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"text", + "text": "Jay Zhangjie Wu $^{1}$ David Junhao Zhang $^{1}$ Wynne Hsu $^{2}$ Mengmi Zhang $^{3,4}$ Mike Zheng Shou $^{1*}$", + "bbox": [ + 91, + 179, + 883, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Show Lab, $^{2}$ National University of Singapore \n $^{3}$ School of Computer Science and Engineering, Nanyang Technological University, Singapore \n $^{4}$ CFAR and I2R, Agency for Science, Technology and Research, Singapore", + "bbox": [ + 112, + 210, + 854, + 265 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 297, + 313, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Humans can watch a continuous video stream and effortlessly perform continual acquisition and transfer of new knowledge with minimal supervision yet retaining previously learnt experiences. In contrast, existing continual learning (CL) methods require fully annotated labels to effectively learn from individual frames in a video stream. Here, we examine a more realistic and challenging problem—Label-Efficient Online Continual Object Detection (LEOCOD) in streaming video. We propose a plug-and-play module, Efficient-CLS, that can be easily inserted into and consistently improve existing CL algorithms for object detection in video streams with reduced data annotation costs and model retraining time. We show that our method has achieved significant improvement with minimal forgetting across all supervision levels on two challenging CL benchmarks for streaming real-world videos. Remarkably, with only $25\\%$ annotated video frames, our proposed method still outperforms the state-of-the-art CL models trained with $100\\%$ annotations on all video frames. The data and source code will be publicly available at https://github.com/showlab/Efficient-CLS.", + "bbox": [ + 73, + 332, + 473, + 650 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 681, + 209, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Humans have the ability to continuously learn from an ever-changing environment, while retaining previously learnt experiences. In contrast to human learning, prior works [3, 2, 11, 34, 7] show that deep neural networks are prone to catastrophic forgetting. To address the forgetting problem, existing works in continual learning (CL) primarily focus on class-incremental image classification or object detection. Their experiment settings are often idealistic and simplified, where i.i.d. static images are usually grouped by class and incrementally presented to computational models in sequence. To learn a particular task containing specific", + "bbox": [ + 75, + 707, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "classes, an agent can go through all the data of current task over multiple epochs. After that, the learned classes in current task become unavailable, i.e., no overlaps between the sets of learned classes and unseen classes.", + "bbox": [ + 500, + 300, + 890, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, these experiment designs deviate from the online continual learning (OCL) setting in the real world, where an agent learns from temporally correlated non-i.i.d. video streams in one single pass. Given context regularities in natural environments, an agent is likely to encounter cases when objects of previously learnt classes co-occur with unknown objects from unseen classes, e.g., a computer mouse and a computer monitor often co-occur. Taking these considerations, [34] introduces OCL on object detection in real-world video streams. They evaluate existing CL approaches on this setting and report a huge performance gap compared with offline training.", + "bbox": [ + 496, + 364, + 892, + 546 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Based on the setting in [34], we take a significant step further and introduce a novel problem setting called Label-Efficient Online Continual Object Detection (LEOCOD), which highlights two unique challenges. First, the setting in [34] is such that the CL algorithms are trained with every mini-batch over multiple passes. We tighten the training recipe in LEOCOD to strictly online, where data is allowed to have one single pass and models are trained on the entire video dataset for only one epoch. Second, existing CL models require fully supervised training where box-level ground truth labels of every object on every video frame have to be obtained from human annotators. Unlike static images, acquiring human annotations for object detection on videos can be expensive and daunting. Thus, in LEOCOD, the video frames per mini-batch are sparsely annotated to alleviate the burdens of extensive human labeling, making LEOCOD one step closer to real world application.", + "bbox": [ + 496, + 549, + 893, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Cognitive science works [35, 19] show that humans are efficient at continuously learning from very few annotated data samples. We get inspirations from the theory of Complementary Learning Systems (CLS) in human brains [18], and propose a plug-and-play module for the LEOCOD task, dubbed as Efficient-CLS. In Efficient-CLS, we introduce", + "bbox": [ + 496, + 809, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author.", + "bbox": [ + 94, + 886, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19246", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a090acd2ce689d64a3637fba2655497866caff7450015ef2e8e9c44ef677bcb6.jpg", + "image_caption": [ + "Figure 1. (a) Problem introduction: An agent continuously learns from a never-ending online video stream over time. In each training step, out of a mini-batch containing 16 consecutive video frames, only a fixed proportion of frames are labeled (green boundary), while the rest of the frames are unlabeled (orange boundary). Following [34], the video frame after every training mini-batch (transparent) is held out for testing. After every 100 training steps, the agent is evaluated on all the video frames from the test set for object detection. (b) Key results: Our proposed method (red) consistently outperforms the best competitive baseline (blue) by a margin of $5\\%$ . Remarkably, our model, trained at $25\\%$ annotation cost, surpasses the best baseline trained at $100\\%$ (grey line). The orange cross denotes the performance of the state-of-the-art model, which is $15\\%$ lower than our method." + ], + "image_footnote": [], + "bbox": [ + 98, + 93, + 529, + 306 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/234e7cabfb9d3c0d9353c67dc8de8cfcc68f8333688ee4fc4fea263dba5918d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 539, + 93, + 870, + 305 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "two feed-forward neural networks as slow and fast learners. In the fast learner, memory is rapidly adapted to the current task. The weights of the slow learner change a little on each reinstatement, and are maintained by taking the exponential moving average (EMA) of the fast learner's weights over time. Though a few continual learning models in previous works [4, 24] also use a similar source of inspiration, they miss the effect of reciprocal connections from slow learners to fast learners, which we intend to address. Inspired by the bidirectional interaction in CLS [14], we reactivate the weights of the slow learners to predict meaningful pseudo labels from the unlabeled video frames and use these pseudo labels to guide the training of the fast learner, closing the loop between the two systems.", + "bbox": [ + 75, + 422, + 470, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate the versatility and effectiveness of our Efficient-CLS on two standard real-world video datasets, OAK [34] and EgoObjects [1]. Our proposed method can be easily integrated into existing CL models and consistently improve their performance by a large margin in LEOCOD. It is worth noting that, with only $25\\%$ labeled data, our method surpasses the comparative baselines trained with full supervision (Figure 1(b)).", + "bbox": [ + 75, + 633, + 468, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, we make the following key contributions:", + "bbox": [ + 96, + 755, + 467, + 770 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a new, challenging and important problem of label-efficient online continual object detection (LEOCOD) in video streams. Solving this problem would greatly benefit real-world applications in reducing annotation cost and model retraining time.", + "- We propose Efficient-CLS, a plug-and-play module inspired from the Complementary Learning Systems (CLS) theory, which can be integrated into existing CL" + ], + "bbox": [ + 94, + 775, + 467, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "models and learn efficiently and effectively with less supervision and minimal forgetting.", + "bbox": [ + 529, + 422, + 890, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We benchmark existing CL methods on the task of LEOCOD and demonstrate the state-of-the-art performance of our method through extensive experiments.", + "bbox": [ + 517, + 458, + 893, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 518, + 640, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Continual Learning", + "text_level": 1, + "bbox": [ + 500, + 544, + 689, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To alleviate catastrophic forgetting, many continual learning methods exploit an external buffer where a limited number of old samples are stored and used for replay when adapting to a new task. iCaRL [26] stores the representative exemplars in past tasks for knowledge distillation and prototype rehearsal. Gradient Episodic Memory (GEM) [21] formulates optimization constraints on the exemplars in memory. Averaged GEM (A-GEM) [8] is an improved version of GEM that achieves faster training and less memory consumption. GDumb [25] greedily stores samples in memory as they come and trains a model using samples only in the memory. Dark Experience Replay++ (DER++) [6] combines replay with knowledge distillation and regularization, and samples logits along the entire optimization trajectory.", + "bbox": [ + 496, + 568, + 890, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast to classical continual learning where data are separated by task boundaries and models are trained with multiple iterations in every task, we examine a more realistic and challenging problem where data are provided in tiny batches and models are trained on these batches only once. Recently, online continual learning (OCL) has gained increasing interests in computer vision [3, 7, 29, 9, 34]. Many OCL methods rely on representative memory replays to pre", + "bbox": [ + 496, + 779, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19247", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "vent forgetting. [3] utilizes gradients of network parameters to select replay samples of maximum diversity. Subsequent works [2, 29] propose to use losses and scoring functions as criteria for selecting the most representative samples for replay. However, these approaches tackle image classification problem in an artificial setting, where new classes appear in a specific order. Their performance in real-world vision tasks remains unclear.", + "bbox": [ + 75, + 90, + 470, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Lately, [34] benchmarks CL methods in the real-world online setting with full supervision. As the video streams arrive endlessly in a real-time manner, assigning annotations to all the video frames for training computational models is laborious and time-consuming. It becomes even more daunting in object detection tasks where class labels and bounding boxes of all objects on a video frame have to be provided. Reducing burdensome costs of labeling remains an under-explored and challenging problem in online continual object detection. We propose a self-sustaining Efficient-CLS, which is capable of exploiting the unlabeled video frames by pseudo-labeling when the number of labeled frames is limited.", + "bbox": [ + 75, + 212, + 470, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Complementary Learning Systems", + "text_level": 1, + "bbox": [ + 76, + 419, + 379, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The essence of fast and slow learning in Complementary Learning Systems (CLS) has benefited several continual learning algorithms in image recognition [24, 23, 28, 4, 15]. However, these methods either require the task boundaries, which are not applicable in our online video setting, or they require to train fast and slow learning systems with replay samples from the same replay buffer, which could easily lead to overfitting problem when the replay buffer has limited capacity. To eliminate overfitting problem, [28] and [15] utilize generative replay models to couple sequential tasks in a latent embedding space. While generative approaches have succeeded in artificial and simple datasets, they often fail in complex vision tasks, e.g., object detection. DualNet [23] also employs a slow-fast learning architecture. However, its update process for the slow learner is more computationally demanding because it leans on both self-supervised and supervised learning objectives. The self-supervised phase demands additional training iterations on extensive batches to yield satisfactory results, thereby delaying the training of the fast learner. In contrast, our method updates the slow learner in real-time using the fast learner's weights, obviating the need for distinct slow learner training. Our approach is optimized for online CL scenarios where computational resources are constrained.", + "bbox": [ + 75, + 443, + 468, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Semi-Supervised Learning", + "text_level": 1, + "bbox": [ + 76, + 816, + 316, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of semi-supervised learning (SSL) [33, 5, 37, 36] is to reduce the demand of labeled data and harness unlabeled data for performance improvement. [31] first introduce SSL to the context of CL, and propose a strategy", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that combines pseudo-labeling, consistency regularization, out-of-distribution detection, and knowledge distillation to solve the problem of class-incremental image classification. However, to distill knowledge from previous tasks, their model relies heavily on the task boundary that identifies the change of training classes, which is not available in our LEOCOD setting. To reduce annotation costs in object detection, several methods [13, 32, 20] capitalize the teacher-student networks. In general, a teacher model predicts pseudo labels or enforces a consistency loss to guide the student networks. However, these previous works on semi-supervised object detection only consider the offline setting on static image datasets, while none of them has been extended to online continual learning on dynamic video streams. We discovered new insights that pseudo-labeling from slow learner to fast learner can not only reduce annotation overhead, but also alleviate forgetting, which is critical to the design of efficient continual learners in real world.", + "bbox": [ + 496, + 90, + 890, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 377, + 589, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Setting", + "text_level": 1, + "bbox": [ + 500, + 402, + 660, + 419 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We advance the online continual object detection in [34] to a label-efficient and computationally-efficient setting—Label-Efficient Online Continual Object Detection (LEOCOD). In contrast to the setting in [34] where video frames are extensively annotated and trained with multiple epochs, an agent in LEOCOD continuously learns from a sparsely annotated video stream in a single pass over time (see Figure 1(a)).", + "bbox": [ + 496, + 426, + 890, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, we consider the online continual object detection on a continuum of video streams $\\mathcal{D} = \\{D_1,\\dots ,D_T\\}$ where at time step $t$ , a learning agent receives a mini-batch of continuous video frames $D_{t}$ from current environment for online training (one single pass). To perform label-efficient object detection, within the batch $D_{t}$ , only a subset of video frames $D_{t}^{s} = (X_{t}^{s},Y_{t}^{s})$ are labeled, while the remaining video frames $D_{t}^{u} = (X_{t}^{u})$ are unlabeled. For each labeled data sample, its annotation contains the bounding box locations and their corresponding class labels.", + "bbox": [ + 496, + 547, + 890, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Efficient Complementary Learning Systems", + "text_level": 1, + "bbox": [ + 500, + 710, + 870, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a plug-and-play module dubbed as EfficientCLS. Specifically, it consists of two feed-forward networks: (i) the fast learner is designed to quickly encode new knowledge from current data stream and then consolidate it to the slow learner; and (ii) the slow learner accumulates the acquired knowledge from fast learner over time and guides the fast learner with meaningful pseudo labels, when full supervision is not available. Same as [26, 8, 25, 6, 34], we maintain an external episodic memory, as a replay buffer, to store exemplars that can be retrieved for replays alongside ongoing video stream. As the fast and slow learners are", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19248", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/02a21dd849294a5f80d943914591152a18efa413983492843b7fea011e65dfed.jpg", + "image_caption": [ + "Figure 2. The framework of Efficient-CLS. At each learning step, the system receives a batch of temporally continuous data $D_{t}$ , including labeled (green) and unlabeled (orange) frames. The fast learner trains the labeled frames alongside a small subset of labeled exemplars retrieved from episodic memory with the supervised loss $\\mathcal{L}_{sup}$ . Meanwhile, the fast learner leverages the pseudo labels generated by the slow learner to optimize a pseudo loss $\\mathcal{L}_{pseudo}$ . To reinstate memory of the slow learner, the weights of the slow learner are updated by taking the Exponential Moving Average (EMA) of the fast learner's weights. The fast and slow learners are complementary to each other, forming a positive feedback loop." + ], + "image_footnote": [], + "bbox": [ + 101, + 92, + 872, + 329 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "model agnostic, our Efficient-CLS can be easily integrated into existing CL models, which leads to less supervision and minimal forgetting.", + "bbox": [ + 75, + 431, + 470, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning with Labeled Frames. The fast learner and slow learner use the same standard Faster-RCNN [27] detector $f$ . Despite the same architecture, the weights of the fast and slow learners are not shared. We use $\\theta_{F}$ and $\\theta_{S}$ to denote the network parameters for fast and slow learners respectively. As shown in Figure 2, at each training step $t$ , we use the labeled video frames $D_{t}^{s} = (X_{t}^{s}, Y_{t}^{s})$ to optimize the fast learner $\\theta_{F}$ with the standard supervised loss $\\mathcal{L}_{sup}$ in Faster-RCNN [27]. It consists of four losses: Region Proposal Network (RPN) classification loss $\\mathcal{L}_{cls}^{rpn}$ , RPN regression loss $\\mathcal{L}_{reg}^{rpn}$ , Region of Interest (ROI) classification loss $\\mathcal{L}_{cls}^{roi}$ , and ROI regression loss $\\mathcal{L}_{reg}^{roi}$ . We define $\\mathcal{L}_{sup}$ as:", + "bbox": [ + 75, + 493, + 468, + 679 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s u p} = \\mathcal {L} _ {c l s} ^ {r p n} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\mathcal {L} _ {r e g} ^ {r p n} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 686, + 468, + 713 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c l s} ^ {r o i} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\mathcal {L} _ {r e g} ^ {r o i} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 710, + 421, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning with Unlabeled Frames. We introduce a pseudo-labeling paradigm to capitalize the information from unlabeled video frames $D_{t}^{u} = (X_{t}^{u})$ for training. In our early exploration, we intuitively use the fast learner for pseudo-labeling as it quickly adapts the knowledge of nearby frames. However, we observe that using the pseudo labels generated by the fast learner for self-replay exhibits biases towards recently seen objects, which is less effective in preventing forgetting. This has also been verified in our ablation study (Section 5.3). In contrast, the slow learner", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "preserves the semantic knowledge over a longer time span which generates pseudo labels with fewer biases. This encourages the fast learner to capture more generic scene representations, hence, in turn, contributing to reinstatement of memory in the slow learner (Section 3.2), resulting in a positive feedback loop.", + "bbox": [ + 496, + 431, + 890, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given all these design considerations, the slow learner takes the unlabeled video frames $D_{t}^{u}$ as inputs to estimate the possible objects of interest and their corresponding bounding box locations. For brevity, we refer these \"pseudo bounding boxes and their corresponding class labels\" as \"pseudo labels\" in the paper. To get rid of false positives, we apply a threshold $\\tau$ to filter out bounding boxes with predicted low confidence scores. Moreover, there also exist repetitive boxes which negatively impact the quality of pseudo-labeling. To address this issue, we use the technique of class-wise non-maximum suppression (NMS) [27] to remove the overlapped boxes and get the high-quality pseudo labels. Formally, the procedure of pseudo label generation is summarized below:", + "bbox": [ + 496, + 523, + 892, + 733 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY _ {t} ^ {u} = \\mathrm {N M S} ([ f (X _ {t} ^ {u}; \\theta_ {S}) ] _ {> \\tau}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 741, + 890, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $[\\cdot ]_{>\\tau}$ denotes the bounding box selection with confidence score larger than $\\tau$", + "bbox": [ + 496, + 763, + 890, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given that the video streams are captured from the egocentric perspective in the real world, head and body motions may lead to undesired motion blur effects on some video frames. To enforce our module to learn invariant object representations from these video frames, same as the previous work [38], we apply data augmentation techniques on the pseudo-labeled frames, including 2D image", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19249", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "crops, rotations, and flipping. Note that different from image classification, the predicted bounding box locations also need to be updated accordingly after image augmentations. We denote these pseudo-labeled video frames and their re-adjusted pseudo labels after data augmentations as $(\\tilde{X}_t^u,\\tilde{Y}_t^u)$ . We can then use these pseudo pairs $(\\tilde{X}_t^u,\\tilde{Y}_t^u)$ to train the fast learner by optimizing the pseudo loss $\\mathcal{L}_{pseudo}:= \\mathcal{L}_{cls}^{roi}(\\tilde{X}_t^u,\\tilde{Y}_t^u) + \\mathcal{L}_{req}^{roi}(\\tilde{X}_t^u,\\tilde{Y}_t^u)$ .", + "bbox": [ + 75, + 90, + 468, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall, our Efficient-CLS is jointly trained with the following losses: $\\mathcal{L}_{total} = \\mathcal{L}_{sup} + \\lambda_{pseudo}\\mathcal{L}_{pseudo}$ , where $\\lambda_{pseudo}$ is the weight of $\\mathcal{L}_{pseudo}$ .", + "bbox": [ + 75, + 212, + 468, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Synapses Consolidation via EMA. To alleviate forgetting of obtained knowledge, we apply Exponential Moving Average (EMA) to gradually update the slow learner with the fast learner's weights. The evolving weight changes in the slow learner are functionally correlated with the memory consolidation mechanism in the hippocampus and the neocortex [4]. Formally, we define EMA process as:", + "bbox": [ + 75, + 268, + 468, + 375 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {S} = \\alpha \\theta_ {S} + (1 - \\alpha) \\theta_ {F}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 380, + 468, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the $\\alpha \\in [0,1]$ is EMA rate. According to the stability-plasticity dilemma, a smaller $\\alpha$ means faster adaptation but less memorization. Empirically, we set $\\alpha = 0.99$ , which leads to best performance.", + "bbox": [ + 75, + 402, + 468, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental details", + "text_level": 1, + "bbox": [ + 76, + 474, + 274, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 500, + 179, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the continual learning methods on two realistic and challenging video datasets, OAK [34] and EgoObjects [1], for the task of online continual object detection.", + "bbox": [ + 75, + 522, + 468, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "OAK [34] is a large egocentric video stream dataset spanning nine months of a graduate student's life, consisting of 7.6 million frames of 460 video clips with a total length of 70.2 hours [30]. The dataset contains 103 object categories. We follow [34] in the ordering of training and testing data splits. One frame every 16 consecutive video frames lasting for 30 seconds is held out to construct a test set and the remaining frames are used for training.", + "bbox": [ + 75, + 568, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "EgoObjects [1] is one of the largest object-centric datasets focusing on object detection task. The dataset contains around 100k video frames with $\\sim 250\\mathrm{k}$ annotations, which correspond to 277 categories and 1110 main objects [22]. Additionally, the dataset follows a long-tailed distribution which makes the task more challenging and real-world oriented. We adopt the same rule as OAK dataset to split the training and testing set.", + "bbox": [ + 75, + 688, + 468, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Baselines", + "text_level": 1, + "bbox": [ + 76, + 816, + 184, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare our model against the following baselines: 1) Vanilla training: Incremental Training is a naive baseline trained sequentially over the entire video stream without any measures to avoid catastrophic forgetting; Offline", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training is an upper bound that can access all the data throughout training; 2) Continual learning algorithms: EWC [16], iCaRL [26], A-GEM [8], GDumb [25], DER++ [6] and iOD [17].", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The iCaRL model implemented by [34] stands as the SOTA method in online continual object detection. We reproduce their results using the released code1. When calculating RPN and ROI losses for replay samples, their iCaRL model neglects the losses of background proposals and penalizes the foreground losses according to the proportion of the current samples and replay samples. We empirically found that this trick hinders the model from effective episodic replay, thus resulting in severe forgetting. Therefore, we re-implement the iCaRL by discarding the reweighting trick and reverting back to the standard RPN and ROI losses. We name these two different implementations as iCaRL(Wang et al.) and iCaRL(our impl.), respectively.", + "bbox": [ + 496, + 152, + 890, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Evaluation", + "text_level": 1, + "bbox": [ + 500, + 357, + 620, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Protocols. First, we define the annotation cost as the proportion of number of labeled frames versus the total 16 frames within a mini-batch $D_{t}$ . For example, if 2 out of 16 consecutive frames within $D_{t}$ get labeled, the annotation cost is $2 / 16 = 12.5\\%$ . The frames to be labeled are randomly selected within each mini-batch $D_{t}$ . Considering that different choices of labeled frames might influence the model performance, for fair comparisons between models, we fix the choice of randomly selected labeled frames and use the same labeled and unlabeled frames for training all models. Based on the various annotation costs, we introduce two training protocols: fully supervised protocol (100% annotation cost) and sparse annotation protocol (where the annotation cost is less than 100%). In sparse annotation protocol, we further split the training experiments based on 50%/25%/12.5%/6.25% annotation costs.", + "bbox": [ + 496, + 380, + 890, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics. We evaluate the models with three standard metrics: continual average precision (CAP), final average precision (FAP) and forgetfulness (F) [34]. We employ an Average Precision (AP) metric at an Intersection over Union (IoU) threshold of 0.5, commonly referred to as AP50.", + "bbox": [ + 496, + 633, + 890, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CAP shows the average performance over the entire video stream. That is,", + "bbox": [ + 500, + 709, + 890, + 738 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {C A P} = \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\mathrm {C A P} _ {t _ {i}} = \\frac {1}{N C} \\sum_ {i = 0} ^ {N} \\sum_ {c = 0} ^ {C} \\mathrm {C A P} _ {t _ {i}} ^ {c}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 750, + 890, + 790 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{CAP}_{t_i}^c$ is the AP of class $c$ on test set at the $i$ -th evaluation step, $N$ is the total number of evaluation steps.", + "bbox": [ + 496, + 801, + 890, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FAP is the final performance of a model after seeing the entire video. That is, $\\mathrm{FAP} = \\mathrm{CAP}_{t_N}$ , where $t_N$ denotes the last evaluation step.", + "bbox": [ + 496, + 832, + 890, + 877 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "$^{1}$ https://github.com/oakdata/benchmark", + "bbox": [ + 517, + 886, + 728, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19250", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/aac219989275d564f8d39834abf219c67bce25adb0da56e6c1ae0309096c1c5d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Annotation CostOAKEgoObjects
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
Incremental100%8.387.720.0310.213.551.48
Offline Training100%48.2835.23-86.1859.81-
EWC100%7.737.02-0.125.151.600.57
iOD100%7.927.140.988.802.640.00
iCaRL(Wang et al.)100%22.8916.60-2.9537.6121.712.79
iCaRL(our impl.)100%36.1426.26-4.8960.8036.41-0.60
w/ Efficient-CLS25%38.36(+2.22)26.64(+0.38)-8.20(-3.31)61.26(+0.46)39.58(+3.17)-3.48(-2.88)
100%40.24(+4.10)28.18(+1.92)-8.10(-3.21)67.05(+6.25)40.36(+3.95)-3.67(-3.07)
A-GEM100%36.9426.19-5.5458.7935.88-8.38
w/ Efficient-CLS25%37.06(+0.12)26.36(+0.17)-7.76(-2.22)63.06(+4.27)39.46(+3.58)-7.49(+0.89)
100%39.87(+2.93)27.97(+1.78)-7.17(-1.63)66.94(+8.15)39.57(+3.69)-11.68(-3.30)
GDumb100%35.2725.29-6.5958.8536.38-5.21
w/ Efficient-CLS25%37.67(+2.40)25.59(+0.30)-9.30(-2.71)62.70(+3.85)38.78(+2.40)-8.86(-3.65)
100%38.61(+3.34)26.04(+0.75)-9.14(-2.55)63.55(+4.70)38.98(+2.60)-7.50(-2.29)
DER++100%37.7925.24-2.8755.8230.84-6.08
w/ Efficient-CLS25%37.93(+0.14)25.64(+0.4)-8.90(-6.03)59.70(+3.88)34.15(+3.31)-11.21(-5.13)
100%39.61(+1.82)26.73(+1.49)-8.30(-5.43)62.01(+6.19)33.09(+2.25)-11.05(-4.97)
", + "bbox": [ + 84, + 87, + 885, + 343 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Overall performance of existing algorithms and Efficient-CLS on OAK and EgoObjects. iCaRL(Wang et al.) denotes the SOTA model presented in [34], and iCaRL(our impl.) is the same method by our implementation.", + "bbox": [ + 75, + 348, + 893, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\mathbf{F}$ estimates the forgetfulness of the model due to the sequential training. It takes into account the time interval between the presence of an object category and its subsequent presence. For a class $c$ , we sort the $\\mathrm{CAP}_{t_i}^c$ according to the time interval $k$ between evaluation time $t_i$ and the last time $t_i - k$ the model is trained on $c$ . After $\\mathrm{CAP}_{t_i}^c$ is sorted, all $\\mathrm{CAP}_{t_i}^c (i = 0,\\dots ,T)$ are divided into $K$ bins $B_{kmin},\\dots ,B_{kmax}$ according to the time interval $k$ . The average CAP $(\\mathrm{aCAP}_k)$ of each bin $B_{k}$ is defined as the model's performance for detecting class $c$ after the model has not been trained on $c$ for $k$ time steps. The forgetfulness (F) of the class $c$ is defined as the weighted sum of the performance decrease at each time:", + "bbox": [ + 75, + 395, + 472, + 592 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nF ^ {c} = \\sum_ {k = k m i n} ^ {k m a x} \\frac {k - k m i n}{\\sum_ {k = k m i n} ^ {k m a x} k - k m i n} \\times \\left(\\mathrm {a C A P} _ {k m i n} - \\mathrm {a C A P} _ {k}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 603, + 482, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall forgetfulness is: $\\mathrm{F} = \\frac{1}{C}\\sum_{c = 0}^{C}\\mathrm{F}^{c}$", + "bbox": [ + 76, + 654, + 383, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 681, + 294, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For a fair comparison, we followed the prior work [34] to use Faster-RCNN [27] with ResNet-50 backbone [12] as our object detection network, which is initialized by the weights pre-trained on PASCAL VOC [10]. We used Adam optimizer with a constant learning rate of 0.0001, and the batch size was set to 16 frames. Same as [34], we maintained a replay buffer with 5 samples per class. At each time step $t$ , we first randomly retrieved 16 video frames from the replay buffer for joint training. We used confidence thresh $\\tau = 0.7$ to generate pseudo-labels for unlabeled frames, and applied EMA rate $\\alpha = 0.99$ to update the slow learner. The weight of pseudo loss $\\lambda_{pseudo}$ was set to 1.0. All the experiments were conducted on 2 NVIDIA RTX 3090 GPUs.", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 498, + 393, + 586, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Fully Supervised Protocol", + "text_level": 1, + "bbox": [ + 500, + 419, + 733, + 435 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As the previous work [34] focuses on online continual object detection (OCOD) in video streams, we first evaluated model performance in fully supervised setting (i.e., $100\\%$ annotation cost), where all video frames are paired with human labels. The reported results were measured by standard metrics (CAP, FAP, and F, Section 4.3) in Table 1.", + "bbox": [ + 496, + 443, + 890, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance of CL baselines. [34] benchmarked Incremental, EWC, iCaRL(Wang et al.), and Offline Training on OAK dataset. They found the replay-based method (i.e. iCaRL(Wang et al.)) outperforms regularization-based method (i.e. EWC) by $10\\%$ in FAP, while iCaRL(Wang et al.) has a huge gap of $30\\%$ compared with Offline Training. Similar observations were made in Table 1, but the performance of Incremental and EWC were $4\\%$ lower than that in [34], as in our setting we only trained each mini-batch of video frames once (they trained each mini-batch 10 times). As mentioned in Section 4.2, we introduce several variations to the original design of iCaRL(Wang et al.). Compared with iCaRL(Wang et al.), we observed a huge performance boost in FAP from $22.89\\%$ to $36.14\\%$ on OAK and from $37.61\\%$ to $60.80\\%$ on EgoObjects, abridging the gap between the baseline and Offline Training.", + "bbox": [ + 496, + 551, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further adapted other standard CL baselines, including iOD, A-GEM, GDumb, DER++, to the OCOD setting for comparisons. iOD is the SOTA method in offline class-incremental object detection. Though it performs well in prior setting, iOD collapses when adapted to online video streams. One explanation is that iOD requires explicit task boundary to trigger the reshape of model gradients that opti", + "bbox": [ + 496, + 795, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19251", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/33fe0a64f37aecc71768e8c1c4c8ff86bb795b645e3f00e83a30203a3e49b417.jpg", + "image_caption": [ + "Figure 3. The changes of $\\mathrm{CAP}_{t_i}^c$ with sampled categories on OAK dataset. The x-axis denotes time step across the entire video stream. The y-axis denotes the AP50 of the category at specific time step (i.e., $\\mathrm{CAP}_{t_i}^c$ ). The grey line indicates the existence of the category." + ], + "image_footnote": [], + "bbox": [ + 88, + 92, + 883, + 256 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "mizes knowledge sharing between adjacent tasks. However, in online video streams, the task boundaries by classes are no longer available and the change of tasks is hard to identify, resulting in the failure to prevent forgetting. In contrast, replay-based methods (i.e., A-GEM, GDumb and DER++) generalize much better to the real-world streaming video.", + "bbox": [ + 75, + 314, + 470, + 405 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance w/ Efficient-CLS. Inheriting from the benefit of fast and slow learning with EMA, our Efficient-CLS consistently improves all the state-of-the-art CL methods (i.e. iCaRL(our impl.), A-GEM, GDumb and DER++) by a significant margin. Taking iCaRL(our impl.) for example, with Efficient-CLS, we observed superior performance and minimal forgetting compared to baseline methods, even when categories appeared infrequently (e.g., sculpture in Figure 3). Since semantic contextual information is more important in indoor environments on EgoObjects compared to the outdoor environments in OAK, we noticed that the improvement brought by our method is even greater on EgoObjects with an increase of $6.25\\%$ in FAP, $3.95\\%$ in CAP $\\%$ and $3.07\\%$ in F. Consistent performance gains are also noticeable for A-GEM, GDumb and DER++, demonstrating the effectiveness and flexibility of our method.", + "bbox": [ + 75, + 416, + 468, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Sparse Annotation Protocol", + "text_level": 1, + "bbox": [ + 76, + 665, + 326, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance of CL baselines. The sparse annotation protocol is more challenging than the previous fully supervised protocol as shown by the performance differences when number of annotated video frames decreases (compare the performance of each colored bar along the x-axis within each subplot in Figure 4). We noted that GDumb is more resilient against the reduce of supervision. Specifically, from Table 2 at the lowest annotation cost of $6.25\\%$ on EgoObjects dataset, GDumb achieves the highest performance of $38.74\\%$ , $22.69\\%$ and $-4.53\\%$ in FAP, CAP and F, which surpasses other baselines by a considerable margin. Same observations can be made on OAK dataset. One possible explanation is that GDumb only trains the data stored in the balanced replay buffer, which makes it less vulnerable", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/88aea2c26004d72c77b0f4cf9ad195f09c2423a021d54903470e4016ed0d6140.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
OAKEgoObjects
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
iCaRL23.0417.75-3.3132.9119.15-1.36
w/ Efficient-CLS29.7220.31-5.3640.1623.95-2.01
A-GEM23.5916.15-2.9921.8412.280.82
w/ Efficient-CLS30.1820.59-5.4438.9623.79-5.64
GDumb27.3719.64-4.2538.7422.69-4.53
w/ Efficient-CLS29.0719.99-6.0140.0923.67-5.16
DER++24.2115.93-3.7916.958.482.03
w/ Efficient-CLS28.6319.64-4.6035.7820.74-4.69
", + "bbox": [ + 500, + 310, + 890, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Performance of Efficient-CLS at low annotation cost of $6.25\\%$ . The best results are bold-faced.", + "bbox": [ + 498, + 429, + 892, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "able to class imbalance problem brought by the reduce of labeled samples in the training set.", + "bbox": [ + 498, + 474, + 892, + 506 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance w/ Efficient-CLS. Our proposed Efficient-CLS is a plug-and-play module that can be easily inserted into and enhance existing continual learning algorithms with the ability to use unlabeled video frames effectively. In both OAK and EgoObjects dataset, Efficient-CLS consistently improves the comparative SOTAs in all three evaluation metrics regardless of various degrees of annotation cost. As shown in Table 2, at a lower annotation cost of $6.25\\%$ , Efficient-CLS doubles the performance of DER++ and A-GEM in terms of FAP and CAP, and achieves an even larger improvement in preventing forgetting. Thanks to the useful information from pseudo labels predicted by the slow learner in Efficient-CLS, our method is more robust to various annotation costs, compared with SOTAs (compare the rate of change of blue bars vs. red bars over different degrees of annotation cost). Most remarkably, Efficient-CLS with $25\\%$ annotation cost has already outperformed comparative SOTAs with $100\\%$ annotation cost (see Table 1).", + "bbox": [ + 496, + 518, + 892, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 801, + 653, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We assessed the importance of our key design choices. The Complementary Learning Systems (CLS) in EfficientCLS is the key for rapidly adapting to learn new tasks, meanwhile, retaining previously learnt knowledge. It constitutes of two memory reinstatement mechanisms: one is", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19252", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dafc29ad3590cc3cfb2a7d358b163bca09c7a2127ab71373a07b5c75f8c90e61.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 88, + 364, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c5dc86c1a627513b4e84ccece2bd45bd5df1c9042492552d7dca3c95edc54efc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 89, + 607, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1ed6f3578d2d9af0843954a429ad7af6532263ab6fad0360d4c62a4e0a890394.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 609, + 90, + 848, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/24693d7cad2f36899b31c8f33ce9bcb2974c9d1836f75eaf87ea557cde227c54.jpg", + "image_caption": [ + "Figure 4. Evaluation of online continual object detection in video streams with three metrics (FAP, CAP and F, Section 4.3) on OAK dataset (first row) and EgoObjects dataset (second row). The higher the bars are, the better. The x-axis denotes the percentage of video frames that are labeled in the video stream. It ranges from $6.25\\%$ to $100\\%$ (full supervision). The y-axis indicates the performance using different evaluation metrics. Ours (iCaRL(our impl.) w/ Efficient-CLS, red) consistently beats the comparative SOTA (iCaRL(our impl.), blue) in all evaluation metrics." + ], + "image_footnote": [], + "bbox": [ + 119, + 219, + 362, + 347 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11853cb1106fcd715fd04101d300b2bdf81ad71ec85abd0a3a6aa42ea914aa0d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 362, + 219, + 604, + 347 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f73a9a17b60c67d99d85868822c5329faa2468187a6784f269ed11e0fc04b41f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 219, + 846, + 347 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3389289ced2f3b4692e364719e4348a28456981109f5af49c9f99a375f80b0f6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
EMAPL50%25%12.5%6.25%
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
XX34.6825.78-4.1533.7024.57-4.3028.7619.80-5.4823.0417.75-3.31
✓X35.7425.77-4.8234.7925.62-4.3531.7221.16-7.2427.8420.03-3.96
X✓35.6125.56-3.7634.9525.65-3.6531.6022.44-4.8326.3919.50-1.99
✓✓38.6126.90-7.2938.3626.64-8.2033.9223.04-7.7129.7220.31-5.36
", + "bbox": [ + 91, + 439, + 874, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Effectiveness of Exponential Moving Average (EMA) and Pseudo-labeling (PL) for iCaRL (our impl.) on OAK dataset at annotation cost $50\\%$ , $25\\%$ , $12.5\\%$ and $6.25\\%$ . The best results are bold-faced.", + "bbox": [ + 75, + 522, + 892, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "synaptic weight transfer from fast to slow learner via exponential moving average (EMA); and the other is reciprocal replay from slow learner to fast learner with pseudolabeling (PL). Here we studied their effects individually.", + "bbox": [ + 75, + 569, + 470, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation: Exponential Moving Average (EMA). We removed EMA by setting the $\\alpha$ in Equation 3 to 1, where the model weights of the fast learner and slow learner are now shared throughout the learning process. Note that in the fully supervised protocol, the pseudo-labeling is turned off and the Efficient-CLS equals to the EMA alone. From Table 1 at $100\\%$ annotation cost, we observed that removing EMA leads to significant performance drops ranging from $2\\%$ to $8\\%$ , for all the comparative baselines on both OAK and EgoObjects. This shows that the slow learner can effectively consolidate the knowledge from the fast learner, and constructively alleviate catastrophic forgetting by synapses consolidation over time. Similar observations were made in Table 3 in the sparse annotation protocol (compare Row 2 vs. Row 1, Row 4 vs. Row 3). It is worth noting that, the performance difference between naive model (Row 1) and its variant with EMA (Row 2) is slightly larger in lower su", + "bbox": [ + 75, + 643, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "pervision (i.e. $12.5\\%$ , $6.25\\%$ ) than higher supervision (i.e. $50\\%$ , $25\\%$ ). One possible reason is that, compared with higher supervision, the fast learner suffers more forgetting in lower supervision; hence, the effect of removing EMA becomes stronger in lower supervision, again highlighting the importance of EMA.", + "bbox": [ + 496, + 569, + 892, + 660 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation: Pseudo-labeling (PL). We ablate our model by removing the PL of the slow learner across varying annotation costs and reported the results in Table 3. The removal of PL (Row 2) leads to a performance drop of around $2\\%$ in FAP, $1\\%$ in CAP and $0.5 - 4\\%$ in F, compared with our full Efficient-CLS (Row 4). It implies that the slow learner captures useful semantic information from unlabeled video frames and these predicted pseudo labels are helpful in training the fast learner.", + "bbox": [ + 496, + 672, + 893, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To investigate whether pseudo labels predicted by the fast learner itself could help stream learning, we conducted another ablation experiment where we performed PL without EMA (Row 3). Compared with the naive model (Row 1), we observed a performance increase from $28.76\\%$ to $31.60\\%$ in FAP and $19.80\\%$ to $22.44\\%$ in CAP. It indicates", + "bbox": [ + 496, + 810, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19253", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "that, due to the temporal correlation in video stream, pseudo labels predicted by the fast learner can serve as an informative supervision for the training of the fast learner itself.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "However, replaying the self-predicted pseudo labels on the fast learner fails to prevent forgetting, as indicated by the drop from $-5.48\\%$ to $-4.83\\%$ in F. It is possible that the pseudo labels generated by the fast learner only bias towards the classes which have already been learnt very well and fail to reinforce the fast learner to improve on the poorly-learnt classes. Different from the fast learner, the slow learner integrates semantic information over time. The predicted pseudo labels carry more semantic information, which is useful for fast learner to capture more generic object representations during pseudo label replays. Again, this emphasizes that the reciprocal replay from the slow learner to the fast learner is critical for memory reinstatement, which has been missing in the computational modeling literature of CLS.", + "bbox": [ + 75, + 137, + 470, + 363 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 378, + 194, + 393 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To imitate what humans see and learn in the real world, we introduce a more realistic and challenging problem of label-efficient online continual object detection (LEOCOD) in video streams. Addressing this problem would greatly benefit real-world applications by reducing model retraining time and data labeling costs. Inspired by the Complementary Learning Systems (CLS) theory, we propose a plug-and-play module, namely Efficient-CLS, that can be easily integrated into and improve existing continual leaning algorithms. We evaluate Efficient-CLS on two challenging real-world video datasets, where our method achieves the state-of-the-art performance in preventing catastrophic forgetting, all while requiring minimal annotation effort.", + "bbox": [ + 75, + 404, + 470, + 602 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements This research is funded by the National Research Foundation, Singapore under its NRFF Award NRF-NRFF13-2021-0008 & NRF-NRFF15-2023-0001, AI Singapore Programme (AISG Award No: AISGC-2019-001-2A & AISG2-RP-2021-025), Mike Zheng Shou's Start-Up Grant from NUS, Mengmi Zhang's Startup Grant from Agency for Science, Technology, and Research (A*STAR), and Early Career Investigatorship from Center for Frontier AI Research (CFAR), A*STAR. The computational work for this article was partially performed on resources of the National Supercomputing Centre, Singapore.", + "bbox": [ + 75, + 622, + 468, + 789 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 804, + 173, + 819 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Egoobjects dataset. https://ai.facebook.com/datasets/egoobjects-dataset/, May 2022. 2, 5", + "[2] Rahaf Aljundi, Eugene Belilovsky, Tinne Tuytelaars, Laurent Charlin, Massimo Caccia, Min Lin, and Lucas Page-Caccia. Online continual learning with maximal interfered" + ], + "bbox": [ + 84, + 828, + 468, + 900 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "retrieval. Advances in neural information processing systems, 32, 2019. 1, 3", + "[3] Rahaf Aljundi, Min Lin, Baptiste Goujaud, and Yoshua Bengio. 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Springer, 2020. 4" + ], + "bbox": [ + 501, + 92, + 890, + 614 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19255", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Label-Efficient Online Continual Object Detection in Streaming Video/bb408240-93f4-4420-9e47-a5facd88851a_model.json b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/bb408240-93f4-4420-9e47-a5facd88851a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1d295ee78c6d617547c0363f9a526045ca8af609 --- /dev/null +++ b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/bb408240-93f4-4420-9e47-a5facd88851a_model.json @@ -0,0 +1,1936 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.131, + 0.131, + 0.842, + 0.154 + ], + "angle": 0, + "content": "Label-Efficient Online Continual Object Detection in Streaming Video" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.18, + 0.884, + 0.201 + ], + "angle": 0, + "content": "Jay Zhangjie Wu\\(^{1}\\) David Junhao Zhang\\(^{1}\\) Wynne Hsu\\(^{2}\\) Mengmi Zhang\\(^{3,4}\\) Mike Zheng Shou\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.211, + 0.856, + 0.266 + ], + "angle": 0, + "content": "\\(^{1}\\)Show Lab, \\(^{2}\\)National University of Singapore \n\\(^{3}\\)School of Computer Science and Engineering, Nanyang Technological University, Singapore \n\\(^{4}\\)CFAR and I2R, Agency for Science, Technology and Research, Singapore" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.299, + 0.314, + 0.317 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.333, + 0.474, + 0.651 + ], + "angle": 0, + "content": "Humans can watch a continuous video stream and effortlessly perform continual acquisition and transfer of new knowledge with minimal supervision yet retaining previously learnt experiences. In contrast, existing continual learning (CL) methods require fully annotated labels to effectively learn from individual frames in a video stream. Here, we examine a more realistic and challenging problem—Label-Efficient Online Continual Object Detection (LEOCOD) in streaming video. We propose a plug-and-play module, Efficient-CLS, that can be easily inserted into and consistently improve existing CL algorithms for object detection in video streams with reduced data annotation costs and model retraining time. We show that our method has achieved significant improvement with minimal forgetting across all supervision levels on two challenging CL benchmarks for streaming real-world videos. Remarkably, with only \\(25\\%\\) annotated video frames, our proposed method still outperforms the state-of-the-art CL models trained with \\(100\\%\\) annotations on all video frames. The data and source code will be publicly available at https://github.com/showlab/Efficient-CLS." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.682, + 0.21, + 0.698 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.708, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Humans have the ability to continuously learn from an ever-changing environment, while retaining previously learnt experiences. In contrast to human learning, prior works [3, 2, 11, 34, 7] show that deep neural networks are prone to catastrophic forgetting. To address the forgetting problem, existing works in continual learning (CL) primarily focus on class-incremental image classification or object detection. Their experiment settings are often idealistic and simplified, where i.i.d. static images are usually grouped by class and incrementally presented to computational models in sequence. To learn a particular task containing specific" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.301, + 0.892, + 0.361 + ], + "angle": 0, + "content": "classes, an agent can go through all the data of current task over multiple epochs. After that, the learned classes in current task become unavailable, i.e., no overlaps between the sets of learned classes and unseen classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.893, + 0.547 + ], + "angle": 0, + "content": "However, these experiment designs deviate from the online continual learning (OCL) setting in the real world, where an agent learns from temporally correlated non-i.i.d. video streams in one single pass. Given context regularities in natural environments, an agent is likely to encounter cases when objects of previously learnt classes co-occur with unknown objects from unseen classes, e.g., a computer mouse and a computer monitor often co-occur. Taking these considerations, [34] introduces OCL on object detection in real-world video streams. They evaluate existing CL approaches on this setting and report a huge performance gap compared with offline training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.895, + 0.807 + ], + "angle": 0, + "content": "Based on the setting in [34], we take a significant step further and introduce a novel problem setting called Label-Efficient Online Continual Object Detection (LEOCOD), which highlights two unique challenges. First, the setting in [34] is such that the CL algorithms are trained with every mini-batch over multiple passes. We tighten the training recipe in LEOCOD to strictly online, where data is allowed to have one single pass and models are trained on the entire video dataset for only one epoch. Second, existing CL models require fully supervised training where box-level ground truth labels of every object on every video frame have to be obtained from human annotators. Unlike static images, acquiring human annotations for object detection on videos can be expensive and daunting. Thus, in LEOCOD, the video frames per mini-batch are sparsely annotated to alleviate the burdens of extensive human labeling, making LEOCOD one step closer to real world application." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Cognitive science works [35, 19] show that humans are efficient at continuously learning from very few annotated data samples. We get inspirations from the theory of Complementary Learning Systems (CLS) in human brains [18], and propose a plug-and-play module for the LEOCOD task, dubbed as Efficient-CLS. In Efficient-CLS, we introduce" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.227, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "19246" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.094, + 0.531, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.54, + 0.094, + 0.871, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.896, + 0.41 + ], + "angle": 0, + "content": "Figure 1. (a) Problem introduction: An agent continuously learns from a never-ending online video stream over time. In each training step, out of a mini-batch containing 16 consecutive video frames, only a fixed proportion of frames are labeled (green boundary), while the rest of the frames are unlabeled (orange boundary). Following [34], the video frame after every training mini-batch (transparent) is held out for testing. After every 100 training steps, the agent is evaluated on all the video frames from the test set for object detection. (b) Key results: Our proposed method (red) consistently outperforms the best competitive baseline (blue) by a margin of \\(5\\%\\). Remarkably, our model, trained at \\(25\\%\\) annotation cost, surpasses the best baseline trained at \\(100\\%\\) (grey line). The orange cross denotes the performance of the state-of-the-art model, which is \\(15\\%\\) lower than our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.471, + 0.635 + ], + "angle": 0, + "content": "two feed-forward neural networks as slow and fast learners. In the fast learner, memory is rapidly adapted to the current task. The weights of the slow learner change a little on each reinstatement, and are maintained by taking the exponential moving average (EMA) of the fast learner's weights over time. Though a few continual learning models in previous works [4, 24] also use a similar source of inspiration, they miss the effect of reciprocal connections from slow learners to fast learners, which we intend to address. Inspired by the bidirectional interaction in CLS [14], we reactivate the weights of the slow learners to predict meaningful pseudo labels from the unlabeled video frames and use these pseudo labels to guide the training of the fast learner, closing the loop between the two systems." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.47, + 0.756 + ], + "angle": 0, + "content": "We demonstrate the versatility and effectiveness of our Efficient-CLS on two standard real-world video datasets, OAK [34] and EgoObjects [1]. Our proposed method can be easily integrated into existing CL models and consistently improve their performance by a large margin in LEOCOD. It is worth noting that, with only \\(25\\%\\) labeled data, our method surpasses the comparative baselines trained with full supervision (Figure 1(b))." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.756, + 0.468, + 0.771 + ], + "angle": 0, + "content": "To summarize, we make the following key contributions:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.776, + 0.468, + 0.852 + ], + "angle": 0, + "content": "- We introduce a new, challenging and important problem of label-efficient online continual object detection (LEOCOD) in video streams. Solving this problem would greatly benefit real-world applications in reducing annotation cost and model retraining time." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.856, + 0.468, + 0.902 + ], + "angle": 0, + "content": "- We propose Efficient-CLS, a plug-and-play module inspired from the Complementary Learning Systems (CLS) theory, which can be integrated into existing CL" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.776, + 0.468, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.424, + 0.892, + 0.455 + ], + "angle": 0, + "content": "models and learn efficiently and effectively with less supervision and minimal forgetting." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.459, + 0.894, + 0.505 + ], + "angle": 0, + "content": "- We benchmark existing CL methods on the task of LEOCOD and demonstrate the state-of-the-art performance of our method through extensive experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.642, + 0.535 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.545, + 0.691, + 0.561 + ], + "angle": 0, + "content": "2.1. Continual Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.78 + ], + "angle": 0, + "content": "To alleviate catastrophic forgetting, many continual learning methods exploit an external buffer where a limited number of old samples are stored and used for replay when adapting to a new task. iCaRL [26] stores the representative exemplars in past tasks for knowledge distillation and prototype rehearsal. Gradient Episodic Memory (GEM) [21] formulates optimization constraints on the exemplars in memory. Averaged GEM (A-GEM) [8] is an improved version of GEM that achieves faster training and less memory consumption. GDumb [25] greedily stores samples in memory as they come and trains a model using samples only in the memory. Dark Experience Replay++ (DER++) [6] combines replay with knowledge distillation and regularization, and samples logits along the entire optimization trajectory." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In contrast to classical continual learning where data are separated by task boundaries and models are trained with multiple iterations in every task, we examine a more realistic and challenging problem where data are provided in tiny batches and models are trained on these batches only once. Recently, online continual learning (OCL) has gained increasing interests in computer vision [3, 7, 29, 9, 34]. Many OCL methods rely on representative memory replays to pre" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19247" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.211 + ], + "angle": 0, + "content": "vent forgetting. [3] utilizes gradients of network parameters to select replay samples of maximum diversity. Subsequent works [2, 29] propose to use losses and scoring functions as criteria for selecting the most representative samples for replay. However, these approaches tackle image classification problem in an artificial setting, where new classes appear in a specific order. Their performance in real-world vision tasks remains unclear." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.471, + 0.409 + ], + "angle": 0, + "content": "Lately, [34] benchmarks CL methods in the real-world online setting with full supervision. As the video streams arrive endlessly in a real-time manner, assigning annotations to all the video frames for training computational models is laborious and time-consuming. It becomes even more daunting in object detection tasks where class labels and bounding boxes of all objects on a video frame have to be provided. Reducing burdensome costs of labeling remains an under-explored and challenging problem in online continual object detection. We propose a self-sustaining Efficient-CLS, which is capable of exploiting the unlabeled video frames by pseudo-labeling when the number of labeled frames is limited." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.42, + 0.38, + 0.436 + ], + "angle": 0, + "content": "2.2. Complementary Learning Systems" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.47, + 0.807 + ], + "angle": 0, + "content": "The essence of fast and slow learning in Complementary Learning Systems (CLS) has benefited several continual learning algorithms in image recognition [24, 23, 28, 4, 15]. However, these methods either require the task boundaries, which are not applicable in our online video setting, or they require to train fast and slow learning systems with replay samples from the same replay buffer, which could easily lead to overfitting problem when the replay buffer has limited capacity. To eliminate overfitting problem, [28] and [15] utilize generative replay models to couple sequential tasks in a latent embedding space. While generative approaches have succeeded in artificial and simple datasets, they often fail in complex vision tasks, e.g., object detection. DualNet [23] also employs a slow-fast learning architecture. However, its update process for the slow learner is more computationally demanding because it leans on both self-supervised and supervised learning objectives. The self-supervised phase demands additional training iterations on extensive batches to yield satisfactory results, thereby delaying the training of the fast learner. In contrast, our method updates the slow learner in real-time using the fast learner's weights, obviating the need for distinct slow learner training. Our approach is optimized for online CL scenarios where computational resources are constrained." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.817, + 0.318, + 0.833 + ], + "angle": 0, + "content": "2.3. Semi-Supervised Learning" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "The goal of semi-supervised learning (SSL) [33, 5, 37, 36] is to reduce the demand of labeled data and harness unlabeled data for performance improvement. [31] first introduce SSL to the context of CL, and propose a strategy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.364 + ], + "angle": 0, + "content": "that combines pseudo-labeling, consistency regularization, out-of-distribution detection, and knowledge distillation to solve the problem of class-incremental image classification. However, to distill knowledge from previous tasks, their model relies heavily on the task boundary that identifies the change of training classes, which is not available in our LEOCOD setting. To reduce annotation costs in object detection, several methods [13, 32, 20] capitalize the teacher-student networks. In general, a teacher model predicts pseudo labels or enforces a consistency loss to guide the student networks. However, these previous works on semi-supervised object detection only consider the offline setting on static image datasets, while none of them has been extended to online continual learning on dynamic video streams. We discovered new insights that pseudo-labeling from slow learner to fast learner can not only reduce annotation overhead, but also alleviate forgetting, which is critical to the design of efficient continual learners in real world." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.378, + 0.591, + 0.394 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.404, + 0.661, + 0.42 + ], + "angle": 0, + "content": "3.1. Problem Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.892, + 0.548 + ], + "angle": 0, + "content": "We advance the online continual object detection in [34] to a label-efficient and computationally-efficient setting—Label-Efficient Online Continual Object Detection (LEOCOD). In contrast to the setting in [34] where video frames are extensively annotated and trained with multiple epochs, an agent in LEOCOD continuously learns from a sparsely annotated video stream in a single pass over time (see Figure 1(a))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Formally, we consider the online continual object detection on a continuum of video streams \\(\\mathcal{D} = \\{D_1,\\dots ,D_T\\}\\) where at time step \\(t\\) , a learning agent receives a mini-batch of continuous video frames \\(D_{t}\\) from current environment for online training (one single pass). To perform label-efficient object detection, within the batch \\(D_{t}\\) , only a subset of video frames \\(D_{t}^{s} = (X_{t}^{s},Y_{t}^{s})\\) are labeled, while the remaining video frames \\(D_{t}^{u} = (X_{t}^{u})\\) are unlabeled. For each labeled data sample, its annotation contains the bounding box locations and their corresponding class labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.871, + 0.727 + ], + "angle": 0, + "content": "3.2. Efficient Complementary Learning Systems" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We propose a plug-and-play module dubbed as EfficientCLS. Specifically, it consists of two feed-forward networks: (i) the fast learner is designed to quickly encode new knowledge from current data stream and then consolidate it to the slow learner; and (ii) the slow learner accumulates the acquired knowledge from fast learner over time and guides the fast learner with meaningful pseudo labels, when full supervision is not available. Same as [26, 8, 25, 6, 34], we maintain an external episodic memory, as a replay buffer, to store exemplars that can be retrieved for replays alongside ongoing video stream. As the fast and slow learners are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19248" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.093, + 0.873, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.335, + 0.895, + 0.42 + ], + "angle": 0, + "content": "Figure 2. The framework of Efficient-CLS. At each learning step, the system receives a batch of temporally continuous data \\( D_{t} \\), including labeled (green) and unlabeled (orange) frames. The fast learner trains the labeled frames alongside a small subset of labeled exemplars retrieved from episodic memory with the supervised loss \\( \\mathcal{L}_{sup} \\). Meanwhile, the fast learner leverages the pseudo labels generated by the slow learner to optimize a pseudo loss \\( \\mathcal{L}_{pseudo} \\). To reinstate memory of the slow learner, the weights of the slow learner are updated by taking the Exponential Moving Average (EMA) of the fast learner's weights. The fast and slow learners are complementary to each other, forming a positive feedback loop." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.471, + 0.48 + ], + "angle": 0, + "content": "model agnostic, our Efficient-CLS can be easily integrated into existing CL models, which leads to less supervision and minimal forgetting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.47, + 0.68 + ], + "angle": 0, + "content": "Learning with Labeled Frames. The fast learner and slow learner use the same standard Faster-RCNN [27] detector \\( f \\). Despite the same architecture, the weights of the fast and slow learners are not shared. We use \\( \\theta_{F} \\) and \\( \\theta_{S} \\) to denote the network parameters for fast and slow learners respectively. As shown in Figure 2, at each training step \\( t \\), we use the labeled video frames \\( D_{t}^{s} = (X_{t}^{s}, Y_{t}^{s}) \\) to optimize the fast learner \\( \\theta_{F} \\) with the standard supervised loss \\( \\mathcal{L}_{sup} \\) in Faster-RCNN [27]. It consists of four losses: Region Proposal Network (RPN) classification loss \\( \\mathcal{L}_{cls}^{rpn} \\), RPN regression loss \\( \\mathcal{L}_{reg}^{rpn} \\), Region of Interest (ROI) classification loss \\( \\mathcal{L}_{cls}^{roi} \\), and ROI regression loss \\( \\mathcal{L}_{reg}^{roi} \\). We define \\( \\mathcal{L}_{sup} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.688, + 0.47, + 0.714 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s u p} = \\mathcal {L} _ {c l s} ^ {r p n} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\mathcal {L} _ {r e g} ^ {r p n} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.711, + 0.422, + 0.728 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c l s} ^ {r o i} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\mathcal {L} _ {r e g} ^ {r o i} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Learning with Unlabeled Frames. We introduce a pseudo-labeling paradigm to capitalize the information from unlabeled video frames \\( D_{t}^{u} = (X_{t}^{u}) \\) for training. In our early exploration, we intuitively use the fast learner for pseudo-labeling as it quickly adapts the knowledge of nearby frames. However, we observe that using the pseudo labels generated by the fast learner for self-replay exhibits biases towards recently seen objects, which is less effective in preventing forgetting. This has also been verified in our ablation study (Section 5.3). In contrast, the slow learner" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.524 + ], + "angle": 0, + "content": "preserves the semantic knowledge over a longer time span which generates pseudo labels with fewer biases. This encourages the fast learner to capture more generic scene representations, hence, in turn, contributing to reinstatement of memory in the slow learner (Section 3.2), resulting in a positive feedback loop." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.893, + 0.734 + ], + "angle": 0, + "content": "Given all these design considerations, the slow learner takes the unlabeled video frames \\( D_{t}^{u} \\) as inputs to estimate the possible objects of interest and their corresponding bounding box locations. For brevity, we refer these \"pseudo bounding boxes and their corresponding class labels\" as \"pseudo labels\" in the paper. To get rid of false positives, we apply a threshold \\( \\tau \\) to filter out bounding boxes with predicted low confidence scores. Moreover, there also exist repetitive boxes which negatively impact the quality of pseudo-labeling. To address this issue, we use the technique of class-wise non-maximum suppression (NMS) [27] to remove the overlapped boxes and get the high-quality pseudo labels. Formally, the procedure of pseudo label generation is summarized below:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.742, + 0.892, + 0.76 + ], + "angle": 0, + "content": "\\[\nY _ {t} ^ {u} = \\mathrm {N M S} ([ f (X _ {t} ^ {u}; \\theta_ {S}) ] _ {> \\tau}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.891, + 0.796 + ], + "angle": 0, + "content": "where \\([\\cdot ]_{>\\tau}\\) denotes the bounding box selection with confidence score larger than \\(\\tau\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Given that the video streams are captured from the egocentric perspective in the real world, head and body motions may lead to undesired motion blur effects on some video frames. To enforce our module to learn invariant object representations from these video frames, same as the previous work [38], we apply data augmentation techniques on the pseudo-labeled frames, including 2D image" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19249" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.213 + ], + "angle": 0, + "content": "crops, rotations, and flipping. Note that different from image classification, the predicted bounding box locations also need to be updated accordingly after image augmentations. We denote these pseudo-labeled video frames and their re-adjusted pseudo labels after data augmentations as \\((\\tilde{X}_t^u,\\tilde{Y}_t^u)\\). We can then use these pseudo pairs \\((\\tilde{X}_t^u,\\tilde{Y}_t^u)\\) to train the fast learner by optimizing the pseudo loss \\(\\mathcal{L}_{pseudo}:= \\mathcal{L}_{cls}^{roi}(\\tilde{X}_t^u,\\tilde{Y}_t^u) + \\mathcal{L}_{req}^{roi}(\\tilde{X}_t^u,\\tilde{Y}_t^u)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.469, + 0.259 + ], + "angle": 0, + "content": "Overall, our Efficient-CLS is jointly trained with the following losses: \\(\\mathcal{L}_{total} = \\mathcal{L}_{sup} + \\lambda_{pseudo}\\mathcal{L}_{pseudo}\\), where \\(\\lambda_{pseudo}\\) is the weight of \\(\\mathcal{L}_{pseudo}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.269, + 0.469, + 0.375 + ], + "angle": 0, + "content": "Synapses Consolidation via EMA. To alleviate forgetting of obtained knowledge, we apply Exponential Moving Average (EMA) to gradually update the slow learner with the fast learner's weights. The evolving weight changes in the slow learner are functionally correlated with the memory consolidation mechanism in the hippocampus and the neocortex [4]. Formally, we define EMA process as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.381, + 0.469, + 0.397 + ], + "angle": 0, + "content": "\\[\n\\theta_ {S} = \\alpha \\theta_ {S} + (1 - \\alpha) \\theta_ {F}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.469, + 0.464 + ], + "angle": 0, + "content": "where the \\(\\alpha \\in [0,1]\\) is EMA rate. According to the stability-plasticity dilemma, a smaller \\(\\alpha\\) means faster adaptation but less memorization. Empirically, we set \\(\\alpha = 0.99\\), which leads to best performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.475, + 0.276, + 0.492 + ], + "angle": 0, + "content": "4. Experimental details" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.5, + 0.18, + 0.515 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.469, + 0.569 + ], + "angle": 0, + "content": "We evaluate the continual learning methods on two realistic and challenging video datasets, OAK [34] and EgoObjects [1], for the task of online continual object detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.689 + ], + "angle": 0, + "content": "OAK [34] is a large egocentric video stream dataset spanning nine months of a graduate student's life, consisting of 7.6 million frames of 460 video clips with a total length of 70.2 hours [30]. The dataset contains 103 object categories. We follow [34] in the ordering of training and testing data splits. One frame every 16 consecutive video frames lasting for 30 seconds is held out to construct a test set and the remaining frames are used for training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.81 + ], + "angle": 0, + "content": "EgoObjects [1] is one of the largest object-centric datasets focusing on object detection task. The dataset contains around 100k video frames with \\(\\sim 250\\mathrm{k}\\) annotations, which correspond to 277 categories and 1110 main objects [22]. Additionally, the dataset follows a long-tailed distribution which makes the task more challenging and real-world oriented. We adopt the same rule as OAK dataset to split the training and testing set." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.185, + 0.832 + ], + "angle": 0, + "content": "4.2. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We compare our model against the following baselines: 1) Vanilla training: Incremental Training is a naive baseline trained sequentially over the entire video stream without any measures to avoid catastrophic forgetting; Offline" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "Training is an upper bound that can access all the data throughout training; 2) Continual learning algorithms: EWC [16], iCaRL [26], A-GEM [8], GDumb [25], DER++ [6] and iOD [17]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.892, + 0.349 + ], + "angle": 0, + "content": "The iCaRL model implemented by [34] stands as the SOTA method in online continual object detection. We reproduce their results using the released code1. When calculating RPN and ROI losses for replay samples, their iCaRL model neglects the losses of background proposals and penalizes the foreground losses according to the proportion of the current samples and replay samples. We empirically found that this trick hinders the model from effective episodic replay, thus resulting in severe forgetting. Therefore, we re-implement the iCaRL by discarding the reweighting trick and reverting back to the standard RPN and ROI losses. We name these two different implementations as iCaRL(Wang et al.) and iCaRL(our impl.), respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.358, + 0.621, + 0.372 + ], + "angle": 0, + "content": "4.3. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.622 + ], + "angle": 0, + "content": "Protocols. First, we define the annotation cost as the proportion of number of labeled frames versus the total 16 frames within a mini-batch \\( D_{t} \\). For example, if 2 out of 16 consecutive frames within \\( D_{t} \\) get labeled, the annotation cost is \\( 2 / 16 = 12.5\\% \\). The frames to be labeled are randomly selected within each mini-batch \\( D_{t} \\). Considering that different choices of labeled frames might influence the model performance, for fair comparisons between models, we fix the choice of randomly selected labeled frames and use the same labeled and unlabeled frames for training all models. Based on the various annotation costs, we introduce two training protocols: fully supervised protocol (100% annotation cost) and sparse annotation protocol (where the annotation cost is less than 100%). In sparse annotation protocol, we further split the training experiments based on 50%/25%/12.5%/6.25% annotation costs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.709 + ], + "angle": 0, + "content": "Metrics. We evaluate the models with three standard metrics: continual average precision (CAP), final average precision (FAP) and forgetfulness (F) [34]. We employ an Average Precision (AP) metric at an Intersection over Union (IoU) threshold of 0.5, commonly referred to as AP50." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.71, + 0.892, + 0.739 + ], + "angle": 0, + "content": "CAP shows the average performance over the entire video stream. That is," + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.75, + 0.892, + 0.791 + ], + "angle": 0, + "content": "\\[\n\\mathrm {C A P} = \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\mathrm {C A P} _ {t _ {i}} = \\frac {1}{N C} \\sum_ {i = 0} ^ {N} \\sum_ {c = 0} ^ {C} \\mathrm {C A P} _ {t _ {i}} ^ {c}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.802, + 0.891, + 0.833 + ], + "angle": 0, + "content": "where \\(\\mathrm{CAP}_{t_i}^c\\) is the AP of class \\(c\\) on test set at the \\(i\\)-th evaluation step, \\(N\\) is the total number of evaluation steps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.833, + 0.892, + 0.878 + ], + "angle": 0, + "content": "FAP is the final performance of a model after seeing the entire video. That is, \\(\\mathrm{FAP} = \\mathrm{CAP}_{t_N}\\), where \\(t_N\\) denotes the last evaluation step." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.729, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)https://github.com/oakdata/benchmark" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19250" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.088, + 0.887, + 0.344 + ], + "angle": 0, + "content": "
Annotation CostOAKEgoObjects
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
Incremental100%8.387.720.0310.213.551.48
Offline Training100%48.2835.23-86.1859.81-
EWC100%7.737.02-0.125.151.600.57
iOD100%7.927.140.988.802.640.00
iCaRL(Wang et al.)100%22.8916.60-2.9537.6121.712.79
iCaRL(our impl.)100%36.1426.26-4.8960.8036.41-0.60
w/ Efficient-CLS25%38.36(+2.22)26.64(+0.38)-8.20(-3.31)61.26(+0.46)39.58(+3.17)-3.48(-2.88)
100%40.24(+4.10)28.18(+1.92)-8.10(-3.21)67.05(+6.25)40.36(+3.95)-3.67(-3.07)
A-GEM100%36.9426.19-5.5458.7935.88-8.38
w/ Efficient-CLS25%37.06(+0.12)26.36(+0.17)-7.76(-2.22)63.06(+4.27)39.46(+3.58)-7.49(+0.89)
100%39.87(+2.93)27.97(+1.78)-7.17(-1.63)66.94(+8.15)39.57(+3.69)-11.68(-3.30)
GDumb100%35.2725.29-6.5958.8536.38-5.21
w/ Efficient-CLS25%37.67(+2.40)25.59(+0.30)-9.30(-2.71)62.70(+3.85)38.78(+2.40)-8.86(-3.65)
100%38.61(+3.34)26.04(+0.75)-9.14(-2.55)63.55(+4.70)38.98(+2.60)-7.50(-2.29)
DER++100%37.7925.24-2.8755.8230.84-6.08
w/ Efficient-CLS25%37.93(+0.14)25.64(+0.4)-8.90(-6.03)59.70(+3.88)34.15(+3.31)-11.21(-5.13)
100%39.61(+1.82)26.73(+1.49)-8.30(-5.43)62.01(+6.19)33.09(+2.25)-11.05(-4.97)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.349, + 0.895, + 0.379 + ], + "angle": 0, + "content": "Table 1. Overall performance of existing algorithms and Efficient-CLS on OAK and EgoObjects. iCaRL(Wang et al.) denotes the SOTA model presented in [34], and iCaRL(our impl.) is the same method by our implementation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.473, + 0.593 + ], + "angle": 0, + "content": "\\(\\mathbf{F}\\) estimates the forgetfulness of the model due to the sequential training. It takes into account the time interval between the presence of an object category and its subsequent presence. For a class \\(c\\), we sort the \\(\\mathrm{CAP}_{t_i}^c\\) according to the time interval \\(k\\) between evaluation time \\(t_i\\) and the last time \\(t_i - k\\) the model is trained on \\(c\\). After \\(\\mathrm{CAP}_{t_i}^c\\) is sorted, all \\(\\mathrm{CAP}_{t_i}^c (i = 0,\\dots ,T)\\) are divided into \\(K\\) bins \\(B_{kmin},\\dots ,B_{kmax}\\) according to the time interval \\(k\\). The average CAP \\((\\mathrm{aCAP}_k)\\) of each bin \\(B_{k}\\) is defined as the model's performance for detecting class \\(c\\) after the model has not been trained on \\(c\\) for \\(k\\) time steps. The forgetfulness (F) of the class \\(c\\) is defined as the weighted sum of the performance decrease at each time:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.604, + 0.483, + 0.656 + ], + "angle": 0, + "content": "\\[\nF ^ {c} = \\sum_ {k = k m i n} ^ {k m a x} \\frac {k - k m i n}{\\sum_ {k = k m i n} ^ {k m a x} k - k m i n} \\times \\left(\\mathrm {a C A P} _ {k m i n} - \\mathrm {a C A P} _ {k}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.655, + 0.385, + 0.675 + ], + "angle": 0, + "content": "The overall forgetfulness is: \\(\\mathrm{F} = \\frac{1}{C}\\sum_{c = 0}^{C}\\mathrm{F}^{c}\\)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.682, + 0.295, + 0.698 + ], + "angle": 0, + "content": "4.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "For a fair comparison, we followed the prior work [34] to use Faster-RCNN [27] with ResNet-50 backbone [12] as our object detection network, which is initialized by the weights pre-trained on PASCAL VOC [10]. We used Adam optimizer with a constant learning rate of 0.0001, and the batch size was set to 16 frames. Same as [34], we maintained a replay buffer with 5 samples per class. At each time step \\( t \\), we first randomly retrieved 16 video frames from the replay buffer for joint training. We used confidence thresh \\( \\tau = 0.7 \\) to generate pseudo-labels for unlabeled frames, and applied EMA rate \\( \\alpha = 0.99 \\) to update the slow learner. The weight of pseudo loss \\( \\lambda_{pseudo} \\) was set to 1.0. All the experiments were conducted on 2 NVIDIA RTX 3090 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.394, + 0.587, + 0.41 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.42, + 0.735, + 0.436 + ], + "angle": 0, + "content": "5.1. Fully Supervised Protocol" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.536 + ], + "angle": 0, + "content": "As the previous work [34] focuses on online continual object detection (OCOD) in video streams, we first evaluated model performance in fully supervised setting (i.e., \\(100\\%\\) annotation cost), where all video frames are paired with human labels. The reported results were measured by standard metrics (CAP, FAP, and F, Section 4.3) in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Performance of CL baselines. [34] benchmarked Incremental, EWC, iCaRL(Wang et al.), and Offline Training on OAK dataset. They found the replay-based method (i.e. iCaRL(Wang et al.)) outperforms regularization-based method (i.e. EWC) by \\(10\\%\\) in FAP, while iCaRL(Wang et al.) has a huge gap of \\(30\\%\\) compared with Offline Training. Similar observations were made in Table 1, but the performance of Incremental and EWC were \\(4\\%\\) lower than that in [34], as in our setting we only trained each mini-batch of video frames once (they trained each mini-batch 10 times). As mentioned in Section 4.2, we introduce several variations to the original design of iCaRL(Wang et al.). Compared with iCaRL(Wang et al.), we observed a huge performance boost in FAP from \\(22.89\\%\\) to \\(36.14\\%\\) on OAK and from \\(37.61\\%\\) to \\(60.80\\%\\) on EgoObjects, abridging the gap between the baseline and Offline Training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We further adapted other standard CL baselines, including iOD, A-GEM, GDumb, DER++, to the OCOD setting for comparisons. iOD is the SOTA method in offline class-incremental object detection. Though it performs well in prior setting, iOD collapses when adapted to online video streams. One explanation is that iOD requires explicit task boundary to trigger the reshape of model gradients that opti" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19251" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.093, + 0.885, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.264, + 0.893, + 0.294 + ], + "angle": 0, + "content": "Figure 3. The changes of \\(\\mathrm{CAP}_{t_i}^c\\) with sampled categories on OAK dataset. The x-axis denotes time step across the entire video stream. The y-axis denotes the AP50 of the category at specific time step (i.e., \\(\\mathrm{CAP}_{t_i}^c\\)). The grey line indicates the existence of the category." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.315, + 0.471, + 0.406 + ], + "angle": 0, + "content": "mizes knowledge sharing between adjacent tasks. However, in online video streams, the task boundaries by classes are no longer available and the change of tasks is hard to identify, resulting in the failure to prevent forgetting. In contrast, replay-based methods (i.e., A-GEM, GDumb and DER++) generalize much better to the real-world streaming video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.47, + 0.658 + ], + "angle": 0, + "content": "Performance w/ Efficient-CLS. Inheriting from the benefit of fast and slow learning with EMA, our Efficient-CLS consistently improves all the state-of-the-art CL methods (i.e. iCaRL(our impl.), A-GEM, GDumb and DER++) by a significant margin. Taking iCaRL(our impl.) for example, with Efficient-CLS, we observed superior performance and minimal forgetting compared to baseline methods, even when categories appeared infrequently (e.g., sculpture in Figure 3). Since semantic contextual information is more important in indoor environments on EgoObjects compared to the outdoor environments in OAK, we noticed that the improvement brought by our method is even greater on EgoObjects with an increase of \\(6.25\\%\\) in FAP, \\(3.95\\%\\) in CAP \\(\\%\\) and \\(3.07\\%\\) in F. Consistent performance gains are also noticeable for A-GEM, GDumb and DER++, demonstrating the effectiveness and flexibility of our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.327, + 0.683 + ], + "angle": 0, + "content": "5.2. Sparse Annotation Protocol" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Performance of CL baselines. The sparse annotation protocol is more challenging than the previous fully supervised protocol as shown by the performance differences when number of annotated video frames decreases (compare the performance of each colored bar along the x-axis within each subplot in Figure 4). We noted that GDumb is more resilient against the reduce of supervision. Specifically, from Table 2 at the lowest annotation cost of \\(6.25\\%\\) on EgoObjects dataset, GDumb achieves the highest performance of \\(38.74\\%\\), \\(22.69\\%\\) and \\(-4.53\\%\\) in FAP, CAP and F, which surpasses other baselines by a considerable margin. Same observations can be made on OAK dataset. One possible explanation is that GDumb only trains the data stored in the balanced replay buffer, which makes it less vulnerable" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.311, + 0.892, + 0.424 + ], + "angle": 0, + "content": "
OAKEgoObjects
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
iCaRL23.0417.75-3.3132.9119.15-1.36
w/ Efficient-CLS29.7220.31-5.3640.1623.95-2.01
A-GEM23.5916.15-2.9921.8412.280.82
w/ Efficient-CLS30.1820.59-5.4438.9623.79-5.64
GDumb27.3719.64-4.2538.7422.69-4.53
w/ Efficient-CLS29.0719.99-6.0140.0923.67-5.16
DER++24.2115.93-3.7916.958.482.03
w/ Efficient-CLS28.6319.64-4.6035.7820.74-4.69
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.43, + 0.893, + 0.459 + ], + "angle": 0, + "content": "Table 2. Performance of Efficient-CLS at low annotation cost of \\(6.25\\%\\). The best results are bold-faced." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.476, + 0.893, + 0.507 + ], + "angle": 0, + "content": "able to class imbalance problem brought by the reduce of labeled samples in the training set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.893, + 0.791 + ], + "angle": 0, + "content": "Performance w/ Efficient-CLS. Our proposed Efficient-CLS is a plug-and-play module that can be easily inserted into and enhance existing continual learning algorithms with the ability to use unlabeled video frames effectively. In both OAK and EgoObjects dataset, Efficient-CLS consistently improves the comparative SOTAs in all three evaluation metrics regardless of various degrees of annotation cost. As shown in Table 2, at a lower annotation cost of \\(6.25\\%\\), Efficient-CLS doubles the performance of DER++ and A-GEM in terms of FAP and CAP, and achieves an even larger improvement in preventing forgetting. Thanks to the useful information from pseudo labels predicted by the slow learner in Efficient-CLS, our method is more robust to various annotation costs, compared with SOTAs (compare the rate of change of blue bars vs. red bars over different degrees of annotation cost). Most remarkably, Efficient-CLS with \\(25\\%\\) annotation cost has already outperformed comparative SOTAs with \\(100\\%\\) annotation cost (see Table 1)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.655, + 0.818 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We assessed the importance of our key design choices. The Complementary Learning Systems (CLS) in EfficientCLS is the key for rapidly adapting to learn new tasks, meanwhile, retaining previously learnt knowledge. It constitutes of two memory reinstatement mechanisms: one is" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19252" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.089, + 0.365, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.09, + 0.609, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.091, + 0.849, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.22, + 0.363, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.363, + 0.22, + 0.605, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.22, + 0.848, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.895, + 0.424 + ], + "angle": 0, + "content": "Figure 4. Evaluation of online continual object detection in video streams with three metrics (FAP, CAP and F, Section 4.3) on OAK dataset (first row) and EgoObjects dataset (second row). The higher the bars are, the better. The x-axis denotes the percentage of video frames that are labeled in the video stream. It ranges from \\(6.25\\%\\) to \\(100\\%\\) (full supervision). The y-axis indicates the performance using different evaluation metrics. Ours (iCaRL(our impl.) w/ Efficient-CLS, red) consistently beats the comparative SOTA (iCaRL(our impl.), blue) in all evaluation metrics." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.44, + 0.875, + 0.519 + ], + "angle": 0, + "content": "
EMAPL50%25%12.5%6.25%
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
XX34.6825.78-4.1533.7024.57-4.3028.7619.80-5.4823.0417.75-3.31
✓X35.7425.77-4.8234.7925.62-4.3531.7221.16-7.2427.8420.03-3.96
X✓35.6125.56-3.7634.9525.65-3.6531.6022.44-4.8326.3919.50-1.99
✓✓38.6126.90-7.2938.3626.64-8.2033.9223.04-7.7129.7220.31-5.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.523, + 0.893, + 0.552 + ], + "angle": 0, + "content": "Table 3. Effectiveness of Exponential Moving Average (EMA) and Pseudo-labeling (PL) for iCaRL (our impl.) on OAK dataset at annotation cost \\(50\\%\\), \\(25\\%\\), \\(12.5\\%\\) and \\(6.25\\%\\). The best results are bold-faced." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.57, + 0.471, + 0.632 + ], + "angle": 0, + "content": "synaptic weight transfer from fast to slow learner via exponential moving average (EMA); and the other is reciprocal replay from slow learner to fast learner with pseudolabeling (PL). Here we studied their effects individually." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Ablation: Exponential Moving Average (EMA). We removed EMA by setting the \\(\\alpha\\) in Equation 3 to 1, where the model weights of the fast learner and slow learner are now shared throughout the learning process. Note that in the fully supervised protocol, the pseudo-labeling is turned off and the Efficient-CLS equals to the EMA alone. From Table 1 at \\(100\\%\\) annotation cost, we observed that removing EMA leads to significant performance drops ranging from \\(2\\%\\) to \\(8\\%\\), for all the comparative baselines on both OAK and EgoObjects. This shows that the slow learner can effectively consolidate the knowledge from the fast learner, and constructively alleviate catastrophic forgetting by synapses consolidation over time. Similar observations were made in Table 3 in the sparse annotation protocol (compare Row 2 vs. Row 1, Row 4 vs. Row 3). It is worth noting that, the performance difference between naive model (Row 1) and its variant with EMA (Row 2) is slightly larger in lower su" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.893, + 0.661 + ], + "angle": 0, + "content": "pervision (i.e. \\(12.5\\%\\), \\(6.25\\%\\)) than higher supervision (i.e. \\(50\\%\\), \\(25\\%\\)). One possible reason is that, compared with higher supervision, the fast learner suffers more forgetting in lower supervision; hence, the effect of removing EMA becomes stronger in lower supervision, again highlighting the importance of EMA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.895, + 0.809 + ], + "angle": 0, + "content": "Ablation: Pseudo-labeling (PL). We ablate our model by removing the PL of the slow learner across varying annotation costs and reported the results in Table 3. The removal of PL (Row 2) leads to a performance drop of around \\(2\\%\\) in FAP, \\(1\\%\\) in CAP and \\(0.5 - 4\\%\\) in F, compared with our full Efficient-CLS (Row 4). It implies that the slow learner captures useful semantic information from unlabeled video frames and these predicted pseudo labels are helpful in training the fast learner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.9 + ], + "angle": 0, + "content": "To investigate whether pseudo labels predicted by the fast learner itself could help stream learning, we conducted another ablation experiment where we performed PL without EMA (Row 3). Compared with the naive model (Row 1), we observed a performance increase from \\(28.76\\%\\) to \\(31.60\\%\\) in FAP and \\(19.80\\%\\) to \\(22.44\\%\\) in CAP. It indicates" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19253" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "that, due to the temporal correlation in video stream, pseudo labels predicted by the fast learner can serve as an informative supervision for the training of the fast learner itself." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.471, + 0.364 + ], + "angle": 0, + "content": "However, replaying the self-predicted pseudo labels on the fast learner fails to prevent forgetting, as indicated by the drop from \\(-5.48\\%\\) to \\(-4.83\\%\\) in F. It is possible that the pseudo labels generated by the fast learner only bias towards the classes which have already been learnt very well and fail to reinforce the fast learner to improve on the poorly-learnt classes. Different from the fast learner, the slow learner integrates semantic information over time. The predicted pseudo labels carry more semantic information, which is useful for fast learner to capture more generic object representations during pseudo label replays. Again, this emphasizes that the reciprocal replay from the slow learner to the fast learner is critical for memory reinstatement, which has been missing in the computational modeling literature of CLS." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.379, + 0.196, + 0.394 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.471, + 0.603 + ], + "angle": 0, + "content": "To imitate what humans see and learn in the real world, we introduce a more realistic and challenging problem of label-efficient online continual object detection (LEOCOD) in video streams. Addressing this problem would greatly benefit real-world applications by reducing model retraining time and data labeling costs. Inspired by the Complementary Learning Systems (CLS) theory, we propose a plug-and-play module, namely Efficient-CLS, that can be easily integrated into and improve existing continual leaning algorithms. We evaluate Efficient-CLS on two challenging real-world video datasets, where our method achieves the state-of-the-art performance in preventing catastrophic forgetting, all while requiring minimal annotation effort." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.47, + 0.79 + ], + "angle": 0, + "content": "Acknowledgements This research is funded by the National Research Foundation, Singapore under its NRFF Award NRF-NRFF13-2021-0008 & NRF-NRFF15-2023-0001, AI Singapore Programme (AISG Award No: AISGC-2019-001-2A & AISG2-RP-2021-025), Mike Zheng Shou's Start-Up Grant from NUS, Mengmi Zhang's Startup Grant from Agency for Science, Technology, and Research (A*STAR), and Early Career Investigatorship from Center for Frontier AI Research (CFAR), A*STAR. 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Springer, 2020. 4" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.615 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19255" + } + ] +] \ No newline at end of file diff --git a/2023/Label-Efficient Online Continual Object Detection in Streaming Video/bb408240-93f4-4420-9e47-a5facd88851a_origin.pdf b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/bb408240-93f4-4420-9e47-a5facd88851a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4fce55bce904af0040e88eb789ac600ccddba8a0 --- /dev/null +++ b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/bb408240-93f4-4420-9e47-a5facd88851a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3f0e80a36f4d370683922f406726e4161653dfb83dd142add2e8cb3e0374866b +size 2745861 diff --git a/2023/Label-Efficient Online Continual Object Detection in Streaming Video/full.md b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/full.md new file mode 100644 index 0000000000000000000000000000000000000000..202d6d56e4f8f5534e085665b5b10c1ff2320fbe --- /dev/null +++ b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/full.md @@ -0,0 +1,282 @@ +# Label-Efficient Online Continual Object Detection in Streaming Video + +Jay Zhangjie Wu $^{1}$ David Junhao Zhang $^{1}$ Wynne Hsu $^{2}$ Mengmi Zhang $^{3,4}$ Mike Zheng Shou $^{1*}$ + +$^{1}$ Show Lab, $^{2}$ National University of Singapore + $^{3}$ School of Computer Science and Engineering, Nanyang Technological University, Singapore + $^{4}$ CFAR and I2R, Agency for Science, Technology and Research, Singapore + +# Abstract + +Humans can watch a continuous video stream and effortlessly perform continual acquisition and transfer of new knowledge with minimal supervision yet retaining previously learnt experiences. In contrast, existing continual learning (CL) methods require fully annotated labels to effectively learn from individual frames in a video stream. Here, we examine a more realistic and challenging problem—Label-Efficient Online Continual Object Detection (LEOCOD) in streaming video. We propose a plug-and-play module, Efficient-CLS, that can be easily inserted into and consistently improve existing CL algorithms for object detection in video streams with reduced data annotation costs and model retraining time. We show that our method has achieved significant improvement with minimal forgetting across all supervision levels on two challenging CL benchmarks for streaming real-world videos. Remarkably, with only $25\%$ annotated video frames, our proposed method still outperforms the state-of-the-art CL models trained with $100\%$ annotations on all video frames. The data and source code will be publicly available at https://github.com/showlab/Efficient-CLS. + +# 1. Introduction + +Humans have the ability to continuously learn from an ever-changing environment, while retaining previously learnt experiences. In contrast to human learning, prior works [3, 2, 11, 34, 7] show that deep neural networks are prone to catastrophic forgetting. To address the forgetting problem, existing works in continual learning (CL) primarily focus on class-incremental image classification or object detection. Their experiment settings are often idealistic and simplified, where i.i.d. static images are usually grouped by class and incrementally presented to computational models in sequence. To learn a particular task containing specific + +classes, an agent can go through all the data of current task over multiple epochs. After that, the learned classes in current task become unavailable, i.e., no overlaps between the sets of learned classes and unseen classes. + +However, these experiment designs deviate from the online continual learning (OCL) setting in the real world, where an agent learns from temporally correlated non-i.i.d. video streams in one single pass. Given context regularities in natural environments, an agent is likely to encounter cases when objects of previously learnt classes co-occur with unknown objects from unseen classes, e.g., a computer mouse and a computer monitor often co-occur. Taking these considerations, [34] introduces OCL on object detection in real-world video streams. They evaluate existing CL approaches on this setting and report a huge performance gap compared with offline training. + +Based on the setting in [34], we take a significant step further and introduce a novel problem setting called Label-Efficient Online Continual Object Detection (LEOCOD), which highlights two unique challenges. First, the setting in [34] is such that the CL algorithms are trained with every mini-batch over multiple passes. We tighten the training recipe in LEOCOD to strictly online, where data is allowed to have one single pass and models are trained on the entire video dataset for only one epoch. Second, existing CL models require fully supervised training where box-level ground truth labels of every object on every video frame have to be obtained from human annotators. Unlike static images, acquiring human annotations for object detection on videos can be expensive and daunting. Thus, in LEOCOD, the video frames per mini-batch are sparsely annotated to alleviate the burdens of extensive human labeling, making LEOCOD one step closer to real world application. + +Cognitive science works [35, 19] show that humans are efficient at continuously learning from very few annotated data samples. We get inspirations from the theory of Complementary Learning Systems (CLS) in human brains [18], and propose a plug-and-play module for the LEOCOD task, dubbed as Efficient-CLS. In Efficient-CLS, we introduce + +![](images/a090acd2ce689d64a3637fba2655497866caff7450015ef2e8e9c44ef677bcb6.jpg) +Figure 1. (a) Problem introduction: An agent continuously learns from a never-ending online video stream over time. In each training step, out of a mini-batch containing 16 consecutive video frames, only a fixed proportion of frames are labeled (green boundary), while the rest of the frames are unlabeled (orange boundary). Following [34], the video frame after every training mini-batch (transparent) is held out for testing. After every 100 training steps, the agent is evaluated on all the video frames from the test set for object detection. (b) Key results: Our proposed method (red) consistently outperforms the best competitive baseline (blue) by a margin of $5\%$ . Remarkably, our model, trained at $25\%$ annotation cost, surpasses the best baseline trained at $100\%$ (grey line). The orange cross denotes the performance of the state-of-the-art model, which is $15\%$ lower than our method. + +![](images/234e7cabfb9d3c0d9353c67dc8de8cfcc68f8333688ee4fc4fea263dba5918d3.jpg) + +two feed-forward neural networks as slow and fast learners. In the fast learner, memory is rapidly adapted to the current task. The weights of the slow learner change a little on each reinstatement, and are maintained by taking the exponential moving average (EMA) of the fast learner's weights over time. Though a few continual learning models in previous works [4, 24] also use a similar source of inspiration, they miss the effect of reciprocal connections from slow learners to fast learners, which we intend to address. Inspired by the bidirectional interaction in CLS [14], we reactivate the weights of the slow learners to predict meaningful pseudo labels from the unlabeled video frames and use these pseudo labels to guide the training of the fast learner, closing the loop between the two systems. + +We demonstrate the versatility and effectiveness of our Efficient-CLS on two standard real-world video datasets, OAK [34] and EgoObjects [1]. Our proposed method can be easily integrated into existing CL models and consistently improve their performance by a large margin in LEOCOD. It is worth noting that, with only $25\%$ labeled data, our method surpasses the comparative baselines trained with full supervision (Figure 1(b)). + +To summarize, we make the following key contributions: + +- We introduce a new, challenging and important problem of label-efficient online continual object detection (LEOCOD) in video streams. Solving this problem would greatly benefit real-world applications in reducing annotation cost and model retraining time. +- We propose Efficient-CLS, a plug-and-play module inspired from the Complementary Learning Systems (CLS) theory, which can be integrated into existing CL + +models and learn efficiently and effectively with less supervision and minimal forgetting. + +- We benchmark existing CL methods on the task of LEOCOD and demonstrate the state-of-the-art performance of our method through extensive experiments. + +# 2. Related Work + +# 2.1. Continual Learning + +To alleviate catastrophic forgetting, many continual learning methods exploit an external buffer where a limited number of old samples are stored and used for replay when adapting to a new task. iCaRL [26] stores the representative exemplars in past tasks for knowledge distillation and prototype rehearsal. Gradient Episodic Memory (GEM) [21] formulates optimization constraints on the exemplars in memory. Averaged GEM (A-GEM) [8] is an improved version of GEM that achieves faster training and less memory consumption. GDumb [25] greedily stores samples in memory as they come and trains a model using samples only in the memory. Dark Experience Replay++ (DER++) [6] combines replay with knowledge distillation and regularization, and samples logits along the entire optimization trajectory. + +In contrast to classical continual learning where data are separated by task boundaries and models are trained with multiple iterations in every task, we examine a more realistic and challenging problem where data are provided in tiny batches and models are trained on these batches only once. Recently, online continual learning (OCL) has gained increasing interests in computer vision [3, 7, 29, 9, 34]. Many OCL methods rely on representative memory replays to pre + +vent forgetting. [3] utilizes gradients of network parameters to select replay samples of maximum diversity. Subsequent works [2, 29] propose to use losses and scoring functions as criteria for selecting the most representative samples for replay. However, these approaches tackle image classification problem in an artificial setting, where new classes appear in a specific order. Their performance in real-world vision tasks remains unclear. + +Lately, [34] benchmarks CL methods in the real-world online setting with full supervision. As the video streams arrive endlessly in a real-time manner, assigning annotations to all the video frames for training computational models is laborious and time-consuming. It becomes even more daunting in object detection tasks where class labels and bounding boxes of all objects on a video frame have to be provided. Reducing burdensome costs of labeling remains an under-explored and challenging problem in online continual object detection. We propose a self-sustaining Efficient-CLS, which is capable of exploiting the unlabeled video frames by pseudo-labeling when the number of labeled frames is limited. + +# 2.2. Complementary Learning Systems + +The essence of fast and slow learning in Complementary Learning Systems (CLS) has benefited several continual learning algorithms in image recognition [24, 23, 28, 4, 15]. However, these methods either require the task boundaries, which are not applicable in our online video setting, or they require to train fast and slow learning systems with replay samples from the same replay buffer, which could easily lead to overfitting problem when the replay buffer has limited capacity. To eliminate overfitting problem, [28] and [15] utilize generative replay models to couple sequential tasks in a latent embedding space. While generative approaches have succeeded in artificial and simple datasets, they often fail in complex vision tasks, e.g., object detection. DualNet [23] also employs a slow-fast learning architecture. However, its update process for the slow learner is more computationally demanding because it leans on both self-supervised and supervised learning objectives. The self-supervised phase demands additional training iterations on extensive batches to yield satisfactory results, thereby delaying the training of the fast learner. In contrast, our method updates the slow learner in real-time using the fast learner's weights, obviating the need for distinct slow learner training. Our approach is optimized for online CL scenarios where computational resources are constrained. + +# 2.3. Semi-Supervised Learning + +The goal of semi-supervised learning (SSL) [33, 5, 37, 36] is to reduce the demand of labeled data and harness unlabeled data for performance improvement. [31] first introduce SSL to the context of CL, and propose a strategy + +that combines pseudo-labeling, consistency regularization, out-of-distribution detection, and knowledge distillation to solve the problem of class-incremental image classification. However, to distill knowledge from previous tasks, their model relies heavily on the task boundary that identifies the change of training classes, which is not available in our LEOCOD setting. To reduce annotation costs in object detection, several methods [13, 32, 20] capitalize the teacher-student networks. In general, a teacher model predicts pseudo labels or enforces a consistency loss to guide the student networks. However, these previous works on semi-supervised object detection only consider the offline setting on static image datasets, while none of them has been extended to online continual learning on dynamic video streams. We discovered new insights that pseudo-labeling from slow learner to fast learner can not only reduce annotation overhead, but also alleviate forgetting, which is critical to the design of efficient continual learners in real world. + +# 3. Method + +# 3.1. Problem Setting + +We advance the online continual object detection in [34] to a label-efficient and computationally-efficient setting—Label-Efficient Online Continual Object Detection (LEOCOD). In contrast to the setting in [34] where video frames are extensively annotated and trained with multiple epochs, an agent in LEOCOD continuously learns from a sparsely annotated video stream in a single pass over time (see Figure 1(a)). + +Formally, we consider the online continual object detection on a continuum of video streams $\mathcal{D} = \{D_1,\dots ,D_T\}$ where at time step $t$ , a learning agent receives a mini-batch of continuous video frames $D_{t}$ from current environment for online training (one single pass). To perform label-efficient object detection, within the batch $D_{t}$ , only a subset of video frames $D_{t}^{s} = (X_{t}^{s},Y_{t}^{s})$ are labeled, while the remaining video frames $D_{t}^{u} = (X_{t}^{u})$ are unlabeled. For each labeled data sample, its annotation contains the bounding box locations and their corresponding class labels. + +# 3.2. Efficient Complementary Learning Systems + +We propose a plug-and-play module dubbed as EfficientCLS. Specifically, it consists of two feed-forward networks: (i) the fast learner is designed to quickly encode new knowledge from current data stream and then consolidate it to the slow learner; and (ii) the slow learner accumulates the acquired knowledge from fast learner over time and guides the fast learner with meaningful pseudo labels, when full supervision is not available. Same as [26, 8, 25, 6, 34], we maintain an external episodic memory, as a replay buffer, to store exemplars that can be retrieved for replays alongside ongoing video stream. As the fast and slow learners are + +![](images/02a21dd849294a5f80d943914591152a18efa413983492843b7fea011e65dfed.jpg) +Figure 2. The framework of Efficient-CLS. At each learning step, the system receives a batch of temporally continuous data $D_{t}$ , including labeled (green) and unlabeled (orange) frames. The fast learner trains the labeled frames alongside a small subset of labeled exemplars retrieved from episodic memory with the supervised loss $\mathcal{L}_{sup}$ . Meanwhile, the fast learner leverages the pseudo labels generated by the slow learner to optimize a pseudo loss $\mathcal{L}_{pseudo}$ . To reinstate memory of the slow learner, the weights of the slow learner are updated by taking the Exponential Moving Average (EMA) of the fast learner's weights. The fast and slow learners are complementary to each other, forming a positive feedback loop. + +model agnostic, our Efficient-CLS can be easily integrated into existing CL models, which leads to less supervision and minimal forgetting. + +Learning with Labeled Frames. The fast learner and slow learner use the same standard Faster-RCNN [27] detector $f$ . Despite the same architecture, the weights of the fast and slow learners are not shared. We use $\theta_{F}$ and $\theta_{S}$ to denote the network parameters for fast and slow learners respectively. As shown in Figure 2, at each training step $t$ , we use the labeled video frames $D_{t}^{s} = (X_{t}^{s}, Y_{t}^{s})$ to optimize the fast learner $\theta_{F}$ with the standard supervised loss $\mathcal{L}_{sup}$ in Faster-RCNN [27]. It consists of four losses: Region Proposal Network (RPN) classification loss $\mathcal{L}_{cls}^{rpn}$ , RPN regression loss $\mathcal{L}_{reg}^{rpn}$ , Region of Interest (ROI) classification loss $\mathcal{L}_{cls}^{roi}$ , and ROI regression loss $\mathcal{L}_{reg}^{roi}$ . We define $\mathcal{L}_{sup}$ as: + +$$ +\mathcal {L} _ {s u p} = \mathcal {L} _ {c l s} ^ {r p n} \left(X _ {t} ^ {s}, Y _ {t} ^ {s}\right) + \mathcal {L} _ {r e g} ^ {r p n} \left(X _ {t} ^ {s}, Y _ {t} ^ {s}\right) + \tag {1} +$$ + +$$ +\mathcal {L} _ {c l s} ^ {r o i} \left(X _ {t} ^ {s}, Y _ {t} ^ {s}\right) + \mathcal {L} _ {r e g} ^ {r o i} \left(X _ {t} ^ {s}, Y _ {t} ^ {s}\right). +$$ + +Learning with Unlabeled Frames. We introduce a pseudo-labeling paradigm to capitalize the information from unlabeled video frames $D_{t}^{u} = (X_{t}^{u})$ for training. In our early exploration, we intuitively use the fast learner for pseudo-labeling as it quickly adapts the knowledge of nearby frames. However, we observe that using the pseudo labels generated by the fast learner for self-replay exhibits biases towards recently seen objects, which is less effective in preventing forgetting. This has also been verified in our ablation study (Section 5.3). In contrast, the slow learner + +preserves the semantic knowledge over a longer time span which generates pseudo labels with fewer biases. This encourages the fast learner to capture more generic scene representations, hence, in turn, contributing to reinstatement of memory in the slow learner (Section 3.2), resulting in a positive feedback loop. + +Given all these design considerations, the slow learner takes the unlabeled video frames $D_{t}^{u}$ as inputs to estimate the possible objects of interest and their corresponding bounding box locations. For brevity, we refer these "pseudo bounding boxes and their corresponding class labels" as "pseudo labels" in the paper. To get rid of false positives, we apply a threshold $\tau$ to filter out bounding boxes with predicted low confidence scores. Moreover, there also exist repetitive boxes which negatively impact the quality of pseudo-labeling. To address this issue, we use the technique of class-wise non-maximum suppression (NMS) [27] to remove the overlapped boxes and get the high-quality pseudo labels. Formally, the procedure of pseudo label generation is summarized below: + +$$ +Y _ {t} ^ {u} = \mathrm {N M S} ([ f (X _ {t} ^ {u}; \theta_ {S}) ] _ {> \tau}), \tag {2} +$$ + +where $[\cdot ]_{>\tau}$ denotes the bounding box selection with confidence score larger than $\tau$ + +Given that the video streams are captured from the egocentric perspective in the real world, head and body motions may lead to undesired motion blur effects on some video frames. To enforce our module to learn invariant object representations from these video frames, same as the previous work [38], we apply data augmentation techniques on the pseudo-labeled frames, including 2D image + +crops, rotations, and flipping. Note that different from image classification, the predicted bounding box locations also need to be updated accordingly after image augmentations. We denote these pseudo-labeled video frames and their re-adjusted pseudo labels after data augmentations as $(\tilde{X}_t^u,\tilde{Y}_t^u)$ . We can then use these pseudo pairs $(\tilde{X}_t^u,\tilde{Y}_t^u)$ to train the fast learner by optimizing the pseudo loss $\mathcal{L}_{pseudo}:= \mathcal{L}_{cls}^{roi}(\tilde{X}_t^u,\tilde{Y}_t^u) + \mathcal{L}_{req}^{roi}(\tilde{X}_t^u,\tilde{Y}_t^u)$ . + +Overall, our Efficient-CLS is jointly trained with the following losses: $\mathcal{L}_{total} = \mathcal{L}_{sup} + \lambda_{pseudo}\mathcal{L}_{pseudo}$ , where $\lambda_{pseudo}$ is the weight of $\mathcal{L}_{pseudo}$ . + +Synapses Consolidation via EMA. To alleviate forgetting of obtained knowledge, we apply Exponential Moving Average (EMA) to gradually update the slow learner with the fast learner's weights. The evolving weight changes in the slow learner are functionally correlated with the memory consolidation mechanism in the hippocampus and the neocortex [4]. Formally, we define EMA process as: + +$$ +\theta_ {S} = \alpha \theta_ {S} + (1 - \alpha) \theta_ {F}, \tag {3} +$$ + +where the $\alpha \in [0,1]$ is EMA rate. According to the stability-plasticity dilemma, a smaller $\alpha$ means faster adaptation but less memorization. Empirically, we set $\alpha = 0.99$ , which leads to best performance. + +# 4. Experimental details + +# 4.1. Datasets + +We evaluate the continual learning methods on two realistic and challenging video datasets, OAK [34] and EgoObjects [1], for the task of online continual object detection. + +OAK [34] is a large egocentric video stream dataset spanning nine months of a graduate student's life, consisting of 7.6 million frames of 460 video clips with a total length of 70.2 hours [30]. The dataset contains 103 object categories. We follow [34] in the ordering of training and testing data splits. One frame every 16 consecutive video frames lasting for 30 seconds is held out to construct a test set and the remaining frames are used for training. + +EgoObjects [1] is one of the largest object-centric datasets focusing on object detection task. The dataset contains around 100k video frames with $\sim 250\mathrm{k}$ annotations, which correspond to 277 categories and 1110 main objects [22]. Additionally, the dataset follows a long-tailed distribution which makes the task more challenging and real-world oriented. We adopt the same rule as OAK dataset to split the training and testing set. + +# 4.2. Baselines + +We compare our model against the following baselines: 1) Vanilla training: Incremental Training is a naive baseline trained sequentially over the entire video stream without any measures to avoid catastrophic forgetting; Offline + +Training is an upper bound that can access all the data throughout training; 2) Continual learning algorithms: EWC [16], iCaRL [26], A-GEM [8], GDumb [25], DER++ [6] and iOD [17]. + +The iCaRL model implemented by [34] stands as the SOTA method in online continual object detection. We reproduce their results using the released code1. When calculating RPN and ROI losses for replay samples, their iCaRL model neglects the losses of background proposals and penalizes the foreground losses according to the proportion of the current samples and replay samples. We empirically found that this trick hinders the model from effective episodic replay, thus resulting in severe forgetting. Therefore, we re-implement the iCaRL by discarding the reweighting trick and reverting back to the standard RPN and ROI losses. We name these two different implementations as iCaRL(Wang et al.) and iCaRL(our impl.), respectively. + +# 4.3. Evaluation + +Protocols. First, we define the annotation cost as the proportion of number of labeled frames versus the total 16 frames within a mini-batch $D_{t}$ . For example, if 2 out of 16 consecutive frames within $D_{t}$ get labeled, the annotation cost is $2 / 16 = 12.5\%$ . The frames to be labeled are randomly selected within each mini-batch $D_{t}$ . Considering that different choices of labeled frames might influence the model performance, for fair comparisons between models, we fix the choice of randomly selected labeled frames and use the same labeled and unlabeled frames for training all models. Based on the various annotation costs, we introduce two training protocols: fully supervised protocol (100% annotation cost) and sparse annotation protocol (where the annotation cost is less than 100%). In sparse annotation protocol, we further split the training experiments based on 50%/25%/12.5%/6.25% annotation costs. + +Metrics. We evaluate the models with three standard metrics: continual average precision (CAP), final average precision (FAP) and forgetfulness (F) [34]. We employ an Average Precision (AP) metric at an Intersection over Union (IoU) threshold of 0.5, commonly referred to as AP50. + +CAP shows the average performance over the entire video stream. That is, + +$$ +\mathrm {C A P} = \frac {1}{N} \sum_ {i = 0} ^ {N} \mathrm {C A P} _ {t _ {i}} = \frac {1}{N C} \sum_ {i = 0} ^ {N} \sum_ {c = 0} ^ {C} \mathrm {C A P} _ {t _ {i}} ^ {c}, \tag {4} +$$ + +where $\mathrm{CAP}_{t_i}^c$ is the AP of class $c$ on test set at the $i$ -th evaluation step, $N$ is the total number of evaluation steps. + +FAP is the final performance of a model after seeing the entire video. That is, $\mathrm{FAP} = \mathrm{CAP}_{t_N}$ , where $t_N$ denotes the last evaluation step. + +
Annotation CostOAKEgoObjects
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
Incremental100%8.387.720.0310.213.551.48
Offline Training100%48.2835.23-86.1859.81-
EWC100%7.737.02-0.125.151.600.57
iOD100%7.927.140.988.802.640.00
iCaRL(Wang et al.)100%22.8916.60-2.9537.6121.712.79
iCaRL(our impl.)100%36.1426.26-4.8960.8036.41-0.60
w/ Efficient-CLS25%38.36(+2.22)26.64(+0.38)-8.20(-3.31)61.26(+0.46)39.58(+3.17)-3.48(-2.88)
100%40.24(+4.10)28.18(+1.92)-8.10(-3.21)67.05(+6.25)40.36(+3.95)-3.67(-3.07)
A-GEM100%36.9426.19-5.5458.7935.88-8.38
w/ Efficient-CLS25%37.06(+0.12)26.36(+0.17)-7.76(-2.22)63.06(+4.27)39.46(+3.58)-7.49(+0.89)
100%39.87(+2.93)27.97(+1.78)-7.17(-1.63)66.94(+8.15)39.57(+3.69)-11.68(-3.30)
GDumb100%35.2725.29-6.5958.8536.38-5.21
w/ Efficient-CLS25%37.67(+2.40)25.59(+0.30)-9.30(-2.71)62.70(+3.85)38.78(+2.40)-8.86(-3.65)
100%38.61(+3.34)26.04(+0.75)-9.14(-2.55)63.55(+4.70)38.98(+2.60)-7.50(-2.29)
DER++100%37.7925.24-2.8755.8230.84-6.08
w/ Efficient-CLS25%37.93(+0.14)25.64(+0.4)-8.90(-6.03)59.70(+3.88)34.15(+3.31)-11.21(-5.13)
100%39.61(+1.82)26.73(+1.49)-8.30(-5.43)62.01(+6.19)33.09(+2.25)-11.05(-4.97)
+ +Table 1. Overall performance of existing algorithms and Efficient-CLS on OAK and EgoObjects. iCaRL(Wang et al.) denotes the SOTA model presented in [34], and iCaRL(our impl.) is the same method by our implementation. + +$\mathbf{F}$ estimates the forgetfulness of the model due to the sequential training. It takes into account the time interval between the presence of an object category and its subsequent presence. For a class $c$ , we sort the $\mathrm{CAP}_{t_i}^c$ according to the time interval $k$ between evaluation time $t_i$ and the last time $t_i - k$ the model is trained on $c$ . After $\mathrm{CAP}_{t_i}^c$ is sorted, all $\mathrm{CAP}_{t_i}^c (i = 0,\dots ,T)$ are divided into $K$ bins $B_{kmin},\dots ,B_{kmax}$ according to the time interval $k$ . The average CAP $(\mathrm{aCAP}_k)$ of each bin $B_{k}$ is defined as the model's performance for detecting class $c$ after the model has not been trained on $c$ for $k$ time steps. The forgetfulness (F) of the class $c$ is defined as the weighted sum of the performance decrease at each time: + +$$ +F ^ {c} = \sum_ {k = k m i n} ^ {k m a x} \frac {k - k m i n}{\sum_ {k = k m i n} ^ {k m a x} k - k m i n} \times \left(\mathrm {a C A P} _ {k m i n} - \mathrm {a C A P} _ {k}\right). \tag {5} +$$ + +The overall forgetfulness is: $\mathrm{F} = \frac{1}{C}\sum_{c = 0}^{C}\mathrm{F}^{c}$ + +# 4.4. Implementation Details + +For a fair comparison, we followed the prior work [34] to use Faster-RCNN [27] with ResNet-50 backbone [12] as our object detection network, which is initialized by the weights pre-trained on PASCAL VOC [10]. We used Adam optimizer with a constant learning rate of 0.0001, and the batch size was set to 16 frames. Same as [34], we maintained a replay buffer with 5 samples per class. At each time step $t$ , we first randomly retrieved 16 video frames from the replay buffer for joint training. We used confidence thresh $\tau = 0.7$ to generate pseudo-labels for unlabeled frames, and applied EMA rate $\alpha = 0.99$ to update the slow learner. The weight of pseudo loss $\lambda_{pseudo}$ was set to 1.0. All the experiments were conducted on 2 NVIDIA RTX 3090 GPUs. + +# 5. Results + +# 5.1. Fully Supervised Protocol + +As the previous work [34] focuses on online continual object detection (OCOD) in video streams, we first evaluated model performance in fully supervised setting (i.e., $100\%$ annotation cost), where all video frames are paired with human labels. The reported results were measured by standard metrics (CAP, FAP, and F, Section 4.3) in Table 1. + +Performance of CL baselines. [34] benchmarked Incremental, EWC, iCaRL(Wang et al.), and Offline Training on OAK dataset. They found the replay-based method (i.e. iCaRL(Wang et al.)) outperforms regularization-based method (i.e. EWC) by $10\%$ in FAP, while iCaRL(Wang et al.) has a huge gap of $30\%$ compared with Offline Training. Similar observations were made in Table 1, but the performance of Incremental and EWC were $4\%$ lower than that in [34], as in our setting we only trained each mini-batch of video frames once (they trained each mini-batch 10 times). As mentioned in Section 4.2, we introduce several variations to the original design of iCaRL(Wang et al.). Compared with iCaRL(Wang et al.), we observed a huge performance boost in FAP from $22.89\%$ to $36.14\%$ on OAK and from $37.61\%$ to $60.80\%$ on EgoObjects, abridging the gap between the baseline and Offline Training. + +We further adapted other standard CL baselines, including iOD, A-GEM, GDumb, DER++, to the OCOD setting for comparisons. iOD is the SOTA method in offline class-incremental object detection. Though it performs well in prior setting, iOD collapses when adapted to online video streams. One explanation is that iOD requires explicit task boundary to trigger the reshape of model gradients that opti + +![](images/33fe0a64f37aecc71768e8c1c4c8ff86bb795b645e3f00e83a30203a3e49b417.jpg) +Figure 3. The changes of $\mathrm{CAP}_{t_i}^c$ with sampled categories on OAK dataset. The x-axis denotes time step across the entire video stream. The y-axis denotes the AP50 of the category at specific time step (i.e., $\mathrm{CAP}_{t_i}^c$ ). The grey line indicates the existence of the category. + +mizes knowledge sharing between adjacent tasks. However, in online video streams, the task boundaries by classes are no longer available and the change of tasks is hard to identify, resulting in the failure to prevent forgetting. In contrast, replay-based methods (i.e., A-GEM, GDumb and DER++) generalize much better to the real-world streaming video. + +Performance w/ Efficient-CLS. Inheriting from the benefit of fast and slow learning with EMA, our Efficient-CLS consistently improves all the state-of-the-art CL methods (i.e. iCaRL(our impl.), A-GEM, GDumb and DER++) by a significant margin. Taking iCaRL(our impl.) for example, with Efficient-CLS, we observed superior performance and minimal forgetting compared to baseline methods, even when categories appeared infrequently (e.g., sculpture in Figure 3). Since semantic contextual information is more important in indoor environments on EgoObjects compared to the outdoor environments in OAK, we noticed that the improvement brought by our method is even greater on EgoObjects with an increase of $6.25\%$ in FAP, $3.95\%$ in CAP $\%$ and $3.07\%$ in F. Consistent performance gains are also noticeable for A-GEM, GDumb and DER++, demonstrating the effectiveness and flexibility of our method. + +# 5.2. Sparse Annotation Protocol + +Performance of CL baselines. The sparse annotation protocol is more challenging than the previous fully supervised protocol as shown by the performance differences when number of annotated video frames decreases (compare the performance of each colored bar along the x-axis within each subplot in Figure 4). We noted that GDumb is more resilient against the reduce of supervision. Specifically, from Table 2 at the lowest annotation cost of $6.25\%$ on EgoObjects dataset, GDumb achieves the highest performance of $38.74\%$ , $22.69\%$ and $-4.53\%$ in FAP, CAP and F, which surpasses other baselines by a considerable margin. Same observations can be made on OAK dataset. One possible explanation is that GDumb only trains the data stored in the balanced replay buffer, which makes it less vulnerable + +
OAKEgoObjects
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
iCaRL23.0417.75-3.3132.9119.15-1.36
w/ Efficient-CLS29.7220.31-5.3640.1623.95-2.01
A-GEM23.5916.15-2.9921.8412.280.82
w/ Efficient-CLS30.1820.59-5.4438.9623.79-5.64
GDumb27.3719.64-4.2538.7422.69-4.53
w/ Efficient-CLS29.0719.99-6.0140.0923.67-5.16
DER++24.2115.93-3.7916.958.482.03
w/ Efficient-CLS28.6319.64-4.6035.7820.74-4.69
+ +Table 2. Performance of Efficient-CLS at low annotation cost of $6.25\%$ . The best results are bold-faced. + +able to class imbalance problem brought by the reduce of labeled samples in the training set. + +Performance w/ Efficient-CLS. Our proposed Efficient-CLS is a plug-and-play module that can be easily inserted into and enhance existing continual learning algorithms with the ability to use unlabeled video frames effectively. In both OAK and EgoObjects dataset, Efficient-CLS consistently improves the comparative SOTAs in all three evaluation metrics regardless of various degrees of annotation cost. As shown in Table 2, at a lower annotation cost of $6.25\%$ , Efficient-CLS doubles the performance of DER++ and A-GEM in terms of FAP and CAP, and achieves an even larger improvement in preventing forgetting. Thanks to the useful information from pseudo labels predicted by the slow learner in Efficient-CLS, our method is more robust to various annotation costs, compared with SOTAs (compare the rate of change of blue bars vs. red bars over different degrees of annotation cost). Most remarkably, Efficient-CLS with $25\%$ annotation cost has already outperformed comparative SOTAs with $100\%$ annotation cost (see Table 1). + +# 5.3. Ablation Study + +We assessed the importance of our key design choices. The Complementary Learning Systems (CLS) in EfficientCLS is the key for rapidly adapting to learn new tasks, meanwhile, retaining previously learnt knowledge. It constitutes of two memory reinstatement mechanisms: one is + +![](images/dafc29ad3590cc3cfb2a7d358b163bca09c7a2127ab71373a07b5c75f8c90e61.jpg) + +![](images/c5dc86c1a627513b4e84ccece2bd45bd5df1c9042492552d7dca3c95edc54efc.jpg) + +![](images/1ed6f3578d2d9af0843954a429ad7af6532263ab6fad0360d4c62a4e0a890394.jpg) + +![](images/24693d7cad2f36899b31c8f33ce9bcb2974c9d1836f75eaf87ea557cde227c54.jpg) +Figure 4. Evaluation of online continual object detection in video streams with three metrics (FAP, CAP and F, Section 4.3) on OAK dataset (first row) and EgoObjects dataset (second row). The higher the bars are, the better. The x-axis denotes the percentage of video frames that are labeled in the video stream. It ranges from $6.25\%$ to $100\%$ (full supervision). The y-axis indicates the performance using different evaluation metrics. Ours (iCaRL(our impl.) w/ Efficient-CLS, red) consistently beats the comparative SOTA (iCaRL(our impl.), blue) in all evaluation metrics. + +![](images/11853cb1106fcd715fd04101d300b2bdf81ad71ec85abd0a3a6aa42ea914aa0d.jpg) + +![](images/f73a9a17b60c67d99d85868822c5329faa2468187a6784f269ed11e0fc04b41f.jpg) + +
EMAPL50%25%12.5%6.25%
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
XX34.6825.78-4.1533.7024.57-4.3028.7619.80-5.4823.0417.75-3.31
✓X35.7425.77-4.8234.7925.62-4.3531.7221.16-7.2427.8420.03-3.96
X✓35.6125.56-3.7634.9525.65-3.6531.6022.44-4.8326.3919.50-1.99
✓✓38.6126.90-7.2938.3626.64-8.2033.9223.04-7.7129.7220.31-5.36
+ +Table 3. Effectiveness of Exponential Moving Average (EMA) and Pseudo-labeling (PL) for iCaRL (our impl.) on OAK dataset at annotation cost $50\%$ , $25\%$ , $12.5\%$ and $6.25\%$ . The best results are bold-faced. + +synaptic weight transfer from fast to slow learner via exponential moving average (EMA); and the other is reciprocal replay from slow learner to fast learner with pseudolabeling (PL). Here we studied their effects individually. + +Ablation: Exponential Moving Average (EMA). We removed EMA by setting the $\alpha$ in Equation 3 to 1, where the model weights of the fast learner and slow learner are now shared throughout the learning process. Note that in the fully supervised protocol, the pseudo-labeling is turned off and the Efficient-CLS equals to the EMA alone. From Table 1 at $100\%$ annotation cost, we observed that removing EMA leads to significant performance drops ranging from $2\%$ to $8\%$ , for all the comparative baselines on both OAK and EgoObjects. This shows that the slow learner can effectively consolidate the knowledge from the fast learner, and constructively alleviate catastrophic forgetting by synapses consolidation over time. Similar observations were made in Table 3 in the sparse annotation protocol (compare Row 2 vs. Row 1, Row 4 vs. Row 3). It is worth noting that, the performance difference between naive model (Row 1) and its variant with EMA (Row 2) is slightly larger in lower su + +pervision (i.e. $12.5\%$ , $6.25\%$ ) than higher supervision (i.e. $50\%$ , $25\%$ ). One possible reason is that, compared with higher supervision, the fast learner suffers more forgetting in lower supervision; hence, the effect of removing EMA becomes stronger in lower supervision, again highlighting the importance of EMA. + +Ablation: Pseudo-labeling (PL). We ablate our model by removing the PL of the slow learner across varying annotation costs and reported the results in Table 3. The removal of PL (Row 2) leads to a performance drop of around $2\%$ in FAP, $1\%$ in CAP and $0.5 - 4\%$ in F, compared with our full Efficient-CLS (Row 4). It implies that the slow learner captures useful semantic information from unlabeled video frames and these predicted pseudo labels are helpful in training the fast learner. + +To investigate whether pseudo labels predicted by the fast learner itself could help stream learning, we conducted another ablation experiment where we performed PL without EMA (Row 3). Compared with the naive model (Row 1), we observed a performance increase from $28.76\%$ to $31.60\%$ in FAP and $19.80\%$ to $22.44\%$ in CAP. It indicates + +that, due to the temporal correlation in video stream, pseudo labels predicted by the fast learner can serve as an informative supervision for the training of the fast learner itself. + +However, replaying the self-predicted pseudo labels on the fast learner fails to prevent forgetting, as indicated by the drop from $-5.48\%$ to $-4.83\%$ in F. It is possible that the pseudo labels generated by the fast learner only bias towards the classes which have already been learnt very well and fail to reinforce the fast learner to improve on the poorly-learnt classes. Different from the fast learner, the slow learner integrates semantic information over time. The predicted pseudo labels carry more semantic information, which is useful for fast learner to capture more generic object representations during pseudo label replays. Again, this emphasizes that the reciprocal replay from the slow learner to the fast learner is critical for memory reinstatement, which has been missing in the computational modeling literature of CLS. + +# 6. Conclusion + +To imitate what humans see and learn in the real world, we introduce a more realistic and challenging problem of label-efficient online continual object detection (LEOCOD) in video streams. Addressing this problem would greatly benefit real-world applications by reducing model retraining time and data labeling costs. Inspired by the Complementary Learning Systems (CLS) theory, we propose a plug-and-play module, namely Efficient-CLS, that can be easily integrated into and improve existing continual leaning algorithms. We evaluate Efficient-CLS on two challenging real-world video datasets, where our method achieves the state-of-the-art performance in preventing catastrophic forgetting, all while requiring minimal annotation effort. + +Acknowledgements This research is funded by the National Research Foundation, Singapore under its NRFF Award NRF-NRFF13-2021-0008 & NRF-NRFF15-2023-0001, AI Singapore Programme (AISG Award No: AISGC-2019-001-2A & AISG2-RP-2021-025), Mike Zheng Shou's Start-Up Grant from NUS, Mengmi Zhang's Startup Grant from Agency for Science, Technology, and Research (A*STAR), and Early Career Investigatorship from Center for Frontier AI Research (CFAR), A*STAR. 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Springer, 2020. 4 \ No newline at end of file diff --git a/2023/Label-Efficient Online Continual Object Detection in Streaming Video/images.zip b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ed1688e3e9e55090dac6f5bb03ca7ab7ca96cb9e --- /dev/null +++ b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fe6b37daa288956d62bd9d8dd3a263202303a3fba0ce74cee6dc13d1a84a6d31 +size 505436 diff --git a/2023/Label-Efficient Online Continual Object Detection in Streaming Video/layout.json b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a06bac441b6eb5eff499d5a65ba3a2dadc58a37e --- /dev/null +++ b/2023/Label-Efficient Online Continual Object Detection in Streaming Video/layout.json @@ -0,0 +1,8488 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 80, + 103, + 515, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 103, + 515, + 121 + ], + "spans": [ + { + "bbox": [ + 80, + 103, + 515, + 121 + ], + "type": "text", + "content": "Label-Efficient Online Continual Object Detection in Streaming Video" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "spans": [ + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "text", + "content": "Jay Zhangjie Wu" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "text", + "content": " David Junhao Zhang" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "text", + "content": " Wynne Hsu" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "text", + "content": " Mengmi Zhang" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "inline_equation", + "content": "^{3,4}" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "text", + "content": " Mike Zheng Shou" + }, + { + "bbox": [ + 56, + 142, + 541, + 159 + ], + "type": "inline_equation", + "content": "^{1*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "spans": [ + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "text", + "content": "Show Lab, " + }, + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "text", + "content": "National University of Singapore \n" + }, + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "text", + "content": "School of Computer Science and Engineering, Nanyang Technological University, Singapore \n" + }, + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 69, + 167, + 523, + 210 + ], + "type": "text", + "content": "CFAR and I2R, Agency for Science, Technology and Research, Singapore" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 236, + 192, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 236, + 192, + 251 + ], + "spans": [ + { + "bbox": [ + 143, + 236, + 192, + 251 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 263, + 290, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 263, + 290, + 515 + ], + "spans": [ + { + "bbox": [ + 45, + 263, + 290, + 515 + ], + "type": "text", + "content": "Humans can watch a continuous video stream and effortlessly perform continual acquisition and transfer of new knowledge with minimal supervision yet retaining previously learnt experiences. In contrast, existing continual learning (CL) methods require fully annotated labels to effectively learn from individual frames in a video stream. Here, we examine a more realistic and challenging problem—Label-Efficient Online Continual Object Detection (LEOCOD) in streaming video. We propose a plug-and-play module, Efficient-CLS, that can be easily inserted into and consistently improve existing CL algorithms for object detection in video streams with reduced data annotation costs and model retraining time. We show that our method has achieved significant improvement with minimal forgetting across all supervision levels on two challenging CL benchmarks for streaming real-world videos. Remarkably, with only " + }, + { + "bbox": [ + 45, + 263, + 290, + 515 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 45, + 263, + 290, + 515 + ], + "type": "text", + "content": " annotated video frames, our proposed method still outperforms the state-of-the-art CL models trained with " + }, + { + "bbox": [ + 45, + 263, + 290, + 515 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 45, + 263, + 290, + 515 + ], + "type": "text", + "content": " annotations on all video frames. The data and source code will be publicly available at https://github.com/showlab/Efficient-CLS." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 540, + 128, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 128, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 128, + 552 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 560, + 288, + 693 + ], + "type": "text", + "content": "Humans have the ability to continuously learn from an ever-changing environment, while retaining previously learnt experiences. In contrast to human learning, prior works [3, 2, 11, 34, 7] show that deep neural networks are prone to catastrophic forgetting. To address the forgetting problem, existing works in continual learning (CL) primarily focus on class-incremental image classification or object detection. Their experiment settings are often idealistic and simplified, where i.i.d. static images are usually grouped by class and incrementally presented to computational models in sequence. To learn a particular task containing specific" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 238, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 238, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 238, + 545, + 285 + ], + "type": "text", + "content": "classes, an agent can go through all the data of current task over multiple epochs. After that, the learned classes in current task become unavailable, i.e., no overlaps between the sets of learned classes and unseen classes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 289, + 546, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 546, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 546, + 433 + ], + "type": "text", + "content": "However, these experiment designs deviate from the online continual learning (OCL) setting in the real world, where an agent learns from temporally correlated non-i.i.d. video streams in one single pass. Given context regularities in natural environments, an agent is likely to encounter cases when objects of previously learnt classes co-occur with unknown objects from unseen classes, e.g., a computer mouse and a computer monitor often co-occur. Taking these considerations, [34] introduces OCL on object detection in real-world video streams. They evaluate existing CL approaches on this setting and report a huge performance gap compared with offline training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 435, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 547, + 639 + ], + "type": "text", + "content": "Based on the setting in [34], we take a significant step further and introduce a novel problem setting called Label-Efficient Online Continual Object Detection (LEOCOD), which highlights two unique challenges. First, the setting in [34] is such that the CL algorithms are trained with every mini-batch over multiple passes. We tighten the training recipe in LEOCOD to strictly online, where data is allowed to have one single pass and models are trained on the entire video dataset for only one epoch. Second, existing CL models require fully supervised training where box-level ground truth labels of every object on every video frame have to be obtained from human annotators. Unlike static images, acquiring human annotations for object detection on videos can be expensive and daunting. Thus, in LEOCOD, the video frames per mini-batch are sparsely annotated to alleviate the burdens of extensive human labeling, making LEOCOD one step closer to real world application." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": "Cognitive science works [35, 19] show that humans are efficient at continuously learning from very few annotated data samples. We get inspirations from the theory of Complementary Learning Systems (CLS) in human brains [18], and propose a plug-and-play module for the LEOCOD task, dubbed as Efficient-CLS. In Efficient-CLS, we introduce" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "text", + "content": "*Corresponding Author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19246" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 74, + 324, + 243 + ], + "blocks": [ + { + "bbox": [ + 60, + 74, + 324, + 243 + ], + "lines": [ + { + "bbox": [ + 60, + 74, + 324, + 243 + ], + "spans": [ + { + "bbox": [ + 60, + 74, + 324, + 243 + ], + "type": "image", + "image_path": "a090acd2ce689d64a3637fba2655497866caff7450015ef2e8e9c44ef677bcb6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "text", + "content": "Figure 1. (a) Problem introduction: An agent continuously learns from a never-ending online video stream over time. In each training step, out of a mini-batch containing 16 consecutive video frames, only a fixed proportion of frames are labeled (green boundary), while the rest of the frames are unlabeled (orange boundary). Following [34], the video frame after every training mini-batch (transparent) is held out for testing. After every 100 training steps, the agent is evaluated on all the video frames from the test set for object detection. (b) Key results: Our proposed method (red) consistently outperforms the best competitive baseline (blue) by a margin of " + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "text", + "content": ". Remarkably, our model, trained at " + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "text", + "content": " annotation cost, surpasses the best baseline trained at " + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "text", + "content": " (grey line). The orange cross denotes the performance of the state-of-the-art model, which is " + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 247, + 548, + 324 + ], + "type": "text", + "content": " lower than our method." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 330, + 74, + 533, + 242 + ], + "blocks": [ + { + "bbox": [ + 330, + 74, + 533, + 242 + ], + "lines": [ + { + "bbox": [ + 330, + 74, + 533, + 242 + ], + "spans": [ + { + "bbox": [ + 330, + 74, + 533, + 242 + ], + "type": "image", + "image_path": "234e7cabfb9d3c0d9353c67dc8de8cfcc68f8333688ee4fc4fea263dba5918d3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 335, + 288, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 288, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 288, + 502 + ], + "type": "text", + "content": "two feed-forward neural networks as slow and fast learners. In the fast learner, memory is rapidly adapted to the current task. The weights of the slow learner change a little on each reinstatement, and are maintained by taking the exponential moving average (EMA) of the fast learner's weights over time. Though a few continual learning models in previous works [4, 24] also use a similar source of inspiration, they miss the effect of reciprocal connections from slow learners to fast learners, which we intend to address. Inspired by the bidirectional interaction in CLS [14], we reactivate the weights of the slow learners to predict meaningful pseudo labels from the unlabeled video frames and use these pseudo labels to guide the training of the fast learner, closing the loop between the two systems." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 502, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 598 + ], + "type": "text", + "content": "We demonstrate the versatility and effectiveness of our Efficient-CLS on two standard real-world video datasets, OAK [34] and EgoObjects [1]. Our proposed method can be easily integrated into existing CL models and consistently improve their performance by a large margin in LEOCOD. It is worth noting that, with only " + }, + { + "bbox": [ + 46, + 502, + 287, + 598 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 502, + 287, + 598 + ], + "type": "text", + "content": " labeled data, our method surpasses the comparative baselines trained with full supervision (Figure 1(b))." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 598, + 286, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 598, + 286, + 610 + ], + "spans": [ + { + "bbox": [ + 59, + 598, + 286, + 610 + ], + "type": "text", + "content": "To summarize, we make the following key contributions:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 614, + 286, + 714 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 58, + 614, + 286, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 614, + 286, + 674 + ], + "spans": [ + { + "bbox": [ + 58, + 614, + 286, + 674 + ], + "type": "text", + "content": "- We introduce a new, challenging and important problem of label-efficient online continual object detection (LEOCOD) in video streams. Solving this problem would greatly benefit real-world applications in reducing annotation cost and model retraining time." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 677, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 677, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 677, + 286, + 714 + ], + "type": "text", + "content": "- We propose Efficient-CLS, a plug-and-play module inspired from the Complementary Learning Systems (CLS) theory, which can be integrated into existing CL" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 335, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 335, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 324, + 335, + 545, + 360 + ], + "type": "text", + "content": "models and learn efficiently and effectively with less supervision and minimal forgetting." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 363, + 547, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 363, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 317, + 363, + 547, + 399 + ], + "type": "text", + "content": "- We benchmark existing CL methods on the task of LEOCOD and demonstrate the state-of-the-art performance of our method through extensive experiments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 411, + 392, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 392, + 423 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 392, + 423 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 431, + 422, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 431, + 422, + 444 + ], + "spans": [ + { + "bbox": [ + 306, + 431, + 422, + 444 + ], + "type": "text", + "content": "2.1. Continual Learning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 450, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 617 + ], + "type": "text", + "content": "To alleviate catastrophic forgetting, many continual learning methods exploit an external buffer where a limited number of old samples are stored and used for replay when adapting to a new task. iCaRL [26] stores the representative exemplars in past tasks for knowledge distillation and prototype rehearsal. Gradient Episodic Memory (GEM) [21] formulates optimization constraints on the exemplars in memory. Averaged GEM (A-GEM) [8] is an improved version of GEM that achieves faster training and less memory consumption. GDumb [25] greedily stores samples in memory as they come and trains a model using samples only in the memory. Dark Experience Replay++ (DER++) [6] combines replay with knowledge distillation and regularization, and samples logits along the entire optimization trajectory." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 714 + ], + "type": "text", + "content": "In contrast to classical continual learning where data are separated by task boundaries and models are trained with multiple iterations in every task, we examine a more realistic and challenging problem where data are provided in tiny batches and models are trained on these batches only once. Recently, online continual learning (OCL) has gained increasing interests in computer vision [3, 7, 29, 9, 34]. Many OCL methods rely on representative memory replays to pre" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19247" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "content": "vent forgetting. [3] utilizes gradients of network parameters to select replay samples of maximum diversity. Subsequent works [2, 29] propose to use losses and scoring functions as criteria for selecting the most representative samples for replay. However, these approaches tackle image classification problem in an artificial setting, where new classes appear in a specific order. Their performance in real-world vision tasks remains unclear." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 288, + 323 + ], + "type": "text", + "content": "Lately, [34] benchmarks CL methods in the real-world online setting with full supervision. As the video streams arrive endlessly in a real-time manner, assigning annotations to all the video frames for training computational models is laborious and time-consuming. It becomes even more daunting in object detection tasks where class labels and bounding boxes of all objects on a video frame have to be provided. Reducing burdensome costs of labeling remains an under-explored and challenging problem in online continual object detection. We propose a self-sustaining Efficient-CLS, which is capable of exploiting the unlabeled video frames by pseudo-labeling when the number of labeled frames is limited." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 332, + 232, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 232, + 345 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 232, + 345 + ], + "type": "text", + "content": "2.2. Complementary Learning Systems" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 351, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 287, + 639 + ], + "type": "text", + "content": "The essence of fast and slow learning in Complementary Learning Systems (CLS) has benefited several continual learning algorithms in image recognition [24, 23, 28, 4, 15]. However, these methods either require the task boundaries, which are not applicable in our online video setting, or they require to train fast and slow learning systems with replay samples from the same replay buffer, which could easily lead to overfitting problem when the replay buffer has limited capacity. To eliminate overfitting problem, [28] and [15] utilize generative replay models to couple sequential tasks in a latent embedding space. While generative approaches have succeeded in artificial and simple datasets, they often fail in complex vision tasks, e.g., object detection. DualNet [23] also employs a slow-fast learning architecture. However, its update process for the slow learner is more computationally demanding because it leans on both self-supervised and supervised learning objectives. The self-supervised phase demands additional training iterations on extensive batches to yield satisfactory results, thereby delaying the training of the fast learner. In contrast, our method updates the slow learner in real-time using the fast learner's weights, obviating the need for distinct slow learner training. Our approach is optimized for online CL scenarios where computational resources are constrained." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 647, + 194, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 194, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 194, + 659 + ], + "type": "text", + "content": "2.3. Semi-Supervised Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "The goal of semi-supervised learning (SSL) [33, 5, 37, 36] is to reduce the demand of labeled data and harness unlabeled data for performance improvement. [31] first introduce SSL to the context of CL, and propose a strategy" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": "that combines pseudo-labeling, consistency regularization, out-of-distribution detection, and knowledge distillation to solve the problem of class-incremental image classification. However, to distill knowledge from previous tasks, their model relies heavily on the task boundary that identifies the change of training classes, which is not available in our LEOCOD setting. To reduce annotation costs in object detection, several methods [13, 32, 20] capitalize the teacher-student networks. In general, a teacher model predicts pseudo labels or enforces a consistency loss to guide the student networks. However, these previous works on semi-supervised object detection only consider the offline setting on static image datasets, while none of them has been extended to online continual learning on dynamic video streams. We discovered new insights that pseudo-labeling from slow learner to fast learner can not only reduce annotation overhead, but also alleviate forgetting, which is critical to the design of efficient continual learners in real world." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 299, + 361, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 299, + 361, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 299, + 361, + 312 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 319, + 404, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 319, + 404, + 332 + ], + "spans": [ + { + "bbox": [ + 306, + 319, + 404, + 332 + ], + "type": "text", + "content": "3.1. Problem Setting" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 338, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 434 + ], + "type": "text", + "content": "We advance the online continual object detection in [34] to a label-efficient and computationally-efficient setting—Label-Efficient Online Continual Object Detection (LEOCOD). In contrast to the setting in [34] where video frames are extensively annotated and trained with multiple epochs, an agent in LEOCOD continuously learns from a sparsely annotated video stream in a single pass over time (see Figure 1(a))." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": "Formally, we consider the online continual object detection on a continuum of video streams " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{D_1,\\dots ,D_T\\}" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " where at time step " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " , a learning agent receives a mini-batch of continuous video frames " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " from current environment for online training (one single pass). To perform label-efficient object detection, within the batch " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " , only a subset of video frames " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "D_{t}^{s} = (X_{t}^{s},Y_{t}^{s})" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " are labeled, while the remaining video frames " + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "inline_equation", + "content": "D_{t}^{u} = (X_{t}^{u})" + }, + { + "bbox": [ + 304, + 434, + 545, + 555 + ], + "type": "text", + "content": " are unlabeled. For each labeled data sample, its annotation contains the bounding box locations and their corresponding class labels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 563, + 533, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 533, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 533, + 575 + ], + "type": "text", + "content": "3.2. Efficient Complementary Learning Systems" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "We propose a plug-and-play module dubbed as EfficientCLS. Specifically, it consists of two feed-forward networks: (i) the fast learner is designed to quickly encode new knowledge from current data stream and then consolidate it to the slow learner; and (ii) the slow learner accumulates the acquired knowledge from fast learner over time and guides the fast learner with meaningful pseudo labels, when full supervision is not available. Same as [26, 8, 25, 6, 34], we maintain an external episodic memory, as a replay buffer, to store exemplars that can be retrieved for replays alongside ongoing video stream. As the fast and slow learners are" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19248" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 73, + 534, + 261 + ], + "blocks": [ + { + "bbox": [ + 62, + 73, + 534, + 261 + ], + "lines": [ + { + "bbox": [ + 62, + 73, + 534, + 261 + ], + "spans": [ + { + "bbox": [ + 62, + 73, + 534, + 261 + ], + "type": "image", + "image_path": "02a21dd849294a5f80d943914591152a18efa413983492843b7fea011e65dfed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "lines": [ + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": "Figure 2. The framework of Efficient-CLS. At each learning step, the system receives a batch of temporally continuous data " + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": ", including labeled (green) and unlabeled (orange) frames. The fast learner trains the labeled frames alongside a small subset of labeled exemplars retrieved from episodic memory with the supervised loss " + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sup}" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": ". Meanwhile, the fast learner leverages the pseudo labels generated by the slow learner to optimize a pseudo loss " + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pseudo}" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": ". To reinstate memory of the slow learner, the weights of the slow learner are updated by taking the Exponential Moving Average (EMA) of the fast learner's weights. The fast and slow learners are complementary to each other, forming a positive feedback loop." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 342, + 288, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 288, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 288, + 380 + ], + "type": "text", + "content": "model agnostic, our Efficient-CLS can be easily integrated into existing CL models, which leads to less supervision and minimal forgetting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": "Learning with Labeled Frames. The fast learner and slow learner use the same standard Faster-RCNN [27] detector " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": ". Despite the same architecture, the weights of the fast and slow learners are not shared. We use " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\theta_{F}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\theta_{S}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": " to denote the network parameters for fast and slow learners respectively. As shown in Figure 2, at each training step " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": ", we use the labeled video frames " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "D_{t}^{s} = (X_{t}^{s}, Y_{t}^{s})" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": " to optimize the fast learner " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\theta_{F}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": " with the standard supervised loss " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sup}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": " in Faster-RCNN [27]. It consists of four losses: Region Proposal Network (RPN) classification loss " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}^{rpn}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": ", RPN regression loss " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}^{rpn}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": ", Region of Interest (ROI) classification loss " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}^{roi}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": ", and ROI regression loss " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}^{roi}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": ". We define " + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sup}" + }, + { + "bbox": [ + 46, + 391, + 287, + 538 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 75, + 544, + 287, + 565 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 544, + 287, + 565 + ], + "spans": [ + { + "bbox": [ + 75, + 544, + 287, + 565 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s u p} = \\mathcal {L} _ {c l s} ^ {r p n} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\mathcal {L} _ {r e g} ^ {r p n} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\tag {1}", + "image_path": "03dbc299f35437f56630efc7cd0b150d50b3c496cbe7541e67f2d9d943582510.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 129, + 563, + 258, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 563, + 258, + 576 + ], + "spans": [ + { + "bbox": [ + 129, + 563, + 258, + 576 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c l s} ^ {r o i} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right) + \\mathcal {L} _ {r e g} ^ {r o i} \\left(X _ {t} ^ {s}, Y _ {t} ^ {s}\\right).", + "image_path": "7a51b4651164e2e42b9c83762a954bbc774eefb73a2689e72e31396914695a7f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "Learning with Unlabeled Frames. We introduce a pseudo-labeling paradigm to capitalize the information from unlabeled video frames " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "D_{t}^{u} = (X_{t}^{u})" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": " for training. In our early exploration, we intuitively use the fast learner for pseudo-labeling as it quickly adapts the knowledge of nearby frames. However, we observe that using the pseudo labels generated by the fast learner for self-replay exhibits biases towards recently seen objects, which is less effective in preventing forgetting. This has also been verified in our ablation study (Section 5.3). In contrast, the slow learner" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 342, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 415 + ], + "type": "text", + "content": "preserves the semantic knowledge over a longer time span which generates pseudo labels with fewer biases. This encourages the fast learner to capture more generic scene representations, hence, in turn, contributing to reinstatement of memory in the slow learner (Section 3.2), resulting in a positive feedback loop." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 415, + 546, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 546, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 546, + 581 + ], + "type": "text", + "content": "Given all these design considerations, the slow learner takes the unlabeled video frames " + }, + { + "bbox": [ + 304, + 415, + 546, + 581 + ], + "type": "inline_equation", + "content": "D_{t}^{u}" + }, + { + "bbox": [ + 304, + 415, + 546, + 581 + ], + "type": "text", + "content": " as inputs to estimate the possible objects of interest and their corresponding bounding box locations. For brevity, we refer these \"pseudo bounding boxes and their corresponding class labels\" as \"pseudo labels\" in the paper. To get rid of false positives, we apply a threshold " + }, + { + "bbox": [ + 304, + 415, + 546, + 581 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 415, + 546, + 581 + ], + "type": "text", + "content": " to filter out bounding boxes with predicted low confidence scores. Moreover, there also exist repetitive boxes which negatively impact the quality of pseudo-labeling. To address this issue, we use the technique of class-wise non-maximum suppression (NMS) [27] to remove the overlapped boxes and get the high-quality pseudo labels. Formally, the procedure of pseudo label generation is summarized below:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 364, + 587, + 545, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 587, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 364, + 587, + 545, + 601 + ], + "type": "interline_equation", + "content": "Y _ {t} ^ {u} = \\mathrm {N M S} ([ f (X _ {t} ^ {u}; \\theta_ {S}) ] _ {> \\tau}), \\tag {2}", + "image_path": "409cf8d2fecef19f243bf17b5df5beb7a1cf9897975678bf408141925411814b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "type": "inline_equation", + "content": "[\\cdot ]_{>\\tau}" + }, + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "type": "text", + "content": " denotes the bounding box selection with confidence score larger than " + }, + { + "bbox": [ + 304, + 605, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\tau" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Given that the video streams are captured from the egocentric perspective in the real world, head and body motions may lead to undesired motion blur effects on some video frames. To enforce our module to learn invariant object representations from these video frames, same as the previous work [38], we apply data augmentation techniques on the pseudo-labeled frames, including 2D image" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19249" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "text", + "content": "crops, rotations, and flipping. Note that different from image classification, the predicted bounding box locations also need to be updated accordingly after image augmentations. We denote these pseudo-labeled video frames and their re-adjusted pseudo labels after data augmentations as " + }, + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "inline_equation", + "content": "(\\tilde{X}_t^u,\\tilde{Y}_t^u)" + }, + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "text", + "content": ". We can then use these pseudo pairs " + }, + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "inline_equation", + "content": "(\\tilde{X}_t^u,\\tilde{Y}_t^u)" + }, + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "text", + "content": " to train the fast learner by optimizing the pseudo loss " + }, + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pseudo}:= \\mathcal{L}_{cls}^{roi}(\\tilde{X}_t^u,\\tilde{Y}_t^u) + \\mathcal{L}_{req}^{roi}(\\tilde{X}_t^u,\\tilde{Y}_t^u)" + }, + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "content": "Overall, our Efficient-CLS is jointly trained with the following losses: " + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{total} = \\mathcal{L}_{sup} + \\lambda_{pseudo}\\mathcal{L}_{pseudo}" + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\lambda_{pseudo}" + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "content": " is the weight of " + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pseudo}" + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 213, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 297 + ], + "type": "text", + "content": "Synapses Consolidation via EMA. To alleviate forgetting of obtained knowledge, we apply Exponential Moving Average (EMA) to gradually update the slow learner with the fast learner's weights. The evolving weight changes in the slow learner are functionally correlated with the memory consolidation mechanism in the hippocampus and the neocortex [4]. Formally, we define EMA process as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 301, + 287, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 301, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 116, + 301, + 287, + 314 + ], + "type": "interline_equation", + "content": "\\theta_ {S} = \\alpha \\theta_ {S} + (1 - \\alpha) \\theta_ {F}, \\tag {3}", + "image_path": "2263bd8c675363bb24d4c50de8a3ec8671feb769e72e972d3c9d145a613634aa.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\alpha \\in [0,1]" + }, + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "type": "text", + "content": " is EMA rate. According to the stability-plasticity dilemma, a smaller " + }, + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "type": "text", + "content": " means faster adaptation but less memorization. Empirically, we set " + }, + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\alpha = 0.99" + }, + { + "bbox": [ + 46, + 319, + 287, + 367 + ], + "type": "text", + "content": ", which leads to best performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 376, + 168, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 168, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 168, + 389 + ], + "type": "text", + "content": "4. Experimental details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 396, + 110, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 110, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 110, + 407 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "text", + "content": "We evaluate the continual learning methods on two realistic and challenging video datasets, OAK [34] and EgoObjects [1], for the task of online continual object detection." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "text", + "content": "OAK [34] is a large egocentric video stream dataset spanning nine months of a graduate student's life, consisting of 7.6 million frames of 460 video clips with a total length of 70.2 hours [30]. The dataset contains 103 object categories. We follow [34] in the ordering of training and testing data splits. One frame every 16 consecutive video frames lasting for 30 seconds is held out to construct a test set and the remaining frames are used for training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "type": "text", + "content": "EgoObjects [1] is one of the largest object-centric datasets focusing on object detection task. The dataset contains around 100k video frames with " + }, + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sim 250\\mathrm{k}" + }, + { + "bbox": [ + 46, + 545, + 287, + 641 + ], + "type": "text", + "content": " annotations, which correspond to 277 categories and 1110 main objects [22]. Additionally, the dataset follows a long-tailed distribution which makes the task more challenging and real-world oriented. We adopt the same rule as OAK dataset to split the training and testing set." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 113, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 113, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 113, + 658 + ], + "type": "text", + "content": "4.2. Baselines" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "We compare our model against the following baselines: 1) Vanilla training: Incremental Training is a naive baseline trained sequentially over the entire video stream without any measures to avoid catastrophic forgetting; Offline" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "Training is an upper bound that can access all the data throughout training; 2) Continual learning algorithms: EWC [16], iCaRL [26], A-GEM [8], GDumb [25], DER++ [6] and iOD [17]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 121, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 545, + 276 + ], + "type": "text", + "content": "The iCaRL model implemented by [34] stands as the SOTA method in online continual object detection. We reproduce their results using the released code1. When calculating RPN and ROI losses for replay samples, their iCaRL model neglects the losses of background proposals and penalizes the foreground losses according to the proportion of the current samples and replay samples. We empirically found that this trick hinders the model from effective episodic replay, thus resulting in severe forgetting. Therefore, we re-implement the iCaRL by discarding the reweighting trick and reverting back to the standard RPN and ROI losses. We name these two different implementations as iCaRL(Wang et al.) and iCaRL(our impl.), respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 283, + 380, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 283, + 380, + 294 + ], + "spans": [ + { + "bbox": [ + 306, + 283, + 380, + 294 + ], + "type": "text", + "content": "4.3. Evaluation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "text", + "content": "Protocols. First, we define the annotation cost as the proportion of number of labeled frames versus the total 16 frames within a mini-batch " + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "text", + "content": ". For example, if 2 out of 16 consecutive frames within " + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "text", + "content": " get labeled, the annotation cost is " + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "inline_equation", + "content": "2 / 16 = 12.5\\%" + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "text", + "content": ". The frames to be labeled are randomly selected within each mini-batch " + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 304, + 301, + 545, + 492 + ], + "type": "text", + "content": ". Considering that different choices of labeled frames might influence the model performance, for fair comparisons between models, we fix the choice of randomly selected labeled frames and use the same labeled and unlabeled frames for training all models. Based on the various annotation costs, we introduce two training protocols: fully supervised protocol (100% annotation cost) and sparse annotation protocol (where the annotation cost is less than 100%). In sparse annotation protocol, we further split the training experiments based on 50%/25%/12.5%/6.25% annotation costs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 502, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 561 + ], + "type": "text", + "content": "Metrics. We evaluate the models with three standard metrics: continual average precision (CAP), final average precision (FAP) and forgetfulness (F) [34]. We employ an Average Precision (AP) metric at an Intersection over Union (IoU) threshold of 0.5, commonly referred to as AP50." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 562, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 545, + 585 + ], + "type": "text", + "content": "CAP shows the average performance over the entire video stream. That is," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 328, + 594, + 545, + 626 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 594, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 328, + 594, + 545, + 626 + ], + "type": "interline_equation", + "content": "\\mathrm {C A P} = \\frac {1}{N} \\sum_ {i = 0} ^ {N} \\mathrm {C A P} _ {t _ {i}} = \\frac {1}{N C} \\sum_ {i = 0} ^ {N} \\sum_ {c = 0} ^ {C} \\mathrm {C A P} _ {t _ {i}} ^ {c}, \\tag {4}", + "image_path": "96c36af357dbf30708d156e6ba435447a8b4ea717d68bf0f98efa5c7573ada27.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "inline_equation", + "content": "\\mathrm{CAP}_{t_i}^c" + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "text", + "content": " is the AP of class " + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "text", + "content": " on test set at the " + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "text", + "content": "-th evaluation step, " + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 635, + 545, + 659 + ], + "type": "text", + "content": " is the total number of evaluation steps." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 659, + 545, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 659, + 545, + 695 + ], + "spans": [ + { + "bbox": [ + 304, + 659, + 545, + 695 + ], + "type": "text", + "content": "FAP is the final performance of a model after seeing the entire video. That is, " + }, + { + "bbox": [ + 304, + 659, + 545, + 695 + ], + "type": "inline_equation", + "content": "\\mathrm{FAP} = \\mathrm{CAP}_{t_N}" + }, + { + "bbox": [ + 304, + 659, + 545, + 695 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 659, + 545, + 695 + ], + "type": "inline_equation", + "content": "t_N" + }, + { + "bbox": [ + 304, + 659, + 545, + 695 + ], + "type": "text", + "content": " denotes the last evaluation step." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 446, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 446, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 446, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 317, + 702, + 446, + 712 + ], + "type": "text", + "content": "https://github.com/oakdata/benchmark" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19250" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 69, + 542, + 272 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 542, + 272 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 542, + 272 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 542, + 272 + ], + "type": "table", + "html": "
Annotation CostOAKEgoObjects
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
Incremental100%8.387.720.0310.213.551.48
Offline Training100%48.2835.23-86.1859.81-
EWC100%7.737.02-0.125.151.600.57
iOD100%7.927.140.988.802.640.00
iCaRL(Wang et al.)100%22.8916.60-2.9537.6121.712.79
iCaRL(our impl.)100%36.1426.26-4.8960.8036.41-0.60
w/ Efficient-CLS25%38.36(+2.22)26.64(+0.38)-8.20(-3.31)61.26(+0.46)39.58(+3.17)-3.48(-2.88)
100%40.24(+4.10)28.18(+1.92)-8.10(-3.21)67.05(+6.25)40.36(+3.95)-3.67(-3.07)
A-GEM100%36.9426.19-5.5458.7935.88-8.38
w/ Efficient-CLS25%37.06(+0.12)26.36(+0.17)-7.76(-2.22)63.06(+4.27)39.46(+3.58)-7.49(+0.89)
100%39.87(+2.93)27.97(+1.78)-7.17(-1.63)66.94(+8.15)39.57(+3.69)-11.68(-3.30)
GDumb100%35.2725.29-6.5958.8536.38-5.21
w/ Efficient-CLS25%37.67(+2.40)25.59(+0.30)-9.30(-2.71)62.70(+3.85)38.78(+2.40)-8.86(-3.65)
100%38.61(+3.34)26.04(+0.75)-9.14(-2.55)63.55(+4.70)38.98(+2.60)-7.50(-2.29)
DER++100%37.7925.24-2.8755.8230.84-6.08
w/ Efficient-CLS25%37.93(+0.14)25.64(+0.4)-8.90(-6.03)59.70(+3.88)34.15(+3.31)-11.21(-5.13)
100%39.61(+1.82)26.73(+1.49)-8.30(-5.43)62.01(+6.19)33.09(+2.25)-11.05(-4.97)
", + "image_path": "aac219989275d564f8d39834abf219c67bce25adb0da56e6c1ae0309096c1c5d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 276, + 547, + 300 + ], + "lines": [ + { + "bbox": [ + 46, + 276, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 547, + 300 + ], + "type": "text", + "content": "Table 1. Overall performance of existing algorithms and Efficient-CLS on OAK and EgoObjects. iCaRL(Wang et al.) denotes the SOTA model presented in [34], and iCaRL(our impl.) is the same method by our implementation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " estimates the forgetfulness of the model due to the sequential training. It takes into account the time interval between the presence of an object category and its subsequent presence. For a class " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": ", we sort the " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "\\mathrm{CAP}_{t_i}^c" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " according to the time interval " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " between evaluation time " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " and the last time " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "t_i - k" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " the model is trained on " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": ". After " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "\\mathrm{CAP}_{t_i}^c" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " is sorted, all " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "\\mathrm{CAP}_{t_i}^c (i = 0,\\dots ,T)" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " are divided into " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " bins " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "B_{kmin},\\dots ,B_{kmax}" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " according to the time interval " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": ". The average CAP " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "(\\mathrm{aCAP}_k)" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " of each bin " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "B_{k}" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " is defined as the model's performance for detecting class " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " after the model has not been trained on " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " time steps. The forgetfulness (F) of the class " + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 313, + 289, + 469 + ], + "type": "text", + "content": " is defined as the weighted sum of the performance decrease at each time:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 478, + 295, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 295, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 295, + 519 + ], + "type": "interline_equation", + "content": "F ^ {c} = \\sum_ {k = k m i n} ^ {k m a x} \\frac {k - k m i n}{\\sum_ {k = k m i n} ^ {k m a x} k - k m i n} \\times \\left(\\mathrm {a C A P} _ {k m i n} - \\mathrm {a C A P} _ {k}\\right). \\tag {5}", + "image_path": "914c229229e560167b5641552b123bbea8d1ebecc17c54b82fa355ffba2c2768.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 518, + 235, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 518, + 235, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 518, + 235, + 534 + ], + "type": "text", + "content": "The overall forgetfulness is: " + }, + { + "bbox": [ + 47, + 518, + 235, + 534 + ], + "type": "inline_equation", + "content": "\\mathrm{F} = \\frac{1}{C}\\sum_{c = 0}^{C}\\mathrm{F}^{c}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 540, + 180, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 180, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 180, + 552 + ], + "type": "text", + "content": "4.4. Implementation Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "For a fair comparison, we followed the prior work [34] to use Faster-RCNN [27] with ResNet-50 backbone [12] as our object detection network, which is initialized by the weights pre-trained on PASCAL VOC [10]. We used Adam optimizer with a constant learning rate of 0.0001, and the batch size was set to 16 frames. Same as [34], we maintained a replay buffer with 5 samples per class. At each time step " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": ", we first randomly retrieved 16 video frames from the replay buffer for joint training. We used confidence thresh " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\tau = 0.7" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " to generate pseudo-labels for unlabeled frames, and applied EMA rate " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\alpha = 0.99" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " to update the slow learner. The weight of pseudo loss " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{pseudo}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " was set to 1.0. All the experiments were conducted on 2 NVIDIA RTX 3090 GPUs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 312, + 359, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 359, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 359, + 324 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 332, + 449, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 332, + 449, + 345 + ], + "spans": [ + { + "bbox": [ + 306, + 332, + 449, + 345 + ], + "type": "text", + "content": "5.1. Fully Supervised Protocol" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 351, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 424 + ], + "type": "text", + "content": "As the previous work [34] focuses on online continual object detection (OCOD) in video streams, we first evaluated model performance in fully supervised setting (i.e., " + }, + { + "bbox": [ + 304, + 351, + 545, + 424 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 351, + 545, + 424 + ], + "type": "text", + "content": " annotation cost), where all video frames are paired with human labels. The reported results were measured by standard metrics (CAP, FAP, and F, Section 4.3) in Table 1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "content": "Performance of CL baselines. [34] benchmarked Incremental, EWC, iCaRL(Wang et al.), and Offline Training on OAK dataset. They found the replay-based method (i.e. iCaRL(Wang et al.)) outperforms regularization-based method (i.e. EWC) by " + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "content": " in FAP, while iCaRL(Wang et al.) has a huge gap of " + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "content": " compared with Offline Training. Similar observations were made in Table 1, but the performance of Incremental and EWC were " + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "content": " lower than that in [34], as in our setting we only trained each mini-batch of video frames once (they trained each mini-batch 10 times). As mentioned in Section 4.2, we introduce several variations to the original design of iCaRL(Wang et al.). Compared with iCaRL(Wang et al.), we observed a huge performance boost in FAP from " + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "inline_equation", + "content": "22.89\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "inline_equation", + "content": "36.14\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "content": " on OAK and from " + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "inline_equation", + "content": "37.61\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "inline_equation", + "content": "60.80\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 628 + ], + "type": "text", + "content": " on EgoObjects, abridging the gap between the baseline and Offline Training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "content": "We further adapted other standard CL baselines, including iOD, A-GEM, GDumb, DER++, to the OCOD setting for comparisons. iOD is the SOTA method in offline class-incremental object detection. Though it performs well in prior setting, iOD collapses when adapted to online video streams. One explanation is that iOD requires explicit task boundary to trigger the reshape of model gradients that opti" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19251" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 73, + 541, + 203 + ], + "blocks": [ + { + "bbox": [ + 54, + 73, + 541, + 203 + ], + "lines": [ + { + "bbox": [ + 54, + 73, + 541, + 203 + ], + "spans": [ + { + "bbox": [ + 54, + 73, + 541, + 203 + ], + "type": "image", + "image_path": "33fe0a64f37aecc71768e8c1c4c8ff86bb795b645e3f00e83a30203a3e49b417.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "type": "text", + "content": "Figure 3. The changes of " + }, + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\mathrm{CAP}_{t_i}^c" + }, + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "type": "text", + "content": " with sampled categories on OAK dataset. The x-axis denotes time step across the entire video stream. The y-axis denotes the AP50 of the category at specific time step (i.e., " + }, + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\mathrm{CAP}_{t_i}^c" + }, + { + "bbox": [ + 46, + 209, + 546, + 232 + ], + "type": "text", + "content": "). The grey line indicates the existence of the category." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 249, + 288, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 249, + 288, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 249, + 288, + 321 + ], + "type": "text", + "content": "mizes knowledge sharing between adjacent tasks. However, in online video streams, the task boundaries by classes are no longer available and the change of tasks is hard to identify, resulting in the failure to prevent forgetting. In contrast, replay-based methods (i.e., A-GEM, GDumb and DER++) generalize much better to the real-world streaming video." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "text", + "content": "Performance w/ Efficient-CLS. Inheriting from the benefit of fast and slow learning with EMA, our Efficient-CLS consistently improves all the state-of-the-art CL methods (i.e. iCaRL(our impl.), A-GEM, GDumb and DER++) by a significant margin. Taking iCaRL(our impl.) for example, with Efficient-CLS, we observed superior performance and minimal forgetting compared to baseline methods, even when categories appeared infrequently (e.g., sculpture in Figure 3). Since semantic contextual information is more important in indoor environments on EgoObjects compared to the outdoor environments in OAK, we noticed that the improvement brought by our method is even greater on EgoObjects with an increase of " + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "inline_equation", + "content": "6.25\\%" + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "text", + "content": " in FAP, " + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "inline_equation", + "content": "3.95\\%" + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "text", + "content": " in CAP " + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\%" + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "inline_equation", + "content": "3.07\\%" + }, + { + "bbox": [ + 46, + 330, + 287, + 521 + ], + "type": "text", + "content": " in F. Consistent performance gains are also noticeable for A-GEM, GDumb and DER++, demonstrating the effectiveness and flexibility of our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 527, + 200, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 200, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 200, + 540 + ], + "type": "text", + "content": "5.2. Sparse Annotation Protocol" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "Performance of CL baselines. The sparse annotation protocol is more challenging than the previous fully supervised protocol as shown by the performance differences when number of annotated video frames decreases (compare the performance of each colored bar along the x-axis within each subplot in Figure 4). We noted that GDumb is more resilient against the reduce of supervision. Specifically, from Table 2 at the lowest annotation cost of " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "6.25\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " on EgoObjects dataset, GDumb achieves the highest performance of " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "38.74\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "22.69\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "-4.53\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " in FAP, CAP and F, which surpasses other baselines by a considerable margin. Same observations can be made on OAK dataset. One possible explanation is that GDumb only trains the data stored in the balanced replay buffer, which makes it less vulnerable" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 306, + 246, + 545, + 335 + ], + "blocks": [ + { + "bbox": [ + 306, + 246, + 545, + 335 + ], + "lines": [ + { + "bbox": [ + 306, + 246, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 246, + 545, + 335 + ], + "type": "table", + "html": "
OAKEgoObjects
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
iCaRL23.0417.75-3.3132.9119.15-1.36
w/ Efficient-CLS29.7220.31-5.3640.1623.95-2.01
A-GEM23.5916.15-2.9921.8412.280.82
w/ Efficient-CLS30.1820.59-5.4438.9623.79-5.64
GDumb27.3719.64-4.2538.7422.69-4.53
w/ Efficient-CLS29.0719.99-6.0140.0923.67-5.16
DER++24.2115.93-3.7916.958.482.03
w/ Efficient-CLS28.6319.64-4.6035.7820.74-4.69
", + "image_path": "88aea2c26004d72c77b0f4cf9ad195f09c2423a021d54903470e4016ed0d6140.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 340, + 546, + 363 + ], + "lines": [ + { + "bbox": [ + 305, + 340, + 546, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 546, + 363 + ], + "type": "text", + "content": "Table 2. Performance of Efficient-CLS at low annotation cost of " + }, + { + "bbox": [ + 305, + 340, + 546, + 363 + ], + "type": "inline_equation", + "content": "6.25\\%" + }, + { + "bbox": [ + 305, + 340, + 546, + 363 + ], + "type": "text", + "content": ". The best results are bold-faced." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 376, + 546, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 546, + 401 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 546, + 401 + ], + "type": "text", + "content": "able to class imbalance problem brought by the reduce of labeled samples in the training set." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "type": "text", + "content": "Performance w/ Efficient-CLS. Our proposed Efficient-CLS is a plug-and-play module that can be easily inserted into and enhance existing continual learning algorithms with the ability to use unlabeled video frames effectively. In both OAK and EgoObjects dataset, Efficient-CLS consistently improves the comparative SOTAs in all three evaluation metrics regardless of various degrees of annotation cost. As shown in Table 2, at a lower annotation cost of " + }, + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "type": "inline_equation", + "content": "6.25\\%" + }, + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "type": "text", + "content": ", Efficient-CLS doubles the performance of DER++ and A-GEM in terms of FAP and CAP, and achieves an even larger improvement in preventing forgetting. Thanks to the useful information from pseudo labels predicted by the slow learner in Efficient-CLS, our method is more robust to various annotation costs, compared with SOTAs (compare the rate of change of blue bars vs. red bars over different degrees of annotation cost). Most remarkably, Efficient-CLS with " + }, + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "type": "text", + "content": " annotation cost has already outperformed comparative SOTAs with " + }, + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 411, + 546, + 626 + ], + "type": "text", + "content": " annotation cost (see Table 1)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 635, + 400, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 400, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 400, + 647 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "We assessed the importance of our key design choices. The Complementary Learning Systems (CLS) in EfficientCLS is the key for rapidly adapting to learn new tasks, meanwhile, retaining previously learnt knowledge. It constitutes of two memory reinstatement mechanisms: one is" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19252" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 70, + 223, + 173 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 223, + 173 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 223, + 173 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 223, + 173 + ], + "type": "image", + "image_path": "dafc29ad3590cc3cfb2a7d358b163bca09c7a2127ab71373a07b5c75f8c90e61.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 223, + 71, + 372, + 173 + ], + "blocks": [ + { + "bbox": [ + 223, + 71, + 372, + 173 + ], + "lines": [ + { + "bbox": [ + 223, + 71, + 372, + 173 + ], + "spans": [ + { + "bbox": [ + 223, + 71, + 372, + 173 + ], + "type": "image", + "image_path": "c5dc86c1a627513b4e84ccece2bd45bd5df1c9042492552d7dca3c95edc54efc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 373, + 72, + 519, + 173 + ], + "blocks": [ + { + "bbox": [ + 373, + 72, + 519, + 173 + ], + "lines": [ + { + "bbox": [ + 373, + 72, + 519, + 173 + ], + "spans": [ + { + "bbox": [ + 373, + 72, + 519, + 173 + ], + "type": "image", + "image_path": "1ed6f3578d2d9af0843954a429ad7af6532263ab6fad0360d4c62a4e0a890394.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 73, + 174, + 222, + 275 + ], + "blocks": [ + { + "bbox": [ + 73, + 174, + 222, + 275 + ], + "lines": [ + { + "bbox": [ + 73, + 174, + 222, + 275 + ], + "spans": [ + { + "bbox": [ + 73, + 174, + 222, + 275 + ], + "type": "image", + "image_path": "24693d7cad2f36899b31c8f33ce9bcb2974c9d1836f75eaf87ea557cde227c54.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 278, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 46, + 278, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 547, + 335 + ], + "type": "text", + "content": "Figure 4. Evaluation of online continual object detection in video streams with three metrics (FAP, CAP and F, Section 4.3) on OAK dataset (first row) and EgoObjects dataset (second row). The higher the bars are, the better. The x-axis denotes the percentage of video frames that are labeled in the video stream. It ranges from " + }, + { + "bbox": [ + 46, + 278, + 547, + 335 + ], + "type": "inline_equation", + "content": "6.25\\%" + }, + { + "bbox": [ + 46, + 278, + 547, + 335 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 278, + 547, + 335 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 278, + 547, + 335 + ], + "type": "text", + "content": " (full supervision). The y-axis indicates the performance using different evaluation metrics. Ours (iCaRL(our impl.) w/ Efficient-CLS, red) consistently beats the comparative SOTA (iCaRL(our impl.), blue) in all evaluation metrics." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 222, + 174, + 370, + 275 + ], + "blocks": [ + { + "bbox": [ + 222, + 174, + 370, + 275 + ], + "lines": [ + { + "bbox": [ + 222, + 174, + 370, + 275 + ], + "spans": [ + { + "bbox": [ + 222, + 174, + 370, + 275 + ], + "type": "image", + "image_path": "11853cb1106fcd715fd04101d300b2bdf81ad71ec85abd0a3a6aa42ea914aa0d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 370, + 174, + 518, + 275 + ], + "blocks": [ + { + "bbox": [ + 370, + 174, + 518, + 275 + ], + "lines": [ + { + "bbox": [ + 370, + 174, + 518, + 275 + ], + "spans": [ + { + "bbox": [ + 370, + 174, + 518, + 275 + ], + "type": "image", + "image_path": "f73a9a17b60c67d99d85868822c5329faa2468187a6784f269ed11e0fc04b41f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 56, + 348, + 535, + 411 + ], + "blocks": [ + { + "bbox": [ + 56, + 348, + 535, + 411 + ], + "lines": [ + { + "bbox": [ + 56, + 348, + 535, + 411 + ], + "spans": [ + { + "bbox": [ + 56, + 348, + 535, + 411 + ], + "type": "table", + "html": "
EMAPL50%25%12.5%6.25%
FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)FAP (↑)CAP (↑)F (↓)
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✓X35.7425.77-4.8234.7925.62-4.3531.7221.16-7.2427.8420.03-3.96
X✓35.6125.56-3.7634.9525.65-3.6531.6022.44-4.8326.3919.50-1.99
✓✓38.6126.90-7.2938.3626.64-8.2033.9223.04-7.7129.7220.31-5.36
", + "image_path": "3389289ced2f3b4692e364719e4348a28456981109f5af49c9f99a375f80b0f6.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "lines": [ + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "text", + "content": "Table 3. Effectiveness of Exponential Moving Average (EMA) and Pseudo-labeling (PL) for iCaRL (our impl.) on OAK dataset at annotation cost " + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "inline_equation", + "content": "12.5\\%" + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "inline_equation", + "content": "6.25\\%" + }, + { + "bbox": [ + 46, + 414, + 546, + 437 + ], + "type": "text", + "content": ". The best results are bold-faced." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 451, + 288, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 451, + 288, + 500 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 288, + 500 + ], + "type": "text", + "content": "synaptic weight transfer from fast to slow learner via exponential moving average (EMA); and the other is reciprocal replay from slow learner to fast learner with pseudolabeling (PL). Here we studied their effects individually." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": "Ablation: Exponential Moving Average (EMA). We removed EMA by setting the " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " in Equation 3 to 1, where the model weights of the fast learner and slow learner are now shared throughout the learning process. Note that in the fully supervised protocol, the pseudo-labeling is turned off and the Efficient-CLS equals to the EMA alone. From Table 1 at " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " annotation cost, we observed that removing EMA leads to significant performance drops ranging from " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": ", for all the comparative baselines on both OAK and EgoObjects. This shows that the slow learner can effectively consolidate the knowledge from the fast learner, and constructively alleviate catastrophic forgetting by synapses consolidation over time. Similar observations were made in Table 3 in the sparse annotation protocol (compare Row 2 vs. Row 1, Row 4 vs. Row 3). It is worth noting that, the performance difference between naive model (Row 1) and its variant with EMA (Row 2) is slightly larger in lower su" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "text", + "content": "pervision (i.e. " + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "inline_equation", + "content": "12.5\\%" + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "inline_equation", + "content": "6.25\\%" + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "text", + "content": ") than higher supervision (i.e. " + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 451, + 546, + 523 + ], + "type": "text", + "content": "). One possible reason is that, compared with higher supervision, the fast learner suffers more forgetting in lower supervision; hence, the effect of removing EMA becomes stronger in lower supervision, again highlighting the importance of EMA." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "type": "text", + "content": "Ablation: Pseudo-labeling (PL). We ablate our model by removing the PL of the slow learner across varying annotation costs and reported the results in Table 3. The removal of PL (Row 2) leads to a performance drop of around " + }, + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "type": "text", + "content": " in FAP, " + }, + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "type": "text", + "content": " in CAP and " + }, + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "type": "inline_equation", + "content": "0.5 - 4\\%" + }, + { + "bbox": [ + 304, + 533, + 547, + 640 + ], + "type": "text", + "content": " in F, compared with our full Efficient-CLS (Row 4). It implies that the slow learner captures useful semantic information from unlabeled video frames and these predicted pseudo labels are helpful in training the fast learner." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "text", + "content": "To investigate whether pseudo labels predicted by the fast learner itself could help stream learning, we conducted another ablation experiment where we performed PL without EMA (Row 3). Compared with the naive model (Row 1), we observed a performance increase from " + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "inline_equation", + "content": "28.76\\%" + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "inline_equation", + "content": "31.60\\%" + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "text", + "content": " in FAP and " + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "inline_equation", + "content": "19.80\\%" + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "inline_equation", + "content": "22.44\\%" + }, + { + "bbox": [ + 304, + 642, + 547, + 712 + ], + "type": "text", + "content": " in CAP. It indicates" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19253" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "that, due to the temporal correlation in video stream, pseudo labels predicted by the fast learner can serve as an informative supervision for the training of the fast learner itself." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 288, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 288, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 288, + 288 + ], + "type": "text", + "content": "However, replaying the self-predicted pseudo labels on the fast learner fails to prevent forgetting, as indicated by the drop from " + }, + { + "bbox": [ + 46, + 109, + 288, + 288 + ], + "type": "inline_equation", + "content": "-5.48\\%" + }, + { + "bbox": [ + 46, + 109, + 288, + 288 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 109, + 288, + 288 + ], + "type": "inline_equation", + "content": "-4.83\\%" + }, + { + "bbox": [ + 46, + 109, + 288, + 288 + ], + "type": "text", + "content": " in F. It is possible that the pseudo labels generated by the fast learner only bias towards the classes which have already been learnt very well and fail to reinforce the fast learner to improve on the poorly-learnt classes. Different from the fast learner, the slow learner integrates semantic information over time. The predicted pseudo labels carry more semantic information, which is useful for fast learner to capture more generic object representations during pseudo label replays. Again, this emphasizes that the reciprocal replay from the slow learner to the fast learner is critical for memory reinstatement, which has been missing in the computational modeling literature of CLS." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 300, + 119, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 119, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 119, + 312 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 320, + 288, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 288, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 288, + 477 + ], + "type": "text", + "content": "To imitate what humans see and learn in the real world, we introduce a more realistic and challenging problem of label-efficient online continual object detection (LEOCOD) in video streams. Addressing this problem would greatly benefit real-world applications by reducing model retraining time and data labeling costs. Inspired by the Complementary Learning Systems (CLS) theory, we propose a plug-and-play module, namely Efficient-CLS, that can be easily integrated into and improve existing continual leaning algorithms. We evaluate Efficient-CLS on two challenging real-world video datasets, where our method achieves the state-of-the-art performance in preventing catastrophic forgetting, all while requiring minimal annotation effort." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 493, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 625 + ], + "type": "text", + "content": "Acknowledgements This research is funded by the National Research Foundation, Singapore under its NRFF Award NRF-NRFF13-2021-0008 & NRF-NRFF15-2023-0001, AI Singapore Programme (AISG Award No: AISGC-2019-001-2A & AISG2-RP-2021-025), Mike Zheng Shou's Start-Up Grant from NUS, Mengmi Zhang's Startup Grant from Agency for Science, Technology, and Research (A*STAR), and Early Career Investigatorship from Center for Frontier AI Research (CFAR), A*STAR. The computational work for this article was partially performed on resources of the National Supercomputing Centre, Singapore." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 637, + 106, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 637, + 106, + 649 + ], + "spans": [ + { + "bbox": [ + 48, + 637, + 106, + 649 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 656, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 52, + 656, + 286, + 678 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 656, + 286, + 678 + ], + "spans": [ + { + "bbox": [ + 52, + 656, + 286, + 678 + ], + "type": "text", + "content": "[1] Egoobjects dataset. https://ai.facebook.com/datasets/egoobjects-dataset/, May 2022. 2, 5" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 680, + 287, + 713 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 680, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 53, + 680, + 287, + 713 + ], + "type": "text", + "content": "[2] Rahaf Aljundi, Eugene Belilovsky, Tinne Tuytelaars, Laurent Charlin, Massimo Caccia, Min Lin, and Lucas Page-Caccia. 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In this paper, we study label-free event-based object recognition where category labels and paired images are not available. To this end, we propose a joint formulation of object recognition and image reconstruction in a complementary manner. Our method first reconstructs images from events and performs object recognition through Contrastive Language-Image Pretraining (CLIP), enabling better recognition through a rich context of images. Since the category information is essential in reconstructing images, we propose category-guided attraction loss and category-agnostic repulsion loss to bridge the textual features of predicted categories and the visual features of reconstructed images using CLIP. Moreover, we introduce a reliable data sampling strategy and local-global reconstruction consistency to boost joint learning of two tasks. To enhance the accuracy of prediction and quality of reconstruction, we also propose a prototype-based approach using unpaired images. Extensive experiments demonstrate the superiority of our method and its extensibility for zero-shot object recognition. Our project code is available at https://github.com/Chohoonhee/Ev-LaFOR.", + "bbox": [ + 75, + 338, + 473, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 684, + 208, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Event cameras are neuromorphic vision sensors that asynchronously perceive per-pixel brightness changes with high temporal resolution. They show advantages over conventional frame-based cameras, such as high dynamic range (HDR) and low latency. However, despite the superiority of cameras, algorithms using events are still in their infancy. Existing event-based object recognition methods [1, 4, 22, 24, 25, 26, 30, 32, 34, 36, 40, 53] have been shown that object recognition is a crucial task for event feature learning [12, 29, 38] and endeavors have successfully", + "bbox": [ + 75, + 707, + 468, + 845 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0284fba41f1963b2940b0ca24aafc41c889a0aaf349f6e097983639d6b731466.jpg", + "image_caption": [ + "Figure 1: We tackle label-free event-based object recognition where category labels and paired images are not available. Our approach can simultaneously perform object recognition and image reconstruction through proposed joint learning framework. Optionally, our method can leverage unpaired images to enhance object recognition performance and reconstructed image quality." + ], + "image_footnote": [], + "bbox": [ + 507, + 307, + 884, + 501 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "classified the object with events. However, they rely on supervision with category labels to achieve high performance. Furthermore, the sparsity of events poses a challenge for users to label them accurately when there are no paired images. Several unsupervised methods [25, 36] have been proposed for object recognition, however, their performances remain subpar. Hence, there is a natural need for robust and effective label-free event-based object recognition methods.", + "bbox": [ + 497, + 640, + 892, + 751 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we study label-free event-based object recognition where category labels and paired images are not available as in Fig. 1. To tackle this task, we focus on two following facts. Firstly, as demonstrated in [45, 60], performing object recognition on reconstructed images with spatially dense information and rich context shows better performance than solely using events. Secondly, during reconstructing images from events, taking the categories into", + "bbox": [ + 497, + 755, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 253, + 48, + 789, + 61 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 332, + 62, + 709, + 74 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 304, + 74, + 739, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The first two authors contributed equally. In alphabetical order.", + "bbox": [ + 95, + 853, + 433, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19866", + "bbox": [ + 465, + 887, + 505, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "account can improve the quality of the reconstructed images. From these observations, we propose a joint learning framework of two closely-linked tasks: event-based object recognition and event-to-image reconstruction.", + "bbox": [ + 75, + 125, + 468, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our joint learning framework, we first reconstruct images from events and perform object recognition on the reconstructed images using Contrastive Language-Image Pretraining (CLIP) [42]. CLIP is an image-text embedding model that has been trained on a large number of image and language pairs sourced from the web. We utilize the textual features encoded from CLIP since they are well-aligned with visual features, which is advantageous for our tasks that lack labels and images. To this end, we propose the category-guided attraction loss that aligns the visual features from reconstructed images close to the texture features of the predicted category from CLIP.", + "bbox": [ + 75, + 184, + 468, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although the above framework enables the joint learning of event-based object recognition and image reconstruction, using the predicted categories brings two issues. (1) Collapsing to the trivial solution, resulting in all outputs being assigned to a single category and (2) Interrupting the learning process due to unreliable (wrong) predictions. To alleviate these problems, we propose (1) category-agnostic repulsion loss to increase the distances between visual features for preventing collapse and (2) a reliable data sampling (RDS) method to reduce the effects of unreliable predictions. For RDS, we devise two reliable indicators named posterior probability indicator (PPI) and temporally reversed consistency indicator (TRCI). The PPI selects reliable samples based on the probability of prediction. For additional sampling, TRCI utilizes the characteristics of events that temporally reversed ones should be categorized into the same category as the original events. This reliable data sampling enables stable learning even with the predicted categories, leading to a substantial performance improvement in object recognition. Furthermore, to restore the local details, we introduce the local-global reconstruction consistency. Finally, to enhance the accuracy of recognition and visual quality of reconstructed images, we expand our method by employing the existing unpaired images. Extensive experiments demonstrate that our method shows outstanding results on the subset of the N-ImageNet dataset over unsupervised and image reconstruction-based approaches and even surpasses the supervised methods on the N-Caltech101 dataset without using labels and images. In addition, we show that our framework can be extended to event-based zero-shot object recognition.", + "bbox": [ + 75, + 351, + 468, + 781 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work presents four main contributions: (I) We propose a novel joint learning framework for event-based object recognition and image reconstruction, without requiring paired images and labels. (II) We introduce a reliable data sampling strategy and local-global reconstruction consistency that enhances label-free joint training. (III) We", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "further introduce employing unpaired images in our framework for boosting performance. (IV) We conduct extensive experiments of our method along with zero-shot object recognition and superset categories learning, and demonstrate our method's superior performance and effectiveness.", + "bbox": [ + 497, + 125, + 890, + 195 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 207, + 640, + 220 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event-based Object Recognition. Concurrent with the success of event-based low-level tasks [9, 10, 11, 23, 52, 54, 63], there has been a surge of active research focused on object recognition [3, 7, 19, 22, 27, 28, 31, 35, 43, 51, 53, 56], which is considered as a fundamental task. Considering the unique features of event data, numerous works [1, 4, 22, 24, 25, 26, 30, 32, 34, 36, 40, 53] have presented models and representations that can effectively extract significant patterns. However, these approaches require labels for each event data for supervised learning, and since event data cannot be crawled from the web like images, the labeling cost of event data is extremely high. On the other hand, our approach enables the learning of event-based object recognition and image reconstruction simultaneously, without requiring category labels and paired images.", + "bbox": [ + 497, + 229, + 890, + 435 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event-based Image Reconstruction is a well-known topic in the field of event-based vision [2, 13, 17, 20, 21, 46, 49, 57]. Recent researches have been utilizing deep learning to generate realistic outcomes [44, 45, 50, 62]. However, these supervised approaches require the paired images of each event stream to be accurately aligned and synchronized in terms of pixels and time. Another line of approach, such as Wang et al. [59] and Pini et al. [41], utilized generative adversarial networks (GANs) to reconstruct intensity with unpaired images that are not related to the events of the scene. However, GANs are prone to be sensitive to various parameters, and when images that are significantly irrelevant to objects are utilized, the quality of the reconstructed images from events is notably low. An alternative solution is a self-supervised method [37] that utilizes photometric consistency, but this approach requires a continuous sequence that spans an adequately long period. Differently, our framework can reconstruct the intensity of event data without images, very long event sequence and GANs. We only exploit the category prompts of a bundle of event data, not the class label of each event data.", + "bbox": [ + 497, + 437, + 890, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Label-free Learning aims to solve the end-task only with unlabeled data, and has been actively explored [8, 58]. HOTS [25] proposed a category-free method for recognizing objects based on events and SSL-E2VID [37] proposed a self-supervised learning method for reconstructing images from only events. However, their performances fall short of supervised learning methods with significant performance gaps. Inspired by the success of using the pretrained model [5, 6, 39, 48, 55], we adopt CLIP [42] for label-free event-based object recognition. We propose a", + "bbox": [ + 497, + 726, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19867", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b9c0ce00c40f448ae65cf3529781931084efaa6040745f51c21d4fd1af0893e9.jpg", + "image_caption": [ + "Figure 2: Overall joint learning framework of event-based object recognition with event-to-image reconstruction. Our approach involves CLIP's textual and visual encoders that derive textual and visual features, respectively, from given class sets and events. Textual features are obtained from category prompts, while visual features are obtained from reconstructed images. Then, logits and corresponding pseudo labels are generated by computing the cosine similarity between visual and textual features. Lastly, our framework employs pseudo labels to facilitate joint learning using category-agnostic repulsion loss and category-guided attraction loss. To mitigate the impact of unreliable pseudo labels and boost performance, we introduce a reliable data sampling strategy and local-global reconstruction consistency." + ], + "image_footnote": [], + "bbox": [ + 80, + 119, + 887, + 391 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "novel joint learning framework that uses visual and textual knowledge to achieve superior performance in event-to-image reconstruction and event-based object recognition without category labels and paired images. To the best of our knowledge, we are the first to incorporate textual knowledge into event vision research, particularly in the context of label-free tasks.", + "bbox": [ + 75, + 505, + 470, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 77, + 612, + 169, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Sec. 3.1, we first introduce our joint formulation of event-to-image reconstruction and object recognition for label-efficient learning. In Sec. 3.2, we describe our reliable data sampling (RDS) strategy for boosting joint learning performance by filtering the unreliable data samples during training. Sec. 3.3 introduces the local-global reconstruction consistency for spatially regularizing the reconstructed images, which ensures capturing the local details. In Sec. 3.4, we propose to further employ the unpaired images for better recognition performance and reconstructed image quality.", + "bbox": [ + 75, + 633, + 468, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Joint Formulation", + "text_level": 1, + "bbox": [ + 77, + 777, + 253, + 790 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a joint formulation of event-to-image reconstruction and object recognition to perform event-based (zero-shot) object recognition without using labels and paired images of event data. Our joint formulation is based on the fact that 1) image reconstruction can be helpful in", + "bbox": [ + 75, + 796, + 470, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "predicting categories from events, and 2) category information is important in reconstructing images from events. Therefore, we propose 1) the process of performing event-to-image reconstruction and CLIP-driven object recognition from the reconstructed images and 2) category-guided attraction loss and category-agnostic repulsion loss for learning this process without labels and paired images. The overall framework is shown in Fig. 2. Note that our joint learning framework can reconstruct intensity images from events without using any images.", + "bbox": [ + 497, + 505, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Event-to-Image Reconstruction. For the joint formulation, we first reconstruct the intensity image $\\mathcal{I}$ from the event stream $\\mathcal{E} = (u_i,t_i,p_i)_i = 1$ , where $u_{i},t_{i}$ , and $p_i$ denote triggered pixel location, time, and polarity of each event, and $N$ is the temporal length of the event stream. We convert the event stream into event spiking tensor (EST) [16], which is then fed into the image reconstruction network $\\mathcal{G}$ to obtain the intensity image. The image reconstruction process is formulated as follows:", + "bbox": [ + 497, + 643, + 892, + 767 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {I} = \\mathcal {G} (\\operatorname {E S T} (\\mathcal {E})). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 775, + 890, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CLIP-driven Object Recognition. We perform object recognition on top of the reconstructed images instead of raw event data. The advantage of using reconstructed images rather than using event data directly for object recognition is that better performance can be achieved by using", + "bbox": [ + 497, + 796, + 892, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19868", + "bbox": [ + 465, + 887, + 505, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a network trained on rich image data [45, 60]. In particular, we use CLIP [42] for object recognition, which also enables zero-shot object recognition. For an event dataset of $C$ classes, the category prompts are constructed by placing each category name into a pre-defined template, \"image of a [CLASS].\" Then, CLIP's textual encoder encodes category prompts to obtain the $D$ -dimensional textual features $F = (f_{i})_{i = 1}^{C}\\in \\mathbb{R}^{C\\times D}$ . Meantime, the reconstructed image $\\mathcal{I}$ is encoded by CLIP's visual encoder to a visual feature $v\\in \\mathbb{R}^{1\\times D}$ and the class probability $p\\in \\mathbb{R}^{1\\times C}$ for the object recognition are obtained as,", + "bbox": [ + 75, + 125, + 472, + 277 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {i} = \\operatorname {s o f t m a x} _ {i} \\left(v F ^ {\\top}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 285, + 468, + 302 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p_i$ and $\\mathrm{softmax}_i(\\cdot)$ denote the probability for category $i$ and the softmax function. By taking the category of maximum probability, we can predict the category $c$ for the event data $\\mathcal{E}$ as,", + "bbox": [ + 75, + 309, + 468, + 365 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc = \\underset {i} {\\operatorname {a r g m a x}} \\left(p _ {i}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 213, + 375, + 468, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Category-guided Attraction Loss. The challenging part of our joint formulation is to train the reconstruction network $\\mathcal{G}$ without using paired images of event data. Once we reconstruct the intensity images from the event stream (Eq. 1), we can perform object recognition using CLIP (Eq. 2). Motivated by the fact that category information is important in reconstructing images from events, we propose category-guided attraction loss to train the reconstruction network. The proposed category-guided attraction loss brings the visual feature $v$ encoded from the reconstructed image $\\mathcal{I}$ closer to the textual feature of the corresponding category, guiding the model to reconstruct the image corresponding to the category. Since category labels are not available for the event data, we use the predicted categories as pseudo labels. For event data with a batch size of $B$ , the category-guided attraction loss $\\mathcal{L}_{att}$ is formulated as InfoNCE loss [33]:", + "bbox": [ + 75, + 403, + 468, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a t t} = - \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(v _ {i} f _ {c _ {i}} ^ {\\top}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(v _ {i} f _ {c _ {j}} ^ {\\top}\\right)}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 149, + 627, + 468, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $v_{i}, c_{i}$ , and $f_{j}$ denote the visual feature and predicted category of the $i^{\\mathrm{th}}$ event data, and the textual feature of category $j$ . Minimizing $\\mathcal{L}_{att}$ enables the image reconstruction network to generate images of the corresponding category label, while object recognition benefits from the reconstructed images.", + "bbox": [ + 75, + 672, + 468, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Category-agnostic Repulsion Loss. Although $\\mathcal{L}_{att}$ enables joint learning, the use of pseudo labels may cause collapsing, resulting in all outputs being assigned to a single category. Therefore, we introduce a category-agnostic repulsion loss to prevent collapsing by increasing the distances between visual features. To be specific, the category-agnostic repulsion loss $\\mathcal{L}_{rep}$ is applied to the set of visual features as follows:", + "bbox": [ + 75, + 755, + 468, + 865 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e p} = \\sum_ {i = 1} ^ {B} \\log \\left(1 + \\sum_ {j = 1, j \\neq i} ^ {B} \\exp \\left(v _ {i} v _ {j} ^ {\\top}\\right)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 559, + 123, + 890, + 163 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With $\\mathcal{L}_{att}$ and $\\mathcal{L}_{rep}$ , we can successfully formulate our joint learning framework, enabling simultaneous event-to-image reconstruction and (zero-shot) object recognition.", + "bbox": [ + 497, + 168, + 890, + 209 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Reliable Data Sampling", + "text_level": 1, + "bbox": [ + 499, + 214, + 717, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As $\\mathcal{L}_{att}$ relies on pseudo labels, the reliability of predictions may affect the overall training procedure and performance. To reduce the effects of unreliable predictions, we devise two reliability indicators named posterior probability indicator (PPI) and temporally reversed consistency indicator (TRCI). Based on the resultant reliability of predictions, we sample data with reliable predictions for $\\mathcal{L}_{att}$ . The remaining unreliable data is excluded from calculating $\\mathcal{L}_{att}$ and used only for $\\mathcal{L}_{rep}$ .", + "bbox": [ + 497, + 232, + 890, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Posterior Probability Indicator. Given the reconstructed image $\\mathcal{I}$ and the predicted category $c$ , the posterior probability $p_c = \\mathbf{p}(c|\\mathcal{I})$ indicates the model confidence for category $c$ . Thus, we use the posterior probability as an indicator of the reliability of the prediction. In particular, we select $K$ data samples corresponding to the top- $K$ posterior probabilities among $B$ data samples in the mini-batch. The set of selected sample indices from PPI, $S_{\\mathrm{PPI}}$ is defined as,", + "bbox": [ + 497, + 357, + 890, + 467 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\mathrm {P P I}} = \\underset {i} {\\operatorname {a r g s o r t}} (\\mathbf {p} (c _ {i} | \\mathcal {I} _ {i})) ] _ {K}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 473, + 890, + 495 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{I}_i$ and $[\\cdot ]_K$ denote the reconstructed image of the $i^{\\mathrm{th}}$ event data in the mini-batch and the set of the first $K$ items. The $\\operatorname {argsort}(\\cdot)$ function returns indices that would sort an input in descending order.", + "bbox": [ + 497, + 497, + 890, + 552 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporally Reversed Consistency Indicator. Considering the temporal aspect of event data, we propose an additional reliability indicator based on the consistency between predictions from the original events and the temporally reversed events. From the fact that the temporally reversed events $\\mathcal{E}^R = (u_i,\\max_j(t_j) - t_i,p_i)_{i = N}^1$ should be categorized into the same category as the original events $\\mathcal{E}$ , we presume that the consistent model prediction would indicate the reliability of the data sample. To be specific, the set of selected sample indices from TRCI, $S_{\\mathrm{TRCI}}$ is defined as follows:", + "bbox": [ + 497, + 553, + 890, + 703 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\mathrm {T R C I}} = \\{i \\mid c _ {i} = c _ {i} ^ {R}, i = 1, 2, \\dots , B \\}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 704, + 890, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $c_{i}^{R}$ denotes a predicted category of $i^{\\mathrm{th}}$ reversed event data $\\mathcal{E}_i^R$ in the mini-batch.", + "bbox": [ + 497, + 725, + 890, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our final set of selected sample indices $S_{\\mathrm{RDS}}$ for reliable data sampling (RDS) is the intersection of $S_{\\mathrm{PPI}}$ and $S_{\\mathrm{TRCI}}$ :", + "bbox": [ + 497, + 754, + 890, + 783 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\mathrm {R D S}} = S _ {\\mathrm {P P I}} \\cap S _ {\\mathrm {T R C I}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 613, + 795, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, the modified attraction loss with RDS is as follows:", + "bbox": [ + 499, + 813, + 880, + 827 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a t t} = - \\sum_ {i \\in S _ {\\mathrm {R D S}}} \\log \\frac {\\exp \\left(v _ {i} f _ {c _ {i}} ^ {\\top}\\right)}{\\sum_ {j \\in S _ {\\mathrm {R D S}}} \\exp \\left(v _ {i} f _ {c _ {j}} ^ {\\top}\\right)}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 832, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19869", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Local-global Reconstruction Consistency", + "text_level": 1, + "bbox": [ + 77, + 125, + 426, + 140 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Along with $\\mathcal{L}_{att}$ and $\\mathcal{L}_{rep}$ , we further introduce the local-global reconstruction consistency for spatially regularizing the reconstructed images in a self-supervised manner. With random crop function $\\mathcal{H}$ , we first crop the EST of original events $\\mathrm{EST}(\\mathcal{E})$ to obtain the cropped tensor $\\mathcal{H}(\\mathrm{EST}(\\mathcal{E}))$ for the local input. Then, the local-global reconstruction consistency loss $L_{con}$ is defined as,", + "bbox": [ + 75, + 144, + 468, + 243 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n}} = \\| \\mathcal {G} (\\mathcal {H} (\\operatorname {E S T} (\\mathcal {E}))) - \\mathcal {H} (\\mathcal {G} (\\operatorname {E S T} (\\mathcal {E}))) \\| _ {1}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 100, + 252, + 468, + 269 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared to $\\mathcal{L}_{att}$ and $\\mathcal{L}_{rep}$ that work on visual features, $L_{con}$ is applied directly to the reconstructed images and considered as a spatial regularization for the reconstruction network $\\mathcal{G}$ . In addition, matching the reconstructed images from local and global inputs enables the network to capture the local details, improving the reconstruction quality.", + "bbox": [ + 75, + 279, + 468, + 363 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total loss function for the joint learning framework is as follows:", + "bbox": [ + 75, + 364, + 468, + 391 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {a t t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {r e p}} + \\lambda_ {3} \\mathcal {L} _ {\\text {c o n}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 144, + 403, + 468, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_1, \\lambda_2,$ and $\\lambda_3$ are weights for $\\mathcal{L}_{att},\\mathcal{L}_{rep}$ , and $\\mathcal{L}_{con}$ .", + "bbox": [ + 75, + 429, + 467, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Employing Unpaired Images", + "text_level": 1, + "bbox": [ + 77, + 453, + 332, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we expand the use case of our method by introducing how to employ the existing unpaired images. Here, we assume that the category of each image is known, which is the common case for web crawling. Although our framework is capable of event-to-image reconstruction and object recognition without using any images and labels, utilizing existing images can possibly improve the image reconstruction quality and consequently improve object recognition performance. As shown in Fig. 3, we replace textual features in $\\mathcal{L}_{att}$ with the prototype features generated from unpaired images. For each category $c$ , we first encode all images of category $c$ and apply a clustering algorithm to obtain $L$ clusters in total. Then, we aggregate the features of each cluster by averaging them, resulting in $L$ prototype features $W^{c} = (w_{i}^{c})_{i=1}^{L} \\in \\mathbb{R}^{L \\times D}$ .", + "bbox": [ + 75, + 473, + 468, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For data sample index $i \\in S_{\\mathrm{RDS}}$ with corresponding visual feature $v_{i}$ and the predicted category $c_{i}$ , we replace the textual features $f_{c_i}$ in Eq. 9 to the closest prototype feature $w_{l_i}^{c_i}$ , where the cluster index $l_{i}$ is calculated as,", + "bbox": [ + 75, + 682, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nl _ {i} = \\underset {j} {\\operatorname {a r g m a x}} \\left(v _ {i} \\left(w _ {j} ^ {c _ {i}}\\right) ^ {\\top}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 749, + 468, + 775 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our modification of $\\mathcal{L}_{att}$ to employ unpaired images is then defined as follows:", + "bbox": [ + 75, + 783, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a t t} = - \\sum_ {i \\in S _ {\\mathrm {R D S}}} \\log \\frac {\\exp \\left(v _ {i} \\left(w _ {l _ {i}} ^ {c _ {i}}\\right) ^ {\\top}\\right)}{\\sum_ {j \\in S _ {\\mathrm {R D S}}} \\exp \\left(v _ {i} \\left(w _ {l _ {j}} ^ {c _ {j}}\\right) ^ {\\top}\\right)}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 100, + 819, + 468, + 858 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1ad5b3a30d84555de23d6033ead8896ecaec074745b65999f993303a6652fe14.jpg", + "image_caption": [ + "Figure 3: Proposed method employing unpaired images in the category-guided attraction loss. Unpaired images are further utilized to enhance object recognition performance and reconstructed image quality." + ], + "image_footnote": [], + "bbox": [ + 504, + 122, + 890, + 346 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Datasets", + "text_level": 1, + "bbox": [ + 499, + 429, + 594, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The experiments are conducted on two widely used event-based object recognition datasets, N-Caltech101 [35] and N-ImageNet [22], which are constructed by filming Caltech101 [15] and ImageNet [14] datasets on LCD monitor with event camera. Since N-Caltech101 and N-ImageNet datasets do not provide APS frames, the image in the original dataset and corresponding event sequence have different resolutions and are not aligned in pixel-level. To create a visual prototype in Sec. 3.4, we scrap images from the original dataset, mimicking the web crawling. To avoid including paired images of events in the train set, we randomly split the event train set in half for each class. One half is used to train the model, while the corresponding images from the other half are used to create the visual prototype.", + "bbox": [ + 497, + 451, + 890, + 644 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "N-Caltech101 dataset consists of 8,246 event stream data belonging to 101 different object classes. Each object is captured with $320 \\times 245$ resolution (average) for 300 milliseconds. Existing works [45, 60] utilized this dataset to evaluate the performance of image reconstruction and event-based object recognition.", + "bbox": [ + 497, + 644, + 890, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "N-ImageNet is recently released large-scale dataset, containing 1,781,167 event stream data of 1,000 object classes. Compared to N-Caltech101, it has a larger resolution of $640 \\times 480$ and a very short capturing time with $5 \\times 10^{-2}$ milliseconds. Therefore, each event stream contains significantly sparse edge information. N-ImageNet is too challenging for unsupervised studies without ground truth, so we utilize a randomly sampled subset of 100 classes called N-ImageNet (Mini). Details about the split of N-ImageNet (Mini) are provided in the supplementary material.", + "bbox": [ + 497, + 726, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19870", + "bbox": [ + 465, + 887, + 505, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3a1715fb6849501fc70c9fa01ac0297af97b30bd9f8f4184985cfb16da0219bc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsImage PairClass LabelN-Caltech101N-ImageNet (Mini)
Accuracy ↑FID ↓IS ↑Accuracy ↑FID ↓IS ↑
Supervised Learning
Histogram [29]✓63.8--49.8--
Ev-gait [61]✓61.9--51.3--
EST [16]✓81.7*--52.5--
DiST [22]✓73.8--57.9--
Unsupervised Learning
HOTS [25]21.0*--1.6--
Image Reconstruction + CLIP
E2VID [44] (Pre-train)64.083.9012.8113.3147.147.82
E2VID [44] (Fine-tune)59.885.3112.9113.4144.577.48
E2VID [44] (Fine-tune)✓59.886.6612.6113.5144.037.40
E2VID [44] (Fine-tune)✓60.185.5012.8512.7145.797.33
E2VID [44] (Scratch)✓9.4302.482.601.0299.701.15
SSL-E2VID [37] (Pre-train)28.2281.092.361.6324.432.08
SSL-E2VID [37] (Scratch)30.5228.304.371.7250.553.00
Wang et al. [59] (Scratch)42.7160.346.8310.1231.945.00
Wang et al. [59] (Scratch)✓43.572.674.5019.0180.764.89
Wang et al. [59] (Scratch)✓39.7179.794.1813.2216.374.70
Ours (Text Prompt)82.4662.2914.8130.16150.587.92
Ours (Visual Prototype)82.6154.1917.5931.28135.959.74
", + "bbox": [ + 85, + 123, + 884, + 444 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: The results of event-based object recognition and event-to-image reconstruction. The **bold** and **underline** denote the best and the second-best performance except for supervised methods, respectively. * denotes the values taken from the original paper and italic denotes the performance of supervised methods.", + "bbox": [ + 75, + 450, + 892, + 492 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 75, + 504, + 208, + 519 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our methods utilizing text prompts or visual prototypes with other existing methods. We adopt four representations (Histogram [29], Ev-gait [61], EST [16], and DiST [22]) for supervised methods and an unsupervised method (HOTS [25]). Additionally, three image reconstruction networks, E2VID [44], SSL-E2VID [37] and Wang et al. [59], are utilized with CLIP. For a fair comparison with image reconstruction networks, we record the performance of three different models for each image reconstruction network: the official pre-trained model, fine-tuned model, and a model trained from scratch. We evaluate these models under three conditions: paired images, images belonging to the same class, and randomly selected images. Some cases are overlooked when the pre-trained model is unavailable or the training setup does not yield meaningful results. For implementation details, see the supplementary material.", + "bbox": [ + 75, + 526, + 470, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Label-free Object Recognition", + "text_level": 1, + "bbox": [ + 75, + 762, + 346, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Text Prompt. The quantitative results are presented in Table 1. The proposed method outperforms supervised object recognition methods on the N-Caltech101 dataset, despite not using category labels. Also, our method surpasses existing unsupervised methods and image reconstruction methods with CLIP by a large margin under all", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "metrics. Specifically, ours surpasses the best image reconstruction with CLIP method, E2VID (Pre-train), by around $28\\%$ increase in accuracy even though it utilizes the image while pre-training. On N-ImageNet, supervised methods record higher accuracy than ours since the dataset is challenging due to the sparse events captured within a short period. However, ours shows a significant improvement in all metrics compared to other unsupervised and image reconstruction-based methods. Our approach demonstrates the ability to perform object recognition and image reconstruction from event data, even when trained solely on textual features without any image data.", + "bbox": [ + 497, + 504, + 890, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visual Prototype. Besides text prompts, our framework can employ visual prototypes generated from scrapped images. By incorporating visual information, our visual prototype-based approach exceeds the performance of relying solely on textual prompts and achieves the best performance among unsupervised and image reconstruction-based methods under all metrics across both datasets. This demonstrates the superiority of the visual prototypes.", + "bbox": [ + 497, + 671, + 890, + 783 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Image-free Image Reconstruction", + "text_level": 1, + "bbox": [ + 499, + 790, + 794, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also compare the reconstruction results of our methods with other event-to-image reconstruction networks in Table 1. Note that, as mentioned in Sec. 4, the resolution and pixel positions of events and corresponding orig-", + "bbox": [ + 497, + 811, + 892, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19871", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7812e7b24f7ef6d5ab6206f30e47da0bd3c45143d93840596bb805df70d09fcc.jpg", + "image_caption": [ + "Events", + "Wang et. al.", + "E2VID", + "E2VID*", + "Ours (Prompt)", + "Ours (Proto.)", + "Ours (Proto.)*", + "Image", + "(a) N-Caltech101" + ], + "image_footnote": [], + "bbox": [ + 94, + 138, + 873, + 346 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e58e7f9c7861d171cda9424194bfc75d07421857ace6eb51493299e456148679.jpg", + "image_caption": [ + "(b) N-ImageNet", + "Figure 4: Visual results of event-to-image reconstruction network on (a) N-Caltech101 and (b) N-ImageNet datasets. Ours shows a higher quality of reconstructed images with fine-grained details than other methods (Wang et al. [59] and pre-trained E2VID [44]). * denotes the images with brightness and contrast adjustment." + ], + "image_footnote": [], + "bbox": [ + 94, + 366, + 873, + 574 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "inal images are not aligned. Therefore, pixel-wise metrics (e.g., L1, PSNR) cannot be used for comparison. Instead, to assess the visual quality of the reconstructed images, we utilize two metrics: inception score (IS) [47] and Fréchet inception distance (FID) [18].", + "bbox": [ + 75, + 657, + 468, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Despite not utilizing any images during training, our text prompt-based approach surpasses all other image reconstruction techniques in terms of FID and IS metrics on the N-Caltech101 dataset. However, in the case of N-ImageNet, our text prompt approach is the strongest by an IS indicator but falls behind pre-trained E2VID in FID. Since ours is trained from events of short periods without paired images, it becomes challenging to learn the distribution of real images. Instead, utilizing the visual prototype results in the highest FID and IS indicators in both datasets. This implies", + "bbox": [ + 75, + 728, + 468, + 865 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that it can acquire the ability to reconstruct images without requiring paired images that correspond to events.", + "bbox": [ + 497, + 657, + 890, + 685 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also present the qualitative results in Fig. 4. Wang et al. [59] utilize the paired image in training but the method lacks the ability to effectively display intensity contrast, resulting in the loss of many details. While pre-trained E2VID shows better image quality over [59], it still struggles to preserve fine details as it operates in a distinct training environment. This is particularly apparent in the N-ImageNet dataset, where E2VID generates results that deviate significantly from the original image. Conversely, our framework is able to recover intensity effectively and preserve details in reconstructed images, even without access to paired images. Our results closely resemble real images, even in the challenging N-ImageNet dataset.", + "bbox": [ + 497, + 687, + 892, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19872", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0cfd7f1f0fb8320a5f80648264f904e3a13da3d8a26c71fecd7dc2eda2a577c6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsImage PairClass LabelN-Caltech101N-ImageNet (Mini)
Accuracy ↑FID ↓IS ↑Accuracy ↑FID ↓IS ↑
Image Reconstruction + CLIP
E2VID [44] (Pre-train)58.4194.266.4731.7203.056.64
E2VID [44] (Fine-tune)61.7203.397.5630.0199.836.73
E2VID [44] (Fine-tune)✓61.1203.407.4530.9199.446.80
E2VID [44] (Fine-tune)✓61.5202.237.5629.4203.976.08
E2VID [44] (Scratch)✓21.3362.082.434.9333.131.36
SSL-E2VID [37] (Pre-train)24.7332.432.075.7352.532.04
SSL-E2VID [37] (Scratch)25.3289.363.936.1287.982.79
Wang et al. [59] (Scratch)47.5228.774.6718.7241.876.12
Wang et al. [59] (Scratch)✓48.5230.744.9120.5236.783.90
Wang et al. [59] (Scratch)✓43.7215.634.6615.6237.384.40
Ours (Text Prompt)84.31147.316.8145.10202.296.31
Ours (Visual Prototype)85.56107.589.3551.50174.247.32
", + "bbox": [ + 85, + 123, + 884, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Zero-shot Object Recognition", + "text_level": 1, + "bbox": [ + 75, + 378, + 339, + 395 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further demonstrate the advantages of our framework over supervised methods by enabling it to be used for zero-shot object recognition. The reconstructed images can be utilized for zero-shot object recognition thanks to CLIP's capacity to align images with any semantic concepts in an open vocabulary for zero-shot object recognition. To define \"unseen\" categories that are not seen during training, we use only 80 of the 100 categories for training and the remaining 20 for zero-shot testing.", + "bbox": [ + 75, + 399, + 468, + 524 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 2, we present the performance of zero-shot object recognition. Without any category labels, our methods with text prompt achieve a promising $84.31\\%$ and $45.10\\%$ on N-Caltech101 and N-ImageNet, respectively. This is $25.91\\%$ and $13.4\\%$ higher than E2VID pretrained with a large number of image pairs. These results validate that although our model learns through the process of being category-aware, generalization is possible for other categories, especially \"unseen\" in this case. Although FID and IS of our method using text prompts are relatively poor compared to pre-trained E2VID on N-ImageNet, this can also be overcome by using visual prototypes. Our method using the visual prototype is able to achieve a substantial improvement under all metrics. Specifically, in the N-Caltech101 dataset, our method increases the IS from 6.81 to 9.35, while in the N-ImageNet dataset, it increases the accuracy from 45.10 to 51.50.", + "bbox": [ + 75, + 526, + 470, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Ablation Study and Discussion", + "text_level": 1, + "bbox": [ + 75, + 777, + 349, + 793 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.1. Ablation Study", + "text_level": 1, + "bbox": [ + 75, + 801, + 231, + 817 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct an ablation study to understand how the components influence performance. Table 3 illustrates the effectiveness of each component on N-ImageNet dataset.", + "bbox": [ + 75, + 824, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3606d8eb0de6e8ed041a6a5e043c5349633a54dc568ac3ebe679df3232df95ca.jpg", + "table_caption": [ + "Table 2: The results of event-based zero-shot object recognition using CLIP." + ], + "table_footnote": [], + "table_body": "
LattLrepLconRDSAccuracy ↑
PPITRCI
(1)✓9.50
(2)✓✓14.00
(3)✓✓✓15.68
(4)✓✓✓28.42
(5)✓✓✓✓28.90
(6)✓✓✓✓28.91
(7)✓✓✓✓✓30.16
", + "bbox": [ + 505, + 378, + 885, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3: Ablation study of the proposed method.", + "bbox": [ + 534, + 513, + 855, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We start with a baseline, which denotes the removal of everything except attraction loss, $\\mathcal{L}_{att}$ . During the experiment, we notice that if we only apply attraction loss towards the network without repulsion loss, $\\mathcal{L}_{rep}$ , the collapse often takes place. Therefore, $\\mathcal{L}_{rep}$ is essential for stable learning of $\\mathcal{L}_{att}$ . It is worth mentioning the impact of the proposed PPI on performance. Upon analyzing (4), which displays the results when PPI is added to (2), it can be seen that the accuracy has increased by 14.42. Upon examining (5) and (7), it can be observed that the accuracy increases by 1.26, validating the impact of the sub-sampling process via TRCI. Furthermore, the ablation results between (6) and (7) show that the reconstruction consistency between global and local preserves the spatial details of the image, leading to performance improvement. Finally, the model (7) that has all of its components incorporated achieves the highest performance.", + "bbox": [ + 497, + 549, + 890, + 774 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.2. Number of Samples in PPI", + "text_level": 1, + "bbox": [ + 499, + 777, + 741, + 793 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The $K$ used in PPI for selecting the sample with the highest probability impacts the performance of object recognition. Fig. 5 shows the evaluation of performance on N-ImageNet dataset based on different values of $K$ . When $K$ is set to 32, which includes all samples in the batch, the", + "bbox": [ + 497, + 796, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19873", + "bbox": [ + 465, + 887, + 505, + 897 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eb8c64942a8dac1e10eb30d1237c9becc4a3d28ea5a4f77e31027d0cad741418.jpg", + "image_caption": [ + "Figure 5: Object recognition accuracy on N-ImageNet (Mini) according to $K$ in PPI." + ], + "image_footnote": [], + "bbox": [ + 84, + 123, + 460, + 197 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/d94d636714e43c46ad2e957cfeb9cc1cfa7d442abd6bce46b365f99be7aa9a4a.jpg", + "image_caption": [ + "Figure 6: Object recognition accuracy on N-Caltech101 according to $K$ in PPI." + ], + "image_footnote": [], + "bbox": [ + 80, + 245, + 463, + 317 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/90b415a0d004f3cb1321bdbf5ec937e872a4c9a47cf2ce06f9fdf56396414993.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
N-Caltech101N-ImageNet (Mini)
λ2\\λ30.5120.512
0.00182.7182.9381.2629.6226.3430.08
0.00583.5282.0281.6629.3826.9228.72
0.0182.2482.4681.9929.3430.1629.80
0.0581.9982.3982.6127.5027.9229.00
0.181.3782.4682.1725.7626.2826.32
", + "bbox": [ + 80, + 366, + 463, + 461 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 4: The accuracy according to hyper-parameter in Eq. 11 when $\\lambda_1 = 1$ .", + "bbox": [ + 75, + 465, + 468, + 492 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "attraction loss, $\\mathcal{L}_{att}$ , is applied to even those samples with low reliability, resulting in the poorest performance. Due to the same reason, the performance is better when $K$ is 16 than when it is 32, but since unreliable samples are also selected, the accuracy is relatively lower than in other favorable situations. As $K$ decreases, the performance improves, but it starts to decline when $K$ is less than 6, indicating that even with high reliability, it is challenging to achieve optimal training if $\\mathcal{L}_{att}$ is applied with very few samples. Similarly, we report the accuracy according to the $K$ value on the N-Caltech101 in Fig 6. Unless an extremely small number of samples are drawn, as the value of $K$ increases, the performance also improves. However, once a certain threshold is reached, there is little significant change, and it starts to decline with further increases. The accuracy exceeds $80\\%$ in all cases, showing robustness to $K$ values. Although the level of sensitivity varies depending on the dataset, we do confirm that satisfactory results can be obtained between $K = 4$ and $K = 10$ .", + "bbox": [ + 75, + 515, + 468, + 777 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6.3. Hyper-parameter Analysis", + "text_level": 1, + "bbox": [ + 75, + 788, + 317, + 804 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In Table 4, we report the accuracy according to $\\lambda_{2}$ and $\\lambda_{3}$ in Eq. 11. If the weight of the repulsion loss, $\\lambda_{2}$ , is set too high, the performance decreases. However, this can be mitigated by increasing the weight of the local-global re", + "bbox": [ + 75, + 809, + 468, + 866 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/d578b2cc4dbd1da4c37ac78ccae19e553041cace94a5a3168bb1d7da94a52d11.jpg", + "image_caption": [ + "Figure 7: Object recognition accuracy on N-Caltech101 according to the number of extra category prompts." + ], + "image_footnote": [], + "bbox": [ + 504, + 124, + 880, + 205 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "construction consistency loss, $\\lambda_3$ . The results verify the robustness of our method according to the $\\lambda$ on both datasets.", + "bbox": [ + 497, + 262, + 890, + 290 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6.4. Learning with Superset Categories", + "text_level": 1, + "bbox": [ + 499, + 302, + 801, + 319 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In practical terms, it can be challenging for users to find corresponding categories of the event dataset. As a result, they often end up taking more categories as prompts. We tackle these issues by demonstrating that our joint learning framework works robustly even when employing more prompts than the categories of the event on the N-Caltech101 dataset. To avoid using additional prompts that are too irrelevant to the N-Caltech101 dataset, we randomly take additional prompts from N-ImageNet. We show the performance results according to the number of extra category prompts in Fig. 7. While the performance decreases with an increase in extra category prompts, it is worth noting that our algorithm remains reliable even when faced with over 100 additional prompts beyond the corresponding category. This suggests that our algorithm can function with superset categories, even in a situation when the number of extra categories is much larger than the actual categories.", + "bbox": [ + 497, + 324, + 890, + 560 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 499, + 577, + 616, + 592 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we propose a joint learning framework for event-based object recognition with image reconstruction from events without labels and paired images. With the proposed losses and the reliable data sampling strategy, our approach allows stable learning of two tasks simultaneously from pseudo labels. As a result, our approach achieves exceptional performance in event-based object recognition and event-to-image reconstruction, all without requiring category labels and paired images. Our approach successfully addresses the challenge of label dependency in event-based research, which has been a significant obstacle. We anticipate that our work can be further extended to other tasks such as event-based zero-shot object detection, zero-shot semantic segmentation, etc., that have not explored so far in the research field for event cameras.", + "bbox": [ + 497, + 600, + 890, + 808 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636).", + "bbox": [ + 497, + 809, + 890, + 866 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "19874", + "bbox": [ + 465, + 887, + 505, + 897 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Arnon Amir, Brian Taba, David Berg, Timothy Melano, Jeffrey McKinstry, Carmelo Di Nolfo, Tapan Nayak, Alexander Andreopoulos, Guillaume Garreau, Marcela Mendoza, et al. A low power, fully event-based gesture recognition system. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7243-7252, 2017. 1, 2", + "[2] Patrick Bardow, Andrew J Davison, and Stefan Leutenegger. 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In Proceedings of the IEEE/CVF International Conference on Com" + ], + "bbox": [ + 78, + 125, + 468, + 859 + ], + "page_idx": 11 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "puter Vision, pages 2563-2572, 2021. 2", + "[63] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. Unsupervised event-based learning of optical flow, depth, and egomotion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 989-997, 2019. 2" + ], + "bbox": [ + 502, + 127, + 892, + 201 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "19877", + "bbox": [ + 465, + 887, + 504, + 897 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/cebb8d22-3e6f-4881-895d-c913e7109230_model.json b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/cebb8d22-3e6f-4881-895d-c913e7109230_model.json new file mode 100644 index 0000000000000000000000000000000000000000..16de94dee1fb10d36356cbe9445b66fbe13253c1 --- /dev/null +++ b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/cebb8d22-3e6f-4881-895d-c913e7109230_model.json @@ -0,0 +1,2457 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.062 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.334, + 0.063, + 0.71, + 0.075 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.305, + 0.076, + 0.74, + 0.088 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.162, + 0.828, + 0.205 + ], + "angle": 0, + "content": "Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events" + }, + { + "type": "text", + "bbox": [ + 0.209, + 0.229, + 0.761, + 0.246 + ], + "angle": 0, + "content": "Hoonhee Cho*, Hyeonseong Kim*, Yujeong Chae, and Kuk-Jin Yoon" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.246, + 0.697, + 0.263 + ], + "angle": 0, + "content": "Korea Advanced Institute of Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.277, + 0.264, + 0.694, + 0.278 + ], + "angle": 0, + "content": "{gnsgnsgml,brian617,yujeong,kjyoon}@kaist.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.474, + 0.671 + ], + "angle": 0, + "content": "Recognizing objects from sparse and noisy events becomes extremely difficult when paired images and category labels do not exist. In this paper, we study label-free event-based object recognition where category labels and paired images are not available. To this end, we propose a joint formulation of object recognition and image reconstruction in a complementary manner. Our method first reconstructs images from events and performs object recognition through Contrastive Language-Image Pretraining (CLIP), enabling better recognition through a rich context of images. Since the category information is essential in reconstructing images, we propose category-guided attraction loss and category-agnostic repulsion loss to bridge the textual features of predicted categories and the visual features of reconstructed images using CLIP. Moreover, we introduce a reliable data sampling strategy and local-global reconstruction consistency to boost joint learning of two tasks. To enhance the accuracy of prediction and quality of reconstruction, we also propose a prototype-based approach using unpaired images. Extensive experiments demonstrate the superiority of our method and its extensibility for zero-shot object recognition. Our project code is available at https://github.com/Chohoonhee/Ev-LaFOR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.685, + 0.21, + 0.699 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.708, + 0.47, + 0.846 + ], + "angle": 0, + "content": "Event cameras are neuromorphic vision sensors that asynchronously perceive per-pixel brightness changes with high temporal resolution. They show advantages over conventional frame-based cameras, such as high dynamic range (HDR) and low latency. However, despite the superiority of cameras, algorithms using events are still in their infancy. Existing event-based object recognition methods [1, 4, 22, 24, 25, 26, 30, 32, 34, 36, 40, 53] have been shown that object recognition is a crucial task for event feature learning [12, 29, 38] and endeavors have successfully" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.308, + 0.885, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.511, + 0.893, + 0.61 + ], + "angle": 0, + "content": "Figure 1: We tackle label-free event-based object recognition where category labels and paired images are not available. Our approach can simultaneously perform object recognition and image reconstruction through proposed joint learning framework. Optionally, our method can leverage unpaired images to enhance object recognition performance and reconstructed image quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.893, + 0.752 + ], + "angle": 0, + "content": "classified the object with events. However, they rely on supervision with category labels to achieve high performance. Furthermore, the sparsity of events poses a challenge for users to label them accurately when there are no paired images. Several unsupervised methods [25, 36] have been proposed for object recognition, however, their performances remain subpar. Hence, there is a natural need for robust and effective label-free event-based object recognition methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.894, + 0.868 + ], + "angle": 0, + "content": "In this paper, we study label-free event-based object recognition where category labels and paired images are not available as in Fig. 1. To tackle this task, we focus on two following facts. Firstly, as demonstrated in [45, 60], performing object recognition on reconstructed images with spatially dense information and rich context shows better performance than solely using events. Secondly, during reconstructing images from events, taking the categories into" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.854, + 0.435, + 0.867 + ], + "angle": 0, + "content": "*The first two authors contributed equally. In alphabetical order." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.506, + 0.899 + ], + "angle": 0, + "content": "19866" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.127, + 0.47, + 0.182 + ], + "angle": 0, + "content": "account can improve the quality of the reconstructed images. From these observations, we propose a joint learning framework of two closely-linked tasks: event-based object recognition and event-to-image reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.185, + 0.47, + 0.35 + ], + "angle": 0, + "content": "In our joint learning framework, we first reconstruct images from events and perform object recognition on the reconstructed images using Contrastive Language-Image Pretraining (CLIP) [42]. CLIP is an image-text embedding model that has been trained on a large number of image and language pairs sourced from the web. We utilize the textual features encoded from CLIP since they are well-aligned with visual features, which is advantageous for our tasks that lack labels and images. To this end, we propose the category-guided attraction loss that aligns the visual features from reconstructed images close to the texture features of the predicted category from CLIP." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.352, + 0.47, + 0.782 + ], + "angle": 0, + "content": "Although the above framework enables the joint learning of event-based object recognition and image reconstruction, using the predicted categories brings two issues. (1) Collapsing to the trivial solution, resulting in all outputs being assigned to a single category and (2) Interrupting the learning process due to unreliable (wrong) predictions. To alleviate these problems, we propose (1) category-agnostic repulsion loss to increase the distances between visual features for preventing collapse and (2) a reliable data sampling (RDS) method to reduce the effects of unreliable predictions. For RDS, we devise two reliable indicators named posterior probability indicator (PPI) and temporally reversed consistency indicator (TRCI). The PPI selects reliable samples based on the probability of prediction. For additional sampling, TRCI utilizes the characteristics of events that temporally reversed ones should be categorized into the same category as the original events. This reliable data sampling enables stable learning even with the predicted categories, leading to a substantial performance improvement in object recognition. Furthermore, to restore the local details, we introduce the local-global reconstruction consistency. Finally, to enhance the accuracy of recognition and visual quality of reconstructed images, we expand our method by employing the existing unpaired images. Extensive experiments demonstrate that our method shows outstanding results on the subset of the N-ImageNet dataset over unsupervised and image reconstruction-based approaches and even surpasses the supervised methods on the N-Caltech101 dataset without using labels and images. In addition, we show that our framework can be extended to event-based zero-shot object recognition." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.784, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Our work presents four main contributions: (I) We propose a novel joint learning framework for event-based object recognition and image reconstruction, without requiring paired images and labels. (II) We introduce a reliable data sampling strategy and local-global reconstruction consistency that enhances label-free joint training. (III) We" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.892, + 0.196 + ], + "angle": 0, + "content": "further introduce employing unpaired images in our framework for boosting performance. (IV) We conduct extensive experiments of our method along with zero-shot object recognition and superset categories learning, and demonstrate our method's superior performance and effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.208, + 0.642, + 0.222 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.23, + 0.892, + 0.437 + ], + "angle": 0, + "content": "Event-based Object Recognition. Concurrent with the success of event-based low-level tasks [9, 10, 11, 23, 52, 54, 63], there has been a surge of active research focused on object recognition [3, 7, 19, 22, 27, 28, 31, 35, 43, 51, 53, 56], which is considered as a fundamental task. Considering the unique features of event data, numerous works [1, 4, 22, 24, 25, 26, 30, 32, 34, 36, 40, 53] have presented models and representations that can effectively extract significant patterns. However, these approaches require labels for each event data for supervised learning, and since event data cannot be crawled from the web like images, the labeling cost of event data is extremely high. On the other hand, our approach enables the learning of event-based object recognition and image reconstruction simultaneously, without requiring category labels and paired images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.438, + 0.892, + 0.727 + ], + "angle": 0, + "content": "Event-based Image Reconstruction is a well-known topic in the field of event-based vision [2, 13, 17, 20, 21, 46, 49, 57]. Recent researches have been utilizing deep learning to generate realistic outcomes [44, 45, 50, 62]. However, these supervised approaches require the paired images of each event stream to be accurately aligned and synchronized in terms of pixels and time. Another line of approach, such as Wang et al. [59] and Pini et al. [41], utilized generative adversarial networks (GANs) to reconstruct intensity with unpaired images that are not related to the events of the scene. However, GANs are prone to be sensitive to various parameters, and when images that are significantly irrelevant to objects are utilized, the quality of the reconstructed images from events is notably low. An alternative solution is a self-supervised method [37] that utilizes photometric consistency, but this approach requires a continuous sequence that spans an adequately long period. Differently, our framework can reconstruct the intensity of event data without images, very long event sequence and GANs. We only exploit the category prompts of a bundle of event data, not the class label of each event data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.728, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Label-free Learning aims to solve the end-task only with unlabeled data, and has been actively explored [8, 58]. HOTS [25] proposed a category-free method for recognizing objects based on events and SSL-E2VID [37] proposed a self-supervised learning method for reconstructing images from only events. However, their performances fall short of supervised learning methods with significant performance gaps. Inspired by the success of using the pretrained model [5, 6, 39, 48, 55], we adopt CLIP [42] for label-free event-based object recognition. We propose a" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "19867" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.121, + 0.889, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.396, + 0.893, + 0.496 + ], + "angle": 0, + "content": "Figure 2: Overall joint learning framework of event-based object recognition with event-to-image reconstruction. Our approach involves CLIP's textual and visual encoders that derive textual and visual features, respectively, from given class sets and events. Textual features are obtained from category prompts, while visual features are obtained from reconstructed images. Then, logits and corresponding pseudo labels are generated by computing the cosine similarity between visual and textual features. Lastly, our framework employs pseudo labels to facilitate joint learning using category-agnostic repulsion loss and category-guided attraction loss. To mitigate the impact of unreliable pseudo labels and boost performance, we introduce a reliable data sampling strategy and local-global reconstruction consistency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.471, + 0.603 + ], + "angle": 0, + "content": "novel joint learning framework that uses visual and textual knowledge to achieve superior performance in event-to-image reconstruction and event-based object recognition without category labels and paired images. To the best of our knowledge, we are the first to incorporate textual knowledge into event vision research, particularly in the context of label-free tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.613, + 0.17, + 0.627 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.47, + 0.773 + ], + "angle": 0, + "content": "In Sec. 3.1, we first introduce our joint formulation of event-to-image reconstruction and object recognition for label-efficient learning. In Sec. 3.2, we describe our reliable data sampling (RDS) strategy for boosting joint learning performance by filtering the unreliable data samples during training. Sec. 3.3 introduces the local-global reconstruction consistency for spatially regularizing the reconstructed images, which ensures capturing the local details. In Sec. 3.4, we propose to further employ the unpaired images for better recognition performance and reconstructed image quality." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.779, + 0.254, + 0.792 + ], + "angle": 0, + "content": "3.1. Joint Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.471, + 0.868 + ], + "angle": 0, + "content": "We propose a joint formulation of event-to-image reconstruction and object recognition to perform event-based (zero-shot) object recognition without using labels and paired images of event data. Our joint formulation is based on the fact that 1) image reconstruction can be helpful in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.644 + ], + "angle": 0, + "content": "predicting categories from events, and 2) category information is important in reconstructing images from events. Therefore, we propose 1) the process of performing event-to-image reconstruction and CLIP-driven object recognition from the reconstructed images and 2) category-guided attraction loss and category-agnostic repulsion loss for learning this process without labels and paired images. The overall framework is shown in Fig. 2. Note that our joint learning framework can reconstruct intensity images from events without using any images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.768 + ], + "angle": 0, + "content": "Event-to-Image Reconstruction. For the joint formulation, we first reconstruct the intensity image \\(\\mathcal{I}\\) from the event stream \\(\\mathcal{E} = (u_i,t_i,p_i)_i = 1\\), where \\(u_{i},t_{i}\\), and \\(p_i\\) denote triggered pixel location, time, and polarity of each event, and \\(N\\) is the temporal length of the event stream. We convert the event stream into event spiking tensor (EST) [16], which is then fed into the image reconstruction network \\(\\mathcal{G}\\) to obtain the intensity image. The image reconstruction process is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.776, + 0.891, + 0.79 + ], + "angle": 0, + "content": "\\[\n\\mathcal {I} = \\mathcal {G} (\\operatorname {E S T} (\\mathcal {E})). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.893, + 0.868 + ], + "angle": 0, + "content": "CLIP-driven Object Recognition. We perform object recognition on top of the reconstructed images instead of raw event data. The advantage of using reconstructed images rather than using event data directly for object recognition is that better performance can be achieved by using" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.506, + 0.898 + ], + "angle": 0, + "content": "19868" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.279 + ], + "angle": 0, + "content": "a network trained on rich image data [45, 60]. In particular, we use CLIP [42] for object recognition, which also enables zero-shot object recognition. For an event dataset of \\(C\\) classes, the category prompts are constructed by placing each category name into a pre-defined template, \"image of a [CLASS].\" Then, CLIP's textual encoder encodes category prompts to obtain the \\(D\\)-dimensional textual features \\(F = (f_{i})_{i = 1}^{C}\\in \\mathbb{R}^{C\\times D}\\). Meantime, the reconstructed image \\(\\mathcal{I}\\) is encoded by CLIP's visual encoder to a visual feature \\(v\\in \\mathbb{R}^{1\\times D}\\) and the class probability \\(p\\in \\mathbb{R}^{1\\times C}\\) for the object recognition are obtained as," + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.286, + 0.47, + 0.303 + ], + "angle": 0, + "content": "\\[\np _ {i} = \\operatorname {s o f t m a x} _ {i} \\left(v F ^ {\\top}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.311, + 0.47, + 0.366 + ], + "angle": 0, + "content": "where \\(p_i\\) and \\(\\mathrm{softmax}_i(\\cdot)\\) denote the probability for category \\(i\\) and the softmax function. By taking the category of maximum probability, we can predict the category \\(c\\) for the event data \\(\\mathcal{E}\\) as," + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.376, + 0.469, + 0.397 + ], + "angle": 0, + "content": "\\[\nc = \\underset {i} {\\operatorname {a r g m a x}} \\left(p _ {i}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.47, + 0.626 + ], + "angle": 0, + "content": "Category-guided Attraction Loss. The challenging part of our joint formulation is to train the reconstruction network \\(\\mathcal{G}\\) without using paired images of event data. Once we reconstruct the intensity images from the event stream (Eq. 1), we can perform object recognition using CLIP (Eq. 2). Motivated by the fact that category information is important in reconstructing images from events, we propose category-guided attraction loss to train the reconstruction network. The proposed category-guided attraction loss brings the visual feature \\(v\\) encoded from the reconstructed image \\(\\mathcal{I}\\) closer to the textual feature of the corresponding category, guiding the model to reconstruct the image corresponding to the category. Since category labels are not available for the event data, we use the predicted categories as pseudo labels. For event data with a batch size of \\(B\\), the category-guided attraction loss \\(\\mathcal{L}_{att}\\) is formulated as InfoNCE loss [33]:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.628, + 0.47, + 0.667 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a t t} = - \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(v _ {i} f _ {c _ {i}} ^ {\\top}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(v _ {i} f _ {c _ {j}} ^ {\\top}\\right)}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.756 + ], + "angle": 0, + "content": "where \\( v_{i}, c_{i} \\), and \\( f_{j} \\) denote the visual feature and predicted category of the \\( i^{\\mathrm{th}} \\) event data, and the textual feature of category \\( j \\). Minimizing \\( \\mathcal{L}_{att} \\) enables the image reconstruction network to generate images of the corresponding category label, while object recognition benefits from the reconstructed images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.469, + 0.866 + ], + "angle": 0, + "content": "Category-agnostic Repulsion Loss. Although \\(\\mathcal{L}_{att}\\) enables joint learning, the use of pseudo labels may cause collapsing, resulting in all outputs being assigned to a single category. Therefore, we introduce a category-agnostic repulsion loss to prevent collapsing by increasing the distances between visual features. To be specific, the category-agnostic repulsion loss \\(\\mathcal{L}_{rep}\\) is applied to the set of visual features as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.124, + 0.892, + 0.164 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e p} = \\sum_ {i = 1} ^ {B} \\log \\left(1 + \\sum_ {j = 1, j \\neq i} ^ {B} \\exp \\left(v _ {i} v _ {j} ^ {\\top}\\right)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.169, + 0.892, + 0.21 + ], + "angle": 0, + "content": "With \\(\\mathcal{L}_{att}\\) and \\(\\mathcal{L}_{rep}\\), we can successfully formulate our joint learning framework, enabling simultaneous event-to-image reconstruction and (zero-shot) object recognition." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.215, + 0.719, + 0.23 + ], + "angle": 0, + "content": "3.2. Reliable Data Sampling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.233, + 0.892, + 0.357 + ], + "angle": 0, + "content": "As \\(\\mathcal{L}_{att}\\) relies on pseudo labels, the reliability of predictions may affect the overall training procedure and performance. To reduce the effects of unreliable predictions, we devise two reliability indicators named posterior probability indicator (PPI) and temporally reversed consistency indicator (TRCI). Based on the resultant reliability of predictions, we sample data with reliable predictions for \\(\\mathcal{L}_{att}\\). The remaining unreliable data is excluded from calculating \\(\\mathcal{L}_{att}\\) and used only for \\(\\mathcal{L}_{rep}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.358, + 0.892, + 0.468 + ], + "angle": 0, + "content": "Posterior Probability Indicator. Given the reconstructed image \\(\\mathcal{I}\\) and the predicted category \\(c\\), the posterior probability \\(p_c = \\mathbf{p}(c|\\mathcal{I})\\) indicates the model confidence for category \\(c\\). Thus, we use the posterior probability as an indicator of the reliability of the prediction. In particular, we select \\(K\\) data samples corresponding to the top-\\(K\\) posterior probabilities among \\(B\\) data samples in the mini-batch. The set of selected sample indices from PPI, \\(S_{\\mathrm{PPI}}\\) is defined as," + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.474, + 0.891, + 0.496 + ], + "angle": 0, + "content": "\\[\nS _ {\\mathrm {P P I}} = \\underset {i} {\\operatorname {a r g s o r t}} (\\mathbf {p} (c _ {i} | \\mathcal {I} _ {i})) ] _ {K}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.891, + 0.553 + ], + "angle": 0, + "content": "where \\(\\mathcal{I}_i\\) and \\([\\cdot ]_K\\) denote the reconstructed image of the \\(i^{\\mathrm{th}}\\) event data in the mini-batch and the set of the first \\(K\\) items. The \\(\\operatorname {argsort}(\\cdot)\\) function returns indices that would sort an input in descending order." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Temporally Reversed Consistency Indicator. Considering the temporal aspect of event data, we propose an additional reliability indicator based on the consistency between predictions from the original events and the temporally reversed events. From the fact that the temporally reversed events \\(\\mathcal{E}^R = (u_i,\\max_j(t_j) - t_i,p_i)_{i = N}^1\\) should be categorized into the same category as the original events \\(\\mathcal{E}\\), we presume that the consistent model prediction would indicate the reliability of the data sample. To be specific, the set of selected sample indices from TRCI, \\(S_{\\mathrm{TRCI}}\\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.705, + 0.891, + 0.722 + ], + "angle": 0, + "content": "\\[\nS _ {\\mathrm {T R C I}} = \\{i \\mid c _ {i} = c _ {i} ^ {R}, i = 1, 2, \\dots , B \\}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.891, + 0.754 + ], + "angle": 0, + "content": "where \\(c_{i}^{R}\\) denotes a predicted category of \\(i^{\\mathrm{th}}\\) reversed event data \\(\\mathcal{E}_i^R\\) in the mini-batch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.755, + 0.891, + 0.784 + ], + "angle": 0, + "content": "Our final set of selected sample indices \\(S_{\\mathrm{RDS}}\\) for reliable data sampling (RDS) is the intersection of \\(S_{\\mathrm{PPI}}\\) and \\(S_{\\mathrm{TRCI}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.796, + 0.891, + 0.811 + ], + "angle": 0, + "content": "\\[\nS _ {\\mathrm {R D S}} = S _ {\\mathrm {P P I}} \\cap S _ {\\mathrm {T R C I}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.814, + 0.882, + 0.828 + ], + "angle": 0, + "content": "Then, the modified attraction loss with RDS is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.833, + 0.891, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a t t} = - \\sum_ {i \\in S _ {\\mathrm {R D S}}} \\log \\frac {\\exp \\left(v _ {i} f _ {c _ {i}} ^ {\\top}\\right)}{\\sum_ {j \\in S _ {\\mathrm {R D S}}} \\exp \\left(v _ {i} f _ {c _ {j}} ^ {\\top}\\right)}, \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.898 + ], + "angle": 0, + "content": "19869" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.126, + 0.427, + 0.141 + ], + "angle": 0, + "content": "3.3. Local-global Reconstruction Consistency" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.146, + 0.47, + 0.244 + ], + "angle": 0, + "content": "Along with \\(\\mathcal{L}_{att}\\) and \\(\\mathcal{L}_{rep}\\), we further introduce the local-global reconstruction consistency for spatially regularizing the reconstructed images in a self-supervised manner. With random crop function \\(\\mathcal{H}\\), we first crop the EST of original events \\(\\mathrm{EST}(\\mathcal{E})\\) to obtain the cropped tensor \\(\\mathcal{H}(\\mathrm{EST}(\\mathcal{E}))\\) for the local input. Then, the local-global reconstruction consistency loss \\(L_{con}\\) is defined as," + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.254, + 0.469, + 0.27 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n}} = \\| \\mathcal {G} (\\mathcal {H} (\\operatorname {E S T} (\\mathcal {E}))) - \\mathcal {H} (\\mathcal {G} (\\operatorname {E S T} (\\mathcal {E}))) \\| _ {1}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.28, + 0.469, + 0.364 + ], + "angle": 0, + "content": "Compared to \\(\\mathcal{L}_{att}\\) and \\(\\mathcal{L}_{rep}\\) that work on visual features, \\(L_{con}\\) is applied directly to the reconstructed images and considered as a spatial regularization for the reconstruction network \\(\\mathcal{G}\\). In addition, matching the reconstructed images from local and global inputs enables the network to capture the local details, improving the reconstruction quality." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.365, + 0.469, + 0.392 + ], + "angle": 0, + "content": "The total loss function for the joint learning framework is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.404, + 0.469, + 0.42 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {a t t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {r e p}} + \\lambda_ {3} \\mathcal {L} _ {\\text {c o n}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.43, + 0.468, + 0.445 + ], + "angle": 0, + "content": "where \\(\\lambda_1, \\lambda_2,\\) and \\(\\lambda_3\\) are weights for \\(\\mathcal{L}_{att},\\mathcal{L}_{rep}\\), and \\(\\mathcal{L}_{con}\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.454, + 0.334, + 0.469 + ], + "angle": 0, + "content": "3.4. Employing Unpaired Images" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.475, + 0.469, + 0.682 + ], + "angle": 0, + "content": "In this section, we expand the use case of our method by introducing how to employ the existing unpaired images. Here, we assume that the category of each image is known, which is the common case for web crawling. Although our framework is capable of event-to-image reconstruction and object recognition without using any images and labels, utilizing existing images can possibly improve the image reconstruction quality and consequently improve object recognition performance. As shown in Fig. 3, we replace textual features in \\(\\mathcal{L}_{att}\\) with the prototype features generated from unpaired images. For each category \\(c\\), we first encode all images of category \\(c\\) and apply a clustering algorithm to obtain \\(L\\) clusters in total. Then, we aggregate the features of each cluster by averaging them, resulting in \\(L\\) prototype features \\(W^{c} = (w_{i}^{c})_{i=1}^{L} \\in \\mathbb{R}^{L \\times D}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.683, + 0.469, + 0.741 + ], + "angle": 0, + "content": "For data sample index \\(i \\in S_{\\mathrm{RDS}}\\) with corresponding visual feature \\(v_{i}\\) and the predicted category \\(c_{i}\\), we replace the textual features \\(f_{c_i}\\) in Eq. 9 to the closest prototype feature \\(w_{l_i}^{c_i}\\), where the cluster index \\(l_{i}\\) is calculated as," + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.75, + 0.469, + 0.776 + ], + "angle": 0, + "content": "\\[\nl _ {i} = \\underset {j} {\\operatorname {a r g m a x}} \\left(v _ {i} \\left(w _ {j} ^ {c _ {i}}\\right) ^ {\\top}\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.785, + 0.469, + 0.812 + ], + "angle": 0, + "content": "Our modification of \\(\\mathcal{L}_{att}\\) to employ unpaired images is then defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.82, + 0.469, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a t t} = - \\sum_ {i \\in S _ {\\mathrm {R D S}}} \\log \\frac {\\exp \\left(v _ {i} \\left(w _ {l _ {i}} ^ {c _ {i}}\\right) ^ {\\top}\\right)}{\\sum_ {j \\in S _ {\\mathrm {R D S}}} \\exp \\left(v _ {i} \\left(w _ {l _ {j}} ^ {c _ {j}}\\right) ^ {\\top}\\right)}, \\tag {13}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.123, + 0.891, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.358, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Figure 3: Proposed method employing unpaired images in the category-guided attraction loss. Unpaired images are further utilized to enhance object recognition performance and reconstructed image quality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.431, + 0.596, + 0.445 + ], + "angle": 0, + "content": "4. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.892, + 0.646 + ], + "angle": 0, + "content": "The experiments are conducted on two widely used event-based object recognition datasets, N-Caltech101 [35] and N-ImageNet [22], which are constructed by filming Caltech101 [15] and ImageNet [14] datasets on LCD monitor with event camera. Since N-Caltech101 and N-ImageNet datasets do not provide APS frames, the image in the original dataset and corresponding event sequence have different resolutions and are not aligned in pixel-level. To create a visual prototype in Sec. 3.4, we scrap images from the original dataset, mimicking the web crawling. To avoid including paired images of events in the train set, we randomly split the event train set in half for each class. One half is used to train the model, while the corresponding images from the other half are used to create the visual prototype." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.892, + 0.728 + ], + "angle": 0, + "content": "N-Caltech101 dataset consists of 8,246 event stream data belonging to 101 different object classes. Each object is captured with \\(320 \\times 245\\) resolution (average) for 300 milliseconds. Existing works [45, 60] utilized this dataset to evaluate the performance of image reconstruction and event-based object recognition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.892, + 0.867 + ], + "angle": 0, + "content": "N-ImageNet is recently released large-scale dataset, containing 1,781,167 event stream data of 1,000 object classes. Compared to N-Caltech101, it has a larger resolution of \\(640 \\times 480\\) and a very short capturing time with \\(5 \\times 10^{-2}\\) milliseconds. Therefore, each event stream contains significantly sparse edge information. N-ImageNet is too challenging for unsupervised studies without ground truth, so we utilize a randomly sampled subset of 100 classes called N-ImageNet (Mini). Details about the split of N-ImageNet (Mini) are provided in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.506, + 0.898 + ], + "angle": 0, + "content": "19870" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.087, + 0.124, + 0.885, + 0.445 + ], + "angle": 0, + "content": "
MethodsImage PairClass LabelN-Caltech101N-ImageNet (Mini)
Accuracy ↑FID ↓IS ↑Accuracy ↑FID ↓IS ↑
Supervised Learning
Histogram [29]✓63.8--49.8--
Ev-gait [61]✓61.9--51.3--
EST [16]✓81.7*--52.5--
DiST [22]✓73.8--57.9--
Unsupervised Learning
HOTS [25]21.0*--1.6--
Image Reconstruction + CLIP
E2VID [44] (Pre-train)64.083.9012.8113.3147.147.82
E2VID [44] (Fine-tune)59.885.3112.9113.4144.577.48
E2VID [44] (Fine-tune)✓59.886.6612.6113.5144.037.40
E2VID [44] (Fine-tune)✓60.185.5012.8512.7145.797.33
E2VID [44] (Scratch)✓9.4302.482.601.0299.701.15
SSL-E2VID [37] (Pre-train)28.2281.092.361.6324.432.08
SSL-E2VID [37] (Scratch)30.5228.304.371.7250.553.00
Wang et al. [59] (Scratch)42.7160.346.8310.1231.945.00
Wang et al. [59] (Scratch)✓43.572.674.5019.0180.764.89
Wang et al. [59] (Scratch)✓39.7179.794.1813.2216.374.70
Ours (Text Prompt)82.4662.2914.8130.16150.587.92
Ours (Visual Prototype)82.6154.1917.5931.28135.959.74
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.451, + 0.893, + 0.493 + ], + "angle": 0, + "content": "Table 1: The results of event-based object recognition and event-to-image reconstruction. The **bold** and **underline** denote the best and the second-best performance except for supervised methods, respectively. * denotes the values taken from the original paper and italic denotes the performance of supervised methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.505, + 0.21, + 0.52 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.471, + 0.749 + ], + "angle": 0, + "content": "We compare our methods utilizing text prompts or visual prototypes with other existing methods. We adopt four representations (Histogram [29], Ev-gait [61], EST [16], and DiST [22]) for supervised methods and an unsupervised method (HOTS [25]). Additionally, three image reconstruction networks, E2VID [44], SSL-E2VID [37] and Wang et al. [59], are utilized with CLIP. For a fair comparison with image reconstruction networks, we record the performance of three different models for each image reconstruction network: the official pre-trained model, fine-tuned model, and a model trained from scratch. We evaluate these models under three conditions: paired images, images belonging to the same class, and randomly selected images. Some cases are overlooked when the pre-trained model is unavailable or the training setup does not yield meaningful results. For implementation details, see the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.763, + 0.347, + 0.779 + ], + "angle": 0, + "content": "5.1. Label-free Object Recognition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Text Prompt. The quantitative results are presented in Table 1. The proposed method outperforms supervised object recognition methods on the N-Caltech101 dataset, despite not using category labels. Also, our method surpasses existing unsupervised methods and image reconstruction methods with CLIP by a large margin under all" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.672 + ], + "angle": 0, + "content": "metrics. Specifically, ours surpasses the best image reconstruction with CLIP method, E2VID (Pre-train), by around \\(28\\%\\) increase in accuracy even though it utilizes the image while pre-training. On N-ImageNet, supervised methods record higher accuracy than ours since the dataset is challenging due to the sparse events captured within a short period. However, ours shows a significant improvement in all metrics compared to other unsupervised and image reconstruction-based methods. Our approach demonstrates the ability to perform object recognition and image reconstruction from event data, even when trained solely on textual features without any image data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.784 + ], + "angle": 0, + "content": "Visual Prototype. Besides text prompts, our framework can employ visual prototypes generated from scrapped images. By incorporating visual information, our visual prototype-based approach exceeds the performance of relying solely on textual prompts and achieves the best performance among unsupervised and image reconstruction-based methods under all metrics across both datasets. This demonstrates the superiority of the visual prototypes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.792, + 0.795, + 0.807 + ], + "angle": 0, + "content": "5.2. Image-free Image Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.893, + 0.868 + ], + "angle": 0, + "content": "We also compare the reconstruction results of our methods with other event-to-image reconstruction networks in Table 1. Note that, as mentioned in Sec. 4, the resolution and pixel positions of events and corresponding orig-" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.899 + ], + "angle": 0, + "content": "19871" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.12, + 0.126, + 0.166, + 0.137 + ], + "angle": 0, + "content": "Events" + }, + { + "type": "image_caption", + "bbox": [ + 0.201, + 0.126, + 0.28, + 0.138 + ], + "angle": 0, + "content": "Wang et. al." + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.126, + 0.362, + 0.137 + ], + "angle": 0, + "content": "E2VID" + }, + { + "type": "image_caption", + "bbox": [ + 0.408, + 0.126, + 0.464, + 0.138 + ], + "angle": 0, + "content": "E2VID*" + }, + { + "type": "image_caption", + "bbox": [ + 0.486, + 0.126, + 0.58, + 0.138 + ], + "angle": 0, + "content": "Ours (Prompt)" + }, + { + "type": "image_caption", + "bbox": [ + 0.584, + 0.126, + 0.672, + 0.138 + ], + "angle": 0, + "content": "Ours (Proto.)" + }, + { + "type": "image_caption", + "bbox": [ + 0.68, + 0.126, + 0.774, + 0.138 + ], + "angle": 0, + "content": "Ours (Proto.)*" + }, + { + "type": "image_caption", + "bbox": [ + 0.804, + 0.127, + 0.845, + 0.138 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.139, + 0.875, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.428, + 0.348, + 0.54, + 0.361 + ], + "angle": 0, + "content": "(a) N-Caltech101" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.368, + 0.875, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.432, + 0.577, + 0.536, + 0.589 + ], + "angle": 0, + "content": "(b) N-ImageNet" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.592, + 0.893, + 0.634 + ], + "angle": 0, + "content": "Figure 4: Visual results of event-to-image reconstruction network on (a) N-Caltech101 and (b) N-ImageNet datasets. Ours shows a higher quality of reconstructed images with fine-grained details than other methods (Wang et al. [59] and pre-trained E2VID [44]). * denotes the images with brightness and contrast adjustment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.727 + ], + "angle": 0, + "content": "inal images are not aligned. Therefore, pixel-wise metrics (e.g., L1, PSNR) cannot be used for comparison. Instead, to assess the visual quality of the reconstructed images, we utilize two metrics: inception score (IS) [47] and Fréchet inception distance (FID) [18]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.469, + 0.866 + ], + "angle": 0, + "content": "Despite not utilizing any images during training, our text prompt-based approach surpasses all other image reconstruction techniques in terms of FID and IS metrics on the N-Caltech101 dataset. However, in the case of N-ImageNet, our text prompt approach is the strongest by an IS indicator but falls behind pre-trained E2VID in FID. Since ours is trained from events of short periods without paired images, it becomes challenging to learn the distribution of real images. Instead, utilizing the visual prototype results in the highest FID and IS indicators in both datasets. This implies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.686 + ], + "angle": 0, + "content": "that it can acquire the ability to reconstruct images without requiring paired images that correspond to events." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.893, + 0.867 + ], + "angle": 0, + "content": "We also present the qualitative results in Fig. 4. Wang et al. [59] utilize the paired image in training but the method lacks the ability to effectively display intensity contrast, resulting in the loss of many details. While pre-trained E2VID shows better image quality over [59], it still struggles to preserve fine details as it operates in a distinct training environment. This is particularly apparent in the N-ImageNet dataset, where E2VID generates results that deviate significantly from the original image. Conversely, our framework is able to recover intensity effectively and preserve details in reconstructed images, even without access to paired images. Our results closely resemble real images, even in the challenging N-ImageNet dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.505, + 0.898 + ], + "angle": 0, + "content": "19872" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.124, + 0.885, + 0.349 + ], + "angle": 0, + "content": "
MethodsImage PairClass LabelN-Caltech101N-ImageNet (Mini)
Accuracy ↑FID ↓IS ↑Accuracy ↑FID ↓IS ↑
Image Reconstruction + CLIP
E2VID [44] (Pre-train)58.4194.266.4731.7203.056.64
E2VID [44] (Fine-tune)61.7203.397.5630.0199.836.73
E2VID [44] (Fine-tune)✓61.1203.407.4530.9199.446.80
E2VID [44] (Fine-tune)✓61.5202.237.5629.4203.976.08
E2VID [44] (Scratch)✓21.3362.082.434.9333.131.36
SSL-E2VID [37] (Pre-train)24.7332.432.075.7352.532.04
SSL-E2VID [37] (Scratch)25.3289.363.936.1287.982.79
Wang et al. [59] (Scratch)47.5228.774.6718.7241.876.12
Wang et al. [59] (Scratch)✓48.5230.744.9120.5236.783.90
Wang et al. [59] (Scratch)✓43.7215.634.6615.6237.384.40
Ours (Text Prompt)84.31147.316.8145.10202.296.31
Ours (Visual Prototype)85.56107.589.3551.50174.247.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.233, + 0.351, + 0.735, + 0.366 + ], + "angle": 0, + "content": "Table 2: The results of event-based zero-shot object recognition using CLIP." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.38, + 0.341, + 0.396 + ], + "angle": 0, + "content": "5.3. Zero-shot Object Recognition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.47, + 0.526 + ], + "angle": 0, + "content": "We further demonstrate the advantages of our framework over supervised methods by enabling it to be used for zero-shot object recognition. The reconstructed images can be utilized for zero-shot object recognition thanks to CLIP's capacity to align images with any semantic concepts in an open vocabulary for zero-shot object recognition. To define \"unseen\" categories that are not seen during training, we use only 80 of the 100 categories for training and the remaining 20 for zero-shot testing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.471, + 0.763 + ], + "angle": 0, + "content": "In Table 2, we present the performance of zero-shot object recognition. Without any category labels, our methods with text prompt achieve a promising \\(84.31\\%\\) and \\(45.10\\%\\) on N-Caltech101 and N-ImageNet, respectively. This is \\(25.91\\%\\) and \\(13.4\\%\\) higher than E2VID pretrained with a large number of image pairs. These results validate that although our model learns through the process of being category-aware, generalization is possible for other categories, especially \"unseen\" in this case. Although FID and IS of our method using text prompts are relatively poor compared to pre-trained E2VID on N-ImageNet, this can also be overcome by using visual prototypes. Our method using the visual prototype is able to achieve a substantial improvement under all metrics. Specifically, in the N-Caltech101 dataset, our method increases the IS from 6.81 to 9.35, while in the N-ImageNet dataset, it increases the accuracy from 45.10 to 51.50." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.778, + 0.351, + 0.794 + ], + "angle": 0, + "content": "6. Ablation Study and Discussion" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.233, + 0.818 + ], + "angle": 0, + "content": "6.1. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.47, + 0.868 + ], + "angle": 0, + "content": "We conduct an ablation study to understand how the components influence performance. Table 3 illustrates the effectiveness of each component on N-ImageNet dataset." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.379, + 0.887, + 0.512 + ], + "angle": 0, + "content": "
LattLrepLconRDSAccuracy ↑
PPITRCI
(1)✓9.50
(2)✓✓14.00
(3)✓✓✓15.68
(4)✓✓✓28.42
(5)✓✓✓✓28.90
(6)✓✓✓✓28.91
(7)✓✓✓✓✓30.16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.535, + 0.514, + 0.856, + 0.528 + ], + "angle": 0, + "content": "Table 3: Ablation study of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.775 + ], + "angle": 0, + "content": "We start with a baseline, which denotes the removal of everything except attraction loss, \\(\\mathcal{L}_{att}\\). During the experiment, we notice that if we only apply attraction loss towards the network without repulsion loss, \\(\\mathcal{L}_{rep}\\), the collapse often takes place. Therefore, \\(\\mathcal{L}_{rep}\\) is essential for stable learning of \\(\\mathcal{L}_{att}\\). It is worth mentioning the impact of the proposed PPI on performance. Upon analyzing (4), which displays the results when PPI is added to (2), it can be seen that the accuracy has increased by 14.42. Upon examining (5) and (7), it can be observed that the accuracy increases by 1.26, validating the impact of the sub-sampling process via TRCI. Furthermore, the ablation results between (6) and (7) show that the reconstruction consistency between global and local preserves the spatial details of the image, leading to performance improvement. Finally, the model (7) that has all of its components incorporated achieves the highest performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.778, + 0.742, + 0.794 + ], + "angle": 0, + "content": "6.2. Number of Samples in PPI" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.797, + 0.892, + 0.868 + ], + "angle": 0, + "content": "The \\(K\\) used in PPI for selecting the sample with the highest probability impacts the performance of object recognition. Fig. 5 shows the evaluation of performance on N-ImageNet dataset based on different values of \\(K\\). When \\(K\\) is set to 32, which includes all samples in the batch, the" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.506, + 0.899 + ], + "angle": 0, + "content": "19873" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.085, + 0.124, + 0.462, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.208, + 0.47, + 0.236 + ], + "angle": 0, + "content": "Figure 5: Object recognition accuracy on N-ImageNet (Mini) according to \\( K \\) in PPI." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.246, + 0.465, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.325, + 0.468, + 0.354 + ], + "angle": 0, + "content": "Figure 6: Object recognition accuracy on N-Caltech101 according to \\(K\\) in PPI." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.367, + 0.465, + 0.462 + ], + "angle": 0, + "content": "
N-Caltech101N-ImageNet (Mini)
λ2\\λ30.5120.512
0.00182.7182.9381.2629.6226.3430.08
0.00583.5282.0281.6629.3826.9228.72
0.0182.2482.4681.9929.3430.1629.80
0.0581.9982.3982.6127.5027.9229.00
0.181.3782.4682.1725.7626.2826.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.466, + 0.469, + 0.494 + ], + "angle": 0, + "content": "Table 4: The accuracy according to hyper-parameter in Eq. 11 when \\( \\lambda_1 = 1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.779 + ], + "angle": 0, + "content": "attraction loss, \\(\\mathcal{L}_{att}\\), is applied to even those samples with low reliability, resulting in the poorest performance. Due to the same reason, the performance is better when \\(K\\) is 16 than when it is 32, but since unreliable samples are also selected, the accuracy is relatively lower than in other favorable situations. As \\(K\\) decreases, the performance improves, but it starts to decline when \\(K\\) is less than 6, indicating that even with high reliability, it is challenging to achieve optimal training if \\(\\mathcal{L}_{att}\\) is applied with very few samples. Similarly, we report the accuracy according to the \\(K\\) value on the N-Caltech101 in Fig 6. Unless an extremely small number of samples are drawn, as the value of \\(K\\) increases, the performance also improves. However, once a certain threshold is reached, there is little significant change, and it starts to decline with further increases. The accuracy exceeds \\(80\\%\\) in all cases, showing robustness to \\(K\\) values. Although the level of sensitivity varies depending on the dataset, we do confirm that satisfactory results can be obtained between \\(K = 4\\) and \\(K = 10\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.789, + 0.318, + 0.805 + ], + "angle": 0, + "content": "6.3. Hyper-parameter Analysis" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.469, + 0.868 + ], + "angle": 0, + "content": "In Table 4, we report the accuracy according to \\(\\lambda_{2}\\) and \\(\\lambda_{3}\\) in Eq. 11. If the weight of the repulsion loss, \\(\\lambda_{2}\\), is set too high, the performance decreases. However, this can be mitigated by increasing the weight of the local-global re" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.125, + 0.882, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.209, + 0.892, + 0.238 + ], + "angle": 0, + "content": "Figure 7: Object recognition accuracy on N-Caltech101 according to the number of extra category prompts." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.263, + 0.892, + 0.291 + ], + "angle": 0, + "content": "construction consistency loss, \\(\\lambda_3\\). The results verify the robustness of our method according to the \\(\\lambda\\) on both datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.304, + 0.803, + 0.32 + ], + "angle": 0, + "content": "6.4. Learning with Superset Categories" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.892, + 0.561 + ], + "angle": 0, + "content": "In practical terms, it can be challenging for users to find corresponding categories of the event dataset. As a result, they often end up taking more categories as prompts. We tackle these issues by demonstrating that our joint learning framework works robustly even when employing more prompts than the categories of the event on the N-Caltech101 dataset. To avoid using additional prompts that are too irrelevant to the N-Caltech101 dataset, we randomly take additional prompts from N-ImageNet. We show the performance results according to the number of extra category prompts in Fig. 7. While the performance decreases with an increase in extra category prompts, it is worth noting that our algorithm remains reliable even when faced with over 100 additional prompts beyond the corresponding category. This suggests that our algorithm can function with superset categories, even in a situation when the number of extra categories is much larger than the actual categories." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.578, + 0.618, + 0.593 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.892, + 0.809 + ], + "angle": 0, + "content": "In this work, we propose a joint learning framework for event-based object recognition with image reconstruction from events without labels and paired images. With the proposed losses and the reliable data sampling strategy, our approach allows stable learning of two tasks simultaneously from pseudo labels. As a result, our approach achieves exceptional performance in event-based object recognition and event-to-image reconstruction, all without requiring category labels and paired images. Our approach successfully addresses the challenge of label dependency in event-based research, which has been a significant obstacle. We anticipate that our work can be further extended to other tasks such as event-based zero-shot object detection, zero-shot semantic segmentation, etc., that have not explored so far in the research field for event cameras." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636)." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.888, + 0.506, + 0.899 + ], + "angle": 0, + "content": "19874" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.173, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.47, + 0.224 + ], + "angle": 0, + "content": "[1] Arnon Amir, Brian Taba, David Berg, Timothy Melano, Jeffrey McKinstry, Carmelo Di Nolfo, Tapan Nayak, Alexander Andreopoulos, Guillaume Garreau, Marcela Mendoza, et al. A low power, fully event-based gesture recognition system. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 989-997, 2019. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.128, + 0.894, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.467, + 0.888, + 0.505, + 0.898 + ], + "angle": 0, + "content": "19877" + } + ] +] \ No newline at end of file diff --git a/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/cebb8d22-3e6f-4881-895d-c913e7109230_origin.pdf b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/cebb8d22-3e6f-4881-895d-c913e7109230_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cae5a500ae843ec4801c47b2e3744e126a88a7a2 --- /dev/null +++ b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/cebb8d22-3e6f-4881-895d-c913e7109230_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c74029b9914930cc74637dc334202b9450d6b575bde49a495fb91cb15b124c81 +size 1816931 diff --git a/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/full.md b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0f5a2abceb97950bdac93f65f006928c04f70d90 --- /dev/null +++ b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/full.md @@ -0,0 +1,343 @@ +# Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events + +Hoonhee Cho*, Hyeonseong Kim*, Yujeong Chae, and Kuk-Jin Yoon + +Korea Advanced Institute of Science and Technology + +{gnsgnsgml,brian617,yujeong,kjyoon}@kaist.ac.kr + +# Abstract + +Recognizing objects from sparse and noisy events becomes extremely difficult when paired images and category labels do not exist. In this paper, we study label-free event-based object recognition where category labels and paired images are not available. To this end, we propose a joint formulation of object recognition and image reconstruction in a complementary manner. Our method first reconstructs images from events and performs object recognition through Contrastive Language-Image Pretraining (CLIP), enabling better recognition through a rich context of images. Since the category information is essential in reconstructing images, we propose category-guided attraction loss and category-agnostic repulsion loss to bridge the textual features of predicted categories and the visual features of reconstructed images using CLIP. Moreover, we introduce a reliable data sampling strategy and local-global reconstruction consistency to boost joint learning of two tasks. To enhance the accuracy of prediction and quality of reconstruction, we also propose a prototype-based approach using unpaired images. Extensive experiments demonstrate the superiority of our method and its extensibility for zero-shot object recognition. Our project code is available at https://github.com/Chohoonhee/Ev-LaFOR. + +# 1. Introduction + +Event cameras are neuromorphic vision sensors that asynchronously perceive per-pixel brightness changes with high temporal resolution. They show advantages over conventional frame-based cameras, such as high dynamic range (HDR) and low latency. However, despite the superiority of cameras, algorithms using events are still in their infancy. Existing event-based object recognition methods [1, 4, 22, 24, 25, 26, 30, 32, 34, 36, 40, 53] have been shown that object recognition is a crucial task for event feature learning [12, 29, 38] and endeavors have successfully + +![](images/0284fba41f1963b2940b0ca24aafc41c889a0aaf349f6e097983639d6b731466.jpg) +Figure 1: We tackle label-free event-based object recognition where category labels and paired images are not available. Our approach can simultaneously perform object recognition and image reconstruction through proposed joint learning framework. Optionally, our method can leverage unpaired images to enhance object recognition performance and reconstructed image quality. + +classified the object with events. However, they rely on supervision with category labels to achieve high performance. Furthermore, the sparsity of events poses a challenge for users to label them accurately when there are no paired images. Several unsupervised methods [25, 36] have been proposed for object recognition, however, their performances remain subpar. Hence, there is a natural need for robust and effective label-free event-based object recognition methods. + +In this paper, we study label-free event-based object recognition where category labels and paired images are not available as in Fig. 1. To tackle this task, we focus on two following facts. Firstly, as demonstrated in [45, 60], performing object recognition on reconstructed images with spatially dense information and rich context shows better performance than solely using events. Secondly, during reconstructing images from events, taking the categories into + +account can improve the quality of the reconstructed images. From these observations, we propose a joint learning framework of two closely-linked tasks: event-based object recognition and event-to-image reconstruction. + +In our joint learning framework, we first reconstruct images from events and perform object recognition on the reconstructed images using Contrastive Language-Image Pretraining (CLIP) [42]. CLIP is an image-text embedding model that has been trained on a large number of image and language pairs sourced from the web. We utilize the textual features encoded from CLIP since they are well-aligned with visual features, which is advantageous for our tasks that lack labels and images. To this end, we propose the category-guided attraction loss that aligns the visual features from reconstructed images close to the texture features of the predicted category from CLIP. + +Although the above framework enables the joint learning of event-based object recognition and image reconstruction, using the predicted categories brings two issues. (1) Collapsing to the trivial solution, resulting in all outputs being assigned to a single category and (2) Interrupting the learning process due to unreliable (wrong) predictions. To alleviate these problems, we propose (1) category-agnostic repulsion loss to increase the distances between visual features for preventing collapse and (2) a reliable data sampling (RDS) method to reduce the effects of unreliable predictions. For RDS, we devise two reliable indicators named posterior probability indicator (PPI) and temporally reversed consistency indicator (TRCI). The PPI selects reliable samples based on the probability of prediction. For additional sampling, TRCI utilizes the characteristics of events that temporally reversed ones should be categorized into the same category as the original events. This reliable data sampling enables stable learning even with the predicted categories, leading to a substantial performance improvement in object recognition. Furthermore, to restore the local details, we introduce the local-global reconstruction consistency. Finally, to enhance the accuracy of recognition and visual quality of reconstructed images, we expand our method by employing the existing unpaired images. Extensive experiments demonstrate that our method shows outstanding results on the subset of the N-ImageNet dataset over unsupervised and image reconstruction-based approaches and even surpasses the supervised methods on the N-Caltech101 dataset without using labels and images. In addition, we show that our framework can be extended to event-based zero-shot object recognition. + +Our work presents four main contributions: (I) We propose a novel joint learning framework for event-based object recognition and image reconstruction, without requiring paired images and labels. (II) We introduce a reliable data sampling strategy and local-global reconstruction consistency that enhances label-free joint training. (III) We + +further introduce employing unpaired images in our framework for boosting performance. (IV) We conduct extensive experiments of our method along with zero-shot object recognition and superset categories learning, and demonstrate our method's superior performance and effectiveness. + +# 2. Related Work + +Event-based Object Recognition. Concurrent with the success of event-based low-level tasks [9, 10, 11, 23, 52, 54, 63], there has been a surge of active research focused on object recognition [3, 7, 19, 22, 27, 28, 31, 35, 43, 51, 53, 56], which is considered as a fundamental task. Considering the unique features of event data, numerous works [1, 4, 22, 24, 25, 26, 30, 32, 34, 36, 40, 53] have presented models and representations that can effectively extract significant patterns. However, these approaches require labels for each event data for supervised learning, and since event data cannot be crawled from the web like images, the labeling cost of event data is extremely high. On the other hand, our approach enables the learning of event-based object recognition and image reconstruction simultaneously, without requiring category labels and paired images. + +Event-based Image Reconstruction is a well-known topic in the field of event-based vision [2, 13, 17, 20, 21, 46, 49, 57]. Recent researches have been utilizing deep learning to generate realistic outcomes [44, 45, 50, 62]. However, these supervised approaches require the paired images of each event stream to be accurately aligned and synchronized in terms of pixels and time. Another line of approach, such as Wang et al. [59] and Pini et al. [41], utilized generative adversarial networks (GANs) to reconstruct intensity with unpaired images that are not related to the events of the scene. However, GANs are prone to be sensitive to various parameters, and when images that are significantly irrelevant to objects are utilized, the quality of the reconstructed images from events is notably low. An alternative solution is a self-supervised method [37] that utilizes photometric consistency, but this approach requires a continuous sequence that spans an adequately long period. Differently, our framework can reconstruct the intensity of event data without images, very long event sequence and GANs. We only exploit the category prompts of a bundle of event data, not the class label of each event data. + +Label-free Learning aims to solve the end-task only with unlabeled data, and has been actively explored [8, 58]. HOTS [25] proposed a category-free method for recognizing objects based on events and SSL-E2VID [37] proposed a self-supervised learning method for reconstructing images from only events. However, their performances fall short of supervised learning methods with significant performance gaps. Inspired by the success of using the pretrained model [5, 6, 39, 48, 55], we adopt CLIP [42] for label-free event-based object recognition. We propose a + +![](images/b9c0ce00c40f448ae65cf3529781931084efaa6040745f51c21d4fd1af0893e9.jpg) +Figure 2: Overall joint learning framework of event-based object recognition with event-to-image reconstruction. Our approach involves CLIP's textual and visual encoders that derive textual and visual features, respectively, from given class sets and events. Textual features are obtained from category prompts, while visual features are obtained from reconstructed images. Then, logits and corresponding pseudo labels are generated by computing the cosine similarity between visual and textual features. Lastly, our framework employs pseudo labels to facilitate joint learning using category-agnostic repulsion loss and category-guided attraction loss. To mitigate the impact of unreliable pseudo labels and boost performance, we introduce a reliable data sampling strategy and local-global reconstruction consistency. + +novel joint learning framework that uses visual and textual knowledge to achieve superior performance in event-to-image reconstruction and event-based object recognition without category labels and paired images. To the best of our knowledge, we are the first to incorporate textual knowledge into event vision research, particularly in the context of label-free tasks. + +# 3. Method + +In Sec. 3.1, we first introduce our joint formulation of event-to-image reconstruction and object recognition for label-efficient learning. In Sec. 3.2, we describe our reliable data sampling (RDS) strategy for boosting joint learning performance by filtering the unreliable data samples during training. Sec. 3.3 introduces the local-global reconstruction consistency for spatially regularizing the reconstructed images, which ensures capturing the local details. In Sec. 3.4, we propose to further employ the unpaired images for better recognition performance and reconstructed image quality. + +# 3.1. Joint Formulation + +We propose a joint formulation of event-to-image reconstruction and object recognition to perform event-based (zero-shot) object recognition without using labels and paired images of event data. Our joint formulation is based on the fact that 1) image reconstruction can be helpful in + +predicting categories from events, and 2) category information is important in reconstructing images from events. Therefore, we propose 1) the process of performing event-to-image reconstruction and CLIP-driven object recognition from the reconstructed images and 2) category-guided attraction loss and category-agnostic repulsion loss for learning this process without labels and paired images. The overall framework is shown in Fig. 2. Note that our joint learning framework can reconstruct intensity images from events without using any images. + +Event-to-Image Reconstruction. For the joint formulation, we first reconstruct the intensity image $\mathcal{I}$ from the event stream $\mathcal{E} = (u_i,t_i,p_i)_i = 1$ , where $u_{i},t_{i}$ , and $p_i$ denote triggered pixel location, time, and polarity of each event, and $N$ is the temporal length of the event stream. We convert the event stream into event spiking tensor (EST) [16], which is then fed into the image reconstruction network $\mathcal{G}$ to obtain the intensity image. The image reconstruction process is formulated as follows: + +$$ +\mathcal {I} = \mathcal {G} (\operatorname {E S T} (\mathcal {E})). \tag {1} +$$ + +CLIP-driven Object Recognition. We perform object recognition on top of the reconstructed images instead of raw event data. The advantage of using reconstructed images rather than using event data directly for object recognition is that better performance can be achieved by using + +a network trained on rich image data [45, 60]. In particular, we use CLIP [42] for object recognition, which also enables zero-shot object recognition. For an event dataset of $C$ classes, the category prompts are constructed by placing each category name into a pre-defined template, "image of a [CLASS]." Then, CLIP's textual encoder encodes category prompts to obtain the $D$ -dimensional textual features $F = (f_{i})_{i = 1}^{C}\in \mathbb{R}^{C\times D}$ . Meantime, the reconstructed image $\mathcal{I}$ is encoded by CLIP's visual encoder to a visual feature $v\in \mathbb{R}^{1\times D}$ and the class probability $p\in \mathbb{R}^{1\times C}$ for the object recognition are obtained as, + +$$ +p _ {i} = \operatorname {s o f t m a x} _ {i} \left(v F ^ {\top}\right), \tag {2} +$$ + +where $p_i$ and $\mathrm{softmax}_i(\cdot)$ denote the probability for category $i$ and the softmax function. By taking the category of maximum probability, we can predict the category $c$ for the event data $\mathcal{E}$ as, + +$$ +c = \underset {i} {\operatorname {a r g m a x}} \left(p _ {i}\right). \tag {3} +$$ + +Category-guided Attraction Loss. The challenging part of our joint formulation is to train the reconstruction network $\mathcal{G}$ without using paired images of event data. Once we reconstruct the intensity images from the event stream (Eq. 1), we can perform object recognition using CLIP (Eq. 2). Motivated by the fact that category information is important in reconstructing images from events, we propose category-guided attraction loss to train the reconstruction network. The proposed category-guided attraction loss brings the visual feature $v$ encoded from the reconstructed image $\mathcal{I}$ closer to the textual feature of the corresponding category, guiding the model to reconstruct the image corresponding to the category. Since category labels are not available for the event data, we use the predicted categories as pseudo labels. For event data with a batch size of $B$ , the category-guided attraction loss $\mathcal{L}_{att}$ is formulated as InfoNCE loss [33]: + +$$ +\mathcal {L} _ {a t t} = - \sum_ {i = 1} ^ {B} \log \frac {\exp \left(v _ {i} f _ {c _ {i}} ^ {\top}\right)}{\sum_ {j = 1} ^ {B} \exp \left(v _ {i} f _ {c _ {j}} ^ {\top}\right)}, \tag {4} +$$ + +where $v_{i}, c_{i}$ , and $f_{j}$ denote the visual feature and predicted category of the $i^{\mathrm{th}}$ event data, and the textual feature of category $j$ . Minimizing $\mathcal{L}_{att}$ enables the image reconstruction network to generate images of the corresponding category label, while object recognition benefits from the reconstructed images. + +Category-agnostic Repulsion Loss. Although $\mathcal{L}_{att}$ enables joint learning, the use of pseudo labels may cause collapsing, resulting in all outputs being assigned to a single category. Therefore, we introduce a category-agnostic repulsion loss to prevent collapsing by increasing the distances between visual features. To be specific, the category-agnostic repulsion loss $\mathcal{L}_{rep}$ is applied to the set of visual features as follows: + +$$ +\mathcal {L} _ {r e p} = \sum_ {i = 1} ^ {B} \log \left(1 + \sum_ {j = 1, j \neq i} ^ {B} \exp \left(v _ {i} v _ {j} ^ {\top}\right)\right). \tag {5} +$$ + +With $\mathcal{L}_{att}$ and $\mathcal{L}_{rep}$ , we can successfully formulate our joint learning framework, enabling simultaneous event-to-image reconstruction and (zero-shot) object recognition. + +# 3.2. Reliable Data Sampling + +As $\mathcal{L}_{att}$ relies on pseudo labels, the reliability of predictions may affect the overall training procedure and performance. To reduce the effects of unreliable predictions, we devise two reliability indicators named posterior probability indicator (PPI) and temporally reversed consistency indicator (TRCI). Based on the resultant reliability of predictions, we sample data with reliable predictions for $\mathcal{L}_{att}$ . The remaining unreliable data is excluded from calculating $\mathcal{L}_{att}$ and used only for $\mathcal{L}_{rep}$ . + +Posterior Probability Indicator. Given the reconstructed image $\mathcal{I}$ and the predicted category $c$ , the posterior probability $p_c = \mathbf{p}(c|\mathcal{I})$ indicates the model confidence for category $c$ . Thus, we use the posterior probability as an indicator of the reliability of the prediction. In particular, we select $K$ data samples corresponding to the top- $K$ posterior probabilities among $B$ data samples in the mini-batch. The set of selected sample indices from PPI, $S_{\mathrm{PPI}}$ is defined as, + +$$ +S _ {\mathrm {P P I}} = \underset {i} {\operatorname {a r g s o r t}} (\mathbf {p} (c _ {i} | \mathcal {I} _ {i})) ] _ {K}, \tag {6} +$$ + +where $\mathcal{I}_i$ and $[\cdot ]_K$ denote the reconstructed image of the $i^{\mathrm{th}}$ event data in the mini-batch and the set of the first $K$ items. The $\operatorname {argsort}(\cdot)$ function returns indices that would sort an input in descending order. + +Temporally Reversed Consistency Indicator. Considering the temporal aspect of event data, we propose an additional reliability indicator based on the consistency between predictions from the original events and the temporally reversed events. From the fact that the temporally reversed events $\mathcal{E}^R = (u_i,\max_j(t_j) - t_i,p_i)_{i = N}^1$ should be categorized into the same category as the original events $\mathcal{E}$ , we presume that the consistent model prediction would indicate the reliability of the data sample. To be specific, the set of selected sample indices from TRCI, $S_{\mathrm{TRCI}}$ is defined as follows: + +$$ +S _ {\mathrm {T R C I}} = \{i \mid c _ {i} = c _ {i} ^ {R}, i = 1, 2, \dots , B \}, \tag {7} +$$ + +where $c_{i}^{R}$ denotes a predicted category of $i^{\mathrm{th}}$ reversed event data $\mathcal{E}_i^R$ in the mini-batch. + +Our final set of selected sample indices $S_{\mathrm{RDS}}$ for reliable data sampling (RDS) is the intersection of $S_{\mathrm{PPI}}$ and $S_{\mathrm{TRCI}}$ : + +$$ +S _ {\mathrm {R D S}} = S _ {\mathrm {P P I}} \cap S _ {\mathrm {T R C I}}. \tag {8} +$$ + +Then, the modified attraction loss with RDS is as follows: + +$$ +\mathcal {L} _ {a t t} = - \sum_ {i \in S _ {\mathrm {R D S}}} \log \frac {\exp \left(v _ {i} f _ {c _ {i}} ^ {\top}\right)}{\sum_ {j \in S _ {\mathrm {R D S}}} \exp \left(v _ {i} f _ {c _ {j}} ^ {\top}\right)}, \tag {9} +$$ + +# 3.3. Local-global Reconstruction Consistency + +Along with $\mathcal{L}_{att}$ and $\mathcal{L}_{rep}$ , we further introduce the local-global reconstruction consistency for spatially regularizing the reconstructed images in a self-supervised manner. With random crop function $\mathcal{H}$ , we first crop the EST of original events $\mathrm{EST}(\mathcal{E})$ to obtain the cropped tensor $\mathcal{H}(\mathrm{EST}(\mathcal{E}))$ for the local input. Then, the local-global reconstruction consistency loss $L_{con}$ is defined as, + +$$ +\mathcal {L} _ {\text {c o n}} = \| \mathcal {G} (\mathcal {H} (\operatorname {E S T} (\mathcal {E}))) - \mathcal {H} (\mathcal {G} (\operatorname {E S T} (\mathcal {E}))) \| _ {1}. \tag {10} +$$ + +Compared to $\mathcal{L}_{att}$ and $\mathcal{L}_{rep}$ that work on visual features, $L_{con}$ is applied directly to the reconstructed images and considered as a spatial regularization for the reconstruction network $\mathcal{G}$ . In addition, matching the reconstructed images from local and global inputs enables the network to capture the local details, improving the reconstruction quality. + +The total loss function for the joint learning framework is as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {\text {a t t}} + \lambda_ {2} \mathcal {L} _ {\text {r e p}} + \lambda_ {3} \mathcal {L} _ {\text {c o n}}, \tag {11} +$$ + +where $\lambda_1, \lambda_2,$ and $\lambda_3$ are weights for $\mathcal{L}_{att},\mathcal{L}_{rep}$ , and $\mathcal{L}_{con}$ . + +# 3.4. Employing Unpaired Images + +In this section, we expand the use case of our method by introducing how to employ the existing unpaired images. Here, we assume that the category of each image is known, which is the common case for web crawling. Although our framework is capable of event-to-image reconstruction and object recognition without using any images and labels, utilizing existing images can possibly improve the image reconstruction quality and consequently improve object recognition performance. As shown in Fig. 3, we replace textual features in $\mathcal{L}_{att}$ with the prototype features generated from unpaired images. For each category $c$ , we first encode all images of category $c$ and apply a clustering algorithm to obtain $L$ clusters in total. Then, we aggregate the features of each cluster by averaging them, resulting in $L$ prototype features $W^{c} = (w_{i}^{c})_{i=1}^{L} \in \mathbb{R}^{L \times D}$ . + +For data sample index $i \in S_{\mathrm{RDS}}$ with corresponding visual feature $v_{i}$ and the predicted category $c_{i}$ , we replace the textual features $f_{c_i}$ in Eq. 9 to the closest prototype feature $w_{l_i}^{c_i}$ , where the cluster index $l_{i}$ is calculated as, + +$$ +l _ {i} = \underset {j} {\operatorname {a r g m a x}} \left(v _ {i} \left(w _ {j} ^ {c _ {i}}\right) ^ {\top}\right). \tag {12} +$$ + +Our modification of $\mathcal{L}_{att}$ to employ unpaired images is then defined as follows: + +$$ +\mathcal {L} _ {a t t} = - \sum_ {i \in S _ {\mathrm {R D S}}} \log \frac {\exp \left(v _ {i} \left(w _ {l _ {i}} ^ {c _ {i}}\right) ^ {\top}\right)}{\sum_ {j \in S _ {\mathrm {R D S}}} \exp \left(v _ {i} \left(w _ {l _ {j}} ^ {c _ {j}}\right) ^ {\top}\right)}, \tag {13} +$$ + +![](images/1ad5b3a30d84555de23d6033ead8896ecaec074745b65999f993303a6652fe14.jpg) +Figure 3: Proposed method employing unpaired images in the category-guided attraction loss. Unpaired images are further utilized to enhance object recognition performance and reconstructed image quality. + +# 4. Datasets + +The experiments are conducted on two widely used event-based object recognition datasets, N-Caltech101 [35] and N-ImageNet [22], which are constructed by filming Caltech101 [15] and ImageNet [14] datasets on LCD monitor with event camera. Since N-Caltech101 and N-ImageNet datasets do not provide APS frames, the image in the original dataset and corresponding event sequence have different resolutions and are not aligned in pixel-level. To create a visual prototype in Sec. 3.4, we scrap images from the original dataset, mimicking the web crawling. To avoid including paired images of events in the train set, we randomly split the event train set in half for each class. One half is used to train the model, while the corresponding images from the other half are used to create the visual prototype. + +N-Caltech101 dataset consists of 8,246 event stream data belonging to 101 different object classes. Each object is captured with $320 \times 245$ resolution (average) for 300 milliseconds. Existing works [45, 60] utilized this dataset to evaluate the performance of image reconstruction and event-based object recognition. + +N-ImageNet is recently released large-scale dataset, containing 1,781,167 event stream data of 1,000 object classes. Compared to N-Caltech101, it has a larger resolution of $640 \times 480$ and a very short capturing time with $5 \times 10^{-2}$ milliseconds. Therefore, each event stream contains significantly sparse edge information. N-ImageNet is too challenging for unsupervised studies without ground truth, so we utilize a randomly sampled subset of 100 classes called N-ImageNet (Mini). Details about the split of N-ImageNet (Mini) are provided in the supplementary material. + +
MethodsImage PairClass LabelN-Caltech101N-ImageNet (Mini)
Accuracy ↑FID ↓IS ↑Accuracy ↑FID ↓IS ↑
Supervised Learning
Histogram [29]✓63.8--49.8--
Ev-gait [61]✓61.9--51.3--
EST [16]✓81.7*--52.5--
DiST [22]✓73.8--57.9--
Unsupervised Learning
HOTS [25]21.0*--1.6--
Image Reconstruction + CLIP
E2VID [44] (Pre-train)64.083.9012.8113.3147.147.82
E2VID [44] (Fine-tune)59.885.3112.9113.4144.577.48
E2VID [44] (Fine-tune)✓59.886.6612.6113.5144.037.40
E2VID [44] (Fine-tune)✓60.185.5012.8512.7145.797.33
E2VID [44] (Scratch)✓9.4302.482.601.0299.701.15
SSL-E2VID [37] (Pre-train)28.2281.092.361.6324.432.08
SSL-E2VID [37] (Scratch)30.5228.304.371.7250.553.00
Wang et al. [59] (Scratch)42.7160.346.8310.1231.945.00
Wang et al. [59] (Scratch)✓43.572.674.5019.0180.764.89
Wang et al. [59] (Scratch)✓39.7179.794.1813.2216.374.70
Ours (Text Prompt)82.4662.2914.8130.16150.587.92
Ours (Visual Prototype)82.6154.1917.5931.28135.959.74
+ +Table 1: The results of event-based object recognition and event-to-image reconstruction. The **bold** and **underline** denote the best and the second-best performance except for supervised methods, respectively. * denotes the values taken from the original paper and italic denotes the performance of supervised methods. + +# 5. Experiments + +We compare our methods utilizing text prompts or visual prototypes with other existing methods. We adopt four representations (Histogram [29], Ev-gait [61], EST [16], and DiST [22]) for supervised methods and an unsupervised method (HOTS [25]). Additionally, three image reconstruction networks, E2VID [44], SSL-E2VID [37] and Wang et al. [59], are utilized with CLIP. For a fair comparison with image reconstruction networks, we record the performance of three different models for each image reconstruction network: the official pre-trained model, fine-tuned model, and a model trained from scratch. We evaluate these models under three conditions: paired images, images belonging to the same class, and randomly selected images. Some cases are overlooked when the pre-trained model is unavailable or the training setup does not yield meaningful results. For implementation details, see the supplementary material. + +# 5.1. Label-free Object Recognition + +Text Prompt. The quantitative results are presented in Table 1. The proposed method outperforms supervised object recognition methods on the N-Caltech101 dataset, despite not using category labels. Also, our method surpasses existing unsupervised methods and image reconstruction methods with CLIP by a large margin under all + +metrics. Specifically, ours surpasses the best image reconstruction with CLIP method, E2VID (Pre-train), by around $28\%$ increase in accuracy even though it utilizes the image while pre-training. On N-ImageNet, supervised methods record higher accuracy than ours since the dataset is challenging due to the sparse events captured within a short period. However, ours shows a significant improvement in all metrics compared to other unsupervised and image reconstruction-based methods. Our approach demonstrates the ability to perform object recognition and image reconstruction from event data, even when trained solely on textual features without any image data. + +Visual Prototype. Besides text prompts, our framework can employ visual prototypes generated from scrapped images. By incorporating visual information, our visual prototype-based approach exceeds the performance of relying solely on textual prompts and achieves the best performance among unsupervised and image reconstruction-based methods under all metrics across both datasets. This demonstrates the superiority of the visual prototypes. + +# 5.2. Image-free Image Reconstruction + +We also compare the reconstruction results of our methods with other event-to-image reconstruction networks in Table 1. Note that, as mentioned in Sec. 4, the resolution and pixel positions of events and corresponding orig- + +![](images/7812e7b24f7ef6d5ab6206f30e47da0bd3c45143d93840596bb805df70d09fcc.jpg) +Events +Wang et. al. +E2VID +E2VID* +Ours (Prompt) +Ours (Proto.) +Ours (Proto.)* +Image +(a) N-Caltech101 + +![](images/e58e7f9c7861d171cda9424194bfc75d07421857ace6eb51493299e456148679.jpg) +(b) N-ImageNet +Figure 4: Visual results of event-to-image reconstruction network on (a) N-Caltech101 and (b) N-ImageNet datasets. Ours shows a higher quality of reconstructed images with fine-grained details than other methods (Wang et al. [59] and pre-trained E2VID [44]). * denotes the images with brightness and contrast adjustment. + +inal images are not aligned. Therefore, pixel-wise metrics (e.g., L1, PSNR) cannot be used for comparison. Instead, to assess the visual quality of the reconstructed images, we utilize two metrics: inception score (IS) [47] and Fréchet inception distance (FID) [18]. + +Despite not utilizing any images during training, our text prompt-based approach surpasses all other image reconstruction techniques in terms of FID and IS metrics on the N-Caltech101 dataset. However, in the case of N-ImageNet, our text prompt approach is the strongest by an IS indicator but falls behind pre-trained E2VID in FID. Since ours is trained from events of short periods without paired images, it becomes challenging to learn the distribution of real images. Instead, utilizing the visual prototype results in the highest FID and IS indicators in both datasets. This implies + +that it can acquire the ability to reconstruct images without requiring paired images that correspond to events. + +We also present the qualitative results in Fig. 4. Wang et al. [59] utilize the paired image in training but the method lacks the ability to effectively display intensity contrast, resulting in the loss of many details. While pre-trained E2VID shows better image quality over [59], it still struggles to preserve fine details as it operates in a distinct training environment. This is particularly apparent in the N-ImageNet dataset, where E2VID generates results that deviate significantly from the original image. Conversely, our framework is able to recover intensity effectively and preserve details in reconstructed images, even without access to paired images. Our results closely resemble real images, even in the challenging N-ImageNet dataset. + +
MethodsImage PairClass LabelN-Caltech101N-ImageNet (Mini)
Accuracy ↑FID ↓IS ↑Accuracy ↑FID ↓IS ↑
Image Reconstruction + CLIP
E2VID [44] (Pre-train)58.4194.266.4731.7203.056.64
E2VID [44] (Fine-tune)61.7203.397.5630.0199.836.73
E2VID [44] (Fine-tune)✓61.1203.407.4530.9199.446.80
E2VID [44] (Fine-tune)✓61.5202.237.5629.4203.976.08
E2VID [44] (Scratch)✓21.3362.082.434.9333.131.36
SSL-E2VID [37] (Pre-train)24.7332.432.075.7352.532.04
SSL-E2VID [37] (Scratch)25.3289.363.936.1287.982.79
Wang et al. [59] (Scratch)47.5228.774.6718.7241.876.12
Wang et al. [59] (Scratch)✓48.5230.744.9120.5236.783.90
Wang et al. [59] (Scratch)✓43.7215.634.6615.6237.384.40
Ours (Text Prompt)84.31147.316.8145.10202.296.31
Ours (Visual Prototype)85.56107.589.3551.50174.247.32
+ +# 5.3. Zero-shot Object Recognition + +We further demonstrate the advantages of our framework over supervised methods by enabling it to be used for zero-shot object recognition. The reconstructed images can be utilized for zero-shot object recognition thanks to CLIP's capacity to align images with any semantic concepts in an open vocabulary for zero-shot object recognition. To define "unseen" categories that are not seen during training, we use only 80 of the 100 categories for training and the remaining 20 for zero-shot testing. + +In Table 2, we present the performance of zero-shot object recognition. Without any category labels, our methods with text prompt achieve a promising $84.31\%$ and $45.10\%$ on N-Caltech101 and N-ImageNet, respectively. This is $25.91\%$ and $13.4\%$ higher than E2VID pretrained with a large number of image pairs. These results validate that although our model learns through the process of being category-aware, generalization is possible for other categories, especially "unseen" in this case. Although FID and IS of our method using text prompts are relatively poor compared to pre-trained E2VID on N-ImageNet, this can also be overcome by using visual prototypes. Our method using the visual prototype is able to achieve a substantial improvement under all metrics. Specifically, in the N-Caltech101 dataset, our method increases the IS from 6.81 to 9.35, while in the N-ImageNet dataset, it increases the accuracy from 45.10 to 51.50. + +# 6. Ablation Study and Discussion + +# 6.1. Ablation Study + +We conduct an ablation study to understand how the components influence performance. Table 3 illustrates the effectiveness of each component on N-ImageNet dataset. + +Table 2: The results of event-based zero-shot object recognition using CLIP. + +
LattLrepLconRDSAccuracy ↑
PPITRCI
(1)✓9.50
(2)✓✓14.00
(3)✓✓✓15.68
(4)✓✓✓28.42
(5)✓✓✓✓28.90
(6)✓✓✓✓28.91
(7)✓✓✓✓✓30.16
+ +Table 3: Ablation study of the proposed method. + +We start with a baseline, which denotes the removal of everything except attraction loss, $\mathcal{L}_{att}$ . During the experiment, we notice that if we only apply attraction loss towards the network without repulsion loss, $\mathcal{L}_{rep}$ , the collapse often takes place. Therefore, $\mathcal{L}_{rep}$ is essential for stable learning of $\mathcal{L}_{att}$ . It is worth mentioning the impact of the proposed PPI on performance. Upon analyzing (4), which displays the results when PPI is added to (2), it can be seen that the accuracy has increased by 14.42. Upon examining (5) and (7), it can be observed that the accuracy increases by 1.26, validating the impact of the sub-sampling process via TRCI. Furthermore, the ablation results between (6) and (7) show that the reconstruction consistency between global and local preserves the spatial details of the image, leading to performance improvement. Finally, the model (7) that has all of its components incorporated achieves the highest performance. + +# 6.2. Number of Samples in PPI + +The $K$ used in PPI for selecting the sample with the highest probability impacts the performance of object recognition. Fig. 5 shows the evaluation of performance on N-ImageNet dataset based on different values of $K$ . When $K$ is set to 32, which includes all samples in the batch, the + +![](images/eb8c64942a8dac1e10eb30d1237c9becc4a3d28ea5a4f77e31027d0cad741418.jpg) +Figure 5: Object recognition accuracy on N-ImageNet (Mini) according to $K$ in PPI. + +![](images/d94d636714e43c46ad2e957cfeb9cc1cfa7d442abd6bce46b365f99be7aa9a4a.jpg) +Figure 6: Object recognition accuracy on N-Caltech101 according to $K$ in PPI. + +
N-Caltech101N-ImageNet (Mini)
λ2\λ30.5120.512
0.00182.7182.9381.2629.6226.3430.08
0.00583.5282.0281.6629.3826.9228.72
0.0182.2482.4681.9929.3430.1629.80
0.0581.9982.3982.6127.5027.9229.00
0.181.3782.4682.1725.7626.2826.32
+ +Table 4: The accuracy according to hyper-parameter in Eq. 11 when $\lambda_1 = 1$ . + +attraction loss, $\mathcal{L}_{att}$ , is applied to even those samples with low reliability, resulting in the poorest performance. Due to the same reason, the performance is better when $K$ is 16 than when it is 32, but since unreliable samples are also selected, the accuracy is relatively lower than in other favorable situations. As $K$ decreases, the performance improves, but it starts to decline when $K$ is less than 6, indicating that even with high reliability, it is challenging to achieve optimal training if $\mathcal{L}_{att}$ is applied with very few samples. Similarly, we report the accuracy according to the $K$ value on the N-Caltech101 in Fig 6. Unless an extremely small number of samples are drawn, as the value of $K$ increases, the performance also improves. However, once a certain threshold is reached, there is little significant change, and it starts to decline with further increases. The accuracy exceeds $80\%$ in all cases, showing robustness to $K$ values. Although the level of sensitivity varies depending on the dataset, we do confirm that satisfactory results can be obtained between $K = 4$ and $K = 10$ . + +# 6.3. Hyper-parameter Analysis + +In Table 4, we report the accuracy according to $\lambda_{2}$ and $\lambda_{3}$ in Eq. 11. If the weight of the repulsion loss, $\lambda_{2}$ , is set too high, the performance decreases. However, this can be mitigated by increasing the weight of the local-global re + +![](images/d578b2cc4dbd1da4c37ac78ccae19e553041cace94a5a3168bb1d7da94a52d11.jpg) +Figure 7: Object recognition accuracy on N-Caltech101 according to the number of extra category prompts. + +construction consistency loss, $\lambda_3$ . The results verify the robustness of our method according to the $\lambda$ on both datasets. + +# 6.4. Learning with Superset Categories + +In practical terms, it can be challenging for users to find corresponding categories of the event dataset. As a result, they often end up taking more categories as prompts. We tackle these issues by demonstrating that our joint learning framework works robustly even when employing more prompts than the categories of the event on the N-Caltech101 dataset. To avoid using additional prompts that are too irrelevant to the N-Caltech101 dataset, we randomly take additional prompts from N-ImageNet. We show the performance results according to the number of extra category prompts in Fig. 7. While the performance decreases with an increase in extra category prompts, it is worth noting that our algorithm remains reliable even when faced with over 100 additional prompts beyond the corresponding category. This suggests that our algorithm can function with superset categories, even in a situation when the number of extra categories is much larger than the actual categories. + +# 7. Conclusion + +In this work, we propose a joint learning framework for event-based object recognition with image reconstruction from events without labels and paired images. With the proposed losses and the reliable data sampling strategy, our approach allows stable learning of two tasks simultaneously from pseudo labels. As a result, our approach achieves exceptional performance in event-based object recognition and event-to-image reconstruction, all without requiring category labels and paired images. Our approach successfully addresses the challenge of label dependency in event-based research, which has been a significant obstacle. 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Dual transfer learning for event-based end-task prediction via pluggable event to image translation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2135-2145, 2021. 2 +[58] Lin Wang, Yujeong Chae, Sung-Hoon Yoon, Tae-Kyun Kim, and Kuk-Jin Yoon. Evdistill: Asynchronous events to end-task learning via bidirectional reconstruction-guided cross-modal knowledge distillation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 608-619, 2021. 2 +[59] Lin Wang, Yo-Sung Ho, Kuk-Jin Yoon, et al. Event-based high dynamic range image and very high frame rate video generation using conditional generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10081-10090, 2019. 2, 6, 7, 8 +[60] Lin Wang, Tae-Kyun Kim, and Kuk-Jin Yoon. Joint framework for single image reconstruction and super-resolution with an event camera. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 989-997, 2019. 2 \ No newline at end of file diff --git a/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/images.zip b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..42d5ae76d9792f915f905ebe060c2abf23cac25a --- /dev/null +++ b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f4c371f5e577a70d9acd57282dd90c666710f7d2f918111b3651f44409509b1e +size 846694 diff --git a/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/layout.json b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e1067242a7121f4d1f22ba6858f4a1c7aa0d8f77 --- /dev/null +++ b/2023/Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events/layout.json @@ -0,0 +1,9838 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 85, + 136, + 492, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 136, + 492, + 172 + ], + "spans": [ + { + "bbox": [ + 85, + 136, + 492, + 172 + ], + "type": "text", + "content": "Label-Free Event-based Object Recognition via Joint Learning with Image Reconstruction from Events" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 124, + 192, + 452, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 192, + 452, + 207 + ], + "spans": [ + { + "bbox": [ + 124, + 192, + 452, + 207 + ], + "type": "text", + "content": "Hoonhee Cho*, Hyeonseong Kim*, Yujeong Chae, and Kuk-Jin Yoon" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 163, + 207, + 414, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 163, + 207, + 414, + 221 + ], + "spans": [ + { + "bbox": [ + 163, + 207, + 414, + 221 + ], + "type": "text", + "content": "Korea Advanced Institute of Science and Technology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 164, + 222, + 412, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 164, + 222, + 412, + 234 + ], + "spans": [ + { + "bbox": [ + 164, + 222, + 412, + 234 + ], + "type": "text", + "content": "{gnsgnsgml,brian617,yujeong,kjyoon}@kaist.ac.kr" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 139, + 260, + 186, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 260, + 186, + 273 + ], + "spans": [ + { + "bbox": [ + 139, + 260, + 186, + 273 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 285, + 282, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 285, + 282, + 564 + ], + "spans": [ + { + "bbox": [ + 45, + 285, + 282, + 564 + ], + "type": "text", + "content": "Recognizing objects from sparse and noisy events becomes extremely difficult when paired images and category labels do not exist. In this paper, we study label-free event-based object recognition where category labels and paired images are not available. To this end, we propose a joint formulation of object recognition and image reconstruction in a complementary manner. Our method first reconstructs images from events and performs object recognition through Contrastive Language-Image Pretraining (CLIP), enabling better recognition through a rich context of images. Since the category information is essential in reconstructing images, we propose category-guided attraction loss and category-agnostic repulsion loss to bridge the textual features of predicted categories and the visual features of reconstructed images using CLIP. Moreover, we introduce a reliable data sampling strategy and local-global reconstruction consistency to boost joint learning of two tasks. To enhance the accuracy of prediction and quality of reconstruction, we also propose a prototype-based approach using unpaired images. Extensive experiments demonstrate the superiority of our method and its extensibility for zero-shot object recognition. Our project code is available at https://github.com/Chohoonhee/Ev-LaFOR." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 576, + 124, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 576, + 124, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 576, + 124, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 596, + 279, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 596, + 279, + 712 + ], + "spans": [ + { + "bbox": [ + 45, + 596, + 279, + 712 + ], + "type": "text", + "content": "Event cameras are neuromorphic vision sensors that asynchronously perceive per-pixel brightness changes with high temporal resolution. They show advantages over conventional frame-based cameras, such as high dynamic range (HDR) and low latency. However, despite the superiority of cameras, algorithms using events are still in their infancy. Existing event-based object recognition methods [1, 4, 22, 24, 25, 26, 30, 32, 34, 36, 40, 53] have been shown that object recognition is a crucial task for event feature learning [12, 29, 38] and endeavors have successfully" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 302, + 259, + 526, + 422 + ], + "blocks": [ + { + "bbox": [ + 302, + 259, + 526, + 422 + ], + "lines": [ + { + "bbox": [ + 302, + 259, + 526, + 422 + ], + "spans": [ + { + "bbox": [ + 302, + 259, + 526, + 422 + ], + "type": "image", + "image_path": "0284fba41f1963b2940b0ca24aafc41c889a0aaf349f6e097983639d6b731466.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 430, + 531, + 513 + ], + "lines": [ + { + "bbox": [ + 296, + 430, + 531, + 513 + ], + "spans": [ + { + "bbox": [ + 296, + 430, + 531, + 513 + ], + "type": "text", + "content": "Figure 1: We tackle label-free event-based object recognition where category labels and paired images are not available. Our approach can simultaneously perform object recognition and image reconstruction through proposed joint learning framework. Optionally, our method can leverage unpaired images to enhance object recognition performance and reconstructed image quality." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 539, + 531, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 539, + 531, + 633 + ], + "spans": [ + { + "bbox": [ + 296, + 539, + 531, + 633 + ], + "type": "text", + "content": "classified the object with events. However, they rely on supervision with category labels to achieve high performance. Furthermore, the sparsity of events poses a challenge for users to label them accurately when there are no paired images. Several unsupervised methods [25, 36] have been proposed for object recognition, however, their performances remain subpar. Hence, there is a natural need for robust and effective label-free event-based object recognition methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 636, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 531, + 730 + ], + "type": "text", + "content": "In this paper, we study label-free event-based object recognition where category labels and paired images are not available as in Fig. 1. To tackle this task, we focus on two following facts. Firstly, as demonstrated in [45, 60], performing object recognition on reconstructed images with spatially dense information and rich context shows better performance than solely using events. Secondly, during reconstructing images from events, taking the categories into" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 151, + 41, + 470, + 52 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 41, + 470, + 52 + ], + "spans": [ + { + "bbox": [ + 151, + 41, + 470, + 52 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 198, + 53, + 422, + 63 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 53, + 422, + 63 + ], + "spans": [ + { + "bbox": [ + 198, + 53, + 422, + 63 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 181, + 63, + 440, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 181, + 63, + 440, + 74 + ], + "spans": [ + { + "bbox": [ + 181, + 63, + 440, + 74 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 719, + 258, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 719, + 258, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 719, + 258, + 730 + ], + "type": "text", + "content": "*The first two authors contributed equally. In alphabetical order." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19866" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 153 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 153 + ], + "type": "text", + "content": "account can improve the quality of the reconstructed images. From these observations, we propose a joint learning framework of two closely-linked tasks: event-based object recognition and event-to-image reconstruction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 155, + 279, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 155, + 279, + 294 + ], + "spans": [ + { + "bbox": [ + 45, + 155, + 279, + 294 + ], + "type": "text", + "content": "In our joint learning framework, we first reconstruct images from events and perform object recognition on the reconstructed images using Contrastive Language-Image Pretraining (CLIP) [42]. CLIP is an image-text embedding model that has been trained on a large number of image and language pairs sourced from the web. We utilize the textual features encoded from CLIP since they are well-aligned with visual features, which is advantageous for our tasks that lack labels and images. To this end, we propose the category-guided attraction loss that aligns the visual features from reconstructed images close to the texture features of the predicted category from CLIP." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 296, + 279, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 296, + 279, + 658 + ], + "spans": [ + { + "bbox": [ + 45, + 296, + 279, + 658 + ], + "type": "text", + "content": "Although the above framework enables the joint learning of event-based object recognition and image reconstruction, using the predicted categories brings two issues. (1) Collapsing to the trivial solution, resulting in all outputs being assigned to a single category and (2) Interrupting the learning process due to unreliable (wrong) predictions. To alleviate these problems, we propose (1) category-agnostic repulsion loss to increase the distances between visual features for preventing collapse and (2) a reliable data sampling (RDS) method to reduce the effects of unreliable predictions. For RDS, we devise two reliable indicators named posterior probability indicator (PPI) and temporally reversed consistency indicator (TRCI). The PPI selects reliable samples based on the probability of prediction. For additional sampling, TRCI utilizes the characteristics of events that temporally reversed ones should be categorized into the same category as the original events. This reliable data sampling enables stable learning even with the predicted categories, leading to a substantial performance improvement in object recognition. Furthermore, to restore the local details, we introduce the local-global reconstruction consistency. Finally, to enhance the accuracy of recognition and visual quality of reconstructed images, we expand our method by employing the existing unpaired images. Extensive experiments demonstrate that our method shows outstanding results on the subset of the N-ImageNet dataset over unsupervised and image reconstruction-based approaches and even surpasses the supervised methods on the N-Caltech101 dataset without using labels and images. In addition, we show that our framework can be extended to event-based zero-shot object recognition." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "Our work presents four main contributions: (I) We propose a novel joint learning framework for event-based object recognition and image reconstruction, without requiring paired images and labels. (II) We introduce a reliable data sampling strategy and local-global reconstruction consistency that enhances label-free joint training. (III) We" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 106, + 530, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 165 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 165 + ], + "type": "text", + "content": "further introduce employing unpaired images in our framework for boosting performance. (IV) We conduct extensive experiments of our method along with zero-shot object recognition and superset categories learning, and demonstrate our method's superior performance and effectiveness." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 297, + 175, + 381, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 175, + 381, + 186 + ], + "spans": [ + { + "bbox": [ + 297, + 175, + 381, + 186 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 193, + 530, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 193, + 530, + 367 + ], + "spans": [ + { + "bbox": [ + 296, + 193, + 530, + 367 + ], + "type": "text", + "content": "Event-based Object Recognition. Concurrent with the success of event-based low-level tasks [9, 10, 11, 23, 52, 54, 63], there has been a surge of active research focused on object recognition [3, 7, 19, 22, 27, 28, 31, 35, 43, 51, 53, 56], which is considered as a fundamental task. Considering the unique features of event data, numerous works [1, 4, 22, 24, 25, 26, 30, 32, 34, 36, 40, 53] have presented models and representations that can effectively extract significant patterns. However, these approaches require labels for each event data for supervised learning, and since event data cannot be crawled from the web like images, the labeling cost of event data is extremely high. On the other hand, our approach enables the learning of event-based object recognition and image reconstruction simultaneously, without requiring category labels and paired images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 368, + 530, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 368, + 530, + 612 + ], + "spans": [ + { + "bbox": [ + 296, + 368, + 530, + 612 + ], + "type": "text", + "content": "Event-based Image Reconstruction is a well-known topic in the field of event-based vision [2, 13, 17, 20, 21, 46, 49, 57]. Recent researches have been utilizing deep learning to generate realistic outcomes [44, 45, 50, 62]. However, these supervised approaches require the paired images of each event stream to be accurately aligned and synchronized in terms of pixels and time. Another line of approach, such as Wang et al. [59] and Pini et al. [41], utilized generative adversarial networks (GANs) to reconstruct intensity with unpaired images that are not related to the events of the scene. However, GANs are prone to be sensitive to various parameters, and when images that are significantly irrelevant to objects are utilized, the quality of the reconstructed images from events is notably low. An alternative solution is a self-supervised method [37] that utilizes photometric consistency, but this approach requires a continuous sequence that spans an adequately long period. Differently, our framework can reconstruct the intensity of event data without images, very long event sequence and GANs. We only exploit the category prompts of a bundle of event data, not the class label of each event data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "content": "Label-free Learning aims to solve the end-task only with unlabeled data, and has been actively explored [8, 58]. HOTS [25] proposed a category-free method for recognizing objects based on events and SSL-E2VID [37] proposed a self-supervised learning method for reconstructing images from only events. However, their performances fall short of supervised learning methods with significant performance gaps. Inspired by the success of using the pretrained model [5, 6, 39, 48, 55], we adopt CLIP [42] for label-free event-based object recognition. We propose a" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "19867" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 101, + 528, + 330 + ], + "blocks": [ + { + "bbox": [ + 48, + 101, + 528, + 330 + ], + "lines": [ + { + "bbox": [ + 48, + 101, + 528, + 330 + ], + "spans": [ + { + "bbox": [ + 48, + 101, + 528, + 330 + ], + "type": "image", + "image_path": "b9c0ce00c40f448ae65cf3529781931084efaa6040745f51c21d4fd1af0893e9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 333, + 531, + 417 + ], + "lines": [ + { + "bbox": [ + 45, + 333, + 531, + 417 + ], + "spans": [ + { + "bbox": [ + 45, + 333, + 531, + 417 + ], + "type": "text", + "content": "Figure 2: Overall joint learning framework of event-based object recognition with event-to-image reconstruction. Our approach involves CLIP's textual and visual encoders that derive textual and visual features, respectively, from given class sets and events. Textual features are obtained from category prompts, while visual features are obtained from reconstructed images. Then, logits and corresponding pseudo labels are generated by computing the cosine similarity between visual and textual features. Lastly, our framework employs pseudo labels to facilitate joint learning using category-agnostic repulsion loss and category-guided attraction loss. To mitigate the impact of unreliable pseudo labels and boost performance, we introduce a reliable data sampling strategy and local-global reconstruction consistency." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 426, + 280, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 426, + 280, + 507 + ], + "spans": [ + { + "bbox": [ + 45, + 426, + 280, + 507 + ], + "type": "text", + "content": "novel joint learning framework that uses visual and textual knowledge to achieve superior performance in event-to-image reconstruction and event-based object recognition without category labels and paired images. To the best of our knowledge, we are the first to incorporate textual knowledge into event vision research, particularly in the context of label-free tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 516, + 101, + 527 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 101, + 527 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 101, + 527 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 533, + 279, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 533, + 279, + 650 + ], + "spans": [ + { + "bbox": [ + 45, + 533, + 279, + 650 + ], + "type": "text", + "content": "In Sec. 3.1, we first introduce our joint formulation of event-to-image reconstruction and object recognition for label-efficient learning. In Sec. 3.2, we describe our reliable data sampling (RDS) strategy for boosting joint learning performance by filtering the unreliable data samples during training. Sec. 3.3 introduces the local-global reconstruction consistency for spatially regularizing the reconstructed images, which ensures capturing the local details. In Sec. 3.4, we propose to further employ the unpaired images for better recognition performance and reconstructed image quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 655, + 151, + 666 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 655, + 151, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 655, + 151, + 666 + ], + "type": "text", + "content": "3.1. Joint Formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": "We propose a joint formulation of event-to-image reconstruction and object recognition to perform event-based (zero-shot) object recognition without using labels and paired images of event data. Our joint formulation is based on the fact that 1) image reconstruction can be helpful in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 426, + 530, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 426, + 530, + 542 + ], + "spans": [ + { + "bbox": [ + 296, + 426, + 530, + 542 + ], + "type": "text", + "content": "predicting categories from events, and 2) category information is important in reconstructing images from events. Therefore, we propose 1) the process of performing event-to-image reconstruction and CLIP-driven object recognition from the reconstructed images and 2) category-guided attraction loss and category-agnostic repulsion loss for learning this process without labels and paired images. The overall framework is shown in Fig. 2. Note that our joint learning framework can reconstruct intensity images from events without using any images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "spans": [ + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "text", + "content": "Event-to-Image Reconstruction. For the joint formulation, we first reconstruct the intensity image " + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "text", + "content": " from the event stream " + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{E} = (u_i,t_i,p_i)_i = 1" + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "inline_equation", + "content": "u_{i},t_{i}" + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "text", + "content": " denote triggered pixel location, time, and polarity of each event, and " + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "text", + "content": " is the temporal length of the event stream. We convert the event stream into event spiking tensor (EST) [16], which is then fed into the image reconstruction network " + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 296, + 542, + 531, + 646 + ], + "type": "text", + "content": " to obtain the intensity image. The image reconstruction process is formulated as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 377, + 653, + 530, + 665 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 653, + 530, + 665 + ], + "spans": [ + { + "bbox": [ + 377, + 653, + 530, + 665 + ], + "type": "interline_equation", + "content": "\\mathcal {I} = \\mathcal {G} (\\operatorname {E S T} (\\mathcal {E})). \\tag {1}", + "image_path": "737a31dec6ebdc9ffd3505ec21eaebae8fa0dcd7986d312c4fa3abb2684d4bf4.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 671, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 671, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 671, + 531, + 730 + ], + "type": "text", + "content": "CLIP-driven Object Recognition. We perform object recognition on top of the reconstructed images instead of raw event data. The advantage of using reconstructed images rather than using event data directly for object recognition is that better performance can be achieved by using" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19868" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": "a network trained on rich image data [45, 60]. In particular, we use CLIP [42] for object recognition, which also enables zero-shot object recognition. For an event dataset of " + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": " classes, the category prompts are constructed by placing each category name into a pre-defined template, \"image of a [CLASS].\" Then, CLIP's textual encoder encodes category prompts to obtain the " + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": "-dimensional textual features " + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "inline_equation", + "content": "F = (f_{i})_{i = 1}^{C}\\in \\mathbb{R}^{C\\times D}" + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": ". Meantime, the reconstructed image " + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": " is encoded by CLIP's visual encoder to a visual feature " + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "inline_equation", + "content": "v\\in \\mathbb{R}^{1\\times D}" + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": " and the class probability " + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "inline_equation", + "content": "p\\in \\mathbb{R}^{1\\times C}" + }, + { + "bbox": [ + 45, + 106, + 281, + 234 + ], + "type": "text", + "content": " for the object recognition are obtained as," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 117, + 240, + 279, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 240, + 279, + 255 + ], + "spans": [ + { + "bbox": [ + 117, + 240, + 279, + 255 + ], + "type": "interline_equation", + "content": "p _ {i} = \\operatorname {s o f t m a x} _ {i} \\left(v F ^ {\\top}\\right), \\tag {2}", + "image_path": "1fa99489cbef65350eb2d57ec0120bc281ba1166a49978c4b2ff0a99c3d53be0.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "spans": [ + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "inline_equation", + "content": "\\mathrm{softmax}_i(\\cdot)" + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "text", + "content": " denote the probability for category " + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "text", + "content": " and the softmax function. By taking the category of maximum probability, we can predict the category " + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "text", + "content": " for the event data " + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 45, + 261, + 279, + 308 + ], + "type": "text", + "content": " as," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 127, + 316, + 279, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 316, + 279, + 334 + ], + "spans": [ + { + "bbox": [ + 127, + 316, + 279, + 334 + ], + "type": "interline_equation", + "content": "c = \\underset {i} {\\operatorname {a r g m a x}} \\left(p _ {i}\\right). \\tag {3}", + "image_path": "98dc519519c59ca70e8065dc08b566a60d58cd956f91323fb272876e23a0b582.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "spans": [ + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "text", + "content": "Category-guided Attraction Loss. The challenging part of our joint formulation is to train the reconstruction network " + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "text", + "content": " without using paired images of event data. Once we reconstruct the intensity images from the event stream (Eq. 1), we can perform object recognition using CLIP (Eq. 2). Motivated by the fact that category information is important in reconstructing images from events, we propose category-guided attraction loss to train the reconstruction network. The proposed category-guided attraction loss brings the visual feature " + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "text", + "content": " encoded from the reconstructed image " + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "text", + "content": " closer to the textual feature of the corresponding category, guiding the model to reconstruct the image corresponding to the category. Since category labels are not available for the event data, we use the predicted categories as pseudo labels. For event data with a batch size of " + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "text", + "content": ", the category-guided attraction loss " + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 45, + 340, + 279, + 527 + ], + "type": "text", + "content": " is formulated as InfoNCE loss [33]:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 89, + 528, + 279, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 528, + 279, + 561 + ], + "spans": [ + { + "bbox": [ + 89, + 528, + 279, + 561 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a t t} = - \\sum_ {i = 1} ^ {B} \\log \\frac {\\exp \\left(v _ {i} f _ {c _ {i}} ^ {\\top}\\right)}{\\sum_ {j = 1} ^ {B} \\exp \\left(v _ {i} f _ {c _ {j}} ^ {\\top}\\right)}, \\tag {4}", + "image_path": "b56e33c1f821c99778f9da48ed95e15d5f09895fa4358fef5a65e1a48697f205.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "spans": [ + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "inline_equation", + "content": "v_{i}, c_{i}" + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "inline_equation", + "content": "f_{j}" + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "text", + "content": " denote the visual feature and predicted category of the " + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "text", + "content": " event data, and the textual feature of category " + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "text", + "content": ". Minimizing " + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 45, + 566, + 279, + 636 + ], + "type": "text", + "content": " enables the image reconstruction network to generate images of the corresponding category label, while object recognition benefits from the reconstructed images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "type": "text", + "content": "Category-agnostic Repulsion Loss. Although " + }, + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "type": "text", + "content": " enables joint learning, the use of pseudo labels may cause collapsing, resulting in all outputs being assigned to a single category. Therefore, we introduce a category-agnostic repulsion loss to prevent collapsing by increasing the distances between visual features. To be specific, the category-agnostic repulsion loss " + }, + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rep}" + }, + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "type": "text", + "content": " is applied to the set of visual features as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 333, + 104, + 530, + 138 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 104, + 530, + 138 + ], + "spans": [ + { + "bbox": [ + 333, + 104, + 530, + 138 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e p} = \\sum_ {i = 1} ^ {B} \\log \\left(1 + \\sum_ {j = 1, j \\neq i} ^ {B} \\exp \\left(v _ {i} v _ {j} ^ {\\top}\\right)\\right). \\tag {5}", + "image_path": "76f153002b05174629c41e0733bbdf38f1a5533455a30db36edc4a9d1a9bd24b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 142, + 530, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 142, + 530, + 176 + ], + "spans": [ + { + "bbox": [ + 296, + 142, + 530, + 176 + ], + "type": "text", + "content": "With " + }, + { + "bbox": [ + 296, + 142, + 530, + 176 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 296, + 142, + 530, + 176 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 142, + 530, + 176 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rep}" + }, + { + "bbox": [ + 296, + 142, + 530, + 176 + ], + "type": "text", + "content": ", we can successfully formulate our joint learning framework, enabling simultaneous event-to-image reconstruction and (zero-shot) object recognition." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 181, + 427, + 193 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 181, + 427, + 193 + ], + "spans": [ + { + "bbox": [ + 297, + 181, + 427, + 193 + ], + "type": "text", + "content": "3.2. Reliable Data Sampling" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "spans": [ + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "text", + "content": "As " + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "text", + "content": " relies on pseudo labels, the reliability of predictions may affect the overall training procedure and performance. To reduce the effects of unreliable predictions, we devise two reliability indicators named posterior probability indicator (PPI) and temporally reversed consistency indicator (TRCI). Based on the resultant reliability of predictions, we sample data with reliable predictions for " + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "text", + "content": ". The remaining unreliable data is excluded from calculating " + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "text", + "content": " and used only for " + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rep}" + }, + { + "bbox": [ + 296, + 196, + 530, + 300 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "spans": [ + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": "Posterior Probability Indicator. Given the reconstructed image " + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": " and the predicted category " + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": ", the posterior probability " + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "inline_equation", + "content": "p_c = \\mathbf{p}(c|\\mathcal{I})" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": " indicates the model confidence for category " + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": ". Thus, we use the posterior probability as an indicator of the reliability of the prediction. In particular, we select " + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": " data samples corresponding to the top-" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": " posterior probabilities among " + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": " data samples in the mini-batch. The set of selected sample indices from PPI, " + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{PPI}}" + }, + { + "bbox": [ + 296, + 301, + 530, + 394 + ], + "type": "text", + "content": " is defined as," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 354, + 399, + 530, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 399, + 530, + 417 + ], + "spans": [ + { + "bbox": [ + 354, + 399, + 530, + 417 + ], + "type": "interline_equation", + "content": "S _ {\\mathrm {P P I}} = \\underset {i} {\\operatorname {a r g s o r t}} (\\mathbf {p} (c _ {i} | \\mathcal {I} _ {i})) ] _ {K}, \\tag {6}", + "image_path": "4bc32a2ef60ccadd241a87db363ea3b455455c50a7bf2d27d674efea114e8ad5.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "spans": [ + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_i" + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "inline_equation", + "content": "[\\cdot ]_K" + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "text", + "content": " denote the reconstructed image of the " + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "text", + "content": " event data in the mini-batch and the set of the first " + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "text", + "content": " items. The " + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "inline_equation", + "content": "\\operatorname {argsort}(\\cdot)" + }, + { + "bbox": [ + 296, + 419, + 530, + 465 + ], + "type": "text", + "content": " function returns indices that would sort an input in descending order." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "spans": [ + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "type": "text", + "content": "Temporally Reversed Consistency Indicator. Considering the temporal aspect of event data, we propose an additional reliability indicator based on the consistency between predictions from the original events and the temporally reversed events. From the fact that the temporally reversed events " + }, + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "type": "inline_equation", + "content": "\\mathcal{E}^R = (u_i,\\max_j(t_j) - t_i,p_i)_{i = N}^1" + }, + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "type": "text", + "content": " should be categorized into the same category as the original events " + }, + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "type": "text", + "content": ", we presume that the consistent model prediction would indicate the reliability of the data sample. To be specific, the set of selected sample indices from TRCI, " + }, + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{TRCI}}" + }, + { + "bbox": [ + 296, + 466, + 530, + 592 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 335, + 593, + 530, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 593, + 530, + 607 + ], + "spans": [ + { + "bbox": [ + 335, + 593, + 530, + 607 + ], + "type": "interline_equation", + "content": "S _ {\\mathrm {T R C I}} = \\{i \\mid c _ {i} = c _ {i} ^ {R}, i = 1, 2, \\dots , B \\}, \\tag {7}", + "image_path": "c0289132679eb9034531ce55086d173f4ab45109b93fbfa0366e5052abac1aab.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "spans": [ + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "type": "inline_equation", + "content": "c_{i}^{R}" + }, + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "type": "text", + "content": " denotes a predicted category of " + }, + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "type": "text", + "content": " reversed event data " + }, + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_i^R" + }, + { + "bbox": [ + 296, + 611, + 530, + 634 + ], + "type": "text", + "content": " in the mini-batch." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "spans": [ + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "type": "text", + "content": "Our final set of selected sample indices " + }, + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{RDS}}" + }, + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "type": "text", + "content": " for reliable data sampling (RDS) is the intersection of " + }, + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{PPI}}" + }, + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{TRCI}}" + }, + { + "bbox": [ + 296, + 635, + 530, + 660 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 365, + 670, + 530, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 670, + 530, + 682 + ], + "spans": [ + { + "bbox": [ + 365, + 670, + 530, + 682 + ], + "type": "interline_equation", + "content": "S _ {\\mathrm {R D S}} = S _ {\\mathrm {P P I}} \\cap S _ {\\mathrm {T R C I}}. \\tag {8}", + "image_path": "2af09d37ff4935244dab98a908cc158a2ef9b37ccbbbc608f413fe20ac56d953.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 297, + 685, + 524, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 685, + 524, + 697 + ], + "spans": [ + { + "bbox": [ + 297, + 685, + 524, + 697 + ], + "type": "text", + "content": "Then, the modified attraction loss with RDS is as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 327, + 701, + 530, + 732 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 701, + 530, + 732 + ], + "spans": [ + { + "bbox": [ + 327, + 701, + 530, + 732 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a t t} = - \\sum_ {i \\in S _ {\\mathrm {R D S}}} \\log \\frac {\\exp \\left(v _ {i} f _ {c _ {i}} ^ {\\top}\\right)}{\\sum_ {j \\in S _ {\\mathrm {R D S}}} \\exp \\left(v _ {i} f _ {c _ {j}} ^ {\\top}\\right)}, \\tag {9}", + "image_path": "006e703921537702524471699f6df0075b0acbf3a48953778ebdc57d025a981f.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "19869" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 106, + 254, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 106, + 254, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 254, + 118 + ], + "type": "text", + "content": "3.3. Local-global Reconstruction Consistency" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "spans": [ + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "text", + "content": "Along with " + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rep}" + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "text", + "content": ", we further introduce the local-global reconstruction consistency for spatially regularizing the reconstructed images in a self-supervised manner. With random crop function " + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "text", + "content": ", we first crop the EST of original events " + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "inline_equation", + "content": "\\mathrm{EST}(\\mathcal{E})" + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "text", + "content": " to obtain the cropped tensor " + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\mathrm{EST}(\\mathcal{E}))" + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "text", + "content": " for the local input. Then, the local-global reconstruction consistency loss " + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "inline_equation", + "content": "L_{con}" + }, + { + "bbox": [ + 45, + 122, + 279, + 205 + ], + "type": "text", + "content": " is defined as," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 60, + 213, + 279, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 213, + 279, + 227 + ], + "spans": [ + { + "bbox": [ + 60, + 213, + 279, + 227 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n}} = \\| \\mathcal {G} (\\mathcal {H} (\\operatorname {E S T} (\\mathcal {E}))) - \\mathcal {H} (\\mathcal {G} (\\operatorname {E S T} (\\mathcal {E}))) \\| _ {1}. \\tag {10}", + "image_path": "389537f350a7038d96d27606c98159e5c11fe2d97b4868f9a2aec3f3c5519dd0.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "spans": [ + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "text", + "content": "Compared to " + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rep}" + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "text", + "content": " that work on visual features, " + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "inline_equation", + "content": "L_{con}" + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "text", + "content": " is applied directly to the reconstructed images and considered as a spatial regularization for the reconstruction network " + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 45, + 235, + 279, + 306 + ], + "type": "text", + "content": ". In addition, matching the reconstructed images from local and global inputs enables the network to capture the local details, improving the reconstruction quality." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 307, + 279, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 307, + 279, + 330 + ], + "spans": [ + { + "bbox": [ + 45, + 307, + 279, + 330 + ], + "type": "text", + "content": "The total loss function for the joint learning framework is as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 340, + 279, + 353 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 340, + 279, + 353 + ], + "spans": [ + { + "bbox": [ + 86, + 340, + 279, + 353 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {a t t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {r e p}} + \\lambda_ {3} \\mathcal {L} _ {\\text {c o n}}, \\tag {11}", + "image_path": "f69c531c895b8e7e63104b73f1ab7a9e85b5950ffdeb400f4cfd133c6b0d4964.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "spans": [ + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2," + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "inline_equation", + "content": "\\lambda_3" + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "text", + "content": " are weights for " + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att},\\mathcal{L}_{rep}" + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{con}" + }, + { + "bbox": [ + 45, + 362, + 278, + 374 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 382, + 198, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 382, + 198, + 394 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 198, + 394 + ], + "type": "text", + "content": "3.4. Employing Unpaired Images" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "spans": [ + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "text", + "content": "In this section, we expand the use case of our method by introducing how to employ the existing unpaired images. Here, we assume that the category of each image is known, which is the common case for web crawling. Although our framework is capable of event-to-image reconstruction and object recognition without using any images and labels, utilizing existing images can possibly improve the image reconstruction quality and consequently improve object recognition performance. As shown in Fig. 3, we replace textual features in " + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "text", + "content": " with the prototype features generated from unpaired images. For each category " + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "text", + "content": ", we first encode all images of category " + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "text", + "content": " and apply a clustering algorithm to obtain " + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "text", + "content": " clusters in total. Then, we aggregate the features of each cluster by averaging them, resulting in " + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "text", + "content": " prototype features " + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "inline_equation", + "content": "W^{c} = (w_{i}^{c})_{i=1}^{L} \\in \\mathbb{R}^{L \\times D}" + }, + { + "bbox": [ + 45, + 399, + 279, + 574 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "spans": [ + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "text", + "content": "For data sample index " + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "inline_equation", + "content": "i \\in S_{\\mathrm{RDS}}" + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "text", + "content": " with corresponding visual feature " + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "text", + "content": " and the predicted category " + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "text", + "content": ", we replace the textual features " + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "inline_equation", + "content": "f_{c_i}" + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "text", + "content": " in Eq. 9 to the closest prototype feature " + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "inline_equation", + "content": "w_{l_i}^{c_i}" + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "text", + "content": ", where the cluster index " + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 45, + 575, + 279, + 623 + ], + "type": "text", + "content": " is calculated as," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 111, + 631, + 279, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 631, + 279, + 653 + ], + "spans": [ + { + "bbox": [ + 111, + 631, + 279, + 653 + ], + "type": "interline_equation", + "content": "l _ {i} = \\underset {j} {\\operatorname {a r g m a x}} \\left(v _ {i} \\left(w _ {j} ^ {c _ {i}}\\right) ^ {\\top}\\right). \\tag {12}", + "image_path": "4731b3053280e92815ce38227fb1d61bb27178c6486e5fb597274e2947bd55ff.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 660, + 279, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 683 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 683 + ], + "type": "text", + "content": "Our modification of " + }, + { + "bbox": [ + 45, + 660, + 279, + 683 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 45, + 660, + 279, + 683 + ], + "type": "text", + "content": " to employ unpaired images is then defined as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 60, + 690, + 279, + 723 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 690, + 279, + 723 + ], + "spans": [ + { + "bbox": [ + 60, + 690, + 279, + 723 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a t t} = - \\sum_ {i \\in S _ {\\mathrm {R D S}}} \\log \\frac {\\exp \\left(v _ {i} \\left(w _ {l _ {i}} ^ {c _ {i}}\\right) ^ {\\top}\\right)}{\\sum_ {j \\in S _ {\\mathrm {R D S}}} \\exp \\left(v _ {i} \\left(w _ {l _ {j}} ^ {c _ {j}}\\right) ^ {\\top}\\right)}, \\tag {13}", + "image_path": "ae3b24f57b67b3862f33374822449da29b8aff6ce56682b8a178e613d01a649a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 300, + 103, + 530, + 292 + ], + "blocks": [ + { + "bbox": [ + 300, + 103, + 530, + 292 + ], + "lines": [ + { + "bbox": [ + 300, + 103, + 530, + 292 + ], + "spans": [ + { + "bbox": [ + 300, + 103, + 530, + 292 + ], + "type": "image", + "image_path": "1ad5b3a30d84555de23d6033ead8896ecaec074745b65999f993303a6652fe14.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 301, + 530, + 348 + ], + "lines": [ + { + "bbox": [ + 296, + 301, + 530, + 348 + ], + "spans": [ + { + "bbox": [ + 296, + 301, + 530, + 348 + ], + "type": "text", + "content": "Figure 3: Proposed method employing unpaired images in the category-guided attraction loss. Unpaired images are further utilized to enhance object recognition performance and reconstructed image quality." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 362, + 354, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 362, + 354, + 374 + ], + "spans": [ + { + "bbox": [ + 297, + 362, + 354, + 374 + ], + "type": "text", + "content": "4. Datasets" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 380, + 530, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 380, + 530, + 543 + ], + "spans": [ + { + "bbox": [ + 296, + 380, + 530, + 543 + ], + "type": "text", + "content": "The experiments are conducted on two widely used event-based object recognition datasets, N-Caltech101 [35] and N-ImageNet [22], which are constructed by filming Caltech101 [15] and ImageNet [14] datasets on LCD monitor with event camera. Since N-Caltech101 and N-ImageNet datasets do not provide APS frames, the image in the original dataset and corresponding event sequence have different resolutions and are not aligned in pixel-level. To create a visual prototype in Sec. 3.4, we scrap images from the original dataset, mimicking the web crawling. To avoid including paired images of events in the train set, we randomly split the event train set in half for each class. One half is used to train the model, while the corresponding images from the other half are used to create the visual prototype." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "spans": [ + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": "N-Caltech101 dataset consists of 8,246 event stream data belonging to 101 different object classes. Each object is captured with " + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "inline_equation", + "content": "320 \\times 245" + }, + { + "bbox": [ + 296, + 543, + 530, + 612 + ], + "type": "text", + "content": " resolution (average) for 300 milliseconds. Existing works [45, 60] utilized this dataset to evaluate the performance of image reconstruction and event-based object recognition." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "content": "N-ImageNet is recently released large-scale dataset, containing 1,781,167 event stream data of 1,000 object classes. Compared to N-Caltech101, it has a larger resolution of " + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "content": " and a very short capturing time with " + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-2}" + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "content": " milliseconds. Therefore, each event stream contains significantly sparse edge information. N-ImageNet is too challenging for unsupervised studies without ground truth, so we utilize a randomly sampled subset of 100 classes called N-ImageNet (Mini). Details about the split of N-ImageNet (Mini) are provided in the supplementary material." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19870" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 104, + 526, + 374 + ], + "blocks": [ + { + "bbox": [ + 51, + 104, + 526, + 374 + ], + "lines": [ + { + "bbox": [ + 51, + 104, + 526, + 374 + ], + "spans": [ + { + "bbox": [ + 51, + 104, + 526, + 374 + ], + "type": "table", + "html": "
MethodsImage PairClass LabelN-Caltech101N-ImageNet (Mini)
Accuracy ↑FID ↓IS ↑Accuracy ↑FID ↓IS ↑
Supervised Learning
Histogram [29]✓63.8--49.8--
Ev-gait [61]✓61.9--51.3--
EST [16]✓81.7*--52.5--
DiST [22]✓73.8--57.9--
Unsupervised Learning
HOTS [25]21.0*--1.6--
Image Reconstruction + CLIP
E2VID [44] (Pre-train)64.083.9012.8113.3147.147.82
E2VID [44] (Fine-tune)59.885.3112.9113.4144.577.48
E2VID [44] (Fine-tune)✓59.886.6612.6113.5144.037.40
E2VID [44] (Fine-tune)✓60.185.5012.8512.7145.797.33
E2VID [44] (Scratch)✓9.4302.482.601.0299.701.15
SSL-E2VID [37] (Pre-train)28.2281.092.361.6324.432.08
SSL-E2VID [37] (Scratch)30.5228.304.371.7250.553.00
Wang et al. [59] (Scratch)42.7160.346.8310.1231.945.00
Wang et al. [59] (Scratch)✓43.572.674.5019.0180.764.89
Wang et al. [59] (Scratch)✓39.7179.794.1813.2216.374.70
Ours (Text Prompt)82.4662.2914.8130.16150.587.92
Ours (Visual Prototype)82.6154.1917.5931.28135.959.74
", + "image_path": "3a1715fb6849501fc70c9fa01ac0297af97b30bd9f8f4184985cfb16da0219bc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 379, + 531, + 415 + ], + "lines": [ + { + "bbox": [ + 45, + 379, + 531, + 415 + ], + "spans": [ + { + "bbox": [ + 45, + 379, + 531, + 415 + ], + "type": "text", + "content": "Table 1: The results of event-based object recognition and event-to-image reconstruction. The **bold** and **underline** denote the best and the second-best performance except for supervised methods, respectively. * denotes the values taken from the original paper and italic denotes the performance of supervised methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 425, + 124, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 425, + 124, + 437 + ], + "spans": [ + { + "bbox": [ + 45, + 425, + 124, + 437 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 443, + 280, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 443, + 280, + 630 + ], + "spans": [ + { + "bbox": [ + 45, + 443, + 280, + 630 + ], + "type": "text", + "content": "We compare our methods utilizing text prompts or visual prototypes with other existing methods. We adopt four representations (Histogram [29], Ev-gait [61], EST [16], and DiST [22]) for supervised methods and an unsupervised method (HOTS [25]). Additionally, three image reconstruction networks, E2VID [44], SSL-E2VID [37] and Wang et al. [59], are utilized with CLIP. For a fair comparison with image reconstruction networks, we record the performance of three different models for each image reconstruction network: the official pre-trained model, fine-tuned model, and a model trained from scratch. We evaluate these models under three conditions: paired images, images belonging to the same class, and randomly selected images. Some cases are overlooked when the pre-trained model is unavailable or the training setup does not yield meaningful results. For implementation details, see the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 642, + 206, + 655 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 642, + 206, + 655 + ], + "spans": [ + { + "bbox": [ + 45, + 642, + 206, + 655 + ], + "type": "text", + "content": "5.1. Label-free Object Recognition" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "Text Prompt. The quantitative results are presented in Table 1. The proposed method outperforms supervised object recognition methods on the N-Caltech101 dataset, despite not using category labels. Also, our method surpasses existing unsupervised methods and image reconstruction methods with CLIP by a large margin under all" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 425, + 530, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 425, + 530, + 565 + ], + "spans": [ + { + "bbox": [ + 296, + 425, + 530, + 565 + ], + "type": "text", + "content": "metrics. Specifically, ours surpasses the best image reconstruction with CLIP method, E2VID (Pre-train), by around " + }, + { + "bbox": [ + 296, + 425, + 530, + 565 + ], + "type": "inline_equation", + "content": "28\\%" + }, + { + "bbox": [ + 296, + 425, + 530, + 565 + ], + "type": "text", + "content": " increase in accuracy even though it utilizes the image while pre-training. On N-ImageNet, supervised methods record higher accuracy than ours since the dataset is challenging due to the sparse events captured within a short period. However, ours shows a significant improvement in all metrics compared to other unsupervised and image reconstruction-based methods. Our approach demonstrates the ability to perform object recognition and image reconstruction from event data, even when trained solely on textual features without any image data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 565, + 530, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 565, + 530, + 660 + ], + "spans": [ + { + "bbox": [ + 296, + 565, + 530, + 660 + ], + "type": "text", + "content": "Visual Prototype. Besides text prompts, our framework can employ visual prototypes generated from scrapped images. By incorporating visual information, our visual prototype-based approach exceeds the performance of relying solely on textual prompts and achieves the best performance among unsupervised and image reconstruction-based methods under all metrics across both datasets. This demonstrates the superiority of the visual prototypes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 297, + 666, + 473, + 679 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 666, + 473, + 679 + ], + "spans": [ + { + "bbox": [ + 297, + 666, + 473, + 679 + ], + "type": "text", + "content": "5.2. Image-free Image Reconstruction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "text", + "content": "We also compare the reconstruction results of our methods with other event-to-image reconstruction networks in Table 1. Note that, as mentioned in Sec. 4, the resolution and pixel positions of events and corresponding orig-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "19871" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 117, + 520, + 292 + ], + "blocks": [ + { + "bbox": [ + 71, + 106, + 98, + 115 + ], + "lines": [ + { + "bbox": [ + 71, + 106, + 98, + 115 + ], + "spans": [ + { + "bbox": [ + 71, + 106, + 98, + 115 + ], + "type": "text", + "content": "Events" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 119, + 106, + 166, + 116 + ], + "lines": [ + { + "bbox": [ + 119, + 106, + 166, + 116 + ], + "spans": [ + { + "bbox": [ + 119, + 106, + 166, + 116 + ], + "type": "text", + "content": "Wang et. al." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 187, + 106, + 215, + 115 + ], + "lines": [ + { + "bbox": [ + 187, + 106, + 215, + 115 + ], + "spans": [ + { + "bbox": [ + 187, + 106, + 215, + 115 + ], + "type": "text", + "content": "E2VID" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 242, + 106, + 276, + 116 + ], + "lines": [ + { + "bbox": [ + 242, + 106, + 276, + 116 + ], + "spans": [ + { + "bbox": [ + 242, + 106, + 276, + 116 + ], + "type": "text", + "content": "E2VID*" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 289, + 106, + 345, + 116 + ], + "lines": [ + { + "bbox": [ + 289, + 106, + 345, + 116 + ], + "spans": [ + { + "bbox": [ + 289, + 106, + 345, + 116 + ], + "type": "text", + "content": "Ours (Prompt)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 347, + 106, + 399, + 116 + ], + "lines": [ + { + "bbox": [ + 347, + 106, + 399, + 116 + ], + "spans": [ + { + "bbox": [ + 347, + 106, + 399, + 116 + ], + "type": "text", + "content": "Ours (Proto.)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 404, + 106, + 460, + 116 + ], + "lines": [ + { + "bbox": [ + 404, + 106, + 460, + 116 + ], + "spans": [ + { + "bbox": [ + 404, + 106, + 460, + 116 + ], + "type": "text", + "content": "Ours (Proto.)*" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 478, + 106, + 502, + 116 + ], + "lines": [ + { + "bbox": [ + 478, + 106, + 502, + 116 + ], + "spans": [ + { + "bbox": [ + 478, + 106, + 502, + 116 + ], + "type": "text", + "content": "Image" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 56, + 117, + 520, + 292 + ], + "lines": [ + { + "bbox": [ + 56, + 117, + 520, + 292 + ], + "spans": [ + { + "bbox": [ + 56, + 117, + 520, + 292 + ], + "type": "image", + "image_path": "7812e7b24f7ef6d5ab6206f30e47da0bd3c45143d93840596bb805df70d09fcc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 254, + 293, + 321, + 303 + ], + "lines": [ + { + "bbox": [ + 254, + 293, + 321, + 303 + ], + "spans": [ + { + "bbox": [ + 254, + 293, + 321, + 303 + ], + "type": "text", + "content": "(a) N-Caltech101" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 56, + 309, + 520, + 484 + ], + "blocks": [ + { + "bbox": [ + 56, + 309, + 520, + 484 + ], + "lines": [ + { + "bbox": [ + 56, + 309, + 520, + 484 + ], + "spans": [ + { + "bbox": [ + 56, + 309, + 520, + 484 + ], + "type": "image", + "image_path": "e58e7f9c7861d171cda9424194bfc75d07421857ace6eb51493299e456148679.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 257, + 485, + 318, + 495 + ], + "lines": [ + { + "bbox": [ + 257, + 485, + 318, + 495 + ], + "spans": [ + { + "bbox": [ + 257, + 485, + 318, + 495 + ], + "type": "text", + "content": "(b) N-ImageNet" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 498, + 531, + 533 + ], + "lines": [ + { + "bbox": [ + 45, + 498, + 531, + 533 + ], + "spans": [ + { + "bbox": [ + 45, + 498, + 531, + 533 + ], + "type": "text", + "content": "Figure 4: Visual results of event-to-image reconstruction network on (a) N-Caltech101 and (b) N-ImageNet datasets. Ours shows a higher quality of reconstructed images with fine-grained details than other methods (Wang et al. [59] and pre-trained E2VID [44]). * denotes the images with brightness and contrast adjustment." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 554, + 279, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 554, + 279, + 612 + ], + "spans": [ + { + "bbox": [ + 45, + 554, + 279, + 612 + ], + "type": "text", + "content": "inal images are not aligned. Therefore, pixel-wise metrics (e.g., L1, PSNR) cannot be used for comparison. Instead, to assess the visual quality of the reconstructed images, we utilize two metrics: inception score (IS) [47] and Fréchet inception distance (FID) [18]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 45, + 613, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 613, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 613, + 279, + 729 + ], + "type": "text", + "content": "Despite not utilizing any images during training, our text prompt-based approach surpasses all other image reconstruction techniques in terms of FID and IS metrics on the N-Caltech101 dataset. However, in the case of N-ImageNet, our text prompt approach is the strongest by an IS indicator but falls behind pre-trained E2VID in FID. Since ours is trained from events of short periods without paired images, it becomes challenging to learn the distribution of real images. Instead, utilizing the visual prototype results in the highest FID and IS indicators in both datasets. This implies" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 554, + 530, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 554, + 530, + 577 + ], + "spans": [ + { + "bbox": [ + 296, + 554, + 530, + 577 + ], + "type": "text", + "content": "that it can acquire the ability to reconstruct images without requiring paired images that correspond to events." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 579, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 579, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 579, + 531, + 730 + ], + "type": "text", + "content": "We also present the qualitative results in Fig. 4. Wang et al. [59] utilize the paired image in training but the method lacks the ability to effectively display intensity contrast, resulting in the loss of many details. While pre-trained E2VID shows better image quality over [59], it still struggles to preserve fine details as it operates in a distinct training environment. This is particularly apparent in the N-ImageNet dataset, where E2VID generates results that deviate significantly from the original image. Conversely, our framework is able to recover intensity effectively and preserve details in reconstructed images, even without access to paired images. Our results closely resemble real images, even in the challenging N-ImageNet dataset." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "19872" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 104, + 526, + 293 + ], + "blocks": [ + { + "bbox": [ + 51, + 104, + 526, + 293 + ], + "lines": [ + { + "bbox": [ + 51, + 104, + 526, + 293 + ], + "spans": [ + { + "bbox": [ + 51, + 104, + 526, + 293 + ], + "type": "table", + "html": "
MethodsImage PairClass LabelN-Caltech101N-ImageNet (Mini)
Accuracy ↑FID ↓IS ↑Accuracy ↑FID ↓IS ↑
Image Reconstruction + CLIP
E2VID [44] (Pre-train)58.4194.266.4731.7203.056.64
E2VID [44] (Fine-tune)61.7203.397.5630.0199.836.73
E2VID [44] (Fine-tune)✓61.1203.407.4530.9199.446.80
E2VID [44] (Fine-tune)✓61.5202.237.5629.4203.976.08
E2VID [44] (Scratch)✓21.3362.082.434.9333.131.36
SSL-E2VID [37] (Pre-train)24.7332.432.075.7352.532.04
SSL-E2VID [37] (Scratch)25.3289.363.936.1287.982.79
Wang et al. [59] (Scratch)47.5228.774.6718.7241.876.12
Wang et al. [59] (Scratch)✓48.5230.744.9120.5236.783.90
Wang et al. [59] (Scratch)✓43.7215.634.6615.6237.384.40
Ours (Text Prompt)84.31147.316.8145.10202.296.31
Ours (Visual Prototype)85.56107.589.3551.50174.247.32
", + "image_path": "0cfd7f1f0fb8320a5f80648264f904e3a13da3d8a26c71fecd7dc2eda2a577c6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 319, + 202, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 319, + 202, + 333 + ], + "spans": [ + { + "bbox": [ + 45, + 319, + 202, + 333 + ], + "type": "text", + "content": "5.3. Zero-shot Object Recognition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 336, + 279, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 336, + 279, + 442 + ], + "spans": [ + { + "bbox": [ + 45, + 336, + 279, + 442 + ], + "type": "text", + "content": "We further demonstrate the advantages of our framework over supervised methods by enabling it to be used for zero-shot object recognition. The reconstructed images can be utilized for zero-shot object recognition thanks to CLIP's capacity to align images with any semantic concepts in an open vocabulary for zero-shot object recognition. To define \"unseen\" categories that are not seen during training, we use only 80 of the 100 categories for training and the remaining 20 for zero-shot testing." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "spans": [ + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "text", + "content": "In Table 2, we present the performance of zero-shot object recognition. Without any category labels, our methods with text prompt achieve a promising " + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "inline_equation", + "content": "84.31\\%" + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "inline_equation", + "content": "45.10\\%" + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "text", + "content": " on N-Caltech101 and N-ImageNet, respectively. This is " + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "inline_equation", + "content": "25.91\\%" + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "inline_equation", + "content": "13.4\\%" + }, + { + "bbox": [ + 45, + 443, + 280, + 642 + ], + "type": "text", + "content": " higher than E2VID pretrained with a large number of image pairs. These results validate that although our model learns through the process of being category-aware, generalization is possible for other categories, especially \"unseen\" in this case. Although FID and IS of our method using text prompts are relatively poor compared to pre-trained E2VID on N-ImageNet, this can also be overcome by using visual prototypes. Our method using the visual prototype is able to achieve a substantial improvement under all metrics. Specifically, in the N-Caltech101 dataset, our method increases the IS from 6.81 to 9.35, while in the N-ImageNet dataset, it increases the accuracy from 45.10 to 51.50." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 655, + 208, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 655, + 208, + 668 + ], + "spans": [ + { + "bbox": [ + 45, + 655, + 208, + 668 + ], + "type": "text", + "content": "6. Ablation Study and Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 675, + 138, + 688 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 675, + 138, + 688 + ], + "spans": [ + { + "bbox": [ + 45, + 675, + 138, + 688 + ], + "type": "text", + "content": "6.1. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": "We conduct an ablation study to understand how the components influence performance. Table 3 illustrates the effectiveness of each component on N-ImageNet dataset." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 301, + 319, + 527, + 431 + ], + "blocks": [ + { + "bbox": [ + 138, + 295, + 437, + 308 + ], + "lines": [ + { + "bbox": [ + 138, + 295, + 437, + 308 + ], + "spans": [ + { + "bbox": [ + 138, + 295, + 437, + 308 + ], + "type": "text", + "content": "Table 2: The results of event-based zero-shot object recognition using CLIP." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 301, + 319, + 527, + 431 + ], + "lines": [ + { + "bbox": [ + 301, + 319, + 527, + 431 + ], + "spans": [ + { + "bbox": [ + 301, + 319, + 527, + 431 + ], + "type": "table", + "html": "
LattLrepLconRDSAccuracy ↑
PPITRCI
(1)✓9.50
(2)✓✓14.00
(3)✓✓✓15.68
(4)✓✓✓28.42
(5)✓✓✓✓28.90
(6)✓✓✓✓28.91
(7)✓✓✓✓✓30.16
", + "image_path": "3606d8eb0de6e8ed041a6a5e043c5349633a54dc568ac3ebe679df3232df95ca.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 432, + 509, + 444 + ], + "lines": [ + { + "bbox": [ + 318, + 432, + 509, + 444 + ], + "spans": [ + { + "bbox": [ + 318, + 432, + 509, + 444 + ], + "type": "text", + "content": "Table 3: Ablation study of the proposed method." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "spans": [ + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "text", + "content": "We start with a baseline, which denotes the removal of everything except attraction loss, " + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "text", + "content": ". During the experiment, we notice that if we only apply attraction loss towards the network without repulsion loss, " + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rep}" + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "text", + "content": ", the collapse often takes place. Therefore, " + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rep}" + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "text", + "content": " is essential for stable learning of " + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 296, + 463, + 530, + 652 + ], + "type": "text", + "content": ". It is worth mentioning the impact of the proposed PPI on performance. Upon analyzing (4), which displays the results when PPI is added to (2), it can be seen that the accuracy has increased by 14.42. Upon examining (5) and (7), it can be observed that the accuracy increases by 1.26, validating the impact of the sub-sampling process via TRCI. Furthermore, the ablation results between (6) and (7) show that the reconstruction consistency between global and local preserves the spatial details of the image, leading to performance improvement. Finally, the model (7) that has all of its components incorporated achieves the highest performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 655, + 441, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 655, + 441, + 668 + ], + "spans": [ + { + "bbox": [ + 297, + 655, + 441, + 668 + ], + "type": "text", + "content": "6.2. Number of Samples in PPI" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": " used in PPI for selecting the sample with the highest probability impacts the performance of object recognition. Fig. 5 shows the evaluation of performance on N-ImageNet dataset based on different values of " + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": " is set to 32, which includes all samples in the batch, the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19873" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 104, + 274, + 166 + ], + "blocks": [ + { + "bbox": [ + 50, + 104, + 274, + 166 + ], + "lines": [ + { + "bbox": [ + 50, + 104, + 274, + 166 + ], + "spans": [ + { + "bbox": [ + 50, + 104, + 274, + 166 + ], + "type": "image", + "image_path": "eb8c64942a8dac1e10eb30d1237c9becc4a3d28ea5a4f77e31027d0cad741418.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 175, + 279, + 198 + ], + "lines": [ + { + "bbox": [ + 45, + 175, + 279, + 198 + ], + "spans": [ + { + "bbox": [ + 45, + 175, + 279, + 198 + ], + "type": "text", + "content": "Figure 5: Object recognition accuracy on N-ImageNet (Mini) according to " + }, + { + "bbox": [ + 45, + 175, + 279, + 198 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 175, + 279, + 198 + ], + "type": "text", + "content": " in PPI." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 207, + 276, + 267 + ], + "blocks": [ + { + "bbox": [ + 48, + 207, + 276, + 267 + ], + "lines": [ + { + "bbox": [ + 48, + 207, + 276, + 267 + ], + "spans": [ + { + "bbox": [ + 48, + 207, + 276, + 267 + ], + "type": "image", + "image_path": "d94d636714e43c46ad2e957cfeb9cc1cfa7d442abd6bce46b365f99be7aa9a4a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 273, + 278, + 298 + ], + "lines": [ + { + "bbox": [ + 45, + 273, + 278, + 298 + ], + "spans": [ + { + "bbox": [ + 45, + 273, + 278, + 298 + ], + "type": "text", + "content": "Figure 6: Object recognition accuracy on N-Caltech101 according to " + }, + { + "bbox": [ + 45, + 273, + 278, + 298 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 273, + 278, + 298 + ], + "type": "text", + "content": " in PPI." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 309, + 276, + 389 + ], + "blocks": [ + { + "bbox": [ + 48, + 309, + 276, + 389 + ], + "lines": [ + { + "bbox": [ + 48, + 309, + 276, + 389 + ], + "spans": [ + { + "bbox": [ + 48, + 309, + 276, + 389 + ], + "type": "table", + "html": "
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Due to the same reason, the performance is better when " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " is 16 than when it is 32, but since unreliable samples are also selected, the accuracy is relatively lower than in other favorable situations. As " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " decreases, the performance improves, but it starts to decline when " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " is less than 6, indicating that even with high reliability, it is challenging to achieve optimal training if " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{att}" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " is applied with very few samples. Similarly, we report the accuracy according to the " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " value on the N-Caltech101 in Fig 6. Unless an extremely small number of samples are drawn, as the value of " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " increases, the performance also improves. However, once a certain threshold is reached, there is little significant change, and it starts to decline with further increases. The accuracy exceeds " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " in all cases, showing robustness to " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " values. Although the level of sensitivity varies depending on the dataset, we do confirm that satisfactory results can be obtained between " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "inline_equation", + "content": "K = 10" + }, + { + "bbox": [ + 45, + 434, + 279, + 655 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 664, + 189, + 677 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 664, + 189, + 677 + ], + "spans": [ + { + "bbox": [ + 45, + 664, + 189, + 677 + ], + "type": "text", + "content": "6.3. Hyper-parameter Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": "In Table 4, we report the accuracy according to " + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\lambda_{3}" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": " in Eq. 11. If the weight of the repulsion loss, " + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": ", is set too high, the performance decreases. However, this can be mitigated by increasing the weight of the local-global re" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 300, + 105, + 524, + 173 + ], + "blocks": [ + { + "bbox": [ + 300, + 105, + 524, + 173 + ], + "lines": [ + { + "bbox": [ + 300, + 105, + 524, + 173 + ], + "spans": [ + { + "bbox": [ + 300, + 105, + 524, + 173 + ], + "type": "image", + "image_path": "d578b2cc4dbd1da4c37ac78ccae19e553041cace94a5a3168bb1d7da94a52d11.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 297, + 175, + 530, + 200 + ], + "lines": [ + { + "bbox": [ + 297, + 175, + 530, + 200 + ], + "spans": [ + { + "bbox": [ + 297, + 175, + 530, + 200 + ], + "type": "text", + "content": "Figure 7: Object recognition accuracy on N-Caltech101 according to the number of extra category prompts." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 221, + 530, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 221, + 530, + 245 + ], + "spans": [ + { + "bbox": [ + 296, + 221, + 530, + 245 + ], + "type": "text", + "content": "construction consistency loss, " + }, + { + "bbox": [ + 296, + 221, + 530, + 245 + ], + "type": "inline_equation", + "content": "\\lambda_3" + }, + { + "bbox": [ + 296, + 221, + 530, + 245 + ], + "type": "text", + "content": ". The results verify the robustness of our method according to the " + }, + { + "bbox": [ + 296, + 221, + 530, + 245 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 296, + 221, + 530, + 245 + ], + "type": "text", + "content": " on both datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 255, + 477, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 255, + 477, + 269 + ], + "spans": [ + { + "bbox": [ + 297, + 255, + 477, + 269 + ], + "type": "text", + "content": "6.4. Learning with Superset Categories" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 273, + 530, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 273, + 530, + 472 + ], + "spans": [ + { + "bbox": [ + 296, + 273, + 530, + 472 + ], + "type": "text", + "content": "In practical terms, it can be challenging for users to find corresponding categories of the event dataset. As a result, they often end up taking more categories as prompts. We tackle these issues by demonstrating that our joint learning framework works robustly even when employing more prompts than the categories of the event on the N-Caltech101 dataset. To avoid using additional prompts that are too irrelevant to the N-Caltech101 dataset, we randomly take additional prompts from N-ImageNet. We show the performance results according to the number of extra category prompts in Fig. 7. While the performance decreases with an increase in extra category prompts, it is worth noting that our algorithm remains reliable even when faced with over 100 additional prompts beyond the corresponding category. This suggests that our algorithm can function with superset categories, even in a situation when the number of extra categories is much larger than the actual categories." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 486, + 367, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 486, + 367, + 499 + ], + "spans": [ + { + "bbox": [ + 297, + 486, + 367, + 499 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 506, + 530, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 506, + 530, + 681 + ], + "spans": [ + { + "bbox": [ + 296, + 506, + 530, + 681 + ], + "type": "text", + "content": "In this work, we propose a joint learning framework for event-based object recognition with image reconstruction from events without labels and paired images. With the proposed losses and the reliable data sampling strategy, our approach allows stable learning of two tasks simultaneously from pseudo labels. As a result, our approach achieves exceptional performance in event-based object recognition and event-to-image reconstruction, all without requiring category labels and paired images. Our approach successfully addresses the challenge of label dependency in event-based research, which has been a significant obstacle. We anticipate that our work can be further extended to other tasks such as event-based zero-shot object detection, zero-shot semantic segmentation, etc., that have not explored so far in the research field for event cameras." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 682, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 682, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 682, + 530, + 730 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19874" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 280, + 720 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 188 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 188 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 188 + ], + "type": "text", + "content": "[1] Arnon Amir, Brian Taba, David Berg, Timothy Melano, Jeffrey McKinstry, Carmelo Di Nolfo, Tapan Nayak, Alexander Andreopoulos, Guillaume Garreau, Marcela Mendoza, et al. 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Naively fine-tuning the old model on new data leads to catastrophic forgetting. A common solution is knowledge distillation (KD), where the output distribution of the new model is regularized to be similar to that of the old model. However, in CSS, this is challenging because of the background shift issue. Existing KD-based CSS methods continue to suffer from confusion between the background and novel classes since they fail to establish a reliable class correspondence for distillation. To address this issue, we propose a new label-guided knowledge distillation (LGKD) loss, where the old model output is expanded and transplanted (with the guidance of the ground truth label) to form a semantically appropriate class correspondence with the new model output. Consequently, the useful knowledge from the old model can be effectively distilled into the new model without causing confusion. We conduct extensive experiments on two prevailing CSS benchmarks, Pascal-VOC and ADE20K, where our LGKD significantly boosts the performance of three competing methods, especially on novel mIoU by up to $+76\\%$ , setting new state-of-the-art. Finally, to further demonstrate its generalization ability, we introduce the first CSS benchmark for 3D point cloud based on ScanNet, along with several re-implemented baselines for comparison. Experiments show that LGKD is versatile in both 2D and 3D modalities without requiring ad hoc design. Codes are available at https://github.com/Ze-Yang/LGKD.", + "bbox": [ + 75, + 358, + 473, + 797 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 823, + 209, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fully supervised semantic segmentation has witnessed tremendous success [33, 63, 27, 8, 16, 22, 47, 65, 9] in re", + "bbox": [ + 76, + 849, + 468, + 880 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5a842318a5f59736e908d670e8a3502e730702509059163ea18e851911ba5ad8.jpg", + "image_caption": [ + "Figure 1. Illustration of knowledge distillation (KD) strategies in continual semantic segmentation. Standard KD and unbiased KD reduce the new class (bicycle) dimension(s) of the probabilities output by the new model via remove and combine respectively, which collapses the class correspondence across incremental steps and raises confusion between background and new classes (see Sec. 1). In contrast, our label-guided KD uses the ground truth label as guidance to expand the probabilities predicted by the old model. It builds a reliable class correspondence across different learning steps without discrepancy (ILT) or entanglement (MiB) (see Sec. 3.2). A $\\xrightarrow{\\text{mimic}}$ B: encourage A to be similar to B." + ], + "image_footnote": [], + "bbox": [ + 501, + 324, + 890, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cent years. These algorithms generally assume a fixed number of classes to be learned. However, in real-world applications, it is often expected that a deployed model can be continuously generalized to handle new classes while not forgetting the old ones. A simple solution is to expand the original dataset with newly available samples and retrain a new model from scratch, dubbed as Joint Training. Obviously, this is computationally expensive and requires an increasing amount of space to store the old data over time.", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: Guosheng Lin", + "bbox": [ + 94, + 886, + 302, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18601", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Further, it may raise privacy issues in some circumstances, e.g., medical images and face data.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this problem, continual semantic segmentation (CSS) has been proposed by [35] as an emerging research direction, where the training scheme is separated into several steps with each step tackling a set of unseen classes. Specifically, given the old model and new training data (only new classes are labeled while others are treated as background), the new model is supposed to recognize both old and new classes. Under this scenario, naively finetuning the old model on new data tends to suffer from catastrophic forgetting [17, 26], where the recognition capability of old classes is quickly lost.", + "bbox": [ + 75, + 123, + 468, + 289 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Knowledge distillation (KD), first proposed in image classification [19], has recently been introduced to CSS [35, 4] to mitigate the forgetting issue. As Fig. 1 shows, $ILT$ [35] removes new class probabilities (green bar) predicted by the new model, and simply distill old classes and background accordingly. However, they ignore the background shift problem [4], where the new class bicycle at current step $t$ was labeled as background at last step $t - 1$ . As a result, the old model, which regards bicycle as background, will output a high background score for the new class bicycle pixels. Via KD, it will mislead the new model to misclassify new classes as background. Obviously, this KD strategy hinders the learning of new classes because the class correspondence for distillation is corrupted, i.e., naively mapping the new background to the old background.", + "bbox": [ + 75, + 291, + 470, + 518 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This issue was highlighted in $MiB$ [4] where they proposed a new class correspondence by combination. Concretely, they combined new classes with the new background via probability summation (Fig. 1) to form a pseudo class, which was treated as the counterpart to the old background for distillation. However, this strategy, though alleviating class mis-correspondence, entangles new classes with the new background and tends to misclassify background as new classes, as detailed in Sec. 3.2. In this paper, we term the error of mistaking background for new (novel) classes or vice-versa as novel-background confusion.", + "bbox": [ + 75, + 520, + 468, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The key insight to overcome the novel-background confusion is to build a reliable class correspondence across different learning steps without corruption or entanglement. To this end, we devise a novel Label-Guided Knowledge Distillation (LGKD) loss, where the class probabilities predicted by the old model are expanded to have the same dimension as the output of the new model (see the blue block in Fig. 1). The background probability is then transplanted to the corresponding ground truth label (class) of the input pixels. In this way, the knowledge from the old background at the last step can be correctly distilled into its corresponding semantic class at the current step, i.e., either the new background or a novel class. Note that our LGKD is a generic regularization term with negligible computa", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tional cost and can be easily incorporated into existing arts. We validate its effectiveness on two prevailing CSS benchmarks Pascal-VOC and ADE20K, where our LGKD consistently yields promising improvements upon three competing methods, especially on novel (new class) mIoU (up to $+76\\%$ ), setting new state-of-the-art. To further demonstrate the generalization ability of our approach, we establish a challenging CSS benchmark based on ScanNet for 3D point cloud and re-implement multiple baselines for comparison. To our best knowledge, this is the first work to conduct CSS on 3D point cloud. Extensive experiments showcase that our LGKD loss is capable to handle both 2D and 3D modalities with no ad hoc design.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this paper can be summarized as:", + "bbox": [ + 500, + 290, + 890, + 306 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a new label-guided knowledge distillation (LGKD) loss for CSS, which builds a reliable class correspondence across incremental steps and alleviates novel-background confusion.", + "- LGKD is a generic regularization term with negligible computational cost, which can be readily combined with existing methods. Extensive experiments on two prevailing CSS benchmarks, Pascal-VOC and ADE20K, showcase that LGKD significantly improves three competitive methods, particularly on novel mIoU by up to $+76\\%$ , setting new state-of-the-art.", + "- To further demonstrate its generalization capability, we establish the first CSS benchmark for 3D point cloud based on ScanNet and re-implement multiple baselines for comparison. Experiments illustrate that our LGKD is versatile in both 2D and 3D modalities without any ad hoc design." + ], + "bbox": [ + 514, + 315, + 890, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 614, + 648, + 630 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic Segmentation, aiming to perform pixel-level classification, has witnessed great advancement [63, 6, 7, 53, 22, 16] in recent years since the pioneering work Fully Convolutional Network (FCN) [33]. Among the above methods, the DeepLab series [6, 7] is well-known for their effective designs, e.g., atrous spatial pyramid pooling (ASPP) [6], atrous convolution in cascade [7]. DeepLabv3 [7] is commonly used as the segmentation framework in prior CSS works [4, 13, 61].", + "bbox": [ + 496, + 643, + 890, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In 3D point cloud modality, PointNet [38] is a pioneering work to directly process unstructured point cloud. Subsequent work PointNet++ [39] learns to capture local structures and recognize fine-grained patterns via a hierarchical neural network that applies PointNet recursively. While more complicated techniques have been proposed in recent works [46, 45, 62, 68, 10], we employ PointNet++ as our 3D segmentation model for its simplicity and efficiency.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18602", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d20b9277ef6bef5cfa08df9dac0ba012aba9e3f4765a82868f524821621afb35.jpg", + "image_caption": [ + "Figure 2. Illustration of our LGKD loss. At learning step $t$ , an input sample $x$ is fed into the old (top) and new (bottom) models to obtain the class probabilities for each element $i \\in \\mathcal{I}$ (pixel or point). These elements are then separated into the novel and background sets according to their ground truth label available at the current step $t$ (yellow and green as novel set). Finally, to build up a reliable class correspondence, we extend the old probabilities (output by the old model) to have the same dimension as the new ones by expand and transplant (for novel set only), such that useful prior knowledge from the old model can be effectively distilled into the new model to facilitate learning new classes. We highlight that our LGKD can effectively alleviate the novel-background confusion issue as occurs in [35, 4]." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Continual Learning aims at training a deep neural network to learn multiple tasks in sequence continually. Distinct from one-step incremental learning [50, 51, 55, 56, 59, 58, 30, 60, 29, 57, 31, 44], continual learning generally confronts more severe forgetting issues during multiple-step learning. Numerous works tackle the catastrophic forgetting issue and they can be classified into three categories. The model growing category [2, 48, 52] tackles this problem by dynamically extending model capacity. The memory replay approaches retain the old-class knowledge by keeping a small amount of old-class data in current training. Those data can be raw data [41, 40, 3], features [18, 23] or generated data [24, 42, 32]. The regularization approaches constrain the model by regularizing the parameters [26, 1, 54], the gradients [21, 5], logits [40, 3, 4] or the features [20, 12, 14] of the model.", + "bbox": [ + 75, + 465, + 472, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Continual Semantic Segmentation. Existing CSS methods can be divided into two categories: 1) replay-based. RECALL [34] rehearses old-class data obtained by web-crawling or generative models. Similarly, [49] utilizes an iterative relabeling strategy with rehearsal-based incremental learning. Following [4], replay-based methods are out of the scope of this paper since accessing old data violates the conventional CSS assumption. 2) regularization-based. ILT [35] is the first work to introduce KD into CSS. MiB [4] raises the background shift problem in CSS and proposes an unbiased KD to tackle it. PLOP [13] distills both short- and long-range spatial relations via local pooled output distilla", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion. SDR [36] leverages prototype matching, feature sparsification and contrastive learning to enforce feature consistency and discrimination. Most recently, class similarity KD, representation compensation, structure-preserving loss and feature projection, and the biased context are investigated by REMINDER [37], RCIL [61], SPPA [28] and RBC [64] respectively. However, the above approaches tend to suffer from the novel-background confusion problem since their distillation term lacks an appropriate class correspondence. Therefore, we propose a generic distillation term, dubbed LGKD, with a reliable class correspondence to alleviate this confusion issue.", + "bbox": [ + 496, + 464, + 893, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 666, + 591, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition and Setups", + "text_level": 1, + "bbox": [ + 500, + 694, + 769, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before introducing the continual learning setting, we first present the setups of the standard semantic segmentation task. To ensure the generality, let $\\mathcal{X} \\in \\mathbb{R}^{N \\times C_{\\mathrm{in}}}$ denote the input space (e.g., image, point cloud, etc.), where $N$ is the number of input elements and $C_{\\mathrm{in}}$ is the number of input channels (typically $C_{\\mathrm{in}} = 3$ , i.e., RGB, for image and $C_{\\mathrm{in}} >= 3$ , e.g., XYZ, RGB, normals, for point cloud). Let $\\mathcal{Y} \\in \\mathcal{C}^N$ denote the output label space, where $\\mathcal{C}$ is a label set that contains all classes including the background class $\\mathsf{b} \\in \\mathcal{C}$ . Note that each sample $x \\in \\mathcal{X}$ comprises a set of elements $\\mathcal{I}$ (e.g., pixels, points, etc.) of corresponding label $y \\in \\mathcal{Y}$ with constant cardinality $|\\mathcal{I}| = N$ .", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18603", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a training set $\\mathcal{T} \\subset \\mathcal{X} \\times \\mathcal{Y}$ , the target of semantic segmentation is to learn a model $f_{\\theta}$ parametrized by $\\theta$ that maps the input space $\\mathcal{X}$ to a set of class probability vectors $f_{\\theta}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}|}$ . The output segmentation mask is then computed as $\\hat{y} = \\{\\arg \\max_{c \\in \\mathcal{C}} f_{\\theta}(x)[i, c]\\}_{i=1}^{N}$ , where $f_{\\theta}(x)[i, c]$ is the probability of element $i$ belonging to category $c$ .", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As opposed to the standard training scheme where the model can access and learn from the full training set $\\mathcal{T} \\subset \\mathcal{X} \\times \\mathcal{C}^N$ all at once, continual learning, instead, involves several learning steps $\\{t\\}_{t=0}^{T}$ each with a subset of label $\\mathcal{C}^t$ . More specifically, at training step $t$ , the previous label set $\\mathcal{C}^{0:t-1}$ will be expanded with a set of unseen classes $\\mathcal{C}^t$ to form a new label set $\\mathcal{C}^{0:t} = \\mathcal{C}^{0:t-1} \\cup \\mathcal{C}^t$ . Then a training set $\\mathcal{T}^t \\subset \\mathcal{X} \\times (\\mathcal{C}^t)^N$ will be provided along with the last model $f_{\\theta^{t-1}}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}^{0:t-1}|}$ to obtain an updated model $f_{\\theta^t}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}^{0:t}|}$ . Note that the training set $\\mathcal{T}^t$ may contain element $i \\in \\mathcal{I}$ from either previous classes $\\mathcal{C}^{0:t-1}$ or future classes $\\mathcal{C}^{t+1:T}$ , though the annotations are collapsed into the background class $b$ at the current step $t$ . This is referred to as overlapped [4] setting. Following the standard incremental setup, we assume that the label sets of each step are disjoint from each other except for the special background class, i.e., $\\mathcal{C}^i \\cap \\mathcal{C}^j = b$ ( $i \\neq j$ ).", + "bbox": [ + 75, + 198, + 470, + 457 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Revisiting Knowledge Distillation Loss", + "text_level": 1, + "bbox": [ + 76, + 465, + 408, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A naive way to tackle the continual learning problem is to initialize a new model $f_{\\theta^t}$ with the weights of the last model $f_{\\theta^{t-1}}$ and then optimize the network with the training set $\\mathcal{T}^t$ . However, this will lead to the catastrophic forgetting of old classes $\\mathcal{C}^{0:t-1}$ . Since no old class samples with annotation are available at the current step.", + "bbox": [ + 75, + 489, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Standard knowledge distillation. To alleviate the forgetting problem, knowledge distillation [19] is a common solution to preserve old knowledge by regularizing the output class probability distribution of the new model $f_{\\theta^t}$ to be close to that of the old model $f_{\\theta^{t-1}}$ given the same input sample. Formally, the standard knowledge distillation loss $\\ell_{\\mathrm{kd}}$ adopted in CSS by ILT [35] can be formulated as:", + "bbox": [ + 75, + 584, + 468, + 690 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y) = - \\frac {1}{| \\mathcal {I} |} \\sum_ {i \\in \\mathcal {I}} \\sum_ {c \\in \\mathcal {C} ^ {0: t - 1}} q _ {x} ^ {t - 1} (i, c) \\log \\hat {q} _ {x} ^ {t} (i, c), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 700, + 468, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{q}_x^t (i,c)$ refers to the probability of class $c$ for element $i$ predicted by $f_{\\theta^t}$ but re-normalized over all old classes:", + "bbox": [ + 76, + 748, + 468, + 780 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {q} _ {x} ^ {t} (i, c) = q _ {x} ^ {t} (i, c) / \\sum_ {k \\in \\mathcal {C} ^ {0: t - 1}} q _ {x} ^ {t} (i, k). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 791, + 468, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, there exists a discrepancy issue in the standard distillation loss. Concretely, it fails to leverage prior knowledge to cope with the new classes, as the new class probabilities $q_{x}^{t}(i,c)$ ( $c \\in \\mathcal{C}^t \\setminus b$ ) are not incorporated in distillation (Eq. 1). Moreover, it wrongly enhances the background", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "probability for novel class elements due to the background shift [4]. Hence, it tends to mistake the novel classes for the background (refer to supp. material for detailed discussion).", + "bbox": [ + 496, + 90, + 890, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unbiased knowledge distillation. To overcome the above issue, MiB [4] proposes an unbiased knowledge distillation loss for CSS by revising $\\hat{q}_x^t (i,c)$ in Eq. 2 as:", + "bbox": [ + 496, + 138, + 890, + 186 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {q} _ {x} ^ {t} (i, c) = \\left\\{ \\begin{array}{l l} q _ {x} ^ {t} (i, c) & \\text {i f} c \\neq \\mathfrak {b} \\\\ \\sum_ {k \\in \\mathcal {C} ^ {t}} q _ {x} ^ {t} (i, k) & \\text {i f} c = \\mathfrak {b}, \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 194, + 890, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where they compare the old background probability $q_{x}^{t - 1}(i,\\mathsf{b})$ with the probability of being either a novel class or the new background, i.e., $\\sum_{k\\in \\mathcal{C}^t}q_x^t (i,k)$ , rather than directly with its counterpart $q_{x}^{t}(i,\\mathsf{b})$ . Such class probability combination mechanism is meant to facilitate distilling the knowledge from the old background class defined at step $t - 1$ to the novel classes at step $t$ . Nevertheless, it entangles the novel classes with the new background due to the probability combination. As a consequence of entanglement, the probabilities of novel classes will be undesirably enhanced when the distillation loss only intends to improve the probabilities of the new background, and vice versa. As opposed to ILT [35], this leads to the other confusion — misclassifying background as novel classes.", + "bbox": [ + 496, + 242, + 892, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Label-Guided Knowledge Distillation", + "text_level": 1, + "bbox": [ + 500, + 462, + 821, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Class separation. Unlike standard KD and unbiased KD, which apply the same KD strategy to all input elements, we propose to separate the input elements into two sets according to the ground truth label available at the current step, namely the background set $S_{\\mathsf{b}} = \\{i|i\\in \\mathcal{I},y_i = \\mathsf{b}\\}$ and the novel set $S_{n} = \\{i|i\\in \\mathcal{I},y_{i}\\in \\mathcal{C}^{t}\\setminus \\mathsf{b}\\}$ . In this way, we can customize the distillation strategy for each class set and establish a more accurate class correspondence, which facilitates more effective knowledge distillation.", + "bbox": [ + 496, + 488, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Class correspondence. As opposed to revising the class probabilities of the new model $q_{x}^{t}(i,c)$ as in [4], we instead resort to correcting the class probabilities of the old model $q_{x}^{t - 1}(i,c)$ according to the ground truth label $y_{i}$ . Our design is inspired by the wireless communication system. In order to improve the useful information captured by the receiver, one should ensure that the signal released by the transmitter is correct and that both transmitter and receiver share the same communication protocol. Likewise, in our case, the objective is to assure the class probabilities (signal) predicted by the old model $f_{\\theta^{t - 1}}$ (transmitter) contain correct class semantics (after background shift) and are well-aligned with (protocol) the output class space of the new model $f_{\\theta^t}$ (receiver). Protocol: For the elements from the novel set $S_{n}$ , we expand the output of the old model $q_{x}^{t - 1}(i,c)$ with zero probability assigned to the extra novel classes $c \\in \\mathcal{C}^t \\setminus \\mathbf{b}$ such that it has the same output class space dimensions with the new model. Signal: Due to the", + "bbox": [ + 496, + 628, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18604", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "background shift, we transplant the probability of the background to the corresponding ground truth novel class and set the background probability to zero while maintaining the others unchanged. The final corrected probability distribution to be distilled from can be formulated as:", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {q} _ {x} ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} ^ {t} \\text {a n d} c \\neq y _ {i} \\\\ q _ {x} ^ {t - 1} (i, \\mathrm {b}) & \\text {i f} c = y _ {i} \\\\ q _ {x} ^ {t - 1} (i, c) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 174, + 468, + 231 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $i \\in S_n$ . We highlight that, this novel set distillation strategy can preserve the knowledge from $f_{\\theta^{t-1}}$ for the old classes while also correcting the class probabilities from the old model for the new classes given the ground truth label $y_i$ as guidance. As for the case of the background set $i \\in S_b$ , it can be treated in a similar yet simpler way by merely expanding zero probability for the extra novel classes as:", + "bbox": [ + 75, + 241, + 468, + 347 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {q} _ {x} ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} ^ {t} \\backslash \\mathfrak {b} \\\\ q _ {x} ^ {t - 1} (i, c) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 358, + 468, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In summary, our distillation loss can be given as:", + "bbox": [ + 76, + 409, + 400, + 422 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y) = \\lambda_ {n} \\cdot \\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S} _ {n}) + \\lambda_ {\\mathfrak {b}} \\cdot \\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S} _ {\\mathfrak {b}}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 433, + 468, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{n}$ and $\\lambda_{\\mathrm{b}}$ balances the contribution of the novel set $S_{n}$ and background set $S_{\\mathrm{b}}$ ; $\\bar{\\ell}_{\\mathrm{kd}}^{\\theta^{t}}(x,y,\\mathcal{S})$ is the distillation loss defined within set $S$ as:", + "bbox": [ + 76, + 464, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S}) = - \\frac {1}{N} \\sum_ {i \\in \\mathcal {S}} \\sum_ {c \\in \\mathcal {C} ^ {0: t}} \\bar {q} _ {x} ^ {t - 1} (i, c) \\log q _ {x} ^ {t} (i, c). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 517, + 468, + 554 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall training objective is then computed as:", + "bbox": [ + 76, + 565, + 411, + 579 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\theta^ {t}\\right) = \\frac {1}{\\left| \\mathcal {T} ^ {t} \\right|} \\sum_ {(x, y) \\in \\mathcal {T} ^ {t}} \\left(\\lambda \\ell_ {c e} ^ {\\theta^ {t}} (x, y) + \\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 590, + 468, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\ell_{ce}^{\\theta^t}(x,y)$ is the cross-entropy loss. $\\lambda$ is the hyperparameter to balance the importance of the two terms, and is set as $\\lambda = 1$ in experiments.", + "bbox": [ + 75, + 641, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 700, + 200, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Benchmarking 3D Continual Segmentation", + "text_level": 1, + "bbox": [ + 76, + 726, + 442, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Existing CSS methods have mainly been evaluated on 2D CSS benchmarks, leaving a significant gap in the exploration of 3D CSS. In order to validate the versatility of LGKD across different modalities, we introduce the first 3D CSS benchmark based on ScanNet [11] and present several baseline methods for comparison.", + "bbox": [ + 75, + 750, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ScanNet contains 1201 and 312 indoor scenes in the training and validation set respectively with 20 classes in total, including a special class for \"other furniture\", i.e. background in the standard segmentation task. In Fig. 3, we", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/695c663d0d51fece92c00017d9f94956c57e4c16cfee9a6c6f6ae5e5d8454d2c.jpg", + "image_caption": [ + "Figure 3. The scene-wise class frequency statistics of our proposed ScanNet benchmark for 3D continual semantic segmentation." + ], + "image_footnote": [], + "bbox": [ + 509, + 94, + 880, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "provide the scene-wise class frequency statistics of ScanNet [11], including both train and validation sets. The scene-wise class frequency indicates the number of scenes that a certain class appears in. Surprisingly, we find that ScanNet exhibits a challenging long-tail category distribution. Additionally, we provide the point-wise class frequency statistics and demonstrate the difficulty of our proposed benchmark in the supp. material. For a challenging CSS benchmark, we split the entire class set into multiple subsets according to the descending order of scene-wise class frequency as in Fig. 3, with the tail classes constituting the novel sets for continual learning. This means that the novel classes to be learned in each step are set to be those rare ones, a.k.a. tail classes in the long-tail field. Following the Pascal-VOC 2012 CSS benchmark [35, 4], we define three different incremental scenarios: adding one class (18-1), adding five classes simultaneously (14-5) and sequentially (14-1). Take 14-5 setting for instance, the last five rare classes, i.e., counter, refrigerator, bookshelf, bathtub, shower curtain, form the novel class set, and likewise for the other settings.", + "bbox": [ + 496, + 369, + 890, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We form the training set by including all the scenes that contain at least one point from the novel classes at the current step, with the others (either previous or future classes) annotated as \"other furniture\". The validation set is established in a similar way except that the label of the previous classes $\\mathcal{C}^{0:t-1}$ are maintained, as the model is required to predict all seen classes up to the current step. Finally, we report the old-, new- and all-class mIoU metrics as well as the background IoU at the end of all incremental steps.", + "bbox": [ + 496, + 686, + 890, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Baselines and Setups", + "text_level": 1, + "bbox": [ + 500, + 832, + 694, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To validate the effectiveness of our approach, we conduct thorough comparison with the latest state-of-the-art CSS methods as well as baselines. FT is a straightforward", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18605", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8e20b00d4cbaca6114da3fa18b73c1377263746772e3341beaaab61db876920c.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Continual Semantic Segmentation performance (mIoU) on Pascal-VOC 2012 under different incremental scenarios. † indicates the results are excerpted from [4]. * suggests the results are reproduced with the official codes. 0 stands for the background class and all represents the mIoU over all classes including the background. Best results are highlighted in Red while runner-up in Blue." + ], + "table_body": "
Method19-1 (2 steps)15-5 (2 steps)15-1 (6 steps)
01-1920all01-1516-20all01-1516-20all
FT†-6.812.9--2.133.1--0.21.8-
EWC† [26]-26.914.0--24.335.5--0.34.3-
LwF-MC† [40]-64.413.3--58.135.0--6.48.4-
ILT† [35]-67.112.3--66.340.6--4.97.8-
ILT* [35]88.666.28.364.589.265.238.159.977.73.77.98.2
SDR* [36]90.068.924.267.890.176.650.971.183.934.113.031.5
REIMINDER* [37]91.975.633.974.490.275.149.169.683.365.227.057.0
SPPA [28]--36.274.6--52.972.1--23.356.0
MiB† [4]-70.222.1--75.549.4--35.113.5-
MiB* [4]90.371.523.270.189.674.246.368.383.238.013.934.5
LGKD+MiB (Ours)91.472.140.471.591.675.254.871.179.739.317.035.9
PLOP* [13]92.175.336.174.289.774.247.568.684.764.621.055.2
LGKD+PLOP (Ours)92.976.542.975.791.478.756.173.989.369.330.961.1
RCIL* [61]90.173.624.572.188.975.948.470.083.967.923.158.0
LGKD+RCIL (Ours)92.876.537.575.591.477.654.372.789.469.029.160.5
Joint93.777.678.178.493.779.073.678.493.779.073.678.4
", + "bbox": [ + 101, + 88, + 870, + 328 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "lower-bound baseline, which simply finetunes the model with the newly available data at each step. On the contrary, Joint, training a standard segmentation model on all classes within a single step, may serve as an upper bound for CSS approaches, though not always true if the CSS benchmark shows a long-tail nature with tail classes as new classes (e.g., ScanNet). For completeness, we include two general continual learning methods [26, 40] that are not specifically designed for semantic segmentation. Further, we mainly benchmark against the recent state-of-the-art methods taylored for segmentation [35, 4, 13, 36, 37, 61]. Following [4], we do not consider replay-based methods, e.g., [40]) in our comparison as the access to previous annotated data violates the standard class-incremental learning assumption. For the sake of generalization, we conduct experiments on both 2D image modality, i.e., Pascal-VOC 2012 [15] and ADE20K [66], and 3D point cloud modality, i.e. ScanNet [11]. Besides the old-, new- and all-class (including the background class) mIoU, we additionally report the background IoU because it is a special category under CSS with its semantic content varying across different learning steps.", + "bbox": [ + 75, + 396, + 472, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CSS protocols. As for the label masking policy for the incremental steps, [4] follows and adapts two different CSS protocols, namely disjoint [35] and overlapped [43]. Both protocols assume that only the novel classes at the current step are labeled while the others are masked out as background. However, in the disjoint protocol, input samples for step $t$ should only contain elements (i.e., pixels or points) that belong to either current or previous classes, i.e., $\\mathcal{C}^{0:t}$ . On the contrary, the overlapped protocol allows the input samples to contain either previous, current or future classes, i.e., $\\mathcal{C}^{0:T}$ . The disjoint protocol makes a strong assumption that the current training data should not contain any samples", + "bbox": [ + 75, + 719, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of the class we would like to learn in the future, which is impracticable. Therefore, we adopt the more realistic overlapped protocol throughout our experiments.", + "bbox": [ + 496, + 396, + 890, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 450, + 718, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In 2D image modality, we follow the framework DeepLabv3 [7] and training hyperparameters of the baselines when building our LGKD upon them, except that we adopt synchronized batch normalization with different batch size and learning rate settings. In 3D point cloud modality, we use PointNet++ [39] with multi-scale grouping as our base model. We use Adam [25] with an initial learning rate $10^{-2}$ for the first step and $5 \\times 10^{-3}$ for the subsequent steps and set the weight decay to 0. The learning rate is decayed by 0.7 every 100 epochs. We train our network for 500 epochs with a batch size of 32. We remove possible duplicated points before calculating the IoU metric. For all benchmarks, we report the mIoU results on the standard validation set. We run our experiments on two NVIDIA RTX 3090 GPUs for Pascal VOC 2012 and ADE20K while one for ScanNet. More details can be found in the supp. material.", + "bbox": [ + 496, + 473, + 890, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Performance", + "text_level": 1, + "bbox": [ + 500, + 738, + 635, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pascal-VOC 2012 consists of 10,582 images for training and 1449 images for validation with 20 foreground categories. Following [4], we conduct three different continual learning scenarios, i.e., adding one class (19-1), five classes simultaneously (15-5) and sequentially (15-1). The split of the class set for each class-incremental step follows the alphabetical order. Table 1 shows comprehensive results of our method along with other baselines. Clearly, FT performs poorly across all the incremental settings as the old", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18606", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/49553776dc6888e2ad3b0fc771d9019bd0f0290b9c3e9e8191daa66ebe224107.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method100-50 (2 steps)100-10 (6 steps)50-50 (3 steps)
01-100101-150all01-100101-150all01-5051-150all
ILT† [35]10.918.414.417.08.50.03.11.18.63.412.99.7
MiB† [4]19.740.717.232.80.038.611.129.20.046.521.029.3
REMINDER* [37]26.642.116.133.424.038.920.332.624.248.020.129.4
SPPA [28]-42.919.9--41.012.5--49.823.9-
PLOP* [13]26.742.114.632.923.939.414.531.124.548.220.729.8
LGKD+PLOP (Ours)27.443.625.737.526.042.122.035.425.349.429.436.0
RCIL* [61]26.341.717.333.50.037.214.929.521.247.823.031.2
LGKD+RCIL (Ours)26.743.325.137.224.042.220.434.925.749.127.234.4
Joint29.142.628.237.729.142.628.237.729.149.232.137.7
", + "bbox": [ + 81, + 88, + 888, + 250 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dc850b93113b3d64538e2e5ad3dfb14299c416837475f7797d36c96aaffa76cc.jpg", + "table_caption": [ + "Table 2. The mIoU(%) of the last step on the ADE20K dataset for different overlapped continual learning scenarios. $\\dagger$ indicates the results are excerpted from [13]. * suggests the results are reproduced with the official codes. Best results are highlighted in Red while runner-up in Blue." + ], + "table_footnote": [], + "table_body": "
Method18-1 (2 steps)14-5 (2 steps)14-1 (6 steps)
01-1819all01-1415-19all01-1415-19all
FT19.20.028.62.418.60.044.312.019.20.07.82.9
ILT [35]23.814.925.815.926.722.243.427.719.30.018.55.6
MiB [4]55.155.032.253.852.957.845.554.545.556.529.749.2
LGKD+MiB (Ours)55.255.540.854.854.357.649.055.351.955.738.451.2
Joint53.255.040.954.253.256.747.554.253.256.747.554.2
", + "bbox": [ + 81, + 301, + 888, + 405 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Continual Semantic Segmentation performance (mIoU) on ScanNet under different incremental scenarios. $\\theta$ stands for the background class and all represents the mIoU over all classes including the background. All results are obtained with our implementation.", + "bbox": [ + 76, + 406, + 890, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "class pixels are masked as background under CSS setup, and the model is explicitly taught to wrongly predict the old classes as background. EWC [26] yields similar results for novel classes while fairly outperforming the FT baseline in terms of base mIoU. Significant improvement on base classes across all settings can be observed when knowledge distillation is introduced in [40, 35]. MiB [4] obtains consistent improvement on both base and novel performance across different settings, due to addressing the background shift problem in CSS. Recent approaches [14, 61] obtain drastically higher performance against MiB when multiple incremental steps are involved (15-1). Despite their promising performance, our LGKD is able to further boost their performance by a large margin, especially on novel performance. For instance, LGKD+MiB achieves $+74\\%$ (40.4 vs. 23.2) improvement against MiB on novel mIoU under 19-1 setting. These promising novel class results along with the improved background performance prove that our LGKD loss can effectively alleviate the novel-background confusion problem.", + "bbox": [ + 75, + 458, + 472, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ADE20K [67] is a challenging dataset consisting of 20,210 training and 2000 testing images of complex scenes. Similar to VOC, we conducted three different CSS scenarios, i.e., 100-50, 100-10 and 50-50, as shown in Table 2. Specifically, we build our LGKD upon two competitive methods, i.e., PLOP [13] and RCIL [61], where LGKD achieves considerable improvement, especially on novel mIoU (up to $+76\\%$ from 14.6 to 25.7 with PLOP under 100-50 setting), setting new state-of-the-art across all incremental scenarios.", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ScanNet. As shown in Table 3, we compare our method with FT baseline, ILT [35] and MiB [4] on our proposed ScanNet benchmark to illustrate the generality of LGKD in 3D modality. Similar to their performance in 2D modality, FT and ILT suffer from catastrophic forgetting when learning new classes. However, MiB significantly outperforms the former methods across all three settings and metrics, in particular, the base class performance, which once again demonstrates the effectiveness of tackling the background shift in CSS. Compared with MiB, our LGKD further improves the novel performance by a large margin: $+27\\%$ (40.8 vs. 32.2) and $+29\\%$ (38.4 vs. 29.7) relative improvement of novel mIoU against MiB are obtained under 18-1 and 14-1 settings respectively, which proves the considerable importance of overcoming the background shift with correct class correspondence. It is also noteworthy that our approach also outperforms joint training, which shows that LGKD is also effective in alleviating long-tail issues.", + "bbox": [ + 496, + 458, + 890, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 738, + 653, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Unless otherwise stated, all ablative studies are conducted upon VOC 15-5 setting with PLOP [13] as the baseline. Refer to the supp. material for the rationale.", + "bbox": [ + 496, + 760, + 890, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Expand & Transplant. We compare three different designs for novel set distillation in Table 5. Firstly, One-hot is a hard-label distillation with all the class probabilities transplanted to the ground truth novel class, making the probability of the ground truth class equal to one. In this case, the distillation loss is equivalent to the standard one-hot cross", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18607", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8bf54184ea3c6ef69c3468d5ef88540764c7263aa98497c36dc727e5d8a6dc40.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
VOC 15-5 (2 steps)VOC 15-1 (6 steps)
01-1516-20all01-1516-20all
PLOP [13]89.774.247.568.684.764.621.055.2
+Standard KD [35]90.774.449.269.288.466.413.454.8
+Unbiased KD [4]90.277.151.871.786.367.122.657.4
+LGKD (Ours)91.478.756.173.989.369.330.961.1
ADE20k 100-50 (2 steps)ADE20k 100-10 (6 steps)
01-100101-150all01-100101-150all
PLOP [13]26.742.114.632.923.939.414.531.1
+Standard KD [35]27.442.513.632.823.239.813.531.0
+Unbiased KD [4]27.042.614.533.223.739.815.131.5
+LGKD (Ours)27.443.625.737.526.042.122.035.4
", + "bbox": [ + 163, + 88, + 810, + 263 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0fe51e8aff0ad7785689832e9c561f338211753f961dee1951db50c4c136b66c.jpg", + "table_caption": [ + "Table 4. Effect of different knowledge distillation terms. Standard KD is adopted in ILT [35] while unbiased KD is adopted in MiB [4]." + ], + "table_footnote": [], + "table_body": "
01-1516-20all
One-hot91.476.751.971.5
Expand only90.478.530.967.7
Expand & Transplant91.478.756.173.9
", + "bbox": [ + 91, + 300, + 459, + 363 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/91f187122e7207ce24e5f6b8b7e3bbfa34290db23a8d2cbe8fef44321564ae96.jpg", + "table_caption": [ + "Table 5. Effect of our novel set distillation design including expand and transplant operations." + ], + "table_footnote": [], + "table_body": "
λbλn01-1516-20all
0090.575.553.671.0
1091.376.953.171.9
2091.677.353.172.2
5091.877.952.072.4
10091.878.349.872.2
50.591.678.655.773.8
5191.478.756.173.9
5291.078.655.573.7
", + "bbox": [ + 120, + 410, + 429, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Effect of the weighted factors ${\\lambda }_{n}$ and ${\\lambda }_{\\mathrm{b}}$ .", + "bbox": [ + 124, + 549, + 419, + 560 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "entropy loss, discarding all the old class probabilities predicted by the old model. As expected, the base performance is slightly compromised compared with Expand & Transplant since the old class knowledge is not distilled. Nevertheless, the novel performance also drops since using hard labels for the novel class pixels will develop a bias toward novel classes, resulting in false positive predictions. This illustrates the significance of retaining the old class probabilities during transplant. Secondly, Expand only will encourage the new model to misclassify a novel class into either background or an old class. Thus, a sharp drop in novel mIoU from 56.1 to 30.9 is observed. This uncovers the importance of correcting the old model output by transplant to handle the background shift. Finally, transplanting the background probability into the corresponding ground truth novel class while retaining the old class probabilities can establish an appropriate class correspondence and facilitate learning new classes, hence yielding the best novel performance.", + "bbox": [ + 75, + 590, + 468, + 878 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Weighted factor. As table 6 shows, increasing $\\lambda_{\\mathrm{b}}$ leads to", + "bbox": [ + 76, + 885, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "higher base performance, but it will compromise the novel performance when $\\lambda_{\\mathrm{b}}$ becomes too large, e.g., $\\lambda_{\\mathrm{b}} = 10$ . It indicates that the background set distillation is mainly responsible for retaining old knowledge. We set $\\lambda_{\\mathrm{b}} = 5$ as the optimal solution as it obtains promising base mIoU while not sacrificing the novel mIoU severely. With the novel set distillation kicking in, the novel mIoU is significantly improved from 52.0 to 56.1 with $\\lambda_{n} = 1$ . Meanwhile, it also boosts the base mIoU from 77.9 to 78.7. This suggests that the novel set distillation facilitates learning new classes while maintaining the old class knowledge distilled from the old model.", + "bbox": [ + 496, + 301, + 890, + 482 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of different KDs. To validate the superiority of LGKD, we compare our LGKD with other knowledge distillation (KD) terms on both VOC and ADE20k upon the same baseline PLOP [13] (Fig. 4), since PLOP does not adopt class probability-wise KD. Firstly, PLOP can hardly benefit from adding the standard KD [35], probably due to its tendency to misclassify new classes as the background (see Sec. 3.2). Secondly, though unbiased KD [4] yields a moderate boost on VOC, it makes almost no difference on the more challenging benchmark ADE20k. In contrast, LGKD consistently surpasses standard KD and unbiased KD by a significant margin, especially in terms of novel mIoU. Concretely, LGKD yields $+8.3 / +11.2 / +6.9$ points improvement against unbiased KD on 15-1/100-50/100-10 setting.", + "bbox": [ + 496, + 487, + 890, + 714 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Error Analysis", + "text_level": 1, + "bbox": [ + 500, + 722, + 650, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We carry out comprehensive error analysis on both Pascal-VOC 2012 and ScanNet datasets to validate the effectiveness of our LGKD in mitigating the novel-background confusion problem.", + "bbox": [ + 496, + 746, + 890, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "2D image. As Fig. 4 shows, under the VOC 15-5 incremental scenario, naive finetuning completely forgets the old class bird while also mistaking the background for the novel class potted plant. Thanks to KD mechanism, ILT [35], REMINDER [37], MiB [4], PLOP [13] and RCIL [61] are capable to retain the old knowledge (bird and chair). Nev", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18608", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5b46f10fce6c80ead65967ac3a82345c812a9e7b6fe052777680b2c8a4d37ab7.jpg", + "image_caption": [ + "Old classes: bird chair", + "New classes: potted plant Sofa", + "Figure 4. Error analysis of baselines along with our LGKD under VOC 15-5 setting. MiB [4], PLOP [13] and RCIL [61] tend to mistake weed and suitcase (background—things of no interest) for potted plant and sofa (novel classes) respectively. Such confusion is effectively alleviated when equipped with our LGKD, except for the bird image with RCIL, where the confusion is slightly mitigated." + ], + "image_footnote": [], + "bbox": [ + 84, + 88, + 767, + 375 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/a0cad4b3110eedc47cfa79b7f07cf95012dbbc554e649b9e231d0e4f5a22cb39.jpg", + "image_caption": [ + "Figure 5. Error analysis of MiB [4] vs. LGKD+MiB on step 4 (with bathtub depicted in pink as the novel class) of the ScanNet 14-1 incremental scenario. Our LGKD effectively alleviates the confusion made by MiB (see the black boxes) — mistaking the background (dark purple) for the novel class bathtub. Meanwhile, LGKD+MiB achieves decent accuracy on the novel class bathtub (see the red boxes)." + ], + "image_footnote": [], + "bbox": [ + 81, + 441, + 468, + 565 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ertheless, these methods are consistently prone to misclassifying the background (weed and suitcase—things of no interest) as novel classes (potted plant and sofa). On the contrary, when incorporating our LGKD into MiB, PLOP and RCIL, the above novel-background confusion is effectively suppressed, except for the bird image with RCIL, where the confusion is slightly alleviated. The above examples demonstrate the effectiveness of LGKD in tackling the novel-background confusion issue. More visualization results can be found in the supp. material.", + "bbox": [ + 75, + 696, + 468, + 849 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "3D point cloud. We show the error results in Fig. 5 for step 4 of the ScanNet 14-1 setting, where the current novel class is bathtub depicted in pink. Clearly, our method effic", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "tively corrects the false prediction made by MiB [4] (see the black boxes), where the background points (highlighted in dark purple) are mistaken for the novel class bathtub. Meanwhile, our LGKD does not sacrifice the capability to recognize the true bathtub points (see red boxes).", + "bbox": [ + 496, + 445, + 893, + 521 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 532, + 619, + 547 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we identify a key issue in continual semantic segmentation (CSS)—novel background confusion. This is generally caused by the corrupted class correspondence during knowledge distillation. To alleviate such confusion, we propose a novel solution termed Label-Guided Knowledge Distillation (LGKD), which can establish an appropriate class correspondence between the output of the old and the new model for distillation, guided by the ground truth label. We validate its effectiveness on both existing 2D benchmarks and our proposed 3D CSS benchmark, where LGKD can consistently outperform competing methods by a large margin, especially on novel mIoU, setting new state-of-the-art. Finally, we hope this work will inspire further in-depth exploration of 3D CSS in the future.", + "bbox": [ + 496, + 558, + 893, + 770 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 781, + 679, + 797 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by the Hyundai research grant (04OIS000252C130).", + "bbox": [ + 500, + 806, + 893, + 835 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 847, + 596, + 863 + ], + "page_idx": 8 + }, + { + "type": "ref_text", + "text": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware", + "bbox": [ + 506, + 872, + 892, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "18609", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "synapses: Learning what (not) to forget. In ECCV, 2018. 3", + "[2] Rahaf Aljundi, Punarjay Chakravarty, and Tinne Tuytelaars. Expert gate: Lifelong learning with a network of experts. 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Cylindrical" + ], + "bbox": [ + 78, + 90, + 467, + 898 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "and asymmetrical 3d convolution networks for lidar segmentation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9939-9948, 2021. 2", + "bbox": [ + 535, + 92, + 890, + 146 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "18612", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/3a801de3-50c8-469a-b26b-c00f633cc663_model.json b/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/3a801de3-50c8-469a-b26b-c00f633cc663_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7dc38a89b4199641e7ca83aa4824a117f1a5b7cc --- /dev/null +++ b/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/3a801de3-50c8-469a-b26b-c00f633cc663_model.json @@ -0,0 +1,2325 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.112, + 0.868, + 0.158 + ], + "angle": 0, + "content": "Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds" + }, + { + "type": "text", + "bbox": [ + 0.233, + 0.185, + 0.744, + 0.221 + ], + "angle": 0, + "content": "Ze Yang\\(^{1}\\), Ruibo Li\\(^{1}\\), Evan Ling\\(^{2}\\), Chi Zhang\\(^{1}\\), Yiming Wang\\(^{1}\\), Dezhao Huang\\(^{2}\\), Keng Teck Ma\\(^{2}\\), Minhoe Hur\\(^{3}\\), Guosheng Lin\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.222, + 0.856, + 0.275 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Computer Science and Engineering, Nanyang Technological University, Singapore \n\\(^{2}\\)Hyundai Motor Group Innovation Center in Singapore (HMGICS) \n\\(^{3}\\)AIRS Company, Hyundai Motor Group" + }, + { + "type": "text", + "bbox": [ + 0.121, + 0.278, + 0.848, + 0.293 + ], + "angle": 0, + "content": "ze001@e.ntu.edu.sg, evan.ling@hmgics.com, minhoe.hur@hyundai.com, gslin@ntu.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.343 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.474, + 0.798 + ], + "angle": 0, + "content": "Continual semantic segmentation (CSS) aims to extend an existing model to tackle unseen tasks while retaining its old knowledge. Naively fine-tuning the old model on new data leads to catastrophic forgetting. A common solution is knowledge distillation (KD), where the output distribution of the new model is regularized to be similar to that of the old model. However, in CSS, this is challenging because of the background shift issue. Existing KD-based CSS methods continue to suffer from confusion between the background and novel classes since they fail to establish a reliable class correspondence for distillation. To address this issue, we propose a new label-guided knowledge distillation (LGKD) loss, where the old model output is expanded and transplanted (with the guidance of the ground truth label) to form a semantically appropriate class correspondence with the new model output. Consequently, the useful knowledge from the old model can be effectively distilled into the new model without causing confusion. We conduct extensive experiments on two prevailing CSS benchmarks, Pascal-VOC and ADE20K, where our LGKD significantly boosts the performance of three competing methods, especially on novel mIoU by up to \\(+76\\%\\), setting new state-of-the-art. Finally, to further demonstrate its generalization ability, we introduce the first CSS benchmark for 3D point cloud based on ScanNet, along with several re-implemented baselines for comparison. Experiments show that LGKD is versatile in both 2D and 3D modalities without requiring ad hoc design. Codes are available at https://github.com/Ze-Yang/LGKD." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.824, + 0.21, + 0.84 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.85, + 0.47, + 0.881 + ], + "angle": 0, + "content": "Fully supervised semantic segmentation has witnessed tremendous success [33, 63, 27, 8, 16, 22, 47, 65, 9] in re" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.325, + 0.892, + 0.573 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.575, + 0.895, + 0.732 + ], + "angle": 0, + "content": "Figure 1. Illustration of knowledge distillation (KD) strategies in continual semantic segmentation. Standard KD and unbiased KD reduce the new class (bicycle) dimension(s) of the probabilities output by the new model via remove and combine respectively, which collapses the class correspondence across incremental steps and raises confusion between background and new classes (see Sec. 1). In contrast, our label-guided KD uses the ground truth label as guidance to expand the probabilities predicted by the old model. It builds a reliable class correspondence across different learning steps without discrepancy (ILT) or entanglement (MiB) (see Sec. 3.2). A \\(\\xrightarrow{\\text{mimic}}\\) B: encourage A to be similar to B." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "cent years. These algorithms generally assume a fixed number of classes to be learned. However, in real-world applications, it is often expected that a deployed model can be continuously generalized to handle new classes while not forgetting the old ones. A simple solution is to expand the original dataset with newly available samples and retrain a new model from scratch, dubbed as Joint Training. Obviously, this is computationally expensive and requires an increasing amount of space to store the old data over time." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.303, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: Guosheng Lin" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18601" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "Further, it may raise privacy issues in some circumstances, e.g., medical images and face data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.124, + 0.47, + 0.29 + ], + "angle": 0, + "content": "To address this problem, continual semantic segmentation (CSS) has been proposed by [35] as an emerging research direction, where the training scheme is separated into several steps with each step tackling a set of unseen classes. Specifically, given the old model and new training data (only new classes are labeled while others are treated as background), the new model is supposed to recognize both old and new classes. Under this scenario, naively finetuning the old model on new data tends to suffer from catastrophic forgetting [17, 26], where the recognition capability of old classes is quickly lost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.471, + 0.519 + ], + "angle": 0, + "content": "Knowledge distillation (KD), first proposed in image classification [19], has recently been introduced to CSS [35, 4] to mitigate the forgetting issue. As Fig. 1 shows, \\(ILT\\) [35] removes new class probabilities (green bar) predicted by the new model, and simply distill old classes and background accordingly. However, they ignore the background shift problem [4], where the new class bicycle at current step \\(t\\) was labeled as background at last step \\(t - 1\\). As a result, the old model, which regards bicycle as background, will output a high background score for the new class bicycle pixels. Via KD, it will mislead the new model to misclassify new classes as background. Obviously, this KD strategy hinders the learning of new classes because the class correspondence for distillation is corrupted, i.e., naively mapping the new background to the old background." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.469, + 0.688 + ], + "angle": 0, + "content": "This issue was highlighted in \\(MiB\\) [4] where they proposed a new class correspondence by combination. Concretely, they combined new classes with the new background via probability summation (Fig. 1) to form a pseudo class, which was treated as the counterpart to the old background for distillation. However, this strategy, though alleviating class mis-correspondence, entangles new classes with the new background and tends to misclassify background as new classes, as detailed in Sec. 3.2. In this paper, we term the error of mistaking background for new (novel) classes or vice-versa as novel-background confusion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The key insight to overcome the novel-background confusion is to build a reliable class correspondence across different learning steps without corruption or entanglement. To this end, we devise a novel Label-Guided Knowledge Distillation (LGKD) loss, where the class probabilities predicted by the old model are expanded to have the same dimension as the output of the new model (see the blue block in Fig. 1). The background probability is then transplanted to the corresponding ground truth label (class) of the input pixels. In this way, the knowledge from the old background at the last step can be correctly distilled into its corresponding semantic class at the current step, i.e., either the new background or a novel class. Note that our LGKD is a generic regularization term with negligible computa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "tional cost and can be easily incorporated into existing arts. We validate its effectiveness on two prevailing CSS benchmarks Pascal-VOC and ADE20K, where our LGKD consistently yields promising improvements upon three competing methods, especially on novel (new class) mIoU (up to \\(+76\\%\\)), setting new state-of-the-art. To further demonstrate the generalization ability of our approach, we establish a challenging CSS benchmark based on ScanNet for 3D point cloud and re-implement multiple baselines for comparison. To our best knowledge, this is the first work to conduct CSS on 3D point cloud. Extensive experiments showcase that our LGKD loss is capable to handle both 2D and 3D modalities with no ad hoc design." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.291, + 0.892, + 0.307 + ], + "angle": 0, + "content": "The main contributions of this paper can be summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.316, + 0.892, + 0.377 + ], + "angle": 0, + "content": "- We propose a new label-guided knowledge distillation (LGKD) loss for CSS, which builds a reliable class correspondence across incremental steps and alleviates novel-background confusion." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.386, + 0.892, + 0.492 + ], + "angle": 0, + "content": "- LGKD is a generic regularization term with negligible computational cost, which can be readily combined with existing methods. Extensive experiments on two prevailing CSS benchmarks, Pascal-VOC and ADE20K, showcase that LGKD significantly improves three competitive methods, particularly on novel mIoU by up to \\(+76\\%\\), setting new state-of-the-art." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.502, + 0.892, + 0.593 + ], + "angle": 0, + "content": "- To further demonstrate its generalization capability, we establish the first CSS benchmark for 3D point cloud based on ScanNet and re-implement multiple baselines for comparison. Experiments illustrate that our LGKD is versatile in both 2D and 3D modalities without any ad hoc design." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.316, + 0.892, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.615, + 0.65, + 0.631 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Semantic Segmentation, aiming to perform pixel-level classification, has witnessed great advancement [63, 6, 7, 53, 22, 16] in recent years since the pioneering work Fully Convolutional Network (FCN) [33]. Among the above methods, the DeepLab series [6, 7] is well-known for their effective designs, e.g., atrous spatial pyramid pooling (ASPP) [6], atrous convolution in cascade [7]. DeepLabv3 [7] is commonly used as the segmentation framework in prior CSS works [4, 13, 61]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In 3D point cloud modality, PointNet [38] is a pioneering work to directly process unstructured point cloud. Subsequent work PointNet++ [39] learns to capture local structures and recognize fine-grained patterns via a hierarchical neural network that applies PointNet recursively. While more complicated techniques have been proposed in recent works [46, 45, 62, 68, 10], we employ PointNet++ as our 3D segmentation model for its simplicity and efficiency." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18602" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.358, + 0.895, + 0.442 + ], + "angle": 0, + "content": "Figure 2. Illustration of our LGKD loss. At learning step \\( t \\), an input sample \\( x \\) is fed into the old (top) and new (bottom) models to obtain the class probabilities for each element \\( i \\in \\mathcal{I} \\) (pixel or point). These elements are then separated into the novel and background sets according to their ground truth label available at the current step \\( t \\) (yellow and green as novel set). Finally, to build up a reliable class correspondence, we extend the old probabilities (output by the old model) to have the same dimension as the new ones by expand and transplant (for novel set only), such that useful prior knowledge from the old model can be effectively distilled into the new model to facilitate learning new classes. We highlight that our LGKD can effectively alleviate the novel-background confusion issue as occurs in [35, 4]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.473, + 0.707 + ], + "angle": 0, + "content": "Continual Learning aims at training a deep neural network to learn multiple tasks in sequence continually. Distinct from one-step incremental learning [50, 51, 55, 56, 59, 58, 30, 60, 29, 57, 31, 44], continual learning generally confronts more severe forgetting issues during multiple-step learning. Numerous works tackle the catastrophic forgetting issue and they can be classified into three categories. The model growing category [2, 48, 52] tackles this problem by dynamically extending model capacity. The memory replay approaches retain the old-class knowledge by keeping a small amount of old-class data in current training. Those data can be raw data [41, 40, 3], features [18, 23] or generated data [24, 42, 32]. The regularization approaches constrain the model by regularizing the parameters [26, 1, 54], the gradients [21, 5], logits [40, 3, 4] or the features [20, 12, 14] of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Continual Semantic Segmentation. Existing CSS methods can be divided into two categories: 1) replay-based. RECALL [34] rehearses old-class data obtained by web-crawling or generative models. Similarly, [49] utilizes an iterative relabeling strategy with rehearsal-based incremental learning. Following [4], replay-based methods are out of the scope of this paper since accessing old data violates the conventional CSS assumption. 2) regularization-based. ILT [35] is the first work to introduce KD into CSS. MiB [4] raises the background shift problem in CSS and proposes an unbiased KD to tackle it. PLOP [13] distills both short- and long-range spatial relations via local pooled output distilla" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.895, + 0.648 + ], + "angle": 0, + "content": "tion. SDR [36] leverages prototype matching, feature sparsification and contrastive learning to enforce feature consistency and discrimination. Most recently, class similarity KD, representation compensation, structure-preserving loss and feature projection, and the biased context are investigated by REMINDER [37], RCIL [61], SPPA [28] and RBC [64] respectively. However, the above approaches tend to suffer from the novel-background confusion problem since their distillation term lacks an appropriate class correspondence. Therefore, we propose a generic distillation term, dubbed LGKD, with a reliable class correspondence to alleviate this confusion issue." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.593, + 0.683 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.771, + 0.711 + ], + "angle": 0, + "content": "3.1. Problem Definition and Setups" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Before introducing the continual learning setting, we first present the setups of the standard semantic segmentation task. To ensure the generality, let \\(\\mathcal{X} \\in \\mathbb{R}^{N \\times C_{\\mathrm{in}}}\\) denote the input space (e.g., image, point cloud, etc.), where \\(N\\) is the number of input elements and \\(C_{\\mathrm{in}}\\) is the number of input channels (typically \\(C_{\\mathrm{in}} = 3\\), i.e., RGB, for image and \\(C_{\\mathrm{in}} >= 3\\), e.g., XYZ, RGB, normals, for point cloud). Let \\(\\mathcal{Y} \\in \\mathcal{C}^N\\) denote the output label space, where \\(\\mathcal{C}\\) is a label set that contains all classes including the background class \\(\\mathsf{b} \\in \\mathcal{C}\\). Note that each sample \\(x \\in \\mathcal{X}\\) comprises a set of elements \\(\\mathcal{I}\\) (e.g., pixels, points, etc.) of corresponding label \\(y \\in \\mathcal{Y}\\) with constant cardinality \\(|\\mathcal{I}| = N\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18603" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "Given a training set \\(\\mathcal{T} \\subset \\mathcal{X} \\times \\mathcal{Y}\\), the target of semantic segmentation is to learn a model \\(f_{\\theta}\\) parametrized by \\(\\theta\\) that maps the input space \\(\\mathcal{X}\\) to a set of class probability vectors \\(f_{\\theta}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}|}\\). The output segmentation mask is then computed as \\(\\hat{y} = \\{\\arg \\max_{c \\in \\mathcal{C}} f_{\\theta}(x)[i, c]\\}_{i=1}^{N}\\), where \\(f_{\\theta}(x)[i, c]\\) is the probability of element \\(i\\) belonging to category \\(c\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.471, + 0.458 + ], + "angle": 0, + "content": "As opposed to the standard training scheme where the model can access and learn from the full training set \\(\\mathcal{T} \\subset \\mathcal{X} \\times \\mathcal{C}^N\\) all at once, continual learning, instead, involves several learning steps \\(\\{t\\}_{t=0}^{T}\\) each with a subset of label \\(\\mathcal{C}^t\\). More specifically, at training step \\(t\\), the previous label set \\(\\mathcal{C}^{0:t-1}\\) will be expanded with a set of unseen classes \\(\\mathcal{C}^t\\) to form a new label set \\(\\mathcal{C}^{0:t} = \\mathcal{C}^{0:t-1} \\cup \\mathcal{C}^t\\). Then a training set \\(\\mathcal{T}^t \\subset \\mathcal{X} \\times (\\mathcal{C}^t)^N\\) will be provided along with the last model \\(f_{\\theta^{t-1}}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}^{0:t-1}|}\\) to obtain an updated model \\(f_{\\theta^t}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}^{0:t}|}\\). Note that the training set \\(\\mathcal{T}^t\\) may contain element \\(i \\in \\mathcal{I}\\) from either previous classes \\(\\mathcal{C}^{0:t-1}\\) or future classes \\(\\mathcal{C}^{t+1:T}\\), though the annotations are collapsed into the background class \\(b\\) at the current step \\(t\\). This is referred to as overlapped [4] setting. Following the standard incremental setup, we assume that the label sets of each step are disjoint from each other except for the special background class, i.e., \\(\\mathcal{C}^i \\cap \\mathcal{C}^j = b\\) (\\(i \\neq j\\))." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.467, + 0.41, + 0.483 + ], + "angle": 0, + "content": "3.2. Revisiting Knowledge Distillation Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.581 + ], + "angle": 0, + "content": "A naive way to tackle the continual learning problem is to initialize a new model \\( f_{\\theta^t} \\) with the weights of the last model \\( f_{\\theta^{t-1}} \\) and then optimize the network with the training set \\( \\mathcal{T}^t \\). However, this will lead to the catastrophic forgetting of old classes \\( \\mathcal{C}^{0:t-1} \\). Since no old class samples with annotation are available at the current step." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.47, + 0.691 + ], + "angle": 0, + "content": "Standard knowledge distillation. To alleviate the forgetting problem, knowledge distillation [19] is a common solution to preserve old knowledge by regularizing the output class probability distribution of the new model \\( f_{\\theta^t} \\) to be close to that of the old model \\( f_{\\theta^{t-1}} \\) given the same input sample. Formally, the standard knowledge distillation loss \\( \\ell_{\\mathrm{kd}} \\) adopted in CSS by ILT [35] can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.701, + 0.47, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y) = - \\frac {1}{| \\mathcal {I} |} \\sum_ {i \\in \\mathcal {I}} \\sum_ {c \\in \\mathcal {C} ^ {0: t - 1}} q _ {x} ^ {t - 1} (i, c) \\log \\hat {q} _ {x} ^ {t} (i, c), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.749, + 0.47, + 0.781 + ], + "angle": 0, + "content": "where \\(\\hat{q}_x^t (i,c)\\) refers to the probability of class \\(c\\) for element \\(i\\) predicted by \\(f_{\\theta^t}\\) but re-normalized over all old classes:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.792, + 0.469, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\hat {q} _ {x} ^ {t} (i, c) = q _ {x} ^ {t} (i, c) / \\sum_ {k \\in \\mathcal {C} ^ {0: t - 1}} q _ {x} ^ {t} (i, k). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "However, there exists a discrepancy issue in the standard distillation loss. Concretely, it fails to leverage prior knowledge to cope with the new classes, as the new class probabilities \\( q_{x}^{t}(i,c) \\) (\\( c \\in \\mathcal{C}^t \\setminus b \\)) are not incorporated in distillation (Eq. 1). Moreover, it wrongly enhances the background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "probability for novel class elements due to the background shift [4]. Hence, it tends to mistake the novel classes for the background (refer to supp. material for detailed discussion)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.14, + 0.892, + 0.187 + ], + "angle": 0, + "content": "Unbiased knowledge distillation. To overcome the above issue, MiB [4] proposes an unbiased knowledge distillation loss for CSS by revising \\(\\hat{q}_x^t (i,c)\\) in Eq. 2 as:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.195, + 0.892, + 0.236 + ], + "angle": 0, + "content": "\\[\n\\hat {q} _ {x} ^ {t} (i, c) = \\left\\{ \\begin{array}{l l} q _ {x} ^ {t} (i, c) & \\text {i f} c \\neq \\mathfrak {b} \\\\ \\sum_ {k \\in \\mathcal {C} ^ {t}} q _ {x} ^ {t} (i, k) & \\text {i f} c = \\mathfrak {b}, \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.893, + 0.456 + ], + "angle": 0, + "content": "where they compare the old background probability \\( q_{x}^{t - 1}(i,\\mathsf{b}) \\) with the probability of being either a novel class or the new background, i.e., \\( \\sum_{k\\in \\mathcal{C}^t}q_x^t (i,k) \\), rather than directly with its counterpart \\( q_{x}^{t}(i,\\mathsf{b}) \\). Such class probability combination mechanism is meant to facilitate distilling the knowledge from the old background class defined at step \\( t - 1 \\) to the novel classes at step \\( t \\). Nevertheless, it entangles the novel classes with the new background due to the probability combination. As a consequence of entanglement, the probabilities of novel classes will be undesirably enhanced when the distillation loss only intends to improve the probabilities of the new background, and vice versa. As opposed to ILT [35], this leads to the other confusion — misclassifying background as novel classes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.463, + 0.822, + 0.48 + ], + "angle": 0, + "content": "3.3. Label-Guided Knowledge Distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.626 + ], + "angle": 0, + "content": "Class separation. Unlike standard KD and unbiased KD, which apply the same KD strategy to all input elements, we propose to separate the input elements into two sets according to the ground truth label available at the current step, namely the background set \\( S_{\\mathsf{b}} = \\{i|i\\in \\mathcal{I},y_i = \\mathsf{b}\\} \\) and the novel set \\( S_{n} = \\{i|i\\in \\mathcal{I},y_{i}\\in \\mathcal{C}^{t}\\setminus \\mathsf{b}\\} \\). In this way, we can customize the distillation strategy for each class set and establish a more accurate class correspondence, which facilitates more effective knowledge distillation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Class correspondence. As opposed to revising the class probabilities of the new model \\( q_{x}^{t}(i,c) \\) as in [4], we instead resort to correcting the class probabilities of the old model \\( q_{x}^{t - 1}(i,c) \\) according to the ground truth label \\( y_{i} \\). Our design is inspired by the wireless communication system. In order to improve the useful information captured by the receiver, one should ensure that the signal released by the transmitter is correct and that both transmitter and receiver share the same communication protocol. Likewise, in our case, the objective is to assure the class probabilities (signal) predicted by the old model \\( f_{\\theta^{t - 1}} \\) (transmitter) contain correct class semantics (after background shift) and are well-aligned with (protocol) the output class space of the new model \\( f_{\\theta^t} \\) (receiver). Protocol: For the elements from the novel set \\( S_{n} \\), we expand the output of the old model \\( q_{x}^{t - 1}(i,c) \\) with zero probability assigned to the extra novel classes \\( c \\in \\mathcal{C}^t \\setminus \\mathbf{b} \\) such that it has the same output class space dimensions with the new model. Signal: Due to the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18604" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "background shift, we transplant the probability of the background to the corresponding ground truth novel class and set the background probability to zero while maintaining the others unchanged. The final corrected probability distribution to be distilled from can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.175, + 0.47, + 0.232 + ], + "angle": 0, + "content": "\\[\n\\bar {q} _ {x} ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} ^ {t} \\text {a n d} c \\neq y _ {i} \\\\ q _ {x} ^ {t - 1} (i, \\mathrm {b}) & \\text {i f} c = y _ {i} \\\\ q _ {x} ^ {t - 1} (i, c) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.242, + 0.469, + 0.348 + ], + "angle": 0, + "content": "where \\( i \\in S_n \\). We highlight that, this novel set distillation strategy can preserve the knowledge from \\( f_{\\theta^{t-1}} \\) for the old classes while also correcting the class probabilities from the old model for the new classes given the ground truth label \\( y_i \\) as guidance. As for the case of the background set \\( i \\in S_b \\), it can be treated in a similar yet simpler way by merely expanding zero probability for the extra novel classes as:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.359, + 0.469, + 0.4 + ], + "angle": 0, + "content": "\\[\n\\bar {q} _ {x} ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} ^ {t} \\backslash \\mathfrak {b} \\\\ q _ {x} ^ {t - 1} (i, c) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.41, + 0.401, + 0.424 + ], + "angle": 0, + "content": "In summary, our distillation loss can be given as:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.434, + 0.469, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y) = \\lambda_ {n} \\cdot \\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S} _ {n}) + \\lambda_ {\\mathfrak {b}} \\cdot \\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S} _ {\\mathfrak {b}}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.465, + 0.469, + 0.51 + ], + "angle": 0, + "content": "where \\(\\lambda_{n}\\) and \\(\\lambda_{\\mathrm{b}}\\) balances the contribution of the novel set \\(S_{n}\\) and background set \\(S_{\\mathrm{b}}\\); \\(\\bar{\\ell}_{\\mathrm{kd}}^{\\theta^{t}}(x,y,\\mathcal{S})\\) is the distillation loss defined within set \\(S\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.518, + 0.469, + 0.555 + ], + "angle": 0, + "content": "\\[\n\\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S}) = - \\frac {1}{N} \\sum_ {i \\in \\mathcal {S}} \\sum_ {c \\in \\mathcal {C} ^ {0: t}} \\bar {q} _ {x} ^ {t - 1} (i, c) \\log q _ {x} ^ {t} (i, c). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.566, + 0.412, + 0.58 + ], + "angle": 0, + "content": "The overall training objective is then computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.591, + 0.469, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\theta^ {t}\\right) = \\frac {1}{\\left| \\mathcal {T} ^ {t} \\right|} \\sum_ {(x, y) \\in \\mathcal {T} ^ {t}} \\left(\\lambda \\ell_ {c e} ^ {\\theta^ {t}} (x, y) + \\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.469, + 0.689 + ], + "angle": 0, + "content": "where \\(\\ell_{ce}^{\\theta^t}(x,y)\\) is the cross-entropy loss. \\(\\lambda\\) is the hyperparameter to balance the importance of the two terms, and is set as \\(\\lambda = 1\\) in experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.702, + 0.201, + 0.719 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.444, + 0.743 + ], + "angle": 0, + "content": "4.1. Benchmarking 3D Continual Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.84 + ], + "angle": 0, + "content": "Existing CSS methods have mainly been evaluated on 2D CSS benchmarks, leaving a significant gap in the exploration of 3D CSS. In order to validate the versatility of LGKD across different modalities, we introduce the first 3D CSS benchmark based on ScanNet [11] and present several baseline methods for comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "ScanNet contains 1201 and 312 indoor scenes in the training and validation set respectively with 20 classes in total, including a special class for \"other furniture\", i.e. background in the standard segmentation task. In Fig. 3, we" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.095, + 0.882, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.318, + 0.892, + 0.346 + ], + "angle": 0, + "content": "Figure 3. The scene-wise class frequency statistics of our proposed ScanNet benchmark for 3D continual semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.892, + 0.687 + ], + "angle": 0, + "content": "provide the scene-wise class frequency statistics of ScanNet [11], including both train and validation sets. The scene-wise class frequency indicates the number of scenes that a certain class appears in. Surprisingly, we find that ScanNet exhibits a challenging long-tail category distribution. Additionally, we provide the point-wise class frequency statistics and demonstrate the difficulty of our proposed benchmark in the supp. material. For a challenging CSS benchmark, we split the entire class set into multiple subsets according to the descending order of scene-wise class frequency as in Fig. 3, with the tail classes constituting the novel sets for continual learning. This means that the novel classes to be learned in each step are set to be those rare ones, a.k.a. tail classes in the long-tail field. Following the Pascal-VOC 2012 CSS benchmark [35, 4], we define three different incremental scenarios: adding one class (18-1), adding five classes simultaneously (14-5) and sequentially (14-1). Take 14-5 setting for instance, the last five rare classes, i.e., counter, refrigerator, bookshelf, bathtub, shower curtain, form the novel class set, and likewise for the other settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.824 + ], + "angle": 0, + "content": "We form the training set by including all the scenes that contain at least one point from the novel classes at the current step, with the others (either previous or future classes) annotated as \"other furniture\". The validation set is established in a similar way except that the label of the previous classes \\(\\mathcal{C}^{0:t-1}\\) are maintained, as the model is required to predict all seen classes up to the current step. Finally, we report the old-, new- and all-class mIoU metrics as well as the background IoU at the end of all incremental steps." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.696, + 0.849 + ], + "angle": 0, + "content": "4.2. Baselines and Setups" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To validate the effectiveness of our approach, we conduct thorough comparison with the latest state-of-the-art CSS methods as well as baselines. FT is a straightforward" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18605" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.089, + 0.871, + 0.329 + ], + "angle": 0, + "content": "
Method19-1 (2 steps)15-5 (2 steps)15-1 (6 steps)
01-1920all01-1516-20all01-1516-20all
FT†-6.812.9--2.133.1--0.21.8-
EWC† [26]-26.914.0--24.335.5--0.34.3-
LwF-MC† [40]-64.413.3--58.135.0--6.48.4-
ILT† [35]-67.112.3--66.340.6--4.97.8-
ILT* [35]88.666.28.364.589.265.238.159.977.73.77.98.2
SDR* [36]90.068.924.267.890.176.650.971.183.934.113.031.5
REIMINDER* [37]91.975.633.974.490.275.149.169.683.365.227.057.0
SPPA [28]--36.274.6--52.972.1--23.356.0
MiB† [4]-70.222.1--75.549.4--35.113.5-
MiB* [4]90.371.523.270.189.674.246.368.383.238.013.934.5
LGKD+MiB (Ours)91.472.140.471.591.675.254.871.179.739.317.035.9
PLOP* [13]92.175.336.174.289.774.247.568.684.764.621.055.2
LGKD+PLOP (Ours)92.976.542.975.791.478.756.173.989.369.330.961.1
RCIL* [61]90.173.624.572.188.975.948.470.083.967.923.158.0
LGKD+RCIL (Ours)92.876.537.575.591.477.654.372.789.469.029.160.5
Joint93.777.678.178.493.779.073.678.493.779.073.678.4
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.33, + 0.894, + 0.375 + ], + "angle": 0, + "content": "Table 1. Continual Semantic Segmentation performance (mIoU) on Pascal-VOC 2012 under different incremental scenarios. † indicates the results are excerpted from [4]. * suggests the results are reproduced with the official codes. 0 stands for the background class and all represents the mIoU over all classes including the background. Best results are highlighted in Red while runner-up in Blue." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.473, + 0.716 + ], + "angle": 0, + "content": "lower-bound baseline, which simply finetunes the model with the newly available data at each step. On the contrary, Joint, training a standard segmentation model on all classes within a single step, may serve as an upper bound for CSS approaches, though not always true if the CSS benchmark shows a long-tail nature with tail classes as new classes (e.g., ScanNet). For completeness, we include two general continual learning methods [26, 40] that are not specifically designed for semantic segmentation. Further, we mainly benchmark against the recent state-of-the-art methods taylored for segmentation [35, 4, 13, 36, 37, 61]. Following [4], we do not consider replay-based methods, e.g., [40]) in our comparison as the access to previous annotated data violates the standard class-incremental learning assumption. For the sake of generalization, we conduct experiments on both 2D image modality, i.e., Pascal-VOC 2012 [15] and ADE20K [66], and 3D point cloud modality, i.e. ScanNet [11]. Besides the old-, new- and all-class (including the background class) mIoU, we additionally report the background IoU because it is a special category under CSS with its semantic content varying across different learning steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.902 + ], + "angle": 0, + "content": "CSS protocols. As for the label masking policy for the incremental steps, [4] follows and adapts two different CSS protocols, namely disjoint [35] and overlapped [43]. Both protocols assume that only the novel classes at the current step are labeled while the others are masked out as background. However, in the disjoint protocol, input samples for step \\( t \\) should only contain elements (i.e., pixels or points) that belong to either current or previous classes, i.e., \\( \\mathcal{C}^{0:t} \\). On the contrary, the overlapped protocol allows the input samples to contain either previous, current or future classes, i.e., \\( \\mathcal{C}^{0:T} \\). The disjoint protocol makes a strong assumption that the current training data should not contain any samples" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.444 + ], + "angle": 0, + "content": "of the class we would like to learn in the future, which is impracticable. Therefore, we adopt the more realistic overlapped protocol throughout our experiments." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.451, + 0.719, + 0.467 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.732 + ], + "angle": 0, + "content": "In 2D image modality, we follow the framework DeepLabv3 [7] and training hyperparameters of the baselines when building our LGKD upon them, except that we adopt synchronized batch normalization with different batch size and learning rate settings. In 3D point cloud modality, we use PointNet++ [39] with multi-scale grouping as our base model. We use Adam [25] with an initial learning rate \\(10^{-2}\\) for the first step and \\(5 \\times 10^{-3}\\) for the subsequent steps and set the weight decay to 0. The learning rate is decayed by 0.7 every 100 epochs. We train our network for 500 epochs with a batch size of 32. We remove possible duplicated points before calculating the IoU metric. For all benchmarks, we report the mIoU results on the standard validation set. We run our experiments on two NVIDIA RTX 3090 GPUs for Pascal VOC 2012 and ADE20K while one for ScanNet. More details can be found in the supp. material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.637, + 0.754 + ], + "angle": 0, + "content": "4.4. Performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Pascal-VOC 2012 consists of 10,582 images for training and 1449 images for validation with 20 foreground categories. Following [4], we conduct three different continual learning scenarios, i.e., adding one class (19-1), five classes simultaneously (15-5) and sequentially (15-1). The split of the class set for each class-incremental step follows the alphabetical order. Table 1 shows comprehensive results of our method along with other baselines. Clearly, FT performs poorly across all the incremental settings as the old" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18606" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.89, + 0.251 + ], + "angle": 0, + "content": "
Method100-50 (2 steps)100-10 (6 steps)50-50 (3 steps)
01-100101-150all01-100101-150all01-5051-150all
ILT† [35]10.918.414.417.08.50.03.11.18.63.412.99.7
MiB† [4]19.740.717.232.80.038.611.129.20.046.521.029.3
REMINDER* [37]26.642.116.133.424.038.920.332.624.248.020.129.4
SPPA [28]-42.919.9--41.012.5--49.823.9-
PLOP* [13]26.742.114.632.923.939.414.531.124.548.220.729.8
LGKD+PLOP (Ours)27.443.625.737.526.042.122.035.425.349.429.436.0
RCIL* [61]26.341.717.333.50.037.214.929.521.247.823.031.2
LGKD+RCIL (Ours)26.743.325.137.224.042.220.434.925.749.127.234.4
Joint29.142.628.237.729.142.628.237.729.149.232.137.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.252, + 0.893, + 0.293 + ], + "angle": 0, + "content": "Table 2. The mIoU(%) of the last step on the ADE20K dataset for different overlapped continual learning scenarios. \\(\\dagger\\) indicates the results are excerpted from [13]. * suggests the results are reproduced with the official codes. Best results are highlighted in Red while runner-up in Blue." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.303, + 0.89, + 0.406 + ], + "angle": 0, + "content": "
Method18-1 (2 steps)14-5 (2 steps)14-1 (6 steps)
01-1819all01-1415-19all01-1415-19all
FT19.20.028.62.418.60.044.312.019.20.07.82.9
ILT [35]23.814.925.815.926.722.243.427.719.30.018.55.6
MiB [4]55.155.032.253.852.957.845.554.545.556.529.749.2
LGKD+MiB (Ours)55.255.540.854.854.357.649.055.351.955.738.451.2
Joint53.255.040.954.253.256.747.554.253.256.747.554.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.407, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Table 3. Continual Semantic Segmentation performance (mIoU) on ScanNet under different incremental scenarios. \\( \\theta \\) stands for the background class and all represents the mIoU over all classes including the background. All results are obtained with our implementation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.473, + 0.761 + ], + "angle": 0, + "content": "class pixels are masked as background under CSS setup, and the model is explicitly taught to wrongly predict the old classes as background. EWC [26] yields similar results for novel classes while fairly outperforming the FT baseline in terms of base mIoU. Significant improvement on base classes across all settings can be observed when knowledge distillation is introduced in [40, 35]. MiB [4] obtains consistent improvement on both base and novel performance across different settings, due to addressing the background shift problem in CSS. Recent approaches [14, 61] obtain drastically higher performance against MiB when multiple incremental steps are involved (15-1). Despite their promising performance, our LGKD is able to further boost their performance by a large margin, especially on novel performance. For instance, LGKD+MiB achieves \\(+74\\%\\) (40.4 vs. 23.2) improvement against MiB on novel mIoU under 19-1 setting. These promising novel class results along with the improved background performance prove that our LGKD loss can effectively alleviate the novel-background confusion problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "ADE20K [67] is a challenging dataset consisting of 20,210 training and 2000 testing images of complex scenes. Similar to VOC, we conducted three different CSS scenarios, i.e., 100-50, 100-10 and 50-50, as shown in Table 2. Specifically, we build our LGKD upon two competitive methods, i.e., PLOP [13] and RCIL [61], where LGKD achieves considerable improvement, especially on novel mIoU (up to \\(+76\\%\\) from 14.6 to 25.7 with PLOP under 100-50 setting), setting new state-of-the-art across all incremental scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.732 + ], + "angle": 0, + "content": "ScanNet. As shown in Table 3, we compare our method with FT baseline, ILT [35] and MiB [4] on our proposed ScanNet benchmark to illustrate the generality of LGKD in 3D modality. Similar to their performance in 2D modality, FT and ILT suffer from catastrophic forgetting when learning new classes. However, MiB significantly outperforms the former methods across all three settings and metrics, in particular, the base class performance, which once again demonstrates the effectiveness of tackling the background shift in CSS. Compared with MiB, our LGKD further improves the novel performance by a large margin: \\(+27\\%\\) (40.8 vs. 32.2) and \\(+29\\%\\) (38.4 vs. 29.7) relative improvement of novel mIoU against MiB are obtained under 18-1 and 14-1 settings respectively, which proves the considerable importance of overcoming the background shift with correct class correspondence. It is also noteworthy that our approach also outperforms joint training, which shows that LGKD is also effective in alleviating long-tail issues." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.655, + 0.755 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.761, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Unless otherwise stated, all ablative studies are conducted upon VOC 15-5 setting with PLOP [13] as the baseline. Refer to the supp. material for the rationale." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Expand & Transplant. We compare three different designs for novel set distillation in Table 5. Firstly, One-hot is a hard-label distillation with all the class probabilities transplanted to the ground truth novel class, making the probability of the ground truth class equal to one. In this case, the distillation loss is equivalent to the standard one-hot cross" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18607" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.164, + 0.089, + 0.812, + 0.265 + ], + "angle": 0, + "content": "
VOC 15-5 (2 steps)VOC 15-1 (6 steps)
01-1516-20all01-1516-20all
PLOP [13]89.774.247.568.684.764.621.055.2
+Standard KD [35]90.774.449.269.288.466.413.454.8
+Unbiased KD [4]90.277.151.871.786.367.122.657.4
+LGKD (Ours)91.478.756.173.989.369.330.961.1
ADE20k 100-50 (2 steps)ADE20k 100-10 (6 steps)
01-100101-150all01-100101-150all
PLOP [13]26.742.114.632.923.939.414.531.1
+Standard KD [35]27.442.513.632.823.239.813.531.0
+Unbiased KD [4]27.042.614.533.223.739.815.131.5
+LGKD (Ours)27.443.625.737.526.042.122.035.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.265, + 0.875, + 0.278 + ], + "angle": 0, + "content": "Table 4. Effect of different knowledge distillation terms. Standard KD is adopted in ILT [35] while unbiased KD is adopted in MiB [4]." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.301, + 0.46, + 0.364 + ], + "angle": 0, + "content": "
01-1516-20all
One-hot91.476.751.971.5
Expand only90.478.530.967.7
Expand & Transplant91.478.756.173.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.365, + 0.468, + 0.392 + ], + "angle": 0, + "content": "Table 5. Effect of our novel set distillation design including expand and transplant operations." + }, + { + "type": "table", + "bbox": [ + 0.122, + 0.411, + 0.43, + 0.549 + ], + "angle": 0, + "content": "
λbλn01-1516-20all
0090.575.553.671.0
1091.376.953.171.9
2091.677.353.172.2
5091.877.952.072.4
10091.878.349.872.2
50.591.678.655.773.8
5191.478.756.173.9
5291.078.655.573.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.125, + 0.55, + 0.421, + 0.561 + ], + "angle": 0, + "content": "Table 6. Effect of the weighted factors \\( {\\lambda }_{n} \\) and \\( {\\lambda }_{\\mathrm{b}} \\) ." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.879 + ], + "angle": 0, + "content": "entropy loss, discarding all the old class probabilities predicted by the old model. As expected, the base performance is slightly compromised compared with Expand & Transplant since the old class knowledge is not distilled. Nevertheless, the novel performance also drops since using hard labels for the novel class pixels will develop a bias toward novel classes, resulting in false positive predictions. This illustrates the significance of retaining the old class probabilities during transplant. Secondly, Expand only will encourage the new model to misclassify a novel class into either background or an old class. Thus, a sharp drop in novel mIoU from 56.1 to 30.9 is observed. This uncovers the importance of correcting the old model output by transplant to handle the background shift. Finally, transplanting the background probability into the corresponding ground truth novel class while retaining the old class probabilities can establish an appropriate class correspondence and facilitate learning new classes, hence yielding the best novel performance." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Weighted factor. As table 6 shows, increasing \\(\\lambda_{\\mathrm{b}}\\) leads to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.483 + ], + "angle": 0, + "content": "higher base performance, but it will compromise the novel performance when \\(\\lambda_{\\mathrm{b}}\\) becomes too large, e.g., \\(\\lambda_{\\mathrm{b}} = 10\\). It indicates that the background set distillation is mainly responsible for retaining old knowledge. We set \\(\\lambda_{\\mathrm{b}} = 5\\) as the optimal solution as it obtains promising base mIoU while not sacrificing the novel mIoU severely. With the novel set distillation kicking in, the novel mIoU is significantly improved from 52.0 to 56.1 with \\(\\lambda_{n} = 1\\). Meanwhile, it also boosts the base mIoU from 77.9 to 78.7. This suggests that the novel set distillation facilitates learning new classes while maintaining the old class knowledge distilled from the old model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.715 + ], + "angle": 0, + "content": "Effect of different KDs. To validate the superiority of LGKD, we compare our LGKD with other knowledge distillation (KD) terms on both VOC and ADE20k upon the same baseline PLOP [13] (Fig. 4), since PLOP does not adopt class probability-wise KD. Firstly, PLOP can hardly benefit from adding the standard KD [35], probably due to its tendency to misclassify new classes as the background (see Sec. 3.2). Secondly, though unbiased KD [4] yields a moderate boost on VOC, it makes almost no difference on the more challenging benchmark ADE20k. In contrast, LGKD consistently surpasses standard KD and unbiased KD by a significant margin, especially in terms of novel mIoU. Concretely, LGKD yields \\(+8.3 / +11.2 / +6.9\\) points improvement against unbiased KD on 15-1/100-50/100-10 setting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.723, + 0.651, + 0.739 + ], + "angle": 0, + "content": "4.6. Error Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.747, + 0.891, + 0.807 + ], + "angle": 0, + "content": "We carry out comprehensive error analysis on both Pascal-VOC 2012 and ScanNet datasets to validate the effectiveness of our LGKD in mitigating the novel-background confusion problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2D image. As Fig. 4 shows, under the VOC 15-5 incremental scenario, naive finetuning completely forgets the old class bird while also mistaking the background for the novel class potted plant. Thanks to KD mechanism, ILT [35], REMINDER [37], MiB [4], PLOP [13] and RCIL [61] are capable to retain the old knowledge (bird and chair). Nev" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18608" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.089, + 0.768, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.179, + 0.88, + 0.231 + ], + "angle": 0, + "content": "Old classes: bird chair" + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.251, + 0.886, + 0.303 + ], + "angle": 0, + "content": "New classes: potted plant Sofa" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.379, + 0.895, + 0.423 + ], + "angle": 0, + "content": "Figure 4. Error analysis of baselines along with our LGKD under VOC 15-5 setting. MiB [4], PLOP [13] and RCIL [61] tend to mistake weed and suitcase (background—things of no interest) for potted plant and sofa (novel classes) respectively. Such confusion is effectively alleviated when equipped with our LGKD, except for the bird image with RCIL, where the confusion is slightly mitigated." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.443, + 0.47, + 0.566 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.57, + 0.471, + 0.668 + ], + "angle": 0, + "content": "Figure 5. Error analysis of MiB [4] vs. LGKD+MiB on step 4 (with bathtub depicted in pink as the novel class) of the ScanNet 14-1 incremental scenario. Our LGKD effectively alleviates the confusion made by MiB (see the black boxes) — mistaking the background (dark purple) for the novel class bathtub. Meanwhile, LGKD+MiB achieves decent accuracy on the novel class bathtub (see the red boxes)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.47, + 0.85 + ], + "angle": 0, + "content": "ertheless, these methods are consistently prone to misclassifying the background (weed and suitcase—things of no interest) as novel classes (potted plant and sofa). On the contrary, when incorporating our LGKD into MiB, PLOP and RCIL, the above novel-background confusion is effectively suppressed, except for the bird image with RCIL, where the confusion is slightly alleviated. The above examples demonstrate the effectiveness of LGKD in tackling the novel-background confusion issue. More visualization results can be found in the supp. material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "3D point cloud. We show the error results in Fig. 5 for step 4 of the ScanNet 14-1 setting, where the current novel class is bathtub depicted in pink. Clearly, our method effic" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.895, + 0.522 + ], + "angle": 0, + "content": "tively corrects the false prediction made by MiB [4] (see the black boxes), where the background points (highlighted in dark purple) are mistaken for the novel class bathtub. Meanwhile, our LGKD does not sacrifice the capability to recognize the true bathtub points (see red boxes)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.533, + 0.62, + 0.549 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.895, + 0.771 + ], + "angle": 0, + "content": "In this work, we identify a key issue in continual semantic segmentation (CSS)—novel background confusion. This is generally caused by the corrupted class correspondence during knowledge distillation. To alleviate such confusion, we propose a novel solution termed Label-Guided Knowledge Distillation (LGKD), which can establish an appropriate class correspondence between the output of the old and the new model for distillation, guided by the ground truth label. We validate its effectiveness on both existing 2D benchmarks and our proposed 3D CSS benchmark, where LGKD can consistently outperform competing methods by a large margin, especially on novel mIoU, setting new state-of-the-art. Finally, we hope this work will inspire further in-depth exploration of 3D CSS in the future." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.782, + 0.681, + 0.799 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.807, + 0.894, + 0.837 + ], + "angle": 0, + "content": "This work is supported by the Hyundai research grant (04OIS000252C130)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.848, + 0.598, + 0.864 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.873, + 0.893, + 0.901 + ], + "angle": 0, + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18609" + } + ], + [ + { + "type": "ref_text", + "bbox": [ + 0.108, + 0.092, + 0.468, + 0.119 + ], + "angle": 0, + "content": "synapses: Learning what (not) to forget. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9939-9948, 2021. 2" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18612" + } + ] +] \ No newline at end of file diff --git a/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/3a801de3-50c8-469a-b26b-c00f633cc663_origin.pdf b/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/3a801de3-50c8-469a-b26b-c00f633cc663_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ee5a6bd7f606d3cc7ac83c3fb7d6b803b56946ac --- /dev/null +++ b/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/3a801de3-50c8-469a-b26b-c00f633cc663_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:70afa47f926dc9f880b001f592a5034800c70f74da93d1a1c31b3612a4f992f2 +size 1275133 diff --git a/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/full.md b/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ca8754b1b9bea2e675f37a3372282c32f5369799 --- /dev/null +++ b/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/full.md @@ -0,0 +1,318 @@ +# Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds + +Ze Yang $^{1}$ , Ruibo Li $^{1}$ , Evan Ling $^{2}$ , Chi Zhang $^{1}$ , Yiming Wang $^{1}$ , Dezhao Huang $^{2}$ , Keng Teck Ma $^{2}$ , Minhoe Hur $^{3}$ , Guosheng Lin $^{1*}$ + +$^{1}$ School of Computer Science and Engineering, Nanyang Technological University, Singapore + $^{2}$ Hyundai Motor Group Innovation Center in Singapore (HMGICS) + $^{3}$ AIRS Company, Hyundai Motor Group + +ze001@e.ntu.edu.sg, evan.ling@hmgics.com, minhoe.hur@hyundai.com, gslin@ntu.edu.sg + +# Abstract + +Continual semantic segmentation (CSS) aims to extend an existing model to tackle unseen tasks while retaining its old knowledge. Naively fine-tuning the old model on new data leads to catastrophic forgetting. A common solution is knowledge distillation (KD), where the output distribution of the new model is regularized to be similar to that of the old model. However, in CSS, this is challenging because of the background shift issue. Existing KD-based CSS methods continue to suffer from confusion between the background and novel classes since they fail to establish a reliable class correspondence for distillation. To address this issue, we propose a new label-guided knowledge distillation (LGKD) loss, where the old model output is expanded and transplanted (with the guidance of the ground truth label) to form a semantically appropriate class correspondence with the new model output. Consequently, the useful knowledge from the old model can be effectively distilled into the new model without causing confusion. We conduct extensive experiments on two prevailing CSS benchmarks, Pascal-VOC and ADE20K, where our LGKD significantly boosts the performance of three competing methods, especially on novel mIoU by up to $+76\%$ , setting new state-of-the-art. Finally, to further demonstrate its generalization ability, we introduce the first CSS benchmark for 3D point cloud based on ScanNet, along with several re-implemented baselines for comparison. Experiments show that LGKD is versatile in both 2D and 3D modalities without requiring ad hoc design. Codes are available at https://github.com/Ze-Yang/LGKD. + +# 1. Introduction + +Fully supervised semantic segmentation has witnessed tremendous success [33, 63, 27, 8, 16, 22, 47, 65, 9] in re + +![](images/5a842318a5f59736e908d670e8a3502e730702509059163ea18e851911ba5ad8.jpg) +Figure 1. Illustration of knowledge distillation (KD) strategies in continual semantic segmentation. Standard KD and unbiased KD reduce the new class (bicycle) dimension(s) of the probabilities output by the new model via remove and combine respectively, which collapses the class correspondence across incremental steps and raises confusion between background and new classes (see Sec. 1). In contrast, our label-guided KD uses the ground truth label as guidance to expand the probabilities predicted by the old model. It builds a reliable class correspondence across different learning steps without discrepancy (ILT) or entanglement (MiB) (see Sec. 3.2). A $\xrightarrow{\text{mimic}}$ B: encourage A to be similar to B. + +cent years. These algorithms generally assume a fixed number of classes to be learned. However, in real-world applications, it is often expected that a deployed model can be continuously generalized to handle new classes while not forgetting the old ones. A simple solution is to expand the original dataset with newly available samples and retrain a new model from scratch, dubbed as Joint Training. Obviously, this is computationally expensive and requires an increasing amount of space to store the old data over time. + +Further, it may raise privacy issues in some circumstances, e.g., medical images and face data. + +To address this problem, continual semantic segmentation (CSS) has been proposed by [35] as an emerging research direction, where the training scheme is separated into several steps with each step tackling a set of unseen classes. Specifically, given the old model and new training data (only new classes are labeled while others are treated as background), the new model is supposed to recognize both old and new classes. Under this scenario, naively finetuning the old model on new data tends to suffer from catastrophic forgetting [17, 26], where the recognition capability of old classes is quickly lost. + +Knowledge distillation (KD), first proposed in image classification [19], has recently been introduced to CSS [35, 4] to mitigate the forgetting issue. As Fig. 1 shows, $ILT$ [35] removes new class probabilities (green bar) predicted by the new model, and simply distill old classes and background accordingly. However, they ignore the background shift problem [4], where the new class bicycle at current step $t$ was labeled as background at last step $t - 1$ . As a result, the old model, which regards bicycle as background, will output a high background score for the new class bicycle pixels. Via KD, it will mislead the new model to misclassify new classes as background. Obviously, this KD strategy hinders the learning of new classes because the class correspondence for distillation is corrupted, i.e., naively mapping the new background to the old background. + +This issue was highlighted in $MiB$ [4] where they proposed a new class correspondence by combination. Concretely, they combined new classes with the new background via probability summation (Fig. 1) to form a pseudo class, which was treated as the counterpart to the old background for distillation. However, this strategy, though alleviating class mis-correspondence, entangles new classes with the new background and tends to misclassify background as new classes, as detailed in Sec. 3.2. In this paper, we term the error of mistaking background for new (novel) classes or vice-versa as novel-background confusion. + +The key insight to overcome the novel-background confusion is to build a reliable class correspondence across different learning steps without corruption or entanglement. To this end, we devise a novel Label-Guided Knowledge Distillation (LGKD) loss, where the class probabilities predicted by the old model are expanded to have the same dimension as the output of the new model (see the blue block in Fig. 1). The background probability is then transplanted to the corresponding ground truth label (class) of the input pixels. In this way, the knowledge from the old background at the last step can be correctly distilled into its corresponding semantic class at the current step, i.e., either the new background or a novel class. Note that our LGKD is a generic regularization term with negligible computa + +tional cost and can be easily incorporated into existing arts. We validate its effectiveness on two prevailing CSS benchmarks Pascal-VOC and ADE20K, where our LGKD consistently yields promising improvements upon three competing methods, especially on novel (new class) mIoU (up to $+76\%$ ), setting new state-of-the-art. To further demonstrate the generalization ability of our approach, we establish a challenging CSS benchmark based on ScanNet for 3D point cloud and re-implement multiple baselines for comparison. To our best knowledge, this is the first work to conduct CSS on 3D point cloud. Extensive experiments showcase that our LGKD loss is capable to handle both 2D and 3D modalities with no ad hoc design. + +The main contributions of this paper can be summarized as: + +- We propose a new label-guided knowledge distillation (LGKD) loss for CSS, which builds a reliable class correspondence across incremental steps and alleviates novel-background confusion. +- LGKD is a generic regularization term with negligible computational cost, which can be readily combined with existing methods. Extensive experiments on two prevailing CSS benchmarks, Pascal-VOC and ADE20K, showcase that LGKD significantly improves three competitive methods, particularly on novel mIoU by up to $+76\%$ , setting new state-of-the-art. +- To further demonstrate its generalization capability, we establish the first CSS benchmark for 3D point cloud based on ScanNet and re-implement multiple baselines for comparison. Experiments illustrate that our LGKD is versatile in both 2D and 3D modalities without any ad hoc design. + +# 2. Related Works + +Semantic Segmentation, aiming to perform pixel-level classification, has witnessed great advancement [63, 6, 7, 53, 22, 16] in recent years since the pioneering work Fully Convolutional Network (FCN) [33]. Among the above methods, the DeepLab series [6, 7] is well-known for their effective designs, e.g., atrous spatial pyramid pooling (ASPP) [6], atrous convolution in cascade [7]. DeepLabv3 [7] is commonly used as the segmentation framework in prior CSS works [4, 13, 61]. + +In 3D point cloud modality, PointNet [38] is a pioneering work to directly process unstructured point cloud. Subsequent work PointNet++ [39] learns to capture local structures and recognize fine-grained patterns via a hierarchical neural network that applies PointNet recursively. While more complicated techniques have been proposed in recent works [46, 45, 62, 68, 10], we employ PointNet++ as our 3D segmentation model for its simplicity and efficiency. + +![](images/d20b9277ef6bef5cfa08df9dac0ba012aba9e3f4765a82868f524821621afb35.jpg) +Figure 2. Illustration of our LGKD loss. At learning step $t$ , an input sample $x$ is fed into the old (top) and new (bottom) models to obtain the class probabilities for each element $i \in \mathcal{I}$ (pixel or point). These elements are then separated into the novel and background sets according to their ground truth label available at the current step $t$ (yellow and green as novel set). Finally, to build up a reliable class correspondence, we extend the old probabilities (output by the old model) to have the same dimension as the new ones by expand and transplant (for novel set only), such that useful prior knowledge from the old model can be effectively distilled into the new model to facilitate learning new classes. We highlight that our LGKD can effectively alleviate the novel-background confusion issue as occurs in [35, 4]. + +Continual Learning aims at training a deep neural network to learn multiple tasks in sequence continually. Distinct from one-step incremental learning [50, 51, 55, 56, 59, 58, 30, 60, 29, 57, 31, 44], continual learning generally confronts more severe forgetting issues during multiple-step learning. Numerous works tackle the catastrophic forgetting issue and they can be classified into three categories. The model growing category [2, 48, 52] tackles this problem by dynamically extending model capacity. The memory replay approaches retain the old-class knowledge by keeping a small amount of old-class data in current training. Those data can be raw data [41, 40, 3], features [18, 23] or generated data [24, 42, 32]. The regularization approaches constrain the model by regularizing the parameters [26, 1, 54], the gradients [21, 5], logits [40, 3, 4] or the features [20, 12, 14] of the model. + +Continual Semantic Segmentation. Existing CSS methods can be divided into two categories: 1) replay-based. RECALL [34] rehearses old-class data obtained by web-crawling or generative models. Similarly, [49] utilizes an iterative relabeling strategy with rehearsal-based incremental learning. Following [4], replay-based methods are out of the scope of this paper since accessing old data violates the conventional CSS assumption. 2) regularization-based. ILT [35] is the first work to introduce KD into CSS. MiB [4] raises the background shift problem in CSS and proposes an unbiased KD to tackle it. PLOP [13] distills both short- and long-range spatial relations via local pooled output distilla + +tion. SDR [36] leverages prototype matching, feature sparsification and contrastive learning to enforce feature consistency and discrimination. Most recently, class similarity KD, representation compensation, structure-preserving loss and feature projection, and the biased context are investigated by REMINDER [37], RCIL [61], SPPA [28] and RBC [64] respectively. However, the above approaches tend to suffer from the novel-background confusion problem since their distillation term lacks an appropriate class correspondence. Therefore, we propose a generic distillation term, dubbed LGKD, with a reliable class correspondence to alleviate this confusion issue. + +# 3. Method + +# 3.1. Problem Definition and Setups + +Before introducing the continual learning setting, we first present the setups of the standard semantic segmentation task. To ensure the generality, let $\mathcal{X} \in \mathbb{R}^{N \times C_{\mathrm{in}}}$ denote the input space (e.g., image, point cloud, etc.), where $N$ is the number of input elements and $C_{\mathrm{in}}$ is the number of input channels (typically $C_{\mathrm{in}} = 3$ , i.e., RGB, for image and $C_{\mathrm{in}} >= 3$ , e.g., XYZ, RGB, normals, for point cloud). Let $\mathcal{Y} \in \mathcal{C}^N$ denote the output label space, where $\mathcal{C}$ is a label set that contains all classes including the background class $\mathsf{b} \in \mathcal{C}$ . Note that each sample $x \in \mathcal{X}$ comprises a set of elements $\mathcal{I}$ (e.g., pixels, points, etc.) of corresponding label $y \in \mathcal{Y}$ with constant cardinality $|\mathcal{I}| = N$ . + +Given a training set $\mathcal{T} \subset \mathcal{X} \times \mathcal{Y}$ , the target of semantic segmentation is to learn a model $f_{\theta}$ parametrized by $\theta$ that maps the input space $\mathcal{X}$ to a set of class probability vectors $f_{\theta}: \mathcal{X} \mapsto \mathbb{R}^{N \times |\mathcal{C}|}$ . The output segmentation mask is then computed as $\hat{y} = \{\arg \max_{c \in \mathcal{C}} f_{\theta}(x)[i, c]\}_{i=1}^{N}$ , where $f_{\theta}(x)[i, c]$ is the probability of element $i$ belonging to category $c$ . + +As opposed to the standard training scheme where the model can access and learn from the full training set $\mathcal{T} \subset \mathcal{X} \times \mathcal{C}^N$ all at once, continual learning, instead, involves several learning steps $\{t\}_{t=0}^{T}$ each with a subset of label $\mathcal{C}^t$ . More specifically, at training step $t$ , the previous label set $\mathcal{C}^{0:t-1}$ will be expanded with a set of unseen classes $\mathcal{C}^t$ to form a new label set $\mathcal{C}^{0:t} = \mathcal{C}^{0:t-1} \cup \mathcal{C}^t$ . Then a training set $\mathcal{T}^t \subset \mathcal{X} \times (\mathcal{C}^t)^N$ will be provided along with the last model $f_{\theta^{t-1}}: \mathcal{X} \mapsto \mathbb{R}^{N \times |\mathcal{C}^{0:t-1}|}$ to obtain an updated model $f_{\theta^t}: \mathcal{X} \mapsto \mathbb{R}^{N \times |\mathcal{C}^{0:t}|}$ . Note that the training set $\mathcal{T}^t$ may contain element $i \in \mathcal{I}$ from either previous classes $\mathcal{C}^{0:t-1}$ or future classes $\mathcal{C}^{t+1:T}$ , though the annotations are collapsed into the background class $b$ at the current step $t$ . This is referred to as overlapped [4] setting. Following the standard incremental setup, we assume that the label sets of each step are disjoint from each other except for the special background class, i.e., $\mathcal{C}^i \cap \mathcal{C}^j = b$ ( $i \neq j$ ). + +# 3.2. Revisiting Knowledge Distillation Loss + +A naive way to tackle the continual learning problem is to initialize a new model $f_{\theta^t}$ with the weights of the last model $f_{\theta^{t-1}}$ and then optimize the network with the training set $\mathcal{T}^t$ . However, this will lead to the catastrophic forgetting of old classes $\mathcal{C}^{0:t-1}$ . Since no old class samples with annotation are available at the current step. + +Standard knowledge distillation. To alleviate the forgetting problem, knowledge distillation [19] is a common solution to preserve old knowledge by regularizing the output class probability distribution of the new model $f_{\theta^t}$ to be close to that of the old model $f_{\theta^{t-1}}$ given the same input sample. Formally, the standard knowledge distillation loss $\ell_{\mathrm{kd}}$ adopted in CSS by ILT [35] can be formulated as: + +$$ +\ell_ {\mathrm {k d}} ^ {\theta^ {t}} (x, y) = - \frac {1}{| \mathcal {I} |} \sum_ {i \in \mathcal {I}} \sum_ {c \in \mathcal {C} ^ {0: t - 1}} q _ {x} ^ {t - 1} (i, c) \log \hat {q} _ {x} ^ {t} (i, c), \tag {1} +$$ + +where $\hat{q}_x^t (i,c)$ refers to the probability of class $c$ for element $i$ predicted by $f_{\theta^t}$ but re-normalized over all old classes: + +$$ +\hat {q} _ {x} ^ {t} (i, c) = q _ {x} ^ {t} (i, c) / \sum_ {k \in \mathcal {C} ^ {0: t - 1}} q _ {x} ^ {t} (i, k). \tag {2} +$$ + +However, there exists a discrepancy issue in the standard distillation loss. Concretely, it fails to leverage prior knowledge to cope with the new classes, as the new class probabilities $q_{x}^{t}(i,c)$ ( $c \in \mathcal{C}^t \setminus b$ ) are not incorporated in distillation (Eq. 1). Moreover, it wrongly enhances the background + +probability for novel class elements due to the background shift [4]. Hence, it tends to mistake the novel classes for the background (refer to supp. material for detailed discussion). + +Unbiased knowledge distillation. To overcome the above issue, MiB [4] proposes an unbiased knowledge distillation loss for CSS by revising $\hat{q}_x^t (i,c)$ in Eq. 2 as: + +$$ +\hat {q} _ {x} ^ {t} (i, c) = \left\{ \begin{array}{l l} q _ {x} ^ {t} (i, c) & \text {i f} c \neq \mathfrak {b} \\ \sum_ {k \in \mathcal {C} ^ {t}} q _ {x} ^ {t} (i, k) & \text {i f} c = \mathfrak {b}, \end{array} \right. \tag {3} +$$ + +where they compare the old background probability $q_{x}^{t - 1}(i,\mathsf{b})$ with the probability of being either a novel class or the new background, i.e., $\sum_{k\in \mathcal{C}^t}q_x^t (i,k)$ , rather than directly with its counterpart $q_{x}^{t}(i,\mathsf{b})$ . Such class probability combination mechanism is meant to facilitate distilling the knowledge from the old background class defined at step $t - 1$ to the novel classes at step $t$ . Nevertheless, it entangles the novel classes with the new background due to the probability combination. As a consequence of entanglement, the probabilities of novel classes will be undesirably enhanced when the distillation loss only intends to improve the probabilities of the new background, and vice versa. As opposed to ILT [35], this leads to the other confusion — misclassifying background as novel classes. + +# 3.3. Label-Guided Knowledge Distillation + +Class separation. Unlike standard KD and unbiased KD, which apply the same KD strategy to all input elements, we propose to separate the input elements into two sets according to the ground truth label available at the current step, namely the background set $S_{\mathsf{b}} = \{i|i\in \mathcal{I},y_i = \mathsf{b}\}$ and the novel set $S_{n} = \{i|i\in \mathcal{I},y_{i}\in \mathcal{C}^{t}\setminus \mathsf{b}\}$ . In this way, we can customize the distillation strategy for each class set and establish a more accurate class correspondence, which facilitates more effective knowledge distillation. + +Class correspondence. As opposed to revising the class probabilities of the new model $q_{x}^{t}(i,c)$ as in [4], we instead resort to correcting the class probabilities of the old model $q_{x}^{t - 1}(i,c)$ according to the ground truth label $y_{i}$ . Our design is inspired by the wireless communication system. In order to improve the useful information captured by the receiver, one should ensure that the signal released by the transmitter is correct and that both transmitter and receiver share the same communication protocol. Likewise, in our case, the objective is to assure the class probabilities (signal) predicted by the old model $f_{\theta^{t - 1}}$ (transmitter) contain correct class semantics (after background shift) and are well-aligned with (protocol) the output class space of the new model $f_{\theta^t}$ (receiver). Protocol: For the elements from the novel set $S_{n}$ , we expand the output of the old model $q_{x}^{t - 1}(i,c)$ with zero probability assigned to the extra novel classes $c \in \mathcal{C}^t \setminus \mathbf{b}$ such that it has the same output class space dimensions with the new model. Signal: Due to the + +background shift, we transplant the probability of the background to the corresponding ground truth novel class and set the background probability to zero while maintaining the others unchanged. The final corrected probability distribution to be distilled from can be formulated as: + +$$ +\bar {q} _ {x} ^ {t - 1} (i, c) = \left\{ \begin{array}{l l} 0 & \text {i f} c \in \mathcal {C} ^ {t} \text {a n d} c \neq y _ {i} \\ q _ {x} ^ {t - 1} (i, \mathrm {b}) & \text {i f} c = y _ {i} \\ q _ {x} ^ {t - 1} (i, c) & \text {o t h e r w i s e ,} \end{array} \right. \tag {4} +$$ + +where $i \in S_n$ . We highlight that, this novel set distillation strategy can preserve the knowledge from $f_{\theta^{t-1}}$ for the old classes while also correcting the class probabilities from the old model for the new classes given the ground truth label $y_i$ as guidance. As for the case of the background set $i \in S_b$ , it can be treated in a similar yet simpler way by merely expanding zero probability for the extra novel classes as: + +$$ +\bar {q} _ {x} ^ {t - 1} (i, c) = \left\{ \begin{array}{l l} 0 & \text {i f} c \in \mathcal {C} ^ {t} \backslash \mathfrak {b} \\ q _ {x} ^ {t - 1} (i, c) & \text {o t h e r w i s e ,} \end{array} \right. \tag {5} +$$ + +In summary, our distillation loss can be given as: + +$$ +\ell_ {\mathrm {k d}} ^ {\theta^ {t}} (x, y) = \lambda_ {n} \cdot \bar {\ell} _ {\mathrm {k d}} ^ {\theta^ {t}} (x, y, \mathcal {S} _ {n}) + \lambda_ {\mathfrak {b}} \cdot \bar {\ell} _ {\mathrm {k d}} ^ {\theta^ {t}} (x, y, \mathcal {S} _ {\mathfrak {b}}), \tag {6} +$$ + +where $\lambda_{n}$ and $\lambda_{\mathrm{b}}$ balances the contribution of the novel set $S_{n}$ and background set $S_{\mathrm{b}}$ ; $\bar{\ell}_{\mathrm{kd}}^{\theta^{t}}(x,y,\mathcal{S})$ is the distillation loss defined within set $S$ as: + +$$ +\bar {\ell} _ {\mathrm {k d}} ^ {\theta^ {t}} (x, y, \mathcal {S}) = - \frac {1}{N} \sum_ {i \in \mathcal {S}} \sum_ {c \in \mathcal {C} ^ {0: t}} \bar {q} _ {x} ^ {t - 1} (i, c) \log q _ {x} ^ {t} (i, c). \tag {7} +$$ + +The overall training objective is then computed as: + +$$ +\mathcal {L} \left(\theta^ {t}\right) = \frac {1}{\left| \mathcal {T} ^ {t} \right|} \sum_ {(x, y) \in \mathcal {T} ^ {t}} \left(\lambda \ell_ {c e} ^ {\theta^ {t}} (x, y) + \ell_ {\mathrm {k d}} ^ {\theta^ {t}} (x, y)\right), \tag {8} +$$ + +where $\ell_{ce}^{\theta^t}(x,y)$ is the cross-entropy loss. $\lambda$ is the hyperparameter to balance the importance of the two terms, and is set as $\lambda = 1$ in experiments. + +# 4. Experiment + +# 4.1. Benchmarking 3D Continual Segmentation + +Existing CSS methods have mainly been evaluated on 2D CSS benchmarks, leaving a significant gap in the exploration of 3D CSS. In order to validate the versatility of LGKD across different modalities, we introduce the first 3D CSS benchmark based on ScanNet [11] and present several baseline methods for comparison. + +ScanNet contains 1201 and 312 indoor scenes in the training and validation set respectively with 20 classes in total, including a special class for "other furniture", i.e. background in the standard segmentation task. In Fig. 3, we + +![](images/695c663d0d51fece92c00017d9f94956c57e4c16cfee9a6c6f6ae5e5d8454d2c.jpg) +Figure 3. The scene-wise class frequency statistics of our proposed ScanNet benchmark for 3D continual semantic segmentation. + +provide the scene-wise class frequency statistics of ScanNet [11], including both train and validation sets. The scene-wise class frequency indicates the number of scenes that a certain class appears in. Surprisingly, we find that ScanNet exhibits a challenging long-tail category distribution. Additionally, we provide the point-wise class frequency statistics and demonstrate the difficulty of our proposed benchmark in the supp. material. For a challenging CSS benchmark, we split the entire class set into multiple subsets according to the descending order of scene-wise class frequency as in Fig. 3, with the tail classes constituting the novel sets for continual learning. This means that the novel classes to be learned in each step are set to be those rare ones, a.k.a. tail classes in the long-tail field. Following the Pascal-VOC 2012 CSS benchmark [35, 4], we define three different incremental scenarios: adding one class (18-1), adding five classes simultaneously (14-5) and sequentially (14-1). Take 14-5 setting for instance, the last five rare classes, i.e., counter, refrigerator, bookshelf, bathtub, shower curtain, form the novel class set, and likewise for the other settings. + +We form the training set by including all the scenes that contain at least one point from the novel classes at the current step, with the others (either previous or future classes) annotated as "other furniture". The validation set is established in a similar way except that the label of the previous classes $\mathcal{C}^{0:t-1}$ are maintained, as the model is required to predict all seen classes up to the current step. Finally, we report the old-, new- and all-class mIoU metrics as well as the background IoU at the end of all incremental steps. + +# 4.2. Baselines and Setups + +To validate the effectiveness of our approach, we conduct thorough comparison with the latest state-of-the-art CSS methods as well as baselines. FT is a straightforward + +
Method19-1 (2 steps)15-5 (2 steps)15-1 (6 steps)
01-1920all01-1516-20all01-1516-20all
FT†-6.812.9--2.133.1--0.21.8-
EWC† [26]-26.914.0--24.335.5--0.34.3-
LwF-MC† [40]-64.413.3--58.135.0--6.48.4-
ILT† [35]-67.112.3--66.340.6--4.97.8-
ILT* [35]88.666.28.364.589.265.238.159.977.73.77.98.2
SDR* [36]90.068.924.267.890.176.650.971.183.934.113.031.5
REIMINDER* [37]91.975.633.974.490.275.149.169.683.365.227.057.0
SPPA [28]--36.274.6--52.972.1--23.356.0
MiB† [4]-70.222.1--75.549.4--35.113.5-
MiB* [4]90.371.523.270.189.674.246.368.383.238.013.934.5
LGKD+MiB (Ours)91.472.140.471.591.675.254.871.179.739.317.035.9
PLOP* [13]92.175.336.174.289.774.247.568.684.764.621.055.2
LGKD+PLOP (Ours)92.976.542.975.791.478.756.173.989.369.330.961.1
RCIL* [61]90.173.624.572.188.975.948.470.083.967.923.158.0
LGKD+RCIL (Ours)92.876.537.575.591.477.654.372.789.469.029.160.5
Joint93.777.678.178.493.779.073.678.493.779.073.678.4
+ +Table 1. Continual Semantic Segmentation performance (mIoU) on Pascal-VOC 2012 under different incremental scenarios. † indicates the results are excerpted from [4]. * suggests the results are reproduced with the official codes. 0 stands for the background class and all represents the mIoU over all classes including the background. Best results are highlighted in Red while runner-up in Blue. + +lower-bound baseline, which simply finetunes the model with the newly available data at each step. On the contrary, Joint, training a standard segmentation model on all classes within a single step, may serve as an upper bound for CSS approaches, though not always true if the CSS benchmark shows a long-tail nature with tail classes as new classes (e.g., ScanNet). For completeness, we include two general continual learning methods [26, 40] that are not specifically designed for semantic segmentation. Further, we mainly benchmark against the recent state-of-the-art methods taylored for segmentation [35, 4, 13, 36, 37, 61]. Following [4], we do not consider replay-based methods, e.g., [40]) in our comparison as the access to previous annotated data violates the standard class-incremental learning assumption. For the sake of generalization, we conduct experiments on both 2D image modality, i.e., Pascal-VOC 2012 [15] and ADE20K [66], and 3D point cloud modality, i.e. ScanNet [11]. Besides the old-, new- and all-class (including the background class) mIoU, we additionally report the background IoU because it is a special category under CSS with its semantic content varying across different learning steps. + +CSS protocols. As for the label masking policy for the incremental steps, [4] follows and adapts two different CSS protocols, namely disjoint [35] and overlapped [43]. Both protocols assume that only the novel classes at the current step are labeled while the others are masked out as background. However, in the disjoint protocol, input samples for step $t$ should only contain elements (i.e., pixels or points) that belong to either current or previous classes, i.e., $\mathcal{C}^{0:t}$ . On the contrary, the overlapped protocol allows the input samples to contain either previous, current or future classes, i.e., $\mathcal{C}^{0:T}$ . The disjoint protocol makes a strong assumption that the current training data should not contain any samples + +of the class we would like to learn in the future, which is impracticable. Therefore, we adopt the more realistic overlapped protocol throughout our experiments. + +# 4.3. Implementation Details + +In 2D image modality, we follow the framework DeepLabv3 [7] and training hyperparameters of the baselines when building our LGKD upon them, except that we adopt synchronized batch normalization with different batch size and learning rate settings. In 3D point cloud modality, we use PointNet++ [39] with multi-scale grouping as our base model. We use Adam [25] with an initial learning rate $10^{-2}$ for the first step and $5 \times 10^{-3}$ for the subsequent steps and set the weight decay to 0. The learning rate is decayed by 0.7 every 100 epochs. We train our network for 500 epochs with a batch size of 32. We remove possible duplicated points before calculating the IoU metric. For all benchmarks, we report the mIoU results on the standard validation set. We run our experiments on two NVIDIA RTX 3090 GPUs for Pascal VOC 2012 and ADE20K while one for ScanNet. More details can be found in the supp. material. + +# 4.4. Performance + +Pascal-VOC 2012 consists of 10,582 images for training and 1449 images for validation with 20 foreground categories. Following [4], we conduct three different continual learning scenarios, i.e., adding one class (19-1), five classes simultaneously (15-5) and sequentially (15-1). The split of the class set for each class-incremental step follows the alphabetical order. Table 1 shows comprehensive results of our method along with other baselines. Clearly, FT performs poorly across all the incremental settings as the old + +
Method100-50 (2 steps)100-10 (6 steps)50-50 (3 steps)
01-100101-150all01-100101-150all01-5051-150all
ILT† [35]10.918.414.417.08.50.03.11.18.63.412.99.7
MiB† [4]19.740.717.232.80.038.611.129.20.046.521.029.3
REMINDER* [37]26.642.116.133.424.038.920.332.624.248.020.129.4
SPPA [28]-42.919.9--41.012.5--49.823.9-
PLOP* [13]26.742.114.632.923.939.414.531.124.548.220.729.8
LGKD+PLOP (Ours)27.443.625.737.526.042.122.035.425.349.429.436.0
RCIL* [61]26.341.717.333.50.037.214.929.521.247.823.031.2
LGKD+RCIL (Ours)26.743.325.137.224.042.220.434.925.749.127.234.4
Joint29.142.628.237.729.142.628.237.729.149.232.137.7
+ +Table 2. The mIoU(%) of the last step on the ADE20K dataset for different overlapped continual learning scenarios. $\dagger$ indicates the results are excerpted from [13]. * suggests the results are reproduced with the official codes. Best results are highlighted in Red while runner-up in Blue. + +
Method18-1 (2 steps)14-5 (2 steps)14-1 (6 steps)
01-1819all01-1415-19all01-1415-19all
FT19.20.028.62.418.60.044.312.019.20.07.82.9
ILT [35]23.814.925.815.926.722.243.427.719.30.018.55.6
MiB [4]55.155.032.253.852.957.845.554.545.556.529.749.2
LGKD+MiB (Ours)55.255.540.854.854.357.649.055.351.955.738.451.2
Joint53.255.040.954.253.256.747.554.253.256.747.554.2
+ +Table 3. Continual Semantic Segmentation performance (mIoU) on ScanNet under different incremental scenarios. $\theta$ stands for the background class and all represents the mIoU over all classes including the background. All results are obtained with our implementation. + +class pixels are masked as background under CSS setup, and the model is explicitly taught to wrongly predict the old classes as background. EWC [26] yields similar results for novel classes while fairly outperforming the FT baseline in terms of base mIoU. Significant improvement on base classes across all settings can be observed when knowledge distillation is introduced in [40, 35]. MiB [4] obtains consistent improvement on both base and novel performance across different settings, due to addressing the background shift problem in CSS. Recent approaches [14, 61] obtain drastically higher performance against MiB when multiple incremental steps are involved (15-1). Despite their promising performance, our LGKD is able to further boost their performance by a large margin, especially on novel performance. For instance, LGKD+MiB achieves $+74\%$ (40.4 vs. 23.2) improvement against MiB on novel mIoU under 19-1 setting. These promising novel class results along with the improved background performance prove that our LGKD loss can effectively alleviate the novel-background confusion problem. + +ADE20K [67] is a challenging dataset consisting of 20,210 training and 2000 testing images of complex scenes. Similar to VOC, we conducted three different CSS scenarios, i.e., 100-50, 100-10 and 50-50, as shown in Table 2. Specifically, we build our LGKD upon two competitive methods, i.e., PLOP [13] and RCIL [61], where LGKD achieves considerable improvement, especially on novel mIoU (up to $+76\%$ from 14.6 to 25.7 with PLOP under 100-50 setting), setting new state-of-the-art across all incremental scenarios. + +ScanNet. As shown in Table 3, we compare our method with FT baseline, ILT [35] and MiB [4] on our proposed ScanNet benchmark to illustrate the generality of LGKD in 3D modality. Similar to their performance in 2D modality, FT and ILT suffer from catastrophic forgetting when learning new classes. However, MiB significantly outperforms the former methods across all three settings and metrics, in particular, the base class performance, which once again demonstrates the effectiveness of tackling the background shift in CSS. Compared with MiB, our LGKD further improves the novel performance by a large margin: $+27\%$ (40.8 vs. 32.2) and $+29\%$ (38.4 vs. 29.7) relative improvement of novel mIoU against MiB are obtained under 18-1 and 14-1 settings respectively, which proves the considerable importance of overcoming the background shift with correct class correspondence. It is also noteworthy that our approach also outperforms joint training, which shows that LGKD is also effective in alleviating long-tail issues. + +# 4.5. Ablation Study + +Unless otherwise stated, all ablative studies are conducted upon VOC 15-5 setting with PLOP [13] as the baseline. Refer to the supp. material for the rationale. + +Expand & Transplant. We compare three different designs for novel set distillation in Table 5. Firstly, One-hot is a hard-label distillation with all the class probabilities transplanted to the ground truth novel class, making the probability of the ground truth class equal to one. In this case, the distillation loss is equivalent to the standard one-hot cross + +
VOC 15-5 (2 steps)VOC 15-1 (6 steps)
01-1516-20all01-1516-20all
PLOP [13]89.774.247.568.684.764.621.055.2
+Standard KD [35]90.774.449.269.288.466.413.454.8
+Unbiased KD [4]90.277.151.871.786.367.122.657.4
+LGKD (Ours)91.478.756.173.989.369.330.961.1
ADE20k 100-50 (2 steps)ADE20k 100-10 (6 steps)
01-100101-150all01-100101-150all
PLOP [13]26.742.114.632.923.939.414.531.1
+Standard KD [35]27.442.513.632.823.239.813.531.0
+Unbiased KD [4]27.042.614.533.223.739.815.131.5
+LGKD (Ours)27.443.625.737.526.042.122.035.4
+ +Table 4. Effect of different knowledge distillation terms. Standard KD is adopted in ILT [35] while unbiased KD is adopted in MiB [4]. + +
01-1516-20all
One-hot91.476.751.971.5
Expand only90.478.530.967.7
Expand & Transplant91.478.756.173.9
+ +Table 5. Effect of our novel set distillation design including expand and transplant operations. + +
λbλn01-1516-20all
0090.575.553.671.0
1091.376.953.171.9
2091.677.353.172.2
5091.877.952.072.4
10091.878.349.872.2
50.591.678.655.773.8
5191.478.756.173.9
5291.078.655.573.7
+ +Table 6. Effect of the weighted factors ${\lambda }_{n}$ and ${\lambda }_{\mathrm{b}}$ . + +entropy loss, discarding all the old class probabilities predicted by the old model. As expected, the base performance is slightly compromised compared with Expand & Transplant since the old class knowledge is not distilled. Nevertheless, the novel performance also drops since using hard labels for the novel class pixels will develop a bias toward novel classes, resulting in false positive predictions. This illustrates the significance of retaining the old class probabilities during transplant. Secondly, Expand only will encourage the new model to misclassify a novel class into either background or an old class. Thus, a sharp drop in novel mIoU from 56.1 to 30.9 is observed. This uncovers the importance of correcting the old model output by transplant to handle the background shift. Finally, transplanting the background probability into the corresponding ground truth novel class while retaining the old class probabilities can establish an appropriate class correspondence and facilitate learning new classes, hence yielding the best novel performance. + +Weighted factor. As table 6 shows, increasing $\lambda_{\mathrm{b}}$ leads to + +higher base performance, but it will compromise the novel performance when $\lambda_{\mathrm{b}}$ becomes too large, e.g., $\lambda_{\mathrm{b}} = 10$ . It indicates that the background set distillation is mainly responsible for retaining old knowledge. We set $\lambda_{\mathrm{b}} = 5$ as the optimal solution as it obtains promising base mIoU while not sacrificing the novel mIoU severely. With the novel set distillation kicking in, the novel mIoU is significantly improved from 52.0 to 56.1 with $\lambda_{n} = 1$ . Meanwhile, it also boosts the base mIoU from 77.9 to 78.7. This suggests that the novel set distillation facilitates learning new classes while maintaining the old class knowledge distilled from the old model. + +Effect of different KDs. To validate the superiority of LGKD, we compare our LGKD with other knowledge distillation (KD) terms on both VOC and ADE20k upon the same baseline PLOP [13] (Fig. 4), since PLOP does not adopt class probability-wise KD. Firstly, PLOP can hardly benefit from adding the standard KD [35], probably due to its tendency to misclassify new classes as the background (see Sec. 3.2). Secondly, though unbiased KD [4] yields a moderate boost on VOC, it makes almost no difference on the more challenging benchmark ADE20k. In contrast, LGKD consistently surpasses standard KD and unbiased KD by a significant margin, especially in terms of novel mIoU. Concretely, LGKD yields $+8.3 / +11.2 / +6.9$ points improvement against unbiased KD on 15-1/100-50/100-10 setting. + +# 4.6. Error Analysis + +We carry out comprehensive error analysis on both Pascal-VOC 2012 and ScanNet datasets to validate the effectiveness of our LGKD in mitigating the novel-background confusion problem. + +2D image. As Fig. 4 shows, under the VOC 15-5 incremental scenario, naive finetuning completely forgets the old class bird while also mistaking the background for the novel class potted plant. Thanks to KD mechanism, ILT [35], REMINDER [37], MiB [4], PLOP [13] and RCIL [61] are capable to retain the old knowledge (bird and chair). Nev + +![](images/5b46f10fce6c80ead65967ac3a82345c812a9e7b6fe052777680b2c8a4d37ab7.jpg) +Old classes: bird chair +New classes: potted plant Sofa +Figure 4. Error analysis of baselines along with our LGKD under VOC 15-5 setting. MiB [4], PLOP [13] and RCIL [61] tend to mistake weed and suitcase (background—things of no interest) for potted plant and sofa (novel classes) respectively. Such confusion is effectively alleviated when equipped with our LGKD, except for the bird image with RCIL, where the confusion is slightly mitigated. + +![](images/a0cad4b3110eedc47cfa79b7f07cf95012dbbc554e649b9e231d0e4f5a22cb39.jpg) +Figure 5. Error analysis of MiB [4] vs. LGKD+MiB on step 4 (with bathtub depicted in pink as the novel class) of the ScanNet 14-1 incremental scenario. Our LGKD effectively alleviates the confusion made by MiB (see the black boxes) — mistaking the background (dark purple) for the novel class bathtub. Meanwhile, LGKD+MiB achieves decent accuracy on the novel class bathtub (see the red boxes). + +ertheless, these methods are consistently prone to misclassifying the background (weed and suitcase—things of no interest) as novel classes (potted plant and sofa). On the contrary, when incorporating our LGKD into MiB, PLOP and RCIL, the above novel-background confusion is effectively suppressed, except for the bird image with RCIL, where the confusion is slightly alleviated. The above examples demonstrate the effectiveness of LGKD in tackling the novel-background confusion issue. More visualization results can be found in the supp. material. + +3D point cloud. We show the error results in Fig. 5 for step 4 of the ScanNet 14-1 setting, where the current novel class is bathtub depicted in pink. Clearly, our method effic + +tively corrects the false prediction made by MiB [4] (see the black boxes), where the background points (highlighted in dark purple) are mistaken for the novel class bathtub. Meanwhile, our LGKD does not sacrifice the capability to recognize the true bathtub points (see red boxes). + +# 5. Conclusion + +In this work, we identify a key issue in continual semantic segmentation (CSS)—novel background confusion. This is generally caused by the corrupted class correspondence during knowledge distillation. To alleviate such confusion, we propose a novel solution termed Label-Guided Knowledge Distillation (LGKD), which can establish an appropriate class correspondence between the output of the old and the new model for distillation, guided by the ground truth label. We validate its effectiveness on both existing 2D benchmarks and our proposed 3D CSS benchmark, where LGKD can consistently outperform competing methods by a large margin, especially on novel mIoU, setting new state-of-the-art. Finally, we hope this work will inspire further in-depth exploration of 3D CSS in the future. + +# 6. Acknowledgement + +This work is supported by the Hyundai research grant (04OIS000252C130). + +# References + +[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. Memory aware + +synapses: Learning what (not) to forget. 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Few-shot incremental learning with continually evolved classifiers. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 12455-12464, 2021. 3 +[61] Chang-Bin Zhang, Jia-Wen Xiao, Xialei Liu, Ying-Cong Chen, and Ming-Ming Cheng. Representation compensation networks for continual semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7053-7064, 2022. 2, 3, 6, 7, 8, 9 +[62] Yang Zhang, Zixiang Zhou, Philip David, Xiangyu Yue, Zerong Xi, Boqing Gong, and Hassan Foroosh. Polarnet: An improved grid representation for online lidar point clouds semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9601-9610, 2020. 2 +[63] Hengshuang Zhao, Jianping Shi, Xiaojuan Qi, Xiaogang Wang, and Jiaya Jia. Pyramid scene parsing network. In CVPR, 2017. 1, 2 +[64] Hanbin Zhao, Fengyu Yang, Xinghe Fu, and Xi Li. Rbc: Rectifying the biased context in continual semantic segmentation. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXXIV, pages 55-72. Springer, 2022. 3 +[65] Sixiao Zheng, Jiachen Lu, Hengshuang Zhao, Xiatian Zhu, Zekun Luo, Yabiao Wang, Yanwei Fu, Jianfeng Feng, Tao Xiang, Philip HS Torr, et al. Rethinking semantic segmentation from a sequence-to-sequence perspective with transformers. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 6881-6890, 2021. 1 +[66] Bolei Zhou, Hang Zhao, Xavier Puig, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Scene parsing through ade20k dataset. In CVPR, 2017. 6 +[67] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ade20k dataset. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9939-9948, 2021. 2 \ No newline at end of file diff --git a/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/images.zip b/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..84a1b3fb886e8668fa9b2fbfa31ab503314b5475 --- /dev/null +++ b/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:acf9ebd154d68e86347b37c030baeb0d92620a4862f4910817fe1e122552fd07 +size 757427 diff --git a/2023/Label-Guided Knowledge Distillation for Continual Semantic Segmentation on 2D Images and 3D Point Clouds/layout.json b/2023/Label-Guided Knowledge Distillation for Continual Semantic 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+ "index": 5 + }, + { + "bbox": [ + 143, + 258, + 192, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 258, + 192, + 271 + ], + "spans": [ + { + "bbox": [ + 143, + 258, + 192, + 271 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 284, + 290, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 290, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 290, + 632 + ], + "type": "text", + "content": "Continual semantic segmentation (CSS) aims to extend an existing model to tackle unseen tasks while retaining its old knowledge. Naively fine-tuning the old model on new data leads to catastrophic forgetting. A common solution is knowledge distillation (KD), where the output distribution of the new model is regularized to be similar to that of the old model. However, in CSS, this is challenging because of the background shift issue. Existing KD-based CSS methods continue to suffer from confusion between the background and novel classes since they fail to establish a reliable class correspondence for distillation. To address this issue, we propose a new label-guided knowledge distillation (LGKD) loss, where the old model output is expanded and transplanted (with the guidance of the ground truth label) to form a semantically appropriate class correspondence with the new model output. Consequently, the useful knowledge from the old model can be effectively distilled into the new model without causing confusion. We conduct extensive experiments on two prevailing CSS benchmarks, Pascal-VOC and ADE20K, where our LGKD significantly boosts the performance of three competing methods, especially on novel mIoU by up to " + }, + { + "bbox": [ + 46, + 284, + 290, + 632 + ], + "type": "inline_equation", + "content": "+76\\%" + }, + { + "bbox": [ + 46, + 284, + 290, + 632 + ], + "type": "text", + "content": ", setting new state-of-the-art. Finally, to further demonstrate its generalization ability, we introduce the first CSS benchmark for 3D point cloud based on ScanNet, along with several re-implemented baselines for comparison. Experiments show that LGKD is versatile in both 2D and 3D modalities without requiring ad hoc design. Codes are available at https://github.com/Ze-Yang/LGKD." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 652, + 128, + 665 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 652, + 128, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 652, + 128, + 665 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 673, + 287, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 287, + 697 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 287, + 697 + ], + "type": "text", + "content": "Fully supervised semantic segmentation has witnessed tremendous success [33, 63, 27, 8, 16, 22, 47, 65, 9] in re" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 257, + 545, + 453 + ], + "blocks": [ + { + "bbox": [ + 307, + 257, + 545, + 453 + ], + "lines": [ + { + "bbox": [ + 307, + 257, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 307, + 257, + 545, + 453 + ], + "type": "image", + "image_path": "5a842318a5f59736e908d670e8a3502e730702509059163ea18e851911ba5ad8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 455, + 547, + 579 + ], + "lines": [ + { + "bbox": [ + 304, + 455, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 547, + 579 + ], + "type": "text", + "content": "Figure 1. Illustration of knowledge distillation (KD) strategies in continual semantic segmentation. Standard KD and unbiased KD reduce the new class (bicycle) dimension(s) of the probabilities output by the new model via remove and combine respectively, which collapses the class correspondence across incremental steps and raises confusion between background and new classes (see Sec. 1). In contrast, our label-guided KD uses the ground truth label as guidance to expand the probabilities predicted by the old model. It builds a reliable class correspondence across different learning steps without discrepancy (ILT) or entanglement (MiB) (see Sec. 3.2). A " + }, + { + "bbox": [ + 304, + 455, + 547, + 579 + ], + "type": "inline_equation", + "content": "\\xrightarrow{\\text{mimic}}" + }, + { + "bbox": [ + 304, + 455, + 547, + 579 + ], + "type": "text", + "content": " B: encourage A to be similar to B." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "cent years. These algorithms generally assume a fixed number of classes to be learned. However, in real-world applications, it is often expected that a deployed model can be continuously generalized to handle new classes while not forgetting the old ones. A simple solution is to expand the original dataset with newly available samples and retrain a new model from scratch, dubbed as Joint Training. Obviously, this is computationally expensive and requires an increasing amount of space to store the old data over time." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 185, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 185, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 185, + 713 + ], + "type": "text", + "content": "*Corresponding author: Guosheng Lin" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18601" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "Further, it may raise privacy issues in some circumstances, e.g., medical images and face data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 98, + 287, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 98, + 287, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 98, + 287, + 229 + ], + "type": "text", + "content": "To address this problem, continual semantic segmentation (CSS) has been proposed by [35] as an emerging research direction, where the training scheme is separated into several steps with each step tackling a set of unseen classes. Specifically, given the old model and new training data (only new classes are labeled while others are treated as background), the new model is supposed to recognize both old and new classes. Under this scenario, naively finetuning the old model on new data tends to suffer from catastrophic forgetting [17, 26], where the recognition capability of old classes is quickly lost." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "type": "text", + "content": "Knowledge distillation (KD), first proposed in image classification [19], has recently been introduced to CSS [35, 4] to mitigate the forgetting issue. As Fig. 1 shows, " + }, + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "type": "inline_equation", + "content": "ILT" + }, + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "type": "text", + "content": " [35] removes new class probabilities (green bar) predicted by the new model, and simply distill old classes and background accordingly. However, they ignore the background shift problem [4], where the new class bicycle at current step " + }, + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "type": "text", + "content": " was labeled as background at last step " + }, + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 46, + 231, + 288, + 411 + ], + "type": "text", + "content": ". As a result, the old model, which regards bicycle as background, will output a high background score for the new class bicycle pixels. Via KD, it will mislead the new model to misclassify new classes as background. Obviously, this KD strategy hinders the learning of new classes because the class correspondence for distillation is corrupted, i.e., naively mapping the new background to the old background." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 412, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 544 + ], + "type": "text", + "content": "This issue was highlighted in " + }, + { + "bbox": [ + 46, + 412, + 287, + 544 + ], + "type": "inline_equation", + "content": "MiB" + }, + { + "bbox": [ + 46, + 412, + 287, + 544 + ], + "type": "text", + "content": " [4] where they proposed a new class correspondence by combination. Concretely, they combined new classes with the new background via probability summation (Fig. 1) to form a pseudo class, which was treated as the counterpart to the old background for distillation. However, this strategy, though alleviating class mis-correspondence, entangles new classes with the new background and tends to misclassify background as new classes, as detailed in Sec. 3.2. In this paper, we term the error of mistaking background for new (novel) classes or vice-versa as novel-background confusion." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "The key insight to overcome the novel-background confusion is to build a reliable class correspondence across different learning steps without corruption or entanglement. To this end, we devise a novel Label-Guided Knowledge Distillation (LGKD) loss, where the class probabilities predicted by the old model are expanded to have the same dimension as the output of the new model (see the blue block in Fig. 1). The background probability is then transplanted to the corresponding ground truth label (class) of the input pixels. In this way, the knowledge from the old background at the last step can be correctly distilled into its corresponding semantic class at the current step, i.e., either the new background or a novel class. Note that our LGKD is a generic regularization term with negligible computa" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "tional cost and can be easily incorporated into existing arts. We validate its effectiveness on two prevailing CSS benchmarks Pascal-VOC and ADE20K, where our LGKD consistently yields promising improvements upon three competing methods, especially on novel (new class) mIoU (up to " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "+76\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "), setting new state-of-the-art. To further demonstrate the generalization ability of our approach, we establish a challenging CSS benchmark based on ScanNet for 3D point cloud and re-implement multiple baselines for comparison. To our best knowledge, this is the first work to conduct CSS on 3D point cloud. Extensive experiments showcase that our LGKD loss is capable to handle both 2D and 3D modalities with no ad hoc design." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 230, + 545, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 230, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 230, + 545, + 243 + ], + "type": "text", + "content": "The main contributions of this paper can be summarized as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 315, + 250, + 545, + 469 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 315, + 250, + 545, + 298 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 250, + 545, + 298 + ], + "spans": [ + { + "bbox": [ + 315, + 250, + 545, + 298 + ], + "type": "text", + "content": "- We propose a new label-guided knowledge distillation (LGKD) loss for CSS, which builds a reliable class correspondence across incremental steps and alleviates novel-background confusion." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 305, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 305, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 315, + 305, + 545, + 389 + ], + "type": "text", + "content": "- LGKD is a generic regularization term with negligible computational cost, which can be readily combined with existing methods. Extensive experiments on two prevailing CSS benchmarks, Pascal-VOC and ADE20K, showcase that LGKD significantly improves three competitive methods, particularly on novel mIoU by up to " + }, + { + "bbox": [ + 315, + 305, + 545, + 389 + ], + "type": "inline_equation", + "content": "+76\\%" + }, + { + "bbox": [ + 315, + 305, + 545, + 389 + ], + "type": "text", + "content": ", setting new state-of-the-art." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 316, + 397, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 397, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 316, + 397, + 545, + 469 + ], + "type": "text", + "content": "- To further demonstrate its generalization capability, we establish the first CSS benchmark for 3D point cloud based on ScanNet and re-implement multiple baselines for comparison. Experiments illustrate that our LGKD is versatile in both 2D and 3D modalities without any ad hoc design." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 487, + 397, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 397, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 397, + 499 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "type": "text", + "content": "Semantic Segmentation, aiming to perform pixel-level classification, has witnessed great advancement [63, 6, 7, 53, 22, 16] in recent years since the pioneering work Fully Convolutional Network (FCN) [33]. Among the above methods, the DeepLab series [6, 7] is well-known for their effective designs, e.g., atrous spatial pyramid pooling (ASPP) [6], atrous convolution in cascade [7]. DeepLabv3 [7] is commonly used as the segmentation framework in prior CSS works [4, 13, 61]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "In 3D point cloud modality, PointNet [38] is a pioneering work to directly process unstructured point cloud. Subsequent work PointNet++ [39] learns to capture local structures and recognize fine-grained patterns via a hierarchical neural network that applies PointNet recursively. While more complicated techniques have been proposed in recent works [46, 45, 62, 68, 10], we employ PointNet++ as our 3D segmentation model for its simplicity and efficiency." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18602" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 281 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 281 + ], + "type": "image", + "image_path": "d20b9277ef6bef5cfa08df9dac0ba012aba9e3f4765a82868f524821621afb35.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "text", + "content": "Figure 2. Illustration of our LGKD loss. At learning step " + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "text", + "content": ", an input sample " + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "text", + "content": " is fed into the old (top) and new (bottom) models to obtain the class probabilities for each element " + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "inline_equation", + "content": "i \\in \\mathcal{I}" + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "text", + "content": " (pixel or point). These elements are then separated into the novel and background sets according to their ground truth label available at the current step " + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 283, + 547, + 350 + ], + "type": "text", + "content": " (yellow and green as novel set). Finally, to build up a reliable class correspondence, we extend the old probabilities (output by the old model) to have the same dimension as the new ones by expand and transplant (for novel set only), such that useful prior knowledge from the old model can be effectively distilled into the new model to facilitate learning new classes. We highlight that our LGKD can effectively alleviate the novel-background confusion issue as occurs in [35, 4]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 369, + 289, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 289, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 289, + 559 + ], + "type": "text", + "content": "Continual Learning aims at training a deep neural network to learn multiple tasks in sequence continually. Distinct from one-step incremental learning [50, 51, 55, 56, 59, 58, 30, 60, 29, 57, 31, 44], continual learning generally confronts more severe forgetting issues during multiple-step learning. Numerous works tackle the catastrophic forgetting issue and they can be classified into three categories. The model growing category [2, 48, 52] tackles this problem by dynamically extending model capacity. The memory replay approaches retain the old-class knowledge by keeping a small amount of old-class data in current training. Those data can be raw data [41, 40, 3], features [18, 23] or generated data [24, 42, 32]. The regularization approaches constrain the model by regularizing the parameters [26, 1, 54], the gradients [21, 5], logits [40, 3, 4] or the features [20, 12, 14] of the model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "Continual Semantic Segmentation. Existing CSS methods can be divided into two categories: 1) replay-based. RECALL [34] rehearses old-class data obtained by web-crawling or generative models. Similarly, [49] utilizes an iterative relabeling strategy with rehearsal-based incremental learning. Following [4], replay-based methods are out of the scope of this paper since accessing old data violates the conventional CSS assumption. 2) regularization-based. ILT [35] is the first work to introduce KD into CSS. MiB [4] raises the background shift problem in CSS and proposes an unbiased KD to tackle it. PLOP [13] distills both short- and long-range spatial relations via local pooled output distilla" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 368, + 547, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 547, + 513 + ], + "type": "text", + "content": "tion. SDR [36] leverages prototype matching, feature sparsification and contrastive learning to enforce feature consistency and discrimination. Most recently, class similarity KD, representation compensation, structure-preserving loss and feature projection, and the biased context are investigated by REMINDER [37], RCIL [61], SPPA [28] and RBC [64] respectively. However, the above approaches tend to suffer from the novel-background confusion problem since their distillation term lacks an appropriate class correspondence. Therefore, we propose a generic distillation term, dubbed LGKD, with a reliable class correspondence to alleviate this confusion issue." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 528, + 362, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 362, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 362, + 540 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 550, + 471, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 471, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 471, + 563 + ], + "type": "text", + "content": "3.1. Problem Definition and Setups" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Before introducing the continual learning setting, we first present the setups of the standard semantic segmentation task. To ensure the generality, let " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X} \\in \\mathbb{R}^{N \\times C_{\\mathrm{in}}}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " denote the input space (e.g., image, point cloud, etc.), where " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " is the number of input elements and " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{in}}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " is the number of input channels (typically " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{in}} = 3" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": ", i.e., RGB, for image and " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{in}} >= 3" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": ", e.g., XYZ, RGB, normals, for point cloud). Let " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} \\in \\mathcal{C}^N" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " denote the output label space, where " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " is a label set that contains all classes including the background class " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathsf{b} \\in \\mathcal{C}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": ". Note that each sample " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "x \\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " comprises a set of elements " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " (e.g., pixels, points, etc.) of corresponding label " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "y \\in \\mathcal{Y}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " with constant cardinality " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "|\\mathcal{I}| = N" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18603" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "Given a training set " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{T} \\subset \\mathcal{X} \\times \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": ", the target of semantic segmentation is to learn a model " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " parametrized by " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " that maps the input space " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " to a set of class probability vectors " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "f_{\\theta}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}|}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": ". The output segmentation mask is then computed as " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\hat{y} = \\{\\arg \\max_{c \\in \\mathcal{C}} f_{\\theta}(x)[i, c]\\}_{i=1}^{N}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x)[i, c]" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " is the probability of element " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " belonging to category " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": "As opposed to the standard training scheme where the model can access and learn from the full training set " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{T} \\subset \\mathcal{X} \\times \\mathcal{C}^N" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " all at once, continual learning, instead, involves several learning steps " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\{t\\}_{t=0}^{T}" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " each with a subset of label " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^t" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": ". More specifically, at training step " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": ", the previous label set " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{0:t-1}" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " will be expanded with a set of unseen classes " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^t" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " to form a new label set " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{0:t} = \\mathcal{C}^{0:t-1} \\cup \\mathcal{C}^t" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": ". Then a training set " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^t \\subset \\mathcal{X} \\times (\\mathcal{C}^t)^N" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " will be provided along with the last model " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "f_{\\theta^{t-1}}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}^{0:t-1}|}" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " to obtain an updated model " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "f_{\\theta^t}: \\mathcal{X} \\mapsto \\mathbb{R}^{N \\times |\\mathcal{C}^{0:t}|}" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": ". Note that the training set " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^t" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " may contain element " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "i \\in \\mathcal{I}" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " from either previous classes " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{0:t-1}" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " or future classes " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{t+1:T}" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": ", though the annotations are collapsed into the background class " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " at the current step " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": ". This is referred to as overlapped [4] setting. Following the standard incremental setup, we assume that the label sets of each step are disjoint from each other except for the special background class, i.e., " + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^i \\cap \\mathcal{C}^j = b" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "inline_equation", + "content": "i \\neq j" + }, + { + "bbox": [ + 46, + 157, + 288, + 362 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 369, + 250, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 250, + 382 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 250, + 382 + ], + "type": "text", + "content": "3.2. Revisiting Knowledge Distillation Loss" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": "A naive way to tackle the continual learning problem is to initialize a new model " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "f_{\\theta^t}" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": " with the weights of the last model " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "f_{\\theta^{t-1}}" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": " and then optimize the network with the training set " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^t" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": ". However, this will lead to the catastrophic forgetting of old classes " + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{0:t-1}" + }, + { + "bbox": [ + 46, + 388, + 287, + 460 + ], + "type": "text", + "content": ". Since no old class samples with annotation are available at the current step." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "type": "text", + "content": "Standard knowledge distillation. To alleviate the forgetting problem, knowledge distillation [19] is a common solution to preserve old knowledge by regularizing the output class probability distribution of the new model " + }, + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "type": "inline_equation", + "content": "f_{\\theta^t}" + }, + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "type": "text", + "content": " to be close to that of the old model " + }, + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "type": "inline_equation", + "content": "f_{\\theta^{t-1}}" + }, + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "type": "text", + "content": " given the same input sample. Formally, the standard knowledge distillation loss " + }, + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "type": "inline_equation", + "content": "\\ell_{\\mathrm{kd}}" + }, + { + "bbox": [ + 46, + 463, + 287, + 547 + ], + "type": "text", + "content": " adopted in CSS by ILT [35] can be formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 555, + 287, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 287, + 583 + ], + "type": "interline_equation", + "content": "\\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y) = - \\frac {1}{| \\mathcal {I} |} \\sum_ {i \\in \\mathcal {I}} \\sum_ {c \\in \\mathcal {C} ^ {0: t - 1}} q _ {x} ^ {t - 1} (i, c) \\log \\hat {q} _ {x} ^ {t} (i, c), \\tag {1}", + "image_path": "3fa793d88fb296a673050f9108e033ba55d60b1126b58dc6745eda011ac16efc.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "spans": [ + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\hat{q}_x^t (i,c)" + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "text", + "content": " refers to the probability of class " + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "text", + "content": " for element " + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "text", + "content": " predicted by " + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "inline_equation", + "content": "f_{\\theta^t}" + }, + { + "bbox": [ + 47, + 593, + 287, + 618 + ], + "type": "text", + "content": " but re-normalized over all old classes:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 84, + 627, + 287, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 627, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 84, + 627, + 287, + 645 + ], + "type": "interline_equation", + "content": "\\hat {q} _ {x} ^ {t} (i, c) = q _ {x} ^ {t} (i, c) / \\sum_ {k \\in \\mathcal {C} ^ {0: t - 1}} q _ {x} ^ {t} (i, k). \\tag {2}", + "image_path": "46c160122ecd1c6bbe0d27533a7b4b3f95aa93a5abbba096f7fb7d0f5fab2559.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "However, there exists a discrepancy issue in the standard distillation loss. Concretely, it fails to leverage prior knowledge to cope with the new classes, as the new class probabilities " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "q_{x}^{t}(i,c)" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{C}^t \\setminus b" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": ") are not incorporated in distillation (Eq. 1). Moreover, it wrongly enhances the background" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "type": "text", + "content": "probability for novel class elements due to the background shift [4]. Hence, it tends to mistake the novel classes for the background (refer to supp. material for detailed discussion)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 110, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 148 + ], + "type": "text", + "content": "Unbiased knowledge distillation. To overcome the above issue, MiB [4] proposes an unbiased knowledge distillation loss for CSS by revising " + }, + { + "bbox": [ + 304, + 110, + 545, + 148 + ], + "type": "inline_equation", + "content": "\\hat{q}_x^t (i,c)" + }, + { + "bbox": [ + 304, + 110, + 545, + 148 + ], + "type": "text", + "content": " in Eq. 2 as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 342, + 154, + 545, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 154, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 342, + 154, + 545, + 186 + ], + "type": "interline_equation", + "content": "\\hat {q} _ {x} ^ {t} (i, c) = \\left\\{ \\begin{array}{l l} q _ {x} ^ {t} (i, c) & \\text {i f} c \\neq \\mathfrak {b} \\\\ \\sum_ {k \\in \\mathcal {C} ^ {t}} q _ {x} ^ {t} (i, k) & \\text {i f} c = \\mathfrak {b}, \\end{array} \\right. \\tag {3}", + "image_path": "5f3a960926e16f3ad5f3c6c2d16a9c35554ffc02bcd3a15e63b614b5429f7610.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "text", + "content": "where they compare the old background probability " + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "inline_equation", + "content": "q_{x}^{t - 1}(i,\\mathsf{b})" + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "text", + "content": " with the probability of being either a novel class or the new background, i.e., " + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\sum_{k\\in \\mathcal{C}^t}q_x^t (i,k)" + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "text", + "content": ", rather than directly with its counterpart " + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "inline_equation", + "content": "q_{x}^{t}(i,\\mathsf{b})" + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "text", + "content": ". Such class probability combination mechanism is meant to facilitate distilling the knowledge from the old background class defined at step " + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "text", + "content": " to the novel classes at step " + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 192, + 546, + 361 + ], + "type": "text", + "content": ". Nevertheless, it entangles the novel classes with the new background due to the probability combination. As a consequence of entanglement, the probabilities of novel classes will be undesirably enhanced when the distillation loss only intends to improve the probabilities of the new background, and vice versa. As opposed to ILT [35], this leads to the other confusion — misclassifying background as novel classes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 366, + 503, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 366, + 503, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 366, + 503, + 380 + ], + "type": "text", + "content": "3.3. Label-Guided Knowledge Distillation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "type": "text", + "content": "Class separation. Unlike standard KD and unbiased KD, which apply the same KD strategy to all input elements, we propose to separate the input elements into two sets according to the ground truth label available at the current step, namely the background set " + }, + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "type": "inline_equation", + "content": "S_{\\mathsf{b}} = \\{i|i\\in \\mathcal{I},y_i = \\mathsf{b}\\}" + }, + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "type": "text", + "content": " and the novel set " + }, + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "type": "inline_equation", + "content": "S_{n} = \\{i|i\\in \\mathcal{I},y_{i}\\in \\mathcal{C}^{t}\\setminus \\mathsf{b}\\}" + }, + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "type": "text", + "content": ". In this way, we can customize the distillation strategy for each class set and establish a more accurate class correspondence, which facilitates more effective knowledge distillation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": "Class correspondence. As opposed to revising the class probabilities of the new model " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "q_{x}^{t}(i,c)" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " as in [4], we instead resort to correcting the class probabilities of the old model " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "q_{x}^{t - 1}(i,c)" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " according to the ground truth label " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": ". Our design is inspired by the wireless communication system. In order to improve the useful information captured by the receiver, one should ensure that the signal released by the transmitter is correct and that both transmitter and receiver share the same communication protocol. Likewise, in our case, the objective is to assure the class probabilities (signal) predicted by the old model " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta^{t - 1}}" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " (transmitter) contain correct class semantics (after background shift) and are well-aligned with (protocol) the output class space of the new model " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta^t}" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " (receiver). Protocol: For the elements from the novel set " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "S_{n}" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": ", we expand the output of the old model " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "q_{x}^{t - 1}(i,c)" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " with zero probability assigned to the extra novel classes " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{C}^t \\setminus \\mathbf{b}" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " such that it has the same output class space dimensions with the new model. Signal: Due to the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18604" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "background shift, we transplant the probability of the background to the corresponding ground truth novel class and set the background probability to zero while maintaining the others unchanged. The final corrected probability distribution to be distilled from can be formulated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 62, + 138, + 287, + 183 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 138, + 287, + 183 + ], + "spans": [ + { + "bbox": [ + 62, + 138, + 287, + 183 + ], + "type": "interline_equation", + "content": "\\bar {q} _ {x} ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} ^ {t} \\text {a n d} c \\neq y _ {i} \\\\ q _ {x} ^ {t - 1} (i, \\mathrm {b}) & \\text {i f} c = y _ {i} \\\\ q _ {x} ^ {t - 1} (i, c) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {4}", + "image_path": "d383d25e5614c839bd2b8fce62d726d0b58f0ed03180d66eaecc594e39e8bd33.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "inline_equation", + "content": "i \\in S_n" + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "text", + "content": ". We highlight that, this novel set distillation strategy can preserve the knowledge from " + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "inline_equation", + "content": "f_{\\theta^{t-1}}" + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "text", + "content": " for the old classes while also correcting the class probabilities from the old model for the new classes given the ground truth label " + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "text", + "content": " as guidance. As for the case of the background set " + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "inline_equation", + "content": "i \\in S_b" + }, + { + "bbox": [ + 46, + 191, + 287, + 275 + ], + "type": "text", + "content": ", it can be treated in a similar yet simpler way by merely expanding zero probability for the extra novel classes as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 84, + 284, + 287, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 284, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 84, + 284, + 287, + 316 + ], + "type": "interline_equation", + "content": "\\bar {q} _ {x} ^ {t - 1} (i, c) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} c \\in \\mathcal {C} ^ {t} \\backslash \\mathfrak {b} \\\\ q _ {x} ^ {t - 1} (i, c) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {5}", + "image_path": "81576dd08b59e55fc5253ecb7eb322c00ab64fc187ffc20b97421b4d0648f04f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 324, + 245, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 245, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 245, + 335 + ], + "type": "text", + "content": "In summary, our distillation loss can be given as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 343, + 287, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 343, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 59, + 343, + 287, + 360 + ], + "type": "interline_equation", + "content": "\\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y) = \\lambda_ {n} \\cdot \\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S} _ {n}) + \\lambda_ {\\mathfrak {b}} \\cdot \\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S} _ {\\mathfrak {b}}), \\tag {6}", + "image_path": "f98527e099318d61dc8d697580c3389609c1938647854739530a2187caaee8c4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\lambda_{n}" + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{b}}" + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "text", + "content": " balances the contribution of the novel set " + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "inline_equation", + "content": "S_{n}" + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "text", + "content": " and background set " + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{b}}" + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\bar{\\ell}_{\\mathrm{kd}}^{\\theta^{t}}(x,y,\\mathcal{S})" + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "text", + "content": " is the distillation loss defined within set " + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 368, + 287, + 403 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 410, + 287, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 410, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 55, + 410, + 287, + 439 + ], + "type": "interline_equation", + "content": "\\bar {\\ell} _ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y, \\mathcal {S}) = - \\frac {1}{N} \\sum_ {i \\in \\mathcal {S}} \\sum_ {c \\in \\mathcal {C} ^ {0: t}} \\bar {q} _ {x} ^ {t - 1} (i, c) \\log q _ {x} ^ {t} (i, c). \\tag {7}", + "image_path": "50482b9cf48d7c04e3e28bd4abdd2535e9735be917d991365a44ec8a619d4aaa.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 448, + 252, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 448, + 252, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 448, + 252, + 459 + ], + "type": "text", + "content": "The overall training objective is then computed as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 60, + 468, + 287, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 468, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 60, + 468, + 287, + 498 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\theta^ {t}\\right) = \\frac {1}{\\left| \\mathcal {T} ^ {t} \\right|} \\sum_ {(x, y) \\in \\mathcal {T} ^ {t}} \\left(\\lambda \\ell_ {c e} ^ {\\theta^ {t}} (x, y) + \\ell_ {\\mathrm {k d}} ^ {\\theta^ {t}} (x, y)\\right), \\tag {8}", + "image_path": "d1d111174ea93eb109b947f0ea9ba37540abcce2824795b47e7e67ce416a8078.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\ell_{ce}^{\\theta^t}(x,y)" + }, + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "type": "text", + "content": " is the cross-entropy loss. " + }, + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "type": "text", + "content": " is the hyperparameter to balance the importance of the two terms, and is set as " + }, + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\lambda = 1" + }, + { + "bbox": [ + 46, + 508, + 287, + 545 + ], + "type": "text", + "content": " in experiments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 555, + 123, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 123, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 123, + 569 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 575, + 271, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 271, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 271, + 588 + ], + "type": "text", + "content": "4.1. Benchmarking 3D Continual Segmentation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "type": "text", + "content": "Existing CSS methods have mainly been evaluated on 2D CSS benchmarks, leaving a significant gap in the exploration of 3D CSS. In order to validate the versatility of LGKD across different modalities, we introduce the first 3D CSS benchmark based on ScanNet [11] and present several baseline methods for comparison." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "ScanNet contains 1201 and 312 indoor scenes in the training and validation set respectively with 20 classes in total, including a special class for \"other furniture\", i.e. background in the standard segmentation task. In Fig. 3, we" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 312, + 75, + 539, + 243 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 539, + 243 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 539, + 243 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 539, + 243 + ], + "type": "image", + "image_path": "695c663d0d51fece92c00017d9f94956c57e4c16cfee9a6c6f6ae5e5d8454d2c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 251, + 545, + 274 + ], + "lines": [ + { + "bbox": [ + 305, + 251, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 545, + 274 + ], + "type": "text", + "content": "Figure 3. The scene-wise class frequency statistics of our proposed ScanNet benchmark for 3D continual semantic segmentation." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 293, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 544 + ], + "type": "text", + "content": "provide the scene-wise class frequency statistics of ScanNet [11], including both train and validation sets. The scene-wise class frequency indicates the number of scenes that a certain class appears in. Surprisingly, we find that ScanNet exhibits a challenging long-tail category distribution. Additionally, we provide the point-wise class frequency statistics and demonstrate the difficulty of our proposed benchmark in the supp. material. For a challenging CSS benchmark, we split the entire class set into multiple subsets according to the descending order of scene-wise class frequency as in Fig. 3, with the tail classes constituting the novel sets for continual learning. This means that the novel classes to be learned in each step are set to be those rare ones, a.k.a. tail classes in the long-tail field. Following the Pascal-VOC 2012 CSS benchmark [35, 4], we define three different incremental scenarios: adding one class (18-1), adding five classes simultaneously (14-5) and sequentially (14-1). Take 14-5 setting for instance, the last five rare classes, i.e., counter, refrigerator, bookshelf, bathtub, shower curtain, form the novel class set, and likewise for the other settings." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 544, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 652 + ], + "type": "text", + "content": "We form the training set by including all the scenes that contain at least one point from the novel classes at the current step, with the others (either previous or future classes) annotated as \"other furniture\". The validation set is established in a similar way except that the label of the previous classes " + }, + { + "bbox": [ + 304, + 544, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{0:t-1}" + }, + { + "bbox": [ + 304, + 544, + 545, + 652 + ], + "type": "text", + "content": " are maintained, as the model is required to predict all seen classes up to the current step. Finally, we report the old-, new- and all-class mIoU metrics as well as the background IoU at the end of all incremental steps." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 659, + 425, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 425, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 425, + 672 + ], + "type": "text", + "content": "4.2. Baselines and Setups" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "To validate the effectiveness of our approach, we conduct thorough comparison with the latest state-of-the-art CSS methods as well as baselines. FT is a straightforward" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18605" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 70, + 533, + 260 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 533, + 260 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 533, + 260 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 533, + 260 + ], + "type": "table", + "html": "
Method19-1 (2 steps)15-5 (2 steps)15-1 (6 steps)
01-1920all01-1516-20all01-1516-20all
FT†-6.812.9--2.133.1--0.21.8-
EWC† [26]-26.914.0--24.335.5--0.34.3-
LwF-MC† [40]-64.413.3--58.135.0--6.48.4-
ILT† [35]-67.112.3--66.340.6--4.97.8-
ILT* [35]88.666.28.364.589.265.238.159.977.73.77.98.2
SDR* [36]90.068.924.267.890.176.650.971.183.934.113.031.5
REIMINDER* [37]91.975.633.974.490.275.149.169.683.365.227.057.0
SPPA [28]--36.274.6--52.972.1--23.356.0
MiB† [4]-70.222.1--75.549.4--35.113.5-
MiB* [4]90.371.523.270.189.674.246.368.383.238.013.934.5
LGKD+MiB (Ours)91.472.140.471.591.675.254.871.179.739.317.035.9
PLOP* [13]92.175.336.174.289.774.247.568.684.764.621.055.2
LGKD+PLOP (Ours)92.976.542.975.791.478.756.173.989.369.330.961.1
RCIL* [61]90.173.624.572.188.975.948.470.083.967.923.158.0
LGKD+RCIL (Ours)92.876.537.575.591.477.654.372.789.469.029.160.5
Joint93.777.678.178.493.779.073.678.493.779.073.678.4
", + "image_path": "8e20b00d4cbaca6114da3fa18b73c1377263746772e3341beaaab61db876920c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 261, + 547, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 547, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 547, + 297 + ], + "type": "text", + "content": "Table 1. Continual Semantic Segmentation performance (mIoU) on Pascal-VOC 2012 under different incremental scenarios. † indicates the results are excerpted from [4]. * suggests the results are reproduced with the official codes. 0 stands for the background class and all represents the mIoU over all classes including the background. Best results are highlighted in Red while runner-up in Blue." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 314, + 289, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 289, + 567 + ], + "type": "text", + "content": "lower-bound baseline, which simply finetunes the model with the newly available data at each step. On the contrary, Joint, training a standard segmentation model on all classes within a single step, may serve as an upper bound for CSS approaches, though not always true if the CSS benchmark shows a long-tail nature with tail classes as new classes (e.g., ScanNet). For completeness, we include two general continual learning methods [26, 40] that are not specifically designed for semantic segmentation. Further, we mainly benchmark against the recent state-of-the-art methods taylored for segmentation [35, 4, 13, 36, 37, 61]. Following [4], we do not consider replay-based methods, e.g., [40]) in our comparison as the access to previous annotated data violates the standard class-incremental learning assumption. For the sake of generalization, we conduct experiments on both 2D image modality, i.e., Pascal-VOC 2012 [15] and ADE20K [66], and 3D point cloud modality, i.e. ScanNet [11]. Besides the old-, new- and all-class (including the background class) mIoU, we additionally report the background IoU because it is a special category under CSS with its semantic content varying across different learning steps." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": "CSS protocols. As for the label masking policy for the incremental steps, [4] follows and adapts two different CSS protocols, namely disjoint [35] and overlapped [43]. Both protocols assume that only the novel classes at the current step are labeled while the others are masked out as background. However, in the disjoint protocol, input samples for step " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " should only contain elements (i.e., pixels or points) that belong to either current or previous classes, i.e., " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{0:t}" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": ". On the contrary, the overlapped protocol allows the input samples to contain either previous, current or future classes, i.e., " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^{0:T}" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": ". The disjoint protocol makes a strong assumption that the current training data should not contain any samples" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 314, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 351 + ], + "type": "text", + "content": "of the class we would like to learn in the future, which is impracticable. Therefore, we adopt the more realistic overlapped protocol throughout our experiments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 357, + 440, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 357, + 440, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 357, + 440, + 369 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 375, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 579 + ], + "type": "text", + "content": "In 2D image modality, we follow the framework DeepLabv3 [7] and training hyperparameters of the baselines when building our LGKD upon them, except that we adopt synchronized batch normalization with different batch size and learning rate settings. In 3D point cloud modality, we use PointNet++ [39] with multi-scale grouping as our base model. We use Adam [25] with an initial learning rate " + }, + { + "bbox": [ + 304, + 375, + 545, + 579 + ], + "type": "inline_equation", + "content": "10^{-2}" + }, + { + "bbox": [ + 304, + 375, + 545, + 579 + ], + "type": "text", + "content": " for the first step and " + }, + { + "bbox": [ + 304, + 375, + 545, + 579 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 375, + 545, + 579 + ], + "type": "text", + "content": " for the subsequent steps and set the weight decay to 0. The learning rate is decayed by 0.7 every 100 epochs. We train our network for 500 epochs with a batch size of 32. We remove possible duplicated points before calculating the IoU metric. For all benchmarks, we report the mIoU results on the standard validation set. We run our experiments on two NVIDIA RTX 3090 GPUs for Pascal VOC 2012 and ADE20K while one for ScanNet. More details can be found in the supp. material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 585, + 389, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 389, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 389, + 597 + ], + "type": "text", + "content": "4.4. Performance" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Pascal-VOC 2012 consists of 10,582 images for training and 1449 images for validation with 20 foreground categories. Following [4], we conduct three different continual learning scenarios, i.e., adding one class (19-1), five classes simultaneously (15-5) and sequentially (15-1). The split of the class set for each class-incremental step follows the alphabetical order. Table 1 shows comprehensive results of our method along with other baselines. Clearly, FT performs poorly across all the incremental settings as the old" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "18606" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 544, + 198 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 544, + 198 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 544, + 198 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 544, + 198 + ], + "type": "table", + "html": "
Method100-50 (2 steps)100-10 (6 steps)50-50 (3 steps)
01-100101-150all01-100101-150all01-5051-150all
ILT† [35]10.918.414.417.08.50.03.11.18.63.412.99.7
MiB† [4]19.740.717.232.80.038.611.129.20.046.521.029.3
REMINDER* [37]26.642.116.133.424.038.920.332.624.248.020.129.4
SPPA [28]-42.919.9--41.012.5--49.823.9-
PLOP* [13]26.742.114.632.923.939.414.531.124.548.220.729.8
LGKD+PLOP (Ours)27.443.625.737.526.042.122.035.425.349.429.436.0
RCIL* [61]26.341.717.333.50.037.214.929.521.247.823.031.2
LGKD+RCIL (Ours)26.743.325.137.224.042.220.434.925.749.127.234.4
Joint29.142.628.237.729.142.628.237.729.149.232.137.7
", + "image_path": "49553776dc6888e2ad3b0fc771d9019bd0f0290b9c3e9e8191daa66ebe224107.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 239, + 544, + 321 + ], + "blocks": [ + { + "bbox": [ + 47, + 199, + 546, + 232 + ], + "lines": [ + { + "bbox": [ + 47, + 199, + 546, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 546, + 232 + ], + "type": "text", + "content": "Table 2. The mIoU(%) of the last step on the ADE20K dataset for different overlapped continual learning scenarios. " + }, + { + "bbox": [ + 47, + 199, + 546, + 232 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 47, + 199, + 546, + 232 + ], + "type": "text", + "content": " indicates the results are excerpted from [13]. * suggests the results are reproduced with the official codes. Best results are highlighted in Red while runner-up in Blue." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 239, + 544, + 321 + ], + "lines": [ + { + "bbox": [ + 50, + 239, + 544, + 321 + ], + "spans": [ + { + "bbox": [ + 50, + 239, + 544, + 321 + ], + "type": "table", + "html": "
Method18-1 (2 steps)14-5 (2 steps)14-1 (6 steps)
01-1819all01-1415-19all01-1415-19all
FT19.20.028.62.418.60.044.312.019.20.07.82.9
ILT [35]23.814.925.815.926.722.243.427.719.30.018.55.6
MiB [4]55.155.032.253.852.957.845.554.545.556.529.749.2
LGKD+MiB (Ours)55.255.540.854.854.357.649.055.351.955.738.451.2
Joint53.255.040.954.253.256.747.554.253.256.747.554.2
", + "image_path": "dc850b93113b3d64538e2e5ad3dfb14299c416837475f7797d36c96aaffa76cc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 322, + 545, + 344 + ], + "lines": [ + { + "bbox": [ + 47, + 322, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 322, + 545, + 344 + ], + "type": "text", + "content": "Table 3. Continual Semantic Segmentation performance (mIoU) on ScanNet under different incremental scenarios. " + }, + { + "bbox": [ + 47, + 322, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 322, + 545, + 344 + ], + "type": "text", + "content": " stands for the background class and all represents the mIoU over all classes including the background. All results are obtained with our implementation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 363, + 289, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 289, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 289, + 602 + ], + "type": "text", + "content": "class pixels are masked as background under CSS setup, and the model is explicitly taught to wrongly predict the old classes as background. EWC [26] yields similar results for novel classes while fairly outperforming the FT baseline in terms of base mIoU. Significant improvement on base classes across all settings can be observed when knowledge distillation is introduced in [40, 35]. MiB [4] obtains consistent improvement on both base and novel performance across different settings, due to addressing the background shift problem in CSS. Recent approaches [14, 61] obtain drastically higher performance against MiB when multiple incremental steps are involved (15-1). Despite their promising performance, our LGKD is able to further boost their performance by a large margin, especially on novel performance. For instance, LGKD+MiB achieves " + }, + { + "bbox": [ + 46, + 363, + 289, + 602 + ], + "type": "inline_equation", + "content": "+74\\%" + }, + { + "bbox": [ + 46, + 363, + 289, + 602 + ], + "type": "text", + "content": " (40.4 vs. 23.2) improvement against MiB on novel mIoU under 19-1 setting. These promising novel class results along with the improved background performance prove that our LGKD loss can effectively alleviate the novel-background confusion problem." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "ADE20K [67] is a challenging dataset consisting of 20,210 training and 2000 testing images of complex scenes. Similar to VOC, we conducted three different CSS scenarios, i.e., 100-50, 100-10 and 50-50, as shown in Table 2. Specifically, we build our LGKD upon two competitive methods, i.e., PLOP [13] and RCIL [61], where LGKD achieves considerable improvement, especially on novel mIoU (up to " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "+76\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " from 14.6 to 25.7 with PLOP under 100-50 setting), setting new state-of-the-art across all incremental scenarios." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 363, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 579 + ], + "type": "text", + "content": "ScanNet. As shown in Table 3, we compare our method with FT baseline, ILT [35] and MiB [4] on our proposed ScanNet benchmark to illustrate the generality of LGKD in 3D modality. Similar to their performance in 2D modality, FT and ILT suffer from catastrophic forgetting when learning new classes. However, MiB significantly outperforms the former methods across all three settings and metrics, in particular, the base class performance, which once again demonstrates the effectiveness of tackling the background shift in CSS. Compared with MiB, our LGKD further improves the novel performance by a large margin: " + }, + { + "bbox": [ + 304, + 363, + 545, + 579 + ], + "type": "inline_equation", + "content": "+27\\%" + }, + { + "bbox": [ + 304, + 363, + 545, + 579 + ], + "type": "text", + "content": " (40.8 vs. 32.2) and " + }, + { + "bbox": [ + 304, + 363, + 545, + 579 + ], + "type": "inline_equation", + "content": "+29\\%" + }, + { + "bbox": [ + 304, + 363, + 545, + 579 + ], + "type": "text", + "content": " (38.4 vs. 29.7) relative improvement of novel mIoU against MiB are obtained under 18-1 and 14-1 settings respectively, which proves the considerable importance of overcoming the background shift with correct class correspondence. It is also noteworthy that our approach also outperforms joint training, which shows that LGKD is also effective in alleviating long-tail issues." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 585, + 400, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 400, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 400, + 597 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 602, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 602, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 602, + 545, + 639 + ], + "type": "text", + "content": "Unless otherwise stated, all ablative studies are conducted upon VOC 15-5 setting with PLOP [13] as the baseline. Refer to the supp. material for the rationale." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Expand & Transplant. We compare three different designs for novel set distillation in Table 5. Firstly, One-hot is a hard-label distillation with all the class probabilities transplanted to the ground truth novel class, making the probability of the ground truth class equal to one. In this case, the distillation loss is equivalent to the standard one-hot cross" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18607" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 100, + 70, + 496, + 209 + ], + "blocks": [ + { + "bbox": [ + 100, + 70, + 496, + 209 + ], + "lines": [ + { + "bbox": [ + 100, + 70, + 496, + 209 + ], + "spans": [ + { + "bbox": [ + 100, + 70, + 496, + 209 + ], + "type": "table", + "html": "
VOC 15-5 (2 steps)VOC 15-1 (6 steps)
01-1516-20all01-1516-20all
PLOP [13]89.774.247.568.684.764.621.055.2
+Standard KD [35]90.774.449.269.288.466.413.454.8
+Unbiased KD [4]90.277.151.871.786.367.122.657.4
+LGKD (Ours)91.478.756.173.989.369.330.961.1
ADE20k 100-50 (2 steps)ADE20k 100-10 (6 steps)
01-100101-150all01-100101-150all
PLOP [13]26.742.114.632.923.939.414.531.1
+Standard KD [35]27.442.513.632.823.239.813.531.0
+Unbiased KD [4]27.042.614.533.223.739.815.131.5
+LGKD (Ours)27.443.625.737.526.042.122.035.4
", + "image_path": "8bf54184ea3c6ef69c3468d5ef88540764c7263aa98497c36dc727e5d8a6dc40.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 238, + 281, + 288 + ], + "blocks": [ + { + "bbox": [ + 47, + 209, + 535, + 220 + ], + "lines": [ + { + "bbox": [ + 47, + 209, + 535, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 535, + 220 + ], + "type": "text", + "content": "Table 4. Effect of different knowledge distillation terms. Standard KD is adopted in ILT [35] while unbiased KD is adopted in MiB [4]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 238, + 281, + 288 + ], + "lines": [ + { + "bbox": [ + 56, + 238, + 281, + 288 + ], + "spans": [ + { + "bbox": [ + 56, + 238, + 281, + 288 + ], + "type": "table", + "html": "
01-1516-20all
One-hot91.476.751.971.5
Expand only90.478.530.967.7
Expand & Transplant91.478.756.173.9
", + "image_path": "0fe51e8aff0ad7785689832e9c561f338211753f961dee1951db50c4c136b66c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 74, + 325, + 263, + 434 + ], + "blocks": [ + { + "bbox": [ + 47, + 289, + 286, + 310 + ], + "lines": [ + { + "bbox": [ + 47, + 289, + 286, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 286, + 310 + ], + "type": "text", + "content": "Table 5. Effect of our novel set distillation design including expand and transplant operations." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 325, + 263, + 434 + ], + "lines": [ + { + "bbox": [ + 74, + 325, + 263, + 434 + ], + "spans": [ + { + "bbox": [ + 74, + 325, + 263, + 434 + ], + "type": "table", + "html": "
λbλn01-1516-20all
0090.575.553.671.0
1091.376.953.171.9
2091.677.353.172.2
5091.877.952.072.4
10091.878.349.872.2
50.591.678.655.773.8
5191.478.756.173.9
5291.078.655.573.7
", + "image_path": "91f187122e7207ce24e5f6b8b7e3bbfa34290db23a8d2cbe8fef44321564ae96.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 76, + 435, + 257, + 444 + ], + "lines": [ + { + "bbox": [ + 76, + 435, + 257, + 444 + ], + "spans": [ + { + "bbox": [ + 76, + 435, + 257, + 444 + ], + "type": "text", + "content": "Table 6. Effect of the weighted factors " + }, + { + "bbox": [ + 76, + 435, + 257, + 444 + ], + "type": "inline_equation", + "content": "{\\lambda }_{n}" + }, + { + "bbox": [ + 76, + 435, + 257, + 444 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 76, + 435, + 257, + 444 + ], + "type": "inline_equation", + "content": "{\\lambda }_{\\mathrm{b}}" + }, + { + "bbox": [ + 76, + 435, + 257, + 444 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 468, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 696 + ], + "type": "text", + "content": "entropy loss, discarding all the old class probabilities predicted by the old model. As expected, the base performance is slightly compromised compared with Expand & Transplant since the old class knowledge is not distilled. Nevertheless, the novel performance also drops since using hard labels for the novel class pixels will develop a bias toward novel classes, resulting in false positive predictions. This illustrates the significance of retaining the old class probabilities during transplant. Secondly, Expand only will encourage the new model to misclassify a novel class into either background or an old class. Thus, a sharp drop in novel mIoU from 56.1 to 30.9 is observed. This uncovers the importance of correcting the old model output by transplant to handle the background shift. Finally, transplanting the background probability into the corresponding ground truth novel class while retaining the old class probabilities can establish an appropriate class correspondence and facilitate learning new classes, hence yielding the best novel performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": "Weighted factor. As table 6 shows, increasing " + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{b}}" + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": " leads to" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "text", + "content": "higher base performance, but it will compromise the novel performance when " + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{b}}" + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "text", + "content": " becomes too large, e.g., " + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{b}} = 10" + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "text", + "content": ". It indicates that the background set distillation is mainly responsible for retaining old knowledge. We set " + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{b}} = 5" + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "text", + "content": " as the optimal solution as it obtains promising base mIoU while not sacrificing the novel mIoU severely. With the novel set distillation kicking in, the novel mIoU is significantly improved from 52.0 to 56.1 with " + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "inline_equation", + "content": "\\lambda_{n} = 1" + }, + { + "bbox": [ + 304, + 239, + 545, + 382 + ], + "type": "text", + "content": ". Meanwhile, it also boosts the base mIoU from 77.9 to 78.7. This suggests that the novel set distillation facilitates learning new classes while maintaining the old class knowledge distilled from the old model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 386, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 566 + ], + "type": "text", + "content": "Effect of different KDs. To validate the superiority of LGKD, we compare our LGKD with other knowledge distillation (KD) terms on both VOC and ADE20k upon the same baseline PLOP [13] (Fig. 4), since PLOP does not adopt class probability-wise KD. Firstly, PLOP can hardly benefit from adding the standard KD [35], probably due to its tendency to misclassify new classes as the background (see Sec. 3.2). Secondly, though unbiased KD [4] yields a moderate boost on VOC, it makes almost no difference on the more challenging benchmark ADE20k. In contrast, LGKD consistently surpasses standard KD and unbiased KD by a significant margin, especially in terms of novel mIoU. Concretely, LGKD yields " + }, + { + "bbox": [ + 304, + 386, + 545, + 566 + ], + "type": "inline_equation", + "content": "+8.3 / +11.2 / +6.9" + }, + { + "bbox": [ + 304, + 386, + 545, + 566 + ], + "type": "text", + "content": " points improvement against unbiased KD on 15-1/100-50/100-10 setting." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 572, + 398, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 572, + 398, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 572, + 398, + 585 + ], + "type": "text", + "content": "4.6. Error Analysis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 591, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 591, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 591, + 545, + 639 + ], + "type": "text", + "content": "We carry out comprehensive error analysis on both Pascal-VOC 2012 and ScanNet datasets to validate the effectiveness of our LGKD in mitigating the novel-background confusion problem." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "2D image. As Fig. 4 shows, under the VOC 15-5 incremental scenario, naive finetuning completely forgets the old class bird while also mistaking the background for the novel class potted plant. Thanks to KD mechanism, ILT [35], REMINDER [37], MiB [4], PLOP [13] and RCIL [61] are capable to retain the old knowledge (bird and chair). Nev" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18608" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 70, + 470, + 297 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 470, + 297 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 470, + 297 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 470, + 297 + ], + "type": "image", + "image_path": "5b46f10fce6c80ead65967ac3a82345c812a9e7b6fe052777680b2c8a4d37ab7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 478, + 141, + 538, + 182 + ], + "lines": [ + { + "bbox": [ + 478, + 141, + 538, + 182 + ], + "spans": [ + { + "bbox": [ + 478, + 141, + 538, + 182 + ], + "type": "text", + "content": "Old classes: bird chair" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 478, + 198, + 542, + 239 + ], + "lines": [ + { + "bbox": [ + 478, + 198, + 542, + 239 + ], + "spans": [ + { + "bbox": [ + 478, + 198, + 542, + 239 + ], + "type": "text", + "content": "New classes: potted plant Sofa" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 300, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 547, + 335 + ], + "type": "text", + "content": "Figure 4. Error analysis of baselines along with our LGKD under VOC 15-5 setting. MiB [4], PLOP [13] and RCIL [61] tend to mistake weed and suitcase (background—things of no interest) for potted plant and sofa (novel classes) respectively. Such confusion is effectively alleviated when equipped with our LGKD, except for the bird image with RCIL, where the confusion is slightly mitigated." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 350, + 287, + 448 + ], + "blocks": [ + { + "bbox": [ + 50, + 350, + 287, + 448 + ], + "lines": [ + { + "bbox": [ + 50, + 350, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 50, + 350, + 287, + 448 + ], + "type": "image", + "image_path": "a0cad4b3110eedc47cfa79b7f07cf95012dbbc554e649b9e231d0e4f5a22cb39.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 451, + 288, + 529 + ], + "lines": [ + { + "bbox": [ + 46, + 451, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 288, + 529 + ], + "type": "text", + "content": "Figure 5. Error analysis of MiB [4] vs. LGKD+MiB on step 4 (with bathtub depicted in pink as the novel class) of the ScanNet 14-1 incremental scenario. Our LGKD effectively alleviates the confusion made by MiB (see the black boxes) — mistaking the background (dark purple) for the novel class bathtub. Meanwhile, LGKD+MiB achieves decent accuracy on the novel class bathtub (see the red boxes)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 552, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 673 + ], + "type": "text", + "content": "ertheless, these methods are consistently prone to misclassifying the background (weed and suitcase—things of no interest) as novel classes (potted plant and sofa). On the contrary, when incorporating our LGKD into MiB, PLOP and RCIL, the above novel-background confusion is effectively suppressed, except for the bird image with RCIL, where the confusion is slightly alleviated. The above examples demonstrate the effectiveness of LGKD in tackling the novel-background confusion issue. More visualization results can be found in the supp. material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "3D point cloud. We show the error results in Fig. 5 for step 4 of the ScanNet 14-1 setting, where the current novel class is bathtub depicted in pink. Clearly, our method effic" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 353, + 547, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 547, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 547, + 413 + ], + "type": "text", + "content": "tively corrects the false prediction made by MiB [4] (see the black boxes), where the background points (highlighted in dark purple) are mistaken for the novel class bathtub. Meanwhile, our LGKD does not sacrifice the capability to recognize the true bathtub points (see red boxes)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 422, + 379, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 379, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 379, + 434 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 442, + 547, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 547, + 610 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 547, + 610 + ], + "type": "text", + "content": "In this work, we identify a key issue in continual semantic segmentation (CSS)—novel background confusion. This is generally caused by the corrupted class correspondence during knowledge distillation. To alleviate such confusion, we propose a novel solution termed Label-Guided Knowledge Distillation (LGKD), which can establish an appropriate class correspondence between the output of the old and the new model for distillation, guided by the ground truth label. We validate its effectiveness on both existing 2D benchmarks and our proposed 3D CSS benchmark, where LGKD can consistently outperform competing methods by a large margin, especially on novel mIoU, setting new state-of-the-art. Finally, we hope this work will inspire further in-depth exploration of 3D CSS in the future." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 619, + 416, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 619, + 416, + 632 + ], + "spans": [ + { + "bbox": [ + 306, + 619, + 416, + 632 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 639, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 639, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 547, + 662 + ], + "type": "text", + "content": "This work is supported by the Hyundai research grant (04OIS000252C130)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 671, + 365, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 365, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 365, + 684 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 691, + 546, + 713 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 691, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 310, + 691, + 546, + 713 + ], + "type": "text", + "content": "[1] Rahaf Aljundi, Francesca Babiloni, Mohamed Elhoseiny, Marcus Rohrbach, and Tinne Tuytelaars. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 9939-9948, 2021. 2" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "18612" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_content_list.json b/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..94c0cb8a75d6584c10602ccc96867e12b65c6823 --- /dev/null +++ b/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_content_list.json @@ -0,0 +1,1569 @@ +[ + { + "type": "text", + "text": "Label-Noise Learning with Intrinsically Long-Tailed Data", + "text_level": 1, + "bbox": [ + 192, + 130, + 777, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yang Lu $^{1,2*}$ Yiliang Zhang $^{1,2}$ Bo Han $^{3}$ Yiu-ming Cheung $^{3}$ Hanzi Wang $^{1,2}$", + "bbox": [ + 158, + 178, + 807, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Fujian Key Laboratory of Sensing and Computing for Smart City, School of Informatics, Xiamen University, Xiamen, China", + "bbox": [ + 114, + 200, + 854, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Key Laboratory of Multimedia Trusted Perception and Efficient Computing,", + "bbox": [ + 254, + 217, + 712, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ministry of Education of China, Xiamen University, Xiamen, China", + "bbox": [ + 281, + 234, + 684, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Department of Computer Science, Hong Kong Baptist University, Hong Kong, China", + "bbox": [ + 228, + 253, + 738, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "luyang@xmu.edu.cn ylzhangcs@hotmail.com {bhanml, ymc}@comp.hkbu.edu.hk hanzi.wang@xmu.edu.cn", + "bbox": [ + 122, + 272, + 844, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 321, + 313, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Label noise is one of the key factors that lead to the poor generalization of deep learning models. Existing label-noise learning methods usually assume that the ground-truth classes of the training data are balanced. However, the real-world data is often imbalanced, leading to the inconsistency between observed and intrinsic class distribution with label noises. In this case, it is hard to distinguish clean samples from noisy samples on the intrinsic tail classes with the unknown intrinsic class distribution. In this paper, we propose a learning framework for label-noise learning with intrinsically long-tailed data. Specifically, we propose two-stage bi-dimensional sample selection (TABASCO) to better separate clean samples from noisy samples, especially for the tail classes. TABASCO consists of two new separation metrics that complement each other to compensate for the limitation of using a single metric in sample separation. Extensive experiments on benchmarks demonstrate the effectiveness of our method. Our code is available at https://github.com/Wakings/TABASCO.", + "bbox": [ + 75, + 353, + 473, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 670, + 209, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Under the support of a large amount of high-quality labeled data, deep neural networks have achieved great success in various fields [27, 40, 7]. However, it is expensive and difficult to obtain a large amount of high-quality labeled data in many practical applications. Instead, the commonly used large-scale training data is usually obtained from the Internet or crowdsourcing platforms like Amazon Mechanical Turk, which is unreliable and may be mislabeled [52, 43]. The models trained on this kind of unreliable data, called noisy-labeled data, often produce poor generalization performance because deep neural networks tend to overfit noisy samples due to their large model capacity. In", + "bbox": [ + 75, + 695, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/22e148d9b056a7487ba405eda466053370f0d945b7ff477a2b438a49a21ec20e.jpg", + "image_caption": [ + "(a) Class distribution" + ], + "image_footnote": [], + "bbox": [ + 500, + 321, + 687, + 425 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/348c53ee3757a4e47bad2047be5b399853813846bb127ad12b77972385732830.jpg", + "image_caption": [ + "(b) Loss distribution", + "Figure 1: (a) An example of observed class distribution with noisy labels with long-tailed intrinsic class distribution. (b) The training loss of each sample under noisy-labeled and long-tailed data." + ], + "image_footnote": [], + "bbox": [ + 694, + 321, + 870, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the literature, there are some works to obtain a robust model trained on noisy-labeled data [11, 44]. Among them, the most straightforward and effective way is to differentiate between clean and noisy samples based on their differences in specific metrics, such as training loss [12, 29, 23].", + "bbox": [ + 496, + 522, + 892, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "These label-noise learning methods generally assume that the intrinsic class distribution of the training data is balanced, where each class has almost the same number of samples in terms of their unknown ground-truth labels. However, the data in real-world applications are often imbalanced, e.g., the LVIS dataset [9] and the iNaturalist dataset [17]. The class imbalance usually exhibits in the form of a long-tail distribution, where a small portion of classes possess a large number of samples, and the other classes possess a small number of samples only [38, 18]. In this case, the model training tends to the head classes and ignores the tail classes [60, 62]. When both noisy labels and long-tail distribution exist, training a robust model is even more challenging. There are two key challenges in this scenario. (1) Distribution inconsistency: The observed and intrinsic distributions are likely inconsistent due to noise labels, making the model more difficult to discover and focus on the intrinsic tail classes. As illustrated in Fig. 1(a), the intrinsic class distribution of the dataset is long-tailed, while the existence of noisy labels makes the distribution more", + "bbox": [ + 496, + 599, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Yang Lu is the corresponding author: luyang@xmu.edu.cn", + "bbox": [ + 94, + 886, + 413, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1369", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "balanced. The intrinsic tail classes, e.g., classes 6 and 9, are occupied by a large number of noisy data, making them no longer tail classes by observation. (2) Tail inseparability: Even if the tail class is identified, it is more difficult than ever to distinguish between clean and noisy samples in the tail class because clean samples are overwhelmed by noises that make their values of the separation metric highly similar. As illustrated in Fig. 1(b), the training loss of clean and noisy samples in the tail class are generally inseparable compared with the ones in the other classes. Several preliminary works have studied the joint problem of label noise and long-tail distribution [21, 49, 24, 2]. These methods implicitly reduce the complexity of the problem by assuming a similar noise rate for each class. However, this assumption is too strong to apply because noisy samples from the head classes may be the majority, resulting in a higher noise rate in the tail class than in other classes.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a Two-stAge Bi-dimensionAl Sample seleCtiOn (TABASCO) strategy to address the problem of label-noise learning with intrinsically long-tailed data. In the first stage, we propose to use two new separation metrics for sample separation, i.e., weighted Jensen-Shannon divergence (WJSD) and adaptive centroid distance (ACD), which work corporately to separate clean samples from noisy samples in the tail classes. The proposed metrics are complementary, where WJSD separates the samples from the output perspective while ACD does that from the feature perspective. In the second stage, we determine the separation dimension with better separability for each class and perform sample selection. In order to evaluate the method uniformly and effectively, we introduce two benchmarks with real-world noise and intrinsically long-tailed distribution. The main contributions of our work can be summarized as follows:", + "bbox": [ + 75, + 348, + 472, + 604 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a more general problem of label-noise learning with intrinsically long-tailed data. The key challenges in this problem are distribution inconsistency and tail inseparability.", + "- We propose an effective solution called TABASCO. With the help of two new separation metrics, it is able to effectively identify and select clean samples of the intrinsic tail class.", + "- We introduce two benchmarks with real-world noise and intrinsically long-tailed distribution. Extensive experiments on them show the effectiveness of our method and the limitations of existing methods." + ], + "bbox": [ + 94, + 614, + 468, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 821, + 218, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Label-Noise Learning", + "text_level": 1, + "bbox": [ + 76, + 845, + 281, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A straightforward strategy to deal with noisy data is to reduce the proportion of noise in training samples by sepa", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "rating noisy samples from clean samples. Methods such as co-teaching [12] and DivideMix [29] adopt the small loss trick, while Jo-SRC [55] and UNICON [23] use Jensen-Shannon divergence instead for sample selection. In contrast to methods that separate at the label level, some methods [30, 34] attempt to separate samples at the feature space. There are also some methods to avoid over-fitting the model to noisy data by imposing regularization constraints on model parameters [50, 10] or labels [37, 58, 32]. Other methods mitigate the influence of noisy data by adjusting the loss functions, such as backward and forward loss correction [36], gold loss correction [16], MW-Net [41] and Dual-T [54].", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Long-tail Learning", + "text_level": 1, + "bbox": [ + 500, + 295, + 683, + 311 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Re-balancing the data for long-tail distributions is a classical strategy to solve the problem of long-tail learning, such as re-sampling [4, 31, 8, 13] and data augmentation [61, 57, 5]. In addition, there are methods to improve the model generalization by introducing long-tail robust loss functions [6, 3, 45, 39]. Methods such as FTL [56], RIDE [46] and DiVE [15] try to solve the problem by using the idea of transfer learning. Recently, approaches based on decoupling [22, 61, 59] split end-to-end learning into feature learning and classifier retraining such that the obtained feature extractor is less affected by the long-tail distribution. In contrast to the above methods with the supervised learning paradigm, CReST [47], ABC [28] and DARP [25] attempt to solve the long-tail problem in the manner of semi-supervised learning.", + "bbox": [ + 496, + 318, + 890, + 546 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Label-Noise Learning on Long-tailed Data", + "text_level": 1, + "bbox": [ + 500, + 553, + 861, + 569 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Research on this joint problem has just been explored. CNLCU [51] relaxes the constraint of the small loss trick by regarding a portion of large loss samples as clean samples to reduce the probability of misclassifying clean samples to noisy samples in the tail class. RoLT [49] uses the distance from the samples to the centroid of the current class instead of the training loss for sample selection. HAR [2] uses an adaptive approach to regularize noise and tail class samples. Karthik et al. [24] uses the idea of decoupling to fine-tune the loss function for better robustness after feature learning by the self-supervised method. ULC [19] introduces uncertainty to enhance the separation ability of noise samples. H2E [53] reduces hard noises to easy ones by learning a classifier as noise identifier invariant to the class and context distributional changes.", + "bbox": [ + 496, + 575, + 890, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Problem Definition", + "text_level": 1, + "bbox": [ + 500, + 815, + 684, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a training set $\\mathcal{D} = \\{x_i, \\hat{y}_i\\}_{i=1}^N$ , where $\\hat{y}_i \\in [M]$ is the observed label of the sample $x_i$ . $N$ is the number of training samples, and $M$ is the number of classes. In our problem, $\\mathcal{D}$ has the following properties:", + "bbox": [ + 496, + 838, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1370", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e2fb5fbcd490fc645823e0de49b016a33494bce676d8b24cf9f2e12b8ee9f4bb.jpg", + "image_caption": [ + "Figure 2: The proposed framework for label-noise learning with intrinsically long-tailed data." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 890, + 272 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Noisy-labeled. There is a subset of samples $\\hat{\\mathcal{D}} \\in \\mathcal{D}$ , where a sample $\\{x, \\hat{y}\\} \\in \\hat{\\mathcal{D}}$ has an unknown ground-truth label $y$ different from its observed label $\\hat{y}$ .", + "- Long-tailed. The ground-truth class distribution is long-tailed. Supposing $n_c$ is the number of the samples in class $c$ , we have $n_1 > n_2 > \\dots > n_M$ ." + ], + "bbox": [ + 94, + 308, + 468, + 405 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We call this kind of training data intrinsically long-tailed because the observed class distribution may not be long-tailed due to the existence of noisy labels. Therefore, our goal is to learn from noisy-labeled data with the intrinsically long-tailed class distribution. The problem is challenging from two aspects. On the one hand, directly applying long-tail learning methods [6, 3, 45] is infeasible because the observed class distribution may be inconsistent with the intrinsic class distribution. On the other hand, label-noise learning methods perform poorly in the tail classes because they usually contain more noisy samples due to insufficient data, as shown in Fig. 1(a). It results in high noise rates in the tail classes, which brings great challenges to separating clean samples and noisy samples for further training. Under this circumstance, the existing sample selection methods [29, 23] often fail to select clean samples in the tail class. The main reason is that it is difficult to distinguish the tail class data from the noisy label data by existing metrics like cross-entropy loss, as shown in Fig. 1(b).", + "bbox": [ + 75, + 410, + 472, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 709, + 250, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we propose a two-stage bi-dimensional sample selection (TABASCO) to address the problem of label-noise learning with intrinsically long-tailed data. TABASCO decouples the sample selection process into two stages: (1) sample separation, and (2) dimension and cluster selection. First, given an initial model $\\theta$ trained on the original training data $\\mathcal{D}$ , we propose to calculate bi-dimension metrics for each sample in each observed class based on the outputs and features of the model. Second, we determine the separation dimension with better separability for each class, and we adopt the corresponding selection strategy to", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "select the cluster with more clean samples based on the selected metric. Last, we adopt semi-supervised learning to update the model by regarding the selected clean cluster as labeled data. The overall framework is shown in Fig. 2.", + "bbox": [ + 496, + 309, + 890, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Bi-Dimensional Separation Metrics", + "text_level": 1, + "bbox": [ + 498, + 378, + 807, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the deficiency of a single separation metric to distinguish clean samples from noisy samples in the complex situation of noisy labels with intrinsic long-tail distribution, we propose to jointly use two metrics from different perspectives: weighted Jensen-Shannon divergence (WJSD) and adaptive centroid distance (ACD). Both metrics are specifically designed for the joint problem and are complementary to cover the case when only one of them cannot separate clean samples from noisy samples well. WJSD fully utilizes the information of prediction confidence, while ACD relies on the distance in the feature space. Thus, using clustering on samples according to the values of their bi-dimensional metrics has the flexibility to separate samples with different imbalance ratios, noise ratios, and noise types.", + "bbox": [ + 496, + 402, + 890, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first reduce the separation granularity to alleviate the interference from the head class to the tail class. Specifically, the separation is performed within each observed class according to the proposed bi-dimensional metrics. We first divide training set $\\mathcal{D}$ into subsets according to the observed labels $\\mathcal{D}_c = \\{(x,\\hat{y})\\mid \\hat{y} = c\\}$ . Given a sample $(x_{i},\\hat{y}_{i})\\in \\mathcal{D}_{c}$ , the model predictions obtained from the model $\\theta$ is denoted as $\\mathbf{p}_i = [p_i^1,p_i^2,\\dots,p_i^M ]$ , where $p_i^j$ is the $j$ 's dimension of vector $\\mathbf{p}_i$ . The one-hot representation of the observed label $\\hat{y}_i$ is denoted as $\\hat{\\mathbf{y}}_i$ .", + "bbox": [ + 496, + 631, + 890, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Weighted Jensen-Shannon Divergence The Jensen-Shannon Divergence (JSD) is a commonly used metric to separate samples by assessing the variability of model predictions [55, 23]. It is defined as:", + "bbox": [ + 496, + 787, + 890, + 848 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nJ S D \\left(x _ {i}\\right) = \\frac {1}{2} K L \\left(\\mathbf {p} _ {i} \\left\\| \\frac {\\mathbf {p} _ {i} + \\hat {\\mathbf {y}} _ {i}}{2}\\right) + \\frac {1}{2} K L \\left(\\hat {\\mathbf {y}} _ {i} \\left\\| \\frac {\\mathbf {p} _ {i} + \\hat {\\mathbf {y}} _ {i}}{2}\\right), \\right. \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 852, + 890, + 896 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1371", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $KL(\\cdot \\|\\cdot)$ is the Kullback-Leibler divergence. When the intrinsic distribution is balanced, the JSD values of clean samples are generally lower than the noisy samples, so the separation can be easily modeled. However, when the distribution is intrinsically long-tailed, the noisy and clean samples in a tail class tend to obtain similar prediction confidence on the observed class $c$ , because their predictions are both towards the head classes. In this case, using JSD as a separation metric fails to separate them. The reason is given by Theorem 1, which shows the upper bound of the absolute value of the JSD difference between two samples.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 (Upper bound of JSD difference) Suppose $x_{i}$ and $x_{j}$ are two samples in class $c$ , $p_{i}^{c}$ and $q_{i}^{c}$ are the $c$ 's dimension of their prediction confidence $\\mathbf{p}_{i} = [p_{i}^{1}, p_{i}^{2}, \\dots, p_{i}^{M}]$ and $\\mathbf{p}_{j} = [p_{j}^{1}, p_{j}^{2}, \\dots, p_{j}^{M}]$ , respectively. The upper bound of the absolute value of the difference between their JSD values is given by:", + "bbox": [ + 76, + 257, + 472, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n| J S D (x _ {i}) - J S D (x _ {j}) | \\leq \\frac {1}{2} \\log \\left(\\frac {p _ {i} ^ {c} + 1}{p _ {i} ^ {c}}\\right) | p _ {i} ^ {c} - p _ {j} ^ {c} |.\n$$\n", + "text_format": "latex", + "bbox": [ + 93, + 352, + 454, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 shows that the difference between values of JSD is only determined by the prediction confidence of the observed class, i.e., $p_i^c$ and $p_j^c$ . In addition, as $|p_i^c - p_j^c|$ gets smaller with a fixed value of $p_i^c$ , $|JSD(x_i) - JSD(x_j)|$ is also smaller. This indicates that when two samples are in the same class $c$ with close values of $p_i^c$ , their JSD values are also close, which makes it difficult to separate them.", + "bbox": [ + 75, + 388, + 468, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Nevertheless, we can utilize the prediction confidence on other classes, i.e., $p_i^d$ for $d \\neq c$ , to distinguish two samples even if their values of $p_i^c$ are close. Specifically, we propose WJSD by imposing an additional weight on JSD to further distinguish samples by inspecting their prediction confidence on other classes rather than the observed class. First, we take the maximum prediction confidence $\\max(\\mathbf{p}_i)$ into account because it may reflect the confidence of a noisy sample's ground-truth class $y_i$ . Then, we calculate the ratio of the maximum prediction confidence to the prediction confidence of the observed class $\\max(\\mathbf{p}_i) / p_i^c$ . In this manner, the additional weight is greater than one only if the class with the maximum prediction confidence is not the observed class. The larger gap between $\\max(\\mathbf{p}_i)$ and $p_i^c$ makes the weight higher. To avoid exceptionally large weights by the division during normalization over all samples in class $c$ for later clustering, we set the upper bound according to the averaged prediction confidence over all samples in class $c$ . Finally, the additional weight can be calculated as follows:", + "bbox": [ + 75, + 494, + 472, + 796 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nW \\left(x _ {i}\\right) = \\min \\left(\\max \\left(\\mathbf {p} _ {i}\\right) / p _ {i} ^ {c}, \\max \\left(\\bar {\\mathbf {p}} _ {c}\\right) / \\bar {p} _ {c} ^ {c}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 801, + 468, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{\\mathbf{p}}_c = [\\bar{p}_c^1,\\bar{p}_c^2,\\dots,\\bar{p}_c^M] = \\frac{1}{|\\mathcal{D}_c|}\\sum_{i = 1}^{|\\mathcal{D}_c|}\\mathbf{p}_i$ is the average prediction confidence of class $c$ . Thus, WJSD can be calculated by:", + "bbox": [ + 76, + 825, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nW J S D \\left(x _ {i}\\right) = W \\left(x _ {i}\\right) \\times J S D \\left(x _ {i}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 880, + 468, + 897 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remarks: Compared with the value of JSD that is only related to the prediction confidence on the observed class, adopting the maximum prediction confidence in WJSD can better separate clean samples from noisy samples.", + "bbox": [ + 496, + 90, + 890, + 152 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Adaptive Centroid Distance. Although the sample separability of WJSD is greatly improved compared with JSD, the separation metric still relies on model prediction. When all the noisy samples labeled in a class are from another class, e.g., asymmetric noise, the model prediction for both noisy and clean samples will be highly similar because it is easy to learn a classifier that maps the features from two different classes into one. It results in low discrimination between the model predictions of clean and noisy samples in this case. Thus, solely using WJSD may not be enough to separate the clean and noisy samples when model predictions (in terms of all classes, not only about $p^c$ ) are close.", + "bbox": [ + 496, + 156, + 890, + 338 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Except for separating the samples in the output space, we propose another metric calculated in the feature space to eliminate the bias from the classifier because the learned features are more robust to noise labels. Specifically, for a given sample, we can calculate the distance between its feature and the class feature centroid to evaluate how the feature of a sample deviates from its class centroid. This approach is only practical when the quality of the centroid is high. Directly calculating the centroid according to the observed label may not be accurate because it involves a certain number of features of the noisy samples. Therefore, we define purity in Definition 1 to assess the quality of the centroid of class $c$ .", + "bbox": [ + 496, + 338, + 890, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 1 (Purity) Suppose a noisy sample set of class $c$ be $\\mathcal{D}_c = \\{(x,\\hat{y})\\mid \\hat{y} = c\\}$ , where the intrinsic label corresponding to the sample is $y$ . The purity $P_{\\mathcal{D}_c}$ of set $\\mathcal{D}_c$ is calculated by:", + "bbox": [ + 496, + 534, + 890, + 594 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {\\mathcal {D} _ {c}} = \\max _ {k = 1, \\dots , M} \\left\\{\\frac {\\sum_ {i = 1} ^ {N} I \\left(y _ {i} = k\\right)}{N} \\right\\}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 598, + 890, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I(\\cdot)$ is an indicator function and $N$ is the number of samples in the set $\\mathcal{D}_c$ .", + "bbox": [ + 496, + 643, + 893, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Purity indicates the proportion of an intrinsic class that takes the majority in the observed class $c$ . The higher the purity of a class set used to calculate the centroid, the better the centroid helps to distinguish between noise and clean samples. RoLT [49] adopts a similar idea to use class feature centroid for noisy sample detection. However it directly calculates the feature centroid on the observed class, such that it inevitably suffers from the existence of noise features when the purity is low, especially in our problem.", + "bbox": [ + 496, + 674, + 890, + 810 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to improve the purity of the class feature centroid for distance calculation between features, we propose ACD as the second separation metric to separate samples jointly with WJSD. The feature centroid for each class is adaptively updated by involving samples with high confidence from the observed class. The class centroid $\\mathbf{o}_c$ based", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1372", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "on a high-confidence sample set $\\mathcal{D}_c^H$ is calculated by:", + "bbox": [ + 76, + 90, + 434, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {o} _ {c} = \\frac {1}{| \\mathcal {D} _ {c} ^ {H} |} \\sum_ {i = 1} ^ {| \\mathcal {D} _ {c} ^ {H} |} \\mathbf {f} _ {i}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 111, + 468, + 155 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {c} ^ {H} = \\left\\{x _ {i} \\mid x _ {i} \\in \\mathcal {D} _ {c}, p _ {i} ^ {t _ {c}} > H _ {c} \\right\\}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 157, + 468, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{f}_i$ is the feature of $x_{i}$ , and $t_c = \\mathrm{argmax}_c\\{\\bar{p}_c^j\\}$ is the class index with the largest average prediction confidence of class $c$ . Thus, we can use the prediction confidence of class $t_c$ for sample $x_{i}$ , e.g., $p_i^{t_c}$ , as the selection criteria compare with the threshold $H_{c}$ . $\\mathcal{D}_c^H$ is constructed by the samples in $D_{c}$ whose corresponding prediction confidence of class $t_c$ is higher than $H_{c}$ . The high-confidence threshold $H_{c}$ is defined as:", + "bbox": [ + 76, + 181, + 472, + 303 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH _ {c} = \\frac {1}{D _ {c}} \\sum_ {i = 1} ^ {| D _ {c} |} w _ {i} \\times p _ {i} ^ {t _ {c}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 305, + 468, + 347 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} = \\max \\left(1, p _ {i} ^ {t _ {c}} / \\bar {p} _ {c} ^ {t _ {c}}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 349, + 468, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$H_{c}$ is calculated by the weighted sum of the prediction confidence of class $t_c$ for all samples $x_{i}$ . The weight $w_{i}$ increases when a sample's prediction confidence of class $t_c$ is higher than its class average. Thus, the threshold is high enough to ensure the purity of the selected samples. High confidence samples are more representative and more likely to be in the same class. It is worth noting that we choose more representative samples rather than clean samples because the clean samples in the tail classes are easily overwhelmed by the noise samples in our problem. In this case, it is difficult to select the clean samples directly because the noise samples may be more representative in the tail class. As for asymmetric noise, the choice of clean or noisy samples to obtain centroid for sample separation is equivalent.", + "bbox": [ + 75, + 373, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In each round, the centroids are adaptively adjusted because the feature extractor in the model is updated, as well as the set $\\mathcal{D}_c^H$ . Therefore, the proposed metric ACD can be calculated by:", + "bbox": [ + 75, + 585, + 470, + 646 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA C D \\left(x _ {i}\\right) = \\cos \\left(\\mathbf {f} _ {i}, \\mathbf {o} _ {c}\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 651, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remarks: The proposed two metrics, WJSD and ACD, are complementary for sample separation in the tail classes. When the ground-truth classes of the noisy samples are diverse, e.g. symmetric noise, WJSD plays the dominant role because the predictions can hardly be unified due to the class diversity of noisy samples. They are more likely to be predicted towards their ground-truth class, which can be captured by $\\max (\\mathbf{p}_i)$ . In this case, ACD may not be effective in separating clean samples from noisy samples because the messy noisy samples may affect the purity of the calculated centroid. On the other hand, when the ground-truth classes of the noisy samples belong to only one class, e.g., asymmetric noise, WJSD tends to produce similar predictions for noisy and clean samples, while the adaptive centroid in ACD can help distinguish them in the feature space.", + "bbox": [ + 75, + 672, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: The Dimension Selection Strategy" + ], + "code_body": "Input: Noise sample set $\\mathcal{D}_c$ in class $c$ , threshold $\\eta$ \nOutput: Cluster $\\mathcal{G}_c^1, \\mathcal{G}_c^2$ \n1 Obtain $\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2$ and separation threshold $d$ by applying GMM with values of WJSD to all samples in $\\mathcal{D}_c$ \n2 Obtain $\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2$ by applying GMM with values of ACD to all samples in $\\mathcal{D}_c$ \n3 Calculate the mean $\\mu_1, \\mu_2$ and variance $\\sigma_1, \\sigma_2$ of WJSD for $\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2$ \n4 if $\\mu_1 < d < \\mu_2$ and $\\sigma_2 / \\sigma_1 < \\eta$ then \n5 return $\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2$ \n6 else if $\\mu_1 > d$ and $\\mu_2 > d$ then \n7 return $\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2$ \n8 else \n9 return $\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2$ \n10 end", + "bbox": [ + 506, + 112, + 862, + 356 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Bi-Dimensional Sample Selection", + "text_level": 1, + "bbox": [ + 500, + 383, + 790, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once the values of the bi-dimensional metrics for all samples in class $c$ are calculated, each sample can be represented by a point in a 2D space. For each dimension, Gaussian mixture model (GMM) can be adopted to separate the samples in class $c$ into two clusters $\\mathcal{G}_c^1$ , $\\mathcal{G}_c^2$ .", + "bbox": [ + 498, + 410, + 892, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dimension Selection. Because each metric shows different separability for different noise types, we first propose a dimension selection strategy to select a proper dimension to separate clean and noisy samples. We consider three cases to select the proper dimension: (a) both of them are acceptable; (b) the separability of WJSD is better; (c) the separability of ACD is better. In short, we only need to figure out if WJSD is suitable for sample separation. If it is certain that WJSD does not show good separability, ACD will be adopted. Fig. 3 shows three cases for dimension selection.", + "bbox": [ + 496, + 494, + 892, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, we use the statistics of WJSD as the criterion of dimension selection. We measure the means $(\\mu_1,\\mu_2)$ and standard deviations $(\\sigma_{1},\\sigma_{2})$ of WJSD for two clusters separated by GMM in terms of ACD. We have two cases that can determine when WJSD is better. We mainly compare", + "bbox": [ + 496, + 647, + 893, + 724 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2de398f5880d8ca6a5cb6c69c9c5ba5bff5667799a17761e1e0b4df02a61fdfb.jpg", + "image_caption": [ + "Figure 3: Examples of three cases of the optimal separation dimension correspond to sample distribution in bidimensional metrics." + ], + "image_footnote": [], + "bbox": [ + 506, + 734, + 877, + 851 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1373", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mu_{1}$ and $\\mu_{2}$ with the threshold $d$ of GMM in WJSD. First, as shown in Fig. 3 (b), if one cluster $\\mathcal{G}_{acd}^{1}$ of ACD has a $\\mu_{1}$ less than $d$ and a $\\sigma_{1}$ much larger than $\\sigma_{2}$ in another cluster with a $\\mu_{2}$ larger than $d$ , it means that cluster $\\mathcal{G}_{acd}^{1}$ has more clean samples but also many noise samples. So in this case, ACD is improper and WJSD is proper. Second, if both $\\mu_{1}, \\mu_{2}$ are greater than $d$ , it means that it is a representation of the previous case in the tail class because there are fewer clean samples in the cluster. So, in this case, WJSD is proper. The strategy is summarized in Algorithm 1.", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cluster Selection. Once we have determined the separation dimension, we can obtain two sample clusters $\\mathcal{G}_c^1$ and $\\mathcal{G}_c^2$ . However, it is not clear which cluster contains more clean samples because the noisy samples may overwhelm the clean samples in some cases. Therefore, we need to further select a cluster between $\\mathcal{G}_c^1$ and $\\mathcal{G}_c^2$ as the clean one. For the cluster separated based on WJSD, we simply choose the one with a smaller average WJSD value as the cluster with more clean samples, denoted as $\\mathcal{D}_c^{clean}$ [29, 23]. For the cluster separated based on ACD, we cannot directly select the cluster closest to the centroid as the cluster with more clean samples since we take more representative samples, which may compose of noisy samples, rather than clean samples as the centroid. Therefore, we need to determine the selection criteria based on whether the current class centroid is obtained by clean samples. Especially, the criterion is based on the similarity between centroids of the current class and other classes. Assume that the sample in $\\mathcal{G}_c^1$ is near the centroid and the sample in $\\mathcal{G}_c^2$ is the opposite. We determined the choice of a more clean cluster $\\mathcal{D}_c^{clean}$ based on the following criteria:", + "bbox": [ + 75, + 247, + 472, + 565 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {c} ^ {\\text {c l e a n}} = \\left\\{ \\begin{array}{l} \\mathcal {G} _ {c} ^ {2}, \\text {i f} | \\cos (o _ {c}, o _ {k}) - 1 | < \\varepsilon \\text {a n d} \\left| \\mathcal {D} _ {c} ^ {H} \\right| < \\left| \\mathcal {D} _ {k} ^ {H} \\right| \\\\ \\mathcal {G} _ {c} ^ {1}, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 570, + 477, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It means that if the centroid of another class is similar to the centroid of the current class, whichever class of high-confidence sample set has fewer samples, then the high-confidence samples in this class are the noise samples. It is because the asymmetric noise ratio cannot exceed $50\\%$ in the past assumption [29, 23]. Therefore, if the centroid is obtained from noise samples, we choose the cluster far away from the centroid as the cluster with more clean samples; otherwise, the cluster close to the centroid is selected.", + "bbox": [ + 75, + 630, + 468, + 767 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Overall Training Process", + "text_level": 1, + "bbox": [ + 76, + 773, + 305, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After sample selection is conducted for each class, we adopt semi-supervised learning [1, 42] to train with all clean samples $\\mathcal{D}^{clean}$ as labeled data and all noisy samples $\\mathcal{D}^{noisy}$ as unlabeled data. The model is thus updated for the next round of training. One may also use long-tailed semi-supervised learning methods instead of normal semi-supervised learning in this stage.", + "bbox": [ + 75, + 799, + 470, + 905 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 90, + 633, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 114, + 689, + 131 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. In order to comprehensively evaluate the effectiveness of method, we perform experiments respectively in the scenarios with synthetic noise and realistic noise in intrinsically long-tailed distribution. We construct synthetic scenarios based on CIFAR-10 and CIFAR-100 [26]. We construct two benchmarks to imitate realistic scenarios, which is built on real-world noise datasets including Red Mini-ImageNet [20], CIFAR-10N and CIFAR-100N [48]. For all datasets, we adopt the standard paradigm of constructing a long-tailed distribution first and injecting noise later. We imitate realistic long-tailed distribution using the same setting in previous long-tailed learning works [3, 35] that long-tailed imbalance follows an exponential decay in sample sizes across different classes. The imbalance factor is denoted by the ratio between the size of the largest class and that of the smallest class.", + "bbox": [ + 496, + 137, + 890, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The details for dataset construction are as follows. (1) As for CIFAR-10/100 [26], we adopt symmetric and asymmetric noise to inject synthetic noise, which is commonly used in the area of label-noise learning [41]. The noise ratio is denoted by the ratio between the number of noisy samples and the total number of samples. It should be noted that different from the previous methods [21, 49] to deal with the joint problem of noisy labeled and long-tailed data, the noise transition matrix is randomly generated only related to the noise ratio. (2) As for CIFAR-10N/100N (10N/100N) [48], we replace sample labels with human-annotated noisy labels after constructing a long-tailed distribution based on real labels. (3) As for Red mini-[ImageNet (Red) [20], we inject web label noise samples after constructing a long-tailed distribution based on the original mini-[ImageNet. Therefore, the observed and intrinsic distribution are likely inconsistent, especially in long-tail distribution.", + "bbox": [ + 496, + 378, + 892, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared Methods. We compare our method with the following three types of approaches: (1) Long-tail learning methods (LT). They are LA [33], LDAM [3] and IB [35]. (2) Label-noise learning methods (NL). They are DivideMix [29] and UNICON [23]; (3) Methods aiming at dealing with noisy label and long-tail distribution (NL-LT). They are MW-Net [41], RoLT [49], HAR [2] and ULC [19].", + "bbox": [ + 496, + 638, + 893, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We use PreAct ResNet18 [14] as backbone for CIFAR datasets and ResNet18 as backbone for Red mini-ImageNet dataset. Both of backbones adopt SGD with an initial learning rate of 0.02, a momentum of 0.9, and a weight decay of $5 \\times 10^{-4}$ and a batch size of 64. For fair comparison, we train all methods for 100 epochs.", + "bbox": [ + 496, + 747, + 893, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparative Results", + "text_level": 1, + "bbox": [ + 500, + 847, + 697, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFAR-10/100. Tab. 1 and 2 report the accuracy of different methods for intrinsically long-tailed CIFAR-10/100", + "bbox": [ + 500, + 869, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1374", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ea9d963df6985beed275a024776a2540336124c053b00ec4ff65e620cbe32b89.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetCIFAR-10CIFAR-100
Imbalance Factor0.1
Noise Ratio (Sym.)0.40.60.40.6
BaselineCE71.6761.1634.5323.63
LTLA70.5654.9229.0723.21
LDAM70.5361.9731.3023.13
IB73.2462.6232.4025.84
NLDivideMix82.6780.1754.7144.98
UNICON84.2582.2952.3445.87
NL-LTMW-Net70.9059.8532.0321.71
RoLT81.6276.5842.9532.59
HAR77.4463.7538.1726.09
ULC84.4683.2554.9144.66
OurTABASCO85.5384.8356.5245.98
", + "bbox": [ + 81, + 88, + 465, + 332 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with symmetric and asymmetric noise, respectively. It can be observed three phenomena as follows: (1) The performance of existing long-tail methods is lower than baseline in most situations. It is because such methods do not have the ability to distinguish the noise samples, and the wrong attention to the noise samples leads to the further decline of the model generalization ability. (2) The advantages of existing methods aiming at both long-tailed distribution and label noise are not obvious compared with single methods. It is because existing methods do not take into account the distribution inconsistency caused by noise labels. (3) Our method significantly improved over other methods in all cases. Moreover, as the proportion of noise increases, the accuracy of our method decreases less compared to other methods. It validates that our method can effectively identify the noise in long-tail distribution.", + "bbox": [ + 75, + 382, + 468, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Red mini-ImageNet and CIFAR-10N/100N. Tab. 4 reports the accuracy of different methods on real-world noise datasets with intrinsically long-tailed distribution. According to the results of label-noise learning methods on CIFAR-10N/100N, it can be observed that real-world noise is more difficult to separate than synthetic noise to some extent. It further increases the difficulty of dealing with such problem. Nevertheless, our method still performs well, which again confirms its effectiveness.", + "bbox": [ + 75, + 627, + 468, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study and Discussions", + "text_level": 1, + "bbox": [ + 76, + 768, + 356, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the following experiments, we analyze each component of the proposed TABASCO on CIFAR-10/100 to verify its effectiveness. We use an imbalance factor of 0.1 and a noise ratio of 0.4 to construct the synthetic noise dataset.", + "bbox": [ + 75, + 792, + 467, + 852 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of WJSD. To validate the effectiveness of the proposed WJSD, we compare the accuracy of models trained by different separation metrics. Specifically, we", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b215880e41e8da7af173718bfa3d28b46dd8ef80e9389bc9e30c3a9930ac3088.jpg", + "table_caption": [ + "Table 1: Performance comparison under symmetric noise. The best results are shown in bold." + ], + "table_footnote": [], + "table_body": "
DatasetCIFAR-10CIFAR-100
Imbalance Factor0.1
Noise Ratio (Asym.)0.20.40.20.4
BaselineCE79.9062.8844.4532.05
LTLA71.4959.8839.3428.49
LDAM74.5862.2940.0633.26
IB73.4958.3645.0235.25
NLDivideMix80.9269.3558.0941.99
UNICON72.8169.0455.9944.70
NL-LTMW-Net79.3465.4942.5230.42
RoLT73.3058.2948.1939.32
HAR82.8569.1948.5033.20
ULC74.0773.1954.4543.20
OurTABASCO82.1080.5759.3950.51
", + "bbox": [ + 504, + 88, + 887, + 332 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8c09be3167e27219cb9986d82e33b13e0a10393aac6ad71bc39d04361880e1ce.jpg", + "table_caption": [ + "Table 2: Performance comparison under asymmetric noise. The best results are shown in bold." + ], + "table_footnote": [], + "table_body": "
DatasetSeparation metricAccuracy
CIFAR-10JSD83.97
WJSD85.57
CIFAR-100JSD55.80
WJSD56.67
", + "bbox": [ + 553, + 388, + 836, + 481 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Performance comparison between JSD and WJSD.", + "bbox": [ + 500, + 491, + 890, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "train the model by using JSD and WJSD for sample separation with a symmetric noise dataset, respectively. As for each separation metric, we simply use the small value strategy [29, 23] for sample selection. As Tab. 3 shows, the model trained by WJSD achieves better results on both symmetric noise datasets compared with JSD owing to the stronger separability of WJSD.", + "bbox": [ + 496, + 513, + 890, + 621 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of ACD. To validate the advantage of the proposed ACD, we compare it with the method which calculates the feature centroid on the observed class (hereinafter referred to as centroid distance or CD) to show their separability in CIFAR-10. Specifically, based on the same backbone, we calculate the distance from the sample to the centroid using ACD and CD in CIFAR-10 with asymmetric noise, respectively. Fig. 4 shows the distributions of samples in the tail class by CD and ACD. The purity of the tail class is 0.53. It can be observed that the CD values of noise and clean samples are highly overlapped, which leads to failure sample separation. It is because the purity of the tail class may be quite low due to the negative effects of both label-noise and long-tailed distribution. The centroid obtained by ACD has a higher purity, so there is a significant difference in ACD between them. As shown in Fig. 4(b), most clean samples are concentrated in the interval of [0.8,1], which is easily clustered by GMM.", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1375", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9ee4f8e0776b34ab050d7b71fb326a4b046e28174c07d9c52c5c21b18b98e4da.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetRed10N100N
Imbalance Factor≈ 0.10.1
Noise Ratio0.20.4≈ 0.4
BaselineCE40.4231.4660.4438.10
LTLA26.8225.8865.7436.50
LDAM26.6423.4662.5038.48
IB23.8022.0865.9142.48
NLDivideMix48.7648.9667.8544.25
UNICON40.1841.6469.5451.93
NL-LTMW-Net42.6640.2669.7344.20
RoLT22.5624.2275.2446.61
HAR46.6138.7174.9744.54
ULC48.1247.0675.7151.72
OurTABASCO50.2049.6880.6153.83
", + "bbox": [ + 81, + 88, + 467, + 333 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4: Performance comparison with real-world noise and long-tail distribution. The best results are shown in bold.", + "bbox": [ + 76, + 343, + 468, + 375 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Bi-dimensional Sample Separation. To validate how the proposed bi-dimensional metrics complement each other, we plot the values of bi-dimensional metrics of both clean and noisy samples under different noise types in Fig. 5. For the case of symmetric noise shown in Fig. 5(a), it can be observed that ACD cannot effectively distinguish clean samples from noisy samples in the tail class. In this case, WJSD shows its advantage because the values of WJSD for most noisy samples are clustered in the top region, and the clean samples are scattered throughout the rest region. For the case of asymmetric noise shown in Fig. 5(b), it can be observed that WJSD cannot distinguish clean samples from noisy samples well for the tail class, while ACD can distinguish them well although the clean and noisy samples are closer in the tail class. The experimental observation is consistent with the previous discussion, which validates the complementarity of bi-dimensional metrics.", + "bbox": [ + 75, + 383, + 468, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Sample Selection. In order to validate the effectiveness of the proposed sample selection in dimension selection and cluster selection, we compare the optimal clean ratio of clusters obtained by WJSD, ACD and our selection method in CIFAR-10 with different noise types. The clean ratio of a cluster is calculated by the proportion of clean samples in the cluster to the total number of cluster samples. As shown in Fig. 6, on the tail class, the clean ratio of the cluster obtained by our selection method is aligned with the higher one between WJSD and ACD for both noise cases. It shows that we can choose the most appropriate separation dimension in different situations. Besides, the clean ratio of the cluster we selected is consistent with that of the optimal cluster in the corresponding dimension, which is sufficient to show that the method we proposed can select clean samples.", + "bbox": [ + 75, + 657, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8978744f5c52019e23a6df9ddbcefd4b3d31544d821d855b90bb486837f20e8a.jpg", + "image_caption": [ + "Figure 4: Comparison of the sample distributions between CD and ACD in the tail class." + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 684, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2ab50acdf51b02f9a848c4538c99922c871944a12dfcdf0eedd93ee4d564c139.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 691, + 90, + 870, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6a8bf68f9db9b8598d1392047cd47c220a1be42a8cd501b7dec94e1c1f3ce57f.jpg", + "image_caption": [ + "(a) Symmetric noise" + ], + "image_footnote": [], + "bbox": [ + 511, + 236, + 687, + 337 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/87cf4887cb473a40cbc410da6221f0e73f402470ce88fd0ef33b08ab0eaab4d3.jpg", + "image_caption": [ + "(b) Asymmetric noise" + ], + "image_footnote": [], + "bbox": [ + 696, + 237, + 867, + 337 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/df444e84913d8f40b83c37295349c5d42fb46363247f2eca2f479539d74cc1f3.jpg", + "image_caption": [ + "Figure 5: Scatter plot of the values of the proposed bidimensional metrics with (a) symmetric noise and (b) asymmetric noise.", + "(a) Symmetric noise", + "Figure 6: The performance of the proposed sample selection with (a) symmetric noise and (b) asymmetric noise." + ], + "image_footnote": [], + "bbox": [ + 504, + 412, + 684, + 517 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/34026ab00885b70d2d07597d1d8b93c9ba16dae610525ee4a0436ad8f17d4e94.jpg", + "image_caption": [ + "(b) Asymmetric noise" + ], + "image_footnote": [], + "bbox": [ + 691, + 412, + 870, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 583, + 617, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper studies a more general and realistic problem of label-noise learning with intrinsically long-tailed data. The major challenge in this problem is that it is hard to distinguish clean samples from noisy samples on intrinsic tail classes. Accordingly, we propose a learning framework TABASCO for this problem. In TABASCO, two new metrics are explicitly proposed to address the problem of sample selection in tail classes. Extensive experiments on noisy-labeled datasets with long-tail distribution demonstrate its effectiveness.", + "bbox": [ + 496, + 607, + 890, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. We thank Dr. Shiquan Ruan for his discussion on the theory proof. This study was supported in part by the National Natural Science Foundation of China under Grants 62002302 and U21A20514; in part by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform under Grant 3502ZCQXT2022008; in part by NSFC/RGC Joint Research Scheme under Grant N_HKBU214/21; and in part by the General Research Fund of RGC under Grants 12201321 and 12202622.", + "bbox": [ + 496, + 760, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1376", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] David Berthelot, Nicholas Carlini, Ian J. Goodfellow, Nicolas Papernot, Avital Oliver, and Colin Raffel. Mixmatch: A holistic approach to semi-supervised learning. 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In AAAI, 2022. 1" + ], + "bbox": [ + 501, + 92, + 890, + 575 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1378", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_model.json b/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e53e6d6c6c0a6a8edfa686eb3dd6c3454fb5b36d --- /dev/null +++ b/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_model.json @@ -0,0 +1,2332 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.194, + 0.131, + 0.778, + 0.154 + ], + "angle": 0, + "content": "Label-Noise Learning with Intrinsically Long-Tailed Data" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.179, + 0.808, + 0.2 + ], + "angle": 0, + "content": "Yang Lu\\(^{1,2*}\\) Yiliang Zhang\\(^{1,2}\\) Bo Han\\(^{3}\\) Yiu-ming Cheung\\(^{3}\\) Hanzi Wang\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.201, + 0.856, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)Fujian Key Laboratory of Sensing and Computing for Smart City, School of Informatics, Xiamen University, Xiamen, China" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.218, + 0.714, + 0.234 + ], + "angle": 0, + "content": "\\(^{2}\\)Key Laboratory of Multimedia Trusted Perception and Efficient Computing," + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.236, + 0.686, + 0.251 + ], + "angle": 0, + "content": "Ministry of Education of China, Xiamen University, Xiamen, China" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.254, + 0.74, + 0.27 + ], + "angle": 0, + "content": "\\(^{3}\\)Department of Computer Science, Hong Kong Baptist University, Hong Kong, China" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.273, + 0.846, + 0.287 + ], + "angle": 0, + "content": "luyang@xmu.edu.cn ylzhangcs@hotmail.com {bhanml, ymc}@comp.hkbu.edu.hk hanzi.wang@xmu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.474, + 0.656 + ], + "angle": 0, + "content": "Label noise is one of the key factors that lead to the poor generalization of deep learning models. Existing label-noise learning methods usually assume that the ground-truth classes of the training data are balanced. However, the real-world data is often imbalanced, leading to the inconsistency between observed and intrinsic class distribution with label noises. In this case, it is hard to distinguish clean samples from noisy samples on the intrinsic tail classes with the unknown intrinsic class distribution. In this paper, we propose a learning framework for label-noise learning with intrinsically long-tailed data. Specifically, we propose two-stage bi-dimensional sample selection (TABASCO) to better separate clean samples from noisy samples, especially for the tail classes. TABASCO consists of two new separation metrics that complement each other to compensate for the limitation of using a single metric in sample separation. Extensive experiments on benchmarks demonstrate the effectiveness of our method. Our code is available at https://github.com/Wakings/TABASCO." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.671, + 0.21, + 0.687 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Under the support of a large amount of high-quality labeled data, deep neural networks have achieved great success in various fields [27, 40, 7]. However, it is expensive and difficult to obtain a large amount of high-quality labeled data in many practical applications. Instead, the commonly used large-scale training data is usually obtained from the Internet or crowdsourcing platforms like Amazon Mechanical Turk, which is unreliable and may be mislabeled [52, 43]. The models trained on this kind of unreliable data, called noisy-labeled data, often produce poor generalization performance because deep neural networks tend to overfit noisy samples due to their large model capacity. In" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.322, + 0.688, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.435, + 0.658, + 0.447 + ], + "angle": 0, + "content": "(a) Class distribution" + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.323, + 0.872, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.435, + 0.844, + 0.447 + ], + "angle": 0, + "content": "(b) Loss distribution" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.455, + 0.893, + 0.515 + ], + "angle": 0, + "content": "Figure 1: (a) An example of observed class distribution with noisy labels with long-tailed intrinsic class distribution. (b) The training loss of each sample under noisy-labeled and long-tailed data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.893, + 0.599 + ], + "angle": 0, + "content": "the literature, there are some works to obtain a robust model trained on noisy-labeled data [11, 44]. Among them, the most straightforward and effective way is to differentiate between clean and noisy samples based on their differences in specific metrics, such as training loss [12, 29, 23]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.895, + 0.901 + ], + "angle": 0, + "content": "These label-noise learning methods generally assume that the intrinsic class distribution of the training data is balanced, where each class has almost the same number of samples in terms of their unknown ground-truth labels. However, the data in real-world applications are often imbalanced, e.g., the LVIS dataset [9] and the iNaturalist dataset [17]. The class imbalance usually exhibits in the form of a long-tail distribution, where a small portion of classes possess a large number of samples, and the other classes possess a small number of samples only [38, 18]. In this case, the model training tends to the head classes and ignores the tail classes [60, 62]. When both noisy labels and long-tail distribution exist, training a robust model is even more challenging. There are two key challenges in this scenario. (1) Distribution inconsistency: The observed and intrinsic distributions are likely inconsistent due to noise labels, making the model more difficult to discover and focus on the intrinsic tail classes. As illustrated in Fig. 1(a), the intrinsic class distribution of the dataset is long-tailed, while the existence of noisy labels makes the distribution more" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.414, + 0.901 + ], + "angle": 0, + "content": "* Yang Lu is the corresponding author: luyang@xmu.edu.cn" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1369" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "balanced. The intrinsic tail classes, e.g., classes 6 and 9, are occupied by a large number of noisy data, making them no longer tail classes by observation. (2) Tail inseparability: Even if the tail class is identified, it is more difficult than ever to distinguish between clean and noisy samples in the tail class because clean samples are overwhelmed by noises that make their values of the separation metric highly similar. As illustrated in Fig. 1(b), the training loss of clean and noisy samples in the tail class are generally inseparable compared with the ones in the other classes. Several preliminary works have studied the joint problem of label noise and long-tail distribution [21, 49, 24, 2]. These methods implicitly reduce the complexity of the problem by assuming a similar noise rate for each class. However, this assumption is too strong to apply because noisy samples from the head classes may be the majority, resulting in a higher noise rate in the tail class than in other classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.473, + 0.606 + ], + "angle": 0, + "content": "In this paper, we propose a Two-stAge Bi-dimensionAl Sample seleCtiOn (TABASCO) strategy to address the problem of label-noise learning with intrinsically long-tailed data. In the first stage, we propose to use two new separation metrics for sample separation, i.e., weighted Jensen-Shannon divergence (WJSD) and adaptive centroid distance (ACD), which work corporately to separate clean samples from noisy samples in the tail classes. The proposed metrics are complementary, where WJSD separates the samples from the output perspective while ACD does that from the feature perspective. In the second stage, we determine the separation dimension with better separability for each class and perform sample selection. In order to evaluate the method uniformly and effectively, we introduce two benchmarks with real-world noise and intrinsically long-tailed distribution. The main contributions of our work can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.616, + 0.47, + 0.678 + ], + "angle": 0, + "content": "- We present a more general problem of label-noise learning with intrinsically long-tailed data. The key challenges in this problem are distribution inconsistency and tail inseparability." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.682, + 0.47, + 0.742 + ], + "angle": 0, + "content": "- We propose an effective solution called TABASCO. With the help of two new separation metrics, it is able to effectively identify and select clean samples of the intrinsic tail class." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.747, + 0.47, + 0.808 + ], + "angle": 0, + "content": "- We introduce two benchmarks with real-world noise and intrinsically long-tailed distribution. Extensive experiments on them show the effectiveness of our method and the limitations of existing methods." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.616, + 0.47, + 0.808 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.822, + 0.22, + 0.837 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.847, + 0.282, + 0.864 + ], + "angle": 0, + "content": "2.1. Label-Noise Learning" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "A straightforward strategy to deal with noisy data is to reduce the proportion of noise in training samples by sepa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "rating noisy samples from clean samples. Methods such as co-teaching [12] and DivideMix [29] adopt the small loss trick, while Jo-SRC [55] and UNICON [23] use Jensen-Shannon divergence instead for sample selection. In contrast to methods that separate at the label level, some methods [30, 34] attempt to separate samples at the feature space. There are also some methods to avoid over-fitting the model to noisy data by imposing regularization constraints on model parameters [50, 10] or labels [37, 58, 32]. Other methods mitigate the influence of noisy data by adjusting the loss functions, such as backward and forward loss correction [36], gold loss correction [16], MW-Net [41] and Dual-T [54]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.296, + 0.684, + 0.312 + ], + "angle": 0, + "content": "2.2. Long-tail Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Re-balancing the data for long-tail distributions is a classical strategy to solve the problem of long-tail learning, such as re-sampling [4, 31, 8, 13] and data augmentation [61, 57, 5]. In addition, there are methods to improve the model generalization by introducing long-tail robust loss functions [6, 3, 45, 39]. Methods such as FTL [56], RIDE [46] and DiVE [15] try to solve the problem by using the idea of transfer learning. Recently, approaches based on decoupling [22, 61, 59] split end-to-end learning into feature learning and classifier retraining such that the obtained feature extractor is less affected by the long-tail distribution. In contrast to the above methods with the supervised learning paradigm, CReST [47], ABC [28] and DARP [25] attempt to solve the long-tail problem in the manner of semi-supervised learning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.554, + 0.862, + 0.57 + ], + "angle": 0, + "content": "2.3. Label-Noise Learning on Long-tailed Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Research on this joint problem has just been explored. CNLCU [51] relaxes the constraint of the small loss trick by regarding a portion of large loss samples as clean samples to reduce the probability of misclassifying clean samples to noisy samples in the tail class. RoLT [49] uses the distance from the samples to the centroid of the current class instead of the training loss for sample selection. HAR [2] uses an adaptive approach to regularize noise and tail class samples. Karthik et al. [24] uses the idea of decoupling to fine-tune the loss function for better robustness after feature learning by the self-supervised method. ULC [19] introduces uncertainty to enhance the separation ability of noise samples. H2E [53] reduces hard noises to easy ones by learning a classifier as noise identifier invariant to the class and context distributional changes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.685, + 0.831 + ], + "angle": 0, + "content": "3. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.839, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Given a training set \\(\\mathcal{D} = \\{x_i, \\hat{y}_i\\}_{i=1}^N\\), where \\(\\hat{y}_i \\in [M]\\) is the observed label of the sample \\(x_i\\). \\(N\\) is the number of training samples, and \\(M\\) is the number of classes. In our problem, \\(\\mathcal{D}\\) has the following properties:" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1370" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.891, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.285, + 0.793, + 0.302 + ], + "angle": 0, + "content": "Figure 2: The proposed framework for label-noise learning with intrinsically long-tailed data." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.309, + 0.469, + 0.356 + ], + "angle": 0, + "content": "- Noisy-labeled. There is a subset of samples \\(\\hat{\\mathcal{D}} \\in \\mathcal{D}\\), where a sample \\(\\{x, \\hat{y}\\} \\in \\hat{\\mathcal{D}}\\) has an unknown ground-truth label \\(y\\) different from its observed label \\(\\hat{y}\\)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.36, + 0.469, + 0.406 + ], + "angle": 0, + "content": "- Long-tailed. The ground-truth class distribution is long-tailed. Supposing \\( n_c \\) is the number of the samples in class \\( c \\), we have \\( n_1 > n_2 > \\dots > n_M \\)." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.309, + 0.469, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.473, + 0.699 + ], + "angle": 0, + "content": "We call this kind of training data intrinsically long-tailed because the observed class distribution may not be long-tailed due to the existence of noisy labels. Therefore, our goal is to learn from noisy-labeled data with the intrinsically long-tailed class distribution. The problem is challenging from two aspects. On the one hand, directly applying long-tail learning methods [6, 3, 45] is infeasible because the observed class distribution may be inconsistent with the intrinsic class distribution. On the other hand, label-noise learning methods perform poorly in the tail classes because they usually contain more noisy samples due to insufficient data, as shown in Fig. 1(a). It results in high noise rates in the tail classes, which brings great challenges to separating clean samples and noisy samples for further training. Under this circumstance, the existing sample selection methods [29, 23] often fail to select clean samples in the tail class. The main reason is that it is difficult to distinguish the tail class data from the noisy label data by existing metrics like cross-entropy loss, as shown in Fig. 1(b)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.251, + 0.727 + ], + "angle": 0, + "content": "4. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a two-stage bi-dimensional sample selection (TABASCO) to address the problem of label-noise learning with intrinsically long-tailed data. TABASCO decouples the sample selection process into two stages: (1) sample separation, and (2) dimension and cluster selection. First, given an initial model \\(\\theta\\) trained on the original training data \\(\\mathcal{D}\\), we propose to calculate bi-dimension metrics for each sample in each observed class based on the outputs and features of the model. Second, we determine the separation dimension with better separability for each class, and we adopt the corresponding selection strategy to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.371 + ], + "angle": 0, + "content": "select the cluster with more clean samples based on the selected metric. Last, we adopt semi-supervised learning to update the model by regarding the selected clean cluster as labeled data. The overall framework is shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.379, + 0.808, + 0.396 + ], + "angle": 0, + "content": "4.1. Bi-Dimensional Separation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.404, + 0.892, + 0.631 + ], + "angle": 0, + "content": "Due to the deficiency of a single separation metric to distinguish clean samples from noisy samples in the complex situation of noisy labels with intrinsic long-tail distribution, we propose to jointly use two metrics from different perspectives: weighted Jensen-Shannon divergence (WJSD) and adaptive centroid distance (ACD). Both metrics are specifically designed for the joint problem and are complementary to cover the case when only one of them cannot separate clean samples from noisy samples well. WJSD fully utilizes the information of prediction confidence, while ACD relies on the distance in the feature space. Thus, using clustering on samples according to the values of their bi-dimensional metrics has the flexibility to separate samples with different imbalance ratios, noise ratios, and noise types." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.892, + 0.784 + ], + "angle": 0, + "content": "We first reduce the separation granularity to alleviate the interference from the head class to the tail class. Specifically, the separation is performed within each observed class according to the proposed bi-dimensional metrics. We first divide training set \\(\\mathcal{D}\\) into subsets according to the observed labels \\(\\mathcal{D}_c = \\{(x,\\hat{y})\\mid \\hat{y} = c\\}\\). Given a sample \\((x_{i},\\hat{y}_{i})\\in \\mathcal{D}_{c}\\), the model predictions obtained from the model \\(\\theta\\) is denoted as \\(\\mathbf{p}_i = [p_i^1,p_i^2,\\dots,p_i^M ]\\), where \\(p_i^j\\) is the \\(j\\)'s dimension of vector \\(\\mathbf{p}_i\\). The one-hot representation of the observed label \\(\\hat{y}_i\\) is denoted as \\(\\hat{\\mathbf{y}}_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.789, + 0.892, + 0.849 + ], + "angle": 0, + "content": "Weighted Jensen-Shannon Divergence The Jensen-Shannon Divergence (JSD) is a commonly used metric to separate samples by assessing the variability of model predictions [55, 23]. It is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.853, + 0.892, + 0.897 + ], + "angle": 0, + "content": "\\[\nJ S D \\left(x _ {i}\\right) = \\frac {1}{2} K L \\left(\\mathbf {p} _ {i} \\left\\| \\frac {\\mathbf {p} _ {i} + \\hat {\\mathbf {y}} _ {i}}{2}\\right) + \\frac {1}{2} K L \\left(\\hat {\\mathbf {y}} _ {i} \\left\\| \\frac {\\mathbf {p} _ {i} + \\hat {\\mathbf {y}} _ {i}}{2}\\right), \\right. \\right. \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1371" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.258 + ], + "angle": 0, + "content": "where \\(KL(\\cdot \\|\\cdot)\\) is the Kullback-Leibler divergence. When the intrinsic distribution is balanced, the JSD values of clean samples are generally lower than the noisy samples, so the separation can be easily modeled. However, when the distribution is intrinsically long-tailed, the noisy and clean samples in a tail class tend to obtain similar prediction confidence on the observed class \\(c\\), because their predictions are both towards the head classes. In this case, using JSD as a separation metric fails to separate them. The reason is given by Theorem 1, which shows the upper bound of the absolute value of the JSD difference between two samples." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.258, + 0.473, + 0.35 + ], + "angle": 0, + "content": "Theorem 1 (Upper bound of JSD difference) Suppose \\( x_{i} \\) and \\( x_{j} \\) are two samples in class \\( c \\), \\( p_{i}^{c} \\) and \\( q_{i}^{c} \\) are the \\( c \\)'s dimension of their prediction confidence \\( \\mathbf{p}_{i} = [p_{i}^{1}, p_{i}^{2}, \\dots, p_{i}^{M}] \\) and \\( \\mathbf{p}_{j} = [p_{j}^{1}, p_{j}^{2}, \\dots, p_{j}^{M}] \\), respectively. The upper bound of the absolute value of the difference between their JSD values is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.094, + 0.353, + 0.455, + 0.387 + ], + "angle": 0, + "content": "\\[\n| J S D (x _ {i}) - J S D (x _ {j}) | \\leq \\frac {1}{2} \\log \\left(\\frac {p _ {i} ^ {c} + 1}{p _ {i} ^ {c}}\\right) | p _ {i} ^ {c} - p _ {j} ^ {c} |.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.47, + 0.496 + ], + "angle": 0, + "content": "Theorem 1 shows that the difference between values of JSD is only determined by the prediction confidence of the observed class, i.e., \\( p_i^c \\) and \\( p_j^c \\). In addition, as \\( |p_i^c - p_j^c| \\) gets smaller with a fixed value of \\( p_i^c \\), \\( |JSD(x_i) - JSD(x_j)| \\) is also smaller. This indicates that when two samples are in the same class \\( c \\) with close values of \\( p_i^c \\), their JSD values are also close, which makes it difficult to separate them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.473, + 0.797 + ], + "angle": 0, + "content": "Nevertheless, we can utilize the prediction confidence on other classes, i.e., \\( p_i^d \\) for \\( d \\neq c \\), to distinguish two samples even if their values of \\( p_i^c \\) are close. Specifically, we propose WJSD by imposing an additional weight on JSD to further distinguish samples by inspecting their prediction confidence on other classes rather than the observed class. First, we take the maximum prediction confidence \\( \\max(\\mathbf{p}_i) \\) into account because it may reflect the confidence of a noisy sample's ground-truth class \\( y_i \\). Then, we calculate the ratio of the maximum prediction confidence to the prediction confidence of the observed class \\( \\max(\\mathbf{p}_i) / p_i^c \\). In this manner, the additional weight is greater than one only if the class with the maximum prediction confidence is not the observed class. The larger gap between \\( \\max(\\mathbf{p}_i) \\) and \\( p_i^c \\) makes the weight higher. To avoid exceptionally large weights by the division during normalization over all samples in class \\( c \\) for later clustering, we set the upper bound according to the averaged prediction confidence over all samples in class \\( c \\). Finally, the additional weight can be calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.803, + 0.47, + 0.821 + ], + "angle": 0, + "content": "\\[\nW \\left(x _ {i}\\right) = \\min \\left(\\max \\left(\\mathbf {p} _ {i}\\right) / p _ {i} ^ {c}, \\max \\left(\\bar {\\mathbf {p}} _ {c}\\right) / \\bar {p} _ {c} ^ {c}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.47, + 0.876 + ], + "angle": 0, + "content": "where \\(\\bar{\\mathbf{p}}_c = [\\bar{p}_c^1,\\bar{p}_c^2,\\dots,\\bar{p}_c^M] = \\frac{1}{|\\mathcal{D}_c|}\\sum_{i = 1}^{|\\mathcal{D}_c|}\\mathbf{p}_i\\) is the average prediction confidence of class \\(c\\). Thus, WJSD can be calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.881, + 0.47, + 0.898 + ], + "angle": 0, + "content": "\\[\nW J S D \\left(x _ {i}\\right) = W \\left(x _ {i}\\right) \\times J S D \\left(x _ {i}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.153 + ], + "angle": 0, + "content": "Remarks: Compared with the value of JSD that is only related to the prediction confidence on the observed class, adopting the maximum prediction confidence in WJSD can better separate clean samples from noisy samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.157, + 0.892, + 0.339 + ], + "angle": 0, + "content": "Adaptive Centroid Distance. Although the sample separability of WJSD is greatly improved compared with JSD, the separation metric still relies on model prediction. When all the noisy samples labeled in a class are from another class, e.g., asymmetric noise, the model prediction for both noisy and clean samples will be highly similar because it is easy to learn a classifier that maps the features from two different classes into one. It results in low discrimination between the model predictions of clean and noisy samples in this case. Thus, solely using WJSD may not be enough to separate the clean and noisy samples when model predictions (in terms of all classes, not only about \\( p^c \\)) are close." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.534 + ], + "angle": 0, + "content": "Except for separating the samples in the output space, we propose another metric calculated in the feature space to eliminate the bias from the classifier because the learned features are more robust to noise labels. Specifically, for a given sample, we can calculate the distance between its feature and the class feature centroid to evaluate how the feature of a sample deviates from its class centroid. This approach is only practical when the quality of the centroid is high. Directly calculating the centroid according to the observed label may not be accurate because it involves a certain number of features of the noisy samples. Therefore, we define purity in Definition 1 to assess the quality of the centroid of class \\( c \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.595 + ], + "angle": 0, + "content": "Definition 1 (Purity) Suppose a noisy sample set of class \\(c\\) be \\(\\mathcal{D}_c = \\{(x,\\hat{y})\\mid \\hat{y} = c\\}\\), where the intrinsic label corresponding to the sample is \\(y\\). The purity \\(P_{\\mathcal{D}_c}\\) of set \\(\\mathcal{D}_c\\) is calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.599, + 0.892, + 0.641 + ], + "angle": 0, + "content": "\\[\nP _ {\\mathcal {D} _ {c}} = \\max _ {k = 1, \\dots , M} \\left\\{\\frac {\\sum_ {i = 1} ^ {N} I \\left(y _ {i} = k\\right)}{N} \\right\\}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.894, + 0.674 + ], + "angle": 0, + "content": "where \\(I(\\cdot)\\) is an indicator function and \\(N\\) is the number of samples in the set \\(\\mathcal{D}_c\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.811 + ], + "angle": 0, + "content": "Purity indicates the proportion of an intrinsic class that takes the majority in the observed class \\( c \\). The higher the purity of a class set used to calculate the centroid, the better the centroid helps to distinguish between noise and clean samples. RoLT [49] adopts a similar idea to use class feature centroid for noisy sample detection. However it directly calculates the feature centroid on the observed class, such that it inevitably suffers from the existence of noise features when the purity is low, especially in our problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In order to improve the purity of the class feature centroid for distance calculation between features, we propose ACD as the second separation metric to separate samples jointly with WJSD. The feature centroid for each class is adaptively updated by involving samples with high confidence from the observed class. The class centroid \\(\\mathbf{o}_c\\) based" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1372" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.435, + 0.108 + ], + "angle": 0, + "content": "on a high-confidence sample set \\(\\mathcal{D}_c^H\\) is calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.112, + 0.47, + 0.156 + ], + "angle": 0, + "content": "\\[\n\\mathbf {o} _ {c} = \\frac {1}{| \\mathcal {D} _ {c} ^ {H} |} \\sum_ {i = 1} ^ {| \\mathcal {D} _ {c} ^ {H} |} \\mathbf {f} _ {i}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.159, + 0.469, + 0.178 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {c} ^ {H} = \\left\\{x _ {i} \\mid x _ {i} \\in \\mathcal {D} _ {c}, p _ {i} ^ {t _ {c}} > H _ {c} \\right\\}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.182, + 0.473, + 0.304 + ], + "angle": 0, + "content": "where \\(\\mathbf{f}_i\\) is the feature of \\(x_{i}\\), and \\(t_c = \\mathrm{argmax}_c\\{\\bar{p}_c^j\\}\\) is the class index with the largest average prediction confidence of class \\(c\\). Thus, we can use the prediction confidence of class \\(t_c\\) for sample \\(x_{i}\\), e.g., \\(p_i^{t_c}\\), as the selection criteria compare with the threshold \\(H_{c}\\). \\(\\mathcal{D}_c^H\\) is constructed by the samples in \\(D_{c}\\) whose corresponding prediction confidence of class \\(t_c\\) is higher than \\(H_{c}\\). The high-confidence threshold \\(H_{c}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.306, + 0.47, + 0.348 + ], + "angle": 0, + "content": "\\[\nH _ {c} = \\frac {1}{D _ {c}} \\sum_ {i = 1} ^ {| D _ {c} |} w _ {i} \\times p _ {i} ^ {t _ {c}}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.351, + 0.469, + 0.37 + ], + "angle": 0, + "content": "\\[\nw _ {i} = \\max \\left(1, p _ {i} ^ {t _ {c}} / \\bar {p} _ {c} ^ {t _ {c}}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.374, + 0.47, + 0.586 + ], + "angle": 0, + "content": "\\(H_{c}\\) is calculated by the weighted sum of the prediction confidence of class \\(t_c\\) for all samples \\(x_{i}\\). The weight \\(w_{i}\\) increases when a sample's prediction confidence of class \\(t_c\\) is higher than its class average. Thus, the threshold is high enough to ensure the purity of the selected samples. High confidence samples are more representative and more likely to be in the same class. It is worth noting that we choose more representative samples rather than clean samples because the clean samples in the tail classes are easily overwhelmed by the noise samples in our problem. In this case, it is difficult to select the clean samples directly because the noise samples may be more representative in the tail class. As for asymmetric noise, the choice of clean or noisy samples to obtain centroid for sample separation is equivalent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.471, + 0.647 + ], + "angle": 0, + "content": "In each round, the centroids are adaptively adjusted because the feature extractor in the model is updated, as well as the set \\(\\mathcal{D}_c^H\\). Therefore, the proposed metric ACD can be calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.652, + 0.469, + 0.669 + ], + "angle": 0, + "content": "\\[\nA C D \\left(x _ {i}\\right) = \\cos \\left(\\mathbf {f} _ {i}, \\mathbf {o} _ {c}\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Remarks: The proposed two metrics, WJSD and ACD, are complementary for sample separation in the tail classes. When the ground-truth classes of the noisy samples are diverse, e.g. symmetric noise, WJSD plays the dominant role because the predictions can hardly be unified due to the class diversity of noisy samples. They are more likely to be predicted towards their ground-truth class, which can be captured by \\(\\max (\\mathbf{p}_i)\\). In this case, ACD may not be effective in separating clean samples from noisy samples because the messy noisy samples may affect the purity of the calculated centroid. On the other hand, when the ground-truth classes of the noisy samples belong to only one class, e.g., asymmetric noise, WJSD tends to produce similar predictions for noisy and clean samples, while the adaptive centroid in ACD can help distinguish them in the feature space." + }, + { + "type": "code_caption", + "bbox": [ + 0.51, + 0.095, + 0.834, + 0.111 + ], + "angle": 0, + "content": "Algorithm 1: The Dimension Selection Strategy" + }, + { + "type": "algorithm", + "bbox": [ + 0.507, + 0.113, + 0.864, + 0.357 + ], + "angle": 0, + "content": "Input: Noise sample set \\(\\mathcal{D}_c\\) in class \\(c\\), threshold \\(\\eta\\) \nOutput: Cluster \\(\\mathcal{G}_c^1, \\mathcal{G}_c^2\\) \n1 Obtain \\(\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2\\) and separation threshold \\(d\\) by applying GMM with values of WJSD to all samples in \\(\\mathcal{D}_c\\) \n2 Obtain \\(\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2\\) by applying GMM with values of ACD to all samples in \\(\\mathcal{D}_c\\) \n3 Calculate the mean \\(\\mu_1, \\mu_2\\) and variance \\(\\sigma_1, \\sigma_2\\) of WJSD for \\(\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2\\) \n4 if \\(\\mu_1 < d < \\mu_2\\) and \\(\\sigma_2 / \\sigma_1 < \\eta\\) then \n5 return \\(\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2\\) \n6 else if \\(\\mu_1 > d\\) and \\(\\mu_2 > d\\) then \n7 return \\(\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2\\) \n8 else \n9 return \\(\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2\\) \n10 end" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.385, + 0.791, + 0.402 + ], + "angle": 0, + "content": "4.2. Bi-Dimensional Sample Selection" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.411, + 0.893, + 0.489 + ], + "angle": 0, + "content": "Once the values of the bi-dimensional metrics for all samples in class \\(c\\) are calculated, each sample can be represented by a point in a 2D space. For each dimension, Gaussian mixture model (GMM) can be adopted to separate the samples in class \\(c\\) into two clusters \\(\\mathcal{G}_c^1\\), \\(\\mathcal{G}_c^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.495, + 0.893, + 0.647 + ], + "angle": 0, + "content": "Dimension Selection. Because each metric shows different separability for different noise types, we first propose a dimension selection strategy to select a proper dimension to separate clean and noisy samples. We consider three cases to select the proper dimension: (a) both of them are acceptable; (b) the separability of WJSD is better; (c) the separability of ACD is better. In short, we only need to figure out if WJSD is suitable for sample separation. If it is certain that WJSD does not show good separability, ACD will be adopted. Fig. 3 shows three cases for dimension selection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.894, + 0.726 + ], + "angle": 0, + "content": "Therefore, we use the statistics of WJSD as the criterion of dimension selection. We measure the means \\((\\mu_1,\\mu_2)\\) and standard deviations \\((\\sigma_{1},\\sigma_{2})\\) of WJSD for two clusters separated by GMM in terms of ACD. We have two cases that can determine when WJSD is better. We mainly compare" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.735, + 0.878, + 0.852 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.858, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Figure 3: Examples of three cases of the optimal separation dimension correspond to sample distribution in bidimensional metrics." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1373" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.244 + ], + "angle": 0, + "content": "\\(\\mu_{1}\\) and \\(\\mu_{2}\\) with the threshold \\(d\\) of GMM in WJSD. First, as shown in Fig. 3 (b), if one cluster \\(\\mathcal{G}_{acd}^{1}\\) of ACD has a \\(\\mu_{1}\\) less than \\(d\\) and a \\(\\sigma_{1}\\) much larger than \\(\\sigma_{2}\\) in another cluster with a \\(\\mu_{2}\\) larger than \\(d\\), it means that cluster \\(\\mathcal{G}_{acd}^{1}\\) has more clean samples but also many noise samples. So in this case, ACD is improper and WJSD is proper. Second, if both \\(\\mu_{1}, \\mu_{2}\\) are greater than \\(d\\), it means that it is a representation of the previous case in the tail class because there are fewer clean samples in the cluster. So, in this case, WJSD is proper. The strategy is summarized in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.473, + 0.566 + ], + "angle": 0, + "content": "Cluster Selection. Once we have determined the separation dimension, we can obtain two sample clusters \\(\\mathcal{G}_c^1\\) and \\(\\mathcal{G}_c^2\\). However, it is not clear which cluster contains more clean samples because the noisy samples may overwhelm the clean samples in some cases. Therefore, we need to further select a cluster between \\(\\mathcal{G}_c^1\\) and \\(\\mathcal{G}_c^2\\) as the clean one. For the cluster separated based on WJSD, we simply choose the one with a smaller average WJSD value as the cluster with more clean samples, denoted as \\(\\mathcal{D}_c^{clean}\\) [29, 23]. For the cluster separated based on ACD, we cannot directly select the cluster closest to the centroid as the cluster with more clean samples since we take more representative samples, which may compose of noisy samples, rather than clean samples as the centroid. Therefore, we need to determine the selection criteria based on whether the current class centroid is obtained by clean samples. Especially, the criterion is based on the similarity between centroids of the current class and other classes. Assume that the sample in \\(\\mathcal{G}_c^1\\) is near the centroid and the sample in \\(\\mathcal{G}_c^2\\) is the opposite. We determined the choice of a more clean cluster \\(\\mathcal{D}_c^{clean}\\) based on the following criteria:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.571, + 0.478, + 0.626 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {c} ^ {\\text {c l e a n}} = \\left\\{ \\begin{array}{l} \\mathcal {G} _ {c} ^ {2}, \\text {i f} | \\cos (o _ {c}, o _ {k}) - 1 | < \\varepsilon \\text {a n d} \\left| \\mathcal {D} _ {c} ^ {H} \\right| < \\left| \\mathcal {D} _ {k} ^ {H} \\right| \\\\ \\mathcal {G} _ {c} ^ {1}, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.631, + 0.47, + 0.768 + ], + "angle": 0, + "content": "It means that if the centroid of another class is similar to the centroid of the current class, whichever class of high-confidence sample set has fewer samples, then the high-confidence samples in this class are the noise samples. It is because the asymmetric noise ratio cannot exceed \\(50\\%\\) in the past assumption [29, 23]. Therefore, if the centroid is obtained from noise samples, we choose the cluster far away from the centroid as the cluster with more clean samples; otherwise, the cluster close to the centroid is selected." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.775, + 0.307, + 0.79 + ], + "angle": 0, + "content": "4.3. Overall Training Process" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.8, + 0.471, + 0.906 + ], + "angle": 0, + "content": "After sample selection is conducted for each class, we adopt semi-supervised learning [1, 42] to train with all clean samples \\( \\mathcal{D}^{clean} \\) as labeled data and all noisy samples \\( \\mathcal{D}^{noisy} \\) as unlabeled data. The model is thus updated for the next round of training. One may also use long-tailed semi-supervised learning methods instead of normal semi-supervised learning in this stage." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.634, + 0.108 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.691, + 0.132 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Datasets. In order to comprehensively evaluate the effectiveness of method, we perform experiments respectively in the scenarios with synthetic noise and realistic noise in intrinsically long-tailed distribution. We construct synthetic scenarios based on CIFAR-10 and CIFAR-100 [26]. We construct two benchmarks to imitate realistic scenarios, which is built on real-world noise datasets including Red Mini-ImageNet [20], CIFAR-10N and CIFAR-100N [48]. For all datasets, we adopt the standard paradigm of constructing a long-tailed distribution first and injecting noise later. We imitate realistic long-tailed distribution using the same setting in previous long-tailed learning works [3, 35] that long-tailed imbalance follows an exponential decay in sample sizes across different classes. The imbalance factor is denoted by the ratio between the size of the largest class and that of the smallest class." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.893, + 0.637 + ], + "angle": 0, + "content": "The details for dataset construction are as follows. (1) As for CIFAR-10/100 [26], we adopt symmetric and asymmetric noise to inject synthetic noise, which is commonly used in the area of label-noise learning [41]. The noise ratio is denoted by the ratio between the number of noisy samples and the total number of samples. It should be noted that different from the previous methods [21, 49] to deal with the joint problem of noisy labeled and long-tailed data, the noise transition matrix is randomly generated only related to the noise ratio. (2) As for CIFAR-10N/100N (10N/100N) [48], we replace sample labels with human-annotated noisy labels after constructing a long-tailed distribution based on real labels. (3) As for Red mini-[ImageNet (Red) [20], we inject web label noise samples after constructing a long-tailed distribution based on the original mini-[ImageNet. Therefore, the observed and intrinsic distribution are likely inconsistent, especially in long-tail distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.894, + 0.746 + ], + "angle": 0, + "content": "Compared Methods. We compare our method with the following three types of approaches: (1) Long-tail learning methods (LT). They are LA [33], LDAM [3] and IB [35]. (2) Label-noise learning methods (NL). They are DivideMix [29] and UNICON [23]; (3) Methods aiming at dealing with noisy label and long-tail distribution (NL-LT). They are MW-Net [41], RoLT [49], HAR [2] and ULC [19]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.894, + 0.839 + ], + "angle": 0, + "content": "Implementation Details. We use PreAct ResNet18 [14] as backbone for CIFAR datasets and ResNet18 as backbone for Red mini-ImageNet dataset. Both of backbones adopt SGD with an initial learning rate of 0.02, a momentum of 0.9, and a weight decay of \\(5 \\times 10^{-4}\\) and a batch size of 64. For fair comparison, we train all methods for 100 epochs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.698, + 0.864 + ], + "angle": 0, + "content": "5.2. Comparative Results" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.901 + ], + "angle": 0, + "content": "CIFAR-10/100. Tab. 1 and 2 report the accuracy of different methods for intrinsically long-tailed CIFAR-10/100" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1374" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.467, + 0.333 + ], + "angle": 0, + "content": "
DatasetCIFAR-10CIFAR-100
Imbalance Factor0.1
Noise Ratio (Sym.)0.40.60.40.6
BaselineCE71.6761.1634.5323.63
LTLA70.5654.9229.0723.21
LDAM70.5361.9731.3023.13
IB73.2462.6232.4025.84
NLDivideMix82.6780.1754.7144.98
UNICON84.2582.2952.3445.87
NL-LTMW-Net70.9059.8532.0321.71
RoLT81.6276.5842.9532.59
HAR77.4463.7538.1726.09
ULC84.4683.2554.9144.66
OurTABASCO85.5384.8356.5245.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.345, + 0.468, + 0.375 + ], + "angle": 0, + "content": "Table 1: Performance comparison under symmetric noise. The best results are shown in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.47, + 0.625 + ], + "angle": 0, + "content": "with symmetric and asymmetric noise, respectively. It can be observed three phenomena as follows: (1) The performance of existing long-tail methods is lower than baseline in most situations. It is because such methods do not have the ability to distinguish the noise samples, and the wrong attention to the noise samples leads to the further decline of the model generalization ability. (2) The advantages of existing methods aiming at both long-tailed distribution and label noise are not obvious compared with single methods. It is because existing methods do not take into account the distribution inconsistency caused by noise labels. (3) Our method significantly improved over other methods in all cases. Moreover, as the proportion of noise increases, the accuracy of our method decreases less compared to other methods. It validates that our method can effectively identify the noise in long-tail distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.765 + ], + "angle": 0, + "content": "Red mini-ImageNet and CIFAR-10N/100N. Tab. 4 reports the accuracy of different methods on real-world noise datasets with intrinsically long-tailed distribution. According to the results of label-noise learning methods on CIFAR-10N/100N, it can be observed that real-world noise is more difficult to separate than synthetic noise to some extent. It further increases the difficulty of dealing with such problem. Nevertheless, our method still performs well, which again confirms its effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.357, + 0.786 + ], + "angle": 0, + "content": "5.3. Ablation Study and Discussions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.468, + 0.853 + ], + "angle": 0, + "content": "In the following experiments, we analyze each component of the proposed TABASCO on CIFAR-10/100 to verify its effectiveness. We use an imbalance factor of 0.1 and a noise ratio of 0.4 to construct the synthetic noise dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Effectiveness of WJSD. To validate the effectiveness of the proposed WJSD, we compare the accuracy of models trained by different separation metrics. Specifically, we" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.888, + 0.333 + ], + "angle": 0, + "content": "
DatasetCIFAR-10CIFAR-100
Imbalance Factor0.1
Noise Ratio (Asym.)0.20.40.20.4
BaselineCE79.9062.8844.4532.05
LTLA71.4959.8839.3428.49
LDAM74.5862.2940.0633.26
IB73.4958.3645.0235.25
NLDivideMix80.9269.3558.0941.99
UNICON72.8169.0455.9944.70
NL-LTMW-Net79.3465.4942.5230.42
RoLT73.3058.2948.1939.32
HAR82.8569.1948.5033.20
ULC74.0773.1954.4543.20
OurTABASCO82.1080.5759.3950.51
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.345, + 0.892, + 0.375 + ], + "angle": 0, + "content": "Table 2: Performance comparison under asymmetric noise. The best results are shown in bold." + }, + { + "type": "table", + "bbox": [ + 0.555, + 0.389, + 0.838, + 0.482 + ], + "angle": 0, + "content": "
DatasetSeparation metricAccuracy
CIFAR-10JSD83.97
WJSD85.57
CIFAR-100JSD55.80
WJSD56.67
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.492, + 0.892, + 0.508 + ], + "angle": 0, + "content": "Table 3: Performance comparison between JSD and WJSD." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.622 + ], + "angle": 0, + "content": "train the model by using JSD and WJSD for sample separation with a symmetric noise dataset, respectively. As for each separation metric, we simply use the small value strategy [29, 23] for sample selection. As Tab. 3 shows, the model trained by WJSD achieves better results on both symmetric noise datasets compared with JSD owing to the stronger separability of WJSD." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of ACD. To validate the advantage of the proposed ACD, we compare it with the method which calculates the feature centroid on the observed class (hereinafter referred to as centroid distance or CD) to show their separability in CIFAR-10. Specifically, based on the same backbone, we calculate the distance from the sample to the centroid using ACD and CD in CIFAR-10 with asymmetric noise, respectively. Fig. 4 shows the distributions of samples in the tail class by CD and ACD. The purity of the tail class is 0.53. It can be observed that the CD values of noise and clean samples are highly overlapped, which leads to failure sample separation. It is because the purity of the tail class may be quite low due to the negative effects of both label-noise and long-tailed distribution. The centroid obtained by ACD has a higher purity, so there is a significant difference in ACD between them. As shown in Fig. 4(b), most clean samples are concentrated in the interval of [0.8,1], which is easily clustered by GMM." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1375" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.334 + ], + "angle": 0, + "content": "
DatasetRed10N100N
Imbalance Factor≈ 0.10.1
Noise Ratio0.20.4≈ 0.4
BaselineCE40.4231.4660.4438.10
LTLA26.8225.8865.7436.50
LDAM26.6423.4662.5038.48
IB23.8022.0865.9142.48
NLDivideMix48.7648.9667.8544.25
UNICON40.1841.6469.5451.93
NL-LTMW-Net42.6640.2669.7344.20
RoLT22.5624.2275.2446.61
HAR46.6138.7174.9744.54
ULC48.1247.0675.7151.72
OurTABASCO50.2049.6880.6153.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.344, + 0.47, + 0.375 + ], + "angle": 0, + "content": "Table 4: Performance comparison with real-world noise and long-tail distribution. The best results are shown in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Effectiveness of Bi-dimensional Sample Separation. To validate how the proposed bi-dimensional metrics complement each other, we plot the values of bi-dimensional metrics of both clean and noisy samples under different noise types in Fig. 5. For the case of symmetric noise shown in Fig. 5(a), it can be observed that ACD cannot effectively distinguish clean samples from noisy samples in the tail class. In this case, WJSD shows its advantage because the values of WJSD for most noisy samples are clustered in the top region, and the clean samples are scattered throughout the rest region. For the case of asymmetric noise shown in Fig. 5(b), it can be observed that WJSD cannot distinguish clean samples from noisy samples well for the tail class, while ACD can distinguish them well although the clean and noisy samples are closer in the tail class. The experimental observation is consistent with the previous discussion, which validates the complementarity of bi-dimensional metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Effectiveness of Sample Selection. In order to validate the effectiveness of the proposed sample selection in dimension selection and cluster selection, we compare the optimal clean ratio of clusters obtained by WJSD, ACD and our selection method in CIFAR-10 with different noise types. The clean ratio of a cluster is calculated by the proportion of clean samples in the cluster to the total number of cluster samples. As shown in Fig. 6, on the tail class, the clean ratio of the cluster obtained by our selection method is aligned with the higher one between WJSD and ACD for both noise cases. It shows that we can choose the most appropriate separation dimension in different situations. Besides, the clean ratio of the cluster we selected is consistent with that of the optimal cluster in the corresponding dimension, which is sufficient to show that the method we proposed can select clean samples." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.685, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.091, + 0.871, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.2, + 0.892, + 0.229 + ], + "angle": 0, + "content": "Figure 4: Comparison of the sample distributions between CD and ACD in the tail class." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.237, + 0.688, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.344, + 0.661, + 0.358 + ], + "angle": 0, + "content": "(a) Symmetric noise" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.238, + 0.869, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.719, + 0.344, + 0.849, + 0.358 + ], + "angle": 0, + "content": "(b) Asymmetric noise" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.363, + 0.892, + 0.408 + ], + "angle": 0, + "content": "Figure 5: Scatter plot of the values of the proposed bidimensional metrics with (a) symmetric noise and (b) asymmetric noise." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.413, + 0.685, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.527, + 0.655, + 0.54 + ], + "angle": 0, + "content": "(a) Symmetric noise" + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.413, + 0.871, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.717, + 0.527, + 0.847, + 0.54 + ], + "angle": 0, + "content": "(b) Asymmetric noise" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.547, + 0.891, + 0.577 + ], + "angle": 0, + "content": "Figure 6: The performance of the proposed sample selection with (a) symmetric noise and (b) asymmetric noise." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.584, + 0.619, + 0.599 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.759 + ], + "angle": 0, + "content": "This paper studies a more general and realistic problem of label-noise learning with intrinsically long-tailed data. The major challenge in this problem is that it is hard to distinguish clean samples from noisy samples on intrinsic tail classes. Accordingly, we propose a learning framework TABASCO for this problem. In TABASCO, two new metrics are explicitly proposed to address the problem of sample selection in tail classes. Extensive experiments on noisy-labeled datasets with long-tail distribution demonstrate its effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.761, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. We thank Dr. Shiquan Ruan for his discussion on the theory proof. This study was supported in part by the National Natural Science Foundation of China under Grants 62002302 and U21A20514; in part by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform under Grant 3502ZCQXT2022008; in part by NSFC/RGC Joint Research Scheme under Grant N_HKBU214/21; and in part by the General Research Fund of RGC under Grants 12201321 and 12202622." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1376" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] David Berthelot, Nicholas Carlini, Ian J. Goodfellow, Nicolas Papernot, Avital Oliver, and Colin Raffel. Mixmatch: A holistic approach to semi-supervised learning. 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In AAAI, 2022. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.576 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "1378" + } + ] +] \ No newline at end of file diff --git a/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_origin.pdf b/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d0fd04577fb656c4bb87d81362452e93590be1e1 --- /dev/null +++ b/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/ca2911cd-1897-45f1-bc9c-ab89b815151c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c3ef382d1e47fe886472c0473e75814315fc5bb063e272c2f13775b89a87382b +size 550494 diff --git a/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/full.md b/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/full.md new file mode 100644 index 0000000000000000000000000000000000000000..38d556f70e92c840f95e52ad505d3dabfa52c805 --- /dev/null +++ b/2023/Label-Noise Learning with Intrinsically Long-Tailed Data/full.md @@ -0,0 +1,339 @@ +# Label-Noise Learning with Intrinsically Long-Tailed Data + +Yang Lu $^{1,2*}$ Yiliang Zhang $^{1,2}$ Bo Han $^{3}$ Yiu-ming Cheung $^{3}$ Hanzi Wang $^{1,2}$ + +$^{1}$ Fujian Key Laboratory of Sensing and Computing for Smart City, School of Informatics, Xiamen University, Xiamen, China + +$^{2}$ Key Laboratory of Multimedia Trusted Perception and Efficient Computing, + +Ministry of Education of China, Xiamen University, Xiamen, China + +$^{3}$ Department of Computer Science, Hong Kong Baptist University, Hong Kong, China + +luyang@xmu.edu.cn ylzhangcs@hotmail.com {bhanml, ymc}@comp.hkbu.edu.hk hanzi.wang@xmu.edu.cn + +# Abstract + +Label noise is one of the key factors that lead to the poor generalization of deep learning models. Existing label-noise learning methods usually assume that the ground-truth classes of the training data are balanced. However, the real-world data is often imbalanced, leading to the inconsistency between observed and intrinsic class distribution with label noises. In this case, it is hard to distinguish clean samples from noisy samples on the intrinsic tail classes with the unknown intrinsic class distribution. In this paper, we propose a learning framework for label-noise learning with intrinsically long-tailed data. Specifically, we propose two-stage bi-dimensional sample selection (TABASCO) to better separate clean samples from noisy samples, especially for the tail classes. TABASCO consists of two new separation metrics that complement each other to compensate for the limitation of using a single metric in sample separation. Extensive experiments on benchmarks demonstrate the effectiveness of our method. Our code is available at https://github.com/Wakings/TABASCO. + +# 1. Introduction + +Under the support of a large amount of high-quality labeled data, deep neural networks have achieved great success in various fields [27, 40, 7]. However, it is expensive and difficult to obtain a large amount of high-quality labeled data in many practical applications. Instead, the commonly used large-scale training data is usually obtained from the Internet or crowdsourcing platforms like Amazon Mechanical Turk, which is unreliable and may be mislabeled [52, 43]. The models trained on this kind of unreliable data, called noisy-labeled data, often produce poor generalization performance because deep neural networks tend to overfit noisy samples due to their large model capacity. In + +![](images/22e148d9b056a7487ba405eda466053370f0d945b7ff477a2b438a49a21ec20e.jpg) +(a) Class distribution + +![](images/348c53ee3757a4e47bad2047be5b399853813846bb127ad12b77972385732830.jpg) +(b) Loss distribution +Figure 1: (a) An example of observed class distribution with noisy labels with long-tailed intrinsic class distribution. (b) The training loss of each sample under noisy-labeled and long-tailed data. + +the literature, there are some works to obtain a robust model trained on noisy-labeled data [11, 44]. Among them, the most straightforward and effective way is to differentiate between clean and noisy samples based on their differences in specific metrics, such as training loss [12, 29, 23]. + +These label-noise learning methods generally assume that the intrinsic class distribution of the training data is balanced, where each class has almost the same number of samples in terms of their unknown ground-truth labels. However, the data in real-world applications are often imbalanced, e.g., the LVIS dataset [9] and the iNaturalist dataset [17]. The class imbalance usually exhibits in the form of a long-tail distribution, where a small portion of classes possess a large number of samples, and the other classes possess a small number of samples only [38, 18]. In this case, the model training tends to the head classes and ignores the tail classes [60, 62]. When both noisy labels and long-tail distribution exist, training a robust model is even more challenging. There are two key challenges in this scenario. (1) Distribution inconsistency: The observed and intrinsic distributions are likely inconsistent due to noise labels, making the model more difficult to discover and focus on the intrinsic tail classes. As illustrated in Fig. 1(a), the intrinsic class distribution of the dataset is long-tailed, while the existence of noisy labels makes the distribution more + +balanced. The intrinsic tail classes, e.g., classes 6 and 9, are occupied by a large number of noisy data, making them no longer tail classes by observation. (2) Tail inseparability: Even if the tail class is identified, it is more difficult than ever to distinguish between clean and noisy samples in the tail class because clean samples are overwhelmed by noises that make their values of the separation metric highly similar. As illustrated in Fig. 1(b), the training loss of clean and noisy samples in the tail class are generally inseparable compared with the ones in the other classes. Several preliminary works have studied the joint problem of label noise and long-tail distribution [21, 49, 24, 2]. These methods implicitly reduce the complexity of the problem by assuming a similar noise rate for each class. However, this assumption is too strong to apply because noisy samples from the head classes may be the majority, resulting in a higher noise rate in the tail class than in other classes. + +In this paper, we propose a Two-stAge Bi-dimensionAl Sample seleCtiOn (TABASCO) strategy to address the problem of label-noise learning with intrinsically long-tailed data. In the first stage, we propose to use two new separation metrics for sample separation, i.e., weighted Jensen-Shannon divergence (WJSD) and adaptive centroid distance (ACD), which work corporately to separate clean samples from noisy samples in the tail classes. The proposed metrics are complementary, where WJSD separates the samples from the output perspective while ACD does that from the feature perspective. In the second stage, we determine the separation dimension with better separability for each class and perform sample selection. In order to evaluate the method uniformly and effectively, we introduce two benchmarks with real-world noise and intrinsically long-tailed distribution. The main contributions of our work can be summarized as follows: + +- We present a more general problem of label-noise learning with intrinsically long-tailed data. The key challenges in this problem are distribution inconsistency and tail inseparability. +- We propose an effective solution called TABASCO. With the help of two new separation metrics, it is able to effectively identify and select clean samples of the intrinsic tail class. +- We introduce two benchmarks with real-world noise and intrinsically long-tailed distribution. Extensive experiments on them show the effectiveness of our method and the limitations of existing methods. + +# 2. Related Work + +# 2.1. Label-Noise Learning + +A straightforward strategy to deal with noisy data is to reduce the proportion of noise in training samples by sepa + +rating noisy samples from clean samples. Methods such as co-teaching [12] and DivideMix [29] adopt the small loss trick, while Jo-SRC [55] and UNICON [23] use Jensen-Shannon divergence instead for sample selection. In contrast to methods that separate at the label level, some methods [30, 34] attempt to separate samples at the feature space. There are also some methods to avoid over-fitting the model to noisy data by imposing regularization constraints on model parameters [50, 10] or labels [37, 58, 32]. Other methods mitigate the influence of noisy data by adjusting the loss functions, such as backward and forward loss correction [36], gold loss correction [16], MW-Net [41] and Dual-T [54]. + +# 2.2. Long-tail Learning + +Re-balancing the data for long-tail distributions is a classical strategy to solve the problem of long-tail learning, such as re-sampling [4, 31, 8, 13] and data augmentation [61, 57, 5]. In addition, there are methods to improve the model generalization by introducing long-tail robust loss functions [6, 3, 45, 39]. Methods such as FTL [56], RIDE [46] and DiVE [15] try to solve the problem by using the idea of transfer learning. Recently, approaches based on decoupling [22, 61, 59] split end-to-end learning into feature learning and classifier retraining such that the obtained feature extractor is less affected by the long-tail distribution. In contrast to the above methods with the supervised learning paradigm, CReST [47], ABC [28] and DARP [25] attempt to solve the long-tail problem in the manner of semi-supervised learning. + +# 2.3. Label-Noise Learning on Long-tailed Data + +Research on this joint problem has just been explored. CNLCU [51] relaxes the constraint of the small loss trick by regarding a portion of large loss samples as clean samples to reduce the probability of misclassifying clean samples to noisy samples in the tail class. RoLT [49] uses the distance from the samples to the centroid of the current class instead of the training loss for sample selection. HAR [2] uses an adaptive approach to regularize noise and tail class samples. Karthik et al. [24] uses the idea of decoupling to fine-tune the loss function for better robustness after feature learning by the self-supervised method. ULC [19] introduces uncertainty to enhance the separation ability of noise samples. H2E [53] reduces hard noises to easy ones by learning a classifier as noise identifier invariant to the class and context distributional changes. + +# 3. Problem Definition + +Given a training set $\mathcal{D} = \{x_i, \hat{y}_i\}_{i=1}^N$ , where $\hat{y}_i \in [M]$ is the observed label of the sample $x_i$ . $N$ is the number of training samples, and $M$ is the number of classes. In our problem, $\mathcal{D}$ has the following properties: + +![](images/e2fb5fbcd490fc645823e0de49b016a33494bce676d8b24cf9f2e12b8ee9f4bb.jpg) +Figure 2: The proposed framework for label-noise learning with intrinsically long-tailed data. + +- Noisy-labeled. There is a subset of samples $\hat{\mathcal{D}} \in \mathcal{D}$ , where a sample $\{x, \hat{y}\} \in \hat{\mathcal{D}}$ has an unknown ground-truth label $y$ different from its observed label $\hat{y}$ . +- Long-tailed. The ground-truth class distribution is long-tailed. Supposing $n_c$ is the number of the samples in class $c$ , we have $n_1 > n_2 > \dots > n_M$ . + +We call this kind of training data intrinsically long-tailed because the observed class distribution may not be long-tailed due to the existence of noisy labels. Therefore, our goal is to learn from noisy-labeled data with the intrinsically long-tailed class distribution. The problem is challenging from two aspects. On the one hand, directly applying long-tail learning methods [6, 3, 45] is infeasible because the observed class distribution may be inconsistent with the intrinsic class distribution. On the other hand, label-noise learning methods perform poorly in the tail classes because they usually contain more noisy samples due to insufficient data, as shown in Fig. 1(a). It results in high noise rates in the tail classes, which brings great challenges to separating clean samples and noisy samples for further training. Under this circumstance, the existing sample selection methods [29, 23] often fail to select clean samples in the tail class. The main reason is that it is difficult to distinguish the tail class data from the noisy label data by existing metrics like cross-entropy loss, as shown in Fig. 1(b). + +# 4. Proposed Method + +In this paper, we propose a two-stage bi-dimensional sample selection (TABASCO) to address the problem of label-noise learning with intrinsically long-tailed data. TABASCO decouples the sample selection process into two stages: (1) sample separation, and (2) dimension and cluster selection. First, given an initial model $\theta$ trained on the original training data $\mathcal{D}$ , we propose to calculate bi-dimension metrics for each sample in each observed class based on the outputs and features of the model. Second, we determine the separation dimension with better separability for each class, and we adopt the corresponding selection strategy to + +select the cluster with more clean samples based on the selected metric. Last, we adopt semi-supervised learning to update the model by regarding the selected clean cluster as labeled data. The overall framework is shown in Fig. 2. + +# 4.1. Bi-Dimensional Separation Metrics + +Due to the deficiency of a single separation metric to distinguish clean samples from noisy samples in the complex situation of noisy labels with intrinsic long-tail distribution, we propose to jointly use two metrics from different perspectives: weighted Jensen-Shannon divergence (WJSD) and adaptive centroid distance (ACD). Both metrics are specifically designed for the joint problem and are complementary to cover the case when only one of them cannot separate clean samples from noisy samples well. WJSD fully utilizes the information of prediction confidence, while ACD relies on the distance in the feature space. Thus, using clustering on samples according to the values of their bi-dimensional metrics has the flexibility to separate samples with different imbalance ratios, noise ratios, and noise types. + +We first reduce the separation granularity to alleviate the interference from the head class to the tail class. Specifically, the separation is performed within each observed class according to the proposed bi-dimensional metrics. We first divide training set $\mathcal{D}$ into subsets according to the observed labels $\mathcal{D}_c = \{(x,\hat{y})\mid \hat{y} = c\}$ . Given a sample $(x_{i},\hat{y}_{i})\in \mathcal{D}_{c}$ , the model predictions obtained from the model $\theta$ is denoted as $\mathbf{p}_i = [p_i^1,p_i^2,\dots,p_i^M ]$ , where $p_i^j$ is the $j$ 's dimension of vector $\mathbf{p}_i$ . The one-hot representation of the observed label $\hat{y}_i$ is denoted as $\hat{\mathbf{y}}_i$ . + +Weighted Jensen-Shannon Divergence The Jensen-Shannon Divergence (JSD) is a commonly used metric to separate samples by assessing the variability of model predictions [55, 23]. It is defined as: + +$$ +J S D \left(x _ {i}\right) = \frac {1}{2} K L \left(\mathbf {p} _ {i} \left\| \frac {\mathbf {p} _ {i} + \hat {\mathbf {y}} _ {i}}{2}\right) + \frac {1}{2} K L \left(\hat {\mathbf {y}} _ {i} \left\| \frac {\mathbf {p} _ {i} + \hat {\mathbf {y}} _ {i}}{2}\right), \right. \right. \tag {1} +$$ + +where $KL(\cdot \|\cdot)$ is the Kullback-Leibler divergence. When the intrinsic distribution is balanced, the JSD values of clean samples are generally lower than the noisy samples, so the separation can be easily modeled. However, when the distribution is intrinsically long-tailed, the noisy and clean samples in a tail class tend to obtain similar prediction confidence on the observed class $c$ , because their predictions are both towards the head classes. In this case, using JSD as a separation metric fails to separate them. The reason is given by Theorem 1, which shows the upper bound of the absolute value of the JSD difference between two samples. + +Theorem 1 (Upper bound of JSD difference) Suppose $x_{i}$ and $x_{j}$ are two samples in class $c$ , $p_{i}^{c}$ and $q_{i}^{c}$ are the $c$ 's dimension of their prediction confidence $\mathbf{p}_{i} = [p_{i}^{1}, p_{i}^{2}, \dots, p_{i}^{M}]$ and $\mathbf{p}_{j} = [p_{j}^{1}, p_{j}^{2}, \dots, p_{j}^{M}]$ , respectively. The upper bound of the absolute value of the difference between their JSD values is given by: + +$$ +| J S D (x _ {i}) - J S D (x _ {j}) | \leq \frac {1}{2} \log \left(\frac {p _ {i} ^ {c} + 1}{p _ {i} ^ {c}}\right) | p _ {i} ^ {c} - p _ {j} ^ {c} |. +$$ + +Theorem 1 shows that the difference between values of JSD is only determined by the prediction confidence of the observed class, i.e., $p_i^c$ and $p_j^c$ . In addition, as $|p_i^c - p_j^c|$ gets smaller with a fixed value of $p_i^c$ , $|JSD(x_i) - JSD(x_j)|$ is also smaller. This indicates that when two samples are in the same class $c$ with close values of $p_i^c$ , their JSD values are also close, which makes it difficult to separate them. + +Nevertheless, we can utilize the prediction confidence on other classes, i.e., $p_i^d$ for $d \neq c$ , to distinguish two samples even if their values of $p_i^c$ are close. Specifically, we propose WJSD by imposing an additional weight on JSD to further distinguish samples by inspecting their prediction confidence on other classes rather than the observed class. First, we take the maximum prediction confidence $\max(\mathbf{p}_i)$ into account because it may reflect the confidence of a noisy sample's ground-truth class $y_i$ . Then, we calculate the ratio of the maximum prediction confidence to the prediction confidence of the observed class $\max(\mathbf{p}_i) / p_i^c$ . In this manner, the additional weight is greater than one only if the class with the maximum prediction confidence is not the observed class. The larger gap between $\max(\mathbf{p}_i)$ and $p_i^c$ makes the weight higher. To avoid exceptionally large weights by the division during normalization over all samples in class $c$ for later clustering, we set the upper bound according to the averaged prediction confidence over all samples in class $c$ . Finally, the additional weight can be calculated as follows: + +$$ +W \left(x _ {i}\right) = \min \left(\max \left(\mathbf {p} _ {i}\right) / p _ {i} ^ {c}, \max \left(\bar {\mathbf {p}} _ {c}\right) / \bar {p} _ {c} ^ {c}\right), \tag {2} +$$ + +where $\bar{\mathbf{p}}_c = [\bar{p}_c^1,\bar{p}_c^2,\dots,\bar{p}_c^M] = \frac{1}{|\mathcal{D}_c|}\sum_{i = 1}^{|\mathcal{D}_c|}\mathbf{p}_i$ is the average prediction confidence of class $c$ . Thus, WJSD can be calculated by: + +$$ +W J S D \left(x _ {i}\right) = W \left(x _ {i}\right) \times J S D \left(x _ {i}\right). \tag {3} +$$ + +Remarks: Compared with the value of JSD that is only related to the prediction confidence on the observed class, adopting the maximum prediction confidence in WJSD can better separate clean samples from noisy samples. + +Adaptive Centroid Distance. Although the sample separability of WJSD is greatly improved compared with JSD, the separation metric still relies on model prediction. When all the noisy samples labeled in a class are from another class, e.g., asymmetric noise, the model prediction for both noisy and clean samples will be highly similar because it is easy to learn a classifier that maps the features from two different classes into one. It results in low discrimination between the model predictions of clean and noisy samples in this case. Thus, solely using WJSD may not be enough to separate the clean and noisy samples when model predictions (in terms of all classes, not only about $p^c$ ) are close. + +Except for separating the samples in the output space, we propose another metric calculated in the feature space to eliminate the bias from the classifier because the learned features are more robust to noise labels. Specifically, for a given sample, we can calculate the distance between its feature and the class feature centroid to evaluate how the feature of a sample deviates from its class centroid. This approach is only practical when the quality of the centroid is high. Directly calculating the centroid according to the observed label may not be accurate because it involves a certain number of features of the noisy samples. Therefore, we define purity in Definition 1 to assess the quality of the centroid of class $c$ . + +Definition 1 (Purity) Suppose a noisy sample set of class $c$ be $\mathcal{D}_c = \{(x,\hat{y})\mid \hat{y} = c\}$ , where the intrinsic label corresponding to the sample is $y$ . The purity $P_{\mathcal{D}_c}$ of set $\mathcal{D}_c$ is calculated by: + +$$ +P _ {\mathcal {D} _ {c}} = \max _ {k = 1, \dots , M} \left\{\frac {\sum_ {i = 1} ^ {N} I \left(y _ {i} = k\right)}{N} \right\}, \tag {4} +$$ + +where $I(\cdot)$ is an indicator function and $N$ is the number of samples in the set $\mathcal{D}_c$ . + +Purity indicates the proportion of an intrinsic class that takes the majority in the observed class $c$ . The higher the purity of a class set used to calculate the centroid, the better the centroid helps to distinguish between noise and clean samples. RoLT [49] adopts a similar idea to use class feature centroid for noisy sample detection. However it directly calculates the feature centroid on the observed class, such that it inevitably suffers from the existence of noise features when the purity is low, especially in our problem. + +In order to improve the purity of the class feature centroid for distance calculation between features, we propose ACD as the second separation metric to separate samples jointly with WJSD. The feature centroid for each class is adaptively updated by involving samples with high confidence from the observed class. The class centroid $\mathbf{o}_c$ based + +on a high-confidence sample set $\mathcal{D}_c^H$ is calculated by: + +$$ +\mathbf {o} _ {c} = \frac {1}{| \mathcal {D} _ {c} ^ {H} |} \sum_ {i = 1} ^ {| \mathcal {D} _ {c} ^ {H} |} \mathbf {f} _ {i}, \tag {5} +$$ + +$$ +\mathcal {D} _ {c} ^ {H} = \left\{x _ {i} \mid x _ {i} \in \mathcal {D} _ {c}, p _ {i} ^ {t _ {c}} > H _ {c} \right\}, \tag {6} +$$ + +where $\mathbf{f}_i$ is the feature of $x_{i}$ , and $t_c = \mathrm{argmax}_c\{\bar{p}_c^j\}$ is the class index with the largest average prediction confidence of class $c$ . Thus, we can use the prediction confidence of class $t_c$ for sample $x_{i}$ , e.g., $p_i^{t_c}$ , as the selection criteria compare with the threshold $H_{c}$ . $\mathcal{D}_c^H$ is constructed by the samples in $D_{c}$ whose corresponding prediction confidence of class $t_c$ is higher than $H_{c}$ . The high-confidence threshold $H_{c}$ is defined as: + +$$ +H _ {c} = \frac {1}{D _ {c}} \sum_ {i = 1} ^ {| D _ {c} |} w _ {i} \times p _ {i} ^ {t _ {c}}, \tag {7} +$$ + +$$ +w _ {i} = \max \left(1, p _ {i} ^ {t _ {c}} / \bar {p} _ {c} ^ {t _ {c}}\right). \tag {8} +$$ + +$H_{c}$ is calculated by the weighted sum of the prediction confidence of class $t_c$ for all samples $x_{i}$ . The weight $w_{i}$ increases when a sample's prediction confidence of class $t_c$ is higher than its class average. Thus, the threshold is high enough to ensure the purity of the selected samples. High confidence samples are more representative and more likely to be in the same class. It is worth noting that we choose more representative samples rather than clean samples because the clean samples in the tail classes are easily overwhelmed by the noise samples in our problem. In this case, it is difficult to select the clean samples directly because the noise samples may be more representative in the tail class. As for asymmetric noise, the choice of clean or noisy samples to obtain centroid for sample separation is equivalent. + +In each round, the centroids are adaptively adjusted because the feature extractor in the model is updated, as well as the set $\mathcal{D}_c^H$ . Therefore, the proposed metric ACD can be calculated by: + +$$ +A C D \left(x _ {i}\right) = \cos \left(\mathbf {f} _ {i}, \mathbf {o} _ {c}\right). \tag {9} +$$ + +Remarks: The proposed two metrics, WJSD and ACD, are complementary for sample separation in the tail classes. When the ground-truth classes of the noisy samples are diverse, e.g. symmetric noise, WJSD plays the dominant role because the predictions can hardly be unified due to the class diversity of noisy samples. They are more likely to be predicted towards their ground-truth class, which can be captured by $\max (\mathbf{p}_i)$ . In this case, ACD may not be effective in separating clean samples from noisy samples because the messy noisy samples may affect the purity of the calculated centroid. On the other hand, when the ground-truth classes of the noisy samples belong to only one class, e.g., asymmetric noise, WJSD tends to produce similar predictions for noisy and clean samples, while the adaptive centroid in ACD can help distinguish them in the feature space. + +Algorithm 1: The Dimension Selection Strategy +Input: Noise sample set $\mathcal{D}_c$ in class $c$ , threshold $\eta$ +Output: Cluster $\mathcal{G}_c^1, \mathcal{G}_c^2$ +1 Obtain $\mathcal{G}_{wjsd}^1, \mathcal{G}_{wjsd}^2$ and separation threshold $d$ by applying GMM with values of WJSD to all samples in $\mathcal{D}_c$ +2 Obtain $\mathcal{G}_{acd}^1, \mathcal{G}_{acd}^2$ by applying GMM with values of ACD to all samples in $\mathcal{D}_c$ +3 Calculate the mean $\mu_1, \mu_2$ and variance $\sigma_1, \sigma_2$ of WJSD for $\mathcal{G}_{acd}^1, \mathcal{G}_{acd}^2$ +4 if $\mu_1 < d < \mu_2$ and $\sigma_2 / \sigma_1 < \eta$ then +5 return $\mathcal{G}_{wjsd}^1, \mathcal{G}_{wjsd}^2$ +6 else if $\mu_1 > d$ and $\mu_2 > d$ then +7 return $\mathcal{G}_{wjsd}^1, \mathcal{G}_{wjsd}^2$ +8 else +9 return $\mathcal{G}_{acd}^1, \mathcal{G}_{acd}^2$ +10 end + +# 4.2. Bi-Dimensional Sample Selection + +Once the values of the bi-dimensional metrics for all samples in class $c$ are calculated, each sample can be represented by a point in a 2D space. For each dimension, Gaussian mixture model (GMM) can be adopted to separate the samples in class $c$ into two clusters $\mathcal{G}_c^1$ , $\mathcal{G}_c^2$ . + +Dimension Selection. Because each metric shows different separability for different noise types, we first propose a dimension selection strategy to select a proper dimension to separate clean and noisy samples. We consider three cases to select the proper dimension: (a) both of them are acceptable; (b) the separability of WJSD is better; (c) the separability of ACD is better. In short, we only need to figure out if WJSD is suitable for sample separation. If it is certain that WJSD does not show good separability, ACD will be adopted. Fig. 3 shows three cases for dimension selection. + +Therefore, we use the statistics of WJSD as the criterion of dimension selection. We measure the means $(\mu_1,\mu_2)$ and standard deviations $(\sigma_{1},\sigma_{2})$ of WJSD for two clusters separated by GMM in terms of ACD. We have two cases that can determine when WJSD is better. We mainly compare + +![](images/2de398f5880d8ca6a5cb6c69c9c5ba5bff5667799a17761e1e0b4df02a61fdfb.jpg) +Figure 3: Examples of three cases of the optimal separation dimension correspond to sample distribution in bidimensional metrics. + +$\mu_{1}$ and $\mu_{2}$ with the threshold $d$ of GMM in WJSD. First, as shown in Fig. 3 (b), if one cluster $\mathcal{G}_{acd}^{1}$ of ACD has a $\mu_{1}$ less than $d$ and a $\sigma_{1}$ much larger than $\sigma_{2}$ in another cluster with a $\mu_{2}$ larger than $d$ , it means that cluster $\mathcal{G}_{acd}^{1}$ has more clean samples but also many noise samples. So in this case, ACD is improper and WJSD is proper. Second, if both $\mu_{1}, \mu_{2}$ are greater than $d$ , it means that it is a representation of the previous case in the tail class because there are fewer clean samples in the cluster. So, in this case, WJSD is proper. The strategy is summarized in Algorithm 1. + +Cluster Selection. Once we have determined the separation dimension, we can obtain two sample clusters $\mathcal{G}_c^1$ and $\mathcal{G}_c^2$ . However, it is not clear which cluster contains more clean samples because the noisy samples may overwhelm the clean samples in some cases. Therefore, we need to further select a cluster between $\mathcal{G}_c^1$ and $\mathcal{G}_c^2$ as the clean one. For the cluster separated based on WJSD, we simply choose the one with a smaller average WJSD value as the cluster with more clean samples, denoted as $\mathcal{D}_c^{clean}$ [29, 23]. For the cluster separated based on ACD, we cannot directly select the cluster closest to the centroid as the cluster with more clean samples since we take more representative samples, which may compose of noisy samples, rather than clean samples as the centroid. Therefore, we need to determine the selection criteria based on whether the current class centroid is obtained by clean samples. Especially, the criterion is based on the similarity between centroids of the current class and other classes. Assume that the sample in $\mathcal{G}_c^1$ is near the centroid and the sample in $\mathcal{G}_c^2$ is the opposite. We determined the choice of a more clean cluster $\mathcal{D}_c^{clean}$ based on the following criteria: + +$$ +\mathcal {D} _ {c} ^ {\text {c l e a n}} = \left\{ \begin{array}{l} \mathcal {G} _ {c} ^ {2}, \text {i f} | \cos (o _ {c}, o _ {k}) - 1 | < \varepsilon \text {a n d} \left| \mathcal {D} _ {c} ^ {H} \right| < \left| \mathcal {D} _ {k} ^ {H} \right| \\ \mathcal {G} _ {c} ^ {1}, \text {o t h e r w i s e} \end{array} \right. \tag {10} +$$ + +It means that if the centroid of another class is similar to the centroid of the current class, whichever class of high-confidence sample set has fewer samples, then the high-confidence samples in this class are the noise samples. It is because the asymmetric noise ratio cannot exceed $50\%$ in the past assumption [29, 23]. Therefore, if the centroid is obtained from noise samples, we choose the cluster far away from the centroid as the cluster with more clean samples; otherwise, the cluster close to the centroid is selected. + +# 4.3. Overall Training Process + +After sample selection is conducted for each class, we adopt semi-supervised learning [1, 42] to train with all clean samples $\mathcal{D}^{clean}$ as labeled data and all noisy samples $\mathcal{D}^{noisy}$ as unlabeled data. The model is thus updated for the next round of training. One may also use long-tailed semi-supervised learning methods instead of normal semi-supervised learning in this stage. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets. In order to comprehensively evaluate the effectiveness of method, we perform experiments respectively in the scenarios with synthetic noise and realistic noise in intrinsically long-tailed distribution. We construct synthetic scenarios based on CIFAR-10 and CIFAR-100 [26]. We construct two benchmarks to imitate realistic scenarios, which is built on real-world noise datasets including Red Mini-ImageNet [20], CIFAR-10N and CIFAR-100N [48]. For all datasets, we adopt the standard paradigm of constructing a long-tailed distribution first and injecting noise later. We imitate realistic long-tailed distribution using the same setting in previous long-tailed learning works [3, 35] that long-tailed imbalance follows an exponential decay in sample sizes across different classes. The imbalance factor is denoted by the ratio between the size of the largest class and that of the smallest class. + +The details for dataset construction are as follows. (1) As for CIFAR-10/100 [26], we adopt symmetric and asymmetric noise to inject synthetic noise, which is commonly used in the area of label-noise learning [41]. The noise ratio is denoted by the ratio between the number of noisy samples and the total number of samples. It should be noted that different from the previous methods [21, 49] to deal with the joint problem of noisy labeled and long-tailed data, the noise transition matrix is randomly generated only related to the noise ratio. (2) As for CIFAR-10N/100N (10N/100N) [48], we replace sample labels with human-annotated noisy labels after constructing a long-tailed distribution based on real labels. (3) As for Red mini-[ImageNet (Red) [20], we inject web label noise samples after constructing a long-tailed distribution based on the original mini-[ImageNet. Therefore, the observed and intrinsic distribution are likely inconsistent, especially in long-tail distribution. + +Compared Methods. We compare our method with the following three types of approaches: (1) Long-tail learning methods (LT). They are LA [33], LDAM [3] and IB [35]. (2) Label-noise learning methods (NL). They are DivideMix [29] and UNICON [23]; (3) Methods aiming at dealing with noisy label and long-tail distribution (NL-LT). They are MW-Net [41], RoLT [49], HAR [2] and ULC [19]. + +Implementation Details. We use PreAct ResNet18 [14] as backbone for CIFAR datasets and ResNet18 as backbone for Red mini-ImageNet dataset. Both of backbones adopt SGD with an initial learning rate of 0.02, a momentum of 0.9, and a weight decay of $5 \times 10^{-4}$ and a batch size of 64. For fair comparison, we train all methods for 100 epochs. + +# 5.2. Comparative Results + +CIFAR-10/100. Tab. 1 and 2 report the accuracy of different methods for intrinsically long-tailed CIFAR-10/100 + +
DatasetCIFAR-10CIFAR-100
Imbalance Factor0.1
Noise Ratio (Sym.)0.40.60.40.6
BaselineCE71.6761.1634.5323.63
LTLA70.5654.9229.0723.21
LDAM70.5361.9731.3023.13
IB73.2462.6232.4025.84
NLDivideMix82.6780.1754.7144.98
UNICON84.2582.2952.3445.87
NL-LTMW-Net70.9059.8532.0321.71
RoLT81.6276.5842.9532.59
HAR77.4463.7538.1726.09
ULC84.4683.2554.9144.66
OurTABASCO85.5384.8356.5245.98
+ +with symmetric and asymmetric noise, respectively. It can be observed three phenomena as follows: (1) The performance of existing long-tail methods is lower than baseline in most situations. It is because such methods do not have the ability to distinguish the noise samples, and the wrong attention to the noise samples leads to the further decline of the model generalization ability. (2) The advantages of existing methods aiming at both long-tailed distribution and label noise are not obvious compared with single methods. It is because existing methods do not take into account the distribution inconsistency caused by noise labels. (3) Our method significantly improved over other methods in all cases. Moreover, as the proportion of noise increases, the accuracy of our method decreases less compared to other methods. It validates that our method can effectively identify the noise in long-tail distribution. + +Red mini-ImageNet and CIFAR-10N/100N. Tab. 4 reports the accuracy of different methods on real-world noise datasets with intrinsically long-tailed distribution. According to the results of label-noise learning methods on CIFAR-10N/100N, it can be observed that real-world noise is more difficult to separate than synthetic noise to some extent. It further increases the difficulty of dealing with such problem. Nevertheless, our method still performs well, which again confirms its effectiveness. + +# 5.3. Ablation Study and Discussions + +In the following experiments, we analyze each component of the proposed TABASCO on CIFAR-10/100 to verify its effectiveness. We use an imbalance factor of 0.1 and a noise ratio of 0.4 to construct the synthetic noise dataset. + +Effectiveness of WJSD. To validate the effectiveness of the proposed WJSD, we compare the accuracy of models trained by different separation metrics. Specifically, we + +Table 1: Performance comparison under symmetric noise. The best results are shown in bold. + +
DatasetCIFAR-10CIFAR-100
Imbalance Factor0.1
Noise Ratio (Asym.)0.20.40.20.4
BaselineCE79.9062.8844.4532.05
LTLA71.4959.8839.3428.49
LDAM74.5862.2940.0633.26
IB73.4958.3645.0235.25
NLDivideMix80.9269.3558.0941.99
UNICON72.8169.0455.9944.70
NL-LTMW-Net79.3465.4942.5230.42
RoLT73.3058.2948.1939.32
HAR82.8569.1948.5033.20
ULC74.0773.1954.4543.20
OurTABASCO82.1080.5759.3950.51
+ +Table 2: Performance comparison under asymmetric noise. The best results are shown in bold. + +
DatasetSeparation metricAccuracy
CIFAR-10JSD83.97
WJSD85.57
CIFAR-100JSD55.80
WJSD56.67
+ +Table 3: Performance comparison between JSD and WJSD. + +train the model by using JSD and WJSD for sample separation with a symmetric noise dataset, respectively. As for each separation metric, we simply use the small value strategy [29, 23] for sample selection. As Tab. 3 shows, the model trained by WJSD achieves better results on both symmetric noise datasets compared with JSD owing to the stronger separability of WJSD. + +Effectiveness of ACD. To validate the advantage of the proposed ACD, we compare it with the method which calculates the feature centroid on the observed class (hereinafter referred to as centroid distance or CD) to show their separability in CIFAR-10. Specifically, based on the same backbone, we calculate the distance from the sample to the centroid using ACD and CD in CIFAR-10 with asymmetric noise, respectively. Fig. 4 shows the distributions of samples in the tail class by CD and ACD. The purity of the tail class is 0.53. It can be observed that the CD values of noise and clean samples are highly overlapped, which leads to failure sample separation. It is because the purity of the tail class may be quite low due to the negative effects of both label-noise and long-tailed distribution. The centroid obtained by ACD has a higher purity, so there is a significant difference in ACD between them. As shown in Fig. 4(b), most clean samples are concentrated in the interval of [0.8,1], which is easily clustered by GMM. + +
DatasetRed10N100N
Imbalance Factor≈ 0.10.1
Noise Ratio0.20.4≈ 0.4
BaselineCE40.4231.4660.4438.10
LTLA26.8225.8865.7436.50
LDAM26.6423.4662.5038.48
IB23.8022.0865.9142.48
NLDivideMix48.7648.9667.8544.25
UNICON40.1841.6469.5451.93
NL-LTMW-Net42.6640.2669.7344.20
RoLT22.5624.2275.2446.61
HAR46.6138.7174.9744.54
ULC48.1247.0675.7151.72
OurTABASCO50.2049.6880.6153.83
+ +Table 4: Performance comparison with real-world noise and long-tail distribution. The best results are shown in bold. + +Effectiveness of Bi-dimensional Sample Separation. To validate how the proposed bi-dimensional metrics complement each other, we plot the values of bi-dimensional metrics of both clean and noisy samples under different noise types in Fig. 5. For the case of symmetric noise shown in Fig. 5(a), it can be observed that ACD cannot effectively distinguish clean samples from noisy samples in the tail class. In this case, WJSD shows its advantage because the values of WJSD for most noisy samples are clustered in the top region, and the clean samples are scattered throughout the rest region. For the case of asymmetric noise shown in Fig. 5(b), it can be observed that WJSD cannot distinguish clean samples from noisy samples well for the tail class, while ACD can distinguish them well although the clean and noisy samples are closer in the tail class. The experimental observation is consistent with the previous discussion, which validates the complementarity of bi-dimensional metrics. + +Effectiveness of Sample Selection. In order to validate the effectiveness of the proposed sample selection in dimension selection and cluster selection, we compare the optimal clean ratio of clusters obtained by WJSD, ACD and our selection method in CIFAR-10 with different noise types. The clean ratio of a cluster is calculated by the proportion of clean samples in the cluster to the total number of cluster samples. As shown in Fig. 6, on the tail class, the clean ratio of the cluster obtained by our selection method is aligned with the higher one between WJSD and ACD for both noise cases. It shows that we can choose the most appropriate separation dimension in different situations. Besides, the clean ratio of the cluster we selected is consistent with that of the optimal cluster in the corresponding dimension, which is sufficient to show that the method we proposed can select clean samples. + +![](images/8978744f5c52019e23a6df9ddbcefd4b3d31544d821d855b90bb486837f20e8a.jpg) +Figure 4: Comparison of the sample distributions between CD and ACD in the tail class. + +![](images/2ab50acdf51b02f9a848c4538c99922c871944a12dfcdf0eedd93ee4d564c139.jpg) + +![](images/6a8bf68f9db9b8598d1392047cd47c220a1be42a8cd501b7dec94e1c1f3ce57f.jpg) +(a) Symmetric noise + +![](images/87cf4887cb473a40cbc410da6221f0e73f402470ce88fd0ef33b08ab0eaab4d3.jpg) +(b) Asymmetric noise + +![](images/df444e84913d8f40b83c37295349c5d42fb46363247f2eca2f479539d74cc1f3.jpg) +Figure 5: Scatter plot of the values of the proposed bidimensional metrics with (a) symmetric noise and (b) asymmetric noise. +(a) Symmetric noise +Figure 6: The performance of the proposed sample selection with (a) symmetric noise and (b) asymmetric noise. + +![](images/34026ab00885b70d2d07597d1d8b93c9ba16dae610525ee4a0436ad8f17d4e94.jpg) +(b) Asymmetric noise + +# 6. Conclusion + +This paper studies a more general and realistic problem of label-noise learning with intrinsically long-tailed data. The major challenge in this problem is that it is hard to distinguish clean samples from noisy samples on intrinsic tail classes. Accordingly, we propose a learning framework TABASCO for this problem. In TABASCO, two new metrics are explicitly proposed to address the problem of sample selection in tail classes. Extensive experiments on noisy-labeled datasets with long-tail distribution demonstrate its effectiveness. + +Acknowledgements. We thank Dr. Shiquan Ruan for his discussion on the theory proof. This study was supported in part by the National Natural Science Foundation of China under Grants 62002302 and U21A20514; in part by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform under Grant 3502ZCQXT2022008; in part by NSFC/RGC Joint Research Scheme under Grant N_HKBU214/21; and in part by the General Research Fund of RGC under Grants 12201321 and 12202622. + +# References + +[1] David Berthelot, Nicholas Carlini, Ian J. Goodfellow, Nicolas Papernot, Avital Oliver, and Colin Raffel. Mixmatch: A holistic approach to semi-supervised learning. In NeurIPS, 2019. 6 +[2] Kaidi Cao, Yining Chen, Junwei Lu, Nikos Aréchiga, Adrien Gaidon, and Tengyu Ma. Heteroskedastic and imbalanced deep learning with adaptive regularization. In ICLR, 2021. 2, 6 +[3] Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. Learning imbalanced datasets with label-distribution-aware margin loss. In NeurIPS, 2019. 2, 3, 6 +[4] Nitesh V. 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"spans": [ + { + "bbox": [ + 46, + 280, + 290, + 519 + ], + "type": "text", + "content": "Label noise is one of the key factors that lead to the poor generalization of deep learning models. Existing label-noise learning methods usually assume that the ground-truth classes of the training data are balanced. However, the real-world data is often imbalanced, leading to the inconsistency between observed and intrinsic class distribution with label noises. In this case, it is hard to distinguish clean samples from noisy samples on the intrinsic tail classes with the unknown intrinsic class distribution. In this paper, we propose a learning framework for label-noise learning with intrinsically long-tailed data. Specifically, we propose two-stage bi-dimensional sample selection (TABASCO) to better separate clean samples from noisy samples, especially for the tail classes. TABASCO consists of two new separation metrics that complement each other to compensate for the limitation of using a single metric in sample separation. Extensive experiments on benchmarks demonstrate the effectiveness of our method. Our code is available at https://github.com/Wakings/TABASCO." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 531, + 128, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 531, + 128, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 531, + 128, + 544 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 551, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 696 + ], + "type": "text", + "content": "Under the support of a large amount of high-quality labeled data, deep neural networks have achieved great success in various fields [27, 40, 7]. However, it is expensive and difficult to obtain a large amount of high-quality labeled data in many practical applications. Instead, the commonly used large-scale training data is usually obtained from the Internet or crowdsourcing platforms like Amazon Mechanical Turk, which is unreliable and may be mislabeled [52, 43]. The models trained on this kind of unreliable data, called noisy-labeled data, often produce poor generalization performance because deep neural networks tend to overfit noisy samples due to their large model capacity. In" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 306, + 255, + 421, + 337 + ], + "blocks": [ + { + "bbox": [ + 306, + 255, + 421, + 337 + ], + "lines": [ + { + "bbox": [ + 306, + 255, + 421, + 337 + ], + "spans": [ + { + "bbox": [ + 306, + 255, + 421, + 337 + ], + "type": "image", + "image_path": "22e148d9b056a7487ba405eda466053370f0d945b7ff477a2b438a49a21ec20e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 325, + 344, + 402, + 354 + ], + "lines": [ + { + "bbox": [ + 325, + 344, + 402, + 354 + ], + "spans": [ + { + "bbox": [ + 325, + 344, + 402, + 354 + ], + "type": "text", + "content": "(a) Class distribution" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 425, + 255, + 533, + 337 + ], + "blocks": [ + { + "bbox": [ + 425, + 255, + 533, + 337 + ], + "lines": [ + { + "bbox": [ + 425, + 255, + 533, + 337 + ], + "spans": [ + { + "bbox": [ + 425, + 255, + 533, + 337 + ], + "type": "image", + "image_path": "348c53ee3757a4e47bad2047be5b399853813846bb127ad12b77972385732830.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 441, + 344, + 516, + 354 + ], + "lines": [ + { + "bbox": [ + 441, + 344, + 516, + 354 + ], + "spans": [ + { + "bbox": [ + 441, + 344, + 516, + 354 + ], + "type": "text", + "content": "(b) Loss distribution" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 360, + 546, + 407 + ], + "lines": [ + { + "bbox": [ + 305, + 360, + 546, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 360, + 546, + 407 + ], + "type": "text", + "content": "Figure 1: (a) An example of observed class distribution with noisy labels with long-tailed intrinsic class distribution. (b) The training loss of each sample under noisy-labeled and long-tailed data." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 414, + 546, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 546, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 546, + 474 + ], + "type": "text", + "content": "the literature, there are some works to obtain a robust model trained on noisy-labeled data [11, 44]. Among them, the most straightforward and effective way is to differentiate between clean and noisy samples based on their differences in specific metrics, such as training loss [12, 29, 23]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 475, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 547, + 713 + ], + "type": "text", + "content": "These label-noise learning methods generally assume that the intrinsic class distribution of the training data is balanced, where each class has almost the same number of samples in terms of their unknown ground-truth labels. However, the data in real-world applications are often imbalanced, e.g., the LVIS dataset [9] and the iNaturalist dataset [17]. The class imbalance usually exhibits in the form of a long-tail distribution, where a small portion of classes possess a large number of samples, and the other classes possess a small number of samples only [38, 18]. In this case, the model training tends to the head classes and ignores the tail classes [60, 62]. When both noisy labels and long-tail distribution exist, training a robust model is even more challenging. There are two key challenges in this scenario. (1) Distribution inconsistency: The observed and intrinsic distributions are likely inconsistent due to noise labels, making the model more difficult to discover and focus on the intrinsic tail classes. As illustrated in Fig. 1(a), the intrinsic class distribution of the dataset is long-tailed, while the existence of noisy labels makes the distribution more" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 253, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 253, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 253, + 713 + ], + "type": "text", + "content": "* Yang Lu is the corresponding author: luyang@xmu.edu.cn" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1369" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "balanced. The intrinsic tail classes, e.g., classes 6 and 9, are occupied by a large number of noisy data, making them no longer tail classes by observation. (2) Tail inseparability: Even if the tail class is identified, it is more difficult than ever to distinguish between clean and noisy samples in the tail class because clean samples are overwhelmed by noises that make their values of the separation metric highly similar. As illustrated in Fig. 1(b), the training loss of clean and noisy samples in the tail class are generally inseparable compared with the ones in the other classes. Several preliminary works have studied the joint problem of label noise and long-tail distribution [21, 49, 24, 2]. These methods implicitly reduce the complexity of the problem by assuming a similar noise rate for each class. However, this assumption is too strong to apply because noisy samples from the head classes may be the majority, resulting in a higher noise rate in the tail class than in other classes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 276, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 289, + 479 + ], + "type": "text", + "content": "In this paper, we propose a Two-stAge Bi-dimensionAl Sample seleCtiOn (TABASCO) strategy to address the problem of label-noise learning with intrinsically long-tailed data. In the first stage, we propose to use two new separation metrics for sample separation, i.e., weighted Jensen-Shannon divergence (WJSD) and adaptive centroid distance (ACD), which work corporately to separate clean samples from noisy samples in the tail classes. The proposed metrics are complementary, where WJSD separates the samples from the output perspective while ACD does that from the feature perspective. In the second stage, we determine the separation dimension with better separability for each class and perform sample selection. In order to evaluate the method uniformly and effectively, we introduce two benchmarks with real-world noise and intrinsically long-tailed distribution. The main contributions of our work can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 487, + 287, + 639 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 487, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 487, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 58, + 487, + 287, + 536 + ], + "type": "text", + "content": "- We present a more general problem of label-noise learning with intrinsically long-tailed data. The key challenges in this problem are distribution inconsistency and tail inseparability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 540, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 540, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 58, + 540, + 287, + 587 + ], + "type": "text", + "content": "- We propose an effective solution called TABASCO. With the help of two new separation metrics, it is able to effectively identify and select clean samples of the intrinsic tail class." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 591, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 591, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 58, + 591, + 287, + 639 + ], + "type": "text", + "content": "- We introduce two benchmarks with real-world noise and intrinsically long-tailed distribution. Extensive experiments on them show the effectiveness of our method and the limitations of existing methods." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 651, + 134, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 134, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 134, + 662 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 670, + 172, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 172, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 172, + 684 + ], + "type": "text", + "content": "2.1. Label-Noise Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "A straightforward strategy to deal with noisy data is to reduce the proportion of noise in training samples by sepa" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "rating noisy samples from clean samples. Methods such as co-teaching [12] and DivideMix [29] adopt the small loss trick, while Jo-SRC [55] and UNICON [23] use Jensen-Shannon divergence instead for sample selection. In contrast to methods that separate at the label level, some methods [30, 34] attempt to separate samples at the feature space. There are also some methods to avoid over-fitting the model to noisy data by imposing regularization constraints on model parameters [50, 10] or labels [37, 58, 32]. Other methods mitigate the influence of noisy data by adjusting the loss functions, such as backward and forward loss correction [36], gold loss correction [16], MW-Net [41] and Dual-T [54]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 234, + 418, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 234, + 418, + 247 + ], + "spans": [ + { + "bbox": [ + 306, + 234, + 418, + 247 + ], + "type": "text", + "content": "2.2. Long-tail Learning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 252, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 545, + 433 + ], + "type": "text", + "content": "Re-balancing the data for long-tail distributions is a classical strategy to solve the problem of long-tail learning, such as re-sampling [4, 31, 8, 13] and data augmentation [61, 57, 5]. In addition, there are methods to improve the model generalization by introducing long-tail robust loss functions [6, 3, 45, 39]. Methods such as FTL [56], RIDE [46] and DiVE [15] try to solve the problem by using the idea of transfer learning. Recently, approaches based on decoupling [22, 61, 59] split end-to-end learning into feature learning and classifier retraining such that the obtained feature extractor is less affected by the long-tail distribution. In contrast to the above methods with the supervised learning paradigm, CReST [47], ABC [28] and DARP [25] attempt to solve the long-tail problem in the manner of semi-supervised learning." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 438, + 527, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 438, + 527, + 451 + ], + "spans": [ + { + "bbox": [ + 306, + 438, + 527, + 451 + ], + "type": "text", + "content": "2.3. Label-Noise Learning on Long-tailed Data" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 456, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 635 + ], + "type": "text", + "content": "Research on this joint problem has just been explored. CNLCU [51] relaxes the constraint of the small loss trick by regarding a portion of large loss samples as clean samples to reduce the probability of misclassifying clean samples to noisy samples in the tail class. RoLT [49] uses the distance from the samples to the centroid of the current class instead of the training loss for sample selection. HAR [2] uses an adaptive approach to regularize noise and tail class samples. Karthik et al. [24] uses the idea of decoupling to fine-tune the loss function for better robustness after feature learning by the self-supervised method. ULC [19] introduces uncertainty to enhance the separation ability of noise samples. H2E [53] reduces hard noises to easy ones by learning a classifier as noise identifier invariant to the class and context distributional changes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 646, + 419, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 419, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 419, + 658 + ], + "type": "text", + "content": "3. Problem Definition" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "text", + "content": "Given a training set " + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{x_i, \\hat{y}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{y}_i \\in [M]" + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "text", + "content": " is the observed label of the sample " + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "text", + "content": " is the number of training samples, and " + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "text", + "content": " is the number of classes. In our problem, " + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 664, + 545, + 714 + ], + "type": "text", + "content": " has the following properties:" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1370" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 545, + 216 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 545, + 216 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 545, + 216 + ], + "type": "image", + "image_path": "e2fb5fbcd490fc645823e0de49b016a33494bce676d8b24cf9f2e12b8ee9f4bb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 108, + 225, + 485, + 239 + ], + "lines": [ + { + "bbox": [ + 108, + 225, + 485, + 239 + ], + "spans": [ + { + "bbox": [ + 108, + 225, + 485, + 239 + ], + "type": "text", + "content": "Figure 2: The proposed framework for label-noise learning with intrinsically long-tailed data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 244, + 287, + 321 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "text", + "content": "- Noisy-labeled. There is a subset of samples " + }, + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{D}} \\in \\mathcal{D}" + }, + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "text", + "content": ", where a sample " + }, + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "inline_equation", + "content": "\\{x, \\hat{y}\\} \\in \\hat{\\mathcal{D}}" + }, + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "text", + "content": " has an unknown ground-truth label " + }, + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "text", + "content": " different from its observed label " + }, + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 58, + 244, + 287, + 281 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "type": "text", + "content": "- Long-tailed. The ground-truth class distribution is long-tailed. Supposing " + }, + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "type": "inline_equation", + "content": "n_c" + }, + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "type": "text", + "content": " is the number of the samples in class " + }, + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "type": "inline_equation", + "content": "n_1 > n_2 > \\dots > n_M" + }, + { + "bbox": [ + 58, + 285, + 287, + 321 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 325, + 289, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 289, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 289, + 553 + ], + "type": "text", + "content": "We call this kind of training data intrinsically long-tailed because the observed class distribution may not be long-tailed due to the existence of noisy labels. Therefore, our goal is to learn from noisy-labeled data with the intrinsically long-tailed class distribution. The problem is challenging from two aspects. On the one hand, directly applying long-tail learning methods [6, 3, 45] is infeasible because the observed class distribution may be inconsistent with the intrinsic class distribution. On the other hand, label-noise learning methods perform poorly in the tail classes because they usually contain more noisy samples due to insufficient data, as shown in Fig. 1(a). It results in high noise rates in the tail classes, which brings great challenges to separating clean samples and noisy samples for further training. Under this circumstance, the existing sample selection methods [29, 23] often fail to select clean samples in the tail class. The main reason is that it is difficult to distinguish the tail class data from the noisy label data by existing metrics like cross-entropy loss, as shown in Fig. 1(b)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 562, + 153, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 153, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 153, + 575 + ], + "type": "text", + "content": "4. Proposed Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we propose a two-stage bi-dimensional sample selection (TABASCO) to address the problem of label-noise learning with intrinsically long-tailed data. TABASCO decouples the sample selection process into two stages: (1) sample separation, and (2) dimension and cluster selection. First, given an initial model " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " trained on the original training data " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": ", we propose to calculate bi-dimension metrics for each sample in each observed class based on the outputs and features of the model. Second, we determine the separation dimension with better separability for each class, and we adopt the corresponding selection strategy to" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 245, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 293 + ], + "type": "text", + "content": "select the cluster with more clean samples based on the selected metric. Last, we adopt semi-supervised learning to update the model by regarding the selected clean cluster as labeled data. The overall framework is shown in Fig. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 300, + 494, + 313 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 494, + 313 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 494, + 313 + ], + "type": "text", + "content": "4.1. Bi-Dimensional Separation Metrics" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 319, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 499 + ], + "type": "text", + "content": "Due to the deficiency of a single separation metric to distinguish clean samples from noisy samples in the complex situation of noisy labels with intrinsic long-tail distribution, we propose to jointly use two metrics from different perspectives: weighted Jensen-Shannon divergence (WJSD) and adaptive centroid distance (ACD). Both metrics are specifically designed for the joint problem and are complementary to cover the case when only one of them cannot separate clean samples from noisy samples well. WJSD fully utilizes the information of prediction confidence, while ACD relies on the distance in the feature space. Thus, using clustering on samples according to the values of their bi-dimensional metrics has the flexibility to separate samples with different imbalance ratios, noise ratios, and noise types." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": "We first reduce the separation granularity to alleviate the interference from the head class to the tail class. Specifically, the separation is performed within each observed class according to the proposed bi-dimensional metrics. We first divide training set " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": " into subsets according to the observed labels " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c = \\{(x,\\hat{y})\\mid \\hat{y} = c\\}" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": ". Given a sample " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "(x_{i},\\hat{y}_{i})\\in \\mathcal{D}_{c}" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": ", the model predictions obtained from the model " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": " is denoted as " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i = [p_i^1,p_i^2,\\dots,p_i^M ]" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "p_i^j" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": "'s dimension of vector " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": ". The one-hot representation of the observed label " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\hat{y}_i" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": " is denoted as " + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}_i" + }, + { + "bbox": [ + 304, + 500, + 545, + 620 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "type": "text", + "content": "Weighted Jensen-Shannon Divergence The Jensen-Shannon Divergence (JSD) is a commonly used metric to separate samples by assessing the variability of model predictions [55, 23]. It is defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 675, + 545, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 675, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 306, + 675, + 545, + 710 + ], + "type": "interline_equation", + "content": "J S D \\left(x _ {i}\\right) = \\frac {1}{2} K L \\left(\\mathbf {p} _ {i} \\left\\| \\frac {\\mathbf {p} _ {i} + \\hat {\\mathbf {y}} _ {i}}{2}\\right) + \\frac {1}{2} K L \\left(\\hat {\\mathbf {y}} _ {i} \\left\\| \\frac {\\mathbf {p} _ {i} + \\hat {\\mathbf {y}} _ {i}}{2}\\right), \\right. \\right. \\tag {1}", + "image_path": "d2d09cbcd018614c3ca430b3592dc32b1189cd546d1ba4e1608fb4fd604e368b.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "1371" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "KL(\\cdot \\|\\cdot)" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " is the Kullback-Leibler divergence. When the intrinsic distribution is balanced, the JSD values of clean samples are generally lower than the noisy samples, so the separation can be easily modeled. However, when the distribution is intrinsically long-tailed, the noisy and clean samples in a tail class tend to obtain similar prediction confidence on the observed class " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", because their predictions are both towards the head classes. In this case, using JSD as a separation metric fails to separate them. The reason is given by Theorem 1, which shows the upper bound of the absolute value of the JSD difference between two samples." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": "Theorem 1 (Upper bound of JSD difference) Suppose " + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "inline_equation", + "content": "x_{j}" + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": " are two samples in class " + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "inline_equation", + "content": "p_{i}^{c}" + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "inline_equation", + "content": "q_{i}^{c}" + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": "'s dimension of their prediction confidence " + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{i} = [p_{i}^{1}, p_{i}^{2}, \\dots, p_{i}^{M}]" + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{j} = [p_{j}^{1}, p_{j}^{2}, \\dots, p_{j}^{M}]" + }, + { + "bbox": [ + 47, + 204, + 289, + 277 + ], + "type": "text", + "content": ", respectively. The upper bound of the absolute value of the difference between their JSD values is given by:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 279, + 278, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 279, + 278, + 306 + ], + "spans": [ + { + "bbox": [ + 57, + 279, + 278, + 306 + ], + "type": "interline_equation", + "content": "| J S D (x _ {i}) - J S D (x _ {j}) | \\leq \\frac {1}{2} \\log \\left(\\frac {p _ {i} ^ {c} + 1}{p _ {i} ^ {c}}\\right) | p _ {i} ^ {c} - p _ {j} ^ {c} |.", + "image_path": "c0768bced81ecbe594d63a284013f0fb38d18c4019734dbb8a6fed61311939d8.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": "Theorem 1 shows that the difference between values of JSD is only determined by the prediction confidence of the observed class, i.e., " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "p_i^c" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "p_j^c" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": ". In addition, as " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "|p_i^c - p_j^c|" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " gets smaller with a fixed value of " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "p_i^c" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "|JSD(x_i) - JSD(x_j)|" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " is also smaller. This indicates that when two samples are in the same class " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " with close values of " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "p_i^c" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": ", their JSD values are also close, which makes it difficult to separate them." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": "Nevertheless, we can utilize the prediction confidence on other classes, i.e., " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "p_i^d" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "d \\neq c" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": ", to distinguish two samples even if their values of " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "p_i^c" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": " are close. Specifically, we propose WJSD by imposing an additional weight on JSD to further distinguish samples by inspecting their prediction confidence on other classes rather than the observed class. First, we take the maximum prediction confidence " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "\\max(\\mathbf{p}_i)" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": " into account because it may reflect the confidence of a noisy sample's ground-truth class " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": ". Then, we calculate the ratio of the maximum prediction confidence to the prediction confidence of the observed class " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "\\max(\\mathbf{p}_i) / p_i^c" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": ". In this manner, the additional weight is greater than one only if the class with the maximum prediction confidence is not the observed class. The larger gap between " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "\\max(\\mathbf{p}_i)" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "p_i^c" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": " makes the weight higher. To avoid exceptionally large weights by the division during normalization over all samples in class " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": " for later clustering, we set the upper bound according to the averaged prediction confidence over all samples in class " + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 392, + 289, + 631 + ], + "type": "text", + "content": ". Finally, the additional weight can be calculated as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 78, + 635, + 287, + 650 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 635, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 78, + 635, + 287, + 650 + ], + "type": "interline_equation", + "content": "W \\left(x _ {i}\\right) = \\min \\left(\\max \\left(\\mathbf {p} _ {i}\\right) / p _ {i} ^ {c}, \\max \\left(\\bar {\\mathbf {p}} _ {c}\\right) / \\bar {p} _ {c} ^ {c}\\right), \\tag {2}", + "image_path": "5e55429bb0d41f2b91ea20410d141205fa3259be7bbaceaf5aa9c72788dfa858.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 654, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 693 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 654, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{p}}_c = [\\bar{p}_c^1,\\bar{p}_c^2,\\dots,\\bar{p}_c^M] = \\frac{1}{|\\mathcal{D}_c|}\\sum_{i = 1}^{|\\mathcal{D}_c|}\\mathbf{p}_i" + }, + { + "bbox": [ + 47, + 654, + 287, + 693 + ], + "type": "text", + "content": " is the average prediction confidence of class " + }, + { + "bbox": [ + 47, + 654, + 287, + 693 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 654, + 287, + 693 + ], + "type": "text", + "content": ". Thus, WJSD can be calculated by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 93, + 697, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 697, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 93, + 697, + 287, + 711 + ], + "type": "interline_equation", + "content": "W J S D \\left(x _ {i}\\right) = W \\left(x _ {i}\\right) \\times J S D \\left(x _ {i}\\right). \\tag {3}", + "image_path": "991df0bbae4bddc211a1b344fe9011fba4098dd76c6b15ded087d6d2b63f631f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 121 + ], + "type": "text", + "content": "Remarks: Compared with the value of JSD that is only related to the prediction confidence on the observed class, adopting the maximum prediction confidence in WJSD can better separate clean samples from noisy samples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 124, + 545, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 124, + 545, + 268 + ], + "spans": [ + { + "bbox": [ + 304, + 124, + 545, + 268 + ], + "type": "text", + "content": "Adaptive Centroid Distance. Although the sample separability of WJSD is greatly improved compared with JSD, the separation metric still relies on model prediction. When all the noisy samples labeled in a class are from another class, e.g., asymmetric noise, the model prediction for both noisy and clean samples will be highly similar because it is easy to learn a classifier that maps the features from two different classes into one. It results in low discrimination between the model predictions of clean and noisy samples in this case. Thus, solely using WJSD may not be enough to separate the clean and noisy samples when model predictions (in terms of all classes, not only about " + }, + { + "bbox": [ + 304, + 124, + 545, + 268 + ], + "type": "inline_equation", + "content": "p^c" + }, + { + "bbox": [ + 304, + 124, + 545, + 268 + ], + "type": "text", + "content": ") are close." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 268, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 422 + ], + "type": "text", + "content": "Except for separating the samples in the output space, we propose another metric calculated in the feature space to eliminate the bias from the classifier because the learned features are more robust to noise labels. Specifically, for a given sample, we can calculate the distance between its feature and the class feature centroid to evaluate how the feature of a sample deviates from its class centroid. This approach is only practical when the quality of the centroid is high. Directly calculating the centroid according to the observed label may not be accurate because it involves a certain number of features of the noisy samples. Therefore, we define purity in Definition 1 to assess the quality of the centroid of class " + }, + { + "bbox": [ + 304, + 268, + 545, + 422 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 268, + 545, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "text", + "content": "Definition 1 (Purity) Suppose a noisy sample set of class " + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "text", + "content": " be " + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c = \\{(x,\\hat{y})\\mid \\hat{y} = c\\}" + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "text", + "content": ", where the intrinsic label corresponding to the sample is " + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "text", + "content": ". The purity " + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{D}_c}" + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "text", + "content": " of set " + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 304, + 423, + 545, + 471 + ], + "type": "text", + "content": " is calculated by:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 345, + 474, + 545, + 507 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 474, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 345, + 474, + 545, + 507 + ], + "type": "interline_equation", + "content": "P _ {\\mathcal {D} _ {c}} = \\max _ {k = 1, \\dots , M} \\left\\{\\frac {\\sum_ {i = 1} ^ {N} I \\left(y _ {i} = k\\right)}{N} \\right\\}, \\tag {4}", + "image_path": "554b2deccfefaf2de821a16eb7e74b4381e66af04607a3ce8f2767fe1f223c14.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "type": "inline_equation", + "content": "I(\\cdot)" + }, + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "type": "text", + "content": " is an indicator function and " + }, + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "type": "text", + "content": " is the number of samples in the set " + }, + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 304, + 510, + 547, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 534, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 642 + ], + "type": "text", + "content": "Purity indicates the proportion of an intrinsic class that takes the majority in the observed class " + }, + { + "bbox": [ + 304, + 534, + 545, + 642 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 534, + 545, + 642 + ], + "type": "text", + "content": ". The higher the purity of a class set used to calculate the centroid, the better the centroid helps to distinguish between noise and clean samples. RoLT [49] adopts a similar idea to use class feature centroid for noisy sample detection. However it directly calculates the feature centroid on the observed class, such that it inevitably suffers from the existence of noise features when the purity is low, especially in our problem." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "In order to improve the purity of the class feature centroid for distance calculation between features, we propose ACD as the second separation metric to separate samples jointly with WJSD. The feature centroid for each class is adaptively updated by involving samples with high confidence from the observed class. The class centroid " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_c" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": " based" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1372" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 266, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 266, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 266, + 85 + ], + "type": "text", + "content": "on a high-confidence sample set " + }, + { + "bbox": [ + 47, + 72, + 266, + 85 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c^H" + }, + { + "bbox": [ + 47, + 72, + 266, + 85 + ], + "type": "text", + "content": " is calculated by:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 88, + 287, + 123 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 88, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 104, + 88, + 287, + 123 + ], + "type": "interline_equation", + "content": "\\mathbf {o} _ {c} = \\frac {1}{| \\mathcal {D} _ {c} ^ {H} |} \\sum_ {i = 1} ^ {| \\mathcal {D} _ {c} ^ {H} |} \\mathbf {f} _ {i}, \\tag {5}", + "image_path": "4b0148011b83ac12c8396216f9f3e23cb560f29e458bf2216e0abc27c4197c4e.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 100, + 125, + 287, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 125, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 100, + 125, + 287, + 140 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {c} ^ {H} = \\left\\{x _ {i} \\mid x _ {i} \\in \\mathcal {D} _ {c}, p _ {i} ^ {t _ {c}} > H _ {c} \\right\\}, \\tag {6}", + "image_path": "2cc58eb5c71beb9a84e6cfab0d439409ca8fb99fb77c47a7c12dda9484a0afc0.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": " is the feature of " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "t_c = \\mathrm{argmax}_c\\{\\bar{p}_c^j\\}" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": " is the class index with the largest average prediction confidence of class " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": ". Thus, we can use the prediction confidence of class " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": " for sample " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": ", e.g., " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "p_i^{t_c}" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": ", as the selection criteria compare with the threshold " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "H_{c}" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c^H" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": " is constructed by the samples in " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "D_{c}" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": " whose corresponding prediction confidence of class " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": " is higher than " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "H_{c}" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": ". The high-confidence threshold " + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "inline_equation", + "content": "H_{c}" + }, + { + "bbox": [ + 47, + 144, + 289, + 240 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 116, + 242, + 287, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 242, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 116, + 242, + 287, + 275 + ], + "type": "interline_equation", + "content": "H _ {c} = \\frac {1}{D _ {c}} \\sum_ {i = 1} ^ {| D _ {c} |} w _ {i} \\times p _ {i} ^ {t _ {c}}, \\tag {7}", + "image_path": "180f0281d7da864b31c9708e192579beaef912538d513a5a2bff3021430d7e95.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 119, + 277, + 287, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 277, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 119, + 277, + 287, + 293 + ], + "type": "interline_equation", + "content": "w _ {i} = \\max \\left(1, p _ {i} ^ {t _ {c}} / \\bar {p} _ {c} ^ {t _ {c}}\\right). \\tag {8}", + "image_path": "d1a8b6d56a49de51699a14aa80b502f60418a3063462d483aa526d410902a820.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "inline_equation", + "content": "H_{c}" + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "text", + "content": " is calculated by the weighted sum of the prediction confidence of class " + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "text", + "content": " for all samples " + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "text", + "content": ". The weight " + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "text", + "content": " increases when a sample's prediction confidence of class " + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "inline_equation", + "content": "t_c" + }, + { + "bbox": [ + 46, + 296, + 287, + 464 + ], + "type": "text", + "content": " is higher than its class average. Thus, the threshold is high enough to ensure the purity of the selected samples. High confidence samples are more representative and more likely to be in the same class. It is worth noting that we choose more representative samples rather than clean samples because the clean samples in the tail classes are easily overwhelmed by the noise samples in our problem. In this case, it is difficult to select the clean samples directly because the noise samples may be more representative in the tail class. As for asymmetric noise, the choice of clean or noisy samples to obtain centroid for sample separation is equivalent." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 464, + 288, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 288, + 512 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 288, + 512 + ], + "type": "text", + "content": "In each round, the centroids are adaptively adjusted because the feature extractor in the model is updated, as well as the set " + }, + { + "bbox": [ + 46, + 464, + 288, + 512 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c^H" + }, + { + "bbox": [ + 46, + 464, + 288, + 512 + ], + "type": "text", + "content": ". Therefore, the proposed metric ACD can be calculated by:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 516, + 287, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 516, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 116, + 516, + 287, + 529 + ], + "type": "interline_equation", + "content": "A C D \\left(x _ {i}\\right) = \\cos \\left(\\mathbf {f} _ {i}, \\mathbf {o} _ {c}\\right). \\tag {9}", + "image_path": "eea0424f24c5b0ae2acdb3b3a3042aeda7ba019cfc03e62c7250e9efd13f8dfc.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 533, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 289, + 714 + ], + "type": "text", + "content": "Remarks: The proposed two metrics, WJSD and ACD, are complementary for sample separation in the tail classes. When the ground-truth classes of the noisy samples are diverse, e.g. symmetric noise, WJSD plays the dominant role because the predictions can hardly be unified due to the class diversity of noisy samples. They are more likely to be predicted towards their ground-truth class, which can be captured by " + }, + { + "bbox": [ + 46, + 533, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\max (\\mathbf{p}_i)" + }, + { + "bbox": [ + 46, + 533, + 289, + 714 + ], + "type": "text", + "content": ". In this case, ACD may not be effective in separating clean samples from noisy samples because the messy noisy samples may affect the purity of the calculated centroid. On the other hand, when the ground-truth classes of the noisy samples belong to only one class, e.g., asymmetric noise, WJSD tends to produce similar predictions for noisy and clean samples, while the adaptive centroid in ACD can help distinguish them in the feature space." + } + ] + } + ], + "index": 9 + }, + { + "type": "code", + "bbox": [ + 310, + 89, + 528, + 282 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 510, + 87 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 510, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 510, + 87 + ], + "type": "text", + "content": "Algorithm 1: The Dimension Selection Strategy" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "lines": [ + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "spans": [ + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": "Input: Noise sample set " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " in class " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": ", threshold " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " \nOutput: Cluster " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^1, \\mathcal{G}_c^2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " \n1 Obtain " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " and separation threshold " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " by applying GMM with values of WJSD to all samples in " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " \n2 Obtain " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " by applying GMM with values of ACD to all samples in " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " \n3 Calculate the mean " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mu_1, \\mu_2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\sigma_1, \\sigma_2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " of WJSD for " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " \n4 if " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mu_1 < d < \\mu_2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\sigma_2 / \\sigma_1 < \\eta" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " then \n5 return " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " \n6 else if " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mu_1 > d" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mu_2 > d" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " then \n7 return " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{wjsd}^1, \\mathcal{G}_{wjsd}^2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " \n8 else \n9 return " + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{acd}^1, \\mathcal{G}_{acd}^2" + }, + { + "bbox": [ + 310, + 89, + 528, + 282 + ], + "type": "text", + "content": " \n10 end" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_body" + } + ], + "index": 11, + "sub_type": "algorithm" + }, + { + "bbox": [ + 306, + 304, + 484, + 318 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 484, + 318 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 484, + 318 + ], + "type": "text", + "content": "4.2. Bi-Dimensional Sample Selection" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "text", + "content": "Once the values of the bi-dimensional metrics for all samples in class " + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "text", + "content": " are calculated, each sample can be represented by a point in a 2D space. For each dimension, Gaussian mixture model (GMM) can be adopted to separate the samples in class " + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "text", + "content": " into two clusters " + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^1" + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^2" + }, + { + "bbox": [ + 305, + 325, + 546, + 387 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 392, + 546, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 546, + 512 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 546, + 512 + ], + "type": "text", + "content": "Dimension Selection. Because each metric shows different separability for different noise types, we first propose a dimension selection strategy to select a proper dimension to separate clean and noisy samples. We consider three cases to select the proper dimension: (a) both of them are acceptable; (b) the separability of WJSD is better; (c) the separability of ACD is better. In short, we only need to figure out if WJSD is suitable for sample separation. If it is certain that WJSD does not show good separability, ACD will be adopted. Fig. 3 shows three cases for dimension selection." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 513, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 547, + 574 + ], + "type": "text", + "content": "Therefore, we use the statistics of WJSD as the criterion of dimension selection. We measure the means " + }, + { + "bbox": [ + 304, + 513, + 547, + 574 + ], + "type": "inline_equation", + "content": "(\\mu_1,\\mu_2)" + }, + { + "bbox": [ + 304, + 513, + 547, + 574 + ], + "type": "text", + "content": " and standard deviations " + }, + { + "bbox": [ + 304, + 513, + 547, + 574 + ], + "type": "inline_equation", + "content": "(\\sigma_{1},\\sigma_{2})" + }, + { + "bbox": [ + 304, + 513, + 547, + 574 + ], + "type": "text", + "content": " of WJSD for two clusters separated by GMM in terms of ACD. We have two cases that can determine when WJSD is better. We mainly compare" + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 310, + 582, + 537, + 674 + ], + "blocks": [ + { + "bbox": [ + 310, + 582, + 537, + 674 + ], + "lines": [ + { + "bbox": [ + 310, + 582, + 537, + 674 + ], + "spans": [ + { + "bbox": [ + 310, + 582, + 537, + 674 + ], + "type": "image", + "image_path": "2de398f5880d8ca6a5cb6c69c9c5ba5bff5667799a17761e1e0b4df02a61fdfb.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 679, + 546, + 715 + ], + "lines": [ + { + "bbox": [ + 304, + 679, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 679, + 546, + 715 + ], + "type": "text", + "content": "Figure 3: Examples of three cases of the optimal separation dimension correspond to sample distribution in bidimensional metrics." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1373" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mu_{1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mu_{2}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " with the threshold " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " of GMM in WJSD. First, as shown in Fig. 3 (b), if one cluster " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{acd}^{1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " of ACD has a " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mu_{1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " less than " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " and a " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\sigma_{1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " much larger than " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\sigma_{2}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " in another cluster with a " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mu_{2}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " larger than " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ", it means that cluster " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{acd}^{1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " has more clean samples but also many noise samples. So in this case, ACD is improper and WJSD is proper. Second, if both " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mu_{1}, \\mu_{2}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " are greater than " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ", it means that it is a representation of the previous case in the tail class because there are fewer clean samples in the cluster. So, in this case, WJSD is proper. The strategy is summarized in Algorithm 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": "Cluster Selection. Once we have determined the separation dimension, we can obtain two sample clusters " + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^1" + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^2" + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": ". However, it is not clear which cluster contains more clean samples because the noisy samples may overwhelm the clean samples in some cases. Therefore, we need to further select a cluster between " + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^1" + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^2" + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": " as the clean one. For the cluster separated based on WJSD, we simply choose the one with a smaller average WJSD value as the cluster with more clean samples, denoted as " + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c^{clean}" + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": " [29, 23]. For the cluster separated based on ACD, we cannot directly select the cluster closest to the centroid as the cluster with more clean samples since we take more representative samples, which may compose of noisy samples, rather than clean samples as the centroid. Therefore, we need to determine the selection criteria based on whether the current class centroid is obtained by clean samples. Especially, the criterion is based on the similarity between centroids of the current class and other classes. Assume that the sample in " + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^1" + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": " is near the centroid and the sample in " + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_c^2" + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": " is the opposite. We determined the choice of a more clean cluster " + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_c^{clean}" + }, + { + "bbox": [ + 46, + 196, + 289, + 448 + ], + "type": "text", + "content": " based on the following criteria:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 452, + 292, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 292, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 292, + 495 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {c} ^ {\\text {c l e a n}} = \\left\\{ \\begin{array}{l} \\mathcal {G} _ {c} ^ {2}, \\text {i f} | \\cos (o _ {c}, o _ {k}) - 1 | < \\varepsilon \\text {a n d} \\left| \\mathcal {D} _ {c} ^ {H} \\right| < \\left| \\mathcal {D} _ {k} ^ {H} \\right| \\\\ \\mathcal {G} _ {c} ^ {1}, \\text {o t h e r w i s e} \\end{array} \\right. \\tag {10}", + "image_path": "9cba070e9bd3bd1cbff878ea308f3209a42ff5807eec33cbd828c8cf1cd03bcc.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": "It means that if the centroid of another class is similar to the centroid of the current class, whichever class of high-confidence sample set has fewer samples, then the high-confidence samples in this class are the noise samples. It is because the asymmetric noise ratio cannot exceed " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " in the past assumption [29, 23]. Therefore, if the centroid is obtained from noise samples, we choose the cluster far away from the centroid as the cluster with more clean samples; otherwise, the cluster close to the centroid is selected." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 613, + 187, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 187, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 187, + 625 + ], + "type": "text", + "content": "4.3. Overall Training Process" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 633, + 288, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 633, + 288, + 717 + ], + "spans": [ + { + "bbox": [ + 46, + 633, + 288, + 717 + ], + "type": "text", + "content": "After sample selection is conducted for each class, we adopt semi-supervised learning [1, 42] to train with all clean samples " + }, + { + "bbox": [ + 46, + 633, + 288, + 717 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^{clean}" + }, + { + "bbox": [ + 46, + 633, + 288, + 717 + ], + "type": "text", + "content": " as labeled data and all noisy samples " + }, + { + "bbox": [ + 46, + 633, + 288, + 717 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^{noisy}" + }, + { + "bbox": [ + 46, + 633, + 288, + 717 + ], + "type": "text", + "content": " as unlabeled data. The model is thus updated for the next round of training. One may also use long-tailed semi-supervised learning methods instead of normal semi-supervised learning in this stage." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 91, + 422, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 422, + 104 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 422, + 104 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 109, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 545, + 300 + ], + "type": "text", + "content": "Datasets. In order to comprehensively evaluate the effectiveness of method, we perform experiments respectively in the scenarios with synthetic noise and realistic noise in intrinsically long-tailed distribution. We construct synthetic scenarios based on CIFAR-10 and CIFAR-100 [26]. We construct two benchmarks to imitate realistic scenarios, which is built on real-world noise datasets including Red Mini-ImageNet [20], CIFAR-10N and CIFAR-100N [48]. For all datasets, we adopt the standard paradigm of constructing a long-tailed distribution first and injecting noise later. We imitate realistic long-tailed distribution using the same setting in previous long-tailed learning works [3, 35] that long-tailed imbalance follows an exponential decay in sample sizes across different classes. The imbalance factor is denoted by the ratio between the size of the largest class and that of the smallest class." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 300, + 546, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 546, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 546, + 504 + ], + "type": "text", + "content": "The details for dataset construction are as follows. (1) As for CIFAR-10/100 [26], we adopt symmetric and asymmetric noise to inject synthetic noise, which is commonly used in the area of label-noise learning [41]. The noise ratio is denoted by the ratio between the number of noisy samples and the total number of samples. It should be noted that different from the previous methods [21, 49] to deal with the joint problem of noisy labeled and long-tailed data, the noise transition matrix is randomly generated only related to the noise ratio. (2) As for CIFAR-10N/100N (10N/100N) [48], we replace sample labels with human-annotated noisy labels after constructing a long-tailed distribution based on real labels. (3) As for Red mini-[ImageNet (Red) [20], we inject web label noise samples after constructing a long-tailed distribution based on the original mini-[ImageNet. Therefore, the observed and intrinsic distribution are likely inconsistent, especially in long-tail distribution." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": "Compared Methods. We compare our method with the following three types of approaches: (1) Long-tail learning methods (LT). They are LA [33], LDAM [3] and IB [35]. (2) Label-noise learning methods (NL). They are DivideMix [29] and UNICON [23]; (3) Methods aiming at dealing with noisy label and long-tail distribution (NL-LT). They are MW-Net [41], RoLT [49], HAR [2] and ULC [19]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 592, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 547, + 664 + ], + "type": "text", + "content": "Implementation Details. We use PreAct ResNet18 [14] as backbone for CIFAR datasets and ResNet18 as backbone for Red mini-ImageNet dataset. Both of backbones adopt SGD with an initial learning rate of 0.02, a momentum of 0.9, and a weight decay of " + }, + { + "bbox": [ + 304, + 592, + 547, + 664 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 592, + 547, + 664 + ], + "type": "text", + "content": " and a batch size of 64. For fair comparison, we train all methods for 100 epochs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 671, + 427, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 427, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 427, + 684 + ], + "type": "text", + "content": "5.2. Comparative Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 713 + ], + "type": "text", + "content": "CIFAR-10/100. Tab. 1 and 2 report the accuracy of different methods for intrinsically long-tailed CIFAR-10/100" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1374" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 285, + 263 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 285, + 263 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 285, + 263 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 285, + 263 + ], + "type": "table", + "html": "
DatasetCIFAR-10CIFAR-100
Imbalance Factor0.1
Noise Ratio (Sym.)0.40.60.40.6
BaselineCE71.6761.1634.5323.63
LTLA70.5654.9229.0723.21
LDAM70.5361.9731.3023.13
IB73.2462.6232.4025.84
NLDivideMix82.6780.1754.7144.98
UNICON84.2582.2952.3445.87
NL-LTMW-Net70.9059.8532.0321.71
RoLT81.6276.5842.9532.59
HAR77.4463.7538.1726.09
ULC84.4683.2554.9144.66
OurTABASCO85.5384.8356.5245.98
", + "image_path": "ea9d963df6985beed275a024776a2540336124c053b00ec4ff65e620cbe32b89.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 303, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 495 + ], + "type": "text", + "content": "with symmetric and asymmetric noise, respectively. It can be observed three phenomena as follows: (1) The performance of existing long-tail methods is lower than baseline in most situations. It is because such methods do not have the ability to distinguish the noise samples, and the wrong attention to the noise samples leads to the further decline of the model generalization ability. (2) The advantages of existing methods aiming at both long-tailed distribution and label noise are not obvious compared with single methods. It is because existing methods do not take into account the distribution inconsistency caused by noise labels. (3) Our method significantly improved over other methods in all cases. Moreover, as the proportion of noise increases, the accuracy of our method decreases less compared to other methods. It validates that our method can effectively identify the noise in long-tail distribution." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "type": "text", + "content": "Red mini-ImageNet and CIFAR-10N/100N. Tab. 4 reports the accuracy of different methods on real-world noise datasets with intrinsically long-tailed distribution. According to the results of label-noise learning methods on CIFAR-10N/100N, it can be observed that real-world noise is more difficult to separate than synthetic noise to some extent. It further increases the difficulty of dealing with such problem. Nevertheless, our method still performs well, which again confirms its effectiveness." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 609, + 218, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 218, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 218, + 622 + ], + "type": "text", + "content": "5.3. Ablation Study and Discussions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 628, + 286, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 286, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 286, + 675 + ], + "type": "text", + "content": "In the following experiments, we analyze each component of the proposed TABASCO on CIFAR-10/100 to verify its effectiveness. We use an imbalance factor of 0.1 and a noise ratio of 0.4 to construct the synthetic noise dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "Effectiveness of WJSD. To validate the effectiveness of the proposed WJSD, we compare the accuracy of models trained by different separation metrics. Specifically, we" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 543, + 263 + ], + "blocks": [ + { + "bbox": [ + 47, + 273, + 286, + 297 + ], + "lines": [ + { + "bbox": [ + 47, + 273, + 286, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 286, + 297 + ], + "type": "text", + "content": "Table 1: Performance comparison under symmetric noise. The best results are shown in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 70, + 543, + 263 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 543, + 263 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 543, + 263 + ], + "type": "table", + "html": "
DatasetCIFAR-10CIFAR-100
Imbalance Factor0.1
Noise Ratio (Asym.)0.20.40.20.4
BaselineCE79.9062.8844.4532.05
LTLA71.4959.8839.3428.49
LDAM74.5862.2940.0633.26
IB73.4958.3645.0235.25
NLDivideMix80.9269.3558.0941.99
UNICON72.8169.0455.9944.70
NL-LTMW-Net79.3465.4942.5230.42
RoLT73.3058.2948.1939.32
HAR82.8569.1948.5033.20
ULC74.0773.1954.4543.20
OurTABASCO82.1080.5759.3950.51
", + "image_path": "b215880e41e8da7af173718bfa3d28b46dd8ef80e9389bc9e30c3a9930ac3088.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 339, + 308, + 512, + 381 + ], + "blocks": [ + { + "bbox": [ + 306, + 273, + 545, + 297 + ], + "lines": [ + { + "bbox": [ + 306, + 273, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 273, + 545, + 297 + ], + "type": "text", + "content": "Table 2: Performance comparison under asymmetric noise. The best results are shown in bold." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 339, + 308, + 512, + 381 + ], + "lines": [ + { + "bbox": [ + 339, + 308, + 512, + 381 + ], + "spans": [ + { + "bbox": [ + 339, + 308, + 512, + 381 + ], + "type": "table", + "html": "
DatasetSeparation metricAccuracy
CIFAR-10JSD83.97
WJSD85.57
CIFAR-100JSD55.80
WJSD56.67
", + "image_path": "8c09be3167e27219cb9986d82e33b13e0a10393aac6ad71bc39d04361880e1ce.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 389, + 545, + 402 + ], + "lines": [ + { + "bbox": [ + 306, + 389, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 306, + 389, + 545, + 402 + ], + "type": "text", + "content": "Table 3: Performance comparison between JSD and WJSD." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 407, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 492 + ], + "type": "text", + "content": "train the model by using JSD and WJSD for sample separation with a symmetric noise dataset, respectively. As for each separation metric, we simply use the small value strategy [29, 23] for sample selection. As Tab. 3 shows, the model trained by WJSD achieves better results on both symmetric noise datasets compared with JSD owing to the stronger separability of WJSD." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of ACD. To validate the advantage of the proposed ACD, we compare it with the method which calculates the feature centroid on the observed class (hereinafter referred to as centroid distance or CD) to show their separability in CIFAR-10. Specifically, based on the same backbone, we calculate the distance from the sample to the centroid using ACD and CD in CIFAR-10 with asymmetric noise, respectively. Fig. 4 shows the distributions of samples in the tail class by CD and ACD. The purity of the tail class is 0.53. It can be observed that the CD values of noise and clean samples are highly overlapped, which leads to failure sample separation. It is because the purity of the tail class may be quite low due to the negative effects of both label-noise and long-tailed distribution. The centroid obtained by ACD has a higher purity, so there is a significant difference in ACD between them. As shown in Fig. 4(b), most clean samples are concentrated in the interval of [0.8,1], which is easily clustered by GMM." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1375" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 264 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 264 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 264 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 264 + ], + "type": "table", + "html": "
DatasetRed10N100N
Imbalance Factor≈ 0.10.1
Noise Ratio0.20.4≈ 0.4
BaselineCE40.4231.4660.4438.10
LTLA26.8225.8865.7436.50
LDAM26.6423.4662.5038.48
IB23.8022.0865.9142.48
NLDivideMix48.7648.9667.8544.25
UNICON40.1841.6469.5451.93
NL-LTMW-Net42.6640.2669.7344.20
RoLT22.5624.2275.2446.61
HAR46.6138.7174.9744.54
ULC48.1247.0675.7151.72
OurTABASCO50.2049.6880.6153.83
", + "image_path": "9ee4f8e0776b34ab050d7b71fb326a4b046e28174c07d9c52c5c21b18b98e4da.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 272, + 287, + 297 + ], + "lines": [ + { + "bbox": [ + 47, + 272, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 287, + 297 + ], + "type": "text", + "content": "Table 4: Performance comparison with real-world noise and long-tail distribution. The best results are shown in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 304, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 519 + ], + "type": "text", + "content": "Effectiveness of Bi-dimensional Sample Separation. To validate how the proposed bi-dimensional metrics complement each other, we plot the values of bi-dimensional metrics of both clean and noisy samples under different noise types in Fig. 5. For the case of symmetric noise shown in Fig. 5(a), it can be observed that ACD cannot effectively distinguish clean samples from noisy samples in the tail class. In this case, WJSD shows its advantage because the values of WJSD for most noisy samples are clustered in the top region, and the clean samples are scattered throughout the rest region. For the case of asymmetric noise shown in Fig. 5(b), it can be observed that WJSD cannot distinguish clean samples from noisy samples well for the tail class, while ACD can distinguish them well although the clean and noisy samples are closer in the tail class. The experimental observation is consistent with the previous discussion, which validates the complementarity of bi-dimensional metrics." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 714 + ], + "type": "text", + "content": "Effectiveness of Sample Selection. In order to validate the effectiveness of the proposed sample selection in dimension selection and cluster selection, we compare the optimal clean ratio of clusters obtained by WJSD, ACD and our selection method in CIFAR-10 with different noise types. The clean ratio of a cluster is calculated by the proportion of clean samples in the cluster to the total number of cluster samples. As shown in Fig. 6, on the tail class, the clean ratio of the cluster obtained by our selection method is aligned with the higher one between WJSD and ACD for both noise cases. It shows that we can choose the most appropriate separation dimension in different situations. Besides, the clean ratio of the cluster we selected is consistent with that of the optimal cluster in the corresponding dimension, which is sufficient to show that the method we proposed can select clean samples." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 419, + 156 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 419, + 156 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 419, + 156 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 419, + 156 + ], + "type": "image", + "image_path": "8978744f5c52019e23a6df9ddbcefd4b3d31544d821d855b90bb486837f20e8a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 158, + 545, + 181 + ], + "lines": [ + { + "bbox": [ + 306, + 158, + 545, + 181 + ], + "spans": [ + { + "bbox": [ + 306, + 158, + 545, + 181 + ], + "type": "text", + "content": "Figure 4: Comparison of the sample distributions between CD and ACD in the tail class." + } + ] + } + ], + "index": 6, + 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"lines": [ + { + "bbox": [ + 329, + 272, + 404, + 283 + ], + "spans": [ + { + "bbox": [ + 329, + 272, + 404, + 283 + ], + "type": "text", + "content": "(a) Symmetric noise" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 426, + 188, + 531, + 267 + ], + "blocks": [ + { + "bbox": [ + 426, + 188, + 531, + 267 + ], + "lines": [ + { + "bbox": [ + 426, + 188, + 531, + 267 + ], + "spans": [ + { + "bbox": [ + 426, + 188, + 531, + 267 + ], + "type": "image", + "image_path": "87cf4887cb473a40cbc410da6221f0e73f402470ce88fd0ef33b08ab0eaab4d3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 272, + 519, + 283 + ], + "lines": [ + { + "bbox": [ + 440, + 272, + 519, + 283 + ], + "spans": [ + { + "bbox": [ + 440, + 272, + 519, + 283 + ], + "type": "text", + "content": "(b) Asymmetric noise" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } 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}, + { + "bbox": [ + 438, + 417, + 518, + 427 + ], + "lines": [ + { + "bbox": [ + 438, + 417, + 518, + 427 + ], + "spans": [ + { + "bbox": [ + 438, + 417, + 518, + 427 + ], + "type": "text", + "content": "(b) Asymmetric noise" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 462, + 378, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 462, + 378, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 462, + 378, + 474 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": "This paper studies a more general and realistic problem of label-noise learning with intrinsically long-tailed data. The major challenge in this problem is that it is hard to distinguish clean samples from noisy samples on intrinsic tail classes. Accordingly, we propose a learning framework TABASCO for this problem. In TABASCO, two new metrics are explicitly proposed to address the problem of sample selection in tail classes. Extensive experiments on noisy-labeled datasets with long-tail distribution demonstrate its effectiveness." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 602, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 602, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 602, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. We thank Dr. Shiquan Ruan for his discussion on the theory proof. This study was supported in part by the National Natural Science Foundation of China under Grants 62002302 and U21A20514; in part by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform under Grant 3502ZCQXT2022008; in part by NSFC/RGC Joint Research Scheme under Grant N_HKBU214/21; and in part by the General Research Fund of RGC under Grants 12201321 and 12202622." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1376" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] David Berthelot, Nicholas Carlini, Ian J. 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In AAAI, 2022. 1" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1378" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_content_list.json b/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9b4b7e755d6a6ac88dfeda20c8d9cd4e9018e0c8 --- /dev/null +++ b/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_content_list.json @@ -0,0 +1,1836 @@ +[ + { + "type": "text", + "text": "Landscape Learning for Neural Network Inversion", + "text_level": 1, + "bbox": [ + 227, + 130, + 743, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ruoshi Liu1 Chengzhi Mao1 Purva Tendulkar1 Hao Wang2 Carl Vondrick1 \n1 Columbia University 2 Rutgers University", + "bbox": [ + 158, + 179, + 803, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 257, + 313, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve gradient descent through a highly non-convex loss landscape, causing the optimization process to be unstable and slow. We introduce a method that learns a loss landscape where gradient descent is efficient, bringing massive improvement and acceleration to the inversion process. We demonstrate this advantage on a number of methods for both generative and discriminative tasks, including GAN inversion, adversarial defense, and 3D human pose reconstruction.", + "bbox": [ + 75, + 277, + 473, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 493, + 209, + 508 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Many inference problems in machine learning are formulated as inverting a forward model $F(x)$ by optimizing an objective over the input space $x$ . This approach, which we term optimization-based inference (OBI), has traditionally been used to solve a range of inverse problems in vision, graphics, robotics, recommendation systems, and security [28, 38, 22, 10, 62, 17]. Recently, neural networks have emerged as the paramterization of choice for forward models [43, 53, 1, 49, 76, 68, 13, 78], which can be pretrained on large collections of data, and inverted at testing time in order to solve inference queries.", + "bbox": [ + 75, + 518, + 470, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Optimization-based inference (OBI) has many advantages over feed-forward or encoder-based inference (EBI). Without encoder, OBI provides flexibility to adapt to new tasks, allowing one to define new constraints into the objective during inference. When observations are partially missing, OBI can adapt without additional training. Moreover, OBI naturally supports generating multiple and diverse hypotheses when there is uncertainty. Finally, OBI has intrinsic advantages for robustness, both adapting to new data distributions as well as defending against adversarial examples.", + "bbox": [ + 75, + 686, + 470, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the key bottleneck for OBI in practice is the computational efficiency and the speed of inference. Feedforward models are fast because they only require a single forward pass of a neural network, but OBI requires many", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5886baaa4e06470f25ae06068a39dd9120e390fe68b37291340f97a2996cbbf0.jpg", + "image_caption": [ + "Figure 1: Loss Landscapes Comparison. The loss landscape of optimization-based inference (OBI) is often highly non-convex. We propose to learn a smoother loss landscape through a mapping network to accelerate the optimization. Plotted from real data." + ], + "image_footnote": [], + "bbox": [ + 501, + 258, + 694, + 386 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ea580b0c066fa2958e2c0629e07c010bdcb00c7fb1d73626bf901eaa0425efd6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 258, + 880, + 386 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(often hundreds) steps of optimization in order to obtain strong results for one example. Forward models in OBI are often trained with generative or discriminative tasks, but they are not trained for the purpose of performing gradient descent in the input space. Fig. 9 visualizes the loss landscape for uncurated examples. The loss landscape is not guaranteed to be an efficient path from the initialization to the solution, causing the instability and inefficiency.", + "bbox": [ + 496, + 476, + 893, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose a framework to accelerate and stabilize the inversion of forward neural networks. Instead of optimizing over the original input space, we learn a new input space such that gradient descent converges quickly. Our approach uses an alternating algorithm to learn the mapping between these spaces. The first step collects optimization trajectories in the new space until convergence. The second step updates the mapping parameters to reduce the distance between the convergence point and each point along the trajectory. By repeating these steps, our approach will learn a mapping between the spaces that allows gradient descent over the input to converge in significantly fewer steps.", + "bbox": [ + 496, + 597, + 895, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Empirical experiments and visualizations on both generative and discriminative models show that our method can largely improve the convergence speed for optimization. We validate our approach on a diverse set of vision tasks, including GAN inversion [1], adversarial defense [45], and 3D human pose reconstruction [53]. Our experiments show that our method converges an order of magnitude faster without loss in absolute performance after convergence. As our ap", + "bbox": [ + 496, + 777, + 895, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2239", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6a230d29c2b6a3599d5ea8047c1a3131a7bc79ba84216272c6c01daec7e57e56.jpg", + "image_caption": [ + "Figure 2: Method. The left and middle figure show the loss landscape for our latent space and the original latent space, respectively. While walking to the optimal solution in a few steps is hard in $X$ space, it can be done in our learned loss landscapes." + ], + "image_footnote": [], + "bbox": [ + 140, + 74, + 834, + 200 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "proach does not require retraining of the forward model, it is compatible to all existing OBI methods with a differentiable forward model and objective function.", + "bbox": [ + 75, + 244, + 468, + 289 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The primary contribution of this paper is an efficient optimization-based inference framework. In Sec. 2, we survey the related literature to provide an overview of forward model inversion problem. In Sec. 3, we formally define OBI (3.1); our method to learn an efficient loss landscape for OBI (3.2); a training algorithm for better generalization and robustness (3.3). In Sec. 4, we experimentally study and analyze the effectiveness of the mapping network for OBI.", + "bbox": [ + 75, + 289, + 470, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 422, + 218, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The different approaches for inference with a neural network can be partitioned into either encoder-based inference, which is feedforward, or optimization-based inference, which is iterative. We briefly review these two approaches in the context of our work. In addition, we also review representative work in meta-learning and discuss the similarities and differences with our work.", + "bbox": [ + 75, + 446, + 472, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Encoder-based Inference", + "text_level": 1, + "bbox": [ + 76, + 560, + 305, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Encoder-based inference trains a neural network $F$ to directly map from the output space to the input space. Autoencoder based approach [55] learns an encoder that maps the input data to the latent space. [59, 65, 70, 54] learn an encoder from the image to the latent space in GAN. Encoder based inference requires training the encoder on the anticipated distribution in advance, which is often less effective and can fail on unexpected samples [21, 33]. In addition, encoder-based method can only produce one reconstruction for under-constrained inverse problems [75], even if multiple outcomes can all be true given the partial input.", + "bbox": [ + 75, + 583, + 470, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Optimization-based Inference", + "text_level": 1, + "bbox": [ + 76, + 756, + 344, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "OBI methods perform inference by solving an optimization problem with gradient-based methods such as Stochastic Gradient Descent (SGD) [60] and Projected Gradient Descent (PGD) [44]. In these cases, the objective function specifies the inference task. Besides these methods which use a point estimate for the latent variable, one can estimate the posterior distribution of the latent variable through Bayesian optimization, such as SGLD [71].", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gradient based optimization methods have been used to infer the latent code of query samples in deep generative models like GANs [26] via GAN inversion [36, 31, 61, 81, 1, 2, 8, 29, 52]. Style transfer relies on gradient based optimization to change the style of the input images [32]. It can also create adversarial attacks that fool the classifier [18, 11, 48, 63]. Recently, back-propagation-based optimization has shown to be effective in defending adversarial examples [45, 47] and compressed sensing [9]. [74] uses MAML [23] to accelerate the optimization process in compressed sensing.", + "bbox": [ + 496, + 244, + 893, + 410 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, constrained optimization was popularized for text-to-image synthesis by [19, 41]. They search in the latent space to produce an image that has the highest similarity with the given text as measured by a multi-modal similarity model like CLIP [56]. Test-time constrained optimization is also related to the idea of 'prompt-tuning' for large language models and vision-language models. [39] learns \"soft prompts\" to condition frozen language models to perform specific downstream tasks. Soft prompts are learned through backpropagation to incorporate signal from just a few labeled examples (few-shot learning). Visual prompting at both training time [7, 46] and testing time [67] also relies on effective latent variable optimization.", + "bbox": [ + 496, + 410, + 893, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A major challenge for optimization-based inference is how to perform efficient optimization in a highly non-convex space. To address this, input convex model [4] was proposed so that gradient descent can be performed in a convex space. [66] introduced a method to retrain the generative model such as it learns a latent manifold that is easy to optimize. When the model cannot be changed and retrained, bidirectional inference [68] and hybrid inference [81, 80] uses an encoder to provide a good initialization for the optimization-based inference in a non-convex space. Our method does not retrain the generative model, but instead maps a new latent space into the original input space, allowing more efficient optimization.", + "bbox": [ + 496, + 607, + 895, + 803 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Meta-Learning", + "text_level": 1, + "bbox": [ + 500, + 811, + 653, + 828 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a distribution of tasks, meta-learning aims to adapt quickly when presented with a previously unseen task. MAML [23] and related methods [25, 24] propose a method to learn a parameter initialization of a neural net", + "bbox": [ + 496, + 835, + 893, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2240", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "work by differentiating through the fine-tuning process. To reduce the computational cost of MAML due to the 2nd degree gradient, [51] proposes a first-order meta-learning algorithm. Unlike MAML which include modifying the forward model (e.g. in [74]), our approach is able to keep the forward model fixed in order to maintain its learned rich priors. Instead of meta-learning of model initialization, a line of work [5, 57, 14, 72] proposed to learn an optimizer, often in the form of an RNN, in order to accelerate gradient descent. Unlike learned optimizers that try to create better optimization algorithms, our approach instead learns to remap the loss landscape which is compatible with any choice of optimizer, including standard SGD or learned ones.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Learning Landscapes for Efficient Inference", + "text_level": 1, + "bbox": [ + 76, + 301, + 470, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We present our framework to learn an efficient loss landscape for optimization-based inference (OBI) methods. In Sec. 3.1, we will define OBI. In Sec. 3.2, we will introduce our framework as well as the training objective. In Sec. 3.3, we will describe how to train our model with an alternating optimization algorithm and an experience-replay buffer.", + "bbox": [ + 75, + 328, + 472, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Optimization-based Inference", + "text_level": 1, + "bbox": [ + 76, + 429, + 344, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $F(\\mathbf{x}) = \\hat{y}$ be a differentiable forward model that generates an output $\\hat{y}$ given an input variable $\\mathbf{x} \\in X$ . For example, $\\hat{y}$ might be an image, and $\\mathbf{x}$ might be the latent variables for a generative model. Given an observation $y$ , the goal of OBI is to find the input $\\hat{\\mathbf{x}} \\in X$ such that an objective function $L(\\hat{y}, y)$ is minimized. Formally, we write this procedure as:", + "bbox": [ + 75, + 452, + 472, + 559 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} = \\underset {\\mathbf {x} \\in X} {\\operatorname {a r g m i n}} L (F (\\mathbf {x}), y) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 571, + 468, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When the objective function $L$ and the model $F$ are both differentiable, we can perform the optimization over input space $X$ with gradient descent.", + "bbox": [ + 75, + 607, + 468, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Remapping the Input Space", + "text_level": 1, + "bbox": [ + 76, + 662, + 328, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instead of operating in the original input space $X$ , we will create a new space $Z$ where gradient descent is efficient and converges in a small number of iterations. We will use a neural network $\\Theta: Z \\to X$ that maps from the new space $Z$ to the original space $X$ . The parameters of the mapping $\\Theta$ is the vector $\\theta$ . The learning problem we need solve is to estimate $\\theta$ so that there is a short gradient descent path in $Z$ from the initialization to the solution. Fig. 2 shows an overview of this setup.", + "bbox": [ + 75, + 686, + 468, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We formulate an objective by rolling out the gradient updates on $\\mathbf{z}$ , where we write $\\mathbf{z}_t \\gets \\mathbf{z}_{t-1} + \\lambda \\frac{\\partial L}{\\partial \\mathbf{z}_{t-1}}$ as the $t^{\\text{th}}$ update with a step size of $\\lambda$ . For gradient descent in space $Z$ to be efficient, the goal of our introduced $\\Theta$ is to move every step $\\mathbf{z}_t$ as close as possible to the global minima:", + "bbox": [ + 75, + 823, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/69201484fa2b47fa9b0c4acbde6be430b7c869aedea1d4120233a92138ff2b2f.jpg", + "image_caption": [ + "Figure 3: Landscape Learning. An optimization trajectory $\\{\\mathbf{z}_t\\}_{t=0}^5$ collected is used to train $\\Theta$ . $\\mathbf{z}_i$ that corresponds to a higher $L_i$ will yield a higher gradient when training $\\Theta$ . Optimization over multiple steps along the trajectory causes $\\Theta$ to learn patterns of trajectories and create a more efficient loss landscape." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 893, + 233 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\theta} = \\underset {\\theta} {\\operatorname {a r g m i n}} \\mathbb {E} _ {(\\mathbf {z}, y)} \\left[ \\sum_ {t = 0} ^ {T} L (F (\\Theta (\\mathbf {z} _ {t})), y) \\right] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 314, + 890, + 363 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\quad \\mathbf {z} _ {t} = \\left\\{ \\begin{array}{l l} 0, & t = 0 \\\\ \\mathbf {z} _ {t - 1} + \\lambda \\frac {\\partial L}{\\partial \\mathbf {z} _ {t - 1}}, & t > 0 \\end{array} \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 359, + 812, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We visualize this process with a toy example in Fig. 3. Gradient updates on $\\Theta$ w.r.t multiple steps $\\mathbf{z}_t$ along a trajectory will cause the loss value on each step to be lowered. By learning the parameters of $\\Theta$ across many examples, $\\Theta$ can learn the patterns of optimization trajectories in $X$ . For example, $\\Theta$ can learn to estimate the step size in $X$ and dynamically adjust it to each example. Moreover, $\\Theta$ can learn to reduce non-convexity of the landscape.", + "bbox": [ + 496, + 409, + 893, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Once we obtain $\\hat{\\Theta}$ with parameters $\\hat{\\theta}$ , we do inference on a new example $y$ through the standard optimization-based inference procedure, except in $Z$ space now. Given the observation $y$ , we find the corresponding $\\hat{\\mathbf{x}}$ through the optimization:", + "bbox": [ + 496, + 530, + 893, + 604 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} = \\hat {\\Theta} (\\hat {\\mathbf {z}}) \\quad \\text {w h e r e} \\quad \\hat {\\mathbf {z}} = \\underset {\\mathbf {z} \\in Z} {\\operatorname {a r g m i n}} L (F (\\hat {\\Theta} (\\mathbf {z})), y) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 616, + 893, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When the inverse problem is under-constrained, one can infer multiple hypotheses for $\\hat{\\mathbf{x}}$ by repeating the above optimization with a different random initialization for $\\mathbf{z}_0$ .", + "bbox": [ + 496, + 652, + 893, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Training", + "text_level": 1, + "bbox": [ + 500, + 707, + 604, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use alternating optimization (AO) in order to train $\\Theta$ jointly with estimating $\\mathbf{z}$ for each example in the training set. Specifically, we first fix parameters of $\\Theta$ and collect $N$ optimization trajectories of $\\mathbf{z}$ , each with length $T$ . Adopting the same terminology from the robotics community for learning on continuous states [50], we term this an experience replay buffer. Subsequently, we randomly sample data from this buffer and train $\\Theta$ to optimize the loss function. We alternate between these two steps for a fixed number of iterations with gradient descent for both. Depending on the application, the training time for $\\Theta$ varied from one hour to", + "bbox": [ + 496, + 731, + 893, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2241", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "one day using a four GPU server. Please see the appendix for more implementation details.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also experimented with an online version of the training algorithm, where we update parameters of $\\Theta$ immediately after one update to $\\mathbf{z}$ . However, in our experiments, we found this resulted in a slower convergence rate. We show these comparisons in the ablation experiments.", + "bbox": [ + 76, + 121, + 468, + 196 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Learning Mapping Network $\\Theta$" + ], + "code_body": "1: Input: Ground truth $y$ , step size $\\lambda_z$ and $\\lambda_{\\theta}$ , number of buffers $B$ , number of data samples in a buffer $N$ , number of optimization steps per sample $T$ , loss function $L$ , and forward model $F$ . \n2: Output: Learned mapping network $\\Theta$ \n3: Randomly initialize a mapping network $\\Theta$ with parameters $\\theta$ \n4: for $b = 1, \\dots, B$ do \n5: Initialize Experience Replay Buffer $[\\{\\mathbf{z}_{t,i}\\}_{t=1}^{T}]_{i=1}^{N}$ \n6: for $i = 1, \\dots, N$ do \n7: $\\mathbf{z}_0 \\gets \\mathbf{0}$ \n8: for $t = 1, \\dots, T$ do \n9: $\\mathbf{z}_t \\gets \\mathbf{z}_{t-1} + \\lambda_z \\frac{\\partial}{\\partial \\mathbf{z}_{t-1}} L(F(\\Theta(\\mathbf{z})), y)$ \n10: $\\mathbf{z}_{t,i} \\gets z_t$ \n11: end for \n12: end for \n13: for $j = 1, \\dots, T \\cdot N$ do \n14: Randomly sample $\\mathbf{z}$ from previously collected buffer \n15: $\\theta_j \\gets \\theta_{j-1} + \\lambda_\\theta \\frac{\\partial}{\\partial \\theta_{j-1}} L(F(\\Theta(\\mathbf{z})), y)$ \n16: end for \n17: end for \n18: Return $\\theta$", + "bbox": [ + 84, + 229, + 472, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 609, + 207, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The goal of our experiments is to analyze how well our proposed method can be applied to various existing OBI methods to improve the optimization efficiency. We demonstrate application of our method to three diverse OBI methods in computer vision, including both generative models and discriminative models. For each OBI method, the inference-time optimization objective of the baseline and ours can be written as:", + "bbox": [ + 75, + 635, + 468, + 755 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {B a s i l e :} \\hat {\\mathbf {x}} = \\min _ {\\mathbf {x} \\in X} L (F (\\mathbf {x}), y) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 766, + 468, + 787 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {O u r s :} \\hat {\\mathbf {z}} = \\min _ {\\mathbf {z} \\in Z} L (F (\\Theta (\\mathbf {z})), y) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 797, + 468, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we provide the specific implementation of the loss term $L$ for each application, along with quantitative and qualitative results. We also perform experiments to understand the loss landscape in Sec. 4.5 and perform ablations on different parts of our approach in Sec. 4.4.", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. GAN Inversion", + "text_level": 1, + "bbox": [ + 500, + 90, + 653, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first validate our method on StyleGAN inversion [1]. We take a pretrained generator of StyleGAN [35] denoted as $F$ . Let $y$ be an observed image whose input variable we are recovering, we optimize the objective of Eq. 5 where the loss can be written as,", + "bbox": [ + 496, + 113, + 893, + 188 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL (\\hat {y}, y) = L _ {l p i p s} (\\hat {y}, y) + \\left\\| \\hat {y} - y \\right\\| _ {2} ^ {2} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 200, + 892, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{lpips}$ is a perceptual similarity loss introduced in [79], $\\hat{y} = F(\\hat{x})$ for baseline and $\\hat{y} = F(\\Theta(\\hat{z}))$ for ours. We train $\\Theta$ on the train split of CelebA-HQ [34] dataset and evaluate on CelebA-HQ validation split for in-distribution experiments and LSUN-Cat[77] for distribution shifting (OOD) experiments. We compare the results from our method against the state-of-the-art encoder-based GAN inversion model [59].", + "bbox": [ + 496, + 229, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Quantitative Results. From Fig. 4a, we see that in all experiments, optimization in our space $Z$ consistently outperforms the baseline from the first optimization step to after convergence. This gap in performance is even larger when evaluated on OOD data. This suggests that the improvement in performance is not caused by memorizing the training data. Note that our image reconstruction performance after only 2 steps of optimization is able to outperform or be on-par with the baseline at 20 steps of optimization, resulting in a 10-fold improvement in efficiency. Even after convergence (after 2000 optimization steps), our reconstruction performance improves over the baseline by $15\\%$ for in-distribution evaluation and $10\\%$ for OOD evaluation. When compared with encoder-based GAN inversion [59], our method achieves better reconstruction after 11 steps of optimization for in-distribution data and 3 steps for OOD data.", + "bbox": [ + 496, + 349, + 893, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Qualitative Results. From Fig. 8, we can see that our method already shows improvements on in-distribution data - it can almost perfectly reconstruct details like fine hair strands, the cap on the person's head, the object in the person's mouth as well-as the text on it. Interestingly, our method is able to discover and reconstruct latents for cats while the encoder-based model fails miserably as shown in Fig 8. The performance on OOD data truly highlights the benefits of our method. We also visualize how the face generations evolve over the process of optimization in Fig. 5. We can see that in just 4 steps, our method is already able to reconstruct coarse features such as face orientation, skin tone and hair color, while the baseline has hardly deviated from the initialization in regard to any of these features. Further, in Fig. 7 we visualize reconstructions from partial observations where only the center of the face (row 1) or everything other than the mouth (row 2) is visible. We can see a variety of feasible possibilities for the hidden regions (e.g., different hairstyles, lip colors, expressions, etc) showcasing the diversity of the new latent space.", + "bbox": [ + 496, + 592, + 893, + 893 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2242", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2daf20a2d6fe761dfa56132ec9e29b47d5dde8a8a850ca1615201afad50035ad.jpg", + "image_caption": [ + "(a) GAN Inversion" + ], + "image_footnote": [], + "bbox": [ + 160, + 89, + 475, + 276 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/82a7d3c0e94e4dd8570ef6f006ec5b47b3e61d5cfec59d603b9e10f242c75ac2.jpg", + "image_caption": [ + "(b) 3D Human Pose Reconstruction" + ], + "image_footnote": [], + "bbox": [ + 483, + 90, + 805, + 275 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/eb62ba9e9a69d0902c6842a6553b58d24853ec7e130a36463ff2845add34e314.jpg", + "image_caption": [ + "Figure 4: Optimization Performance. We visualize the trends of optimization performance compared with the baseline. In GAN Inversion (Left), we evaluate all models on test splits of CelebA-HQ [34] and LSUN-cat [77] (OOD) with loss defined in Eq. 6. Since encoder-based inference doesn't involve optimization, we use a flat line to represent it. We perform 2000 steps of gradient descent for all models except encoder-based models. In 3D Human Pose Reconstruction (Right), we evaluate all models on test splits of GRAB [64] and PROX [27] (OOD) with loss defined in Eq. 7. We perform 200 steps of gradient descent for all models. For each step, we plot the average loss value of test splits.", + "Figure 5: Optimization Process for GAN Inversion. Comparing optimization process of our method and the baseline in order to reconstruct the ground truth image. Left shows the results from the baseline where optimization is done in the original input space $X$ . Middle shows the results from our method where optimization is done in our space $Z$ . Right column contains the ground truth image to each example. Each row corresponds to the same example." + ], + "image_footnote": [], + "bbox": [ + 142, + 367, + 831, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.3D Human Pose Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 683, + 359, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition to image generation, our framework also works for 3D reconstruction. For this, we use VPoser [53] – a variational autoencoder [37] that has learnt a pose prior over body pose. VPoser was trained on SMPL-X body pose parameters $y \\in \\mathbb{R}^{63}$ obtained by applying MoSh [42] on three publicly available human motion capture datasets: CMU Mocap [16], training set of Human3.6M [30], and the PosePrior dataset [3].", + "bbox": [ + 73, + 705, + 470, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We take a pretrained VPoser decoder denoted as $F$ . Our trained mapping network $\\Theta$ projects a vector from the new input space $\\mathbf{z} \\in Z$ to a vector in the original VPoser decoder's input space $\\mathbf{x} \\in X$ . Similar to GAN Inversion, we optimize the objective of Eq. 5, where the loss function", + "bbox": [ + 75, + 827, + 472, + 905 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "between predicted and ground truth pose parameters is,", + "bbox": [ + 498, + 684, + 864, + 700 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL (\\hat {y}, y) = \\left\\| \\hat {y} - y \\right\\| _ {2} ^ {2} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 710, + 893, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{y} = F(\\hat{x})$ for the baseline and $\\hat{y} = F(\\Theta(\\hat{z}))$ for ours. For training $\\Theta$ , we use the GRAB dataset [64] which contains poses of humans interacting with everyday objects. We construct splits for novel video sequences – thus the test split will contain a seen human subject but a potentially unseen pose / demonstration by that subject. We evaluate on this test split for in-distribution experiments and on the PROX dataset [27] for OOD experiments, which contains poses of humans interacting in 3D scenes (e.g., living room, office, etc).", + "bbox": [ + 496, + 738, + 893, + 888 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative Results. For SMPL-X human pose recon", + "bbox": [ + 517, + 890, + 893, + 906 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2243", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/583c9ad7156d0677d7f63e45a5447bf6c025fb747bbcfdadd1c56eac1fd1e3a5.jpg", + "image_caption": [ + "Figure 6: Optimization Process for 3D Human Pose Reconstruction. Results shown are for out-of-distribution PROX dataset for sitting (Top) and standing (Bottom) poses." + ], + "image_footnote": [], + "bbox": [ + 138, + 74, + 830, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "struction experiment, the results follow a similar trend as GAN inversion, with massive improvement in both convergence speed and final loss values after convergence (see Fig. 4b). Our method outperforms the baseline by $19\\%$ for in-distribution evaluation and $11\\%$ for OOD evaluation.", + "bbox": [ + 75, + 375, + 470, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Results. In Fig. 6 we visualize how the human pose reconstructions evolve over the process of optimization. Here, we observe that the reconstructions from steps 0 to 6 of the baseline are similar for both examples. On the other hand, our method caters to fast convergence for the varying examples, highlighting the general, yet efficient properties of our search space. Further, in Fig. 7 we visualize reconstructions from partial observations where the only joints visible are that of the upper body (row 3) or lower body (row 4). We obtain a wide range of feasible possibilities for the hidden joints demonstrating the diversity of the latent space.", + "bbox": [ + 75, + 450, + 473, + 632 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Defending Adversarial Attacks", + "text_level": 1, + "bbox": [ + 76, + 640, + 352, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method is also applicable to discriminative models. A state-of-the-art defense [45] for adversarial attack optimizes the self-supervision task at inference time, such that the model can dynamically restore the corrupted structure from the input image for robust inference. Following the existing algorithm implementation, we optimize the input image via our method by minimizing the following discriminative loss function:", + "bbox": [ + 75, + 662, + 468, + 785 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L (F (\\mathbf {r} + \\mathbf {a}), y) = L (F (\\Theta (\\mathbf {z}) + \\mathbf {a}), y) \\\\ = \\mathbb {E} _ {i, j} \\left[ - y _ {i j} ^ {(s)} \\log \\frac {\\exp (\\cos (\\mathbf {f} _ {i} , \\mathbf {f} _ {j}))}{\\sum_ {k} \\exp (\\cos (\\mathbf {f} _ {i} , \\mathbf {f} _ {k}))} \\right] + \\lambda | | \\Theta (\\mathbf {z}) | | _ {2} ^ {2}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 792, + 455, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{a}$ is the adversarial attacks that we aim to defend against, $\\mathbf{r} = \\Theta (\\mathbf{z})$ is our additive defense vector to optimize, $\\mathbf{f}_i$ are the contrastive features produced by the neural network", + "bbox": [ + 76, + 854, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$F$ from the $i^{\\mathrm{th}}$ image instance, and $\\mathbf{y}_{ij}^{(s)}$ is the indicator for the positive pairs and negative pairs.", + "bbox": [ + 498, + 375, + 890, + 406 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After obtaining the mapping network $\\Theta$ and the input variable $\\hat{\\mathbf{z}}$ , the prediction is $\\hat{\\mathbf{y}} = F'(\\mathbf{a} + \\Theta (\\mathbf{z}))$ , where $F^{\\prime}$ is the classification model. Note that the self-supervision loss is optimized as a proxy for increasing the robust classification accuracy. In addition, we add a $L_{2}$ norm decay term for the generated noise $z$ to avoid generating reversal vector that is too large.", + "bbox": [ + 496, + 406, + 892, + 512 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4558638513fc0c2eb65fbd49d8071a116d781a8ff2e97de897e12d7dd675c482.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelOptimization Steps
None1 step3 steps5 steps
BLOursBLOursBLOurs
RO31.9934.6244.6536.7744.2338.3843.43
AWP35.6139.5451.3942.8151.6744.9651.05
MART35.6639.7751.7742.5051.7745.4250.96
SemiSL29.7834.5352.1137.2751.2340.9349.83
", + "bbox": [ + 504, + 523, + 888, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Results. We evaluate our method on four popular pretrained robust models [58, 69, 73, 12] on CIFAR-10 dataset. The results in [45] require many steps to optimize the objective to improve the adversarial robustness, which slows down the inference by hundreds of times than the original forward pass. Ideally, we desire test-time optimization that can adapt to the attacked images in just one step,", + "bbox": [ + 496, + 685, + 893, + 792 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/624b755753205044a76e21533495571167f9dc117854b1eb23495d16f5b5a1c6.jpg", + "table_caption": [ + "Table 1: Experiment on improving adversarial robust accuracy. Our goal is to defend 200 steps of $L_{2} = 256 / 255$ norm bounded attack [44], where the attack's step size is 64/255. Our baseline (BL) is the SOTA test-time optimization-based defense [45], which minimizes the loss of self-supervision task." + ], + "table_footnote": [], + "table_body": "
Defense Steps0135
Reversal (Baseline)29.5331.3634.0736.81
OBI (Ours)29.5344.4846.8450.42
", + "bbox": [ + 514, + 813, + 877, + 875 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2: Adaptive attack experiments with BPDA (SemiSL). When the attacker adapts to the defense, we can still improve robustness.", + "bbox": [ + 498, + 876, + 890, + 905 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2244", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dcb86b669b6740b4ba9ea94d12806f2e3854d659d434a086ad906bc8f905d78a.jpg", + "image_caption": [ + "Figure 7: Diversity of Masked Reconstructions. We visualize reconstructions for partially observable inputs from random initializations. The masked regions are not considered for loss computation, i.e., the gradient is set to be zero. By optimizing only on the partial observation, we obtain diverse, feasible solutions for the hidden regions. 5 or 4 out of 20 most representative samples are presented." + ], + "image_footnote": [], + "bbox": [ + 151, + 74, + 821, + 436 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/62729aff825b347aded27aa88e9ba7a231605d53bf0db4a15ac72f061549356f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Number of StepsFull ModelWithout AO and BufferRandom ΘBaseline
In-distribution203.0823.5834.4174.456
OOD204.9325.1275.1355.292
In-distribution2001.9643.0342.7232.569
OOD2003.4984.7563.8234.617
", + "bbox": [ + 76, + 492, + 470, + 594 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Ablation Study on mapping network. Number of Steps indicates the number of optimization steps performed during inference.", + "bbox": [ + 75, + 604, + 470, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "causing the minimal delay at inference time. In Table 1, our method outperforms the gradient descent method in [45] by up to $18\\%$ robust accuracy using a single step, providing a real-time robust inference method. In Table 2, even under the adaptive attack BPDA [6], our method also improves accuracy by up to $14\\%$ . Note that our method converges after 1 step of optimization, demonstrating the effectiveness of our approach.", + "bbox": [ + 75, + 661, + 468, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 787, + 230, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we present an ablation study by removing the proposed alternating optimization (AO) scheme and the experience replay buffer. We also compare against a $\\Theta$ that is randomly initialized. From Table 3 in appendix, we discovered that for in-distribution, AO and training of Theta improves the optimization performance by $14\\%$ and $30\\%$", + "bbox": [ + 75, + 805, + 470, + 896 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "respectively. Such gap becomes $35\\%$ and $28\\%$ for evaluation on 200 steps. For OOD data, the advantage is furthered enlarged as shown in Table 3.", + "bbox": [ + 496, + 494, + 892, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "One surprising result we discovered experimentally is that OBI under a randomly initialized mapping network $\\Theta$ consistently outperforms the baseline. We believe this is due to the fact that adding a Gaussian distribution to an underlying latent distribution of StyleGAN is beneficial in smoothing out loss landscape, making it easier to perform OBI. Similar random projection can also be found in [74].", + "bbox": [ + 496, + 542, + 893, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Loss Landscape", + "text_level": 1, + "bbox": [ + 500, + 662, + 660, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To understand the underlying cause of the significant improvement in optimization brought by our mapping network $\\theta$ , we visualize in Fig. 9 the loss landscape for performing optimization in the original input space $X$ , and our projected space $Z$ . To generate this visualization, we first perform 20 steps of optimization on the validation dataset to collect a set of recovered latents. We then perform principle component analysis (PCA) on these recovered latents to obtain two principle directions. Finally, for individual examples, we evaluate the loss for vertices on a meshgrid spanned by the two principle directions where the center is the last step of optimization.", + "bbox": [ + 496, + 686, + 893, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From the visualization, we can see that the loss landscapes of the baseline are highly non-convex and contain", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2245", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4989d1af3ecdd68a877d72ca94a3441b4a17d62a06c6ce8e7b5f208a9c0b1cab.jpg", + "image_caption": [ + "In-Distribution", + "Encoder", + "Ours", + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 161, + 107, + 480, + 354 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 375, + 191, + 480, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d1a31fd19b5cdb469c4da96c60e6ee20716775786cb911d3761d9fd6c4f496dd.jpg", + "image_caption": [ + "Out-of-Distribution", + "Encoder", + "Ours", + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 488, + 107, + 807, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/53b4913a7839fced8f224bb719df4235681cc332cf2ddb564415a29b685dd227.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 158, + 416, + 320, + 512 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b3b1463c7a5a2c1e7915da3c1b95e5ebf1a627e742c368d6dcd1d0123675edec.jpg", + "image_caption": [ + "Figure 8: Comparison Against Encoder-Based Inference. Left shows the results on the test split of CelebA-HQ; Right shows the results on the LSUN-cat dataset." + ], + "image_footnote": [], + "bbox": [ + 321, + 415, + 480, + 512 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/69afcfa8539fd65e8bb4e8be3a416b9ca34ddff77f40cf1a285b5eed6aa4f637.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 415, + 640, + 512 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0b15995df62b7fd6efe12425d4f1aaa5f0bf943796309e5ac13111bc299506ca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 642, + 415, + 803, + 512 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/37f9e7d3fab8c35a691240b0efe20708bd672bca55d45784606a0450aca620da.jpg", + "image_caption": [ + "Figure 9: Visualizing Loss Landscape (Uncurated). Visualizing the loss landscape of StyleGAN inversion spanned by two principle directions. Top row shows 4 examples of the loss landscapes corresponding to our space $Z$ . Bottom row shows the loss landscapes corresponding to the original input space $X$ for the same 4 examples. Note that the top row and the bottom row have different minimum loss values on the landscape because the minimas are obtained by performing independent optimization runs in space $Z$ and $X$ respectively. Given a fixed number of optimization steps, optimization in $Z$ reaches lower loss values than optimization in $X$ ." + ], + "image_footnote": [], + "bbox": [ + 156, + 520, + 321, + 617 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d97445046b79e18a36a67a3ceb47b8f90ec9093be9b1c95045d4d5e3968e4ab6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 521, + 480, + 616 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/83720abffbc6a5c377b720bd81e988339fce701fd224bb63921ab9f17f736a39.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 521, + 638, + 616 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51c5ab68c7753665d5fea9a93da9d269916673ee362f3194915de8f7ee83c30b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 521, + 803, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "points whose loss are significantly higher than its neighboring regions, while our loss landscapes are significantly smoother, with the \"spikes\" removed. Besides, our loss landscapes also tend to be steeper than the baseline ones. These two phenomena directly cause our method to perform gradient descent faster and stabler.", + "bbox": [ + 75, + 712, + 470, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Analysis", + "text_level": 1, + "bbox": [ + 76, + 820, + 171, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.1. L-BFGS", + "text_level": 1, + "bbox": [ + 76, + 845, + 179, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "After learning the mapping network $\\theta$ , in addition to the main results presented in Fig. 4a, we also run the same ex", + "bbox": [ + 76, + 869, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "periments but with L-BFGS as optimizer [40], which tends to perform better empirically with a smoother loss landscape. As shown in table 5, after 10 steps of optimization, L-BFGS achieves much better results than Adam in our learned landscape, which is already significantly better than the baseline. Notably, applying L-BFGS in the original landscape does not achieve significant speedup, and for Celeb-HQ, around $18\\%$ of the examples failed to converge due to instability. These results further verify that our method successfully learns a smoother landscape for efficient optimization.", + "bbox": [ + 496, + 712, + 893, + 864 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2246", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1f056855aaebce7f361d28a23f0c3b2589590e8539d156dc7f46056f9a42af9c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
level of CorruptionN(0,0.02)N(0,0.12)N(0,0.22)N(0,0.32)N(0,0.42)
Improvement29.53%18.95%12.57%6.30%6.72%
", + "bbox": [ + 179, + 88, + 787, + 135 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/0b37228c72ca54287adb99aa5e9103054a9715204e9a921f47fefc2b2d4fd48a.jpg", + "table_caption": [ + "Table 4: Evaluation of a mapping network trained with Celeba-HQ trainset and tested on the Celeba-HQ testset corrupted with different levels of Gaussian noise. The improvement is calculated by the percentage improvement of loss defined by Eq. 6 from baseline (no mapping network) to ours (with mapping network) after 200 steps of optimization." + ], + "table_footnote": [], + "table_body": "
datasetCelebA-HQAFHQ-CatLSUN-CatContainer-ShipN(0.5, 0.52)
Improvement29.53%35.99%24.36%16.87%6.60%
", + "bbox": [ + 176, + 204, + 794, + 250 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/aacf76d00fd80c3b90c304c11695ad7ea8418a709a9e04b0a59aa5bbb4febaec.jpg", + "table_caption": [ + "Table 6: Evaluation of a mapping network trained with Celeba-HQ trainset and tested on a spectrum of datasets from the original CelebA-HQ (in-distribution) to Gaussian noise (OOD). AFHQ-Cat [15] is a dataset with aligned cat faces. LSUN-Cat [77] is a dataset with unaligned cat images. Container-Ship is 200 images sampled from \"Container Ship\" class of ImageNet [20]. The improvement is calculated by the percentage improvement of loss defined by Eq. 6 from baseline (without $\\theta$ ) to ours (with $\\theta$ ) after 200 steps of optimization." + ], + "table_footnote": [ + "Table 5: L-BFGS vs. Adam in Leanred Landscape (Ours)" + ], + "table_body": "
ours\nL-BFGSours\nAdambaseline\nL-BFGSbaseline\nAdam
Human2.2393.504N/A4.875
Cat (OOD)4.0665.0875.2275.475
", + "bbox": [ + 91, + 318, + 454, + 395 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.2. More Evaluation on OOD Generalization", + "text_level": 1, + "bbox": [ + 76, + 416, + 431, + 431 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Since our proposed mapping network $\\Theta$ is parameterized by a neural network, there's no guarantee that the learned mapping function is surjective. Therefore, we empirically study the generalization performance by testing a mapping network trained on CelebA-HQ against a spectrum of datasets from very similar ones (in-distribution) to completely different ones (OOD).", + "bbox": [ + 75, + 439, + 470, + 545 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Synthetic Spectrum We first created a synthetic version of this spectrum of datasets by varying the level of Gaussian noise injected into the images of CelebA-HQ. With a higher level of Gaussian noise injected into the original images, more of the original image content is corrupted, creating a distribution of images further away from the original images.", + "bbox": [ + 75, + 545, + 468, + 636 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Natural Image Spectrum We also created a natural image version of this spectrum of datasets containing: CelebA-HQ (original in-distribution testset), AFHQ-Cat (center-aligned cat faces), LSUN-Cat (unaligned cat images), Container-Ship (\"Container Ship\" class from ImageNet), and Gaussian noise with individual pixel sampled from $\\mathcal{N}(0.5, 0.5^2)$ . From left to right, images vary from very similar to human faces to very different.", + "bbox": [ + 75, + 636, + 470, + 756 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "From results evaluated on both synthetic spectrum and real spectrum, we observed consistent improvements of our method over the baseline, which shows the generalization performance of our method when applied to OOD data. From table 6, we see the improvements drop as the evaluation data is less and less in-distribution with the training data, which indicates that the mapping network does learn a prior from the training data.", + "bbox": [ + 75, + 757, + 470, + 878 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/6e592a18fdce047f8fc40b97a05228ac9702873e8f2b302df7c6efe2f390af9a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BaselineOursImprovement
CelebA-HQ2.5692.3966.72%
LSUN-Cat4.6173.71719.49%
", + "bbox": [ + 524, + 329, + 867, + 392 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 7: Evaluation of a mapping network trained with images of Gaussian noise sampled from $\\mathcal{N}(0.5,0.5^2)$ clipped to [0, 1]. Numbers show the average loss defined in Eq. 6 evaluated on testset of CelebA-HQ and LSUN-Cat.", + "bbox": [ + 498, + 392, + 893, + 449 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.3. Dependence on Training Dataset", + "text_level": 1, + "bbox": [ + 500, + 460, + 785, + 477 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "From previous section, we know that the learned mapping network contains priors learned from the training data. To exclude such influence, we train our mapping network using randomly generated images made of Gaussian noise and evaluate on testset of CelebA-HQ. From table 7, we see that even trained with the task of reconstructing images of Gaussian noise, our mapping network still bring some improvement over the baseline model, though less significant.", + "bbox": [ + 496, + 484, + 893, + 606 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 618, + 617, + 633 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This paper presents a method to accelerate optimization-based inference to invert a forward model. We propose an approach that learns a new space that is easier than the original input space to optimize with gradient descent at testing time. Our experiments and analysis on three different applications in computer vision have shown that by learning this mapping function, optimization becomes more efficient and generalizes better to out-of-distribution data. Through quantitative and qualitative analysis, we found that such improvement in optimization performance comes from a more efficient loss landscape. Since optimization-based inference has many advantages over encoder-based inference, we believe methods to accelerate them will have many impacts in a variety of applications.", + "bbox": [ + 496, + 643, + 893, + 853 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement This research is based on work partially supported by the NSF NRI Award 1925157, NSF STC LEAP, DARPA MCS program, and DARPA CCU program.", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "2247", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? 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Springer, 2016. 2" + ], + "bbox": [ + 501, + 90, + 893, + 529 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "2250", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_model.json b/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c1d5e73a447fda1203891d073ef4e4de1aecc1de --- /dev/null +++ b/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_model.json @@ -0,0 +1,2798 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.228, + 0.131, + 0.745, + 0.154 + ], + "angle": 0, + "content": "Landscape Learning for Neural Network Inversion" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.18, + 0.804, + 0.222 + ], + "angle": 0, + "content": "Ruoshi Liu1 Chengzhi Mao1 Purva Tendulkar1 Hao Wang2 Carl Vondrick1 \n1 Columbia University 2 Rutgers University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.258, + 0.314, + 0.274 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.279, + 0.474, + 0.461 + ], + "angle": 0, + "content": "Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve gradient descent through a highly non-convex loss landscape, causing the optimization process to be unstable and slow. We introduce a method that learns a loss landscape where gradient descent is efficient, bringing massive improvement and acceleration to the inversion process. We demonstrate this advantage on a number of methods for both generative and discriminative tasks, including GAN inversion, adversarial defense, and 3D human pose reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.494, + 0.21, + 0.51 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.471, + 0.687 + ], + "angle": 0, + "content": "Many inference problems in machine learning are formulated as inverting a forward model \\( F(x) \\) by optimizing an objective over the input space \\( x \\). This approach, which we term optimization-based inference (OBI), has traditionally been used to solve a range of inverse problems in vision, graphics, robotics, recommendation systems, and security [28, 38, 22, 10, 62, 17]. Recently, neural networks have emerged as the paramterization of choice for forward models [43, 53, 1, 49, 76, 68, 13, 78], which can be pretrained on large collections of data, and inverted at testing time in order to solve inference queries." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.471, + 0.839 + ], + "angle": 0, + "content": "Optimization-based inference (OBI) has many advantages over feed-forward or encoder-based inference (EBI). Without encoder, OBI provides flexibility to adapt to new tasks, allowing one to define new constraints into the objective during inference. When observations are partially missing, OBI can adapt without additional training. Moreover, OBI naturally supports generating multiple and diverse hypotheses when there is uncertainty. Finally, OBI has intrinsic advantages for robustness, both adapting to new data distributions as well as defending against adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "However, the key bottleneck for OBI in practice is the computational efficiency and the speed of inference. Feedforward models are fast because they only require a single forward pass of a neural network, but OBI requires many" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.259, + 0.695, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.259, + 0.882, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.389, + 0.895, + 0.445 + ], + "angle": 0, + "content": "Figure 1: Loss Landscapes Comparison. The loss landscape of optimization-based inference (OBI) is often highly non-convex. We propose to learn a smoother loss landscape through a mapping network to accelerate the optimization. Plotted from real data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.895, + 0.597 + ], + "angle": 0, + "content": "(often hundreds) steps of optimization in order to obtain strong results for one example. Forward models in OBI are often trained with generative or discriminative tasks, but they are not trained for the purpose of performing gradient descent in the input space. Fig. 9 visualizes the loss landscape for uncurated examples. The loss landscape is not guaranteed to be an efficient path from the initialization to the solution, causing the instability and inefficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.896, + 0.779 + ], + "angle": 0, + "content": "In this paper, we propose a framework to accelerate and stabilize the inversion of forward neural networks. Instead of optimizing over the original input space, we learn a new input space such that gradient descent converges quickly. Our approach uses an alternating algorithm to learn the mapping between these spaces. The first step collects optimization trajectories in the new space until convergence. The second step updates the mapping parameters to reduce the distance between the convergence point and each point along the trajectory. By repeating these steps, our approach will learn a mapping between the spaces that allows gradient descent over the input to converge in significantly fewer steps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.779, + 0.897, + 0.9 + ], + "angle": 0, + "content": "Empirical experiments and visualizations on both generative and discriminative models show that our method can largely improve the convergence speed for optimization. We validate our approach on a diverse set of vision tasks, including GAN inversion [1], adversarial defense [45], and 3D human pose reconstruction [53]. Our experiments show that our method converges an order of magnitude faster without loss in absolute performance after convergence. As our ap" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2239" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.075, + 0.835, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.203, + 0.893, + 0.233 + ], + "angle": 0, + "content": "Figure 2: Method. The left and middle figure show the loss landscape for our latent space and the original latent space, respectively. While walking to the optimal solution in a few steps is hard in \\( X \\) space, it can be done in our learned loss landscapes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.47, + 0.29 + ], + "angle": 0, + "content": "proach does not require retraining of the forward model, it is compatible to all existing OBI methods with a differentiable forward model and objective function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.29, + 0.471, + 0.412 + ], + "angle": 0, + "content": "The primary contribution of this paper is an efficient optimization-based inference framework. In Sec. 2, we survey the related literature to provide an overview of forward model inversion problem. In Sec. 3, we formally define OBI (3.1); our method to learn an efficient loss landscape for OBI (3.2); a training algorithm for better generalization and robustness (3.3). In Sec. 4, we experimentally study and analyze the effectiveness of the mapping network for OBI." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.423, + 0.22, + 0.437 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.473, + 0.553 + ], + "angle": 0, + "content": "The different approaches for inference with a neural network can be partitioned into either encoder-based inference, which is feedforward, or optimization-based inference, which is iterative. We briefly review these two approaches in the context of our work. In addition, we also review representative work in meta-learning and discuss the similarities and differences with our work." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.561, + 0.307, + 0.575 + ], + "angle": 0, + "content": "2.1. Encoder-based Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.751 + ], + "angle": 0, + "content": "Encoder-based inference trains a neural network \\( F \\) to directly map from the output space to the input space. Autoencoder based approach [55] learns an encoder that maps the input data to the latent space. [59, 65, 70, 54] learn an encoder from the image to the latent space in GAN. Encoder based inference requires training the encoder on the anticipated distribution in advance, which is often less effective and can fail on unexpected samples [21, 33]. In addition, encoder-based method can only produce one reconstruction for under-constrained inverse problems [75], even if multiple outcomes can all be true given the partial input." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.345, + 0.773 + ], + "angle": 0, + "content": "2.2. Optimization-based Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "OBI methods perform inference by solving an optimization problem with gradient-based methods such as Stochastic Gradient Descent (SGD) [60] and Projected Gradient Descent (PGD) [44]. In these cases, the objective function specifies the inference task. Besides these methods which use a point estimate for the latent variable, one can estimate the posterior distribution of the latent variable through Bayesian optimization, such as SGLD [71]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.895, + 0.411 + ], + "angle": 0, + "content": "Gradient based optimization methods have been used to infer the latent code of query samples in deep generative models like GANs [26] via GAN inversion [36, 31, 61, 81, 1, 2, 8, 29, 52]. Style transfer relies on gradient based optimization to change the style of the input images [32]. It can also create adversarial attacks that fool the classifier [18, 11, 48, 63]. Recently, back-propagation-based optimization has shown to be effective in defending adversarial examples [45, 47] and compressed sensing [9]. [74] uses MAML [23] to accelerate the optimization process in compressed sensing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.895, + 0.607 + ], + "angle": 0, + "content": "Recently, constrained optimization was popularized for text-to-image synthesis by [19, 41]. They search in the latent space to produce an image that has the highest similarity with the given text as measured by a multi-modal similarity model like CLIP [56]. Test-time constrained optimization is also related to the idea of 'prompt-tuning' for large language models and vision-language models. [39] learns \"soft prompts\" to condition frozen language models to perform specific downstream tasks. Soft prompts are learned through backpropagation to incorporate signal from just a few labeled examples (few-shot learning). Visual prompting at both training time [7, 46] and testing time [67] also relies on effective latent variable optimization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.896, + 0.804 + ], + "angle": 0, + "content": "A major challenge for optimization-based inference is how to perform efficient optimization in a highly non-convex space. To address this, input convex model [4] was proposed so that gradient descent can be performed in a convex space. [66] introduced a method to retrain the generative model such as it learns a latent manifold that is easy to optimize. When the model cannot be changed and retrained, bidirectional inference [68] and hybrid inference [81, 80] uses an encoder to provide a good initialization for the optimization-based inference in a non-convex space. Our method does not retrain the generative model, but instead maps a new latent space into the original input space, allowing more efficient optimization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.813, + 0.655, + 0.829 + ], + "angle": 0, + "content": "2.3. Meta-Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.836, + 0.895, + 0.898 + ], + "angle": 0, + "content": "Given a distribution of tasks, meta-learning aims to adapt quickly when presented with a previously unseen task. MAML [23] and related methods [25, 24] propose a method to learn a parameter initialization of a neural net" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2240" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "work by differentiating through the fine-tuning process. To reduce the computational cost of MAML due to the 2nd degree gradient, [51] proposes a first-order meta-learning algorithm. Unlike MAML which include modifying the forward model (e.g. in [74]), our approach is able to keep the forward model fixed in order to maintain its learned rich priors. Instead of meta-learning of model initialization, a line of work [5, 57, 14, 72] proposed to learn an optimizer, often in the form of an RNN, in order to accelerate gradient descent. Unlike learned optimizers that try to create better optimization algorithms, our approach instead learns to remap the loss landscape which is compatible with any choice of optimizer, including standard SGD or learned ones." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.303, + 0.471, + 0.32 + ], + "angle": 0, + "content": "3. Learning Landscapes for Efficient Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.473, + 0.421 + ], + "angle": 0, + "content": "We present our framework to learn an efficient loss landscape for optimization-based inference (OBI) methods. In Sec. 3.1, we will define OBI. In Sec. 3.2, we will introduce our framework as well as the training objective. In Sec. 3.3, we will describe how to train our model with an alternating optimization algorithm and an experience-replay buffer." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.43, + 0.345, + 0.446 + ], + "angle": 0, + "content": "3.1. Optimization-based Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.473, + 0.56 + ], + "angle": 0, + "content": "Let \\( F(\\mathbf{x}) = \\hat{y} \\) be a differentiable forward model that generates an output \\( \\hat{y} \\) given an input variable \\( \\mathbf{x} \\in X \\). For example, \\( \\hat{y} \\) might be an image, and \\( \\mathbf{x} \\) might be the latent variables for a generative model. Given an observation \\( y \\), the goal of OBI is to find the input \\( \\hat{\\mathbf{x}} \\in X \\) such that an objective function \\( L(\\hat{y}, y) \\) is minimized. Formally, we write this procedure as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.572, + 0.47, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} = \\underset {\\mathbf {x} \\in X} {\\operatorname {a r g m i n}} L (F (\\mathbf {x}), y) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.655 + ], + "angle": 0, + "content": "When the objective function \\( L \\) and the model \\( F \\) are both differentiable, we can perform the optimization over input space \\( X \\) with gradient descent." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.33, + 0.681 + ], + "angle": 0, + "content": "3.2. Remapping the Input Space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.824 + ], + "angle": 0, + "content": "Instead of operating in the original input space \\( X \\), we will create a new space \\( Z \\) where gradient descent is efficient and converges in a small number of iterations. We will use a neural network \\( \\Theta: Z \\to X \\) that maps from the new space \\( Z \\) to the original space \\( X \\). The parameters of the mapping \\( \\Theta \\) is the vector \\( \\theta \\). The learning problem we need solve is to estimate \\( \\theta \\) so that there is a short gradient descent path in \\( Z \\) from the initialization to the solution. Fig. 2 shows an overview of this setup." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.824, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We formulate an objective by rolling out the gradient updates on \\(\\mathbf{z}\\), where we write \\(\\mathbf{z}_t \\gets \\mathbf{z}_{t-1} + \\lambda \\frac{\\partial L}{\\partial \\mathbf{z}_{t-1}}\\) as the \\(t^{\\text{th}}\\) update with a step size of \\(\\lambda\\). For gradient descent in space \\(Z\\) to be efficient, the goal of our introduced \\(\\Theta\\) is to move every step \\(\\mathbf{z}_t\\) as close as possible to the global minima:" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.895, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.235, + 0.895, + 0.305 + ], + "angle": 0, + "content": "Figure 3: Landscape Learning. An optimization trajectory \\(\\{\\mathbf{z}_t\\}_{t=0}^5\\) collected is used to train \\(\\Theta\\). \\(\\mathbf{z}_i\\) that corresponds to a higher \\(L_i\\) will yield a higher gradient when training \\(\\Theta\\). Optimization over multiple steps along the trajectory causes \\(\\Theta\\) to learn patterns of trajectories and create a more efficient loss landscape." + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.315, + 0.892, + 0.364 + ], + "angle": 0, + "content": "\\[\n\\hat {\\theta} = \\underset {\\theta} {\\operatorname {a r g m i n}} \\mathbb {E} _ {(\\mathbf {z}, y)} \\left[ \\sum_ {t = 0} ^ {T} L (F (\\Theta (\\mathbf {z} _ {t})), y) \\right] \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.361, + 0.813, + 0.401 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\quad \\mathbf {z} _ {t} = \\left\\{ \\begin{array}{l l} 0, & t = 0 \\\\ \\mathbf {z} _ {t - 1} + \\lambda \\frac {\\partial L}{\\partial \\mathbf {z} _ {t - 1}}, & t > 0 \\end{array} \\right.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.895, + 0.531 + ], + "angle": 0, + "content": "We visualize this process with a toy example in Fig. 3. Gradient updates on \\(\\Theta\\) w.r.t multiple steps \\(\\mathbf{z}_t\\) along a trajectory will cause the loss value on each step to be lowered. By learning the parameters of \\(\\Theta\\) across many examples, \\(\\Theta\\) can learn the patterns of optimization trajectories in \\(X\\). For example, \\(\\Theta\\) can learn to estimate the step size in \\(X\\) and dynamically adjust it to each example. Moreover, \\(\\Theta\\) can learn to reduce non-convexity of the landscape." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.895, + 0.605 + ], + "angle": 0, + "content": "Once we obtain \\(\\hat{\\Theta}\\) with parameters \\(\\hat{\\theta}\\), we do inference on a new example \\(y\\) through the standard optimization-based inference procedure, except in \\(Z\\) space now. Given the observation \\(y\\), we find the corresponding \\(\\hat{\\mathbf{x}}\\) through the optimization:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.617, + 0.895, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} = \\hat {\\Theta} (\\hat {\\mathbf {z}}) \\quad \\text {w h e r e} \\quad \\hat {\\mathbf {z}} = \\underset {\\mathbf {z} \\in Z} {\\operatorname {a r g m i n}} L (F (\\hat {\\Theta} (\\mathbf {z})), y) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.895, + 0.699 + ], + "angle": 0, + "content": "When the inverse problem is under-constrained, one can infer multiple hypotheses for \\(\\hat{\\mathbf{x}}\\) by repeating the above optimization with a different random initialization for \\(\\mathbf{z}_0\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.708, + 0.606, + 0.725 + ], + "angle": 0, + "content": "3.3. Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.895, + 0.899 + ], + "angle": 0, + "content": "We use alternating optimization (AO) in order to train \\(\\Theta\\) jointly with estimating \\(\\mathbf{z}\\) for each example in the training set. Specifically, we first fix parameters of \\(\\Theta\\) and collect \\(N\\) optimization trajectories of \\(\\mathbf{z}\\), each with length \\(T\\). Adopting the same terminology from the robotics community for learning on continuous states [50], we term this an experience replay buffer. Subsequently, we randomly sample data from this buffer and train \\(\\Theta\\) to optimize the loss function. We alternate between these two steps for a fixed number of iterations with gradient descent for both. Depending on the application, the training time for \\(\\Theta\\) varied from one hour to" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2241" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "one day using a four GPU server. Please see the appendix for more implementation details." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.122, + 0.47, + 0.198 + ], + "angle": 0, + "content": "We also experimented with an online version of the training algorithm, where we update parameters of \\(\\Theta\\) immediately after one update to \\(\\mathbf{z}\\). However, in our experiments, we found this resulted in a slower convergence rate. We show these comparisons in the ablation experiments." + }, + { + "type": "code_caption", + "bbox": [ + 0.08, + 0.212, + 0.37, + 0.227 + ], + "angle": 0, + "content": "Algorithm 1 Learning Mapping Network \\(\\Theta\\)" + }, + { + "type": "algorithm", + "bbox": [ + 0.085, + 0.23, + 0.473, + 0.58 + ], + "angle": 0, + "content": "1: Input: Ground truth \\(y\\), step size \\(\\lambda_z\\) and \\(\\lambda_{\\theta}\\), number of buffers \\(B\\), number of data samples in a buffer \\(N\\), number of optimization steps per sample \\(T\\), loss function \\(L\\), and forward model \\(F\\). \n2: Output: Learned mapping network \\(\\Theta\\) \n3: Randomly initialize a mapping network \\(\\Theta\\) with parameters \\(\\theta\\) \n4: for \\(b = 1, \\dots, B\\) do \n5: Initialize Experience Replay Buffer \\([\\{\\mathbf{z}_{t,i}\\}_{t=1}^{T}]_{i=1}^{N}\\) \n6: for \\(i = 1, \\dots, N\\) do \n7: \\(\\mathbf{z}_0 \\gets \\mathbf{0}\\) \n8: for \\(t = 1, \\dots, T\\) do \n9: \\(\\mathbf{z}_t \\gets \\mathbf{z}_{t-1} + \\lambda_z \\frac{\\partial}{\\partial \\mathbf{z}_{t-1}} L(F(\\Theta(\\mathbf{z})), y)\\) \n10: \\(\\mathbf{z}_{t,i} \\gets z_t\\) \n11: end for \n12: end for \n13: for \\(j = 1, \\dots, T \\cdot N\\) do \n14: Randomly sample \\(\\mathbf{z}\\) from previously collected buffer \n15: \\(\\theta_j \\gets \\theta_{j-1} + \\lambda_\\theta \\frac{\\partial}{\\partial \\theta_{j-1}} L(F(\\Theta(\\mathbf{z})), y)\\) \n16: end for \n17: end for \n18: Return \\(\\theta\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.611, + 0.209, + 0.627 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.756 + ], + "angle": 0, + "content": "The goal of our experiments is to analyze how well our proposed method can be applied to various existing OBI methods to improve the optimization efficiency. We demonstrate application of our method to three diverse OBI methods in computer vision, including both generative models and discriminative models. For each OBI method, the inference-time optimization objective of the baseline and ours can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.767, + 0.47, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\text {B a s i l e :} \\hat {\\mathbf {x}} = \\min _ {\\mathbf {x} \\in X} L (F (\\mathbf {x}), y) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.799, + 0.47, + 0.821 + ], + "angle": 0, + "content": "\\[\n\\text {O u r s :} \\hat {\\mathbf {z}} = \\min _ {\\mathbf {z} \\in Z} L (F (\\Theta (\\mathbf {z})), y) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Next, we provide the specific implementation of the loss term \\( L \\) for each application, along with quantitative and qualitative results. We also perform experiments to understand the loss landscape in Sec. 4.5 and perform ablations on different parts of our approach in Sec. 4.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.654, + 0.106 + ], + "angle": 0, + "content": "4.1. GAN Inversion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.894, + 0.189 + ], + "angle": 0, + "content": "We first validate our method on StyleGAN inversion [1]. We take a pretrained generator of StyleGAN [35] denoted as \\( F \\). Let \\( y \\) be an observed image whose input variable we are recovering, we optimize the objective of Eq. 5 where the loss can be written as," + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.201, + 0.893, + 0.219 + ], + "angle": 0, + "content": "\\[\nL (\\hat {y}, y) = L _ {l p i p s} (\\hat {y}, y) + \\left\\| \\hat {y} - y \\right\\| _ {2} ^ {2} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.892, + 0.35 + ], + "angle": 0, + "content": "where \\( L_{lpips} \\) is a perceptual similarity loss introduced in [79], \\( \\hat{y} = F(\\hat{x}) \\) for baseline and \\( \\hat{y} = F(\\Theta(\\hat{z})) \\) for ours. We train \\( \\Theta \\) on the train split of CelebA-HQ [34] dataset and evaluate on CelebA-HQ validation split for in-distribution experiments and LSUN-Cat[77] for distribution shifting (OOD) experiments. We compare the results from our method against the state-of-the-art encoder-based GAN inversion model [59]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.895, + 0.592 + ], + "angle": 0, + "content": "Quantitative Results. From Fig. 4a, we see that in all experiments, optimization in our space \\( Z \\) consistently outperforms the baseline from the first optimization step to after convergence. This gap in performance is even larger when evaluated on OOD data. This suggests that the improvement in performance is not caused by memorizing the training data. Note that our image reconstruction performance after only 2 steps of optimization is able to outperform or be on-par with the baseline at 20 steps of optimization, resulting in a 10-fold improvement in efficiency. Even after convergence (after 2000 optimization steps), our reconstruction performance improves over the baseline by \\( 15\\% \\) for in-distribution evaluation and \\( 10\\% \\) for OOD evaluation. When compared with encoder-based GAN inversion [59], our method achieves better reconstruction after 11 steps of optimization for in-distribution data and 3 steps for OOD data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.895, + 0.895 + ], + "angle": 0, + "content": "Qualitative Results. From Fig. 8, we can see that our method already shows improvements on in-distribution data - it can almost perfectly reconstruct details like fine hair strands, the cap on the person's head, the object in the person's mouth as well-as the text on it. Interestingly, our method is able to discover and reconstruct latents for cats while the encoder-based model fails miserably as shown in Fig 8. The performance on OOD data truly highlights the benefits of our method. We also visualize how the face generations evolve over the process of optimization in Fig. 5. We can see that in just 4 steps, our method is already able to reconstruct coarse features such as face orientation, skin tone and hair color, while the baseline has hardly deviated from the initialization in regard to any of these features. Further, in Fig. 7 we visualize reconstructions from partial observations where only the center of the face (row 1) or everything other than the mouth (row 2) is visible. We can see a variety of feasible possibilities for the hidden regions (e.g., different hairstyles, lip colors, expressions, etc) showcasing the diversity of the new latent space." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2242" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.161, + 0.09, + 0.476, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.271, + 0.282, + 0.372, + 0.294 + ], + "angle": 0, + "content": "(a) GAN Inversion" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.091, + 0.807, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.282, + 0.742, + 0.294 + ], + "angle": 0, + "content": "(b) 3D Human Pose Reconstruction" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.897, + 0.366 + ], + "angle": 0, + "content": "Figure 4: Optimization Performance. We visualize the trends of optimization performance compared with the baseline. In GAN Inversion (Left), we evaluate all models on test splits of CelebA-HQ [34] and LSUN-cat [77] (OOD) with loss defined in Eq. 6. Since encoder-based inference doesn't involve optimization, we use a flat line to represent it. We perform 2000 steps of gradient descent for all models except encoder-based models. In 3D Human Pose Reconstruction (Right), we evaluate all models on test splits of GRAB [64] and PROX [27] (OOD) with loss defined in Eq. 7. We perform 200 steps of gradient descent for all models. For each step, we plot the average loss value of test splits." + }, + { + "type": "image", + "bbox": [ + 0.143, + 0.368, + 0.832, + 0.613 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.615, + 0.895, + 0.673 + ], + "angle": 0, + "content": "Figure 5: Optimization Process for GAN Inversion. Comparing optimization process of our method and the baseline in order to reconstruct the ground truth image. Left shows the results from the baseline where optimization is done in the original input space \\( X \\). Middle shows the results from our method where optimization is done in our space \\( Z \\). Right column contains the ground truth image to each example. Each row corresponds to the same example." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.684, + 0.36, + 0.699 + ], + "angle": 0, + "content": "4.2.3D Human Pose Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.707, + 0.471, + 0.827 + ], + "angle": 0, + "content": "In addition to image generation, our framework also works for 3D reconstruction. For this, we use VPoser [53] – a variational autoencoder [37] that has learnt a pose prior over body pose. VPoser was trained on SMPL-X body pose parameters \\( y \\in \\mathbb{R}^{63} \\) obtained by applying MoSh [42] on three publicly available human motion capture datasets: CMU Mocap [16], training set of Human3.6M [30], and the PosePrior dataset [3]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.828, + 0.473, + 0.906 + ], + "angle": 0, + "content": "We take a pretrained VPoser decoder denoted as \\( F \\). Our trained mapping network \\( \\Theta \\) projects a vector from the new input space \\( \\mathbf{z} \\in Z \\) to a vector in the original VPoser decoder's input space \\( \\mathbf{x} \\in X \\). Similar to GAN Inversion, we optimize the objective of Eq. 5, where the loss function" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.685, + 0.866, + 0.701 + ], + "angle": 0, + "content": "between predicted and ground truth pose parameters is," + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.711, + 0.894, + 0.73 + ], + "angle": 0, + "content": "\\[\nL (\\hat {y}, y) = \\left\\| \\hat {y} - y \\right\\| _ {2} ^ {2} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.739, + 0.895, + 0.89 + ], + "angle": 0, + "content": "where \\(\\hat{y} = F(\\hat{x})\\) for the baseline and \\(\\hat{y} = F(\\Theta(\\hat{z}))\\) for ours. For training \\(\\Theta\\), we use the GRAB dataset [64] which contains poses of humans interacting with everyday objects. We construct splits for novel video sequences – thus the test split will contain a seen human subject but a potentially unseen pose / demonstration by that subject. We evaluate on this test split for in-distribution experiments and on the PROX dataset [27] for OOD experiments, which contains poses of humans interacting in 3D scenes (e.g., living room, office, etc)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.891, + 0.895, + 0.907 + ], + "angle": 0, + "content": "Quantitative Results. For SMPL-X human pose recon" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2243" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.075, + 0.831, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.334, + 0.894, + 0.363 + ], + "angle": 0, + "content": "Figure 6: Optimization Process for 3D Human Pose Reconstruction. Results shown are for out-of-distribution PROX dataset for sitting (Top) and standing (Bottom) poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.471, + 0.451 + ], + "angle": 0, + "content": "struction experiment, the results follow a similar trend as GAN inversion, with massive improvement in both convergence speed and final loss values after convergence (see Fig. 4b). Our method outperforms the baseline by \\(19\\%\\) for in-distribution evaluation and \\(11\\%\\) for OOD evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.474, + 0.633 + ], + "angle": 0, + "content": "Qualitative Results. In Fig. 6 we visualize how the human pose reconstructions evolve over the process of optimization. Here, we observe that the reconstructions from steps 0 to 6 of the baseline are similar for both examples. On the other hand, our method caters to fast convergence for the varying examples, highlighting the general, yet efficient properties of our search space. Further, in Fig. 7 we visualize reconstructions from partial observations where the only joints visible are that of the upper body (row 3) or lower body (row 4). We obtain a wide range of feasible possibilities for the hidden joints demonstrating the diversity of the latent space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.641, + 0.353, + 0.657 + ], + "angle": 0, + "content": "4.3. Defending Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Our method is also applicable to discriminative models. A state-of-the-art defense [45] for adversarial attack optimizes the self-supervision task at inference time, such that the model can dynamically restore the corrupted structure from the input image for robust inference. Following the existing algorithm implementation, we optimize the input image via our method by minimizing the following discriminative loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.794, + 0.457, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L (F (\\mathbf {r} + \\mathbf {a}), y) = L (F (\\Theta (\\mathbf {z}) + \\mathbf {a}), y) \\\\ = \\mathbb {E} _ {i, j} \\left[ - y _ {i j} ^ {(s)} \\log \\frac {\\exp (\\cos (\\mathbf {f} _ {i} , \\mathbf {f} _ {j}))}{\\sum_ {k} \\exp (\\cos (\\mathbf {f} _ {i} , \\mathbf {f} _ {k}))} \\right] + \\lambda | | \\Theta (\\mathbf {z}) | | _ {2} ^ {2}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{a}\\) is the adversarial attacks that we aim to defend against, \\(\\mathbf{r} = \\Theta (\\mathbf{z})\\) is our additive defense vector to optimize, \\(\\mathbf{f}_i\\) are the contrastive features produced by the neural network" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.375, + 0.892, + 0.407 + ], + "angle": 0, + "content": "\\(F\\) from the \\(i^{\\mathrm{th}}\\) image instance, and \\(\\mathbf{y}_{ij}^{(s)}\\) is the indicator for the positive pairs and negative pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.893, + 0.513 + ], + "angle": 0, + "content": "After obtaining the mapping network \\(\\Theta\\) and the input variable \\(\\hat{\\mathbf{z}}\\), the prediction is \\(\\hat{\\mathbf{y}} = F'(\\mathbf{a} + \\Theta (\\mathbf{z}))\\), where \\(F^{\\prime}\\) is the classification model. Note that the self-supervision loss is optimized as a proxy for increasing the robust classification accuracy. In addition, we add a \\(L_{2}\\) norm decay term for the generated noise \\(z\\) to avoid generating reversal vector that is too large." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.525, + 0.889, + 0.611 + ], + "angle": 0, + "content": "
ModelOptimization Steps
None1 step3 steps5 steps
BLOursBLOursBLOurs
RO31.9934.6244.6536.7744.2338.3843.43
AWP35.6139.5451.3942.8151.6744.9651.05
MART35.6639.7751.7742.5051.7745.4250.96
SemiSL29.7834.5352.1137.2751.2340.9349.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.613, + 0.894, + 0.682 + ], + "angle": 0, + "content": "Table 1: Experiment on improving adversarial robust accuracy. Our goal is to defend 200 steps of \\( L_{2} = 256 / 255 \\) norm bounded attack [44], where the attack's step size is 64/255. Our baseline (BL) is the SOTA test-time optimization-based defense [45], which minimizes the loss of self-supervision task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.895, + 0.793 + ], + "angle": 0, + "content": "Quantitative Results. We evaluate our method on four popular pretrained robust models [58, 69, 73, 12] on CIFAR-10 dataset. The results in [45] require many steps to optimize the objective to improve the adversarial robustness, which slows down the inference by hundreds of times than the original forward pass. Ideally, we desire test-time optimization that can adapt to the attacked images in just one step," + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.814, + 0.878, + 0.876 + ], + "angle": 0, + "content": "
Defense Steps0135
Reversal (Baseline)29.5331.3634.0736.81
OBI (Ours)29.5344.4846.8450.42
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.877, + 0.892, + 0.906 + ], + "angle": 0, + "content": "Table 2: Adaptive attack experiments with BPDA (SemiSL). When the attacker adapts to the defense, we can still improve robustness." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2244" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.152, + 0.075, + 0.822, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.44, + 0.897, + 0.484 + ], + "angle": 0, + "content": "Figure 7: Diversity of Masked Reconstructions. We visualize reconstructions for partially observable inputs from random initializations. The masked regions are not considered for loss computation, i.e., the gradient is set to be zero. By optimizing only on the partial observation, we obtain diverse, feasible solutions for the hidden regions. 5 or 4 out of 20 most representative samples are presented." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.493, + 0.472, + 0.595 + ], + "angle": 0, + "content": "
Number of StepsFull ModelWithout AO and BufferRandom ΘBaseline
In-distribution203.0823.5834.4174.456
OOD204.9325.1275.1355.292
In-distribution2001.9643.0342.7232.569
OOD2003.4984.7563.8234.617
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.606, + 0.472, + 0.648 + ], + "angle": 0, + "content": "Table 3: Ablation Study on mapping network. Number of Steps indicates the number of optimization steps performed during inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.662, + 0.47, + 0.784 + ], + "angle": 0, + "content": "causing the minimal delay at inference time. In Table 1, our method outperforms the gradient descent method in [45] by up to \\(18\\%\\) robust accuracy using a single step, providing a real-time robust inference method. In Table 2, even under the adaptive attack BPDA [6], our method also improves accuracy by up to \\(14\\%\\). Note that our method converges after 1 step of optimization, demonstrating the effectiveness of our approach." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.789, + 0.231, + 0.805 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.806, + 0.471, + 0.897 + ], + "angle": 0, + "content": "In this section, we present an ablation study by removing the proposed alternating optimization (AO) scheme and the experience replay buffer. We also compare against a \\(\\Theta\\) that is randomly initialized. From Table 3 in appendix, we discovered that for in-distribution, AO and training of Theta improves the optimization performance by \\(14\\%\\) and \\(30\\%\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.496, + 0.893, + 0.542 + ], + "angle": 0, + "content": "respectively. Such gap becomes \\(35\\%\\) and \\(28\\%\\) for evaluation on 200 steps. For OOD data, the advantage is furthered enlarged as shown in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.894, + 0.65 + ], + "angle": 0, + "content": "One surprising result we discovered experimentally is that OBI under a randomly initialized mapping network \\(\\Theta\\) consistently outperforms the baseline. We believe this is due to the fact that adding a Gaussian distribution to an underlying latent distribution of StyleGAN is beneficial in smoothing out loss landscape, making it easier to perform OBI. Similar random projection can also be found in [74]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.663, + 0.661, + 0.68 + ], + "angle": 0, + "content": "4.5. Loss Landscape" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.895, + 0.869 + ], + "angle": 0, + "content": "To understand the underlying cause of the significant improvement in optimization brought by our mapping network \\(\\theta\\), we visualize in Fig. 9 the loss landscape for performing optimization in the original input space \\(X\\), and our projected space \\(Z\\). To generate this visualization, we first perform 20 steps of optimization on the validation dataset to collect a set of recovered latents. We then perform principle component analysis (PCA) on these recovered latents to obtain two principle directions. Finally, for individual examples, we evaluate the loss for vertices on a meshgrid spanned by the two principle directions where the center is the last step of optimization." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.901 + ], + "angle": 0, + "content": "From the visualization, we can see that the loss landscapes of the baseline are highly non-convex and contain" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2245" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.272, + 0.091, + 0.372, + 0.104 + ], + "angle": 0, + "content": "In-Distribution" + }, + { + "type": "image", + "bbox": [ + 0.162, + 0.108, + 0.482, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.189, + 0.359, + 0.245, + 0.37 + ], + "angle": 0, + "content": "Encoder" + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.358, + 0.34, + 0.369 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.376, + 0.192, + 0.482, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.383, + 0.359, + 0.474, + 0.37 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.585, + 0.091, + 0.712, + 0.104 + ], + "angle": 0, + "content": "Out-of-Distribution" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.108, + 0.808, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.359, + 0.571, + 0.37 + ], + "angle": 0, + "content": "Encoder" + }, + { + "type": "image_caption", + "bbox": [ + 0.632, + 0.359, + 0.665, + 0.37 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.71, + 0.359, + 0.799, + 0.37 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.374, + 0.893, + 0.401 + ], + "angle": 0, + "content": "Figure 8: Comparison Against Encoder-Based Inference. Left shows the results on the test split of CelebA-HQ; Right shows the results on the LSUN-cat dataset." + }, + { + "type": "image", + "bbox": [ + 0.159, + 0.417, + 0.321, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.416, + 0.481, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.416, + 0.642, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.643, + 0.416, + 0.804, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.158, + 0.521, + 0.322, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.322, + 0.522, + 0.481, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.481, + 0.522, + 0.64, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.522, + 0.804, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.629, + 0.895, + 0.7 + ], + "angle": 0, + "content": "Figure 9: Visualizing Loss Landscape (Uncurated). Visualizing the loss landscape of StyleGAN inversion spanned by two principle directions. Top row shows 4 examples of the loss landscapes corresponding to our space \\( Z \\). Bottom row shows the loss landscapes corresponding to the original input space \\( X \\) for the same 4 examples. Note that the top row and the bottom row have different minimum loss values on the landscape because the minimas are obtained by performing independent optimization runs in space \\( Z \\) and \\( X \\) respectively. Given a fixed number of optimization steps, optimization in \\( Z \\) reaches lower loss values than optimization in \\( X \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.471, + 0.804 + ], + "angle": 0, + "content": "points whose loss are significantly higher than its neighboring regions, while our loss landscapes are significantly smoother, with the \"spikes\" removed. Besides, our loss landscapes also tend to be steeper than the baseline ones. These two phenomena directly cause our method to perform gradient descent faster and stabler." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.821, + 0.173, + 0.837 + ], + "angle": 0, + "content": "5. Analysis" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.846, + 0.18, + 0.86 + ], + "angle": 0, + "content": "5.1. L-BFGS" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "After learning the mapping network \\(\\theta\\), in addition to the main results presented in Fig. 4a, we also run the same ex" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.895, + 0.865 + ], + "angle": 0, + "content": "periments but with L-BFGS as optimizer [40], which tends to perform better empirically with a smoother loss landscape. As shown in table 5, after 10 steps of optimization, L-BFGS achieves much better results than Adam in our learned landscape, which is already significantly better than the baseline. Notably, applying L-BFGS in the original landscape does not achieve significant speedup, and for Celeb-HQ, around \\(18\\%\\) of the examples failed to converge due to instability. These results further verify that our method successfully learns a smoother landscape for efficient optimization." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2246" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.18, + 0.089, + 0.788, + 0.136 + ], + "angle": 0, + "content": "
level of CorruptionN(0,0.02)N(0,0.12)N(0,0.22)N(0,0.32)N(0,0.42)
Improvement29.53%18.95%12.57%6.30%6.72%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.149, + 0.895, + 0.193 + ], + "angle": 0, + "content": "Table 4: Evaluation of a mapping network trained with Celeba-HQ trainset and tested on the Celeba-HQ testset corrupted with different levels of Gaussian noise. The improvement is calculated by the percentage improvement of loss defined by Eq. 6 from baseline (no mapping network) to ours (with mapping network) after 200 steps of optimization." + }, + { + "type": "table", + "bbox": [ + 0.178, + 0.205, + 0.795, + 0.251 + ], + "angle": 0, + "content": "
datasetCelebA-HQAFHQ-CatLSUN-CatContainer-ShipN(0.5, 0.52)
Improvement29.53%35.99%24.36%16.87%6.60%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.252, + 0.895, + 0.31 + ], + "angle": 0, + "content": "Table 6: Evaluation of a mapping network trained with Celeba-HQ trainset and tested on a spectrum of datasets from the original CelebA-HQ (in-distribution) to Gaussian noise (OOD). AFHQ-Cat [15] is a dataset with aligned cat faces. LSUN-Cat [77] is a dataset with unaligned cat images. Container-Ship is 200 images sampled from \"Container Ship\" class of ImageNet [20]. The improvement is calculated by the percentage improvement of loss defined by Eq. 6 from baseline (without \\(\\theta\\)) to ours (with \\(\\theta\\)) after 200 steps of optimization." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.319, + 0.455, + 0.396 + ], + "angle": 0, + "content": "
ours\nL-BFGSours\nAdambaseline\nL-BFGSbaseline\nAdam
Human2.2393.504N/A4.875
Cat (OOD)4.0665.0875.2275.475
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.102, + 0.397, + 0.444, + 0.411 + ], + "angle": 0, + "content": "Table 5: L-BFGS vs. Adam in Leanred Landscape (Ours)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.417, + 0.432, + 0.433 + ], + "angle": 0, + "content": "5.2. More Evaluation on OOD Generalization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.471, + 0.546 + ], + "angle": 0, + "content": "Since our proposed mapping network \\(\\Theta\\) is parameterized by a neural network, there's no guarantee that the learned mapping function is surjective. Therefore, we empirically study the generalization performance by testing a mapping network trained on CelebA-HQ against a spectrum of datasets from very similar ones (in-distribution) to completely different ones (OOD)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.47, + 0.637 + ], + "angle": 0, + "content": "Synthetic Spectrum We first created a synthetic version of this spectrum of datasets by varying the level of Gaussian noise injected into the images of CelebA-HQ. With a higher level of Gaussian noise injected into the original images, more of the original image content is corrupted, creating a distribution of images further away from the original images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.471, + 0.757 + ], + "angle": 0, + "content": "Natural Image Spectrum We also created a natural image version of this spectrum of datasets containing: CelebA-HQ (original in-distribution testset), AFHQ-Cat (center-aligned cat faces), LSUN-Cat (unaligned cat images), Container-Ship (\"Container Ship\" class from ImageNet), and Gaussian noise with individual pixel sampled from \\(\\mathcal{N}(0.5, 0.5^2)\\). From left to right, images vary from very similar to human faces to very different." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.471, + 0.879 + ], + "angle": 0, + "content": "From results evaluated on both synthetic spectrum and real spectrum, we observed consistent improvements of our method over the baseline, which shows the generalization performance of our method when applied to OOD data. From table 6, we see the improvements drop as the evaluation data is less and less in-distribution with the training data, which indicates that the mapping network does learn a prior from the training data." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.33, + 0.868, + 0.393 + ], + "angle": 0, + "content": "
BaselineOursImprovement
CelebA-HQ2.5692.3966.72%
LSUN-Cat4.6173.71719.49%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.393, + 0.894, + 0.45 + ], + "angle": 0, + "content": "Table 7: Evaluation of a mapping network trained with images of Gaussian noise sampled from \\(\\mathcal{N}(0.5,0.5^2)\\) clipped to [0, 1]. Numbers show the average loss defined in Eq. 6 evaluated on testset of CelebA-HQ and LSUN-Cat." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.461, + 0.787, + 0.478 + ], + "angle": 0, + "content": "5.3. Dependence on Training Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.895, + 0.607 + ], + "angle": 0, + "content": "From previous section, we know that the learned mapping network contains priors learned from the training data. To exclude such influence, we train our mapping network using randomly generated images made of Gaussian noise and evaluate on testset of CelebA-HQ. From table 7, we see that even trained with the task of reconstructing images of Gaussian noise, our mapping network still bring some improvement over the baseline model, though less significant." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.619, + 0.619, + 0.635 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.854 + ], + "angle": 0, + "content": "This paper presents a method to accelerate optimization-based inference to invert a forward model. We propose an approach that learns a new space that is easier than the original input space to optimize with gradient descent at testing time. Our experiments and analysis on three different applications in computer vision have shown that by learning this mapping function, optimization becomes more efficient and generalizes better to out-of-distribution data. Through quantitative and qualitative analysis, we found that such improvement in optimization performance comes from a more efficient loss landscape. Since optimization-based inference has many advantages over encoder-based inference, we believe methods to accelerate them will have many impacts in a variety of applications." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement This research is based on work partially supported by the NSF NRI Award 1925157, NSF STC LEAP, DARPA MCS program, and DARPA CCU program." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2247" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.473, + 0.183 + ], + "angle": 0, + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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Springer, 2016. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.894, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "2250" + } + ] +] \ No newline at end of file diff --git a/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_origin.pdf b/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5dd919bc9b75264934e4c36f3075522a0dc931d9 --- /dev/null +++ b/2023/Landscape Learning for Neural Network Inversion/f1107abc-1d35-4283-b4db-d9fd38f81a61_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ee99da27cdc693a7248ce42861519c67152e6be157461c040f4713054ea53690 +size 4728297 diff --git a/2023/Landscape Learning for Neural Network Inversion/full.md b/2023/Landscape Learning for Neural Network Inversion/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b0072e1c399925a38b77779af6b0b4ef5042a390 --- /dev/null +++ b/2023/Landscape Learning for Neural Network Inversion/full.md @@ -0,0 +1,405 @@ +# Landscape Learning for Neural Network Inversion + +Ruoshi Liu1 Chengzhi Mao1 Purva Tendulkar1 Hao Wang2 Carl Vondrick1 +1 Columbia University 2 Rutgers University + +# Abstract + +Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve gradient descent through a highly non-convex loss landscape, causing the optimization process to be unstable and slow. We introduce a method that learns a loss landscape where gradient descent is efficient, bringing massive improvement and acceleration to the inversion process. We demonstrate this advantage on a number of methods for both generative and discriminative tasks, including GAN inversion, adversarial defense, and 3D human pose reconstruction. + +# 1. Introduction + +Many inference problems in machine learning are formulated as inverting a forward model $F(x)$ by optimizing an objective over the input space $x$ . This approach, which we term optimization-based inference (OBI), has traditionally been used to solve a range of inverse problems in vision, graphics, robotics, recommendation systems, and security [28, 38, 22, 10, 62, 17]. Recently, neural networks have emerged as the paramterization of choice for forward models [43, 53, 1, 49, 76, 68, 13, 78], which can be pretrained on large collections of data, and inverted at testing time in order to solve inference queries. + +Optimization-based inference (OBI) has many advantages over feed-forward or encoder-based inference (EBI). Without encoder, OBI provides flexibility to adapt to new tasks, allowing one to define new constraints into the objective during inference. When observations are partially missing, OBI can adapt without additional training. Moreover, OBI naturally supports generating multiple and diverse hypotheses when there is uncertainty. Finally, OBI has intrinsic advantages for robustness, both adapting to new data distributions as well as defending against adversarial examples. + +However, the key bottleneck for OBI in practice is the computational efficiency and the speed of inference. Feedforward models are fast because they only require a single forward pass of a neural network, but OBI requires many + +![](images/5886baaa4e06470f25ae06068a39dd9120e390fe68b37291340f97a2996cbbf0.jpg) +Figure 1: Loss Landscapes Comparison. The loss landscape of optimization-based inference (OBI) is often highly non-convex. We propose to learn a smoother loss landscape through a mapping network to accelerate the optimization. Plotted from real data. + +![](images/ea580b0c066fa2958e2c0629e07c010bdcb00c7fb1d73626bf901eaa0425efd6.jpg) + +(often hundreds) steps of optimization in order to obtain strong results for one example. Forward models in OBI are often trained with generative or discriminative tasks, but they are not trained for the purpose of performing gradient descent in the input space. Fig. 9 visualizes the loss landscape for uncurated examples. The loss landscape is not guaranteed to be an efficient path from the initialization to the solution, causing the instability and inefficiency. + +In this paper, we propose a framework to accelerate and stabilize the inversion of forward neural networks. Instead of optimizing over the original input space, we learn a new input space such that gradient descent converges quickly. Our approach uses an alternating algorithm to learn the mapping between these spaces. The first step collects optimization trajectories in the new space until convergence. The second step updates the mapping parameters to reduce the distance between the convergence point and each point along the trajectory. By repeating these steps, our approach will learn a mapping between the spaces that allows gradient descent over the input to converge in significantly fewer steps. + +Empirical experiments and visualizations on both generative and discriminative models show that our method can largely improve the convergence speed for optimization. We validate our approach on a diverse set of vision tasks, including GAN inversion [1], adversarial defense [45], and 3D human pose reconstruction [53]. Our experiments show that our method converges an order of magnitude faster without loss in absolute performance after convergence. As our ap + +![](images/6a230d29c2b6a3599d5ea8047c1a3131a7bc79ba84216272c6c01daec7e57e56.jpg) +Figure 2: Method. The left and middle figure show the loss landscape for our latent space and the original latent space, respectively. While walking to the optimal solution in a few steps is hard in $X$ space, it can be done in our learned loss landscapes. + +proach does not require retraining of the forward model, it is compatible to all existing OBI methods with a differentiable forward model and objective function. + +The primary contribution of this paper is an efficient optimization-based inference framework. In Sec. 2, we survey the related literature to provide an overview of forward model inversion problem. In Sec. 3, we formally define OBI (3.1); our method to learn an efficient loss landscape for OBI (3.2); a training algorithm for better generalization and robustness (3.3). In Sec. 4, we experimentally study and analyze the effectiveness of the mapping network for OBI. + +# 2. Related Work + +The different approaches for inference with a neural network can be partitioned into either encoder-based inference, which is feedforward, or optimization-based inference, which is iterative. We briefly review these two approaches in the context of our work. In addition, we also review representative work in meta-learning and discuss the similarities and differences with our work. + +# 2.1. Encoder-based Inference + +Encoder-based inference trains a neural network $F$ to directly map from the output space to the input space. Autoencoder based approach [55] learns an encoder that maps the input data to the latent space. [59, 65, 70, 54] learn an encoder from the image to the latent space in GAN. Encoder based inference requires training the encoder on the anticipated distribution in advance, which is often less effective and can fail on unexpected samples [21, 33]. In addition, encoder-based method can only produce one reconstruction for under-constrained inverse problems [75], even if multiple outcomes can all be true given the partial input. + +# 2.2. Optimization-based Inference + +OBI methods perform inference by solving an optimization problem with gradient-based methods such as Stochastic Gradient Descent (SGD) [60] and Projected Gradient Descent (PGD) [44]. In these cases, the objective function specifies the inference task. Besides these methods which use a point estimate for the latent variable, one can estimate the posterior distribution of the latent variable through Bayesian optimization, such as SGLD [71]. + +Gradient based optimization methods have been used to infer the latent code of query samples in deep generative models like GANs [26] via GAN inversion [36, 31, 61, 81, 1, 2, 8, 29, 52]. Style transfer relies on gradient based optimization to change the style of the input images [32]. It can also create adversarial attacks that fool the classifier [18, 11, 48, 63]. Recently, back-propagation-based optimization has shown to be effective in defending adversarial examples [45, 47] and compressed sensing [9]. [74] uses MAML [23] to accelerate the optimization process in compressed sensing. + +Recently, constrained optimization was popularized for text-to-image synthesis by [19, 41]. They search in the latent space to produce an image that has the highest similarity with the given text as measured by a multi-modal similarity model like CLIP [56]. Test-time constrained optimization is also related to the idea of 'prompt-tuning' for large language models and vision-language models. [39] learns "soft prompts" to condition frozen language models to perform specific downstream tasks. Soft prompts are learned through backpropagation to incorporate signal from just a few labeled examples (few-shot learning). Visual prompting at both training time [7, 46] and testing time [67] also relies on effective latent variable optimization. + +A major challenge for optimization-based inference is how to perform efficient optimization in a highly non-convex space. To address this, input convex model [4] was proposed so that gradient descent can be performed in a convex space. [66] introduced a method to retrain the generative model such as it learns a latent manifold that is easy to optimize. When the model cannot be changed and retrained, bidirectional inference [68] and hybrid inference [81, 80] uses an encoder to provide a good initialization for the optimization-based inference in a non-convex space. Our method does not retrain the generative model, but instead maps a new latent space into the original input space, allowing more efficient optimization. + +# 2.3. Meta-Learning + +Given a distribution of tasks, meta-learning aims to adapt quickly when presented with a previously unseen task. MAML [23] and related methods [25, 24] propose a method to learn a parameter initialization of a neural net + +work by differentiating through the fine-tuning process. To reduce the computational cost of MAML due to the 2nd degree gradient, [51] proposes a first-order meta-learning algorithm. Unlike MAML which include modifying the forward model (e.g. in [74]), our approach is able to keep the forward model fixed in order to maintain its learned rich priors. Instead of meta-learning of model initialization, a line of work [5, 57, 14, 72] proposed to learn an optimizer, often in the form of an RNN, in order to accelerate gradient descent. Unlike learned optimizers that try to create better optimization algorithms, our approach instead learns to remap the loss landscape which is compatible with any choice of optimizer, including standard SGD or learned ones. + +# 3. Learning Landscapes for Efficient Inference + +We present our framework to learn an efficient loss landscape for optimization-based inference (OBI) methods. In Sec. 3.1, we will define OBI. In Sec. 3.2, we will introduce our framework as well as the training objective. In Sec. 3.3, we will describe how to train our model with an alternating optimization algorithm and an experience-replay buffer. + +# 3.1. Optimization-based Inference + +Let $F(\mathbf{x}) = \hat{y}$ be a differentiable forward model that generates an output $\hat{y}$ given an input variable $\mathbf{x} \in X$ . For example, $\hat{y}$ might be an image, and $\mathbf{x}$ might be the latent variables for a generative model. Given an observation $y$ , the goal of OBI is to find the input $\hat{\mathbf{x}} \in X$ such that an objective function $L(\hat{y}, y)$ is minimized. Formally, we write this procedure as: + +$$ +\hat {\mathbf {x}} = \underset {\mathbf {x} \in X} {\operatorname {a r g m i n}} L (F (\mathbf {x}), y) \tag {1} +$$ + +When the objective function $L$ and the model $F$ are both differentiable, we can perform the optimization over input space $X$ with gradient descent. + +# 3.2. Remapping the Input Space + +Instead of operating in the original input space $X$ , we will create a new space $Z$ where gradient descent is efficient and converges in a small number of iterations. We will use a neural network $\Theta: Z \to X$ that maps from the new space $Z$ to the original space $X$ . The parameters of the mapping $\Theta$ is the vector $\theta$ . The learning problem we need solve is to estimate $\theta$ so that there is a short gradient descent path in $Z$ from the initialization to the solution. Fig. 2 shows an overview of this setup. + +We formulate an objective by rolling out the gradient updates on $\mathbf{z}$ , where we write $\mathbf{z}_t \gets \mathbf{z}_{t-1} + \lambda \frac{\partial L}{\partial \mathbf{z}_{t-1}}$ as the $t^{\text{th}}$ update with a step size of $\lambda$ . For gradient descent in space $Z$ to be efficient, the goal of our introduced $\Theta$ is to move every step $\mathbf{z}_t$ as close as possible to the global minima: + +![](images/69201484fa2b47fa9b0c4acbde6be430b7c869aedea1d4120233a92138ff2b2f.jpg) +Figure 3: Landscape Learning. An optimization trajectory $\{\mathbf{z}_t\}_{t=0}^5$ collected is used to train $\Theta$ . $\mathbf{z}_i$ that corresponds to a higher $L_i$ will yield a higher gradient when training $\Theta$ . Optimization over multiple steps along the trajectory causes $\Theta$ to learn patterns of trajectories and create a more efficient loss landscape. + +$$ +\hat {\theta} = \underset {\theta} {\operatorname {a r g m i n}} \mathbb {E} _ {(\mathbf {z}, y)} \left[ \sum_ {t = 0} ^ {T} L (F (\Theta (\mathbf {z} _ {t})), y) \right] \tag {2} +$$ + +$$ +\text {w h e r e} \quad \mathbf {z} _ {t} = \left\{ \begin{array}{l l} 0, & t = 0 \\ \mathbf {z} _ {t - 1} + \lambda \frac {\partial L}{\partial \mathbf {z} _ {t - 1}}, & t > 0 \end{array} \right. +$$ + +We visualize this process with a toy example in Fig. 3. Gradient updates on $\Theta$ w.r.t multiple steps $\mathbf{z}_t$ along a trajectory will cause the loss value on each step to be lowered. By learning the parameters of $\Theta$ across many examples, $\Theta$ can learn the patterns of optimization trajectories in $X$ . For example, $\Theta$ can learn to estimate the step size in $X$ and dynamically adjust it to each example. Moreover, $\Theta$ can learn to reduce non-convexity of the landscape. + +Once we obtain $\hat{\Theta}$ with parameters $\hat{\theta}$ , we do inference on a new example $y$ through the standard optimization-based inference procedure, except in $Z$ space now. Given the observation $y$ , we find the corresponding $\hat{\mathbf{x}}$ through the optimization: + +$$ +\hat {\mathbf {x}} = \hat {\Theta} (\hat {\mathbf {z}}) \quad \text {w h e r e} \quad \hat {\mathbf {z}} = \underset {\mathbf {z} \in Z} {\operatorname {a r g m i n}} L (F (\hat {\Theta} (\mathbf {z})), y) \tag {3} +$$ + +When the inverse problem is under-constrained, one can infer multiple hypotheses for $\hat{\mathbf{x}}$ by repeating the above optimization with a different random initialization for $\mathbf{z}_0$ . + +# 3.3. Training + +We use alternating optimization (AO) in order to train $\Theta$ jointly with estimating $\mathbf{z}$ for each example in the training set. Specifically, we first fix parameters of $\Theta$ and collect $N$ optimization trajectories of $\mathbf{z}$ , each with length $T$ . Adopting the same terminology from the robotics community for learning on continuous states [50], we term this an experience replay buffer. Subsequently, we randomly sample data from this buffer and train $\Theta$ to optimize the loss function. We alternate between these two steps for a fixed number of iterations with gradient descent for both. Depending on the application, the training time for $\Theta$ varied from one hour to + +one day using a four GPU server. Please see the appendix for more implementation details. + +We also experimented with an online version of the training algorithm, where we update parameters of $\Theta$ immediately after one update to $\mathbf{z}$ . However, in our experiments, we found this resulted in a slower convergence rate. We show these comparisons in the ablation experiments. + +Algorithm 1 Learning Mapping Network $\Theta$ +1: Input: Ground truth $y$ , step size $\lambda_z$ and $\lambda_{\theta}$ , number of buffers $B$ , number of data samples in a buffer $N$ , number of optimization steps per sample $T$ , loss function $L$ , and forward model $F$ . +2: Output: Learned mapping network $\Theta$ +3: Randomly initialize a mapping network $\Theta$ with parameters $\theta$ +4: for $b = 1, \dots, B$ do +5: Initialize Experience Replay Buffer $[\{\mathbf{z}_{t,i}\}_{t=1}^{T}]_{i=1}^{N}$ +6: for $i = 1, \dots, N$ do +7: $\mathbf{z}_0 \gets \mathbf{0}$ +8: for $t = 1, \dots, T$ do +9: $\mathbf{z}_t \gets \mathbf{z}_{t-1} + \lambda_z \frac{\partial}{\partial \mathbf{z}_{t-1}} L(F(\Theta(\mathbf{z})), y)$ +10: $\mathbf{z}_{t,i} \gets z_t$ +11: end for +12: end for +13: for $j = 1, \dots, T \cdot N$ do +14: Randomly sample $\mathbf{z}$ from previously collected buffer +15: $\theta_j \gets \theta_{j-1} + \lambda_\theta \frac{\partial}{\partial \theta_{j-1}} L(F(\Theta(\mathbf{z})), y)$ +16: end for +17: end for +18: Return $\theta$ + +# 4. Experiments + +The goal of our experiments is to analyze how well our proposed method can be applied to various existing OBI methods to improve the optimization efficiency. We demonstrate application of our method to three diverse OBI methods in computer vision, including both generative models and discriminative models. For each OBI method, the inference-time optimization objective of the baseline and ours can be written as: + +$$ +\text {B a s i l e :} \hat {\mathbf {x}} = \min _ {\mathbf {x} \in X} L (F (\mathbf {x}), y) \tag {4} +$$ + +$$ +\text {O u r s :} \hat {\mathbf {z}} = \min _ {\mathbf {z} \in Z} L (F (\Theta (\mathbf {z})), y) \tag {5} +$$ + +Next, we provide the specific implementation of the loss term $L$ for each application, along with quantitative and qualitative results. We also perform experiments to understand the loss landscape in Sec. 4.5 and perform ablations on different parts of our approach in Sec. 4.4. + +# 4.1. GAN Inversion + +We first validate our method on StyleGAN inversion [1]. We take a pretrained generator of StyleGAN [35] denoted as $F$ . Let $y$ be an observed image whose input variable we are recovering, we optimize the objective of Eq. 5 where the loss can be written as, + +$$ +L (\hat {y}, y) = L _ {l p i p s} (\hat {y}, y) + \left\| \hat {y} - y \right\| _ {2} ^ {2} \tag {6} +$$ + +where $L_{lpips}$ is a perceptual similarity loss introduced in [79], $\hat{y} = F(\hat{x})$ for baseline and $\hat{y} = F(\Theta(\hat{z}))$ for ours. We train $\Theta$ on the train split of CelebA-HQ [34] dataset and evaluate on CelebA-HQ validation split for in-distribution experiments and LSUN-Cat[77] for distribution shifting (OOD) experiments. We compare the results from our method against the state-of-the-art encoder-based GAN inversion model [59]. + +Quantitative Results. From Fig. 4a, we see that in all experiments, optimization in our space $Z$ consistently outperforms the baseline from the first optimization step to after convergence. This gap in performance is even larger when evaluated on OOD data. This suggests that the improvement in performance is not caused by memorizing the training data. Note that our image reconstruction performance after only 2 steps of optimization is able to outperform or be on-par with the baseline at 20 steps of optimization, resulting in a 10-fold improvement in efficiency. Even after convergence (after 2000 optimization steps), our reconstruction performance improves over the baseline by $15\%$ for in-distribution evaluation and $10\%$ for OOD evaluation. When compared with encoder-based GAN inversion [59], our method achieves better reconstruction after 11 steps of optimization for in-distribution data and 3 steps for OOD data. + +Qualitative Results. From Fig. 8, we can see that our method already shows improvements on in-distribution data - it can almost perfectly reconstruct details like fine hair strands, the cap on the person's head, the object in the person's mouth as well-as the text on it. Interestingly, our method is able to discover and reconstruct latents for cats while the encoder-based model fails miserably as shown in Fig 8. The performance on OOD data truly highlights the benefits of our method. We also visualize how the face generations evolve over the process of optimization in Fig. 5. We can see that in just 4 steps, our method is already able to reconstruct coarse features such as face orientation, skin tone and hair color, while the baseline has hardly deviated from the initialization in regard to any of these features. Further, in Fig. 7 we visualize reconstructions from partial observations where only the center of the face (row 1) or everything other than the mouth (row 2) is visible. We can see a variety of feasible possibilities for the hidden regions (e.g., different hairstyles, lip colors, expressions, etc) showcasing the diversity of the new latent space. + +![](images/2daf20a2d6fe761dfa56132ec9e29b47d5dde8a8a850ca1615201afad50035ad.jpg) +(a) GAN Inversion + +![](images/82a7d3c0e94e4dd8570ef6f006ec5b47b3e61d5cfec59d603b9e10f242c75ac2.jpg) +(b) 3D Human Pose Reconstruction + +![](images/eb62ba9e9a69d0902c6842a6553b58d24853ec7e130a36463ff2845add34e314.jpg) +Figure 4: Optimization Performance. We visualize the trends of optimization performance compared with the baseline. In GAN Inversion (Left), we evaluate all models on test splits of CelebA-HQ [34] and LSUN-cat [77] (OOD) with loss defined in Eq. 6. Since encoder-based inference doesn't involve optimization, we use a flat line to represent it. We perform 2000 steps of gradient descent for all models except encoder-based models. In 3D Human Pose Reconstruction (Right), we evaluate all models on test splits of GRAB [64] and PROX [27] (OOD) with loss defined in Eq. 7. We perform 200 steps of gradient descent for all models. For each step, we plot the average loss value of test splits. +Figure 5: Optimization Process for GAN Inversion. Comparing optimization process of our method and the baseline in order to reconstruct the ground truth image. Left shows the results from the baseline where optimization is done in the original input space $X$ . Middle shows the results from our method where optimization is done in our space $Z$ . Right column contains the ground truth image to each example. Each row corresponds to the same example. + +# 4.2.3D Human Pose Reconstruction + +In addition to image generation, our framework also works for 3D reconstruction. For this, we use VPoser [53] – a variational autoencoder [37] that has learnt a pose prior over body pose. VPoser was trained on SMPL-X body pose parameters $y \in \mathbb{R}^{63}$ obtained by applying MoSh [42] on three publicly available human motion capture datasets: CMU Mocap [16], training set of Human3.6M [30], and the PosePrior dataset [3]. + +We take a pretrained VPoser decoder denoted as $F$ . Our trained mapping network $\Theta$ projects a vector from the new input space $\mathbf{z} \in Z$ to a vector in the original VPoser decoder's input space $\mathbf{x} \in X$ . Similar to GAN Inversion, we optimize the objective of Eq. 5, where the loss function + +between predicted and ground truth pose parameters is, + +$$ +L (\hat {y}, y) = \left\| \hat {y} - y \right\| _ {2} ^ {2} \tag {7} +$$ + +where $\hat{y} = F(\hat{x})$ for the baseline and $\hat{y} = F(\Theta(\hat{z}))$ for ours. For training $\Theta$ , we use the GRAB dataset [64] which contains poses of humans interacting with everyday objects. We construct splits for novel video sequences – thus the test split will contain a seen human subject but a potentially unseen pose / demonstration by that subject. We evaluate on this test split for in-distribution experiments and on the PROX dataset [27] for OOD experiments, which contains poses of humans interacting in 3D scenes (e.g., living room, office, etc). + +Quantitative Results. For SMPL-X human pose recon + +![](images/583c9ad7156d0677d7f63e45a5447bf6c025fb747bbcfdadd1c56eac1fd1e3a5.jpg) +Figure 6: Optimization Process for 3D Human Pose Reconstruction. Results shown are for out-of-distribution PROX dataset for sitting (Top) and standing (Bottom) poses. + +struction experiment, the results follow a similar trend as GAN inversion, with massive improvement in both convergence speed and final loss values after convergence (see Fig. 4b). Our method outperforms the baseline by $19\%$ for in-distribution evaluation and $11\%$ for OOD evaluation. + +Qualitative Results. In Fig. 6 we visualize how the human pose reconstructions evolve over the process of optimization. Here, we observe that the reconstructions from steps 0 to 6 of the baseline are similar for both examples. On the other hand, our method caters to fast convergence for the varying examples, highlighting the general, yet efficient properties of our search space. Further, in Fig. 7 we visualize reconstructions from partial observations where the only joints visible are that of the upper body (row 3) or lower body (row 4). We obtain a wide range of feasible possibilities for the hidden joints demonstrating the diversity of the latent space. + +# 4.3. Defending Adversarial Attacks + +Our method is also applicable to discriminative models. A state-of-the-art defense [45] for adversarial attack optimizes the self-supervision task at inference time, such that the model can dynamically restore the corrupted structure from the input image for robust inference. Following the existing algorithm implementation, we optimize the input image via our method by minimizing the following discriminative loss function: + +$$ +\begin{array}{l} L (F (\mathbf {r} + \mathbf {a}), y) = L (F (\Theta (\mathbf {z}) + \mathbf {a}), y) \\ = \mathbb {E} _ {i, j} \left[ - y _ {i j} ^ {(s)} \log \frac {\exp (\cos (\mathbf {f} _ {i} , \mathbf {f} _ {j}))}{\sum_ {k} \exp (\cos (\mathbf {f} _ {i} , \mathbf {f} _ {k}))} \right] + \lambda | | \Theta (\mathbf {z}) | | _ {2} ^ {2}, \\ \end{array} +$$ + +where $\mathbf{a}$ is the adversarial attacks that we aim to defend against, $\mathbf{r} = \Theta (\mathbf{z})$ is our additive defense vector to optimize, $\mathbf{f}_i$ are the contrastive features produced by the neural network + +$F$ from the $i^{\mathrm{th}}$ image instance, and $\mathbf{y}_{ij}^{(s)}$ is the indicator for the positive pairs and negative pairs. + +After obtaining the mapping network $\Theta$ and the input variable $\hat{\mathbf{z}}$ , the prediction is $\hat{\mathbf{y}} = F'(\mathbf{a} + \Theta (\mathbf{z}))$ , where $F^{\prime}$ is the classification model. Note that the self-supervision loss is optimized as a proxy for increasing the robust classification accuracy. In addition, we add a $L_{2}$ norm decay term for the generated noise $z$ to avoid generating reversal vector that is too large. + +
ModelOptimization Steps
None1 step3 steps5 steps
BLOursBLOursBLOurs
RO31.9934.6244.6536.7744.2338.3843.43
AWP35.6139.5451.3942.8151.6744.9651.05
MART35.6639.7751.7742.5051.7745.4250.96
SemiSL29.7834.5352.1137.2751.2340.9349.83
+ +Quantitative Results. We evaluate our method on four popular pretrained robust models [58, 69, 73, 12] on CIFAR-10 dataset. The results in [45] require many steps to optimize the objective to improve the adversarial robustness, which slows down the inference by hundreds of times than the original forward pass. Ideally, we desire test-time optimization that can adapt to the attacked images in just one step, + +Table 1: Experiment on improving adversarial robust accuracy. Our goal is to defend 200 steps of $L_{2} = 256 / 255$ norm bounded attack [44], where the attack's step size is 64/255. Our baseline (BL) is the SOTA test-time optimization-based defense [45], which minimizes the loss of self-supervision task. + +
Defense Steps0135
Reversal (Baseline)29.5331.3634.0736.81
OBI (Ours)29.5344.4846.8450.42
+ +Table 2: Adaptive attack experiments with BPDA (SemiSL). When the attacker adapts to the defense, we can still improve robustness. + +![](images/dcb86b669b6740b4ba9ea94d12806f2e3854d659d434a086ad906bc8f905d78a.jpg) +Figure 7: Diversity of Masked Reconstructions. We visualize reconstructions for partially observable inputs from random initializations. The masked regions are not considered for loss computation, i.e., the gradient is set to be zero. By optimizing only on the partial observation, we obtain diverse, feasible solutions for the hidden regions. 5 or 4 out of 20 most representative samples are presented. + +
Number of StepsFull ModelWithout AO and BufferRandom ΘBaseline
In-distribution203.0823.5834.4174.456
OOD204.9325.1275.1355.292
In-distribution2001.9643.0342.7232.569
OOD2003.4984.7563.8234.617
+ +Table 3: Ablation Study on mapping network. Number of Steps indicates the number of optimization steps performed during inference. + +causing the minimal delay at inference time. In Table 1, our method outperforms the gradient descent method in [45] by up to $18\%$ robust accuracy using a single step, providing a real-time robust inference method. In Table 2, even under the adaptive attack BPDA [6], our method also improves accuracy by up to $14\%$ . Note that our method converges after 1 step of optimization, demonstrating the effectiveness of our approach. + +# 4.4. Ablation Study + +In this section, we present an ablation study by removing the proposed alternating optimization (AO) scheme and the experience replay buffer. We also compare against a $\Theta$ that is randomly initialized. From Table 3 in appendix, we discovered that for in-distribution, AO and training of Theta improves the optimization performance by $14\%$ and $30\%$ + +respectively. Such gap becomes $35\%$ and $28\%$ for evaluation on 200 steps. For OOD data, the advantage is furthered enlarged as shown in Table 3. + +One surprising result we discovered experimentally is that OBI under a randomly initialized mapping network $\Theta$ consistently outperforms the baseline. We believe this is due to the fact that adding a Gaussian distribution to an underlying latent distribution of StyleGAN is beneficial in smoothing out loss landscape, making it easier to perform OBI. Similar random projection can also be found in [74]. + +# 4.5. Loss Landscape + +To understand the underlying cause of the significant improvement in optimization brought by our mapping network $\theta$ , we visualize in Fig. 9 the loss landscape for performing optimization in the original input space $X$ , and our projected space $Z$ . To generate this visualization, we first perform 20 steps of optimization on the validation dataset to collect a set of recovered latents. We then perform principle component analysis (PCA) on these recovered latents to obtain two principle directions. Finally, for individual examples, we evaluate the loss for vertices on a meshgrid spanned by the two principle directions where the center is the last step of optimization. + +From the visualization, we can see that the loss landscapes of the baseline are highly non-convex and contain + +![](images/4989d1af3ecdd68a877d72ca94a3441b4a17d62a06c6ce8e7b5f208a9c0b1cab.jpg) +In-Distribution +Encoder +Ours +Ground Truth + +![](images/d1a31fd19b5cdb469c4da96c60e6ee20716775786cb911d3761d9fd6c4f496dd.jpg) +Out-of-Distribution +Encoder +Ours +Ground Truth + +![](images/53b4913a7839fced8f224bb719df4235681cc332cf2ddb564415a29b685dd227.jpg) + +![](images/b3b1463c7a5a2c1e7915da3c1b95e5ebf1a627e742c368d6dcd1d0123675edec.jpg) +Figure 8: Comparison Against Encoder-Based Inference. Left shows the results on the test split of CelebA-HQ; Right shows the results on the LSUN-cat dataset. + +![](images/69afcfa8539fd65e8bb4e8be3a416b9ca34ddff77f40cf1a285b5eed6aa4f637.jpg) + +![](images/0b15995df62b7fd6efe12425d4f1aaa5f0bf943796309e5ac13111bc299506ca.jpg) + +![](images/37f9e7d3fab8c35a691240b0efe20708bd672bca55d45784606a0450aca620da.jpg) +Figure 9: Visualizing Loss Landscape (Uncurated). Visualizing the loss landscape of StyleGAN inversion spanned by two principle directions. Top row shows 4 examples of the loss landscapes corresponding to our space $Z$ . Bottom row shows the loss landscapes corresponding to the original input space $X$ for the same 4 examples. Note that the top row and the bottom row have different minimum loss values on the landscape because the minimas are obtained by performing independent optimization runs in space $Z$ and $X$ respectively. Given a fixed number of optimization steps, optimization in $Z$ reaches lower loss values than optimization in $X$ . + +![](images/d97445046b79e18a36a67a3ceb47b8f90ec9093be9b1c95045d4d5e3968e4ab6.jpg) + +![](images/83720abffbc6a5c377b720bd81e988339fce701fd224bb63921ab9f17f736a39.jpg) + +![](images/51c5ab68c7753665d5fea9a93da9d269916673ee362f3194915de8f7ee83c30b.jpg) + +points whose loss are significantly higher than its neighboring regions, while our loss landscapes are significantly smoother, with the "spikes" removed. Besides, our loss landscapes also tend to be steeper than the baseline ones. These two phenomena directly cause our method to perform gradient descent faster and stabler. + +# 5. Analysis + +# 5.1. L-BFGS + +After learning the mapping network $\theta$ , in addition to the main results presented in Fig. 4a, we also run the same ex + +periments but with L-BFGS as optimizer [40], which tends to perform better empirically with a smoother loss landscape. As shown in table 5, after 10 steps of optimization, L-BFGS achieves much better results than Adam in our learned landscape, which is already significantly better than the baseline. Notably, applying L-BFGS in the original landscape does not achieve significant speedup, and for Celeb-HQ, around $18\%$ of the examples failed to converge due to instability. These results further verify that our method successfully learns a smoother landscape for efficient optimization. + +
level of CorruptionN(0,0.02)N(0,0.12)N(0,0.22)N(0,0.32)N(0,0.42)
Improvement29.53%18.95%12.57%6.30%6.72%
+ +Table 4: Evaluation of a mapping network trained with Celeba-HQ trainset and tested on the Celeba-HQ testset corrupted with different levels of Gaussian noise. The improvement is calculated by the percentage improvement of loss defined by Eq. 6 from baseline (no mapping network) to ours (with mapping network) after 200 steps of optimization. + +
datasetCelebA-HQAFHQ-CatLSUN-CatContainer-ShipN(0.5, 0.52)
Improvement29.53%35.99%24.36%16.87%6.60%
+ +Table 6: Evaluation of a mapping network trained with Celeba-HQ trainset and tested on a spectrum of datasets from the original CelebA-HQ (in-distribution) to Gaussian noise (OOD). AFHQ-Cat [15] is a dataset with aligned cat faces. LSUN-Cat [77] is a dataset with unaligned cat images. Container-Ship is 200 images sampled from "Container Ship" class of ImageNet [20]. The improvement is calculated by the percentage improvement of loss defined by Eq. 6 from baseline (without $\theta$ ) to ours (with $\theta$ ) after 200 steps of optimization. + +
ours +L-BFGSours +Adambaseline +L-BFGSbaseline +Adam
Human2.2393.504N/A4.875
Cat (OOD)4.0665.0875.2275.475
+ +Table 5: L-BFGS vs. Adam in Leanred Landscape (Ours) + +# 5.2. More Evaluation on OOD Generalization + +Since our proposed mapping network $\Theta$ is parameterized by a neural network, there's no guarantee that the learned mapping function is surjective. Therefore, we empirically study the generalization performance by testing a mapping network trained on CelebA-HQ against a spectrum of datasets from very similar ones (in-distribution) to completely different ones (OOD). + +Synthetic Spectrum We first created a synthetic version of this spectrum of datasets by varying the level of Gaussian noise injected into the images of CelebA-HQ. With a higher level of Gaussian noise injected into the original images, more of the original image content is corrupted, creating a distribution of images further away from the original images. + +Natural Image Spectrum We also created a natural image version of this spectrum of datasets containing: CelebA-HQ (original in-distribution testset), AFHQ-Cat (center-aligned cat faces), LSUN-Cat (unaligned cat images), Container-Ship ("Container Ship" class from ImageNet), and Gaussian noise with individual pixel sampled from $\mathcal{N}(0.5, 0.5^2)$ . From left to right, images vary from very similar to human faces to very different. + +From results evaluated on both synthetic spectrum and real spectrum, we observed consistent improvements of our method over the baseline, which shows the generalization performance of our method when applied to OOD data. From table 6, we see the improvements drop as the evaluation data is less and less in-distribution with the training data, which indicates that the mapping network does learn a prior from the training data. + +
BaselineOursImprovement
CelebA-HQ2.5692.3966.72%
LSUN-Cat4.6173.71719.49%
+ +Table 7: Evaluation of a mapping network trained with images of Gaussian noise sampled from $\mathcal{N}(0.5,0.5^2)$ clipped to [0, 1]. Numbers show the average loss defined in Eq. 6 evaluated on testset of CelebA-HQ and LSUN-Cat. + +# 5.3. Dependence on Training Dataset + +From previous section, we know that the learned mapping network contains priors learned from the training data. To exclude such influence, we train our mapping network using randomly generated images made of Gaussian noise and evaluate on testset of CelebA-HQ. From table 7, we see that even trained with the task of reconstructing images of Gaussian noise, our mapping network still bring some improvement over the baseline model, though less significant. + +# 6. Conclusion + +This paper presents a method to accelerate optimization-based inference to invert a forward model. We propose an approach that learns a new space that is easier than the original input space to optimize with gradient descent at testing time. Our experiments and analysis on three different applications in computer vision have shown that by learning this mapping function, optimization becomes more efficient and generalizes better to out-of-distribution data. Through quantitative and qualitative analysis, we found that such improvement in optimization performance comes from a more efficient loss landscape. Since optimization-based inference has many advantages over encoder-based inference, we believe methods to accelerate them will have many impacts in a variety of applications. + +Acknowledgement This research is based on work partially supported by the NSF NRI Award 1925157, NSF STC LEAP, DARPA MCS program, and DARPA CCU program. + +# References + +[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4432-4441, 2019. 1, 2, 4 +[2] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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Springer, 2016. 2 \ No newline at end of file diff --git a/2023/Landscape Learning for Neural Network Inversion/images.zip b/2023/Landscape Learning for Neural Network Inversion/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..acb396b4e8e5f7f779798735d1ffe1dcd5d9682d --- /dev/null +++ b/2023/Landscape Learning for Neural Network Inversion/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9434e349eeb07fe67d9cecf9b2fddf7a3b9404602f31b69367e49520ba278560 +size 768865 diff --git a/2023/Landscape Learning for Neural Network Inversion/layout.json b/2023/Landscape Learning for Neural Network Inversion/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..32499b650f6b60033a30ebcc53bb856fe2e8cabf --- /dev/null +++ b/2023/Landscape Learning for Neural Network Inversion/layout.json @@ -0,0 +1,11541 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 139, + 103, + 455, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 103, + 455, + 121 + ], + "spans": [ + { + "bbox": [ + 139, + 103, + 455, + 121 + ], + "type": "text", + "content": "Landscape Learning for Neural Network Inversion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 142, + 492, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 142, + 492, + 175 + ], + "spans": [ + { + "bbox": [ + 97, + 142, + 492, + 175 + ], + "type": "text", + "content": "Ruoshi Liu1 Chengzhi Mao1 Purva Tendulkar1 Hao Wang2 Carl Vondrick1 \n1 Columbia University 2 Rutgers University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 204, + 192, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 204, + 192, + 217 + ], + "spans": [ + { + "bbox": [ + 143, + 204, + 192, + 217 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 220, + 290, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 290, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 290, + 365 + ], + "type": "text", + "content": "Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve gradient descent through a highly non-convex loss landscape, causing the optimization process to be unstable and slow. We introduce a method that learns a loss landscape where gradient descent is efficient, bringing massive improvement and acceleration to the inversion process. We demonstrate this advantage on a number of methods for both generative and discriminative tasks, including GAN inversion, adversarial defense, and 3D human pose reconstruction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 391, + 128, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 391, + 128, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 391, + 128, + 403 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 411, + 288, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 288, + 544 + ], + "type": "text", + "content": "Many inference problems in machine learning are formulated as inverting a forward model " + }, + { + "bbox": [ + 46, + 411, + 288, + 544 + ], + "type": "inline_equation", + "content": "F(x)" + }, + { + "bbox": [ + 46, + 411, + 288, + 544 + ], + "type": "text", + "content": " by optimizing an objective over the input space " + }, + { + "bbox": [ + 46, + 411, + 288, + 544 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 411, + 288, + 544 + ], + "type": "text", + "content": ". This approach, which we term optimization-based inference (OBI), has traditionally been used to solve a range of inverse problems in vision, graphics, robotics, recommendation systems, and security [28, 38, 22, 10, 62, 17]. Recently, neural networks have emerged as the paramterization of choice for forward models [43, 53, 1, 49, 76, 68, 13, 78], which can be pretrained on large collections of data, and inverted at testing time in order to solve inference queries." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 544, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 288, + 664 + ], + "type": "text", + "content": "Optimization-based inference (OBI) has many advantages over feed-forward or encoder-based inference (EBI). Without encoder, OBI provides flexibility to adapt to new tasks, allowing one to define new constraints into the objective during inference. When observations are partially missing, OBI can adapt without additional training. Moreover, OBI naturally supports generating multiple and diverse hypotheses when there is uncertainty. Finally, OBI has intrinsic advantages for robustness, both adapting to new data distributions as well as defending against adversarial examples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "However, the key bottleneck for OBI in practice is the computational efficiency and the speed of inference. Feedforward models are fast because they only require a single forward pass of a neural network, but OBI requires many" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 205, + 425, + 306 + ], + "blocks": [ + { + "bbox": [ + 307, + 205, + 425, + 306 + ], + "lines": [ + { + "bbox": [ + 307, + 205, + 425, + 306 + ], + "spans": [ + { + "bbox": [ + 307, + 205, + 425, + 306 + ], + "type": "image", + "image_path": "5886baaa4e06470f25ae06068a39dd9120e390fe68b37291340f97a2996cbbf0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 308, + 547, + 352 + ], + "lines": [ + { + "bbox": [ + 305, + 308, + 547, + 352 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 547, + 352 + ], + "type": "text", + "content": "Figure 1: Loss Landscapes Comparison. The loss landscape of optimization-based inference (OBI) is often highly non-convex. We propose to learn a smoother loss landscape through a mapping network to accelerate the optimization. Plotted from real data." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 426, + 205, + 539, + 306 + ], + "blocks": [ + { + "bbox": [ + 426, + 205, + 539, + 306 + ], + "lines": [ + { + "bbox": [ + 426, + 205, + 539, + 306 + ], + "spans": [ + { + "bbox": [ + 426, + 205, + 539, + 306 + ], + "type": "image", + "image_path": "ea580b0c066fa2958e2c0629e07c010bdcb00c7fb1d73626bf901eaa0425efd6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 377, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 547, + 472 + ], + "type": "text", + "content": "(often hundreds) steps of optimization in order to obtain strong results for one example. Forward models in OBI are often trained with generative or discriminative tasks, but they are not trained for the purpose of performing gradient descent in the input space. Fig. 9 visualizes the loss landscape for uncurated examples. The loss landscape is not guaranteed to be an efficient path from the initialization to the solution, causing the instability and inefficiency." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 473, + 548, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 548, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 548, + 616 + ], + "type": "text", + "content": "In this paper, we propose a framework to accelerate and stabilize the inversion of forward neural networks. Instead of optimizing over the original input space, we learn a new input space such that gradient descent converges quickly. Our approach uses an alternating algorithm to learn the mapping between these spaces. The first step collects optimization trajectories in the new space until convergence. The second step updates the mapping parameters to reduce the distance between the convergence point and each point along the trajectory. By repeating these steps, our approach will learn a mapping between the spaces that allows gradient descent over the input to converge in significantly fewer steps." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 616, + 548, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 548, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 548, + 712 + ], + "type": "text", + "content": "Empirical experiments and visualizations on both generative and discriminative models show that our method can largely improve the convergence speed for optimization. We validate our approach on a diverse set of vision tasks, including GAN inversion [1], adversarial defense [45], and 3D human pose reconstruction [53]. Our experiments show that our method converges an order of magnitude faster without loss in absolute performance after convergence. As our ap" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2239" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 59, + 511, + 159 + ], + "blocks": [ + { + "bbox": [ + 86, + 59, + 511, + 159 + ], + "lines": [ + { + "bbox": [ + 86, + 59, + 511, + 159 + ], + "spans": [ + { + "bbox": [ + 86, + 59, + 511, + 159 + ], + "type": "image", + "image_path": "6a230d29c2b6a3599d5ea8047c1a3131a7bc79ba84216272c6c01daec7e57e56.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 160, + 546, + 184 + ], + "lines": [ + { + "bbox": [ + 46, + 160, + 546, + 184 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 546, + 184 + ], + "type": "text", + "content": "Figure 2: Method. The left and middle figure show the loss landscape for our latent space and the original latent space, respectively. While walking to the optimal solution in a few steps is hard in " + }, + { + "bbox": [ + 46, + 160, + 546, + 184 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 160, + 546, + 184 + ], + "type": "text", + "content": " space, it can be done in our learned loss landscapes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 287, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 229 + ], + "type": "text", + "content": "proach does not require retraining of the forward model, it is compatible to all existing OBI methods with a differentiable forward model and objective function." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 229, + 288, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 229, + 288, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 288, + 326 + ], + "type": "text", + "content": "The primary contribution of this paper is an efficient optimization-based inference framework. In Sec. 2, we survey the related literature to provide an overview of forward model inversion problem. In Sec. 3, we formally define OBI (3.1); our method to learn an efficient loss landscape for OBI (3.2); a training algorithm for better generalization and robustness (3.3). In Sec. 4, we experimentally study and analyze the effectiveness of the mapping network for OBI." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 335, + 134, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 134, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 134, + 346 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 354, + 289, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 289, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 289, + 437 + ], + "type": "text", + "content": "The different approaches for inference with a neural network can be partitioned into either encoder-based inference, which is feedforward, or optimization-based inference, which is iterative. We briefly review these two approaches in the context of our work. In addition, we also review representative work in meta-learning and discuss the similarities and differences with our work." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 444, + 187, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 444, + 187, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 444, + 187, + 455 + ], + "type": "text", + "content": "2.1. Encoder-based Inference" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 462, + 288, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 594 + ], + "type": "text", + "content": "Encoder-based inference trains a neural network " + }, + { + "bbox": [ + 46, + 462, + 288, + 594 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 462, + 288, + 594 + ], + "type": "text", + "content": " to directly map from the output space to the input space. Autoencoder based approach [55] learns an encoder that maps the input data to the latent space. [59, 65, 70, 54] learn an encoder from the image to the latent space in GAN. Encoder based inference requires training the encoder on the anticipated distribution in advance, which is often less effective and can fail on unexpected samples [21, 33]. In addition, encoder-based method can only produce one reconstruction for under-constrained inverse problems [75], even if multiple outcomes can all be true given the partial input." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 599, + 211, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 211, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 211, + 612 + ], + "type": "text", + "content": "2.2. Optimization-based Inference" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "OBI methods perform inference by solving an optimization problem with gradient-based methods such as Stochastic Gradient Descent (SGD) [60] and Projected Gradient Descent (PGD) [44]. In these cases, the objective function specifies the inference task. Besides these methods which use a point estimate for the latent variable, one can estimate the posterior distribution of the latent variable through Bayesian optimization, such as SGLD [71]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 194, + 547, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 547, + 325 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 547, + 325 + ], + "type": "text", + "content": "Gradient based optimization methods have been used to infer the latent code of query samples in deep generative models like GANs [26] via GAN inversion [36, 31, 61, 81, 1, 2, 8, 29, 52]. Style transfer relies on gradient based optimization to change the style of the input images [32]. It can also create adversarial attacks that fool the classifier [18, 11, 48, 63]. Recently, back-propagation-based optimization has shown to be effective in defending adversarial examples [45, 47] and compressed sensing [9]. [74] uses MAML [23] to accelerate the optimization process in compressed sensing." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 325, + 547, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 547, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 547, + 480 + ], + "type": "text", + "content": "Recently, constrained optimization was popularized for text-to-image synthesis by [19, 41]. They search in the latent space to produce an image that has the highest similarity with the given text as measured by a multi-modal similarity model like CLIP [56]. Test-time constrained optimization is also related to the idea of 'prompt-tuning' for large language models and vision-language models. [39] learns \"soft prompts\" to condition frozen language models to perform specific downstream tasks. Soft prompts are learned through backpropagation to incorporate signal from just a few labeled examples (few-shot learning). Visual prompting at both training time [7, 46] and testing time [67] also relies on effective latent variable optimization." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 481, + 548, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 548, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 548, + 636 + ], + "type": "text", + "content": "A major challenge for optimization-based inference is how to perform efficient optimization in a highly non-convex space. To address this, input convex model [4] was proposed so that gradient descent can be performed in a convex space. [66] introduced a method to retrain the generative model such as it learns a latent manifold that is easy to optimize. When the model cannot be changed and retrained, bidirectional inference [68] and hybrid inference [81, 80] uses an encoder to provide a good initialization for the optimization-based inference in a non-convex space. Our method does not retrain the generative model, but instead maps a new latent space into the original input space, allowing more efficient optimization." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 643, + 400, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 400, + 656 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 400, + 656 + ], + "type": "text", + "content": "2.3. Meta-Learning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 662, + 547, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 662, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 662, + 547, + 711 + ], + "type": "text", + "content": "Given a distribution of tasks, meta-learning aims to adapt quickly when presented with a previously unseen task. MAML [23] and related methods [25, 24] propose a method to learn a parameter initialization of a neural net" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2240" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "work by differentiating through the fine-tuning process. To reduce the computational cost of MAML due to the 2nd degree gradient, [51] proposes a first-order meta-learning algorithm. Unlike MAML which include modifying the forward model (e.g. in [74]), our approach is able to keep the forward model fixed in order to maintain its learned rich priors. Instead of meta-learning of model initialization, a line of work [5, 57, 14, 72] proposed to learn an optimizer, often in the form of an RNN, in order to accelerate gradient descent. Unlike learned optimizers that try to create better optimization algorithms, our approach instead learns to remap the loss landscape which is compatible with any choice of optimizer, including standard SGD or learned ones." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 239, + 288, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 288, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 288, + 253 + ], + "type": "text", + "content": "3. Learning Landscapes for Efficient Inference" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 260, + 289, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 289, + 333 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 289, + 333 + ], + "type": "text", + "content": "We present our framework to learn an efficient loss landscape for optimization-based inference (OBI) methods. In Sec. 3.1, we will define OBI. In Sec. 3.2, we will introduce our framework as well as the training objective. In Sec. 3.3, we will describe how to train our model with an alternating optimization algorithm and an experience-replay buffer." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 340, + 211, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 211, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 211, + 353 + ], + "type": "text", + "content": "3.1. Optimization-based Inference" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "inline_equation", + "content": "F(\\mathbf{x}) = \\hat{y}" + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": " be a differentiable forward model that generates an output " + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": " given an input variable " + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in X" + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": ". For example, " + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": " might be an image, and " + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": " might be the latent variables for a generative model. Given an observation " + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": ", the goal of OBI is to find the input " + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}} \\in X" + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": " such that an objective function " + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "inline_equation", + "content": "L(\\hat{y}, y)" + }, + { + "bbox": [ + 46, + 358, + 289, + 443 + ], + "type": "text", + "content": " is minimized. Formally, we write this procedure as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 453, + 287, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 453, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 116, + 453, + 287, + 472 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} = \\underset {\\mathbf {x} \\in X} {\\operatorname {a r g m i n}} L (F (\\mathbf {x}), y) \\tag {1}", + "image_path": "eb30eef66216e086aec3c9b749216a58e8c549ec4fa69da5a27d8cdd699010a6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "text", + "content": "When the objective function " + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "text", + "content": " and the model " + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "text", + "content": " are both differentiable, we can perform the optimization over input space " + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "text", + "content": " with gradient descent." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 525, + 201, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 201, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 201, + 539 + ], + "type": "text", + "content": "3.2. Remapping the Input Space" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": "Instead of operating in the original input space " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": ", we will create a new space " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " where gradient descent is efficient and converges in a small number of iterations. We will use a neural network " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\Theta: Z \\to X" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " that maps from the new space " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " to the original space " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": ". The parameters of the mapping " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " is the vector " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": ". The learning problem we need solve is to estimate " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " so that there is a short gradient descent path in " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " from the initialization to the solution. Fig. 2 shows an overview of this setup." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "content": "We formulate an objective by rolling out the gradient updates on " + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "content": ", where we write " + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t \\gets \\mathbf{z}_{t-1} + \\lambda \\frac{\\partial L}{\\partial \\mathbf{z}_{t-1}}" + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "content": " as the " + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "inline_equation", + "content": "t^{\\text{th}}" + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "content": " update with a step size of " + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "content": ". For gradient descent in space " + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "content": " to be efficient, the goal of our introduced " + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "content": " is to move every step " + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 46, + 652, + 288, + 715 + ], + "type": "text", + "content": " as close as possible to the global minima:" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 547, + 185 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 547, + 185 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 547, + 185 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 547, + 185 + ], + "type": "image", + "image_path": "69201484fa2b47fa9b0c4acbde6be430b7c869aedea1d4120233a92138ff2b2f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "lines": [ + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "text", + "content": "Figure 3: Landscape Learning. An optimization trajectory " + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_t\\}_{t=0}^5" + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "text", + "content": " collected is used to train " + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "text", + "content": " that corresponds to a higher " + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "inline_equation", + "content": "L_i" + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "text", + "content": " will yield a higher gradient when training " + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "text", + "content": ". Optimization over multiple steps along the trajectory causes " + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 306, + 186, + 547, + 241 + ], + "type": "text", + "content": " to learn patterns of trajectories and create a more efficient loss landscape." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 332, + 249, + 545, + 288 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 249, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 332, + 249, + 545, + 288 + ], + "type": "interline_equation", + "content": "\\hat {\\theta} = \\underset {\\theta} {\\operatorname {a r g m i n}} \\mathbb {E} _ {(\\mathbf {z}, y)} \\left[ \\sum_ {t = 0} ^ {T} L (F (\\Theta (\\mathbf {z} _ {t})), y) \\right] \\tag {2}", + "image_path": "2300f30f26622bb63ee657d5c29d59f5a7bdad0de626e0f9e9f4c1797547d2fa.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 334, + 285, + 497, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 285, + 497, + 317 + ], + "spans": [ + { + "bbox": [ + 334, + 285, + 497, + 317 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\quad \\mathbf {z} _ {t} = \\left\\{ \\begin{array}{l l} 0, & t = 0 \\\\ \\mathbf {z} _ {t - 1} + \\lambda \\frac {\\partial L}{\\partial \\mathbf {z} _ {t - 1}}, & t > 0 \\end{array} \\right.", + "image_path": "94409d27060257f3babddbc924cd34d9dd9559c116370454e01e0307dd562d76.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": "We visualize this process with a toy example in Fig. 3. Gradient updates on " + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": " w.r.t multiple steps " + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": " along a trajectory will cause the loss value on each step to be lowered. By learning the parameters of " + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": " across many examples, " + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": " can learn the patterns of optimization trajectories in " + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": ". For example, " + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": " can learn to estimate the step size in " + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": " and dynamically adjust it to each example. Moreover, " + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 324, + 547, + 420 + ], + "type": "text", + "content": " can learn to reduce non-convexity of the landscape." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "text", + "content": "Once we obtain " + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "inline_equation", + "content": "\\hat{\\Theta}" + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "text", + "content": ", we do inference on a new example " + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "text", + "content": " through the standard optimization-based inference procedure, except in " + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "text", + "content": " space now. Given the observation " + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "text", + "content": ", we find the corresponding " + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 420, + 547, + 479 + ], + "type": "text", + "content": " through the optimization:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 319, + 488, + 547, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 488, + 547, + 510 + ], + "spans": [ + { + "bbox": [ + 319, + 488, + 547, + 510 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} = \\hat {\\Theta} (\\hat {\\mathbf {z}}) \\quad \\text {w h e r e} \\quad \\hat {\\mathbf {z}} = \\underset {\\mathbf {z} \\in Z} {\\operatorname {a r g m i n}} L (F (\\hat {\\Theta} (\\mathbf {z})), y) \\tag {3}", + "image_path": "0a25b961db1aeb1f8c3e50698566690f3576f2b697dd19e84ca7b64321c4fba8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 517, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 553 + ], + "type": "text", + "content": "When the inverse problem is under-constrained, one can infer multiple hypotheses for " + }, + { + "bbox": [ + 304, + 517, + 547, + 553 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 517, + 547, + 553 + ], + "type": "text", + "content": " by repeating the above optimization with a different random initialization for " + }, + { + "bbox": [ + 304, + 517, + 547, + 553 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 304, + 517, + 547, + 553 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 560, + 370, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 560, + 370, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 370, + 574 + ], + "type": "text", + "content": "3.3. Training" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": "We use alternating optimization (AO) in order to train " + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": " jointly with estimating " + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": " for each example in the training set. Specifically, we first fix parameters of " + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": " and collect " + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": " optimization trajectories of " + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": ", each with length " + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": ". Adopting the same terminology from the robotics community for learning on continuous states [50], we term this an experience replay buffer. Subsequently, we randomly sample data from this buffer and train " + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": " to optimize the loss function. We alternate between these two steps for a fixed number of iterations with gradient descent for both. Depending on the application, the training time for " + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 579, + 547, + 712 + ], + "type": "text", + "content": " varied from one hour to" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2241" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "one day using a four GPU server. Please see the appendix for more implementation details." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 96, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 96, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 96, + 287, + 156 + ], + "type": "text", + "content": "We also experimented with an online version of the training algorithm, where we update parameters of " + }, + { + "bbox": [ + 47, + 96, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 47, + 96, + 287, + 156 + ], + "type": "text", + "content": " immediately after one update to " + }, + { + "bbox": [ + 47, + 96, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 47, + 96, + 287, + 156 + ], + "type": "text", + "content": ". However, in our experiments, we found this resulted in a slower convergence rate. We show these comparisons in the ablation experiments." + } + ] + } + ], + "index": 1 + }, + { + "type": "code", + "bbox": [ + 52, + 182, + 289, + 459 + ], + "blocks": [ + { + "bbox": [ + 48, + 167, + 226, + 179 + ], + "lines": [ + { + "bbox": [ + 48, + 167, + 226, + 179 + ], + "spans": [ + { + "bbox": [ + 48, + 167, + 226, + 179 + ], + "type": "text", + "content": "Algorithm 1 Learning Mapping Network " + }, + { + "bbox": [ + 48, + 167, + 226, + 179 + ], + "type": "inline_equation", + "content": "\\Theta" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "lines": [ + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "spans": [ + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": "1: Input: Ground truth " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": ", step size " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\lambda_z" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\lambda_{\\theta}" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": ", number of buffers " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": ", number of data samples in a buffer " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": ", number of optimization steps per sample " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": ", loss function " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": ", and forward model " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": ". \n2: Output: Learned mapping network " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " \n3: Randomly initialize a mapping network " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " \n4: for " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "b = 1, \\dots, B" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " do \n5: Initialize Experience Replay Buffer " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "[\\{\\mathbf{z}_{t,i}\\}_{t=1}^{T}]_{i=1}^{N}" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " \n6: for " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, N" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " do \n7: " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0 \\gets \\mathbf{0}" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " \n8: for " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "t = 1, \\dots, T" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " do \n9: " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t \\gets \\mathbf{z}_{t-1} + \\lambda_z \\frac{\\partial}{\\partial \\mathbf{z}_{t-1}} L(F(\\Theta(\\mathbf{z})), y)" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " \n10: " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t,i} \\gets z_t" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " \n11: end for \n12: end for \n13: for " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "j = 1, \\dots, T \\cdot N" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " do \n14: Randomly sample " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " from previously collected buffer \n15: " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\theta_j \\gets \\theta_{j-1} + \\lambda_\\theta \\frac{\\partial}{\\partial \\theta_{j-1}} L(F(\\Theta(\\mathbf{z})), y)" + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "text", + "content": " \n16: end for \n17: end for \n18: Return " + }, + { + "bbox": [ + 52, + 182, + 289, + 459 + ], + "type": "inline_equation", + "content": "\\theta" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "code_body" + } + ], + "index": 3, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 483, + 127, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 127, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 127, + 496 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 503, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 598 + ], + "type": "text", + "content": "The goal of our experiments is to analyze how well our proposed method can be applied to various existing OBI methods to improve the optimization efficiency. We demonstrate application of our method to three diverse OBI methods in computer vision, including both generative models and discriminative models. For each OBI method, the inference-time optimization objective of the baseline and ours can be written as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 102, + 607, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 607, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 102, + 607, + 287, + 624 + ], + "type": "interline_equation", + "content": "\\text {B a s i l e :} \\hat {\\mathbf {x}} = \\min _ {\\mathbf {x} \\in X} L (F (\\mathbf {x}), y) \\tag {4}", + "image_path": "73a3781fa6a4413eb8829ef3ccaf1c16877bf0a492a74f49908b50fef12f7ba5.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 632, + 287, + 650 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 632, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 104, + 632, + 287, + 650 + ], + "type": "interline_equation", + "content": "\\text {O u r s :} \\hat {\\mathbf {z}} = \\min _ {\\mathbf {z} \\in Z} L (F (\\Theta (\\mathbf {z})), y) \\tag {5}", + "image_path": "f7b4bf059d01a5c4940035657c8af4e60900badc93f8dbb72fdb8feaf9fda924.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "Next, we provide the specific implementation of the loss term " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " for each application, along with quantitative and qualitative results. We also perform experiments to understand the loss landscape in Sec. 4.5 and perform ablations on different parts of our approach in Sec. 4.4." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 400, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 400, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 400, + 83 + ], + "type": "text", + "content": "4.1. GAN Inversion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 90, + 547, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 149 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 149 + ], + "type": "text", + "content": "We first validate our method on StyleGAN inversion [1]. We take a pretrained generator of StyleGAN [35] denoted as " + }, + { + "bbox": [ + 304, + 90, + 547, + 149 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 90, + 547, + 149 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 90, + 547, + 149 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 90, + 547, + 149 + ], + "type": "text", + "content": " be an observed image whose input variable we are recovering, we optimize the objective of Eq. 5 where the loss can be written as," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 353, + 159, + 546, + 173 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 159, + 546, + 173 + ], + "spans": [ + { + "bbox": [ + 353, + 159, + 546, + 173 + ], + "type": "interline_equation", + "content": "L (\\hat {y}, y) = L _ {l p i p s} (\\hat {y}, y) + \\left\\| \\hat {y} - y \\right\\| _ {2} ^ {2} \\tag {6}", + "image_path": "97c86bd366fd2bf28a3a05c4fd3878329c4e654e10af62002c51b1ce796b2cf9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "inline_equation", + "content": "L_{lpips}" + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "text", + "content": " is a perceptual similarity loss introduced in [79], " + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\hat{y} = F(\\hat{x})" + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "text", + "content": " for baseline and " + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\hat{y} = F(\\Theta(\\hat{z}))" + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "text", + "content": " for ours. We train " + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 182, + 545, + 277 + ], + "type": "text", + "content": " on the train split of CelebA-HQ [34] dataset and evaluate on CelebA-HQ validation split for in-distribution experiments and LSUN-Cat[77] for distribution shifting (OOD) experiments. We compare the results from our method against the state-of-the-art encoder-based GAN inversion model [59]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "type": "text", + "content": "Quantitative Results. From Fig. 4a, we see that in all experiments, optimization in our space " + }, + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "type": "text", + "content": " consistently outperforms the baseline from the first optimization step to after convergence. This gap in performance is even larger when evaluated on OOD data. This suggests that the improvement in performance is not caused by memorizing the training data. Note that our image reconstruction performance after only 2 steps of optimization is able to outperform or be on-par with the baseline at 20 steps of optimization, resulting in a 10-fold improvement in efficiency. Even after convergence (after 2000 optimization steps), our reconstruction performance improves over the baseline by " + }, + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "type": "text", + "content": " for in-distribution evaluation and " + }, + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 277, + 547, + 468 + ], + "type": "text", + "content": " for OOD evaluation. When compared with encoder-based GAN inversion [59], our method achieves better reconstruction after 11 steps of optimization for in-distribution data and 3 steps for OOD data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 469, + 547, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 547, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 547, + 708 + ], + "type": "text", + "content": "Qualitative Results. From Fig. 8, we can see that our method already shows improvements on in-distribution data - it can almost perfectly reconstruct details like fine hair strands, the cap on the person's head, the object in the person's mouth as well-as the text on it. Interestingly, our method is able to discover and reconstruct latents for cats while the encoder-based model fails miserably as shown in Fig 8. The performance on OOD data truly highlights the benefits of our method. We also visualize how the face generations evolve over the process of optimization in Fig. 5. We can see that in just 4 steps, our method is already able to reconstruct coarse features such as face orientation, skin tone and hair color, while the baseline has hardly deviated from the initialization in regard to any of these features. Further, in Fig. 7 we visualize reconstructions from partial observations where only the center of the face (row 1) or everything other than the mouth (row 2) is visible. We can see a variety of feasible possibilities for the hidden regions (e.g., different hairstyles, lip colors, expressions, etc) showcasing the diversity of the new latent space." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "2242" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 98, + 71, + 291, + 219 + ], + "blocks": [ + { + "bbox": [ + 98, + 71, + 291, + 219 + ], + "lines": [ + { + "bbox": [ + 98, + 71, + 291, + 219 + ], + "spans": [ + { + "bbox": [ + 98, + 71, + 291, + 219 + ], + "type": "image", + "image_path": "2daf20a2d6fe761dfa56132ec9e29b47d5dde8a8a850ca1615201afad50035ad.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 165, + 223, + 227, + 232 + ], + "lines": [ + { + "bbox": [ + 165, + 223, + 227, + 232 + ], + "spans": [ + { + "bbox": [ + 165, + 223, + 227, + 232 + ], + "type": "text", + "content": "(a) GAN Inversion" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 72, + 493, + 218 + ], + "blocks": [ + { + "bbox": [ + 296, + 72, + 493, + 218 + ], + "lines": [ + { + "bbox": [ + 296, + 72, + 493, + 218 + ], + "spans": [ + { + "bbox": [ + 296, + 72, + 493, + 218 + ], + "type": "image", + "image_path": "82a7d3c0e94e4dd8570ef6f006ec5b47b3e61d5cfec59d603b9e10f242c75ac2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 223, + 454, + 232 + ], + "lines": [ + { + "bbox": [ + 337, + 223, + 454, + 232 + ], + "spans": [ + { + "bbox": [ + 337, + 223, + 454, + 232 + ], + "type": "text", + "content": "(b) 3D Human Pose Reconstruction" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 87, + 291, + 509, + 485 + ], + "blocks": [ + { + "bbox": [ + 46, + 235, + 548, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 548, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 548, + 289 + ], + "type": "text", + "content": "Figure 4: Optimization Performance. We visualize the trends of optimization performance compared with the baseline. In GAN Inversion (Left), we evaluate all models on test splits of CelebA-HQ [34] and LSUN-cat [77] (OOD) with loss defined in Eq. 6. Since encoder-based inference doesn't involve optimization, we use a flat line to represent it. We perform 2000 steps of gradient descent for all models except encoder-based models. In 3D Human Pose Reconstruction (Right), we evaluate all models on test splits of GRAB [64] and PROX [27] (OOD) with loss defined in Eq. 7. We perform 200 steps of gradient descent for all models. For each step, we plot the average loss value of test splits." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 87, + 291, + 509, + 485 + ], + "lines": [ + { + "bbox": [ + 87, + 291, + 509, + 485 + ], + "spans": [ + { + "bbox": [ + 87, + 291, + 509, + 485 + ], + "type": "image", + "image_path": "eb62ba9e9a69d0902c6842a6553b58d24853ec7e130a36463ff2845add34e314.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 487, + 547, + 533 + ], + "lines": [ + { + "bbox": [ + 46, + 487, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 547, + 533 + ], + "type": "text", + "content": "Figure 5: Optimization Process for GAN Inversion. Comparing optimization process of our method and the baseline in order to reconstruct the ground truth image. Left shows the results from the baseline where optimization is done in the original input space " + }, + { + "bbox": [ + 46, + 487, + 547, + 533 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 487, + 547, + 533 + ], + "type": "text", + "content": ". Middle shows the results from our method where optimization is done in our space " + }, + { + "bbox": [ + 46, + 487, + 547, + 533 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 487, + 547, + 533 + ], + "type": "text", + "content": ". Right column contains the ground truth image to each example. Each row corresponds to the same example." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 541, + 220, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 541, + 220, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 541, + 220, + 553 + ], + "type": "text", + "content": "4.2.3D Human Pose Reconstruction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 559, + 288, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 559, + 288, + 654 + ], + "spans": [ + { + "bbox": [ + 45, + 559, + 288, + 654 + ], + "type": "text", + "content": "In addition to image generation, our framework also works for 3D reconstruction. For this, we use VPoser [53] – a variational autoencoder [37] that has learnt a pose prior over body pose. VPoser was trained on SMPL-X body pose parameters " + }, + { + "bbox": [ + 45, + 559, + 288, + 654 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{63}" + }, + { + "bbox": [ + 45, + 559, + 288, + 654 + ], + "type": "text", + "content": " obtained by applying MoSh [42] on three publicly available human motion capture datasets: CMU Mocap [16], training set of Human3.6M [30], and the PosePrior dataset [3]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "spans": [ + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "text", + "content": "We take a pretrained VPoser decoder denoted as " + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "text", + "content": ". Our trained mapping network " + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "text", + "content": " projects a vector from the new input space " + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\in Z" + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "text", + "content": " to a vector in the original VPoser decoder's input space " + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in X" + }, + { + "bbox": [ + 46, + 655, + 289, + 717 + ], + "type": "text", + "content": ". Similar to GAN Inversion, we optimize the objective of Eq. 5, where the loss function" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 542, + 529, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 542, + 529, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 542, + 529, + 555 + ], + "type": "text", + "content": "between predicted and ground truth pose parameters is," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 383, + 563, + 547, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 563, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 383, + 563, + 547, + 578 + ], + "type": "interline_equation", + "content": "L (\\hat {y}, y) = \\left\\| \\hat {y} - y \\right\\| _ {2} ^ {2} \\tag {7}", + "image_path": "1040159958f6c7ecafa98a5c7f8eadf9293098d9e1dc8a0b6d0735ae795747b6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "type": "inline_equation", + "content": "\\hat{y} = F(\\hat{x})" + }, + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "type": "text", + "content": " for the baseline and " + }, + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "type": "inline_equation", + "content": "\\hat{y} = F(\\Theta(\\hat{z}))" + }, + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "type": "text", + "content": " for ours. For training " + }, + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 585, + 547, + 704 + ], + "type": "text", + "content": ", we use the GRAB dataset [64] which contains poses of humans interacting with everyday objects. We construct splits for novel video sequences – thus the test split will contain a seen human subject but a potentially unseen pose / demonstration by that subject. We evaluate on this test split for in-distribution experiments and on the PROX dataset [27] for OOD experiments, which contains poses of humans interacting in 3D scenes (e.g., living room, office, etc)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 705, + 547, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 705, + 547, + 718 + ], + "spans": [ + { + "bbox": [ + 317, + 705, + 547, + 718 + ], + "type": "text", + "content": "Quantitative Results. For SMPL-X human pose recon" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2243" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 59, + 508, + 263 + ], + "blocks": [ + { + "bbox": [ + 85, + 59, + 508, + 263 + ], + "lines": [ + { + "bbox": [ + 85, + 59, + 508, + 263 + ], + "spans": [ + { + "bbox": [ + 85, + 59, + 508, + 263 + ], + "type": "image", + "image_path": "583c9ad7156d0677d7f63e45a5447bf6c025fb747bbcfdadd1c56eac1fd1e3a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 264, + 547, + 287 + ], + "lines": [ + { + "bbox": [ + 46, + 264, + 547, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 547, + 287 + ], + "type": "text", + "content": "Figure 6: Optimization Process for 3D Human Pose Reconstruction. Results shown are for out-of-distribution PROX dataset for sitting (Top) and standing (Bottom) poses." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 288, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 288, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 288, + 357 + ], + "type": "text", + "content": "struction experiment, the results follow a similar trend as GAN inversion, with massive improvement in both convergence speed and final loss values after convergence (see Fig. 4b). Our method outperforms the baseline by " + }, + { + "bbox": [ + 46, + 297, + 288, + 357 + ], + "type": "inline_equation", + "content": "19\\%" + }, + { + "bbox": [ + 46, + 297, + 288, + 357 + ], + "type": "text", + "content": " for in-distribution evaluation and " + }, + { + "bbox": [ + 46, + 297, + 288, + 357 + ], + "type": "inline_equation", + "content": "11\\%" + }, + { + "bbox": [ + 46, + 297, + 288, + 357 + ], + "type": "text", + "content": " for OOD evaluation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 357, + 290, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 290, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 290, + 501 + ], + "type": "text", + "content": "Qualitative Results. In Fig. 6 we visualize how the human pose reconstructions evolve over the process of optimization. Here, we observe that the reconstructions from steps 0 to 6 of the baseline are similar for both examples. On the other hand, our method caters to fast convergence for the varying examples, highlighting the general, yet efficient properties of our search space. Further, in Fig. 7 we visualize reconstructions from partial observations where the only joints visible are that of the upper body (row 3) or lower body (row 4). We obtain a wide range of feasible possibilities for the hidden joints demonstrating the diversity of the latent space." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 507, + 216, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 507, + 216, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 507, + 216, + 520 + ], + "type": "text", + "content": "4.3. Defending Adversarial Attacks" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 525, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 622 + ], + "type": "text", + "content": "Our method is also applicable to discriminative models. A state-of-the-art defense [45] for adversarial attack optimizes the self-supervision task at inference time, such that the model can dynamically restore the corrupted structure from the input image for robust inference. Following the existing algorithm implementation, we optimize the input image via our method by minimizing the following discriminative loss function:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 628, + 279, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 279, + 673 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 279, + 673 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L (F (\\mathbf {r} + \\mathbf {a}), y) = L (F (\\Theta (\\mathbf {z}) + \\mathbf {a}), y) \\\\ = \\mathbb {E} _ {i, j} \\left[ - y _ {i j} ^ {(s)} \\log \\frac {\\exp (\\cos (\\mathbf {f} _ {i} , \\mathbf {f} _ {j}))}{\\sum_ {k} \\exp (\\cos (\\mathbf {f} _ {i} , \\mathbf {f} _ {k}))} \\right] + \\lambda | | \\Theta (\\mathbf {z}) | | _ {2} ^ {2}, \\\\ \\end{array}", + "image_path": "a0ca7f78ec9deec392b9cdc70e43252604165405b49f7a6b87bc7dc2f93d4927.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": " is the adversarial attacks that we aim to defend against, " + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{r} = \\Theta (\\mathbf{z})" + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": " is our additive defense vector to optimize, " + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i" + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": " are the contrastive features produced by the neural network" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 297, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 545, + 322 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 297, + 545, + 322 + ], + "type": "text", + "content": " from the " + }, + { + "bbox": [ + 305, + 297, + 545, + 322 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 305, + 297, + 545, + 322 + ], + "type": "text", + "content": " image instance, and " + }, + { + "bbox": [ + 305, + 297, + 545, + 322 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{ij}^{(s)}" + }, + { + "bbox": [ + 305, + 297, + 545, + 322 + ], + "type": "text", + "content": " is the indicator for the positive pairs and negative pairs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "text", + "content": "After obtaining the mapping network " + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "text", + "content": " and the input variable " + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "text", + "content": ", the prediction is " + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}} = F'(\\mathbf{a} + \\Theta (\\mathbf{z}))" + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "inline_equation", + "content": "F^{\\prime}" + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "text", + "content": " is the classification model. Note that the self-supervision loss is optimized as a proxy for increasing the robust classification accuracy. In addition, we add a " + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "text", + "content": " norm decay term for the generated noise " + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 322, + 546, + 406 + ], + "type": "text", + "content": " to avoid generating reversal vector that is too large." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 309, + 415, + 544, + 483 + ], + "blocks": [ + { + "bbox": [ + 309, + 415, + 544, + 483 + ], + "lines": [ + { + "bbox": [ + 309, + 415, + 544, + 483 + ], + "spans": [ + { + "bbox": [ + 309, + 415, + 544, + 483 + ], + "type": "table", + "html": "
ModelOptimization Steps
None1 step3 steps5 steps
BLOursBLOursBLOurs
RO31.9934.6244.6536.7744.2338.3843.43
AWP35.6139.5451.3942.8151.6744.9651.05
MART35.6639.7751.7742.5051.7745.4250.96
SemiSL29.7834.5352.1137.2751.2340.9349.83
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Defense Steps0135
Reversal (Baseline)29.5331.3634.0736.81
OBI (Ours)29.5344.4846.8450.42
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Number of StepsFull ModelWithout AO and BufferRandom ΘBaseline
In-distribution203.0823.5834.4174.456
OOD204.9325.1275.1355.292
In-distribution2001.9643.0342.7232.569
OOD2003.4984.7563.8234.617
", + "image_path": "62729aff825b347aded27aa88e9ba7a231605d53bf0db4a15ac72f061549356f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 479, + 288, + 513 + ], + "lines": [ + { + "bbox": [ + 46, + 479, + 288, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 288, + 513 + ], + "type": "text", + "content": "Table 3: Ablation Study on mapping network. Number of Steps indicates the number of optimization steps performed during inference." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 524, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 524, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 524, + 287, + 620 + ], + "type": "text", + "content": "causing the minimal delay at inference time. In Table 1, our method outperforms the gradient descent method in [45] by up to " + }, + { + "bbox": [ + 46, + 524, + 287, + 620 + ], + "type": "inline_equation", + "content": "18\\%" + }, + { + "bbox": [ + 46, + 524, + 287, + 620 + ], + "type": "text", + "content": " robust accuracy using a single step, providing a real-time robust inference method. In Table 2, even under the adaptive attack BPDA [6], our method also improves accuracy by up to " + }, + { + "bbox": [ + 46, + 524, + 287, + 620 + ], + "type": "inline_equation", + "content": "14\\%" + }, + { + "bbox": [ + 46, + 524, + 287, + 620 + ], + "type": "text", + "content": ". Note that our method converges after 1 step of optimization, demonstrating the effectiveness of our approach." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 624, + 141, + 637 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 141, + 637 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 141, + 637 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 638, + 288, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 638, + 288, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 638, + 288, + 710 + ], + "type": "text", + "content": "In this section, we present an ablation study by removing the proposed alternating optimization (AO) scheme and the experience replay buffer. We also compare against a " + }, + { + "bbox": [ + 46, + 638, + 288, + 710 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 638, + 288, + 710 + ], + "type": "text", + "content": " that is randomly initialized. From Table 3 in appendix, we discovered that for in-distribution, AO and training of Theta improves the optimization performance by " + }, + { + "bbox": [ + 46, + 638, + 288, + 710 + ], + "type": "inline_equation", + "content": "14\\%" + }, + { + "bbox": [ + 46, + 638, + 288, + 710 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 638, + 288, + 710 + ], + "type": "inline_equation", + "content": "30\\%" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 392, + 546, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 546, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 546, + 429 + ], + "type": "text", + "content": "respectively. Such gap becomes " + }, + { + "bbox": [ + 304, + 392, + 546, + 429 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 304, + 392, + 546, + 429 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 392, + 546, + 429 + ], + "type": "inline_equation", + "content": "28\\%" + }, + { + "bbox": [ + 304, + 392, + 546, + 429 + ], + "type": "text", + "content": " for evaluation on 200 steps. For OOD data, the advantage is furthered enlarged as shown in Table 3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 430, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 547, + 514 + ], + "type": "text", + "content": "One surprising result we discovered experimentally is that OBI under a randomly initialized mapping network " + }, + { + "bbox": [ + 304, + 430, + 547, + 514 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 430, + 547, + 514 + ], + "type": "text", + "content": " consistently outperforms the baseline. We believe this is due to the fact that adding a Gaussian distribution to an underlying latent distribution of StyleGAN is beneficial in smoothing out loss landscape, making it easier to perform OBI. Similar random projection can also be found in [74]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 525, + 404, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 404, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 404, + 538 + ], + "type": "text", + "content": "4.5. Loss Landscape" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "type": "text", + "content": "To understand the underlying cause of the significant improvement in optimization brought by our mapping network " + }, + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "type": "text", + "content": ", we visualize in Fig. 9 the loss landscape for performing optimization in the original input space " + }, + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "type": "text", + "content": ", and our projected space " + }, + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 544, + 547, + 688 + ], + "type": "text", + "content": ". To generate this visualization, we first perform 20 steps of optimization on the validation dataset to collect a set of recovered latents. We then perform principle component analysis (PCA) on these recovered latents to obtain two principle directions. Finally, for individual examples, we evaluate the loss for vertices on a meshgrid spanned by the two principle directions where the center is the last step of optimization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "From the visualization, we can see that the loss landscapes of the baseline are highly non-convex and contain" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2245" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": 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Visualizing the loss landscape of StyleGAN inversion spanned by two principle directions. Top row shows 4 examples of the loss landscapes corresponding to our space " + }, + { + "bbox": [ + 46, + 498, + 547, + 554 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 498, + 547, + 554 + ], + "type": "text", + "content": ". Bottom row shows the loss landscapes corresponding to the original input space " + }, + { + "bbox": [ + 46, + 498, + 547, + 554 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 498, + 547, + 554 + ], + "type": "text", + "content": " for the same 4 examples. Note that the top row and the bottom row have different minimum loss values on the landscape because the minimas are obtained by performing independent optimization runs in space " + }, + { + "bbox": [ + 46, + 498, + 547, + 554 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 498, + 547, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 547, + 554 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 498, + 547, + 554 + ], + "type": "text", + "content": " respectively. 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Besides, our loss landscapes also tend to be steeper than the baseline ones. These two phenomena directly cause our method to perform gradient descent faster and stabler." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 650, + 105, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 650, + 105, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 650, + 105, + 662 + ], + "type": "text", + "content": "5. Analysis" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 670, + 110, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 110, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 110, + 681 + ], + "type": "text", + "content": "5.1. 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As shown in table 5, after 10 steps of optimization, L-BFGS achieves much better results than Adam in our learned landscape, which is already significantly better than the baseline. Notably, applying L-BFGS in the original landscape does not achieve significant speedup, and for Celeb-HQ, around " + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "inline_equation", + "content": "18\\%" + }, + { + "bbox": [ + 304, + 564, + 547, + 685 + ], + "type": "text", + "content": " of the examples failed to converge due to instability. These results further verify that our method successfully learns a smoother landscape for efficient optimization." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "2246" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 110, + 70, + 482, + 107 + ], + "blocks": [ + { + "bbox": [ + 110, + 70, + 482, + 107 + ], + "lines": [ + { + "bbox": [ + 110, + 70, + 482, + 107 + ], + "spans": [ + { + "bbox": [ + 110, + 70, + 482, + 107 + ], + "type": "table", + "html": "
level of CorruptionN(0,0.02)N(0,0.12)N(0,0.22)N(0,0.32)N(0,0.42)
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", + "image_path": "1f056855aaebce7f361d28a23f0c3b2589590e8539d156dc7f46056f9a42af9c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 108, + 162, + 486, + 198 + ], + "blocks": [ + { + "bbox": [ + 46, + 118, + 547, + 152 + ], + "lines": [ + { + "bbox": [ + 46, + 118, + 547, + 152 + ], + "spans": [ + { + "bbox": [ + 46, + 118, + 547, + 152 + ], + "type": "text", + "content": "Table 4: Evaluation of a mapping network trained with Celeba-HQ trainset and tested on the Celeba-HQ testset corrupted with different levels of Gaussian noise. The improvement is calculated by the percentage improvement of loss defined by Eq. 6 from baseline (no mapping network) to ours (with mapping network) after 200 steps of optimization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 108, + 162, + 486, + 198 + ], + "lines": [ + { + "bbox": [ + 108, + 162, + 486, + 198 + ], + "spans": [ + { + "bbox": [ + 108, + 162, + 486, + 198 + ], + "type": "table", + "html": "
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Numbers show the average loss defined in Eq. 6 evaluated on testset of CelebA-HQ and LSUN-Cat." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 365, + 481, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 481, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 481, + 378 + ], + "type": "text", + "content": "5.3. Dependence on Training Dataset" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 384, + 547, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 547, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 547, + 480 + ], + "type": "text", + "content": "From previous section, we know that the learned mapping network contains priors learned from the training data. To exclude such influence, we train our mapping network using randomly generated images made of Gaussian noise and evaluate on testset of CelebA-HQ. From table 7, we see that even trained with the task of reconstructing images of Gaussian noise, our mapping network still bring some improvement over the baseline model, though less significant." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 490, + 378, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 378, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 378, + 502 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 510, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 676 + ], + "type": "text", + "content": "This paper presents a method to accelerate optimization-based inference to invert a forward model. We propose an approach that learns a new space that is easier than the original input space to optimize with gradient descent at testing time. Our experiments and analysis on three different applications in computer vision have shown that by learning this mapping function, optimization becomes more efficient and generalizes better to out-of-distribution data. Through quantitative and qualitative analysis, we found that such improvement in optimization performance comes from a more efficient loss landscape. Since optimization-based inference has many advantages over encoder-based inference, we believe methods to accelerate them will have many impacts in a variety of applications." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgement This research is based on work partially supported by the NSF NRI Award 1925157, NSF STC LEAP, DARPA MCS program, and DARPA CCU program." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2247" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 289, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 289, + 144 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 289, + 144 + ], + "type": "text", + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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Springer, 2016. 2" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "2250" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_content_list.json b/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3505fcd7f069350be854725fd6083448f3e6f024 --- /dev/null +++ b/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_content_list.json @@ -0,0 +1,2103 @@ +[ + { + "type": "text", + "text": "Large Selective Kernel Network for Remote Sensing Object Detection", + "text_level": 1, + "bbox": [ + 135, + 130, + 833, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yuxuan Li†, Qibin Hou, Zhaohui Zheng, Ming-Ming Cheng, Jian Yang* and Xiang Li* \nVCIP, CS, Nankai University", + "bbox": [ + 135, + 180, + 839, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "yuxuan.li.17@ucl.ac.uk†, {csjyang, xiang.li.implus}@nankai.edu.cn*", + "bbox": [ + 194, + 218, + 774, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent research on remote sensing object detection has largely focused on improving the representation of oriented bounding boxes but has overlooked the unique prior knowledge presented in remote sensing scenarios. Such prior knowledge can be useful because tiny remote sensing objects may be mistakenly detected without referencing a sufficiently long-range context, which can vary for different objects. This paper considers these priors and proposes the lightweight Large Selective Kernel Network (LSKNet). LSKNet can dynamically adjust its large spatial receptive field to better model the ranging context of various objects in remote sensing scenarios. To our knowledge, large and selective kernel mechanisms have not been previously explored in remote sensing object detection. Without bells and whistles, our lightweight LSKNet sets new state-of-the-art scores on standard benchmarks, i.e., HRSC2016 $(98.46\\% \\text{mAP})$ , DOTA-v1.0 $(81.85\\% \\text{mAP})$ , and FAIR1M-v1.0 $(47.87\\% \\text{mAP})$ .", + "bbox": [ + 73, + 300, + 473, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 601, + 209, + 617 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Remote sensing object detection [47, 57, 82] focuses on identifying and locating objects of interest in aerial images, such as vehicles, ships or aircraft. In recent years, one mainstream trend has been to generate bounding boxes that accurately fit the orientation of the objects being detected rather than simply drawing horizontal boxes around them. Consequently, much research has focused on improving the representation of oriented bounding boxes for remote sensing object detection. This has largely been achieved through the development of specialized detection frameworks (i.e., RoI Transformer [12], Oriented R-CNN [69], and R3Det [75]) and oriented box encoding (i.e., gliding vertex [71] and midpoint offset box encoding [69]). Additionally, several loss functions, including GWD [77], KLD [79], and Modulated Loss [54], have been further proposed to enhance the", + "bbox": [ + 73, + 627, + 470, + 854 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c3bb16fa2ce72726663a286ca45a641a4d1fbd556a43bec0cac9b91882fe8b49.jpg", + "image_caption": [ + "Ship or Vehicle?" + ], + "image_footnote": [], + "bbox": [ + 501, + 280, + 560, + 308 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6db7f7b631b5099d1fc4667c304046d7449724738601f65a7fa3b3c761dc2f65.jpg", + "image_caption": [ + "Figure 1. Successfully detecting remote sensing objects requires using a wide range of contextual information. Detectors with a limited receptive field may easily lead to incorrect results." + ], + "image_footnote": [], + "bbox": [ + 571, + 267, + 730, + 391 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/910dff187a27be78cab0ab7c96a028b932c451fc85de589cb9fbfa24ca5b559a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 268, + 890, + 391 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "performance of these approaches.", + "bbox": [ + 500, + 454, + 723, + 468 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite these advances, relatively few works have considered the strong prior knowledge of remote sensing images. Aerial images are typically captured at high resolutions from a bird's eye view. In particular, most objects in aerial images may be small and difficult to identify based on their appearance alone. Instead, recognizing these objects relies on their context, as the surrounding environment can provide valuable clues about their shape, orientation, and other characteristics. According to an analysis of the remote sensing data, we identify two important priors:", + "bbox": [ + 496, + 469, + 892, + 619 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Accurate detection often requires a wide range of contextual information. As illustrated in Fig. 1, the limited context used by object detectors in remote sensing images can often lead to incorrect classifications. Rather than their appearance, the context distinguishes the ship from the vehicle.", + "- The contextual information required for different objects is very different. As shown in Fig. 2, the soccer field requires relatively less contextual information because of the unique distinguishable court borderlines. In contrast, the roundabout may require more context information to distinguish between gardens and ring-like buildings. Intersections, especially those partially covered by trees, require an extremely large receptive field due to the long-range dependencies between the intersecting roads." + ], + "bbox": [ + 517, + 627, + 893, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the challenge of accurately detecting objects", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors.", + "bbox": [ + 98, + 863, + 227, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Team URL: https://github.com/IMPlus-PCALab", + "bbox": [ + 78, + 876, + 398, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Project page: https://github.com/zcablii/LSKNet", + "bbox": [ + 78, + 888, + 411, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16794", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/84fbfd0eeb92108394a7ef9b0a7e672251aa231fbdfdf86c42802e44b6f03bb8.jpg", + "image_caption": [ + "Figure 2. The wide range of contextual information required for different object types is very different by human criteria. The objects with red boxes are the exact ground-truth annotations." + ], + "image_footnote": [], + "bbox": [ + 107, + 85, + 441, + 281 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "in remote sensing images, which often require a wide and dynamic range of contextual information, we propose a novel lightweight detection backbone called Large Selective Kernel Network (LSKNet). Our approach involves dynamically adjusting the receptive field of the feature extraction backbone to more effectively process the varying wide context of the objects being detected. This is achieved through a spatial selective mechanism, which efficiently weights the features processed by a sequence of large depth-wise kernels and then spatially merge them. The weights of these kernels are determined dynamically based on the input, allowing the model to adaptively use different large kernels and adjust the receptive field for each target in space as needed.", + "bbox": [ + 75, + 349, + 468, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To our knowledge, the proposed LSKNet is the first to investigate using large and selective kernels for remote sensing object detection. Despite its simplicity and lightweight nature, our model achieves state-of-the-art performance on three popular datasets: HRSC2016 (98.46% mAP), DOTAv1.0 (81.85% mAP), and FAIR1M-v1.0 (47.87% mAP), surpassing previously published results. Furthermore, we demonstrate that our model's behaviour aligns with the two priors above, which in turn verifies the effectiveness of the proposed mechanism.", + "bbox": [ + 75, + 561, + 468, + 712 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 729, + 218, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Remote Sensing Object Detection Framework", + "text_level": 1, + "bbox": [ + 76, + 753, + 464, + 771 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "High-performance remote sensing object detectors often rely on the RCNN [56] framework, which consists of a region proposal network and regional CNN detection heads. The RPN proposes high-quality regions of interest (RoIs) from the backbone feature maps, while the regional CNN detection heads are responsible for object classification and bounding box regression. Several variations on the RCNN framework have been proposed in recent years. The two-", + "bbox": [ + 75, + 780, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "stage RoI transformer [12] uses fully-connected layers to rotate candidate horizontal anchor boxes in the first stage, and then features within the boxes are extracted for further regression and classification. SCRDet [78] uses an attention mechanism to reduce background noise and improve the modelling of crowded and small objects. Oriented RCNN [69] and Gliding Vertex [71] introduce new box encoding systems to address the instability of training losses caused by rotation angle periodicity. Some approaches [32, 61, 87] treat remote sensing detection as a point detection task [74], providing an alternative way of addressing remote sensing detection problems.", + "bbox": [ + 496, + 90, + 890, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rather than relying on the proposed anchors, one-stage detection frameworks classify and regress oriented bounding boxes directly from grid densely sampled anchors. The one-stage S²A network [23] extracts robust object features via oriented feature alignment and orientation-invariant feature extraction. DRN [50], on the other hand, leverages attention mechanisms to dynamically refined the backbone's extracted features for more accurate predictions. In contrast with Oriented RCNN and Gliding Vertex, RSDet [54] addresses the discontinuity of regression loss by introducing a modulated loss. LD [86] enhances the localization quality of oriented bounding boxes by distillation. AOPG [6] and R3Det [75] adopt a progressive regression approach, refining bounding boxes from coarse to fine granularity. In addition to CNN, AO2-DETR [9] introduces a transformer-based detection framework, DETR [4], into remote sensing detection tasks, which brings more research diversity.", + "bbox": [ + 496, + 273, + 890, + 529 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While these approaches have achieved promising results in addressing the issue of rotation variance, they do not consider the strong and valuable prior information presented in aerial images. Instead, our approach uses the large kernel and spatial selective mechanism to better model these priors without modifying the current detection framework.", + "bbox": [ + 496, + 531, + 890, + 621 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Large Kernel Networks", + "text_level": 1, + "bbox": [ + 500, + 633, + 718, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformer-based [59] models, such as the Vision Transformer (ViT) [1, 11, 14, 53, 60], Swin transformer [25, 39, 51, 64, 70, 83], and pyramid transformer [62, 67], have gained popularity in computer vision. Research [17, 45, 55, 72, 85] has demonstrated that the large receptive field is a key factor in their success. Recent work has shown that well-designed convolutional networks with large receptive fields can also be highly competitive with transformer-based models. For example, ConvNeXt [40] uses $7 \\times 7$ depth-wise convolutions in its backbone, resulting in significant performance improvements in downstream tasks. In addition, RepLKNet [13] even uses a $31 \\times 31$ convolutional kernel via re-parameterization, achieving compelling performance. A subsequent work SLaK [38], further expands the kernel size to $51 \\times 51$ through kernel decomposition and sparse group techniques. RF-Next [18] automatically searches for a fixed", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16795", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c5a076b661b5d458804786abcc0a7b8380a683b072777292ba4b9ea3993b0fdd.jpg", + "image_caption": [ + "Figure 3. Architectural comparison between our proposed LSK module and other representative selective mechanism modules. K: Kernel." + ], + "image_footnote": [], + "bbox": [ + 99, + 106, + 251, + 257 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2cebb7e29b6ec97ac377dd67b9c69e0c2d7594fc42c85702b004e2241f3172b8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 104, + 449, + 257 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8ce330c0dfca81cc999baa38a4d05a2bc2de3eed51e13836546f3c7d641b9c8f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 527, + 107, + 663, + 257 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a52af307ee375073e004c1f68353bc71e84e097d84aadeed78c7291c2e00b1e7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 740, + 107, + 864, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "large kernel for various tasks. VAN [19] introduces an efficient decomposition of large kernels as convolutional attention. Similarly, SegNeXt [20] and Conv2Former [28] demonstrate that large kernel convolution plays an important role in modulating the convolutional features with a richer context.", + "bbox": [ + 75, + 289, + 467, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although large kernel convolutions have received attention in general object recognition, there has been a lack of research examining their significance in remote sensing detection. As previously noted in Sec. 1, aerial images possess unique characteristics that make large kernels particularly well-suited for remote sensing. As far as we know, our work represents the first attempt to introduce large kernel convolutions for remote sensing and to examine their importance in this field.", + "bbox": [ + 75, + 380, + 467, + 515 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Attention/Selective Mechanism", + "text_level": 1, + "bbox": [ + 76, + 527, + 352, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The attention mechanism [21] is a simple but effective way to enhance neural representations for various tasks. The channel attention SE block [30] uses global average information to reweight feature channels, while spatial attention modules like GENet [29], GCNet [3], and SGE [34] enhance a network's ability to model context information via spatial masks. CBAM [66] and BAM [52] combine both channel and spatial attention.", + "bbox": [ + 75, + 551, + 467, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In addition to channel/spatial attention mechanisms, kernel selection is a self-adaptive and effective technique for dynamic context modelling. CondConv [73] and Dynamic convolution [5] use parallel kernels to adaptively aggregate features from multiple convolution kernels. SKNet [33] introduces multiple branches with different convolutional kernels and selectively combines them along the channel dimension. ResNeSt [84] extends the idea of SKNet by partitioning the input feature map into several groups. Similarly to the SKNet, SCNet [37] uses branch attention to capturing richer information and spatial attention to improve localization ability. Deformable Convnets [8, 89] introduce a flexible kernel shape for convolution units.", + "bbox": [ + 75, + 672, + 467, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach bears the most similarity to SKNet [33]. However, there are two key distinctions between the two", + "bbox": [ + 76, + 869, + 467, + 898 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4d4de59c7dcfa5bf07dbaba2286cf630d5a38a4e92187d05be2691e3bf643343.jpg", + "image_caption": [ + "Figure 4. A block of LSKNet." + ], + "image_footnote": [], + "bbox": [ + 558, + 289, + 815, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "methods. Firstly, our proposed selective mechanism relies explicitly on a sequence of large kernels via decomposition, a departure from most existing attention-based approaches. Secondly, our method adaptively aggregates information across large kernels in the spatial dimension rather than the channel dimension utilized by SKNet. This design is more intuitive and effective for remote sensing tasks because channel-wise selection fails to model the spatial variance for different targets across the image space. The detailed structural comparisons are listed in Fig. 3.", + "bbox": [ + 496, + 542, + 890, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 500, + 712, + 598, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. LSKNet Architecture", + "text_level": 1, + "bbox": [ + 500, + 738, + 700, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall architecture of the LSKNet backbone is simply built upon repeated LSKNet Blocks. Fig 4 illustrates an LSKNet Block, which is inspired by ConvNeXt [41], MetaFormer [81], PVT-v2 [63], Conv2Former [28] and VAN [19]. Each LSKNet block consists of two residual sub-blocks: the Large Kernel Selection (LK Selection) subblock and the Feed-forward Network (FFN) sub-block.", + "bbox": [ + 496, + 762, + 890, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The LK Selection sub-block dynamically adjusts the network's receptive field as needed. The core LSK module", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16796", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4fc7ef940ab39965d1a30be538f026fe14d1fd03f7677f06bb30cbb8a0c2c15d.jpg", + "image_caption": [ + "Figure 5. A conceptual illustration of LSK module." + ], + "image_footnote": [], + "bbox": [ + 122, + 93, + 851, + 247 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/ca9b26db964d6f1888e9278be6cfff170f668af2eead7236694fadac1aab4e9f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Model{C1,C2,C3,C4}{D1,D2,D3,D4}#P
★LSKNet-T{32,64,160,256}{3,3,5,2}4.3M
★LSKNet-S{64,128,320,512}{2,2,4,2}14.4M
", + "bbox": [ + 83, + 277, + 460, + 323 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/0eeb9c3ea461c102fb676ab3812ac0d9759e0080fa09f9b72b6da55112f79d51.jpg", + "table_caption": [ + "Table 1. Variants of LSKNet used in this paper. $C_i$ : feature channel number; $D_i$ : number of LSKNet blocks of each stage $i$ ." + ], + "table_footnote": [], + "table_body": "
RF(k,d) sequence#PFLOPs
23(23,1)40.4K42.4G
(5,1) → (7,3)11.3K11.9G
29(29,1)60.4K63.3G
(3,1) → (5,2) → (7,3)11.3K13.6G
", + "bbox": [ + 89, + 367, + 455, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 2. Theoretical efficiency comparisons of two representative examples by expanding a single large depth-wise kernel into a sequence, given channels being 64. $k$ : kernel size; $d$ : dilation.", + "bbox": [ + 76, + 446, + 468, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(Fig. 5) is embedded in the LK Selection sub-block. It consists of a sequence of large kernel convolutions and a spatial kernel selection mechanism, which will be elaborated on later. The FFN sub-block is used for channel mixing and feature refinement, which consists of a sequence of a fully connected layer, a depth-wise convolution, a GELU [26] activation, and a second fully connected layer.", + "bbox": [ + 75, + 503, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The detailed configuration of different variants of LSKNet used in this paper is listed in Tab. 1.", + "bbox": [ + 76, + 609, + 470, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Large Kernel Convolutions", + "text_level": 1, + "bbox": [ + 76, + 648, + 321, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to the prior (2), as stated in Sec. 1, it is suggested to model a series of multiple long-range contexts for adaptive selection. Therefore, we propose constructing a larger kernel convolution by explicitly decomposing it into a sequence of depth-wise convolutions with a large growing kernel and increasing dilation. Specifically, for the $i$ -th depth-wise convolution, the expansion of the kernel size $k$ , dilation rate $d$ , and the receptive field $RF$ are defined as follows:", + "bbox": [ + 75, + 672, + 468, + 808 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nk _ {i - 1} \\leq k _ {i}; d _ {1} = 1, d _ {i - 1} < d _ {i} \\leq R F _ {i - 1}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 821, + 468, + 838 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR F _ {1} = k _ {1}, R F _ {i} = d _ {i} \\left(k _ {i} - 1\\right) + R F _ {i - 1}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 845, + 468, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The increasing kernel size and dilation rate ensure that the receptive field expands quickly enough. We set an upper", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "bound on the dilation rate to guarantee that the dilation convolution does not introduce gaps between feature maps. For instance, we can decompose a large kernel into 2 or 3 depth-wise convolutions as in Tab. 2, which have a theoretical receptive field of 23 and 29, respectively.", + "bbox": [ + 496, + 280, + 890, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are two advantages of the proposed designs. First, it explicitly yields multiple features with various large receptive fields, which makes it easier for the later kernel selection. Second, sequential decomposition is more efficient than simply applying a single larger kernel. As shown in Tab. 2, under the same resulted theoretical receptive field, our decomposition greatly reduces the number of parameters compared to the standard large convolution kernels. To obtain features with rich contextual information from different ranges for input $\\mathbf{X}$ , a series of decomposed depth-wise convolutions with different receptive fields are applied:", + "bbox": [ + 496, + 354, + 892, + 522 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {U} _ {0} = \\mathbf {X}, \\quad \\mathbf {U} _ {i + 1} = \\mathcal {F} _ {i} ^ {d w} (\\mathbf {U} _ {i}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 529, + 890, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_i^{dw}(\\cdot)$ are depth-wise convolutions with kernel $k_{i}$ and dilation $d_{i}$ . Assuming there are $N$ decomposed kernels, each of which is further processed by a $1\\times 1$ convolution layer $\\mathcal{F}^{1\\times 1}(\\cdot)$ :", + "bbox": [ + 496, + 555, + 890, + 616 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {U}} _ {i} = \\mathcal {F} _ {i} ^ {1 \\times 1} \\left(\\mathbf {U} _ {i}\\right), \\text {f o r} i \\text {i n} [ 1, N ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 625, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "allowing channel mixing for each spatial feature vector. Then, a selection mechanism is proposed to dynamically select kernels for various objects based on the multi-scale features obtained, which would be introduced next.", + "bbox": [ + 496, + 652, + 890, + 713 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Spatial Kernel Selection", + "text_level": 1, + "bbox": [ + 500, + 720, + 720, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enhance the network's ability to focus on the most relevant spatial context regions for detecting targets, we use a spatial selection mechanism to spatially select the feature maps from large convolution kernels at different scales. Firstly, we concatenate the features obtained from different kernels with different ranges of receptive field:", + "bbox": [ + 496, + 744, + 890, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {U}} = \\left[ \\widetilde {\\mathbf {U}} _ {1}; \\dots ; \\widetilde {\\mathbf {U}} _ {i} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 842, + 890, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and then efficiently extract the spatial relationship by applying channel-based average and maximum pooling (denoted", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16797", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "as $\\mathcal{P}_{avg}(\\cdot)$ and $\\mathcal{P}_{max}(\\cdot)$ to $\\tilde{\\mathbf{U}}$ :", + "bbox": [ + 76, + 89, + 282, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S A} _ {a v g} = \\mathcal {P} _ {a v g} (\\widetilde {\\mathbf {U}}), \\mathbf {S A} _ {m a x} = \\mathcal {P} _ {m a x} (\\widetilde {\\mathbf {U}}), \\qquad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 116, + 468, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{SA}_{avg}$ and $\\mathbf{SA}_{max}$ are the average and maximum pooled spatial feature descriptors. To allow information interaction among different spatial descriptors, we concatenate the spatially pooled features and use a convolution layer $\\mathcal{F}^{2\\rightarrow N}(\\cdot)$ to transform the pooled features (with 2 channels) into $N$ spatial attention maps:", + "bbox": [ + 76, + 146, + 468, + 238 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathbf {S A}} = \\mathcal {F} ^ {2 \\rightarrow N} \\left(\\left[ \\mathbf {S A} _ {a v g}; \\mathbf {S A} _ {m a x} \\right]\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 247, + 468, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each of the spatial attention maps, $\\widehat{\\mathbf{SA}_i}$ , a sigmoid activation function is applied to obtain the individual spatial selection mask for each of the decomposed large kernels:", + "bbox": [ + 76, + 279, + 468, + 325 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {S A} _ {i}} = \\sigma (\\widehat {\\mathbf {S A} _ {i}}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 335, + 468, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma(\\cdot)$ denotes the sigmoid function. The feature maps from the sequence of decomposed large kernels are weighted by their corresponding spatial selection masks and then fused by a convolution layer $\\mathcal{F}(\\cdot)$ to obtain the attention feature $\\mathbf{S}$ :", + "bbox": [ + 76, + 364, + 468, + 441 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} = \\mathcal {F} \\left(\\sum_ {i = 1} ^ {N} \\left(\\widetilde {\\mathbf {S A}} _ {i} \\cdot \\widetilde {\\mathbf {U}} _ {i}\\right)\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 449, + 468, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final output of the LSK module is the element-wise product between the input feature $\\mathbf{X}$ and $\\mathbf{S}$ , similarly in [19, 20, 28]:", + "bbox": [ + 76, + 500, + 468, + 545 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} = \\mathbf {X} \\cdot \\mathbf {S}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 232, + 545, + 468, + 560 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 5 shows a detailed conceptual illustration of an LSK module where we intuitively demonstrate how the large selective kernel works by adaptively collecting the corresponding large receptive field for different objects.", + "bbox": [ + 76, + 566, + 468, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 641, + 207, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 665, + 178, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "HRSC2016 [42] is a high-resolution remote sensing dataset which is collected for ship detection. It consists of 1,061 images which contain 2,976 instances of ships.", + "bbox": [ + 76, + 688, + 468, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DOTA-v1.0 [68] consists of 2,806 remote sensing images. It contains 188,282 instances of 15 categories: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), and Helicopter (HC).", + "bbox": [ + 76, + 734, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FAIR1M-v1.0 [58] is a recently published remote sensing dataset that consists of 15,266 high-resolution images and more than 1 million instances. It contains 5 categories and 37 sub-categories objects.", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 90, + 715, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our experiment, we report the results of the oriented object detection models on HRSC2016, DOTA-v1.0 and FAIR1M-v1.0 datasets. To ensure fairness, we follow the same dataset processing approach as other mainstream methods [23, 24, 69]. For DOTA-v1.0 and FAIR1M-v1.0 datasets, we adopt multi-scale training and testing strategy by first rescaling the images into three scales (0.5, 1.0, 1.5), and then cropping each scaled image into $1024 \\times 1024$ sub-images with a patch overlap of 500 pixels. For the HRSC2016 dataset, we rescale the images by setting the longer side of the image to 800 pixels, without changing their aspect ratios.", + "bbox": [ + 496, + 113, + 890, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During our experiments, the backbones are first pretrained on the ImageNet-1K [10] dataset and then finetuned on the target remote sensing benchmarks. In ablation studies, we adopt the 100-epoch backbone pretraining schedule for experimental efficiency (Tab. 3, 5, 4, 6, 7). We adopt a 300-epoch backbone pretraining strategy to pursue higher accuracy in main results (Tab. 8, 9, 10), similarly to [6,23,69,75]. In main results (Tab. 8, 9), the \"Pre.\" column stands for the dataset on which the networks/backbones are pretrained (IN: Imagenet [10] dataset; CO: Microsoft COCO [36] dataset; MA: Million-AID [43] dataset). Unless otherwise stated, LSKNet is defaulting to be built within the framework of Oriented RCNN [69] due to its compelling performance and efficiency. All the models are trained on the training and validation sets and tested on the testing set. Following [69], we train the models for 36 epochs on the HRSC2016 datasets and 12 epochs on the DOTA-v1.0 and FAIR1M-v1.0 datasets, with the AdamW [44] optimizer. The initial learning rate is set to 0.0004 for HRSC2016, and 0.0002 for the other two datasets, with a weight decay of 0.05. The models are implemented under MMRotate [88] framework. We use 8 RTX3090 GPUs with a batch size of 8 for model training and use a single RTX3090 GPU for testing. All the FLOPs we report in this paper are calculated with a $1024 \\times 1024$ image input.", + "bbox": [ + 496, + 295, + 892, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 681, + 651, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we report ablation study results on the DOTA-v1.0 test set to investigate its effectiveness.", + "bbox": [ + 500, + 704, + 888, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Large Kernel Decomposition. Deciding on the number of kernels to decompose is a critical choice for the LSK module. We follow Eq. (1) to configure the decomposed kernels. The results of the ablation study on the number of large kernel decompositions, when the theoretical receptive field is fixed at 29, are shown in Tab. 3. It suggests that decomposing the large kernel into two depth-wise large kernels results in a good trade-off between speed and accuracy, achieving the best performance in terms of both FPS (frames per second) and mAP (mean average precision).", + "bbox": [ + 496, + 734, + 890, + 885 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Receptive Field Size and Selection Type. Based on our", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16798", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/df43f8e7b611b22b7873d006f922653fd2df8bebbabbeada48cf0144622c1fca.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
(k,d) sequenceRFNum.FPSmAP (%)
(29,1)29118.680.66
(5,1)→(7,4)29220.580.91
(3,1)→(5,2)→(7,3)29319.280.77
", + "bbox": [ + 81, + 89, + 460, + 148 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f03af539651190f12e54b6ff334d2c7cfcf41ae9a09776bd1954b6eed25fc345.jpg", + "table_caption": [ + "Table 3. The effects of the number of decomposed large kernels on the inference FPS and mAP, given the theoretical receptive field being 29. We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. Decomposing the large kernel into two depth-wise kernels achieves the best performance of speed and accuracy." + ], + "table_footnote": [], + "table_body": "
(k1, d1)(k2, d2)CSSSRFFPSmAP (%)
(3, 1)(5, 2)--1122.180.80
(5, 1)(7, 3)--2321.780.94
(5, 1)(7, 4)--2920.580.91
(7, 1)(9, 4)--3921.380.84
(5, 1)(7, 3)✓-2319.680.57
(5, 1)(7, 3)-✓2320.781.31
", + "bbox": [ + 84, + 237, + 457, + 340 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/487fe5e23e6f1e7b52f24ede47ea63da15e9e4e71da7e6c009d33a71ba27f11a.jpg", + "table_caption": [ + "Table 4. The effectiveness of the key design components of the LSKNet when the large kernel is decomposed into a sequence of two depth-wise kernels. CS: channel selection (likewise in SKNet [33]); SS: spatial selection (ours). We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. The LSKNet achieves the best performance when using a reasonably large receptive field with spatial selection." + ], + "table_footnote": [], + "table_body": "
PoolingFPSmAP (%)
Max.Avg.
✓20.781.23
✓20.781.12
✓✓20.781.31
", + "bbox": [ + 166, + 455, + 377, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "evaluations presented in Tab. 3, we find that the optimal solution for our proposed LSKNet is to decompose the large kernel into two depth-wise kernels in series. Furthermore, Tab. 4 shows that excessively small or large receptive fields can hinder the performance of the LSKNet, and a receptive field size of approximately 23 is determined to be the most effective. In addition, our experiments indicate that the proposed spatial selection approach is more effective than channel attention (similarly in SKNet [33]) for remote sensing object detection tasks. It suggests that in detection tasks, spatial information is more critical.", + "bbox": [ + 75, + 611, + 467, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pooling Layers in Spatial Selection. We conduct experiments to determine the optimal pooling layers for spatial selection, as reported in Tab. 5. The results suggest that using both max and average pooling in the spatial selection component of our LSK module provides the best performance without sacrificing inference speed.", + "bbox": [ + 75, + 777, + 467, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance of LSKNet backbone under different detection frameworks. To validate the generality and ef", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cac52e7c077eba67ec70bb466fc719b26672a1b01e4d3f816258a70eb7b027ab.jpg", + "table_caption": [ + "Table 5. Ablation study on the effectiveness of the maximum and average pooling in spatial selection of our proposed LSK module. We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. The best result is obtained when using both." + ], + "table_footnote": [], + "table_body": "
FrameworksResNet-18★ LSKNet-T
ORCNN [69]79.2781.31 (+2.04)
RoI Trans. [12]78.3280.89 (+2.57)
S²A-Net [23]76.8280.15 (+3.33)
R3Det [75]74.1678.39 (+4.23)
#P (backbone only)11.2M4.3M (-62%)
FLOPs (backbone only)38.1G19.1G (-50%)
", + "bbox": [ + 522, + 89, + 870, + 191 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/df9368342ad6a44dcc1865af32885fbf79574ae6b6599f0dcbe9eaaaaeb9ba9f.jpg", + "table_caption": [ + "Table 6. Comparison of LSKNet-T and ResNet-18 as backbones with different detection frameworks on DOTA-v1.0. The LSKNet-T backbone is pretrained on ImageNet for 100 epochs. The lightweight LSKNet-T achieves significantly higher mAP in various frameworks than ResNet-18." + ], + "table_footnote": [], + "table_body": "
GroupModel (backbone only)#PFLOPsmAP (%)
BaselineResNet-1811.2M38.1G79.27
Large KernelVAN-B1 [19]13.4M52.7G81.15
ConvNeXt V2-N [65]15.0M51.2G80.81
MSCAN-S [20]13.1M45.0G81.12
Selective AttentionSKNet-26 [33]14.5M58.5G80.67
ResNeSt-14 [84]8.6M57.9G79.51
SCNet-18 [37]14.0M50.7G79.69
Ours★ LSKNet-S14.4M54.4G81.48
Prev BestCSPNeXt [46]26.1M87.6G81.33
", + "bbox": [ + 504, + 272, + 883, + 421 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b47c85492142e31e01aa4a8c0cafafd92269f7f7e10d8f8d725e37060cf5375a.jpg", + "table_caption": [ + "Table 7. Comparison on LSKNet-S and other (large kernel/selective attention) backbones under O-RCNN [69] framework on DOTA-v1.0, except that the Prev Best is under RT-MDet [46] framework. All backbones are pretrained on ImageNet for 100 epochs. Our LSKNet achieves the best mAP under similar complexity budgets." + ], + "table_footnote": [], + "table_body": "
MethodPre.mAP(07)↑mAP(12)↑#P↓FLOPs↓
DRN [50]IN-92.70--
CenterMap [61]IN-92.8041.1M198G
Rol Trans. [12]IN86.20-55.1M200G
G. V. [71]IN88.20-41.1M198G
R3Det [75]IN89.2696.0141.9M336G
DAL [48]IN89.77-36.4M216G
GWD [77]IN89.8597.3747.4M456G
S2ANet [23]IN90.1795.0138.6M198G
AOPG [6]IN90.3496.22--
ReDet [24]IN90.4697.6331.6M-
O-RCNN [69]IN90.5097.6041.1M199G
RTMDet [46]CO90.6097.1052.3M205G
★LSKNet-TIN90.5498.1321.0M124G
★LSKNet-SIN90.6598.4631.0M161G
", + "bbox": [ + 503, + 521, + 887, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 8. Comparison with state-of-the-art methods on the HRSC2016 dataset. The LSKNet-S backbone is pretrained on ImageNet for 300 epochs, the same with most compared methods [23,69,75]. mAP (07/12): VOC 2007 [15]/2012 [16] metrics.", + "bbox": [ + 498, + 742, + 890, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "fectiveness of our proposed LSKNet backbone, we evaluate its performance under various remote sensing detection frameworks, including two-stage frameworks O-RCNN [69] and RoI Transformer [12] as well as one-stage frameworks $\\mathrm{S}^2\\mathrm{A}$ -Net [23] and R3Det [75]. The re", + "bbox": [ + 498, + 824, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16799", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1caf5c0dfa09ac0787b641816b3ac2732266c3e421c5f4613c11e0073720bbcd.jpg", + "table_caption": [ + "Method |Pre. $\\left|\\mathbf{mAP}\\uparrow\\right|\\# \\mathbf{P}\\downarrow$ FLOPs↓ PL BD BR GTF SV LV SH TC BC ST SBF RA HA SP HC" + ], + "table_footnote": [], + "table_body": "
One-stage
R3Det [75]IN76.4741.9M336G89.8083.7748.1166.7778.7683.2787.8490.8285.3885.5165.5762.6867.5378.5672.62
CFA [22]IN76.67--89.0883.2054.3766.8781.2380.9687.1790.2184.3286.0952.3469.9475.5280.7667.96
DAFNe [31]IN76.95--89.4086.2753.7060.5182.0481.1788.6690.3783.8187.2753.9369.3875.6181.2670.86
SASM [27]IN79.17--89.5485.9457.7378.4179.7884.1989.2590.8758.8087.2763.8267.8178.6779.3569.37
AO2-DETR [9]IN79.2274.3M304G89.9584.5256.9074.8380.8683.4788.4790.8786.1288.5563.2165.0979.0982.8873.46
\\( S^2ANet \\) [23]IN79.42--88.8983.6057.7481.9579.9483.1989.1190.7884.8787.8170.3068.2578.3077.0169.58
R3Det-GWD [77]IN80.2341.9M336G89.6684.9959.2682.1978.9784.8387.7090.2186.5486.8573.4767.7776.9279.2274.92
RTMDet-R [46]IN80.5452.3M205G88.3684.9657.3380.4680.5884.8888.0890.9086.3287.5769.2970.6178.6380.9779.24
R3Det-KLD [79]IN80.6341.9M336G89.9285.1359.1981.3378.8284.3887.5089.8087.3387.0072.5771.3577.1279.3478.68
RTMDet-R [46]CO81.3352.3M205G88.0186.1758.5482.4481.3084.8288.7190.8988.7787.3771.9671.1881.2381.4077.13
Two-stage
SCRDet [78]IN72.61--89.9880.6552.0968.3668.3660.3272.4190.8587.9486.8665.0266.6866.2568.2465.21
Rol Trans. [12]IN74.6155.1M200G88.6582.6052.5370.8777.9376.6786.8790.7183.8382.5153.9567.6174.6768.7561.03
G.V. [71]IN75.0241.1M198G89.6485.0052.2677.3473.0173.1486.8290.7479.0286.8159.5570.9172.9470.8657.32
CenterMap [61]IN76.0341.1M198G89.8384.4154.6070.2577.6678.3287.1990.6684.8985.2756.4669.2374.1371.5666.06
CSL [76]IN76.1737.4M236G90.2585.5354.6475.3170.4473.5177.6290.8486.1586.6969.6068.0473.8371.1068.93
ReDet [24]IN80.10--88.8182.4860.8380.8278.3486.0688.3190.8788.7787.0368.6566.9079.2679.7174.67
DODet [7]IN80.62--89.9685.5258.0181.2278.7185.4688.5990.8987.1287.8070.5071.5482.0677.4374.47
AOPG [6]IN80.66--89.8885.5760.9081.5178.7085.2988.8590.8987.6087.6571.6668.6982.3177.3273.10
O-RCNN [69]IN80.8741.1M199G89.8485.4361.0979.8279.7185.3588.8290.8886.6887.7372.2170.8082.4278.1874.11
KFloU [80]IN80.9358.8M206G89.4484.4162.2282.5180.1086.0788.6890.9087.3288.3872.8071.9578.9674.9575.27
RVSA [60]MA81.24114.4M414G88.9785.7661.4681.2779.9885.3188.3090.8485.0687.5066.7773.1184.7581.8877.58
★LSKNet-T (ours)IN81.3721.0M124G89.1484.9061.7883.5081.5485.8788.6490.8988.0287.3171.5570.7478.6679.8178.16
★LSKNet-S (ours)IN81.6431.0M161G89.5786.3463.1383.6782.2086.1088.6690.8988.4187.4271.7269.5878.8881.7776.52
★LSKNet-S* (ours)IN81.8531.0M161G89.6985.7061.4783.2381.3786.0588.6490.8888.4987.4071.6771.3579.1981.7780.86
", + "bbox": [ + 80, + 104, + 890, + 481 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1b7bd30d77ff0abe814eb9b58774dfece235c0993fcd64c4749db17a4bd9e907.jpg", + "table_caption": [ + "Table 9. Comparison with state-of-the-art methods on the DOTA-v1.0 dataset with multi-scale training and testing. The LSKNet backbones are pretrained on ImageNet for 300 epochs, similarly to [23, 69, 75]. *: With EMA finetune similarly to the compared methods [46]." + ], + "table_footnote": [], + "table_body": "
ModelG. V.* [71]RetinaNet* [35]C-RCNN* [2]F-RCNN* [56]RoI Trans.* [12]O-RCNN [69]★ LSKNet-T★ LSKNet-S
mAP(%)29.9230.6731.1832.1235.2945.6046.9347.87
", + "bbox": [ + 84, + 523, + 879, + 560 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 10. Comparison with state-of-the-art methods on the FAIR1M-v1.0 dataset. The LSKNet backbones are pretrained on ImageNet for 300 epochs, similarly to [23,69,75].*: Results are referenced from FAIR1M paper [58].", + "bbox": [ + 76, + 563, + 892, + 592 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sults in Tab. 6 show that our proposed LSKNet-T backbone significantly improves detection performance compared to ResNet-18, while using only $38\\%$ of its parameters and with $50\\%$ fewer FLOPs.", + "bbox": [ + 75, + 611, + 468, + 670 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with Other Large Kernel/Selective Attention Backbones. We also compare our LSKNet with 6 popular high-performance backbone models with large kernels or selective attention. As shown in Tab. 7, under similar model sizes and complexity budgets, our LSKNet outperforms all other models on the DOTA-v1.0 dataset.", + "bbox": [ + 75, + 671, + 470, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Main Results", + "text_level": 1, + "bbox": [ + 76, + 771, + 217, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on HRSC2016. We evaluated the performance of our LSKNet against 12 state-of-the-art methods on the HRSC2016 dataset. The results presented in Tab. 8 demonstrate that our LSKNet-S outperforms all other methods with an mAP of $90.65\\%$ and $98.46\\%$ under the PASCAL VOC 2007 [15] and VOC 2012 [16] metrics, respectively.", + "bbox": [ + 75, + 794, + 468, + 885 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on DOTA-v1.0. We compare our LSKNet with", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "20 state-of-the-art methods on the DOTA-v1.0 dataset, as reported in Tab. 9. Our LSKNet-T, LSKNet-S and LSKNet-S* achieve state-of-the-art with mAP of $81.37\\%$ , $81.64\\%$ and $81.85\\%$ respectively. Notably, our high-performing LSKNet-S reaches an inference speed of 18.1 FPS on 1024x1024 images with a single RTX3090 GPU.", + "bbox": [ + 496, + 611, + 890, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on FAIR1M-v1.0. We compare our LSKNet against 6 other models on the FAIR1M-v1.0 dataset, as shown in Tab. 10. The results reveal that our LSKNet-T and LSKNet-S perform exceptionally well, achieving state-of-the-art mAP scores of $46.93\\%$ and $47.87\\%$ respectively, surpassing all other models by a significant margin.", + "bbox": [ + 496, + 700, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Analysis", + "text_level": 1, + "bbox": [ + 500, + 801, + 602, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Detection Results Visualization. Visualization examples of detection results and Eigen-CAM [49] are shown in Fig. 6. LSKNet can capture much more context information relevant to the detected targets, leading to better performance in various hard cases, which justifies our prior (1).", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16800", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d7a8ed27195bfe79d5b31025d48d78e26b0cf161cd1c956ec42cbe49a8b53159.jpg", + "image_caption": [ + "(a) Robustness to obstacles" + ], + "image_footnote": [], + "bbox": [ + 99, + 89, + 395, + 356 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f1cf7274765a362675051a08069ec03e4afad2981538c85f047aa29184ccefb7.jpg", + "image_caption": [ + "(b) Accurate Object Classification" + ], + "image_footnote": [], + "bbox": [ + 400, + 90, + 630, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/20c4bb773aecb4dfaa342f1407399b8017616b0288915928d51eca7471115d0d.jpg", + "image_caption": [ + "(c) Accurate Object Localization", + "Figure 6. Eigen-CAM visualization of Oriented RCNN detection framework with ResNet-50 and LSKNet-S. Our proposed LSKNet can model a much long range of context information, leading to better performance in various hard cases." + ], + "image_footnote": [], + "bbox": [ + 635, + 90, + 867, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7ebedb060824893151b42938746c503367c232b389eb40f079979e13898ef94d.jpg", + "image_caption": [ + "Figure 7. Normalised Ratio $R_{c}$ of Expected Selective RF Area and GT Bounding Box Area for object categories in DOTA-v1.0. The relative range of context required for different object categories varies a lot. Examples of Bridge and Soccer-ball-field are given, where the visualized receptive field is obtained from Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model." + ], + "image_footnote": [], + "bbox": [ + 94, + 425, + 447, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Relative Context Range for Different Objects. To investigate the relative range of receptive field for each object category, we define $R_{c}$ as the Ratio of Expected Selective RF Area and GT Bounding Box Area for category $c$ :", + "bbox": [ + 75, + 724, + 470, + 786 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nR _ {c} = \\frac {\\sum_ {i = 1} ^ {I _ {c}} A _ {i} / B _ {i}}{I _ {c}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 794, + 468, + 829 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nA _ {i} = \\sum_ {d = 1} ^ {D} \\sum_ {n = 1} ^ {N} | \\widetilde {\\mathbf {S A}} _ {n} ^ {d} \\cdot R F _ {n} |, B _ {i} = \\sum_ {j = 1} ^ {J _ {i}} \\operatorname {A r e a} \\left(\\mathrm {G T} _ {j}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 838, + 468, + 881 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $I_{c}$ is the number of images that contain the object", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2cea3cd55e85b011419d017dc50c7bf5a4d9ed7c8006248b9021ae97b8a82202.jpg", + "image_caption": [ + "Figure 8. Normalised Kernel Selection Difference in the LSKNet-T blocks for Bridge, Roundabout and Soccer-ball-field. B.i.j represents the j-th LSK block in stage i. A greater value is indicative of a dependence on a broader context." + ], + "image_footnote": [], + "bbox": [ + 517, + 425, + 870, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "category $c$ only. The $A_{i}$ is the sum of spatial selection activation in all LSK blocks for input image $i$ , where $D$ is the number of blocks in an LSKNet, and $N$ is the number of decomposed large kernels in an LSK module. $B_{i}$ is the total pixel area of all $J_{i}$ annotated oriented object bounding boxes (GT). We plot the normalized $R_{c}$ in Fig. 7 which represents the relative range of context required for different object categories for a better view.", + "bbox": [ + 496, + 654, + 890, + 775 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results suggest that the Bridge category stands out as requiring a greater amount of additional contextual information compared to other categories, primarily due to its similarity in features with roads and the necessity of contextual clues to ascertain whether it is enveloped by water. Conversely, the Court categories, such as Soccer-ball-field, necessitate minimal contextual information owing to their distinctive textural attributes, specifically the court bound-", + "bbox": [ + 496, + 780, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16801", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/512746ec2faceb1f4d3f46b3c748134cc1ed9cd1b4b997a852ac398188fdc385.jpg", + "image_caption": [ + "Bridge" + ], + "image_footnote": [], + "bbox": [ + 143, + 99, + 307, + 184 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/774d319db09b06d7db67c5605096e6b694516cfcfa790b7b542c00b5d59ea0f0.jpg", + "image_caption": [ + "Roundabout" + ], + "image_footnote": [], + "bbox": [ + 318, + 99, + 480, + 184 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/9beac37f773233e704842ffe7f81a23da7b961f5aed405c42fa90713a3b3e76d.jpg", + "image_caption": [ + "Small Vehicle" + ], + "image_footnote": [], + "bbox": [ + 493, + 99, + 656, + 184 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/7b6c39586a57fb0f698de55b9729fdff4f3165450b308e73fb43cf1a8c48e0b9.jpg", + "image_caption": [ + "Swimming Pool" + ], + "image_footnote": [], + "bbox": [ + 666, + 99, + 831, + 184 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/14125c3a6618e4fe0f91e7083dfe795d4cd53808d21b584b272c5953042ea552.jpg", + "image_caption": [ + "Ship" + ], + "image_footnote": [], + "bbox": [ + 143, + 208, + 307, + 294 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/3338637b3ebcde3702afc0b4ad60f0e84901eb63040f50d49a4f244714c25a21.jpg", + "image_caption": [ + "Storage tank" + ], + "image_footnote": [], + "bbox": [ + 316, + 208, + 480, + 294 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/c00d4df859a995651d0ab7c8e189bd3f6ead78cbb8164e8fa4ec9be90673080a.jpg", + "image_caption": [ + "Baseball diamond" + ], + "image_footnote": [], + "bbox": [ + 493, + 208, + 656, + 294 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/00181f35da6ab9d12fb110f9895f6c76c877a742f654a3f8d066eee074c16625.jpg", + "image_caption": [ + "Large Vehicle" + ], + "image_footnote": [], + "bbox": [ + 666, + 208, + 831, + 294 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/a2363b95673378b8e57f9ac7a60a2158b40c320a68867e0cbe9d13e7234cbc09.jpg", + "image_caption": [ + "Harbor" + ], + "image_footnote": [], + "bbox": [ + 143, + 316, + 307, + 402 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0a790f8e132bbd87c9e1c168efde2a477c333e87deed8d4e8136587cb3c4ec06.jpg", + "image_caption": [ + "Tennis court" + ], + "image_footnote": [], + "bbox": [ + 318, + 316, + 480, + 402 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/e496d46bd283e0c36260a9d4452442e62c87f0a15a93235d83e1178fe29dcc57.jpg", + "image_caption": [ + "Plane", + "Figure 9. Receptive field activation for more object categories in DOTA-v1.0, where the activation map is obtained from the Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model." + ], + "image_footnote": [], + "bbox": [ + 493, + 316, + 656, + 402 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0604412e8dcab7a2f7eacbee42261b7d60ceda6a452313709ee4c2b3385f7d7f.jpg", + "image_caption": [ + "Soccer-ball field" + ], + "image_footnote": [], + "bbox": [ + 666, + 316, + 831, + 402 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ary lines. It aligns with our knowledge and further supports prior (2) that the relative range of contextual information required for different object categories varies greatly.", + "bbox": [ + 75, + 460, + 468, + 507 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Kernel Selection Behaviour. We further investigate the kernel selection behaviour in our LSKNet. For object category $c$ , the Kernel Selection Difference $\\Delta A_{c}$ (i.e., larger kernel selection - smaller kernel selection) of an LSKNet-T block is defined as:", + "bbox": [ + 75, + 507, + 468, + 580 + ], + "page_idx": 8 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta A _ {c} = \\left| \\widetilde {\\mathbf {S A}} _ {\\text {l a r g e r}} - \\widetilde {\\mathbf {S A}} _ {\\text {s m a l l e r}} \\right|. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 595, + 468, + 614 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We demonstrate the normalised $\\Delta A_{c}$ over all images for three typical categories: Bridge, Roundabout and Soccerball-field and for each LSKNet-T block in Fig. 8. As expected, the participation of larger kernels of all blocks for Bridge is higher than that of Roundabout, and Roundabout is higher than Soccer-ball-field. This aligns with the common sense that Soccer-ball-field indeed does not require a large amount of context, since its own texture characteristics are already sufficiently distinct and discriminatory.", + "bbox": [ + 75, + 627, + 468, + 762 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We also surprisingly discover another selection pattern of LSKNet across network depth: LSKNet usually utilizes larger kernels in its shallow layers and smaller kernels in higher levels. This indicates that networks tend to quickly focus on capturing information from large receptive fields in low-level layers so that higher-level semantics can contain sufficient receptive fields for better discrimination.", + "bbox": [ + 75, + 763, + 468, + 868 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Spatial Activation Visualisations. Spatial activation map examples for more object categories in DOTA-v1.0", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "are shown in Fig. 9, where the activation map is obtained from Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model. The object categories are arranged in decreasing order from top left to bottom right based on the Ratio of Expected Selective RF Area and GT Bounding Box Area as illustrated in Fig. 7. The spatial activation visualisation results also demonstrate that the model's behaviour aligns with our proposed two priors and the above analysis, which in turn verifies the effectiveness of the proposed mechanism.", + "bbox": [ + 496, + 460, + 890, + 611 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 630, + 617, + 645 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose the Large Selective Kernel Network (LSKNet) for remote sensing object detection tasks, which is designed to utilize the inherent characteristics in remote sensing images: the need for a wider and adaptable contextual understanding. By adapting its large spatial receptive field, LSKNet can effectively model the varying contextual nuances of different object types. Extensive experiments demonstrate that our proposed lightweight model achieves state-of-the-art performance on competitive remote sensing benchmarks.", + "bbox": [ + 496, + 656, + 890, + 808 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement. This research was supported by the NSFC (NO. 62176130, 62206134, 62225604) and the Fundamental Research Funds for the Central Universities (Nankai University, 070-63233084, 070-63233089). Computation is supported by the Supercomputing Center of Nankai University.", + "bbox": [ + 496, + 830, + 890, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "16802", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yakoub Bazi, Laila Bashmal, Mohamad M. Al Rahhal, Reham Al Dayil, and Naif Al Ajan. Vision transformers for remote sensing image classification. Remote Sensing, 2021. 2", + "[2] Zhaowei Cai and Nuno Vasconcelos. Cascade R-CNN: Delving into high quality object detection. In CVPR, 2018. 7", + "[3] Yue Cao, Jiarui Xu, Stephen Lin, Fangyun Wei, and Han Hu. GCNet: Non-local networks meet squeeze-excitation networks and beyond. 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In CVPR, 2019. 3" + ], + "bbox": [ + 501, + 92, + 890, + 415 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "16805", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_model.json b/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3063bd0d93bf93189180fb4b577ed4bd0aab87ca --- /dev/null +++ b/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_model.json @@ -0,0 +1,3227 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.136, + 0.131, + 0.834, + 0.154 + ], + "angle": 0, + "content": "Large Selective Kernel Network for Remote Sensing Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.181, + 0.84, + 0.217 + ], + "angle": 0, + "content": "Yuxuan Li†, Qibin Hou, Zhaohui Zheng, Ming-Ming Cheng, Jian Yang* and Xiang Li* \nVCIP, CS, Nankai University" + }, + { + "type": "text", + "bbox": [ + 0.195, + 0.219, + 0.775, + 0.235 + ], + "angle": 0, + "content": "yuxuan.li.17@ucl.ac.uk†, {csjyang, xiang.li.implus}@nankai.edu.cn*" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.301, + 0.474, + 0.573 + ], + "angle": 0, + "content": "Recent research on remote sensing object detection has largely focused on improving the representation of oriented bounding boxes but has overlooked the unique prior knowledge presented in remote sensing scenarios. Such prior knowledge can be useful because tiny remote sensing objects may be mistakenly detected without referencing a sufficiently long-range context, which can vary for different objects. This paper considers these priors and proposes the lightweight Large Selective Kernel Network (LSKNet). LSKNet can dynamically adjust its large spatial receptive field to better model the ranging context of various objects in remote sensing scenarios. To our knowledge, large and selective kernel mechanisms have not been previously explored in remote sensing object detection. Without bells and whistles, our lightweight LSKNet sets new state-of-the-art scores on standard benchmarks, i.e., HRSC2016 \\((98.46\\% \\text{mAP})\\), DOTA-v1.0 \\((81.85\\% \\text{mAP})\\), and FAIR1M-v1.0 \\((47.87\\% \\text{mAP})\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.602, + 0.21, + 0.618 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.628, + 0.471, + 0.855 + ], + "angle": 0, + "content": "Remote sensing object detection [47, 57, 82] focuses on identifying and locating objects of interest in aerial images, such as vehicles, ships or aircraft. In recent years, one mainstream trend has been to generate bounding boxes that accurately fit the orientation of the objects being detected rather than simply drawing horizontal boxes around them. Consequently, much research has focused on improving the representation of oriented bounding boxes for remote sensing object detection. This has largely been achieved through the development of specialized detection frameworks (i.e., RoI Transformer [12], Oriented R-CNN [69], and R3Det [75]) and oriented box encoding (i.e., gliding vertex [71] and midpoint offset box encoding [69]). Additionally, several loss functions, including GWD [77], KLD [79], and Modulated Loss [54], have been further proposed to enhance the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.281, + 0.561, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.311, + 0.562, + 0.34 + ], + "angle": 0, + "content": "Ship or Vehicle?" + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.268, + 0.731, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.269, + 0.892, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.399, + 0.893, + 0.442 + ], + "angle": 0, + "content": "Figure 1. Successfully detecting remote sensing objects requires using a wide range of contextual information. Detectors with a limited receptive field may easily lead to incorrect results." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.455, + 0.724, + 0.469 + ], + "angle": 0, + "content": "performance of these approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.893, + 0.621 + ], + "angle": 0, + "content": "Despite these advances, relatively few works have considered the strong prior knowledge of remote sensing images. Aerial images are typically captured at high resolutions from a bird's eye view. In particular, most objects in aerial images may be small and difficult to identify based on their appearance alone. Instead, recognizing these objects relies on their context, as the surrounding environment can provide valuable clues about their shape, orientation, and other characteristics. According to an analysis of the remote sensing data, we identify two important priors:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.628, + 0.894, + 0.719 + ], + "angle": 0, + "content": "- Accurate detection often requires a wide range of contextual information. As illustrated in Fig. 1, the limited context used by object detectors in remote sensing images can often lead to incorrect classifications. Rather than their appearance, the context distinguishes the ship from the vehicle." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.727, + 0.894, + 0.879 + ], + "angle": 0, + "content": "- The contextual information required for different objects is very different. As shown in Fig. 2, the soccer field requires relatively less contextual information because of the unique distinguishable court borderlines. In contrast, the roundabout may require more context information to distinguish between gardens and ring-like buildings. Intersections, especially those partially covered by trees, require an extremely large receptive field due to the long-range dependencies between the intersecting roads." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.628, + 0.894, + 0.879 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To address the challenge of accurately detecting objects" + }, + { + "type": "page_footnote", + "bbox": [ + 0.099, + 0.864, + 0.228, + 0.876 + ], + "angle": 0, + "content": "*Corresponding authors." + }, + { + "type": "page_footnote", + "bbox": [ + 0.079, + 0.877, + 0.399, + 0.888 + ], + "angle": 0, + "content": "Team URL: https://github.com/IMPlus-PCALab" + }, + { + "type": "page_footnote", + "bbox": [ + 0.08, + 0.889, + 0.412, + 0.9 + ], + "angle": 0, + "content": "Project page: https://github.com/zcablii/LSKNet" + }, + { + "type": "list", + "bbox": [ + 0.079, + 0.864, + 0.412, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16794" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.087, + 0.442, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.285, + 0.471, + 0.327 + ], + "angle": 0, + "content": "Figure 2. The wide range of contextual information required for different object types is very different by human criteria. The objects with red boxes are the exact ground-truth annotations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.47, + 0.56 + ], + "angle": 0, + "content": "in remote sensing images, which often require a wide and dynamic range of contextual information, we propose a novel lightweight detection backbone called Large Selective Kernel Network (LSKNet). Our approach involves dynamically adjusting the receptive field of the feature extraction backbone to more effectively process the varying wide context of the objects being detected. This is achieved through a spatial selective mechanism, which efficiently weights the features processed by a sequence of large depth-wise kernels and then spatially merge them. The weights of these kernels are determined dynamically based on the input, allowing the model to adaptively use different large kernels and adjust the receptive field for each target in space as needed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.47, + 0.713 + ], + "angle": 0, + "content": "To our knowledge, the proposed LSKNet is the first to investigate using large and selective kernels for remote sensing object detection. Despite its simplicity and lightweight nature, our model achieves state-of-the-art performance on three popular datasets: HRSC2016 (98.46% mAP), DOTAv1.0 (81.85% mAP), and FAIR1M-v1.0 (47.87% mAP), surpassing previously published results. Furthermore, we demonstrate that our model's behaviour aligns with the two priors above, which in turn verifies the effectiveness of the proposed mechanism." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.73, + 0.219, + 0.745 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.465, + 0.772 + ], + "angle": 0, + "content": "2.1. Remote Sensing Object Detection Framework" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.903 + ], + "angle": 0, + "content": "High-performance remote sensing object detectors often rely on the RCNN [56] framework, which consists of a region proposal network and regional CNN detection heads. The RPN proposes high-quality regions of interest (RoIs) from the backbone feature maps, while the regional CNN detection heads are responsible for object classification and bounding box regression. Several variations on the RCNN framework have been proposed in recent years. The two-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.273 + ], + "angle": 0, + "content": "stage RoI transformer [12] uses fully-connected layers to rotate candidate horizontal anchor boxes in the first stage, and then features within the boxes are extracted for further regression and classification. SCRDet [78] uses an attention mechanism to reduce background noise and improve the modelling of crowded and small objects. Oriented RCNN [69] and Gliding Vertex [71] introduce new box encoding systems to address the instability of training losses caused by rotation angle periodicity. Some approaches [32, 61, 87] treat remote sensing detection as a point detection task [74], providing an alternative way of addressing remote sensing detection problems." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.892, + 0.53 + ], + "angle": 0, + "content": "Rather than relying on the proposed anchors, one-stage detection frameworks classify and regress oriented bounding boxes directly from grid densely sampled anchors. The one-stage S²A network [23] extracts robust object features via oriented feature alignment and orientation-invariant feature extraction. DRN [50], on the other hand, leverages attention mechanisms to dynamically refined the backbone's extracted features for more accurate predictions. In contrast with Oriented RCNN and Gliding Vertex, RSDet [54] addresses the discontinuity of regression loss by introducing a modulated loss. LD [86] enhances the localization quality of oriented bounding boxes by distillation. AOPG [6] and R3Det [75] adopt a progressive regression approach, refining bounding boxes from coarse to fine granularity. In addition to CNN, AO2-DETR [9] introduces a transformer-based detection framework, DETR [4], into remote sensing detection tasks, which brings more research diversity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.892, + 0.622 + ], + "angle": 0, + "content": "While these approaches have achieved promising results in addressing the issue of rotation variance, they do not consider the strong and valuable prior information presented in aerial images. Instead, our approach uses the large kernel and spatial selective mechanism to better model these priors without modifying the current detection framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.635, + 0.719, + 0.651 + ], + "angle": 0, + "content": "2.2. Large Kernel Networks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Transformer-based [59] models, such as the Vision Transformer (ViT) [1, 11, 14, 53, 60], Swin transformer [25, 39, 51, 64, 70, 83], and pyramid transformer [62, 67], have gained popularity in computer vision. Research [17, 45, 55, 72, 85] has demonstrated that the large receptive field is a key factor in their success. Recent work has shown that well-designed convolutional networks with large receptive fields can also be highly competitive with transformer-based models. For example, ConvNeXt [40] uses \\(7 \\times 7\\) depth-wise convolutions in its backbone, resulting in significant performance improvements in downstream tasks. In addition, RepLKNet [13] even uses a \\(31 \\times 31\\) convolutional kernel via re-parameterization, achieving compelling performance. A subsequent work SLaK [38], further expands the kernel size to \\(51 \\times 51\\) through kernel decomposition and sparse group techniques. RF-Next [18] automatically searches for a fixed" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16795" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.107, + 0.252, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.106, + 0.45, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.108, + 0.664, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.741, + 0.108, + 0.865, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.256, + 0.892, + 0.271 + ], + "angle": 0, + "content": "Figure 3. Architectural comparison between our proposed LSK module and other representative selective mechanism modules. K: Kernel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.29, + 0.468, + 0.38 + ], + "angle": 0, + "content": "large kernel for various tasks. VAN [19] introduces an efficient decomposition of large kernels as convolutional attention. Similarly, SegNeXt [20] and Conv2Former [28] demonstrate that large kernel convolution plays an important role in modulating the convolutional features with a richer context." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.468, + 0.516 + ], + "angle": 0, + "content": "Although large kernel convolutions have received attention in general object recognition, there has been a lack of research examining their significance in remote sensing detection. As previously noted in Sec. 1, aerial images possess unique characteristics that make large kernels particularly well-suited for remote sensing. As far as we know, our work represents the first attempt to introduce large kernel convolutions for remote sensing and to examine their importance in this field." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.528, + 0.353, + 0.543 + ], + "angle": 0, + "content": "2.3. Attention/Selective Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.468, + 0.673 + ], + "angle": 0, + "content": "The attention mechanism [21] is a simple but effective way to enhance neural representations for various tasks. The channel attention SE block [30] uses global average information to reweight feature channels, while spatial attention modules like GENet [29], GCNet [3], and SGE [34] enhance a network's ability to model context information via spatial masks. CBAM [66] and BAM [52] combine both channel and spatial attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.468, + 0.869 + ], + "angle": 0, + "content": "In addition to channel/spatial attention mechanisms, kernel selection is a self-adaptive and effective technique for dynamic context modelling. CondConv [73] and Dynamic convolution [5] use parallel kernels to adaptively aggregate features from multiple convolution kernels. SKNet [33] introduces multiple branches with different convolutional kernels and selectively combines them along the channel dimension. ResNeSt [84] extends the idea of SKNet by partitioning the input feature map into several groups. Similarly to the SKNet, SCNet [37] uses branch attention to capturing richer information and spatial attention to improve localization ability. Deformable Convnets [8, 89] introduce a flexible kernel shape for convolution units." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Our approach bears the most similarity to SKNet [33]. However, there are two key distinctions between the two" + }, + { + "type": "image", + "bbox": [ + 0.559, + 0.29, + 0.816, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.605, + 0.511, + 0.788, + 0.526 + ], + "angle": 0, + "content": "Figure 4. A block of LSKNet." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.544, + 0.892, + 0.695 + ], + "angle": 0, + "content": "methods. Firstly, our proposed selective mechanism relies explicitly on a sequence of large kernels via decomposition, a departure from most existing attention-based approaches. Secondly, our method adaptively aggregates information across large kernels in the spatial dimension rather than the channel dimension utilized by SKNet. This design is more intuitive and effective for remote sensing tasks because channel-wise selection fails to model the spatial variance for different targets across the image space. The detailed structural comparisons are listed in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.713, + 0.599, + 0.727 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.702, + 0.753 + ], + "angle": 0, + "content": "3.1. LSKNet Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.868 + ], + "angle": 0, + "content": "The overall architecture of the LSKNet backbone is simply built upon repeated LSKNet Blocks. Fig 4 illustrates an LSKNet Block, which is inspired by ConvNeXt [41], MetaFormer [81], PVT-v2 [63], Conv2Former [28] and VAN [19]. Each LSKNet block consists of two residual sub-blocks: the Large Kernel Selection (LK Selection) subblock and the Feed-forward Network (FFN) sub-block." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "The LK Selection sub-block dynamically adjusts the network's receptive field as needed. The core LSK module" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16796" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.124, + 0.094, + 0.852, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.331, + 0.251, + 0.64, + 0.266 + ], + "angle": 0, + "content": "Figure 5. A conceptual illustration of LSK module." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.278, + 0.462, + 0.324 + ], + "angle": 0, + "content": "
Model{C1,C2,C3,C4}{D1,D2,D3,D4}#P
★LSKNet-T{32,64,160,256}{3,3,5,2}4.3M
★LSKNet-S{64,128,320,512}{2,2,4,2}14.4M
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.327, + 0.47, + 0.356 + ], + "angle": 0, + "content": "Table 1. Variants of LSKNet used in this paper. \\( C_i \\): feature channel number; \\( D_i \\): number of LSKNet blocks of each stage \\( i \\)." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.368, + 0.456, + 0.445 + ], + "angle": 0, + "content": "
RF(k,d) sequence#PFLOPs
23(23,1)40.4K42.4G
(5,1) → (7,3)11.3K11.9G
29(29,1)60.4K63.3G
(3,1) → (5,2) → (7,3)11.3K13.6G
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.447, + 0.47, + 0.489 + ], + "angle": 0, + "content": "Table 2. Theoretical efficiency comparisons of two representative examples by expanding a single large depth-wise kernel into a sequence, given channels being 64. \\( k \\): kernel size; \\( d \\): dilation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.61 + ], + "angle": 0, + "content": "(Fig. 5) is embedded in the LK Selection sub-block. It consists of a sequence of large kernel convolutions and a spatial kernel selection mechanism, which will be elaborated on later. The FFN sub-block is used for channel mixing and feature refinement, which consists of a sequence of a fully connected layer, a depth-wise convolution, a GELU [26] activation, and a second fully connected layer." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.61, + 0.472, + 0.641 + ], + "angle": 0, + "content": "The detailed configuration of different variants of LSKNet used in this paper is listed in Tab. 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.65, + 0.323, + 0.667 + ], + "angle": 0, + "content": "3.2. Large Kernel Convolutions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.809 + ], + "angle": 0, + "content": "According to the prior (2), as stated in Sec. 1, it is suggested to model a series of multiple long-range contexts for adaptive selection. Therefore, we propose constructing a larger kernel convolution by explicitly decomposing it into a sequence of depth-wise convolutions with a large growing kernel and increasing dilation. Specifically, for the \\(i\\)-th depth-wise convolution, the expansion of the kernel size \\(k\\), dilation rate \\(d\\), and the receptive field \\(RF\\) are defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.823, + 0.469, + 0.839 + ], + "angle": 0, + "content": "\\[\nk _ {i - 1} \\leq k _ {i}; d _ {1} = 1, d _ {i - 1} < d _ {i} \\leq R F _ {i - 1}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.846, + 0.469, + 0.863 + ], + "angle": 0, + "content": "\\[\nR F _ {1} = k _ {1}, R F _ {i} = d _ {i} \\left(k _ {i} - 1\\right) + R F _ {i - 1}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The increasing kernel size and dilation rate ensure that the receptive field expands quickly enough. We set an upper" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.281, + 0.892, + 0.356 + ], + "angle": 0, + "content": "bound on the dilation rate to guarantee that the dilation convolution does not introduce gaps between feature maps. For instance, we can decompose a large kernel into 2 or 3 depth-wise convolutions as in Tab. 2, which have a theoretical receptive field of 23 and 29, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.893, + 0.523 + ], + "angle": 0, + "content": "There are two advantages of the proposed designs. First, it explicitly yields multiple features with various large receptive fields, which makes it easier for the later kernel selection. Second, sequential decomposition is more efficient than simply applying a single larger kernel. As shown in Tab. 2, under the same resulted theoretical receptive field, our decomposition greatly reduces the number of parameters compared to the standard large convolution kernels. To obtain features with rich contextual information from different ranges for input \\(\\mathbf{X}\\), a series of decomposed depth-wise convolutions with different receptive fields are applied:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.53, + 0.892, + 0.549 + ], + "angle": 0, + "content": "\\[\n\\mathbf {U} _ {0} = \\mathbf {X}, \\quad \\mathbf {U} _ {i + 1} = \\mathcal {F} _ {i} ^ {d w} (\\mathbf {U} _ {i}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.556, + 0.892, + 0.617 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_i^{dw}(\\cdot)\\) are depth-wise convolutions with kernel \\(k_{i}\\) and dilation \\(d_{i}\\). Assuming there are \\(N\\) decomposed kernels, each of which is further processed by a \\(1\\times 1\\) convolution layer \\(\\mathcal{F}^{1\\times 1}(\\cdot)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.626, + 0.892, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {U}} _ {i} = \\mathcal {F} _ {i} ^ {1 \\times 1} \\left(\\mathbf {U} _ {i}\\right), \\text {f o r} i \\text {i n} [ 1, N ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.714 + ], + "angle": 0, + "content": "allowing channel mixing for each spatial feature vector. Then, a selection mechanism is proposed to dynamically select kernels for various objects based on the multi-scale features obtained, which would be introduced next." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.722, + 0.722, + 0.739 + ], + "angle": 0, + "content": "3.3. Spatial Kernel Selection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.746, + 0.892, + 0.837 + ], + "angle": 0, + "content": "To enhance the network's ability to focus on the most relevant spatial context regions for detecting targets, we use a spatial selection mechanism to spatially select the feature maps from large convolution kernels at different scales. Firstly, we concatenate the features obtained from different kernels with different ranges of receptive field:" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.843, + 0.892, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {U}} = \\left[ \\widetilde {\\mathbf {U}} _ {1}; \\dots ; \\widetilde {\\mathbf {U}} _ {i} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "and then efficiently extract the spatial relationship by applying channel-based average and maximum pooling (denoted" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16797" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.09, + 0.283, + 0.108 + ], + "angle": 0, + "content": "as \\(\\mathcal{P}_{avg}(\\cdot)\\) and \\(\\mathcal{P}_{max}(\\cdot)\\) to \\(\\tilde{\\mathbf{U}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.117, + 0.47, + 0.138 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S A} _ {a v g} = \\mathcal {P} _ {a v g} (\\widetilde {\\mathbf {U}}), \\mathbf {S A} _ {m a x} = \\mathcal {P} _ {m a x} (\\widetilde {\\mathbf {U}}), \\qquad (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.147, + 0.47, + 0.239 + ], + "angle": 0, + "content": "where \\(\\mathbf{SA}_{avg}\\) and \\(\\mathbf{SA}_{max}\\) are the average and maximum pooled spatial feature descriptors. To allow information interaction among different spatial descriptors, we concatenate the spatially pooled features and use a convolution layer \\(\\mathcal{F}^{2\\rightarrow N}(\\cdot)\\) to transform the pooled features (with 2 channels) into \\(N\\) spatial attention maps:" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.248, + 0.469, + 0.268 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathbf {S A}} = \\mathcal {F} ^ {2 \\rightarrow N} \\left(\\left[ \\mathbf {S A} _ {a v g}; \\mathbf {S A} _ {m a x} \\right]\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.28, + 0.469, + 0.327 + ], + "angle": 0, + "content": "For each of the spatial attention maps, \\(\\widehat{\\mathbf{SA}_i}\\), a sigmoid activation function is applied to obtain the individual spatial selection mask for each of the decomposed large kernels:" + }, + { + "type": "equation", + "bbox": [ + 0.216, + 0.336, + 0.469, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {S A} _ {i}} = \\sigma (\\widehat {\\mathbf {S A} _ {i}}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.366, + 0.469, + 0.442 + ], + "angle": 0, + "content": "where \\(\\sigma(\\cdot)\\) denotes the sigmoid function. The feature maps from the sequence of decomposed large kernels are weighted by their corresponding spatial selection masks and then fused by a convolution layer \\(\\mathcal{F}(\\cdot)\\) to obtain the attention feature \\(\\mathbf{S}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.45, + 0.469, + 0.491 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} = \\mathcal {F} \\left(\\sum_ {i = 1} ^ {N} \\left(\\widetilde {\\mathbf {S A}} _ {i} \\cdot \\widetilde {\\mathbf {U}} _ {i}\\right)\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.501, + 0.469, + 0.546 + ], + "angle": 0, + "content": "The final output of the LSK module is the element-wise product between the input feature \\(\\mathbf{X}\\) and \\(\\mathbf{S}\\), similarly in [19, 20, 28]:" + }, + { + "type": "equation", + "bbox": [ + 0.233, + 0.546, + 0.469, + 0.561 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} = \\mathbf {X} \\cdot \\mathbf {S}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.568, + 0.469, + 0.629 + ], + "angle": 0, + "content": "Fig. 5 shows a detailed conceptual illustration of an LSK module where we intuitively demonstrate how the large selective kernel works by adaptively collecting the corresponding large receptive field for different objects." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.642, + 0.208, + 0.658 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.179, + 0.681 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.689, + 0.469, + 0.735 + ], + "angle": 0, + "content": "HRSC2016 [42] is a high-resolution remote sensing dataset which is collected for ship detection. It consists of 1,061 images which contain 2,976 instances of ships." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.469, + 0.84 + ], + "angle": 0, + "content": "DOTA-v1.0 [68] consists of 2,806 remote sensing images. It contains 188,282 instances of 15 categories: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), and Helicopter (HC)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "FAIR1M-v1.0 [58] is a recently published remote sensing dataset that consists of 15,266 high-resolution images and more than 1 million instances. It contains 5 categories and 37 sub-categories objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.717, + 0.107 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.295 + ], + "angle": 0, + "content": "In our experiment, we report the results of the oriented object detection models on HRSC2016, DOTA-v1.0 and FAIR1M-v1.0 datasets. To ensure fairness, we follow the same dataset processing approach as other mainstream methods [23, 24, 69]. For DOTA-v1.0 and FAIR1M-v1.0 datasets, we adopt multi-scale training and testing strategy by first rescaling the images into three scales (0.5, 1.0, 1.5), and then cropping each scaled image into \\(1024 \\times 1024\\) sub-images with a patch overlap of 500 pixels. For the HRSC2016 dataset, we rescale the images by setting the longer side of the image to 800 pixels, without changing their aspect ratios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.893, + 0.673 + ], + "angle": 0, + "content": "During our experiments, the backbones are first pretrained on the ImageNet-1K [10] dataset and then finetuned on the target remote sensing benchmarks. In ablation studies, we adopt the 100-epoch backbone pretraining schedule for experimental efficiency (Tab. 3, 5, 4, 6, 7). We adopt a 300-epoch backbone pretraining strategy to pursue higher accuracy in main results (Tab. 8, 9, 10), similarly to [6,23,69,75]. In main results (Tab. 8, 9), the \"Pre.\" column stands for the dataset on which the networks/backbones are pretrained (IN: Imagenet [10] dataset; CO: Microsoft COCO [36] dataset; MA: Million-AID [43] dataset). Unless otherwise stated, LSKNet is defaulting to be built within the framework of Oriented RCNN [69] due to its compelling performance and efficiency. All the models are trained on the training and validation sets and tested on the testing set. Following [69], we train the models for 36 epochs on the HRSC2016 datasets and 12 epochs on the DOTA-v1.0 and FAIR1M-v1.0 datasets, with the AdamW [44] optimizer. The initial learning rate is set to 0.0004 for HRSC2016, and 0.0002 for the other two datasets, with a weight decay of 0.05. The models are implemented under MMRotate [88] framework. We use 8 RTX3090 GPUs with a batch size of 8 for model training and use a single RTX3090 GPU for testing. All the FLOPs we report in this paper are calculated with a \\(1024 \\times 1024\\) image input." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.653, + 0.698 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.705, + 0.89, + 0.735 + ], + "angle": 0, + "content": "In this section, we report ablation study results on the DOTA-v1.0 test set to investigate its effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.886 + ], + "angle": 0, + "content": "Large Kernel Decomposition. Deciding on the number of kernels to decompose is a critical choice for the LSK module. We follow Eq. (1) to configure the decomposed kernels. The results of the ablation study on the number of large kernel decompositions, when the theoretical receptive field is fixed at 29, are shown in Tab. 3. It suggests that decomposing the large kernel into two depth-wise large kernels results in a good trade-off between speed and accuracy, achieving the best performance in terms of both FPS (frames per second) and mAP (mean average precision)." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Receptive Field Size and Selection Type. Based on our" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16798" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.462, + 0.15 + ], + "angle": 0, + "content": "
(k,d) sequenceRFNum.FPSmAP (%)
(29,1)29118.680.66
(5,1)→(7,4)29220.580.91
(3,1)→(5,2)→(7,3)29319.280.77
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.154, + 0.47, + 0.224 + ], + "angle": 0, + "content": "Table 3. The effects of the number of decomposed large kernels on the inference FPS and mAP, given the theoretical receptive field being 29. We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. Decomposing the large kernel into two depth-wise kernels achieves the best performance of speed and accuracy." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.238, + 0.459, + 0.342 + ], + "angle": 0, + "content": "
(k1, d1)(k2, d2)CSSSRFFPSmAP (%)
(3, 1)(5, 2)--1122.180.80
(5, 1)(7, 3)--2321.780.94
(5, 1)(7, 4)--2920.580.91
(7, 1)(9, 4)--3921.380.84
(5, 1)(7, 3)✓-2319.680.57
(5, 1)(7, 3)-✓2320.781.31
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.442 + ], + "angle": 0, + "content": "Table 4. The effectiveness of the key design components of the LSKNet when the large kernel is decomposed into a sequence of two depth-wise kernels. CS: channel selection (likewise in SKNet [33]); SS: spatial selection (ours). We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. The LSKNet achieves the best performance when using a reasonably large receptive field with spatial selection." + }, + { + "type": "table", + "bbox": [ + 0.167, + 0.456, + 0.378, + 0.531 + ], + "angle": 0, + "content": "
PoolingFPSmAP (%)
Max.Avg.
✓20.781.23
✓20.781.12
✓✓20.781.31
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.59 + ], + "angle": 0, + "content": "Table 5. Ablation study on the effectiveness of the maximum and average pooling in spatial selection of our proposed LSK module. We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. The best result is obtained when using both." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.468, + 0.778 + ], + "angle": 0, + "content": "evaluations presented in Tab. 3, we find that the optimal solution for our proposed LSKNet is to decompose the large kernel into two depth-wise kernels in series. Furthermore, Tab. 4 shows that excessively small or large receptive fields can hinder the performance of the LSKNet, and a receptive field size of approximately 23 is determined to be the most effective. In addition, our experiments indicate that the proposed spatial selection approach is more effective than channel attention (similarly in SKNet [33]) for remote sensing object detection tasks. It suggests that in detection tasks, spatial information is more critical." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.468, + 0.869 + ], + "angle": 0, + "content": "Pooling Layers in Spatial Selection. We conduct experiments to determine the optimal pooling layers for spatial selection, as reported in Tab. 5. The results suggest that using both max and average pooling in the spatial selection component of our LSK module provides the best performance without sacrificing inference speed." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Performance of LSKNet backbone under different detection frameworks. To validate the generality and ef" + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.09, + 0.871, + 0.193 + ], + "angle": 0, + "content": "
FrameworksResNet-18★ LSKNet-T
ORCNN [69]79.2781.31 (+2.04)
RoI Trans. [12]78.3280.89 (+2.57)
S²A-Net [23]76.8280.15 (+3.33)
R3Det [75]74.1678.39 (+4.23)
#P (backbone only)11.2M4.3M (-62%)
FLOPs (backbone only)38.1G19.1G (-50%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.194, + 0.892, + 0.263 + ], + "angle": 0, + "content": "Table 6. Comparison of LSKNet-T and ResNet-18 as backbones with different detection frameworks on DOTA-v1.0. The LSKNet-T backbone is pretrained on ImageNet for 100 epochs. The lightweight LSKNet-T achieves significantly higher mAP in various frameworks than ResNet-18." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.273, + 0.885, + 0.422 + ], + "angle": 0, + "content": "
GroupModel (backbone only)#PFLOPsmAP (%)
BaselineResNet-1811.2M38.1G79.27
Large KernelVAN-B1 [19]13.4M52.7G81.15
ConvNeXt V2-N [65]15.0M51.2G80.81
MSCAN-S [20]13.1M45.0G81.12
Selective AttentionSKNet-26 [33]14.5M58.5G80.67
ResNeSt-14 [84]8.6M57.9G79.51
SCNet-18 [37]14.0M50.7G79.69
Ours★ LSKNet-S14.4M54.4G81.48
Prev BestCSPNeXt [46]26.1M87.6G81.33
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.423, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Table 7. Comparison on LSKNet-S and other (large kernel/selective attention) backbones under O-RCNN [69] framework on DOTA-v1.0, except that the Prev Best is under RT-MDet [46] framework. All backbones are pretrained on ImageNet for 100 epochs. Our LSKNet achieves the best mAP under similar complexity budgets." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.522, + 0.888, + 0.74 + ], + "angle": 0, + "content": "
MethodPre.mAP(07)↑mAP(12)↑#P↓FLOPs↓
DRN [50]IN-92.70--
CenterMap [61]IN-92.8041.1M198G
Rol Trans. [12]IN86.20-55.1M200G
G. V. [71]IN88.20-41.1M198G
R3Det [75]IN89.2696.0141.9M336G
DAL [48]IN89.77-36.4M216G
GWD [77]IN89.8597.3747.4M456G
S2ANet [23]IN90.1795.0138.6M198G
AOPG [6]IN90.3496.22--
ReDet [24]IN90.4697.6331.6M-
O-RCNN [69]IN90.5097.6041.1M199G
RTMDet [46]CO90.6097.1052.3M205G
★LSKNet-TIN90.5498.1321.0M124G
★LSKNet-SIN90.6598.4631.0M161G
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.743, + 0.892, + 0.798 + ], + "angle": 0, + "content": "Table 8. Comparison with state-of-the-art methods on the HRSC2016 dataset. The LSKNet-S backbone is pretrained on ImageNet for 300 epochs, the same with most compared methods [23,69,75]. mAP (07/12): VOC 2007 [15]/2012 [16] metrics." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "fectiveness of our proposed LSKNet backbone, we evaluate its performance under various remote sensing detection frameworks, including two-stage frameworks O-RCNN [69] and RoI Transformer [12] as well as one-stage frameworks \\(\\mathrm{S}^2\\mathrm{A}\\) -Net [23] and R3Det [75]. The re" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16799" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.09, + 0.887, + 0.103 + ], + "angle": 0, + "content": "Method |Pre. \\(\\left|\\mathbf{mAP}\\uparrow\\right|\\# \\mathbf{P}\\downarrow\\) FLOPs↓ PL BD BR GTF SV LV SH TC BC ST SBF RA HA SP HC" + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.106, + 0.892, + 0.482 + ], + "angle": 0, + "content": "
One-stage
R3Det [75]IN76.4741.9M336G89.8083.7748.1166.7778.7683.2787.8490.8285.3885.5165.5762.6867.5378.5672.62
CFA [22]IN76.67--89.0883.2054.3766.8781.2380.9687.1790.2184.3286.0952.3469.9475.5280.7667.96
DAFNe [31]IN76.95--89.4086.2753.7060.5182.0481.1788.6690.3783.8187.2753.9369.3875.6181.2670.86
SASM [27]IN79.17--89.5485.9457.7378.4179.7884.1989.2590.8758.8087.2763.8267.8178.6779.3569.37
AO2-DETR [9]IN79.2274.3M304G89.9584.5256.9074.8380.8683.4788.4790.8786.1288.5563.2165.0979.0982.8873.46
\\( S^2ANet \\) [23]IN79.42--88.8983.6057.7481.9579.9483.1989.1190.7884.8787.8170.3068.2578.3077.0169.58
R3Det-GWD [77]IN80.2341.9M336G89.6684.9959.2682.1978.9784.8387.7090.2186.5486.8573.4767.7776.9279.2274.92
RTMDet-R [46]IN80.5452.3M205G88.3684.9657.3380.4680.5884.8888.0890.9086.3287.5769.2970.6178.6380.9779.24
R3Det-KLD [79]IN80.6341.9M336G89.9285.1359.1981.3378.8284.3887.5089.8087.3387.0072.5771.3577.1279.3478.68
RTMDet-R [46]CO81.3352.3M205G88.0186.1758.5482.4481.3084.8288.7190.8988.7787.3771.9671.1881.2381.4077.13
Two-stage
SCRDet [78]IN72.61--89.9880.6552.0968.3668.3660.3272.4190.8587.9486.8665.0266.6866.2568.2465.21
Rol Trans. [12]IN74.6155.1M200G88.6582.6052.5370.8777.9376.6786.8790.7183.8382.5153.9567.6174.6768.7561.03
G.V. [71]IN75.0241.1M198G89.6485.0052.2677.3473.0173.1486.8290.7479.0286.8159.5570.9172.9470.8657.32
CenterMap [61]IN76.0341.1M198G89.8384.4154.6070.2577.6678.3287.1990.6684.8985.2756.4669.2374.1371.5666.06
CSL [76]IN76.1737.4M236G90.2585.5354.6475.3170.4473.5177.6290.8486.1586.6969.6068.0473.8371.1068.93
ReDet [24]IN80.10--88.8182.4860.8380.8278.3486.0688.3190.8788.7787.0368.6566.9079.2679.7174.67
DODet [7]IN80.62--89.9685.5258.0181.2278.7185.4688.5990.8987.1287.8070.5071.5482.0677.4374.47
AOPG [6]IN80.66--89.8885.5760.9081.5178.7085.2988.8590.8987.6087.6571.6668.6982.3177.3273.10
O-RCNN [69]IN80.8741.1M199G89.8485.4361.0979.8279.7185.3588.8290.8886.6887.7372.2170.8082.4278.1874.11
KFloU [80]IN80.9358.8M206G89.4484.4162.2282.5180.1086.0788.6890.9087.3288.3872.8071.9578.9674.9575.27
RVSA [60]MA81.24114.4M414G88.9785.7661.4681.2779.9885.3188.3090.8485.0687.5066.7773.1184.7581.8877.58
★LSKNet-T (ours)IN81.3721.0M124G89.1484.9061.7883.5081.5485.8788.6490.8988.0287.3171.5570.7478.6679.8178.16
★LSKNet-S (ours)IN81.6431.0M161G89.5786.3463.1383.6782.2086.1088.6690.8988.4187.4271.7269.5878.8881.7776.52
★LSKNet-S* (ours)IN81.8531.0M161G89.6985.7061.4783.2381.3786.0588.6490.8888.4987.4071.6771.3579.1981.7780.86
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.485, + 0.893, + 0.514 + ], + "angle": 0, + "content": "Table 9. Comparison with state-of-the-art methods on the DOTA-v1.0 dataset with multi-scale training and testing. The LSKNet backbones are pretrained on ImageNet for 300 epochs, similarly to [23, 69, 75]. *: With EMA finetune similarly to the compared methods [46]." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.525, + 0.88, + 0.561 + ], + "angle": 0, + "content": "
ModelG. V.* [71]RetinaNet* [35]C-RCNN* [2]F-RCNN* [56]RoI Trans.* [12]O-RCNN [69]★ LSKNet-T★ LSKNet-S
mAP(%)29.9230.6731.1832.1235.2945.6046.9347.87
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.564, + 0.893, + 0.593 + ], + "angle": 0, + "content": "Table 10. Comparison with state-of-the-art methods on the FAIR1M-v1.0 dataset. The LSKNet backbones are pretrained on ImageNet for 300 epochs, similarly to [23,69,75].*: Results are referenced from FAIR1M paper [58]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.671 + ], + "angle": 0, + "content": "sults in Tab. 6 show that our proposed LSKNet-T backbone significantly improves detection performance compared to ResNet-18, while using only \\(38\\%\\) of its parameters and with \\(50\\%\\) fewer FLOPs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.471, + 0.763 + ], + "angle": 0, + "content": "Comparison with Other Large Kernel/Selective Attention Backbones. We also compare our LSKNet with 6 popular high-performance backbone models with large kernels or selective attention. As shown in Tab. 7, under similar model sizes and complexity budgets, our LSKNet outperforms all other models on the DOTA-v1.0 dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.218, + 0.787 + ], + "angle": 0, + "content": "4.4. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.886 + ], + "angle": 0, + "content": "Results on HRSC2016. We evaluated the performance of our LSKNet against 12 state-of-the-art methods on the HRSC2016 dataset. The results presented in Tab. 8 demonstrate that our LSKNet-S outperforms all other methods with an mAP of \\(90.65\\%\\) and \\(98.46\\%\\) under the PASCAL VOC 2007 [15] and VOC 2012 [16] metrics, respectively." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Results on DOTA-v1.0. We compare our LSKNet with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.702 + ], + "angle": 0, + "content": "20 state-of-the-art methods on the DOTA-v1.0 dataset, as reported in Tab. 9. Our LSKNet-T, LSKNet-S and LSKNet-S* achieve state-of-the-art with mAP of \\(81.37\\%\\), \\(81.64\\%\\) and \\(81.85\\%\\) respectively. Notably, our high-performing LSKNet-S reaches an inference speed of 18.1 FPS on 1024x1024 images with a single RTX3090 GPU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Results on FAIR1M-v1.0. We compare our LSKNet against 6 other models on the FAIR1M-v1.0 dataset, as shown in Tab. 10. The results reveal that our LSKNet-T and LSKNet-S perform exceptionally well, achieving state-of-the-art mAP scores of \\(46.93\\%\\) and \\(47.87\\%\\) respectively, surpassing all other models by a significant margin." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.603, + 0.818 + ], + "angle": 0, + "content": "4.5. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Detection Results Visualization. Visualization examples of detection results and Eigen-CAM [49] are shown in Fig. 6. LSKNet can capture much more context information relevant to the detected targets, leading to better performance in various hard cases, which justifies our prior (1)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16800" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.09, + 0.396, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.207, + 0.359, + 0.347, + 0.37 + ], + "angle": 0, + "content": "(a) Robustness to obstacles" + }, + { + "type": "image", + "bbox": [ + 0.401, + 0.092, + 0.631, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.427, + 0.358, + 0.602, + 0.37 + ], + "angle": 0, + "content": "(b) Accurate Object Classification" + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.092, + 0.868, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.667, + 0.358, + 0.836, + 0.37 + ], + "angle": 0, + "content": "(c) Accurate Object Localization" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.376, + 0.893, + 0.404 + ], + "angle": 0, + "content": "Figure 6. Eigen-CAM visualization of Oriented RCNN detection framework with ResNet-50 and LSKNet-S. Our proposed LSKNet can model a much long range of context information, leading to better performance in various hard cases." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.426, + 0.449, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.704 + ], + "angle": 0, + "content": "Figure 7. Normalised Ratio \\( R_{c} \\) of Expected Selective RF Area and GT Bounding Box Area for object categories in DOTA-v1.0. The relative range of context required for different object categories varies a lot. Examples of Bridge and Soccer-ball-field are given, where the visualized receptive field is obtained from Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.471, + 0.787 + ], + "angle": 0, + "content": "Relative Context Range for Different Objects. To investigate the relative range of receptive field for each object category, we define \\( R_{c} \\) as the Ratio of Expected Selective RF Area and GT Bounding Box Area for category \\( c \\):" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.795, + 0.47, + 0.83 + ], + "angle": 0, + "content": "\\[\nR _ {c} = \\frac {\\sum_ {i = 1} ^ {I _ {c}} A _ {i} / B _ {i}}{I _ {c}}, \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.839, + 0.469, + 0.882 + ], + "angle": 0, + "content": "\\[\nA _ {i} = \\sum_ {d = 1} ^ {D} \\sum_ {n = 1} ^ {N} | \\widetilde {\\mathbf {S A}} _ {n} ^ {d} \\cdot R F _ {n} |, B _ {i} = \\sum_ {j = 1} ^ {J _ {i}} \\operatorname {A r e a} \\left(\\mathrm {G T} _ {j}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(I_{c}\\) is the number of images that contain the object" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.426, + 0.872, + 0.562 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.565, + 0.892, + 0.62 + ], + "angle": 0, + "content": "Figure 8. Normalised Kernel Selection Difference in the LSKNet-T blocks for Bridge, Roundabout and Soccer-ball-field. B.i.j represents the j-th LSK block in stage i. A greater value is indicative of a dependence on a broader context." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.776 + ], + "angle": 0, + "content": "category \\(c\\) only. The \\(A_{i}\\) is the sum of spatial selection activation in all LSK blocks for input image \\(i\\), where \\(D\\) is the number of blocks in an LSKNet, and \\(N\\) is the number of decomposed large kernels in an LSK module. \\(B_{i}\\) is the total pixel area of all \\(J_{i}\\) annotated oriented object bounding boxes (GT). We plot the normalized \\(R_{c}\\) in Fig. 7 which represents the relative range of context required for different object categories for a better view." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The results suggest that the Bridge category stands out as requiring a greater amount of additional contextual information compared to other categories, primarily due to its similarity in features with roads and the necessity of contextual clues to ascertain whether it is enveloped by water. Conversely, the Court categories, such as Soccer-ball-field, necessitate minimal contextual information owing to their distinctive textural attributes, specifically the court bound-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16801" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.145, + 0.1, + 0.308, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.186, + 0.251, + 0.199 + ], + "angle": 0, + "content": "Bridge" + }, + { + "type": "image", + "bbox": [ + 0.319, + 0.1, + 0.482, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.186, + 0.437, + 0.197 + ], + "angle": 0, + "content": "Roundabout" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.1, + 0.657, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.186, + 0.614, + 0.197 + ], + "angle": 0, + "content": "Small Vehicle" + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.1, + 0.833, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.709, + 0.186, + 0.796, + 0.198 + ], + "angle": 0, + "content": "Swimming Pool" + }, + { + "type": "image", + "bbox": [ + 0.144, + 0.209, + 0.308, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.296, + 0.239, + 0.308 + ], + "angle": 0, + "content": "Ship" + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.209, + 0.482, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.296, + 0.438, + 0.308 + ], + "angle": 0, + "content": "Storage tank" + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.209, + 0.657, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.296, + 0.633, + 0.306 + ], + "angle": 0, + "content": "Baseball diamond" + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.209, + 0.832, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.709, + 0.296, + 0.786, + 0.308 + ], + "angle": 0, + "content": "Large Vehicle" + }, + { + "type": "image", + "bbox": [ + 0.144, + 0.318, + 0.308, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.404, + 0.252, + 0.414 + ], + "angle": 0, + "content": "Harbor" + }, + { + "type": "image", + "bbox": [ + 0.319, + 0.318, + 0.482, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.404, + 0.438, + 0.414 + ], + "angle": 0, + "content": "Tennis court" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.318, + 0.657, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.404, + 0.592, + 0.414 + ], + "angle": 0, + "content": "Plane" + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.318, + 0.832, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.709, + 0.404, + 0.798, + 0.414 + ], + "angle": 0, + "content": "Soccer-ball field" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.419, + 0.892, + 0.447 + ], + "angle": 0, + "content": "Figure 9. Receptive field activation for more object categories in DOTA-v1.0, where the activation map is obtained from the Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.469, + 0.508 + ], + "angle": 0, + "content": "ary lines. It aligns with our knowledge and further supports prior (2) that the relative range of contextual information required for different object categories varies greatly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.582 + ], + "angle": 0, + "content": "Kernel Selection Behaviour. We further investigate the kernel selection behaviour in our LSKNet. For object category \\( c \\), the Kernel Selection Difference \\( \\Delta A_{c} \\) (i.e., larger kernel selection - smaller kernel selection) of an LSKNet-T block is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.596, + 0.469, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\Delta A _ {c} = \\left| \\widetilde {\\mathbf {S A}} _ {\\text {l a r g e r}} - \\widetilde {\\mathbf {S A}} _ {\\text {s m a l l e r}} \\right|. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.469, + 0.763 + ], + "angle": 0, + "content": "We demonstrate the normalised \\(\\Delta A_{c}\\) over all images for three typical categories: Bridge, Roundabout and Soccerball-field and for each LSKNet-T block in Fig. 8. As expected, the participation of larger kernels of all blocks for Bridge is higher than that of Roundabout, and Roundabout is higher than Soccer-ball-field. This aligns with the common sense that Soccer-ball-field indeed does not require a large amount of context, since its own texture characteristics are already sufficiently distinct and discriminatory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.469, + 0.869 + ], + "angle": 0, + "content": "We also surprisingly discover another selection pattern of LSKNet across network depth: LSKNet usually utilizes larger kernels in its shallow layers and smaller kernels in higher levels. This indicates that networks tend to quickly focus on capturing information from large receptive fields in low-level layers so that higher-level semantics can contain sufficient receptive fields for better discrimination." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Spatial Activation Visualisations. Spatial activation map examples for more object categories in DOTA-v1.0" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.612 + ], + "angle": 0, + "content": "are shown in Fig. 9, where the activation map is obtained from Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model. The object categories are arranged in decreasing order from top left to bottom right based on the Ratio of Expected Selective RF Area and GT Bounding Box Area as illustrated in Fig. 7. The spatial activation visualisation results also demonstrate that the model's behaviour aligns with our proposed two priors and the above analysis, which in turn verifies the effectiveness of the proposed mechanism." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.631, + 0.619, + 0.646 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.809 + ], + "angle": 0, + "content": "In this paper, we propose the Large Selective Kernel Network (LSKNet) for remote sensing object detection tasks, which is designed to utilize the inherent characteristics in remote sensing images: the need for a wider and adaptable contextual understanding. By adapting its large spatial receptive field, LSKNet can effectively model the varying contextual nuances of different object types. Extensive experiments demonstrate that our proposed lightweight model achieves state-of-the-art performance on competitive remote sensing benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.831, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This research was supported by the NSFC (NO. 62176130, 62206134, 62225604) and the Fundamental Research Funds for the Central Universities (Nankai University, 070-63233084, 070-63233089). 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In CVPR, 2019. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16805" + } + ] +] \ No newline at end of file diff --git a/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_origin.pdf b/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..dbc608c2771fa98f4c530fa95577b6c8b03f2ae8 --- /dev/null +++ b/2023/Large Selective Kernel Network for Remote Sensing Object Detection/1c2f7154-2a88-4538-ac11-efbaf0ea97b7_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fc141ba277e97ab6af94fe4a451a2675c1f391aa837736812f84fa1d50558e85 +size 1302487 diff --git a/2023/Large Selective Kernel Network for Remote Sensing Object Detection/full.md b/2023/Large Selective Kernel Network for Remote Sensing Object Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f8c51a668fe91e187447048c6582180d35c09402 --- /dev/null +++ b/2023/Large Selective Kernel Network for Remote Sensing Object Detection/full.md @@ -0,0 +1,448 @@ +# Large Selective Kernel Network for Remote Sensing Object Detection + +Yuxuan Li†, Qibin Hou, Zhaohui Zheng, Ming-Ming Cheng, Jian Yang* and Xiang Li* +VCIP, CS, Nankai University + +yuxuan.li.17@ucl.ac.uk†, {csjyang, xiang.li.implus}@nankai.edu.cn* + +# Abstract + +Recent research on remote sensing object detection has largely focused on improving the representation of oriented bounding boxes but has overlooked the unique prior knowledge presented in remote sensing scenarios. Such prior knowledge can be useful because tiny remote sensing objects may be mistakenly detected without referencing a sufficiently long-range context, which can vary for different objects. This paper considers these priors and proposes the lightweight Large Selective Kernel Network (LSKNet). LSKNet can dynamically adjust its large spatial receptive field to better model the ranging context of various objects in remote sensing scenarios. To our knowledge, large and selective kernel mechanisms have not been previously explored in remote sensing object detection. Without bells and whistles, our lightweight LSKNet sets new state-of-the-art scores on standard benchmarks, i.e., HRSC2016 $(98.46\% \text{mAP})$ , DOTA-v1.0 $(81.85\% \text{mAP})$ , and FAIR1M-v1.0 $(47.87\% \text{mAP})$ . + +# 1. Introduction + +Remote sensing object detection [47, 57, 82] focuses on identifying and locating objects of interest in aerial images, such as vehicles, ships or aircraft. In recent years, one mainstream trend has been to generate bounding boxes that accurately fit the orientation of the objects being detected rather than simply drawing horizontal boxes around them. Consequently, much research has focused on improving the representation of oriented bounding boxes for remote sensing object detection. This has largely been achieved through the development of specialized detection frameworks (i.e., RoI Transformer [12], Oriented R-CNN [69], and R3Det [75]) and oriented box encoding (i.e., gliding vertex [71] and midpoint offset box encoding [69]). Additionally, several loss functions, including GWD [77], KLD [79], and Modulated Loss [54], have been further proposed to enhance the + +![](images/c3bb16fa2ce72726663a286ca45a641a4d1fbd556a43bec0cac9b91882fe8b49.jpg) +Ship or Vehicle? + +![](images/6db7f7b631b5099d1fc4667c304046d7449724738601f65a7fa3b3c761dc2f65.jpg) +Figure 1. Successfully detecting remote sensing objects requires using a wide range of contextual information. Detectors with a limited receptive field may easily lead to incorrect results. + +![](images/910dff187a27be78cab0ab7c96a028b932c451fc85de589cb9fbfa24ca5b559a.jpg) + +performance of these approaches. + +Despite these advances, relatively few works have considered the strong prior knowledge of remote sensing images. Aerial images are typically captured at high resolutions from a bird's eye view. In particular, most objects in aerial images may be small and difficult to identify based on their appearance alone. Instead, recognizing these objects relies on their context, as the surrounding environment can provide valuable clues about their shape, orientation, and other characteristics. According to an analysis of the remote sensing data, we identify two important priors: + +- Accurate detection often requires a wide range of contextual information. As illustrated in Fig. 1, the limited context used by object detectors in remote sensing images can often lead to incorrect classifications. Rather than their appearance, the context distinguishes the ship from the vehicle. +- The contextual information required for different objects is very different. As shown in Fig. 2, the soccer field requires relatively less contextual information because of the unique distinguishable court borderlines. In contrast, the roundabout may require more context information to distinguish between gardens and ring-like buildings. Intersections, especially those partially covered by trees, require an extremely large receptive field due to the long-range dependencies between the intersecting roads. + +To address the challenge of accurately detecting objects + +![](images/84fbfd0eeb92108394a7ef9b0a7e672251aa231fbdfdf86c42802e44b6f03bb8.jpg) +Figure 2. The wide range of contextual information required for different object types is very different by human criteria. The objects with red boxes are the exact ground-truth annotations. + +in remote sensing images, which often require a wide and dynamic range of contextual information, we propose a novel lightweight detection backbone called Large Selective Kernel Network (LSKNet). Our approach involves dynamically adjusting the receptive field of the feature extraction backbone to more effectively process the varying wide context of the objects being detected. This is achieved through a spatial selective mechanism, which efficiently weights the features processed by a sequence of large depth-wise kernels and then spatially merge them. The weights of these kernels are determined dynamically based on the input, allowing the model to adaptively use different large kernels and adjust the receptive field for each target in space as needed. + +To our knowledge, the proposed LSKNet is the first to investigate using large and selective kernels for remote sensing object detection. Despite its simplicity and lightweight nature, our model achieves state-of-the-art performance on three popular datasets: HRSC2016 (98.46% mAP), DOTAv1.0 (81.85% mAP), and FAIR1M-v1.0 (47.87% mAP), surpassing previously published results. Furthermore, we demonstrate that our model's behaviour aligns with the two priors above, which in turn verifies the effectiveness of the proposed mechanism. + +# 2. Related Work + +# 2.1. Remote Sensing Object Detection Framework + +High-performance remote sensing object detectors often rely on the RCNN [56] framework, which consists of a region proposal network and regional CNN detection heads. The RPN proposes high-quality regions of interest (RoIs) from the backbone feature maps, while the regional CNN detection heads are responsible for object classification and bounding box regression. Several variations on the RCNN framework have been proposed in recent years. The two- + +stage RoI transformer [12] uses fully-connected layers to rotate candidate horizontal anchor boxes in the first stage, and then features within the boxes are extracted for further regression and classification. SCRDet [78] uses an attention mechanism to reduce background noise and improve the modelling of crowded and small objects. Oriented RCNN [69] and Gliding Vertex [71] introduce new box encoding systems to address the instability of training losses caused by rotation angle periodicity. Some approaches [32, 61, 87] treat remote sensing detection as a point detection task [74], providing an alternative way of addressing remote sensing detection problems. + +Rather than relying on the proposed anchors, one-stage detection frameworks classify and regress oriented bounding boxes directly from grid densely sampled anchors. The one-stage S²A network [23] extracts robust object features via oriented feature alignment and orientation-invariant feature extraction. DRN [50], on the other hand, leverages attention mechanisms to dynamically refined the backbone's extracted features for more accurate predictions. In contrast with Oriented RCNN and Gliding Vertex, RSDet [54] addresses the discontinuity of regression loss by introducing a modulated loss. LD [86] enhances the localization quality of oriented bounding boxes by distillation. AOPG [6] and R3Det [75] adopt a progressive regression approach, refining bounding boxes from coarse to fine granularity. In addition to CNN, AO2-DETR [9] introduces a transformer-based detection framework, DETR [4], into remote sensing detection tasks, which brings more research diversity. + +While these approaches have achieved promising results in addressing the issue of rotation variance, they do not consider the strong and valuable prior information presented in aerial images. Instead, our approach uses the large kernel and spatial selective mechanism to better model these priors without modifying the current detection framework. + +# 2.2. Large Kernel Networks + +Transformer-based [59] models, such as the Vision Transformer (ViT) [1, 11, 14, 53, 60], Swin transformer [25, 39, 51, 64, 70, 83], and pyramid transformer [62, 67], have gained popularity in computer vision. Research [17, 45, 55, 72, 85] has demonstrated that the large receptive field is a key factor in their success. Recent work has shown that well-designed convolutional networks with large receptive fields can also be highly competitive with transformer-based models. For example, ConvNeXt [40] uses $7 \times 7$ depth-wise convolutions in its backbone, resulting in significant performance improvements in downstream tasks. In addition, RepLKNet [13] even uses a $31 \times 31$ convolutional kernel via re-parameterization, achieving compelling performance. A subsequent work SLaK [38], further expands the kernel size to $51 \times 51$ through kernel decomposition and sparse group techniques. RF-Next [18] automatically searches for a fixed + +![](images/c5a076b661b5d458804786abcc0a7b8380a683b072777292ba4b9ea3993b0fdd.jpg) +Figure 3. Architectural comparison between our proposed LSK module and other representative selective mechanism modules. K: Kernel. + +![](images/2cebb7e29b6ec97ac377dd67b9c69e0c2d7594fc42c85702b004e2241f3172b8.jpg) + +![](images/8ce330c0dfca81cc999baa38a4d05a2bc2de3eed51e13836546f3c7d641b9c8f.jpg) + +![](images/a52af307ee375073e004c1f68353bc71e84e097d84aadeed78c7291c2e00b1e7.jpg) + +large kernel for various tasks. VAN [19] introduces an efficient decomposition of large kernels as convolutional attention. Similarly, SegNeXt [20] and Conv2Former [28] demonstrate that large kernel convolution plays an important role in modulating the convolutional features with a richer context. + +Although large kernel convolutions have received attention in general object recognition, there has been a lack of research examining their significance in remote sensing detection. As previously noted in Sec. 1, aerial images possess unique characteristics that make large kernels particularly well-suited for remote sensing. As far as we know, our work represents the first attempt to introduce large kernel convolutions for remote sensing and to examine their importance in this field. + +# 2.3. Attention/Selective Mechanism + +The attention mechanism [21] is a simple but effective way to enhance neural representations for various tasks. The channel attention SE block [30] uses global average information to reweight feature channels, while spatial attention modules like GENet [29], GCNet [3], and SGE [34] enhance a network's ability to model context information via spatial masks. CBAM [66] and BAM [52] combine both channel and spatial attention. + +In addition to channel/spatial attention mechanisms, kernel selection is a self-adaptive and effective technique for dynamic context modelling. CondConv [73] and Dynamic convolution [5] use parallel kernels to adaptively aggregate features from multiple convolution kernels. SKNet [33] introduces multiple branches with different convolutional kernels and selectively combines them along the channel dimension. ResNeSt [84] extends the idea of SKNet by partitioning the input feature map into several groups. Similarly to the SKNet, SCNet [37] uses branch attention to capturing richer information and spatial attention to improve localization ability. Deformable Convnets [8, 89] introduce a flexible kernel shape for convolution units. + +Our approach bears the most similarity to SKNet [33]. However, there are two key distinctions between the two + +![](images/4d4de59c7dcfa5bf07dbaba2286cf630d5a38a4e92187d05be2691e3bf643343.jpg) +Figure 4. A block of LSKNet. + +methods. Firstly, our proposed selective mechanism relies explicitly on a sequence of large kernels via decomposition, a departure from most existing attention-based approaches. Secondly, our method adaptively aggregates information across large kernels in the spatial dimension rather than the channel dimension utilized by SKNet. This design is more intuitive and effective for remote sensing tasks because channel-wise selection fails to model the spatial variance for different targets across the image space. The detailed structural comparisons are listed in Fig. 3. + +# 3. Methods + +# 3.1. LSKNet Architecture + +The overall architecture of the LSKNet backbone is simply built upon repeated LSKNet Blocks. Fig 4 illustrates an LSKNet Block, which is inspired by ConvNeXt [41], MetaFormer [81], PVT-v2 [63], Conv2Former [28] and VAN [19]. Each LSKNet block consists of two residual sub-blocks: the Large Kernel Selection (LK Selection) subblock and the Feed-forward Network (FFN) sub-block. + +The LK Selection sub-block dynamically adjusts the network's receptive field as needed. The core LSK module + +![](images/4fc7ef940ab39965d1a30be538f026fe14d1fd03f7677f06bb30cbb8a0c2c15d.jpg) +Figure 5. A conceptual illustration of LSK module. + +
Model{C1,C2,C3,C4}{D1,D2,D3,D4}#P
★LSKNet-T{32,64,160,256}{3,3,5,2}4.3M
★LSKNet-S{64,128,320,512}{2,2,4,2}14.4M
+ +Table 1. Variants of LSKNet used in this paper. $C_i$ : feature channel number; $D_i$ : number of LSKNet blocks of each stage $i$ . + +
RF(k,d) sequence#PFLOPs
23(23,1)40.4K42.4G
(5,1) → (7,3)11.3K11.9G
29(29,1)60.4K63.3G
(3,1) → (5,2) → (7,3)11.3K13.6G
+ +Table 2. Theoretical efficiency comparisons of two representative examples by expanding a single large depth-wise kernel into a sequence, given channels being 64. $k$ : kernel size; $d$ : dilation. + +(Fig. 5) is embedded in the LK Selection sub-block. It consists of a sequence of large kernel convolutions and a spatial kernel selection mechanism, which will be elaborated on later. The FFN sub-block is used for channel mixing and feature refinement, which consists of a sequence of a fully connected layer, a depth-wise convolution, a GELU [26] activation, and a second fully connected layer. + +The detailed configuration of different variants of LSKNet used in this paper is listed in Tab. 1. + +# 3.2. Large Kernel Convolutions + +According to the prior (2), as stated in Sec. 1, it is suggested to model a series of multiple long-range contexts for adaptive selection. Therefore, we propose constructing a larger kernel convolution by explicitly decomposing it into a sequence of depth-wise convolutions with a large growing kernel and increasing dilation. Specifically, for the $i$ -th depth-wise convolution, the expansion of the kernel size $k$ , dilation rate $d$ , and the receptive field $RF$ are defined as follows: + +$$ +k _ {i - 1} \leq k _ {i}; d _ {1} = 1, d _ {i - 1} < d _ {i} \leq R F _ {i - 1}, \tag {1} +$$ + +$$ +R F _ {1} = k _ {1}, R F _ {i} = d _ {i} \left(k _ {i} - 1\right) + R F _ {i - 1}. \tag {2} +$$ + +The increasing kernel size and dilation rate ensure that the receptive field expands quickly enough. We set an upper + +bound on the dilation rate to guarantee that the dilation convolution does not introduce gaps between feature maps. For instance, we can decompose a large kernel into 2 or 3 depth-wise convolutions as in Tab. 2, which have a theoretical receptive field of 23 and 29, respectively. + +There are two advantages of the proposed designs. First, it explicitly yields multiple features with various large receptive fields, which makes it easier for the later kernel selection. Second, sequential decomposition is more efficient than simply applying a single larger kernel. As shown in Tab. 2, under the same resulted theoretical receptive field, our decomposition greatly reduces the number of parameters compared to the standard large convolution kernels. To obtain features with rich contextual information from different ranges for input $\mathbf{X}$ , a series of decomposed depth-wise convolutions with different receptive fields are applied: + +$$ +\mathbf {U} _ {0} = \mathbf {X}, \quad \mathbf {U} _ {i + 1} = \mathcal {F} _ {i} ^ {d w} (\mathbf {U} _ {i}), \tag {3} +$$ + +where $\mathcal{F}_i^{dw}(\cdot)$ are depth-wise convolutions with kernel $k_{i}$ and dilation $d_{i}$ . Assuming there are $N$ decomposed kernels, each of which is further processed by a $1\times 1$ convolution layer $\mathcal{F}^{1\times 1}(\cdot)$ : + +$$ +\widetilde {\mathbf {U}} _ {i} = \mathcal {F} _ {i} ^ {1 \times 1} \left(\mathbf {U} _ {i}\right), \text {f o r} i \text {i n} [ 1, N ], \tag {4} +$$ + +allowing channel mixing for each spatial feature vector. Then, a selection mechanism is proposed to dynamically select kernels for various objects based on the multi-scale features obtained, which would be introduced next. + +# 3.3. Spatial Kernel Selection + +To enhance the network's ability to focus on the most relevant spatial context regions for detecting targets, we use a spatial selection mechanism to spatially select the feature maps from large convolution kernels at different scales. Firstly, we concatenate the features obtained from different kernels with different ranges of receptive field: + +$$ +\widetilde {\mathbf {U}} = \left[ \widetilde {\mathbf {U}} _ {1}; \dots ; \widetilde {\mathbf {U}} _ {i} \right], \tag {5} +$$ + +and then efficiently extract the spatial relationship by applying channel-based average and maximum pooling (denoted + +as $\mathcal{P}_{avg}(\cdot)$ and $\mathcal{P}_{max}(\cdot)$ to $\tilde{\mathbf{U}}$ : + +$$ +\mathbf {S A} _ {a v g} = \mathcal {P} _ {a v g} (\widetilde {\mathbf {U}}), \mathbf {S A} _ {m a x} = \mathcal {P} _ {m a x} (\widetilde {\mathbf {U}}), \qquad (6) +$$ + +where $\mathbf{SA}_{avg}$ and $\mathbf{SA}_{max}$ are the average and maximum pooled spatial feature descriptors. To allow information interaction among different spatial descriptors, we concatenate the spatially pooled features and use a convolution layer $\mathcal{F}^{2\rightarrow N}(\cdot)$ to transform the pooled features (with 2 channels) into $N$ spatial attention maps: + +$$ +\widehat {\mathbf {S A}} = \mathcal {F} ^ {2 \rightarrow N} \left(\left[ \mathbf {S A} _ {a v g}; \mathbf {S A} _ {m a x} \right]\right). \tag {7} +$$ + +For each of the spatial attention maps, $\widehat{\mathbf{SA}_i}$ , a sigmoid activation function is applied to obtain the individual spatial selection mask for each of the decomposed large kernels: + +$$ +\widetilde {\mathbf {S A} _ {i}} = \sigma (\widehat {\mathbf {S A} _ {i}}), \tag {8} +$$ + +where $\sigma(\cdot)$ denotes the sigmoid function. The feature maps from the sequence of decomposed large kernels are weighted by their corresponding spatial selection masks and then fused by a convolution layer $\mathcal{F}(\cdot)$ to obtain the attention feature $\mathbf{S}$ : + +$$ +\mathbf {S} = \mathcal {F} \left(\sum_ {i = 1} ^ {N} \left(\widetilde {\mathbf {S A}} _ {i} \cdot \widetilde {\mathbf {U}} _ {i}\right)\right). \tag {9} +$$ + +The final output of the LSK module is the element-wise product between the input feature $\mathbf{X}$ and $\mathbf{S}$ , similarly in [19, 20, 28]: + +$$ +\mathbf {Y} = \mathbf {X} \cdot \mathbf {S}. \tag {10} +$$ + +Fig. 5 shows a detailed conceptual illustration of an LSK module where we intuitively demonstrate how the large selective kernel works by adaptively collecting the corresponding large receptive field for different objects. + +# 4. Experiments + +# 4.1. Datasets + +HRSC2016 [42] is a high-resolution remote sensing dataset which is collected for ship detection. It consists of 1,061 images which contain 2,976 instances of ships. + +DOTA-v1.0 [68] consists of 2,806 remote sensing images. It contains 188,282 instances of 15 categories: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), and Helicopter (HC). + +FAIR1M-v1.0 [58] is a recently published remote sensing dataset that consists of 15,266 high-resolution images and more than 1 million instances. It contains 5 categories and 37 sub-categories objects. + +# 4.2. Implementation Details + +In our experiment, we report the results of the oriented object detection models on HRSC2016, DOTA-v1.0 and FAIR1M-v1.0 datasets. To ensure fairness, we follow the same dataset processing approach as other mainstream methods [23, 24, 69]. For DOTA-v1.0 and FAIR1M-v1.0 datasets, we adopt multi-scale training and testing strategy by first rescaling the images into three scales (0.5, 1.0, 1.5), and then cropping each scaled image into $1024 \times 1024$ sub-images with a patch overlap of 500 pixels. For the HRSC2016 dataset, we rescale the images by setting the longer side of the image to 800 pixels, without changing their aspect ratios. + +During our experiments, the backbones are first pretrained on the ImageNet-1K [10] dataset and then finetuned on the target remote sensing benchmarks. In ablation studies, we adopt the 100-epoch backbone pretraining schedule for experimental efficiency (Tab. 3, 5, 4, 6, 7). We adopt a 300-epoch backbone pretraining strategy to pursue higher accuracy in main results (Tab. 8, 9, 10), similarly to [6,23,69,75]. In main results (Tab. 8, 9), the "Pre." column stands for the dataset on which the networks/backbones are pretrained (IN: Imagenet [10] dataset; CO: Microsoft COCO [36] dataset; MA: Million-AID [43] dataset). Unless otherwise stated, LSKNet is defaulting to be built within the framework of Oriented RCNN [69] due to its compelling performance and efficiency. All the models are trained on the training and validation sets and tested on the testing set. Following [69], we train the models for 36 epochs on the HRSC2016 datasets and 12 epochs on the DOTA-v1.0 and FAIR1M-v1.0 datasets, with the AdamW [44] optimizer. The initial learning rate is set to 0.0004 for HRSC2016, and 0.0002 for the other two datasets, with a weight decay of 0.05. The models are implemented under MMRotate [88] framework. We use 8 RTX3090 GPUs with a batch size of 8 for model training and use a single RTX3090 GPU for testing. All the FLOPs we report in this paper are calculated with a $1024 \times 1024$ image input. + +# 4.3. Ablation Study + +In this section, we report ablation study results on the DOTA-v1.0 test set to investigate its effectiveness. + +Large Kernel Decomposition. Deciding on the number of kernels to decompose is a critical choice for the LSK module. We follow Eq. (1) to configure the decomposed kernels. The results of the ablation study on the number of large kernel decompositions, when the theoretical receptive field is fixed at 29, are shown in Tab. 3. It suggests that decomposing the large kernel into two depth-wise large kernels results in a good trade-off between speed and accuracy, achieving the best performance in terms of both FPS (frames per second) and mAP (mean average precision). + +Receptive Field Size and Selection Type. Based on our + +
(k,d) sequenceRFNum.FPSmAP (%)
(29,1)29118.680.66
(5,1)→(7,4)29220.580.91
(3,1)→(5,2)→(7,3)29319.280.77
+ +Table 3. The effects of the number of decomposed large kernels on the inference FPS and mAP, given the theoretical receptive field being 29. We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. Decomposing the large kernel into two depth-wise kernels achieves the best performance of speed and accuracy. + +
(k1, d1)(k2, d2)CSSSRFFPSmAP (%)
(3, 1)(5, 2)--1122.180.80
(5, 1)(7, 3)--2321.780.94
(5, 1)(7, 4)--2920.580.91
(7, 1)(9, 4)--3921.380.84
(5, 1)(7, 3)✓-2319.680.57
(5, 1)(7, 3)-✓2320.781.31
+ +Table 4. The effectiveness of the key design components of the LSKNet when the large kernel is decomposed into a sequence of two depth-wise kernels. CS: channel selection (likewise in SKNet [33]); SS: spatial selection (ours). We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. The LSKNet achieves the best performance when using a reasonably large receptive field with spatial selection. + +
PoolingFPSmAP (%)
Max.Avg.
✓20.781.23
✓20.781.12
✓✓20.781.31
+ +evaluations presented in Tab. 3, we find that the optimal solution for our proposed LSKNet is to decompose the large kernel into two depth-wise kernels in series. Furthermore, Tab. 4 shows that excessively small or large receptive fields can hinder the performance of the LSKNet, and a receptive field size of approximately 23 is determined to be the most effective. In addition, our experiments indicate that the proposed spatial selection approach is more effective than channel attention (similarly in SKNet [33]) for remote sensing object detection tasks. It suggests that in detection tasks, spatial information is more critical. + +Pooling Layers in Spatial Selection. We conduct experiments to determine the optimal pooling layers for spatial selection, as reported in Tab. 5. The results suggest that using both max and average pooling in the spatial selection component of our LSK module provides the best performance without sacrificing inference speed. + +Performance of LSKNet backbone under different detection frameworks. To validate the generality and ef + +Table 5. Ablation study on the effectiveness of the maximum and average pooling in spatial selection of our proposed LSK module. We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. The best result is obtained when using both. + +
FrameworksResNet-18★ LSKNet-T
ORCNN [69]79.2781.31 (+2.04)
RoI Trans. [12]78.3280.89 (+2.57)
S²A-Net [23]76.8280.15 (+3.33)
R3Det [75]74.1678.39 (+4.23)
#P (backbone only)11.2M4.3M (-62%)
FLOPs (backbone only)38.1G19.1G (-50%)
+ +Table 6. Comparison of LSKNet-T and ResNet-18 as backbones with different detection frameworks on DOTA-v1.0. The LSKNet-T backbone is pretrained on ImageNet for 100 epochs. The lightweight LSKNet-T achieves significantly higher mAP in various frameworks than ResNet-18. + +
GroupModel (backbone only)#PFLOPsmAP (%)
BaselineResNet-1811.2M38.1G79.27
Large KernelVAN-B1 [19]13.4M52.7G81.15
ConvNeXt V2-N [65]15.0M51.2G80.81
MSCAN-S [20]13.1M45.0G81.12
Selective AttentionSKNet-26 [33]14.5M58.5G80.67
ResNeSt-14 [84]8.6M57.9G79.51
SCNet-18 [37]14.0M50.7G79.69
Ours★ LSKNet-S14.4M54.4G81.48
Prev BestCSPNeXt [46]26.1M87.6G81.33
+ +Table 7. Comparison on LSKNet-S and other (large kernel/selective attention) backbones under O-RCNN [69] framework on DOTA-v1.0, except that the Prev Best is under RT-MDet [46] framework. All backbones are pretrained on ImageNet for 100 epochs. Our LSKNet achieves the best mAP under similar complexity budgets. + +
MethodPre.mAP(07)↑mAP(12)↑#P↓FLOPs↓
DRN [50]IN-92.70--
CenterMap [61]IN-92.8041.1M198G
Rol Trans. [12]IN86.20-55.1M200G
G. V. [71]IN88.20-41.1M198G
R3Det [75]IN89.2696.0141.9M336G
DAL [48]IN89.77-36.4M216G
GWD [77]IN89.8597.3747.4M456G
S2ANet [23]IN90.1795.0138.6M198G
AOPG [6]IN90.3496.22--
ReDet [24]IN90.4697.6331.6M-
O-RCNN [69]IN90.5097.6041.1M199G
RTMDet [46]CO90.6097.1052.3M205G
★LSKNet-TIN90.5498.1321.0M124G
★LSKNet-SIN90.6598.4631.0M161G
+ +Table 8. Comparison with state-of-the-art methods on the HRSC2016 dataset. The LSKNet-S backbone is pretrained on ImageNet for 300 epochs, the same with most compared methods [23,69,75]. mAP (07/12): VOC 2007 [15]/2012 [16] metrics. + +fectiveness of our proposed LSKNet backbone, we evaluate its performance under various remote sensing detection frameworks, including two-stage frameworks O-RCNN [69] and RoI Transformer [12] as well as one-stage frameworks $\mathrm{S}^2\mathrm{A}$ -Net [23] and R3Det [75]. The re + +Method |Pre. $\left|\mathbf{mAP}\uparrow\right|\# \mathbf{P}\downarrow$ FLOPs↓ PL BD BR GTF SV LV SH TC BC ST SBF RA HA SP HC + +
One-stage
R3Det [75]IN76.4741.9M336G89.8083.7748.1166.7778.7683.2787.8490.8285.3885.5165.5762.6867.5378.5672.62
CFA [22]IN76.67--89.0883.2054.3766.8781.2380.9687.1790.2184.3286.0952.3469.9475.5280.7667.96
DAFNe [31]IN76.95--89.4086.2753.7060.5182.0481.1788.6690.3783.8187.2753.9369.3875.6181.2670.86
SASM [27]IN79.17--89.5485.9457.7378.4179.7884.1989.2590.8758.8087.2763.8267.8178.6779.3569.37
AO2-DETR [9]IN79.2274.3M304G89.9584.5256.9074.8380.8683.4788.4790.8786.1288.5563.2165.0979.0982.8873.46
\( S^2ANet \) [23]IN79.42--88.8983.6057.7481.9579.9483.1989.1190.7884.8787.8170.3068.2578.3077.0169.58
R3Det-GWD [77]IN80.2341.9M336G89.6684.9959.2682.1978.9784.8387.7090.2186.5486.8573.4767.7776.9279.2274.92
RTMDet-R [46]IN80.5452.3M205G88.3684.9657.3380.4680.5884.8888.0890.9086.3287.5769.2970.6178.6380.9779.24
R3Det-KLD [79]IN80.6341.9M336G89.9285.1359.1981.3378.8284.3887.5089.8087.3387.0072.5771.3577.1279.3478.68
RTMDet-R [46]CO81.3352.3M205G88.0186.1758.5482.4481.3084.8288.7190.8988.7787.3771.9671.1881.2381.4077.13
Two-stage
SCRDet [78]IN72.61--89.9880.6552.0968.3668.3660.3272.4190.8587.9486.8665.0266.6866.2568.2465.21
Rol Trans. [12]IN74.6155.1M200G88.6582.6052.5370.8777.9376.6786.8790.7183.8382.5153.9567.6174.6768.7561.03
G.V. [71]IN75.0241.1M198G89.6485.0052.2677.3473.0173.1486.8290.7479.0286.8159.5570.9172.9470.8657.32
CenterMap [61]IN76.0341.1M198G89.8384.4154.6070.2577.6678.3287.1990.6684.8985.2756.4669.2374.1371.5666.06
CSL [76]IN76.1737.4M236G90.2585.5354.6475.3170.4473.5177.6290.8486.1586.6969.6068.0473.8371.1068.93
ReDet [24]IN80.10--88.8182.4860.8380.8278.3486.0688.3190.8788.7787.0368.6566.9079.2679.7174.67
DODet [7]IN80.62--89.9685.5258.0181.2278.7185.4688.5990.8987.1287.8070.5071.5482.0677.4374.47
AOPG [6]IN80.66--89.8885.5760.9081.5178.7085.2988.8590.8987.6087.6571.6668.6982.3177.3273.10
O-RCNN [69]IN80.8741.1M199G89.8485.4361.0979.8279.7185.3588.8290.8886.6887.7372.2170.8082.4278.1874.11
KFloU [80]IN80.9358.8M206G89.4484.4162.2282.5180.1086.0788.6890.9087.3288.3872.8071.9578.9674.9575.27
RVSA [60]MA81.24114.4M414G88.9785.7661.4681.2779.9885.3188.3090.8485.0687.5066.7773.1184.7581.8877.58
★LSKNet-T (ours)IN81.3721.0M124G89.1484.9061.7883.5081.5485.8788.6490.8988.0287.3171.5570.7478.6679.8178.16
★LSKNet-S (ours)IN81.6431.0M161G89.5786.3463.1383.6782.2086.1088.6690.8988.4187.4271.7269.5878.8881.7776.52
★LSKNet-S* (ours)IN81.8531.0M161G89.6985.7061.4783.2381.3786.0588.6490.8888.4987.4071.6771.3579.1981.7780.86
+ +Table 9. Comparison with state-of-the-art methods on the DOTA-v1.0 dataset with multi-scale training and testing. The LSKNet backbones are pretrained on ImageNet for 300 epochs, similarly to [23, 69, 75]. *: With EMA finetune similarly to the compared methods [46]. + +
ModelG. V.* [71]RetinaNet* [35]C-RCNN* [2]F-RCNN* [56]RoI Trans.* [12]O-RCNN [69]★ LSKNet-T★ LSKNet-S
mAP(%)29.9230.6731.1832.1235.2945.6046.9347.87
+ +Table 10. Comparison with state-of-the-art methods on the FAIR1M-v1.0 dataset. The LSKNet backbones are pretrained on ImageNet for 300 epochs, similarly to [23,69,75].*: Results are referenced from FAIR1M paper [58]. + +sults in Tab. 6 show that our proposed LSKNet-T backbone significantly improves detection performance compared to ResNet-18, while using only $38\%$ of its parameters and with $50\%$ fewer FLOPs. + +Comparison with Other Large Kernel/Selective Attention Backbones. We also compare our LSKNet with 6 popular high-performance backbone models with large kernels or selective attention. As shown in Tab. 7, under similar model sizes and complexity budgets, our LSKNet outperforms all other models on the DOTA-v1.0 dataset. + +# 4.4. Main Results + +Results on HRSC2016. We evaluated the performance of our LSKNet against 12 state-of-the-art methods on the HRSC2016 dataset. The results presented in Tab. 8 demonstrate that our LSKNet-S outperforms all other methods with an mAP of $90.65\%$ and $98.46\%$ under the PASCAL VOC 2007 [15] and VOC 2012 [16] metrics, respectively. + +Results on DOTA-v1.0. We compare our LSKNet with + +20 state-of-the-art methods on the DOTA-v1.0 dataset, as reported in Tab. 9. Our LSKNet-T, LSKNet-S and LSKNet-S* achieve state-of-the-art with mAP of $81.37\%$ , $81.64\%$ and $81.85\%$ respectively. Notably, our high-performing LSKNet-S reaches an inference speed of 18.1 FPS on 1024x1024 images with a single RTX3090 GPU. + +Results on FAIR1M-v1.0. We compare our LSKNet against 6 other models on the FAIR1M-v1.0 dataset, as shown in Tab. 10. The results reveal that our LSKNet-T and LSKNet-S perform exceptionally well, achieving state-of-the-art mAP scores of $46.93\%$ and $47.87\%$ respectively, surpassing all other models by a significant margin. + +# 4.5. Analysis + +Detection Results Visualization. Visualization examples of detection results and Eigen-CAM [49] are shown in Fig. 6. LSKNet can capture much more context information relevant to the detected targets, leading to better performance in various hard cases, which justifies our prior (1). + +![](images/d7a8ed27195bfe79d5b31025d48d78e26b0cf161cd1c956ec42cbe49a8b53159.jpg) +(a) Robustness to obstacles + +![](images/f1cf7274765a362675051a08069ec03e4afad2981538c85f047aa29184ccefb7.jpg) +(b) Accurate Object Classification + +![](images/20c4bb773aecb4dfaa342f1407399b8017616b0288915928d51eca7471115d0d.jpg) +(c) Accurate Object Localization +Figure 6. Eigen-CAM visualization of Oriented RCNN detection framework with ResNet-50 and LSKNet-S. Our proposed LSKNet can model a much long range of context information, leading to better performance in various hard cases. + +![](images/7ebedb060824893151b42938746c503367c232b389eb40f079979e13898ef94d.jpg) +Figure 7. Normalised Ratio $R_{c}$ of Expected Selective RF Area and GT Bounding Box Area for object categories in DOTA-v1.0. The relative range of context required for different object categories varies a lot. Examples of Bridge and Soccer-ball-field are given, where the visualized receptive field is obtained from Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model. + +Relative Context Range for Different Objects. To investigate the relative range of receptive field for each object category, we define $R_{c}$ as the Ratio of Expected Selective RF Area and GT Bounding Box Area for category $c$ : + +$$ +R _ {c} = \frac {\sum_ {i = 1} ^ {I _ {c}} A _ {i} / B _ {i}}{I _ {c}}, \tag {11} +$$ + +$$ +A _ {i} = \sum_ {d = 1} ^ {D} \sum_ {n = 1} ^ {N} | \widetilde {\mathbf {S A}} _ {n} ^ {d} \cdot R F _ {n} |, B _ {i} = \sum_ {j = 1} ^ {J _ {i}} \operatorname {A r e a} \left(\mathrm {G T} _ {j}\right), \tag {12} +$$ + +where $I_{c}$ is the number of images that contain the object + +![](images/2cea3cd55e85b011419d017dc50c7bf5a4d9ed7c8006248b9021ae97b8a82202.jpg) +Figure 8. Normalised Kernel Selection Difference in the LSKNet-T blocks for Bridge, Roundabout and Soccer-ball-field. B.i.j represents the j-th LSK block in stage i. A greater value is indicative of a dependence on a broader context. + +category $c$ only. The $A_{i}$ is the sum of spatial selection activation in all LSK blocks for input image $i$ , where $D$ is the number of blocks in an LSKNet, and $N$ is the number of decomposed large kernels in an LSK module. $B_{i}$ is the total pixel area of all $J_{i}$ annotated oriented object bounding boxes (GT). We plot the normalized $R_{c}$ in Fig. 7 which represents the relative range of context required for different object categories for a better view. + +The results suggest that the Bridge category stands out as requiring a greater amount of additional contextual information compared to other categories, primarily due to its similarity in features with roads and the necessity of contextual clues to ascertain whether it is enveloped by water. Conversely, the Court categories, such as Soccer-ball-field, necessitate minimal contextual information owing to their distinctive textural attributes, specifically the court bound- + +![](images/512746ec2faceb1f4d3f46b3c748134cc1ed9cd1b4b997a852ac398188fdc385.jpg) +Bridge + +![](images/774d319db09b06d7db67c5605096e6b694516cfcfa790b7b542c00b5d59ea0f0.jpg) +Roundabout + +![](images/9beac37f773233e704842ffe7f81a23da7b961f5aed405c42fa90713a3b3e76d.jpg) +Small Vehicle + +![](images/7b6c39586a57fb0f698de55b9729fdff4f3165450b308e73fb43cf1a8c48e0b9.jpg) +Swimming Pool + +![](images/14125c3a6618e4fe0f91e7083dfe795d4cd53808d21b584b272c5953042ea552.jpg) +Ship + +![](images/3338637b3ebcde3702afc0b4ad60f0e84901eb63040f50d49a4f244714c25a21.jpg) +Storage tank + +![](images/c00d4df859a995651d0ab7c8e189bd3f6ead78cbb8164e8fa4ec9be90673080a.jpg) +Baseball diamond + +![](images/00181f35da6ab9d12fb110f9895f6c76c877a742f654a3f8d066eee074c16625.jpg) +Large Vehicle + +![](images/a2363b95673378b8e57f9ac7a60a2158b40c320a68867e0cbe9d13e7234cbc09.jpg) +Harbor + +![](images/0a790f8e132bbd87c9e1c168efde2a477c333e87deed8d4e8136587cb3c4ec06.jpg) +Tennis court + +![](images/e496d46bd283e0c36260a9d4452442e62c87f0a15a93235d83e1178fe29dcc57.jpg) +Plane +Figure 9. Receptive field activation for more object categories in DOTA-v1.0, where the activation map is obtained from the Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model. + +![](images/0604412e8dcab7a2f7eacbee42261b7d60ceda6a452313709ee4c2b3385f7d7f.jpg) +Soccer-ball field + +ary lines. It aligns with our knowledge and further supports prior (2) that the relative range of contextual information required for different object categories varies greatly. + +Kernel Selection Behaviour. We further investigate the kernel selection behaviour in our LSKNet. For object category $c$ , the Kernel Selection Difference $\Delta A_{c}$ (i.e., larger kernel selection - smaller kernel selection) of an LSKNet-T block is defined as: + +$$ +\Delta A _ {c} = \left| \widetilde {\mathbf {S A}} _ {\text {l a r g e r}} - \widetilde {\mathbf {S A}} _ {\text {s m a l l e r}} \right|. \tag {13} +$$ + +We demonstrate the normalised $\Delta A_{c}$ over all images for three typical categories: Bridge, Roundabout and Soccerball-field and for each LSKNet-T block in Fig. 8. As expected, the participation of larger kernels of all blocks for Bridge is higher than that of Roundabout, and Roundabout is higher than Soccer-ball-field. This aligns with the common sense that Soccer-ball-field indeed does not require a large amount of context, since its own texture characteristics are already sufficiently distinct and discriminatory. + +We also surprisingly discover another selection pattern of LSKNet across network depth: LSKNet usually utilizes larger kernels in its shallow layers and smaller kernels in higher levels. This indicates that networks tend to quickly focus on capturing information from large receptive fields in low-level layers so that higher-level semantics can contain sufficient receptive fields for better discrimination. + +Spatial Activation Visualisations. Spatial activation map examples for more object categories in DOTA-v1.0 + +are shown in Fig. 9, where the activation map is obtained from Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model. The object categories are arranged in decreasing order from top left to bottom right based on the Ratio of Expected Selective RF Area and GT Bounding Box Area as illustrated in Fig. 7. The spatial activation visualisation results also demonstrate that the model's behaviour aligns with our proposed two priors and the above analysis, which in turn verifies the effectiveness of the proposed mechanism. + +# 5. Conclusion + +In this paper, we propose the Large Selective Kernel Network (LSKNet) for remote sensing object detection tasks, which is designed to utilize the inherent characteristics in remote sensing images: the need for a wider and adaptable contextual understanding. By adapting its large spatial receptive field, LSKNet can effectively model the varying contextual nuances of different object types. Extensive experiments demonstrate that our proposed lightweight model achieves state-of-the-art performance on competitive remote sensing benchmarks. + +Acknowledgement. This research was supported by the NSFC (NO. 62176130, 62206134, 62225604) and the Fundamental Research Funds for the Central Universities (Nankai University, 070-63233084, 070-63233089). Computation is supported by the Supercomputing Center of Nankai University. + +# References + +[1] Yakoub Bazi, Laila Bashmal, Mohamad M. Al Rahhal, Reham Al Dayil, and Naif Al Ajan. Vision transformers for remote sensing image classification. Remote Sensing, 2021. 2 +[2] Zhaowei Cai and Nuno Vasconcelos. Cascade R-CNN: Delving into high quality object detection. In CVPR, 2018. 7 +[3] Yue Cao, Jiarui Xu, Stephen Lin, Fangyun Wei, and Han Hu. GCNet: Non-local networks meet squeeze-excitation networks and beyond. In ICCV Workshops, 2019. 3 +[4] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In ECCV, 2020. 2 +[5] Yinpeng Chen, Xiyang Dai, Mengchen Liu, Dongdong Chen, Lu Yuan, and Zicheng Liu. 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Such prior knowledge can be useful because tiny remote sensing objects may be mistakenly detected without referencing a sufficiently long-range context, which can vary for different objects. This paper considers these priors and proposes the lightweight Large Selective Kernel Network (LSKNet). LSKNet can dynamically adjust its large spatial receptive field to better model the ranging context of various objects in remote sensing scenarios. To our knowledge, large and selective kernel mechanisms have not been previously explored in remote sensing object detection. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 497, + 288, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 497, + 288, + 677 + ], + "spans": [ + { + "bbox": [ + 45, + 497, + 288, + 677 + ], + "type": "text", + "content": "Remote sensing object detection [47, 57, 82] focuses on identifying and locating objects of interest in aerial images, such as vehicles, ships or aircraft. In recent years, one mainstream trend has been to generate bounding boxes that accurately fit the orientation of the objects being detected rather than simply drawing horizontal boxes around them. Consequently, much research has focused on improving the representation of oriented bounding boxes for remote sensing object detection. This has largely been achieved through the development of specialized detection frameworks (i.e., RoI Transformer [12], Oriented R-CNN [69], and R3Det [75]) and oriented box encoding (i.e., gliding vertex [71] and midpoint offset box encoding [69]). Additionally, several loss functions, including GWD [77], KLD [79], and Modulated Loss [54], have been further proposed to enhance the" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 222, + 343, + 244 + ], + "blocks": [ + { + "bbox": [ + 307, + 222, + 343, + 244 + ], + "lines": [ + { + "bbox": [ + 307, + 222, + 343, + 244 + ], + "spans": [ + { + "bbox": [ + 307, + 222, + 343, + 244 + ], + "type": "image", + "image_path": "c3bb16fa2ce72726663a286ca45a641a4d1fbd556a43bec0cac9b91882fe8b49.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 246, + 343, + 269 + ], + "lines": [ + { + "bbox": [ + 307, + 246, + 343, + 269 + ], + "spans": [ + { + "bbox": [ + 307, + 246, + 343, + 269 + ], + "type": "text", + "content": "Ship or Vehicle?" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 350, + 212, + 447, + 310 + ], + "blocks": [ + { + "bbox": [ + 350, + 212, + 447, + 310 + ], + "lines": [ + { + "bbox": [ + 350, + 212, + 447, + 310 + ], + "spans": [ + { + "bbox": [ + 350, + 212, + 447, + 310 + ], + "type": "image", + "image_path": "6db7f7b631b5099d1fc4667c304046d7449724738601f65a7fa3b3c761dc2f65.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 316, + 546, + 350 + ], + "lines": [ + { + "bbox": [ + 305, + 316, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 546, + 350 + ], + "type": "text", + "content": "Figure 1. Successfully detecting remote sensing objects requires using a wide range of contextual information. Detectors with a limited receptive field may easily lead to incorrect results." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 449, + 213, + 545, + 310 + ], + "blocks": [ + { + "bbox": [ + 449, + 213, + 545, + 310 + ], + "lines": [ + { + "bbox": [ + 449, + 213, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 449, + 213, + 545, + 310 + ], + "type": "image", + "image_path": "910dff187a27be78cab0ab7c96a028b932c451fc85de589cb9fbfa24ca5b559a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 360, + 443, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 443, + 371 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 443, + 371 + ], + "type": "text", + "content": "performance of these approaches." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 372, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 546, + 491 + ], + "type": "text", + "content": "Despite these advances, relatively few works have considered the strong prior knowledge of remote sensing images. Aerial images are typically captured at high resolutions from a bird's eye view. In particular, most objects in aerial images may be small and difficult to identify based on their appearance alone. Instead, recognizing these objects relies on their context, as the surrounding environment can provide valuable clues about their shape, orientation, and other characteristics. According to an analysis of the remote sensing data, we identify two important priors:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 497, + 547, + 696 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 317, + 497, + 547, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 497, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 317, + 497, + 547, + 569 + ], + "type": "text", + "content": "- Accurate detection often requires a wide range of contextual information. As illustrated in Fig. 1, the limited context used by object detectors in remote sensing images can often lead to incorrect classifications. Rather than their appearance, the context distinguishes the ship from the vehicle." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 575, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 575, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 317, + 575, + 547, + 696 + ], + "type": "text", + "content": "- The contextual information required for different objects is very different. As shown in Fig. 2, the soccer field requires relatively less contextual information because of the unique distinguishable court borderlines. In contrast, the roundabout may require more context information to distinguish between gardens and ring-like buildings. Intersections, especially those partially covered by trees, require an extremely large receptive field due to the long-range dependencies between the intersecting roads." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "To address the challenge of accurately detecting objects" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 60, + 684, + 139, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 684, + 139, + 693 + ], + "spans": [ + { + "bbox": [ + 60, + 684, + 139, + 693 + ], + "type": "text", + "content": "*Corresponding authors." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 48, + 694, + 244, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 694, + 244, + 703 + ], + "spans": [ + { + "bbox": [ + 48, + 694, + 244, + 703 + ], + "type": "text", + "content": "Team URL: https://github.com/IMPlus-PCALab" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 48, + 704, + 252, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 704, + 252, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 704, + 252, + 712 + ], + "type": "text", + "content": "Project page: https://github.com/zcablii/LSKNet" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16794" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 68, + 270, + 223 + ], + "blocks": [ + { + "bbox": [ + 66, + 68, + 270, + 223 + ], + "lines": [ + { + "bbox": [ + 66, + 68, + 270, + 223 + ], + "spans": [ + { + "bbox": [ + 66, + 68, + 270, + 223 + ], + "type": "image", + "image_path": "84fbfd0eeb92108394a7ef9b0a7e672251aa231fbdfdf86c42802e44b6f03bb8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 225, + 288, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 225, + 288, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 288, + 258 + ], + "type": "text", + "content": "Figure 2. The wide range of contextual information required for different object types is very different by human criteria. The objects with red boxes are the exact ground-truth annotations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 443 + ], + "type": "text", + "content": "in remote sensing images, which often require a wide and dynamic range of contextual information, we propose a novel lightweight detection backbone called Large Selective Kernel Network (LSKNet). Our approach involves dynamically adjusting the receptive field of the feature extraction backbone to more effectively process the varying wide context of the objects being detected. This is achieved through a spatial selective mechanism, which efficiently weights the features processed by a sequence of large depth-wise kernels and then spatially merge them. The weights of these kernels are determined dynamically based on the input, allowing the model to adaptively use different large kernels and adjust the receptive field for each target in space as needed." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 445, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 564 + ], + "type": "text", + "content": "To our knowledge, the proposed LSKNet is the first to investigate using large and selective kernels for remote sensing object detection. Despite its simplicity and lightweight nature, our model achieves state-of-the-art performance on three popular datasets: HRSC2016 (98.46% mAP), DOTAv1.0 (81.85% mAP), and FAIR1M-v1.0 (47.87% mAP), surpassing previously published results. Furthermore, we demonstrate that our model's behaviour aligns with the two priors above, which in turn verifies the effectiveness of the proposed mechanism." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 578, + 134, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 134, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 134, + 590 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 284, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 284, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 284, + 611 + ], + "type": "text", + "content": "2.1. Remote Sensing Object Detection Framework" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "content": "High-performance remote sensing object detectors often rely on the RCNN [56] framework, which consists of a region proposal network and regional CNN detection heads. The RPN proposes high-quality regions of interest (RoIs) from the backbone feature maps, while the regional CNN detection heads are responsible for object classification and bounding box regression. Several variations on the RCNN framework have been proposed in recent years. The two-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": "stage RoI transformer [12] uses fully-connected layers to rotate candidate horizontal anchor boxes in the first stage, and then features within the boxes are extracted for further regression and classification. SCRDet [78] uses an attention mechanism to reduce background noise and improve the modelling of crowded and small objects. Oriented RCNN [69] and Gliding Vertex [71] introduce new box encoding systems to address the instability of training losses caused by rotation angle periodicity. Some approaches [32, 61, 87] treat remote sensing detection as a point detection task [74], providing an alternative way of addressing remote sensing detection problems." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 217, + 545, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 419 + ], + "type": "text", + "content": "Rather than relying on the proposed anchors, one-stage detection frameworks classify and regress oriented bounding boxes directly from grid densely sampled anchors. The one-stage S²A network [23] extracts robust object features via oriented feature alignment and orientation-invariant feature extraction. DRN [50], on the other hand, leverages attention mechanisms to dynamically refined the backbone's extracted features for more accurate predictions. In contrast with Oriented RCNN and Gliding Vertex, RSDet [54] addresses the discontinuity of regression loss by introducing a modulated loss. LD [86] enhances the localization quality of oriented bounding boxes by distillation. AOPG [6] and R3Det [75] adopt a progressive regression approach, refining bounding boxes from coarse to fine granularity. In addition to CNN, AO2-DETR [9] introduces a transformer-based detection framework, DETR [4], into remote sensing detection tasks, which brings more research diversity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 421, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 545, + 492 + ], + "type": "text", + "content": "While these approaches have achieved promising results in addressing the issue of rotation variance, they do not consider the strong and valuable prior information presented in aerial images. Instead, our approach uses the large kernel and spatial selective mechanism to better model these priors without modifying the current detection framework." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 502, + 440, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 440, + 515 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 440, + 515 + ], + "type": "text", + "content": "2.2. Large Kernel Networks" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "Transformer-based [59] models, such as the Vision Transformer (ViT) [1, 11, 14, 53, 60], Swin transformer [25, 39, 51, 64, 70, 83], and pyramid transformer [62, 67], have gained popularity in computer vision. Research [17, 45, 55, 72, 85] has demonstrated that the large receptive field is a key factor in their success. Recent work has shown that well-designed convolutional networks with large receptive fields can also be highly competitive with transformer-based models. For example, ConvNeXt [40] uses " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " depth-wise convolutions in its backbone, resulting in significant performance improvements in downstream tasks. In addition, RepLKNet [13] even uses a " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "31 \\times 31" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " convolutional kernel via re-parameterization, achieving compelling performance. A subsequent work SLaK [38], further expands the kernel size to " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "51 \\times 51" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " through kernel decomposition and sparse group techniques. RF-Next [18] automatically searches for a fixed" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16795" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 84, + 154, + 204 + ], + "blocks": [ + { + "bbox": [ + 61, + 84, + 154, + 204 + ], + "lines": [ + { + "bbox": [ + 61, + 84, + 154, + 204 + ], + "spans": [ + { + "bbox": [ + 61, + 84, + 154, + 204 + ], + "type": "image", + "image_path": "c5a076b661b5d458804786abcc0a7b8380a683b072777292ba4b9ea3993b0fdd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 202, + 545, + 214 + ], + "lines": [ + { + "bbox": [ + 46, + 202, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 545, + 214 + ], + "type": "text", + "content": "Figure 3. Architectural comparison between our proposed LSK module and other representative selective mechanism modules. K: Kernel." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 197, + 83, + 275, + 204 + ], + "blocks": [ + { + "bbox": [ + 197, + 83, + 275, + 204 + ], + "lines": [ + { + "bbox": [ + 197, + 83, + 275, + 204 + ], + "spans": [ + { + "bbox": [ + 197, + 83, + 275, + 204 + ], + "type": "image", + "image_path": "2cebb7e29b6ec97ac377dd67b9c69e0c2d7594fc42c85702b004e2241f3172b8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 323, + 85, + 406, + 204 + ], + "blocks": [ + { + "bbox": [ + 323, + 85, + 406, + 204 + ], + "lines": [ + { + "bbox": [ + 323, + 85, + 406, + 204 + ], + "spans": [ + { + "bbox": [ + 323, + 85, + 406, + 204 + ], + "type": "image", + "image_path": "8ce330c0dfca81cc999baa38a4d05a2bc2de3eed51e13836546f3c7d641b9c8f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 453, + 85, + 529, + 204 + ], + "blocks": [ + { + "bbox": [ + 453, + 85, + 529, + 204 + ], + "lines": [ + { + "bbox": [ + 453, + 85, + 529, + 204 + ], + "spans": [ + { + "bbox": [ + 453, + 85, + 529, + 204 + ], + "type": "image", + "image_path": "a52af307ee375073e004c1f68353bc71e84e097d84aadeed78c7291c2e00b1e7.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 229, + 286, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 229, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 286, + 300 + ], + "type": "text", + "content": "large kernel for various tasks. VAN [19] introduces an efficient decomposition of large kernels as convolutional attention. Similarly, SegNeXt [20] and Conv2Former [28] demonstrate that large kernel convolution plays an important role in modulating the convolutional features with a richer context." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 301, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 286, + 408 + ], + "type": "text", + "content": "Although large kernel convolutions have received attention in general object recognition, there has been a lack of research examining their significance in remote sensing detection. As previously noted in Sec. 1, aerial images possess unique characteristics that make large kernels particularly well-suited for remote sensing. As far as we know, our work represents the first attempt to introduce large kernel convolutions for remote sensing and to examine their importance in this field." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 418, + 216, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 216, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 216, + 430 + ], + "type": "text", + "content": "2.3. Attention/Selective Mechanism" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 437, + 286, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 286, + 533 + ], + "type": "text", + "content": "The attention mechanism [21] is a simple but effective way to enhance neural representations for various tasks. The channel attention SE block [30] uses global average information to reweight feature channels, while spatial attention modules like GENet [29], GCNet [3], and SGE [34] enhance a network's ability to model context information via spatial masks. CBAM [66] and BAM [52] combine both channel and spatial attention." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 533, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 286, + 688 + ], + "type": "text", + "content": "In addition to channel/spatial attention mechanisms, kernel selection is a self-adaptive and effective technique for dynamic context modelling. CondConv [73] and Dynamic convolution [5] use parallel kernels to adaptively aggregate features from multiple convolution kernels. SKNet [33] introduces multiple branches with different convolutional kernels and selectively combines them along the channel dimension. ResNeSt [84] extends the idea of SKNet by partitioning the input feature map into several groups. Similarly to the SKNet, SCNet [37] uses branch attention to capturing richer information and spatial attention to improve localization ability. Deformable Convnets [8, 89] introduce a flexible kernel shape for convolution units." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 712 + ], + "type": "text", + "content": "Our approach bears the most similarity to SKNet [33]. However, there are two key distinctions between the two" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 342, + 229, + 499, + 398 + ], + "blocks": [ + { + "bbox": [ + 342, + 229, + 499, + 398 + ], + "lines": [ + { + "bbox": [ + 342, + 229, + 499, + 398 + ], + "spans": [ + { + "bbox": [ + 342, + 229, + 499, + 398 + ], + "type": "image", + "image_path": "4d4de59c7dcfa5bf07dbaba2286cf630d5a38a4e92187d05be2691e3bf643343.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 370, + 404, + 482, + 416 + ], + "lines": [ + { + "bbox": [ + 370, + 404, + 482, + 416 + ], + "spans": [ + { + "bbox": [ + 370, + 404, + 482, + 416 + ], + "type": "text", + "content": "Figure 4. A block of LSKNet." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "text", + "content": "methods. Firstly, our proposed selective mechanism relies explicitly on a sequence of large kernels via decomposition, a departure from most existing attention-based approaches. Secondly, our method adaptively aggregates information across large kernels in the spatial dimension rather than the channel dimension utilized by SKNet. This design is more intuitive and effective for remote sensing tasks because channel-wise selection fails to model the spatial variance for different targets across the image space. The detailed structural comparisons are listed in Fig. 3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 564, + 366, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 564, + 366, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 564, + 366, + 575 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 585, + 429, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 429, + 596 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 429, + 596 + ], + "type": "text", + "content": "3.1. LSKNet Architecture" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 687 + ], + "type": "text", + "content": "The overall architecture of the LSKNet backbone is simply built upon repeated LSKNet Blocks. Fig 4 illustrates an LSKNet Block, which is inspired by ConvNeXt [41], MetaFormer [81], PVT-v2 [63], Conv2Former [28] and VAN [19]. Each LSKNet block consists of two residual sub-blocks: the Large Kernel Selection (LK Selection) subblock and the Feed-forward Network (FFN) sub-block." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "The LK Selection sub-block dynamically adjusts the network's receptive field as needed. The core LSK module" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16796" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 74, + 521, + 196 + ], + "blocks": [ + { + "bbox": [ + 75, + 74, + 521, + 196 + ], + "lines": [ + { + "bbox": [ + 75, + 74, + 521, + 196 + ], + "spans": [ + { + "bbox": [ + 75, + 74, + 521, + 196 + ], + "type": "image", + "image_path": "4fc7ef940ab39965d1a30be538f026fe14d1fd03f7677f06bb30cbb8a0c2c15d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 202, + 198, + 391, + 210 + ], + "lines": [ + { + "bbox": [ + 202, + 198, + 391, + 210 + ], + "spans": [ + { + "bbox": [ + 202, + 198, + 391, + 210 + ], + "type": "text", + "content": "Figure 5. A conceptual illustration of LSK module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 220, + 282, + 256 + ], + "blocks": [ + { + "bbox": [ + 51, + 220, + 282, + 256 + ], + "lines": [ + { + "bbox": [ + 51, + 220, + 282, + 256 + ], + "spans": [ + { + "bbox": [ + 51, + 220, + 282, + 256 + ], + "type": "table", + "html": "
Model{C1,C2,C3,C4}{D1,D2,D3,D4}#P
★LSKNet-T{32,64,160,256}{3,3,5,2}4.3M
★LSKNet-S{64,128,320,512}{2,2,4,2}14.4M
", + "image_path": "ca9b26db964d6f1888e9278be6cfff170f668af2eead7236694fadac1aab4e9f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 55, + 291, + 279, + 352 + ], + "blocks": [ + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "type": "text", + "content": "Table 1. Variants of LSKNet used in this paper. " + }, + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "type": "text", + "content": ": feature channel number; " + }, + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "type": "inline_equation", + "content": "D_i" + }, + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "type": "text", + "content": ": number of LSKNet blocks of each stage " + }, + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 258, + 287, + 281 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 291, + 279, + 352 + ], + "lines": [ + { + "bbox": [ + 55, + 291, + 279, + 352 + ], + "spans": [ + { + "bbox": [ + 55, + 291, + 279, + 352 + ], + "type": "table", + "html": "
RF(k,d) sequence#PFLOPs
23(23,1)40.4K42.4G
(5,1) → (7,3)11.3K11.9G
29(29,1)60.4K63.3G
(3,1) → (5,2) → (7,3)11.3K13.6G
", + "image_path": "0eeb9c3ea461c102fb676ab3812ac0d9759e0080fa09f9b72b6da55112f79d51.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 354, + 287, + 387 + ], + "lines": [ + { + "bbox": [ + 47, + 354, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 287, + 387 + ], + "type": "text", + "content": "Table 2. Theoretical efficiency comparisons of two representative examples by expanding a single large depth-wise kernel into a sequence, given channels being 64. " + }, + { + "bbox": [ + 47, + 354, + 287, + 387 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 354, + 287, + 387 + ], + "type": "text", + "content": ": kernel size; " + }, + { + "bbox": [ + 47, + 354, + 287, + 387 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 354, + 287, + 387 + ], + "type": "text", + "content": ": dilation." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 399, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 483 + ], + "type": "text", + "content": "(Fig. 5) is embedded in the LK Selection sub-block. It consists of a sequence of large kernel convolutions and a spatial kernel selection mechanism, which will be elaborated on later. The FFN sub-block is used for channel mixing and feature refinement, which consists of a sequence of a fully connected layer, a depth-wise convolution, a GELU [26] activation, and a second fully connected layer." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 483, + 288, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 288, + 507 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 288, + 507 + ], + "type": "text", + "content": "The detailed configuration of different variants of LSKNet used in this paper is listed in Tab. 1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 514, + 197, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 197, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 197, + 528 + ], + "type": "text", + "content": "3.2. Large Kernel Convolutions" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "text", + "content": "According to the prior (2), as stated in Sec. 1, it is suggested to model a series of multiple long-range contexts for adaptive selection. Therefore, we propose constructing a larger kernel convolution by explicitly decomposing it into a sequence of depth-wise convolutions with a large growing kernel and increasing dilation. Specifically, for the " + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "text", + "content": "-th depth-wise convolution, the expansion of the kernel size " + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "text", + "content": ", dilation rate " + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "text", + "content": ", and the receptive field " + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "inline_equation", + "content": "RF" + }, + { + "bbox": [ + 46, + 533, + 287, + 640 + ], + "type": "text", + "content": " are defined as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 82, + 651, + 287, + 664 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 651, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 82, + 651, + 287, + 664 + ], + "type": "interline_equation", + "content": "k _ {i - 1} \\leq k _ {i}; d _ {1} = 1, d _ {i - 1} < d _ {i} \\leq R F _ {i - 1}, \\tag {1}", + "image_path": "e2696d86473ae4c7d13476d28d5963698b7a22ed9102fd2a35ed451cd53d4c32.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 84, + 670, + 287, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 670, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 84, + 670, + 287, + 683 + ], + "type": "interline_equation", + "content": "R F _ {1} = k _ {1}, R F _ {i} = d _ {i} \\left(k _ {i} - 1\\right) + R F _ {i - 1}. \\tag {2}", + "image_path": "d4b23c8728b4494bba6d76a62172b8a2d0dbe5f620cd2cb7012eddc910e36d3e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "The increasing kernel size and dilation rate ensure that the receptive field expands quickly enough. We set an upper" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 222, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 222, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 222, + 545, + 281 + ], + "type": "text", + "content": "bound on the dilation rate to guarantee that the dilation convolution does not introduce gaps between feature maps. For instance, we can decompose a large kernel into 2 or 3 depth-wise convolutions as in Tab. 2, which have a theoretical receptive field of 23 and 29, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 281, + 546, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 546, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 546, + 414 + ], + "type": "text", + "content": "There are two advantages of the proposed designs. First, it explicitly yields multiple features with various large receptive fields, which makes it easier for the later kernel selection. Second, sequential decomposition is more efficient than simply applying a single larger kernel. As shown in Tab. 2, under the same resulted theoretical receptive field, our decomposition greatly reduces the number of parameters compared to the standard large convolution kernels. To obtain features with rich contextual information from different ranges for input " + }, + { + "bbox": [ + 304, + 281, + 546, + 414 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 281, + 546, + 414 + ], + "type": "text", + "content": ", a series of decomposed depth-wise convolutions with different receptive fields are applied:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 361, + 419, + 545, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 419, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 361, + 419, + 545, + 434 + ], + "type": "interline_equation", + "content": "\\mathbf {U} _ {0} = \\mathbf {X}, \\quad \\mathbf {U} _ {i + 1} = \\mathcal {F} _ {i} ^ {d w} (\\mathbf {U} _ {i}), \\tag {3}", + "image_path": "6c0b9c5faf49e2b1b1844c72c92d2f58fa439755fdaac11a35f9d2b3db0817a4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_i^{dw}(\\cdot)" + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "text", + "content": " are depth-wise convolutions with kernel " + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "text", + "content": " and dilation " + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "text", + "content": ". Assuming there are " + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "text", + "content": " decomposed kernels, each of which is further processed by a " + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "text", + "content": " convolution layer " + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{1\\times 1}(\\cdot)" + }, + { + "bbox": [ + 304, + 440, + 545, + 488 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 358, + 495, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 495, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 358, + 495, + 545, + 510 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {U}} _ {i} = \\mathcal {F} _ {i} ^ {1 \\times 1} \\left(\\mathbf {U} _ {i}\\right), \\text {f o r} i \\text {i n} [ 1, N ], \\tag {4}", + "image_path": "c79d103eb3912a1867b1eb8a462510704d8666076f91c7db7d33a691ff9ad288.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 517, + 545, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 565 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 565 + ], + "type": "text", + "content": "allowing channel mixing for each spatial feature vector. Then, a selection mechanism is proposed to dynamically select kernels for various objects based on the multi-scale features obtained, which would be introduced next." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 571, + 441, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 571, + 441, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 571, + 441, + 585 + ], + "type": "text", + "content": "3.3. Spatial Kernel Selection" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 590, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 545, + 662 + ], + "type": "text", + "content": "To enhance the network's ability to focus on the most relevant spatial context regions for detecting targets, we use a spatial selection mechanism to spatially select the feature maps from large convolution kernels at different scales. Firstly, we concatenate the features obtained from different kernels with different ranges of receptive field:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 388, + 667, + 545, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 667, + 545, + 683 + ], + "spans": [ + { + "bbox": [ + 388, + 667, + 545, + 683 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {U}} = \\left[ \\widetilde {\\mathbf {U}} _ {1}; \\dots ; \\widetilde {\\mathbf {U}} _ {i} \\right], \\tag {5}", + "image_path": "9680eca14c9d392a46c40ab11578ee5472b29b6ae218edaf08fdce286fda4b95.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "and then efficiently extract the spatial relationship by applying channel-based average and maximum pooling (denoted" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16797" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "text", + "content": "as " + }, + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{avg}(\\cdot)" + }, + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{max}(\\cdot)" + }, + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{U}}" + }, + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 78, + 92, + 287, + 109 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 92, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 78, + 92, + 287, + 109 + ], + "type": "interline_equation", + "content": "\\mathbf {S A} _ {a v g} = \\mathcal {P} _ {a v g} (\\widetilde {\\mathbf {U}}), \\mathbf {S A} _ {m a x} = \\mathcal {P} _ {m a x} (\\widetilde {\\mathbf {U}}), \\qquad (6)", + "image_path": "64927dfb7615b207435f48dc5bad83885a5d0ce94a4960f8cf190a0932980995.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "spans": [ + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "inline_equation", + "content": "\\mathbf{SA}_{avg}" + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "inline_equation", + "content": "\\mathbf{SA}_{max}" + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "text", + "content": " are the average and maximum pooled spatial feature descriptors. To allow information interaction among different spatial descriptors, we concatenate the spatially pooled features and use a convolution layer " + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{2\\rightarrow N}(\\cdot)" + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "text", + "content": " to transform the pooled features (with 2 channels) into " + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 116, + 287, + 189 + ], + "type": "text", + "content": " spatial attention maps:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 196, + 287, + 212 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 196, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 97, + 196, + 287, + 212 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathbf {S A}} = \\mathcal {F} ^ {2 \\rightarrow N} \\left(\\left[ \\mathbf {S A} _ {a v g}; \\mathbf {S A} _ {m a x} \\right]\\right). \\tag {7}", + "image_path": "2dc59f7961adcef02270d06dc451e5b2ae4fdf398c19cf1bf6b53b8e3db4e528.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 221, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 287, + 258 + ], + "type": "text", + "content": "For each of the spatial attention maps, " + }, + { + "bbox": [ + 47, + 221, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{SA}_i}" + }, + { + "bbox": [ + 47, + 221, + 287, + 258 + ], + "type": "text", + "content": ", a sigmoid activation function is applied to obtain the individual spatial selection mask for each of the decomposed large kernels:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 132, + 266, + 287, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 266, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 132, + 266, + 287, + 281 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {S A} _ {i}} = \\sigma (\\widehat {\\mathbf {S A} _ {i}}), \\tag {8}", + "image_path": "e5883112ee1d7c1908ecaa6435f5c4d94ae21d23c5d50506547b268aa15ccfe2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "type": "text", + "content": " denotes the sigmoid function. The feature maps from the sequence of decomposed large kernels are weighted by their corresponding spatial selection masks and then fused by a convolution layer " + }, + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\cdot)" + }, + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "type": "text", + "content": " to obtain the attention feature " + }, + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 47, + 289, + 287, + 350 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 356, + 287, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 356, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 115, + 356, + 287, + 388 + ], + "type": "interline_equation", + "content": "\\mathbf {S} = \\mathcal {F} \\left(\\sum_ {i = 1} ^ {N} \\left(\\widetilde {\\mathbf {S A}} _ {i} \\cdot \\widetilde {\\mathbf {U}} _ {i}\\right)\\right). \\tag {9}", + "image_path": "865ef3e8738ac79e8c352654d216a55f806a80d07372e098d1b59e3edd373506.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 396, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 287, + 432 + ], + "type": "text", + "content": "The final output of the LSK module is the element-wise product between the input feature " + }, + { + "bbox": [ + 47, + 396, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 47, + 396, + 287, + 432 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 396, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 47, + 396, + 287, + 432 + ], + "type": "text", + "content": ", similarly in [19, 20, 28]:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 142, + 432, + 287, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 142, + 432, + 287, + 444 + ], + "spans": [ + { + "bbox": [ + 142, + 432, + 287, + 444 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} = \\mathbf {X} \\cdot \\mathbf {S}. \\tag {10}", + "image_path": "9e75df8b8a0f241a6f5a271a5e940b27d30beeef6a6315f2ea0d24481ed8e7fb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 449, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 287, + 498 + ], + "type": "text", + "content": "Fig. 5 shows a detailed conceptual illustration of an LSK module where we intuitively demonstrate how the large selective kernel works by adaptively collecting the corresponding large receptive field for different objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 508, + 127, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 508, + 127, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 508, + 127, + 521 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 527, + 109, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 109, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 109, + 539 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 545, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 545, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 545, + 287, + 582 + ], + "type": "text", + "content": "HRSC2016 [42] is a high-resolution remote sensing dataset which is collected for ship detection. It consists of 1,061 images which contain 2,976 instances of ships." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 582, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 665 + ], + "type": "text", + "content": "DOTA-v1.0 [68] consists of 2,806 remote sensing images. It contains 188,282 instances of 15 categories: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), and Helicopter (HC)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "FAIR1M-v1.0 [58] is a recently published remote sensing dataset that consists of 15,266 high-resolution images and more than 1 million instances. It contains 5 categories and 37 sub-categories objects." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 72, + 438, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 438, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 438, + 84 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 90, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 233 + ], + "type": "text", + "content": "In our experiment, we report the results of the oriented object detection models on HRSC2016, DOTA-v1.0 and FAIR1M-v1.0 datasets. To ensure fairness, we follow the same dataset processing approach as other mainstream methods [23, 24, 69]. For DOTA-v1.0 and FAIR1M-v1.0 datasets, we adopt multi-scale training and testing strategy by first rescaling the images into three scales (0.5, 1.0, 1.5), and then cropping each scaled image into " + }, + { + "bbox": [ + 304, + 90, + 545, + 233 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 90, + 545, + 233 + ], + "type": "text", + "content": " sub-images with a patch overlap of 500 pixels. For the HRSC2016 dataset, we rescale the images by setting the longer side of the image to 800 pixels, without changing their aspect ratios." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 234, + 546, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 546, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 546, + 533 + ], + "type": "text", + "content": "During our experiments, the backbones are first pretrained on the ImageNet-1K [10] dataset and then finetuned on the target remote sensing benchmarks. In ablation studies, we adopt the 100-epoch backbone pretraining schedule for experimental efficiency (Tab. 3, 5, 4, 6, 7). We adopt a 300-epoch backbone pretraining strategy to pursue higher accuracy in main results (Tab. 8, 9, 10), similarly to [6,23,69,75]. In main results (Tab. 8, 9), the \"Pre.\" column stands for the dataset on which the networks/backbones are pretrained (IN: Imagenet [10] dataset; CO: Microsoft COCO [36] dataset; MA: Million-AID [43] dataset). Unless otherwise stated, LSKNet is defaulting to be built within the framework of Oriented RCNN [69] due to its compelling performance and efficiency. All the models are trained on the training and validation sets and tested on the testing set. Following [69], we train the models for 36 epochs on the HRSC2016 datasets and 12 epochs on the DOTA-v1.0 and FAIR1M-v1.0 datasets, with the AdamW [44] optimizer. The initial learning rate is set to 0.0004 for HRSC2016, and 0.0002 for the other two datasets, with a weight decay of 0.05. The models are implemented under MMRotate [88] framework. We use 8 RTX3090 GPUs with a batch size of 8 for model training and use a single RTX3090 GPU for testing. All the FLOPs we report in this paper are calculated with a " + }, + { + "bbox": [ + 304, + 234, + 546, + 533 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 234, + 546, + 533 + ], + "type": "text", + "content": " image input." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 540, + 399, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 399, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 399, + 552 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 558, + 544, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 558, + 544, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 558, + 544, + 582 + ], + "type": "text", + "content": "In this section, we report ablation study results on the DOTA-v1.0 test set to investigate its effectiveness." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 582, + 545, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 701 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 701 + ], + "type": "text", + "content": "Large Kernel Decomposition. Deciding on the number of kernels to decompose is a critical choice for the LSK module. We follow Eq. (1) to configure the decomposed kernels. The results of the ablation study on the number of large kernel decompositions, when the theoretical receptive field is fixed at 29, are shown in Tab. 3. It suggests that decomposing the large kernel into two depth-wise large kernels results in a good trade-off between speed and accuracy, achieving the best performance in terms of both FPS (frames per second) and mAP (mean average precision)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "Receptive Field Size and Selection Type. Based on our" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16798" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 71, + 282, + 118 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 282, + 118 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 282, + 118 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 282, + 118 + ], + "type": "table", + "html": "
(k,d) sequenceRFNum.FPSmAP (%)
(29,1)29118.680.66
(5,1)→(7,4)29220.580.91
(3,1)→(5,2)→(7,3)29319.280.77
", + "image_path": "df43f8e7b611b22b7873d006f922653fd2df8bebbabbeada48cf0144622c1fca.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 188, + 280, + 270 + ], + "blocks": [ + { + "bbox": [ + 46, + 121, + 287, + 177 + ], + "lines": [ + { + "bbox": [ + 46, + 121, + 287, + 177 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 287, + 177 + ], + "type": "text", + "content": "Table 3. The effects of the number of decomposed large kernels on the inference FPS and mAP, given the theoretical receptive field being 29. We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. Decomposing the large kernel into two depth-wise kernels achieves the best performance of speed and accuracy." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 188, + 280, + 270 + ], + "lines": [ + { + "bbox": [ + 52, + 188, + 280, + 270 + ], + "spans": [ + { + "bbox": [ + 52, + 188, + 280, + 270 + ], + "type": "table", + "html": "
(k1, d1)(k2, d2)CSSSRFFPSmAP (%)
(3, 1)(5, 2)--1122.180.80
(5, 1)(7, 3)--2321.780.94
(5, 1)(7, 4)--2920.580.91
(7, 1)(9, 4)--3921.380.84
(5, 1)(7, 3)✓-2319.680.57
(5, 1)(7, 3)-✓2320.781.31
", + "image_path": "f03af539651190f12e54b6ff334d2c7cfcf41ae9a09776bd1954b6eed25fc345.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 102, + 361, + 231, + 420 + ], + "blocks": [ + { + "bbox": [ + 46, + 273, + 287, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 350 + ], + "type": "text", + "content": "Table 4. The effectiveness of the key design components of the LSKNet when the large kernel is decomposed into a sequence of two depth-wise kernels. CS: channel selection (likewise in SKNet [33]); SS: spatial selection (ours). We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. The LSKNet achieves the best performance when using a reasonably large receptive field with spatial selection." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 102, + 361, + 231, + 420 + ], + "lines": [ + { + "bbox": [ + 102, + 361, + 231, + 420 + ], + "spans": [ + { + "bbox": [ + 102, + 361, + 231, + 420 + ], + "type": "table", + "html": "
PoolingFPSmAP (%)
Max.Avg.
✓20.781.23
✓20.781.12
✓✓20.781.31
", + "image_path": "487fe5e23e6f1e7b52f24ede47ea63da15e9e4e71da7e6c009d33a71ba27f11a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 484, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 286, + 616 + ], + "type": "text", + "content": "evaluations presented in Tab. 3, we find that the optimal solution for our proposed LSKNet is to decompose the large kernel into two depth-wise kernels in series. Furthermore, Tab. 4 shows that excessively small or large receptive fields can hinder the performance of the LSKNet, and a receptive field size of approximately 23 is determined to be the most effective. In addition, our experiments indicate that the proposed spatial selection approach is more effective than channel attention (similarly in SKNet [33]) for remote sensing object detection tasks. It suggests that in detection tasks, spatial information is more critical." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 616, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 286, + 688 + ], + "type": "text", + "content": "Pooling Layers in Spatial Selection. We conduct experiments to determine the optimal pooling layers for spatial selection, as reported in Tab. 5. The results suggest that using both max and average pooling in the spatial selection component of our LSK module provides the best performance without sacrificing inference speed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "Performance of LSKNet backbone under different detection frameworks. To validate the generality and ef" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 320, + 71, + 533, + 152 + ], + "blocks": [ + { + "bbox": [ + 46, + 423, + 287, + 467 + ], + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 467 + ], + "type": "text", + "content": "Table 5. Ablation study on the effectiveness of the maximum and average pooling in spatial selection of our proposed LSK module. We adopt LSKNet-T backbones pretrained on ImageNet for 100 epochs. The best result is obtained when using both." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 71, + 533, + 152 + ], + "lines": [ + { + "bbox": [ + 320, + 71, + 533, + 152 + ], + "spans": [ + { + "bbox": [ + 320, + 71, + 533, + 152 + ], + "type": "table", + "html": "
FrameworksResNet-18★ LSKNet-T
ORCNN [69]79.2781.31 (+2.04)
RoI Trans. [12]78.3280.89 (+2.57)
S²A-Net [23]76.8280.15 (+3.33)
R3Det [75]74.1678.39 (+4.23)
#P (backbone only)11.2M4.3M (-62%)
FLOPs (backbone only)38.1G19.1G (-50%)
", + "image_path": "cac52e7c077eba67ec70bb466fc719b26672a1b01e4d3f816258a70eb7b027ab.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 309, + 216, + 541, + 334 + ], + "blocks": [ + { + "bbox": [ + 305, + 153, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 305, + 153, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 305, + 153, + 545, + 208 + ], + "type": "text", + "content": "Table 6. Comparison of LSKNet-T and ResNet-18 as backbones with different detection frameworks on DOTA-v1.0. The LSKNet-T backbone is pretrained on ImageNet for 100 epochs. The lightweight LSKNet-T achieves significantly higher mAP in various frameworks than ResNet-18." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 216, + 541, + 334 + ], + "lines": [ + { + "bbox": [ + 309, + 216, + 541, + 334 + ], + "spans": [ + { + "bbox": [ + 309, + 216, + 541, + 334 + ], + "type": "table", + "html": "
GroupModel (backbone only)#PFLOPsmAP (%)
BaselineResNet-1811.2M38.1G79.27
Large KernelVAN-B1 [19]13.4M52.7G81.15
ConvNeXt V2-N [65]15.0M51.2G80.81
MSCAN-S [20]13.1M45.0G81.12
Selective AttentionSKNet-26 [33]14.5M58.5G80.67
ResNeSt-14 [84]8.6M57.9G79.51
SCNet-18 [37]14.0M50.7G79.69
Ours★ LSKNet-S14.4M54.4G81.48
Prev BestCSPNeXt [46]26.1M87.6G81.33
", + "image_path": "df9368342ad6a44dcc1865af32885fbf79574ae6b6599f0dcbe9eaaaaeb9ba9f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 308, + 413, + 543, + 586 + ], + "blocks": [ + { + "bbox": [ + 305, + 335, + 545, + 400 + ], + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 400 + ], + "type": "text", + "content": "Table 7. Comparison on LSKNet-S and other (large kernel/selective attention) backbones under O-RCNN [69] framework on DOTA-v1.0, except that the Prev Best is under RT-MDet [46] framework. All backbones are pretrained on ImageNet for 100 epochs. Our LSKNet achieves the best mAP under similar complexity budgets." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 413, + 543, + 586 + ], + "lines": [ + { + "bbox": [ + 308, + 413, + 543, + 586 + ], + "spans": [ + { + "bbox": [ + 308, + 413, + 543, + 586 + ], + "type": "table", + "html": "
MethodPre.mAP(07)↑mAP(12)↑#P↓FLOPs↓
DRN [50]IN-92.70--
CenterMap [61]IN-92.8041.1M198G
Rol Trans. [12]IN86.20-55.1M200G
G. V. [71]IN88.20-41.1M198G
R3Det [75]IN89.2696.0141.9M336G
DAL [48]IN89.77-36.4M216G
GWD [77]IN89.8597.3747.4M456G
S2ANet [23]IN90.1795.0138.6M198G
AOPG [6]IN90.3496.22--
ReDet [24]IN90.4697.6331.6M-
O-RCNN [69]IN90.5097.6041.1M199G
RTMDet [46]CO90.6097.1052.3M205G
★LSKNet-TIN90.5498.1321.0M124G
★LSKNet-SIN90.6598.4631.0M161G
", + "image_path": "b47c85492142e31e01aa4a8c0cafafd92269f7f7e10d8f8d725e37060cf5375a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 588, + 545, + 632 + ], + "lines": [ + { + "bbox": [ + 305, + 588, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 305, + 588, + 545, + 632 + ], + "type": "text", + "content": "Table 8. Comparison with state-of-the-art methods on the HRSC2016 dataset. The LSKNet-S backbone is pretrained on ImageNet for 300 epochs, the same with most compared methods [23,69,75]. mAP (07/12): VOC 2007 [15]/2012 [16] metrics." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": "fectiveness of our proposed LSKNet backbone, we evaluate its performance under various remote sensing detection frameworks, including two-stage frameworks O-RCNN [69] and RoI Transformer [12] as well as one-stage frameworks " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{S}^2\\mathrm{A}" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " -Net [23] and R3Det [75]. The re" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16799" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 83, + 545, + 381 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 542, + 81 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 542, + 81 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 542, + 81 + ], + "type": "text", + "content": "Method |Pre. " + }, + { + "bbox": [ + 49, + 71, + 542, + 81 + ], + "type": "inline_equation", + "content": "\\left|\\mathbf{mAP}\\uparrow\\right|\\# \\mathbf{P}\\downarrow" + }, + { + "bbox": [ + 49, + 71, + 542, + 81 + ], + "type": "text", + "content": " FLOPs↓ PL BD BR GTF SV LV SH TC BC ST SBF RA HA SP HC" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 83, + 545, + 381 + ], + "lines": [ + { + "bbox": [ + 49, + 83, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 49, + 83, + 545, + 381 + ], + "type": "table", + "html": "
One-stage
R3Det [75]IN76.4741.9M336G89.8083.7748.1166.7778.7683.2787.8490.8285.3885.5165.5762.6867.5378.5672.62
CFA [22]IN76.67--89.0883.2054.3766.8781.2380.9687.1790.2184.3286.0952.3469.9475.5280.7667.96
DAFNe [31]IN76.95--89.4086.2753.7060.5182.0481.1788.6690.3783.8187.2753.9369.3875.6181.2670.86
SASM [27]IN79.17--89.5485.9457.7378.4179.7884.1989.2590.8758.8087.2763.8267.8178.6779.3569.37
AO2-DETR [9]IN79.2274.3M304G89.9584.5256.9074.8380.8683.4788.4790.8786.1288.5563.2165.0979.0982.8873.46
\\( S^2ANet \\) [23]IN79.42--88.8983.6057.7481.9579.9483.1989.1190.7884.8787.8170.3068.2578.3077.0169.58
R3Det-GWD [77]IN80.2341.9M336G89.6684.9959.2682.1978.9784.8387.7090.2186.5486.8573.4767.7776.9279.2274.92
RTMDet-R [46]IN80.5452.3M205G88.3684.9657.3380.4680.5884.8888.0890.9086.3287.5769.2970.6178.6380.9779.24
R3Det-KLD [79]IN80.6341.9M336G89.9285.1359.1981.3378.8284.3887.5089.8087.3387.0072.5771.3577.1279.3478.68
RTMDet-R [46]CO81.3352.3M205G88.0186.1758.5482.4481.3084.8288.7190.8988.7787.3771.9671.1881.2381.4077.13
Two-stage
SCRDet [78]IN72.61--89.9880.6552.0968.3668.3660.3272.4190.8587.9486.8665.0266.6866.2568.2465.21
Rol Trans. [12]IN74.6155.1M200G88.6582.6052.5370.8777.9376.6786.8790.7183.8382.5153.9567.6174.6768.7561.03
G.V. [71]IN75.0241.1M198G89.6485.0052.2677.3473.0173.1486.8290.7479.0286.8159.5570.9172.9470.8657.32
CenterMap [61]IN76.0341.1M198G89.8384.4154.6070.2577.6678.3287.1990.6684.8985.2756.4669.2374.1371.5666.06
CSL [76]IN76.1737.4M236G90.2585.5354.6475.3170.4473.5177.6290.8486.1586.6969.6068.0473.8371.1068.93
ReDet [24]IN80.10--88.8182.4860.8380.8278.3486.0688.3190.8788.7787.0368.6566.9079.2679.7174.67
DODet [7]IN80.62--89.9685.5258.0181.2278.7185.4688.5990.8987.1287.8070.5071.5482.0677.4374.47
AOPG [6]IN80.66--89.8885.5760.9081.5178.7085.2988.8590.8987.6087.6571.6668.6982.3177.3273.10
O-RCNN [69]IN80.8741.1M199G89.8485.4361.0979.8279.7185.3588.8290.8886.6887.7372.2170.8082.4278.1874.11
KFloU [80]IN80.9358.8M206G89.4484.4162.2282.5180.1086.0788.6890.9087.3288.3872.8071.9578.9674.9575.27
RVSA [60]MA81.24114.4M414G88.9785.7661.4681.2779.9885.3188.3090.8485.0687.5066.7773.1184.7581.8877.58
★LSKNet-T (ours)IN81.3721.0M124G89.1484.9061.7883.5081.5485.8788.6490.8988.0287.3171.5570.7478.6679.8178.16
★LSKNet-S (ours)IN81.6431.0M161G89.5786.3463.1383.6782.2086.1088.6690.8988.4187.4271.7269.5878.8881.7776.52
★LSKNet-S* (ours)IN81.8531.0M161G89.6985.7061.4783.2381.3786.0588.6490.8888.4987.4071.6771.3579.1981.7780.86
", + "image_path": "1caf5c0dfa09ac0787b641816b3ac2732266c3e421c5f4613c11e0073720bbcd.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 415, + 538, + 444 + ], + "blocks": [ + { + "bbox": [ + 47, + 384, + 546, + 407 + ], + "lines": [ + { + "bbox": [ + 47, + 384, + 546, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 546, + 407 + ], + "type": "text", + "content": "Table 9. Comparison with state-of-the-art methods on the DOTA-v1.0 dataset with multi-scale training and testing. The LSKNet backbones are pretrained on ImageNet for 300 epochs, similarly to [23, 69, 75]. *: With EMA finetune similarly to the compared methods [46]." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 415, + 538, + 444 + ], + "lines": [ + { + "bbox": [ + 52, + 415, + 538, + 444 + ], + "spans": [ + { + "bbox": [ + 52, + 415, + 538, + 444 + ], + "type": "table", + "html": "
ModelG. V.* [71]RetinaNet* [35]C-RCNN* [2]F-RCNN* [56]RoI Trans.* [12]O-RCNN [69]★ LSKNet-T★ LSKNet-S
mAP(%)29.9230.6731.1832.1235.2945.6046.9347.87
", + "image_path": "1b7bd30d77ff0abe814eb9b58774dfece235c0993fcd64c4749db17a4bd9e907.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 446, + 546, + 469 + ], + "lines": [ + { + "bbox": [ + 47, + 446, + 546, + 469 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 546, + 469 + ], + "type": "text", + "content": "Table 10. Comparison with state-of-the-art methods on the FAIR1M-v1.0 dataset. The LSKNet backbones are pretrained on ImageNet for 300 epochs, similarly to [23,69,75].*: Results are referenced from FAIR1M paper [58]." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 484, + 287, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 531 + ], + "type": "text", + "content": "sults in Tab. 6 show that our proposed LSKNet-T backbone significantly improves detection performance compared to ResNet-18, while using only " + }, + { + "bbox": [ + 46, + 484, + 287, + 531 + ], + "type": "inline_equation", + "content": "38\\%" + }, + { + "bbox": [ + 46, + 484, + 287, + 531 + ], + "type": "text", + "content": " of its parameters and with " + }, + { + "bbox": [ + 46, + 484, + 287, + 531 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 484, + 287, + 531 + ], + "type": "text", + "content": " fewer FLOPs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 532, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 288, + 604 + ], + "type": "text", + "content": "Comparison with Other Large Kernel/Selective Attention Backbones. We also compare our LSKNet with 6 popular high-performance backbone models with large kernels or selective attention. As shown in Tab. 7, under similar model sizes and complexity budgets, our LSKNet outperforms all other models on the DOTA-v1.0 dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 611, + 133, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 133, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 133, + 623 + ], + "type": "text", + "content": "4.4. Main Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 701 + ], + "type": "text", + "content": "Results on HRSC2016. We evaluated the performance of our LSKNet against 12 state-of-the-art methods on the HRSC2016 dataset. The results presented in Tab. 8 demonstrate that our LSKNet-S outperforms all other methods with an mAP of " + }, + { + "bbox": [ + 46, + 629, + 287, + 701 + ], + "type": "inline_equation", + "content": "90.65\\%" + }, + { + "bbox": [ + 46, + 629, + 287, + 701 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 701 + ], + "type": "inline_equation", + "content": "98.46\\%" + }, + { + "bbox": [ + 46, + 629, + 287, + 701 + ], + "type": "text", + "content": " under the PASCAL VOC 2007 [15] and VOC 2012 [16] metrics, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Results on DOTA-v1.0. We compare our LSKNet with" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": "20 state-of-the-art methods on the DOTA-v1.0 dataset, as reported in Tab. 9. Our LSKNet-T, LSKNet-S and LSKNet-S* achieve state-of-the-art with mAP of " + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "inline_equation", + "content": "81.37\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "inline_equation", + "content": "81.64\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "inline_equation", + "content": "81.85\\%" + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": " respectively. Notably, our high-performing LSKNet-S reaches an inference speed of 18.1 FPS on 1024x1024 images with a single RTX3090 GPU." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "type": "text", + "content": "Results on FAIR1M-v1.0. We compare our LSKNet against 6 other models on the FAIR1M-v1.0 dataset, as shown in Tab. 10. The results reveal that our LSKNet-T and LSKNet-S perform exceptionally well, achieving state-of-the-art mAP scores of " + }, + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "type": "inline_equation", + "content": "46.93\\%" + }, + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "type": "inline_equation", + "content": "47.87\\%" + }, + { + "bbox": [ + 304, + 555, + 545, + 628 + ], + "type": "text", + "content": " respectively, surpassing all other models by a significant margin." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 635, + 369, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 369, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 369, + 647 + ], + "type": "text", + "content": "4.5. Analysis" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Detection Results Visualization. Visualization examples of detection results and Eigen-CAM [49] are shown in Fig. 6. LSKNet can capture much more context information relevant to the detected targets, leading to better performance in various hard cases, which justifies our prior (1)." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16800" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 242, + 282 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 242, + 282 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 242, + 282 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 242, + 282 + ], + "type": "image", + "image_path": "d7a8ed27195bfe79d5b31025d48d78e26b0cf161cd1c956ec42cbe49a8b53159.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 126, + 284, + 212, + 293 + ], + "lines": [ + { + "bbox": [ + 126, + 284, + 212, + 293 + ], + "spans": [ + { + "bbox": [ + 126, + 284, + 212, + 293 + ], + "type": "text", + "content": "(a) Robustness to obstacles" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 245, + 72, + 386, + 281 + ], + "blocks": [ + { + "bbox": [ + 245, + 72, + 386, + 281 + ], + "lines": [ + { + "bbox": [ + 245, + 72, + 386, + 281 + ], + "spans": [ + { + "bbox": [ + 245, + 72, + 386, + 281 + ], + "type": "image", + "image_path": "f1cf7274765a362675051a08069ec03e4afad2981538c85f047aa29184ccefb7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 261, + 283, + 368, + 293 + ], + "lines": [ + { + "bbox": [ + 261, + 283, + 368, + 293 + ], + "spans": [ + { + "bbox": [ + 261, + 283, + 368, + 293 + ], + "type": "text", + "content": "(b) Accurate Object Classification" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 389, + 72, + 531, + 281 + ], + "blocks": [ + { + "bbox": [ + 389, + 72, + 531, + 281 + ], + "lines": [ + { + "bbox": [ + 389, + 72, + 531, + 281 + ], + "spans": [ + { + "bbox": [ + 389, + 72, + 531, + 281 + ], + "type": "image", + "image_path": "20c4bb773aecb4dfaa342f1407399b8017616b0288915928d51eca7471115d0d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 408, + 283, + 511, + 293 + ], + "lines": [ + { + "bbox": [ + 408, + 283, + 511, + 293 + ], + "spans": [ + { + "bbox": [ + 408, + 283, + 511, + 293 + ], + "type": "text", + "content": "(c) Accurate Object Localization" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 297, + 546, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 297, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 546, + 319 + ], + "type": "text", + "content": "Figure 6. Eigen-CAM visualization of Oriented RCNN detection framework with ResNet-50 and LSKNet-S. Our proposed LSKNet can model a much long range of context information, leading to better performance in various hard cases." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 58, + 337, + 274, + 487 + ], + "blocks": [ + { + "bbox": [ + 58, + 337, + 274, + 487 + ], + "lines": [ + { + "bbox": [ + 58, + 337, + 274, + 487 + ], + "spans": [ + { + "bbox": [ + 58, + 337, + 274, + 487 + ], + "type": "image", + "image_path": "7ebedb060824893151b42938746c503367c232b389eb40f079979e13898ef94d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 490, + 287, + 557 + ], + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 557 + ], + "type": "text", + "content": "Figure 7. Normalised Ratio " + }, + { + "bbox": [ + 46, + 490, + 287, + 557 + ], + "type": "inline_equation", + "content": "R_{c}" + }, + { + "bbox": [ + 46, + 490, + 287, + 557 + ], + "type": "text", + "content": " of Expected Selective RF Area and GT Bounding Box Area for object categories in DOTA-v1.0. The relative range of context required for different object categories varies a lot. Examples of Bridge and Soccer-ball-field are given, where the visualized receptive field is obtained from Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 574, + 288, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 288, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 288, + 623 + ], + "type": "text", + "content": "Relative Context Range for Different Objects. To investigate the relative range of receptive field for each object category, we define " + }, + { + "bbox": [ + 46, + 574, + 288, + 623 + ], + "type": "inline_equation", + "content": "R_{c}" + }, + { + "bbox": [ + 46, + 574, + 288, + 623 + ], + "type": "text", + "content": " as the Ratio of Expected Selective RF Area and GT Bounding Box Area for category " + }, + { + "bbox": [ + 46, + 574, + 288, + 623 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 574, + 288, + 623 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 124, + 629, + 287, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 629, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 124, + 629, + 287, + 657 + ], + "type": "interline_equation", + "content": "R _ {c} = \\frac {\\sum_ {i = 1} ^ {I _ {c}} A _ {i} / B _ {i}}{I _ {c}}, \\tag {11}", + "image_path": "d1ce8d50d931c6048c398640d66a6224e06bd98ed4dd4fece44b19f904b36386.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 53, + 664, + 287, + 698 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 664, + 287, + 698 + ], + "spans": [ + { + "bbox": [ + 53, + 664, + 287, + 698 + ], + "type": "interline_equation", + "content": "A _ {i} = \\sum_ {d = 1} ^ {D} \\sum_ {n = 1} ^ {N} | \\widetilde {\\mathbf {S A}} _ {n} ^ {d} \\cdot R F _ {n} |, B _ {i} = \\sum_ {j = 1} ^ {J _ {i}} \\operatorname {A r e a} \\left(\\mathrm {G T} _ {j}\\right), \\tag {12}", + "image_path": "ce09b4442a9ef6c1bcd3ecce26c776d599c34288eb5069b895b8d13939168857.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": " is the number of images that contain the object" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 317, + 337, + 533, + 445 + ], + "blocks": [ + { + "bbox": [ + 317, + 337, + 533, + 445 + ], + "lines": [ + { + "bbox": [ + 317, + 337, + 533, + 445 + ], + "spans": [ + { + "bbox": [ + 317, + 337, + 533, + 445 + ], + "type": "image", + "image_path": "2cea3cd55e85b011419d017dc50c7bf5a4d9ed7c8006248b9021ae97b8a82202.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 447, + 545, + 491 + ], + "lines": [ + { + "bbox": [ + 305, + 447, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 545, + 491 + ], + "type": "text", + "content": "Figure 8. Normalised Kernel Selection Difference in the LSKNet-T blocks for Bridge, Roundabout and Soccer-ball-field. B.i.j represents the j-th LSK block in stage i. A greater value is indicative of a dependence on a broader context." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": "category " + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": " only. The " + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "inline_equation", + "content": "A_{i}" + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": " is the sum of spatial selection activation in all LSK blocks for input image " + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": " is the number of blocks in an LSKNet, and " + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": " is the number of decomposed large kernels in an LSK module. " + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "inline_equation", + "content": "B_{i}" + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": " is the total pixel area of all " + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "inline_equation", + "content": "J_{i}" + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": " annotated oriented object bounding boxes (GT). 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Receptive field activation for more object categories in DOTA-v1.0, where the activation map is obtained from the Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 408, + 251, + 509, + 319 + ], + "blocks": [ + { + "bbox": [ + 408, + 251, + 509, + 319 + ], + "lines": [ + { + "bbox": [ + 408, + 251, + 509, + 319 + ], + "spans": [ + { + "bbox": [ + 408, + 251, + 509, + 319 + ], + "type": "image", + "image_path": "0604412e8dcab7a2f7eacbee42261b7d60ceda6a452313709ee4c2b3385f7d7f.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 433, + 319, + 488, + 327 + ], + "lines": [ + { + "bbox": [ + 433, + 319, + 488, + 327 + ], + "spans": [ + { + "bbox": [ + 433, + 319, + 488, + 327 + ], + "type": "text", + "content": "Soccer-ball field" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 365, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 402 + ], + "type": "text", + "content": "ary lines. It aligns with our knowledge and further supports prior (2) that the relative range of contextual information required for different object categories varies greatly." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 402, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 460 + ], + "type": "text", + "content": "Kernel Selection Behaviour. We further investigate the kernel selection behaviour in our LSKNet. For object category " + }, + { + "bbox": [ + 46, + 402, + 287, + 460 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 402, + 287, + 460 + ], + "type": "text", + "content": ", the Kernel Selection Difference " + }, + { + "bbox": [ + 46, + 402, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\Delta A_{c}" + }, + { + "bbox": [ + 46, + 402, + 287, + 460 + ], + "type": "text", + "content": " (i.e., larger kernel selection - smaller kernel selection) of an LSKNet-T block is defined as:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 96, + 472, + 287, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 472, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 96, + 472, + 287, + 487 + ], + "type": "interline_equation", + "content": "\\Delta A _ {c} = \\left| \\widetilde {\\mathbf {S A}} _ {\\text {l a r g e r}} - \\widetilde {\\mathbf {S A}} _ {\\text {s m a l l e r}} \\right|. \\tag {13}", + "image_path": "7d714b90b196d40f5696213cbbb52ee470289e102ebdcda793e3a342f8e36935.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 497, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 604 + ], + "type": "text", + "content": "We demonstrate the normalised " + }, + { + "bbox": [ + 46, + 497, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\Delta A_{c}" + }, + { + "bbox": [ + 46, + 497, + 287, + 604 + ], + "type": "text", + "content": " over all images for three typical categories: Bridge, Roundabout and Soccerball-field and for each LSKNet-T block in Fig. 8. As expected, the participation of larger kernels of all blocks for Bridge is higher than that of Roundabout, and Roundabout is higher than Soccer-ball-field. This aligns with the common sense that Soccer-ball-field indeed does not require a large amount of context, since its own texture characteristics are already sufficiently distinct and discriminatory." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "content": "We also surprisingly discover another selection pattern of LSKNet across network depth: LSKNet usually utilizes larger kernels in its shallow layers and smaller kernels in higher levels. This indicates that networks tend to quickly focus on capturing information from large receptive fields in low-level layers so that higher-level semantics can contain sufficient receptive fields for better discrimination." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Spatial Activation Visualisations. Spatial activation map examples for more object categories in DOTA-v1.0" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 365, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 484 + ], + "type": "text", + "content": "are shown in Fig. 9, where the activation map is obtained from Eq. (8) (i.e., the spatial activation) of our well-trained LSKNet model. The object categories are arranged in decreasing order from top left to bottom right based on the Ratio of Expected Selective RF Area and GT Bounding Box Area as illustrated in Fig. 7. The spatial activation visualisation results also demonstrate that the model's behaviour aligns with our proposed two priors and the above analysis, which in turn verifies the effectiveness of the proposed mechanism." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 499, + 378, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 499, + 378, + 511 + ], + "spans": [ + { + "bbox": [ + 306, + 499, + 378, + 511 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 520, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 640 + ], + "type": "text", + "content": "In this paper, we propose the Large Selective Kernel Network (LSKNet) for remote sensing object detection tasks, which is designed to utilize the inherent characteristics in remote sensing images: the need for a wider and adaptable contextual understanding. By adapting its large spatial receptive field, LSKNet can effectively model the varying contextual nuances of different object types. Extensive experiments demonstrate that our proposed lightweight model achieves state-of-the-art performance on competitive remote sensing benchmarks." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 658, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 658, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 658, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This research was supported by the NSFC (NO. 62176130, 62206134, 62225604) and the Fundamental Research Funds for the Central Universities (Nankai University, 070-63233084, 070-63233089). Computation is supported by the Supercomputing Center of Nankai University." + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16802" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Yakoub Bazi, Laila Bashmal, Mohamad M. 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However, existing methods overlook the potential to alleviate the class imbalance problem by selecting a suitable set of unlabeled data. Besides, in class-imbalanced scenarios, existing pseudo-labeling methods mostly only pick confident samples, failing to exploit the hard samples during training. To tackle these issues, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation framework. The proposed framework consists of three key components. To construct a better semi-supervised learning dataset, we propose a class-aware unlabeled data selection method that is more balanced towards the minority classes. Based on the built dataset with improved class balance, we propose a Class-Balanced Cross Entropy loss, jointly considering the annotation bias and the class bias to re-weight the loss in both sample and class levels to alleviate the class imbalance problem. Moreover, we propose the Class Center Contrast method to jointly utilize the labeled and unlabeled data. Specifically, we decompose the feature embedding space using the ground truth and pseudo-labels, and employ the embedding centers for hard and easy samples of each class per image in the contrast loss to exploit the hard samples during training. Compared with state-of-the-art class-balanced pseudo-labeling methods, the proposed method improves the mean accuracy and mIoU by $4.28\\%$ and $1.70\\%$ , respectively, on the large-scale Sentinel-2 dataset with 24 land cover classes.", + "bbox": [ + 76, + 358, + 473, + 781 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 808, + 209, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Land cover mapping provides pixel-level information for urban management, climate change research, ecosystem protection, and other sustainability-related applica", + "bbox": [ + 76, + 834, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7b5448a33ca75d31ea5097cb4e3ad58bf9f15c5950fbe43a104bff7189823f84.jpg", + "image_caption": [ + "Figure 1. Examples of the labeled data. The top row shows Sentinel-2 images containing 13 bands. The bottom row shows the corresponding labels. We use a fine-grained classification system with 24 land cover classes in this work." + ], + "image_footnote": [], + "bbox": [ + 504, + 328, + 893, + 554 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tions [21, 27]. With the rapid progress of computer vision technology, it is desired to automatically gain large-scale and fine-grained land cover information from remote sensing images to support the demand of existing earth system science studies and bring new opportunities for intelligent city study [31]. However, fine-grained annotations for land cover mapping are high-cost and time-consuming, limiting labeled data collection for large-scale applications. Semi-supervised learning (SSL) is a potential solution to this problem, as it utilizes both existing labeled data and a large number of unlabeled data [37].", + "bbox": [ + 496, + 655, + 893, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large-scale land cover mapping with fine-grained classes usually suffers from class imbalance, as shown in Figure 1 and 3. The labeled data tends to be biased due to the difficulty of data collection and label annotation varying by class. The class imbalance leads to suboptimal per", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16783", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "formance in the minority classes. Most SSL methods for large-scale land cover mapping are typically based on the assumption that labeled and unlabeled data have the same class distribution [41, 37]. However, this assumption does not hold in most scenarios, resulting in the bias of class estimation. As such, it is non-trivial to jointly utilize the labeled and unlabeled data to train the network for semi-supervised semantic segmentation. Although many pseudo-labeling methods aim to assign pseudo-labels more steadily and correctly for different classes on the unlabeled data, e.g., dynamically setting threshold or proportion [17, 44], they still rely on setting hyperparameters and empirical principles, resulting in a lack of flexibility and generalization ability in applications. Besides, pseudo-labeling methods mostly rely on easy samples with high confidence scores, thus failing to exploit the hard samples on the unlabeled data.", + "bbox": [ + 80, + 90, + 467, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To alleviate the above issues, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation framework. We exploit the potential of the unlabeled data and alleviate the class imbalance problem in large-scale land cover mapping with fine-grained classes. The proposed class-aware unlabeled data selection method constructs an SSL dataset and compensates for the class imbalance on the labeled data. Based on the built SSL dataset, we propose a class-balanced learning method to remove the annotation bias and class bias on the SSL dataset. We dynamically estimate the class prior information on the entire SSL dataset during training to re-weight both samples and classes of the loss function for the labeled data. Finally, we propose the Class Center Contrast method to jointly use the labeled and unlabeled data for training. The ground truth and pseudolabels are leveraged as the guide to decompose the feature embedding space. We estimate the hard, easy, and overall embedding centers for each class per image and apply the contrastive loss to optimize the distances between class centers to utilize both easy and hard samples. The class imbalance issue is alleviated by utilizing the proposed method, and the performance of large-scale land cover mapping with fine-grained classes is effectively improved.", + "bbox": [ + 80, + 333, + 467, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 80, + 694, + 215, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Large-Scale Land Cover Mapping. Land cover mapping classifies each pixel of images into a unique class, which can be regarded as a semantic segmentation problem [6, 11]. Large-scale land cover mapping with fine-grained classes can provide necessary information for earth system science studies and land spatial layout optimization. However, manual or semi-manual labeling is high-cost and time-consuming [34]. Besides, the classification systems of most large-scale studies are coarse. Thus the provided land cover information is limited. For example, the Chesapeake dataset covering $160,000\\mathrm{km}^2$ costs $1.3 million but only contains four classes [33]. DynamicEarthNet", + "bbox": [ + 80, + 720, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "dataset covers $17,000\\mathrm{km}^2$ and includes 7 basic land cover classes [36]. To overcome the limited area of the labeled data and improve the model generalization, some works utilize openly available produced data (e.g., OpenStreetMap data and land cover products), which contains many noisy labels but can provide prior information in a large-scale area [19, 10]. These works still use coarse classification systems of land cover mapping. Five-Billion-Pixels [37] is a large-scale land cover dataset with 24 categories, covering about $60,000\\mathrm{km}^2$ , which opens the door to large-scale land cover mapping with fine-grained classes. However, this dataset suffers from a severe class-imbalance problem (the common categories cover hundreds of times more pixels than the rare ones), due to the difficulty of data collection and label annotation varying by class.", + "bbox": [ + 503, + 90, + 888, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Class-Imbalanced Learning. To solve the class-imbalance problem, related works include data resampling [3, 4], loss re-weighting [22, 32, 18], margin modification [5, 35], and decoupled learning [20, 47]. In self-supervised learning and SSL, recent works devote to rebalancing the class distribution of SSL data by assigning pseudo-labels for the unlabeled data to address the class imbalance issue [41, 15]. For example, Gui et al. [14] propose a class-aware pseudo-labeling method for SSL, dynamically adjusting the threshold for selecting pseudo-labels to obtain better performance on minority classes. Similarly, Hu et al. [17] propose a label bias removal method and dynamically determine the threshold for each class to assign more pseudo-labels for minority classes. However, the hard samples with relatively low confidence scores are ignored for optimizing the model, leading to sub-optimal performance.", + "bbox": [ + 503, + 321, + 888, + 563 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semi-Supervised Semantic Segmentation. SSL methods leverage the relationships between the labeled and unlabeled data to improve the model accuracy and generalization, alleviating the limited area of the labeled data [8]. Semi-supervised semantic segmentation methods include entropy minimization [38], consistency regularization [30], and pseudo-labeling [42]. Pseudo-labeling is widely used in semi-supervised semantic segmentation, and many works contribute to selecting pseudo-labels more steadily and correctly [29]. For example, Tong et al. [37] propose a dynamic pseudo-label assignment method, in which the number of pseudo-labels is dynamically increased with training iterations. However, these methods still rely on the manual setting of hyperparameters and suffer from the uncertainty of pseudo-labels. Alternatively, contrastive learning methods in supervised learning [39, 16] and SSL [46, 40] constrain the representations of positive samples against these negative samples in feature space, leading to promising results. Different from the manner of data augmentation-based positive sample construction [43, 23] and memory bank-based negative sample construction [1, 40], we leverage the ground-truth and pseudo-labels as a guide to decom", + "bbox": [ + 503, + 569, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16784", + "bbox": [ + 482, + 946, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pose the feature embedding space, and estimate the embedding centers for each class per image to stably select easy and hard samples for the proposed Class Center Contrast method.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 166, + 212, + 184 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. The Overall Workflow of Our Approach", + "text_level": 1, + "bbox": [ + 76, + 191, + 421, + 209 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach consists of four steps. First, a baseline model is trained on the labeled data. Second, we propose a class-aware unlabeled data selection method to build an SSL dataset that is more balanced towards minority classes. The baseline model is used to predict land cover classes on all collected data from a large unlabeled data pool and calculate the statistics of the class distribution for each image patch. The image patches containing pixels of minority classes are selected as unlabeled data. Then the SSL dataset is constructed by combining the labeled data and the selected unlabeled data. Third, we propose a Class-Balanced Cross Entropy loss and a Class Center Contrast method. To alleviate the class imbalance problem, we reweight the cross entropy loss on labeled data in both sample and class level by jointly considering the annotation bias and the class bias on the built SSL dataset. Besides, we decompose the feature embedding space using the ground truth and pseudo-labels, and propose an embedding center selection and contrast method for class-balanced and annotation-guided learning on unlabeled data. The pipeline of the proposed class-aware SSL model is shown in Figure 2. Finally, we perform model inference for large-scale land cover mapping.", + "bbox": [ + 75, + 215, + 472, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Class-Aware Unlabeled Data Selection", + "text_level": 1, + "bbox": [ + 76, + 574, + 406, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A suitable set selection of unlabeled data is important for SSL model development. Inspired by the observation in [41] that existing SSL algorithms can produce pseudolabels on minority classes with high precision, we propose an unlabeled data selection strategy that tends to select unlabeled image patches containing pixels with minority classes.", + "bbox": [ + 75, + 598, + 468, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, we train a semantic segmentation model using labeled data. We apply the off-the-shelf class balance strategy [4] designed for supervised learning to guarantee the model ability of minority class estimation. The definition of minority classes depends on the class proportion and the class accuracy on the labeled data. Then, we perform model inference on all candidate unlabeled data to predict the land cover class of each pixel, thereby obtaining the class distribution of each candidate image patch. We denote the proportion of pixels of all minority classes in an image patch as $P_{m}$ . Finally, we formulate a principle to automatically select unlabeled data according to the class distribution of each candidate image patch. Specifically, the pro", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "portions of the 24 classes on the labeled dataset are shown in Figure 3. The classes with a proportion lower than $1\\%$ generally achieve an accuracy of less than $30\\%$ within our dataset. We collect all the images with $P_{m} \\geq 1\\%$ , which leads to about 25,000 images over the about 500,000 candidates (see Section 4.3). Then we randomly select another 25,000 images from those with $0 < P_{m} < 1\\%$ , leading to a total of 50,000 unlabeled images, which is five times the number of the labeled training data. The authors suggest selecting unlabeled patches with relatively more pixels of minority classes (i.e., larger $P_{m}$ ), and those encompassing rare classes characterized by fewer pixels within the minority classes. Note that although the prediction on the unlabeled data is not absolutely accurate, it can preserve image patches that are most likely to contain pixels with minority classes, which contributes to building a more balanced SSL dataset.", + "bbox": [ + 496, + 90, + 893, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Class-Balanced Learning", + "text_level": 1, + "bbox": [ + 498, + 357, + 730, + 373 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our built SSL dataset, the class distribution of unlabeled data differs from that of the labeled data. It can be regarded as an annotation bias problem on the entire dataset. Besides, the SSL dataset still suffers from a class imbalance issue. Consequently, using the class prior information estimated on the labeled data to the re-weight loss function is inappropriate. To solve the above issues, we propose a class-balanced learning method to jointly remove the annotation bias and class bias on the SSL dataset.", + "bbox": [ + 496, + 380, + 890, + 515 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, we re-weight samples of labeled data to remove the annotation bias. Owing to our unlabeled data selection method, the entire SSL dataset is more balanced towards minority classes than the original labeled dataset. Therefore, we can estimate the class prior on the entire SSL dataset to partially remove the annotation bias. Specifically, we denote $L$ as a label indicator, where $L = 0$ and $L = 1$ represent the unlabeled and labeled data, respectively. The model parameters $\\theta$ of labeled data in traditional SSL methods are obtained by maximizing likelihood estimation in the formula (1).", + "bbox": [ + 496, + 516, + 892, + 681 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\theta} = \\arg \\max _ {\\theta} \\log P (Y | X, L = 1; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log P (y | x; \\theta), \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 704, + 890, + 766 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\hat{\\theta}$ is the estimated model parameter, $X$ represents samples, $Y$ represents classes, and $D_{L = 1}$ denotes the set of labeled data. Due to the annotation bias in the SSL dataset, we have $P(y|x;L = 1)\\neq P(y|x)$ . According to causal inference [13, 17], in the entire SSL dataset, $X\\rightarrow Y\\rightarrow L$ can be regarded as a one-way chain, where the class is dependent on its pixel, and whether the pixel has a label or not depends on its class. According to the", + "bbox": [ + 496, + 777, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16785", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4374f975a37edd04ac6a43821175eb63e023e918e341f7644a90e03609a8add0.jpg", + "image_caption": [ + "Figure 2. The pipeline of the proposed Class-Aware Semi-Supervised Semantic Segmentation framework with class-balanced learning, embedding center estimation, and class center contrast. The class-aware unlabeled data selection process is not shown in the figure." + ], + "image_footnote": [], + "bbox": [ + 117, + 92, + 851, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "conditional independence rule, we obtain the expression, $P(X|Y,L = 1) = P(X|Y)$ when conditioning on Y. Therefore, estimating the model parameters of the entire SSL dataset can be formalized as in the formula (2) [17], where $s(x,y) = \\frac{\\log P(y|x;\\theta) - \\log P(y;\\theta)}{\\log P(y|x;\\theta)}$ is the loss weight of each labeled sample $(x,y)$ . Thus, it can be interpreted as modifying the class prior $P(y;\\theta)$ to remove the annotation bias of the labeled data.", + "bbox": [ + 75, + 424, + 473, + 547 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\theta} = \\arg \\max _ {\\theta} \\log P (X | Y; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log P (x | y; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log \\frac {P (y | x ; \\theta) P (x ; \\theta)}{P (y ; \\theta)} \\tag {2} \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log \\frac {P (y | x ; \\theta)}{P (y ; \\theta)} \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} s (x, y) \\cdot \\log P (y | x; \\theta), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 569, + 468, + 751 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Second, although the SSL dataset is more balanced than the labeled data, it still suffers from the class imbalance problem. Therefore, we further estimate the class bias on the SSL dataset. A widely used class re-weighting loss function on supervised learning can be formalized as follows:", + "bbox": [ + 75, + 760, + 468, + 849 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {w c e} = \\sum_ {k = 1} ^ {K} W _ {k} \\sum_ {i = 1} ^ {n _ {k}} y _ {i k} \\log p _ {i k}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 862, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_{k} = \\frac{1}{\\log(1 + r_{k})}$ and $r_k$ is the ratio of the class $k$ on the labeled data. $K$ is the number of classes, $n_k$ is the number of samples of class $k$ , $y_{ik}$ and $p_{ik}$ is the ground-truth and predicted probability of the $i$ -th sample for class $k$ , respectively. In SSL, we approximate $r_k$ with $P(y; \\theta)$ , the class distribution on the entire dataset.", + "bbox": [ + 496, + 422, + 890, + 516 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we perform an online estimation strategy for $P(y; \\theta)$ to simplify the training process. We compute the average of class probability distributions over all pixels in a mini-batch, which is denoted as $P(Y; B_t, \\theta_t)$ . $B_t$ and $\\theta_t$ are the samples and model parameters of the current batch, respectively. Then the approximate class distribution, denoted as $\\tilde{P}(Y)$ , is updated by the weighted sum of the obtained class distribution of this mini-batch and the approximate class distribution in the previous iteration, which is formalized as follows:", + "bbox": [ + 496, + 520, + 892, + 671 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {P} (Y) \\leftarrow \\mu \\tilde {P} (Y) + (1 - \\mu) P (Y; B _ {t}, \\theta_ {t}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 700, + 890, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu \\in [0,1]$ is a weighting coefficient. We set $\\mu = \\frac{B}{N}$ , in which $B$ is the batch size and $N$ is the total number of samples in the dataset. We initialize $\\tilde{P}(Y)$ with the class distribution calculated on the labeled data. As such, the proposed Class-Balanced Cross Entropy loss on the labeled data is formulated as follows:", + "bbox": [ + 496, + 742, + 892, + 833 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c b c e} = \\sum_ {k = 1} ^ {K} W _ {k} \\sum_ {i = 1} ^ {n _ {k}} s \\left(x _ {i k}, y _ {i k}\\right) y _ {i k} \\log p _ {i k}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 862, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16786", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Class Center Contrast", + "text_level": 1, + "bbox": [ + 76, + 90, + 284, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training via pseudo-labeling is commonly used to utilize unlabeled data in SSL. In fine-grained classes, assigning reliable labels for minority classes is challenging because the segmentation model tends to be biased towards the majority classes [26]. Besides, existing label assignment methods usually use only high-confidence predictions, which may offer limited information to model learning. In this work, our method selects reliable and hard samples. Moreover, instead of directly using the pseudo-labels for supervised learning on unlabeled data, we leverage the pseudo-labels as the guide to decompose the feature embedding space. In general, the distance of feature embeddings from the same class should be minimized, while the distance of those from different classes should be maximized. Therefore, we propose an online embedding center selection method that divides each class into hard and easy sample regions on each image. Specifically, we use the prediction probabilities of ground truth or pseudo-labels to separate easy and hard samples. The predicted probability of each pixel is associated with its feature embedding, and we then calculate the average prediction probability of each class for each image. Feature embeddings with above-average probabilities for the corresponding class are considered easy samples and vice versa. Thus we can obtain three feature embedding centers, including easy, hard, and all feature embedding centers, as contrastive samples. With this method, on the one hand, the obtained feature embeddings for each class are with relatively high confidence, as the samples are close to feature local centers for each class in the embedding space. On the other hand, these feature embeddings include hard samples of each class.", + "bbox": [ + 76, + 113, + 472, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by the existing contrastive learning method [39], we perform cross-image contrastive learning in each mini-batch. Since both labeled and unlabeled data are trained in a mini-batch, the embeddings of the labeled data could help the feature embedding learning of the unlabeled data. Formally, denote $P_{m}$ and $N_{m}$ as the feature embedding collections of the positive and negative samples in a mini-batch for the $m$ -th feature embedding center $c_{m}$ . The proposed Class Center Contrastive loss for the $m$ -th feature embedding center is formulated as follows:", + "bbox": [ + 75, + 583, + 470, + 734 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c c t} ^ {m} = - \\frac {1}{| P _ {m} |} \\sum_ {\\boldsymbol {c} _ {m} ^ {+} \\in P _ {m}} \\log \\frac {e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {+} / \\tau\\right)}}{e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {+} / \\tau\\right)} + \\sum_ {\\boldsymbol {c} _ {m} ^ {-} \\in N _ {m}} e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {-} / \\tau\\right)}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 758, + 485, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which $\\tau$ is the temperature parameter, $c_{m}^{+}$ and $c_{m}^{-}$ are the positive and negative samples, respectively.", + "bbox": [ + 76, + 823, + 467, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss function can be formulated as follows:", + "bbox": [ + 96, + 854, + 460, + 868 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c b c e} + \\lambda \\mathcal {L} _ {c c t}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 885, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is the loss weight.", + "bbox": [ + 500, + 90, + 679, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Data", + "text_level": 1, + "bbox": [ + 500, + 125, + 566, + 138 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Image Collection and Preparation", + "text_level": 1, + "bbox": [ + 500, + 148, + 797, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering free access, multispectral bands, and relatively high spatial resolution, all satellite images used in this work are acquired from Sentinel-2 satellites. Sentinel-2 imagery has 13 spectral bands at $10\\mathrm{m}$ (R, G, B, and near-infrared bands), $20\\mathrm{m}$ (six red edge and shortwave infrared bands), and $60\\mathrm{m}$ (three atmospheric correction bands) resolutions [12]. The abundant multispectral information and up to $10\\mathrm{m}$ spatial resolution benefit land cover mapping with a fine-grained classification system.", + "bbox": [ + 496, + 174, + 890, + 309 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We collect Sentinel-2 images with radiometric correction, geometric corrections, and atmospheric correction, covering more than 60 cities in China. We apply an off-the-shelf Sentinel-2 sharpening method, DSen2Net [24], to reconstruct low-resolution bands and uniform the resolution of all bands of Sentinel-2 images to $10\\mathrm{m}$ .", + "bbox": [ + 496, + 311, + 890, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Label Collection and Classification System", + "text_level": 1, + "bbox": [ + 500, + 415, + 862, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The land cover labels and classification system are from the Five-Billion-Pixels dataset [37], labeled with $4\\mathrm{m}$ resolution. It includes 24 land cover classes. We resize the $4\\mathrm{m}$ labels to $10\\mathrm{m}$ to match Sentinel-2 images. The labeled area covers about $60,000\\mathrm{km}^2$ in China. The classification system includes the industrial area (C1), paddy field (C2), irrigated field (C3), dry cropland (C4), garden land (C5), arbor forest (C6), shrub forest (C7), park (C8), natural meadow (C9), artificial meadow (C10), river (C11), urban residential (C12), lake (C13), pond (C14), fish pond (C15), snow (C16), bare land (C17), rural residential (C18), stadium (C19), square (C20), road (C21), overpass (C22), railway station (C23), and airport (C24).", + "bbox": [ + 496, + 440, + 890, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Dataset", + "text_level": 1, + "bbox": [ + 500, + 648, + 594, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Examples of the labeled data are shown in Figure 1. The training, validation, and test datasets include 9,995, 2,000, and 2,503 images with a size of $256 \\times 256$ , respectively, according to the geographical division. The unlabeled data is from more than 60 dispersed administrative districts in China and has no overlap with the labeled data. The number of candidate unlabeled images is about 500,000, each with a size of $256 \\times 256$ . According to our minority class-biased unlabeled data selection strategy, we filter 50,000 images to build the unlabeled set, which covers more scenes with minority classes. Figure 3 shows the proportion of each land cover class on labeled training data, unlabeled training data, and all training data. The majority classes cover hundreds of times more pixels than the minority classes on the labeled training data.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16787", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/66af3d5eaff49cc0c9ef9bd8aca6e0f9f856cf57c02cf9dde286574d88af7d03.jpg", + "image_caption": [ + "Figure 3. Percentage of each land cover class on the labeled training data, unlabeled training data, and all training data." + ], + "image_footnote": [], + "bbox": [ + 81, + 92, + 890, + 390 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1e6d46ac96b704cc9c89296589fcec31ff0587896a4d10eea3a4cdc437201d23.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodOAmAccmIoUC1C2C3C4C5C6C7C8C9C10
Baseline73.2445.7735.6171.2466.2588.6617.9016.9362.2627.0117.2644.6511.33
SimCLR [7] +finetune74.0745.8135.1774.4963.3390.8814.1017.8062.1023.5718.3948.4221.02
Pseudo -labeling [25]74.6148.8338.0376.8569.6091.5513.4720.5259.1931.6337.5344.9010.68
Advent [38]74.8149.2538.9875.8868.3891.9812.2015.0162.4625.9144.7754.758.10
CADR [17]75.4947.8336.6376.3252.4391.4821.5424.3564.7431.8522.5959.8817.25
DPA [37]75.3648.5737.7776.0569.4092.3315.5119.7966.3027.0523.2552.4112.48
Ours75.9753.5340.6881.7180.0788.8922.2737.3267.0634.8726.4456.7317.16
C11C12C13C14C15C16C17C18C19C20C21C22C23C24
70.8682.7678.9324.4957.713.0448.6777.2310.807.9071.4245.8334.9560.34
71.4783.2779.4130.5464.730.7548.7768.822.00073.5944.5333.8763.72
72.4082.9083.5616.9452.4413.6655.0672.5821.0513.0370.2760.6038.7862.83
69.9883.1983.3819.7249.3415.5046.5675.1622.4017.5570.9958.0441.6269.23
65.9086.2784.5326.0972.57051.7874.960.95065.2348.5133.6475.02
71.9783.3381.8016.7750.660.8852.3772.6121.426.6472.1559.1049.1572.37
70.6182.8681.6917.1378.5326.2855.8080.6931.8326.4966.2364.6546.3942.97
", + "bbox": [ + 86, + 435, + 883, + 693 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison with different methods. We also show the precision of each class. Bold indicates the best results $(\\%)$", + "bbox": [ + 76, + 696, + 875, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 734, + 209, + 752 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Implementation Details and Metrics", + "text_level": 1, + "bbox": [ + 76, + 763, + 390, + 781 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We choose ResUNet [9] in our experiments, as it is stable and lightweight for land cover mapping. We train for 100 epochs for all experiments using stochastic gradient descent (SGD) with a momentum of 0.9 and a weight decay of $10^{-4}$ . The initial learning rate is set to 0.05. We adopt the batch size as 12, including 6 labeled images and 6 unlabeled images. The loss weight $\\lambda$ is set to 0.005. The temperature", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\tau$ of contrastive loss is set to 0.07.", + "bbox": [ + 500, + 736, + 723, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The performance of the proposed approach and other competing methods are assessed with overall accuracy (OA), mean accuracy (mAcc), mean intersection over union (mIoU), and precision of each class.", + "bbox": [ + 498, + 753, + 890, + 814 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison Results", + "text_level": 1, + "bbox": [ + 500, + 829, + 692, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 shows the comparison results with typical and state-of-the-art class-balanced pseudo-labeling methods. For a fair comparison, all competing methods and our", + "bbox": [ + 498, + 854, + 892, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16788", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a6759b955130e942fd9658c3df227bdcea20218473c6fb420ad98b36f2536fd3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodOAmAccmIoU
Random selection75.5051.3539.09
Majority class -biased selection75.7549.9839.33
Minority class -biased selection75.9753.5340.68
", + "bbox": [ + 130, + 88, + 416, + 189 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/53c82a41da47d48dd81f00bdb2d8097ccbb54a351ff4aa10a5e1221579f63e06.jpg", + "table_caption": [ + "Table 2. Ablation study on the proposed class-aware unlabeled data selection method. Bold indicates the best results $(\\%)$ ." + ], + "table_footnote": [], + "table_body": "
MethodOAmAccmIoU
Without class balance75.4148.1637.27
Class-balanced method in [38]73.6151.3338.61
Class-balanced method in [37]75.5149.6635.51
Ours75.9753.5340.68
", + "bbox": [ + 78, + 239, + 475, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Comparison results on different class-balanced learning methods. Bold indicates the best results $(\\%)$ .", + "bbox": [ + 76, + 330, + 467, + 357 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "method use the same model architecture. All experiments are measured on the same computing platform. The baseline applies the supervised learning method to the labeled data. The SimCLR+finetune method uses a self-supervised learning method [7] on the unlabeled data to obtain a pretrain model and performs fine-tuning on the labeled data. Pseudo-labeling method [25] first generates pseudo-labels of the unlabeled data by using the baseline model, then retransmits the model with ground truth and pseudo-labels. Advent [38], DPA [37], and CADR [17] are three state-of-the-art SSL methods.", + "bbox": [ + 75, + 383, + 467, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results demonstrate that our approach significantly improved over $4.28\\%$ in mAcc, $1.70\\%$ in mIoU, and $0.58\\%$ in OA. Compared to the baseline for each class, our method can significantly improve the accuracy of the minority classes and maintain the accuracy of the majority classes simultaneously. In contrast, the competing methods often tend to predict the pixels to majority classes and suffer from low precision on minority classes. Regarding the computational cost, our method incurs $53\\%$ additional training time than the basic SSL algorithm (i.e., Advent) due to Class-Balanced Learning and Class Center Contrast. The inference times are the same for all SSL methods, as we use the same backbone. Please find the visual comparison in the supplementary.", + "bbox": [ + 75, + 549, + 467, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 770, + 228, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Class-Aware Unlabeled Data Selection. We compare our method with the opposite strategy (i.e., majority class-biased data selection) and widely opted random selection method. Table 2 shows that our method achieves the best results. On the contrary, the mAcc value of the majority class-biased data selection method is unsatisfactory because the SSL model is biased toward predicting the majority classes.", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/10d83bb2ceae84f2e5bf7fb6a2db8ac3888294dc074b804f6a1d10733d745232.jpg", + "image_caption": [ + "Figure 4. Results of using the different number of labeled images (i.e., 500, 1,000, and 3,000) and the different ratios of unlabeled to labeled images in SSL." + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 890, + 263 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Besides, to verify the effectiveness of unlabeled data selection, we show the statistics of class distribution in Figure 3. Estimating the class distribution of unlabeled data is based on the pseudo-labels produced by the baseline model. Owing to the proposed class-aware unlabeled data selection method, the class distribution of the unlabeled data is more balanced than that of the labeled data. As a result, the entire training dataset is more balanced towards minority classes than the original labeled dataset. Therefore, we can estimate the class prior information on the entire dataset to partially remove the annotation bias.", + "bbox": [ + 496, + 351, + 890, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Class-Balanced Learning. In general, class weighting sacrifices the accuracy of majority classes to improve the accuracy of minority classes, which decreases OA and mIoU. From Table 3, two comparison methods suffer from the above problem, while our method improves the mAcc, OA, and mIoU compared to the baseline (i.e., without loss weights). The reason is that the two comparison methods use class prior information of labeled data and ignore the discrepancy of class distributions between labeled and unlabeled data in SSL. Besides, Table 4 shows the ablation study on Class-Balanced Cross Entropy loss. Utilizing sample re-weighting improves performance by removing the annotation bias on the semi-supervised learning dataset. Using class re-weighting for cross-entropy loss removes class bias and improves the performance of mAcc and mIoU by a large margin. Furthermore, jointly utilizing the sample and class weights achieves the best results in Table 4.", + "bbox": [ + 496, + 520, + 890, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Class Center Contrast Method. Table 5 shows the ablation study on the proposed class center contrast method. Contrastive loss utilizes inter-class and intra-class information and achieves better results than center loss used in [28]. Compared with only training contrastive loss with pseudolabels on unlabeled data, using pseudo-labels on both labeled and unlabeled data achieves better results. Further-", + "bbox": [ + 496, + 794, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16789", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a32f4d62a56ee63264f1724813b1316e98741cd4edf88c634ee78c788460f4d3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Cross entropy lossSample re-weightingClass re-weightingOAmAccmIoU
✓75.4148.1637.27
✓✓75.7448.9638.40
✓✓75.4352.0640.07
✓✓✓75.9753.5340.68
", + "bbox": [ + 166, + 87, + 803, + 167 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3a3ef5b9cf4e13b3adf267b42001abaab364006405379d2ac79606baa42796f0.jpg", + "table_caption": [ + "Table 4. Ablation study on class-balanced cross entropy loss. Bold indicates the best results $(\\%)$ ." + ], + "table_footnote": [], + "table_body": "
Center lossContrastive lossPseudo labelGround truthOn labeled dataOn unlabeled dataOAmAccmIoU
✓✓✓74.0748.1337.34
✓✓✓75.2350.0639.29
✓✓✓✓75.2651.4239.43
✓✓✓✓✓75.9753.5340.68
", + "bbox": [ + 135, + 203, + 834, + 299 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/45efef6b56a47580d8a4a354b5af92acbf71321f28fc5d16b255426c7de47944.jpg", + "table_caption": [ + "Table 5. Ablation study on the class center contrast method. Bold indicates the best results $(\\%)$" + ], + "table_footnote": [], + "table_body": "
MethodOAmAccmIoU
Random sample selection74.6849.3138.80
Simple sample selection74.7451.5740.42
Hard sample selection74.5751.1440.31
Feature embedding centers75.9753.5340.68
", + "bbox": [ + 86, + 345, + 460, + 425 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e259d892fbe004a71ca134cd182697c5d7c50116bbad327954eaca1f14937489.jpg", + "table_caption": [ + "Table 6. Results of different contrastive sample selection manners. Bold indicates the best results $(\\%)$ ." + ], + "table_footnote": [], + "table_body": "
MethodOAmAccmIoU
Within-image method73.3653.4840.03
Cross-image method75.9753.5340.68
", + "bbox": [ + 102, + 479, + 444, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "more, introducing the ground truth of labeled data to the training of contrastive loss can significantly improve performance. We also compare different sample selection strategies for contrastive learning. We select three contrastive samples for each class per image for a fair comparison. As shown in Table 6, leveraging high-confidence predicted samples from the unlabeled data for semi-supervised learning yields better results than employing uncertain samples. Nonetheless, samples with high-confidence predictions provide limited information for model learning, leading to only marginal enhancements. The proposed Class Center Contrast method involves both high-confidence and hard samples, achieving the best results. Besides, we compare within-image and cross-image contrastive learning results in Table 7. Cross-image method uses labeled and unlabeled images in a mini-batch and achieves better results, while the within-image method only uses local information of labeled or unlabeled images.", + "bbox": [ + 75, + 595, + 468, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyperparameter Tuning of Loss Weight. $\\lambda$ is to balance two loss terms in the formula (7). Table 8 shows the", + "bbox": [ + 76, + 869, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/11eb0834942d54c4f2a712e19739ea1fba553cf61a5ca055604034830108765f.jpg", + "table_caption": [ + "Table 7. Results of within-image and cross-image contrastive learning. Bold indicates the best results $(\\%)$ ." + ], + "table_footnote": [], + "table_body": "
Loss weightOAmAccmIoU
λ = 0.0575.0751.6240.15
λ = 0.0175.2651.4239.43
λ = 0.00575.9753.5340.68
λ = 0.00175.2753.8440.26
", + "bbox": [ + 555, + 345, + 836, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Hyperparameter tuning of loss weight. Bold indicates the best results $(\\%)$ .", + "bbox": [ + 500, + 435, + 890, + 462 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "results using different loss weights $\\lambda$ . We conclude that a large loss weight for $\\mathcal{L}_{cct}$ reduces the model performance. In this work, we set $\\lambda = 0.005$ .", + "bbox": [ + 498, + 488, + 890, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Number and Ratio of Labeled Images in SSL. We conduct a comparative analysis of the enhancement in accuracy resulting from the increase of unlabeled data. As shown in Figure 4, the utilization of a larger quantity of unlabeled data, specifically ten times the amount of labeled training data containing only 500 images, has been observed to result in a substantial improvement in accuracy. Meanwhile, the performance becomes unstable as the ratio between unlabeled and labeled images increases further because of the limited number of labeled images. As the amount of labeled data increased, using the unlabeled data, which is five times the amount of labeled data, can yield superior results compared to using just one time the amount of labeled data. Subsequently, the performance is relatively stable as the number of unlabeled data increases. Therefore, to balance the computational cost and improvement in accuracy, we use a ratio of 5:1 for unlabeled and labeled data.", + "bbox": [ + 496, + 534, + 890, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Examples of Land Cover Mapping in China", + "text_level": 1, + "bbox": [ + 500, + 801, + 870, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As an application of the proposed method, we produce large-scale land cover maps with 24 classes over 1 million $\\mathrm{km}^2$ . As shown in Figure 5, we compare our land cover mapping results with two existing public products produced by ESA [45] and Google [2]. The example in the top row", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16790", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/99ab48134b1f93faa14350de580fb1f22554bef78b70c53c9974b5cf369dd558.jpg", + "image_caption": [ + "Tree cover", + "Shrubland", + "Grassland", + "Cropland", + "Built-up", + "Bare/sparse.", + "vegetation", + "Snow and ice", + "Perm", + "water bodies", + "Herbaceous wetland", + "Mangroves", + "Moss and lichen", + "(a) ESA" + ], + "image_footnote": [], + "bbox": [ + 83, + 98, + 269, + 239 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/f7f357d0a572cca03a1ba1ff2bd5083e6e4a81c05ae6d022c9b05c5dd55adfd2.jpg", + "image_caption": [ + "Water", + "Trees", + "Grass", + "Flooded", + "vegetation", + "Crops", + "Shrub &", + "Scrub", + "Built", + "Bare ground", + "Snow & ice" + ], + "image_footnote": [], + "bbox": [ + 349, + 98, + 531, + 238 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0aa2424f575f40c7123070bad49ed39ca9a28a3c17339dbbfcbb6f86bc0e8fae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 98, + 883, + 239 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/e7b8435da0c4cbe62f2e8d8cc0317ea4202a3afe0372c0b324bbe76068c871f6.jpg", + "image_caption": [ + "(b) Google", + "(c) Ours", + "Figure 5. Examples of Land Cover Mapping in China. The land cover products of ESA and Google are also generated from Sentinel-2 images but use different classification systems. In the black rectangles, our land cover results with fine-grained classes can provide more land cover information. In the red rectangles, our method recognizes the paddy field correctly, while the other two products classify it as cropland and water, respectively, due to the coarse classification system and the misleading spectral information of the paddy field." + ], + "image_footnote": [], + "bbox": [ + 614, + 243, + 879, + 383 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "shows the results of an urban area located in the east of China, and that in the bottom row gives the results of a rural area located in the center of China. The land cover products of ESA and Google contain 11 and 9 classes, while our classification system includes 24 classes. From the black rectangles, the two comparison products mainly distinguish built areas, water, trees, and crops. Owing to the fine-grained classification system and the proposed class-aware SSL methods, our results can recognize more land cover categories, including industrial area, urban residential, rural residential, road, overpass, railway station, arbor forest, artificial meadow, irrigated field, bare land, lake, river, pond, and fish pond. Our land cover maps with fine-grained classes can provide more land cover information. Besides, from the red rectangles, our method recognizes the paddy field correctly, while the other two products classify it as cropland and water, respectively, due to the coarse classification system and the misleading spectral information of the paddy field. From the above qualitative comparison, our method provides land cover maps with fine-grained classes, significantly improving the land cover information.", + "bbox": [ + 75, + 505, + 472, + 824 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 843, + 194, + 858 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation approach for large-", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "scale land cover mapping with fine-grained classes. To address the class-imbalance issue, we propose a class-aware unlabeled data selection method to build an SSL dataset more balanced towards minority classes. Then, we propose a Class-Balanced Cross Entropy loss, considering the annotation and class biases on the built SSL dataset. Moreover, we propose the Class Center Contrast method to jointly use the labeled and unlabeled data for training. Experimental results validate the effectiveness of our method in large-scale land cover mapping with fine-grained classes.", + "bbox": [ + 496, + 505, + 893, + 657 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 710, + 666, + 728 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research was supported in part by the National Natural Science Foundation of China (Grant No. T2125006), Jiangsu Innovation Capacity Building Program (Project No. BM2022028), China Postdoctoral Science Foundation (Grant No. 2023M731871), the German Federal Ministry of Education and Research (BMBF) in the framework of the international future AI lab \"AI4EO - Artificial Intelligence for Earth Observation: Reasoning, Uncertainties, Ethics and Beyond\" (Grant No. 01DD20001), and Shuimu Tsinghua Scholar Project.", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "16791", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9719–9728, 2020. 2" + ], + "bbox": [ + 501, + 92, + 893, + 897 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16793", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/85af6521-8e24-45e3-ac82-fb3352f9480e_model.json b/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/85af6521-8e24-45e3-ac82-fb3352f9480e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d2cc3d86e708b09a62cce6585c08a1e51630b827 --- /dev/null +++ b/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/85af6521-8e24-45e3-ac82-fb3352f9480e_model.json @@ -0,0 +1,2279 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.13, + 0.88, + 0.177 + ], + "angle": 0, + "content": "Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.203, + 0.834, + 0.277 + ], + "angle": 0, + "content": "Runmin Dong\\(^{1,4}\\), Lichao Mou\\(^{2}\\), Mengxuan Chen\\(^{1,4}\\), Weijia Li\\(^{3}\\), Xin-Yi Tong\\(^{2}\\), Shuai Yuan\\(^{1,4}\\), Lixian Zhang\\(^{1,4}\\), Juepeng Zheng\\(^{3,4}\\), Xiao Xiang Zhu\\(^{2}\\), Haohuan Fu\\(^{1,4,*}\\), Tsinghua University \\({}^{2}\\)Technical University of Munich \\({}^{3}\\)Sun Yat-Sen University \\({}^{4}\\)Tsinghua University - Xi'an Institute of Surveying and Mapping Joint Research Center" + }, + { + "type": "text", + "bbox": [ + 0.266, + 0.278, + 0.704, + 0.292 + ], + "angle": 0, + "content": "drm@mail.tsinghua.edu.cn, haohuan@tsinghua.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.359, + 0.474, + 0.782 + ], + "angle": 0, + "content": "Semi-supervised learning has attracted increasing attention in the large-scale land cover mapping task. However, existing methods overlook the potential to alleviate the class imbalance problem by selecting a suitable set of unlabeled data. Besides, in class-imbalanced scenarios, existing pseudo-labeling methods mostly only pick confident samples, failing to exploit the hard samples during training. To tackle these issues, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation framework. The proposed framework consists of three key components. To construct a better semi-supervised learning dataset, we propose a class-aware unlabeled data selection method that is more balanced towards the minority classes. Based on the built dataset with improved class balance, we propose a Class-Balanced Cross Entropy loss, jointly considering the annotation bias and the class bias to re-weight the loss in both sample and class levels to alleviate the class imbalance problem. Moreover, we propose the Class Center Contrast method to jointly utilize the labeled and unlabeled data. Specifically, we decompose the feature embedding space using the ground truth and pseudo-labels, and employ the embedding centers for hard and easy samples of each class per image in the contrast loss to exploit the hard samples during training. Compared with state-of-the-art class-balanced pseudo-labeling methods, the proposed method improves the mean accuracy and mIoU by \\(4.28\\%\\) and \\(1.70\\%\\), respectively, on the large-scale Sentinel-2 dataset with 24 land cover classes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.809, + 0.21, + 0.825 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.835, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Land cover mapping provides pixel-level information for urban management, climate change research, ecosystem protection, and other sustainability-related applica" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.329, + 0.895, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.571, + 0.895, + 0.627 + ], + "angle": 0, + "content": "Figure 1. Examples of the labeled data. The top row shows Sentinel-2 images containing 13 bands. The bottom row shows the corresponding labels. We use a fine-grained classification system with 24 land cover classes in this work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.895, + 0.822 + ], + "angle": 0, + "content": "tions [21, 27]. With the rapid progress of computer vision technology, it is desired to automatically gain large-scale and fine-grained land cover information from remote sensing images to support the demand of existing earth system science studies and bring new opportunities for intelligent city study [31]. However, fine-grained annotations for land cover mapping are high-cost and time-consuming, limiting labeled data collection for large-scale applications. Semi-supervised learning (SSL) is a potential solution to this problem, as it utilizes both existing labeled data and a large number of unlabeled data [37]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Large-scale land cover mapping with fine-grained classes usually suffers from class imbalance, as shown in Figure 1 and 3. The labeled data tends to be biased due to the difficulty of data collection and label annotation varying by class. The class imbalance leads to suboptimal per" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16783" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.332 + ], + "angle": 0, + "content": "formance in the minority classes. Most SSL methods for large-scale land cover mapping are typically based on the assumption that labeled and unlabeled data have the same class distribution [41, 37]. However, this assumption does not hold in most scenarios, resulting in the bias of class estimation. As such, it is non-trivial to jointly utilize the labeled and unlabeled data to train the network for semi-supervised semantic segmentation. Although many pseudo-labeling methods aim to assign pseudo-labels more steadily and correctly for different classes on the unlabeled data, e.g., dynamically setting threshold or proportion [17, 44], they still rely on setting hyperparameters and empirical principles, resulting in a lack of flexibility and generalization ability in applications. Besides, pseudo-labeling methods mostly rely on easy samples with high confidence scores, thus failing to exploit the hard samples on the unlabeled data." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.334, + 0.468, + 0.68 + ], + "angle": 0, + "content": "To alleviate the above issues, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation framework. We exploit the potential of the unlabeled data and alleviate the class imbalance problem in large-scale land cover mapping with fine-grained classes. The proposed class-aware unlabeled data selection method constructs an SSL dataset and compensates for the class imbalance on the labeled data. Based on the built SSL dataset, we propose a class-balanced learning method to remove the annotation bias and class bias on the SSL dataset. We dynamically estimate the class prior information on the entire SSL dataset during training to re-weight both samples and classes of the loss function for the labeled data. Finally, we propose the Class Center Contrast method to jointly use the labeled and unlabeled data for training. The ground truth and pseudolabels are leveraged as the guide to decompose the feature embedding space. We estimate the hard, easy, and overall embedding centers for each class per image and apply the contrastive loss to optimize the distances between class centers to utilize both easy and hard samples. The class imbalance issue is alleviated by utilizing the proposed method, and the performance of large-scale land cover mapping with fine-grained classes is effectively improved." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.695, + 0.216, + 0.71 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.721, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Large-Scale Land Cover Mapping. Land cover mapping classifies each pixel of images into a unique class, which can be regarded as a semantic segmentation problem [6, 11]. Large-scale land cover mapping with fine-grained classes can provide necessary information for earth system science studies and land spatial layout optimization. However, manual or semi-manual labeling is high-cost and time-consuming [34]. Besides, the classification systems of most large-scale studies are coarse. Thus the provided land cover information is limited. For example, the Chesapeake dataset covering \\(160,000\\mathrm{km}^2\\) costs $1.3 million but only contains four classes [33]. DynamicEarthNet" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.318 + ], + "angle": 0, + "content": "dataset covers \\(17,000\\mathrm{km}^2\\) and includes 7 basic land cover classes [36]. To overcome the limited area of the labeled data and improve the model generalization, some works utilize openly available produced data (e.g., OpenStreetMap data and land cover products), which contains many noisy labels but can provide prior information in a large-scale area [19, 10]. These works still use coarse classification systems of land cover mapping. Five-Billion-Pixels [37] is a large-scale land cover dataset with 24 categories, covering about \\(60,000\\mathrm{km}^2\\), which opens the door to large-scale land cover mapping with fine-grained classes. However, this dataset suffers from a severe class-imbalance problem (the common categories cover hundreds of times more pixels than the rare ones), due to the difficulty of data collection and label annotation varying by class." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.323, + 0.89, + 0.564 + ], + "angle": 0, + "content": "Class-Imbalanced Learning. To solve the class-imbalance problem, related works include data resampling [3, 4], loss re-weighting [22, 32, 18], margin modification [5, 35], and decoupled learning [20, 47]. In self-supervised learning and SSL, recent works devote to rebalancing the class distribution of SSL data by assigning pseudo-labels for the unlabeled data to address the class imbalance issue [41, 15]. For example, Gui et al. [14] propose a class-aware pseudo-labeling method for SSL, dynamically adjusting the threshold for selecting pseudo-labels to obtain better performance on minority classes. Similarly, Hu et al. [17] propose a label bias removal method and dynamically determine the threshold for each class to assign more pseudo-labels for minority classes. However, the hard samples with relatively low confidence scores are ignored for optimizing the model, leading to sub-optimal performance." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.57, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Semi-Supervised Semantic Segmentation. SSL methods leverage the relationships between the labeled and unlabeled data to improve the model accuracy and generalization, alleviating the limited area of the labeled data [8]. Semi-supervised semantic segmentation methods include entropy minimization [38], consistency regularization [30], and pseudo-labeling [42]. Pseudo-labeling is widely used in semi-supervised semantic segmentation, and many works contribute to selecting pseudo-labels more steadily and correctly [29]. For example, Tong et al. [37] propose a dynamic pseudo-label assignment method, in which the number of pseudo-labels is dynamically increased with training iterations. However, these methods still rely on the manual setting of hyperparameters and suffer from the uncertainty of pseudo-labels. Alternatively, contrastive learning methods in supervised learning [39, 16] and SSL [46, 40] constrain the representations of positive samples against these negative samples in feature space, leading to promising results. Different from the manner of data augmentation-based positive sample construction [43, 23] and memory bank-based negative sample construction [1, 40], we leverage the ground-truth and pseudo-labels as a guide to decom" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.947, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16784" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "pose the feature embedding space, and estimate the embedding centers for each class per image to stably select easy and hard samples for the proposed Class Center Contrast method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.167, + 0.214, + 0.185 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.192, + 0.423, + 0.21 + ], + "angle": 0, + "content": "3.1. The Overall Workflow of Our Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.216, + 0.473, + 0.565 + ], + "angle": 0, + "content": "Our approach consists of four steps. First, a baseline model is trained on the labeled data. Second, we propose a class-aware unlabeled data selection method to build an SSL dataset that is more balanced towards minority classes. The baseline model is used to predict land cover classes on all collected data from a large unlabeled data pool and calculate the statistics of the class distribution for each image patch. The image patches containing pixels of minority classes are selected as unlabeled data. Then the SSL dataset is constructed by combining the labeled data and the selected unlabeled data. Third, we propose a Class-Balanced Cross Entropy loss and a Class Center Contrast method. To alleviate the class imbalance problem, we reweight the cross entropy loss on labeled data in both sample and class level by jointly considering the annotation bias and the class bias on the built SSL dataset. Besides, we decompose the feature embedding space using the ground truth and pseudo-labels, and propose an embedding center selection and contrast method for class-balanced and annotation-guided learning on unlabeled data. The pipeline of the proposed class-aware SSL model is shown in Figure 2. Finally, we perform model inference for large-scale land cover mapping." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.575, + 0.407, + 0.59 + ], + "angle": 0, + "content": "3.2. Class-Aware Unlabeled Data Selection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.704 + ], + "angle": 0, + "content": "A suitable set selection of unlabeled data is important for SSL model development. Inspired by the observation in [41] that existing SSL algorithms can produce pseudolabels on minority classes with high precision, we propose an unlabeled data selection strategy that tends to select unlabeled image patches containing pixels with minority classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "First, we train a semantic segmentation model using labeled data. We apply the off-the-shelf class balance strategy [4] designed for supervised learning to guarantee the model ability of minority class estimation. The definition of minority classes depends on the class proportion and the class accuracy on the labeled data. Then, we perform model inference on all candidate unlabeled data to predict the land cover class of each pixel, thereby obtaining the class distribution of each candidate image patch. We denote the proportion of pixels of all minority classes in an image patch as \\( P_{m} \\). Finally, we formulate a principle to automatically select unlabeled data according to the class distribution of each candidate image patch. Specifically, the pro" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.348 + ], + "angle": 0, + "content": "portions of the 24 classes on the labeled dataset are shown in Figure 3. The classes with a proportion lower than \\(1\\%\\) generally achieve an accuracy of less than \\(30\\%\\) within our dataset. We collect all the images with \\(P_{m} \\geq 1\\%\\), which leads to about 25,000 images over the about 500,000 candidates (see Section 4.3). Then we randomly select another 25,000 images from those with \\(0 < P_{m} < 1\\%\\), leading to a total of 50,000 unlabeled images, which is five times the number of the labeled training data. The authors suggest selecting unlabeled patches with relatively more pixels of minority classes (i.e., larger \\(P_{m}\\)), and those encompassing rare classes characterized by fewer pixels within the minority classes. Note that although the prediction on the unlabeled data is not absolutely accurate, it can preserve image patches that are most likely to contain pixels with minority classes, which contributes to building a more balanced SSL dataset." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.358, + 0.731, + 0.374 + ], + "angle": 0, + "content": "3.3. Class-Balanced Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.516 + ], + "angle": 0, + "content": "In our built SSL dataset, the class distribution of unlabeled data differs from that of the labeled data. It can be regarded as an annotation bias problem on the entire dataset. Besides, the SSL dataset still suffers from a class imbalance issue. Consequently, using the class prior information estimated on the labeled data to the re-weight loss function is inappropriate. To solve the above issues, we propose a class-balanced learning method to jointly remove the annotation bias and class bias on the SSL dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.893, + 0.683 + ], + "angle": 0, + "content": "First, we re-weight samples of labeled data to remove the annotation bias. Owing to our unlabeled data selection method, the entire SSL dataset is more balanced towards minority classes than the original labeled dataset. Therefore, we can estimate the class prior on the entire SSL dataset to partially remove the annotation bias. Specifically, we denote \\( L \\) as a label indicator, where \\( L = 0 \\) and \\( L = 1 \\) represent the unlabeled and labeled data, respectively. The model parameters \\( \\theta \\) of labeled data in traditional SSL methods are obtained by maximizing likelihood estimation in the formula (1)." + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.705, + 0.891, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\theta} = \\arg \\max _ {\\theta} \\log P (Y | X, L = 1; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log P (y | x; \\theta), \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.779, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(\\hat{\\theta}\\) is the estimated model parameter, \\(X\\) represents samples, \\(Y\\) represents classes, and \\(D_{L = 1}\\) denotes the set of labeled data. Due to the annotation bias in the SSL dataset, we have \\(P(y|x;L = 1)\\neq P(y|x)\\). According to causal inference [13, 17], in the entire SSL dataset, \\(X\\rightarrow Y\\rightarrow L\\) can be regarded as a one-way chain, where the class is dependent on its pixel, and whether the pixel has a label or not depends on its class. According to the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16785" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.093, + 0.852, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.372, + 0.89, + 0.401 + ], + "angle": 0, + "content": "Figure 2. The pipeline of the proposed Class-Aware Semi-Supervised Semantic Segmentation framework with class-balanced learning, embedding center estimation, and class center contrast. The class-aware unlabeled data selection process is not shown in the figure." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.474, + 0.548 + ], + "angle": 0, + "content": "conditional independence rule, we obtain the expression, \\( P(X|Y,L = 1) = P(X|Y) \\) when conditioning on Y. Therefore, estimating the model parameters of the entire SSL dataset can be formalized as in the formula (2) [17], where \\( s(x,y) = \\frac{\\log P(y|x;\\theta) - \\log P(y;\\theta)}{\\log P(y|x;\\theta)} \\) is the loss weight of each labeled sample \\( (x,y) \\). Thus, it can be interpreted as modifying the class prior \\( P(y;\\theta) \\) to remove the annotation bias of the labeled data." + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.57, + 0.469, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\theta} = \\arg \\max _ {\\theta} \\log P (X | Y; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log P (x | y; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log \\frac {P (y | x ; \\theta) P (x ; \\theta)}{P (y ; \\theta)} \\tag {2} \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log \\frac {P (y | x ; \\theta)}{P (y ; \\theta)} \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} s (x, y) \\cdot \\log P (y | x; \\theta), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.761, + 0.47, + 0.85 + ], + "angle": 0, + "content": "Second, although the SSL dataset is more balanced than the labeled data, it still suffers from the class imbalance problem. Therefore, we further estimate the class bias on the SSL dataset. A widely used class re-weighting loss function on supervised learning can be formalized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.863, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {w c e} = \\sum_ {k = 1} ^ {K} W _ {k} \\sum_ {i = 1} ^ {n _ {k}} y _ {i k} \\log p _ {i k}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.517 + ], + "angle": 0, + "content": "where \\( W_{k} = \\frac{1}{\\log(1 + r_{k})} \\) and \\( r_k \\) is the ratio of the class \\( k \\) on the labeled data. \\( K \\) is the number of classes, \\( n_k \\) is the number of samples of class \\( k \\), \\( y_{ik} \\) and \\( p_{ik} \\) is the ground-truth and predicted probability of the \\( i \\)-th sample for class \\( k \\), respectively. In SSL, we approximate \\( r_k \\) with \\( P(y; \\theta) \\), the class distribution on the entire dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.893, + 0.672 + ], + "angle": 0, + "content": "Finally, we perform an online estimation strategy for \\( P(y; \\theta) \\) to simplify the training process. We compute the average of class probability distributions over all pixels in a mini-batch, which is denoted as \\( P(Y; B_t, \\theta_t) \\). \\( B_t \\) and \\( \\theta_t \\) are the samples and model parameters of the current batch, respectively. Then the approximate class distribution, denoted as \\( \\tilde{P}(Y) \\), is updated by the weighted sum of the obtained class distribution of this mini-batch and the approximate class distribution in the previous iteration, which is formalized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.702, + 0.892, + 0.72 + ], + "angle": 0, + "content": "\\[\n\\tilde {P} (Y) \\leftarrow \\mu \\tilde {P} (Y) + (1 - \\mu) P (Y; B _ {t}, \\theta_ {t}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.743, + 0.893, + 0.834 + ], + "angle": 0, + "content": "where \\(\\mu \\in [0,1]\\) is a weighting coefficient. We set \\(\\mu = \\frac{B}{N}\\), in which \\(B\\) is the batch size and \\(N\\) is the total number of samples in the dataset. We initialize \\(\\tilde{P}(Y)\\) with the class distribution calculated on the labeled data. As such, the proposed Class-Balanced Cross Entropy loss on the labeled data is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.863, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c b c e} = \\sum_ {k = 1} ^ {K} W _ {k} \\sum_ {i = 1} ^ {n _ {k}} s \\left(x _ {i k}, y _ {i k}\\right) y _ {i k} \\log p _ {i k}. \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16786" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.285, + 0.105 + ], + "angle": 0, + "content": "3.4. Class Center Contrast" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.114, + 0.473, + 0.584 + ], + "angle": 0, + "content": "Training via pseudo-labeling is commonly used to utilize unlabeled data in SSL. In fine-grained classes, assigning reliable labels for minority classes is challenging because the segmentation model tends to be biased towards the majority classes [26]. Besides, existing label assignment methods usually use only high-confidence predictions, which may offer limited information to model learning. In this work, our method selects reliable and hard samples. Moreover, instead of directly using the pseudo-labels for supervised learning on unlabeled data, we leverage the pseudo-labels as the guide to decompose the feature embedding space. In general, the distance of feature embeddings from the same class should be minimized, while the distance of those from different classes should be maximized. Therefore, we propose an online embedding center selection method that divides each class into hard and easy sample regions on each image. Specifically, we use the prediction probabilities of ground truth or pseudo-labels to separate easy and hard samples. The predicted probability of each pixel is associated with its feature embedding, and we then calculate the average prediction probability of each class for each image. Feature embeddings with above-average probabilities for the corresponding class are considered easy samples and vice versa. Thus we can obtain three feature embedding centers, including easy, hard, and all feature embedding centers, as contrastive samples. With this method, on the one hand, the obtained feature embeddings for each class are with relatively high confidence, as the samples are close to feature local centers for each class in the embedding space. On the other hand, these feature embeddings include hard samples of each class." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.472, + 0.735 + ], + "angle": 0, + "content": "Inspired by the existing contrastive learning method [39], we perform cross-image contrastive learning in each mini-batch. Since both labeled and unlabeled data are trained in a mini-batch, the embeddings of the labeled data could help the feature embedding learning of the unlabeled data. Formally, denote \\( P_{m} \\) and \\( N_{m} \\) as the feature embedding collections of the positive and negative samples in a mini-batch for the \\( m \\)-th feature embedding center \\( c_{m} \\). The proposed Class Center Contrastive loss for the \\( m \\)-th feature embedding center is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.759, + 0.486, + 0.823 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c c t} ^ {m} = - \\frac {1}{| P _ {m} |} \\sum_ {\\boldsymbol {c} _ {m} ^ {+} \\in P _ {m}} \\log \\frac {e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {+} / \\tau\\right)}}{e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {+} / \\tau\\right)} + \\sum_ {\\boldsymbol {c} _ {m} ^ {-} \\in N _ {m}} e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {-} / \\tau\\right)}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.824, + 0.468, + 0.854 + ], + "angle": 0, + "content": "in which \\(\\tau\\) is the temperature parameter, \\(c_{m}^{+}\\) and \\(c_{m}^{-}\\) are the positive and negative samples, respectively." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.855, + 0.462, + 0.869 + ], + "angle": 0, + "content": "The overall loss function can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {c b c e} + \\lambda \\mathcal {L} _ {c c t}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.68, + 0.107 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the loss weight." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.125, + 0.567, + 0.14 + ], + "angle": 0, + "content": "4. Data" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.15, + 0.798, + 0.166 + ], + "angle": 0, + "content": "4.1. Image Collection and Preparation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.175, + 0.892, + 0.31 + ], + "angle": 0, + "content": "Considering free access, multispectral bands, and relatively high spatial resolution, all satellite images used in this work are acquired from Sentinel-2 satellites. Sentinel-2 imagery has 13 spectral bands at \\(10\\mathrm{m}\\) (R, G, B, and near-infrared bands), \\(20\\mathrm{m}\\) (six red edge and shortwave infrared bands), and \\(60\\mathrm{m}\\) (three atmospheric correction bands) resolutions [12]. The abundant multispectral information and up to \\(10\\mathrm{m}\\) spatial resolution benefit land cover mapping with a fine-grained classification system." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.402 + ], + "angle": 0, + "content": "We collect Sentinel-2 images with radiometric correction, geometric corrections, and atmospheric correction, covering more than 60 cities in China. We apply an off-the-shelf Sentinel-2 sharpening method, DSen2Net [24], to reconstruct low-resolution bands and uniform the resolution of all bands of Sentinel-2 images to \\(10\\mathrm{m}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.416, + 0.863, + 0.433 + ], + "angle": 0, + "content": "4.2. Label Collection and Classification System" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.892, + 0.637 + ], + "angle": 0, + "content": "The land cover labels and classification system are from the Five-Billion-Pixels dataset [37], labeled with \\(4\\mathrm{m}\\) resolution. It includes 24 land cover classes. We resize the \\(4\\mathrm{m}\\) labels to \\(10\\mathrm{m}\\) to match Sentinel-2 images. The labeled area covers about \\(60,000\\mathrm{km}^2\\) in China. The classification system includes the industrial area (C1), paddy field (C2), irrigated field (C3), dry cropland (C4), garden land (C5), arbor forest (C6), shrub forest (C7), park (C8), natural meadow (C9), artificial meadow (C10), river (C11), urban residential (C12), lake (C13), pond (C14), fish pond (C15), snow (C16), bare land (C17), rural residential (C18), stadium (C19), square (C20), road (C21), overpass (C22), railway station (C23), and airport (C24)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.596, + 0.665 + ], + "angle": 0, + "content": "4.3. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Examples of the labeled data are shown in Figure 1. The training, validation, and test datasets include 9,995, 2,000, and 2,503 images with a size of \\(256 \\times 256\\), respectively, according to the geographical division. The unlabeled data is from more than 60 dispersed administrative districts in China and has no overlap with the labeled data. The number of candidate unlabeled images is about 500,000, each with a size of \\(256 \\times 256\\). According to our minority class-biased unlabeled data selection strategy, we filter 50,000 images to build the unlabeled set, which covers more scenes with minority classes. Figure 3 shows the proportion of each land cover class on labeled training data, unlabeled training data, and all training data. The majority classes cover hundreds of times more pixels than the minority classes on the labeled training data." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16787" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.093, + 0.891, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.41, + 0.835, + 0.426 + ], + "angle": 0, + "content": "Figure 3. Percentage of each land cover class on the labeled training data, unlabeled training data, and all training data." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.436, + 0.885, + 0.694 + ], + "angle": 0, + "content": "
MethodOAmAccmIoUC1C2C3C4C5C6C7C8C9C10
Baseline73.2445.7735.6171.2466.2588.6617.9016.9362.2627.0117.2644.6511.33
SimCLR [7] +finetune74.0745.8135.1774.4963.3390.8814.1017.8062.1023.5718.3948.4221.02
Pseudo -labeling [25]74.6148.8338.0376.8569.6091.5513.4720.5259.1931.6337.5344.9010.68
Advent [38]74.8149.2538.9875.8868.3891.9812.2015.0162.4625.9144.7754.758.10
CADR [17]75.4947.8336.6376.3252.4391.4821.5424.3564.7431.8522.5959.8817.25
DPA [37]75.3648.5737.7776.0569.4092.3315.5119.7966.3027.0523.2552.4112.48
Ours75.9753.5340.6881.7180.0788.8922.2737.3267.0634.8726.4456.7317.16
C11C12C13C14C15C16C17C18C19C20C21C22C23C24
70.8682.7678.9324.4957.713.0448.6777.2310.807.9071.4245.8334.9560.34
71.4783.2779.4130.5464.730.7548.7768.822.00073.5944.5333.8763.72
72.4082.9083.5616.9452.4413.6655.0672.5821.0513.0370.2760.6038.7862.83
69.9883.1983.3819.7249.3415.5046.5675.1622.4017.5570.9958.0441.6269.23
65.9086.2784.5326.0972.57051.7874.960.95065.2348.5133.6475.02
71.9783.3381.8016.7750.660.8852.3772.6121.426.6472.1559.1049.1572.37
70.6182.8681.6917.1378.5326.2855.8080.6931.8326.4966.2364.6546.3942.97
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.697, + 0.877, + 0.713 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with different methods. We also show the precision of each class. Bold indicates the best results \\((\\%)\\)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.735, + 0.21, + 0.753 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.765, + 0.392, + 0.782 + ], + "angle": 0, + "content": "5.1. Implementation Details and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We choose ResUNet [9] in our experiments, as it is stable and lightweight for land cover mapping. We train for 100 epochs for all experiments using stochastic gradient descent (SGD) with a momentum of 0.9 and a weight decay of \\(10^{-4}\\). The initial learning rate is set to 0.05. We adopt the batch size as 12, including 6 labeled images and 6 unlabeled images. The loss weight \\(\\lambda\\) is set to 0.005. The temperature" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.737, + 0.725, + 0.751 + ], + "angle": 0, + "content": "\\(\\tau\\) of contrastive loss is set to 0.07." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.754, + 0.892, + 0.815 + ], + "angle": 0, + "content": "The performance of the proposed approach and other competing methods are assessed with overall accuracy (OA), mean accuracy (mAcc), mean intersection over union (mIoU), and precision of each class." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.693, + 0.847 + ], + "angle": 0, + "content": "5.2. Comparison Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Table 1 shows the comparison results with typical and state-of-the-art class-balanced pseudo-labeling methods. For a fair comparison, all competing methods and our" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16788" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.132, + 0.089, + 0.418, + 0.19 + ], + "angle": 0, + "content": "
MethodOAmAccmIoU
Random selection75.5051.3539.09
Majority class -biased selection75.7549.9839.33
Minority class -biased selection75.9753.5340.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.2, + 0.47, + 0.227 + ], + "angle": 0, + "content": "Table 2. Ablation study on the proposed class-aware unlabeled data selection method. Bold indicates the best results \\((\\%)\\)." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.241, + 0.477, + 0.322 + ], + "angle": 0, + "content": "
MethodOAmAccmIoU
Without class balance75.4148.1637.27
Class-balanced method in [38]73.6151.3338.61
Class-balanced method in [37]75.5149.6635.51
Ours75.9753.5340.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.331, + 0.468, + 0.358 + ], + "angle": 0, + "content": "Table 3. Comparison results on different class-balanced learning methods. Bold indicates the best results \\((\\%)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.468, + 0.548 + ], + "angle": 0, + "content": "method use the same model architecture. All experiments are measured on the same computing platform. The baseline applies the supervised learning method to the labeled data. The SimCLR+finetune method uses a self-supervised learning method [7] on the unlabeled data to obtain a pretrain model and performs fine-tuning on the labeled data. Pseudo-labeling method [25] first generates pseudo-labels of the unlabeled data by using the baseline model, then retransmits the model with ground truth and pseudo-labels. Advent [38], DPA [37], and CADR [17] are three state-of-the-art SSL methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.468, + 0.763 + ], + "angle": 0, + "content": "The results demonstrate that our approach significantly improved over \\(4.28\\%\\) in mAcc, \\(1.70\\%\\) in mIoU, and \\(0.58\\%\\) in OA. Compared to the baseline for each class, our method can significantly improve the accuracy of the minority classes and maintain the accuracy of the majority classes simultaneously. In contrast, the competing methods often tend to predict the pixels to majority classes and suffer from low precision on minority classes. Regarding the computational cost, our method incurs \\(53\\%\\) additional training time than the basic SSL algorithm (i.e., Advent) due to Class-Balanced Learning and Class Center Contrast. The inference times are the same for all SSL methods, as we use the same backbone. Please find the visual comparison in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.229, + 0.788 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Class-Aware Unlabeled Data Selection. We compare our method with the opposite strategy (i.e., majority class-biased data selection) and widely opted random selection method. Table 2 shows that our method achieves the best results. On the contrary, the mAcc value of the majority class-biased data selection method is unsatisfactory because the SSL model is biased toward predicting the majority classes." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.891, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.281, + 0.892, + 0.323 + ], + "angle": 0, + "content": "Figure 4. Results of using the different number of labeled images (i.e., 500, 1,000, and 3,000) and the different ratios of unlabeled to labeled images in SSL." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Besides, to verify the effectiveness of unlabeled data selection, we show the statistics of class distribution in Figure 3. Estimating the class distribution of unlabeled data is based on the pseudo-labels produced by the baseline model. Owing to the proposed class-aware unlabeled data selection method, the class distribution of the unlabeled data is more balanced than that of the labeled data. As a result, the entire training dataset is more balanced towards minority classes than the original labeled dataset. Therefore, we can estimate the class prior information on the entire dataset to partially remove the annotation bias." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.791 + ], + "angle": 0, + "content": "Class-Balanced Learning. In general, class weighting sacrifices the accuracy of majority classes to improve the accuracy of minority classes, which decreases OA and mIoU. From Table 3, two comparison methods suffer from the above problem, while our method improves the mAcc, OA, and mIoU compared to the baseline (i.e., without loss weights). The reason is that the two comparison methods use class prior information of labeled data and ignore the discrepancy of class distributions between labeled and unlabeled data in SSL. Besides, Table 4 shows the ablation study on Class-Balanced Cross Entropy loss. Utilizing sample re-weighting improves performance by removing the annotation bias on the semi-supervised learning dataset. Using class re-weighting for cross-entropy loss removes class bias and improves the performance of mAcc and mIoU by a large margin. Furthermore, jointly utilizing the sample and class weights achieves the best results in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Class Center Contrast Method. Table 5 shows the ablation study on the proposed class center contrast method. Contrastive loss utilizes inter-class and intra-class information and achieves better results than center loss used in [28]. Compared with only training contrastive loss with pseudolabels on unlabeled data, using pseudo-labels on both labeled and unlabeled data achieves better results. Further-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16789" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.167, + 0.088, + 0.805, + 0.169 + ], + "angle": 0, + "content": "
Cross entropy lossSample re-weightingClass re-weightingOAmAccmIoU
✓75.4148.1637.27
✓✓75.7448.9638.40
✓✓75.4352.0640.07
✓✓✓75.9753.5340.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.199, + 0.179, + 0.771, + 0.193 + ], + "angle": 0, + "content": "Table 4. Ablation study on class-balanced cross entropy loss. Bold indicates the best results \\((\\%)\\)." + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.204, + 0.836, + 0.3 + ], + "angle": 0, + "content": "
Center lossContrastive lossPseudo labelGround truthOn labeled dataOn unlabeled dataOAmAccmIoU
✓✓✓74.0748.1337.34
✓✓✓75.2350.0639.29
✓✓✓✓75.2651.4239.43
✓✓✓✓✓75.9753.5340.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.202, + 0.31, + 0.766, + 0.324 + ], + "angle": 0, + "content": "Table 5. Ablation study on the class center contrast method. Bold indicates the best results \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.346, + 0.462, + 0.426 + ], + "angle": 0, + "content": "
MethodOAmAccmIoU
Random sample selection74.6849.3138.80
Simple sample selection74.7451.5740.42
Hard sample selection74.5751.1440.31
Feature embedding centers75.9753.5340.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.436, + 0.468, + 0.464 + ], + "angle": 0, + "content": "Table 6. Results of different contrastive sample selection manners. Bold indicates the best results \\((\\%)\\)." + }, + { + "type": "table", + "bbox": [ + 0.103, + 0.48, + 0.445, + 0.53 + ], + "angle": 0, + "content": "
MethodOAmAccmIoU
Within-image method73.3653.4840.03
Cross-image method75.9753.5340.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.54, + 0.469, + 0.567 + ], + "angle": 0, + "content": "Table 7. Results of within-image and cross-image contrastive learning. Bold indicates the best results \\((\\%)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.469, + 0.868 + ], + "angle": 0, + "content": "more, introducing the ground truth of labeled data to the training of contrastive loss can significantly improve performance. We also compare different sample selection strategies for contrastive learning. We select three contrastive samples for each class per image for a fair comparison. As shown in Table 6, leveraging high-confidence predicted samples from the unlabeled data for semi-supervised learning yields better results than employing uncertain samples. Nonetheless, samples with high-confidence predictions provide limited information for model learning, leading to only marginal enhancements. The proposed Class Center Contrast method involves both high-confidence and hard samples, achieving the best results. Besides, we compare within-image and cross-image contrastive learning results in Table 7. Cross-image method uses labeled and unlabeled images in a mini-batch and achieves better results, while the within-image method only uses local information of labeled or unlabeled images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Hyperparameter Tuning of Loss Weight. \\(\\lambda\\) is to balance two loss terms in the formula (7). Table 8 shows the" + }, + { + "type": "table", + "bbox": [ + 0.557, + 0.346, + 0.837, + 0.426 + ], + "angle": 0, + "content": "
Loss weightOAmAccmIoU
λ = 0.0575.0751.6240.15
λ = 0.0175.2651.4239.43
λ = 0.00575.9753.5340.68
λ = 0.00175.2753.8440.26
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.436, + 0.892, + 0.463 + ], + "angle": 0, + "content": "Table 8. Hyperparameter tuning of loss weight. Bold indicates the best results \\((\\%)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.489, + 0.891, + 0.534 + ], + "angle": 0, + "content": "results using different loss weights \\(\\lambda\\). We conclude that a large loss weight for \\(\\mathcal{L}_{cct}\\) reduces the model performance. In this work, we set \\(\\lambda = 0.005\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.791 + ], + "angle": 0, + "content": "The Number and Ratio of Labeled Images in SSL. We conduct a comparative analysis of the enhancement in accuracy resulting from the increase of unlabeled data. As shown in Figure 4, the utilization of a larger quantity of unlabeled data, specifically ten times the amount of labeled training data containing only 500 images, has been observed to result in a substantial improvement in accuracy. Meanwhile, the performance becomes unstable as the ratio between unlabeled and labeled images increases further because of the limited number of labeled images. As the amount of labeled data increased, using the unlabeled data, which is five times the amount of labeled data, can yield superior results compared to using just one time the amount of labeled data. Subsequently, the performance is relatively stable as the number of unlabeled data increases. Therefore, to balance the computational cost and improvement in accuracy, we use a ratio of 5:1 for unlabeled and labeled data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.871, + 0.818 + ], + "angle": 0, + "content": "5.4. Examples of Land Cover Mapping in China" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As an application of the proposed method, we produce large-scale land cover maps with 24 classes over 1 million \\(\\mathrm{km}^2\\). As shown in Figure 5, we compare our land cover mapping results with two existing public products produced by ESA [45] and Google [2]. The example in the top row" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16790" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.099, + 0.27, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.276, + 0.101, + 0.332, + 0.111 + ], + "angle": 0, + "content": "Tree cover" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.113, + 0.329, + 0.122 + ], + "angle": 0, + "content": "Shrubland" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.123, + 0.328, + 0.132 + ], + "angle": 0, + "content": "Grassland" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.134, + 0.327, + 0.143 + ], + "angle": 0, + "content": "Cropland" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.144, + 0.323, + 0.153 + ], + "angle": 0, + "content": "Built-up" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.155, + 0.335, + 0.164 + ], + "angle": 0, + "content": "Bare/sparse." + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.165, + 0.331, + 0.175 + ], + "angle": 0, + "content": "vegetation" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.176, + 0.339, + 0.186 + ], + "angle": 0, + "content": "Snow and ice" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.188, + 0.311, + 0.197 + ], + "angle": 0, + "content": "Perm" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.198, + 0.335, + 0.207 + ], + "angle": 0, + "content": "water bodies" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.208, + 0.335, + 0.223 + ], + "angle": 0, + "content": "Herbaceous wetland" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.225, + 0.333, + 0.234 + ], + "angle": 0, + "content": "Mangroves" + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.236, + 0.328, + 0.254 + ], + "angle": 0, + "content": "Moss and lichen" + }, + { + "type": "image", + "bbox": [ + 0.351, + 0.099, + 0.532, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.101, + 0.576, + 0.11 + ], + "angle": 0, + "content": "Water" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.113, + 0.574, + 0.122 + ], + "angle": 0, + "content": "Trees" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.123, + 0.574, + 0.132 + ], + "angle": 0, + "content": "Grass" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.134, + 0.586, + 0.143 + ], + "angle": 0, + "content": "Flooded" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.144, + 0.586, + 0.153 + ], + "angle": 0, + "content": "vegetation" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.154, + 0.576, + 0.162 + ], + "angle": 0, + "content": "Crops" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.164, + 0.585, + 0.173 + ], + "angle": 0, + "content": "Shrub &" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.174, + 0.574, + 0.181 + ], + "angle": 0, + "content": "Scrub" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.182, + 0.574, + 0.191 + ], + "angle": 0, + "content": "Built" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.193, + 0.6, + 0.202 + ], + "angle": 0, + "content": "Bare ground" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.204, + 0.598, + 0.214 + ], + "angle": 0, + "content": "Snow & ice" + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.099, + 0.884, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.244, + 0.88, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.392, + 0.233, + 0.404 + ], + "angle": 0, + "content": "(a) ESA" + }, + { + "type": "image_caption", + "bbox": [ + 0.45, + 0.392, + 0.504, + 0.404 + ], + "angle": 0, + "content": "(b) Google" + }, + { + "type": "image_caption", + "bbox": [ + 0.73, + 0.392, + 0.771, + 0.404 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.424, + 0.895, + 0.482 + ], + "angle": 0, + "content": "Figure 5. Examples of Land Cover Mapping in China. The land cover products of ESA and Google are also generated from Sentinel-2 images but use different classification systems. In the black rectangles, our land cover results with fine-grained classes can provide more land cover information. In the red rectangles, our method recognizes the paddy field correctly, while the other two products classify it as cropland and water, respectively, due to the coarse classification system and the misleading spectral information of the paddy field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.473, + 0.825 + ], + "angle": 0, + "content": "shows the results of an urban area located in the east of China, and that in the bottom row gives the results of a rural area located in the center of China. The land cover products of ESA and Google contain 11 and 9 classes, while our classification system includes 24 classes. From the black rectangles, the two comparison products mainly distinguish built areas, water, trees, and crops. Owing to the fine-grained classification system and the proposed class-aware SSL methods, our results can recognize more land cover categories, including industrial area, urban residential, rural residential, road, overpass, railway station, arbor forest, artificial meadow, irrigated field, bare land, lake, river, pond, and fish pond. Our land cover maps with fine-grained classes can provide more land cover information. Besides, from the red rectangles, our method recognizes the paddy field correctly, while the other two products classify it as cropland and water, respectively, due to the coarse classification system and the misleading spectral information of the paddy field. From the above qualitative comparison, our method provides land cover maps with fine-grained classes, significantly improving the land cover information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.844, + 0.196, + 0.859 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this work, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation approach for large-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.895, + 0.658 + ], + "angle": 0, + "content": "scale land cover mapping with fine-grained classes. To address the class-imbalance issue, we propose a class-aware unlabeled data selection method to build an SSL dataset more balanced towards minority classes. Then, we propose a Class-Balanced Cross Entropy loss, considering the annotation and class biases on the built SSL dataset. Moreover, we propose the Class Center Contrast method to jointly use the labeled and unlabeled data for training. Experimental results validate the effectiveness of our method in large-scale land cover mapping with fine-grained classes." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.711, + 0.667, + 0.729 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "This research was supported in part by the National Natural Science Foundation of China (Grant No. T2125006), Jiangsu Innovation Capacity Building Program (Project No. BM2022028), China Postdoctoral Science Foundation (Grant No. 2023M731871), the German Federal Ministry of Education and Research (BMBF) in the framework of the international future AI lab \"AI4EO - Artificial Intelligence for Earth Observation: Reasoning, Uncertainties, Ethics and Beyond\" (Grant No. 01DD20001), and Shuimu Tsinghua Scholar Project." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16791" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9719–9728, 2020. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.895, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16793" + } + ] +] \ No newline at end of file diff --git a/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/85af6521-8e24-45e3-ac82-fb3352f9480e_origin.pdf b/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/85af6521-8e24-45e3-ac82-fb3352f9480e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..362a46d215a5a5a51c57c7dcbb2968653462764c --- /dev/null +++ b/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/85af6521-8e24-45e3-ac82-fb3352f9480e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1814308282930a153d77fd16ab314ddb8e5b10d019eda4ccba093ca30f6b6121 +size 5430027 diff --git a/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/full.md b/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f9d98a5ee6f067bb6a3d60e51fffdb614911e985 --- /dev/null +++ b/2023/Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation/full.md @@ -0,0 +1,309 @@ +# Large-Scale Land Cover Mapping with Fine-Grained Classes via Class-Aware Semi-Supervised Semantic Segmentation + +Runmin Dong $^{1,4}$ , Lichao Mou $^{2}$ , Mengxuan Chen $^{1,4}$ , Weijia Li $^{3}$ , Xin-Yi Tong $^{2}$ , Shuai Yuan $^{1,4}$ , Lixian Zhang $^{1,4}$ , Juepeng Zheng $^{3,4}$ , Xiao Xiang Zhu $^{2}$ , Haohuan Fu $^{1,4,*}$ , Tsinghua University ${}^{2}$ Technical University of Munich ${}^{3}$ Sun Yat-Sen University ${}^{4}$ Tsinghua University - Xi'an Institute of Surveying and Mapping Joint Research Center + +drm@mail.tsinghua.edu.cn, haohuan@tsinghua.edu.cn + +# Abstract + +Semi-supervised learning has attracted increasing attention in the large-scale land cover mapping task. However, existing methods overlook the potential to alleviate the class imbalance problem by selecting a suitable set of unlabeled data. Besides, in class-imbalanced scenarios, existing pseudo-labeling methods mostly only pick confident samples, failing to exploit the hard samples during training. To tackle these issues, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation framework. The proposed framework consists of three key components. To construct a better semi-supervised learning dataset, we propose a class-aware unlabeled data selection method that is more balanced towards the minority classes. Based on the built dataset with improved class balance, we propose a Class-Balanced Cross Entropy loss, jointly considering the annotation bias and the class bias to re-weight the loss in both sample and class levels to alleviate the class imbalance problem. Moreover, we propose the Class Center Contrast method to jointly utilize the labeled and unlabeled data. Specifically, we decompose the feature embedding space using the ground truth and pseudo-labels, and employ the embedding centers for hard and easy samples of each class per image in the contrast loss to exploit the hard samples during training. Compared with state-of-the-art class-balanced pseudo-labeling methods, the proposed method improves the mean accuracy and mIoU by $4.28\%$ and $1.70\%$ , respectively, on the large-scale Sentinel-2 dataset with 24 land cover classes. + +# 1. Introduction + +Land cover mapping provides pixel-level information for urban management, climate change research, ecosystem protection, and other sustainability-related applica + +![](images/7b5448a33ca75d31ea5097cb4e3ad58bf9f15c5950fbe43a104bff7189823f84.jpg) +Figure 1. Examples of the labeled data. The top row shows Sentinel-2 images containing 13 bands. The bottom row shows the corresponding labels. We use a fine-grained classification system with 24 land cover classes in this work. + +tions [21, 27]. With the rapid progress of computer vision technology, it is desired to automatically gain large-scale and fine-grained land cover information from remote sensing images to support the demand of existing earth system science studies and bring new opportunities for intelligent city study [31]. However, fine-grained annotations for land cover mapping are high-cost and time-consuming, limiting labeled data collection for large-scale applications. Semi-supervised learning (SSL) is a potential solution to this problem, as it utilizes both existing labeled data and a large number of unlabeled data [37]. + +Large-scale land cover mapping with fine-grained classes usually suffers from class imbalance, as shown in Figure 1 and 3. The labeled data tends to be biased due to the difficulty of data collection and label annotation varying by class. The class imbalance leads to suboptimal per + +formance in the minority classes. Most SSL methods for large-scale land cover mapping are typically based on the assumption that labeled and unlabeled data have the same class distribution [41, 37]. However, this assumption does not hold in most scenarios, resulting in the bias of class estimation. As such, it is non-trivial to jointly utilize the labeled and unlabeled data to train the network for semi-supervised semantic segmentation. Although many pseudo-labeling methods aim to assign pseudo-labels more steadily and correctly for different classes on the unlabeled data, e.g., dynamically setting threshold or proportion [17, 44], they still rely on setting hyperparameters and empirical principles, resulting in a lack of flexibility and generalization ability in applications. Besides, pseudo-labeling methods mostly rely on easy samples with high confidence scores, thus failing to exploit the hard samples on the unlabeled data. + +To alleviate the above issues, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation framework. We exploit the potential of the unlabeled data and alleviate the class imbalance problem in large-scale land cover mapping with fine-grained classes. The proposed class-aware unlabeled data selection method constructs an SSL dataset and compensates for the class imbalance on the labeled data. Based on the built SSL dataset, we propose a class-balanced learning method to remove the annotation bias and class bias on the SSL dataset. We dynamically estimate the class prior information on the entire SSL dataset during training to re-weight both samples and classes of the loss function for the labeled data. Finally, we propose the Class Center Contrast method to jointly use the labeled and unlabeled data for training. The ground truth and pseudolabels are leveraged as the guide to decompose the feature embedding space. We estimate the hard, easy, and overall embedding centers for each class per image and apply the contrastive loss to optimize the distances between class centers to utilize both easy and hard samples. The class imbalance issue is alleviated by utilizing the proposed method, and the performance of large-scale land cover mapping with fine-grained classes is effectively improved. + +# 2. Related Work + +Large-Scale Land Cover Mapping. Land cover mapping classifies each pixel of images into a unique class, which can be regarded as a semantic segmentation problem [6, 11]. Large-scale land cover mapping with fine-grained classes can provide necessary information for earth system science studies and land spatial layout optimization. However, manual or semi-manual labeling is high-cost and time-consuming [34]. Besides, the classification systems of most large-scale studies are coarse. Thus the provided land cover information is limited. For example, the Chesapeake dataset covering $160,000\mathrm{km}^2$ costs $1.3 million but only contains four classes [33]. DynamicEarthNet + +dataset covers $17,000\mathrm{km}^2$ and includes 7 basic land cover classes [36]. To overcome the limited area of the labeled data and improve the model generalization, some works utilize openly available produced data (e.g., OpenStreetMap data and land cover products), which contains many noisy labels but can provide prior information in a large-scale area [19, 10]. These works still use coarse classification systems of land cover mapping. Five-Billion-Pixels [37] is a large-scale land cover dataset with 24 categories, covering about $60,000\mathrm{km}^2$ , which opens the door to large-scale land cover mapping with fine-grained classes. However, this dataset suffers from a severe class-imbalance problem (the common categories cover hundreds of times more pixels than the rare ones), due to the difficulty of data collection and label annotation varying by class. + +Class-Imbalanced Learning. To solve the class-imbalance problem, related works include data resampling [3, 4], loss re-weighting [22, 32, 18], margin modification [5, 35], and decoupled learning [20, 47]. In self-supervised learning and SSL, recent works devote to rebalancing the class distribution of SSL data by assigning pseudo-labels for the unlabeled data to address the class imbalance issue [41, 15]. For example, Gui et al. [14] propose a class-aware pseudo-labeling method for SSL, dynamically adjusting the threshold for selecting pseudo-labels to obtain better performance on minority classes. Similarly, Hu et al. [17] propose a label bias removal method and dynamically determine the threshold for each class to assign more pseudo-labels for minority classes. However, the hard samples with relatively low confidence scores are ignored for optimizing the model, leading to sub-optimal performance. + +Semi-Supervised Semantic Segmentation. SSL methods leverage the relationships between the labeled and unlabeled data to improve the model accuracy and generalization, alleviating the limited area of the labeled data [8]. Semi-supervised semantic segmentation methods include entropy minimization [38], consistency regularization [30], and pseudo-labeling [42]. Pseudo-labeling is widely used in semi-supervised semantic segmentation, and many works contribute to selecting pseudo-labels more steadily and correctly [29]. For example, Tong et al. [37] propose a dynamic pseudo-label assignment method, in which the number of pseudo-labels is dynamically increased with training iterations. However, these methods still rely on the manual setting of hyperparameters and suffer from the uncertainty of pseudo-labels. Alternatively, contrastive learning methods in supervised learning [39, 16] and SSL [46, 40] constrain the representations of positive samples against these negative samples in feature space, leading to promising results. Different from the manner of data augmentation-based positive sample construction [43, 23] and memory bank-based negative sample construction [1, 40], we leverage the ground-truth and pseudo-labels as a guide to decom + +pose the feature embedding space, and estimate the embedding centers for each class per image to stably select easy and hard samples for the proposed Class Center Contrast method. + +# 3. Methodology + +# 3.1. The Overall Workflow of Our Approach + +Our approach consists of four steps. First, a baseline model is trained on the labeled data. Second, we propose a class-aware unlabeled data selection method to build an SSL dataset that is more balanced towards minority classes. The baseline model is used to predict land cover classes on all collected data from a large unlabeled data pool and calculate the statistics of the class distribution for each image patch. The image patches containing pixels of minority classes are selected as unlabeled data. Then the SSL dataset is constructed by combining the labeled data and the selected unlabeled data. Third, we propose a Class-Balanced Cross Entropy loss and a Class Center Contrast method. To alleviate the class imbalance problem, we reweight the cross entropy loss on labeled data in both sample and class level by jointly considering the annotation bias and the class bias on the built SSL dataset. Besides, we decompose the feature embedding space using the ground truth and pseudo-labels, and propose an embedding center selection and contrast method for class-balanced and annotation-guided learning on unlabeled data. The pipeline of the proposed class-aware SSL model is shown in Figure 2. Finally, we perform model inference for large-scale land cover mapping. + +# 3.2. Class-Aware Unlabeled Data Selection + +A suitable set selection of unlabeled data is important for SSL model development. Inspired by the observation in [41] that existing SSL algorithms can produce pseudolabels on minority classes with high precision, we propose an unlabeled data selection strategy that tends to select unlabeled image patches containing pixels with minority classes. + +First, we train a semantic segmentation model using labeled data. We apply the off-the-shelf class balance strategy [4] designed for supervised learning to guarantee the model ability of minority class estimation. The definition of minority classes depends on the class proportion and the class accuracy on the labeled data. Then, we perform model inference on all candidate unlabeled data to predict the land cover class of each pixel, thereby obtaining the class distribution of each candidate image patch. We denote the proportion of pixels of all minority classes in an image patch as $P_{m}$ . Finally, we formulate a principle to automatically select unlabeled data according to the class distribution of each candidate image patch. Specifically, the pro + +portions of the 24 classes on the labeled dataset are shown in Figure 3. The classes with a proportion lower than $1\%$ generally achieve an accuracy of less than $30\%$ within our dataset. We collect all the images with $P_{m} \geq 1\%$ , which leads to about 25,000 images over the about 500,000 candidates (see Section 4.3). Then we randomly select another 25,000 images from those with $0 < P_{m} < 1\%$ , leading to a total of 50,000 unlabeled images, which is five times the number of the labeled training data. The authors suggest selecting unlabeled patches with relatively more pixels of minority classes (i.e., larger $P_{m}$ ), and those encompassing rare classes characterized by fewer pixels within the minority classes. Note that although the prediction on the unlabeled data is not absolutely accurate, it can preserve image patches that are most likely to contain pixels with minority classes, which contributes to building a more balanced SSL dataset. + +# 3.3. Class-Balanced Learning + +In our built SSL dataset, the class distribution of unlabeled data differs from that of the labeled data. It can be regarded as an annotation bias problem on the entire dataset. Besides, the SSL dataset still suffers from a class imbalance issue. Consequently, using the class prior information estimated on the labeled data to the re-weight loss function is inappropriate. To solve the above issues, we propose a class-balanced learning method to jointly remove the annotation bias and class bias on the SSL dataset. + +First, we re-weight samples of labeled data to remove the annotation bias. Owing to our unlabeled data selection method, the entire SSL dataset is more balanced towards minority classes than the original labeled dataset. Therefore, we can estimate the class prior on the entire SSL dataset to partially remove the annotation bias. Specifically, we denote $L$ as a label indicator, where $L = 0$ and $L = 1$ represent the unlabeled and labeled data, respectively. The model parameters $\theta$ of labeled data in traditional SSL methods are obtained by maximizing likelihood estimation in the formula (1). + +$$ +\begin{array}{l} \hat {\theta} = \arg \max _ {\theta} \log P (Y | X, L = 1; \theta) \\ = \arg \max _ {\theta} \sum_ {(x, y) \in D _ {L = 1}} \log P (y | x; \theta), \tag {1} \\ \end{array} +$$ + +where $\hat{\theta}$ is the estimated model parameter, $X$ represents samples, $Y$ represents classes, and $D_{L = 1}$ denotes the set of labeled data. Due to the annotation bias in the SSL dataset, we have $P(y|x;L = 1)\neq P(y|x)$ . According to causal inference [13, 17], in the entire SSL dataset, $X\rightarrow Y\rightarrow L$ can be regarded as a one-way chain, where the class is dependent on its pixel, and whether the pixel has a label or not depends on its class. According to the + +![](images/4374f975a37edd04ac6a43821175eb63e023e918e341f7644a90e03609a8add0.jpg) +Figure 2. The pipeline of the proposed Class-Aware Semi-Supervised Semantic Segmentation framework with class-balanced learning, embedding center estimation, and class center contrast. The class-aware unlabeled data selection process is not shown in the figure. + +conditional independence rule, we obtain the expression, $P(X|Y,L = 1) = P(X|Y)$ when conditioning on Y. Therefore, estimating the model parameters of the entire SSL dataset can be formalized as in the formula (2) [17], where $s(x,y) = \frac{\log P(y|x;\theta) - \log P(y;\theta)}{\log P(y|x;\theta)}$ is the loss weight of each labeled sample $(x,y)$ . Thus, it can be interpreted as modifying the class prior $P(y;\theta)$ to remove the annotation bias of the labeled data. + +$$ +\begin{array}{l} \hat {\theta} = \arg \max _ {\theta} \log P (X | Y; \theta) \\ = \arg \max _ {\theta} \sum_ {(x, y) \in D _ {L = 1}} \log P (x | y; \theta) \\ = \arg \max _ {\theta} \sum_ {(x, y) \in D _ {L = 1}} \log \frac {P (y | x ; \theta) P (x ; \theta)}{P (y ; \theta)} \tag {2} \\ = \arg \max _ {\theta} \sum_ {(x, y) \in D _ {L = 1}} \log \frac {P (y | x ; \theta)}{P (y ; \theta)} \\ = \arg \max _ {\theta} \sum_ {(x, y) \in D _ {L = 1}} s (x, y) \cdot \log P (y | x; \theta), \\ \end{array} +$$ + +Second, although the SSL dataset is more balanced than the labeled data, it still suffers from the class imbalance problem. Therefore, we further estimate the class bias on the SSL dataset. A widely used class re-weighting loss function on supervised learning can be formalized as follows: + +$$ +\mathcal {L} _ {w c e} = \sum_ {k = 1} ^ {K} W _ {k} \sum_ {i = 1} ^ {n _ {k}} y _ {i k} \log p _ {i k}, \tag {3} +$$ + +where $W_{k} = \frac{1}{\log(1 + r_{k})}$ and $r_k$ is the ratio of the class $k$ on the labeled data. $K$ is the number of classes, $n_k$ is the number of samples of class $k$ , $y_{ik}$ and $p_{ik}$ is the ground-truth and predicted probability of the $i$ -th sample for class $k$ , respectively. In SSL, we approximate $r_k$ with $P(y; \theta)$ , the class distribution on the entire dataset. + +Finally, we perform an online estimation strategy for $P(y; \theta)$ to simplify the training process. We compute the average of class probability distributions over all pixels in a mini-batch, which is denoted as $P(Y; B_t, \theta_t)$ . $B_t$ and $\theta_t$ are the samples and model parameters of the current batch, respectively. Then the approximate class distribution, denoted as $\tilde{P}(Y)$ , is updated by the weighted sum of the obtained class distribution of this mini-batch and the approximate class distribution in the previous iteration, which is formalized as follows: + +$$ +\tilde {P} (Y) \leftarrow \mu \tilde {P} (Y) + (1 - \mu) P (Y; B _ {t}, \theta_ {t}), \tag {4} +$$ + +where $\mu \in [0,1]$ is a weighting coefficient. We set $\mu = \frac{B}{N}$ , in which $B$ is the batch size and $N$ is the total number of samples in the dataset. We initialize $\tilde{P}(Y)$ with the class distribution calculated on the labeled data. As such, the proposed Class-Balanced Cross Entropy loss on the labeled data is formulated as follows: + +$$ +\mathcal {L} _ {c b c e} = \sum_ {k = 1} ^ {K} W _ {k} \sum_ {i = 1} ^ {n _ {k}} s \left(x _ {i k}, y _ {i k}\right) y _ {i k} \log p _ {i k}. \tag {5} +$$ + +# 3.4. Class Center Contrast + +Training via pseudo-labeling is commonly used to utilize unlabeled data in SSL. In fine-grained classes, assigning reliable labels for minority classes is challenging because the segmentation model tends to be biased towards the majority classes [26]. Besides, existing label assignment methods usually use only high-confidence predictions, which may offer limited information to model learning. In this work, our method selects reliable and hard samples. Moreover, instead of directly using the pseudo-labels for supervised learning on unlabeled data, we leverage the pseudo-labels as the guide to decompose the feature embedding space. In general, the distance of feature embeddings from the same class should be minimized, while the distance of those from different classes should be maximized. Therefore, we propose an online embedding center selection method that divides each class into hard and easy sample regions on each image. Specifically, we use the prediction probabilities of ground truth or pseudo-labels to separate easy and hard samples. The predicted probability of each pixel is associated with its feature embedding, and we then calculate the average prediction probability of each class for each image. Feature embeddings with above-average probabilities for the corresponding class are considered easy samples and vice versa. Thus we can obtain three feature embedding centers, including easy, hard, and all feature embedding centers, as contrastive samples. With this method, on the one hand, the obtained feature embeddings for each class are with relatively high confidence, as the samples are close to feature local centers for each class in the embedding space. On the other hand, these feature embeddings include hard samples of each class. + +Inspired by the existing contrastive learning method [39], we perform cross-image contrastive learning in each mini-batch. Since both labeled and unlabeled data are trained in a mini-batch, the embeddings of the labeled data could help the feature embedding learning of the unlabeled data. Formally, denote $P_{m}$ and $N_{m}$ as the feature embedding collections of the positive and negative samples in a mini-batch for the $m$ -th feature embedding center $c_{m}$ . The proposed Class Center Contrastive loss for the $m$ -th feature embedding center is formulated as follows: + +$$ +\mathcal {L} _ {c c t} ^ {m} = - \frac {1}{| P _ {m} |} \sum_ {\boldsymbol {c} _ {m} ^ {+} \in P _ {m}} \log \frac {e ^ {\left(\boldsymbol {c} _ {m} \cdot \boldsymbol {c} _ {m} ^ {+} / \tau\right)}}{e ^ {\left(\boldsymbol {c} _ {m} \cdot \boldsymbol {c} _ {m} ^ {+} / \tau\right)} + \sum_ {\boldsymbol {c} _ {m} ^ {-} \in N _ {m}} e ^ {\left(\boldsymbol {c} _ {m} \cdot \boldsymbol {c} _ {m} ^ {-} / \tau\right)}}, \tag {6} +$$ + +in which $\tau$ is the temperature parameter, $c_{m}^{+}$ and $c_{m}^{-}$ are the positive and negative samples, respectively. + +The overall loss function can be formulated as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {c b c e} + \lambda \mathcal {L} _ {c c t}, \tag {7} +$$ + +where $\lambda$ is the loss weight. + +# 4. Data + +# 4.1. Image Collection and Preparation + +Considering free access, multispectral bands, and relatively high spatial resolution, all satellite images used in this work are acquired from Sentinel-2 satellites. Sentinel-2 imagery has 13 spectral bands at $10\mathrm{m}$ (R, G, B, and near-infrared bands), $20\mathrm{m}$ (six red edge and shortwave infrared bands), and $60\mathrm{m}$ (three atmospheric correction bands) resolutions [12]. The abundant multispectral information and up to $10\mathrm{m}$ spatial resolution benefit land cover mapping with a fine-grained classification system. + +We collect Sentinel-2 images with radiometric correction, geometric corrections, and atmospheric correction, covering more than 60 cities in China. We apply an off-the-shelf Sentinel-2 sharpening method, DSen2Net [24], to reconstruct low-resolution bands and uniform the resolution of all bands of Sentinel-2 images to $10\mathrm{m}$ . + +# 4.2. Label Collection and Classification System + +The land cover labels and classification system are from the Five-Billion-Pixels dataset [37], labeled with $4\mathrm{m}$ resolution. It includes 24 land cover classes. We resize the $4\mathrm{m}$ labels to $10\mathrm{m}$ to match Sentinel-2 images. The labeled area covers about $60,000\mathrm{km}^2$ in China. The classification system includes the industrial area (C1), paddy field (C2), irrigated field (C3), dry cropland (C4), garden land (C5), arbor forest (C6), shrub forest (C7), park (C8), natural meadow (C9), artificial meadow (C10), river (C11), urban residential (C12), lake (C13), pond (C14), fish pond (C15), snow (C16), bare land (C17), rural residential (C18), stadium (C19), square (C20), road (C21), overpass (C22), railway station (C23), and airport (C24). + +# 4.3. Dataset + +Examples of the labeled data are shown in Figure 1. The training, validation, and test datasets include 9,995, 2,000, and 2,503 images with a size of $256 \times 256$ , respectively, according to the geographical division. The unlabeled data is from more than 60 dispersed administrative districts in China and has no overlap with the labeled data. The number of candidate unlabeled images is about 500,000, each with a size of $256 \times 256$ . According to our minority class-biased unlabeled data selection strategy, we filter 50,000 images to build the unlabeled set, which covers more scenes with minority classes. Figure 3 shows the proportion of each land cover class on labeled training data, unlabeled training data, and all training data. The majority classes cover hundreds of times more pixels than the minority classes on the labeled training data. + +![](images/66af3d5eaff49cc0c9ef9bd8aca6e0f9f856cf57c02cf9dde286574d88af7d03.jpg) +Figure 3. Percentage of each land cover class on the labeled training data, unlabeled training data, and all training data. + +
MethodOAmAccmIoUC1C2C3C4C5C6C7C8C9C10
Baseline73.2445.7735.6171.2466.2588.6617.9016.9362.2627.0117.2644.6511.33
SimCLR [7] +finetune74.0745.8135.1774.4963.3390.8814.1017.8062.1023.5718.3948.4221.02
Pseudo -labeling [25]74.6148.8338.0376.8569.6091.5513.4720.5259.1931.6337.5344.9010.68
Advent [38]74.8149.2538.9875.8868.3891.9812.2015.0162.4625.9144.7754.758.10
CADR [17]75.4947.8336.6376.3252.4391.4821.5424.3564.7431.8522.5959.8817.25
DPA [37]75.3648.5737.7776.0569.4092.3315.5119.7966.3027.0523.2552.4112.48
Ours75.9753.5340.6881.7180.0788.8922.2737.3267.0634.8726.4456.7317.16
C11C12C13C14C15C16C17C18C19C20C21C22C23C24
70.8682.7678.9324.4957.713.0448.6777.2310.807.9071.4245.8334.9560.34
71.4783.2779.4130.5464.730.7548.7768.822.00073.5944.5333.8763.72
72.4082.9083.5616.9452.4413.6655.0672.5821.0513.0370.2760.6038.7862.83
69.9883.1983.3819.7249.3415.5046.5675.1622.4017.5570.9958.0441.6269.23
65.9086.2784.5326.0972.57051.7874.960.95065.2348.5133.6475.02
71.9783.3381.8016.7750.660.8852.3772.6121.426.6472.1559.1049.1572.37
70.6182.8681.6917.1378.5326.2855.8080.6931.8326.4966.2364.6546.3942.97
+ +Table 1. Quantitative comparison with different methods. We also show the precision of each class. Bold indicates the best results $(\%)$ + +# 5. Experiments + +# 5.1. Implementation Details and Metrics + +We choose ResUNet [9] in our experiments, as it is stable and lightweight for land cover mapping. We train for 100 epochs for all experiments using stochastic gradient descent (SGD) with a momentum of 0.9 and a weight decay of $10^{-4}$ . The initial learning rate is set to 0.05. We adopt the batch size as 12, including 6 labeled images and 6 unlabeled images. The loss weight $\lambda$ is set to 0.005. The temperature + +$\tau$ of contrastive loss is set to 0.07. + +The performance of the proposed approach and other competing methods are assessed with overall accuracy (OA), mean accuracy (mAcc), mean intersection over union (mIoU), and precision of each class. + +# 5.2. Comparison Results + +Table 1 shows the comparison results with typical and state-of-the-art class-balanced pseudo-labeling methods. For a fair comparison, all competing methods and our + +
MethodOAmAccmIoU
Random selection75.5051.3539.09
Majority class -biased selection75.7549.9839.33
Minority class -biased selection75.9753.5340.68
+ +Table 2. Ablation study on the proposed class-aware unlabeled data selection method. Bold indicates the best results $(\%)$ . + +
MethodOAmAccmIoU
Without class balance75.4148.1637.27
Class-balanced method in [38]73.6151.3338.61
Class-balanced method in [37]75.5149.6635.51
Ours75.9753.5340.68
+ +Table 3. Comparison results on different class-balanced learning methods. Bold indicates the best results $(\%)$ . + +method use the same model architecture. All experiments are measured on the same computing platform. The baseline applies the supervised learning method to the labeled data. The SimCLR+finetune method uses a self-supervised learning method [7] on the unlabeled data to obtain a pretrain model and performs fine-tuning on the labeled data. Pseudo-labeling method [25] first generates pseudo-labels of the unlabeled data by using the baseline model, then retransmits the model with ground truth and pseudo-labels. Advent [38], DPA [37], and CADR [17] are three state-of-the-art SSL methods. + +The results demonstrate that our approach significantly improved over $4.28\%$ in mAcc, $1.70\%$ in mIoU, and $0.58\%$ in OA. Compared to the baseline for each class, our method can significantly improve the accuracy of the minority classes and maintain the accuracy of the majority classes simultaneously. In contrast, the competing methods often tend to predict the pixels to majority classes and suffer from low precision on minority classes. Regarding the computational cost, our method incurs $53\%$ additional training time than the basic SSL algorithm (i.e., Advent) due to Class-Balanced Learning and Class Center Contrast. The inference times are the same for all SSL methods, as we use the same backbone. Please find the visual comparison in the supplementary. + +# 5.3. Ablation Study + +Class-Aware Unlabeled Data Selection. We compare our method with the opposite strategy (i.e., majority class-biased data selection) and widely opted random selection method. Table 2 shows that our method achieves the best results. On the contrary, the mAcc value of the majority class-biased data selection method is unsatisfactory because the SSL model is biased toward predicting the majority classes. + +![](images/10d83bb2ceae84f2e5bf7fb6a2db8ac3888294dc074b804f6a1d10733d745232.jpg) +Figure 4. Results of using the different number of labeled images (i.e., 500, 1,000, and 3,000) and the different ratios of unlabeled to labeled images in SSL. + +Besides, to verify the effectiveness of unlabeled data selection, we show the statistics of class distribution in Figure 3. Estimating the class distribution of unlabeled data is based on the pseudo-labels produced by the baseline model. Owing to the proposed class-aware unlabeled data selection method, the class distribution of the unlabeled data is more balanced than that of the labeled data. As a result, the entire training dataset is more balanced towards minority classes than the original labeled dataset. Therefore, we can estimate the class prior information on the entire dataset to partially remove the annotation bias. + +Class-Balanced Learning. In general, class weighting sacrifices the accuracy of majority classes to improve the accuracy of minority classes, which decreases OA and mIoU. From Table 3, two comparison methods suffer from the above problem, while our method improves the mAcc, OA, and mIoU compared to the baseline (i.e., without loss weights). The reason is that the two comparison methods use class prior information of labeled data and ignore the discrepancy of class distributions between labeled and unlabeled data in SSL. Besides, Table 4 shows the ablation study on Class-Balanced Cross Entropy loss. Utilizing sample re-weighting improves performance by removing the annotation bias on the semi-supervised learning dataset. Using class re-weighting for cross-entropy loss removes class bias and improves the performance of mAcc and mIoU by a large margin. Furthermore, jointly utilizing the sample and class weights achieves the best results in Table 4. + +Class Center Contrast Method. Table 5 shows the ablation study on the proposed class center contrast method. Contrastive loss utilizes inter-class and intra-class information and achieves better results than center loss used in [28]. Compared with only training contrastive loss with pseudolabels on unlabeled data, using pseudo-labels on both labeled and unlabeled data achieves better results. Further- + +
Cross entropy lossSample re-weightingClass re-weightingOAmAccmIoU
✓75.4148.1637.27
✓✓75.7448.9638.40
✓✓75.4352.0640.07
✓✓✓75.9753.5340.68
+ +Table 4. Ablation study on class-balanced cross entropy loss. Bold indicates the best results $(\%)$ . + +
Center lossContrastive lossPseudo labelGround truthOn labeled dataOn unlabeled dataOAmAccmIoU
✓✓✓74.0748.1337.34
✓✓✓75.2350.0639.29
✓✓✓✓75.2651.4239.43
✓✓✓✓✓75.9753.5340.68
+ +Table 5. Ablation study on the class center contrast method. Bold indicates the best results $(\%)$ + +
MethodOAmAccmIoU
Random sample selection74.6849.3138.80
Simple sample selection74.7451.5740.42
Hard sample selection74.5751.1440.31
Feature embedding centers75.9753.5340.68
+ +Table 6. Results of different contrastive sample selection manners. Bold indicates the best results $(\%)$ . + +
MethodOAmAccmIoU
Within-image method73.3653.4840.03
Cross-image method75.9753.5340.68
+ +more, introducing the ground truth of labeled data to the training of contrastive loss can significantly improve performance. We also compare different sample selection strategies for contrastive learning. We select three contrastive samples for each class per image for a fair comparison. As shown in Table 6, leveraging high-confidence predicted samples from the unlabeled data for semi-supervised learning yields better results than employing uncertain samples. Nonetheless, samples with high-confidence predictions provide limited information for model learning, leading to only marginal enhancements. The proposed Class Center Contrast method involves both high-confidence and hard samples, achieving the best results. Besides, we compare within-image and cross-image contrastive learning results in Table 7. Cross-image method uses labeled and unlabeled images in a mini-batch and achieves better results, while the within-image method only uses local information of labeled or unlabeled images. + +Hyperparameter Tuning of Loss Weight. $\lambda$ is to balance two loss terms in the formula (7). Table 8 shows the + +Table 7. Results of within-image and cross-image contrastive learning. Bold indicates the best results $(\%)$ . + +
Loss weightOAmAccmIoU
λ = 0.0575.0751.6240.15
λ = 0.0175.2651.4239.43
λ = 0.00575.9753.5340.68
λ = 0.00175.2753.8440.26
+ +Table 8. Hyperparameter tuning of loss weight. Bold indicates the best results $(\%)$ . + +results using different loss weights $\lambda$ . We conclude that a large loss weight for $\mathcal{L}_{cct}$ reduces the model performance. In this work, we set $\lambda = 0.005$ . + +The Number and Ratio of Labeled Images in SSL. We conduct a comparative analysis of the enhancement in accuracy resulting from the increase of unlabeled data. As shown in Figure 4, the utilization of a larger quantity of unlabeled data, specifically ten times the amount of labeled training data containing only 500 images, has been observed to result in a substantial improvement in accuracy. Meanwhile, the performance becomes unstable as the ratio between unlabeled and labeled images increases further because of the limited number of labeled images. As the amount of labeled data increased, using the unlabeled data, which is five times the amount of labeled data, can yield superior results compared to using just one time the amount of labeled data. Subsequently, the performance is relatively stable as the number of unlabeled data increases. Therefore, to balance the computational cost and improvement in accuracy, we use a ratio of 5:1 for unlabeled and labeled data. + +# 5.4. Examples of Land Cover Mapping in China + +As an application of the proposed method, we produce large-scale land cover maps with 24 classes over 1 million $\mathrm{km}^2$ . As shown in Figure 5, we compare our land cover mapping results with two existing public products produced by ESA [45] and Google [2]. The example in the top row + +![](images/99ab48134b1f93faa14350de580fb1f22554bef78b70c53c9974b5cf369dd558.jpg) +Tree cover +Shrubland +Grassland +Cropland +Built-up +Bare/sparse. +vegetation +Snow and ice +Perm +water bodies +Herbaceous wetland +Mangroves +Moss and lichen +(a) ESA + +![](images/f7f357d0a572cca03a1ba1ff2bd5083e6e4a81c05ae6d022c9b05c5dd55adfd2.jpg) +Water +Trees +Grass +Flooded +vegetation +Crops +Shrub & +Scrub +Built +Bare ground +Snow & ice + +![](images/0aa2424f575f40c7123070bad49ed39ca9a28a3c17339dbbfcbb6f86bc0e8fae.jpg) + +![](images/e7b8435da0c4cbe62f2e8d8cc0317ea4202a3afe0372c0b324bbe76068c871f6.jpg) +(b) Google +(c) Ours +Figure 5. Examples of Land Cover Mapping in China. The land cover products of ESA and Google are also generated from Sentinel-2 images but use different classification systems. In the black rectangles, our land cover results with fine-grained classes can provide more land cover information. In the red rectangles, our method recognizes the paddy field correctly, while the other two products classify it as cropland and water, respectively, due to the coarse classification system and the misleading spectral information of the paddy field. + +shows the results of an urban area located in the east of China, and that in the bottom row gives the results of a rural area located in the center of China. The land cover products of ESA and Google contain 11 and 9 classes, while our classification system includes 24 classes. From the black rectangles, the two comparison products mainly distinguish built areas, water, trees, and crops. Owing to the fine-grained classification system and the proposed class-aware SSL methods, our results can recognize more land cover categories, including industrial area, urban residential, rural residential, road, overpass, railway station, arbor forest, artificial meadow, irrigated field, bare land, lake, river, pond, and fish pond. Our land cover maps with fine-grained classes can provide more land cover information. Besides, from the red rectangles, our method recognizes the paddy field correctly, while the other two products classify it as cropland and water, respectively, due to the coarse classification system and the misleading spectral information of the paddy field. From the above qualitative comparison, our method provides land cover maps with fine-grained classes, significantly improving the land cover information. + +# 6. Conclusion + +In this work, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation approach for large- + +scale land cover mapping with fine-grained classes. To address the class-imbalance issue, we propose a class-aware unlabeled data selection method to build an SSL dataset more balanced towards minority classes. Then, we propose a Class-Balanced Cross Entropy loss, considering the annotation and class biases on the built SSL dataset. Moreover, we propose the Class Center Contrast method to jointly use the labeled and unlabeled data for training. Experimental results validate the effectiveness of our method in large-scale land cover mapping with fine-grained classes. + +# Acknowledgements + +This research was supported in part by the National Natural Science Foundation of China (Grant No. T2125006), Jiangsu Innovation Capacity Building Program (Project No. BM2022028), China Postdoctoral Science Foundation (Grant No. 2023M731871), the German Federal Ministry of Education and Research (BMBF) in the framework of the international future AI lab "AI4EO - Artificial Intelligence for Earth Observation: Reasoning, Uncertainties, Ethics and Beyond" (Grant No. 01DD20001), and Shuimu Tsinghua Scholar Project. + +# References + +[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. Semi-supervised semantic segmentation with pixel-level contrastive learning from a class-wise memory bank. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4268-4277, 2022. 2 +[45] D Zanaga, R Van De Kerchove, W De Keersmaecker, N Souverijns, C Brockmann, R Quast, J Wevers, A Grosu, A Paccini, S Vergnaud, et al. Esa worldwide 10 m 2020 v100. zenodo, 2021. 8 +[46] Yuanyi Zhong, Bodi Yuan, Hong Wu, Zhiqiang Yuan, Jian Peng, and Yu-Xiong Wang. Pixel contrastive-consistent semi-supervised semantic segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 7273-7282, 2021. 2 +[47] Boyan Zhou, Quan Cui, Xiu-Shen Wei, and Zhao-Min Chen. Bbn: Bilateral-branch network with cumulative learning for long-tailed visual recognition. 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However, existing methods overlook the potential to alleviate the class imbalance problem by selecting a suitable set of unlabeled data. Besides, in class-imbalanced scenarios, existing pseudo-labeling methods mostly only pick confident samples, failing to exploit the hard samples during training. To tackle these issues, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation framework. The proposed framework consists of three key components. To construct a better semi-supervised learning dataset, we propose a class-aware unlabeled data selection method that is more balanced towards the minority classes. Based on the built dataset with improved class balance, we propose a Class-Balanced Cross Entropy loss, jointly considering the annotation bias and the class bias to re-weight the loss in both sample and class levels to alleviate the class imbalance problem. Moreover, we propose the Class Center Contrast method to jointly utilize the labeled and unlabeled data. Specifically, we decompose the feature embedding space using the ground truth and pseudo-labels, and employ the embedding centers for hard and easy samples of each class per image in the contrast loss to exploit the hard samples during training. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 661, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 661, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 661, + 287, + 696 + ], + "type": "text", + "content": "Land cover mapping provides pixel-level information for urban management, climate change research, ecosystem protection, and other sustainability-related applica" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 260, + 547, + 439 + ], + "blocks": [ + { + "bbox": [ + 309, + 260, + 547, + 439 + ], + "lines": [ + { + "bbox": [ + 309, + 260, + 547, + 439 + ], + "spans": [ + { + "bbox": [ + 309, + 260, + 547, + 439 + ], + "type": "image", + "image_path": "7b5448a33ca75d31ea5097cb4e3ad58bf9f15c5950fbe43a104bff7189823f84.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 452, + 547, + 496 + ], + "lines": [ + { + "bbox": [ + 305, + 452, + 547, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 452, + 547, + 496 + ], + "type": "text", + "content": "Figure 1. Examples of the labeled data. The top row shows Sentinel-2 images containing 13 bands. The bottom row shows the corresponding labels. We use a fine-grained classification system with 24 land cover classes in this work." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 519, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 547, + 651 + ], + "type": "text", + "content": "tions [21, 27]. With the rapid progress of computer vision technology, it is desired to automatically gain large-scale and fine-grained land cover information from remote sensing images to support the demand of existing earth system science studies and bring new opportunities for intelligent city study [31]. However, fine-grained annotations for land cover mapping are high-cost and time-consuming, limiting labeled data collection for large-scale applications. Semi-supervised learning (SSL) is a potential solution to this problem, as it utilizes both existing labeled data and a large number of unlabeled data [37]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Large-scale land cover mapping with fine-grained classes usually suffers from class imbalance, as shown in Figure 1 and 3. The labeled data tends to be biased due to the difficulty of data collection and label annotation varying by class. The class imbalance leads to suboptimal per" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16783" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 262 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 262 + ], + "type": "text", + "content": "formance in the minority classes. Most SSL methods for large-scale land cover mapping are typically based on the assumption that labeled and unlabeled data have the same class distribution [41, 37]. However, this assumption does not hold in most scenarios, resulting in the bias of class estimation. As such, it is non-trivial to jointly utilize the labeled and unlabeled data to train the network for semi-supervised semantic segmentation. Although many pseudo-labeling methods aim to assign pseudo-labels more steadily and correctly for different classes on the unlabeled data, e.g., dynamically setting threshold or proportion [17, 44], they still rely on setting hyperparameters and empirical principles, resulting in a lack of flexibility and generalization ability in applications. Besides, pseudo-labeling methods mostly rely on easy samples with high confidence scores, thus failing to exploit the hard samples on the unlabeled data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 264, + 286, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 264, + 286, + 538 + ], + "spans": [ + { + "bbox": [ + 49, + 264, + 286, + 538 + ], + "type": "text", + "content": "To alleviate the above issues, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation framework. We exploit the potential of the unlabeled data and alleviate the class imbalance problem in large-scale land cover mapping with fine-grained classes. The proposed class-aware unlabeled data selection method constructs an SSL dataset and compensates for the class imbalance on the labeled data. Based on the built SSL dataset, we propose a class-balanced learning method to remove the annotation bias and class bias on the SSL dataset. We dynamically estimate the class prior information on the entire SSL dataset during training to re-weight both samples and classes of the loss function for the labeled data. Finally, we propose the Class Center Contrast method to jointly use the labeled and unlabeled data for training. The ground truth and pseudolabels are leveraged as the guide to decompose the feature embedding space. We estimate the hard, easy, and overall embedding centers for each class per image and apply the contrastive loss to optimize the distances between class centers to utilize both easy and hard samples. The class imbalance issue is alleviated by utilizing the proposed method, and the performance of large-scale land cover mapping with fine-grained classes is effectively improved." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 550, + 132, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 550, + 132, + 562 + ], + "spans": [ + { + "bbox": [ + 49, + 550, + 132, + 562 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 571, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 571, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 571, + 286, + 712 + ], + "type": "text", + "content": "Large-Scale Land Cover Mapping. Land cover mapping classifies each pixel of images into a unique class, which can be regarded as a semantic segmentation problem [6, 11]. Large-scale land cover mapping with fine-grained classes can provide necessary information for earth system science studies and land spatial layout optimization. However, manual or semi-manual labeling is high-cost and time-consuming [34]. Besides, the classification systems of most large-scale studies are coarse. Thus the provided land cover information is limited. For example, the Chesapeake dataset covering " + }, + { + "bbox": [ + 49, + 571, + 286, + 712 + ], + "type": "inline_equation", + "content": "160,000\\mathrm{km}^2" + }, + { + "bbox": [ + 49, + 571, + 286, + 712 + ], + "type": "text", + "content": " costs $1.3 million but only contains four classes [33]. DynamicEarthNet" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 72, + 544, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 251 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 251 + ], + "type": "text", + "content": "dataset covers " + }, + { + "bbox": [ + 308, + 72, + 544, + 251 + ], + "type": "inline_equation", + "content": "17,000\\mathrm{km}^2" + }, + { + "bbox": [ + 308, + 72, + 544, + 251 + ], + "type": "text", + "content": " and includes 7 basic land cover classes [36]. To overcome the limited area of the labeled data and improve the model generalization, some works utilize openly available produced data (e.g., OpenStreetMap data and land cover products), which contains many noisy labels but can provide prior information in a large-scale area [19, 10]. These works still use coarse classification systems of land cover mapping. Five-Billion-Pixels [37] is a large-scale land cover dataset with 24 categories, covering about " + }, + { + "bbox": [ + 308, + 72, + 544, + 251 + ], + "type": "inline_equation", + "content": "60,000\\mathrm{km}^2" + }, + { + "bbox": [ + 308, + 72, + 544, + 251 + ], + "type": "text", + "content": ", which opens the door to large-scale land cover mapping with fine-grained classes. However, this dataset suffers from a severe class-imbalance problem (the common categories cover hundreds of times more pixels than the rare ones), due to the difficulty of data collection and label annotation varying by class." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 255, + 544, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 255, + 544, + 446 + ], + "spans": [ + { + "bbox": [ + 308, + 255, + 544, + 446 + ], + "type": "text", + "content": "Class-Imbalanced Learning. To solve the class-imbalance problem, related works include data resampling [3, 4], loss re-weighting [22, 32, 18], margin modification [5, 35], and decoupled learning [20, 47]. In self-supervised learning and SSL, recent works devote to rebalancing the class distribution of SSL data by assigning pseudo-labels for the unlabeled data to address the class imbalance issue [41, 15]. For example, Gui et al. [14] propose a class-aware pseudo-labeling method for SSL, dynamically adjusting the threshold for selecting pseudo-labels to obtain better performance on minority classes. Similarly, Hu et al. [17] propose a label bias removal method and dynamically determine the threshold for each class to assign more pseudo-labels for minority classes. However, the hard samples with relatively low confidence scores are ignored for optimizing the model, leading to sub-optimal performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 451, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 451, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 451, + 544, + 712 + ], + "type": "text", + "content": "Semi-Supervised Semantic Segmentation. SSL methods leverage the relationships between the labeled and unlabeled data to improve the model accuracy and generalization, alleviating the limited area of the labeled data [8]. Semi-supervised semantic segmentation methods include entropy minimization [38], consistency regularization [30], and pseudo-labeling [42]. Pseudo-labeling is widely used in semi-supervised semantic segmentation, and many works contribute to selecting pseudo-labels more steadily and correctly [29]. For example, Tong et al. [37] propose a dynamic pseudo-label assignment method, in which the number of pseudo-labels is dynamically increased with training iterations. However, these methods still rely on the manual setting of hyperparameters and suffer from the uncertainty of pseudo-labels. Alternatively, contrastive learning methods in supervised learning [39, 16] and SSL [46, 40] constrain the representations of positive samples against these negative samples in feature space, leading to promising results. Different from the manner of data augmentation-based positive sample construction [43, 23] and memory bank-based negative sample construction [1, 40], we leverage the ground-truth and pseudo-labels as a guide to decom" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 750, + 317, + 757 + ], + "type": "text", + "content": "16784" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "pose the feature embedding space, and estimate the embedding centers for each class per image to stably select easy and hard samples for the proposed Class Center Contrast method." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 132, + 130, + 146 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 132, + 130, + 146 + ], + "spans": [ + { + "bbox": [ + 47, + 132, + 130, + 146 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 152, + 258, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 258, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 258, + 166 + ], + "type": "text", + "content": "3.1. The Overall Workflow of Our Approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 171, + 289, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 289, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 289, + 447 + ], + "type": "text", + "content": "Our approach consists of four steps. First, a baseline model is trained on the labeled data. Second, we propose a class-aware unlabeled data selection method to build an SSL dataset that is more balanced towards minority classes. The baseline model is used to predict land cover classes on all collected data from a large unlabeled data pool and calculate the statistics of the class distribution for each image patch. The image patches containing pixels of minority classes are selected as unlabeled data. Then the SSL dataset is constructed by combining the labeled data and the selected unlabeled data. Third, we propose a Class-Balanced Cross Entropy loss and a Class Center Contrast method. To alleviate the class imbalance problem, we reweight the cross entropy loss on labeled data in both sample and class level by jointly considering the annotation bias and the class bias on the built SSL dataset. Besides, we decompose the feature embedding space using the ground truth and pseudo-labels, and propose an embedding center selection and contrast method for class-balanced and annotation-guided learning on unlabeled data. The pipeline of the proposed class-aware SSL model is shown in Figure 2. Finally, we perform model inference for large-scale land cover mapping." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 455, + 249, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 249, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 249, + 467 + ], + "type": "text", + "content": "3.2. Class-Aware Unlabeled Data Selection" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "content": "A suitable set selection of unlabeled data is important for SSL model development. Inspired by the observation in [41] that existing SSL algorithms can produce pseudolabels on minority classes with high precision, we propose an unlabeled data selection strategy that tends to select unlabeled image patches containing pixels with minority classes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "First, we train a semantic segmentation model using labeled data. We apply the off-the-shelf class balance strategy [4] designed for supervised learning to guarantee the model ability of minority class estimation. The definition of minority classes depends on the class proportion and the class accuracy on the labeled data. Then, we perform model inference on all candidate unlabeled data to predict the land cover class of each pixel, thereby obtaining the class distribution of each candidate image patch. We denote the proportion of pixels of all minority classes in an image patch as " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "P_{m}" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": ". Finally, we formulate a principle to automatically select unlabeled data according to the class distribution of each candidate image patch. Specifically, the pro" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": "portions of the 24 classes on the labeled dataset are shown in Figure 3. The classes with a proportion lower than " + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": " generally achieve an accuracy of less than " + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": " within our dataset. We collect all the images with " + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "inline_equation", + "content": "P_{m} \\geq 1\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": ", which leads to about 25,000 images over the about 500,000 candidates (see Section 4.3). Then we randomly select another 25,000 images from those with " + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "inline_equation", + "content": "0 < P_{m} < 1\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": ", leading to a total of 50,000 unlabeled images, which is five times the number of the labeled training data. The authors suggest selecting unlabeled patches with relatively more pixels of minority classes (i.e., larger " + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "inline_equation", + "content": "P_{m}" + }, + { + "bbox": [ + 304, + 72, + 547, + 275 + ], + "type": "text", + "content": "), and those encompassing rare classes characterized by fewer pixels within the minority classes. Note that although the prediction on the unlabeled data is not absolutely accurate, it can preserve image patches that are most likely to contain pixels with minority classes, which contributes to building a more balanced SSL dataset." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 283, + 447, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 283, + 447, + 296 + ], + "spans": [ + { + "bbox": [ + 305, + 283, + 447, + 296 + ], + "type": "text", + "content": "3.3. Class-Balanced Learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 301, + 545, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 408 + ], + "type": "text", + "content": "In our built SSL dataset, the class distribution of unlabeled data differs from that of the labeled data. It can be regarded as an annotation bias problem on the entire dataset. Besides, the SSL dataset still suffers from a class imbalance issue. Consequently, using the class prior information estimated on the labeled data to the re-weight loss function is inappropriate. To solve the above issues, we propose a class-balanced learning method to jointly remove the annotation bias and class bias on the SSL dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "text", + "content": "First, we re-weight samples of labeled data to remove the annotation bias. Owing to our unlabeled data selection method, the entire SSL dataset is more balanced towards minority classes than the original labeled dataset. Therefore, we can estimate the class prior on the entire SSL dataset to partially remove the annotation bias. Specifically, we denote " + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "text", + "content": " as a label indicator, where " + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "inline_equation", + "content": "L = 0" + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "inline_equation", + "content": "L = 1" + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "text", + "content": " represent the unlabeled and labeled data, respectively. The model parameters " + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 409, + 546, + 540 + ], + "type": "text", + "content": " of labeled data in traditional SSL methods are obtained by maximizing likelihood estimation in the formula (1)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 345, + 558, + 545, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 558, + 545, + 607 + ], + "spans": [ + { + "bbox": [ + 345, + 558, + 545, + 607 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\theta} = \\arg \\max _ {\\theta} \\log P (Y | X, L = 1; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log P (y | x; \\theta), \\tag {1} \\\\ \\end{array}", + "image_path": "950f72e43d5f45c3a13146f63c3267bca818c28d3980a6512636d514b8baf39b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "text", + "content": " is the estimated model parameter, " + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "text", + "content": " represents samples, " + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "text", + "content": " represents classes, and " + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "inline_equation", + "content": "D_{L = 1}" + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "text", + "content": " denotes the set of labeled data. Due to the annotation bias in the SSL dataset, we have " + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "inline_equation", + "content": "P(y|x;L = 1)\\neq P(y|x)" + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "text", + "content": ". According to causal inference [13, 17], in the entire SSL dataset, " + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "inline_equation", + "content": "X\\rightarrow Y\\rightarrow L" + }, + { + "bbox": [ + 304, + 616, + 547, + 715 + ], + "type": "text", + "content": " can be regarded as a one-way chain, where the class is dependent on its pixel, and whether the pixel has a label or not depends on its class. According to the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16785" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 73, + 521, + 277 + ], + "blocks": [ + { + "bbox": [ + 72, + 73, + 521, + 277 + ], + "lines": [ + { + "bbox": [ + 72, + 73, + 521, + 277 + ], + "spans": [ + { + "bbox": [ + 72, + 73, + 521, + 277 + ], + "type": "image", + "image_path": "4374f975a37edd04ac6a43821175eb63e023e918e341f7644a90e03609a8add0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 294, + 544, + 317 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 544, + 317 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 544, + 317 + ], + "type": "text", + "content": "Figure 2. The pipeline of the proposed Class-Aware Semi-Supervised Semantic Segmentation framework with class-balanced learning, embedding center estimation, and class center contrast. The class-aware unlabeled data selection process is not shown in the figure." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "text", + "content": "conditional independence rule, we obtain the expression, " + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "inline_equation", + "content": "P(X|Y,L = 1) = P(X|Y)" + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "text", + "content": " when conditioning on Y. Therefore, estimating the model parameters of the entire SSL dataset can be formalized as in the formula (2) [17], where " + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "inline_equation", + "content": "s(x,y) = \\frac{\\log P(y|x;\\theta) - \\log P(y;\\theta)}{\\log P(y|x;\\theta)}" + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "text", + "content": " is the loss weight of each labeled sample " + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "text", + "content": ". Thus, it can be interpreted as modifying the class prior " + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "inline_equation", + "content": "P(y;\\theta)" + }, + { + "bbox": [ + 46, + 336, + 290, + 434 + ], + "type": "text", + "content": " to remove the annotation bias of the labeled data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 451, + 287, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 451, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 66, + 451, + 287, + 595 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\theta} = \\arg \\max _ {\\theta} \\log P (X | Y; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log P (x | y; \\theta) \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log \\frac {P (y | x ; \\theta) P (x ; \\theta)}{P (y ; \\theta)} \\tag {2} \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} \\log \\frac {P (y | x ; \\theta)}{P (y ; \\theta)} \\\\ = \\arg \\max _ {\\theta} \\sum_ {(x, y) \\in D _ {L = 1}} s (x, y) \\cdot \\log P (y | x; \\theta), \\\\ \\end{array}", + "image_path": "c95320160bd362817a339d5324b0d9810beefd39c9a62d68cdfdd5bfbd601c01.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 602, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 602, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 602, + 287, + 673 + ], + "type": "text", + "content": "Second, although the SSL dataset is more balanced than the labeled data, it still suffers from the class imbalance problem. Therefore, we further estimate the class bias on the SSL dataset. A widely used class re-weighting loss function on supervised learning can be formalized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 102, + 683, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 683, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 102, + 683, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {w c e} = \\sum_ {k = 1} ^ {K} W _ {k} \\sum_ {i = 1} ^ {n _ {k}} y _ {i k} \\log p _ {i k}, \\tag {3}", + "image_path": "7eb853c507430a440c01f08ac0941895c9c69672a01fd8c1787dac01174dee33.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "W_{k} = \\frac{1}{\\log(1 + r_{k})}" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "r_k" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": " is the ratio of the class " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": " on the labeled data. " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": " is the number of classes, " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "n_k" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": " is the number of samples of class " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "y_{ik}" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "p_{ik}" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": " is the ground-truth and predicted probability of the " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": "-th sample for class " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": ", respectively. In SSL, we approximate " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "r_k" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "inline_equation", + "content": "P(y; \\theta)" + }, + { + "bbox": [ + 304, + 335, + 545, + 409 + ], + "type": "text", + "content": ", the class distribution on the entire dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "content": "Finally, we perform an online estimation strategy for " + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "inline_equation", + "content": "P(y; \\theta)" + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "content": " to simplify the training process. We compute the average of class probability distributions over all pixels in a mini-batch, which is denoted as " + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "inline_equation", + "content": "P(Y; B_t, \\theta_t)" + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "inline_equation", + "content": "B_t" + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "content": " are the samples and model parameters of the current batch, respectively. Then the approximate class distribution, denoted as " + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "inline_equation", + "content": "\\tilde{P}(Y)" + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "content": ", is updated by the weighted sum of the obtained class distribution of this mini-batch and the approximate class distribution in the previous iteration, which is formalized as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 341, + 555, + 545, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 555, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 341, + 555, + 545, + 570 + ], + "type": "interline_equation", + "content": "\\tilde {P} (Y) \\leftarrow \\mu \\tilde {P} (Y) + (1 - \\mu) P (Y; B _ {t}, \\theta_ {t}), \\tag {4}", + "image_path": "8d07e3604a3610afaae859fd2a55ac5c44c9e6b5bb304cb5911b7b6e7a87cc11.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "inline_equation", + "content": "\\mu \\in [0,1]" + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "text", + "content": " is a weighting coefficient. We set " + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "inline_equation", + "content": "\\mu = \\frac{B}{N}" + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "text", + "content": ", in which " + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "text", + "content": " is the batch size and " + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "text", + "content": " is the total number of samples in the dataset. We initialize " + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "inline_equation", + "content": "\\tilde{P}(Y)" + }, + { + "bbox": [ + 304, + 588, + 546, + 660 + ], + "type": "text", + "content": " with the class distribution calculated on the labeled data. As such, the proposed Class-Balanced Cross Entropy loss on the labeled data is formulated as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 339, + 683, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 683, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 339, + 683, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c b c e} = \\sum_ {k = 1} ^ {K} W _ {k} \\sum_ {i = 1} ^ {n _ {k}} s \\left(x _ {i k}, y _ {i k}\\right) y _ {i k} \\log p _ {i k}. \\tag {5}", + "image_path": "772e7e8383e0ee8cb3434e5b04f052de99cfd190a57c59de8fcb42b8c3510d20.jpg" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16786" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 174, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 174, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 174, + 83 + ], + "type": "text", + "content": "3.4. Class Center Contrast" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 289, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 289, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 289, + 462 + ], + "type": "text", + "content": "Training via pseudo-labeling is commonly used to utilize unlabeled data in SSL. In fine-grained classes, assigning reliable labels for minority classes is challenging because the segmentation model tends to be biased towards the majority classes [26]. Besides, existing label assignment methods usually use only high-confidence predictions, which may offer limited information to model learning. In this work, our method selects reliable and hard samples. Moreover, instead of directly using the pseudo-labels for supervised learning on unlabeled data, we leverage the pseudo-labels as the guide to decompose the feature embedding space. In general, the distance of feature embeddings from the same class should be minimized, while the distance of those from different classes should be maximized. Therefore, we propose an online embedding center selection method that divides each class into hard and easy sample regions on each image. Specifically, we use the prediction probabilities of ground truth or pseudo-labels to separate easy and hard samples. The predicted probability of each pixel is associated with its feature embedding, and we then calculate the average prediction probability of each class for each image. Feature embeddings with above-average probabilities for the corresponding class are considered easy samples and vice versa. Thus we can obtain three feature embedding centers, including easy, hard, and all feature embedding centers, as contrastive samples. With this method, on the one hand, the obtained feature embeddings for each class are with relatively high confidence, as the samples are close to feature local centers for each class in the embedding space. On the other hand, these feature embeddings include hard samples of each class." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "text", + "content": "Inspired by the existing contrastive learning method [39], we perform cross-image contrastive learning in each mini-batch. Since both labeled and unlabeled data are trained in a mini-batch, the embeddings of the labeled data could help the feature embedding learning of the unlabeled data. Formally, denote " + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "inline_equation", + "content": "P_{m}" + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "inline_equation", + "content": "N_{m}" + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "text", + "content": " as the feature embedding collections of the positive and negative samples in a mini-batch for the " + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "text", + "content": "-th feature embedding center " + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "inline_equation", + "content": "c_{m}" + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "text", + "content": ". The proposed Class Center Contrastive loss for the " + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 462, + 288, + 582 + ], + "type": "text", + "content": "-th feature embedding center is formulated as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 601, + 297, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 297, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 297, + 651 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c c t} ^ {m} = - \\frac {1}{| P _ {m} |} \\sum_ {\\boldsymbol {c} _ {m} ^ {+} \\in P _ {m}} \\log \\frac {e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {+} / \\tau\\right)}}{e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {+} / \\tau\\right)} + \\sum_ {\\boldsymbol {c} _ {m} ^ {-} \\in N _ {m}} e ^ {\\left(\\boldsymbol {c} _ {m} \\cdot \\boldsymbol {c} _ {m} ^ {-} / \\tau\\right)}}, \\tag {6}", + "image_path": "9a7275ed1b9cfd82736005e85851476c8506a7357798ef395c858993a2262996.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "type": "text", + "content": " is the temperature parameter, " + }, + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "type": "inline_equation", + "content": "c_{m}^{+}" + }, + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "type": "inline_equation", + "content": "c_{m}^{-}" + }, + { + "bbox": [ + 47, + 652, + 286, + 676 + ], + "type": "text", + "content": " are the positive and negative samples, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 677, + 282, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 677, + 282, + 688 + ], + "spans": [ + { + "bbox": [ + 59, + 677, + 282, + 688 + ], + "type": "text", + "content": "The overall loss function can be formulated as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 125, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 125, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {c b c e} + \\lambda \\mathcal {L} _ {c c t}, \\tag {7}", + "image_path": "eb096b3ad1b1571052228e5d77715b1830e2ecccca98d79eb24b1fcb6d0fd2f4.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 416, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 416, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 416, + 84 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 72, + 416, + 84 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 306, + 72, + 416, + 84 + ], + "type": "text", + "content": " is the loss weight." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 99, + 347, + 110 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 99, + 347, + 110 + ], + "spans": [ + { + "bbox": [ + 306, + 99, + 347, + 110 + ], + "type": "text", + "content": "4. Data" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 118, + 488, + 131 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 118, + 488, + 131 + ], + "spans": [ + { + "bbox": [ + 306, + 118, + 488, + 131 + ], + "type": "text", + "content": "4.1. Image Collection and Preparation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "spans": [ + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "text", + "content": "Considering free access, multispectral bands, and relatively high spatial resolution, all satellite images used in this work are acquired from Sentinel-2 satellites. Sentinel-2 imagery has 13 spectral bands at " + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "inline_equation", + "content": "10\\mathrm{m}" + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "text", + "content": " (R, G, B, and near-infrared bands), " + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "inline_equation", + "content": "20\\mathrm{m}" + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "text", + "content": " (six red edge and shortwave infrared bands), and " + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "inline_equation", + "content": "60\\mathrm{m}" + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "text", + "content": " (three atmospheric correction bands) resolutions [12]. The abundant multispectral information and up to " + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "inline_equation", + "content": "10\\mathrm{m}" + }, + { + "bbox": [ + 304, + 138, + 545, + 245 + ], + "type": "text", + "content": " spatial resolution benefit land cover mapping with a fine-grained classification system." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 247, + 545, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 318 + ], + "type": "text", + "content": "We collect Sentinel-2 images with radiometric correction, geometric corrections, and atmospheric correction, covering more than 60 cities in China. We apply an off-the-shelf Sentinel-2 sharpening method, DSen2Net [24], to reconstruct low-resolution bands and uniform the resolution of all bands of Sentinel-2 images to " + }, + { + "bbox": [ + 304, + 247, + 545, + 318 + ], + "type": "inline_equation", + "content": "10\\mathrm{m}" + }, + { + "bbox": [ + 304, + 247, + 545, + 318 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 329, + 528, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 329, + 528, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 329, + 528, + 342 + ], + "type": "text", + "content": "4.2. Label Collection and Classification System" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "text", + "content": "The land cover labels and classification system are from the Five-Billion-Pixels dataset [37], labeled with " + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "inline_equation", + "content": "4\\mathrm{m}" + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "text", + "content": " resolution. It includes 24 land cover classes. We resize the " + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "inline_equation", + "content": "4\\mathrm{m}" + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "text", + "content": " labels to " + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "inline_equation", + "content": "10\\mathrm{m}" + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "text", + "content": " to match Sentinel-2 images. The labeled area covers about " + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "inline_equation", + "content": "60,000\\mathrm{km}^2" + }, + { + "bbox": [ + 304, + 349, + 545, + 504 + ], + "type": "text", + "content": " in China. The classification system includes the industrial area (C1), paddy field (C2), irrigated field (C3), dry cropland (C4), garden land (C5), arbor forest (C6), shrub forest (C7), park (C8), natural meadow (C9), artificial meadow (C10), river (C11), urban residential (C12), lake (C13), pond (C14), fish pond (C15), snow (C16), bare land (C17), rural residential (C18), stadium (C19), square (C20), road (C21), overpass (C22), railway station (C23), and airport (C24)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 514, + 364, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 364, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 364, + 526 + ], + "type": "text", + "content": "4.3. Dataset" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Examples of the labeled data are shown in Figure 1. The training, validation, and test datasets include 9,995, 2,000, and 2,503 images with a size of " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", respectively, according to the geographical division. The unlabeled data is from more than 60 dispersed administrative districts in China and has no overlap with the labeled data. The number of candidate unlabeled images is about 500,000, each with a size of " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ". According to our minority class-biased unlabeled data selection strategy, we filter 50,000 images to build the unlabeled set, which covers more scenes with minority classes. Figure 3 shows the proportion of each land cover class on labeled training data, unlabeled training data, and all training data. The majority classes cover hundreds of times more pixels than the minority classes on the labeled training data." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16787" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 73, + 545, + 309 + ], + "blocks": [ + { + "bbox": [ + 50, + 73, + 545, + 309 + ], + "lines": [ + { + "bbox": [ + 50, + 73, + 545, + 309 + ], + "spans": [ + { + "bbox": [ + 50, + 73, + 545, + 309 + ], + "type": "image", + "image_path": "66af3d5eaff49cc0c9ef9bd8aca6e0f9f856cf57c02cf9dde286574d88af7d03.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 81, + 324, + 511, + 337 + ], + "lines": [ + { + "bbox": [ + 81, + 324, + 511, + 337 + ], + "spans": [ + { + "bbox": [ + 81, + 324, + 511, + 337 + ], + "type": "text", + "content": "Figure 3. Percentage of each land cover class on the labeled training data, unlabeled training data, and all training data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 345, + 541, + 549 + ], + "blocks": [ + { + "bbox": [ + 53, + 345, + 541, + 549 + ], + "lines": [ + { + "bbox": [ + 53, + 345, + 541, + 549 + ], + "spans": [ + { + "bbox": [ + 53, + 345, + 541, + 549 + ], + "type": "table", + "html": "
MethodOAmAccmIoUC1C2C3C4C5C6C7C8C9C10
Baseline73.2445.7735.6171.2466.2588.6617.9016.9362.2627.0117.2644.6511.33
SimCLR [7] +finetune74.0745.8135.1774.4963.3390.8814.1017.8062.1023.5718.3948.4221.02
Pseudo -labeling [25]74.6148.8338.0376.8569.6091.5513.4720.5259.1931.6337.5344.9010.68
Advent [38]74.8149.2538.9875.8868.3891.9812.2015.0162.4625.9144.7754.758.10
CADR [17]75.4947.8336.6376.3252.4391.4821.5424.3564.7431.8522.5959.8817.25
DPA [37]75.3648.5737.7776.0569.4092.3315.5119.7966.3027.0523.2552.4112.48
Ours75.9753.5340.6881.7180.0788.8922.2737.3267.0634.8726.4456.7317.16
C11C12C13C14C15C16C17C18C19C20C21C22C23C24
70.8682.7678.9324.4957.713.0448.6777.2310.807.9071.4245.8334.9560.34
71.4783.2779.4130.5464.730.7548.7768.822.00073.5944.5333.8763.72
72.4082.9083.5616.9452.4413.6655.0672.5821.0513.0370.2760.6038.7862.83
69.9883.1983.3819.7249.3415.5046.5675.1622.4017.5570.9958.0441.6269.23
65.9086.2784.5326.0972.57051.7874.960.95065.2348.5133.6475.02
71.9783.3381.8016.7750.660.8852.3772.6121.426.6472.1559.1049.1572.37
70.6182.8681.6917.1378.5326.2855.8080.6931.8326.4966.2364.6546.3942.97
", + "image_path": "1e6d46ac96b704cc9c89296589fcec31ff0587896a4d10eea3a4cdc437201d23.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 552, + 536, + 564 + ], + "lines": [ + { + "bbox": [ + 47, + 552, + 536, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 536, + 564 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with different methods. We also show the precision of each class. Bold indicates the best results " + }, + { + "bbox": [ + 47, + 552, + 536, + 564 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 582, + 128, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 128, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 128, + 596 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 605, + 239, + 619 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 239, + 619 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 239, + 619 + ], + "type": "text", + "content": "5.1. Implementation Details and Metrics" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "We choose ResUNet [9] in our experiments, as it is stable and lightweight for land cover mapping. We train for 100 epochs for all experiments using stochastic gradient descent (SGD) with a momentum of 0.9 and a weight decay of " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": ". The initial learning rate is set to 0.05. We adopt the batch size as 12, including 6 labeled images and 6 unlabeled images. The loss weight " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": " is set to 0.005. The temperature" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 583, + 443, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 583, + 443, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 583, + 443, + 594 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 583, + 443, + 594 + ], + "type": "text", + "content": " of contrastive loss is set to 0.07." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 597, + 545, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 597, + 545, + 645 + ], + "spans": [ + { + "bbox": [ + 305, + 597, + 545, + 645 + ], + "type": "text", + "content": "The performance of the proposed approach and other competing methods are assessed with overall accuracy (OA), mean accuracy (mAcc), mean intersection over union (mIoU), and precision of each class." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 657, + 424, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 424, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 424, + 670 + ], + "type": "text", + "content": "5.2. Comparison Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 677, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 715 + ], + "type": "text", + "content": "Table 1 shows the comparison results with typical and state-of-the-art class-balanced pseudo-labeling methods. For a fair comparison, all competing methods and our" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16788" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 80, + 70, + 255, + 150 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 255, + 150 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 255, + 150 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 255, + 150 + ], + "type": "table", + "html": "
MethodOAmAccmIoU
Random selection75.5051.3539.09
Majority class -biased selection75.7549.9839.33
Minority class -biased selection75.9753.5340.68
", + "image_path": "a6759b955130e942fd9658c3df227bdcea20218473c6fb420ad98b36f2536fd3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 190, + 291, + 255 + ], + "blocks": [ + { + "bbox": [ + 47, + 158, + 287, + 179 + ], + "lines": [ + { + "bbox": [ + 47, + 158, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 47, + 158, + 287, + 179 + ], + "type": "text", + "content": "Table 2. Ablation study on the proposed class-aware unlabeled data selection method. Bold indicates the best results " + }, + { + "bbox": [ + 47, + 158, + 287, + 179 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 158, + 287, + 179 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 190, + 291, + 255 + ], + "lines": [ + { + "bbox": [ + 48, + 190, + 291, + 255 + ], + "spans": [ + { + "bbox": [ + 48, + 190, + 291, + 255 + ], + "type": "table", + "html": "
MethodOAmAccmIoU
Without class balance75.4148.1637.27
Class-balanced method in [38]73.6151.3338.61
Class-balanced method in [37]75.5149.6635.51
Ours75.9753.5340.68
", + "image_path": "53c82a41da47d48dd81f00bdb2d8097ccbb54a351ff4aa10a5e1221579f63e06.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 262, + 286, + 283 + ], + "lines": [ + { + "bbox": [ + 47, + 262, + 286, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 286, + 283 + ], + "type": "text", + "content": "Table 3. Comparison results on different class-balanced learning methods. Bold indicates the best results " + }, + { + "bbox": [ + 47, + 262, + 286, + 283 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 262, + 286, + 283 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 304, + 286, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 286, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 286, + 434 + ], + "type": "text", + "content": "method use the same model architecture. All experiments are measured on the same computing platform. The baseline applies the supervised learning method to the labeled data. The SimCLR+finetune method uses a self-supervised learning method [7] on the unlabeled data to obtain a pretrain model and performs fine-tuning on the labeled data. Pseudo-labeling method [25] first generates pseudo-labels of the unlabeled data by using the baseline model, then retransmits the model with ground truth and pseudo-labels. Advent [38], DPA [37], and CADR [17] are three state-of-the-art SSL methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "text", + "content": "The results demonstrate that our approach significantly improved over " + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "inline_equation", + "content": "4.28\\%" + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "text", + "content": " in mAcc, " + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "inline_equation", + "content": "1.70\\%" + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "text", + "content": " in mIoU, and " + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "inline_equation", + "content": "0.58\\%" + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "text", + "content": " in OA. Compared to the baseline for each class, our method can significantly improve the accuracy of the minority classes and maintain the accuracy of the majority classes simultaneously. In contrast, the competing methods often tend to predict the pixels to majority classes and suffer from low precision on minority classes. Regarding the computational cost, our method incurs " + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "inline_equation", + "content": "53\\%" + }, + { + "bbox": [ + 46, + 435, + 286, + 604 + ], + "type": "text", + "content": " additional training time than the basic SSL algorithm (i.e., Advent) due to Class-Balanced Learning and Class Center Contrast. The inference times are the same for all SSL methods, as we use the same backbone. Please find the visual comparison in the supplementary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 610, + 140, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 140, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 140, + 624 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "Class-Aware Unlabeled Data Selection. We compare our method with the opposite strategy (i.e., majority class-biased data selection) and widely opted random selection method. Table 2 shows that our method achieves the best results. On the contrary, the mAcc value of the majority class-biased data selection method is unsatisfactory because the SSL model is biased toward predicting the majority classes." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 545, + 209 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 545, + 209 + ], + "type": "image", + "image_path": "10d83bb2ceae84f2e5bf7fb6a2db8ac3888294dc074b804f6a1d10733d745232.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 222, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 305, + 222, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 222, + 545, + 255 + ], + "type": "text", + "content": "Figure 4. Results of using the different number of labeled images (i.e., 500, 1,000, and 3,000) and the different ratios of unlabeled to labeled images in SSL." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 278, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 410 + ], + "type": "text", + "content": "Besides, to verify the effectiveness of unlabeled data selection, we show the statistics of class distribution in Figure 3. Estimating the class distribution of unlabeled data is based on the pseudo-labels produced by the baseline model. Owing to the proposed class-aware unlabeled data selection method, the class distribution of the unlabeled data is more balanced than that of the labeled data. As a result, the entire training dataset is more balanced towards minority classes than the original labeled dataset. Therefore, we can estimate the class prior information on the entire dataset to partially remove the annotation bias." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 412, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 626 + ], + "type": "text", + "content": "Class-Balanced Learning. In general, class weighting sacrifices the accuracy of majority classes to improve the accuracy of minority classes, which decreases OA and mIoU. From Table 3, two comparison methods suffer from the above problem, while our method improves the mAcc, OA, and mIoU compared to the baseline (i.e., without loss weights). The reason is that the two comparison methods use class prior information of labeled data and ignore the discrepancy of class distributions between labeled and unlabeled data in SSL. Besides, Table 4 shows the ablation study on Class-Balanced Cross Entropy loss. Utilizing sample re-weighting improves performance by removing the annotation bias on the semi-supervised learning dataset. Using class re-weighting for cross-entropy loss removes class bias and improves the performance of mAcc and mIoU by a large margin. Furthermore, jointly utilizing the sample and class weights achieves the best results in Table 4." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "type": "text", + "content": "Class Center Contrast Method. Table 5 shows the ablation study on the proposed class center contrast method. Contrastive loss utilizes inter-class and intra-class information and achieves better results than center loss used in [28]. Compared with only training contrastive loss with pseudolabels on unlabeled data, using pseudo-labels on both labeled and unlabeled data achieves better results. Further-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16789" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 102, + 69, + 492, + 133 + ], + "blocks": [ + { + "bbox": [ + 102, + 69, + 492, + 133 + ], + "lines": [ + { + "bbox": [ + 102, + 69, + 492, + 133 + ], + "spans": [ + { + "bbox": [ + 102, + 69, + 492, + 133 + ], + "type": "table", + "html": "
Cross entropy lossSample re-weightingClass re-weightingOAmAccmIoU
✓75.4148.1637.27
✓✓75.7448.9638.40
✓✓75.4352.0640.07
✓✓✓75.9753.5340.68
", + "image_path": "a32f4d62a56ee63264f1724813b1316e98741cd4edf88c634ee78c788460f4d3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 83, + 161, + 511, + 237 + ], + "blocks": [ + { + "bbox": [ + 121, + 141, + 471, + 152 + ], + "lines": [ + { + "bbox": [ + 121, + 141, + 471, + 152 + ], + "spans": [ + { + "bbox": [ + 121, + 141, + 471, + 152 + ], + "type": "text", + "content": "Table 4. Ablation study on class-balanced cross entropy loss. Bold indicates the best results " + }, + { + "bbox": [ + 121, + 141, + 471, + 152 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 121, + 141, + 471, + 152 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 161, + 511, + 237 + ], + "lines": [ + { + "bbox": [ + 83, + 161, + 511, + 237 + ], + "spans": [ + { + "bbox": [ + 83, + 161, + 511, + 237 + ], + "type": "table", + "html": "
Center lossContrastive lossPseudo labelGround truthOn labeled dataOn unlabeled dataOAmAccmIoU
✓✓✓74.0748.1337.34
✓✓✓75.2350.0639.29
✓✓✓✓75.2651.4239.43
✓✓✓✓✓75.9753.5340.68
", + "image_path": "3a3ef5b9cf4e13b3adf267b42001abaab364006405379d2ac79606baa42796f0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 53, + 274, + 282, + 337 + ], + "blocks": [ + { + "bbox": [ + 123, + 245, + 468, + 256 + ], + "lines": [ + { + "bbox": [ + 123, + 245, + 468, + 256 + ], + "spans": [ + { + "bbox": [ + 123, + 245, + 468, + 256 + ], + "type": "text", + "content": "Table 5. Ablation study on the class center contrast method. Bold indicates the best results " + }, + { + "bbox": [ + 123, + 245, + 468, + 256 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 274, + 282, + 337 + ], + "lines": [ + { + "bbox": [ + 53, + 274, + 282, + 337 + ], + "spans": [ + { + "bbox": [ + 53, + 274, + 282, + 337 + ], + "type": "table", + "html": "
MethodOAmAccmIoU
Random sample selection74.6849.3138.80
Simple sample selection74.7451.5740.42
Hard sample selection74.5751.1440.31
Feature embedding centers75.9753.5340.68
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MethodOAmAccmIoU
Within-image method73.3653.4840.03
Cross-image method75.9753.5340.68
", + "image_path": "e259d892fbe004a71ca134cd182697c5d7c50116bbad327954eaca1f14937489.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 472, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 687 + ], + "type": "text", + "content": "more, introducing the ground truth of labeled data to the training of contrastive loss can significantly improve performance. We also compare different sample selection strategies for contrastive learning. We select three contrastive samples for each class per image for a fair comparison. As shown in Table 6, leveraging high-confidence predicted samples from the unlabeled data for semi-supervised learning yields better results than employing uncertain samples. Nonetheless, samples with high-confidence predictions provide limited information for model learning, leading to only marginal enhancements. The proposed Class Center Contrast method involves both high-confidence and hard samples, achieving the best results. Besides, we compare within-image and cross-image contrastive learning results in Table 7. Cross-image method uses labeled and unlabeled images in a mini-batch and achieves better results, while the within-image method only uses local information of labeled or unlabeled images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "content": "Hyperparameter Tuning of Loss Weight. " + }, + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "content": " is to balance two loss terms in the formula (7). Table 8 shows the" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 340, + 274, + 512, + 337 + ], + "blocks": [ + { + "bbox": [ + 47, + 427, + 287, + 449 + ], + "lines": [ + { + "bbox": [ + 47, + 427, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 287, + 449 + ], + "type": "text", + "content": "Table 7. Results of within-image and cross-image contrastive learning. Bold indicates the best results " + }, + { + "bbox": [ + 47, + 427, + 287, + 449 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 427, + 287, + 449 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 340, + 274, + 512, + 337 + ], + "lines": [ + { + "bbox": [ + 340, + 274, + 512, + 337 + ], + "spans": [ + { + "bbox": [ + 340, + 274, + 512, + 337 + ], + "type": "table", + "html": "
Loss weightOAmAccmIoU
λ = 0.0575.0751.6240.15
λ = 0.0175.2651.4239.43
λ = 0.00575.9753.5340.68
λ = 0.00175.2753.8440.26
", + "image_path": "11eb0834942d54c4f2a712e19739ea1fba553cf61a5ca055604034830108765f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 345, + 545, + 366 + ], + "lines": [ + { + "bbox": [ + 306, + 345, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 306, + 345, + 545, + 366 + ], + "type": "text", + "content": "Table 8. Hyperparameter tuning of loss weight. Bold indicates the best results " + }, + { + "bbox": [ + 306, + 345, + 545, + 366 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 306, + 345, + 545, + 366 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "type": "text", + "content": "results using different loss weights " + }, + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "type": "text", + "content": ". We conclude that a large loss weight for " + }, + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cct}" + }, + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "type": "text", + "content": " reduces the model performance. In this work, we set " + }, + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\lambda = 0.005" + }, + { + "bbox": [ + 305, + 387, + 545, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 423, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 626 + ], + "type": "text", + "content": "The Number and Ratio of Labeled Images in SSL. We conduct a comparative analysis of the enhancement in accuracy resulting from the increase of unlabeled data. As shown in Figure 4, the utilization of a larger quantity of unlabeled data, specifically ten times the amount of labeled training data containing only 500 images, has been observed to result in a substantial improvement in accuracy. Meanwhile, the performance becomes unstable as the ratio between unlabeled and labeled images increases further because of the limited number of labeled images. As the amount of labeled data increased, using the unlabeled data, which is five times the amount of labeled data, can yield superior results compared to using just one time the amount of labeled data. Subsequently, the performance is relatively stable as the number of unlabeled data increases. Therefore, to balance the computational cost and improvement in accuracy, we use a ratio of 5:1 for unlabeled and labeled data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 635, + 533, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 533, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 533, + 647 + ], + "type": "text", + "content": "5.4. Examples of Land Cover Mapping in China" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "As an application of the proposed method, we produce large-scale land cover maps with 24 classes over 1 million " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{km}^2" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ". As shown in Figure 5, we compare our land cover mapping results with two existing public products produced by ESA [45] and Google [2]. 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Examples of Land Cover Mapping in China. The land cover products of ESA and Google are also generated from Sentinel-2 images but use different classification systems. In the black rectangles, our land cover results with fine-grained classes can provide more land cover information. In the red rectangles, our method recognizes the paddy field correctly, while the other two products classify it as cropland and water, respectively, due to the coarse classification system and the misleading spectral information of the paddy field." + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 400, + 289, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 289, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 289, + 653 + ], + "type": "text", + "content": "shows the results of an urban area located in the east of China, and that in the bottom row gives the results of a rural area located in the center of China. The land cover products of ESA and Google contain 11 and 9 classes, while our classification system includes 24 classes. From the black rectangles, the two comparison products mainly distinguish built areas, water, trees, and crops. Owing to the fine-grained classification system and the proposed class-aware SSL methods, our results can recognize more land cover categories, including industrial area, urban residential, rural residential, road, overpass, railway station, arbor forest, artificial meadow, irrigated field, bare land, lake, river, pond, and fish pond. Our land cover maps with fine-grained classes can provide more land cover information. Besides, from the red rectangles, our method recognizes the paddy field correctly, while the other two products classify it as cropland and water, respectively, due to the coarse classification system and the misleading spectral information of the paddy field. From the above qualitative comparison, our method provides land cover maps with fine-grained classes, significantly improving the land cover information." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 47, + 668, + 119, + 680 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 668, + 119, + 680 + ], + "spans": [ + { + "bbox": [ + 47, + 668, + 119, + 680 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "In this work, we propose a unified Class-Aware Semi-Supervised Semantic Segmentation approach for large-" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 400, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 547, + 521 + ], + "type": "text", + "content": "scale land cover mapping with fine-grained classes. To address the class-imbalance issue, we propose a class-aware unlabeled data selection method to build an SSL dataset more balanced towards minority classes. Then, we propose a Class-Balanced Cross Entropy loss, considering the annotation and class biases on the built SSL dataset. Moreover, we propose the Class Center Contrast method to jointly use the labeled and unlabeled data for training. Experimental results validate the effectiveness of our method in large-scale land cover mapping with fine-grained classes." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 563, + 408, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 408, + 577 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 408, + 577 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "This research was supported in part by the National Natural Science Foundation of China (Grant No. T2125006), Jiangsu Innovation Capacity Building Program (Project No. BM2022028), China Postdoctoral Science Foundation (Grant No. 2023M731871), the German Federal Ministry of Education and Research (BMBF) in the framework of the international future AI lab \"AI4EO - Artificial Intelligence for Earth Observation: Reasoning, Uncertainties, Ethics and Beyond\" (Grant No. 01DD20001), and Shuimu Tsinghua Scholar Project." + } + ] + } + ], + "index": 37 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16791" + } + ] + } + ], + "index": 38 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. 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Instead of existing efforts devoted to localizing tourist photos captured by perspective cameras, in this article, we focus on devising person positioning solutions using overhead fisheye cameras. Such solutions are advantageous in large field of view (FOV), low cost, anti-occlusion, and unaggressive work mode (without the necessity of cameras carried by persons). However, related studies are quite scarce, due to the paucity of data. To stimulate research in this exciting area, we present LOAF, the first large-scale overhead fisheye dataset for person detection and localization. LOAF is built with many essential features, e.g., i) the data cover abundant diversities in scenes, human pose, density, and location; ii) it contains currently the largest number of annotated pedestrian, i.e., 457K bounding boxes with ground-truth location information; iii) the body-boxes are labeled as radius-aligned so as to fully address the positioning challenge. To approach localization, we build a fisheye person detection network, which exploits the fisheye distortions by a rotation-equivariant training strategy and predict radius-aligned human boxes end-to-end. Then, the actual locations of the detected persons are calculated by a numerical solution on the fisheye model and camera altitude data. Extensive experiments on LOAF validate the superiority of our fisheye detector w.r.t. previous methods, and show that our whole fisheye positioning solution is able to locate all persons in FOV with an accuracy of $0.5\\mathrm{m}$ , within $0.1\\mathrm{s}$ .", + "bbox": [ + 75, + 318, + 473, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 744, + 209, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Accurate position finding of persons attracts growing interest from both research and industrial communities, since it plays a crucial role in numerous location-sensitive application scenarios (e.g., surveillance, smart home, public health). Nevertheless, due to the line-of-sight (LOS) issue, GPS is unreliable in interior spaces and urban canyon. To overcome", + "bbox": [ + 75, + 771, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d9da8daa5ab5af46460ee1950a50f23e4df131a028e1412294e5dd9b1422a0c5.jpg", + "image_caption": [ + "Figure 1: Person positioning using overhead fisheye camera: We detect humans on omnidirectional images and then project detects onto the real world coordinates to obtain physical locations. Compared with using perspective cameras, our fisheye camera based solution is favored in low cost, high accuracy, and fast speed." + ], + "image_footnote": [], + "bbox": [ + 506, + 277, + 885, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "such limitation, various alternative solutions are investigated. Signal based solutions, including Bluetooth [13] and WiFi [74], are popular, but they are easily interfered by changing environments and nearby human bodies [73]. A complementary stream of work is vision based; they typically make use of traditional cameras, RGBD cameras, or in-built smartphone cameras, and enjoy the advantage of reliable services. To get location information, visual positioning solutions usually refer to a pre-acquired 3D map or a geotagged database as the scene representation [63], or directly utilize the captured image to estimate the camera pose [39].", + "bbox": [ + 496, + 609, + 893, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although visual localization has been a hotspot issue for many years, existing efforts are mainly dedicated to urban place recognition or indoor camera localization, based on perspective cameras [63, 39, 62, 43]. None of them addresses person positioning by using overhead fisheye cameras, even though fisheye cameras are widely used in visual surveillance applications. One possible reason is the lack of accessible datasets, compounded by considerable costs in-", + "bbox": [ + 496, + 779, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "The first two authors contribute equally to this work.", + "bbox": [ + 93, + 875, + 380, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{2}$ Corresponding author: Wenguan Wang.", + "bbox": [ + 96, + 887, + 310, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19961", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "volved in data collection. In this article, we provide a large-scale overhead fisheye dataset, LOAF, for person detection and localization in both indoor and outdoor scenes.", + "bbox": [ + 76, + 90, + 468, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared with perspective cameras, overhead (top-view) fisheye cameras are promoted due to less occlusion among people and larger field of view (FOV) - allowing the coverage of a large space using a single, low-cost camera. Only few public datasets [21, 42, 24] provide top-view fisheye data. Unfortunately, they only cover quite few scenes and their people-box annotations do not adequately address the positioning challenge, negatively affecting location approximation (see §3.2 for detailed analysis). Differently, LOAF specifically targets at person localization in surveillance applications, and has the following appealing characteristics:", + "bbox": [ + 75, + 137, + 468, + 303 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Large-scale: LOAF is the largest in the filed, to our best knowledge. It consists of over 70 videos, with more than 43K frame images, 457K person-detection annotations as well as corresponding location information.", + "- High diversity: LOAF contains a wide variety of surveillance scenarios; it includes a total of 11 indoor and 40 outdoor scenes, and the data are captured at different times of day and cover different illumination conditions.", + "- Positioning-aware person-box annotation: LOAF offers radius-aligned human-box annotations. Compared with other person representations, i.e., head center [21], axis-aligned [60] or body-aligned box [42, 24], used in previous fisheye datasets, the radius-aligned box is promoted, as it fits well radially-oriented bodies [42], and, more importantly, it is better aware of the positioning problem." + ], + "bbox": [ + 76, + 306, + 468, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, we devise a person positioning system that first detects persons from raw fisheye images, and then calculates physical locations based on fisheye visual model and altitude information (see Fig. 1). Clearly, high-quality person detection is the crucial premise for precise localization using overhead fisheye cameras. Fisheye lenses provide large FOV, at the cost of strong radial distortion. This makes pedestrian detection in top-view fisheye images a much harder task, compared with using perspective cameras. Studies on overhead fisheye pedestrian detection are very scarce [60, 42, 51, 24, 64]; they rarely concern the link with person positioning, and many of them [60, 42] are even not trainable due to the lack of fisheye data. With our LOAF dataset, we develop a novel query based fisheye human detector. It explicitly exploits fisheye geometry by accommodating rotation equivariance into the matching between queries and human instances during network training. The insight here is intuitive: for a robust fisheye detector, rotation of a fisheye image should result in correspondingly rotated detections. In addition, our detection algorithm learns to predict radius-aligned person boxes, facilitating localization estimation.", + "bbox": [ + 75, + 537, + 468, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We test our fisheye person detection algorithm as well as our whole positioning system over LOAF. We find that our detector significantly outperforms previous methods, and", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "our full system delivers precise localization results. We also empirically show that our algorithm generalizes well on previous top-view fisheye person detection datasets [24, 65].", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 148, + 640, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accurate Positioning. GPS is the most popular system for outdoor localization. As it requires LOS between the satellites and the handset, GPS does not function well in urban canyons, indoors and basements [30, 26]. This triggered the development of alternative positioning solutions, following a multi-disciplinary approach. Concretely, there are two main schemes of the alternatives: signal-based and vision-based.", + "bbox": [ + 496, + 170, + 890, + 276 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Signal-based positioning systems typically lean on sound wave [50], geomagnetism [32], radio frequency (RF) [26, 74, 54, 13, 1], and infrared radiation (IR) [71], as well as different location determination techniques, such as TOA (time of arrival) [30] and RSS (received signal strength) [26]. The main challenge to signal-based systems is the sensitivity to environment changes, such as object moving, diffraction and reflection, which affect signal propagation [26].", + "bbox": [ + 496, + 277, + 890, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual data is another potential information source for precise localization. Since put forward [61], visual positioning has become a hot topic in robotics and computer vision. Some methods adopt a pre-built geo-tagged database or a 3D scene model, as the reference for camera location estimation [33, 77, 66, 78, 76]. Some others rely on recognizing some deployed coded targets [27, 59, 20, 31, 36], e.g., concentric rings, barcodes, colored dots, etc. Some recent ones utilize deep learning techniques to replace some components (e.g., image retrieval, descriptor matching) in traditional systems [4, 16], or regress the camera pose directly [39, 38, 7]. Though promising, existing visual positioning systems are mostly founded on perspective cameras.", + "bbox": [ + 496, + 400, + 892, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to the problem complexity, there is no persuasive solution for precise positioning yet, and hybrid schemes are often applied in practice. Fisheye cameras have advantage of providing wide FOV with low cost and reduced occlusion, while the research landscape is sparse for fisheye camera based localization [79, 21]. To foster research in this direction and facilitate practical deployment, we contribute the first overhead fisheye dataset, to our knowledge, that allows to conduct the task of person localization at large scale.", + "bbox": [ + 496, + 597, + 892, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep Learning based Visual (Camera) Localization. Regarding application scenarios, scholars in computer vision community are mainly aware of city-scale location recognition [2, 72, 58, 57] and indoor camera localization [5, 67]. Popular visual localization approaches can be divided as retrieval-based, regression-based, and structure-based, according to the camera pose estimation strategy. Retrieval-based methods [58, 3, 23, 75, 56] represent a scene as a database of geo-tagged photos and use geo-tag of the most relevant database photo as an approximation to the camera position [58]. Regression-based methods learn to encode", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19962", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the scene into a deep network and directly regress a 6DOF camera pose [39, 67, 38] from a captured image. Structure-based methods [6, 55, 29] pose the localization problem as a camera resection task [58]. They first represent scenes via 3D models and establish a set of 2D-3D matches, then recover the full camera pose by employing a PnP solver [34] inside a RANSAC [28] loop.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These visual positioning techniques seek to localize images captured by handheld devices [43, 11] or vehicle cameras [48] and demand pre-created geo-tagged databases or 3D maps. And they work on an active mode – users need to carry the cameras. Differently, we address person localization in surveillance scenarios, by using stationary, overhead fisheye cameras. This yields a passive, low-cost scheme, where the localization is completed by a numerical solution on the fisheye model fused with altitude information. Thus our scheme faces a different challenge, i.e., conducting robust person detection from non-rectilinear fisheye images. Overall, our scheme fills the gap left by conventional studies and is complementary to existing positioning systems.", + "bbox": [ + 75, + 199, + 468, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Person Detection in Overhead Fisheye Images. As a canonical subproblem of object detection, pedestrian detection has long received great interest owing to its broad applications such as intelligent surveillance and autonomous vehicles [12, 8]. By contrast, people detection in overhead fisheye images has been studied much less, due to the absence of such datasets. Moreover, adapting standard pedestrian detectors to top-view fisheye cameras is difficult [15]: First, the appearance of people in fisheye images is arbitrary-oriented, while in perspective images, people typically appear upright. Second, people suffer from severe geometric distortions, particularly in the fisheye image's periphery.", + "bbox": [ + 75, + 397, + 468, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Faced with the above challenges, early attempts make use of handcrafted features (e.g., HOG, LBP) as well as standard pedestrian detectors with slight modifications to account for fisheye geometry [40, 14, 17, 69]. The common approach is dewarping fisheye images [14] or features [40] so as to approximate normal people' appearances from the deformed ones. Though this simplifies the classification of features, approximation errors are inevitable, causing performance degradation [64]. Later, a few CNN-based fisheye detectors were developed. Some of them are training-free. For example, [60] runs standard YOLOv2 [52] on dewarped versions of overlapped windows extracted from a fisheye image. Li et al. [42] rotate a fisheye image in $15^{\\circ}$ increments, and apply off-the-shelf YOLOv3 [53] only to the top-center region of each rotated image, where people usually appear upright. Some more recent methods are trainable: [64] trains YOLOv2 with rotated perspective images so as to handle omnidirectional images without test-time transformation; [24] trains YOLOv3 with human-aligned boxes.", + "bbox": [ + 75, + 580, + 470, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although many prior arts [60, 42, 64] allowing to detect persons without any fisheye training data, they require a cer-", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tain amount of computation time for post-processing: [60] carries out detection in multiple perspective images dewarped from one omnidirectional image; [42] applies YOLOv3 24 times to each fisheye image; [64] needs a grouping process to eliminate numerous redundant results, caused by a rotation-invariant training strategy. Hence, the utility of previous methods is limited in the context of visual positioning. Our analysis in §3.2 sheds light on the weaknesses of human representations adopted by existing fisheye detectors (e.g., head center [21], horizontal or body-aligned box [60, 42, 24]) in regard to localization. Thus we supply our large-scale dataset with positioning-aware person-detection annotation. As a result, our human detector can benefit from end-to-end, fisheye visual pattern learning and output radius-aligned body-boxes for precise positioning. Further, by regularizing the learning of image representations and instance queries with rotation equivariance, our algorithm naturally addresses the omnidirectional nature of fisheye images, yet using standard detection network architecture designed for perspective images.", + "bbox": [ + 496, + 90, + 893, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. LOAF Dataset", + "text_level": 1, + "bbox": [ + 500, + 387, + 648, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Dataset Acquisition", + "text_level": 1, + "bbox": [ + 500, + 409, + 686, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first describe how our fisheye images are collected. Apparatus and Technical Specifications. A TL-IPC59AE fisheye camera with $1.1\\mathrm{mm}$ focal length is adopted for data recording. It has a wide FOV, reaching the full circle in the horizontal plane and $180^{\\circ}$ in the vertical plane. This offers a clear advantage in reducing deployment cost – installing just one fisheye camera instead of multiple conventional cameras to monitor the same region. However, the severe geometric distortions introduced prevent the use of standard detectors, which are designed for conventional cameras [8]. Data Capturing. The fisheye camera is mounted on the ceiling (indoors) or poles (outdoors), $2.5\\sim 4.0\\mathrm{m}$ from the ground with $200\\sim 300\\mathrm{m}^2$ FOV. Considering the factors such as scenario diversity, pedestrians density and weather condition, we capture 110 fisheye image sequences in 80 realistic scenarios as the raw data pool. The recorded sequences span 14 hrs; the image resolution is $2952\\times 2952$ pixels, and the frame rate is $10\\sim 20$ fps. Eventually, 42,942 images, sampled at 1 fps, are collected to construct our LOAF dataset.", + "bbox": [ + 496, + 430, + 890, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Dataset Annotation", + "text_level": 1, + "bbox": [ + 500, + 728, + 684, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We next describe how our fisheye images are annotated. Person Detection. As the performance of localization relies critically on the quality of person detections, significant effort should be spent on the fisheye person-detection annotation. Some human-detection representations were explored in previous datasets: [21] labels the center point of each human head; [42, 24] opt for human-aligned person-boxes. However, these representations have several shortcomings, especially with regards to the localization task. First, they suffer from some inherent limitations. The point-based rep", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19963", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/0a223e2c69ab10176ea19643a29696846404e75a7d4986b7ede427712ae801ed.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Dataset#Scene#Video#Image#PeopleMax ResolutionFOV (m2)AnnotationFPS
IndoorOutdoorTotalAvg.MaxPeople DetectionLocationAttribute
PIROPO [21]2027----800×600<50Head Center10
HABBOF [42]2045,83720,4663.552,048×2,048<36Human-aligned box12~30
MW-R [24]60198,75222,8252.661,488×1,488<36Human-aligned box15
CEPDOF [24]50825,504173,0736.8132,048×2,048<36Human-aligned box1~10
WEPDTOF [65]1401610,54493,3638.9352,592×1,944<36Human-aligned box1~10
LOAF11397442,942457,76210.5652,952×2,952200~300Radius-aligned box✓✓10~20
", + "bbox": [ + 91, + 82, + 887, + 185 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1: Overhead fisheye datasets comparison (§3.4). LOAF is the largest in terms of the total number of pedestrian and scene categories.", + "bbox": [ + 76, + 186, + 893, + 202 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e8ecf0dabec41382c1f4818a5fcc12928e67a8a026178700fedcc287896a15a8.jpg", + "image_caption": [ + "Figure 2: Human annotation comparison for visual positioning (§3.2). Previous methods typically use the detected human head [21] ( $\\bullet$ ) or the center ( $\\bullet$ ) of human-aligned body-box ( $\\langle \\rangle$ ) [42, 24] to determine the physical location $P$ , bringing positioning errors (i.e., $PP_{1}$ , $PP_{2}$ ). We instead leverage the radius-aligned box ( $\\square$ ) as human representation. The midpoint ( $\\bullet$ ) of side $AB$ , i.e., the closest point to the image center on the radius-aligned box, better corresponds to the human actual position." + ], + "image_footnote": [], + "bbox": [ + 117, + 210, + 426, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "resentation is not applicable in other analysis tasks (e.g., re-identification, attribute recognition); the human-aligned box has ambiguity [10, 68] – the ground-truths of human-aligned boxes are not uniquely determined [24]. Second, and most important, these human-detection representations cannot meet the need of precise localization. Clearly, based on the fisheye camera model, one can project 2D detections on the 3D world for localization. However, the center of human head or of human-aligned box is not the exact placement occupied by human on the image plane, causing errors to estimations of human physical position (see Fig. 2).", + "bbox": [ + 75, + 507, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We instead label each person through a radius-aligned rectangular box. Such representation is favored as it: i) allows unique groundtruth box assignment; ii) fits well radially-oriented human bodies presented in fisheye images; and iii) better corresponds to the actual position of human on the image plane, facilitating physical localization. Notably, although the radially-oriented box constraint was explored in a prior fisheye detector [42], there is no previous datasets provide such kind of annotation, neither is there any literature points out the advantage of such representation in localization. Finally, around 457K human box annotations are obtained. High-quality annotation is ensured via a rigorous quality check, conducted by highly skilled reviewers.", + "bbox": [ + 75, + 674, + 470, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Person Localization. For each scene, a $10\\mathrm{m}$ ruler (with $0.05\\mathrm{m}$ accuracy) is placed on the ground, and one end of the", + "bbox": [ + 76, + 869, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e3f4fafde1e206055214c00a1cb3f0019fe43878e6a4b6156eb82f5574ed418b.jpg", + "image_caption": [ + "(a)", + "Figure 3: Calibration for groundtruth person location annotation. (a) Ground makers (with $0.05\\mathrm{m}$ precision). (b) Top-view fisheye image capture for calibration. See §3.2 for details." + ], + "image_footnote": [], + "bbox": [ + 521, + 210, + 666, + 358 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9af3d095353cd10aa67ed5028cc2c96b6e9c92936d06344f43b061731640c848.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 681, + 210, + 870, + 358 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ruler is directly under the fisheye lens (cf. Fig. 3 (a)). We take a fisheye picture and use this marked picture as the calibration for all the dataset images recorded in this scene (cf. Fig. 3(b)). Finally, for each annotated human, the physical location, at sub-decimeter precision, is provided (cf. Fig. 4).", + "bbox": [ + 498, + 430, + 890, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Scene Attribute. To enable in-depth analysis, each image is annotated with multiple attributes, including day/night, outdoor/indoor, and sunny/rain/foggy/snow.", + "bbox": [ + 498, + 506, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Dataset Design", + "text_level": 1, + "bbox": [ + 500, + 559, + 650, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then list several key aspects of our dataset design.", + "bbox": [ + 519, + 580, + 872, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Privacy Protection. To protect personal information, we apply the gaussian filter to blur all the visible facial regions in our dataset, and conduct experiments on the blurred data. Dataset Splits. LOAF contains 29,569 training, 4,600 validation, and 8,773 testing images (approximately 7 train, 1 val, and 2 test). Moreover, to better evaluate models' generalization ability, LOAF is split into five sets: train (7/28 indoor/outdoor scenes, 29,569 images), val seen (1/2 indoor/outdoor scenes, 1,700 images), val unseen (2/3 indoor/outdoor scenes, 2,900 images), test seen (2/3 indoor/outdoor scenes, 2,774 images), test unseen (2/8 indoor/outdoor scenes, 5,999 images). There are no overlapping scenes between unseen and train sets.", + "bbox": [ + 498, + 595, + 890, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dataset Accessibility. Only the desensitized version of our dataset will be released online, under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License [19].", + "bbox": [ + 498, + 792, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Dataset Features and Analysis", + "text_level": 1, + "bbox": [ + 500, + 845, + 766, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we present statistic analysis of LOAF in comparison with existing overhead fisheye datasets [21, 42, 24].", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19964", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3874faf83a1f87cb98734690d995bab419a5c4bb1b11818c892a2d4d0c5ea112.jpg", + "image_caption": [ + "playground | winter | noon", + "(a) Our proposed LOAF" + ], + "image_footnote": [], + "bbox": [ + 81, + 78, + 222, + 185 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/332e247dd4cce7a72e8f56e8da89acb758c6b3780779aaf43250a19015b116b1.jpg", + "image_caption": [ + "hall | fall | afternoon" + ], + "image_footnote": [], + "bbox": [ + 222, + 85, + 352, + 185 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0dd1005fd968575b6b564258bbd47967bdea814f2b54863d087f91051fbd04f7.jpg", + "image_caption": [ + "street | spring | morning" + ], + "image_footnote": [], + "bbox": [ + 352, + 84, + 480, + 185 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bb593de8269c91711ec122fba21d20b3c712e93d2109b6d365dc78eb87390715.jpg", + "image_caption": [ + "(b) PIROPO [21]" + ], + "image_footnote": [], + "bbox": [ + 486, + 78, + 596, + 185 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4c39d8656378ebc5b2543cd9cef2012dc6d391329b153e7985a695ed7d3edc11.jpg", + "image_caption": [ + "(c) HABBOF [42]" + ], + "image_footnote": [], + "bbox": [ + 604, + 78, + 741, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/32395c7927e4611b23622ac2de31d9ebe2025fcce7026c2ffac12a12b84ee047.jpg", + "image_caption": [ + "(d) CEPDOF [24]" + ], + "image_footnote": [], + "bbox": [ + 751, + 78, + 890, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f0a4041d8b3e2c825a8308c3dd8591271ef49dd0be458a169b8a4a5b487e57d6.jpg", + "image_caption": [ + "Figure 4: Example images from different datasets ( $\\S 3.2-\\S 3.4$ ). Prior datasets [21, 42, 24] are restricted to few indoor scenes with person detection annotation only, i.e., head center $(\\bullet)$ or human-aligned box $(\\square)$ . In contrast, LOAF covers challenging indoor and outdoor scenes with human detection, localization and scene attribute annotations. The person-detection annotation is given as the radius-aligned box $(- \\square)$ , which is more suitable for localization. For better visualization, we only present location ground-truths for some of persons.", + "(a) Person scale" + ], + "image_footnote": [], + "bbox": [ + 78, + 277, + 254, + 426 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/72e18a3c6c6a1f9edf9be646ab56ad26f35e65015842e43e9b4f596851fb8106.jpg", + "image_caption": [ + "(b) Person locations" + ], + "image_footnote": [], + "bbox": [ + 267, + 277, + 452, + 349 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/327c7873cd49ad6ddcd326dc87d87ad1e4a0e473f74ebe418369c540a32c6724.jpg", + "image_caption": [ + "(c) Person density", + "Figure 5: Dataset Statistics (§3.4): We summarize LOAF with the distribution of (a) person scale (area in pixel), (b) person locations (horizontal distance between human and the fisheye lens in the real world), and (c) person density (number of person per image)." + ], + "image_footnote": [], + "bbox": [ + 267, + 359, + 452, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LOAF distinguishes itself from three aspects (cf. Table 1):", + "bbox": [ + 75, + 506, + 460, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Large-scale: LOAF has 42,942 fisheye images with more than 457K person boxes. Moreover, LOAF data are captured by an advanced fisheye camera, which is capable of covering a larger area $(200\\sim 300\\mathrm{m}^2)$ with higher pedestrian density (2~65 persons per scene, 10.5 in average). This makes LOAF the largest overhead fisheye dataset in terms of the total number of pedestrian and scene categories.", + "bbox": [ + 75, + 521, + 468, + 627 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "High Diversity: Existing datasets limit in data diversities, i.e., only containing very few indoor scenes (2~14) and completely missing outdoor scenarios (cf. Fig. 4). In contrast, LOAF involves 51 realistic scenes, including 11 indoor scenes (e.g., lab, office, library, classroom) and 40 outdoor scenes (e.g., street, playground, parking lot, square). The recorded data cover four seasons under different illumination (e.g., morning, noon, afternoon) and weather (e.g., sunny, rain, snow) conditions, and involve vast variance of human pose (e.g., walking, standing, and sitting), scale, location, and density (cf. Fig. 5). Thus our dataset better reflects the distribution in real-world surveillance scenarios.", + "bbox": [ + 75, + 628, + 468, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Rich and Positioning-aware Annotation: LOAF is provided with rich ground-truths for detection, localization, and scene attribute, which lays a solid foundation for fisheye camera based human-centric analysis. Hence, as demonstrated in §3.2, the radius-aligned human-box representation is adopted during our annotation. Compared with human-", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "head center based point annotation [21] and human-aligned person-boxes [42, 24] used in previous datasets, radius-aligned human-boxes are more suitable for the position task.", + "bbox": [ + 496, + 275, + 890, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Our Approach", + "text_level": 1, + "bbox": [ + 498, + 329, + 648, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our overhead fisheye camera based person localization solution comprises two parts. The former computes 2D detections that locate the people on the image plane (§4.1). The latter converts the 2D detections to 3D-world coordinates, obtaining the physical location of the people (§4.2).", + "bbox": [ + 496, + 351, + 890, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Overhead Fisheye Person Detection", + "text_level": 1, + "bbox": [ + 498, + 431, + 807, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Core Idea: Rotation Equivariance. One of the reasons for the tremendous success of CNNs is their equivariance to horizontal and vertical shifts and the resulting invariance to local deformations [41, 25]. This stimulates a line of efforts to learn robust representations equivariant to generic types of transformations [35, 18, 70]. Formally, a representation $f$ is said to be equivariant with a geometric transformation $g$ (e.g., cropping, flipping) for an input (image) $I$ if:", + "bbox": [ + 496, + 452, + 892, + 573 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf (g (I)) \\approx g (f (I)). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 578, + 890, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "That is to say, the output representation $f(I)$ is changed in the same way as the transformation $g$ imposed to the input $I$ .", + "bbox": [ + 496, + 598, + 890, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this work, we devise a query-based fisheye person detector that exhibits $360^{\\circ}$ -rotational equivariance through an elaborately designed training protocol. Our key insight is derived from the omnidirectional nature of this task: if one rotates the input fisheye image by an arbitrary angle, then the outputs of a robust fisheye detector should change accordingly. We thus design a rotation equivariant training strategy, which forces the matching between object queries and image representations to be equivariant against $360^{\\circ}$ -rotations. In this way, the rotational symmetry of omnidirectional images is explicitly addressed, without architectural modification of standard detectors developed for perspective images. Rotation Equivariant Training for Query-based Fisheye Detection. As shown in Fig. 6, our fisheye detector is built upon DETR [9], promoted by a rotation equivariant training strategy. Basically, DETR conducts detection in a query-based fashion. Denote $\\mathcal{F}$ as a feature encoder that extracts representation $I$ of image $I$ , and $\\kappa$ as a query creator", + "bbox": [ + 496, + 628, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19965", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/84ddbf217cfe1d9f63999d77f1d13c59b4542d4725a8091df5c551f2f2bd612a.jpg", + "image_caption": [ + "Figure 6: Our rotation equivariant training strategy for query-based fisheye person detection (§4.1). For equivariant training, object queries $\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N$ created for rotated image $g^r(I)$ and the rotated representation $g^r(I)$ are fed into the decoder $\\mathcal{D}$ ; the rotated ground-truths $\\{\\pmb{b}_{\\ell(n)}^{g^r}\\}_{n=1}^N$ are set as the training targets." + ], + "image_footnote": [], + "bbox": [ + 78, + 80, + 472, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "that outputs a set of $N$ object-aware descriptors $\\{\\pmb{q}_n\\}_{n=1}^N$ from $\\pmb{I}$ . DETR employs $\\{\\pmb{q}_n\\}_{n=1}^N$ as queries to retrieve target objects from $\\pmb{I}$ :", + "bbox": [ + 75, + 338, + 468, + 385 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\hat {\\boldsymbol {b}} _ {n} \\right\\} _ {n = 1} ^ {N} = \\mathcal {D} (\\boldsymbol {I}, \\left\\{\\boldsymbol {q} _ {n} \\right\\} _ {n = 1} ^ {N}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 388, + 468, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\pmb{I} = \\mathcal{F}(I)$ , $\\{\\pmb{q}_n\\}_{n=1}^N = \\kappa(\\pmb{I})$ , and $\\mathcal{D}$ refers to the Transformer decoder which formulates the object-query matching process via neural cross-attention computation. $\\{\\hat{\\pmb{b}}_n\\}_{n=1}^N$ are the set of predicted parameterized object bounding boxes.", + "bbox": [ + 76, + 416, + 468, + 478 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our rotation equivariant training further encourages robust object-query matching which is equivariant against rotations. First, given an input rotation transformation $g^r$ , a robust fisheye detector is desired to be able to extract rotation-equivariant representation. Analogous to Eq. 1, we have:", + "bbox": [ + 75, + 479, + 468, + 554 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} \\left(g ^ {r} (I)\\right) \\approx g (\\mathcal {F} (I)) = g ^ {r} (\\boldsymbol {I}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 559, + 468, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Also, it is reasonable to assume that the final output of a robust fisheye detector should be changed in the same way to the rotation $g^{r}$ applied to the input fisheye image $I$ :", + "bbox": [ + 75, + 579, + 468, + 625 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {b} _ {\\ell (n)} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N} \\approx \\mathcal {D} \\left(\\boldsymbol {I} ^ {g ^ {r}}, \\left\\{\\boldsymbol {q} _ {n} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 631, + 468, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $I^{g^r}$ indicates the feature of rotated image $g^{r}(I)$ , i.e., $\\pmb{I}^{g^{r}} = \\mathcal{F}(g^{r}(I))$ . Similarly, $\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N$ denote the object queries derived from $g^{r}(I)$ , i.e., $\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N = \\kappa(I^{g^r})$ . $\\{\\pmb{b}_{\\ell(n)}^{g^{r}}\\}_{n=1}^N$ are the rotated groundtruth bounding boxes, where $\\ell(n)$ returns the groundtruth index for $n$ -th query.", + "bbox": [ + 76, + 660, + 468, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Considering Eq.3 and Eq.4, we can have: $\\{\\pmb{b}_{\\ell(n)}^{g^r}\\}_{n=1}^N \\approx \\mathcal{D}(g^r(\\pmb{I}), \\{\\pmb{q}_n^{g^r}\\}_{n=1}^N)$ . Hence our rotation equivariant training objective is given as:", + "bbox": [ + 76, + 739, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r o t a t - e q u i}} = \\mathcal {L} _ {\\det } \\left(\\left\\{\\boldsymbol {b} _ {\\ell (n)} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}, \\mathcal {D} \\left(g ^ {r} (\\boldsymbol {I}), \\left\\{\\boldsymbol {q} _ {n} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}\\right)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 797, + 468, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here $\\mathcal{L}_{\\mathrm{det}}$ is the standard detection loss in DETR [9]. As such, the rotation equivariance properties for both fisheye representation $\\mathcal{F}$ (cf. Eq.3) and the query-based detection prediction $\\mathcal{D}(\\boldsymbol {I},\\{\\pmb {q}_n\\}_{n = 1}^N)$ (cf. Eq.4) are sought in a single training target. This also allows us to effortlessly adapt standard", + "bbox": [ + 76, + 824, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d9515f35afae0c94c683b1ac86271a358c47042b91c37bf32e6d1296edf330e5.jpg", + "image_caption": [ + "Figure 7: Our fisheye camera model based person localization (§4.2). Here $\\pmb{p}$ and $\\pmb{p}'$ denote the projection point of the distortion point $P$ by fisheye lens and normal perspective lens, respectively." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 741, + 252 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DETR to our omnidirectional detection setting. Note that our rotation equivariant training differs from rotational data augmentation technique which only views rotated images as individual training samples (see §5.4 for detailed experiments).", + "bbox": [ + 498, + 267, + 890, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. 2D-3D Projection based Person Localization", + "text_level": 1, + "bbox": [ + 498, + 337, + 874, + 352 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "General Fisheye Camera Model. The perspective projection of a normal pinhole camera can be written as $r = f \\tan \\theta$ , where $r$ indicates the projection distance between the principal point and the image point, $f$ is the focal length, and $\\theta$ is the angle between the incident ray and the camera's optical axis. However, fisheye lens does not follow this perspective projection model [49], as the FOV equals to $180^{\\circ}$ (cf. Fig. 7). Fortunately, the image formation of different kinds of fisheye lenses can be approximated by a general polynomial projection model [37], i.e.,", + "bbox": [ + 496, + 359, + 890, + 511 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nr (\\theta) = \\sum_ {i = 1} ^ {n} k _ {i} \\theta^ {2 i - 1}, \\quad n = 1, 2, 3, 4, \\dots \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 520, + 890, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "High distortions can be handled well when $n = 5$ [37]. The coefficients $k_{s}$ can be obtained from camera calibration.", + "bbox": [ + 496, + 549, + 890, + 579 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2D-3D Projection. Given a detected human location point $\\pmb{p} = (u,v)^{\\top}$ in the fisheye image pixel coordinate system, our target is to calculate its 3D location $\\pmb{P} = (X,Y,Z)^{\\top}$ in the camera coordinate system, where $Z$ is the altitude of the fisheye camera and primarily known. To do so, one can first calculate $r$ as: $r = \\sqrt{(x^2 + y^2)}$ , where $x = (u - u_0) / f$ and $y = (v - v_0) / f$ , and $(u_0,v_0)^{\\top}$ are the coordinates of the principal point in the fisheye image. Then $\\theta$ can be obtained by solving Eq. 6 using a numerical means [37]. With the altitude $Z$ of the camera, the actual location $(X,Y)^{\\top}$ is given as:", + "bbox": [ + 496, + 580, + 890, + 742 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\binom {X} {Y} = Z \\binom {\\tan \\theta \\cos \\phi} {\\tan \\theta \\sin \\phi}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 739, + 890, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\phi = \\arctan (y,x)$ refers to the polar angle, which is shared by both $\\pmb{p}$ and $\\pmb{P}$ .", + "bbox": [ + 496, + 780, + 888, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It can be seen that precise determination of the person location point $\\pmb{p}$ on the image plane is vital for estimating the corresponding physical position $\\pmb{P}$ . However, most previous approaches, restricted to axis-aligned [79, 60] or person-aligned [24] human-box representation, use the center of the detection box to approximate $\\pmb{p}$ . Few excep", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19966", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d9366d37d95e9c6516309e1b7688079db46eddb141649ec873cb7425d391972c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodvaltestFPS↑
mAP↑AP50↑AP75↑APn↑APm↑APf↑APseen↑APunseen↑mAP↑AP50↑AP75↑APn↑APm↑APf↑APseen↑APunseen↑
Seide et al. [60]21.859.87.632.828.52.323.219.520.258.27.132.228.33.922.418.910.2
Li et al. [42]28.563.320.146.824.21.333.829.327.265.221.347.224.81.331.827.60.6
Tamura et al. [64]34.872.127.751.738.88.738.832.934.272.828.753.737.36.539.533.210.2
RAPiD [24]40.377.934.855.341.99.244.737.639.277.935.454.840.17.944.237.38.4
Ours47.482.648.464.154.314.150.845.746.281.147.366.153.512.649.344.912.1
", + "bbox": [ + 91, + 83, + 883, + 176 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cea33104a3275bb7c6dee67b760a6eeed7d43e0b6fa2c50010e32121d3523418.jpg", + "table_caption": [ + "Table 2: Person detection results on val and test sets of LOAF (§5.2)." + ], + "table_footnote": [], + "table_body": "
MethodmAP↑AP50↑AP75↑Precision↑Recall↑F-Score↑
Seide et al. [60]20.950.610.280.639.553.0
Li et al. [42]34.275.728.686.365.474.4
Tamura et al. [64]29.361.023.488.851.265.0
RAPiD [24]39.385.426.089.278.783.6
Ours47.288.538.290.387.688.9
", + "bbox": [ + 88, + 202, + 475, + 282 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tions [21], built on point-based human representation, treat the center of the detected human head as $\\pmb{p}$ . However, they suffer from a similar issue as the human head center is even often far from the exact position $\\pmb{p}$ human stand on, w.r.t. the image plane. Instead, with our radius-aligned human-box representation, the closest point to the principal point on the bounding box better corresponds to $\\pmb{p}$ .", + "bbox": [ + 75, + 310, + 468, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 425, + 294, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network Architecture. Our fisheye person detector is built upon DAB-DETR [45], a prevalent variant of DETR [9] but converges much faster. Swin-T [46] is utilized as the backbone. For our LOAF with radius-aligned person boxes, the output of our detector is a 4D vector $\\pmb{b} \\in [0,1]^4$ that parameterizes 2D center coordinates, height, and width. Note that, for traditional fisheye detection datasets like [24, 65] with arbitrary-oriented person box annotations, an extra output dimension is needed for rotation angle regression.", + "bbox": [ + 75, + 448, + 468, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training Objective. Our fisheye person detector is end-to-end trained by jointly optimizing the vanilla detection loss used in DETR [9, 45] (referred as $\\mathcal{L}_{\\mathrm{Det}}$ ) and our proposed rotation-equivariant constraint (i.e., $\\mathcal{L}_{\\mathrm{rotat - equi}}$ in Eq. 5):", + "bbox": [ + 75, + 585, + 468, + 646 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {d e t}} + \\lambda \\mathcal {L} _ {\\text {r o t a t - e q u i}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 652, + 468, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where the coefficient $\\lambda$ is empirically set to 0.5.", + "bbox": [ + 75, + 674, + 393, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training. Our fisheye detector is trained with a batch size of 8 for 50 epochs, where the AdamW [47] optimizer is employed with base learning rate 2e-4 and decayed by 0.1 at epoch 40. The remaining hyper-parameters are determined following [64, 24]. Specifically, we initialize backbones with ImageNet [22] pre-trained weights and adopt standard data augmentation techniques, i.e., color jitter, horizontal flip, and random scaling, with a base training size of $608 \\times 608$ . For CEPDOF [24] and WEPDTOF [65], we use a batch size of 128 and pre-train the detector on COCO [44] for 50 epochs to prevent over-fitting, as in [24, 65]. For the computation of our rotation-equivariant loss $\\mathcal{L}_{\\mathrm{rotat - equi}}$ , the training images are rotated by a degree randomly sampled from 0 to 360. Our detector is implemented in PyTorch and trained on eight", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2fa67e3ee0acaec53ca67bbf1ddee0fd7571e712b6346cf3d20f534fee02d67f.jpg", + "table_caption": [ + "Table 3: Person detection results on CEPDOF [24] (\\$5.2)." + ], + "table_footnote": [], + "table_body": "
MethodmAP↑AP50↑AP75↑Precision↑Recall↑F-Score↑
Seide et al. [60]16.139.49.070.938.650.0
Li et al. [42]25.269.930.281.464.572.0
Tamura et al. [64]28.859.824.277.052.462.4
RAPiD [24]37.772.026.873.367.870.4
Ours45.885.636.684.974.679.8
", + "bbox": [ + 511, + 202, + 898, + 282 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4: Person detection results on WEPDTOF [65] (\\$5.2).", + "bbox": [ + 511, + 285, + 879, + 299 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "NVIDIA Tesla V100 GPUs with a 32GB memory per-card. Inference. Once trained, our fisheye detector can be directly applied for locating persons on the omnidirectional image plane. After that, the physical locations of the detected persons can be easily obtained through the numerical solution described in §4.2. For fisheye person detection, we follow prior work [60, 42, 64, 24] to use $1024 \\times 1024$ input resolution without any test-time augmentation or post-processing. Testing is conducted on a single NVIDIA V100 GPU with 16 GB memory.", + "bbox": [ + 496, + 311, + 890, + 463 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 500, + 474, + 624, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 497, + 689, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation Protocol. On the top of LOAF, we conduct experiments for fisheye based person detection and localization. Following the dataset splitting (cf. §3.3), performance are reported on seen and unseen scenes, respectively, for both val and test sets. This allows us to assess the generalization ability over different surveillance scenarios. For comprehensive study, we further report person detection performance on two existing fisheye datasets, CEPDOF[24] and WEPDTOF[65]. Note that localization cannot be test since [24, 65] only provide person bounding box annotations. Evaluation Metrics. For fisheye person detection, we follow COCO [44] to report the mean average precision (mAP) for IoU $\\in$ [0.5:0.05:0.95]. We also employ AP $_{50}$ and AP $_{75}$ for further analysis. For fisheye person localization, we measure positional error (PE) in meters, i.e., Euclidean distance of calculated position and ground-truth position, as the conventions in visual localization [43, 58, 73, 79]. For detailed evaluation, on our LOAF, we report performance w.r.t. horizontal distance between human and the fisheye lens, i.e., near (0~10 m), middle (10~20 m), and far (larger than 20 m). Hence we have AP $_{n,m,f}$ and PE $_{n,m,f}$ accordingly.", + "bbox": [ + 496, + 518, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Performance on Person Detection", + "text_level": 1, + "bbox": [ + 500, + 845, + 792, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "LOAF. We first report the person detection performance on LOAF. Specifically, four recent deep learning based fisheye", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19967", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/09880f0396cde8565da3ece75e8f2537fa4beb87f3b4b85c1c5032add3283d97.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodvaltest
mPE↓PEn↓PEm↓PEf↓PEseen↓PEunseen↓mPE↓PEn↓PEm↓PEf↓PEseen↓PEunseen↓
Seide et al. [60]1.2980.5611.3323.1091.2061.3821.3210.7061.3093.4821.3061.386
Li et al. [42]0.8980.5020.8712.6500.8320.9620.9130.5430.8842.7800.9040.998
Tamura et al. [64]0.7550.4290.7361.8620.7090.8210.7780.4710.8262.1600.7240.836
RAPiD [24]0.6740.4260.6231.4030.6250.7570.6820.4610.6641.4450.6380.776
Ours0.3680.1440.3630.7750.3180.4020.3740.1480.3750.8190.3260.398
", + "bbox": [ + 91, + 88, + 885, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "person detectors [60, 42, 64, 24] are involved for comparison. Among them, [60, 42] are training-free, thus their scores are obtained by directly running the algorithms on the val and test data. As [64, 24] are trainable methods, we first train them on the train set of LOAF following their official setups, and then report the scores on the val and test sets. Quantitative comparison results are presented in Table 2. Some essential observations are as follows:", + "bbox": [ + 75, + 209, + 468, + 329 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Our fisheye person detector significantly outperforms existing methods across all the metrics. For example, our detector provides a considerable performance gain in mAP, i.e., $7.1\\%$ and $7.0\\%$ higher than the second best, RAPiD [24], on the val and test sets, respectively.", + "- Our detector not only handles nearby persons but also approaches distant targets well. Specifically, for the targets at $10\\sim 20\\mathrm{m}$ away from the fisheye lens, our performance gain over other methods is more significant than the improvement reported with the persons at $0\\sim 10\\mathrm{m}$ distance.", + "- Our detector also yields small performance gap between the seen and unseen scenes (e.g., $49.3 \\rightarrow 44.9$ in terms of mAP), validating our good generalizability.", + "- For those persons at very far distance ( $>20\\mathrm{~m}$ ), our algorithm, though still giving higher scores than other competitors, suffers from great performance degradation. This sheds light on the direction of our future efforts." + ], + "bbox": [ + 76, + 335, + 467, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "CEPDOF [24]. CEPDOF contains eight videos with 25,504 frames in total. Following the official setup, we train our fisheye person detector on HABBOF [42] and MW-R [24] datasets, and report performance on CEPDOF. As shown in Table 3, our fisheye detector delivers state-of-the-art performance: it significantly outperforms RAPiD [24], the current top-leading algorithm, by $7.9\\%$ in terms of mAP.", + "bbox": [ + 75, + 595, + 467, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "WEPDTOF [65]. WEPDTOF has 16 videos with 10,544 frames in total. Following the official setup, we use HAB-BOF [42], MW-R [24], and CEPDOF [24] for training and WEPDTOF for testing. Table 4 summarizes the results. Impressively, our detector greatly suppresses all the other competitors across all the evaluation metrics.", + "bbox": [ + 75, + 700, + 467, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Performance on Person Localization", + "text_level": 1, + "bbox": [ + 76, + 801, + 390, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Then we study the person localization performance on LOAF. None of previous fisheye person detectors [60, 42, 64, 24] are aware of the task of person localization. We therefore follow the common practice [79, 21] in the field of visual localization: for [60, 42, 64, 24], we project", + "bbox": [ + 75, + 825, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6e87ce99dda350089a3e9385459bdfa3bf8606525e04e844a9190506454a97f6.jpg", + "table_caption": [ + "Table 5: Person localization results on val and test sets of LOAF (§5.3)." + ], + "table_footnote": [], + "table_body": "
MethodmAP↑val seenval unseen
mAP↑AP50↑AP75↑mAP↑AP50↑AP75↑
Baseline [45]43.146.481.248.440.976.238.9
+ Rotation Aug.45.649.282.852.843.278.943.9
+ Rotation Equ.47.450.883.854.845.780.547.3
", + "bbox": [ + 511, + 210, + 898, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6: Diagnostic results on val set of LOAF (§5.4).", + "bbox": [ + 526, + 284, + 861, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "centers of their detected human boxes on the 3D world, based on the same strategy of ours (cf. §4.2), for physical position estimation. As shown in Table 5, our system produces much small localization errors in comparison with [60, 42, 64, 24], i.e., $\\mathbf{0.374m}$ vs $0.682\\mathrm{m}[24]$ and 0.773 m of [64] on the test set of LOAF. In addition, for all the methods, the localization performance is declined as target distance increases, but our system suffers from the smallest drop. Moreover, the results suggest there is still large room for improvement, thus we hope that our dataset could encourage continuous efforts in this challenging task.", + "bbox": [ + 496, + 310, + 890, + 476 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Diagnostic Study", + "text_level": 1, + "bbox": [ + 500, + 493, + 666, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6 studies the efficacy of our rotation equivariant training strategy (§4.1), on the val set of LOAF. Our baseline model [45] (row #1) gains $43.1\\%$ mAP. After adopting rotational data augmentation (row #2), the performance boosts by $2.5\\%$ mAP. By contrast, our rotation equivariant training brings much larger improvements over the baseline, e.g., $4.3\\%$ mAP gain. It is remarkable that, training with standard rotational data augmentation technique can be viewed as a specific case of our equivariant training - only learning rotation-equivariant object-querying (cf. Eq. 4).", + "bbox": [ + 496, + 518, + 890, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 691, + 617, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented LOAF – the first top-view fisheye dataset that supports large-scale study for person localization in realistic surveillance scenarios. With radius-aligned personbox annotations and precise location ground-truths, LOAF closes a crucial gap in the literature as these cases are not covered by previous datasets and annotation protocols. We further proposed an efficient fisheye person detection model that is equipped with a rotation-equivariant training strategy. The physical locations of detected persons are formulated based on the fisheye model and the altitude of the camera. We empirically verified the effectiveness and promising performance of our algorithm.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19968", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This work was sponsored in part by the CCF-Tencent Open Fund, China Postdoctoral Science Foundation (2022M710467) and National Key Research and Development Program of China (Grant No. 2021YFF0500900).", + "bbox": [ + 76, + 92, + 468, + 148 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 159, + 173, + 174 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdulrahman Alarifi, AbdulMalik Al-Salman, Mansour Alsaleh, Ahmad Alnafessah, Suheer Al-Hadhrami, Mai A Al-Ammar, and Hend S Al-Khalifa. Ultra wideband indoor positioning technologies: Analysis and recent advances. 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Journal of Visual Communication and Image Representation, 59:128-139, 2019. 2, 6, 7, 8" + ], + "bbox": [ + 78, + 92, + 468, + 617 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "19971", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/b691cb26-f3c1-4d93-ba53-9242b6258c4e_model.json b/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/b691cb26-f3c1-4d93-ba53-9242b6258c4e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ff16cd0f1d3b530fa6bbcbe237ff3d9686db77e1 --- /dev/null +++ b/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/b691cb26-f3c1-4d93-ba53-9242b6258c4e_model.json @@ -0,0 +1,2884 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.131, + 0.895, + 0.155 + ], + "angle": 0, + "content": "Large-Scale Person Detection and Localization using Overhead Fisheye Cameras" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.18, + 0.808, + 0.201 + ], + "angle": 0, + "content": "Lu Yang\\(^{1*}\\), Lulei Li\\(^{2*}\\), Xueshi Xin\\(^{1}\\), Yifan Sun\\(^{3}\\), Qing Song\\(^{1}\\), Wenguan Wang\\(^{4\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.201, + 0.798, + 0.217 + ], + "angle": 0, + "content": "1 Beijing University of Posts and Telecommunications 2 ReLER, AAI, University of Technology Sydney" + }, + { + "type": "text", + "bbox": [ + 0.348, + 0.218, + 0.623, + 0.234 + ], + "angle": 0, + "content": "3Baidu 4ReLU, CCAI, Zhejiang University" + }, + { + "type": "text", + "bbox": [ + 0.355, + 0.238, + 0.613, + 0.251 + ], + "angle": 0, + "content": "https://LOAFisheye.github.io/" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.729 + ], + "angle": 0, + "content": "Location determination finds wide applications in daily life. Instead of existing efforts devoted to localizing tourist photos captured by perspective cameras, in this article, we focus on devising person positioning solutions using overhead fisheye cameras. Such solutions are advantageous in large field of view (FOV), low cost, anti-occlusion, and unaggressive work mode (without the necessity of cameras carried by persons). However, related studies are quite scarce, due to the paucity of data. To stimulate research in this exciting area, we present LOAF, the first large-scale overhead fisheye dataset for person detection and localization. LOAF is built with many essential features, e.g., i) the data cover abundant diversities in scenes, human pose, density, and location; ii) it contains currently the largest number of annotated pedestrian, i.e., 457K bounding boxes with ground-truth location information; iii) the body-boxes are labeled as radius-aligned so as to fully address the positioning challenge. To approach localization, we build a fisheye person detection network, which exploits the fisheye distortions by a rotation-equivariant training strategy and predict radius-aligned human boxes end-to-end. Then, the actual locations of the detected persons are calculated by a numerical solution on the fisheye model and camera altitude data. Extensive experiments on LOAF validate the superiority of our fisheye detector w.r.t. previous methods, and show that our whole fisheye positioning solution is able to locate all persons in FOV with an accuracy of \\(0.5\\mathrm{m}\\), within \\(0.1\\mathrm{s}\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.746, + 0.21, + 0.761 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.772, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Accurate position finding of persons attracts growing interest from both research and industrial communities, since it plays a crucial role in numerous location-sensitive application scenarios (e.g., surveillance, smart home, public health). Nevertheless, due to the line-of-sight (LOS) issue, GPS is unreliable in interior spaces and urban canyon. To overcome" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.279, + 0.887, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.527, + 0.895, + 0.598 + ], + "angle": 0, + "content": "Figure 1: Person positioning using overhead fisheye camera: We detect humans on omnidirectional images and then project detects onto the real world coordinates to obtain physical locations. Compared with using perspective cameras, our fisheye camera based solution is favored in low cost, high accuracy, and fast speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.895, + 0.778 + ], + "angle": 0, + "content": "such limitation, various alternative solutions are investigated. Signal based solutions, including Bluetooth [13] and WiFi [74], are popular, but they are easily interfered by changing environments and nearby human bodies [73]. A complementary stream of work is vision based; they typically make use of traditional cameras, RGBD cameras, or in-built smartphone cameras, and enjoy the advantage of reliable services. To get location information, visual positioning solutions usually refer to a pre-acquired 3D map or a geotagged database as the scene representation [63], or directly utilize the captured image to estimate the camera pose [39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Although visual localization has been a hotspot issue for many years, existing efforts are mainly dedicated to urban place recognition or indoor camera localization, based on perspective cameras [63, 39, 62, 43]. None of them addresses person positioning by using overhead fisheye cameras, even though fisheye cameras are widely used in visual surveillance applications. One possible reason is the lack of accessible datasets, compounded by considerable costs in-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.875, + 0.381, + 0.888 + ], + "angle": 0, + "content": "The first two authors contribute equally to this work." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.312, + 0.9 + ], + "angle": 0, + "content": "\\(^{2}\\)Corresponding author: Wenguan Wang." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.875, + 0.381, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19961" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "volved in data collection. In this article, we provide a large-scale overhead fisheye dataset, LOAF, for person detection and localization in both indoor and outdoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.47, + 0.304 + ], + "angle": 0, + "content": "Compared with perspective cameras, overhead (top-view) fisheye cameras are promoted due to less occlusion among people and larger field of view (FOV) - allowing the coverage of a large space using a single, low-cost camera. Only few public datasets [21, 42, 24] provide top-view fisheye data. Unfortunately, they only cover quite few scenes and their people-box annotations do not adequately address the positioning challenge, negatively affecting location approximation (see §3.2 for detailed analysis). Differently, LOAF specifically targets at person localization in surveillance applications, and has the following appealing characteristics:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.307, + 0.469, + 0.367 + ], + "angle": 0, + "content": "- Large-scale: LOAF is the largest in the filed, to our best knowledge. It consists of over 70 videos, with more than 43K frame images, 457K person-detection annotations as well as corresponding location information." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.367, + 0.469, + 0.426 + ], + "angle": 0, + "content": "- High diversity: LOAF contains a wide variety of surveillance scenarios; it includes a total of 11 indoor and 40 outdoor scenes, and the data are captured at different times of day and cover different illumination conditions." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.428, + 0.469, + 0.533 + ], + "angle": 0, + "content": "- Positioning-aware person-box annotation: LOAF offers radius-aligned human-box annotations. Compared with other person representations, i.e., head center [21], axis-aligned [60] or body-aligned box [42, 24], used in previous fisheye datasets, the radius-aligned box is promoted, as it fits well radially-oriented bodies [42], and, more importantly, it is better aware of the positioning problem." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.307, + 0.469, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Moreover, we devise a person positioning system that first detects persons from raw fisheye images, and then calculates physical locations based on fisheye visual model and altitude information (see Fig. 1). Clearly, high-quality person detection is the crucial premise for precise localization using overhead fisheye cameras. Fisheye lenses provide large FOV, at the cost of strong radial distortion. This makes pedestrian detection in top-view fisheye images a much harder task, compared with using perspective cameras. Studies on overhead fisheye pedestrian detection are very scarce [60, 42, 51, 24, 64]; they rarely concern the link with person positioning, and many of them [60, 42] are even not trainable due to the lack of fisheye data. With our LOAF dataset, we develop a novel query based fisheye human detector. It explicitly exploits fisheye geometry by accommodating rotation equivariance into the matching between queries and human instances during network training. The insight here is intuitive: for a robust fisheye detector, rotation of a fisheye image should result in correspondingly rotated detections. In addition, our detection algorithm learns to predict radius-aligned person boxes, facilitating localization estimation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We test our fisheye person detection algorithm as well as our whole positioning system over LOAF. We find that our detector significantly outperforms previous methods, and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "our full system delivers precise localization results. We also empirically show that our algorithm generalizes well on previous top-view fisheye person detection datasets [24, 65]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.149, + 0.642, + 0.166 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.171, + 0.892, + 0.277 + ], + "angle": 0, + "content": "Accurate Positioning. GPS is the most popular system for outdoor localization. As it requires LOS between the satellites and the handset, GPS does not function well in urban canyons, indoors and basements [30, 26]. This triggered the development of alternative positioning solutions, following a multi-disciplinary approach. Concretely, there are two main schemes of the alternatives: signal-based and vision-based." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.399 + ], + "angle": 0, + "content": "Signal-based positioning systems typically lean on sound wave [50], geomagnetism [32], radio frequency (RF) [26, 74, 54, 13, 1], and infrared radiation (IR) [71], as well as different location determination techniques, such as TOA (time of arrival) [30] and RSS (received signal strength) [26]. The main challenge to signal-based systems is the sensitivity to environment changes, such as object moving, diffraction and reflection, which affect signal propagation [26]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.893, + 0.596 + ], + "angle": 0, + "content": "Visual data is another potential information source for precise localization. Since put forward [61], visual positioning has become a hot topic in robotics and computer vision. Some methods adopt a pre-built geo-tagged database or a 3D scene model, as the reference for camera location estimation [33, 77, 66, 78, 76]. Some others rely on recognizing some deployed coded targets [27, 59, 20, 31, 36], e.g., concentric rings, barcodes, colored dots, etc. Some recent ones utilize deep learning techniques to replace some components (e.g., image retrieval, descriptor matching) in traditional systems [4, 16], or regress the camera pose directly [39, 38, 7]. Though promising, existing visual positioning systems are mostly founded on perspective cameras." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.893, + 0.735 + ], + "angle": 0, + "content": "Due to the problem complexity, there is no persuasive solution for precise positioning yet, and hybrid schemes are often applied in practice. Fisheye cameras have advantage of providing wide FOV with low cost and reduced occlusion, while the research landscape is sparse for fisheye camera based localization [79, 21]. To foster research in this direction and facilitate practical deployment, we contribute the first overhead fisheye dataset, to our knowledge, that allows to conduct the task of person localization at large scale." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Deep Learning based Visual (Camera) Localization. Regarding application scenarios, scholars in computer vision community are mainly aware of city-scale location recognition [2, 72, 58, 57] and indoor camera localization [5, 67]. Popular visual localization approaches can be divided as retrieval-based, regression-based, and structure-based, according to the camera pose estimation strategy. Retrieval-based methods [58, 3, 23, 75, 56] represent a scene as a database of geo-tagged photos and use geo-tag of the most relevant database photo as an approximation to the camera position [58]. Regression-based methods learn to encode" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19962" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "the scene into a deep network and directly regress a 6DOF camera pose [39, 67, 38] from a captured image. Structure-based methods [6, 55, 29] pose the localization problem as a camera resection task [58]. They first represent scenes via 3D models and establish a set of 2D-3D matches, then recover the full camera pose by employing a PnP solver [34] inside a RANSAC [28] loop." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.47, + 0.397 + ], + "angle": 0, + "content": "These visual positioning techniques seek to localize images captured by handheld devices [43, 11] or vehicle cameras [48] and demand pre-created geo-tagged databases or 3D maps. And they work on an active mode – users need to carry the cameras. Differently, we address person localization in surveillance scenarios, by using stationary, overhead fisheye cameras. This yields a passive, low-cost scheme, where the localization is completed by a numerical solution on the fisheye model fused with altitude information. Thus our scheme faces a different challenge, i.e., conducting robust person detection from non-rectilinear fisheye images. Overall, our scheme fills the gap left by conventional studies and is complementary to existing positioning systems." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Person Detection in Overhead Fisheye Images. As a canonical subproblem of object detection, pedestrian detection has long received great interest owing to its broad applications such as intelligent surveillance and autonomous vehicles [12, 8]. By contrast, people detection in overhead fisheye images has been studied much less, due to the absence of such datasets. Moreover, adapting standard pedestrian detectors to top-view fisheye cameras is difficult [15]: First, the appearance of people in fisheye images is arbitrary-oriented, while in perspective images, people typically appear upright. Second, people suffer from severe geometric distortions, particularly in the fisheye image's periphery." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.471, + 0.869 + ], + "angle": 0, + "content": "Faced with the above challenges, early attempts make use of handcrafted features (e.g., HOG, LBP) as well as standard pedestrian detectors with slight modifications to account for fisheye geometry [40, 14, 17, 69]. The common approach is dewarping fisheye images [14] or features [40] so as to approximate normal people' appearances from the deformed ones. Though this simplifies the classification of features, approximation errors are inevitable, causing performance degradation [64]. Later, a few CNN-based fisheye detectors were developed. Some of them are training-free. For example, [60] runs standard YOLOv2 [52] on dewarped versions of overlapped windows extracted from a fisheye image. Li et al. [42] rotate a fisheye image in \\(15^{\\circ}\\) increments, and apply off-the-shelf YOLOv3 [53] only to the top-center region of each rotated image, where people usually appear upright. Some more recent methods are trainable: [64] trains YOLOv2 with rotated perspective images so as to handle omnidirectional images without test-time transformation; [24] trains YOLOv3 with human-aligned boxes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Although many prior arts [60, 42, 64] allowing to detect persons without any fisheye training data, they require a cer-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.38 + ], + "angle": 0, + "content": "tain amount of computation time for post-processing: [60] carries out detection in multiple perspective images dewarped from one omnidirectional image; [42] applies YOLOv3 24 times to each fisheye image; [64] needs a grouping process to eliminate numerous redundant results, caused by a rotation-invariant training strategy. Hence, the utility of previous methods is limited in the context of visual positioning. Our analysis in §3.2 sheds light on the weaknesses of human representations adopted by existing fisheye detectors (e.g., head center [21], horizontal or body-aligned box [60, 42, 24]) in regard to localization. Thus we supply our large-scale dataset with positioning-aware person-detection annotation. As a result, our human detector can benefit from end-to-end, fisheye visual pattern learning and output radius-aligned body-boxes for precise positioning. Further, by regularizing the learning of image representations and instance queries with rotation equivariance, our algorithm naturally addresses the omnidirectional nature of fisheye images, yet using standard detection network architecture designed for perspective images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.388, + 0.649, + 0.403 + ], + "angle": 0, + "content": "3. LOAF Dataset" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.687, + 0.426 + ], + "angle": 0, + "content": "3.1. Dataset Acquisition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.892, + 0.719 + ], + "angle": 0, + "content": "We first describe how our fisheye images are collected. Apparatus and Technical Specifications. A TL-IPC59AE fisheye camera with \\(1.1\\mathrm{mm}\\) focal length is adopted for data recording. It has a wide FOV, reaching the full circle in the horizontal plane and \\(180^{\\circ}\\) in the vertical plane. This offers a clear advantage in reducing deployment cost – installing just one fisheye camera instead of multiple conventional cameras to monitor the same region. However, the severe geometric distortions introduced prevent the use of standard detectors, which are designed for conventional cameras [8]. Data Capturing. The fisheye camera is mounted on the ceiling (indoors) or poles (outdoors), \\(2.5\\sim 4.0\\mathrm{m}\\) from the ground with \\(200\\sim 300\\mathrm{m}^2\\) FOV. Considering the factors such as scenario diversity, pedestrians density and weather condition, we capture 110 fisheye image sequences in 80 realistic scenarios as the raw data pool. The recorded sequences span 14 hrs; the image resolution is \\(2952\\times 2952\\) pixels, and the frame rate is \\(10\\sim 20\\) fps. Eventually, 42,942 images, sampled at 1 fps, are collected to construct our LOAF dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.729, + 0.686, + 0.743 + ], + "angle": 0, + "content": "3.2. Dataset Annotation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We next describe how our fisheye images are annotated. Person Detection. As the performance of localization relies critically on the quality of person detections, significant effort should be spent on the fisheye person-detection annotation. Some human-detection representations were explored in previous datasets: [21] labels the center point of each human head; [42, 24] opt for human-aligned person-boxes. However, these representations have several shortcomings, especially with regards to the localization task. First, they suffer from some inherent limitations. The point-based rep" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19963" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.083, + 0.888, + 0.186 + ], + "angle": 0, + "content": "
Dataset#Scene#Video#Image#PeopleMax ResolutionFOV (m2)AnnotationFPS
IndoorOutdoorTotalAvg.MaxPeople DetectionLocationAttribute
PIROPO [21]2027----800×600<50Head Center10
HABBOF [42]2045,83720,4663.552,048×2,048<36Human-aligned box12~30
MW-R [24]60198,75222,8252.661,488×1,488<36Human-aligned box15
CEPDOF [24]50825,504173,0736.8132,048×2,048<36Human-aligned box1~10
WEPDTOF [65]1401610,54493,3638.9352,592×1,944<36Human-aligned box1~10
LOAF11397442,942457,76210.5652,952×2,952200~300Radius-aligned box✓✓10~20
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.188, + 0.895, + 0.203 + ], + "angle": 0, + "content": "Table 1: Overhead fisheye datasets comparison (§3.4). LOAF is the largest in terms of the total number of pedestrian and scene categories." + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.211, + 0.428, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.499 + ], + "angle": 0, + "content": "Figure 2: Human annotation comparison for visual positioning (§3.2). Previous methods typically use the detected human head [21] (\\(\\bullet\\)) or the center (\\(\\bullet\\)) of human-aligned body-box (\\(\\langle \\rangle\\)) [42, 24] to determine the physical location \\(P\\), bringing positioning errors (i.e., \\(PP_{1}\\), \\(PP_{2}\\)). We instead leverage the radius-aligned box (\\(\\square\\)) as human representation. The midpoint (\\(\\bullet\\)) of side \\(AB\\), i.e., the closest point to the image center on the radius-aligned box, better corresponds to the human actual position." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.674 + ], + "angle": 0, + "content": "resentation is not applicable in other analysis tasks (e.g., re-identification, attribute recognition); the human-aligned box has ambiguity [10, 68] – the ground-truths of human-aligned boxes are not uniquely determined [24]. Second, and most important, these human-detection representations cannot meet the need of precise localization. Clearly, based on the fisheye camera model, one can project 2D detections on the 3D world for localization. However, the center of human head or of human-aligned box is not the exact placement occupied by human on the image plane, causing errors to estimations of human physical position (see Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.87 + ], + "angle": 0, + "content": "We instead label each person through a radius-aligned rectangular box. Such representation is favored as it: i) allows unique groundtruth box assignment; ii) fits well radially-oriented human bodies presented in fisheye images; and iii) better corresponds to the actual position of human on the image plane, facilitating physical localization. Notably, although the radially-oriented box constraint was explored in a prior fisheye detector [42], there is no previous datasets provide such kind of annotation, neither is there any literature points out the advantage of such representation in localization. Finally, around 457K human box annotations are obtained. High-quality annotation is ensured via a rigorous quality check, conducted by highly skilled reviewers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Person Localization. For each scene, a \\(10\\mathrm{m}\\) ruler (with \\(0.05\\mathrm{m}\\) accuracy) is placed on the ground, and one end of the" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.211, + 0.667, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.587, + 0.361, + 0.608, + 0.375 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.212, + 0.872, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.361, + 0.786, + 0.374 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.378, + 0.892, + 0.42 + ], + "angle": 0, + "content": "Figure 3: Calibration for groundtruth person location annotation. (a) Ground makers (with \\(0.05\\mathrm{m}\\) precision). (b) Top-view fisheye image capture for calibration. See §3.2 for details." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.431, + 0.892, + 0.506 + ], + "angle": 0, + "content": "ruler is directly under the fisheye lens (cf. Fig. 3 (a)). We take a fisheye picture and use this marked picture as the calibration for all the dataset images recorded in this scene (cf. Fig. 3(b)). Finally, for each annotated human, the physical location, at sub-decimeter precision, is provided (cf. Fig. 4)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.892, + 0.553 + ], + "angle": 0, + "content": "Scene Attribute. To enable in-depth analysis, each image is annotated with multiple attributes, including day/night, outdoor/indoor, and sunny/rain/foggy/snow." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.56, + 0.651, + 0.575 + ], + "angle": 0, + "content": "3.3. Dataset Design" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.581, + 0.874, + 0.596 + ], + "angle": 0, + "content": "We then list several key aspects of our dataset design." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.597, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Privacy Protection. To protect personal information, we apply the gaussian filter to blur all the visible facial regions in our dataset, and conduct experiments on the blurred data. Dataset Splits. LOAF contains 29,569 training, 4,600 validation, and 8,773 testing images (approximately 7 train, 1 val, and 2 test). Moreover, to better evaluate models' generalization ability, LOAF is split into five sets: train (7/28 indoor/outdoor scenes, 29,569 images), val seen (1/2 indoor/outdoor scenes, 1,700 images), val unseen (2/3 indoor/outdoor scenes, 2,900 images), test seen (2/3 indoor/outdoor scenes, 2,774 images), test unseen (2/8 indoor/outdoor scenes, 5,999 images). There are no overlapping scenes between unseen and train sets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.794, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Dataset Accessibility. Only the desensitized version of our dataset will be released online, under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License [19]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.767, + 0.862 + ], + "angle": 0, + "content": "3.4. Dataset Features and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Finally, we present statistic analysis of LOAF in comparison with existing overhead fisheye datasets [21, 42, 24]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19964" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.079, + 0.223, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.186, + 0.214, + 0.195 + ], + "angle": 0, + "content": "playground | winter | noon" + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.086, + 0.353, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.187, + 0.335, + 0.195 + ], + "angle": 0, + "content": "hall | fall | afternoon" + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.085, + 0.481, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.364, + 0.187, + 0.467, + 0.195 + ], + "angle": 0, + "content": "street | spring | morning" + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.195, + 0.358, + 0.208 + ], + "angle": 0, + "content": "(a) Our proposed LOAF" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.079, + 0.597, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.494, + 0.194, + 0.596, + 0.207 + ], + "angle": 0, + "content": "(b) PIROPO [21]" + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.079, + 0.743, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.62, + 0.194, + 0.73, + 0.207 + ], + "angle": 0, + "content": "(c) HABBOF [42]" + }, + { + "type": "image", + "bbox": [ + 0.752, + 0.079, + 0.891, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.194, + 0.882, + 0.207 + ], + "angle": 0, + "content": "(d) CEPDOF [24]" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.212, + 0.894, + 0.269 + ], + "angle": 0, + "content": "Figure 4: Example images from different datasets (\\(\\S 3.2-\\S 3.4\\)). Prior datasets [21, 42, 24] are restricted to few indoor scenes with person detection annotation only, i.e., head center \\((\\bullet)\\) or human-aligned box \\((\\square)\\). In contrast, LOAF covers challenging indoor and outdoor scenes with human detection, localization and scene attribute annotations. The person-detection annotation is given as the radius-aligned box \\((- \\square)\\), which is more suitable for localization. For better visualization, we only present location ground-truths for some of persons." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.279, + 0.255, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.431, + 0.216, + 0.441 + ], + "angle": 0, + "content": "(a) Person scale" + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.279, + 0.453, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.32, + 0.351, + 0.425, + 0.361 + ], + "angle": 0, + "content": "(b) Person locations" + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.361, + 0.453, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.432, + 0.421, + 0.442 + ], + "angle": 0, + "content": "(c) Person density" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.498 + ], + "angle": 0, + "content": "Figure 5: Dataset Statistics (§3.4): We summarize LOAF with the distribution of (a) person scale (area in pixel), (b) person locations (horizontal distance between human and the fisheye lens in the real world), and (c) person density (number of person per image)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.462, + 0.522 + ], + "angle": 0, + "content": "LOAF distinguishes itself from three aspects (cf. Table 1):" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.628 + ], + "angle": 0, + "content": "Large-scale: LOAF has 42,942 fisheye images with more than 457K person boxes. Moreover, LOAF data are captured by an advanced fisheye camera, which is capable of covering a larger area \\((200\\sim 300\\mathrm{m}^2)\\) with higher pedestrian density (2~65 persons per scene, 10.5 in average). This makes LOAF the largest overhead fisheye dataset in terms of the total number of pedestrian and scene categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.809 + ], + "angle": 0, + "content": "High Diversity: Existing datasets limit in data diversities, i.e., only containing very few indoor scenes (2~14) and completely missing outdoor scenarios (cf. Fig. 4). In contrast, LOAF involves 51 realistic scenes, including 11 indoor scenes (e.g., lab, office, library, classroom) and 40 outdoor scenes (e.g., street, playground, parking lot, square). The recorded data cover four seasons under different illumination (e.g., morning, noon, afternoon) and weather (e.g., sunny, rain, snow) conditions, and involve vast variance of human pose (e.g., walking, standing, and sitting), scale, location, and density (cf. Fig. 5). Thus our dataset better reflects the distribution in real-world surveillance scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Rich and Positioning-aware Annotation: LOAF is provided with rich ground-truths for detection, localization, and scene attribute, which lays a solid foundation for fisheye camera based human-centric analysis. Hence, as demonstrated in §3.2, the radius-aligned human-box representation is adopted during our annotation. Compared with human-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.892, + 0.322 + ], + "angle": 0, + "content": "head center based point annotation [21] and human-aligned person-boxes [42, 24] used in previous datasets, radius-aligned human-boxes are more suitable for the position task." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.33, + 0.649, + 0.347 + ], + "angle": 0, + "content": "4. Our Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.429 + ], + "angle": 0, + "content": "Our overhead fisheye camera based person localization solution comprises two parts. The former computes 2D detections that locate the people on the image plane (§4.1). The latter converts the 2D detections to 3D-world coordinates, obtaining the physical location of the people (§4.2)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.433, + 0.808, + 0.449 + ], + "angle": 0, + "content": "4.1. Overhead Fisheye Person Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.893, + 0.574 + ], + "angle": 0, + "content": "Core Idea: Rotation Equivariance. One of the reasons for the tremendous success of CNNs is their equivariance to horizontal and vertical shifts and the resulting invariance to local deformations [41, 25]. This stimulates a line of efforts to learn robust representations equivariant to generic types of transformations [35, 18, 70]. Formally, a representation \\( f \\) is said to be equivariant with a geometric transformation \\( g \\) (e.g., cropping, flipping) for an input (image) \\( I \\) if:" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.579, + 0.891, + 0.595 + ], + "angle": 0, + "content": "\\[\nf (g (I)) \\approx g (f (I)). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.891, + 0.629 + ], + "angle": 0, + "content": "That is to say, the output representation \\( f(I) \\) is changed in the same way as the transformation \\( g \\) imposed to the input \\( I \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In this work, we devise a query-based fisheye person detector that exhibits \\(360^{\\circ}\\)-rotational equivariance through an elaborately designed training protocol. Our key insight is derived from the omnidirectional nature of this task: if one rotates the input fisheye image by an arbitrary angle, then the outputs of a robust fisheye detector should change accordingly. We thus design a rotation equivariant training strategy, which forces the matching between object queries and image representations to be equivariant against \\(360^{\\circ}\\)-rotations. In this way, the rotational symmetry of omnidirectional images is explicitly addressed, without architectural modification of standard detectors developed for perspective images. Rotation Equivariant Training for Query-based Fisheye Detection. As shown in Fig. 6, our fisheye detector is built upon DETR [9], promoted by a rotation equivariant training strategy. Basically, DETR conducts detection in a query-based fashion. Denote \\(\\mathcal{F}\\) as a feature encoder that extracts representation \\(I\\) of image \\(I\\), and \\(\\kappa\\) as a query creator" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19965" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.082, + 0.473, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.47, + 0.325 + ], + "angle": 0, + "content": "Figure 6: Our rotation equivariant training strategy for query-based fisheye person detection (§4.1). For equivariant training, object queries \\(\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N\\) created for rotated image \\(g^r(I)\\) and the rotated representation \\(g^r(I)\\) are fed into the decoder \\(\\mathcal{D}\\); the rotated ground-truths \\(\\{\\pmb{b}_{\\ell(n)}^{g^r}\\}_{n=1}^N\\) are set as the training targets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.469, + 0.386 + ], + "angle": 0, + "content": "that outputs a set of \\(N\\) object-aware descriptors \\(\\{\\pmb{q}_n\\}_{n=1}^N\\) from \\(\\pmb{I}\\). DETR employs \\(\\{\\pmb{q}_n\\}_{n=1}^N\\) as queries to retrieve target objects from \\(\\pmb{I}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.39, + 0.469, + 0.408 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\hat {\\boldsymbol {b}} _ {n} \\right\\} _ {n = 1} ^ {N} = \\mathcal {D} (\\boldsymbol {I}, \\left\\{\\boldsymbol {q} _ {n} \\right\\} _ {n = 1} ^ {N}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.417, + 0.469, + 0.479 + ], + "angle": 0, + "content": "where \\(\\pmb{I} = \\mathcal{F}(I)\\), \\(\\{\\pmb{q}_n\\}_{n=1}^N = \\kappa(\\pmb{I})\\), and \\(\\mathcal{D}\\) refers to the Transformer decoder which formulates the object-query matching process via neural cross-attention computation. \\(\\{\\hat{\\pmb{b}}_n\\}_{n=1}^N\\) are the set of predicted parameterized object bounding boxes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.469, + 0.555 + ], + "angle": 0, + "content": "Our rotation equivariant training further encourages robust object-query matching which is equivariant against rotations. First, given an input rotation transformation \\( g^r \\), a robust fisheye detector is desired to be able to extract rotation-equivariant representation. Analogous to Eq. 1, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.56, + 0.469, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} \\left(g ^ {r} (I)\\right) \\approx g (\\mathcal {F} (I)) = g ^ {r} (\\boldsymbol {I}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.469, + 0.626 + ], + "angle": 0, + "content": "Also, it is reasonable to assume that the final output of a robust fisheye detector should be changed in the same way to the rotation \\( g^{r} \\) applied to the input fisheye image \\( I \\):" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.632, + 0.469, + 0.652 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {b} _ {\\ell (n)} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N} \\approx \\mathcal {D} \\left(\\boldsymbol {I} ^ {g ^ {r}}, \\left\\{\\boldsymbol {q} _ {n} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.661, + 0.47, + 0.741 + ], + "angle": 0, + "content": "where \\(I^{g^r}\\) indicates the feature of rotated image \\(g^{r}(I)\\), i.e., \\(\\pmb{I}^{g^{r}} = \\mathcal{F}(g^{r}(I))\\). Similarly, \\(\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N\\) denote the object queries derived from \\(g^{r}(I)\\), i.e., \\(\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N = \\kappa(I^{g^r})\\). \\(\\{\\pmb{b}_{\\ell(n)}^{g^{r}}\\}_{n=1}^N\\) are the rotated groundtruth bounding boxes, where \\(\\ell(n)\\) returns the groundtruth index for \\(n\\)-th query." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.741, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Considering Eq.3 and Eq.4, we can have: \\(\\{\\pmb{b}_{\\ell(n)}^{g^r}\\}_{n=1}^N \\approx \\mathcal{D}(g^r(\\pmb{I}), \\{\\pmb{q}_n^{g^r}\\}_{n=1}^N)\\). Hence our rotation equivariant training objective is given as:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.798, + 0.469, + 0.818 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r o t a t - e q u i}} = \\mathcal {L} _ {\\det } \\left(\\left\\{\\boldsymbol {b} _ {\\ell (n)} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}, \\mathcal {D} \\left(g ^ {r} (\\boldsymbol {I}), \\left\\{\\boldsymbol {q} _ {n} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}\\right)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Here \\(\\mathcal{L}_{\\mathrm{det}}\\) is the standard detection loss in DETR [9]. As such, the rotation equivariance properties for both fisheye representation \\(\\mathcal{F}\\) (cf. Eq.3) and the query-based detection prediction \\(\\mathcal{D}(\\boldsymbol {I},\\{\\pmb {q}_n\\}_{n = 1}^N)\\) (cf. Eq.4) are sought in a single training target. This also allows us to effortlessly adapt standard" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.743, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.749, + 0.116, + 0.888, + 0.241 + ], + "angle": 0, + "content": "Figure 7: Our fisheye camera model based person localization (§4.2). Here \\( \\pmb{p} \\) and \\( \\pmb{p}' \\) denote the projection point of the distortion point \\( P \\) by fisheye lens and normal perspective lens, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.268, + 0.892, + 0.328 + ], + "angle": 0, + "content": "DETR to our omnidirectional detection setting. Note that our rotation equivariant training differs from rotational data augmentation technique which only views rotated images as individual training samples (see §5.4 for detailed experiments)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.338, + 0.875, + 0.353 + ], + "angle": 0, + "content": "4.2. 2D-3D Projection based Person Localization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.36, + 0.892, + 0.512 + ], + "angle": 0, + "content": "General Fisheye Camera Model. The perspective projection of a normal pinhole camera can be written as \\( r = f \\tan \\theta \\), where \\( r \\) indicates the projection distance between the principal point and the image point, \\( f \\) is the focal length, and \\( \\theta \\) is the angle between the incident ray and the camera's optical axis. However, fisheye lens does not follow this perspective projection model [49], as the FOV equals to \\( 180^{\\circ} \\) (cf. Fig. 7). Fortunately, the image formation of different kinds of fisheye lenses can be approximated by a general polynomial projection model [37], i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.521, + 0.891, + 0.543 + ], + "angle": 0, + "content": "\\[\nr (\\theta) = \\sum_ {i = 1} ^ {n} k _ {i} \\theta^ {2 i - 1}, \\quad n = 1, 2, 3, 4, \\dots \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.891, + 0.58 + ], + "angle": 0, + "content": "High distortions can be handled well when \\( n = 5 \\) [37]. The coefficients \\( k_{s} \\) can be obtained from camera calibration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.743 + ], + "angle": 0, + "content": "2D-3D Projection. Given a detected human location point \\(\\pmb{p} = (u,v)^{\\top}\\) in the fisheye image pixel coordinate system, our target is to calculate its 3D location \\(\\pmb{P} = (X,Y,Z)^{\\top}\\) in the camera coordinate system, where \\(Z\\) is the altitude of the fisheye camera and primarily known. To do so, one can first calculate \\(r\\) as: \\(r = \\sqrt{(x^2 + y^2)}\\), where \\(x = (u - u_0) / f\\) and \\(y = (v - v_0) / f\\), and \\((u_0,v_0)^{\\top}\\) are the coordinates of the principal point in the fisheye image. Then \\(\\theta\\) can be obtained by solving Eq. 6 using a numerical means [37]. With the altitude \\(Z\\) of the camera, the actual location \\((X,Y)^{\\top}\\) is given as:" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.74, + 0.891, + 0.777 + ], + "angle": 0, + "content": "\\[\n\\binom {X} {Y} = Z \\binom {\\tan \\theta \\cos \\phi} {\\tan \\theta \\sin \\phi}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.89, + 0.81 + ], + "angle": 0, + "content": "where \\(\\phi = \\arctan (y,x)\\) refers to the polar angle, which is shared by both \\(\\pmb{p}\\) and \\(\\pmb{P}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "It can be seen that precise determination of the person location point \\( \\pmb{p} \\) on the image plane is vital for estimating the corresponding physical position \\( \\pmb{P} \\). However, most previous approaches, restricted to axis-aligned [79, 60] or person-aligned [24] human-box representation, use the center of the detection box to approximate \\( \\pmb{p} \\). Few excep" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19966" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.084, + 0.885, + 0.178 + ], + "angle": 0, + "content": "
MethodvaltestFPS↑
mAP↑AP50↑AP75↑APn↑APm↑APf↑APseen↑APunseen↑mAP↑AP50↑AP75↑APn↑APm↑APf↑APseen↑APunseen↑
Seide et al. [60]21.859.87.632.828.52.323.219.520.258.27.132.228.33.922.418.910.2
Li et al. [42]28.563.320.146.824.21.333.829.327.265.221.347.224.81.331.827.60.6
Tamura et al. [64]34.872.127.751.738.88.738.832.934.272.828.753.737.36.539.533.210.2
RAPiD [24]40.377.934.855.341.99.244.737.639.277.935.454.840.17.944.237.38.4
Ours47.482.648.464.154.314.150.845.746.281.147.366.153.512.649.344.912.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.263, + 0.181, + 0.706, + 0.194 + ], + "angle": 0, + "content": "Table 2: Person detection results on val and test sets of LOAF (§5.2)." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.203, + 0.476, + 0.284 + ], + "angle": 0, + "content": "
MethodmAP↑AP50↑AP75↑Precision↑Recall↑F-Score↑
Seide et al. [60]20.950.610.280.639.553.0
Li et al. [42]34.275.728.686.365.474.4
Tamura et al. [64]29.361.023.488.851.265.0
RAPiD [24]39.385.426.089.278.783.6
Ours47.288.538.290.387.688.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.096, + 0.286, + 0.45, + 0.3 + ], + "angle": 0, + "content": "Table 3: Person detection results on CEPDOF [24] (\\$5.2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.47, + 0.417 + ], + "angle": 0, + "content": "tions [21], built on point-based human representation, treat the center of the detected human head as \\( \\pmb{p} \\). However, they suffer from a similar issue as the human head center is even often far from the exact position \\( \\pmb{p} \\) human stand on, w.r.t. the image plane. Instead, with our radius-aligned human-box representation, the closest point to the principal point on the bounding box better corresponds to \\( \\pmb{p} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.426, + 0.295, + 0.442 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.47, + 0.586 + ], + "angle": 0, + "content": "Network Architecture. Our fisheye person detector is built upon DAB-DETR [45], a prevalent variant of DETR [9] but converges much faster. Swin-T [46] is utilized as the backbone. For our LOAF with radius-aligned person boxes, the output of our detector is a 4D vector \\(\\pmb{b} \\in [0,1]^4\\) that parameterizes 2D center coordinates, height, and width. Note that, for traditional fisheye detection datasets like [24, 65] with arbitrary-oriented person box annotations, an extra output dimension is needed for rotation angle regression." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.647 + ], + "angle": 0, + "content": "Training Objective. Our fisheye person detector is end-to-end trained by jointly optimizing the vanilla detection loss used in DETR [9, 45] (referred as \\(\\mathcal{L}_{\\mathrm{Det}}\\)) and our proposed rotation-equivariant constraint (i.e., \\(\\mathcal{L}_{\\mathrm{rotat - equi}}\\) in Eq. 5):" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.653, + 0.47, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {d e t}} + \\lambda \\mathcal {L} _ {\\text {r o t a t - e q u i}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.394, + 0.689 + ], + "angle": 0, + "content": "where the coefficient \\(\\lambda\\) is empirically set to 0.5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Training. Our fisheye detector is trained with a batch size of 8 for 50 epochs, where the AdamW [47] optimizer is employed with base learning rate 2e-4 and decayed by 0.1 at epoch 40. The remaining hyper-parameters are determined following [64, 24]. Specifically, we initialize backbones with ImageNet [22] pre-trained weights and adopt standard data augmentation techniques, i.e., color jitter, horizontal flip, and random scaling, with a base training size of \\(608 \\times 608\\). For CEPDOF [24] and WEPDTOF [65], we use a batch size of 128 and pre-train the detector on COCO [44] for 50 epochs to prevent over-fitting, as in [24, 65]. For the computation of our rotation-equivariant loss \\(\\mathcal{L}_{\\mathrm{rotat - equi}}\\), the training images are rotated by a degree randomly sampled from 0 to 360. Our detector is implemented in PyTorch and trained on eight" + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.203, + 0.899, + 0.284 + ], + "angle": 0, + "content": "
MethodmAP↑AP50↑AP75↑Precision↑Recall↑F-Score↑
Seide et al. [60]16.139.49.070.938.650.0
Li et al. [42]25.269.930.281.464.572.0
Tamura et al. [64]28.859.824.277.052.462.4
RAPiD [24]37.772.026.873.367.870.4
Ours45.885.636.684.974.679.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.286, + 0.88, + 0.3 + ], + "angle": 0, + "content": "Table 4: Person detection results on WEPDTOF [65] (\\$5.2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.464 + ], + "angle": 0, + "content": "NVIDIA Tesla V100 GPUs with a 32GB memory per-card. Inference. Once trained, our fisheye detector can be directly applied for locating persons on the omnidirectional image plane. After that, the physical locations of the detected persons can be easily obtained through the numerical solution described in §4.2. For fisheye person detection, we follow prior work [60, 42, 64, 24] to use \\(1024 \\times 1024\\) input resolution without any test-time augmentation or post-processing. Testing is conducted on a single NVIDIA V100 GPU with 16 GB memory." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.476, + 0.625, + 0.492 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.691, + 0.515 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Evaluation Protocol. On the top of LOAF, we conduct experiments for fisheye based person detection and localization. Following the dataset splitting (cf. §3.3), performance are reported on seen and unseen scenes, respectively, for both val and test sets. This allows us to assess the generalization ability over different surveillance scenarios. For comprehensive study, we further report person detection performance on two existing fisheye datasets, CEPDOF[24] and WEPDTOF[65]. Note that localization cannot be test since [24, 65] only provide person bounding box annotations. Evaluation Metrics. For fisheye person detection, we follow COCO [44] to report the mean average precision (mAP) for IoU \\(\\in\\) [0.5:0.05:0.95]. We also employ AP\\(_{50}\\) and AP\\(_{75}\\) for further analysis. For fisheye person localization, we measure positional error (PE) in meters, i.e., Euclidean distance of calculated position and ground-truth position, as the conventions in visual localization [43, 58, 73, 79]. For detailed evaluation, on our LOAF, we report performance w.r.t. horizontal distance between human and the fisheye lens, i.e., near (0~10 m), middle (10~20 m), and far (larger than 20 m). Hence we have AP\\(_{n,m,f}\\) and PE\\(_{n,m,f}\\) accordingly." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.794, + 0.862 + ], + "angle": 0, + "content": "5.2. Performance on Person Detection" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "LOAF. We first report the person detection performance on LOAF. Specifically, four recent deep learning based fisheye" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19967" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.093, + 0.089, + 0.887, + 0.182 + ], + "angle": 0, + "content": "
Methodvaltest
mPE↓PEn↓PEm↓PEf↓PEseen↓PEunseen↓mPE↓PEn↓PEm↓PEf↓PEseen↓PEunseen↓
Seide et al. [60]1.2980.5611.3323.1091.2061.3821.3210.7061.3093.4821.3061.386
Li et al. [42]0.8980.5020.8712.6500.8320.9620.9130.5430.8842.7800.9040.998
Tamura et al. [64]0.7550.4290.7361.8620.7090.8210.7780.4710.8262.1600.7240.836
RAPiD [24]0.6740.4260.6231.4030.6250.7570.6820.4610.6641.4450.6380.776
Ours0.3680.1440.3630.7750.3180.4020.3740.1480.3750.8190.3260.398
" + }, + { + "type": "table_caption", + "bbox": [ + 0.255, + 0.184, + 0.713, + 0.197 + ], + "angle": 0, + "content": "Table 5: Person localization results on val and test sets of LOAF (§5.3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.21, + 0.47, + 0.33 + ], + "angle": 0, + "content": "person detectors [60, 42, 64, 24] are involved for comparison. Among them, [60, 42] are training-free, thus their scores are obtained by directly running the algorithms on the val and test data. As [64, 24] are trainable methods, we first train them on the train set of LOAF following their official setups, and then report the scores on the val and test sets. Quantitative comparison results are presented in Table 2. Some essential observations are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.468, + 0.412 + ], + "angle": 0, + "content": "- Our fisheye person detector significantly outperforms existing methods across all the metrics. For example, our detector provides a considerable performance gain in mAP, i.e., \\(7.1\\%\\) and \\(7.0\\%\\) higher than the second best, RAPiD [24], on the val and test sets, respectively." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.413, + 0.468, + 0.488 + ], + "angle": 0, + "content": "- Our detector not only handles nearby persons but also approaches distant targets well. Specifically, for the targets at \\(10\\sim 20\\mathrm{m}\\) away from the fisheye lens, our performance gain over other methods is more significant than the improvement reported with the persons at \\(0\\sim 10\\mathrm{m}\\) distance." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.488, + 0.468, + 0.533 + ], + "angle": 0, + "content": "- Our detector also yields small performance gap between the seen and unseen scenes (e.g., \\(49.3 \\rightarrow 44.9\\) in terms of mAP), validating our good generalizability." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.534, + 0.468, + 0.593 + ], + "angle": 0, + "content": "- For those persons at very far distance (\\(>20\\mathrm{~m}\\)), our algorithm, though still giving higher scores than other competitors, suffers from great performance degradation. This sheds light on the direction of our future efforts." + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.337, + 0.468, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.468, + 0.702 + ], + "angle": 0, + "content": "CEPDOF [24]. CEPDOF contains eight videos with 25,504 frames in total. Following the official setup, we train our fisheye person detector on HABBOF [42] and MW-R [24] datasets, and report performance on CEPDOF. As shown in Table 3, our fisheye detector delivers state-of-the-art performance: it significantly outperforms RAPiD [24], the current top-leading algorithm, by \\(7.9\\%\\) in terms of mAP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.468, + 0.792 + ], + "angle": 0, + "content": "WEPDTOF [65]. WEPDTOF has 16 videos with 10,544 frames in total. Following the official setup, we use HAB-BOF [42], MW-R [24], and CEPDOF [24] for training and WEPDTOF for testing. Table 4 summarizes the results. Impressively, our detector greatly suppresses all the other competitors across all the evaluation metrics." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.392, + 0.817 + ], + "angle": 0, + "content": "5.3. Performance on Person Localization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Then we study the person localization performance on LOAF. None of previous fisheye person detectors [60, 42, 64, 24] are aware of the task of person localization. We therefore follow the common practice [79, 21] in the field of visual localization: for [60, 42, 64, 24], we project" + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.212, + 0.899, + 0.284 + ], + "angle": 0, + "content": "
MethodmAP↑val seenval unseen
mAP↑AP50↑AP75↑mAP↑AP50↑AP75↑
Baseline [45]43.146.481.248.440.976.238.9
+ Rotation Aug.45.649.282.852.843.278.943.9
+ Rotation Equ.47.450.883.854.845.780.547.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.527, + 0.285, + 0.862, + 0.298 + ], + "angle": 0, + "content": "Table 6: Diagnostic results on val set of LOAF (§5.4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.892, + 0.477 + ], + "angle": 0, + "content": "centers of their detected human boxes on the 3D world, based on the same strategy of ours (cf. §4.2), for physical position estimation. As shown in Table 5, our system produces much small localization errors in comparison with [60, 42, 64, 24], i.e., \\( \\mathbf{0.374m} \\) vs \\( 0.682\\mathrm{m}[24] \\) and 0.773 m of [64] on the test set of LOAF. In addition, for all the methods, the localization performance is declined as target distance increases, but our system suffers from the smallest drop. Moreover, the results suggest there is still large room for improvement, thus we hope that our dataset could encourage continuous efforts in this challenging task." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.494, + 0.667, + 0.51 + ], + "angle": 0, + "content": "5.4. Diagnostic Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Table 6 studies the efficacy of our rotation equivariant training strategy (§4.1), on the val set of LOAF. Our baseline model [45] (row #1) gains \\(43.1\\%\\) mAP. After adopting rotational data augmentation (row #2), the performance boosts by \\(2.5\\%\\) mAP. By contrast, our rotation equivariant training brings much larger improvements over the baseline, e.g., \\(4.3\\%\\) mAP gain. It is remarkable that, training with standard rotational data augmentation technique can be viewed as a specific case of our equivariant training - only learning rotation-equivariant object-querying (cf. Eq. 4)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.692, + 0.619, + 0.708 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We presented LOAF – the first top-view fisheye dataset that supports large-scale study for person localization in realistic surveillance scenarios. With radius-aligned personbox annotations and precise location ground-truths, LOAF closes a crucial gap in the literature as these cases are not covered by previous datasets and annotation protocols. We further proposed an efficient fisheye person detection model that is equipped with a rotation-equivariant training strategy. The physical locations of detected persons are formulated based on the fisheye model and the altitude of the camera. We empirically verified the effectiveness and promising performance of our algorithm." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19968" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.093, + 0.47, + 0.149 + ], + "angle": 0, + "content": "Acknowledgements This work was sponsored in part by the CCF-Tencent Open Fund, China Postdoctoral Science Foundation (2022M710467) and National Key Research and Development Program of China (Grant No. 2021YFF0500900)." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.16, + 0.174, + 0.175 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.185, + 0.47, + 0.253 + ], + "angle": 0, + "content": "[1] Abdulrahman Alarifi, AbdulMalik Al-Salman, Mansour Alsaleh, Ahmad Alnafessah, Suheer Al-Hadhrami, Mai A Al-Ammar, and Hend S Al-Khalifa. Ultra wideband indoor positioning technologies: Analysis and recent advances. 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Journal of Visual Communication and Image Representation, 59:128-139, 2019. 2, 6, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.093, + 0.469, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19971" + } + ] +] \ No newline at end of file diff --git a/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/b691cb26-f3c1-4d93-ba53-9242b6258c4e_origin.pdf b/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/b691cb26-f3c1-4d93-ba53-9242b6258c4e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f318a6236f3bd2406efb40af9fca4311b282e17a --- /dev/null +++ b/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/b691cb26-f3c1-4d93-ba53-9242b6258c4e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:79d95cbe36bc6141f304440235a7619be257b2a49c322e9686c28b04753108f6 +size 6491089 diff --git a/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/full.md b/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8ac14ee70fe3b1075c13a272bd691e410545728f --- /dev/null +++ b/2023/Large-Scale Person Detection and Localization Using Overhead Fisheye Cameras/full.md @@ -0,0 +1,387 @@ +# Large-Scale Person Detection and Localization using Overhead Fisheye Cameras + +Lu Yang $^{1*}$ , Lulei Li $^{2*}$ , Xueshi Xin $^{1}$ , Yifan Sun $^{3}$ , Qing Song $^{1}$ , Wenguan Wang $^{4\dagger}$ + +1 Beijing University of Posts and Telecommunications 2 ReLER, AAI, University of Technology Sydney + +3Baidu 4ReLU, CCAI, Zhejiang University + +https://LOAFisheye.github.io/ + +# Abstract + +Location determination finds wide applications in daily life. Instead of existing efforts devoted to localizing tourist photos captured by perspective cameras, in this article, we focus on devising person positioning solutions using overhead fisheye cameras. Such solutions are advantageous in large field of view (FOV), low cost, anti-occlusion, and unaggressive work mode (without the necessity of cameras carried by persons). However, related studies are quite scarce, due to the paucity of data. To stimulate research in this exciting area, we present LOAF, the first large-scale overhead fisheye dataset for person detection and localization. LOAF is built with many essential features, e.g., i) the data cover abundant diversities in scenes, human pose, density, and location; ii) it contains currently the largest number of annotated pedestrian, i.e., 457K bounding boxes with ground-truth location information; iii) the body-boxes are labeled as radius-aligned so as to fully address the positioning challenge. To approach localization, we build a fisheye person detection network, which exploits the fisheye distortions by a rotation-equivariant training strategy and predict radius-aligned human boxes end-to-end. Then, the actual locations of the detected persons are calculated by a numerical solution on the fisheye model and camera altitude data. Extensive experiments on LOAF validate the superiority of our fisheye detector w.r.t. previous methods, and show that our whole fisheye positioning solution is able to locate all persons in FOV with an accuracy of $0.5\mathrm{m}$ , within $0.1\mathrm{s}$ . + +# 1. Introduction + +Accurate position finding of persons attracts growing interest from both research and industrial communities, since it plays a crucial role in numerous location-sensitive application scenarios (e.g., surveillance, smart home, public health). Nevertheless, due to the line-of-sight (LOS) issue, GPS is unreliable in interior spaces and urban canyon. To overcome + +![](images/d9da8daa5ab5af46460ee1950a50f23e4df131a028e1412294e5dd9b1422a0c5.jpg) +Figure 1: Person positioning using overhead fisheye camera: We detect humans on omnidirectional images and then project detects onto the real world coordinates to obtain physical locations. Compared with using perspective cameras, our fisheye camera based solution is favored in low cost, high accuracy, and fast speed. + +such limitation, various alternative solutions are investigated. Signal based solutions, including Bluetooth [13] and WiFi [74], are popular, but they are easily interfered by changing environments and nearby human bodies [73]. A complementary stream of work is vision based; they typically make use of traditional cameras, RGBD cameras, or in-built smartphone cameras, and enjoy the advantage of reliable services. To get location information, visual positioning solutions usually refer to a pre-acquired 3D map or a geotagged database as the scene representation [63], or directly utilize the captured image to estimate the camera pose [39]. + +Although visual localization has been a hotspot issue for many years, existing efforts are mainly dedicated to urban place recognition or indoor camera localization, based on perspective cameras [63, 39, 62, 43]. None of them addresses person positioning by using overhead fisheye cameras, even though fisheye cameras are widely used in visual surveillance applications. One possible reason is the lack of accessible datasets, compounded by considerable costs in- + +volved in data collection. In this article, we provide a large-scale overhead fisheye dataset, LOAF, for person detection and localization in both indoor and outdoor scenes. + +Compared with perspective cameras, overhead (top-view) fisheye cameras are promoted due to less occlusion among people and larger field of view (FOV) - allowing the coverage of a large space using a single, low-cost camera. Only few public datasets [21, 42, 24] provide top-view fisheye data. Unfortunately, they only cover quite few scenes and their people-box annotations do not adequately address the positioning challenge, negatively affecting location approximation (see §3.2 for detailed analysis). Differently, LOAF specifically targets at person localization in surveillance applications, and has the following appealing characteristics: + +- Large-scale: LOAF is the largest in the filed, to our best knowledge. It consists of over 70 videos, with more than 43K frame images, 457K person-detection annotations as well as corresponding location information. +- High diversity: LOAF contains a wide variety of surveillance scenarios; it includes a total of 11 indoor and 40 outdoor scenes, and the data are captured at different times of day and cover different illumination conditions. +- Positioning-aware person-box annotation: LOAF offers radius-aligned human-box annotations. Compared with other person representations, i.e., head center [21], axis-aligned [60] or body-aligned box [42, 24], used in previous fisheye datasets, the radius-aligned box is promoted, as it fits well radially-oriented bodies [42], and, more importantly, it is better aware of the positioning problem. + +Moreover, we devise a person positioning system that first detects persons from raw fisheye images, and then calculates physical locations based on fisheye visual model and altitude information (see Fig. 1). Clearly, high-quality person detection is the crucial premise for precise localization using overhead fisheye cameras. Fisheye lenses provide large FOV, at the cost of strong radial distortion. This makes pedestrian detection in top-view fisheye images a much harder task, compared with using perspective cameras. Studies on overhead fisheye pedestrian detection are very scarce [60, 42, 51, 24, 64]; they rarely concern the link with person positioning, and many of them [60, 42] are even not trainable due to the lack of fisheye data. With our LOAF dataset, we develop a novel query based fisheye human detector. It explicitly exploits fisheye geometry by accommodating rotation equivariance into the matching between queries and human instances during network training. The insight here is intuitive: for a robust fisheye detector, rotation of a fisheye image should result in correspondingly rotated detections. In addition, our detection algorithm learns to predict radius-aligned person boxes, facilitating localization estimation. + +We test our fisheye person detection algorithm as well as our whole positioning system over LOAF. We find that our detector significantly outperforms previous methods, and + +our full system delivers precise localization results. We also empirically show that our algorithm generalizes well on previous top-view fisheye person detection datasets [24, 65]. + +# 2. Related Work + +Accurate Positioning. GPS is the most popular system for outdoor localization. As it requires LOS between the satellites and the handset, GPS does not function well in urban canyons, indoors and basements [30, 26]. This triggered the development of alternative positioning solutions, following a multi-disciplinary approach. Concretely, there are two main schemes of the alternatives: signal-based and vision-based. + +Signal-based positioning systems typically lean on sound wave [50], geomagnetism [32], radio frequency (RF) [26, 74, 54, 13, 1], and infrared radiation (IR) [71], as well as different location determination techniques, such as TOA (time of arrival) [30] and RSS (received signal strength) [26]. The main challenge to signal-based systems is the sensitivity to environment changes, such as object moving, diffraction and reflection, which affect signal propagation [26]. + +Visual data is another potential information source for precise localization. Since put forward [61], visual positioning has become a hot topic in robotics and computer vision. Some methods adopt a pre-built geo-tagged database or a 3D scene model, as the reference for camera location estimation [33, 77, 66, 78, 76]. Some others rely on recognizing some deployed coded targets [27, 59, 20, 31, 36], e.g., concentric rings, barcodes, colored dots, etc. Some recent ones utilize deep learning techniques to replace some components (e.g., image retrieval, descriptor matching) in traditional systems [4, 16], or regress the camera pose directly [39, 38, 7]. Though promising, existing visual positioning systems are mostly founded on perspective cameras. + +Due to the problem complexity, there is no persuasive solution for precise positioning yet, and hybrid schemes are often applied in practice. Fisheye cameras have advantage of providing wide FOV with low cost and reduced occlusion, while the research landscape is sparse for fisheye camera based localization [79, 21]. To foster research in this direction and facilitate practical deployment, we contribute the first overhead fisheye dataset, to our knowledge, that allows to conduct the task of person localization at large scale. + +Deep Learning based Visual (Camera) Localization. Regarding application scenarios, scholars in computer vision community are mainly aware of city-scale location recognition [2, 72, 58, 57] and indoor camera localization [5, 67]. Popular visual localization approaches can be divided as retrieval-based, regression-based, and structure-based, according to the camera pose estimation strategy. Retrieval-based methods [58, 3, 23, 75, 56] represent a scene as a database of geo-tagged photos and use geo-tag of the most relevant database photo as an approximation to the camera position [58]. Regression-based methods learn to encode + +the scene into a deep network and directly regress a 6DOF camera pose [39, 67, 38] from a captured image. Structure-based methods [6, 55, 29] pose the localization problem as a camera resection task [58]. They first represent scenes via 3D models and establish a set of 2D-3D matches, then recover the full camera pose by employing a PnP solver [34] inside a RANSAC [28] loop. + +These visual positioning techniques seek to localize images captured by handheld devices [43, 11] or vehicle cameras [48] and demand pre-created geo-tagged databases or 3D maps. And they work on an active mode – users need to carry the cameras. Differently, we address person localization in surveillance scenarios, by using stationary, overhead fisheye cameras. This yields a passive, low-cost scheme, where the localization is completed by a numerical solution on the fisheye model fused with altitude information. Thus our scheme faces a different challenge, i.e., conducting robust person detection from non-rectilinear fisheye images. Overall, our scheme fills the gap left by conventional studies and is complementary to existing positioning systems. + +Person Detection in Overhead Fisheye Images. As a canonical subproblem of object detection, pedestrian detection has long received great interest owing to its broad applications such as intelligent surveillance and autonomous vehicles [12, 8]. By contrast, people detection in overhead fisheye images has been studied much less, due to the absence of such datasets. Moreover, adapting standard pedestrian detectors to top-view fisheye cameras is difficult [15]: First, the appearance of people in fisheye images is arbitrary-oriented, while in perspective images, people typically appear upright. Second, people suffer from severe geometric distortions, particularly in the fisheye image's periphery. + +Faced with the above challenges, early attempts make use of handcrafted features (e.g., HOG, LBP) as well as standard pedestrian detectors with slight modifications to account for fisheye geometry [40, 14, 17, 69]. The common approach is dewarping fisheye images [14] or features [40] so as to approximate normal people' appearances from the deformed ones. Though this simplifies the classification of features, approximation errors are inevitable, causing performance degradation [64]. Later, a few CNN-based fisheye detectors were developed. Some of them are training-free. For example, [60] runs standard YOLOv2 [52] on dewarped versions of overlapped windows extracted from a fisheye image. Li et al. [42] rotate a fisheye image in $15^{\circ}$ increments, and apply off-the-shelf YOLOv3 [53] only to the top-center region of each rotated image, where people usually appear upright. Some more recent methods are trainable: [64] trains YOLOv2 with rotated perspective images so as to handle omnidirectional images without test-time transformation; [24] trains YOLOv3 with human-aligned boxes. + +Although many prior arts [60, 42, 64] allowing to detect persons without any fisheye training data, they require a cer- + +tain amount of computation time for post-processing: [60] carries out detection in multiple perspective images dewarped from one omnidirectional image; [42] applies YOLOv3 24 times to each fisheye image; [64] needs a grouping process to eliminate numerous redundant results, caused by a rotation-invariant training strategy. Hence, the utility of previous methods is limited in the context of visual positioning. Our analysis in §3.2 sheds light on the weaknesses of human representations adopted by existing fisheye detectors (e.g., head center [21], horizontal or body-aligned box [60, 42, 24]) in regard to localization. Thus we supply our large-scale dataset with positioning-aware person-detection annotation. As a result, our human detector can benefit from end-to-end, fisheye visual pattern learning and output radius-aligned body-boxes for precise positioning. Further, by regularizing the learning of image representations and instance queries with rotation equivariance, our algorithm naturally addresses the omnidirectional nature of fisheye images, yet using standard detection network architecture designed for perspective images. + +# 3. LOAF Dataset + +# 3.1. Dataset Acquisition + +We first describe how our fisheye images are collected. Apparatus and Technical Specifications. A TL-IPC59AE fisheye camera with $1.1\mathrm{mm}$ focal length is adopted for data recording. It has a wide FOV, reaching the full circle in the horizontal plane and $180^{\circ}$ in the vertical plane. This offers a clear advantage in reducing deployment cost – installing just one fisheye camera instead of multiple conventional cameras to monitor the same region. However, the severe geometric distortions introduced prevent the use of standard detectors, which are designed for conventional cameras [8]. Data Capturing. The fisheye camera is mounted on the ceiling (indoors) or poles (outdoors), $2.5\sim 4.0\mathrm{m}$ from the ground with $200\sim 300\mathrm{m}^2$ FOV. Considering the factors such as scenario diversity, pedestrians density and weather condition, we capture 110 fisheye image sequences in 80 realistic scenarios as the raw data pool. The recorded sequences span 14 hrs; the image resolution is $2952\times 2952$ pixels, and the frame rate is $10\sim 20$ fps. Eventually, 42,942 images, sampled at 1 fps, are collected to construct our LOAF dataset. + +# 3.2. Dataset Annotation + +We next describe how our fisheye images are annotated. Person Detection. As the performance of localization relies critically on the quality of person detections, significant effort should be spent on the fisheye person-detection annotation. Some human-detection representations were explored in previous datasets: [21] labels the center point of each human head; [42, 24] opt for human-aligned person-boxes. However, these representations have several shortcomings, especially with regards to the localization task. First, they suffer from some inherent limitations. The point-based rep + +
Dataset#Scene#Video#Image#PeopleMax ResolutionFOV (m2)AnnotationFPS
IndoorOutdoorTotalAvg.MaxPeople DetectionLocationAttribute
PIROPO [21]2027----800×600<50Head Center10
HABBOF [42]2045,83720,4663.552,048×2,048<36Human-aligned box12~30
MW-R [24]60198,75222,8252.661,488×1,488<36Human-aligned box15
CEPDOF [24]50825,504173,0736.8132,048×2,048<36Human-aligned box1~10
WEPDTOF [65]1401610,54493,3638.9352,592×1,944<36Human-aligned box1~10
LOAF11397442,942457,76210.5652,952×2,952200~300Radius-aligned box✓✓10~20
+ +Table 1: Overhead fisheye datasets comparison (§3.4). LOAF is the largest in terms of the total number of pedestrian and scene categories. + +![](images/e8ecf0dabec41382c1f4818a5fcc12928e67a8a026178700fedcc287896a15a8.jpg) +Figure 2: Human annotation comparison for visual positioning (§3.2). Previous methods typically use the detected human head [21] ( $\bullet$ ) or the center ( $\bullet$ ) of human-aligned body-box ( $\langle \rangle$ ) [42, 24] to determine the physical location $P$ , bringing positioning errors (i.e., $PP_{1}$ , $PP_{2}$ ). We instead leverage the radius-aligned box ( $\square$ ) as human representation. The midpoint ( $\bullet$ ) of side $AB$ , i.e., the closest point to the image center on the radius-aligned box, better corresponds to the human actual position. + +resentation is not applicable in other analysis tasks (e.g., re-identification, attribute recognition); the human-aligned box has ambiguity [10, 68] – the ground-truths of human-aligned boxes are not uniquely determined [24]. Second, and most important, these human-detection representations cannot meet the need of precise localization. Clearly, based on the fisheye camera model, one can project 2D detections on the 3D world for localization. However, the center of human head or of human-aligned box is not the exact placement occupied by human on the image plane, causing errors to estimations of human physical position (see Fig. 2). + +We instead label each person through a radius-aligned rectangular box. Such representation is favored as it: i) allows unique groundtruth box assignment; ii) fits well radially-oriented human bodies presented in fisheye images; and iii) better corresponds to the actual position of human on the image plane, facilitating physical localization. Notably, although the radially-oriented box constraint was explored in a prior fisheye detector [42], there is no previous datasets provide such kind of annotation, neither is there any literature points out the advantage of such representation in localization. Finally, around 457K human box annotations are obtained. High-quality annotation is ensured via a rigorous quality check, conducted by highly skilled reviewers. + +Person Localization. For each scene, a $10\mathrm{m}$ ruler (with $0.05\mathrm{m}$ accuracy) is placed on the ground, and one end of the + +![](images/e3f4fafde1e206055214c00a1cb3f0019fe43878e6a4b6156eb82f5574ed418b.jpg) +(a) +Figure 3: Calibration for groundtruth person location annotation. (a) Ground makers (with $0.05\mathrm{m}$ precision). (b) Top-view fisheye image capture for calibration. See §3.2 for details. + +![](images/9af3d095353cd10aa67ed5028cc2c96b6e9c92936d06344f43b061731640c848.jpg) +(b) + +ruler is directly under the fisheye lens (cf. Fig. 3 (a)). We take a fisheye picture and use this marked picture as the calibration for all the dataset images recorded in this scene (cf. Fig. 3(b)). Finally, for each annotated human, the physical location, at sub-decimeter precision, is provided (cf. Fig. 4). + +Scene Attribute. To enable in-depth analysis, each image is annotated with multiple attributes, including day/night, outdoor/indoor, and sunny/rain/foggy/snow. + +# 3.3. Dataset Design + +We then list several key aspects of our dataset design. + +Privacy Protection. To protect personal information, we apply the gaussian filter to blur all the visible facial regions in our dataset, and conduct experiments on the blurred data. Dataset Splits. LOAF contains 29,569 training, 4,600 validation, and 8,773 testing images (approximately 7 train, 1 val, and 2 test). Moreover, to better evaluate models' generalization ability, LOAF is split into five sets: train (7/28 indoor/outdoor scenes, 29,569 images), val seen (1/2 indoor/outdoor scenes, 1,700 images), val unseen (2/3 indoor/outdoor scenes, 2,900 images), test seen (2/3 indoor/outdoor scenes, 2,774 images), test unseen (2/8 indoor/outdoor scenes, 5,999 images). There are no overlapping scenes between unseen and train sets. + +Dataset Accessibility. Only the desensitized version of our dataset will be released online, under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License [19]. + +# 3.4. Dataset Features and Analysis + +Finally, we present statistic analysis of LOAF in comparison with existing overhead fisheye datasets [21, 42, 24]. + +![](images/3874faf83a1f87cb98734690d995bab419a5c4bb1b11818c892a2d4d0c5ea112.jpg) +playground | winter | noon +(a) Our proposed LOAF + +![](images/332e247dd4cce7a72e8f56e8da89acb758c6b3780779aaf43250a19015b116b1.jpg) +hall | fall | afternoon + +![](images/0dd1005fd968575b6b564258bbd47967bdea814f2b54863d087f91051fbd04f7.jpg) +street | spring | morning + +![](images/bb593de8269c91711ec122fba21d20b3c712e93d2109b6d365dc78eb87390715.jpg) +(b) PIROPO [21] + +![](images/4c39d8656378ebc5b2543cd9cef2012dc6d391329b153e7985a695ed7d3edc11.jpg) +(c) HABBOF [42] + +![](images/32395c7927e4611b23622ac2de31d9ebe2025fcce7026c2ffac12a12b84ee047.jpg) +(d) CEPDOF [24] + +![](images/f0a4041d8b3e2c825a8308c3dd8591271ef49dd0be458a169b8a4a5b487e57d6.jpg) +Figure 4: Example images from different datasets ( $\S 3.2-\S 3.4$ ). Prior datasets [21, 42, 24] are restricted to few indoor scenes with person detection annotation only, i.e., head center $(\bullet)$ or human-aligned box $(\square)$ . In contrast, LOAF covers challenging indoor and outdoor scenes with human detection, localization and scene attribute annotations. The person-detection annotation is given as the radius-aligned box $(- \square)$ , which is more suitable for localization. For better visualization, we only present location ground-truths for some of persons. +(a) Person scale + +![](images/72e18a3c6c6a1f9edf9be646ab56ad26f35e65015842e43e9b4f596851fb8106.jpg) +(b) Person locations + +![](images/327c7873cd49ad6ddcd326dc87d87ad1e4a0e473f74ebe418369c540a32c6724.jpg) +(c) Person density +Figure 5: Dataset Statistics (§3.4): We summarize LOAF with the distribution of (a) person scale (area in pixel), (b) person locations (horizontal distance between human and the fisheye lens in the real world), and (c) person density (number of person per image). + +LOAF distinguishes itself from three aspects (cf. Table 1): + +Large-scale: LOAF has 42,942 fisheye images with more than 457K person boxes. Moreover, LOAF data are captured by an advanced fisheye camera, which is capable of covering a larger area $(200\sim 300\mathrm{m}^2)$ with higher pedestrian density (2~65 persons per scene, 10.5 in average). This makes LOAF the largest overhead fisheye dataset in terms of the total number of pedestrian and scene categories. + +High Diversity: Existing datasets limit in data diversities, i.e., only containing very few indoor scenes (2~14) and completely missing outdoor scenarios (cf. Fig. 4). In contrast, LOAF involves 51 realistic scenes, including 11 indoor scenes (e.g., lab, office, library, classroom) and 40 outdoor scenes (e.g., street, playground, parking lot, square). The recorded data cover four seasons under different illumination (e.g., morning, noon, afternoon) and weather (e.g., sunny, rain, snow) conditions, and involve vast variance of human pose (e.g., walking, standing, and sitting), scale, location, and density (cf. Fig. 5). Thus our dataset better reflects the distribution in real-world surveillance scenarios. + +Rich and Positioning-aware Annotation: LOAF is provided with rich ground-truths for detection, localization, and scene attribute, which lays a solid foundation for fisheye camera based human-centric analysis. Hence, as demonstrated in §3.2, the radius-aligned human-box representation is adopted during our annotation. Compared with human- + +head center based point annotation [21] and human-aligned person-boxes [42, 24] used in previous datasets, radius-aligned human-boxes are more suitable for the position task. + +# 4. Our Approach + +Our overhead fisheye camera based person localization solution comprises two parts. The former computes 2D detections that locate the people on the image plane (§4.1). The latter converts the 2D detections to 3D-world coordinates, obtaining the physical location of the people (§4.2). + +# 4.1. Overhead Fisheye Person Detection + +Core Idea: Rotation Equivariance. One of the reasons for the tremendous success of CNNs is their equivariance to horizontal and vertical shifts and the resulting invariance to local deformations [41, 25]. This stimulates a line of efforts to learn robust representations equivariant to generic types of transformations [35, 18, 70]. Formally, a representation $f$ is said to be equivariant with a geometric transformation $g$ (e.g., cropping, flipping) for an input (image) $I$ if: + +$$ +f (g (I)) \approx g (f (I)). \tag {1} +$$ + +That is to say, the output representation $f(I)$ is changed in the same way as the transformation $g$ imposed to the input $I$ . + +In this work, we devise a query-based fisheye person detector that exhibits $360^{\circ}$ -rotational equivariance through an elaborately designed training protocol. Our key insight is derived from the omnidirectional nature of this task: if one rotates the input fisheye image by an arbitrary angle, then the outputs of a robust fisheye detector should change accordingly. We thus design a rotation equivariant training strategy, which forces the matching between object queries and image representations to be equivariant against $360^{\circ}$ -rotations. In this way, the rotational symmetry of omnidirectional images is explicitly addressed, without architectural modification of standard detectors developed for perspective images. Rotation Equivariant Training for Query-based Fisheye Detection. As shown in Fig. 6, our fisheye detector is built upon DETR [9], promoted by a rotation equivariant training strategy. Basically, DETR conducts detection in a query-based fashion. Denote $\mathcal{F}$ as a feature encoder that extracts representation $I$ of image $I$ , and $\kappa$ as a query creator + +![](images/84ddbf217cfe1d9f63999d77f1d13c59b4542d4725a8091df5c551f2f2bd612a.jpg) +Figure 6: Our rotation equivariant training strategy for query-based fisheye person detection (§4.1). For equivariant training, object queries $\{\pmb{q}_n^{g^r}\}_{n=1}^N$ created for rotated image $g^r(I)$ and the rotated representation $g^r(I)$ are fed into the decoder $\mathcal{D}$ ; the rotated ground-truths $\{\pmb{b}_{\ell(n)}^{g^r}\}_{n=1}^N$ are set as the training targets. + +that outputs a set of $N$ object-aware descriptors $\{\pmb{q}_n\}_{n=1}^N$ from $\pmb{I}$ . DETR employs $\{\pmb{q}_n\}_{n=1}^N$ as queries to retrieve target objects from $\pmb{I}$ : + +$$ +\left\{\hat {\boldsymbol {b}} _ {n} \right\} _ {n = 1} ^ {N} = \mathcal {D} (\boldsymbol {I}, \left\{\boldsymbol {q} _ {n} \right\} _ {n = 1} ^ {N}), \tag {2} +$$ + +where $\pmb{I} = \mathcal{F}(I)$ , $\{\pmb{q}_n\}_{n=1}^N = \kappa(\pmb{I})$ , and $\mathcal{D}$ refers to the Transformer decoder which formulates the object-query matching process via neural cross-attention computation. $\{\hat{\pmb{b}}_n\}_{n=1}^N$ are the set of predicted parameterized object bounding boxes. + +Our rotation equivariant training further encourages robust object-query matching which is equivariant against rotations. First, given an input rotation transformation $g^r$ , a robust fisheye detector is desired to be able to extract rotation-equivariant representation. Analogous to Eq. 1, we have: + +$$ +\mathcal {F} \left(g ^ {r} (I)\right) \approx g (\mathcal {F} (I)) = g ^ {r} (\boldsymbol {I}). \tag {3} +$$ + +Also, it is reasonable to assume that the final output of a robust fisheye detector should be changed in the same way to the rotation $g^{r}$ applied to the input fisheye image $I$ : + +$$ +\left\{\boldsymbol {b} _ {\ell (n)} ^ {g ^ {r}} \right\} _ {n = 1} ^ {N} \approx \mathcal {D} \left(\boldsymbol {I} ^ {g ^ {r}}, \left\{\boldsymbol {q} _ {n} ^ {g ^ {r}} \right\} _ {n = 1} ^ {N}\right), \tag {4} +$$ + +where $I^{g^r}$ indicates the feature of rotated image $g^{r}(I)$ , i.e., $\pmb{I}^{g^{r}} = \mathcal{F}(g^{r}(I))$ . Similarly, $\{\pmb{q}_n^{g^r}\}_{n=1}^N$ denote the object queries derived from $g^{r}(I)$ , i.e., $\{\pmb{q}_n^{g^r}\}_{n=1}^N = \kappa(I^{g^r})$ . $\{\pmb{b}_{\ell(n)}^{g^{r}}\}_{n=1}^N$ are the rotated groundtruth bounding boxes, where $\ell(n)$ returns the groundtruth index for $n$ -th query. + +Considering Eq.3 and Eq.4, we can have: $\{\pmb{b}_{\ell(n)}^{g^r}\}_{n=1}^N \approx \mathcal{D}(g^r(\pmb{I}), \{\pmb{q}_n^{g^r}\}_{n=1}^N)$ . Hence our rotation equivariant training objective is given as: + +$$ +\mathcal {L} _ {\text {r o t a t - e q u i}} = \mathcal {L} _ {\det } \left(\left\{\boldsymbol {b} _ {\ell (n)} ^ {g ^ {r}} \right\} _ {n = 1} ^ {N}, \mathcal {D} \left(g ^ {r} (\boldsymbol {I}), \left\{\boldsymbol {q} _ {n} ^ {g ^ {r}} \right\} _ {n = 1} ^ {N}\right)\right). \tag {5} +$$ + +Here $\mathcal{L}_{\mathrm{det}}$ is the standard detection loss in DETR [9]. As such, the rotation equivariance properties for both fisheye representation $\mathcal{F}$ (cf. Eq.3) and the query-based detection prediction $\mathcal{D}(\boldsymbol {I},\{\pmb {q}_n\}_{n = 1}^N)$ (cf. Eq.4) are sought in a single training target. This also allows us to effortlessly adapt standard + +![](images/d9515f35afae0c94c683b1ac86271a358c47042b91c37bf32e6d1296edf330e5.jpg) +Figure 7: Our fisheye camera model based person localization (§4.2). Here $\pmb{p}$ and $\pmb{p}'$ denote the projection point of the distortion point $P$ by fisheye lens and normal perspective lens, respectively. + +DETR to our omnidirectional detection setting. Note that our rotation equivariant training differs from rotational data augmentation technique which only views rotated images as individual training samples (see §5.4 for detailed experiments). + +# 4.2. 2D-3D Projection based Person Localization + +General Fisheye Camera Model. The perspective projection of a normal pinhole camera can be written as $r = f \tan \theta$ , where $r$ indicates the projection distance between the principal point and the image point, $f$ is the focal length, and $\theta$ is the angle between the incident ray and the camera's optical axis. However, fisheye lens does not follow this perspective projection model [49], as the FOV equals to $180^{\circ}$ (cf. Fig. 7). Fortunately, the image formation of different kinds of fisheye lenses can be approximated by a general polynomial projection model [37], i.e., + +$$ +r (\theta) = \sum_ {i = 1} ^ {n} k _ {i} \theta^ {2 i - 1}, \quad n = 1, 2, 3, 4, \dots \tag {6} +$$ + +High distortions can be handled well when $n = 5$ [37]. The coefficients $k_{s}$ can be obtained from camera calibration. + +2D-3D Projection. Given a detected human location point $\pmb{p} = (u,v)^{\top}$ in the fisheye image pixel coordinate system, our target is to calculate its 3D location $\pmb{P} = (X,Y,Z)^{\top}$ in the camera coordinate system, where $Z$ is the altitude of the fisheye camera and primarily known. To do so, one can first calculate $r$ as: $r = \sqrt{(x^2 + y^2)}$ , where $x = (u - u_0) / f$ and $y = (v - v_0) / f$ , and $(u_0,v_0)^{\top}$ are the coordinates of the principal point in the fisheye image. Then $\theta$ can be obtained by solving Eq. 6 using a numerical means [37]. With the altitude $Z$ of the camera, the actual location $(X,Y)^{\top}$ is given as: + +$$ +\binom {X} {Y} = Z \binom {\tan \theta \cos \phi} {\tan \theta \sin \phi}, \tag {7} +$$ + +where $\phi = \arctan (y,x)$ refers to the polar angle, which is shared by both $\pmb{p}$ and $\pmb{P}$ . + +It can be seen that precise determination of the person location point $\pmb{p}$ on the image plane is vital for estimating the corresponding physical position $\pmb{P}$ . However, most previous approaches, restricted to axis-aligned [79, 60] or person-aligned [24] human-box representation, use the center of the detection box to approximate $\pmb{p}$ . Few excep + +
MethodvaltestFPS↑
mAP↑AP50↑AP75↑APn↑APm↑APf↑APseen↑APunseen↑mAP↑AP50↑AP75↑APn↑APm↑APf↑APseen↑APunseen↑
Seide et al. [60]21.859.87.632.828.52.323.219.520.258.27.132.228.33.922.418.910.2
Li et al. [42]28.563.320.146.824.21.333.829.327.265.221.347.224.81.331.827.60.6
Tamura et al. [64]34.872.127.751.738.88.738.832.934.272.828.753.737.36.539.533.210.2
RAPiD [24]40.377.934.855.341.99.244.737.639.277.935.454.840.17.944.237.38.4
Ours47.482.648.464.154.314.150.845.746.281.147.366.153.512.649.344.912.1
+ +Table 2: Person detection results on val and test sets of LOAF (§5.2). + +
MethodmAP↑AP50↑AP75↑Precision↑Recall↑F-Score↑
Seide et al. [60]20.950.610.280.639.553.0
Li et al. [42]34.275.728.686.365.474.4
Tamura et al. [64]29.361.023.488.851.265.0
RAPiD [24]39.385.426.089.278.783.6
Ours47.288.538.290.387.688.9
+ +tions [21], built on point-based human representation, treat the center of the detected human head as $\pmb{p}$ . However, they suffer from a similar issue as the human head center is even often far from the exact position $\pmb{p}$ human stand on, w.r.t. the image plane. Instead, with our radius-aligned human-box representation, the closest point to the principal point on the bounding box better corresponds to $\pmb{p}$ . + +# 4.3. Implementation Details + +Network Architecture. Our fisheye person detector is built upon DAB-DETR [45], a prevalent variant of DETR [9] but converges much faster. Swin-T [46] is utilized as the backbone. For our LOAF with radius-aligned person boxes, the output of our detector is a 4D vector $\pmb{b} \in [0,1]^4$ that parameterizes 2D center coordinates, height, and width. Note that, for traditional fisheye detection datasets like [24, 65] with arbitrary-oriented person box annotations, an extra output dimension is needed for rotation angle regression. + +Training Objective. Our fisheye person detector is end-to-end trained by jointly optimizing the vanilla detection loss used in DETR [9, 45] (referred as $\mathcal{L}_{\mathrm{Det}}$ ) and our proposed rotation-equivariant constraint (i.e., $\mathcal{L}_{\mathrm{rotat - equi}}$ in Eq. 5): + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {d e t}} + \lambda \mathcal {L} _ {\text {r o t a t - e q u i}}, \tag {8} +$$ + +where the coefficient $\lambda$ is empirically set to 0.5. + +Training. Our fisheye detector is trained with a batch size of 8 for 50 epochs, where the AdamW [47] optimizer is employed with base learning rate 2e-4 and decayed by 0.1 at epoch 40. The remaining hyper-parameters are determined following [64, 24]. Specifically, we initialize backbones with ImageNet [22] pre-trained weights and adopt standard data augmentation techniques, i.e., color jitter, horizontal flip, and random scaling, with a base training size of $608 \times 608$ . For CEPDOF [24] and WEPDTOF [65], we use a batch size of 128 and pre-train the detector on COCO [44] for 50 epochs to prevent over-fitting, as in [24, 65]. For the computation of our rotation-equivariant loss $\mathcal{L}_{\mathrm{rotat - equi}}$ , the training images are rotated by a degree randomly sampled from 0 to 360. Our detector is implemented in PyTorch and trained on eight + +Table 3: Person detection results on CEPDOF [24] (\$5.2). + +
MethodmAP↑AP50↑AP75↑Precision↑Recall↑F-Score↑
Seide et al. [60]16.139.49.070.938.650.0
Li et al. [42]25.269.930.281.464.572.0
Tamura et al. [64]28.859.824.277.052.462.4
RAPiD [24]37.772.026.873.367.870.4
Ours45.885.636.684.974.679.8
+ +Table 4: Person detection results on WEPDTOF [65] (\$5.2). + +NVIDIA Tesla V100 GPUs with a 32GB memory per-card. Inference. Once trained, our fisheye detector can be directly applied for locating persons on the omnidirectional image plane. After that, the physical locations of the detected persons can be easily obtained through the numerical solution described in §4.2. For fisheye person detection, we follow prior work [60, 42, 64, 24] to use $1024 \times 1024$ input resolution without any test-time augmentation or post-processing. Testing is conducted on a single NVIDIA V100 GPU with 16 GB memory. + +# 5. Experiment + +# 5.1. Experimental Setup + +Evaluation Protocol. On the top of LOAF, we conduct experiments for fisheye based person detection and localization. Following the dataset splitting (cf. §3.3), performance are reported on seen and unseen scenes, respectively, for both val and test sets. This allows us to assess the generalization ability over different surveillance scenarios. For comprehensive study, we further report person detection performance on two existing fisheye datasets, CEPDOF[24] and WEPDTOF[65]. Note that localization cannot be test since [24, 65] only provide person bounding box annotations. Evaluation Metrics. For fisheye person detection, we follow COCO [44] to report the mean average precision (mAP) for IoU $\in$ [0.5:0.05:0.95]. We also employ AP $_{50}$ and AP $_{75}$ for further analysis. For fisheye person localization, we measure positional error (PE) in meters, i.e., Euclidean distance of calculated position and ground-truth position, as the conventions in visual localization [43, 58, 73, 79]. For detailed evaluation, on our LOAF, we report performance w.r.t. horizontal distance between human and the fisheye lens, i.e., near (0~10 m), middle (10~20 m), and far (larger than 20 m). Hence we have AP $_{n,m,f}$ and PE $_{n,m,f}$ accordingly. + +# 5.2. Performance on Person Detection + +LOAF. We first report the person detection performance on LOAF. Specifically, four recent deep learning based fisheye + +
Methodvaltest
mPE↓PEn↓PEm↓PEf↓PEseen↓PEunseen↓mPE↓PEn↓PEm↓PEf↓PEseen↓PEunseen↓
Seide et al. [60]1.2980.5611.3323.1091.2061.3821.3210.7061.3093.4821.3061.386
Li et al. [42]0.8980.5020.8712.6500.8320.9620.9130.5430.8842.7800.9040.998
Tamura et al. [64]0.7550.4290.7361.8620.7090.8210.7780.4710.8262.1600.7240.836
RAPiD [24]0.6740.4260.6231.4030.6250.7570.6820.4610.6641.4450.6380.776
Ours0.3680.1440.3630.7750.3180.4020.3740.1480.3750.8190.3260.398
+ +person detectors [60, 42, 64, 24] are involved for comparison. Among them, [60, 42] are training-free, thus their scores are obtained by directly running the algorithms on the val and test data. As [64, 24] are trainable methods, we first train them on the train set of LOAF following their official setups, and then report the scores on the val and test sets. Quantitative comparison results are presented in Table 2. Some essential observations are as follows: + +- Our fisheye person detector significantly outperforms existing methods across all the metrics. For example, our detector provides a considerable performance gain in mAP, i.e., $7.1\%$ and $7.0\%$ higher than the second best, RAPiD [24], on the val and test sets, respectively. +- Our detector not only handles nearby persons but also approaches distant targets well. Specifically, for the targets at $10\sim 20\mathrm{m}$ away from the fisheye lens, our performance gain over other methods is more significant than the improvement reported with the persons at $0\sim 10\mathrm{m}$ distance. +- Our detector also yields small performance gap between the seen and unseen scenes (e.g., $49.3 \rightarrow 44.9$ in terms of mAP), validating our good generalizability. +- For those persons at very far distance ( $>20\mathrm{~m}$ ), our algorithm, though still giving higher scores than other competitors, suffers from great performance degradation. This sheds light on the direction of our future efforts. + +CEPDOF [24]. CEPDOF contains eight videos with 25,504 frames in total. Following the official setup, we train our fisheye person detector on HABBOF [42] and MW-R [24] datasets, and report performance on CEPDOF. As shown in Table 3, our fisheye detector delivers state-of-the-art performance: it significantly outperforms RAPiD [24], the current top-leading algorithm, by $7.9\%$ in terms of mAP. + +WEPDTOF [65]. WEPDTOF has 16 videos with 10,544 frames in total. Following the official setup, we use HAB-BOF [42], MW-R [24], and CEPDOF [24] for training and WEPDTOF for testing. Table 4 summarizes the results. Impressively, our detector greatly suppresses all the other competitors across all the evaluation metrics. + +# 5.3. Performance on Person Localization + +Then we study the person localization performance on LOAF. None of previous fisheye person detectors [60, 42, 64, 24] are aware of the task of person localization. We therefore follow the common practice [79, 21] in the field of visual localization: for [60, 42, 64, 24], we project + +Table 5: Person localization results on val and test sets of LOAF (§5.3). + +
MethodmAP↑val seenval unseen
mAP↑AP50↑AP75↑mAP↑AP50↑AP75↑
Baseline [45]43.146.481.248.440.976.238.9
+ Rotation Aug.45.649.282.852.843.278.943.9
+ Rotation Equ.47.450.883.854.845.780.547.3
+ +Table 6: Diagnostic results on val set of LOAF (§5.4). + +centers of their detected human boxes on the 3D world, based on the same strategy of ours (cf. §4.2), for physical position estimation. As shown in Table 5, our system produces much small localization errors in comparison with [60, 42, 64, 24], i.e., $\mathbf{0.374m}$ vs $0.682\mathrm{m}[24]$ and 0.773 m of [64] on the test set of LOAF. In addition, for all the methods, the localization performance is declined as target distance increases, but our system suffers from the smallest drop. Moreover, the results suggest there is still large room for improvement, thus we hope that our dataset could encourage continuous efforts in this challenging task. + +# 5.4. Diagnostic Study + +Table 6 studies the efficacy of our rotation equivariant training strategy (§4.1), on the val set of LOAF. Our baseline model [45] (row #1) gains $43.1\%$ mAP. After adopting rotational data augmentation (row #2), the performance boosts by $2.5\%$ mAP. By contrast, our rotation equivariant training brings much larger improvements over the baseline, e.g., $4.3\%$ mAP gain. It is remarkable that, training with standard rotational data augmentation technique can be viewed as a specific case of our equivariant training - only learning rotation-equivariant object-querying (cf. Eq. 4). + +# 6. Conclusion + +We presented LOAF – the first top-view fisheye dataset that supports large-scale study for person localization in realistic surveillance scenarios. With radius-aligned personbox annotations and precise location ground-truths, LOAF closes a crucial gap in the literature as these cases are not covered by previous datasets and annotation protocols. We further proposed an efficient fisheye person detection model that is equipped with a rotation-equivariant training strategy. The physical locations of detected persons are formulated based on the fisheye model and the altitude of the camera. 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Instead of existing efforts devoted to localizing tourist photos captured by perspective cameras, in this article, we focus on devising person positioning solutions using overhead fisheye cameras. Such solutions are advantageous in large field of view (FOV), low cost, anti-occlusion, and unaggressive work mode (without the necessity of cameras carried by persons). However, related studies are quite scarce, due to the paucity of data. To stimulate research in this exciting area, we present LOAF, the first large-scale overhead fisheye dataset for person detection and localization. LOAF is built with many essential features, e.g., i) the data cover abundant diversities in scenes, human pose, density, and location; ii) it contains currently the largest number of annotated pedestrian, i.e., 457K bounding boxes with ground-truth location information; iii) the body-boxes are labeled as radius-aligned so as to fully address the positioning challenge. 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Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 611, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 611, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 611, + 287, + 684 + ], + "type": "text", + "content": "Accurate position finding of persons attracts growing interest from both research and industrial communities, since it plays a crucial role in numerous location-sensitive application scenarios (e.g., surveillance, smart home, public health). Nevertheless, due to the line-of-sight (LOS) issue, GPS is unreliable in interior spaces and urban canyon. To overcome" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 220, + 542, + 411 + ], + "blocks": [ + { + "bbox": [ + 310, + 220, + 542, + 411 + ], + "lines": [ + { + "bbox": [ + 310, + 220, + 542, + 411 + ], + "spans": [ + { + "bbox": [ + 310, + 220, + 542, + 411 + ], + "type": "image", + "image_path": "d9da8daa5ab5af46460ee1950a50f23e4df131a028e1412294e5dd9b1422a0c5.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 417, + 547, + 473 + ], + "lines": [ + { + "bbox": [ + 305, + 417, + 547, + 473 + ], + "spans": [ + { + "bbox": [ + 305, + 417, + 547, + 473 + ], + "type": "text", + "content": "Figure 1: Person positioning using overhead fisheye camera: We detect humans on omnidirectional images and then project detects onto the real world coordinates to obtain physical locations. Compared with using perspective cameras, our fisheye camera based solution is favored in low cost, high accuracy, and fast speed." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 483, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 616 + ], + "type": "text", + "content": "such limitation, various alternative solutions are investigated. Signal based solutions, including Bluetooth [13] and WiFi [74], are popular, but they are easily interfered by changing environments and nearby human bodies [73]. A complementary stream of work is vision based; they typically make use of traditional cameras, RGBD cameras, or in-built smartphone cameras, and enjoy the advantage of reliable services. To get location information, visual positioning solutions usually refer to a pre-acquired 3D map or a geotagged database as the scene representation [63], or directly utilize the captured image to estimate the camera pose [39]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "Although visual localization has been a hotspot issue for many years, existing efforts are mainly dedicated to urban place recognition or indoor camera localization, based on perspective cameras [63, 39, 62, 43]. None of them addresses person positioning by using overhead fisheye cameras, even though fisheye cameras are widely used in visual surveillance applications. One possible reason is the lack of accessible datasets, compounded by considerable costs in-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 693, + 233, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 233, + 703 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 233, + 703 + ], + "type": "text", + "content": "The first two authors contribute equally to this work." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 703, + 190, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 190, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 190, + 712 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 59, + 703, + 190, + 712 + ], + "type": "text", + "content": "Corresponding author: Wenguan Wang." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19961" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": "volved in data collection. In this article, we provide a large-scale overhead fisheye dataset, LOAF, for person detection and localization in both indoor and outdoor scenes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 287, + 240 + ], + "type": "text", + "content": "Compared with perspective cameras, overhead (top-view) fisheye cameras are promoted due to less occlusion among people and larger field of view (FOV) - allowing the coverage of a large space using a single, low-cost camera. Only few public datasets [21, 42, 24] provide top-view fisheye data. Unfortunately, they only cover quite few scenes and their people-box annotations do not adequately address the positioning challenge, negatively affecting location approximation (see §3.2 for detailed analysis). Differently, LOAF specifically targets at person localization in surveillance applications, and has the following appealing characteristics:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 243, + 287, + 422 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 243, + 287, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 287, + 290 + ], + "type": "text", + "content": "- Large-scale: LOAF is the largest in the filed, to our best knowledge. It consists of over 70 videos, with more than 43K frame images, 457K person-detection annotations as well as corresponding location information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 290, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 290, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 290, + 287, + 337 + ], + "type": "text", + "content": "- High diversity: LOAF contains a wide variety of surveillance scenarios; it includes a total of 11 indoor and 40 outdoor scenes, and the data are captured at different times of day and cover different illumination conditions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 338, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 338, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 338, + 287, + 422 + ], + "type": "text", + "content": "- Positioning-aware person-box annotation: LOAF offers radius-aligned human-box annotations. Compared with other person representations, i.e., head center [21], axis-aligned [60] or body-aligned box [42, 24], used in previous fisheye datasets, the radius-aligned box is promoted, as it fits well radially-oriented bodies [42], and, more importantly, it is better aware of the positioning problem." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 426, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 677 + ], + "type": "text", + "content": "Moreover, we devise a person positioning system that first detects persons from raw fisheye images, and then calculates physical locations based on fisheye visual model and altitude information (see Fig. 1). Clearly, high-quality person detection is the crucial premise for precise localization using overhead fisheye cameras. Fisheye lenses provide large FOV, at the cost of strong radial distortion. This makes pedestrian detection in top-view fisheye images a much harder task, compared with using perspective cameras. Studies on overhead fisheye pedestrian detection are very scarce [60, 42, 51, 24, 64]; they rarely concern the link with person positioning, and many of them [60, 42] are even not trainable due to the lack of fisheye data. With our LOAF dataset, we develop a novel query based fisheye human detector. It explicitly exploits fisheye geometry by accommodating rotation equivariance into the matching between queries and human instances during network training. The insight here is intuitive: for a robust fisheye detector, rotation of a fisheye image should result in correspondingly rotated detections. In addition, our detection algorithm learns to predict radius-aligned person boxes, facilitating localization estimation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "We test our fisheye person detection algorithm as well as our whole positioning system over LOAF. We find that our detector significantly outperforms previous methods, and" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "our full system delivers precise localization results. We also empirically show that our algorithm generalizes well on previous top-view fisheye person detection datasets [24, 65]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 118, + 392, + 131 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 118, + 392, + 131 + ], + "spans": [ + { + "bbox": [ + 306, + 118, + 392, + 131 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 135, + 545, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 135, + 545, + 219 + ], + "spans": [ + { + "bbox": [ + 304, + 135, + 545, + 219 + ], + "type": "text", + "content": "Accurate Positioning. GPS is the most popular system for outdoor localization. As it requires LOS between the satellites and the handset, GPS does not function well in urban canyons, indoors and basements [30, 26]. This triggered the development of alternative positioning solutions, following a multi-disciplinary approach. Concretely, there are two main schemes of the alternatives: signal-based and vision-based." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 220, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 316 + ], + "type": "text", + "content": "Signal-based positioning systems typically lean on sound wave [50], geomagnetism [32], radio frequency (RF) [26, 74, 54, 13, 1], and infrared radiation (IR) [71], as well as different location determination techniques, such as TOA (time of arrival) [30] and RSS (received signal strength) [26]. The main challenge to signal-based systems is the sensitivity to environment changes, such as object moving, diffraction and reflection, which affect signal propagation [26]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 317, + 546, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 546, + 472 + ], + "type": "text", + "content": "Visual data is another potential information source for precise localization. Since put forward [61], visual positioning has become a hot topic in robotics and computer vision. Some methods adopt a pre-built geo-tagged database or a 3D scene model, as the reference for camera location estimation [33, 77, 66, 78, 76]. Some others rely on recognizing some deployed coded targets [27, 59, 20, 31, 36], e.g., concentric rings, barcodes, colored dots, etc. Some recent ones utilize deep learning techniques to replace some components (e.g., image retrieval, descriptor matching) in traditional systems [4, 16], or regress the camera pose directly [39, 38, 7]. Though promising, existing visual positioning systems are mostly founded on perspective cameras." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 473, + 546, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 546, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 546, + 582 + ], + "type": "text", + "content": "Due to the problem complexity, there is no persuasive solution for precise positioning yet, and hybrid schemes are often applied in practice. Fisheye cameras have advantage of providing wide FOV with low cost and reduced occlusion, while the research landscape is sparse for fisheye camera based localization [79, 21]. To foster research in this direction and facilitate practical deployment, we contribute the first overhead fisheye dataset, to our knowledge, that allows to conduct the task of person localization at large scale." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Deep Learning based Visual (Camera) Localization. Regarding application scenarios, scholars in computer vision community are mainly aware of city-scale location recognition [2, 72, 58, 57] and indoor camera localization [5, 67]. Popular visual localization approaches can be divided as retrieval-based, regression-based, and structure-based, according to the camera pose estimation strategy. Retrieval-based methods [58, 3, 23, 75, 56] represent a scene as a database of geo-tagged photos and use geo-tag of the most relevant database photo as an approximation to the camera position [58]. Regression-based methods learn to encode" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19962" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "the scene into a deep network and directly regress a 6DOF camera pose [39, 67, 38] from a captured image. Structure-based methods [6, 55, 29] pose the localization problem as a camera resection task [58]. They first represent scenes via 3D models and establish a set of 2D-3D matches, then recover the full camera pose by employing a PnP solver [34] inside a RANSAC [28] loop." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 287, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 287, + 314 + ], + "type": "text", + "content": "These visual positioning techniques seek to localize images captured by handheld devices [43, 11] or vehicle cameras [48] and demand pre-created geo-tagged databases or 3D maps. And they work on an active mode – users need to carry the cameras. Differently, we address person localization in surveillance scenarios, by using stationary, overhead fisheye cameras. This yields a passive, low-cost scheme, where the localization is completed by a numerical solution on the fisheye model fused with altitude information. Thus our scheme faces a different challenge, i.e., conducting robust person detection from non-rectilinear fisheye images. Overall, our scheme fills the gap left by conventional studies and is complementary to existing positioning systems." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 315, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 287, + 460 + ], + "type": "text", + "content": "Person Detection in Overhead Fisheye Images. As a canonical subproblem of object detection, pedestrian detection has long received great interest owing to its broad applications such as intelligent surveillance and autonomous vehicles [12, 8]. By contrast, people detection in overhead fisheye images has been studied much less, due to the absence of such datasets. Moreover, adapting standard pedestrian detectors to top-view fisheye cameras is difficult [15]: First, the appearance of people in fisheye images is arbitrary-oriented, while in perspective images, people typically appear upright. Second, people suffer from severe geometric distortions, particularly in the fisheye image's periphery." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 460, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 288, + 688 + ], + "type": "text", + "content": "Faced with the above challenges, early attempts make use of handcrafted features (e.g., HOG, LBP) as well as standard pedestrian detectors with slight modifications to account for fisheye geometry [40, 14, 17, 69]. The common approach is dewarping fisheye images [14] or features [40] so as to approximate normal people' appearances from the deformed ones. Though this simplifies the classification of features, approximation errors are inevitable, causing performance degradation [64]. Later, a few CNN-based fisheye detectors were developed. Some of them are training-free. For example, [60] runs standard YOLOv2 [52] on dewarped versions of overlapped windows extracted from a fisheye image. Li et al. [42] rotate a fisheye image in " + }, + { + "bbox": [ + 46, + 460, + 288, + 688 + ], + "type": "inline_equation", + "content": "15^{\\circ}" + }, + { + "bbox": [ + 46, + 460, + 288, + 688 + ], + "type": "text", + "content": " increments, and apply off-the-shelf YOLOv3 [53] only to the top-center region of each rotated image, where people usually appear upright. Some more recent methods are trainable: [64] trains YOLOv2 with rotated perspective images so as to handle omnidirectional images without test-time transformation; [24] trains YOLOv3 with human-aligned boxes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Although many prior arts [60, 42, 64] allowing to detect persons without any fisheye training data, they require a cer-" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": "tain amount of computation time for post-processing: [60] carries out detection in multiple perspective images dewarped from one omnidirectional image; [42] applies YOLOv3 24 times to each fisheye image; [64] needs a grouping process to eliminate numerous redundant results, caused by a rotation-invariant training strategy. Hence, the utility of previous methods is limited in the context of visual positioning. Our analysis in §3.2 sheds light on the weaknesses of human representations adopted by existing fisheye detectors (e.g., head center [21], horizontal or body-aligned box [60, 42, 24]) in regard to localization. Thus we supply our large-scale dataset with positioning-aware person-detection annotation. As a result, our human detector can benefit from end-to-end, fisheye visual pattern learning and output radius-aligned body-boxes for precise positioning. Further, by regularizing the learning of image representations and instance queries with rotation equivariance, our algorithm naturally addresses the omnidirectional nature of fisheye images, yet using standard detection network architecture designed for perspective images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 307, + 397, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 307, + 397, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 307, + 397, + 319 + ], + "type": "text", + "content": "3. LOAF Dataset" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 324, + 420, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 420, + 337 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 420, + 337 + ], + "type": "text", + "content": "3.1. Dataset Acquisition" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "text", + "content": "We first describe how our fisheye images are collected. Apparatus and Technical Specifications. A TL-IPC59AE fisheye camera with " + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "inline_equation", + "content": "1.1\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "text", + "content": " focal length is adopted for data recording. It has a wide FOV, reaching the full circle in the horizontal plane and " + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "text", + "content": " in the vertical plane. This offers a clear advantage in reducing deployment cost – installing just one fisheye camera instead of multiple conventional cameras to monitor the same region. However, the severe geometric distortions introduced prevent the use of standard detectors, which are designed for conventional cameras [8]. Data Capturing. The fisheye camera is mounted on the ceiling (indoors) or poles (outdoors), " + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "inline_equation", + "content": "2.5\\sim 4.0\\mathrm{m}" + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "text", + "content": " from the ground with " + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "inline_equation", + "content": "200\\sim 300\\mathrm{m}^2" + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "text", + "content": " FOV. Considering the factors such as scenario diversity, pedestrians density and weather condition, we capture 110 fisheye image sequences in 80 realistic scenarios as the raw data pool. The recorded sequences span 14 hrs; the image resolution is " + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "inline_equation", + "content": "2952\\times 2952" + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "text", + "content": " pixels, and the frame rate is " + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "inline_equation", + "content": "10\\sim 20" + }, + { + "bbox": [ + 304, + 341, + 545, + 569 + ], + "type": "text", + "content": " fps. Eventually, 42,942 images, sampled at 1 fps, are collected to construct our LOAF dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 577, + 419, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 577, + 419, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 577, + 419, + 588 + ], + "type": "text", + "content": "3.2. Dataset Annotation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "We next describe how our fisheye images are annotated. Person Detection. As the performance of localization relies critically on the quality of person detections, significant effort should be spent on the fisheye person-detection annotation. Some human-detection representations were explored in previous datasets: [21] labels the center point of each human head; [42, 24] opt for human-aligned person-boxes. However, these representations have several shortcomings, especially with regards to the localization task. First, they suffer from some inherent limitations. The point-based rep" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19963" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 65, + 543, + 147 + ], + "blocks": [ + { + "bbox": [ + 56, + 65, + 543, + 147 + ], + "lines": [ + { + "bbox": [ + 56, + 65, + 543, + 147 + ], + "spans": [ + { + "bbox": [ + 56, + 65, + 543, + 147 + ], + "type": "table", + "html": "
Dataset#Scene#Video#Image#PeopleMax ResolutionFOV (m2)AnnotationFPS
IndoorOutdoorTotalAvg.MaxPeople DetectionLocationAttribute
PIROPO [21]2027----800×600<50Head Center10
HABBOF [42]2045,83720,4663.552,048×2,048<36Human-aligned box12~30
MW-R [24]60198,75222,8252.661,488×1,488<36Human-aligned box15
CEPDOF [24]50825,504173,0736.8132,048×2,048<36Human-aligned box1~10
WEPDTOF [65]1401610,54493,3638.9352,592×1,944<36Human-aligned box1~10
LOAF11397442,942457,76210.5652,952×2,952200~300Radius-aligned box✓✓10~20
", + "image_path": "0a223e2c69ab10176ea19643a29696846404e75a7d4986b7ede427712ae801ed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 148, + 547, + 160 + ], + "lines": [ + { + "bbox": [ + 47, + 148, + 547, + 160 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 547, + 160 + ], + "type": "text", + "content": "Table 1: Overhead fisheye datasets comparison (§3.4). LOAF is the largest in terms of the total number of pedestrian and scene categories." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 72, + 167, + 261, + 301 + ], + "blocks": [ + { + "bbox": [ + 72, + 167, + 261, + 301 + ], + "lines": [ + { + "bbox": [ + 72, + 167, + 261, + 301 + ], + "spans": [ + { + "bbox": [ + 72, + 167, + 261, + 301 + ], + "type": "image", + "image_path": "e8ecf0dabec41382c1f4818a5fcc12928e67a8a026178700fedcc287896a15a8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": "Figure 2: Human annotation comparison for visual positioning (§3.2). Previous methods typically use the detected human head [21] (" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": ") or the center (" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": ") of human-aligned body-box (" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\langle \\rangle" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": ") [42, 24] to determine the physical location " + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": ", bringing positioning errors (i.e., " + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "PP_{1}" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "PP_{2}" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": "). We instead leverage the radius-aligned box (" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\square" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": ") as human representation. The midpoint (" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": ") of side " + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "inline_equation", + "content": "AB" + }, + { + "bbox": [ + 46, + 306, + 287, + 395 + ], + "type": "text", + "content": ", i.e., the closest point to the image center on the radius-aligned box, better corresponds to the human actual position." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 402, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 533 + ], + "type": "text", + "content": "resentation is not applicable in other analysis tasks (e.g., re-identification, attribute recognition); the human-aligned box has ambiguity [10, 68] – the ground-truths of human-aligned boxes are not uniquely determined [24]. Second, and most important, these human-detection representations cannot meet the need of precise localization. Clearly, based on the fisheye camera model, one can project 2D detections on the 3D world for localization. However, the center of human head or of human-aligned box is not the exact placement occupied by human on the image plane, causing errors to estimations of human physical position (see Fig. 2)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 534, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 689 + ], + "type": "text", + "content": "We instead label each person through a radius-aligned rectangular box. Such representation is favored as it: i) allows unique groundtruth box assignment; ii) fits well radially-oriented human bodies presented in fisheye images; and iii) better corresponds to the actual position of human on the image plane, facilitating physical localization. Notably, although the radially-oriented box constraint was explored in a prior fisheye detector [42], there is no previous datasets provide such kind of annotation, neither is there any literature points out the advantage of such representation in localization. Finally, around 457K human box annotations are obtained. High-quality annotation is ensured via a rigorous quality check, conducted by highly skilled reviewers." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "content": "Person Localization. For each scene, a " + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "inline_equation", + "content": "10\\mathrm{m}" + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "content": " ruler (with " + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "inline_equation", + "content": "0.05\\mathrm{m}" + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "content": " accuracy) is placed on the ground, and one end of the" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 319, + 167, + 408, + 284 + ], + "blocks": [ + { + "bbox": [ + 319, + 167, + 408, + 284 + ], + "lines": [ + { + "bbox": [ + 319, + 167, + 408, + 284 + ], + "spans": [ + { + "bbox": [ + 319, + 167, + 408, + 284 + ], + "type": "image", + "image_path": "e3f4fafde1e206055214c00a1cb3f0019fe43878e6a4b6156eb82f5574ed418b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 359, + 285, + 372, + 297 + ], + "lines": [ + { + "bbox": [ + 359, + 285, + 372, + 297 + ], + "spans": [ + { + "bbox": [ + 359, + 285, + 372, + 297 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 299, + 545, + 332 + ], + "lines": [ + { + "bbox": [ + 305, + 299, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 305, + 299, + 545, + 332 + ], + "type": "text", + "content": "Figure 3: Calibration for groundtruth person location annotation. (a) Ground makers (with " + }, + { + "bbox": [ + 305, + 299, + 545, + 332 + ], + "type": "inline_equation", + "content": "0.05\\mathrm{m}" + }, + { + "bbox": [ + 305, + 299, + 545, + 332 + ], + "type": "text", + "content": " precision). (b) Top-view fisheye image capture for calibration. See §3.2 for details." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 417, + 167, + 533, + 284 + ], + "blocks": [ + { + "bbox": [ + 417, + 167, + 533, + 284 + ], + "lines": [ + { + "bbox": [ + 417, + 167, + 533, + 284 + ], + "spans": [ + { + "bbox": [ + 417, + 167, + 533, + 284 + ], + "type": "image", + "image_path": "9af3d095353cd10aa67ed5028cc2c96b6e9c92936d06344f43b061731640c848.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 285, + 481, + 296 + ], + "lines": [ + { + "bbox": [ + 468, + 285, + 481, + 296 + ], + "spans": [ + { + "bbox": [ + 468, + 285, + 481, + 296 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 341, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 341, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 305, + 341, + 545, + 400 + ], + "type": "text", + "content": "ruler is directly under the fisheye lens (cf. Fig. 3 (a)). We take a fisheye picture and use this marked picture as the calibration for all the dataset images recorded in this scene (cf. Fig. 3(b)). Finally, for each annotated human, the physical location, at sub-decimeter precision, is provided (cf. Fig. 4)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 401, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 401, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 401, + 545, + 437 + ], + "type": "text", + "content": "Scene Attribute. To enable in-depth analysis, each image is annotated with multiple attributes, including day/night, outdoor/indoor, and sunny/rain/foggy/snow." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 443, + 398, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 443, + 398, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 443, + 398, + 455 + ], + "type": "text", + "content": "3.3. Dataset Design" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 460, + 534, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 460, + 534, + 472 + ], + "spans": [ + { + "bbox": [ + 318, + 460, + 534, + 472 + ], + "type": "text", + "content": "We then list several key aspects of our dataset design." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 472, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 545, + 628 + ], + "type": "text", + "content": "Privacy Protection. To protect personal information, we apply the gaussian filter to blur all the visible facial regions in our dataset, and conduct experiments on the blurred data. Dataset Splits. LOAF contains 29,569 training, 4,600 validation, and 8,773 testing images (approximately 7 train, 1 val, and 2 test). Moreover, to better evaluate models' generalization ability, LOAF is split into five sets: train (7/28 indoor/outdoor scenes, 29,569 images), val seen (1/2 indoor/outdoor scenes, 1,700 images), val unseen (2/3 indoor/outdoor scenes, 2,900 images), test seen (2/3 indoor/outdoor scenes, 2,774 images), test unseen (2/8 indoor/outdoor scenes, 5,999 images). There are no overlapping scenes between unseen and train sets." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 628, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 628, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 305, + 628, + 545, + 664 + ], + "type": "text", + "content": "Dataset Accessibility. Only the desensitized version of our dataset will be released online, under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License [19]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 670, + 469, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 469, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 469, + 682 + ], + "type": "text", + "content": "3.4. Dataset Features and Analysis" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Finally, we present statistic analysis of LOAF in comparison with existing overhead fisheye datasets [21, 42, 24]." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19964" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 62, + 136, + 147 + ], + "blocks": [ + { + "bbox": [ + 50, + 62, + 136, + 147 + ], + "lines": [ + { + "bbox": 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"type": "text", + "content": "(b) PIROPO [21]" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 370, + 62, + 454, + 148 + ], + "blocks": [ + { + "bbox": [ + 370, + 62, + 454, + 148 + ], + "lines": [ + { + "bbox": [ + 370, + 62, + 454, + 148 + ], + "spans": [ + { + "bbox": [ + 370, + 62, + 454, + 148 + ], + "type": "image", + "image_path": "4c39d8656378ebc5b2543cd9cef2012dc6d391329b153e7985a695ed7d3edc11.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 379, + 153, + 446, + 163 + ], + "lines": [ + { + "bbox": [ + 379, + 153, + 446, + 163 + ], + "spans": [ + { + "bbox": [ + 379, + 153, + 446, + 163 + ], + "type": "text", + "content": "(c) HABBOF [42]" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 460, + 62, + 545, + 148 + ], + "blocks": [ + { + "bbox": [ + 460, + 62, + 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+ 547, + 213 + ], + "type": "inline_equation", + "content": "\\S 3.2-\\S 3.4" + }, + { + "bbox": [ + 46, + 167, + 547, + 213 + ], + "type": "text", + "content": "). Prior datasets [21, 42, 24] are restricted to few indoor scenes with person detection annotation only, i.e., head center " + }, + { + "bbox": [ + 46, + 167, + 547, + 213 + ], + "type": "inline_equation", + "content": "(\\bullet)" + }, + { + "bbox": [ + 46, + 167, + 547, + 213 + ], + "type": "text", + "content": " or human-aligned box " + }, + { + "bbox": [ + 46, + 167, + 547, + 213 + ], + "type": "inline_equation", + "content": "(\\square)" + }, + { + "bbox": [ + 46, + 167, + 547, + 213 + ], + "type": "text", + "content": ". In contrast, LOAF covers challenging indoor and outdoor scenes with human detection, localization and scene attribute annotations. The person-detection annotation is given as the radius-aligned box " + }, + { + "bbox": [ + 46, + 167, + 547, + 213 + ], + "type": "inline_equation", + "content": "(- \\square)" + }, + { + "bbox": [ + 46, + 167, + 547, + 213 + ], + "type": "text", + "content": ", which is more suitable for localization. For better visualization, we only present location ground-truths for some of persons." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 220, + 156, + 338 + ], + "lines": [ + { + "bbox": [ + 48, + 220, + 156, + 338 + ], + "spans": [ + { + "bbox": [ + 48, + 220, + 156, + 338 + ], + "type": "image", + "image_path": "f0a4041d8b3e2c825a8308c3dd8591271ef49dd0be458a169b8a4a5b487e57d6.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 341, + 132, + 349 + ], + "lines": [ + { + "bbox": [ + 80, + 341, + 132, + 349 + ], + "spans": [ + { + "bbox": [ + 80, + 341, + 132, + 349 + ], + "type": "text", + "content": "(a) Person scale" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 164, + 220, + 277, + 277 + ], + "blocks": [ + { + "bbox": [ + 164, + 220, + 277, + 277 + ], + "lines": [ + { + "bbox": [ + 164, + 220, + 277, + 277 + ], + "spans": [ + { + "bbox": [ + 164, + 220, + 277, + 277 + ], + "type": "image", + "image_path": "72e18a3c6c6a1f9edf9be646ab56ad26f35e65015842e43e9b4f596851fb8106.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 195, + 277, + 260, + 285 + ], + "lines": [ + { + "bbox": [ + 195, + 277, + 260, + 285 + ], + "spans": [ + { + "bbox": [ + 195, + 277, + 260, + 285 + ], + "type": "text", + "content": "(b) Person locations" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 164, + 285, + 277, + 341 + ], + "blocks": [ + { + "bbox": [ + 164, + 285, + 277, + 341 + ], + "lines": [ + { + "bbox": [ + 164, + 285, + 277, + 341 + ], + "spans": [ + { + "bbox": [ + 164, + 285, + 277, + 341 + ], + "type": "image", + "image_path": "327c7873cd49ad6ddcd326dc87d87ad1e4a0e473f74ebe418369c540a32c6724.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 198, + 342, + 257, + 350 + ], + "lines": [ + { + "bbox": [ + 198, + 342, + 257, + 350 + ], + "spans": [ + { + "bbox": [ + 198, + 342, + 257, + 350 + ], + "type": "text", + "content": "(c) Person density" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 350, + 287, + 394 + ], + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 394 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 394 + ], + "type": "text", + "content": "Figure 5: Dataset Statistics (§3.4): We summarize LOAF with the distribution of (a) person scale (area in pixel), (b) person locations (horizontal distance between human and the fisheye lens in the real world), and (c) person density (number of person per image)." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 401, + 282, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 282, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 282, + 413 + ], + "type": "text", + "content": "LOAF distinguishes itself from three aspects (cf. Table 1):" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 413, + 287, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 497 + ], + "type": "text", + "content": "Large-scale: LOAF has 42,942 fisheye images with more than 457K person boxes. Moreover, LOAF data are captured by an advanced fisheye camera, which is capable of covering a larger area " + }, + { + "bbox": [ + 46, + 413, + 287, + 497 + ], + "type": "inline_equation", + "content": "(200\\sim 300\\mathrm{m}^2)" + }, + { + "bbox": [ + 46, + 413, + 287, + 497 + ], + "type": "text", + "content": " with higher pedestrian density (2~65 persons per scene, 10.5 in average). This makes LOAF the largest overhead fisheye dataset in terms of the total number of pedestrian and scene categories." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 498, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 640 + ], + "type": "text", + "content": "High Diversity: Existing datasets limit in data diversities, i.e., only containing very few indoor scenes (2~14) and completely missing outdoor scenarios (cf. Fig. 4). In contrast, LOAF involves 51 realistic scenes, including 11 indoor scenes (e.g., lab, office, library, classroom) and 40 outdoor scenes (e.g., street, playground, parking lot, square). The recorded data cover four seasons under different illumination (e.g., morning, noon, afternoon) and weather (e.g., sunny, rain, snow) conditions, and involve vast variance of human pose (e.g., walking, standing, and sitting), scale, location, and density (cf. Fig. 5). Thus our dataset better reflects the distribution in real-world surveillance scenarios." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "Rich and Positioning-aware Annotation: LOAF is provided with rich ground-truths for detection, localization, and scene attribute, which lays a solid foundation for fisheye camera based human-centric analysis. Hence, as demonstrated in §3.2, the radius-aligned human-box representation is adopted during our annotation. Compared with human-" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 218, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 545, + 255 + ], + "type": "text", + "content": "head center based point annotation [21] and human-aligned person-boxes [42, 24] used in previous datasets, radius-aligned human-boxes are more suitable for the position task." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 261, + 397, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 261, + 397, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 261, + 397, + 274 + ], + "type": "text", + "content": "4. Our Approach" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 278, + 545, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 339 + ], + "type": "text", + "content": "Our overhead fisheye camera based person localization solution comprises two parts. The former computes 2D detections that locate the people on the image plane (§4.1). The latter converts the 2D detections to 3D-world coordinates, obtaining the physical location of the people (§4.2)." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 342, + 494, + 355 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 494, + 355 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 494, + 355 + ], + "type": "text", + "content": "4.1. Overhead Fisheye Person Detection" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "type": "text", + "content": "Core Idea: Rotation Equivariance. One of the reasons for the tremendous success of CNNs is their equivariance to horizontal and vertical shifts and the resulting invariance to local deformations [41, 25]. This stimulates a line of efforts to learn robust representations equivariant to generic types of transformations [35, 18, 70]. Formally, a representation " + }, + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "type": "text", + "content": " is said to be equivariant with a geometric transformation " + }, + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "type": "text", + "content": " (e.g., cropping, flipping) for an input (image) " + }, + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 358, + 546, + 454 + ], + "type": "text", + "content": " if:" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 387, + 458, + 545, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 458, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 387, + 458, + 545, + 471 + ], + "type": "interline_equation", + "content": "f (g (I)) \\approx g (f (I)). \\tag {1}", + "image_path": "7bd83573390bfce71743d5deb151af43ce7d529736e4a7c7bed20d75492bba6f.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "type": "text", + "content": "That is to say, the output representation " + }, + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "type": "inline_equation", + "content": "f(I)" + }, + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "type": "text", + "content": " is changed in the same way as the transformation " + }, + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "type": "text", + "content": " imposed to the input " + }, + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 474, + 545, + 498 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "In this work, we devise a query-based fisheye person detector that exhibits " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "-rotational equivariance through an elaborately designed training protocol. Our key insight is derived from the omnidirectional nature of this task: if one rotates the input fisheye image by an arbitrary angle, then the outputs of a robust fisheye detector should change accordingly. We thus design a rotation equivariant training strategy, which forces the matching between object queries and image representations to be equivariant against " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "-rotations. In this way, the rotational symmetry of omnidirectional images is explicitly addressed, without architectural modification of standard detectors developed for perspective images. Rotation Equivariant Training for Query-based Fisheye Detection. As shown in Fig. 6, our fisheye detector is built upon DETR [9], promoted by a rotation equivariant training strategy. Basically, DETR conducts detection in a query-based fashion. Denote " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " as a feature encoder that extracts representation " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " of image " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " as a query creator" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19965" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 64, + 289, + 194 + ], + "blocks": [ + { + "bbox": [ + 48, + 64, + 289, + 194 + ], + "lines": [ + { + "bbox": [ + 48, + 64, + 289, + 194 + ], + "spans": [ + { + "bbox": [ + 48, + 64, + 289, + 194 + ], + "type": "image", + "image_path": "84ddbf217cfe1d9f63999d77f1d13c59b4542d4725a8091df5c551f2f2bd612a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "text", + "content": "Figure 6: Our rotation equivariant training strategy for query-based fisheye person detection (§4.1). For equivariant training, object queries " + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "inline_equation", + "content": "\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N" + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "text", + "content": " created for rotated image " + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "inline_equation", + "content": "g^r(I)" + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "text", + "content": " and the rotated representation " + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "inline_equation", + "content": "g^r(I)" + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "text", + "content": " are fed into the decoder " + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "text", + "content": "; the rotated ground-truths " + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "inline_equation", + "content": "\\{\\pmb{b}_{\\ell(n)}^{g^r}\\}_{n=1}^N" + }, + { + "bbox": [ + 46, + 198, + 287, + 257 + ], + "type": "text", + "content": " are set as the training targets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "text", + "content": "that outputs a set of " + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "text", + "content": " object-aware descriptors " + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "inline_equation", + "content": "\\{\\pmb{q}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "text", + "content": ". DETR employs " + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "inline_equation", + "content": "\\{\\pmb{q}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "text", + "content": " as queries to retrieve target objects from " + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 46, + 268, + 287, + 305 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 113, + 308, + 287, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 308, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 113, + 308, + 287, + 323 + ], + "type": "interline_equation", + "content": "\\left\\{\\hat {\\boldsymbol {b}} _ {n} \\right\\} _ {n = 1} ^ {N} = \\mathcal {D} (\\boldsymbol {I}, \\left\\{\\boldsymbol {q} _ {n} \\right\\} _ {n = 1} ^ {N}), \\tag {2}", + "image_path": "a6481700024b9d90624bed659dbb54e97f804ba2087839753f862d5185d81044.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\pmb{I} = \\mathcal{F}(I)" + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\{\\pmb{q}_n\\}_{n=1}^N = \\kappa(\\pmb{I})" + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "text", + "content": " refers to the Transformer decoder which formulates the object-query matching process via neural cross-attention computation. " + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\{\\hat{\\pmb{b}}_n\\}_{n=1}^N" + }, + { + "bbox": [ + 47, + 330, + 287, + 379 + ], + "type": "text", + "content": " are the set of predicted parameterized object bounding boxes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 380, + 287, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 439 + ], + "type": "text", + "content": "Our rotation equivariant training further encourages robust object-query matching which is equivariant against rotations. First, given an input rotation transformation " + }, + { + "bbox": [ + 46, + 380, + 287, + 439 + ], + "type": "inline_equation", + "content": "g^r" + }, + { + "bbox": [ + 46, + 380, + 287, + 439 + ], + "type": "text", + "content": ", a robust fisheye detector is desired to be able to extract rotation-equivariant representation. Analogous to Eq. 1, we have:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 443, + 287, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 443, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 107, + 443, + 287, + 455 + ], + "type": "interline_equation", + "content": "\\mathcal {F} \\left(g ^ {r} (I)\\right) \\approx g (\\mathcal {F} (I)) = g ^ {r} (\\boldsymbol {I}). \\tag {3}", + "image_path": "e90599b01e3f6580c15bf2279198fd6f148d7df03f5881dc77548c7880f9d467.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "text", + "content": "Also, it is reasonable to assume that the final output of a robust fisheye detector should be changed in the same way to the rotation " + }, + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "inline_equation", + "content": "g^{r}" + }, + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "text", + "content": " applied to the input fisheye image " + }, + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 459, + 287, + 495 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 102, + 500, + 287, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 500, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 102, + 500, + 287, + 516 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {b} _ {\\ell (n)} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N} \\approx \\mathcal {D} \\left(\\boldsymbol {I} ^ {g ^ {r}}, \\left\\{\\boldsymbol {q} _ {n} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}\\right), \\tag {4}", + "image_path": "73ab243bbe5505f8616300c3091df6bdde7d3b469d80d1313effd8cd49b12d0f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "I^{g^r}" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": " indicates the feature of rotated image " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "g^{r}(I)" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\pmb{I}^{g^{r}} = \\mathcal{F}(g^{r}(I))" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": ". Similarly, " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": " denote the object queries derived from " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "g^{r}(I)" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\{\\pmb{q}_n^{g^r}\\}_{n=1}^N = \\kappa(I^{g^r})" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\{\\pmb{b}_{\\ell(n)}^{g^{r}}\\}_{n=1}^N" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": " are the rotated groundtruth bounding boxes, where " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\ell(n)" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": " returns the groundtruth index for " + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 523, + 287, + 586 + ], + "type": "text", + "content": "-th query." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 586, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 287, + 628 + ], + "type": "text", + "content": "Considering Eq.3 and Eq.4, we can have: " + }, + { + "bbox": [ + 47, + 586, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\{\\pmb{b}_{\\ell(n)}^{g^r}\\}_{n=1}^N \\approx \\mathcal{D}(g^r(\\pmb{I}), \\{\\pmb{q}_n^{g^r}\\}_{n=1}^N)" + }, + { + "bbox": [ + 47, + 586, + 287, + 628 + ], + "type": "text", + "content": ". Hence our rotation equivariant training objective is given as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 70, + 632, + 287, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 632, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 70, + 632, + 287, + 647 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r o t a t - e q u i}} = \\mathcal {L} _ {\\det } \\left(\\left\\{\\boldsymbol {b} _ {\\ell (n)} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}, \\mathcal {D} \\left(g ^ {r} (\\boldsymbol {I}), \\left\\{\\boldsymbol {q} _ {n} ^ {g ^ {r}} \\right\\} _ {n = 1} ^ {N}\\right)\\right). \\tag {5}", + "image_path": "b1616819e50e407972c5f44e8d40ae7ca2735706c5f22f807c67e3cb4ffa8aa3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{det}}" + }, + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "text", + "content": " is the standard detection loss in DETR [9]. As such, the rotation equivariance properties for both fisheye representation " + }, + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "text", + "content": " (cf. Eq.3) and the query-based detection prediction " + }, + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\boldsymbol {I},\\{\\pmb {q}_n\\}_{n = 1}^N)" + }, + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "text", + "content": " (cf. Eq.4) are sought in a single training target. This also allows us to effortlessly adapt standard" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 454, + 200 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 454, + 200 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 454, + 200 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 454, + 200 + ], + "type": "image", + "image_path": "d9515f35afae0c94c683b1ac86271a358c47042b91c37bf32e6d1296edf330e5.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "lines": [ + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "spans": [ + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "type": "text", + "content": "Figure 7: Our fisheye camera model based person localization (§4.2). Here " + }, + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "type": "inline_equation", + "content": "\\pmb{p}'" + }, + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "type": "text", + "content": " denote the projection point of the distortion point " + }, + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 458, + 91, + 543, + 190 + ], + "type": "text", + "content": " by fisheye lens and normal perspective lens, respectively." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 212, + 545, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 212, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 305, + 212, + 545, + 259 + ], + "type": "text", + "content": "DETR to our omnidirectional detection setting. Note that our rotation equivariant training differs from rotational data augmentation technique which only views rotated images as individual training samples (see §5.4 for detailed experiments)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 267, + 535, + 279 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 267, + 535, + 279 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 535, + 279 + ], + "type": "text", + "content": "4.2. 2D-3D Projection based Person Localization" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": "General Fisheye Camera Model. The perspective projection of a normal pinhole camera can be written as " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "r = f \\tan \\theta" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": " indicates the projection distance between the principal point and the image point, " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": " is the focal length, and " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": " is the angle between the incident ray and the camera's optical axis. However, fisheye lens does not follow this perspective projection model [49], as the FOV equals to " + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 304, + 285, + 545, + 405 + ], + "type": "text", + "content": " (cf. Fig. 7). Fortunately, the image formation of different kinds of fisheye lenses can be approximated by a general polynomial projection model [37], i.e.," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 343, + 412, + 545, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 412, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 343, + 412, + 545, + 430 + ], + "type": "interline_equation", + "content": "r (\\theta) = \\sum_ {i = 1} ^ {n} k _ {i} \\theta^ {2 i - 1}, \\quad n = 1, 2, 3, 4, \\dots \\tag {6}", + "image_path": "da3a6aed716b7a4cabbad6e721c0421c63bbab56fcf4c1c4ad558e682cf61b0f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 435, + 545, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 459 + ], + "type": "text", + "content": "High distortions can be handled well when " + }, + { + "bbox": [ + 304, + 435, + 545, + 459 + ], + "type": "inline_equation", + "content": "n = 5" + }, + { + "bbox": [ + 304, + 435, + 545, + 459 + ], + "type": "text", + "content": " [37]. The coefficients " + }, + { + "bbox": [ + 304, + 435, + 545, + 459 + ], + "type": "inline_equation", + "content": "k_{s}" + }, + { + "bbox": [ + 304, + 435, + 545, + 459 + ], + "type": "text", + "content": " can be obtained from camera calibration." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": "2D-3D Projection. Given a detected human location point " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "\\pmb{p} = (u,v)^{\\top}" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " in the fisheye image pixel coordinate system, our target is to calculate its 3D location " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "\\pmb{P} = (X,Y,Z)^{\\top}" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " in the camera coordinate system, where " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " is the altitude of the fisheye camera and primarily known. To do so, one can first calculate " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " as: " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "r = \\sqrt{(x^2 + y^2)}" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "x = (u - u_0) / f" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "y = (v - v_0) / f" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "(u_0,v_0)^{\\top}" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " are the coordinates of the principal point in the fisheye image. Then " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " can be obtained by solving Eq. 6 using a numerical means [37]. With the altitude " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " of the camera, the actual location " + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "inline_equation", + "content": "(X,Y)^{\\top}" + }, + { + "bbox": [ + 304, + 460, + 545, + 588 + ], + "type": "text", + "content": " is given as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 375, + 586, + 545, + 615 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 586, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 375, + 586, + 545, + 615 + ], + "type": "interline_equation", + "content": "\\binom {X} {Y} = Z \\binom {\\tan \\theta \\cos \\phi} {\\tan \\theta \\sin \\phi}, \\tag {7}", + "image_path": "201dffb195662c5be1817832e7c2f1672060ae9c1c9458f282c9b019509eeeb7.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "inline_equation", + "content": "\\phi = \\arctan (y,x)" + }, + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "text", + "content": " refers to the polar angle, which is shared by both " + }, + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "inline_equation", + "content": "\\pmb{P}" + }, + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "It can be seen that precise determination of the person location point " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " on the image plane is vital for estimating the corresponding physical position " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{P}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": ". However, most previous approaches, restricted to axis-aligned [79, 60] or person-aligned [24] human-box representation, use the center of the detection box to approximate " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": ". Few excep" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19966" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 66, + 541, + 140 + ], + "blocks": [ + { + "bbox": [ + 56, + 66, + 541, + 140 + ], + "lines": [ + { + "bbox": [ + 56, + 66, + 541, + 140 + ], + "spans": [ + { + "bbox": [ + 56, + 66, + 541, + 140 + ], + "type": "table", + "html": "
MethodvaltestFPS↑
mAP↑AP50↑AP75↑APn↑APm↑APf↑APseen↑APunseen↑mAP↑AP50↑AP75↑APn↑APm↑APf↑APseen↑APunseen↑
Seide et al. [60]21.859.87.632.828.52.323.219.520.258.27.132.228.33.922.418.910.2
Li et al. [42]28.563.320.146.824.21.333.829.327.265.221.347.224.81.331.827.60.6
Tamura et al. [64]34.872.127.751.738.88.738.832.934.272.828.753.737.36.539.533.210.2
RAPiD [24]40.377.934.855.341.99.244.737.639.277.935.454.840.17.944.237.38.4
Ours47.482.648.464.154.314.150.845.746.281.147.366.153.512.649.344.912.1
", + "image_path": "d9366d37d95e9c6516309e1b7688079db46eddb141649ec873cb7425d391972c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 54, + 160, + 291, + 224 + ], + "blocks": [ + { + "bbox": [ + 160, + 143, + 432, + 153 + ], + "lines": [ + { + "bbox": [ + 160, + 143, + 432, + 153 + ], + "spans": [ + { + "bbox": [ + 160, + 143, + 432, + 153 + ], + "type": "text", + "content": "Table 2: Person detection results on val and test sets of LOAF (§5.2)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 54, + 160, + 291, + 224 + ], + "lines": [ + { + "bbox": [ + 54, + 160, + 291, + 224 + ], + "spans": [ + { + "bbox": [ + 54, + 160, + 291, + 224 + ], + "type": "table", + "html": "
MethodmAP↑AP50↑AP75↑Precision↑Recall↑F-Score↑
Seide et al. [60]20.950.610.280.639.553.0
Li et al. [42]34.275.728.686.365.474.4
Tamura et al. [64]29.361.023.488.851.265.0
RAPiD [24]39.385.426.089.278.783.6
Ours47.288.538.290.387.688.9
", + "image_path": "cea33104a3275bb7c6dee67b760a6eeed7d43e0b6fa2c50010e32121d3523418.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "text", + "content": "tions [21], built on point-based human representation, treat the center of the detected human head as " + }, + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "text", + "content": ". However, they suffer from a similar issue as the human head center is even often far from the exact position " + }, + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "text", + "content": " human stand on, w.r.t. the image plane. Instead, with our radius-aligned human-box representation, the closest point to the principal point on the bounding box better corresponds to " + }, + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 337, + 180, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 337, + 180, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 180, + 350 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 355, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 464 + ], + "type": "text", + "content": "Network Architecture. Our fisheye person detector is built upon DAB-DETR [45], a prevalent variant of DETR [9] but converges much faster. Swin-T [46] is utilized as the backbone. For our LOAF with radius-aligned person boxes, the output of our detector is a 4D vector " + }, + { + "bbox": [ + 46, + 355, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\pmb{b} \\in [0,1]^4" + }, + { + "bbox": [ + 46, + 355, + 287, + 464 + ], + "type": "text", + "content": " that parameterizes 2D center coordinates, height, and width. Note that, for traditional fisheye detection datasets like [24, 65] with arbitrary-oriented person box annotations, an extra output dimension is needed for rotation angle regression." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 464, + 287, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 512 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 512 + ], + "type": "text", + "content": "Training Objective. Our fisheye person detector is end-to-end trained by jointly optimizing the vanilla detection loss used in DETR [9, 45] (referred as " + }, + { + "bbox": [ + 46, + 464, + 287, + 512 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Det}}" + }, + { + "bbox": [ + 46, + 464, + 287, + 512 + ], + "type": "text", + "content": ") and our proposed rotation-equivariant constraint (i.e., " + }, + { + "bbox": [ + 46, + 464, + 287, + 512 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rotat - equi}}" + }, + { + "bbox": [ + 46, + 464, + 287, + 512 + ], + "type": "text", + "content": " in Eq. 5):" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 124, + 517, + 287, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 517, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 124, + 517, + 287, + 529 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {d e t}} + \\lambda \\mathcal {L} _ {\\text {r o t a t - e q u i}}, \\tag {8}", + "image_path": "a5f6d26892ce0d309aff6d023d6de49c175612142d4c613afc50bd58d93530e3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 534, + 241, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 241, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 241, + 545 + ], + "type": "text", + "content": "where the coefficient " + }, + { + "bbox": [ + 46, + 534, + 241, + 545 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 534, + 241, + 545 + ], + "type": "text", + "content": " is empirically set to 0.5." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "Training. Our fisheye detector is trained with a batch size of 8 for 50 epochs, where the AdamW [47] optimizer is employed with base learning rate 2e-4 and decayed by 0.1 at epoch 40. The remaining hyper-parameters are determined following [64, 24]. Specifically, we initialize backbones with ImageNet [22] pre-trained weights and adopt standard data augmentation techniques, i.e., color jitter, horizontal flip, and random scaling, with a base training size of " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "608 \\times 608" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ". For CEPDOF [24] and WEPDTOF [65], we use a batch size of 128 and pre-train the detector on COCO [44] for 50 epochs to prevent over-fitting, as in [24, 65]. For the computation of our rotation-equivariant loss " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rotat - equi}}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ", the training images are rotated by a degree randomly sampled from 0 to 360. Our detector is implemented in PyTorch and trained on eight" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 313, + 160, + 550, + 224 + ], + "blocks": [ + { + "bbox": [ + 58, + 226, + 275, + 237 + ], + "lines": [ + { + "bbox": [ + 58, + 226, + 275, + 237 + ], + "spans": [ + { + "bbox": [ + 58, + 226, + 275, + 237 + ], + "type": "text", + "content": "Table 3: Person detection results on CEPDOF [24] (\\$5.2)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 160, + 550, + 224 + ], + "lines": [ + { + "bbox": [ + 313, + 160, + 550, + 224 + ], + "spans": [ + { + "bbox": [ + 313, + 160, + 550, + 224 + ], + "type": "table", + "html": "
MethodmAP↑AP50↑AP75↑Precision↑Recall↑F-Score↑
Seide et al. [60]16.139.49.070.938.650.0
Li et al. [42]25.269.930.281.464.572.0
Tamura et al. [64]28.859.824.277.052.462.4
RAPiD [24]37.772.026.873.367.870.4
Ours45.885.636.684.974.679.8
", + "image_path": "2fa67e3ee0acaec53ca67bbf1ddee0fd7571e712b6346cf3d20f534fee02d67f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 226, + 538, + 237 + ], + "lines": [ + { + "bbox": [ + 313, + 226, + 538, + 237 + ], + "spans": [ + { + "bbox": [ + 313, + 226, + 538, + 237 + ], + "type": "text", + "content": "Table 4: Person detection results on WEPDTOF [65] (\\$5.2)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 247, + 545, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 367 + ], + "type": "text", + "content": "NVIDIA Tesla V100 GPUs with a 32GB memory per-card. Inference. Once trained, our fisheye detector can be directly applied for locating persons on the omnidirectional image plane. After that, the physical locations of the detected persons can be easily obtained through the numerical solution described in §4.2. For fisheye person detection, we follow prior work [60, 42, 64, 24] to use " + }, + { + "bbox": [ + 304, + 247, + 545, + 367 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 247, + 545, + 367 + ], + "type": "text", + "content": " input resolution without any test-time augmentation or post-processing. Testing is conducted on a single NVIDIA V100 GPU with 16 GB memory." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 376, + 382, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 382, + 389 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 382, + 389 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 394, + 422, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 422, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 422, + 407 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "text", + "content": "Evaluation Protocol. On the top of LOAF, we conduct experiments for fisheye based person detection and localization. Following the dataset splitting (cf. §3.3), performance are reported on seen and unseen scenes, respectively, for both val and test sets. This allows us to assess the generalization ability over different surveillance scenarios. For comprehensive study, we further report person detection performance on two existing fisheye datasets, CEPDOF[24] and WEPDTOF[65]. Note that localization cannot be test since [24, 65] only provide person bounding box annotations. Evaluation Metrics. For fisheye person detection, we follow COCO [44] to report the mean average precision (mAP) for IoU " + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\in" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "text", + "content": " [0.5:0.05:0.95]. We also employ AP" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "inline_equation", + "content": "_{50}" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "text", + "content": " and AP" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "inline_equation", + "content": "_{75}" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "text", + "content": " for further analysis. For fisheye person localization, we measure positional error (PE) in meters, i.e., Euclidean distance of calculated position and ground-truth position, as the conventions in visual localization [43, 58, 73, 79]. For detailed evaluation, on our LOAF, we report performance w.r.t. horizontal distance between human and the fisheye lens, i.e., near (0~10 m), middle (10~20 m), and far (larger than 20 m). Hence we have AP" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "inline_equation", + "content": "_{n,m,f}" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "text", + "content": " and PE" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "inline_equation", + "content": "_{n,m,f}" + }, + { + "bbox": [ + 304, + 411, + 545, + 665 + ], + "type": "text", + "content": " accordingly." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 670, + 485, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 485, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 485, + 682 + ], + "type": "text", + "content": "5.2. Performance on Person Detection" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "LOAF. We first report the person detection performance on LOAF. Specifically, four recent deep learning based fisheye" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19967" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 542, + 144 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 542, + 144 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 542, + 144 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 542, + 144 + ], + "type": "table", + "html": "
Methodvaltest
mPE↓PEn↓PEm↓PEf↓PEseen↓PEunseen↓mPE↓PEn↓PEm↓PEf↓PEseen↓PEunseen↓
Seide et al. [60]1.2980.5611.3323.1091.2061.3821.3210.7061.3093.4821.3061.386
Li et al. [42]0.8980.5020.8712.6500.8320.9620.9130.5430.8842.7800.9040.998
Tamura et al. [64]0.7550.4290.7361.8620.7090.8210.7780.4710.8262.1600.7240.836
RAPiD [24]0.6740.4260.6231.4030.6250.7570.6820.4610.6641.4450.6380.776
Ours0.3680.1440.3630.7750.3180.4020.3740.1480.3750.8190.3260.398
", + "image_path": "09880f0396cde8565da3ece75e8f2537fa4beb87f3b4b85c1c5032add3283d97.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 166, + 287, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 166, + 287, + 261 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 287, + 261 + ], + "type": "text", + "content": "person detectors [60, 42, 64, 24] are involved for comparison. Among them, [60, 42] are training-free, thus their scores are obtained by directly running the algorithms on the val and test data. As [64, 24] are trainable methods, we first train them on the train set of LOAF following their official setups, and then report the scores on the val and test sets. Quantitative comparison results are presented in Table 2. Some essential observations are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 266, + 286, + 469 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 266, + 286, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 286, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 286, + 326 + ], + "type": "text", + "content": "- Our fisheye person detector significantly outperforms existing methods across all the metrics. For example, our detector provides a considerable performance gain in mAP, i.e., " + }, + { + "bbox": [ + 47, + 266, + 286, + 326 + ], + "type": "inline_equation", + "content": "7.1\\%" + }, + { + "bbox": [ + 47, + 266, + 286, + 326 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 266, + 286, + 326 + ], + "type": "inline_equation", + "content": "7.0\\%" + }, + { + "bbox": [ + 47, + 266, + 286, + 326 + ], + "type": "text", + "content": " higher than the second best, RAPiD [24], on the val and test sets, respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 327, + 286, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 286, + 386 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 286, + 386 + ], + "type": "text", + "content": "- Our detector not only handles nearby persons but also approaches distant targets well. Specifically, for the targets at " + }, + { + "bbox": [ + 47, + 327, + 286, + 386 + ], + "type": "inline_equation", + "content": "10\\sim 20\\mathrm{m}" + }, + { + "bbox": [ + 47, + 327, + 286, + 386 + ], + "type": "text", + "content": " away from the fisheye lens, our performance gain over other methods is more significant than the improvement reported with the persons at " + }, + { + "bbox": [ + 47, + 327, + 286, + 386 + ], + "type": "inline_equation", + "content": "0\\sim 10\\mathrm{m}" + }, + { + "bbox": [ + 47, + 327, + 286, + 386 + ], + "type": "text", + "content": " distance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 386, + 286, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 386, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 386, + 286, + 422 + ], + "type": "text", + "content": "- Our detector also yields small performance gap between the seen and unseen scenes (e.g., " + }, + { + "bbox": [ + 47, + 386, + 286, + 422 + ], + "type": "inline_equation", + "content": "49.3 \\rightarrow 44.9" + }, + { + "bbox": [ + 47, + 386, + 286, + 422 + ], + "type": "text", + "content": " in terms of mAP), validating our good generalizability." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 422, + 286, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 422, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 47, + 422, + 286, + 469 + ], + "type": "text", + "content": "- For those persons at very far distance (" + }, + { + "bbox": [ + 47, + 422, + 286, + 469 + ], + "type": "inline_equation", + "content": ">20\\mathrm{~m}" + }, + { + "bbox": [ + 47, + 422, + 286, + 469 + ], + "type": "text", + "content": "), our algorithm, though still giving higher scores than other competitors, suffers from great performance degradation. This sheds light on the direction of our future efforts." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 472, + 286, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 286, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 286, + 555 + ], + "type": "text", + "content": "CEPDOF [24]. CEPDOF contains eight videos with 25,504 frames in total. Following the official setup, we train our fisheye person detector on HABBOF [42] and MW-R [24] datasets, and report performance on CEPDOF. As shown in Table 3, our fisheye detector delivers state-of-the-art performance: it significantly outperforms RAPiD [24], the current top-leading algorithm, by " + }, + { + "bbox": [ + 46, + 472, + 286, + 555 + ], + "type": "inline_equation", + "content": "7.9\\%" + }, + { + "bbox": [ + 46, + 472, + 286, + 555 + ], + "type": "text", + "content": " in terms of mAP." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 555, + 286, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 286, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 286, + 627 + ], + "type": "text", + "content": "WEPDTOF [65]. WEPDTOF has 16 videos with 10,544 frames in total. Following the official setup, we use HAB-BOF [42], MW-R [24], and CEPDOF [24] for training and WEPDTOF for testing. Table 4 summarizes the results. Impressively, our detector greatly suppresses all the other competitors across all the evaluation metrics." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 635, + 239, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 239, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 239, + 647 + ], + "type": "text", + "content": "5.3. Performance on Person Localization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": "Then we study the person localization performance on LOAF. None of previous fisheye person detectors [60, 42, 64, 24] are aware of the task of person localization. We therefore follow the common practice [79, 21] in the field of visual localization: for [60, 42, 64, 24], we project" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 313, + 167, + 550, + 224 + ], + "blocks": [ + { + "bbox": [ + 156, + 145, + 436, + 156 + ], + "lines": [ + { + "bbox": [ + 156, + 145, + 436, + 156 + ], + "spans": [ + { + "bbox": [ + 156, + 145, + 436, + 156 + ], + "type": "text", + "content": "Table 5: Person localization results on val and test sets of LOAF (§5.3)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 167, + 550, + 224 + ], + "lines": [ + { + "bbox": [ + 313, + 167, + 550, + 224 + ], + "spans": [ + { + "bbox": [ + 313, + 167, + 550, + 224 + ], + "type": "table", + "html": "
MethodmAP↑val seenval unseen
mAP↑AP50↑AP75↑mAP↑AP50↑AP75↑
Baseline [45]43.146.481.248.440.976.238.9
+ Rotation Aug.45.649.282.852.843.278.943.9
+ Rotation Equ.47.450.883.854.845.780.547.3
", + "image_path": "6e87ce99dda350089a3e9385459bdfa3bf8606525e04e844a9190506454a97f6.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 322, + 225, + 527, + 236 + ], + "lines": [ + { + "bbox": [ + 322, + 225, + 527, + 236 + ], + "spans": [ + { + "bbox": [ + 322, + 225, + 527, + 236 + ], + "type": "text", + "content": "Table 6: Diagnostic results on val set of LOAF (§5.4)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 246, + 545, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 545, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 545, + 377 + ], + "type": "text", + "content": "centers of their detected human boxes on the 3D world, based on the same strategy of ours (cf. §4.2), for physical position estimation. As shown in Table 5, our system produces much small localization errors in comparison with [60, 42, 64, 24], i.e., " + }, + { + "bbox": [ + 304, + 246, + 545, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{0.374m}" + }, + { + "bbox": [ + 304, + 246, + 545, + 377 + ], + "type": "text", + "content": " vs " + }, + { + "bbox": [ + 304, + 246, + 545, + 377 + ], + "type": "inline_equation", + "content": "0.682\\mathrm{m}[24]" + }, + { + "bbox": [ + 304, + 246, + 545, + 377 + ], + "type": "text", + "content": " and 0.773 m of [64] on the test set of LOAF. In addition, for all the methods, the localization performance is declined as target distance increases, but our system suffers from the smallest drop. Moreover, the results suggest there is still large room for improvement, thus we hope that our dataset could encourage continuous efforts in this challenging task." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 391, + 408, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 391, + 408, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 391, + 408, + 403 + ], + "type": "text", + "content": "5.4. Diagnostic Study" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": "Table 6 studies the efficacy of our rotation equivariant training strategy (§4.1), on the val set of LOAF. Our baseline model [45] (row #1) gains " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "43.1\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": " mAP. After adopting rotational data augmentation (row #2), the performance boosts by " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": " mAP. By contrast, our rotation equivariant training brings much larger improvements over the baseline, e.g., " + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "inline_equation", + "content": "4.3\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 532 + ], + "type": "text", + "content": " mAP gain. It is remarkable that, training with standard rotational data augmentation technique can be viewed as a specific case of our equivariant training - only learning rotation-equivariant object-querying (cf. Eq. 4)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "We presented LOAF – the first top-view fisheye dataset that supports large-scale study for person localization in realistic surveillance scenarios. With radius-aligned personbox annotations and precise location ground-truths, LOAF closes a crucial gap in the literature as these cases are not covered by previous datasets and annotation protocols. We further proposed an efficient fisheye person detection model that is equipped with a rotation-equivariant training strategy. The physical locations of detected persons are formulated based on the fisheye model and the altitude of the camera. We empirically verified the effectiveness and promising performance of our algorithm." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19968" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 73, + 287, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 73, + 287, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 73, + 287, + 118 + ], + "type": "text", + "content": "Acknowledgements This work was sponsored in part by the CCF-Tencent Open Fund, China Postdoctoral Science Foundation (2022M710467) and National Key Research and Development Program of China (Grant No. 2021YFF0500900)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 126, + 106, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 126, + 106, + 138 + ], + "spans": [ + { + "bbox": [ + 48, + 126, + 106, + 138 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 146, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 146, + 287, + 200 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 146, + 287, + 200 + ], + "spans": [ + { + "bbox": [ + 53, + 146, + 287, + 200 + ], + "type": "text", + "content": "[1] Abdulrahman Alarifi, AbdulMalik Al-Salman, Mansour Alsaleh, Ahmad Alnafessah, Suheer Al-Hadhrami, Mai A Al-Ammar, and Hend S Al-Khalifa. 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Journal of Visual Communication and Image Representation, 59:128-139, 2019. 2, 6, 7, 8" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19971" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/c0b4cc8e-d6dd-4adb-8592-11f986f8c0fc_content_list.json b/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/c0b4cc8e-d6dd-4adb-8592-11f986f8c0fc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9128ce17889e342e932eb4d745b35e7e86264805 --- /dev/null +++ b/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/c0b4cc8e-d6dd-4adb-8592-11f986f8c0fc_content_list.json @@ -0,0 +1,1360 @@ +[ + { + "type": "text", + "text": "Late Stopping: Avoiding Confidently Learning from Mislabeled Examples", + "text_level": 1, + "bbox": [ + 112, + 130, + 856, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Suqin Yuan $^{1}$ Lei Feng $^{2*}$ Tongliang Liu $^{1*}$ $^{1}$ The University of Sydney $^{2}$ Nanyang Technological University", + "bbox": [ + 225, + 179, + 743, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 312, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which are critical for achieving the model's close-to-optimal generalization performance. In this paper, we propose a new framework, Late Stopping, which leverages the intrinsic robust learning ability of DNNs through a prolonged training process. Specifically, Late Stopping gradually shrinks the noisy dataset by removing high-probability mislabeled examples while retaining the majority of clean hard examples in the training set throughout the learning process. We empirically observe that mislabeled and clean examples exhibit differences in the number of epochs required for them to be consistently and correctly classified, and thus high-probability mislabeled examples can be removed. Experimental results on benchmark-simulated and real-world noisy datasets demonstrate that the proposed method outperforms state-of-the-art counterparts.", + "bbox": [ + 75, + 282, + 472, + 570 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 589, + 209, + 604 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep Neural Networks (DNNs) have achieved outstanding success in various tasks, while the success largely relies on data with high-quality annotations [13, 55, 41, 19]. In many real-world scenarios, it would be quite difficult to collect large-scale accurately labeled data, which could inevitably contain noisy labels. Unfortunately, previous studies [1, 56] showed that DNNs can easily overfit random labels, resulting in poor generalization performance. Therefore, an increasing number of methods have been proposed for Learning with Noisy Labels (LNL).", + "bbox": [ + 75, + 614, + 468, + 766 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One mainstream solution in existing methods of LNL is to train the classifier with confident examples [20, 14, 46, 34, 36], which is based on the memorization effect of DNNs, i.e., DNNs learn example with dominant patterns first and then overfit rare ones [1]. Given only noisy data, to exploit the memorization effect, the typical strategy starts from a small confident clean dataset and then", + "bbox": [ + 75, + 767, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "gradually expands the dataset, which prevents DNNs from over-fitting noisy data. In general, there are two primary approaches to exploit confident examples in the learning process. The first approach involves identifying examples with high-probability clean labels and training the classifier based on these examples, which is commonly referred to as the \"small-loss trick\" [20, 14, 12, 28, 52]. The second approach involves controlling the learning process of the classifier to primarily learn high-probability clean examples in noisy datasets, which is commonly referred to as \"early stopping\" [37, 42, 17, 25, 3].", + "bbox": [ + 496, + 252, + 893, + 417 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite providing satisfactory performance, these approaches present an unintended consequence in their methods to prevent over-fitting noise. Specifically, to reduce the impact of mislabeled examples, these approaches limit the capability of the model to effectively learn clean hard examples (CHEs) in noisy datasets, where CHEs are defined as clean examples that are close to the decision boundary, and a significant proportion of CHEs are non-dominated sub-population examples [9]. Identifying CHEs in noisy data is quite challenging [2, 22], as both the CHEs and the mislabeled examples are often characterized by large losses [52, 11, 6], causing them to become entangled. To maintain the purity of the dataset of confident examples, existing LNL methods [34, 2] normally try to eliminate potential examples that are likely to be mislabeled, which inevitably contain many CHEs. However, it is necessary to consider the positive impact of memorization effects on underrepresented sub-populations [10] (i.e., CHEs) when learning from natural datasets, as this is crucial for achieving close-to-optimal generalization performance.", + "bbox": [ + 496, + 417, + 893, + 719 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, our goal is to enable the classifier to learn as many useful non-dominated sub-population examples in the training set as possible during the process of learning with noisy labels. This entails selecting as many clean examples as possible, particularly the clean hard examples, during the sample selection process. In relation to this context, we introduce a novel concept termed First-time $k$ -epoch Learning (FkL), which is defined as the index of the epoch during the training procedure where an example has been predicted to its given label for consecutive $k$ epochs for the first time, as shown in Figure 1(a).", + "bbox": [ + 496, + 720, + 893, + 886 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors.", + "bbox": [ + 94, + 887, + 227, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16079", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8447846622861a9cee5d4f28f3f3d1bbc44d3f359d99f06c02ddc5be8aa762b3.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 112, + 85, + 315, + 328 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3ee4c5efc137a5350c63ffbd5465764dbc038deaa61fe00f82238f8df48c3782.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 338, + 89, + 602, + 321 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d99cd1818e22dd2eb077d300100d3b39ea0745cc934bed036a57620be3aaa668.jpg", + "image_caption": [ + "Figure 1. (a) We propose the First-time $k$ -epoch Learning (FkL) metric, which determines the minimum index of the training epoch until which an example has been predicted as its given label for consecutive $k$ epochs. (b) The normalised histogram of CIFAR-10 examples with $40\\%$ symmetric label noise w.r.t. the sequence they meet the FkL metric during training procedure. The horizontal axis represents the sequential order in which training examples meet the FkL metric. The vertical axis represents the normalised histogram of examples. (c) Rather than the methods that start from a small yet clean training set ('Early' Stopping), our proposed framework starts from a large training set ('Late' Stopping) that retains as many clean examples as possible." + ], + "image_footnote": [], + "bbox": [ + 629, + 90, + 736, + 325 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/92929d3565c32fbf4e1d033d9a5b330e55d91b52dab584bce45e04747d74cd59.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 750, + 90, + 854, + 325 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Using First-time $k$ -epoch Learning (FkL) as a metric, we sequence the examples in the noisy dataset according to the order they meet the FkL metric during the training procedure, as shown in Figure 1(b). As shown in the same figure, most unlabeled examples can only be classified into their given labels for consecutive $k$ epochs in the later stages of training (i.e., larger in the sequence), which implies a relatively large FkL value. This observation suggests that the examples with large FkL values (i.e., those examples that are classified to their given labels for consecutive $k$ epochs only in the late training stage) are predominantly those with incorrect labels. Therefore, the FkL values of different training examples can be used to distinguish whether an example is unlabeled or not.", + "bbox": [ + 75, + 445, + 468, + 655 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the above observations, we propose a novel method based on reverse thinking of the conventional confident example selection strategy. Our proposed method, called Late Stopping, employs an iterative sample selection process that gradually reduces the noise rate of the dataset, leading to a positive feedback loop. Instead of selecting high-probability clean examples in the early stage, our method focuses on selecting high-probability mislabeled examples in the late stage to retain as many CHEs as possible in the training set throughout the learning process, even though this method may lead to the retention of an acceptable level of mislabeled examples, as shown in 1(c). Building on this, we introduce a novel sample selection criterion, FkL, which works effectively in selecting mislabeled examples under the Late Stopping framework, and empirical results show that the FkL is more ef", + "bbox": [ + 75, + 659, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "fective than the loss criterion. We evaluate our method on benchmark-simulated and real-world noisy datasets. Empirical results demonstrate that the Late Stopping method achieves superior performance compared with state-of-the-art counterparts of learning with noisy labels.", + "bbox": [ + 496, + 445, + 890, + 521 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 539, + 640, + 555 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing methods of learning with noisy labels can be broadly categorized into two types. The first category includes classifier-consistent algorithms that use the noise transition matrix [27, 29, 54, 35, 8], which indicates the probabilities of clean labels flipping to noisy labels. The second category focuses on heuristic methods to mitigate the impact of label noise [36, 50, 39, 45, 30, 49, 36], which is also the primary focus of our work. Many existing heuristic methods in LNL are based on the memorization effect, where the algorithm attempts to only learn from confident clean examples [20, 14, 46, 34]. Alternatively optimizing the classifier and updating the training set is not a new idea in LNL. For instance, Joint Optim [42], Co-teaching [14], SELF [34], and Me-Momentum [2] employ a similar positive feedback loop to our proposed Late Stopping.", + "bbox": [ + 496, + 566, + 890, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Previous research on the dynamics of DNNs has demonstrated that hard examples are typically learned during the late stage of the learning process [1, 43, 31]. Furthermore, many recent studies have employed various training-time metrics to quantify the \"hardness\" of examples [32, 16, 7, 4, 21, 31], leading to an increase in LNL approaches that use learning dynamics to select clean examples. For instance,", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16080", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Late Stopping" + ], + "code_body": "Input: Original noisy training set $\\mathcal{D}_1$ , iteration rate $m\\%$ , noise rate $n\\%$ , epoch $T_{max}$ and iteration $I_{max}$ . \nOutput: Extracted final training set and the classifier. \n1: for $I = 1, \\dots, I_{max}$ do \n2: Initialize $\\mathcal{D}_i$ , $S_{F_i} = 0$ and $\\mathcal{D}_{F_i} = [\\ldots]$ . \n3: //Initialize new training set, the number/dataset of examples that meet the First-time k-epoch Learning, respectively. \n4: for $T = 1, \\dots, T_{max}$ do \n5: Train $f_i$ on $\\mathcal{D}_i$ . \n6: Update $\\mathcal{D}_{F_i}$ , $S_{F_i}$ . \n7: Break and Output $\\mathcal{D}_{i+1} = \\mathcal{D}_{F_i}$ , if $S_{F_i} > S_{F_{i-1}} \\times (1 - m\\%)$ . \n8: end for \n9: Break and Output $f_i$ and $\\mathcal{D}_{F_i}$ , if $m \\times i > n$ . \n10: end for", + "bbox": [ + 76, + 108, + 883, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "FSLT&SSFT [31], Self-Filtering [48], SELFIE [40], and RoCL [57] adopt a criterion similar to our proposed FkL criterion. Specifically, FSLT&SSFT and Self-Filtering use the classifier's error prediction to pinpoint clean examples, SELFIE employs entropy values from prediction histories for selection, and RoCL leverages the variance of training losses to select clean examples. Instead of quantifying the \"hardness\" of examples based on the characteristics of individual examples in the dataset, our proposed method focuses on extracting the intrinsic robust learning ability of DNNs from the model trained on noisy datasets.", + "bbox": [ + 75, + 319, + 473, + 487 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Late Stopping", + "text_level": 1, + "bbox": [ + 76, + 503, + 220, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we elaborate on our proposed Late Stopping method. As shown in Figure 1, the primary goal of the Late Stopping framework is to maximize the retention of clean examples in the training set throughout the learning process, enabling our method to learn clean hard examples (CHEs) from a noisy training set. Therefore, we halt the training process in the late training stage, leveraging First-time $k$ -epoch Learning (FkL) to exploit the results of the intrinsic robust learning ability of DNNs for sample selection. Iteratively performing this operation allows for a gradual reduction of noise while maximizing the retention of clean samples in the training dataset.", + "bbox": [ + 75, + 529, + 470, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Algorithm Flow", + "text_level": 1, + "bbox": [ + 76, + 723, + 235, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For a comprehensive explanation of Late Stopping, we begin by formally defining First-time $k$ -epoch Learning (FkL). In learning with noisy labels, let us consider a model $f_{i}$ trained on a noisy training set $\\mathcal{D}_i$ composed of $n$ training examples $\\{\\mathbf{x}_j,y_j\\}_{j = 1}^n$ where $y_{j}$ denotes the given label (which may not be true) of $\\mathbf{x}_j$ . After $t$ training epochs, the predicted label $\\hat{y}_j^t$ for the instance $\\mathbf{x}_j$ can be obtained. Let $\\mathrm{acc}_j^t = \\mathbb{1}_{\\hat{y}_j^t = y_j}$ denote a binary variable indicating whether $f_{i}$ predicts the given label $y_{j}$ of the instance $\\mathbf{x}_j$ at epoch $t$ . The FkL for the instance $\\mathbf{x}_j$ is defined as the minimum", + "bbox": [ + 75, + 748, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "index of the training epoch that the instance $\\mathbf{x}_j$ has been predicted to its given label $y_{j}$ for $k$ consecutive epochs:", + "bbox": [ + 496, + 320, + 890, + 351 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {F k L} _ {j} = \\underset {t ^ {*} \\in t} {\\operatorname {a r g m i n}} \\left(\\mathrm {a c c} _ {j} ^ {t ^ {*}} \\wedge \\ldots \\wedge \\mathrm {a c c} _ {j} ^ {(t ^ {*} - k + 1)} = 1\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 354, + 864, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "If $\\mathrm{FkL}_j = t^*$ , it implies that the classifier $f_{i}$ \"learns\" the instance $\\mathbf{x}_j$ after $t^*$ epochs. Notably, if $\\mathbf{x}_j$ is \"learned\" by the classifier early in the training, it will have a small FkL value, however, if it is \"learned\" in the late stage, it will have a large FkL value. Based on our FkL definition, we observed that the majority of examples with large FkL values are mislabeled, as shown in Figure 1(a). This observation provides a rationale for selecting examples with large FkL values, those learned in the late training stage, as high-probability mislabeled examples.", + "bbox": [ + 496, + 386, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With the FkL selection criterion, we present the algorithmic framework of Late Stopping. At the low level (Steps 4-8 of Algorithm 1), the sample selection strategy follows a \"from easy to hard\" curriculum learning procedure [5, 18]. During the $i$ -th iteration, the classifier $f_{i}$ is trained on a new training set $\\mathcal{D}_i$ (Step 5), and newly identified FkL examples are added to $\\mathcal{D}_{F_i}$ (Step 6). If the size of $\\mathcal{D}_{F_i}$ , represented as $S_{F_i}$ , exceeds a predefined threshold, the training in this iteration will halt, and the output becomes $\\mathcal{D}_{F_i}$ (Step 7). At the higher level (Steps 1-10 of Algorithm 1), our method learns through a \"from hard to easy\" positive feedback loop, distinguishing it from most existing LNL approaches. The algorithm starts with initializing $\\mathcal{D}_1$ and training $f_{1}$ (Iteration 1). In subsequent iterations, the new training set $\\mathcal{D}_i$ (Step 2, Iteration $i$ ) is updated from the previous iteration's $\\mathcal{D}_{F_{i - 1}}$ (Step 8, Iteration $i - 1$ ). When the stopping condition is met, the output is $f_{i}$ and $\\mathcal{D}_{F_i}$ (Step 10).", + "bbox": [ + 496, + 537, + 892, + 795 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Learning CHEs by Positive Feedback Loop", + "text_level": 1, + "bbox": [ + 500, + 801, + 867, + 818 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we delve deeper into the typical positive feedback loop in LNL, highlighting its limitations in effectively learning CHEs. We then elucidate how our proposed method overcomes these limitations and maximizes the retention of clean examples throughout the learning process.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16081", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Typical positive feedback loop in LNL. According to statistical learning theory [33], training data with better quality yields a better classifier. Therefore, we can improve the classifier's generalization performance in LNL through the construction of a positive feedback loop. The goal of the positive feedback loop is that, after each training step, the new classifier showcases enhanced generalization performance compared with its predecessor. By doing so, it can more robustly guide the sample selection process, enabling the use of improved training data for classifier training in the succeeding steps [2].", + "bbox": [ + 76, + 90, + 472, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Most LNL methods, relying on confident examples, initiate with either a small yet clean training set or a weak yet reliable classifier. To enhance the classifier's generalization performance during initialization, they often rigorously limit memorization effects and eliminate potential mislabeled examples, even if this entails removing many CHEs. By restricting the memorization of mislabeled examples, they achieve superior generalization performance compared with unrestricted training on the original set. Then, they either iteratively or incrementally, train classifiers, ultimately obtaining either a larger clean training set or a more robust classifier. This strategy is effective when the classes or subclasses within the dataset are well-balanced and the examples within each class are interrelated, allowing the classifier to learn harder examples from easier ones.", + "bbox": [ + 76, + 260, + 472, + 487 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Limitations of typical positive feedback loop. Although LNL methods that rely on a typical positive feedback loop achieve good generalization performance in a variety of benchmark tasks, natural datasets are often highly imbalanced. This imbalance poses a challenge to achieving close-to-optimal generalization performance with existing LNL methods. Specifically, such challenges are because CHEs are often characterized by large losses and non-dominant patterns. As a result, substantial learning about CHEs predominantly transpires during the late stages of training, driven by memorization effects [2, 52]. The conventional positive feedback loop, aimed at preventing overfitting, often strictly limits the memorization effects of DNNs. Consequently, this strict constraint reduces a classifier's ability to learn from under-represented subpopulations in datasets [9], and thus limits its learning primarily to typical (dominant) classes and subclasses. Such constraints ultimately lead to a situation where the learning ability of rare classes and subclasses, i.e., CHEs, is continuously neglected, while the learning ability of the classes and subclasses representing the dominant pattern is continuously enhanced.", + "bbox": [ + 76, + 489, + 472, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Positive feedback loop in Late Stopping. Based on our previous discussions, to achieve close-to-optimal generalization performance on natural datasets, we need to focus on learning from CHEs throughout the training process. To achieve this, we prolong the training process for each train-", + "bbox": [ + 76, + 825, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ing iteration to make use of the memorization effects to help memorize CHEs. With a loose sample selection process, we can ensure that we maximize the retention of clean examples in the training set throughout the learning process. However, retaining as many clean examples as possible during the training initialization requires accepting a significant amount of label noise in the initial training set. Additionally, relying on the \"memorization effects in the late training stage\" to learn CHEs might result in poor generalization performance, as the classifier may seriously overfit label noise in this stage.", + "bbox": [ + 496, + 90, + 893, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To counter these negative effects, we propose a \"from hard to easy\" positive feedback loop within the Late Stopping framework. While we prolong the training process in each training iteration, we simultaneously use the classifier's robust learning capabilities as the criterion for sample selection, i.e., FkL. In each iteration, we train a new classifier on a new training set, using it solely to guide the sample selection for the current iteration. In this positive feedback loop, we opt to disregard the generalization performance of the classifier in each iteration. Instead, we exploit the robust learning capabilities of each new classifier, $f_{i}$ , in its $i$ iteration on $\\mathcal{D}_i$ from its learning dynamics, i.e., using the FkL criterion to select examples for the next iteration.", + "bbox": [ + 496, + 260, + 893, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The new training set, obtained by the FkL criterion from the previous iteration, will have less noise. This enables the training of a better new classifier, which can learn more from the CHEs before it begins to memorize mislabeled examples. Therefore, tracking learning dynamics using the FkL criterion can better distinguish between CHEs and mislabeled examples, resulting in a new training set with even less noise than the previous one but contains CHEs. By observing each classifier's learning dynamics through FkL in every iteration, we can iteratively refine our training set, reducing noise while retaining the majority of clean examples, as shown in Figure 2.", + "bbox": [ + 496, + 459, + 893, + 641 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discussion. Our proposed method is motivated by the seemingly conflicting views on the ability of DNNs to handle label noise as presented in recent studies: \"Deep neural networks easily fit random labels [56]\" and \"Deep learning is robust to massive label noises [37]\". Empirical evidence [1] suggests that DNNs first learn simple patterns before over-fitting in the late training stage. However, there is a scarcity of studies on the behavior of DNNs during the intermediate stages of training, which may be a critical factor for understanding the robustness of DNNs to label noise - DNNs might exhibit spontaneously robust learning to massive label noises in all periods of training, though the generalization performance is over-fitting noisy labels. Thus, we aim to separate the robust learning ability of DNNs from their generalization performance. To this end, we leverage the intrinsic robust learning ability of DNNs by continuing the training process until the generalization performance se", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16082", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0bb0cf552779ea2d7d338e7ad3a121554314ee42301076f0542b61a316dd11ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 95, + 295, + 305 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8fad7cead5903932755b2f00bc7dd9c76e89556aec67dd378b77e65d22dba3bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 305, + 95, + 483, + 304 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/35340cd50c450ee8c74a49181468d1b2650c7db2c36740a911b14ceb1e96ad41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 95, + 673, + 304 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d5116a105fc06502ef1c75a082b10053ab028240597fe2ef44cf1ccdebe98cee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 95, + 864, + 304 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a6a93e6d9452aafb9b41fe113129918007448a49fe81938f85cbceb640ac6010.jpg", + "image_caption": [ + "Figure 2. We refer to one update of the classifier and the training set as one iteration. Top subfigures: We illustrate the changes in the Test-set Accuracy and the Training-set Accuracy of the classifier during the training process of Late Stopping. There are ten peaks in each figure because we set the number of iterations $= 10$ and the classifiers are re-initialized at the beginning of each new iteration. Bottom subfigures: We illustrate the changes in the noise rate of the training set in each iteration. There are ten bars in each figure because we set the number of iterations $= 10$ and the training set of each iteration is obtained from the previous iteration." + ], + "image_footnote": [], + "bbox": [ + 112, + 309, + 292, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7fccf7d2d3a6a3bbe2811305228f9405440e05bba75c70001bbf14ae7446220f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 303, + 311, + 480, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b9be724f8ac70093670aa00831aa917c795c01e624a5767017bae51d2f58f3bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 311, + 669, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/67f65b7a20cff59ecadc867180a36b27facc844bff3eea3aa0c89169e852d1d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 311, + 864, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "riously deteriorates (i.e., Late Stopping) and we extract the robust learning results during this process (i.e., FkL).", + "bbox": [ + 75, + 523, + 470, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 569, + 209, + 588 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we conduct experiments on both synthetic and real-world datasets containing label noise to validate the effectiveness of our proposed Late Stopping.", + "bbox": [ + 75, + 595, + 468, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We use two popular benchmark datasets i.e., CIFAR-10 and CIFAR-100 [23], to test the generalization performance of our proposed method. Following previous works [2, 51], we manually corrupt CIFAR-10 and CIFAR-100 with Symmetric noise (abbreviated as Sym.) [44] and Instance-dependent (abbreviated as Ins.) noise [53]. For Sym. noise and Ins. noise, the noise rate is set to $20\\%$ and $40\\%$ . For a fair comparison, we leave out $10\\%$ of the noisy training data. We employ the real-world noisy dataset CIFAR-10N [47], which equips the training datasets of CIFAR-10 with human-annotated real-world noisy labels. More details about the above datasets and noise types are provided in Appendix A1.", + "bbox": [ + 75, + 643, + 470, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared methods. We compare the Late Stopping method (Algorithm 1) with the following well-known methods: (1) Statistically inconsistent approaches (small-loss trick): MentorNet [20], Co-teaching [14], and JoCoR [46];", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(2) Statistically inconsistent approaches (other tricks): Joint Optim [42], CDR [51], and Me-Momentum [2]; (3) Statistically consistent approaches: Forward [35] and DMI [54]. Note that drawing a direct comparison with certain semi-supervised approaches, especially those with multiple technical aggregations such as SELF [34], DivideMix [24], ELR+ [26], and Unicon [22]. The results for baselines are copied from original papers and [2, 47].", + "bbox": [ + 496, + 523, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Network structure and experimental setup. We utilize a typical warming-up strategy to ensure stable predictions of the DNNs. The optimizer settings used in our experiments are as follows: SGD with a momentum of 0.9, weight decay of 5e-4, batch size of 128, and initial learning rate of 0.02. In our experiments, we applied typical data augmentations such as horizontal flipping and random cropping. For the experiments on synthetic noisy datasets, ResNet-18 and ResNet-34 [15] are used for CIFAR-10 and CIFAR-100, respectively. For the experiments on real-world noisy datasets, ResNet-34 is used for CIFAR-10N. More details about our experimental setup are provided in Appendix A2.", + "bbox": [ + 496, + 643, + 892, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Effectiveness of Late Stopping", + "text_level": 1, + "bbox": [ + 500, + 832, + 769, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, we aim to provide empirical evidence to verify the effectiveness of Late Stopping. We conduct experiments on the CIFAR-10 and CIFAR-100 datasets, as their", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16083", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/15304dee3243407b58892187e9aa4e0abd280f9a9e4e627067536ca30318710f.jpg", + "table_caption": [ + "Table 1. Label precision of the selected examples (45k in total, with 27k clean examples)." + ], + "table_footnote": [], + "table_body": "
Data&NoisecriterionSelecting Clean ExamplesSelecting Mislabeled Examples
0-10k0-15k0-25k30k-45k35k-45k40k-45k
CIFAR-10loss92.73%89.56%82.89%75.67%83.49%91.54%
Sym. 40%FkL(Ours)95.49%95.59%93.56%96.39%99.81%99.94%
CIFAR-10loss75.55%72.33%71.38%60.27%68.69%77.28%
Ins. 40%FkL(Ours)81.88%81.67%81.51%78.51%88.85%99.30%
CIFAR-100loss88.43%84.72%78.49%68.02%75.73%84.68%
Sym. 40%FkL(Ours)97.45%96.78%95.06%94.63%97.91%98.86%
CIFAR-100loss71.30%68.23%65.29%45.91%44.23%42.56%
Ins. 40%FkL(Ours)89.25%88.56%84.40%78.22%86.28%91.76%
", + "bbox": [ + 86, + 101, + 883, + 284 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b287010e5edc6dadd6e08c0380aeacc50bf98552a4b763d313566128bfa7169d.jpg", + "table_caption": [ + "Table 2. Numbers of clean examples of the final training set (27k in total)." + ], + "table_footnote": [], + "table_body": "
CIFAR-10 (Sym. 40%)CIFAR-10 (Ins. 40%)CIFAR-100 (Sym. 40%)CIFAR-100 (Ins. 40%)
Me-Momentum [2]25,79125,69422,24420,779
Late Stopping (Ours)26,56225,91526,12023,979
", + "bbox": [ + 86, + 305, + 883, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ground-truth labels are available. The average results of five runs of our experiments are presented in Figure 2, which demonstrates the iterative improvement in the quality of the training set when Late Stopping is applied in the learning process. And a classifier with better generalization performance is obtained. We demonstrate the ability of our proposed FkL criterion to select mislabeled examples under the Late Stopping framework, compared with the loss criterion. Additionally, we show the effectiveness of our proposed Late Stopping in retaining clean examples in the training set by comparing it with Me-Momentum [2], which is also an sample selection method that focuses on extracting clean hard examples.", + "bbox": [ + 75, + 385, + 468, + 582 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with loss criterion. The selection of confident clean examples based on the small-loss criterion is a commonly used approach in LNL and has been shown to be effective [20, 14, 46]. However, the approach of selecting mislabeled examples based on the large-loss [6] can be tricky since it fails to distinguish between mislabeled and clean hard examples [52]. We conducted experiments on the CIFAR-10 and CIFAR-100 datasets to compare the effectiveness of the FkL and loss criterion for selecting examples during the same training process. Specifically, we ranked all examples (45k in total, with 27k clean examples) using the FkL criterion and the loss criterion, respectively, from the smallest 0k to the largest 45k. We then compared the precision of the two criteria in selecting clean examples and mislabeled examples in different ranges. The details of the experiments and the results are presented in Table 1. Our experimental results demonstrate that the FkL criterion outperforms the loss criterion in selecting both clean and mislabeled examples under the Late Stopping framework. The largest performance gap was observed in the $40k - 45k$ range. These results provide empirical evidence that the FkL cri", + "bbox": [ + 75, + 583, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "terion is more effective than the loss criterion for selecting mislabeled examples in the Late Stopping framework.", + "bbox": [ + 496, + 385, + 890, + 414 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with hard example selection approach. In Table 2, we compare our proposed method with Me-Momentum [2] which also focuses on selecting clean hard examples. Since there are no clear definitions of clean hard examples, we cannot directly compare the effectiveness of selecting such examples. Nevertheless, we can make an indirect comparison by comparing the ability to select clean examples. Our experimental results demonstrate that Late Stopping is an effective approach for retaining clean hard examples. On the CIFAR-10 dataset, both Late Stopping and Me-Momentum showed comparable performance. However, on the more challenging CIFAR-100 dataset, Late Stopping significantly achieved better performance in selecting clean hard examples.", + "bbox": [ + 496, + 415, + 892, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Classification Accuracy", + "text_level": 1, + "bbox": [ + 500, + 635, + 718, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Synthetic datasets. The experimental results on test accuracy on synthetic datasets with class-dependent and instance-dependent label noise are provided in Table 3 and 4. Each trial is repeated five times and the mean value and standard deviation are recorded. On CIFAR-10, our method achieves varying degrees of lead over baselines. In the $20\\%$ symmetric noise task, which is the simplest task in all cases, the Me-Momentum baseline outperforms ours, which illustrates the effectiveness of conventional sample selection based on confident clean examples for simple LNL. For the more challenging CIFAR-100 dataset, our proposed method consistently achieved the best results. The size of each class in CIFAR-100 is ten times smaller than that of CIFAR-10, making it difficult to retain sufficient CHEs while maintaining a small yet clean training set using conventional sample selection methods. Methods that focus on improving the", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16084", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bb51523ffb97f7b2aa4a3a85ec020d7c7f9a7e33cf12d47c9a6fd199cc068955.jpg", + "table_caption": [ + "Table 3. Test performance (mean±std) of each approach using ResNet-18 on CIFAR-10." + ], + "table_footnote": [], + "table_body": "
Sym. 20%Sym. 40%Ins. 20%Ins. 40%
Late Stopping(Ours)91.06±0.22%88.92±0.38%91.08±0.23%87.41±0.38%
Cross-Entropy [38]85.00±0.43%79.59±1.31%85.92±1.09%79.91±1.41%
MentorNet [20]80.49±0.11%77.48±3.45%79.12±0.42%70.27±1.52%
Forward [35]85.63±0.11%74.30±0.26%85.29±0.38%74.72±3.24%
Co-teaching [14]87.16±0.52%83.59±0.28%86.54±0.11%80.98±0.39%
JoCoR [46]88.69±0.19%85.44±0.29%87.31±0.27%82.49±0.57%
DMI [54]88.18±0.13%83.98±0.48%89.14±0.36%84.78±1.97%
Joint Optim [42]89.70±0.36%87.79±0.20%89.69±0.42%82.62±0.57%
CDR [51]89.68±0.38%86.13±0.44%90.24±0.39%83.07±1.33%
Me-Momentum [2]91.44±0.33%88.39±0.34%90.86±0.21%86.66±0.91%
", + "bbox": [ + 86, + 101, + 883, + 284 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a2f8a0f48b28f0c7201c92c4c1df03b20c6c335d2ed80467e32aa6c32065b7e7.jpg", + "table_caption": [ + "Table 4. Test performance (mean±std) of each approach using ResNet-34 on CIFAR-100." + ], + "table_footnote": [], + "table_body": "
Sym. 20%Sym. 40%Ins. 20%Ins. 40%
Late Stopping(Ours)68.67±0.67%64.10±0.40%68.59±0.70%59.28±0.46%
Cross-Entropy [38]57.59±2.55%45.74±2.61%59.85±1.56%43.74±1.54%
MentorNet [20]52.11±0.10%35.12±1.13%51.73±0.17%40.90±0.45%
Forward [35]57.75±0.37%38.59±1.62%58.76±0.66%44.50±0.72%
Co-teaching [14]59.28±0.47%51.60±0.49%57.24±0.69%45.69±0.99%
JoCoR [46]64.17±0.19%55.97±0.46%61.98±0.39%50.59±0.71%
DMI [54]58.73±0.70%49.81±1.22%58.05±0.20%47.36±0.68%
Joint Optim [42]64.55±0.38%57.97±0.67%65.15±0.31%55.57±0.41%
CDR [51]66.52±0.24%60.18±0.22%67.06±0.50%56.86±0.62%
Me-Momentum [2]68.03±0.53%63.48±0.72%68.11±0.57%58.38±1.28%
", + "bbox": [ + 86, + 309, + 883, + 494 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/537bdfeb6899fe709f7f8ffa939c9fab15ea18a19a3223a703446f7d757f11ed.jpg", + "table_caption": [ + "Table 5. Test accuracy of each approach using ResNet-34 on CIFAR-10N (Worst)." + ], + "table_footnote": [], + "table_body": "
Cross-Entropy [38]Forward [35]Co-teaching [14]JoCoR [46]Me-Momentum [2]Late Stopping(Ours)
77.69±1.55%79.79±0.46%83.83±0.13%83.37±0.30%84.71±0.37%85.24±0.38%
", + "bbox": [ + 86, + 518, + 883, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "number of CHEs in the training set can achieve better generalization performance in this task. For instance, DMI and Co-teaching show a much larger performance gap with our proposed method on CIFAR-100 compared with CIFAR-10. Furthermore, Table 2 validates our method's superior capability to retain clean examples, resulting in a larger performance gap with Me-Momentum on CIFAR-100.", + "bbox": [ + 75, + 585, + 468, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Real-world dataset. To validate the efficacy of our proposed method on real-world datasets, we assess our method using the CIFAR-10N dataset in Table 4, a recognized benchmark in learning with noisy labels tasks with both ground-truth labels and human-annotated real-world noisy labels. We utilized the most challenging real-world noisy labels from CIFAR-10N, i.e., the \"Worst\" setting. In this setting, for each image, if there are any incorrectly labeled examples, the given label is randomly selected from human-annotated false labels. Each trial is repeated five times and the mean value and standard deviation are recorded. As shown in Table 4, our method achieves the best performance compared with other methods.", + "bbox": [ + 75, + 703, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Further analysis", + "text_level": 1, + "bbox": [ + 500, + 585, + 663, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Here, we conduct further analysis of our proposed method with the same experimental settings as those used in Section 4.2 unless stated otherwise.", + "bbox": [ + 498, + 609, + 890, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Limitations. While our method achieves good robustness by simply removing the lately learned examples, it is not immune to errors. Some clean examples might be incorrectly removed from the training set, i.e., falsely removed examples, and some mislabeled examples are incorrectly retained in the training set, i.e., falsely retained examples. We visualize such typical examples in Figure 3 and provide the following empirical analysis.", + "bbox": [ + 496, + 657, + 890, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Falsely retained examples are mislabeled with the wrong label $L_{w}$ , however, such examples often possess patterns similar to the dominant subclasses in the $L_{w}$ class, making it difficult to identify them as high probability mislabeled examples by the FkL criterion. As shown in Table 6, based on the FkL criterion and the loss criterion, the \"hardness\" of these examples decreases after being mislabeled. In particular, we named the examples with a decrease in", + "bbox": [ + 496, + 779, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16085", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bb131935bcded0d1eb98a2305e21cd862c8533fcdcbe93795ec04ac5c2e49096.jpg", + "image_caption": [ + "Figure 3. The labels in the figure are ground-truth labels for each example. Falsely Removed (1-3) are typical examples that are incorrectly removed in the first iteration of Late Stopping; Falsely Retained (1-3) are typical examples that are incorrectly marked by FkL in the last iteration of Late Stopping. In the training set, Falsely Retained (1) is incorrectly labeled as \"deer\", Falsely Retained (2) is incorrectly labeled as \"truck\", and Falsely Retained (3) is incorrectly labeled as \"frog\"." + ], + "image_footnote": [], + "bbox": [ + 104, + 99, + 272, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/34340c5b7fdfaff1f2a036501159a9ecad1650462804b4a3d0b6478abda668ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 99, + 356, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d1fe7ce62347848503949b305d2a414cfc467b064263998ee36fac42839e70b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 99, + 437, + 250 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4f12463c5d7bf1bee38740de148e269351f4e68317fc1f4208326fc69a0e7a79.jpg", + "table_caption": [ + "Table 6. The comparison of the average ranking of falsely retained examples using the loss criterion and the FkL criterion before and after fixing the noisy labels (CIFAR-10, Before: Sym. $40\\%$ noise)." + ], + "table_footnote": [], + "table_body": "
LabelCriterionAvg. Ranking
Before fixing (Given label)FkL22340.66
loss23673.50
After fixing (Ground-truth label)FkL28452.08 (+27.36%)
loss29476.46 (+24.51%)
", + "bbox": [ + 84, + 434, + 460, + 520 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1775aba9b41305aef3d313a10049072f7e00abf1d76be5af1255e13dfe05a671.jpg", + "table_caption": [ + "Table 7. Comparison of the number of clean examples in datasets before and after applying our method as a pre-processing approach to decrease the noise level of a $40\\%$ noisy training set to $20\\%$ ." + ], + "table_footnote": [], + "table_body": "
Training setBefore (40% noise)After (20% noise)
CIFAR-10 (Sym.)2722827139 (-0.33%)
CIFAR-10 (Ins.)2709426710 (-1.42%)
CIFAR-100 (Sym.)2734127037 (-1.11%)
CIFAR-100 (Ins.)2724925079 (-7.96%)
CIFAR-10N (Worst)2989629613 (-0.95%)
", + "bbox": [ + 84, + 578, + 460, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "training losses after being mislabeled as \"hard mislabeled examples\". Our experimental results indicate that hard mislabeled examples pose a challenge for all sample selection-based LNL methods. More details about Table 6 are provided in Appendix B1.", + "bbox": [ + 75, + 702, + 468, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Falsely removed examples refer to the examples that are too hard to remove in practice. To limit the computational resources consumed by our proposed method, we set the removal rate (Algorithm 1, iteration rate $m\\%$ ) to a large value. Thus, our proposed method cannot completely distinguish between rare patterns and mislabeled examples, which can result in a small number of examples from rare subclasses being mistakenly removed from the training set.", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2efc3115f78fce9d87ca5a0555f44dc8464716ac4ec32c955a3abca30183633d.jpg", + "table_caption": [ + "Table 8. Comparison of the total training hours on CIFAR-100." + ], + "table_footnote": [], + "table_body": "
Co-teaching [14]Me-Momentum [2]Late Stopping (Ours)
3.3h7.1h9.5h
", + "bbox": [ + 508, + 101, + 883, + 140 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/70c7769ec338a69881711bf58e86cba66bebdc465732d24fead3c802151bc71f.jpg", + "image_caption": [ + "Figure 4. Illustrates the performance of classifiers with the change in iteration rate $m$ ." + ], + "image_footnote": [], + "bbox": [ + 550, + 157, + 834, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Versatility. We are focusing on demonstrating the concept, i.e., using Late Stopping to retain clean hard examples in the training set, but not on boosting the classification performance. However, to cope with even more complex noisy scenarios, our method works well in combination with other advanced techniques. In particular, our approach has excellent performance as a pre-processing approach for reducing the noise rate of the noisy training set. As shown in Table 7, we evaluate Late Stopping as a pre-processing approach to decrease the noise level of a $40\\%$ noisy training set to $20\\%$ . Our experimental results indicate that our proposed method performs exceptionally well in reducing label noise. It can substantially reduce the noise level of the training set with minimal loss of clean examples.", + "bbox": [ + 496, + 344, + 890, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Training time. Our proposed method involves training the classifier on a larger training set for a longer period, which may not be advantageous in terms of efficiency. Despite this, as the noise rate decreases, the size of the training set decreases, and the speed of obtaining FkL-examples is accelerated (see Figure 2). As shown in Table 8, we compare the training time with typical baseline methods on CIFAR-100 (Sym. $40\\%$ ). Our experimental results indicate that the training time of our proposed method is in a comparable range with other approaches.", + "bbox": [ + 496, + 561, + 890, + 713 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sensitivity of the iteration rate. The iteration rate $m$ (see Algorithm 1) determines the iteration number for Late Stopping and the number of examples removed in each iteration. To investigate the sensitivity of $m$ , we conducted experiments on CIFAR10 with $40\\%$ Sym. noise and Ins. noise by varying $m$ in the range $\\{10,5,4,3,2\\}$ . Figure 4 shows the performance of classifiers, which gradually improves as $m$ decreases. This observation aligns with the findings presented in Table 1, where a decrease in the range of selected high-probability unlabeled examples leads to higher accuracy in selecting such examples, ultimately benefiting the classifier's performance.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16086", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 89, + 194, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we focused on the challenge of the inability of existing sample selection methods to effectively select clean hard examples. To address this challenge, we proposed a novel method called Late Stopping. In contrast to traditional early-stopping strategies, our method is rooted in a prolonged training process that distinguishes between mislabeled and clean examples by pinpointing the number of training epochs required for each example to be consistently classified to its given label for the first time. We coin this new sample selection criterion as First-time $k$ -epoch Learning. Experimental results on synthetic and real-world datasets demonstrate that our proposed method is both straightforward and effective in handling learning with noisy labels. In future work, we plan to enhance the FkL criterion to more accurately capture the intrinsic robust learning ability of DNNs, which could potentially bolster the effectiveness of our Late Stopping framework, especially under more intricate noise conditions.", + "bbox": [ + 75, + 114, + 472, + 387 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 76, + 400, + 236, + 417 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Lei Feng was supported by the National Natural Science Foundation of China (Grant No. 62106028), Chongqing Overseas Chinese Entrepreneurship and Innovation Support Program, CAAI-Huawei MindSpore Open Fund, and Chongqing Artificial Intelligence Innovation Center. Tongliang Liu was partially supported by Australian Research Council Projects IC-190100031, LP-220100527, DP-220102121, and FT-220100318. 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In ICLR, 2021." + ], + "bbox": [ + 501, + 92, + 890, + 843 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16088", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/c0b4cc8e-d6dd-4adb-8592-11f986f8c0fc_model.json b/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/c0b4cc8e-d6dd-4adb-8592-11f986f8c0fc_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1c0d8e5de4a8bbb42f6c8ea73c1c5a6cf707eb --- /dev/null +++ b/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/c0b4cc8e-d6dd-4adb-8592-11f986f8c0fc_model.json @@ -0,0 +1,2013 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.131, + 0.857, + 0.153 + ], + "angle": 0, + "content": "Late Stopping: Avoiding Confidently Learning from Mislabeled Examples" + }, + { + "type": "text", + "bbox": [ + 0.226, + 0.18, + 0.744, + 0.218 + ], + "angle": 0, + "content": "Suqin Yuan\\(^{1}\\) Lei Feng\\(^{2*}\\) Tongliang Liu\\(^{1*}\\) \n\\(^{1}\\)The University of Sydney \\(^{2}\\)Nanyang Technological University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.313, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.473, + 0.571 + ], + "angle": 0, + "content": "Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which are critical for achieving the model's close-to-optimal generalization performance. In this paper, we propose a new framework, Late Stopping, which leverages the intrinsic robust learning ability of DNNs through a prolonged training process. Specifically, Late Stopping gradually shrinks the noisy dataset by removing high-probability mislabeled examples while retaining the majority of clean hard examples in the training set throughout the learning process. We empirically observe that mislabeled and clean examples exhibit differences in the number of epochs required for them to be consistently and correctly classified, and thus high-probability mislabeled examples can be removed. Experimental results on benchmark-simulated and real-world noisy datasets demonstrate that the proposed method outperforms state-of-the-art counterparts." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.59, + 0.21, + 0.606 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.767 + ], + "angle": 0, + "content": "Deep Neural Networks (DNNs) have achieved outstanding success in various tasks, while the success largely relies on data with high-quality annotations [13, 55, 41, 19]. In many real-world scenarios, it would be quite difficult to collect large-scale accurately labeled data, which could inevitably contain noisy labels. Unfortunately, previous studies [1, 56] showed that DNNs can easily overfit random labels, resulting in poor generalization performance. Therefore, an increasing number of methods have been proposed for Learning with Noisy Labels (LNL)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.768, + 0.47, + 0.875 + ], + "angle": 0, + "content": "One mainstream solution in existing methods of LNL is to train the classifier with confident examples [20, 14, 46, 34, 36], which is based on the memorization effect of DNNs, i.e., DNNs learn example with dominant patterns first and then overfit rare ones [1]. Given only noisy data, to exploit the memorization effect, the typical strategy starts from a small confident clean dataset and then" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.253, + 0.895, + 0.419 + ], + "angle": 0, + "content": "gradually expands the dataset, which prevents DNNs from over-fitting noisy data. In general, there are two primary approaches to exploit confident examples in the learning process. The first approach involves identifying examples with high-probability clean labels and training the classifier based on these examples, which is commonly referred to as the \"small-loss trick\" [20, 14, 12, 28, 52]. The second approach involves controlling the learning process of the classifier to primarily learn high-probability clean examples in noisy datasets, which is commonly referred to as \"early stopping\" [37, 42, 17, 25, 3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.895, + 0.72 + ], + "angle": 0, + "content": "Despite providing satisfactory performance, these approaches present an unintended consequence in their methods to prevent over-fitting noise. Specifically, to reduce the impact of mislabeled examples, these approaches limit the capability of the model to effectively learn clean hard examples (CHEs) in noisy datasets, where CHEs are defined as clean examples that are close to the decision boundary, and a significant proportion of CHEs are non-dominated sub-population examples [9]. Identifying CHEs in noisy data is quite challenging [2, 22], as both the CHEs and the mislabeled examples are often characterized by large losses [52, 11, 6], causing them to become entangled. To maintain the purity of the dataset of confident examples, existing LNL methods [34, 2] normally try to eliminate potential examples that are likely to be mislabeled, which inevitably contain many CHEs. However, it is necessary to consider the positive impact of memorization effects on underrepresented sub-populations [10] (i.e., CHEs) when learning from natural datasets, as this is crucial for achieving close-to-optimal generalization performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.721, + 0.895, + 0.887 + ], + "angle": 0, + "content": "In this work, our goal is to enable the classifier to learn as many useful non-dominated sub-population examples in the training set as possible during the process of learning with noisy labels. This entails selecting as many clean examples as possible, particularly the clean hard examples, during the sample selection process. In relation to this context, we introduce a novel concept termed First-time \\( k \\)-epoch Learning (FkL), which is defined as the index of the epoch during the training procedure where an example has been predicted to its given label for consecutive \\( k \\) epochs for the first time, as shown in Figure 1(a)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.228, + 0.9 + ], + "angle": 0, + "content": "*Corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16079" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.087, + 0.316, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.207, + 0.332, + 0.223, + 0.342 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.09, + 0.604, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.331, + 0.482, + 0.342 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.091, + 0.738, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.091, + 0.855, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.332, + 0.751, + 0.342 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.346, + 0.892, + 0.43 + ], + "angle": 0, + "content": "Figure 1. (a) We propose the First-time \\( k \\)-epoch Learning (FkL) metric, which determines the minimum index of the training epoch until which an example has been predicted as its given label for consecutive \\( k \\) epochs. (b) The normalised histogram of CIFAR-10 examples with \\( 40\\% \\) symmetric label noise w.r.t. the sequence they meet the FkL metric during training procedure. The horizontal axis represents the sequential order in which training examples meet the FkL metric. The vertical axis represents the normalised histogram of examples. (c) Rather than the methods that start from a small yet clean training set ('Early' Stopping), our proposed framework starts from a large training set ('Late' Stopping) that retains as many clean examples as possible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Using First-time \\( k \\)-epoch Learning (FkL) as a metric, we sequence the examples in the noisy dataset according to the order they meet the FkL metric during the training procedure, as shown in Figure 1(b). As shown in the same figure, most unlabeled examples can only be classified into their given labels for consecutive \\( k \\) epochs in the later stages of training (i.e., larger in the sequence), which implies a relatively large FkL value. This observation suggests that the examples with large FkL values (i.e., those examples that are classified to their given labels for consecutive \\( k \\) epochs only in the late training stage) are predominantly those with incorrect labels. Therefore, the FkL values of different training examples can be used to distinguish whether an example is unlabeled or not." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Motivated by the above observations, we propose a novel method based on reverse thinking of the conventional confident example selection strategy. Our proposed method, called Late Stopping, employs an iterative sample selection process that gradually reduces the noise rate of the dataset, leading to a positive feedback loop. Instead of selecting high-probability clean examples in the early stage, our method focuses on selecting high-probability mislabeled examples in the late stage to retain as many CHEs as possible in the training set throughout the learning process, even though this method may lead to the retention of an acceptable level of mislabeled examples, as shown in 1(c). Building on this, we introduce a novel sample selection criterion, FkL, which works effectively in selecting mislabeled examples under the Late Stopping framework, and empirical results show that the FkL is more ef" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.522 + ], + "angle": 0, + "content": "fective than the loss criterion. We evaluate our method on benchmark-simulated and real-world noisy datasets. Empirical results demonstrate that the Late Stopping method achieves superior performance compared with state-of-the-art counterparts of learning with noisy labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.54, + 0.642, + 0.556 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Existing methods of learning with noisy labels can be broadly categorized into two types. The first category includes classifier-consistent algorithms that use the noise transition matrix [27, 29, 54, 35, 8], which indicates the probabilities of clean labels flipping to noisy labels. The second category focuses on heuristic methods to mitigate the impact of label noise [36, 50, 39, 45, 30, 49, 36], which is also the primary focus of our work. Many existing heuristic methods in LNL are based on the memorization effect, where the algorithm attempts to only learn from confident clean examples [20, 14, 46, 34]. Alternatively optimizing the classifier and updating the training set is not a new idea in LNL. For instance, Joint Optim [42], Co-teaching [14], SELF [34], and Me-Momentum [2] employ a similar positive feedback loop to our proposed Late Stopping." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Previous research on the dynamics of DNNs has demonstrated that hard examples are typically learned during the late stage of the learning process [1, 43, 31]. Furthermore, many recent studies have employed various training-time metrics to quantify the \"hardness\" of examples [32, 16, 7, 4, 21, 31], leading to an increase in LNL approaches that use learning dynamics to select clean examples. For instance," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16080" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.078, + 0.09, + 0.265, + 0.108 + ], + "angle": 0, + "content": "Algorithm 1 Late Stopping" + }, + { + "type": "algorithm", + "bbox": [ + 0.078, + 0.109, + 0.884, + 0.293 + ], + "angle": 0, + "content": "Input: Original noisy training set \\(\\mathcal{D}_1\\), iteration rate \\(m\\%\\), noise rate \\(n\\%\\), epoch \\(T_{max}\\) and iteration \\(I_{max}\\). \nOutput: Extracted final training set and the classifier. \n1: for \\(I = 1, \\dots, I_{max}\\) do \n2: Initialize \\(\\mathcal{D}_i\\), \\(S_{F_i} = 0\\) and \\(\\mathcal{D}_{F_i} = [\\ldots]\\). \n3: //Initialize new training set, the number/dataset of examples that meet the First-time k-epoch Learning, respectively. \n4: for \\(T = 1, \\dots, T_{max}\\) do \n5: Train \\(f_i\\) on \\(\\mathcal{D}_i\\). \n6: Update \\(\\mathcal{D}_{F_i}\\), \\(S_{F_i}\\). \n7: Break and Output \\(\\mathcal{D}_{i+1} = \\mathcal{D}_{F_i}\\), if \\(S_{F_i} > S_{F_{i-1}} \\times (1 - m\\%)\\). \n8: end for \n9: Break and Output \\(f_i\\) and \\(\\mathcal{D}_{F_i}\\), if \\(m \\times i > n\\). \n10: end for" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.474, + 0.488 + ], + "angle": 0, + "content": "FSLT&SSFT [31], Self-Filtering [48], SELFIE [40], and RoCL [57] adopt a criterion similar to our proposed FkL criterion. Specifically, FSLT&SSFT and Self-Filtering use the classifier's error prediction to pinpoint clean examples, SELFIE employs entropy values from prediction histories for selection, and RoCL leverages the variance of training losses to select clean examples. Instead of quantifying the \"hardness\" of examples based on the characteristics of individual examples in the dataset, our proposed method focuses on extracting the intrinsic robust learning ability of DNNs from the model trained on noisy datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.504, + 0.222, + 0.522 + ], + "angle": 0, + "content": "3. Late Stopping" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.471, + 0.712 + ], + "angle": 0, + "content": "In this section, we elaborate on our proposed Late Stopping method. As shown in Figure 1, the primary goal of the Late Stopping framework is to maximize the retention of clean examples in the training set throughout the learning process, enabling our method to learn clean hard examples (CHEs) from a noisy training set. Therefore, we halt the training process in the late training stage, leveraging First-time \\( k \\)-epoch Learning (FkL) to exploit the results of the intrinsic robust learning ability of DNNs for sample selection. Iteratively performing this operation allows for a gradual reduction of noise while maximizing the retention of clean samples in the training dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.236, + 0.74 + ], + "angle": 0, + "content": "3.1. Algorithm Flow" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.903 + ], + "angle": 0, + "content": "For a comprehensive explanation of Late Stopping, we begin by formally defining First-time \\(k\\)-epoch Learning (FkL). In learning with noisy labels, let us consider a model \\(f_{i}\\) trained on a noisy training set \\(\\mathcal{D}_i\\) composed of \\(n\\) training examples \\(\\{\\mathbf{x}_j,y_j\\}_{j = 1}^n\\) where \\(y_{j}\\) denotes the given label (which may not be true) of \\(\\mathbf{x}_j\\). After \\(t\\) training epochs, the predicted label \\(\\hat{y}_j^t\\) for the instance \\(\\mathbf{x}_j\\) can be obtained. Let \\(\\mathrm{acc}_j^t = \\mathbb{1}_{\\hat{y}_j^t = y_j}\\) denote a binary variable indicating whether \\(f_{i}\\) predicts the given label \\(y_{j}\\) of the instance \\(\\mathbf{x}_j\\) at epoch \\(t\\). The FkL for the instance \\(\\mathbf{x}_j\\) is defined as the minimum" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.352 + ], + "angle": 0, + "content": "index of the training epoch that the instance \\(\\mathbf{x}_j\\) has been predicted to its given label \\(y_{j}\\) for \\(k\\) consecutive epochs:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.356, + 0.866, + 0.385 + ], + "angle": 0, + "content": "\\[\n\\mathrm {F k L} _ {j} = \\underset {t ^ {*} \\in t} {\\operatorname {a r g m i n}} \\left(\\mathrm {a c c} _ {j} ^ {t ^ {*}} \\wedge \\ldots \\wedge \\mathrm {a c c} _ {j} ^ {(t ^ {*} - k + 1)} = 1\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.538 + ], + "angle": 0, + "content": "If \\(\\mathrm{FkL}_j = t^*\\), it implies that the classifier \\(f_{i}\\) \"learns\" the instance \\(\\mathbf{x}_j\\) after \\(t^*\\) epochs. Notably, if \\(\\mathbf{x}_j\\) is \"learned\" by the classifier early in the training, it will have a small FkL value, however, if it is \"learned\" in the late stage, it will have a large FkL value. Based on our FkL definition, we observed that the majority of examples with large FkL values are mislabeled, as shown in Figure 1(a). This observation provides a rationale for selecting examples with large FkL values, those learned in the late training stage, as high-probability mislabeled examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.893, + 0.796 + ], + "angle": 0, + "content": "With the FkL selection criterion, we present the algorithmic framework of Late Stopping. At the low level (Steps 4-8 of Algorithm 1), the sample selection strategy follows a \"from easy to hard\" curriculum learning procedure [5, 18]. During the \\(i\\)-th iteration, the classifier \\(f_{i}\\) is trained on a new training set \\(\\mathcal{D}_i\\) (Step 5), and newly identified FkL examples are added to \\(\\mathcal{D}_{F_i}\\) (Step 6). If the size of \\(\\mathcal{D}_{F_i}\\), represented as \\(S_{F_i}\\), exceeds a predefined threshold, the training in this iteration will halt, and the output becomes \\(\\mathcal{D}_{F_i}\\) (Step 7). At the higher level (Steps 1-10 of Algorithm 1), our method learns through a \"from hard to easy\" positive feedback loop, distinguishing it from most existing LNL approaches. The algorithm starts with initializing \\(\\mathcal{D}_1\\) and training \\(f_{1}\\) (Iteration 1). In subsequent iterations, the new training set \\(\\mathcal{D}_i\\) (Step 2, Iteration \\(i\\)) is updated from the previous iteration's \\(\\mathcal{D}_{F_{i - 1}}\\) (Step 8, Iteration \\(i - 1\\)). When the stopping condition is met, the output is \\(f_{i}\\) and \\(\\mathcal{D}_{F_i}\\) (Step 10)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.868, + 0.819 + ], + "angle": 0, + "content": "3.2. Learning CHEs by Positive Feedback Loop" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Here, we delve deeper into the typical positive feedback loop in LNL, highlighting its limitations in effectively learning CHEs. We then elucidate how our proposed method overcomes these limitations and maximizes the retention of clean examples throughout the learning process." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16081" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "Typical positive feedback loop in LNL. According to statistical learning theory [33], training data with better quality yields a better classifier. Therefore, we can improve the classifier's generalization performance in LNL through the construction of a positive feedback loop. The goal of the positive feedback loop is that, after each training step, the new classifier showcases enhanced generalization performance compared with its predecessor. By doing so, it can more robustly guide the sample selection process, enabling the use of improved training data for classifier training in the succeeding steps [2]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.261, + 0.473, + 0.488 + ], + "angle": 0, + "content": "Most LNL methods, relying on confident examples, initiate with either a small yet clean training set or a weak yet reliable classifier. To enhance the classifier's generalization performance during initialization, they often rigorously limit memorization effects and eliminate potential mislabeled examples, even if this entails removing many CHEs. By restricting the memorization of mislabeled examples, they achieve superior generalization performance compared with unrestricted training on the original set. Then, they either iteratively or incrementally, train classifiers, ultimately obtaining either a larger clean training set or a more robust classifier. This strategy is effective when the classes or subclasses within the dataset are well-balanced and the examples within each class are interrelated, allowing the classifier to learn harder examples from easier ones." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.491, + 0.473, + 0.822 + ], + "angle": 0, + "content": "Limitations of typical positive feedback loop. Although LNL methods that rely on a typical positive feedback loop achieve good generalization performance in a variety of benchmark tasks, natural datasets are often highly imbalanced. This imbalance poses a challenge to achieving close-to-optimal generalization performance with existing LNL methods. Specifically, such challenges are because CHEs are often characterized by large losses and non-dominant patterns. As a result, substantial learning about CHEs predominantly transpires during the late stages of training, driven by memorization effects [2, 52]. The conventional positive feedback loop, aimed at preventing overfitting, often strictly limits the memorization effects of DNNs. Consequently, this strict constraint reduces a classifier's ability to learn from under-represented subpopulations in datasets [9], and thus limits its learning primarily to typical (dominant) classes and subclasses. Such constraints ultimately lead to a situation where the learning ability of rare classes and subclasses, i.e., CHEs, is continuously neglected, while the learning ability of the classes and subclasses representing the dominant pattern is continuously enhanced." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Positive feedback loop in Late Stopping. Based on our previous discussions, to achieve close-to-optimal generalization performance on natural datasets, we need to focus on learning from CHEs throughout the training process. To achieve this, we prolong the training process for each train-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.258 + ], + "angle": 0, + "content": "ing iteration to make use of the memorization effects to help memorize CHEs. With a loose sample selection process, we can ensure that we maximize the retention of clean examples in the training set throughout the learning process. However, retaining as many clean examples as possible during the training initialization requires accepting a significant amount of label noise in the initial training set. Additionally, relying on the \"memorization effects in the late training stage\" to learn CHEs might result in poor generalization performance, as the classifier may seriously overfit label noise in this stage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.895, + 0.457 + ], + "angle": 0, + "content": "To counter these negative effects, we propose a \"from hard to easy\" positive feedback loop within the Late Stopping framework. While we prolong the training process in each training iteration, we simultaneously use the classifier's robust learning capabilities as the criterion for sample selection, i.e., FkL. In each iteration, we train a new classifier on a new training set, using it solely to guide the sample selection for the current iteration. In this positive feedback loop, we opt to disregard the generalization performance of the classifier in each iteration. Instead, we exploit the robust learning capabilities of each new classifier, \\( f_{i} \\), in its \\( i \\) iteration on \\( \\mathcal{D}_i \\) from its learning dynamics, i.e., using the FkL criterion to select examples for the next iteration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.642 + ], + "angle": 0, + "content": "The new training set, obtained by the FkL criterion from the previous iteration, will have less noise. This enables the training of a better new classifier, which can learn more from the CHEs before it begins to memorize mislabeled examples. Therefore, tracking learning dynamics using the FkL criterion can better distinguish between CHEs and mislabeled examples, resulting in a new training set with even less noise than the previous one but contains CHEs. By observing each classifier's learning dynamics through FkL in every iteration, we can iteratively refine our training set, reducing noise while retaining the majority of clean examples, as shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Discussion. Our proposed method is motivated by the seemingly conflicting views on the ability of DNNs to handle label noise as presented in recent studies: \"Deep neural networks easily fit random labels [56]\" and \"Deep learning is robust to massive label noises [37]\". Empirical evidence [1] suggests that DNNs first learn simple patterns before over-fitting in the late training stage. However, there is a scarcity of studies on the behavior of DNNs during the intermediate stages of training, which may be a critical factor for understanding the robustness of DNNs to label noise - DNNs might exhibit spontaneously robust learning to massive label noises in all periods of training, though the generalization performance is over-fitting noisy labels. Thus, we aim to separate the robust learning ability of DNNs from their generalization performance. To this end, we leverage the intrinsic robust learning ability of DNNs by continuing the training process until the generalization performance se" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16082" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.096, + 0.296, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.306, + 0.096, + 0.485, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.097, + 0.674, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.097, + 0.865, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.31, + 0.293, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.305, + 0.312, + 0.481, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.312, + 0.67, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.312, + 0.865, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.44, + 0.895, + 0.511 + ], + "angle": 0, + "content": "Figure 2. We refer to one update of the classifier and the training set as one iteration. Top subfigures: We illustrate the changes in the Test-set Accuracy and the Training-set Accuracy of the classifier during the training process of Late Stopping. There are ten peaks in each figure because we set the number of iterations \\(= 10\\) and the classifiers are re-initialized at the beginning of each new iteration. Bottom subfigures: We illustrate the changes in the noise rate of the training set in each iteration. There are ten bars in each figure because we set the number of iterations \\(= 10\\) and the training set of each iteration is obtained from the previous iteration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.471, + 0.556 + ], + "angle": 0, + "content": "riously deteriorates (i.e., Late Stopping) and we extract the robust learning results during this process (i.e., FkL)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.57, + 0.21, + 0.589 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.643 + ], + "angle": 0, + "content": "In this section, we conduct experiments on both synthetic and real-world datasets containing label noise to validate the effectiveness of our proposed Late Stopping." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.839 + ], + "angle": 0, + "content": "Datasets. We use two popular benchmark datasets i.e., CIFAR-10 and CIFAR-100 [23], to test the generalization performance of our proposed method. Following previous works [2, 51], we manually corrupt CIFAR-10 and CIFAR-100 with Symmetric noise (abbreviated as Sym.) [44] and Instance-dependent (abbreviated as Ins.) noise [53]. For Sym. noise and Ins. noise, the noise rate is set to \\(20\\%\\) and \\(40\\%\\). For a fair comparison, we leave out \\(10\\%\\) of the noisy training data. We employ the real-world noisy dataset CIFAR-10N [47], which equips the training datasets of CIFAR-10 with human-annotated real-world noisy labels. More details about the above datasets and noise types are provided in Appendix A1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Compared methods. We compare the Late Stopping method (Algorithm 1) with the following well-known methods: (1) Statistically inconsistent approaches (small-loss trick): MentorNet [20], Co-teaching [14], and JoCoR [46];" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.644 + ], + "angle": 0, + "content": "(2) Statistically inconsistent approaches (other tricks): Joint Optim [42], CDR [51], and Me-Momentum [2]; (3) Statistically consistent approaches: Forward [35] and DMI [54]. Note that drawing a direct comparison with certain semi-supervised approaches, especially those with multiple technical aggregations such as SELF [34], DivideMix [24], ELR+ [26], and Unicon [22]. The results for baselines are copied from original papers and [2, 47]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.826 + ], + "angle": 0, + "content": "Network structure and experimental setup. We utilize a typical warming-up strategy to ensure stable predictions of the DNNs. The optimizer settings used in our experiments are as follows: SGD with a momentum of 0.9, weight decay of 5e-4, batch size of 128, and initial learning rate of 0.02. In our experiments, we applied typical data augmentations such as horizontal flipping and random cropping. For the experiments on synthetic noisy datasets, ResNet-18 and ResNet-34 [15] are used for CIFAR-10 and CIFAR-100, respectively. For the experiments on real-world noisy datasets, ResNet-34 is used for CIFAR-10N. More details about our experimental setup are provided in Appendix A2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.77, + 0.85 + ], + "angle": 0, + "content": "4.1. Effectiveness of Late Stopping" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Here, we aim to provide empirical evidence to verify the effectiveness of Late Stopping. We conduct experiments on the CIFAR-10 and CIFAR-100 datasets, as their" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16083" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.218, + 0.088, + 0.748, + 0.102 + ], + "angle": 0, + "content": "Table 1. Label precision of the selected examples (45k in total, with 27k clean examples)." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.102, + 0.884, + 0.285 + ], + "angle": 0, + "content": "
Data&NoisecriterionSelecting Clean ExamplesSelecting Mislabeled Examples
0-10k0-15k0-25k30k-45k35k-45k40k-45k
CIFAR-10loss92.73%89.56%82.89%75.67%83.49%91.54%
Sym. 40%FkL(Ours)95.49%95.59%93.56%96.39%99.81%99.94%
CIFAR-10loss75.55%72.33%71.38%60.27%68.69%77.28%
Ins. 40%FkL(Ours)81.88%81.67%81.51%78.51%88.85%99.30%
CIFAR-100loss88.43%84.72%78.49%68.02%75.73%84.68%
Sym. 40%FkL(Ours)97.45%96.78%95.06%94.63%97.91%98.86%
CIFAR-100loss71.30%68.23%65.29%45.91%44.23%42.56%
Ins. 40%FkL(Ours)89.25%88.56%84.40%78.22%86.28%91.76%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.265, + 0.293, + 0.704, + 0.306 + ], + "angle": 0, + "content": "Table 2. Numbers of clean examples of the final training set (27k in total)." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.306, + 0.884, + 0.364 + ], + "angle": 0, + "content": "
CIFAR-10 (Sym. 40%)CIFAR-10 (Ins. 40%)CIFAR-100 (Sym. 40%)CIFAR-100 (Ins. 40%)
Me-Momentum [2]25,79125,69422,24420,779
Late Stopping (Ours)26,56225,91526,12023,979
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.47, + 0.583 + ], + "angle": 0, + "content": "ground-truth labels are available. The average results of five runs of our experiments are presented in Figure 2, which demonstrates the iterative improvement in the quality of the training set when Late Stopping is applied in the learning process. And a classifier with better generalization performance is obtained. We demonstrate the ability of our proposed FkL criterion to select mislabeled examples under the Late Stopping framework, compared with the loss criterion. Additionally, we show the effectiveness of our proposed Late Stopping in retaining clean examples in the training set by comparing it with Me-Momentum [2], which is also an sample selection method that focuses on extracting clean hard examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Comparison with loss criterion. The selection of confident clean examples based on the small-loss criterion is a commonly used approach in LNL and has been shown to be effective [20, 14, 46]. However, the approach of selecting mislabeled examples based on the large-loss [6] can be tricky since it fails to distinguish between mislabeled and clean hard examples [52]. We conducted experiments on the CIFAR-10 and CIFAR-100 datasets to compare the effectiveness of the FkL and loss criterion for selecting examples during the same training process. Specifically, we ranked all examples (45k in total, with 27k clean examples) using the FkL criterion and the loss criterion, respectively, from the smallest 0k to the largest 45k. We then compared the precision of the two criteria in selecting clean examples and mislabeled examples in different ranges. The details of the experiments and the results are presented in Table 1. Our experimental results demonstrate that the FkL criterion outperforms the loss criterion in selecting both clean and mislabeled examples under the Late Stopping framework. The largest performance gap was observed in the \\(40k - 45k\\) range. These results provide empirical evidence that the FkL cri" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.386, + 0.892, + 0.415 + ], + "angle": 0, + "content": "terion is more effective than the loss criterion for selecting mislabeled examples in the Late Stopping framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.893, + 0.628 + ], + "angle": 0, + "content": "Comparison with hard example selection approach. In Table 2, we compare our proposed method with Me-Momentum [2] which also focuses on selecting clean hard examples. Since there are no clear definitions of clean hard examples, we cannot directly compare the effectiveness of selecting such examples. Nevertheless, we can make an indirect comparison by comparing the ability to select clean examples. Our experimental results demonstrate that Late Stopping is an effective approach for retaining clean hard examples. On the CIFAR-10 dataset, both Late Stopping and Me-Momentum showed comparable performance. However, on the more challenging CIFAR-100 dataset, Late Stopping significantly achieved better performance in selecting clean hard examples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.719, + 0.652 + ], + "angle": 0, + "content": "4.2. Classification Accuracy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Synthetic datasets. The experimental results on test accuracy on synthetic datasets with class-dependent and instance-dependent label noise are provided in Table 3 and 4. Each trial is repeated five times and the mean value and standard deviation are recorded. On CIFAR-10, our method achieves varying degrees of lead over baselines. In the \\(20\\%\\) symmetric noise task, which is the simplest task in all cases, the Me-Momentum baseline outperforms ours, which illustrates the effectiveness of conventional sample selection based on confident clean examples for simple LNL. For the more challenging CIFAR-100 dataset, our proposed method consistently achieved the best results. The size of each class in CIFAR-100 is ten times smaller than that of CIFAR-10, making it difficult to retain sufficient CHEs while maintaining a small yet clean training set using conventional sample selection methods. Methods that focus on improving the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16084" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.223, + 0.088, + 0.746, + 0.102 + ], + "angle": 0, + "content": "Table 3. Test performance (mean±std) of each approach using ResNet-18 on CIFAR-10." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.102, + 0.884, + 0.285 + ], + "angle": 0, + "content": "
Sym. 20%Sym. 40%Ins. 20%Ins. 40%
Late Stopping(Ours)91.06±0.22%88.92±0.38%91.08±0.23%87.41±0.38%
Cross-Entropy [38]85.00±0.43%79.59±1.31%85.92±1.09%79.91±1.41%
MentorNet [20]80.49±0.11%77.48±3.45%79.12±0.42%70.27±1.52%
Forward [35]85.63±0.11%74.30±0.26%85.29±0.38%74.72±3.24%
Co-teaching [14]87.16±0.52%83.59±0.28%86.54±0.11%80.98±0.39%
JoCoR [46]88.69±0.19%85.44±0.29%87.31±0.27%82.49±0.57%
DMI [54]88.18±0.13%83.98±0.48%89.14±0.36%84.78±1.97%
Joint Optim [42]89.70±0.36%87.79±0.20%89.69±0.42%82.62±0.57%
CDR [51]89.68±0.38%86.13±0.44%90.24±0.39%83.07±1.33%
Me-Momentum [2]91.44±0.33%88.39±0.34%90.86±0.21%86.66±0.91%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.218, + 0.296, + 0.749, + 0.31 + ], + "angle": 0, + "content": "Table 4. Test performance (mean±std) of each approach using ResNet-34 on CIFAR-100." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.31, + 0.884, + 0.495 + ], + "angle": 0, + "content": "
Sym. 20%Sym. 40%Ins. 20%Ins. 40%
Late Stopping(Ours)68.67±0.67%64.10±0.40%68.59±0.70%59.28±0.46%
Cross-Entropy [38]57.59±2.55%45.74±2.61%59.85±1.56%43.74±1.54%
MentorNet [20]52.11±0.10%35.12±1.13%51.73±0.17%40.90±0.45%
Forward [35]57.75±0.37%38.59±1.62%58.76±0.66%44.50±0.72%
Co-teaching [14]59.28±0.47%51.60±0.49%57.24±0.69%45.69±0.99%
JoCoR [46]64.17±0.19%55.97±0.46%61.98±0.39%50.59±0.71%
DMI [54]58.73±0.70%49.81±1.22%58.05±0.20%47.36±0.68%
Joint Optim [42]64.55±0.38%57.97±0.67%65.15±0.31%55.57±0.41%
CDR [51]66.52±0.24%60.18±0.22%67.06±0.50%56.86±0.62%
Me-Momentum [2]68.03±0.53%63.48±0.72%68.11±0.57%58.38±1.28%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.241, + 0.505, + 0.726, + 0.519 + ], + "angle": 0, + "content": "Table 5. Test accuracy of each approach using ResNet-34 on CIFAR-10N (Worst)." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.519, + 0.884, + 0.562 + ], + "angle": 0, + "content": "
Cross-Entropy [38]Forward [35]Co-teaching [14]JoCoR [46]Me-Momentum [2]Late Stopping(Ours)
77.69±1.55%79.79±0.46%83.83±0.13%83.37±0.30%84.71±0.37%85.24±0.38%
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.692 + ], + "angle": 0, + "content": "number of CHEs in the training set can achieve better generalization performance in this task. For instance, DMI and Co-teaching show a much larger performance gap with our proposed method on CIFAR-100 compared with CIFAR-10. Furthermore, Table 2 validates our method's superior capability to retain clean examples, resulting in a larger performance gap with Me-Momentum on CIFAR-100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Real-world dataset. To validate the efficacy of our proposed method on real-world datasets, we assess our method using the CIFAR-10N dataset in Table 4, a recognized benchmark in learning with noisy labels tasks with both ground-truth labels and human-annotated real-world noisy labels. We utilized the most challenging real-world noisy labels from CIFAR-10N, i.e., the \"Worst\" setting. In this setting, for each image, if there are any incorrectly labeled examples, the given label is randomly selected from human-annotated false labels. Each trial is repeated five times and the mean value and standard deviation are recorded. As shown in Table 4, our method achieves the best performance compared with other methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.586, + 0.664, + 0.603 + ], + "angle": 0, + "content": "4.3. Further analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.611, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Here, we conduct further analysis of our proposed method with the same experimental settings as those used in Section 4.2 unless stated otherwise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Limitations. While our method achieves good robustness by simply removing the lately learned examples, it is not immune to errors. Some clean examples might be incorrectly removed from the training set, i.e., falsely removed examples, and some mislabeled examples are incorrectly retained in the training set, i.e., falsely retained examples. We visualize such typical examples in Figure 3 and provide the following empirical analysis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Falsely retained examples are mislabeled with the wrong label \\( L_{w} \\), however, such examples often possess patterns similar to the dominant subclasses in the \\( L_{w} \\) class, making it difficult to identify them as high probability mislabeled examples by the FkL criterion. As shown in Table 6, based on the FkL criterion and the loss criterion, the \"hardness\" of these examples decreases after being mislabeled. In particular, we named the examples with a decrease in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16085" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.105, + 0.1, + 0.273, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.101, + 0.357, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.101, + 0.439, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.266, + 0.47, + 0.378 + ], + "angle": 0, + "content": "Figure 3. The labels in the figure are ground-truth labels for each example. Falsely Removed (1-3) are typical examples that are incorrectly removed in the first iteration of Late Stopping; Falsely Retained (1-3) are typical examples that are incorrectly marked by FkL in the last iteration of Late Stopping. In the training set, Falsely Retained (1) is incorrectly labeled as \"deer\", Falsely Retained (2) is incorrectly labeled as \"truck\", and Falsely Retained (3) is incorrectly labeled as \"frog\"." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.393, + 0.471, + 0.434 + ], + "angle": 0, + "content": "Table 6. The comparison of the average ranking of falsely retained examples using the loss criterion and the FkL criterion before and after fixing the noisy labels (CIFAR-10, Before: Sym. \\(40\\%\\) noise)." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.435, + 0.462, + 0.521 + ], + "angle": 0, + "content": "
LabelCriterionAvg. Ranking
Before fixing (Given label)FkL22340.66
loss23673.50
After fixing (Ground-truth label)FkL28452.08 (+27.36%)
loss29476.46 (+24.51%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.537, + 0.47, + 0.578 + ], + "angle": 0, + "content": "Table 7. Comparison of the number of clean examples in datasets before and after applying our method as a pre-processing approach to decrease the noise level of a \\(40\\%\\) noisy training set to \\(20\\%\\)." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.579, + 0.462, + 0.673 + ], + "angle": 0, + "content": "
Training setBefore (40% noise)After (20% noise)
CIFAR-10 (Sym.)2722827139 (-0.33%)
CIFAR-10 (Ins.)2709426710 (-1.42%)
CIFAR-100 (Sym.)2734127037 (-1.11%)
CIFAR-100 (Ins.)2724925079 (-7.96%)
CIFAR-10N (Worst)2989629613 (-0.95%)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.47, + 0.779 + ], + "angle": 0, + "content": "training losses after being mislabeled as \"hard mislabeled examples\". Our experimental results indicate that hard mislabeled examples pose a challenge for all sample selection-based LNL methods. More details about Table 6 are provided in Appendix B1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Falsely removed examples refer to the examples that are too hard to remove in practice. To limit the computational resources consumed by our proposed method, we set the removal rate (Algorithm 1, iteration rate \\( m\\% \\)) to a large value. Thus, our proposed method cannot completely distinguish between rare patterns and mislabeled examples, which can result in a small number of examples from rare subclasses being mistakenly removed from the training set." + }, + { + "type": "table_caption", + "bbox": [ + 0.501, + 0.088, + 0.875, + 0.102 + ], + "angle": 0, + "content": "Table 8. Comparison of the total training hours on CIFAR-100." + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.102, + 0.885, + 0.141 + ], + "angle": 0, + "content": "
Co-teaching [14]Me-Momentum [2]Late Stopping (Ours)
3.3h7.1h9.5h
" + }, + { + "type": "image", + "bbox": [ + 0.552, + 0.158, + 0.835, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.3, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Figure 4. Illustrates the performance of classifiers with the change in iteration rate \\( m \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.892, + 0.557 + ], + "angle": 0, + "content": "Versatility. We are focusing on demonstrating the concept, i.e., using Late Stopping to retain clean hard examples in the training set, but not on boosting the classification performance. However, to cope with even more complex noisy scenarios, our method works well in combination with other advanced techniques. In particular, our approach has excellent performance as a pre-processing approach for reducing the noise rate of the noisy training set. As shown in Table 7, we evaluate Late Stopping as a pre-processing approach to decrease the noise level of a \\(40\\%\\) noisy training set to \\(20\\%\\). Our experimental results indicate that our proposed method performs exceptionally well in reducing label noise. It can substantially reduce the noise level of the training set with minimal loss of clean examples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.714 + ], + "angle": 0, + "content": "Training time. Our proposed method involves training the classifier on a larger training set for a longer period, which may not be advantageous in terms of efficiency. Despite this, as the noise rate decreases, the size of the training set decreases, and the speed of obtaining FkL-examples is accelerated (see Figure 2). As shown in Table 8, we compare the training time with typical baseline methods on CIFAR-100 (Sym. \\(40\\%\\)). Our experimental results indicate that the training time of our proposed method is in a comparable range with other approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Sensitivity of the iteration rate. The iteration rate \\( m \\) (see Algorithm 1) determines the iteration number for Late Stopping and the number of examples removed in each iteration. To investigate the sensitivity of \\( m \\), we conducted experiments on CIFAR10 with \\( 40\\% \\) Sym. noise and Ins. noise by varying \\( m \\) in the range \\( \\{10,5,4,3,2\\} \\). Figure 4 shows the performance of classifiers, which gradually improves as \\( m \\) decreases. This observation aligns with the findings presented in Table 1, where a decrease in the range of selected high-probability unlabeled examples leads to higher accuracy in selecting such examples, ultimately benefiting the classifier's performance." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16086" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.196, + 0.106 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.473, + 0.388 + ], + "angle": 0, + "content": "In this paper, we focused on the challenge of the inability of existing sample selection methods to effectively select clean hard examples. To address this challenge, we proposed a novel method called Late Stopping. In contrast to traditional early-stopping strategies, our method is rooted in a prolonged training process that distinguishes between mislabeled and clean examples by pinpointing the number of training epochs required for each example to be consistently classified to its given label for the first time. We coin this new sample selection criterion as First-time \\(k\\)-epoch Learning. Experimental results on synthetic and real-world datasets demonstrate that our proposed method is both straightforward and effective in handling learning with noisy labels. In future work, we plan to enhance the FkL criterion to more accurately capture the intrinsic robust learning ability of DNNs, which could potentially bolster the effectiveness of our Late Stopping framework, especially under more intricate noise conditions." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.401, + 0.238, + 0.419 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.473, + 0.581 + ], + "angle": 0, + "content": "Lei Feng was supported by the National Natural Science Foundation of China (Grant No. 62106028), Chongqing Overseas Chinese Entrepreneurship and Innovation Support Program, CAAI-Huawei MindSpore Open Fund, and Chongqing Artificial Intelligence Innovation Center. Tongliang Liu was partially supported by Australian Research Council Projects IC-190100031, LP-220100527, DP-220102121, and FT-220100318. 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However, this method may not effectively identify clean hard examples with large losses, which are critical for achieving the model's close-to-optimal generalization performance. In this paper, we propose a new framework, Late Stopping, which leverages the intrinsic robust learning ability of DNNs through a prolonged training process. Specifically, Late Stopping gradually shrinks the noisy dataset by removing high-probability mislabeled examples while retaining the majority of clean hard examples in the training set throughout the learning process. We empirically observe that mislabeled and clean examples exhibit differences in the number of epochs required for them to be consistently and correctly classified, and thus high-probability mislabeled examples can be removed. Experimental results on benchmark-simulated and real-world noisy datasets demonstrate that the proposed method outperforms state-of-the-art counterparts. + +# 1. Introduction + +Deep Neural Networks (DNNs) have achieved outstanding success in various tasks, while the success largely relies on data with high-quality annotations [13, 55, 41, 19]. In many real-world scenarios, it would be quite difficult to collect large-scale accurately labeled data, which could inevitably contain noisy labels. Unfortunately, previous studies [1, 56] showed that DNNs can easily overfit random labels, resulting in poor generalization performance. Therefore, an increasing number of methods have been proposed for Learning with Noisy Labels (LNL). + +One mainstream solution in existing methods of LNL is to train the classifier with confident examples [20, 14, 46, 34, 36], which is based on the memorization effect of DNNs, i.e., DNNs learn example with dominant patterns first and then overfit rare ones [1]. Given only noisy data, to exploit the memorization effect, the typical strategy starts from a small confident clean dataset and then + +gradually expands the dataset, which prevents DNNs from over-fitting noisy data. In general, there are two primary approaches to exploit confident examples in the learning process. The first approach involves identifying examples with high-probability clean labels and training the classifier based on these examples, which is commonly referred to as the "small-loss trick" [20, 14, 12, 28, 52]. The second approach involves controlling the learning process of the classifier to primarily learn high-probability clean examples in noisy datasets, which is commonly referred to as "early stopping" [37, 42, 17, 25, 3]. + +Despite providing satisfactory performance, these approaches present an unintended consequence in their methods to prevent over-fitting noise. Specifically, to reduce the impact of mislabeled examples, these approaches limit the capability of the model to effectively learn clean hard examples (CHEs) in noisy datasets, where CHEs are defined as clean examples that are close to the decision boundary, and a significant proportion of CHEs are non-dominated sub-population examples [9]. Identifying CHEs in noisy data is quite challenging [2, 22], as both the CHEs and the mislabeled examples are often characterized by large losses [52, 11, 6], causing them to become entangled. To maintain the purity of the dataset of confident examples, existing LNL methods [34, 2] normally try to eliminate potential examples that are likely to be mislabeled, which inevitably contain many CHEs. However, it is necessary to consider the positive impact of memorization effects on underrepresented sub-populations [10] (i.e., CHEs) when learning from natural datasets, as this is crucial for achieving close-to-optimal generalization performance. + +In this work, our goal is to enable the classifier to learn as many useful non-dominated sub-population examples in the training set as possible during the process of learning with noisy labels. This entails selecting as many clean examples as possible, particularly the clean hard examples, during the sample selection process. In relation to this context, we introduce a novel concept termed First-time $k$ -epoch Learning (FkL), which is defined as the index of the epoch during the training procedure where an example has been predicted to its given label for consecutive $k$ epochs for the first time, as shown in Figure 1(a). + +![](images/8447846622861a9cee5d4f28f3f3d1bbc44d3f359d99f06c02ddc5be8aa762b3.jpg) +(a) + +![](images/3ee4c5efc137a5350c63ffbd5465764dbc038deaa61fe00f82238f8df48c3782.jpg) +(b) + +![](images/d99cd1818e22dd2eb077d300100d3b39ea0745cc934bed036a57620be3aaa668.jpg) +Figure 1. (a) We propose the First-time $k$ -epoch Learning (FkL) metric, which determines the minimum index of the training epoch until which an example has been predicted as its given label for consecutive $k$ epochs. (b) The normalised histogram of CIFAR-10 examples with $40\%$ symmetric label noise w.r.t. the sequence they meet the FkL metric during training procedure. The horizontal axis represents the sequential order in which training examples meet the FkL metric. The vertical axis represents the normalised histogram of examples. (c) Rather than the methods that start from a small yet clean training set ('Early' Stopping), our proposed framework starts from a large training set ('Late' Stopping) that retains as many clean examples as possible. + +![](images/92929d3565c32fbf4e1d033d9a5b330e55d91b52dab584bce45e04747d74cd59.jpg) +(c) + +Using First-time $k$ -epoch Learning (FkL) as a metric, we sequence the examples in the noisy dataset according to the order they meet the FkL metric during the training procedure, as shown in Figure 1(b). As shown in the same figure, most unlabeled examples can only be classified into their given labels for consecutive $k$ epochs in the later stages of training (i.e., larger in the sequence), which implies a relatively large FkL value. This observation suggests that the examples with large FkL values (i.e., those examples that are classified to their given labels for consecutive $k$ epochs only in the late training stage) are predominantly those with incorrect labels. Therefore, the FkL values of different training examples can be used to distinguish whether an example is unlabeled or not. + +Motivated by the above observations, we propose a novel method based on reverse thinking of the conventional confident example selection strategy. Our proposed method, called Late Stopping, employs an iterative sample selection process that gradually reduces the noise rate of the dataset, leading to a positive feedback loop. Instead of selecting high-probability clean examples in the early stage, our method focuses on selecting high-probability mislabeled examples in the late stage to retain as many CHEs as possible in the training set throughout the learning process, even though this method may lead to the retention of an acceptable level of mislabeled examples, as shown in 1(c). Building on this, we introduce a novel sample selection criterion, FkL, which works effectively in selecting mislabeled examples under the Late Stopping framework, and empirical results show that the FkL is more ef + +fective than the loss criterion. We evaluate our method on benchmark-simulated and real-world noisy datasets. Empirical results demonstrate that the Late Stopping method achieves superior performance compared with state-of-the-art counterparts of learning with noisy labels. + +# 2. Related Work + +Existing methods of learning with noisy labels can be broadly categorized into two types. The first category includes classifier-consistent algorithms that use the noise transition matrix [27, 29, 54, 35, 8], which indicates the probabilities of clean labels flipping to noisy labels. The second category focuses on heuristic methods to mitigate the impact of label noise [36, 50, 39, 45, 30, 49, 36], which is also the primary focus of our work. Many existing heuristic methods in LNL are based on the memorization effect, where the algorithm attempts to only learn from confident clean examples [20, 14, 46, 34]. Alternatively optimizing the classifier and updating the training set is not a new idea in LNL. For instance, Joint Optim [42], Co-teaching [14], SELF [34], and Me-Momentum [2] employ a similar positive feedback loop to our proposed Late Stopping. + +Previous research on the dynamics of DNNs has demonstrated that hard examples are typically learned during the late stage of the learning process [1, 43, 31]. Furthermore, many recent studies have employed various training-time metrics to quantify the "hardness" of examples [32, 16, 7, 4, 21, 31], leading to an increase in LNL approaches that use learning dynamics to select clean examples. For instance, + +Algorithm 1 Late Stopping +Input: Original noisy training set $\mathcal{D}_1$ , iteration rate $m\%$ , noise rate $n\%$ , epoch $T_{max}$ and iteration $I_{max}$ . +Output: Extracted final training set and the classifier. +1: for $I = 1, \dots, I_{max}$ do +2: Initialize $\mathcal{D}_i$ , $S_{F_i} = 0$ and $\mathcal{D}_{F_i} = [\ldots]$ . +3: //Initialize new training set, the number/dataset of examples that meet the First-time k-epoch Learning, respectively. +4: for $T = 1, \dots, T_{max}$ do +5: Train $f_i$ on $\mathcal{D}_i$ . +6: Update $\mathcal{D}_{F_i}$ , $S_{F_i}$ . +7: Break and Output $\mathcal{D}_{i+1} = \mathcal{D}_{F_i}$ , if $S_{F_i} > S_{F_{i-1}} \times (1 - m\%)$ . +8: end for +9: Break and Output $f_i$ and $\mathcal{D}_{F_i}$ , if $m \times i > n$ . +10: end for + +FSLT&SSFT [31], Self-Filtering [48], SELFIE [40], and RoCL [57] adopt a criterion similar to our proposed FkL criterion. Specifically, FSLT&SSFT and Self-Filtering use the classifier's error prediction to pinpoint clean examples, SELFIE employs entropy values from prediction histories for selection, and RoCL leverages the variance of training losses to select clean examples. Instead of quantifying the "hardness" of examples based on the characteristics of individual examples in the dataset, our proposed method focuses on extracting the intrinsic robust learning ability of DNNs from the model trained on noisy datasets. + +# 3. Late Stopping + +In this section, we elaborate on our proposed Late Stopping method. As shown in Figure 1, the primary goal of the Late Stopping framework is to maximize the retention of clean examples in the training set throughout the learning process, enabling our method to learn clean hard examples (CHEs) from a noisy training set. Therefore, we halt the training process in the late training stage, leveraging First-time $k$ -epoch Learning (FkL) to exploit the results of the intrinsic robust learning ability of DNNs for sample selection. Iteratively performing this operation allows for a gradual reduction of noise while maximizing the retention of clean samples in the training dataset. + +# 3.1. Algorithm Flow + +For a comprehensive explanation of Late Stopping, we begin by formally defining First-time $k$ -epoch Learning (FkL). In learning with noisy labels, let us consider a model $f_{i}$ trained on a noisy training set $\mathcal{D}_i$ composed of $n$ training examples $\{\mathbf{x}_j,y_j\}_{j = 1}^n$ where $y_{j}$ denotes the given label (which may not be true) of $\mathbf{x}_j$ . After $t$ training epochs, the predicted label $\hat{y}_j^t$ for the instance $\mathbf{x}_j$ can be obtained. Let $\mathrm{acc}_j^t = \mathbb{1}_{\hat{y}_j^t = y_j}$ denote a binary variable indicating whether $f_{i}$ predicts the given label $y_{j}$ of the instance $\mathbf{x}_j$ at epoch $t$ . The FkL for the instance $\mathbf{x}_j$ is defined as the minimum + +index of the training epoch that the instance $\mathbf{x}_j$ has been predicted to its given label $y_{j}$ for $k$ consecutive epochs: + +$$ +\mathrm {F k L} _ {j} = \underset {t ^ {*} \in t} {\operatorname {a r g m i n}} \left(\mathrm {a c c} _ {j} ^ {t ^ {*}} \wedge \ldots \wedge \mathrm {a c c} _ {j} ^ {(t ^ {*} - k + 1)} = 1\right). +$$ + +If $\mathrm{FkL}_j = t^*$ , it implies that the classifier $f_{i}$ "learns" the instance $\mathbf{x}_j$ after $t^*$ epochs. Notably, if $\mathbf{x}_j$ is "learned" by the classifier early in the training, it will have a small FkL value, however, if it is "learned" in the late stage, it will have a large FkL value. Based on our FkL definition, we observed that the majority of examples with large FkL values are mislabeled, as shown in Figure 1(a). This observation provides a rationale for selecting examples with large FkL values, those learned in the late training stage, as high-probability mislabeled examples. + +With the FkL selection criterion, we present the algorithmic framework of Late Stopping. At the low level (Steps 4-8 of Algorithm 1), the sample selection strategy follows a "from easy to hard" curriculum learning procedure [5, 18]. During the $i$ -th iteration, the classifier $f_{i}$ is trained on a new training set $\mathcal{D}_i$ (Step 5), and newly identified FkL examples are added to $\mathcal{D}_{F_i}$ (Step 6). If the size of $\mathcal{D}_{F_i}$ , represented as $S_{F_i}$ , exceeds a predefined threshold, the training in this iteration will halt, and the output becomes $\mathcal{D}_{F_i}$ (Step 7). At the higher level (Steps 1-10 of Algorithm 1), our method learns through a "from hard to easy" positive feedback loop, distinguishing it from most existing LNL approaches. The algorithm starts with initializing $\mathcal{D}_1$ and training $f_{1}$ (Iteration 1). In subsequent iterations, the new training set $\mathcal{D}_i$ (Step 2, Iteration $i$ ) is updated from the previous iteration's $\mathcal{D}_{F_{i - 1}}$ (Step 8, Iteration $i - 1$ ). When the stopping condition is met, the output is $f_{i}$ and $\mathcal{D}_{F_i}$ (Step 10). + +# 3.2. Learning CHEs by Positive Feedback Loop + +Here, we delve deeper into the typical positive feedback loop in LNL, highlighting its limitations in effectively learning CHEs. We then elucidate how our proposed method overcomes these limitations and maximizes the retention of clean examples throughout the learning process. + +Typical positive feedback loop in LNL. According to statistical learning theory [33], training data with better quality yields a better classifier. Therefore, we can improve the classifier's generalization performance in LNL through the construction of a positive feedback loop. The goal of the positive feedback loop is that, after each training step, the new classifier showcases enhanced generalization performance compared with its predecessor. By doing so, it can more robustly guide the sample selection process, enabling the use of improved training data for classifier training in the succeeding steps [2]. + +Most LNL methods, relying on confident examples, initiate with either a small yet clean training set or a weak yet reliable classifier. To enhance the classifier's generalization performance during initialization, they often rigorously limit memorization effects and eliminate potential mislabeled examples, even if this entails removing many CHEs. By restricting the memorization of mislabeled examples, they achieve superior generalization performance compared with unrestricted training on the original set. Then, they either iteratively or incrementally, train classifiers, ultimately obtaining either a larger clean training set or a more robust classifier. This strategy is effective when the classes or subclasses within the dataset are well-balanced and the examples within each class are interrelated, allowing the classifier to learn harder examples from easier ones. + +Limitations of typical positive feedback loop. Although LNL methods that rely on a typical positive feedback loop achieve good generalization performance in a variety of benchmark tasks, natural datasets are often highly imbalanced. This imbalance poses a challenge to achieving close-to-optimal generalization performance with existing LNL methods. Specifically, such challenges are because CHEs are often characterized by large losses and non-dominant patterns. As a result, substantial learning about CHEs predominantly transpires during the late stages of training, driven by memorization effects [2, 52]. The conventional positive feedback loop, aimed at preventing overfitting, often strictly limits the memorization effects of DNNs. Consequently, this strict constraint reduces a classifier's ability to learn from under-represented subpopulations in datasets [9], and thus limits its learning primarily to typical (dominant) classes and subclasses. Such constraints ultimately lead to a situation where the learning ability of rare classes and subclasses, i.e., CHEs, is continuously neglected, while the learning ability of the classes and subclasses representing the dominant pattern is continuously enhanced. + +Positive feedback loop in Late Stopping. Based on our previous discussions, to achieve close-to-optimal generalization performance on natural datasets, we need to focus on learning from CHEs throughout the training process. To achieve this, we prolong the training process for each train- + +ing iteration to make use of the memorization effects to help memorize CHEs. With a loose sample selection process, we can ensure that we maximize the retention of clean examples in the training set throughout the learning process. However, retaining as many clean examples as possible during the training initialization requires accepting a significant amount of label noise in the initial training set. Additionally, relying on the "memorization effects in the late training stage" to learn CHEs might result in poor generalization performance, as the classifier may seriously overfit label noise in this stage. + +To counter these negative effects, we propose a "from hard to easy" positive feedback loop within the Late Stopping framework. While we prolong the training process in each training iteration, we simultaneously use the classifier's robust learning capabilities as the criterion for sample selection, i.e., FkL. In each iteration, we train a new classifier on a new training set, using it solely to guide the sample selection for the current iteration. In this positive feedback loop, we opt to disregard the generalization performance of the classifier in each iteration. Instead, we exploit the robust learning capabilities of each new classifier, $f_{i}$ , in its $i$ iteration on $\mathcal{D}_i$ from its learning dynamics, i.e., using the FkL criterion to select examples for the next iteration. + +The new training set, obtained by the FkL criterion from the previous iteration, will have less noise. This enables the training of a better new classifier, which can learn more from the CHEs before it begins to memorize mislabeled examples. Therefore, tracking learning dynamics using the FkL criterion can better distinguish between CHEs and mislabeled examples, resulting in a new training set with even less noise than the previous one but contains CHEs. By observing each classifier's learning dynamics through FkL in every iteration, we can iteratively refine our training set, reducing noise while retaining the majority of clean examples, as shown in Figure 2. + +Discussion. Our proposed method is motivated by the seemingly conflicting views on the ability of DNNs to handle label noise as presented in recent studies: "Deep neural networks easily fit random labels [56]" and "Deep learning is robust to massive label noises [37]". Empirical evidence [1] suggests that DNNs first learn simple patterns before over-fitting in the late training stage. However, there is a scarcity of studies on the behavior of DNNs during the intermediate stages of training, which may be a critical factor for understanding the robustness of DNNs to label noise - DNNs might exhibit spontaneously robust learning to massive label noises in all periods of training, though the generalization performance is over-fitting noisy labels. Thus, we aim to separate the robust learning ability of DNNs from their generalization performance. To this end, we leverage the intrinsic robust learning ability of DNNs by continuing the training process until the generalization performance se + +![](images/0bb0cf552779ea2d7d338e7ad3a121554314ee42301076f0542b61a316dd11ab.jpg) + +![](images/8fad7cead5903932755b2f00bc7dd9c76e89556aec67dd378b77e65d22dba3bb.jpg) + +![](images/35340cd50c450ee8c74a49181468d1b2650c7db2c36740a911b14ceb1e96ad41.jpg) + +![](images/d5116a105fc06502ef1c75a082b10053ab028240597fe2ef44cf1ccdebe98cee.jpg) + +![](images/a6a93e6d9452aafb9b41fe113129918007448a49fe81938f85cbceb640ac6010.jpg) +Figure 2. We refer to one update of the classifier and the training set as one iteration. Top subfigures: We illustrate the changes in the Test-set Accuracy and the Training-set Accuracy of the classifier during the training process of Late Stopping. There are ten peaks in each figure because we set the number of iterations $= 10$ and the classifiers are re-initialized at the beginning of each new iteration. Bottom subfigures: We illustrate the changes in the noise rate of the training set in each iteration. There are ten bars in each figure because we set the number of iterations $= 10$ and the training set of each iteration is obtained from the previous iteration. + +![](images/7fccf7d2d3a6a3bbe2811305228f9405440e05bba75c70001bbf14ae7446220f.jpg) + +![](images/b9be724f8ac70093670aa00831aa917c795c01e624a5767017bae51d2f58f3bb.jpg) + +![](images/67f65b7a20cff59ecadc867180a36b27facc844bff3eea3aa0c89169e852d1d3.jpg) + +riously deteriorates (i.e., Late Stopping) and we extract the robust learning results during this process (i.e., FkL). + +# 4. Experiments + +In this section, we conduct experiments on both synthetic and real-world datasets containing label noise to validate the effectiveness of our proposed Late Stopping. + +Datasets. We use two popular benchmark datasets i.e., CIFAR-10 and CIFAR-100 [23], to test the generalization performance of our proposed method. Following previous works [2, 51], we manually corrupt CIFAR-10 and CIFAR-100 with Symmetric noise (abbreviated as Sym.) [44] and Instance-dependent (abbreviated as Ins.) noise [53]. For Sym. noise and Ins. noise, the noise rate is set to $20\%$ and $40\%$ . For a fair comparison, we leave out $10\%$ of the noisy training data. We employ the real-world noisy dataset CIFAR-10N [47], which equips the training datasets of CIFAR-10 with human-annotated real-world noisy labels. More details about the above datasets and noise types are provided in Appendix A1. + +Compared methods. We compare the Late Stopping method (Algorithm 1) with the following well-known methods: (1) Statistically inconsistent approaches (small-loss trick): MentorNet [20], Co-teaching [14], and JoCoR [46]; + +(2) Statistically inconsistent approaches (other tricks): Joint Optim [42], CDR [51], and Me-Momentum [2]; (3) Statistically consistent approaches: Forward [35] and DMI [54]. Note that drawing a direct comparison with certain semi-supervised approaches, especially those with multiple technical aggregations such as SELF [34], DivideMix [24], ELR+ [26], and Unicon [22]. The results for baselines are copied from original papers and [2, 47]. + +Network structure and experimental setup. We utilize a typical warming-up strategy to ensure stable predictions of the DNNs. The optimizer settings used in our experiments are as follows: SGD with a momentum of 0.9, weight decay of 5e-4, batch size of 128, and initial learning rate of 0.02. In our experiments, we applied typical data augmentations such as horizontal flipping and random cropping. For the experiments on synthetic noisy datasets, ResNet-18 and ResNet-34 [15] are used for CIFAR-10 and CIFAR-100, respectively. For the experiments on real-world noisy datasets, ResNet-34 is used for CIFAR-10N. More details about our experimental setup are provided in Appendix A2. + +# 4.1. Effectiveness of Late Stopping + +Here, we aim to provide empirical evidence to verify the effectiveness of Late Stopping. We conduct experiments on the CIFAR-10 and CIFAR-100 datasets, as their + +Table 1. Label precision of the selected examples (45k in total, with 27k clean examples). + +
Data&NoisecriterionSelecting Clean ExamplesSelecting Mislabeled Examples
0-10k0-15k0-25k30k-45k35k-45k40k-45k
CIFAR-10loss92.73%89.56%82.89%75.67%83.49%91.54%
Sym. 40%FkL(Ours)95.49%95.59%93.56%96.39%99.81%99.94%
CIFAR-10loss75.55%72.33%71.38%60.27%68.69%77.28%
Ins. 40%FkL(Ours)81.88%81.67%81.51%78.51%88.85%99.30%
CIFAR-100loss88.43%84.72%78.49%68.02%75.73%84.68%
Sym. 40%FkL(Ours)97.45%96.78%95.06%94.63%97.91%98.86%
CIFAR-100loss71.30%68.23%65.29%45.91%44.23%42.56%
Ins. 40%FkL(Ours)89.25%88.56%84.40%78.22%86.28%91.76%
+ +Table 2. Numbers of clean examples of the final training set (27k in total). + +
CIFAR-10 (Sym. 40%)CIFAR-10 (Ins. 40%)CIFAR-100 (Sym. 40%)CIFAR-100 (Ins. 40%)
Me-Momentum [2]25,79125,69422,24420,779
Late Stopping (Ours)26,56225,91526,12023,979
+ +ground-truth labels are available. The average results of five runs of our experiments are presented in Figure 2, which demonstrates the iterative improvement in the quality of the training set when Late Stopping is applied in the learning process. And a classifier with better generalization performance is obtained. We demonstrate the ability of our proposed FkL criterion to select mislabeled examples under the Late Stopping framework, compared with the loss criterion. Additionally, we show the effectiveness of our proposed Late Stopping in retaining clean examples in the training set by comparing it with Me-Momentum [2], which is also an sample selection method that focuses on extracting clean hard examples. + +Comparison with loss criterion. The selection of confident clean examples based on the small-loss criterion is a commonly used approach in LNL and has been shown to be effective [20, 14, 46]. However, the approach of selecting mislabeled examples based on the large-loss [6] can be tricky since it fails to distinguish between mislabeled and clean hard examples [52]. We conducted experiments on the CIFAR-10 and CIFAR-100 datasets to compare the effectiveness of the FkL and loss criterion for selecting examples during the same training process. Specifically, we ranked all examples (45k in total, with 27k clean examples) using the FkL criterion and the loss criterion, respectively, from the smallest 0k to the largest 45k. We then compared the precision of the two criteria in selecting clean examples and mislabeled examples in different ranges. The details of the experiments and the results are presented in Table 1. Our experimental results demonstrate that the FkL criterion outperforms the loss criterion in selecting both clean and mislabeled examples under the Late Stopping framework. The largest performance gap was observed in the $40k - 45k$ range. These results provide empirical evidence that the FkL cri + +terion is more effective than the loss criterion for selecting mislabeled examples in the Late Stopping framework. + +Comparison with hard example selection approach. In Table 2, we compare our proposed method with Me-Momentum [2] which also focuses on selecting clean hard examples. Since there are no clear definitions of clean hard examples, we cannot directly compare the effectiveness of selecting such examples. Nevertheless, we can make an indirect comparison by comparing the ability to select clean examples. Our experimental results demonstrate that Late Stopping is an effective approach for retaining clean hard examples. On the CIFAR-10 dataset, both Late Stopping and Me-Momentum showed comparable performance. However, on the more challenging CIFAR-100 dataset, Late Stopping significantly achieved better performance in selecting clean hard examples. + +# 4.2. Classification Accuracy + +Synthetic datasets. The experimental results on test accuracy on synthetic datasets with class-dependent and instance-dependent label noise are provided in Table 3 and 4. Each trial is repeated five times and the mean value and standard deviation are recorded. On CIFAR-10, our method achieves varying degrees of lead over baselines. In the $20\%$ symmetric noise task, which is the simplest task in all cases, the Me-Momentum baseline outperforms ours, which illustrates the effectiveness of conventional sample selection based on confident clean examples for simple LNL. For the more challenging CIFAR-100 dataset, our proposed method consistently achieved the best results. The size of each class in CIFAR-100 is ten times smaller than that of CIFAR-10, making it difficult to retain sufficient CHEs while maintaining a small yet clean training set using conventional sample selection methods. Methods that focus on improving the + +Table 3. Test performance (mean±std) of each approach using ResNet-18 on CIFAR-10. + +
Sym. 20%Sym. 40%Ins. 20%Ins. 40%
Late Stopping(Ours)91.06±0.22%88.92±0.38%91.08±0.23%87.41±0.38%
Cross-Entropy [38]85.00±0.43%79.59±1.31%85.92±1.09%79.91±1.41%
MentorNet [20]80.49±0.11%77.48±3.45%79.12±0.42%70.27±1.52%
Forward [35]85.63±0.11%74.30±0.26%85.29±0.38%74.72±3.24%
Co-teaching [14]87.16±0.52%83.59±0.28%86.54±0.11%80.98±0.39%
JoCoR [46]88.69±0.19%85.44±0.29%87.31±0.27%82.49±0.57%
DMI [54]88.18±0.13%83.98±0.48%89.14±0.36%84.78±1.97%
Joint Optim [42]89.70±0.36%87.79±0.20%89.69±0.42%82.62±0.57%
CDR [51]89.68±0.38%86.13±0.44%90.24±0.39%83.07±1.33%
Me-Momentum [2]91.44±0.33%88.39±0.34%90.86±0.21%86.66±0.91%
+ +Table 4. Test performance (mean±std) of each approach using ResNet-34 on CIFAR-100. + +
Sym. 20%Sym. 40%Ins. 20%Ins. 40%
Late Stopping(Ours)68.67±0.67%64.10±0.40%68.59±0.70%59.28±0.46%
Cross-Entropy [38]57.59±2.55%45.74±2.61%59.85±1.56%43.74±1.54%
MentorNet [20]52.11±0.10%35.12±1.13%51.73±0.17%40.90±0.45%
Forward [35]57.75±0.37%38.59±1.62%58.76±0.66%44.50±0.72%
Co-teaching [14]59.28±0.47%51.60±0.49%57.24±0.69%45.69±0.99%
JoCoR [46]64.17±0.19%55.97±0.46%61.98±0.39%50.59±0.71%
DMI [54]58.73±0.70%49.81±1.22%58.05±0.20%47.36±0.68%
Joint Optim [42]64.55±0.38%57.97±0.67%65.15±0.31%55.57±0.41%
CDR [51]66.52±0.24%60.18±0.22%67.06±0.50%56.86±0.62%
Me-Momentum [2]68.03±0.53%63.48±0.72%68.11±0.57%58.38±1.28%
+ +Table 5. Test accuracy of each approach using ResNet-34 on CIFAR-10N (Worst). + +
Cross-Entropy [38]Forward [35]Co-teaching [14]JoCoR [46]Me-Momentum [2]Late Stopping(Ours)
77.69±1.55%79.79±0.46%83.83±0.13%83.37±0.30%84.71±0.37%85.24±0.38%
+ +number of CHEs in the training set can achieve better generalization performance in this task. For instance, DMI and Co-teaching show a much larger performance gap with our proposed method on CIFAR-100 compared with CIFAR-10. Furthermore, Table 2 validates our method's superior capability to retain clean examples, resulting in a larger performance gap with Me-Momentum on CIFAR-100. + +Real-world dataset. To validate the efficacy of our proposed method on real-world datasets, we assess our method using the CIFAR-10N dataset in Table 4, a recognized benchmark in learning with noisy labels tasks with both ground-truth labels and human-annotated real-world noisy labels. We utilized the most challenging real-world noisy labels from CIFAR-10N, i.e., the "Worst" setting. In this setting, for each image, if there are any incorrectly labeled examples, the given label is randomly selected from human-annotated false labels. Each trial is repeated five times and the mean value and standard deviation are recorded. As shown in Table 4, our method achieves the best performance compared with other methods. + +# 4.3. Further analysis + +Here, we conduct further analysis of our proposed method with the same experimental settings as those used in Section 4.2 unless stated otherwise. + +Limitations. While our method achieves good robustness by simply removing the lately learned examples, it is not immune to errors. Some clean examples might be incorrectly removed from the training set, i.e., falsely removed examples, and some mislabeled examples are incorrectly retained in the training set, i.e., falsely retained examples. We visualize such typical examples in Figure 3 and provide the following empirical analysis. + +Falsely retained examples are mislabeled with the wrong label $L_{w}$ , however, such examples often possess patterns similar to the dominant subclasses in the $L_{w}$ class, making it difficult to identify them as high probability mislabeled examples by the FkL criterion. As shown in Table 6, based on the FkL criterion and the loss criterion, the "hardness" of these examples decreases after being mislabeled. In particular, we named the examples with a decrease in + +![](images/bb131935bcded0d1eb98a2305e21cd862c8533fcdcbe93795ec04ac5c2e49096.jpg) +Figure 3. The labels in the figure are ground-truth labels for each example. Falsely Removed (1-3) are typical examples that are incorrectly removed in the first iteration of Late Stopping; Falsely Retained (1-3) are typical examples that are incorrectly marked by FkL in the last iteration of Late Stopping. In the training set, Falsely Retained (1) is incorrectly labeled as "deer", Falsely Retained (2) is incorrectly labeled as "truck", and Falsely Retained (3) is incorrectly labeled as "frog". + +![](images/34340c5b7fdfaff1f2a036501159a9ecad1650462804b4a3d0b6478abda668ce.jpg) + +![](images/d1fe7ce62347848503949b305d2a414cfc467b064263998ee36fac42839e70b7.jpg) + +Table 6. The comparison of the average ranking of falsely retained examples using the loss criterion and the FkL criterion before and after fixing the noisy labels (CIFAR-10, Before: Sym. $40\%$ noise). + +
LabelCriterionAvg. Ranking
Before fixing (Given label)FkL22340.66
loss23673.50
After fixing (Ground-truth label)FkL28452.08 (+27.36%)
loss29476.46 (+24.51%)
+ +Table 7. Comparison of the number of clean examples in datasets before and after applying our method as a pre-processing approach to decrease the noise level of a $40\%$ noisy training set to $20\%$ . + +
Training setBefore (40% noise)After (20% noise)
CIFAR-10 (Sym.)2722827139 (-0.33%)
CIFAR-10 (Ins.)2709426710 (-1.42%)
CIFAR-100 (Sym.)2734127037 (-1.11%)
CIFAR-100 (Ins.)2724925079 (-7.96%)
CIFAR-10N (Worst)2989629613 (-0.95%)
+ +training losses after being mislabeled as "hard mislabeled examples". Our experimental results indicate that hard mislabeled examples pose a challenge for all sample selection-based LNL methods. More details about Table 6 are provided in Appendix B1. + +Falsely removed examples refer to the examples that are too hard to remove in practice. To limit the computational resources consumed by our proposed method, we set the removal rate (Algorithm 1, iteration rate $m\%$ ) to a large value. Thus, our proposed method cannot completely distinguish between rare patterns and mislabeled examples, which can result in a small number of examples from rare subclasses being mistakenly removed from the training set. + +Table 8. Comparison of the total training hours on CIFAR-100. + +
Co-teaching [14]Me-Momentum [2]Late Stopping (Ours)
3.3h7.1h9.5h
+ +![](images/70c7769ec338a69881711bf58e86cba66bebdc465732d24fead3c802151bc71f.jpg) +Figure 4. Illustrates the performance of classifiers with the change in iteration rate $m$ . + +Versatility. We are focusing on demonstrating the concept, i.e., using Late Stopping to retain clean hard examples in the training set, but not on boosting the classification performance. However, to cope with even more complex noisy scenarios, our method works well in combination with other advanced techniques. In particular, our approach has excellent performance as a pre-processing approach for reducing the noise rate of the noisy training set. As shown in Table 7, we evaluate Late Stopping as a pre-processing approach to decrease the noise level of a $40\%$ noisy training set to $20\%$ . Our experimental results indicate that our proposed method performs exceptionally well in reducing label noise. It can substantially reduce the noise level of the training set with minimal loss of clean examples. + +Training time. Our proposed method involves training the classifier on a larger training set for a longer period, which may not be advantageous in terms of efficiency. Despite this, as the noise rate decreases, the size of the training set decreases, and the speed of obtaining FkL-examples is accelerated (see Figure 2). As shown in Table 8, we compare the training time with typical baseline methods on CIFAR-100 (Sym. $40\%$ ). Our experimental results indicate that the training time of our proposed method is in a comparable range with other approaches. + +Sensitivity of the iteration rate. The iteration rate $m$ (see Algorithm 1) determines the iteration number for Late Stopping and the number of examples removed in each iteration. To investigate the sensitivity of $m$ , we conducted experiments on CIFAR10 with $40\%$ Sym. noise and Ins. noise by varying $m$ in the range $\{10,5,4,3,2\}$ . Figure 4 shows the performance of classifiers, which gradually improves as $m$ decreases. This observation aligns with the findings presented in Table 1, where a decrease in the range of selected high-probability unlabeled examples leads to higher accuracy in selecting such examples, ultimately benefiting the classifier's performance. + +# 5. Conclusion + +In this paper, we focused on the challenge of the inability of existing sample selection methods to effectively select clean hard examples. To address this challenge, we proposed a novel method called Late Stopping. In contrast to traditional early-stopping strategies, our method is rooted in a prolonged training process that distinguishes between mislabeled and clean examples by pinpointing the number of training epochs required for each example to be consistently classified to its given label for the first time. We coin this new sample selection criterion as First-time $k$ -epoch Learning. Experimental results on synthetic and real-world datasets demonstrate that our proposed method is both straightforward and effective in handling learning with noisy labels. In future work, we plan to enhance the FkL criterion to more accurately capture the intrinsic robust learning ability of DNNs, which could potentially bolster the effectiveness of our Late Stopping framework, especially under more intricate noise conditions. + +# Acknowledgement + +Lei Feng was supported by the National Natural Science Foundation of China (Grant No. 62106028), Chongqing Overseas Chinese Entrepreneurship and Innovation Support Program, CAAI-Huawei MindSpore Open Fund, and Chongqing Artificial Intelligence Innovation Center. Tongliang Liu was partially supported by Australian Research Council Projects IC-190100031, LP-220100527, DP-220102121, and FT-220100318. We would like to thank anonymous reviewers for their constructive feedback that improved our paper. + +# References + +[1] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. 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In ICLR, 2021. \ No newline at end of file diff --git a/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/images.zip b/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a54032b19d29dc2e7753660c8037f307c6076421 --- /dev/null +++ b/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:89da5e22dbeb9e23ec1fca0335e5fbdf73c00fd5d8b8226637a3707a3ba54bf9 +size 605273 diff --git a/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/layout.json b/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..14153aae520d2b2c58a934c25f842e3308ba05a9 --- /dev/null +++ b/2023/Late Stopping_ Avoiding Confidently Learning from Mislabeled Examples/layout.json @@ -0,0 +1,8293 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 69, + 103, + 524, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 103, + 524, + 121 + ], + "spans": [ + { + "bbox": [ + 69, + 103, + 524, + 121 + ], + "type": "text", + "content": "Late Stopping: Avoiding Confidently Learning from Mislabeled Examples" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "spans": [ + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "text", + "content": "Suqin Yuan" + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "text", + "content": " Lei Feng" + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "text", + "content": " Tongliang Liu" + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "text", + "content": "The University of Sydney " + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 138, + 142, + 455, + 172 + ], + "type": "text", + "content": "Nanyang Technological University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 199, + 191, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 199, + 191, + 211 + ], + "spans": [ + { + "bbox": [ + 143, + 199, + 191, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 224, + 289, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 289, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 289, + 452 + ], + "type": "text", + "content": "Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which are critical for achieving the model's close-to-optimal generalization performance. In this paper, we propose a new framework, Late Stopping, which leverages the intrinsic robust learning ability of DNNs through a prolonged training process. Specifically, Late Stopping gradually shrinks the noisy dataset by removing high-probability mislabeled examples while retaining the majority of clean hard examples in the training set throughout the learning process. We empirically observe that mislabeled and clean examples exhibit differences in the number of epochs required for them to be consistently and correctly classified, and thus high-probability mislabeled examples can be removed. Experimental results on benchmark-simulated and real-world noisy datasets demonstrate that the proposed method outperforms state-of-the-art counterparts." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 467, + 128, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 128, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 128, + 479 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 487, + 287, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 607 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 607 + ], + "type": "text", + "content": "Deep Neural Networks (DNNs) have achieved outstanding success in various tasks, while the success largely relies on data with high-quality annotations [13, 55, 41, 19]. In many real-world scenarios, it would be quite difficult to collect large-scale accurately labeled data, which could inevitably contain noisy labels. Unfortunately, previous studies [1, 56] showed that DNNs can easily overfit random labels, resulting in poor generalization performance. Therefore, an increasing number of methods have been proposed for Learning with Noisy Labels (LNL)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 608, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 608, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 608, + 287, + 693 + ], + "type": "text", + "content": "One mainstream solution in existing methods of LNL is to train the classifier with confident examples [20, 14, 46, 34, 36], which is based on the memorization effect of DNNs, i.e., DNNs learn example with dominant patterns first and then overfit rare ones [1]. Given only noisy data, to exploit the memorization effect, the typical strategy starts from a small confident clean dataset and then" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 200, + 547, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 200, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 547, + 331 + ], + "type": "text", + "content": "gradually expands the dataset, which prevents DNNs from over-fitting noisy data. In general, there are two primary approaches to exploit confident examples in the learning process. The first approach involves identifying examples with high-probability clean labels and training the classifier based on these examples, which is commonly referred to as the \"small-loss trick\" [20, 14, 12, 28, 52]. The second approach involves controlling the learning process of the classifier to primarily learn high-probability clean examples in noisy datasets, which is commonly referred to as \"early stopping\" [37, 42, 17, 25, 3]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 331, + 547, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 570 + ], + "type": "text", + "content": "Despite providing satisfactory performance, these approaches present an unintended consequence in their methods to prevent over-fitting noise. Specifically, to reduce the impact of mislabeled examples, these approaches limit the capability of the model to effectively learn clean hard examples (CHEs) in noisy datasets, where CHEs are defined as clean examples that are close to the decision boundary, and a significant proportion of CHEs are non-dominated sub-population examples [9]. Identifying CHEs in noisy data is quite challenging [2, 22], as both the CHEs and the mislabeled examples are often characterized by large losses [52, 11, 6], causing them to become entangled. To maintain the purity of the dataset of confident examples, existing LNL methods [34, 2] normally try to eliminate potential examples that are likely to be mislabeled, which inevitably contain many CHEs. However, it is necessary to consider the positive impact of memorization effects on underrepresented sub-populations [10] (i.e., CHEs) when learning from natural datasets, as this is crucial for achieving close-to-optimal generalization performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 571, + 547, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 571, + 547, + 702 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 547, + 702 + ], + "type": "text", + "content": "In this work, our goal is to enable the classifier to learn as many useful non-dominated sub-population examples in the training set as possible during the process of learning with noisy labels. This entails selecting as many clean examples as possible, particularly the clean hard examples, during the sample selection process. In relation to this context, we introduce a novel concept termed First-time " + }, + { + "bbox": [ + 304, + 571, + 547, + 702 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 571, + 547, + 702 + ], + "type": "text", + "content": "-epoch Learning (FkL), which is defined as the index of the epoch during the training procedure where an example has been predicted to its given label for consecutive " + }, + { + "bbox": [ + 304, + 571, + 547, + 702 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 571, + 547, + 702 + ], + "type": "text", + "content": " epochs for the first time, as shown in Figure 1(a)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 139, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 139, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 139, + 712 + ], + "type": "text", + "content": "*Corresponding authors." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16079" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 68, + 193, + 260 + ], + "blocks": [ + { + "bbox": [ + 69, + 68, + 193, + 260 + ], + "lines": [ + { + "bbox": [ + 69, + 68, + 193, + 260 + ], + "spans": [ + { + "bbox": [ + 69, + 68, + 193, + 260 + ], + "type": "image", + "image_path": "8447846622861a9cee5d4f28f3f3d1bbc44d3f359d99f06c02ddc5be8aa762b3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 126, + 262, + 136, + 270 + ], + "lines": [ + { + "bbox": [ + 126, + 262, + 136, + 270 + ], + "spans": [ + { + "bbox": [ + 126, + 262, + 136, + 270 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 207, + 71, + 369, + 255 + ], + "blocks": [ + { + "bbox": [ + 207, + 71, + 369, + 255 + ], + "lines": [ + { + "bbox": [ + 207, + 71, + 369, + 255 + ], + "spans": [ + { + "bbox": [ + 207, + 71, + 369, + 255 + ], + "type": "image", + "image_path": "3ee4c5efc137a5350c63ffbd5465764dbc038deaa61fe00f82238f8df48c3782.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 284, + 262, + 294, + 270 + ], + "lines": [ + { + "bbox": [ + 284, + 262, + 294, + 270 + ], + "spans": [ + { + "bbox": [ + 284, + 262, + 294, + 270 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 385, + 72, + 451, + 258 + ], + "blocks": [ + { + "bbox": [ + 385, + 72, + 451, + 258 + ], + "lines": [ + { + "bbox": [ + 385, + 72, + 451, + 258 + ], + "spans": [ + { + "bbox": [ + 385, + 72, + 451, + 258 + ], + "type": "image", + "image_path": "d99cd1818e22dd2eb077d300100d3b39ea0745cc934bed036a57620be3aaa668.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "type": "text", + "content": "Figure 1. (a) We propose the First-time " + }, + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "type": "text", + "content": "-epoch Learning (FkL) metric, which determines the minimum index of the training epoch until which an example has been predicted as its given label for consecutive " + }, + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "type": "text", + "content": " epochs. (b) The normalised histogram of CIFAR-10 examples with " + }, + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 274, + 545, + 340 + ], + "type": "text", + "content": " symmetric label noise w.r.t. the sequence they meet the FkL metric during training procedure. The horizontal axis represents the sequential order in which training examples meet the FkL metric. The vertical axis represents the normalised histogram of examples. (c) Rather than the methods that start from a small yet clean training set ('Early' Stopping), our proposed framework starts from a large training set ('Late' Stopping) that retains as many clean examples as possible." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 459, + 72, + 523, + 258 + ], + "blocks": [ + { + "bbox": [ + 459, + 72, + 523, + 258 + ], + "lines": [ + { + "bbox": [ + 459, + 72, + 523, + 258 + ], + "spans": [ + { + "bbox": [ + 459, + 72, + 523, + 258 + ], + "type": "image", + "image_path": "92929d3565c32fbf4e1d033d9a5b330e55d91b52dab584bce45e04747d74cd59.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 262, + 459, + 270 + ], + "lines": [ + { + "bbox": [ + 449, + 262, + 459, + 270 + ], + "spans": [ + { + "bbox": [ + 449, + 262, + 459, + 270 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "type": "text", + "content": "Using First-time " + }, + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "type": "text", + "content": "-epoch Learning (FkL) as a metric, we sequence the examples in the noisy dataset according to the order they meet the FkL metric during the training procedure, as shown in Figure 1(b). As shown in the same figure, most unlabeled examples can only be classified into their given labels for consecutive " + }, + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "type": "text", + "content": " epochs in the later stages of training (i.e., larger in the sequence), which implies a relatively large FkL value. This observation suggests that the examples with large FkL values (i.e., those examples that are classified to their given labels for consecutive " + }, + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 353, + 287, + 519 + ], + "type": "text", + "content": " epochs only in the late training stage) are predominantly those with incorrect labels. Therefore, the FkL values of different training examples can be used to distinguish whether an example is unlabeled or not." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "Motivated by the above observations, we propose a novel method based on reverse thinking of the conventional confident example selection strategy. Our proposed method, called Late Stopping, employs an iterative sample selection process that gradually reduces the noise rate of the dataset, leading to a positive feedback loop. Instead of selecting high-probability clean examples in the early stage, our method focuses on selecting high-probability mislabeled examples in the late stage to retain as many CHEs as possible in the training set throughout the learning process, even though this method may lead to the retention of an acceptable level of mislabeled examples, as shown in 1(c). Building on this, we introduce a novel sample selection criterion, FkL, which works effectively in selecting mislabeled examples under the Late Stopping framework, and empirical results show that the FkL is more ef" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "type": "text", + "content": "fective than the loss criterion. We evaluate our method on benchmark-simulated and real-world noisy datasets. Empirical results demonstrate that the Late Stopping method achieves superior performance compared with state-of-the-art counterparts of learning with noisy labels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 427, + 392, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 427, + 392, + 440 + ], + "spans": [ + { + "bbox": [ + 306, + 427, + 392, + 440 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": "Existing methods of learning with noisy labels can be broadly categorized into two types. The first category includes classifier-consistent algorithms that use the noise transition matrix [27, 29, 54, 35, 8], which indicates the probabilities of clean labels flipping to noisy labels. The second category focuses on heuristic methods to mitigate the impact of label noise [36, 50, 39, 45, 30, 49, 36], which is also the primary focus of our work. Many existing heuristic methods in LNL are based on the memorization effect, where the algorithm attempts to only learn from confident clean examples [20, 14, 46, 34]. Alternatively optimizing the classifier and updating the training set is not a new idea in LNL. For instance, Joint Optim [42], Co-teaching [14], SELF [34], and Me-Momentum [2] employ a similar positive feedback loop to our proposed Late Stopping." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Previous research on the dynamics of DNNs has demonstrated that hard examples are typically learned during the late stage of the learning process [1, 43, 31]. Furthermore, many recent studies have employed various training-time metrics to quantify the \"hardness\" of examples [32, 16, 7, 4, 21, 31], leading to an increase in LNL approaches that use learning dynamics to select clean examples. For instance," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16080" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 86, + 541, + 232 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 162, + 85 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 162, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 162, + 85 + ], + "type": "text", + "content": "Algorithm 1 Late Stopping" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "lines": [ + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": "Input: Original noisy training set " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_1" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ", iteration rate " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "m\\%" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ", noise rate " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "n\\%" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ", epoch " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "T_{max}" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": " and iteration " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "I_{max}" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ". \nOutput: Extracted final training set and the classifier. \n1: for " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "I = 1, \\dots, I_{max}" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": " do \n2: Initialize " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "S_{F_i} = 0" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{F_i} = [\\ldots]" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ". \n3: //Initialize new training set, the number/dataset of examples that meet the First-time k-epoch Learning, respectively. \n4: for " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "T = 1, \\dots, T_{max}" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": " do \n5: Train " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "f_i" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ". \n6: Update " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{F_i}" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "S_{F_i}" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ". \n7: Break and Output " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{i+1} = \\mathcal{D}_{F_i}" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ", if " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "S_{F_i} > S_{F_{i-1}} \\times (1 - m\\%)" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ". \n8: end for \n9: Break and Output " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "f_i" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{F_i}" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ", if " + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "inline_equation", + "content": "m \\times i > n" + }, + { + "bbox": [ + 47, + 86, + 541, + 232 + ], + "type": "text", + "content": ". \n10: end for" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 46, + 253, + 290, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 290, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 290, + 386 + ], + "type": "text", + "content": "FSLT&SSFT [31], Self-Filtering [48], SELFIE [40], and RoCL [57] adopt a criterion similar to our proposed FkL criterion. Specifically, FSLT&SSFT and Self-Filtering use the classifier's error prediction to pinpoint clean examples, SELFIE employs entropy values from prediction histories for selection, and RoCL leverages the variance of training losses to select clean examples. Instead of quantifying the \"hardness\" of examples based on the characteristics of individual examples in the dataset, our proposed method focuses on extracting the intrinsic robust learning ability of DNNs from the model trained on noisy datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 399, + 135, + 413 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 135, + 413 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 135, + 413 + ], + "type": "text", + "content": "3. Late Stopping" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 419, + 288, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 288, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 288, + 563 + ], + "type": "text", + "content": "In this section, we elaborate on our proposed Late Stopping method. As shown in Figure 1, the primary goal of the Late Stopping framework is to maximize the retention of clean examples in the training set throughout the learning process, enabling our method to learn clean hard examples (CHEs) from a noisy training set. Therefore, we halt the training process in the late training stage, leveraging First-time " + }, + { + "bbox": [ + 46, + 419, + 288, + 563 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 419, + 288, + 563 + ], + "type": "text", + "content": "-epoch Learning (FkL) to exploit the results of the intrinsic robust learning ability of DNNs for sample selection. Iteratively performing this operation allows for a gradual reduction of noise while maximizing the retention of clean samples in the training dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 573, + 144, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 144, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 144, + 586 + ], + "type": "text", + "content": "3.1. Algorithm Flow" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": "For a comprehensive explanation of Late Stopping, we begin by formally defining First-time " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": "-epoch Learning (FkL). In learning with noisy labels, let us consider a model " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " trained on a noisy training set " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " composed of " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " training examples " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_j,y_j\\}_{j = 1}^n" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "y_{j}" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " denotes the given label (which may not be true) of " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": ". After " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " training epochs, the predicted label " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\hat{y}_j^t" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " for the instance " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " can be obtained. Let " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{acc}_j^t = \\mathbb{1}_{\\hat{y}_j^t = y_j}" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " denote a binary variable indicating whether " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " predicts the given label " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "y_{j}" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " of the instance " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " at epoch " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": ". The FkL for the instance " + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 46, + 593, + 287, + 715 + ], + "type": "text", + "content": " is defined as the minimum" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "type": "text", + "content": "index of the training epoch that the instance " + }, + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "type": "text", + "content": " has been predicted to its given label " + }, + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "type": "inline_equation", + "content": "y_{j}" + }, + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 254, + 545, + 278 + ], + "type": "text", + "content": " consecutive epochs:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 322, + 281, + 529, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 281, + 529, + 304 + ], + "spans": [ + { + "bbox": [ + 322, + 281, + 529, + 304 + ], + "type": "interline_equation", + "content": "\\mathrm {F k L} _ {j} = \\underset {t ^ {*} \\in t} {\\operatorname {a r g m i n}} \\left(\\mathrm {a c c} _ {j} ^ {t ^ {*}} \\wedge \\ldots \\wedge \\mathrm {a c c} _ {j} ^ {(t ^ {*} - k + 1)} = 1\\right).", + "image_path": "0477b143bb58469a2fe918532f68adbb0c7f68b4ca78c32a99117dbbf939a05b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "text", + "content": "If " + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\mathrm{FkL}_j = t^*" + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "text", + "content": ", it implies that the classifier " + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "text", + "content": " \"learns\" the instance " + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "text", + "content": " after " + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "inline_equation", + "content": "t^*" + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "text", + "content": " epochs. Notably, if " + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 304, + 306, + 545, + 426 + ], + "type": "text", + "content": " is \"learned\" by the classifier early in the training, it will have a small FkL value, however, if it is \"learned\" in the late stage, it will have a large FkL value. Based on our FkL definition, we observed that the majority of examples with large FkL values are mislabeled, as shown in Figure 1(a). This observation provides a rationale for selecting examples with large FkL values, those learned in the late training stage, as high-probability mislabeled examples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": "With the FkL selection criterion, we present the algorithmic framework of Late Stopping. At the low level (Steps 4-8 of Algorithm 1), the sample selection strategy follows a \"from easy to hard\" curriculum learning procedure [5, 18]. During the " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": "-th iteration, the classifier " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " is trained on a new training set " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " (Step 5), and newly identified FkL examples are added to " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{F_i}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " (Step 6). If the size of " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{F_i}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": ", represented as " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "S_{F_i}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": ", exceeds a predefined threshold, the training in this iteration will halt, and the output becomes " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{F_i}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " (Step 7). At the higher level (Steps 1-10 of Algorithm 1), our method learns through a \"from hard to easy\" positive feedback loop, distinguishing it from most existing LNL approaches. The algorithm starts with initializing " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_1" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " and training " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "f_{1}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " (Iteration 1). In subsequent iterations, the new training set " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " (Step 2, Iteration " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": ") is updated from the previous iteration's " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{F_{i - 1}}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " (Step 8, Iteration " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "i - 1" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": "). When the stopping condition is met, the output is " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{F_i}" + }, + { + "bbox": [ + 304, + 426, + 546, + 630 + ], + "type": "text", + "content": " (Step 10)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 635, + 531, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 531, + 648 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 531, + 648 + ], + "type": "text", + "content": "3.2. Learning CHEs by Positive Feedback Loop" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Here, we delve deeper into the typical positive feedback loop in LNL, highlighting its limitations in effectively learning CHEs. We then elucidate how our proposed method overcomes these limitations and maximizes the retention of clean examples throughout the learning process." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16081" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": "Typical positive feedback loop in LNL. According to statistical learning theory [33], training data with better quality yields a better classifier. Therefore, we can improve the classifier's generalization performance in LNL through the construction of a positive feedback loop. The goal of the positive feedback loop is that, after each training step, the new classifier showcases enhanced generalization performance compared with its predecessor. By doing so, it can more robustly guide the sample selection process, enabling the use of improved training data for classifier training in the succeeding steps [2]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 206, + 289, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 206, + 289, + 386 + ], + "spans": [ + { + "bbox": [ + 47, + 206, + 289, + 386 + ], + "type": "text", + "content": "Most LNL methods, relying on confident examples, initiate with either a small yet clean training set or a weak yet reliable classifier. To enhance the classifier's generalization performance during initialization, they often rigorously limit memorization effects and eliminate potential mislabeled examples, even if this entails removing many CHEs. By restricting the memorization of mislabeled examples, they achieve superior generalization performance compared with unrestricted training on the original set. Then, they either iteratively or incrementally, train classifiers, ultimately obtaining either a larger clean training set or a more robust classifier. This strategy is effective when the classes or subclasses within the dataset are well-balanced and the examples within each class are interrelated, allowing the classifier to learn harder examples from easier ones." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 388, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 289, + 651 + ], + "type": "text", + "content": "Limitations of typical positive feedback loop. Although LNL methods that rely on a typical positive feedback loop achieve good generalization performance in a variety of benchmark tasks, natural datasets are often highly imbalanced. This imbalance poses a challenge to achieving close-to-optimal generalization performance with existing LNL methods. Specifically, such challenges are because CHEs are often characterized by large losses and non-dominant patterns. As a result, substantial learning about CHEs predominantly transpires during the late stages of training, driven by memorization effects [2, 52]. The conventional positive feedback loop, aimed at preventing overfitting, often strictly limits the memorization effects of DNNs. Consequently, this strict constraint reduces a classifier's ability to learn from under-represented subpopulations in datasets [9], and thus limits its learning primarily to typical (dominant) classes and subclasses. Such constraints ultimately lead to a situation where the learning ability of rare classes and subclasses, i.e., CHEs, is continuously neglected, while the learning ability of the classes and subclasses representing the dominant pattern is continuously enhanced." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 654, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 289, + 715 + ], + "type": "text", + "content": "Positive feedback loop in Late Stopping. Based on our previous discussions, to achieve close-to-optimal generalization performance on natural datasets, we need to focus on learning from CHEs throughout the training process. To achieve this, we prolong the training process for each train-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": "ing iteration to make use of the memorization effects to help memorize CHEs. With a loose sample selection process, we can ensure that we maximize the retention of clean examples in the training set throughout the learning process. However, retaining as many clean examples as possible during the training initialization requires accepting a significant amount of label noise in the initial training set. Additionally, relying on the \"memorization effects in the late training stage\" to learn CHEs might result in poor generalization performance, as the classifier may seriously overfit label noise in this stage." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "type": "text", + "content": "To counter these negative effects, we propose a \"from hard to easy\" positive feedback loop within the Late Stopping framework. While we prolong the training process in each training iteration, we simultaneously use the classifier's robust learning capabilities as the criterion for sample selection, i.e., FkL. In each iteration, we train a new classifier on a new training set, using it solely to guide the sample selection for the current iteration. In this positive feedback loop, we opt to disregard the generalization performance of the classifier in each iteration. Instead, we exploit the robust learning capabilities of each new classifier, " + }, + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "type": "text", + "content": ", in its " + }, + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "type": "text", + "content": " iteration on " + }, + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 304, + 206, + 547, + 361 + ], + "type": "text", + "content": " from its learning dynamics, i.e., using the FkL criterion to select examples for the next iteration." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 364, + 547, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 508 + ], + "type": "text", + "content": "The new training set, obtained by the FkL criterion from the previous iteration, will have less noise. This enables the training of a better new classifier, which can learn more from the CHEs before it begins to memorize mislabeled examples. Therefore, tracking learning dynamics using the FkL criterion can better distinguish between CHEs and mislabeled examples, resulting in a new training set with even less noise than the previous one but contains CHEs. By observing each classifier's learning dynamics through FkL in every iteration, we can iteratively refine our training set, reducing noise while retaining the majority of clean examples, as shown in Figure 2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "Discussion. Our proposed method is motivated by the seemingly conflicting views on the ability of DNNs to handle label noise as presented in recent studies: \"Deep neural networks easily fit random labels [56]\" and \"Deep learning is robust to massive label noises [37]\". Empirical evidence [1] suggests that DNNs first learn simple patterns before over-fitting in the late training stage. However, there is a scarcity of studies on the behavior of DNNs during the intermediate stages of training, which may be a critical factor for understanding the robustness of DNNs to label noise - DNNs might exhibit spontaneously robust learning to massive label noises in all periods of training, though the generalization performance is over-fitting noisy labels. Thus, we aim to separate the robust learning ability of DNNs from their generalization performance. To this end, we leverage the intrinsic robust learning ability of DNNs by continuing the training process until the generalization performance se" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16082" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 76, + 181, + 242 + ], + "blocks": [ + { + "bbox": [ + 62, + 76, + 181, + 242 + ], + "lines": [ + { + "bbox": [ + 62, + 76, + 181, + 242 + ], + "spans": [ + { + "bbox": [ + 62, + 76, + 181, + 242 + ], + "type": "image", + "image_path": "0bb0cf552779ea2d7d338e7ad3a121554314ee42301076f0542b61a316dd11ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 187, + 76, + 296, + 241 + ], + "blocks": [ + { + "bbox": [ + 187, + 76, + 296, + 241 + ], + "lines": [ + { + "bbox": [ + 187, + 76, + 296, + 241 + ], + "spans": [ + { + "bbox": [ + 187, + 76, + 296, + 241 + ], + "type": "image", + "image_path": "8fad7cead5903932755b2f00bc7dd9c76e89556aec67dd378b77e65d22dba3bb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 303, + 76, + 412, + 241 + ], + "blocks": [ + { + "bbox": [ + 303, + 76, + 412, + 241 + ], + "lines": [ + { + "bbox": [ + 303, + 76, + 412, + 241 + ], + "spans": [ + { + "bbox": [ + 303, + 76, + 412, + 241 + ], + "type": "image", + "image_path": "35340cd50c450ee8c74a49181468d1b2650c7db2c36740a911b14ceb1e96ad41.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 420, + 76, + 529, + 241 + ], + "blocks": [ + { + "bbox": [ + 420, + 76, + 529, + 241 + ], + "lines": [ + { + "bbox": [ + 420, + 76, + 529, + 241 + ], + "spans": [ + { + "bbox": [ + 420, + 76, + 529, + 241 + ], + "type": "image", + "image_path": "d5116a105fc06502ef1c75a082b10053ab028240597fe2ef44cf1ccdebe98cee.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 69, + 245, + 179, + 335 + ], + "blocks": [ + { + "bbox": [ + 69, + 245, + 179, + 335 + ], + "lines": [ + { + "bbox": [ + 69, + 245, + 179, + 335 + ], + "spans": [ + { + "bbox": [ + 69, + 245, + 179, + 335 + ], + "type": "image", + "image_path": "a6a93e6d9452aafb9b41fe113129918007448a49fe81938f85cbceb640ac6010.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 348, + 547, + 404 + ], + "lines": [ + { + "bbox": [ + 46, + 348, + 547, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 547, + 404 + ], + "type": "text", + "content": "Figure 2. We refer to one update of the classifier and the training set as one iteration. Top subfigures: We illustrate the changes in the Test-set Accuracy and the Training-set Accuracy of the classifier during the training process of Late Stopping. There are ten peaks in each figure because we set the number of iterations " + }, + { + "bbox": [ + 46, + 348, + 547, + 404 + ], + "type": "inline_equation", + "content": "= 10" + }, + { + "bbox": [ + 46, + 348, + 547, + 404 + ], + "type": "text", + "content": " and the classifiers are re-initialized at the beginning of each new iteration. Bottom subfigures: We illustrate the changes in the noise rate of the training set in each iteration. There are ten bars in each figure because we set the number of iterations " + }, + { + "bbox": [ + 46, + 348, + 547, + 404 + ], + "type": "inline_equation", + "content": "= 10" + }, + { + "bbox": [ + 46, + 348, + 547, + 404 + ], + "type": "text", + "content": " and the training set of each iteration is obtained from the previous iteration." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 186, + 247, + 294, + 335 + ], + "blocks": [ + { + "bbox": [ + 186, + 247, + 294, + 335 + ], + "lines": [ + { + "bbox": [ + 186, + 247, + 294, + 335 + ], + "spans": [ + { + "bbox": [ + 186, + 247, + 294, + 335 + ], + "type": "image", + "image_path": "7fccf7d2d3a6a3bbe2811305228f9405440e05bba75c70001bbf14ae7446220f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 301, + 247, + 410, + 335 + ], + "blocks": [ + { + "bbox": [ + 301, + 247, + 410, + 335 + ], + "lines": [ + { + "bbox": [ + 301, + 247, + 410, + 335 + ], + "spans": [ + { + "bbox": [ + 301, + 247, + 410, + 335 + ], + "type": "image", + "image_path": "b9be724f8ac70093670aa00831aa917c795c01e624a5767017bae51d2f58f3bb.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 421, + 247, + 529, + 335 + ], + "blocks": [ + { + "bbox": [ + 421, + 247, + 529, + 335 + ], + "lines": [ + { + "bbox": [ + 421, + 247, + 529, + 335 + ], + "spans": [ + { + "bbox": [ + 421, + 247, + 529, + 335 + ], + "type": "image", + "image_path": "67f65b7a20cff59ecadc867180a36b27facc844bff3eea3aa0c89169e852d1d3.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 415, + 288, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 288, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 288, + 440 + ], + "type": "text", + "content": "riously deteriorates (i.e., Late Stopping) and we extract the robust learning results during this process (i.e., FkL)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 451, + 128, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 128, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 128, + 466 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 472, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 509 + ], + "type": "text", + "content": "In this section, we conduct experiments on both synthetic and real-world datasets containing label noise to validate the effectiveness of our proposed Late Stopping." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "type": "text", + "content": "Datasets. We use two popular benchmark datasets i.e., CIFAR-10 and CIFAR-100 [23], to test the generalization performance of our proposed method. Following previous works [2, 51], we manually corrupt CIFAR-10 and CIFAR-100 with Symmetric noise (abbreviated as Sym.) [44] and Instance-dependent (abbreviated as Ins.) noise [53]. For Sym. noise and Ins. noise, the noise rate is set to " + }, + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "type": "text", + "content": ". For a fair comparison, we leave out " + }, + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 510, + 288, + 664 + ], + "type": "text", + "content": " of the noisy training data. We employ the real-world noisy dataset CIFAR-10N [47], which equips the training datasets of CIFAR-10 with human-annotated real-world noisy labels. More details about the above datasets and noise types are provided in Appendix A1." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Compared methods. We compare the Late Stopping method (Algorithm 1) with the following well-known methods: (1) Statistically inconsistent approaches (small-loss trick): MentorNet [20], Co-teaching [14], and JoCoR [46];" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 415, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 510 + ], + "type": "text", + "content": "(2) Statistically inconsistent approaches (other tricks): Joint Optim [42], CDR [51], and Me-Momentum [2]; (3) Statistically consistent approaches: Forward [35] and DMI [54]. Note that drawing a direct comparison with certain semi-supervised approaches, especially those with multiple technical aggregations such as SELF [34], DivideMix [24], ELR+ [26], and Unicon [22]. The results for baselines are copied from original papers and [2, 47]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 510, + 546, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 654 + ], + "type": "text", + "content": "Network structure and experimental setup. We utilize a typical warming-up strategy to ensure stable predictions of the DNNs. The optimizer settings used in our experiments are as follows: SGD with a momentum of 0.9, weight decay of 5e-4, batch size of 128, and initial learning rate of 0.02. In our experiments, we applied typical data augmentations such as horizontal flipping and random cropping. For the experiments on synthetic noisy datasets, ResNet-18 and ResNet-34 [15] are used for CIFAR-10 and CIFAR-100, respectively. For the experiments on real-world noisy datasets, ResNet-34 is used for CIFAR-10N. More details about our experimental setup are provided in Appendix A2." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 659, + 471, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 471, + 673 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 471, + 673 + ], + "type": "text", + "content": "4.1. Effectiveness of Late Stopping" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Here, we aim to provide empirical evidence to verify the effectiveness of Late Stopping. We conduct experiments on the CIFAR-10 and CIFAR-100 datasets, as their" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16083" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 80, + 541, + 225 + ], + "blocks": [ + { + "bbox": [ + 133, + 69, + 457, + 80 + ], + "lines": [ + { + "bbox": [ + 133, + 69, + 457, + 80 + ], + "spans": [ + { + "bbox": [ + 133, + 69, + 457, + 80 + ], + "type": "text", + "content": "Table 1. Label precision of the selected examples (45k in total, with 27k clean examples)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 80, + 541, + 225 + ], + "lines": [ + { + "bbox": [ + 53, + 80, + 541, + 225 + ], + "spans": [ + { + "bbox": [ + 53, + 80, + 541, + 225 + ], + "type": "table", + "html": "
Data&NoisecriterionSelecting Clean ExamplesSelecting Mislabeled Examples
0-10k0-15k0-25k30k-45k35k-45k40k-45k
CIFAR-10loss92.73%89.56%82.89%75.67%83.49%91.54%
Sym. 40%FkL(Ours)95.49%95.59%93.56%96.39%99.81%99.94%
CIFAR-10loss75.55%72.33%71.38%60.27%68.69%77.28%
Ins. 40%FkL(Ours)81.88%81.67%81.51%78.51%88.85%99.30%
CIFAR-100loss88.43%84.72%78.49%68.02%75.73%84.68%
Sym. 40%FkL(Ours)97.45%96.78%95.06%94.63%97.91%98.86%
CIFAR-100loss71.30%68.23%65.29%45.91%44.23%42.56%
Ins. 40%FkL(Ours)89.25%88.56%84.40%78.22%86.28%91.76%
", + "image_path": "15304dee3243407b58892187e9aa4e0abd280f9a9e4e627067536ca30318710f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 53, + 242, + 541, + 288 + ], + "blocks": [ + { + "bbox": [ + 162, + 232, + 430, + 242 + ], + "lines": [ + { + "bbox": [ + 162, + 232, + 430, + 242 + ], + "spans": [ + { + "bbox": [ + 162, + 232, + 430, + 242 + ], + "type": "text", + "content": "Table 2. Numbers of clean examples of the final training set (27k in total)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 242, + 541, + 288 + ], + "lines": [ + { + "bbox": [ + 53, + 242, + 541, + 288 + ], + "spans": [ + { + "bbox": [ + 53, + 242, + 541, + 288 + ], + "type": "table", + "html": "
CIFAR-10 (Sym. 40%)CIFAR-10 (Ins. 40%)CIFAR-100 (Sym. 40%)CIFAR-100 (Ins. 40%)
Me-Momentum [2]25,79125,69422,24420,779
Late Stopping (Ours)26,56225,91526,12023,979
", + "image_path": "b287010e5edc6dadd6e08c0380aeacc50bf98552a4b763d313566128bfa7169d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 305, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 287, + 461 + ], + "type": "text", + "content": "ground-truth labels are available. The average results of five runs of our experiments are presented in Figure 2, which demonstrates the iterative improvement in the quality of the training set when Late Stopping is applied in the learning process. And a classifier with better generalization performance is obtained. We demonstrate the ability of our proposed FkL criterion to select mislabeled examples under the Late Stopping framework, compared with the loss criterion. Additionally, we show the effectiveness of our proposed Late Stopping in retaining clean examples in the training set by comparing it with Me-Momentum [2], which is also an sample selection method that focuses on extracting clean hard examples." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": "Comparison with loss criterion. The selection of confident clean examples based on the small-loss criterion is a commonly used approach in LNL and has been shown to be effective [20, 14, 46]. However, the approach of selecting mislabeled examples based on the large-loss [6] can be tricky since it fails to distinguish between mislabeled and clean hard examples [52]. We conducted experiments on the CIFAR-10 and CIFAR-100 datasets to compare the effectiveness of the FkL and loss criterion for selecting examples during the same training process. Specifically, we ranked all examples (45k in total, with 27k clean examples) using the FkL criterion and the loss criterion, respectively, from the smallest 0k to the largest 45k. We then compared the precision of the two criteria in selecting clean examples and mislabeled examples in different ranges. The details of the experiments and the results are presented in Table 1. Our experimental results demonstrate that the FkL criterion outperforms the loss criterion in selecting both clean and mislabeled examples under the Late Stopping framework. The largest performance gap was observed in the " + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "inline_equation", + "content": "40k - 45k" + }, + { + "bbox": [ + 46, + 462, + 288, + 713 + ], + "type": "text", + "content": " range. These results provide empirical evidence that the FkL cri" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "text", + "content": "terion is more effective than the loss criterion for selecting mislabeled examples in the Late Stopping framework." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 329, + 546, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 546, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 546, + 497 + ], + "type": "text", + "content": "Comparison with hard example selection approach. In Table 2, we compare our proposed method with Me-Momentum [2] which also focuses on selecting clean hard examples. Since there are no clear definitions of clean hard examples, we cannot directly compare the effectiveness of selecting such examples. Nevertheless, we can make an indirect comparison by comparing the ability to select clean examples. Our experimental results demonstrate that Late Stopping is an effective approach for retaining clean hard examples. On the CIFAR-10 dataset, both Late Stopping and Me-Momentum showed comparable performance. However, on the more challenging CIFAR-100 dataset, Late Stopping significantly achieved better performance in selecting clean hard examples." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 503, + 440, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 440, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 440, + 516 + ], + "type": "text", + "content": "4.2. Classification Accuracy" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "Synthetic datasets. The experimental results on test accuracy on synthetic datasets with class-dependent and instance-dependent label noise are provided in Table 3 and 4. Each trial is repeated five times and the mean value and standard deviation are recorded. On CIFAR-10, our method achieves varying degrees of lead over baselines. In the " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " symmetric noise task, which is the simplest task in all cases, the Me-Momentum baseline outperforms ours, which illustrates the effectiveness of conventional sample selection based on confident clean examples for simple LNL. For the more challenging CIFAR-100 dataset, our proposed method consistently achieved the best results. The size of each class in CIFAR-100 is ten times smaller than that of CIFAR-10, making it difficult to retain sufficient CHEs while maintaining a small yet clean training set using conventional sample selection methods. Methods that focus on improving the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16084" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 80, + 541, + 225 + ], + "blocks": [ + { + "bbox": [ + 136, + 69, + 456, + 80 + ], + "lines": [ + { + "bbox": [ + 136, + 69, + 456, + 80 + ], + "spans": [ + { + "bbox": [ + 136, + 69, + 456, + 80 + ], + "type": "text", + "content": "Table 3. Test performance (mean±std) of each approach using ResNet-18 on CIFAR-10." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 80, + 541, + 225 + ], + "lines": [ + { + "bbox": [ + 53, + 80, + 541, + 225 + ], + "spans": [ + { + "bbox": [ + 53, + 80, + 541, + 225 + ], + "type": "table", + "html": "
Sym. 20%Sym. 40%Ins. 20%Ins. 40%
Late Stopping(Ours)91.06±0.22%88.92±0.38%91.08±0.23%87.41±0.38%
Cross-Entropy [38]85.00±0.43%79.59±1.31%85.92±1.09%79.91±1.41%
MentorNet [20]80.49±0.11%77.48±3.45%79.12±0.42%70.27±1.52%
Forward [35]85.63±0.11%74.30±0.26%85.29±0.38%74.72±3.24%
Co-teaching [14]87.16±0.52%83.59±0.28%86.54±0.11%80.98±0.39%
JoCoR [46]88.69±0.19%85.44±0.29%87.31±0.27%82.49±0.57%
DMI [54]88.18±0.13%83.98±0.48%89.14±0.36%84.78±1.97%
Joint Optim [42]89.70±0.36%87.79±0.20%89.69±0.42%82.62±0.57%
CDR [51]89.68±0.38%86.13±0.44%90.24±0.39%83.07±1.33%
Me-Momentum [2]91.44±0.33%88.39±0.34%90.86±0.21%86.66±0.91%
", + "image_path": "bb51523ffb97f7b2aa4a3a85ec020d7c7f9a7e33cf12d47c9a6fd199cc068955.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 53, + 245, + 541, + 392 + ], + "blocks": [ + { + "bbox": [ + 133, + 234, + 458, + 245 + ], + "lines": [ + { + "bbox": [ + 133, + 234, + 458, + 245 + ], + "spans": [ + { + "bbox": [ + 133, + 234, + 458, + 245 + ], + "type": "text", + "content": "Table 4. Test performance (mean±std) of each approach using ResNet-34 on CIFAR-100." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 245, + 541, + 392 + ], + "lines": [ + { + "bbox": [ + 53, + 245, + 541, + 392 + ], + "spans": [ + { + "bbox": [ + 53, + 245, + 541, + 392 + ], + "type": "table", + "html": "
Sym. 20%Sym. 40%Ins. 20%Ins. 40%
Late Stopping(Ours)68.67±0.67%64.10±0.40%68.59±0.70%59.28±0.46%
Cross-Entropy [38]57.59±2.55%45.74±2.61%59.85±1.56%43.74±1.54%
MentorNet [20]52.11±0.10%35.12±1.13%51.73±0.17%40.90±0.45%
Forward [35]57.75±0.37%38.59±1.62%58.76±0.66%44.50±0.72%
Co-teaching [14]59.28±0.47%51.60±0.49%57.24±0.69%45.69±0.99%
JoCoR [46]64.17±0.19%55.97±0.46%61.98±0.39%50.59±0.71%
DMI [54]58.73±0.70%49.81±1.22%58.05±0.20%47.36±0.68%
Joint Optim [42]64.55±0.38%57.97±0.67%65.15±0.31%55.57±0.41%
CDR [51]66.52±0.24%60.18±0.22%67.06±0.50%56.86±0.62%
Me-Momentum [2]68.03±0.53%63.48±0.72%68.11±0.57%58.38±1.28%
", + "image_path": "a2f8a0f48b28f0c7201c92c4c1df03b20c6c335d2ed80467e32aa6c32065b7e7.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 53, + 411, + 541, + 445 + ], + "blocks": [ + { + "bbox": [ + 147, + 399, + 444, + 411 + ], + "lines": [ + { + "bbox": [ + 147, + 399, + 444, + 411 + ], + "spans": [ + { + "bbox": [ + 147, + 399, + 444, + 411 + ], + "type": "text", + "content": "Table 5. Test accuracy of each approach using ResNet-34 on CIFAR-10N (Worst)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 411, + 541, + 445 + ], + "lines": [ + { + "bbox": [ + 53, + 411, + 541, + 445 + ], + "spans": [ + { + "bbox": [ + 53, + 411, + 541, + 445 + ], + "type": "table", + "html": "
Cross-Entropy [38]Forward [35]Co-teaching [14]JoCoR [46]Me-Momentum [2]Late Stopping(Ours)
77.69±1.55%79.79±0.46%83.83±0.13%83.37±0.30%84.71±0.37%85.24±0.38%
", + "image_path": "537bdfeb6899fe709f7f8ffa939c9fab15ea18a19a3223a703446f7d757f11ed.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "type": "text", + "content": "number of CHEs in the training set can achieve better generalization performance in this task. For instance, DMI and Co-teaching show a much larger performance gap with our proposed method on CIFAR-100 compared with CIFAR-10. Furthermore, Table 2 validates our method's superior capability to retain clean examples, resulting in a larger performance gap with Me-Momentum on CIFAR-100." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": "Real-world dataset. To validate the efficacy of our proposed method on real-world datasets, we assess our method using the CIFAR-10N dataset in Table 4, a recognized benchmark in learning with noisy labels tasks with both ground-truth labels and human-annotated real-world noisy labels. We utilized the most challenging real-world noisy labels from CIFAR-10N, i.e., the \"Worst\" setting. In this setting, for each image, if there are any incorrectly labeled examples, the given label is randomly selected from human-annotated false labels. Each trial is repeated five times and the mean value and standard deviation are recorded. As shown in Table 4, our method achieves the best performance compared with other methods." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 464, + 406, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 406, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 406, + 477 + ], + "type": "text", + "content": "4.3. Further analysis" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 483, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 483, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 483, + 545, + 519 + ], + "type": "text", + "content": "Here, we conduct further analysis of our proposed method with the same experimental settings as those used in Section 4.2 unless stated otherwise." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "type": "text", + "content": "Limitations. While our method achieves good robustness by simply removing the lately learned examples, it is not immune to errors. Some clean examples might be incorrectly removed from the training set, i.e., falsely removed examples, and some mislabeled examples are incorrectly retained in the training set, i.e., falsely retained examples. We visualize such typical examples in Figure 3 and provide the following empirical analysis." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "Falsely retained examples are mislabeled with the wrong label " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "L_{w}" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": ", however, such examples often possess patterns similar to the dominant subclasses in the " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "L_{w}" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": " class, making it difficult to identify them as high probability mislabeled examples by the FkL criterion. As shown in Table 6, based on the FkL criterion and the loss criterion, the \"hardness\" of these examples decreases after being mislabeled. In particular, we named the examples with a decrease in" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16085" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 64, + 79, + 167, + 198 + ], + "blocks": [ + { + "bbox": [ + 64, + 79, + 167, + 198 + ], + "lines": [ + { + "bbox": [ + 64, + 79, + 167, + 198 + ], + "spans": [ + { + "bbox": [ + 64, + 79, + 167, + 198 + ], + "type": "image", + "image_path": "bb131935bcded0d1eb98a2305e21cd862c8533fcdcbe93795ec04ac5c2e49096.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 210, + 287, + 299 + ], + "lines": [ + { + "bbox": [ + 46, + 210, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 287, + 299 + ], + "type": "text", + "content": "Figure 3. The labels in the figure are ground-truth labels for each example. Falsely Removed (1-3) are typical examples that are incorrectly removed in the first iteration of Late Stopping; Falsely Retained (1-3) are typical examples that are incorrectly marked by FkL in the last iteration of Late Stopping. In the training set, Falsely Retained (1) is incorrectly labeled as \"deer\", Falsely Retained (2) is incorrectly labeled as \"truck\", and Falsely Retained (3) is incorrectly labeled as \"frog\"." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 170, + 79, + 218, + 198 + ], + "blocks": [ + { + "bbox": [ + 170, + 79, + 218, + 198 + ], + "lines": [ + { + "bbox": [ + 170, + 79, + 218, + 198 + ], + "spans": [ + { + "bbox": [ + 170, + 79, + 218, + 198 + ], + "type": "image", + "image_path": "34340c5b7fdfaff1f2a036501159a9ecad1650462804b4a3d0b6478abda668ce.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 220, + 79, + 268, + 198 + ], + "blocks": [ + { + "bbox": [ + 220, + 79, + 268, + 198 + ], + "lines": [ + { + "bbox": [ + 220, + 79, + 268, + 198 + ], + "spans": [ + { + "bbox": [ + 220, + 79, + 268, + 198 + ], + "type": "image", + "image_path": "d1fe7ce62347848503949b305d2a414cfc467b064263998ee36fac42839e70b7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 52, + 344, + 282, + 412 + ], + "blocks": [ + { + "bbox": [ + 47, + 311, + 288, + 343 + ], + "lines": [ + { + "bbox": [ + 47, + 311, + 288, + 343 + ], + "spans": [ + { + "bbox": [ + 47, + 311, + 288, + 343 + ], + "type": "text", + "content": "Table 6. The comparison of the average ranking of falsely retained examples using the loss criterion and the FkL criterion before and after fixing the noisy labels (CIFAR-10, Before: Sym. " + }, + { + "bbox": [ + 47, + 311, + 288, + 343 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 47, + 311, + 288, + 343 + ], + "type": "text", + "content": " noise)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 344, + 282, + 412 + ], + "lines": [ + { + "bbox": [ + 52, + 344, + 282, + 412 + ], + "spans": [ + { + "bbox": [ + 52, + 344, + 282, + 412 + ], + "type": "table", + "html": "
LabelCriterionAvg. Ranking
Before fixing (Given label)FkL22340.66
loss23673.50
After fixing (Ground-truth label)FkL28452.08 (+27.36%)
loss29476.46 (+24.51%)
", + "image_path": "4f12463c5d7bf1bee38740de148e269351f4e68317fc1f4208326fc69a0e7a79.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 52, + 458, + 282, + 533 + ], + "blocks": [ + { + "bbox": [ + 47, + 425, + 287, + 457 + ], + "lines": [ + { + "bbox": [ + 47, + 425, + 287, + 457 + ], + "spans": [ + { + "bbox": [ + 47, + 425, + 287, + 457 + ], + "type": "text", + "content": "Table 7. Comparison of the number of clean examples in datasets before and after applying our method as a pre-processing approach to decrease the noise level of a " + }, + { + "bbox": [ + 47, + 425, + 287, + 457 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 47, + 425, + 287, + 457 + ], + "type": "text", + "content": " noisy training set to " + }, + { + "bbox": [ + 47, + 425, + 287, + 457 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 47, + 425, + 287, + 457 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 458, + 282, + 533 + ], + "lines": [ + { + "bbox": [ + 52, + 458, + 282, + 533 + ], + "spans": [ + { + "bbox": [ + 52, + 458, + 282, + 533 + ], + "type": "table", + "html": "
Training setBefore (40% noise)After (20% noise)
CIFAR-10 (Sym.)2722827139 (-0.33%)
CIFAR-10 (Ins.)2709426710 (-1.42%)
CIFAR-100 (Sym.)2734127037 (-1.11%)
CIFAR-100 (Ins.)2724925079 (-7.96%)
CIFAR-10N (Worst)2989629613 (-0.95%)
", + "image_path": "1775aba9b41305aef3d313a10049072f7e00abf1d76be5af1255e13dfe05a671.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 616 + ], + "type": "text", + "content": "training losses after being mislabeled as \"hard mislabeled examples\". Our experimental results indicate that hard mislabeled examples pose a challenge for all sample selection-based LNL methods. More details about Table 6 are provided in Appendix B1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Falsely removed examples refer to the examples that are too hard to remove in practice. To limit the computational resources consumed by our proposed method, we set the removal rate (Algorithm 1, iteration rate " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "m\\%" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": ") to a large value. Thus, our proposed method cannot completely distinguish between rare patterns and mislabeled examples, which can result in a small number of examples from rare subclasses being mistakenly removed from the training set." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 311, + 80, + 541, + 111 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 535, + 80 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 535, + 80 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 535, + 80 + ], + "type": "text", + "content": "Table 8. Comparison of the total training hours on CIFAR-100." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 311, + 80, + 541, + 111 + ], + "lines": [ + { + "bbox": [ + 311, + 80, + 541, + 111 + ], + "spans": [ + { + "bbox": [ + 311, + 80, + 541, + 111 + ], + "type": "table", + "html": "
Co-teaching [14]Me-Momentum [2]Late Stopping (Ours)
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Illustrates the performance of classifiers with the change in iteration rate " + }, + { + "bbox": [ + 306, + 237, + 545, + 258 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 306, + 237, + 545, + 258 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 273, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 545, + 441 + ], + "type": "text", + "content": "Versatility. We are focusing on demonstrating the concept, i.e., using Late Stopping to retain clean hard examples in the training set, but not on boosting the classification performance. However, to cope with even more complex noisy scenarios, our method works well in combination with other advanced techniques. In particular, our approach has excellent performance as a pre-processing approach for reducing the noise rate of the noisy training set. As shown in Table 7, we evaluate Late Stopping as a pre-processing approach to decrease the noise level of a " + }, + { + "bbox": [ + 304, + 273, + 545, + 441 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 273, + 545, + 441 + ], + "type": "text", + "content": " noisy training set to " + }, + { + "bbox": [ + 304, + 273, + 545, + 441 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 273, + 545, + 441 + ], + "type": "text", + "content": ". Our experimental results indicate that our proposed method performs exceptionally well in reducing label noise. It can substantially reduce the noise level of the training set with minimal loss of clean examples." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 445, + 545, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 565 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 565 + ], + "type": "text", + "content": "Training time. Our proposed method involves training the classifier on a larger training set for a longer period, which may not be advantageous in terms of efficiency. Despite this, as the noise rate decreases, the size of the training set decreases, and the speed of obtaining FkL-examples is accelerated (see Figure 2). As shown in Table 8, we compare the training time with typical baseline methods on CIFAR-100 (Sym. " + }, + { + "bbox": [ + 304, + 445, + 545, + 565 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 445, + 545, + 565 + ], + "type": "text", + "content": "). Our experimental results indicate that the training time of our proposed method is in a comparable range with other approaches." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Sensitivity of the iteration rate. The iteration rate " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " (see Algorithm 1) determines the iteration number for Late Stopping and the number of examples removed in each iteration. To investigate the sensitivity of " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ", we conducted experiments on CIFAR10 with " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " Sym. noise and Ins. noise by varying " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " in the range " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{10,5,4,3,2\\}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ". Figure 4 shows the performance of classifiers, which gradually improves as " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " decreases. This observation aligns with the findings presented in Table 1, where a decrease in the range of selected high-probability unlabeled examples leads to higher accuracy in selecting such examples, ultimately benefiting the classifier's performance." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16086" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 289, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 289, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 289, + 307 + ], + "type": "text", + "content": "In this paper, we focused on the challenge of the inability of existing sample selection methods to effectively select clean hard examples. To address this challenge, we proposed a novel method called Late Stopping. In contrast to traditional early-stopping strategies, our method is rooted in a prolonged training process that distinguishes between mislabeled and clean examples by pinpointing the number of training epochs required for each example to be consistently classified to its given label for the first time. We coin this new sample selection criterion as First-time " + }, + { + "bbox": [ + 46, + 91, + 289, + 307 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 91, + 289, + 307 + ], + "type": "text", + "content": "-epoch Learning. Experimental results on synthetic and real-world datasets demonstrate that our proposed method is both straightforward and effective in handling learning with noisy labels. In future work, we plan to enhance the FkL criterion to more accurately capture the intrinsic robust learning ability of DNNs, which could potentially bolster the effectiveness of our Late Stopping framework, especially under more intricate noise conditions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 317, + 145, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 145, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 145, + 331 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 338, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 289, + 460 + ], + "type": "text", + "content": "Lei Feng was supported by the National Natural Science Foundation of China (Grant No. 62106028), Chongqing Overseas Chinese Entrepreneurship and Innovation Support Program, CAAI-Huawei MindSpore Open Fund, and Chongqing Artificial Intelligence Innovation Center. Tongliang Liu was partially supported by Australian Research Council Projects IC-190100031, LP-220100527, DP-220102121, and FT-220100318. 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This is because when unexpected objects occlude the face, the FER network faces difficulties extracting facial features and accurately predicting facial expressions. Therefore, occluded FER (OFER) is a challenging problem. Previous studies on occlusion-aware FER have typically required fully annotated facial images for training. However, collecting facial images with various occlusions and expression annotations is time-consuming and expensive. Latent-OFER, the proposed method, can detect occlusions, restore occluded parts of the face as if they were unoccluded, and recognize them, improving FER accuracy. This approach involves three steps: First, the vision transformer (ViT)-based occlusion patch detector masks the occluded position by training only latent vectors from the unoccluded patches using the support vector data description algorithm. Second, the hybrid reconstruction network generates the masking position as a complete image using the ViT and convolutional neural network (CNN). Last, the expression-relevant latent vector extractor retrieves and uses expression-related information from all latent vectors by applying a CNN-based class activation map. This mechanism has a significant advantage in preventing performance degradation from occlusion by unseen objects. The experimental results on several databases demonstrate the superiority of the proposed method over state-of-the-art methods. This code is available at https://github.com/leeisack/Latent-OFER.", + "bbox": [ + 76, + 323, + 473, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 790, + 209, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Facial expression recognition (FER) has undergone remarkable advancements in recent years and is now widely used across various industries. However, the ability of FER models in the presence of occlusion remains a challenge.", + "bbox": [ + 76, + 816, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9ca4025bf30451ff5fcdf737fd83ae6fdc94da3d1e3d9c323b118c9b8cbf2bbd.jpg", + "image_caption": [ + "Figure 1. Facial expression recognition (FER) performance on RAF-DB according to the occluded proportions." + ], + "image_footnote": [], + "bbox": [ + 516, + 290, + 857, + 465 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1 illustrates the accuracy of the previous state-of-the-art model for FER [58] for various occlusion proportions. In this study, we evaluated the robustness of the typical model in recognizing facial expressions using two types of occlusions: random sampling occlusion and grad occlusion. Random sampling occlusion divides the entire image into 196 patches and randomly masks them according to the proportion. Grad occlusion processes an image with an intentionally occluded area that affects FER using gradient-weighted class activation mapping (Grad-CAM) [46]. This study reveals a more substantial decrease in performance with the second type of occlusion, particularly when the occluded area is crucial for accurate FER. This finding has been objectively measured using Grad-CAM [46].", + "bbox": [ + 496, + 502, + 893, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous studies on FER [1, 2, 3, 5, 7, 13, 14, 15, 21, 23, 29, 31, 38, 43, 44, 49, 50, 54, 57, 60, 62, 63, 68, 69, 70] have not given adequate attention to the influence of occlusions. However, addressing this challenge is crucial for enhancing the practical applications of FER in real-world scenarios. Although research on occluded FER (OFER) is relatively scarce, its importance is increasingly recognized [66].", + "bbox": [ + 496, + 715, + 893, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Currently, several approaches address OFER. The occlusion-robust feature extraction approach [9, 53] aims to identify an occlusion-insensitive and discriminative representation, but it is challenging because the types and locations of occlusion are often unknown. The sub region anal", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 886, + 220, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1536", + "bbox": [ + 483, + 945, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ysis approach [26, 55] divides regions based on facial landmarks and uses attention mechanisms to focus on crucial areas. However, the inability to detect facial landmarks due to occlusions can lead to errors in the FER process. The unoccluded image network assist approach [35, 61] uses two distinct networks: one trained on unoccluded images and the other trained on occluded images. This approach leverages unoccluded images as privileged information to assist in expression recognition in the presence of occlusion. It is unsuitable in real-world situations because it cannot differentiate between occluded and unoccluded images.", + "bbox": [ + 80, + 90, + 467, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Hence, the proposed approach is the occlusion recovery-based approach, which aims to transform occluded images into complete images through a deocclusion process. We propose the deocclusive autoencoder for reconstructing facial images. The deocclusive autoencoder can be functionally divided into an occlusion detector and reconstruction module. The occlusion detector uses the vision transformer (ViT) support vector data description (SVDD) for the reconstruction module. This approach enables the model to detect occlusion caused by unseen objects, an essential step in accurately generating deoccluded facial images. The reconstruction network consists of the ViT structure and convolutional neural network (CNN) structure for facial image reconstruction. We leverage the strengths of the ViT in generating realistic facial images despite varying poses and further refine them using the CNN. We call it the hybrid reconstruction network. The hybrid reconstruction network enhances FER performance by generating deoccluded images that express detailed and vivid facial expression attributes. This enhancement is achieved by incorporating a self-assembly layer and semantic consistency loss. In contrast, previous work on image reconstruction has primarily focused on achieving naturalness, which can result in dull facial expressions. Additionally, we use informative ViT-latent vectors obtained from the reconstruction process. We combine the CNN features and ViT-latent vectors for enhanced facial expression predictions. The main contributions in this work are summarized as follows:", + "bbox": [ + 80, + 261, + 467, + 681 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose an expression-relevant feature extractor that uses spatial attention to assign a higher weight to specific facial features, allowing us to identify critical positions for FER. We can retrieve expression-relevant latent vectors from the ViT-latent space to extract valuable information using these positions as critical values.", + "bbox": [ + 78, + 689, + 467, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose ViT-SVDD, a patch-based occlusion detection module optimized for ViT-based networks. As a self-supervised local classifier, the ViT-SVDD module is trained only on latent vectors of unoccluded facial images. This method accurately classifies occlusions caused by unseen objects for subsequent reconstruction.", + "bbox": [ + 78, + 780, + 467, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose a hybrid reconstruction network that combines the strengths of the ViT and CNN architectures with", + "bbox": [ + 78, + 869, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a self-assembly layer and semantic consistency loss to generate facial images naturalness and rich in expression. This approach enhances the quality of deoccluded images and improves the accuracy of FER in challenging conditions.", + "bbox": [ + 503, + 92, + 888, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 503, + 167, + 638, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Occluded Object Detection", + "text_level": 1, + "bbox": [ + 503, + 191, + 740, + 207 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Several early studies [8] have attempted to detect occlusions in images for OFER tasks. The conventional methods provide location information about the occlusions and are called occlusion-aware methods [26, 55]. However, these methods are not practical for real-world scenarios. Another approach [30] is to train models using synthesized images with various occlusions to detect the occluded positions. Although this approach can determine occlusion positions, it requires a diverse set of object images, which can be challenging to obtain. Moreover, the performance of these models [26, 30, 55] degrades when they encounter unseen objects as input. We drew inspiration from anomaly detection tasks [10, 45, 47, 64] with one-class classification algorithms [20, 32, 39, 40, 52] and proposed a model that learns only from unoccluded datasets and can generalize well to unseen datasets.", + "bbox": [ + 503, + 215, + 888, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Occluded Facial Expression Recognition", + "text_level": 1, + "bbox": [ + 503, + 468, + 841, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We have no prior knowledge of where occlusions may appear on a facial image or how large or complex they might be. These occlusions can significantly reduce the accuracy of FER by either increasing the intra-class variability or inter-class similarity. Four categories address this issue: occlusion-robust feature extraction, subregion analysis, unoccluded image network-assisted, and occlusion recovery.", + "bbox": [ + 503, + 492, + 888, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Occlusion-robust feature extraction approach. This approach aims to extract features less affected by occlusions while maintaining discriminative capability. Wang et al. [53] used self-supervised and contrastive learning to explore robust representations with synthesized occlusions.", + "bbox": [ + 503, + 598, + 888, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Subregion analysis approach. This approach excludes the occluded parts from recognition. By focusing only on the unoccluded facial parts, the influence of occlusion on recognition performance can be reduced. Li et al. [26] proposed a gate unit with an attention mechanism that allows the model to focus on informative unoccluded facial areas.", + "bbox": [ + 503, + 674, + 888, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unoccluded image network-assisted approach. This approach employs unoccluded facial images as guidance to assist with OFER. Pan et al. [35] trained two deep neural networks from occluded and unoccluded facial images. Then, the unoccluded network guides the occluded network. Xia et al. [61] measured the complexity of unoccluded data using distribution density in a feature space. The classifier can be guided by unoccluded data and subsequently leverage more meaningful and discriminative samples.", + "bbox": [ + 503, + 765, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1537", + "bbox": [ + 485, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/184900aecb48fa1c83b2b6ad20352e27e427fd17fafd389d0c3748337749cb68.jpg", + "image_caption": [ + "Figure 2. Framework of the Latent-OFER that creates a deoccluded image that erases the occlusion. In this process, the expression-relevant latent vectors are extracted by mapping the vision transformer (ViT)-latent vector and the convolutional neural network (CNN) class activation map. Latent-OFER predicts facial expressions that combine CNN-based features with specific VIT-based latent vectors." + ], + "image_footnote": [], + "bbox": [ + 98, + 90, + 870, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Occlusion recovery-based approach. This approach uses face completion as a basis to deal with occlusion. To reconstruct occluded faces, Lu et al. [30] suggested using a WGAN consisting of an autoencoder-based generator and discriminators. By reconstructing the occlusion, these approaches provide necessary information while avoiding the interference of noisy information and obtaining informative appearance. Therefore, we adopt an image-inpainting technique as a recovery-based approach, to deal with occlusion. A notable point of differentiation between our method and existing approaches lies in our specific emphasis on the reconstruction of occluded regions while simultaneously retaining the facial expression information. Furthermore, we employ ViT-based latent vectors extracted throughout the reconstruction process to enhance the performance of FER.", + "bbox": [ + 75, + 349, + 472, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Image inpainting", + "text_level": 1, + "bbox": [ + 76, + 588, + 246, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Several approaches based on CNN have been developed to generate semantically coherent content. Pathak et al. [37] employed context encoders to generate plausible features for the area requiring restoration. Yu et al. [65] introduced a contextual attention module to refine by referencing the surrounding features. Song et al. [51] used a patch-swap layer that replaces each patch within the masking areas of a feature map with the most comparable patch in the unoccluded areas. Liu et al. [28] developed a coherent semantic attention layer to ensure semantic relevance between the swapped features.", + "bbox": [ + 75, + 612, + 468, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In recent years, transformer-based methods have also significantly contributed to computer vision. The ViT [11] achieves better results for image recognition than CNN-based methods. Furthermore, MAE [17] demonstrated that transformer-based models are well-suited for image inpainting tasks. However, transformer-based algorithms have a limitation in that they may produce blurry results when restoring large block areas [17]. Another work [25]", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "presents MAT, a transformer-based model for large-hole inpainting. Nevertheless, in cases where the eyes or mouth are fully occluded, the ViT cannot generate images in detail because it is significantly less biased toward local textures [34]. Therefore, the challenge remains.", + "bbox": [ + 496, + 349, + 892, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed method", + "text_level": 1, + "bbox": [ + 498, + 436, + 671, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 2, we propose multi-stage approach to address OFER, involving detecting, masking, and reconstructing occlusions to recognize facial expressions. The proposed approach enhances recognition accuracy through cooperative learning ViT-latent vectors extracted from the image reconstruction process and the existing CNN features. We divided the facial image into patches, classified each patch as occluded or unoccluded, and reconstructed the occluded patches to be deoccluded. Subsequently, we leveraged the reconstructed image and expression-relevant latent vectors to predict facial expressions.", + "bbox": [ + 496, + 460, + 892, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Occlusion detection module: ViT-SVDD", + "text_level": 1, + "bbox": [ + 498, + 635, + 843, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "General object detection and segmentation models may not be suitable for real-world scenarios because they may be unable to detect unseen objects. To address this limitation, we use one-class classification, which is often employed in anomaly detection. This approach makes it possible to classify unused occlusion during training through self-supervised learning, which only uses unoccluded patches for learning, providing a more effective solution for real-world applications.", + "bbox": [ + 496, + 659, + 890, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "One-class classification methods for classifying normal or abnormal can operate at various levels of granularity, ranging from low-level anomaly detection [47] at the pixel level to high-level anomaly detection [40] at the image level. Detection and classification are performed based on the size of the unit, which can be customized to suit the user's needs. We used a ViT-based reconstruction method;", + "bbox": [ + 496, + 795, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1538", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "thus, we propose a middle-level anomaly detector specifically optimized for ViT. We divided the image to match the size of the ViT patch and created ViT-latent vectors. These patches are encoded with informative features to produce ViT-latent vectors. To generate the smallest feature space for unoccluded patches, we used the deep SVDD algorithm [39]. One-class deep SVDD employs quadratic loss to penalize the distance of every network representation. This objective is defined as", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\| \\Phi (x _ {i}; \\mathcal {W}) - c \\| ^ {2} + \\frac {\\lambda}{2} \\sum_ {l = 1} ^ {L} \\| w ^ {l} \\| _ {F} ^ {2}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 227, + 468, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $n$ denotes number of training data, $L$ denote number of layer, $\\mathcal{W}$ denotes set of weights $\\mathcal{W} = \\{w^1, \\dots, w^L\\}$ and $c$ represents a hypersphere characterized by the center. The first term induces the features of all normal images to converge at the center point $c$ , whereas the last term is a weight decay regularizer on the network parameter $W$ with hyperparameter $\\lambda > 0$ , where $\\| \\cdot \\|_F$ denotes the Frobenius norm. Eq (1) simply employs a quadratic loss for penalizing the distance of every network representation $\\Phi(x_i; \\mathcal{W})$ to $c \\in \\mathcal{F}$ , Where $\\mathcal{F}$ is output feature space. The network learn parameters $\\mathcal{W}$ such that data points are closely mapped to $c$ of the hypersphere. To determine whether a patch is occluded, we calculated the distance between the new input information and the center $c$ of the feature space for each patch. If the distance exceeds the pre-defined radius, the corresponding patch is classified as occluded and masked. The optimal value of the radius is automatically determined in the SVDD procedure. Through this process, occlusion patch detection is possible for unseen objects. The proposed ViT-SVDD approach allows for validating the performance of synthetic images with occlusion patch annotations. By detecting occlusion patches, we can improve the accuracy of the reconstruction method and make it more suitable for real-world applications.", + "bbox": [ + 75, + 271, + 472, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Image reconstruction module: hybrid reconstruction network", + "text_level": 1, + "bbox": [ + 76, + 645, + 468, + 675 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The facial image reconstruction process employs an occlusion-masked image generated by the occlusion detector. The hybrid reconstruction network is designed to cooperate by fusing ViT-based and CNN-based networks. Through this mechanism, we leverage both the strengths of ViT and CNN. The ViT-based method employs $16 \\times 16$ patches as input image; however, we used the outputs of the occlusion detector as input because the image has already been partitioned into patch units by the occlusion detector.", + "bbox": [ + 75, + 684, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Network structure", + "text_level": 1, + "bbox": [ + 76, + 830, + 261, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The ViT-based approach encodes the input patches and positively embeds all tokens. The occluded patch reconstruction is achieved through correlation with other patches.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e15a46d6198aa4dc7abd7a8bf76a973c1c1e9708eb0a28697a3174adb9145035.jpg", + "image_caption": [ + "Figure 3. Illustration of the self-assembly operation. (a) Feature map in the self-assembly layer. (b) Flip of (a). The patch in masked region is generated by combining three patch information." + ], + "image_footnote": [], + "bbox": [ + 540, + 69, + 854, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The ViT has low inductive bias and a high degree of freedom [34], enabling it to generate credible images despite diverse occlusion shapes, positions, and facial poses. As discussed in Section 2.3, the ViT-based approach may sometimes not supply detailed results. To address this limitation, we combined the ViT and CNN. The network consists of a U-Net architecture. Additionally, we added a self-assembly layer inside the encoder to generate a detailed representation. This multi structure approach effectively combines the strengths of the ViT and CNN-based networks to generate high-quality facial image reconstructions that represent facial expressions well.", + "bbox": [ + 498, + 262, + 890, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Self-assembly layer", + "text_level": 1, + "bbox": [ + 500, + 449, + 689, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We implemented a self-assembly layer to improve image reconstruction for FER. We reconstructed masked regions like [17] but made enhancements specific to facial images. Based on the concept that the left and right characteristics of a person's face are symmetrical[42, 48, 67], we used the feature information present in the corresponding location of the horizontally flipped image when reconstructing a masked region. We expanded the range of candidate patches used in the generation process by incorporating information from three sources, the previously generated patch, the most similar patch in the unmasked region, and patches located in the corresponding position of the horizontally flipped image. In this process, the masked region contains the reconstruction results with the ViT network. We assigned weights to each based on the similarity value with the current patch. The weight calculation is based on a cross-correlation metric:", + "bbox": [ + 498, + 472, + 890, + 714 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS (p, p _ {x}) = \\frac {\\langle p , p _ {x} \\rangle}{\\| p \\| \\cdot \\| p _ {x} \\|}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 723, + 890, + 757 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p$ represents a patch in the masked region, and the patch $p_x$ is the comparison target. The similarity value between $p$ and $p_x$ is denoted by $S$ .", + "bbox": [ + 498, + 763, + 890, + 810 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The self-assembly operation is defined in Eq (3), which generates a patch value $p_i$ . Figure 3 depicts the operation process, where $p_s$ denotes the patch value symmetrically positioned with respect to $p$ and averaged by considering the peripheral patches. The $S_{sym}$ is calculated as Eq (2) through $p_i$ and $p_{s_i}$ . In addition, $p_k$ is the most similar patch", + "bbox": [ + 498, + 810, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1539", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to $p$ among the unmasked region, and $S_{\\text{known}}$ is calculated as $S(p_i, p_{k_i})$ . Further, $p_{i-1}$ represents the previously generated patch, and $S_{i-1}$ is obtained by $S(p_i, p_{i-1})$ . The similarity value $S$ is normalized to be used as the weight.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Figure 3, the red patch in (a) is $p_i$ , which is a combined result of $p_k$ (the orange patch), $p_{i-1}$ (the yellow patch), and $p_s$ (the blue patch in (b)). Because $p_1$ has no prior generated patch, $S_0$ is zero. In certain cases, such as side-face images, the patches in symmetrical positions may not be relevant for generating the patch. Thus, the value of $S_{sym}$ in this situation is minimal and is rarely used to generate the patch.", + "bbox": [ + 75, + 151, + 470, + 257 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p _ {i} = \\frac {S _ {s y m}}{S _ {s y m} + S _ {k n o w n} + S _ {i - 1}} \\times p _ {s _ {i}} \\\\ + \\frac {S _ {\\text {k n o w n}}}{S _ {\\text {s y m}} + S _ {\\text {k n o w n}} + S _ {i - 1}} \\times p _ {k _ {i}}. \\tag {3} \\\\ + \\frac {S _ {i - 1}}{S _ {s y m} + S _ {k n o w n} + S _ {i - 1}} \\times p _ {i - 1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 277, + 468, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.3 Objective", + "text_level": 1, + "bbox": [ + 76, + 396, + 197, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The aim of image reconstruction is to fill in the masked portion to provide supplementary information for FER. In pursuit of this, we incorporated a semantic consistency loss that enables optimizing the task while maintaining the reconstruction loss $L_{re}$ , consistency $L_{c}$ [28], feature patch discriminator $L_{d_f}$ [19], and patch discriminator $L_{d}$ [36].", + "bbox": [ + 75, + 420, + 468, + 511 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The semantic consistency loss $L_{sc}$ emphasizes facial expression attributes. The $L_{sc}$ has the effect of reducing intraclass variability and can be defined as:", + "bbox": [ + 75, + 511, + 468, + 555 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s c} = \\sum_ {c = 1} ^ {7} p _ {c} \\left(z _ {g t}\\right) \\log \\left(p _ {c} \\left(z _ {r e c}\\right)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 556, + 468, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $c$ represents seven basic expressions, $p_c(z_{gt})$ denotes the predicted probability of $c$ in the ground-truth image, and $p_c(z_{rec})$ indicates the predicted probability of $c$ in the reconstruction result. The predicted probability distributions are obtained via the pretrained FER network. During training, the overall loss function is defined as:", + "bbox": [ + 75, + 603, + 468, + 693 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = \\lambda_ {r e} L _ {r e} + \\lambda_ {c} L _ {c} + \\lambda_ {s c} L _ {s c} + \\lambda_ {d} \\left(L _ {d} + L _ {d _ {f}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 705, + 468, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{re},\\lambda_{c},\\lambda_{sc},\\lambda_{d}$ denote the trade-off parameters for the reconstruction, consistency, semantic consistency, discriminator losses, respectively. Furthermore, the FER network is trained with the same feature extraction architecture using probability distributions about the ground-truth label and prediction of FER.", + "bbox": [ + 75, + 732, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Facial expression recognition network", + "text_level": 1, + "bbox": [ + 76, + 832, + 403, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed FER network is designed as an attention-based model for predicting facial expressions. We employed spatial and channel-attention mechanisms [59].", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4b750f4a56a6c628cefd3fcbcc8d4747d6c4a57f60bf9c2e83a932a192b6ac54.jpg", + "image_caption": [ + "Figure 4. Expression-relevant vision transformer (ViT)-latent vector extraction method." + ], + "image_footnote": [], + "bbox": [ + 500, + 89, + 888, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We obtained the refined feature map and CAM using the attention-based model. In addition, we obtained the expression-relevant latent vectors from the ViT using the CAM. As depicted in Figure 2, the Latent-OFER cooperatively uses a CNN-based feature and ViT-based latent vectors. Thus, the model performs better.", + "bbox": [ + 496, + 357, + 890, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Expression-relevant ViT-latent vectors. The proposed method employs only expression-relevant latent vectors rather than the entire latent space to improve FER performance. During the reconstruction process, ViT-based latent vectors are extracted by embedding the input image. We used a CAM to identify spatially significant areas within the image for FER, and the class activation map is generated through a CNN.", + "bbox": [ + 496, + 449, + 890, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The position of the area is stored as a key, and the attention weight for each space is recorded. The key of the region where the weight of the spatial attention exceeds the top $50\\%$ is used. This key is retrieved from the entire ViT-latent vectors, and the corresponding value is read. The activation map is used to identify expression-relevant latent vectors, as presented in Figure 4. This process enables the selection of positions that are relevant to FER while avoiding extraneous details, such as appearance information irrelevant to expressions, which can increase inter-class dissimilarity and lead to more accurate and effective learning results.", + "bbox": [ + 496, + 571, + 890, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In cases where patch detection fails, the occluded patch's latent vectors are used for training and inference. However, spatial attention is not focused on the occluded area, and the latent vector of the occlusion patch is neither searched nor used for training and inference. The proposed extractor is not significantly affected in this situation.", + "bbox": [ + 496, + 739, + 890, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 844, + 632, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this part, we describe three FER benchmark datasets and several occluded FER datasets used to evaluate this", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1540", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0aef81f360a17b0ef13206eed6593eb208903499ec6702c3b6080fd8f49e4a34.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Accuracy (%)Precision (%)Recall (%)
One class SVM [39]91.190.289.4
Patch-SVDD [64]85.280.194.1
ViT-SVDD98.394.198.7
", + "bbox": [ + 99, + 88, + 446, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Comparison of occlusion patch detection performance.", + "bbox": [ + 80, + 138, + 452, + 152 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fa6926fe9939294850e591e2d75ac4684f0e7246cd9dd68065f045c301344546.jpg", + "image_caption": [ + "Figure 5. Occlusion patch classification results." + ], + "image_footnote": [], + "bbox": [ + 99, + 161, + 449, + 241 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "model and explain the results. We demonstrate that the proposed method performs better on both the FER task and occluded FER task. Last, an ablation study demonstrates how each model element contributes to the final performance.", + "bbox": [ + 76, + 271, + 468, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 76, + 344, + 171, + 358 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RAF-DB [24] is a large-scale facial expression database with around 30,000 images. We used data on seven basic expressions, 12,271 images as the training set, and 3,068 images as the testing set.", + "bbox": [ + 76, + 371, + 468, + 433 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "AffectNet [33] is the largest facial expression database with annotations. We used seven basic expressions facial images, about 287,568 training and 3,500 testing images.", + "bbox": [ + 76, + 434, + 468, + 481 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "KDEF [4] is a set of 4,900 images of facial expressions. Each expression is viewed from five viewpoints.", + "bbox": [ + 76, + 483, + 467, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Syn-AffectNet and Syn-RAF-DB consist of FER benchmark datasets that synthesize a real object to occlude.", + "bbox": [ + 76, + 516, + 468, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Occlusion-AffectNet and Occlusion-RAF-DB are real-world occlusion datasets selected from the AffectNet validation set and RAF-DB testing set by Wang et al. [53].", + "bbox": [ + 76, + 549, + 468, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FED-RO dataset is also a real-world occlusion dataset collected by Li et al. [26]. It contains 400 images labeled with seven basic emotions. We trained the proposed model using RAF-DB and AffectNet when testing the FED-RO datasets, following the protocol suggested in [26].", + "bbox": [ + 76, + 598, + 468, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 691, + 290, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We trained a self-supervised occlusion detection module with the KDEF dataset [4] synthesized by randomly copy-pasting objects such as hands and cups for occlusion. We used a ViT-based network pretrained with ImageNet [6] and a CNN-based network trained on several FER training datasets [24, 33] for detailed representation in the image reconstruction module. The FER network uses ResNet-18 [18] backbone architecture. It is pretrained on MS-Celeb-1M [16]. The trade-off parameters in hybrid reconstruction module are set as $\\lambda_{re} = 1$ , $\\lambda_c = 0.01$ , $\\lambda_{sc} = 1$ , $\\lambda_d = 0.002$ . The experimental source code is implemented with PyTorch, and the models are trained with a GTX-3090 GPU.", + "bbox": [ + 76, + 719, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6e8a401e819ab056cc57f52a5055003fa9020d7c56e48b4009b83cd0cb37b22d.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison of synthesis and real occlusion. Facial expression recognition prediction results according to image reconstruction. Labels highlighted in green indicate matching the correct expression, whereas red indicates a misprediction." + ], + "image_footnote": [], + "bbox": [ + 526, + 90, + 867, + 228 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison of occlusion detection module", + "text_level": 1, + "bbox": [ + 500, + 306, + 859, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proposed ViT-SVDD detects occlusion for each patch using a suitable detector for ViT-based image reconstruction. We compared the module with existing one-class classification methods trained solely on unoccluded images to evaluate its effectiveness. We used a test set consisting of occluded and unoccluded images.", + "bbox": [ + 496, + 330, + 890, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Patch-SVDD, which trains in a hierarchical structure from small pixels to large pixels and segments anomaly positions into small pixel units, was also included in the comparison. The proposed module achieved the highest occlusion detection accuracy among all methods, as demonstrated in Table 1.", + "bbox": [ + 496, + 422, + 890, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on these results, the proposed method is particularly well-suited for the patch-by-patch processing rather than being the optimal solution for all anomaly detection tasks. While several proposed anomaly detection methods are suitable for various units, such as whole images and pixels, this approach is specifically designed to fit the ViTSVDD framework and detect anomalies in a patch-specific manner. As illustrated in Figure 5, the results demonstrate improved performance in patch-specific occlusion detection, indicating that the proposed method is best suited for special situations that require this processing type.", + "bbox": [ + 496, + 515, + 890, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Comparison of reconstruction module", + "text_level": 1, + "bbox": [ + 500, + 694, + 826, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The hybrid reconstruction network is compared to MAE [17] and CSA [28]. All reconstruction results are the direct output of the model without post processing. Figure 6 compares the results of deocclusion for synthesis and real occlusion on RAF-DB and AffectNet. As displayed in Figure 6 and Table 2, we present qualitative and quantitative comparisons and the FER result. The self-assembly layer enlarge the facial expression information and increase the number of patch candidates involved in the generation process to reconstruct visually pleasing and natural, and semantic consistency loss induces rich in expression of facial images, providing an advantage for FER. While other com", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1541", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b32812f1a474116b26f19e974bff4f6a097e988f88b12a4c3cea014e299f9fbd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MAE [17]CSA [28]Self-assembly
Accuracy (%)72.675.677.3
", + "bbox": [ + 114, + 88, + 424, + 114 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5065cafd4a27c031164ffdfee7c894e6ab296d905eae43235d78bb5b54c43bcd.jpg", + "table_caption": [ + "Table 2. Facial expression recognition prediction results according to image reconstruction on Syn-RAF-DB." + ], + "table_footnote": [], + "table_body": "
InputMAECSASelf-assemblyGround truth
SurpriseSurpriseSurpriseHappinessHappiness
SurpriseFearDisgustSadnessAnger
", + "bbox": [ + 117, + 148, + 426, + 258 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e4991f7797f98ac58eb8dd3658bb5676ed878798bb81e43f17920f0389efd5b4.jpg", + "table_caption": [ + "Figure 7. Comparison of reconstruction results and the results of each expression probability." + ], + "table_footnote": [], + "table_body": "
MethodAffect NetSyn-Affect NetRAF DBSyn-RAF DBKDEFSyn-KDEF
DACL [15]62.549.688.876.087.968.9
RUL [68]62.652.288.977.183.151.2
DAN [58]63.851.189.776.186.870.8
EAC [69]63.254.988.078.687.567.6
Latent -OFER63.956.189.680.188.386.7
", + "bbox": [ + 114, + 300, + 424, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "parative models generate reasonable content, the proposed approach offers a superior representation of FER.", + "bbox": [ + 76, + 441, + 467, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As presented in Figure 7, the first row shows a partially masked facial image, ground truth image, the corresponding reconstruction results of MAE, CSA and self-assembly. The second row is depicted for better visibility of the influence on FER. The proposed method displays the highest probability of a ground truth label.", + "bbox": [ + 76, + 473, + 467, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Comparison of FER accuracy in occlusion", + "text_level": 1, + "bbox": [ + 76, + 574, + 434, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with Typical FER-model. As listed in Table 3, we compared the proposed model with several state-of-the-art methods for FER on the AffectNet (C7), RAF-DB, and KDEF datasets, all available as open source. We conducted experiments by separately testing these models with synthesized occlusion images and the original dataset for each dataset. In the field of FER, recent models [15, 58, 68, 69, 41, 22] demonstrated satisfactory performance on the original dataset. However, they fail to achieve acceptable accuracy on occluded datasets. In contrast, the proposed model was designed to be robust to occlusion and outperformed other models in terms of accuracy on occluded images. Moreover, the proposed model also achieved nearly the best performance on the original images compared to typical models.", + "bbox": [ + 75, + 598, + 467, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with the OFER-model. We compared the performance of the proposed FER model targeting occlusion with other state-of-the-art models using FED-RO. As the code for other models is unavailable, we used the reported accuracy from the respective papers. Table 4 reveals", + "bbox": [ + 75, + 825, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/08348f89eac0eb4a6530ba3320a6bf465859e417cc2979c2529a2ab2669432f2.jpg", + "table_caption": [ + "Table 3. Accuracy (%) comparison to the state-of-the-art results on the various facial expression recognition datasets." + ], + "table_footnote": [], + "table_body": "
gACNN [26]Pan's [35]Xia's [61]RAN [55]OADN [9]Wang's [53]Latent -OFER
FED-RO66.569.370.568.068.170.071.8
", + "bbox": [ + 540, + 88, + 848, + 118 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/abbb9bb6330206cb2a15229710d36ed1d8b146193d47d6b7ee0956537855ae4d.jpg", + "table_caption": [ + "Table 4. Accuracy (%) comparison to the state-of-the-art results on the FED-RO dataset." + ], + "table_footnote": [], + "table_body": "
BoostGAN [12]RAN [55]OADN [9]Latent -OFER
Occlusion-AffectNet43.458.564.066.1
", + "bbox": [ + 537, + 147, + 846, + 181 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9436548407e33b2a324d400b2f17914d18fc97e1363dbcfb55663e72416d8ed9.jpg", + "table_caption": [ + "Table 5. Accuracy (\\%) comparison to the state-of-the-art results on the occlusion-AffectNet dataset." + ], + "table_footnote": [], + "table_body": "
BoostGAN [12]RAN [55]Wang's [53]Latent -OFER
Occlusion-RAF-DB55.482.782.584.2
", + "bbox": [ + 537, + 223, + 846, + 257 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/86ee1110cc547b6e2c898d0947ff1d15a3e4c273efc4e32b9794eeeb519cead3.jpg", + "table_caption": [ + "Table 6. Accuracy $(\\%)$ comparison to the state-of-the-art results on the occlusion-RAF-DB dataset." + ], + "table_footnote": [], + "table_body": "
MethodAccuracyComplexity
AffectNetRAF-DBFlops(G)Parameters(M)
gACNN [26]58.885.1331370
WGAN AE [30]59.783.5353400
Pan's [35]57.180.2525
Xia's [61]57.582.7230360
RAN [55]52.686.9390300
OADN [9]61.987.2122250
Wang's [53]60.286.0102210
Latent-OFER63.989.6156373
", + "bbox": [ + 508, + 299, + 880, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7. Accuracy (%) and complexity comparison to the occluded FER models on the typical FER datasets", + "bbox": [ + 500, + 411, + 890, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that the proposed model achieved an accuracy of $71.8\\%$ with the default setting, a new state-of-the-art performance for this dataset, to the best of our knowledge.", + "bbox": [ + 500, + 446, + 890, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tables 5 and 6 present the FER performance for occluded images in AffectNet and RAF-DB, where the proposed Latent-OFER model achieved an accuracy of $66.5\\%$ and $84.2\\%$ with the default setting $(2.5\\% p$ and $1.5\\% p$ better than OADN [9] and RAN [55]), respectively.", + "bbox": [ + 496, + 492, + 890, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 7 compares the accuracy and complexity of the OFER models. The complexity is estimated by ourselves. As demonstrated in Table 7, OFER models exhibit poor performance on typical FER datasets. This limitation makes them unsuitable for general use unless the unoccluded image network-assisted approach described in Section 1 is employed. In contrast, the proposed model demonstrates acceptable performance on typical and occluded FER datasets. Specifically, the proposed model achieves accuracy rates of $63.9\\%$ and $89.6\\%$ , which represent improvements of $2.0\\% p$ and $2.4\\% p$ , respectively, over OADN.", + "bbox": [ + 496, + 569, + 890, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 753, + 648, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This section presents the experiments investigating the effects of several modules on FER performance", + "bbox": [ + 500, + 779, + 888, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of self-assembly layer. We use RAF-DB test dataset and synthesize irregular masks [27] for each image to make comparison. We replaced the self-assembly layer with a conventional $3 \\times 3$ layer and the CSA layer [28]. As presented in Table 8, we used standard evaluation metrics, the PSNR [56] and SSIM [56], to quantify the module per", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1542", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/22e0a5ac66f2d7fa7365970bbdf5427ecb1157928a385ef100846fd095f3ef55.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPSNR(↑)SSIM(↑)
Conventional26.360.868
CSA25.480.860
Self-assembly26.650.880
", + "bbox": [ + 168, + 88, + 379, + 133 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b81cc1066dfe2afa2107a94a5a1b44c50d613446170478dd3ebd52b55f80de06.jpg", + "image_caption": [ + "Figure 8. Effect of the self-assembly layer. Conventional and CSA [28] are results of the proposed module which replaces the self-assembly layer with the conventional and CSA layers respectively." + ], + "image_footnote": [], + "bbox": [ + 106, + 172, + 439, + 232 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fc3ced8b0cf236e8d0f3c91482c6958583bd107b2745bcc127859ec0f71c5401.jpg", + "table_caption": [ + "Table 8. Quantitative comparisons results between conventional, CSA [28], and self-assembly." + ], + "table_footnote": [], + "table_body": "
MAE [17]CSA [28]Hybrid reconstruction
Reconstructed-RAF-DB72.671.677.3
", + "bbox": [ + 114, + 292, + 428, + 327 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance. Moreover, as illustrated in Figure 8, the mask part fails to reconstruct reasonable content when we used conventional $3 \\times 3$ layer. Although the CSA [28] can improve the performance compared to conventional. Table 9 reveals that the reconstruction results of CSA inpainting still lack facial expression attributes. Table 9 shows the average accuracy of facial expression prediction with images regenerated by MAE, CSA, and hybrid reconstruction network. For fair comparison, the same expression recognition network and the same partially masked test set were used. Compared with them, the proposed method performs better. The effect of semantic consistency loss is included in the Supplementary Material.", + "bbox": [ + 75, + 376, + 468, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of occlusion detection and reconstruction module. We demonstrated the effectiveness of the deocclusive auto-encoder with occluded KDEF images created through synthesis. As presented in Table 10, image reconstruction is not performed when the occlusion detector is not used, leading to low FER performance. However, even without the proposed module, the proposed model performed well compared to typical models.", + "bbox": [ + 75, + 577, + 467, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of latent vectors and expression-relevant feature extractor. As shown Table 10, this study evaluates the efficiency of the deocclusive autoencoder and expression-related feature extractor in FER. The results reveal that using only the ViT-latent vector extracted from occluded data results in poor performance. Although using only CNN features improved the performance, it remained unacceptable. However, training with the ViT-latent vectors and CNN features improves performance by about $4.0\\% p$ compared to only CNN features. Additionally, performance improves by $8.2\\% p$ when images are deoccluded via a hybrid reconstruction network. These results indicate that all proposed modules contribute to performance improvement,", + "bbox": [ + 75, + 704, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/26b5ec749cf4ebac0367d618d9b1cc78035d9f2ced8df61c3f4c426c36ad03aa.jpg", + "table_caption": [ + "Table 9. Accuracy $(\\%)$ comparison of FER using irregular masked facial image reconstruction results by MAE, CSA, Hybrid reconstruction network." + ], + "table_footnote": [], + "table_body": "
Image recon-stuctionCNN-featuresFull ViT-latent vectorsExtracted ViT-latent vectorsAccuracy (%)
✓15.2
✓20.1
✓75.4
✓✓76.5
✓✓78.5
✓✓64.9
✓✓66.4
✓✓82.7
✓✓✓84.2
✓✓✓86.7
", + "bbox": [ + 537, + 88, + 851, + 237 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 10. Module evaluation in Latent-OFER on Syn-KDEF.", + "bbox": [ + 498, + 238, + 862, + 252 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and the best performance is achieved when CNN features and expression-relevant ViT-latent vectors are trained cooperatively.", + "bbox": [ + 498, + 257, + 890, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 500, + 308, + 612, + 323 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This section discusses two topics. First, the performance of the occluded patch detector can be considered dominant. The proposed model restores images and extracts latent vectors to use for FER. In cases where occlusion patch detection fails to perform adequately, latent vectors are not extracted correctly because the image is not fully restored. However, the model uses spatial attention to extract expression-relevant features. In images with poor occlusion patch detection, the corresponding patch has lower weights. As a result, the influence of poor detection on the overall performance is mitigated. The second is the potential limitations of scalability when using image reconstruction modules trained with a single dataset. These models may not be adaptable enough to handle a variety of datasets, thereby making it difficult to reconstruct a complete image. To overcome this challenge, extra training on diverse datasets or the adoption of uniform alignment across datasets is necessary. Therefore, to enhance the flexibility of image reconstruction modules, a multi-dataset training approach or standardized alignment methods can be implemented.", + "bbox": [ + 496, + 333, + 890, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 642, + 617, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper addresses FER in real-world occlusion. Our method involves detecting the occluded parts of the face and then reconstructing them using a specially designed reconstruction network to produce images as if they were unoccluded. In addition, expression-relevant latent vectors were extracted and learned cooperatively with the CNN features. The proposed Latent-OFER model works well under occluded and unoccluded conditions. We evaluate this method on occluded FER datasets and typical FER datasets, and the proposed method achieves state-of-the-art accuracy.", + "bbox": [ + 496, + 667, + 890, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This work was supported by the Industrial Fundamental Technology Development Program (No. 20018699) funded by MOTIE of Korea and IITP grant funded by the Korea government (MSIT; No.2021-0-02068, RS-2023-00256629).", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1543", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mouath Aouayeb, Wassim Hamidouche, Catherine Soladie, Kidiyo Kpalma, and Renaud Seguier. 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In Proceedings of the AAAI conference on artificial intelligence, pages 3510-3519, 2021." + ], + "bbox": [ + 501, + 92, + 890, + 387 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1546", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Latent-OFER_ Detect, Mask, and Reconstruct with Latent Vectors for Occluded Facial Expression Recognition/b49e72cb-c8b1-4c66-830a-4cce4a977773_model.json b/2023/Latent-OFER_ Detect, Mask, and Reconstruct with Latent Vectors for Occluded Facial Expression Recognition/b49e72cb-c8b1-4c66-830a-4cce4a977773_model.json new file mode 100644 index 0000000000000000000000000000000000000000..be0ef30ac931af1a622ac0102f4d8b4879bab679 --- /dev/null +++ b/2023/Latent-OFER_ Detect, Mask, and Reconstruct with Latent Vectors for Occluded Facial Expression Recognition/b49e72cb-c8b1-4c66-830a-4cce4a977773_model.json @@ -0,0 +1,2565 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.13, + 0.89, + 0.178 + ], + "angle": 0, + "content": "Latent-OFER: Detect, Mask, and Reconstruct with Latent Vectors for Occluded Facial Expression Recognition" + }, + { + "type": "text", + "bbox": [ + 0.332, + 0.204, + 0.644, + 0.222 + ], + "angle": 0, + "content": "Isack Lee, Eungi Lee, Seok Bong Yoo*" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.222, + 0.877, + 0.241 + ], + "angle": 0, + "content": "Department of Artificial Intelligence Convergence, Chonnam National University, Gwangju, Korea" + }, + { + "type": "text", + "bbox": [ + 0.331, + 0.242, + 0.641, + 0.258 + ], + "angle": 0, + "content": "{sackda24，181061，sbyoo}@jnu.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.324, + 0.474, + 0.764 + ], + "angle": 0, + "content": "Most research on facial expression recognition (FER) is conducted in highly controlled environments, but its performance is often unacceptable when applied to real-world situations. This is because when unexpected objects occlude the face, the FER network faces difficulties extracting facial features and accurately predicting facial expressions. Therefore, occluded FER (OFER) is a challenging problem. Previous studies on occlusion-aware FER have typically required fully annotated facial images for training. However, collecting facial images with various occlusions and expression annotations is time-consuming and expensive. Latent-OFER, the proposed method, can detect occlusions, restore occluded parts of the face as if they were unoccluded, and recognize them, improving FER accuracy. This approach involves three steps: First, the vision transformer (ViT)-based occlusion patch detector masks the occluded position by training only latent vectors from the unoccluded patches using the support vector data description algorithm. Second, the hybrid reconstruction network generates the masking position as a complete image using the ViT and convolutional neural network (CNN). Last, the expression-relevant latent vector extractor retrieves and uses expression-related information from all latent vectors by applying a CNN-based class activation map. This mechanism has a significant advantage in preventing performance degradation from occlusion by unseen objects. The experimental results on several databases demonstrate the superiority of the proposed method over state-of-the-art methods. This code is available at https://github.com/leeisack/Latent-OFER." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.791, + 0.21, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.817, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Facial expression recognition (FER) has undergone remarkable advancements in recent years and is now widely used across various industries. However, the ability of FER models in the presence of occlusion remains a challenge." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.291, + 0.859, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.469, + 0.895, + 0.498 + ], + "angle": 0, + "content": "Figure 1. Facial expression recognition (FER) performance on RAF-DB according to the occluded proportions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.895, + 0.715 + ], + "angle": 0, + "content": "Figure 1 illustrates the accuracy of the previous state-of-the-art model for FER [58] for various occlusion proportions. In this study, we evaluated the robustness of the typical model in recognizing facial expressions using two types of occlusions: random sampling occlusion and grad occlusion. Random sampling occlusion divides the entire image into 196 patches and randomly masks them according to the proportion. Grad occlusion processes an image with an intentionally occluded area that affects FER using gradient-weighted class activation mapping (Grad-CAM) [46]. This study reveals a more substantial decrease in performance with the second type of occlusion, particularly when the occluded area is crucial for accurate FER. This finding has been objectively measured using Grad-CAM [46]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.895, + 0.824 + ], + "angle": 0, + "content": "Previous studies on FER [1, 2, 3, 5, 7, 13, 14, 15, 21, 23, 29, 31, 38, 43, 44, 49, 50, 54, 57, 60, 62, 63, 68, 69, 70] have not given adequate attention to the influence of occlusions. However, addressing this challenge is crucial for enhancing the practical applications of FER in real-world scenarios. Although research on occluded FER (OFER) is relatively scarce, its importance is increasingly recognized [66]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Currently, several approaches address OFER. The occlusion-robust feature extraction approach [9, 53] aims to identify an occlusion-insensitive and discriminative representation, but it is challenging because the types and locations of occlusion are often unknown. The sub region anal" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.517, + 0.957 + ], + "angle": 0, + "content": "1536" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.257 + ], + "angle": 0, + "content": "ysis approach [26, 55] divides regions based on facial landmarks and uses attention mechanisms to focus on crucial areas. However, the inability to detect facial landmarks due to occlusions can lead to errors in the FER process. The unoccluded image network assist approach [35, 61] uses two distinct networks: one trained on unoccluded images and the other trained on occluded images. This approach leverages unoccluded images as privileged information to assist in expression recognition in the presence of occlusion. It is unsuitable in real-world situations because it cannot differentiate between occluded and unoccluded images." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.262, + 0.468, + 0.683 + ], + "angle": 0, + "content": "Hence, the proposed approach is the occlusion recovery-based approach, which aims to transform occluded images into complete images through a deocclusion process. We propose the deocclusive autoencoder for reconstructing facial images. The deocclusive autoencoder can be functionally divided into an occlusion detector and reconstruction module. The occlusion detector uses the vision transformer (ViT) support vector data description (SVDD) for the reconstruction module. This approach enables the model to detect occlusion caused by unseen objects, an essential step in accurately generating deoccluded facial images. The reconstruction network consists of the ViT structure and convolutional neural network (CNN) structure for facial image reconstruction. We leverage the strengths of the ViT in generating realistic facial images despite varying poses and further refine them using the CNN. We call it the hybrid reconstruction network. The hybrid reconstruction network enhances FER performance by generating deoccluded images that express detailed and vivid facial expression attributes. This enhancement is achieved by incorporating a self-assembly layer and semantic consistency loss. In contrast, previous work on image reconstruction has primarily focused on achieving naturalness, which can result in dull facial expressions. Additionally, we use informative ViT-latent vectors obtained from the reconstruction process. We combine the CNN features and ViT-latent vectors for enhanced facial expression predictions. The main contributions in this work are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.69, + 0.468, + 0.779 + ], + "angle": 0, + "content": "- We propose an expression-relevant feature extractor that uses spatial attention to assign a higher weight to specific facial features, allowing us to identify critical positions for FER. We can retrieve expression-relevant latent vectors from the ViT-latent space to extract valuable information using these positions as critical values." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.781, + 0.468, + 0.87 + ], + "angle": 0, + "content": "- We propose ViT-SVDD, a patch-based occlusion detection module optimized for ViT-based networks. As a self-supervised local classifier, the ViT-SVDD module is trained only on latent vectors of unoccluded facial images. This method accurately classifies occlusions caused by unseen objects for subsequent reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.871, + 0.468, + 0.899 + ], + "angle": 0, + "content": "- We propose a hybrid reconstruction network that combines the strengths of the ViT and CNN architectures with" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.093, + 0.89, + 0.151 + ], + "angle": 0, + "content": "a self-assembly layer and semantic consistency loss to generate facial images naturalness and rich in expression. This approach enhances the quality of deoccluded images and improves the accuracy of FER in challenging conditions." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.168, + 0.64, + 0.183 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.193, + 0.741, + 0.208 + ], + "angle": 0, + "content": "2.1. Occluded Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.216, + 0.89, + 0.455 + ], + "angle": 0, + "content": "Several early studies [8] have attempted to detect occlusions in images for OFER tasks. The conventional methods provide location information about the occlusions and are called occlusion-aware methods [26, 55]. However, these methods are not practical for real-world scenarios. Another approach [30] is to train models using synthesized images with various occlusions to detect the occluded positions. Although this approach can determine occlusion positions, it requires a diverse set of object images, which can be challenging to obtain. Moreover, the performance of these models [26, 30, 55] degrades when they encounter unseen objects as input. We drew inspiration from anomaly detection tasks [10, 45, 47, 64] with one-class classification algorithms [20, 32, 39, 40, 52] and proposed a model that learns only from unoccluded datasets and can generalize well to unseen datasets." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.469, + 0.843, + 0.484 + ], + "angle": 0, + "content": "2.2. Occluded Facial Expression Recognition" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.493, + 0.89, + 0.597 + ], + "angle": 0, + "content": "We have no prior knowledge of where occlusions may appear on a facial image or how large or complex they might be. These occlusions can significantly reduce the accuracy of FER by either increasing the intra-class variability or inter-class similarity. Four categories address this issue: occlusion-robust feature extraction, subregion analysis, unoccluded image network-assisted, and occlusion recovery." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.599, + 0.89, + 0.673 + ], + "angle": 0, + "content": "Occlusion-robust feature extraction approach. This approach aims to extract features less affected by occlusions while maintaining discriminative capability. Wang et al. [53] used self-supervised and contrastive learning to explore robust representations with synthesized occlusions." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.675, + 0.89, + 0.763 + ], + "angle": 0, + "content": "Subregion analysis approach. This approach excludes the occluded parts from recognition. By focusing only on the unoccluded facial parts, the influence of occlusion on recognition performance can be reduced. Li et al. [26] proposed a gate unit with an attention mechanism that allows the model to focus on informative unoccluded facial areas." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.766, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Unoccluded image network-assisted approach. This approach employs unoccluded facial images as guidance to assist with OFER. Pan et al. [35] trained two deep neural networks from occluded and unoccluded facial images. Then, the unoccluded network guides the occluded network. Xia et al. [61] measured the complexity of unoccluded data using distribution density in a feature space. The classifier can be guided by unoccluded data and subsequently leverage more meaningful and discriminative samples." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1537" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.092, + 0.872, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.893, + 0.339 + ], + "angle": 0, + "content": "Figure 2. Framework of the Latent-OFER that creates a deoccluded image that erases the occlusion. In this process, the expression-relevant latent vectors are extracted by mapping the vision transformer (ViT)-latent vector and the convolutional neural network (CNN) class activation map. Latent-OFER predicts facial expressions that combine CNN-based features with specific VIT-based latent vectors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.473, + 0.576 + ], + "angle": 0, + "content": "Occlusion recovery-based approach. This approach uses face completion as a basis to deal with occlusion. To reconstruct occluded faces, Lu et al. [30] suggested using a WGAN consisting of an autoencoder-based generator and discriminators. By reconstructing the occlusion, these approaches provide necessary information while avoiding the interference of noisy information and obtaining informative appearance. Therefore, we adopt an image-inpainting technique as a recovery-based approach, to deal with occlusion. A notable point of differentiation between our method and existing approaches lies in our specific emphasis on the reconstruction of occluded regions while simultaneously retaining the facial expression information. Furthermore, we employ ViT-based latent vectors extracted throughout the reconstruction process to enhance the performance of FER." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.589, + 0.248, + 0.606 + ], + "angle": 0, + "content": "2.3. Image inpainting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.779 + ], + "angle": 0, + "content": "Several approaches based on CNN have been developed to generate semantically coherent content. Pathak et al. [37] employed context encoders to generate plausible features for the area requiring restoration. Yu et al. [65] introduced a contextual attention module to refine by referencing the surrounding features. Song et al. [51] used a patch-swap layer that replaces each patch within the masking areas of a feature map with the most comparable patch in the unoccluded areas. Liu et al. [28] developed a coherent semantic attention layer to ensure semantic relevance between the swapped features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In recent years, transformer-based methods have also significantly contributed to computer vision. The ViT [11] achieves better results for image recognition than CNN-based methods. Furthermore, MAE [17] demonstrated that transformer-based models are well-suited for image inpainting tasks. However, transformer-based algorithms have a limitation in that they may produce blurry results when restoring large block areas [17]. Another work [25]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.893, + 0.426 + ], + "angle": 0, + "content": "presents MAT, a transformer-based model for large-hole inpainting. Nevertheless, in cases where the eyes or mouth are fully occluded, the ViT cannot generate images in detail because it is significantly less biased toward local textures [34]. Therefore, the challenge remains." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.437, + 0.673, + 0.455 + ], + "angle": 0, + "content": "3. Proposed method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.893, + 0.63 + ], + "angle": 0, + "content": "As shown in Figure 2, we propose multi-stage approach to address OFER, involving detecting, masking, and reconstructing occlusions to recognize facial expressions. The proposed approach enhances recognition accuracy through cooperative learning ViT-latent vectors extracted from the image reconstruction process and the existing CNN features. We divided the facial image into patches, classified each patch as occluded or unoccluded, and reconstructed the occluded patches to be deoccluded. Subsequently, we leveraged the reconstructed image and expression-relevant latent vectors to predict facial expressions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.636, + 0.844, + 0.652 + ], + "angle": 0, + "content": "3.1. Occlusion detection module: ViT-SVDD" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.795 + ], + "angle": 0, + "content": "General object detection and segmentation models may not be suitable for real-world scenarios because they may be unable to detect unseen objects. To address this limitation, we use one-class classification, which is often employed in anomaly detection. This approach makes it possible to classify unused occlusion during training through self-supervised learning, which only uses unoccluded patches for learning, providing a more effective solution for real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.893, + 0.901 + ], + "angle": 0, + "content": "One-class classification methods for classifying normal or abnormal can operate at various levels of granularity, ranging from low-level anomaly detection [47] at the pixel level to high-level anomaly detection [40] at the image level. Detection and classification are performed based on the size of the unit, which can be customized to suit the user's needs. We used a ViT-based reconstruction method;" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1538" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "thus, we propose a middle-level anomaly detector specifically optimized for ViT. We divided the image to match the size of the ViT patch and created ViT-latent vectors. These patches are encoded with informative features to produce ViT-latent vectors. To generate the smallest feature space for unoccluded patches, we used the deep SVDD algorithm [39]. One-class deep SVDD employs quadratic loss to penalize the distance of every network representation. This objective is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.228, + 0.47, + 0.27 + ], + "angle": 0, + "content": "\\[\n\\min \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\| \\Phi (x _ {i}; \\mathcal {W}) - c \\| ^ {2} + \\frac {\\lambda}{2} \\sum_ {l = 1} ^ {L} \\| w ^ {l} \\| _ {F} ^ {2}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.473, + 0.635 + ], + "angle": 0, + "content": "where \\( n \\) denotes number of training data, \\( L \\) denote number of layer, \\( \\mathcal{W} \\) denotes set of weights \\( \\mathcal{W} = \\{w^1, \\dots, w^L\\} \\) and \\( c \\) represents a hypersphere characterized by the center. The first term induces the features of all normal images to converge at the center point \\( c \\), whereas the last term is a weight decay regularizer on the network parameter \\( W \\) with hyperparameter \\( \\lambda > 0 \\), where \\( \\| \\cdot \\|_F \\) denotes the Frobenius norm. Eq (1) simply employs a quadratic loss for penalizing the distance of every network representation \\( \\Phi(x_i; \\mathcal{W}) \\) to \\( c \\in \\mathcal{F} \\), Where \\( \\mathcal{F} \\) is output feature space. The network learn parameters \\( \\mathcal{W} \\) such that data points are closely mapped to \\( c \\) of the hypersphere. To determine whether a patch is occluded, we calculated the distance between the new input information and the center \\( c \\) of the feature space for each patch. If the distance exceeds the pre-defined radius, the corresponding patch is classified as occluded and masked. The optimal value of the radius is automatically determined in the SVDD procedure. Through this process, occlusion patch detection is possible for unseen objects. The proposed ViT-SVDD approach allows for validating the performance of synthetic images with occlusion patch annotations. By detecting occlusion patches, we can improve the accuracy of the reconstruction method and make it more suitable for real-world applications." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.646, + 0.47, + 0.676 + ], + "angle": 0, + "content": "3.2. Image reconstruction module: hybrid reconstruction network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.822 + ], + "angle": 0, + "content": "The facial image reconstruction process employs an occlusion-masked image generated by the occlusion detector. The hybrid reconstruction network is designed to cooperate by fusing ViT-based and CNN-based networks. Through this mechanism, we leverage both the strengths of ViT and CNN. The ViT-based method employs \\(16 \\times 16\\) patches as input image; however, we used the outputs of the occlusion detector as input because the image has already been partitioned into patch units by the occlusion detector." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.262, + 0.845 + ], + "angle": 0, + "content": "3.2.1 Network structure" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The ViT-based approach encodes the input patches and positively embeds all tokens. The occluded patch reconstruction is achieved through correlation with other patches." + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.07, + 0.856, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.21, + 0.892, + 0.253 + ], + "angle": 0, + "content": "Figure 3. Illustration of the self-assembly operation. (a) Feature map in the self-assembly layer. (b) Flip of (a). The patch in masked region is generated by combining three patch information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.263, + 0.892, + 0.445 + ], + "angle": 0, + "content": "The ViT has low inductive bias and a high degree of freedom [34], enabling it to generate credible images despite diverse occlusion shapes, positions, and facial poses. As discussed in Section 2.3, the ViT-based approach may sometimes not supply detailed results. To address this limitation, we combined the ViT and CNN. The network consists of a U-Net architecture. Additionally, we added a self-assembly layer inside the encoder to generate a detailed representation. This multi structure approach effectively combines the strengths of the ViT and CNN-based networks to generate high-quality facial image reconstructions that represent facial expressions well." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.691, + 0.465 + ], + "angle": 0, + "content": "3.2.2 Self-assembly layer" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.473, + 0.892, + 0.715 + ], + "angle": 0, + "content": "We implemented a self-assembly layer to improve image reconstruction for FER. We reconstructed masked regions like [17] but made enhancements specific to facial images. Based on the concept that the left and right characteristics of a person's face are symmetrical[42, 48, 67], we used the feature information present in the corresponding location of the horizontally flipped image when reconstructing a masked region. We expanded the range of candidate patches used in the generation process by incorporating information from three sources, the previously generated patch, the most similar patch in the unmasked region, and patches located in the corresponding position of the horizontally flipped image. In this process, the masked region contains the reconstruction results with the ViT network. We assigned weights to each based on the similarity value with the current patch. The weight calculation is based on a cross-correlation metric:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.724, + 0.892, + 0.758 + ], + "angle": 0, + "content": "\\[\nS (p, p _ {x}) = \\frac {\\langle p , p _ {x} \\rangle}{\\| p \\| \\cdot \\| p _ {x} \\|}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.765, + 0.891, + 0.811 + ], + "angle": 0, + "content": "where \\( p \\) represents a patch in the masked region, and the patch \\( p_x \\) is the comparison target. The similarity value between \\( p \\) and \\( p_x \\) is denoted by \\( S \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The self-assembly operation is defined in Eq (3), which generates a patch value \\( p_i \\). Figure 3 depicts the operation process, where \\( p_s \\) denotes the patch value symmetrically positioned with respect to \\( p \\) and averaged by considering the peripheral patches. The \\( S_{sym} \\) is calculated as Eq (2) through \\( p_i \\) and \\( p_{s_i} \\). In addition, \\( p_k \\) is the most similar patch" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1539" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "to \\( p \\) among the unmasked region, and \\( S_{\\text{known}} \\) is calculated as \\( S(p_i, p_{k_i}) \\). Further, \\( p_{i-1} \\) represents the previously generated patch, and \\( S_{i-1} \\) is obtained by \\( S(p_i, p_{i-1}) \\). The similarity value \\( S \\) is normalized to be used as the weight." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.152, + 0.471, + 0.258 + ], + "angle": 0, + "content": "In Figure 3, the red patch in (a) is \\( p_i \\), which is a combined result of \\( p_k \\) (the orange patch), \\( p_{i-1} \\) (the yellow patch), and \\( p_s \\) (the blue patch in (b)). Because \\( p_1 \\) has no prior generated patch, \\( S_0 \\) is zero. In certain cases, such as side-face images, the patches in symmetrical positions may not be relevant for generating the patch. Thus, the value of \\( S_{sym} \\) in this situation is minimal and is rarely used to generate the patch." + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.278, + 0.469, + 0.381 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p _ {i} = \\frac {S _ {s y m}}{S _ {s y m} + S _ {k n o w n} + S _ {i - 1}} \\times p _ {s _ {i}} \\\\ + \\frac {S _ {\\text {k n o w n}}}{S _ {\\text {s y m}} + S _ {\\text {k n o w n}} + S _ {i - 1}} \\times p _ {k _ {i}}. \\tag {3} \\\\ + \\frac {S _ {i - 1}}{S _ {s y m} + S _ {k n o w n} + S _ {i - 1}} \\times p _ {i - 1} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.397, + 0.199, + 0.413 + ], + "angle": 0, + "content": "3.2.3 Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.469, + 0.512 + ], + "angle": 0, + "content": "The aim of image reconstruction is to fill in the masked portion to provide supplementary information for FER. In pursuit of this, we incorporated a semantic consistency loss that enables optimizing the task while maintaining the reconstruction loss \\( L_{re} \\), consistency \\( L_{c} \\) [28], feature patch discriminator \\( L_{d_f} \\) [19], and patch discriminator \\( L_{d} \\) [36]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.469, + 0.556 + ], + "angle": 0, + "content": "The semantic consistency loss \\( L_{sc} \\) emphasizes facial expression attributes. The \\( L_{sc} \\) has the effect of reducing intraclass variability and can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.558, + 0.469, + 0.599 + ], + "angle": 0, + "content": "\\[\nL _ {s c} = \\sum_ {c = 1} ^ {7} p _ {c} \\left(z _ {g t}\\right) \\log \\left(p _ {c} \\left(z _ {r e c}\\right)\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.469, + 0.694 + ], + "angle": 0, + "content": "where \\(c\\) represents seven basic expressions, \\(p_c(z_{gt})\\) denotes the predicted probability of \\(c\\) in the ground-truth image, and \\(p_c(z_{rec})\\) indicates the predicted probability of \\(c\\) in the reconstruction result. The predicted probability distributions are obtained via the pretrained FER network. During training, the overall loss function is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.707, + 0.469, + 0.725 + ], + "angle": 0, + "content": "\\[\nL = \\lambda_ {r e} L _ {r e} + \\lambda_ {c} L _ {c} + \\lambda_ {s c} L _ {s c} + \\lambda_ {d} \\left(L _ {d} + L _ {d _ {f}}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.469, + 0.824 + ], + "angle": 0, + "content": "where \\(\\lambda_{re},\\lambda_{c},\\lambda_{sc},\\lambda_{d}\\) denote the trade-off parameters for the reconstruction, consistency, semantic consistency, discriminator losses, respectively. Furthermore, the FER network is trained with the same feature extraction architecture using probability distributions about the ground-truth label and prediction of FER." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.405, + 0.849 + ], + "angle": 0, + "content": "3.3. Facial expression recognition network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The proposed FER network is designed as an attention-based model for predicting facial expressions. We employed spatial and channel-attention mechanisms [59]." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.09, + 0.889, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.32, + 0.892, + 0.348 + ], + "angle": 0, + "content": "Figure 4. Expression-relevant vision transformer (ViT)-latent vector extraction method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.358, + 0.892, + 0.448 + ], + "angle": 0, + "content": "We obtained the refined feature map and CAM using the attention-based model. In addition, we obtained the expression-relevant latent vectors from the ViT using the CAM. As depicted in Figure 2, the Latent-OFER cooperatively uses a CNN-based feature and ViT-based latent vectors. Thus, the model performs better." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.892, + 0.57 + ], + "angle": 0, + "content": "Expression-relevant ViT-latent vectors. The proposed method employs only expression-relevant latent vectors rather than the entire latent space to improve FER performance. During the reconstruction process, ViT-based latent vectors are extracted by embedding the input image. We used a CAM to identify spatially significant areas within the image for FER, and the class activation map is generated through a CNN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.892, + 0.739 + ], + "angle": 0, + "content": "The position of the area is stored as a key, and the attention weight for each space is recorded. The key of the region where the weight of the spatial attention exceeds the top \\(50\\%\\) is used. This key is retrieved from the entire ViT-latent vectors, and the corresponding value is read. The activation map is used to identify expression-relevant latent vectors, as presented in Figure 4. This process enables the selection of positions that are relevant to FER while avoiding extraneous details, such as appearance information irrelevant to expressions, which can increase inter-class dissimilarity and lead to more accurate and effective learning results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.741, + 0.892, + 0.831 + ], + "angle": 0, + "content": "In cases where patch detection fails, the occluded patch's latent vectors are used for training and inference. However, spatial attention is not focused on the occluded area, and the latent vector of the occlusion patch is neither searched nor used for training and inference. The proposed extractor is not significantly affected in this situation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.633, + 0.862 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In this part, we describe three FER benchmark datasets and several occluded FER datasets used to evaluate this" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1540" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.447, + 0.138 + ], + "angle": 0, + "content": "
Accuracy (%)Precision (%)Recall (%)
One class SVM [39]91.190.289.4
Patch-SVDD [64]85.280.194.1
ViT-SVDD98.394.198.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.14, + 0.453, + 0.153 + ], + "angle": 0, + "content": "Table 1. Comparison of occlusion patch detection performance." + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.162, + 0.45, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.132, + 0.246, + 0.414, + 0.26 + ], + "angle": 0, + "content": "Figure 5. Occlusion patch classification results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.272, + 0.469, + 0.334 + ], + "angle": 0, + "content": "model and explain the results. We demonstrate that the proposed method performs better on both the FER task and occluded FER task. Last, an ablation study demonstrates how each model element contributes to the final performance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.345, + 0.172, + 0.359 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.372, + 0.469, + 0.434 + ], + "angle": 0, + "content": "RAF-DB [24] is a large-scale facial expression database with around 30,000 images. We used data on seven basic expressions, 12,271 images as the training set, and 3,068 images as the testing set." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.435, + 0.469, + 0.482 + ], + "angle": 0, + "content": "AffectNet [33] is the largest facial expression database with annotations. We used seven basic expressions facial images, about 287,568 training and 3,500 testing images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.484, + 0.468, + 0.514 + ], + "angle": 0, + "content": "KDEF [4] is a set of 4,900 images of facial expressions. Each expression is viewed from five viewpoints." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.517, + 0.469, + 0.547 + ], + "angle": 0, + "content": "Syn-AffectNet and Syn-RAF-DB consist of FER benchmark datasets that synthesize a real object to occlude." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.55, + 0.469, + 0.597 + ], + "angle": 0, + "content": "Occlusion-AffectNet and Occlusion-RAF-DB are real-world occlusion datasets selected from the AffectNet validation set and RAF-DB testing set by Wang et al. [53]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.599, + 0.469, + 0.675 + ], + "angle": 0, + "content": "FED-RO dataset is also a real-world occlusion dataset collected by Li et al. [26]. It contains 400 images labeled with seven basic emotions. We trained the proposed model using RAF-DB and AffectNet when testing the FED-RO datasets, following the protocol suggested in [26]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.693, + 0.291, + 0.71 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.469, + 0.9 + ], + "angle": 0, + "content": "We trained a self-supervised occlusion detection module with the KDEF dataset [4] synthesized by randomly copy-pasting objects such as hands and cups for occlusion. We used a ViT-based network pretrained with ImageNet [6] and a CNN-based network trained on several FER training datasets [24, 33] for detailed representation in the image reconstruction module. The FER network uses ResNet-18 [18] backbone architecture. It is pretrained on MS-Celeb-1M [16]. The trade-off parameters in hybrid reconstruction module are set as \\(\\lambda_{re} = 1\\), \\(\\lambda_c = 0.01\\), \\(\\lambda_{sc} = 1\\), \\(\\lambda_d = 0.002\\). The experimental source code is implemented with PyTorch, and the models are trained with a GTX-3090 GPU." + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.092, + 0.868, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.232, + 0.892, + 0.287 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison of synthesis and real occlusion. Facial expression recognition prediction results according to image reconstruction. Labels highlighted in green indicate matching the correct expression, whereas red indicates a misprediction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.308, + 0.861, + 0.324 + ], + "angle": 0, + "content": "4.3. Comparison of occlusion detection module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.892, + 0.422 + ], + "angle": 0, + "content": "The proposed ViT-SVDD detects occlusion for each patch using a suitable detector for ViT-based image reconstruction. We compared the module with existing one-class classification methods trained solely on unoccluded images to evaluate its effectiveness. We used a test set consisting of occluded and unoccluded images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.514 + ], + "angle": 0, + "content": "Patch-SVDD, which trains in a hierarchical structure from small pixels to large pixels and segments anomaly positions into small pixel units, was also included in the comparison. The proposed module achieved the highest occlusion detection accuracy among all methods, as demonstrated in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.516, + 0.892, + 0.682 + ], + "angle": 0, + "content": "Based on these results, the proposed method is particularly well-suited for the patch-by-patch processing rather than being the optimal solution for all anomaly detection tasks. While several proposed anomaly detection methods are suitable for various units, such as whole images and pixels, this approach is specifically designed to fit the ViTSVDD framework and detect anomalies in a patch-specific manner. As illustrated in Figure 5, the results demonstrate improved performance in patch-specific occlusion detection, indicating that the proposed method is best suited for special situations that require this processing type." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.827, + 0.71 + ], + "angle": 0, + "content": "4.4. Comparison of reconstruction module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The hybrid reconstruction network is compared to MAE [17] and CSA [28]. All reconstruction results are the direct output of the model without post processing. Figure 6 compares the results of deocclusion for synthesis and real occlusion on RAF-DB and AffectNet. As displayed in Figure 6 and Table 2, we present qualitative and quantitative comparisons and the FER result. The self-assembly layer enlarge the facial expression information and increase the number of patch candidates involved in the generation process to reconstruct visually pleasing and natural, and semantic consistency loss induces rich in expression of facial images, providing an advantage for FER. While other com" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1541" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.116, + 0.089, + 0.425, + 0.116 + ], + "angle": 0, + "content": "
MAE [17]CSA [28]Self-assembly
Accuracy (%)72.675.677.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.12, + 0.47, + 0.147 + ], + "angle": 0, + "content": "Table 2. Facial expression recognition prediction results according to image reconstruction on Syn-RAF-DB." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.149, + 0.428, + 0.259 + ], + "angle": 0, + "content": "
InputMAECSASelf-assemblyGround truth
SurpriseSurpriseSurpriseHappinessHappiness
SurpriseFearDisgustSadnessAnger
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.26, + 0.47, + 0.287 + ], + "angle": 0, + "content": "Figure 7. Comparison of reconstruction results and the results of each expression probability." + }, + { + "type": "table", + "bbox": [ + 0.116, + 0.301, + 0.426, + 0.399 + ], + "angle": 0, + "content": "
MethodAffect NetSyn-Affect NetRAF DBSyn-RAF DBKDEFSyn-KDEF
DACL [15]62.549.688.876.087.968.9
RUL [68]62.652.288.977.183.151.2
DAN [58]63.851.189.776.186.870.8
EAC [69]63.254.988.078.687.567.6
Latent -OFER63.956.189.680.188.386.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.402, + 0.468, + 0.429 + ], + "angle": 0, + "content": "Table 3. Accuracy (%) comparison to the state-of-the-art results on the various facial expression recognition datasets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.443, + 0.468, + 0.472 + ], + "angle": 0, + "content": "parative models generate reasonable content, the proposed approach offers a superior representation of FER." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.468, + 0.563 + ], + "angle": 0, + "content": "As presented in Figure 7, the first row shows a partially masked facial image, ground truth image, the corresponding reconstruction results of MAE, CSA and self-assembly. The second row is depicted for better visibility of the influence on FER. The proposed method displays the highest probability of a ground truth label." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.575, + 0.436, + 0.59 + ], + "angle": 0, + "content": "4.5. Comparison of FER accuracy in occlusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.468, + 0.825 + ], + "angle": 0, + "content": "Comparison with Typical FER-model. As listed in Table 3, we compared the proposed model with several state-of-the-art methods for FER on the AffectNet (C7), RAF-DB, and KDEF datasets, all available as open source. We conducted experiments by separately testing these models with synthesized occlusion images and the original dataset for each dataset. In the field of FER, recent models [15, 58, 68, 69, 41, 22] demonstrated satisfactory performance on the original dataset. However, they fail to achieve acceptable accuracy on occluded datasets. In contrast, the proposed model was designed to be robust to occlusion and outperformed other models in terms of accuracy on occluded images. Moreover, the proposed model also achieved nearly the best performance on the original images compared to typical models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Comparison with the OFER-model. We compared the performance of the proposed FER model targeting occlusion with other state-of-the-art models using FED-RO. As the code for other models is unavailable, we used the reported accuracy from the respective papers. Table 4 reveals" + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.089, + 0.849, + 0.119 + ], + "angle": 0, + "content": "
gACNN [26]Pan's [35]Xia's [61]RAN [55]OADN [9]Wang's [53]Latent -OFER
FED-RO66.569.370.568.068.170.071.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.121, + 0.892, + 0.146 + ], + "angle": 0, + "content": "Table 4. Accuracy (%) comparison to the state-of-the-art results on the FED-RO dataset." + }, + { + "type": "table", + "bbox": [ + 0.539, + 0.148, + 0.848, + 0.182 + ], + "angle": 0, + "content": "
BoostGAN [12]RAN [55]OADN [9]Latent -OFER
Occlusion-AffectNet43.458.564.066.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.185, + 0.891, + 0.21 + ], + "angle": 0, + "content": "Table 5. Accuracy (\\%) comparison to the state-of-the-art results on the occlusion-AffectNet dataset." + }, + { + "type": "table", + "bbox": [ + 0.539, + 0.224, + 0.848, + 0.258 + ], + "angle": 0, + "content": "
BoostGAN [12]RAN [55]Wang's [53]Latent -OFER
Occlusion-RAF-DB55.482.782.584.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.261, + 0.891, + 0.287 + ], + "angle": 0, + "content": "Table 6. Accuracy \\((\\%)\\) comparison to the state-of-the-art results on the occlusion-RAF-DB dataset." + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.3, + 0.882, + 0.408 + ], + "angle": 0, + "content": "
MethodAccuracyComplexity
AffectNetRAF-DBFlops(G)Parameters(M)
gACNN [26]58.885.1331370
WGAN AE [30]59.783.5353400
Pan's [35]57.180.2525
Xia's [61]57.582.7230360
RAN [55]52.686.9390300
OADN [9]61.987.2122250
Wang's [53]60.286.0102210
Latent-OFER63.989.6156373
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.412, + 0.891, + 0.439 + ], + "angle": 0, + "content": "Table 7. Accuracy (%) and complexity comparison to the occluded FER models on the typical FER datasets" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.447, + 0.891, + 0.492 + ], + "angle": 0, + "content": "that the proposed model achieved an accuracy of \\(71.8\\%\\) with the default setting, a new state-of-the-art performance for this dataset, to the best of our knowledge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.891, + 0.569 + ], + "angle": 0, + "content": "Tables 5 and 6 present the FER performance for occluded images in AffectNet and RAF-DB, where the proposed Latent-OFER model achieved an accuracy of \\(66.5\\%\\) and \\(84.2\\%\\) with the default setting \\((2.5\\% p\\) and \\(1.5\\% p\\) better than OADN [9] and RAN [55]), respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.736 + ], + "angle": 0, + "content": "Table 7 compares the accuracy and complexity of the OFER models. The complexity is estimated by ourselves. As demonstrated in Table 7, OFER models exhibit poor performance on typical FER datasets. This limitation makes them unsuitable for general use unless the unoccluded image network-assisted approach described in Section 1 is employed. In contrast, the proposed model demonstrates acceptable performance on typical and occluded FER datasets. Specifically, the proposed model achieves accuracy rates of \\(63.9\\%\\) and \\(89.6\\%\\), which represent improvements of \\(2.0\\% p\\) and \\(2.4\\% p\\), respectively, over OADN." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.754, + 0.649, + 0.77 + ], + "angle": 0, + "content": "5. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.78, + 0.89, + 0.809 + ], + "angle": 0, + "content": "This section presents the experiments investigating the effects of several modules on FER performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect of self-assembly layer. We use RAF-DB test dataset and synthesize irregular masks [27] for each image to make comparison. We replaced the self-assembly layer with a conventional \\(3 \\times 3\\) layer and the CSA layer [28]. As presented in Table 8, we used standard evaluation metrics, the PSNR [56] and SSIM [56], to quantify the module per" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1542" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.169, + 0.089, + 0.38, + 0.134 + ], + "angle": 0, + "content": "
MethodPSNR(↑)SSIM(↑)
Conventional26.360.868
CSA25.480.860
Self-assembly26.650.880
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.138, + 0.47, + 0.166 + ], + "angle": 0, + "content": "Table 8. Quantitative comparisons results between conventional, CSA [28], and self-assembly." + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.173, + 0.44, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.237, + 0.47, + 0.28 + ], + "angle": 0, + "content": "Figure 8. Effect of the self-assembly layer. Conventional and CSA [28] are results of the proposed module which replaces the self-assembly layer with the conventional and CSA layers respectively." + }, + { + "type": "table", + "bbox": [ + 0.116, + 0.293, + 0.429, + 0.328 + ], + "angle": 0, + "content": "
MAE [17]CSA [28]Hybrid reconstruction
Reconstructed-RAF-DB72.671.677.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.329, + 0.468, + 0.37 + ], + "angle": 0, + "content": "Table 9. Accuracy \\((\\%)\\) comparison of FER using irregular masked facial image reconstruction results by MAE, CSA, Hybrid reconstruction network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.47, + 0.573 + ], + "angle": 0, + "content": "formance. Moreover, as illustrated in Figure 8, the mask part fails to reconstruct reasonable content when we used conventional \\(3 \\times 3\\) layer. Although the CSA [28] can improve the performance compared to conventional. Table 9 reveals that the reconstruction results of CSA inpainting still lack facial expression attributes. Table 9 shows the average accuracy of facial expression prediction with images regenerated by MAE, CSA, and hybrid reconstruction network. For fair comparison, the same expression recognition network and the same partially masked test set were used. Compared with them, the proposed method performs better. The effect of semantic consistency loss is included in the Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.468, + 0.699 + ], + "angle": 0, + "content": "Effect of occlusion detection and reconstruction module. We demonstrated the effectiveness of the deocclusive auto-encoder with occluded KDEF images created through synthesis. As presented in Table 10, image reconstruction is not performed when the occlusion detector is not used, leading to low FER performance. However, even without the proposed module, the proposed model performed well compared to typical models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Effect of latent vectors and expression-relevant feature extractor. As shown Table 10, this study evaluates the efficiency of the deocclusive autoencoder and expression-related feature extractor in FER. The results reveal that using only the ViT-latent vector extracted from occluded data results in poor performance. Although using only CNN features improved the performance, it remained unacceptable. However, training with the ViT-latent vectors and CNN features improves performance by about \\(4.0\\% p\\) compared to only CNN features. Additionally, performance improves by \\(8.2\\% p\\) when images are deoccluded via a hybrid reconstruction network. These results indicate that all proposed modules contribute to performance improvement," + }, + { + "type": "table", + "bbox": [ + 0.539, + 0.089, + 0.852, + 0.238 + ], + "angle": 0, + "content": "
Image recon-stuctionCNN-featuresFull ViT-latent vectorsExtracted ViT-latent vectorsAccuracy (%)
✓15.2
✓20.1
✓75.4
✓✓76.5
✓✓78.5
✓✓64.9
✓✓66.4
✓✓82.7
✓✓✓84.2
✓✓✓86.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.239, + 0.864, + 0.253 + ], + "angle": 0, + "content": "Table 10. Module evaluation in Latent-OFER on Syn-KDEF." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.258, + 0.892, + 0.303 + ], + "angle": 0, + "content": "and the best performance is achieved when CNN features and expression-relevant ViT-latent vectors are trained cooperatively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.309, + 0.613, + 0.324 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.892, + 0.636 + ], + "angle": 0, + "content": "This section discusses two topics. First, the performance of the occluded patch detector can be considered dominant. The proposed model restores images and extracts latent vectors to use for FER. In cases where occlusion patch detection fails to perform adequately, latent vectors are not extracted correctly because the image is not fully restored. However, the model uses spatial attention to extract expression-relevant features. In images with poor occlusion patch detection, the corresponding patch has lower weights. As a result, the influence of poor detection on the overall performance is mitigated. The second is the potential limitations of scalability when using image reconstruction modules trained with a single dataset. These models may not be adaptable enough to handle a variety of datasets, thereby making it difficult to reconstruct a complete image. To overcome this challenge, extra training on diverse datasets or the adoption of uniform alignment across datasets is necessary. Therefore, to enhance the flexibility of image reconstruction modules, a multi-dataset training approach or standardized alignment methods can be implemented." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.643, + 0.619, + 0.658 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.892, + 0.82 + ], + "angle": 0, + "content": "This paper addresses FER in real-world occlusion. Our method involves detecting the occluded parts of the face and then reconstructing them using a specially designed reconstruction network to produce images as if they were unoccluded. In addition, expression-relevant latent vectors were extracted and learned cooperatively with the CNN features. The proposed Latent-OFER model works well under occluded and unoccluded conditions. We evaluate this method on occluded FER datasets and typical FER datasets, and the proposed method achieves state-of-the-art accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements This work was supported by the Industrial Fundamental Technology Development Program (No. 20018699) funded by MOTIE of Korea and IITP grant funded by the Korea government (MSIT; No.2021-0-02068, RS-2023-00256629)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1543" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Mouath Aouayeb, Wassim Hamidouche, Catherine Soladie, Kidiyo Kpalma, and Renaud Seguier. 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This is because when unexpected objects occlude the face, the FER network faces difficulties extracting facial features and accurately predicting facial expressions. Therefore, occluded FER (OFER) is a challenging problem. Previous studies on occlusion-aware FER have typically required fully annotated facial images for training. However, collecting facial images with various occlusions and expression annotations is time-consuming and expensive. Latent-OFER, the proposed method, can detect occlusions, restore occluded parts of the face as if they were unoccluded, and recognize them, improving FER accuracy. This approach involves three steps: First, the vision transformer (ViT)-based occlusion patch detector masks the occluded position by training only latent vectors from the unoccluded patches using the support vector data description algorithm. Second, the hybrid reconstruction network generates the masking position as a complete image using the ViT and convolutional neural network (CNN). Last, the expression-relevant latent vector extractor retrieves and uses expression-related information from all latent vectors by applying a CNN-based class activation map. This mechanism has a significant advantage in preventing performance degradation from occlusion by unseen objects. The experimental results on several databases demonstrate the superiority of the proposed method over state-of-the-art methods. This code is available at https://github.com/leeisack/Latent-OFER. + +# 1. Introduction + +Facial expression recognition (FER) has undergone remarkable advancements in recent years and is now widely used across various industries. However, the ability of FER models in the presence of occlusion remains a challenge. + +![](images/9ca4025bf30451ff5fcdf737fd83ae6fdc94da3d1e3d9c323b118c9b8cbf2bbd.jpg) +Figure 1. Facial expression recognition (FER) performance on RAF-DB according to the occluded proportions. + +Figure 1 illustrates the accuracy of the previous state-of-the-art model for FER [58] for various occlusion proportions. In this study, we evaluated the robustness of the typical model in recognizing facial expressions using two types of occlusions: random sampling occlusion and grad occlusion. Random sampling occlusion divides the entire image into 196 patches and randomly masks them according to the proportion. Grad occlusion processes an image with an intentionally occluded area that affects FER using gradient-weighted class activation mapping (Grad-CAM) [46]. This study reveals a more substantial decrease in performance with the second type of occlusion, particularly when the occluded area is crucial for accurate FER. This finding has been objectively measured using Grad-CAM [46]. + +Previous studies on FER [1, 2, 3, 5, 7, 13, 14, 15, 21, 23, 29, 31, 38, 43, 44, 49, 50, 54, 57, 60, 62, 63, 68, 69, 70] have not given adequate attention to the influence of occlusions. However, addressing this challenge is crucial for enhancing the practical applications of FER in real-world scenarios. Although research on occluded FER (OFER) is relatively scarce, its importance is increasingly recognized [66]. + +Currently, several approaches address OFER. The occlusion-robust feature extraction approach [9, 53] aims to identify an occlusion-insensitive and discriminative representation, but it is challenging because the types and locations of occlusion are often unknown. The sub region anal + +ysis approach [26, 55] divides regions based on facial landmarks and uses attention mechanisms to focus on crucial areas. However, the inability to detect facial landmarks due to occlusions can lead to errors in the FER process. The unoccluded image network assist approach [35, 61] uses two distinct networks: one trained on unoccluded images and the other trained on occluded images. This approach leverages unoccluded images as privileged information to assist in expression recognition in the presence of occlusion. It is unsuitable in real-world situations because it cannot differentiate between occluded and unoccluded images. + +Hence, the proposed approach is the occlusion recovery-based approach, which aims to transform occluded images into complete images through a deocclusion process. We propose the deocclusive autoencoder for reconstructing facial images. The deocclusive autoencoder can be functionally divided into an occlusion detector and reconstruction module. The occlusion detector uses the vision transformer (ViT) support vector data description (SVDD) for the reconstruction module. This approach enables the model to detect occlusion caused by unseen objects, an essential step in accurately generating deoccluded facial images. The reconstruction network consists of the ViT structure and convolutional neural network (CNN) structure for facial image reconstruction. We leverage the strengths of the ViT in generating realistic facial images despite varying poses and further refine them using the CNN. We call it the hybrid reconstruction network. The hybrid reconstruction network enhances FER performance by generating deoccluded images that express detailed and vivid facial expression attributes. This enhancement is achieved by incorporating a self-assembly layer and semantic consistency loss. In contrast, previous work on image reconstruction has primarily focused on achieving naturalness, which can result in dull facial expressions. Additionally, we use informative ViT-latent vectors obtained from the reconstruction process. We combine the CNN features and ViT-latent vectors for enhanced facial expression predictions. The main contributions in this work are summarized as follows: + +- We propose an expression-relevant feature extractor that uses spatial attention to assign a higher weight to specific facial features, allowing us to identify critical positions for FER. We can retrieve expression-relevant latent vectors from the ViT-latent space to extract valuable information using these positions as critical values. + +- We propose ViT-SVDD, a patch-based occlusion detection module optimized for ViT-based networks. As a self-supervised local classifier, the ViT-SVDD module is trained only on latent vectors of unoccluded facial images. This method accurately classifies occlusions caused by unseen objects for subsequent reconstruction. + +- We propose a hybrid reconstruction network that combines the strengths of the ViT and CNN architectures with + +a self-assembly layer and semantic consistency loss to generate facial images naturalness and rich in expression. This approach enhances the quality of deoccluded images and improves the accuracy of FER in challenging conditions. + +# 2. Related Work + +# 2.1. Occluded Object Detection + +Several early studies [8] have attempted to detect occlusions in images for OFER tasks. The conventional methods provide location information about the occlusions and are called occlusion-aware methods [26, 55]. However, these methods are not practical for real-world scenarios. Another approach [30] is to train models using synthesized images with various occlusions to detect the occluded positions. Although this approach can determine occlusion positions, it requires a diverse set of object images, which can be challenging to obtain. Moreover, the performance of these models [26, 30, 55] degrades when they encounter unseen objects as input. We drew inspiration from anomaly detection tasks [10, 45, 47, 64] with one-class classification algorithms [20, 32, 39, 40, 52] and proposed a model that learns only from unoccluded datasets and can generalize well to unseen datasets. + +# 2.2. Occluded Facial Expression Recognition + +We have no prior knowledge of where occlusions may appear on a facial image or how large or complex they might be. These occlusions can significantly reduce the accuracy of FER by either increasing the intra-class variability or inter-class similarity. Four categories address this issue: occlusion-robust feature extraction, subregion analysis, unoccluded image network-assisted, and occlusion recovery. + +Occlusion-robust feature extraction approach. This approach aims to extract features less affected by occlusions while maintaining discriminative capability. Wang et al. [53] used self-supervised and contrastive learning to explore robust representations with synthesized occlusions. + +Subregion analysis approach. This approach excludes the occluded parts from recognition. By focusing only on the unoccluded facial parts, the influence of occlusion on recognition performance can be reduced. Li et al. [26] proposed a gate unit with an attention mechanism that allows the model to focus on informative unoccluded facial areas. + +Unoccluded image network-assisted approach. This approach employs unoccluded facial images as guidance to assist with OFER. Pan et al. [35] trained two deep neural networks from occluded and unoccluded facial images. Then, the unoccluded network guides the occluded network. Xia et al. [61] measured the complexity of unoccluded data using distribution density in a feature space. The classifier can be guided by unoccluded data and subsequently leverage more meaningful and discriminative samples. + +![](images/184900aecb48fa1c83b2b6ad20352e27e427fd17fafd389d0c3748337749cb68.jpg) +Figure 2. Framework of the Latent-OFER that creates a deoccluded image that erases the occlusion. In this process, the expression-relevant latent vectors are extracted by mapping the vision transformer (ViT)-latent vector and the convolutional neural network (CNN) class activation map. Latent-OFER predicts facial expressions that combine CNN-based features with specific VIT-based latent vectors. + +Occlusion recovery-based approach. This approach uses face completion as a basis to deal with occlusion. To reconstruct occluded faces, Lu et al. [30] suggested using a WGAN consisting of an autoencoder-based generator and discriminators. By reconstructing the occlusion, these approaches provide necessary information while avoiding the interference of noisy information and obtaining informative appearance. Therefore, we adopt an image-inpainting technique as a recovery-based approach, to deal with occlusion. A notable point of differentiation between our method and existing approaches lies in our specific emphasis on the reconstruction of occluded regions while simultaneously retaining the facial expression information. Furthermore, we employ ViT-based latent vectors extracted throughout the reconstruction process to enhance the performance of FER. + +# 2.3. Image inpainting + +Several approaches based on CNN have been developed to generate semantically coherent content. Pathak et al. [37] employed context encoders to generate plausible features for the area requiring restoration. Yu et al. [65] introduced a contextual attention module to refine by referencing the surrounding features. Song et al. [51] used a patch-swap layer that replaces each patch within the masking areas of a feature map with the most comparable patch in the unoccluded areas. Liu et al. [28] developed a coherent semantic attention layer to ensure semantic relevance between the swapped features. + +In recent years, transformer-based methods have also significantly contributed to computer vision. The ViT [11] achieves better results for image recognition than CNN-based methods. Furthermore, MAE [17] demonstrated that transformer-based models are well-suited for image inpainting tasks. However, transformer-based algorithms have a limitation in that they may produce blurry results when restoring large block areas [17]. Another work [25] + +presents MAT, a transformer-based model for large-hole inpainting. Nevertheless, in cases where the eyes or mouth are fully occluded, the ViT cannot generate images in detail because it is significantly less biased toward local textures [34]. Therefore, the challenge remains. + +# 3. Proposed method + +As shown in Figure 2, we propose multi-stage approach to address OFER, involving detecting, masking, and reconstructing occlusions to recognize facial expressions. The proposed approach enhances recognition accuracy through cooperative learning ViT-latent vectors extracted from the image reconstruction process and the existing CNN features. We divided the facial image into patches, classified each patch as occluded or unoccluded, and reconstructed the occluded patches to be deoccluded. Subsequently, we leveraged the reconstructed image and expression-relevant latent vectors to predict facial expressions. + +# 3.1. Occlusion detection module: ViT-SVDD + +General object detection and segmentation models may not be suitable for real-world scenarios because they may be unable to detect unseen objects. To address this limitation, we use one-class classification, which is often employed in anomaly detection. This approach makes it possible to classify unused occlusion during training through self-supervised learning, which only uses unoccluded patches for learning, providing a more effective solution for real-world applications. + +One-class classification methods for classifying normal or abnormal can operate at various levels of granularity, ranging from low-level anomaly detection [47] at the pixel level to high-level anomaly detection [40] at the image level. Detection and classification are performed based on the size of the unit, which can be customized to suit the user's needs. We used a ViT-based reconstruction method; + +thus, we propose a middle-level anomaly detector specifically optimized for ViT. We divided the image to match the size of the ViT patch and created ViT-latent vectors. These patches are encoded with informative features to produce ViT-latent vectors. To generate the smallest feature space for unoccluded patches, we used the deep SVDD algorithm [39]. One-class deep SVDD employs quadratic loss to penalize the distance of every network representation. This objective is defined as + +$$ +\min \frac {1}{n} \sum_ {i = 1} ^ {n} \| \Phi (x _ {i}; \mathcal {W}) - c \| ^ {2} + \frac {\lambda}{2} \sum_ {l = 1} ^ {L} \| w ^ {l} \| _ {F} ^ {2}. \tag {1} +$$ + +where $n$ denotes number of training data, $L$ denote number of layer, $\mathcal{W}$ denotes set of weights $\mathcal{W} = \{w^1, \dots, w^L\}$ and $c$ represents a hypersphere characterized by the center. The first term induces the features of all normal images to converge at the center point $c$ , whereas the last term is a weight decay regularizer on the network parameter $W$ with hyperparameter $\lambda > 0$ , where $\| \cdot \|_F$ denotes the Frobenius norm. Eq (1) simply employs a quadratic loss for penalizing the distance of every network representation $\Phi(x_i; \mathcal{W})$ to $c \in \mathcal{F}$ , Where $\mathcal{F}$ is output feature space. The network learn parameters $\mathcal{W}$ such that data points are closely mapped to $c$ of the hypersphere. To determine whether a patch is occluded, we calculated the distance between the new input information and the center $c$ of the feature space for each patch. If the distance exceeds the pre-defined radius, the corresponding patch is classified as occluded and masked. The optimal value of the radius is automatically determined in the SVDD procedure. Through this process, occlusion patch detection is possible for unseen objects. The proposed ViT-SVDD approach allows for validating the performance of synthetic images with occlusion patch annotations. By detecting occlusion patches, we can improve the accuracy of the reconstruction method and make it more suitable for real-world applications. + +# 3.2. Image reconstruction module: hybrid reconstruction network + +The facial image reconstruction process employs an occlusion-masked image generated by the occlusion detector. The hybrid reconstruction network is designed to cooperate by fusing ViT-based and CNN-based networks. Through this mechanism, we leverage both the strengths of ViT and CNN. The ViT-based method employs $16 \times 16$ patches as input image; however, we used the outputs of the occlusion detector as input because the image has already been partitioned into patch units by the occlusion detector. + +# 3.2.1 Network structure + +The ViT-based approach encodes the input patches and positively embeds all tokens. The occluded patch reconstruction is achieved through correlation with other patches. + +![](images/e15a46d6198aa4dc7abd7a8bf76a973c1c1e9708eb0a28697a3174adb9145035.jpg) +Figure 3. Illustration of the self-assembly operation. (a) Feature map in the self-assembly layer. (b) Flip of (a). The patch in masked region is generated by combining three patch information. + +The ViT has low inductive bias and a high degree of freedom [34], enabling it to generate credible images despite diverse occlusion shapes, positions, and facial poses. As discussed in Section 2.3, the ViT-based approach may sometimes not supply detailed results. To address this limitation, we combined the ViT and CNN. The network consists of a U-Net architecture. Additionally, we added a self-assembly layer inside the encoder to generate a detailed representation. This multi structure approach effectively combines the strengths of the ViT and CNN-based networks to generate high-quality facial image reconstructions that represent facial expressions well. + +# 3.2.2 Self-assembly layer + +We implemented a self-assembly layer to improve image reconstruction for FER. We reconstructed masked regions like [17] but made enhancements specific to facial images. Based on the concept that the left and right characteristics of a person's face are symmetrical[42, 48, 67], we used the feature information present in the corresponding location of the horizontally flipped image when reconstructing a masked region. We expanded the range of candidate patches used in the generation process by incorporating information from three sources, the previously generated patch, the most similar patch in the unmasked region, and patches located in the corresponding position of the horizontally flipped image. In this process, the masked region contains the reconstruction results with the ViT network. We assigned weights to each based on the similarity value with the current patch. The weight calculation is based on a cross-correlation metric: + +$$ +S (p, p _ {x}) = \frac {\langle p , p _ {x} \rangle}{\| p \| \cdot \| p _ {x} \|}, \tag {2} +$$ + +where $p$ represents a patch in the masked region, and the patch $p_x$ is the comparison target. The similarity value between $p$ and $p_x$ is denoted by $S$ . + +The self-assembly operation is defined in Eq (3), which generates a patch value $p_i$ . Figure 3 depicts the operation process, where $p_s$ denotes the patch value symmetrically positioned with respect to $p$ and averaged by considering the peripheral patches. The $S_{sym}$ is calculated as Eq (2) through $p_i$ and $p_{s_i}$ . In addition, $p_k$ is the most similar patch + +to $p$ among the unmasked region, and $S_{\text{known}}$ is calculated as $S(p_i, p_{k_i})$ . Further, $p_{i-1}$ represents the previously generated patch, and $S_{i-1}$ is obtained by $S(p_i, p_{i-1})$ . The similarity value $S$ is normalized to be used as the weight. + +In Figure 3, the red patch in (a) is $p_i$ , which is a combined result of $p_k$ (the orange patch), $p_{i-1}$ (the yellow patch), and $p_s$ (the blue patch in (b)). Because $p_1$ has no prior generated patch, $S_0$ is zero. In certain cases, such as side-face images, the patches in symmetrical positions may not be relevant for generating the patch. Thus, the value of $S_{sym}$ in this situation is minimal and is rarely used to generate the patch. + +$$ +\begin{array}{l} p _ {i} = \frac {S _ {s y m}}{S _ {s y m} + S _ {k n o w n} + S _ {i - 1}} \times p _ {s _ {i}} \\ + \frac {S _ {\text {k n o w n}}}{S _ {\text {s y m}} + S _ {\text {k n o w n}} + S _ {i - 1}} \times p _ {k _ {i}}. \tag {3} \\ + \frac {S _ {i - 1}}{S _ {s y m} + S _ {k n o w n} + S _ {i - 1}} \times p _ {i - 1} \\ \end{array} +$$ + +# 3.2.3 Objective + +The aim of image reconstruction is to fill in the masked portion to provide supplementary information for FER. In pursuit of this, we incorporated a semantic consistency loss that enables optimizing the task while maintaining the reconstruction loss $L_{re}$ , consistency $L_{c}$ [28], feature patch discriminator $L_{d_f}$ [19], and patch discriminator $L_{d}$ [36]. + +The semantic consistency loss $L_{sc}$ emphasizes facial expression attributes. The $L_{sc}$ has the effect of reducing intraclass variability and can be defined as: + +$$ +L _ {s c} = \sum_ {c = 1} ^ {7} p _ {c} \left(z _ {g t}\right) \log \left(p _ {c} \left(z _ {r e c}\right)\right), \tag {4} +$$ + +where $c$ represents seven basic expressions, $p_c(z_{gt})$ denotes the predicted probability of $c$ in the ground-truth image, and $p_c(z_{rec})$ indicates the predicted probability of $c$ in the reconstruction result. The predicted probability distributions are obtained via the pretrained FER network. During training, the overall loss function is defined as: + +$$ +L = \lambda_ {r e} L _ {r e} + \lambda_ {c} L _ {c} + \lambda_ {s c} L _ {s c} + \lambda_ {d} \left(L _ {d} + L _ {d _ {f}}\right), \tag {5} +$$ + +where $\lambda_{re},\lambda_{c},\lambda_{sc},\lambda_{d}$ denote the trade-off parameters for the reconstruction, consistency, semantic consistency, discriminator losses, respectively. Furthermore, the FER network is trained with the same feature extraction architecture using probability distributions about the ground-truth label and prediction of FER. + +# 3.3. Facial expression recognition network + +The proposed FER network is designed as an attention-based model for predicting facial expressions. We employed spatial and channel-attention mechanisms [59]. + +![](images/4b750f4a56a6c628cefd3fcbcc8d4747d6c4a57f60bf9c2e83a932a192b6ac54.jpg) +Figure 4. Expression-relevant vision transformer (ViT)-latent vector extraction method. + +We obtained the refined feature map and CAM using the attention-based model. In addition, we obtained the expression-relevant latent vectors from the ViT using the CAM. As depicted in Figure 2, the Latent-OFER cooperatively uses a CNN-based feature and ViT-based latent vectors. Thus, the model performs better. + +Expression-relevant ViT-latent vectors. The proposed method employs only expression-relevant latent vectors rather than the entire latent space to improve FER performance. During the reconstruction process, ViT-based latent vectors are extracted by embedding the input image. We used a CAM to identify spatially significant areas within the image for FER, and the class activation map is generated through a CNN. + +The position of the area is stored as a key, and the attention weight for each space is recorded. The key of the region where the weight of the spatial attention exceeds the top $50\%$ is used. This key is retrieved from the entire ViT-latent vectors, and the corresponding value is read. The activation map is used to identify expression-relevant latent vectors, as presented in Figure 4. This process enables the selection of positions that are relevant to FER while avoiding extraneous details, such as appearance information irrelevant to expressions, which can increase inter-class dissimilarity and lead to more accurate and effective learning results. + +In cases where patch detection fails, the occluded patch's latent vectors are used for training and inference. However, spatial attention is not focused on the occluded area, and the latent vector of the occlusion patch is neither searched nor used for training and inference. The proposed extractor is not significantly affected in this situation. + +# 4. Experiments + +In this part, we describe three FER benchmark datasets and several occluded FER datasets used to evaluate this + +
Accuracy (%)Precision (%)Recall (%)
One class SVM [39]91.190.289.4
Patch-SVDD [64]85.280.194.1
ViT-SVDD98.394.198.7
+ +Table 1. Comparison of occlusion patch detection performance. + +![](images/fa6926fe9939294850e591e2d75ac4684f0e7246cd9dd68065f045c301344546.jpg) +Figure 5. Occlusion patch classification results. + +model and explain the results. We demonstrate that the proposed method performs better on both the FER task and occluded FER task. Last, an ablation study demonstrates how each model element contributes to the final performance. + +# 4.1. Dataset + +RAF-DB [24] is a large-scale facial expression database with around 30,000 images. We used data on seven basic expressions, 12,271 images as the training set, and 3,068 images as the testing set. + +AffectNet [33] is the largest facial expression database with annotations. We used seven basic expressions facial images, about 287,568 training and 3,500 testing images. + +KDEF [4] is a set of 4,900 images of facial expressions. Each expression is viewed from five viewpoints. + +Syn-AffectNet and Syn-RAF-DB consist of FER benchmark datasets that synthesize a real object to occlude. + +Occlusion-AffectNet and Occlusion-RAF-DB are real-world occlusion datasets selected from the AffectNet validation set and RAF-DB testing set by Wang et al. [53]. + +FED-RO dataset is also a real-world occlusion dataset collected by Li et al. [26]. It contains 400 images labeled with seven basic emotions. We trained the proposed model using RAF-DB and AffectNet when testing the FED-RO datasets, following the protocol suggested in [26]. + +# 4.2. Implementation details + +We trained a self-supervised occlusion detection module with the KDEF dataset [4] synthesized by randomly copy-pasting objects such as hands and cups for occlusion. We used a ViT-based network pretrained with ImageNet [6] and a CNN-based network trained on several FER training datasets [24, 33] for detailed representation in the image reconstruction module. The FER network uses ResNet-18 [18] backbone architecture. It is pretrained on MS-Celeb-1M [16]. The trade-off parameters in hybrid reconstruction module are set as $\lambda_{re} = 1$ , $\lambda_c = 0.01$ , $\lambda_{sc} = 1$ , $\lambda_d = 0.002$ . The experimental source code is implemented with PyTorch, and the models are trained with a GTX-3090 GPU. + +![](images/6e8a401e819ab056cc57f52a5055003fa9020d7c56e48b4009b83cd0cb37b22d.jpg) +Figure 6. Qualitative comparison of synthesis and real occlusion. Facial expression recognition prediction results according to image reconstruction. Labels highlighted in green indicate matching the correct expression, whereas red indicates a misprediction. + +# 4.3. Comparison of occlusion detection module + +The proposed ViT-SVDD detects occlusion for each patch using a suitable detector for ViT-based image reconstruction. We compared the module with existing one-class classification methods trained solely on unoccluded images to evaluate its effectiveness. We used a test set consisting of occluded and unoccluded images. + +Patch-SVDD, which trains in a hierarchical structure from small pixels to large pixels and segments anomaly positions into small pixel units, was also included in the comparison. The proposed module achieved the highest occlusion detection accuracy among all methods, as demonstrated in Table 1. + +Based on these results, the proposed method is particularly well-suited for the patch-by-patch processing rather than being the optimal solution for all anomaly detection tasks. While several proposed anomaly detection methods are suitable for various units, such as whole images and pixels, this approach is specifically designed to fit the ViTSVDD framework and detect anomalies in a patch-specific manner. As illustrated in Figure 5, the results demonstrate improved performance in patch-specific occlusion detection, indicating that the proposed method is best suited for special situations that require this processing type. + +# 4.4. Comparison of reconstruction module + +The hybrid reconstruction network is compared to MAE [17] and CSA [28]. All reconstruction results are the direct output of the model without post processing. Figure 6 compares the results of deocclusion for synthesis and real occlusion on RAF-DB and AffectNet. As displayed in Figure 6 and Table 2, we present qualitative and quantitative comparisons and the FER result. The self-assembly layer enlarge the facial expression information and increase the number of patch candidates involved in the generation process to reconstruct visually pleasing and natural, and semantic consistency loss induces rich in expression of facial images, providing an advantage for FER. While other com + +
MAE [17]CSA [28]Self-assembly
Accuracy (%)72.675.677.3
+ +Table 2. Facial expression recognition prediction results according to image reconstruction on Syn-RAF-DB. + +
InputMAECSASelf-assemblyGround truth
SurpriseSurpriseSurpriseHappinessHappiness
SurpriseFearDisgustSadnessAnger
+ +Figure 7. Comparison of reconstruction results and the results of each expression probability. + +
MethodAffect NetSyn-Affect NetRAF DBSyn-RAF DBKDEFSyn-KDEF
DACL [15]62.549.688.876.087.968.9
RUL [68]62.652.288.977.183.151.2
DAN [58]63.851.189.776.186.870.8
EAC [69]63.254.988.078.687.567.6
Latent -OFER63.956.189.680.188.386.7
+ +parative models generate reasonable content, the proposed approach offers a superior representation of FER. + +As presented in Figure 7, the first row shows a partially masked facial image, ground truth image, the corresponding reconstruction results of MAE, CSA and self-assembly. The second row is depicted for better visibility of the influence on FER. The proposed method displays the highest probability of a ground truth label. + +# 4.5. Comparison of FER accuracy in occlusion + +Comparison with Typical FER-model. As listed in Table 3, we compared the proposed model with several state-of-the-art methods for FER on the AffectNet (C7), RAF-DB, and KDEF datasets, all available as open source. We conducted experiments by separately testing these models with synthesized occlusion images and the original dataset for each dataset. In the field of FER, recent models [15, 58, 68, 69, 41, 22] demonstrated satisfactory performance on the original dataset. However, they fail to achieve acceptable accuracy on occluded datasets. In contrast, the proposed model was designed to be robust to occlusion and outperformed other models in terms of accuracy on occluded images. Moreover, the proposed model also achieved nearly the best performance on the original images compared to typical models. + +Comparison with the OFER-model. We compared the performance of the proposed FER model targeting occlusion with other state-of-the-art models using FED-RO. As the code for other models is unavailable, we used the reported accuracy from the respective papers. Table 4 reveals + +Table 3. Accuracy (%) comparison to the state-of-the-art results on the various facial expression recognition datasets. + +
gACNN [26]Pan's [35]Xia's [61]RAN [55]OADN [9]Wang's [53]Latent -OFER
FED-RO66.569.370.568.068.170.071.8
+ +Table 4. Accuracy (%) comparison to the state-of-the-art results on the FED-RO dataset. + +
BoostGAN [12]RAN [55]OADN [9]Latent -OFER
Occlusion-AffectNet43.458.564.066.1
+ +Table 5. Accuracy (\%) comparison to the state-of-the-art results on the occlusion-AffectNet dataset. + +
BoostGAN [12]RAN [55]Wang's [53]Latent -OFER
Occlusion-RAF-DB55.482.782.584.2
+ +Table 6. Accuracy $(\%)$ comparison to the state-of-the-art results on the occlusion-RAF-DB dataset. + +
MethodAccuracyComplexity
AffectNetRAF-DBFlops(G)Parameters(M)
gACNN [26]58.885.1331370
WGAN AE [30]59.783.5353400
Pan's [35]57.180.2525
Xia's [61]57.582.7230360
RAN [55]52.686.9390300
OADN [9]61.987.2122250
Wang's [53]60.286.0102210
Latent-OFER63.989.6156373
+ +Table 7. Accuracy (%) and complexity comparison to the occluded FER models on the typical FER datasets + +that the proposed model achieved an accuracy of $71.8\%$ with the default setting, a new state-of-the-art performance for this dataset, to the best of our knowledge. + +Tables 5 and 6 present the FER performance for occluded images in AffectNet and RAF-DB, where the proposed Latent-OFER model achieved an accuracy of $66.5\%$ and $84.2\%$ with the default setting $(2.5\% p$ and $1.5\% p$ better than OADN [9] and RAN [55]), respectively. + +Table 7 compares the accuracy and complexity of the OFER models. The complexity is estimated by ourselves. As demonstrated in Table 7, OFER models exhibit poor performance on typical FER datasets. This limitation makes them unsuitable for general use unless the unoccluded image network-assisted approach described in Section 1 is employed. In contrast, the proposed model demonstrates acceptable performance on typical and occluded FER datasets. Specifically, the proposed model achieves accuracy rates of $63.9\%$ and $89.6\%$ , which represent improvements of $2.0\% p$ and $2.4\% p$ , respectively, over OADN. + +# 5. Ablation study + +This section presents the experiments investigating the effects of several modules on FER performance + +Effect of self-assembly layer. We use RAF-DB test dataset and synthesize irregular masks [27] for each image to make comparison. We replaced the self-assembly layer with a conventional $3 \times 3$ layer and the CSA layer [28]. As presented in Table 8, we used standard evaluation metrics, the PSNR [56] and SSIM [56], to quantify the module per + +
MethodPSNR(↑)SSIM(↑)
Conventional26.360.868
CSA25.480.860
Self-assembly26.650.880
+ +![](images/b81cc1066dfe2afa2107a94a5a1b44c50d613446170478dd3ebd52b55f80de06.jpg) +Figure 8. Effect of the self-assembly layer. Conventional and CSA [28] are results of the proposed module which replaces the self-assembly layer with the conventional and CSA layers respectively. + +Table 8. Quantitative comparisons results between conventional, CSA [28], and self-assembly. + +
MAE [17]CSA [28]Hybrid reconstruction
Reconstructed-RAF-DB72.671.677.3
+ +formance. Moreover, as illustrated in Figure 8, the mask part fails to reconstruct reasonable content when we used conventional $3 \times 3$ layer. Although the CSA [28] can improve the performance compared to conventional. Table 9 reveals that the reconstruction results of CSA inpainting still lack facial expression attributes. Table 9 shows the average accuracy of facial expression prediction with images regenerated by MAE, CSA, and hybrid reconstruction network. For fair comparison, the same expression recognition network and the same partially masked test set were used. Compared with them, the proposed method performs better. The effect of semantic consistency loss is included in the Supplementary Material. + +Effect of occlusion detection and reconstruction module. We demonstrated the effectiveness of the deocclusive auto-encoder with occluded KDEF images created through synthesis. As presented in Table 10, image reconstruction is not performed when the occlusion detector is not used, leading to low FER performance. However, even without the proposed module, the proposed model performed well compared to typical models. + +Effect of latent vectors and expression-relevant feature extractor. As shown Table 10, this study evaluates the efficiency of the deocclusive autoencoder and expression-related feature extractor in FER. The results reveal that using only the ViT-latent vector extracted from occluded data results in poor performance. Although using only CNN features improved the performance, it remained unacceptable. However, training with the ViT-latent vectors and CNN features improves performance by about $4.0\% p$ compared to only CNN features. Additionally, performance improves by $8.2\% p$ when images are deoccluded via a hybrid reconstruction network. These results indicate that all proposed modules contribute to performance improvement, + +Table 9. Accuracy $(\%)$ comparison of FER using irregular masked facial image reconstruction results by MAE, CSA, Hybrid reconstruction network. + +
Image recon-stuctionCNN-featuresFull ViT-latent vectorsExtracted ViT-latent vectorsAccuracy (%)
✓15.2
✓20.1
✓75.4
✓✓76.5
✓✓78.5
✓✓64.9
✓✓66.4
✓✓82.7
✓✓✓84.2
✓✓✓86.7
+ +Table 10. Module evaluation in Latent-OFER on Syn-KDEF. + +and the best performance is achieved when CNN features and expression-relevant ViT-latent vectors are trained cooperatively. + +# 6. Discussion + +This section discusses two topics. First, the performance of the occluded patch detector can be considered dominant. The proposed model restores images and extracts latent vectors to use for FER. In cases where occlusion patch detection fails to perform adequately, latent vectors are not extracted correctly because the image is not fully restored. However, the model uses spatial attention to extract expression-relevant features. In images with poor occlusion patch detection, the corresponding patch has lower weights. As a result, the influence of poor detection on the overall performance is mitigated. The second is the potential limitations of scalability when using image reconstruction modules trained with a single dataset. These models may not be adaptable enough to handle a variety of datasets, thereby making it difficult to reconstruct a complete image. To overcome this challenge, extra training on diverse datasets or the adoption of uniform alignment across datasets is necessary. Therefore, to enhance the flexibility of image reconstruction modules, a multi-dataset training approach or standardized alignment methods can be implemented. + +# 7. Conclusion + +This paper addresses FER in real-world occlusion. Our method involves detecting the occluded parts of the face and then reconstructing them using a specially designed reconstruction network to produce images as if they were unoccluded. In addition, expression-relevant latent vectors were extracted and learned cooperatively with the CNN features. The proposed Latent-OFER model works well under occluded and unoccluded conditions. We evaluate this method on occluded FER datasets and typical FER datasets, and the proposed method achieves state-of-the-art accuracy. + +Acknowledgements This work was supported by the Industrial Fundamental Technology Development Program (No. 20018699) funded by MOTIE of Korea and IITP grant funded by the Korea government (MSIT; No.2021-0-02068, RS-2023-00256629). + +# References + +[1] Mouath Aouayeb, Wassim Hamidouche, Catherine Soladie, Kidiyo Kpalma, and Renaud Seguier. Learning vision transformer with squeeze and excitation for facial expression recognition. arXiv preprint arXiv:2107.03107, 2021. +[2] Emad Barsoum, Cha Zhang, Cristian Canton Ferrer, and Zhengyou Zhang. Training deep networks for facial expression recognition with crowd-sourced label distribution. In Proceedings of the 18th ACM international conference on multimodal interaction, pages 279-283, 2016. +[3] Jie Cai, Zibo Meng, Ahmed Shehab Khan, Zhiyuan Li, James O'Reilly, and Yan Tong. 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This is because when unexpected objects occlude the face, the FER network faces difficulties extracting facial features and accurately predicting facial expressions. Therefore, occluded FER (OFER) is a challenging problem. Previous studies on occlusion-aware FER have typically required fully annotated facial images for training. However, collecting facial images with various occlusions and expression annotations is time-consuming and expensive. Latent-OFER, the proposed method, can detect occlusions, restore occluded parts of the face as if they were unoccluded, and recognize them, improving FER accuracy. This approach involves three steps: First, the vision transformer (ViT)-based occlusion patch detector masks the occluded position by training only latent vectors from the unoccluded patches using the support vector data description algorithm. Second, the hybrid reconstruction network generates the masking position as a complete image using the ViT and convolutional neural network (CNN). Last, the expression-relevant latent vector extractor retrieves and uses expression-related information from all latent vectors by applying a CNN-based class activation map. This mechanism has a significant advantage in preventing performance degradation from occlusion by unseen objects. The experimental results on several databases demonstrate the superiority of the proposed method over state-of-the-art methods. This code is available at https://github.com/leeisack/Latent-OFER." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "type": "text", + "content": "Facial expression recognition (FER) has undergone remarkable advancements in recent years and is now widely used across various industries. However, the ability of FER models in the presence of occlusion remains a challenge." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 316, + 230, + 525, + 369 + ], + "blocks": [ + { + "bbox": [ + 316, + 230, + 525, + 369 + ], + "lines": [ + { + "bbox": [ + 316, + 230, + 525, + 369 + ], + "spans": [ + { + "bbox": [ + 316, + 230, + 525, + 369 + ], + "type": "image", + "image_path": "9ca4025bf30451ff5fcdf737fd83ae6fdc94da3d1e3d9c323b118c9b8cbf2bbd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 371, + 547, + 394 + ], + "lines": [ + { + "bbox": [ + 305, + 371, + 547, + 394 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 547, + 394 + ], + "type": "text", + "content": "Figure 1. Facial expression recognition (FER) performance on RAF-DB according to the occluded proportions." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 398, + 547, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 547, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 547, + 566 + ], + "type": "text", + "content": "Figure 1 illustrates the accuracy of the previous state-of-the-art model for FER [58] for various occlusion proportions. In this study, we evaluated the robustness of the typical model in recognizing facial expressions using two types of occlusions: random sampling occlusion and grad occlusion. Random sampling occlusion divides the entire image into 196 patches and randomly masks them according to the proportion. Grad occlusion processes an image with an intentionally occluded area that affects FER using gradient-weighted class activation mapping (Grad-CAM) [46]. This study reveals a more substantial decrease in performance with the second type of occlusion, particularly when the occluded area is crucial for accurate FER. This finding has been objectively measured using Grad-CAM [46]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 567, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 547, + 652 + ], + "type": "text", + "content": "Previous studies on FER [1, 2, 3, 5, 7, 13, 14, 15, 21, 23, 29, 31, 38, 43, 44, 49, 50, 54, 57, 60, 62, 63, 68, 69, 70] have not given adequate attention to the influence of occlusions. However, addressing this challenge is crucial for enhancing the practical applications of FER in real-world scenarios. Although research on occluded FER (OFER) is relatively scarce, its importance is increasingly recognized [66]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Currently, several approaches address OFER. The occlusion-robust feature extraction approach [9, 53] aims to identify an occlusion-insensitive and discriminative representation, but it is challenging because the types and locations of occlusion are often unknown. The sub region anal" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 713 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 749, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 316, + 757 + ], + "type": "text", + "content": "1536" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 203 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 203 + ], + "type": "text", + "content": "ysis approach [26, 55] divides regions based on facial landmarks and uses attention mechanisms to focus on crucial areas. However, the inability to detect facial landmarks due to occlusions can lead to errors in the FER process. The unoccluded image network assist approach [35, 61] uses two distinct networks: one trained on unoccluded images and the other trained on occluded images. This approach leverages unoccluded images as privileged information to assist in expression recognition in the presence of occlusion. It is unsuitable in real-world situations because it cannot differentiate between occluded and unoccluded images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 207, + 286, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 207, + 286, + 540 + ], + "spans": [ + { + "bbox": [ + 49, + 207, + 286, + 540 + ], + "type": "text", + "content": "Hence, the proposed approach is the occlusion recovery-based approach, which aims to transform occluded images into complete images through a deocclusion process. We propose the deocclusive autoencoder for reconstructing facial images. The deocclusive autoencoder can be functionally divided into an occlusion detector and reconstruction module. The occlusion detector uses the vision transformer (ViT) support vector data description (SVDD) for the reconstruction module. This approach enables the model to detect occlusion caused by unseen objects, an essential step in accurately generating deoccluded facial images. The reconstruction network consists of the ViT structure and convolutional neural network (CNN) structure for facial image reconstruction. We leverage the strengths of the ViT in generating realistic facial images despite varying poses and further refine them using the CNN. We call it the hybrid reconstruction network. The hybrid reconstruction network enhances FER performance by generating deoccluded images that express detailed and vivid facial expression attributes. This enhancement is achieved by incorporating a self-assembly layer and semantic consistency loss. In contrast, previous work on image reconstruction has primarily focused on achieving naturalness, which can result in dull facial expressions. Additionally, we use informative ViT-latent vectors obtained from the reconstruction process. We combine the CNN features and ViT-latent vectors for enhanced facial expression predictions. The main contributions in this work are summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 546, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 546, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 48, + 546, + 286, + 616 + ], + "type": "text", + "content": "- We propose an expression-relevant feature extractor that uses spatial attention to assign a higher weight to specific facial features, allowing us to identify critical positions for FER. We can retrieve expression-relevant latent vectors from the ViT-latent space to extract valuable information using these positions as critical values." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 618, + 286, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 618, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 48, + 618, + 286, + 689 + ], + "type": "text", + "content": "- We propose ViT-SVDD, a patch-based occlusion detection module optimized for ViT-based networks. As a self-supervised local classifier, the ViT-SVDD module is trained only on latent vectors of unoccluded facial images. This method accurately classifies occlusions caused by unseen objects for subsequent reconstruction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "type": "text", + "content": "- We propose a hybrid reconstruction network that combines the strengths of the ViT and CNN architectures with" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 73, + 544, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 73, + 544, + 119 + ], + "spans": [ + { + "bbox": [ + 308, + 73, + 544, + 119 + ], + "type": "text", + "content": "a self-assembly layer and semantic consistency loss to generate facial images naturalness and rich in expression. This approach enhances the quality of deoccluded images and improves the accuracy of FER in challenging conditions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 133, + 391, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 133, + 391, + 144 + ], + "spans": [ + { + "bbox": [ + 308, + 133, + 391, + 144 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 152, + 453, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 152, + 453, + 164 + ], + "spans": [ + { + "bbox": [ + 308, + 152, + 453, + 164 + ], + "type": "text", + "content": "2.1. Occluded Object Detection" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 171, + 544, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 171, + 544, + 360 + ], + "spans": [ + { + "bbox": [ + 308, + 171, + 544, + 360 + ], + "type": "text", + "content": "Several early studies [8] have attempted to detect occlusions in images for OFER tasks. The conventional methods provide location information about the occlusions and are called occlusion-aware methods [26, 55]. However, these methods are not practical for real-world scenarios. Another approach [30] is to train models using synthesized images with various occlusions to detect the occluded positions. Although this approach can determine occlusion positions, it requires a diverse set of object images, which can be challenging to obtain. Moreover, the performance of these models [26, 30, 55] degrades when they encounter unseen objects as input. We drew inspiration from anomaly detection tasks [10, 45, 47, 64] with one-class classification algorithms [20, 32, 39, 40, 52] and proposed a model that learns only from unoccluded datasets and can generalize well to unseen datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 371, + 515, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 371, + 515, + 383 + ], + "spans": [ + { + "bbox": [ + 308, + 371, + 515, + 383 + ], + "type": "text", + "content": "2.2. Occluded Facial Expression Recognition" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 390, + 544, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 390, + 544, + 472 + ], + "spans": [ + { + "bbox": [ + 308, + 390, + 544, + 472 + ], + "type": "text", + "content": "We have no prior knowledge of where occlusions may appear on a facial image or how large or complex they might be. These occlusions can significantly reduce the accuracy of FER by either increasing the intra-class variability or inter-class similarity. Four categories address this issue: occlusion-robust feature extraction, subregion analysis, unoccluded image network-assisted, and occlusion recovery." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 474, + 544, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 474, + 544, + 533 + ], + "spans": [ + { + "bbox": [ + 308, + 474, + 544, + 533 + ], + "type": "text", + "content": "Occlusion-robust feature extraction approach. This approach aims to extract features less affected by occlusions while maintaining discriminative capability. Wang et al. [53] used self-supervised and contrastive learning to explore robust representations with synthesized occlusions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 534, + 544, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 534, + 544, + 604 + ], + "spans": [ + { + "bbox": [ + 308, + 534, + 544, + 604 + ], + "type": "text", + "content": "Subregion analysis approach. This approach excludes the occluded parts from recognition. By focusing only on the unoccluded facial parts, the influence of occlusion on recognition performance can be reduced. Li et al. [26] proposed a gate unit with an attention mechanism that allows the model to focus on informative unoccluded facial areas." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 606, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 606, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 606, + 544, + 712 + ], + "type": "text", + "content": "Unoccluded image network-assisted approach. This approach employs unoccluded facial images as guidance to assist with OFER. Pan et al. [35] trained two deep neural networks from occluded and unoccluded facial images. Then, the unoccluded network guides the occluded network. Xia et al. [61] measured the complexity of unoccluded data using distribution density in a feature space. The classifier can be guided by unoccluded data and subsequently leverage more meaningful and discriminative samples." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 750, + 314, + 757 + ], + "type": "text", + "content": "1537" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 72, + 533, + 232 + ], + "blocks": [ + { + "bbox": [ + 60, + 72, + 533, + 232 + ], + "lines": [ + { + "bbox": [ + 60, + 72, + 533, + 232 + ], + "spans": [ + { + "bbox": [ + 60, + 72, + 533, + 232 + ], + "type": "image", + "image_path": "184900aecb48fa1c83b2b6ad20352e27e427fd17fafd389d0c3748337749cb68.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 234, + 546, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 546, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 546, + 268 + ], + "type": "text", + "content": "Figure 2. Framework of the Latent-OFER that creates a deoccluded image that erases the occlusion. In this process, the expression-relevant latent vectors are extracted by mapping the vision transformer (ViT)-latent vector and the convolutional neural network (CNN) class activation map. Latent-OFER predicts facial expressions that combine CNN-based features with specific VIT-based latent vectors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 456 + ], + "type": "text", + "content": "Occlusion recovery-based approach. This approach uses face completion as a basis to deal with occlusion. To reconstruct occluded faces, Lu et al. [30] suggested using a WGAN consisting of an autoencoder-based generator and discriminators. By reconstructing the occlusion, these approaches provide necessary information while avoiding the interference of noisy information and obtaining informative appearance. Therefore, we adopt an image-inpainting technique as a recovery-based approach, to deal with occlusion. A notable point of differentiation between our method and existing approaches lies in our specific emphasis on the reconstruction of occluded regions while simultaneously retaining the facial expression information. Furthermore, we employ ViT-based latent vectors extracted throughout the reconstruction process to enhance the performance of FER." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 466, + 151, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 151, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 151, + 479 + ], + "type": "text", + "content": "2.3. Image inpainting" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 485, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 616 + ], + "type": "text", + "content": "Several approaches based on CNN have been developed to generate semantically coherent content. Pathak et al. [37] employed context encoders to generate plausible features for the area requiring restoration. Yu et al. [65] introduced a contextual attention module to refine by referencing the surrounding features. Song et al. [51] used a patch-swap layer that replaces each patch within the masking areas of a feature map with the most comparable patch in the unoccluded areas. Liu et al. [28] developed a coherent semantic attention layer to ensure semantic relevance between the swapped features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "In recent years, transformer-based methods have also significantly contributed to computer vision. The ViT [11] achieves better results for image recognition than CNN-based methods. Furthermore, MAE [17] demonstrated that transformer-based models are well-suited for image inpainting tasks. However, transformer-based algorithms have a limitation in that they may produce blurry results when restoring large block areas [17]. Another work [25]" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 277, + 546, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 546, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 546, + 337 + ], + "type": "text", + "content": "presents MAT, a transformer-based model for large-hole inpainting. Nevertheless, in cases where the eyes or mouth are fully occluded, the ViT cannot generate images in detail because it is significantly less biased toward local textures [34]. Therefore, the challenge remains." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 346, + 411, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 346, + 411, + 360 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 411, + 360 + ], + "type": "text", + "content": "3. Proposed method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 365, + 546, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 546, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 546, + 498 + ], + "type": "text", + "content": "As shown in Figure 2, we propose multi-stage approach to address OFER, involving detecting, masking, and reconstructing occlusions to recognize facial expressions. The proposed approach enhances recognition accuracy through cooperative learning ViT-latent vectors extracted from the image reconstruction process and the existing CNN features. We divided the facial image into patches, classified each patch as occluded or unoccluded, and reconstructed the occluded patches to be deoccluded. Subsequently, we leveraged the reconstructed image and expression-relevant latent vectors to predict facial expressions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 503, + 516, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 503, + 516, + 516 + ], + "spans": [ + { + "bbox": [ + 305, + 503, + 516, + 516 + ], + "type": "text", + "content": "3.1. Occlusion detection module: ViT-SVDD" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "type": "text", + "content": "General object detection and segmentation models may not be suitable for real-world scenarios because they may be unable to detect unseen objects. To address this limitation, we use one-class classification, which is often employed in anomaly detection. This approach makes it possible to classify unused occlusion during training through self-supervised learning, which only uses unoccluded patches for learning, providing a more effective solution for real-world applications." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "type": "text", + "content": "One-class classification methods for classifying normal or abnormal can operate at various levels of granularity, ranging from low-level anomaly detection [47] at the pixel level to high-level anomaly detection [40] at the image level. Detection and classification are performed based on the size of the unit, which can be customized to suit the user's needs. We used a ViT-based reconstruction method;" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1538" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "thus, we propose a middle-level anomaly detector specifically optimized for ViT. We divided the image to match the size of the ViT patch and created ViT-latent vectors. These patches are encoded with informative features to produce ViT-latent vectors. To generate the smallest feature space for unoccluded patches, we used the deep SVDD algorithm [39]. One-class deep SVDD employs quadratic loss to penalize the distance of every network representation. This objective is defined as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 72, + 180, + 287, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 180, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 72, + 180, + 287, + 213 + ], + "type": "interline_equation", + "content": "\\min \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\| \\Phi (x _ {i}; \\mathcal {W}) - c \\| ^ {2} + \\frac {\\lambda}{2} \\sum_ {l = 1} ^ {L} \\| w ^ {l} \\| _ {F} ^ {2}. \\tag {1}", + "image_path": "ff268fe6e1638d29a468d3fd7ea01c0c409b63ceeb322c9f1654ba4db1db1057.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " denotes number of training data, " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " denote number of layer, " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " denotes set of weights " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{W} = \\{w^1, \\dots, w^L\\}" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " represents a hypersphere characterized by the center. The first term induces the features of all normal images to converge at the center point " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": ", whereas the last term is a weight decay regularizer on the network parameter " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " with hyperparameter " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "\\lambda > 0" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|_F" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " denotes the Frobenius norm. Eq (1) simply employs a quadratic loss for penalizing the distance of every network representation " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "\\Phi(x_i; \\mathcal{W})" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{F}" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": ", Where " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " is output feature space. The network learn parameters " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " such that data points are closely mapped to " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " of the hypersphere. To determine whether a patch is occluded, we calculated the distance between the new input information and the center " + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 215, + 289, + 502 + ], + "type": "text", + "content": " of the feature space for each patch. If the distance exceeds the pre-defined radius, the corresponding patch is classified as occluded and masked. The optimal value of the radius is automatically determined in the SVDD procedure. Through this process, occlusion patch detection is possible for unseen objects. The proposed ViT-SVDD approach allows for validating the performance of synthetic images with occlusion patch annotations. By detecting occlusion patches, we can improve the accuracy of the reconstruction method and make it more suitable for real-world applications." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 511, + 287, + 535 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 287, + 535 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 287, + 535 + ], + "type": "text", + "content": "3.2. Image reconstruction module: hybrid reconstruction network" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 542, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 651 + ], + "type": "text", + "content": "The facial image reconstruction process employs an occlusion-masked image generated by the occlusion detector. The hybrid reconstruction network is designed to cooperate by fusing ViT-based and CNN-based networks. Through this mechanism, we leverage both the strengths of ViT and CNN. The ViT-based method employs " + }, + { + "bbox": [ + 46, + 542, + 287, + 651 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 542, + 287, + 651 + ], + "type": "text", + "content": " patches as input image; however, we used the outputs of the occlusion detector as input because the image has already been partitioned into patch units by the occlusion detector." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 160, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 160, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 160, + 669 + ], + "type": "text", + "content": "3.2.1 Network structure" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "The ViT-based approach encodes the input patches and positively embeds all tokens. The occluded patch reconstruction is achieved through correlation with other patches." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 331, + 55, + 523, + 163 + ], + "blocks": [ + { + "bbox": [ + 331, + 55, + 523, + 163 + ], + "lines": [ + { + "bbox": [ + 331, + 55, + 523, + 163 + ], + "spans": [ + { + "bbox": [ + 331, + 55, + 523, + 163 + ], + "type": "image", + "image_path": "e15a46d6198aa4dc7abd7a8bf76a973c1c1e9708eb0a28697a3174adb9145035.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 166, + 545, + 200 + ], + "lines": [ + { + "bbox": [ + 305, + 166, + 545, + 200 + ], + "spans": [ + { + "bbox": [ + 305, + 166, + 545, + 200 + ], + "type": "text", + "content": "Figure 3. Illustration of the self-assembly operation. (a) Feature map in the self-assembly layer. (b) Flip of (a). The patch in masked region is generated by combining three patch information." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 208, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 208, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 305, + 208, + 545, + 352 + ], + "type": "text", + "content": "The ViT has low inductive bias and a high degree of freedom [34], enabling it to generate credible images despite diverse occlusion shapes, positions, and facial poses. As discussed in Section 2.3, the ViT-based approach may sometimes not supply detailed results. To address this limitation, we combined the ViT and CNN. The network consists of a U-Net architecture. Additionally, we added a self-assembly layer inside the encoder to generate a detailed representation. This multi structure approach effectively combines the strengths of the ViT and CNN-based networks to generate high-quality facial image reconstructions that represent facial expressions well." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 356, + 422, + 368 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 422, + 368 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 422, + 368 + ], + "type": "text", + "content": "3.2.2 Self-assembly layer" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 374, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 374, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 305, + 374, + 545, + 566 + ], + "type": "text", + "content": "We implemented a self-assembly layer to improve image reconstruction for FER. We reconstructed masked regions like [17] but made enhancements specific to facial images. Based on the concept that the left and right characteristics of a person's face are symmetrical[42, 48, 67], we used the feature information present in the corresponding location of the horizontally flipped image when reconstructing a masked region. We expanded the range of candidate patches used in the generation process by incorporating information from three sources, the previously generated patch, the most similar patch in the unmasked region, and patches located in the corresponding position of the horizontally flipped image. In this process, the masked region contains the reconstruction results with the ViT network. We assigned weights to each based on the similarity value with the current patch. The weight calculation is based on a cross-correlation metric:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 376, + 573, + 545, + 600 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 573, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 376, + 573, + 545, + 600 + ], + "type": "interline_equation", + "content": "S (p, p _ {x}) = \\frac {\\langle p , p _ {x} \\rangle}{\\| p \\| \\cdot \\| p _ {x} \\|}, \\tag {2}", + "image_path": "87cac0a72f9166197a9ae03d8fa67e15fc91088eb2f2f483decebf8ce3588403.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "text", + "content": " represents a patch in the masked region, and the patch " + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "inline_equation", + "content": "p_x" + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "text", + "content": " is the comparison target. The similarity value between " + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "inline_equation", + "content": "p_x" + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "text", + "content": " is denoted by " + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 605, + 545, + 642 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": "The self-assembly operation is defined in Eq (3), which generates a patch value " + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": ". Figure 3 depicts the operation process, where " + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "p_s" + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": " denotes the patch value symmetrically positioned with respect to " + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": " and averaged by considering the peripheral patches. The " + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "S_{sym}" + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": " is calculated as Eq (2) through " + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "p_{s_i}" + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": ". In addition, " + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "p_k" + }, + { + "bbox": [ + 305, + 642, + 545, + 714 + ], + "type": "text", + "content": " is the most similar patch" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1539" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "to " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " among the unmasked region, and " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "S_{\\text{known}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " is calculated as " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "S(p_i, p_{k_i})" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ". Further, " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "p_{i-1}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " represents the previously generated patch, and " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "S_{i-1}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " is obtained by " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "S(p_i, p_{i-1})" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ". The similarity value " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " is normalized to be used as the weight." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": "In Figure 3, the red patch in (a) is " + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": ", which is a combined result of " + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "inline_equation", + "content": "p_k" + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": " (the orange patch), " + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "inline_equation", + "content": "p_{i-1}" + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": " (the yellow patch), and " + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "inline_equation", + "content": "p_s" + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": " (the blue patch in (b)). Because " + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": " has no prior generated patch, " + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "inline_equation", + "content": "S_0" + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": " is zero. In certain cases, such as side-face images, the patches in symmetrical positions may not be relevant for generating the patch. Thus, the value of " + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "inline_equation", + "content": "S_{sym}" + }, + { + "bbox": [ + 46, + 120, + 288, + 204 + ], + "type": "text", + "content": " in this situation is minimal and is rarely used to generate the patch." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 92, + 220, + 287, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 220, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 92, + 220, + 287, + 301 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p _ {i} = \\frac {S _ {s y m}}{S _ {s y m} + S _ {k n o w n} + S _ {i - 1}} \\times p _ {s _ {i}} \\\\ + \\frac {S _ {\\text {k n o w n}}}{S _ {\\text {s y m}} + S _ {\\text {k n o w n}} + S _ {i - 1}} \\times p _ {k _ {i}}. \\tag {3} \\\\ + \\frac {S _ {i - 1}}{S _ {s y m} + S _ {k n o w n} + S _ {i - 1}} \\times p _ {i - 1} \\\\ \\end{array}", + "image_path": "83b156a165677e73f5027469f8680baa4cba1b6b9ad897c61be83d78f6793d30.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 314, + 121, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 314, + 121, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 314, + 121, + 327 + ], + "type": "text", + "content": "3.2.3 Objective" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": "The aim of image reconstruction is to fill in the masked portion to provide supplementary information for FER. In pursuit of this, we incorporated a semantic consistency loss that enables optimizing the task while maintaining the reconstruction loss " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "L_{re}" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": ", consistency " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "L_{c}" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": " [28], feature patch discriminator " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "L_{d_f}" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": " [19], and patch discriminator " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "L_{d}" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": " [36]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 405, + 287, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 440 + ], + "type": "text", + "content": "The semantic consistency loss " + }, + { + "bbox": [ + 46, + 405, + 287, + 440 + ], + "type": "inline_equation", + "content": "L_{sc}" + }, + { + "bbox": [ + 46, + 405, + 287, + 440 + ], + "type": "text", + "content": " emphasizes facial expression attributes. The " + }, + { + "bbox": [ + 46, + 405, + 287, + 440 + ], + "type": "inline_equation", + "content": "L_{sc}" + }, + { + "bbox": [ + 46, + 405, + 287, + 440 + ], + "type": "text", + "content": " has the effect of reducing intraclass variability and can be defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 96, + 441, + 287, + 474 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 441, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 96, + 441, + 287, + 474 + ], + "type": "interline_equation", + "content": "L _ {s c} = \\sum_ {c = 1} ^ {7} p _ {c} \\left(z _ {g t}\\right) \\log \\left(p _ {c} \\left(z _ {r e c}\\right)\\right), \\tag {4}", + "image_path": "f7b23a45b758c149fd3f47268900b1fe03c2e8b3793da87f8dae6b90edc51f5c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "text", + "content": " represents seven basic expressions, " + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "inline_equation", + "content": "p_c(z_{gt})" + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "text", + "content": " denotes the predicted probability of " + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "text", + "content": " in the ground-truth image, and " + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "inline_equation", + "content": "p_c(z_{rec})" + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "text", + "content": " indicates the predicted probability of " + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 478, + 287, + 549 + ], + "type": "text", + "content": " in the reconstruction result. The predicted probability distributions are obtained via the pretrained FER network. During training, the overall loss function is defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 62, + 559, + 287, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 559, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 62, + 559, + 287, + 574 + ], + "type": "interline_equation", + "content": "L = \\lambda_ {r e} L _ {r e} + \\lambda_ {c} L _ {c} + \\lambda_ {s c} L _ {s c} + \\lambda_ {d} \\left(L _ {d} + L _ {d _ {f}}\\right), \\tag {5}", + "image_path": "391d99a5dd858b2b7a1c430165a00838933fb79e8334ff35b88fc8c4fd7bc351.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 580, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 580, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\lambda_{re},\\lambda_{c},\\lambda_{sc},\\lambda_{d}" + }, + { + "bbox": [ + 46, + 580, + 287, + 652 + ], + "type": "text", + "content": " denote the trade-off parameters for the reconstruction, consistency, semantic consistency, discriminator losses, respectively. Furthermore, the FER network is trained with the same feature extraction architecture using probability distributions about the ground-truth label and prediction of FER." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 659, + 247, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 247, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 247, + 672 + ], + "type": "text", + "content": "3.3. Facial expression recognition network" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "The proposed FER network is designed as an attention-based model for predicting facial expressions. We employed spatial and channel-attention mechanisms [59]." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 306, + 71, + 544, + 247 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 544, + 247 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 544, + 247 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 544, + 247 + ], + "type": "image", + "image_path": "4b750f4a56a6c628cefd3fcbcc8d4747d6c4a57f60bf9c2e83a932a192b6ac54.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 253, + 545, + 275 + ], + "lines": [ + { + "bbox": [ + 305, + 253, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 305, + 253, + 545, + 275 + ], + "type": "text", + "content": "Figure 4. Expression-relevant vision transformer (ViT)-latent vector extraction method." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 283, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 283, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 545, + 354 + ], + "type": "text", + "content": "We obtained the refined feature map and CAM using the attention-based model. In addition, we obtained the expression-relevant latent vectors from the ViT using the CAM. As depicted in Figure 2, the Latent-OFER cooperatively uses a CNN-based feature and ViT-based latent vectors. Thus, the model performs better." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 356, + 545, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 545, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 545, + 451 + ], + "type": "text", + "content": "Expression-relevant ViT-latent vectors. The proposed method employs only expression-relevant latent vectors rather than the entire latent space to improve FER performance. During the reconstruction process, ViT-based latent vectors are extracted by embedding the input image. We used a CAM to identify spatially significant areas within the image for FER, and the class activation map is generated through a CNN." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 453, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 585 + ], + "type": "text", + "content": "The position of the area is stored as a key, and the attention weight for each space is recorded. The key of the region where the weight of the spatial attention exceeds the top " + }, + { + "bbox": [ + 304, + 453, + 545, + 585 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 453, + 545, + 585 + ], + "type": "text", + "content": " is used. This key is retrieved from the entire ViT-latent vectors, and the corresponding value is read. The activation map is used to identify expression-relevant latent vectors, as presented in Figure 4. This process enables the selection of positions that are relevant to FER while avoiding extraneous details, such as appearance information irrelevant to expressions, which can increase inter-class dissimilarity and lead to more accurate and effective learning results." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 586, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 586, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 586, + 545, + 658 + ], + "type": "text", + "content": "In cases where patch detection fails, the occluded patch's latent vectors are used for training and inference. However, spatial attention is not focused on the occluded area, and the latent vector of the occlusion patch is neither searched nor used for training and inference. The proposed extractor is not significantly affected in this situation." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 669, + 387, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 387, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 387, + 682 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "In this part, we describe three FER benchmark datasets and several occluded FER datasets used to evaluate this" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1540" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 273, + 109 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 273, + 109 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 273, + 109 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 273, + 109 + ], + "type": "table", + "html": "
Accuracy (%)Precision (%)Recall (%)
One class SVM [39]91.190.289.4
Patch-SVDD [64]85.280.194.1
ViT-SVDD98.394.198.7
", + "image_path": "0aef81f360a17b0ef13206eed6593eb208903499ec6702c3b6080fd8f49e4a34.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 110, + 277, + 121 + ], + "lines": [ + { + "bbox": [ + 49, + 110, + 277, + 121 + ], + "spans": [ + { + "bbox": [ + 49, + 110, + 277, + 121 + ], + "type": "text", + "content": "Table 1. Comparison of occlusion patch detection performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 61, + 128, + 275, + 191 + ], + "blocks": [ + { + "bbox": [ + 61, + 128, + 275, + 191 + ], + "lines": [ + { + "bbox": [ + 61, + 128, + 275, + 191 + ], + "spans": [ + { + "bbox": [ + 61, + 128, + 275, + 191 + ], + "type": "image", + "image_path": "fa6926fe9939294850e591e2d75ac4684f0e7246cd9dd68065f045c301344546.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 194, + 253, + 205 + ], + "lines": [ + { + "bbox": [ + 80, + 194, + 253, + 205 + ], + "spans": [ + { + "bbox": [ + 80, + 194, + 253, + 205 + ], + "type": "text", + "content": "Figure 5. Occlusion patch classification results." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 215, + 287, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 215, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 215, + 287, + 264 + ], + "type": "text", + "content": "model and explain the results. We demonstrate that the proposed method performs better on both the FER task and occluded FER task. Last, an ablation study demonstrates how each model element contributes to the final performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 273, + 105, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 273, + 105, + 284 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 105, + 284 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 294, + 287, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 294, + 287, + 343 + ], + "spans": [ + { + "bbox": [ + 47, + 294, + 287, + 343 + ], + "type": "text", + "content": "RAF-DB [24] is a large-scale facial expression database with around 30,000 images. We used data on seven basic expressions, 12,271 images as the training set, and 3,068 images as the testing set." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 344, + 287, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 287, + 381 + ], + "type": "text", + "content": "AffectNet [33] is the largest facial expression database with annotations. We used seven basic expressions facial images, about 287,568 training and 3,500 testing images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 383, + 286, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 286, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 286, + 407 + ], + "type": "text", + "content": "KDEF [4] is a set of 4,900 images of facial expressions. Each expression is viewed from five viewpoints." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 409, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 409, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 47, + 409, + 287, + 433 + ], + "type": "text", + "content": "Syn-AffectNet and Syn-RAF-DB consist of FER benchmark datasets that synthesize a real object to occlude." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "type": "text", + "content": "Occlusion-AffectNet and Occlusion-RAF-DB are real-world occlusion datasets selected from the AffectNet validation set and RAF-DB testing set by Wang et al. [53]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 474, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 474, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 287, + 534 + ], + "type": "text", + "content": "FED-RO dataset is also a real-world occlusion dataset collected by Li et al. [26]. It contains 400 images labeled with seven basic emotions. We trained the proposed model using RAF-DB and AffectNet when testing the FED-RO datasets, following the protocol suggested in [26]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 548, + 178, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 178, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 178, + 562 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "text", + "content": "We trained a self-supervised occlusion detection module with the KDEF dataset [4] synthesized by randomly copy-pasting objects such as hands and cups for occlusion. We used a ViT-based network pretrained with ImageNet [6] and a CNN-based network trained on several FER training datasets [24, 33] for detailed representation in the image reconstruction module. The FER network uses ResNet-18 [18] backbone architecture. It is pretrained on MS-Celeb-1M [16]. The trade-off parameters in hybrid reconstruction module are set as " + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{re} = 1" + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_c = 0.01" + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{sc} = 1" + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_d = 0.002" + }, + { + "bbox": [ + 47, + 570, + 287, + 712 + ], + "type": "text", + "content": ". The experimental source code is implemented with PyTorch, and the models are trained with a GTX-3090 GPU." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 322, + 72, + 531, + 181 + ], + "blocks": [ + { + "bbox": [ + 322, + 72, + 531, + 181 + ], + "lines": [ + { + "bbox": [ + 322, + 72, + 531, + 181 + ], + "spans": [ + { + "bbox": [ + 322, + 72, + 531, + 181 + ], + "type": "image", + "image_path": "6e8a401e819ab056cc57f52a5055003fa9020d7c56e48b4009b83cd0cb37b22d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 183, + 545, + 227 + ], + "lines": [ + { + "bbox": [ + 305, + 183, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 305, + 183, + 545, + 227 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison of synthesis and real occlusion. Facial expression recognition prediction results according to image reconstruction. Labels highlighted in green indicate matching the correct expression, whereas red indicates a misprediction." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 243, + 526, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 243, + 526, + 256 + ], + "spans": [ + { + "bbox": [ + 306, + 243, + 526, + 256 + ], + "type": "text", + "content": "4.3. Comparison of occlusion detection module" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 262, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 334 + ], + "type": "text", + "content": "The proposed ViT-SVDD detects occlusion for each patch using a suitable detector for ViT-based image reconstruction. We compared the module with existing one-class classification methods trained solely on unoccluded images to evaluate its effectiveness. We used a test set consisting of occluded and unoccluded images." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 407 + ], + "type": "text", + "content": "Patch-SVDD, which trains in a hierarchical structure from small pixels to large pixels and segments anomaly positions into small pixel units, was also included in the comparison. The proposed module achieved the highest occlusion detection accuracy among all methods, as demonstrated in Table 1." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 408, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 408, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 408, + 545, + 540 + ], + "type": "text", + "content": "Based on these results, the proposed method is particularly well-suited for the patch-by-patch processing rather than being the optimal solution for all anomaly detection tasks. While several proposed anomaly detection methods are suitable for various units, such as whole images and pixels, this approach is specifically designed to fit the ViTSVDD framework and detect anomalies in a patch-specific manner. As illustrated in Figure 5, the results demonstrate improved performance in patch-specific occlusion detection, indicating that the proposed method is best suited for special situations that require this processing type." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 550, + 506, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 506, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 506, + 562 + ], + "type": "text", + "content": "4.4. Comparison of reconstruction module" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "The hybrid reconstruction network is compared to MAE [17] and CSA [28]. All reconstruction results are the direct output of the model without post processing. Figure 6 compares the results of deocclusion for synthesis and real occlusion on RAF-DB and AffectNet. As displayed in Figure 6 and Table 2, we present qualitative and quantitative comparisons and the FER result. The self-assembly layer enlarge the facial expression information and increase the number of patch candidates involved in the generation process to reconstruct visually pleasing and natural, and semantic consistency loss induces rich in expression of facial images, providing an advantage for FER. While other com" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1541" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 70, + 260, + 91 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 260, + 91 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 260, + 91 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 260, + 91 + ], + "type": "table", + "html": "
MAE [17]CSA [28]Self-assembly
Accuracy (%)72.675.677.3
", + "image_path": "b32812f1a474116b26f19e974bff4f6a097e988f88b12a4c3cea014e299f9fbd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 72, + 118, + 261, + 205 + ], + "blocks": [ + { + "bbox": [ + 47, + 95, + 287, + 116 + ], + "lines": [ + { + "bbox": [ + 47, + 95, + 287, + 116 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 287, + 116 + ], + "type": "text", + "content": "Table 2. Facial expression recognition prediction results according to image reconstruction on Syn-RAF-DB." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 118, + 261, + 205 + ], + "lines": [ + { + "bbox": [ + 72, + 118, + 261, + 205 + ], + "spans": [ + { + "bbox": [ + 72, + 118, + 261, + 205 + ], + "type": "table", + "html": "
InputMAECSASelf-assemblyGround truth
SurpriseSurpriseSurpriseHappinessHappiness
SurpriseFearDisgustSadnessAnger
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MethodAffect NetSyn-Affect NetRAF DBSyn-RAF DBKDEFSyn-KDEF
DACL [15]62.549.688.876.087.968.9
RUL [68]62.652.288.977.183.151.2
DAN [58]63.851.189.776.186.870.8
EAC [69]63.254.988.078.687.567.6
Latent -OFER63.956.189.680.188.386.7
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gACNN [26]Pan's [35]Xia's [61]RAN [55]OADN [9]Wang's [53]Latent -OFER
FED-RO66.569.370.568.068.170.071.8
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BoostGAN [12]RAN [55]OADN [9]Latent -OFER
Occlusion-AffectNet43.458.564.066.1
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BoostGAN [12]RAN [55]Wang's [53]Latent -OFER
Occlusion-RAF-DB55.482.782.584.2
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MethodAccuracyComplexity
AffectNetRAF-DBFlops(G)Parameters(M)
gACNN [26]58.885.1331370
WGAN AE [30]59.783.5353400
Pan's [35]57.180.2525
Xia's [61]57.582.7230360
RAN [55]52.686.9390300
OADN [9]61.987.2122250
Wang's [53]60.286.0102210
Latent-OFER63.989.6156373
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Accuracy (%) and complexity comparison to the occluded FER models on the typical FER datasets" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 354, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 354, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 306, + 354, + 545, + 389 + ], + "type": "text", + "content": "that the proposed model achieved an accuracy of " + }, + { + "bbox": [ + 306, + 354, + 545, + 389 + ], + "type": "inline_equation", + "content": "71.8\\%" + }, + { + "bbox": [ + 306, + 354, + 545, + 389 + ], + "type": "text", + "content": " with the default setting, a new state-of-the-art performance for this dataset, to the best of our knowledge." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "text", + "content": "Tables 5 and 6 present the FER performance for occluded images in AffectNet and RAF-DB, where the proposed Latent-OFER model achieved an accuracy of " + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "inline_equation", + "content": "66.5\\%" + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "inline_equation", + "content": "84.2\\%" + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "text", + "content": " with the default setting " + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "inline_equation", + "content": "(2.5\\% p" + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "inline_equation", + "content": "1.5\\% p" + }, + { + "bbox": [ + 304, + 390, + 545, + 450 + ], + "type": "text", + "content": " better than OADN [9] and RAN [55]), respectively." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "text", + "content": "Table 7 compares the accuracy and complexity of the OFER models. The complexity is estimated by ourselves. As demonstrated in Table 7, OFER models exhibit poor performance on typical FER datasets. This limitation makes them unsuitable for general use unless the unoccluded image network-assisted approach described in Section 1 is employed. In contrast, the proposed model demonstrates acceptable performance on typical and occluded FER datasets. Specifically, the proposed model achieves accuracy rates of " + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "inline_equation", + "content": "63.9\\%" + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "inline_equation", + "content": "89.6\\%" + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "text", + "content": ", which represent improvements of " + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "inline_equation", + "content": "2.0\\% p" + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "inline_equation", + "content": "2.4\\% p" + }, + { + "bbox": [ + 304, + 451, + 545, + 582 + ], + "type": "text", + "content": ", respectively, over OADN." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 597, + 397, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 397, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 397, + 609 + ], + "type": "text", + "content": "5. Ablation study" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 617, + 544, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 617, + 544, + 640 + ], + "spans": [ + { + "bbox": [ + 306, + 617, + 544, + 640 + ], + "type": "text", + "content": "This section presents the experiments investigating the effects of several modules on FER performance" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Effect of self-assembly layer. We use RAF-DB test dataset and synthesize irregular masks [27] for each image to make comparison. We replaced the self-assembly layer with a conventional " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " layer and the CSA layer [28]. As presented in Table 8, we used standard evaluation metrics, the PSNR [56] and SSIM [56], to quantify the module per" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1542" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 103, + 70, + 232, + 106 + ], + "blocks": [ + { + "bbox": [ + 103, + 70, + 232, + 106 + ], + "lines": [ + { + "bbox": [ + 103, + 70, + 232, + 106 + ], + "spans": [ + { + "bbox": [ + 103, + 70, + 232, + 106 + ], + "type": "table", + "html": "
MethodPSNR(↑)SSIM(↑)
Conventional26.360.868
CSA25.480.860
Self-assembly26.650.880
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MAE [17]CSA [28]Hybrid reconstruction
Reconstructed-RAF-DB72.671.677.3
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Image recon-stuctionCNN-featuresFull ViT-latent vectorsExtracted ViT-latent vectorsAccuracy (%)
✓15.2
✓20.1
✓75.4
✓✓76.5
✓✓78.5
✓✓64.9
✓✓66.4
✓✓82.7
✓✓✓84.2
✓✓✓86.7
", + "image_path": "26b5ec749cf4ebac0367d618d9b1cc78035d9f2ced8df61c3f4c426c36ad03aa.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 189, + 528, + 200 + ], + "lines": [ + { + "bbox": [ + 305, + 189, + 528, + 200 + ], + "spans": [ + { + "bbox": [ + 305, + 189, + 528, + 200 + ], + "type": "text", + "content": "Table 10. Module evaluation in Latent-OFER on Syn-KDEF." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 204, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 204, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 204, + 545, + 239 + ], + "type": "text", + "content": "and the best performance is achieved when CNN features and expression-relevant ViT-latent vectors are trained cooperatively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 244, + 375, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 244, + 375, + 256 + ], + "spans": [ + { + "bbox": [ + 306, + 244, + 375, + 256 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 264, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 545, + 503 + ], + "type": "text", + "content": "This section discusses two topics. First, the performance of the occluded patch detector can be considered dominant. The proposed model restores images and extracts latent vectors to use for FER. In cases where occlusion patch detection fails to perform adequately, latent vectors are not extracted correctly because the image is not fully restored. However, the model uses spatial attention to extract expression-relevant features. In images with poor occlusion patch detection, the corresponding patch has lower weights. As a result, the influence of poor detection on the overall performance is mitigated. The second is the potential limitations of scalability when using image reconstruction modules trained with a single dataset. These models may not be adaptable enough to handle a variety of datasets, thereby making it difficult to reconstruct a complete image. To overcome this challenge, extra training on diverse datasets or the adoption of uniform alignment across datasets is necessary. Therefore, to enhance the flexibility of image reconstruction modules, a multi-dataset training approach or standardized alignment methods can be implemented." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 509, + 378, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 378, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 378, + 521 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 529, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 649 + ], + "type": "text", + "content": "This paper addresses FER in real-world occlusion. Our method involves detecting the occluded parts of the face and then reconstructing them using a specially designed reconstruction network to produce images as if they were unoccluded. In addition, expression-relevant latent vectors were extracted and learned cooperatively with the CNN features. The proposed Latent-OFER model works well under occluded and unoccluded conditions. We evaluate this method on occluded FER datasets and typical FER datasets, and the proposed method achieves state-of-the-art accuracy." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements This work was supported by the Industrial Fundamental Technology Development Program (No. 20018699) funded by MOTIE of Korea and IITP grant funded by the Korea government (MSIT; No.2021-0-02068, RS-2023-00256629)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1543" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Mouath Aouayeb, Wassim Hamidouche, Catherine Soladie, Kidiyo Kpalma, and Renaud Seguier. 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In Proceedings of the AAAI conference on artificial intelligence, pages 3510-3519, 2021." + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1546" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_content_list.json b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e3cb976562e5a6f9bf4a86251c981eb2202ed4e0 --- /dev/null +++ b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_content_list.json @@ -0,0 +1,1625 @@ +[ + { + "type": "text", + "text": "LayoutDiffusion: Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models", + "text_level": 1, + "bbox": [ + 181, + 130, + 789, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Junyi Zhang $^{1*}$ Jiaqi Guo $^{2}$ Shizhao Sun $^{2}$ Jian-Guang Lou $^{2}$ Dongmei Zhang $^{2}$ \\\n $^{1}$ Shanghai Jiao Tong University\\\n $^{2}$ Microsoft Research Asia\\\njunyizhang@sjtu.edu.cn $\\{\\mathrm{jiaqiguo, shizsu, jlou, dongmeiz}\\} @$ microsoft.com", + "bbox": [ + 111, + 202, + 856, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 287, + 313, + 305 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Creating graphic layouts is a fundamental step in graphic designs. In this work, we present a novel generative model named LayoutDiffusion for automatic layout generation. As layout is typically represented as a sequence of discrete tokens, LayoutDiffusion models layout generation as a discrete denoising diffusion process. It learns to reverse a mild forward process, in which layouts become increasingly chaotic with the growth of forward steps and layouts in the neighboring steps do not differ too much. Designing such a mild forward process is however very challenging as layout has both categorical attributes and ordinal attributes. To tackle the challenge, we summarize three critical factors for achieving a mild forward process for the layout, i.e., legality, coordinate proximity and type disruption. Based on the factors, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule. Experiments on RICO and PubLayNet datasets show that LayoutDiffusion outperforms state-of-the-art approaches significantly. Moreover, it enables two conditional layout generation tasks in a plug-and-play manner without re-training and achieves better performance than existing methods. Project page: https://layoutdiffusion.github.io.", + "bbox": [ + 75, + 320, + 473, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 672, + 209, + 689 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Graphic layout, i.e., the sizes and positions of elements, is important to the interaction between the viewer and the information. Recently, layout generation attracts growing research interest. Leading approaches [11, 16, 17, 20] often represent a layout as a sequence of elements and leverage Transformer [40] to model element relationships. As the placement of one element could depends on any part of a layout, global context modeling plays a critical role in layout generation. However, there is no satisfactory solution to it. Some studies simply consider biased context [1, 11, 16, 17]. They generate layout sequences autoregressively, where the generation order for elements is pre", + "bbox": [ + 75, + 698, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fcf5c4b158a73d0b20c006ae07879b2daadf8903a0c1ef572201376b09dad8e7.jpg", + "image_caption": [ + "(a) Mild forward corruption process" + ], + "image_footnote": [], + "bbox": [ + 500, + 287, + 893, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c9f8dcf37399839b0bf6ae0aa23d19b9b74bc911ab947b7482c6d486cee54f9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 369, + 892, + 436 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e152f1bed53ff2fb0e353bde6a597d3eede0b4b19328045e5f31a99ed033b313.jpg", + "image_caption": [ + "(b) Absorbing [2]", + "(c) Uniform [37]" + ], + "image_footnote": [], + "bbox": [ + 501, + 450, + 892, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ebcb95395f98c4b6af2d501c918586647c49b107bdaf85213a9105aeb96d2aca.jpg", + "image_caption": [ + "(d) The mapping between colors and element types used in Figs. 1a to 1c", + "Figure 1. Comparison of different forward corruption processes. We sample the layouts at the timesteps 0, 1/6, 2/6, 3/6, 4/6, 5/6, and 1 of the total timestep. The blank page is used when the format of the layout sequence is destroyed." + ], + "image_footnote": [], + "bbox": [ + 501, + 534, + 890, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "defined and the placement of one element only depends on a certain part of layout. A few other studies try to utilize global context by non-autoregressive generation [22]. Unfortunately, they fail to improve the generation quality significantly since it is too challenging to generate a sequence in a single pass [7].", + "bbox": [ + 496, + 642, + 890, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Meanwhile, the emerging diffusion probabilistic model (DDPM) [13, 38] achieves amazing performance on many generation tasks [12, 21, 33-36, 44]. It consists of multiple rounds, each of which gradually denoises the latent variables towards the desired data distribution. This sort of process seems to be a promising solution to layout generation. First, the layout generated in the last round could serve as the global context for the generation in the next round. Second, by multiple rounds of denoising, a layout could be refined iteratively, overcoming the challenge of single-pass generation from non-autoregressive models.", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at Microsoft Research Asia.", + "bbox": [ + 94, + 886, + 419, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7226", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, we propose LayoutDiffusion to improve graphic layout generation. As a layout is represented as a sequence of discrete tokens [11, 16, 20], we formulate layout generation as a discrete diffusion process. Roughly speaking, it samples a layout by reversing a forward process. The forward process corrupts the real data into a sequence of increasingly noisy latent variables by a fixed Markov Chain. The reverse process starts from noise and denoises it step by step via learning the posterior distribution.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To ease the estimation of the posterior distribution, it is critical to design a mild forward corruption process [29], in which latent variables in neighboring steps do not differ too much and become increasingly chaotic with the growth of forward steps (see Fig. 1a). However, designing such a process for layout is non-trivial, due to the heterogeneous nature of the layout sequence, where the tokens representing element types are categorical while the tokens representing element coordinates are ordinal. Existing discrete forward processes hardly consider heterogeneous tokens. Directly applying them to layout data often leads to harsh corruptions, where a layout is changed dramatically at each step (see Figs. 1b and 1c). For example, the uniform process in Fig. 1c will transition an element type token to a coordinate token, drastically violating the layout semantics.", + "bbox": [ + 75, + 229, + 472, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To realize a mild corruption process for layout, we make three important observations. (i) Legality. The transition between type tokens and coordinate tokens will lead to an illegal layout sequence, resulting in an unpredictable change between forward steps. Hence, it is vital to impose legality during the corruption process. (ii) Coordinate Proximity. Coordinate tokens are ordinal, and thus transitioning a coordinate token to its proximal tokens (e.g., from 0 to 1) will introduce a milder change to a layout compared with transitioning to distant ones (e.g., from 0 to 127). (iii) Type Disruption. Unlike coordinate tokens, type tokens are categorical and do not have particular proximity. Simply transitioning one type to another may cause abrupt semantic changes to a layout (e.g., from a button to a background image).", + "bbox": [ + 75, + 459, + 472, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the above observations, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule in LayoutDiffusion. The transition matrix is designed as follows. First, to achieve legality, we only allow the internal transition between coordinate tokens and that between type tokens. Second, regarding coordinate proximity, we leverage discretized Gaussian [2], where the transition between more proximal tokens takes a higher probability, for the transition between coordinate tokens. Third, as for type disruption, we introduce absorbing state [2]. Each type token either stays the same or transitions to the absorbing state. To further alleviate type disruption, we propose a piece-wise linear noise schedule to make the transition for element types only occur in the late stage of the forward process. With above techniques, LayoutDiffusion", + "bbox": [ + 75, + 674, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "fusion achieves the mild forward process shown in Fig. 1a.", + "bbox": [ + 498, + 90, + 887, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our design also enables LayoutDiffusion to perform certain conditional layout generation tasks in a plug-and-play manner without re-training, which has never been explored by previous work. Specifically, owning to the mild forward process achieved by LayoutDiffusion, its reverse process is to iteratively improve a layout, which naturally supports the task of layout refinement [32]. Besides, as the transition of element types only occurs in the late forward process, LayoutDiffusion will determine the element types in a layout quickly in the reverse process. Thus, it can perform generation conditioned on types by simply keeping the types fixed and running the reverse process.", + "bbox": [ + 496, + 107, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, this work makes four key contributions:", + "bbox": [ + 517, + 287, + 870, + 301 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We formulate layout generation as a discrete diffusion process, which addresses biased context modeling by iterative refinement from a non-autoregressive model.", + "2. We design a new diffusion process based on the heterogeneous nature of layout sequence (legality, coordinate proximity and type disruption). It not only better suits layout data but also showcases a promising way of applying diffusion models to other heterogeneous data.", + "3. We enable certain conditional layout generation tasks in a plug-and-play manner without re-training.", + "4. We make extensive experiments and user studies. LayoutDiffusion outperforms existing methods on all the tasks in terms of most evaluation metrics, even if it is not re-trained for conditional generation tasks." + ], + "bbox": [ + 511, + 303, + 890, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 527, + 640, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Graphic Layout Generation. Early work on graphic layout generation has explored classical optimization approaches [30, 31], as well as generative models such as Generative Adversarial Networks (GANs) [19, 23] and Variational Autoencoders (VAEs) [1, 17, 18, 42].", + "bbox": [ + 496, + 551, + 890, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, inspired by the success of NLP, masking strategies [20], language models [11], and encoder-decoder architectures [16] have been studied. These approaches represent the layout as a sequence of elements and use Transformer [40] as the basic model architecture. As the placement of one element can depend on any part of a layout, one critical issue in layout generation is global context modeling. Some previous studies introduce unnatural biases and fail to model global context effectively [1, 11, 16, 17, 42]. They generate the layout sequence in an autoregressive manner, where there is a predefined generation order and the placement of one element can only depend on the generated part of the layout. On the other hand, a few other studies consider global context but do not achieve significantly better performance [19, 20, 23]. They generate the layout sequence in a non-autoregressive manner, where there is no predefined generation order, and all the tokens are generated in parallel. However, generating a sequence in a single pass", + "bbox": [ + 496, + 628, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7227", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "is too challenging [8]. BLT [20] explored an iterative refinement mechanism to alleviate the difficulty. However, it relies on heuristic rules instead of being learned from the data. The above limitation motivates us to seek a better model for layout generation. We think diffusion models are well-suited. By multiple rounds of denoising, it naturally takes the layout in the last step as the global context and generates a layout iteratively instead of by a single pass.", + "bbox": [ + 75, + 90, + 468, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another branch of studies has explored incorporating diverse user constraints into the layout generation [22, 24, 32, 45, 47]. They treat layout generation tasks with different constraints separately, which introduces repetitive training and hinders knowledge sharing across different tasks. By utilizing the flexible forward process of diffusion models [3], we enable some conditional generation tasks without re-training for the first time, which can be potentially extended to handle more conditional generation tasks.", + "bbox": [ + 75, + 214, + 468, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Models for Discrete Data. Diffusion models on continuous data have achieved outstanding results [43]. Recently, diffusion models on discrete data are also emerging. They can be grouped into two categories. The first category [5, 9, 25] maps discrete data to continuous state space via a learnable or fixed embedding, and then utilizes techniques from classical continuous diffusion models. These approaches enable simple technology migration from continuous diffusion models, but make the fine-grained control of the forward corruption process much difficult. Another category [2, 4, 10, 15, 39, 41] chooses to directly perform diffusion in discrete state space by modeling the forward corruption process as a random walk between different states. This category makes it easy to incorporate domain-dependent structure to the transition matrices and thus enables flexible control of the forward process. Different to the discrete data (e.g., images and texts) explored by previous work, the layout data studied in this work is heterogeneous by nature. Thus, we fully consider such characteristic and propose a new transition matrix coupled with noise schedules to achieve a mild corruption process.", + "bbox": [ + 75, + 352, + 470, + 670 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 689, + 284, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Graphic Layout. A graphic layout $x$ is composed of a set of graphic elements $\\{e_i\\}_{i=1}^N$ , where $N$ denotes the number of elements. Each element $e_i$ has an element type $c_i$ and a bounding box indicating its left $l_i$ , top $t_i$ , right $r_i$ , and bottom $b_i$ coordinates. Following the advanced layout generation methods [1, 11, 17, 27, 32, 42], we represent an element as a sequence with 5 discrete tokens, i.e., $e_i = \\{c_i l_i t_i r_i b_i\\}$ , where the continuous bounding box coordinates are uniformly discretized into integers between $[0, K)$ . Then, we represent a layout as a concatenation of element sequences:", + "bbox": [ + 75, + 715, + 468, + 867 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} = \\left\\{\\langle \\mathrm {s o s} \\rangle c _ {1} l _ {1} t _ {1} r _ {1} b _ {1} \\| \\dots \\| c _ {N} l _ {N} t _ {N} r _ {N} b _ {N} \\langle \\mathrm {e o s} \\rangle \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 878, + 468, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\langle \\mathrm{sos}\\rangle$ and $\\langle \\mathrm{eos}\\rangle$ are special tokens indicating the start and end of a sequence, and token $\\parallel$ indicates the separator between any two elements. Obviously, the layout sequence is heterogeneous. The element type tokens are categorical, while the coordinate tokens are ordinal.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Graphic Layout Generation. In this work, we primarily focus on unconditional layout generation. Specifically, we learn a generative model $p_{\\theta}(\\mathbf{x})$ parameterized by $\\theta$ , which synthesizes diverse and high-quality graphic layouts.", + "bbox": [ + 496, + 167, + 890, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. LayoutDiffusion", + "text_level": 1, + "bbox": [ + 498, + 241, + 661, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We formulate the layout generation problem as a discrete denoising diffusion process (see Fig. 2). It consists of two Markov chains, where the forward process is hand-designed and fixed while the reverse process is parameterized.", + "bbox": [ + 496, + 266, + 890, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Give a real layout $\\mathbf{x}_0\\sim q(\\mathbf{x}_0)$ , the forward process corrupts it into a sequence of increasingly noisy latent variables $\\mathbf{x}_{1:T} = \\mathbf{x_1},\\mathbf{x}_2,\\ldots ,\\mathbf{x}_T$", + "bbox": [ + 496, + 327, + 890, + 372 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {1: T} \\mid \\mathbf {x} _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 383, + 890, + 424 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t} \\mid x _ {t - 1}\\right) = x _ {t} \\mathbf {Q} _ {t} x _ {t - 1}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 428, + 890, + 444 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $x_{t}$ denotes the one-hot version of a single discrete token in the layout sequence $\\mathbf{x}_t$ . $\\mathbf{Q}_t$ is the transition matrix, where $[\\mathbf{Q}_t]_{ij} = q(x_t = j|x_{t-1} = i)$ represents the probabilities that $x_{t-1}$ transitions to $x_{t}$ . Due to the property of Markov chain, the cumulative probability of $x_{t}$ at arbitrary timestep from $x_0$ can be derived as $q(x_t|x_0) = \\mathbf{x}_t\\overline{\\mathbf{Q}}_t\\mathbf{x}_0$ , where $\\overline{\\mathbf{Q}}_t = \\mathbf{Q}_1\\mathbf{Q}_2\\dots \\mathbf{Q}_t$ (refer to [2] for details).", + "bbox": [ + 496, + 455, + 890, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To generate a layout, the reverse process starts with a random noise $\\mathbf{x}_T$ and gradually recovers it relying on the learned posterior distribution $p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)$", + "bbox": [ + 496, + 561, + 890, + 607 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 619, + 890, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following, we will introduce how to construct a mild forward process $q(\\mathbf{x}_t|\\mathbf{x}_{t - 1})$ for layout generation (Sec. 4.1), and how to learn the generative model $p_{\\theta}(\\mathbf{x}_0)$ in the reverse process (Sec. 4.2).", + "bbox": [ + 496, + 671, + 890, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1.Forward Process", + "text_level": 1, + "bbox": [ + 500, + 741, + 666, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In LayoutDiffusion, we propose a block-wise transition matrix $\\mathbf{Q}_t$ and a piece-wise linear noise schedule to realize a mild forward process, in which layouts in the neighboring steps do not differ too much and become increasingly disordered as the forward step grows (see Fig. 1a).", + "bbox": [ + 496, + 763, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The design of the transition matrix and noise schedule stems from our three important observations. (i) Legality. As defined in Sec. 3, layout sequence has a rigorous format. Any transition between element type tokens and coordinate", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7228", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d36222b7feb2aeb21a3dce1019e992d52d504429d2438d9d4fb70489a7d39958.jpg", + "image_caption": [ + "Figure 2. An illustration for LayoutDiffusion. In the forward process, the coordinates are mildly corrupted into stationary distribution, and the element types are absorbed into $\\mathsf{MASK}$ in the late stage. In the reverse process, the element types are first recovered, and then the rough coordinates are gradually refined. For brevity, only two elements are shown, while the other elements and the special tokens are omitted." + ], + "image_footnote": [], + "bbox": [ + 133, + 95, + 825, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tokens will lead to an illegal layout sequence, resulting in a disruptive change between forward steps. Hence, it is vital to impose sequence legality in the transition matrix. (ii) Coordinate Proximity. Coordinate tokens in layout sequence are ordinal and have a meaningful proximity. Transitioning a coordinate token to its proximal tokens (e.g., from 0 to 1) will introduce a milder change to a layout, compared with transitioning to distant ones (e.g., from 0 to 127). Thus, it is helpful to encode the proximity prior in the transition matrix. (iii) Type Disruption. Type tokens are categorical and do not present particular proximity. Each type of element has its unique coordinate distribution. For example, a background image tends to have a large size, while a button has a small size. Transitioning a type to another type may produce an abnormal element (e.g., a button has a large size and is placed at the top-left corner), leading to abrupt changes in layout. This is also consistent with the observation from diffusion models on other categorical data, e.g., latent code and text [2, 10]. Therefore, it is beneficial to alleviate type disruption in the transition matrix and noise schedule.", + "bbox": [ + 75, + 332, + 472, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transition Matrices. There are three kinds of tokens in the layout sequence, including type tokens (i.e., $c_{i}$ ), coordinate tokens (i.e., $l_{i}, t_{i}, r_{i}$ and $b_{i}$ ) and special tokens (i.e., $\\langle \\mathrm{sos} \\rangle$ , $\\langle \\mathrm{eos} \\rangle$ , ||, and PAD). Denote the number of different coordinate tokens and type tokens as $K$ and $C$ . Then, the transition matrix is denoted as $\\mathbf{Q}_t \\in \\mathbb{R}^{V \\times V}$ , where $V = K + C + 4$ .", + "bbox": [ + 76, + 633, + 468, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve the legality of the layout sequence, we only allow the internal transition within each kind of tokens. Thus, $\\mathbf{Q}_t$ can be reduced to a block-wise diagonal matrix,", + "bbox": [ + 75, + 739, + 468, + 786 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {t} = \\left[ \\begin{array}{c c c} \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} & & \\\\ & \\mathbf {Q} _ {t} ^ {\\text {t y p e}} & \\\\ & & \\mathbf {Q} _ {t} ^ {\\text {s p e c}} \\end{array} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 794, + 468, + 843 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{Q}_t^{\\mathrm{coord}}$ , $\\mathbf{Q}_t^{\\mathrm{type}}$ and $\\mathbf{Q}_t^{\\mathrm{spec}}$ depicts the probabilities of the internal transition within coordinate tokens, type tokens and special tokens, respectively.", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For $\\mathbf{Q}_t^{\\mathrm{coord}}$ , to encode the ordinal proximity, we introduce the discretized Gaussian matrix [2] for coordinate tokens, which assigns a higher probability to the transition between more proximal tokens,", + "bbox": [ + 498, + 330, + 890, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} \\right] _ {i j} = \\left\\{ \\begin{array}{l l} \\frac {\\exp \\left(- \\frac {4 | i - j | ^ {2}}{(K - 1) ^ {2} \\beta_ {t}}\\right)}{\\sum_ {n = - (K - 1)} ^ {(K - 1)} \\exp \\left(- \\frac {4 n ^ {2}}{(K - 1) ^ {2} \\beta_ {t}}\\right)}, & i \\neq j \\\\ 1 - \\sum_ {l = 0, l \\neq i} ^ {(K - 1)} \\left[ \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} \\right] _ {i l}, & i = j \\end{array} \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 402, + 890, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the parameters $\\beta_{t}$ influence the variance of the forward process distributions.", + "bbox": [ + 498, + 498, + 888, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For $\\mathbf{Q}_t^{\\mathrm{type}}$ , to alleviate the type disruption, we choose to transit a type token to a special MASK token instead of another meaningful type token. Therefore, we introduce the absorbing state transition matrix [2] for type tokens,", + "bbox": [ + 498, + 527, + 890, + 588 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {t} ^ {\\text {t y p e}} = \\left[ \\begin{array}{c c c c} 1 - \\gamma_ {t} & 0 & \\dots & 0 \\\\ 0 & 1 - \\gamma_ {t} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\gamma_ {t} & \\gamma_ {t} & \\dots & 1 \\end{array} \\right], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 598, + 890, + 670 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{t}$ indicates the probability that a token is absorbed into a MASK token, and $1 - \\gamma_{t}$ is the probability that a token stays unchanged.", + "bbox": [ + 498, + 680, + 890, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For $\\mathbf{Q}_t^{\\mathrm{spec}}$ , as special tokens describe the structure of the layout sequence, any transition between them will lead to an invalid layout sequence. Therefore, we choose to disable any transition between them,", + "bbox": [ + 498, + 724, + 890, + 785 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {t} ^ {\\text {s p e c}} = \\mathbf {I}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 796, + 890, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{I}$ is an identity matrix.", + "bbox": [ + 500, + 825, + 694, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Noise Schedules. An early absorbing of type tokens (i.e., transitioning to MASK token) will bring an abrupt change to the layout. Hence, to further eliminate type disruption, we choose to make the element type begin to change only", + "bbox": [ + 498, + 840, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7229", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in the late stage of the forward process. Specifically, we design $\\overline{\\gamma}_t = 1 - \\prod_{i=1}^t (1 - \\gamma_i)$ for the cumulative probability $q_t(x_t|x_0)$ as a piece-wise linear function,", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\gamma} _ {t} = \\left\\{ \\begin{array}{l l} 0, & t < \\tilde {T} \\\\ (t - \\tilde {T}) / (T - \\tilde {T}), & t \\geq \\tilde {T} \\end{array} \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 145, + 468, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\tilde{T}$ is the timestep where the absorbing is enabled, and $T$ is the terminal timestep.", + "bbox": [ + 75, + 194, + 468, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides, although existing work often uses linear schedule for Gaussian transition process, we choose to use $\\beta_{t} = g / (T - t + \\epsilon)^{h}$ for the transition of coordinate tokens $\\mathbf{Q}_t^{\\mathrm{coord}}$ . Here $g$ and $h$ are hyper-parameters, and $\\epsilon$ denotes a small positive quantity. It is generalized from a commonly used noise schedule $1 / (T - t + 1)$ [2,37]. We find that with $h > 1$ , it achieves a slower and more smooth corruption to the layout in the early forward process, which helps the model in the reverse process better learn the posterior distribution.", + "bbox": [ + 75, + 224, + 468, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Reverse Process", + "text_level": 1, + "bbox": [ + 76, + 369, + 235, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To reverse the forward process, we optimize the generative model $p_{\\theta}(\\mathbf{x}_0)$ to fit the data distribution $q(\\mathbf{x}_0)$ by minimizing the variational lower bound (VLB) [2],", + "bbox": [ + 75, + 392, + 468, + 438 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {V L B}} = - \\log p _ {\\theta} (\\mathbf {x} _ {0} | \\mathbf {x} _ {1}) + D _ {\\mathrm {K L}} (q (\\mathbf {x} _ {T} | \\mathbf {x} _ {0}) \\| p (\\mathbf {x} _ {T})) \\tag {10} \\\\ + \\sum_ {t = 2} ^ {T} D _ {\\mathrm {K L}} \\left(q \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) \\| p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right)\\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 446, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following recent work [2, 10], we predict $p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t)$ instead of $p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)$ , and encourage good predictions of $\\mathbf{x}_0$ at each step by combining $\\mathcal{L}_{\\mathrm{VLB}}$ with an auxiliary objective,", + "bbox": [ + 75, + 516, + 468, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {V L B}} - \\lambda \\log p _ {\\theta} \\left(\\mathbf {x} _ {0} \\mid \\mathbf {x} _ {t}\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 575, + 468, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we leverage Transformer encoder [40] to learn $p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t)$ . Denote the embedding of $i$ -th token in the layout sequence $\\mathbf{x}_t$ as $\\mathrm{emb}(x_{t,i})$ and its positional embedding as $p_i$ . Denote the embedding of the timestep $t$ as $\\mathrm{emb}(t)$ . Then, Transformer takes the aggregation of them, i.e., $\\{\\mathrm{emb}(x_{t,i}) + p_i + \\mathrm{emb}(t)\\}_{i=1}^M$ , as the input and predicts a new layout sequence $\\tilde{\\mathbf{x}}_0 = \\{\\tilde{x}_{0,i}\\}_{i=1}^M$ as the output.", + "bbox": [ + 75, + 597, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, we set an $N$ as the maximum number of elements. During inference, we first sample an element count $n$ from the training set's prior distribution. For constructing $\\mathbf{x}_T$ , we assign MASK tokens for the type and random coordinate tokens for bounding boxes of the first $n$ elements. For the remaining $(N - n)$ elements, PAD tokens are utilized to ensure a consistent length. By performing denoising from timestep $T$ to 0, we derive the layout $\\mathbf{x}_0$ .", + "bbox": [ + 75, + 703, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Enabling Conditional Layout Generation in a Plug-and-Play Manner", + "text_level": 1, + "bbox": [ + 76, + 830, + 468, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although LayoutDiffusion is trained for unconditional layout generation, it can handle some conditional gener", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ation tasks without re-training, which has never been explored by previous work. Such a plug-and-play feature of conditional generation is enabled by the design of transition matrices and noise schedules. In the following, we introduce how LayoutDiffusion achieves it.", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Refinement is a user-oriented layout generation task first posed in ROUTE [32], and is recently studied by Layout-Former++ [16]. Its goal is to take a user given flawed layout as input and provide a high-quality layout for the user while maintaining the original design style. With the proposed transition matrices and noise schedules, a layout is gradually corrupted in the forward process. With such a forward process, the reverse process learned by LayoutDiffusion is to iteratively improve a layout, which naturally enables refinement. Specifically, in LayoutDiffusion, we achieve refinement by feeding the flawed layout into the model and then running reverse process from a certain timestep. Here the timestep is related to how noisy the input layout is.", + "bbox": [ + 496, + 167, + 890, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generation Conditioned on Types (Gen-Type) is also a widely studied conditional layout generation task [16, 20, 22] to satisfy the needs of user. It aims to generate layouts with the given element types. In LayoutDiffusion, there is no transition between coordinates and types (see Eq. (5)). Besides, with the noise schedule in Eq. (9), the change of the types only occurs in the late forward process. With the above two mechanisms, LayoutDiffusion will determine the element types in the early reverse steps very quickly and then continue to improve the coordinates in the remaining reverse steps without changing the types (see the transformation of the layout from right to left in Fig. 2). In other words, the generation for coordinates and that for element types are approximately decoupled. Thus, in LayoutDiffusion, we achieve Gen-Type by feeding in the element types in the early stage and running the reverse process.", + "bbox": [ + 496, + 364, + 890, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 623, + 630, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Setups", + "text_level": 1, + "bbox": [ + 500, + 648, + 586, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We employ two widely-used public datasets of graphic layouts. RICO [6] is a dataset of user interface designs for mobile applications, which contains $66\\mathrm{K}+$ UI layouts with 25 element types. PublayNet [46] includes $360\\mathrm{K}+$ annotated scientific document layouts with 5 element types. Both datasets contain a few over-length entries. We filter out the layouts longer than 20 elements as in LayoutFormer++ [16]. Then, we split the filtered data into a training, validation, and test set by $90\\%$ , $5\\%$ , and $5\\%$ .", + "bbox": [ + 496, + 672, + 890, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. First, we compare LayoutDiffusion with leading approaches for layout generation. Specifically, we compare against LayoutTransformer [11], VTN [1], Coarse2Fine [17], and LayoutFormer++ [16] on unconditional generation (UGen); against NDN-none [22], LayoutGan++ [19], BLT [20], and LayoutFormer++ [16]", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7230", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b5828e0e15c1253b8774d78aab1f47e2b1280ac4a7d24dd5ed7cc03e5c1bfd61.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SubtasksMethodsRICOPubLayNet
mIoU (↑)Overlap (→)Align. (→)FID (↓)mIoU (↑)Overlap (→)Align. (→)FID (↓)
Un-GenLayoutTransformer0.5870.5420.03724.3200.3590.00450.06730.048
VTN0.3360.5610.47788.1150.3120.2210.207105.909
Coarse2Fine0.3600.6760.12846.4830.3610.1420.22150.854
LayoutFormer++0.6340.5460.05120.1980.4010.00100.02847.082
Diffusion-LM°0.6620.6310.18411.4480.4390.01250.07611.895
D3PM (absorbing)°0.5850.6190.1574.9850.4010.04270.07512.218
D3PM (uniform)°0.5950.6580.2295.5760.4050.05710.09911.212
LayoutDiffusion° (ours)0.6200.5020.0692.4900.4170.00300.0658.625
Gen-TypeNDN-none0.350.550.5613.760.310.170.3535.67
LayoutGan++0.2980.6200.2615.9540.2970.1480.12414.875
BLT0.2160.9830.15025.6330.1400.1960.03638.684
LayoutFormer++0.3770.5370.1242.4830.3330.0090.02510.151
Diffusion-LM°0.3240.5740.1996.5300.3160.0260.0467.396
D3PM (absorbing)°0.3370.5940.1923.5060.3330.0580.0578.858
D3PM (uniform)°0.3170.6210.2185.7710.3510.0630.0648.275
LayoutDiffusion° (ours)0.3450.4910.1241.5570.3430.0050.0293.731
RefinementRUITE0.6580.4920.1777.9260.6370.03750.0737.890
LayoutFormer++0.6560.5030.1413.6660.6420.01260.0422.937
Diffusion-LM°0.6210.4990.1818.5780.5730.04080.14013.985
D3PM (uniform)°0.5680.5260.2668.4070.5640.05150.11014.553
LayoutDiffusion° (ours)0.7190.4690.1020.5490.6600.00790.0352.045
Real Data-0.4660.093--0.00310.022-
", + "bbox": [ + 80, + 88, + 893, + 385 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative results. Methods with $\\diamond$ are diffusion-based, which achieve conditional generation (i.e., Gen-Type and Refinement) in a plug-and-play manner, while other methods require re-training for each subtask. The best and the second best values of each metric are bold and underlined respectively. For mIoU, the higher the score, the better the performance (indicated by $\\uparrow$ ). For Overlap and Align, the closer to real data, the better (indicated by $\\rightarrow$ ). For FID, the lower the score, the better the performance (indicated by $\\downarrow$ ).", + "bbox": [ + 75, + 388, + 892, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "on generation conditioned on type (Gen-Type); against ROUTE [32], and LayoutFormer++ [16] on refinement. Moreover, we compare LayoutDiffusion with the existing diffusion models that do not consider the characteristics of layouts. Diffusion-LM [25] maps discrete data to continuous state space, while D3PM (uniform) [2] and D3PM (absorbing) [2] perform diffusion in discrete state space using different transition matrices.", + "bbox": [ + 75, + 453, + 472, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We set the weight of auxiliary loss as $\\lambda = 0.0001$ (see Eq. (11)). In the training, we set the timestep as $T = 200$ ; in the inference, we set the timesteps $T_{\\mathrm{UGen}} = 200$ , $T_{\\mathrm{Gen-Type}} = 160$ , and $T_{\\mathrm{Refine}} = 50$ for different generation tasks. For the layout sequence (see Eq. (1)), we arrange elements in the alphabetical order of the type, and each token is embedded with $d = 128$ dimensions. For the denoising network $p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t)$ , we apply a 12-layer Transformer encoder with 12 attention heads. We train the model using AdamW optimizer [26] with $2 \\sim 4$ NVIDIA V100 GPUs. We also employ importance timestep sampling [29] during the training. See Supplementals for more details.", + "bbox": [ + 75, + 578, + 468, + 761 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. We adopt four metrics to measure the performance comprehensively. Among them, Frechet Inception Distance (FID) measures the overall performance, while Maximum Interaction over Union (mIoU), Alignment (Align.) and Overlap measure the quality from a specific aspect. Specifically, FID computes the distance between the distribution of the generated layouts and that of real layouts. Following the previous practice [19, 22], we train a classification-based neural network to get the feature", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "embedding for the layout. $mIoU$ calculates the maximum IoU between bounding boxes of the generated layouts and those of the real layouts with the same type set [19]. Align measures whether the elements in a generated layout are well-aligned, either by center or by edges. In addition to the original implementation [22], a normalization over the number of elements is applied. Overlap measures the overlapping area between elements in the generated layout. Following LayoutFormer++ [16], we ignore normal overlaps, e.g., elements on top of the background.", + "bbox": [ + 496, + 453, + 893, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison with Existing Approaches for Layout Generation", + "text_level": 1, + "bbox": [ + 498, + 616, + 890, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Analysis. In Tab. 1, the methods without the symbol $\\diamond$ are existing approaches for layout generation.", + "bbox": [ + 496, + 656, + 890, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "First, we compare FID as it is an overall metric for generation performance. LayoutDiffusion achieves significantly better FID scores than all other methods. For example, on Un-Gen, LayoutDiffusion achieves 2.490 and 8.625 on RICO and PubLayNet datasets, respectively, while the best existing work only achieves 20.198 and 30.048.", + "bbox": [ + 496, + 688, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, we examine individual metrics, including mIoU, Overlap, and Align., each of which measures the quality from a specific aspect. LayoutDiffusion is in the top two on almost every metric and frequently achieves the best performance. On the contrary, existing approaches may perform well on a certain metric but fail on the other individual metrics and the overall metric (i.e., FID), indicating that LayoutDiffusion is a well-rounded approach. For ex", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7231", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cc9cf75c86949b32c319c31d9e76de77a3a40c9f39f250bea606767f2bb810aa.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison against strongest baselines selected by FID (better view in color and $2 \\times$ zoom). The first three row is for RICO and the last three is for PubLayNet. LayoutDiffusion generates high-quality and diverse layouts. Layouts from LayoutFormer++ either lack diversity (Un-Gen) or are flawed (Gen-Type and Refinement). Layouts from other methods misalign and overlap frequently." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 885, + 510 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ample, on Un-Gen, LayoutTransformer has a good overlap score, but it does not perform well on Align., mIoU and FID; LayoutFormer++ has the best Align. for PubLayNet, but underperforms in mIoU, overlap and FID.", + "bbox": [ + 75, + 563, + 468, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Moreover, on conditional generation tasks (i.e., GenType and Refinement), the above observations still hold, even though LayoutDiffusion is not re-trained on these tasks (see Sec. 4.3) while existing approaches are re-trained.", + "bbox": [ + 75, + 625, + 468, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Analysis. Fig. 3 shows qualitative results. On Un-Gen, LayoutDiffusion generates diverse and high-quality layouts. In contrast, LayoutTransformer mainly suffers from incorrect spacing and overlap, and LayoutFormer++ is deficient in diversity. For example, for LayoutFormer++, most layouts on RICO contain a top toolbar and several list items, and most layouts on PublayNet are double-columned and have many texts. Besides, on Gen-Type and Refinement, LayoutDiffusion outperforms other methods (e.g., alignment, overlap and spacing) while it is not re-trained. For more qualitative results, please refer to Supplemental Sec. E.", + "bbox": [ + 75, + 686, + 468, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "User Study. On each task, we select the best two baselines by FID for the user study. We design two kinds of evalua", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion. One is quality evaluation. We show three layouts from three models respectively (two from baselines and one from LayoutDiffusion) and invite the user to choose which one has the best quality (e.g., more plausible overall structure and pleasing details). Another one is diversity evaluation. We show three sets of layouts from three models respectively, where each set contains five layouts from the same model. Then, we invite the user to choose which set has the most diverse layouts. For Refinement, we do not conduct diversity evaluation as it is not necessary for this scenario.", + "bbox": [ + 496, + 563, + 890, + 713 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 4 shows the results. Across different datasets, tasks and evaluation modes, there are 10 groups of user studies in total, in each of which we invite 15 people and everyone labels 50 groups of layouts. The user study shows that LayoutDiffusion outperforms other methods significantly.", + "bbox": [ + 496, + 714, + 890, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Comparison with Traditional Diffusion Models", + "text_level": 1, + "bbox": [ + 500, + 800, + 890, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Analysis. In Tab. 1, methods marked with $\\diamond$ are traditional diffusion models. They are originally proposed for other generation tasks (e.g., image and text). We adapt them for layout generation. On Un-Gen, LayoutDiffusion achieves the best performance on most metrics. On", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7232", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a66066b385de55820d707129c78bbb3dc8a33a7ce40b9eb42d649072bf7013a9.jpg", + "image_caption": [ + "Figure 4. Results of the user study. For each model, we count how many people prefer the layouts generated from this model. The study shows that the results generated by LayoutDiffusion were favored by users over the other methods, particularly in terms of diversity." + ], + "image_footnote": [], + "bbox": [ + 102, + 89, + 861, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c98228eaa61ef76c62f4529279fe9a62ad963bf8d933d7aa5d716159f5ad0ef3.jpg", + "image_caption": [ + "Figure 5. Reverse denoising process for unconditional generation on RICO (from left to right). Each row is for one model. The blank page is used when the generated layout sequence is invalid." + ], + "image_footnote": [], + "bbox": [ + 96, + 241, + 447, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Gen-Type and Refinement, while traditional diffusion models can be used for conditional generation tasks without retraining, their performance is usually worse than existing methods for layout generation (e.g., LayoutFormer++, not to mention LayoutDiffusion. These observations demonstrate that our consideration of the heterogeneous nature of layout data is critical for both achieving good performance and realizing plug-and-play conditional generation.", + "bbox": [ + 75, + 489, + 468, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Analysis. Fig. 3 shows a qualitative comparison with the best traditional diffusion model (selected by FID). LayoutDiffusion consistently generates better layouts, e.g., better alignment and less overlap. Moreover, Fig. 5 compares the reverse denoising processes of different diffusion models. LayoutDiffusion quickly generates a draft layout and then gradually refines it to a pleasing layout, while other diffusion models take many steps to generate a rough layout and fewer steps for iterative refinement, which may limit the modeling of precise relationships between elements, such as strict alignment and no overlap.", + "bbox": [ + 75, + 611, + 470, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Ablation Studies and Discussions", + "text_level": 1, + "bbox": [ + 76, + 786, + 366, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Transition Matrices. Our transition matrices are designed by considering three critical factors, i.e., legality, coordinate proximity and type disruption (see Sec. 4.1). We remove the technique corresponding to each factor. First, without considering the legality, the techniques for the other two factors cannot be applied. Thus, LayoutDiffusion degrades to", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0d7425b163ed85b884fa42960578396bd7545534473e324f559a049cd446b8fa.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodmIoU↑Overlap→Align.→FID↓
Uniform Qtcoord0.6140.6330.1193.174
Absorbing Qtcoord0.6360.6070.1143.672
Uniform Qttype0.5930.4780.1392.534
Linear γt0.5800.5220.1562.846
Linear βt0.5890.5170.2022.598
LayoutDiffusion0.6200.5020.0692.490
Real Data-0.4660.093-
", + "bbox": [ + 500, + 238, + 885, + 368 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8642babd0fb25f15af443a5355b312f86333ac156d6d164509e7dca12a8a5132.jpg", + "table_caption": [ + "Table 2. Ablation studies on RICO with unconditional generation." + ], + "table_footnote": [], + "table_body": "
FID↓Number of Steps
10020050010002000
Diffusion-LM17.75917.16411.98411.74111.448
D3PM (absorbing)7.4646.1026.0914.9855.110
D3PM (uniform)6.9866.9105.3515.5755.239
LayoutDiffusion3.8752.4902.3872.2952.360
", + "bbox": [ + 503, + 393, + 879, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation study on timesteps for diffusion models. All the experiments are on RICO with unconditional generation. The training and inference steps are set as the same. 2000 and 1000 are default settings used in Diffusion-LM [25] and D3PMs [2].", + "bbox": [ + 498, + 487, + 890, + 544 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "D3PM (absorbing or uniform). Tab. 1 shows that Layout-Diffusion achieves better performance. Second, to ignore coordinate proximity, we use uniform or absorbing transition for coordinate tokens, denoted as Uniform $\\mathbf{Q}_t^{\\mathrm{coord}}$ and Absorbing $\\mathbf{Q}_t^{\\mathrm{coord}}$ in Tab. 2. LayoutDiffusion outperforms these two variations on most metrics, especially Overlap and FID. Third, to study type disruption, we use uniform transition for type tokens, denoted as Uniform $\\mathbf{Q}_t^{\\mathrm{type}}$ in Tab. 2. LayoutDiffusion outperforms this variation, where the improvement of mIoU is most significant.", + "bbox": [ + 496, + 550, + 892, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Noise Schedules. To make the corruption of element types occur throughout the forward process, we set $\\tilde{T}$ as 0 for $\\overline{\\gamma}_t$ (see Eq. (9)), which results in a linear schedule (denoted as Linear $\\overline{\\gamma}_t$ in Tab. 2). We replace the noise schedule for $\\beta_t$ with the original linear schedule in previous work [2] (denoted as Linear $\\beta_t$ in Tab. 2). LayoutDiffusion outperforms both of them on most metrics, especially mIoU and Align.", + "bbox": [ + 496, + 702, + 892, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Timesteps. Tab. 3 shows FID of diffusion models with different timesteps. While 200 steps are enough for LayoutDiffusion, the performance of Diffusion-LM, D3PM (absorbing), and D3PM (uniform) saturates at 500, 1000, and 500 timesteps respectively. Besides, even the fastest version of LayoutDiffusion surpasses all the other diffusion models.", + "bbox": [ + 496, + 809, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7233", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Additional Analyses. For a detailed discussion on the diversity of the generated layouts, see Supplemental Sec. B. Experiments on additional settings of conditional generation are available in Sec. C. Ablation studies concerning conditional generation tasks, noise schedules, and sequence ordering can be found in Sec. D.", + "bbox": [ + 76, + 90, + 472, + 183 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 196, + 194, + 213 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we propose LayoutDiffusion to improve graphic layout generation by discrete diffusion models. The core of our method lies in realizing a mild forward process by considering the heterogeneous characteristics of the layout. Our method also enables two conditional generation tasks without re-training. Experiments demonstrate the superiority of LayoutDiffusion over leading approaches for layout generation and existing diffusion models. In the future, we plan to incorporate diverse conditions [14, 28] in LayoutDiffusion. Besides, we will also explore how to extend LayoutDiffusion to handle other heterogeneous data.", + "bbox": [ + 75, + 220, + 472, + 387 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 76, + 402, + 256, + 420 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We would like to thank Zhaoyun Jiang for helpful discussions. We also appreciate Zhaoyun Jiang's support in providing the pre-processed datasets and pretrained models for the FID evaluations.", + "bbox": [ + 76, + 428, + 470, + 488 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 505, + 174, + 520 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Diego Martin Arroyo, Janis Postels, and Federico Tombari. Variational transformer networks for layout generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13642-13652, 2021. 1, 2, 3, 5", + "[2] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. Structured denoising diffusion models in discrete state-spaces. 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Composition-aware graphic layout gan for visual-textual presentation designs. arXiv preprint arXiv:2205.00303, 2022. 3" + ], + "bbox": [ + 78, + 90, + 468, + 232 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7236", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_model.json b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f958cb9ef6dd728f007c3577c85b3b196efdd014 --- /dev/null +++ b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_model.json @@ -0,0 +1,2224 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.182, + 0.131, + 0.79, + 0.175 + ], + "angle": 0, + "content": "LayoutDiffusion: Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.203, + 0.857, + 0.258 + ], + "angle": 0, + "content": "Junyi Zhang\\(^{1*}\\) Jiaqi Guo\\(^{2}\\) Shizhao Sun\\(^{2}\\) Jian-Guang Lou\\(^{2}\\) Dongmei Zhang\\(^{2}\\)\\\n\\(^{1}\\)Shanghai Jiao Tong University\\\n\\(^{2}\\)Microsoft Research Asia\\\njunyizhang@sjtu.edu.cn \\(\\{\\mathrm{jiaqiguo, shizsu, jlou, dongmeiz}\\} @\\)microsoft.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.289, + 0.314, + 0.306 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.474, + 0.655 + ], + "angle": 0, + "content": "Creating graphic layouts is a fundamental step in graphic designs. In this work, we present a novel generative model named LayoutDiffusion for automatic layout generation. As layout is typically represented as a sequence of discrete tokens, LayoutDiffusion models layout generation as a discrete denoising diffusion process. It learns to reverse a mild forward process, in which layouts become increasingly chaotic with the growth of forward steps and layouts in the neighboring steps do not differ too much. Designing such a mild forward process is however very challenging as layout has both categorical attributes and ordinal attributes. To tackle the challenge, we summarize three critical factors for achieving a mild forward process for the layout, i.e., legality, coordinate proximity and type disruption. Based on the factors, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule. Experiments on RICO and PubLayNet datasets show that LayoutDiffusion outperforms state-of-the-art approaches significantly. Moreover, it enables two conditional layout generation tasks in a plug-and-play manner without re-training and achieves better performance than existing methods. Project page: https://layoutdiffusion.github.io." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.674, + 0.21, + 0.69 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Graphic layout, i.e., the sizes and positions of elements, is important to the interaction between the viewer and the information. Recently, layout generation attracts growing research interest. Leading approaches [11, 16, 17, 20] often represent a layout as a sequence of elements and leverage Transformer [40] to model element relationships. As the placement of one element could depends on any part of a layout, global context modeling plays a critical role in layout generation. However, there is no satisfactory solution to it. Some studies simply consider biased context [1, 11, 16, 17]. They generate layout sequences autoregressively, where the generation order for elements is pre" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.288, + 0.895, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.602, + 0.357, + 0.793, + 0.369 + ], + "angle": 0, + "content": "(a) Mild forward corruption process" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.37, + 0.893, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.439, + 0.745, + 0.451 + ], + "angle": 0, + "content": "(b) Absorbing [2]" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.452, + 0.893, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.652, + 0.52, + 0.743, + 0.532 + ], + "angle": 0, + "content": "(c) Uniform [37]" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.535, + 0.892, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.552, + 0.891, + 0.566 + ], + "angle": 0, + "content": "(d) The mapping between colors and element types used in Figs. 1a to 1c" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.573, + 0.892, + 0.63 + ], + "angle": 0, + "content": "Figure 1. Comparison of different forward corruption processes. We sample the layouts at the timesteps 0, 1/6, 2/6, 3/6, 4/6, 5/6, and 1 of the total timestep. The blank page is used when the format of the layout sequence is destroyed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.734 + ], + "angle": 0, + "content": "defined and the placement of one element only depends on a certain part of layout. A few other studies try to utilize global context by non-autoregressive generation [22]. Unfortunately, they fail to improve the generation quality significantly since it is too challenging to generate a sequence in a single pass [7]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Meanwhile, the emerging diffusion probabilistic model (DDPM) [13, 38] achieves amazing performance on many generation tasks [12, 21, 33-36, 44]. It consists of multiple rounds, each of which gradually denoises the latent variables towards the desired data distribution. This sort of process seems to be a promising solution to layout generation. First, the layout generated in the last round could serve as the global context for the generation in the next round. Second, by multiple rounds of denoising, a layout could be refined iteratively, overcoming the challenge of single-pass generation from non-autoregressive models." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.42, + 0.9 + ], + "angle": 0, + "content": "*Work done during an internship at Microsoft Research Asia." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7226" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "To this end, we propose LayoutDiffusion to improve graphic layout generation. As a layout is represented as a sequence of discrete tokens [11, 16, 20], we formulate layout generation as a discrete diffusion process. Roughly speaking, it samples a layout by reversing a forward process. The forward process corrupts the real data into a sequence of increasingly noisy latent variables by a fixed Markov Chain. The reverse process starts from noise and denoises it step by step via learning the posterior distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.473, + 0.457 + ], + "angle": 0, + "content": "To ease the estimation of the posterior distribution, it is critical to design a mild forward corruption process [29], in which latent variables in neighboring steps do not differ too much and become increasingly chaotic with the growth of forward steps (see Fig. 1a). However, designing such a process for layout is non-trivial, due to the heterogeneous nature of the layout sequence, where the tokens representing element types are categorical while the tokens representing element coordinates are ordinal. Existing discrete forward processes hardly consider heterogeneous tokens. Directly applying them to layout data often leads to harsh corruptions, where a layout is changed dramatically at each step (see Figs. 1b and 1c). For example, the uniform process in Fig. 1c will transition an element type token to a coordinate token, drastically violating the layout semantics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.673 + ], + "angle": 0, + "content": "To realize a mild corruption process for layout, we make three important observations. (i) Legality. The transition between type tokens and coordinate tokens will lead to an illegal layout sequence, resulting in an unpredictable change between forward steps. Hence, it is vital to impose legality during the corruption process. (ii) Coordinate Proximity. Coordinate tokens are ordinal, and thus transitioning a coordinate token to its proximal tokens (e.g., from 0 to 1) will introduce a milder change to a layout compared with transitioning to distant ones (e.g., from 0 to 127). (iii) Type Disruption. Unlike coordinate tokens, type tokens are categorical and do not have particular proximity. Simply transitioning one type to another may cause abrupt semantic changes to a layout (e.g., from a button to a background image)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Motivated by the above observations, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule in LayoutDiffusion. The transition matrix is designed as follows. First, to achieve legality, we only allow the internal transition between coordinate tokens and that between type tokens. Second, regarding coordinate proximity, we leverage discretized Gaussian [2], where the transition between more proximal tokens takes a higher probability, for the transition between coordinate tokens. Third, as for type disruption, we introduce absorbing state [2]. Each type token either stays the same or transitions to the absorbing state. To further alleviate type disruption, we propose a piece-wise linear noise schedule to make the transition for element types only occur in the late stage of the forward process. With above techniques, LayoutDiffusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.888, + 0.107 + ], + "angle": 0, + "content": "fusion achieves the mild forward process shown in Fig. 1a." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.892, + 0.288 + ], + "angle": 0, + "content": "Our design also enables LayoutDiffusion to perform certain conditional layout generation tasks in a plug-and-play manner without re-training, which has never been explored by previous work. Specifically, owning to the mild forward process achieved by LayoutDiffusion, its reverse process is to iteratively improve a layout, which naturally supports the task of layout refinement [32]. Besides, as the transition of element types only occurs in the late forward process, LayoutDiffusion will determine the element types in a layout quickly in the reverse process. Thus, it can perform generation conditioned on types by simply keeping the types fixed and running the reverse process." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.289, + 0.871, + 0.303 + ], + "angle": 0, + "content": "In summary, this work makes four key contributions:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.304, + 0.892, + 0.348 + ], + "angle": 0, + "content": "1. We formulate layout generation as a discrete diffusion process, which addresses biased context modeling by iterative refinement from a non-autoregressive model." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.349, + 0.892, + 0.424 + ], + "angle": 0, + "content": "2. We design a new diffusion process based on the heterogeneous nature of layout sequence (legality, coordinate proximity and type disruption). It not only better suits layout data but also showcases a promising way of applying diffusion models to other heterogeneous data." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.424, + 0.892, + 0.454 + ], + "angle": 0, + "content": "3. We enable certain conditional layout generation tasks in a plug-and-play manner without re-training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.455, + 0.892, + 0.515 + ], + "angle": 0, + "content": "4. We make extensive experiments and user studies. LayoutDiffusion outperforms existing methods on all the tasks in terms of most evaluation metrics, even if it is not re-trained for conditional generation tasks." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.304, + 0.892, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.528, + 0.642, + 0.544 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Graphic Layout Generation. Early work on graphic layout generation has explored classical optimization approaches [30, 31], as well as generative models such as Generative Adversarial Networks (GANs) [19, 23] and Variational Autoencoders (VAEs) [1, 17, 18, 42]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Recently, inspired by the success of NLP, masking strategies [20], language models [11], and encoder-decoder architectures [16] have been studied. These approaches represent the layout as a sequence of elements and use Transformer [40] as the basic model architecture. As the placement of one element can depend on any part of a layout, one critical issue in layout generation is global context modeling. Some previous studies introduce unnatural biases and fail to model global context effectively [1, 11, 16, 17, 42]. They generate the layout sequence in an autoregressive manner, where there is a predefined generation order and the placement of one element can only depend on the generated part of the layout. On the other hand, a few other studies consider global context but do not achieve significantly better performance [19, 20, 23]. They generate the layout sequence in a non-autoregressive manner, where there is no predefined generation order, and all the tokens are generated in parallel. However, generating a sequence in a single pass" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7227" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.213 + ], + "angle": 0, + "content": "is too challenging [8]. BLT [20] explored an iterative refinement mechanism to alleviate the difficulty. However, it relies on heuristic rules instead of being learned from the data. The above limitation motivates us to seek a better model for layout generation. We think diffusion models are well-suited. By multiple rounds of denoising, it naturally takes the layout in the last step as the global context and generates a layout iteratively instead of by a single pass." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.469, + 0.35 + ], + "angle": 0, + "content": "Another branch of studies has explored incorporating diverse user constraints into the layout generation [22, 24, 32, 45, 47]. They treat layout generation tasks with different constraints separately, which introduces repetitive training and hinders knowledge sharing across different tasks. By utilizing the flexible forward process of diffusion models [3], we enable some conditional generation tasks without re-training for the first time, which can be potentially extended to handle more conditional generation tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.471, + 0.671 + ], + "angle": 0, + "content": "Diffusion Models for Discrete Data. Diffusion models on continuous data have achieved outstanding results [43]. Recently, diffusion models on discrete data are also emerging. They can be grouped into two categories. The first category [5, 9, 25] maps discrete data to continuous state space via a learnable or fixed embedding, and then utilizes techniques from classical continuous diffusion models. These approaches enable simple technology migration from continuous diffusion models, but make the fine-grained control of the forward corruption process much difficult. Another category [2, 4, 10, 15, 39, 41] chooses to directly perform diffusion in discrete state space by modeling the forward corruption process as a random walk between different states. This category makes it easy to incorporate domain-dependent structure to the transition matrices and thus enables flexible control of the forward process. Different to the discrete data (e.g., images and texts) explored by previous work, the layout data studied in this work is heterogeneous by nature. Thus, we fully consider such characteristic and propose a new transition matrix coupled with noise schedules to achieve a mild corruption process." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.69, + 0.285, + 0.705 + ], + "angle": 0, + "content": "3. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Graphic Layout. A graphic layout \\( x \\) is composed of a set of graphic elements \\( \\{e_i\\}_{i=1}^N \\), where \\( N \\) denotes the number of elements. Each element \\( e_i \\) has an element type \\( c_i \\) and a bounding box indicating its left \\( l_i \\), top \\( t_i \\), right \\( r_i \\), and bottom \\( b_i \\) coordinates. Following the advanced layout generation methods [1, 11, 17, 27, 32, 42], we represent an element as a sequence with 5 discrete tokens, i.e., \\( e_i = \\{c_i l_i t_i r_i b_i\\} \\), where the continuous bounding box coordinates are uniformly discretized into integers between \\( [0, K) \\). Then, we represent a layout as a concatenation of element sequences:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.88, + 0.47, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} = \\left\\{\\langle \\mathrm {s o s} \\rangle c _ {1} l _ {1} t _ {1} r _ {1} b _ {1} \\| \\dots \\| c _ {N} l _ {N} t _ {N} r _ {N} b _ {N} \\langle \\mathrm {e o s} \\rangle \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "where \\(\\langle \\mathrm{sos}\\rangle\\) and \\(\\langle \\mathrm{eos}\\rangle\\) are special tokens indicating the start and end of a sequence, and token \\(\\parallel\\) indicates the separator between any two elements. Obviously, the layout sequence is heterogeneous. The element type tokens are categorical, while the coordinate tokens are ordinal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Graphic Layout Generation. In this work, we primarily focus on unconditional layout generation. Specifically, we learn a generative model \\( p_{\\theta}(\\mathbf{x}) \\) parameterized by \\( \\theta \\), which synthesizes diverse and high-quality graphic layouts." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.242, + 0.663, + 0.259 + ], + "angle": 0, + "content": "4. LayoutDiffusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.327 + ], + "angle": 0, + "content": "We formulate the layout generation problem as a discrete denoising diffusion process (see Fig. 2). It consists of two Markov chains, where the forward process is hand-designed and fixed while the reverse process is parameterized." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.373 + ], + "angle": 0, + "content": "Give a real layout \\(\\mathbf{x}_0\\sim q(\\mathbf{x}_0)\\), the forward process corrupts it into a sequence of increasingly noisy latent variables \\(\\mathbf{x}_{1:T} = \\mathbf{x_1},\\mathbf{x}_2,\\ldots ,\\mathbf{x}_T\\)" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.384, + 0.891, + 0.425 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {1: T} \\mid \\mathbf {x} _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.429, + 0.891, + 0.445 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t} \\mid x _ {t - 1}\\right) = x _ {t} \\mathbf {Q} _ {t} x _ {t - 1}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.563 + ], + "angle": 0, + "content": "Here, \\( x_{t} \\) denotes the one-hot version of a single discrete token in the layout sequence \\( \\mathbf{x}_t \\). \\( \\mathbf{Q}_t \\) is the transition matrix, where \\( [\\mathbf{Q}_t]_{ij} = q(x_t = j|x_{t-1} = i) \\) represents the probabilities that \\( x_{t-1} \\) transitions to \\( x_{t} \\). Due to the property of Markov chain, the cumulative probability of \\( x_{t} \\) at arbitrary timestep from \\( x_0 \\) can be derived as \\( q(x_t|x_0) = \\mathbf{x}_t\\overline{\\mathbf{Q}}_t\\mathbf{x}_0 \\), where \\( \\overline{\\mathbf{Q}}_t = \\mathbf{Q}_1\\mathbf{Q}_2\\dots \\mathbf{Q}_t \\) (refer to [2] for details)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.608 + ], + "angle": 0, + "content": "To generate a layout, the reverse process starts with a random noise \\(\\mathbf{x}_T\\) and gradually recovers it relying on the learned posterior distribution \\(p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)\\)" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.62, + 0.891, + 0.66 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.732 + ], + "angle": 0, + "content": "In the following, we will introduce how to construct a mild forward process \\( q(\\mathbf{x}_t|\\mathbf{x}_{t - 1}) \\) for layout generation (Sec. 4.1), and how to learn the generative model \\( p_{\\theta}(\\mathbf{x}_0) \\) in the reverse process (Sec. 4.2)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.667, + 0.756 + ], + "angle": 0, + "content": "4.1.Forward Process" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.84 + ], + "angle": 0, + "content": "In LayoutDiffusion, we propose a block-wise transition matrix \\(\\mathbf{Q}_t\\) and a piece-wise linear noise schedule to realize a mild forward process, in which layouts in the neighboring steps do not differ too much and become increasingly disordered as the forward step grows (see Fig. 1a)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The design of the transition matrix and noise schedule stems from our three important observations. (i) Legality. As defined in Sec. 3, layout sequence has a rigorous format. Any transition between element type tokens and coordinate" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7228" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.096, + 0.826, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.283, + 0.895, + 0.325 + ], + "angle": 0, + "content": "Figure 2. An illustration for LayoutDiffusion. In the forward process, the coordinates are mildly corrupted into stationary distribution, and the element types are absorbed into \\(\\mathsf{MASK}\\) in the late stage. In the reverse process, the element types are first recovered, and then the rough coordinates are gradually refined. For brevity, only two elements are shown, while the other elements and the special tokens are omitted." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.473, + 0.634 + ], + "angle": 0, + "content": "tokens will lead to an illegal layout sequence, resulting in a disruptive change between forward steps. Hence, it is vital to impose sequence legality in the transition matrix. (ii) Coordinate Proximity. Coordinate tokens in layout sequence are ordinal and have a meaningful proximity. Transitioning a coordinate token to its proximal tokens (e.g., from 0 to 1) will introduce a milder change to a layout, compared with transitioning to distant ones (e.g., from 0 to 127). Thus, it is helpful to encode the proximity prior in the transition matrix. (iii) Type Disruption. Type tokens are categorical and do not present particular proximity. Each type of element has its unique coordinate distribution. For example, a background image tends to have a large size, while a button has a small size. Transitioning a type to another type may produce an abnormal element (e.g., a button has a large size and is placed at the top-left corner), leading to abrupt changes in layout. This is also consistent with the observation from diffusion models on other categorical data, e.g., latent code and text [2, 10]. Therefore, it is beneficial to alleviate type disruption in the transition matrix and noise schedule." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.635, + 0.47, + 0.739 + ], + "angle": 0, + "content": "Transition Matrices. There are three kinds of tokens in the layout sequence, including type tokens (i.e., \\( c_{i} \\)), coordinate tokens (i.e., \\( l_{i}, t_{i}, r_{i} \\) and \\( b_{i} \\)) and special tokens (i.e., \\( \\langle \\mathrm{sos} \\rangle \\), \\( \\langle \\mathrm{eos} \\rangle \\), ||, and PAD). Denote the number of different coordinate tokens and type tokens as \\( K \\) and \\( C \\). Then, the transition matrix is denoted as \\( \\mathbf{Q}_t \\in \\mathbb{R}^{V \\times V} \\), where \\( V = K + C + 4 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.741, + 0.47, + 0.787 + ], + "angle": 0, + "content": "To achieve the legality of the layout sequence, we only allow the internal transition within each kind of tokens. Thus, \\(\\mathbf{Q}_t\\) can be reduced to a block-wise diagonal matrix," + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.795, + 0.47, + 0.844 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {t} = \\left[ \\begin{array}{c c c} \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} & & \\\\ & \\mathbf {Q} _ {t} ^ {\\text {t y p e}} & \\\\ & & \\mathbf {Q} _ {t} ^ {\\text {s p e c}} \\end{array} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.855, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{Q}_t^{\\mathrm{coord}}\\), \\(\\mathbf{Q}_t^{\\mathrm{type}}\\) and \\(\\mathbf{Q}_t^{\\mathrm{spec}}\\) depicts the probabilities of the internal transition within coordinate tokens, type tokens and special tokens, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.892, + 0.394 + ], + "angle": 0, + "content": "For \\(\\mathbf{Q}_t^{\\mathrm{coord}}\\), to encode the ordinal proximity, we introduce the discretized Gaussian matrix [2] for coordinate tokens, which assigns a higher probability to the transition between more proximal tokens," + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.403, + 0.891, + 0.497 + ], + "angle": 0, + "content": "\\[\n\\left[ \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} \\right] _ {i j} = \\left\\{ \\begin{array}{l l} \\frac {\\exp \\left(- \\frac {4 | i - j | ^ {2}}{(K - 1) ^ {2} \\beta_ {t}}\\right)}{\\sum_ {n = - (K - 1)} ^ {(K - 1)} \\exp \\left(- \\frac {4 n ^ {2}}{(K - 1) ^ {2} \\beta_ {t}}\\right)}, & i \\neq j \\\\ 1 - \\sum_ {l = 0, l \\neq i} ^ {(K - 1)} \\left[ \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} \\right] _ {i l}, & i = j \\end{array} \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.499, + 0.89, + 0.528 + ], + "angle": 0, + "content": "where the parameters \\(\\beta_{t}\\) influence the variance of the forward process distributions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.529, + 0.892, + 0.589 + ], + "angle": 0, + "content": "For \\(\\mathbf{Q}_t^{\\mathrm{type}}\\), to alleviate the type disruption, we choose to transit a type token to a special MASK token instead of another meaningful type token. Therefore, we introduce the absorbing state transition matrix [2] for type tokens," + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.599, + 0.892, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {t} ^ {\\text {t y p e}} = \\left[ \\begin{array}{c c c c} 1 - \\gamma_ {t} & 0 & \\dots & 0 \\\\ 0 & 1 - \\gamma_ {t} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\gamma_ {t} & \\gamma_ {t} & \\dots & 1 \\end{array} \\right], \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.681, + 0.891, + 0.725 + ], + "angle": 0, + "content": "where \\(\\gamma_{t}\\) indicates the probability that a token is absorbed into a MASK token, and \\(1 - \\gamma_{t}\\) is the probability that a token stays unchanged." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.726, + 0.892, + 0.786 + ], + "angle": 0, + "content": "For \\(\\mathbf{Q}_t^{\\mathrm{spec}}\\), as special tokens describe the structure of the layout sequence, any transition between them will lead to an invalid layout sequence. Therefore, we choose to disable any transition between them," + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.797, + 0.891, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {t} ^ {\\text {s p e c}} = \\mathbf {I}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.826, + 0.695, + 0.84 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}\\) is an identity matrix." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Noise Schedules. An early absorbing of type tokens (i.e., transitioning to MASK token) will bring an abrupt change to the layout. Hence, to further eliminate type disruption, we choose to make the element type begin to change only" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7229" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "in the late stage of the forward process. Specifically, we design \\(\\overline{\\gamma}_t = 1 - \\prod_{i=1}^t (1 - \\gamma_i)\\) for the cumulative probability \\(q_t(x_t|x_0)\\) as a piece-wise linear function," + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.146, + 0.47, + 0.186 + ], + "angle": 0, + "content": "\\[\n\\bar {\\gamma} _ {t} = \\left\\{ \\begin{array}{l l} 0, & t < \\tilde {T} \\\\ (t - \\tilde {T}) / (T - \\tilde {T}), & t \\geq \\tilde {T} \\end{array} \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.195, + 0.469, + 0.226 + ], + "angle": 0, + "content": "Here, \\(\\tilde{T}\\) is the timestep where the absorbing is enabled, and \\(T\\) is the terminal timestep." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.226, + 0.469, + 0.362 + ], + "angle": 0, + "content": "Besides, although existing work often uses linear schedule for Gaussian transition process, we choose to use \\(\\beta_{t} = g / (T - t + \\epsilon)^{h}\\) for the transition of coordinate tokens \\(\\mathbf{Q}_t^{\\mathrm{coord}}\\). Here \\(g\\) and \\(h\\) are hyper-parameters, and \\(\\epsilon\\) denotes a small positive quantity. It is generalized from a commonly used noise schedule \\(1 / (T - t + 1)\\) [2,37]. We find that with \\(h > 1\\), it achieves a slower and more smooth corruption to the layout in the early forward process, which helps the model in the reverse process better learn the posterior distribution." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.37, + 0.236, + 0.385 + ], + "angle": 0, + "content": "4.2. Reverse Process" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.469, + 0.439 + ], + "angle": 0, + "content": "To reverse the forward process, we optimize the generative model \\(p_{\\theta}(\\mathbf{x}_0)\\) to fit the data distribution \\(q(\\mathbf{x}_0)\\) by minimizing the variational lower bound (VLB) [2]," + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.447, + 0.469, + 0.509 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {V L B}} = - \\log p _ {\\theta} (\\mathbf {x} _ {0} | \\mathbf {x} _ {1}) + D _ {\\mathrm {K L}} (q (\\mathbf {x} _ {T} | \\mathbf {x} _ {0}) \\| p (\\mathbf {x} _ {T})) \\tag {10} \\\\ + \\sum_ {t = 2} ^ {T} D _ {\\mathrm {K L}} \\left(q \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) \\| p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right)\\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.469, + 0.563 + ], + "angle": 0, + "content": "Following recent work [2, 10], we predict \\( p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t) \\) instead of \\( p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t) \\), and encourage good predictions of \\( \\mathbf{x}_0 \\) at each step by combining \\( \\mathcal{L}_{\\mathrm{VLB}} \\) with an auxiliary objective," + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.577, + 0.469, + 0.593 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {V L B}} - \\lambda \\log p _ {\\theta} \\left(\\mathbf {x} _ {0} \\mid \\mathbf {x} _ {t}\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.469, + 0.704 + ], + "angle": 0, + "content": "Specifically, we leverage Transformer encoder [40] to learn \\( p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t) \\). Denote the embedding of \\( i \\)-th token in the layout sequence \\( \\mathbf{x}_t \\) as \\( \\mathrm{emb}(x_{t,i}) \\) and its positional embedding as \\( p_i \\). Denote the embedding of the timestep \\( t \\) as \\( \\mathrm{emb}(t) \\). Then, Transformer takes the aggregation of them, i.e., \\( \\{\\mathrm{emb}(x_{t,i}) + p_i + \\mathrm{emb}(t)\\}_{i=1}^M \\), as the input and predicts a new layout sequence \\( \\tilde{\\mathbf{x}}_0 = \\{\\tilde{x}_{0,i}\\}_{i=1}^M \\) as the output." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.469, + 0.824 + ], + "angle": 0, + "content": "In practice, we set an \\(N\\) as the maximum number of elements. During inference, we first sample an element count \\(n\\) from the training set's prior distribution. For constructing \\(\\mathbf{x}_T\\), we assign MASK tokens for the type and random coordinate tokens for bounding boxes of the first \\(n\\) elements. For the remaining \\((N - n)\\) elements, PAD tokens are utilized to ensure a consistent length. By performing denoising from timestep \\(T\\) to 0, we derive the layout \\(\\mathbf{x}_0\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.469, + 0.864 + ], + "angle": 0, + "content": "4.3. Enabling Conditional Layout Generation in a Plug-and-Play Manner" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Although LayoutDiffusion is trained for unconditional layout generation, it can handle some conditional gener" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "ation tasks without re-training, which has never been explored by previous work. Such a plug-and-play feature of conditional generation is enabled by the design of transition matrices and noise schedules. In the following, we introduce how LayoutDiffusion achieves it." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.365 + ], + "angle": 0, + "content": "Refinement is a user-oriented layout generation task first posed in ROUTE [32], and is recently studied by Layout-Former++ [16]. Its goal is to take a user given flawed layout as input and provide a high-quality layout for the user while maintaining the original design style. With the proposed transition matrices and noise schedules, a layout is gradually corrupted in the forward process. With such a forward process, the reverse process learned by LayoutDiffusion is to iteratively improve a layout, which naturally enables refinement. Specifically, in LayoutDiffusion, we achieve refinement by feeding the flawed layout into the model and then running reverse process from a certain timestep. Here the timestep is related to how noisy the input layout is." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.607 + ], + "angle": 0, + "content": "Generation Conditioned on Types (Gen-Type) is also a widely studied conditional layout generation task [16, 20, 22] to satisfy the needs of user. It aims to generate layouts with the given element types. In LayoutDiffusion, there is no transition between coordinates and types (see Eq. (5)). Besides, with the noise schedule in Eq. (9), the change of the types only occurs in the late forward process. With the above two mechanisms, LayoutDiffusion will determine the element types in the early reverse steps very quickly and then continue to improve the coordinates in the remaining reverse steps without changing the types (see the transformation of the layout from right to left in Fig. 2). In other words, the generation for coordinates and that for element types are approximately decoupled. Thus, in LayoutDiffusion, we achieve Gen-Type by feeding in the element types in the early stage and running the reverse process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.624, + 0.632, + 0.64 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.588, + 0.665 + ], + "angle": 0, + "content": "5.1. Setups" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Datasets. We employ two widely-used public datasets of graphic layouts. RICO [6] is a dataset of user interface designs for mobile applications, which contains \\(66\\mathrm{K}+\\) UI layouts with 25 element types. PublayNet [46] includes \\(360\\mathrm{K}+\\) annotated scientific document layouts with 5 element types. Both datasets contain a few over-length entries. We filter out the layouts longer than 20 elements as in LayoutFormer++ [16]. Then, we split the filtered data into a training, validation, and test set by \\(90\\%\\), \\(5\\%\\), and \\(5\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Baselines. First, we compare LayoutDiffusion with leading approaches for layout generation. Specifically, we compare against LayoutTransformer [11], VTN [1], Coarse2Fine [17], and LayoutFormer++ [16] on unconditional generation (UGen); against NDN-none [22], LayoutGan++ [19], BLT [20], and LayoutFormer++ [16]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7230" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.894, + 0.386 + ], + "angle": 0, + "content": "
SubtasksMethodsRICOPubLayNet
mIoU (↑)Overlap (→)Align. (→)FID (↓)mIoU (↑)Overlap (→)Align. (→)FID (↓)
Un-GenLayoutTransformer0.5870.5420.03724.3200.3590.00450.06730.048
VTN0.3360.5610.47788.1150.3120.2210.207105.909
Coarse2Fine0.3600.6760.12846.4830.3610.1420.22150.854
LayoutFormer++0.6340.5460.05120.1980.4010.00100.02847.082
Diffusion-LM°0.6620.6310.18411.4480.4390.01250.07611.895
D3PM (absorbing)°0.5850.6190.1574.9850.4010.04270.07512.218
D3PM (uniform)°0.5950.6580.2295.5760.4050.05710.09911.212
LayoutDiffusion° (ours)0.6200.5020.0692.4900.4170.00300.0658.625
Gen-TypeNDN-none0.350.550.5613.760.310.170.3535.67
LayoutGan++0.2980.6200.2615.9540.2970.1480.12414.875
BLT0.2160.9830.15025.6330.1400.1960.03638.684
LayoutFormer++0.3770.5370.1242.4830.3330.0090.02510.151
Diffusion-LM°0.3240.5740.1996.5300.3160.0260.0467.396
D3PM (absorbing)°0.3370.5940.1923.5060.3330.0580.0578.858
D3PM (uniform)°0.3170.6210.2185.7710.3510.0630.0648.275
LayoutDiffusion° (ours)0.3450.4910.1241.5570.3430.0050.0293.731
RefinementRUITE0.6580.4920.1777.9260.6370.03750.0737.890
LayoutFormer++0.6560.5030.1413.6660.6420.01260.0422.937
Diffusion-LM°0.6210.4990.1818.5780.5730.04080.14013.985
D3PM (uniform)°0.5680.5260.2668.4070.5640.05150.11014.553
LayoutDiffusion° (ours)0.7190.4690.1020.5490.6600.00790.0352.045
Real Data-0.4660.093--0.00310.022-
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.39, + 0.893, + 0.448 + ], + "angle": 0, + "content": "Table 1. Quantitative results. Methods with \\(\\diamond\\) are diffusion-based, which achieve conditional generation (i.e., Gen-Type and Refinement) in a plug-and-play manner, while other methods require re-training for each subtask. The best and the second best values of each metric are bold and underlined respectively. For mIoU, the higher the score, the better the performance (indicated by \\(\\uparrow\\)). For Overlap and Align, the closer to real data, the better (indicated by \\(\\rightarrow\\)). For FID, the lower the score, the better the performance (indicated by \\(\\downarrow\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.473, + 0.573 + ], + "angle": 0, + "content": "on generation conditioned on type (Gen-Type); against ROUTE [32], and LayoutFormer++ [16] on refinement. Moreover, we compare LayoutDiffusion with the existing diffusion models that do not consider the characteristics of layouts. Diffusion-LM [25] maps discrete data to continuous state space, while D3PM (uniform) [2] and D3PM (absorbing) [2] perform diffusion in discrete state space using different transition matrices." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.47, + 0.762 + ], + "angle": 0, + "content": "Implementation Details. We set the weight of auxiliary loss as \\(\\lambda = 0.0001\\) (see Eq. (11)). In the training, we set the timestep as \\(T = 200\\); in the inference, we set the timesteps \\(T_{\\mathrm{UGen}} = 200\\), \\(T_{\\mathrm{Gen-Type}} = 160\\), and \\(T_{\\mathrm{Refine}} = 50\\) for different generation tasks. For the layout sequence (see Eq. (1)), we arrange elements in the alphabetical order of the type, and each token is embedded with \\(d = 128\\) dimensions. For the denoising network \\(p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t)\\), we apply a 12-layer Transformer encoder with 12 attention heads. We train the model using AdamW optimizer [26] with \\(2 \\sim 4\\) NVIDIA V100 GPUs. We also employ importance timestep sampling [29] during the training. See Supplementals for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Evaluation Metrics. We adopt four metrics to measure the performance comprehensively. Among them, Frechet Inception Distance (FID) measures the overall performance, while Maximum Interaction over Union (mIoU), Alignment (Align.) and Overlap measure the quality from a specific aspect. Specifically, FID computes the distance between the distribution of the generated layouts and that of real layouts. Following the previous practice [19, 22], we train a classification-based neural network to get the feature" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.895, + 0.606 + ], + "angle": 0, + "content": "embedding for the layout. \\(mIoU\\) calculates the maximum IoU between bounding boxes of the generated layouts and those of the real layouts with the same type set [19]. Align measures whether the elements in a generated layout are well-aligned, either by center or by edges. In addition to the original implementation [22], a normalization over the number of elements is applied. Overlap measures the overlapping area between elements in the generated layout. Following LayoutFormer++ [16], we ignore normal overlaps, e.g., elements on top of the background." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.617, + 0.892, + 0.648 + ], + "angle": 0, + "content": "5.2. Comparison with Existing Approaches for Layout Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.688 + ], + "angle": 0, + "content": "Quantitative Analysis. In Tab. 1, the methods without the symbol \\(\\diamond\\) are existing approaches for layout generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.779 + ], + "angle": 0, + "content": "First, we compare FID as it is an overall metric for generation performance. LayoutDiffusion achieves significantly better FID scores than all other methods. For example, on Un-Gen, LayoutDiffusion achieves 2.490 and 8.625 on RICO and PubLayNet datasets, respectively, while the best existing work only achieves 20.198 and 30.048." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Furthermore, we examine individual metrics, including mIoU, Overlap, and Align., each of which measures the quality from a specific aspect. LayoutDiffusion is in the top two on almost every metric and frequently achieves the best performance. On the contrary, existing approaches may perform well on a certain metric but fail on the other individual metrics and the overall metric (i.e., FID), indicating that LayoutDiffusion is a well-rounded approach. For ex" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7231" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.887, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.515, + 0.895, + 0.557 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison against strongest baselines selected by FID (better view in color and \\(2 \\times\\) zoom). The first three row is for RICO and the last three is for PubLayNet. LayoutDiffusion generates high-quality and diverse layouts. Layouts from LayoutFormer++ either lack diversity (Un-Gen) or are flawed (Gen-Type and Refinement). Layouts from other methods misalign and overlap frequently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.47, + 0.625 + ], + "angle": 0, + "content": "ample, on Un-Gen, LayoutTransformer has a good overlap score, but it does not perform well on Align., mIoU and FID; LayoutFormer++ has the best Align. for PubLayNet, but underperforms in mIoU, overlap and FID." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Moreover, on conditional generation tasks (i.e., GenType and Refinement), the above observations still hold, even though LayoutDiffusion is not re-trained on these tasks (see Sec. 4.3) while existing approaches are re-trained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Qualitative Analysis. Fig. 3 shows qualitative results. On Un-Gen, LayoutDiffusion generates diverse and high-quality layouts. In contrast, LayoutTransformer mainly suffers from incorrect spacing and overlap, and LayoutFormer++ is deficient in diversity. For example, for LayoutFormer++, most layouts on RICO contain a top toolbar and several list items, and most layouts on PublayNet are double-columned and have many texts. Besides, on Gen-Type and Refinement, LayoutDiffusion outperforms other methods (e.g., alignment, overlap and spacing) while it is not re-trained. For more qualitative results, please refer to Supplemental Sec. E." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "User Study. On each task, we select the best two baselines by FID for the user study. We design two kinds of evalua" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.892, + 0.714 + ], + "angle": 0, + "content": "tion. One is quality evaluation. We show three layouts from three models respectively (two from baselines and one from LayoutDiffusion) and invite the user to choose which one has the best quality (e.g., more plausible overall structure and pleasing details). Another one is diversity evaluation. We show three sets of layouts from three models respectively, where each set contains five layouts from the same model. Then, we invite the user to choose which set has the most diverse layouts. For Refinement, we do not conduct diversity evaluation as it is not necessary for this scenario." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.791 + ], + "angle": 0, + "content": "Fig. 4 shows the results. Across different datasets, tasks and evaluation modes, there are 10 groups of user studies in total, in each of which we invite 15 people and everyone labels 50 groups of layouts. The user study shows that LayoutDiffusion outperforms other methods significantly." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.892, + 0.818 + ], + "angle": 0, + "content": "5.3. Comparison with Traditional Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantitative Analysis. In Tab. 1, methods marked with \\(\\diamond\\) are traditional diffusion models. They are originally proposed for other generation tasks (e.g., image and text). We adapt them for layout generation. On Un-Gen, LayoutDiffusion achieves the best performance on most metrics. On" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7232" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.09, + 0.862, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.207, + 0.892, + 0.234 + ], + "angle": 0, + "content": "Figure 4. Results of the user study. For each model, we count how many people prefer the layouts generated from this model. The study shows that the results generated by LayoutDiffusion were favored by users over the other methods, particularly in terms of diversity." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.242, + 0.449, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Figure 5. Reverse denoising process for unconditional generation on RICO (from left to right). Each row is for one model. The blank page is used when the generated layout sequence is invalid." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.612 + ], + "angle": 0, + "content": "Gen-Type and Refinement, while traditional diffusion models can be used for conditional generation tasks without retraining, their performance is usually worse than existing methods for layout generation (e.g., LayoutFormer++, not to mention LayoutDiffusion. These observations demonstrate that our consideration of the heterogeneous nature of layout data is critical for both achieving good performance and realizing plug-and-play conditional generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.471, + 0.779 + ], + "angle": 0, + "content": "Qualitative Analysis. Fig. 3 shows a qualitative comparison with the best traditional diffusion model (selected by FID). LayoutDiffusion consistently generates better layouts, e.g., better alignment and less overlap. Moreover, Fig. 5 compares the reverse denoising processes of different diffusion models. LayoutDiffusion quickly generates a draft layout and then gradually refines it to a pleasing layout, while other diffusion models take many steps to generate a rough layout and fewer steps for iterative refinement, which may limit the modeling of precise relationships between elements, such as strict alignment and no overlap." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.367, + 0.803 + ], + "angle": 0, + "content": "5.4. Ablation Studies and Discussions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Transition Matrices. Our transition matrices are designed by considering three critical factors, i.e., legality, coordinate proximity and type disruption (see Sec. 4.1). We remove the technique corresponding to each factor. First, without considering the legality, the techniques for the other two factors cannot be applied. Thus, LayoutDiffusion degrades to" + }, + { + "type": "table", + "bbox": [ + 0.5, + 0.239, + 0.886, + 0.369 + ], + "angle": 0, + "content": "
MethodmIoU↑Overlap→Align.→FID↓
Uniform Qtcoord0.6140.6330.1193.174
Absorbing Qtcoord0.6360.6070.1143.672
Uniform Qttype0.5930.4780.1392.534
Linear γt0.5800.5220.1562.846
Linear βt0.5890.5170.2022.598
LayoutDiffusion0.6200.5020.0692.490
Real Data-0.4660.093-
" + }, + { + "type": "table_caption", + "bbox": [ + 0.501, + 0.374, + 0.89, + 0.388 + ], + "angle": 0, + "content": "Table 2. Ablation studies on RICO with unconditional generation." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.395, + 0.88, + 0.484 + ], + "angle": 0, + "content": "
FID↓Number of Steps
10020050010002000
Diffusion-LM17.75917.16411.98411.74111.448
D3PM (absorbing)7.4646.1026.0914.9855.110
D3PM (uniform)6.9866.9105.3515.5755.239
LayoutDiffusion3.8752.4902.3872.2952.360
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.488, + 0.892, + 0.545 + ], + "angle": 0, + "content": "Table 3. Ablation study on timesteps for diffusion models. All the experiments are on RICO with unconditional generation. The training and inference steps are set as the same. 2000 and 1000 are default settings used in Diffusion-LM [25] and D3PMs [2]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.893, + 0.702 + ], + "angle": 0, + "content": "D3PM (absorbing or uniform). Tab. 1 shows that Layout-Diffusion achieves better performance. Second, to ignore coordinate proximity, we use uniform or absorbing transition for coordinate tokens, denoted as Uniform \\(\\mathbf{Q}_t^{\\mathrm{coord}}\\) and Absorbing \\(\\mathbf{Q}_t^{\\mathrm{coord}}\\) in Tab. 2. LayoutDiffusion outperforms these two variations on most metrics, especially Overlap and FID. Third, to study type disruption, we use uniform transition for type tokens, denoted as Uniform \\(\\mathbf{Q}_t^{\\mathrm{type}}\\) in Tab. 2. LayoutDiffusion outperforms this variation, where the improvement of mIoU is most significant." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.893, + 0.809 + ], + "angle": 0, + "content": "Noise Schedules. To make the corruption of element types occur throughout the forward process, we set \\(\\tilde{T}\\) as 0 for \\(\\overline{\\gamma}_t\\) (see Eq. (9)), which results in a linear schedule (denoted as Linear \\(\\overline{\\gamma}_t\\) in Tab. 2). We replace the noise schedule for \\(\\beta_t\\) with the original linear schedule in previous work [2] (denoted as Linear \\(\\beta_t\\) in Tab. 2). LayoutDiffusion outperforms both of them on most metrics, especially mIoU and Align." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Timesteps. Tab. 3 shows FID of diffusion models with different timesteps. While 200 steps are enough for LayoutDiffusion, the performance of Diffusion-LM, D3PM (absorbing), and D3PM (uniform) saturates at 500, 1000, and 500 timesteps respectively. Besides, even the fastest version of LayoutDiffusion surpasses all the other diffusion models." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7233" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "Additional Analyses. For a detailed discussion on the diversity of the generated layouts, see Supplemental Sec. B. Experiments on additional settings of conditional generation are available in Sec. C. Ablation studies concerning conditional generation tasks, noise schedules, and sequence ordering can be found in Sec. D." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.198, + 0.196, + 0.214 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.221, + 0.473, + 0.388 + ], + "angle": 0, + "content": "In this work, we propose LayoutDiffusion to improve graphic layout generation by discrete diffusion models. The core of our method lies in realizing a mild forward process by considering the heterogeneous characteristics of the layout. Our method also enables two conditional generation tasks without re-training. Experiments demonstrate the superiority of LayoutDiffusion over leading approaches for layout generation and existing diffusion models. In the future, we plan to incorporate diverse conditions [14, 28] in LayoutDiffusion. Besides, we will also explore how to extend LayoutDiffusion to handle other heterogeneous data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.403, + 0.258, + 0.421 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.429, + 0.471, + 0.489 + ], + "angle": 0, + "content": "We would like to thank Zhaoyun Jiang for helpful discussions. We also appreciate Zhaoyun Jiang's support in providing the pre-processed datasets and pretrained models for the FID evaluations." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.506, + 0.175, + 0.521 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.531, + 0.47, + 0.6 + ], + "angle": 0, + "content": "[1] Diego Martin Arroyo, Janis Postels, and Federico Tombari. Variational transformer networks for layout generation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13642-13652, 2021. 1, 2, 3, 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.603, + 0.472, + 0.671 + ], + "angle": 0, + "content": "[2] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. 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Composition-aware graphic layout gan for visual-textual presentation designs. arXiv preprint arXiv:2205.00303, 2022. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.517, + 0.956 + ], + "angle": 0, + "content": "7236" + } + ] +] \ No newline at end of file diff --git a/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_origin.pdf b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..903b2b050d74d427e2030d8696c78a0c3a4a9c02 --- /dev/null +++ b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/77145711-9475-40d3-bb1f-4deba9a37184_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d7045fe75bcb4d1b047a5faf1f89dbffcfd93694eb03ac8f7df757df240977e6 +size 1366014 diff --git a/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/full.md b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0c4dd699afa8b1400f5130a8436f1d6950deaa48 --- /dev/null +++ b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/full.md @@ -0,0 +1,326 @@ +# LayoutDiffusion: Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models + +Junyi Zhang $^{1*}$ Jiaqi Guo $^{2}$ Shizhao Sun $^{2}$ Jian-Guang Lou $^{2}$ Dongmei Zhang $^{2}$ \ + $^{1}$ Shanghai Jiao Tong University\ + $^{2}$ Microsoft Research Asia\ +junyizhang@sjtu.edu.cn $\{\mathrm{jiaqiguo, shizsu, jlou, dongmeiz}\} @$ microsoft.com + +# Abstract + +Creating graphic layouts is a fundamental step in graphic designs. In this work, we present a novel generative model named LayoutDiffusion for automatic layout generation. As layout is typically represented as a sequence of discrete tokens, LayoutDiffusion models layout generation as a discrete denoising diffusion process. It learns to reverse a mild forward process, in which layouts become increasingly chaotic with the growth of forward steps and layouts in the neighboring steps do not differ too much. Designing such a mild forward process is however very challenging as layout has both categorical attributes and ordinal attributes. To tackle the challenge, we summarize three critical factors for achieving a mild forward process for the layout, i.e., legality, coordinate proximity and type disruption. Based on the factors, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule. Experiments on RICO and PubLayNet datasets show that LayoutDiffusion outperforms state-of-the-art approaches significantly. Moreover, it enables two conditional layout generation tasks in a plug-and-play manner without re-training and achieves better performance than existing methods. Project page: https://layoutdiffusion.github.io. + +# 1. Introduction + +Graphic layout, i.e., the sizes and positions of elements, is important to the interaction between the viewer and the information. Recently, layout generation attracts growing research interest. Leading approaches [11, 16, 17, 20] often represent a layout as a sequence of elements and leverage Transformer [40] to model element relationships. As the placement of one element could depends on any part of a layout, global context modeling plays a critical role in layout generation. However, there is no satisfactory solution to it. Some studies simply consider biased context [1, 11, 16, 17]. They generate layout sequences autoregressively, where the generation order for elements is pre + +![](images/fcf5c4b158a73d0b20c006ae07879b2daadf8903a0c1ef572201376b09dad8e7.jpg) +(a) Mild forward corruption process + +![](images/4c9f8dcf37399839b0bf6ae0aa23d19b9b74bc911ab947b7482c6d486cee54f9.jpg) + +![](images/e152f1bed53ff2fb0e353bde6a597d3eede0b4b19328045e5f31a99ed033b313.jpg) +(b) Absorbing [2] +(c) Uniform [37] + +![](images/ebcb95395f98c4b6af2d501c918586647c49b107bdaf85213a9105aeb96d2aca.jpg) +(d) The mapping between colors and element types used in Figs. 1a to 1c +Figure 1. Comparison of different forward corruption processes. We sample the layouts at the timesteps 0, 1/6, 2/6, 3/6, 4/6, 5/6, and 1 of the total timestep. The blank page is used when the format of the layout sequence is destroyed. + +defined and the placement of one element only depends on a certain part of layout. A few other studies try to utilize global context by non-autoregressive generation [22]. Unfortunately, they fail to improve the generation quality significantly since it is too challenging to generate a sequence in a single pass [7]. + +Meanwhile, the emerging diffusion probabilistic model (DDPM) [13, 38] achieves amazing performance on many generation tasks [12, 21, 33-36, 44]. It consists of multiple rounds, each of which gradually denoises the latent variables towards the desired data distribution. This sort of process seems to be a promising solution to layout generation. First, the layout generated in the last round could serve as the global context for the generation in the next round. Second, by multiple rounds of denoising, a layout could be refined iteratively, overcoming the challenge of single-pass generation from non-autoregressive models. + +To this end, we propose LayoutDiffusion to improve graphic layout generation. As a layout is represented as a sequence of discrete tokens [11, 16, 20], we formulate layout generation as a discrete diffusion process. Roughly speaking, it samples a layout by reversing a forward process. The forward process corrupts the real data into a sequence of increasingly noisy latent variables by a fixed Markov Chain. The reverse process starts from noise and denoises it step by step via learning the posterior distribution. + +To ease the estimation of the posterior distribution, it is critical to design a mild forward corruption process [29], in which latent variables in neighboring steps do not differ too much and become increasingly chaotic with the growth of forward steps (see Fig. 1a). However, designing such a process for layout is non-trivial, due to the heterogeneous nature of the layout sequence, where the tokens representing element types are categorical while the tokens representing element coordinates are ordinal. Existing discrete forward processes hardly consider heterogeneous tokens. Directly applying them to layout data often leads to harsh corruptions, where a layout is changed dramatically at each step (see Figs. 1b and 1c). For example, the uniform process in Fig. 1c will transition an element type token to a coordinate token, drastically violating the layout semantics. + +To realize a mild corruption process for layout, we make three important observations. (i) Legality. The transition between type tokens and coordinate tokens will lead to an illegal layout sequence, resulting in an unpredictable change between forward steps. Hence, it is vital to impose legality during the corruption process. (ii) Coordinate Proximity. Coordinate tokens are ordinal, and thus transitioning a coordinate token to its proximal tokens (e.g., from 0 to 1) will introduce a milder change to a layout compared with transitioning to distant ones (e.g., from 0 to 127). (iii) Type Disruption. Unlike coordinate tokens, type tokens are categorical and do not have particular proximity. Simply transitioning one type to another may cause abrupt semantic changes to a layout (e.g., from a button to a background image). + +Motivated by the above observations, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule in LayoutDiffusion. The transition matrix is designed as follows. First, to achieve legality, we only allow the internal transition between coordinate tokens and that between type tokens. Second, regarding coordinate proximity, we leverage discretized Gaussian [2], where the transition between more proximal tokens takes a higher probability, for the transition between coordinate tokens. Third, as for type disruption, we introduce absorbing state [2]. Each type token either stays the same or transitions to the absorbing state. To further alleviate type disruption, we propose a piece-wise linear noise schedule to make the transition for element types only occur in the late stage of the forward process. With above techniques, LayoutDiffusion + +fusion achieves the mild forward process shown in Fig. 1a. + +Our design also enables LayoutDiffusion to perform certain conditional layout generation tasks in a plug-and-play manner without re-training, which has never been explored by previous work. Specifically, owning to the mild forward process achieved by LayoutDiffusion, its reverse process is to iteratively improve a layout, which naturally supports the task of layout refinement [32]. Besides, as the transition of element types only occurs in the late forward process, LayoutDiffusion will determine the element types in a layout quickly in the reverse process. Thus, it can perform generation conditioned on types by simply keeping the types fixed and running the reverse process. + +In summary, this work makes four key contributions: + +1. We formulate layout generation as a discrete diffusion process, which addresses biased context modeling by iterative refinement from a non-autoregressive model. +2. We design a new diffusion process based on the heterogeneous nature of layout sequence (legality, coordinate proximity and type disruption). It not only better suits layout data but also showcases a promising way of applying diffusion models to other heterogeneous data. +3. We enable certain conditional layout generation tasks in a plug-and-play manner without re-training. +4. We make extensive experiments and user studies. LayoutDiffusion outperforms existing methods on all the tasks in terms of most evaluation metrics, even if it is not re-trained for conditional generation tasks. + +# 2. Related Work + +Graphic Layout Generation. Early work on graphic layout generation has explored classical optimization approaches [30, 31], as well as generative models such as Generative Adversarial Networks (GANs) [19, 23] and Variational Autoencoders (VAEs) [1, 17, 18, 42]. + +Recently, inspired by the success of NLP, masking strategies [20], language models [11], and encoder-decoder architectures [16] have been studied. These approaches represent the layout as a sequence of elements and use Transformer [40] as the basic model architecture. As the placement of one element can depend on any part of a layout, one critical issue in layout generation is global context modeling. Some previous studies introduce unnatural biases and fail to model global context effectively [1, 11, 16, 17, 42]. They generate the layout sequence in an autoregressive manner, where there is a predefined generation order and the placement of one element can only depend on the generated part of the layout. On the other hand, a few other studies consider global context but do not achieve significantly better performance [19, 20, 23]. They generate the layout sequence in a non-autoregressive manner, where there is no predefined generation order, and all the tokens are generated in parallel. However, generating a sequence in a single pass + +is too challenging [8]. BLT [20] explored an iterative refinement mechanism to alleviate the difficulty. However, it relies on heuristic rules instead of being learned from the data. The above limitation motivates us to seek a better model for layout generation. We think diffusion models are well-suited. By multiple rounds of denoising, it naturally takes the layout in the last step as the global context and generates a layout iteratively instead of by a single pass. + +Another branch of studies has explored incorporating diverse user constraints into the layout generation [22, 24, 32, 45, 47]. They treat layout generation tasks with different constraints separately, which introduces repetitive training and hinders knowledge sharing across different tasks. By utilizing the flexible forward process of diffusion models [3], we enable some conditional generation tasks without re-training for the first time, which can be potentially extended to handle more conditional generation tasks. + +Diffusion Models for Discrete Data. Diffusion models on continuous data have achieved outstanding results [43]. Recently, diffusion models on discrete data are also emerging. They can be grouped into two categories. The first category [5, 9, 25] maps discrete data to continuous state space via a learnable or fixed embedding, and then utilizes techniques from classical continuous diffusion models. These approaches enable simple technology migration from continuous diffusion models, but make the fine-grained control of the forward corruption process much difficult. Another category [2, 4, 10, 15, 39, 41] chooses to directly perform diffusion in discrete state space by modeling the forward corruption process as a random walk between different states. This category makes it easy to incorporate domain-dependent structure to the transition matrices and thus enables flexible control of the forward process. Different to the discrete data (e.g., images and texts) explored by previous work, the layout data studied in this work is heterogeneous by nature. Thus, we fully consider such characteristic and propose a new transition matrix coupled with noise schedules to achieve a mild corruption process. + +# 3. Problem Formulation + +Graphic Layout. A graphic layout $x$ is composed of a set of graphic elements $\{e_i\}_{i=1}^N$ , where $N$ denotes the number of elements. Each element $e_i$ has an element type $c_i$ and a bounding box indicating its left $l_i$ , top $t_i$ , right $r_i$ , and bottom $b_i$ coordinates. Following the advanced layout generation methods [1, 11, 17, 27, 32, 42], we represent an element as a sequence with 5 discrete tokens, i.e., $e_i = \{c_i l_i t_i r_i b_i\}$ , where the continuous bounding box coordinates are uniformly discretized into integers between $[0, K)$ . Then, we represent a layout as a concatenation of element sequences: + +$$ +\mathbf {x} = \left\{\langle \mathrm {s o s} \rangle c _ {1} l _ {1} t _ {1} r _ {1} b _ {1} \| \dots \| c _ {N} l _ {N} t _ {N} r _ {N} b _ {N} \langle \mathrm {e o s} \rangle \right\}, \tag {1} +$$ + +where $\langle \mathrm{sos}\rangle$ and $\langle \mathrm{eos}\rangle$ are special tokens indicating the start and end of a sequence, and token $\parallel$ indicates the separator between any two elements. Obviously, the layout sequence is heterogeneous. The element type tokens are categorical, while the coordinate tokens are ordinal. + +Graphic Layout Generation. In this work, we primarily focus on unconditional layout generation. Specifically, we learn a generative model $p_{\theta}(\mathbf{x})$ parameterized by $\theta$ , which synthesizes diverse and high-quality graphic layouts. + +# 4. LayoutDiffusion + +We formulate the layout generation problem as a discrete denoising diffusion process (see Fig. 2). It consists of two Markov chains, where the forward process is hand-designed and fixed while the reverse process is parameterized. + +Give a real layout $\mathbf{x}_0\sim q(\mathbf{x}_0)$ , the forward process corrupts it into a sequence of increasingly noisy latent variables $\mathbf{x}_{1:T} = \mathbf{x_1},\mathbf{x}_2,\ldots ,\mathbf{x}_T$ + +$$ +q \left(\mathbf {x} _ {1: T} \mid \mathbf {x} _ {0}\right) = \prod_ {t = 1} ^ {T} q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right), \tag {2} +$$ + +$$ +q \left(x _ {t} \mid x _ {t - 1}\right) = x _ {t} \mathbf {Q} _ {t} x _ {t - 1}. \tag {3} +$$ + +Here, $x_{t}$ denotes the one-hot version of a single discrete token in the layout sequence $\mathbf{x}_t$ . $\mathbf{Q}_t$ is the transition matrix, where $[\mathbf{Q}_t]_{ij} = q(x_t = j|x_{t-1} = i)$ represents the probabilities that $x_{t-1}$ transitions to $x_{t}$ . Due to the property of Markov chain, the cumulative probability of $x_{t}$ at arbitrary timestep from $x_0$ can be derived as $q(x_t|x_0) = \mathbf{x}_t\overline{\mathbf{Q}}_t\mathbf{x}_0$ , where $\overline{\mathbf{Q}}_t = \mathbf{Q}_1\mathbf{Q}_2\dots \mathbf{Q}_t$ (refer to [2] for details). + +To generate a layout, the reverse process starts with a random noise $\mathbf{x}_T$ and gradually recovers it relying on the learned posterior distribution $p_{\theta}(\mathbf{x}_{t - 1}|\mathbf{x}_t)$ + +$$ +p _ {\theta} \left(\mathbf {x} _ {0: T}\right) = p \left(\mathbf {x} _ {T}\right) \prod_ {t = 1} ^ {T} p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right). \tag {4} +$$ + +In the following, we will introduce how to construct a mild forward process $q(\mathbf{x}_t|\mathbf{x}_{t - 1})$ for layout generation (Sec. 4.1), and how to learn the generative model $p_{\theta}(\mathbf{x}_0)$ in the reverse process (Sec. 4.2). + +# 4.1.Forward Process + +In LayoutDiffusion, we propose a block-wise transition matrix $\mathbf{Q}_t$ and a piece-wise linear noise schedule to realize a mild forward process, in which layouts in the neighboring steps do not differ too much and become increasingly disordered as the forward step grows (see Fig. 1a). + +The design of the transition matrix and noise schedule stems from our three important observations. (i) Legality. As defined in Sec. 3, layout sequence has a rigorous format. Any transition between element type tokens and coordinate + +![](images/d36222b7feb2aeb21a3dce1019e992d52d504429d2438d9d4fb70489a7d39958.jpg) +Figure 2. An illustration for LayoutDiffusion. In the forward process, the coordinates are mildly corrupted into stationary distribution, and the element types are absorbed into $\mathsf{MASK}$ in the late stage. In the reverse process, the element types are first recovered, and then the rough coordinates are gradually refined. For brevity, only two elements are shown, while the other elements and the special tokens are omitted. + +tokens will lead to an illegal layout sequence, resulting in a disruptive change between forward steps. Hence, it is vital to impose sequence legality in the transition matrix. (ii) Coordinate Proximity. Coordinate tokens in layout sequence are ordinal and have a meaningful proximity. Transitioning a coordinate token to its proximal tokens (e.g., from 0 to 1) will introduce a milder change to a layout, compared with transitioning to distant ones (e.g., from 0 to 127). Thus, it is helpful to encode the proximity prior in the transition matrix. (iii) Type Disruption. Type tokens are categorical and do not present particular proximity. Each type of element has its unique coordinate distribution. For example, a background image tends to have a large size, while a button has a small size. Transitioning a type to another type may produce an abnormal element (e.g., a button has a large size and is placed at the top-left corner), leading to abrupt changes in layout. This is also consistent with the observation from diffusion models on other categorical data, e.g., latent code and text [2, 10]. Therefore, it is beneficial to alleviate type disruption in the transition matrix and noise schedule. + +Transition Matrices. There are three kinds of tokens in the layout sequence, including type tokens (i.e., $c_{i}$ ), coordinate tokens (i.e., $l_{i}, t_{i}, r_{i}$ and $b_{i}$ ) and special tokens (i.e., $\langle \mathrm{sos} \rangle$ , $\langle \mathrm{eos} \rangle$ , ||, and PAD). Denote the number of different coordinate tokens and type tokens as $K$ and $C$ . Then, the transition matrix is denoted as $\mathbf{Q}_t \in \mathbb{R}^{V \times V}$ , where $V = K + C + 4$ . + +To achieve the legality of the layout sequence, we only allow the internal transition within each kind of tokens. Thus, $\mathbf{Q}_t$ can be reduced to a block-wise diagonal matrix, + +$$ +\mathbf {Q} _ {t} = \left[ \begin{array}{c c c} \mathbf {Q} _ {t} ^ {\text {c o o r d}} & & \\ & \mathbf {Q} _ {t} ^ {\text {t y p e}} & \\ & & \mathbf {Q} _ {t} ^ {\text {s p e c}} \end{array} \right], \tag {5} +$$ + +where $\mathbf{Q}_t^{\mathrm{coord}}$ , $\mathbf{Q}_t^{\mathrm{type}}$ and $\mathbf{Q}_t^{\mathrm{spec}}$ depicts the probabilities of the internal transition within coordinate tokens, type tokens and special tokens, respectively. + +For $\mathbf{Q}_t^{\mathrm{coord}}$ , to encode the ordinal proximity, we introduce the discretized Gaussian matrix [2] for coordinate tokens, which assigns a higher probability to the transition between more proximal tokens, + +$$ +\left[ \mathbf {Q} _ {t} ^ {\text {c o o r d}} \right] _ {i j} = \left\{ \begin{array}{l l} \frac {\exp \left(- \frac {4 | i - j | ^ {2}}{(K - 1) ^ {2} \beta_ {t}}\right)}{\sum_ {n = - (K - 1)} ^ {(K - 1)} \exp \left(- \frac {4 n ^ {2}}{(K - 1) ^ {2} \beta_ {t}}\right)}, & i \neq j \\ 1 - \sum_ {l = 0, l \neq i} ^ {(K - 1)} \left[ \mathbf {Q} _ {t} ^ {\text {c o o r d}} \right] _ {i l}, & i = j \end{array} \right. \tag {6} +$$ + +where the parameters $\beta_{t}$ influence the variance of the forward process distributions. + +For $\mathbf{Q}_t^{\mathrm{type}}$ , to alleviate the type disruption, we choose to transit a type token to a special MASK token instead of another meaningful type token. Therefore, we introduce the absorbing state transition matrix [2] for type tokens, + +$$ +\mathbf {Q} _ {t} ^ {\text {t y p e}} = \left[ \begin{array}{c c c c} 1 - \gamma_ {t} & 0 & \dots & 0 \\ 0 & 1 - \gamma_ {t} & \dots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ \gamma_ {t} & \gamma_ {t} & \dots & 1 \end{array} \right], \tag {7} +$$ + +where $\gamma_{t}$ indicates the probability that a token is absorbed into a MASK token, and $1 - \gamma_{t}$ is the probability that a token stays unchanged. + +For $\mathbf{Q}_t^{\mathrm{spec}}$ , as special tokens describe the structure of the layout sequence, any transition between them will lead to an invalid layout sequence. Therefore, we choose to disable any transition between them, + +$$ +\mathbf {Q} _ {t} ^ {\text {s p e c}} = \mathbf {I}, \tag {8} +$$ + +where $\mathbf{I}$ is an identity matrix. + +Noise Schedules. An early absorbing of type tokens (i.e., transitioning to MASK token) will bring an abrupt change to the layout. Hence, to further eliminate type disruption, we choose to make the element type begin to change only + +in the late stage of the forward process. Specifically, we design $\overline{\gamma}_t = 1 - \prod_{i=1}^t (1 - \gamma_i)$ for the cumulative probability $q_t(x_t|x_0)$ as a piece-wise linear function, + +$$ +\bar {\gamma} _ {t} = \left\{ \begin{array}{l l} 0, & t < \tilde {T} \\ (t - \tilde {T}) / (T - \tilde {T}), & t \geq \tilde {T} \end{array} \right. \tag {9} +$$ + +Here, $\tilde{T}$ is the timestep where the absorbing is enabled, and $T$ is the terminal timestep. + +Besides, although existing work often uses linear schedule for Gaussian transition process, we choose to use $\beta_{t} = g / (T - t + \epsilon)^{h}$ for the transition of coordinate tokens $\mathbf{Q}_t^{\mathrm{coord}}$ . Here $g$ and $h$ are hyper-parameters, and $\epsilon$ denotes a small positive quantity. It is generalized from a commonly used noise schedule $1 / (T - t + 1)$ [2,37]. We find that with $h > 1$ , it achieves a slower and more smooth corruption to the layout in the early forward process, which helps the model in the reverse process better learn the posterior distribution. + +# 4.2. Reverse Process + +To reverse the forward process, we optimize the generative model $p_{\theta}(\mathbf{x}_0)$ to fit the data distribution $q(\mathbf{x}_0)$ by minimizing the variational lower bound (VLB) [2], + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {V L B}} = - \log p _ {\theta} (\mathbf {x} _ {0} | \mathbf {x} _ {1}) + D _ {\mathrm {K L}} (q (\mathbf {x} _ {T} | \mathbf {x} _ {0}) \| p (\mathbf {x} _ {T})) \tag {10} \\ + \sum_ {t = 2} ^ {T} D _ {\mathrm {K L}} \left(q \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) \| p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right)\right). \\ \end{array} +$$ + +Following recent work [2, 10], we predict $p_{\theta}(\mathbf{x}_0|\mathbf{x}_t)$ instead of $p_{\theta}(\mathbf{x}_{t - 1}|\mathbf{x}_t)$ , and encourage good predictions of $\mathbf{x}_0$ at each step by combining $\mathcal{L}_{\mathrm{VLB}}$ with an auxiliary objective, + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {V L B}} - \lambda \log p _ {\theta} \left(\mathbf {x} _ {0} \mid \mathbf {x} _ {t}\right). \tag {11} +$$ + +Specifically, we leverage Transformer encoder [40] to learn $p_{\theta}(\mathbf{x}_0|\mathbf{x}_t)$ . Denote the embedding of $i$ -th token in the layout sequence $\mathbf{x}_t$ as $\mathrm{emb}(x_{t,i})$ and its positional embedding as $p_i$ . Denote the embedding of the timestep $t$ as $\mathrm{emb}(t)$ . Then, Transformer takes the aggregation of them, i.e., $\{\mathrm{emb}(x_{t,i}) + p_i + \mathrm{emb}(t)\}_{i=1}^M$ , as the input and predicts a new layout sequence $\tilde{\mathbf{x}}_0 = \{\tilde{x}_{0,i}\}_{i=1}^M$ as the output. + +In practice, we set an $N$ as the maximum number of elements. During inference, we first sample an element count $n$ from the training set's prior distribution. For constructing $\mathbf{x}_T$ , we assign MASK tokens for the type and random coordinate tokens for bounding boxes of the first $n$ elements. For the remaining $(N - n)$ elements, PAD tokens are utilized to ensure a consistent length. By performing denoising from timestep $T$ to 0, we derive the layout $\mathbf{x}_0$ . + +# 4.3. Enabling Conditional Layout Generation in a Plug-and-Play Manner + +Although LayoutDiffusion is trained for unconditional layout generation, it can handle some conditional gener + +ation tasks without re-training, which has never been explored by previous work. Such a plug-and-play feature of conditional generation is enabled by the design of transition matrices and noise schedules. In the following, we introduce how LayoutDiffusion achieves it. + +Refinement is a user-oriented layout generation task first posed in ROUTE [32], and is recently studied by Layout-Former++ [16]. Its goal is to take a user given flawed layout as input and provide a high-quality layout for the user while maintaining the original design style. With the proposed transition matrices and noise schedules, a layout is gradually corrupted in the forward process. With such a forward process, the reverse process learned by LayoutDiffusion is to iteratively improve a layout, which naturally enables refinement. Specifically, in LayoutDiffusion, we achieve refinement by feeding the flawed layout into the model and then running reverse process from a certain timestep. Here the timestep is related to how noisy the input layout is. + +Generation Conditioned on Types (Gen-Type) is also a widely studied conditional layout generation task [16, 20, 22] to satisfy the needs of user. It aims to generate layouts with the given element types. In LayoutDiffusion, there is no transition between coordinates and types (see Eq. (5)). Besides, with the noise schedule in Eq. (9), the change of the types only occurs in the late forward process. With the above two mechanisms, LayoutDiffusion will determine the element types in the early reverse steps very quickly and then continue to improve the coordinates in the remaining reverse steps without changing the types (see the transformation of the layout from right to left in Fig. 2). In other words, the generation for coordinates and that for element types are approximately decoupled. Thus, in LayoutDiffusion, we achieve Gen-Type by feeding in the element types in the early stage and running the reverse process. + +# 5. Experiments + +# 5.1. Setups + +Datasets. We employ two widely-used public datasets of graphic layouts. RICO [6] is a dataset of user interface designs for mobile applications, which contains $66\mathrm{K}+$ UI layouts with 25 element types. PublayNet [46] includes $360\mathrm{K}+$ annotated scientific document layouts with 5 element types. Both datasets contain a few over-length entries. We filter out the layouts longer than 20 elements as in LayoutFormer++ [16]. Then, we split the filtered data into a training, validation, and test set by $90\%$ , $5\%$ , and $5\%$ . + +Baselines. First, we compare LayoutDiffusion with leading approaches for layout generation. Specifically, we compare against LayoutTransformer [11], VTN [1], Coarse2Fine [17], and LayoutFormer++ [16] on unconditional generation (UGen); against NDN-none [22], LayoutGan++ [19], BLT [20], and LayoutFormer++ [16] + +
SubtasksMethodsRICOPubLayNet
mIoU (↑)Overlap (→)Align. (→)FID (↓)mIoU (↑)Overlap (→)Align. (→)FID (↓)
Un-GenLayoutTransformer0.5870.5420.03724.3200.3590.00450.06730.048
VTN0.3360.5610.47788.1150.3120.2210.207105.909
Coarse2Fine0.3600.6760.12846.4830.3610.1420.22150.854
LayoutFormer++0.6340.5460.05120.1980.4010.00100.02847.082
Diffusion-LM°0.6620.6310.18411.4480.4390.01250.07611.895
D3PM (absorbing)°0.5850.6190.1574.9850.4010.04270.07512.218
D3PM (uniform)°0.5950.6580.2295.5760.4050.05710.09911.212
LayoutDiffusion° (ours)0.6200.5020.0692.4900.4170.00300.0658.625
Gen-TypeNDN-none0.350.550.5613.760.310.170.3535.67
LayoutGan++0.2980.6200.2615.9540.2970.1480.12414.875
BLT0.2160.9830.15025.6330.1400.1960.03638.684
LayoutFormer++0.3770.5370.1242.4830.3330.0090.02510.151
Diffusion-LM°0.3240.5740.1996.5300.3160.0260.0467.396
D3PM (absorbing)°0.3370.5940.1923.5060.3330.0580.0578.858
D3PM (uniform)°0.3170.6210.2185.7710.3510.0630.0648.275
LayoutDiffusion° (ours)0.3450.4910.1241.5570.3430.0050.0293.731
RefinementRUITE0.6580.4920.1777.9260.6370.03750.0737.890
LayoutFormer++0.6560.5030.1413.6660.6420.01260.0422.937
Diffusion-LM°0.6210.4990.1818.5780.5730.04080.14013.985
D3PM (uniform)°0.5680.5260.2668.4070.5640.05150.11014.553
LayoutDiffusion° (ours)0.7190.4690.1020.5490.6600.00790.0352.045
Real Data-0.4660.093--0.00310.022-
+ +Table 1. Quantitative results. Methods with $\diamond$ are diffusion-based, which achieve conditional generation (i.e., Gen-Type and Refinement) in a plug-and-play manner, while other methods require re-training for each subtask. The best and the second best values of each metric are bold and underlined respectively. For mIoU, the higher the score, the better the performance (indicated by $\uparrow$ ). For Overlap and Align, the closer to real data, the better (indicated by $\rightarrow$ ). For FID, the lower the score, the better the performance (indicated by $\downarrow$ ). + +on generation conditioned on type (Gen-Type); against ROUTE [32], and LayoutFormer++ [16] on refinement. Moreover, we compare LayoutDiffusion with the existing diffusion models that do not consider the characteristics of layouts. Diffusion-LM [25] maps discrete data to continuous state space, while D3PM (uniform) [2] and D3PM (absorbing) [2] perform diffusion in discrete state space using different transition matrices. + +Implementation Details. We set the weight of auxiliary loss as $\lambda = 0.0001$ (see Eq. (11)). In the training, we set the timestep as $T = 200$ ; in the inference, we set the timesteps $T_{\mathrm{UGen}} = 200$ , $T_{\mathrm{Gen-Type}} = 160$ , and $T_{\mathrm{Refine}} = 50$ for different generation tasks. For the layout sequence (see Eq. (1)), we arrange elements in the alphabetical order of the type, and each token is embedded with $d = 128$ dimensions. For the denoising network $p_{\theta}(\mathbf{x}_0|\mathbf{x}_t)$ , we apply a 12-layer Transformer encoder with 12 attention heads. We train the model using AdamW optimizer [26] with $2 \sim 4$ NVIDIA V100 GPUs. We also employ importance timestep sampling [29] during the training. See Supplementals for more details. + +Evaluation Metrics. We adopt four metrics to measure the performance comprehensively. Among them, Frechet Inception Distance (FID) measures the overall performance, while Maximum Interaction over Union (mIoU), Alignment (Align.) and Overlap measure the quality from a specific aspect. Specifically, FID computes the distance between the distribution of the generated layouts and that of real layouts. Following the previous practice [19, 22], we train a classification-based neural network to get the feature + +embedding for the layout. $mIoU$ calculates the maximum IoU between bounding boxes of the generated layouts and those of the real layouts with the same type set [19]. Align measures whether the elements in a generated layout are well-aligned, either by center or by edges. In addition to the original implementation [22], a normalization over the number of elements is applied. Overlap measures the overlapping area between elements in the generated layout. Following LayoutFormer++ [16], we ignore normal overlaps, e.g., elements on top of the background. + +# 5.2. Comparison with Existing Approaches for Layout Generation + +Quantitative Analysis. In Tab. 1, the methods without the symbol $\diamond$ are existing approaches for layout generation. + +First, we compare FID as it is an overall metric for generation performance. LayoutDiffusion achieves significantly better FID scores than all other methods. For example, on Un-Gen, LayoutDiffusion achieves 2.490 and 8.625 on RICO and PubLayNet datasets, respectively, while the best existing work only achieves 20.198 and 30.048. + +Furthermore, we examine individual metrics, including mIoU, Overlap, and Align., each of which measures the quality from a specific aspect. LayoutDiffusion is in the top two on almost every metric and frequently achieves the best performance. On the contrary, existing approaches may perform well on a certain metric but fail on the other individual metrics and the overall metric (i.e., FID), indicating that LayoutDiffusion is a well-rounded approach. For ex + +![](images/cc9cf75c86949b32c319c31d9e76de77a3a40c9f39f250bea606767f2bb810aa.jpg) +Figure 3. Qualitative comparison against strongest baselines selected by FID (better view in color and $2 \times$ zoom). The first three row is for RICO and the last three is for PubLayNet. LayoutDiffusion generates high-quality and diverse layouts. Layouts from LayoutFormer++ either lack diversity (Un-Gen) or are flawed (Gen-Type and Refinement). Layouts from other methods misalign and overlap frequently. + +ample, on Un-Gen, LayoutTransformer has a good overlap score, but it does not perform well on Align., mIoU and FID; LayoutFormer++ has the best Align. for PubLayNet, but underperforms in mIoU, overlap and FID. + +Moreover, on conditional generation tasks (i.e., GenType and Refinement), the above observations still hold, even though LayoutDiffusion is not re-trained on these tasks (see Sec. 4.3) while existing approaches are re-trained. + +Qualitative Analysis. Fig. 3 shows qualitative results. On Un-Gen, LayoutDiffusion generates diverse and high-quality layouts. In contrast, LayoutTransformer mainly suffers from incorrect spacing and overlap, and LayoutFormer++ is deficient in diversity. For example, for LayoutFormer++, most layouts on RICO contain a top toolbar and several list items, and most layouts on PublayNet are double-columned and have many texts. Besides, on Gen-Type and Refinement, LayoutDiffusion outperforms other methods (e.g., alignment, overlap and spacing) while it is not re-trained. For more qualitative results, please refer to Supplemental Sec. E. + +User Study. On each task, we select the best two baselines by FID for the user study. We design two kinds of evalua + +tion. One is quality evaluation. We show three layouts from three models respectively (two from baselines and one from LayoutDiffusion) and invite the user to choose which one has the best quality (e.g., more plausible overall structure and pleasing details). Another one is diversity evaluation. We show three sets of layouts from three models respectively, where each set contains five layouts from the same model. Then, we invite the user to choose which set has the most diverse layouts. For Refinement, we do not conduct diversity evaluation as it is not necessary for this scenario. + +Fig. 4 shows the results. Across different datasets, tasks and evaluation modes, there are 10 groups of user studies in total, in each of which we invite 15 people and everyone labels 50 groups of layouts. The user study shows that LayoutDiffusion outperforms other methods significantly. + +# 5.3. Comparison with Traditional Diffusion Models + +Quantitative Analysis. In Tab. 1, methods marked with $\diamond$ are traditional diffusion models. They are originally proposed for other generation tasks (e.g., image and text). We adapt them for layout generation. On Un-Gen, LayoutDiffusion achieves the best performance on most metrics. On + +![](images/a66066b385de55820d707129c78bbb3dc8a33a7ce40b9eb42d649072bf7013a9.jpg) +Figure 4. Results of the user study. For each model, we count how many people prefer the layouts generated from this model. The study shows that the results generated by LayoutDiffusion were favored by users over the other methods, particularly in terms of diversity. + +![](images/c98228eaa61ef76c62f4529279fe9a62ad963bf8d933d7aa5d716159f5ad0ef3.jpg) +Figure 5. Reverse denoising process for unconditional generation on RICO (from left to right). Each row is for one model. The blank page is used when the generated layout sequence is invalid. + +Gen-Type and Refinement, while traditional diffusion models can be used for conditional generation tasks without retraining, their performance is usually worse than existing methods for layout generation (e.g., LayoutFormer++, not to mention LayoutDiffusion. These observations demonstrate that our consideration of the heterogeneous nature of layout data is critical for both achieving good performance and realizing plug-and-play conditional generation. + +Qualitative Analysis. Fig. 3 shows a qualitative comparison with the best traditional diffusion model (selected by FID). LayoutDiffusion consistently generates better layouts, e.g., better alignment and less overlap. Moreover, Fig. 5 compares the reverse denoising processes of different diffusion models. LayoutDiffusion quickly generates a draft layout and then gradually refines it to a pleasing layout, while other diffusion models take many steps to generate a rough layout and fewer steps for iterative refinement, which may limit the modeling of precise relationships between elements, such as strict alignment and no overlap. + +# 5.4. Ablation Studies and Discussions + +Transition Matrices. Our transition matrices are designed by considering three critical factors, i.e., legality, coordinate proximity and type disruption (see Sec. 4.1). We remove the technique corresponding to each factor. First, without considering the legality, the techniques for the other two factors cannot be applied. Thus, LayoutDiffusion degrades to + +
MethodmIoU↑Overlap→Align.→FID↓
Uniform Qtcoord0.6140.6330.1193.174
Absorbing Qtcoord0.6360.6070.1143.672
Uniform Qttype0.5930.4780.1392.534
Linear γt0.5800.5220.1562.846
Linear βt0.5890.5170.2022.598
LayoutDiffusion0.6200.5020.0692.490
Real Data-0.4660.093-
+ +Table 2. Ablation studies on RICO with unconditional generation. + +
FID↓Number of Steps
10020050010002000
Diffusion-LM17.75917.16411.98411.74111.448
D3PM (absorbing)7.4646.1026.0914.9855.110
D3PM (uniform)6.9866.9105.3515.5755.239
LayoutDiffusion3.8752.4902.3872.2952.360
+ +Table 3. Ablation study on timesteps for diffusion models. All the experiments are on RICO with unconditional generation. The training and inference steps are set as the same. 2000 and 1000 are default settings used in Diffusion-LM [25] and D3PMs [2]. + +D3PM (absorbing or uniform). Tab. 1 shows that Layout-Diffusion achieves better performance. Second, to ignore coordinate proximity, we use uniform or absorbing transition for coordinate tokens, denoted as Uniform $\mathbf{Q}_t^{\mathrm{coord}}$ and Absorbing $\mathbf{Q}_t^{\mathrm{coord}}$ in Tab. 2. LayoutDiffusion outperforms these two variations on most metrics, especially Overlap and FID. Third, to study type disruption, we use uniform transition for type tokens, denoted as Uniform $\mathbf{Q}_t^{\mathrm{type}}$ in Tab. 2. LayoutDiffusion outperforms this variation, where the improvement of mIoU is most significant. + +Noise Schedules. To make the corruption of element types occur throughout the forward process, we set $\tilde{T}$ as 0 for $\overline{\gamma}_t$ (see Eq. (9)), which results in a linear schedule (denoted as Linear $\overline{\gamma}_t$ in Tab. 2). We replace the noise schedule for $\beta_t$ with the original linear schedule in previous work [2] (denoted as Linear $\beta_t$ in Tab. 2). LayoutDiffusion outperforms both of them on most metrics, especially mIoU and Align. + +Timesteps. Tab. 3 shows FID of diffusion models with different timesteps. While 200 steps are enough for LayoutDiffusion, the performance of Diffusion-LM, D3PM (absorbing), and D3PM (uniform) saturates at 500, 1000, and 500 timesteps respectively. Besides, even the fastest version of LayoutDiffusion surpasses all the other diffusion models. + +Additional Analyses. For a detailed discussion on the diversity of the generated layouts, see Supplemental Sec. B. Experiments on additional settings of conditional generation are available in Sec. C. Ablation studies concerning conditional generation tasks, noise schedules, and sequence ordering can be found in Sec. D. + +# 6. Conclusion + +In this work, we propose LayoutDiffusion to improve graphic layout generation by discrete diffusion models. The core of our method lies in realizing a mild forward process by considering the heterogeneous characteristics of the layout. Our method also enables two conditional generation tasks without re-training. Experiments demonstrate the superiority of LayoutDiffusion over leading approaches for layout generation and existing diffusion models. In the future, we plan to incorporate diverse conditions [14, 28] in LayoutDiffusion. Besides, we will also explore how to extend LayoutDiffusion to handle other heterogeneous data. + +# 7. Acknowledgement + +We would like to thank Zhaoyun Jiang for helpful discussions. 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Composition-aware graphic layout gan for visual-textual presentation designs. arXiv preprint arXiv:2205.00303, 2022. 3 \ No newline at end of file diff --git a/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/images.zip b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..aaff25900b8e801853825d8d30cb3add80a4f550 --- /dev/null +++ b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:eee3e7593304b70be718ff5b0c3d54d6fa3d8611dfde17483a88e3ac741b8744 +size 635295 diff --git a/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/layout.json b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7fa67a343ba76c86a8fd6d96662d3846235408f0 --- /dev/null +++ b/2023/LayoutDiffusion_ Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models/layout.json @@ -0,0 +1,9219 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 111, + 103, + 483, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 103, + 483, + 138 + ], + "spans": [ + { + "bbox": [ + 111, + 103, + 483, + 138 + ], + "type": "text", + "content": "LayoutDiffusion: Improving Graphic Layout Generation by Discrete Diffusion Probabilistic Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "spans": [ + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": "Junyi Zhang" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": " Jiaqi Guo" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": " Shizhao Sun" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": " Jian-Guang Lou" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": " Dongmei Zhang" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": "\\\n" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": "Shanghai Jiao Tong University\\\n" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": "Microsoft Research Asia\\\njunyizhang@sjtu.edu.cn " + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{jiaqiguo, shizsu, jlou, dongmeiz}\\} @" + }, + { + "bbox": [ + 68, + 160, + 524, + 204 + ], + "type": "text", + "content": "microsoft.com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 228, + 192, + 242 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 228, + 192, + 242 + ], + "spans": [ + { + "bbox": [ + 143, + 228, + 192, + 242 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 254, + 290, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 290, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 290, + 518 + ], + "type": "text", + "content": "Creating graphic layouts is a fundamental step in graphic designs. In this work, we present a novel generative model named LayoutDiffusion for automatic layout generation. As layout is typically represented as a sequence of discrete tokens, LayoutDiffusion models layout generation as a discrete denoising diffusion process. It learns to reverse a mild forward process, in which layouts become increasingly chaotic with the growth of forward steps and layouts in the neighboring steps do not differ too much. Designing such a mild forward process is however very challenging as layout has both categorical attributes and ordinal attributes. To tackle the challenge, we summarize three critical factors for achieving a mild forward process for the layout, i.e., legality, coordinate proximity and type disruption. Based on the factors, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule. Experiments on RICO and PubLayNet datasets show that LayoutDiffusion outperforms state-of-the-art approaches significantly. Moreover, it enables two conditional layout generation tasks in a plug-and-play manner without re-training and achieves better performance than existing methods. Project page: https://layoutdiffusion.github.io." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 533, + 128, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 128, + 546 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 128, + 546 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 553, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 696 + ], + "type": "text", + "content": "Graphic layout, i.e., the sizes and positions of elements, is important to the interaction between the viewer and the information. Recently, layout generation attracts growing research interest. Leading approaches [11, 16, 17, 20] often represent a layout as a sequence of elements and leverage Transformer [40] to model element relationships. As the placement of one element could depends on any part of a layout, global context modeling plays a critical role in layout generation. However, there is no satisfactory solution to it. Some studies simply consider biased context [1, 11, 16, 17]. They generate layout sequences autoregressively, where the generation order for elements is pre" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 228, + 547, + 281 + ], + "blocks": [ + { + "bbox": [ + 306, + 228, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 306, + 228, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 547, + 281 + ], + "type": "image", + "image_path": "fcf5c4b158a73d0b20c006ae07879b2daadf8903a0c1ef572201376b09dad8e7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 368, + 282, + 485, + 292 + ], + "lines": [ + { + "bbox": [ + 368, + 282, + 485, + 292 + ], + "spans": [ + { + "bbox": [ + 368, + 282, + 485, + 292 + ], + "type": "text", + "content": "(a) Mild forward corruption process" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 293, + 546, + 346 + ], + "blocks": [ + { + "bbox": [ + 307, + 293, + 546, + 346 + ], + "lines": [ + { + "bbox": [ + 307, + 293, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 307, + 293, + 546, + 346 + ], + "type": "image", + "image_path": "4c9f8dcf37399839b0bf6ae0aa23d19b9b74bc911ab947b7482c6d486cee54f9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 357, + 546, + 411 + ], + "blocks": [ + { + "bbox": [ + 397, + 347, + 455, + 357 + ], + "lines": [ + { + "bbox": [ + 397, + 347, + 455, + 357 + ], + "spans": [ + { + "bbox": [ + 397, + 347, + 455, + 357 + ], + "type": "text", + "content": "(b) Absorbing [2]" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 357, + 546, + 411 + ], + "lines": [ + { + "bbox": [ + 307, + 357, + 546, + 411 + ], + "spans": [ + { + "bbox": [ + 307, + 357, + 546, + 411 + ], + "type": "image", + "image_path": "e152f1bed53ff2fb0e353bde6a597d3eede0b4b19328045e5f31a99ed033b313.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 399, + 411, + 454, + 421 + ], + "lines": [ + { + "bbox": [ + 399, + 411, + 454, + 421 + ], + "spans": [ + { + "bbox": [ + 399, + 411, + 454, + 421 + ], + "type": "text", + "content": "(c) Uniform [37]" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 423, + 545, + 434 + ], + "blocks": [ + { + "bbox": [ + 307, + 423, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 307, + 423, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 307, + 423, + 545, + 434 + ], + "type": "image", + "image_path": "ebcb95395f98c4b6af2d501c918586647c49b107bdaf85213a9105aeb96d2aca.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 437, + 545, + 448 + ], + "lines": [ + { + "bbox": [ + 307, + 437, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 307, + 437, + 545, + 448 + ], + "type": "text", + "content": "(d) The mapping between colors and element types used in Figs. 1a to 1c" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 453, + 545, + 498 + ], + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 498 + ], + "type": "text", + "content": "Figure 1. Comparison of different forward corruption processes. We sample the layouts at the timesteps 0, 1/6, 2/6, 3/6, 4/6, 5/6, and 1 of the total timestep. The blank page is used when the format of the layout sequence is destroyed." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 509, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 581 + ], + "type": "text", + "content": "defined and the placement of one element only depends on a certain part of layout. A few other studies try to utilize global context by non-autoregressive generation [22]. Unfortunately, they fail to improve the generation quality significantly since it is too challenging to generate a sequence in a single pass [7]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "Meanwhile, the emerging diffusion probabilistic model (DDPM) [13, 38] achieves amazing performance on many generation tasks [12, 21, 33-36, 44]. It consists of multiple rounds, each of which gradually denoises the latent variables towards the desired data distribution. This sort of process seems to be a promising solution to layout generation. First, the layout generated in the last round could serve as the global context for the generation in the next round. Second, by multiple rounds of denoising, a layout could be refined iteratively, overcoming the challenge of single-pass generation from non-autoregressive models." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 257, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 257, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 257, + 712 + ], + "type": "text", + "content": "*Work done during an internship at Microsoft Research Asia." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7226" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "To this end, we propose LayoutDiffusion to improve graphic layout generation. As a layout is represented as a sequence of discrete tokens [11, 16, 20], we formulate layout generation as a discrete diffusion process. Roughly speaking, it samples a layout by reversing a forward process. The forward process corrupts the real data into a sequence of increasingly noisy latent variables by a fixed Markov Chain. The reverse process starts from noise and denoises it step by step via learning the posterior distribution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 289, + 361 + ], + "type": "text", + "content": "To ease the estimation of the posterior distribution, it is critical to design a mild forward corruption process [29], in which latent variables in neighboring steps do not differ too much and become increasingly chaotic with the growth of forward steps (see Fig. 1a). However, designing such a process for layout is non-trivial, due to the heterogeneous nature of the layout sequence, where the tokens representing element types are categorical while the tokens representing element coordinates are ordinal. Existing discrete forward processes hardly consider heterogeneous tokens. Directly applying them to layout data often leads to harsh corruptions, where a layout is changed dramatically at each step (see Figs. 1b and 1c). For example, the uniform process in Fig. 1c will transition an element type token to a coordinate token, drastically violating the layout semantics." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 364, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 533 + ], + "type": "text", + "content": "To realize a mild corruption process for layout, we make three important observations. (i) Legality. The transition between type tokens and coordinate tokens will lead to an illegal layout sequence, resulting in an unpredictable change between forward steps. Hence, it is vital to impose legality during the corruption process. (ii) Coordinate Proximity. Coordinate tokens are ordinal, and thus transitioning a coordinate token to its proximal tokens (e.g., from 0 to 1) will introduce a milder change to a layout compared with transitioning to distant ones (e.g., from 0 to 127). (iii) Type Disruption. Unlike coordinate tokens, type tokens are categorical and do not have particular proximity. Simply transitioning one type to another may cause abrupt semantic changes to a layout (e.g., from a button to a background image)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "content": "Motivated by the above observations, we propose a block-wise transition matrix coupled with a piece-wise linear noise schedule in LayoutDiffusion. The transition matrix is designed as follows. First, to achieve legality, we only allow the internal transition between coordinate tokens and that between type tokens. Second, regarding coordinate proximity, we leverage discretized Gaussian [2], where the transition between more proximal tokens takes a higher probability, for the transition between coordinate tokens. Third, as for type disruption, we introduce absorbing state [2]. Each type token either stays the same or transitions to the absorbing state. To further alleviate type disruption, we propose a piece-wise linear noise schedule to make the transition for element types only occur in the late stage of the forward process. With above techniques, LayoutDiffusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 543, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 543, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 543, + 84 + ], + "type": "text", + "content": "fusion achieves the mild forward process shown in Fig. 1a." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 85, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 228 + ], + "type": "text", + "content": "Our design also enables LayoutDiffusion to perform certain conditional layout generation tasks in a plug-and-play manner without re-training, which has never been explored by previous work. Specifically, owning to the mild forward process achieved by LayoutDiffusion, its reverse process is to iteratively improve a layout, which naturally supports the task of layout refinement [32]. Besides, as the transition of element types only occurs in the late forward process, LayoutDiffusion will determine the element types in a layout quickly in the reverse process. Thus, it can perform generation conditioned on types by simply keeping the types fixed and running the reverse process." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 228, + 533, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 228, + 533, + 239 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 533, + 239 + ], + "type": "text", + "content": "In summary, this work makes four key contributions:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 240, + 545, + 407 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 313, + 240, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 240, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 313, + 240, + 545, + 275 + ], + "type": "text", + "content": "1. We formulate layout generation as a discrete diffusion process, which addresses biased context modeling by iterative refinement from a non-autoregressive model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 276, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 276, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 276, + 545, + 335 + ], + "type": "text", + "content": "2. We design a new diffusion process based on the heterogeneous nature of layout sequence (legality, coordinate proximity and type disruption). It not only better suits layout data but also showcases a promising way of applying diffusion models to other heterogeneous data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 335, + 545, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 335, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 545, + 359 + ], + "type": "text", + "content": "3. We enable certain conditional layout generation tasks in a plug-and-play manner without re-training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 360, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 360, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 313, + 360, + 545, + 407 + ], + "type": "text", + "content": "4. We make extensive experiments and user studies. LayoutDiffusion outperforms existing methods on all the tasks in terms of most evaluation metrics, even if it is not re-trained for conditional generation tasks." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 418, + 392, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 392, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 392, + 430 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 437, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 498 + ], + "type": "text", + "content": "Graphic Layout Generation. Early work on graphic layout generation has explored classical optimization approaches [30, 31], as well as generative models such as Generative Adversarial Networks (GANs) [19, 23] and Variational Autoencoders (VAEs) [1, 17, 18, 42]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 714 + ], + "type": "text", + "content": "Recently, inspired by the success of NLP, masking strategies [20], language models [11], and encoder-decoder architectures [16] have been studied. These approaches represent the layout as a sequence of elements and use Transformer [40] as the basic model architecture. As the placement of one element can depend on any part of a layout, one critical issue in layout generation is global context modeling. Some previous studies introduce unnatural biases and fail to model global context effectively [1, 11, 16, 17, 42]. They generate the layout sequence in an autoregressive manner, where there is a predefined generation order and the placement of one element can only depend on the generated part of the layout. On the other hand, a few other studies consider global context but do not achieve significantly better performance [19, 20, 23]. They generate the layout sequence in a non-autoregressive manner, where there is no predefined generation order, and all the tokens are generated in parallel. However, generating a sequence in a single pass" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7227" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 168 + ], + "type": "text", + "content": "is too challenging [8]. BLT [20] explored an iterative refinement mechanism to alleviate the difficulty. However, it relies on heuristic rules instead of being learned from the data. The above limitation motivates us to seek a better model for layout generation. We think diffusion models are well-suited. By multiple rounds of denoising, it naturally takes the layout in the last step as the global context and generates a layout iteratively instead of by a single pass." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 170, + 287, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 287, + 277 + ], + "type": "text", + "content": "Another branch of studies has explored incorporating diverse user constraints into the layout generation [22, 24, 32, 45, 47]. They treat layout generation tasks with different constraints separately, which introduces repetitive training and hinders knowledge sharing across different tasks. By utilizing the flexible forward process of diffusion models [3], we enable some conditional generation tasks without re-training for the first time, which can be potentially extended to handle more conditional generation tasks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 279, + 288, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 288, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 288, + 531 + ], + "type": "text", + "content": "Diffusion Models for Discrete Data. Diffusion models on continuous data have achieved outstanding results [43]. Recently, diffusion models on discrete data are also emerging. They can be grouped into two categories. The first category [5, 9, 25] maps discrete data to continuous state space via a learnable or fixed embedding, and then utilizes techniques from classical continuous diffusion models. These approaches enable simple technology migration from continuous diffusion models, but make the fine-grained control of the forward corruption process much difficult. Another category [2, 4, 10, 15, 39, 41] chooses to directly perform diffusion in discrete state space by modeling the forward corruption process as a random walk between different states. This category makes it easy to incorporate domain-dependent structure to the transition matrices and thus enables flexible control of the forward process. Different to the discrete data (e.g., images and texts) explored by previous work, the layout data studied in this work is heterogeneous by nature. Thus, we fully consider such characteristic and propose a new transition matrix coupled with noise schedules to achieve a mild corruption process." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 546, + 174, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 174, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 174, + 558 + ], + "type": "text", + "content": "3. Problem Formulation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": "Graphic Layout. A graphic layout " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": " is composed of a set of graphic elements " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\{e_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": " denotes the number of elements. Each element " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": " has an element type " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": " and a bounding box indicating its left " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": ", top " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": ", right " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": ", and bottom " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "b_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": " coordinates. Following the advanced layout generation methods [1, 11, 17, 27, 32, 42], we represent an element as a sequence with 5 discrete tokens, i.e., " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "e_i = \\{c_i l_i t_i r_i b_i\\}" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": ", where the continuous bounding box coordinates are uniformly discretized into integers between " + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "inline_equation", + "content": "[0, K)" + }, + { + "bbox": [ + 46, + 567, + 287, + 687 + ], + "type": "text", + "content": ". Then, we represent a layout as a concatenation of element sequences:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 696, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 696, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 59, + 696, + 287, + 711 + ], + "type": "interline_equation", + "content": "\\mathbf {x} = \\left\\{\\langle \\mathrm {s o s} \\rangle c _ {1} l _ {1} t _ {1} r _ {1} b _ {1} \\| \\dots \\| c _ {N} l _ {N} t _ {N} r _ {N} b _ {N} \\langle \\mathrm {e o s} \\rangle \\right\\}, \\tag {1}", + "image_path": "18e7f7a70803a373873cce7257a0288870f7d231d28a3508494b70a713594cd2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{sos}\\rangle" + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{eos}\\rangle" + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": " are special tokens indicating the start and end of a sequence, and token " + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "inline_equation", + "content": "\\parallel" + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": " indicates the separator between any two elements. Obviously, the layout sequence is heterogeneous. The element type tokens are categorical, while the coordinate tokens are ordinal." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 133, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 180 + ], + "type": "text", + "content": "Graphic Layout Generation. In this work, we primarily focus on unconditional layout generation. Specifically, we learn a generative model " + }, + { + "bbox": [ + 304, + 133, + 545, + 180 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 133, + 545, + 180 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 304, + 133, + 545, + 180 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 133, + 545, + 180 + ], + "type": "text", + "content": ", which synthesizes diverse and high-quality graphic layouts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 191, + 405, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 191, + 405, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 405, + 205 + ], + "type": "text", + "content": "4. LayoutDiffusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 258 + ], + "type": "text", + "content": "We formulate the layout generation problem as a discrete denoising diffusion process (see Fig. 2). It consists of two Markov chains, where the forward process is hand-designed and fixed while the reverse process is parameterized." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 259, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 295 + ], + "type": "text", + "content": "Give a real layout " + }, + { + "bbox": [ + 304, + 259, + 545, + 295 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0\\sim q(\\mathbf{x}_0)" + }, + { + "bbox": [ + 304, + 259, + 545, + 295 + ], + "type": "text", + "content": ", the forward process corrupts it into a sequence of increasingly noisy latent variables " + }, + { + "bbox": [ + 304, + 259, + 545, + 295 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{1:T} = \\mathbf{x_1},\\mathbf{x}_2,\\ldots ,\\mathbf{x}_T" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 364, + 304, + 545, + 336 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 304, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 364, + 304, + 545, + 336 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {1: T} \\mid \\mathbf {x} _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right), \\tag {2}", + "image_path": "e3a9134004733fa51fd9c19c3fb52930b245b9bd822b88795961f94ea33afae2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 364, + 339, + 545, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 339, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 364, + 339, + 545, + 352 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t} \\mid x _ {t - 1}\\right) = x _ {t} \\mathbf {Q} _ {t} x _ {t - 1}. \\tag {3}", + "image_path": "8a9abcaf53f8d217a23f1350cb3dbf8b8c92efb899088081a6d6758ce9f49d31.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": " denotes the one-hot version of a single discrete token in the layout sequence " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": " is the transition matrix, where " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "[\\mathbf{Q}_t]_{ij} = q(x_t = j|x_{t-1} = i)" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": " represents the probabilities that " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "x_{t-1}" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": " transitions to " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": ". Due to the property of Markov chain, the cumulative probability of " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": " at arbitrary timestep from " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": " can be derived as " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "q(x_t|x_0) = \\mathbf{x}_t\\overline{\\mathbf{Q}}_t\\mathbf{x}_0" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{Q}}_t = \\mathbf{Q}_1\\mathbf{Q}_2\\dots \\mathbf{Q}_t" + }, + { + "bbox": [ + 304, + 361, + 545, + 445 + ], + "type": "text", + "content": " (refer to [2] for details)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 445, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 481 + ], + "type": "text", + "content": "To generate a layout, the reverse process starts with a random noise " + }, + { + "bbox": [ + 304, + 445, + 545, + 481 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 304, + 445, + 545, + 481 + ], + "type": "text", + "content": " and gradually recovers it relying on the learned posterior distribution " + }, + { + "bbox": [ + 304, + 445, + 545, + 481 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 351, + 491, + 545, + 522 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 491, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 351, + 491, + 545, + 522 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {x} _ {0: T}\\right) = p \\left(\\mathbf {x} _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right). \\tag {4}", + "image_path": "4770550d49d2dcbd31f562cc6244f4c2de440943669e38ff7538b3a7cd31dc0e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 532, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 579 + ], + "type": "text", + "content": "In the following, we will introduce how to construct a mild forward process " + }, + { + "bbox": [ + 304, + 532, + 545, + 579 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_t|\\mathbf{x}_{t - 1})" + }, + { + "bbox": [ + 304, + 532, + 545, + 579 + ], + "type": "text", + "content": " for layout generation (Sec. 4.1), and how to learn the generative model " + }, + { + "bbox": [ + 304, + 532, + 545, + 579 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_0)" + }, + { + "bbox": [ + 304, + 532, + 545, + 579 + ], + "type": "text", + "content": " in the reverse process (Sec. 4.2)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 587, + 408, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 408, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 408, + 598 + ], + "type": "text", + "content": "4.1.Forward Process" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "content": "In LayoutDiffusion, we propose a block-wise transition matrix " + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t" + }, + { + "bbox": [ + 304, + 605, + 545, + 665 + ], + "type": "text", + "content": " and a piece-wise linear noise schedule to realize a mild forward process, in which layouts in the neighboring steps do not differ too much and become increasingly disordered as the forward step grows (see Fig. 1a)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "The design of the transition matrix and noise schedule stems from our three important observations. (i) Legality. As defined in Sec. 3, layout sequence has a rigorous format. Any transition between element type tokens and coordinate" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7228" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 76, + 505, + 222 + ], + "blocks": [ + { + "bbox": [ + 82, + 76, + 505, + 222 + ], + "lines": [ + { + "bbox": [ + 82, + 76, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 82, + 76, + 505, + 222 + ], + "type": "image", + "image_path": "d36222b7feb2aeb21a3dce1019e992d52d504429d2438d9d4fb70489a7d39958.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 224, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 224, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 547, + 257 + ], + "type": "text", + "content": "Figure 2. An illustration for LayoutDiffusion. In the forward process, the coordinates are mildly corrupted into stationary distribution, and the element types are absorbed into " + }, + { + "bbox": [ + 46, + 224, + 547, + 257 + ], + "type": "inline_equation", + "content": "\\mathsf{MASK}" + }, + { + "bbox": [ + 46, + 224, + 547, + 257 + ], + "type": "text", + "content": " in the late stage. In the reverse process, the element types are first recovered, and then the rough coordinates are gradually refined. For brevity, only two elements are shown, while the other elements and the special tokens are omitted." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 263, + 289, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 289, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 289, + 502 + ], + "type": "text", + "content": "tokens will lead to an illegal layout sequence, resulting in a disruptive change between forward steps. Hence, it is vital to impose sequence legality in the transition matrix. (ii) Coordinate Proximity. Coordinate tokens in layout sequence are ordinal and have a meaningful proximity. Transitioning a coordinate token to its proximal tokens (e.g., from 0 to 1) will introduce a milder change to a layout, compared with transitioning to distant ones (e.g., from 0 to 127). Thus, it is helpful to encode the proximity prior in the transition matrix. (iii) Type Disruption. Type tokens are categorical and do not present particular proximity. Each type of element has its unique coordinate distribution. For example, a background image tends to have a large size, while a button has a small size. Transitioning a type to another type may produce an abnormal element (e.g., a button has a large size and is placed at the top-left corner), leading to abrupt changes in layout. This is also consistent with the observation from diffusion models on other categorical data, e.g., latent code and text [2, 10]. Therefore, it is beneficial to alleviate type disruption in the transition matrix and noise schedule." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": "Transition Matrices. There are three kinds of tokens in the layout sequence, including type tokens (i.e., " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": "), coordinate tokens (i.e., " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "l_{i}, t_{i}, r_{i}" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": ") and special tokens (i.e., " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{sos} \\rangle" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{eos} \\rangle" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": ", ||, and PAD). Denote the number of different coordinate tokens and type tokens as " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": ". Then, the transition matrix is denoted as " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t \\in \\mathbb{R}^{V \\times V}" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "inline_equation", + "content": "V = K + C + 4" + }, + { + "bbox": [ + 47, + 502, + 287, + 585 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 586, + 287, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 287, + 623 + ], + "type": "text", + "content": "To achieve the legality of the layout sequence, we only allow the internal transition within each kind of tokens. Thus, " + }, + { + "bbox": [ + 46, + 586, + 287, + 623 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t" + }, + { + "bbox": [ + 46, + 586, + 287, + 623 + ], + "type": "text", + "content": " can be reduced to a block-wise diagonal matrix," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 95, + 629, + 287, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 629, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 95, + 629, + 287, + 668 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {t} = \\left[ \\begin{array}{c c c} \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} & & \\\\ & \\mathbf {Q} _ {t} ^ {\\text {t y p e}} & \\\\ & & \\mathbf {Q} _ {t} ^ {\\text {s p e c}} \\end{array} \\right], \\tag {5}", + "image_path": "55d5aa4a35160d2320437f882b9352ebb220403a5c0e458806ec18d2e86efc48.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{coord}}" + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{type}}" + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{spec}}" + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": " depicts the probabilities of the internal transition within coordinate tokens, type tokens and special tokens, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 262, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 312 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 305, + 262, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{coord}}" + }, + { + "bbox": [ + 305, + 262, + 545, + 312 + ], + "type": "text", + "content": ", to encode the ordinal proximity, we introduce the discretized Gaussian matrix [2] for coordinate tokens, which assigns a higher probability to the transition between more proximal tokens," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 310, + 319, + 545, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 319, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 310, + 319, + 545, + 393 + ], + "type": "interline_equation", + "content": "\\left[ \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} \\right] _ {i j} = \\left\\{ \\begin{array}{l l} \\frac {\\exp \\left(- \\frac {4 | i - j | ^ {2}}{(K - 1) ^ {2} \\beta_ {t}}\\right)}{\\sum_ {n = - (K - 1)} ^ {(K - 1)} \\exp \\left(- \\frac {4 n ^ {2}}{(K - 1) ^ {2} \\beta_ {t}}\\right)}, & i \\neq j \\\\ 1 - \\sum_ {l = 0, l \\neq i} ^ {(K - 1)} \\left[ \\mathbf {Q} _ {t} ^ {\\text {c o o r d}} \\right] _ {i l}, & i = j \\end{array} \\right. \\tag {6}", + "image_path": "31f0444da613b65918fdc256ced7452c3c59152f93e72f4148d8957f18f7468a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 395, + 544, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 395, + 544, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 395, + 544, + 418 + ], + "type": "text", + "content": "where the parameters " + }, + { + "bbox": [ + 305, + 395, + 544, + 418 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 305, + 395, + 544, + 418 + ], + "type": "text", + "content": " influence the variance of the forward process distributions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 418, + 545, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 418, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 305, + 418, + 545, + 466 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 305, + 418, + 545, + 466 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{type}}" + }, + { + "bbox": [ + 305, + 418, + 545, + 466 + ], + "type": "text", + "content": ", to alleviate the type disruption, we choose to transit a type token to a special MASK token instead of another meaningful type token. Therefore, we introduce the absorbing state transition matrix [2] for type tokens," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 344, + 474, + 545, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 474, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 344, + 474, + 545, + 531 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {t} ^ {\\text {t y p e}} = \\left[ \\begin{array}{c c c c} 1 - \\gamma_ {t} & 0 & \\dots & 0 \\\\ 0 & 1 - \\gamma_ {t} & \\dots & 0 \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\gamma_ {t} & \\gamma_ {t} & \\dots & 1 \\end{array} \\right], \\tag {7}", + "image_path": "909a75621aab4cf69e789795e87fbc947eafab80d33d73be95afa1e95f12331f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 539, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 539, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 305, + 539, + 545, + 574 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 539, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 305, + 539, + 545, + 574 + ], + "type": "text", + "content": " indicates the probability that a token is absorbed into a MASK token, and " + }, + { + "bbox": [ + 305, + 539, + 545, + 574 + ], + "type": "inline_equation", + "content": "1 - \\gamma_{t}" + }, + { + "bbox": [ + 305, + 539, + 545, + 574 + ], + "type": "text", + "content": " is the probability that a token stays unchanged." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{spec}}" + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "content": ", as special tokens describe the structure of the layout sequence, any transition between them will lead to an invalid layout sequence. Therefore, we choose to disable any transition between them," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 402, + 631, + 545, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 631, + 545, + 645 + ], + "spans": [ + { + "bbox": [ + 402, + 631, + 545, + 645 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {t} ^ {\\text {s p e c}} = \\mathbf {I}, \\tag {8}", + "image_path": "40fae9bc3d9ddd29aa6af1e47130cee900ed51bebbcaaacc1cdec558173c3e3d.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 654, + 425, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 654, + 425, + 665 + ], + "spans": [ + { + "bbox": [ + 306, + 654, + 425, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 654, + 425, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 306, + 654, + 425, + 665 + ], + "type": "text", + "content": " is an identity matrix." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "content": "Noise Schedules. An early absorbing of type tokens (i.e., transitioning to MASK token) will bring an abrupt change to the layout. Hence, to further eliminate type disruption, we choose to make the element type begin to change only" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7229" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "in the late stage of the forward process. Specifically, we design " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\overline{\\gamma}_t = 1 - \\prod_{i=1}^t (1 - \\gamma_i)" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " for the cumulative probability " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "q_t(x_t|x_0)" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " as a piece-wise linear function," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 95, + 115, + 287, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 115, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 95, + 115, + 287, + 147 + ], + "type": "interline_equation", + "content": "\\bar {\\gamma} _ {t} = \\left\\{ \\begin{array}{l l} 0, & t < \\tilde {T} \\\\ (t - \\tilde {T}) / (T - \\tilde {T}), & t \\geq \\tilde {T} \\end{array} \\right. \\tag {9}", + "image_path": "b17674fda5748c744ca5b66cdc6b61e9fa05909f2b547dfcef4d9b7482de42a2.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 154, + 287, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 154, + 287, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 154, + 287, + 178 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 154, + 287, + 178 + ], + "type": "inline_equation", + "content": "\\tilde{T}" + }, + { + "bbox": [ + 46, + 154, + 287, + 178 + ], + "type": "text", + "content": " is the timestep where the absorbing is enabled, and " + }, + { + "bbox": [ + 46, + 154, + 287, + 178 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 154, + 287, + 178 + ], + "type": "text", + "content": " is the terminal timestep." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "content": "Besides, although existing work often uses linear schedule for Gaussian transition process, we choose to use " + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\beta_{t} = g / (T - t + \\epsilon)^{h}" + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "content": " for the transition of coordinate tokens " + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{coord}}" + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "content": " are hyper-parameters, and " + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "content": " denotes a small positive quantity. It is generalized from a commonly used noise schedule " + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "inline_equation", + "content": "1 / (T - t + 1)" + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "content": " [2,37]. We find that with " + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "inline_equation", + "content": "h > 1" + }, + { + "bbox": [ + 46, + 178, + 287, + 286 + ], + "type": "text", + "content": ", it achieves a slower and more smooth corruption to the layout in the early forward process, which helps the model in the reverse process better learn the posterior distribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 293, + 144, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 144, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 144, + 304 + ], + "type": "text", + "content": "4.2. Reverse Process" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "type": "text", + "content": "To reverse the forward process, we optimize the generative model " + }, + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_0)" + }, + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "type": "text", + "content": " to fit the data distribution " + }, + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_0)" + }, + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "type": "text", + "content": " by minimizing the variational lower bound (VLB) [2]," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 354, + 287, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 354, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 53, + 354, + 287, + 403 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {V L B}} = - \\log p _ {\\theta} (\\mathbf {x} _ {0} | \\mathbf {x} _ {1}) + D _ {\\mathrm {K L}} (q (\\mathbf {x} _ {T} | \\mathbf {x} _ {0}) \\| p (\\mathbf {x} _ {T})) \\tag {10} \\\\ + \\sum_ {t = 2} ^ {T} D _ {\\mathrm {K L}} \\left(q \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) \\| p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right)\\right). \\\\ \\end{array}", + "image_path": "b8176a8176c931054752303c222595f29d2365bb38a96040119409c6d6dff598.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "text", + "content": "Following recent work [2, 10], we predict " + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t)" + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)" + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "text", + "content": ", and encourage good predictions of " + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "text", + "content": " at each step by combining " + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{VLB}}" + }, + { + "bbox": [ + 46, + 409, + 287, + 445 + ], + "type": "text", + "content": " with an auxiliary objective," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 456, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 456, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 287, + 469 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {V L B}} - \\lambda \\log p _ {\\theta} \\left(\\mathbf {x} _ {0} \\mid \\mathbf {x} _ {t}\\right). \\tag {11}", + "image_path": "3ba48ef15396728e626872bf02241090ae652ac53da4d06426e9c66341ede1c4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": "Specifically, we leverage Transformer encoder [40] to learn " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t)" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": ". Denote the embedding of " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": "-th token in the layout sequence " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathrm{emb}(x_{t,i})" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": " and its positional embedding as " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": ". Denote the embedding of the timestep " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathrm{emb}(t)" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": ". Then, Transformer takes the aggregation of them, i.e., " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{emb}(x_{t,i}) + p_i + \\mathrm{emb}(t)\\}_{i=1}^M" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": ", as the input and predicts a new layout sequence " + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}}_0 = \\{\\tilde{x}_{0,i}\\}_{i=1}^M" + }, + { + "bbox": [ + 46, + 473, + 287, + 557 + ], + "type": "text", + "content": " as the output." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "content": "In practice, we set an " + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "content": " as the maximum number of elements. During inference, we first sample an element count " + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "content": " from the training set's prior distribution. For constructing " + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "content": ", we assign MASK tokens for the type and random coordinate tokens for bounding boxes of the first " + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "content": " elements. For the remaining " + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "inline_equation", + "content": "(N - n)" + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "content": " elements, PAD tokens are utilized to ensure a consistent length. By performing denoising from timestep " + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "content": " to 0, we derive the layout " + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 557, + 287, + 652 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 658, + 287, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 287, + 684 + ], + "type": "text", + "content": "4.3. Enabling Conditional Layout Generation in a Plug-and-Play Manner" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Although LayoutDiffusion is trained for unconditional layout generation, it can handle some conditional gener" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "ation tasks without re-training, which has never been explored by previous work. Such a plug-and-play feature of conditional generation is enabled by the design of transition matrices and noise schedules. In the following, we introduce how LayoutDiffusion achieves it." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 133, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 289 + ], + "type": "text", + "content": "Refinement is a user-oriented layout generation task first posed in ROUTE [32], and is recently studied by Layout-Former++ [16]. Its goal is to take a user given flawed layout as input and provide a high-quality layout for the user while maintaining the original design style. With the proposed transition matrices and noise schedules, a layout is gradually corrupted in the forward process. With such a forward process, the reverse process learned by LayoutDiffusion is to iteratively improve a layout, which naturally enables refinement. Specifically, in LayoutDiffusion, we achieve refinement by feeding the flawed layout into the model and then running reverse process from a certain timestep. Here the timestep is related to how noisy the input layout is." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 289, + 545, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 480 + ], + "type": "text", + "content": "Generation Conditioned on Types (Gen-Type) is also a widely studied conditional layout generation task [16, 20, 22] to satisfy the needs of user. It aims to generate layouts with the given element types. In LayoutDiffusion, there is no transition between coordinates and types (see Eq. (5)). Besides, with the noise schedule in Eq. (9), the change of the types only occurs in the late forward process. With the above two mechanisms, LayoutDiffusion will determine the element types in the early reverse steps very quickly and then continue to improve the coordinates in the remaining reverse steps without changing the types (see the transformation of the layout from right to left in Fig. 2). In other words, the generation for coordinates and that for element types are approximately decoupled. Thus, in LayoutDiffusion, we achieve Gen-Type by feeding in the element types in the early stage and running the reverse process." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 494, + 386, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 494, + 386, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 494, + 386, + 506 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 514, + 359, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 359, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 359, + 526 + ], + "type": "text", + "content": "5.1. Setups" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": "Datasets. We employ two widely-used public datasets of graphic layouts. RICO [6] is a dataset of user interface designs for mobile applications, which contains " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "66\\mathrm{K}+" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": " UI layouts with 25 element types. PublayNet [46] includes " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "360\\mathrm{K}+" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": " annotated scientific document layouts with 5 element types. Both datasets contain a few over-length entries. We filter out the layouts longer than 20 elements as in LayoutFormer++ [16]. Then, we split the filtered data into a training, validation, and test set by " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Baselines. First, we compare LayoutDiffusion with leading approaches for layout generation. Specifically, we compare against LayoutTransformer [11], VTN [1], Coarse2Fine [17], and LayoutFormer++ [16] on unconditional generation (UGen); against NDN-none [22], LayoutGan++ [19], BLT [20], and LayoutFormer++ [16]" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7230" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 547, + 305 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 547, + 305 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 547, + 305 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 547, + 305 + ], + "type": "table", + "html": "
SubtasksMethodsRICOPubLayNet
mIoU (↑)Overlap (→)Align. (→)FID (↓)mIoU (↑)Overlap (→)Align. (→)FID (↓)
Un-GenLayoutTransformer0.5870.5420.03724.3200.3590.00450.06730.048
VTN0.3360.5610.47788.1150.3120.2210.207105.909
Coarse2Fine0.3600.6760.12846.4830.3610.1420.22150.854
LayoutFormer++0.6340.5460.05120.1980.4010.00100.02847.082
Diffusion-LM°0.6620.6310.18411.4480.4390.01250.07611.895
D3PM (absorbing)°0.5850.6190.1574.9850.4010.04270.07512.218
D3PM (uniform)°0.5950.6580.2295.5760.4050.05710.09911.212
LayoutDiffusion° (ours)0.6200.5020.0692.4900.4170.00300.0658.625
Gen-TypeNDN-none0.350.550.5613.760.310.170.3535.67
LayoutGan++0.2980.6200.2615.9540.2970.1480.12414.875
BLT0.2160.9830.15025.6330.1400.1960.03638.684
LayoutFormer++0.3770.5370.1242.4830.3330.0090.02510.151
Diffusion-LM°0.3240.5740.1996.5300.3160.0260.0467.396
D3PM (absorbing)°0.3370.5940.1923.5060.3330.0580.0578.858
D3PM (uniform)°0.3170.6210.2185.7710.3510.0630.0648.275
LayoutDiffusion° (ours)0.3450.4910.1241.5570.3430.0050.0293.731
RefinementRUITE0.6580.4920.1777.9260.6370.03750.0737.890
LayoutFormer++0.6560.5030.1413.6660.6420.01260.0422.937
Diffusion-LM°0.6210.4990.1818.5780.5730.04080.14013.985
D3PM (uniform)°0.5680.5260.2668.4070.5640.05150.11014.553
LayoutDiffusion° (ours)0.7190.4690.1020.5490.6600.00790.0352.045
Real Data-0.4660.093--0.00310.022-
", + "image_path": "b5828e0e15c1253b8774d78aab1f47e2b1280ac4a7d24dd5ed7cc03e5c1bfd61.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "text", + "content": "Table 1. Quantitative results. Methods with " + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "text", + "content": " are diffusion-based, which achieve conditional generation (i.e., Gen-Type and Refinement) in a plug-and-play manner, while other methods require re-training for each subtask. The best and the second best values of each metric are bold and underlined respectively. For mIoU, the higher the score, the better the performance (indicated by " + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "text", + "content": "). For Overlap and Align, the closer to real data, the better (indicated by " + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "text", + "content": "). For FID, the lower the score, the better the performance (indicated by " + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 308, + 546, + 354 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 359, + 289, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 289, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 289, + 453 + ], + "type": "text", + "content": "on generation conditioned on type (Gen-Type); against ROUTE [32], and LayoutFormer++ [16] on refinement. Moreover, we compare LayoutDiffusion with the existing diffusion models that do not consider the characteristics of layouts. Diffusion-LM [25] maps discrete data to continuous state space, while D3PM (uniform) [2] and D3PM (absorbing) [2] perform diffusion in discrete state space using different transition matrices." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": "Implementation Details. We set the weight of auxiliary loss as " + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\lambda = 0.0001" + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": " (see Eq. (11)). In the training, we set the timestep as " + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "inline_equation", + "content": "T = 200" + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": "; in the inference, we set the timesteps " + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{UGen}} = 200" + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{Gen-Type}} = 160" + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{Refine}} = 50" + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": " for different generation tasks. For the layout sequence (see Eq. (1)), we arrange elements in the alphabetical order of the type, and each token is embedded with " + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "inline_equation", + "content": "d = 128" + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": " dimensions. For the denoising network " + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_0|\\mathbf{x}_t)" + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": ", we apply a 12-layer Transformer encoder with 12 attention heads. We train the model using AdamW optimizer [26] with " + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "inline_equation", + "content": "2 \\sim 4" + }, + { + "bbox": [ + 46, + 458, + 287, + 603 + ], + "type": "text", + "content": " NVIDIA V100 GPUs. We also employ importance timestep sampling [29] during the training. See Supplementals for more details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Evaluation Metrics. We adopt four metrics to measure the performance comprehensively. Among them, Frechet Inception Distance (FID) measures the overall performance, while Maximum Interaction over Union (mIoU), Alignment (Align.) and Overlap measure the quality from a specific aspect. Specifically, FID computes the distance between the distribution of the generated layouts and that of real layouts. Following the previous practice [19, 22], we train a classification-based neural network to get the feature" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "content": "embedding for the layout. " + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "inline_equation", + "content": "mIoU" + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "content": " calculates the maximum IoU between bounding boxes of the generated layouts and those of the real layouts with the same type set [19]. Align measures whether the elements in a generated layout are well-aligned, either by center or by edges. In addition to the original implementation [22], a normalization over the number of elements is applied. Overlap measures the overlapping area between elements in the generated layout. Following LayoutFormer++ [16], we ignore normal overlaps, e.g., elements on top of the background." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 488, + 545, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 488, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 488, + 545, + 513 + ], + "type": "text", + "content": "5.2. Comparison with Existing Approaches for Layout Generation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "type": "text", + "content": "Quantitative Analysis. In Tab. 1, the methods without the symbol " + }, + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 304, + 520, + 545, + 544 + ], + "type": "text", + "content": " are existing approaches for layout generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 545, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 616 + ], + "type": "text", + "content": "First, we compare FID as it is an overall metric for generation performance. LayoutDiffusion achieves significantly better FID scores than all other methods. For example, on Un-Gen, LayoutDiffusion achieves 2.490 and 8.625 on RICO and PubLayNet datasets, respectively, while the best existing work only achieves 20.198 and 30.048." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "Furthermore, we examine individual metrics, including mIoU, Overlap, and Align., each of which measures the quality from a specific aspect. LayoutDiffusion is in the top two on almost every metric and frequently achieves the best performance. On the contrary, existing approaches may perform well on a certain metric but fail on the other individual metrics and the overall metric (i.e., FID), indicating that LayoutDiffusion is a well-rounded approach. For ex" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7231" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 542, + 404 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 542, + 404 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 542, + 404 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 542, + 404 + ], + "type": "image", + "image_path": "cc9cf75c86949b32c319c31d9e76de77a3a40c9f39f250bea606767f2bb810aa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 407, + 547, + 441 + ], + "lines": [ + { + "bbox": [ + 46, + 407, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 547, + 441 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison against strongest baselines selected by FID (better view in color and " + }, + { + "bbox": [ + 46, + 407, + 547, + 441 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 407, + 547, + 441 + ], + "type": "text", + "content": " zoom). The first three row is for RICO and the last three is for PubLayNet. LayoutDiffusion generates high-quality and diverse layouts. Layouts from LayoutFormer++ either lack diversity (Un-Gen) or are flawed (Gen-Type and Refinement). Layouts from other methods misalign and overlap frequently." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 446, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 287, + 495 + ], + "type": "text", + "content": "ample, on Un-Gen, LayoutTransformer has a good overlap score, but it does not perform well on Align., mIoU and FID; LayoutFormer++ has the best Align. for PubLayNet, but underperforms in mIoU, overlap and FID." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 495, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 544 + ], + "type": "text", + "content": "Moreover, on conditional generation tasks (i.e., GenType and Refinement), the above observations still hold, even though LayoutDiffusion is not re-trained on these tasks (see Sec. 4.3) while existing approaches are re-trained." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 544, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 688 + ], + "type": "text", + "content": "Qualitative Analysis. Fig. 3 shows qualitative results. On Un-Gen, LayoutDiffusion generates diverse and high-quality layouts. In contrast, LayoutTransformer mainly suffers from incorrect spacing and overlap, and LayoutFormer++ is deficient in diversity. For example, for LayoutFormer++, most layouts on RICO contain a top toolbar and several list items, and most layouts on PublayNet are double-columned and have many texts. Besides, on Gen-Type and Refinement, LayoutDiffusion outperforms other methods (e.g., alignment, overlap and spacing) while it is not re-trained. For more qualitative results, please refer to Supplemental Sec. E." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "User Study. On each task, we select the best two baselines by FID for the user study. We design two kinds of evalua" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 446, + 545, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 545, + 565 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 545, + 565 + ], + "type": "text", + "content": "tion. One is quality evaluation. We show three layouts from three models respectively (two from baselines and one from LayoutDiffusion) and invite the user to choose which one has the best quality (e.g., more plausible overall structure and pleasing details). Another one is diversity evaluation. We show three sets of layouts from three models respectively, where each set contains five layouts from the same model. Then, we invite the user to choose which set has the most diverse layouts. For Refinement, we do not conduct diversity evaluation as it is not necessary for this scenario." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 566, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 626 + ], + "type": "text", + "content": "Fig. 4 shows the results. Across different datasets, tasks and evaluation modes, there are 10 groups of user studies in total, in each of which we invite 15 people and everyone labels 50 groups of layouts. The user study shows that LayoutDiffusion outperforms other methods significantly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 634, + 545, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 545, + 647 + ], + "type": "text", + "content": "5.3. Comparison with Traditional Diffusion Models" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Quantitative Analysis. In Tab. 1, methods marked with " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " are traditional diffusion models. They are originally proposed for other generation tasks (e.g., image and text). We adapt them for layout generation. On Un-Gen, LayoutDiffusion achieves the best performance on most metrics. On" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7232" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 71, + 527, + 163 + ], + "blocks": [ + { + "bbox": [ + 63, + 71, + 527, + 163 + ], + "lines": [ + { + "bbox": [ + 63, + 71, + 527, + 163 + ], + "spans": [ + { + "bbox": [ + 63, + 71, + 527, + 163 + ], + "type": "image", + "image_path": "a66066b385de55820d707129c78bbb3dc8a33a7ce40b9eb42d649072bf7013a9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 545, + 185 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 545, + 185 + ], + "type": "text", + "content": "Figure 4. Results of the user study. For each model, we count how many people prefer the layouts generated from this model. The study shows that the results generated by LayoutDiffusion were favored by users over the other methods, particularly in terms of diversity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 191, + 274, + 344 + ], + "blocks": [ + { + "bbox": [ + 59, + 191, + 274, + 344 + ], + "lines": [ + { + "bbox": [ + 59, + 191, + 274, + 344 + ], + "spans": [ + { + "bbox": [ + 59, + 191, + 274, + 344 + ], + "type": "image", + "image_path": "c98228eaa61ef76c62f4529279fe9a62ad963bf8d933d7aa5d716159f5ad0ef3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 345, + 287, + 378 + ], + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 378 + ], + "type": "text", + "content": "Figure 5. Reverse denoising process for unconditional generation on RICO (from left to right). Each row is for one model. The blank page is used when the generated layout sequence is invalid." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 388, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 484 + ], + "type": "text", + "content": "Gen-Type and Refinement, while traditional diffusion models can be used for conditional generation tasks without retraining, their performance is usually worse than existing methods for layout generation (e.g., LayoutFormer++, not to mention LayoutDiffusion. These observations demonstrate that our consideration of the heterogeneous nature of layout data is critical for both achieving good performance and realizing plug-and-play conditional generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 484, + 288, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 288, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 288, + 616 + ], + "type": "text", + "content": "Qualitative Analysis. Fig. 3 shows a qualitative comparison with the best traditional diffusion model (selected by FID). LayoutDiffusion consistently generates better layouts, e.g., better alignment and less overlap. Moreover, Fig. 5 compares the reverse denoising processes of different diffusion models. LayoutDiffusion quickly generates a draft layout and then gradually refines it to a pleasing layout, while other diffusion models take many steps to generate a rough layout and fewer steps for iterative refinement, which may limit the modeling of precise relationships between elements, such as strict alignment and no overlap." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 623, + 224, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 224, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 224, + 635 + ], + "type": "text", + "content": "5.4. Ablation Studies and Discussions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Transition Matrices. Our transition matrices are designed by considering three critical factors, i.e., legality, coordinate proximity and type disruption (see Sec. 4.1). We remove the technique corresponding to each factor. First, without considering the legality, the techniques for the other two factors cannot be applied. Thus, LayoutDiffusion degrades to" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 306, + 189, + 542, + 292 + ], + "blocks": [ + { + "bbox": [ + 306, + 189, + 542, + 292 + ], + "lines": [ + { + "bbox": [ + 306, + 189, + 542, + 292 + ], + "spans": [ + { + "bbox": [ + 306, + 189, + 542, + 292 + ], + "type": "table", + "html": "
MethodmIoU↑Overlap→Align.→FID↓
Uniform Qtcoord0.6140.6330.1193.174
Absorbing Qtcoord0.6360.6070.1143.672
Uniform Qttype0.5930.4780.1392.534
Linear γt0.5800.5220.1562.846
Linear βt0.5890.5170.2022.598
LayoutDiffusion0.6200.5020.0692.490
Real Data-0.4660.093-
", + "image_path": "0d7425b163ed85b884fa42960578396bd7545534473e324f559a049cd446b8fa.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 312, + 538, + 383 + ], + "blocks": [ + { + "bbox": [ + 306, + 296, + 544, + 307 + ], + "lines": [ + { + "bbox": [ + 306, + 296, + 544, + 307 + ], + "spans": [ + { + "bbox": [ + 306, + 296, + 544, + 307 + ], + "type": "text", + "content": "Table 2. Ablation studies on RICO with unconditional generation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 312, + 538, + 383 + ], + "lines": [ + { + "bbox": [ + 308, + 312, + 538, + 383 + ], + "spans": [ + { + "bbox": [ + 308, + 312, + 538, + 383 + ], + "type": "table", + "html": "
FID↓Number of Steps
10020050010002000
Diffusion-LM17.75917.16411.98411.74111.448
D3PM (absorbing)7.4646.1026.0914.9855.110
D3PM (uniform)6.9866.9105.3515.5755.239
LayoutDiffusion3.8752.4902.3872.2952.360
", + "image_path": "8642babd0fb25f15af443a5355b312f86333ac156d6d164509e7dca12a8a5132.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 386, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 386, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 305, + 386, + 545, + 431 + ], + "type": "text", + "content": "Table 3. Ablation study on timesteps for diffusion models. All the experiments are on RICO with unconditional generation. The training and inference steps are set as the same. 2000 and 1000 are default settings used in Diffusion-LM [25] and D3PMs [2]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "type": "text", + "content": "D3PM (absorbing or uniform). Tab. 1 shows that Layout-Diffusion achieves better performance. Second, to ignore coordinate proximity, we use uniform or absorbing transition for coordinate tokens, denoted as Uniform " + }, + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{coord}}" + }, + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "type": "text", + "content": " and Absorbing " + }, + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{coord}}" + }, + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "type": "text", + "content": " in Tab. 2. LayoutDiffusion outperforms these two variations on most metrics, especially Overlap and FID. Third, to study type disruption, we use uniform transition for type tokens, denoted as Uniform " + }, + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^{\\mathrm{type}}" + }, + { + "bbox": [ + 304, + 436, + 546, + 555 + ], + "type": "text", + "content": " in Tab. 2. LayoutDiffusion outperforms this variation, where the improvement of mIoU is most significant." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "text", + "content": "Noise Schedules. To make the corruption of element types occur throughout the forward process, we set " + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\tilde{T}" + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "text", + "content": " as 0 for " + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\overline{\\gamma}_t" + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "text", + "content": " (see Eq. (9)), which results in a linear schedule (denoted as Linear " + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\overline{\\gamma}_t" + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "text", + "content": " in Tab. 2). We replace the noise schedule for " + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\beta_t" + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "text", + "content": " with the original linear schedule in previous work [2] (denoted as Linear " + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\beta_t" + }, + { + "bbox": [ + 304, + 556, + 546, + 640 + ], + "type": "text", + "content": " in Tab. 2). LayoutDiffusion outperforms both of them on most metrics, especially mIoU and Align." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": "Timesteps. Tab. 3 shows FID of diffusion models with different timesteps. While 200 steps are enough for LayoutDiffusion, the performance of Diffusion-LM, D3PM (absorbing), and D3PM (uniform) saturates at 500, 1000, and 500 timesteps respectively. Besides, even the fastest version of LayoutDiffusion surpasses all the other diffusion models." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7233" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 145 + ], + "type": "text", + "content": "Additional Analyses. For a detailed discussion on the diversity of the generated layouts, see Supplemental Sec. B. Experiments on additional settings of conditional generation are available in Sec. C. Ablation studies concerning conditional generation tasks, noise schedules, and sequence ordering can be found in Sec. D." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 156, + 119, + 169 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 119, + 169 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 119, + 169 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 175, + 289, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 289, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 289, + 307 + ], + "type": "text", + "content": "In this work, we propose LayoutDiffusion to improve graphic layout generation by discrete diffusion models. The core of our method lies in realizing a mild forward process by considering the heterogeneous characteristics of the layout. Our method also enables two conditional generation tasks without re-training. Experiments demonstrate the superiority of LayoutDiffusion over leading approaches for layout generation and existing diffusion models. In the future, we plan to incorporate diverse conditions [14, 28] in LayoutDiffusion. Besides, we will also explore how to extend LayoutDiffusion to handle other heterogeneous data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 319, + 157, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 157, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 157, + 333 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 339, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 288, + 387 + ], + "type": "text", + "content": "We would like to thank Zhaoyun Jiang for helpful discussions. 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Existing works usually develop generic 4D learning tools without leveraging the prior that a 4D sequence comes from a single 3D scene with local dynamics. Based on this observation, we propose to learn region-wise coordinate frames that transform together with the underlying geometry. With such frames, we can factorize geometry and motion to facilitate a feature-space geometric reconstruction for more effective 4D learning. To learn such region frames, we develop a rotation equivariant network with a frame stabilization strategy. To leverage such frames for better spatial-temporal feature learning, we develop a frame-guided 4D learning scheme. Experiments show that this approach significantly outperforms previous state-of-the-art methods on a wide range of 4D understanding benchmarks.", + "bbox": [ + 75, + 317, + 473, + 540 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 565, + 208, + 579 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We have recently witnessed a surge of interest in understanding point cloud sequences in 4D (3D space + 1D time). As the direct sensory input in a large number of modern AI applications including robotics and AR/VR, point cloud sequences can faithfully depict the geometry and motion of a dynamic scene, and therefore become critical for an intelligent agent to perceive and interact with the physical world.", + "bbox": [ + 75, + 589, + 468, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, learning on such 4D data is very challenging and is still in an immature stage. 4D point cloud sequences usually couple 3D geometry and its dynamic motion together, resulting in quite redundant data in a very high dimensional space. This causes severe learning issues against an effective and compact spatial-temporal representation.", + "bbox": [ + 75, + 686, + 468, + 769 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some existing efforts tackle the challenge through novel 4D backbone designs [8, 30, 7]. However, most of these works treat the point cloud sequence as unstructured 4D data and exploit generic 4D learning methods without leveraging the prior that the whole 4D sequence just depicts a single 3D scene with dynamic objects. As a result, such 4D learning is usually not super effective and the learned", + "bbox": [ + 75, + 769, + 470, + 866 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a456efa32dba68f9a2a4bfd473caa3454ae1c977217f0c5575ca345c9cf944d4.jpg", + "image_caption": [ + "Figure 1. Frame-aware spatial-temporal convolution. We propose to learn frames for point cloud sequence. Upon obtaining the frames, we could easily align the geometry regardless of the underlying motion toward a more canonical and complete geometry understanding. The motion-agnostic geometric features also allow easier temporal association toward a better motion understanding." + ], + "image_footnote": [], + "bbox": [ + 502, + 286, + 890, + 451 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "spatial-temporal feature barely outperforms the spatial feature alone. Another line of works [7] uses self-supervised representation learning to encourage geometry and motion learning in a loosely decoupled manner. However, the decoupling still happens on the whole-scene level with a special focus on camera ego-motion, restricting their efficacy in modeling local dynamics on the object-level. We envision that successful geometry and motion decoupling is the key toward effective 4D representation learning. This essentially requires depicting the low-dimensional manifold of the dynamic scenes from the redundant high-dimensional 4D data. This highly correlates to dynamic scene reconstruction which requires understanding both camera ego-motion and object motion and is an ongoing research topic itself. Instead of explicitly reconstructing the dynamic scene without a quality guarantee, we seek a more lightweight and flexible solution.", + "bbox": [ + 497, + 543, + 890, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our solution is based upon the following observation. For a specific region in the scene, we can understand its dynamic motion through establishing geometry-based and temporally-consistent local coordinate frames. Specifically, if we can establish a local coordinate frame based upon the 3D geometry in each timestamp and also make sure such", + "bbox": [ + 497, + 783, + 890, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 84 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 253, + 48, + 789, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "604", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "frame transforms in the same way as the underlying geometry, then we can estimate the local rigid motion via comparing such frames among corresponding regions across timestamps. Such local frames allow us to factorize the local geometry understanding from its motion in a similar spirit to equivariant 3D analysis [22, 14]. In particular, once we establish temporally-consistent local coordinate frames, we essentially have a way to align the geometry regardless of the underlying motion toward a more canonical and complete geometry understanding. In addition, the motion-agnostic geometric features also allow easier temporal association toward a better motion understanding.", + "bbox": [ + 75, + 125, + 468, + 290 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based upon the above observations, we present a novel 4D learning framework named LeaF. LeaF contains a frame learning module and a frame-guided 4D learning module. The frame learning module aims at producing geometry-based temporally consistent coordinate frames at different scales so that corresponding regions across timestamps can be well-aligned. This allows for factorizing geometry learning from motion learning. And then the frame-guided 4D learning module leverages the learned frames to facilitate a more effective spatial-temporal feature aggregation. Specifically, in the frame learning module, we design a hierarchical FrameNet which is essentially a rotation-equivariant neural network able to produce coordinate frames equivariant to the rotation of input geometry. The frame learning process is very challenging though since apart from rotations different observations from a point cloud sequence can vary significantly due to sampling differences, density variation, or sensor noises. To make sure the rotation equivariance of hierarchical FrameNet is not broken in practice, we introduce a frame stabilization scheme to further regularize the frame learning process. In the frame-guided 4D learning module, we first modify popular 4D operators (e.g. 4D point conv) into their frame-guided version and then leverage frame-guided 4D convolution to process 4D point cloud sequences. Since the motion information is factorized away while convolving with the learned region frames, we additionally process the 4D sequences with just a globally constant camera frame so that the motion information is faithfully kept. We fuse the learned features both from using region frames and from using camera frames, allowing a very effective 4D feature learning.", + "bbox": [ + 75, + 294, + 470, + 722 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To verify the effectiveness of LeaF, we conduct experiments on a wide range of 4D understanding tasks. And we demonstrate significant improvements over previous state-of-the-art methods $(+2.0\\%)$ accuracy on HOI4D action segmentation [21], $+1.51\\%$ accuracy on MSR action recognition [17], $+2.4\\%$ mIoU on HOI4D indoor semantic segmentation [21], and $+1.81\\%$ mIoU on Synthia4D outdoor semantic segmentation [25]).", + "bbox": [ + 75, + 725, + 468, + 836 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are threefold: 1) we propose to learn effective spatial-temporal 4D features via learning and ex", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ploiting region-wise coordinate frames and our framework LeaF achieves state-of-the-art performance on a wide range of 4D understanding benchmarks; 2) we design a hierarchical FrameNet along with a frame stabilization scheme to learn equivariant region frames for motion-invariant geometry feature learning; 3) we present a frame-guided 4D learning method that is able to benefit from equivariant region frames without losing the motion information.", + "bbox": [ + 497, + 125, + 890, + 237 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 252, + 640, + 268 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "4D point cloud sequence understanding. Compared with understanding static 3D point clouds, understanding 4D point cloud sequences requires more on aggregating and leveraging spatial-temporal information to perceive the geometry and dynamics. Several 4D backbones have been proposed to address such challenges, and they can be divided into two categories based on their representations. The first is to voxelize raw point clouds and extract features on 4D voxels, including MinkwoskiNet [3] which employs 4D spatial-temporal convolutions on 4D voxels. The second is to perform directly on raw points, including Meteor Net [19] which extends PointNet++[23] with a temporal dimension and explicitly tracks points' motion for grouping, and PSTNet[11] which constructs a point tube along temporal dimension for 4D point convolution. State of The Art methods such as Point 4d Transformer [9] and PPTr [30] belong to the second category and introduce transformer architecture, in order to avoid point-tracking and to better capture spatio-temporal correlation. There are works [7] focusing on improving the optimization of a transformer.", + "bbox": [ + 497, + 283, + 890, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Equivariant feature learning. The seminal work of Group Equivariant Convolution Networks [4] (G-CNN) starts a trend of leveraging group equivariance for neural networks. For 3D data, rotation group equivariance or SO(3) equivariance is significant, and there are roughly two categories of SO(3) equivariant networks. The first category is the \"filter orbit\" method. Inspired by group-equivariant convolution on 2D images proposed in G-CNN [4], Equivariant Point Network [2] and successive works [16, 18, 32] discretizes SO(3) and analogously design group-equivariant operations on point clouds. However, as such networks extend the original features to multiple oriented features, they encounter memory issues and may not be suitable for 4D point cloud sequences understanding. The second category is the \"filter design\" method. These methods [28, 5, 14] design the filter forms to achieve exact SO(3) equivariance. \"Filter design\" methods get rid of memory issues, but their representation capability is usually limited due to the restricted filter form.", + "bbox": [ + 497, + 568, + 890, + 818 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rotation-invariant local descriptors. Local descriptor is a synonym for local feature, which is widely used in tasks such as 3D point cloud matching. Some of the rotation-", + "bbox": [ + 497, + 825, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "605", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e5f1fdf35f0bc84845deafc7be410da222a78c4f38035c56c985baaa17c652ac.jpg", + "image_caption": [ + "Figure 2. Illustration of the proposed Learning Frame for 4D Point Cloud Sequence Understanding (LeaF). We use an SO(3) equivariant network proposed in [22] to learn hierarchical frames denoted as region frames. We denote the identity frames as camera frames. Under region frames and camera frames, region frame feature and camera frame feature can be extracted by frame-aware 4D backbones, and are then fused by region frame-guided transformer to do downstream tasks such as action recognition, action segmentation, and semantic segmentation. Data augmentation and regularization losses are also added to make the equivariant Hierarchical frame network robust to re-sampling, down-sampling, and jittering." + ], + "image_footnote": [], + "bbox": [ + 171, + 122, + 806, + 413 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "invariant local descriptors first obtain rotation-equivariant local reference frames (LRFs) either via PCA methods [29, 13, 29, 31, 12, 15], or by incorporating learning methods to decide the axis in the tangent plane aside from normal [33], or completely by 3D rotation equivariant networks [22]. Under those LRFs, local support sets can be transformed into canonical representation, and thus invariant local features can be extracted either by hand-crafted method [29, 13, 29, 31] or by learning methods [12, 15]. Some other methods [27, 26, 1, 6] directly extract invariant local features from invariant local geometry property, e.g., the dot product of point pair normals.", + "bbox": [ + 75, + 503, + 472, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 77, + 682, + 168, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first provide an overview of our method in Section 3.1. Next, in Sections 3.2, 3.3 we describe our approach in detail in terms of how to learn hierarchical frames and how to use the learned frames, respectively.", + "bbox": [ + 75, + 707, + 468, + 764 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 77, + 774, + 186, + 788 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our core idea is to establish geometry-based and temporally-consistent local coordinate frames to factorize the local geometry understanding from its underlying motion. Such frames would allow us to align the local geometry from different timestamps toward a more complete geo", + "bbox": [ + 75, + 796, + 470, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "metric understanding. Such geometric features are motion-agnostic, which also allows easier temporal association toward a better motion understanding. Realizing the idea above requires addressing two challenges: how to learn such frames and how to use such frames for 4D learning.", + "bbox": [ + 497, + 503, + 890, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Regarding the first challenge, we introduce a frame learning module as shown in Figure 2. Since geometric features are naturally hierarchical, the frames have to be hierarchical as well. We, therefore, propose to learn such frames through a hierarchical Frame Network. We leverage rotation equivariant networks [12] to design the FrameNet so that its output transforms in the same way as the underlying geometry. This network produces a hierarchy of frames covering regions from local to global. The global region frame allows factorizing ego-motion and aligning different observations to a unified view. The local region frame can align local geometry to a canonical space.", + "bbox": [ + 497, + 573, + 892, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To stabilize the frame learning processing so that the FrameNet could learn temporally consistent region frames at different scales, we design a frame stabilization strategy. Given an input point cloud, we first apply data augmentation to obtain the augmented version of it. Then we feed both the original point cloud and the augmented one through the FrameNet and enforce their predictions to be consistent. Through various data augmentation strategies, we can keep the rotation equivariance of our predicted frames regardless", + "bbox": [ + 497, + 741, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "606", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of the time-dependent data corruptions.", + "bbox": [ + 75, + 125, + 339, + 138 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Regarding the second challenge of how to use the frames, we design a frame-guided 4D learning scheme as shown in Figure 2. Particularly, we design a frame-guided 4D convolution operator which can generate local and global features based on different frames at different scales. By cascading a series of frame-guided 4D convolution operators in a similar way to existing 4D backbones [9, 11], we can extract 4D features under the guidance of hierarchical frames. To keep the motion information from the 4D input, we leverage two frame-guided 4D convolution branches with shared weights. For one branch, the frames are just our learned region frames from the frame learning module. For the other branch, we use a constant camera frame across all timestamps and at all scales. The first branch focuses on motion-agnostic geometric feature learning while the second branch complements the motion cues. A region frame-guided transformer is designed to fuse the two branches for effective spatial-temporal features.", + "bbox": [ + 75, + 140, + 468, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The designs above enable us to achieve various 4D point cloud understanding tasks effectively including 3D action segmentation, 3D action recognition, and 4D semantic segmentation for both indoor and outdoor scenarios.", + "bbox": [ + 75, + 389, + 468, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Hierarchical Frame Learning Module", + "text_level": 1, + "bbox": [ + 75, + 454, + 403, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we first revisit the concept of SO(3)-equivariance and SO(3)-invariance of 3D point cloud. Then we introduce the local-global frame learning pipeline with equivariant neural network in detail. Besides, in order to learn geometrically-stable and temporally-consistent local coordinate frames, we also introduce a frame stabilization scheme to regularize the frame learning process.", + "bbox": [ + 75, + 476, + 468, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Revisit equivariance and invariance. Given a group $G$ and a certain domain $\\mathbb{V}$ , a group action of $G$ on $\\mathbb{V}$ is a mapping from $G\\times \\mathbb{V}$ to $\\mathbb{V}$ (written as $g\\cdot v$ for all $g\\in G$ and $v\\in \\mathbb{V}$ ), where each $g$ corresponds to a bijection on $\\mathbb{V}$ . A mapping $\\Phi :\\mathbb{X}\\to \\mathbb{Y}$ is equivariant with respect to a group $G$ (and its group action on $\\mathbb{X},\\mathbb{Y}$ ), if for every $g\\in G,x\\in \\mathbb{X}$", + "bbox": [ + 75, + 579, + 468, + 663 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi (g \\cdot x) = g \\cdot \\Phi (x). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 201, + 676, + 468, + 692 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Further, if the group action of $G$ on $\\mathbb{Y}$ is trivial, (i.e., $g \\cdot y = y$ for any $g \\in G, y \\in \\mathbb{Y}$ ), we say $\\Phi$ is invariant with respect to $G$ . For convenience, we also say $\\Phi(x)$ is equivariant or invariant if $\\Phi$ is equivariant or invariant.", + "bbox": [ + 75, + 699, + 468, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For point clouds, let $\\mathbb{X} = \\mathbb{R}^{n\\times 3}$ be the input domain, and $\\mathbb{Y}$ be the output domain. Permutation, translation, and $SO(3)$ rotation equivariance are usually taken into consideration for point cloud networks. Consider a point cloud $\\mathbf{X} = (\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_n)^T\\in \\mathbb{X}$ . For the permutation group $S_{n}$ , for some $\\sigma \\in S_n$ , $\\sigma \\cdot \\mathbf{X} = (\\mathbf{x}_{\\sigma (1)},\\mathbf{x}_{\\sigma (2)},\\dots ,\\mathbf{x}_{\\sigma (n)})^T$ . For the translation group $\\mathbb{R}^3$ , for some $\\mathbf{v}\\in \\mathbb{R}^3$ , $\\mathbf{v}\\cdot \\mathbf{X} = (\\mathbf{x}_1 + \\mathbf{v},\\mathbf{x}_2 + \\mathbf{v},\\dots ,\\mathbf{x}_n + \\mathbf{v})^T$ . For the rotation group $SO(3)$ ,", + "bbox": [ + 75, + 755, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1c539144d47707d39729681c3f002667d82a084438589f7d1c245db2839701ab.jpg", + "image_caption": [ + "Figure 3. Illustration of hierarchical Frame Learning Module. Invariant features and equivariant features are extracted progressively by EquivLayer, and are then used to generate frames by FrameGen at each scale." + ], + "image_footnote": [], + "bbox": [ + 521, + 123, + 870, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$g\\cdot \\mathbf{X} = (g\\cdot \\mathbf{x}_1,g\\cdot \\mathbf{x}_2,\\dots ,g\\cdot \\mathbf{x}_n)^T$ , where each $g$ corresponds to a rotation matrix $R\\in \\mathbb{R}^{3\\times 3}$ and $g\\cdot \\mathbf{x} = R\\mathbf{x}$", + "bbox": [ + 497, + 435, + 890, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hierarchical frame learning. It is a challenging problem to learn geometry-based and temporally-consistent local coordinate frames to align the local region and factorize the underlying geometry feature from its motion. We need to construct hierarchical local region frames to accurately depict the orientations of local regions. And the established local coordinate frames should be based upon the 3D geometry in each timestamp and transform in the same way as the underlying geometry changes. To satisfy such requirements, we draw inspiration from the equivariant 3D point cloud analysis [22] and propose to use an equivariant network to learn the geometry-based rotation equivariant local coordinate frames $F$ at different scales as shown in Figure 3.", + "bbox": [ + 497, + 469, + 892, + 649 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathbf{X}^l$ denote the downsampled point cloud at layer $l$ with $N^l$ points. Let $H^l$ and $\\mathbf{V}^l$ denote per-point invariant scalar features and equivariant vector features of $\\mathbf{X}^l$ , respectively. We use $\\mathbf{X}^0, H^0, \\mathbf{V}^0$ to denote the input point cloud, invariant scalar and equivariant vector features, where $H^0, \\mathbf{V}^0$ are all zeros. And we pass the featured point cloud to a hierarchical equivariant network that aims to extract hierarchical invariant and equivariant features. Our EquivLayer is adapted from the GVP-GNN layer [14] and we defer the details to the supplementary material.", + "bbox": [ + 497, + 649, + 892, + 788 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\mathbf {X} ^ {l + 1}, H ^ {l + 1}, \\mathbf {V} ^ {l + 1}\\right) \\leftarrow \\operatorname {E q u i v L a y e r} ^ {l + 1} \\left(\\mathbf {X} ^ {l}, H ^ {l}, \\mathbf {V} ^ {l}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 796, + 890, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since $\\mathrm{EquivLayer}^{l + 1}$ is equivariant at all the layers, and the inputs $H^0,\\mathbf{V}^0$ are invariant and equivariant features, the output $H^{l},\\mathbf{V}^{l}$ of each layer are also invariant and equivari", + "bbox": [ + 497, + 823, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "607", + "bbox": [ + 472, + 885, + 497, + 897 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b1693772c6bc247b0780bb45cd9399d91f0f0abef6cc9d98b04a8989329bd0e8.jpg", + "image_caption": [ + "Expected Frame", + "Figure 4. The learned frames are sensitive to disruptions if not regularized, above are the frames' possible distortions resulting from the impact of sampling, density, and noise." + ], + "image_footnote": [], + "bbox": [ + 99, + 125, + 171, + 169 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/47e81066027f97e60fa3f9bcfe6dba90622fadad33ddd4af23cb0c42c549e2af.jpg", + "image_caption": [ + "(a) Impact of Sampling" + ], + "image_footnote": [], + "bbox": [ + 184, + 125, + 265, + 169 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0a2275289cb137697f5ce0995d46dea4b192d6efe8b6719bde063a308fa9471f.jpg", + "image_caption": [ + "(b) Impact of Density" + ], + "image_footnote": [], + "bbox": [ + 270, + 124, + 354, + 168 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1f2519934b42e55e72ab1322b167d34ee999d9e74f93f64738b47b5aac1365b2.jpg", + "image_caption": [ + "(c) Impact of Noise" + ], + "image_footnote": [], + "bbox": [ + 359, + 125, + 447, + 168 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ant features, respectively.", + "bbox": [ + 75, + 230, + 248, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain hierarchical frames from hierarchical invariant and equivariant features, we use another set of equivariant networks adapted from the GVP layers [14]. We use FrameGen to denote the network for the $l$ -th layer.", + "bbox": [ + 75, + 244, + 468, + 299 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {V} _ {\\text {o u t}} ^ {l} \\leftarrow \\operatorname {F r a m e G e n} ^ {l} \\left(H ^ {l}, \\mathbf {V} ^ {l}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 309, + 468, + 326 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where hierarchical frames will be constructed from $\\mathbf{V}_{\\mathrm{out}}^{l} = (\\mathbf{v}_{\\mathrm{out},1}^{l},\\dots ,\\mathbf{v}_{\\mathrm{out},N^{l}}^{l})(\\mathbf{v}_{\\mathrm{out},i}^{l}\\in \\mathbb{R}^{2\\times 3})$ . We orthonormalize the two vectors $\\mathbf{v}_{\\mathrm{out},i,1}^{l},\\mathbf{v}_{\\mathrm{out},i,2}^{l}$ for each point to get $\\mathbf{u}_{i,1}^{l},\\mathbf{u}_{i,2}^{l}$ using the Gram-Schmidt method. Then we get the frame $F_{i}^{l} = \\left[\\mathbf{u}_{i,1}^{l},\\mathbf{u}_{i,2}^{l},\\mathbf{u}_{i,1}^{l}\\times \\mathbf{u}_{i,2}^{l}\\right]\\in \\mathbb{R}^{3\\times 3}(i = 1,\\dots ,N^{l})$ Since $\\mathbf{V}_{\\mathrm{out}}^l$ is rotation equivariant, the constructed frames are also rotation equivariant.", + "bbox": [ + 75, + 339, + 468, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We refer to the whole module to generate hierarchical frames as FrameNet.", + "bbox": [ + 75, + 442, + 468, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Frame stabilization schemes. Frame learning is not an easy task since the corresponding regions in different timestamps can vary significantly due to reasons beyond motion such as sampling variation. To make sure the rotation equivariance of FrameNet is not broken, we introduce a frame stabilization scheme to further regularize the frame learning process.", + "bbox": [ + 75, + 475, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We expect the region frame of anchor points to represent the orientation of a local region regardless of how the anchor points are sampled. However, our FrameNet is point cloud-based and its prediction could vary dramatically as the anchor points in the region vary (Figure 4 (a)). Besides, the local region frame is also affected by the density of point clouds. When a local region is very sparse while the shape intensely deforms, the estimated region frame will also be extremely disrupted (Figure 4 (b)). The density of the same local region in different timestamps changes due to the egomotion and the occlusion variation or when the noise of the point cloud is very large (Figure 4 (c)). Such disruptions can break the temporal consistency of the region frame, and we expect FrameNet to be sampling, density, and noise invariant for stable and temporally-consistent region frames.", + "bbox": [ + 75, + 573, + 468, + 780 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To achieve the goal above, we introduce several self-supervised losses to encourage the learned frame to be invariant under different point cloud augmentation strategies:", + "bbox": [ + 75, + 780, + 468, + 821 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {a u g}} = \\sum_ {i} \\frac {\\operatorname {c o s i n e S i m} \\left(\\hat {F} _ {i} ^ {\\mathrm {a u g}} , F _ {i}\\right)}{N}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 833, + 468, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where cosineSim means cosine similarity, $N$ is the number of anchor points, $\\hat{F}^{\\mathrm{aug}}$ is the frame of anchor points after augmentation, and $F$ is the frame of original anchor points. Since the anchor points do not strictly match after the augmentation, we take the nearest neighbors of the original anchors in the augmented anchors as the corresponding points.", + "bbox": [ + 497, + 125, + 890, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More specifically, we apply three types of augmentations including point cloud re-sampling, down-sampling, and jittering. Therefore, the final self-supervised loss is:", + "bbox": [ + 497, + 209, + 890, + 250 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s t a b l i z e r}} = \\alpha L _ {\\text {r e - s a m p l i n g}} + \\beta L _ {\\text {d o w n - s a m p l i n g}} + \\gamma L _ {\\text {j i t t e r i n g}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 510, + 260, + 890, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha, \\beta, \\gamma$ are balancing coefficients set as 1.", + "bbox": [ + 499, + 285, + 811, + 299 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Frame-guided 4D Learning Module", + "text_level": 1, + "bbox": [ + 499, + 307, + 808, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the hierarchical region frames which are geometrically stable and temporally consistent, we can use these frames to factorize the region-wise geometry feature from its motion by aligning corresponding regions. Instead of explicitly aligning regions at all different scales, we modify popular 4D operators including point 4D convolution and point 4D transformer so that they could learn the geometry feature as if corresponding regions are aligned.", + "bbox": [ + 497, + 328, + 890, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Frame-aware 4D operations. We first modify the point 4D convolution [9] into a frame-aware operator. Unlike the traditional point 4D convolution convolving directly between an anchor point and its spatiotemporal neighbor points, the frame-aware version first divides the neighbor points based on their timestamps, then picks up the nearest point from the anchor point in each division, aligns different divisions to the anchor point frame based upon the frames of the picked points, and finally conduct convolution in the aligned space. The frame-aware convolution layer can be mathematically described as:", + "bbox": [ + 497, + 444, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} ^ {l + 1} = \\sum_ {j \\in N (i)} M _ {1} ^ {l} \\left(F _ {i, t _ {j}} ^ {l \\top} \\left(x _ {j} - x _ {i}\\right), t _ {j} - t _ {i}\\right) \\odot M _ {2} ^ {l} \\left(f _ {j} ^ {l}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 507, + 617, + 890, + 649 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N(i)$ is the spatiotemporal neighbor of the anchor point $i$ , while $\\mathbf{x}_i$ is its coordinate and $f_i^l$ is its feature on the $l$ -th level. $F_{i,t}^{l}$ is the $l$ -th frame of the nearest neighbor of $x_i$ in timestamp $t$ . $\\sum$ is aggregation implemented with sum-pooling or max-pooling, $M_1^l, M_2^l$ are MLP networks, and $\\odot$ is summation. The output feature can be seen as the representation under the region frames, and we denote such feature as \"region frame feature\". In particular, if we let the frames be identity matrices, this operation will be exactly the vanilla P4Dconv, and the output feature would be the representation under the original camera frame and we refer to it as \"camera frame feature\".", + "bbox": [ + 497, + 657, + 890, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We then modify the point 4D transformer [9] into a frame-aware version. Since the transformer operator usually follows the 4D convolution, we consider its input as", + "bbox": [ + 497, + 824, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "608", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "a set of point tokens each equipped with a region frame as well as its feature within the frame. In this case, what we need to do is to make the positional embedding frame-aware so that the whole transformer is frame-aware. To be specific, we use $F_{\\mathrm{global},t}$ to represent the global frame at timestamp $t$ and use $W_{p}$ to represent a linear transformation. Then considering a point token with a spatiotemporal coordinate of $(\\mathbf{x},t)$ , its positional embedding can be written as $p = W_{p} \\cdot \\binom{F_{\\mathrm{global},t}^{\\intercal}\\mathbf{x}}{t}$ .", + "bbox": [ + 75, + 125, + 472, + 264 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is worth mentioning that the frame-aware method can be plug-and-play for many other operators, for example, we can also transform RS-CNN into a frame-aware RS-CNN to extract invariant features using hierarchical frames. Specifically, the frame-aware RS-CNN is [14]:", + "bbox": [ + 75, + 264, + 470, + 334 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nh _ {i} ^ {l + 1} \\leftarrow \\max _ {j \\in N (i)} \\left(M \\left(\\| F _ {i} ^ {l \\mathbf {T}} r _ {i j} \\|, F _ {i} ^ {l \\mathbf {T}} r _ {i j}\\right) \\odot h _ {j} ^ {l}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 115, + 340, + 468, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where max denotes the max pooling operation, $M$ is an MLP network, $\\odot$ denotes element-wise multiplication, $N(i)$ denotes the neighbors of point $i$ , $r_{ij}$ denotes the relative coordinates between point $i$ and $j$ , $h$ denotes the features and $F$ denotes the learned region frames.", + "bbox": [ + 75, + 376, + 468, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Frame-guided feature learning. With the frame-aware 4D operation we can extract hierarchical region frame features, which are inherent representations of the underlying geometry but lacks the motion information. So such region frame features are not enough to fully encode the 4D spatiotemporal information. On the other hand, the camera frame feature computed under the camera coordinate frame faithfully retain the motion information and can be a good complement to the region frame features. We then propose to combine both features to obtain a more powerful and representative 4D feature. In particular, we design a two-tower framework to extract the region frame feature and camera frame feature. To fuse features from the two towers, we propose to use the region frame feature to guide the camera frame feature learning through an attention map which aligns the local region across different timestamps into a canonical space and allows easier temporal associations for better motion understanding, as shown in Figure 5.", + "bbox": [ + 75, + 450, + 468, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To be specific, the queries and keys are generated from the region frame feature but the values are generated from the camera frame feature. We formulate the fusion process as a self-attention operation below:", + "bbox": [ + 75, + 699, + 468, + 755 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {r} = W _ {q} f _ {r}, K _ {r} = W _ {k} f _ {r}, V _ {c} = W _ {v} f _ {c},\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 763, + 391, + 779 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {a t t e n t i o n} \\left(Q _ {r}, K _ {r}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {r} , K _ {r}}{\\sqrt {C _ {k}}}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 781, + 468, + 812 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nO = V _ {c} \\cdot \\text {a t t e n t i o n} \\left(Q _ {r}, K _ {r}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 131, + 814, + 321, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $f_{r}$ is the region frame feature, $f_{c}$ is the camera frame feature. The output $O$ is the camera frame feature fused", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e89feeecc9888320e359b2d479909549ea84b25601a381c4259b6c01100425aa.jpg", + "image_caption": [ + "Figure 5. An illustration of the region frame-guided transformer. The input is the feature of multiple timestamps, For each timestamp (take timestamp 1 for example), the attention scores are computed by the correlations between timestamp 1 and all the other timestamps, then the output of timestamp 1 is the weighted sum of values encoded from the camera frame feature." + ], + "image_footnote": [], + "bbox": [ + 521, + 122, + 870, + 342 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "under the guidance of the region frame feature. Then, we can add different task heads to complete various 4D point cloud sequence understanding tasks.", + "bbox": [ + 497, + 431, + 892, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 499, + 486, + 631, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we cover four 4D point cloud sequence understanding tasks: action segmentation on HOI4D [21], action recognition on MSR-action3D [17], indoor semantic segmentation on HOI4D [21], and outdoor semantic segmentation on Synthia4D [25], in Section 4.1, 4.2, 4.3 and 4.4 respectively. In addition, we provide extensive ablation studies to validate our design choices in Section 4.5.", + "bbox": [ + 497, + 510, + 890, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Action Segmentation on HOI4D", + "text_level": 1, + "bbox": [ + 499, + 617, + 781, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup. To demonstrate the effectiveness of our method, we first conducted experiments on the HOI4D action segmentation task. For each point cloud sequence, we need to predict the action labels for each timestamp. We followed the official data split with 2971 sequences as the training set and 892 as the test set. Each sequence has 150 timestamps with 2048 points per timestamp. We use PPTr, an improved variant of the P4Transformer, as our backbone, which leverages two hierarchical transformers to process point cloud sequences and supports appending invariant features as additional inputs. We compare our method with baseline methods including P4Transformer and original PPTr. In this experiment, we use a two-scale FrameNet to learn 128 local frames and one global frame. We use frame-aware 4DConv to extract the invariant feature. The following metrics are reported: framewise accuracy (Acc), segmental edit", + "bbox": [ + 497, + 644, + 892, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "609", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/608fbb146e96383055b319aaf9e2ed3ce824e2746b1eaca34e519fc181284072.jpg", + "table_caption": [ + "Table 1. Action segmentation on HOI4D dataset" + ], + "table_footnote": [], + "table_body": "
MethodClip LengthAccEditF1@10F1@25F1@50
P4Transformer [8]15071.273.173.869.258.2
PPTr [30]15077.480.181.778.569.5
PPTr+Ours15079.4+2.0↑83.9+3.8↑85.0+3.3↑81.9+3.4↑73.3+3.8↑
", + "bbox": [ + 78, + 134, + 468, + 204 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "distance, as well as segmental F1 scores at the overlapping thresholds of $10\\%$ , $25\\%$ , and $50\\%$ . Overlapping thresholds are determined by the IoU ratio.", + "bbox": [ + 75, + 209, + 468, + 251 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Result. As reported in Table 1, our method consistently has big improvements over previous state-of-the-art method in all metrics. This demonstrates that the region frame feature can significantly improve the communication of point clouds at different timestamps, to extract a more effective spatiotemporal representation. By introducing the region frame features for 4D point cloud sequence, we can factorize the local geometry understanding from its motion so that the network can have a better understanding of geometry and motion respectively.", + "bbox": [ + 75, + 257, + 468, + 396 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Action Recognition on MSR-Action3D", + "text_level": 1, + "bbox": [ + 77, + 406, + 406, + 420 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setup. Following P4Transformer and PPTr, we used the MAR-Action3D dataset, which consists of 567 human point cloud sequences, including 20 action categories. Each timestamp is sampled with 2,048 points. The point cloud sequences are segmented into multiple segments. During training, video-level labels are used as segment-level labels. As in action segmentation, we use PPTr as the base network. A two-layer FrameNet is used to extract local and global frames. And a frame-aware 4DConv is used to extract invariant features. To ensure a fair comparison, we also use primitive fitting to divide each human point cloud into four regions. To estimate the sequence-level probabilities, we take the mean of all segment-level probability predictions.", + "bbox": [ + 75, + 433, + 468, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Result. As reported in Table 2, our method also outperforms previous methods in 3D action recognition tasks. We find that when the clip length is 8, the improvement of our method is 0.48, while the improvement of our method is 1.51 when clip length is 24. This indicates that our method performs better in longer sequences. This also demonstrates that the proposed region frame feature can factorize geometry learning from motion learning and achieve better temporal correlation.", + "bbox": [ + 75, + 619, + 468, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Indoor Semantic Segmentation on HOI4D", + "text_level": 1, + "bbox": [ + 77, + 755, + 433, + 769 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setup. To verify that our approach can be effective for fine-grained tasks as well, we conducted further experiments on HOI4D for 4D semantic segmentation. The dataset consists of 3863 4D sequences, each including 300 timestamps of point clouds, for a total of 1.158M timestamps of point clouds. For one timestamp, there are 8192", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8a8fd18dc2faa201287e297c544d8ea4eece1e31a33ef1c534a95b47618f0e00.jpg", + "table_caption": [ + "Table 2. Action recognition on MSR-Action3D dataset [17]" + ], + "table_footnote": [], + "table_body": "
MethodInputClip LengthVideo Acc@1
PointNet++ [24]point161.61
MeteorNet [20]point881.14
point1688.21
point2488.50
PSTNet [10]point883.50
point1689.90
point2491.20
P4Transformer [9]point883.17
point1689.56
point2490.94
PPT [30]point884.02
point1690.31
point2492.33
PPTr+Ourspoint884.50+0.48↑
point1691.50+1.19↑
point2493.84+1.51↑
", + "bbox": [ + 557, + 135, + 828, + 343 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/44810e7519c1e0799795a1fbfabe14739f1421a5c226fdf907268190a795a216.jpg", + "table_caption": [ + "Table 3. Semantic segmentation on HOI4D dataset [21]" + ], + "table_footnote": [], + "table_body": "
MethodClip LengthmIoU
P4Transformer [8]340.1
PPTr [30]341.0
P4T+Ours343.5+2.4↑
", + "bbox": [ + 500, + 362, + 890, + 429 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "points. We follow the official data segmentation of HOI4D with 2971 training scenes and 892 test scenes. In this task, to avoid the complicated primitive fitting process, we choose P4Transformer as the base network. A three-scale FrameNet is used to learn three scales of the frames, respectively 512 and 128 local region frames as well as the global frame. In the semantic segmentation tasks, we all use a frame-aware RS-CNN to demonstrate that the framework method can be plug-and-play for other operators. Accordingly, we use a three-scale RS-CNN to extract \"region frame\" features. We use mean IoU(mIoU) % over 39 categories as an evaluation metric.", + "bbox": [ + 497, + 432, + 890, + 598 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Result. The results are shown in Table 3. We can observe that we improve the performance by a large margin compared with previous methods. Even without a primitive fitting process, our method still outperforms PPTr by $2.4\\%$ , which demonstrates that our local region feature is also helpful in the fine-grained 4D understanding task.", + "bbox": [ + 497, + 603, + 890, + 687 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Outdoor Semantic Segmentation on Synthia4D", + "text_level": 1, + "bbox": [ + 499, + 695, + 890, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setup. Synthia 4D is a synthetic dataset generated from Synthia dataset. It consists of six sequences of driving scenarios where both objects and cameras are moving. Following previous works, we use the same training/validation/test split, with 19,888/815/1,886 timestamps, respectively. We use P4Transformer as the base network, and other settings are the same as the experiments on semantic segmentation on HOI4D. The mean Intersection over Union (mIoU) is used as the evaluation metric.", + "bbox": [ + 497, + 722, + 890, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Result. As shown in Table 4, there is still a per", + "bbox": [ + 499, + 852, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "610", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/304b58f664816f43c41235013ebc75568878583a91300fe7b4b59e0f073fd2e4.jpg", + "table_caption": [ + "Table 4. Evaluation for semantic segmentation on Synthia 4D" + ], + "table_footnote": [], + "table_body": "
MethodClip LengthBldnRoadSdwkFenceVegittPoleCarT. SignPedstmBicyclLaneT.LightmloU
3D MinkNet14189.3997.6869.4386.5298.1197.2693.5079.4592.270.0044.6166.6976.24
4D MinkNet14390.1398.2673.4787.1999.1097.5094.0179.0492.620.0050.0168.1477.24
PointNet++196.8897.7286.2092.7597.1297.0990.8566.8778.640.0072.9375.1779.35
MeteorNet-m298.2297.7990.9893.1898.3197.4594.3076.3581.050.0074.0975.9281.47
MeteorNet-1398.1097.7288.6594.0097.9897.6593.8384.0780.900.0071.1477.6081.80
P4Transformer196.7698.2392.1195.2398.6297.7795.4680.7585.480.0074.2874.2282.41
P4Transformer396.7398.3594.0395.2398.2898.0195.6081.5485.180.0075.9579.0783.16
PPTr197.1498.4294.1297.0099.5997.8698.5479.6889.200.0077.2677.4283.85
PPTr397.5198.2195.1196.8199.6597.8698.0180.9890.600.0078.2176.8984.15
PPTr3098.0198.6395.2697.0399.7097.9598.7681.9991.200.0078.2977.0984.49
P4T+Ours398.2298.8997.9796.8599.6097.9099.0082.7391.500.0078.0378.9284.97+1.81↑
", + "bbox": [ + 77, + 138, + 490, + 264 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance improvement, which also shows the effectiveness of our approach for outdoor 4D semantic segmentation tasks. It is worth mentioning that our network is based on P4Transformer, so a fair comparison is between P4Transformer with 3 timestamps and our method with 3 timestamps. The mIoU going from $83.16\\%$ to $84.97\\% (+1.81\\%)$ demonstrates the effectiveness of our method. Moreover, our method associates 3 point clouds by region frame feature, which is even better than PPTr's method of using 30 sequential point clouds.", + "bbox": [ + 75, + 276, + 468, + 414 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation and Discussion", + "text_level": 1, + "bbox": [ + 75, + 423, + 299, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Efficacy of frame stabilization schemes. The frame learning process is challenging due to sampling differences, density variation, or sensor noises. To make sure the rotation equivariance of MS-FrameNet is not broken, we introduce a frame stabilization scheme to regularize the frame learning process. We run ablation studies with and without frame stabilization schemes to quantify their efficacy. We find that learning region frames without frame stabilization schemes results in a $0.8\\%$ accuracy and $1.8\\%$ segmental edit distance drop on the HOI4D action segmentation task. This result proves that our frame stabilization schemes play an important role in learning high-quality region frames.", + "bbox": [ + 75, + 451, + 468, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Learning frames vs. non-learning frames. In the frame learning module, we design an MS-FrameNet which is essentially a rotation-equivariant neural network able to produce region frames equivariant to the rotation of input geometry. To demonstrate the advantages of learning frames, we compare our method with PCA which is a non-learning method to obtain local reference frames(LRFs). When replacing our frame-learning module with PCA frames, the best result we can get is $78.3\\%$ accuracy on HOI4D action segmentation task, which is $1.1\\%$ lower than our method. This experiment confirms the value of learning frames compared with the non-learning method.", + "bbox": [ + 75, + 624, + 468, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Compared with random frames and identity frames. To further examine the value of the frame learning process, we conduct another two experiments that frame-guided 4D learning with random frames and identity frames.", + "bbox": [ + 75, + 796, + 468, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With random frames, we can only achieve $78.0\\%$ accu", + "bbox": [ + 95, + 852, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "racy on HOI4D action segmentation which is $1.4\\%$ lower than our method. This demonstrates that random frames are not friendly for cross-time association and temporally consistent frames are important for frame-guided learning. With identity frames, the best result we can get is $76.3\\%$ which is even $1.1\\%$ lower than PPTr without frame learning, showing that the improvement is not brought about by a simple ensemble strategy.", + "bbox": [ + 497, + 125, + 890, + 237 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Action segmentation with large motion. To better verify that the motion-agnostic geometric features allow easier temporal association toward a better motion understanding, we conduct experiments on HOI4D action segmentation tasks with large motion. We only select the sequences where the maximum distance of the object movement exceeds $0.5\\mathrm{m}$ to construct a subset of HOI4D with 900 training scenes and 300 test scenes. Without learning frames, PPTr can get 29.22 accuracy on action segmentation, while our method can achieve $36.39\\%$ accuracy. This result proves that our method has a stronger ability to deal with point cloud sequences with large motion.", + "bbox": [ + 497, + 245, + 890, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The efficiency comparison. Our method does not introduce a significant increase in computational overhead. The 4D backbone requires much heavier computation compared with the lightweight FrameNet. So as shown in Table 5, introducing FrameNet in Frame-aware P4DConv does not significantly increase FLOPs or parameters compared with P4DConv. Worth to mention, since our method relies on both the invariant and non-invariant feature branches, the overall computational overhead is roughly twice that of a single branch P4DConv.", + "bbox": [ + 497, + 421, + 890, + 559 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5908c04979bfc0bba562cf313a91af6abf6264b11594e26fa933bd63b25b1074.jpg", + "table_caption": [ + "Table 5. LeaF does not introduce a significant increase in computational overhead. All tests were conducted on a single NVIDIA GeForce RTX 3090 graphics card, with a batch size of 1." + ], + "table_footnote": [], + "table_body": "
MethodFLOPsParameters
P4DConv7.550G8.192K
Frame-aware P4DConv8.428G8.314k
Only FrameNet878.2M122.0B
", + "bbox": [ + 524, + 610, + 863, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 499, + 714, + 626, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes to use SO(3) equivariant networks to learn orientations for 4D point cloud videos and to obtain inherent features of the point clouds. The core idea is that the inherent features are motion-independent and this feature can be better correlated between contexts. We also propose three constraint terms to guide the learning of frame in order to obtain stable and consistent point cloud orientations. Experiments prove that our proposed method is effective and significantly outperforms existing methods.", + "bbox": [ + 497, + 741, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "611", + "bbox": [ + 472, + 887, + 495, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 173, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tolga Birdal and Slobodan Ilic. Point pair features based object detection and pose estimation revisited. In 2015 International conference on 3D vision, pages 527-535. IEEE, 2015. 3", + "[2] Haiwei Chen, Shichen Liu, Weikai Chen, Hao Li, and Randall Hill. Equivariant point network for 3d point cloud analysis. 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Unique signatures of histograms for local surface description. In Computer Vision-ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part III 11, pages 356-369. Springer, 2010. 3", + "[30] Hao Wen, Yunze Liu, Jingwei Huang, Bo Duan, and Li Yi. Point primitive transformer for long-term 4d point cloud video understanding. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXIX, pages 19-35. Springer, 2022. 1, 2, 7", + "[31] Jiaqi Yang, Qian Zhang, Yang Xiao, and Zhiguo Cao. Toldi: An effective and robust approach for 3d local shape description. Pattern Recognition, 65:175-187, 2017. 3", + "[32] Hong-Xing Yu, Jiajun Wu, and Li Yi. Rotationally equivariant 3d object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1456-1464, 2022. 2", + "[33] Angfan Zhu, Jiaqi Yang, Weiyue Zhao, and Zhiguo Cao. Lrf-net: learning local reference frames for 3d local shape description and matching. Sensors, 20(18):5086, 2020. 3" + ], + "bbox": [ + 78, + 127, + 468, + 564 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "613", + "bbox": [ + 472, + 887, + 497, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/51c2f292-724b-40e6-8771-779ef4bbccc4_model.json b/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/51c2f292-724b-40e6-8771-779ef4bbccc4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cf0229c0777db3fdc21ef6b3d1504d7f9ae1f54b --- /dev/null +++ b/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/51c2f292-724b-40e6-8771-779ef4bbccc4_model.json @@ -0,0 +1,1947 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.085 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.088 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.137, + 0.162, + 0.834, + 0.184 + ], + "angle": 0, + "content": "LeaF: Learning Frames for 4D Point Cloud Sequence Understanding" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.207, + 0.882, + 0.256 + ], + "angle": 0, + "content": "Yunze Liu \\(^{1,3}\\), Junyu Chen \\(^{1}\\), Zekai Zhang \\(^{1}\\), Jingwei Huang \\(^{4}\\), Li Yi \\(^{1,2,3}\\), Tsinghua University, \\(^{2}\\) Shanghai Artificial Intelligence Laboratory, \\(^{3}\\) Shanghai Qi Zhi Institute Huawei" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.289, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.541 + ], + "angle": 0, + "content": "We focus on learning descriptive geometry and motion features from 4D point cloud sequences in this work. Existing works usually develop generic 4D learning tools without leveraging the prior that a 4D sequence comes from a single 3D scene with local dynamics. Based on this observation, we propose to learn region-wise coordinate frames that transform together with the underlying geometry. With such frames, we can factorize geometry and motion to facilitate a feature-space geometric reconstruction for more effective 4D learning. To learn such region frames, we develop a rotation equivariant network with a frame stabilization strategy. To leverage such frames for better spatial-temporal feature learning, we develop a frame-guided 4D learning scheme. Experiments show that this approach significantly outperforms previous state-of-the-art methods on a wide range of 4D understanding benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.566, + 0.21, + 0.58 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.47, + 0.687 + ], + "angle": 0, + "content": "We have recently witnessed a surge of interest in understanding point cloud sequences in 4D (3D space + 1D time). As the direct sensory input in a large number of modern AI applications including robotics and AR/VR, point cloud sequences can faithfully depict the geometry and motion of a dynamic scene, and therefore become critical for an intelligent agent to perceive and interact with the physical world." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.77 + ], + "angle": 0, + "content": "However, learning on such 4D data is very challenging and is still in an immature stage. 4D point cloud sequences usually couple 3D geometry and its dynamic motion together, resulting in quite redundant data in a very high dimensional space. This causes severe learning issues against an effective and compact spatial-temporal representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Some existing efforts tackle the challenge through novel 4D backbone designs [8, 30, 7]. However, most of these works treat the point cloud sequence as unstructured 4D data and exploit generic 4D learning methods without leveraging the prior that the whole 4D sequence just depicts a single 3D scene with dynamic objects. As a result, such 4D learning is usually not super effective and the learned" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.287, + 0.891, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.452, + 0.893, + 0.53 + ], + "angle": 0, + "content": "Figure 1. Frame-aware spatial-temporal convolution. We propose to learn frames for point cloud sequence. Upon obtaining the frames, we could easily align the geometry regardless of the underlying motion toward a more canonical and complete geometry understanding. The motion-agnostic geometric features also allow easier temporal association toward a better motion understanding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.892, + 0.78 + ], + "angle": 0, + "content": "spatial-temporal feature barely outperforms the spatial feature alone. Another line of works [7] uses self-supervised representation learning to encourage geometry and motion learning in a loosely decoupled manner. However, the decoupling still happens on the whole-scene level with a special focus on camera ego-motion, restricting their efficacy in modeling local dynamics on the object-level. We envision that successful geometry and motion decoupling is the key toward effective 4D representation learning. This essentially requires depicting the low-dimensional manifold of the dynamic scenes from the redundant high-dimensional 4D data. This highly correlates to dynamic scene reconstruction which requires understanding both camera ego-motion and object motion and is an ongoing research topic itself. Instead of explicitly reconstructing the dynamic scene without a quality guarantee, we seek a more lightweight and flexible solution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.784, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Our solution is based upon the following observation. For a specific region in the scene, we can understand its dynamic motion through establishing geometry-based and temporally-consistent local coordinate frames. Specifically, if we can establish a local coordinate frame based upon the 3D geometry in each timestamp and also make sure such" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "604" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.127, + 0.47, + 0.292 + ], + "angle": 0, + "content": "frame transforms in the same way as the underlying geometry, then we can estimate the local rigid motion via comparing such frames among corresponding regions across timestamps. Such local frames allow us to factorize the local geometry understanding from its motion in a similar spirit to equivariant 3D analysis [22, 14]. In particular, once we establish temporally-consistent local coordinate frames, we essentially have a way to align the geometry regardless of the underlying motion toward a more canonical and complete geometry understanding. In addition, the motion-agnostic geometric features also allow easier temporal association toward a better motion understanding." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.295, + 0.471, + 0.723 + ], + "angle": 0, + "content": "Based upon the above observations, we present a novel 4D learning framework named LeaF. LeaF contains a frame learning module and a frame-guided 4D learning module. The frame learning module aims at producing geometry-based temporally consistent coordinate frames at different scales so that corresponding regions across timestamps can be well-aligned. This allows for factorizing geometry learning from motion learning. And then the frame-guided 4D learning module leverages the learned frames to facilitate a more effective spatial-temporal feature aggregation. Specifically, in the frame learning module, we design a hierarchical FrameNet which is essentially a rotation-equivariant neural network able to produce coordinate frames equivariant to the rotation of input geometry. The frame learning process is very challenging though since apart from rotations different observations from a point cloud sequence can vary significantly due to sampling differences, density variation, or sensor noises. To make sure the rotation equivariance of hierarchical FrameNet is not broken in practice, we introduce a frame stabilization scheme to further regularize the frame learning process. In the frame-guided 4D learning module, we first modify popular 4D operators (e.g. 4D point conv) into their frame-guided version and then leverage frame-guided 4D convolution to process 4D point cloud sequences. Since the motion information is factorized away while convolving with the learned region frames, we additionally process the 4D sequences with just a globally constant camera frame so that the motion information is faithfully kept. We fuse the learned features both from using region frames and from using camera frames, allowing a very effective 4D feature learning." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.726, + 0.47, + 0.837 + ], + "angle": 0, + "content": "To verify the effectiveness of LeaF, we conduct experiments on a wide range of 4D understanding tasks. And we demonstrate significant improvements over previous state-of-the-art methods \\((+2.0\\%)\\) accuracy on HOI4D action segmentation [21], \\(+1.51\\%\\) accuracy on MSR action recognition [17], \\(+2.4\\%\\) mIoU on HOI4D indoor semantic segmentation [21], and \\(+1.81\\%\\) mIoU on Synthia4D outdoor semantic segmentation [25])." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Our contributions are threefold: 1) we propose to learn effective spatial-temporal 4D features via learning and ex" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.238 + ], + "angle": 0, + "content": "ploiting region-wise coordinate frames and our framework LeaF achieves state-of-the-art performance on a wide range of 4D understanding benchmarks; 2) we design a hierarchical FrameNet along with a frame stabilization scheme to learn equivariant region frames for motion-invariant geometry feature learning; 3) we present a frame-guided 4D learning method that is able to benefit from equivariant region frames without losing the motion information." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.254, + 0.642, + 0.269 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.285, + 0.892, + 0.562 + ], + "angle": 0, + "content": "4D point cloud sequence understanding. Compared with understanding static 3D point clouds, understanding 4D point cloud sequences requires more on aggregating and leveraging spatial-temporal information to perceive the geometry and dynamics. Several 4D backbones have been proposed to address such challenges, and they can be divided into two categories based on their representations. The first is to voxelize raw point clouds and extract features on 4D voxels, including MinkwoskiNet [3] which employs 4D spatial-temporal convolutions on 4D voxels. The second is to perform directly on raw points, including Meteor Net [19] which extends PointNet++[23] with a temporal dimension and explicitly tracks points' motion for grouping, and PSTNet[11] which constructs a point tube along temporal dimension for 4D point convolution. State of The Art methods such as Point 4d Transformer [9] and PPTr [30] belong to the second category and introduce transformer architecture, in order to avoid point-tracking and to better capture spatio-temporal correlation. There are works [7] focusing on improving the optimization of a transformer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.819 + ], + "angle": 0, + "content": "Equivariant feature learning. The seminal work of Group Equivariant Convolution Networks [4] (G-CNN) starts a trend of leveraging group equivariance for neural networks. For 3D data, rotation group equivariance or SO(3) equivariance is significant, and there are roughly two categories of SO(3) equivariant networks. The first category is the \"filter orbit\" method. Inspired by group-equivariant convolution on 2D images proposed in G-CNN [4], Equivariant Point Network [2] and successive works [16, 18, 32] discretizes SO(3) and analogously design group-equivariant operations on point clouds. However, as such networks extend the original features to multiple oriented features, they encounter memory issues and may not be suitable for 4D point cloud sequences understanding. The second category is the \"filter design\" method. These methods [28, 5, 14] design the filter forms to achieve exact SO(3) equivariance. \"Filter design\" methods get rid of memory issues, but their representation capability is usually limited due to the restricted filter form." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Rotation-invariant local descriptors. Local descriptor is a synonym for local feature, which is widely used in tasks such as 3D point cloud matching. Some of the rotation-" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "605" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.173, + 0.123, + 0.808, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.418, + 0.892, + 0.496 + ], + "angle": 0, + "content": "Figure 2. Illustration of the proposed Learning Frame for 4D Point Cloud Sequence Understanding (LeaF). We use an SO(3) equivariant network proposed in [22] to learn hierarchical frames denoted as region frames. We denote the identity frames as camera frames. Under region frames and camera frames, region frame feature and camera frame feature can be extracted by frame-aware 4D backbones, and are then fused by region frame-guided transformer to do downstream tasks such as action recognition, action segmentation, and semantic segmentation. Data augmentation and regularization losses are also added to make the equivariant Hierarchical frame network robust to re-sampling, down-sampling, and jittering." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.473, + 0.671 + ], + "angle": 0, + "content": "invariant local descriptors first obtain rotation-equivariant local reference frames (LRFs) either via PCA methods [29, 13, 29, 31, 12, 15], or by incorporating learning methods to decide the axis in the tangent plane aside from normal [33], or completely by 3D rotation equivariant networks [22]. Under those LRFs, local support sets can be transformed into canonical representation, and thus invariant local features can be extracted either by hand-crafted method [29, 13, 29, 31] or by learning methods [12, 15]. Some other methods [27, 26, 1, 6] directly extract invariant local features from invariant local geometry property, e.g., the dot product of point pair normals." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.684, + 0.169, + 0.699 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.47, + 0.765 + ], + "angle": 0, + "content": "We first provide an overview of our method in Section 3.1. Next, in Sections 3.2, 3.3 we describe our approach in detail in terms of how to learn hierarchical frames and how to use the learned frames, respectively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.775, + 0.188, + 0.789 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Our core idea is to establish geometry-based and temporally-consistent local coordinate frames to factorize the local geometry understanding from its underlying motion. Such frames would allow us to align the local geometry from different timestamps toward a more complete geo" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.892, + 0.572 + ], + "angle": 0, + "content": "metric understanding. Such geometric features are motion-agnostic, which also allows easier temporal association toward a better motion understanding. Realizing the idea above requires addressing two challenges: how to learn such frames and how to use such frames for 4D learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.893, + 0.74 + ], + "angle": 0, + "content": "Regarding the first challenge, we introduce a frame learning module as shown in Figure 2. Since geometric features are naturally hierarchical, the frames have to be hierarchical as well. We, therefore, propose to learn such frames through a hierarchical Frame Network. We leverage rotation equivariant networks [12] to design the FrameNet so that its output transforms in the same way as the underlying geometry. This network produces a hierarchy of frames covering regions from local to global. The global region frame allows factorizing ego-motion and aligning different observations to a unified view. The local region frame can align local geometry to a canonical space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.868 + ], + "angle": 0, + "content": "To stabilize the frame learning processing so that the FrameNet could learn temporally consistent region frames at different scales, we design a frame stabilization strategy. Given an input point cloud, we first apply data augmentation to obtain the augmented version of it. Then we feed both the original point cloud and the augmented one through the FrameNet and enforce their predictions to be consistent. Through various data augmentation strategies, we can keep the rotation equivariance of our predicted frames regardless" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "606" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.127, + 0.34, + 0.14 + ], + "angle": 0, + "content": "of the time-dependent data corruptions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.141, + 0.47, + 0.389 + ], + "angle": 0, + "content": "Regarding the second challenge of how to use the frames, we design a frame-guided 4D learning scheme as shown in Figure 2. Particularly, we design a frame-guided 4D convolution operator which can generate local and global features based on different frames at different scales. By cascading a series of frame-guided 4D convolution operators in a similar way to existing 4D backbones [9, 11], we can extract 4D features under the guidance of hierarchical frames. To keep the motion information from the 4D input, we leverage two frame-guided 4D convolution branches with shared weights. For one branch, the frames are just our learned region frames from the frame learning module. For the other branch, we use a constant camera frame across all timestamps and at all scales. The first branch focuses on motion-agnostic geometric feature learning while the second branch complements the motion cues. A region frame-guided transformer is designed to fuse the two branches for effective spatial-temporal features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.47, + 0.445 + ], + "angle": 0, + "content": "The designs above enable us to achieve various 4D point cloud understanding tasks effectively including 3D action segmentation, 3D action recognition, and 4D semantic segmentation for both indoor and outdoor scenarios." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.455, + 0.405, + 0.47 + ], + "angle": 0, + "content": "3.2. Hierarchical Frame Learning Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.574 + ], + "angle": 0, + "content": "In this section, we first revisit the concept of SO(3)-equivariance and SO(3)-invariance of 3D point cloud. Then we introduce the local-global frame learning pipeline with equivariant neural network in detail. Besides, in order to learn geometrically-stable and temporally-consistent local coordinate frames, we also introduce a frame stabilization scheme to regularize the frame learning process." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.58, + 0.47, + 0.664 + ], + "angle": 0, + "content": "Revisit equivariance and invariance. Given a group \\(G\\) and a certain domain \\(\\mathbb{V}\\), a group action of \\(G\\) on \\(\\mathbb{V}\\) is a mapping from \\(G\\times \\mathbb{V}\\) to \\(\\mathbb{V}\\) (written as \\(g\\cdot v\\) for all \\(g\\in G\\) and \\(v\\in \\mathbb{V}\\)), where each \\(g\\) corresponds to a bijection on \\(\\mathbb{V}\\). A mapping \\(\\Phi :\\mathbb{X}\\to \\mathbb{Y}\\) is equivariant with respect to a group \\(G\\) (and its group action on \\(\\mathbb{X},\\mathbb{Y}\\)), if for every \\(g\\in G,x\\in \\mathbb{X}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.678, + 0.469, + 0.693 + ], + "angle": 0, + "content": "\\[\n\\Phi (g \\cdot x) = g \\cdot \\Phi (x). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.469, + 0.756 + ], + "angle": 0, + "content": "Further, if the group action of \\( G \\) on \\( \\mathbb{Y} \\) is trivial, (i.e., \\( g \\cdot y = y \\) for any \\( g \\in G, y \\in \\mathbb{Y} \\)), we say \\( \\Phi \\) is invariant with respect to \\( G \\). For convenience, we also say \\( \\Phi(x) \\) is equivariant or invariant if \\( \\Phi \\) is equivariant or invariant." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.756, + 0.47, + 0.868 + ], + "angle": 0, + "content": "For point clouds, let \\(\\mathbb{X} = \\mathbb{R}^{n\\times 3}\\) be the input domain, and \\(\\mathbb{Y}\\) be the output domain. Permutation, translation, and \\(SO(3)\\) rotation equivariance are usually taken into consideration for point cloud networks. Consider a point cloud \\(\\mathbf{X} = (\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_n)^T\\in \\mathbb{X}\\). For the permutation group \\(S_{n}\\), for some \\(\\sigma \\in S_n\\), \\(\\sigma \\cdot \\mathbf{X} = (\\mathbf{x}_{\\sigma (1)},\\mathbf{x}_{\\sigma (2)},\\dots ,\\mathbf{x}_{\\sigma (n)})^T\\). For the translation group \\(\\mathbb{R}^3\\), for some \\(\\mathbf{v}\\in \\mathbb{R}^3\\), \\(\\mathbf{v}\\cdot \\mathbf{X} = (\\mathbf{x}_1 + \\mathbf{v},\\mathbf{x}_2 + \\mathbf{v},\\dots ,\\mathbf{x}_n + \\mathbf{v})^T\\). For the rotation group \\(SO(3)\\)," + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.124, + 0.871, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.376, + 0.892, + 0.427 + ], + "angle": 0, + "content": "Figure 3. Illustration of hierarchical Frame Learning Module. Invariant features and equivariant features are extracted progressively by EquivLayer, and are then used to generate frames by FrameGen at each scale." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.437, + 0.892, + 0.465 + ], + "angle": 0, + "content": "\\(g\\cdot \\mathbf{X} = (g\\cdot \\mathbf{x}_1,g\\cdot \\mathbf{x}_2,\\dots ,g\\cdot \\mathbf{x}_n)^T\\) , where each \\(g\\) corresponds to a rotation matrix \\(R\\in \\mathbb{R}^{3\\times 3}\\) and \\(g\\cdot \\mathbf{x} = R\\mathbf{x}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.893, + 0.65 + ], + "angle": 0, + "content": "Hierarchical frame learning. It is a challenging problem to learn geometry-based and temporally-consistent local coordinate frames to align the local region and factorize the underlying geometry feature from its motion. We need to construct hierarchical local region frames to accurately depict the orientations of local regions. And the established local coordinate frames should be based upon the 3D geometry in each timestamp and transform in the same way as the underlying geometry changes. To satisfy such requirements, we draw inspiration from the equivariant 3D point cloud analysis [22] and propose to use an equivariant network to learn the geometry-based rotation equivariant local coordinate frames \\( F \\) at different scales as shown in Figure 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.894, + 0.789 + ], + "angle": 0, + "content": "Let \\(\\mathbf{X}^l\\) denote the downsampled point cloud at layer \\(l\\) with \\(N^l\\) points. Let \\(H^l\\) and \\(\\mathbf{V}^l\\) denote per-point invariant scalar features and equivariant vector features of \\(\\mathbf{X}^l\\), respectively. We use \\(\\mathbf{X}^0, H^0, \\mathbf{V}^0\\) to denote the input point cloud, invariant scalar and equivariant vector features, where \\(H^0, \\mathbf{V}^0\\) are all zeros. And we pass the featured point cloud to a hierarchical equivariant network that aims to extract hierarchical invariant and equivariant features. Our EquivLayer is adapted from the GVP-GNN layer [14] and we defer the details to the supplementary material." + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.797, + 0.892, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\left(\\mathbf {X} ^ {l + 1}, H ^ {l + 1}, \\mathbf {V} ^ {l + 1}\\right) \\leftarrow \\operatorname {E q u i v L a y e r} ^ {l + 1} \\left(\\mathbf {X} ^ {l}, H ^ {l}, \\mathbf {V} ^ {l}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.824, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Since \\(\\mathrm{EquivLayer}^{l + 1}\\) is equivariant at all the layers, and the inputs \\(H^0,\\mathbf{V}^0\\) are invariant and equivariant features, the output \\(H^{l},\\mathbf{V}^{l}\\) of each layer are also invariant and equivari" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.887, + 0.498, + 0.898 + ], + "angle": 0, + "content": "607" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.127, + 0.172, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.171, + 0.168, + 0.177 + ], + "angle": 0, + "content": "Expected Frame" + }, + { + "type": "image", + "bbox": [ + 0.186, + 0.127, + 0.266, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.181, + 0.171, + 0.265, + 0.178 + ], + "angle": 0, + "content": "(a) Impact of Sampling" + }, + { + "type": "image", + "bbox": [ + 0.272, + 0.125, + 0.355, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.276, + 0.171, + 0.352, + 0.177 + ], + "angle": 0, + "content": "(b) Impact of Density" + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.127, + 0.448, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.367, + 0.171, + 0.437, + 0.178 + ], + "angle": 0, + "content": "(c) Impact of Noise" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.182, + 0.47, + 0.22 + ], + "angle": 0, + "content": "Figure 4. The learned frames are sensitive to disruptions if not regularized, above are the frames' possible distortions resulting from the impact of sampling, density, and noise." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.231, + 0.249, + 0.243 + ], + "angle": 0, + "content": "ant features, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.469, + 0.3 + ], + "angle": 0, + "content": "To obtain hierarchical frames from hierarchical invariant and equivariant features, we use another set of equivariant networks adapted from the GVP layers [14]. We use FrameGen to denote the network for the \\(l\\)-th layer." + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.31, + 0.469, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\mathbf {V} _ {\\text {o u t}} ^ {l} \\leftarrow \\operatorname {F r a m e G e n} ^ {l} \\left(H ^ {l}, \\mathbf {V} ^ {l}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.34, + 0.469, + 0.442 + ], + "angle": 0, + "content": "where hierarchical frames will be constructed from \\(\\mathbf{V}_{\\mathrm{out}}^{l} = (\\mathbf{v}_{\\mathrm{out},1}^{l},\\dots ,\\mathbf{v}_{\\mathrm{out},N^{l}}^{l})(\\mathbf{v}_{\\mathrm{out},i}^{l}\\in \\mathbb{R}^{2\\times 3})\\) . We orthonormalize the two vectors \\(\\mathbf{v}_{\\mathrm{out},i,1}^{l},\\mathbf{v}_{\\mathrm{out},i,2}^{l}\\) for each point to get \\(\\mathbf{u}_{i,1}^{l},\\mathbf{u}_{i,2}^{l}\\) using the Gram-Schmidt method. Then we get the frame \\(F_{i}^{l} = \\left[\\mathbf{u}_{i,1}^{l},\\mathbf{u}_{i,2}^{l},\\mathbf{u}_{i,1}^{l}\\times \\mathbf{u}_{i,2}^{l}\\right]\\in \\mathbb{R}^{3\\times 3}(i = 1,\\dots ,N^{l})\\) Since \\(\\mathbf{V}_{\\mathrm{out}}^l\\) is rotation equivariant, the constructed frames are also rotation equivariant." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.443, + 0.469, + 0.469 + ], + "angle": 0, + "content": "We refer to the whole module to generate hierarchical frames as FrameNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.469, + 0.572 + ], + "angle": 0, + "content": "Frame stabilization schemes. Frame learning is not an easy task since the corresponding regions in different timestamps can vary significantly due to reasons beyond motion such as sampling variation. To make sure the rotation equivariance of FrameNet is not broken, we introduce a frame stabilization scheme to further regularize the frame learning process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.469, + 0.781 + ], + "angle": 0, + "content": "We expect the region frame of anchor points to represent the orientation of a local region regardless of how the anchor points are sampled. However, our FrameNet is point cloud-based and its prediction could vary dramatically as the anchor points in the region vary (Figure 4 (a)). Besides, the local region frame is also affected by the density of point clouds. When a local region is very sparse while the shape intensely deforms, the estimated region frame will also be extremely disrupted (Figure 4 (b)). The density of the same local region in different timestamps changes due to the egomotion and the occlusion variation or when the noise of the point cloud is very large (Figure 4 (c)). Such disruptions can break the temporal consistency of the region frame, and we expect FrameNet to be sampling, density, and noise invariant for stable and temporally-consistent region frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.823 + ], + "angle": 0, + "content": "To achieve the goal above, we introduce several self-supervised losses to encourage the learned frame to be invariant under different point cloud augmentation strategies:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.834, + 0.469, + 0.869 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {a u g}} = \\sum_ {i} \\frac {\\operatorname {c o s i n e S i m} \\left(\\hat {F} _ {i} ^ {\\mathrm {a u g}} , F _ {i}\\right)}{N}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.209 + ], + "angle": 0, + "content": "where cosineSim means cosine similarity, \\(N\\) is the number of anchor points, \\(\\hat{F}^{\\mathrm{aug}}\\) is the frame of anchor points after augmentation, and \\(F\\) is the frame of original anchor points. Since the anchor points do not strictly match after the augmentation, we take the nearest neighbors of the original anchors in the augmented anchors as the corresponding points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.21, + 0.892, + 0.251 + ], + "angle": 0, + "content": "More specifically, we apply three types of augmentations including point cloud re-sampling, down-sampling, and jittering. Therefore, the final self-supervised loss is:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.261, + 0.892, + 0.277 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s t a b l i z e r}} = \\alpha L _ {\\text {r e - s a m p l i n g}} + \\beta L _ {\\text {d o w n - s a m p l i n g}} + \\gamma L _ {\\text {j i t t e r i n g}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.286, + 0.813, + 0.3 + ], + "angle": 0, + "content": "where \\(\\alpha, \\beta, \\gamma\\) are balancing coefficients set as 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.308, + 0.81, + 0.323 + ], + "angle": 0, + "content": "3.3. Frame-guided 4D Learning Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.44 + ], + "angle": 0, + "content": "After obtaining the hierarchical region frames which are geometrically stable and temporally consistent, we can use these frames to factorize the region-wise geometry feature from its motion by aligning corresponding regions. Instead of explicitly aligning regions at all different scales, we modify popular 4D operators including point 4D convolution and point 4D transformer so that they could learn the geometry feature as if corresponding regions are aligned." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.596 + ], + "angle": 0, + "content": "Frame-aware 4D operations. We first modify the point 4D convolution [9] into a frame-aware operator. Unlike the traditional point 4D convolution convolving directly between an anchor point and its spatiotemporal neighbor points, the frame-aware version first divides the neighbor points based on their timestamps, then picks up the nearest point from the anchor point in each division, aligns different divisions to the anchor point frame based upon the frames of the picked points, and finally conduct convolution in the aligned space. The frame-aware convolution layer can be mathematically described as:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.618, + 0.891, + 0.65 + ], + "angle": 0, + "content": "\\[\nf _ {i} ^ {l + 1} = \\sum_ {j \\in N (i)} M _ {1} ^ {l} \\left(F _ {i, t _ {j}} ^ {l \\top} \\left(x _ {j} - x _ {i}\\right), t _ {j} - t _ {i}\\right) \\odot M _ {2} ^ {l} \\left(f _ {j} ^ {l}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.824 + ], + "angle": 0, + "content": "where \\( N(i) \\) is the spatiotemporal neighbor of the anchor point \\( i \\), while \\( \\mathbf{x}_i \\) is its coordinate and \\( f_i^l \\) is its feature on the \\( l \\)-th level. \\( F_{i,t}^{l} \\) is the \\( l \\)-th frame of the nearest neighbor of \\( x_i \\) in timestamp \\( t \\). \\( \\sum \\) is aggregation implemented with sum-pooling or max-pooling, \\( M_1^l, M_2^l \\) are MLP networks, and \\( \\odot \\) is summation. The output feature can be seen as the representation under the region frames, and we denote such feature as \"region frame feature\". In particular, if we let the frames be identity matrices, this operation will be exactly the vanilla P4Dconv, and the output feature would be the representation under the original camera frame and we refer to it as \"camera frame feature\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.867 + ], + "angle": 0, + "content": "We then modify the point 4D transformer [9] into a frame-aware version. Since the transformer operator usually follows the 4D convolution, we consider its input as" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "608" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.127, + 0.473, + 0.265 + ], + "angle": 0, + "content": "a set of point tokens each equipped with a region frame as well as its feature within the frame. In this case, what we need to do is to make the positional embedding frame-aware so that the whole transformer is frame-aware. To be specific, we use \\( F_{\\mathrm{global},t} \\) to represent the global frame at timestamp \\( t \\) and use \\( W_{p} \\) to represent a linear transformation. Then considering a point token with a spatiotemporal coordinate of \\( (\\mathbf{x},t) \\), its positional embedding can be written as \\( p = W_{p} \\cdot \\binom{F_{\\mathrm{global},t}^{\\intercal}\\mathbf{x}}{t} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.472, + 0.335 + ], + "angle": 0, + "content": "It is worth mentioning that the frame-aware method can be plug-and-play for many other operators, for example, we can also transform RS-CNN into a frame-aware RS-CNN to extract invariant features using hierarchical frames. Specifically, the frame-aware RS-CNN is [14]:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.342, + 0.47, + 0.369 + ], + "angle": 0, + "content": "\\[\nh _ {i} ^ {l + 1} \\leftarrow \\max _ {j \\in N (i)} \\left(M \\left(\\| F _ {i} ^ {l \\mathbf {T}} r _ {i j} \\|, F _ {i} ^ {l \\mathbf {T}} r _ {i j}\\right) \\odot h _ {j} ^ {l}\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.377, + 0.47, + 0.446 + ], + "angle": 0, + "content": "where max denotes the max pooling operation, \\(M\\) is an MLP network, \\(\\odot\\) denotes element-wise multiplication, \\(N(i)\\) denotes the neighbors of point \\(i\\), \\(r_{ij}\\) denotes the relative coordinates between point \\(i\\) and \\(j\\), \\(h\\) denotes the features and \\(F\\) denotes the learned region frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.47, + 0.699 + ], + "angle": 0, + "content": "Frame-guided feature learning. With the frame-aware 4D operation we can extract hierarchical region frame features, which are inherent representations of the underlying geometry but lacks the motion information. So such region frame features are not enough to fully encode the 4D spatiotemporal information. On the other hand, the camera frame feature computed under the camera coordinate frame faithfully retain the motion information and can be a good complement to the region frame features. We then propose to combine both features to obtain a more powerful and representative 4D feature. In particular, we design a two-tower framework to extract the region frame feature and camera frame feature. To fuse features from the two towers, we propose to use the region frame feature to guide the camera frame feature learning through an attention map which aligns the local region across different timestamps into a canonical space and allows easier temporal associations for better motion understanding, as shown in Figure 5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.47, + 0.756 + ], + "angle": 0, + "content": "To be specific, the queries and keys are generated from the region frame feature but the values are generated from the camera frame feature. We formulate the fusion process as a self-attention operation below:" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.764, + 0.393, + 0.78 + ], + "angle": 0, + "content": "\\[\nQ _ {r} = W _ {q} f _ {r}, K _ {r} = W _ {k} f _ {r}, V _ {c} = W _ {v} f _ {c},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.782, + 0.469, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\operatorname {a t t e n t i o n} \\left(Q _ {r}, K _ {r}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {r} , K _ {r}}{\\sqrt {C _ {k}}}\\right), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.815, + 0.322, + 0.831 + ], + "angle": 0, + "content": "\\[\nO = V _ {c} \\cdot \\text {a t t e n t i o n} \\left(Q _ {r}, K _ {r}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.47, + 0.867 + ], + "angle": 0, + "content": "where \\(f_{r}\\) is the region frame feature, \\(f_{c}\\) is the camera frame feature. The output \\(O\\) is the camera frame feature fused" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.123, + 0.872, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.346, + 0.893, + 0.422 + ], + "angle": 0, + "content": "Figure 5. An illustration of the region frame-guided transformer. The input is the feature of multiple timestamps, For each timestamp (take timestamp 1 for example), the attention scores are computed by the correlations between timestamp 1 and all the other timestamps, then the output of timestamp 1 is the weighted sum of values encoded from the camera frame feature." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.893, + 0.474 + ], + "angle": 0, + "content": "under the guidance of the region frame feature. Then, we can add different task heads to complete various 4D point cloud sequence understanding tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.488, + 0.633, + 0.503 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.892, + 0.608 + ], + "angle": 0, + "content": "In this section, we cover four 4D point cloud sequence understanding tasks: action segmentation on HOI4D [21], action recognition on MSR-action3D [17], indoor semantic segmentation on HOI4D [21], and outdoor semantic segmentation on Synthia4D [25], in Section 4.1, 4.2, 4.3 and 4.4 respectively. In addition, we provide extensive ablation studies to validate our design choices in Section 4.5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.618, + 0.783, + 0.633 + ], + "angle": 0, + "content": "4.1. Action Segmentation on HOI4D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.893, + 0.868 + ], + "angle": 0, + "content": "Setup. To demonstrate the effectiveness of our method, we first conducted experiments on the HOI4D action segmentation task. For each point cloud sequence, we need to predict the action labels for each timestamp. We followed the official data split with 2971 sequences as the training set and 892 as the test set. Each sequence has 150 timestamps with 2048 points per timestamp. We use PPTr, an improved variant of the P4Transformer, as our backbone, which leverages two hierarchical transformers to process point cloud sequences and supports appending invariant features as additional inputs. We compare our method with baseline methods including P4Transformer and original PPTr. In this experiment, we use a two-scale FrameNet to learn 128 local frames and one global frame. We use frame-aware 4DConv to extract the invariant feature. The following metrics are reported: framewise accuracy (Acc), segmental edit" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "609" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.123, + 0.417, + 0.135 + ], + "angle": 0, + "content": "Table 1. Action segmentation on HOI4D dataset" + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.135, + 0.47, + 0.205 + ], + "angle": 0, + "content": "
MethodClip LengthAccEditF1@10F1@25F1@50
P4Transformer [8]15071.273.173.869.258.2
PPTr [30]15077.480.181.778.569.5
PPTr+Ours15079.4+2.0↑83.9+3.8↑85.0+3.3↑81.9+3.4↑73.3+3.8↑
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.21, + 0.469, + 0.252 + ], + "angle": 0, + "content": "distance, as well as segmental F1 scores at the overlapping thresholds of \\(10\\%\\), \\(25\\%\\), and \\(50\\%\\). Overlapping thresholds are determined by the IoU ratio." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.258, + 0.469, + 0.397 + ], + "angle": 0, + "content": "Result. As reported in Table 1, our method consistently has big improvements over previous state-of-the-art method in all metrics. This demonstrates that the region frame feature can significantly improve the communication of point clouds at different timestamps, to extract a more effective spatiotemporal representation. By introducing the region frame features for 4D point cloud sequence, we can factorize the local geometry understanding from its motion so that the network can have a better understanding of geometry and motion respectively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.407, + 0.407, + 0.421 + ], + "angle": 0, + "content": "4.2. Action Recognition on MSR-Action3D" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.434, + 0.469, + 0.614 + ], + "angle": 0, + "content": "Setup. Following P4Transformer and PPTr, we used the MAR-Action3D dataset, which consists of 567 human point cloud sequences, including 20 action categories. Each timestamp is sampled with 2,048 points. The point cloud sequences are segmented into multiple segments. During training, video-level labels are used as segment-level labels. As in action segmentation, we use PPTr as the base network. A two-layer FrameNet is used to extract local and global frames. And a frame-aware 4DConv is used to extract invariant features. To ensure a fair comparison, we also use primitive fitting to divide each human point cloud into four regions. To estimate the sequence-level probabilities, we take the mean of all segment-level probability predictions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.62, + 0.469, + 0.745 + ], + "angle": 0, + "content": "Result. As reported in Table 2, our method also outperforms previous methods in 3D action recognition tasks. We find that when the clip length is 8, the improvement of our method is 0.48, while the improvement of our method is 1.51 when clip length is 24. This indicates that our method performs better in longer sequences. This also demonstrates that the proposed region frame feature can factorize geometry learning from motion learning and achieve better temporal correlation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.756, + 0.435, + 0.77 + ], + "angle": 0, + "content": "4.3. Indoor Semantic Segmentation on HOI4D" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.784, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Setup. To verify that our approach can be effective for fine-grained tasks as well, we conducted further experiments on HOI4D for 4D semantic segmentation. The dataset consists of 3863 4D sequences, each including 300 timestamps of point clouds, for a total of 1.158M timestamps of point clouds. For one timestamp, there are 8192" + }, + { + "type": "table_caption", + "bbox": [ + 0.501, + 0.123, + 0.854, + 0.136 + ], + "angle": 0, + "content": "Table 2. Action recognition on MSR-Action3D dataset [17]" + }, + { + "type": "table", + "bbox": [ + 0.559, + 0.136, + 0.83, + 0.344 + ], + "angle": 0, + "content": "
MethodInputClip LengthVideo Acc@1
PointNet++ [24]point161.61
MeteorNet [20]point881.14
point1688.21
point2488.50
PSTNet [10]point883.50
point1689.90
point2491.20
P4Transformer [9]point883.17
point1689.56
point2490.94
PPT [30]point884.02
point1690.31
point2492.33
PPTr+Ourspoint884.50+0.48↑
point1691.50+1.19↑
point2493.84+1.51↑
" + }, + { + "type": "table_caption", + "bbox": [ + 0.531, + 0.351, + 0.86, + 0.363 + ], + "angle": 0, + "content": "Table 3. Semantic segmentation on HOI4D dataset [21]" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.363, + 0.891, + 0.431 + ], + "angle": 0, + "content": "
MethodClip LengthmIoU
P4Transformer [8]340.1
PPTr [30]341.0
P4T+Ours343.5+2.4↑
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.599 + ], + "angle": 0, + "content": "points. We follow the official data segmentation of HOI4D with 2971 training scenes and 892 test scenes. In this task, to avoid the complicated primitive fitting process, we choose P4Transformer as the base network. A three-scale FrameNet is used to learn three scales of the frames, respectively 512 and 128 local region frames as well as the global frame. In the semantic segmentation tasks, we all use a frame-aware RS-CNN to demonstrate that the framework method can be plug-and-play for other operators. Accordingly, we use a three-scale RS-CNN to extract \"region frame\" features. We use mean IoU(mIoU) % over 39 categories as an evaluation metric." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.891, + 0.688 + ], + "angle": 0, + "content": "Result. The results are shown in Table 3. We can observe that we improve the performance by a large margin compared with previous methods. Even without a primitive fitting process, our method still outperforms PPTr by \\(2.4\\%\\), which demonstrates that our local region feature is also helpful in the fine-grained 4D understanding task." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.891, + 0.71 + ], + "angle": 0, + "content": "4.4. Outdoor Semantic Segmentation on Synthia4D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.892, + 0.846 + ], + "angle": 0, + "content": "Setup. Synthia 4D is a synthetic dataset generated from Synthia dataset. It consists of six sequences of driving scenarios where both objects and cameras are moving. Following previous works, we use the same training/validation/test split, with 19,888/815/1,886 timestamps, respectively. We use P4Transformer as the base network, and other settings are the same as the experiments on semantic segmentation on HOI4D. The mean Intersection over Union (mIoU) is used as the evaluation metric." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.853, + 0.891, + 0.867 + ], + "angle": 0, + "content": "Result. As shown in Table 4, there is still a per" + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "610" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.123, + 0.443, + 0.136 + ], + "angle": 0, + "content": "Table 4. Evaluation for semantic segmentation on Synthia 4D" + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.139, + 0.491, + 0.266 + ], + "angle": 0, + "content": "
MethodClip LengthBldnRoadSdwkFenceVegittPoleCarT. SignPedstmBicyclLaneT.LightmloU
3D MinkNet14189.3997.6869.4386.5298.1197.2693.5079.4592.270.0044.6166.6976.24
4D MinkNet14390.1398.2673.4787.1999.1097.5094.0179.0492.620.0050.0168.1477.24
PointNet++196.8897.7286.2092.7597.1297.0990.8566.8778.640.0072.9375.1779.35
MeteorNet-m298.2297.7990.9893.1898.3197.4594.3076.3581.050.0074.0975.9281.47
MeteorNet-1398.1097.7288.6594.0097.9897.6593.8384.0780.900.0071.1477.6081.80
P4Transformer196.7698.2392.1195.2398.6297.7795.4680.7585.480.0074.2874.2282.41
P4Transformer396.7398.3594.0395.2398.2898.0195.6081.5485.180.0075.9579.0783.16
PPTr197.1498.4294.1297.0099.5997.8698.5479.6889.200.0077.2677.4283.85
PPTr397.5198.2195.1196.8199.6597.8698.0180.9890.600.0078.2176.8984.15
PPTr3098.0198.6395.2697.0399.7097.9598.7681.9991.200.0078.2977.0984.49
P4T+Ours398.2298.8997.9796.8599.6097.9099.0082.7391.500.0078.0378.9284.97+1.81↑
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.47, + 0.415 + ], + "angle": 0, + "content": "formance improvement, which also shows the effectiveness of our approach for outdoor 4D semantic segmentation tasks. It is worth mentioning that our network is based on P4Transformer, so a fair comparison is between P4Transformer with 3 timestamps and our method with 3 timestamps. The mIoU going from \\(83.16\\%\\) to \\(84.97\\% (+1.81\\%)\\) demonstrates the effectiveness of our method. Moreover, our method associates 3 point clouds by region frame feature, which is even better than PPTr's method of using 30 sequential point clouds." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.425, + 0.3, + 0.439 + ], + "angle": 0, + "content": "4.5. Ablation and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.619 + ], + "angle": 0, + "content": "Efficacy of frame stabilization schemes. The frame learning process is challenging due to sampling differences, density variation, or sensor noises. To make sure the rotation equivariance of MS-FrameNet is not broken, we introduce a frame stabilization scheme to regularize the frame learning process. We run ablation studies with and without frame stabilization schemes to quantify their efficacy. We find that learning region frames without frame stabilization schemes results in a \\(0.8\\%\\) accuracy and \\(1.8\\%\\) segmental edit distance drop on the HOI4D action segmentation task. This result proves that our frame stabilization schemes play an important role in learning high-quality region frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.47, + 0.791 + ], + "angle": 0, + "content": "Learning frames vs. non-learning frames. In the frame learning module, we design an MS-FrameNet which is essentially a rotation-equivariant neural network able to produce region frames equivariant to the rotation of input geometry. To demonstrate the advantages of learning frames, we compare our method with PCA which is a non-learning method to obtain local reference frames(LRFs). When replacing our frame-learning module with PCA frames, the best result we can get is \\(78.3\\%\\) accuracy on HOI4D action segmentation task, which is \\(1.1\\%\\) lower than our method. This experiment confirms the value of learning frames compared with the non-learning method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.469, + 0.852 + ], + "angle": 0, + "content": "Compared with random frames and identity frames. To further examine the value of the frame learning process, we conduct another two experiments that frame-guided 4D learning with random frames and identity frames." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.853, + 0.469, + 0.867 + ], + "angle": 0, + "content": "With random frames, we can only achieve \\(78.0\\%\\) accu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.238 + ], + "angle": 0, + "content": "racy on HOI4D action segmentation which is \\(1.4\\%\\) lower than our method. This demonstrates that random frames are not friendly for cross-time association and temporally consistent frames are important for frame-guided learning. With identity frames, the best result we can get is \\(76.3\\%\\) which is even \\(1.1\\%\\) lower than PPTr without frame learning, showing that the improvement is not brought about by a simple ensemble strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.413 + ], + "angle": 0, + "content": "Action segmentation with large motion. To better verify that the motion-agnostic geometric features allow easier temporal association toward a better motion understanding, we conduct experiments on HOI4D action segmentation tasks with large motion. We only select the sequences where the maximum distance of the object movement exceeds \\(0.5\\mathrm{m}\\) to construct a subset of HOI4D with 900 training scenes and 300 test scenes. Without learning frames, PPTr can get 29.22 accuracy on action segmentation, while our method can achieve \\(36.39\\%\\) accuracy. This result proves that our method has a stronger ability to deal with point cloud sequences with large motion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.56 + ], + "angle": 0, + "content": "The efficiency comparison. Our method does not introduce a significant increase in computational overhead. The 4D backbone requires much heavier computation compared with the lightweight FrameNet. So as shown in Table 5, introducing FrameNet in Frame-aware P4DConv does not significantly increase FLOPs or parameters compared with P4DConv. Worth to mention, since our method relies on both the invariant and non-invariant feature branches, the overall computational overhead is roughly twice that of a single branch P4DConv." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.573, + 0.891, + 0.611 + ], + "angle": 0, + "content": "Table 5. LeaF does not introduce a significant increase in computational overhead. All tests were conducted on a single NVIDIA GeForce RTX 3090 graphics card, with a batch size of 1." + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.611, + 0.865, + 0.681 + ], + "angle": 0, + "content": "
MethodFLOPsParameters
P4DConv7.550G8.192K
Frame-aware P4DConv8.428G8.314k
Only FrameNet878.2M122.0B
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.715, + 0.627, + 0.73 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.867 + ], + "angle": 0, + "content": "This paper proposes to use SO(3) equivariant networks to learn orientations for 4D point cloud videos and to obtain inherent features of the point clouds. The core idea is that the inherent features are motion-independent and this feature can be better correlated between contexts. We also propose three constraint terms to guide the learning of frame in order to obtain stable and consistent point cloud orientations. Experiments prove that our proposed method is effective and significantly outperforms existing methods." + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.496, + 0.898 + ], + "angle": 0, + "content": "611" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.174, + 0.14 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Tolga Birdal and Slobodan Ilic. Point pair features based object detection and pose estimation revisited. In 2015 International conference on 3D vision, pages 527-535. IEEE, 2015. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.201, + 0.472, + 0.252 + ], + "angle": 0, + "content": "[2] Haiwei Chen, Shichen Liu, Weikai Chen, Hao Li, and Randall Hill. Equivariant point network for 3d point cloud analysis. 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Sensors, 20(18):5086, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.128, + 0.469, + 0.565 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.473, + 0.888, + 0.498, + 0.898 + ], + "angle": 0, + "content": "613" + } + ] +] \ No newline at end of file diff --git a/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/51c2f292-724b-40e6-8771-779ef4bbccc4_origin.pdf b/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/51c2f292-724b-40e6-8771-779ef4bbccc4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d94f6ef757e42a1400f26d14cb1ae14b5c37c6a7 --- /dev/null +++ b/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/51c2f292-724b-40e6-8771-779ef4bbccc4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f1651f5153d6bab3b169f5aec82408ed06d6732e80ea3e9429bfd6326716ef63 +size 1008368 diff --git a/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/full.md b/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/full.md new file mode 100644 index 0000000000000000000000000000000000000000..57cdb637f5f64b87287716318bf3039c90ded6eb --- /dev/null +++ b/2023/LeaF_ Learning Frames for 4D Point Cloud Sequence Understanding/full.md @@ -0,0 +1,299 @@ +# LeaF: Learning Frames for 4D Point Cloud Sequence Understanding + +Yunze Liu $^{1,3}$ , Junyu Chen $^{1}$ , Zekai Zhang $^{1}$ , Jingwei Huang $^{4}$ , Li Yi $^{1,2,3}$ , Tsinghua University, $^{2}$ Shanghai Artificial Intelligence Laboratory, $^{3}$ Shanghai Qi Zhi Institute Huawei + +# Abstract + +We focus on learning descriptive geometry and motion features from 4D point cloud sequences in this work. Existing works usually develop generic 4D learning tools without leveraging the prior that a 4D sequence comes from a single 3D scene with local dynamics. Based on this observation, we propose to learn region-wise coordinate frames that transform together with the underlying geometry. With such frames, we can factorize geometry and motion to facilitate a feature-space geometric reconstruction for more effective 4D learning. To learn such region frames, we develop a rotation equivariant network with a frame stabilization strategy. To leverage such frames for better spatial-temporal feature learning, we develop a frame-guided 4D learning scheme. Experiments show that this approach significantly outperforms previous state-of-the-art methods on a wide range of 4D understanding benchmarks. + +# 1. Introduction + +We have recently witnessed a surge of interest in understanding point cloud sequences in 4D (3D space + 1D time). As the direct sensory input in a large number of modern AI applications including robotics and AR/VR, point cloud sequences can faithfully depict the geometry and motion of a dynamic scene, and therefore become critical for an intelligent agent to perceive and interact with the physical world. + +However, learning on such 4D data is very challenging and is still in an immature stage. 4D point cloud sequences usually couple 3D geometry and its dynamic motion together, resulting in quite redundant data in a very high dimensional space. This causes severe learning issues against an effective and compact spatial-temporal representation. + +Some existing efforts tackle the challenge through novel 4D backbone designs [8, 30, 7]. However, most of these works treat the point cloud sequence as unstructured 4D data and exploit generic 4D learning methods without leveraging the prior that the whole 4D sequence just depicts a single 3D scene with dynamic objects. As a result, such 4D learning is usually not super effective and the learned + +![](images/a456efa32dba68f9a2a4bfd473caa3454ae1c977217f0c5575ca345c9cf944d4.jpg) +Figure 1. Frame-aware spatial-temporal convolution. We propose to learn frames for point cloud sequence. Upon obtaining the frames, we could easily align the geometry regardless of the underlying motion toward a more canonical and complete geometry understanding. The motion-agnostic geometric features also allow easier temporal association toward a better motion understanding. + +spatial-temporal feature barely outperforms the spatial feature alone. Another line of works [7] uses self-supervised representation learning to encourage geometry and motion learning in a loosely decoupled manner. However, the decoupling still happens on the whole-scene level with a special focus on camera ego-motion, restricting their efficacy in modeling local dynamics on the object-level. We envision that successful geometry and motion decoupling is the key toward effective 4D representation learning. This essentially requires depicting the low-dimensional manifold of the dynamic scenes from the redundant high-dimensional 4D data. This highly correlates to dynamic scene reconstruction which requires understanding both camera ego-motion and object motion and is an ongoing research topic itself. Instead of explicitly reconstructing the dynamic scene without a quality guarantee, we seek a more lightweight and flexible solution. + +Our solution is based upon the following observation. For a specific region in the scene, we can understand its dynamic motion through establishing geometry-based and temporally-consistent local coordinate frames. Specifically, if we can establish a local coordinate frame based upon the 3D geometry in each timestamp and also make sure such + +frame transforms in the same way as the underlying geometry, then we can estimate the local rigid motion via comparing such frames among corresponding regions across timestamps. Such local frames allow us to factorize the local geometry understanding from its motion in a similar spirit to equivariant 3D analysis [22, 14]. In particular, once we establish temporally-consistent local coordinate frames, we essentially have a way to align the geometry regardless of the underlying motion toward a more canonical and complete geometry understanding. In addition, the motion-agnostic geometric features also allow easier temporal association toward a better motion understanding. + +Based upon the above observations, we present a novel 4D learning framework named LeaF. LeaF contains a frame learning module and a frame-guided 4D learning module. The frame learning module aims at producing geometry-based temporally consistent coordinate frames at different scales so that corresponding regions across timestamps can be well-aligned. This allows for factorizing geometry learning from motion learning. And then the frame-guided 4D learning module leverages the learned frames to facilitate a more effective spatial-temporal feature aggregation. Specifically, in the frame learning module, we design a hierarchical FrameNet which is essentially a rotation-equivariant neural network able to produce coordinate frames equivariant to the rotation of input geometry. The frame learning process is very challenging though since apart from rotations different observations from a point cloud sequence can vary significantly due to sampling differences, density variation, or sensor noises. To make sure the rotation equivariance of hierarchical FrameNet is not broken in practice, we introduce a frame stabilization scheme to further regularize the frame learning process. In the frame-guided 4D learning module, we first modify popular 4D operators (e.g. 4D point conv) into their frame-guided version and then leverage frame-guided 4D convolution to process 4D point cloud sequences. Since the motion information is factorized away while convolving with the learned region frames, we additionally process the 4D sequences with just a globally constant camera frame so that the motion information is faithfully kept. We fuse the learned features both from using region frames and from using camera frames, allowing a very effective 4D feature learning. + +To verify the effectiveness of LeaF, we conduct experiments on a wide range of 4D understanding tasks. And we demonstrate significant improvements over previous state-of-the-art methods $(+2.0\%)$ accuracy on HOI4D action segmentation [21], $+1.51\%$ accuracy on MSR action recognition [17], $+2.4\%$ mIoU on HOI4D indoor semantic segmentation [21], and $+1.81\%$ mIoU on Synthia4D outdoor semantic segmentation [25]). + +Our contributions are threefold: 1) we propose to learn effective spatial-temporal 4D features via learning and ex + +ploiting region-wise coordinate frames and our framework LeaF achieves state-of-the-art performance on a wide range of 4D understanding benchmarks; 2) we design a hierarchical FrameNet along with a frame stabilization scheme to learn equivariant region frames for motion-invariant geometry feature learning; 3) we present a frame-guided 4D learning method that is able to benefit from equivariant region frames without losing the motion information. + +# 2. Related Work + +4D point cloud sequence understanding. Compared with understanding static 3D point clouds, understanding 4D point cloud sequences requires more on aggregating and leveraging spatial-temporal information to perceive the geometry and dynamics. Several 4D backbones have been proposed to address such challenges, and they can be divided into two categories based on their representations. The first is to voxelize raw point clouds and extract features on 4D voxels, including MinkwoskiNet [3] which employs 4D spatial-temporal convolutions on 4D voxels. The second is to perform directly on raw points, including Meteor Net [19] which extends PointNet++[23] with a temporal dimension and explicitly tracks points' motion for grouping, and PSTNet[11] which constructs a point tube along temporal dimension for 4D point convolution. State of The Art methods such as Point 4d Transformer [9] and PPTr [30] belong to the second category and introduce transformer architecture, in order to avoid point-tracking and to better capture spatio-temporal correlation. There are works [7] focusing on improving the optimization of a transformer. + +Equivariant feature learning. The seminal work of Group Equivariant Convolution Networks [4] (G-CNN) starts a trend of leveraging group equivariance for neural networks. For 3D data, rotation group equivariance or SO(3) equivariance is significant, and there are roughly two categories of SO(3) equivariant networks. The first category is the "filter orbit" method. Inspired by group-equivariant convolution on 2D images proposed in G-CNN [4], Equivariant Point Network [2] and successive works [16, 18, 32] discretizes SO(3) and analogously design group-equivariant operations on point clouds. However, as such networks extend the original features to multiple oriented features, they encounter memory issues and may not be suitable for 4D point cloud sequences understanding. The second category is the "filter design" method. These methods [28, 5, 14] design the filter forms to achieve exact SO(3) equivariance. "Filter design" methods get rid of memory issues, but their representation capability is usually limited due to the restricted filter form. + +Rotation-invariant local descriptors. Local descriptor is a synonym for local feature, which is widely used in tasks such as 3D point cloud matching. Some of the rotation- + +![](images/e5f1fdf35f0bc84845deafc7be410da222a78c4f38035c56c985baaa17c652ac.jpg) +Figure 2. Illustration of the proposed Learning Frame for 4D Point Cloud Sequence Understanding (LeaF). We use an SO(3) equivariant network proposed in [22] to learn hierarchical frames denoted as region frames. We denote the identity frames as camera frames. Under region frames and camera frames, region frame feature and camera frame feature can be extracted by frame-aware 4D backbones, and are then fused by region frame-guided transformer to do downstream tasks such as action recognition, action segmentation, and semantic segmentation. Data augmentation and regularization losses are also added to make the equivariant Hierarchical frame network robust to re-sampling, down-sampling, and jittering. + +invariant local descriptors first obtain rotation-equivariant local reference frames (LRFs) either via PCA methods [29, 13, 29, 31, 12, 15], or by incorporating learning methods to decide the axis in the tangent plane aside from normal [33], or completely by 3D rotation equivariant networks [22]. Under those LRFs, local support sets can be transformed into canonical representation, and thus invariant local features can be extracted either by hand-crafted method [29, 13, 29, 31] or by learning methods [12, 15]. Some other methods [27, 26, 1, 6] directly extract invariant local features from invariant local geometry property, e.g., the dot product of point pair normals. + +# 3. Method + +We first provide an overview of our method in Section 3.1. Next, in Sections 3.2, 3.3 we describe our approach in detail in terms of how to learn hierarchical frames and how to use the learned frames, respectively. + +# 3.1. Overview + +Our core idea is to establish geometry-based and temporally-consistent local coordinate frames to factorize the local geometry understanding from its underlying motion. Such frames would allow us to align the local geometry from different timestamps toward a more complete geo + +metric understanding. Such geometric features are motion-agnostic, which also allows easier temporal association toward a better motion understanding. Realizing the idea above requires addressing two challenges: how to learn such frames and how to use such frames for 4D learning. + +Regarding the first challenge, we introduce a frame learning module as shown in Figure 2. Since geometric features are naturally hierarchical, the frames have to be hierarchical as well. We, therefore, propose to learn such frames through a hierarchical Frame Network. We leverage rotation equivariant networks [12] to design the FrameNet so that its output transforms in the same way as the underlying geometry. This network produces a hierarchy of frames covering regions from local to global. The global region frame allows factorizing ego-motion and aligning different observations to a unified view. The local region frame can align local geometry to a canonical space. + +To stabilize the frame learning processing so that the FrameNet could learn temporally consistent region frames at different scales, we design a frame stabilization strategy. Given an input point cloud, we first apply data augmentation to obtain the augmented version of it. Then we feed both the original point cloud and the augmented one through the FrameNet and enforce their predictions to be consistent. Through various data augmentation strategies, we can keep the rotation equivariance of our predicted frames regardless + +of the time-dependent data corruptions. + +Regarding the second challenge of how to use the frames, we design a frame-guided 4D learning scheme as shown in Figure 2. Particularly, we design a frame-guided 4D convolution operator which can generate local and global features based on different frames at different scales. By cascading a series of frame-guided 4D convolution operators in a similar way to existing 4D backbones [9, 11], we can extract 4D features under the guidance of hierarchical frames. To keep the motion information from the 4D input, we leverage two frame-guided 4D convolution branches with shared weights. For one branch, the frames are just our learned region frames from the frame learning module. For the other branch, we use a constant camera frame across all timestamps and at all scales. The first branch focuses on motion-agnostic geometric feature learning while the second branch complements the motion cues. A region frame-guided transformer is designed to fuse the two branches for effective spatial-temporal features. + +The designs above enable us to achieve various 4D point cloud understanding tasks effectively including 3D action segmentation, 3D action recognition, and 4D semantic segmentation for both indoor and outdoor scenarios. + +# 3.2. Hierarchical Frame Learning Module + +In this section, we first revisit the concept of SO(3)-equivariance and SO(3)-invariance of 3D point cloud. Then we introduce the local-global frame learning pipeline with equivariant neural network in detail. Besides, in order to learn geometrically-stable and temporally-consistent local coordinate frames, we also introduce a frame stabilization scheme to regularize the frame learning process. + +Revisit equivariance and invariance. Given a group $G$ and a certain domain $\mathbb{V}$ , a group action of $G$ on $\mathbb{V}$ is a mapping from $G\times \mathbb{V}$ to $\mathbb{V}$ (written as $g\cdot v$ for all $g\in G$ and $v\in \mathbb{V}$ ), where each $g$ corresponds to a bijection on $\mathbb{V}$ . A mapping $\Phi :\mathbb{X}\to \mathbb{Y}$ is equivariant with respect to a group $G$ (and its group action on $\mathbb{X},\mathbb{Y}$ ), if for every $g\in G,x\in \mathbb{X}$ + +$$ +\Phi (g \cdot x) = g \cdot \Phi (x). \tag {1} +$$ + +Further, if the group action of $G$ on $\mathbb{Y}$ is trivial, (i.e., $g \cdot y = y$ for any $g \in G, y \in \mathbb{Y}$ ), we say $\Phi$ is invariant with respect to $G$ . For convenience, we also say $\Phi(x)$ is equivariant or invariant if $\Phi$ is equivariant or invariant. + +For point clouds, let $\mathbb{X} = \mathbb{R}^{n\times 3}$ be the input domain, and $\mathbb{Y}$ be the output domain. Permutation, translation, and $SO(3)$ rotation equivariance are usually taken into consideration for point cloud networks. Consider a point cloud $\mathbf{X} = (\mathbf{x}_1,\mathbf{x}_2,\dots ,\mathbf{x}_n)^T\in \mathbb{X}$ . For the permutation group $S_{n}$ , for some $\sigma \in S_n$ , $\sigma \cdot \mathbf{X} = (\mathbf{x}_{\sigma (1)},\mathbf{x}_{\sigma (2)},\dots ,\mathbf{x}_{\sigma (n)})^T$ . For the translation group $\mathbb{R}^3$ , for some $\mathbf{v}\in \mathbb{R}^3$ , $\mathbf{v}\cdot \mathbf{X} = (\mathbf{x}_1 + \mathbf{v},\mathbf{x}_2 + \mathbf{v},\dots ,\mathbf{x}_n + \mathbf{v})^T$ . For the rotation group $SO(3)$ , + +![](images/1c539144d47707d39729681c3f002667d82a084438589f7d1c245db2839701ab.jpg) +Figure 3. Illustration of hierarchical Frame Learning Module. Invariant features and equivariant features are extracted progressively by EquivLayer, and are then used to generate frames by FrameGen at each scale. + +$g\cdot \mathbf{X} = (g\cdot \mathbf{x}_1,g\cdot \mathbf{x}_2,\dots ,g\cdot \mathbf{x}_n)^T$ , where each $g$ corresponds to a rotation matrix $R\in \mathbb{R}^{3\times 3}$ and $g\cdot \mathbf{x} = R\mathbf{x}$ + +Hierarchical frame learning. It is a challenging problem to learn geometry-based and temporally-consistent local coordinate frames to align the local region and factorize the underlying geometry feature from its motion. We need to construct hierarchical local region frames to accurately depict the orientations of local regions. And the established local coordinate frames should be based upon the 3D geometry in each timestamp and transform in the same way as the underlying geometry changes. To satisfy such requirements, we draw inspiration from the equivariant 3D point cloud analysis [22] and propose to use an equivariant network to learn the geometry-based rotation equivariant local coordinate frames $F$ at different scales as shown in Figure 3. + +Let $\mathbf{X}^l$ denote the downsampled point cloud at layer $l$ with $N^l$ points. Let $H^l$ and $\mathbf{V}^l$ denote per-point invariant scalar features and equivariant vector features of $\mathbf{X}^l$ , respectively. We use $\mathbf{X}^0, H^0, \mathbf{V}^0$ to denote the input point cloud, invariant scalar and equivariant vector features, where $H^0, \mathbf{V}^0$ are all zeros. And we pass the featured point cloud to a hierarchical equivariant network that aims to extract hierarchical invariant and equivariant features. Our EquivLayer is adapted from the GVP-GNN layer [14] and we defer the details to the supplementary material. + +$$ +\left(\mathbf {X} ^ {l + 1}, H ^ {l + 1}, \mathbf {V} ^ {l + 1}\right) \leftarrow \operatorname {E q u i v L a y e r} ^ {l + 1} \left(\mathbf {X} ^ {l}, H ^ {l}, \mathbf {V} ^ {l}\right). \tag {2} +$$ + +Since $\mathrm{EquivLayer}^{l + 1}$ is equivariant at all the layers, and the inputs $H^0,\mathbf{V}^0$ are invariant and equivariant features, the output $H^{l},\mathbf{V}^{l}$ of each layer are also invariant and equivari + +![](images/b1693772c6bc247b0780bb45cd9399d91f0f0abef6cc9d98b04a8989329bd0e8.jpg) +Expected Frame +Figure 4. The learned frames are sensitive to disruptions if not regularized, above are the frames' possible distortions resulting from the impact of sampling, density, and noise. + +![](images/47e81066027f97e60fa3f9bcfe6dba90622fadad33ddd4af23cb0c42c549e2af.jpg) +(a) Impact of Sampling + +![](images/0a2275289cb137697f5ce0995d46dea4b192d6efe8b6719bde063a308fa9471f.jpg) +(b) Impact of Density + +![](images/1f2519934b42e55e72ab1322b167d34ee999d9e74f93f64738b47b5aac1365b2.jpg) +(c) Impact of Noise + +ant features, respectively. + +To obtain hierarchical frames from hierarchical invariant and equivariant features, we use another set of equivariant networks adapted from the GVP layers [14]. We use FrameGen to denote the network for the $l$ -th layer. + +$$ +\mathbf {V} _ {\text {o u t}} ^ {l} \leftarrow \operatorname {F r a m e G e n} ^ {l} \left(H ^ {l}, \mathbf {V} ^ {l}\right), \tag {3} +$$ + +where hierarchical frames will be constructed from $\mathbf{V}_{\mathrm{out}}^{l} = (\mathbf{v}_{\mathrm{out},1}^{l},\dots ,\mathbf{v}_{\mathrm{out},N^{l}}^{l})(\mathbf{v}_{\mathrm{out},i}^{l}\in \mathbb{R}^{2\times 3})$ . We orthonormalize the two vectors $\mathbf{v}_{\mathrm{out},i,1}^{l},\mathbf{v}_{\mathrm{out},i,2}^{l}$ for each point to get $\mathbf{u}_{i,1}^{l},\mathbf{u}_{i,2}^{l}$ using the Gram-Schmidt method. Then we get the frame $F_{i}^{l} = \left[\mathbf{u}_{i,1}^{l},\mathbf{u}_{i,2}^{l},\mathbf{u}_{i,1}^{l}\times \mathbf{u}_{i,2}^{l}\right]\in \mathbb{R}^{3\times 3}(i = 1,\dots ,N^{l})$ Since $\mathbf{V}_{\mathrm{out}}^l$ is rotation equivariant, the constructed frames are also rotation equivariant. + +We refer to the whole module to generate hierarchical frames as FrameNet. + +Frame stabilization schemes. Frame learning is not an easy task since the corresponding regions in different timestamps can vary significantly due to reasons beyond motion such as sampling variation. To make sure the rotation equivariance of FrameNet is not broken, we introduce a frame stabilization scheme to further regularize the frame learning process. + +We expect the region frame of anchor points to represent the orientation of a local region regardless of how the anchor points are sampled. However, our FrameNet is point cloud-based and its prediction could vary dramatically as the anchor points in the region vary (Figure 4 (a)). Besides, the local region frame is also affected by the density of point clouds. When a local region is very sparse while the shape intensely deforms, the estimated region frame will also be extremely disrupted (Figure 4 (b)). The density of the same local region in different timestamps changes due to the egomotion and the occlusion variation or when the noise of the point cloud is very large (Figure 4 (c)). Such disruptions can break the temporal consistency of the region frame, and we expect FrameNet to be sampling, density, and noise invariant for stable and temporally-consistent region frames. + +To achieve the goal above, we introduce several self-supervised losses to encourage the learned frame to be invariant under different point cloud augmentation strategies: + +$$ +L _ {\mathrm {a u g}} = \sum_ {i} \frac {\operatorname {c o s i n e S i m} \left(\hat {F} _ {i} ^ {\mathrm {a u g}} , F _ {i}\right)}{N}, \tag {4} +$$ + +where cosineSim means cosine similarity, $N$ is the number of anchor points, $\hat{F}^{\mathrm{aug}}$ is the frame of anchor points after augmentation, and $F$ is the frame of original anchor points. Since the anchor points do not strictly match after the augmentation, we take the nearest neighbors of the original anchors in the augmented anchors as the corresponding points. + +More specifically, we apply three types of augmentations including point cloud re-sampling, down-sampling, and jittering. Therefore, the final self-supervised loss is: + +$$ +L _ {\text {s t a b l i z e r}} = \alpha L _ {\text {r e - s a m p l i n g}} + \beta L _ {\text {d o w n - s a m p l i n g}} + \gamma L _ {\text {j i t t e r i n g}}, \tag {5} +$$ + +where $\alpha, \beta, \gamma$ are balancing coefficients set as 1. + +# 3.3. Frame-guided 4D Learning Module + +After obtaining the hierarchical region frames which are geometrically stable and temporally consistent, we can use these frames to factorize the region-wise geometry feature from its motion by aligning corresponding regions. Instead of explicitly aligning regions at all different scales, we modify popular 4D operators including point 4D convolution and point 4D transformer so that they could learn the geometry feature as if corresponding regions are aligned. + +Frame-aware 4D operations. We first modify the point 4D convolution [9] into a frame-aware operator. Unlike the traditional point 4D convolution convolving directly between an anchor point and its spatiotemporal neighbor points, the frame-aware version first divides the neighbor points based on their timestamps, then picks up the nearest point from the anchor point in each division, aligns different divisions to the anchor point frame based upon the frames of the picked points, and finally conduct convolution in the aligned space. The frame-aware convolution layer can be mathematically described as: + +$$ +f _ {i} ^ {l + 1} = \sum_ {j \in N (i)} M _ {1} ^ {l} \left(F _ {i, t _ {j}} ^ {l \top} \left(x _ {j} - x _ {i}\right), t _ {j} - t _ {i}\right) \odot M _ {2} ^ {l} \left(f _ {j} ^ {l}\right), \tag {6} +$$ + +where $N(i)$ is the spatiotemporal neighbor of the anchor point $i$ , while $\mathbf{x}_i$ is its coordinate and $f_i^l$ is its feature on the $l$ -th level. $F_{i,t}^{l}$ is the $l$ -th frame of the nearest neighbor of $x_i$ in timestamp $t$ . $\sum$ is aggregation implemented with sum-pooling or max-pooling, $M_1^l, M_2^l$ are MLP networks, and $\odot$ is summation. The output feature can be seen as the representation under the region frames, and we denote such feature as "region frame feature". In particular, if we let the frames be identity matrices, this operation will be exactly the vanilla P4Dconv, and the output feature would be the representation under the original camera frame and we refer to it as "camera frame feature". + +We then modify the point 4D transformer [9] into a frame-aware version. Since the transformer operator usually follows the 4D convolution, we consider its input as + +a set of point tokens each equipped with a region frame as well as its feature within the frame. In this case, what we need to do is to make the positional embedding frame-aware so that the whole transformer is frame-aware. To be specific, we use $F_{\mathrm{global},t}$ to represent the global frame at timestamp $t$ and use $W_{p}$ to represent a linear transformation. Then considering a point token with a spatiotemporal coordinate of $(\mathbf{x},t)$ , its positional embedding can be written as $p = W_{p} \cdot \binom{F_{\mathrm{global},t}^{\intercal}\mathbf{x}}{t}$ . + +It is worth mentioning that the frame-aware method can be plug-and-play for many other operators, for example, we can also transform RS-CNN into a frame-aware RS-CNN to extract invariant features using hierarchical frames. Specifically, the frame-aware RS-CNN is [14]: + +$$ +h _ {i} ^ {l + 1} \leftarrow \max _ {j \in N (i)} \left(M \left(\| F _ {i} ^ {l \mathbf {T}} r _ {i j} \|, F _ {i} ^ {l \mathbf {T}} r _ {i j}\right) \odot h _ {j} ^ {l}\right) \tag {7} +$$ + +where max denotes the max pooling operation, $M$ is an MLP network, $\odot$ denotes element-wise multiplication, $N(i)$ denotes the neighbors of point $i$ , $r_{ij}$ denotes the relative coordinates between point $i$ and $j$ , $h$ denotes the features and $F$ denotes the learned region frames. + +Frame-guided feature learning. With the frame-aware 4D operation we can extract hierarchical region frame features, which are inherent representations of the underlying geometry but lacks the motion information. So such region frame features are not enough to fully encode the 4D spatiotemporal information. On the other hand, the camera frame feature computed under the camera coordinate frame faithfully retain the motion information and can be a good complement to the region frame features. We then propose to combine both features to obtain a more powerful and representative 4D feature. In particular, we design a two-tower framework to extract the region frame feature and camera frame feature. To fuse features from the two towers, we propose to use the region frame feature to guide the camera frame feature learning through an attention map which aligns the local region across different timestamps into a canonical space and allows easier temporal associations for better motion understanding, as shown in Figure 5. + +To be specific, the queries and keys are generated from the region frame feature but the values are generated from the camera frame feature. We formulate the fusion process as a self-attention operation below: + +$$ +Q _ {r} = W _ {q} f _ {r}, K _ {r} = W _ {k} f _ {r}, V _ {c} = W _ {v} f _ {c}, +$$ + +$$ +\operatorname {a t t e n t i o n} \left(Q _ {r}, K _ {r}\right) = \operatorname {s o f t m a x} \left(\frac {Q _ {r} , K _ {r}}{\sqrt {C _ {k}}}\right), \tag {8} +$$ + +$$ +O = V _ {c} \cdot \text {a t t e n t i o n} \left(Q _ {r}, K _ {r}\right), +$$ + +where $f_{r}$ is the region frame feature, $f_{c}$ is the camera frame feature. The output $O$ is the camera frame feature fused + +![](images/e89feeecc9888320e359b2d479909549ea84b25601a381c4259b6c01100425aa.jpg) +Figure 5. An illustration of the region frame-guided transformer. The input is the feature of multiple timestamps, For each timestamp (take timestamp 1 for example), the attention scores are computed by the correlations between timestamp 1 and all the other timestamps, then the output of timestamp 1 is the weighted sum of values encoded from the camera frame feature. + +under the guidance of the region frame feature. Then, we can add different task heads to complete various 4D point cloud sequence understanding tasks. + +# 4. Experiments + +In this section, we cover four 4D point cloud sequence understanding tasks: action segmentation on HOI4D [21], action recognition on MSR-action3D [17], indoor semantic segmentation on HOI4D [21], and outdoor semantic segmentation on Synthia4D [25], in Section 4.1, 4.2, 4.3 and 4.4 respectively. In addition, we provide extensive ablation studies to validate our design choices in Section 4.5. + +# 4.1. Action Segmentation on HOI4D + +Setup. To demonstrate the effectiveness of our method, we first conducted experiments on the HOI4D action segmentation task. For each point cloud sequence, we need to predict the action labels for each timestamp. We followed the official data split with 2971 sequences as the training set and 892 as the test set. Each sequence has 150 timestamps with 2048 points per timestamp. We use PPTr, an improved variant of the P4Transformer, as our backbone, which leverages two hierarchical transformers to process point cloud sequences and supports appending invariant features as additional inputs. We compare our method with baseline methods including P4Transformer and original PPTr. In this experiment, we use a two-scale FrameNet to learn 128 local frames and one global frame. We use frame-aware 4DConv to extract the invariant feature. The following metrics are reported: framewise accuracy (Acc), segmental edit + +Table 1. Action segmentation on HOI4D dataset + +
MethodClip LengthAccEditF1@10F1@25F1@50
P4Transformer [8]15071.273.173.869.258.2
PPTr [30]15077.480.181.778.569.5
PPTr+Ours15079.4+2.0↑83.9+3.8↑85.0+3.3↑81.9+3.4↑73.3+3.8↑
+ +distance, as well as segmental F1 scores at the overlapping thresholds of $10\%$ , $25\%$ , and $50\%$ . Overlapping thresholds are determined by the IoU ratio. + +Result. As reported in Table 1, our method consistently has big improvements over previous state-of-the-art method in all metrics. This demonstrates that the region frame feature can significantly improve the communication of point clouds at different timestamps, to extract a more effective spatiotemporal representation. By introducing the region frame features for 4D point cloud sequence, we can factorize the local geometry understanding from its motion so that the network can have a better understanding of geometry and motion respectively. + +# 4.2. Action Recognition on MSR-Action3D + +Setup. Following P4Transformer and PPTr, we used the MAR-Action3D dataset, which consists of 567 human point cloud sequences, including 20 action categories. Each timestamp is sampled with 2,048 points. The point cloud sequences are segmented into multiple segments. During training, video-level labels are used as segment-level labels. As in action segmentation, we use PPTr as the base network. A two-layer FrameNet is used to extract local and global frames. And a frame-aware 4DConv is used to extract invariant features. To ensure a fair comparison, we also use primitive fitting to divide each human point cloud into four regions. To estimate the sequence-level probabilities, we take the mean of all segment-level probability predictions. + +Result. As reported in Table 2, our method also outperforms previous methods in 3D action recognition tasks. We find that when the clip length is 8, the improvement of our method is 0.48, while the improvement of our method is 1.51 when clip length is 24. This indicates that our method performs better in longer sequences. This also demonstrates that the proposed region frame feature can factorize geometry learning from motion learning and achieve better temporal correlation. + +# 4.3. Indoor Semantic Segmentation on HOI4D + +Setup. To verify that our approach can be effective for fine-grained tasks as well, we conducted further experiments on HOI4D for 4D semantic segmentation. The dataset consists of 3863 4D sequences, each including 300 timestamps of point clouds, for a total of 1.158M timestamps of point clouds. For one timestamp, there are 8192 + +Table 2. Action recognition on MSR-Action3D dataset [17] + +
MethodInputClip LengthVideo Acc@1
PointNet++ [24]point161.61
MeteorNet [20]point881.14
point1688.21
point2488.50
PSTNet [10]point883.50
point1689.90
point2491.20
P4Transformer [9]point883.17
point1689.56
point2490.94
PPT [30]point884.02
point1690.31
point2492.33
PPTr+Ourspoint884.50+0.48↑
point1691.50+1.19↑
point2493.84+1.51↑
+ +Table 3. Semantic segmentation on HOI4D dataset [21] + +
MethodClip LengthmIoU
P4Transformer [8]340.1
PPTr [30]341.0
P4T+Ours343.5+2.4↑
+ +points. We follow the official data segmentation of HOI4D with 2971 training scenes and 892 test scenes. In this task, to avoid the complicated primitive fitting process, we choose P4Transformer as the base network. A three-scale FrameNet is used to learn three scales of the frames, respectively 512 and 128 local region frames as well as the global frame. In the semantic segmentation tasks, we all use a frame-aware RS-CNN to demonstrate that the framework method can be plug-and-play for other operators. Accordingly, we use a three-scale RS-CNN to extract "region frame" features. We use mean IoU(mIoU) % over 39 categories as an evaluation metric. + +Result. The results are shown in Table 3. We can observe that we improve the performance by a large margin compared with previous methods. Even without a primitive fitting process, our method still outperforms PPTr by $2.4\%$ , which demonstrates that our local region feature is also helpful in the fine-grained 4D understanding task. + +# 4.4. Outdoor Semantic Segmentation on Synthia4D + +Setup. Synthia 4D is a synthetic dataset generated from Synthia dataset. It consists of six sequences of driving scenarios where both objects and cameras are moving. Following previous works, we use the same training/validation/test split, with 19,888/815/1,886 timestamps, respectively. We use P4Transformer as the base network, and other settings are the same as the experiments on semantic segmentation on HOI4D. The mean Intersection over Union (mIoU) is used as the evaluation metric. + +Result. As shown in Table 4, there is still a per + +Table 4. Evaluation for semantic segmentation on Synthia 4D + +
MethodClip LengthBldnRoadSdwkFenceVegittPoleCarT. SignPedstmBicyclLaneT.LightmloU
3D MinkNet14189.3997.6869.4386.5298.1197.2693.5079.4592.270.0044.6166.6976.24
4D MinkNet14390.1398.2673.4787.1999.1097.5094.0179.0492.620.0050.0168.1477.24
PointNet++196.8897.7286.2092.7597.1297.0990.8566.8778.640.0072.9375.1779.35
MeteorNet-m298.2297.7990.9893.1898.3197.4594.3076.3581.050.0074.0975.9281.47
MeteorNet-1398.1097.7288.6594.0097.9897.6593.8384.0780.900.0071.1477.6081.80
P4Transformer196.7698.2392.1195.2398.6297.7795.4680.7585.480.0074.2874.2282.41
P4Transformer396.7398.3594.0395.2398.2898.0195.6081.5485.180.0075.9579.0783.16
PPTr197.1498.4294.1297.0099.5997.8698.5479.6889.200.0077.2677.4283.85
PPTr397.5198.2195.1196.8199.6597.8698.0180.9890.600.0078.2176.8984.15
PPTr3098.0198.6395.2697.0399.7097.9598.7681.9991.200.0078.2977.0984.49
P4T+Ours398.2298.8997.9796.8599.6097.9099.0082.7391.500.0078.0378.9284.97+1.81↑
+ +formance improvement, which also shows the effectiveness of our approach for outdoor 4D semantic segmentation tasks. It is worth mentioning that our network is based on P4Transformer, so a fair comparison is between P4Transformer with 3 timestamps and our method with 3 timestamps. The mIoU going from $83.16\%$ to $84.97\% (+1.81\%)$ demonstrates the effectiveness of our method. Moreover, our method associates 3 point clouds by region frame feature, which is even better than PPTr's method of using 30 sequential point clouds. + +# 4.5. Ablation and Discussion + +Efficacy of frame stabilization schemes. The frame learning process is challenging due to sampling differences, density variation, or sensor noises. To make sure the rotation equivariance of MS-FrameNet is not broken, we introduce a frame stabilization scheme to regularize the frame learning process. We run ablation studies with and without frame stabilization schemes to quantify their efficacy. We find that learning region frames without frame stabilization schemes results in a $0.8\%$ accuracy and $1.8\%$ segmental edit distance drop on the HOI4D action segmentation task. This result proves that our frame stabilization schemes play an important role in learning high-quality region frames. + +Learning frames vs. non-learning frames. In the frame learning module, we design an MS-FrameNet which is essentially a rotation-equivariant neural network able to produce region frames equivariant to the rotation of input geometry. To demonstrate the advantages of learning frames, we compare our method with PCA which is a non-learning method to obtain local reference frames(LRFs). When replacing our frame-learning module with PCA frames, the best result we can get is $78.3\%$ accuracy on HOI4D action segmentation task, which is $1.1\%$ lower than our method. This experiment confirms the value of learning frames compared with the non-learning method. + +Compared with random frames and identity frames. To further examine the value of the frame learning process, we conduct another two experiments that frame-guided 4D learning with random frames and identity frames. + +With random frames, we can only achieve $78.0\%$ accu + +racy on HOI4D action segmentation which is $1.4\%$ lower than our method. This demonstrates that random frames are not friendly for cross-time association and temporally consistent frames are important for frame-guided learning. With identity frames, the best result we can get is $76.3\%$ which is even $1.1\%$ lower than PPTr without frame learning, showing that the improvement is not brought about by a simple ensemble strategy. + +Action segmentation with large motion. To better verify that the motion-agnostic geometric features allow easier temporal association toward a better motion understanding, we conduct experiments on HOI4D action segmentation tasks with large motion. We only select the sequences where the maximum distance of the object movement exceeds $0.5\mathrm{m}$ to construct a subset of HOI4D with 900 training scenes and 300 test scenes. Without learning frames, PPTr can get 29.22 accuracy on action segmentation, while our method can achieve $36.39\%$ accuracy. This result proves that our method has a stronger ability to deal with point cloud sequences with large motion. + +The efficiency comparison. Our method does not introduce a significant increase in computational overhead. The 4D backbone requires much heavier computation compared with the lightweight FrameNet. So as shown in Table 5, introducing FrameNet in Frame-aware P4DConv does not significantly increase FLOPs or parameters compared with P4DConv. Worth to mention, since our method relies on both the invariant and non-invariant feature branches, the overall computational overhead is roughly twice that of a single branch P4DConv. + +Table 5. LeaF does not introduce a significant increase in computational overhead. All tests were conducted on a single NVIDIA GeForce RTX 3090 graphics card, with a batch size of 1. + +
MethodFLOPsParameters
P4DConv7.550G8.192K
Frame-aware P4DConv8.428G8.314k
Only FrameNet878.2M122.0B
+ +# 5. Conclusions + +This paper proposes to use SO(3) equivariant networks to learn orientations for 4D point cloud videos and to obtain inherent features of the point clouds. The core idea is that the inherent features are motion-independent and this feature can be better correlated between contexts. We also propose three constraint terms to guide the learning of frame in order to obtain stable and consistent point cloud orientations. Experiments prove that our proposed method is effective and significantly outperforms existing methods. + +# References + +[1] Tolga Birdal and Slobodan Ilic. Point pair features based object detection and pose estimation revisited. In 2015 International conference on 3D vision, pages 527-535. IEEE, 2015. 3 +[2] Haiwei Chen, Shichen Liu, Weikai Chen, Hao Li, and Randall Hill. Equivariant point network for 3d point cloud analysis. 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Existing works usually develop generic 4D learning tools without leveraging the prior that a 4D sequence comes from a single 3D scene with local dynamics. Based on this observation, we propose to learn region-wise coordinate frames that transform together with the underlying geometry. With such frames, we can factorize geometry and motion to facilitate a feature-space geometric reconstruction for more effective 4D learning. To learn such region frames, we develop a rotation equivariant network with a frame stabilization strategy. To leverage such frames for better spatial-temporal feature learning, we develop a frame-guided 4D learning scheme. Experiments show that this approach significantly outperforms previous state-of-the-art methods on a wide range of 4D understanding benchmarks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 476, + 124, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 124, + 488 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 124, + 488 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 496, + 279, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 496, + 279, + 578 + ], + "spans": [ + { + "bbox": [ + 45, + 496, + 279, + 578 + ], + "type": "text", + "content": "We have recently witnessed a surge of interest in understanding point cloud sequences in 4D (3D space + 1D time). As the direct sensory input in a large number of modern AI applications including robotics and AR/VR, point cloud sequences can faithfully depict the geometry and motion of a dynamic scene, and therefore become critical for an intelligent agent to perceive and interact with the physical world." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 578, + 279, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 578, + 279, + 648 + ], + "spans": [ + { + "bbox": [ + 45, + 578, + 279, + 648 + ], + "type": "text", + "content": "However, learning on such 4D data is very challenging and is still in an immature stage. 4D point cloud sequences usually couple 3D geometry and its dynamic motion together, resulting in quite redundant data in a very high dimensional space. This causes severe learning issues against an effective and compact spatial-temporal representation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 280, + 730 + ], + "type": "text", + "content": "Some existing efforts tackle the challenge through novel 4D backbone designs [8, 30, 7]. However, most of these works treat the point cloud sequence as unstructured 4D data and exploit generic 4D learning methods without leveraging the prior that the whole 4D sequence just depicts a single 3D scene with dynamic objects. As a result, such 4D learning is usually not super effective and the learned" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 299, + 241, + 530, + 380 + ], + "blocks": [ + { + "bbox": [ + 299, + 241, + 530, + 380 + ], + "lines": [ + { + "bbox": [ + 299, + 241, + 530, + 380 + ], + "spans": [ + { + "bbox": [ + 299, + 241, + 530, + 380 + ], + "type": "image", + "image_path": "a456efa32dba68f9a2a4bfd473caa3454ae1c977217f0c5575ca345c9cf944d4.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 380, + 531, + 446 + ], + "lines": [ + { + "bbox": [ + 296, + 380, + 531, + 446 + ], + "spans": [ + { + "bbox": [ + 296, + 380, + 531, + 446 + ], + "type": "text", + "content": "Figure 1. Frame-aware spatial-temporal convolution. We propose to learn frames for point cloud sequence. Upon obtaining the frames, we could easily align the geometry regardless of the underlying motion toward a more canonical and complete geometry understanding. The motion-agnostic geometric features also allow easier temporal association toward a better motion understanding." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 458, + 530, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 458, + 530, + 656 + ], + "spans": [ + { + "bbox": [ + 296, + 458, + 530, + 656 + ], + "type": "text", + "content": "spatial-temporal feature barely outperforms the spatial feature alone. Another line of works [7] uses self-supervised representation learning to encourage geometry and motion learning in a loosely decoupled manner. However, the decoupling still happens on the whole-scene level with a special focus on camera ego-motion, restricting their efficacy in modeling local dynamics on the object-level. We envision that successful geometry and motion decoupling is the key toward effective 4D representation learning. This essentially requires depicting the low-dimensional manifold of the dynamic scenes from the redundant high-dimensional 4D data. This highly correlates to dynamic scene reconstruction which requires understanding both camera ego-motion and object motion and is an ongoing research topic itself. Instead of explicitly reconstructing the dynamic scene without a quality guarantee, we seek a more lightweight and flexible solution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 660, + 530, + 730 + ], + "type": "text", + "content": "Our solution is based upon the following observation. For a specific region in the scene, we can understand its dynamic motion through establishing geometry-based and temporally-consistent local coordinate frames. Specifically, if we can establish a local coordinate frame based upon the 3D geometry in each timestamp and also make sure such" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "spans": [ + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "604" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 245 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 245 + ], + "type": "text", + "content": "frame transforms in the same way as the underlying geometry, then we can estimate the local rigid motion via comparing such frames among corresponding regions across timestamps. Such local frames allow us to factorize the local geometry understanding from its motion in a similar spirit to equivariant 3D analysis [22, 14]. In particular, once we establish temporally-consistent local coordinate frames, we essentially have a way to align the geometry regardless of the underlying motion toward a more canonical and complete geometry understanding. In addition, the motion-agnostic geometric features also allow easier temporal association toward a better motion understanding." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 248, + 280, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 248, + 280, + 608 + ], + "spans": [ + { + "bbox": [ + 45, + 248, + 280, + 608 + ], + "type": "text", + "content": "Based upon the above observations, we present a novel 4D learning framework named LeaF. LeaF contains a frame learning module and a frame-guided 4D learning module. The frame learning module aims at producing geometry-based temporally consistent coordinate frames at different scales so that corresponding regions across timestamps can be well-aligned. This allows for factorizing geometry learning from motion learning. And then the frame-guided 4D learning module leverages the learned frames to facilitate a more effective spatial-temporal feature aggregation. Specifically, in the frame learning module, we design a hierarchical FrameNet which is essentially a rotation-equivariant neural network able to produce coordinate frames equivariant to the rotation of input geometry. The frame learning process is very challenging though since apart from rotations different observations from a point cloud sequence can vary significantly due to sampling differences, density variation, or sensor noises. To make sure the rotation equivariance of hierarchical FrameNet is not broken in practice, we introduce a frame stabilization scheme to further regularize the frame learning process. In the frame-guided 4D learning module, we first modify popular 4D operators (e.g. 4D point conv) into their frame-guided version and then leverage frame-guided 4D convolution to process 4D point cloud sequences. Since the motion information is factorized away while convolving with the learned region frames, we additionally process the 4D sequences with just a globally constant camera frame so that the motion information is faithfully kept. We fuse the learned features both from using region frames and from using camera frames, allowing a very effective 4D feature learning." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "spans": [ + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "text", + "content": "To verify the effectiveness of LeaF, we conduct experiments on a wide range of 4D understanding tasks. And we demonstrate significant improvements over previous state-of-the-art methods " + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "inline_equation", + "content": "(+2.0\\%)" + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "text", + "content": " accuracy on HOI4D action segmentation [21], " + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "inline_equation", + "content": "+1.51\\%" + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "text", + "content": " accuracy on MSR action recognition [17], " + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "inline_equation", + "content": "+2.4\\%" + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "text", + "content": " mIoU on HOI4D indoor semantic segmentation [21], and " + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "inline_equation", + "content": "+1.81\\%" + }, + { + "bbox": [ + 45, + 611, + 279, + 704 + ], + "type": "text", + "content": " mIoU on Synthia4D outdoor semantic segmentation [25])." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "Our contributions are threefold: 1) we propose to learn effective spatial-temporal 4D features via learning and ex" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "text", + "content": "ploiting region-wise coordinate frames and our framework LeaF achieves state-of-the-art performance on a wide range of 4D understanding benchmarks; 2) we design a hierarchical FrameNet along with a frame stabilization scheme to learn equivariant region frames for motion-invariant geometry feature learning; 3) we present a frame-guided 4D learning method that is able to benefit from equivariant region frames without losing the motion information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 297, + 213, + 381, + 226 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 213, + 381, + 226 + ], + "spans": [ + { + "bbox": [ + 297, + 213, + 381, + 226 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 239, + 530, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 239, + 530, + 473 + ], + "spans": [ + { + "bbox": [ + 296, + 239, + 530, + 473 + ], + "type": "text", + "content": "4D point cloud sequence understanding. Compared with understanding static 3D point clouds, understanding 4D point cloud sequences requires more on aggregating and leveraging spatial-temporal information to perceive the geometry and dynamics. Several 4D backbones have been proposed to address such challenges, and they can be divided into two categories based on their representations. The first is to voxelize raw point clouds and extract features on 4D voxels, including MinkwoskiNet [3] which employs 4D spatial-temporal convolutions on 4D voxels. The second is to perform directly on raw points, including Meteor Net [19] which extends PointNet++[23] with a temporal dimension and explicitly tracks points' motion for grouping, and PSTNet[11] which constructs a point tube along temporal dimension for 4D point convolution. State of The Art methods such as Point 4d Transformer [9] and PPTr [30] belong to the second category and introduce transformer architecture, in order to avoid point-tracking and to better capture spatio-temporal correlation. There are works [7] focusing on improving the optimization of a transformer." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 479, + 530, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 479, + 530, + 689 + ], + "spans": [ + { + "bbox": [ + 296, + 479, + 530, + 689 + ], + "type": "text", + "content": "Equivariant feature learning. The seminal work of Group Equivariant Convolution Networks [4] (G-CNN) starts a trend of leveraging group equivariance for neural networks. For 3D data, rotation group equivariance or SO(3) equivariance is significant, and there are roughly two categories of SO(3) equivariant networks. The first category is the \"filter orbit\" method. Inspired by group-equivariant convolution on 2D images proposed in G-CNN [4], Equivariant Point Network [2] and successive works [16, 18, 32] discretizes SO(3) and analogously design group-equivariant operations on point clouds. However, as such networks extend the original features to multiple oriented features, they encounter memory issues and may not be suitable for 4D point cloud sequences understanding. The second category is the \"filter design\" method. These methods [28, 5, 14] design the filter forms to achieve exact SO(3) equivariance. \"Filter design\" methods get rid of memory issues, but their representation capability is usually limited due to the restricted filter form." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "type": "text", + "content": "Rotation-invariant local descriptors. Local descriptor is a synonym for local feature, which is widely used in tasks such as 3D point cloud matching. Some of the rotation-" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "605" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 102, + 103, + 480, + 348 + ], + "blocks": [ + { + "bbox": [ + 102, + 103, + 480, + 348 + ], + "lines": [ + { + "bbox": [ + 102, + 103, + 480, + 348 + ], + "spans": [ + { + "bbox": [ + 102, + 103, + 480, + 348 + ], + "type": "image", + "image_path": "e5f1fdf35f0bc84845deafc7be410da222a78c4f38035c56c985baaa17c652ac.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 351, + 530, + 417 + ], + "lines": [ + { + "bbox": [ + 45, + 351, + 530, + 417 + ], + "spans": [ + { + "bbox": [ + 45, + 351, + 530, + 417 + ], + "type": "text", + "content": "Figure 2. Illustration of the proposed Learning Frame for 4D Point Cloud Sequence Understanding (LeaF). We use an SO(3) equivariant network proposed in [22] to learn hierarchical frames denoted as region frames. We denote the identity frames as camera frames. Under region frames and camera frames, region frame feature and camera frame feature can be extracted by frame-aware 4D backbones, and are then fused by region frame-guided transformer to do downstream tasks such as action recognition, action segmentation, and semantic segmentation. Data augmentation and regularization losses are also added to make the equivariant Hierarchical frame network robust to re-sampling, down-sampling, and jittering." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 424, + 281, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 424, + 281, + 564 + ], + "spans": [ + { + "bbox": [ + 45, + 424, + 281, + 564 + ], + "type": "text", + "content": "invariant local descriptors first obtain rotation-equivariant local reference frames (LRFs) either via PCA methods [29, 13, 29, 31, 12, 15], or by incorporating learning methods to decide the axis in the tangent plane aside from normal [33], or completely by 3D rotation equivariant networks [22]. Under those LRFs, local support sets can be transformed into canonical representation, and thus invariant local features can be extracted either by hand-crafted method [29, 13, 29, 31] or by learning methods [12, 15]. Some other methods [27, 26, 1, 6] directly extract invariant local features from invariant local geometry property, e.g., the dot product of point pair normals." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 575, + 100, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 100, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 100, + 588 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 596, + 279, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 596, + 279, + 644 + ], + "spans": [ + { + "bbox": [ + 45, + 596, + 279, + 644 + ], + "type": "text", + "content": "We first provide an overview of our method in Section 3.1. Next, in Sections 3.2, 3.3 we describe our approach in detail in terms of how to learn hierarchical frames and how to use the learned frames, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 652, + 111, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 652, + 111, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 652, + 111, + 664 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": "Our core idea is to establish geometry-based and temporally-consistent local coordinate frames to factorize the local geometry understanding from its underlying motion. Such frames would allow us to align the local geometry from different timestamps toward a more complete geo" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 424, + 530, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 424, + 530, + 481 + ], + "spans": [ + { + "bbox": [ + 296, + 424, + 530, + 481 + ], + "type": "text", + "content": "metric understanding. Such geometric features are motion-agnostic, which also allows easier temporal association toward a better motion understanding. Realizing the idea above requires addressing two challenges: how to learn such frames and how to use such frames for 4D learning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 483, + 531, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 483, + 531, + 623 + ], + "spans": [ + { + "bbox": [ + 296, + 483, + 531, + 623 + ], + "type": "text", + "content": "Regarding the first challenge, we introduce a frame learning module as shown in Figure 2. Since geometric features are naturally hierarchical, the frames have to be hierarchical as well. We, therefore, propose to learn such frames through a hierarchical Frame Network. We leverage rotation equivariant networks [12] to design the FrameNet so that its output transforms in the same way as the underlying geometry. This network produces a hierarchy of frames covering regions from local to global. The global region frame allows factorizing ego-motion and aligning different observations to a unified view. The local region frame can align local geometry to a canonical space." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": "To stabilize the frame learning processing so that the FrameNet could learn temporally consistent region frames at different scales, we design a frame stabilization strategy. Given an input point cloud, we first apply data augmentation to obtain the augmented version of it. Then we feed both the original point cloud and the augmented one through the FrameNet and enforce their predictions to be consistent. Through various data augmentation strategies, we can keep the rotation equivariance of our predicted frames regardless" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "606" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 202, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 202, + 117 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 202, + 117 + ], + "type": "text", + "content": "of the time-dependent data corruptions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 118, + 279, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 118, + 279, + 327 + ], + "spans": [ + { + "bbox": [ + 45, + 118, + 279, + 327 + ], + "type": "text", + "content": "Regarding the second challenge of how to use the frames, we design a frame-guided 4D learning scheme as shown in Figure 2. Particularly, we design a frame-guided 4D convolution operator which can generate local and global features based on different frames at different scales. By cascading a series of frame-guided 4D convolution operators in a similar way to existing 4D backbones [9, 11], we can extract 4D features under the guidance of hierarchical frames. To keep the motion information from the 4D input, we leverage two frame-guided 4D convolution branches with shared weights. For one branch, the frames are just our learned region frames from the frame learning module. For the other branch, we use a constant camera frame across all timestamps and at all scales. The first branch focuses on motion-agnostic geometric feature learning while the second branch complements the motion cues. A region frame-guided transformer is designed to fuse the two branches for effective spatial-temporal features." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 328, + 279, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 328, + 279, + 374 + ], + "spans": [ + { + "bbox": [ + 45, + 328, + 279, + 374 + ], + "type": "text", + "content": "The designs above enable us to achieve various 4D point cloud understanding tasks effectively including 3D action segmentation, 3D action recognition, and 4D semantic segmentation for both indoor and outdoor scenarios." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 383, + 240, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 383, + 240, + 395 + ], + "spans": [ + { + "bbox": [ + 45, + 383, + 240, + 395 + ], + "type": "text", + "content": "3.2. Hierarchical Frame Learning Module" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 401, + 279, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 401, + 279, + 483 + ], + "spans": [ + { + "bbox": [ + 45, + 401, + 279, + 483 + ], + "type": "text", + "content": "In this section, we first revisit the concept of SO(3)-equivariance and SO(3)-invariance of 3D point cloud. Then we introduce the local-global frame learning pipeline with equivariant neural network in detail. Besides, in order to learn geometrically-stable and temporally-consistent local coordinate frames, we also introduce a frame stabilization scheme to regularize the frame learning process." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "spans": [ + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": "Revisit equivariance and invariance. Given a group " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " and a certain domain " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "\\mathbb{V}" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": ", a group action of " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "\\mathbb{V}" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " is a mapping from " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "G\\times \\mathbb{V}" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "\\mathbb{V}" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " (written as " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "g\\cdot v" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "g\\in G" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "v\\in \\mathbb{V}" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": "), where each " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " corresponds to a bijection on " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "\\mathbb{V}" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": ". A mapping " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "\\Phi :\\mathbb{X}\\to \\mathbb{Y}" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " is equivariant with respect to a group " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": " (and its group action on " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "\\mathbb{X},\\mathbb{Y}" + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "text", + "content": "), if for every " + }, + { + "bbox": [ + 45, + 488, + 279, + 559 + ], + "type": "inline_equation", + "content": "g\\in G,x\\in \\mathbb{X}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 120, + 570, + 279, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 570, + 279, + 583 + ], + "spans": [ + { + "bbox": [ + 120, + 570, + 279, + 583 + ], + "type": "interline_equation", + "content": "\\Phi (g \\cdot x) = g \\cdot \\Phi (x). \\tag {1}", + "image_path": "99cc97f5e912d5569351731fe8e4eb325f70295656efd1568338823658f02ca5.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "spans": [ + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": "Further, if the group action of " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "\\mathbb{Y}" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": " is trivial, (i.e., " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "g \\cdot y = y" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "g \\in G, y \\in \\mathbb{Y}" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": "), we say " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": " is invariant with respect to " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": ". For convenience, we also say " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "\\Phi(x)" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": " is equivariant or invariant if " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": " is equivariant or invariant." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": "For point clouds, let " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbb{X} = \\mathbb{R}^{n\\times 3}" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": " be the input domain, and " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbb{Y}" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": " be the output domain. Permutation, translation, and " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "SO(3)" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": " rotation equivariance are usually taken into consideration for point cloud networks. Consider a point cloud " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = (\\mathbf{x}_1,\\mathbf{x}_2,\\dots ,\\mathbf{x}_n)^T\\in \\mathbb{X}" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ". For the permutation group " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "S_{n}" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ", for some " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\sigma \\in S_n" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\sigma \\cdot \\mathbf{X} = (\\mathbf{x}_{\\sigma (1)},\\mathbf{x}_{\\sigma (2)},\\dots ,\\mathbf{x}_{\\sigma (n)})^T" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ". For the translation group " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^3" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ", for some " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{v}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{v}\\cdot \\mathbf{X} = (\\mathbf{x}_1 + \\mathbf{v},\\mathbf{x}_2 + \\mathbf{v},\\dots ,\\mathbf{x}_n + \\mathbf{v})^T" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ". For the rotation group " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "SO(3)" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 104, + 518, + 314 + ], + "blocks": [ + { + "bbox": [ + 310, + 104, + 518, + 314 + ], + "lines": [ + { + "bbox": [ + 310, + 104, + 518, + 314 + ], + "spans": [ + { + "bbox": [ + 310, + 104, + 518, + 314 + ], + "type": "image", + "image_path": "1c539144d47707d39729681c3f002667d82a084438589f7d1c245db2839701ab.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 316, + 530, + 359 + ], + "lines": [ + { + "bbox": [ + 296, + 316, + 530, + 359 + ], + "spans": [ + { + "bbox": [ + 296, + 316, + 530, + 359 + ], + "type": "text", + "content": "Figure 3. Illustration of hierarchical Frame Learning Module. Invariant features and equivariant features are extracted progressively by EquivLayer, and are then used to generate frames by FrameGen at each scale." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "spans": [ + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "type": "inline_equation", + "content": "g\\cdot \\mathbf{X} = (g\\cdot \\mathbf{x}_1,g\\cdot \\mathbf{x}_2,\\dots ,g\\cdot \\mathbf{x}_n)^T" + }, + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "type": "text", + "content": " , where each " + }, + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "type": "text", + "content": " corresponds to a rotation matrix " + }, + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "type": "inline_equation", + "content": "R\\in \\mathbb{R}^{3\\times 3}" + }, + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 367, + 530, + 391 + ], + "type": "inline_equation", + "content": "g\\cdot \\mathbf{x} = R\\mathbf{x}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 395, + 531, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 395, + 531, + 547 + ], + "spans": [ + { + "bbox": [ + 296, + 395, + 531, + 547 + ], + "type": "text", + "content": "Hierarchical frame learning. It is a challenging problem to learn geometry-based and temporally-consistent local coordinate frames to align the local region and factorize the underlying geometry feature from its motion. We need to construct hierarchical local region frames to accurately depict the orientations of local regions. And the established local coordinate frames should be based upon the 3D geometry in each timestamp and transform in the same way as the underlying geometry changes. To satisfy such requirements, we draw inspiration from the equivariant 3D point cloud analysis [22] and propose to use an equivariant network to learn the geometry-based rotation equivariant local coordinate frames " + }, + { + "bbox": [ + 296, + 395, + 531, + 547 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 296, + 395, + 531, + 547 + ], + "type": "text", + "content": " at different scales as shown in Figure 3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "spans": [ + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^l" + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": " denote the downsampled point cloud at layer " + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "inline_equation", + "content": "N^l" + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": " points. Let " + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "inline_equation", + "content": "H^l" + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^l" + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": " denote per-point invariant scalar features and equivariant vector features of " + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^l" + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": ", respectively. We use " + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^0, H^0, \\mathbf{V}^0" + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": " to denote the input point cloud, invariant scalar and equivariant vector features, where " + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "inline_equation", + "content": "H^0, \\mathbf{V}^0" + }, + { + "bbox": [ + 296, + 547, + 531, + 664 + ], + "type": "text", + "content": " are all zeros. And we pass the featured point cloud to a hierarchical equivariant network that aims to extract hierarchical invariant and equivariant features. Our EquivLayer is adapted from the GVP-GNN layer [14] and we defer the details to the supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 303, + 671, + 530, + 686 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 671, + 530, + 686 + ], + "spans": [ + { + "bbox": [ + 303, + 671, + 530, + 686 + ], + "type": "interline_equation", + "content": "\\left(\\mathbf {X} ^ {l + 1}, H ^ {l + 1}, \\mathbf {V} ^ {l + 1}\\right) \\leftarrow \\operatorname {E q u i v L a y e r} ^ {l + 1} \\left(\\mathbf {X} ^ {l}, H ^ {l}, \\mathbf {V} ^ {l}\\right). \\tag {2}", + "image_path": "2d9fc07d51dac5e50e897e5985c6e652dd5dcb1563cde5b5d6b37165940b3dea.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathrm{EquivLayer}^{l + 1}" + }, + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "type": "text", + "content": " is equivariant at all the layers, and the inputs " + }, + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "type": "inline_equation", + "content": "H^0,\\mathbf{V}^0" + }, + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "type": "text", + "content": " are invariant and equivariant features, the output " + }, + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "type": "inline_equation", + "content": "H^{l},\\mathbf{V}^{l}" + }, + { + "bbox": [ + 296, + 693, + 530, + 730 + ], + "type": "text", + "content": " of each layer are also invariant and equivari" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 746, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 746, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 746, + 296, + 756 + ], + "type": "text", + "content": "607" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 106, + 102, + 143 + ], + "blocks": [ + { + "bbox": [ + 59, + 106, + 102, + 143 + ], + "lines": [ + { + "bbox": [ + 59, + 106, + 102, + 143 + ], + "spans": [ + { + "bbox": [ + 59, + 106, + 102, + 143 + ], + "type": "image", + "image_path": "b1693772c6bc247b0780bb45cd9399d91f0f0abef6cc9d98b04a8989329bd0e8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 63, + 143, + 99, + 149 + ], + "lines": [ + { + "bbox": [ + 63, + 143, + 99, + 149 + ], + "spans": [ + { + "bbox": [ + 63, + 143, + 99, + 149 + ], + "type": "text", + "content": "Expected Frame" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 153, + 279, + 185 + ], + "lines": [ + { + "bbox": [ + 45, + 153, + 279, + 185 + ], + "spans": [ + { + "bbox": [ + 45, + 153, + 279, + 185 + ], + "type": "text", + "content": "Figure 4. The learned frames are sensitive to disruptions if not regularized, above are the frames' possible distortions resulting from the impact of sampling, density, and noise." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 110, + 106, + 158, + 143 + ], + "blocks": [ + { + "bbox": [ + 110, + 106, + 158, + 143 + ], + "lines": [ + { + "bbox": [ + 110, + 106, + 158, + 143 + ], + "spans": [ + { + "bbox": [ + 110, + 106, + 158, + 143 + ], + "type": "image", + "image_path": "47e81066027f97e60fa3f9bcfe6dba90622fadad33ddd4af23cb0c42c549e2af.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 143, + 157, + 149 + ], + "lines": [ + { + "bbox": [ + 107, + 143, + 157, + 149 + ], + "spans": [ + { + "bbox": [ + 107, + 143, + 157, + 149 + ], + "type": "text", + "content": "(a) Impact of Sampling" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 161, + 105, + 211, + 142 + ], + "blocks": [ + { + "bbox": [ + 161, + 105, + 211, + 142 + ], + "lines": [ + { + "bbox": [ + 161, + 105, + 211, + 142 + ], + "spans": [ + { + "bbox": [ + 161, + 105, + 211, + 142 + ], + "type": "image", + "image_path": "0a2275289cb137697f5ce0995d46dea4b192d6efe8b6719bde063a308fa9471f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 164, + 143, + 209, + 149 + ], + "lines": [ + { + "bbox": [ + 164, + 143, + 209, + 149 + ], + "spans": [ + { + "bbox": [ + 164, + 143, + 209, + 149 + ], + "type": "text", + "content": "(b) Impact of Density" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 214, + 106, + 266, + 142 + ], + "blocks": [ + { + "bbox": [ + 214, + 106, + 266, + 142 + ], + "lines": [ + { + "bbox": [ + 214, + 106, + 266, + 142 + ], + "spans": [ + { + "bbox": [ + 214, + 106, + 266, + 142 + ], + "type": "image", + "image_path": "1f2519934b42e55e72ab1322b167d34ee999d9e74f93f64738b47b5aac1365b2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 218, + 143, + 260, + 149 + ], + "lines": [ + { + "bbox": [ + 218, + 143, + 260, + 149 + ], + "spans": [ + { + "bbox": [ + 218, + 143, + 260, + 149 + ], + "type": "text", + "content": "(c) Impact of Noise" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 194, + 148, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 194, + 148, + 204 + ], + "spans": [ + { + "bbox": [ + 45, + 194, + 148, + 204 + ], + "type": "text", + "content": "ant features, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 206, + 279, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 206, + 279, + 252 + ], + "spans": [ + { + "bbox": [ + 45, + 206, + 279, + 252 + ], + "type": "text", + "content": "To obtain hierarchical frames from hierarchical invariant and equivariant features, we use another set of equivariant networks adapted from the GVP layers [14]. We use FrameGen to denote the network for the " + }, + { + "bbox": [ + 45, + 206, + 279, + 252 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 45, + 206, + 279, + 252 + ], + "type": "text", + "content": "-th layer." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 261, + 279, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 261, + 279, + 275 + ], + "spans": [ + { + "bbox": [ + 104, + 261, + 279, + 275 + ], + "type": "interline_equation", + "content": "\\mathbf {V} _ {\\text {o u t}} ^ {l} \\leftarrow \\operatorname {F r a m e G e n} ^ {l} \\left(H ^ {l}, \\mathbf {V} ^ {l}\\right), \\tag {3}", + "image_path": "aab291cf3c700c8dcefe40fd980b5aa3cd67ab162008750835bedd4230a1e8b2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "spans": [ + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "text", + "content": "where hierarchical frames will be constructed from " + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{\\mathrm{out}}^{l} = (\\mathbf{v}_{\\mathrm{out},1}^{l},\\dots ,\\mathbf{v}_{\\mathrm{out},N^{l}}^{l})(\\mathbf{v}_{\\mathrm{out},i}^{l}\\in \\mathbb{R}^{2\\times 3})" + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "text", + "content": " . We orthonormalize the two vectors " + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{\\mathrm{out},i,1}^{l},\\mathbf{v}_{\\mathrm{out},i,2}^{l}" + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "text", + "content": " for each point to get " + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{u}_{i,1}^{l},\\mathbf{u}_{i,2}^{l}" + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "text", + "content": " using the Gram-Schmidt method. Then we get the frame " + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "inline_equation", + "content": "F_{i}^{l} = \\left[\\mathbf{u}_{i,1}^{l},\\mathbf{u}_{i,2}^{l},\\mathbf{u}_{i,1}^{l}\\times \\mathbf{u}_{i,2}^{l}\\right]\\in \\mathbb{R}^{3\\times 3}(i = 1,\\dots ,N^{l})" + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "text", + "content": " Since " + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{\\mathrm{out}}^l" + }, + { + "bbox": [ + 45, + 286, + 279, + 372 + ], + "type": "text", + "content": " is rotation equivariant, the constructed frames are also rotation equivariant." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 373, + 279, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 373, + 279, + 394 + ], + "spans": [ + { + "bbox": [ + 45, + 373, + 279, + 394 + ], + "type": "text", + "content": "We refer to the whole module to generate hierarchical frames as FrameNet." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 45, + 400, + 279, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 400, + 279, + 481 + ], + "spans": [ + { + "bbox": [ + 45, + 400, + 279, + 481 + ], + "type": "text", + "content": "Frame stabilization schemes. Frame learning is not an easy task since the corresponding regions in different timestamps can vary significantly due to reasons beyond motion such as sampling variation. To make sure the rotation equivariance of FrameNet is not broken, we introduce a frame stabilization scheme to further regularize the frame learning process." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 45, + 483, + 279, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 483, + 279, + 657 + ], + "spans": [ + { + "bbox": [ + 45, + 483, + 279, + 657 + ], + "type": "text", + "content": "We expect the region frame of anchor points to represent the orientation of a local region regardless of how the anchor points are sampled. However, our FrameNet is point cloud-based and its prediction could vary dramatically as the anchor points in the region vary (Figure 4 (a)). Besides, the local region frame is also affected by the density of point clouds. When a local region is very sparse while the shape intensely deforms, the estimated region frame will also be extremely disrupted (Figure 4 (b)). The density of the same local region in different timestamps changes due to the egomotion and the occlusion variation or when the noise of the point cloud is very large (Figure 4 (c)). Such disruptions can break the temporal consistency of the region frame, and we expect FrameNet to be sampling, density, and noise invariant for stable and temporally-consistent region frames." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 45, + 657, + 279, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 657, + 279, + 692 + ], + "spans": [ + { + "bbox": [ + 45, + 657, + 279, + 692 + ], + "type": "text", + "content": "To achieve the goal above, we introduce several self-supervised losses to encourage the learned frame to be invariant under different point cloud augmentation strategies:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 95, + 702, + 279, + 731 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 702, + 279, + 731 + ], + "spans": [ + { + "bbox": [ + 95, + 702, + 279, + 731 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {a u g}} = \\sum_ {i} \\frac {\\operatorname {c o s i n e S i m} \\left(\\hat {F} _ {i} ^ {\\mathrm {a u g}} , F _ {i}\\right)}{N}, \\tag {4}", + "image_path": "ff6ddb66c334d6ad8d2bb805b1fcc3240241ae5adc6f58d934981873c390bcc2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": "where cosineSim means cosine similarity, " + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": " is the number of anchor points, " + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "inline_equation", + "content": "\\hat{F}^{\\mathrm{aug}}" + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": " is the frame of anchor points after augmentation, and " + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": " is the frame of original anchor points. Since the anchor points do not strictly match after the augmentation, we take the nearest neighbors of the original anchors in the augmented anchors as the corresponding points." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 176, + 530, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 176, + 530, + 211 + ], + "spans": [ + { + "bbox": [ + 296, + 176, + 530, + 211 + ], + "type": "text", + "content": "More specifically, we apply three types of augmentations including point cloud re-sampling, down-sampling, and jittering. Therefore, the final self-supervised loss is:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 219, + 530, + 233 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 530, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 530, + 233 + ], + "type": "interline_equation", + "content": "L _ {\\text {s t a b l i z e r}} = \\alpha L _ {\\text {r e - s a m p l i n g}} + \\beta L _ {\\text {d o w n - s a m p l i n g}} + \\gamma L _ {\\text {j i t t e r i n g}}, \\tag {5}", + "image_path": "7880f31c43731a41e0c3f08aa26df87e08fb9b6e34c776045ba455191d4b450d.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 297, + 240, + 483, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 240, + 483, + 252 + ], + "spans": [ + { + "bbox": [ + 297, + 240, + 483, + 252 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 297, + 240, + 483, + 252 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta, \\gamma" + }, + { + "bbox": [ + 297, + 240, + 483, + 252 + ], + "type": "text", + "content": " are balancing coefficients set as 1." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 297, + 259, + 481, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 259, + 481, + 271 + ], + "spans": [ + { + "bbox": [ + 297, + 259, + 481, + 271 + ], + "type": "text", + "content": "3.3. Frame-guided 4D Learning Module" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 277, + 530, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 277, + 530, + 370 + ], + "spans": [ + { + "bbox": [ + 296, + 277, + 530, + 370 + ], + "type": "text", + "content": "After obtaining the hierarchical region frames which are geometrically stable and temporally consistent, we can use these frames to factorize the region-wise geometry feature from its motion by aligning corresponding regions. Instead of explicitly aligning regions at all different scales, we modify popular 4D operators including point 4D convolution and point 4D transformer so that they could learn the geometry feature as if corresponding regions are aligned." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 296, + 374, + 530, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 374, + 530, + 501 + ], + "spans": [ + { + "bbox": [ + 296, + 374, + 530, + 501 + ], + "type": "text", + "content": "Frame-aware 4D operations. We first modify the point 4D convolution [9] into a frame-aware operator. Unlike the traditional point 4D convolution convolving directly between an anchor point and its spatiotemporal neighbor points, the frame-aware version first divides the neighbor points based on their timestamps, then picks up the nearest point from the anchor point in each division, aligns different divisions to the anchor point frame based upon the frames of the picked points, and finally conduct convolution in the aligned space. The frame-aware convolution layer can be mathematically described as:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 302, + 520, + 530, + 547 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 520, + 530, + 547 + ], + "spans": [ + { + "bbox": [ + 302, + 520, + 530, + 547 + ], + "type": "interline_equation", + "content": "f _ {i} ^ {l + 1} = \\sum_ {j \\in N (i)} M _ {1} ^ {l} \\left(F _ {i, t _ {j}} ^ {l \\top} \\left(x _ {j} - x _ {i}\\right), t _ {j} - t _ {i}\\right) \\odot M _ {2} ^ {l} \\left(f _ {j} ^ {l}\\right), \\tag {6}", + "image_path": "0b213f4eff2c0757fe168acd8de5838acb45182fb628e13a1ca92042dcb9416a.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "spans": [ + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "N(i)" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": " is the spatiotemporal neighbor of the anchor point " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": " is its coordinate and " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "f_i^l" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": " is its feature on the " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": "-th level. " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "F_{i,t}^{l}" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": "-th frame of the nearest neighbor of " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": " in timestamp " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "\\sum" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": " is aggregation implemented with sum-pooling or max-pooling, " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "M_1^l, M_2^l" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": " are MLP networks, and " + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 296, + 554, + 530, + 693 + ], + "type": "text", + "content": " is summation. The output feature can be seen as the representation under the region frames, and we denote such feature as \"region frame feature\". In particular, if we let the frames be identity matrices, this operation will be exactly the vanilla P4Dconv, and the output feature would be the representation under the original camera frame and we refer to it as \"camera frame feature\"." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": "We then modify the point 4D transformer [9] into a frame-aware version. Since the transformer operator usually follows the 4D convolution, we consider its input as" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "608" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "content": "a set of point tokens each equipped with a region frame as well as its feature within the frame. In this case, what we need to do is to make the positional embedding frame-aware so that the whole transformer is frame-aware. To be specific, we use " + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{global},t}" + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "content": " to represent the global frame at timestamp " + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "content": " and use " + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "inline_equation", + "content": "W_{p}" + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "content": " to represent a linear transformation. Then considering a point token with a spatiotemporal coordinate of " + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},t)" + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "content": ", its positional embedding can be written as " + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "inline_equation", + "content": "p = W_{p} \\cdot \\binom{F_{\\mathrm{global},t}^{\\intercal}\\mathbf{x}}{t}" + }, + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 223, + 280, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 223, + 280, + 282 + ], + "spans": [ + { + "bbox": [ + 45, + 223, + 280, + 282 + ], + "type": "text", + "content": "It is worth mentioning that the frame-aware method can be plug-and-play for many other operators, for example, we can also transform RS-CNN into a frame-aware RS-CNN to extract invariant features using hierarchical frames. Specifically, the frame-aware RS-CNN is [14]:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 287, + 279, + 310 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 287, + 279, + 310 + ], + "spans": [ + { + "bbox": [ + 69, + 287, + 279, + 310 + ], + "type": "interline_equation", + "content": "h _ {i} ^ {l + 1} \\leftarrow \\max _ {j \\in N (i)} \\left(M \\left(\\| F _ {i} ^ {l \\mathbf {T}} r _ {i j} \\|, F _ {i} ^ {l \\mathbf {T}} r _ {i j}\\right) \\odot h _ {j} ^ {l}\\right) \\tag {7}", + "image_path": "2be487bb30b32ed1309de9e69dc7400913e698b98acef01d7fe1a0451baf93c3.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "spans": [ + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": "where max denotes the max pooling operation, " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": " is an MLP network, " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": " denotes element-wise multiplication, " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "N(i)" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": " denotes the neighbors of point " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "r_{ij}" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": " denotes the relative coordinates between point " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": " denotes the features and " + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 45, + 317, + 279, + 375 + ], + "type": "text", + "content": " denotes the learned region frames." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 379, + 279, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 379, + 279, + 588 + ], + "spans": [ + { + "bbox": [ + 45, + 379, + 279, + 588 + ], + "type": "text", + "content": "Frame-guided feature learning. With the frame-aware 4D operation we can extract hierarchical region frame features, which are inherent representations of the underlying geometry but lacks the motion information. So such region frame features are not enough to fully encode the 4D spatiotemporal information. On the other hand, the camera frame feature computed under the camera coordinate frame faithfully retain the motion information and can be a good complement to the region frame features. We then propose to combine both features to obtain a more powerful and representative 4D feature. In particular, we design a two-tower framework to extract the region frame feature and camera frame feature. To fuse features from the two towers, we propose to use the region frame feature to guide the camera frame feature learning through an attention map which aligns the local region across different timestamps into a canonical space and allows easier temporal associations for better motion understanding, as shown in Figure 5." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "spans": [ + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": "To be specific, the queries and keys are generated from the region frame feature but the values are generated from the camera frame feature. We formulate the fusion process as a self-attention operation below:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 77, + 643, + 233, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 643, + 233, + 656 + ], + "spans": [ + { + "bbox": [ + 77, + 643, + 233, + 656 + ], + "type": "interline_equation", + "content": "Q _ {r} = W _ {q} f _ {r}, K _ {r} = W _ {k} f _ {r}, V _ {c} = W _ {v} f _ {c},", + "image_path": "1027fef465662aa72da183e23a39940c4619f57fb4ea50cdc5b09b8ad75a3d5a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 77, + 658, + 279, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 658, + 279, + 684 + ], + "spans": [ + { + "bbox": [ + 77, + 658, + 279, + 684 + ], + "type": "interline_equation", + "content": "\\operatorname {a t t e n t i o n} \\left(Q _ {r}, K _ {r}\\right) = \\operatorname {s o f t m a x} \\left(\\frac {Q _ {r} , K _ {r}}{\\sqrt {C _ {k}}}\\right), \\tag {8}", + "image_path": "3cc632346dea70bba83979aa1cb340c8a1666d137e25d8341c9e61a882110844.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 78, + 686, + 191, + 699 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 686, + 191, + 699 + ], + "spans": [ + { + "bbox": [ + 78, + 686, + 191, + 699 + ], + "type": "interline_equation", + "content": "O = V _ {c} \\cdot \\text {a t t e n t i o n} \\left(Q _ {r}, K _ {r}\\right),", + "image_path": "cd1cc6771d5a4623de4fee76f77b598aafd5bd8380fa92365b4175c38903f788.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "inline_equation", + "content": "f_{r}" + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": " is the region frame feature, " + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": " is the camera frame feature. The output " + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": " is the camera frame feature fused" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 103, + 518, + 288 + ], + "blocks": [ + { + "bbox": [ + 310, + 103, + 518, + 288 + ], + "lines": [ + { + "bbox": [ + 310, + 103, + 518, + 288 + ], + "spans": [ + { + "bbox": [ + 310, + 103, + 518, + 288 + ], + "type": "image", + "image_path": "e89feeecc9888320e359b2d479909549ea84b25601a381c4259b6c01100425aa.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 291, + 531, + 355 + ], + "lines": [ + { + "bbox": [ + 296, + 291, + 531, + 355 + ], + "spans": [ + { + "bbox": [ + 296, + 291, + 531, + 355 + ], + "type": "text", + "content": "Figure 5. An illustration of the region frame-guided transformer. The input is the feature of multiple timestamps, For each timestamp (take timestamp 1 for example), the attention scores are computed by the correlations between timestamp 1 and all the other timestamps, then the output of timestamp 1 is the weighted sum of values encoded from the camera frame feature." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 363, + 531, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 363, + 531, + 399 + ], + "spans": [ + { + "bbox": [ + 296, + 363, + 531, + 399 + ], + "type": "text", + "content": "under the guidance of the region frame feature. Then, we can add different task heads to complete various 4D point cloud sequence understanding tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 410, + 376, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 410, + 376, + 423 + ], + "spans": [ + { + "bbox": [ + 297, + 410, + 376, + 423 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 430, + 530, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 430, + 530, + 511 + ], + "spans": [ + { + "bbox": [ + 296, + 430, + 530, + 511 + ], + "type": "text", + "content": "In this section, we cover four 4D point cloud sequence understanding tasks: action segmentation on HOI4D [21], action recognition on MSR-action3D [17], indoor semantic segmentation on HOI4D [21], and outdoor semantic segmentation on Synthia4D [25], in Section 4.1, 4.2, 4.3 and 4.4 respectively. In addition, we provide extensive ablation studies to validate our design choices in Section 4.5." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 520, + 465, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 520, + 465, + 532 + ], + "spans": [ + { + "bbox": [ + 297, + 520, + 465, + 532 + ], + "type": "text", + "content": "4.1. Action Segmentation on HOI4D" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 543, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 543, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 543, + 531, + 730 + ], + "type": "text", + "content": "Setup. To demonstrate the effectiveness of our method, we first conducted experiments on the HOI4D action segmentation task. For each point cloud sequence, we need to predict the action labels for each timestamp. We followed the official data split with 2971 sequences as the training set and 892 as the test set. Each sequence has 150 timestamps with 2048 points per timestamp. We use PPTr, an improved variant of the P4Transformer, as our backbone, which leverages two hierarchical transformers to process point cloud sequences and supports appending invariant features as additional inputs. We compare our method with baseline methods including P4Transformer and original PPTr. In this experiment, we use a two-scale FrameNet to learn 128 local frames and one global frame. We use frame-aware 4DConv to extract the invariant feature. The following metrics are reported: framewise accuracy (Acc), segmental edit" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "609" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 113, + 279, + 172 + ], + "blocks": [ + { + "bbox": [ + 77, + 103, + 248, + 113 + ], + "lines": [ + { + "bbox": [ + 77, + 103, + 248, + 113 + ], + "spans": [ + { + "bbox": [ + 77, + 103, + 248, + 113 + ], + "type": "text", + "content": "Table 1. Action segmentation on HOI4D dataset" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 113, + 279, + 172 + ], + "lines": [ + { + "bbox": [ + 47, + 113, + 279, + 172 + ], + "spans": [ + { + "bbox": [ + 47, + 113, + 279, + 172 + ], + "type": "table", + "html": "
MethodClip LengthAccEditF1@10F1@25F1@50
P4Transformer [8]15071.273.173.869.258.2
PPTr [30]15077.480.181.778.569.5
PPTr+Ours15079.4+2.0↑83.9+3.8↑85.0+3.3↑81.9+3.4↑73.3+3.8↑
", + "image_path": "608fbb146e96383055b319aaf9e2ed3ce824e2746b1eaca34e519fc181284072.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "spans": [ + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "type": "text", + "content": "distance, as well as segmental F1 scores at the overlapping thresholds of " + }, + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 45, + 176, + 279, + 212 + ], + "type": "text", + "content": ". Overlapping thresholds are determined by the IoU ratio." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 217, + 279, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 217, + 279, + 334 + ], + "spans": [ + { + "bbox": [ + 45, + 217, + 279, + 334 + ], + "type": "text", + "content": "Result. As reported in Table 1, our method consistently has big improvements over previous state-of-the-art method in all metrics. This demonstrates that the region frame feature can significantly improve the communication of point clouds at different timestamps, to extract a more effective spatiotemporal representation. By introducing the region frame features for 4D point cloud sequence, we can factorize the local geometry understanding from its motion so that the network can have a better understanding of geometry and motion respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 242, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 242, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 242, + 354 + ], + "type": "text", + "content": "4.2. Action Recognition on MSR-Action3D" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 365, + 279, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 365, + 279, + 516 + ], + "spans": [ + { + "bbox": [ + 45, + 365, + 279, + 516 + ], + "type": "text", + "content": "Setup. Following P4Transformer and PPTr, we used the MAR-Action3D dataset, which consists of 567 human point cloud sequences, including 20 action categories. Each timestamp is sampled with 2,048 points. The point cloud sequences are segmented into multiple segments. During training, video-level labels are used as segment-level labels. As in action segmentation, we use PPTr as the base network. A two-layer FrameNet is used to extract local and global frames. And a frame-aware 4DConv is used to extract invariant features. To ensure a fair comparison, we also use primitive fitting to divide each human point cloud into four regions. To estimate the sequence-level probabilities, we take the mean of all segment-level probability predictions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 522, + 279, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 522, + 279, + 627 + ], + "spans": [ + { + "bbox": [ + 45, + 522, + 279, + 627 + ], + "type": "text", + "content": "Result. As reported in Table 2, our method also outperforms previous methods in 3D action recognition tasks. We find that when the clip length is 8, the improvement of our method is 0.48, while the improvement of our method is 1.51 when clip length is 24. This indicates that our method performs better in longer sequences. This also demonstrates that the proposed region frame feature can factorize geometry learning from motion learning and achieve better temporal correlation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 636, + 258, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 258, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 258, + 648 + ], + "type": "text", + "content": "4.3. Indoor Semantic Segmentation on HOI4D" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "Setup. To verify that our approach can be effective for fine-grained tasks as well, we conducted further experiments on HOI4D for 4D semantic segmentation. The dataset consists of 3863 4D sequences, each including 300 timestamps of point clouds, for a total of 1.158M timestamps of point clouds. For one timestamp, there are 8192" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 332, + 114, + 493, + 289 + ], + "blocks": [ + { + "bbox": [ + 298, + 103, + 508, + 114 + ], + "lines": [ + { + "bbox": [ + 298, + 103, + 508, + 114 + ], + "spans": [ + { + "bbox": [ + 298, + 103, + 508, + 114 + ], + "type": "text", + "content": "Table 2. Action recognition on MSR-Action3D dataset [17]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 332, + 114, + 493, + 289 + ], + "lines": [ + { + "bbox": [ + 332, + 114, + 493, + 289 + ], + "spans": [ + { + "bbox": [ + 332, + 114, + 493, + 289 + ], + "type": "table", + "html": "
MethodInputClip LengthVideo Acc@1
PointNet++ [24]point161.61
MeteorNet [20]point881.14
point1688.21
point2488.50
PSTNet [10]point883.50
point1689.90
point2491.20
P4Transformer [9]point883.17
point1689.56
point2490.94
PPT [30]point884.02
point1690.31
point2492.33
PPTr+Ourspoint884.50+0.48↑
point1691.50+1.19↑
point2493.84+1.51↑
", + "image_path": "8a8fd18dc2faa201287e297c544d8ea4eece1e31a33ef1c534a95b47618f0e00.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 298, + 305, + 530, + 362 + ], + "blocks": [ + { + "bbox": [ + 315, + 295, + 511, + 305 + ], + "lines": [ + { + "bbox": [ + 315, + 295, + 511, + 305 + ], + "spans": [ + { + "bbox": [ + 315, + 295, + 511, + 305 + ], + "type": "text", + "content": "Table 3. Semantic segmentation on HOI4D dataset [21]" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 298, + 305, + 530, + 362 + ], + "lines": [ + { + "bbox": [ + 298, + 305, + 530, + 362 + ], + "spans": [ + { + "bbox": [ + 298, + 305, + 530, + 362 + ], + "type": "table", + "html": "
MethodClip LengthmIoU
P4Transformer [8]340.1
PPTr [30]341.0
P4T+Ours343.5+2.4↑
", + "image_path": "44810e7519c1e0799795a1fbfabe14739f1421a5c226fdf907268190a795a216.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 364, + 530, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 364, + 530, + 504 + ], + "spans": [ + { + "bbox": [ + 296, + 364, + 530, + 504 + ], + "type": "text", + "content": "points. We follow the official data segmentation of HOI4D with 2971 training scenes and 892 test scenes. In this task, to avoid the complicated primitive fitting process, we choose P4Transformer as the base network. A three-scale FrameNet is used to learn three scales of the frames, respectively 512 and 128 local region frames as well as the global frame. In the semantic segmentation tasks, we all use a frame-aware RS-CNN to demonstrate that the framework method can be plug-and-play for other operators. Accordingly, we use a three-scale RS-CNN to extract \"region frame\" features. We use mean IoU(mIoU) % over 39 categories as an evaluation metric." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 508, + 530, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 508, + 530, + 579 + ], + "spans": [ + { + "bbox": [ + 296, + 508, + 530, + 579 + ], + "type": "text", + "content": "Result. The results are shown in Table 3. We can observe that we improve the performance by a large margin compared with previous methods. Even without a primitive fitting process, our method still outperforms PPTr by " + }, + { + "bbox": [ + 296, + 508, + 530, + 579 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 296, + 508, + 530, + 579 + ], + "type": "text", + "content": ", which demonstrates that our local region feature is also helpful in the fine-grained 4D understanding task." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 586, + 530, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 586, + 530, + 597 + ], + "spans": [ + { + "bbox": [ + 297, + 586, + 530, + 597 + ], + "type": "text", + "content": "4.4. Outdoor Semantic Segmentation on Synthia4D" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 608, + 530, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 608, + 530, + 712 + ], + "spans": [ + { + "bbox": [ + 296, + 608, + 530, + 712 + ], + "type": "text", + "content": "Setup. Synthia 4D is a synthetic dataset generated from Synthia dataset. It consists of six sequences of driving scenarios where both objects and cameras are moving. Following previous works, we use the same training/validation/test split, with 19,888/815/1,886 timestamps, respectively. We use P4Transformer as the base network, and other settings are the same as the experiments on semantic segmentation on HOI4D. The mean Intersection over Union (mIoU) is used as the evaluation metric." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 718, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 718, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 297, + 718, + 530, + 730 + ], + "type": "text", + "content": "Result. As shown in Table 4, there is still a per" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "610" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 46, + 117, + 292, + 223 + ], + "blocks": [ + { + "bbox": [ + 46, + 103, + 263, + 114 + ], + "lines": [ + { + "bbox": [ + 46, + 103, + 263, + 114 + ], + "spans": [ + { + "bbox": [ + 46, + 103, + 263, + 114 + ], + "type": "text", + "content": "Table 4. Evaluation for semantic segmentation on Synthia 4D" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 46, + 117, + 292, + 223 + ], + "lines": [ + { + "bbox": [ + 46, + 117, + 292, + 223 + ], + "spans": [ + { + "bbox": [ + 46, + 117, + 292, + 223 + ], + "type": "table", + "html": "
MethodClip LengthBldnRoadSdwkFenceVegittPoleCarT. SignPedstmBicyclLaneT.LightmloU
3D MinkNet14189.3997.6869.4386.5298.1197.2693.5079.4592.270.0044.6166.6976.24
4D MinkNet14390.1398.2673.4787.1999.1097.5094.0179.0492.620.0050.0168.1477.24
PointNet++196.8897.7286.2092.7597.1297.0990.8566.8778.640.0072.9375.1779.35
MeteorNet-m298.2297.7990.9893.1898.3197.4594.3076.3581.050.0074.0975.9281.47
MeteorNet-1398.1097.7288.6594.0097.9897.6593.8384.0780.900.0071.1477.6081.80
P4Transformer196.7698.2392.1195.2398.6297.7795.4680.7585.480.0074.2874.2282.41
P4Transformer396.7398.3594.0395.2398.2898.0195.6081.5485.180.0075.9579.0783.16
PPTr197.1498.4294.1297.0099.5997.8698.5479.6889.200.0077.2677.4283.85
PPTr397.5198.2195.1196.8199.6597.8698.0180.9890.600.0078.2176.8984.15
PPTr3098.0198.6395.2697.0399.7097.9598.7681.9991.200.0078.2977.0984.49
P4T+Ours398.2298.8997.9796.8599.6097.9099.0082.7391.500.0078.0378.9284.97+1.81↑
", + "image_path": "304b58f664816f43c41235013ebc75568878583a91300fe7b4b59e0f073fd2e4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 233, + 279, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 233, + 279, + 349 + ], + "spans": [ + { + "bbox": [ + 45, + 233, + 279, + 349 + ], + "type": "text", + "content": "formance improvement, which also shows the effectiveness of our approach for outdoor 4D semantic segmentation tasks. It is worth mentioning that our network is based on P4Transformer, so a fair comparison is between P4Transformer with 3 timestamps and our method with 3 timestamps. The mIoU going from " + }, + { + "bbox": [ + 45, + 233, + 279, + 349 + ], + "type": "inline_equation", + "content": "83.16\\%" + }, + { + "bbox": [ + 45, + 233, + 279, + 349 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 233, + 279, + 349 + ], + "type": "inline_equation", + "content": "84.97\\% (+1.81\\%)" + }, + { + "bbox": [ + 45, + 233, + 279, + 349 + ], + "type": "text", + "content": " demonstrates the effectiveness of our method. Moreover, our method associates 3 point clouds by region frame feature, which is even better than PPTr's method of using 30 sequential point clouds." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 357, + 178, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 357, + 178, + 369 + ], + "spans": [ + { + "bbox": [ + 45, + 357, + 178, + 369 + ], + "type": "text", + "content": "4.5. Ablation and Discussion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 380, + 279, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 380, + 279, + 521 + ], + "spans": [ + { + "bbox": [ + 45, + 380, + 279, + 521 + ], + "type": "text", + "content": "Efficacy of frame stabilization schemes. The frame learning process is challenging due to sampling differences, density variation, or sensor noises. To make sure the rotation equivariance of MS-FrameNet is not broken, we introduce a frame stabilization scheme to regularize the frame learning process. We run ablation studies with and without frame stabilization schemes to quantify their efficacy. We find that learning region frames without frame stabilization schemes results in a " + }, + { + "bbox": [ + 45, + 380, + 279, + 521 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 45, + 380, + 279, + 521 + ], + "type": "text", + "content": " accuracy and " + }, + { + "bbox": [ + 45, + 380, + 279, + 521 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 45, + 380, + 279, + 521 + ], + "type": "text", + "content": " segmental edit distance drop on the HOI4D action segmentation task. This result proves that our frame stabilization schemes play an important role in learning high-quality region frames." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 526, + 279, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 526, + 279, + 666 + ], + "spans": [ + { + "bbox": [ + 45, + 526, + 279, + 666 + ], + "type": "text", + "content": "Learning frames vs. non-learning frames. In the frame learning module, we design an MS-FrameNet which is essentially a rotation-equivariant neural network able to produce region frames equivariant to the rotation of input geometry. To demonstrate the advantages of learning frames, we compare our method with PCA which is a non-learning method to obtain local reference frames(LRFs). When replacing our frame-learning module with PCA frames, the best result we can get is " + }, + { + "bbox": [ + 45, + 526, + 279, + 666 + ], + "type": "inline_equation", + "content": "78.3\\%" + }, + { + "bbox": [ + 45, + 526, + 279, + 666 + ], + "type": "text", + "content": " accuracy on HOI4D action segmentation task, which is " + }, + { + "bbox": [ + 45, + 526, + 279, + 666 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 45, + 526, + 279, + 666 + ], + "type": "text", + "content": " lower than our method. This experiment confirms the value of learning frames compared with the non-learning method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 671, + 279, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 717 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 717 + ], + "type": "text", + "content": "Compared with random frames and identity frames. To further examine the value of the frame learning process, we conduct another two experiments that frame-guided 4D learning with random frames and identity frames." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 57, + 718, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 718, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 718, + 279, + 730 + ], + "type": "text", + "content": "With random frames, we can only achieve " + }, + { + "bbox": [ + 57, + 718, + 279, + 730 + ], + "type": "inline_equation", + "content": "78.0\\%" + }, + { + "bbox": [ + 57, + 718, + 279, + 730 + ], + "type": "text", + "content": " accu" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "text", + "content": "racy on HOI4D action segmentation which is " + }, + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "text", + "content": " lower than our method. This demonstrates that random frames are not friendly for cross-time association and temporally consistent frames are important for frame-guided learning. With identity frames, the best result we can get is " + }, + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "inline_equation", + "content": "76.3\\%" + }, + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "text", + "content": " which is even " + }, + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 296, + 106, + 530, + 200 + ], + "type": "text", + "content": " lower than PPTr without frame learning, showing that the improvement is not brought about by a simple ensemble strategy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 207, + 530, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 207, + 530, + 347 + ], + "spans": [ + { + "bbox": [ + 296, + 207, + 530, + 347 + ], + "type": "text", + "content": "Action segmentation with large motion. To better verify that the motion-agnostic geometric features allow easier temporal association toward a better motion understanding, we conduct experiments on HOI4D action segmentation tasks with large motion. We only select the sequences where the maximum distance of the object movement exceeds " + }, + { + "bbox": [ + 296, + 207, + 530, + 347 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{m}" + }, + { + "bbox": [ + 296, + 207, + 530, + 347 + ], + "type": "text", + "content": " to construct a subset of HOI4D with 900 training scenes and 300 test scenes. Without learning frames, PPTr can get 29.22 accuracy on action segmentation, while our method can achieve " + }, + { + "bbox": [ + 296, + 207, + 530, + 347 + ], + "type": "inline_equation", + "content": "36.39\\%" + }, + { + "bbox": [ + 296, + 207, + 530, + 347 + ], + "type": "text", + "content": " accuracy. This result proves that our method has a stronger ability to deal with point cloud sequences with large motion." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 355, + 530, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 355, + 530, + 471 + ], + "spans": [ + { + "bbox": [ + 296, + 355, + 530, + 471 + ], + "type": "text", + "content": "The efficiency comparison. Our method does not introduce a significant increase in computational overhead. The 4D backbone requires much heavier computation compared with the lightweight FrameNet. So as shown in Table 5, introducing FrameNet in Frame-aware P4DConv does not significantly increase FLOPs or parameters compared with P4DConv. Worth to mention, since our method relies on both the invariant and non-invariant feature branches, the overall computational overhead is roughly twice that of a single branch P4DConv." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 312, + 514, + 514, + 573 + ], + "blocks": [ + { + "bbox": [ + 296, + 482, + 530, + 514 + ], + "lines": [ + { + "bbox": [ + 296, + 482, + 530, + 514 + ], + "spans": [ + { + "bbox": [ + 296, + 482, + 530, + 514 + ], + "type": "text", + "content": "Table 5. LeaF does not introduce a significant increase in computational overhead. All tests were conducted on a single NVIDIA GeForce RTX 3090 graphics card, with a batch size of 1." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 514, + 514, + 573 + ], + "lines": [ + { + "bbox": [ + 312, + 514, + 514, + 573 + ], + "spans": [ + { + "bbox": [ + 312, + 514, + 514, + 573 + ], + "type": "table", + "html": "
MethodFLOPsParameters
P4DConv7.550G8.192K
Frame-aware P4DConv8.428G8.314k
Only FrameNet878.2M122.0B
", + "image_path": "5908c04979bfc0bba562cf313a91af6abf6264b11594e26fa933bd63b25b1074.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 602, + 373, + 614 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 602, + 373, + 614 + ], + "spans": [ + { + "bbox": [ + 297, + 602, + 373, + 614 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": "This paper proposes to use SO(3) equivariant networks to learn orientations for 4D point cloud videos and to obtain inherent features of the point clouds. The core idea is that the inherent features are motion-independent and this feature can be better correlated between contexts. We also propose three constraint terms to guide the learning of frame in order to obtain stable and consistent point cloud orientations. 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Sensors, 20(18):5086, 2020. 3" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "spans": [ + { + "bbox": [ + 281, + 747, + 296, + 756 + ], + "type": "text", + "content": "613" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Leaping Into Memories_ Space-Time Deep Feature Synthesis/5ad3f2c3-b163-4339-b33a-6f2219ed23a6_content_list.json b/2023/Leaping Into Memories_ Space-Time Deep Feature Synthesis/5ad3f2c3-b163-4339-b33a-6f2219ed23a6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d7684ac2d8198397f08656129d52a5567dd6f1dd --- /dev/null +++ b/2023/Leaping Into Memories_ Space-Time Deep Feature Synthesis/5ad3f2c3-b163-4339-b33a-6f2219ed23a6_content_list.json @@ -0,0 +1,1533 @@ +[ + { + "type": "text", + "text": "Leaping Into Memories: Space-Time Deep Feature Synthesis", + "text_level": 1, + "bbox": [ + 178, + 130, + 792, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Alexandros Stergiou Nikos Deligiannis", + "bbox": [ + 305, + 181, + 661, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vrije Universiteit Brussel, Belgium & imec, Belgium", + "bbox": [ + 274, + 199, + 694, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": ".@vub.be", + "bbox": [ + 388, + 219, + 580, + 232 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9b6e4b76a31a2fc6aaa7cbc3ff4594a4b97a21c0e08978254f0f917d284b0f36.jpg", + "image_caption": [ + "Figure 1: Illustration of our proposed LEAPS model inversion. Given a video input $\\mathbf{x}^*$ initialized with noise, we use a stimulus video $\\mathbf{v}$ of target class $y$ , to prime video model $\\Phi(\\cdot)$ . We iteratively optimize $\\mathbf{x}^*$ to synthesize and visually represent the internal spatiotemporal features of $\\Phi(\\cdot)$ . To impose diversity over the synthesized videos, feature statistics from a domain-specific verifier network $S(\\cdot)$ are distilled to regularize $\\mathbf{x}^*$ . To preserve the continuity of motions across frames, $\\mathbf{x}^*$ is temporally regularized at each training iteration. Although the illustration visualizes internal representations as $C \\times T \\times H \\times W$ volumes, they can also be flattened patches $CP^3 \\times \\frac{THW}{P^3}$ of $P^3$ resolution as in Vision Transformers." + ], + "image_footnote": [], + "bbox": [ + 98, + 250, + 869, + 453 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 566, + 313, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of deep learning models has led to their adaptation and adoption by prominent video understanding methods. The majority of these approaches encode features in a joint space-time modality for which the inner workings and learned representations are difficult to visually interpret. We propose LEArned Preconscious Synthesis (LEAPS), an architecture-independent method for synthesizing videos from the internal spatiotemporal representations of models. Using a stimulus video and a target class, we prime a fixed space-time model and iteratively optimize a video initialized with random noise. Additional regularizers are used to improve the feature diversity of the synthesized videos alongside the cross-frame temporal coherence of motions. We quantitatively and qualitatively evaluate the applicability of LEAPS by inverting a range of spatiotemporal convolutional and attention-based architectures trained on Kinetics-400, which to the best of our knowledge has not been previously accomplished.", + "bbox": [ + 75, + 585, + 472, + 857 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 566, + 630, + 583 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inverting deep networks' learned internal representations has been a difficult task to achieve. The adaptation and deployment of CNNs and more recently Transformers, to a variety of vision tasks has led to significant breakthroughs. The field of video action recognition has experienced drastic growth in recent years through the convergence of models with increased complexities and capacities [2, 4, 32, 63] as well as large accuracy improvements [11, 12, 27, 26, 29]. Despite great progress in their applicability, there is still a large gap in the interpretability of video models. As these models compositionally encode space and time modalities of videos over large feature spaces and require a lot of parameters, conceptualizing their internal representations remains challenging. In this paper, we propose a method to invert learned features of video models associated with specific actions by optimizing a parameterized input to synthesize conceptually and visually coherent representations.", + "bbox": [ + 496, + 595, + 890, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In cognitive science, stages of consciousness include the conscious, the unconscious, and the preconscious. In contrast to the conscious and unconscious, the preconscious is", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "See alexandrosstergiou/LEAPS for video examples and code.", + "bbox": [ + 94, + 886, + 424, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1966", + "bbox": [ + 483, + 925, + 514, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "responsible for learned information currently outside conscious awareness to remain readily available [18]. One way of accessing learned preconscious information and making it part of conscious awareness is through priming [38]. Priming uses a stimulus to activate related learned concepts in memory and make them easily and readily accessible [33, 34]; e.g., one can remember their bedroom if primed with a picture of a bed.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by visual priming in cognitive science, we demonstrate that learned representations of video models can become accessible through model priming. By using a video stimulus and a target action class, we synthesize the dominant learned concepts corresponding to actions. In turn, the visual features of the synthesized videos provide a conceptual view of the models' learned internal representations. We term these features as the learned preconscious of the video model associated with a specific action.", + "bbox": [ + 75, + 212, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce LEArned Preconscious Synthesis (LEAPS), illustrated in Figure 1, a spatiotemporal model inversion method that synthesizes interpretable videos by minimizing a classification and priming loss without prior knowledge of the training data. LEAPS uses a video of a target action class as stimulus, to prime a fixed spatiotemporal model. We additionally include two regularization terms. The first term enforces motion coherence across frames by constraining their representations at each update. The second enhances the diversity of the synthesized videos by using a domain-specific verifier network that exploits disagreements between feature statistics similar to [64]. Through the same architecture-independent approach, we show that LEAPS can invert the spatiotemporal features of 3D-CNNs and spatiotemporal Transformers.", + "bbox": [ + 75, + 347, + 472, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are as follows. First, we introduce LEAPS, a general approach for inverting video models, which to the best of our knowledge, is the first attempt to create videos of conceptual representations from jointly encoded space-time features. Second, we use LEAPS on multiple convolution and attention models and compare it to prior image-based inversion methods that we extend to video. Finally, we show that LEAPS can invert both video CNNs and transformers, with the same architecture-independent method without any modifications.", + "bbox": [ + 75, + 575, + 472, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 739, + 218, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Approaches for visualizing and interpreting deep models can be divided into three groups which we detail below.", + "bbox": [ + 75, + 763, + 468, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attribution-based visualizations. These methods have been used to visualize feature contributions over an input. Attribution methods for images have primarily been based on back-propagating activations of classes [8, 48, 61], or individual neurons [3, 5, 49, 52] to localize regions in the input that are informative for a given class or feature. Such approaches include Integrated gradients (IG) [56] which", + "bbox": [ + 75, + 795, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "produce pixel-wise attributions from integrating computed backprop gradients. Subsequent works have also included gradient smoothing [51], gradient accumulation in saturated regions [35], and adaptation of the gradient path [23]. Another set of approaches that rely on attribution-based visualizations use perturbations of the input [17, 16, 44]. Given their straightforward applicability, image attribution methods have also been extended to video. The majority of works; e.g., Saliency Tubes [55, 54], STEP [28], video OSA [59], and BOREx [24], have focused on the localization of spatiotemporal salient regions by extending GradCAM [48], Extremal Perturbations (EP) [16], Occlusion Sensitivity Analysis (OSA) [66], and Gaussian processes regression (GPR) [6, 37] respectively. In contrast to these approaches that localize salient class features, we offer a visual feature synthesis method to conceptualize the learned representations of video models through priming.", + "bbox": [ + 496, + 90, + 893, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Input synthesis. Network-centric approaches invert models to either visualize particular classes [41, 65, 64] or features [43, 53]. One of the main methods employed for visualizing internal network features is Gradient Ascent (GA) [10], which optimizes the input by increasing the activation of a specific neuron. Activation Maximization (AM) [50] later adapted GA to visualize CNN features. Following works have been built on top of AM by including additional regularizers; e.g., total variation [31], blurring [60], and gradient masking [41]. One of the most popular extensions of AM has been DeepDream [1] which optimizes the input to yield high responses for a chosen class while keeping internal representations constraint-free. The produced images include repetitions of recognizable concepts without representing a coherent whole. In addition to AM, model inversion [9, 19, 30, 64, 66] includes the task of maximizing the classification score of the synthesized image instead of maximizing class activations. The only extension of input synthesis approaches to videos has been introduced by Feichtenhofer et al. [13] in which AM is used to create visual representations of class features from two-steam models [14, 62], trained on RGB frames (spatial stream) and optical flow (temporal stream). In this paper, we instead propose a model inversion method for inverting video models concurrently encoding space and time modalities.", + "bbox": [ + 496, + 352, + 893, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual feature generation. These methods utilize activation maximization by including an additional generator network [39, 40, 42], with the cost of requiring access to the training data. Huang et al. [21] adapted feature generation on video data by modeling the temporal signal with a temporal generator network. Despite the high fidelity of the produced results, these approaches are less suitable for interpreting internal model behaviors, as they do not solely depend on the model under inspection. Instead, they are primarily influenced by the training data used as well as the capacity and complexity of the generator model trained.", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1967", + "bbox": [ + 483, + 924, + 514, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Learned Preconscious Synthesis", + "text_level": 1, + "bbox": [ + 76, + 89, + 369, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we overview our LEAPS method, shown in Figure 1. We start by formally introducing model priming for video models in Section 3.1. A stimulus video of a target class is used to initially prime the network. The training process uses the primed representations to update a randomly initialized input alongside two regularizers. The first regularizer is used to enforce temporal coherence, explained in Section 3.2. The second is used to improve synthesized feature diversity, overviewed in Section 3.3. We present the final aggregated function in Section 3.4.", + "bbox": [ + 75, + 114, + 470, + 267 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Model Priming", + "text_level": 1, + "bbox": [ + 76, + 276, + 230, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Priming deep models is influenced by cognitive science [38] in which a stimulus is used to recall prior knowledge. We extend this approach to visualizing the learned preconscious of deep video models associated with a specific action class $y$ . Given a video $\\mathbf{v}$ of size $C\\times T\\times H\\times W$ , with $C$ channels, $T$ frames, $H$ height, and $W$ width, as a visual cue for action class $y$ , and a randomly initialized input $\\mathbf{x}^*$ of $C\\times T\\times H\\times W$ size to optimize. We define a priming loss $\\mathcal{L}_{prim}(\\mathbf{x}^*,\\mathbf{v})$ between the internal representations $\\mathbf{z}^l (\\cdot)$ of the optimized input $\\mathbf{x}^*$ and stimulus $\\mathbf{v}$ across $l\\in \\Lambda = \\{1,\\dots,L\\}$ layers:", + "bbox": [ + 75, + 299, + 470, + 474 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p r i m} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}\\right) = \\frac {1}{L} \\sum_ {l \\in \\boldsymbol {\\Lambda}} \\lambda_ {l} J V S \\left(\\mu \\left(\\mathbf {z} ^ {l} \\left(\\mathbf {x} ^ {*}\\right)\\right), \\mu \\left(\\mathbf {z} ^ {l} (\\mathbf {v})\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 484, + 468, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mu (\\mathbf{z}^l (\\cdot))$ is the $C$ -length spatiotemporal mean vector of representations $\\mathbf{z}^l (\\cdot)$ . $JVS(\\cdot)$ denotes the Jaccard vector similarity [15]. To integrate a degree of freedom and avoid hard constraints on the internal representations of $\\mathbf{x}^*$ , we define $0 < \\lambda_{l}\\leq 1$ as priming weight for layer $l$ . An overview of updating $\\mathbf{x}^*$ by priming appears in Figure 1.", + "bbox": [ + 75, + 532, + 468, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the vastness of the feature space when optimizing (1), we include two additional regularization terms to constrain the input. Specifically, we apply a temporal coherence regularization $\\mathcal{R}$ and a feature diversity regularization $\\mathcal{R}_{coh}$ which we detail below.", + "bbox": [ + 75, + 625, + 468, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Temporal Coherence Regularization", + "text_level": 1, + "bbox": [ + 76, + 720, + 393, + 738 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the first regularizer, we aim to enforce similarity between representations of consecutive frames in order to enable consistent feature transitions in the synthesized video. Therefore, we include a coherence regularizer $\\mathcal{R}$ , formulated based on the temporal coherence loss from [36].", + "bbox": [ + 75, + 744, + 468, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given two spatiotemporal representations $\\mathbf{z}^L (\\mathbf{x}^*)_{t_1}$ and $\\mathbf{z}^{L}(\\mathbf{x}^{*})_{t_{2}}$ at layer $L$ , for temporal locations $t_1$ and $t_2$ , we use their $l_{1}$ norm to enforce similarity if $t_1$ and $t_2$ are consecutive in the video. In non-consecutive cases, the divergence between $\\mathbf{z}^L (\\mathbf{x}^*)_{t_1}$ and $\\mathbf{z}^{L}(\\mathbf{x}^{*})_{t_{2}}$ should increase. The", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/06a8bb79959d74222cf8c0b423df200da78072f431cc7bc918bfd377c3eb7d4f.jpg", + "image_caption": [ + "Figure 2: Temporal Coherence regularization of zumba target action label. Applying temporal coherence regularization on representations from all layers $l \\in \\Lambda$ synthesizes static videos (bottom row). Instead, regularizing only the final network layer $L$ synthesizes videos with consistent frame transitions and motions (top row). We note that the video stimulus is shown as a reference as the regularizations are only applied to synthesized video representations." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 893, + 252 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "coherence regularizer is formulated as:", + "bbox": [ + 498, + 402, + 758, + 416 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {c o h} \\left(\\mathbf {x} ^ {*}\\right) = \\left\\{ \\begin{array}{l} \\left\\| \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {1}} - \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {2}} \\right\\| _ {1}, \\text {i f c o n s e c u t i v e} \\\\ \\max \\left(0, \\delta - \\left\\| \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {1}} - \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {2}} \\right\\| _ {1}\\right), \\text {e l s e w i s e} \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 431, + 890, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\delta$ is a margin hyperparameter. Temporal coherence is enforced at layer $L$ as in [36]. Although $\\mathcal{R}_{coh}$ can be applied to any layer $l\\in \\Lambda$ , in practice, minimizing (2) for all layers enforces a very strong regularization, producing synthesized videos with minimal to no cross-frame variations as shown in Figure 2. We note that for Transformers using patches of $P^3$ resolution, we first reshape $\\mathbf{z}^{L}(\\mathbf{x}^{*})$ from $C^\\prime P^3\\times \\frac{T'H'W'}{P^3}$ to $C^\\prime \\times T^\\prime \\times H^\\prime W^\\prime$ before calculating (2).", + "bbox": [ + 496, + 484, + 892, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Feature Diversity Regularization", + "text_level": 1, + "bbox": [ + 498, + 626, + 787, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our second regularization term $\\mathcal{R}_{\\text {feat }}$ is responsible for improving the diversity of features generated by model priming. Although priming provides a strong signal based on which the input can be updated, the diversity of features is limited compared to observing multiple instances. Thus, class features varying from those in the stimulus, or features not present in the stimulus, may not be explored during optimization. In order to enhance the search space we introduce an additional domain-specific verifier network $S(\\cdot)$ . Our goal is to use high- and low-level feature distribution statistics as proposed in [64] incorporating the verifier's prior knowledge during optimization.", + "bbox": [ + 496, + 651, + 890, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on input $\\mathbf{x}^*$ , we run inference on the verifier $S(\\mathbf{x}^*)$ to obtain representations $\\mathbf{a}^k (\\mathbf{x}^*)$ across each verifier layer $k\\in$ $\\mathbf{K}$ . The feature statistics are then obtained by the $C$ -length space-time mean $\\mu\\left(\\mathbf{a}^k (\\mathbf{x}^*)\\right)$ and variance $\\sigma^2\\left(\\mathbf{a}^k (\\mathbf{x}^*)\\right)$ vec", + "bbox": [ + 496, + 839, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1968", + "bbox": [ + 483, + 924, + 514, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/70a8585fdbdbddc249b29069ee043a2ac37425009731682e453188fb6b5a67bb.jpg", + "image_caption": [ + "Figure 3: Feature diversity regularization. Given the video stimulus in blue, synthesized videos in orange are optimized only from the stimulus. Synthesized videos with feature diversity regularization are shown in red. The regularized videos can also include general class features different from or not existing in the stimulus." + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 472, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tors. The feature diversity regularizer is defined as:", + "bbox": [ + 76, + 297, + 413, + 313 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\underset {f e a t} {\\mathcal {R}} \\left(\\mathbf {x} ^ {*}\\right) = \\sum_ {k \\in \\mathbf {K}} \\left\\| \\mu \\left(\\mathbf {a} ^ {k} \\left(\\mathbf {x} ^ {*}\\right)\\right) - \\mathbb {E} \\left(\\mu \\left(\\mathbf {a} ^ {k} (\\mathbf {x})\\right) \\mid \\mathcal {X}\\right) \\right\\| _ {2} + (3) \\\\ \\sum_ {k \\in \\mathbf {K}} | | \\sigma^ {2} (\\mathbf {a} ^ {k} (\\mathbf {x} ^ {*})) - \\mathbb {E} \\left(\\sigma^ {2} (\\mathbf {a} ^ {k} (\\mathbf {x})) | \\mathcal {X}\\right) | | _ {2} (3) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 323, + 467, + 391 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{E}(\\cdot)$ corresponds to the expected value of representation $\\mathbf{a}(\\cdot)$ for video input $\\mathbf{x}$ part of video dataset $\\mathcal{X}$ . Instead of requiring access to the dataset to train over $\\mathbf{x} \\in \\mathcal{X}$ videos, we use the Batch Normalization [22] running mean and variance to approximate the expected mean and variance as in [64]. The mean and variance estimates are then reformulated as $\\mathbb{E}\\left(\\mu\\left(\\mathbf{a}^k(\\mathbf{x})\\right) \\mid \\mathcal{X}\\right) \\simeq BN^k(\\text{running\\_mean})$ and $\\mathbb{E}\\left(\\sigma^2\\left(\\mathbf{a}^k(\\mathbf{x})\\right) \\mid \\mathcal{X}\\right) \\simeq BN^k(\\text{running\\_variance})$ . An illustration of the improved search space achieved with the inclusion of feature diversity is shown in Figure 3.", + "bbox": [ + 75, + 402, + 468, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Aggregation for Model Inversion", + "text_level": 1, + "bbox": [ + 76, + 564, + 364, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We have introduced model priming as a method to obtain a strong signal from a stimulus video with which noise-initialized videos can be optimized. To implicitly enforce transition continuity across frames, we include a temporal coherence regularizer. In addition, as the stimulus does not provide prior intuition about the diversity of features, we use a feature diversity regularizer to enhance the search space. Given their complementary properties, we formulate the final LEAPS objective as the combination of model priming, temporal coherence, and feature diversity regularizers. In line with spatial feature visualization losses that synthesize distinguishable features from noise [1, 36, 47, 64], we include a cross-entropy loss $\\mathcal{L}_{CE}$ from class predictions given the synthesized input $\\mathbf{x}^*$ :", + "bbox": [ + 75, + 587, + 468, + 803 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}, y\\right) = \\mathcal {L} _ {C E} \\left(\\mathbf {x} ^ {*}, y\\right) + \\mathcal {L} _ {p r i m} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}\\right) + r \\mathcal {R} \\left(\\mathbf {x} ^ {*}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 814, + 468, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the regularizer term combines (2) and (3): $\\mathcal{R}(\\mathbf{x}^{*}) = \\mathcal{R} + \\mathcal{R}$ . Respectively, $r$ is a regularizer scaling factor. The final LEAPS objective enables the synthesis of high-fidelity", + "bbox": [ + 76, + 849, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "features without being constrained by data availability or architecture types as shown in the results section.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Main Results", + "text_level": 1, + "bbox": [ + 498, + 138, + 635, + 155 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first detail the train scheme and implementation settings used in Section 4.1. We then compare our proposed LEAPS method to image-based feature visualization methods that we extend to video and use as baselines in Section 4.2. We also qualitatively and quantitatively investigate the synthesized videos across a variety of video models in Section 4.3. Finally, in Section 4.4 we perform ablation studies for the LEAPS objective as well as different updatable input spatiotemporal resolutions.", + "bbox": [ + 496, + 165, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Experimental details", + "text_level": 1, + "bbox": [ + 498, + 314, + 694, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model details. We invert 3D [20]/(2+1)D [58]/CSN [57] ResNet-50 (R50), X3D [11], TimeSformer [4], Video Swin [29], MViTv2 [27], rev-MViT [32], and UniFormerv2 [26] networks. For all our experiments, we use the official networks available from their respective repositories pretrained on Kinetics-400 [7]. Due to its limited computational overhead and requirement of BN layers by the feature diversity regularizer in (3), we use $\\mathrm{X3DS}$ as the verifier network $S(\\cdot)$ . We note that only the internal representations and predictions from the inverted and verifier models are used. Both models only run inference and remain fixed throughout the feature synthesis.", + "bbox": [ + 496, + 338, + 890, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Feature synthesis optimization details. Video input $\\mathbf{x}^*$ is initialized with size of $8 \\times 224^2$ . For models [11, 4, 29, 27, 32, 26] which use inputs of fixed size, we first interpolate $\\mathbf{x}^*$ to match the required size2. Priming stimuli are selected from the Kinetics-400 validation set randomly. For transformer models, $\\mathbf{x}^*$ and $\\mathbf{v}$ are first tokenized. We use Adam [25] with a learning rate of 0.2 and a cosine decrease policy as in [64]. We use a total of 2K gradient updates. As in [36], we set $\\delta = 1$ . To discover the optimal $\\lambda$ and $r$ hyperparameters for each network we use Mango [46] to perform a simple grid search for 1K gradient updates. A full overview of the hyperparameters used by each model is available in Table S1 in the supplementary material.", + "bbox": [ + 496, + 521, + 890, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Baseline results", + "text_level": 1, + "bbox": [ + 500, + 729, + 655, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first assess the quality of the synthesized videos. We invert 3D R50, $\\mathrm{X3D_M}$ , and Video Swin-B models and report the averaged top-1 classification accuracies and Inception Scores (IS) [45] on synthesized videos using each video from the validation set of Kinetics-400 as a stimulus. We extend two prominent image-based feature visualization methods making them applicable to spatiotemporal models:", + "bbox": [ + 496, + 753, + 890, + 861 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2Due to space limitations in Figures 5 to 8 the last 2 frames of $\\mathbf{x}^*$ are not shown.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1969", + "bbox": [ + 483, + 924, + 514, + 936 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/f71af7da34559e233d89fded369f5f0cd854fb67c21349288d7cbcb1914d4f36.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Visualization methodtop-1 (%)Inception Score (IS)
modelver.modelverifier
3D R50
3D Deep Dream [1]34.52.61.1 ± 0.11.0
3D AM [13]41.45.81.4 ± 0.31.2 ± 0.2
LEAPSours( L )prim67.953.13.9 ± 0.93.2 ± 0.6
LEAPSours( L + R )primfeat74.360.25.1 ± 0.83.9 ± 1.4
LEAPSours(full)86.768.59.0 ± 1.05.7 ± 0.7
X3DM
3D Deep Dream [1]18.11.91.1 ± 0.11.1 ± 0.1
3D AM [13]33.25.61.3 ± 0.31.2 ± 0.2
LEAPSours( L )prim73.459.85.1 ± 1.13.9 ± 0.4
LEAPSours( L + R )primfeat81.169.38.8 ± 1.56.3 ± 0.8
LEAPSours(full)90.382.511.4 ± 0.98.0 ± 1.4
Video Swin-B
3D Deep Dream [1]15.91.41.4 ± 0.21.1 ± 0.1
3D AM [13]25.62.21.6 ± 0.41.1 ± 0.1
LEAPSours( L )prim71.258.64.4 ± 0.83.5 ± 0.6
LEAPSours( L + R )primfeat76.065.45.3 ± 1.54.1 ± 1.1
LEAPSours(full)87.474.39.8 ± 1.36.5 ± 0.9
", + "bbox": [ + 78, + 88, + 467, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1: Quantitative results for mean top-1 accuracy and Inception Score (IS). The best results per metric are in bold and per architecture are underlined.", + "bbox": [ + 75, + 417, + 468, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DeepDream [1] optimizes the input by a cross-entropy loss. It uses two regularizers including the total variance and $l_{2}$ norm on the input to improve convergence.", + "bbox": [ + 75, + 476, + 468, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Activation Maximization (AM) [31] optimizes a random noise image by gradient ascent to maximize the activation of a specific class. We specifically adapt [13] for visualizing concurrent spatiotemporal representations, as it is the only prior method for visualizing features over space and time.", + "bbox": [ + 75, + 522, + 468, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative evaluation. Table 1 shows the average top-1 accuracies and IS obtained by both the inverted models and verifier when inferring synthesized videos. For DeepDream and AM that do not use priming, the statistics are averaged across 10 runs per class. In LEAPS the statistics are calculated using each video in the Kinetics validation set as stimulus. For both measures, LEAPS yields consistently higher accuracies and IS compared to DeepDream and AM. Notably, it significantly improves the verifier accuracy across all three architectures. This demonstrates the merits of model priming as both DeepDream and AM optimize inputs solely by maximizing feature or class activations, without using the information-rich internal representations provided by a stimulus. This trend is also visible in the IS, as LEAPS regularizes the synthesized features in order to better represent learned temporally coherent motions.", + "bbox": [ + 75, + 598, + 468, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Qualitative examples. Videos for the class salsa spin synthesized from different methods are shown in Figure 4. Features synthesized with LEAPS are significantly more visually distinct compared to those of baseline methods. As", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8784158481e24f3387f319d444bc084e7a00f7396a31522acfb31122b0855db7.jpg", + "image_caption": [ + "(a) 3D DeepDream [1]" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 689, + 161 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a160190ca42e31869edd94b575cff0482966d8c1608a5359c934848388bdfa81.jpg", + "image_caption": [ + "(b) 3D AM [13]" + ], + "image_footnote": [], + "bbox": [ + 702, + 89, + 890, + 162 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e277a2aa298b51bee470690cde9a1d49a12275670a8c964515b8fd3e82b55a34.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 162, + 710, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/da45d9d4c817bb98b216719aad851caddac28d6925666272a81811033c88999d.jpg", + "image_caption": [ + "(c) stimulus video" + ], + "image_footnote": [], + "bbox": [ + 501, + 186, + 689, + 262 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5e9e79b62a196a4a974bf328534e5fe1d9d2a24d00da6fee1e98855f0d605797.jpg", + "image_caption": [ + "(d) LEAPS" + ], + "image_footnote": [], + "bbox": [ + 697, + 186, + 885, + 261 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4ba066fe583282977d3e21a552af9a9ff2fa6060937a01064bfa489acb56b4f5.jpg", + "image_caption": [ + "Figure 4: Different feature synthesis methods for visualizing $\\mathbf{X3D_M}$ features corresponding to class salsa dancing. Stimulus video is only used for LEAPS.", + "Figure 5: Feature synthesis over different runs for action class bartending. MViTv2 features are from different runs based on the same priming stimulus." + ], + "image_footnote": [], + "bbox": [ + 504, + 345, + 888, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "shown, videos produced by image-based methods extended to videos fail to represent learned spatiotemporal deep features. The visual quality of the synthesized videos also correlates with the accuracies and IS in Table 1.", + "bbox": [ + 496, + 580, + 890, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 5 illustrates synthesized videos from different runs given the same stimulus for class bartending. A substantial difference in the quality and representability of the visualizations between LEAPS and the extended 3D AM can be seen across runs. Despite the use of a video stimulus to prime the network, LEAPS visualizations are not constrained by the representations of the stimulus video. Each run of our LEAPS method shows a distinct visual style as feature diversity is encouraged during optimization through the homonym regularizer term. Effectively, LEAPS can be used as a tool for investigating the different class-specific features learned by each model.", + "bbox": [ + 496, + 641, + 892, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Analysis of LEAPS synthesized video", + "text_level": 1, + "bbox": [ + 500, + 832, + 820, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The generalizability of feature visualization methods across multiple architectures is largely neglected with features from only a small subset of models being visualized.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1970", + "bbox": [ + 483, + 924, + 514, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/be1c6339db0b3a265302cb88a6bc6188e3b2495ff6ef2f79cb0b9cb02baf3e62.jpg", + "image_caption": [ + "Figure 6: Qualitative examples of synthesized spatiotemporal features with LEAPS. Models are primed with a stimulus video, shown on the left of each row of synthesized videos." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 486, + 440 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a68c8a8f6e36180220d2b660e44d2540b6a4788673f27253cc3c7fb6a8d78840.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 89, + 890, + 439 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7fcddab8bb524f93ae2b5158aef000af1f79e78d4727bb3989f876183f6e6b71.jpg", + "image_caption": [ + "(a) stimulus video for doing aerobics" + ], + "image_footnote": [], + "bbox": [ + 81, + 494, + 465, + 607 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/da76de2388190c903513f14cba84a307fc30d9edf46e1bfaae0cfe508d47db4a.jpg", + "image_caption": [ + "(b) LEAPS synthesized video", + "Figure 7: SSIM and PSNR statistics over real and synthesized videos using Video Swin-B features. Lower values correspond to larger cross-frame differences." + ], + "image_footnote": [], + "bbox": [ + 86, + 625, + 467, + 736 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the architecture-independent nature of LEAPS and better understand the visual fidelity of the synthesized videos, we investigate the applicability of LEAPS over a range of convolutional and attention-based video models.", + "bbox": [ + 75, + 824, + 467, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Generalizability. The quality of the produced feature vi", + "bbox": [ + 76, + 885, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sualizations may depend on the architecture used, as models vary in terms of their complexities and feature spaces that they employ. We compare our proposed LEAPS visualization method by inverting common video models shown in Figure 6 for an arbitrary number of Kinetics classes. A common theme that arises for all models is the association of objects with specific actions. For example, the feature visualizations for the throwing ball, catching/throwing frisbee, eating spaghetti, and snatch weight lifting actions from inverted features of 3D R50, (2+1)D R50, Video Swin-B, and rev-MViT-B respectively, all optimize the video to primarily focus on the objects associated with the specific actions. Instead, for actions that are primarily perceived by motions performed, e.g. running on treadmill and dancing ballet, the actors/performers of the target actions are shown to be more conceptually influential to the model's learned preconscious of an action, with their associated motions and movements captured by the produced visualizations. In addition, the visualizations for cases eating spaghetti, blowing out candles, and sword fighting reveal that networks also learn to temporally bound distinct spatiotemporal features of certain actions. This is an important ability to be learned by video models as it effectively demonstrates their capacity to filter temporal information alongside the spatial signal. Notably, LEAPS visualizations for both convolutional and attention-based models show that learned features have", + "bbox": [ + 496, + 496, + 890, + 888 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1971", + "bbox": [ + 483, + 924, + 513, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d7ff5f0265891765d366eb7a38a4d1cb58f6c99ded332b974218d68985d4e8b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 89, + 465, + 142 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/38502353adebc055cd25a338a85dfe49d8c1e913d81296ab0d45d1450b34f444.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 152, + 465, + 203 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/da530fe95c3602b4046aecdaf8a6d6ffdb44bf0f177ebf8e64596e1fda192e7f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 205, + 465, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/20c5ea8a1cd50a2707580e19042d6d02581baf2cc2ab3b8ab5aca8c651333ec7.jpg", + "image_caption": [ + "Figure 8: Video synthesis at different optimization stages for class riding on a bike. $\\mathrm{X3D_M}$ features are used." + ], + "image_footnote": [], + "bbox": [ + 80, + 257, + 465, + 306 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a good correspondence to their classes across architectures. Temporal coherence. As we show in Figure 7, LEAPS can visualize motions performed over different speeds (slow/fast). We report the Peak Signal Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) for consecutive frame pairs to analyze the variations observed by both fast and slow motions within a video. We observe that the speeds with which motions are performed within the same video can be fundamentally different with both large and small changes occurring between frames. In contrast to image-based methods extended to video, LEAPS shows the ability to represent such variations in the produced feature visualizations. As shown, the PSNR and SSIM statistics from the stimulus video of class doing aerobics in Figure 7a, follow similar trends as those produced by the synthesized LEAPS video in Figure 7b.", + "bbox": [ + 75, + 366, + 468, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Video synthesis optimization. We visualize the resulting synthesized video $\\mathbf{x}^*$ at different iteration steps during optimization in Figure 8. General features such as the outlines of objects and actors as well as their movements are synthesized first by our proposed method. Interestingly, later iterations show to refine the visualized features by further synthesizing visual details. This demonstrates a level of learned hierarchy by video models as to the types of spatiotemporal learned features that are associated with a specific action. Our proposed use of model priming in tandem with temporal coherence and feature diversity regularization terms shows to enable the visualization of models' spatiotemporal representations of actions, at a finer quality and detail.", + "bbox": [ + 75, + 609, + 468, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation studies", + "text_level": 1, + "bbox": [ + 76, + 816, + 236, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies reporting model statistics over synthesized videos. We initially consider the effect of the distance function used during model priming. Additionally, we report statistics over different", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/65d72218e05741524f7ecb04962181556f36301f476499550bde493abf45e937.jpg", + "table_caption": [ + "(a) 3D R50." + ], + "table_footnote": [], + "table_body": "
MetricDistance function
l2l1cosJVS
top-1 (m)84.382.472.186.7
top-1 (v)65.863.746.168.5
", + "bbox": [ + 503, + 107, + 687, + 156 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c2ddba3e609975a8302f6afa168241cdeaa0cb2029c7720b9e4ae99808e41aef.jpg", + "table_caption": [ + "(b) $\\mathbf{X3D_M}$" + ], + "table_footnote": [], + "table_body": "
MetricDistance function
l2l1cosJVS
top-1 (m)88.186.878.990.3
top-1 (v)79.778.470.282.5
", + "bbox": [ + 702, + 107, + 887, + 156 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/836398ac302dd38a306c0876fda647f0359808e24c568f74872b5669d9ce7eb8.jpg", + "table_caption": [ + "(c) Video Swin-B." + ], + "table_footnote": [], + "table_body": "
MetricDistance function
l2l1cosJVS
top-1 (m)85.583.069.287.4
top-1 (v)72.871.641.474.3
", + "bbox": [ + 501, + 179, + 687, + 227 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a286148ce898eaf8d8011d43617049db105f8e9a1ef6b3db4e7f795359e2e792.jpg", + "table_caption": [ + "(d) MViTv2-B." + ], + "table_footnote": [], + "table_body": "
MetricDistance function
l2l1cosJVS
top-1 (m)83.581.970.785.9
top-1 (v)72.469.745.673.1
", + "bbox": [ + 702, + 179, + 887, + 227 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2: Top-1 accuracies of the inverted model (m) and verifier (v) on synthesized videos over different priming distance functions. Best results are in bold.", + "bbox": [ + 498, + 238, + 890, + 282 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "combinations of priming and introduced regularizers across the tested architectures. Finally, we present quantitative results when using inputs of different spatiotemporal sizes alongside the resulting averaged latency times.", + "bbox": [ + 496, + 301, + 890, + 362 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Priming distance methods. In Table 2, we evaluate the impact of the distance functions used during model priming at (1). We test three different magnitude-based methods including $l_{2}$ , $l_{1}$ , and $JVS$ , as well the cosine similarity $cos$ . Across all four spatiotemporal models, 3D R50, X3DM, Video Swin-B, and MViTv2-B, the magnitude-based methods perform favorably over the cosine similarity. This is due to $cos$ not taking into account the magnitude of the feature activation vectors from the synthesized and stimulus videos, which in turn limits the ability to synthesize representations relevant to the stimulus. Across magnitude-based methods, an average improvement of $+2.2\\%$ and $+4.1\\%$ to the inverted model's (m) accuracy is observed with JVS compared to $l_{2}$ and $l_{1}$ respectively. The same trend also holds true for the verifier (v), with $+1.9\\%$ and $+3.7\\%$ accuracy improvements from $l_{2}$ and $l_{1}$ when using JVS. Comparatively to $l_{2}$ and $l_{1}$ , JVS uses a combination of vector magnitudes and angles [15], providing a more balanced approach than magnitude-only or angle-only metrics. Therefore, we adopt $JVS$ as the priming distance method used between stimulus and synthesized feature vectors.", + "bbox": [ + 496, + 364, + 890, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Regularizers. In Table 3 we provide comparisons over different priming and regularizer combinations for our LEAPS objective. We report the top-1 accuracies of the inverted model (m), and verifier (v), as well as the IS of the inverted model across a range of spatiotemporal convolutional and attention-based architectures. We note that in the case of inverting $\\mathrm{X3D_S}$ the same model is used for both model inversion and as the verifier, evidently resulting in matching verifier/inverted model accuracies. Overall, the priming objective $\\mathcal{L}$ combined with either regularizer term yields clear improvements compared to the sole use of model priming. Modest improvements are observed with the combination of priming and the feature diversity regularizer over priming with temporal coherence. We believe that this is due to the", + "bbox": [ + 496, + 683, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1972", + "bbox": [ + 483, + 924, + 514, + 936 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3a7e07646c42a8f08ac4c7f1169e28cd10cda7a7ac00e3c5d168966bfb6a6128.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Video model architectures and variants
MetricR50X3D [11]TS [4]Video Swin [29]MViTv2 [27]rev-MViT-B [32]UniFormerv2 [26]
3D(2+1)D [58]CSN [57]XSSMLTSBSBBL
LEAPS L prim
top-1 (m)67.963.872.467.468.573.473.864.969.169.571.270.671.564.572.373.0
top-1 (v)53.149.555.851.968.559.860.452.652.353.557.654.656.750.756.456.9
IS3.9±0.92.4±0.54.2±0.64.0±1.04.3±0.65.1±1.15.5±1.32.7±0.74.1±1.64.2±1.14.4±0.84.3±1.24.6±0.73.1±1.74.3±0.84.5±1.2
LEAPS L + R prim coh
top-1 (m)70.465.776.174.875.678.078.573.172.873.274.573.774.269.274.975.3
top-1 (v)55.854.360.161.075.665.670.063.462.963.363.863.563.952.963.764.5
IS4.6±1.23.5±0.84.8±1.64.3±0.95.0±1.57.2±1.37.5±1.03.9±0.94.5±0.74.8±1.35.4±0.65.0±0.85.3±1.03.3±2.15.5±0.65.9±0.4
LEAPS L + R prim feat
top-1 (m)74.367.476.278.979.481.181.571.974.174.776.075.676.370.475.876.6
top-1 (v)60.256.964.365.879.469.370.867.263.264.565.466.768.058.269.069.8
IS5.1±0.84.2±1.45.6±1.27.3±1.17.6±0.88.8±1.59.1±1.23.8±1.24.7±1.14.9±0.55.3±1.55.1±0.65.5±1.24.0±1.85.7±1.06.2±0.9
LEAPS (full)
top-1 (m)86.778.088.386.287.090.390.883.685.786.287.485.185.982.587.188.3
top-1 (v)68.565.271.676.487.082.583.769.771.973.574.372.473.167.375.476.2
IS9.0±1.06.4±1.39.7±0.79.6±0.410.4±1.211.4±0.911.9±1.57.5±1.68.5±0.79.4±1.59.8±1.38.7±1.39.3±0.87.1±2.69.1±1.39.6±1.2
", + "bbox": [ + 76, + 88, + 890, + 286 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/55f9e974deaf011f63b3469228998b805e903a0b9f45ca12ed64a83969a0d855.jpg", + "table_caption": [ + "Table 3: Top-1 accuracies and Inceprion Scores (IS) over different objectives across different architectures and model variants. X3Ds is used as the verifier (v) for all experiments. The best results per variant are in bold. The verifier accuracy is denoted in gray for the case of using X3Ds for both model inversion and as the verifier." + ], + "table_footnote": [], + "table_body": "
Modeltemp.×spatial2top-1ISLatency (secs) (↓I / ↑B)
mv
3D R508 × 182284.367.28.1±1.30.591 / 0.913
8 × 224286.768.59.7±1.00.832 / 1.205
16 × 224287.068.79.8±1.61.140 / 1.681
(2+1)D R508 × 182275.462.94.2±1.81.684/2.325
8 × 224278.065.26.4±1.31.858/2.793
16 × 224278.565.46.6±1.52.343/3.176
", + "bbox": [ + 78, + 354, + 467, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4: Synthesized video size comparisons based on the top-1 accuracies of the inverted model, and verifier, IS, and latency times for inference $(\\downarrow \\mathrm{I})$ and backprop $(\\uparrow \\mathrm{B})$ . Best settings per architecture are in bold.", + "bbox": [ + 75, + 469, + 468, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "enhanced search space of $\\mathcal{L}_{prim} + \\mathcal{R}_{feat}$ as more diverse class features not in the stimulus are also explored. The combination of the priming objective with both regularizer terms for our proposed LEAPS consistently achieves the best results by a large margin compared to all other settings. LEAPS improves accuracy, for both the inverted model and verifier, as well as the quality of the generated videos based on the IS. These results further demonstrate that our proposed LEAPS optimization can be used across a range of architectures as a general spatiotemporal feature visualization method. Further qualitative examples for each network over different Kinetics classes are shown in Figures S1 to S4 in the supplementary alongside embeddings projections of LEAPS with different regularizer regimes in Section S3.", + "bbox": [ + 75, + 546, + 468, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Synthesized video resolution. Finally, we compare the accuracies, IS, and latency times when optimizing video inputs of different spatiotemporal sizes. Due to the majority of architectures requiring fixed-size inputs, we use 3D R50 and $(2 + 1)\\mathrm{D}$ R50 as they are input size independent. From the top-1 (m/v) accuracies and IS summarized in Table 4, the best-performing setting across metrics is obtained with $16\\times 224^{2}$ -sized inputs. We observe comparable performance on the temporally-reduced $8\\times 224^{2}$ setting with", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a significantly more balanced performance-to-latency. Notable decreases in accuracies and IS are observed with the potentially limited spatial resolution $8 \\times 182^{2}$ setting, making it less suitable. Due to the significant improvements in the per-iteration latency of the $8 \\times 224^{2}$ inputs, we adopt this setting throughout our experiments.", + "bbox": [ + 496, + 353, + 890, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 472, + 627, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have introduced LEAPS, a novel spatiotemporal model inversion method for visualizing the learned internal representations of networks through video synthesis. LEAPS uses a stimulus video to prime a model and iteratively optimize an input by minimizing the classification and priming loss. The resulting synthesized video visualizes learned concepts that are associated with classes without prior knowledge of the training data. During optimization, LEAPS uses two regularizers. The first enforces temporal coherence between feature transitions across frames in the updatable input. The second improves the diversity of the synthesized features through a domain-specific verifier network to enhance the search space. The proposed architecture-independent method has shown qualitatively and quantitatively that it can produce high-quality and visually coherent synthesized videos over a wide range of spatiotemporal convolutional and attention-based video models. The high classification scores and synthesized video quality metrics make LEAPS a generalizable and effective spatiotemporal feature visualization method. We believe that this first step towards learned spatiotemporal representations synthesis is a promising direction in understanding video models.", + "bbox": [ + 496, + 502, + 890, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. We use publicly available datasets and models. Research is funded by imec.icon Surv-AI-llance project and FWO (Grant G0A4720N).", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1973", + "bbox": [ + 483, + 924, + 514, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mordvintsev Alexander, Olah Christopher, and Tyka Mike. Inceptionism: Going deeper into neural networks. 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Springer, 2014. 2" + ], + "bbox": [ + 78, + 90, + 468, + 854 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1976", + "bbox": [ + 483, + 924, + 514, + 936 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Leaping Into Memories_ Space-Time Deep Feature Synthesis/5ad3f2c3-b163-4339-b33a-6f2219ed23a6_model.json b/2023/Leaping Into Memories_ Space-Time Deep Feature Synthesis/5ad3f2c3-b163-4339-b33a-6f2219ed23a6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bfe8b26140cf442cdeb47c3d1c5386d05819c401 --- /dev/null +++ b/2023/Leaping Into Memories_ Space-Time Deep Feature Synthesis/5ad3f2c3-b163-4339-b33a-6f2219ed23a6_model.json @@ -0,0 +1,2323 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.179, + 0.131, + 0.793, + 0.154 + ], + "angle": 0, + "content": "Leaping Into Memories: Space-Time Deep Feature Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.307, + 0.182, + 0.662, + 0.199 + ], + "angle": 0, + "content": "Alexandros Stergiou Nikos Deligiannis" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.2, + 0.696, + 0.218 + ], + "angle": 0, + "content": "Vrije Universiteit Brussel, Belgium & imec, Belgium" + }, + { + "type": "text", + "bbox": [ + 0.39, + 0.22, + 0.581, + 0.233 + ], + "angle": 0, + "content": ".@vub.be" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.25, + 0.87, + 0.454 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.465, + 0.893, + 0.556 + ], + "angle": 0, + "content": "Figure 1: Illustration of our proposed LEAPS model inversion. Given a video input \\(\\mathbf{x}^*\\) initialized with noise, we use a stimulus video \\(\\mathbf{v}\\) of target class \\(y\\), to prime video model \\(\\Phi(\\cdot)\\). We iteratively optimize \\(\\mathbf{x}^*\\) to synthesize and visually represent the internal spatiotemporal features of \\(\\Phi(\\cdot)\\). To impose diversity over the synthesized videos, feature statistics from a domain-specific verifier network \\(S(\\cdot)\\) are distilled to regularize \\(\\mathbf{x}^*\\). To preserve the continuity of motions across frames, \\(\\mathbf{x}^*\\) is temporally regularized at each training iteration. Although the illustration visualizes internal representations as \\(C \\times T \\times H \\times W\\) volumes, they can also be flattened patches \\(CP^3 \\times \\frac{THW}{P^3}\\) of \\(P^3\\) resolution as in Vision Transformers." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.568, + 0.314, + 0.583 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.473, + 0.858 + ], + "angle": 0, + "content": "The success of deep learning models has led to their adaptation and adoption by prominent video understanding methods. The majority of these approaches encode features in a joint space-time modality for which the inner workings and learned representations are difficult to visually interpret. We propose LEArned Preconscious Synthesis (LEAPS), an architecture-independent method for synthesizing videos from the internal spatiotemporal representations of models. Using a stimulus video and a target class, we prime a fixed space-time model and iteratively optimize a video initialized with random noise. Additional regularizers are used to improve the feature diversity of the synthesized videos alongside the cross-frame temporal coherence of motions. We quantitatively and qualitatively evaluate the applicability of LEAPS by inverting a range of spatiotemporal convolutional and attention-based architectures trained on Kinetics-400, which to the best of our knowledge has not been previously accomplished." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.568, + 0.631, + 0.584 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.892, + 0.853 + ], + "angle": 0, + "content": "Inverting deep networks' learned internal representations has been a difficult task to achieve. The adaptation and deployment of CNNs and more recently Transformers, to a variety of vision tasks has led to significant breakthroughs. The field of video action recognition has experienced drastic growth in recent years through the convergence of models with increased complexities and capacities [2, 4, 32, 63] as well as large accuracy improvements [11, 12, 27, 26, 29]. Despite great progress in their applicability, there is still a large gap in the interpretability of video models. As these models compositionally encode space and time modalities of videos over large feature spaces and require a lot of parameters, conceptualizing their internal representations remains challenging. In this paper, we propose a method to invert learned features of video models associated with specific actions by optimizing a parameterized input to synthesize conceptually and visually coherent representations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In cognitive science, stages of consciousness include the conscious, the unconscious, and the preconscious. In contrast to the conscious and unconscious, the preconscious is" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.425, + 0.9 + ], + "angle": 0, + "content": "See alexandrosstergiou/LEAPS for video examples and code." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.926, + 0.516, + 0.937 + ], + "angle": 0, + "content": "1966" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "responsible for learned information currently outside conscious awareness to remain readily available [18]. One way of accessing learned preconscious information and making it part of conscious awareness is through priming [38]. Priming uses a stimulus to activate related learned concepts in memory and make them easily and readily accessible [33, 34]; e.g., one can remember their bedroom if primed with a picture of a bed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.348 + ], + "angle": 0, + "content": "Motivated by visual priming in cognitive science, we demonstrate that learned representations of video models can become accessible through model priming. By using a video stimulus and a target action class, we synthesize the dominant learned concepts corresponding to actions. In turn, the visual features of the synthesized videos provide a conceptual view of the models' learned internal representations. We term these features as the learned preconscious of the video model associated with a specific action." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.575 + ], + "angle": 0, + "content": "We introduce LEArned Preconscious Synthesis (LEAPS), illustrated in Figure 1, a spatiotemporal model inversion method that synthesizes interpretable videos by minimizing a classification and priming loss without prior knowledge of the training data. LEAPS uses a video of a target action class as stimulus, to prime a fixed spatiotemporal model. We additionally include two regularization terms. The first term enforces motion coherence across frames by constraining their representations at each update. The second enhances the diversity of the synthesized videos by using a domain-specific verifier network that exploits disagreements between feature statistics similar to [64]. Through the same architecture-independent approach, we show that LEAPS can invert the spatiotemporal features of 3D-CNNs and spatiotemporal Transformers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.473, + 0.727 + ], + "angle": 0, + "content": "Our main contributions are as follows. First, we introduce LEAPS, a general approach for inverting video models, which to the best of our knowledge, is the first attempt to create videos of conceptual representations from jointly encoded space-time features. Second, we use LEAPS on multiple convolution and attention models and compare it to prior image-based inversion methods that we extend to video. Finally, we show that LEAPS can invert both video CNNs and transformers, with the same architecture-independent method without any modifications." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.22, + 0.755 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Approaches for visualizing and interpreting deep models can be divided into three groups which we detail below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Attribution-based visualizations. These methods have been used to visualize feature contributions over an input. Attribution methods for images have primarily been based on back-propagating activations of classes [8, 48, 61], or individual neurons [3, 5, 49, 52] to localize regions in the input that are informative for a given class or feature. Such approaches include Integrated gradients (IG) [56] which" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.35 + ], + "angle": 0, + "content": "produce pixel-wise attributions from integrating computed backprop gradients. Subsequent works have also included gradient smoothing [51], gradient accumulation in saturated regions [35], and adaptation of the gradient path [23]. Another set of approaches that rely on attribution-based visualizations use perturbations of the input [17, 16, 44]. Given their straightforward applicability, image attribution methods have also been extended to video. The majority of works; e.g., Saliency Tubes [55, 54], STEP [28], video OSA [59], and BOREx [24], have focused on the localization of spatiotemporal salient regions by extending GradCAM [48], Extremal Perturbations (EP) [16], Occlusion Sensitivity Analysis (OSA) [66], and Gaussian processes regression (GPR) [6, 37] respectively. In contrast to these approaches that localize salient class features, we offer a visual feature synthesis method to conceptualize the learned representations of video models through priming." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.895, + 0.732 + ], + "angle": 0, + "content": "Input synthesis. Network-centric approaches invert models to either visualize particular classes [41, 65, 64] or features [43, 53]. One of the main methods employed for visualizing internal network features is Gradient Ascent (GA) [10], which optimizes the input by increasing the activation of a specific neuron. Activation Maximization (AM) [50] later adapted GA to visualize CNN features. Following works have been built on top of AM by including additional regularizers; e.g., total variation [31], blurring [60], and gradient masking [41]. One of the most popular extensions of AM has been DeepDream [1] which optimizes the input to yield high responses for a chosen class while keeping internal representations constraint-free. The produced images include repetitions of recognizable concepts without representing a coherent whole. In addition to AM, model inversion [9, 19, 30, 64, 66] includes the task of maximizing the classification score of the synthesized image instead of maximizing class activations. The only extension of input synthesis approaches to videos has been introduced by Feichtenhofer et al. [13] in which AM is used to create visual representations of class features from two-steam models [14, 62], trained on RGB frames (spatial stream) and optical flow (temporal stream). In this paper, we instead propose a model inversion method for inverting video models concurrently encoding space and time modalities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Visual feature generation. These methods utilize activation maximization by including an additional generator network [39, 40, 42], with the cost of requiring access to the training data. Huang et al. [21] adapted feature generation on video data by modeling the temporal signal with a temporal generator network. Despite the high fidelity of the produced results, these approaches are less suitable for interpreting internal model behaviors, as they do not solely depend on the model under inspection. Instead, they are primarily influenced by the training data used as well as the capacity and complexity of the generator model trained." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "1967" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.37, + 0.108 + ], + "angle": 0, + "content": "3. Learned Preconscious Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.471, + 0.268 + ], + "angle": 0, + "content": "In this section, we overview our LEAPS method, shown in Figure 1. We start by formally introducing model priming for video models in Section 3.1. A stimulus video of a target class is used to initially prime the network. The training process uses the primed representations to update a randomly initialized input alongside two regularizers. The first regularizer is used to enforce temporal coherence, explained in Section 3.2. The second is used to improve synthesized feature diversity, overviewed in Section 3.3. We present the final aggregated function in Section 3.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.277, + 0.232, + 0.293 + ], + "angle": 0, + "content": "3.1. Model Priming" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.471, + 0.476 + ], + "angle": 0, + "content": "Priming deep models is influenced by cognitive science [38] in which a stimulus is used to recall prior knowledge. We extend this approach to visualizing the learned preconscious of deep video models associated with a specific action class \\( y \\). Given a video \\( \\mathbf{v} \\) of size \\( C\\times T\\times H\\times W \\), with \\( C \\) channels, \\( T \\) frames, \\( H \\) height, and \\( W \\) width, as a visual cue for action class \\( y \\), and a randomly initialized input \\( \\mathbf{x}^* \\) of \\( C\\times T\\times H\\times W \\) size to optimize. We define a priming loss \\( \\mathcal{L}_{prim}(\\mathbf{x}^*,\\mathbf{v}) \\) between the internal representations \\( \\mathbf{z}^l (\\cdot) \\) of the optimized input \\( \\mathbf{x}^* \\) and stimulus \\( \\mathbf{v} \\) across \\( l\\in \\Lambda = \\{1,\\dots,L\\} \\) layers:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.486, + 0.47, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p r i m} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}\\right) = \\frac {1}{L} \\sum_ {l \\in \\boldsymbol {\\Lambda}} \\lambda_ {l} J V S \\left(\\mu \\left(\\mathbf {z} ^ {l} \\left(\\mathbf {x} ^ {*}\\right)\\right), \\mu \\left(\\mathbf {z} ^ {l} (\\mathbf {v})\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.626 + ], + "angle": 0, + "content": "where \\(\\mu (\\mathbf{z}^l (\\cdot))\\) is the \\(C\\)-length spatiotemporal mean vector of representations \\(\\mathbf{z}^l (\\cdot)\\). \\(JVS(\\cdot)\\) denotes the Jaccard vector similarity [15]. To integrate a degree of freedom and avoid hard constraints on the internal representations of \\(\\mathbf{x}^*\\), we define \\(0 < \\lambda_{l}\\leq 1\\) as priming weight for layer \\(l\\). An overview of updating \\(\\mathbf{x}^*\\) by priming appears in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Due to the vastness of the feature space when optimizing (1), we include two additional regularization terms to constrain the input. Specifically, we apply a temporal coherence regularization \\(\\mathcal{R}\\) and a feature diversity regularization \\(\\mathcal{R}_{coh}\\) which we detail below." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.394, + 0.739 + ], + "angle": 0, + "content": "3.2. Temporal Coherence Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.745, + 0.469, + 0.825 + ], + "angle": 0, + "content": "For the first regularizer, we aim to enforce similarity between representations of consecutive frames in order to enable consistent feature transitions in the synthesized video. Therefore, we include a coherence regularizer \\(\\mathcal{R}\\), formulated based on the temporal coherence loss from [36]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Given two spatiotemporal representations \\(\\mathbf{z}^L (\\mathbf{x}^*)_{t_1}\\) and \\(\\mathbf{z}^{L}(\\mathbf{x}^{*})_{t_{2}}\\) at layer \\(L\\), for temporal locations \\(t_1\\) and \\(t_2\\), we use their \\(l_{1}\\) norm to enforce similarity if \\(t_1\\) and \\(t_2\\) are consecutive in the video. In non-consecutive cases, the divergence between \\(\\mathbf{z}^L (\\mathbf{x}^*)_{t_1}\\) and \\(\\mathbf{z}^{L}(\\mathbf{x}^{*})_{t_{2}}\\) should increase. The" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.092, + 0.895, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.265, + 0.894, + 0.386 + ], + "angle": 0, + "content": "Figure 2: Temporal Coherence regularization of zumba target action label. Applying temporal coherence regularization on representations from all layers \\( l \\in \\Lambda \\) synthesizes static videos (bottom row). Instead, regularizing only the final network layer \\( L \\) synthesizes videos with consistent frame transitions and motions (top row). We note that the video stimulus is shown as a reference as the regularizations are only applied to synthesized video representations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.403, + 0.759, + 0.417 + ], + "angle": 0, + "content": "coherence regularizer is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.432, + 0.892, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {c o h} \\left(\\mathbf {x} ^ {*}\\right) = \\left\\{ \\begin{array}{l} \\left\\| \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {1}} - \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {2}} \\right\\| _ {1}, \\text {i f c o n s e c u t i v e} \\\\ \\max \\left(0, \\delta - \\left\\| \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {1}} - \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {2}} \\right\\| _ {1}\\right), \\text {e l s e w i s e} \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.893, + 0.614 + ], + "angle": 0, + "content": "where \\(\\delta\\) is a margin hyperparameter. Temporal coherence is enforced at layer \\(L\\) as in [36]. Although \\(\\mathcal{R}_{coh}\\) can be applied to any layer \\(l\\in \\Lambda\\), in practice, minimizing (2) for all layers enforces a very strong regularization, producing synthesized videos with minimal to no cross-frame variations as shown in Figure 2. We note that for Transformers using patches of \\(P^3\\) resolution, we first reshape \\(\\mathbf{z}^{L}(\\mathbf{x}^{*})\\) from \\(C^\\prime P^3\\times \\frac{T'H'W'}{P^3}\\) to \\(C^\\prime \\times T^\\prime \\times H^\\prime W^\\prime\\) before calculating (2)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.627, + 0.788, + 0.643 + ], + "angle": 0, + "content": "3.3. Feature Diversity Regularization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Our second regularization term \\(\\mathcal{R}_{\\text {feat }}\\) is responsible for improving the diversity of features generated by model priming. Although priming provides a strong signal based on which the input can be updated, the diversity of features is limited compared to observing multiple instances. Thus, class features varying from those in the stimulus, or features not present in the stimulus, may not be explored during optimization. In order to enhance the search space we introduce an additional domain-specific verifier network \\(S(\\cdot)\\). Our goal is to use high- and low-level feature distribution statistics as proposed in [64] incorporating the verifier's prior knowledge during optimization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Based on input \\(\\mathbf{x}^*\\), we run inference on the verifier \\(S(\\mathbf{x}^*)\\) to obtain representations \\(\\mathbf{a}^k (\\mathbf{x}^*)\\) across each verifier layer \\(k\\in\\) \\(\\mathbf{K}\\). The feature statistics are then obtained by the \\(C\\)-length space-time mean \\(\\mu\\left(\\mathbf{a}^k (\\mathbf{x}^*)\\right)\\) and variance \\(\\sigma^2\\left(\\mathbf{a}^k (\\mathbf{x}^*)\\right)\\) vec" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "1968" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.088, + 0.473, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.195, + 0.47, + 0.286 + ], + "angle": 0, + "content": "Figure 3: Feature diversity regularization. Given the video stimulus in blue, synthesized videos in orange are optimized only from the stimulus. Synthesized videos with feature diversity regularization are shown in red. The regularized videos can also include general class features different from or not existing in the stimulus." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.299, + 0.415, + 0.314 + ], + "angle": 0, + "content": "tors. The feature diversity regularizer is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.324, + 0.468, + 0.392 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\underset {f e a t} {\\mathcal {R}} \\left(\\mathbf {x} ^ {*}\\right) = \\sum_ {k \\in \\mathbf {K}} \\left\\| \\mu \\left(\\mathbf {a} ^ {k} \\left(\\mathbf {x} ^ {*}\\right)\\right) - \\mathbb {E} \\left(\\mu \\left(\\mathbf {a} ^ {k} (\\mathbf {x})\\right) \\mid \\mathcal {X}\\right) \\right\\| _ {2} + (3) \\\\ \\sum_ {k \\in \\mathbf {K}} | | \\sigma^ {2} (\\mathbf {a} ^ {k} (\\mathbf {x} ^ {*})) - \\mathbb {E} \\left(\\sigma^ {2} (\\mathbf {a} ^ {k} (\\mathbf {x})) | \\mathcal {X}\\right) | | _ {2} (3) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.47, + 0.556 + ], + "angle": 0, + "content": "where \\(\\mathbb{E}(\\cdot)\\) corresponds to the expected value of representation \\(\\mathbf{a}(\\cdot)\\) for video input \\(\\mathbf{x}\\) part of video dataset \\(\\mathcal{X}\\). Instead of requiring access to the dataset to train over \\(\\mathbf{x} \\in \\mathcal{X}\\) videos, we use the Batch Normalization [22] running mean and variance to approximate the expected mean and variance as in [64]. The mean and variance estimates are then reformulated as \\(\\mathbb{E}\\left(\\mu\\left(\\mathbf{a}^k(\\mathbf{x})\\right) \\mid \\mathcal{X}\\right) \\simeq BN^k(\\text{running\\_mean})\\) and \\(\\mathbb{E}\\left(\\sigma^2\\left(\\mathbf{a}^k(\\mathbf{x})\\right) \\mid \\mathcal{X}\\right) \\simeq BN^k(\\text{running\\_variance})\\). An illustration of the improved search space achieved with the inclusion of feature diversity is shown in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.565, + 0.365, + 0.58 + ], + "angle": 0, + "content": "3.4. Aggregation for Model Inversion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.47, + 0.804 + ], + "angle": 0, + "content": "We have introduced model priming as a method to obtain a strong signal from a stimulus video with which noise-initialized videos can be optimized. To implicitly enforce transition continuity across frames, we include a temporal coherence regularizer. In addition, as the stimulus does not provide prior intuition about the diversity of features, we use a feature diversity regularizer to enhance the search space. Given their complementary properties, we formulate the final LEAPS objective as the combination of model priming, temporal coherence, and feature diversity regularizers. In line with spatial feature visualization losses that synthesize distinguishable features from noise [1, 36, 47, 64], we include a cross-entropy loss \\(\\mathcal{L}_{CE}\\) from class predictions given the synthesized input \\(\\mathbf{x}^*\\):" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.815, + 0.47, + 0.839 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}, y\\right) = \\mathcal {L} _ {C E} \\left(\\mathbf {x} ^ {*}, y\\right) + \\mathcal {L} _ {p r i m} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}\\right) + r \\mathcal {R} \\left(\\mathbf {x} ^ {*}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.85, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where the regularizer term combines (2) and (3): \\(\\mathcal{R}(\\mathbf{x}^{*}) = \\mathcal{R} + \\mathcal{R}\\). Respectively, \\(r\\) is a regularizer scaling factor. The final LEAPS objective enables the synthesis of high-fidelity" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "features without being constrained by data availability or architecture types as shown in the results section." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.139, + 0.636, + 0.156 + ], + "angle": 0, + "content": "4. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.166, + 0.892, + 0.302 + ], + "angle": 0, + "content": "We first detail the train scheme and implementation settings used in Section 4.1. We then compare our proposed LEAPS method to image-based feature visualization methods that we extend to video and use as baselines in Section 4.2. We also qualitatively and quantitatively investigate the synthesized videos across a variety of video models in Section 4.3. Finally, in Section 4.4 we perform ablation studies for the LEAPS objective as well as different updatable input spatiotemporal resolutions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.315, + 0.696, + 0.331 + ], + "angle": 0, + "content": "4.1. Experimental details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Model details. We invert 3D [20]/(2+1)D [58]/CSN [57] ResNet-50 (R50), X3D [11], TimeSformer [4], Video Swin [29], MViTv2 [27], rev-MViT [32], and UniFormerv2 [26] networks. For all our experiments, we use the official networks available from their respective repositories pretrained on Kinetics-400 [7]. Due to its limited computational overhead and requirement of BN layers by the feature diversity regularizer in (3), we use \\(\\mathrm{X3DS}\\) as the verifier network \\(S(\\cdot)\\). We note that only the internal representations and predictions from the inverted and verifier models are used. Both models only run inference and remain fixed throughout the feature synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Feature synthesis optimization details. Video input \\(\\mathbf{x}^*\\) is initialized with size of \\(8 \\times 224^2\\). For models [11, 4, 29, 27, 32, 26] which use inputs of fixed size, we first interpolate \\(\\mathbf{x}^*\\) to match the required size2. Priming stimuli are selected from the Kinetics-400 validation set randomly. For transformer models, \\(\\mathbf{x}^*\\) and \\(\\mathbf{v}\\) are first tokenized. We use Adam [25] with a learning rate of 0.2 and a cosine decrease policy as in [64]. We use a total of 2K gradient updates. As in [36], we set \\(\\delta = 1\\). To discover the optimal \\(\\lambda\\) and \\(r\\) hyperparameters for each network we use Mango [46] to perform a simple grid search for 1K gradient updates. A full overview of the hyperparameters used by each model is available in Table S1 in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.731, + 0.656, + 0.746 + ], + "angle": 0, + "content": "4.2. Baseline results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.755, + 0.892, + 0.862 + ], + "angle": 0, + "content": "We first assess the quality of the synthesized videos. We invert 3D R50, \\(\\mathrm{X3D_M}\\), and Video Swin-B models and report the averaged top-1 classification accuracies and Inception Scores (IS) [45] on synthesized videos using each video from the validation set of Kinetics-400 as a stimulus. We extend two prominent image-based feature visualization methods making them applicable to spatiotemporal models:" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": "2Due to space limitations in Figures 5 to 8 the last 2 frames of \\(\\mathbf{x}^*\\) are not shown." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "1969" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.41 + ], + "angle": 0, + "content": "
Visualization methodtop-1 (%)Inception Score (IS)
modelver.modelverifier
3D R50
3D Deep Dream [1]34.52.61.1 ± 0.11.0
3D AM [13]41.45.81.4 ± 0.31.2 ± 0.2
LEAPSours( L )prim67.953.13.9 ± 0.93.2 ± 0.6
LEAPSours( L + R )primfeat74.360.25.1 ± 0.83.9 ± 1.4
LEAPSours(full)86.768.59.0 ± 1.05.7 ± 0.7
X3DM
3D Deep Dream [1]18.11.91.1 ± 0.11.1 ± 0.1
3D AM [13]33.25.61.3 ± 0.31.2 ± 0.2
LEAPSours( L )prim73.459.85.1 ± 1.13.9 ± 0.4
LEAPSours( L + R )primfeat81.169.38.8 ± 1.56.3 ± 0.8
LEAPSours(full)90.382.511.4 ± 0.98.0 ± 1.4
Video Swin-B
3D Deep Dream [1]15.91.41.4 ± 0.21.1 ± 0.1
3D AM [13]25.62.21.6 ± 0.41.1 ± 0.1
LEAPSours( L )prim71.258.64.4 ± 0.83.5 ± 0.6
LEAPSours( L + R )primfeat76.065.45.3 ± 1.54.1 ± 1.1
LEAPSours(full)87.474.39.8 ± 1.36.5 ± 0.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.464 + ], + "angle": 0, + "content": "Table 1: Quantitative results for mean top-1 accuracy and Inception Score (IS). The best results per metric are in bold and per architecture are underlined." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.469, + 0.522 + ], + "angle": 0, + "content": "DeepDream [1] optimizes the input by a cross-entropy loss. It uses two regularizers including the total variance and \\( l_{2} \\) norm on the input to improve convergence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.469, + 0.599 + ], + "angle": 0, + "content": "Activation Maximization (AM) [31] optimizes a random noise image by gradient ascent to maximize the activation of a specific class. We specifically adapt [13] for visualizing concurrent spatiotemporal representations, as it is the only prior method for visualizing features over space and time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.469, + 0.841 + ], + "angle": 0, + "content": "Quantitative evaluation. Table 1 shows the average top-1 accuracies and IS obtained by both the inverted models and verifier when inferring synthesized videos. For DeepDream and AM that do not use priming, the statistics are averaged across 10 runs per class. In LEAPS the statistics are calculated using each video in the Kinetics validation set as stimulus. For both measures, LEAPS yields consistently higher accuracies and IS compared to DeepDream and AM. Notably, it significantly improves the verifier accuracy across all three architectures. This demonstrates the merits of model priming as both DeepDream and AM optimize inputs solely by maximizing feature or class activations, without using the information-rich internal representations provided by a stimulus. This trend is also visible in the IS, as LEAPS regularizes the synthesized features in order to better represent learned temporally coherent motions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Qualitative examples. Videos for the class salsa spin synthesized from different methods are shown in Figure 4. Features synthesized with LEAPS are significantly more visually distinct compared to those of baseline methods. As" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.691, + 0.162 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.17, + 0.665, + 0.184 + ], + "angle": 0, + "content": "(a) 3D DeepDream [1]" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.09, + 0.892, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.164, + 0.712, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.17, + 0.845, + 0.183 + ], + "angle": 0, + "content": "(b) 3D AM [13]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.188, + 0.69, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.269, + 0.651, + 0.281 + ], + "angle": 0, + "content": "(c) stimulus video" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.188, + 0.887, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.76, + 0.268, + 0.827, + 0.281 + ], + "angle": 0, + "content": "(d) LEAPS" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.288, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Figure 4: Different feature synthesis methods for visualizing \\(\\mathbf{X3D_M}\\) features corresponding to class salsa dancing. Stimulus video is only used for LEAPS." + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.346, + 0.89, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.571 + ], + "angle": 0, + "content": "Figure 5: Feature synthesis over different runs for action class bartending. MViTv2 features are from different runs based on the same priming stimulus." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.642 + ], + "angle": 0, + "content": "shown, videos produced by image-based methods extended to videos fail to represent learned spatiotemporal deep features. The visual quality of the synthesized videos also correlates with the accuracies and IS in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.893, + 0.824 + ], + "angle": 0, + "content": "Figure 5 illustrates synthesized videos from different runs given the same stimulus for class bartending. A substantial difference in the quality and representability of the visualizations between LEAPS and the extended 3D AM can be seen across runs. Despite the use of a video stimulus to prime the network, LEAPS visualizations are not constrained by the representations of the stimulus video. Each run of our LEAPS method shows a distinct visual style as feature diversity is encouraged during optimization through the homonym regularizer term. Effectively, LEAPS can be used as a tool for investigating the different class-specific features learned by each model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.821, + 0.849 + ], + "angle": 0, + "content": "4.3. Analysis of LEAPS synthesized video" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The generalizability of feature visualization methods across multiple architectures is largely neglected with features from only a small subset of models being visualized." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "1970" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.487, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.09, + 0.892, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.453, + 0.892, + 0.484 + ], + "angle": 0, + "content": "Figure 6: Qualitative examples of synthesized spatiotemporal features with LEAPS. Models are primed with a stimulus video, shown on the left of each row of synthesized videos." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.495, + 0.466, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.164, + 0.61, + 0.384, + 0.622 + ], + "angle": 0, + "content": "(a) stimulus video for doing aerobics" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.625, + 0.468, + 0.737 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.186, + 0.738, + 0.362, + 0.75 + ], + "angle": 0, + "content": "(b) LEAPS synthesized video" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.811 + ], + "angle": 0, + "content": "Figure 7: SSIM and PSNR statistics over real and synthesized videos using Video Swin-B features. Lower values correspond to larger cross-frame differences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.884 + ], + "angle": 0, + "content": "To evaluate the architecture-independent nature of LEAPS and better understand the visual fidelity of the synthesized videos, we investigate the applicability of LEAPS over a range of convolutional and attention-based video models." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Generalizability. The quality of the produced feature vi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.892, + 0.89 + ], + "angle": 0, + "content": "sualizations may depend on the architecture used, as models vary in terms of their complexities and feature spaces that they employ. We compare our proposed LEAPS visualization method by inverting common video models shown in Figure 6 for an arbitrary number of Kinetics classes. A common theme that arises for all models is the association of objects with specific actions. For example, the feature visualizations for the throwing ball, catching/throwing frisbee, eating spaghetti, and snatch weight lifting actions from inverted features of 3D R50, (2+1)D R50, Video Swin-B, and rev-MViT-B respectively, all optimize the video to primarily focus on the objects associated with the specific actions. Instead, for actions that are primarily perceived by motions performed, e.g. running on treadmill and dancing ballet, the actors/performers of the target actions are shown to be more conceptually influential to the model's learned preconscious of an action, with their associated motions and movements captured by the produced visualizations. In addition, the visualizations for cases eating spaghetti, blowing out candles, and sword fighting reveal that networks also learn to temporally bound distinct spatiotemporal features of certain actions. This is an important ability to be learned by video models as it effectively demonstrates their capacity to filter temporal information alongside the spatial signal. Notably, LEAPS visualizations for both convolutional and attention-based models show that learned features have" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.925, + 0.514, + 0.937 + ], + "angle": 0, + "content": "1971" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.467, + 0.143 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.153, + 0.466, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.206, + 0.466, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.258, + 0.466, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.323, + 0.469, + 0.354 + ], + "angle": 0, + "content": "Figure 8: Video synthesis at different optimization stages for class riding on a bike. \\(\\mathrm{X3D_M}\\) features are used." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.469, + 0.609 + ], + "angle": 0, + "content": "a good correspondence to their classes across architectures. Temporal coherence. As we show in Figure 7, LEAPS can visualize motions performed over different speeds (slow/fast). We report the Peak Signal Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) for consecutive frame pairs to analyze the variations observed by both fast and slow motions within a video. We observe that the speeds with which motions are performed within the same video can be fundamentally different with both large and small changes occurring between frames. In contrast to image-based methods extended to video, LEAPS shows the ability to represent such variations in the produced feature visualizations. As shown, the PSNR and SSIM statistics from the stimulus video of class doing aerobics in Figure 7a, follow similar trends as those produced by the synthesized LEAPS video in Figure 7b." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.469, + 0.806 + ], + "angle": 0, + "content": "Video synthesis optimization. We visualize the resulting synthesized video \\(\\mathbf{x}^*\\) at different iteration steps during optimization in Figure 8. General features such as the outlines of objects and actors as well as their movements are synthesized first by our proposed method. Interestingly, later iterations show to refine the visualized features by further synthesizing visual details. This demonstrates a level of learned hierarchy by video models as to the types of spatiotemporal learned features that are associated with a specific action. Our proposed use of model priming in tandem with temporal coherence and feature diversity regularization terms shows to enable the visualization of models' spatiotemporal representations of actions, at a finer quality and detail." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.238, + 0.832 + ], + "angle": 0, + "content": "4.4. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies reporting model statistics over synthesized videos. We initially consider the effect of the distance function used during model priming. Additionally, we report statistics over different" + }, + { + "type": "table_caption", + "bbox": [ + 0.56, + 0.094, + 0.632, + 0.107 + ], + "angle": 0, + "content": "(a) 3D R50." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.108, + 0.688, + 0.157 + ], + "angle": 0, + "content": "
MetricDistance function
l2l1cosJVS
top-1 (m)84.382.472.186.7
top-1 (v)65.863.746.168.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.765, + 0.094, + 0.829, + 0.107 + ], + "angle": 0, + "content": "(b) \\(\\mathbf{X3D_M}\\)" + }, + { + "type": "table", + "bbox": [ + 0.704, + 0.108, + 0.888, + 0.157 + ], + "angle": 0, + "content": "
MetricDistance function
l2l1cosJVS
top-1 (m)88.186.878.990.3
top-1 (v)79.778.470.282.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.541, + 0.166, + 0.652, + 0.179 + ], + "angle": 0, + "content": "(c) Video Swin-B." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.18, + 0.688, + 0.228 + ], + "angle": 0, + "content": "
MetricDistance function
l2l1cosJVS
top-1 (m)85.583.069.287.4
top-1 (v)72.871.641.474.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.751, + 0.166, + 0.843, + 0.179 + ], + "angle": 0, + "content": "(d) MViTv2-B." + }, + { + "type": "table", + "bbox": [ + 0.704, + 0.18, + 0.888, + 0.228 + ], + "angle": 0, + "content": "
MetricDistance function
l2l1cosJVS
top-1 (m)83.581.970.785.9
top-1 (v)72.469.745.673.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.239, + 0.892, + 0.284 + ], + "angle": 0, + "content": "Table 2: Top-1 accuracies of the inverted model (m) and verifier (v) on synthesized videos over different priming distance functions. Best results are in bold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.302, + 0.892, + 0.363 + ], + "angle": 0, + "content": "combinations of priming and introduced regularizers across the tested architectures. Finally, we present quantitative results when using inputs of different spatiotemporal sizes alongside the resulting averaged latency times." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.892, + 0.681 + ], + "angle": 0, + "content": "Priming distance methods. In Table 2, we evaluate the impact of the distance functions used during model priming at (1). We test three different magnitude-based methods including \\( l_{2} \\), \\( l_{1} \\), and \\( JVS \\), as well the cosine similarity \\( cos \\). Across all four spatiotemporal models, 3D R50, X3DM, Video Swin-B, and MViTv2-B, the magnitude-based methods perform favorably over the cosine similarity. This is due to \\( cos \\) not taking into account the magnitude of the feature activation vectors from the synthesized and stimulus videos, which in turn limits the ability to synthesize representations relevant to the stimulus. Across magnitude-based methods, an average improvement of \\( +2.2\\% \\) and \\( +4.1\\% \\) to the inverted model's (m) accuracy is observed with JVS compared to \\( l_{2} \\) and \\( l_{1} \\) respectively. The same trend also holds true for the verifier (v), with \\( +1.9\\% \\) and \\( +3.7\\% \\) accuracy improvements from \\( l_{2} \\) and \\( l_{1} \\) when using JVS. Comparatively to \\( l_{2} \\) and \\( l_{1} \\), JVS uses a combination of vector magnitudes and angles [15], providing a more balanced approach than magnitude-only or angle-only metrics. Therefore, we adopt \\( JVS \\) as the priming distance method used between stimulus and synthesized feature vectors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.684, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Regularizers. In Table 3 we provide comparisons over different priming and regularizer combinations for our LEAPS objective. We report the top-1 accuracies of the inverted model (m), and verifier (v), as well as the IS of the inverted model across a range of spatiotemporal convolutional and attention-based architectures. We note that in the case of inverting \\(\\mathrm{X3D_S}\\) the same model is used for both model inversion and as the verifier, evidently resulting in matching verifier/inverted model accuracies. Overall, the priming objective \\(\\mathcal{L}\\) combined with either regularizer term yields clear improvements compared to the sole use of model priming. Modest improvements are observed with the combination of priming and the feature diversity regularizer over priming with temporal coherence. We believe that this is due to the" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "1972" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.891, + 0.287 + ], + "angle": 0, + "content": "
Video model architectures and variants
MetricR50X3D [11]TS [4]Video Swin [29]MViTv2 [27]rev-MViT-B [32]UniFormerv2 [26]
3D(2+1)D [58]CSN [57]XSSMLTSBSBBL
LEAPS L prim
top-1 (m)67.963.872.467.468.573.473.864.969.169.571.270.671.564.572.373.0
top-1 (v)53.149.555.851.968.559.860.452.652.353.557.654.656.750.756.456.9
IS3.9±0.92.4±0.54.2±0.64.0±1.04.3±0.65.1±1.15.5±1.32.7±0.74.1±1.64.2±1.14.4±0.84.3±1.24.6±0.73.1±1.74.3±0.84.5±1.2
LEAPS L + R prim coh
top-1 (m)70.465.776.174.875.678.078.573.172.873.274.573.774.269.274.975.3
top-1 (v)55.854.360.161.075.665.670.063.462.963.363.863.563.952.963.764.5
IS4.6±1.23.5±0.84.8±1.64.3±0.95.0±1.57.2±1.37.5±1.03.9±0.94.5±0.74.8±1.35.4±0.65.0±0.85.3±1.03.3±2.15.5±0.65.9±0.4
LEAPS L + R prim feat
top-1 (m)74.367.476.278.979.481.181.571.974.174.776.075.676.370.475.876.6
top-1 (v)60.256.964.365.879.469.370.867.263.264.565.466.768.058.269.069.8
IS5.1±0.84.2±1.45.6±1.27.3±1.17.6±0.88.8±1.59.1±1.23.8±1.24.7±1.14.9±0.55.3±1.55.1±0.65.5±1.24.0±1.85.7±1.06.2±0.9
LEAPS (full)
top-1 (m)86.778.088.386.287.090.390.883.685.786.287.485.185.982.587.188.3
top-1 (v)68.565.271.676.487.082.583.769.771.973.574.372.473.167.375.476.2
IS9.0±1.06.4±1.39.7±0.79.6±0.410.4±1.211.4±0.911.9±1.57.5±1.68.5±0.79.4±1.59.8±1.38.7±1.39.3±0.87.1±2.69.1±1.39.6±1.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.295, + 0.893, + 0.342 + ], + "angle": 0, + "content": "Table 3: Top-1 accuracies and Inceprion Scores (IS) over different objectives across different architectures and model variants. X3Ds is used as the verifier (v) for all experiments. The best results per variant are in bold. The verifier accuracy is denoted in gray for the case of using X3Ds for both model inversion and as the verifier." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.356, + 0.468, + 0.462 + ], + "angle": 0, + "content": "
Modeltemp.×spatial2top-1ISLatency (secs) (↓I / ↑B)
mv
3D R508 × 182284.367.28.1±1.30.591 / 0.913
8 × 224286.768.59.7±1.00.832 / 1.205
16 × 224287.068.79.8±1.61.140 / 1.681
(2+1)D R508 × 182275.462.94.2±1.81.684/2.325
8 × 224278.065.26.4±1.31.858/2.793
16 × 224278.565.46.6±1.52.343/3.176
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.47, + 0.47, + 0.531 + ], + "angle": 0, + "content": "Table 4: Synthesized video size comparisons based on the top-1 accuracies of the inverted model, and verifier, IS, and latency times for inference \\((\\downarrow \\mathrm{I})\\) and backprop \\((\\uparrow \\mathrm{B})\\). Best settings per architecture are in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.763 + ], + "angle": 0, + "content": "enhanced search space of \\(\\mathcal{L}_{prim} + \\mathcal{R}_{feat}\\) as more diverse class features not in the stimulus are also explored. The combination of the priming objective with both regularizer terms for our proposed LEAPS consistently achieves the best results by a large margin compared to all other settings. LEAPS improves accuracy, for both the inverted model and verifier, as well as the quality of the generated videos based on the IS. These results further demonstrate that our proposed LEAPS optimization can be used across a range of architectures as a general spatiotemporal feature visualization method. Further qualitative examples for each network over different Kinetics classes are shown in Figures S1 to S4 in the supplementary alongside embeddings projections of LEAPS with different regularizer regimes in Section S3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Synthesized video resolution. Finally, we compare the accuracies, IS, and latency times when optimizing video inputs of different spatiotemporal sizes. Due to the majority of architectures requiring fixed-size inputs, we use 3D R50 and \\((2 + 1)\\mathrm{D}\\) R50 as they are input size independent. From the top-1 (m/v) accuracies and IS summarized in Table 4, the best-performing setting across metrics is obtained with \\(16\\times 224^{2}\\)-sized inputs. We observe comparable performance on the temporally-reduced \\(8\\times 224^{2}\\) setting with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.354, + 0.892, + 0.446 + ], + "angle": 0, + "content": "a significantly more balanced performance-to-latency. Notable decreases in accuracies and IS are observed with the potentially limited spatial resolution \\(8 \\times 182^{2}\\) setting, making it less suitable. Due to the significant improvements in the per-iteration latency of the \\(8 \\times 224^{2}\\) inputs, we adopt this setting throughout our experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.473, + 0.628, + 0.489 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.85 + ], + "angle": 0, + "content": "We have introduced LEAPS, a novel spatiotemporal model inversion method for visualizing the learned internal representations of networks through video synthesis. LEAPS uses a stimulus video to prime a model and iteratively optimize an input by minimizing the classification and priming loss. The resulting synthesized video visualizes learned concepts that are associated with classes without prior knowledge of the training data. During optimization, LEAPS uses two regularizers. The first enforces temporal coherence between feature transitions across frames in the updatable input. The second improves the diversity of the synthesized features through a domain-specific verifier network to enhance the search space. The proposed architecture-independent method has shown qualitatively and quantitatively that it can produce high-quality and visually coherent synthesized videos over a wide range of spatiotemporal convolutional and attention-based video models. The high classification scores and synthesized video quality metrics make LEAPS a generalizable and effective spatiotemporal feature visualization method. We believe that this first step towards learned spatiotemporal representations synthesis is a promising direction in understanding video models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. We use publicly available datasets and models. Research is funded by imec.icon Surv-AI-llance project and FWO (Grant G0A4720N)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "1973" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Mordvintsev Alexander, Olah Christopher, and Tyka Mike. Inceptionism: Going deeper into neural networks. 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Given a video input $\mathbf{x}^*$ initialized with noise, we use a stimulus video $\mathbf{v}$ of target class $y$ , to prime video model $\Phi(\cdot)$ . We iteratively optimize $\mathbf{x}^*$ to synthesize and visually represent the internal spatiotemporal features of $\Phi(\cdot)$ . To impose diversity over the synthesized videos, feature statistics from a domain-specific verifier network $S(\cdot)$ are distilled to regularize $\mathbf{x}^*$ . To preserve the continuity of motions across frames, $\mathbf{x}^*$ is temporally regularized at each training iteration. Although the illustration visualizes internal representations as $C \times T \times H \times W$ volumes, they can also be flattened patches $CP^3 \times \frac{THW}{P^3}$ of $P^3$ resolution as in Vision Transformers. + +# Abstract + +The success of deep learning models has led to their adaptation and adoption by prominent video understanding methods. The majority of these approaches encode features in a joint space-time modality for which the inner workings and learned representations are difficult to visually interpret. We propose LEArned Preconscious Synthesis (LEAPS), an architecture-independent method for synthesizing videos from the internal spatiotemporal representations of models. Using a stimulus video and a target class, we prime a fixed space-time model and iteratively optimize a video initialized with random noise. Additional regularizers are used to improve the feature diversity of the synthesized videos alongside the cross-frame temporal coherence of motions. We quantitatively and qualitatively evaluate the applicability of LEAPS by inverting a range of spatiotemporal convolutional and attention-based architectures trained on Kinetics-400, which to the best of our knowledge has not been previously accomplished. + +# 1. Introduction + +Inverting deep networks' learned internal representations has been a difficult task to achieve. The adaptation and deployment of CNNs and more recently Transformers, to a variety of vision tasks has led to significant breakthroughs. The field of video action recognition has experienced drastic growth in recent years through the convergence of models with increased complexities and capacities [2, 4, 32, 63] as well as large accuracy improvements [11, 12, 27, 26, 29]. Despite great progress in their applicability, there is still a large gap in the interpretability of video models. As these models compositionally encode space and time modalities of videos over large feature spaces and require a lot of parameters, conceptualizing their internal representations remains challenging. In this paper, we propose a method to invert learned features of video models associated with specific actions by optimizing a parameterized input to synthesize conceptually and visually coherent representations. + +In cognitive science, stages of consciousness include the conscious, the unconscious, and the preconscious. In contrast to the conscious and unconscious, the preconscious is + +responsible for learned information currently outside conscious awareness to remain readily available [18]. One way of accessing learned preconscious information and making it part of conscious awareness is through priming [38]. Priming uses a stimulus to activate related learned concepts in memory and make them easily and readily accessible [33, 34]; e.g., one can remember their bedroom if primed with a picture of a bed. + +Motivated by visual priming in cognitive science, we demonstrate that learned representations of video models can become accessible through model priming. By using a video stimulus and a target action class, we synthesize the dominant learned concepts corresponding to actions. In turn, the visual features of the synthesized videos provide a conceptual view of the models' learned internal representations. We term these features as the learned preconscious of the video model associated with a specific action. + +We introduce LEArned Preconscious Synthesis (LEAPS), illustrated in Figure 1, a spatiotemporal model inversion method that synthesizes interpretable videos by minimizing a classification and priming loss without prior knowledge of the training data. LEAPS uses a video of a target action class as stimulus, to prime a fixed spatiotemporal model. We additionally include two regularization terms. The first term enforces motion coherence across frames by constraining their representations at each update. The second enhances the diversity of the synthesized videos by using a domain-specific verifier network that exploits disagreements between feature statistics similar to [64]. Through the same architecture-independent approach, we show that LEAPS can invert the spatiotemporal features of 3D-CNNs and spatiotemporal Transformers. + +Our main contributions are as follows. First, we introduce LEAPS, a general approach for inverting video models, which to the best of our knowledge, is the first attempt to create videos of conceptual representations from jointly encoded space-time features. Second, we use LEAPS on multiple convolution and attention models and compare it to prior image-based inversion methods that we extend to video. Finally, we show that LEAPS can invert both video CNNs and transformers, with the same architecture-independent method without any modifications. + +# 2. Related Work + +Approaches for visualizing and interpreting deep models can be divided into three groups which we detail below. + +Attribution-based visualizations. These methods have been used to visualize feature contributions over an input. Attribution methods for images have primarily been based on back-propagating activations of classes [8, 48, 61], or individual neurons [3, 5, 49, 52] to localize regions in the input that are informative for a given class or feature. Such approaches include Integrated gradients (IG) [56] which + +produce pixel-wise attributions from integrating computed backprop gradients. Subsequent works have also included gradient smoothing [51], gradient accumulation in saturated regions [35], and adaptation of the gradient path [23]. Another set of approaches that rely on attribution-based visualizations use perturbations of the input [17, 16, 44]. Given their straightforward applicability, image attribution methods have also been extended to video. The majority of works; e.g., Saliency Tubes [55, 54], STEP [28], video OSA [59], and BOREx [24], have focused on the localization of spatiotemporal salient regions by extending GradCAM [48], Extremal Perturbations (EP) [16], Occlusion Sensitivity Analysis (OSA) [66], and Gaussian processes regression (GPR) [6, 37] respectively. In contrast to these approaches that localize salient class features, we offer a visual feature synthesis method to conceptualize the learned representations of video models through priming. + +Input synthesis. Network-centric approaches invert models to either visualize particular classes [41, 65, 64] or features [43, 53]. One of the main methods employed for visualizing internal network features is Gradient Ascent (GA) [10], which optimizes the input by increasing the activation of a specific neuron. Activation Maximization (AM) [50] later adapted GA to visualize CNN features. Following works have been built on top of AM by including additional regularizers; e.g., total variation [31], blurring [60], and gradient masking [41]. One of the most popular extensions of AM has been DeepDream [1] which optimizes the input to yield high responses for a chosen class while keeping internal representations constraint-free. The produced images include repetitions of recognizable concepts without representing a coherent whole. In addition to AM, model inversion [9, 19, 30, 64, 66] includes the task of maximizing the classification score of the synthesized image instead of maximizing class activations. The only extension of input synthesis approaches to videos has been introduced by Feichtenhofer et al. [13] in which AM is used to create visual representations of class features from two-steam models [14, 62], trained on RGB frames (spatial stream) and optical flow (temporal stream). In this paper, we instead propose a model inversion method for inverting video models concurrently encoding space and time modalities. + +Visual feature generation. These methods utilize activation maximization by including an additional generator network [39, 40, 42], with the cost of requiring access to the training data. Huang et al. [21] adapted feature generation on video data by modeling the temporal signal with a temporal generator network. Despite the high fidelity of the produced results, these approaches are less suitable for interpreting internal model behaviors, as they do not solely depend on the model under inspection. Instead, they are primarily influenced by the training data used as well as the capacity and complexity of the generator model trained. + +# 3. Learned Preconscious Synthesis + +In this section, we overview our LEAPS method, shown in Figure 1. We start by formally introducing model priming for video models in Section 3.1. A stimulus video of a target class is used to initially prime the network. The training process uses the primed representations to update a randomly initialized input alongside two regularizers. The first regularizer is used to enforce temporal coherence, explained in Section 3.2. The second is used to improve synthesized feature diversity, overviewed in Section 3.3. We present the final aggregated function in Section 3.4. + +# 3.1. Model Priming + +Priming deep models is influenced by cognitive science [38] in which a stimulus is used to recall prior knowledge. We extend this approach to visualizing the learned preconscious of deep video models associated with a specific action class $y$ . Given a video $\mathbf{v}$ of size $C\times T\times H\times W$ , with $C$ channels, $T$ frames, $H$ height, and $W$ width, as a visual cue for action class $y$ , and a randomly initialized input $\mathbf{x}^*$ of $C\times T\times H\times W$ size to optimize. We define a priming loss $\mathcal{L}_{prim}(\mathbf{x}^*,\mathbf{v})$ between the internal representations $\mathbf{z}^l (\cdot)$ of the optimized input $\mathbf{x}^*$ and stimulus $\mathbf{v}$ across $l\in \Lambda = \{1,\dots,L\}$ layers: + +$$ +\mathcal {L} _ {p r i m} \left(\mathbf {x} ^ {*}, \mathbf {v}\right) = \frac {1}{L} \sum_ {l \in \boldsymbol {\Lambda}} \lambda_ {l} J V S \left(\mu \left(\mathbf {z} ^ {l} \left(\mathbf {x} ^ {*}\right)\right), \mu \left(\mathbf {z} ^ {l} (\mathbf {v})\right)\right) \tag {1} +$$ + +where $\mu (\mathbf{z}^l (\cdot))$ is the $C$ -length spatiotemporal mean vector of representations $\mathbf{z}^l (\cdot)$ . $JVS(\cdot)$ denotes the Jaccard vector similarity [15]. To integrate a degree of freedom and avoid hard constraints on the internal representations of $\mathbf{x}^*$ , we define $0 < \lambda_{l}\leq 1$ as priming weight for layer $l$ . An overview of updating $\mathbf{x}^*$ by priming appears in Figure 1. + +Due to the vastness of the feature space when optimizing (1), we include two additional regularization terms to constrain the input. Specifically, we apply a temporal coherence regularization $\mathcal{R}$ and a feature diversity regularization $\mathcal{R}_{coh}$ which we detail below. + +# 3.2. Temporal Coherence Regularization + +For the first regularizer, we aim to enforce similarity between representations of consecutive frames in order to enable consistent feature transitions in the synthesized video. Therefore, we include a coherence regularizer $\mathcal{R}$ , formulated based on the temporal coherence loss from [36]. + +Given two spatiotemporal representations $\mathbf{z}^L (\mathbf{x}^*)_{t_1}$ and $\mathbf{z}^{L}(\mathbf{x}^{*})_{t_{2}}$ at layer $L$ , for temporal locations $t_1$ and $t_2$ , we use their $l_{1}$ norm to enforce similarity if $t_1$ and $t_2$ are consecutive in the video. In non-consecutive cases, the divergence between $\mathbf{z}^L (\mathbf{x}^*)_{t_1}$ and $\mathbf{z}^{L}(\mathbf{x}^{*})_{t_{2}}$ should increase. The + +![](images/06a8bb79959d74222cf8c0b423df200da78072f431cc7bc918bfd377c3eb7d4f.jpg) +Figure 2: Temporal Coherence regularization of zumba target action label. Applying temporal coherence regularization on representations from all layers $l \in \Lambda$ synthesizes static videos (bottom row). Instead, regularizing only the final network layer $L$ synthesizes videos with consistent frame transitions and motions (top row). We note that the video stimulus is shown as a reference as the regularizations are only applied to synthesized video representations. + +coherence regularizer is formulated as: + +$$ +\mathcal {R} _ {c o h} \left(\mathbf {x} ^ {*}\right) = \left\{ \begin{array}{l} \left\| \mathbf {z} ^ {L} \left(\mathbf {x} ^ {*}\right) _ {t _ {1}} - \mathbf {z} ^ {L} \left(\mathbf {x} ^ {*}\right) _ {t _ {2}} \right\| _ {1}, \text {i f c o n s e c u t i v e} \\ \max \left(0, \delta - \left\| \mathbf {z} ^ {L} \left(\mathbf {x} ^ {*}\right) _ {t _ {1}} - \mathbf {z} ^ {L} \left(\mathbf {x} ^ {*}\right) _ {t _ {2}} \right\| _ {1}\right), \text {e l s e w i s e} \end{array} \right. \tag {2} +$$ + +where $\delta$ is a margin hyperparameter. Temporal coherence is enforced at layer $L$ as in [36]. Although $\mathcal{R}_{coh}$ can be applied to any layer $l\in \Lambda$ , in practice, minimizing (2) for all layers enforces a very strong regularization, producing synthesized videos with minimal to no cross-frame variations as shown in Figure 2. We note that for Transformers using patches of $P^3$ resolution, we first reshape $\mathbf{z}^{L}(\mathbf{x}^{*})$ from $C^\prime P^3\times \frac{T'H'W'}{P^3}$ to $C^\prime \times T^\prime \times H^\prime W^\prime$ before calculating (2). + +# 3.3. Feature Diversity Regularization + +Our second regularization term $\mathcal{R}_{\text {feat }}$ is responsible for improving the diversity of features generated by model priming. Although priming provides a strong signal based on which the input can be updated, the diversity of features is limited compared to observing multiple instances. Thus, class features varying from those in the stimulus, or features not present in the stimulus, may not be explored during optimization. In order to enhance the search space we introduce an additional domain-specific verifier network $S(\cdot)$ . Our goal is to use high- and low-level feature distribution statistics as proposed in [64] incorporating the verifier's prior knowledge during optimization. + +Based on input $\mathbf{x}^*$ , we run inference on the verifier $S(\mathbf{x}^*)$ to obtain representations $\mathbf{a}^k (\mathbf{x}^*)$ across each verifier layer $k\in$ $\mathbf{K}$ . The feature statistics are then obtained by the $C$ -length space-time mean $\mu\left(\mathbf{a}^k (\mathbf{x}^*)\right)$ and variance $\sigma^2\left(\mathbf{a}^k (\mathbf{x}^*)\right)$ vec + +![](images/70a8585fdbdbddc249b29069ee043a2ac37425009731682e453188fb6b5a67bb.jpg) +Figure 3: Feature diversity regularization. Given the video stimulus in blue, synthesized videos in orange are optimized only from the stimulus. Synthesized videos with feature diversity regularization are shown in red. The regularized videos can also include general class features different from or not existing in the stimulus. + +tors. The feature diversity regularizer is defined as: + +$$ +\begin{array}{l} \underset {f e a t} {\mathcal {R}} \left(\mathbf {x} ^ {*}\right) = \sum_ {k \in \mathbf {K}} \left\| \mu \left(\mathbf {a} ^ {k} \left(\mathbf {x} ^ {*}\right)\right) - \mathbb {E} \left(\mu \left(\mathbf {a} ^ {k} (\mathbf {x})\right) \mid \mathcal {X}\right) \right\| _ {2} + (3) \\ \sum_ {k \in \mathbf {K}} | | \sigma^ {2} (\mathbf {a} ^ {k} (\mathbf {x} ^ {*})) - \mathbb {E} \left(\sigma^ {2} (\mathbf {a} ^ {k} (\mathbf {x})) | \mathcal {X}\right) | | _ {2} (3) \\ \end{array} +$$ + +where $\mathbb{E}(\cdot)$ corresponds to the expected value of representation $\mathbf{a}(\cdot)$ for video input $\mathbf{x}$ part of video dataset $\mathcal{X}$ . Instead of requiring access to the dataset to train over $\mathbf{x} \in \mathcal{X}$ videos, we use the Batch Normalization [22] running mean and variance to approximate the expected mean and variance as in [64]. The mean and variance estimates are then reformulated as $\mathbb{E}\left(\mu\left(\mathbf{a}^k(\mathbf{x})\right) \mid \mathcal{X}\right) \simeq BN^k(\text{running\_mean})$ and $\mathbb{E}\left(\sigma^2\left(\mathbf{a}^k(\mathbf{x})\right) \mid \mathcal{X}\right) \simeq BN^k(\text{running\_variance})$ . An illustration of the improved search space achieved with the inclusion of feature diversity is shown in Figure 3. + +# 3.4. Aggregation for Model Inversion + +We have introduced model priming as a method to obtain a strong signal from a stimulus video with which noise-initialized videos can be optimized. To implicitly enforce transition continuity across frames, we include a temporal coherence regularizer. In addition, as the stimulus does not provide prior intuition about the diversity of features, we use a feature diversity regularizer to enhance the search space. Given their complementary properties, we formulate the final LEAPS objective as the combination of model priming, temporal coherence, and feature diversity regularizers. In line with spatial feature visualization losses that synthesize distinguishable features from noise [1, 36, 47, 64], we include a cross-entropy loss $\mathcal{L}_{CE}$ from class predictions given the synthesized input $\mathbf{x}^*$ : + +$$ +\mathcal {L} \left(\mathbf {x} ^ {*}, \mathbf {v}, y\right) = \mathcal {L} _ {C E} \left(\mathbf {x} ^ {*}, y\right) + \mathcal {L} _ {p r i m} \left(\mathbf {x} ^ {*}, \mathbf {v}\right) + r \mathcal {R} \left(\mathbf {x} ^ {*}\right) \tag {4} +$$ + +where the regularizer term combines (2) and (3): $\mathcal{R}(\mathbf{x}^{*}) = \mathcal{R} + \mathcal{R}$ . Respectively, $r$ is a regularizer scaling factor. The final LEAPS objective enables the synthesis of high-fidelity + +features without being constrained by data availability or architecture types as shown in the results section. + +# 4. Main Results + +We first detail the train scheme and implementation settings used in Section 4.1. We then compare our proposed LEAPS method to image-based feature visualization methods that we extend to video and use as baselines in Section 4.2. We also qualitatively and quantitatively investigate the synthesized videos across a variety of video models in Section 4.3. Finally, in Section 4.4 we perform ablation studies for the LEAPS objective as well as different updatable input spatiotemporal resolutions. + +# 4.1. Experimental details + +Model details. We invert 3D [20]/(2+1)D [58]/CSN [57] ResNet-50 (R50), X3D [11], TimeSformer [4], Video Swin [29], MViTv2 [27], rev-MViT [32], and UniFormerv2 [26] networks. For all our experiments, we use the official networks available from their respective repositories pretrained on Kinetics-400 [7]. Due to its limited computational overhead and requirement of BN layers by the feature diversity regularizer in (3), we use $\mathrm{X3DS}$ as the verifier network $S(\cdot)$ . We note that only the internal representations and predictions from the inverted and verifier models are used. Both models only run inference and remain fixed throughout the feature synthesis. + +Feature synthesis optimization details. Video input $\mathbf{x}^*$ is initialized with size of $8 \times 224^2$ . For models [11, 4, 29, 27, 32, 26] which use inputs of fixed size, we first interpolate $\mathbf{x}^*$ to match the required size2. Priming stimuli are selected from the Kinetics-400 validation set randomly. For transformer models, $\mathbf{x}^*$ and $\mathbf{v}$ are first tokenized. We use Adam [25] with a learning rate of 0.2 and a cosine decrease policy as in [64]. We use a total of 2K gradient updates. As in [36], we set $\delta = 1$ . To discover the optimal $\lambda$ and $r$ hyperparameters for each network we use Mango [46] to perform a simple grid search for 1K gradient updates. A full overview of the hyperparameters used by each model is available in Table S1 in the supplementary material. + +# 4.2. Baseline results + +We first assess the quality of the synthesized videos. We invert 3D R50, $\mathrm{X3D_M}$ , and Video Swin-B models and report the averaged top-1 classification accuracies and Inception Scores (IS) [45] on synthesized videos using each video from the validation set of Kinetics-400 as a stimulus. We extend two prominent image-based feature visualization methods making them applicable to spatiotemporal models: + +
Visualization methodtop-1 (%)Inception Score (IS)
modelver.modelverifier
3D R50
3D Deep Dream [1]34.52.61.1 ± 0.11.0
3D AM [13]41.45.81.4 ± 0.31.2 ± 0.2
LEAPSours( L )prim67.953.13.9 ± 0.93.2 ± 0.6
LEAPSours( L + R )primfeat74.360.25.1 ± 0.83.9 ± 1.4
LEAPSours(full)86.768.59.0 ± 1.05.7 ± 0.7
X3DM
3D Deep Dream [1]18.11.91.1 ± 0.11.1 ± 0.1
3D AM [13]33.25.61.3 ± 0.31.2 ± 0.2
LEAPSours( L )prim73.459.85.1 ± 1.13.9 ± 0.4
LEAPSours( L + R )primfeat81.169.38.8 ± 1.56.3 ± 0.8
LEAPSours(full)90.382.511.4 ± 0.98.0 ± 1.4
Video Swin-B
3D Deep Dream [1]15.91.41.4 ± 0.21.1 ± 0.1
3D AM [13]25.62.21.6 ± 0.41.1 ± 0.1
LEAPSours( L )prim71.258.64.4 ± 0.83.5 ± 0.6
LEAPSours( L + R )primfeat76.065.45.3 ± 1.54.1 ± 1.1
LEAPSours(full)87.474.39.8 ± 1.36.5 ± 0.9
+ +Table 1: Quantitative results for mean top-1 accuracy and Inception Score (IS). The best results per metric are in bold and per architecture are underlined. + +DeepDream [1] optimizes the input by a cross-entropy loss. It uses two regularizers including the total variance and $l_{2}$ norm on the input to improve convergence. + +Activation Maximization (AM) [31] optimizes a random noise image by gradient ascent to maximize the activation of a specific class. We specifically adapt [13] for visualizing concurrent spatiotemporal representations, as it is the only prior method for visualizing features over space and time. + +Quantitative evaluation. Table 1 shows the average top-1 accuracies and IS obtained by both the inverted models and verifier when inferring synthesized videos. For DeepDream and AM that do not use priming, the statistics are averaged across 10 runs per class. In LEAPS the statistics are calculated using each video in the Kinetics validation set as stimulus. For both measures, LEAPS yields consistently higher accuracies and IS compared to DeepDream and AM. Notably, it significantly improves the verifier accuracy across all three architectures. This demonstrates the merits of model priming as both DeepDream and AM optimize inputs solely by maximizing feature or class activations, without using the information-rich internal representations provided by a stimulus. This trend is also visible in the IS, as LEAPS regularizes the synthesized features in order to better represent learned temporally coherent motions. + +Qualitative examples. Videos for the class salsa spin synthesized from different methods are shown in Figure 4. Features synthesized with LEAPS are significantly more visually distinct compared to those of baseline methods. As + +![](images/8784158481e24f3387f319d444bc084e7a00f7396a31522acfb31122b0855db7.jpg) +(a) 3D DeepDream [1] + +![](images/a160190ca42e31869edd94b575cff0482966d8c1608a5359c934848388bdfa81.jpg) +(b) 3D AM [13] + +![](images/e277a2aa298b51bee470690cde9a1d49a12275670a8c964515b8fd3e82b55a34.jpg) + +![](images/da45d9d4c817bb98b216719aad851caddac28d6925666272a81811033c88999d.jpg) +(c) stimulus video + +![](images/5e9e79b62a196a4a974bf328534e5fe1d9d2a24d00da6fee1e98855f0d605797.jpg) +(d) LEAPS + +![](images/4ba066fe583282977d3e21a552af9a9ff2fa6060937a01064bfa489acb56b4f5.jpg) +Figure 4: Different feature synthesis methods for visualizing $\mathbf{X3D_M}$ features corresponding to class salsa dancing. Stimulus video is only used for LEAPS. +Figure 5: Feature synthesis over different runs for action class bartending. MViTv2 features are from different runs based on the same priming stimulus. + +shown, videos produced by image-based methods extended to videos fail to represent learned spatiotemporal deep features. The visual quality of the synthesized videos also correlates with the accuracies and IS in Table 1. + +Figure 5 illustrates synthesized videos from different runs given the same stimulus for class bartending. A substantial difference in the quality and representability of the visualizations between LEAPS and the extended 3D AM can be seen across runs. Despite the use of a video stimulus to prime the network, LEAPS visualizations are not constrained by the representations of the stimulus video. Each run of our LEAPS method shows a distinct visual style as feature diversity is encouraged during optimization through the homonym regularizer term. Effectively, LEAPS can be used as a tool for investigating the different class-specific features learned by each model. + +# 4.3. Analysis of LEAPS synthesized video + +The generalizability of feature visualization methods across multiple architectures is largely neglected with features from only a small subset of models being visualized. + +![](images/be1c6339db0b3a265302cb88a6bc6188e3b2495ff6ef2f79cb0b9cb02baf3e62.jpg) +Figure 6: Qualitative examples of synthesized spatiotemporal features with LEAPS. Models are primed with a stimulus video, shown on the left of each row of synthesized videos. + +![](images/a68c8a8f6e36180220d2b660e44d2540b6a4788673f27253cc3c7fb6a8d78840.jpg) + +![](images/7fcddab8bb524f93ae2b5158aef000af1f79e78d4727bb3989f876183f6e6b71.jpg) +(a) stimulus video for doing aerobics + +![](images/da76de2388190c903513f14cba84a307fc30d9edf46e1bfaae0cfe508d47db4a.jpg) +(b) LEAPS synthesized video +Figure 7: SSIM and PSNR statistics over real and synthesized videos using Video Swin-B features. Lower values correspond to larger cross-frame differences. + +To evaluate the architecture-independent nature of LEAPS and better understand the visual fidelity of the synthesized videos, we investigate the applicability of LEAPS over a range of convolutional and attention-based video models. + +Generalizability. The quality of the produced feature vi + +sualizations may depend on the architecture used, as models vary in terms of their complexities and feature spaces that they employ. We compare our proposed LEAPS visualization method by inverting common video models shown in Figure 6 for an arbitrary number of Kinetics classes. A common theme that arises for all models is the association of objects with specific actions. For example, the feature visualizations for the throwing ball, catching/throwing frisbee, eating spaghetti, and snatch weight lifting actions from inverted features of 3D R50, (2+1)D R50, Video Swin-B, and rev-MViT-B respectively, all optimize the video to primarily focus on the objects associated with the specific actions. Instead, for actions that are primarily perceived by motions performed, e.g. running on treadmill and dancing ballet, the actors/performers of the target actions are shown to be more conceptually influential to the model's learned preconscious of an action, with their associated motions and movements captured by the produced visualizations. In addition, the visualizations for cases eating spaghetti, blowing out candles, and sword fighting reveal that networks also learn to temporally bound distinct spatiotemporal features of certain actions. This is an important ability to be learned by video models as it effectively demonstrates their capacity to filter temporal information alongside the spatial signal. Notably, LEAPS visualizations for both convolutional and attention-based models show that learned features have + +![](images/d7ff5f0265891765d366eb7a38a4d1cb58f6c99ded332b974218d68985d4e8b1.jpg) + +![](images/38502353adebc055cd25a338a85dfe49d8c1e913d81296ab0d45d1450b34f444.jpg) + +![](images/da530fe95c3602b4046aecdaf8a6d6ffdb44bf0f177ebf8e64596e1fda192e7f.jpg) + +![](images/20c5ea8a1cd50a2707580e19042d6d02581baf2cc2ab3b8ab5aca8c651333ec7.jpg) +Figure 8: Video synthesis at different optimization stages for class riding on a bike. $\mathrm{X3D_M}$ features are used. + +a good correspondence to their classes across architectures. Temporal coherence. As we show in Figure 7, LEAPS can visualize motions performed over different speeds (slow/fast). We report the Peak Signal Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) for consecutive frame pairs to analyze the variations observed by both fast and slow motions within a video. We observe that the speeds with which motions are performed within the same video can be fundamentally different with both large and small changes occurring between frames. In contrast to image-based methods extended to video, LEAPS shows the ability to represent such variations in the produced feature visualizations. As shown, the PSNR and SSIM statistics from the stimulus video of class doing aerobics in Figure 7a, follow similar trends as those produced by the synthesized LEAPS video in Figure 7b. + +Video synthesis optimization. We visualize the resulting synthesized video $\mathbf{x}^*$ at different iteration steps during optimization in Figure 8. General features such as the outlines of objects and actors as well as their movements are synthesized first by our proposed method. Interestingly, later iterations show to refine the visualized features by further synthesizing visual details. This demonstrates a level of learned hierarchy by video models as to the types of spatiotemporal learned features that are associated with a specific action. Our proposed use of model priming in tandem with temporal coherence and feature diversity regularization terms shows to enable the visualization of models' spatiotemporal representations of actions, at a finer quality and detail. + +# 4.4. Ablation studies + +In this section, we conduct ablation studies reporting model statistics over synthesized videos. We initially consider the effect of the distance function used during model priming. Additionally, we report statistics over different + +(a) 3D R50. + +
MetricDistance function
l2l1cosJVS
top-1 (m)84.382.472.186.7
top-1 (v)65.863.746.168.5
+ +(b) $\mathbf{X3D_M}$ + +
MetricDistance function
l2l1cosJVS
top-1 (m)88.186.878.990.3
top-1 (v)79.778.470.282.5
+ +(c) Video Swin-B. + +
MetricDistance function
l2l1cosJVS
top-1 (m)85.583.069.287.4
top-1 (v)72.871.641.474.3
+ +(d) MViTv2-B. + +
MetricDistance function
l2l1cosJVS
top-1 (m)83.581.970.785.9
top-1 (v)72.469.745.673.1
+ +Table 2: Top-1 accuracies of the inverted model (m) and verifier (v) on synthesized videos over different priming distance functions. Best results are in bold. + +combinations of priming and introduced regularizers across the tested architectures. Finally, we present quantitative results when using inputs of different spatiotemporal sizes alongside the resulting averaged latency times. + +Priming distance methods. In Table 2, we evaluate the impact of the distance functions used during model priming at (1). We test three different magnitude-based methods including $l_{2}$ , $l_{1}$ , and $JVS$ , as well the cosine similarity $cos$ . Across all four spatiotemporal models, 3D R50, X3DM, Video Swin-B, and MViTv2-B, the magnitude-based methods perform favorably over the cosine similarity. This is due to $cos$ not taking into account the magnitude of the feature activation vectors from the synthesized and stimulus videos, which in turn limits the ability to synthesize representations relevant to the stimulus. Across magnitude-based methods, an average improvement of $+2.2\%$ and $+4.1\%$ to the inverted model's (m) accuracy is observed with JVS compared to $l_{2}$ and $l_{1}$ respectively. The same trend also holds true for the verifier (v), with $+1.9\%$ and $+3.7\%$ accuracy improvements from $l_{2}$ and $l_{1}$ when using JVS. Comparatively to $l_{2}$ and $l_{1}$ , JVS uses a combination of vector magnitudes and angles [15], providing a more balanced approach than magnitude-only or angle-only metrics. Therefore, we adopt $JVS$ as the priming distance method used between stimulus and synthesized feature vectors. + +Regularizers. In Table 3 we provide comparisons over different priming and regularizer combinations for our LEAPS objective. We report the top-1 accuracies of the inverted model (m), and verifier (v), as well as the IS of the inverted model across a range of spatiotemporal convolutional and attention-based architectures. We note that in the case of inverting $\mathrm{X3D_S}$ the same model is used for both model inversion and as the verifier, evidently resulting in matching verifier/inverted model accuracies. Overall, the priming objective $\mathcal{L}$ combined with either regularizer term yields clear improvements compared to the sole use of model priming. Modest improvements are observed with the combination of priming and the feature diversity regularizer over priming with temporal coherence. We believe that this is due to the + +
Video model architectures and variants
MetricR50X3D [11]TS [4]Video Swin [29]MViTv2 [27]rev-MViT-B [32]UniFormerv2 [26]
3D(2+1)D [58]CSN [57]XSSMLTSBSBBL
LEAPS L prim
top-1 (m)67.963.872.467.468.573.473.864.969.169.571.270.671.564.572.373.0
top-1 (v)53.149.555.851.968.559.860.452.652.353.557.654.656.750.756.456.9
IS3.9±0.92.4±0.54.2±0.64.0±1.04.3±0.65.1±1.15.5±1.32.7±0.74.1±1.64.2±1.14.4±0.84.3±1.24.6±0.73.1±1.74.3±0.84.5±1.2
LEAPS L + R prim coh
top-1 (m)70.465.776.174.875.678.078.573.172.873.274.573.774.269.274.975.3
top-1 (v)55.854.360.161.075.665.670.063.462.963.363.863.563.952.963.764.5
IS4.6±1.23.5±0.84.8±1.64.3±0.95.0±1.57.2±1.37.5±1.03.9±0.94.5±0.74.8±1.35.4±0.65.0±0.85.3±1.03.3±2.15.5±0.65.9±0.4
LEAPS L + R prim feat
top-1 (m)74.367.476.278.979.481.181.571.974.174.776.075.676.370.475.876.6
top-1 (v)60.256.964.365.879.469.370.867.263.264.565.466.768.058.269.069.8
IS5.1±0.84.2±1.45.6±1.27.3±1.17.6±0.88.8±1.59.1±1.23.8±1.24.7±1.14.9±0.55.3±1.55.1±0.65.5±1.24.0±1.85.7±1.06.2±0.9
LEAPS (full)
top-1 (m)86.778.088.386.287.090.390.883.685.786.287.485.185.982.587.188.3
top-1 (v)68.565.271.676.487.082.583.769.771.973.574.372.473.167.375.476.2
IS9.0±1.06.4±1.39.7±0.79.6±0.410.4±1.211.4±0.911.9±1.57.5±1.68.5±0.79.4±1.59.8±1.38.7±1.39.3±0.87.1±2.69.1±1.39.6±1.2
+ +Table 3: Top-1 accuracies and Inceprion Scores (IS) over different objectives across different architectures and model variants. X3Ds is used as the verifier (v) for all experiments. The best results per variant are in bold. The verifier accuracy is denoted in gray for the case of using X3Ds for both model inversion and as the verifier. + +
Modeltemp.×spatial2top-1ISLatency (secs) (↓I / ↑B)
mv
3D R508 × 182284.367.28.1±1.30.591 / 0.913
8 × 224286.768.59.7±1.00.832 / 1.205
16 × 224287.068.79.8±1.61.140 / 1.681
(2+1)D R508 × 182275.462.94.2±1.81.684/2.325
8 × 224278.065.26.4±1.31.858/2.793
16 × 224278.565.46.6±1.52.343/3.176
+ +Table 4: Synthesized video size comparisons based on the top-1 accuracies of the inverted model, and verifier, IS, and latency times for inference $(\downarrow \mathrm{I})$ and backprop $(\uparrow \mathrm{B})$ . Best settings per architecture are in bold. + +enhanced search space of $\mathcal{L}_{prim} + \mathcal{R}_{feat}$ as more diverse class features not in the stimulus are also explored. The combination of the priming objective with both regularizer terms for our proposed LEAPS consistently achieves the best results by a large margin compared to all other settings. LEAPS improves accuracy, for both the inverted model and verifier, as well as the quality of the generated videos based on the IS. These results further demonstrate that our proposed LEAPS optimization can be used across a range of architectures as a general spatiotemporal feature visualization method. Further qualitative examples for each network over different Kinetics classes are shown in Figures S1 to S4 in the supplementary alongside embeddings projections of LEAPS with different regularizer regimes in Section S3. + +Synthesized video resolution. Finally, we compare the accuracies, IS, and latency times when optimizing video inputs of different spatiotemporal sizes. Due to the majority of architectures requiring fixed-size inputs, we use 3D R50 and $(2 + 1)\mathrm{D}$ R50 as they are input size independent. From the top-1 (m/v) accuracies and IS summarized in Table 4, the best-performing setting across metrics is obtained with $16\times 224^{2}$ -sized inputs. We observe comparable performance on the temporally-reduced $8\times 224^{2}$ setting with + +a significantly more balanced performance-to-latency. Notable decreases in accuracies and IS are observed with the potentially limited spatial resolution $8 \times 182^{2}$ setting, making it less suitable. Due to the significant improvements in the per-iteration latency of the $8 \times 224^{2}$ inputs, we adopt this setting throughout our experiments. + +# 5. Conclusions + +We have introduced LEAPS, a novel spatiotemporal model inversion method for visualizing the learned internal representations of networks through video synthesis. LEAPS uses a stimulus video to prime a model and iteratively optimize an input by minimizing the classification and priming loss. The resulting synthesized video visualizes learned concepts that are associated with classes without prior knowledge of the training data. During optimization, LEAPS uses two regularizers. The first enforces temporal coherence between feature transitions across frames in the updatable input. The second improves the diversity of the synthesized features through a domain-specific verifier network to enhance the search space. The proposed architecture-independent method has shown qualitatively and quantitatively that it can produce high-quality and visually coherent synthesized videos over a wide range of spatiotemporal convolutional and attention-based video models. The high classification scores and synthesized video quality metrics make LEAPS a generalizable and effective spatiotemporal feature visualization method. We believe that this first step towards learned spatiotemporal representations synthesis is a promising direction in understanding video models. + +Acknowledgments. We use publicly available datasets and models. Research is funded by imec.icon Surv-AI-llance project and FWO (Grant G0A4720N). + +# References + +[1] Mordvintsev Alexander, Olah Christopher, and Tyka Mike. Inceptionism: Going deeper into neural networks. Google Research Blog, 2015. 2, 4, 5 +[2] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. 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The majority of these approaches encode features in a joint space-time modality for which the inner workings and learned representations are difficult to visually interpret. We propose LEArned Preconscious Synthesis (LEAPS), an architecture-independent method for synthesizing videos from the internal spatiotemporal representations of models. Using a stimulus video and a target class, we prime a fixed space-time model and iteratively optimize a video initialized with random noise. Additional regularizers are used to improve the feature diversity of the synthesized videos alongside the cross-frame temporal coherence of motions. We quantitatively and qualitatively evaluate the applicability of LEAPS by inverting a range of spatiotemporal convolutional and attention-based architectures trained on Kinetics-400, which to the best of our knowledge has not been previously accomplished." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 449, + 386, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 449, + 386, + 462 + ], + "spans": [ + { + "bbox": [ + 306, + 449, + 386, + 462 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 472, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 675 + ], + "type": "text", + "content": "Inverting deep networks' learned internal representations has been a difficult task to achieve. The adaptation and deployment of CNNs and more recently Transformers, to a variety of vision tasks has led to significant breakthroughs. The field of video action recognition has experienced drastic growth in recent years through the convergence of models with increased complexities and capacities [2, 4, 32, 63] as well as large accuracy improvements [11, 12, 27, 26, 29]. Despite great progress in their applicability, there is still a large gap in the interpretability of video models. As these models compositionally encode space and time modalities of videos over large feature spaces and require a lot of parameters, conceptualizing their internal representations remains challenging. In this paper, we propose a method to invert learned features of video models associated with specific actions by optimizing a parameterized input to synthesize conceptually and visually coherent representations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": "In cognitive science, stages of consciousness include the conscious, the unconscious, and the preconscious. In contrast to the conscious and unconscious, the preconscious is" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 260, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 260, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 260, + 712 + ], + "type": "text", + "content": "See alexandrosstergiou/LEAPS for video examples and code." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 733, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 733, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 733, + 315, + 742 + ], + "type": "text", + "content": "1966" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "responsible for learned information currently outside conscious awareness to remain readily available [18]. One way of accessing learned preconscious information and making it part of conscious awareness is through priming [38]. Priming uses a stimulus to activate related learned concepts in memory and make them easily and readily accessible [33, 34]; e.g., one can remember their bedroom if primed with a picture of a bed." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 275 + ], + "type": "text", + "content": "Motivated by visual priming in cognitive science, we demonstrate that learned representations of video models can become accessible through model priming. By using a video stimulus and a target action class, we synthesize the dominant learned concepts corresponding to actions. In turn, the visual features of the synthesized videos provide a conceptual view of the models' learned internal representations. We term these features as the learned preconscious of the video model associated with a specific action." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 275, + 289, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 455 + ], + "type": "text", + "content": "We introduce LEArned Preconscious Synthesis (LEAPS), illustrated in Figure 1, a spatiotemporal model inversion method that synthesizes interpretable videos by minimizing a classification and priming loss without prior knowledge of the training data. LEAPS uses a video of a target action class as stimulus, to prime a fixed spatiotemporal model. We additionally include two regularization terms. The first term enforces motion coherence across frames by constraining their representations at each update. The second enhances the diversity of the synthesized videos by using a domain-specific verifier network that exploits disagreements between feature statistics similar to [64]. Through the same architecture-independent approach, we show that LEAPS can invert the spatiotemporal features of 3D-CNNs and spatiotemporal Transformers." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 456, + 289, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 289, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 289, + 575 + ], + "type": "text", + "content": "Our main contributions are as follows. First, we introduce LEAPS, a general approach for inverting video models, which to the best of our knowledge, is the first attempt to create videos of conceptual representations from jointly encoded space-time features. Second, we use LEAPS on multiple convolution and attention models and compare it to prior image-based inversion methods that we extend to video. Finally, we show that LEAPS can invert both video CNNs and transformers, with the same architecture-independent method without any modifications." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "content": "Approaches for visualizing and interpreting deep models can be divided into three groups which we detail below." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": "Attribution-based visualizations. These methods have been used to visualize feature contributions over an input. Attribution methods for images have primarily been based on back-propagating activations of classes [8, 48, 61], or individual neurons [3, 5, 49, 52] to localize regions in the input that are informative for a given class or feature. Such approaches include Integrated gradients (IG) [56] which" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": "produce pixel-wise attributions from integrating computed backprop gradients. Subsequent works have also included gradient smoothing [51], gradient accumulation in saturated regions [35], and adaptation of the gradient path [23]. Another set of approaches that rely on attribution-based visualizations use perturbations of the input [17, 16, 44]. Given their straightforward applicability, image attribution methods have also been extended to video. The majority of works; e.g., Saliency Tubes [55, 54], STEP [28], video OSA [59], and BOREx [24], have focused on the localization of spatiotemporal salient regions by extending GradCAM [48], Extremal Perturbations (EP) [16], Occlusion Sensitivity Analysis (OSA) [66], and Gaussian processes regression (GPR) [6, 37] respectively. In contrast to these approaches that localize salient class features, we offer a visual feature synthesis method to conceptualize the learned representations of video models through priming." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 279, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 547, + 579 + ], + "type": "text", + "content": "Input synthesis. Network-centric approaches invert models to either visualize particular classes [41, 65, 64] or features [43, 53]. One of the main methods employed for visualizing internal network features is Gradient Ascent (GA) [10], which optimizes the input by increasing the activation of a specific neuron. Activation Maximization (AM) [50] later adapted GA to visualize CNN features. Following works have been built on top of AM by including additional regularizers; e.g., total variation [31], blurring [60], and gradient masking [41]. One of the most popular extensions of AM has been DeepDream [1] which optimizes the input to yield high responses for a chosen class while keeping internal representations constraint-free. The produced images include repetitions of recognizable concepts without representing a coherent whole. In addition to AM, model inversion [9, 19, 30, 64, 66] includes the task of maximizing the classification score of the synthesized image instead of maximizing class activations. The only extension of input synthesis approaches to videos has been introduced by Feichtenhofer et al. [13] in which AM is used to create visual representations of class features from two-steam models [14, 62], trained on RGB frames (spatial stream) and optical flow (temporal stream). In this paper, we instead propose a model inversion method for inverting video models concurrently encoding space and time modalities." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Visual feature generation. These methods utilize activation maximization by including an additional generator network [39, 40, 42], with the cost of requiring access to the training data. Huang et al. [21] adapted feature generation on video data by modeling the temporal signal with a temporal generator network. Despite the high fidelity of the produced results, these approaches are less suitable for interpreting internal model behaviors, as they do not solely depend on the model under inspection. Instead, they are primarily influenced by the training data used as well as the capacity and complexity of the generator model trained." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "text", + "content": "1967" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 226, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 226, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 226, + 85 + ], + "type": "text", + "content": "3. Learned Preconscious Synthesis" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "type": "text", + "content": "In this section, we overview our LEAPS method, shown in Figure 1. We start by formally introducing model priming for video models in Section 3.1. A stimulus video of a target class is used to initially prime the network. The training process uses the primed representations to update a randomly initialized input alongside two regularizers. The first regularizer is used to enforce temporal coherence, explained in Section 3.2. The second is used to improve synthesized feature diversity, overviewed in Section 3.3. We present the final aggregated function in Section 3.4." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 219, + 141, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 219, + 141, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 219, + 141, + 232 + ], + "type": "text", + "content": "3.1. Model Priming" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "text", + "content": "Priming deep models is influenced by cognitive science [38] in which a stimulus is used to recall prior knowledge. We extend this approach to visualizing the learned preconscious of deep video models associated with a specific action class " + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "text", + "content": ". 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We define a priming loss " + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{prim}(\\mathbf{x}^*,\\mathbf{v})" + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "text", + "content": " between the internal representations " + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^l (\\cdot)" + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "text", + "content": " of the optimized input " + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "text", + "content": " and stimulus " + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "text", + "content": " across " + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "inline_equation", + "content": "l\\in \\Lambda = \\{1,\\dots,L\\}" + }, + { + "bbox": [ + 46, + 237, + 288, + 376 + ], + "type": "text", + "content": " layers:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 384, + 287, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 384, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 53, + 384, + 287, + 413 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p r i m} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}\\right) = \\frac {1}{L} \\sum_ {l \\in \\boldsymbol {\\Lambda}} \\lambda_ {l} J V S \\left(\\mu \\left(\\mathbf {z} ^ {l} \\left(\\mathbf {x} ^ {*}\\right)\\right), \\mu \\left(\\mathbf {z} ^ {l} (\\mathbf {v})\\right)\\right) \\tag {1}", + "image_path": "874fea13b43d9e34df59edfe448e4f8b0186f147392e7f68e69dd5e4f5c32334.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mu (\\mathbf{z}^l (\\cdot))" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": "-length spatiotemporal mean vector of representations " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^l (\\cdot)" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "JVS(\\cdot)" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": " denotes the Jaccard vector similarity [15]. To integrate a degree of freedom and avoid hard constraints on the internal representations of " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": ", we define " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "0 < \\lambda_{l}\\leq 1" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": " as priming weight for layer " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": ". An overview of updating " + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 46, + 422, + 287, + 495 + ], + "type": "text", + "content": " by priming appears in Figure 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 495, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 564 + ], + "type": "text", + "content": "Due to the vastness of the feature space when optimizing (1), we include two additional regularization terms to constrain the input. Specifically, we apply a temporal coherence regularization " + }, + { + "bbox": [ + 46, + 495, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 495, + 287, + 564 + ], + "type": "text", + "content": " and a feature diversity regularization " + }, + { + "bbox": [ + 46, + 495, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{coh}" + }, + { + "bbox": [ + 46, + 495, + 287, + 564 + ], + "type": "text", + "content": " which we detail below." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 571, + 241, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 241, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 241, + 585 + ], + "type": "text", + "content": "3.2. Temporal Coherence Regularization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 590, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 653 + ], + "type": "text", + "content": "For the first regularizer, we aim to enforce similarity between representations of consecutive frames in order to enable consistent feature transitions in the synthesized video. Therefore, we include a coherence regularizer " + }, + { + "bbox": [ + 46, + 590, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 590, + 287, + 653 + ], + "type": "text", + "content": ", formulated based on the temporal coherence loss from [36]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "Given two spatiotemporal representations " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^L (\\mathbf{x}^*)_{t_1}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{L}(\\mathbf{x}^{*})_{t_{2}}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " at layer " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": ", for temporal locations " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "t_1" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": ", we use their " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " norm to enforce similarity if " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "t_1" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " are consecutive in the video. In non-consecutive cases, the divergence between " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^L (\\mathbf{x}^*)_{t_1}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{L}(\\mathbf{x}^{*})_{t_{2}}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " should increase. The" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 547, + 200 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 547, + 200 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 547, + 200 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 547, + 200 + ], + "type": "image", + "image_path": "06a8bb79959d74222cf8c0b423df200da78072f431cc7bc918bfd377c3eb7d4f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 209, + 547, + 305 + ], + "lines": [ + { + "bbox": [ + 304, + 209, + 547, + 305 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 547, + 305 + ], + "type": "text", + "content": "Figure 2: Temporal Coherence regularization of zumba target action label. Applying temporal coherence regularization on representations from all layers " + }, + { + "bbox": [ + 304, + 209, + 547, + 305 + ], + "type": "inline_equation", + "content": "l \\in \\Lambda" + }, + { + "bbox": [ + 304, + 209, + 547, + 305 + ], + "type": "text", + "content": " synthesizes static videos (bottom row). Instead, regularizing only the final network layer " + }, + { + "bbox": [ + 304, + 209, + 547, + 305 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 209, + 547, + 305 + ], + "type": "text", + "content": " synthesizes videos with consistent frame transitions and motions (top row). We note that the video stimulus is shown as a reference as the regularizations are only applied to synthesized video representations." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 319, + 464, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 464, + 330 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 464, + 330 + ], + "type": "text", + "content": "coherence regularizer is formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 307, + 342, + 545, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 342, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 307, + 342, + 545, + 384 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {c o h} \\left(\\mathbf {x} ^ {*}\\right) = \\left\\{ \\begin{array}{l} \\left\\| \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {1}} - \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {2}} \\right\\| _ {1}, \\text {i f c o n s e c u t i v e} \\\\ \\max \\left(0, \\delta - \\left\\| \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {1}} - \\mathbf {z} ^ {L} \\left(\\mathbf {x} ^ {*}\\right) _ {t _ {2}} \\right\\| _ {1}\\right), \\text {e l s e w i s e} \\end{array} \\right. \\tag {2}", + "image_path": "5bf6e6cf9897a7faf0fe478ad8f95a03f5a47dfee899f3b8431d53e62c3892de.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": " is a margin hyperparameter. Temporal coherence is enforced at layer " + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": " as in [36]. Although " + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{coh}" + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": " can be applied to any layer " + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "inline_equation", + "content": "l\\in \\Lambda" + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": ", in practice, minimizing (2) for all layers enforces a very strong regularization, producing synthesized videos with minimal to no cross-frame variations as shown in Figure 2. We note that for Transformers using patches of " + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "inline_equation", + "content": "P^3" + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": " resolution, we first reshape " + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{L}(\\mathbf{x}^{*})" + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "inline_equation", + "content": "C^\\prime P^3\\times \\frac{T'H'W'}{P^3}" + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "inline_equation", + "content": "C^\\prime \\times T^\\prime \\times H^\\prime W^\\prime" + }, + { + "bbox": [ + 304, + 384, + 546, + 486 + ], + "type": "text", + "content": " before calculating (2)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 496, + 482, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 496, + 482, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 496, + 482, + 509 + ], + "type": "text", + "content": "3.3. Feature Diversity Regularization" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 516, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 664 + ], + "type": "text", + "content": "Our second regularization term " + }, + { + "bbox": [ + 304, + 516, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\text {feat }}" + }, + { + "bbox": [ + 304, + 516, + 545, + 664 + ], + "type": "text", + "content": " is responsible for improving the diversity of features generated by model priming. Although priming provides a strong signal based on which the input can be updated, the diversity of features is limited compared to observing multiple instances. Thus, class features varying from those in the stimulus, or features not present in the stimulus, may not be explored during optimization. In order to enhance the search space we introduce an additional domain-specific verifier network " + }, + { + "bbox": [ + 304, + 516, + 545, + 664 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 304, + 516, + 545, + 664 + ], + "type": "text", + "content": ". Our goal is to use high- and low-level feature distribution statistics as proposed in [64] incorporating the verifier's prior knowledge during optimization." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": "Based on input " + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": ", we run inference on the verifier " + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "S(\\mathbf{x}^*)" + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": " to obtain representations " + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{a}^k (\\mathbf{x}^*)" + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": " across each verifier layer " + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "k\\in" + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": ". The feature statistics are then obtained by the " + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": "-length space-time mean " + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mu\\left(\\mathbf{a}^k (\\mathbf{x}^*)\\right)" + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\sigma^2\\left(\\mathbf{a}^k (\\mathbf{x}^*)\\right)" + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": " vec" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "text", + "content": "1968" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 289, + 144 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 289, + 144 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 289, + 144 + ], + "type": "image", + "image_path": "70a8585fdbdbddc249b29069ee043a2ac37425009731682e453188fb6b5a67bb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 154, + 287, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 154, + 287, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 154, + 287, + 226 + ], + "type": "text", + "content": "Figure 3: Feature diversity regularization. Given the video stimulus in blue, synthesized videos in orange are optimized only from the stimulus. Synthesized videos with feature diversity regularization are shown in red. The regularized videos can also include general class features different from or not existing in the stimulus." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 236, + 253, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 236, + 253, + 248 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 253, + 248 + ], + "type": "text", + "content": "tors. The feature diversity regularizer is defined as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 256, + 286, + 310 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 256, + 286, + 310 + ], + "spans": [ + { + "bbox": [ + 53, + 256, + 286, + 310 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\underset {f e a t} {\\mathcal {R}} \\left(\\mathbf {x} ^ {*}\\right) = \\sum_ {k \\in \\mathbf {K}} \\left\\| \\mu \\left(\\mathbf {a} ^ {k} \\left(\\mathbf {x} ^ {*}\\right)\\right) - \\mathbb {E} \\left(\\mu \\left(\\mathbf {a} ^ {k} (\\mathbf {x})\\right) \\mid \\mathcal {X}\\right) \\right\\| _ {2} + (3) \\\\ \\sum_ {k \\in \\mathbf {K}} | | \\sigma^ {2} (\\mathbf {a} ^ {k} (\\mathbf {x} ^ {*})) - \\mathbb {E} \\left(\\sigma^ {2} (\\mathbf {a} ^ {k} (\\mathbf {x})) | \\mathcal {X}\\right) | | _ {2} (3) \\\\ \\end{array}", + "image_path": "cd895ffbe0d726093444a3dbf5fb6ea05d80608e397941cf8b11684c5ad5fac8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\mathbb{E}(\\cdot)" + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "content": " corresponds to the expected value of representation " + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\mathbf{a}(\\cdot)" + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "content": " for video input " + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "content": " part of video dataset " + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "content": ". Instead of requiring access to the dataset to train over " + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "content": " videos, we use the Batch Normalization [22] running mean and variance to approximate the expected mean and variance as in [64]. The mean and variance estimates are then reformulated as " + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\mathbb{E}\\left(\\mu\\left(\\mathbf{a}^k(\\mathbf{x})\\right) \\mid \\mathcal{X}\\right) \\simeq BN^k(\\text{running\\_mean})" + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "inline_equation", + "content": "\\mathbb{E}\\left(\\sigma^2\\left(\\mathbf{a}^k(\\mathbf{x})\\right) \\mid \\mathcal{X}\\right) \\simeq BN^k(\\text{running\\_variance})" + }, + { + "bbox": [ + 46, + 319, + 287, + 440 + ], + "type": "text", + "content": ". An illustration of the improved search space achieved with the inclusion of feature diversity is shown in Figure 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 447, + 223, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 223, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 223, + 459 + ], + "type": "text", + "content": "3.4. Aggregation for Model Inversion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 465, + 287, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 287, + 636 + ], + "type": "text", + "content": "We have introduced model priming as a method to obtain a strong signal from a stimulus video with which noise-initialized videos can be optimized. To implicitly enforce transition continuity across frames, we include a temporal coherence regularizer. In addition, as the stimulus does not provide prior intuition about the diversity of features, we use a feature diversity regularizer to enhance the search space. Given their complementary properties, we formulate the final LEAPS objective as the combination of model priming, temporal coherence, and feature diversity regularizers. In line with spatial feature visualization losses that synthesize distinguishable features from noise [1, 36, 47, 64], we include a cross-entropy loss " + }, + { + "bbox": [ + 46, + 465, + 287, + 636 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CE}" + }, + { + "bbox": [ + 46, + 465, + 287, + 636 + ], + "type": "text", + "content": " from class predictions given the synthesized input " + }, + { + "bbox": [ + 46, + 465, + 287, + 636 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 46, + 465, + 287, + 636 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 645, + 287, + 664 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 645, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 59, + 645, + 287, + 664 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}, y\\right) = \\mathcal {L} _ {C E} \\left(\\mathbf {x} ^ {*}, y\\right) + \\mathcal {L} _ {p r i m} \\left(\\mathbf {x} ^ {*}, \\mathbf {v}\\right) + r \\mathcal {R} \\left(\\mathbf {x} ^ {*}\\right) \\tag {4}", + "image_path": "6fd1750b6fa64177602091e92066e8842ba901e41a1f1c358e0fb01a8a948318.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 673, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 287, + 714 + ], + "type": "text", + "content": "where the regularizer term combines (2) and (3): " + }, + { + "bbox": [ + 47, + 673, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\mathbf{x}^{*}) = \\mathcal{R} + \\mathcal{R}" + }, + { + "bbox": [ + 47, + 673, + 287, + 714 + ], + "type": "text", + "content": ". Respectively, " + }, + { + "bbox": [ + 47, + 673, + 287, + 714 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 47, + 673, + 287, + 714 + ], + "type": "text", + "content": " is a regularizer scaling factor. The final LEAPS objective enables the synthesis of high-fidelity" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "features without being constrained by data availability or architecture types as shown in the results section." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 110, + 389, + 123 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 110, + 389, + 123 + ], + "spans": [ + { + "bbox": [ + 305, + 110, + 389, + 123 + ], + "type": "text", + "content": "4. Main Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 131, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 131, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 131, + 545, + 239 + ], + "type": "text", + "content": "We first detail the train scheme and implementation settings used in Section 4.1. We then compare our proposed LEAPS method to image-based feature visualization methods that we extend to video and use as baselines in Section 4.2. We also qualitatively and quantitatively investigate the synthesized videos across a variety of video models in Section 4.3. Finally, in Section 4.4 we perform ablation studies for the LEAPS objective as well as different updatable input spatiotemporal resolutions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 249, + 425, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 249, + 425, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 249, + 425, + 262 + ], + "type": "text", + "content": "4.1. Experimental details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 268, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 411 + ], + "type": "text", + "content": "Model details. We invert 3D [20]/(2+1)D [58]/CSN [57] ResNet-50 (R50), X3D [11], TimeSformer [4], Video Swin [29], MViTv2 [27], rev-MViT [32], and UniFormerv2 [26] networks. For all our experiments, we use the official networks available from their respective repositories pretrained on Kinetics-400 [7]. Due to its limited computational overhead and requirement of BN layers by the feature diversity regularizer in (3), we use " + }, + { + "bbox": [ + 304, + 268, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\mathrm{X3DS}" + }, + { + "bbox": [ + 304, + 268, + 545, + 411 + ], + "type": "text", + "content": " as the verifier network " + }, + { + "bbox": [ + 304, + 268, + 545, + 411 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 304, + 268, + 545, + 411 + ], + "type": "text", + "content": ". We note that only the internal representations and predictions from the inverted and verifier models are used. Both models only run inference and remain fixed throughout the feature synthesis." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": "Feature synthesis optimization details. Video input " + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": " is initialized with size of " + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "inline_equation", + "content": "8 \\times 224^2" + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": ". For models [11, 4, 29, 27, 32, 26] which use inputs of fixed size, we first interpolate " + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": " to match the required size2. Priming stimuli are selected from the Kinetics-400 validation set randomly. For transformer models, " + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": " are first tokenized. We use Adam [25] with a learning rate of 0.2 and a cosine decrease policy as in [64]. We use a total of 2K gradient updates. As in [36], we set " + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\delta = 1" + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": ". To discover the optimal " + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 413, + 545, + 568 + ], + "type": "text", + "content": " hyperparameters for each network we use Mango [46] to perform a simple grid search for 1K gradient updates. A full overview of the hyperparameters used by each model is available in Table S1 in the supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 578, + 401, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 578, + 401, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 578, + 401, + 590 + ], + "type": "text", + "content": "4.2. Baseline results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 597, + 545, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 545, + 682 + ], + "type": "text", + "content": "We first assess the quality of the synthesized videos. We invert 3D R50, " + }, + { + "bbox": [ + 304, + 597, + 545, + 682 + ], + "type": "inline_equation", + "content": "\\mathrm{X3D_M}" + }, + { + "bbox": [ + 304, + 597, + 545, + 682 + ], + "type": "text", + "content": ", and Video Swin-B models and report the averaged top-1 classification accuracies and Inception Scores (IS) [45] on synthesized videos using each video from the validation set of Kinetics-400 as a stimulus. We extend two prominent image-based feature visualization methods making them applicable to spatiotemporal models:" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "2Due to space limitations in Figures 5 to 8 the last 2 frames of " + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": " are not shown." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "text", + "content": "1969" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 286, + 324 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 324 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 324 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 324 + ], + "type": "table", + "html": "
Visualization methodtop-1 (%)Inception Score (IS)
modelver.modelverifier
3D R50
3D Deep Dream [1]34.52.61.1 ± 0.11.0
3D AM [13]41.45.81.4 ± 0.31.2 ± 0.2
LEAPSours( L )prim67.953.13.9 ± 0.93.2 ± 0.6
LEAPSours( L + R )primfeat74.360.25.1 ± 0.83.9 ± 1.4
LEAPSours(full)86.768.59.0 ± 1.05.7 ± 0.7
X3DM
3D Deep Dream [1]18.11.91.1 ± 0.11.1 ± 0.1
3D AM [13]33.25.61.3 ± 0.31.2 ± 0.2
LEAPSours( L )prim73.459.85.1 ± 1.13.9 ± 0.4
LEAPSours( L + R )primfeat81.169.38.8 ± 1.56.3 ± 0.8
LEAPSours(full)90.382.511.4 ± 0.98.0 ± 1.4
Video Swin-B
3D Deep Dream [1]15.91.41.4 ± 0.21.1 ± 0.1
3D AM [13]25.62.21.6 ± 0.41.1 ± 0.1
LEAPSours( L )prim71.258.64.4 ± 0.83.5 ± 0.6
LEAPSours( L + R )primfeat76.065.45.3 ± 1.54.1 ± 1.1
LEAPSours(full)87.474.39.8 ± 1.36.5 ± 0.9
", + "image_path": "f71af7da34559e233d89fded369f5f0cd854fb67c21349288d7cbcb1914d4f36.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 287, + 367 + ], + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 367 + ], + "type": "text", + "content": "Table 1: Quantitative results for mean top-1 accuracy and Inception Score (IS). The best results per metric are in bold and per architecture are underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 377, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 413 + ], + "type": "text", + "content": "DeepDream [1] optimizes the input by a cross-entropy loss. It uses two regularizers including the total variance and " + }, + { + "bbox": [ + 46, + 377, + 287, + 413 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 46, + 377, + 287, + 413 + ], + "type": "text", + "content": " norm on the input to improve convergence." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 414, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 474 + ], + "type": "text", + "content": "Activation Maximization (AM) [31] optimizes a random noise image by gradient ascent to maximize the activation of a specific class. We specifically adapt [13] for visualizing concurrent spatiotemporal representations, as it is the only prior method for visualizing features over space and time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 666 + ], + "type": "text", + "content": "Quantitative evaluation. Table 1 shows the average top-1 accuracies and IS obtained by both the inverted models and verifier when inferring synthesized videos. For DeepDream and AM that do not use priming, the statistics are averaged across 10 runs per class. In LEAPS the statistics are calculated using each video in the Kinetics validation set as stimulus. For both measures, LEAPS yields consistently higher accuracies and IS compared to DeepDream and AM. Notably, it significantly improves the verifier accuracy across all three architectures. This demonstrates the merits of model priming as both DeepDream and AM optimize inputs solely by maximizing feature or class activations, without using the information-rich internal representations provided by a stimulus. This trend is also visible in the IS, as LEAPS regularizes the synthesized features in order to better represent learned temporally coherent motions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "Qualitative examples. Videos for the class salsa spin synthesized from different methods are shown in Figure 4. Features synthesized with LEAPS are significantly more visually distinct compared to those of baseline methods. As" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 422, + 128 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 422, + 128 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 422, + 128 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 422, + 128 + ], + "type": "image", + "image_path": "8784158481e24f3387f319d444bc084e7a00f7396a31522acfb31122b0855db7.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 134, + 406, + 145 + ], + "lines": [ + { + "bbox": [ + 323, + 134, + 406, + 145 + ], + "spans": [ + { + "bbox": [ + 323, + 134, + 406, + 145 + ], + "type": "text", + "content": "(a) 3D DeepDream [1]" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 430, + 71, + 545, + 129 + ], + "blocks": [ + { + "bbox": [ + 430, + 71, + 545, + 129 + ], + "lines": [ + { + "bbox": [ + 430, + 71, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 430, + 71, + 545, + 129 + ], + "type": "image", + "image_path": "a160190ca42e31869edd94b575cff0482966d8c1608a5359c934848388bdfa81.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 459, + 134, + 517, + 144 + ], + "lines": [ + { + "bbox": [ + 459, + 134, + 517, + 144 + ], + "spans": [ + { + "bbox": [ + 459, + 134, + 517, + 144 + ], + "type": "text", + "content": "(b) 3D AM [13]" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 419, + 129, + 435, + 146 + ], + "blocks": [ + { + "bbox": [ + 419, + 129, + 435, + 146 + ], + "lines": [ + { + "bbox": [ + 419, + 129, + 435, + 146 + ], + "spans": [ + { + "bbox": [ + 419, + 129, + 435, + 146 + ], + "type": "image", + "image_path": "e277a2aa298b51bee470690cde9a1d49a12275670a8c964515b8fd3e82b55a34.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 148, + 422, + 208 + ], + "blocks": [ + { + "bbox": [ + 307, + 148, + 422, + 208 + ], + "lines": [ + { + "bbox": [ + 307, + 148, + 422, + 208 + ], + "spans": [ + { + "bbox": [ + 307, + 148, + 422, + 208 + ], + "type": "image", + "image_path": "da45d9d4c817bb98b216719aad851caddac28d6925666272a81811033c88999d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 213, + 398, + 222 + ], + "lines": [ + { + "bbox": [ + 331, + 213, + 398, + 222 + ], + "spans": [ + { + "bbox": [ + 331, + 213, + 398, + 222 + ], + "type": "text", + "content": "(c) stimulus video" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 148, + 542, + 207 + ], + "blocks": [ + { + "bbox": [ + 427, + 148, + 542, + 207 + ], + "lines": [ + { + "bbox": [ + 427, + 148, + 542, + 207 + ], + "spans": [ + { + "bbox": [ + 427, + 148, + 542, + 207 + ], + "type": "image", + "image_path": "5e9e79b62a196a4a974bf328534e5fe1d9d2a24d00da6fee1e98855f0d605797.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 465, + 212, + 506, + 222 + ], + "lines": [ + { + "bbox": [ + 465, + 212, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 465, + 212, + 506, + 222 + ], + "type": "text", + "content": "(d) LEAPS" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 309, + 274, + 544, + 407 + ], + "blocks": [ + { + "bbox": [ + 305, + 228, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 264 + ], + "type": "text", + "content": "Figure 4: Different feature synthesis methods for visualizing " + }, + { + "bbox": [ + 305, + 228, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\mathbf{X3D_M}" + }, + { + "bbox": [ + 305, + 228, + 545, + 264 + ], + "type": "text", + "content": " features corresponding to class salsa dancing. Stimulus video is only used for LEAPS." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 274, + 544, + 407 + ], + "lines": [ + { + "bbox": [ + 309, + 274, + 544, + 407 + ], + "spans": [ + { + "bbox": [ + 309, + 274, + 544, + 407 + ], + "type": "image", + "image_path": "4ba066fe583282977d3e21a552af9a9ff2fa6060937a01064bfa489acb56b4f5.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 415, + 545, + 452 + ], + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 452 + ], + "type": "text", + "content": "Figure 5: Feature synthesis over different runs for action class bartending. MViTv2 features are from different runs based on the same priming stimulus." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "content": "shown, videos produced by image-based methods extended to videos fail to represent learned spatiotemporal deep features. The visual quality of the synthesized videos also correlates with the accuracies and IS in Table 1." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 508, + 546, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 546, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 546, + 652 + ], + "type": "text", + "content": "Figure 5 illustrates synthesized videos from different runs given the same stimulus for class bartending. A substantial difference in the quality and representability of the visualizations between LEAPS and the extended 3D AM can be seen across runs. Despite the use of a video stimulus to prime the network, LEAPS visualizations are not constrained by the representations of the stimulus video. Each run of our LEAPS method shows a distinct visual style as feature diversity is encouraged during optimization through the homonym regularizer term. Effectively, LEAPS can be used as a tool for investigating the different class-specific features learned by each model." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 659, + 502, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 502, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 502, + 672 + ], + "type": "text", + "content": "4.3. Analysis of LEAPS synthesized video" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "The generalizability of feature visualization methods across multiple architectures is largely neglected with features from only a small subset of models being visualized." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "text", + "content": "1970" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 298, + 349 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 298, + 349 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 298, + 349 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 298, + 349 + ], + "type": "image", + "image_path": "be1c6339db0b3a265302cb88a6bc6188e3b2495ff6ef2f79cb0b9cb02baf3e62.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 358, + 545, + 383 + ], + "lines": [ + { + "bbox": [ + 47, + 358, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 545, + 383 + ], + "type": "text", + "content": "Figure 6: Qualitative examples of synthesized spatiotemporal features with LEAPS. Models are primed with a stimulus video, shown on the left of each row of synthesized videos." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 299, + 71, + 545, + 348 + ], + "blocks": [ + { + "bbox": [ + 299, + 71, + 545, + 348 + ], + "lines": [ + { + "bbox": [ + 299, + 71, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 299, + 71, + 545, + 348 + ], + "type": "image", + "image_path": "a68c8a8f6e36180220d2b660e44d2540b6a4788673f27253cc3c7fb6a8d78840.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 392, + 285, + 481 + ], + "blocks": [ + { + "bbox": [ + 50, + 392, + 285, + 481 + ], + "lines": [ + { + "bbox": [ + 50, + 392, + 285, + 481 + ], + "spans": [ + { + "bbox": [ + 50, + 392, + 285, + 481 + ], + "type": "image", + "image_path": "7fcddab8bb524f93ae2b5158aef000af1f79e78d4727bb3989f876183f6e6b71.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 100, + 483, + 235, + 492 + ], + "lines": [ + { + "bbox": [ + 100, + 483, + 235, + 492 + ], + "spans": [ + { + "bbox": [ + 100, + 483, + 235, + 492 + ], + "type": "text", + "content": "(a) stimulus video for doing aerobics" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 53, + 495, + 286, + 583 + ], + "blocks": [ + { + "bbox": [ + 53, + 495, + 286, + 583 + ], + "lines": [ + { + "bbox": [ + 53, + 495, + 286, + 583 + ], + "spans": [ + { + "bbox": [ + 53, + 495, + 286, + 583 + ], + "type": "image", + "image_path": "da76de2388190c903513f14cba84a307fc30d9edf46e1bfaae0cfe508d47db4a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 113, + 584, + 221, + 594 + ], + "lines": [ + { + "bbox": [ + 113, + 584, + 221, + 594 + ], + "spans": [ + { + "bbox": [ + 113, + 584, + 221, + 594 + ], + "type": "text", + "content": "(b) LEAPS synthesized video" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 605, + 287, + 642 + ], + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 642 + ], + "type": "text", + "content": "Figure 7: SSIM and PSNR statistics over real and synthesized videos using Video Swin-B features. Lower values correspond to larger cross-frame differences." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 700 + ], + "type": "text", + "content": "To evaluate the architecture-independent nature of LEAPS and better understand the visual fidelity of the synthesized videos, we investigate the applicability of LEAPS over a range of convolutional and attention-based video models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 713 + ], + "type": "text", + "content": "Generalizability. The quality of the produced feature vi" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 393, + 545, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 545, + 704 + ], + "type": "text", + "content": "sualizations may depend on the architecture used, as models vary in terms of their complexities and feature spaces that they employ. We compare our proposed LEAPS visualization method by inverting common video models shown in Figure 6 for an arbitrary number of Kinetics classes. A common theme that arises for all models is the association of objects with specific actions. For example, the feature visualizations for the throwing ball, catching/throwing frisbee, eating spaghetti, and snatch weight lifting actions from inverted features of 3D R50, (2+1)D R50, Video Swin-B, and rev-MViT-B respectively, all optimize the video to primarily focus on the objects associated with the specific actions. Instead, for actions that are primarily perceived by motions performed, e.g. running on treadmill and dancing ballet, the actors/performers of the target actions are shown to be more conceptually influential to the model's learned preconscious of an action, with their associated motions and movements captured by the produced visualizations. In addition, the visualizations for cases eating spaghetti, blowing out candles, and sword fighting reveal that networks also learn to temporally bound distinct spatiotemporal features of certain actions. This is an important ability to be learned by video models as it effectively demonstrates their capacity to filter temporal information alongside the spatial signal. Notably, LEAPS visualizations for both convolutional and attention-based models show that learned features have" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 732, + 314, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 732, + 314, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 732, + 314, + 742 + ], + "type": "text", + "content": "1971" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 285, + 113 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 285, + 113 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 285, + 113 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 285, + 113 + ], + "type": "image", + "image_path": "d7ff5f0265891765d366eb7a38a4d1cb58f6c99ded332b974218d68985d4e8b1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 121, + 285, + 161 + ], + "blocks": [ + { + "bbox": [ + 49, + 121, + 285, + 161 + ], + "lines": [ + { + "bbox": [ + 49, + 121, + 285, + 161 + ], + "spans": [ + { + "bbox": [ + 49, + 121, + 285, + 161 + ], + "type": "image", + "image_path": "38502353adebc055cd25a338a85dfe49d8c1e913d81296ab0d45d1450b34f444.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 163, + 285, + 202 + ], + "blocks": [ + { + "bbox": [ + 49, + 163, + 285, + 202 + ], + "lines": [ + { + "bbox": [ + 49, + 163, + 285, + 202 + ], + "spans": [ + { + "bbox": [ + 49, + 163, + 285, + 202 + ], + "type": "image", + "image_path": "da530fe95c3602b4046aecdaf8a6d6ffdb44bf0f177ebf8e64596e1fda192e7f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 49, + 204, + 285, + 243 + ], + "blocks": [ + { + "bbox": [ + 49, + 204, + 285, + 243 + ], + "lines": [ + { + "bbox": [ + 49, + 204, + 285, + 243 + ], + "spans": [ + { + "bbox": [ + 49, + 204, + 285, + 243 + ], + "type": "image", + "image_path": "20c5ea8a1cd50a2707580e19042d6d02581baf2cc2ab3b8ab5aca8c651333ec7.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 255, + 287, + 280 + ], + "lines": [ + { + "bbox": [ + 47, + 255, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 287, + 280 + ], + "type": "text", + "content": "Figure 8: Video synthesis at different optimization stages for class riding on a bike. " + }, + { + "bbox": [ + 47, + 255, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathrm{X3D_M}" + }, + { + "bbox": [ + 47, + 255, + 287, + 280 + ], + "type": "text", + "content": " features are used." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "content": "a good correspondence to their classes across architectures. Temporal coherence. As we show in Figure 7, LEAPS can visualize motions performed over different speeds (slow/fast). We report the Peak Signal Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) for consecutive frame pairs to analyze the variations observed by both fast and slow motions within a video. We observe that the speeds with which motions are performed within the same video can be fundamentally different with both large and small changes occurring between frames. In contrast to image-based methods extended to video, LEAPS shows the ability to represent such variations in the produced feature visualizations. As shown, the PSNR and SSIM statistics from the stimulus video of class doing aerobics in Figure 7a, follow similar trends as those produced by the synthesized LEAPS video in Figure 7b." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": "Video synthesis optimization. We visualize the resulting synthesized video " + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^*" + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": " at different iteration steps during optimization in Figure 8. General features such as the outlines of objects and actors as well as their movements are synthesized first by our proposed method. Interestingly, later iterations show to refine the visualized features by further synthesizing visual details. This demonstrates a level of learned hierarchy by video models as to the types of spatiotemporal learned features that are associated with a specific action. Our proposed use of model priming in tandem with temporal coherence and feature diversity regularization terms shows to enable the visualization of models' spatiotemporal representations of actions, at a finer quality and detail." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 145, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 145, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 145, + 658 + ], + "type": "text", + "content": "4.4. Ablation studies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "In this section, we conduct ablation studies reporting model statistics over synthesized videos. We initially consider the effect of the distance function used during model priming. Additionally, we report statistics over different" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 85, + 421, + 124 + ], + "blocks": [ + { + "bbox": [ + 342, + 74, + 386, + 84 + ], + "lines": [ + { + "bbox": [ + 342, + 74, + 386, + 84 + ], + "spans": [ + { + "bbox": [ + 342, + 74, + 386, + 84 + ], + "type": "text", + "content": "(a) 3D R50." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 85, + 421, + 124 + ], + "lines": [ + { + "bbox": [ + 308, + 85, + 421, + 124 + ], + "spans": [ + { + "bbox": [ + 308, + 85, + 421, + 124 + ], + "type": "table", + "html": "
MetricDistance function
l2l1cosJVS
top-1 (m)84.382.472.186.7
top-1 (v)65.863.746.168.5
", + "image_path": "65d72218e05741524f7ecb04962181556f36301f476499550bde493abf45e937.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 430, + 85, + 543, + 124 + ], + "blocks": [ + { + "bbox": [ + 468, + 74, + 507, + 84 + ], + "lines": [ + { + "bbox": [ + 468, + 74, + 507, + 84 + ], + "spans": [ + { + "bbox": [ + 468, + 74, + 507, + 84 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 468, + 74, + 507, + 84 + ], + "type": "inline_equation", + "content": "\\mathbf{X3D_M}" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 430, + 85, + 543, + 124 + ], + "lines": [ + { + "bbox": [ + 430, + 85, + 543, + 124 + ], + "spans": [ + { + "bbox": [ + 430, + 85, + 543, + 124 + ], + "type": "table", + "html": "
MetricDistance function
l2l1cosJVS
top-1 (m)88.186.878.990.3
top-1 (v)79.778.470.282.5
", + "image_path": "c2ddba3e609975a8302f6afa168241cdeaa0cb2029c7720b9e4ae99808e41aef.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 307, + 142, + 421, + 180 + ], + "blocks": [ + { + "bbox": [ + 331, + 131, + 399, + 141 + ], + "lines": [ + { + "bbox": [ + 331, + 131, + 399, + 141 + ], + "spans": [ + { + "bbox": [ + 331, + 131, + 399, + 141 + ], + "type": "text", + "content": "(c) Video Swin-B." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 142, + 421, + 180 + ], + "lines": [ + { + "bbox": [ + 307, + 142, + 421, + 180 + ], + "spans": [ + { + "bbox": [ + 307, + 142, + 421, + 180 + ], + "type": "table", + "html": "
MetricDistance function
l2l1cosJVS
top-1 (m)85.583.069.287.4
top-1 (v)72.871.641.474.3
", + "image_path": "836398ac302dd38a306c0876fda647f0359808e24c568f74872b5669d9ce7eb8.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 430, + 142, + 543, + 180 + ], + "blocks": [ + { + "bbox": [ + 459, + 131, + 515, + 141 + ], + "lines": [ + { + "bbox": [ + 459, + 131, + 515, + 141 + ], + "spans": [ + { + "bbox": [ + 459, + 131, + 515, + 141 + ], + "type": "text", + "content": "(d) MViTv2-B." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 430, + 142, + 543, + 180 + ], + "lines": [ + { + "bbox": [ + 430, + 142, + 543, + 180 + ], + "spans": [ + { + "bbox": [ + 430, + 142, + 543, + 180 + ], + "type": "table", + "html": "
MetricDistance function
l2l1cosJVS
top-1 (m)83.581.970.785.9
top-1 (v)72.469.745.673.1
", + "image_path": "a286148ce898eaf8d8011d43617049db105f8e9a1ef6b3db4e7f795359e2e792.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 189, + 545, + 224 + ], + "lines": [ + { + "bbox": [ + 305, + 189, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 189, + 545, + 224 + ], + "type": "text", + "content": "Table 2: Top-1 accuracies of the inverted model (m) and verifier (v) on synthesized videos over different priming distance functions. Best results are in bold." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 239, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 287 + ], + "type": "text", + "content": "combinations of priming and introduced regularizers across the tested architectures. Finally, we present quantitative results when using inputs of different spatiotemporal sizes alongside the resulting averaged latency times." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": "Priming distance methods. In Table 2, we evaluate the impact of the distance functions used during model priming at (1). We test three different magnitude-based methods including " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "JVS" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": ", as well the cosine similarity " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "cos" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": ". Across all four spatiotemporal models, 3D R50, X3DM, Video Swin-B, and MViTv2-B, the magnitude-based methods perform favorably over the cosine similarity. This is due to " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "cos" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " not taking into account the magnitude of the feature activation vectors from the synthesized and stimulus videos, which in turn limits the ability to synthesize representations relevant to the stimulus. Across magnitude-based methods, an average improvement of " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "+2.2\\%" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "+4.1\\%" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " to the inverted model's (m) accuracy is observed with JVS compared to " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " respectively. The same trend also holds true for the verifier (v), with " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "+1.9\\%" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "+3.7\\%" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " accuracy improvements from " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " when using JVS. Comparatively to " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": ", JVS uses a combination of vector magnitudes and angles [15], providing a more balanced approach than magnitude-only or angle-only metrics. Therefore, we adopt " + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "inline_equation", + "content": "JVS" + }, + { + "bbox": [ + 304, + 289, + 545, + 539 + ], + "type": "text", + "content": " as the priming distance method used between stimulus and synthesized feature vectors." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 541, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 541, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 541, + 545, + 712 + ], + "type": "text", + "content": "Regularizers. In Table 3 we provide comparisons over different priming and regularizer combinations for our LEAPS objective. We report the top-1 accuracies of the inverted model (m), and verifier (v), as well as the IS of the inverted model across a range of spatiotemporal convolutional and attention-based architectures. We note that in the case of inverting " + }, + { + "bbox": [ + 304, + 541, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{X3D_S}" + }, + { + "bbox": [ + 304, + 541, + 545, + 712 + ], + "type": "text", + "content": " the same model is used for both model inversion and as the verifier, evidently resulting in matching verifier/inverted model accuracies. Overall, the priming objective " + }, + { + "bbox": [ + 304, + 541, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 541, + 545, + 712 + ], + "type": "text", + "content": " combined with either regularizer term yields clear improvements compared to the sole use of model priming. Modest improvements are observed with the combination of priming and the feature diversity regularizer over priming with temporal coherence. We believe that this is due to the" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "text", + "content": "1972" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 545, + 227 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 227 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 227 + ], + "type": "table", + "html": "
Video model architectures and variants
MetricR50X3D [11]TS [4]Video Swin [29]MViTv2 [27]rev-MViT-B [32]UniFormerv2 [26]
3D(2+1)D [58]CSN [57]XSSMLTSBSBBL
LEAPS L prim
top-1 (m)67.963.872.467.468.573.473.864.969.169.571.270.671.564.572.373.0
top-1 (v)53.149.555.851.968.559.860.452.652.353.557.654.656.750.756.456.9
IS3.9±0.92.4±0.54.2±0.64.0±1.04.3±0.65.1±1.15.5±1.32.7±0.74.1±1.64.2±1.14.4±0.84.3±1.24.6±0.73.1±1.74.3±0.84.5±1.2
LEAPS L + R prim coh
top-1 (m)70.465.776.174.875.678.078.573.172.873.274.573.774.269.274.975.3
top-1 (v)55.854.360.161.075.665.670.063.462.963.363.863.563.952.963.764.5
IS4.6±1.23.5±0.84.8±1.64.3±0.95.0±1.57.2±1.37.5±1.03.9±0.94.5±0.74.8±1.35.4±0.65.0±0.85.3±1.03.3±2.15.5±0.65.9±0.4
LEAPS L + R prim feat
top-1 (m)74.367.476.278.979.481.181.571.974.174.776.075.676.370.475.876.6
top-1 (v)60.256.964.365.879.469.370.867.263.264.565.466.768.058.269.069.8
IS5.1±0.84.2±1.45.6±1.27.3±1.17.6±0.88.8±1.59.1±1.23.8±1.24.7±1.14.9±0.55.3±1.55.1±0.65.5±1.24.0±1.85.7±1.06.2±0.9
LEAPS (full)
top-1 (m)86.778.088.386.287.090.390.883.685.786.287.485.185.982.587.188.3
top-1 (v)68.565.271.676.487.082.583.769.771.973.574.372.473.167.375.476.2
IS9.0±1.06.4±1.39.7±0.79.6±0.410.4±1.211.4±0.911.9±1.57.5±1.68.5±0.79.4±1.59.8±1.38.7±1.39.3±0.87.1±2.69.1±1.39.6±1.2
", + "image_path": "3a7e07646c42a8f08ac4c7f1169e28cd10cda7a7ac00e3c5d168966bfb6a6128.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 281, + 286, + 365 + ], + "blocks": [ + { + "bbox": [ + 46, + 233, + 546, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 546, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 546, + 270 + ], + "type": "text", + "content": "Table 3: Top-1 accuracies and Inceprion Scores (IS) over different objectives across different architectures and model variants. X3Ds is used as the verifier (v) for all experiments. The best results per variant are in bold. The verifier accuracy is denoted in gray for the case of using X3Ds for both model inversion and as the verifier." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 281, + 286, + 365 + ], + "lines": [ + { + "bbox": [ + 48, + 281, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 48, + 281, + 286, + 365 + ], + "type": "table", + "html": "
Modeltemp.×spatial2top-1ISLatency (secs) (↓I / ↑B)
mv
3D R508 × 182284.367.28.1±1.30.591 / 0.913
8 × 224286.768.59.7±1.00.832 / 1.205
16 × 224287.068.79.8±1.61.140 / 1.681
(2+1)D R508 × 182275.462.94.2±1.81.684/2.325
8 × 224278.065.26.4±1.31.858/2.793
16 × 224278.565.46.6±1.52.343/3.176
", + "image_path": "55f9e974deaf011f63b3469228998b805e903a0b9f45ca12ed64a83969a0d855.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "text", + "content": "Table 4: Synthesized video size comparisons based on the top-1 accuracies of the inverted model, and verifier, IS, and latency times for inference " + }, + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "inline_equation", + "content": "(\\downarrow \\mathrm{I})" + }, + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "text", + "content": " and backprop " + }, + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "inline_equation", + "content": "(\\uparrow \\mathrm{B})" + }, + { + "bbox": [ + 46, + 372, + 287, + 420 + ], + "type": "text", + "content": ". Best settings per architecture are in bold." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 433, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 433, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 287, + 604 + ], + "type": "text", + "content": "enhanced search space of " + }, + { + "bbox": [ + 46, + 433, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{prim} + \\mathcal{R}_{feat}" + }, + { + "bbox": [ + 46, + 433, + 287, + 604 + ], + "type": "text", + "content": " as more diverse class features not in the stimulus are also explored. The combination of the priming objective with both regularizer terms for our proposed LEAPS consistently achieves the best results by a large margin compared to all other settings. LEAPS improves accuracy, for both the inverted model and verifier, as well as the quality of the generated videos based on the IS. These results further demonstrate that our proposed LEAPS optimization can be used across a range of architectures as a general spatiotemporal feature visualization method. Further qualitative examples for each network over different Kinetics classes are shown in Figures S1 to S4 in the supplementary alongside embeddings projections of LEAPS with different regularizer regimes in Section S3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Synthesized video resolution. Finally, we compare the accuracies, IS, and latency times when optimizing video inputs of different spatiotemporal sizes. Due to the majority of architectures requiring fixed-size inputs, we use 3D R50 and " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "(2 + 1)\\mathrm{D}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " R50 as they are input size independent. From the top-1 (m/v) accuracies and IS summarized in Table 4, the best-performing setting across metrics is obtained with " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "16\\times 224^{2}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "-sized inputs. We observe comparable performance on the temporally-reduced " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "8\\times 224^{2}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " setting with" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 280, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 280, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 280, + 545, + 353 + ], + "type": "text", + "content": "a significantly more balanced performance-to-latency. Notable decreases in accuracies and IS are observed with the potentially limited spatial resolution " + }, + { + "bbox": [ + 304, + 280, + 545, + 353 + ], + "type": "inline_equation", + "content": "8 \\times 182^{2}" + }, + { + "bbox": [ + 304, + 280, + 545, + 353 + ], + "type": "text", + "content": " setting, making it less suitable. Due to the significant improvements in the per-iteration latency of the " + }, + { + "bbox": [ + 304, + 280, + 545, + 353 + ], + "type": "inline_equation", + "content": "8 \\times 224^{2}" + }, + { + "bbox": [ + 304, + 280, + 545, + 353 + ], + "type": "text", + "content": " inputs, we adopt this setting throughout our experiments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 374, + 384, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 374, + 384, + 387 + ], + "spans": [ + { + "bbox": [ + 306, + 374, + 384, + 387 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 398, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 673 + ], + "type": "text", + "content": "We have introduced LEAPS, a novel spatiotemporal model inversion method for visualizing the learned internal representations of networks through video synthesis. LEAPS uses a stimulus video to prime a model and iteratively optimize an input by minimizing the classification and priming loss. The resulting synthesized video visualizes learned concepts that are associated with classes without prior knowledge of the training data. During optimization, LEAPS uses two regularizers. The first enforces temporal coherence between feature transitions across frames in the updatable input. The second improves the diversity of the synthesized features through a domain-specific verifier network to enhance the search space. The proposed architecture-independent method has shown qualitatively and quantitatively that it can produce high-quality and visually coherent synthesized videos over a wide range of spatiotemporal convolutional and attention-based video models. The high classification scores and synthesized video quality metrics make LEAPS a generalizable and effective spatiotemporal feature visualization method. We believe that this first step towards learned spatiotemporal representations synthesis is a promising direction in understanding video models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. We use publicly available datasets and models. 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Springer, 2014. 2" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 732, + 315, + 742 + ], + "type": "text", + "content": "1976" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learn TAROT with MENTOR_ A Meta-Learned Self-Supervised Approach for Trajectory Prediction/e84db066-834e-41d1-b5a0-8e0c6af0f9b7_content_list.json b/2023/Learn TAROT with MENTOR_ A Meta-Learned Self-Supervised Approach for Trajectory Prediction/e84db066-834e-41d1-b5a0-8e0c6af0f9b7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5390d07f398c3c2e090fad30d616381f13c521ab --- /dev/null +++ b/2023/Learn TAROT with MENTOR_ A Meta-Learned Self-Supervised Approach for Trajectory Prediction/e84db066-834e-41d1-b5a0-8e0c6af0f9b7_content_list.json @@ -0,0 +1,1453 @@ +[ + { + "type": "text", + "text": "Learn TAROT with MENTOR: A Meta-Learned Self-supervised Approach for Trajectory Prediction", + "text_level": 1, + "bbox": [ + 89, + 128, + 880, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mozhgan Pourkeshavarz, Changhe Chen, Amir Rasouli", + "bbox": [ + 264, + 203, + 702, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Noah's Ark Lab, Huawei", + "bbox": [ + 385, + 222, + 583, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Toronto, Canada", + "bbox": [ + 418, + 239, + 550, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "firstname_lastname@huawei.com", + "bbox": [ + 357, + 260, + 614, + 272 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predicting diverse yet admissible trajectories that adhere to the map constraints is challenging. Graph-based scene encoders have been proven effective for preserving local structures of maps by defining lane-level connections. However, such encoders do not capture more complex patterns emerging from long-range heterogeneous connections between nonadjacent interacting lanes. To this end, we shed new light on learning common driving patterns by introducing meTA ROad paTh (TAROT) to formulate combinations of various relations between lanes on the road topology. Intuitively, this can be viewed as finding feasible routes. Furthermore, we propose MEta-road NeTwORk (MENTOR) that helps trajectory prediction by providing it with TAROT as navigation tips. More specifically, 1) we define TAROT prediction as a novel self-supervised proxy task to identify the complex heterogeneous structure of the map. 2) For typical driving actions, we establish several TAROTs that result in multiple Heterogeneous Structure Learning (HSL) tasks. These tasks are used in MENTOR, which performs meta-learning by simultaneously predicting trajectories along with proxy tasks, identifying an optimal combination of them, and automatically balancing them to improve the primary task. We show that our model achieves state-of-the-art performance on the Argoverse dataset, especially on diversity and admissibility metrics, achieving up to $20\\%$ improvements in challenging scenarios. We further investigate the contribution of proposed modules in ablation studies.", + "bbox": [ + 75, + 340, + 472, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vehicle trajectory prediction is one of the main building blocks of autonomous driving. Prediction demonstrates how the future might unfold based on the road structure and the behavior of road users. To operate safely, self-driving cars must accurately perceive the geometric and semantic information in the driving scene and predict diverse yet scene-compliant trajectories. High-definition maps provide useful cues since the behaviors of agents and the interac", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tions among them are largely influenced by the road topology and governed by the map constraints. For example, a vehicle is unlikely to change to a lane that runs in the opposite direction. In this light, learning the structure of the map efficiently is essential to predict a variety of feasible trajectories.", + "bbox": [ + 496, + 310, + 893, + 400 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by the structural nature of the road, map vectorization has become prevalent in recent works, in which lanes are converted into vectors [15, 56, 18]. Consequently, graph structures can be leveraged to learn the relationships between vectorized entities [28, 54, 11, 16]. In this way, connected lanes in various formations, e.g. successor, predecessor, right, and left, represent admissible ways to traverse the terrain. For example, two lanes positioned consecutively in space and connected by a sequential link can be driven successively, whereas two lanes connected by a lateral link enable a lane change maneuver. Hence, the HD map lane graph has edges with different semantic meanings, indicating its heterogeneous nature.", + "bbox": [ + 496, + 401, + 893, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although existing lane graphs are shown to be effective in learning local structures through the adjacent lanes, they lack the ability to model more complex patterns imposed by long-range heterogeneous connections between nonadjacent yet interacting lanes. These connections are important to capture high-level intentions, such as overtaking, merging, and double turns, and can potentially represent the constraints and rules of the road. To model such connections, some methods propose adopting self-supervised tasks on top of the lane graph [15, 4] to encourage the model to learn the semantics associated with lane connectivities. Since scene structure contains various semantics, having only one proxy task at a time is insufficient to provide diverse traffic patterns. Alternatively, anchor-based models incorporate prior knowledge by identifying candidate trajectories based on sampling or clustering of training data [6, 43]. However, these methods are less robust and generalizable due to their dependency on the distribution of data.", + "bbox": [ + 496, + 598, + 895, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motivated by this insight, we introduce a novel self-supervised task for trajectory prediction, termed Heteroge-", + "bbox": [ + 500, + 869, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8384", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "aneous Structure Learning (HSL), to formulate traffic patterns imposed by road constraints. In particular, we formulate the road structure by meTA ROad paTh (TAROT) as a composite relation of heterogeneous edges in the scene graph that can model diverse abstractions from the map without additional data and labels. Therefore, by predicting the presence of TAROT in the driving scene as an HSL task, the model gets a sense of feasible transitions on the map as navigation tips for traversing the road. Furthermore, we propose MEta-road NeTwORk (MENTOR), a novel trajectory prediction framework that provides insight into the structural perspective of the map by simultaneously predicting a set of HSL tasks. In detail, inspired by the meta-learning concept, MENTOR is learning to learn road topology by automatically selecting the HSL tasks that assist the target trajectory prediction.", + "bbox": [ + 80, + 90, + 467, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are as follows: (1) For the first time, to the best of our knowledge, we investigate the idea of learning to learn in trajectory prediction through the proposed MEta-road NeTwORk (MENTOR), which determines an optimal combination of Heterogeneous Structure Learning (HSL) tasks and automatically balances them to assist the primary task of predicting diverse and admissible trajectories. (2) We propose meTA ROad paTh (TAROT) prediction as a novel HSL task capable of modeling high-level semantics within the map structure. Thus, diverse semantic aspects of road configuration can be captured by defining various TAROTs, resulting in multiple HSL tasks that are learned simultaneously. (3) We conduct extensive experimental evaluations to show our model's effectiveness in predicting not only precise but also diverse and admissible trajectories.", + "bbox": [ + 80, + 333, + 467, + 573 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 80, + 588, + 215, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Trajectory Prediction has been the subject of interest in a large body of literature. Existing methods explore different representations and methods to learn scene context, including rasterized images [6, 38, 16] and point-clouds [49] with CNNs, and vectorized representations with GNNs [15, 32, 18, 54], or transformers [21, 58, 17, 30], which are often associated with sophisticated fusion mechanisms [28]. These models focus on finding more powerful ways of extracting features from HD maps and modeling agents' interactions. They, however, require substantial model capacity, heavy parameterization, extensive augmentations, or a large amount of data to produce accurate results.", + "bbox": [ + 80, + 613, + 467, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Some methods investigate the ways to improve prediction precision by incorporating prior knowledge as predefined candidate trajectories generated using sampling or clustering techniques [32, 55]. Nevertheless, the main limitation of these methods is that their performance is highly dependent on the quality of trajectory proposals, which becomes a dependency. To resolve this issue, end-to-end", + "bbox": [ + 80, + 795, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "solutions optimize the endpoints of candidate trajectories [18, 16] resulting in improved accuracy while maintaining a reasonable parameter budget. However, using an online goal candidate optimization strategy is computationally very expensive, therefore it is prohibitive for real-time applications, such as autonomous driving. More recently, ensemble techniques have become more prevalent and demonstrated good prediction performance [43, 50]. However, their major disadvantages are high memory cost for training and computationally expensive inference.", + "bbox": [ + 503, + 90, + 888, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Besides designing high-precision models, researchers have focused on diversity, admissibility, and map conformity of the predicted trajectories. To generate diverse trajectories, state-of-the-art models use Generative Adversarial Networks (GANs) [25, 37, 57], and Conditional Variational Autoencoders (CVAEs) [38, 42, 53, 26], sophisticated sampling functions, such as diversity sampling [52] and latent semantic sampling [20]. However, most works sacrifice map conformity for prediction diversity. To improve conformity, map data can be incorporated as a part of the loss function [44, 9], or as a post-processing step [48]. To better evaluate the diversity and admissibility of predicted trajectories, new metrics, such as RF and DAO, have been proposed [34]. In this paper, we use these as well as common metrics to further assess our model's performance.", + "bbox": [ + 503, + 244, + 888, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-Supervised Learning (SSL) is a learning method that uses appropriately designed proxy tasks to generate additional supervised signals to train models. In trajectory prediction, SSL has been utilized by defining various proxy tasks laid on top of the agent/map information [15, 4]. For instance, a recent work, SSL-Lane [4], uses four different tasks and shows how they can be incorporated to improve performance. However, this model uses only one proxy task at a time and does not explore combinations of different tasks. Additionally, SSL-Lane employs different losses in its formulation only in a 1:1 ratio without tuning them. These shortcomings motivated our proposed framework for simultaneously learning proxy tasks without letting them compete with the target trajectory prediction task.", + "bbox": [ + 503, + 474, + 888, + 685 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Meta-learning originates from the concept of learning to learn, a topic of continued interest in machine-learning research. Meta-learning has been used for finding optimal hyper-parameters and good initialization [27, 13], metric-learning, and non-parametric methods for few-shot learning [40, 41]. This paper uses meta-learning to learn the road topology across several tasks by transferring the knowledge from self-supervised tasks, defined on the map structure, to the primary trajectory prediction task. In a closely related category of works, sample weighting, a meta-learning mechanism is used for adaptively extracting sample weights to guarantee robust deep learning in the presence of training data bias [23, 39]. In practice, instead of manually setting the form of weight functions, these methods learn an ex", + "bbox": [ + 503, + 688, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8385", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3c6682fd7fff9337898f362c727cc188baf6587cdce6ae1ec51fdac8ae4aa2f1.jpg", + "image_caption": [ + "Figure 1: Overview of the proposed approach. Given directed HIN $\\mathcal{G}$ of the scene and $N$ predefined TAROTs, the HSL engine $\\mathcal{H}(\\mathrm{TAROTs})$ defines $N$ HSL tasks each predicting the presence of a specific TAROT. Within each TAROT task $p_n$ , positive samples are two arbitrary nodes from $\\mathcal{G}$ that can be reached by $p_n$ , and negative samples are those that cannot. For the HSL tasks and the primary task, we find learned representations $\\mathcal{Z}$ from GNN model $f$ . To find the loss values, samples are fed through the task-specific transformations $\\Phi_t$ followed by task-specific loss functions $\\mathcal{L}^n$ . Lastly, by Providing loss values of the primary task's samples and the HSL tasks' samples (as a concatenation of [task id, label(Pos/Neg), loss value]), we train MENTOR to learn weight function $\\mathcal{V}$ in a way to find an optimal combination of the HSL tasks in a meta-learning manner." + ], + "image_footnote": [], + "bbox": [ + 140, + 89, + 831, + 290 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "plicit weighting function directly from the data.", + "bbox": [ + 76, + 436, + 393, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-supervised learning and meta-learning both contribute to improving model generalization capability. To the best of our knowledge, this is the first study in trajectory prediction to exploit the benefit of scene-based self-supervised tasks through a meta-learning paradigm.", + "bbox": [ + 75, + 460, + 470, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 571, + 250, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Traffic transitions are complex and cannot simply be modeled by learning the local relationships. What required is modeling patterns of traveling through the road as a combination of relationships, not only in the adjacent lanes but also between nonadjacent yet interacting lanes. This can, for example, refer to a merge pattern in the road structure that involves both lateral and sequential relations.", + "bbox": [ + 75, + 604, + 468, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The main idea behind our proposed model is to provide high-order combinations of basic adjacent-adjacent patterns as the full gamut of lane interactions when predicting vehicle trajectories. To this end, we first discuss the procedure for generating a Heterogeneous Information Network (HIN) from scenes, followed by the introduction of the Heterogeneous Structural Learning (HSL) tasks designed to capture relations between lanes. Next, we describe our novel MEtaroad NeTwork (MENTOR) that learns an explicit weighting function to softly select HSL tasks and balance them to improve the performance of the primary task via meta-learning (see Fig. 1).", + "bbox": [ + 75, + 720, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Scene Encoding", + "text_level": 1, + "bbox": [ + 500, + 436, + 658, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Contrary to the common approach that treats the scene as a homogeneous graph [54], we model the scene as a Heterogeneous Information Network (HIN) [24].", + "bbox": [ + 498, + 460, + 890, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 1. Heterogeneous Information Network (HIN) a HIN is defined as a graph $\\mathcal{G} = (\\mathcal{V},\\mathcal{E})$ , where $\\mathcal{V}$ is the set of nodes and $\\mathcal{E}$ is the set of edges, each representing a binary relation between two nodes in $\\mathcal{V}$ . $\\mathcal{G}$ is associated with two mappings: (1) node type mapping function $\\phi :\\mathcal{V}\\to \\mathcal{T}$ and (2) edge type mapping function $\\psi :\\mathcal{E}\\rightarrow \\mathcal{R}$ where $\\mathcal{T}$ and $\\mathcal{R}$ denote sets of node and edge types, respectively. If $|\\mathcal{T}| + |\\mathcal{R}| > 2$ , network $\\mathcal{G}$ is an HIN, otherwise it is homogeneous.", + "bbox": [ + 498, + 506, + 892, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We encode the scene as a directed HIN with node types $\\mathcal{T} = \\{\\text{lane, agent}\\}$ and $\\mathcal{R} = \\{\\text{left, right, successor, predecessor}\\}$ as basic relations between adjacent lanes. To initialize node features in the HIN, we use the simplified PointNet [36] with multi-layer perception (MLP) to process polyline features and a 1D convolution with a feature pyramid network [29] to process agents' observations similar to [28]. One advantage of our method is that any type of GNN can be used to process the HIN. Hence, we employ Heterogeneous Graph Transformer (HGT) as a simple yet effective model similar to [19].", + "bbox": [ + 498, + 643, + 893, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Heterogeneous Structural Learning", + "text_level": 1, + "bbox": [ + 500, + 816, + 808, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Traffic transitions follow patterns governed by high-level constraints stemming from long-range structural connections between lanes of the road. For learning the map structure, heterogeneity helps interpret a series of relations,", + "bbox": [ + 498, + 839, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8386", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which our model learns with meTA ROad paTh (TAROT).", + "bbox": [ + 76, + 90, + 464, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 2. Meta-Path. A meta-path $\\mathcal{P} = v_{1} \\xrightarrow{r_{1}} v_{2} \\xrightarrow{r_{2}} \\ldots \\xrightarrow{r_{\\ell}} v_{\\ell + 1}$ expresses a composite relation $R = r_{1} \\circ r_{2} \\dots \\circ r_{\\ell}$ between nodes $v_{1}$ and $v_{\\ell + 1}$ , where $\\circ$ denotes the composition operator on relations. If two nodes $v_{i}$ and $v_{j}$ are related by the composite relation $R$ , then there exists a path that connects $v_{i}$ to $v_{j}$ in $\\mathcal{G}$ , denoted by $\\mathcal{P}_{v_{i} \\rightsquigarrow v_{j}}$ . Moreover, the nodes and edges types in $\\mathcal{P}_{x_{i} \\rightsquigarrow x_{j}}$ match with types in $\\mathcal{T}$ and $\\mathcal{R}$ , respectively.", + "bbox": [ + 75, + 104, + 467, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The features obtained from the meta-path analysis in HINs are notably useful in improving graph-based models since they encode indirect semantic relations between nodes that are not directly connected. These features also aid in establishing new relations between vertices. As such, metapath analysis has been frequently used in graph domains to enhance graph representation learning power and improve downstream tasks, such as node classification and link prediction [51, 46, 22, 8]. This means meta-paths can help find new patterns and relations in HINs.", + "bbox": [ + 75, + 229, + 467, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By focusing on the long-range relations that impose transitions on the road, we define TAROT $p$ though the HIN as a path instance of $p_{v_i\\sim v_j}\\vdash \\mathcal{P}$ where node types are the same. Thus, the TAROT can formulate a combination of basic road relations corresponding to transition patterns imposed by map constraints. Predicting the presence of a TAROT between two nodes $v_{i}$ and $v_{j}$ is similar to link prediction. Here, the link means heterogeneous composite relations between nodes. Contrary to link prediction problems, the proposed TAROT prediction can be treated as a self-supervised task. In detail, we follow a simple rule to provide the additional supervised signals for proxy tasks: If node $v$ is reachable from node $u$ by TAROT $p$ , then $y_{u,v}^{p} = 1$ , otherwise $y_{u,v}^{p} = 0$ . This means the HSL task, associated with the TAROT will be formed as a simple link prediction task without the need for any additional data or manual labeling. Hence, by obtaining the hidden representations of two arbitrary nodes learned by a GNN and using a simple operator $\\hat{y}_{u,v}^{p} = \\sigma \\left(\\Phi_{t}(z_{u})^{\\top}\\Phi_{t}(z_{v})\\right)$ we can predict whether a TAROT between two nodes is present or absent. Here, $\\Phi_t$ is a type-specific transformation $t\\in \\mathcal{T}$ and $z_{u}$ and $z_{v}$ are the node embeddings of nodes $u$ and $v$ .", + "bbox": [ + 75, + 381, + 468, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using the proposed TAROT as a type of meta-path we can model a common pattern of driving that adhere to the map constraints. Hence, we define several TAROTs to formulate diverse traffic patterns within the driving scene, resulting in several HSL tasks that can be used to predict diverse and admissible trajectories. We provided a complimentary figure in the supplementary material to further show TAROT's motivation.", + "bbox": [ + 75, + 719, + 467, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Meta Road Network", + "text_level": 1, + "bbox": [ + 76, + 845, + 269, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed HSL task is designed to identify diverse patterns within the road structure, for which we explore the", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "idea of defining various TAROTs resulting in several self-supervised HSL tasks to be learned simultaneously with the primary trajectory prediction task. However, as with any multi-task learning method, the HSL tasks should be carefully chosen and properly weighted so that learning the map structure does not compete with the primary task, especially when the capacity of graph neural networks (GNNs) is limited. To this end, we propose MEta-road NeTwORk (MENTOR), a learning framework for trajectory prediction that offers the possibility of learning to learn the road configuration while learning the main task. Below, we discuss a naive multi-task combination of self-supervision tasks to explain the motivation behind the design of MENTOR, followed by describing the meta-learning objective using MENTOR, and a detailed look at the learning procedure.", + "bbox": [ + 496, + 90, + 890, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Naive Multi-task Combination of HSL Tasks", + "text_level": 1, + "bbox": [ + 498, + 325, + 862, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Self-supervised learning has already been explored in trajectory prediction for autonomous driving and has proven beneficial [15, 4]. Adopting a combination of Self-Supervised Learning (SSL) tasks, namely proxy tasks, to improve the primary task has not yet been addressed, even though it has been shown to be effective in visual learning [12]. Here, we formulate a naive multi-task combination of HSL tasks, as SSL tasks, with a shared backbone network with parameters $\\mathbf{w}$ , between the primary and all proxy tasks. Each task has a specific loss function $\\mathcal{L}^n$ incorporated by a task-specific parameter $\\lambda_{n}$ . So the optimal parameter $\\mathbf{w}^{*}$ can be extracted by the following objective function:", + "bbox": [ + 496, + 351, + 890, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {w}} \\quad \\mathbb {E} \\left[ \\lambda_ {0} \\mathcal {L} ^ {0} (.; \\mathbf {w}) + \\sum_ {n = 1} ^ {N} \\lambda_ {n} \\mathcal {L} ^ {n} (.; \\mathbf {w}) \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 546, + 890, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where index zero stands for the primary task $n = 0$ , and index $n|_1^N$ denotes $n^{th}$ task of $N$ proxy tasks.", + "bbox": [ + 498, + 599, + 890, + 631 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 Meta-learning Objective", + "text_level": 1, + "bbox": [ + 500, + 656, + 723, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning road topology should enhance rather than compete with trajectory prediction, hence determining an effective combination of $\\lambda$ parameters is crucial. To achieve this, we adopt MENTOR to parameterize model $\\mathbf{w}(\\Theta)$ to determine an optimal combination of HSL tasks and automatically balance them for improved prediction as shown below,", + "bbox": [ + 496, + 681, + 890, + 773 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {w}, \\boldsymbol {\\Theta}} \\quad \\mathbb {E} \\left[ \\mathcal {L} ^ {0} \\left(\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})\\right) \\right] \\\\ \\text {s . t .} \\mathbf {w} ^ {*} (\\boldsymbol {\\Theta}) = \\underset {\\mathbf {w}} {\\operatorname {a r g m i n}} \\quad \\mathbb {E} \\left[ \\mathcal {L} ^ {n | _ {0} ^ {N}} (\\mathbf {w}; \\boldsymbol {\\Theta}) \\right]. \\end{array} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 785, + 890, + 842 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, to parametrize the model parameters $\\mathbf{w}$ , we can impose a learnable weighting function $\\mathcal{V}(\\cdot ,\\Theta)$ to the objective function in (2) as MENTOR similar to [39]. Thus, the", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8387", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: MEta-road NeTwORk (MENTOR)" + ], + "code_body": "Input : primary data $D^{\\mathrm{pr}}$ , HSL proxy tasks data $D^{\\mathrm{hsl}}$ , batch size $n$ $m$ , max iteration $T$ folds for cross-validation $K$ , model parameters w, MENTOR parameters $\\Theta$ Output: model parameter $\\hat{\\mathbf{w}}^T$ \n1 Initialize w, $\\Theta$ \n2 for $t = 0$ to $T - 1$ do \n3 $\\left\\{x^{(\\mathrm{pr})},y^{(\\mathrm{pr})}\\right\\} \\gets$ SampleMiniBatch $(D^{pr},n)$ . \n4 $\\left\\{x^{(\\mathrm{hsl})},y^{(\\mathrm{hsl})}\\right\\} \\gets$ SampleMiniBatch $(D^{\\mathrm{hsl}},m)$ //cross validation \n5 for $k = 1$ to $K$ do \n6 $\\left\\{x^{(\\mathrm{meta})},y^{(\\mathrm{meta})}\\right\\} ,\\left\\{x^{(\\mathrm{train})},y^{(\\mathrm{train})}\\right\\} \\gets$ CVSplit $(D^{pr},k)$ . Formulate model parameter $\\mathbf{w}^t$ by Eq 6 \n8 Keep $\\Theta_{k}^{t + 1}$ on fold $= k$ by Eq.7 \n9 end \n10 Update $\\Theta^{t + 1}$ with $\\frac{1}{K}\\sum_{k}^{K}\\Theta_{k}^{t + 1}$ \n11 Update $\\mathbf{w}^{t + 1}$ by Eq 8 \n12 end", + "bbox": [ + 78, + 109, + 468, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "objective function can be written as follows:", + "bbox": [ + 76, + 439, + 372, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta}) = \\operatorname * {a r g m i n} _ {\\mathbf {w}}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 460, + 250, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {n = 0} ^ {N} \\sum_ {i = 1} ^ {M _ {n}} \\frac {1}{M _ {n}} \\mathcal {V} \\left(\\Psi_ {i} ^ {n}; \\Theta\\right) \\mathcal {L} ^ {n} \\left(y _ {i} ^ {n}, f ^ {n} \\left(x _ {i} ^ {n}; \\mathbf {w}\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 487, + 468, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where each task has $M_{n}$ samples and $f^n$ is the model for task $n$ . For $i^{th}$ sample of task $n$ , $y_i^n$ is the label, and $\\Psi_i^n$ is an embedding vector expressing as the concatenation of one-hot vector of task types, the label (positive/negative), and the loss value of the sample. Therefore, following Eq. (3), the model learns how to assist the primary task by optimizing MENTOR's parameters $\\Theta$ . These parameters can be optimized using the meta-learning idea [47, 1, 10, 14]. Specifically, using a small amount of meta-data $D^{\\mathrm{meta}}$ , representing the meta-knowledge of ground-truth $D^{\\mathrm{gt}}$ , $D^{\\mathrm{meta}} \\cup D^{\\mathrm{train}} = D^{\\mathrm{gt}}$ , the optimal parameter $\\Theta^*$ can be obtained by minimizing the following loss:", + "bbox": [ + 75, + 534, + 468, + 715 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Theta} ^ {*} = \\underset {\\boldsymbol {\\Theta}} {\\operatorname {a r g m i n}} \\mathcal {L} ^ {\\text {m e t a}} (\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})) \\triangleq \\frac {1}{m} \\sum_ {i = 1} ^ {m} \\mathcal {L} _ {i} ^ {\\text {m e t a}} (\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 715, + 468, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $m$ and $r$ , $m \\ll r$ , are the number of meta-samples and training samples, respectively, and meta-loss is,", + "bbox": [ + 76, + 768, + 468, + 797 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i} ^ {\\mathrm {m e t a}} (\\mathbf {w}) = \\mathcal {L} \\left(y _ {i} ^ {\\mathrm {m e t a}}, f \\left(x _ {i} ^ {\\mathrm {m e t a}}, \\mathbf {w}\\right)\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 804, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $(x,y)\\sim D^{\\mathrm{meta}}$", + "bbox": [ + 76, + 828, + 225, + 843 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Meta-road Network Learning Procedure", + "text_level": 1, + "bbox": [ + 76, + 847, + 413, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To overcome the complexity of the bi-level optimization, following [13, 39], we use an online strategy to approximate", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathbf{w}^*$ and $\\Theta^{*}$ with the updated parameters $\\hat{\\mathbf{w}}$ and $\\hat{\\Theta}$ , respectively through a single optimization loop. In each iteration of training, given training data $D^{\\mathrm{train}}$ , HSL proxy tasks data $D^{\\mathrm{hsl}}$ , and meta-data $D^{\\mathrm{meta}}$ , we follow three steps:", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Formulating Model Parameter: We formulate the updating equation of model parameter $\\mathbf{w}$ by moving the current $\\mathbf{w}^t$ along the descent direction of the loss in Eq. (3),", + "bbox": [ + 498, + 152, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {D ^ {\\text {t r a i n}} \\cup D ^ {\\mathrm {h s l}}} {\\hat {\\mathbf {w}} ^ {(t)}} (\\boldsymbol {\\Theta}) = \\mathbf {w} ^ {(t)} - \\alpha \\frac {1}{N} \\sum_ {n = 0} ^ {N} \\mathcal {V} (\\cdot ; \\boldsymbol {\\Theta}) \\nabla_ {\\mathbf {w}} \\mathcal {L} ^ {n} (\\mathbf {w}) \\Bigg | _ {\\mathbf {w} ^ {(t)}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 217, + 890, + 261 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ is the learning rate for $\\mathbf{w}$ and $\\mathcal{L}^n$ denotes the loss function for the task number $n$ . To avoid cluttered notation, the summation of task samples is omitted.", + "bbox": [ + 498, + 267, + 890, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Updating Parameters of MENTOR: After updating model parameter $\\hat{\\mathbf{w}}^{(t)}(\\Theta)$ , parameter $\\Theta$ of MENTOR can be updated guided by Eq. (4), i.e., moving the current parameter $\\Theta^{(t)}$ along the objective gradient of Eq. (4) calculated on the meta-data,", + "bbox": [ + 498, + 313, + 890, + 387 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Theta_ {D ^ {\\mathrm {m e t a}}} ^ {(t + 1)} = \\Theta^ {(t)} - \\beta \\mathcal {V} (\\cdot ; \\Theta) \\mathcal {L} ^ {0} \\left(\\hat {\\mathbf {w}} ^ {(t)} (\\Theta)\\right) \\Big | _ {\\Theta^ {(t)}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 407, + 890, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta$ is the learning rate for $\\Theta$ . This update allows the soft selection of useful HSL proxy tasks and balances them with the main motion prediction task to improve the performance of the main task. Without balancing tasks with the weighting function $\\mathcal{V}(\\cdot;\\Theta)$ , proxy tasks can dominate training and degrade the performance of the primary task.", + "bbox": [ + 498, + 441, + 890, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Updating Model Parameters: Model parameters $\\mathbf{w}$ for tasks can be updated with optimized $\\Theta^{t + 1}$ in Eq. (7) as,", + "bbox": [ + 498, + 532, + 890, + 564 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\mathbf {w}} _ {D ^ {\\mathrm {t r a i n}} \\cup D ^ {\\mathrm {h s l}}} ^ {(t + 1)} (\\boldsymbol {\\Theta}) = \\mathbf {w} ^ {(t)} \\\\ - \\alpha \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\mathcal {V} \\left(\\because \\Theta^ {(t + 1)}\\right) \\nabla_ {\\mathbf {w}} \\mathcal {L} ^ {n} (\\mathbf {w}) \\Bigg | _ {\\mathbf {w} ^ {(t)}}. \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 571, + 890, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lastly, to circumvent the problem of meta-overfitting, meaning that parameters $\\Theta$ overfit to the small meta-dataset, we follow the meta-validation solution as in [2, 59]. In particular, to make $\\Theta$ generalizable across meta-training sets, we optimize it using $K$ different meta-datasets with k-fold cross-validation. The gradients of $\\Theta$ from different meta-datasets are then averaged to update $\\Theta^{(t)}$ . The MENTOR learning procedure is summarized in Algorithm 1.", + "bbox": [ + 498, + 651, + 890, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 784, + 630, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our goal is to investigate ways for improving map representational learning power to predict diverse and admissible trajectories. For this purpose, we seek to answer the following questions: Q1: Are predicted trajectories diverse and admissible? Q2: Is MEta-road NeTwORk (MENTOR) effective regardless of the type of HSL task? Q3: How much", + "bbox": [ + 498, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8388", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7eb96df774651e3c2440517d11d8979e2146246552f1d971f2fb290c4953f563.jpg", + "table_caption": [ + "Table 1: Comparison to SOTA models on challenging scenarios. Arrows show lower (↓) or higher (↑) values are better." + ], + "table_footnote": [], + "table_body": "
MethodTurnsStationary
minADE(↓)minFDE(↓)DAO(↑)RF(↑)MR(↓)minADE(↓)minFDE(↓)DAO(↑)RF(↑)MR(↓)
LaneGCN [28]1.082.1867.632.8935.761.232.5261.692.6936.80
MMTransformer[21]1.052.0769.763.3532.001.132.2864.853.2135.69
FTGN [3]1.062.0470.723.2534.061.162.2263.953.0632.49
HiVT [58]1.062.2366.842.7935.451.252.7458.432.5139.61
SSL-Lane [4]1.072.1169.653.2133.341.162.3462.453.2234.54
MENTOR (Ours)1.032.0079.213.7631.301.132.1969.233.8732.76
", + "bbox": [ + 81, + 104, + 888, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "does our proposed HSL task contribute to diversity and admissibility?", + "bbox": [ + 78, + 224, + 467, + 256 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 78, + 260, + 264, + 276 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset: We evaluated our method on the Argoverse benchmark dataset [7]. Here the task is to predict 3 seconds of future trajectories given 2 seconds of past observations. This dataset consists of more than $300K$ real-world driving sequences, which are split into the train (205K), validation (39K), and test (78K) sets without geographical overlap along with corresponding HD maps.", + "bbox": [ + 78, + 284, + 467, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics: We selected a set of metrics to measure the precision, diversity, and admissibility of predictions. For precision, we use minADE (Average Displacement Error), minFDE (Final Displacement Error), and MR (Miss Rate). For diversity, we use the Ratio of avgFDE to minFDE (RF) [34], which measures the spread of predictions in Euclidean distance. We use Drivable Area Occupancy (DAO) [34] to determine the proportion of pixels that predicted trajectories occupy in the drivable area. RF and DAO work in a complementary way to measure diversity along with admissibility.", + "bbox": [ + 78, + 390, + 467, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details: To normalize the data, we translate and rotate the coordinate system of each sequence so that the origin is at the agent's current location at $t = 0$ . We use the orientation from the agent's location at $t = -1$ to its location at $t = 0$ as the positive x axis. We use all actors and lanes whose distance from the agent is smaller than 100 meters as the input. As a model architecture, we use three layers of HGT with the hidden dimension of size 128. For the HSL tasks, we define five TAROTs with variable lengths of 4 to 7. The intuition behind the number of TAROTs is to model turning right/left, lane changing (right-to-left and left-to-right), and going straight. We formulate Mentor as an MLP with two hidden layers with 100 nodes each, with ReLU activations for hidden nodes and sigmoid output to ensure it is in range [0, 1]. For the loss functions, we follow the widely used regression-MLP plus classification-MLP combination [28, 24, 33] for trajectory prediction and cross-entropy for the HSL task. For the training, we use the AdamW [31] optimizer with an initial learning rate of 5e-4, weight decay 1e-4, and batch size of 64.", + "bbox": [ + 78, + 541, + 467, + 842 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Analysis on Challenging Scenarios", + "text_level": 1, + "bbox": [ + 78, + 847, + 375, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Existing prediction datasets are highly imbalanced in terms of scenario diversity, with the majority of traffic ac", + "bbox": [ + 78, + 869, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tors simply driving straight [35]. Calculating metrics by aggregating over scenarios is therefore influenced by the most common maneuvers, where prediction models often do well. In practice, scenarios, such as turning at intersections could be of greater interest to practitioners and accurately predicting these scenarios are even more crucial for the safe operation of autonomous vehicles. Hence, to verify the effectiveness of our model, we extracted challenging scenarios including left/right/blind turns and stationary scenarios where the vehicle's observed trajectory is very short, thus the model has minimal motion information from the vehicle. By blind turns, we refer to the cases where the observed trajectory is straight and the turn occurs during the unobserved portion of the trajectory.", + "bbox": [ + 501, + 224, + 888, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method against several vectorized-based SOTA models with public implementations, including two graph-based models, LaneGCN [28] and FTGN [3], two transformer-based models, MMTransformer [21] and HiVT [58], and SSL-Lane [4], which extends the lane graph by adding four different self-supervised tasks based on agent/map information. As shown in Table 1, our method significantly improves upon the state-of-the-art models on most metrics in both scenarios. Particularly, our method, MENTOR achieves notable improvements in diversity and admissibility metrics, namely DAO and RF by up to $13\\%$ and $20\\%$ respectively in the challenging scenarios.", + "bbox": [ + 503, + 436, + 888, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative analysis. Fig. 2 depicts a number of qualitative examples to better highlight our method's performance. The first two rows represent turn-right scenarios, and the third and fourth rows show left-turn and stationary scenarios. As can be seen in the last column, our method consistently generates diverse predictions that are also admissible by correctly aligning with the road topology. The behavior of competing methods, however, varies often resulting in the generation of infeasible trajectories. In the supplementary materials, we discuss the algorithm used to find challenging scenarios and present additional per-scenario metrics to further elaborate on the correlation of metrics.", + "bbox": [ + 503, + 619, + 888, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 503, + 808, + 661, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.1 MENTOR Acting as a Mentor", + "text_level": 1, + "bbox": [ + 503, + 832, + 761, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To assess the ability of MENTOR, we analyze the weighting function $\\mathcal{V}(\\Psi_i^n;\\Theta)$ for $i^{th}$ sample of task $n$ . Particularly, we present the learned weight function at the last epoch of", + "bbox": [ + 503, + 854, + 888, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8389", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e59793ae8e717bb09121fe124ec54d8443715c5a2d9752e288c9567473e35f7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 117, + 80, + 854, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/00468cf7409b7b596e7b0dbadcd2cc73ce182e1c858ca235575814d185efbf12.jpg", + "image_caption": [ + "Figure 2: Qualitative examples on Argoverse showing diversity and admissibility of the predicted trajectories by MENTOR. Red, green, and blue trajectories represent observation, ground truth, and 6 predicted trajectories, respectively.", + "Figure 3: The weighting function in MENTOR. The green line is the primary task, and solid and dashed color lines represent positive and negative HSL samples, respectively. Each color corresponds to a specific HSL task." + ], + "image_footnote": [], + "bbox": [ + 142, + 467, + 403, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the training. As shown in Fig. 3, MENTOR has two main benefits. Firstly, even when the model's loss is low, as the model is learning less challenging scenarios, trajectory prediction task (green line) samples have a higher weight than HSL tasks. Hence, MENTOR is more focused on learning the primary trajectory prediction task as there is no competition between HSL tasks and the primary task. Secondly, in all tasks, hard samples with higher losses are given more weight than easy samples with lower losses, indicating that MENTOR is mining hard samples. Here, MENTOR acts as a mentor by learning TAROTs and transferring that knowledge to the primary task.", + "bbox": [ + 75, + 684, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of MENTOR: To analyze the effectiveness of MENTOR, we borrow a lane-graph-based baseline", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and four self-supervised learning (SSL) tasks introduced in [4] and use them in MENTOR to improve the baseline. The SSL tasks are as follows: A) Lane masking, which recovers feature information from the perturbed lane graphs; B) Predicting distance to the intersection in terms of the shortest path length from all lane nodes to the intersection nodes; C) Maneuver classification, which predicts the form of a maneuver that the agent of interest intends to execute; And D) success/failure classification, which trains an agent specialized in achieving end-points.", + "bbox": [ + 496, + 491, + 890, + 643 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We report the results in Tab. 2 where the SSL tasks are termed A-D and $\\text{MENTOR}_{\\sum \\mathrm{A}, \\mathrm{B}, \\mathrm{C}, \\mathrm{D}}$ denotes the proposed model. According to the table, among the proposed tasks, maneuver classification, task C, has the best DAO (admissibility), indicating that predicting the form of maneuver can reveal more information about the road structure. Additionally, predicting the distance to the intersection, task B, gives a better estimate of the agent to the intersection, and the possibility of branching roads, hence improving RF (diversity) metric. In summary, individual tasks are shown to be effective by providing auxiliary information that helps improve different aspects of prediction. Once combined together, SSL tasks through the MENTOR framework improve distance-based metrics, minADE and minFDE as well as admissibility and diversity metrics, DAO and RF. These results validate the effectiveness of MENTOR as a learning framework to enhance prediction models", + "bbox": [ + 496, + 643, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8390", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6e58fce6617ed0410bc93c9bcad51292704155d67c0b7b9fde62bba46f1001fc.jpg", + "table_caption": [ + "Table 2: Results of the ablation studies. $\\mathrm{SSL}_{-}x$ indicates self-supervised tasks as in [4] and $\\mathrm{MENTOR}_{\\sum \\mathrm{A,B,C,D}}$ indicates the original model augmented with MENTOR." + ], + "table_footnote": [], + "table_body": "
ModelminADE(↓)minFDE(↓)DAO(↑)RF(↑)
Baseline0.731.1265.873.00
SSLA0.701.0268.212.98
SSLB0.711.0468.653.87
SSLC0.721.0569.973.14
SSLD0.701.0168.023.01
MENTORΣA,B,C,D0.690.9877.914.18
", + "bbox": [ + 80, + 133, + 467, + 222 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/73b2bc42c18adfc96af31e97aa174bf65c6243d20f42006ce1ff387ed5f48622.jpg", + "table_caption": [ + "Table 3: Results of the ablation studies. $\\mathrm{TAROT}^x$ indicates the length of the TAROT through the HSL task and MENTOR represents our full model, which includes several HSL tasks." + ], + "table_footnote": [], + "table_body": "
TurnsValidation
ModelminFDE(↓)DAO(↑)RF(↑)minFDE(↓)DAO(↑)RF(↑)
Baseline2.37268.452.981.13274.024.21
TAROT42.26771.013.191.12875.524.43
TAROT52.20873.673.231.10777.114.48
TAROT62.15376.933.711.11278.894.50
TAROT72.08276.173.561.12178.004.51
TAROT82.10973.653.411.12077.214.38
MENTOR2.00379.213.760.97485.314.65
", + "bbox": [ + 80, + 297, + 465, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "by providing additional information as SSL tasks.", + "bbox": [ + 76, + 417, + 406, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of TAROT Prediction as an HSL Task: for the purpose of analyzing the impact of the TAROT prediction, we conduct several experiments on the entire validation set and challenging turn scenarios by designing different models named $\\mathrm{TAROT}^x$ where $x$ refers to the length of TAROT through the HSL task. For example, $\\mathrm{TAROT}^4$ could be any of these patterns [S-S-S-R, S-L-S-S, S-L-P-P...] (S: Successor, L: Left, R: Right, P: Predecessor as the basic relation of adjacent lanes). We average the metrics over all of the members in the list. A baseline model does not have any HSL tasks, and therefore does not have MENTOR. The last model is our final model which is loaded by multiple HSL tasks through MENTOR. As shown in Tab. 3, augmenting the model with the HSL task improves the baseline model performance. Moreover, from the experiments, we found that by predicting a longer TAROT, corresponding to a longer pattern in the road configuration with a higher abstraction, we can improve the model in turns scenarios. However, the length of TAROTs should be set carefully, as if set too long, the model would have a tendency to predict a turn maneuver even when several alternatives, such as driving straight, are available. To take advantage of this phenomenon, we define multiple TAROTs with variable lengths representing both short and long patterns. Thus, once used through MENTOR we enable the model to identify the best combination of HSL tasks, as TAROT prediction, by weighting them properly. In this way, our full model outperforms other models significantly. Based on the obtained results, we can conclude that 1) TAROTs are capable of modeling patterns in the map structure, thus formulating multiple TAROTs and subsequently multiple HST", + "bbox": [ + 76, + 433, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a5de450bb87c292fdc7c9ea3fbfac9438669363709f88abff1921dfbd6ca39fb.jpg", + "table_caption": [ + "Table 4: Comparisons with SOTA on Argoverse test set." + ], + "table_footnote": [], + "table_body": "
MethodminADE(↓)minFDE(↓)MR(↓)
TNT [56]0.941.5413.30
DenseTNT [18]0.881.2812.58
TPCN [49]0.871.3615.80
mmTransformer [30]0.871.3415.40
LaneRCNN [54]0.901.4512.32
LTP [45]0.831.2914.72
AutoBot [17]0.891.4116.00
SceneTransformer [33]0.801.2312.55
HiVT [58]0.771.1612.67
MENTOR (Ours)0.791.2113.01
", + "bbox": [ + 501, + 104, + 890, + 258 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tasks, can capture diverse lane connection patterns in the map topology. 2) MENTOR is good at adopting HSL tasks to transfer their knowledge to the primary task, and consequently resulting in significant improvement in terms of diverse (RF) and admissible (DAO) trajectory prediction.", + "bbox": [ + 496, + 263, + 890, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Comparison to SOTA", + "text_level": 1, + "bbox": [ + 500, + 344, + 700, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare our method to SOTA models on the Argov-verse benchmark. Even though the focus of our method was on improving diversity and admissibility of generated trajectories in challenging scenarios, as shown in Tab. 4, our model's performance is comparable to best models, on the distance-based metrics on the benchmark. Particularly, compared to HiVT [58], our model achieves the second rank on minADE and minFDE, while in challenging scenarios it outperforms HiVT on the diversity and admissibility metrics as well as the distance-based metrics with a large margin, as is evident in Tab. 1. We further verify the effectiveness of our approach on a smaller dataset, nuScenes [5], and report the results in the supplementary material.", + "bbox": [ + 496, + 368, + 890, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 573, + 617, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented a novel trajectory prediction model based on the concept of meta-learning. We formulated various lane connection relations on the map topology as meTA ROad paTh (TAROT), and used a model, MEtaroad NeTwORk (MENTOR), to supply TAROT tips in the form of Heterogeneous Structural Learning (HSL) tasks to improve trajectory prediction. Besides, focusing on enhancing the map representational learning power, MENTOR can mentor any proxy task to further improve the primary motion forecasting task. Via extensive experimental evaluations, we showed that HSL tasks are capable of modeling high-level semantics stemming from long-range heterogeneous connections between lanes. Additionally, we showed that our proposed MENTOR model acts as a mentor to gain the maximum benefit from the existing structural information of the map. The results also highlighted that, besides significantly improving diversity and admissibility of predictions, our method can obtain improved or comparable results on common distance-based metrics compared to the past arts with a larger number of parameters.", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8391", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W Hoffman, David Pfau, Tom Schaul, Brendan Shillingford, and Nando De Freitas. Learning to learn by gradient descent by gradient descent. In NeurIPS, 2016. 5", + "[2] Antreas Antoniou, Harrison Edwards, and Amos Storkey. How to train your MAML. 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In ICML, 2019. 5" + ], + "bbox": [ + 501, + 92, + 890, + 588 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8393", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learn TAROT with MENTOR_ A Meta-Learned Self-Supervised Approach for Trajectory Prediction/e84db066-834e-41d1-b5a0-8e0c6af0f9b7_model.json b/2023/Learn TAROT with MENTOR_ A Meta-Learned Self-Supervised Approach for Trajectory Prediction/e84db066-834e-41d1-b5a0-8e0c6af0f9b7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9ebb1872b78e5b40be8fc24c94c32a17796cbee2 --- /dev/null +++ b/2023/Learn TAROT with MENTOR_ A Meta-Learned Self-Supervised Approach for Trajectory Prediction/e84db066-834e-41d1-b5a0-8e0c6af0f9b7_model.json @@ -0,0 +1,2090 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.13, + 0.882, + 0.176 + ], + "angle": 0, + "content": "Learn TAROT with MENTOR: A Meta-Learned Self-supervised Approach for Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.266, + 0.204, + 0.703, + 0.221 + ], + "angle": 0, + "content": "Mozhgan Pourkeshavarz, Changhe Chen, Amir Rasouli" + }, + { + "type": "text", + "bbox": [ + 0.386, + 0.223, + 0.584, + 0.239 + ], + "angle": 0, + "content": "Noah's Ark Lab, Huawei" + }, + { + "type": "text", + "bbox": [ + 0.419, + 0.24, + 0.551, + 0.256 + ], + "angle": 0, + "content": "Toronto, Canada" + }, + { + "type": "text", + "bbox": [ + 0.358, + 0.261, + 0.615, + 0.273 + ], + "angle": 0, + "content": "firstname_lastname@huawei.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.473, + 0.751 + ], + "angle": 0, + "content": "Predicting diverse yet admissible trajectories that adhere to the map constraints is challenging. Graph-based scene encoders have been proven effective for preserving local structures of maps by defining lane-level connections. However, such encoders do not capture more complex patterns emerging from long-range heterogeneous connections between nonadjacent interacting lanes. To this end, we shed new light on learning common driving patterns by introducing meTA ROad paTh (TAROT) to formulate combinations of various relations between lanes on the road topology. Intuitively, this can be viewed as finding feasible routes. Furthermore, we propose MEta-road NeTwORk (MENTOR) that helps trajectory prediction by providing it with TAROT as navigation tips. More specifically, 1) we define TAROT prediction as a novel self-supervised proxy task to identify the complex heterogeneous structure of the map. 2) For typical driving actions, we establish several TAROTs that result in multiple Heterogeneous Structure Learning (HSL) tasks. These tasks are used in MENTOR, which performs meta-learning by simultaneously predicting trajectories along with proxy tasks, identifying an optimal combination of them, and automatically balancing them to improve the primary task. We show that our model achieves state-of-the-art performance on the Argoverse dataset, especially on diversity and admissibility metrics, achieving up to \\(20\\%\\) improvements in challenging scenarios. We further investigate the contribution of proposed modules in ablation studies." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Vehicle trajectory prediction is one of the main building blocks of autonomous driving. Prediction demonstrates how the future might unfold based on the road structure and the behavior of road users. To operate safely, self-driving cars must accurately perceive the geometric and semantic information in the driving scene and predict diverse yet scene-compliant trajectories. High-definition maps provide useful cues since the behaviors of agents and the interac" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.895, + 0.401 + ], + "angle": 0, + "content": "tions among them are largely influenced by the road topology and governed by the map constraints. For example, a vehicle is unlikely to change to a lane that runs in the opposite direction. In this light, learning the structure of the map efficiently is essential to predict a variety of feasible trajectories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.895, + 0.599 + ], + "angle": 0, + "content": "Inspired by the structural nature of the road, map vectorization has become prevalent in recent works, in which lanes are converted into vectors [15, 56, 18]. Consequently, graph structures can be leveraged to learn the relationships between vectorized entities [28, 54, 11, 16]. In this way, connected lanes in various formations, e.g. successor, predecessor, right, and left, represent admissible ways to traverse the terrain. For example, two lanes positioned consecutively in space and connected by a sequential link can be driven successively, whereas two lanes connected by a lateral link enable a lane change maneuver. Hence, the HD map lane graph has edges with different semantic meanings, indicating its heterogeneous nature." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.896, + 0.87 + ], + "angle": 0, + "content": "Although existing lane graphs are shown to be effective in learning local structures through the adjacent lanes, they lack the ability to model more complex patterns imposed by long-range heterogeneous connections between nonadjacent yet interacting lanes. These connections are important to capture high-level intentions, such as overtaking, merging, and double turns, and can potentially represent the constraints and rules of the road. To model such connections, some methods propose adopting self-supervised tasks on top of the lane graph [15, 4] to encourage the model to learn the semantics associated with lane connectivities. Since scene structure contains various semantics, having only one proxy task at a time is insufficient to provide diverse traffic patterns. Alternatively, anchor-based models incorporate prior knowledge by identifying candidate trajectories based on sampling or clustering of training data [6, 43]. However, these methods are less robust and generalizable due to their dependency on the distribution of data." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Motivated by this insight, we introduce a novel self-supervised task for trajectory prediction, termed Heteroge-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8384" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.332 + ], + "angle": 0, + "content": "aneous Structure Learning (HSL), to formulate traffic patterns imposed by road constraints. In particular, we formulate the road structure by meTA ROad paTh (TAROT) as a composite relation of heterogeneous edges in the scene graph that can model diverse abstractions from the map without additional data and labels. Therefore, by predicting the presence of TAROT in the driving scene as an HSL task, the model gets a sense of feasible transitions on the map as navigation tips for traversing the road. Furthermore, we propose MEta-road NeTwORk (MENTOR), a novel trajectory prediction framework that provides insight into the structural perspective of the map by simultaneously predicting a set of HSL tasks. In detail, inspired by the meta-learning concept, MENTOR is learning to learn road topology by automatically selecting the HSL tasks that assist the target trajectory prediction." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.334, + 0.468, + 0.574 + ], + "angle": 0, + "content": "The contributions of this paper are as follows: (1) For the first time, to the best of our knowledge, we investigate the idea of learning to learn in trajectory prediction through the proposed MEta-road NeTwORk (MENTOR), which determines an optimal combination of Heterogeneous Structure Learning (HSL) tasks and automatically balances them to assist the primary task of predicting diverse and admissible trajectories. (2) We propose meTA ROad paTh (TAROT) prediction as a novel HSL task capable of modeling high-level semantics within the map structure. Thus, diverse semantic aspects of road configuration can be captured by defining various TAROTs, resulting in multiple HSL tasks that are learned simultaneously. (3) We conduct extensive experimental evaluations to show our model's effectiveness in predicting not only precise but also diverse and admissible trajectories." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.589, + 0.216, + 0.604 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.614, + 0.468, + 0.794 + ], + "angle": 0, + "content": "Trajectory Prediction has been the subject of interest in a large body of literature. Existing methods explore different representations and methods to learn scene context, including rasterized images [6, 38, 16] and point-clouds [49] with CNNs, and vectorized representations with GNNs [15, 32, 18, 54], or transformers [21, 58, 17, 30], which are often associated with sophisticated fusion mechanisms [28]. These models focus on finding more powerful ways of extracting features from HD maps and modeling agents' interactions. They, however, require substantial model capacity, heavy parameterization, extensive augmentations, or a large amount of data to produce accurate results." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.796, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Some methods investigate the ways to improve prediction precision by incorporating prior knowledge as predefined candidate trajectories generated using sampling or clustering techniques [32, 55]. Nevertheless, the main limitation of these methods is that their performance is highly dependent on the quality of trajectory proposals, which becomes a dependency. To resolve this issue, end-to-end" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.242 + ], + "angle": 0, + "content": "solutions optimize the endpoints of candidate trajectories [18, 16] resulting in improved accuracy while maintaining a reasonable parameter budget. However, using an online goal candidate optimization strategy is computationally very expensive, therefore it is prohibitive for real-time applications, such as autonomous driving. More recently, ensemble techniques have become more prevalent and demonstrated good prediction performance [43, 50]. However, their major disadvantages are high memory cost for training and computationally expensive inference." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.246, + 0.89, + 0.472 + ], + "angle": 0, + "content": "Besides designing high-precision models, researchers have focused on diversity, admissibility, and map conformity of the predicted trajectories. To generate diverse trajectories, state-of-the-art models use Generative Adversarial Networks (GANs) [25, 37, 57], and Conditional Variational Autoencoders (CVAEs) [38, 42, 53, 26], sophisticated sampling functions, such as diversity sampling [52] and latent semantic sampling [20]. However, most works sacrifice map conformity for prediction diversity. To improve conformity, map data can be incorporated as a part of the loss function [44, 9], or as a post-processing step [48]. To better evaluate the diversity and admissibility of predicted trajectories, new metrics, such as RF and DAO, have been proposed [34]. In this paper, we use these as well as common metrics to further assess our model's performance." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.476, + 0.89, + 0.686 + ], + "angle": 0, + "content": "Self-Supervised Learning (SSL) is a learning method that uses appropriately designed proxy tasks to generate additional supervised signals to train models. In trajectory prediction, SSL has been utilized by defining various proxy tasks laid on top of the agent/map information [15, 4]. For instance, a recent work, SSL-Lane [4], uses four different tasks and shows how they can be incorporated to improve performance. However, this model uses only one proxy task at a time and does not explore combinations of different tasks. Additionally, SSL-Lane employs different losses in its formulation only in a 1:1 ratio without tuning them. These shortcomings motivated our proposed framework for simultaneously learning proxy tasks without letting them compete with the target trajectory prediction task." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.689, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Meta-learning originates from the concept of learning to learn, a topic of continued interest in machine-learning research. Meta-learning has been used for finding optimal hyper-parameters and good initialization [27, 13], metric-learning, and non-parametric methods for few-shot learning [40, 41]. This paper uses meta-learning to learn the road topology across several tasks by transferring the knowledge from self-supervised tasks, defined on the map structure, to the primary trajectory prediction task. In a closely related category of works, sample weighting, a meta-learning mechanism is used for adaptively extracting sample weights to guarantee robust deep learning in the presence of training data bias [23, 39]. In practice, instead of manually setting the form of weight functions, these methods learn an ex" + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8385" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.09, + 0.833, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.303, + 0.895, + 0.425 + ], + "angle": 0, + "content": "Figure 1: Overview of the proposed approach. Given directed HIN \\(\\mathcal{G}\\) of the scene and \\(N\\) predefined TAROTs, the HSL engine \\(\\mathcal{H}(\\mathrm{TAROTs})\\) defines \\(N\\) HSL tasks each predicting the presence of a specific TAROT. Within each TAROT task \\(p_n\\), positive samples are two arbitrary nodes from \\(\\mathcal{G}\\) that can be reached by \\(p_n\\), and negative samples are those that cannot. For the HSL tasks and the primary task, we find learned representations \\(\\mathcal{Z}\\) from GNN model \\(f\\). To find the loss values, samples are fed through the task-specific transformations \\(\\Phi_t\\) followed by task-specific loss functions \\(\\mathcal{L}^n\\). Lastly, by Providing loss values of the primary task's samples and the HSL tasks' samples (as a concatenation of [task id, label(Pos/Neg), loss value]), we train MENTOR to learn weight function \\(\\mathcal{V}\\) in a way to find an optimal combination of the HSL tasks in a meta-learning manner." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.438, + 0.395, + 0.453 + ], + "angle": 0, + "content": "plicit weighting function directly from the data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.471, + 0.537 + ], + "angle": 0, + "content": "Self-supervised learning and meta-learning both contribute to improving model generalization capability. To the best of our knowledge, this is the first study in trajectory prediction to exploit the benefit of scene-based self-supervised tasks through a meta-learning paradigm." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.572, + 0.251, + 0.59 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Traffic transitions are complex and cannot simply be modeled by learning the local relationships. What required is modeling patterns of traveling through the road as a combination of relationships, not only in the adjacent lanes but also between nonadjacent yet interacting lanes. This can, for example, refer to a merge pattern in the road structure that involves both lateral and sequential relations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.721, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The main idea behind our proposed model is to provide high-order combinations of basic adjacent-adjacent patterns as the full gamut of lane interactions when predicting vehicle trajectories. To this end, we first discuss the procedure for generating a Heterogeneous Information Network (HIN) from scenes, followed by the introduction of the Heterogeneous Structural Learning (HSL) tasks designed to capture relations between lanes. Next, we describe our novel MEtaroad NeTwork (MENTOR) that learns an explicit weighting function to softly select HSL tasks and balance them to improve the performance of the primary task via meta-learning (see Fig. 1)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.66, + 0.453 + ], + "angle": 0, + "content": "3.1. Scene Encoding" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.461, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Contrary to the common approach that treats the scene as a homogeneous graph [54], we model the scene as a Heterogeneous Information Network (HIN) [24]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.893, + 0.643 + ], + "angle": 0, + "content": "Definition 1. Heterogeneous Information Network (HIN) a HIN is defined as a graph \\(\\mathcal{G} = (\\mathcal{V},\\mathcal{E})\\), where \\(\\mathcal{V}\\) is the set of nodes and \\(\\mathcal{E}\\) is the set of edges, each representing a binary relation between two nodes in \\(\\mathcal{V}\\). \\(\\mathcal{G}\\) is associated with two mappings: (1) node type mapping function \\(\\phi :\\mathcal{V}\\to \\mathcal{T}\\) and (2) edge type mapping function \\(\\psi :\\mathcal{E}\\rightarrow \\mathcal{R}\\) where \\(\\mathcal{T}\\) and \\(\\mathcal{R}\\) denote sets of node and edge types, respectively. If \\(|\\mathcal{T}| + |\\mathcal{R}| > 2\\), network \\(\\mathcal{G}\\) is an HIN, otherwise it is homogeneous." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.644, + 0.894, + 0.81 + ], + "angle": 0, + "content": "We encode the scene as a directed HIN with node types \\(\\mathcal{T} = \\{\\text{lane, agent}\\}\\) and \\(\\mathcal{R} = \\{\\text{left, right, successor, predecessor}\\}\\) as basic relations between adjacent lanes. To initialize node features in the HIN, we use the simplified PointNet [36] with multi-layer perception (MLP) to process polyline features and a 1D convolution with a feature pyramid network [29] to process agents' observations similar to [28]. One advantage of our method is that any type of GNN can be used to process the HIN. Hence, we employ Heterogeneous Graph Transformer (HGT) as a simple yet effective model similar to [19]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.81, + 0.833 + ], + "angle": 0, + "content": "3.2. Heterogeneous Structural Learning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Traffic transitions follow patterns governed by high-level constraints stemming from long-range structural connections between lanes of the road. For learning the map structure, heterogeneity helps interpret a series of relations," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8386" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.465, + 0.106 + ], + "angle": 0, + "content": "which our model learns with meTA ROad paTh (TAROT)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.106, + 0.468, + 0.228 + ], + "angle": 0, + "content": "Definition 2. Meta-Path. A meta-path \\(\\mathcal{P} = v_{1} \\xrightarrow{r_{1}} v_{2} \\xrightarrow{r_{2}} \\ldots \\xrightarrow{r_{\\ell}} v_{\\ell + 1}\\) expresses a composite relation \\(R = r_{1} \\circ r_{2} \\dots \\circ r_{\\ell}\\) between nodes \\(v_{1}\\) and \\(v_{\\ell + 1}\\), where \\(\\circ\\) denotes the composition operator on relations. If two nodes \\(v_{i}\\) and \\(v_{j}\\) are related by the composite relation \\(R\\), then there exists a path that connects \\(v_{i}\\) to \\(v_{j}\\) in \\(\\mathcal{G}\\), denoted by \\(\\mathcal{P}_{v_{i} \\rightsquigarrow v_{j}}\\). Moreover, the nodes and edges types in \\(\\mathcal{P}_{x_{i} \\rightsquigarrow x_{j}}\\) match with types in \\(\\mathcal{T}\\) and \\(\\mathcal{R}\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.468, + 0.38 + ], + "angle": 0, + "content": "The features obtained from the meta-path analysis in HINs are notably useful in improving graph-based models since they encode indirect semantic relations between nodes that are not directly connected. These features also aid in establishing new relations between vertices. As such, metapath analysis has been frequently used in graph domains to enhance graph representation learning power and improve downstream tasks, such as node classification and link prediction [51, 46, 22, 8]. This means meta-paths can help find new patterns and relations in HINs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.719 + ], + "angle": 0, + "content": "By focusing on the long-range relations that impose transitions on the road, we define TAROT \\( p \\) though the HIN as a path instance of \\( p_{v_i\\sim v_j}\\vdash \\mathcal{P} \\) where node types are the same. Thus, the TAROT can formulate a combination of basic road relations corresponding to transition patterns imposed by map constraints. Predicting the presence of a TAROT between two nodes \\( v_{i} \\) and \\( v_{j} \\) is similar to link prediction. Here, the link means heterogeneous composite relations between nodes. Contrary to link prediction problems, the proposed TAROT prediction can be treated as a self-supervised task. In detail, we follow a simple rule to provide the additional supervised signals for proxy tasks: If node \\( v \\) is reachable from node \\( u \\) by TAROT \\( p \\), then \\( y_{u,v}^{p} = 1 \\), otherwise \\( y_{u,v}^{p} = 0 \\). This means the HSL task, associated with the TAROT will be formed as a simple link prediction task without the need for any additional data or manual labeling. Hence, by obtaining the hidden representations of two arbitrary nodes learned by a GNN and using a simple operator \\( \\hat{y}_{u,v}^{p} = \\sigma \\left(\\Phi_{t}(z_{u})^{\\top}\\Phi_{t}(z_{v})\\right) \\) we can predict whether a TAROT between two nodes is present or absent. Here, \\( \\Phi_t \\) is a type-specific transformation \\( t\\in \\mathcal{T} \\) and \\( z_{u} \\) and \\( z_{v} \\) are the node embeddings of nodes \\( u \\) and \\( v \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.468, + 0.84 + ], + "angle": 0, + "content": "Using the proposed TAROT as a type of meta-path we can model a common pattern of driving that adhere to the map constraints. Hence, we define several TAROTs to formulate diverse traffic patterns within the driving scene, resulting in several HSL tasks that can be used to predict diverse and admissible trajectories. We provided a complimentary figure in the supplementary material to further show TAROT's motivation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.847, + 0.27, + 0.862 + ], + "angle": 0, + "content": "3.3. Meta Road Network" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The proposed HSL task is designed to identify diverse patterns within the road structure, for which we explore the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.318 + ], + "angle": 0, + "content": "idea of defining various TAROTs resulting in several self-supervised HSL tasks to be learned simultaneously with the primary trajectory prediction task. However, as with any multi-task learning method, the HSL tasks should be carefully chosen and properly weighted so that learning the map structure does not compete with the primary task, especially when the capacity of graph neural networks (GNNs) is limited. To this end, we propose MEta-road NeTwORk (MENTOR), a learning framework for trajectory prediction that offers the possibility of learning to learn the road configuration while learning the main task. Below, we discuss a naive multi-task combination of self-supervision tasks to explain the motivation behind the design of MENTOR, followed by describing the meta-learning objective using MENTOR, and a detailed look at the learning procedure." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.326, + 0.864, + 0.34 + ], + "angle": 0, + "content": "3.3.1 Naive Multi-task Combination of HSL Tasks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.533 + ], + "angle": 0, + "content": "Self-supervised learning has already been explored in trajectory prediction for autonomous driving and has proven beneficial [15, 4]. Adopting a combination of Self-Supervised Learning (SSL) tasks, namely proxy tasks, to improve the primary task has not yet been addressed, even though it has been shown to be effective in visual learning [12]. Here, we formulate a naive multi-task combination of HSL tasks, as SSL tasks, with a shared backbone network with parameters \\(\\mathbf{w}\\), between the primary and all proxy tasks. Each task has a specific loss function \\(\\mathcal{L}^n\\) incorporated by a task-specific parameter \\(\\lambda_{n}\\). So the optimal parameter \\(\\mathbf{w}^{*}\\) can be extracted by the following objective function:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.547, + 0.892, + 0.589 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {w}} \\quad \\mathbb {E} \\left[ \\lambda_ {0} \\mathcal {L} ^ {0} (.; \\mathbf {w}) + \\sum_ {n = 1} ^ {N} \\lambda_ {n} \\mathcal {L} ^ {n} (.; \\mathbf {w}) \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.601, + 0.891, + 0.632 + ], + "angle": 0, + "content": "where index zero stands for the primary task \\( n = 0 \\), and index \\( n|_1^N \\) denotes \\( n^{th} \\) task of \\( N \\) proxy tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.657, + 0.725, + 0.672 + ], + "angle": 0, + "content": "3.3.2 Meta-learning Objective" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.891, + 0.774 + ], + "angle": 0, + "content": "Learning road topology should enhance rather than compete with trajectory prediction, hence determining an effective combination of \\(\\lambda\\) parameters is crucial. To achieve this, we adopt MENTOR to parameterize model \\(\\mathbf{w}(\\Theta)\\) to determine an optimal combination of HSL tasks and automatically balance them for improved prediction as shown below," + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.786, + 0.891, + 0.843 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {w}, \\boldsymbol {\\Theta}} \\quad \\mathbb {E} \\left[ \\mathcal {L} ^ {0} \\left(\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})\\right) \\right] \\\\ \\text {s . t .} \\mathbf {w} ^ {*} (\\boldsymbol {\\Theta}) = \\underset {\\mathbf {w}} {\\operatorname {a r g m i n}} \\quad \\mathbb {E} \\left[ \\mathcal {L} ^ {n | _ {0} ^ {N}} (\\mathbf {w}; \\boldsymbol {\\Theta}) \\right]. \\end{array} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Specifically, to parametrize the model parameters \\(\\mathbf{w}\\), we can impose a learnable weighting function \\(\\mathcal{V}(\\cdot ,\\Theta)\\) to the objective function in (2) as MENTOR similar to [39]. Thus, the" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8387" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.088, + 0.095, + 0.415, + 0.109 + ], + "angle": 0, + "content": "Algorithm 1: MEta-road NeTwORk (MENTOR)" + }, + { + "type": "algorithm", + "bbox": [ + 0.08, + 0.111, + 0.47, + 0.41 + ], + "angle": 0, + "content": "Input : primary data \\(D^{\\mathrm{pr}}\\) , HSL proxy tasks data \\(D^{\\mathrm{hsl}}\\) , batch size \\(n\\) \\(m\\) , max iteration \\(T\\) folds for cross-validation \\(K\\) , model parameters w, MENTOR parameters \\(\\Theta\\) Output: model parameter \\(\\hat{\\mathbf{w}}^T\\) \n1 Initialize w, \\(\\Theta\\) \n2 for \\(t = 0\\) to \\(T - 1\\) do \n3 \\(\\left\\{x^{(\\mathrm{pr})},y^{(\\mathrm{pr})}\\right\\} \\gets\\) SampleMiniBatch \\((D^{pr},n)\\) . \n4 \\(\\left\\{x^{(\\mathrm{hsl})},y^{(\\mathrm{hsl})}\\right\\} \\gets\\) SampleMiniBatch \\((D^{\\mathrm{hsl}},m)\\) //cross validation \n5 for \\(k = 1\\) to \\(K\\) do \n6 \\(\\left\\{x^{(\\mathrm{meta})},y^{(\\mathrm{meta})}\\right\\} ,\\left\\{x^{(\\mathrm{train})},y^{(\\mathrm{train})}\\right\\} \\gets\\) CVSplit \\((D^{pr},k)\\) . Formulate model parameter \\(\\mathbf{w}^t\\) by Eq 6 \n8 Keep \\(\\Theta_{k}^{t + 1}\\) on fold \\(= k\\) by Eq.7 \n9 end \n10 Update \\(\\Theta^{t + 1}\\) with \\(\\frac{1}{K}\\sum_{k}^{K}\\Theta_{k}^{t + 1}\\) \n11 Update \\(\\mathbf{w}^{t + 1}\\) by Eq 8 \n12 end" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.44, + 0.373, + 0.456 + ], + "angle": 0, + "content": "objective function can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.461, + 0.251, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta}) = \\operatorname * {a r g m i n} _ {\\mathbf {w}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.488, + 0.469, + 0.529 + ], + "angle": 0, + "content": "\\[\n\\sum_ {n = 0} ^ {N} \\sum_ {i = 1} ^ {M _ {n}} \\frac {1}{M _ {n}} \\mathcal {V} \\left(\\Psi_ {i} ^ {n}; \\Theta\\right) \\mathcal {L} ^ {n} \\left(y _ {i} ^ {n}, f ^ {n} \\left(x _ {i} ^ {n}; \\mathbf {w}\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.716 + ], + "angle": 0, + "content": "where each task has \\(M_{n}\\) samples and \\(f^n\\) is the model for task \\(n\\). For \\(i^{th}\\) sample of task \\(n\\), \\(y_i^n\\) is the label, and \\(\\Psi_i^n\\) is an embedding vector expressing as the concatenation of one-hot vector of task types, the label (positive/negative), and the loss value of the sample. Therefore, following Eq. (3), the model learns how to assist the primary task by optimizing MENTOR's parameters \\(\\Theta\\). These parameters can be optimized using the meta-learning idea [47, 1, 10, 14]. Specifically, using a small amount of meta-data \\(D^{\\mathrm{meta}}\\), representing the meta-knowledge of ground-truth \\(D^{\\mathrm{gt}}\\), \\(D^{\\mathrm{meta}} \\cup D^{\\mathrm{train}} = D^{\\mathrm{gt}}\\), the optimal parameter \\(\\Theta^*\\) can be obtained by minimizing the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.717, + 0.469, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Theta} ^ {*} = \\underset {\\boldsymbol {\\Theta}} {\\operatorname {a r g m i n}} \\mathcal {L} ^ {\\text {m e t a}} (\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})) \\triangleq \\frac {1}{m} \\sum_ {i = 1} ^ {m} \\mathcal {L} _ {i} ^ {\\text {m e t a}} (\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.769, + 0.469, + 0.799 + ], + "angle": 0, + "content": "where \\(m\\) and \\(r\\), \\(m \\ll r\\), are the number of meta-samples and training samples, respectively, and meta-loss is," + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.805, + 0.469, + 0.824 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i} ^ {\\mathrm {m e t a}} (\\mathbf {w}) = \\mathcal {L} \\left(y _ {i} ^ {\\mathrm {m e t a}}, f \\left(x _ {i} ^ {\\mathrm {m e t a}}, \\mathbf {w}\\right)\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.829, + 0.226, + 0.844 + ], + "angle": 0, + "content": "where \\((x,y)\\sim D^{\\mathrm{meta}}\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.414, + 0.863 + ], + "angle": 0, + "content": "3.3.3 Meta-road Network Learning Procedure" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "To overcome the complexity of the bi-level optimization, following [13, 39], we use an online strategy to approximate" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.152 + ], + "angle": 0, + "content": "\\(\\mathbf{w}^*\\) and \\(\\Theta^{*}\\) with the updated parameters \\(\\hat{\\mathbf{w}}\\) and \\(\\hat{\\Theta}\\), respectively through a single optimization loop. In each iteration of training, given training data \\(D^{\\mathrm{train}}\\), HSL proxy tasks data \\(D^{\\mathrm{hsl}}\\), and meta-data \\(D^{\\mathrm{meta}}\\), we follow three steps:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.153, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Formulating Model Parameter: We formulate the updating equation of model parameter \\(\\mathbf{w}\\) by moving the current \\(\\mathbf{w}^t\\) along the descent direction of the loss in Eq. (3)," + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.218, + 0.892, + 0.262 + ], + "angle": 0, + "content": "\\[\n\\underset {D ^ {\\text {t r a i n}} \\cup D ^ {\\mathrm {h s l}}} {\\hat {\\mathbf {w}} ^ {(t)}} (\\boldsymbol {\\Theta}) = \\mathbf {w} ^ {(t)} - \\alpha \\frac {1}{N} \\sum_ {n = 0} ^ {N} \\mathcal {V} (\\cdot ; \\boldsymbol {\\Theta}) \\nabla_ {\\mathbf {w}} \\mathcal {L} ^ {n} (\\mathbf {w}) \\Bigg | _ {\\mathbf {w} ^ {(t)}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.268, + 0.892, + 0.313 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is the learning rate for \\(\\mathbf{w}\\) and \\(\\mathcal{L}^n\\) denotes the loss function for the task number \\(n\\). To avoid cluttered notation, the summation of task samples is omitted." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.314, + 0.892, + 0.388 + ], + "angle": 0, + "content": "Updating Parameters of MENTOR: After updating model parameter \\(\\hat{\\mathbf{w}}^{(t)}(\\Theta)\\), parameter \\(\\Theta\\) of MENTOR can be updated guided by Eq. (4), i.e., moving the current parameter \\(\\Theta^{(t)}\\) along the objective gradient of Eq. (4) calculated on the meta-data," + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.409, + 0.892, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\Theta_ {D ^ {\\mathrm {m e t a}}} ^ {(t + 1)} = \\Theta^ {(t)} - \\beta \\mathcal {V} (\\cdot ; \\Theta) \\mathcal {L} ^ {0} \\left(\\hat {\\mathbf {w}} ^ {(t)} (\\Theta)\\right) \\Big | _ {\\Theta^ {(t)}} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.443, + 0.892, + 0.533 + ], + "angle": 0, + "content": "where \\(\\beta\\) is the learning rate for \\(\\Theta\\). This update allows the soft selection of useful HSL proxy tasks and balances them with the main motion prediction task to improve the performance of the main task. Without balancing tasks with the weighting function \\(\\mathcal{V}(\\cdot;\\Theta)\\), proxy tasks can dominate training and degrade the performance of the primary task." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.534, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Updating Model Parameters: Model parameters \\(\\mathbf{w}\\) for tasks can be updated with optimized \\(\\Theta^{t + 1}\\) in Eq. (7) as," + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.572, + 0.892, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\mathbf {w}} _ {D ^ {\\mathrm {t r a i n}} \\cup D ^ {\\mathrm {h s l}}} ^ {(t + 1)} (\\boldsymbol {\\Theta}) = \\mathbf {w} ^ {(t)} \\\\ - \\alpha \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\mathcal {V} \\left(\\because \\Theta^ {(t + 1)}\\right) \\nabla_ {\\mathbf {w}} \\mathcal {L} ^ {n} (\\mathbf {w}) \\Bigg | _ {\\mathbf {w} ^ {(t)}}. \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.652, + 0.892, + 0.773 + ], + "angle": 0, + "content": "Lastly, to circumvent the problem of meta-overfitting, meaning that parameters \\(\\Theta\\) overfit to the small meta-dataset, we follow the meta-validation solution as in [2, 59]. In particular, to make \\(\\Theta\\) generalizable across meta-training sets, we optimize it using \\(K\\) different meta-datasets with k-fold cross-validation. The gradients of \\(\\Theta\\) from different meta-datasets are then averaged to update \\(\\Theta^{(t)}\\). The MENTOR learning procedure is summarized in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.632, + 0.802 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our goal is to investigate ways for improving map representational learning power to predict diverse and admissible trajectories. For this purpose, we seek to answer the following questions: Q1: Are predicted trajectories diverse and admissible? Q2: Is MEta-road NeTwORk (MENTOR) effective regardless of the type of HSL task? Q3: How much" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8388" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.096, + 0.09, + 0.874, + 0.104 + ], + "angle": 0, + "content": "Table 1: Comparison to SOTA models on challenging scenarios. Arrows show lower (↓) or higher (↑) values are better." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.105, + 0.89, + 0.213 + ], + "angle": 0, + "content": "
MethodTurnsStationary
minADE(↓)minFDE(↓)DAO(↑)RF(↑)MR(↓)minADE(↓)minFDE(↓)DAO(↑)RF(↑)MR(↓)
LaneGCN [28]1.082.1867.632.8935.761.232.5261.692.6936.80
MMTransformer[21]1.052.0769.763.3532.001.132.2864.853.2135.69
FTGN [3]1.062.0470.723.2534.061.162.2263.953.0632.49
HiVT [58]1.062.2366.842.7935.451.252.7458.432.5139.61
SSL-Lane [4]1.072.1169.653.2133.341.162.3462.453.2234.54
MENTOR (Ours)1.032.0079.213.7631.301.132.1969.233.8732.76
" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.226, + 0.468, + 0.257 + ], + "angle": 0, + "content": "does our proposed HSL task contribute to diversity and admissibility?" + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.261, + 0.266, + 0.277 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.285, + 0.468, + 0.389 + ], + "angle": 0, + "content": "Dataset: We evaluated our method on the Argoverse benchmark dataset [7]. Here the task is to predict 3 seconds of future trajectories given 2 seconds of past observations. This dataset consists of more than \\(300K\\) real-world driving sequences, which are split into the train (205K), validation (39K), and test (78K) sets without geographical overlap along with corresponding HD maps." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.391, + 0.468, + 0.541 + ], + "angle": 0, + "content": "Metrics: We selected a set of metrics to measure the precision, diversity, and admissibility of predictions. For precision, we use minADE (Average Displacement Error), minFDE (Final Displacement Error), and MR (Miss Rate). For diversity, we use the Ratio of avgFDE to minFDE (RF) [34], which measures the spread of predictions in Euclidean distance. We use Drivable Area Occupancy (DAO) [34] to determine the proportion of pixels that predicted trajectories occupy in the drivable area. RF and DAO work in a complementary way to measure diversity along with admissibility." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.542, + 0.468, + 0.843 + ], + "angle": 0, + "content": "Implementation Details: To normalize the data, we translate and rotate the coordinate system of each sequence so that the origin is at the agent's current location at \\( t = 0 \\). We use the orientation from the agent's location at \\( t = -1 \\) to its location at \\( t = 0 \\) as the positive x axis. We use all actors and lanes whose distance from the agent is smaller than 100 meters as the input. As a model architecture, we use three layers of HGT with the hidden dimension of size 128. For the HSL tasks, we define five TAROTs with variable lengths of 4 to 7. The intuition behind the number of TAROTs is to model turning right/left, lane changing (right-to-left and left-to-right), and going straight. We formulate Mentor as an MLP with two hidden layers with 100 nodes each, with ReLU activations for hidden nodes and sigmoid output to ensure it is in range [0, 1]. For the loss functions, we follow the widely used regression-MLP plus classification-MLP combination [28, 24, 33] for trajectory prediction and cross-entropy for the HSL task. For the training, we use the AdamW [31] optimizer with an initial learning rate of 5e-4, weight decay 1e-4, and batch size of 64." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.848, + 0.377, + 0.864 + ], + "angle": 0, + "content": "4.2. Analysis on Challenging Scenarios" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Existing prediction datasets are highly imbalanced in terms of scenario diversity, with the majority of traffic ac" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.226, + 0.89, + 0.437 + ], + "angle": 0, + "content": "tors simply driving straight [35]. Calculating metrics by aggregating over scenarios is therefore influenced by the most common maneuvers, where prediction models often do well. In practice, scenarios, such as turning at intersections could be of greater interest to practitioners and accurately predicting these scenarios are even more crucial for the safe operation of autonomous vehicles. Hence, to verify the effectiveness of our model, we extracted challenging scenarios including left/right/blind turns and stationary scenarios where the vehicle's observed trajectory is very short, thus the model has minimal motion information from the vehicle. By blind turns, we refer to the cases where the observed trajectory is straight and the turn occurs during the unobserved portion of the trajectory." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.438, + 0.89, + 0.619 + ], + "angle": 0, + "content": "We compare our method against several vectorized-based SOTA models with public implementations, including two graph-based models, LaneGCN [28] and FTGN [3], two transformer-based models, MMTransformer [21] and HiVT [58], and SSL-Lane [4], which extends the lane graph by adding four different self-supervised tasks based on agent/map information. As shown in Table 1, our method significantly improves upon the state-of-the-art models on most metrics in both scenarios. Particularly, our method, MENTOR achieves notable improvements in diversity and admissibility metrics, namely DAO and RF by up to \\(13\\%\\) and \\(20\\%\\) respectively in the challenging scenarios." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.62, + 0.89, + 0.799 + ], + "angle": 0, + "content": "Qualitative analysis. Fig. 2 depicts a number of qualitative examples to better highlight our method's performance. The first two rows represent turn-right scenarios, and the third and fourth rows show left-turn and stationary scenarios. As can be seen in the last column, our method consistently generates diverse predictions that are also admissible by correctly aligning with the road topology. The behavior of competing methods, however, varies often resulting in the generation of infeasible trajectories. In the supplementary materials, we discuss the algorithm used to find challenging scenarios and present additional per-scenario metrics to further elaborate on the correlation of metrics." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.809, + 0.663, + 0.823 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.833, + 0.763, + 0.847 + ], + "angle": 0, + "content": "4.3.1 MENTOR Acting as a Mentor" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.856, + 0.89, + 0.9 + ], + "angle": 0, + "content": "To assess the ability of MENTOR, we analyze the weighting function \\(\\mathcal{V}(\\Psi_i^n;\\Theta)\\) for \\(i^{th}\\) sample of task \\(n\\). Particularly, we present the learned weight function at the last epoch of" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8389" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.082, + 0.855, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.435, + 0.891, + 0.467 + ], + "angle": 0, + "content": "Figure 2: Qualitative examples on Argoverse showing diversity and admissibility of the predicted trajectories by MENTOR. Red, green, and blue trajectories represent observation, ground truth, and 6 predicted trajectories, respectively." + }, + { + "type": "image", + "bbox": [ + 0.143, + 0.468, + 0.404, + 0.607 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.669 + ], + "angle": 0, + "content": "Figure 3: The weighting function in MENTOR. The green line is the primary task, and solid and dashed color lines represent positive and negative HSL samples, respectively. Each color corresponds to a specific HSL task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.867 + ], + "angle": 0, + "content": "the training. As shown in Fig. 3, MENTOR has two main benefits. Firstly, even when the model's loss is low, as the model is learning less challenging scenarios, trajectory prediction task (green line) samples have a higher weight than HSL tasks. Hence, MENTOR is more focused on learning the primary trajectory prediction task as there is no competition between HSL tasks and the primary task. Secondly, in all tasks, hard samples with higher losses are given more weight than easy samples with lower losses, indicating that MENTOR is mining hard samples. Here, MENTOR acts as a mentor by learning TAROTs and transferring that knowledge to the primary task." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of MENTOR: To analyze the effectiveness of MENTOR, we borrow a lane-graph-based baseline" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.644 + ], + "angle": 0, + "content": "and four self-supervised learning (SSL) tasks introduced in [4] and use them in MENTOR to improve the baseline. The SSL tasks are as follows: A) Lane masking, which recovers feature information from the perturbed lane graphs; B) Predicting distance to the intersection in terms of the shortest path length from all lane nodes to the intersection nodes; C) Maneuver classification, which predicts the form of a maneuver that the agent of interest intends to execute; And D) success/failure classification, which trains an agent specialized in achieving end-points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.893, + 0.901 + ], + "angle": 0, + "content": "We report the results in Tab. 2 where the SSL tasks are termed A-D and \\( \\text{MENTOR}_{\\sum \\mathrm{A}, \\mathrm{B}, \\mathrm{C}, \\mathrm{D}} \\) denotes the proposed model. According to the table, among the proposed tasks, maneuver classification, task C, has the best DAO (admissibility), indicating that predicting the form of maneuver can reveal more information about the road structure. Additionally, predicting the distance to the intersection, task B, gives a better estimate of the agent to the intersection, and the possibility of branching roads, hence improving RF (diversity) metric. In summary, individual tasks are shown to be effective by providing auxiliary information that helps improve different aspects of prediction. Once combined together, SSL tasks through the MENTOR framework improve distance-based metrics, minADE and minFDE as well as admissibility and diversity metrics, DAO and RF. These results validate the effectiveness of MENTOR as a learning framework to enhance prediction models" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8390" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.134 + ], + "angle": 0, + "content": "Table 2: Results of the ablation studies. \\(\\mathrm{SSL}_{-}x\\) indicates self-supervised tasks as in [4] and \\(\\mathrm{MENTOR}_{\\sum \\mathrm{A,B,C,D}}\\) indicates the original model augmented with MENTOR." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.135, + 0.468, + 0.223 + ], + "angle": 0, + "content": "
ModelminADE(↓)minFDE(↓)DAO(↑)RF(↑)
Baseline0.731.1265.873.00
SSLA0.701.0268.212.98
SSLB0.711.0468.653.87
SSLC0.721.0569.973.14
SSLD0.701.0168.023.01
MENTORΣA,B,C,D0.690.9877.914.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.238, + 0.468, + 0.297 + ], + "angle": 0, + "content": "Table 3: Results of the ablation studies. \\(\\mathrm{TAROT}^x\\) indicates the length of the TAROT through the HSL task and MENTOR represents our full model, which includes several HSL tasks." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.299, + 0.466, + 0.4 + ], + "angle": 0, + "content": "
TurnsValidation
ModelminFDE(↓)DAO(↑)RF(↑)minFDE(↓)DAO(↑)RF(↑)
Baseline2.37268.452.981.13274.024.21
TAROT42.26771.013.191.12875.524.43
TAROT52.20873.673.231.10777.114.48
TAROT62.15376.933.711.11278.894.50
TAROT72.08276.173.561.12178.004.51
TAROT82.10973.653.411.12077.214.38
MENTOR2.00379.213.760.97485.314.65
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.418, + 0.408, + 0.432 + ], + "angle": 0, + "content": "by providing additional information as SSL tasks." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.434, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Impact of TAROT Prediction as an HSL Task: for the purpose of analyzing the impact of the TAROT prediction, we conduct several experiments on the entire validation set and challenging turn scenarios by designing different models named \\(\\mathrm{TAROT}^x\\) where \\(x\\) refers to the length of TAROT through the HSL task. For example, \\(\\mathrm{TAROT}^4\\) could be any of these patterns [S-S-S-R, S-L-S-S, S-L-P-P...] (S: Successor, L: Left, R: Right, P: Predecessor as the basic relation of adjacent lanes). We average the metrics over all of the members in the list. A baseline model does not have any HSL tasks, and therefore does not have MENTOR. The last model is our final model which is loaded by multiple HSL tasks through MENTOR. As shown in Tab. 3, augmenting the model with the HSL task improves the baseline model performance. Moreover, from the experiments, we found that by predicting a longer TAROT, corresponding to a longer pattern in the road configuration with a higher abstraction, we can improve the model in turns scenarios. However, the length of TAROTs should be set carefully, as if set too long, the model would have a tendency to predict a turn maneuver even when several alternatives, such as driving straight, are available. To take advantage of this phenomenon, we define multiple TAROTs with variable lengths representing both short and long patterns. Thus, once used through MENTOR we enable the model to identify the best combination of HSL tasks, as TAROT prediction, by weighting them properly. In this way, our full model outperforms other models significantly. Based on the obtained results, we can conclude that 1) TAROTs are capable of modeling patterns in the map structure, thus formulating multiple TAROTs and subsequently multiple HST" + }, + { + "type": "table_caption", + "bbox": [ + 0.51, + 0.09, + 0.88, + 0.104 + ], + "angle": 0, + "content": "Table 4: Comparisons with SOTA on Argoverse test set." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.105, + 0.892, + 0.259 + ], + "angle": 0, + "content": "
MethodminADE(↓)minFDE(↓)MR(↓)
TNT [56]0.941.5413.30
DenseTNT [18]0.881.2812.58
TPCN [49]0.871.3615.80
mmTransformer [30]0.871.3415.40
LaneRCNN [54]0.901.4512.32
LTP [45]0.831.2914.72
AutoBot [17]0.891.4116.00
SceneTransformer [33]0.801.2312.55
HiVT [58]0.771.1612.67
MENTOR (Ours)0.791.2113.01
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.892, + 0.341 + ], + "angle": 0, + "content": "tasks, can capture diverse lane connection patterns in the map topology. 2) MENTOR is good at adopting HSL tasks to transfer their knowledge to the primary task, and consequently resulting in significant improvement in terms of diverse (RF) and admissible (DAO) trajectory prediction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.345, + 0.702, + 0.361 + ], + "angle": 0, + "content": "4.4. Comparison to SOTA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.565 + ], + "angle": 0, + "content": "We compare our method to SOTA models on the Argov-verse benchmark. Even though the focus of our method was on improving diversity and admissibility of generated trajectories in challenging scenarios, as shown in Tab. 4, our model's performance is comparable to best models, on the distance-based metrics on the benchmark. Particularly, compared to HiVT [58], our model achieves the second rank on minADE and minFDE, while in challenging scenarios it outperforms HiVT on the diversity and admissibility metrics as well as the distance-based metrics with a large margin, as is evident in Tab. 1. We further verify the effectiveness of our approach on a smaller dataset, nuScenes [5], and report the results in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.619, + 0.589 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we presented a novel trajectory prediction model based on the concept of meta-learning. We formulated various lane connection relations on the map topology as meTA ROad paTh (TAROT), and used a model, MEtaroad NeTwORk (MENTOR), to supply TAROT tips in the form of Heterogeneous Structural Learning (HSL) tasks to improve trajectory prediction. Besides, focusing on enhancing the map representational learning power, MENTOR can mentor any proxy task to further improve the primary motion forecasting task. Via extensive experimental evaluations, we showed that HSL tasks are capable of modeling high-level semantics stemming from long-range heterogeneous connections between lanes. Additionally, we showed that our proposed MENTOR model acts as a mentor to gain the maximum benefit from the existing structural information of the map. The results also highlighted that, besides significantly improving diversity and admissibility of predictions, our method can obtain improved or comparable results on common distance-based metrics compared to the past arts with a larger number of parameters." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8391" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W Hoffman, David Pfau, Tom Schaul, Brendan Shillingford, and Nando De Freitas. Learning to learn by gradient descent by gradient descent. 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Graph-based scene encoders have been proven effective for preserving local structures of maps by defining lane-level connections. However, such encoders do not capture more complex patterns emerging from long-range heterogeneous connections between nonadjacent interacting lanes. To this end, we shed new light on learning common driving patterns by introducing meTA ROad paTh (TAROT) to formulate combinations of various relations between lanes on the road topology. Intuitively, this can be viewed as finding feasible routes. Furthermore, we propose MEta-road NeTwORk (MENTOR) that helps trajectory prediction by providing it with TAROT as navigation tips. More specifically, 1) we define TAROT prediction as a novel self-supervised proxy task to identify the complex heterogeneous structure of the map. 2) For typical driving actions, we establish several TAROTs that result in multiple Heterogeneous Structure Learning (HSL) tasks. These tasks are used in MENTOR, which performs meta-learning by simultaneously predicting trajectories along with proxy tasks, identifying an optimal combination of them, and automatically balancing them to improve the primary task. We show that our model achieves state-of-the-art performance on the Argoverse dataset, especially on diversity and admissibility metrics, achieving up to $20\%$ improvements in challenging scenarios. We further investigate the contribution of proposed modules in ablation studies. + +# 1. Introduction + +Vehicle trajectory prediction is one of the main building blocks of autonomous driving. Prediction demonstrates how the future might unfold based on the road structure and the behavior of road users. To operate safely, self-driving cars must accurately perceive the geometric and semantic information in the driving scene and predict diverse yet scene-compliant trajectories. High-definition maps provide useful cues since the behaviors of agents and the interac + +tions among them are largely influenced by the road topology and governed by the map constraints. For example, a vehicle is unlikely to change to a lane that runs in the opposite direction. In this light, learning the structure of the map efficiently is essential to predict a variety of feasible trajectories. + +Inspired by the structural nature of the road, map vectorization has become prevalent in recent works, in which lanes are converted into vectors [15, 56, 18]. Consequently, graph structures can be leveraged to learn the relationships between vectorized entities [28, 54, 11, 16]. In this way, connected lanes in various formations, e.g. successor, predecessor, right, and left, represent admissible ways to traverse the terrain. For example, two lanes positioned consecutively in space and connected by a sequential link can be driven successively, whereas two lanes connected by a lateral link enable a lane change maneuver. Hence, the HD map lane graph has edges with different semantic meanings, indicating its heterogeneous nature. + +Although existing lane graphs are shown to be effective in learning local structures through the adjacent lanes, they lack the ability to model more complex patterns imposed by long-range heterogeneous connections between nonadjacent yet interacting lanes. These connections are important to capture high-level intentions, such as overtaking, merging, and double turns, and can potentially represent the constraints and rules of the road. To model such connections, some methods propose adopting self-supervised tasks on top of the lane graph [15, 4] to encourage the model to learn the semantics associated with lane connectivities. Since scene structure contains various semantics, having only one proxy task at a time is insufficient to provide diverse traffic patterns. Alternatively, anchor-based models incorporate prior knowledge by identifying candidate trajectories based on sampling or clustering of training data [6, 43]. However, these methods are less robust and generalizable due to their dependency on the distribution of data. + +Motivated by this insight, we introduce a novel self-supervised task for trajectory prediction, termed Heteroge- + +aneous Structure Learning (HSL), to formulate traffic patterns imposed by road constraints. In particular, we formulate the road structure by meTA ROad paTh (TAROT) as a composite relation of heterogeneous edges in the scene graph that can model diverse abstractions from the map without additional data and labels. Therefore, by predicting the presence of TAROT in the driving scene as an HSL task, the model gets a sense of feasible transitions on the map as navigation tips for traversing the road. Furthermore, we propose MEta-road NeTwORk (MENTOR), a novel trajectory prediction framework that provides insight into the structural perspective of the map by simultaneously predicting a set of HSL tasks. In detail, inspired by the meta-learning concept, MENTOR is learning to learn road topology by automatically selecting the HSL tasks that assist the target trajectory prediction. + +The contributions of this paper are as follows: (1) For the first time, to the best of our knowledge, we investigate the idea of learning to learn in trajectory prediction through the proposed MEta-road NeTwORk (MENTOR), which determines an optimal combination of Heterogeneous Structure Learning (HSL) tasks and automatically balances them to assist the primary task of predicting diverse and admissible trajectories. (2) We propose meTA ROad paTh (TAROT) prediction as a novel HSL task capable of modeling high-level semantics within the map structure. Thus, diverse semantic aspects of road configuration can be captured by defining various TAROTs, resulting in multiple HSL tasks that are learned simultaneously. (3) We conduct extensive experimental evaluations to show our model's effectiveness in predicting not only precise but also diverse and admissible trajectories. + +# 2. Related Work + +Trajectory Prediction has been the subject of interest in a large body of literature. Existing methods explore different representations and methods to learn scene context, including rasterized images [6, 38, 16] and point-clouds [49] with CNNs, and vectorized representations with GNNs [15, 32, 18, 54], or transformers [21, 58, 17, 30], which are often associated with sophisticated fusion mechanisms [28]. These models focus on finding more powerful ways of extracting features from HD maps and modeling agents' interactions. They, however, require substantial model capacity, heavy parameterization, extensive augmentations, or a large amount of data to produce accurate results. + +Some methods investigate the ways to improve prediction precision by incorporating prior knowledge as predefined candidate trajectories generated using sampling or clustering techniques [32, 55]. Nevertheless, the main limitation of these methods is that their performance is highly dependent on the quality of trajectory proposals, which becomes a dependency. To resolve this issue, end-to-end + +solutions optimize the endpoints of candidate trajectories [18, 16] resulting in improved accuracy while maintaining a reasonable parameter budget. However, using an online goal candidate optimization strategy is computationally very expensive, therefore it is prohibitive for real-time applications, such as autonomous driving. More recently, ensemble techniques have become more prevalent and demonstrated good prediction performance [43, 50]. However, their major disadvantages are high memory cost for training and computationally expensive inference. + +Besides designing high-precision models, researchers have focused on diversity, admissibility, and map conformity of the predicted trajectories. To generate diverse trajectories, state-of-the-art models use Generative Adversarial Networks (GANs) [25, 37, 57], and Conditional Variational Autoencoders (CVAEs) [38, 42, 53, 26], sophisticated sampling functions, such as diversity sampling [52] and latent semantic sampling [20]. However, most works sacrifice map conformity for prediction diversity. To improve conformity, map data can be incorporated as a part of the loss function [44, 9], or as a post-processing step [48]. To better evaluate the diversity and admissibility of predicted trajectories, new metrics, such as RF and DAO, have been proposed [34]. In this paper, we use these as well as common metrics to further assess our model's performance. + +Self-Supervised Learning (SSL) is a learning method that uses appropriately designed proxy tasks to generate additional supervised signals to train models. In trajectory prediction, SSL has been utilized by defining various proxy tasks laid on top of the agent/map information [15, 4]. For instance, a recent work, SSL-Lane [4], uses four different tasks and shows how they can be incorporated to improve performance. However, this model uses only one proxy task at a time and does not explore combinations of different tasks. Additionally, SSL-Lane employs different losses in its formulation only in a 1:1 ratio without tuning them. These shortcomings motivated our proposed framework for simultaneously learning proxy tasks without letting them compete with the target trajectory prediction task. + +Meta-learning originates from the concept of learning to learn, a topic of continued interest in machine-learning research. Meta-learning has been used for finding optimal hyper-parameters and good initialization [27, 13], metric-learning, and non-parametric methods for few-shot learning [40, 41]. This paper uses meta-learning to learn the road topology across several tasks by transferring the knowledge from self-supervised tasks, defined on the map structure, to the primary trajectory prediction task. In a closely related category of works, sample weighting, a meta-learning mechanism is used for adaptively extracting sample weights to guarantee robust deep learning in the presence of training data bias [23, 39]. In practice, instead of manually setting the form of weight functions, these methods learn an ex + +![](images/3c6682fd7fff9337898f362c727cc188baf6587cdce6ae1ec51fdac8ae4aa2f1.jpg) +Figure 1: Overview of the proposed approach. Given directed HIN $\mathcal{G}$ of the scene and $N$ predefined TAROTs, the HSL engine $\mathcal{H}(\mathrm{TAROTs})$ defines $N$ HSL tasks each predicting the presence of a specific TAROT. Within each TAROT task $p_n$ , positive samples are two arbitrary nodes from $\mathcal{G}$ that can be reached by $p_n$ , and negative samples are those that cannot. For the HSL tasks and the primary task, we find learned representations $\mathcal{Z}$ from GNN model $f$ . To find the loss values, samples are fed through the task-specific transformations $\Phi_t$ followed by task-specific loss functions $\mathcal{L}^n$ . Lastly, by Providing loss values of the primary task's samples and the HSL tasks' samples (as a concatenation of [task id, label(Pos/Neg), loss value]), we train MENTOR to learn weight function $\mathcal{V}$ in a way to find an optimal combination of the HSL tasks in a meta-learning manner. + +plicit weighting function directly from the data. + +Self-supervised learning and meta-learning both contribute to improving model generalization capability. To the best of our knowledge, this is the first study in trajectory prediction to exploit the benefit of scene-based self-supervised tasks through a meta-learning paradigm. + +# 3. Proposed Method + +Traffic transitions are complex and cannot simply be modeled by learning the local relationships. What required is modeling patterns of traveling through the road as a combination of relationships, not only in the adjacent lanes but also between nonadjacent yet interacting lanes. This can, for example, refer to a merge pattern in the road structure that involves both lateral and sequential relations. + +The main idea behind our proposed model is to provide high-order combinations of basic adjacent-adjacent patterns as the full gamut of lane interactions when predicting vehicle trajectories. To this end, we first discuss the procedure for generating a Heterogeneous Information Network (HIN) from scenes, followed by the introduction of the Heterogeneous Structural Learning (HSL) tasks designed to capture relations between lanes. Next, we describe our novel MEtaroad NeTwork (MENTOR) that learns an explicit weighting function to softly select HSL tasks and balance them to improve the performance of the primary task via meta-learning (see Fig. 1). + +# 3.1. Scene Encoding + +Contrary to the common approach that treats the scene as a homogeneous graph [54], we model the scene as a Heterogeneous Information Network (HIN) [24]. + +Definition 1. Heterogeneous Information Network (HIN) a HIN is defined as a graph $\mathcal{G} = (\mathcal{V},\mathcal{E})$ , where $\mathcal{V}$ is the set of nodes and $\mathcal{E}$ is the set of edges, each representing a binary relation between two nodes in $\mathcal{V}$ . $\mathcal{G}$ is associated with two mappings: (1) node type mapping function $\phi :\mathcal{V}\to \mathcal{T}$ and (2) edge type mapping function $\psi :\mathcal{E}\rightarrow \mathcal{R}$ where $\mathcal{T}$ and $\mathcal{R}$ denote sets of node and edge types, respectively. If $|\mathcal{T}| + |\mathcal{R}| > 2$ , network $\mathcal{G}$ is an HIN, otherwise it is homogeneous. + +We encode the scene as a directed HIN with node types $\mathcal{T} = \{\text{lane, agent}\}$ and $\mathcal{R} = \{\text{left, right, successor, predecessor}\}$ as basic relations between adjacent lanes. To initialize node features in the HIN, we use the simplified PointNet [36] with multi-layer perception (MLP) to process polyline features and a 1D convolution with a feature pyramid network [29] to process agents' observations similar to [28]. One advantage of our method is that any type of GNN can be used to process the HIN. Hence, we employ Heterogeneous Graph Transformer (HGT) as a simple yet effective model similar to [19]. + +# 3.2. Heterogeneous Structural Learning + +Traffic transitions follow patterns governed by high-level constraints stemming from long-range structural connections between lanes of the road. For learning the map structure, heterogeneity helps interpret a series of relations, + +which our model learns with meTA ROad paTh (TAROT). + +Definition 2. Meta-Path. A meta-path $\mathcal{P} = v_{1} \xrightarrow{r_{1}} v_{2} \xrightarrow{r_{2}} \ldots \xrightarrow{r_{\ell}} v_{\ell + 1}$ expresses a composite relation $R = r_{1} \circ r_{2} \dots \circ r_{\ell}$ between nodes $v_{1}$ and $v_{\ell + 1}$ , where $\circ$ denotes the composition operator on relations. If two nodes $v_{i}$ and $v_{j}$ are related by the composite relation $R$ , then there exists a path that connects $v_{i}$ to $v_{j}$ in $\mathcal{G}$ , denoted by $\mathcal{P}_{v_{i} \rightsquigarrow v_{j}}$ . Moreover, the nodes and edges types in $\mathcal{P}_{x_{i} \rightsquigarrow x_{j}}$ match with types in $\mathcal{T}$ and $\mathcal{R}$ , respectively. + +The features obtained from the meta-path analysis in HINs are notably useful in improving graph-based models since they encode indirect semantic relations between nodes that are not directly connected. These features also aid in establishing new relations between vertices. As such, metapath analysis has been frequently used in graph domains to enhance graph representation learning power and improve downstream tasks, such as node classification and link prediction [51, 46, 22, 8]. This means meta-paths can help find new patterns and relations in HINs. + +By focusing on the long-range relations that impose transitions on the road, we define TAROT $p$ though the HIN as a path instance of $p_{v_i\sim v_j}\vdash \mathcal{P}$ where node types are the same. Thus, the TAROT can formulate a combination of basic road relations corresponding to transition patterns imposed by map constraints. Predicting the presence of a TAROT between two nodes $v_{i}$ and $v_{j}$ is similar to link prediction. Here, the link means heterogeneous composite relations between nodes. Contrary to link prediction problems, the proposed TAROT prediction can be treated as a self-supervised task. In detail, we follow a simple rule to provide the additional supervised signals for proxy tasks: If node $v$ is reachable from node $u$ by TAROT $p$ , then $y_{u,v}^{p} = 1$ , otherwise $y_{u,v}^{p} = 0$ . This means the HSL task, associated with the TAROT will be formed as a simple link prediction task without the need for any additional data or manual labeling. Hence, by obtaining the hidden representations of two arbitrary nodes learned by a GNN and using a simple operator $\hat{y}_{u,v}^{p} = \sigma \left(\Phi_{t}(z_{u})^{\top}\Phi_{t}(z_{v})\right)$ we can predict whether a TAROT between two nodes is present or absent. Here, $\Phi_t$ is a type-specific transformation $t\in \mathcal{T}$ and $z_{u}$ and $z_{v}$ are the node embeddings of nodes $u$ and $v$ . + +Using the proposed TAROT as a type of meta-path we can model a common pattern of driving that adhere to the map constraints. Hence, we define several TAROTs to formulate diverse traffic patterns within the driving scene, resulting in several HSL tasks that can be used to predict diverse and admissible trajectories. We provided a complimentary figure in the supplementary material to further show TAROT's motivation. + +# 3.3. Meta Road Network + +The proposed HSL task is designed to identify diverse patterns within the road structure, for which we explore the + +idea of defining various TAROTs resulting in several self-supervised HSL tasks to be learned simultaneously with the primary trajectory prediction task. However, as with any multi-task learning method, the HSL tasks should be carefully chosen and properly weighted so that learning the map structure does not compete with the primary task, especially when the capacity of graph neural networks (GNNs) is limited. To this end, we propose MEta-road NeTwORk (MENTOR), a learning framework for trajectory prediction that offers the possibility of learning to learn the road configuration while learning the main task. Below, we discuss a naive multi-task combination of self-supervision tasks to explain the motivation behind the design of MENTOR, followed by describing the meta-learning objective using MENTOR, and a detailed look at the learning procedure. + +# 3.3.1 Naive Multi-task Combination of HSL Tasks + +Self-supervised learning has already been explored in trajectory prediction for autonomous driving and has proven beneficial [15, 4]. Adopting a combination of Self-Supervised Learning (SSL) tasks, namely proxy tasks, to improve the primary task has not yet been addressed, even though it has been shown to be effective in visual learning [12]. Here, we formulate a naive multi-task combination of HSL tasks, as SSL tasks, with a shared backbone network with parameters $\mathbf{w}$ , between the primary and all proxy tasks. Each task has a specific loss function $\mathcal{L}^n$ incorporated by a task-specific parameter $\lambda_{n}$ . So the optimal parameter $\mathbf{w}^{*}$ can be extracted by the following objective function: + +$$ +\min _ {\mathbf {w}} \quad \mathbb {E} \left[ \lambda_ {0} \mathcal {L} ^ {0} (.; \mathbf {w}) + \sum_ {n = 1} ^ {N} \lambda_ {n} \mathcal {L} ^ {n} (.; \mathbf {w}) \right] \tag {1} +$$ + +where index zero stands for the primary task $n = 0$ , and index $n|_1^N$ denotes $n^{th}$ task of $N$ proxy tasks. + +# 3.3.2 Meta-learning Objective + +Learning road topology should enhance rather than compete with trajectory prediction, hence determining an effective combination of $\lambda$ parameters is crucial. To achieve this, we adopt MENTOR to parameterize model $\mathbf{w}(\Theta)$ to determine an optimal combination of HSL tasks and automatically balance them for improved prediction as shown below, + +$$ +\begin{array}{l} \min _ {\mathbf {w}, \boldsymbol {\Theta}} \quad \mathbb {E} \left[ \mathcal {L} ^ {0} \left(\mathbf {w} ^ {*} (\boldsymbol {\Theta})\right) \right] \\ \text {s . t .} \mathbf {w} ^ {*} (\boldsymbol {\Theta}) = \underset {\mathbf {w}} {\operatorname {a r g m i n}} \quad \mathbb {E} \left[ \mathcal {L} ^ {n | _ {0} ^ {N}} (\mathbf {w}; \boldsymbol {\Theta}) \right]. \end{array} \tag {2} +$$ + +Specifically, to parametrize the model parameters $\mathbf{w}$ , we can impose a learnable weighting function $\mathcal{V}(\cdot ,\Theta)$ to the objective function in (2) as MENTOR similar to [39]. Thus, the + +Algorithm 1: MEta-road NeTwORk (MENTOR) +Input : primary data $D^{\mathrm{pr}}$ , HSL proxy tasks data $D^{\mathrm{hsl}}$ , batch size $n$ $m$ , max iteration $T$ folds for cross-validation $K$ , model parameters w, MENTOR parameters $\Theta$ Output: model parameter $\hat{\mathbf{w}}^T$ +1 Initialize w, $\Theta$ +2 for $t = 0$ to $T - 1$ do +3 $\left\{x^{(\mathrm{pr})},y^{(\mathrm{pr})}\right\} \gets$ SampleMiniBatch $(D^{pr},n)$ . +4 $\left\{x^{(\mathrm{hsl})},y^{(\mathrm{hsl})}\right\} \gets$ SampleMiniBatch $(D^{\mathrm{hsl}},m)$ //cross validation +5 for $k = 1$ to $K$ do +6 $\left\{x^{(\mathrm{meta})},y^{(\mathrm{meta})}\right\} ,\left\{x^{(\mathrm{train})},y^{(\mathrm{train})}\right\} \gets$ CVSplit $(D^{pr},k)$ . Formulate model parameter $\mathbf{w}^t$ by Eq 6 +8 Keep $\Theta_{k}^{t + 1}$ on fold $= k$ by Eq.7 +9 end +10 Update $\Theta^{t + 1}$ with $\frac{1}{K}\sum_{k}^{K}\Theta_{k}^{t + 1}$ +11 Update $\mathbf{w}^{t + 1}$ by Eq 8 +12 end + +objective function can be written as follows: + +$$ +\mathbf {w} ^ {*} (\boldsymbol {\Theta}) = \operatorname * {a r g m i n} _ {\mathbf {w}} +$$ + +$$ +\sum_ {n = 0} ^ {N} \sum_ {i = 1} ^ {M _ {n}} \frac {1}{M _ {n}} \mathcal {V} \left(\Psi_ {i} ^ {n}; \Theta\right) \mathcal {L} ^ {n} \left(y _ {i} ^ {n}, f ^ {n} \left(x _ {i} ^ {n}; \mathbf {w}\right)\right) \tag {3} +$$ + +where each task has $M_{n}$ samples and $f^n$ is the model for task $n$ . For $i^{th}$ sample of task $n$ , $y_i^n$ is the label, and $\Psi_i^n$ is an embedding vector expressing as the concatenation of one-hot vector of task types, the label (positive/negative), and the loss value of the sample. Therefore, following Eq. (3), the model learns how to assist the primary task by optimizing MENTOR's parameters $\Theta$ . These parameters can be optimized using the meta-learning idea [47, 1, 10, 14]. Specifically, using a small amount of meta-data $D^{\mathrm{meta}}$ , representing the meta-knowledge of ground-truth $D^{\mathrm{gt}}$ , $D^{\mathrm{meta}} \cup D^{\mathrm{train}} = D^{\mathrm{gt}}$ , the optimal parameter $\Theta^*$ can be obtained by minimizing the following loss: + +$$ +\boldsymbol {\Theta} ^ {*} = \underset {\boldsymbol {\Theta}} {\operatorname {a r g m i n}} \mathcal {L} ^ {\text {m e t a}} (\mathbf {w} ^ {*} (\boldsymbol {\Theta})) \triangleq \frac {1}{m} \sum_ {i = 1} ^ {m} \mathcal {L} _ {i} ^ {\text {m e t a}} (\mathbf {w} ^ {*} (\boldsymbol {\Theta})) \tag {4} +$$ + +where $m$ and $r$ , $m \ll r$ , are the number of meta-samples and training samples, respectively, and meta-loss is, + +$$ +\mathcal {L} _ {i} ^ {\mathrm {m e t a}} (\mathbf {w}) = \mathcal {L} \left(y _ {i} ^ {\mathrm {m e t a}}, f \left(x _ {i} ^ {\mathrm {m e t a}}, \mathbf {w}\right)\right) \tag {5} +$$ + +where $(x,y)\sim D^{\mathrm{meta}}$ + +# 3.3.3 Meta-road Network Learning Procedure + +To overcome the complexity of the bi-level optimization, following [13, 39], we use an online strategy to approximate + +$\mathbf{w}^*$ and $\Theta^{*}$ with the updated parameters $\hat{\mathbf{w}}$ and $\hat{\Theta}$ , respectively through a single optimization loop. In each iteration of training, given training data $D^{\mathrm{train}}$ , HSL proxy tasks data $D^{\mathrm{hsl}}$ , and meta-data $D^{\mathrm{meta}}$ , we follow three steps: + +Formulating Model Parameter: We formulate the updating equation of model parameter $\mathbf{w}$ by moving the current $\mathbf{w}^t$ along the descent direction of the loss in Eq. (3), + +$$ +\underset {D ^ {\text {t r a i n}} \cup D ^ {\mathrm {h s l}}} {\hat {\mathbf {w}} ^ {(t)}} (\boldsymbol {\Theta}) = \mathbf {w} ^ {(t)} - \alpha \frac {1}{N} \sum_ {n = 0} ^ {N} \mathcal {V} (\cdot ; \boldsymbol {\Theta}) \nabla_ {\mathbf {w}} \mathcal {L} ^ {n} (\mathbf {w}) \Bigg | _ {\mathbf {w} ^ {(t)}} \tag {6} +$$ + +where $\alpha$ is the learning rate for $\mathbf{w}$ and $\mathcal{L}^n$ denotes the loss function for the task number $n$ . To avoid cluttered notation, the summation of task samples is omitted. + +Updating Parameters of MENTOR: After updating model parameter $\hat{\mathbf{w}}^{(t)}(\Theta)$ , parameter $\Theta$ of MENTOR can be updated guided by Eq. (4), i.e., moving the current parameter $\Theta^{(t)}$ along the objective gradient of Eq. (4) calculated on the meta-data, + +$$ +\Theta_ {D ^ {\mathrm {m e t a}}} ^ {(t + 1)} = \Theta^ {(t)} - \beta \mathcal {V} (\cdot ; \Theta) \mathcal {L} ^ {0} \left(\hat {\mathbf {w}} ^ {(t)} (\Theta)\right) \Big | _ {\Theta^ {(t)}} \tag {7} +$$ + +where $\beta$ is the learning rate for $\Theta$ . This update allows the soft selection of useful HSL proxy tasks and balances them with the main motion prediction task to improve the performance of the main task. Without balancing tasks with the weighting function $\mathcal{V}(\cdot;\Theta)$ , proxy tasks can dominate training and degrade the performance of the primary task. + +Updating Model Parameters: Model parameters $\mathbf{w}$ for tasks can be updated with optimized $\Theta^{t + 1}$ in Eq. (7) as, + +$$ +\begin{array}{l} \hat {\mathbf {w}} _ {D ^ {\mathrm {t r a i n}} \cup D ^ {\mathrm {h s l}}} ^ {(t + 1)} (\boldsymbol {\Theta}) = \mathbf {w} ^ {(t)} \\ - \alpha \frac {1}{N} \sum_ {n = 1} ^ {N} \mathcal {V} \left(\because \Theta^ {(t + 1)}\right) \nabla_ {\mathbf {w}} \mathcal {L} ^ {n} (\mathbf {w}) \Bigg | _ {\mathbf {w} ^ {(t)}}. \tag {8} \\ \end{array} +$$ + +Lastly, to circumvent the problem of meta-overfitting, meaning that parameters $\Theta$ overfit to the small meta-dataset, we follow the meta-validation solution as in [2, 59]. In particular, to make $\Theta$ generalizable across meta-training sets, we optimize it using $K$ different meta-datasets with k-fold cross-validation. The gradients of $\Theta$ from different meta-datasets are then averaged to update $\Theta^{(t)}$ . The MENTOR learning procedure is summarized in Algorithm 1. + +# 4. Experiments + +Our goal is to investigate ways for improving map representational learning power to predict diverse and admissible trajectories. For this purpose, we seek to answer the following questions: Q1: Are predicted trajectories diverse and admissible? Q2: Is MEta-road NeTwORk (MENTOR) effective regardless of the type of HSL task? Q3: How much + +Table 1: Comparison to SOTA models on challenging scenarios. Arrows show lower (↓) or higher (↑) values are better. + +
MethodTurnsStationary
minADE(↓)minFDE(↓)DAO(↑)RF(↑)MR(↓)minADE(↓)minFDE(↓)DAO(↑)RF(↑)MR(↓)
LaneGCN [28]1.082.1867.632.8935.761.232.5261.692.6936.80
MMTransformer[21]1.052.0769.763.3532.001.132.2864.853.2135.69
FTGN [3]1.062.0470.723.2534.061.162.2263.953.0632.49
HiVT [58]1.062.2366.842.7935.451.252.7458.432.5139.61
SSL-Lane [4]1.072.1169.653.2133.341.162.3462.453.2234.54
MENTOR (Ours)1.032.0079.213.7631.301.132.1969.233.8732.76
+ +does our proposed HSL task contribute to diversity and admissibility? + +# 4.1. Experimental Setup + +Dataset: We evaluated our method on the Argoverse benchmark dataset [7]. Here the task is to predict 3 seconds of future trajectories given 2 seconds of past observations. This dataset consists of more than $300K$ real-world driving sequences, which are split into the train (205K), validation (39K), and test (78K) sets without geographical overlap along with corresponding HD maps. + +Metrics: We selected a set of metrics to measure the precision, diversity, and admissibility of predictions. For precision, we use minADE (Average Displacement Error), minFDE (Final Displacement Error), and MR (Miss Rate). For diversity, we use the Ratio of avgFDE to minFDE (RF) [34], which measures the spread of predictions in Euclidean distance. We use Drivable Area Occupancy (DAO) [34] to determine the proportion of pixels that predicted trajectories occupy in the drivable area. RF and DAO work in a complementary way to measure diversity along with admissibility. + +Implementation Details: To normalize the data, we translate and rotate the coordinate system of each sequence so that the origin is at the agent's current location at $t = 0$ . We use the orientation from the agent's location at $t = -1$ to its location at $t = 0$ as the positive x axis. We use all actors and lanes whose distance from the agent is smaller than 100 meters as the input. As a model architecture, we use three layers of HGT with the hidden dimension of size 128. For the HSL tasks, we define five TAROTs with variable lengths of 4 to 7. The intuition behind the number of TAROTs is to model turning right/left, lane changing (right-to-left and left-to-right), and going straight. We formulate Mentor as an MLP with two hidden layers with 100 nodes each, with ReLU activations for hidden nodes and sigmoid output to ensure it is in range [0, 1]. For the loss functions, we follow the widely used regression-MLP plus classification-MLP combination [28, 24, 33] for trajectory prediction and cross-entropy for the HSL task. For the training, we use the AdamW [31] optimizer with an initial learning rate of 5e-4, weight decay 1e-4, and batch size of 64. + +# 4.2. Analysis on Challenging Scenarios + +Existing prediction datasets are highly imbalanced in terms of scenario diversity, with the majority of traffic ac + +tors simply driving straight [35]. Calculating metrics by aggregating over scenarios is therefore influenced by the most common maneuvers, where prediction models often do well. In practice, scenarios, such as turning at intersections could be of greater interest to practitioners and accurately predicting these scenarios are even more crucial for the safe operation of autonomous vehicles. Hence, to verify the effectiveness of our model, we extracted challenging scenarios including left/right/blind turns and stationary scenarios where the vehicle's observed trajectory is very short, thus the model has minimal motion information from the vehicle. By blind turns, we refer to the cases where the observed trajectory is straight and the turn occurs during the unobserved portion of the trajectory. + +We compare our method against several vectorized-based SOTA models with public implementations, including two graph-based models, LaneGCN [28] and FTGN [3], two transformer-based models, MMTransformer [21] and HiVT [58], and SSL-Lane [4], which extends the lane graph by adding four different self-supervised tasks based on agent/map information. As shown in Table 1, our method significantly improves upon the state-of-the-art models on most metrics in both scenarios. Particularly, our method, MENTOR achieves notable improvements in diversity and admissibility metrics, namely DAO and RF by up to $13\%$ and $20\%$ respectively in the challenging scenarios. + +Qualitative analysis. Fig. 2 depicts a number of qualitative examples to better highlight our method's performance. The first two rows represent turn-right scenarios, and the third and fourth rows show left-turn and stationary scenarios. As can be seen in the last column, our method consistently generates diverse predictions that are also admissible by correctly aligning with the road topology. The behavior of competing methods, however, varies often resulting in the generation of infeasible trajectories. In the supplementary materials, we discuss the algorithm used to find challenging scenarios and present additional per-scenario metrics to further elaborate on the correlation of metrics. + +# 4.3. Ablation Studies + +# 4.3.1 MENTOR Acting as a Mentor + +To assess the ability of MENTOR, we analyze the weighting function $\mathcal{V}(\Psi_i^n;\Theta)$ for $i^{th}$ sample of task $n$ . Particularly, we present the learned weight function at the last epoch of + +![](images/2e59793ae8e717bb09121fe124ec54d8443715c5a2d9752e288c9567473e35f7.jpg) + +![](images/00468cf7409b7b596e7b0dbadcd2cc73ce182e1c858ca235575814d185efbf12.jpg) +Figure 2: Qualitative examples on Argoverse showing diversity and admissibility of the predicted trajectories by MENTOR. Red, green, and blue trajectories represent observation, ground truth, and 6 predicted trajectories, respectively. +Figure 3: The weighting function in MENTOR. The green line is the primary task, and solid and dashed color lines represent positive and negative HSL samples, respectively. Each color corresponds to a specific HSL task. + +the training. As shown in Fig. 3, MENTOR has two main benefits. Firstly, even when the model's loss is low, as the model is learning less challenging scenarios, trajectory prediction task (green line) samples have a higher weight than HSL tasks. Hence, MENTOR is more focused on learning the primary trajectory prediction task as there is no competition between HSL tasks and the primary task. Secondly, in all tasks, hard samples with higher losses are given more weight than easy samples with lower losses, indicating that MENTOR is mining hard samples. Here, MENTOR acts as a mentor by learning TAROTs and transferring that knowledge to the primary task. + +Effectiveness of MENTOR: To analyze the effectiveness of MENTOR, we borrow a lane-graph-based baseline + +and four self-supervised learning (SSL) tasks introduced in [4] and use them in MENTOR to improve the baseline. The SSL tasks are as follows: A) Lane masking, which recovers feature information from the perturbed lane graphs; B) Predicting distance to the intersection in terms of the shortest path length from all lane nodes to the intersection nodes; C) Maneuver classification, which predicts the form of a maneuver that the agent of interest intends to execute; And D) success/failure classification, which trains an agent specialized in achieving end-points. + +We report the results in Tab. 2 where the SSL tasks are termed A-D and $\text{MENTOR}_{\sum \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}}$ denotes the proposed model. According to the table, among the proposed tasks, maneuver classification, task C, has the best DAO (admissibility), indicating that predicting the form of maneuver can reveal more information about the road structure. Additionally, predicting the distance to the intersection, task B, gives a better estimate of the agent to the intersection, and the possibility of branching roads, hence improving RF (diversity) metric. In summary, individual tasks are shown to be effective by providing auxiliary information that helps improve different aspects of prediction. Once combined together, SSL tasks through the MENTOR framework improve distance-based metrics, minADE and minFDE as well as admissibility and diversity metrics, DAO and RF. These results validate the effectiveness of MENTOR as a learning framework to enhance prediction models + +Table 2: Results of the ablation studies. $\mathrm{SSL}_{-}x$ indicates self-supervised tasks as in [4] and $\mathrm{MENTOR}_{\sum \mathrm{A,B,C,D}}$ indicates the original model augmented with MENTOR. + +
ModelminADE(↓)minFDE(↓)DAO(↑)RF(↑)
Baseline0.731.1265.873.00
SSLA0.701.0268.212.98
SSLB0.711.0468.653.87
SSLC0.721.0569.973.14
SSLD0.701.0168.023.01
MENTORΣA,B,C,D0.690.9877.914.18
+ +Table 3: Results of the ablation studies. $\mathrm{TAROT}^x$ indicates the length of the TAROT through the HSL task and MENTOR represents our full model, which includes several HSL tasks. + +
TurnsValidation
ModelminFDE(↓)DAO(↑)RF(↑)minFDE(↓)DAO(↑)RF(↑)
Baseline2.37268.452.981.13274.024.21
TAROT42.26771.013.191.12875.524.43
TAROT52.20873.673.231.10777.114.48
TAROT62.15376.933.711.11278.894.50
TAROT72.08276.173.561.12178.004.51
TAROT82.10973.653.411.12077.214.38
MENTOR2.00379.213.760.97485.314.65
+ +by providing additional information as SSL tasks. + +Impact of TAROT Prediction as an HSL Task: for the purpose of analyzing the impact of the TAROT prediction, we conduct several experiments on the entire validation set and challenging turn scenarios by designing different models named $\mathrm{TAROT}^x$ where $x$ refers to the length of TAROT through the HSL task. For example, $\mathrm{TAROT}^4$ could be any of these patterns [S-S-S-R, S-L-S-S, S-L-P-P...] (S: Successor, L: Left, R: Right, P: Predecessor as the basic relation of adjacent lanes). We average the metrics over all of the members in the list. A baseline model does not have any HSL tasks, and therefore does not have MENTOR. The last model is our final model which is loaded by multiple HSL tasks through MENTOR. As shown in Tab. 3, augmenting the model with the HSL task improves the baseline model performance. Moreover, from the experiments, we found that by predicting a longer TAROT, corresponding to a longer pattern in the road configuration with a higher abstraction, we can improve the model in turns scenarios. However, the length of TAROTs should be set carefully, as if set too long, the model would have a tendency to predict a turn maneuver even when several alternatives, such as driving straight, are available. To take advantage of this phenomenon, we define multiple TAROTs with variable lengths representing both short and long patterns. Thus, once used through MENTOR we enable the model to identify the best combination of HSL tasks, as TAROT prediction, by weighting them properly. In this way, our full model outperforms other models significantly. Based on the obtained results, we can conclude that 1) TAROTs are capable of modeling patterns in the map structure, thus formulating multiple TAROTs and subsequently multiple HST + +Table 4: Comparisons with SOTA on Argoverse test set. + +
MethodminADE(↓)minFDE(↓)MR(↓)
TNT [56]0.941.5413.30
DenseTNT [18]0.881.2812.58
TPCN [49]0.871.3615.80
mmTransformer [30]0.871.3415.40
LaneRCNN [54]0.901.4512.32
LTP [45]0.831.2914.72
AutoBot [17]0.891.4116.00
SceneTransformer [33]0.801.2312.55
HiVT [58]0.771.1612.67
MENTOR (Ours)0.791.2113.01
+ +tasks, can capture diverse lane connection patterns in the map topology. 2) MENTOR is good at adopting HSL tasks to transfer their knowledge to the primary task, and consequently resulting in significant improvement in terms of diverse (RF) and admissible (DAO) trajectory prediction. + +# 4.4. Comparison to SOTA + +We compare our method to SOTA models on the Argov-verse benchmark. Even though the focus of our method was on improving diversity and admissibility of generated trajectories in challenging scenarios, as shown in Tab. 4, our model's performance is comparable to best models, on the distance-based metrics on the benchmark. Particularly, compared to HiVT [58], our model achieves the second rank on minADE and minFDE, while in challenging scenarios it outperforms HiVT on the diversity and admissibility metrics as well as the distance-based metrics with a large margin, as is evident in Tab. 1. We further verify the effectiveness of our approach on a smaller dataset, nuScenes [5], and report the results in the supplementary material. + +# 5. Conclusion + +In this paper, we presented a novel trajectory prediction model based on the concept of meta-learning. We formulated various lane connection relations on the map topology as meTA ROad paTh (TAROT), and used a model, MEtaroad NeTwORk (MENTOR), to supply TAROT tips in the form of Heterogeneous Structural Learning (HSL) tasks to improve trajectory prediction. Besides, focusing on enhancing the map representational learning power, MENTOR can mentor any proxy task to further improve the primary motion forecasting task. Via extensive experimental evaluations, we showed that HSL tasks are capable of modeling high-level semantics stemming from long-range heterogeneous connections between lanes. Additionally, we showed that our proposed MENTOR model acts as a mentor to gain the maximum benefit from the existing structural information of the map. The results also highlighted that, besides significantly improving diversity and admissibility of predictions, our method can obtain improved or comparable results on common distance-based metrics compared to the past arts with a larger number of parameters. + +# References + +[1] Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W Hoffman, David Pfau, Tom Schaul, Brendan Shillingford, and Nando De Freitas. Learning to learn by gradient descent by gradient descent. In NeurIPS, 2016. 5 +[2] Antreas Antoniou, Harrison Edwards, and Amos Storkey. How to train your MAML. In ICLR, 2019. 5 +[3] Görkay Aydemir, Adil Kaan Akan, and Fatma Güney. Trajectory forecasting on temporal graphs. arXiv:2207.00255, 2022.6 +[4] Prarthana Bhattacharyya, Chengjie Huang, and Krzysztof Czarnecki. 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Graph-based scene encoders have been proven effective for preserving local structures of maps by defining lane-level connections. However, such encoders do not capture more complex patterns emerging from long-range heterogeneous connections between nonadjacent interacting lanes. To this end, we shed new light on learning common driving patterns by introducing meTA ROad paTh (TAROT) to formulate combinations of various relations between lanes on the road topology. Intuitively, this can be viewed as finding feasible routes. Furthermore, we propose MEta-road NeTwORk (MENTOR) that helps trajectory prediction by providing it with TAROT as navigation tips. More specifically, 1) we define TAROT prediction as a novel self-supervised proxy task to identify the complex heterogeneous structure of the map. 2) For typical driving actions, we establish several TAROTs that result in multiple Heterogeneous Structure Learning (HSL) tasks. These tasks are used in MENTOR, which performs meta-learning by simultaneously predicting trajectories along with proxy tasks, identifying an optimal combination of them, and automatically balancing them to improve the primary task. We show that our model achieves state-of-the-art performance on the Argoverse dataset, especially on diversity and admissibility metrics, achieving up to " + }, + { + "bbox": [ + 46, + 270, + 289, + 594 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 270, + 289, + 594 + ], + "type": "text", + "content": " improvements in challenging scenarios. We further investigate the contribution of proposed modules in ablation studies." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "Vehicle trajectory prediction is one of the main building blocks of autonomous driving. Prediction demonstrates how the future might unfold based on the road structure and the behavior of road users. To operate safely, self-driving cars must accurately perceive the geometric and semantic information in the driving scene and predict diverse yet scene-compliant trajectories. High-definition maps provide useful cues since the behaviors of agents and the interac" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 246, + 547, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 547, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 547, + 317 + ], + "type": "text", + "content": "tions among them are largely influenced by the road topology and governed by the map constraints. For example, a vehicle is unlikely to change to a lane that runs in the opposite direction. In this light, learning the structure of the map efficiently is essential to predict a variety of feasible trajectories." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 318, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 547, + 474 + ], + "type": "text", + "content": "Inspired by the structural nature of the road, map vectorization has become prevalent in recent works, in which lanes are converted into vectors [15, 56, 18]. Consequently, graph structures can be leveraged to learn the relationships between vectorized entities [28, 54, 11, 16]. In this way, connected lanes in various formations, e.g. successor, predecessor, right, and left, represent admissible ways to traverse the terrain. For example, two lanes positioned consecutively in space and connected by a sequential link can be driven successively, whereas two lanes connected by a lateral link enable a lane change maneuver. Hence, the HD map lane graph has edges with different semantic meanings, indicating its heterogeneous nature." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 548, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 548, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 548, + 689 + ], + "type": "text", + "content": "Although existing lane graphs are shown to be effective in learning local structures through the adjacent lanes, they lack the ability to model more complex patterns imposed by long-range heterogeneous connections between nonadjacent yet interacting lanes. These connections are important to capture high-level intentions, such as overtaking, merging, and double turns, and can potentially represent the constraints and rules of the road. To model such connections, some methods propose adopting self-supervised tasks on top of the lane graph [15, 4] to encourage the model to learn the semantics associated with lane connectivities. Since scene structure contains various semantics, having only one proxy task at a time is insufficient to provide diverse traffic patterns. Alternatively, anchor-based models incorporate prior knowledge by identifying candidate trajectories based on sampling or clustering of training data [6, 43]. However, these methods are less robust and generalizable due to their dependency on the distribution of data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "content": "Motivated by this insight, we introduce a novel self-supervised task for trajectory prediction, termed Heteroge-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8384" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 262 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 262 + ], + "type": "text", + "content": "aneous Structure Learning (HSL), to formulate traffic patterns imposed by road constraints. In particular, we formulate the road structure by meTA ROad paTh (TAROT) as a composite relation of heterogeneous edges in the scene graph that can model diverse abstractions from the map without additional data and labels. Therefore, by predicting the presence of TAROT in the driving scene as an HSL task, the model gets a sense of feasible transitions on the map as navigation tips for traversing the road. Furthermore, we propose MEta-road NeTwORk (MENTOR), a novel trajectory prediction framework that provides insight into the structural perspective of the map by simultaneously predicting a set of HSL tasks. In detail, inspired by the meta-learning concept, MENTOR is learning to learn road topology by automatically selecting the HSL tasks that assist the target trajectory prediction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 264, + 286, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 264, + 286, + 454 + ], + "spans": [ + { + "bbox": [ + 49, + 264, + 286, + 454 + ], + "type": "text", + "content": "The contributions of this paper are as follows: (1) For the first time, to the best of our knowledge, we investigate the idea of learning to learn in trajectory prediction through the proposed MEta-road NeTwORk (MENTOR), which determines an optimal combination of Heterogeneous Structure Learning (HSL) tasks and automatically balances them to assist the primary task of predicting diverse and admissible trajectories. (2) We propose meTA ROad paTh (TAROT) prediction as a novel HSL task capable of modeling high-level semantics within the map structure. Thus, diverse semantic aspects of road configuration can be captured by defining various TAROTs, resulting in multiple HSL tasks that are learned simultaneously. (3) We conduct extensive experimental evaluations to show our model's effectiveness in predicting not only precise but also diverse and admissible trajectories." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 466, + 132, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 466, + 132, + 478 + ], + "spans": [ + { + "bbox": [ + 49, + 466, + 132, + 478 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 486, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 486, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 49, + 486, + 286, + 628 + ], + "type": "text", + "content": "Trajectory Prediction has been the subject of interest in a large body of literature. Existing methods explore different representations and methods to learn scene context, including rasterized images [6, 38, 16] and point-clouds [49] with CNNs, and vectorized representations with GNNs [15, 32, 18, 54], or transformers [21, 58, 17, 30], which are often associated with sophisticated fusion mechanisms [28]. These models focus on finding more powerful ways of extracting features from HD maps and modeling agents' interactions. They, however, require substantial model capacity, heavy parameterization, extensive augmentations, or a large amount of data to produce accurate results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 630, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 630, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 630, + 286, + 712 + ], + "type": "text", + "content": "Some methods investigate the ways to improve prediction precision by incorporating prior knowledge as predefined candidate trajectories generated using sampling or clustering techniques [32, 55]. Nevertheless, the main limitation of these methods is that their performance is highly dependent on the quality of trajectory proposals, which becomes a dependency. To resolve this issue, end-to-end" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 72, + 544, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 191 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 191 + ], + "type": "text", + "content": "solutions optimize the endpoints of candidate trajectories [18, 16] resulting in improved accuracy while maintaining a reasonable parameter budget. However, using an online goal candidate optimization strategy is computationally very expensive, therefore it is prohibitive for real-time applications, such as autonomous driving. More recently, ensemble techniques have become more prevalent and demonstrated good prediction performance [43, 50]. However, their major disadvantages are high memory cost for training and computationally expensive inference." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 194, + 544, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 194, + 544, + 373 + ], + "spans": [ + { + "bbox": [ + 308, + 194, + 544, + 373 + ], + "type": "text", + "content": "Besides designing high-precision models, researchers have focused on diversity, admissibility, and map conformity of the predicted trajectories. To generate diverse trajectories, state-of-the-art models use Generative Adversarial Networks (GANs) [25, 37, 57], and Conditional Variational Autoencoders (CVAEs) [38, 42, 53, 26], sophisticated sampling functions, such as diversity sampling [52] and latent semantic sampling [20]. However, most works sacrifice map conformity for prediction diversity. To improve conformity, map data can be incorporated as a part of the loss function [44, 9], or as a post-processing step [48]. To better evaluate the diversity and admissibility of predicted trajectories, new metrics, such as RF and DAO, have been proposed [34]. In this paper, we use these as well as common metrics to further assess our model's performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 376, + 544, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 376, + 544, + 543 + ], + "spans": [ + { + "bbox": [ + 308, + 376, + 544, + 543 + ], + "type": "text", + "content": "Self-Supervised Learning (SSL) is a learning method that uses appropriately designed proxy tasks to generate additional supervised signals to train models. In trajectory prediction, SSL has been utilized by defining various proxy tasks laid on top of the agent/map information [15, 4]. For instance, a recent work, SSL-Lane [4], uses four different tasks and shows how they can be incorporated to improve performance. However, this model uses only one proxy task at a time and does not explore combinations of different tasks. Additionally, SSL-Lane employs different losses in its formulation only in a 1:1 ratio without tuning them. These shortcomings motivated our proposed framework for simultaneously learning proxy tasks without letting them compete with the target trajectory prediction task." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 545, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 545, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 545, + 544, + 712 + ], + "type": "text", + "content": "Meta-learning originates from the concept of learning to learn, a topic of continued interest in machine-learning research. Meta-learning has been used for finding optimal hyper-parameters and good initialization [27, 13], metric-learning, and non-parametric methods for few-shot learning [40, 41]. This paper uses meta-learning to learn the road topology across several tasks by transferring the knowledge from self-supervised tasks, defined on the map structure, to the primary trajectory prediction task. In a closely related category of works, sample weighting, a meta-learning mechanism is used for adaptively extracting sample weights to guarantee robust deep learning in the presence of training data bias [23, 39]. In practice, instead of manually setting the form of weight functions, these methods learn an ex" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "8385" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 71, + 509, + 230 + ], + "blocks": [ + { + "bbox": [ + 86, + 71, + 509, + 230 + ], + "lines": [ + { + "bbox": [ + 86, + 71, + 509, + 230 + ], + "spans": [ + { + "bbox": [ + 86, + 71, + 509, + 230 + ], + "type": "image", + "image_path": "3c6682fd7fff9337898f362c727cc188baf6587cdce6ae1ec51fdac8ae4aa2f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": "Figure 1: Overview of the proposed approach. Given directed HIN " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": " of the scene and " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": " predefined TAROTs, the HSL engine " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\mathrm{TAROTs})" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": " defines " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": " HSL tasks each predicting the presence of a specific TAROT. Within each TAROT task " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "p_n" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": ", positive samples are two arbitrary nodes from " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": " that can be reached by " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "p_n" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": ", and negative samples are those that cannot. For the HSL tasks and the primary task, we find learned representations " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": " from GNN model " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": ". To find the loss values, samples are fed through the task-specific transformations " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "\\Phi_t" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": " followed by task-specific loss functions " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^n" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": ". Lastly, by Providing loss values of the primary task's samples and the HSL tasks' samples (as a concatenation of [task id, label(Pos/Neg), loss value]), we train MENTOR to learn weight function " + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 239, + 547, + 336 + ], + "type": "text", + "content": " in a way to find an optimal combination of the HSL tasks in a meta-learning manner." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 346, + 241, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 241, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 241, + 358 + ], + "type": "text", + "content": "plicit weighting function directly from the data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 288, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 288, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 288, + 425 + ], + "type": "text", + "content": "Self-supervised learning and meta-learning both contribute to improving model generalization capability. To the best of our knowledge, this is the first study in trajectory prediction to exploit the benefit of scene-based self-supervised tasks through a meta-learning paradigm." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 453, + 153, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 153, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 153, + 467 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 479, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 564 + ], + "type": "text", + "content": "Traffic transitions are complex and cannot simply be modeled by learning the local relationships. What required is modeling patterns of traveling through the road as a combination of relationships, not only in the adjacent lanes but also between nonadjacent yet interacting lanes. This can, for example, refer to a merge pattern in the road structure that involves both lateral and sequential relations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 571, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 288, + 715 + ], + "type": "text", + "content": "The main idea behind our proposed model is to provide high-order combinations of basic adjacent-adjacent patterns as the full gamut of lane interactions when predicting vehicle trajectories. To this end, we first discuss the procedure for generating a Heterogeneous Information Network (HIN) from scenes, followed by the introduction of the Heterogeneous Structural Learning (HSL) tasks designed to capture relations between lanes. Next, we describe our novel MEtaroad NeTwork (MENTOR) that learns an explicit weighting function to softly select HSL tasks and balance them to improve the performance of the primary task via meta-learning (see Fig. 1)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 346, + 403, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 403, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 403, + 358 + ], + "type": "text", + "content": "3.1. Scene Encoding" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 365, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 400 + ], + "type": "text", + "content": "Contrary to the common approach that treats the scene as a homogeneous graph [54], we model the scene as a Heterogeneous Information Network (HIN) [24]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": "Definition 1. Heterogeneous Information Network (HIN) a HIN is defined as a graph " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = (\\mathcal{V},\\mathcal{E})" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": " is the set of nodes and " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": " is the set of edges, each representing a binary relation between two nodes in " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": " is associated with two mappings: (1) node type mapping function " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\phi :\\mathcal{V}\\to \\mathcal{T}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": " and (2) edge type mapping function " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\psi :\\mathcal{E}\\rightarrow \\mathcal{R}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": " denote sets of node and edge types, respectively. If " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "|\\mathcal{T}| + |\\mathcal{R}| > 2" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": ", network " + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 305, + 401, + 546, + 509 + ], + "type": "text", + "content": " is an HIN, otherwise it is homogeneous." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 510, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 510, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 305, + 510, + 547, + 641 + ], + "type": "text", + "content": "We encode the scene as a directed HIN with node types " + }, + { + "bbox": [ + 305, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{\\text{lane, agent}\\}" + }, + { + "bbox": [ + 305, + 510, + 547, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 510, + 547, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{R} = \\{\\text{left, right, successor, predecessor}\\}" + }, + { + "bbox": [ + 305, + 510, + 547, + 641 + ], + "type": "text", + "content": " as basic relations between adjacent lanes. To initialize node features in the HIN, we use the simplified PointNet [36] with multi-layer perception (MLP) to process polyline features and a 1D convolution with a feature pyramid network [29] to process agents' observations similar to [28]. One advantage of our method is that any type of GNN can be used to process the HIN. Hence, we employ Heterogeneous Graph Transformer (HGT) as a simple yet effective model similar to [19]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 647, + 495, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 495, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 495, + 659 + ], + "type": "text", + "content": "3.2. Heterogeneous Structural Learning" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 665, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 546, + 713 + ], + "type": "text", + "content": "Traffic transitions follow patterns governed by high-level constraints stemming from long-range structural connections between lanes of the road. For learning the map structure, heterogeneity helps interpret a series of relations," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8386" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 284, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 284, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 284, + 83 + ], + "type": "text", + "content": "which our model learns with meTA ROad paTh (TAROT)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": "Definition 2. Meta-Path. A meta-path " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = v_{1} \\xrightarrow{r_{1}} v_{2} \\xrightarrow{r_{2}} \\ldots \\xrightarrow{r_{\\ell}} v_{\\ell + 1}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " expresses a composite relation " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "R = r_{1} \\circ r_{2} \\dots \\circ r_{\\ell}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " between nodes " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "v_{1}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "v_{\\ell + 1}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " denotes the composition operator on relations. If two nodes " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "v_{j}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " are related by the composite relation " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": ", then there exists a path that connects " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "v_{j}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{v_{i} \\rightsquigarrow v_{j}}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": ". Moreover, the nodes and edges types in " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{x_{i} \\rightsquigarrow x_{j}}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " match with types in " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 83, + 286, + 180 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 182, + 286, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 286, + 300 + ], + "type": "text", + "content": "The features obtained from the meta-path analysis in HINs are notably useful in improving graph-based models since they encode indirect semantic relations between nodes that are not directly connected. These features also aid in establishing new relations between vertices. As such, metapath analysis has been frequently used in graph domains to enhance graph representation learning power and improve downstream tasks, such as node classification and link prediction [51, 46, 22, 8]. This means meta-paths can help find new patterns and relations in HINs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": "By focusing on the long-range relations that impose transitions on the road, we define TAROT " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " though the HIN as a path instance of " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "p_{v_i\\sim v_j}\\vdash \\mathcal{P}" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " where node types are the same. Thus, the TAROT can formulate a combination of basic road relations corresponding to transition patterns imposed by map constraints. Predicting the presence of a TAROT between two nodes " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "v_{j}" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " is similar to link prediction. Here, the link means heterogeneous composite relations between nodes. Contrary to link prediction problems, the proposed TAROT prediction can be treated as a self-supervised task. In detail, we follow a simple rule to provide the additional supervised signals for proxy tasks: If node " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " is reachable from node " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " by TAROT " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "y_{u,v}^{p} = 1" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": ", otherwise " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "y_{u,v}^{p} = 0" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": ". This means the HSL task, associated with the TAROT will be formed as a simple link prediction task without the need for any additional data or manual labeling. Hence, by obtaining the hidden representations of two arbitrary nodes learned by a GNN and using a simple operator " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\hat{y}_{u,v}^{p} = \\sigma \\left(\\Phi_{t}(z_{u})^{\\top}\\Phi_{t}(z_{v})\\right)" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " we can predict whether a TAROT between two nodes is present or absent. Here, " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\Phi_t" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " is a type-specific transformation " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "t\\in \\mathcal{T}" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "z_{u}" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "z_{v}" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " are the node embeddings of nodes " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 302, + 287, + 569 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 286, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 286, + 665 + ], + "type": "text", + "content": "Using the proposed TAROT as a type of meta-path we can model a common pattern of driving that adhere to the map constraints. Hence, we define several TAROTs to formulate diverse traffic patterns within the driving scene, resulting in several HSL tasks that can be used to predict diverse and admissible trajectories. We provided a complimentary figure in the supplementary material to further show TAROT's motivation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 165, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 165, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 165, + 682 + ], + "type": "text", + "content": "3.3. Meta Road Network" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "The proposed HSL task is designed to identify diverse patterns within the road structure, for which we explore the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "idea of defining various TAROTs resulting in several self-supervised HSL tasks to be learned simultaneously with the primary trajectory prediction task. However, as with any multi-task learning method, the HSL tasks should be carefully chosen and properly weighted so that learning the map structure does not compete with the primary task, especially when the capacity of graph neural networks (GNNs) is limited. To this end, we propose MEta-road NeTwORk (MENTOR), a learning framework for trajectory prediction that offers the possibility of learning to learn the road configuration while learning the main task. Below, we discuss a naive multi-task combination of self-supervision tasks to explain the motivation behind the design of MENTOR, followed by describing the meta-learning objective using MENTOR, and a detailed look at the learning procedure." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 258, + 528, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 528, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 528, + 269 + ], + "type": "text", + "content": "3.3.1 Naive Multi-task Combination of HSL Tasks" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "text", + "content": "Self-supervised learning has already been explored in trajectory prediction for autonomous driving and has proven beneficial [15, 4]. Adopting a combination of Self-Supervised Learning (SSL) tasks, namely proxy tasks, to improve the primary task has not yet been addressed, even though it has been shown to be effective in visual learning [12]. Here, we formulate a naive multi-task combination of HSL tasks, as SSL tasks, with a shared backbone network with parameters " + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "text", + "content": ", between the primary and all proxy tasks. Each task has a specific loss function " + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^n" + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "text", + "content": " incorporated by a task-specific parameter " + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\lambda_{n}" + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "text", + "content": ". So the optimal parameter " + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^{*}" + }, + { + "bbox": [ + 304, + 278, + 545, + 422 + ], + "type": "text", + "content": " can be extracted by the following objective function:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 337, + 433, + 545, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 433, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 337, + 433, + 545, + 466 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {w}} \\quad \\mathbb {E} \\left[ \\lambda_ {0} \\mathcal {L} ^ {0} (.; \\mathbf {w}) + \\sum_ {n = 1} ^ {N} \\lambda_ {n} \\mathcal {L} ^ {n} (.; \\mathbf {w}) \\right] \\tag {1}", + "image_path": "f798d429d7cd1469db0143bbb231b847436171091fbc8350d8731c578901b1e6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "text", + "content": "where index zero stands for the primary task " + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "inline_equation", + "content": "n = 0" + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "text", + "content": ", and index " + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "inline_equation", + "content": "n|_1^N" + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "inline_equation", + "content": "n^{th}" + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "text", + "content": " task of " + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 475, + 545, + 500 + ], + "type": "text", + "content": " proxy tasks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 520, + 443, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 443, + 532 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 443, + 532 + ], + "type": "text", + "content": "3.3.2 Meta-learning Objective" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 540, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 613 + ], + "type": "text", + "content": "Learning road topology should enhance rather than compete with trajectory prediction, hence determining an effective combination of " + }, + { + "bbox": [ + 304, + 540, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 540, + 545, + 613 + ], + "type": "text", + "content": " parameters is crucial. To achieve this, we adopt MENTOR to parameterize model " + }, + { + "bbox": [ + 304, + 540, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{w}(\\Theta)" + }, + { + "bbox": [ + 304, + 540, + 545, + 613 + ], + "type": "text", + "content": " to determine an optimal combination of HSL tasks and automatically balance them for improved prediction as shown below," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 337, + 622, + 545, + 667 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 622, + 545, + 667 + ], + "spans": [ + { + "bbox": [ + 337, + 622, + 545, + 667 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {w}, \\boldsymbol {\\Theta}} \\quad \\mathbb {E} \\left[ \\mathcal {L} ^ {0} \\left(\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})\\right) \\right] \\\\ \\text {s . t .} \\mathbf {w} ^ {*} (\\boldsymbol {\\Theta}) = \\underset {\\mathbf {w}} {\\operatorname {a r g m i n}} \\quad \\mathbb {E} \\left[ \\mathcal {L} ^ {n | _ {0} ^ {N}} (\\mathbf {w}; \\boldsymbol {\\Theta}) \\right]. \\end{array} \\tag {2}", + "image_path": "66658d944e60fbb116a7fc7dbc379a8e8e125b3c2f4ea08456f2fe8bc62cb3d9.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Specifically, to parametrize the model parameters " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": ", we can impose a learnable weighting function " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}(\\cdot ,\\Theta)" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " to the objective function in (2) as MENTOR similar to [39]. Thus, the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8387" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 48, + 87, + 287, + 324 + ], + "blocks": [ + { + "bbox": [ + 53, + 75, + 253, + 86 + ], + "lines": [ + { + "bbox": [ + 53, + 75, + 253, + 86 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 253, + 86 + ], + "type": "text", + "content": "Algorithm 1: MEta-road NeTwORk (MENTOR)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "lines": [ + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": "Input : primary data " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{pr}}" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " , HSL proxy tasks data " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{hsl}}" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " , batch size " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " , max iteration " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " folds for cross-validation " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " , model parameters w, MENTOR parameters " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " Output: model parameter " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}^T" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " \n1 Initialize w, " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " \n2 for " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "T - 1" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " do \n3 " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\left\\{x^{(\\mathrm{pr})},y^{(\\mathrm{pr})}\\right\\} \\gets" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " SampleMiniBatch " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "(D^{pr},n)" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " . \n4 " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\left\\{x^{(\\mathrm{hsl})},y^{(\\mathrm{hsl})}\\right\\} \\gets" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " SampleMiniBatch " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "(D^{\\mathrm{hsl}},m)" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " //cross validation \n5 for " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " do \n6 " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\left\\{x^{(\\mathrm{meta})},y^{(\\mathrm{meta})}\\right\\} ,\\left\\{x^{(\\mathrm{train})},y^{(\\mathrm{train})}\\right\\} \\gets" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " CVSplit " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "(D^{pr},k)" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " . Formulate model parameter " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^t" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " by Eq 6 \n8 Keep " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\Theta_{k}^{t + 1}" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " on fold " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "= k" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " by Eq.7 \n9 end \n10 Update " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\Theta^{t + 1}" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\frac{1}{K}\\sum_{k}^{K}\\Theta_{k}^{t + 1}" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " \n11 Update " + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^{t + 1}" + }, + { + "bbox": [ + 48, + 87, + 287, + 324 + ], + "type": "text", + "content": " by Eq 8 \n12 end" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 348, + 228, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 228, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 228, + 361 + ], + "type": "text", + "content": "objective function can be written as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 77, + 365, + 153, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 365, + 153, + 384 + ], + "spans": [ + { + "bbox": [ + 77, + 365, + 153, + 384 + ], + "type": "interline_equation", + "content": "\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta}) = \\operatorname * {a r g m i n} _ {\\mathbf {w}}", + "image_path": "ab9dd432b695f71800eecfd2324381cca14b77759a617162b39dab1b18c46215.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 78, + 386, + 287, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 386, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 78, + 386, + 287, + 418 + ], + "type": "interline_equation", + "content": "\\sum_ {n = 0} ^ {N} \\sum_ {i = 1} ^ {M _ {n}} \\frac {1}{M _ {n}} \\mathcal {V} \\left(\\Psi_ {i} ^ {n}; \\Theta\\right) \\mathcal {L} ^ {n} \\left(y _ {i} ^ {n}, f ^ {n} \\left(x _ {i} ^ {n}; \\mathbf {w}\\right)\\right) \\tag {3}", + "image_path": "42e482ed27e737f20e28cdf3e4b6341b7e53cdfdc6dcf9c3c4c834cdd68af98c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": "where each task has " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "M_{n}" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " samples and " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "f^n" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " is the model for task " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " sample of task " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "y_i^n" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " is the label, and " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\Psi_i^n" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " is an embedding vector expressing as the concatenation of one-hot vector of task types, the label (positive/negative), and the loss value of the sample. Therefore, following Eq. (3), the model learns how to assist the primary task by optimizing MENTOR's parameters " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ". These parameters can be optimized using the meta-learning idea [47, 1, 10, 14]. Specifically, using a small amount of meta-data " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{meta}}" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ", representing the meta-knowledge of ground-truth " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{gt}}" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{meta}} \\cup D^{\\mathrm{train}} = D^{\\mathrm{gt}}" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": ", the optimal parameter " + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\Theta^*" + }, + { + "bbox": [ + 46, + 423, + 287, + 567 + ], + "type": "text", + "content": " can be obtained by minimizing the following loss:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 567, + 287, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 567, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 53, + 567, + 287, + 608 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Theta} ^ {*} = \\underset {\\boldsymbol {\\Theta}} {\\operatorname {a r g m i n}} \\mathcal {L} ^ {\\text {m e t a}} (\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})) \\triangleq \\frac {1}{m} \\sum_ {i = 1} ^ {m} \\mathcal {L} _ {i} ^ {\\text {m e t a}} (\\mathbf {w} ^ {*} (\\boldsymbol {\\Theta})) \\tag {4}", + "image_path": "f69f22b5b2099e58e03b812f7f47f63b271b7d3f708690158c145f31ba0afb89.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "type": "inline_equation", + "content": "m \\ll r" + }, + { + "bbox": [ + 47, + 609, + 287, + 632 + ], + "type": "text", + "content": ", are the number of meta-samples and training samples, respectively, and meta-loss is," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 94, + 637, + 287, + 652 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 637, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 94, + 637, + 287, + 652 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i} ^ {\\mathrm {m e t a}} (\\mathbf {w}) = \\mathcal {L} \\left(y _ {i} ^ {\\mathrm {m e t a}}, f \\left(x _ {i} ^ {\\mathrm {m e t a}}, \\mathbf {w}\\right)\\right) \\tag {5}", + "image_path": "237d6317b4ae4db45a8d74e7826ec011bcdd3d3e89ee3bfd02deadb980032aa0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 656, + 138, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 138, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 138, + 668 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 656, + 138, + 668 + ], + "type": "inline_equation", + "content": "(x,y)\\sim D^{\\mathrm{meta}}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 253, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 253, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 253, + 683 + ], + "type": "text", + "content": "3.3.3 Meta-road Network Learning Procedure" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "To overcome the complexity of the bi-level optimization, following [13, 39], we use an online strategy to approximate" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^*" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\Theta^{*}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " with the updated parameters " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\hat{\\Theta}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": ", respectively through a single optimization loop. In each iteration of training, given training data " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{train}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": ", HSL proxy tasks data " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{hsl}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": ", and meta-data " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "D^{\\mathrm{meta}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": ", we follow three steps:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "type": "text", + "content": "Formulating Model Parameter: We formulate the updating equation of model parameter " + }, + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "type": "text", + "content": " by moving the current " + }, + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^t" + }, + { + "bbox": [ + 305, + 121, + 545, + 156 + ], + "type": "text", + "content": " along the descent direction of the loss in Eq. (3)," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 311, + 172, + 545, + 207 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 172, + 545, + 207 + ], + "spans": [ + { + "bbox": [ + 311, + 172, + 545, + 207 + ], + "type": "interline_equation", + "content": "\\underset {D ^ {\\text {t r a i n}} \\cup D ^ {\\mathrm {h s l}}} {\\hat {\\mathbf {w}} ^ {(t)}} (\\boldsymbol {\\Theta}) = \\mathbf {w} ^ {(t)} - \\alpha \\frac {1}{N} \\sum_ {n = 0} ^ {N} \\mathcal {V} (\\cdot ; \\boldsymbol {\\Theta}) \\nabla_ {\\mathbf {w}} \\mathcal {L} ^ {n} (\\mathbf {w}) \\Bigg | _ {\\mathbf {w} ^ {(t)}} \\tag {6}", + "image_path": "e9ae120b5aa86c4fac020f7b0e43ca2ff855e6b4d2ac9d668591e4863f066f49.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "text", + "content": " is the learning rate for " + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^n" + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "text", + "content": " denotes the loss function for the task number " + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 212, + 545, + 247 + ], + "type": "text", + "content": ". To avoid cluttered notation, the summation of task samples is omitted." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "type": "text", + "content": "Updating Parameters of MENTOR: After updating model parameter " + }, + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}^{(t)}(\\Theta)" + }, + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "type": "text", + "content": ", parameter " + }, + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "type": "text", + "content": " of MENTOR can be updated guided by Eq. (4), i.e., moving the current parameter " + }, + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\Theta^{(t)}" + }, + { + "bbox": [ + 305, + 248, + 545, + 307 + ], + "type": "text", + "content": " along the objective gradient of Eq. (4) calculated on the meta-data," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 323, + 323, + 545, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 323, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 323, + 323, + 545, + 345 + ], + "type": "interline_equation", + "content": "\\Theta_ {D ^ {\\mathrm {m e t a}}} ^ {(t + 1)} = \\Theta^ {(t)} - \\beta \\mathcal {V} (\\cdot ; \\Theta) \\mathcal {L} ^ {0} \\left(\\hat {\\mathbf {w}} ^ {(t)} (\\Theta)\\right) \\Big | _ {\\Theta^ {(t)}} \\tag {7}", + "image_path": "b72f4198af02371c33a2c1066ba587d760e09f6a22541f6a6a4d4718e8906bd1.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "type": "text", + "content": " is the learning rate for " + }, + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "type": "text", + "content": ". This update allows the soft selection of useful HSL proxy tasks and balances them with the main motion prediction task to improve the performance of the main task. Without balancing tasks with the weighting function " + }, + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{V}(\\cdot;\\Theta)" + }, + { + "bbox": [ + 305, + 350, + 545, + 422 + ], + "type": "text", + "content": ", proxy tasks can dominate training and degrade the performance of the primary task." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 422, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 545, + 447 + ], + "type": "text", + "content": "Updating Model Parameters: Model parameters " + }, + { + "bbox": [ + 305, + 422, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 305, + 422, + 545, + 447 + ], + "type": "text", + "content": " for tasks can be updated with optimized " + }, + { + "bbox": [ + 305, + 422, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\Theta^{t + 1}" + }, + { + "bbox": [ + 305, + 422, + 545, + 447 + ], + "type": "text", + "content": " in Eq. (7) as," + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 336, + 453, + 545, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 453, + 545, + 512 + ], + "spans": [ + { + "bbox": [ + 336, + 453, + 545, + 512 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\mathbf {w}} _ {D ^ {\\mathrm {t r a i n}} \\cup D ^ {\\mathrm {h s l}}} ^ {(t + 1)} (\\boldsymbol {\\Theta}) = \\mathbf {w} ^ {(t)} \\\\ - \\alpha \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\mathcal {V} \\left(\\because \\Theta^ {(t + 1)}\\right) \\nabla_ {\\mathbf {w}} \\mathcal {L} ^ {n} (\\mathbf {w}) \\Bigg | _ {\\mathbf {w} ^ {(t)}}. \\tag {8} \\\\ \\end{array}", + "image_path": "c3acbd9f03baa82e63516ab34ac2c36a148929357217e9a0bf51beebb4302f51.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "text", + "content": "Lastly, to circumvent the problem of meta-overfitting, meaning that parameters " + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "text", + "content": " overfit to the small meta-dataset, we follow the meta-validation solution as in [2, 59]. In particular, to make " + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "text", + "content": " generalizable across meta-training sets, we optimize it using " + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "text", + "content": " different meta-datasets with k-fold cross-validation. The gradients of " + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "text", + "content": " from different meta-datasets are then averaged to update " + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "inline_equation", + "content": "\\Theta^{(t)}" + }, + { + "bbox": [ + 305, + 516, + 545, + 612 + ], + "type": "text", + "content": ". The MENTOR learning procedure is summarized in Algorithm 1." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 621, + 386, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 386, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 386, + 635 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": "Our goal is to investigate ways for improving map representational learning power to predict diverse and admissible trajectories. For this purpose, we seek to answer the following questions: Q1: Are predicted trajectories diverse and admissible? Q2: Is MEta-road NeTwORk (MENTOR) effective regardless of the type of HSL task? Q3: How much" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8388" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 83, + 544, + 168 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 534, + 82 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 534, + 82 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 534, + 82 + ], + "type": "text", + "content": "Table 1: Comparison to SOTA models on challenging scenarios. Arrows show lower (↓) or higher (↑) values are better." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 83, + 544, + 168 + ], + "lines": [ + { + "bbox": [ + 50, + 83, + 544, + 168 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 544, + 168 + ], + "type": "table", + "html": "
MethodTurnsStationary
minADE(↓)minFDE(↓)DAO(↑)RF(↑)MR(↓)minADE(↓)minFDE(↓)DAO(↑)RF(↑)MR(↓)
LaneGCN [28]1.082.1867.632.8935.761.232.5261.692.6936.80
MMTransformer[21]1.052.0769.763.3532.001.132.2864.853.2135.69
FTGN [3]1.062.0470.723.2534.061.162.2263.953.0632.49
HiVT [58]1.062.2366.842.7935.451.252.7458.432.5139.61
SSL-Lane [4]1.072.1169.653.2133.341.162.3462.453.2234.54
MENTOR (Ours)1.032.0079.213.7631.301.132.1969.233.8732.76
", + "image_path": "7eb96df774651e3c2440517d11d8979e2146246552f1d971f2fb290c4953f563.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 178, + 286, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 178, + 286, + 203 + ], + "spans": [ + { + "bbox": [ + 48, + 178, + 286, + 203 + ], + "type": "text", + "content": "does our proposed HSL task contribute to diversity and admissibility?" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 206, + 162, + 219 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 206, + 162, + 219 + ], + "spans": [ + { + "bbox": [ + 48, + 206, + 162, + 219 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 225, + 286, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 225, + 286, + 308 + ], + "spans": [ + { + "bbox": [ + 48, + 225, + 286, + 308 + ], + "type": "text", + "content": "Dataset: We evaluated our method on the Argoverse benchmark dataset [7]. Here the task is to predict 3 seconds of future trajectories given 2 seconds of past observations. This dataset consists of more than " + }, + { + "bbox": [ + 48, + 225, + 286, + 308 + ], + "type": "inline_equation", + "content": "300K" + }, + { + "bbox": [ + 48, + 225, + 286, + 308 + ], + "type": "text", + "content": " real-world driving sequences, which are split into the train (205K), validation (39K), and test (78K) sets without geographical overlap along with corresponding HD maps." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 309, + 286, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 309, + 286, + 428 + ], + "spans": [ + { + "bbox": [ + 48, + 309, + 286, + 428 + ], + "type": "text", + "content": "Metrics: We selected a set of metrics to measure the precision, diversity, and admissibility of predictions. For precision, we use minADE (Average Displacement Error), minFDE (Final Displacement Error), and MR (Miss Rate). For diversity, we use the Ratio of avgFDE to minFDE (RF) [34], which measures the spread of predictions in Euclidean distance. We use Drivable Area Occupancy (DAO) [34] to determine the proportion of pixels that predicted trajectories occupy in the drivable area. RF and DAO work in a complementary way to measure diversity along with admissibility." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "spans": [ + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "type": "text", + "content": "Implementation Details: To normalize the data, we translate and rotate the coordinate system of each sequence so that the origin is at the agent's current location at " + }, + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "type": "text", + "content": ". We use the orientation from the agent's location at " + }, + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "type": "inline_equation", + "content": "t = -1" + }, + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "type": "text", + "content": " to its location at " + }, + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 48, + 429, + 286, + 667 + ], + "type": "text", + "content": " as the positive x axis. We use all actors and lanes whose distance from the agent is smaller than 100 meters as the input. As a model architecture, we use three layers of HGT with the hidden dimension of size 128. For the HSL tasks, we define five TAROTs with variable lengths of 4 to 7. The intuition behind the number of TAROTs is to model turning right/left, lane changing (right-to-left and left-to-right), and going straight. We formulate Mentor as an MLP with two hidden layers with 100 nodes each, with ReLU activations for hidden nodes and sigmoid output to ensure it is in range [0, 1]. For the loss functions, we follow the widely used regression-MLP plus classification-MLP combination [28, 24, 33] for trajectory prediction and cross-entropy for the HSL task. For the training, we use the AdamW [31] optimizer with an initial learning rate of 5e-4, weight decay 1e-4, and batch size of 64." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 671, + 230, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 671, + 230, + 684 + ], + "spans": [ + { + "bbox": [ + 48, + 671, + 230, + 684 + ], + "type": "text", + "content": "4.2. Analysis on Challenging Scenarios" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 689, + 286, + 712 + ], + "type": "text", + "content": "Existing prediction datasets are highly imbalanced in terms of scenario diversity, with the majority of traffic ac" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 178, + 544, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 178, + 544, + 346 + ], + "spans": [ + { + "bbox": [ + 307, + 178, + 544, + 346 + ], + "type": "text", + "content": "tors simply driving straight [35]. Calculating metrics by aggregating over scenarios is therefore influenced by the most common maneuvers, where prediction models often do well. In practice, scenarios, such as turning at intersections could be of greater interest to practitioners and accurately predicting these scenarios are even more crucial for the safe operation of autonomous vehicles. Hence, to verify the effectiveness of our model, we extracted challenging scenarios including left/right/blind turns and stationary scenarios where the vehicle's observed trajectory is very short, thus the model has minimal motion information from the vehicle. By blind turns, we refer to the cases where the observed trajectory is straight and the turn occurs during the unobserved portion of the trajectory." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 346, + 544, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 346, + 544, + 490 + ], + "spans": [ + { + "bbox": [ + 308, + 346, + 544, + 490 + ], + "type": "text", + "content": "We compare our method against several vectorized-based SOTA models with public implementations, including two graph-based models, LaneGCN [28] and FTGN [3], two transformer-based models, MMTransformer [21] and HiVT [58], and SSL-Lane [4], which extends the lane graph by adding four different self-supervised tasks based on agent/map information. As shown in Table 1, our method significantly improves upon the state-of-the-art models on most metrics in both scenarios. Particularly, our method, MENTOR achieves notable improvements in diversity and admissibility metrics, namely DAO and RF by up to " + }, + { + "bbox": [ + 308, + 346, + 544, + 490 + ], + "type": "inline_equation", + "content": "13\\%" + }, + { + "bbox": [ + 308, + 346, + 544, + 490 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 308, + 346, + 544, + 490 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 308, + 346, + 544, + 490 + ], + "type": "text", + "content": " respectively in the challenging scenarios." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 491, + 544, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 491, + 544, + 632 + ], + "spans": [ + { + "bbox": [ + 308, + 491, + 544, + 632 + ], + "type": "text", + "content": "Qualitative analysis. Fig. 2 depicts a number of qualitative examples to better highlight our method's performance. The first two rows represent turn-right scenarios, and the third and fourth rows show left-turn and stationary scenarios. As can be seen in the last column, our method consistently generates diverse predictions that are also admissible by correctly aligning with the road topology. The behavior of competing methods, however, varies often resulting in the generation of infeasible trajectories. In the supplementary materials, we discuss the algorithm used to find challenging scenarios and present additional per-scenario metrics to further elaborate on the correlation of metrics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 640, + 405, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 640, + 405, + 651 + ], + "spans": [ + { + "bbox": [ + 308, + 640, + 405, + 651 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 659, + 466, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 659, + 466, + 670 + ], + "spans": [ + { + "bbox": [ + 308, + 659, + 466, + 670 + ], + "type": "text", + "content": "4.3.1 MENTOR Acting as a Mentor" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "text", + "content": "To assess the ability of MENTOR, we analyze the weighting function " + }, + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{V}(\\Psi_i^n;\\Theta)" + }, + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "text", + "content": " sample of task " + }, + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "text", + "content": ". Particularly, we present the learned weight function at the last epoch of" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "8389" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 64, + 523, + 340 + ], + "blocks": [ + { + "bbox": [ + 72, + 64, + 523, + 340 + ], + "lines": [ + { + "bbox": [ + 72, + 64, + 523, + 340 + ], + "spans": [ + { + "bbox": [ + 72, + 64, + 523, + 340 + ], + "type": "image", + "image_path": "2e59793ae8e717bb09121fe124ec54d8443715c5a2d9752e288c9567473e35f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 87, + 370, + 247, + 480 + ], + "blocks": [ + { + "bbox": [ + 46, + 344, + 545, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 344, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 344, + 545, + 369 + ], + "type": "text", + "content": "Figure 2: Qualitative examples on Argoverse showing diversity and admissibility of the predicted trajectories by MENTOR. Red, green, and blue trajectories represent observation, ground truth, and 6 predicted trajectories, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 87, + 370, + 247, + 480 + ], + "lines": [ + { + "bbox": [ + 87, + 370, + 247, + 480 + ], + "spans": [ + { + "bbox": [ + 87, + 370, + 247, + 480 + ], + "type": "image", + "image_path": "00468cf7409b7b596e7b0dbadcd2cc73ce182e1c858ca235575814d185efbf12.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "text", + "content": "Figure 3: The weighting function in MENTOR. The green line is the primary task, and solid and dashed color lines represent positive and negative HSL samples, respectively. Each color corresponds to a specific HSL task." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 542, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 686 + ], + "type": "text", + "content": "the training. As shown in Fig. 3, MENTOR has two main benefits. Firstly, even when the model's loss is low, as the model is learning less challenging scenarios, trajectory prediction task (green line) samples have a higher weight than HSL tasks. Hence, MENTOR is more focused on learning the primary trajectory prediction task as there is no competition between HSL tasks and the primary task. Secondly, in all tasks, hard samples with higher losses are given more weight than easy samples with lower losses, indicating that MENTOR is mining hard samples. Here, MENTOR acts as a mentor by learning TAROTs and transferring that knowledge to the primary task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Effectiveness of MENTOR: To analyze the effectiveness of MENTOR, we borrow a lane-graph-based baseline" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": "and four self-supervised learning (SSL) tasks introduced in [4] and use them in MENTOR to improve the baseline. The SSL tasks are as follows: A) Lane masking, which recovers feature information from the perturbed lane graphs; B) Predicting distance to the intersection in terms of the shortest path length from all lane nodes to the intersection nodes; C) Maneuver classification, which predicts the form of a maneuver that the agent of interest intends to execute; And D) success/failure classification, which trains an agent specialized in achieving end-points." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": "We report the results in Tab. 2 where the SSL tasks are termed A-D and " + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\text{MENTOR}_{\\sum \\mathrm{A}, \\mathrm{B}, \\mathrm{C}, \\mathrm{D}}" + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": " denotes the proposed model. According to the table, among the proposed tasks, maneuver classification, task C, has the best DAO (admissibility), indicating that predicting the form of maneuver can reveal more information about the road structure. Additionally, predicting the distance to the intersection, task B, gives a better estimate of the agent to the intersection, and the possibility of branching roads, hence improving RF (diversity) metric. In summary, individual tasks are shown to be effective by providing auxiliary information that helps improve different aspects of prediction. Once combined together, SSL tasks through the MENTOR framework improve distance-based metrics, minADE and minFDE as well as admissibility and diversity metrics, DAO and RF. These results validate the effectiveness of MENTOR as a learning framework to enhance prediction models" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8390" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 106, + 286, + 176 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 106 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 106 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 106 + ], + "type": "text", + "content": "Table 2: Results of the ablation studies. " + }, + { + "bbox": [ + 47, + 70, + 287, + 106 + ], + "type": "inline_equation", + "content": "\\mathrm{SSL}_{-}x" + }, + { + "bbox": [ + 47, + 70, + 287, + 106 + ], + "type": "text", + "content": " indicates self-supervised tasks as in [4] and " + }, + { + "bbox": [ + 47, + 70, + 287, + 106 + ], + "type": "inline_equation", + "content": "\\mathrm{MENTOR}_{\\sum \\mathrm{A,B,C,D}}" + }, + { + "bbox": [ + 47, + 70, + 287, + 106 + ], + "type": "text", + "content": " indicates the original model augmented with MENTOR." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 106, + 286, + 176 + ], + "lines": [ + { + "bbox": [ + 49, + 106, + 286, + 176 + ], + "spans": [ + { + "bbox": [ + 49, + 106, + 286, + 176 + ], + "type": "table", + "html": "
ModelminADE(↓)minFDE(↓)DAO(↑)RF(↑)
Baseline0.731.1265.873.00
SSLA0.701.0268.212.98
SSLB0.711.0468.653.87
SSLC0.721.0569.973.14
SSLD0.701.0168.023.01
MENTORΣA,B,C,D0.690.9877.914.18
", + "image_path": "6e58fce6617ed0410bc93c9bcad51292704155d67c0b7b9fde62bba46f1001fc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 236, + 285, + 316 + ], + "blocks": [ + { + "bbox": [ + 47, + 188, + 286, + 235 + ], + "lines": [ + { + "bbox": [ + 47, + 188, + 286, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 188, + 286, + 235 + ], + "type": "text", + "content": "Table 3: Results of the ablation studies. " + }, + { + "bbox": [ + 47, + 188, + 286, + 235 + ], + "type": "inline_equation", + "content": "\\mathrm{TAROT}^x" + }, + { + "bbox": [ + 47, + 188, + 286, + 235 + ], + "type": "text", + "content": " indicates the length of the TAROT through the HSL task and MENTOR represents our full model, which includes several HSL tasks." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 236, + 285, + 316 + ], + "lines": [ + { + "bbox": [ + 49, + 236, + 285, + 316 + ], + "spans": [ + { + "bbox": [ + 49, + 236, + 285, + 316 + ], + "type": "table", + "html": "
TurnsValidation
ModelminFDE(↓)DAO(↑)RF(↑)minFDE(↓)DAO(↑)RF(↑)
Baseline2.37268.452.981.13274.024.21
TAROT42.26771.013.191.12875.524.43
TAROT52.20873.673.231.10777.114.48
TAROT62.15376.933.711.11278.894.50
TAROT72.08276.173.561.12178.004.51
TAROT82.10973.653.411.12077.214.38
MENTOR2.00379.213.760.97485.314.65
", + "image_path": "73b2bc42c18adfc96af31e97aa174bf65c6243d20f42006ce1ff387ed5f48622.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 331, + 249, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 249, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 249, + 342 + ], + "type": "text", + "content": "by providing additional information as SSL tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "type": "text", + "content": "Impact of TAROT Prediction as an HSL Task: for the purpose of analyzing the impact of the TAROT prediction, we conduct several experiments on the entire validation set and challenging turn scenarios by designing different models named " + }, + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{TAROT}^x" + }, + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "type": "text", + "content": " refers to the length of TAROT through the HSL task. For example, " + }, + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{TAROT}^4" + }, + { + "bbox": [ + 47, + 343, + 287, + 713 + ], + "type": "text", + "content": " could be any of these patterns [S-S-S-R, S-L-S-S, S-L-P-P...] (S: Successor, L: Left, R: Right, P: Predecessor as the basic relation of adjacent lanes). We average the metrics over all of the members in the list. A baseline model does not have any HSL tasks, and therefore does not have MENTOR. The last model is our final model which is loaded by multiple HSL tasks through MENTOR. As shown in Tab. 3, augmenting the model with the HSL task improves the baseline model performance. Moreover, from the experiments, we found that by predicting a longer TAROT, corresponding to a longer pattern in the road configuration with a higher abstraction, we can improve the model in turns scenarios. However, the length of TAROTs should be set carefully, as if set too long, the model would have a tendency to predict a turn maneuver even when several alternatives, such as driving straight, are available. To take advantage of this phenomenon, we define multiple TAROTs with variable lengths representing both short and long patterns. Thus, once used through MENTOR we enable the model to identify the best combination of HSL tasks, as TAROT prediction, by weighting them properly. In this way, our full model outperforms other models significantly. Based on the obtained results, we can conclude that 1) TAROTs are capable of modeling patterns in the map structure, thus formulating multiple TAROTs and subsequently multiple HST" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 83, + 545, + 205 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 538, + 82 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 538, + 82 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 538, + 82 + ], + "type": "text", + "content": "Table 4: Comparisons with SOTA on Argoverse test set." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 83, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 307, + 83, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 307, + 83, + 545, + 205 + ], + "type": "table", + "html": "
MethodminADE(↓)minFDE(↓)MR(↓)
TNT [56]0.941.5413.30
DenseTNT [18]0.881.2812.58
TPCN [49]0.871.3615.80
mmTransformer [30]0.871.3415.40
LaneRCNN [54]0.901.4512.32
LTP [45]0.831.2914.72
AutoBot [17]0.891.4116.00
SceneTransformer [33]0.801.2312.55
HiVT [58]0.771.1612.67
MENTOR (Ours)0.791.2113.01
", + "image_path": "a5de450bb87c292fdc7c9ea3fbfac9438669363709f88abff1921dfbd6ca39fb.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 209, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 270 + ], + "type": "text", + "content": "tasks, can capture diverse lane connection patterns in the map topology. 2) MENTOR is good at adopting HSL tasks to transfer their knowledge to the primary task, and consequently resulting in significant improvement in terms of diverse (RF) and admissible (DAO) trajectory prediction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 273, + 429, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 273, + 429, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 273, + 429, + 285 + ], + "type": "text", + "content": "4.4. Comparison to SOTA" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 292, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 447 + ], + "type": "text", + "content": "We compare our method to SOTA models on the Argov-verse benchmark. Even though the focus of our method was on improving diversity and admissibility of generated trajectories in challenging scenarios, as shown in Tab. 4, our model's performance is comparable to best models, on the distance-based metrics on the benchmark. Particularly, compared to HiVT [58], our model achieves the second rank on minADE and minFDE, while in challenging scenarios it outperforms HiVT on the diversity and admissibility metrics as well as the distance-based metrics with a large margin, as is evident in Tab. 1. We further verify the effectiveness of our approach on a smaller dataset, nuScenes [5], and report the results in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 454, + 378, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 378, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 378, + 466 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we presented a novel trajectory prediction model based on the concept of meta-learning. We formulated various lane connection relations on the map topology as meTA ROad paTh (TAROT), and used a model, MEtaroad NeTwORk (MENTOR), to supply TAROT tips in the form of Heterogeneous Structural Learning (HSL) tasks to improve trajectory prediction. Besides, focusing on enhancing the map representational learning power, MENTOR can mentor any proxy task to further improve the primary motion forecasting task. Via extensive experimental evaluations, we showed that HSL tasks are capable of modeling high-level semantics stemming from long-range heterogeneous connections between lanes. Additionally, we showed that our proposed MENTOR model acts as a mentor to gain the maximum benefit from the existing structural information of the map. The results also highlighted that, besides significantly improving diversity and admissibility of predictions, our method can obtain improved or comparable results on common distance-based metrics compared to the past arts with a larger number of parameters." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "8391" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W Hoffman, David Pfau, Tom Schaul, Brendan Shillingford, and Nando De Freitas. 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In ICML, 2019. 5" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8393" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_content_list.json b/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1f4c0a27b96b68a32883a86c2ad90c15f0169c39 --- /dev/null +++ b/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_content_list.json @@ -0,0 +1,1669 @@ +[ + { + "type": "text", + "text": "Learned Compressive Representations for Single-Photon 3D Imaging", + "text_level": 1, + "bbox": [ + 135, + 130, + 833, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Felipe Gutierrez-Barragan $^{1\\ddagger}$ , Fangzhou Mu $^{1}$ , Andrei Ardelean $^{3}$ , Atul Ingle $^{2}$ , Claudio Bruschini $^{3}$ , Edoardo Charbon $^{3}$ , Yin Li $^{1}$ , Mohit Gupta $^{1}$ , Andreas Velten $^{1}$", + "bbox": [ + 102, + 156, + 867, + 191 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Wisconsin-Madison, 2Portland State University,", + "bbox": [ + 236, + 193, + 733, + 210 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Ecole Polytechnique Federale de Lausanne", + "bbox": [ + 305, + 210, + 656, + 229 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 253, + 313, + 270 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Single-photon 3D cameras can record the time-of-arrival of billions of photons per second with picosecond accuracy. One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that encodes distances along the time axis. As the spatio-temporal resolution of the histogram tensor increases, the in-pixel memory requirements and output data rates can quickly become impractical. To overcome this limitation, we propose a family of linear compressive representations of histogram tensors that can be computed efficiently, in an online fashion, as a matrix operation. We design practical lightweight compressive representations that are amenable to an in-pixel implementation and consider the spatio-temporal information of each timestamp. Furthermore, we implement our proposed framework as the first layer of a neural network, which enables the joint end-to-end optimization of the compressive representations and a downstream SPAD data processing model. We find that a well-designed compressive representation can reduce in-sensor memory and data rates up to 2 orders of magnitude without significantly reducing 3D imaging quality. Finally, we analyze the power consumption implications through an on-chip implementation.", + "bbox": [ + 75, + 286, + 473, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 657, + 209, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D cameras based on single-photon avalanche diode technology (SPAD) are becoming increasingly popular for a wide range of applications that require high-resolution and low-power depth sensing, ranging from autonomous vehicles [1] to consumer smartphones [2]. Kilo-to-megapixel resolution SPAD pixel arrays [27, 28] have the capability of capturing the time-of-arrival of billions of individual photons per frame with extremely high (picosecond) time resolution [31]. Unfortunately, this extreme sensitivity and high speed comes at a cost — the raw timestamp data causes a severe bottleneck between the image sensor and the image signal processor (ISP) that processes this data (Fig. 1(a)). This data bottleneck severely limits the wider use of high-", + "bbox": [ + 75, + 681, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e6bf66f7edf47a672e7fb68c930b15195df549b9a7d885a6f362ba4d25bf7c77.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 257, + 861, + 362 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ed1878b6bbec76a0902ee2bc93d51cea753f43822d10ea7c417ed927ce4e404b.jpg", + "image_caption": [ + "Figure 1. Resolving SPAD data bottleneck with learned compression. (a) Conventional SPAD-based 3D cameras stream raw photon timestamps or summary histograms off the image sensor which causes a data bottleneck between the image sensor and the on-camera image and signal processing (ISP) module. (b) Our method applies a lightweight, on-sensor compressive coding scheme to the photon timestamp data which is later decoded at the ISP, resolving the data bandwidth limitation." + ], + "image_footnote": [], + "bbox": [ + 532, + 363, + 849, + 460 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "resolution SPAD arrays in 3D sensing applications.", + "bbox": [ + 500, + 585, + 839, + 601 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One common approach to avoid transferring individual photon timestamps is to build a histogram in each pixel. This results in a 3D histogram tensor that is transferred off-sensor for processing. Although this may be practical at low spatio-temporal resolutions (e.g., $64 \\times 32$ pixels with 16 time bins [15]), it requires higher in-sensor memory. Moreover, the data rates of this histogram tensor representation also scale rapidly with the spatio-temporal resolution and maximum depth range. For example, a megapixel SPAD-based 3D camera operating at 30 fps that outputs a histogram tensor with a thousand 8-bit bins per pixel would require an unmanageable data transfer rate of 240 Gbps.", + "bbox": [ + 496, + 602, + 892, + 780 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome the above limitations, we seek to design compressive representations of 3D histogram tensors. In order to reduce the data rates output by the SPAD camera, the compact representation needs to be built in-pixel or inside the focal plane array (FPA). This is illustrated in Fig. 1(b). Due to the limited in-pixel memory and compute, the compressive representation needs to be built in a streaming manner, with minimal computations per photon. Photon", + "bbox": [ + 496, + 781, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{\\ddagger}$ Email: fgutierrez3@wisc.edu", + "bbox": [ + 94, + 886, + 300, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10756", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "histogram tensors are very different from conventional RGB images/video data. Therefore, traditional compression algorithms such as MPEG are not directly applicable.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose a family of compressive representations for 3D histogram tensors that can be computed in an online fashion with limited memory and compute. They are based on the linear spatio-temporal projection of each photon timestamp, which can be expressed as a simple matrix operation. Instead of constructing per-pixel timestamp histograms, a compressive encoding maps its spatio-temporal information into a compressive histogram. To exploit local spatio-temporal correlations, a single compressive histogram is built for a local 3D histogram block as illustrated in Fig. 2. Instead of building and storing the full 3D histogram tensor in-sensor, multiple compressive histograms are built and transferred off-sensor for processing, effectively reducing the required in-sensor memory and data rates. Recent works proposed a similar compression framework based on compressive histograms [13] or sketches [36]. In Sec. 4, we show that these prior works can be viewed as special cases of our proposed framework.", + "bbox": [ + 75, + 136, + 468, + 400 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we explore the design space of spatiotemporal compressive encodings and analyze the trade-offs between different design choices. Furthermore, we present a method to integrate our compression framework with data-driven SPAD data processing methods using convolutional neural networks (CNNs), which enables end-to-end optimization of the compressive encoding and a SPAD data processing CNN. We demonstrate the feasibility of compressive histograms through an on-chip implementation.", + "bbox": [ + 75, + 402, + 468, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For our experimental evaluation, we integrate the compressive histograms framework with a state-of-the-art learning-based denoising model for SPAD-based 3D imaging [32]. Our results show that the jointly optimized compressive encoding and CNN can consistently reduce data rates up to 2 orders of magnitude in a wide range of signal and noise levels. Moreover, for a given compression level, it can increase 3D imaging accuracy over previous hand-designed compressive histograms that only exploit temporal information [13, 36], especially in low signal-to-background ratio (SBR) scenarios and at higher compression rates. Furthermore, we show that learned compressive histograms can perform comparably and sometimes even outperform a theoretical SPAD sensor design where the full 3D histogram tensor is stored in-sensor and only per-pixel depths are transferred off-sensor. Finally, we analyze the power consumption of a compressive histogram implemented on the UltraPhase SPAD processing chip [4].", + "bbox": [ + 75, + 535, + 468, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 813, + 218, + 828 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compressive histograms, also called sketches, are an emerging framework for online in-sensor compression of SPAD timestamp data [13, 41, 36, 33]. A coarse histogram is one common compressive histogram approach [13] to re", + "bbox": [ + 75, + 840, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "duce data rates and in-pixel memory [15, 8, 18]. Despite their practical hardware implementation, coarse histograms achieve sub-optimal depth accuracy compared to compressive histograms based on Fourier [36, 37, 13] and Gray [13] codes. One limitation of these approaches is that the compressive representation only exploits the temporal information of the incident timestamp, and disregards the spatial redundancy. In this work, we generalize the compressive histogram framework to utilize the spatio-temporal information of each timestamp. Moreover, instead of relying on hand-designed coded projections, in this paper we learn them as the first layer of a CNN.", + "bbox": [ + 496, + 90, + 890, + 268 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Shared In-Pixel Histograms: One common design is to have multiple neighboring SPAD pixels have a single shared memory where all timestamps are aggregated into a coarse histogram (e.g., $4 \\times 4$ [18, 15], $3 \\times 3$ [20]). This approach throws away the local spatial information (i.e., pixel location) of the detected photon timestamps. A compressive histogram is well-suited for these shared memory designs because it can be shared among multiple SPAD pixels and preserves spatial information through the coded projection.", + "bbox": [ + 496, + 273, + 890, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Sensors and Pixel Processor Arrays: Pixel processor arrays (PPAs) are an emerging sensing technology that embeds processing electronics inside each pixel [9]. This new sensing paradigm begins processing the image at the focal plane array, which allows it to reduce the sensor data rates by transmitting only the relevant information, and consequently, it increases the sensor's throughput [9] which can enable computer vision at 3,000 fps [6, 7]. PPAs have also become building blocks of novel computational imaging systems optimized end-to-end for HDR imaging [25, 39], motion deblurring [30], video compressive sensing [25], and light field imaging [43]. A compressive histogram relies on a similar in-pixel processing paradigm. Similar to previous works, we jointly optimize the sensor parameters (i.e., the compressive histogram) and the processing algorithm (i.e., the CNN), but to our knowledge, this work is the first to use this approach for SPAD data compression.", + "bbox": [ + 496, + 412, + 890, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Single-Photon 3D Histogram Tensors", + "text_level": 1, + "bbox": [ + 500, + 680, + 834, + 698 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SPAD-based 3D cameras consist of a SPAD sensor and a pulsed laser that illuminates the scene. The photon flux signal arriving at pixel, $p$ , can be written as:", + "bbox": [ + 496, + 705, + 890, + 751 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi_ {\\boldsymbol {p}} (t) = a _ {\\boldsymbol {p}} h \\left(t - 2 d _ {\\boldsymbol {p}} / c\\right) + \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}} = \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {s i g}} (t) + \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 763, + 890, + 782 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $a_{p}$ is the amplitude of the returning signal accounting for laser power, reflectivity, and light fall-off; $h(t)$ is the system's impulse response function (IRF) which accounts for pulse waveform and sensor IRF; $d_{p}$ is the distance to the point imaged by $p$ ; $c$ is the speed of light; and $\\Phi_{p}^{\\mathrm{bkg}}$ is the constant photon flux due to background illumination (e.g., sunlight). This model assumes direct-only reflections", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10757", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ccb75f2aaef93d94c8ba5be029ed2f756361ca7ab11b161cf5e2081f6d5461ea.jpg", + "image_caption": [ + "Figure 2. Compressive Histogram Formation. Histogram tensors, $H$ , are a 3D spatio-temporal grid whose elements store the number of photons that arrived within a short time interval. (a) In SPAD-based 3D imaging, the temporal axis of $H$ encodes distances. (b) A histogram block, $H_{b}$ , can be expressed as the sum of $J$ one-hot encoding tensors, where each tensor represents a photon timestamp. (c) A compact representation of $H_{b}$ can be built by applying $K$ linear projections (i.e., dot product) with pre-designed coding tensors. (d) The compressive histogram, will be a vector with $K$ elements whose compression capacity is given by $\\frac{M_t \\cdot M_r \\cdot M_c}{K}$ ." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 573, + 279 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3dab483cae28c9552f5efd54c97c53c2380536942ed77069c51ba3e6cbc230eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 576, + 88, + 888, + 279 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which is a valid approximation, in particular, for scanning-based ToF 3D imaging systems [3].", + "bbox": [ + 75, + 366, + 468, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "TCSPC-based SPAD cameras measure $\\Phi_p(t)$ by building a per-pixel timing histogram, where the $i$ th histogram bin records the number of photons that arrived in a time interval of length $\\Delta$ , which follows a Poisson process $\\mathcal{P}$ :", + "bbox": [ + 75, + 395, + 468, + 455 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi_ {i, \\boldsymbol {p}} = \\mathcal {P} \\left(\\Phi_ {i, \\boldsymbol {p}} ^ {\\mathrm {s i g}} + \\Delta \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 463, + 468, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The pulse repetition period, $\\tau$ , determines the maximum timestamp value and the length of the histogram vector $\\Phi_p = (\\Phi_{i,p})_{i=0}^{N_t - 1}$ , where $N_t = \\tau / \\Delta$ . Therefore, one assumption built into $\\Phi_p$ , is that no signal photons had a timestamp larger than $\\tau$ , which means that the maximum distance that $\\Phi_p$ can encode is $d_{\\max} = \\frac{c\\tau}{2}$ . Furthermore, we assume that pile-up distortions are minimized through various SPAD data acquisition techniques [11, 15, 16, 12].", + "bbox": [ + 75, + 489, + 468, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This process generates a $N_{t} \\times N_{r} \\times N_{c}$ 3D histogram tensor, $\\pmb{H} = (\\Phi_p)_{p=0,0}^{(N_r - 1, N_c - 1)}$ . In challenging 3D imaging scenarios with high background illumination, building $\\pmb{H}$ off-sensor requires transferring thousands of photon timestamps per-pixel leading to data rates of hundreds of GB/s in a megapixel sensor. Moreover, building and storing a high-resolution $\\pmb{H}$ in-sensor would require significant memory (1GB for a megapixel SPAD camera with 1000 time bins per-pixel), and transferring it would continue to lead to impractical data rates of tens of GB/s on a SPAD-based 3D camera operating at 30fps. Overall, a practical SPAD-based 3D camera would build and store a compact representation of $\\pmb{H}$ in-sensor and then transfer it to a processing chip (e.g., FPGA, ISP, embedded computer) where it is processed.", + "bbox": [ + 75, + 607, + 468, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Spatio-temporal Compressive Histograms", + "text_level": 1, + "bbox": [ + 76, + 830, + 450, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A natural approach to compress $\\pmb{H}$ that exploits its local correlations due to smooth depths and photon flux, is to build a compressive representation of a local 3D histogram", + "bbox": [ + 75, + 856, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "block as illustrated in Fig. 2. To avoid storing or transferring the photon timestamp stream, the compressive representation is built as each timestamp arrives. In this section, we present an online compression framework for histogram blocks based on the coded projection of photon timestamps.", + "bbox": [ + 496, + 364, + 890, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $H_{b}$ be the $b$ th histogram block of $H$ with dimensions $M_{t} \\times M_{r} \\times M_{c}$ , where $M_{t} \\leq N_{t}$ , $M_{r} \\leq N_{c}$ , and $M_{c} \\leq N_{c}$ . First, we observe that $H_{b}$ can be expressed as the sum of $J$ one-hot encoding tensors, each representing one photon detection within $H_{b}$ (Fig. 2b). Specifically, let $t_{b,j}$ be a $M_{t} \\times M_{r} \\times M_{c}$ one-hot encoding tensor representing the $j^{\\mathrm{th}}$ photon timestamp detected in histogram block $H_{b}$ , whose elements are all 0 except for $t_{b,j,l,p'} = 1$ , where $l = \\left\\lfloor \\frac{T_j \\mod (\\Delta M_t)}{\\Delta} \\right\\rfloor$ , $T_{j}$ is the timestamp value, and $p'$ is the pixel where the timestamps was detected. Using this representation we can write $H_{b}$ as follows:", + "bbox": [ + 496, + 439, + 892, + 604 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {H} _ {b} = \\sum_ {j = 0} ^ {J - 1} \\boldsymbol {t} _ {b, j}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 612, + 890, + 655 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$H_{b}$ can be compressed in an online fashion through the linear projection of each timestamp tensor; expressed as the inner product with $K$ pre-designed coding tensors, $\\mathbf{C}_k$ , with dimensions $M_t\\times M_r\\times M_c$ , as in Fig. 2. Mathematically,", + "bbox": [ + 496, + 661, + 890, + 722 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {Y} _ {b, k} = \\mathbf {C} _ {k} \\cdot \\boldsymbol {H} _ {b} = \\sum_ {j = 0} ^ {J - 1} \\mathbf {C} _ {k} \\cdot \\boldsymbol {t} _ {b, j} = \\sum_ {j = 0} ^ {J - 1} \\mathbf {C} _ {k, l, \\boldsymbol {p} ^ {\\prime}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 727, + 890, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\cdot$ denotes element-wise multiplication, and $l$ and $\\pmb{p}^{\\prime}$ are the indices where $\\pmb{t}_{b,j,l,\\pmb{p}^{\\prime}} = 1$ . We define $\\widehat{\\mathbf{Y}}_b = (\\widehat{Y}_{b,k})_{k=0}^{K-1}$ as the compressive histogram of $\\pmb{H}_b$ . Compressive histograms, as defined in [13, 36], are a special case of Eq. 4 where $\\mathbf{C}$ compresses individual histograms and disregards spatial information (i.e., $M_t = N_t$ , $M_r = 1$ , $M_c = 1$ ). Note that each timestamp in Eq. 4 is processed efficiently on-the-fly after each photon detection through a simple lookup", + "bbox": [ + 496, + 777, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10758", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "operation. Moreover, individual histogram blocks or timestamps are never explicitly stored or transferred off-sensor.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Practical Coding Tensor Design", + "text_level": 1, + "bbox": [ + 76, + 128, + 357, + 145 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compressive histograms, when implemented as in Eq. 4, introduce an in-sensor memory overhead because, in addition to storing $\\widehat{\\mathbf{Y}}_b$ , $\\mathbf{C}$ needs to be stored in-sensor for efficient lookup operations. Therefore, a practical compressive single-photon camera implementation would rely on parameter-efficient coding tensors that minimize this overhead. Here, we present two strategies to design practical coding tensors that are evaluated in Sec. 6.", + "bbox": [ + 75, + 152, + 468, + 271 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The memory overhead makes certain coding tensor designs impractical. Consider a set of coding tensors that operate on the full histogram tensor, i.e., $\\pmb{H}_b = \\pmb{H}$ . In this case, the number of elements in $\\mathbf{C}$ will exceed the number of elements of $\\pmb{H}$ . Consequently, although the data rates are reduced in this scenario since $K < (N_t \\cdot N_r \\cdot N_c)$ , the insensor memory required exceeds the size of the histogram tensor. To circumvent this issue, we propose two complementary strategies to design lightweight coding tensors: local block-based and separable.", + "bbox": [ + 75, + 272, + 468, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Local Block-based Coding Tensors: As we reduce the size of the histogram block, $H_{b}$ , represented by a compressive histogram, the size of the coding tensors decreases. Therefore, compressing local histogram blocks is not only beneficial due to local spatio-temporal redundancies, but also because these local coding tensors have fewer parameters. One example of local block-based coding tensors are the ones used in temporal compressive histograms [13, 36] where $H_{b}$ is a per-pixel histogram.", + "bbox": [ + 75, + 422, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Separable Coding Tensors: One approach to designing lightweight coding tensors is to make them separable along the temporal and spatial dimensions. This approach is used in parameter-efficient CNN models that use separable depth-wise convolutional layers [17] to reduce model size. Formally, we can write a separable coding tensor as the outer product of two smaller tensors:", + "bbox": [ + 75, + 561, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} _ {k} = \\mathbf {C} _ {k} ^ {\\text {t e m p o r a l}} \\otimes \\mathbf {C} _ {k} ^ {\\text {s p a t i a l}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 674, + 468, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{C}_k^{\\mathrm{temporal}}$ is a $M_t\\times 1\\times 1$ tensor, and $\\mathbf{C}_k^{\\mathrm{spatial}}$ is a $1\\times M_r\\times M_c$ tensor. This design is also motivated by the differences between the temporal and spatial correlations encountered in histogram blocks. In addition to local correlations present in both dimensions, the temporal dimension also exhibits long-range correlations due to the background illumination offset ( $\\Phi_p^{\\mathrm{bkg}}$ ) in every histogram bin. Therefore, Eq. 5 may be able to represent this prior by encoding the temporal and spatial information independently.", + "bbox": [ + 75, + 704, + 468, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One assumption made in our memory overhead analysis is that a compressive SPAD-based 3D camera only needs to store a single $\\mathbf{C}$ that is shared across the full sensor, which can be implemented in two general ways. One approach", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(a) Compressive Histogram Encoding", + "bbox": [ + 509, + 93, + 792, + 106 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c2bba31eee76afb3167d1320314952ba3a71f8787afa493aae6dde99cb0fcd4a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 108, + 888, + 209 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(b) Compressive Histogram Decoding", + "bbox": [ + 509, + 212, + 792, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/405e3bd80fef08f7449db58138a71fe29574ed8303f506fd8f8aabfdad9a9104.jpg", + "image_caption": [ + "Figure 3. Convolutional Compressive Histogram Layer. (a) Building a compressive histogram for each block in the histogram tensor, can be viewed as applying $K$ stripped convolutional filters whose weights are the coding tensors. The compressed histogram tensor will be $K\\frac{N_t}{M_t}\\times \\frac{N_r}{M_r}\\times \\frac{N_c}{M_c}$ tensors. (b) To lift the compressed histogram tensor back to its original domain an unfiltered backprojection operation can be applied on each compressive histogram which decodes a single block. The decoded histogram tensor can then be assembled by concatenating all the decoded blocks." + ], + "image_footnote": [], + "bbox": [ + 511, + 227, + 887, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "could distribute $\\mathbf{C}$ across the local memory of all pixels and then allow communication across pixels as in PPAs [6]. A second approach could store $\\mathbf{C}$ in a global memory that can be accessed by all pixels which could be enabled in 3D-stacked SPAD cameras [44]. Finally, some of the coding tensor designs explored in this paper have as few as 640 parameters. In this case, even if $\\mathbf{C}$ is stored for every $4 \\times 4$ group of pixels, the in-sensor memory is still reduced by $20 \\times$ compared to storing a 1024 bin per-pixel histogram.", + "bbox": [ + 496, + 465, + 890, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Convolutional Compressive Histogram Layer", + "text_level": 1, + "bbox": [ + 500, + 613, + 883, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A compressive histogram is built for each histogram block. Therefore, multiple compressive histograms are used to encode the complete histogram tensor. In this way, the coding tensors can be viewed as a set of 3D convolutional filters, which can be implemented as the first layer of a 3D CNN. For simplicity, we assume that histogram blocks do not overlap, and therefore, the stride of the convolutional filters will equal their dimensions. Fig. 3(a) illustrates this convolutional compressive histogram encoding.", + "bbox": [ + 496, + 638, + 890, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unfortunately, the compressed histogram tensor representation is not directly compatible with 3D CNNs that have been designed for SPAD-based 3D imaging (e.g., [32, 21]). To this end, each compressive histogram is lifted back to the original 3D domain through an unfiltered backprojection:", + "bbox": [ + 496, + 773, + 890, + 848 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\boldsymbol {H}} _ {b} = \\sum_ {k = 0} ^ {K - 1} \\mathbf {C} _ {k} \\widehat {Y} _ {b, k}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 861, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10759", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $\\widehat{H}_b$ is the decoded compressive histogram for block $b$ , which is the weighted linear combination of the coding tensors. The decoded histogram blocks are then concatenated and given as input to the processing 3D CNN. Fig. 3(b) illustrates this decoding step. The decoding step in Eq. 6 will occur off-sensor, after the compressive histograms have been moved to the camera compute module which has access to larger memory and computational resources than sensor module. One benefit of using the unfiltered backprojection as the upsampling operator is that if all coding tensors are mutually orthogonal, in the limit when $K$ approaches the size of $H_b$ (i.e., no compression), then $\\widehat{H}_b \\approx H_b$ . This suggests that at compression rates close to unity, an appropriately trained compressive histogram layer should be approximately equal to an identity transformation applied to $H_b$ .", + "bbox": [ + 76, + 89, + 472, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To summarize, a compressive histogram layer comprises an encoding/compression step followed by a decoding step, which uses the coding tensors as the convolutional filters. This layer can be appended to the beginning of any CNN that has been designed to process 3D histogram tensors. Finally, the coding tensors can be jointly optimized with the downstream CNN in an end-to-end manner.", + "bbox": [ + 76, + 330, + 470, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Datasets and Implementation", + "text_level": 1, + "bbox": [ + 76, + 449, + 348, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we describe the datasets used for model training and testing, and also provide implementation details for the compressive histogram layer and the 3D CNN used for the experiments.", + "bbox": [ + 76, + 474, + 468, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 546, + 181, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For training, we generate a synthetic SPAD measurement dataset containing different scenes at a wide range of illumination settings. We use a similar synthetic data generation pipeline used in previous learning-based SPAD-based 3D imaging works [21, 32, 40]. Using Eq. 2, SPAD measurements can be simulated given an RGB-D image, the pulse waveform $(h(t))$ , and the average number of detected signal and background photons per pixel. Please refer to the supplement for a detailed overview of the simulation pipeline.", + "bbox": [ + 76, + 569, + 468, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Simulated Training Dataset: We use the RGB-D images from the NYU v2 dataset [38]. The simulated histograms have $N_{t} = 1024$ bins and a $\\Delta = 80$ ps bin size (12.3m depth range). The pulse waveform used has a full-width half maximum (FWHM) of 400ps obtained from [21]. For each scene, we randomly set the average number of signal and background photons detected per pixel to [2, 5, or 10] and [2, 10, 50], respectively. With appropriate normalization, the models generalize to other photon levels despite being trained on this photon-starved dataset. A total of 16,628 histogram tensors with dimensions $1024 \\times 64 \\times 64$ are simulated and split into a training and a validation set with 13,851 and 2,777 examples, respectively.", + "bbox": [ + 76, + 707, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Simulated Test Dataset: For testing we use 8 RGB-D images from the Middlebury stereo dataset [35]. The simulated histograms have $N_{t} = 1024$ bins and a $\\Delta = 100\\mathrm{ps}$ bin size (15.3m depth range). The pulse waveform used is a Gaussian pulse with an FWHM of 318ps ( $\\sigma = 135\\mathrm{ps}$ ). A total of 128 test histogram tensors are generated by simulating each scene with the following average number of detected signal/background photons: 2/2, 2/5, 2/50, 5/2, 5/10, 5/50, 10/2, 10/10, 10/50, 10/200, 10/500, 10/1000, 50/50, 50/200, 50/500, and 50/1000.", + "bbox": [ + 496, + 90, + 890, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Real-world Experimental Data: To evaluate the generalization of the proposed models, we downloaded raw histogram tensor captured in [21] with a line-scanning SPAD-based 3D camera prototype. Please refer to the supplementary document for details on this dataset.", + "bbox": [ + 496, + 242, + 890, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Training and Implementation", + "text_level": 1, + "bbox": [ + 500, + 325, + 764, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To simplify training, the input to all models is a 3D histogram tensor, even though compressive histograms can work directly on streams of photon timestamps (Eq. 4).", + "bbox": [ + 496, + 348, + 890, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compressive Histogram Layer: The encoder is implemented as a 3D convolution with a stride equal to the filter size, whose learned filters are the coding tensors, $\\mathbf{C}_k$ . We constraint $\\mathbf{C}_k$ to be zero-mean along the time dimension. The unfiltered backprojection decoder is implemented as a 3D transposed convolution with a stride equal to its filter size. To help the CNN model generalize to different photon count levels we apply zero-normalization along the channel dimension (i.e., $K$ ) to the inputs $(\\widehat{\\mathbf{Y}}_b)$ and the weights ( $\\mathbf{C}$ ) of the transposed convolution, also known as layer-norm [5]. This normalization is also commonly used in depth decoding algorithms [14, 13, 26].", + "bbox": [ + 496, + 396, + 892, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth Estimation 3D CNN: To estimate depths from the decoded histogram tensor we use the 3D deep boosting CNN model proposed by [32] for single-photon 3D imaging, without the non-local block. Similar to [21, 32] we use the pixel-wise KL-divergence between the output histogram tensor and a normalized true histogram tensor as our objective, and estimate depths using a softargmax.", + "bbox": [ + 496, + 578, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training: At each training iteration we randomly sample patches of size $1024 \\times 32 \\times 32$ . We train all models using the ADAM optimizer [19] with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ , batch size of 4, and a learning rate of 0.001 that decays by 0.9 after every epoch. We train all models for 30 epochs with periodical checkpoints, and for a given model we choose the checkpoint that achieves the lowest root mean squared error (RMSE) on the validation set.", + "bbox": [ + 496, + 685, + 890, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Experiments and Results", + "text_level": 1, + "bbox": [ + 500, + 816, + 735, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present the performance at various compression levels for different coding tensor designs jointly optimized with the depth estimation CNN described in Sec. 5. A coding tensor design is determined by the", + "bbox": [ + 496, + 840, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10760", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/aebcfa17b70af6abf98e05ac51128e01b34278264fbc3e4150e2841b7427cf8c.jpg", + "image_caption": [ + "Compression vs. Mean Absolute Error (mm)" + ], + "image_footnote": [], + "bbox": [ + 81, + 104, + 475, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a3e2bc1e72a74c6e5abdc63d240035a42c4e3b6f18f5b2f940850268f9c429fb.jpg", + "image_caption": [ + "Figure 4. Compression vs. Test Set Metrics. The two left-most plots show the mean absolute error computed over the test set as we increase compression. Similarly, the two right-most plots show the mean percent of pixels whose absolute depth errors were $< 10\\mathrm{mm}$ . The simulated test set images were divided into low (SBR $\\leq 0.1$ ) and high (SBR $>0.1$ ) SBR groups to be able to disentangle the impact of SBR on the performance of each model. The dashed lines show the peak and no compression baselines whose compression levels do not vary. Each line corresponds to a fixed coding tensor design for which we vary $K$ to control the compression level. Moreover, each point for a given compression level corresponds to a single set of coding tensors jointly optimized with the depth estimation 3D CNN." + ], + "image_footnote": [], + "bbox": [ + 86, + 226, + 885, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8e06c1940d217b41f4fd313955fdb8048859ec5195721267c9b6b5256b0e6b74.jpg", + "image_caption": [ + "Compression vs. Percent Pixels with Errors $< 10\\mathrm{mm}$" + ], + "image_footnote": [], + "bbox": [ + 488, + 104, + 890, + 226 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "dimensions of $\\mathbf{C}_k$ (i.e., $M_t \\times M_r \\times M_c$ ), the size of the compressive histogram (i.e., $K$ ), and if $\\mathbf{C}_k$ is separable.", + "bbox": [ + 75, + 359, + 468, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Baselines and Performance Metrics", + "text_level": 1, + "bbox": [ + 76, + 401, + 385, + 416 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare against the following baselines:", + "bbox": [ + 94, + 425, + 392, + 440 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Temporal Truncated Fourier C [36, 13]: A compressive histogram that uses coding tensors with dimensions $1024 \\times 1 \\times 1$ and whose weights are set using the first $K / 2$ frequencies of the Fourier matrix. In the supplement, we compare against additional Fourier-based C [13].", + "- Temporal Coarse Histogram C: Here C is a box down-sampling operator along the temporal dimensions which produces a coarse histogram with $K$ bins.", + "- No Compression Oracle: In this baseline, we assume the ideal scenario where the histogram tensor is transferred off-sensor and processed with the depth estimation 3D CNN. Similar to [32], we train this model with an initial learning rate of $10^{-4}$ and total variation regularization.", + "- Peak Compression Oracle: This baseline implements an ideal SPAD camera with sufficient in-sensor memory to store the histogram tensor and sufficient computation power to compute per-pixel depths through an \"argmax\" along the time axis. To process the noisy 2D depth images with the 3D CNN, we generate a 3D grid where all elements are zero except for one element per spatial location whose index is proportional to the depth. This model is trained like the no-compression oracle." + ], + "bbox": [ + 76, + 443, + 468, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Similar to our proposed approach, all compressive histogram baselines described here, implemented their C as a compressive histogram layer, with fixed weights, whose outputs are processed by the depth estimation 3D CNN.", + "bbox": [ + 75, + 791, + 468, + 851 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics: The 3D imaging performance of each model is summarized using two metrics: (1) the mean absolute depth error (MAE), (2) and the percent of pixels with", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "absolute depth errors that are lower than $10\\mathrm{mm}$ . To understand the performance under these metrics we divide the test set into different SBR ranges and report the metrics for each range individually. We also visualize the overall dataset performance as scatter plots (e.g., Fig. 7) where each point shows the MAE for a given test scene and their color hue represents the mean SBR of the scene. Outliers with an MAE larger than $50\\mathrm{mm}$ are not visible in the plot, however, they are included in the calculation of the statistics. Finally, when comparing different compressive histogram strategies the compression ratio is fixed. The compression ratio (CR) is the ratio of the block size and the length of the compressive histogram (i.e., $\\mathrm{CR} = (M_t \\cdot M_r \\cdot M_c) / K$ ).", + "bbox": [ + 496, + 359, + 890, + 553 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.2.3D Imaging Performance", + "text_level": 1, + "bbox": [ + 500, + 560, + 730, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compression vs. Performance: Fig. 4 shows the performance of compressive histograms as a function of the compression ratio. The learned coding tensors consistently outperform the temporal Fourier-based C. At low SBR and $\\mathrm{CR} > 100$ , it becomes essential for the learned coding tensors to utilize spatio-temporal information (i.e., green and red lines). Moreover, the proposed models can outperform the peak compression oracle for $\\mathrm{CR} \\leq 64$ . Overall, learned spatio-temporal coding tensors provide robust performance that degrades gracefully as compression increases.", + "bbox": [ + 496, + 585, + 890, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Importance of Learned Coding Tensors: Fig. 5 compares the depth reconstructions of compressive histograms with coding tensors that were optimized (ours) against coding tensors that were fixed and not optimized throughout training. The extreme quantization in coarse histograms causes large systematic depth errors. Random unoptimized coding tensors consistently produce lower-quality depth reconstructions. A well-designed coding tensor based on Fourier codes can produce reasonable depth reconstructions at $64\\mathrm{x}$ compression, however, at $128\\mathrm{x}$ compression, scene details become blurred. The proposed learned coding tensors are", + "bbox": [ + 496, + 737, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10761", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1acdcfb5f9ed672dbfd42a85440f83f4509dc395363474fa4d291bdca5e68a9b.jpg", + "image_caption": [ + "Figure 5. Importance of Learned Coding Tensors. Depth reconstructions at $64\\mathrm{x}$ (top) and $128\\mathrm{x}$ (bottom) compression for compressive histogram models whose coding tensors were hand-designed (coarse histogram and Fourier-based), learned (proposed), and not learned (randomly initialized). The simulated scene had an $\\mathrm{SBR} = 0.1$ , where the mean signal and background photon levels were [50, 500]." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 890, + 281 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/37ae801c01dea273e49d3fed2244e0ce80bdeac1a0db27554c5a349df13531ae.jpg", + "image_caption": [ + "Figure 6. What if we could compute depths in-pixel? Depth reconstructions at high and low SBR with mean signal and background photon levels of [10, 10] and [10, 1000], respectively. The compressive histograms have a compression of 64." + ], + "image_footnote": [], + "bbox": [ + 81, + 335, + 465, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "able to generate high-quality reconstructions comparable to the no-compression oracle. Overall, optimizing the coding tensors can provide non-trivial performance gains.", + "bbox": [ + 75, + 550, + 468, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "What if we could compute depths in-pixel? Fig. 6 compares the depth reconstruction quality of two learned coding tensors at $64\\mathrm{x}$ compression with the peak compression oracle described in Sec. 6.1. At high SBR, all methods recover the fine and coarse scene details. At low SBR the peak compression oracle fails to reconstruct high-level scene structures such as the rings in the red box, while the learned coding tensors better preserve these coarse and fine details.", + "bbox": [ + 75, + 598, + 468, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3. Exploring the Coding Tensor Design Space", + "text_level": 1, + "bbox": [ + 76, + 724, + 441, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "When does spatio-temporal coding help? Fig. 7 shows the effect of increasing the spatial dimension of C, at 64x compression. At high SBR, all methods have similar MAE, but, coding tensors with smaller spatial dimensions better preserve fine details (e.g., sticks). On the other hand, at low SBR, coding tensors with larger spatial dimensions preserve high-level details such as the pot handle. This difference is also observed in the scatter plot where the mean and median of the $256 \\times 1 \\times 1$ C do not match which indicates multiple low SBR scenes with high MAE.", + "bbox": [ + 75, + 752, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3e7aec92c344bb8012c473390d45fe8e4b9b688400bd7eb00a13752daa8a3c95.jpg", + "image_caption": [ + "Figure 7. When do spatio-temporal coding tensors help? Each scatter plot point corresponds to the MAE of a test scene. The images directly below each model correspond to the depth reconstructions for two test examples at high and low SBR levels whose mean signal and background photons per pixel are [10, 10] and [10, 1000], respectively. For a fixed compression level, the spatial block size of each model is increased from left to right and $K$ is adjusted to maintain the same compression level. The coding tensors for all models in this plot are learned and separable." + ], + "image_footnote": [], + "bbox": [ + 506, + 337, + 890, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "How does reducing the size of C affect performance? Fig. 8 shows the effect of reducing the size of C at $128\\mathrm{x}$ compression. The coding tensors size is reduced by training models with separable coding tensors that operate on smaller histogram blocks. The performance difference between full and separable coding tensors $(1024\\times 4\\times 4)$ is negligible. As we further reduce the number of parameters in C, the overall performance degrades. Coding tensors with fewer parameters that operate on smaller histogram blocks tend to produce blurrier reconstructions. This can be observed in the red box where the coding tensors with less than 10,000 parameters blurs the spikes. Nonetheless, as discussed in Sec. 4.1, a parameter-efficient C is desirable due to the limited in-sensor memory. Ultimately, a practical", + "bbox": [ + 496, + 693, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10762", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/820f2c20befd626ed26778c03e802af27661f9b8991e64cdd54e7da08f3753f8.jpg", + "image_caption": [ + "Figure 8. How does Reducing Size of C Affect Performance?. Each scatter plot point corresponds to the MAE of a test scene. The images directly below each model correspond to the depth reconstructions for two test scenes at high and low SBR levels whose mean signal and background photons per pixel are [10, 10] and [10, 1000], respectively. The size of C is reduced from left to right by making it separable or reducing the $M_{t}$ ." + ], + "image_footnote": [], + "bbox": [ + 83, + 92, + 467, + 303 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "compressive SPAD-based 3D camera design requires determining the trade-off between parameter efficiency and 3D imaging quality, which may depend on the application.", + "bbox": [ + 75, + 417, + 468, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.4. Evaluation on Real-world Data", + "text_level": 1, + "bbox": [ + 76, + 473, + 352, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 9 shows the depth reconstructions at $256\\mathrm{x}$ compression of multiple compressive histograms and the no compression baseline on the real-world experimental data from [21]. In low SBR scenes, such as the outdoor capture of the ball falling down stairs (first row), Truncated Fourier blurs the staircase edges, while the learned spatio-temporal C preserved these details. Compared to the no compression oracle, compressive histogram models produce less smooth depth images with some small artifacts. This suggests that the compressive histogram models could benefit from a spatial regularizer such as the one used when training the no compression oracle. Additional results and details on this evaluation are available in the supplement.", + "bbox": [ + 75, + 496, + 470, + 690 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.5. On-chip Implementation and Power Analysis", + "text_level": 1, + "bbox": [ + 76, + 699, + 459, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To validate the feasibility of compressive histograms, we implement them on the UltraPhase chip which has a $3 \\times 6$ processor core array [4]. At this time, UltraPhase has not been 3D stacked on a SPAD sensor, thus we only evaluate its compute and data readout power consumption. Fig. 10 shows the power dissipated by UltraPhase when processing photon timestamps with different methods and transferring data off-sensor. Although compressive histograms dissipate more power on computation (blue), this is less than $0.3\\%$ of the overall power consumption, which is dominated by data readout. Due to limited memory in UltraPhase (4096 bits per core), our method learns $\\mathbf{C}^{\\mathrm{spatial}}$ and uses Fourier codes", + "bbox": [ + 75, + 722, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ec85109e03b0c08584b6f8ee8fa8cca029a09e73d3a013edeca40d0f6f79490a.jpg", + "image_caption": [ + "Figure 9. Depth Reconstructions of Real-world SPAD Data at $256\\mathrm{x}$ Compression. Depth reconstructions of different scenes captured with a SPAD-based 3D camera prototype [21]." + ], + "image_footnote": [], + "bbox": [ + 504, + 92, + 890, + 287 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a99aad7ded3d12d585c2eed772a438c9d8fd9325417498c04cfb9160352afd10.jpg", + "image_caption": [ + "Figure 10. Compute vs. Data Readout Power. Average power dissipated by $2 \\times 2$ SPADs processing 500 timestamps per depth frame and operating at 30 depth frames per second. Compute power is obtained from the implementation on the UltraPhase SPAD processors [4]. Readout power is estimated from the output data rate assuming the readout scheme of the SwissSPAD2 [42]. Coarse histograms use 8-bit precision, while compressive histograms use 16-bit precision. Note the difference in blue and orange scales." + ], + "image_footnote": [], + "bbox": [ + 506, + 351, + 887, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "for $\\mathbf{C}^{\\mathrm{temporal}}$ due to their memory efficient implementation. We also quantize $\\mathbf{C}$ to 8 bits and find no degradation in performance. Refer to the supplement for additional details.", + "bbox": [ + 498, + 575, + 890, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Discussion", + "text_level": 1, + "bbox": [ + 500, + 633, + 612, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SPAD-based 3D cameras encounter a data bottleneck between the SPAD array and the compute module when transferring the photon timestamps. A histogram tensor can help summarize timestamps at low resolutions, but as megapixel SPAD arrays become available, histogram tensors also lead to a data bottleneck. To overcome this limitation we proposed compressive histograms as a compact representation that can be built on-the-fly, as each photon is detected. As a consequence, compressive histograms can reduce the insensor memory and data rates because neither the photon data stream nor a histogram tensor needs to be stored or transferred. Our results show that high-quality depth information can be recovered from a learnt compressive histogram representation that is up to 2 orders of magnitude smaller than a histogram tensor representation.", + "bbox": [ + 496, + 659, + 890, + 882 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Practical compressive histogram operating points: The", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10763", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "learned separable $256 \\times 4 \\times 4$ and $256 \\times 2 \\times 2$ C, achieved a good balance between parameter efficiency vs. reconstruction quality, and require on the order of 10-100kbits of memory. In an UltraPhase-like chip this would require distributing C among at least 8x8 cores (4kbits per core). If the temporal dimension is fixed to Fourier-based Ctemporal such as the ones from [13, 36], the number of parameters can be reduced by 10-40x (see Suppl. Sec. 3.3) which enables storing C on a per-pixel basis and made the Ultra-Phase evaluation possible. Overall, for a 1MP SPAD sensor with 1000 bins per-pixel, compressive histograms that can provide more than 50x compression would result in practical data rates of $\\sim 0.6\\mathrm{GB/s}$ which USB 3.2 can support.", + "bbox": [ + 75, + 90, + 472, + 282 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Trade-off space: Compressive histograms establish a trade-off between reconstruction fidelity, data bandwidth, and in-sensor compute and memory resources. For a fixed bandwidth, a coarse histogram requires arguably the lowest in-sensor resources but leads to poor reconstructions. Fourier-based histograms can improve reconstruction fidelity, at the expense of increased in-sensor computation and memory. The proposed generalization of compressive histograms allows further increasing reconstruction accuracy, at the expense of additional in-sensor memory over Fourier-based methods. Ultimately, the correct trade-off for a given scenario will be determined by power, application, and hardware constraints.", + "bbox": [ + 75, + 287, + 472, + 479 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Although compressive histograms require more insensor computation than coarse histograms, our method presents a practical solution from a power consumption and a real-time application perspective. Power consumption is primarily determined by data rates. Fig. 10 and Suppl. Fig. 4 shows that despite compressive histograms dissipating $100\\mathrm{x}$ more processing power than coarse histograms, their overall power consumption is still lower even when data rates are only reduced by $2\\mathrm{x}$ . The processing time for building compressive histograms is $\\sim 0.5\\mathrm{ms}$ (Suppl. Fig. 5). From a real-time (i.e., 30 FPS) or a high-speed application standpoint, this additional processing time is nearly negligible since it is overlapped with acquisition/exposure time.", + "bbox": [ + 75, + 481, + 472, + 672 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "From a hardware perspective, the importance of reducing the memory overhead of $\\mathbf{C}$ depends on resolution. In low-resolution SPAD cameras, memory-efficient $\\mathbf{C}$ are essential because they are stored among a single or a few pixels. The proposed method allowed integrating memory-efficient Fourier codes with learned spatial codes, which were implemented on the 2x2 pixels of UltraPhase (Suppl. Sec. 2). As resolution increases and $\\mathbf{C}$ is shared among more pixels, the memory overhead reduces, and less parameter-efficient $\\mathbf{C}$ with increased reconstruction fidelity can be considered.", + "bbox": [ + 75, + 674, + 472, + 823 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Bias in Learned C: In the supplement, we show that coding tensors with $M_{t} = N_{t}$ develop a depth range bias. These coding tensors learn to zero out photons coming from distances that are less common in the dataset since they are usually background/noise photons. Interestingly, learned", + "bbox": [ + 75, + 825, + 472, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "coding tensors with $M_t < N_t$ avoid this bias and generalize to depths that are less common in the training set.", + "bbox": [ + 496, + 90, + 890, + 121 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Generalization: There are multiple generalization axes including signal and ambient light levels, sensor and laser parameters (e.g., resolution, pulse waveform), and scene response complexity (e.g., depth range, indirect reflections). Our evaluation has probed some of them. Specifically, our training set only included a subset of the signal and ambient light levels that the test set contained. Furthermore, the model was trained and tested on histogram tensors with different resolutions. Finally, the dataset bias investigation showed that models with $N_{t} \\leq 256$ generalized well to less prevalent depths during training (Suppl. Sec. 1).", + "bbox": [ + 496, + 128, + 890, + 291 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We further discuss the model's ability to generalize in other scenarios. For instance, all learned models (including baselines) are unlikely to generalize well to wider laser pulses, because if the model is trained with a narrow pulse width, it learns to extract signal information from high frequencies which will only contain noise in the wider pulse. Similarly, these learned models may generalize to narrower pulse widths. Furthermore, we anticipate a learned C with the properties described in [13] to be robust to diffuse indirect reflections but may require data augmentation to generalize to other light transport scenarios.", + "bbox": [ + 496, + 292, + 890, + 455 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Why not compute depths in-sensor? SPAD-based 3D cameras with large in-pixel memory could store per-pixel histograms and reduce data rates by computing depths in-pixel (i.e., peak compression oracle). Our results show that compressive histogram can provide similar reconstruction quality and outperform this method at low SBR without requiring the storage of the full histogram tensor in-sensor.", + "bbox": [ + 496, + 462, + 890, + 568 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Additional Coding Tensor Designs: Although we find promising empirical results for the coding tensor representations described in this paper, the optimal set of coding tensors will depend on the exact hardware specifications (e.g., in-pixel memory, system bandwidth) and scene-dependent parameters (e.g., SBR, geometry, albedo). Additional lightweight C designs could rely on other factorization techniques and weight quantization.", + "bbox": [ + 496, + 574, + 890, + 694 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Task-specific Compressive Histograms: Histogram tensors are used in other active single-photon imaging modalities such as fluorescence lifetime microscopy [34], nonline-of-sight [10, 23, 29], and diffuse optical tomography [22, 45, 24]. Our framework could be used to find compressive representations optimized for these applications.", + "bbox": [ + 496, + 700, + 890, + 790 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments: This work was supported by the Department of Energy and National Nuclear Security Administration (DE-NA0003921), Air Force (FA9550-21-1-0341), Swiss National Science Foundation (200021_166289), and NSF Awards 1846884 (A.V.), 1943149 (M.G.), 2107060 (M.G.), 2138471 (A.I.). 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Luminance-depth reconstruction from compressed time-of-flight histograms. IEEE Transactions on Computational Imaging, 8:148-161, 2022. 2", + "[34] Kayvan Samimi, Danielle E Desa, Wei Lin, Kurt Weiss, Joe Li, Jan Huisken, Veronika Miskolci, Anna Huttenlocher, Jenu V Chacko, Andreas Velten, et al. Light sheet autofluorescence lifetime imaging with a single photon avalanche diode array. bioRxiv, pages 2023-02, 2023. 9", + "[35] Daniel Scharstein and Chris Pal. Learning conditional random fields for stereo. In 2007 IEEE Conference on Computer Vision and Pattern Recognition, pages 1-8. IEEE, 2007. 5", + "[36] Michael P. Sheehan, Julián Tachella, and Mike E. Davies. A sketching framework for reduced data transfer in photon counting lidar. IEEE Transactions on Computational Imaging, 7:989-1004, 2021. 2, 3, 4, 6, 9", + "[37] Michael P Sheehan, Julián Tachella, and Mike E Davies. Surface detection for sketched single photon lidar. arXiv preprint arXiv:2105.06920, 2021. 2", + "[38] Nathan Silberman, Derek Hoiem, Pushmeet Kohli, and Rob Fergus. Indoor segmentation and support inference from rgbd images. In European conference on computer vision, pages 746-760. Springer, 2012. 5", + "[39] Haley M So, Julien NP Martel, Piotr Dudek, and Gordon Wetzstein. Mantissacam: Learning snapshot high-dynamic-range imaging with perceptually-based in-pixel irradiance encoding. arXiv preprint arXiv:2112.05221, 2021. 2", + "[40] Zhanghao Sun, David B Lindell, Olav Solgaard, and Gordon Wetzstein. Spadnet: deep rgb-spad sensor fusion assisted by monocular depth estimation. Optics express, 28(10):14948-14962, 2020. 5" + ], + "bbox": [ + 78, + 90, + 470, + 898 + ], + "page_idx": 10 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[41] Julián Tachella, Michael P Sheehan, and Mike E Davies. Sketched rt3d: How to reconstruct billions of photons per second. In ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1566-1570. IEEE, 2022. 2", + "[42] Arin Can Ulku, Claudio Bruschini, Ivan Michel Antolović, Yung Kuo, Rinet Ankri, Shimon Weiss, Xavier Michalet, and Edoardo Charbon. A $512 \\times 512$ spad image sensor with integrated gating for widefield film. IEEE Journal of Selected Topics in Quantum Electronics, 25(1):1-12, 2018. 8", + "[43] Edwin Vargas, Julien NP Martel, Gordon Wetzstein, and Henry Arguello. Time-multiplexed coded aperture imaging: Learned coded aperture and pixel exposures for compressive imaging systems. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2692-2702, 2021. 2", + "[44] Chao Zhang, Ning Zhang, Zhijie Ma, Letian Wang, Yu Qin, Jieyang Jia, and Kai Zang. A $240 \\times 160$ 3d-stacked spad dtof image sensor with rolling shutter and in-pixel histogram for mobile devices. IEEE Open Journal of the Solid-State Circuits Society, 2:3-11, 2021. 4", + "[45] Yongyi Zhao, Ankit Raghuram, Hyun Kim, Andreas Hielscher, Jacob T Robinson, and Ashok Narayanan Veeraraghavan. High resolution, deep imaging using confocal time-of-flight diffuse optical tomography. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021. 9" + ], + "bbox": [ + 501, + 90, + 892, + 460 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10766", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_model.json b/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_model.json new file mode 100644 index 0000000000000000000000000000000000000000..13dad8ef5b75f255efae757dd4bfef193a7d72aa --- /dev/null +++ b/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_model.json @@ -0,0 +1,2224 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.048 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.137, + 0.131, + 0.834, + 0.153 + ], + "angle": 0, + "content": "Learned Compressive Representations for Single-Photon 3D Imaging" + }, + { + "type": "text", + "bbox": [ + 0.103, + 0.157, + 0.868, + 0.192 + ], + "angle": 0, + "content": "Felipe Gutierrez-Barragan\\(^{1\\ddagger}\\), Fangzhou Mu\\(^{1}\\), Andrei Ardelean\\(^{3}\\), Atul Ingle\\(^{2}\\), Claudio Bruschini\\(^{3}\\), Edoardo Charbon\\(^{3}\\), Yin Li\\(^{1}\\), Mohit Gupta\\(^{1}\\), Andreas Velten\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.238, + 0.194, + 0.734, + 0.212 + ], + "angle": 0, + "content": "1University of Wisconsin-Madison, 2Portland State University," + }, + { + "type": "text", + "bbox": [ + 0.307, + 0.212, + 0.658, + 0.23 + ], + "angle": 0, + "content": "\\(^{3}\\)Ecole Polytechnique Federale de Lausanne" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.255, + 0.314, + 0.271 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.474, + 0.629 + ], + "angle": 0, + "content": "Single-photon 3D cameras can record the time-of-arrival of billions of photons per second with picosecond accuracy. One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that encodes distances along the time axis. As the spatio-temporal resolution of the histogram tensor increases, the in-pixel memory requirements and output data rates can quickly become impractical. To overcome this limitation, we propose a family of linear compressive representations of histogram tensors that can be computed efficiently, in an online fashion, as a matrix operation. We design practical lightweight compressive representations that are amenable to an in-pixel implementation and consider the spatio-temporal information of each timestamp. Furthermore, we implement our proposed framework as the first layer of a neural network, which enables the joint end-to-end optimization of the compressive representations and a downstream SPAD data processing model. We find that a well-designed compressive representation can reduce in-sensor memory and data rates up to 2 orders of magnitude without significantly reducing 3D imaging quality. Finally, we analyze the power consumption implications through an on-chip implementation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.658, + 0.21, + 0.673 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.47, + 0.877 + ], + "angle": 0, + "content": "3D cameras based on single-photon avalanche diode technology (SPAD) are becoming increasingly popular for a wide range of applications that require high-resolution and low-power depth sensing, ranging from autonomous vehicles [1] to consumer smartphones [2]. Kilo-to-megapixel resolution SPAD pixel arrays [27, 28] have the capability of capturing the time-of-arrival of billions of individual photons per frame with extremely high (picosecond) time resolution [31]. Unfortunately, this extreme sensitivity and high speed comes at a cost — the raw timestamp data causes a severe bottleneck between the image sensor and the image signal processor (ISP) that processes this data (Fig. 1(a)). This data bottleneck severely limits the wider use of high-" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.258, + 0.862, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.364, + 0.85, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.467, + 0.893, + 0.576 + ], + "angle": 0, + "content": "Figure 1. Resolving SPAD data bottleneck with learned compression. (a) Conventional SPAD-based 3D cameras stream raw photon timestamps or summary histograms off the image sensor which causes a data bottleneck between the image sensor and the on-camera image and signal processing (ISP) module. (b) Our method applies a lightweight, on-sensor compressive coding scheme to the photon timestamp data which is later decoded at the ISP, resolving the data bandwidth limitation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.587, + 0.84, + 0.602 + ], + "angle": 0, + "content": "resolution SPAD arrays in 3D sensing applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.893, + 0.781 + ], + "angle": 0, + "content": "One common approach to avoid transferring individual photon timestamps is to build a histogram in each pixel. This results in a 3D histogram tensor that is transferred off-sensor for processing. Although this may be practical at low spatio-temporal resolutions (e.g., \\(64 \\times 32\\) pixels with 16 time bins [15]), it requires higher in-sensor memory. Moreover, the data rates of this histogram tensor representation also scale rapidly with the spatio-temporal resolution and maximum depth range. For example, a megapixel SPAD-based 3D camera operating at 30 fps that outputs a histogram tensor with a thousand 8-bit bins per pixel would require an unmanageable data transfer rate of 240 Gbps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.782, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To overcome the above limitations, we seek to design compressive representations of 3D histogram tensors. In order to reduce the data rates output by the SPAD camera, the compact representation needs to be built in-pixel or inside the focal plane array (FPA). This is illustrated in Fig. 1(b). Due to the limited in-pixel memory and compute, the compressive representation needs to be built in a streaming manner, with minimal computations per photon. Photon" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.302, + 0.9 + ], + "angle": 0, + "content": "\\(^{\\ddagger}\\)Email: fgutierrez3@wisc.edu" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10756" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "histogram tensors are very different from conventional RGB images/video data. Therefore, traditional compression algorithms such as MPEG are not directly applicable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.47, + 0.401 + ], + "angle": 0, + "content": "We propose a family of compressive representations for 3D histogram tensors that can be computed in an online fashion with limited memory and compute. They are based on the linear spatio-temporal projection of each photon timestamp, which can be expressed as a simple matrix operation. Instead of constructing per-pixel timestamp histograms, a compressive encoding maps its spatio-temporal information into a compressive histogram. To exploit local spatio-temporal correlations, a single compressive histogram is built for a local 3D histogram block as illustrated in Fig. 2. Instead of building and storing the full 3D histogram tensor in-sensor, multiple compressive histograms are built and transferred off-sensor for processing, effectively reducing the required in-sensor memory and data rates. Recent works proposed a similar compression framework based on compressive histograms [13] or sketches [36]. In Sec. 4, we show that these prior works can be viewed as special cases of our proposed framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.47, + 0.535 + ], + "angle": 0, + "content": "In this paper, we explore the design space of spatiotemporal compressive encodings and analyze the trade-offs between different design choices. Furthermore, we present a method to integrate our compression framework with data-driven SPAD data processing methods using convolutional neural networks (CNNs), which enables end-to-end optimization of the compressive encoding and a SPAD data processing CNN. We demonstrate the feasibility of compressive histograms through an on-chip implementation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.803 + ], + "angle": 0, + "content": "For our experimental evaluation, we integrate the compressive histograms framework with a state-of-the-art learning-based denoising model for SPAD-based 3D imaging [32]. Our results show that the jointly optimized compressive encoding and CNN can consistently reduce data rates up to 2 orders of magnitude in a wide range of signal and noise levels. Moreover, for a given compression level, it can increase 3D imaging accuracy over previous hand-designed compressive histograms that only exploit temporal information [13, 36], especially in low signal-to-background ratio (SBR) scenarios and at higher compression rates. Furthermore, we show that learned compressive histograms can perform comparably and sometimes even outperform a theoretical SPAD sensor design where the full 3D histogram tensor is stored in-sensor and only per-pixel depths are transferred off-sensor. Finally, we analyze the power consumption of a compressive histogram implemented on the UltraPhase SPAD processing chip [4]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.814, + 0.22, + 0.829 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.842, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Compressive histograms, also called sketches, are an emerging framework for online in-sensor compression of SPAD timestamp data [13, 41, 36, 33]. A coarse histogram is one common compressive histogram approach [13] to re" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.27 + ], + "angle": 0, + "content": "duce data rates and in-pixel memory [15, 8, 18]. Despite their practical hardware implementation, coarse histograms achieve sub-optimal depth accuracy compared to compressive histograms based on Fourier [36, 37, 13] and Gray [13] codes. One limitation of these approaches is that the compressive representation only exploits the temporal information of the incident timestamp, and disregards the spatial redundancy. In this work, we generalize the compressive histogram framework to utilize the spatio-temporal information of each timestamp. Moreover, instead of relying on hand-designed coded projections, in this paper we learn them as the first layer of a CNN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.892, + 0.409 + ], + "angle": 0, + "content": "- Shared In-Pixel Histograms: One common design is to have multiple neighboring SPAD pixels have a single shared memory where all timestamps are aggregated into a coarse histogram (e.g., \\(4 \\times 4\\) [18, 15], \\(3 \\times 3\\) [20]). This approach throws away the local spatial information (i.e., pixel location) of the detected photon timestamps. A compressive histogram is well-suited for these shared memory designs because it can be shared among multiple SPAD pixels and preserves spatial information through the coded projection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Neural Sensors and Pixel Processor Arrays: Pixel processor arrays (PPAs) are an emerging sensing technology that embeds processing electronics inside each pixel [9]. This new sensing paradigm begins processing the image at the focal plane array, which allows it to reduce the sensor data rates by transmitting only the relevant information, and consequently, it increases the sensor's throughput [9] which can enable computer vision at 3,000 fps [6, 7]. PPAs have also become building blocks of novel computational imaging systems optimized end-to-end for HDR imaging [25, 39], motion deblurring [30], video compressive sensing [25], and light field imaging [43]. A compressive histogram relies on a similar in-pixel processing paradigm. Similar to previous works, we jointly optimize the sensor parameters (i.e., the compressive histogram) and the processing algorithm (i.e., the CNN), but to our knowledge, this work is the first to use this approach for SPAD data compression." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.836, + 0.699 + ], + "angle": 0, + "content": "3. Single-Photon 3D Histogram Tensors" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.707, + 0.892, + 0.752 + ], + "angle": 0, + "content": "SPAD-based 3D cameras consist of a SPAD sensor and a pulsed laser that illuminates the scene. The photon flux signal arriving at pixel, \\( p \\), can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.764, + 0.892, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\Phi_ {\\boldsymbol {p}} (t) = a _ {\\boldsymbol {p}} h \\left(t - 2 d _ {\\boldsymbol {p}} / c\\right) + \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}} = \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {s i g}} (t) + \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( a_{p} \\) is the amplitude of the returning signal accounting for laser power, reflectivity, and light fall-off; \\( h(t) \\) is the system's impulse response function (IRF) which accounts for pulse waveform and sensor IRF; \\( d_{p} \\) is the distance to the point imaged by \\( p \\); \\( c \\) is the speed of light; and \\( \\Phi_{p}^{\\mathrm{bkg}} \\) is the constant photon flux due to background illumination (e.g., sunlight). This model assumes direct-only reflections" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10757" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.574, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.577, + 0.089, + 0.89, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.281, + 0.893, + 0.351 + ], + "angle": 0, + "content": "Figure 2. Compressive Histogram Formation. Histogram tensors, \\( H \\), are a 3D spatio-temporal grid whose elements store the number of photons that arrived within a short time interval. (a) In SPAD-based 3D imaging, the temporal axis of \\( H \\) encodes distances. (b) A histogram block, \\( H_{b} \\), can be expressed as the sum of \\( J \\) one-hot encoding tensors, where each tensor represents a photon timestamp. (c) A compact representation of \\( H_{b} \\) can be built by applying \\( K \\) linear projections (i.e., dot product) with pre-designed coding tensors. (d) The compressive histogram, will be a vector with \\( K \\) elements whose compression capacity is given by \\( \\frac{M_t \\cdot M_r \\cdot M_c}{K} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.469, + 0.396 + ], + "angle": 0, + "content": "which is a valid approximation, in particular, for scanning-based ToF 3D imaging systems [3]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.469, + 0.456 + ], + "angle": 0, + "content": "TCSPC-based SPAD cameras measure \\(\\Phi_p(t)\\) by building a per-pixel timing histogram, where the \\(i\\)th histogram bin records the number of photons that arrived in a time interval of length \\(\\Delta\\), which follows a Poisson process \\(\\mathcal{P}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.464, + 0.469, + 0.484 + ], + "angle": 0, + "content": "\\[\n\\Phi_ {i, \\boldsymbol {p}} = \\mathcal {P} \\left(\\Phi_ {i, \\boldsymbol {p}} ^ {\\mathrm {s i g}} + \\Delta \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.469, + 0.608 + ], + "angle": 0, + "content": "The pulse repetition period, \\(\\tau\\), determines the maximum timestamp value and the length of the histogram vector \\(\\Phi_p = (\\Phi_{i,p})_{i=0}^{N_t - 1}\\), where \\(N_t = \\tau / \\Delta\\). Therefore, one assumption built into \\(\\Phi_p\\), is that no signal photons had a timestamp larger than \\(\\tau\\), which means that the maximum distance that \\(\\Phi_p\\) can encode is \\(d_{\\max} = \\frac{c\\tau}{2}\\). Furthermore, we assume that pile-up distortions are minimized through various SPAD data acquisition techniques [11, 15, 16, 12]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.469, + 0.82 + ], + "angle": 0, + "content": "This process generates a \\(N_{t} \\times N_{r} \\times N_{c}\\) 3D histogram tensor, \\(\\pmb{H} = (\\Phi_p)_{p=0,0}^{(N_r - 1, N_c - 1)}\\). In challenging 3D imaging scenarios with high background illumination, building \\(\\pmb{H}\\) off-sensor requires transferring thousands of photon timestamps per-pixel leading to data rates of hundreds of GB/s in a megapixel sensor. Moreover, building and storing a high-resolution \\(\\pmb{H}\\) in-sensor would require significant memory (1GB for a megapixel SPAD camera with 1000 time bins per-pixel), and transferring it would continue to lead to impractical data rates of tens of GB/s on a SPAD-based 3D camera operating at 30fps. Overall, a practical SPAD-based 3D camera would build and store a compact representation of \\(\\pmb{H}\\) in-sensor and then transfer it to a processing chip (e.g., FPGA, ISP, embedded computer) where it is processed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.452, + 0.849 + ], + "angle": 0, + "content": "4. Spatio-temporal Compressive Histograms" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.857, + 0.47, + 0.902 + ], + "angle": 0, + "content": "A natural approach to compress \\( \\pmb{H} \\) that exploits its local correlations due to smooth depths and photon flux, is to build a compressive representation of a local 3D histogram" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.44 + ], + "angle": 0, + "content": "block as illustrated in Fig. 2. To avoid storing or transferring the photon timestamp stream, the compressive representation is built as each timestamp arrives. In this section, we present an online compression framework for histogram blocks based on the coded projection of photon timestamps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.893, + 0.606 + ], + "angle": 0, + "content": "Let \\( H_{b} \\) be the \\( b \\)th histogram block of \\( H \\) with dimensions \\( M_{t} \\times M_{r} \\times M_{c} \\), where \\( M_{t} \\leq N_{t} \\), \\( M_{r} \\leq N_{c} \\), and \\( M_{c} \\leq N_{c} \\). First, we observe that \\( H_{b} \\) can be expressed as the sum of \\( J \\) one-hot encoding tensors, each representing one photon detection within \\( H_{b} \\) (Fig. 2b). Specifically, let \\( t_{b,j} \\) be a \\( M_{t} \\times M_{r} \\times M_{c} \\) one-hot encoding tensor representing the \\( j^{\\mathrm{th}} \\) photon timestamp detected in histogram block \\( H_{b} \\), whose elements are all 0 except for \\( t_{b,j,l,p'} = 1 \\), where \\( l = \\left\\lfloor \\frac{T_j \\mod (\\Delta M_t)}{\\Delta} \\right\\rfloor \\), \\( T_{j} \\) is the timestamp value, and \\( p' \\) is the pixel where the timestamps was detected. Using this representation we can write \\( H_{b} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.642, + 0.613, + 0.892, + 0.656 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {H} _ {b} = \\sum_ {j = 0} ^ {J - 1} \\boldsymbol {t} _ {b, j}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.662, + 0.892, + 0.723 + ], + "angle": 0, + "content": "\\(H_{b}\\) can be compressed in an online fashion through the linear projection of each timestamp tensor; expressed as the inner product with \\(K\\) pre-designed coding tensors, \\(\\mathbf{C}_k\\), with dimensions \\(M_t\\times M_r\\times M_c\\), as in Fig. 2. Mathematically," + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.728, + 0.892, + 0.772 + ], + "angle": 0, + "content": "\\[\n\\widehat {Y} _ {b, k} = \\mathbf {C} _ {k} \\cdot \\boldsymbol {H} _ {b} = \\sum_ {j = 0} ^ {J - 1} \\mathbf {C} _ {k} \\cdot \\boldsymbol {t} _ {b, j} = \\sum_ {j = 0} ^ {J - 1} \\mathbf {C} _ {k, l, \\boldsymbol {p} ^ {\\prime}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.893, + 0.902 + ], + "angle": 0, + "content": "where \\(\\cdot\\) denotes element-wise multiplication, and \\(l\\) and \\(\\pmb{p}^{\\prime}\\) are the indices where \\(\\pmb{t}_{b,j,l,\\pmb{p}^{\\prime}} = 1\\). We define \\(\\widehat{\\mathbf{Y}}_b = (\\widehat{Y}_{b,k})_{k=0}^{K-1}\\) as the compressive histogram of \\(\\pmb{H}_b\\). Compressive histograms, as defined in [13, 36], are a special case of Eq. 4 where \\(\\mathbf{C}\\) compresses individual histograms and disregards spatial information (i.e., \\(M_t = N_t\\), \\(M_r = 1\\), \\(M_c = 1\\)). Note that each timestamp in Eq. 4 is processed efficiently on-the-fly after each photon detection through a simple lookup" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10758" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "operation. Moreover, individual histogram blocks or timestamps are never explicitly stored or transferred off-sensor." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.13, + 0.358, + 0.146 + ], + "angle": 0, + "content": "4.1. Practical Coding Tensor Design" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.469, + 0.272 + ], + "angle": 0, + "content": "Compressive histograms, when implemented as in Eq. 4, introduce an in-sensor memory overhead because, in addition to storing \\(\\widehat{\\mathbf{Y}}_b\\), \\(\\mathbf{C}\\) needs to be stored in-sensor for efficient lookup operations. Therefore, a practical compressive single-photon camera implementation would rely on parameter-efficient coding tensors that minimize this overhead. Here, we present two strategies to design practical coding tensors that are evaluated in Sec. 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.469, + 0.42 + ], + "angle": 0, + "content": "The memory overhead makes certain coding tensor designs impractical. Consider a set of coding tensors that operate on the full histogram tensor, i.e., \\( \\pmb{H}_b = \\pmb{H} \\). In this case, the number of elements in \\( \\mathbf{C} \\) will exceed the number of elements of \\( \\pmb{H} \\). Consequently, although the data rates are reduced in this scenario since \\( K < (N_t \\cdot N_r \\cdot N_c) \\), the insensor memory required exceeds the size of the histogram tensor. To circumvent this issue, we propose two complementary strategies to design lightweight coding tensors: local block-based and separable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.469, + 0.558 + ], + "angle": 0, + "content": "Local Block-based Coding Tensors: As we reduce the size of the histogram block, \\( H_{b} \\), represented by a compressive histogram, the size of the coding tensors decreases. Therefore, compressing local histogram blocks is not only beneficial due to local spatio-temporal redundancies, but also because these local coding tensors have fewer parameters. One example of local block-based coding tensors are the ones used in temporal compressive histograms [13, 36] where \\( H_{b} \\) is a per-pixel histogram." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.469, + 0.664 + ], + "angle": 0, + "content": "Separable Coding Tensors: One approach to designing lightweight coding tensors is to make them separable along the temporal and spatial dimensions. This approach is used in parameter-efficient CNN models that use separable depth-wise convolutional layers [17] to reduce model size. Formally, we can write a separable coding tensor as the outer product of two smaller tensors:" + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.675, + 0.469, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} _ {k} = \\mathbf {C} _ {k} ^ {\\text {t e m p o r a l}} \\otimes \\mathbf {C} _ {k} ^ {\\text {s p a t i a l}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.469, + 0.841 + ], + "angle": 0, + "content": "where \\(\\mathbf{C}_k^{\\mathrm{temporal}}\\) is a \\(M_t\\times 1\\times 1\\) tensor, and \\(\\mathbf{C}_k^{\\mathrm{spatial}}\\) is a \\(1\\times M_r\\times M_c\\) tensor. This design is also motivated by the differences between the temporal and spatial correlations encountered in histogram blocks. In addition to local correlations present in both dimensions, the temporal dimension also exhibits long-range correlations due to the background illumination offset (\\(\\Phi_p^{\\mathrm{bkg}}\\)) in every histogram bin. Therefore, Eq. 5 may be able to represent this prior by encoding the temporal and spatial information independently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.842, + 0.469, + 0.901 + ], + "angle": 0, + "content": "One assumption made in our memory overhead analysis is that a compressive SPAD-based 3D camera only needs to store a single \\(\\mathbf{C}\\) that is shared across the full sensor, which can be implemented in two general ways. One approach" + }, + { + "type": "code_caption", + "bbox": [ + 0.51, + 0.094, + 0.793, + 0.107 + ], + "angle": 0, + "content": "(a) Compressive Histogram Encoding" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.109, + 0.89, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "code_caption", + "bbox": [ + 0.51, + 0.213, + 0.793, + 0.226 + ], + "angle": 0, + "content": "(b) Compressive Histogram Decoding" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.228, + 0.888, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.325, + 0.892, + 0.448 + ], + "angle": 0, + "content": "Figure 3. Convolutional Compressive Histogram Layer. (a) Building a compressive histogram for each block in the histogram tensor, can be viewed as applying \\( K \\) stripped convolutional filters whose weights are the coding tensors. The compressed histogram tensor will be \\( K\\frac{N_t}{M_t}\\times \\frac{N_r}{M_r}\\times \\frac{N_c}{M_c} \\) tensors. (b) To lift the compressed histogram tensor back to its original domain an unfiltered backprojection operation can be applied on each compressive histogram which decodes a single block. The decoded histogram tensor can then be assembled by concatenating all the decoded blocks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.601 + ], + "angle": 0, + "content": "could distribute \\(\\mathbf{C}\\) across the local memory of all pixels and then allow communication across pixels as in PPAs [6]. A second approach could store \\(\\mathbf{C}\\) in a global memory that can be accessed by all pixels which could be enabled in 3D-stacked SPAD cameras [44]. Finally, some of the coding tensor designs explored in this paper have as few as 640 parameters. In this case, even if \\(\\mathbf{C}\\) is stored for every \\(4 \\times 4\\) group of pixels, the in-sensor memory is still reduced by \\(20 \\times\\) compared to storing a 1024 bin per-pixel histogram." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.614, + 0.884, + 0.631 + ], + "angle": 0, + "content": "4.2. Convolutional Compressive Histogram Layer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.772 + ], + "angle": 0, + "content": "A compressive histogram is built for each histogram block. Therefore, multiple compressive histograms are used to encode the complete histogram tensor. In this way, the coding tensors can be viewed as a set of 3D convolutional filters, which can be implemented as the first layer of a 3D CNN. For simplicity, we assume that histogram blocks do not overlap, and therefore, the stride of the convolutional filters will equal their dimensions. Fig. 3(a) illustrates this convolutional compressive histogram encoding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.774, + 0.892, + 0.849 + ], + "angle": 0, + "content": "Unfortunately, the compressed histogram tensor representation is not directly compatible with 3D CNNs that have been designed for SPAD-based 3D imaging (e.g., [32, 21]). To this end, each compressive histogram is lifted back to the original 3D domain through an unfiltered backprojection:" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.862, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\boldsymbol {H}} _ {b} = \\sum_ {k = 0} ^ {K - 1} \\mathbf {C} _ {k} \\widehat {Y} _ {b, k}. \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10759" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.09, + 0.473, + 0.33 + ], + "angle": 0, + "content": "Here \\(\\widehat{H}_b\\) is the decoded compressive histogram for block \\(b\\), which is the weighted linear combination of the coding tensors. The decoded histogram blocks are then concatenated and given as input to the processing 3D CNN. Fig. 3(b) illustrates this decoding step. The decoding step in Eq. 6 will occur off-sensor, after the compressive histograms have been moved to the camera compute module which has access to larger memory and computational resources than sensor module. One benefit of using the unfiltered backprojection as the upsampling operator is that if all coding tensors are mutually orthogonal, in the limit when \\(K\\) approaches the size of \\(H_b\\) (i.e., no compression), then \\(\\widehat{H}_b \\approx H_b\\). This suggests that at compression rates close to unity, an appropriately trained compressive histogram layer should be approximately equal to an identity transformation applied to \\(H_b\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.331, + 0.472, + 0.435 + ], + "angle": 0, + "content": "To summarize, a compressive histogram layer comprises an encoding/compression step followed by a decoding step, which uses the coding tensors as the convolutional filters. This layer can be appended to the beginning of any CNN that has been designed to process 3D histogram tensors. Finally, the coding tensors can be jointly optimized with the downstream CNN in an end-to-end manner." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.45, + 0.349, + 0.468 + ], + "angle": 0, + "content": "5. Datasets and Implementation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.476, + 0.47, + 0.536 + ], + "angle": 0, + "content": "In this section, we describe the datasets used for model training and testing, and also provide implementation details for the compressive histogram layer and the 3D CNN used for the experiments." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.547, + 0.182, + 0.563 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.57, + 0.47, + 0.706 + ], + "angle": 0, + "content": "For training, we generate a synthetic SPAD measurement dataset containing different scenes at a wide range of illumination settings. We use a similar synthetic data generation pipeline used in previous learning-based SPAD-based 3D imaging works [21, 32, 40]. Using Eq. 2, SPAD measurements can be simulated given an RGB-D image, the pulse waveform \\((h(t))\\), and the average number of detected signal and background photons per pixel. Please refer to the supplement for a detailed overview of the simulation pipeline." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.708, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Simulated Training Dataset: We use the RGB-D images from the NYU v2 dataset [38]. The simulated histograms have \\( N_{t} = 1024 \\) bins and a \\( \\Delta = 80 \\) ps bin size (12.3m depth range). The pulse waveform used has a full-width half maximum (FWHM) of 400ps obtained from [21]. For each scene, we randomly set the average number of signal and background photons detected per pixel to [2, 5, or 10] and [2, 10, 50], respectively. With appropriate normalization, the models generalize to other photon levels despite being trained on this photon-starved dataset. A total of 16,628 histogram tensors with dimensions \\( 1024 \\times 64 \\times 64 \\) are simulated and split into a training and a validation set with 13,851 and 2,777 examples, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.24 + ], + "angle": 0, + "content": "Simulated Test Dataset: For testing we use 8 RGB-D images from the Middlebury stereo dataset [35]. The simulated histograms have \\( N_{t} = 1024 \\) bins and a \\( \\Delta = 100\\mathrm{ps} \\) bin size (15.3m depth range). The pulse waveform used is a Gaussian pulse with an FWHM of 318ps (\\( \\sigma = 135\\mathrm{ps} \\)). A total of 128 test histogram tensors are generated by simulating each scene with the following average number of detected signal/background photons: 2/2, 2/5, 2/50, 5/2, 5/10, 5/50, 10/2, 10/10, 10/50, 10/200, 10/500, 10/1000, 50/50, 50/200, 50/500, and 50/1000." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.318 + ], + "angle": 0, + "content": "Real-world Experimental Data: To evaluate the generalization of the proposed models, we downloaded raw histogram tensor captured in [21] with a line-scanning SPAD-based 3D camera prototype. Please refer to the supplementary document for details on this dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.326, + 0.766, + 0.342 + ], + "angle": 0, + "content": "5.2. Training and Implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.395 + ], + "angle": 0, + "content": "To simplify training, the input to all models is a 3D histogram tensor, even though compressive histograms can work directly on streams of photon timestamps (Eq. 4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.893, + 0.576 + ], + "angle": 0, + "content": "Compressive Histogram Layer: The encoder is implemented as a 3D convolution with a stride equal to the filter size, whose learned filters are the coding tensors, \\(\\mathbf{C}_k\\). We constraint \\(\\mathbf{C}_k\\) to be zero-mean along the time dimension. The unfiltered backprojection decoder is implemented as a 3D transposed convolution with a stride equal to its filter size. To help the CNN model generalize to different photon count levels we apply zero-normalization along the channel dimension (i.e., \\(K\\)) to the inputs \\((\\widehat{\\mathbf{Y}}_b)\\) and the weights (\\(\\mathbf{C}\\)) of the transposed convolution, also known as layer-norm [5]. This normalization is also commonly used in depth decoding algorithms [14, 13, 26]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.892, + 0.683 + ], + "angle": 0, + "content": "Depth Estimation 3D CNN: To estimate depths from the decoded histogram tensor we use the 3D deep boosting CNN model proposed by [32] for single-photon 3D imaging, without the non-local block. Similar to [21, 32] we use the pixel-wise KL-divergence between the output histogram tensor and a normalized true histogram tensor as our objective, and estimate depths using a softargmax." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.892, + 0.805 + ], + "angle": 0, + "content": "Training: At each training iteration we randomly sample patches of size \\(1024 \\times 32 \\times 32\\). We train all models using the ADAM optimizer [19] with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\), batch size of 4, and a learning rate of 0.001 that decays by 0.9 after every epoch. We train all models for 30 epochs with periodical checkpoints, and for a given model we choose the checkpoint that achieves the lowest root mean squared error (RMSE) on the validation set." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.736, + 0.833 + ], + "angle": 0, + "content": "6. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.842, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this section, we present the performance at various compression levels for different coding tensor designs jointly optimized with the depth estimation CNN described in Sec. 5. A coding tensor design is determined by the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "10760" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.173, + 0.092, + 0.404, + 0.103 + ], + "angle": 0, + "content": "Compression vs. Mean Absolute Error (mm)" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.106, + 0.476, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.227, + 0.887, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.092, + 0.838, + 0.103 + ], + "angle": 0, + "content": "Compression vs. Percent Pixels with Errors \\(< 10\\mathrm{mm}\\)" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.106, + 0.892, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.894, + 0.346 + ], + "angle": 0, + "content": "Figure 4. Compression vs. Test Set Metrics. The two left-most plots show the mean absolute error computed over the test set as we increase compression. Similarly, the two right-most plots show the mean percent of pixels whose absolute depth errors were \\(< 10\\mathrm{mm}\\). The simulated test set images were divided into low (SBR \\(\\leq 0.1\\)) and high (SBR \\(>0.1\\)) SBR groups to be able to disentangle the impact of SBR on the performance of each model. The dashed lines show the peak and no compression baselines whose compression levels do not vary. Each line corresponds to a fixed coding tensor design for which we vary \\(K\\) to control the compression level. Moreover, each point for a given compression level corresponds to a single set of coding tensors jointly optimized with the depth estimation 3D CNN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.392 + ], + "angle": 0, + "content": "dimensions of \\(\\mathbf{C}_k\\) (i.e., \\(M_t \\times M_r \\times M_c\\)), the size of the compressive histogram (i.e., \\(K\\)), and if \\(\\mathbf{C}_k\\) is separable." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.402, + 0.386, + 0.417 + ], + "angle": 0, + "content": "6.1. Baselines and Performance Metrics" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.426, + 0.393, + 0.441 + ], + "angle": 0, + "content": "We compare against the following baselines:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.444, + 0.47, + 0.519 + ], + "angle": 0, + "content": "- Temporal Truncated Fourier C [36, 13]: A compressive histogram that uses coding tensors with dimensions \\(1024 \\times 1 \\times 1\\) and whose weights are set using the first \\(K / 2\\) frequencies of the Fourier matrix. In the supplement, we compare against additional Fourier-based C [13]." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.524, + 0.469, + 0.569 + ], + "angle": 0, + "content": "- Temporal Coarse Histogram C: Here C is a box down-sampling operator along the temporal dimensions which produces a coarse histogram with \\( K \\) bins." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.575, + 0.469, + 0.649 + ], + "angle": 0, + "content": "- No Compression Oracle: In this baseline, we assume the ideal scenario where the histogram tensor is transferred off-sensor and processed with the depth estimation 3D CNN. Similar to [32], we train this model with an initial learning rate of \\(10^{-4}\\) and total variation regularization." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.656, + 0.469, + 0.789 + ], + "angle": 0, + "content": "- Peak Compression Oracle: This baseline implements an ideal SPAD camera with sufficient in-sensor memory to store the histogram tensor and sufficient computation power to compute per-pixel depths through an \"argmax\" along the time axis. To process the noisy 2D depth images with the 3D CNN, we generate a 3D grid where all elements are zero except for one element per spatial location whose index is proportional to the depth. This model is trained like the no-compression oracle." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.444, + 0.47, + 0.789 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.792, + 0.469, + 0.852 + ], + "angle": 0, + "content": "Similar to our proposed approach, all compressive histogram baselines described here, implemented their C as a compressive histogram layer, with fixed weights, whose outputs are processed by the depth estimation 3D CNN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics: The 3D imaging performance of each model is summarized using two metrics: (1) the mean absolute depth error (MAE), (2) and the percent of pixels with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.554 + ], + "angle": 0, + "content": "absolute depth errors that are lower than \\(10\\mathrm{mm}\\). To understand the performance under these metrics we divide the test set into different SBR ranges and report the metrics for each range individually. We also visualize the overall dataset performance as scatter plots (e.g., Fig. 7) where each point shows the MAE for a given test scene and their color hue represents the mean SBR of the scene. Outliers with an MAE larger than \\(50\\mathrm{mm}\\) are not visible in the plot, however, they are included in the calculation of the statistics. Finally, when comparing different compressive histogram strategies the compression ratio is fixed. The compression ratio (CR) is the ratio of the block size and the length of the compressive histogram (i.e., \\(\\mathrm{CR} = (M_t \\cdot M_r \\cdot M_c) / K\\))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.731, + 0.577 + ], + "angle": 0, + "content": "6.2.3D Imaging Performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.892, + 0.736 + ], + "angle": 0, + "content": "Compression vs. Performance: Fig. 4 shows the performance of compressive histograms as a function of the compression ratio. The learned coding tensors consistently outperform the temporal Fourier-based C. At low SBR and \\(\\mathrm{CR} > 100\\), it becomes essential for the learned coding tensors to utilize spatio-temporal information (i.e., green and red lines). Moreover, the proposed models can outperform the peak compression oracle for \\(\\mathrm{CR} \\leq 64\\). Overall, learned spatio-temporal coding tensors provide robust performance that degrades gracefully as compression increases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.738, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Importance of Learned Coding Tensors: Fig. 5 compares the depth reconstructions of compressive histograms with coding tensors that were optimized (ours) against coding tensors that were fixed and not optimized throughout training. The extreme quantization in coarse histograms causes large systematic depth errors. Random unoptimized coding tensors consistently produce lower-quality depth reconstructions. A well-designed coding tensor based on Fourier codes can produce reasonable depth reconstructions at \\(64\\mathrm{x}\\) compression, however, at \\(128\\mathrm{x}\\) compression, scene details become blurred. The proposed learned coding tensors are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10761" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.891, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.283, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Figure 5. Importance of Learned Coding Tensors. Depth reconstructions at \\(64\\mathrm{x}\\) (top) and \\(128\\mathrm{x}\\) (bottom) compression for compressive histogram models whose coding tensors were hand-designed (coarse histogram and Fourier-based), learned (proposed), and not learned (randomly initialized). The simulated scene had an \\(\\mathrm{SBR} = 0.1\\) , where the mean signal and background photon levels were [50, 500]." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.337, + 0.466, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.481, + 0.47, + 0.536 + ], + "angle": 0, + "content": "Figure 6. What if we could compute depths in-pixel? Depth reconstructions at high and low SBR with mean signal and background photon levels of [10, 10] and [10, 1000], respectively. The compressive histograms have a compression of 64." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.596 + ], + "angle": 0, + "content": "able to generate high-quality reconstructions comparable to the no-compression oracle. Overall, optimizing the coding tensors can provide non-trivial performance gains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.718 + ], + "angle": 0, + "content": "What if we could compute depths in-pixel? Fig. 6 compares the depth reconstruction quality of two learned coding tensors at \\(64\\mathrm{x}\\) compression with the peak compression oracle described in Sec. 6.1. At high SBR, all methods recover the fine and coarse scene details. At low SBR the peak compression oracle fails to reconstruct high-level scene structures such as the rings in the red box, while the learned coding tensors better preserve these coarse and fine details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.442, + 0.743 + ], + "angle": 0, + "content": "6.3. Exploring the Coding Tensor Design Space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.753, + 0.471, + 0.902 + ], + "angle": 0, + "content": "When does spatio-temporal coding help? Fig. 7 shows the effect of increasing the spatial dimension of C, at 64x compression. At high SBR, all methods have similar MAE, but, coding tensors with smaller spatial dimensions better preserve fine details (e.g., sticks). On the other hand, at low SBR, coding tensors with larger spatial dimensions preserve high-level details such as the pot handle. This difference is also observed in the scatter plot where the mean and median of the \\(256 \\times 1 \\times 1\\) C do not match which indicates multiple low SBR scenes with high MAE." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.338, + 0.891, + 0.548 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.553, + 0.893, + 0.678 + ], + "angle": 0, + "content": "Figure 7. When do spatio-temporal coding tensors help? Each scatter plot point corresponds to the MAE of a test scene. The images directly below each model correspond to the depth reconstructions for two test examples at high and low SBR levels whose mean signal and background photons per pixel are [10, 10] and [10, 1000], respectively. For a fixed compression level, the spatial block size of each model is increased from left to right and \\( K \\) is adjusted to maintain the same compression level. The coding tensors for all models in this plot are learned and separable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.901 + ], + "angle": 0, + "content": "How does reducing the size of C affect performance? Fig. 8 shows the effect of reducing the size of C at \\(128\\mathrm{x}\\) compression. The coding tensors size is reduced by training models with separable coding tensors that operate on smaller histogram blocks. The performance difference between full and separable coding tensors \\((1024\\times 4\\times 4)\\) is negligible. As we further reduce the number of parameters in C, the overall performance degrades. Coding tensors with fewer parameters that operate on smaller histogram blocks tend to produce blurrier reconstructions. This can be observed in the red box where the coding tensors with less than 10,000 parameters blurs the spikes. Nonetheless, as discussed in Sec. 4.1, a parameter-efficient C is desirable due to the limited in-sensor memory. Ultimately, a practical" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10762" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.093, + 0.468, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.307, + 0.47, + 0.404 + ], + "angle": 0, + "content": "Figure 8. How does Reducing Size of C Affect Performance?. Each scatter plot point corresponds to the MAE of a test scene. The images directly below each model correspond to the depth reconstructions for two test scenes at high and low SBR levels whose mean signal and background photons per pixel are [10, 10] and [10, 1000], respectively. The size of C is reduced from left to right by making it separable or reducing the \\( M_{t} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.47, + 0.466 + ], + "angle": 0, + "content": "compressive SPAD-based 3D camera design requires determining the trade-off between parameter efficiency and 3D imaging quality, which may depend on the application." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.474, + 0.353, + 0.489 + ], + "angle": 0, + "content": "6.4. Evaluation on Real-world Data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.471, + 0.691 + ], + "angle": 0, + "content": "Fig. 9 shows the depth reconstructions at \\(256\\mathrm{x}\\) compression of multiple compressive histograms and the no compression baseline on the real-world experimental data from [21]. In low SBR scenes, such as the outdoor capture of the ball falling down stairs (first row), Truncated Fourier blurs the staircase edges, while the learned spatio-temporal C preserved these details. Compared to the no compression oracle, compressive histogram models produce less smooth depth images with some small artifacts. This suggests that the compressive histogram models could benefit from a spatial regularizer such as the one used when training the no compression oracle. Additional results and details on this evaluation are available in the supplement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.7, + 0.46, + 0.716 + ], + "angle": 0, + "content": "6.5. On-chip Implementation and Power Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To validate the feasibility of compressive histograms, we implement them on the UltraPhase chip which has a \\(3 \\times 6\\) processor core array [4]. At this time, UltraPhase has not been 3D stacked on a SPAD sensor, thus we only evaluate its compute and data readout power consumption. Fig. 10 shows the power dissipated by UltraPhase when processing photon timestamps with different methods and transferring data off-sensor. Although compressive histograms dissipate more power on computation (blue), this is less than \\(0.3\\%\\) of the overall power consumption, which is dominated by data readout. Due to limited memory in UltraPhase (4096 bits per core), our method learns \\(\\mathbf{C}^{\\mathrm{spatial}}\\) and uses Fourier codes" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.093, + 0.891, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.292, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Figure 9. Depth Reconstructions of Real-world SPAD Data at \\(256\\mathrm{x}\\) Compression. Depth reconstructions of different scenes captured with a SPAD-based 3D camera prototype [21]." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.352, + 0.888, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.44, + 0.893, + 0.563 + ], + "angle": 0, + "content": "Figure 10. Compute vs. Data Readout Power. Average power dissipated by \\(2 \\times 2\\) SPADs processing 500 timestamps per depth frame and operating at 30 depth frames per second. Compute power is obtained from the implementation on the UltraPhase SPAD processors [4]. Readout power is estimated from the output data rate assuming the readout scheme of the SwissSPAD2 [42]. Coarse histograms use 8-bit precision, while compressive histograms use 16-bit precision. Note the difference in blue and orange scales." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.577, + 0.892, + 0.624 + ], + "angle": 0, + "content": "for \\(\\mathbf{C}^{\\mathrm{temporal}}\\) due to their memory efficient implementation. We also quantize \\(\\mathbf{C}\\) to 8 bits and find no degradation in performance. Refer to the supplement for additional details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.635, + 0.614, + 0.65 + ], + "angle": 0, + "content": "7. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.883 + ], + "angle": 0, + "content": "SPAD-based 3D cameras encounter a data bottleneck between the SPAD array and the compute module when transferring the photon timestamps. A histogram tensor can help summarize timestamps at low resolutions, but as megapixel SPAD arrays become available, histogram tensors also lead to a data bottleneck. To overcome this limitation we proposed compressive histograms as a compact representation that can be built on-the-fly, as each photon is detected. As a consequence, compressive histograms can reduce the insensor memory and data rates because neither the photon data stream nor a histogram tensor needs to be stored or transferred. Our results show that high-quality depth information can be recovered from a learnt compressive histogram representation that is up to 2 orders of magnitude smaller than a histogram tensor representation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.891, + 0.902 + ], + "angle": 0, + "content": "Practical compressive histogram operating points: The" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10763" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.284 + ], + "angle": 0, + "content": "learned separable \\(256 \\times 4 \\times 4\\) and \\(256 \\times 2 \\times 2\\) C, achieved a good balance between parameter efficiency vs. reconstruction quality, and require on the order of 10-100kbits of memory. In an UltraPhase-like chip this would require distributing C among at least 8x8 cores (4kbits per core). If the temporal dimension is fixed to Fourier-based Ctemporal such as the ones from [13, 36], the number of parameters can be reduced by 10-40x (see Suppl. Sec. 3.3) which enables storing C on a per-pixel basis and made the Ultra-Phase evaluation possible. Overall, for a 1MP SPAD sensor with 1000 bins per-pixel, compressive histograms that can provide more than 50x compression would result in practical data rates of \\(\\sim 0.6\\mathrm{GB/s}\\) which USB 3.2 can support." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.48 + ], + "angle": 0, + "content": "Trade-off space: Compressive histograms establish a trade-off between reconstruction fidelity, data bandwidth, and in-sensor compute and memory resources. For a fixed bandwidth, a coarse histogram requires arguably the lowest in-sensor resources but leads to poor reconstructions. Fourier-based histograms can improve reconstruction fidelity, at the expense of increased in-sensor computation and memory. The proposed generalization of compressive histograms allows further increasing reconstruction accuracy, at the expense of additional in-sensor memory over Fourier-based methods. Ultimately, the correct trade-off for a given scenario will be determined by power, application, and hardware constraints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.482, + 0.473, + 0.674 + ], + "angle": 0, + "content": "Although compressive histograms require more insensor computation than coarse histograms, our method presents a practical solution from a power consumption and a real-time application perspective. Power consumption is primarily determined by data rates. Fig. 10 and Suppl. Fig. 4 shows that despite compressive histograms dissipating \\(100\\mathrm{x}\\) more processing power than coarse histograms, their overall power consumption is still lower even when data rates are only reduced by \\(2\\mathrm{x}\\). The processing time for building compressive histograms is \\(\\sim 0.5\\mathrm{ms}\\) (Suppl. Fig. 5). From a real-time (i.e., 30 FPS) or a high-speed application standpoint, this additional processing time is nearly negligible since it is overlapped with acquisition/exposure time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.824 + ], + "angle": 0, + "content": "From a hardware perspective, the importance of reducing the memory overhead of \\(\\mathbf{C}\\) depends on resolution. In low-resolution SPAD cameras, memory-efficient \\(\\mathbf{C}\\) are essential because they are stored among a single or a few pixels. The proposed method allowed integrating memory-efficient Fourier codes with learned spatial codes, which were implemented on the 2x2 pixels of UltraPhase (Suppl. Sec. 2). As resolution increases and \\(\\mathbf{C}\\) is shared among more pixels, the memory overhead reduces, and less parameter-efficient \\(\\mathbf{C}\\) with increased reconstruction fidelity can be considered." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Bias in Learned C: In the supplement, we show that coding tensors with \\( M_{t} = N_{t} \\) develop a depth range bias. These coding tensors learn to zero out photons coming from distances that are less common in the dataset since they are usually background/noise photons. Interestingly, learned" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "coding tensors with \\( M_t < N_t \\) avoid this bias and generalize to depths that are less common in the training set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.129, + 0.892, + 0.292 + ], + "angle": 0, + "content": "Generalization: There are multiple generalization axes including signal and ambient light levels, sensor and laser parameters (e.g., resolution, pulse waveform), and scene response complexity (e.g., depth range, indirect reflections). Our evaluation has probed some of them. Specifically, our training set only included a subset of the signal and ambient light levels that the test set contained. Furthermore, the model was trained and tested on histogram tensors with different resolutions. Finally, the dataset bias investigation showed that models with \\( N_{t} \\leq 256 \\) generalized well to less prevalent depths during training (Suppl. Sec. 1)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.892, + 0.457 + ], + "angle": 0, + "content": "We further discuss the model's ability to generalize in other scenarios. For instance, all learned models (including baselines) are unlikely to generalize well to wider laser pulses, because if the model is trained with a narrow pulse width, it learns to extract signal information from high frequencies which will only contain noise in the wider pulse. Similarly, these learned models may generalize to narrower pulse widths. Furthermore, we anticipate a learned C with the properties described in [13] to be robust to diffuse indirect reflections but may require data augmentation to generalize to other light transport scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.569 + ], + "angle": 0, + "content": "Why not compute depths in-sensor? SPAD-based 3D cameras with large in-pixel memory could store per-pixel histograms and reduce data rates by computing depths in-pixel (i.e., peak compression oracle). Our results show that compressive histogram can provide similar reconstruction quality and outperform this method at low SBR without requiring the storage of the full histogram tensor in-sensor." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Additional Coding Tensor Designs: Although we find promising empirical results for the coding tensor representations described in this paper, the optimal set of coding tensors will depend on the exact hardware specifications (e.g., in-pixel memory, system bandwidth) and scene-dependent parameters (e.g., SBR, geometry, albedo). Additional lightweight C designs could rely on other factorization techniques and weight quantization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.791 + ], + "angle": 0, + "content": "Task-specific Compressive Histograms: Histogram tensors are used in other active single-photon imaging modalities such as fluorescence lifetime microscopy [34], nonline-of-sight [10, 23, 29], and diffuse optical tomography [22, 45, 24]. Our framework could be used to find compressive representations optimized for these applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments: This work was supported by the Department of Energy and National Nuclear Security Administration (DE-NA0003921), Air Force (FA9550-21-1-0341), Swiss National Science Foundation (200021_166289), and NSF Awards 1846884 (A.V.), 1943149 (M.G.), 2107060 (M.G.), 2138471 (A.I.). 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021. 9" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.893, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10766" + } + ] +] \ No newline at end of file diff --git a/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_origin.pdf b/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1941557ca72771d45bd4792bda2248ec11d2a6b5 --- /dev/null +++ b/2023/Learned Compressive Representations for Single-Photon 3D Imaging/78c901d2-1e87-453e-b9f2-75e42afe6005_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e037231165aca589c8c7193237a75502c76620d55031ff391b5f887a62d2741f +size 4136404 diff --git a/2023/Learned Compressive Representations for Single-Photon 3D Imaging/full.md b/2023/Learned Compressive Representations for Single-Photon 3D Imaging/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a6bfc1b415404ea225e145f16e69b657c24a1018 --- /dev/null +++ b/2023/Learned Compressive Representations for Single-Photon 3D Imaging/full.md @@ -0,0 +1,317 @@ +# Learned Compressive Representations for Single-Photon 3D Imaging + +Felipe Gutierrez-Barragan $^{1\ddagger}$ , Fangzhou Mu $^{1}$ , Andrei Ardelean $^{3}$ , Atul Ingle $^{2}$ , Claudio Bruschini $^{3}$ , Edoardo Charbon $^{3}$ , Yin Li $^{1}$ , Mohit Gupta $^{1}$ , Andreas Velten $^{1}$ + +1University of Wisconsin-Madison, 2Portland State University, + +$^{3}$ Ecole Polytechnique Federale de Lausanne + +# Abstract + +Single-photon 3D cameras can record the time-of-arrival of billions of photons per second with picosecond accuracy. One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that encodes distances along the time axis. As the spatio-temporal resolution of the histogram tensor increases, the in-pixel memory requirements and output data rates can quickly become impractical. To overcome this limitation, we propose a family of linear compressive representations of histogram tensors that can be computed efficiently, in an online fashion, as a matrix operation. We design practical lightweight compressive representations that are amenable to an in-pixel implementation and consider the spatio-temporal information of each timestamp. Furthermore, we implement our proposed framework as the first layer of a neural network, which enables the joint end-to-end optimization of the compressive representations and a downstream SPAD data processing model. We find that a well-designed compressive representation can reduce in-sensor memory and data rates up to 2 orders of magnitude without significantly reducing 3D imaging quality. Finally, we analyze the power consumption implications through an on-chip implementation. + +# 1. Introduction + +3D cameras based on single-photon avalanche diode technology (SPAD) are becoming increasingly popular for a wide range of applications that require high-resolution and low-power depth sensing, ranging from autonomous vehicles [1] to consumer smartphones [2]. Kilo-to-megapixel resolution SPAD pixel arrays [27, 28] have the capability of capturing the time-of-arrival of billions of individual photons per frame with extremely high (picosecond) time resolution [31]. Unfortunately, this extreme sensitivity and high speed comes at a cost — the raw timestamp data causes a severe bottleneck between the image sensor and the image signal processor (ISP) that processes this data (Fig. 1(a)). This data bottleneck severely limits the wider use of high- + +![](images/e6bf66f7edf47a672e7fb68c930b15195df549b9a7d885a6f362ba4d25bf7c77.jpg) + +![](images/ed1878b6bbec76a0902ee2bc93d51cea753f43822d10ea7c417ed927ce4e404b.jpg) +Figure 1. Resolving SPAD data bottleneck with learned compression. (a) Conventional SPAD-based 3D cameras stream raw photon timestamps or summary histograms off the image sensor which causes a data bottleneck between the image sensor and the on-camera image and signal processing (ISP) module. (b) Our method applies a lightweight, on-sensor compressive coding scheme to the photon timestamp data which is later decoded at the ISP, resolving the data bandwidth limitation. + +resolution SPAD arrays in 3D sensing applications. + +One common approach to avoid transferring individual photon timestamps is to build a histogram in each pixel. This results in a 3D histogram tensor that is transferred off-sensor for processing. Although this may be practical at low spatio-temporal resolutions (e.g., $64 \times 32$ pixels with 16 time bins [15]), it requires higher in-sensor memory. Moreover, the data rates of this histogram tensor representation also scale rapidly with the spatio-temporal resolution and maximum depth range. For example, a megapixel SPAD-based 3D camera operating at 30 fps that outputs a histogram tensor with a thousand 8-bit bins per pixel would require an unmanageable data transfer rate of 240 Gbps. + +To overcome the above limitations, we seek to design compressive representations of 3D histogram tensors. In order to reduce the data rates output by the SPAD camera, the compact representation needs to be built in-pixel or inside the focal plane array (FPA). This is illustrated in Fig. 1(b). Due to the limited in-pixel memory and compute, the compressive representation needs to be built in a streaming manner, with minimal computations per photon. Photon + +histogram tensors are very different from conventional RGB images/video data. Therefore, traditional compression algorithms such as MPEG are not directly applicable. + +We propose a family of compressive representations for 3D histogram tensors that can be computed in an online fashion with limited memory and compute. They are based on the linear spatio-temporal projection of each photon timestamp, which can be expressed as a simple matrix operation. Instead of constructing per-pixel timestamp histograms, a compressive encoding maps its spatio-temporal information into a compressive histogram. To exploit local spatio-temporal correlations, a single compressive histogram is built for a local 3D histogram block as illustrated in Fig. 2. Instead of building and storing the full 3D histogram tensor in-sensor, multiple compressive histograms are built and transferred off-sensor for processing, effectively reducing the required in-sensor memory and data rates. Recent works proposed a similar compression framework based on compressive histograms [13] or sketches [36]. In Sec. 4, we show that these prior works can be viewed as special cases of our proposed framework. + +In this paper, we explore the design space of spatiotemporal compressive encodings and analyze the trade-offs between different design choices. Furthermore, we present a method to integrate our compression framework with data-driven SPAD data processing methods using convolutional neural networks (CNNs), which enables end-to-end optimization of the compressive encoding and a SPAD data processing CNN. We demonstrate the feasibility of compressive histograms through an on-chip implementation. + +For our experimental evaluation, we integrate the compressive histograms framework with a state-of-the-art learning-based denoising model for SPAD-based 3D imaging [32]. Our results show that the jointly optimized compressive encoding and CNN can consistently reduce data rates up to 2 orders of magnitude in a wide range of signal and noise levels. Moreover, for a given compression level, it can increase 3D imaging accuracy over previous hand-designed compressive histograms that only exploit temporal information [13, 36], especially in low signal-to-background ratio (SBR) scenarios and at higher compression rates. Furthermore, we show that learned compressive histograms can perform comparably and sometimes even outperform a theoretical SPAD sensor design where the full 3D histogram tensor is stored in-sensor and only per-pixel depths are transferred off-sensor. Finally, we analyze the power consumption of a compressive histogram implemented on the UltraPhase SPAD processing chip [4]. + +# 2. Related Work + +Compressive histograms, also called sketches, are an emerging framework for online in-sensor compression of SPAD timestamp data [13, 41, 36, 33]. A coarse histogram is one common compressive histogram approach [13] to re + +duce data rates and in-pixel memory [15, 8, 18]. Despite their practical hardware implementation, coarse histograms achieve sub-optimal depth accuracy compared to compressive histograms based on Fourier [36, 37, 13] and Gray [13] codes. One limitation of these approaches is that the compressive representation only exploits the temporal information of the incident timestamp, and disregards the spatial redundancy. In this work, we generalize the compressive histogram framework to utilize the spatio-temporal information of each timestamp. Moreover, instead of relying on hand-designed coded projections, in this paper we learn them as the first layer of a CNN. + +- Shared In-Pixel Histograms: One common design is to have multiple neighboring SPAD pixels have a single shared memory where all timestamps are aggregated into a coarse histogram (e.g., $4 \times 4$ [18, 15], $3 \times 3$ [20]). This approach throws away the local spatial information (i.e., pixel location) of the detected photon timestamps. A compressive histogram is well-suited for these shared memory designs because it can be shared among multiple SPAD pixels and preserves spatial information through the coded projection. + +Neural Sensors and Pixel Processor Arrays: Pixel processor arrays (PPAs) are an emerging sensing technology that embeds processing electronics inside each pixel [9]. This new sensing paradigm begins processing the image at the focal plane array, which allows it to reduce the sensor data rates by transmitting only the relevant information, and consequently, it increases the sensor's throughput [9] which can enable computer vision at 3,000 fps [6, 7]. PPAs have also become building blocks of novel computational imaging systems optimized end-to-end for HDR imaging [25, 39], motion deblurring [30], video compressive sensing [25], and light field imaging [43]. A compressive histogram relies on a similar in-pixel processing paradigm. Similar to previous works, we jointly optimize the sensor parameters (i.e., the compressive histogram) and the processing algorithm (i.e., the CNN), but to our knowledge, this work is the first to use this approach for SPAD data compression. + +# 3. Single-Photon 3D Histogram Tensors + +SPAD-based 3D cameras consist of a SPAD sensor and a pulsed laser that illuminates the scene. The photon flux signal arriving at pixel, $p$ , can be written as: + +$$ +\Phi_ {\boldsymbol {p}} (t) = a _ {\boldsymbol {p}} h \left(t - 2 d _ {\boldsymbol {p}} / c\right) + \Phi_ {\boldsymbol {p}} ^ {\mathrm {b k g}} = \Phi_ {\boldsymbol {p}} ^ {\mathrm {s i g}} (t) + \Phi_ {\boldsymbol {p}} ^ {\mathrm {b k g}}, \tag {1} +$$ + +where $a_{p}$ is the amplitude of the returning signal accounting for laser power, reflectivity, and light fall-off; $h(t)$ is the system's impulse response function (IRF) which accounts for pulse waveform and sensor IRF; $d_{p}$ is the distance to the point imaged by $p$ ; $c$ is the speed of light; and $\Phi_{p}^{\mathrm{bkg}}$ is the constant photon flux due to background illumination (e.g., sunlight). This model assumes direct-only reflections + +![](images/ccb75f2aaef93d94c8ba5be029ed2f756361ca7ab11b161cf5e2081f6d5461ea.jpg) +Figure 2. Compressive Histogram Formation. Histogram tensors, $H$ , are a 3D spatio-temporal grid whose elements store the number of photons that arrived within a short time interval. (a) In SPAD-based 3D imaging, the temporal axis of $H$ encodes distances. (b) A histogram block, $H_{b}$ , can be expressed as the sum of $J$ one-hot encoding tensors, where each tensor represents a photon timestamp. (c) A compact representation of $H_{b}$ can be built by applying $K$ linear projections (i.e., dot product) with pre-designed coding tensors. (d) The compressive histogram, will be a vector with $K$ elements whose compression capacity is given by $\frac{M_t \cdot M_r \cdot M_c}{K}$ . + +![](images/3dab483cae28c9552f5efd54c97c53c2380536942ed77069c51ba3e6cbc230eb.jpg) + +which is a valid approximation, in particular, for scanning-based ToF 3D imaging systems [3]. + +TCSPC-based SPAD cameras measure $\Phi_p(t)$ by building a per-pixel timing histogram, where the $i$ th histogram bin records the number of photons that arrived in a time interval of length $\Delta$ , which follows a Poisson process $\mathcal{P}$ : + +$$ +\Phi_ {i, \boldsymbol {p}} = \mathcal {P} \left(\Phi_ {i, \boldsymbol {p}} ^ {\mathrm {s i g}} + \Delta \Phi_ {\boldsymbol {p}} ^ {\mathrm {b k g}}\right). \tag {2} +$$ + +The pulse repetition period, $\tau$ , determines the maximum timestamp value and the length of the histogram vector $\Phi_p = (\Phi_{i,p})_{i=0}^{N_t - 1}$ , where $N_t = \tau / \Delta$ . Therefore, one assumption built into $\Phi_p$ , is that no signal photons had a timestamp larger than $\tau$ , which means that the maximum distance that $\Phi_p$ can encode is $d_{\max} = \frac{c\tau}{2}$ . Furthermore, we assume that pile-up distortions are minimized through various SPAD data acquisition techniques [11, 15, 16, 12]. + +This process generates a $N_{t} \times N_{r} \times N_{c}$ 3D histogram tensor, $\pmb{H} = (\Phi_p)_{p=0,0}^{(N_r - 1, N_c - 1)}$ . In challenging 3D imaging scenarios with high background illumination, building $\pmb{H}$ off-sensor requires transferring thousands of photon timestamps per-pixel leading to data rates of hundreds of GB/s in a megapixel sensor. Moreover, building and storing a high-resolution $\pmb{H}$ in-sensor would require significant memory (1GB for a megapixel SPAD camera with 1000 time bins per-pixel), and transferring it would continue to lead to impractical data rates of tens of GB/s on a SPAD-based 3D camera operating at 30fps. Overall, a practical SPAD-based 3D camera would build and store a compact representation of $\pmb{H}$ in-sensor and then transfer it to a processing chip (e.g., FPGA, ISP, embedded computer) where it is processed. + +# 4. Spatio-temporal Compressive Histograms + +A natural approach to compress $\pmb{H}$ that exploits its local correlations due to smooth depths and photon flux, is to build a compressive representation of a local 3D histogram + +block as illustrated in Fig. 2. To avoid storing or transferring the photon timestamp stream, the compressive representation is built as each timestamp arrives. In this section, we present an online compression framework for histogram blocks based on the coded projection of photon timestamps. + +Let $H_{b}$ be the $b$ th histogram block of $H$ with dimensions $M_{t} \times M_{r} \times M_{c}$ , where $M_{t} \leq N_{t}$ , $M_{r} \leq N_{c}$ , and $M_{c} \leq N_{c}$ . First, we observe that $H_{b}$ can be expressed as the sum of $J$ one-hot encoding tensors, each representing one photon detection within $H_{b}$ (Fig. 2b). Specifically, let $t_{b,j}$ be a $M_{t} \times M_{r} \times M_{c}$ one-hot encoding tensor representing the $j^{\mathrm{th}}$ photon timestamp detected in histogram block $H_{b}$ , whose elements are all 0 except for $t_{b,j,l,p'} = 1$ , where $l = \left\lfloor \frac{T_j \mod (\Delta M_t)}{\Delta} \right\rfloor$ , $T_{j}$ is the timestamp value, and $p'$ is the pixel where the timestamps was detected. Using this representation we can write $H_{b}$ as follows: + +$$ +\boldsymbol {H} _ {b} = \sum_ {j = 0} ^ {J - 1} \boldsymbol {t} _ {b, j}. \tag {3} +$$ + +$H_{b}$ can be compressed in an online fashion through the linear projection of each timestamp tensor; expressed as the inner product with $K$ pre-designed coding tensors, $\mathbf{C}_k$ , with dimensions $M_t\times M_r\times M_c$ , as in Fig. 2. Mathematically, + +$$ +\widehat {Y} _ {b, k} = \mathbf {C} _ {k} \cdot \boldsymbol {H} _ {b} = \sum_ {j = 0} ^ {J - 1} \mathbf {C} _ {k} \cdot \boldsymbol {t} _ {b, j} = \sum_ {j = 0} ^ {J - 1} \mathbf {C} _ {k, l, \boldsymbol {p} ^ {\prime}}, \tag {4} +$$ + +where $\cdot$ denotes element-wise multiplication, and $l$ and $\pmb{p}^{\prime}$ are the indices where $\pmb{t}_{b,j,l,\pmb{p}^{\prime}} = 1$ . We define $\widehat{\mathbf{Y}}_b = (\widehat{Y}_{b,k})_{k=0}^{K-1}$ as the compressive histogram of $\pmb{H}_b$ . Compressive histograms, as defined in [13, 36], are a special case of Eq. 4 where $\mathbf{C}$ compresses individual histograms and disregards spatial information (i.e., $M_t = N_t$ , $M_r = 1$ , $M_c = 1$ ). Note that each timestamp in Eq. 4 is processed efficiently on-the-fly after each photon detection through a simple lookup + +operation. Moreover, individual histogram blocks or timestamps are never explicitly stored or transferred off-sensor. + +# 4.1. Practical Coding Tensor Design + +Compressive histograms, when implemented as in Eq. 4, introduce an in-sensor memory overhead because, in addition to storing $\widehat{\mathbf{Y}}_b$ , $\mathbf{C}$ needs to be stored in-sensor for efficient lookup operations. Therefore, a practical compressive single-photon camera implementation would rely on parameter-efficient coding tensors that minimize this overhead. Here, we present two strategies to design practical coding tensors that are evaluated in Sec. 6. + +The memory overhead makes certain coding tensor designs impractical. Consider a set of coding tensors that operate on the full histogram tensor, i.e., $\pmb{H}_b = \pmb{H}$ . In this case, the number of elements in $\mathbf{C}$ will exceed the number of elements of $\pmb{H}$ . Consequently, although the data rates are reduced in this scenario since $K < (N_t \cdot N_r \cdot N_c)$ , the insensor memory required exceeds the size of the histogram tensor. To circumvent this issue, we propose two complementary strategies to design lightweight coding tensors: local block-based and separable. + +Local Block-based Coding Tensors: As we reduce the size of the histogram block, $H_{b}$ , represented by a compressive histogram, the size of the coding tensors decreases. Therefore, compressing local histogram blocks is not only beneficial due to local spatio-temporal redundancies, but also because these local coding tensors have fewer parameters. One example of local block-based coding tensors are the ones used in temporal compressive histograms [13, 36] where $H_{b}$ is a per-pixel histogram. + +Separable Coding Tensors: One approach to designing lightweight coding tensors is to make them separable along the temporal and spatial dimensions. This approach is used in parameter-efficient CNN models that use separable depth-wise convolutional layers [17] to reduce model size. Formally, we can write a separable coding tensor as the outer product of two smaller tensors: + +$$ +\mathbf {C} _ {k} = \mathbf {C} _ {k} ^ {\text {t e m p o r a l}} \otimes \mathbf {C} _ {k} ^ {\text {s p a t i a l}}, \tag {5} +$$ + +where $\mathbf{C}_k^{\mathrm{temporal}}$ is a $M_t\times 1\times 1$ tensor, and $\mathbf{C}_k^{\mathrm{spatial}}$ is a $1\times M_r\times M_c$ tensor. This design is also motivated by the differences between the temporal and spatial correlations encountered in histogram blocks. In addition to local correlations present in both dimensions, the temporal dimension also exhibits long-range correlations due to the background illumination offset ( $\Phi_p^{\mathrm{bkg}}$ ) in every histogram bin. Therefore, Eq. 5 may be able to represent this prior by encoding the temporal and spatial information independently. + +One assumption made in our memory overhead analysis is that a compressive SPAD-based 3D camera only needs to store a single $\mathbf{C}$ that is shared across the full sensor, which can be implemented in two general ways. One approach + +(a) Compressive Histogram Encoding + +![](images/c2bba31eee76afb3167d1320314952ba3a71f8787afa493aae6dde99cb0fcd4a.jpg) + +(b) Compressive Histogram Decoding + +![](images/405e3bd80fef08f7449db58138a71fe29574ed8303f506fd8f8aabfdad9a9104.jpg) +Figure 3. Convolutional Compressive Histogram Layer. (a) Building a compressive histogram for each block in the histogram tensor, can be viewed as applying $K$ stripped convolutional filters whose weights are the coding tensors. The compressed histogram tensor will be $K\frac{N_t}{M_t}\times \frac{N_r}{M_r}\times \frac{N_c}{M_c}$ tensors. (b) To lift the compressed histogram tensor back to its original domain an unfiltered backprojection operation can be applied on each compressive histogram which decodes a single block. The decoded histogram tensor can then be assembled by concatenating all the decoded blocks. + +could distribute $\mathbf{C}$ across the local memory of all pixels and then allow communication across pixels as in PPAs [6]. A second approach could store $\mathbf{C}$ in a global memory that can be accessed by all pixels which could be enabled in 3D-stacked SPAD cameras [44]. Finally, some of the coding tensor designs explored in this paper have as few as 640 parameters. In this case, even if $\mathbf{C}$ is stored for every $4 \times 4$ group of pixels, the in-sensor memory is still reduced by $20 \times$ compared to storing a 1024 bin per-pixel histogram. + +# 4.2. Convolutional Compressive Histogram Layer + +A compressive histogram is built for each histogram block. Therefore, multiple compressive histograms are used to encode the complete histogram tensor. In this way, the coding tensors can be viewed as a set of 3D convolutional filters, which can be implemented as the first layer of a 3D CNN. For simplicity, we assume that histogram blocks do not overlap, and therefore, the stride of the convolutional filters will equal their dimensions. Fig. 3(a) illustrates this convolutional compressive histogram encoding. + +Unfortunately, the compressed histogram tensor representation is not directly compatible with 3D CNNs that have been designed for SPAD-based 3D imaging (e.g., [32, 21]). To this end, each compressive histogram is lifted back to the original 3D domain through an unfiltered backprojection: + +$$ +\widehat {\boldsymbol {H}} _ {b} = \sum_ {k = 0} ^ {K - 1} \mathbf {C} _ {k} \widehat {Y} _ {b, k}. \tag {6} +$$ + +Here $\widehat{H}_b$ is the decoded compressive histogram for block $b$ , which is the weighted linear combination of the coding tensors. The decoded histogram blocks are then concatenated and given as input to the processing 3D CNN. Fig. 3(b) illustrates this decoding step. The decoding step in Eq. 6 will occur off-sensor, after the compressive histograms have been moved to the camera compute module which has access to larger memory and computational resources than sensor module. One benefit of using the unfiltered backprojection as the upsampling operator is that if all coding tensors are mutually orthogonal, in the limit when $K$ approaches the size of $H_b$ (i.e., no compression), then $\widehat{H}_b \approx H_b$ . This suggests that at compression rates close to unity, an appropriately trained compressive histogram layer should be approximately equal to an identity transformation applied to $H_b$ . + +To summarize, a compressive histogram layer comprises an encoding/compression step followed by a decoding step, which uses the coding tensors as the convolutional filters. This layer can be appended to the beginning of any CNN that has been designed to process 3D histogram tensors. Finally, the coding tensors can be jointly optimized with the downstream CNN in an end-to-end manner. + +# 5. Datasets and Implementation + +In this section, we describe the datasets used for model training and testing, and also provide implementation details for the compressive histogram layer and the 3D CNN used for the experiments. + +# 5.1. Datasets + +For training, we generate a synthetic SPAD measurement dataset containing different scenes at a wide range of illumination settings. We use a similar synthetic data generation pipeline used in previous learning-based SPAD-based 3D imaging works [21, 32, 40]. Using Eq. 2, SPAD measurements can be simulated given an RGB-D image, the pulse waveform $(h(t))$ , and the average number of detected signal and background photons per pixel. Please refer to the supplement for a detailed overview of the simulation pipeline. + +Simulated Training Dataset: We use the RGB-D images from the NYU v2 dataset [38]. The simulated histograms have $N_{t} = 1024$ bins and a $\Delta = 80$ ps bin size (12.3m depth range). The pulse waveform used has a full-width half maximum (FWHM) of 400ps obtained from [21]. For each scene, we randomly set the average number of signal and background photons detected per pixel to [2, 5, or 10] and [2, 10, 50], respectively. With appropriate normalization, the models generalize to other photon levels despite being trained on this photon-starved dataset. A total of 16,628 histogram tensors with dimensions $1024 \times 64 \times 64$ are simulated and split into a training and a validation set with 13,851 and 2,777 examples, respectively. + +Simulated Test Dataset: For testing we use 8 RGB-D images from the Middlebury stereo dataset [35]. The simulated histograms have $N_{t} = 1024$ bins and a $\Delta = 100\mathrm{ps}$ bin size (15.3m depth range). The pulse waveform used is a Gaussian pulse with an FWHM of 318ps ( $\sigma = 135\mathrm{ps}$ ). A total of 128 test histogram tensors are generated by simulating each scene with the following average number of detected signal/background photons: 2/2, 2/5, 2/50, 5/2, 5/10, 5/50, 10/2, 10/10, 10/50, 10/200, 10/500, 10/1000, 50/50, 50/200, 50/500, and 50/1000. + +Real-world Experimental Data: To evaluate the generalization of the proposed models, we downloaded raw histogram tensor captured in [21] with a line-scanning SPAD-based 3D camera prototype. Please refer to the supplementary document for details on this dataset. + +# 5.2. Training and Implementation + +To simplify training, the input to all models is a 3D histogram tensor, even though compressive histograms can work directly on streams of photon timestamps (Eq. 4). + +Compressive Histogram Layer: The encoder is implemented as a 3D convolution with a stride equal to the filter size, whose learned filters are the coding tensors, $\mathbf{C}_k$ . We constraint $\mathbf{C}_k$ to be zero-mean along the time dimension. The unfiltered backprojection decoder is implemented as a 3D transposed convolution with a stride equal to its filter size. To help the CNN model generalize to different photon count levels we apply zero-normalization along the channel dimension (i.e., $K$ ) to the inputs $(\widehat{\mathbf{Y}}_b)$ and the weights ( $\mathbf{C}$ ) of the transposed convolution, also known as layer-norm [5]. This normalization is also commonly used in depth decoding algorithms [14, 13, 26]. + +Depth Estimation 3D CNN: To estimate depths from the decoded histogram tensor we use the 3D deep boosting CNN model proposed by [32] for single-photon 3D imaging, without the non-local block. Similar to [21, 32] we use the pixel-wise KL-divergence between the output histogram tensor and a normalized true histogram tensor as our objective, and estimate depths using a softargmax. + +Training: At each training iteration we randomly sample patches of size $1024 \times 32 \times 32$ . We train all models using the ADAM optimizer [19] with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ , batch size of 4, and a learning rate of 0.001 that decays by 0.9 after every epoch. We train all models for 30 epochs with periodical checkpoints, and for a given model we choose the checkpoint that achieves the lowest root mean squared error (RMSE) on the validation set. + +# 6. Experiments and Results + +In this section, we present the performance at various compression levels for different coding tensor designs jointly optimized with the depth estimation CNN described in Sec. 5. A coding tensor design is determined by the + +![](images/aebcfa17b70af6abf98e05ac51128e01b34278264fbc3e4150e2841b7427cf8c.jpg) +Compression vs. Mean Absolute Error (mm) + +![](images/a3e2bc1e72a74c6e5abdc63d240035a42c4e3b6f18f5b2f940850268f9c429fb.jpg) +Figure 4. Compression vs. Test Set Metrics. The two left-most plots show the mean absolute error computed over the test set as we increase compression. Similarly, the two right-most plots show the mean percent of pixels whose absolute depth errors were $< 10\mathrm{mm}$ . The simulated test set images were divided into low (SBR $\leq 0.1$ ) and high (SBR $>0.1$ ) SBR groups to be able to disentangle the impact of SBR on the performance of each model. The dashed lines show the peak and no compression baselines whose compression levels do not vary. Each line corresponds to a fixed coding tensor design for which we vary $K$ to control the compression level. Moreover, each point for a given compression level corresponds to a single set of coding tensors jointly optimized with the depth estimation 3D CNN. + +![](images/8e06c1940d217b41f4fd313955fdb8048859ec5195721267c9b6b5256b0e6b74.jpg) +Compression vs. Percent Pixels with Errors $< 10\mathrm{mm}$ + +dimensions of $\mathbf{C}_k$ (i.e., $M_t \times M_r \times M_c$ ), the size of the compressive histogram (i.e., $K$ ), and if $\mathbf{C}_k$ is separable. + +# 6.1. Baselines and Performance Metrics + +We compare against the following baselines: + +- Temporal Truncated Fourier C [36, 13]: A compressive histogram that uses coding tensors with dimensions $1024 \times 1 \times 1$ and whose weights are set using the first $K / 2$ frequencies of the Fourier matrix. In the supplement, we compare against additional Fourier-based C [13]. +- Temporal Coarse Histogram C: Here C is a box down-sampling operator along the temporal dimensions which produces a coarse histogram with $K$ bins. +- No Compression Oracle: In this baseline, we assume the ideal scenario where the histogram tensor is transferred off-sensor and processed with the depth estimation 3D CNN. Similar to [32], we train this model with an initial learning rate of $10^{-4}$ and total variation regularization. +- Peak Compression Oracle: This baseline implements an ideal SPAD camera with sufficient in-sensor memory to store the histogram tensor and sufficient computation power to compute per-pixel depths through an "argmax" along the time axis. To process the noisy 2D depth images with the 3D CNN, we generate a 3D grid where all elements are zero except for one element per spatial location whose index is proportional to the depth. This model is trained like the no-compression oracle. + +Similar to our proposed approach, all compressive histogram baselines described here, implemented their C as a compressive histogram layer, with fixed weights, whose outputs are processed by the depth estimation 3D CNN. + +Evaluation Metrics: The 3D imaging performance of each model is summarized using two metrics: (1) the mean absolute depth error (MAE), (2) and the percent of pixels with + +absolute depth errors that are lower than $10\mathrm{mm}$ . To understand the performance under these metrics we divide the test set into different SBR ranges and report the metrics for each range individually. We also visualize the overall dataset performance as scatter plots (e.g., Fig. 7) where each point shows the MAE for a given test scene and their color hue represents the mean SBR of the scene. Outliers with an MAE larger than $50\mathrm{mm}$ are not visible in the plot, however, they are included in the calculation of the statistics. Finally, when comparing different compressive histogram strategies the compression ratio is fixed. The compression ratio (CR) is the ratio of the block size and the length of the compressive histogram (i.e., $\mathrm{CR} = (M_t \cdot M_r \cdot M_c) / K$ ). + +# 6.2.3D Imaging Performance + +Compression vs. Performance: Fig. 4 shows the performance of compressive histograms as a function of the compression ratio. The learned coding tensors consistently outperform the temporal Fourier-based C. At low SBR and $\mathrm{CR} > 100$ , it becomes essential for the learned coding tensors to utilize spatio-temporal information (i.e., green and red lines). Moreover, the proposed models can outperform the peak compression oracle for $\mathrm{CR} \leq 64$ . Overall, learned spatio-temporal coding tensors provide robust performance that degrades gracefully as compression increases. + +Importance of Learned Coding Tensors: Fig. 5 compares the depth reconstructions of compressive histograms with coding tensors that were optimized (ours) against coding tensors that were fixed and not optimized throughout training. The extreme quantization in coarse histograms causes large systematic depth errors. Random unoptimized coding tensors consistently produce lower-quality depth reconstructions. A well-designed coding tensor based on Fourier codes can produce reasonable depth reconstructions at $64\mathrm{x}$ compression, however, at $128\mathrm{x}$ compression, scene details become blurred. The proposed learned coding tensors are + +![](images/1acdcfb5f9ed672dbfd42a85440f83f4509dc395363474fa4d291bdca5e68a9b.jpg) +Figure 5. Importance of Learned Coding Tensors. Depth reconstructions at $64\mathrm{x}$ (top) and $128\mathrm{x}$ (bottom) compression for compressive histogram models whose coding tensors were hand-designed (coarse histogram and Fourier-based), learned (proposed), and not learned (randomly initialized). The simulated scene had an $\mathrm{SBR} = 0.1$ , where the mean signal and background photon levels were [50, 500]. + +![](images/37ae801c01dea273e49d3fed2244e0ce80bdeac1a0db27554c5a349df13531ae.jpg) +Figure 6. What if we could compute depths in-pixel? Depth reconstructions at high and low SBR with mean signal and background photon levels of [10, 10] and [10, 1000], respectively. The compressive histograms have a compression of 64. + +able to generate high-quality reconstructions comparable to the no-compression oracle. Overall, optimizing the coding tensors can provide non-trivial performance gains. + +What if we could compute depths in-pixel? Fig. 6 compares the depth reconstruction quality of two learned coding tensors at $64\mathrm{x}$ compression with the peak compression oracle described in Sec. 6.1. At high SBR, all methods recover the fine and coarse scene details. At low SBR the peak compression oracle fails to reconstruct high-level scene structures such as the rings in the red box, while the learned coding tensors better preserve these coarse and fine details. + +# 6.3. Exploring the Coding Tensor Design Space + +When does spatio-temporal coding help? Fig. 7 shows the effect of increasing the spatial dimension of C, at 64x compression. At high SBR, all methods have similar MAE, but, coding tensors with smaller spatial dimensions better preserve fine details (e.g., sticks). On the other hand, at low SBR, coding tensors with larger spatial dimensions preserve high-level details such as the pot handle. This difference is also observed in the scatter plot where the mean and median of the $256 \times 1 \times 1$ C do not match which indicates multiple low SBR scenes with high MAE. + +![](images/3e7aec92c344bb8012c473390d45fe8e4b9b688400bd7eb00a13752daa8a3c95.jpg) +Figure 7. When do spatio-temporal coding tensors help? Each scatter plot point corresponds to the MAE of a test scene. The images directly below each model correspond to the depth reconstructions for two test examples at high and low SBR levels whose mean signal and background photons per pixel are [10, 10] and [10, 1000], respectively. For a fixed compression level, the spatial block size of each model is increased from left to right and $K$ is adjusted to maintain the same compression level. The coding tensors for all models in this plot are learned and separable. + +How does reducing the size of C affect performance? Fig. 8 shows the effect of reducing the size of C at $128\mathrm{x}$ compression. The coding tensors size is reduced by training models with separable coding tensors that operate on smaller histogram blocks. The performance difference between full and separable coding tensors $(1024\times 4\times 4)$ is negligible. As we further reduce the number of parameters in C, the overall performance degrades. Coding tensors with fewer parameters that operate on smaller histogram blocks tend to produce blurrier reconstructions. This can be observed in the red box where the coding tensors with less than 10,000 parameters blurs the spikes. Nonetheless, as discussed in Sec. 4.1, a parameter-efficient C is desirable due to the limited in-sensor memory. Ultimately, a practical + +![](images/820f2c20befd626ed26778c03e802af27661f9b8991e64cdd54e7da08f3753f8.jpg) +Figure 8. How does Reducing Size of C Affect Performance?. Each scatter plot point corresponds to the MAE of a test scene. The images directly below each model correspond to the depth reconstructions for two test scenes at high and low SBR levels whose mean signal and background photons per pixel are [10, 10] and [10, 1000], respectively. The size of C is reduced from left to right by making it separable or reducing the $M_{t}$ . + +compressive SPAD-based 3D camera design requires determining the trade-off between parameter efficiency and 3D imaging quality, which may depend on the application. + +# 6.4. Evaluation on Real-world Data + +Fig. 9 shows the depth reconstructions at $256\mathrm{x}$ compression of multiple compressive histograms and the no compression baseline on the real-world experimental data from [21]. In low SBR scenes, such as the outdoor capture of the ball falling down stairs (first row), Truncated Fourier blurs the staircase edges, while the learned spatio-temporal C preserved these details. Compared to the no compression oracle, compressive histogram models produce less smooth depth images with some small artifacts. This suggests that the compressive histogram models could benefit from a spatial regularizer such as the one used when training the no compression oracle. Additional results and details on this evaluation are available in the supplement. + +# 6.5. On-chip Implementation and Power Analysis + +To validate the feasibility of compressive histograms, we implement them on the UltraPhase chip which has a $3 \times 6$ processor core array [4]. At this time, UltraPhase has not been 3D stacked on a SPAD sensor, thus we only evaluate its compute and data readout power consumption. Fig. 10 shows the power dissipated by UltraPhase when processing photon timestamps with different methods and transferring data off-sensor. Although compressive histograms dissipate more power on computation (blue), this is less than $0.3\%$ of the overall power consumption, which is dominated by data readout. Due to limited memory in UltraPhase (4096 bits per core), our method learns $\mathbf{C}^{\mathrm{spatial}}$ and uses Fourier codes + +![](images/ec85109e03b0c08584b6f8ee8fa8cca029a09e73d3a013edeca40d0f6f79490a.jpg) +Figure 9. Depth Reconstructions of Real-world SPAD Data at $256\mathrm{x}$ Compression. Depth reconstructions of different scenes captured with a SPAD-based 3D camera prototype [21]. + +![](images/a99aad7ded3d12d585c2eed772a438c9d8fd9325417498c04cfb9160352afd10.jpg) +Figure 10. Compute vs. Data Readout Power. Average power dissipated by $2 \times 2$ SPADs processing 500 timestamps per depth frame and operating at 30 depth frames per second. Compute power is obtained from the implementation on the UltraPhase SPAD processors [4]. Readout power is estimated from the output data rate assuming the readout scheme of the SwissSPAD2 [42]. Coarse histograms use 8-bit precision, while compressive histograms use 16-bit precision. Note the difference in blue and orange scales. + +for $\mathbf{C}^{\mathrm{temporal}}$ due to their memory efficient implementation. We also quantize $\mathbf{C}$ to 8 bits and find no degradation in performance. Refer to the supplement for additional details. + +# 7. Discussion + +SPAD-based 3D cameras encounter a data bottleneck between the SPAD array and the compute module when transferring the photon timestamps. A histogram tensor can help summarize timestamps at low resolutions, but as megapixel SPAD arrays become available, histogram tensors also lead to a data bottleneck. To overcome this limitation we proposed compressive histograms as a compact representation that can be built on-the-fly, as each photon is detected. As a consequence, compressive histograms can reduce the insensor memory and data rates because neither the photon data stream nor a histogram tensor needs to be stored or transferred. Our results show that high-quality depth information can be recovered from a learnt compressive histogram representation that is up to 2 orders of magnitude smaller than a histogram tensor representation. + +Practical compressive histogram operating points: The + +learned separable $256 \times 4 \times 4$ and $256 \times 2 \times 2$ C, achieved a good balance between parameter efficiency vs. reconstruction quality, and require on the order of 10-100kbits of memory. In an UltraPhase-like chip this would require distributing C among at least 8x8 cores (4kbits per core). If the temporal dimension is fixed to Fourier-based Ctemporal such as the ones from [13, 36], the number of parameters can be reduced by 10-40x (see Suppl. Sec. 3.3) which enables storing C on a per-pixel basis and made the Ultra-Phase evaluation possible. Overall, for a 1MP SPAD sensor with 1000 bins per-pixel, compressive histograms that can provide more than 50x compression would result in practical data rates of $\sim 0.6\mathrm{GB/s}$ which USB 3.2 can support. + +Trade-off space: Compressive histograms establish a trade-off between reconstruction fidelity, data bandwidth, and in-sensor compute and memory resources. For a fixed bandwidth, a coarse histogram requires arguably the lowest in-sensor resources but leads to poor reconstructions. Fourier-based histograms can improve reconstruction fidelity, at the expense of increased in-sensor computation and memory. The proposed generalization of compressive histograms allows further increasing reconstruction accuracy, at the expense of additional in-sensor memory over Fourier-based methods. Ultimately, the correct trade-off for a given scenario will be determined by power, application, and hardware constraints. + +Although compressive histograms require more insensor computation than coarse histograms, our method presents a practical solution from a power consumption and a real-time application perspective. Power consumption is primarily determined by data rates. Fig. 10 and Suppl. Fig. 4 shows that despite compressive histograms dissipating $100\mathrm{x}$ more processing power than coarse histograms, their overall power consumption is still lower even when data rates are only reduced by $2\mathrm{x}$ . The processing time for building compressive histograms is $\sim 0.5\mathrm{ms}$ (Suppl. Fig. 5). From a real-time (i.e., 30 FPS) or a high-speed application standpoint, this additional processing time is nearly negligible since it is overlapped with acquisition/exposure time. + +From a hardware perspective, the importance of reducing the memory overhead of $\mathbf{C}$ depends on resolution. In low-resolution SPAD cameras, memory-efficient $\mathbf{C}$ are essential because they are stored among a single or a few pixels. The proposed method allowed integrating memory-efficient Fourier codes with learned spatial codes, which were implemented on the 2x2 pixels of UltraPhase (Suppl. Sec. 2). As resolution increases and $\mathbf{C}$ is shared among more pixels, the memory overhead reduces, and less parameter-efficient $\mathbf{C}$ with increased reconstruction fidelity can be considered. + +Bias in Learned C: In the supplement, we show that coding tensors with $M_{t} = N_{t}$ develop a depth range bias. These coding tensors learn to zero out photons coming from distances that are less common in the dataset since they are usually background/noise photons. Interestingly, learned + +coding tensors with $M_t < N_t$ avoid this bias and generalize to depths that are less common in the training set. + +Generalization: There are multiple generalization axes including signal and ambient light levels, sensor and laser parameters (e.g., resolution, pulse waveform), and scene response complexity (e.g., depth range, indirect reflections). Our evaluation has probed some of them. Specifically, our training set only included a subset of the signal and ambient light levels that the test set contained. Furthermore, the model was trained and tested on histogram tensors with different resolutions. Finally, the dataset bias investigation showed that models with $N_{t} \leq 256$ generalized well to less prevalent depths during training (Suppl. Sec. 1). + +We further discuss the model's ability to generalize in other scenarios. For instance, all learned models (including baselines) are unlikely to generalize well to wider laser pulses, because if the model is trained with a narrow pulse width, it learns to extract signal information from high frequencies which will only contain noise in the wider pulse. Similarly, these learned models may generalize to narrower pulse widths. Furthermore, we anticipate a learned C with the properties described in [13] to be robust to diffuse indirect reflections but may require data augmentation to generalize to other light transport scenarios. + +Why not compute depths in-sensor? SPAD-based 3D cameras with large in-pixel memory could store per-pixel histograms and reduce data rates by computing depths in-pixel (i.e., peak compression oracle). Our results show that compressive histogram can provide similar reconstruction quality and outperform this method at low SBR without requiring the storage of the full histogram tensor in-sensor. + +Additional Coding Tensor Designs: Although we find promising empirical results for the coding tensor representations described in this paper, the optimal set of coding tensors will depend on the exact hardware specifications (e.g., in-pixel memory, system bandwidth) and scene-dependent parameters (e.g., SBR, geometry, albedo). Additional lightweight C designs could rely on other factorization techniques and weight quantization. + +Task-specific Compressive Histograms: Histogram tensors are used in other active single-photon imaging modalities such as fluorescence lifetime microscopy [34], nonline-of-sight [10, 23, 29], and diffuse optical tomography [22, 45, 24]. 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Surface detection for sketched single photon lidar. arXiv preprint arXiv:2105.06920, 2021. 2 +[38] Nathan Silberman, Derek Hoiem, Pushmeet Kohli, and Rob Fergus. Indoor segmentation and support inference from rgbd images. In European conference on computer vision, pages 746-760. Springer, 2012. 5 +[39] Haley M So, Julien NP Martel, Piotr Dudek, and Gordon Wetzstein. Mantissacam: Learning snapshot high-dynamic-range imaging with perceptually-based in-pixel irradiance encoding. arXiv preprint arXiv:2112.05221, 2021. 2 +[40] Zhanghao Sun, David B Lindell, Olav Solgaard, and Gordon Wetzstein. Spadnet: deep rgb-spad sensor fusion assisted by monocular depth estimation. Optics express, 28(10):14948-14962, 2020. 5 + +[41] Julián Tachella, Michael P Sheehan, and Mike E Davies. Sketched rt3d: How to reconstruct billions of photons per second. In ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1566-1570. IEEE, 2022. 2 +[42] Arin Can Ulku, Claudio Bruschini, Ivan Michel Antolović, Yung Kuo, Rinet Ankri, Shimon Weiss, Xavier Michalet, and Edoardo Charbon. A $512 \times 512$ spad image sensor with integrated gating for widefield film. IEEE Journal of Selected Topics in Quantum Electronics, 25(1):1-12, 2018. 8 +[43] Edwin Vargas, Julien NP Martel, Gordon Wetzstein, and Henry Arguello. Time-multiplexed coded aperture imaging: Learned coded aperture and pixel exposures for compressive imaging systems. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2692-2702, 2021. 2 +[44] Chao Zhang, Ning Zhang, Zhijie Ma, Letian Wang, Yu Qin, Jieyang Jia, and Kai Zang. A $240 \times 160$ 3d-stacked spad dtof image sensor with rolling shutter and in-pixel histogram for mobile devices. IEEE Open Journal of the Solid-State Circuits Society, 2:3-11, 2021. 4 +[45] Yongyi Zhao, Ankit Raghuram, Hyun Kim, Andreas Hielscher, Jacob T Robinson, and Ashok Narayanan Veeraraghavan. High resolution, deep imaging using confocal time-of-flight diffuse optical tomography. 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One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that encodes distances along the time axis. As the spatio-temporal resolution of the histogram tensor increases, the in-pixel memory requirements and output data rates can quickly become impractical. To overcome this limitation, we propose a family of linear compressive representations of histogram tensors that can be computed efficiently, in an online fashion, as a matrix operation. We design practical lightweight compressive representations that are amenable to an in-pixel implementation and consider the spatio-temporal information of each timestamp. Furthermore, we implement our proposed framework as the first layer of a neural network, which enables the joint end-to-end optimization of the compressive representations and a downstream SPAD data processing model. We find that a well-designed compressive representation can reduce in-sensor memory and data rates up to 2 orders of magnitude without significantly reducing 3D imaging quality. Finally, we analyze the power consumption implications through an on-chip implementation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 521, + 128, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 128, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 128, + 533 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 540, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 694 + ], + "type": "text", + "content": "3D cameras based on single-photon avalanche diode technology (SPAD) are becoming increasingly popular for a wide range of applications that require high-resolution and low-power depth sensing, ranging from autonomous vehicles [1] to consumer smartphones [2]. Kilo-to-megapixel resolution SPAD pixel arrays [27, 28] have the capability of capturing the time-of-arrival of billions of individual photons per frame with extremely high (picosecond) time resolution [31]. Unfortunately, this extreme sensitivity and high speed comes at a cost — the raw timestamp data causes a severe bottleneck between the image sensor and the image signal processor (ISP) that processes this data (Fig. 1(a)). This data bottleneck severely limits the wider use of high-" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 326, + 204, + 527, + 287 + ], + "blocks": [ + { + "bbox": [ + 326, + 204, + 527, + 287 + ], + "lines": [ + { + "bbox": [ + 326, + 204, + 527, + 287 + ], + "spans": [ + { + "bbox": [ + 326, + 204, + 527, + 287 + ], + "type": "image", + "image_path": "e6bf66f7edf47a672e7fb68c930b15195df549b9a7d885a6f362ba4d25bf7c77.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 326, + 288, + 520, + 365 + ], + "blocks": [ + { + "bbox": [ + 326, + 288, + 520, + 365 + ], + "lines": [ + { + "bbox": [ + 326, + 288, + 520, + 365 + ], + "spans": [ + { + "bbox": [ + 326, + 288, + 520, + 365 + ], + "type": "image", + "image_path": "ed1878b6bbec76a0902ee2bc93d51cea753f43822d10ea7c417ed927ce4e404b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 369, + 546, + 456 + ], + "lines": [ + { + "bbox": [ + 305, + 369, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 546, + 456 + ], + "type": "text", + "content": "Figure 1. Resolving SPAD data bottleneck with learned compression. (a) Conventional SPAD-based 3D cameras stream raw photon timestamps or summary histograms off the image sensor which causes a data bottleneck between the image sensor and the on-camera image and signal processing (ISP) module. (b) Our method applies a lightweight, on-sensor compressive coding scheme to the photon timestamp data which is later decoded at the ISP, resolving the data bandwidth limitation." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 464, + 514, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 514, + 476 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 514, + 476 + ], + "type": "text", + "content": "resolution SPAD arrays in 3D sensing applications." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 477, + 546, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 546, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 546, + 618 + ], + "type": "text", + "content": "One common approach to avoid transferring individual photon timestamps is to build a histogram in each pixel. This results in a 3D histogram tensor that is transferred off-sensor for processing. Although this may be practical at low spatio-temporal resolutions (e.g., " + }, + { + "bbox": [ + 304, + 477, + 546, + 618 + ], + "type": "inline_equation", + "content": "64 \\times 32" + }, + { + "bbox": [ + 304, + 477, + 546, + 618 + ], + "type": "text", + "content": " pixels with 16 time bins [15]), it requires higher in-sensor memory. Moreover, the data rates of this histogram tensor representation also scale rapidly with the spatio-temporal resolution and maximum depth range. For example, a megapixel SPAD-based 3D camera operating at 30 fps that outputs a histogram tensor with a thousand 8-bit bins per pixel would require an unmanageable data transfer rate of 240 Gbps." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 619, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 619, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 619, + 547, + 715 + ], + "type": "text", + "content": "To overcome the above limitations, we seek to design compressive representations of 3D histogram tensors. In order to reduce the data rates output by the SPAD camera, the compact representation needs to be built in-pixel or inside the focal plane array (FPA). This is illustrated in Fig. 1(b). Due to the limited in-pixel memory and compute, the compressive representation needs to be built in a streaming manner, with minimal computations per photon. Photon" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 38 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 184, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 184, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 184, + 712 + ], + "type": "inline_equation", + "content": "^{\\ddagger}" + }, + { + "bbox": [ + 58, + 702, + 184, + 712 + ], + "type": "text", + "content": "Email: fgutierrez3@wisc.edu" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10756" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "histogram tensors are very different from conventional RGB images/video data. Therefore, traditional compression algorithms such as MPEG are not directly applicable." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 287, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 287, + 317 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 287, + 317 + ], + "type": "text", + "content": "We propose a family of compressive representations for 3D histogram tensors that can be computed in an online fashion with limited memory and compute. They are based on the linear spatio-temporal projection of each photon timestamp, which can be expressed as a simple matrix operation. Instead of constructing per-pixel timestamp histograms, a compressive encoding maps its spatio-temporal information into a compressive histogram. To exploit local spatio-temporal correlations, a single compressive histogram is built for a local 3D histogram block as illustrated in Fig. 2. Instead of building and storing the full 3D histogram tensor in-sensor, multiple compressive histograms are built and transferred off-sensor for processing, effectively reducing the required in-sensor memory and data rates. Recent works proposed a similar compression framework based on compressive histograms [13] or sketches [36]. In Sec. 4, we show that these prior works can be viewed as special cases of our proposed framework." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 319, + 287, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 423 + ], + "type": "text", + "content": "In this paper, we explore the design space of spatiotemporal compressive encodings and analyze the trade-offs between different design choices. Furthermore, we present a method to integrate our compression framework with data-driven SPAD data processing methods using convolutional neural networks (CNNs), which enables end-to-end optimization of the compressive encoding and a SPAD data processing CNN. We demonstrate the feasibility of compressive histograms through an on-chip implementation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 424, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 635 + ], + "type": "text", + "content": "For our experimental evaluation, we integrate the compressive histograms framework with a state-of-the-art learning-based denoising model for SPAD-based 3D imaging [32]. Our results show that the jointly optimized compressive encoding and CNN can consistently reduce data rates up to 2 orders of magnitude in a wide range of signal and noise levels. Moreover, for a given compression level, it can increase 3D imaging accuracy over previous hand-designed compressive histograms that only exploit temporal information [13, 36], especially in low signal-to-background ratio (SBR) scenarios and at higher compression rates. Furthermore, we show that learned compressive histograms can perform comparably and sometimes even outperform a theoretical SPAD sensor design where the full 3D histogram tensor is stored in-sensor and only per-pixel depths are transferred off-sensor. Finally, we analyze the power consumption of a compressive histogram implemented on the UltraPhase SPAD processing chip [4]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 644, + 134, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 134, + 656 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 134, + 656 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "content": "Compressive histograms, also called sketches, are an emerging framework for online in-sensor compression of SPAD timestamp data [13, 41, 36, 33]. A coarse histogram is one common compressive histogram approach [13] to re" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 213 + ], + "type": "text", + "content": "duce data rates and in-pixel memory [15, 8, 18]. Despite their practical hardware implementation, coarse histograms achieve sub-optimal depth accuracy compared to compressive histograms based on Fourier [36, 37, 13] and Gray [13] codes. One limitation of these approaches is that the compressive representation only exploits the temporal information of the incident timestamp, and disregards the spatial redundancy. In this work, we generalize the compressive histogram framework to utilize the spatio-temporal information of each timestamp. Moreover, instead of relying on hand-designed coded projections, in this paper we learn them as the first layer of a CNN." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 217, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 323 + ], + "type": "text", + "content": "- Shared In-Pixel Histograms: One common design is to have multiple neighboring SPAD pixels have a single shared memory where all timestamps are aggregated into a coarse histogram (e.g., " + }, + { + "bbox": [ + 304, + 217, + 545, + 323 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 304, + 217, + 545, + 323 + ], + "type": "text", + "content": " [18, 15], " + }, + { + "bbox": [ + 304, + 217, + 545, + 323 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 217, + 545, + 323 + ], + "type": "text", + "content": " [20]). This approach throws away the local spatial information (i.e., pixel location) of the detected photon timestamps. A compressive histogram is well-suited for these shared memory designs because it can be shared among multiple SPAD pixels and preserves spatial information through the coded projection." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 327, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 526 + ], + "type": "text", + "content": "Neural Sensors and Pixel Processor Arrays: Pixel processor arrays (PPAs) are an emerging sensing technology that embeds processing electronics inside each pixel [9]. This new sensing paradigm begins processing the image at the focal plane array, which allows it to reduce the sensor data rates by transmitting only the relevant information, and consequently, it increases the sensor's throughput [9] which can enable computer vision at 3,000 fps [6, 7]. PPAs have also become building blocks of novel computational imaging systems optimized end-to-end for HDR imaging [25, 39], motion deblurring [30], video compressive sensing [25], and light field imaging [43]. A compressive histogram relies on a similar in-pixel processing paradigm. Similar to previous works, we jointly optimize the sensor parameters (i.e., the compressive histogram) and the processing algorithm (i.e., the CNN), but to our knowledge, this work is the first to use this approach for SPAD data compression." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 539, + 511, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 511, + 553 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 511, + 553 + ], + "type": "text", + "content": "3. Single-Photon 3D Histogram Tensors" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 559, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 595 + ], + "type": "text", + "content": "SPAD-based 3D cameras consist of a SPAD sensor and a pulsed laser that illuminates the scene. The photon flux signal arriving at pixel, " + }, + { + "bbox": [ + 304, + 559, + 545, + 595 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 559, + 545, + 595 + ], + "type": "text", + "content": ", can be written as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 605, + 545, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 605, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 315, + 605, + 545, + 620 + ], + "type": "interline_equation", + "content": "\\Phi_ {\\boldsymbol {p}} (t) = a _ {\\boldsymbol {p}} h \\left(t - 2 d _ {\\boldsymbol {p}} / c\\right) + \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}} = \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {s i g}} (t) + \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}}, \\tag {1}", + "image_path": "95c55bd328f5a32b48cc2eb148400975cd29b193b81f83b2a7e5f1f0af4a72e0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "a_{p}" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " is the amplitude of the returning signal accounting for laser power, reflectivity, and light fall-off; " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "h(t)" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " is the system's impulse response function (IRF) which accounts for pulse waveform and sensor IRF; " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "d_{p}" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " is the distance to the point imaged by " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " is the speed of light; and " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Phi_{p}^{\\mathrm{bkg}}" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " is the constant photon flux due to background illumination (e.g., sunlight). This model assumes direct-only reflections" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10757" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 351, + 221 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 351, + 221 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 351, + 221 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 351, + 221 + ], + "type": "image", + "image_path": "ccb75f2aaef93d94c8ba5be029ed2f756361ca7ab11b161cf5e2081f6d5461ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": "Figure 2. Compressive Histogram Formation. Histogram tensors, " + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": ", are a 3D spatio-temporal grid whose elements store the number of photons that arrived within a short time interval. (a) In SPAD-based 3D imaging, the temporal axis of " + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": " encodes distances. (b) A histogram block, " + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": ", can be expressed as the sum of " + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": " one-hot encoding tensors, where each tensor represents a photon timestamp. (c) A compact representation of " + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": " can be built by applying " + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": " linear projections (i.e., dot product) with pre-designed coding tensors. (d) The compressive histogram, will be a vector with " + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": " elements whose compression capacity is given by " + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "inline_equation", + "content": "\\frac{M_t \\cdot M_r \\cdot M_c}{K}" + }, + { + "bbox": [ + 46, + 222, + 546, + 277 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 353, + 70, + 544, + 221 + ], + "blocks": [ + { + "bbox": [ + 353, + 70, + 544, + 221 + ], + "lines": [ + { + "bbox": [ + 353, + 70, + 544, + 221 + ], + "spans": [ + { + "bbox": [ + 353, + 70, + 544, + 221 + ], + "type": "image", + "image_path": "3dab483cae28c9552f5efd54c97c53c2380536942ed77069c51ba3e6cbc230eb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 290, + 287, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 313 + ], + "type": "text", + "content": "which is a valid approximation, in particular, for scanning-based ToF 3D imaging systems [3]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "text", + "content": "TCSPC-based SPAD cameras measure " + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\Phi_p(t)" + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "text", + "content": " by building a per-pixel timing histogram, where the " + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "text", + "content": "th histogram bin records the number of photons that arrived in a time interval of length " + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "text", + "content": ", which follows a Poisson process " + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 313, + 287, + 361 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 112, + 367, + 287, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 367, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 112, + 367, + 287, + 383 + ], + "type": "interline_equation", + "content": "\\Phi_ {i, \\boldsymbol {p}} = \\mathcal {P} \\left(\\Phi_ {i, \\boldsymbol {p}} ^ {\\mathrm {s i g}} + \\Delta \\Phi_ {\\boldsymbol {p}} ^ {\\mathrm {b k g}}\\right). \\tag {2}", + "image_path": "91ffc397577c22991f4fcd6fca8e99e721ecd4ad85c3605dbfa8cc417a34bb3d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "content": "The pulse repetition period, " + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "content": ", determines the maximum timestamp value and the length of the histogram vector " + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\Phi_p = (\\Phi_{i,p})_{i=0}^{N_t - 1}" + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "inline_equation", + "content": "N_t = \\tau / \\Delta" + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "content": ". Therefore, one assumption built into " + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\Phi_p" + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "content": ", is that no signal photons had a timestamp larger than " + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "content": ", which means that the maximum distance that " + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\Phi_p" + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "content": " can encode is " + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "inline_equation", + "content": "d_{\\max} = \\frac{c\\tau}{2}" + }, + { + "bbox": [ + 46, + 388, + 287, + 481 + ], + "type": "text", + "content": ". Furthermore, we assume that pile-up distortions are minimized through various SPAD data acquisition techniques [11, 15, 16, 12]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": "This process generates a " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "N_{t} \\times N_{r} \\times N_{c}" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " 3D histogram tensor, " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\pmb{H} = (\\Phi_p)_{p=0,0}^{(N_r - 1, N_c - 1)}" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": ". In challenging 3D imaging scenarios with high background illumination, building " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\pmb{H}" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " off-sensor requires transferring thousands of photon timestamps per-pixel leading to data rates of hundreds of GB/s in a megapixel sensor. Moreover, building and storing a high-resolution " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\pmb{H}" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " in-sensor would require significant memory (1GB for a megapixel SPAD camera with 1000 time bins per-pixel), and transferring it would continue to lead to impractical data rates of tens of GB/s on a SPAD-based 3D camera operating at 30fps. Overall, a practical SPAD-based 3D camera would build and store a compact representation of " + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\pmb{H}" + }, + { + "bbox": [ + 46, + 481, + 287, + 649 + ], + "type": "text", + "content": " in-sensor and then transfer it to a processing chip (e.g., FPGA, ISP, embedded computer) where it is processed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 658, + 276, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 276, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 276, + 672 + ], + "type": "text", + "content": "4. Spatio-temporal Compressive Histograms" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "type": "text", + "content": "A natural approach to compress " + }, + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{H}" + }, + { + "bbox": [ + 46, + 678, + 287, + 714 + ], + "type": "text", + "content": " that exploits its local correlations due to smooth depths and photon flux, is to build a compressive representation of a local 3D histogram" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 289, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 348 + ], + "type": "text", + "content": "block as illustrated in Fig. 2. To avoid storing or transferring the photon timestamp stream, the compressive representation is built as each timestamp arrives. In this section, we present an online compression framework for histogram blocks based on the coded projection of photon timestamps." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " be the " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": "th histogram block of " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " with dimensions " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "M_{t} \\times M_{r} \\times M_{c}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "M_{t} \\leq N_{t}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "M_{r} \\leq N_{c}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "M_{c} \\leq N_{c}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ". First, we observe that " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " can be expressed as the sum of " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " one-hot encoding tensors, each representing one photon detection within " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " (Fig. 2b). Specifically, let " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "t_{b,j}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " be a " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "M_{t} \\times M_{r} \\times M_{c}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " one-hot encoding tensor representing the " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "j^{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " photon timestamp detected in histogram block " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", whose elements are all 0 except for " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "t_{b,j,l,p'} = 1" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "l = \\left\\lfloor \\frac{T_j \\mod (\\Delta M_t)}{\\Delta} \\right\\rfloor" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "T_{j}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " is the timestamp value, and " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "p'" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " is the pixel where the timestamps was detected. Using this representation we can write " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 392, + 485, + 545, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 485, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 392, + 485, + 545, + 519 + ], + "type": "interline_equation", + "content": "\\boldsymbol {H} _ {b} = \\sum_ {j = 0} ^ {J - 1} \\boldsymbol {t} _ {b, j}. \\tag {3}", + "image_path": "b150be95239310210eb4c52f4f6590d26375d03f623cc3adf1ddeec227c8182f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "text", + "content": " can be compressed in an online fashion through the linear projection of each timestamp tensor; expressed as the inner product with " + }, + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "text", + "content": " pre-designed coding tensors, " + }, + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_k" + }, + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "text", + "content": ", with dimensions " + }, + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "inline_equation", + "content": "M_t\\times M_r\\times M_c" + }, + { + "bbox": [ + 304, + 524, + 545, + 572 + ], + "type": "text", + "content": ", as in Fig. 2. Mathematically," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 328, + 576, + 545, + 611 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 576, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 328, + 576, + 545, + 611 + ], + "type": "interline_equation", + "content": "\\widehat {Y} _ {b, k} = \\mathbf {C} _ {k} \\cdot \\boldsymbol {H} _ {b} = \\sum_ {j = 0} ^ {J - 1} \\mathbf {C} _ {k} \\cdot \\boldsymbol {t} _ {b, j} = \\sum_ {j = 0} ^ {J - 1} \\mathbf {C} _ {k, l, \\boldsymbol {p} ^ {\\prime}}, \\tag {4}", + "image_path": "fbcaeaf81764798dbe920464e82133256c66bdbcfed76ab9695cd8dcc7ba5c2a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": " denotes element-wise multiplication, and " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{p}^{\\prime}" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": " are the indices where " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{t}_{b,j,l,\\pmb{p}^{\\prime}} = 1" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": ". We define " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_b = (\\widehat{Y}_{b,k})_{k=0}^{K-1}" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": " as the compressive histogram of " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{H}_b" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": ". Compressive histograms, as defined in [13, 36], are a special case of Eq. 4 where " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": " compresses individual histograms and disregards spatial information (i.e., " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "M_t = N_t" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "M_r = 1" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "inline_equation", + "content": "M_c = 1" + }, + { + "bbox": [ + 304, + 616, + 546, + 714 + ], + "type": "text", + "content": "). Note that each timestamp in Eq. 4 is processed efficiently on-the-fly after each photon detection through a simple lookup" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10758" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "operation. Moreover, individual histogram blocks or timestamps are never explicitly stored or transferred off-sensor." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 102, + 219, + 115 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 102, + 219, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 102, + 219, + 115 + ], + "type": "text", + "content": "4.1. Practical Coding Tensor Design" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 121, + 287, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 287, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 287, + 215 + ], + "type": "text", + "content": "Compressive histograms, when implemented as in Eq. 4, introduce an in-sensor memory overhead because, in addition to storing " + }, + { + "bbox": [ + 46, + 121, + 287, + 215 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_b" + }, + { + "bbox": [ + 46, + 121, + 287, + 215 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 121, + 287, + 215 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 121, + 287, + 215 + ], + "type": "text", + "content": " needs to be stored in-sensor for efficient lookup operations. Therefore, a practical compressive single-photon camera implementation would rely on parameter-efficient coding tensors that minimize this overhead. Here, we present two strategies to design practical coding tensors that are evaluated in Sec. 6." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "text", + "content": "The memory overhead makes certain coding tensor designs impractical. Consider a set of coding tensors that operate on the full histogram tensor, i.e., " + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "inline_equation", + "content": "\\pmb{H}_b = \\pmb{H}" + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "text", + "content": ". In this case, the number of elements in " + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "text", + "content": " will exceed the number of elements of " + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "inline_equation", + "content": "\\pmb{H}" + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "text", + "content": ". Consequently, although the data rates are reduced in this scenario since " + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "inline_equation", + "content": "K < (N_t \\cdot N_r \\cdot N_c)" + }, + { + "bbox": [ + 46, + 216, + 287, + 332 + ], + "type": "text", + "content": ", the insensor memory required exceeds the size of the histogram tensor. To circumvent this issue, we propose two complementary strategies to design lightweight coding tensors: local block-based and separable." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": "Local Block-based Coding Tensors: As we reduce the size of the histogram block, " + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": ", represented by a compressive histogram, the size of the coding tensors decreases. Therefore, compressing local histogram blocks is not only beneficial due to local spatio-temporal redundancies, but also because these local coding tensors have fewer parameters. One example of local block-based coding tensors are the ones used in temporal compressive histograms [13, 36] where " + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "inline_equation", + "content": "H_{b}" + }, + { + "bbox": [ + 46, + 335, + 287, + 441 + ], + "type": "text", + "content": " is a per-pixel histogram." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 445, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 525 + ], + "type": "text", + "content": "Separable Coding Tensors: One approach to designing lightweight coding tensors is to make them separable along the temporal and spatial dimensions. This approach is used in parameter-efficient CNN models that use separable depth-wise convolutional layers [17] to reduce model size. Formally, we can write a separable coding tensor as the outer product of two smaller tensors:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 114, + 534, + 287, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 534, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 114, + 534, + 287, + 550 + ], + "type": "interline_equation", + "content": "\\mathbf {C} _ {k} = \\mathbf {C} _ {k} ^ {\\text {t e m p o r a l}} \\otimes \\mathbf {C} _ {k} ^ {\\text {s p a t i a l}}, \\tag {5}", + "image_path": "2333c8ce4071e408e30d920d647df94eab198ee5e86de5a63b89861a7f5bbc64.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_k^{\\mathrm{temporal}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "M_t\\times 1\\times 1" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": " tensor, and " + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_k^{\\mathrm{spatial}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "1\\times M_r\\times M_c" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": " tensor. This design is also motivated by the differences between the temporal and spatial correlations encountered in histogram blocks. In addition to local correlations present in both dimensions, the temporal dimension also exhibits long-range correlations due to the background illumination offset (" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\Phi_p^{\\mathrm{bkg}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": ") in every histogram bin. Therefore, Eq. 5 may be able to represent this prior by encoding the temporal and spatial information independently." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "One assumption made in our memory overhead analysis is that a compressive SPAD-based 3D camera only needs to store a single " + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": " that is shared across the full sensor, which can be implemented in two general ways. One approach" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 74, + 485, + 84 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 74, + 485, + 84 + ], + "spans": [ + { + "bbox": [ + 312, + 74, + 485, + 84 + ], + "type": "text", + "content": "(a) Compressive Histogram Encoding" + } + ] + } + ], + "index": 9, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 310, + 86, + 544, + 166 + ], + "blocks": [ + { + "bbox": [ + 310, + 86, + 544, + 166 + ], + "lines": [ + { + "bbox": [ + 310, + 86, + 544, + 166 + ], + "spans": [ + { + "bbox": [ + 310, + 86, + 544, + 166 + ], + "type": "image", + "image_path": "c2bba31eee76afb3167d1320314952ba3a71f8787afa493aae6dde99cb0fcd4a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 168, + 485, + 178 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 168, + 485, + 178 + ], + "spans": [ + { + "bbox": [ + 312, + 168, + 485, + 178 + ], + "type": "text", + "content": "(b) Compressive Histogram Decoding" + } + ] + } + ], + "index": 11, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 313, + 180, + 543, + 255 + ], + "blocks": [ + { + "bbox": [ + 313, + 180, + 543, + 255 + ], + "lines": [ + { + "bbox": [ + 313, + 180, + 543, + 255 + ], + "spans": [ + { + "bbox": [ + 313, + 180, + 543, + 255 + ], + "type": "image", + "image_path": "405e3bd80fef08f7449db58138a71fe29574ed8303f506fd8f8aabfdad9a9104.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 257, + 545, + 354 + ], + "lines": [ + { + "bbox": [ + 305, + 257, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 545, + 354 + ], + "type": "text", + "content": "Figure 3. Convolutional Compressive Histogram Layer. (a) Building a compressive histogram for each block in the histogram tensor, can be viewed as applying " + }, + { + "bbox": [ + 305, + 257, + 545, + 354 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 257, + 545, + 354 + ], + "type": "text", + "content": " stripped convolutional filters whose weights are the coding tensors. The compressed histogram tensor will be " + }, + { + "bbox": [ + 305, + 257, + 545, + 354 + ], + "type": "inline_equation", + "content": "K\\frac{N_t}{M_t}\\times \\frac{N_r}{M_r}\\times \\frac{N_c}{M_c}" + }, + { + "bbox": [ + 305, + 257, + 545, + 354 + ], + "type": "text", + "content": " tensors. (b) To lift the compressed histogram tensor back to its original domain an unfiltered backprojection operation can be applied on each compressive histogram which decodes a single block. The decoded histogram tensor can then be assembled by concatenating all the decoded blocks." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "text", + "content": "could distribute " + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "text", + "content": " across the local memory of all pixels and then allow communication across pixels as in PPAs [6]. A second approach could store " + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "text", + "content": " in a global memory that can be accessed by all pixels which could be enabled in 3D-stacked SPAD cameras [44]. Finally, some of the coding tensor designs explored in this paper have as few as 640 parameters. In this case, even if " + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "text", + "content": " is stored for every " + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "text", + "content": " group of pixels, the in-sensor memory is still reduced by " + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "inline_equation", + "content": "20 \\times" + }, + { + "bbox": [ + 304, + 369, + 545, + 475 + ], + "type": "text", + "content": " compared to storing a 1024 bin per-pixel histogram." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 486, + 541, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 486, + 541, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 486, + 541, + 499 + ], + "type": "text", + "content": "4.2. Convolutional Compressive Histogram Layer" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 506, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 611 + ], + "type": "text", + "content": "A compressive histogram is built for each histogram block. Therefore, multiple compressive histograms are used to encode the complete histogram tensor. In this way, the coding tensors can be viewed as a set of 3D convolutional filters, which can be implemented as the first layer of a 3D CNN. For simplicity, we assume that histogram blocks do not overlap, and therefore, the stride of the convolutional filters will equal their dimensions. Fig. 3(a) illustrates this convolutional compressive histogram encoding." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 613, + 545, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 672 + ], + "type": "text", + "content": "Unfortunately, the compressed histogram tensor representation is not directly compatible with 3D CNNs that have been designed for SPAD-based 3D imaging (e.g., [32, 21]). To this end, each compressive histogram is lifted back to the original 3D domain through an unfiltered backprojection:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 383, + 682, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 682, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 383, + 682, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\widehat {\\boldsymbol {H}} _ {b} = \\sum_ {k = 0} ^ {K - 1} \\mathbf {C} _ {k} \\widehat {Y} _ {b, k}. \\tag {6}", + "image_path": "a867727791cbfbf5156627d8ad1aa5022c3579925c9f3e1b752cec14f32f0d18.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10759" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "inline_equation", + "content": "\\widehat{H}_b" + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "text", + "content": " is the decoded compressive histogram for block " + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "text", + "content": ", which is the weighted linear combination of the coding tensors. The decoded histogram blocks are then concatenated and given as input to the processing 3D CNN. Fig. 3(b) illustrates this decoding step. The decoding step in Eq. 6 will occur off-sensor, after the compressive histograms have been moved to the camera compute module which has access to larger memory and computational resources than sensor module. One benefit of using the unfiltered backprojection as the upsampling operator is that if all coding tensors are mutually orthogonal, in the limit when " + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "text", + "content": " approaches the size of " + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "inline_equation", + "content": "H_b" + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "text", + "content": " (i.e., no compression), then " + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "inline_equation", + "content": "\\widehat{H}_b \\approx H_b" + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "text", + "content": ". This suggests that at compression rates close to unity, an appropriately trained compressive histogram layer should be approximately equal to an identity transformation applied to " + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "inline_equation", + "content": "H_b" + }, + { + "bbox": [ + 47, + 71, + 289, + 261 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 262, + 288, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 288, + 344 + ], + "type": "text", + "content": "To summarize, a compressive histogram layer comprises an encoding/compression step followed by a decoding step, which uses the coding tensors as the convolutional filters. This layer can be appended to the beginning of any CNN that has been designed to process 3D histogram tensors. Finally, the coding tensors can be jointly optimized with the downstream CNN in an end-to-end manner." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 356, + 213, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 356, + 213, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 213, + 370 + ], + "type": "text", + "content": "5. Datasets and Implementation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 376, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 287, + 424 + ], + "type": "text", + "content": "In this section, we describe the datasets used for model training and testing, and also provide implementation details for the compressive histogram layer and the 3D CNN used for the experiments." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 433, + 111, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 111, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 111, + 445 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 451, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 287, + 559 + ], + "type": "text", + "content": "For training, we generate a synthetic SPAD measurement dataset containing different scenes at a wide range of illumination settings. We use a similar synthetic data generation pipeline used in previous learning-based SPAD-based 3D imaging works [21, 32, 40]. Using Eq. 2, SPAD measurements can be simulated given an RGB-D image, the pulse waveform " + }, + { + "bbox": [ + 47, + 451, + 287, + 559 + ], + "type": "inline_equation", + "content": "(h(t))" + }, + { + "bbox": [ + 47, + 451, + 287, + 559 + ], + "type": "text", + "content": ", and the average number of detected signal and background photons per pixel. Please refer to the supplement for a detailed overview of the simulation pipeline." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "type": "text", + "content": "Simulated Training Dataset: We use the RGB-D images from the NYU v2 dataset [38]. The simulated histograms have " + }, + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "type": "inline_equation", + "content": "N_{t} = 1024" + }, + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "type": "text", + "content": " bins and a " + }, + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Delta = 80" + }, + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "type": "text", + "content": " ps bin size (12.3m depth range). The pulse waveform used has a full-width half maximum (FWHM) of 400ps obtained from [21]. For each scene, we randomly set the average number of signal and background photons detected per pixel to [2, 5, or 10] and [2, 10, 50], respectively. With appropriate normalization, the models generalize to other photon levels despite being trained on this photon-starved dataset. A total of 16,628 histogram tensors with dimensions " + }, + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "type": "inline_equation", + "content": "1024 \\times 64 \\times 64" + }, + { + "bbox": [ + 47, + 560, + 289, + 715 + ], + "type": "text", + "content": " are simulated and split into a training and a validation set with 13,851 and 2,777 examples, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "type": "text", + "content": "Simulated Test Dataset: For testing we use 8 RGB-D images from the Middlebury stereo dataset [35]. The simulated histograms have " + }, + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "N_{t} = 1024" + }, + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "type": "text", + "content": " bins and a " + }, + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\Delta = 100\\mathrm{ps}" + }, + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "type": "text", + "content": " bin size (15.3m depth range). The pulse waveform used is a Gaussian pulse with an FWHM of 318ps (" + }, + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\sigma = 135\\mathrm{ps}" + }, + { + "bbox": [ + 304, + 72, + 545, + 190 + ], + "type": "text", + "content": "). A total of 128 test histogram tensors are generated by simulating each scene with the following average number of detected signal/background photons: 2/2, 2/5, 2/50, 5/2, 5/10, 5/50, 10/2, 10/10, 10/50, 10/200, 10/500, 10/1000, 50/50, 50/200, 50/500, and 50/1000." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 192, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 251 + ], + "type": "text", + "content": "Real-world Experimental Data: To evaluate the generalization of the proposed models, we downloaded raw histogram tensor captured in [21] with a line-scanning SPAD-based 3D camera prototype. Please refer to the supplementary document for details on this dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 258, + 468, + 270 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 258, + 468, + 270 + ], + "spans": [ + { + "bbox": [ + 306, + 258, + 468, + 270 + ], + "type": "text", + "content": "5.2. Training and Implementation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 276, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 312 + ], + "type": "text", + "content": "To simplify training, the input to all models is a 3D histogram tensor, even though compressive histograms can work directly on streams of photon timestamps (Eq. 4)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "text", + "content": "Compressive Histogram Layer: The encoder is implemented as a 3D convolution with a stride equal to the filter size, whose learned filters are the coding tensors, " + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_k" + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "text", + "content": ". We constraint " + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_k" + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "text", + "content": " to be zero-mean along the time dimension. The unfiltered backprojection decoder is implemented as a 3D transposed convolution with a stride equal to its filter size. To help the CNN model generalize to different photon count levels we apply zero-normalization along the channel dimension (i.e., " + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "text", + "content": ") to the inputs " + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "inline_equation", + "content": "(\\widehat{\\mathbf{Y}}_b)" + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "text", + "content": " and the weights (" + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 314, + 546, + 456 + ], + "type": "text", + "content": ") of the transposed convolution, also known as layer-norm [5]. This normalization is also commonly used in depth decoding algorithms [14, 13, 26]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 458, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 545, + 540 + ], + "type": "text", + "content": "Depth Estimation 3D CNN: To estimate depths from the decoded histogram tensor we use the 3D deep boosting CNN model proposed by [32] for single-photon 3D imaging, without the non-local block. Similar to [21, 32] we use the pixel-wise KL-divergence between the output histogram tensor and a normalized true histogram tensor as our objective, and estimate depths using a softargmax." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "type": "text", + "content": "Training: At each training iteration we randomly sample patches of size " + }, + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "type": "inline_equation", + "content": "1024 \\times 32 \\times 32" + }, + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "type": "text", + "content": ". We train all models using the ADAM optimizer [19] with " + }, + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 543, + 545, + 637 + ], + "type": "text", + "content": ", batch size of 4, and a learning rate of 0.001 that decays by 0.9 after every epoch. We train all models for 30 epochs with periodical checkpoints, and for a given model we choose the checkpoint that achieves the lowest root mean squared error (RMSE) on the validation set." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 647, + 450, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 450, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 450, + 659 + ], + "type": "text", + "content": "6. Experiments and Results" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": "In this section, we present the performance at various compression levels for different coding tensor designs jointly optimized with the depth estimation CNN described in Sec. 5. A coding tensor design is determined by the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10760" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 83, + 291, + 178 + ], + "blocks": [ + { + "bbox": [ + 105, + 72, + 247, + 81 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 247, + 81 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 247, + 81 + ], + "type": "text", + "content": "Compression vs. Mean Absolute Error (mm)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 83, + 291, + 178 + ], + "lines": [ + { + "bbox": [ + 50, + 83, + 291, + 178 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 291, + 178 + ], + "type": "image", + "image_path": "aebcfa17b70af6abf98e05ac51128e01b34278264fbc3e4150e2841b7427cf8c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 179, + 542, + 205 + ], + "blocks": [ + { + "bbox": [ + 53, + 179, + 542, + 205 + ], + "lines": [ + { + "bbox": [ + 53, + 179, + 542, + 205 + ], + "spans": [ + { + "bbox": [ + 53, + 179, + 542, + 205 + ], + "type": "image", + "image_path": "a3e2bc1e72a74c6e5abdc63d240035a42c4e3b6f18f5b2f940850268f9c429fb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "text", + "content": "Figure 4. Compression vs. Test Set Metrics. The two left-most plots show the mean absolute error computed over the test set as we increase compression. Similarly, the two right-most plots show the mean percent of pixels whose absolute depth errors were " + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "inline_equation", + "content": "< 10\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "text", + "content": ". The simulated test set images were divided into low (SBR " + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "inline_equation", + "content": "\\leq 0.1" + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "text", + "content": ") and high (SBR " + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "inline_equation", + "content": ">0.1" + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "text", + "content": ") SBR groups to be able to disentangle the impact of SBR on the performance of each model. The dashed lines show the peak and no compression baselines whose compression levels do not vary. Each line corresponds to a fixed coding tensor design for which we vary " + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 208, + 547, + 274 + ], + "type": "text", + "content": " to control the compression level. Moreover, each point for a given compression level corresponds to a single set of coding tensors jointly optimized with the depth estimation 3D CNN." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 299, + 83, + 545, + 179 + ], + "blocks": [ + { + "bbox": [ + 345, + 72, + 512, + 81 + ], + "lines": [ + { + "bbox": [ + 345, + 72, + 512, + 81 + ], + "spans": [ + { + "bbox": [ + 345, + 72, + 512, + 81 + ], + "type": "text", + "content": "Compression vs. Percent Pixels with Errors " + }, + { + "bbox": [ + 345, + 72, + 512, + 81 + ], + "type": "inline_equation", + "content": "< 10\\mathrm{mm}" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 299, + 83, + 545, + 179 + ], + "lines": [ + { + "bbox": [ + 299, + 83, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 299, + 83, + 545, + 179 + ], + "type": "image", + "image_path": "8e06c1940d217b41f4fd313955fdb8048859ec5195721267c9b6b5256b0e6b74.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "text", + "content": "dimensions of " + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_k" + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "inline_equation", + "content": "M_t \\times M_r \\times M_c" + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "text", + "content": "), the size of the compressive histogram (i.e., " + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "text", + "content": "), and if " + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_k" + }, + { + "bbox": [ + 46, + 285, + 287, + 310 + ], + "type": "text", + "content": " is separable." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 318, + 236, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 318, + 236, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 318, + 236, + 330 + ], + "type": "text", + "content": "6.1. Baselines and Performance Metrics" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 337, + 240, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 337, + 240, + 349 + ], + "spans": [ + { + "bbox": [ + 58, + 337, + 240, + 349 + ], + "type": "text", + "content": "We compare against the following baselines:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 351, + 287, + 624 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 47, + 351, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 351, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 287, + 411 + ], + "type": "text", + "content": "- Temporal Truncated Fourier C [36, 13]: A compressive histogram that uses coding tensors with dimensions " + }, + { + "bbox": [ + 47, + 351, + 287, + 411 + ], + "type": "inline_equation", + "content": "1024 \\times 1 \\times 1" + }, + { + "bbox": [ + 47, + 351, + 287, + 411 + ], + "type": "text", + "content": " and whose weights are set using the first " + }, + { + "bbox": [ + 47, + 351, + 287, + 411 + ], + "type": "inline_equation", + "content": "K / 2" + }, + { + "bbox": [ + 47, + 351, + 287, + 411 + ], + "type": "text", + "content": " frequencies of the Fourier matrix. In the supplement, we compare against additional Fourier-based C [13]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 415, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 287, + 450 + ], + "type": "text", + "content": "- Temporal Coarse Histogram C: Here C is a box down-sampling operator along the temporal dimensions which produces a coarse histogram with " + }, + { + "bbox": [ + 47, + 415, + 287, + 450 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 415, + 287, + 450 + ], + "type": "text", + "content": " bins." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 455, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 287, + 514 + ], + "type": "text", + "content": "- No Compression Oracle: In this baseline, we assume the ideal scenario where the histogram tensor is transferred off-sensor and processed with the depth estimation 3D CNN. Similar to [32], we train this model with an initial learning rate of " + }, + { + "bbox": [ + 47, + 455, + 287, + 514 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 47, + 455, + 287, + 514 + ], + "type": "text", + "content": " and total variation regularization." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 519, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 519, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 519, + 287, + 624 + ], + "type": "text", + "content": "- Peak Compression Oracle: This baseline implements an ideal SPAD camera with sufficient in-sensor memory to store the histogram tensor and sufficient computation power to compute per-pixel depths through an \"argmax\" along the time axis. To process the noisy 2D depth images with the 3D CNN, we generate a 3D grid where all elements are zero except for one element per spatial location whose index is proportional to the depth. This model is trained like the no-compression oracle." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 627, + 287, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 627, + 287, + 674 + ], + "spans": [ + { + "bbox": [ + 46, + 627, + 287, + 674 + ], + "type": "text", + "content": "Similar to our proposed approach, all compressive histogram baselines described here, implemented their C as a compressive histogram layer, with fixed weights, whose outputs are processed by the depth estimation 3D CNN." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Evaluation Metrics: The 3D imaging performance of each model is summarized using two metrics: (1) the mean absolute depth error (MAE), (2) and the percent of pixels with" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "type": "text", + "content": "absolute depth errors that are lower than " + }, + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "type": "inline_equation", + "content": "10\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "type": "text", + "content": ". To understand the performance under these metrics we divide the test set into different SBR ranges and report the metrics for each range individually. We also visualize the overall dataset performance as scatter plots (e.g., Fig. 7) where each point shows the MAE for a given test scene and their color hue represents the mean SBR of the scene. Outliers with an MAE larger than " + }, + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "type": "inline_equation", + "content": "50\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "type": "text", + "content": " are not visible in the plot, however, they are included in the calculation of the statistics. Finally, when comparing different compressive histogram strategies the compression ratio is fixed. The compression ratio (CR) is the ratio of the block size and the length of the compressive histogram (i.e., " + }, + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "type": "inline_equation", + "content": "\\mathrm{CR} = (M_t \\cdot M_r \\cdot M_c) / K" + }, + { + "bbox": [ + 304, + 285, + 545, + 438 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 444, + 447, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 447, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 447, + 456 + ], + "type": "text", + "content": "6.2.3D Imaging Performance" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 464, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 545, + 582 + ], + "type": "text", + "content": "Compression vs. Performance: Fig. 4 shows the performance of compressive histograms as a function of the compression ratio. The learned coding tensors consistently outperform the temporal Fourier-based C. At low SBR and " + }, + { + "bbox": [ + 304, + 464, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathrm{CR} > 100" + }, + { + "bbox": [ + 304, + 464, + 545, + 582 + ], + "type": "text", + "content": ", it becomes essential for the learned coding tensors to utilize spatio-temporal information (i.e., green and red lines). Moreover, the proposed models can outperform the peak compression oracle for " + }, + { + "bbox": [ + 304, + 464, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathrm{CR} \\leq 64" + }, + { + "bbox": [ + 304, + 464, + 545, + 582 + ], + "type": "text", + "content": ". Overall, learned spatio-temporal coding tensors provide robust performance that degrades gracefully as compression increases." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 584, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 584, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 584, + 545, + 713 + ], + "type": "text", + "content": "Importance of Learned Coding Tensors: Fig. 5 compares the depth reconstructions of compressive histograms with coding tensors that were optimized (ours) against coding tensors that were fixed and not optimized throughout training. The extreme quantization in coarse histograms causes large systematic depth errors. Random unoptimized coding tensors consistently produce lower-quality depth reconstructions. A well-designed coding tensor based on Fourier codes can produce reasonable depth reconstructions at " + }, + { + "bbox": [ + 304, + 584, + 545, + 713 + ], + "type": "inline_equation", + "content": "64\\mathrm{x}" + }, + { + "bbox": [ + 304, + 584, + 545, + 713 + ], + "type": "text", + "content": " compression, however, at " + }, + { + "bbox": [ + 304, + 584, + 545, + 713 + ], + "type": "inline_equation", + "content": "128\\mathrm{x}" + }, + { + "bbox": [ + 304, + 584, + 545, + 713 + ], + "type": "text", + "content": " compression, scene details become blurred. The proposed learned coding tensors are" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10761" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 545, + 223 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 545, + 223 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 545, + 223 + ], + "type": "image", + "image_path": "1acdcfb5f9ed672dbfd42a85440f83f4509dc395363474fa4d291bdca5e68a9b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "type": "text", + "content": "Figure 5. Importance of Learned Coding Tensors. Depth reconstructions at " + }, + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "type": "inline_equation", + "content": "64\\mathrm{x}" + }, + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "type": "text", + "content": " (top) and " + }, + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "type": "inline_equation", + "content": "128\\mathrm{x}" + }, + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "type": "text", + "content": " (bottom) compression for compressive histogram models whose coding tensors were hand-designed (coarse histogram and Fourier-based), learned (proposed), and not learned (randomly initialized). The simulated scene had an " + }, + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "type": "inline_equation", + "content": "\\mathrm{SBR} = 0.1" + }, + { + "bbox": [ + 46, + 224, + 546, + 257 + ], + "type": "text", + "content": " , where the mean signal and background photon levels were [50, 500]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 266, + 285, + 376 + ], + "blocks": [ + { + "bbox": [ + 50, + 266, + 285, + 376 + ], + "lines": [ + { + "bbox": [ + 50, + 266, + 285, + 376 + ], + "spans": [ + { + "bbox": [ + 50, + 266, + 285, + 376 + ], + "type": "image", + "image_path": "37ae801c01dea273e49d3fed2244e0ce80bdeac1a0db27554c5a349df13531ae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 424 + ], + "type": "text", + "content": "Figure 6. What if we could compute depths in-pixel? Depth reconstructions at high and low SBR with mean signal and background photon levels of [10, 10] and [10, 1000], respectively. The compressive histograms have a compression of 64." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 436, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 472 + ], + "type": "text", + "content": "able to generate high-quality reconstructions comparable to the no-compression oracle. Overall, optimizing the coding tensors can provide non-trivial performance gains." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 568 + ], + "type": "text", + "content": "What if we could compute depths in-pixel? Fig. 6 compares the depth reconstruction quality of two learned coding tensors at " + }, + { + "bbox": [ + 46, + 474, + 287, + 568 + ], + "type": "inline_equation", + "content": "64\\mathrm{x}" + }, + { + "bbox": [ + 46, + 474, + 287, + 568 + ], + "type": "text", + "content": " compression with the peak compression oracle described in Sec. 6.1. At high SBR, all methods recover the fine and coarse scene details. At low SBR the peak compression oracle fails to reconstruct high-level scene structures such as the rings in the red box, while the learned coding tensors better preserve these coarse and fine details." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 574, + 270, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 270, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 270, + 588 + ], + "type": "text", + "content": "6.3. Exploring the Coding Tensor Design Space" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 596, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 596, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 596, + 288, + 714 + ], + "type": "text", + "content": "When does spatio-temporal coding help? Fig. 7 shows the effect of increasing the spatial dimension of C, at 64x compression. At high SBR, all methods have similar MAE, but, coding tensors with smaller spatial dimensions better preserve fine details (e.g., sticks). On the other hand, at low SBR, coding tensors with larger spatial dimensions preserve high-level details such as the pot handle. This difference is also observed in the scatter plot where the mean and median of the " + }, + { + "bbox": [ + 46, + 596, + 288, + 714 + ], + "type": "inline_equation", + "content": "256 \\times 1 \\times 1" + }, + { + "bbox": [ + 46, + 596, + 288, + 714 + ], + "type": "text", + "content": " C do not match which indicates multiple low SBR scenes with high MAE." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 267, + 545, + 434 + ], + "blocks": [ + { + "bbox": [ + 310, + 267, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 310, + 267, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 310, + 267, + 545, + 434 + ], + "type": "image", + "image_path": "3e7aec92c344bb8012c473390d45fe8e4b9b688400bd7eb00a13752daa8a3c95.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 437, + 546, + 536 + ], + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 536 + ], + "type": "text", + "content": "Figure 7. When do spatio-temporal coding tensors help? Each scatter plot point corresponds to the MAE of a test scene. The images directly below each model correspond to the depth reconstructions for two test examples at high and low SBR levels whose mean signal and background photons per pixel are [10, 10] and [10, 1000], respectively. For a fixed compression level, the spatial block size of each model is increased from left to right and " + }, + { + "bbox": [ + 304, + 437, + 546, + 536 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 437, + 546, + 536 + ], + "type": "text", + "content": " is adjusted to maintain the same compression level. The coding tensors for all models in this plot are learned and separable." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 549, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 713 + ], + "type": "text", + "content": "How does reducing the size of C affect performance? Fig. 8 shows the effect of reducing the size of C at " + }, + { + "bbox": [ + 304, + 549, + 545, + 713 + ], + "type": "inline_equation", + "content": "128\\mathrm{x}" + }, + { + "bbox": [ + 304, + 549, + 545, + 713 + ], + "type": "text", + "content": " compression. The coding tensors size is reduced by training models with separable coding tensors that operate on smaller histogram blocks. The performance difference between full and separable coding tensors " + }, + { + "bbox": [ + 304, + 549, + 545, + 713 + ], + "type": "inline_equation", + "content": "(1024\\times 4\\times 4)" + }, + { + "bbox": [ + 304, + 549, + 545, + 713 + ], + "type": "text", + "content": " is negligible. As we further reduce the number of parameters in C, the overall performance degrades. Coding tensors with fewer parameters that operate on smaller histogram blocks tend to produce blurrier reconstructions. This can be observed in the red box where the coding tensors with less than 10,000 parameters blurs the spikes. Nonetheless, as discussed in Sec. 4.1, a parameter-efficient C is desirable due to the limited in-sensor memory. Ultimately, a practical" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10762" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 73, + 286, + 240 + ], + "blocks": [ + { + "bbox": [ + 51, + 73, + 286, + 240 + ], + "lines": [ + { + "bbox": [ + 51, + 73, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 51, + 73, + 286, + 240 + ], + "type": "image", + "image_path": "820f2c20befd626ed26778c03e802af27661f9b8991e64cdd54e7da08f3753f8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 287, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 287, + 319 + ], + "type": "text", + "content": "Figure 8. How does Reducing Size of C Affect Performance?. Each scatter plot point corresponds to the MAE of a test scene. The images directly below each model correspond to the depth reconstructions for two test scenes at high and low SBR levels whose mean signal and background photons per pixel are [10, 10] and [10, 1000], respectively. The size of C is reduced from left to right by making it separable or reducing the " + }, + { + "bbox": [ + 46, + 243, + 287, + 319 + ], + "type": "inline_equation", + "content": "M_{t}" + }, + { + "bbox": [ + 46, + 243, + 287, + 319 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 369 + ], + "type": "text", + "content": "compressive SPAD-based 3D camera design requires determining the trade-off between parameter efficiency and 3D imaging quality, which may depend on the application." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 375, + 216, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 216, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 216, + 387 + ], + "type": "text", + "content": "6.4. Evaluation on Real-world Data" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 393, + 288, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 288, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 288, + 547 + ], + "type": "text", + "content": "Fig. 9 shows the depth reconstructions at " + }, + { + "bbox": [ + 46, + 393, + 288, + 547 + ], + "type": "inline_equation", + "content": "256\\mathrm{x}" + }, + { + "bbox": [ + 46, + 393, + 288, + 547 + ], + "type": "text", + "content": " compression of multiple compressive histograms and the no compression baseline on the real-world experimental data from [21]. In low SBR scenes, such as the outdoor capture of the ball falling down stairs (first row), Truncated Fourier blurs the staircase edges, while the learned spatio-temporal C preserved these details. Compared to the no compression oracle, compressive histogram models produce less smooth depth images with some small artifacts. This suggests that the compressive histogram models could benefit from a spatial regularizer such as the one used when training the no compression oracle. Additional results and details on this evaluation are available in the supplement." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 554, + 281, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 554, + 281, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 281, + 567 + ], + "type": "text", + "content": "6.5. On-chip Implementation and Power Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "type": "text", + "content": "To validate the feasibility of compressive histograms, we implement them on the UltraPhase chip which has a " + }, + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 6" + }, + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "type": "text", + "content": " processor core array [4]. At this time, UltraPhase has not been 3D stacked on a SPAD sensor, thus we only evaluate its compute and data readout power consumption. Fig. 10 shows the power dissipated by UltraPhase when processing photon timestamps with different methods and transferring data off-sensor. Although compressive histograms dissipate more power on computation (blue), this is less than " + }, + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "type": "text", + "content": " of the overall power consumption, which is dominated by data readout. Due to limited memory in UltraPhase (4096 bits per core), our method learns " + }, + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^{\\mathrm{spatial}}" + }, + { + "bbox": [ + 46, + 572, + 288, + 713 + ], + "type": "text", + "content": " and uses Fourier codes" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 73, + 545, + 228 + ], + "blocks": [ + { + "bbox": [ + 309, + 73, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 309, + 73, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 309, + 73, + 545, + 228 + ], + "type": "image", + "image_path": "ec85109e03b0c08584b6f8ee8fa8cca029a09e73d3a013edeca40d0f6f79490a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 231, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 306, + 231, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 231, + 545, + 264 + ], + "type": "text", + "content": "Figure 9. Depth Reconstructions of Real-world SPAD Data at " + }, + { + "bbox": [ + 306, + 231, + 545, + 264 + ], + "type": "inline_equation", + "content": "256\\mathrm{x}" + }, + { + "bbox": [ + 306, + 231, + 545, + 264 + ], + "type": "text", + "content": " Compression. Depth reconstructions of different scenes captured with a SPAD-based 3D camera prototype [21]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 278, + 543, + 346 + ], + "blocks": [ + { + "bbox": [ + 310, + 278, + 543, + 346 + ], + "lines": [ + { + "bbox": [ + 310, + 278, + 543, + 346 + ], + "spans": [ + { + "bbox": [ + 310, + 278, + 543, + 346 + ], + "type": "image", + "image_path": "a99aad7ded3d12d585c2eed772a438c9d8fd9325417498c04cfb9160352afd10.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 348, + 546, + 445 + ], + "lines": [ + { + "bbox": [ + 304, + 348, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 546, + 445 + ], + "type": "text", + "content": "Figure 10. Compute vs. Data Readout Power. Average power dissipated by " + }, + { + "bbox": [ + 304, + 348, + 546, + 445 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 304, + 348, + 546, + 445 + ], + "type": "text", + "content": " SPADs processing 500 timestamps per depth frame and operating at 30 depth frames per second. Compute power is obtained from the implementation on the UltraPhase SPAD processors [4]. Readout power is estimated from the output data rate assuming the readout scheme of the SwissSPAD2 [42]. Coarse histograms use 8-bit precision, while compressive histograms use 16-bit precision. Note the difference in blue and orange scales." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 456, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 456, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 545, + 494 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 305, + 456, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^{\\mathrm{temporal}}" + }, + { + "bbox": [ + 305, + 456, + 545, + 494 + ], + "type": "text", + "content": " due to their memory efficient implementation. We also quantize " + }, + { + "bbox": [ + 305, + 456, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 305, + 456, + 545, + 494 + ], + "type": "text", + "content": " to 8 bits and find no degradation in performance. Refer to the supplement for additional details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 502, + 375, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 375, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 375, + 514 + ], + "type": "text", + "content": "7. Discussion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 545, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 699 + ], + "type": "text", + "content": "SPAD-based 3D cameras encounter a data bottleneck between the SPAD array and the compute module when transferring the photon timestamps. A histogram tensor can help summarize timestamps at low resolutions, but as megapixel SPAD arrays become available, histogram tensors also lead to a data bottleneck. To overcome this limitation we proposed compressive histograms as a compact representation that can be built on-the-fly, as each photon is detected. As a consequence, compressive histograms can reduce the insensor memory and data rates because neither the photon data stream nor a histogram tensor needs to be stored or transferred. Our results show that high-quality depth information can be recovered from a learnt compressive histogram representation that is up to 2 orders of magnitude smaller than a histogram tensor representation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Practical compressive histogram operating points: The" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10763" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "type": "text", + "content": "learned separable " + }, + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "type": "inline_equation", + "content": "256 \\times 4 \\times 4" + }, + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "type": "inline_equation", + "content": "256 \\times 2 \\times 2" + }, + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "type": "text", + "content": " C, achieved a good balance between parameter efficiency vs. reconstruction quality, and require on the order of 10-100kbits of memory. In an UltraPhase-like chip this would require distributing C among at least 8x8 cores (4kbits per core). If the temporal dimension is fixed to Fourier-based Ctemporal such as the ones from [13, 36], the number of parameters can be reduced by 10-40x (see Suppl. Sec. 3.3) which enables storing C on a per-pixel basis and made the Ultra-Phase evaluation possible. Overall, for a 1MP SPAD sensor with 1000 bins per-pixel, compressive histograms that can provide more than 50x compression would result in practical data rates of " + }, + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "type": "inline_equation", + "content": "\\sim 0.6\\mathrm{GB/s}" + }, + { + "bbox": [ + 46, + 72, + 289, + 224 + ], + "type": "text", + "content": " which USB 3.2 can support." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 380 + ], + "type": "text", + "content": "Trade-off space: Compressive histograms establish a trade-off between reconstruction fidelity, data bandwidth, and in-sensor compute and memory resources. For a fixed bandwidth, a coarse histogram requires arguably the lowest in-sensor resources but leads to poor reconstructions. Fourier-based histograms can improve reconstruction fidelity, at the expense of increased in-sensor computation and memory. The proposed generalization of compressive histograms allows further increasing reconstruction accuracy, at the expense of additional in-sensor memory over Fourier-based methods. Ultimately, the correct trade-off for a given scenario will be determined by power, application, and hardware constraints." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "type": "text", + "content": "Although compressive histograms require more insensor computation than coarse histograms, our method presents a practical solution from a power consumption and a real-time application perspective. Power consumption is primarily determined by data rates. Fig. 10 and Suppl. Fig. 4 shows that despite compressive histograms dissipating " + }, + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "type": "inline_equation", + "content": "100\\mathrm{x}" + }, + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "type": "text", + "content": " more processing power than coarse histograms, their overall power consumption is still lower even when data rates are only reduced by " + }, + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "type": "inline_equation", + "content": "2\\mathrm{x}" + }, + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "type": "text", + "content": ". The processing time for building compressive histograms is " + }, + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "type": "inline_equation", + "content": "\\sim 0.5\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 381, + 289, + 533 + ], + "type": "text", + "content": " (Suppl. Fig. 5). From a real-time (i.e., 30 FPS) or a high-speed application standpoint, this additional processing time is nearly negligible since it is overlapped with acquisition/exposure time." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "text", + "content": "From a hardware perspective, the importance of reducing the memory overhead of " + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "text", + "content": " depends on resolution. In low-resolution SPAD cameras, memory-efficient " + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "text", + "content": " are essential because they are stored among a single or a few pixels. The proposed method allowed integrating memory-efficient Fourier codes with learned spatial codes, which were implemented on the 2x2 pixels of UltraPhase (Suppl. Sec. 2). As resolution increases and " + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "text", + "content": " is shared among more pixels, the memory overhead reduces, and less parameter-efficient " + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 534, + 289, + 652 + ], + "type": "text", + "content": " with increased reconstruction fidelity can be considered." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": "Bias in Learned C: In the supplement, we show that coding tensors with " + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "inline_equation", + "content": "M_{t} = N_{t}" + }, + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": " develop a depth range bias. These coding tensors learn to zero out photons coming from distances that are less common in the dataset since they are usually background/noise photons. Interestingly, learned" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": "coding tensors with " + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "M_t < N_t" + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": " avoid this bias and generalize to depths that are less common in the training set." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 102, + 545, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 102, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 304, + 102, + 545, + 231 + ], + "type": "text", + "content": "Generalization: There are multiple generalization axes including signal and ambient light levels, sensor and laser parameters (e.g., resolution, pulse waveform), and scene response complexity (e.g., depth range, indirect reflections). Our evaluation has probed some of them. Specifically, our training set only included a subset of the signal and ambient light levels that the test set contained. Furthermore, the model was trained and tested on histogram tensors with different resolutions. Finally, the dataset bias investigation showed that models with " + }, + { + "bbox": [ + 304, + 102, + 545, + 231 + ], + "type": "inline_equation", + "content": "N_{t} \\leq 256" + }, + { + "bbox": [ + 304, + 102, + 545, + 231 + ], + "type": "text", + "content": " generalized well to less prevalent depths during training (Suppl. Sec. 1)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 232, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 361 + ], + "type": "text", + "content": "We further discuss the model's ability to generalize in other scenarios. For instance, all learned models (including baselines) are unlikely to generalize well to wider laser pulses, because if the model is trained with a narrow pulse width, it learns to extract signal information from high frequencies which will only contain noise in the wider pulse. Similarly, these learned models may generalize to narrower pulse widths. Furthermore, we anticipate a learned C with the properties described in [13] to be robust to diffuse indirect reflections but may require data augmentation to generalize to other light transport scenarios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 366, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 450 + ], + "type": "text", + "content": "Why not compute depths in-sensor? SPAD-based 3D cameras with large in-pixel memory could store per-pixel histograms and reduce data rates by computing depths in-pixel (i.e., peak compression oracle). Our results show that compressive histogram can provide similar reconstruction quality and outperform this method at low SBR without requiring the storage of the full histogram tensor in-sensor." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 455, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 550 + ], + "type": "text", + "content": "Additional Coding Tensor Designs: Although we find promising empirical results for the coding tensor representations described in this paper, the optimal set of coding tensors will depend on the exact hardware specifications (e.g., in-pixel memory, system bandwidth) and scene-dependent parameters (e.g., SBR, geometry, albedo). Additional lightweight C designs could rely on other factorization techniques and weight quantization." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 555, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 626 + ], + "type": "text", + "content": "Task-specific Compressive Histograms: Histogram tensors are used in other active single-photon imaging modalities such as fluorescence lifetime microscopy [34], nonline-of-sight [10, 23, 29], and diffuse optical tomography [22, 45, 24]. Our framework could be used to find compressive representations optimized for these applications." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments: This work was supported by the Department of Energy and National Nuclear Security Administration (DE-NA0003921), Air Force (FA9550-21-1-0341), Swiss National Science Foundation (200021_166289), and NSF Awards 1846884 (A.V.), 1943149 (M.G.), 2107060 (M.G.), 2138471 (A.I.). U.S. DOE full legal disclaimer: https://www.osti.gov/stip/about/disclaimer." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10764" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] How multi-beam flash lidar works. https://ouster.com/blog/ how-multi-beam-flash-lidar-works/. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021. 9" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10766" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_content_list.json b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..cd9080e6e76b4ed59dec71534858e5ea802e1175 --- /dev/null +++ b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_content_list.json @@ -0,0 +1,2308 @@ +[ + { + "type": "text", + "text": "Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-Spectral Image Fusion", + "text_level": 1, + "bbox": [ + 120, + 128, + 849, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Man Zhou $^{1*}$ , Jie Huang $^{2*}$ , Naishan Zheng $^{2}$ , Chongyi Li $^{3\\dagger}$", + "bbox": [ + 263, + 202, + 702, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ S-Lab, Nanyang Technological University, Singapore", + "bbox": [ + 263, + 220, + 699, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ University of Science and Technology of China, China", + "bbox": [ + 263, + 238, + 704, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Nankai University, China", + "bbox": [ + 380, + 256, + 589, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 324 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of deep neural networks for pan-sharpening is commonly in a form of black box, lacking transparency and interpretability. To alleviate this issue, we propose a novel model-driven deep unfolding framework with image reasoning prior tailored for the pan-sharpening task. Different from existing unfolding solutions that deliver the proximal operator networks as the uncertain and vague priors, our framework is motivated by the content reasoning ability of masked autoencoders (MAE) with insightful designs. Specifically, the pre-trained MAE with spatial masking strategy, acting as intrinsic reasoning prior, is embedded into unfolding architecture. Meanwhile, the pre-trained MAE with spatial-spectral masking strategy is treated as the regularization term within loss function to constrain the spatial-spectral consistency. Such designs penetrate the image reasoning prior into deep unfolding networks while improving its interpretability and representation capability. The uniqueness of our framework is that the holistic learning process is explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Extensive experiments on multiple satellite datasets demonstrate the superiority of our method over the existing state-of-the-art approaches. Code will be released at https://manman1995.github.io/.", + "bbox": [ + 76, + 340, + 473, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 734, + 209, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pan-sharpening, a texture-rich panchromatic image-guided multi-spectral image super-resolution task, is to reason the unknown content at the pre-defined pixel positions according to the context of low-resolution (LR) multispectral (MS) image and high-resolution (HR) panchromatic (PAN) image. Owing to the physical constraints,", + "bbox": [ + 76, + 760, + 468, + 852 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/00f16f38456c671d51af36c000007f6ed520a5070b266de7a70415bf99d11a98.jpg", + "image_caption": [ + "Figure 1: Motivation. Pan-sharpening is to reason the unknown content at the pre-defined pixel positions according to the context of low-resolution multi-spectral image and high-resolution panchromatic image." + ], + "image_footnote": [], + "bbox": [ + 529, + 314, + 859, + 483 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "satellites usually adopt both MS and PAN sensors to observe scenes, providing the MS images with high spectral but limited spatial resolution and the PAN images with high spatial but low spectral resolution. To obtain observation with both high spectral and high spatial resolutions, the pan-sharpening technique has drawn increasing attention in both image processing and remote sensing communities.", + "bbox": [ + 496, + 565, + 892, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Many research efforts have been devoted to solving the pan-sharpening problem, which can be categorized into two groups: traditional optimization methods and deep learning-based methods. Since an infinite number of HR-MS images can be downsampled to produce the same LR-MS image, reasoning the HR-MS images from the LR counterparts is highly ill-posed. To solve the ill-posedness, various natural images priors as regularization terms have been developed in traditional optimization methods, e.g., low-rank prior [29] and sparse image priors [44]. However, these priors are not easy to be devised. Moreover, it is challenging to optimize these methods, hampering the practical applications. Besides, due to the hand-crafted designs, their limited representation ability results in unsatisfactory performance.", + "bbox": [ + 496, + 672, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The powerful learning capability of deep neural net", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Co-first authors contributed equally, † corresponding author. We also gratefully acknowledge the support of MindSpore, CANN, and Ascend AI Processor used for this research.", + "bbox": [ + 76, + 862, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12398", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8cdcfb74689abd0753ddf1a6f48b58fd604a292375d718f500adae3f232d1189.jpg", + "image_caption": [ + "Figure 2: Motivation. The comparison between prior unfolding frameworks and ours." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 477, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "works ignites renewed interest in this problem. As a pioneering work, PNN [18] employs three-layer convolution neural networks to account for pan-sharpening learning. Since then, more and more complicated and deeper architectures have been proposed to improve the performance of pan-sharpening [25, 28, 30]. Despite the remarkable progress, most of them focus on heuristically constructing network architectures in a black box fashion without considering the underlying rationality of pan-sharpening task, lacking transparency and interpretability.", + "bbox": [ + 75, + 450, + 468, + 602 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To improve interpretability, model-driven deep unfolding methods have been proposed. Xu et al. [26] propose the first deep unfolding network for pan-sharpening. The basic idea behind it is to formulate pan-sharpening as an optimization problem and employ the proximal gradient descent algorithm to solve it. The optimization process can be reformulated as:", + "bbox": [ + 75, + 607, + 468, + 712 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {H}} = \\min _ {\\mathbf {H}} \\frac {1}{2} | | \\mathbf {L} - \\mathbf {D K H} | | _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {H} | \\mathbf {P}), \\qquad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 731, + 468, + 761 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyper-parameter to weight the first term (data fidelity term accords with the degradation) and the second term (regularization term $\\Omega(\\cdot)$ ). $\\mathbf{D}$ , and $\\mathbf{K}$ denote the down-sampling and blur operators, respectively. L, P, and H respectively represent the LR-MS image, PAN image, and HR-MS image. Technically, the proximal gradient descent algorithm can be approximatively expressed as an iterative convergence problem by solving the following iterative", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "function:", + "bbox": [ + 500, + 92, + 563, + 104 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} ^ {(k)} = \\operatorname {p r o x} _ {\\lambda , \\Omega , P} \\left(\\mathbf {H} ^ {(k - 1)} + \\delta (\\mathbf {D K}) ^ {T} (\\mathbf {L} - \\mathbf {D K H} ^ {(k - 1)})\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 111, + 893, + 143 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathrm{k}$ and $\\delta$ denote the iterative step and learning factor. Motivation. In terms of the function $\\mathrm{prox}_{\\lambda, \\Omega, \\mathrm{P}}$ that involves the embedded prior term $\\Omega(\\cdot)$ , existing works usually heuristically employ diverse network architectures in a black box fashion and deliver the proximal operator networks as the uncertain and vague priors, visized in Figure 2. These methods thus lack clear physical meanings of the prior terms. In addition, most deep unfolding-based methods [26, 27] cannot extract the pan-sharpening customized prior with clear physical patterns well, which is caused by weak interpretable prior operations. Hence, we argue that the deep unfolding framework with sufficient interpretability has the potential of improving performance.", + "bbox": [ + 496, + 151, + 890, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Solution. The first function of pan-sharpening is to reason the unknown information at the pre-defined pixel positions using the context, detailed in Figure 1. In this work, we propose a novel model-driven deep unfolding framework for pan-sharpening with interpretability. Inspired by the content reasoning ability of masked autoencoders (MAE) [9], our framework endows the holistic learning process of deep unfolding with the explicitly integrated with inherent physical mechanism underlying the pan-sharpening task. The key insights of our framework are (1) we embed the pretrained MAE with spatial masking strategy into the unfolding architecture, acting as intrinsic reasoning prior and (2) we treat the pre-trained MAE with spatial-spectral masking as the regularization term within loss function to constrain the spatial-spectral consistency. Such new designs penetrate the image reasoning prior into deep unfolding network while improving the interpretability and representation ability. Besides, our framework also outperforms existing state-of-the-art approaches on multiple satellite datasets.", + "bbox": [ + 496, + 347, + 892, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are summarized as follows:", + "bbox": [ + 517, + 633, + 857, + 648 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to embed the pre-trained MAE into deep unfolding architecture, resorting to its image reasoning ability for pan-sharpening. Such reasoning prior makes the framework transparent and interpretable.", + "- We creatively treat the pre-trained MAE with spatial-spectral masking strategy as regularization term within loss function to constrain the spatial-spectral consistency. The tailored regularization term with intrinsic knowledge of spatial-spectral reasoning empowers the unfolding framework.", + "- In contrast to previous works, our framework as the first attempt pushes the frontiers of pan-sharpening towards the designs of the deep prior term. It shows outstanding performance on three satellite datasets, outperforming the state-of-the-art algorithms." + ], + "bbox": [ + 517, + 657, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12399", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Traditional Methods. Traditional pan-sharpening methods can be roughly divided into three main categories: CS-based methods, MRA-based methods, and VO-based methods. The CS-based approaches separate spatial and spectral information from the LRMS image and replace spatial information with a PAN image. Intensity hue-saturation (IHS) fusion [3], the principal component analysis (PCA) methods [13, 22], Brovey transforms [6], and Gram-Schmidt (GS) orthogonalization method [14] are CS-based approaches. These CS-based approaches are fast since LR-MS images simply need spectral treatment to remove and replace spatial components, but the resultant HR-MS images show severe spectral distortion. The MRA-based methods inject high-frequency features of PAN derived by multi-resolution decomposition techniques into upsampled multi-spectral images. Decimated wavelet transform (DWT) [17], high-pass filter fusion (HPF) [21], Laplacian pyramid (LP) [23], smoothing filter-based intensity modulation (SFIM) [16], and atrous wavelet transform (ATWT) [19] are typical MRA-based methods that reduce spectral distortion and improve resolution, but they heavily rely on multi-resolution techniques, which may cause local spatial artifacts. In recent years, VO-based methods are used because of the fine fusion effect on ill-posed problems. These various constraints can only inadequately reflect the limited structural relations of the images.", + "bbox": [ + 76, + 135, + 472, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Deep Learning-based Methods. Deep learning-based methods have been widely used for pan-sharpening [41, 27, 34, 35, 11, 32, 40, 43, 39, 36, 37, 33, 42]. PNN [18] uses three convolutional units to directly map the relationship between PAN, LR-MS, and HR-MS images. Inspired by PNN, a large number of pan-sharpening studies based on deep learning emerge. For example, PANNet [28] adopts the residual learning module in Resnet [10]. MSDCNN [30] adds multi-scale modules on the basis of residual connection. SRPPNN [2] refers to the design idea of SRCNN [4].", + "bbox": [ + 76, + 547, + 468, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, some model-driven deep models with physical meaning emerge. The basic idea is to use prior knowledge to formulate optimization problems, then unfold the optimization algorithms and replace the steps in the algorithm with deep neural networks. For example, Xu et al. [26] propose the model-based deep learning network MH-Net and GPPNN for pan-sharpening, respectively. In terms of the function design $\\mathrm{prox}_{\\lambda,\\Omega}$ that takes for the embedded prior term, existing works heuristically employ diverse network architectures in the black-box fashion, thus resulting in weak physical meanings. It motivates us to explore the task-driven customized prior with clear physical patterns.", + "bbox": [ + 76, + 719, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 89, + 635, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Model Formulation", + "text_level": 1, + "bbox": [ + 500, + 114, + 686, + 128 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In general, pan-sharpening aims to obtain the HR-MS image $\\mathbf{H}$ from its degradation observation $\\mathbf{L} = (\\mathbf{H} \\otimes \\mathbf{K}) \\downarrow_{s} + \\mathbf{n}_{\\mathbf{s}}$ , where $\\mathbf{K}$ and $\\downarrow_{s}$ denote blur kernel and down-sampling operation, and $\\mathbf{n}_{\\mathbf{s}}$ is usually assumed to be additive white Gaussian noise (AWGN). The degradation process by using the maximum a posteriori (MAP) principle can be reformulated as:", + "bbox": [ + 498, + 137, + 893, + 243 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {H}} \\frac {1}{2} \\left\\| \\mathbf {L} - \\mathbf {D K H} \\right\\| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {H} | \\mathbf {P}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 251, + 890, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyper-parameter to weight the first term (data fidelity term accords with degradation) and the regularization term $\\Omega(.)$ . We solve the optimization problem using the half-quadratic splitting (HQS) algorithm. By introducing one auxiliary variables $\\mathbf{U}$ , Eq. (3) can be reformulated as a non-constrained optimization problem:", + "bbox": [ + 498, + 290, + 893, + 381 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {H}, \\mathbf {U}} \\frac {1}{2} \\left\\| \\mathbf {L} - \\mathbf {D K H} \\right\\| _ {2} ^ {2} + \\frac {\\eta}{2} \\left\\| \\mathbf {U} - \\mathbf {H} \\right\\| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {U} | \\mathbf {P}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 391, + 890, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\eta$ is the penalty parameter. When $\\eta$ approaches infinity, Eq. (4) converges to Eq. (3). Minimizing Eq. (4) involves updating $\\mathbf{U}$ and $\\mathbf{H}$ alternately.", + "bbox": [ + 498, + 431, + 890, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Updating U. Given the estimated HR-MS image $\\mathbf{H}^{(k)}$ at iteration $k$ , the auxiliary variable $\\mathbf{U}$ can be updated as:", + "bbox": [ + 500, + 477, + 890, + 508 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {U} ^ {(k)} = \\underset {\\mathbf {U}} {\\arg \\min } \\frac {\\eta}{2} \\left| \\left| \\mathbf {U} - \\mathbf {H} ^ {(k)} \\right| \\right| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {U} | \\mathbf {P}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 518, + 890, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We can derive the solution of Eq. (5) as", + "bbox": [ + 500, + 560, + 764, + 575 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {U} ^ {(k)} = \\operatorname {p r o x} _ {\\Omega (.) , \\lambda , \\eta} (\\mathbf {H} ^ {(k)}, P), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 585, + 890, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathrm{prox}_{\\Omega}(\\cdot)$ is the proximal operator corresponding to the implicit local prior $\\Omega (\\cdot)$ .", + "bbox": [ + 498, + 614, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Updating H. Given $\\mathbf{U}^{(k)}$ , $\\mathbf{H}$ is updated as:", + "bbox": [ + 500, + 645, + 790, + 660 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} ^ {(k + 1)} = \\underset {\\mathbf {H}} {\\arg \\min } \\frac {1}{2} \\left| \\left| \\mathbf {L} - \\mathbf {D K H} \\right| \\right| _ {2} ^ {2} + \\frac {\\eta}{2} \\left| \\left| \\mathbf {U} ^ {(k)} - \\mathbf {H} \\right| \\right| _ {2} ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 670, + 890, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By applying the proximal gradient method [20] to Eq. (7), we update $\\mathbf{H}$ using the gradient decent method. Consequently, the updated equation for $\\mathbf{H}$ is", + "bbox": [ + 498, + 729, + 890, + 773 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} ^ {(k + 1)} = \\mathbf {H} ^ {(k)} - \\delta_ {2} \\nabla f _ {2} (\\mathbf {H} ^ {(k)}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 784, + 890, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\delta_{2}$ is the step size, and the gradient $\\nabla f_2(\\mathbf{H}^{(k)})$ is", + "bbox": [ + 500, + 814, + 870, + 832 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla f _ {2} \\left(\\mathbf {H} ^ {(k)}\\right) = \\left(\\mathbf {D K}\\right) ^ {T} \\left(\\mathbf {D K H} ^ {(k)} - \\mathbf {L}\\right) + \\eta \\left(\\mathbf {H} ^ {(k)} - \\mathbf {U} ^ {(k)}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 840, + 890, + 873 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $T$ is the matrix transpose operation.", + "bbox": [ + 500, + 885, + 781, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12400", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ca04489f45f52a3dcbf0aa40559ce422eb82e1cd71ee049140f3bb73eafd3204.jpg", + "image_caption": [ + "Stage 1: Image Reasoning Prior Pre-training" + ], + "image_footnote": [], + "bbox": [ + 122, + 112, + 480, + 258 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0e1735fe0814b2cfeb417d658f90088fd53317c54374592308c41c532809f520.jpg", + "image_caption": [ + "Stage 2: Spatial-spectral Consistency Pre-training" + ], + "image_footnote": [], + "bbox": [ + 506, + 119, + 844, + 261 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a080c7a2f3376d5118e7dc11405887357b5e4d97306cf330be47416726ff60f7.jpg", + "image_caption": [ + "Stage 3: Penetrating Reasoning Prior into Unfolding", + "Conv block", + "Spatial-domain operator", + "Frequency-domain operator", + "Element-wise subtraction", + "Downsample convolution", + "Upsample convolution", + "Frozen" + ], + "image_footnote": [], + "bbox": [ + 117, + 276, + 844, + 479 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6be4df005ba60cae04e4a62d2269d25a44777385b4fb3aaf3222ee73492f8e27.jpg", + "image_caption": [ + "Figure 3: The overall architecture of our proposed method. In detail, LR-MS image is firstly up-sampled and then performs the stage-wise iteration, updating U and H in the overall K stages where the pre-trained MAE acting as reasoning prior penetrates Deep Unfolding process. To promote the spatial-spectral consistency, the pre-trained extension version is employed as the loss constraint. (Best viewed in color.)" + ], + "image_footnote": [], + "bbox": [ + 125, + 473, + 148, + 489 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8105cf22368db16857de7d0d46c95820be475df198bd60ef114826e97c75870c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 205, + 474, + 222, + 489 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/990ba5e7c66d29e1a7486cd6e299773d07a6d437ddfa1dcd1cf0585b61322125.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 313, + 474, + 330, + 489 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c8576a0d77efb06b19b18ca688453c50bdc4c7e2353b9a45ff6060826f7f00de.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 441, + 477, + 457, + 486 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4dcc4955b4fd58cfc87bf708527ae3e4f33d916141ad8402c8877965b70dfd53.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 560, + 474, + 578, + 489 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/46a11b45603de31b0d9d0f33ab688ae01d83e0b32e8a8c529fe30a89f447e975.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 474, + 702, + 489 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ddb13d1d6f5c0400e04a6023b744a583eeafb1ead12bfbbcad0736282c3d97ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 795, + 474, + 813, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Model Flowchart", + "text_level": 1, + "bbox": [ + 76, + 566, + 246, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As detailed in Figure 3, the proposed image reasoning prior-embedded framework consists of four training stages:", + "bbox": [ + 75, + 590, + 468, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stage 1: Image Reasoning Prior Pre-training; Stage 2: Spatial-Spectral Consistency Pre-training; Stage 3: Penetrating Reasoning Prior into Unfolding Network; Stage 4: Spatial-Spectral Consistency Constraint as loss function.", + "bbox": [ + 76, + 619, + 468, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Structure Flow", + "text_level": 1, + "bbox": [ + 76, + 693, + 228, + 708 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the iterative algorithm, we construct deep unfolding network for pan-sharpening as shown in Figure 3. This network is an implementation of the algorithm for solving Eq. (3). In terms of the function design $\\mathrm{prox}_{\\lambda,\\Omega}$ that takes for the embedded prior term $\\Omega(.)$ , we stand on the shoulder of MAE proposed by He et al, where the MAE is trained in a self-supervised manner and empowered with the reasoning ability, acting as the image prior. Based on the above analysis, the MAE is naturally treated as the prior term $\\Omega(.)$ and meets the function of pan-sharpening.", + "bbox": [ + 75, + 718, + 468, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stage 1: Based on the original MAE, we employ the pure convolution neural network as the encoder and de", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "coder to implement its network architecture with masking patch strategies: (1) evenly divide the input image, randomly sample the small subset of regions and mask the remaining ones while keeping the whole image architecture; and (2) both the small subset of visible patches and mask tokens are processed by the encoder and decoder that reconstructs the original image in pixels. Note that the input into the encoder is the whole image, not the image patch.", + "bbox": [ + 496, + 566, + 890, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stage 3: UNet. Based on the pre-trained MAE encoder $\\mathrm{f_{CMAE}(.,)}$ we implement the whole architecture of UNet that is presented in Figure 5. To be specific, the k-th iteration $\\mathbf{H}^{(k - 1)}$ is fed into the encoder part $\\mathrm{E_{CMAE}(.,)}$ of the pre-trained MAE to generate the reasoning feature representation as", + "bbox": [ + 496, + 686, + 890, + 775 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} _ {\\mathrm {r s}} = \\operatorname {E} _ {\\mathrm {C M A E}} \\left(\\mathbf {H} ^ {(\\mathrm {k} - 1)}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 776, + 890, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, PAN image $\\mathrm{P}$ is projected into the shallow feature space by the convolution units as", + "bbox": [ + 496, + 800, + 890, + 830 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {\\mathrm {p}} = \\operatorname {C o n v} (\\mathbf {P}). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 638, + 842, + 890, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Referring to the representation $\\mathbf{H}_{\\mathrm{rs}}$ and the texture-rich PAN information $\\mathbf{F}_{\\mathrm{p}}$ , we further incorporate them to re", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12401", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8f0b0bd9a8b871ccd38b7f351e2235aa82bf18adb5eca8f87ab650836e4dd90f.jpg", + "image_caption": [ + "Figure 6: Motivation. Masked Autoencoders as spatiotemporal learners. It masks a large subset of random patches in spacetime. An encoder operates on a set of visible patches. A decoder then processes the full set of encoded patches and mask tokens to reconstruct the input. Except for patch and positional embeddings, the encoder, the decoder, and the masking strategy have no spatiotemporal inductive bias." + ], + "image_footnote": [], + "bbox": [ + 76, + 90, + 488, + 406 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a976430df081b0e22c57f83ef9acf6c69dd323ef8243f5f76c10b5f5fc175b33.jpg", + "image_caption": [ + "Figure 4: Motivation. Masked Autoencoders as the image reasoning learners. During pre-training, a large random subset of image patches is masked out, remarked as yellow ones. The encoder is applied to the small subset of visible patches. Mask tokens are introduced after the encoder, and the full set of encoded patches and mask tokens is processed by a decoder that reconstructs the original image in pixels.", + "Figure 5: The detailed structure of UNet." + ], + "image_footnote": [], + "bbox": [ + 76, + 525, + 472, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "construct the HR-MS image by the spatial-frequency information transformation module $SFT$ that derived from [38], which is shown in Figure 5. The information transformation process is detailed as", + "bbox": [ + 75, + 727, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {F} _ {\\text {f u s e}} = \\mathrm {S F T} \\left(\\mathrm {H} _ {\\mathrm {r s l}}, \\mathrm {F} _ {\\mathrm {p}}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 797, + 468, + 815 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "HNet. To transform the update process of $\\mathbf{H}^{(k + 1)}$ in Eq. (8) into a network. Firstly, we need to implement two operations, i.e., Down $\\downarrow_{s}$ and $Up\\uparrow_{s}$ , using the network. Specifically, Down $\\downarrow_{s}$ is implemented by a spatial identify transformation convolution operator, and an additional $s-$", + "bbox": [ + 75, + 824, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e83d625ffb1c45c0e98981a497204a17c8001ff5e4e7a308ef808d456625a2f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 87, + 911, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "strides followed convolution module with spatial resolution reduction:", + "bbox": [ + 498, + 357, + 890, + 386 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {D K H} ^ {(k)} = \\operatorname {C o n v} ^ {(s)} \\downarrow \\left(\\mathbf {K H} ^ {(k)}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 397, + 890, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\operatorname{Conv} \\downarrow_{(s)}$ aims to perform the $s$ times down-sampling. The latter operation $Up \\uparrow_{s}$ is implemented by a deconvolution layer containing the $s$ -strides convolution module with spatial resolution expansion and a convolution module with spatial identify transformation:", + "bbox": [ + 496, + 426, + 890, + 503 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {U} \\mathbf {H} ^ {(k)} = \\operatorname {C o n v} ^ {(s)} \\uparrow (\\mathbf {L} - \\mathbf {D K H} ^ {(k)}), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 512, + 890, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{Conv}\\uparrow_{(s)}$ aims to perform the $s$ times up-sampling.", + "bbox": [ + 498, + 542, + 887, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Optimization Flow", + "text_level": 1, + "bbox": [ + 500, + 566, + 679, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stage 2: To highlight, the uniqueness of our proposed method is that the entire learning process is fully and explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Specifically, based on the MAE with spatial-spectral masking strategy that is tailored with the spatial-frequency representation learner, we redevelop the MAE as the regularization term within the loss function to constrain the spatial-spectral consistency of the model output and its corresponding ground truth. As shown in Figure 6, standing on the shoulders of the video-version extension of masked Autoencoders [5] proposed by He et al, we redevelop the masked image modeling as \"learned loss function\" to constraint the spatial-spectral representation consistency by the following implementation details:", + "bbox": [ + 496, + 590, + 890, + 801 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- randomly mask out spatial-spectral patches in the ground truth image and then learn an autoencoder to reconstruct them;", + "- the only spatial-spectral specific inductive bias is on embedding the patches and their positions; all other" + ], + "bbox": [ + 517, + 815, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12402", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2c971dd856a29d405a8910f664a14355d5c0bc6fda9b4b6968cedb1f2bdec313.jpg", + "table_caption": [ + "Table 1: Quantitative comparison with the state-of-the-art methods. The best results are highlighted in bold." + ], + "table_footnote": [], + "table_body": "
MethodWordView IIGaoFen2WordView III
PSNR ↑SSIM↑SAM↓ERGAS↓PSNR ↑SSIM↑SAM↓ERGAS↓PSNR ↑SSIM↑SAM↓ERGAS↓
SFIM34.12970.89750.04392.344936.90600.88820.03181.739821.82120.54570.12088.9730
Brovey35.86460.92160.04031.823837.79740.90260.02181.372022.5060.54660.11598.2331
GS35.63760.91760.04231.877437.22600.90340.03091.673622.56080.54700.12178.2433
IHS35.29620.90270.04612.027838.17540.91000.02431.533622.55790.53540.12668.3616
GFPCA34.55810.90380.04882.141137.94430.92040.03141.560422.33440.48260.12948.3964
PNN (RS'16)40.75500.96240.02591.064643.12080.97040.01720.852829.94180.91210.08243.3206
PANNet (ICCV'17)40.81760.96260.02571.055743.06590.96850.01780.857729.6840.90720.08513.4263
MSDCNN (TGRS'21)41.33550.96640.02420.994045.68740.98270.01350.638930.30380.91840.07823.1884
SRPPNN (TGRS'20)41.45380.96790.02330.989947.19980.98770.01060.558630.43460.92020.07703.1553
GPPNN (CVPR'21)41.16220.96840.02441.031544.21450.98150.01370.736130.17850.91750.07763.2596
MutNet (CVPR'22)41.67730.97050.02240.951947.30420.98920.01020.548130.49070.92230.07493.1125
MANet (ECCV'22)41.85770.96970.02290.942047.26680.98900.01020.547230.54510.92140.07693.1032
Ours41.87350.97310.02200.941347.39310.98920.00890.543530.55600.92250.07333.0072
", + "bbox": [ + 78, + 116, + 895, + 364 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/513208b11f3f919b24a7f0e1e6b1b9c310ae81b651dfe6424a019a0ecf325fa0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 378, + 205, + 469 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/34f567426b9acc2266d2dacdc91ca1bf814a5e0fe33c32f5289cec8251cd582b.jpg", + "image_caption": [ + "MS", + "SRPPNN" + ], + "image_footnote": [], + "bbox": [ + 84, + 481, + 205, + 571 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5b8ba8a544439ff457b5b7e0c1ae2aab798e0b94578a0b9e1368dd222532bab8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 218, + 378, + 336, + 469 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1ee113541177b87afe7ed4b2e0ffb7de69445e9c8524738569c3b04dc67fc70e.jpg", + "image_caption": [ + "PAN", + "GPPNN" + ], + "image_footnote": [], + "bbox": [ + 218, + 481, + 336, + 571 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/22cde19a0a3a908653057f13dc93c7ed099da9995c0eed6e425d1f6edca6201b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 378, + 470, + 469 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8a37bd7f47a68bc72bb3035daf18b8e6f62b871e35c3ccf80f0e0bd9fc7214b9.jpg", + "image_caption": [ + "GFPCA", + "MutNet" + ], + "image_footnote": [], + "bbox": [ + 351, + 481, + 470, + 571 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/16d6384aec15aa8e51c0aa1aa67588d42a876c405e9e1bf36656c5c170fc523f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 378, + 602, + 469 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/90a9e8b0ad804f0e56bc0e6d4ed4274c758ff18c1b29548a7f814354800a6cb0.jpg", + "image_caption": [ + "GS", + "MANet" + ], + "image_footnote": [], + "bbox": [ + 483, + 481, + 602, + 571 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fa219f19a8a6570880bd567c1895e809d3002634268aef9a943494c2ca8feec9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 378, + 736, + 469 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7286d82b10165c11d0d1dbd1db1c12613410561d9460084a8fe7c03ca483794a.jpg", + "image_caption": [ + "SFIM", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 617, + 481, + 736, + 574 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d5a3c3b62aa2178ccc482f22148bfd585fa0c784e4108cc5aa5909215b1318a2.jpg", + "image_caption": [ + "PANNET" + ], + "image_footnote": [], + "bbox": [ + 751, + 378, + 870, + 469 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/77c61cd59339511971c5f64fbea7ea4c2ac3834891c33d6d28ea782c0af374e5.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 751, + 481, + 870, + 571 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/437bf59159cb8ced0820231cb5b4a8afe8590607937c2fcf5b0ef64c34dab069.jpg", + "image_caption": [ + "GFPCA" + ], + "image_footnote": [], + "bbox": [ + 84, + 588, + 169, + 650 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/47a2337151d54c6cb4fa4ac3261a1e2f1501d92ee640bb227d52d2c0d71eff19.jpg", + "image_caption": [ + "GS", + "Figure 7: Visual comparison of the HR-MS images produced by different methods for processing the LR-MS image from the WorldView-II dataset. Images in the last row visualize the mean squared error image between the output and ground truth." + ], + "image_footnote": [], + "bbox": [ + 171, + 588, + 256, + 652 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5d26900746a30128119292c9d4e114245336f7233461ee5ce03feef6fa4390f1.jpg", + "image_caption": [ + "SFIM" + ], + "image_footnote": [], + "bbox": [ + 256, + 588, + 341, + 652 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/978ee199b8b726ed3eeb2f2911716efe9d4849b80ebee0f9fa80fc09ec7edb02.jpg", + "image_caption": [ + "PANNET" + ], + "image_footnote": [], + "bbox": [ + 341, + 588, + 426, + 652 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f41e7068fabe898242303e51ce395f129644f470aff0a8df07f997b83f4dbb74.jpg", + "image_caption": [ + "SRPPNN" + ], + "image_footnote": [], + "bbox": [ + 426, + 588, + 511, + 652 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3d9b1eac280ceb59bc9a85d21b4c3dbcd635dfe3d2ca3e758db2d9e412151853.jpg", + "image_caption": [ + "GPPNN" + ], + "image_footnote": [], + "bbox": [ + 511, + 588, + 596, + 652 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5c6d7852dd28f11662b2dea0a1979c22466b6a2d8f77a9d658c0aab0e700a43e.jpg", + "image_caption": [ + "MutNet" + ], + "image_footnote": [], + "bbox": [ + 596, + 588, + 679, + 652 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/25c08c2402b76b9f55c73afc37f2d677bbc701f9e6ae2d8597789bb63bfa6488.jpg", + "image_caption": [ + "MANet" + ], + "image_footnote": [], + "bbox": [ + 681, + 588, + 764, + 652 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fa563574a1e350c9ebf3af419a81f92fd523dab193da64d97c1e327de4c22b0e.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 766, + 588, + 851, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "components are agnostic to the spatial-spectral nature of the problem. In particular, the encoder and decoder are both vanilla Vision Transformers with no factorization or hierarchy, and our random mask sampling is agnostic to the spatial-spectral structures.", + "bbox": [ + 107, + 720, + 470, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To generate pleasing pan-sharpening results, we construct our training objective function using the mean absolute error loss over image-level measurement, which is", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "defined as", + "bbox": [ + 500, + 720, + 571, + 733 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} _ {\\mathrm {i m g}} = \\sum_ {i = 1} ^ {N} \\left\\| \\mathbf {H} _ {i} ^ {(K + 1)} - \\mathbf {H} _ {g t, i} \\right\\| _ {1}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 747, + 890, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{H}_i^{(K + 1)}$ denotes the $i$ -th estimated HR-MS image, $\\mathbf{H}_{gt,i}$ is $i$ -th ground truth HR-MS image, and $N$ is the number of training pairs.", + "bbox": [ + 500, + 805, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Stage 4: Suppose that the pre-trained MAE model is $f_{mae}(.)$ and its encoder part is $E_{mae}(.)$ , it is employed as the complementary loss function to the original image-level", + "bbox": [ + 500, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12403", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/dae672a4229ff0cc507a9db63c43499dffedf25caea2802e2707f2017bf2c0ea.jpg", + "table_caption": [ + "Table 2: The average quantitative results on the GaoFen2 dataset in the full resolution case." + ], + "table_footnote": [], + "table_body": "
MetricsSFIMGSBroveyIHSGFPCAPNNPANNETMSDCNNSRPPNNGPPNNMutNetMANetOurs
Dλ↓0.08220.06960.13780.07700.09140.07460.07370.07340.07670.07820.06940.06810.0676
Ds↓0.10870.24560.26050.29850.16350.11640.12240.11510.11620.12530.11180.11190.1112
QNR↑0.82140.70250.63900.64850.76150.81910.81430.82510.81730.80730.82590.82660.8287
", + "bbox": [ + 81, + 114, + 893, + 189 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/41007f5f3cb9d5e5f94fad0b7f8a87b1815b0d94ce81f64fc513f76072b0b5c9.jpg", + "image_caption": [ + "MS" + ], + "image_footnote": [], + "bbox": [ + 86, + 200, + 205, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bfdcedfc8906629addf31e026e64aff5c16229fa6aa71a05cc1c3c7dfcccfe58.jpg", + "image_caption": [ + "SRPPNN" + ], + "image_footnote": [], + "bbox": [ + 86, + 305, + 204, + 396 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b0bec9fa061dcd7df29e7ca166e33c300fb92eccba316a657298da8905e7ad6.jpg", + "image_caption": [ + "PAN" + ], + "image_footnote": [], + "bbox": [ + 220, + 200, + 338, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/273949b8b1f3d37c3227237fe944f88ba313a1d8ea4cad87366b3483fe19190b.jpg", + "image_caption": [ + "GPPNN" + ], + "image_footnote": [], + "bbox": [ + 220, + 305, + 336, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/07a1f80314074b1c86612e788dcd91ccdb41540f53634d525e1fbb283e01486f.jpg", + "image_caption": [ + "GFPCA" + ], + "image_footnote": [], + "bbox": [ + 352, + 200, + 470, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f9df7beaa8ce8aefc48eb7ecefbcf7ea32db050b1449ccf8004721ee241b8ca6.jpg", + "image_caption": [ + "MutNet" + ], + "image_footnote": [], + "bbox": [ + 352, + 305, + 470, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/810ca38e1bb525ba543f40e9c6ce328ce56e9574ad5df7a6244ed4083dc01f30.jpg", + "image_caption": [ + "GS" + ], + "image_footnote": [], + "bbox": [ + 486, + 200, + 602, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0ec41ea3ee760d6505390fd79990dda0851ce89e77e7a099c8a0a361bd22cb39.jpg", + "image_caption": [ + "MANet" + ], + "image_footnote": [], + "bbox": [ + 486, + 305, + 602, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9326816e46cfbb93f4cf2f289e6438ab616cf588042bac686fd58daa1d8a198e.jpg", + "image_caption": [ + "SFIM" + ], + "image_footnote": [], + "bbox": [ + 620, + 200, + 736, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/af652fb7fe0568d61e9d30f6d7857b3bf4a044e3e2f9df828dcea66af8d10c83.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 620, + 305, + 736, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/286ab977f0513d0b05042b750e70a4e749863bebb624a1f3f2f8d4137b762bf9.jpg", + "image_caption": [ + "PANNET" + ], + "image_footnote": [], + "bbox": [ + 754, + 200, + 870, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/add18749bd986910a63e7dc869d3ee311c668783f2e36ff415e6c0780ecbd426.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 305, + 870, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0d69c6e901b0126aad42b6b2c40dce4d352bd5a92f546e653ec61d2ca2326b6f.jpg", + "image_caption": [ + "GFPCA" + ], + "image_footnote": [], + "bbox": [ + 86, + 412, + 169, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3f86bf6a96400c6867b7cb0f00fa59770cd69d193ae25e3f675e55853292cfc1.jpg", + "image_caption": [ + "GS" + ], + "image_footnote": [], + "bbox": [ + 171, + 412, + 254, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/981c6f86901f32afab435b44a9a223dc0855a30bc9bb66ba34fa92e064cba2ae.jpg", + "image_caption": [ + "SFIM" + ], + "image_footnote": [], + "bbox": [ + 256, + 412, + 339, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/39ff2097971f79ce9fd7096a921791aba093f54173903cc44c9ada9e1530d768.jpg", + "image_caption": [ + "PANNET" + ], + "image_footnote": [], + "bbox": [ + 341, + 412, + 424, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6c36325675010a9edc5a4ed98c3129b2e5e3edcd7662a3e3827832504d0ece81.jpg", + "image_caption": [ + "SRPPNN", + "Figure 8: Qualitative visualization comparison of our method with other representative counterparts on a typical satellite image pair from the GaoFen2 dataset. Images in the last row visualize the MSE between the output and ground truth." + ], + "image_footnote": [], + "bbox": [ + 426, + 412, + 509, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9b9261cf8f7ab2fbb373536428ed244081bd18ce2a2e8dc5004262472131f946.jpg", + "image_caption": [ + "GPPNN" + ], + "image_footnote": [], + "bbox": [ + 511, + 412, + 596, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/553c4165dcc8e9d6ddddc81a4a45a5dfbd0593874b8a465d0fb82513f7c86eae.jpg", + "image_caption": [ + "MutNet" + ], + "image_footnote": [], + "bbox": [ + 598, + 412, + 681, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e87ba7158fcb17fd4a04f3647c0b0b0030e803ea1e28bf49fb29abeb7f7de7f.jpg", + "image_caption": [ + "MANet" + ], + "image_footnote": [], + "bbox": [ + 683, + 412, + 767, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/699a382eb3d691f91dc5cce8ea4900cdb78cd9f3a7da052a31eb0319c3939e49.jpg", + "image_caption": [ + "Ground Truth", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 767, + 411, + 854, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "loss function $\\mathbf{L}_{\\mathrm{img}}$ as", + "bbox": [ + 76, + 566, + 223, + 583 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} _ {\\mathbf {s s}} = \\sum_ {i = 1} ^ {N} \\left| \\left| E _ {m a e} \\left(\\mathbf {H} _ {g t, i}\\right) - E _ {m a e} \\left(\\mathbf {H} _ {i} ^ {(K + 1)}\\right) \\right| \\right| _ {1}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 594, + 468, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The total loss function is remarked as", + "bbox": [ + 76, + 646, + 326, + 659 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} = L _ {i m g} + \\lambda \\times L _ {s s}. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 674, + 468, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\lambda$ is weighted factor and set as 1 in our work.", + "bbox": [ + 76, + 702, + 419, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 731, + 207, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Settings", + "text_level": 1, + "bbox": [ + 76, + 756, + 174, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets. Due to the unavailability of ground-truth MS images, we follow the previous works to generate the training set by employing the Wald protocol tool [24]. Specifically, given the MS image $\\mathrm{H} \\in \\mathrm{R}^{\\mathrm{M} \\times \\mathrm{N} \\times \\mathrm{C}}$ and the PAN image $\\mathrm{P_H} \\in \\mathrm{R}^{\\mathrm{rM} \\times \\mathrm{rN} \\times \\mathrm{b}}$ , both of them are downsampled by a ratio $\\mathbf{r}$ , and then are denoted as $\\mathrm{L} \\in \\mathrm{R}^{\\mathrm{M} / \\mathrm{r} \\times \\mathrm{N} / \\mathrm{r} \\times \\mathrm{C}}$ and $\\mathrm{P} \\in \\mathrm{R}^{\\mathrm{M} \\times \\mathrm{N} \\times \\mathrm{b}}$ , respectively. In the training set, $\\mathbf{L}$ and $\\mathbf{p}$ are regarded as the inputs, while $\\mathrm{H}$ is the ground truth. In our", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "work, three satellite images of WorldView II, GaoFen2, and WorldView III are adopted to construct image datasets. For each database, PAN images are cropped into patches with a size of $128 \\times 128$ while the corresponding MS patches are with a size of $32 \\times 32$ .", + "bbox": [ + 500, + 566, + 890, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. Several state-of-the-art Pan-sharpening methods are compared, including seven representative deep learning-based methods: PNN [18], PANNET [28], MSDCNN [30], SRPPNN [2], GPPNN [26], MANet [27], and MutNet [41] and five promising traditional methods: SFIM [16], Brovey [7], GS [14], IHS [8], and GFPCA [15].", + "bbox": [ + 500, + 643, + 890, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics. Several widely-used image quality assessment (IQA) metrics are employed for performance measurement, including PSNR, SSIM, SAM [31], ERGAS [1], and three non-reference metrics $D_{\\lambda}$ , $D_{S}$ , and QNR for real-world full-resolution scenes.", + "bbox": [ + 500, + 734, + 890, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementations. In our experiments, all the designed networks are implemented with PyTorch framework and trained on the PC with a single NVIDIA GeForce GTX 3090 GPU. In the training phase, these networks are optimized by the Adam optimizer [12] over 1000 epochs with a mini-batch size of 4. The learning rate is initialized with", + "bbox": [ + 500, + 810, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12404", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$5 \\times 10^{-4}$ . When reaching 200 epochs, the learning rate is decayed by multiplying 0.5.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Comparisons", + "text_level": 1, + "bbox": [ + 76, + 131, + 217, + 147 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation on reduced-resolution scenes. The comparison results on three satellite datasets are reported in Table 1. As can be seen, our proposed method achieves the best overall results than other pan-sharpening methods across all the satellite datasets. Specifically, the average gains of our method over the second-best MANet are 0.12dB, 0.32dB, and 0.10dB in terms of PSNR on WorldView-II, GaoFen2, and WorldView-III datasets, respectively. In addition to PSNR, consistent improvements can be observed in the other metrics, indicating lower spectral distortion and spatial texture preservation. Our method outperforms other compared methods by a large margin. The corresponding visual comparisons shown in Figure 7 and Figure 8 also support the above claim. More visual results can be found in the supplementary material.", + "bbox": [ + 75, + 154, + 468, + 380 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation on full-resolution scenes. In order to demonstrate the real-world application, we further perform experiments on 200 sets of full-resolution data obtained by the additional Gaofen2. Due to the unavailability of ground-truth MS images in real-world full-resolution scenes, the commonly-used three non-reference metrics of $D_{\\lambda}$ , $D_{s}$ , and QNR are adopted for evaluation. The quantitative comparisons between representative deep learning-based methods and our method are shown in Table 2. Our methods surpass other pan-sharpening methods in all metrics.", + "bbox": [ + 75, + 381, + 468, + 532 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f024170fa58196ad7d43b133fc8d71fc4234fc74563702ba9b406aac9cf1d25f.jpg", + "table_caption": [ + "Table 3: Quantitative results of the model with different number stages." + ], + "table_footnote": [], + "table_body": "
Stage Number (K)PSNR↑SSIM↑SAM↓ERGAS↓
141.24590.96550.02501.0123
241.49620.96790.02400.9838
341.71520.97220.02230.9506
441.87350.97310.02200.9413
541.84610.96970.02260.9421
641.74290.97330.02210.9506
", + "bbox": [ + 78, + 587, + 468, + 710 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/997e4ea05aaccfb75e3d2b6ee0516af5fe7931bc68da65d7767f8e187f03e9e8.jpg", + "table_caption": [ + "Table 4: Quantitative results with the ablation of key components." + ], + "table_footnote": [], + "table_body": "
UMAELMAEPSNR↑SSIM↑SAM↓ERGAS↓
41.46550.96690.02530.9724
✓41.65760.96810.02410.9679
✓41.83820.96950.02310.9423
✓✓41.87350.97310.02200.9413
", + "bbox": [ + 81, + 781, + 467, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 90, + 653, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To explore the contribution of different hyper-parameters and the key components, we conduct ablation studies on the WorldView-II dataset.", + "bbox": [ + 498, + 113, + 890, + 157 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of the Stage Numbers. To investigate the impact of the number of unfolded stages, we experiment proposed method with varying numbers of stages K. Observing the results from Table 3, we found that the model's performance has obtained considerable improvement as the number of stages increases until reaching 4. When further increasing the K, the results show a decreasing trend, which may be caused by the difficulty of gradient propagation. We set $\\mathrm{K} = 4$ as default stage number to balance the performance and computational complexity.", + "bbox": [ + 496, + 157, + 890, + 309 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Key Components. To investigate the contribution of the devised modules in our network, we take the model with $K = 4$ as the baseline and then conduct the comparison by observing the difference before and after removing the components. The corresponding quantitative comparisons are reported in Table 4, where $\\mathrm{U}_{\\mathrm{MAE}}$ represents the MAE within the UNet network and $\\mathrm{L}_{\\mathrm{MAE}}$ represents the MAE within loss function. As can be observed, equipping with both the MAE priors significantly improves the model performance.", + "bbox": [ + 496, + 310, + 890, + 460 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b67b0abb19629cc7683e93fd07b5e6a35d88be54b49df6066f2a3b908063b4ca.jpg", + "image_caption": [ + "Figure 9: The feature visualization in Unet upon the iterative stage increasing of deep unfolding network." + ], + "image_footnote": [], + "bbox": [ + 504, + 476, + 890, + 627 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Effect of MAE prior", + "text_level": 1, + "bbox": [ + 500, + 689, + 692, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To verify the effect of the designed MAE prior, we deepen into the feature maps of $F_{rs}$ , $F_{use}$ . As illustrated in section 3.3 that the MAE prior takes account for predicting the missing information of $F_{rs}$ and then enhances the representation $F_{use}$ , with the stage increasing, the MAE-prior reasoned feature $F_{rs}$ is gradually enhanced and the resulted $F_{use}$ becomes more informative, thus supporting the powerful capability of the MAE prior, detailed in Figure 9.", + "bbox": [ + 496, + 712, + 890, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 844, + 617, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed the first work to focus on the designs of the deep prior term. We employ the learned", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12405", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "MAE in a self-supervised manner acting as an image prior and then embed the pre-trained MAE with reasoning ability to penetrate deep unfolding architecture, thus making it more transparent. We also redevelop the pre-trained MAE with a spatial-spectral masking strategy and employ it as the regularization term within loss function to constrain the spatial-spectral consistency. The contained intrinsic knowledge over MAE loss term empowers the main unfolding network learning ability. Extensive experiments on three satellite datasets demonstrate its superiority.", + "bbox": [ + 76, + 90, + 472, + 243 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 258, + 174, + 273 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] L. Alparone, L. Wald, J. Chanussot, C. Thomas, P. Gamba, and L. M. Bruce. Comparison of pansharpening algorithms: Outcome of the 2006 grs-s data fusion contest. IEEE Transactions on Geoscience and Remote Sensing, 45(10):3012-3021, 2007.", + "[2] Jiajun Cai and Bo Huang. Super-resolution-guided progressive pansharpening based on a deep convolutional neural network. IEEE Transactions on Geoscience and Remote Sensing, 2020.", + "[3] WJOSEPH CARPER, THOMASM LILLESAND, and RALPHW KIEFER. The use of intensity-hue-saturation transformations for merging spot panchromatic and multispectral image data. 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Curran Associates, Inc., 2022.", + "[44] Xiao Xiang Zhu and Richard Bamler. A sparse image fusion algorithm with application to pan-sharpening. IEEE transactions on geoscience and remote sensing, 51(5):2827-2836, 2012." + ], + "bbox": [ + 503, + 92, + 890, + 513 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12407", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_model.json b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1c0b1c4b81a7925df7e2982f2ba5597663263b3a --- /dev/null +++ b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_model.json @@ -0,0 +1,3256 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.122, + 0.13, + 0.85, + 0.177 + ], + "angle": 0, + "content": "Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-Spectral Image Fusion" + }, + { + "type": "text", + "bbox": [ + 0.264, + 0.203, + 0.704, + 0.222 + ], + "angle": 0, + "content": "Man Zhou\\(^{1*}\\), Jie Huang\\(^{2*}\\), Naishan Zheng\\(^{2}\\), Chongyi Li\\(^{3\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.264, + 0.222, + 0.7, + 0.239 + ], + "angle": 0, + "content": "\\(^{1}\\)S-Lab, Nanyang Technological University, Singapore" + }, + { + "type": "text", + "bbox": [ + 0.264, + 0.239, + 0.705, + 0.257 + ], + "angle": 0, + "content": "\\(^{2}\\)University of Science and Technology of China, China" + }, + { + "type": "text", + "bbox": [ + 0.382, + 0.257, + 0.59, + 0.275 + ], + "angle": 0, + "content": "\\(^{3}\\)Nankai University, China" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.474, + 0.706 + ], + "angle": 0, + "content": "The success of deep neural networks for pan-sharpening is commonly in a form of black box, lacking transparency and interpretability. To alleviate this issue, we propose a novel model-driven deep unfolding framework with image reasoning prior tailored for the pan-sharpening task. Different from existing unfolding solutions that deliver the proximal operator networks as the uncertain and vague priors, our framework is motivated by the content reasoning ability of masked autoencoders (MAE) with insightful designs. Specifically, the pre-trained MAE with spatial masking strategy, acting as intrinsic reasoning prior, is embedded into unfolding architecture. Meanwhile, the pre-trained MAE with spatial-spectral masking strategy is treated as the regularization term within loss function to constrain the spatial-spectral consistency. Such designs penetrate the image reasoning prior into deep unfolding networks while improving its interpretability and representation capability. The uniqueness of our framework is that the holistic learning process is explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Extensive experiments on multiple satellite datasets demonstrate the superiority of our method over the existing state-of-the-art approaches. Code will be released at https://manman1995.github.io/." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.735, + 0.21, + 0.751 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.761, + 0.47, + 0.853 + ], + "angle": 0, + "content": "Pan-sharpening, a texture-rich panchromatic image-guided multi-spectral image super-resolution task, is to reason the unknown content at the pre-defined pixel positions according to the context of low-resolution (LR) multispectral (MS) image and high-resolution (HR) panchromatic (PAN) image. Owing to the physical constraints," + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.315, + 0.861, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.487, + 0.895, + 0.548 + ], + "angle": 0, + "content": "Figure 1: Motivation. Pan-sharpening is to reason the unknown content at the pre-defined pixel positions according to the context of low-resolution multi-spectral image and high-resolution panchromatic image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.893, + 0.672 + ], + "angle": 0, + "content": "satellites usually adopt both MS and PAN sensors to observe scenes, providing the MS images with high spectral but limited spatial resolution and the PAN images with high spatial but low spectral resolution. To obtain observation with both high spectral and high spatial resolutions, the pan-sharpening technique has drawn increasing attention in both image processing and remote sensing communities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.895, + 0.884 + ], + "angle": 0, + "content": "Many research efforts have been devoted to solving the pan-sharpening problem, which can be categorized into two groups: traditional optimization methods and deep learning-based methods. Since an infinite number of HR-MS images can be downsampled to produce the same LR-MS image, reasoning the HR-MS images from the LR counterparts is highly ill-posed. To solve the ill-posedness, various natural images priors as regularization terms have been developed in traditional optimization methods, e.g., low-rank prior [29] and sparse image priors [44]. However, these priors are not easy to be devised. Moreover, it is challenging to optimize these methods, hampering the practical applications. Besides, due to the hand-crafted designs, their limited representation ability results in unsatisfactory performance." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The powerful learning capability of deep neural net" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.863, + 0.47, + 0.9 + ], + "angle": 0, + "content": "*Co-first authors contributed equally, † corresponding author. We also gratefully acknowledge the support of MindSpore, CANN, and Ascend AI Processor used for this research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12398" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.478, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.396, + 0.471, + 0.426 + ], + "angle": 0, + "content": "Figure 2: Motivation. The comparison between prior unfolding frameworks and ours." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.603 + ], + "angle": 0, + "content": "works ignites renewed interest in this problem. As a pioneering work, PNN [18] employs three-layer convolution neural networks to account for pan-sharpening learning. Since then, more and more complicated and deeper architectures have been proposed to improve the performance of pan-sharpening [25, 28, 30]. Despite the remarkable progress, most of them focus on heuristically constructing network architectures in a black box fashion without considering the underlying rationality of pan-sharpening task, lacking transparency and interpretability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.713 + ], + "angle": 0, + "content": "To improve interpretability, model-driven deep unfolding methods have been proposed. Xu et al. [26] propose the first deep unfolding network for pan-sharpening. The basic idea behind it is to formulate pan-sharpening as an optimization problem and employ the proximal gradient descent algorithm to solve it. The optimization process can be reformulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.732, + 0.47, + 0.762 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {H}} = \\min _ {\\mathbf {H}} \\frac {1}{2} | | \\mathbf {L} - \\mathbf {D K H} | | _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {H} | \\mathbf {P}), \\qquad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyper-parameter to weight the first term (data fidelity term accords with the degradation) and the second term (regularization term \\(\\Omega(\\cdot)\\)). \\(\\mathbf{D}\\), and \\(\\mathbf{K}\\) denote the down-sampling and blur operators, respectively. L, P, and H respectively represent the LR-MS image, PAN image, and HR-MS image. Technically, the proximal gradient descent algorithm can be approximatively expressed as an iterative convergence problem by solving the following iterative" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.093, + 0.565, + 0.105 + ], + "angle": 0, + "content": "function:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.112, + 0.894, + 0.145 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} ^ {(k)} = \\operatorname {p r o x} _ {\\lambda , \\Omega , P} \\left(\\mathbf {H} ^ {(k - 1)} + \\delta (\\mathbf {D K}) ^ {T} (\\mathbf {L} - \\mathbf {D K H} ^ {(k - 1)})\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.892, + 0.348 + ], + "angle": 0, + "content": "where \\( \\mathrm{k} \\) and \\( \\delta \\) denote the iterative step and learning factor. Motivation. In terms of the function \\( \\mathrm{prox}_{\\lambda, \\Omega, \\mathrm{P}} \\) that involves the embedded prior term \\( \\Omega(\\cdot) \\), existing works usually heuristically employ diverse network architectures in a black box fashion and deliver the proximal operator networks as the uncertain and vague priors, visized in Figure 2. These methods thus lack clear physical meanings of the prior terms. In addition, most deep unfolding-based methods [26, 27] cannot extract the pan-sharpening customized prior with clear physical patterns well, which is caused by weak interpretable prior operations. Hence, we argue that the deep unfolding framework with sufficient interpretability has the potential of improving performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.893, + 0.635 + ], + "angle": 0, + "content": "Solution. The first function of pan-sharpening is to reason the unknown information at the pre-defined pixel positions using the context, detailed in Figure 1. In this work, we propose a novel model-driven deep unfolding framework for pan-sharpening with interpretability. Inspired by the content reasoning ability of masked autoencoders (MAE) [9], our framework endows the holistic learning process of deep unfolding with the explicitly integrated with inherent physical mechanism underlying the pan-sharpening task. The key insights of our framework are (1) we embed the pretrained MAE with spatial masking strategy into the unfolding architecture, acting as intrinsic reasoning prior and (2) we treat the pre-trained MAE with spatial-spectral masking as the regularization term within loss function to constrain the spatial-spectral consistency. Such new designs penetrate the image reasoning prior into deep unfolding network while improving the interpretability and representation ability. Besides, our framework also outperforms existing state-of-the-art approaches on multiple satellite datasets." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.635, + 0.858, + 0.649 + ], + "angle": 0, + "content": "Our main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.658, + 0.892, + 0.719 + ], + "angle": 0, + "content": "- We propose to embed the pre-trained MAE into deep unfolding architecture, resorting to its image reasoning ability for pan-sharpening. Such reasoning prior makes the framework transparent and interpretable." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.727, + 0.892, + 0.817 + ], + "angle": 0, + "content": "- We creatively treat the pre-trained MAE with spatial-spectral masking strategy as regularization term within loss function to constrain the spatial-spectral consistency. The tailored regularization term with intrinsic knowledge of spatial-spectral reasoning empowers the unfolding framework." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- In contrast to previous works, our framework as the first attempt pushes the frontiers of pan-sharpening towards the designs of the deep prior term. It shows outstanding performance on three satellite datasets, outperforming the state-of-the-art algorithms." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.658, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12399" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.136, + 0.473, + 0.53 + ], + "angle": 0, + "content": "Traditional Methods. Traditional pan-sharpening methods can be roughly divided into three main categories: CS-based methods, MRA-based methods, and VO-based methods. The CS-based approaches separate spatial and spectral information from the LRMS image and replace spatial information with a PAN image. Intensity hue-saturation (IHS) fusion [3], the principal component analysis (PCA) methods [13, 22], Brovey transforms [6], and Gram-Schmidt (GS) orthogonalization method [14] are CS-based approaches. These CS-based approaches are fast since LR-MS images simply need spectral treatment to remove and replace spatial components, but the resultant HR-MS images show severe spectral distortion. The MRA-based methods inject high-frequency features of PAN derived by multi-resolution decomposition techniques into upsampled multi-spectral images. Decimated wavelet transform (DWT) [17], high-pass filter fusion (HPF) [21], Laplacian pyramid (LP) [23], smoothing filter-based intensity modulation (SFIM) [16], and atrous wavelet transform (ATWT) [19] are typical MRA-based methods that reduce spectral distortion and improve resolution, but they heavily rely on multi-resolution techniques, which may cause local spatial artifacts. In recent years, VO-based methods are used because of the fine fusion effect on ill-posed problems. These various constraints can only inadequately reflect the limited structural relations of the images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.549, + 0.47, + 0.701 + ], + "angle": 0, + "content": "Deep Learning-based Methods. Deep learning-based methods have been widely used for pan-sharpening [41, 27, 34, 35, 11, 32, 40, 43, 39, 36, 37, 33, 42]. PNN [18] uses three convolutional units to directly map the relationship between PAN, LR-MS, and HR-MS images. Inspired by PNN, a large number of pan-sharpening studies based on deep learning emerge. For example, PANNet [28] adopts the residual learning module in Resnet [10]. MSDCNN [30] adds multi-scale modules on the basis of residual connection. SRPPNN [2] refers to the design idea of SRCNN [4]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Recently, some model-driven deep models with physical meaning emerge. The basic idea is to use prior knowledge to formulate optimization problems, then unfold the optimization algorithms and replace the steps in the algorithm with deep neural networks. For example, Xu et al. [26] propose the model-based deep learning network MH-Net and GPPNN for pan-sharpening, respectively. In terms of the function design \\(\\mathrm{prox}_{\\lambda,\\Omega}\\) that takes for the embedded prior term, existing works heuristically employ diverse network architectures in the black-box fashion, thus resulting in weak physical meanings. It motivates us to explore the task-driven customized prior with clear physical patterns." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.636, + 0.108 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.687, + 0.13 + ], + "angle": 0, + "content": "3.1. Model Formulation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.138, + 0.895, + 0.244 + ], + "angle": 0, + "content": "In general, pan-sharpening aims to obtain the HR-MS image \\(\\mathbf{H}\\) from its degradation observation \\(\\mathbf{L} = (\\mathbf{H} \\otimes \\mathbf{K}) \\downarrow_{s} + \\mathbf{n}_{\\mathbf{s}}\\), where \\(\\mathbf{K}\\) and \\(\\downarrow_{s}\\) denote blur kernel and down-sampling operation, and \\(\\mathbf{n}_{\\mathbf{s}}\\) is usually assumed to be additive white Gaussian noise (AWGN). The degradation process by using the maximum a posteriori (MAP) principle can be reformulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.252, + 0.892, + 0.282 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {H}} \\frac {1}{2} \\left\\| \\mathbf {L} - \\mathbf {D K H} \\right\\| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {H} | \\mathbf {P}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.291, + 0.895, + 0.382 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyper-parameter to weight the first term (data fidelity term accords with degradation) and the regularization term \\(\\Omega(.)\\). We solve the optimization problem using the half-quadratic splitting (HQS) algorithm. By introducing one auxiliary variables \\(\\mathbf{U}\\), Eq. (3) can be reformulated as a non-constrained optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.392, + 0.892, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {H}, \\mathbf {U}} \\frac {1}{2} \\left\\| \\mathbf {L} - \\mathbf {D K H} \\right\\| _ {2} ^ {2} + \\frac {\\eta}{2} \\left\\| \\mathbf {U} - \\mathbf {H} \\right\\| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {U} | \\mathbf {P}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.433, + 0.892, + 0.478 + ], + "angle": 0, + "content": "where \\(\\eta\\) is the penalty parameter. When \\(\\eta\\) approaches infinity, Eq. (4) converges to Eq. (3). Minimizing Eq. (4) involves updating \\(\\mathbf{U}\\) and \\(\\mathbf{H}\\) alternately." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.478, + 0.892, + 0.509 + ], + "angle": 0, + "content": "Updating U. Given the estimated HR-MS image \\(\\mathbf{H}^{(k)}\\) at iteration \\(k\\), the auxiliary variable \\(\\mathbf{U}\\) can be updated as:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.519, + 0.892, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\mathbf {U} ^ {(k)} = \\underset {\\mathbf {U}} {\\arg \\min } \\frac {\\eta}{2} \\left| \\left| \\mathbf {U} - \\mathbf {H} ^ {(k)} \\right| \\right| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {U} | \\mathbf {P}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.561, + 0.766, + 0.576 + ], + "angle": 0, + "content": "We can derive the solution of Eq. (5) as" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.586, + 0.892, + 0.607 + ], + "angle": 0, + "content": "\\[\n\\mathbf {U} ^ {(k)} = \\operatorname {p r o x} _ {\\Omega (.) , \\lambda , \\eta} (\\mathbf {H} ^ {(k)}, P), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.615, + 0.892, + 0.645 + ], + "angle": 0, + "content": "where \\(\\mathrm{prox}_{\\Omega}(\\cdot)\\) is the proximal operator corresponding to the implicit local prior \\(\\Omega (\\cdot)\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.646, + 0.792, + 0.661 + ], + "angle": 0, + "content": "Updating H. Given \\(\\mathbf{U}^{(k)}\\), \\(\\mathbf{H}\\) is updated as:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.671, + 0.892, + 0.719 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} ^ {(k + 1)} = \\underset {\\mathbf {H}} {\\arg \\min } \\frac {1}{2} \\left| \\left| \\mathbf {L} - \\mathbf {D K H} \\right| \\right| _ {2} ^ {2} + \\frac {\\eta}{2} \\left| \\left| \\mathbf {U} ^ {(k)} - \\mathbf {H} \\right| \\right| _ {2} ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.73, + 0.892, + 0.775 + ], + "angle": 0, + "content": "By applying the proximal gradient method [20] to Eq. (7), we update \\(\\mathbf{H}\\) using the gradient decent method. Consequently, the updated equation for \\(\\mathbf{H}\\) is" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.785, + 0.892, + 0.804 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} ^ {(k + 1)} = \\mathbf {H} ^ {(k)} - \\delta_ {2} \\nabla f _ {2} (\\mathbf {H} ^ {(k)}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.815, + 0.871, + 0.833 + ], + "angle": 0, + "content": "where \\(\\delta_{2}\\) is the step size, and the gradient \\(\\nabla f_2(\\mathbf{H}^{(k)})\\) is" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.841, + 0.892, + 0.874 + ], + "angle": 0, + "content": "\\[\n\\nabla f _ {2} \\left(\\mathbf {H} ^ {(k)}\\right) = \\left(\\mathbf {D K}\\right) ^ {T} \\left(\\mathbf {D K H} ^ {(k)} - \\mathbf {L}\\right) + \\eta \\left(\\mathbf {H} ^ {(k)} - \\mathbf {U} ^ {(k)}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.782, + 0.901 + ], + "angle": 0, + "content": "where \\(T\\) is the matrix transpose operation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12400" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.093, + 0.362, + 0.106 + ], + "angle": 0, + "content": "Stage 1: Image Reasoning Prior Pre-training" + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.113, + 0.481, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.093, + 0.776, + 0.106 + ], + "angle": 0, + "content": "Stage 2: Spatial-spectral Consistency Pre-training" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.12, + 0.845, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.264, + 0.408, + 0.276 + ], + "angle": 0, + "content": "Stage 3: Penetrating Reasoning Prior into Unfolding" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.277, + 0.846, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.474, + 0.149, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.478, + 0.19, + 0.488 + ], + "angle": 0, + "content": "Conv block" + }, + { + "type": "image", + "bbox": [ + 0.207, + 0.476, + 0.223, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.478, + 0.307, + 0.487 + ], + "angle": 0, + "content": "Spatial-domain operator" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.475, + 0.331, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.33, + 0.478, + 0.43, + 0.487 + ], + "angle": 0, + "content": "Frequency-domain operator" + }, + { + "type": "image", + "bbox": [ + 0.442, + 0.478, + 0.458, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.458, + 0.478, + 0.547, + 0.487 + ], + "angle": 0, + "content": "Element-wise subtraction" + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.476, + 0.58, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.478, + 0.672, + 0.487 + ], + "angle": 0, + "content": "Downsample convolution" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.476, + 0.703, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.709, + 0.478, + 0.789, + 0.487 + ], + "angle": 0, + "content": "Upsample convolution" + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.475, + 0.814, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.816, + 0.478, + 0.844, + 0.487 + ], + "angle": 0, + "content": "Frozen" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.492, + 0.895, + 0.553 + ], + "angle": 0, + "content": "Figure 3: The overall architecture of our proposed method. In detail, LR-MS image is firstly up-sampled and then performs the stage-wise iteration, updating U and H in the overall K stages where the pre-trained MAE acting as reasoning prior penetrates Deep Unfolding process. To promote the spatial-spectral consistency, the pre-trained extension version is employed as the loss constraint. (Best viewed in color.)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.567, + 0.248, + 0.582 + ], + "angle": 0, + "content": "3.2. Model Flowchart" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.47, + 0.621 + ], + "angle": 0, + "content": "As detailed in Figure 3, the proposed image reasoning prior-embedded framework consists of four training stages:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.621, + 0.47, + 0.682 + ], + "angle": 0, + "content": "Stage 1: Image Reasoning Prior Pre-training; Stage 2: Spatial-Spectral Consistency Pre-training; Stage 3: Penetrating Reasoning Prior into Unfolding Network; Stage 4: Spatial-Spectral Consistency Constraint as loss function." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.694, + 0.229, + 0.709 + ], + "angle": 0, + "content": "3.3. Structure Flow" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Based on the iterative algorithm, we construct deep unfolding network for pan-sharpening as shown in Figure 3. This network is an implementation of the algorithm for solving Eq. (3). In terms of the function design \\(\\mathrm{prox}_{\\lambda,\\Omega}\\) that takes for the embedded prior term \\(\\Omega(.)\\), we stand on the shoulder of MAE proposed by He et al, where the MAE is trained in a self-supervised manner and empowered with the reasoning ability, acting as the image prior. Based on the above analysis, the MAE is naturally treated as the prior term \\(\\Omega(.)\\) and meets the function of pan-sharpening." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Stage 1: Based on the original MAE, we employ the pure convolution neural network as the encoder and de" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.688 + ], + "angle": 0, + "content": "coder to implement its network architecture with masking patch strategies: (1) evenly divide the input image, randomly sample the small subset of regions and mask the remaining ones while keeping the whole image architecture; and (2) both the small subset of visible patches and mask tokens are processed by the encoder and decoder that reconstructs the original image in pixels. Note that the input into the encoder is the whole image, not the image patch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.776 + ], + "angle": 0, + "content": "Stage 3: UNet. Based on the pre-trained MAE encoder \\(\\mathrm{f_{CMAE}(.,)}\\) we implement the whole architecture of UNet that is presented in Figure 5. To be specific, the k-th iteration \\(\\mathbf{H}^{(k - 1)}\\) is fed into the encoder part \\(\\mathrm{E_{CMAE}(.,)}\\) of the pre-trained MAE to generate the reasoning feature representation as" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.777, + 0.892, + 0.795 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} _ {\\mathrm {r s}} = \\operatorname {E} _ {\\mathrm {C M A E}} \\left(\\mathbf {H} ^ {(\\mathrm {k} - 1)}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.801, + 0.892, + 0.831 + ], + "angle": 0, + "content": "Then, PAN image \\(\\mathrm{P}\\) is projected into the shallow feature space by the convolution units as" + }, + { + "type": "equation", + "bbox": [ + 0.639, + 0.843, + 0.892, + 0.861 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {\\mathrm {p}} = \\operatorname {C o n v} (\\mathbf {P}). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Referring to the representation \\(\\mathbf{H}_{\\mathrm{rs}}\\) and the texture-rich PAN information \\(\\mathbf{F}_{\\mathrm{p}}\\), we further incorporate them to re" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12401" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.092, + 0.489, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.416, + 0.471, + 0.522 + ], + "angle": 0, + "content": "Figure 4: Motivation. Masked Autoencoders as the image reasoning learners. During pre-training, a large random subset of image patches is masked out, remarked as yellow ones. The encoder is applied to the small subset of visible patches. Mask tokens are introduced after the encoder, and the full set of encoded patches and mask tokens is processed by a decoder that reconstructs the original image in pixels." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.526, + 0.473, + 0.691 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.7, + 0.411, + 0.715 + ], + "angle": 0, + "content": "Figure 5: The detailed structure of UNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.47, + 0.789 + ], + "angle": 0, + "content": "construct the HR-MS image by the spatial-frequency information transformation module \\(SFT\\) that derived from [38], which is shown in Figure 5. The information transformation process is detailed as" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.799, + 0.469, + 0.816 + ], + "angle": 0, + "content": "\\[\n\\mathrm {F} _ {\\text {f u s e}} = \\mathrm {S F T} \\left(\\mathrm {H} _ {\\mathrm {r s l}}, \\mathrm {F} _ {\\mathrm {p}}\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.901 + ], + "angle": 0, + "content": "HNet. To transform the update process of \\(\\mathbf{H}^{(k + 1)}\\) in Eq. (8) into a network. Firstly, we need to implement two operations, i.e., Down \\(\\downarrow_{s}\\) and \\(Up\\uparrow_{s}\\), using the network. Specifically, Down \\(\\downarrow_{s}\\) is implemented by a spatial identify transformation convolution operator, and an additional \\(s-\\)" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.912, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.235, + 0.892, + 0.342 + ], + "angle": 0, + "content": "Figure 6: Motivation. Masked Autoencoders as spatiotemporal learners. It masks a large subset of random patches in spacetime. An encoder operates on a set of visible patches. A decoder then processes the full set of encoded patches and mask tokens to reconstruct the input. Except for patch and positional embeddings, the encoder, the decoder, and the masking strategy have no spatiotemporal inductive bias." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.358, + 0.892, + 0.387 + ], + "angle": 0, + "content": "strides followed convolution module with spatial resolution reduction:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.398, + 0.892, + 0.416 + ], + "angle": 0, + "content": "\\[\n\\mathbf {D K H} ^ {(k)} = \\operatorname {C o n v} ^ {(s)} \\downarrow \\left(\\mathbf {K H} ^ {(k)}\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.892, + 0.504 + ], + "angle": 0, + "content": "where \\(\\operatorname{Conv} \\downarrow_{(s)}\\) aims to perform the \\(s\\) times down-sampling. The latter operation \\(Up \\uparrow_{s}\\) is implemented by a deconvolution layer containing the \\(s\\)-strides convolution module with spatial resolution expansion and a convolution module with spatial identify transformation:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.513, + 0.892, + 0.532 + ], + "angle": 0, + "content": "\\[\n\\mathbf {U} \\mathbf {H} ^ {(k)} = \\operatorname {C o n v} ^ {(s)} \\uparrow (\\mathbf {L} - \\mathbf {D K H} ^ {(k)}), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.544, + 0.888, + 0.56 + ], + "angle": 0, + "content": "where \\(\\mathrm{Conv}\\uparrow_{(s)}\\) aims to perform the \\(s\\) times up-sampling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.568, + 0.681, + 0.584 + ], + "angle": 0, + "content": "3.4. Optimization Flow" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.592, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Stage 2: To highlight, the uniqueness of our proposed method is that the entire learning process is fully and explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Specifically, based on the MAE with spatial-spectral masking strategy that is tailored with the spatial-frequency representation learner, we redevelop the MAE as the regularization term within the loss function to constrain the spatial-spectral consistency of the model output and its corresponding ground truth. As shown in Figure 6, standing on the shoulders of the video-version extension of masked Autoencoders [5] proposed by He et al, we redevelop the masked image modeling as \"learned loss function\" to constraint the spatial-spectral representation consistency by the following implementation details:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.816, + 0.892, + 0.86 + ], + "angle": 0, + "content": "- randomly mask out spatial-spectral patches in the ground truth image and then learn an autoencoder to reconstruct them;" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "- the only spatial-spectral specific inductive bias is on embedding the patches and their positions; all other" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.816, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12402" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.09, + 0.842, + 0.107 + ], + "angle": 0, + "content": "Table 1: Quantitative comparison with the state-of-the-art methods. The best results are highlighted in bold." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.117, + 0.896, + 0.366 + ], + "angle": 0, + "content": "
MethodWordView IIGaoFen2WordView III
PSNR ↑SSIM↑SAM↓ERGAS↓PSNR ↑SSIM↑SAM↓ERGAS↓PSNR ↑SSIM↑SAM↓ERGAS↓
SFIM34.12970.89750.04392.344936.90600.88820.03181.739821.82120.54570.12088.9730
Brovey35.86460.92160.04031.823837.79740.90260.02181.372022.5060.54660.11598.2331
GS35.63760.91760.04231.877437.22600.90340.03091.673622.56080.54700.12178.2433
IHS35.29620.90270.04612.027838.17540.91000.02431.533622.55790.53540.12668.3616
GFPCA34.55810.90380.04882.141137.94430.92040.03141.560422.33440.48260.12948.3964
PNN (RS'16)40.75500.96240.02591.064643.12080.97040.01720.852829.94180.91210.08243.3206
PANNet (ICCV'17)40.81760.96260.02571.055743.06590.96850.01780.857729.6840.90720.08513.4263
MSDCNN (TGRS'21)41.33550.96640.02420.994045.68740.98270.01350.638930.30380.91840.07823.1884
SRPPNN (TGRS'20)41.45380.96790.02330.989947.19980.98770.01060.558630.43460.92020.07703.1553
GPPNN (CVPR'21)41.16220.96840.02441.031544.21450.98150.01370.736130.17850.91750.07763.2596
MutNet (CVPR'22)41.67730.97050.02240.951947.30420.98920.01020.548130.49070.92230.07493.1125
MANet (ECCV'22)41.85770.96970.02290.942047.26680.98900.01020.547230.54510.92140.07693.1032
Ours41.87350.97310.02200.941347.39310.98920.00890.543530.55600.92250.07333.0072
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+ "type": "image", + "bbox": [ + 0.512, + 0.589, + 0.597, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.655, + 0.576, + 0.665 + ], + "angle": 0, + "content": "GPPNN" + }, + { + "type": "image", + "bbox": [ + 0.597, + 0.589, + 0.681, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.614, + 0.655, + 0.663, + 0.665 + ], + "angle": 0, + "content": "MutNet" + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.589, + 0.766, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.655, + 0.746, + 0.665 + ], + "angle": 0, + "content": "MANet" + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.589, + 0.852, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.655, + 0.824, + 0.665 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.668, + 0.894, + 0.699 + ], + "angle": 0, + "content": "Figure 7: Visual comparison of the HR-MS images produced by different methods for processing the LR-MS image from the WorldView-II dataset. Images in the last row visualize the mean squared error image between the output and ground truth." + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.721, + 0.471, + 0.797 + ], + "angle": 0, + "content": "components are agnostic to the spatial-spectral nature of the problem. In particular, the encoder and decoder are both vanilla Vision Transformers with no factorization or hierarchy, and our random mask sampling is agnostic to the spatial-spectral structures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To generate pleasing pan-sharpening results, we construct our training objective function using the mean absolute error loss over image-level measurement, which is" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.721, + 0.572, + 0.734 + ], + "angle": 0, + "content": "defined as" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.748, + 0.892, + 0.79 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} _ {\\mathrm {i m g}} = \\sum_ {i = 1} ^ {N} \\left\\| \\mathbf {H} _ {i} ^ {(K + 1)} - \\mathbf {H} _ {g t, i} \\right\\| _ {1}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.806, + 0.892, + 0.854 + ], + "angle": 0, + "content": "where \\(\\mathbf{H}_i^{(K + 1)}\\) denotes the \\(i\\)-th estimated HR-MS image, \\(\\mathbf{H}_{gt,i}\\) is \\(i\\)-th ground truth HR-MS image, and \\(N\\) is the number of training pairs." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Stage 4: Suppose that the pre-trained MAE model is \\( f_{mae}(.) \\) and its encoder part is \\( E_{mae}(.) \\), it is employed as the complementary loss function to the original image-level" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12403" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.185, + 0.09, + 0.784, + 0.105 + ], + "angle": 0, + "content": "Table 2: The average quantitative results on the GaoFen2 dataset in the full resolution case." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.116, + 0.895, + 0.19 + ], + "angle": 0, + "content": "
MetricsSFIMGSBroveyIHSGFPCAPNNPANNETMSDCNNSRPPNNGPPNNMutNetMANetOurs
Dλ↓0.08220.06960.13780.07700.09140.07460.07370.07340.07670.07820.06940.06810.0676
Ds↓0.10870.24560.26050.29850.16350.11640.12240.11510.11620.12530.11180.11190.1112
QNR↑0.82140.70250.63900.64850.76150.81910.81430.82510.81730.80730.82590.82660.8287
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0.471, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.392, + 0.295, + 0.434, + 0.305 + ], + "angle": 0, + "content": "GFPCA" + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.306, + 0.471, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.388, + 0.399, + 0.437, + 0.41 + ], + "angle": 0, + "content": "MutNet" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.202, + 0.604, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.295, + 0.556, + 0.305 + ], + "angle": 0, + "content": "GS" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.306, + 0.604, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.399, + 0.569, + 0.41 + ], + "angle": 0, + "content": "MANet" + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.202, + 0.738, + 0.293 + ], + "angle": 0, + "content": null + }, + { + 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0.15, + 0.49 + ], + "angle": 0, + "content": "GFPCA" + }, + { + "type": "image", + "bbox": [ + 0.172, + 0.413, + 0.256, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.207, + 0.479, + 0.225, + 0.49 + ], + "angle": 0, + "content": "GS" + }, + { + "type": "image", + "bbox": [ + 0.258, + 0.413, + 0.341, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.284, + 0.479, + 0.316, + 0.49 + ], + "angle": 0, + "content": "SFIM" + }, + { + "type": "image", + "bbox": [ + 0.343, + 0.413, + 0.426, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.479, + 0.41, + 0.49 + ], + "angle": 0, + "content": "PANNET" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.413, + 0.511, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.445, + 0.479, + 0.496, + 0.49 + ], + "angle": 0, + "content": "SRPPNN" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.413, + 0.598, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.479, + 0.578, + 0.49 + ], + "angle": 0, + "content": "GPPNN" + }, + { + "type": "image", + "bbox": [ + 0.599, + 0.413, + 0.683, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.479, + 0.666, + 0.49 + ], + "angle": 0, + "content": "MutNet" + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.413, + 0.768, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.479, + 0.749, + 0.49 + ], + "angle": 0, + "content": "MANet" + }, + { + "type": "image", + "bbox": [ + 0.769, + 0.412, + 0.855, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.798, + 0.479, + 0.827, + 0.49 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.51, + 0.893, + 0.542 + ], + "angle": 0, + "content": "Figure 8: Qualitative visualization comparison of our method with other representative counterparts on a typical satellite image pair from the GaoFen2 dataset. Images in the last row visualize the MSE between the output and ground truth." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.568, + 0.225, + 0.584 + ], + "angle": 0, + "content": "loss function \\(\\mathbf{L}_{\\mathrm{img}}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.595, + 0.47, + 0.636 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} _ {\\mathbf {s s}} = \\sum_ {i = 1} ^ {N} \\left| \\left| E _ {m a e} \\left(\\mathbf {H} _ {g t, i}\\right) - E _ {m a e} \\left(\\mathbf {H} _ {i} ^ {(K + 1)}\\right) \\right| \\right| _ {1}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.647, + 0.328, + 0.66 + ], + "angle": 0, + "content": "The total loss function is remarked as" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.675, + 0.469, + 0.692 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} = L _ {i m g} + \\lambda \\times L _ {s s}. \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.703, + 0.42, + 0.717 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is weighted factor and set as 1 in our work." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.732, + 0.209, + 0.749 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.175, + 0.773 + ], + "angle": 0, + "content": "4.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Datasets. Due to the unavailability of ground-truth MS images, we follow the previous works to generate the training set by employing the Wald protocol tool [24]. Specifically, given the MS image \\(\\mathrm{H} \\in \\mathrm{R}^{\\mathrm{M} \\times \\mathrm{N} \\times \\mathrm{C}}\\) and the PAN image \\(\\mathrm{P_H} \\in \\mathrm{R}^{\\mathrm{rM} \\times \\mathrm{rN} \\times \\mathrm{b}}\\), both of them are downsampled by a ratio \\(\\mathbf{r}\\), and then are denoted as \\(\\mathrm{L} \\in \\mathrm{R}^{\\mathrm{M} / \\mathrm{r} \\times \\mathrm{N} / \\mathrm{r} \\times \\mathrm{C}}\\) and \\(\\mathrm{P} \\in \\mathrm{R}^{\\mathrm{M} \\times \\mathrm{N} \\times \\mathrm{b}}\\), respectively. In the training set, \\(\\mathbf{L}\\) and \\(\\mathbf{p}\\) are regarded as the inputs, while \\(\\mathrm{H}\\) is the ground truth. In our" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.568, + 0.892, + 0.642 + ], + "angle": 0, + "content": "work, three satellite images of WorldView II, GaoFen2, and WorldView III are adopted to construct image datasets. For each database, PAN images are cropped into patches with a size of \\(128 \\times 128\\) while the corresponding MS patches are with a size of \\(32 \\times 32\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.644, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Baselines. Several state-of-the-art Pan-sharpening methods are compared, including seven representative deep learning-based methods: PNN [18], PANNET [28], MSDCNN [30], SRPPNN [2], GPPNN [26], MANet [27], and MutNet [41] and five promising traditional methods: SFIM [16], Brovey [7], GS [14], IHS [8], and GFPCA [15]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.735, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Metrics. Several widely-used image quality assessment (IQA) metrics are employed for performance measurement, including PSNR, SSIM, SAM [31], ERGAS [1], and three non-reference metrics \\( D_{\\lambda} \\), \\( D_{S} \\), and QNR for real-world full-resolution scenes." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.811, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Implementations. In our experiments, all the designed networks are implemented with PyTorch framework and trained on the PC with a single NVIDIA GeForce GTX 3090 GPU. In the training phase, these networks are optimized by the Adam optimizer [12] over 1000 epochs with a mini-batch size of 4. The learning rate is initialized with" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12404" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.122 + ], + "angle": 0, + "content": "\\(5 \\times 10^{-4}\\). When reaching 200 epochs, the learning rate is decayed by multiplying 0.5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.132, + 0.218, + 0.148 + ], + "angle": 0, + "content": "4.2. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.155, + 0.47, + 0.381 + ], + "angle": 0, + "content": "Evaluation on reduced-resolution scenes. The comparison results on three satellite datasets are reported in Table 1. As can be seen, our proposed method achieves the best overall results than other pan-sharpening methods across all the satellite datasets. Specifically, the average gains of our method over the second-best MANet are 0.12dB, 0.32dB, and 0.10dB in terms of PSNR on WorldView-II, GaoFen2, and WorldView-III datasets, respectively. In addition to PSNR, consistent improvements can be observed in the other metrics, indicating lower spectral distortion and spatial texture preservation. Our method outperforms other compared methods by a large margin. The corresponding visual comparisons shown in Figure 7 and Figure 8 also support the above claim. More visual results can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.534 + ], + "angle": 0, + "content": "Evaluation on full-resolution scenes. In order to demonstrate the real-world application, we further perform experiments on 200 sets of full-resolution data obtained by the additional Gaofen2. Due to the unavailability of ground-truth MS images in real-world full-resolution scenes, the commonly-used three non-reference metrics of \\( D_{\\lambda} \\), \\( D_{s} \\), and QNR are adopted for evaluation. The quantitative comparisons between representative deep learning-based methods and our method are shown in Table 2. Our methods surpass other pan-sharpening methods in all metrics." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.546, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Table 3: Quantitative results of the model with different number stages." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.588, + 0.47, + 0.711 + ], + "angle": 0, + "content": "
Stage Number (K)PSNR↑SSIM↑SAM↓ERGAS↓
141.24590.96550.02501.0123
241.49620.96790.02400.9838
341.71520.97220.02230.9506
441.87350.97310.02200.9413
541.84610.96970.02260.9421
641.74290.97330.02210.9506
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.74, + 0.468, + 0.771 + ], + "angle": 0, + "content": "Table 4: Quantitative results with the ablation of key components." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.782, + 0.468, + 0.884 + ], + "angle": 0, + "content": "
UMAELMAEPSNR↑SSIM↑SAM↓ERGAS↓
41.46550.96690.02530.9724
✓41.65760.96810.02410.9679
✓41.83820.96950.02310.9423
✓✓41.87350.97310.02200.9413
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.655, + 0.108 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.114, + 0.892, + 0.158 + ], + "angle": 0, + "content": "To explore the contribution of different hyper-parameters and the key components, we conduct ablation studies on the WorldView-II dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.159, + 0.892, + 0.31 + ], + "angle": 0, + "content": "Impact of the Stage Numbers. To investigate the impact of the number of unfolded stages, we experiment proposed method with varying numbers of stages K. Observing the results from Table 3, we found that the model's performance has obtained considerable improvement as the number of stages increases until reaching 4. When further increasing the K, the results show a decreasing trend, which may be caused by the difficulty of gradient propagation. We set \\( \\mathrm{K} = 4 \\) as default stage number to balance the performance and computational complexity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.892, + 0.461 + ], + "angle": 0, + "content": "Effect of Key Components. To investigate the contribution of the devised modules in our network, we take the model with \\( K = 4 \\) as the baseline and then conduct the comparison by observing the difference before and after removing the components. The corresponding quantitative comparisons are reported in Table 4, where \\( \\mathrm{U}_{\\mathrm{MAE}} \\) represents the MAE within the UNet network and \\( \\mathrm{L}_{\\mathrm{MAE}} \\) represents the MAE within loss function. As can be observed, equipping with both the MAE priors significantly improves the model performance." + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.477, + 0.892, + 0.628 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.639, + 0.892, + 0.67 + ], + "angle": 0, + "content": "Figure 9: The feature visualization in Unet upon the iterative stage increasing of deep unfolding network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.69, + 0.694, + 0.707 + ], + "angle": 0, + "content": "4.4. Effect of MAE prior" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.892, + 0.835 + ], + "angle": 0, + "content": "To verify the effect of the designed MAE prior, we deepen into the feature maps of \\( F_{rs} \\), \\( F_{use} \\). As illustrated in section 3.3 that the MAE prior takes account for predicting the missing information of \\( F_{rs} \\) and then enhances the representation \\( F_{use} \\), with the stage increasing, the MAE-prior reasoned feature \\( F_{rs} \\) is gradually enhanced and the resulted \\( F_{use} \\) becomes more informative, thus supporting the powerful capability of the MAE prior, detailed in Figure 9." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.619, + 0.861 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this paper, we proposed the first work to focus on the designs of the deep prior term. We employ the learned" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12405" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "MAE in a self-supervised manner acting as an image prior and then embed the pre-trained MAE with reasoning ability to penetrate deep unfolding architecture, thus making it more transparent. We also redevelop the pre-trained MAE with a spatial-spectral masking strategy and employ it as the regularization term within loss function to constrain the spatial-spectral consistency. The contained intrinsic knowledge over MAE loss term empowers the main unfolding network learning ability. Extensive experiments on three satellite datasets demonstrate its superiority." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.26, + 0.175, + 0.275 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.285, + 0.47, + 0.354 + ], + "angle": 0, + "content": "[1] L. Alparone, L. Wald, J. Chanussot, C. Thomas, P. Gamba, and L. M. Bruce. Comparison of pansharpening algorithms: Outcome of the 2006 grs-s data fusion contest. IEEE Transactions on Geoscience and Remote Sensing, 45(10):3012-3021, 2007." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.357, + 0.47, + 0.412 + ], + "angle": 0, + "content": "[2] Jiajun Cai and Bo Huang. Super-resolution-guided progressive pansharpening based on a deep convolutional neural network. 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IEEE transactions on geoscience and remote sensing, 51(5):2827-2836, 2012." + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12407" + } + ] +] \ No newline at end of file diff --git a/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_origin.pdf b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7dfc74a405ba2108b5ffa0697ef9115a370d4187 --- /dev/null +++ b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/e7814c90-67a9-4d35-afdb-629b41a8c850_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7d4261b3ac4b7bb86dec6b465bf886126d32cf2aac27fcba4f66082991d1368c +size 10523095 diff --git a/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/full.md b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5178859a9f4e285ac1346259f3e28e7e4e826f8d --- /dev/null +++ b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/full.md @@ -0,0 +1,478 @@ +# Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-Spectral Image Fusion + +Man Zhou $^{1*}$ , Jie Huang $^{2*}$ , Naishan Zheng $^{2}$ , Chongyi Li $^{3\dagger}$ + +$^{1}$ S-Lab, Nanyang Technological University, Singapore + +$^{2}$ University of Science and Technology of China, China + +$^{3}$ Nankai University, China + +# Abstract + +The success of deep neural networks for pan-sharpening is commonly in a form of black box, lacking transparency and interpretability. To alleviate this issue, we propose a novel model-driven deep unfolding framework with image reasoning prior tailored for the pan-sharpening task. Different from existing unfolding solutions that deliver the proximal operator networks as the uncertain and vague priors, our framework is motivated by the content reasoning ability of masked autoencoders (MAE) with insightful designs. Specifically, the pre-trained MAE with spatial masking strategy, acting as intrinsic reasoning prior, is embedded into unfolding architecture. Meanwhile, the pre-trained MAE with spatial-spectral masking strategy is treated as the regularization term within loss function to constrain the spatial-spectral consistency. Such designs penetrate the image reasoning prior into deep unfolding networks while improving its interpretability and representation capability. The uniqueness of our framework is that the holistic learning process is explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Extensive experiments on multiple satellite datasets demonstrate the superiority of our method over the existing state-of-the-art approaches. Code will be released at https://manman1995.github.io/. + +# 1. Introduction + +Pan-sharpening, a texture-rich panchromatic image-guided multi-spectral image super-resolution task, is to reason the unknown content at the pre-defined pixel positions according to the context of low-resolution (LR) multispectral (MS) image and high-resolution (HR) panchromatic (PAN) image. Owing to the physical constraints, + +![](images/00f16f38456c671d51af36c000007f6ed520a5070b266de7a70415bf99d11a98.jpg) +Figure 1: Motivation. Pan-sharpening is to reason the unknown content at the pre-defined pixel positions according to the context of low-resolution multi-spectral image and high-resolution panchromatic image. + +satellites usually adopt both MS and PAN sensors to observe scenes, providing the MS images with high spectral but limited spatial resolution and the PAN images with high spatial but low spectral resolution. To obtain observation with both high spectral and high spatial resolutions, the pan-sharpening technique has drawn increasing attention in both image processing and remote sensing communities. + +Many research efforts have been devoted to solving the pan-sharpening problem, which can be categorized into two groups: traditional optimization methods and deep learning-based methods. Since an infinite number of HR-MS images can be downsampled to produce the same LR-MS image, reasoning the HR-MS images from the LR counterparts is highly ill-posed. To solve the ill-posedness, various natural images priors as regularization terms have been developed in traditional optimization methods, e.g., low-rank prior [29] and sparse image priors [44]. However, these priors are not easy to be devised. Moreover, it is challenging to optimize these methods, hampering the practical applications. Besides, due to the hand-crafted designs, their limited representation ability results in unsatisfactory performance. + +The powerful learning capability of deep neural net + +![](images/8cdcfb74689abd0753ddf1a6f48b58fd604a292375d718f500adae3f232d1189.jpg) +Figure 2: Motivation. The comparison between prior unfolding frameworks and ours. + +works ignites renewed interest in this problem. As a pioneering work, PNN [18] employs three-layer convolution neural networks to account for pan-sharpening learning. Since then, more and more complicated and deeper architectures have been proposed to improve the performance of pan-sharpening [25, 28, 30]. Despite the remarkable progress, most of them focus on heuristically constructing network architectures in a black box fashion without considering the underlying rationality of pan-sharpening task, lacking transparency and interpretability. + +To improve interpretability, model-driven deep unfolding methods have been proposed. Xu et al. [26] propose the first deep unfolding network for pan-sharpening. The basic idea behind it is to formulate pan-sharpening as an optimization problem and employ the proximal gradient descent algorithm to solve it. The optimization process can be reformulated as: + +$$ +\hat {\mathbf {H}} = \min _ {\mathbf {H}} \frac {1}{2} | | \mathbf {L} - \mathbf {D K H} | | _ {2} ^ {2} + \lambda \Omega (\mathbf {H} | \mathbf {P}), \qquad (1) +$$ + +where $\lambda$ is a hyper-parameter to weight the first term (data fidelity term accords with the degradation) and the second term (regularization term $\Omega(\cdot)$ ). $\mathbf{D}$ , and $\mathbf{K}$ denote the down-sampling and blur operators, respectively. L, P, and H respectively represent the LR-MS image, PAN image, and HR-MS image. Technically, the proximal gradient descent algorithm can be approximatively expressed as an iterative convergence problem by solving the following iterative + +function: + +$$ +\mathbf {H} ^ {(k)} = \operatorname {p r o x} _ {\lambda , \Omega , P} \left(\mathbf {H} ^ {(k - 1)} + \delta (\mathbf {D K}) ^ {T} (\mathbf {L} - \mathbf {D K H} ^ {(k - 1)})\right), \tag {2} +$$ + +where $\mathrm{k}$ and $\delta$ denote the iterative step and learning factor. Motivation. In terms of the function $\mathrm{prox}_{\lambda, \Omega, \mathrm{P}}$ that involves the embedded prior term $\Omega(\cdot)$ , existing works usually heuristically employ diverse network architectures in a black box fashion and deliver the proximal operator networks as the uncertain and vague priors, visized in Figure 2. These methods thus lack clear physical meanings of the prior terms. In addition, most deep unfolding-based methods [26, 27] cannot extract the pan-sharpening customized prior with clear physical patterns well, which is caused by weak interpretable prior operations. Hence, we argue that the deep unfolding framework with sufficient interpretability has the potential of improving performance. + +Solution. The first function of pan-sharpening is to reason the unknown information at the pre-defined pixel positions using the context, detailed in Figure 1. In this work, we propose a novel model-driven deep unfolding framework for pan-sharpening with interpretability. Inspired by the content reasoning ability of masked autoencoders (MAE) [9], our framework endows the holistic learning process of deep unfolding with the explicitly integrated with inherent physical mechanism underlying the pan-sharpening task. The key insights of our framework are (1) we embed the pretrained MAE with spatial masking strategy into the unfolding architecture, acting as intrinsic reasoning prior and (2) we treat the pre-trained MAE with spatial-spectral masking as the regularization term within loss function to constrain the spatial-spectral consistency. Such new designs penetrate the image reasoning prior into deep unfolding network while improving the interpretability and representation ability. Besides, our framework also outperforms existing state-of-the-art approaches on multiple satellite datasets. + +Our main contributions are summarized as follows: + +- We propose to embed the pre-trained MAE into deep unfolding architecture, resorting to its image reasoning ability for pan-sharpening. Such reasoning prior makes the framework transparent and interpretable. +- We creatively treat the pre-trained MAE with spatial-spectral masking strategy as regularization term within loss function to constrain the spatial-spectral consistency. The tailored regularization term with intrinsic knowledge of spatial-spectral reasoning empowers the unfolding framework. +- In contrast to previous works, our framework as the first attempt pushes the frontiers of pan-sharpening towards the designs of the deep prior term. It shows outstanding performance on three satellite datasets, outperforming the state-of-the-art algorithms. + +# 2. Related Work + +Traditional Methods. Traditional pan-sharpening methods can be roughly divided into three main categories: CS-based methods, MRA-based methods, and VO-based methods. The CS-based approaches separate spatial and spectral information from the LRMS image and replace spatial information with a PAN image. Intensity hue-saturation (IHS) fusion [3], the principal component analysis (PCA) methods [13, 22], Brovey transforms [6], and Gram-Schmidt (GS) orthogonalization method [14] are CS-based approaches. These CS-based approaches are fast since LR-MS images simply need spectral treatment to remove and replace spatial components, but the resultant HR-MS images show severe spectral distortion. The MRA-based methods inject high-frequency features of PAN derived by multi-resolution decomposition techniques into upsampled multi-spectral images. Decimated wavelet transform (DWT) [17], high-pass filter fusion (HPF) [21], Laplacian pyramid (LP) [23], smoothing filter-based intensity modulation (SFIM) [16], and atrous wavelet transform (ATWT) [19] are typical MRA-based methods that reduce spectral distortion and improve resolution, but they heavily rely on multi-resolution techniques, which may cause local spatial artifacts. In recent years, VO-based methods are used because of the fine fusion effect on ill-posed problems. These various constraints can only inadequately reflect the limited structural relations of the images. + +Deep Learning-based Methods. Deep learning-based methods have been widely used for pan-sharpening [41, 27, 34, 35, 11, 32, 40, 43, 39, 36, 37, 33, 42]. PNN [18] uses three convolutional units to directly map the relationship between PAN, LR-MS, and HR-MS images. Inspired by PNN, a large number of pan-sharpening studies based on deep learning emerge. For example, PANNet [28] adopts the residual learning module in Resnet [10]. MSDCNN [30] adds multi-scale modules on the basis of residual connection. SRPPNN [2] refers to the design idea of SRCNN [4]. + +Recently, some model-driven deep models with physical meaning emerge. The basic idea is to use prior knowledge to formulate optimization problems, then unfold the optimization algorithms and replace the steps in the algorithm with deep neural networks. For example, Xu et al. [26] propose the model-based deep learning network MH-Net and GPPNN for pan-sharpening, respectively. In terms of the function design $\mathrm{prox}_{\lambda,\Omega}$ that takes for the embedded prior term, existing works heuristically employ diverse network architectures in the black-box fashion, thus resulting in weak physical meanings. It motivates us to explore the task-driven customized prior with clear physical patterns. + +# 3. Methodology + +# 3.1. Model Formulation + +In general, pan-sharpening aims to obtain the HR-MS image $\mathbf{H}$ from its degradation observation $\mathbf{L} = (\mathbf{H} \otimes \mathbf{K}) \downarrow_{s} + \mathbf{n}_{\mathbf{s}}$ , where $\mathbf{K}$ and $\downarrow_{s}$ denote blur kernel and down-sampling operation, and $\mathbf{n}_{\mathbf{s}}$ is usually assumed to be additive white Gaussian noise (AWGN). The degradation process by using the maximum a posteriori (MAP) principle can be reformulated as: + +$$ +\min _ {\mathbf {H}} \frac {1}{2} \left\| \mathbf {L} - \mathbf {D K H} \right\| _ {2} ^ {2} + \lambda \Omega (\mathbf {H} | \mathbf {P}), \tag {3} +$$ + +where $\lambda$ is a hyper-parameter to weight the first term (data fidelity term accords with degradation) and the regularization term $\Omega(.)$ . We solve the optimization problem using the half-quadratic splitting (HQS) algorithm. By introducing one auxiliary variables $\mathbf{U}$ , Eq. (3) can be reformulated as a non-constrained optimization problem: + +$$ +\min _ {\mathbf {H}, \mathbf {U}} \frac {1}{2} \left\| \mathbf {L} - \mathbf {D K H} \right\| _ {2} ^ {2} + \frac {\eta}{2} \left\| \mathbf {U} - \mathbf {H} \right\| _ {2} ^ {2} + \lambda \Omega (\mathbf {U} | \mathbf {P}), \tag {4} +$$ + +where $\eta$ is the penalty parameter. When $\eta$ approaches infinity, Eq. (4) converges to Eq. (3). Minimizing Eq. (4) involves updating $\mathbf{U}$ and $\mathbf{H}$ alternately. + +Updating U. Given the estimated HR-MS image $\mathbf{H}^{(k)}$ at iteration $k$ , the auxiliary variable $\mathbf{U}$ can be updated as: + +$$ +\mathbf {U} ^ {(k)} = \underset {\mathbf {U}} {\arg \min } \frac {\eta}{2} \left| \left| \mathbf {U} - \mathbf {H} ^ {(k)} \right| \right| _ {2} ^ {2} + \lambda \Omega (\mathbf {U} | \mathbf {P}). \tag {5} +$$ + +We can derive the solution of Eq. (5) as + +$$ +\mathbf {U} ^ {(k)} = \operatorname {p r o x} _ {\Omega (.) , \lambda , \eta} (\mathbf {H} ^ {(k)}, P), \tag {6} +$$ + +where $\mathrm{prox}_{\Omega}(\cdot)$ is the proximal operator corresponding to the implicit local prior $\Omega (\cdot)$ . + +Updating H. Given $\mathbf{U}^{(k)}$ , $\mathbf{H}$ is updated as: + +$$ +\mathbf {H} ^ {(k + 1)} = \underset {\mathbf {H}} {\arg \min } \frac {1}{2} \left| \left| \mathbf {L} - \mathbf {D K H} \right| \right| _ {2} ^ {2} + \frac {\eta}{2} \left| \left| \mathbf {U} ^ {(k)} - \mathbf {H} \right| \right| _ {2} ^ {2}. \tag {7} +$$ + +By applying the proximal gradient method [20] to Eq. (7), we update $\mathbf{H}$ using the gradient decent method. Consequently, the updated equation for $\mathbf{H}$ is + +$$ +\mathbf {H} ^ {(k + 1)} = \mathbf {H} ^ {(k)} - \delta_ {2} \nabla f _ {2} (\mathbf {H} ^ {(k)}), \tag {8} +$$ + +where $\delta_{2}$ is the step size, and the gradient $\nabla f_2(\mathbf{H}^{(k)})$ is + +$$ +\nabla f _ {2} \left(\mathbf {H} ^ {(k)}\right) = \left(\mathbf {D K}\right) ^ {T} \left(\mathbf {D K H} ^ {(k)} - \mathbf {L}\right) + \eta \left(\mathbf {H} ^ {(k)} - \mathbf {U} ^ {(k)}\right), \tag {9} +$$ + +where $T$ is the matrix transpose operation. + +![](images/ca04489f45f52a3dcbf0aa40559ce422eb82e1cd71ee049140f3bb73eafd3204.jpg) +Stage 1: Image Reasoning Prior Pre-training + +![](images/0e1735fe0814b2cfeb417d658f90088fd53317c54374592308c41c532809f520.jpg) +Stage 2: Spatial-spectral Consistency Pre-training + +![](images/a080c7a2f3376d5118e7dc11405887357b5e4d97306cf330be47416726ff60f7.jpg) +Stage 3: Penetrating Reasoning Prior into Unfolding +Conv block +Spatial-domain operator +Frequency-domain operator +Element-wise subtraction +Downsample convolution +Upsample convolution +Frozen + +![](images/6be4df005ba60cae04e4a62d2269d25a44777385b4fb3aaf3222ee73492f8e27.jpg) +Figure 3: The overall architecture of our proposed method. In detail, LR-MS image is firstly up-sampled and then performs the stage-wise iteration, updating U and H in the overall K stages where the pre-trained MAE acting as reasoning prior penetrates Deep Unfolding process. To promote the spatial-spectral consistency, the pre-trained extension version is employed as the loss constraint. (Best viewed in color.) + +![](images/8105cf22368db16857de7d0d46c95820be475df198bd60ef114826e97c75870c.jpg) + +![](images/990ba5e7c66d29e1a7486cd6e299773d07a6d437ddfa1dcd1cf0585b61322125.jpg) + +![](images/c8576a0d77efb06b19b18ca688453c50bdc4c7e2353b9a45ff6060826f7f00de.jpg) + +![](images/4dcc4955b4fd58cfc87bf708527ae3e4f33d916141ad8402c8877965b70dfd53.jpg) + +![](images/46a11b45603de31b0d9d0f33ab688ae01d83e0b32e8a8c529fe30a89f447e975.jpg) + +![](images/ddb13d1d6f5c0400e04a6023b744a583eeafb1ead12bfbbcad0736282c3d97ce.jpg) + +# 3.2. Model Flowchart + +As detailed in Figure 3, the proposed image reasoning prior-embedded framework consists of four training stages: + +Stage 1: Image Reasoning Prior Pre-training; Stage 2: Spatial-Spectral Consistency Pre-training; Stage 3: Penetrating Reasoning Prior into Unfolding Network; Stage 4: Spatial-Spectral Consistency Constraint as loss function. + +# 3.3. Structure Flow + +Based on the iterative algorithm, we construct deep unfolding network for pan-sharpening as shown in Figure 3. This network is an implementation of the algorithm for solving Eq. (3). In terms of the function design $\mathrm{prox}_{\lambda,\Omega}$ that takes for the embedded prior term $\Omega(.)$ , we stand on the shoulder of MAE proposed by He et al, where the MAE is trained in a self-supervised manner and empowered with the reasoning ability, acting as the image prior. Based on the above analysis, the MAE is naturally treated as the prior term $\Omega(.)$ and meets the function of pan-sharpening. + +Stage 1: Based on the original MAE, we employ the pure convolution neural network as the encoder and de + +coder to implement its network architecture with masking patch strategies: (1) evenly divide the input image, randomly sample the small subset of regions and mask the remaining ones while keeping the whole image architecture; and (2) both the small subset of visible patches and mask tokens are processed by the encoder and decoder that reconstructs the original image in pixels. Note that the input into the encoder is the whole image, not the image patch. + +Stage 3: UNet. Based on the pre-trained MAE encoder $\mathrm{f_{CMAE}(.,)}$ we implement the whole architecture of UNet that is presented in Figure 5. To be specific, the k-th iteration $\mathbf{H}^{(k - 1)}$ is fed into the encoder part $\mathrm{E_{CMAE}(.,)}$ of the pre-trained MAE to generate the reasoning feature representation as + +$$ +\mathbf {H} _ {\mathrm {r s}} = \operatorname {E} _ {\mathrm {C M A E}} \left(\mathbf {H} ^ {(\mathrm {k} - 1)}\right), \tag {10} +$$ + +Then, PAN image $\mathrm{P}$ is projected into the shallow feature space by the convolution units as + +$$ +\mathbf {F} _ {\mathrm {p}} = \operatorname {C o n v} (\mathbf {P}). \tag {11} +$$ + +Referring to the representation $\mathbf{H}_{\mathrm{rs}}$ and the texture-rich PAN information $\mathbf{F}_{\mathrm{p}}$ , we further incorporate them to re + +![](images/8f0b0bd9a8b871ccd38b7f351e2235aa82bf18adb5eca8f87ab650836e4dd90f.jpg) +Figure 6: Motivation. Masked Autoencoders as spatiotemporal learners. It masks a large subset of random patches in spacetime. An encoder operates on a set of visible patches. A decoder then processes the full set of encoded patches and mask tokens to reconstruct the input. Except for patch and positional embeddings, the encoder, the decoder, and the masking strategy have no spatiotemporal inductive bias. + +![](images/a976430df081b0e22c57f83ef9acf6c69dd323ef8243f5f76c10b5f5fc175b33.jpg) +Figure 4: Motivation. Masked Autoencoders as the image reasoning learners. During pre-training, a large random subset of image patches is masked out, remarked as yellow ones. The encoder is applied to the small subset of visible patches. Mask tokens are introduced after the encoder, and the full set of encoded patches and mask tokens is processed by a decoder that reconstructs the original image in pixels. +Figure 5: The detailed structure of UNet. + +construct the HR-MS image by the spatial-frequency information transformation module $SFT$ that derived from [38], which is shown in Figure 5. The information transformation process is detailed as + +$$ +\mathrm {F} _ {\text {f u s e}} = \mathrm {S F T} \left(\mathrm {H} _ {\mathrm {r s l}}, \mathrm {F} _ {\mathrm {p}}\right). \tag {12} +$$ + +HNet. To transform the update process of $\mathbf{H}^{(k + 1)}$ in Eq. (8) into a network. Firstly, we need to implement two operations, i.e., Down $\downarrow_{s}$ and $Up\uparrow_{s}$ , using the network. Specifically, Down $\downarrow_{s}$ is implemented by a spatial identify transformation convolution operator, and an additional $s-$ + +![](images/e83d625ffb1c45c0e98981a497204a17c8001ff5e4e7a308ef808d456625a2f8.jpg) + +strides followed convolution module with spatial resolution reduction: + +$$ +\mathbf {D K H} ^ {(k)} = \operatorname {C o n v} ^ {(s)} \downarrow \left(\mathbf {K H} ^ {(k)}\right), \tag {13} +$$ + +where $\operatorname{Conv} \downarrow_{(s)}$ aims to perform the $s$ times down-sampling. The latter operation $Up \uparrow_{s}$ is implemented by a deconvolution layer containing the $s$ -strides convolution module with spatial resolution expansion and a convolution module with spatial identify transformation: + +$$ +\mathbf {U} \mathbf {H} ^ {(k)} = \operatorname {C o n v} ^ {(s)} \uparrow (\mathbf {L} - \mathbf {D K H} ^ {(k)}), \tag {14} +$$ + +where $\mathrm{Conv}\uparrow_{(s)}$ aims to perform the $s$ times up-sampling. + +# 3.4. Optimization Flow + +Stage 2: To highlight, the uniqueness of our proposed method is that the entire learning process is fully and explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Specifically, based on the MAE with spatial-spectral masking strategy that is tailored with the spatial-frequency representation learner, we redevelop the MAE as the regularization term within the loss function to constrain the spatial-spectral consistency of the model output and its corresponding ground truth. As shown in Figure 6, standing on the shoulders of the video-version extension of masked Autoencoders [5] proposed by He et al, we redevelop the masked image modeling as "learned loss function" to constraint the spatial-spectral representation consistency by the following implementation details: + +- randomly mask out spatial-spectral patches in the ground truth image and then learn an autoencoder to reconstruct them; +- the only spatial-spectral specific inductive bias is on embedding the patches and their positions; all other + +Table 1: Quantitative comparison with the state-of-the-art methods. The best results are highlighted in bold. + +
MethodWordView IIGaoFen2WordView III
PSNR ↑SSIM↑SAM↓ERGAS↓PSNR ↑SSIM↑SAM↓ERGAS↓PSNR ↑SSIM↑SAM↓ERGAS↓
SFIM34.12970.89750.04392.344936.90600.88820.03181.739821.82120.54570.12088.9730
Brovey35.86460.92160.04031.823837.79740.90260.02181.372022.5060.54660.11598.2331
GS35.63760.91760.04231.877437.22600.90340.03091.673622.56080.54700.12178.2433
IHS35.29620.90270.04612.027838.17540.91000.02431.533622.55790.53540.12668.3616
GFPCA34.55810.90380.04882.141137.94430.92040.03141.560422.33440.48260.12948.3964
PNN (RS'16)40.75500.96240.02591.064643.12080.97040.01720.852829.94180.91210.08243.3206
PANNet (ICCV'17)40.81760.96260.02571.055743.06590.96850.01780.857729.6840.90720.08513.4263
MSDCNN (TGRS'21)41.33550.96640.02420.994045.68740.98270.01350.638930.30380.91840.07823.1884
SRPPNN (TGRS'20)41.45380.96790.02330.989947.19980.98770.01060.558630.43460.92020.07703.1553
GPPNN (CVPR'21)41.16220.96840.02441.031544.21450.98150.01370.736130.17850.91750.07763.2596
MutNet (CVPR'22)41.67730.97050.02240.951947.30420.98920.01020.548130.49070.92230.07493.1125
MANet (ECCV'22)41.85770.96970.02290.942047.26680.98900.01020.547230.54510.92140.07693.1032
Ours41.87350.97310.02200.941347.39310.98920.00890.543530.55600.92250.07333.0072
+ +![](images/513208b11f3f919b24a7f0e1e6b1b9c310ae81b651dfe6424a019a0ecf325fa0.jpg) + +![](images/34f567426b9acc2266d2dacdc91ca1bf814a5e0fe33c32f5289cec8251cd582b.jpg) +MS +SRPPNN + +![](images/5b8ba8a544439ff457b5b7e0c1ae2aab798e0b94578a0b9e1368dd222532bab8.jpg) + +![](images/1ee113541177b87afe7ed4b2e0ffb7de69445e9c8524738569c3b04dc67fc70e.jpg) +PAN +GPPNN + +![](images/22cde19a0a3a908653057f13dc93c7ed099da9995c0eed6e425d1f6edca6201b.jpg) + +![](images/8a37bd7f47a68bc72bb3035daf18b8e6f62b871e35c3ccf80f0e0bd9fc7214b9.jpg) +GFPCA +MutNet + +![](images/16d6384aec15aa8e51c0aa1aa67588d42a876c405e9e1bf36656c5c170fc523f.jpg) + +![](images/90a9e8b0ad804f0e56bc0e6d4ed4274c758ff18c1b29548a7f814354800a6cb0.jpg) +GS +MANet + +![](images/fa219f19a8a6570880bd567c1895e809d3002634268aef9a943494c2ca8feec9.jpg) + +![](images/7286d82b10165c11d0d1dbd1db1c12613410561d9460084a8fe7c03ca483794a.jpg) +SFIM +Ours + +![](images/d5a3c3b62aa2178ccc482f22148bfd585fa0c784e4108cc5aa5909215b1318a2.jpg) +PANNET + +![](images/77c61cd59339511971c5f64fbea7ea4c2ac3834891c33d6d28ea782c0af374e5.jpg) +Ground Truth + +![](images/437bf59159cb8ced0820231cb5b4a8afe8590607937c2fcf5b0ef64c34dab069.jpg) +GFPCA + +![](images/47a2337151d54c6cb4fa4ac3261a1e2f1501d92ee640bb227d52d2c0d71eff19.jpg) +GS +Figure 7: Visual comparison of the HR-MS images produced by different methods for processing the LR-MS image from the WorldView-II dataset. Images in the last row visualize the mean squared error image between the output and ground truth. + +![](images/5d26900746a30128119292c9d4e114245336f7233461ee5ce03feef6fa4390f1.jpg) +SFIM + +![](images/978ee199b8b726ed3eeb2f2911716efe9d4849b80ebee0f9fa80fc09ec7edb02.jpg) +PANNET + +![](images/f41e7068fabe898242303e51ce395f129644f470aff0a8df07f997b83f4dbb74.jpg) +SRPPNN + +![](images/3d9b1eac280ceb59bc9a85d21b4c3dbcd635dfe3d2ca3e758db2d9e412151853.jpg) +GPPNN + +![](images/5c6d7852dd28f11662b2dea0a1979c22466b6a2d8f77a9d658c0aab0e700a43e.jpg) +MutNet + +![](images/25c08c2402b76b9f55c73afc37f2d677bbc701f9e6ae2d8597789bb63bfa6488.jpg) +MANet + +![](images/fa563574a1e350c9ebf3af419a81f92fd523dab193da64d97c1e327de4c22b0e.jpg) +Ours + +components are agnostic to the spatial-spectral nature of the problem. In particular, the encoder and decoder are both vanilla Vision Transformers with no factorization or hierarchy, and our random mask sampling is agnostic to the spatial-spectral structures. + +To generate pleasing pan-sharpening results, we construct our training objective function using the mean absolute error loss over image-level measurement, which is + +defined as + +$$ +\mathbf {L} _ {\mathrm {i m g}} = \sum_ {i = 1} ^ {N} \left\| \mathbf {H} _ {i} ^ {(K + 1)} - \mathbf {H} _ {g t, i} \right\| _ {1}, \tag {15} +$$ + +where $\mathbf{H}_i^{(K + 1)}$ denotes the $i$ -th estimated HR-MS image, $\mathbf{H}_{gt,i}$ is $i$ -th ground truth HR-MS image, and $N$ is the number of training pairs. + +Stage 4: Suppose that the pre-trained MAE model is $f_{mae}(.)$ and its encoder part is $E_{mae}(.)$ , it is employed as the complementary loss function to the original image-level + +Table 2: The average quantitative results on the GaoFen2 dataset in the full resolution case. + +
MetricsSFIMGSBroveyIHSGFPCAPNNPANNETMSDCNNSRPPNNGPPNNMutNetMANetOurs
Dλ↓0.08220.06960.13780.07700.09140.07460.07370.07340.07670.07820.06940.06810.0676
Ds↓0.10870.24560.26050.29850.16350.11640.12240.11510.11620.12530.11180.11190.1112
QNR↑0.82140.70250.63900.64850.76150.81910.81430.82510.81730.80730.82590.82660.8287
+ +![](images/41007f5f3cb9d5e5f94fad0b7f8a87b1815b0d94ce81f64fc513f76072b0b5c9.jpg) +MS + +![](images/bfdcedfc8906629addf31e026e64aff5c16229fa6aa71a05cc1c3c7dfcccfe58.jpg) +SRPPNN + +![](images/5b0bec9fa061dcd7df29e7ca166e33c300fb92eccba316a657298da8905e7ad6.jpg) +PAN + +![](images/273949b8b1f3d37c3227237fe944f88ba313a1d8ea4cad87366b3483fe19190b.jpg) +GPPNN + +![](images/07a1f80314074b1c86612e788dcd91ccdb41540f53634d525e1fbb283e01486f.jpg) +GFPCA + +![](images/f9df7beaa8ce8aefc48eb7ecefbcf7ea32db050b1449ccf8004721ee241b8ca6.jpg) +MutNet + +![](images/810ca38e1bb525ba543f40e9c6ce328ce56e9574ad5df7a6244ed4083dc01f30.jpg) +GS + +![](images/0ec41ea3ee760d6505390fd79990dda0851ce89e77e7a099c8a0a361bd22cb39.jpg) +MANet + +![](images/9326816e46cfbb93f4cf2f289e6438ab616cf588042bac686fd58daa1d8a198e.jpg) +SFIM + +![](images/af652fb7fe0568d61e9d30f6d7857b3bf4a044e3e2f9df828dcea66af8d10c83.jpg) +Ours + +![](images/286ab977f0513d0b05042b750e70a4e749863bebb624a1f3f2f8d4137b762bf9.jpg) +PANNET + +![](images/add18749bd986910a63e7dc869d3ee311c668783f2e36ff415e6c0780ecbd426.jpg) + +![](images/0d69c6e901b0126aad42b6b2c40dce4d352bd5a92f546e653ec61d2ca2326b6f.jpg) +GFPCA + +![](images/3f86bf6a96400c6867b7cb0f00fa59770cd69d193ae25e3f675e55853292cfc1.jpg) +GS + +![](images/981c6f86901f32afab435b44a9a223dc0855a30bc9bb66ba34fa92e064cba2ae.jpg) +SFIM + +![](images/39ff2097971f79ce9fd7096a921791aba093f54173903cc44c9ada9e1530d768.jpg) +PANNET + +![](images/6c36325675010a9edc5a4ed98c3129b2e5e3edcd7662a3e3827832504d0ece81.jpg) +SRPPNN +Figure 8: Qualitative visualization comparison of our method with other representative counterparts on a typical satellite image pair from the GaoFen2 dataset. Images in the last row visualize the MSE between the output and ground truth. + +![](images/9b9261cf8f7ab2fbb373536428ed244081bd18ce2a2e8dc5004262472131f946.jpg) +GPPNN + +![](images/553c4165dcc8e9d6ddddc81a4a45a5dfbd0593874b8a465d0fb82513f7c86eae.jpg) +MutNet + +![](images/6e87ba7158fcb17fd4a04f3647c0b0b0030e803ea1e28bf49fb29abeb7f7de7f.jpg) +MANet + +![](images/699a382eb3d691f91dc5cce8ea4900cdb78cd9f3a7da052a31eb0319c3939e49.jpg) +Ground Truth +Ours + +loss function $\mathbf{L}_{\mathrm{img}}$ as + +$$ +\mathbf {L} _ {\mathbf {s s}} = \sum_ {i = 1} ^ {N} \left| \left| E _ {m a e} \left(\mathbf {H} _ {g t, i}\right) - E _ {m a e} \left(\mathbf {H} _ {i} ^ {(K + 1)}\right) \right| \right| _ {1}. \tag {16} +$$ + +The total loss function is remarked as + +$$ +\mathbf {L} = L _ {i m g} + \lambda \times L _ {s s}. \tag {17} +$$ + +where $\lambda$ is weighted factor and set as 1 in our work. + +# 4. Experiments + +# 4.1. Settings + +Datasets. Due to the unavailability of ground-truth MS images, we follow the previous works to generate the training set by employing the Wald protocol tool [24]. Specifically, given the MS image $\mathrm{H} \in \mathrm{R}^{\mathrm{M} \times \mathrm{N} \times \mathrm{C}}$ and the PAN image $\mathrm{P_H} \in \mathrm{R}^{\mathrm{rM} \times \mathrm{rN} \times \mathrm{b}}$ , both of them are downsampled by a ratio $\mathbf{r}$ , and then are denoted as $\mathrm{L} \in \mathrm{R}^{\mathrm{M} / \mathrm{r} \times \mathrm{N} / \mathrm{r} \times \mathrm{C}}$ and $\mathrm{P} \in \mathrm{R}^{\mathrm{M} \times \mathrm{N} \times \mathrm{b}}$ , respectively. In the training set, $\mathbf{L}$ and $\mathbf{p}$ are regarded as the inputs, while $\mathrm{H}$ is the ground truth. In our + +work, three satellite images of WorldView II, GaoFen2, and WorldView III are adopted to construct image datasets. For each database, PAN images are cropped into patches with a size of $128 \times 128$ while the corresponding MS patches are with a size of $32 \times 32$ . + +Baselines. Several state-of-the-art Pan-sharpening methods are compared, including seven representative deep learning-based methods: PNN [18], PANNET [28], MSDCNN [30], SRPPNN [2], GPPNN [26], MANet [27], and MutNet [41] and five promising traditional methods: SFIM [16], Brovey [7], GS [14], IHS [8], and GFPCA [15]. + +Metrics. Several widely-used image quality assessment (IQA) metrics are employed for performance measurement, including PSNR, SSIM, SAM [31], ERGAS [1], and three non-reference metrics $D_{\lambda}$ , $D_{S}$ , and QNR for real-world full-resolution scenes. + +Implementations. In our experiments, all the designed networks are implemented with PyTorch framework and trained on the PC with a single NVIDIA GeForce GTX 3090 GPU. In the training phase, these networks are optimized by the Adam optimizer [12] over 1000 epochs with a mini-batch size of 4. The learning rate is initialized with + +$5 \times 10^{-4}$ . When reaching 200 epochs, the learning rate is decayed by multiplying 0.5. + +# 4.2. Comparisons + +Evaluation on reduced-resolution scenes. The comparison results on three satellite datasets are reported in Table 1. As can be seen, our proposed method achieves the best overall results than other pan-sharpening methods across all the satellite datasets. Specifically, the average gains of our method over the second-best MANet are 0.12dB, 0.32dB, and 0.10dB in terms of PSNR on WorldView-II, GaoFen2, and WorldView-III datasets, respectively. In addition to PSNR, consistent improvements can be observed in the other metrics, indicating lower spectral distortion and spatial texture preservation. Our method outperforms other compared methods by a large margin. The corresponding visual comparisons shown in Figure 7 and Figure 8 also support the above claim. More visual results can be found in the supplementary material. + +Evaluation on full-resolution scenes. In order to demonstrate the real-world application, we further perform experiments on 200 sets of full-resolution data obtained by the additional Gaofen2. Due to the unavailability of ground-truth MS images in real-world full-resolution scenes, the commonly-used three non-reference metrics of $D_{\lambda}$ , $D_{s}$ , and QNR are adopted for evaluation. The quantitative comparisons between representative deep learning-based methods and our method are shown in Table 2. Our methods surpass other pan-sharpening methods in all metrics. + +Table 3: Quantitative results of the model with different number stages. + +
Stage Number (K)PSNR↑SSIM↑SAM↓ERGAS↓
141.24590.96550.02501.0123
241.49620.96790.02400.9838
341.71520.97220.02230.9506
441.87350.97310.02200.9413
541.84610.96970.02260.9421
641.74290.97330.02210.9506
+ +Table 4: Quantitative results with the ablation of key components. + +
UMAELMAEPSNR↑SSIM↑SAM↓ERGAS↓
41.46550.96690.02530.9724
✓41.65760.96810.02410.9679
✓41.83820.96950.02310.9423
✓✓41.87350.97310.02200.9413
+ +# 4.3. Ablation Study + +To explore the contribution of different hyper-parameters and the key components, we conduct ablation studies on the WorldView-II dataset. + +Impact of the Stage Numbers. To investigate the impact of the number of unfolded stages, we experiment proposed method with varying numbers of stages K. Observing the results from Table 3, we found that the model's performance has obtained considerable improvement as the number of stages increases until reaching 4. When further increasing the K, the results show a decreasing trend, which may be caused by the difficulty of gradient propagation. We set $\mathrm{K} = 4$ as default stage number to balance the performance and computational complexity. + +Effect of Key Components. To investigate the contribution of the devised modules in our network, we take the model with $K = 4$ as the baseline and then conduct the comparison by observing the difference before and after removing the components. The corresponding quantitative comparisons are reported in Table 4, where $\mathrm{U}_{\mathrm{MAE}}$ represents the MAE within the UNet network and $\mathrm{L}_{\mathrm{MAE}}$ represents the MAE within loss function. As can be observed, equipping with both the MAE priors significantly improves the model performance. + +![](images/b67b0abb19629cc7683e93fd07b5e6a35d88be54b49df6066f2a3b908063b4ca.jpg) +Figure 9: The feature visualization in Unet upon the iterative stage increasing of deep unfolding network. + +# 4.4. Effect of MAE prior + +To verify the effect of the designed MAE prior, we deepen into the feature maps of $F_{rs}$ , $F_{use}$ . As illustrated in section 3.3 that the MAE prior takes account for predicting the missing information of $F_{rs}$ and then enhances the representation $F_{use}$ , with the stage increasing, the MAE-prior reasoned feature $F_{rs}$ is gradually enhanced and the resulted $F_{use}$ becomes more informative, thus supporting the powerful capability of the MAE prior, detailed in Figure 9. + +# 5. Conclusion + +In this paper, we proposed the first work to focus on the designs of the deep prior term. We employ the learned + +MAE in a self-supervised manner acting as an image prior and then embed the pre-trained MAE with reasoning ability to penetrate deep unfolding architecture, thus making it more transparent. We also redevelop the pre-trained MAE with a spatial-spectral masking strategy and employ it as the regularization term within loss function to constrain the spatial-spectral consistency. 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IEEE transactions on geoscience and remote sensing, 51(5):2827-2836, 2012. \ No newline at end of file diff --git a/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/images.zip b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..48244d80e38062549b39aedb7e82e56d7834e583 --- /dev/null +++ b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:208f28c7e41da4f5a7a3eeea5dacfa5e21553ec647a4eed24eb79a978dbff95e +size 1010951 diff --git a/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/layout.json b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..70b75240cd11a06defb601ef20cb968cdb9ed94e --- /dev/null +++ b/2023/Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-spectral Image Fusion/layout.json @@ -0,0 +1,12309 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 74, + 102, + 520, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 102, + 520, + 140 + ], + "spans": [ + { + "bbox": [ + 74, + 102, + 520, + 140 + ], + "type": "text", + "content": "Learned Image Reasoning Prior Penetrates Deep Unfolding Network for Panchromatic and Multi-Spectral Image Fusion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "spans": [ + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "text", + "content": "Man Zhou" + }, + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "text", + "content": ", Jie Huang" + }, + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "text", + "content": ", Naishan Zheng" + }, + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "text", + "content": ", Chongyi Li" + }, + { + "bbox": [ + 161, + 160, + 430, + 175 + ], + "type": "inline_equation", + "content": "^{3\\dagger}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 161, + 175, + 428, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 161, + 175, + 428, + 189 + ], + "spans": [ + { + "bbox": [ + 161, + 175, + 428, + 189 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 161, + 175, + 428, + 189 + ], + "type": "text", + "content": "S-Lab, Nanyang Technological University, Singapore" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 161, + 189, + 431, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 161, + 189, + 431, + 203 + ], + "spans": [ + { + "bbox": [ + 161, + 189, + 431, + 203 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 161, + 189, + 431, + 203 + ], + "type": "text", + "content": "University of Science and Technology of China, China" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 233, + 203, + 361, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 233, + 203, + 361, + 217 + ], + "spans": [ + { + "bbox": [ + 233, + 203, + 361, + 217 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 233, + 203, + 361, + 217 + ], + "type": "text", + "content": "Nankai University, China" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 244, + 192, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 257 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 257 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 270, + 290, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 290, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 290, + 559 + ], + "type": "text", + "content": "The success of deep neural networks for pan-sharpening is commonly in a form of black box, lacking transparency and interpretability. To alleviate this issue, we propose a novel model-driven deep unfolding framework with image reasoning prior tailored for the pan-sharpening task. Different from existing unfolding solutions that deliver the proximal operator networks as the uncertain and vague priors, our framework is motivated by the content reasoning ability of masked autoencoders (MAE) with insightful designs. Specifically, the pre-trained MAE with spatial masking strategy, acting as intrinsic reasoning prior, is embedded into unfolding architecture. Meanwhile, the pre-trained MAE with spatial-spectral masking strategy is treated as the regularization term within loss function to constrain the spatial-spectral consistency. Such designs penetrate the image reasoning prior into deep unfolding networks while improving its interpretability and representation capability. The uniqueness of our framework is that the holistic learning process is explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Extensive experiments on multiple satellite datasets demonstrate the superiority of our method over the existing state-of-the-art approaches. Code will be released at https://manman1995.github.io/." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 582, + 128, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 128, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 128, + 594 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 602, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 602, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 47, + 602, + 287, + 675 + ], + "type": "text", + "content": "Pan-sharpening, a texture-rich panchromatic image-guided multi-spectral image super-resolution task, is to reason the unknown content at the pre-defined pixel positions according to the context of low-resolution (LR) multispectral (MS) image and high-resolution (HR) panchromatic (PAN) image. Owing to the physical constraints," + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 324, + 249, + 526, + 383 + ], + "blocks": [ + { + "bbox": [ + 324, + 249, + 526, + 383 + ], + "lines": [ + { + "bbox": [ + 324, + 249, + 526, + 383 + ], + "spans": [ + { + "bbox": [ + 324, + 249, + 526, + 383 + ], + "type": "image", + "image_path": "00f16f38456c671d51af36c000007f6ed520a5070b266de7a70415bf99d11a98.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 385, + 547, + 434 + ], + "lines": [ + { + "bbox": [ + 305, + 385, + 547, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 385, + 547, + 434 + ], + "type": "text", + "content": "Figure 1: Motivation. Pan-sharpening is to reason the unknown content at the pre-defined pixel positions according to the context of low-resolution multi-spectral image and high-resolution panchromatic image." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 448, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 546, + 532 + ], + "type": "text", + "content": "satellites usually adopt both MS and PAN sensors to observe scenes, providing the MS images with high spectral but limited spatial resolution and the PAN images with high spatial but low spectral resolution. To obtain observation with both high spectral and high spatial resolutions, the pan-sharpening technique has drawn increasing attention in both image processing and remote sensing communities." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 533, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 700 + ], + "type": "text", + "content": "Many research efforts have been devoted to solving the pan-sharpening problem, which can be categorized into two groups: traditional optimization methods and deep learning-based methods. Since an infinite number of HR-MS images can be downsampled to produce the same LR-MS image, reasoning the HR-MS images from the LR counterparts is highly ill-posed. To solve the ill-posedness, various natural images priors as regularization terms have been developed in traditional optimization methods, e.g., low-rank prior [29] and sparse image priors [44]. However, these priors are not easy to be devised. Moreover, it is challenging to optimize these methods, hampering the practical applications. Besides, due to the hand-crafted designs, their limited representation ability results in unsatisfactory performance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "The powerful learning capability of deep neural net" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 683, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 287, + 712 + ], + "type": "text", + "content": "*Co-first authors contributed equally, † corresponding author. We also gratefully acknowledge the support of MindSpore, CANN, and Ascend AI Processor used for this research." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12398" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 292, + 304 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 292, + 304 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 292, + 304 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 292, + 304 + ], + "type": "image", + "image_path": "8cdcfb74689abd0753ddf1a6f48b58fd604a292375d718f500adae3f232d1189.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 313, + 288, + 337 + ], + "lines": [ + { + "bbox": [ + 46, + 313, + 288, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 288, + 337 + ], + "type": "text", + "content": "Figure 2: Motivation. The comparison between prior unfolding frameworks and ours." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 357, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 477 + ], + "type": "text", + "content": "works ignites renewed interest in this problem. As a pioneering work, PNN [18] employs three-layer convolution neural networks to account for pan-sharpening learning. Since then, more and more complicated and deeper architectures have been proposed to improve the performance of pan-sharpening [25, 28, 30]. Despite the remarkable progress, most of them focus on heuristically constructing network architectures in a black box fashion without considering the underlying rationality of pan-sharpening task, lacking transparency and interpretability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 481, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 564 + ], + "type": "text", + "content": "To improve interpretability, model-driven deep unfolding methods have been proposed. Xu et al. [26] propose the first deep unfolding network for pan-sharpening. The basic idea behind it is to formulate pan-sharpening as an optimization problem and employ the proximal gradient descent algorithm to solve it. The optimization process can be reformulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 82, + 579, + 287, + 603 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 579, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 82, + 579, + 287, + 603 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {H}} = \\min _ {\\mathbf {H}} \\frac {1}{2} | | \\mathbf {L} - \\mathbf {D K H} | | _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {H} | \\mathbf {P}), \\qquad (1)", + "image_path": "ad62ec809a1738929fc1cbaa05a0a6f227619bfcf5b1a03f97d8a4ad3720addc.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " is a hyper-parameter to weight the first term (data fidelity term accords with the degradation) and the second term (regularization term " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Omega(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "). " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " denote the down-sampling and blur operators, respectively. L, P, and H respectively represent the LR-MS image, PAN image, and HR-MS image. Technically, the proximal gradient descent algorithm can be approximatively expressed as an iterative convergence problem by solving the following iterative" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 73, + 345, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 73, + 345, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 73, + 345, + 83 + ], + "type": "text", + "content": "function:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 88, + 547, + 114 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 88, + 547, + 114 + ], + "spans": [ + { + "bbox": [ + 306, + 88, + 547, + 114 + ], + "type": "interline_equation", + "content": "\\mathbf {H} ^ {(k)} = \\operatorname {p r o x} _ {\\lambda , \\Omega , P} \\left(\\mathbf {H} ^ {(k - 1)} + \\delta (\\mathbf {D K}) ^ {T} (\\mathbf {L} - \\mathbf {D K H} ^ {(k - 1)})\\right), \\tag {2}", + "image_path": "65f1afebc14aba96c88bc2b6215387aabad36c6e08fe1941941986ccb8745082.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "inline_equation", + "content": "\\mathrm{k}" + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "text", + "content": " denote the iterative step and learning factor. Motivation. In terms of the function " + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "inline_equation", + "content": "\\mathrm{prox}_{\\lambda, \\Omega, \\mathrm{P}}" + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "text", + "content": " that involves the embedded prior term " + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "inline_equation", + "content": "\\Omega(\\cdot)" + }, + { + "bbox": [ + 304, + 120, + 545, + 275 + ], + "type": "text", + "content": ", existing works usually heuristically employ diverse network architectures in a black box fashion and deliver the proximal operator networks as the uncertain and vague priors, visized in Figure 2. These methods thus lack clear physical meanings of the prior terms. In addition, most deep unfolding-based methods [26, 27] cannot extract the pan-sharpening customized prior with clear physical patterns well, which is caused by weak interpretable prior operations. Hence, we argue that the deep unfolding framework with sufficient interpretability has the potential of improving performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 275, + 546, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 546, + 502 + ], + "type": "text", + "content": "Solution. The first function of pan-sharpening is to reason the unknown information at the pre-defined pixel positions using the context, detailed in Figure 1. In this work, we propose a novel model-driven deep unfolding framework for pan-sharpening with interpretability. Inspired by the content reasoning ability of masked autoencoders (MAE) [9], our framework endows the holistic learning process of deep unfolding with the explicitly integrated with inherent physical mechanism underlying the pan-sharpening task. The key insights of our framework are (1) we embed the pretrained MAE with spatial masking strategy into the unfolding architecture, acting as intrinsic reasoning prior and (2) we treat the pre-trained MAE with spatial-spectral masking as the regularization term within loss function to constrain the spatial-spectral consistency. Such new designs penetrate the image reasoning prior into deep unfolding network while improving the interpretability and representation ability. Besides, our framework also outperforms existing state-of-the-art approaches on multiple satellite datasets." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 502, + 525, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 502, + 525, + 514 + ], + "spans": [ + { + "bbox": [ + 317, + 502, + 525, + 514 + ], + "type": "text", + "content": "Our main contributions are summarized as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 521, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 317, + 521, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 521, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 317, + 521, + 545, + 569 + ], + "type": "text", + "content": "- We propose to embed the pre-trained MAE into deep unfolding architecture, resorting to its image reasoning ability for pan-sharpening. Such reasoning prior makes the framework transparent and interpretable." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 575, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 575, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 317, + 575, + 545, + 647 + ], + "type": "text", + "content": "- We creatively treat the pre-trained MAE with spatial-spectral masking strategy as regularization term within loss function to constrain the spatial-spectral consistency. The tailored regularization term with intrinsic knowledge of spatial-spectral reasoning empowers the unfolding framework." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 654, + 545, + 713 + ], + "type": "text", + "content": "- In contrast to previous works, our framework as the first attempt pushes the frontiers of pan-sharpening towards the designs of the deep prior term. It shows outstanding performance on three satellite datasets, outperforming the state-of-the-art algorithms." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12399" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 107, + 289, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 107, + 289, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 107, + 289, + 419 + ], + "type": "text", + "content": "Traditional Methods. Traditional pan-sharpening methods can be roughly divided into three main categories: CS-based methods, MRA-based methods, and VO-based methods. The CS-based approaches separate spatial and spectral information from the LRMS image and replace spatial information with a PAN image. Intensity hue-saturation (IHS) fusion [3], the principal component analysis (PCA) methods [13, 22], Brovey transforms [6], and Gram-Schmidt (GS) orthogonalization method [14] are CS-based approaches. These CS-based approaches are fast since LR-MS images simply need spectral treatment to remove and replace spatial components, but the resultant HR-MS images show severe spectral distortion. The MRA-based methods inject high-frequency features of PAN derived by multi-resolution decomposition techniques into upsampled multi-spectral images. Decimated wavelet transform (DWT) [17], high-pass filter fusion (HPF) [21], Laplacian pyramid (LP) [23], smoothing filter-based intensity modulation (SFIM) [16], and atrous wavelet transform (ATWT) [19] are typical MRA-based methods that reduce spectral distortion and improve resolution, but they heavily rely on multi-resolution techniques, which may cause local spatial artifacts. In recent years, VO-based methods are used because of the fine fusion effect on ill-posed problems. These various constraints can only inadequately reflect the limited structural relations of the images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 434, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 287, + 555 + ], + "type": "text", + "content": "Deep Learning-based Methods. Deep learning-based methods have been widely used for pan-sharpening [41, 27, 34, 35, 11, 32, 40, 43, 39, 36, 37, 33, 42]. PNN [18] uses three convolutional units to directly map the relationship between PAN, LR-MS, and HR-MS images. Inspired by PNN, a large number of pan-sharpening studies based on deep learning emerge. For example, PANNet [28] adopts the residual learning module in Resnet [10]. MSDCNN [30] adds multi-scale modules on the basis of residual connection. SRPPNN [2] refers to the design idea of SRCNN [4]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 289, + 715 + ], + "type": "text", + "content": "Recently, some model-driven deep models with physical meaning emerge. The basic idea is to use prior knowledge to formulate optimization problems, then unfold the optimization algorithms and replace the steps in the algorithm with deep neural networks. For example, Xu et al. [26] propose the model-based deep learning network MH-Net and GPPNN for pan-sharpening, respectively. In terms of the function design " + }, + { + "bbox": [ + 47, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{prox}_{\\lambda,\\Omega}" + }, + { + "bbox": [ + 47, + 570, + 289, + 715 + ], + "type": "text", + "content": " that takes for the embedded prior term, existing works heuristically employ diverse network architectures in the black-box fashion, thus resulting in weak physical meanings. It motivates us to explore the task-driven customized prior with clear physical patterns." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 91, + 420, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 420, + 102 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 420, + 102 + ], + "type": "text", + "content": "3.1. Model Formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "text", + "content": "In general, pan-sharpening aims to obtain the HR-MS image " + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "text", + "content": " from its degradation observation " + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{L} = (\\mathbf{H} \\otimes \\mathbf{K}) \\downarrow_{s} + \\mathbf{n}_{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "inline_equation", + "content": "\\downarrow_{s}" + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "text", + "content": " denote blur kernel and down-sampling operation, and " + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 109, + 547, + 193 + ], + "type": "text", + "content": " is usually assumed to be additive white Gaussian noise (AWGN). The degradation process by using the maximum a posteriori (MAP) principle can be reformulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 351, + 199, + 545, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 199, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 351, + 199, + 545, + 223 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {H}} \\frac {1}{2} \\left\\| \\mathbf {L} - \\mathbf {D K H} \\right\\| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {H} | \\mathbf {P}), \\tag {3}", + "image_path": "a3295f5c667c38011cec5ff4172595cb2dde876aa8e982e1c2fbe602043d3e6a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "spans": [ + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "type": "text", + "content": " is a hyper-parameter to weight the first term (data fidelity term accords with degradation) and the regularization term " + }, + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "type": "inline_equation", + "content": "\\Omega(.)" + }, + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "type": "text", + "content": ". We solve the optimization problem using the half-quadratic splitting (HQS) algorithm. By introducing one auxiliary variables " + }, + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 305, + 230, + 547, + 302 + ], + "type": "text", + "content": ", Eq. (3) can be reformulated as a non-constrained optimization problem:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 310, + 545, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 310, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 313, + 310, + 545, + 334 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {H}, \\mathbf {U}} \\frac {1}{2} \\left\\| \\mathbf {L} - \\mathbf {D K H} \\right\\| _ {2} ^ {2} + \\frac {\\eta}{2} \\left\\| \\mathbf {U} - \\mathbf {H} \\right\\| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {U} | \\mathbf {P}), \\tag {4}", + "image_path": "71d771744bce8b8d9703d071665a1b7095528e084b26722cce2d89dea9becf79.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "text", + "content": " is the penalty parameter. When " + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "text", + "content": " approaches infinity, Eq. (4) converges to Eq. (3). Minimizing Eq. (4) involves updating " + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 305, + 342, + 545, + 378 + ], + "type": "text", + "content": " alternately." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "type": "text", + "content": "Updating U. Given the estimated HR-MS image " + }, + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{(k)}" + }, + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "type": "text", + "content": " at iteration " + }, + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "type": "text", + "content": ", the auxiliary variable " + }, + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 306, + 378, + 545, + 403 + ], + "type": "text", + "content": " can be updated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 323, + 411, + 545, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 411, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 323, + 411, + 545, + 435 + ], + "type": "interline_equation", + "content": "\\mathbf {U} ^ {(k)} = \\underset {\\mathbf {U}} {\\arg \\min } \\frac {\\eta}{2} \\left| \\left| \\mathbf {U} - \\mathbf {H} ^ {(k)} \\right| \\right| _ {2} ^ {2} + \\lambda \\Omega (\\mathbf {U} | \\mathbf {P}). \\tag {5}", + "image_path": "acf64958b44ed9e962fcbb251c372fdbd02bf17311b9e650476ca3305e784657.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 444, + 468, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 468, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 468, + 456 + ], + "type": "text", + "content": "We can derive the solution of Eq. (5) as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 362, + 464, + 545, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 464, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 362, + 464, + 545, + 480 + ], + "type": "interline_equation", + "content": "\\mathbf {U} ^ {(k)} = \\operatorname {p r o x} _ {\\Omega (.) , \\lambda , \\eta} (\\mathbf {H} ^ {(k)}, P), \\tag {6}", + "image_path": "0c244fb048337a3399f12f73a578504a08e26439df8f1e41841c51b38d2d1db4.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 487, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 487, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 487, + 545, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 487, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\mathrm{prox}_{\\Omega}(\\cdot)" + }, + { + "bbox": [ + 305, + 487, + 545, + 510 + ], + "type": "text", + "content": " is the proximal operator corresponding to the implicit local prior " + }, + { + "bbox": [ + 305, + 487, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\Omega (\\cdot)" + }, + { + "bbox": [ + 305, + 487, + 545, + 510 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 511, + 484, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 511, + 484, + 523 + ], + "spans": [ + { + "bbox": [ + 306, + 511, + 484, + 523 + ], + "type": "text", + "content": "Updating H. Given " + }, + { + "bbox": [ + 306, + 511, + 484, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{U}^{(k)}" + }, + { + "bbox": [ + 306, + 511, + 484, + 523 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 511, + 484, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 306, + 511, + 484, + 523 + ], + "type": "text", + "content": " is updated as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 307, + 531, + 545, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 531, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 307, + 531, + 545, + 569 + ], + "type": "interline_equation", + "content": "\\mathbf {H} ^ {(k + 1)} = \\underset {\\mathbf {H}} {\\arg \\min } \\frac {1}{2} \\left| \\left| \\mathbf {L} - \\mathbf {D K H} \\right| \\right| _ {2} ^ {2} + \\frac {\\eta}{2} \\left| \\left| \\mathbf {U} ^ {(k)} - \\mathbf {H} \\right| \\right| _ {2} ^ {2}. \\tag {7}", + "image_path": "468aedb9a267fec8add57e63dea10ced6dca95e741f40b037bb626c49d6b70a0.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 578, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 578, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 305, + 578, + 545, + 613 + ], + "type": "text", + "content": "By applying the proximal gradient method [20] to Eq. (7), we update " + }, + { + "bbox": [ + 305, + 578, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 305, + 578, + 545, + 613 + ], + "type": "text", + "content": " using the gradient decent method. Consequently, the updated equation for " + }, + { + "bbox": [ + 305, + 578, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{H}" + }, + { + "bbox": [ + 305, + 578, + 545, + 613 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 358, + 621, + 545, + 636 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 621, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 358, + 621, + 545, + 636 + ], + "type": "interline_equation", + "content": "\\mathbf {H} ^ {(k + 1)} = \\mathbf {H} ^ {(k)} - \\delta_ {2} \\nabla f _ {2} (\\mathbf {H} ^ {(k)}), \\tag {8}", + "image_path": "212e85568b99d24811cb70490f9f8967f79cbfb61a20e5e1fd498d6b1233b04a.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 645, + 533, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 533, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 533, + 659 + ], + "type": "text", + 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"image_path": "3b8dee126b07e1375ab47ec5f491db2498c3d63e2f29a0ae8d6b95b665885683.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 701, + 478, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 478, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 478, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 701, + 478, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 306, + 701, + 478, + 713 + ], + "type": "text", + "content": " is the matrix transpose operation." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12400" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + 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In detail, LR-MS image is firstly up-sampled and then performs the stage-wise iteration, updating U and H in the overall K stages where the pre-trained MAE acting as reasoning prior penetrates Deep Unfolding process. To promote the spatial-spectral consistency, the pre-trained extension version is employed as the loss constraint. 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Model Flowchart" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 468, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 491 + ], + "type": "text", + "content": "As detailed in Figure 3, the proposed image reasoning prior-embedded framework consists of four training stages:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 491, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 287, + 540 + ], + "type": "text", + "content": "Stage 1: Image Reasoning Prior Pre-training; Stage 2: Spatial-Spectral Consistency Pre-training; Stage 3: Penetrating Reasoning Prior into Unfolding Network; Stage 4: Spatial-Spectral Consistency Constraint as loss function." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 549, + 140, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 140, + 561 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 140, + 561 + ], + "type": "text", + "content": "3.3. Structure Flow" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "type": "text", + "content": "Based on the iterative algorithm, we construct deep unfolding network for pan-sharpening as shown in Figure 3. This network is an implementation of the algorithm for solving Eq. (3). In terms of the function design " + }, + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{prox}_{\\lambda,\\Omega}" + }, + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "type": "text", + "content": " that takes for the embedded prior term " + }, + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\Omega(.)" + }, + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "type": "text", + "content": ", we stand on the shoulder of MAE proposed by He et al, where the MAE is trained in a self-supervised manner and empowered with the reasoning ability, acting as the image prior. Based on the above analysis, the MAE is naturally treated as the prior term " + }, + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\Omega(.)" + }, + { + "bbox": [ + 46, + 569, + 287, + 688 + ], + "type": "text", + "content": " and meets the function of pan-sharpening." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Stage 1: Based on the original MAE, we employ the pure convolution neural network as the encoder and de" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 449, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 544 + ], + "type": "text", + "content": "coder to implement its network architecture with masking patch strategies: (1) evenly divide the input image, randomly sample the small subset of regions and mask the remaining ones while keeping the whole image architecture; and (2) both the small subset of visible patches and mask tokens are processed by the encoder and decoder that reconstructs the original image in pixels. Note that the input into the encoder is the whole image, not the image patch." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "type": "text", + "content": "Stage 3: UNet. Based on the pre-trained MAE encoder " + }, + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\mathrm{f_{CMAE}(.,)}" + }, + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "type": "text", + "content": " we implement the whole architecture of UNet that is presented in Figure 5. To be specific, the k-th iteration " + }, + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{(k - 1)}" + }, + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "type": "text", + "content": " is fed into the encoder part " + }, + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\mathrm{E_{CMAE}(.,)}" + }, + { + "bbox": [ + 304, + 544, + 545, + 614 + ], + "type": "text", + "content": " of the pre-trained MAE to generate the reasoning feature representation as" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 373, + 615, + 545, + 629 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 615, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 373, + 615, + 545, + 629 + ], + "type": "interline_equation", + "content": "\\mathbf {H} _ {\\mathrm {r s}} = \\operatorname {E} _ {\\mathrm {C M A E}} \\left(\\mathbf {H} ^ {(\\mathrm {k} - 1)}\\right), \\tag {10}", + "image_path": "f2aad2e547a56f1e4636c623530194001e261cca6e6b0c1223476921fabd6d01.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 634, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 634, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 634, + 545, + 658 + ], + "type": "text", + "content": "Then, PAN image " + }, + { + "bbox": [ + 304, + 634, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathrm{P}" + }, + { + "bbox": [ + 304, + 634, + 545, + 658 + ], + "type": "text", + "content": " is projected into the shallow feature space by the convolution units as" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 391, + 667, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 667, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 391, + 667, + 545, + 681 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {\\mathrm {p}} = \\operatorname {C o n v} (\\mathbf {P}). \\tag {11}", + "image_path": "99208a15e4980891fbd9a457b952fc0b2746c21be998cd6dc99b7ca6cf18946b.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "Referring to the representation " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_{\\mathrm{rs}}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " and the texture-rich PAN information " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathrm{p}}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": ", we further incorporate them to re" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12401" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 72, + 299, + 322 + ], + "blocks": [ + { + "bbox": [ + 47, + 72, + 299, + 322 + ], + "lines": [ + { + "bbox": [ + 47, + 72, + 299, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 299, + 322 + ], + "type": "image", + "image_path": "8f0b0bd9a8b871ccd38b7f351e2235aa82bf18adb5eca8f87ab650836e4dd90f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 186, + 545, + 270 + ], + "lines": [ + { + "bbox": [ + 304, + 186, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 545, + 270 + ], + "type": "text", + "content": "Figure 6: Motivation. Masked Autoencoders as spatiotemporal learners. It masks a large subset of random patches in spacetime. An encoder operates on a set of visible patches. A decoder then processes the full set of encoded patches and mask tokens to reconstruct the input. Except for patch and positional embeddings, the encoder, the decoder, and the masking strategy have no spatiotemporal inductive bias." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 416, + 289, + 547 + ], + "blocks": [ + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "lines": [ + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": "Figure 4: Motivation. Masked Autoencoders as the image reasoning learners. During pre-training, a large random subset of image patches is masked out, remarked as yellow ones. The encoder is applied to the small subset of visible patches. Mask tokens are introduced after the encoder, and the full set of encoded patches and mask tokens is processed by a decoder that reconstructs the original image in pixels." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 416, + 289, + 547 + ], + "lines": [ + { + "bbox": [ + 47, + 416, + 289, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 289, + 547 + ], + "type": "image", + "image_path": "a976430df081b0e22c57f83ef9acf6c69dd323ef8243f5f76c10b5f5fc175b33.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 554, + 251, + 566 + ], + "lines": [ + { + "bbox": [ + 83, + 554, + 251, + 566 + ], + "spans": [ + { + "bbox": [ + 83, + 554, + 251, + 566 + ], + "type": "text", + "content": "Figure 5: The detailed structure of UNet." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 576, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 576, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 576, + 287, + 624 + ], + "type": "text", + "content": "construct the HR-MS image by the spatial-frequency information transformation module " + }, + { + "bbox": [ + 46, + 576, + 287, + 624 + ], + "type": "inline_equation", + "content": "SFT" + }, + { + "bbox": [ + 46, + 576, + 287, + 624 + ], + "type": "text", + "content": " that derived from [38], which is shown in Figure 5. The information transformation process is detailed as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 117, + 632, + 287, + 646 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 632, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 117, + 632, + 287, + 646 + ], + "type": "interline_equation", + "content": "\\mathrm {F} _ {\\text {f u s e}} = \\mathrm {S F T} \\left(\\mathrm {H} _ {\\mathrm {r s l}}, \\mathrm {F} _ {\\mathrm {p}}\\right). \\tag {12}", + "image_path": "8d2ac35445e61f9b9d156a80a9365401090198c885c297e013f76c9178c0324f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": "HNet. To transform the update process of " + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{H}^{(k + 1)}" + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": " in Eq. (8) into a network. Firstly, we need to implement two operations, i.e., Down " + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\downarrow_{s}" + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "Up\\uparrow_{s}" + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": ", using the network. Specifically, Down " + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\downarrow_{s}" + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": " is implemented by a spatial identify transformation convolution operator, and an additional " + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "s-" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 558, + 178 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 558, + 178 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 558, + 178 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 558, + 178 + ], + "type": "image", + "image_path": "e83d625ffb1c45c0e98981a497204a17c8001ff5e4e7a308ef808d456625a2f8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 283, + 545, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 283, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 305, + 283, + 545, + 306 + ], + "type": "text", + "content": "strides followed convolution module with spatial resolution reduction:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 356, + 315, + 545, + 329 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 315, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 356, + 315, + 545, + 329 + ], + "type": "interline_equation", + "content": "\\mathbf {D K H} ^ {(k)} = \\operatorname {C o n v} ^ {(s)} \\downarrow \\left(\\mathbf {K H} ^ {(k)}\\right), \\tag {13}", + "image_path": "ba6f789afc6a5c031834e2dc0e37fac63d1b658d3e6467489d4826f0d85458a4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\operatorname{Conv} \\downarrow_{(s)}" + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "text", + "content": " aims to perform the " + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "text", + "content": " times down-sampling. The latter operation " + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "inline_equation", + "content": "Up \\uparrow_{s}" + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "text", + "content": " is implemented by a deconvolution layer containing the " + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 338, + 545, + 399 + ], + "type": "text", + "content": "-strides convolution module with spatial resolution expansion and a convolution module with spatial identify transformation:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 347, + 406, + 545, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 406, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 347, + 406, + 545, + 421 + ], + "type": "interline_equation", + "content": "\\mathbf {U} \\mathbf {H} ^ {(k)} = \\operatorname {C o n v} ^ {(s)} \\uparrow (\\mathbf {L} - \\mathbf {D K H} ^ {(k)}), \\tag {14}", + "image_path": "3638fd329e2a2e5dd2c6b1041ec039bc8307c755f11140cce4b26a727377bc3e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 430, + 543, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 543, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 543, + 443 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 430, + 543, + 443 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}\\uparrow_{(s)}" + }, + { + "bbox": [ + 305, + 430, + 543, + 443 + ], + "type": "text", + "content": " aims to perform the " + }, + { + "bbox": [ + 305, + 430, + 543, + 443 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 430, + 543, + 443 + ], + "type": "text", + "content": " times up-sampling." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 449, + 416, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 449, + 416, + 462 + ], + "spans": [ + { + "bbox": [ + 306, + 449, + 416, + 462 + ], + "type": "text", + "content": "3.4. Optimization Flow" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 468, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 635 + ], + "type": "text", + "content": "Stage 2: To highlight, the uniqueness of our proposed method is that the entire learning process is fully and explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Specifically, based on the MAE with spatial-spectral masking strategy that is tailored with the spatial-frequency representation learner, we redevelop the MAE as the regularization term within the loss function to constrain the spatial-spectral consistency of the model output and its corresponding ground truth. As shown in Figure 6, standing on the shoulders of the video-version extension of masked Autoencoders [5] proposed by He et al, we redevelop the masked image modeling as \"learned loss function\" to constraint the spatial-spectral representation consistency by the following implementation details:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 646, + 545, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 317, + 646, + 545, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 646, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 317, + 646, + 545, + 681 + ], + "type": "text", + "content": "- randomly mask out spatial-spectral patches in the ground truth image and then learn an autoencoder to reconstruct them;" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 689, + 545, + 713 + ], + "type": "text", + "content": "- the only spatial-spectral specific inductive bias is on embedding the patches and their positions; all other" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12402" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 92, + 548, + 289 + ], + "blocks": [ + { + "bbox": [ + 79, + 71, + 515, + 84 + ], + "lines": [ + { + "bbox": [ + 79, + 71, + 515, + 84 + ], + "spans": [ + { + "bbox": [ + 79, + 71, + 515, + 84 + ], + "type": "text", + "content": "Table 1: Quantitative comparison with the state-of-the-art methods. The best results are highlighted in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 92, + 548, + 289 + ], + "lines": [ + { + "bbox": [ + 48, + 92, + 548, + 289 + ], + "spans": [ + { + "bbox": [ + 48, + 92, + 548, + 289 + ], + "type": "table", + "html": "
MethodWordView IIGaoFen2WordView III
PSNR ↑SSIM↑SAM↓ERGAS↓PSNR ↑SSIM↑SAM↓ERGAS↓PSNR ↑SSIM↑SAM↓ERGAS↓
SFIM34.12970.89750.04392.344936.90600.88820.03181.739821.82120.54570.12088.9730
Brovey35.86460.92160.04031.823837.79740.90260.02181.372022.5060.54660.11598.2331
GS35.63760.91760.04231.877437.22600.90340.03091.673622.56080.54700.12178.2433
IHS35.29620.90270.04612.027838.17540.91000.02431.533622.55790.53540.12668.3616
GFPCA34.55810.90380.04882.141137.94430.92040.03141.560422.33440.48260.12948.3964
PNN (RS'16)40.75500.96240.02591.064643.12080.97040.01720.852829.94180.91210.08243.3206
PANNet (ICCV'17)40.81760.96260.02571.055743.06590.96850.01780.857729.6840.90720.08513.4263
MSDCNN (TGRS'21)41.33550.96640.02420.994045.68740.98270.01350.638930.30380.91840.07823.1884
SRPPNN (TGRS'20)41.45380.96790.02330.989947.19980.98770.01060.558630.43460.92020.07703.1553
GPPNN (CVPR'21)41.16220.96840.02441.031544.21450.98150.01370.736130.17850.91750.07763.2596
MutNet (CVPR'22)41.67730.97050.02240.951947.30420.98920.01020.548130.49070.92230.07493.1125
MANet (ECCV'22)41.85770.96970.02290.942047.26680.98900.01020.547230.54510.92140.07693.1032
Ours41.87350.97310.02200.941347.39310.98920.00890.543530.55600.92250.07333.0072
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MetricsSFIMGSBroveyIHSGFPCAPNNPANNETMSDCNNSRPPNNGPPNNMutNetMANetOurs
Dλ↓0.08220.06960.13780.07700.09140.07460.07370.07340.07670.07820.06940.06810.0676
Ds↓0.10870.24560.26050.29850.16350.11640.12240.11510.11620.12530.11180.11190.1112
QNR↑0.82140.70250.63900.64850.76150.81910.81430.82510.81730.80730.82590.82660.8287
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Experiments" + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 47, + 599, + 107, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 107, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 107, + 612 + ], + "type": "text", + "content": "4.1. Settings" + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Datasets. Due to the unavailability of ground-truth MS images, we follow the previous works to generate the training set by employing the Wald protocol tool [24]. Specifically, given the MS image " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{H} \\in \\mathrm{R}^{\\mathrm{M} \\times \\mathrm{N} \\times \\mathrm{C}}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " and the PAN image " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{P_H} \\in \\mathrm{R}^{\\mathrm{rM} \\times \\mathrm{rN} \\times \\mathrm{b}}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": ", both of them are downsampled by a ratio " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": ", and then are denoted as " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{L} \\in \\mathrm{R}^{\\mathrm{M} / \\mathrm{r} \\times \\mathrm{N} / \\mathrm{r} \\times \\mathrm{C}}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{P} \\in \\mathrm{R}^{\\mathrm{M} \\times \\mathrm{N} \\times \\mathrm{b}}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": ", respectively. In the training set, " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{L}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " are regarded as the inputs, while " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{H}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " is the ground truth. In our" + } + ] + } + ], + "index": 52 + }, + { + "bbox": [ + 306, + 449, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 449, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 306, + 449, + 545, + 508 + ], + "type": "text", + "content": "work, three satellite images of WorldView II, GaoFen2, and WorldView III are adopted to construct image datasets. For each database, PAN images are cropped into patches with a size of " + }, + { + "bbox": [ + 306, + 449, + 545, + 508 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 306, + 449, + 545, + 508 + ], + "type": "text", + "content": " while the corresponding MS patches are with a size of " + }, + { + "bbox": [ + 306, + 449, + 545, + 508 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 306, + 449, + 545, + 508 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 53 + }, + { + "bbox": [ + 306, + 510, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 545, + 581 + ], + "type": "text", + "content": "Baselines. Several state-of-the-art Pan-sharpening methods are compared, including seven representative deep learning-based methods: PNN [18], PANNET [28], MSDCNN [30], SRPPNN [2], GPPNN [26], MANet [27], and MutNet [41] and five promising traditional methods: SFIM [16], Brovey [7], GS [14], IHS [8], and GFPCA [15]." + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 306, + 582, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 545, + 640 + ], + "type": "text", + "content": "Metrics. Several widely-used image quality assessment (IQA) metrics are employed for performance measurement, including PSNR, SSIM, SAM [31], ERGAS [1], and three non-reference metrics " + }, + { + "bbox": [ + 306, + 582, + 545, + 640 + ], + "type": "inline_equation", + "content": "D_{\\lambda}" + }, + { + "bbox": [ + 306, + 582, + 545, + 640 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 582, + 545, + 640 + ], + "type": "inline_equation", + "content": "D_{S}" + }, + { + "bbox": [ + 306, + 582, + 545, + 640 + ], + "type": "text", + "content": ", and QNR for real-world full-resolution scenes." + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 306, + 642, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 546, + 713 + ], + "type": "text", + "content": "Implementations. In our experiments, all the designed networks are implemented with PyTorch framework and trained on the PC with a single NVIDIA GeForce GTX 3090 GPU. In the training phase, these networks are optimized by the Adam optimizer [12] over 1000 epochs with a mini-batch size of 4. The learning rate is initialized with" + } + ] + } + ], + "index": 56 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12404" + } + ] + } + ], + "index": 57 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": ". When reaching 200 epochs, the learning rate is decayed by multiplying 0.5." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 104, + 133, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 104, + 133, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 104, + 133, + 117 + ], + "type": "text", + "content": "4.2. Comparisons" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 122, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 122, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 122, + 287, + 301 + ], + "type": "text", + "content": "Evaluation on reduced-resolution scenes. The comparison results on three satellite datasets are reported in Table 1. As can be seen, our proposed method achieves the best overall results than other pan-sharpening methods across all the satellite datasets. Specifically, the average gains of our method over the second-best MANet are 0.12dB, 0.32dB, and 0.10dB in terms of PSNR on WorldView-II, GaoFen2, and WorldView-III datasets, respectively. In addition to PSNR, consistent improvements can be observed in the other metrics, indicating lower spectral distortion and spatial texture preservation. Our method outperforms other compared methods by a large margin. The corresponding visual comparisons shown in Figure 7 and Figure 8 also support the above claim. More visual results can be found in the supplementary material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 302, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 422 + ], + "type": "text", + "content": "Evaluation on full-resolution scenes. In order to demonstrate the real-world application, we further perform experiments on 200 sets of full-resolution data obtained by the additional Gaofen2. Due to the unavailability of ground-truth MS images in real-world full-resolution scenes, the commonly-used three non-reference metrics of " + }, + { + "bbox": [ + 46, + 302, + 287, + 422 + ], + "type": "inline_equation", + "content": "D_{\\lambda}" + }, + { + "bbox": [ + 46, + 302, + 287, + 422 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 302, + 287, + 422 + ], + "type": "inline_equation", + "content": "D_{s}" + }, + { + "bbox": [ + 46, + 302, + 287, + 422 + ], + "type": "text", + "content": ", and QNR are adopted for evaluation. The quantitative comparisons between representative deep learning-based methods and our method are shown in Table 2. Our methods surpass other pan-sharpening methods in all metrics." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 465, + 287, + 563 + ], + "blocks": [ + { + "bbox": [ + 47, + 432, + 287, + 456 + ], + "lines": [ + { + "bbox": [ + 47, + 432, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 287, + 456 + ], + "type": "text", + "content": "Table 3: Quantitative results of the model with different number stages." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 465, + 287, + 563 + ], + "lines": [ + { + "bbox": [ + 48, + 465, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 48, + 465, + 287, + 563 + ], + "type": "table", + "html": "
Stage Number (K)PSNR↑SSIM↑SAM↓ERGAS↓
141.24590.96550.02501.0123
241.49620.96790.02400.9838
341.71520.97220.02230.9506
441.87350.97310.02200.9413
541.84610.96970.02260.9421
641.74290.97330.02210.9506
", + "image_path": "f024170fa58196ad7d43b133fc8d71fc4234fc74563702ba9b406aac9cf1d25f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 50, + 619, + 286, + 700 + ], + "blocks": [ + { + "bbox": [ + 47, + 586, + 286, + 610 + ], + "lines": [ + { + "bbox": [ + 47, + 586, + 286, + 610 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 286, + 610 + ], + "type": "text", + "content": "Table 4: Quantitative results with the ablation of key components." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 619, + 286, + 700 + ], + "lines": [ + { + "bbox": [ + 50, + 619, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 50, + 619, + 286, + 700 + ], + "type": "table", + "html": "
UMAELMAEPSNR↑SSIM↑SAM↓ERGAS↓
41.46550.96690.02530.9724
✓41.65760.96810.02410.9679
✓41.83820.96950.02310.9423
✓✓41.87350.97310.02200.9413
", + "image_path": "997e4ea05aaccfb75e3d2b6ee0516af5fe7931bc68da65d7767f8e187f03e9e8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 400, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 400, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 400, + 85 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 90, + 545, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 90, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 305, + 90, + 545, + 125 + ], + "type": "text", + "content": "To explore the contribution of different hyper-parameters and the key components, we conduct ablation studies on the WorldView-II dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 125, + 545, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 125, + 545, + 245 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 545, + 245 + ], + "type": "text", + "content": "Impact of the Stage Numbers. To investigate the impact of the number of unfolded stages, we experiment proposed method with varying numbers of stages K. Observing the results from Table 3, we found that the model's performance has obtained considerable improvement as the number of stages increases until reaching 4. When further increasing the K, the results show a decreasing trend, which may be caused by the difficulty of gradient propagation. We set " + }, + { + "bbox": [ + 304, + 125, + 545, + 245 + ], + "type": "inline_equation", + "content": "\\mathrm{K} = 4" + }, + { + "bbox": [ + 304, + 125, + 545, + 245 + ], + "type": "text", + "content": " as default stage number to balance the performance and computational complexity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "type": "text", + "content": "Effect of Key Components. To investigate the contribution of the devised modules in our network, we take the model with " + }, + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "type": "text", + "content": " as the baseline and then conduct the comparison by observing the difference before and after removing the components. The corresponding quantitative comparisons are reported in Table 4, where " + }, + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathrm{U}_{\\mathrm{MAE}}" + }, + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "type": "text", + "content": " represents the MAE within the UNet network and " + }, + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathrm{L}_{\\mathrm{MAE}}" + }, + { + "bbox": [ + 304, + 246, + 545, + 365 + ], + "type": "text", + "content": " represents the MAE within loss function. As can be observed, equipping with both the MAE priors significantly improves the model performance." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 309, + 377, + 545, + 497 + ], + "blocks": [ + { + "bbox": [ + 309, + 377, + 545, + 497 + ], + "lines": [ + { + "bbox": [ + 309, + 377, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 309, + 377, + 545, + 497 + ], + "type": "image", + "image_path": "b67b0abb19629cc7683e93fd07b5e6a35d88be54b49df6066f2a3b908063b4ca.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 506, + 545, + 530 + ], + "lines": [ + { + "bbox": [ + 305, + 506, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 305, + 506, + 545, + 530 + ], + "type": "text", + "content": "Figure 9: The feature visualization in Unet upon the iterative stage increasing of deep unfolding network." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 546, + 424, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 546, + 424, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 546, + 424, + 559 + ], + "type": "text", + "content": "4.4. Effect of MAE prior" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "text", + "content": "To verify the effect of the designed MAE prior, we deepen into the feature maps of " + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "inline_equation", + "content": "F_{rs}" + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "inline_equation", + "content": "F_{use}" + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "text", + "content": ". As illustrated in section 3.3 that the MAE prior takes account for predicting the missing information of " + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "inline_equation", + "content": "F_{rs}" + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "text", + "content": " and then enhances the representation " + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "inline_equation", + "content": "F_{use}" + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "text", + "content": ", with the stage increasing, the MAE-prior reasoned feature " + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "inline_equation", + "content": "F_{rs}" + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "text", + "content": " is gradually enhanced and the resulted " + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "inline_equation", + "content": "F_{use}" + }, + { + "bbox": [ + 304, + 564, + 545, + 661 + ], + "type": "text", + "content": " becomes more informative, thus supporting the powerful capability of the MAE prior, detailed in Figure 9." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 669, + 378, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 378, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 378, + 681 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "In this paper, we proposed the first work to focus on the designs of the deep prior term. We employ the learned" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12405" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "content": "MAE in a self-supervised manner acting as an image prior and then embed the pre-trained MAE with reasoning ability to penetrate deep unfolding architecture, thus making it more transparent. We also redevelop the pre-trained MAE with a spatial-spectral masking strategy and employ it as the regularization term within loss function to constrain the spatial-spectral consistency. The contained intrinsic knowledge over MAE loss term empowers the main unfolding network learning ability. Extensive experiments on three satellite datasets demonstrate its superiority." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 205, + 107, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 205, + 107, + 217 + ], + "spans": [ + { + "bbox": [ + 48, + 205, + 107, + 217 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 225, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 225, + 287, + 280 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 225, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 53, + 225, + 287, + 280 + ], + "type": "text", + "content": "[1] L. Alparone, L. Wald, J. Chanussot, C. Thomas, P. Gamba, and L. M. Bruce. Comparison of pansharpening algorithms: Outcome of the 2006 grs-s data fusion contest. 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IEEE transactions on geoscience and remote sensing, 51(5):2827-2836, 2012." + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12407" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_content_list.json b/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ddb68e75b140990ec210c14912a918e3c0cdf617 --- /dev/null +++ b/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_content_list.json @@ -0,0 +1,1571 @@ +[ + { + "type": "text", + "text": "Learning Adaptive Neighborhoods for Graph Neural Networks", + "text_level": 1, + "bbox": [ + 166, + 130, + 803, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Avishkar Saha1, Oscar Mendez1, Chris Russell2, Richard Bowden1 \n1Centre for Vision Speech and Signal Processing, University of Surrey, Guildford, UK \n2University of Oxford, Oxford, UK", + "bbox": [ + 143, + 180, + 823, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{a.saha, o.mendez, r.bowden}@surrey.ac.uk, Christopher.m.russell@gmail.com", + "bbox": [ + 156, + 236, + 812, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Graph convolutional networks (GCNs) enable end-to-end learning on graph structured data. However, many works assume a given graph structure. When the input graph is noisy or unavailable, one approach is to construct or learn a latent graph structure. These methods typically fix the choice of node degree for the entire graph, which is suboptimal. Instead, we propose a novel end-to-end differentiable graph generator which builds graph topologies where each node selects both its neighborhood and its size. Our module can be readily integrated into existing pipelines involving graph convolution operations, replacing the predetermined or existing adjacency matrix with one that is learned, and optimized, as part of the general objective. As such it is applicable to any GCN. We integrate our module into trajectory prediction, point cloud classification and node classification pipelines resulting in improved accuracy over other structure-learning methods across a wide range of datasets and GCN backbones. We will release the code.", + "bbox": [ + 75, + 316, + 473, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 618, + 209, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of Graph Neural Networks (GNNs) [6, 1, 24], has led to a surge in graph-based representation learning. GNNs provide an efficient framework to learn from graph-structured data, making them widely applicable where data can be represented as a relation or interaction system. They have been effectively applied in a wide range of tasks [25], [33] including particle physics [4] and protein science [10].", + "bbox": [ + 75, + 643, + 470, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In a GNN, each node iteratively updates its state by interacting with its neighbors, typically through message passing. However, a fundamental limitation of such architectures is the assumption that the underlying graph is provided. While node or edge features may be updated during message passing, the graph topology remains fixed, and its choice may be suboptimal for various reasons. For instance, when classifying nodes on a citation network, an edge connecting nodes of different classes can diminish classification accuracy. These edges can degrade performance by propagating irrelevant", + "bbox": [ + 75, + 750, + 473, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "information across the graph. When no graph is explicitly provided, such domain knowledge can be exploited to learn structures optimized for the task at hand [8, 3, 9, 7]. However, in tasks where knowledge of the optimal graph structure is unknown, one common practice is to generate a $k$ -nearest neighbor ( $k$ -NN) graph. In such cases, $k$ is a hyperparameter and tuned to find the model with the best performance. For many applications, fixing $k$ is overly restrictive as the optimal choice of $k$ may vary for each node in the graph. While there has been an emergence of approaches which learn the graph structure for use in downstream GNNs [43, 13, 15], all of them treat the node degree $k$ as a fixed hyperparameter.", + "bbox": [ + 496, + 287, + 895, + 469 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a general differentiable graph-generator (DGG) module for learning graph topology with or without an initial edge structure. Rather than learning graphs with fixed node degrees $k$ , our module generates local topologies with an adaptive neighborhood size. This module can be placed within any graph convolutional network, and jointly optimized with the rest of the network's parameters, learning topologies which favor the downstream task without hyperparameter selection or indeed any additional training signal. The primary contributions of this paper are as follows:", + "bbox": [ + 496, + 473, + 895, + 625 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We propose a novel, differentiable graph-generator (DGG) module which jointly optimizes both the neighborhood size, and the edges that should belong to each neighborhood. Note a key limitation of existing approaches [43, 15, 13, 8, 3, 7, 37] is their inability to learn neighborhood sizes.", + "2. Our DGG module is directly integrable into any pipeline involving graph convolutions, where either the given adjacency matrix is noisy, or unavailable and must be determined heuristically. In both cases, our DGG generates the adjacency matrix as part of the GNN training and can be trained end-to-end to optimize performance on the downstream task. Should a good graph structure be known, the generated adjacency matrix can be learned to remain close to it while optimizing performance.", + "3. To demonstrate the power of the approach, we integrate our DGG into a range of SOTA pipelines — without" + ], + "bbox": [ + 511, + 628, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22541", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "modification — across different datasets in trajectory prediction, point cloud classification and node classification and show improvements in model accuracy.", + "bbox": [ + 107, + 90, + 470, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 150, + 215, + 166 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Graph Representation Learning: GNNs [1] are a broad class of neural architectures for modelling data which can be represented as a set of nodes and relations (edges). Most use message-passing to build node representations by aggregating neighborhood information. A common formulation is the Graph Convolution Network (GCNs) which generalizes the convolution operation to graphs [16, 5, 38, 11]. More recently, the Graph Attention Network (GAT) [35] utilizes a self-attention mechanism to aggregate neighborhood information. However, these works assumed that the underlying graph structure is fixed in advance, with the graph convolutions learning features that describe pre-existing nodes and edges. In contrast, we simultaneously learn the graph structure while using our generated adjacency matrix in downstream graph convolutions. The generated graph topology of our module is jointly optimized alongside other network parameters with feedback signals from the downstream task.", + "bbox": [ + 76, + 176, + 472, + 431 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Graph Structure Learning: In many applications, the optimal graph is unknown, and a graph is constructed before training a GNN. One question to ask is: \"Why isn't a fully-connected graph suitable?\" Constructing adjacency matrices weighted by distance or even an attention mechanism [35] over a fully-connected graph incorporates many task-irrelevant edges, even if their weights are small. While an attention mechanism can zero these out — i.e., discover a subgraph within the complete graph — discovering this subgraph is challenging given the combinatorial complexity of graphs. A common remedy is to sparsify a complete graph by selecting the $k$ -nearest neighbors ( $k$ -NN). Although this can prevent the propagation of irrelevant information between nodes, the topology of the constructed graph may have no relation to the downstream task. Not only can irrelevant edges still exist, but pairs of relevant nodes may remain unconnected and can lead GCNs to learn representations with poor generalization [43].", + "bbox": [ + 76, + 433, + 472, + 704 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome this, recent works constructed bespoke frameworks which learn the graph's adjacency matrix for specific tasks. For instance, in human pose estimation, some methods [31, 20] treat the elements of the adjacency matrix as a set of learnable weights. However, as each element is treated as a learnable parameter, the learned adjacency matrix is unlinked to the representation space and can only be used in tasks where there is a known correspondence between training and test nodes. This is not the case for many vision and graph tasks. Others have [15, 7, 17] employed variational inference frameworks to sample the entire adjacency matrix. Franceschi et al. [9] jointly learned the graph structure and the parameters of a GCN by approximately", + "bbox": [ + 76, + 705, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "solving a bilevel program. NodeFormer [37] and IDGL [3] instead learned latent topologies using multi-head attention [34]. There are two key differences between these methods and ours. First, we simplify optimization by factorizing the adjacency matrix distribution from which we sample the neighborhood for each node, as opposed to sampling the entire matrix. Second, these methods are bespoke frameworks specifically designed for node and graph classification. They leverage knowledge of the task in their loss functions, such as graph smoothness and sparsity [3]. As these methods are tailored to graph-based tasks only, they cannot be dropped into any GCN without modification, limiting their applicability to non-graph tasks like vision. In contrast, our module is both GCN and task-agnostic, and can be integrated into any GCN pipeline and trained using the downstream task loss.", + "bbox": [ + 496, + 90, + 893, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast to the bespoke frameworks above, recent methods [43, 21, 13] took a more module-based approach similar to ours. As these approaches learned the graph structure entirely from the downstream task loss, there is less domain knowledge to leverage compared to methods constructed for specific tasks. Consequently, sparsity is often induced through a $k$ -NN graph. Here, $k$ is a scalar hyperparameter selected to control the learned graph's node degree.", + "bbox": [ + 496, + 318, + 893, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unlike these works, we generate neighborhoods of varying size by learning a distribution over the edges and over the node degree $k$ . Each node samples its top- $k$ neighbors (where $k$ is now a continuous variable), allowing it to individually select its neighborhood and the edges that should belong to it, in a differentiable manner. Additionally, a known 'ideal' graph structure can be used as intermediate supervision to further constrain the latent space.", + "bbox": [ + 496, + 438, + 893, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 571, + 591, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Here, we provide details of our differentiable graph generation (DGG) module. We begin with notation and the statistical learning framework guiding its design, before describing the module, and how it is combined with graph convolutional backbone architectures.", + "bbox": [ + 496, + 595, + 893, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Notation We represent a graph of $N$ nodes as $G = (V, E)$ : where $V$ is the set of nodes or vertices, and $E$ the edge set. A graph's structure can be described by its adjacency matrix $A$ , with $a_{ij} = 1$ if an edge connects nodes $i$ and $j$ and $a_{ij} = 0$ otherwise. This binary adjacency matrix $A$ is directed, and potentially asymmetrical.", + "bbox": [ + 496, + 671, + 893, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Problem definition We reformulate the baseline prediction task based on a fixed graph with an adaptive variant where the graph is learned. Typically, such baseline tasks make learned predictions $Y$ given a set of input features $X$ and a graph structure $A$ of node degree $k$ :", + "bbox": [ + 496, + 762, + 893, + 838 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nY = Q _ {\\phi} (X, A (k)), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 845, + 893, + 864 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $Q_{\\phi}$ is an end-to-end neural network parameterized by learnable weights $\\phi$ . These formulations require a pre", + "bbox": [ + 496, + 869, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22542", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9e86ce1a616f21e37fef8197dde29fc047cd8a0ce363a56fbd2ee6e1b7b80c8e.jpg", + "image_caption": [ + "Figure 1. (Left) A typical prediction task using graphs $Y = Q_{\\phi}(X, A)$ where $A$ and $k$ are predetermined. (Right) Our reformulation $P(Y|X) \\approx \\sum_{A} \\sum_{k} Q_{\\phi}(X, A) Q_{\\theta}(A|X, k) Q_{\\rho}(k|X)$ which learns a distribution over $A$ and $k$ alongside the downstream task." + ], + "image_footnote": [], + "bbox": [ + 78, + 85, + 472, + 175 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "determined graph-structure $A(k)$ , typically based on choice of node degree $k$ , and take $A(k)$ as additional input to the model. In contrast, we learn both $A$ and $k$ in an end-to-end manner, and use them to make predictions $Y$ . As graphs are inherently binary, with edges either present or absent, they are not directly estimizable using gradient descent. Instead, we consider a distribution of graphs, $\\mathcal{G}$ , which then induce a distribution of labels, $\\mathcal{V}$ , in the downstream task. This distribution takes the factorized form:", + "bbox": [ + 75, + 268, + 473, + 405 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP (Y | X) = \\sum_ {A \\in \\mathcal {G}} \\sum_ {k \\in \\mathbb {N} ^ {| V |}} Q _ {\\phi} (X, A) P (A | X, k) P (k | X), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 412, + 470, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $P(k|X)$ is the distribution of node degree $k$ given $X$ (i.e., the choice of $k$ in $k - \\mathrm{NN}$ ), $P(A|X, k)$ the distribution of graph structures $A$ conditioned on the learned $k$ and input $X$ , and $P(Y|X)$ is the downstream distribution of labels conditioned on data $X$ . For clarity, the adjacency $A$ represents a subgraph of a complete graph over $X$ , and $k$ is a multidimensional variable controlling the number of top- $k$ neighbors for each node individually. To avoid learning individual probabilities for each possible graph $A$ in an exponential state space, we further assume that $P(A|X, k)$ has a factorized distribution where each neighborhood is sampled independently, i.e. $P(A|X, k) = \\prod_{i \\in V} P(a_i|X, k)$ .", + "bbox": [ + 75, + 457, + 470, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We model the distributions over adjacencies $A$ and $k$ with tractable functions:", + "bbox": [ + 76, + 638, + 470, + 667 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP (Y | X) \\approx \\sum_ {A} \\sum_ {k} Q _ {\\phi} (X, A) Q _ {\\theta} (A | X, k) Q _ {\\rho} (k | X), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 676, + 472, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $Q_{\\theta}$ and $Q_{\\rho}$ are functions parameterized by $\\theta$ and $\\rho$ to approximate $P(A|X, k)$ and $P(k|X)$ , respectively. In Fig. 1, we illustrate the functions of our method compared to the typical prediction task in Eq. 1.", + "bbox": [ + 75, + 719, + 472, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Using this formulation, we train the entire system end-to-end to minimize the expected loss when sampling $Y$ . This can be efficiently performed using stochastic gradient descent. In the forward pass, we first sample a subgraph/set of nodes $X$ from the space of datapoints, and conditioning on $X$ we sample $A$ and compute the associated label $Y$ . When computing the gradient step, we update $Q_{\\phi}(X,A)$ as normal and update the distributions using two standard", + "bbox": [ + 75, + 780, + 473, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d82569931c8d3a382ededdac190bf12cd83c74fbaa3d5965766e845816f8d177.jpg", + "image_caption": [ + "Figure 2. Our differentiable graph-generator (DGG) takes input nodes $\\mathbf{X}$ and generates an adjacency matrix $\\mathbf{A}$ . It consists of: (1) Degree-estimator: generates samples of $k_{i}$ for each node, (2) Edge-ranker: generates edge samples $\\mathbf{e}_i$ for each node and (3) Top-k selector: takes $k_{i}$ and edge samples $\\mathbf{e}_i$ and selects top-k elements in a differentiable manner to output a final adjacency $\\mathbf{A}$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 883, + 178 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "reparametrization tricks: one for discrete variables [12] such that $Q_{\\theta}(A|X, k)$ can generate differentiable graph samples $A'$ , and another for continuous variables [14] of $k'$ drawn from $Q_{\\rho}(k|X)$ :", + "bbox": [ + 496, + 290, + 893, + 351 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP (Y | X) \\approx \\sum_ {A ^ {\\prime}} \\sum_ {k ^ {\\prime}} Q _ {\\phi} \\left(X, A ^ {\\prime}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 363, + 892, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $A^{\\prime}\\sim Q_{\\theta}(A|X,k^{\\prime})$ and $k^{\\prime}\\sim Q_{\\rho}(k|X)$", + "bbox": [ + 542, + 398, + 846, + 416 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As both the graph structure $A'$ and variable $k'$ samplers are differentiable, our DGG module can be readily integrated into pipelines involving graph convolutions and jointly trained end-to-end.", + "bbox": [ + 496, + 428, + 893, + 487 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Differentiable Graph Generation", + "text_level": 1, + "bbox": [ + 500, + 498, + 790, + 515 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our differentiable graph-generator (DGG) takes a set of nodes $V = \\{v_{1},\\dots,v_{N}\\}$ with $d$ -dimensional features $\\mathbf{X} \\in \\mathbb{R}^{N\\times d}$ and generates a (potentially) asymmetric adjacency matrix $\\mathbf{A} \\in \\mathbb{R}^{N\\times N}$ . This adjacency matrix can be used directly in any downstream graph convolution operation (see Module Instantiation below). As illustrated by Fig. 2, the DGG module consists of four components:", + "bbox": [ + 496, + 522, + 893, + 627 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Node encoding: this component projects the input node features $\\mathbf{X} \\in \\mathbb{R}^{N \\times d}$ to a latent representation $\\hat{\\mathbf{X}} \\in \\mathbb{R}^{N \\times d'}$ , which forms the primary representation space of the model.", + "2. Edge ranking: this takes the latent node features $\\hat{\\mathbf{X}}\\in \\mathbb{R}^{N\\times d^{\\prime}}$ and generates a matrix representing a stochastic ordering of edges $\\mathbf{E}\\in \\mathbb{R}^{N\\times N}$ drawn from a learned distribution over the edge-probabilities $(A^{\\prime}\\sim Q_{\\theta}(A|X,k^{\\prime})$ from Eq. 4).", + "3. Degree estimation: this component estimates the number of neighbors each individual node is connected to. It takes as input the latent node features $\\hat{\\mathbf{X}}\\in \\mathbb{R}^{N\\times d^{\\prime}}$ and generates random samples $k\\in \\mathbb{R}^N$ drawn from a learned distribution over the node degree $(k^{\\prime}\\sim Q_{\\rho}(k|X)$ from Eq. 4).", + "4. Differentiable top- $k$ edge selector: takes $k$ and the edge-samples $e$ and performs a soft thresholding that probabilistically selects the most important elements," + ], + "bbox": [ + 511, + 628, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22543", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "based on the output of the Edge-ranking to output an adjacency matrix $\\mathbf{A}\\in \\mathbb{R}^{N\\times N}$", + "bbox": [ + 107, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now explain these steps in more detail:", + "bbox": [ + 76, + 122, + 359, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Node encoding We construct a single latent space from the input node features, and use it for edge ranking and degree estimation. We first map input node features $\\mathbf{X} \\in \\mathbb{R}^{N \\times d}$ into latent features $\\hat{\\mathbf{X}} \\in \\mathbb{R}^{N \\times d'}$ using a multi-layer perceptron (MLP) $N_{\\phi}$ with weights $\\phi$ : $\\hat{\\mathbf{X}} = N_{\\phi}(\\mathbf{X})$ . These latent features form the input for the rest of the DGG. Furthermore, they are output by the DGG and passed to the GCN downstream to prevent vanishing gradients.", + "bbox": [ + 75, + 137, + 470, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Edge ranking The edge ranking returns an implicit distribution of edge orderings, from which we sample the neighborhood for each node. For each node $v_{i}$ , it draws a set of scores $\\mathbf{e}_i = \\{e_{ij}\\}_{j}^N$ quantifying its relevance to all nodes $v_{j} \\in V$ including itself. To generate differentiable edge samples $\\mathbf{e}_i$ we use the Gumbel-Softmax [12].", + "bbox": [ + 76, + 258, + 470, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Before locally scoring each edge embedding $e_{ij} \\in \\mathbf{e}_i$ for node $v_i$ , we implement a global stage which constructs edge embeddings with both local and global dependencies:", + "bbox": [ + 76, + 349, + 470, + 395 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1. Using latent node features $\\hat{\\mathbf{x}}_i\\in \\hat{\\mathbf{X}}$ , determine local edge embeddings $\\hat{\\mathbf{c}}_{ij}\\in \\mathbb{R}^{d^{\\prime}}$ by passing each pair of node features through an MLP $l_{\\phi}$ .. $\\hat{\\mathbf{c}}_{ij} = l_{\\phi}(\\hat{\\mathbf{x}}_i,\\hat{\\mathbf{x}}_j)$ These embeddings now form a complete graph $\\mathcal{G}$ over the nodes, with each edge attributed $\\hat{\\mathbf{c}}_{ij}$", + "bbox": [ + 89, + 396, + 470, + 472 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2. As each edge embedding $\\hat{\\mathbf{c}}_{ij} \\in \\mathbf{C}$ is calculated independently of the others, we refine it to account for its dependencies to adjacent edges. We do this through edge-to-edge message passing. However, we avoid computing dependencies between all edges of the complete graph for two reasons: first, some edges may not have any common nodes, so passing messages between them could propagate irrelevant information, and secondly, it could be prohibitively expensive. To restrict message-passing between adjacent edges only, we first compute the adjoint graph $\\mathcal{H}$ of the complete graph $\\mathcal{G}$ . In the adjoint $\\mathcal{H}$ , each edge is associated with a node, and two nodes are connected if and only if their corresponding edges in $\\mathcal{G}$ have a node in common. The adjoint's adjacency $A^{\\mathcal{H}}$ can be calculated using its incidence matrix $L$ , $A^{\\mathcal{H}} = L^{T}L - 2I$ . In the adjoint, each node embedding $\\hat{\\mathbf{c}}_i$ is then updated using an average of its neighboring nodes $\\hat{\\mathbf{c}}_j$ and passed through an MLP $h_\\phi$ :", + "bbox": [ + 88, + 472, + 472, + 744 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {c}} _ {i} ^ {\\prime} = \\sum_ {j \\in \\mathcal {N} (i)} h _ {\\phi} \\left(\\hat {\\mathbf {c}} _ {i} \\| \\mathbf {c} _ {i} - \\mathbf {c} _ {j}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 757, + 470, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Having computed edge embeddings $\\mathbf{C} \\in \\mathbb{R}^{N \\times N \\times d'}$ with global dependencies, we rank these edges for each node. Without loss of generality, we focus on a single node $v_i \\in V$ , with latent features $\\hat{\\mathbf{x}}_i \\in \\mathbb{R}^d$ . We implement the approximation function $Q_{\\theta}(A|X,k)$ of the Edge-ranker as follows:", + "bbox": [ + 76, + 792, + 470, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1. Using edge embeddings $\\hat{\\mathbf{c}}_{ij} \\in \\mathbb{R}^{d'}$ , calculate edge prob", + "bbox": [ + 89, + 883, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "abilities $\\mathbf{p}_i\\in \\mathbb{R}^N$ for node $v_{i}$ using an MLP $m_{\\theta}$ ..", + "bbox": [ + 531, + 90, + 854, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} _ {i} = \\left\\{m _ {\\theta} \\left(\\hat {\\mathbf {c}} _ {i j}\\right) | \\forall j \\in N \\right\\}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 117, + 893, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Each element $p_{ij} \\in \\mathbf{p}_i$ represents a similarity measure between the latent features of node $v_i$ and $v_j$ . In practice, any distance measure can be used here.", + "bbox": [ + 529, + 145, + 893, + 189 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2. Using Gumbel-Softmax over the edge probabilities $\\mathbf{p}_i\\in \\mathbb{R}^N$ , we generate differentiable samples $\\mathbf{e}_i\\in \\mathbb{R}^N$ with Gumbel noise $g$ :", + "bbox": [ + 511, + 190, + 890, + 236 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {i} = \\left\\{\\frac {\\exp \\left(\\left(\\log \\left(p _ {i j}\\right) + g _ {i}\\right) + \\tau\\right)}{\\sum_ {j} \\exp \\left(\\left(\\log \\left(p _ {i j}\\right) + g _ {i}\\right) + \\tau\\right)} \\mid \\forall j \\in N \\right\\}, \\quad g _ {i} \\sim \\operatorname {G u m b e l} (0, 1) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 244, + 890, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is a temperature hyperparameter controlling the interpolation between a discrete one-hot categorical distribution and a continuous categorical density. When $\\tau \\rightarrow 0$ , the edge energies $e_{ij} \\in \\mathbf{e}_i$ approach a degenerate distribution. The temperature $\\tau$ is important for inducing sparsity, but given the exponential function, this results in a single element in $\\mathbf{e}_i$ given much more weighting than the rest, i.e., it approaches a one-hot argmax over $\\mathbf{e}_i$ . As we want a variable number of edges to be given higher importance and others to be close to zero, we select a higher temperature and use the top- $k$ selection procedure (detailed below) to induce sparsity. This additionally avoids the high-variance gradients induced by lower temperatures.", + "bbox": [ + 529, + 333, + 893, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Degree estimation A key limitation of existing graph generation methods [13, 15, 43] is their use of a fixed node degree $k$ across the entire graph. This can be suboptimal as mentioned previously. In our approach, rather than fixing $k$ for the entire graph, we sample it per node from a learned distribution. Focusing on a single node as before, the approximation function $Q_{\\rho}(k|X)$ of the Degree-estimator works as follows:", + "bbox": [ + 496, + 544, + 893, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1. We approximate the distribution of latent node features $\\hat{\\mathbf{x}}_i\\in \\mathbb{R}^d$ following a VAE-like formulation [14]. We encode its mean $\\pmb {\\mu}_i\\in \\mathbb{R}^d$ and variance $\\sigma_{i}\\in \\mathbb{R}^{d}$ using two MLPs $M_{\\rho}$ and $S_{\\rho}$ , and then reparametrize with noise $\\epsilon$ to obtain latent variable $\\mathbf{z}_i\\in \\mathbb{R}^d$ :", + "bbox": [ + 511, + 664, + 893, + 739 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {i}, \\boldsymbol {\\sigma} _ {i} = M _ {\\rho} (\\hat {\\mathbf {x}} _ {i}), S _ {\\rho} (\\hat {\\mathbf {x}} _ {i}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 750, + 890, + 775 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {i} = \\boldsymbol {\\mu} _ {i} + \\epsilon_ {i} \\boldsymbol {\\sigma} _ {i}, \\epsilon_ {i} \\sim \\mathcal {N} (0, 1).\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 770, + 826, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2. Finally, we concatenate each latent variable $\\mathbf{z}_i\\in \\mathbb{R}^d$ with the L1-norm of the edge samples $\\mathbf{h}_i = ||\\mathbf{e}_i||_1$ and decode it into a scalar $k_{i}\\in \\mathbb{R}$ with another MLP $D_{\\rho}$ representing a continuous relaxation of the neighborhood size for node $v_{i}$ :", + "bbox": [ + 511, + 797, + 893, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nk _ {i} = D _ {\\rho} \\left(\\mathbf {z} _ {i}\\right) + \\mathbf {h} _ {i}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 647, + 885, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22544", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since $\\mathbf{h}_i$ is a summation of a node's edge probabilities, it can be understood as representing an initial estimate of the node degree which is then improved by combining with a second node representation $\\mathbf{z}_i$ based entirely on the node's features. Using the edge samples to estimate the node degree links these representation spaces back to the primary latent space of node features $\\hat{\\mathbf{X}}$ .", + "bbox": [ + 107, + 90, + 470, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Top- $k$ Edge-Selector Having sampled edge weights, and node degrees $k$ , this function selects the top- $k$ edges for each node. The top- $k$ operation, i.e. finding the indices corresponding to the $k$ largest elements in a set of values, is a piecewise constant function and cannot be directly used in gradient-based optimization. Previous work [40] framed the top- $k$ operation as an optimal transport problem, providing a smoothed top- $k$ approximator. However, as their function is only defined for discrete values of $k$ it cannot be optimized with gradient descent. As an alternative that is differentiable with respect to $k$ , we relax the discrete constraint on $k$ , and instead use it to control the $x$ -axis value of the inflection point on a smoothed-Heaviside function (Fig. 3). For a node $v_{i} \\in V$ , of smoothed degree $k_{i} \\in \\mathbb{R}$ and edges $\\mathbf{e}_{i} \\in \\mathbb{R}^{N}$ , our Top- $k$ Edge Selector outputs an adjacency vector $\\mathbf{a}_{i} \\in \\mathbb{R}^{N}$ where the $k$ largest elements from $\\mathbf{e}_{i}$ are close to 1, and the rest close to 0. Focusing on a single node $v_{i}$ as before, the implementation is as follows:", + "bbox": [ + 76, + 196, + 472, + 467 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Draw 1D input points $\\mathbf{d}_i = \\{1,\\dots,N\\}$ where $N$ is the number of nodes in $V$ .", + "2. Pass $\\mathbf{d}_i$ through a hyperbolic tangent (tanh) which serves as a smooth approximation of the Heaviside function:" + ], + "bbox": [ + 88, + 468, + 468, + 542 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} _ {i} = 1 - 0. 5 * \\left\\{1 + \\tanh \\left(\\lambda^ {- 1} d _ {i} - \\lambda^ {- 1} k _ {i}\\right) \\right\\}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 554, + 468, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "here $\\lambda > 0$ is a temperature parameter controlling the gradient of the function's inflection point. As $\\lambda \\to 0$ , the smooth function approaches the Heaviside step function. The first- $k$ values in $\\mathbf{h}_i = \\{h_{ij}\\}_{j}^N$ will now be closer to 1, while the rest closer to 0.", + "bbox": [ + 107, + 583, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3. Finally, for each node $i$ we sort its edge-energies $\\mathbf{e}_i = \\{e_{ij}\\}_{j}^{N}$ in descending order, multiply by $\\mathbf{h}_i = \\{h_{ij}\\}_{j}^{N}$ and then restore the original order to obtain the final adjacency vector $\\mathbf{a}_i = \\{a_{ij}\\}_{j}^{N}$ . Stacking $\\mathbf{a}_i$ over all nodes $v_i \\in V$ creates the final adjacency matrix $\\mathbf{A} \\in \\mathbb{R}^{N \\times N}$ .", + "bbox": [ + 89, + 659, + 468, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Symmetric adjacency matrix If the adjacency matrix $A$ must be symmetric, this can be enforced by replacing it with $A_{sym}$ where: $\\mathbf{A}_{sym} = (\\mathbf{A} + \\mathbf{A}^T) / 2$ .", + "bbox": [ + 76, + 750, + 468, + 795 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Straight through Top- $k$ Edge Selector To make our final adjacency matrix $\\mathbf{A} \\in \\mathbb{R}^{N \\times N}$ discrete, we follow the trick used in the Straight-Through Gumbel Softmax [12]: we output the discretized version of $\\mathbf{A}$ in the forward pass and the continuous version in the backwards pass. For the discretized version in the forward pass, we replace the smooth-Heaviside function in Eq. 10 with a step function.", + "bbox": [ + 75, + 796, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Module Instantiation: The DGG module can be easily combined with any graph convolution operation. A typical graph convolution [16] is defined as follows: $\\mathbf{X}' = \\hat{\\mathbf{D}}^{-1/2} \\hat{\\mathbf{A}} \\hat{\\mathbf{D}}^{-1/2} \\mathbf{X} \\Theta$ . Here, $\\hat{\\mathbf{A}} = \\mathbf{A} + \\mathbf{I}$ denotes the adjacency matrix with inserted self-loops, $\\hat{\\mathbf{D}}$ its diagonal degree matrix and $\\Theta$ its weights. To use this graph convolution with the DGG, we simply use our module to generate the adjacency matrix $\\hat{\\mathbf{A}}$ .", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 224, + 633, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our DGG on node classification, point cloud classification and trajectory prediction. We chose these tasks as they demonstrate the wide applicability of our module: (1) graphs for node classification require models that can generate edge structures from noisy input graphs, (2) point cloud classification tasks have no input graph structures and (3) trajectory prediction additionally requires models which can handle a variable number of nodes per batch. We compare against state-of-the-art structure learning methods in each domain. As far as we know, our structure-learning approach is the only one that can be easily applied without modification to any GCN pipeline in such a range of tasks.", + "bbox": [ + 496, + 250, + 893, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Node classification", + "text_level": 1, + "bbox": [ + 500, + 439, + 679, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Beginning with node classification, we conduct ablations examining the behavior of different parts of the DGG, followed by comparisons to other state-of-the-art structure learning approaches. In the supplementary we include experiments investigating the effect of the DGG on downstream models under the addition of noisy edges to input graphs. We perform these experiments under both transductive and inductive scenarios, as well as semi-supervised and fully-supervised settings.", + "bbox": [ + 496, + 462, + 893, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets In the transductive setting, we evaluate on three citation benchmark datasets Cora, Citeseer and Pubmed [26] introduced by [41]. In an inductive setting, we evaluate on Reddit [42] and PPI [11]. Further dataset details can be found in the supplementary. Baselines and Implementation As our DGG is a GCN-agnostic module that can be integrated alongside any graph convolution operation, we compare its performance to both other GCN-agnostic approaches and bespoke structure-learning architectures. To compare against other GCN-agnostic methods, we integrate our DGG into four representative GCN backbones: GCN [16], GraphSage [11], GAT [35] and GCNII [2]. On these backbones, we compare against other GCN-agnostic structure learning methods: DropEdge [29], NeuralSparse [43], PTDNet [21]. Then we compare against bespoke architectures IDGL [3], LDS [9], SLAPS [8], NodeFormer [37] and VGCN [7]. To make our comparison fair against these bespoke architectures which learn the structure specifically for node classification, we integrate our DGG into a GCN backbone that is comparable to the bespoke architecture in design. Please see the", + "bbox": [ + 496, + 599, + 895, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22545", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/678a2bd19dc1970d2e5608459adbcd451c2e2fcdc004e529cc504652718eb851.jpg", + "image_caption": [ + "Figure 3. The differentiable Top- $k$ Edge Selector. This component uses the node degree $k_{i}$ output by the Degree Estimator to control the inflection point on a smooth-Heaviside function and uses it to select the top edges from $\\mathbf{e}_i$ output by the Edge Ranker. This produces an adjacency vector $\\mathbf{a}_i$ for each node, and stacking $\\mathbf{a}_i$ across all nodes produces the final adjacency matrix $\\mathbf{A}$ ." + ], + "image_footnote": [], + "bbox": [ + 238, + 89, + 733, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "supplementary for implementation details.", + "bbox": [ + 75, + 313, + 357, + 328 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training details A node classification model partitions the latent space of node embeddings into separate classes. However, when message-passing, there is one phenomenon of the input graph that can limit classification accuracy: two nodes with different classes but similar features and an edge connecting them. Classifying these nodes is challenging as their feature similarity can be compounded by passing messages between them. The goal of the DGG is to move such nodes apart in the latent space such that there is no edge and communication between them. However, traversing the loss landscape from the initial random initialization of the network to one where the model is able to discriminate between these nodes can take several iterations using only the downstream classification loss. To speed up training, we add an intermediate loss to further partition the latent space. We do this by supervising the adjacency matrix generated by the DGG to remove all edges between classes and only maintain those within a class. We then anneal this loss over the training cycle, eventually leaving only the downstream classification loss. We provide more details in the supplementary.", + "bbox": [ + 75, + 329, + 473, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.1 Ablations", + "text_level": 1, + "bbox": [ + 76, + 650, + 199, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 1, we explore the effect of disabling different components of our DGG module when integrated into a GCN [16] for node classification: 1. DGG without Degree Estimation and Differentiable Top-k Edge Selection — we remove the Degree Estimator and instead fix $k$ to select the top-k stochastically ordered edges. 2. DGG with deterministic Edge Ranking — we remove the noise in Eq. 7 of the Edge Ranker. 3. DGG with deterministic Degree Estimation — we remove the noise in Eq. 8 of the Degree Estimator. We perform these on Cora [41] and omit the annealed intermediate loss during training.", + "bbox": [ + 75, + 672, + 470, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 shows the benefit of learning a distribution over the node degree. When learning it deterministically, the accuracy decreases by $0.5\\%$ . This becomes significantly worse when the node degree is fixed for the entire graph", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ccc582ffadd73620476b37cbc02c7e49ba0634eb9cdf77e5bc54976f604d57e7.jpg", + "table_caption": [ + "Table 1. Ablation study. DGG integrated into a GCN for node classification on Cora [41]." + ], + "table_footnote": [], + "table_body": "
ModelAccuracy
Fixed node degree, k = {1, 5, 10, 100}{49.7, 78.9, 55.0, 37.0}
With deterministic Edge Ranking and Degree Estimation82.4
With deterministic Edge Ranking82.7
With deterministic Degree Estimation82.8
DGG83.2
", + "bbox": [ + 501, + 335, + 890, + 401 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "rather than learned per node. Note also, the sensitivity with respect to choice of $k$ . A fixed node degree of $k = 10$ or $k = 1$ reduces accuracy by almost $30\\%$ vs a graph of 5. This is due to the graph convolution operation: as it has no adaptive weighting mechanism for a node's neighborhood, each of the neighbors is given the same weight. Naturally, this leads to information sharing between unrelated nodes, reducing the quality of node representation after message-passing. In contrast, by learning a distribution over the node degree we are able to select only the most relevant neighbors, even though these are then weighted equally in the graph convolution. Finally, the inclusion of noise in any of the DGG components does increase accuracy, but only by approximately $0.5\\%$ — demonstrating both its benefit and the robustness of the DGG without it.", + "bbox": [ + 496, + 415, + 893, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.2 Results", + "text_level": 1, + "bbox": [ + 500, + 664, + 606, + 678 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison to GCN-agnostic modules In Table 2 we compare against GCN-agnostic structure learning methods. For fair comparison, we present two versions of our method: DGG-wl trained with the downstream loss only and DGG* trained with both the downstream and intermediate loss.", + "bbox": [ + 496, + 688, + 893, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DGG improves performance across all baselines and datasets. Against other approaches, DGG-wl generally outperforms the state-of-the-art NeuralSparse and PTDNet-wl (both trained with only the downstream loss). This can be attributed to our method for modelling sparsity, which explicitly lets each node to select the size of its neighborhood based on the downstream training signal. This training signal helps partition the node representation space, while the estimated node-degree additionally prevents communication", + "bbox": [ + 496, + 763, + 895, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22546", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a66a0df4ba53012141d76bbc996dd5b4529d459de05ed9c6d5a0a752be2ea479.jpg", + "table_caption": [ + "Table 2. Semi-supervised node classification compared to other architecture agnostic SOTA structure learning methods. We compare against prior methods reported in [21, 43, 2], using the official results where available. Those with ' -' have no official results or we ran into out-of-memory errors." + ], + "table_footnote": [], + "table_body": "
BackboneMethodCoraCiteseerPubmedRedditPPI
GCNOriginal81.170.379.092.253.2
DropEdge80.972.278.596.154.8
NeuralSparse82.171.578.896.665.1
PTDNet-wl82.471.779.1-75.2
DGG-wl83.272.680.296.877.1
PTDNet-wl + low rank82.872.779.8-80.3
DGG*84.174.984.097.381.6
GraphSageOriginal79.267.676.793.861.8
NeuralSparse79.367.475.196.762.6
PTDNet-wl79.467.877.0-64.5
DGG-wl79.468.277.696.665.3
PTDNet-wl + low rank80.367.977.1-64.8
DGG*80.570.880.296.967.3
GATOriginal83.072.179.0-97.3
DropEdge83.270.977.9-85.1
NeuralSparse83.472.478.0-92.1
PTDNet-wl83.772.379.2-97.8
DGG-wl84.673.279.7-97.4
PTDNet-wl + low rank84.473.779.3-98.0
DGG*85.376.482.0-97.6
GCNIIOriginal85.373.280.2-99.5
DropEdge84.973.479.4-99.0
DGG-wl86.974.581.5-99.6
DGG*87.875.781.9-99.7
", + "bbox": [ + 80, + 156, + 467, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "between distant nodes. Although PTDNet-wl does this implicitly through its attention mechanism, discovering this sparse subgraph of the input graph is challenging given its complexity. NeuralSparse on the other hand selects $k$ for its entire generated subgraph, which is both suboptimal and requires additional hyperparameter tuning.", + "bbox": [ + 75, + 441, + 470, + 532 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8d415e5272affed7c8fb788ee9bd0dbccb44c7db93d80f0ea18b19a2a584504a.jpg", + "table_caption": [ + "Table 3. Adjacency matrix constraints: our intermediate annealed loss vs. PTDNet's low rank regularizer [21] for semi-supervised node classification with a GCN backbone." + ], + "table_footnote": [], + "table_body": "
MethodCoraCiteseerPubmedPPI
DGG-wl86.874.481.299.5
DGG-wl + low rank87.175.381.499.5
DGG-wl + int. loss (aka DGG*)87.775.881.999.7
DGG-wl + int. loss + low rank87.876.282.199.7
", + "bbox": [ + 78, + 580, + 467, + 645 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparing methods which enforce additional constraints on the adjacency matrix, DGG* demonstrates larger accuracy gains than PTDNet*. PTDNet* regularizes its adjacency matrix to be of low-rank, as previous work [30] has shown that the rank of an adjacency matrix can reflect the number of clusters. This regularizer reasons about the graph's topology globally. While this may aid generalization, the accuracy difference may then be attributed to our intermediate loss providing stronger signals to discriminate between nodes with similar features but different classes (and therefore remove the edges between them). Furthermore, their regularizer uses the sum of the top- $k$ singular values during training, where $k$ again is a hyperparameter tuned to each dataset individually. Our method requires no additional parameters to be chosen.", + "bbox": [ + 75, + 659, + 470, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally in Table 3 we compare the low-rank constraint of PTDNet with our intermediate annealed loss. Our interme", + "bbox": [ + 76, + 869, + 472, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fc8d0eff7aee23a7a36b1f1c6ae10554b38c248823abccbaa5f2ef2a0663255b.jpg", + "table_caption": [ + "Table 4. Node classification results against bespoke SOTA architectures which learn the graph structure." + ], + "table_footnote": [], + "table_body": "
ModelCoraCiteseer
Setting 1IDGL [3]84.574.1
originalDGG* + GAT85.476.4
Setting 2LDS [9]71.573.3
Input graph = noneSLAPS [8]74.273.1
train split = {train + 1/2 val}DGG* + GCN82.474.0
Setting 3NodeFormer [37]88.776.2
split = 0.5/0.25/0.25DGG* + GAT90.177.8
Setting 4VGCN [7]85.976.5
train split = {train + 1/2 val}DGG* + GAT87.677.1
", + "bbox": [ + 501, + 114, + 890, + 253 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ca0b9ed8f6cc9a6f399cbfc8a6c931c0f984e9b33038984abcaa2d6f33b4bed2.jpg", + "table_caption": [ + "Table 5. ADE/FDE on the ETH & UCY datasets using SocialSTGCNN (first table), and Stanford Drone Dataset (SDD) using DAGNet (second table). For DGM [13], $k = 2$ for both datasets." + ], + "table_footnote": [], + "table_body": "
DatasetOriginalDGM [13] Gain (%)DGG Gain (%)
ADE↓FDE ↓ADE ↑FDE↑ADE ↑FDE ↑
ETH0.641.112.4%6.4%7.8%21.4%
Hotel0.490.8514.2%18.9%22.7%37.5%
Univ0.440.796.2%3.5%11.8%14.9%
Zara10.340.533.8%13.7%7.7%23.8%
Zara20.300.485.0%5.0%12.8%17.3%
Mean0.440.756.3%10.6%12.6%23.0%
SDD0.531.041.9%3.0%10.9%9.5%
", + "bbox": [ + 501, + 306, + 890, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "diate loss ('DGG-wl + int. loss') outperforms the low-rank constraint ('DGG-wl + low rank'). However, using both constraints ('DGG-wl + int. loss + low rank') increases classification accuracy further, suggesting the edges removed by both methods are complementary.", + "bbox": [ + 496, + 453, + 893, + 529 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with bespoke architectures In Table 4 we compare against bespoke architectures specifically designed for node classification. As each of these methods uses different experiment settings, we train our DGG-integrated architecture separately for each. See the supplementary for details on each setting and reasons for our choice of backbone. Our performance gains here can generally be attributed to factors: (1) our intermediate loss on the adjacency matrix and (2) our adjacency matrix factorizations where we learn the neighborhood for each node. Our intermediate loss particularly benefits from the experimental settings adopted by the other methods as they use larger training splits involving half the validation graph. Additionally, constructing the adjacency matrix by learning nodewise neighborhoods restricts the graph search space, making optimization easier. However, we note that some of these other methods are designed for node-classification on graphs which are orders of magnitude larger than Cora and Citeseer. In such cases, factorizing the adjacency per node, as we do, may be unfeasible.", + "bbox": [ + 496, + 531, + 893, + 818 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Trajectory prediction", + "text_level": 1, + "bbox": [ + 500, + 830, + 700, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate on trajectory prediction tasks as these have neither an input or ground truth graph structure, thus the ideal structure has to be generated entirely from the data. We", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22547", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/070ff4a41fec7a8bd509de208040856f81c528475a6353a6659b19468ebb5d99.jpg", + "table_caption": [ + "Table 6. ADE/FDE metrics on the SportVU Basketball dataset using DAGNet. For DGM [13], $k = 3$ ." + ], + "table_footnote": [], + "table_body": "
SplitTeamOriginalDGM [13] Gain (%)DGG Gain (%)
ADEFDEADEFDEADEFDE
10-40ATK2.744.29-0.4%-0.2%6.7%5.1%
DEF2.092.97-0.5%-0.1%9.7%6.4%
20-30ATK2.033.980.1%0.1%7.2%8.2%
DEF1.533.070.2%0.3%21.4%19.1%
40-10ATK0.811.711.3%0.9%15.5%17.0%
DEF0.721.490.8%0.8%10.9%16.2%
Mean—1.652.920.3%0.3%11.9%12.0%
", + "bbox": [ + 76, + 114, + 467, + 226 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "consider four datasets covering a range of scenarios from basketball to crowded urban environments. On each, we integrate our DGG into a SOTA GCN trajectory prediction pipeline and compare results to another task-agnostic structure learning approach, DGM [13].", + "bbox": [ + 75, + 231, + 470, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Datasets We evaluate on four trajectory prediction benchmarks. 1. ETH [27] and UCY [18] — 5 subsets of widely used real-world pedestrian trajectories. 2. STATS SportVU [32] — multiple NBA seasons tracking trajectories of basketball players over a game. Stanford Drone Dataset (SDD) [28] — top-down scenes across multiple areas at Stanford University. Further details on these datasets can be found in the supplementary. Baselines and Implementation We integrate our DGG module into two state-of-the-art trajectory prediction pipelines: Social-STGCNN [22] and DAGNet [23]. Our DGG is placed within both networks to generate the adjacency matrix on the fly and forms part of its forward and backward pass. Please see the supplementary for implementation details. Evaluation metrics. Model performance is measured with Average Displacement Error (ADE) and Final Displacement Error (FDE). ADE measures the average Euclidean distance along the entire predicted trajectory, while the FDE is that of the last timestep only.", + "bbox": [ + 75, + 306, + 473, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results In Table 5, the integration of our DGG into Social-STGCNN reduces ADE/FDE compared to both the baseline and the integration of DGM. In Table 5 and 6 we demonstrate similar gains over DGM when integrated into DAGNet. First, this shows the benefit of inducing sparsity when message-passing over a distance weighted adjacency matrix like Social-STGCNN or even an attention-mechanism like DAGNet. The larger error reduction of our DGG compared to DGM may be attributed to DGM's use of a fixed node-degree $k$ across its learned graph. While this can prevent the propagation of irrelevant information across the graph in some cases, in others it might limit the context available to certain nodes. We provide qualitative analysis in the supplementary.", + "bbox": [ + 75, + 579, + 470, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Point Cloud Classification", + "text_level": 1, + "bbox": [ + 76, + 801, + 313, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We evaluate on another vision task of point cloud classification for models which use GCNs. This task differs from the previous two as predictions are made for the entire graph as opposed to node-wise. As with our trajectory prediction experiments, we integrate our DGG into SOTA classification", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8fa34207ace01cf1db1ba3524e9c1ff3e6583d4b21df988d6bb0f665b6128958.jpg", + "table_caption": [ + "Table 7. Point Cloud classification on ModelNet40 with our module and DGM [13] integrated into two different point cloud labelling architectures." + ], + "table_footnote": [], + "table_body": "
BaselineMethodMean degreeS.D. degreeAccuracy
ResGCN [19]Original9093.3
DGM [13]20093.5
DGG14.87.494.4
DGCNN [36]Original40092.9
DGM [13]20093.3
DGG19.35.293.8
", + "bbox": [ + 501, + 126, + 890, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "architectures and compare against the other task-agnostic graph-learning module DGM [13].", + "bbox": [ + 498, + 237, + 890, + 267 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Datasets We evaluate on ModelNet40 [39], consisting of CAD models for a variety of object categories. Baselines and Implementation We integrate our DGG into a SOTA ResGCN [19] and DGCNN [36]. Both models use a $k$ -NN sampling scheme to construct its graph. We simply replace this sampler with our DGG and keep the rest of the network and training protocol the same.", + "bbox": [ + 496, + 267, + 893, + 372 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results Our results in Table 7 demonstrate the benefits of learning an adaptive neighborhood size across the latent graph. DGM [13] learns a fully-connected latent graph and then imposes a fixed node degree of $k = 20$ across it (i.e. selecting the top 20 neighbors for each node). This marginally improves upon the baselines ResGCN [19] and DGCNN[36], which both also used fixed node-degrees $k$ . In contrast, we learn a distribution over the node degree from which we sample each node's neighborhood size. As shown in Table 7, the node degree varies in our models with a standard deviation of around 5-7 across both baselines. Our accuracy gains over the baseline and DGM can be attributed to this variance in neighborhood sizes across the graph. These gains can be understood when viewing an input point cloud as a composition of object parts. Building semantic representations for different parts may naturally require varying amounts of contextual points. For instance, the wheels of a car might be identifiable with a smaller neighborhood than the car's body. This may suggest why an adaptive neighborhood size is helpful in this case.", + "bbox": [ + 496, + 373, + 895, + 675 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 688, + 619, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a novel approach for learning graph topologies, and shown how it obtains state-of-the-art performance across multiple baselines and datasets for trajectory prediction, point cloud classification and node classification. The principal advantage of our approach is that it can be combined with any existing graph convolution layer, under the presence of noisy, incomplete or unavailable edge structures.", + "bbox": [ + 496, + 713, + 893, + 820 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 830, + 668, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This project was supported by the EPSRC project ROSSINI (EP/S016317/1) and studentship 2327211 (EP/T517616/1).", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22548", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Michael M Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. 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PMLR, 2020." + ], + "bbox": [ + 501, + 92, + 893, + 217 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22550", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_model.json b/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_model.json new file mode 100644 index 0000000000000000000000000000000000000000..92a9245064cafb028f8540a1807c3d9a55337009 --- /dev/null +++ b/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.167, + 0.131, + 0.804, + 0.153 + ], + "angle": 0, + "content": "Learning Adaptive Neighborhoods for Graph Neural Networks" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.181, + 0.825, + 0.234 + ], + "angle": 0, + "content": "Avishkar Saha1, Oscar Mendez1, Chris Russell2, Richard Bowden1 \n1Centre for Vision Speech and Signal Processing, University of Surrey, Guildford, UK \n2University of Oxford, Oxford, UK" + }, + { + "type": "text", + "bbox": [ + 0.158, + 0.237, + 0.813, + 0.252 + ], + "angle": 0, + "content": "{a.saha, o.mendez, r.bowden}@surrey.ac.uk, Christopher.m.russell@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.591 + ], + "angle": 0, + "content": "Graph convolutional networks (GCNs) enable end-to-end learning on graph structured data. However, many works assume a given graph structure. When the input graph is noisy or unavailable, one approach is to construct or learn a latent graph structure. These methods typically fix the choice of node degree for the entire graph, which is suboptimal. Instead, we propose a novel end-to-end differentiable graph generator which builds graph topologies where each node selects both its neighborhood and its size. Our module can be readily integrated into existing pipelines involving graph convolution operations, replacing the predetermined or existing adjacency matrix with one that is learned, and optimized, as part of the general objective. As such it is applicable to any GCN. We integrate our module into trajectory prediction, point cloud classification and node classification pipelines resulting in improved accuracy over other structure-learning methods across a wide range of datasets and GCN backbones. We will release the code." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.619, + 0.21, + 0.635 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.472, + 0.75 + ], + "angle": 0, + "content": "The success of Graph Neural Networks (GNNs) [6, 1, 24], has led to a surge in graph-based representation learning. GNNs provide an efficient framework to learn from graph-structured data, making them widely applicable where data can be represented as a relation or interaction system. They have been effectively applied in a wide range of tasks [25], [33] including particle physics [4] and protein science [10]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.751, + 0.474, + 0.902 + ], + "angle": 0, + "content": "In a GNN, each node iteratively updates its state by interacting with its neighbors, typically through message passing. However, a fundamental limitation of such architectures is the assumption that the underlying graph is provided. While node or edge features may be updated during message passing, the graph topology remains fixed, and its choice may be suboptimal for various reasons. For instance, when classifying nodes on a citation network, an edge connecting nodes of different classes can diminish classification accuracy. These edges can degrade performance by propagating irrelevant" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.896, + 0.47 + ], + "angle": 0, + "content": "information across the graph. When no graph is explicitly provided, such domain knowledge can be exploited to learn structures optimized for the task at hand [8, 3, 9, 7]. However, in tasks where knowledge of the optimal graph structure is unknown, one common practice is to generate a \\( k \\)-nearest neighbor (\\( k \\)-NN) graph. In such cases, \\( k \\) is a hyperparameter and tuned to find the model with the best performance. For many applications, fixing \\( k \\) is overly restrictive as the optimal choice of \\( k \\) may vary for each node in the graph. While there has been an emergence of approaches which learn the graph structure for use in downstream GNNs [43, 13, 15], all of them treat the node degree \\( k \\) as a fixed hyperparameter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.897, + 0.626 + ], + "angle": 0, + "content": "We propose a general differentiable graph-generator (DGG) module for learning graph topology with or without an initial edge structure. Rather than learning graphs with fixed node degrees \\( k \\), our module generates local topologies with an adaptive neighborhood size. This module can be placed within any graph convolutional network, and jointly optimized with the rest of the network's parameters, learning topologies which favor the downstream task without hyperparameter selection or indeed any additional training signal. The primary contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.895, + 0.719 + ], + "angle": 0, + "content": "1. We propose a novel, differentiable graph-generator (DGG) module which jointly optimizes both the neighborhood size, and the edges that should belong to each neighborhood. Note a key limitation of existing approaches [43, 15, 13, 8, 3, 7, 37] is their inability to learn neighborhood sizes." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.72, + 0.896, + 0.869 + ], + "angle": 0, + "content": "2. Our DGG module is directly integrable into any pipeline involving graph convolutions, where either the given adjacency matrix is noisy, or unavailable and must be determined heuristically. In both cases, our DGG generates the adjacency matrix as part of the GNN training and can be trained end-to-end to optimize performance on the downstream task. Should a good graph structure be known, the generated adjacency matrix can be learned to remain close to it while optimizing performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "3. To demonstrate the power of the approach, we integrate our DGG into a range of SOTA pipelines — without" + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.629, + 0.896, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22541" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.109, + 0.092, + 0.471, + 0.138 + ], + "angle": 0, + "content": "modification — across different datasets in trajectory prediction, point cloud classification and node classification and show improvements in model accuracy." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.151, + 0.216, + 0.167 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.177, + 0.473, + 0.433 + ], + "angle": 0, + "content": "Graph Representation Learning: GNNs [1] are a broad class of neural architectures for modelling data which can be represented as a set of nodes and relations (edges). Most use message-passing to build node representations by aggregating neighborhood information. A common formulation is the Graph Convolution Network (GCNs) which generalizes the convolution operation to graphs [16, 5, 38, 11]. More recently, the Graph Attention Network (GAT) [35] utilizes a self-attention mechanism to aggregate neighborhood information. However, these works assumed that the underlying graph structure is fixed in advance, with the graph convolutions learning features that describe pre-existing nodes and edges. In contrast, we simultaneously learn the graph structure while using our generated adjacency matrix in downstream graph convolutions. The generated graph topology of our module is jointly optimized alongside other network parameters with feedback signals from the downstream task." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.434, + 0.473, + 0.705 + ], + "angle": 0, + "content": "Graph Structure Learning: In many applications, the optimal graph is unknown, and a graph is constructed before training a GNN. One question to ask is: \"Why isn't a fully-connected graph suitable?\" Constructing adjacency matrices weighted by distance or even an attention mechanism [35] over a fully-connected graph incorporates many task-irrelevant edges, even if their weights are small. While an attention mechanism can zero these out — i.e., discover a subgraph within the complete graph — discovering this subgraph is challenging given the combinatorial complexity of graphs. A common remedy is to sparsify a complete graph by selecting the \\( k \\)-nearest neighbors (\\( k \\)-NN). Although this can prevent the propagation of irrelevant information between nodes, the topology of the constructed graph may have no relation to the downstream task. Not only can irrelevant edges still exist, but pairs of relevant nodes may remain unconnected and can lead GCNs to learn representations with poor generalization [43]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.706, + 0.473, + 0.902 + ], + "angle": 0, + "content": "To overcome this, recent works constructed bespoke frameworks which learn the graph's adjacency matrix for specific tasks. For instance, in human pose estimation, some methods [31, 20] treat the elements of the adjacency matrix as a set of learnable weights. However, as each element is treated as a learnable parameter, the learned adjacency matrix is unlinked to the representation space and can only be used in tasks where there is a known correspondence between training and test nodes. This is not the case for many vision and graph tasks. Others have [15, 7, 17] employed variational inference frameworks to sample the entire adjacency matrix. Franceschi et al. [9] jointly learned the graph structure and the parameters of a GCN by approximately" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.318 + ], + "angle": 0, + "content": "solving a bilevel program. NodeFormer [37] and IDGL [3] instead learned latent topologies using multi-head attention [34]. There are two key differences between these methods and ours. First, we simplify optimization by factorizing the adjacency matrix distribution from which we sample the neighborhood for each node, as opposed to sampling the entire matrix. Second, these methods are bespoke frameworks specifically designed for node and graph classification. They leverage knowledge of the task in their loss functions, such as graph smoothness and sparsity [3]. As these methods are tailored to graph-based tasks only, they cannot be dropped into any GCN without modification, limiting their applicability to non-graph tasks like vision. In contrast, our module is both GCN and task-agnostic, and can be integrated into any GCN pipeline and trained using the downstream task loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.895, + 0.438 + ], + "angle": 0, + "content": "In contrast to the bespoke frameworks above, recent methods [43, 21, 13] took a more module-based approach similar to ours. As these approaches learned the graph structure entirely from the downstream task loss, there is less domain knowledge to leverage compared to methods constructed for specific tasks. Consequently, sparsity is often induced through a \\(k\\)-NN graph. Here, \\(k\\) is a scalar hyperparameter selected to control the learned graph's node degree." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.895, + 0.56 + ], + "angle": 0, + "content": "Unlike these works, we generate neighborhoods of varying size by learning a distribution over the edges and over the node degree \\( k \\). Each node samples its top-\\( k \\) neighbors (where \\( k \\) is now a continuous variable), allowing it to individually select its neighborhood and the edges that should belong to it, in a differentiable manner. Additionally, a known 'ideal' graph structure can be used as intermediate supervision to further constrain the latent space." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.572, + 0.593, + 0.587 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.895, + 0.671 + ], + "angle": 0, + "content": "Here, we provide details of our differentiable graph generation (DGG) module. We begin with notation and the statistical learning framework guiding its design, before describing the module, and how it is combined with graph convolutional backbone architectures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.895, + 0.763 + ], + "angle": 0, + "content": "Notation We represent a graph of \\( N \\) nodes as \\( G = (V, E) \\): where \\( V \\) is the set of nodes or vertices, and \\( E \\) the edge set. A graph's structure can be described by its adjacency matrix \\( A \\), with \\( a_{ij} = 1 \\) if an edge connects nodes \\( i \\) and \\( j \\) and \\( a_{ij} = 0 \\) otherwise. This binary adjacency matrix \\( A \\) is directed, and potentially asymmetrical." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.895, + 0.839 + ], + "angle": 0, + "content": "Problem definition We reformulate the baseline prediction task based on a fixed graph with an adaptive variant where the graph is learned. Typically, such baseline tasks make learned predictions \\( Y \\) given a set of input features \\( X \\) and a graph structure \\( A \\) of node degree \\( k \\):" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.847, + 0.894, + 0.865 + ], + "angle": 0, + "content": "\\[\nY = Q _ {\\phi} (X, A (k)), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "where \\(Q_{\\phi}\\) is an end-to-end neural network parameterized by learnable weights \\(\\phi\\). These formulations require a pre" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22542" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.087, + 0.473, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.178, + 0.473, + 0.248 + ], + "angle": 0, + "content": "Figure 1. (Left) A typical prediction task using graphs \\( Y = Q_{\\phi}(X, A) \\) where \\( A \\) and \\( k \\) are predetermined. (Right) Our reformulation \\( P(Y|X) \\approx \\sum_{A} \\sum_{k} Q_{\\phi}(X, A) Q_{\\theta}(A|X, k) Q_{\\rho}(k|X) \\) which learns a distribution over \\( A \\) and \\( k \\) alongside the downstream task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.27, + 0.474, + 0.406 + ], + "angle": 0, + "content": "determined graph-structure \\( A(k) \\), typically based on choice of node degree \\( k \\), and take \\( A(k) \\) as additional input to the model. In contrast, we learn both \\( A \\) and \\( k \\) in an end-to-end manner, and use them to make predictions \\( Y \\). As graphs are inherently binary, with edges either present or absent, they are not directly estimizable using gradient descent. Instead, we consider a distribution of graphs, \\( \\mathcal{G} \\), which then induce a distribution of labels, \\( \\mathcal{V} \\), in the downstream task. This distribution takes the factorized form:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.414, + 0.472, + 0.448 + ], + "angle": 0, + "content": "\\[\nP (Y | X) = \\sum_ {A \\in \\mathcal {G}} \\sum_ {k \\in \\mathbb {N} ^ {| V |}} Q _ {\\phi} (X, A) P (A | X, k) P (k | X), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.472, + 0.64 + ], + "angle": 0, + "content": "where \\( P(k|X) \\) is the distribution of node degree \\( k \\) given \\( X \\) (i.e., the choice of \\( k \\) in \\( k - \\mathrm{NN} \\)), \\( P(A|X, k) \\) the distribution of graph structures \\( A \\) conditioned on the learned \\( k \\) and input \\( X \\), and \\( P(Y|X) \\) is the downstream distribution of labels conditioned on data \\( X \\). For clarity, the adjacency \\( A \\) represents a subgraph of a complete graph over \\( X \\), and \\( k \\) is a multidimensional variable controlling the number of top- \\( k \\) neighbors for each node individually. To avoid learning individual probabilities for each possible graph \\( A \\) in an exponential state space, we further assume that \\( P(A|X, k) \\) has a factorized distribution where each neighborhood is sampled independently, i.e. \\( P(A|X, k) = \\prod_{i \\in V} P(a_i|X, k) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.64, + 0.471, + 0.669 + ], + "angle": 0, + "content": "We model the distributions over adjacencies \\(A\\) and \\(k\\) with tractable functions:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.678, + 0.473, + 0.711 + ], + "angle": 0, + "content": "\\[\nP (Y | X) \\approx \\sum_ {A} \\sum_ {k} Q _ {\\phi} (X, A) Q _ {\\theta} (A | X, k) Q _ {\\rho} (k | X), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.78 + ], + "angle": 0, + "content": "where \\( Q_{\\theta} \\) and \\( Q_{\\rho} \\) are functions parameterized by \\( \\theta \\) and \\( \\rho \\) to approximate \\( P(A|X, k) \\) and \\( P(k|X) \\), respectively. In Fig. 1, we illustrate the functions of our method compared to the typical prediction task in Eq. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.474, + 0.902 + ], + "angle": 0, + "content": "Using this formulation, we train the entire system end-to-end to minimize the expected loss when sampling \\( Y \\). This can be efficiently performed using stochastic gradient descent. In the forward pass, we first sample a subgraph/set of nodes \\( X \\) from the space of datapoints, and conditioning on \\( X \\) we sample \\( A \\) and compute the associated label \\( Y \\). When computing the gradient step, we update \\( Q_{\\phi}(X,A) \\) as normal and update the distributions using two standard" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.088, + 0.885, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.182, + 0.895, + 0.267 + ], + "angle": 0, + "content": "Figure 2. Our differentiable graph-generator (DGG) takes input nodes \\(\\mathbf{X}\\) and generates an adjacency matrix \\(\\mathbf{A}\\). It consists of: (1) Degree-estimator: generates samples of \\(k_{i}\\) for each node, (2) Edge-ranker: generates edge samples \\(\\mathbf{e}_i\\) for each node and (3) Top-k selector: takes \\(k_{i}\\) and edge samples \\(\\mathbf{e}_i\\) and selects top-k elements in a differentiable manner to output a final adjacency \\(\\mathbf{A}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.895, + 0.352 + ], + "angle": 0, + "content": "reparametrization tricks: one for discrete variables [12] such that \\( Q_{\\theta}(A|X, k) \\) can generate differentiable graph samples \\( A' \\), and another for continuous variables [14] of \\( k' \\) drawn from \\( Q_{\\rho}(k|X) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.364, + 0.893, + 0.398 + ], + "angle": 0, + "content": "\\[\nP (Y | X) \\approx \\sum_ {A ^ {\\prime}} \\sum_ {k ^ {\\prime}} Q _ {\\phi} \\left(X, A ^ {\\prime}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.543, + 0.399, + 0.848, + 0.417 + ], + "angle": 0, + "content": "where \\(A^{\\prime}\\sim Q_{\\theta}(A|X,k^{\\prime})\\) and \\(k^{\\prime}\\sim Q_{\\rho}(k|X)\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.895, + 0.488 + ], + "angle": 0, + "content": "As both the graph structure \\( A' \\) and variable \\( k' \\) samplers are differentiable, our DGG module can be readily integrated into pipelines involving graph convolutions and jointly trained end-to-end." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.499, + 0.792, + 0.516 + ], + "angle": 0, + "content": "3.1. Differentiable Graph Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.894, + 0.628 + ], + "angle": 0, + "content": "Our differentiable graph-generator (DGG) takes a set of nodes \\( V = \\{v_{1},\\dots,v_{N}\\} \\) with \\( d \\)-dimensional features \\( \\mathbf{X} \\in \\mathbb{R}^{N\\times d} \\) and generates a (potentially) asymmetric adjacency matrix \\( \\mathbf{A} \\in \\mathbb{R}^{N\\times N} \\). This adjacency matrix can be used directly in any downstream graph convolution operation (see Module Instantiation below). As illustrated by Fig. 2, the DGG module consists of four components:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.629, + 0.894, + 0.689 + ], + "angle": 0, + "content": "1. Node encoding: this component projects the input node features \\(\\mathbf{X} \\in \\mathbb{R}^{N \\times d}\\) to a latent representation \\(\\hat{\\mathbf{X}} \\in \\mathbb{R}^{N \\times d'}\\), which forms the primary representation space of the model." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.69, + 0.894, + 0.765 + ], + "angle": 0, + "content": "2. Edge ranking: this takes the latent node features \\(\\hat{\\mathbf{X}}\\in \\mathbb{R}^{N\\times d^{\\prime}}\\) and generates a matrix representing a stochastic ordering of edges \\(\\mathbf{E}\\in \\mathbb{R}^{N\\times N}\\) drawn from a learned distribution over the edge-probabilities \\((A^{\\prime}\\sim Q_{\\theta}(A|X,k^{\\prime})\\) from Eq. 4)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.765, + 0.895, + 0.856 + ], + "angle": 0, + "content": "3. Degree estimation: this component estimates the number of neighbors each individual node is connected to. It takes as input the latent node features \\(\\hat{\\mathbf{X}}\\in \\mathbb{R}^{N\\times d^{\\prime}}\\) and generates random samples \\(k\\in \\mathbb{R}^N\\) drawn from a learned distribution over the node degree \\((k^{\\prime}\\sim Q_{\\rho}(k|X)\\) from Eq. 4)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "4. Differentiable top-\\(k\\) edge selector: takes \\(k\\) and the edge-samples \\(e\\) and performs a soft thresholding that probabilistically selects the most important elements," + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.629, + 0.895, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22543" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.109, + 0.092, + 0.469, + 0.121 + ], + "angle": 0, + "content": "based on the output of the Edge-ranking to output an adjacency matrix \\(\\mathbf{A}\\in \\mathbb{R}^{N\\times N}\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.123, + 0.36, + 0.137 + ], + "angle": 0, + "content": "We now explain these steps in more detail:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.471, + 0.259 + ], + "angle": 0, + "content": "Node encoding We construct a single latent space from the input node features, and use it for edge ranking and degree estimation. We first map input node features \\(\\mathbf{X} \\in \\mathbb{R}^{N \\times d}\\) into latent features \\(\\hat{\\mathbf{X}} \\in \\mathbb{R}^{N \\times d'}\\) using a multi-layer perceptron (MLP) \\(N_{\\phi}\\) with weights \\(\\phi\\): \\(\\hat{\\mathbf{X}} = N_{\\phi}(\\mathbf{X})\\). These latent features form the input for the rest of the DGG. Furthermore, they are output by the DGG and passed to the GCN downstream to prevent vanishing gradients." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.26, + 0.472, + 0.349 + ], + "angle": 0, + "content": "Edge ranking The edge ranking returns an implicit distribution of edge orderings, from which we sample the neighborhood for each node. For each node \\( v_{i} \\), it draws a set of scores \\( \\mathbf{e}_i = \\{e_{ij}\\}_{j}^N \\) quantifying its relevance to all nodes \\( v_{j} \\in V \\) including itself. To generate differentiable edge samples \\( \\mathbf{e}_i \\) we use the Gumbel-Softmax [12]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.351, + 0.471, + 0.396 + ], + "angle": 0, + "content": "Before locally scoring each edge embedding \\( e_{ij} \\in \\mathbf{e}_i \\) for node \\( v_i \\), we implement a global stage which constructs edge embeddings with both local and global dependencies:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.397, + 0.472, + 0.473 + ], + "angle": 0, + "content": "1. Using latent node features \\(\\hat{\\mathbf{x}}_i\\in \\hat{\\mathbf{X}}\\) , determine local edge embeddings \\(\\hat{\\mathbf{c}}_{ij}\\in \\mathbb{R}^{d^{\\prime}}\\) by passing each pair of node features through an MLP \\(l_{\\phi}\\) .. \\(\\hat{\\mathbf{c}}_{ij} = l_{\\phi}(\\hat{\\mathbf{x}}_i,\\hat{\\mathbf{x}}_j)\\) These embeddings now form a complete graph \\(\\mathcal{G}\\) over the nodes, with each edge attributed \\(\\hat{\\mathbf{c}}_{ij}\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.473, + 0.473, + 0.746 + ], + "angle": 0, + "content": "2. As each edge embedding \\(\\hat{\\mathbf{c}}_{ij} \\in \\mathbf{C}\\) is calculated independently of the others, we refine it to account for its dependencies to adjacent edges. We do this through edge-to-edge message passing. However, we avoid computing dependencies between all edges of the complete graph for two reasons: first, some edges may not have any common nodes, so passing messages between them could propagate irrelevant information, and secondly, it could be prohibitively expensive. To restrict message-passing between adjacent edges only, we first compute the adjoint graph \\(\\mathcal{H}\\) of the complete graph \\(\\mathcal{G}\\). In the adjoint \\(\\mathcal{H}\\), each edge is associated with a node, and two nodes are connected if and only if their corresponding edges in \\(\\mathcal{G}\\) have a node in common. The adjoint's adjacency \\(A^{\\mathcal{H}}\\) can be calculated using its incidence matrix \\(L\\), \\(A^{\\mathcal{H}} = L^{T}L - 2I\\). In the adjoint, each node embedding \\(\\hat{\\mathbf{c}}_i\\) is then updated using an average of its neighboring nodes \\(\\hat{\\mathbf{c}}_j\\) and passed through an MLP \\(h_\\phi\\):" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.758, + 0.471, + 0.793 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {c}} _ {i} ^ {\\prime} = \\sum_ {j \\in \\mathcal {N} (i)} h _ {\\phi} \\left(\\hat {\\mathbf {c}} _ {i} \\| \\mathbf {c} _ {i} - \\mathbf {c} _ {j}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.794, + 0.472, + 0.871 + ], + "angle": 0, + "content": "Having computed edge embeddings \\(\\mathbf{C} \\in \\mathbb{R}^{N \\times N \\times d'}\\) with global dependencies, we rank these edges for each node. Without loss of generality, we focus on a single node \\(v_i \\in V\\), with latent features \\(\\hat{\\mathbf{x}}_i \\in \\mathbb{R}^d\\). We implement the approximation function \\(Q_{\\theta}(A|X,k)\\) of the Edge-ranker as follows:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.885, + 0.473, + 0.902 + ], + "angle": 0, + "content": "1. Using edge embeddings \\(\\hat{\\mathbf{c}}_{ij} \\in \\mathbb{R}^{d'}\\), calculate edge prob" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.091, + 0.856, + 0.107 + ], + "angle": 0, + "content": "abilities \\(\\mathbf{p}_i\\in \\mathbb{R}^N\\) for node \\(v_{i}\\) using an MLP \\(m_{\\theta}\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.118, + 0.894, + 0.136 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} _ {i} = \\left\\{m _ {\\theta} \\left(\\hat {\\mathbf {c}} _ {i j}\\right) | \\forall j \\in N \\right\\}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.146, + 0.894, + 0.19 + ], + "angle": 0, + "content": "Each element \\( p_{ij} \\in \\mathbf{p}_i \\) represents a similarity measure between the latent features of node \\( v_i \\) and \\( v_j \\). In practice, any distance measure can be used here." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.191, + 0.892, + 0.237 + ], + "angle": 0, + "content": "2. Using Gumbel-Softmax over the edge probabilities \\(\\mathbf{p}_i\\in \\mathbb{R}^N\\), we generate differentiable samples \\(\\mathbf{e}_i\\in \\mathbb{R}^N\\) with Gumbel noise \\(g\\):" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.246, + 0.892, + 0.322 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {i} = \\left\\{\\frac {\\exp \\left(\\left(\\log \\left(p _ {i j}\\right) + g _ {i}\\right) + \\tau\\right)}{\\sum_ {j} \\exp \\left(\\left(\\log \\left(p _ {i j}\\right) + g _ {i}\\right) + \\tau\\right)} \\mid \\forall j \\in N \\right\\}, \\quad g _ {i} \\sim \\operatorname {G u m b e l} (0, 1) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.334, + 0.895, + 0.544 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a temperature hyperparameter controlling the interpolation between a discrete one-hot categorical distribution and a continuous categorical density. When \\(\\tau \\rightarrow 0\\), the edge energies \\(e_{ij} \\in \\mathbf{e}_i\\) approach a degenerate distribution. The temperature \\(\\tau\\) is important for inducing sparsity, but given the exponential function, this results in a single element in \\(\\mathbf{e}_i\\) given much more weighting than the rest, i.e., it approaches a one-hot argmax over \\(\\mathbf{e}_i\\). As we want a variable number of edges to be given higher importance and others to be close to zero, we select a higher temperature and use the top-\\(k\\) selection procedure (detailed below) to induce sparsity. This additionally avoids the high-variance gradients induced by lower temperatures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.895, + 0.663 + ], + "angle": 0, + "content": "Degree estimation A key limitation of existing graph generation methods [13, 15, 43] is their use of a fixed node degree \\( k \\) across the entire graph. This can be suboptimal as mentioned previously. In our approach, rather than fixing \\( k \\) for the entire graph, we sample it per node from a learned distribution. Focusing on a single node as before, the approximation function \\( Q_{\\rho}(k|X) \\) of the Degree-estimator works as follows:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.665, + 0.894, + 0.741 + ], + "angle": 0, + "content": "1. We approximate the distribution of latent node features \\(\\hat{\\mathbf{x}}_i\\in \\mathbb{R}^d\\) following a VAE-like formulation [14]. We encode its mean \\(\\pmb {\\mu}_i\\in \\mathbb{R}^d\\) and variance \\(\\sigma_{i}\\in \\mathbb{R}^{d}\\) using two MLPs \\(M_{\\rho}\\) and \\(S_{\\rho}\\), and then reparametrize with noise \\(\\epsilon\\) to obtain latent variable \\(\\mathbf{z}_i\\in \\mathbb{R}^d\\):" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.751, + 0.892, + 0.776 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {i}, \\boldsymbol {\\sigma} _ {i} = M _ {\\rho} (\\hat {\\mathbf {x}} _ {i}), S _ {\\rho} (\\hat {\\mathbf {x}} _ {i}), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.771, + 0.828, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {i} = \\boldsymbol {\\mu} _ {i} + \\epsilon_ {i} \\boldsymbol {\\sigma} _ {i}, \\epsilon_ {i} \\sim \\mathcal {N} (0, 1).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.798, + 0.895, + 0.873 + ], + "angle": 0, + "content": "2. Finally, we concatenate each latent variable \\(\\mathbf{z}_i\\in \\mathbb{R}^d\\) with the L1-norm of the edge samples \\(\\mathbf{h}_i = ||\\mathbf{e}_i||_1\\) and decode it into a scalar \\(k_{i}\\in \\mathbb{R}\\) with another MLP \\(D_{\\rho}\\) representing a continuous relaxation of the neighborhood size for node \\(v_{i}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.648, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "\\[\nk _ {i} = D _ {\\rho} \\left(\\mathbf {z} _ {i}\\right) + \\mathbf {h} _ {i}. \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "22544" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.108, + 0.092, + 0.471, + 0.197 + ], + "angle": 0, + "content": "Since \\(\\mathbf{h}_i\\) is a summation of a node's edge probabilities, it can be understood as representing an initial estimate of the node degree which is then improved by combining with a second node representation \\(\\mathbf{z}_i\\) based entirely on the node's features. Using the edge samples to estimate the node degree links these representation spaces back to the primary latent space of node features \\(\\hat{\\mathbf{X}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.198, + 0.473, + 0.468 + ], + "angle": 0, + "content": "Top-\\(k\\) Edge-Selector Having sampled edge weights, and node degrees \\(k\\), this function selects the top-\\(k\\) edges for each node. The top-\\(k\\) operation, i.e. finding the indices corresponding to the \\(k\\) largest elements in a set of values, is a piecewise constant function and cannot be directly used in gradient-based optimization. Previous work [40] framed the top-\\(k\\) operation as an optimal transport problem, providing a smoothed top-\\(k\\) approximator. However, as their function is only defined for discrete values of \\(k\\) it cannot be optimized with gradient descent. As an alternative that is differentiable with respect to \\(k\\), we relax the discrete constraint on \\(k\\), and instead use it to control the \\(x\\)-axis value of the inflection point on a smoothed-Heaviside function (Fig. 3). For a node \\(v_{i} \\in V\\), of smoothed degree \\(k_{i} \\in \\mathbb{R}\\) and edges \\(\\mathbf{e}_{i} \\in \\mathbb{R}^{N}\\), our Top-\\(k\\) Edge Selector outputs an adjacency vector \\(\\mathbf{a}_{i} \\in \\mathbb{R}^{N}\\) where the \\(k\\) largest elements from \\(\\mathbf{e}_{i}\\) are close to 1, and the rest close to 0. Focusing on a single node \\(v_{i}\\) as before, the implementation is as follows:" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.469, + 0.469, + 0.498 + ], + "angle": 0, + "content": "1. Draw 1D input points \\(\\mathbf{d}_i = \\{1,\\dots,N\\}\\) where \\(N\\) is the number of nodes in \\(V\\)." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.499, + 0.469, + 0.543 + ], + "angle": 0, + "content": "2. Pass \\(\\mathbf{d}_i\\) through a hyperbolic tangent (tanh) which serves as a smooth approximation of the Heaviside function:" + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.469, + 0.469, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.555, + 0.47, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} _ {i} = 1 - 0. 5 * \\left\\{1 + \\tanh \\left(\\lambda^ {- 1} d _ {i} - \\lambda^ {- 1} k _ {i}\\right) \\right\\}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.584, + 0.47, + 0.659 + ], + "angle": 0, + "content": "here \\(\\lambda > 0\\) is a temperature parameter controlling the gradient of the function's inflection point. As \\(\\lambda \\to 0\\), the smooth function approaches the Heaviside step function. The first-\\(k\\) values in \\(\\mathbf{h}_i = \\{h_{ij}\\}_{j}^N\\) will now be closer to 1, while the rest closer to 0." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.66, + 0.47, + 0.748 + ], + "angle": 0, + "content": "3. Finally, for each node \\(i\\) we sort its edge-energies \\(\\mathbf{e}_i = \\{e_{ij}\\}_{j}^{N}\\) in descending order, multiply by \\(\\mathbf{h}_i = \\{h_{ij}\\}_{j}^{N}\\) and then restore the original order to obtain the final adjacency vector \\(\\mathbf{a}_i = \\{a_{ij}\\}_{j}^{N}\\). Stacking \\(\\mathbf{a}_i\\) over all nodes \\(v_i \\in V\\) creates the final adjacency matrix \\(\\mathbf{A} \\in \\mathbb{R}^{N \\times N}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.47, + 0.796 + ], + "angle": 0, + "content": "Symmetric adjacency matrix If the adjacency matrix \\( A \\) must be symmetric, this can be enforced by replacing it with \\( A_{sym} \\) where: \\( \\mathbf{A}_{sym} = (\\mathbf{A} + \\mathbf{A}^T) / 2 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Straight through Top-\\(k\\) Edge Selector To make our final adjacency matrix \\(\\mathbf{A} \\in \\mathbb{R}^{N \\times N}\\) discrete, we follow the trick used in the Straight-Through Gumbel Softmax [12]: we output the discretized version of \\(\\mathbf{A}\\) in the forward pass and the continuous version in the backwards pass. For the discretized version in the forward pass, we replace the smooth-Heaviside function in Eq. 10 with a step function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.213 + ], + "angle": 0, + "content": "Module Instantiation: The DGG module can be easily combined with any graph convolution operation. A typical graph convolution [16] is defined as follows: \\(\\mathbf{X}' = \\hat{\\mathbf{D}}^{-1/2} \\hat{\\mathbf{A}} \\hat{\\mathbf{D}}^{-1/2} \\mathbf{X} \\Theta\\). Here, \\(\\hat{\\mathbf{A}} = \\mathbf{A} + \\mathbf{I}\\) denotes the adjacency matrix with inserted self-loops, \\(\\hat{\\mathbf{D}}\\) its diagonal degree matrix and \\(\\Theta\\) its weights. To use this graph convolution with the DGG, we simply use our module to generate the adjacency matrix \\(\\hat{\\mathbf{A}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.225, + 0.634, + 0.243 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.25, + 0.895, + 0.432 + ], + "angle": 0, + "content": "We evaluate our DGG on node classification, point cloud classification and trajectory prediction. We chose these tasks as they demonstrate the wide applicability of our module: (1) graphs for node classification require models that can generate edge structures from noisy input graphs, (2) point cloud classification tasks have no input graph structures and (3) trajectory prediction additionally requires models which can handle a variable number of nodes per batch. We compare against state-of-the-art structure learning methods in each domain. As far as we know, our structure-learning approach is the only one that can be easily applied without modification to any GCN pipeline in such a range of tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.44, + 0.68, + 0.455 + ], + "angle": 0, + "content": "4.1. Node classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.895, + 0.599 + ], + "angle": 0, + "content": "Beginning with node classification, we conduct ablations examining the behavior of different parts of the DGG, followed by comparisons to other state-of-the-art structure learning approaches. In the supplementary we include experiments investigating the effect of the DGG on downstream models under the addition of noisy edges to input graphs. We perform these experiments under both transductive and inductive scenarios, as well as semi-supervised and fully-supervised settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Datasets In the transductive setting, we evaluate on three citation benchmark datasets Cora, Citeseer and Pubmed [26] introduced by [41]. In an inductive setting, we evaluate on Reddit [42] and PPI [11]. Further dataset details can be found in the supplementary. Baselines and Implementation As our DGG is a GCN-agnostic module that can be integrated alongside any graph convolution operation, we compare its performance to both other GCN-agnostic approaches and bespoke structure-learning architectures. To compare against other GCN-agnostic methods, we integrate our DGG into four representative GCN backbones: GCN [16], GraphSage [11], GAT [35] and GCNII [2]. On these backbones, we compare against other GCN-agnostic structure learning methods: DropEdge [29], NeuralSparse [43], PTDNet [21]. Then we compare against bespoke architectures IDGL [3], LDS [9], SLAPS [8], NodeFormer [37] and VGCN [7]. To make our comparison fair against these bespoke architectures which learn the structure specifically for node classification, we integrate our DGG into a GCN backbone that is comparable to the bespoke architecture in design. Please see the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22545" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.24, + 0.09, + 0.734, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.247, + 0.895, + 0.29 + ], + "angle": 0, + "content": "Figure 3. The differentiable Top-\\(k\\) Edge Selector. This component uses the node degree \\(k_{i}\\) output by the Degree Estimator to control the inflection point on a smooth-Heaviside function and uses it to select the top edges from \\(\\mathbf{e}_i\\) output by the Edge Ranker. This produces an adjacency vector \\(\\mathbf{a}_i\\) for each node, and stacking \\(\\mathbf{a}_i\\) across all nodes produces the final adjacency matrix \\(\\mathbf{A}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.358, + 0.329 + ], + "angle": 0, + "content": "supplementary for implementation details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.474, + 0.631 + ], + "angle": 0, + "content": "Training details A node classification model partitions the latent space of node embeddings into separate classes. However, when message-passing, there is one phenomenon of the input graph that can limit classification accuracy: two nodes with different classes but similar features and an edge connecting them. Classifying these nodes is challenging as their feature similarity can be compounded by passing messages between them. The goal of the DGG is to move such nodes apart in the latent space such that there is no edge and communication between them. However, traversing the loss landscape from the initial random initialization of the network to one where the model is able to discriminate between these nodes can take several iterations using only the downstream classification loss. To speed up training, we add an intermediate loss to further partition the latent space. We do this by supervising the adjacency matrix generated by the DGG to remove all edges between classes and only maintain those within a class. We then anneal this loss over the training cycle, eventually leaving only the downstream classification loss. We provide more details in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.2, + 0.665 + ], + "angle": 0, + "content": "4.1.1 Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.472, + 0.84 + ], + "angle": 0, + "content": "In Table 1, we explore the effect of disabling different components of our DGG module when integrated into a GCN [16] for node classification: 1. DGG without Degree Estimation and Differentiable Top-k Edge Selection — we remove the Degree Estimator and instead fix \\( k \\) to select the top-k stochastically ordered edges. 2. DGG with deterministic Edge Ranking — we remove the noise in Eq. 7 of the Edge Ranker. 3. DGG with deterministic Degree Estimation — we remove the noise in Eq. 8 of the Degree Estimator. We perform these on Cora [41] and omit the annealed intermediate loss during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Table 1 shows the benefit of learning a distribution over the node degree. When learning it deterministically, the accuracy decreases by \\(0.5\\%\\). This becomes significantly worse when the node degree is fixed for the entire graph" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.31, + 0.892, + 0.337 + ], + "angle": 0, + "content": "Table 1. Ablation study. DGG integrated into a GCN for node classification on Cora [41]." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.337, + 0.891, + 0.402 + ], + "angle": 0, + "content": "
ModelAccuracy
Fixed node degree, k = {1, 5, 10, 100}{49.7, 78.9, 55.0, 37.0}
With deterministic Edge Ranking and Degree Estimation82.4
With deterministic Edge Ranking82.7
With deterministic Degree Estimation82.8
DGG83.2
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.895, + 0.642 + ], + "angle": 0, + "content": "rather than learned per node. Note also, the sensitivity with respect to choice of \\( k \\). A fixed node degree of \\( k = 10 \\) or \\( k = 1 \\) reduces accuracy by almost \\( 30\\% \\) vs a graph of 5. This is due to the graph convolution operation: as it has no adaptive weighting mechanism for a node's neighborhood, each of the neighbors is given the same weight. Naturally, this leads to information sharing between unrelated nodes, reducing the quality of node representation after message-passing. In contrast, by learning a distribution over the node degree we are able to select only the most relevant neighbors, even though these are then weighted equally in the graph convolution. Finally, the inclusion of noise in any of the DGG components does increase accuracy, but only by approximately \\( 0.5\\% \\) — demonstrating both its benefit and the robustness of the DGG without it." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.665, + 0.607, + 0.679 + ], + "angle": 0, + "content": "4.1.2 Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.764 + ], + "angle": 0, + "content": "Comparison to GCN-agnostic modules In Table 2 we compare against GCN-agnostic structure learning methods. For fair comparison, we present two versions of our method: DGG-wl trained with the downstream loss only and DGG* trained with both the downstream and intermediate loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.897, + 0.901 + ], + "angle": 0, + "content": "DGG improves performance across all baselines and datasets. Against other approaches, DGG-wl generally outperforms the state-of-the-art NeuralSparse and PTDNet-wl (both trained with only the downstream loss). This can be attributed to our method for modelling sparsity, which explicitly lets each node to select the size of its neighborhood based on the downstream training signal. This training signal helps partition the node representation space, while the estimated node-degree additionally prevents communication" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22546" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.472, + 0.156 + ], + "angle": 0, + "content": "Table 2. Semi-supervised node classification compared to other architecture agnostic SOTA structure learning methods. We compare against prior methods reported in [21, 43, 2], using the official results where available. Those with ' -' have no official results or we ran into out-of-memory errors." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.157, + 0.468, + 0.419 + ], + "angle": 0, + "content": "
BackboneMethodCoraCiteseerPubmedRedditPPI
GCNOriginal81.170.379.092.253.2
DropEdge80.972.278.596.154.8
NeuralSparse82.171.578.896.665.1
PTDNet-wl82.471.779.1-75.2
DGG-wl83.272.680.296.877.1
PTDNet-wl + low rank82.872.779.8-80.3
DGG*84.174.984.097.381.6
GraphSageOriginal79.267.676.793.861.8
NeuralSparse79.367.475.196.762.6
PTDNet-wl79.467.877.0-64.5
DGG-wl79.468.277.696.665.3
PTDNet-wl + low rank80.367.977.1-64.8
DGG*80.570.880.296.967.3
GATOriginal83.072.179.0-97.3
DropEdge83.270.977.9-85.1
NeuralSparse83.472.478.0-92.1
PTDNet-wl83.772.379.2-97.8
DGG-wl84.673.279.7-97.4
PTDNet-wl + low rank84.473.779.3-98.0
DGG*85.376.482.0-97.6
GCNIIOriginal85.373.280.2-99.5
DropEdge84.973.479.4-99.0
DGG-wl86.974.581.5-99.6
DGG*87.875.781.9-99.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.472, + 0.534 + ], + "angle": 0, + "content": "between distant nodes. Although PTDNet-wl does this implicitly through its attention mechanism, discovering this sparse subgraph of the input graph is challenging given its complexity. NeuralSparse on the other hand selects \\( k \\) for its entire generated subgraph, which is both suboptimal and requires additional hyperparameter tuning." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.543, + 0.47, + 0.582 + ], + "angle": 0, + "content": "Table 3. Adjacency matrix constraints: our intermediate annealed loss vs. PTDNet's low rank regularizer [21] for semi-supervised node classification with a GCN backbone." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.582, + 0.468, + 0.646 + ], + "angle": 0, + "content": "
MethodCoraCiteseerPubmedPPI
DGG-wl86.874.481.299.5
DGG-wl + low rank87.175.381.499.5
DGG-wl + int. loss (aka DGG*)87.775.881.999.7
DGG-wl + int. loss + low rank87.876.282.199.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.472, + 0.871 + ], + "angle": 0, + "content": "Comparing methods which enforce additional constraints on the adjacency matrix, DGG* demonstrates larger accuracy gains than PTDNet*. PTDNet* regularizes its adjacency matrix to be of low-rank, as previous work [30] has shown that the rank of an adjacency matrix can reflect the number of clusters. This regularizer reasons about the graph's topology globally. While this may aid generalization, the accuracy difference may then be attributed to our intermediate loss providing stronger signals to discriminate between nodes with similar features but different classes (and therefore remove the edges between them). Furthermore, their regularizer uses the sum of the top-\\(k\\) singular values during training, where \\(k\\) again is a hyperparameter tuned to each dataset individually. Our method requires no additional parameters to be chosen." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.473, + 0.9 + ], + "angle": 0, + "content": "Finally in Table 3 we compare the low-rank constraint of PTDNet with our intermediate annealed loss. Our interme" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.088, + 0.895, + 0.114 + ], + "angle": 0, + "content": "Table 4. Node classification results against bespoke SOTA architectures which learn the graph structure." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.115, + 0.892, + 0.255 + ], + "angle": 0, + "content": "
ModelCoraCiteseer
Setting 1IDGL [3]84.574.1
originalDGG* + GAT85.476.4
Setting 2LDS [9]71.573.3
Input graph = noneSLAPS [8]74.273.1
train split = {train + 1/2 val}DGG* + GCN82.474.0
Setting 3NodeFormer [37]88.776.2
split = 0.5/0.25/0.25DGG* + GAT90.177.8
Setting 4VGCN [7]85.976.5
train split = {train + 1/2 val}DGG* + GAT87.677.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.265, + 0.895, + 0.306 + ], + "angle": 0, + "content": "Table 5. ADE/FDE on the ETH & UCY datasets using SocialSTGCNN (first table), and Stanford Drone Dataset (SDD) using DAGNet (second table). For DGM [13], \\( k = 2 \\) for both datasets." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.307, + 0.891, + 0.428 + ], + "angle": 0, + "content": "
DatasetOriginalDGM [13] Gain (%)DGG Gain (%)
ADE↓FDE ↓ADE ↑FDE↑ADE ↑FDE ↑
ETH0.641.112.4%6.4%7.8%21.4%
Hotel0.490.8514.2%18.9%22.7%37.5%
Univ0.440.796.2%3.5%11.8%14.9%
Zara10.340.533.8%13.7%7.7%23.8%
Zara20.300.485.0%5.0%12.8%17.3%
Mean0.440.756.3%10.6%12.6%23.0%
SDD0.531.041.9%3.0%10.9%9.5%
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.894, + 0.53 + ], + "angle": 0, + "content": "diate loss ('DGG-wl + int. loss') outperforms the low-rank constraint ('DGG-wl + low rank'). However, using both constraints ('DGG-wl + int. loss + low rank') increases classification accuracy further, suggesting the edges removed by both methods are complementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.895, + 0.819 + ], + "angle": 0, + "content": "Comparison with bespoke architectures In Table 4 we compare against bespoke architectures specifically designed for node classification. As each of these methods uses different experiment settings, we train our DGG-integrated architecture separately for each. See the supplementary for details on each setting and reasons for our choice of backbone. Our performance gains here can generally be attributed to factors: (1) our intermediate loss on the adjacency matrix and (2) our adjacency matrix factorizations where we learn the neighborhood for each node. Our intermediate loss particularly benefits from the experimental settings adopted by the other methods as they use larger training splits involving half the validation graph. Additionally, constructing the adjacency matrix by learning nodewise neighborhoods restricts the graph search space, making optimization easier. However, we note that some of these other methods are designed for node-classification on graphs which are orders of magnitude larger than Cora and Citeseer. In such cases, factorizing the adjacency per node, as we do, may be unfeasible." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.702, + 0.848 + ], + "angle": 0, + "content": "4.2. Trajectory prediction" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We evaluate on trajectory prediction tasks as these have neither an input or ground truth graph structure, thus the ideal structure has to be generated entirely from the data. We" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22547" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.114 + ], + "angle": 0, + "content": "Table 6. ADE/FDE metrics on the SportVU Basketball dataset using DAGNet. For DGM [13], \\( k = 3 \\)." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.115, + 0.468, + 0.227 + ], + "angle": 0, + "content": "
SplitTeamOriginalDGM [13] Gain (%)DGG Gain (%)
ADEFDEADEFDEADEFDE
10-40ATK2.744.29-0.4%-0.2%6.7%5.1%
DEF2.092.97-0.5%-0.1%9.7%6.4%
20-30ATK2.033.980.1%0.1%7.2%8.2%
DEF1.533.070.2%0.3%21.4%19.1%
40-10ATK0.811.711.3%0.9%15.5%17.0%
DEF0.721.490.8%0.8%10.9%16.2%
Mean—1.652.920.3%0.3%11.9%12.0%
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.232, + 0.471, + 0.307 + ], + "angle": 0, + "content": "consider four datasets covering a range of scenarios from basketball to crowded urban environments. On each, we integrate our DGG into a SOTA GCN trajectory prediction pipeline and compare results to another task-agnostic structure learning approach, DGM [13]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.474, + 0.58 + ], + "angle": 0, + "content": "Datasets We evaluate on four trajectory prediction benchmarks. 1. ETH [27] and UCY [18] — 5 subsets of widely used real-world pedestrian trajectories. 2. STATS SportVU [32] — multiple NBA seasons tracking trajectories of basketball players over a game. Stanford Drone Dataset (SDD) [28] — top-down scenes across multiple areas at Stanford University. Further details on these datasets can be found in the supplementary. Baselines and Implementation We integrate our DGG module into two state-of-the-art trajectory prediction pipelines: Social-STGCNN [22] and DAGNet [23]. Our DGG is placed within both networks to generate the adjacency matrix on the fly and forms part of its forward and backward pass. Please see the supplementary for implementation details. Evaluation metrics. Model performance is measured with Average Displacement Error (ADE) and Final Displacement Error (FDE). ADE measures the average Euclidean distance along the entire predicted trajectory, while the FDE is that of the last timestep only." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.472, + 0.793 + ], + "angle": 0, + "content": "Results In Table 5, the integration of our DGG into Social-STGCNN reduces ADE/FDE compared to both the baseline and the integration of DGM. In Table 5 and 6 we demonstrate similar gains over DGM when integrated into DAGNet. First, this shows the benefit of inducing sparsity when message-passing over a distance weighted adjacency matrix like Social-STGCNN or even an attention-mechanism like DAGNet. The larger error reduction of our DGG compared to DGM may be attributed to DGM's use of a fixed node-degree \\( k \\) across its learned graph. While this can prevent the propagation of irrelevant information across the graph in some cases, in others it might limit the context available to certain nodes. We provide qualitative analysis in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.315, + 0.818 + ], + "angle": 0, + "content": "4.3. Point Cloud Classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We evaluate on another vision task of point cloud classification for models which use GCNs. This task differs from the previous two as predictions are made for the entire graph as opposed to node-wise. As with our trajectory prediction experiments, we integrate our DGG into SOTA classification" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.087, + 0.892, + 0.128 + ], + "angle": 0, + "content": "Table 7. Point Cloud classification on ModelNet40 with our module and DGM [13] integrated into two different point cloud labelling architectures." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.127, + 0.892, + 0.213 + ], + "angle": 0, + "content": "
BaselineMethodMean degreeS.D. degreeAccuracy
ResGCN [19]Original9093.3
DGM [13]20093.5
DGG14.87.494.4
DGCNN [36]Original40092.9
DGM [13]20093.3
DGG19.35.293.8
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.238, + 0.892, + 0.268 + ], + "angle": 0, + "content": "architectures and compare against the other task-agnostic graph-learning module DGM [13]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.895, + 0.373 + ], + "angle": 0, + "content": "Datasets We evaluate on ModelNet40 [39], consisting of CAD models for a variety of object categories. Baselines and Implementation We integrate our DGG into a SOTA ResGCN [19] and DGCNN [36]. Both models use a \\(k\\)-NN sampling scheme to construct its graph. We simply replace this sampler with our DGG and keep the rest of the network and training protocol the same." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.374, + 0.896, + 0.676 + ], + "angle": 0, + "content": "Results Our results in Table 7 demonstrate the benefits of learning an adaptive neighborhood size across the latent graph. DGM [13] learns a fully-connected latent graph and then imposes a fixed node degree of \\( k = 20 \\) across it (i.e. selecting the top 20 neighbors for each node). This marginally improves upon the baselines ResGCN [19] and DGCNN[36], which both also used fixed node-degrees \\( k \\). In contrast, we learn a distribution over the node degree from which we sample each node's neighborhood size. As shown in Table 7, the node degree varies in our models with a standard deviation of around 5-7 across both baselines. Our accuracy gains over the baseline and DGM can be attributed to this variance in neighborhood sizes across the graph. These gains can be understood when viewing an input point cloud as a composition of object parts. Building semantic representations for different parts may naturally require varying amounts of contextual points. For instance, the wheels of a car might be identifiable with a smaller neighborhood than the car's body. This may suggest why an adaptive neighborhood size is helpful in this case." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.689, + 0.62, + 0.705 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.895, + 0.821 + ], + "angle": 0, + "content": "We have presented a novel approach for learning graph topologies, and shown how it obtains state-of-the-art performance across multiple baselines and datasets for trajectory prediction, point cloud classification and node classification. The principal advantage of our approach is that it can be combined with any existing graph convolution layer, under the presence of noisy, incomplete or unavailable edge structures." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.669, + 0.848 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This project was supported by the EPSRC project ROSSINI (EP/S016317/1) and studentship 2327211 (EP/T517616/1)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22548" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.472, + 0.17 + ], + "angle": 0, + "content": "[1] Michael M Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. 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PMLR, 2020." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.895, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22550" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_origin.pdf b/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..67a6b5846280fb48b195849099e4b95cee6e459f --- /dev/null +++ b/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/002465ad-e9c1-4d74-bc7a-fd7e74285b28_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:41b6e8571e03a878cd16c48a03a11dd6dbea486e35d2e635a73f624a29fcdbda +size 1143956 diff --git a/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/full.md b/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8d60a9cdbe114f11ca1bb13acb5ab08a3d30d27e --- /dev/null +++ b/2023/Learning Adaptive Neighborhoods for Graph Neural Networks/full.md @@ -0,0 +1,321 @@ +# Learning Adaptive Neighborhoods for Graph Neural Networks + +Avishkar Saha1, Oscar Mendez1, Chris Russell2, Richard Bowden1 +1Centre for Vision Speech and Signal Processing, University of Surrey, Guildford, UK +2University of Oxford, Oxford, UK + +{a.saha, o.mendez, r.bowden}@surrey.ac.uk, Christopher.m.russell@gmail.com + +# Abstract + +Graph convolutional networks (GCNs) enable end-to-end learning on graph structured data. However, many works assume a given graph structure. When the input graph is noisy or unavailable, one approach is to construct or learn a latent graph structure. These methods typically fix the choice of node degree for the entire graph, which is suboptimal. Instead, we propose a novel end-to-end differentiable graph generator which builds graph topologies where each node selects both its neighborhood and its size. Our module can be readily integrated into existing pipelines involving graph convolution operations, replacing the predetermined or existing adjacency matrix with one that is learned, and optimized, as part of the general objective. As such it is applicable to any GCN. We integrate our module into trajectory prediction, point cloud classification and node classification pipelines resulting in improved accuracy over other structure-learning methods across a wide range of datasets and GCN backbones. We will release the code. + +# 1. Introduction + +The success of Graph Neural Networks (GNNs) [6, 1, 24], has led to a surge in graph-based representation learning. GNNs provide an efficient framework to learn from graph-structured data, making them widely applicable where data can be represented as a relation or interaction system. They have been effectively applied in a wide range of tasks [25], [33] including particle physics [4] and protein science [10]. + +In a GNN, each node iteratively updates its state by interacting with its neighbors, typically through message passing. However, a fundamental limitation of such architectures is the assumption that the underlying graph is provided. While node or edge features may be updated during message passing, the graph topology remains fixed, and its choice may be suboptimal for various reasons. For instance, when classifying nodes on a citation network, an edge connecting nodes of different classes can diminish classification accuracy. These edges can degrade performance by propagating irrelevant + +information across the graph. When no graph is explicitly provided, such domain knowledge can be exploited to learn structures optimized for the task at hand [8, 3, 9, 7]. However, in tasks where knowledge of the optimal graph structure is unknown, one common practice is to generate a $k$ -nearest neighbor ( $k$ -NN) graph. In such cases, $k$ is a hyperparameter and tuned to find the model with the best performance. For many applications, fixing $k$ is overly restrictive as the optimal choice of $k$ may vary for each node in the graph. While there has been an emergence of approaches which learn the graph structure for use in downstream GNNs [43, 13, 15], all of them treat the node degree $k$ as a fixed hyperparameter. + +We propose a general differentiable graph-generator (DGG) module for learning graph topology with or without an initial edge structure. Rather than learning graphs with fixed node degrees $k$ , our module generates local topologies with an adaptive neighborhood size. This module can be placed within any graph convolutional network, and jointly optimized with the rest of the network's parameters, learning topologies which favor the downstream task without hyperparameter selection or indeed any additional training signal. The primary contributions of this paper are as follows: + +1. We propose a novel, differentiable graph-generator (DGG) module which jointly optimizes both the neighborhood size, and the edges that should belong to each neighborhood. Note a key limitation of existing approaches [43, 15, 13, 8, 3, 7, 37] is their inability to learn neighborhood sizes. +2. Our DGG module is directly integrable into any pipeline involving graph convolutions, where either the given adjacency matrix is noisy, or unavailable and must be determined heuristically. In both cases, our DGG generates the adjacency matrix as part of the GNN training and can be trained end-to-end to optimize performance on the downstream task. Should a good graph structure be known, the generated adjacency matrix can be learned to remain close to it while optimizing performance. +3. To demonstrate the power of the approach, we integrate our DGG into a range of SOTA pipelines — without + +modification — across different datasets in trajectory prediction, point cloud classification and node classification and show improvements in model accuracy. + +# 2. Related work + +Graph Representation Learning: GNNs [1] are a broad class of neural architectures for modelling data which can be represented as a set of nodes and relations (edges). Most use message-passing to build node representations by aggregating neighborhood information. A common formulation is the Graph Convolution Network (GCNs) which generalizes the convolution operation to graphs [16, 5, 38, 11]. More recently, the Graph Attention Network (GAT) [35] utilizes a self-attention mechanism to aggregate neighborhood information. However, these works assumed that the underlying graph structure is fixed in advance, with the graph convolutions learning features that describe pre-existing nodes and edges. In contrast, we simultaneously learn the graph structure while using our generated adjacency matrix in downstream graph convolutions. The generated graph topology of our module is jointly optimized alongside other network parameters with feedback signals from the downstream task. + +Graph Structure Learning: In many applications, the optimal graph is unknown, and a graph is constructed before training a GNN. One question to ask is: "Why isn't a fully-connected graph suitable?" Constructing adjacency matrices weighted by distance or even an attention mechanism [35] over a fully-connected graph incorporates many task-irrelevant edges, even if their weights are small. While an attention mechanism can zero these out — i.e., discover a subgraph within the complete graph — discovering this subgraph is challenging given the combinatorial complexity of graphs. A common remedy is to sparsify a complete graph by selecting the $k$ -nearest neighbors ( $k$ -NN). Although this can prevent the propagation of irrelevant information between nodes, the topology of the constructed graph may have no relation to the downstream task. Not only can irrelevant edges still exist, but pairs of relevant nodes may remain unconnected and can lead GCNs to learn representations with poor generalization [43]. + +To overcome this, recent works constructed bespoke frameworks which learn the graph's adjacency matrix for specific tasks. For instance, in human pose estimation, some methods [31, 20] treat the elements of the adjacency matrix as a set of learnable weights. However, as each element is treated as a learnable parameter, the learned adjacency matrix is unlinked to the representation space and can only be used in tasks where there is a known correspondence between training and test nodes. This is not the case for many vision and graph tasks. Others have [15, 7, 17] employed variational inference frameworks to sample the entire adjacency matrix. Franceschi et al. [9] jointly learned the graph structure and the parameters of a GCN by approximately + +solving a bilevel program. NodeFormer [37] and IDGL [3] instead learned latent topologies using multi-head attention [34]. There are two key differences between these methods and ours. First, we simplify optimization by factorizing the adjacency matrix distribution from which we sample the neighborhood for each node, as opposed to sampling the entire matrix. Second, these methods are bespoke frameworks specifically designed for node and graph classification. They leverage knowledge of the task in their loss functions, such as graph smoothness and sparsity [3]. As these methods are tailored to graph-based tasks only, they cannot be dropped into any GCN without modification, limiting their applicability to non-graph tasks like vision. In contrast, our module is both GCN and task-agnostic, and can be integrated into any GCN pipeline and trained using the downstream task loss. + +In contrast to the bespoke frameworks above, recent methods [43, 21, 13] took a more module-based approach similar to ours. As these approaches learned the graph structure entirely from the downstream task loss, there is less domain knowledge to leverage compared to methods constructed for specific tasks. Consequently, sparsity is often induced through a $k$ -NN graph. Here, $k$ is a scalar hyperparameter selected to control the learned graph's node degree. + +Unlike these works, we generate neighborhoods of varying size by learning a distribution over the edges and over the node degree $k$ . Each node samples its top- $k$ neighbors (where $k$ is now a continuous variable), allowing it to individually select its neighborhood and the edges that should belong to it, in a differentiable manner. Additionally, a known 'ideal' graph structure can be used as intermediate supervision to further constrain the latent space. + +# 3. Method + +Here, we provide details of our differentiable graph generation (DGG) module. We begin with notation and the statistical learning framework guiding its design, before describing the module, and how it is combined with graph convolutional backbone architectures. + +Notation We represent a graph of $N$ nodes as $G = (V, E)$ : where $V$ is the set of nodes or vertices, and $E$ the edge set. A graph's structure can be described by its adjacency matrix $A$ , with $a_{ij} = 1$ if an edge connects nodes $i$ and $j$ and $a_{ij} = 0$ otherwise. This binary adjacency matrix $A$ is directed, and potentially asymmetrical. + +Problem definition We reformulate the baseline prediction task based on a fixed graph with an adaptive variant where the graph is learned. Typically, such baseline tasks make learned predictions $Y$ given a set of input features $X$ and a graph structure $A$ of node degree $k$ : + +$$ +Y = Q _ {\phi} (X, A (k)), \tag {1} +$$ + +where $Q_{\phi}$ is an end-to-end neural network parameterized by learnable weights $\phi$ . These formulations require a pre + +![](images/9e86ce1a616f21e37fef8197dde29fc047cd8a0ce363a56fbd2ee6e1b7b80c8e.jpg) +Figure 1. (Left) A typical prediction task using graphs $Y = Q_{\phi}(X, A)$ where $A$ and $k$ are predetermined. (Right) Our reformulation $P(Y|X) \approx \sum_{A} \sum_{k} Q_{\phi}(X, A) Q_{\theta}(A|X, k) Q_{\rho}(k|X)$ which learns a distribution over $A$ and $k$ alongside the downstream task. + +determined graph-structure $A(k)$ , typically based on choice of node degree $k$ , and take $A(k)$ as additional input to the model. In contrast, we learn both $A$ and $k$ in an end-to-end manner, and use them to make predictions $Y$ . As graphs are inherently binary, with edges either present or absent, they are not directly estimizable using gradient descent. Instead, we consider a distribution of graphs, $\mathcal{G}$ , which then induce a distribution of labels, $\mathcal{V}$ , in the downstream task. This distribution takes the factorized form: + +$$ +P (Y | X) = \sum_ {A \in \mathcal {G}} \sum_ {k \in \mathbb {N} ^ {| V |}} Q _ {\phi} (X, A) P (A | X, k) P (k | X), \tag {2} +$$ + +where $P(k|X)$ is the distribution of node degree $k$ given $X$ (i.e., the choice of $k$ in $k - \mathrm{NN}$ ), $P(A|X, k)$ the distribution of graph structures $A$ conditioned on the learned $k$ and input $X$ , and $P(Y|X)$ is the downstream distribution of labels conditioned on data $X$ . For clarity, the adjacency $A$ represents a subgraph of a complete graph over $X$ , and $k$ is a multidimensional variable controlling the number of top- $k$ neighbors for each node individually. To avoid learning individual probabilities for each possible graph $A$ in an exponential state space, we further assume that $P(A|X, k)$ has a factorized distribution where each neighborhood is sampled independently, i.e. $P(A|X, k) = \prod_{i \in V} P(a_i|X, k)$ . + +We model the distributions over adjacencies $A$ and $k$ with tractable functions: + +$$ +P (Y | X) \approx \sum_ {A} \sum_ {k} Q _ {\phi} (X, A) Q _ {\theta} (A | X, k) Q _ {\rho} (k | X), \tag {3} +$$ + +where $Q_{\theta}$ and $Q_{\rho}$ are functions parameterized by $\theta$ and $\rho$ to approximate $P(A|X, k)$ and $P(k|X)$ , respectively. In Fig. 1, we illustrate the functions of our method compared to the typical prediction task in Eq. 1. + +Using this formulation, we train the entire system end-to-end to minimize the expected loss when sampling $Y$ . This can be efficiently performed using stochastic gradient descent. In the forward pass, we first sample a subgraph/set of nodes $X$ from the space of datapoints, and conditioning on $X$ we sample $A$ and compute the associated label $Y$ . When computing the gradient step, we update $Q_{\phi}(X,A)$ as normal and update the distributions using two standard + +![](images/d82569931c8d3a382ededdac190bf12cd83c74fbaa3d5965766e845816f8d177.jpg) +Figure 2. Our differentiable graph-generator (DGG) takes input nodes $\mathbf{X}$ and generates an adjacency matrix $\mathbf{A}$ . It consists of: (1) Degree-estimator: generates samples of $k_{i}$ for each node, (2) Edge-ranker: generates edge samples $\mathbf{e}_i$ for each node and (3) Top-k selector: takes $k_{i}$ and edge samples $\mathbf{e}_i$ and selects top-k elements in a differentiable manner to output a final adjacency $\mathbf{A}$ . + +reparametrization tricks: one for discrete variables [12] such that $Q_{\theta}(A|X, k)$ can generate differentiable graph samples $A'$ , and another for continuous variables [14] of $k'$ drawn from $Q_{\rho}(k|X)$ : + +$$ +P (Y | X) \approx \sum_ {A ^ {\prime}} \sum_ {k ^ {\prime}} Q _ {\phi} \left(X, A ^ {\prime}\right), \tag {4} +$$ + +where $A^{\prime}\sim Q_{\theta}(A|X,k^{\prime})$ and $k^{\prime}\sim Q_{\rho}(k|X)$ + +As both the graph structure $A'$ and variable $k'$ samplers are differentiable, our DGG module can be readily integrated into pipelines involving graph convolutions and jointly trained end-to-end. + +# 3.1. Differentiable Graph Generation + +Our differentiable graph-generator (DGG) takes a set of nodes $V = \{v_{1},\dots,v_{N}\}$ with $d$ -dimensional features $\mathbf{X} \in \mathbb{R}^{N\times d}$ and generates a (potentially) asymmetric adjacency matrix $\mathbf{A} \in \mathbb{R}^{N\times N}$ . This adjacency matrix can be used directly in any downstream graph convolution operation (see Module Instantiation below). As illustrated by Fig. 2, the DGG module consists of four components: + +1. Node encoding: this component projects the input node features $\mathbf{X} \in \mathbb{R}^{N \times d}$ to a latent representation $\hat{\mathbf{X}} \in \mathbb{R}^{N \times d'}$ , which forms the primary representation space of the model. +2. Edge ranking: this takes the latent node features $\hat{\mathbf{X}}\in \mathbb{R}^{N\times d^{\prime}}$ and generates a matrix representing a stochastic ordering of edges $\mathbf{E}\in \mathbb{R}^{N\times N}$ drawn from a learned distribution over the edge-probabilities $(A^{\prime}\sim Q_{\theta}(A|X,k^{\prime})$ from Eq. 4). +3. Degree estimation: this component estimates the number of neighbors each individual node is connected to. It takes as input the latent node features $\hat{\mathbf{X}}\in \mathbb{R}^{N\times d^{\prime}}$ and generates random samples $k\in \mathbb{R}^N$ drawn from a learned distribution over the node degree $(k^{\prime}\sim Q_{\rho}(k|X)$ from Eq. 4). +4. Differentiable top- $k$ edge selector: takes $k$ and the edge-samples $e$ and performs a soft thresholding that probabilistically selects the most important elements, + +based on the output of the Edge-ranking to output an adjacency matrix $\mathbf{A}\in \mathbb{R}^{N\times N}$ + +We now explain these steps in more detail: + +Node encoding We construct a single latent space from the input node features, and use it for edge ranking and degree estimation. We first map input node features $\mathbf{X} \in \mathbb{R}^{N \times d}$ into latent features $\hat{\mathbf{X}} \in \mathbb{R}^{N \times d'}$ using a multi-layer perceptron (MLP) $N_{\phi}$ with weights $\phi$ : $\hat{\mathbf{X}} = N_{\phi}(\mathbf{X})$ . These latent features form the input for the rest of the DGG. Furthermore, they are output by the DGG and passed to the GCN downstream to prevent vanishing gradients. + +Edge ranking The edge ranking returns an implicit distribution of edge orderings, from which we sample the neighborhood for each node. For each node $v_{i}$ , it draws a set of scores $\mathbf{e}_i = \{e_{ij}\}_{j}^N$ quantifying its relevance to all nodes $v_{j} \in V$ including itself. To generate differentiable edge samples $\mathbf{e}_i$ we use the Gumbel-Softmax [12]. + +Before locally scoring each edge embedding $e_{ij} \in \mathbf{e}_i$ for node $v_i$ , we implement a global stage which constructs edge embeddings with both local and global dependencies: + +1. Using latent node features $\hat{\mathbf{x}}_i\in \hat{\mathbf{X}}$ , determine local edge embeddings $\hat{\mathbf{c}}_{ij}\in \mathbb{R}^{d^{\prime}}$ by passing each pair of node features through an MLP $l_{\phi}$ .. $\hat{\mathbf{c}}_{ij} = l_{\phi}(\hat{\mathbf{x}}_i,\hat{\mathbf{x}}_j)$ These embeddings now form a complete graph $\mathcal{G}$ over the nodes, with each edge attributed $\hat{\mathbf{c}}_{ij}$ + +2. As each edge embedding $\hat{\mathbf{c}}_{ij} \in \mathbf{C}$ is calculated independently of the others, we refine it to account for its dependencies to adjacent edges. We do this through edge-to-edge message passing. However, we avoid computing dependencies between all edges of the complete graph for two reasons: first, some edges may not have any common nodes, so passing messages between them could propagate irrelevant information, and secondly, it could be prohibitively expensive. To restrict message-passing between adjacent edges only, we first compute the adjoint graph $\mathcal{H}$ of the complete graph $\mathcal{G}$ . In the adjoint $\mathcal{H}$ , each edge is associated with a node, and two nodes are connected if and only if their corresponding edges in $\mathcal{G}$ have a node in common. The adjoint's adjacency $A^{\mathcal{H}}$ can be calculated using its incidence matrix $L$ , $A^{\mathcal{H}} = L^{T}L - 2I$ . In the adjoint, each node embedding $\hat{\mathbf{c}}_i$ is then updated using an average of its neighboring nodes $\hat{\mathbf{c}}_j$ and passed through an MLP $h_\phi$ : + +$$ +\hat {\mathbf {c}} _ {i} ^ {\prime} = \sum_ {j \in \mathcal {N} (i)} h _ {\phi} \left(\hat {\mathbf {c}} _ {i} \| \mathbf {c} _ {i} - \mathbf {c} _ {j}\right) \tag {5} +$$ + +Having computed edge embeddings $\mathbf{C} \in \mathbb{R}^{N \times N \times d'}$ with global dependencies, we rank these edges for each node. Without loss of generality, we focus on a single node $v_i \in V$ , with latent features $\hat{\mathbf{x}}_i \in \mathbb{R}^d$ . We implement the approximation function $Q_{\theta}(A|X,k)$ of the Edge-ranker as follows: + +1. Using edge embeddings $\hat{\mathbf{c}}_{ij} \in \mathbb{R}^{d'}$ , calculate edge prob + +abilities $\mathbf{p}_i\in \mathbb{R}^N$ for node $v_{i}$ using an MLP $m_{\theta}$ .. + +$$ +\mathbf {p} _ {i} = \left\{m _ {\theta} \left(\hat {\mathbf {c}} _ {i j}\right) | \forall j \in N \right\}. \tag {6} +$$ + +Each element $p_{ij} \in \mathbf{p}_i$ represents a similarity measure between the latent features of node $v_i$ and $v_j$ . In practice, any distance measure can be used here. + +2. Using Gumbel-Softmax over the edge probabilities $\mathbf{p}_i\in \mathbb{R}^N$ , we generate differentiable samples $\mathbf{e}_i\in \mathbb{R}^N$ with Gumbel noise $g$ : + +$$ +\mathbf {e} _ {i} = \left\{\frac {\exp \left(\left(\log \left(p _ {i j}\right) + g _ {i}\right) + \tau\right)}{\sum_ {j} \exp \left(\left(\log \left(p _ {i j}\right) + g _ {i}\right) + \tau\right)} \mid \forall j \in N \right\}, \quad g _ {i} \sim \operatorname {G u m b e l} (0, 1) \tag {7} +$$ + +where $\tau$ is a temperature hyperparameter controlling the interpolation between a discrete one-hot categorical distribution and a continuous categorical density. When $\tau \rightarrow 0$ , the edge energies $e_{ij} \in \mathbf{e}_i$ approach a degenerate distribution. The temperature $\tau$ is important for inducing sparsity, but given the exponential function, this results in a single element in $\mathbf{e}_i$ given much more weighting than the rest, i.e., it approaches a one-hot argmax over $\mathbf{e}_i$ . As we want a variable number of edges to be given higher importance and others to be close to zero, we select a higher temperature and use the top- $k$ selection procedure (detailed below) to induce sparsity. This additionally avoids the high-variance gradients induced by lower temperatures. + +Degree estimation A key limitation of existing graph generation methods [13, 15, 43] is their use of a fixed node degree $k$ across the entire graph. This can be suboptimal as mentioned previously. In our approach, rather than fixing $k$ for the entire graph, we sample it per node from a learned distribution. Focusing on a single node as before, the approximation function $Q_{\rho}(k|X)$ of the Degree-estimator works as follows: + +1. We approximate the distribution of latent node features $\hat{\mathbf{x}}_i\in \mathbb{R}^d$ following a VAE-like formulation [14]. We encode its mean $\pmb {\mu}_i\in \mathbb{R}^d$ and variance $\sigma_{i}\in \mathbb{R}^{d}$ using two MLPs $M_{\rho}$ and $S_{\rho}$ , and then reparametrize with noise $\epsilon$ to obtain latent variable $\mathbf{z}_i\in \mathbb{R}^d$ : + +$$ +\boldsymbol {\mu} _ {i}, \boldsymbol {\sigma} _ {i} = M _ {\rho} (\hat {\mathbf {x}} _ {i}), S _ {\rho} (\hat {\mathbf {x}} _ {i}), \tag {8} +$$ + +$$ +\mathbf {z} _ {i} = \boldsymbol {\mu} _ {i} + \epsilon_ {i} \boldsymbol {\sigma} _ {i}, \epsilon_ {i} \sim \mathcal {N} (0, 1). +$$ + +2. Finally, we concatenate each latent variable $\mathbf{z}_i\in \mathbb{R}^d$ with the L1-norm of the edge samples $\mathbf{h}_i = ||\mathbf{e}_i||_1$ and decode it into a scalar $k_{i}\in \mathbb{R}$ with another MLP $D_{\rho}$ representing a continuous relaxation of the neighborhood size for node $v_{i}$ : + +$$ +k _ {i} = D _ {\rho} \left(\mathbf {z} _ {i}\right) + \mathbf {h} _ {i}. \tag {9} +$$ + +Since $\mathbf{h}_i$ is a summation of a node's edge probabilities, it can be understood as representing an initial estimate of the node degree which is then improved by combining with a second node representation $\mathbf{z}_i$ based entirely on the node's features. Using the edge samples to estimate the node degree links these representation spaces back to the primary latent space of node features $\hat{\mathbf{X}}$ . + +Top- $k$ Edge-Selector Having sampled edge weights, and node degrees $k$ , this function selects the top- $k$ edges for each node. The top- $k$ operation, i.e. finding the indices corresponding to the $k$ largest elements in a set of values, is a piecewise constant function and cannot be directly used in gradient-based optimization. Previous work [40] framed the top- $k$ operation as an optimal transport problem, providing a smoothed top- $k$ approximator. However, as their function is only defined for discrete values of $k$ it cannot be optimized with gradient descent. As an alternative that is differentiable with respect to $k$ , we relax the discrete constraint on $k$ , and instead use it to control the $x$ -axis value of the inflection point on a smoothed-Heaviside function (Fig. 3). For a node $v_{i} \in V$ , of smoothed degree $k_{i} \in \mathbb{R}$ and edges $\mathbf{e}_{i} \in \mathbb{R}^{N}$ , our Top- $k$ Edge Selector outputs an adjacency vector $\mathbf{a}_{i} \in \mathbb{R}^{N}$ where the $k$ largest elements from $\mathbf{e}_{i}$ are close to 1, and the rest close to 0. Focusing on a single node $v_{i}$ as before, the implementation is as follows: + +1. Draw 1D input points $\mathbf{d}_i = \{1,\dots,N\}$ where $N$ is the number of nodes in $V$ . +2. Pass $\mathbf{d}_i$ through a hyperbolic tangent (tanh) which serves as a smooth approximation of the Heaviside function: + +$$ +\mathbf {h} _ {i} = 1 - 0. 5 * \left\{1 + \tanh \left(\lambda^ {- 1} d _ {i} - \lambda^ {- 1} k _ {i}\right) \right\}, \tag {10} +$$ + +here $\lambda > 0$ is a temperature parameter controlling the gradient of the function's inflection point. As $\lambda \to 0$ , the smooth function approaches the Heaviside step function. The first- $k$ values in $\mathbf{h}_i = \{h_{ij}\}_{j}^N$ will now be closer to 1, while the rest closer to 0. + +3. Finally, for each node $i$ we sort its edge-energies $\mathbf{e}_i = \{e_{ij}\}_{j}^{N}$ in descending order, multiply by $\mathbf{h}_i = \{h_{ij}\}_{j}^{N}$ and then restore the original order to obtain the final adjacency vector $\mathbf{a}_i = \{a_{ij}\}_{j}^{N}$ . Stacking $\mathbf{a}_i$ over all nodes $v_i \in V$ creates the final adjacency matrix $\mathbf{A} \in \mathbb{R}^{N \times N}$ . + +Symmetric adjacency matrix If the adjacency matrix $A$ must be symmetric, this can be enforced by replacing it with $A_{sym}$ where: $\mathbf{A}_{sym} = (\mathbf{A} + \mathbf{A}^T) / 2$ . + +Straight through Top- $k$ Edge Selector To make our final adjacency matrix $\mathbf{A} \in \mathbb{R}^{N \times N}$ discrete, we follow the trick used in the Straight-Through Gumbel Softmax [12]: we output the discretized version of $\mathbf{A}$ in the forward pass and the continuous version in the backwards pass. For the discretized version in the forward pass, we replace the smooth-Heaviside function in Eq. 10 with a step function. + +Module Instantiation: The DGG module can be easily combined with any graph convolution operation. A typical graph convolution [16] is defined as follows: $\mathbf{X}' = \hat{\mathbf{D}}^{-1/2} \hat{\mathbf{A}} \hat{\mathbf{D}}^{-1/2} \mathbf{X} \Theta$ . Here, $\hat{\mathbf{A}} = \mathbf{A} + \mathbf{I}$ denotes the adjacency matrix with inserted self-loops, $\hat{\mathbf{D}}$ its diagonal degree matrix and $\Theta$ its weights. To use this graph convolution with the DGG, we simply use our module to generate the adjacency matrix $\hat{\mathbf{A}}$ . + +# 4. Experiments + +We evaluate our DGG on node classification, point cloud classification and trajectory prediction. We chose these tasks as they demonstrate the wide applicability of our module: (1) graphs for node classification require models that can generate edge structures from noisy input graphs, (2) point cloud classification tasks have no input graph structures and (3) trajectory prediction additionally requires models which can handle a variable number of nodes per batch. We compare against state-of-the-art structure learning methods in each domain. As far as we know, our structure-learning approach is the only one that can be easily applied without modification to any GCN pipeline in such a range of tasks. + +# 4.1. Node classification + +Beginning with node classification, we conduct ablations examining the behavior of different parts of the DGG, followed by comparisons to other state-of-the-art structure learning approaches. In the supplementary we include experiments investigating the effect of the DGG on downstream models under the addition of noisy edges to input graphs. We perform these experiments under both transductive and inductive scenarios, as well as semi-supervised and fully-supervised settings. + +Datasets In the transductive setting, we evaluate on three citation benchmark datasets Cora, Citeseer and Pubmed [26] introduced by [41]. In an inductive setting, we evaluate on Reddit [42] and PPI [11]. Further dataset details can be found in the supplementary. Baselines and Implementation As our DGG is a GCN-agnostic module that can be integrated alongside any graph convolution operation, we compare its performance to both other GCN-agnostic approaches and bespoke structure-learning architectures. To compare against other GCN-agnostic methods, we integrate our DGG into four representative GCN backbones: GCN [16], GraphSage [11], GAT [35] and GCNII [2]. On these backbones, we compare against other GCN-agnostic structure learning methods: DropEdge [29], NeuralSparse [43], PTDNet [21]. Then we compare against bespoke architectures IDGL [3], LDS [9], SLAPS [8], NodeFormer [37] and VGCN [7]. To make our comparison fair against these bespoke architectures which learn the structure specifically for node classification, we integrate our DGG into a GCN backbone that is comparable to the bespoke architecture in design. Please see the + +![](images/678a2bd19dc1970d2e5608459adbcd451c2e2fcdc004e529cc504652718eb851.jpg) +Figure 3. The differentiable Top- $k$ Edge Selector. This component uses the node degree $k_{i}$ output by the Degree Estimator to control the inflection point on a smooth-Heaviside function and uses it to select the top edges from $\mathbf{e}_i$ output by the Edge Ranker. This produces an adjacency vector $\mathbf{a}_i$ for each node, and stacking $\mathbf{a}_i$ across all nodes produces the final adjacency matrix $\mathbf{A}$ . + +supplementary for implementation details. + +Training details A node classification model partitions the latent space of node embeddings into separate classes. However, when message-passing, there is one phenomenon of the input graph that can limit classification accuracy: two nodes with different classes but similar features and an edge connecting them. Classifying these nodes is challenging as their feature similarity can be compounded by passing messages between them. The goal of the DGG is to move such nodes apart in the latent space such that there is no edge and communication between them. However, traversing the loss landscape from the initial random initialization of the network to one where the model is able to discriminate between these nodes can take several iterations using only the downstream classification loss. To speed up training, we add an intermediate loss to further partition the latent space. We do this by supervising the adjacency matrix generated by the DGG to remove all edges between classes and only maintain those within a class. We then anneal this loss over the training cycle, eventually leaving only the downstream classification loss. We provide more details in the supplementary. + +# 4.1.1 Ablations + +In Table 1, we explore the effect of disabling different components of our DGG module when integrated into a GCN [16] for node classification: 1. DGG without Degree Estimation and Differentiable Top-k Edge Selection — we remove the Degree Estimator and instead fix $k$ to select the top-k stochastically ordered edges. 2. DGG with deterministic Edge Ranking — we remove the noise in Eq. 7 of the Edge Ranker. 3. DGG with deterministic Degree Estimation — we remove the noise in Eq. 8 of the Degree Estimator. We perform these on Cora [41] and omit the annealed intermediate loss during training. + +Table 1 shows the benefit of learning a distribution over the node degree. When learning it deterministically, the accuracy decreases by $0.5\%$ . This becomes significantly worse when the node degree is fixed for the entire graph + +Table 1. Ablation study. DGG integrated into a GCN for node classification on Cora [41]. + +
ModelAccuracy
Fixed node degree, k = {1, 5, 10, 100}{49.7, 78.9, 55.0, 37.0}
With deterministic Edge Ranking and Degree Estimation82.4
With deterministic Edge Ranking82.7
With deterministic Degree Estimation82.8
DGG83.2
+ +rather than learned per node. Note also, the sensitivity with respect to choice of $k$ . A fixed node degree of $k = 10$ or $k = 1$ reduces accuracy by almost $30\%$ vs a graph of 5. This is due to the graph convolution operation: as it has no adaptive weighting mechanism for a node's neighborhood, each of the neighbors is given the same weight. Naturally, this leads to information sharing between unrelated nodes, reducing the quality of node representation after message-passing. In contrast, by learning a distribution over the node degree we are able to select only the most relevant neighbors, even though these are then weighted equally in the graph convolution. Finally, the inclusion of noise in any of the DGG components does increase accuracy, but only by approximately $0.5\%$ — demonstrating both its benefit and the robustness of the DGG without it. + +# 4.1.2 Results + +Comparison to GCN-agnostic modules In Table 2 we compare against GCN-agnostic structure learning methods. For fair comparison, we present two versions of our method: DGG-wl trained with the downstream loss only and DGG* trained with both the downstream and intermediate loss. + +DGG improves performance across all baselines and datasets. Against other approaches, DGG-wl generally outperforms the state-of-the-art NeuralSparse and PTDNet-wl (both trained with only the downstream loss). This can be attributed to our method for modelling sparsity, which explicitly lets each node to select the size of its neighborhood based on the downstream training signal. This training signal helps partition the node representation space, while the estimated node-degree additionally prevents communication + +Table 2. Semi-supervised node classification compared to other architecture agnostic SOTA structure learning methods. We compare against prior methods reported in [21, 43, 2], using the official results where available. Those with ' -' have no official results or we ran into out-of-memory errors. + +
BackboneMethodCoraCiteseerPubmedRedditPPI
GCNOriginal81.170.379.092.253.2
DropEdge80.972.278.596.154.8
NeuralSparse82.171.578.896.665.1
PTDNet-wl82.471.779.1-75.2
DGG-wl83.272.680.296.877.1
PTDNet-wl + low rank82.872.779.8-80.3
DGG*84.174.984.097.381.6
GraphSageOriginal79.267.676.793.861.8
NeuralSparse79.367.475.196.762.6
PTDNet-wl79.467.877.0-64.5
DGG-wl79.468.277.696.665.3
PTDNet-wl + low rank80.367.977.1-64.8
DGG*80.570.880.296.967.3
GATOriginal83.072.179.0-97.3
DropEdge83.270.977.9-85.1
NeuralSparse83.472.478.0-92.1
PTDNet-wl83.772.379.2-97.8
DGG-wl84.673.279.7-97.4
PTDNet-wl + low rank84.473.779.3-98.0
DGG*85.376.482.0-97.6
GCNIIOriginal85.373.280.2-99.5
DropEdge84.973.479.4-99.0
DGG-wl86.974.581.5-99.6
DGG*87.875.781.9-99.7
+ +between distant nodes. Although PTDNet-wl does this implicitly through its attention mechanism, discovering this sparse subgraph of the input graph is challenging given its complexity. NeuralSparse on the other hand selects $k$ for its entire generated subgraph, which is both suboptimal and requires additional hyperparameter tuning. + +Table 3. Adjacency matrix constraints: our intermediate annealed loss vs. PTDNet's low rank regularizer [21] for semi-supervised node classification with a GCN backbone. + +
MethodCoraCiteseerPubmedPPI
DGG-wl86.874.481.299.5
DGG-wl + low rank87.175.381.499.5
DGG-wl + int. loss (aka DGG*)87.775.881.999.7
DGG-wl + int. loss + low rank87.876.282.199.7
+ +Comparing methods which enforce additional constraints on the adjacency matrix, DGG* demonstrates larger accuracy gains than PTDNet*. PTDNet* regularizes its adjacency matrix to be of low-rank, as previous work [30] has shown that the rank of an adjacency matrix can reflect the number of clusters. This regularizer reasons about the graph's topology globally. While this may aid generalization, the accuracy difference may then be attributed to our intermediate loss providing stronger signals to discriminate between nodes with similar features but different classes (and therefore remove the edges between them). Furthermore, their regularizer uses the sum of the top- $k$ singular values during training, where $k$ again is a hyperparameter tuned to each dataset individually. Our method requires no additional parameters to be chosen. + +Finally in Table 3 we compare the low-rank constraint of PTDNet with our intermediate annealed loss. Our interme + +Table 4. Node classification results against bespoke SOTA architectures which learn the graph structure. + +
ModelCoraCiteseer
Setting 1IDGL [3]84.574.1
originalDGG* + GAT85.476.4
Setting 2LDS [9]71.573.3
Input graph = noneSLAPS [8]74.273.1
train split = {train + 1/2 val}DGG* + GCN82.474.0
Setting 3NodeFormer [37]88.776.2
split = 0.5/0.25/0.25DGG* + GAT90.177.8
Setting 4VGCN [7]85.976.5
train split = {train + 1/2 val}DGG* + GAT87.677.1
+ +Table 5. ADE/FDE on the ETH & UCY datasets using SocialSTGCNN (first table), and Stanford Drone Dataset (SDD) using DAGNet (second table). For DGM [13], $k = 2$ for both datasets. + +
DatasetOriginalDGM [13] Gain (%)DGG Gain (%)
ADE↓FDE ↓ADE ↑FDE↑ADE ↑FDE ↑
ETH0.641.112.4%6.4%7.8%21.4%
Hotel0.490.8514.2%18.9%22.7%37.5%
Univ0.440.796.2%3.5%11.8%14.9%
Zara10.340.533.8%13.7%7.7%23.8%
Zara20.300.485.0%5.0%12.8%17.3%
Mean0.440.756.3%10.6%12.6%23.0%
SDD0.531.041.9%3.0%10.9%9.5%
+ +diate loss ('DGG-wl + int. loss') outperforms the low-rank constraint ('DGG-wl + low rank'). However, using both constraints ('DGG-wl + int. loss + low rank') increases classification accuracy further, suggesting the edges removed by both methods are complementary. + +Comparison with bespoke architectures In Table 4 we compare against bespoke architectures specifically designed for node classification. As each of these methods uses different experiment settings, we train our DGG-integrated architecture separately for each. See the supplementary for details on each setting and reasons for our choice of backbone. Our performance gains here can generally be attributed to factors: (1) our intermediate loss on the adjacency matrix and (2) our adjacency matrix factorizations where we learn the neighborhood for each node. Our intermediate loss particularly benefits from the experimental settings adopted by the other methods as they use larger training splits involving half the validation graph. Additionally, constructing the adjacency matrix by learning nodewise neighborhoods restricts the graph search space, making optimization easier. However, we note that some of these other methods are designed for node-classification on graphs which are orders of magnitude larger than Cora and Citeseer. In such cases, factorizing the adjacency per node, as we do, may be unfeasible. + +# 4.2. Trajectory prediction + +We evaluate on trajectory prediction tasks as these have neither an input or ground truth graph structure, thus the ideal structure has to be generated entirely from the data. We + +Table 6. ADE/FDE metrics on the SportVU Basketball dataset using DAGNet. For DGM [13], $k = 3$ . + +
SplitTeamOriginalDGM [13] Gain (%)DGG Gain (%)
ADEFDEADEFDEADEFDE
10-40ATK2.744.29-0.4%-0.2%6.7%5.1%
DEF2.092.97-0.5%-0.1%9.7%6.4%
20-30ATK2.033.980.1%0.1%7.2%8.2%
DEF1.533.070.2%0.3%21.4%19.1%
40-10ATK0.811.711.3%0.9%15.5%17.0%
DEF0.721.490.8%0.8%10.9%16.2%
Mean—1.652.920.3%0.3%11.9%12.0%
+ +consider four datasets covering a range of scenarios from basketball to crowded urban environments. On each, we integrate our DGG into a SOTA GCN trajectory prediction pipeline and compare results to another task-agnostic structure learning approach, DGM [13]. + +Datasets We evaluate on four trajectory prediction benchmarks. 1. ETH [27] and UCY [18] — 5 subsets of widely used real-world pedestrian trajectories. 2. STATS SportVU [32] — multiple NBA seasons tracking trajectories of basketball players over a game. Stanford Drone Dataset (SDD) [28] — top-down scenes across multiple areas at Stanford University. Further details on these datasets can be found in the supplementary. Baselines and Implementation We integrate our DGG module into two state-of-the-art trajectory prediction pipelines: Social-STGCNN [22] and DAGNet [23]. Our DGG is placed within both networks to generate the adjacency matrix on the fly and forms part of its forward and backward pass. Please see the supplementary for implementation details. Evaluation metrics. Model performance is measured with Average Displacement Error (ADE) and Final Displacement Error (FDE). ADE measures the average Euclidean distance along the entire predicted trajectory, while the FDE is that of the last timestep only. + +Results In Table 5, the integration of our DGG into Social-STGCNN reduces ADE/FDE compared to both the baseline and the integration of DGM. In Table 5 and 6 we demonstrate similar gains over DGM when integrated into DAGNet. First, this shows the benefit of inducing sparsity when message-passing over a distance weighted adjacency matrix like Social-STGCNN or even an attention-mechanism like DAGNet. The larger error reduction of our DGG compared to DGM may be attributed to DGM's use of a fixed node-degree $k$ across its learned graph. While this can prevent the propagation of irrelevant information across the graph in some cases, in others it might limit the context available to certain nodes. We provide qualitative analysis in the supplementary. + +# 4.3. Point Cloud Classification + +We evaluate on another vision task of point cloud classification for models which use GCNs. This task differs from the previous two as predictions are made for the entire graph as opposed to node-wise. As with our trajectory prediction experiments, we integrate our DGG into SOTA classification + +Table 7. Point Cloud classification on ModelNet40 with our module and DGM [13] integrated into two different point cloud labelling architectures. + +
BaselineMethodMean degreeS.D. degreeAccuracy
ResGCN [19]Original9093.3
DGM [13]20093.5
DGG14.87.494.4
DGCNN [36]Original40092.9
DGM [13]20093.3
DGG19.35.293.8
+ +architectures and compare against the other task-agnostic graph-learning module DGM [13]. + +Datasets We evaluate on ModelNet40 [39], consisting of CAD models for a variety of object categories. Baselines and Implementation We integrate our DGG into a SOTA ResGCN [19] and DGCNN [36]. Both models use a $k$ -NN sampling scheme to construct its graph. We simply replace this sampler with our DGG and keep the rest of the network and training protocol the same. + +Results Our results in Table 7 demonstrate the benefits of learning an adaptive neighborhood size across the latent graph. DGM [13] learns a fully-connected latent graph and then imposes a fixed node degree of $k = 20$ across it (i.e. selecting the top 20 neighbors for each node). This marginally improves upon the baselines ResGCN [19] and DGCNN[36], which both also used fixed node-degrees $k$ . In contrast, we learn a distribution over the node degree from which we sample each node's neighborhood size. As shown in Table 7, the node degree varies in our models with a standard deviation of around 5-7 across both baselines. Our accuracy gains over the baseline and DGM can be attributed to this variance in neighborhood sizes across the graph. These gains can be understood when viewing an input point cloud as a composition of object parts. Building semantic representations for different parts may naturally require varying amounts of contextual points. For instance, the wheels of a car might be identifiable with a smaller neighborhood than the car's body. This may suggest why an adaptive neighborhood size is helpful in this case. + +# 5. Conclusion + +We have presented a novel approach for learning graph topologies, and shown how it obtains state-of-the-art performance across multiple baselines and datasets for trajectory prediction, point cloud classification and node classification. The principal advantage of our approach is that it can be combined with any existing graph convolution layer, under the presence of noisy, incomplete or unavailable edge structures. + +# Acknowledgements + +This project was supported by the EPSRC project ROSSINI (EP/S016317/1) and studentship 2327211 (EP/T517616/1). + +# References + +[1] Michael M Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. Geometric deep learning: going beyond euclidean data. IEEE Signal Processing Magazine, 34(4):18-42, 2017. +[2] Ming Chen, Zhewei Wei, Zengfeng Huang, Bolin Ding, and Yaliang Li. Simple and deep graph convolutional networks. In International Conference on Machine Learning, pages 1725-1735. PMLR, 2020. +[3] Yu Chen, Lingfei Wu, and Mohammed Zaki. Iterative deep graph learning for graph neural networks: Better and robust node embeddings. 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However, many works assume a given graph structure. When the input graph is noisy or unavailable, one approach is to construct or learn a latent graph structure. These methods typically fix the choice of node degree for the entire graph, which is suboptimal. Instead, we propose a novel end-to-end differentiable graph generator which builds graph topologies where each node selects both its neighborhood and its size. Our module can be readily integrated into existing pipelines involving graph convolution operations, replacing the predetermined or existing adjacency matrix with one that is learned, and optimized, as part of the general objective. As such it is applicable to any GCN. We integrate our module into trajectory prediction, point cloud classification and node classification pipelines resulting in improved accuracy over other structure-learning methods across a wide range of datasets and GCN backbones. We will release the code." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 490, + 128, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 128, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 128, + 502 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 510, + 288, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 594 + ], + "type": "text", + "content": "The success of Graph Neural Networks (GNNs) [6, 1, 24], has led to a surge in graph-based representation learning. GNNs provide an efficient framework to learn from graph-structured data, making them widely applicable where data can be represented as a relation or interaction system. They have been effectively applied in a wide range of tasks [25], [33] including particle physics [4] and protein science [10]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 290, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 290, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 290, + 714 + ], + "type": "text", + "content": "In a GNN, each node iteratively updates its state by interacting with its neighbors, typically through message passing. However, a fundamental limitation of such architectures is the assumption that the underlying graph is provided. While node or edge features may be updated during message passing, the graph topology remains fixed, and its choice may be suboptimal for various reasons. For instance, when classifying nodes on a citation network, an edge connecting nodes of different classes can diminish classification accuracy. These edges can degrade performance by propagating irrelevant" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "text", + "content": "information across the graph. When no graph is explicitly provided, such domain knowledge can be exploited to learn structures optimized for the task at hand [8, 3, 9, 7]. However, in tasks where knowledge of the optimal graph structure is unknown, one common practice is to generate a " + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "text", + "content": "-nearest neighbor (" + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "text", + "content": "-NN) graph. In such cases, " + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "text", + "content": " is a hyperparameter and tuned to find the model with the best performance. For many applications, fixing " + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "text", + "content": " is overly restrictive as the optimal choice of " + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "text", + "content": " may vary for each node in the graph. While there has been an emergence of approaches which learn the graph structure for use in downstream GNNs [43, 13, 15], all of them treat the node degree " + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 228, + 548, + 372 + ], + "type": "text", + "content": " as a fixed hyperparameter." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 375, + 548, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 548, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 548, + 495 + ], + "type": "text", + "content": "We propose a general differentiable graph-generator (DGG) module for learning graph topology with or without an initial edge structure. Rather than learning graphs with fixed node degrees " + }, + { + "bbox": [ + 304, + 375, + 548, + 495 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 375, + 548, + 495 + ], + "type": "text", + "content": ", our module generates local topologies with an adaptive neighborhood size. This module can be placed within any graph convolutional network, and jointly optimized with the rest of the network's parameters, learning topologies which favor the downstream task without hyperparameter selection or indeed any additional training signal. The primary contributions of this paper are as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 498, + 548, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 313, + 498, + 547, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 547, + 569 + ], + "type": "text", + "content": "1. We propose a novel, differentiable graph-generator (DGG) module which jointly optimizes both the neighborhood size, and the edges that should belong to each neighborhood. Note a key limitation of existing approaches [43, 15, 13, 8, 3, 7, 37] is their inability to learn neighborhood sizes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 570, + 548, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 570, + 548, + 688 + ], + "spans": [ + { + "bbox": [ + 313, + 570, + 548, + 688 + ], + "type": "text", + "content": "2. Our DGG module is directly integrable into any pipeline involving graph convolutions, where either the given adjacency matrix is noisy, or unavailable and must be determined heuristically. In both cases, our DGG generates the adjacency matrix as part of the GNN training and can be trained end-to-end to optimize performance on the downstream task. Should a good graph structure be known, the generated adjacency matrix can be learned to remain close to it while optimizing performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 689, + 547, + 714 + ], + "type": "text", + "content": "3. To demonstrate the power of the approach, we integrate our DGG into a range of SOTA pipelines — without" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22541" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 66, + 72, + 288, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 72, + 288, + 109 + ], + "spans": [ + { + "bbox": [ + 66, + 72, + 288, + 109 + ], + "type": "text", + "content": "modification — across different datasets in trajectory prediction, point cloud classification and node classification and show improvements in model accuracy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 119, + 132, + 132 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 119, + 132, + 132 + ], + "spans": [ + { + "bbox": [ + 47, + 119, + 132, + 132 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 140, + 289, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 289, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 289, + 342 + ], + "type": "text", + "content": "Graph Representation Learning: GNNs [1] are a broad class of neural architectures for modelling data which can be represented as a set of nodes and relations (edges). Most use message-passing to build node representations by aggregating neighborhood information. A common formulation is the Graph Convolution Network (GCNs) which generalizes the convolution operation to graphs [16, 5, 38, 11]. More recently, the Graph Attention Network (GAT) [35] utilizes a self-attention mechanism to aggregate neighborhood information. However, these works assumed that the underlying graph structure is fixed in advance, with the graph convolutions learning features that describe pre-existing nodes and edges. In contrast, we simultaneously learn the graph structure while using our generated adjacency matrix in downstream graph convolutions. The generated graph topology of our module is jointly optimized alongside other network parameters with feedback signals from the downstream task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 343, + 289, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 343, + 289, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 343, + 289, + 558 + ], + "type": "text", + "content": "Graph Structure Learning: In many applications, the optimal graph is unknown, and a graph is constructed before training a GNN. One question to ask is: \"Why isn't a fully-connected graph suitable?\" Constructing adjacency matrices weighted by distance or even an attention mechanism [35] over a fully-connected graph incorporates many task-irrelevant edges, even if their weights are small. While an attention mechanism can zero these out — i.e., discover a subgraph within the complete graph — discovering this subgraph is challenging given the combinatorial complexity of graphs. A common remedy is to sparsify a complete graph by selecting the " + }, + { + "bbox": [ + 47, + 343, + 289, + 558 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 343, + 289, + 558 + ], + "type": "text", + "content": "-nearest neighbors (" + }, + { + "bbox": [ + 47, + 343, + 289, + 558 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 343, + 289, + 558 + ], + "type": "text", + "content": "-NN). Although this can prevent the propagation of irrelevant information between nodes, the topology of the constructed graph may have no relation to the downstream task. Not only can irrelevant edges still exist, but pairs of relevant nodes may remain unconnected and can lead GCNs to learn representations with poor generalization [43]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 559, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 289, + 714 + ], + "type": "text", + "content": "To overcome this, recent works constructed bespoke frameworks which learn the graph's adjacency matrix for specific tasks. For instance, in human pose estimation, some methods [31, 20] treat the elements of the adjacency matrix as a set of learnable weights. However, as each element is treated as a learnable parameter, the learned adjacency matrix is unlinked to the representation space and can only be used in tasks where there is a known correspondence between training and test nodes. This is not the case for many vision and graph tasks. Others have [15, 7, 17] employed variational inference frameworks to sample the entire adjacency matrix. Franceschi et al. [9] jointly learned the graph structure and the parameters of a GCN by approximately" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 251 + ], + "type": "text", + "content": "solving a bilevel program. NodeFormer [37] and IDGL [3] instead learned latent topologies using multi-head attention [34]. There are two key differences between these methods and ours. First, we simplify optimization by factorizing the adjacency matrix distribution from which we sample the neighborhood for each node, as opposed to sampling the entire matrix. Second, these methods are bespoke frameworks specifically designed for node and graph classification. They leverage knowledge of the task in their loss functions, such as graph smoothness and sparsity [3]. As these methods are tailored to graph-based tasks only, they cannot be dropped into any GCN without modification, limiting their applicability to non-graph tasks like vision. In contrast, our module is both GCN and task-agnostic, and can be integrated into any GCN pipeline and trained using the downstream task loss." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 252, + 547, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 547, + 346 + ], + "type": "text", + "content": "In contrast to the bespoke frameworks above, recent methods [43, 21, 13] took a more module-based approach similar to ours. As these approaches learned the graph structure entirely from the downstream task loss, there is less domain knowledge to leverage compared to methods constructed for specific tasks. Consequently, sparsity is often induced through a " + }, + { + "bbox": [ + 304, + 252, + 547, + 346 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 252, + 547, + 346 + ], + "type": "text", + "content": "-NN graph. Here, " + }, + { + "bbox": [ + 304, + 252, + 547, + 346 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 252, + 547, + 346 + ], + "type": "text", + "content": " is a scalar hyperparameter selected to control the learned graph's node degree." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "text", + "content": "Unlike these works, we generate neighborhoods of varying size by learning a distribution over the edges and over the node degree " + }, + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "text", + "content": ". Each node samples its top-" + }, + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "text", + "content": " neighbors (where " + }, + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "text", + "content": " is now a continuous variable), allowing it to individually select its neighborhood and the edges that should belong to it, in a differentiable manner. Additionally, a known 'ideal' graph structure can be used as intermediate supervision to further constrain the latent space." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 453, + 362, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 453, + 362, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 453, + 362, + 464 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 472, + 547, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 531 + ], + "type": "text", + "content": "Here, we provide details of our differentiable graph generation (DGG) module. We begin with notation and the statistical learning framework guiding its design, before describing the module, and how it is combined with graph convolutional backbone architectures." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": "Notation We represent a graph of " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": " nodes as " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "G = (V, E)" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": ": where " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": " is the set of nodes or vertices, and " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": " the edge set. A graph's structure can be described by its adjacency matrix " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "a_{ij} = 1" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": " if an edge connects nodes " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "a_{ij} = 0" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": " otherwise. This binary adjacency matrix " + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 532, + 547, + 604 + ], + "type": "text", + "content": " is directed, and potentially asymmetrical." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "text", + "content": "Problem definition We reformulate the baseline prediction task based on a fixed graph with an adaptive variant where the graph is learned. Typically, such baseline tasks make learned predictions " + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "text", + "content": " given a set of input features " + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "text", + "content": " and a graph structure " + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "text", + "content": " of node degree " + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 604, + 547, + 664 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 384, + 670, + 547, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 670, + 547, + 685 + ], + "spans": [ + { + "bbox": [ + 384, + 670, + 547, + 685 + ], + "type": "interline_equation", + "content": "Y = Q _ {\\phi} (X, A (k)), \\tag {1}", + "image_path": "c4ce1baef40872a69c45732b9dc0164a9b21a6928d5d7931a0f538fe106d289c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 547, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 689, + 547, + 714 + ], + "type": "inline_equation", + "content": "Q_{\\phi}" + }, + { + "bbox": [ + 304, + 689, + 547, + 714 + ], + "type": "text", + "content": " is an end-to-end neural network parameterized by learnable weights " + }, + { + "bbox": [ + 304, + 689, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 689, + 547, + 714 + ], + "type": "text", + "content": ". These formulations require a pre" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22542" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 289, + 139 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 289, + 139 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 289, + 139 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 289, + 139 + ], + "type": "image", + "image_path": "9e86ce1a616f21e37fef8197dde29fc047cd8a0ce363a56fbd2ee6e1b7b80c8e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "lines": [ + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "text", + "content": "Figure 1. (Left) A typical prediction task using graphs " + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "inline_equation", + "content": "Y = Q_{\\phi}(X, A)" + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "text", + "content": " are predetermined. (Right) Our reformulation " + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "inline_equation", + "content": "P(Y|X) \\approx \\sum_{A} \\sum_{k} Q_{\\phi}(X, A) Q_{\\theta}(A|X, k) Q_{\\rho}(k|X)" + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "text", + "content": " which learns a distribution over " + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 140, + 289, + 196 + ], + "type": "text", + "content": " alongside the downstream task." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": "determined graph-structure " + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "inline_equation", + "content": "A(k)" + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": ", typically based on choice of node degree " + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": ", and take " + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "inline_equation", + "content": "A(k)" + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": " as additional input to the model. In contrast, we learn both " + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": " in an end-to-end manner, and use them to make predictions " + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": ". As graphs are inherently binary, with edges either present or absent, they are not directly estimizable using gradient descent. Instead, we consider a distribution of graphs, " + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": ", which then induce a distribution of labels, " + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 213, + 290, + 321 + ], + "type": "text", + "content": ", in the downstream task. This distribution takes the factorized form:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 327, + 288, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 327, + 288, + 354 + ], + "spans": [ + { + "bbox": [ + 52, + 327, + 288, + 354 + ], + "type": "interline_equation", + "content": "P (Y | X) = \\sum_ {A \\in \\mathcal {G}} \\sum_ {k \\in \\mathbb {N} ^ {| V |}} Q _ {\\phi} (X, A) P (A | X, k) P (k | X), \\tag {2}", + "image_path": "3c66b6fa99240c531379f1fd938f508ba36091609b4cef7262d1b9ac2dfc0758.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "P(k|X)" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " is the distribution of node degree " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " (i.e., the choice of " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "k - \\mathrm{NN}" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "P(A|X, k)" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " the distribution of graph structures " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " conditioned on the learned " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " and input " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "P(Y|X)" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " is the downstream distribution of labels conditioned on data " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": ". For clarity, the adjacency " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " represents a subgraph of a complete graph over " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " is a multidimensional variable controlling the number of top- " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " neighbors for each node individually. To avoid learning individual probabilities for each possible graph " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " in an exponential state space, we further assume that " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "P(A|X, k)" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": " has a factorized distribution where each neighborhood is sampled independently, i.e. " + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "inline_equation", + "content": "P(A|X, k) = \\prod_{i \\in V} P(a_i|X, k)" + }, + { + "bbox": [ + 46, + 362, + 288, + 506 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 506, + 288, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 288, + 529 + ], + "type": "text", + "content": "We model the distributions over adjacencies " + }, + { + "bbox": [ + 47, + 506, + 288, + 529 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 506, + 288, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 506, + 288, + 529 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 506, + 288, + 529 + ], + "type": "text", + "content": " with tractable functions:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 536, + 289, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 536, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 55, + 536, + 289, + 563 + ], + "type": "interline_equation", + "content": "P (Y | X) \\approx \\sum_ {A} \\sum_ {k} Q _ {\\phi} (X, A) Q _ {\\theta} (A | X, k) Q _ {\\rho} (k | X), \\tag {3}", + "image_path": "aa04bc2963068b9cb7695c20b96fcdeaf1680247cb9aa48b431cacb2cf05cfce.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "inline_equation", + "content": "Q_{\\theta}" + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "inline_equation", + "content": "Q_{\\rho}" + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "text", + "content": " are functions parameterized by " + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "text", + "content": " to approximate " + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "inline_equation", + "content": "P(A|X, k)" + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "inline_equation", + "content": "P(k|X)" + }, + { + "bbox": [ + 46, + 570, + 289, + 617 + ], + "type": "text", + "content": ", respectively. In Fig. 1, we illustrate the functions of our method compared to the typical prediction task in Eq. 1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "text", + "content": "Using this formulation, we train the entire system end-to-end to minimize the expected loss when sampling " + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "text", + "content": ". This can be efficiently performed using stochastic gradient descent. In the forward pass, we first sample a subgraph/set of nodes " + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "text", + "content": " from the space of datapoints, and conditioning on " + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "text", + "content": " we sample " + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "text", + "content": " and compute the associated label " + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "text", + "content": ". When computing the gradient step, we update " + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "inline_equation", + "content": "Q_{\\phi}(X,A)" + }, + { + "bbox": [ + 46, + 618, + 290, + 714 + ], + "type": "text", + "content": " as normal and update the distributions using two standard" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 541, + 141 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 541, + 141 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 541, + 141 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 541, + 141 + ], + "type": "image", + "image_path": "d82569931c8d3a382ededdac190bf12cd83c74fbaa3d5965766e845816f8d177.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "lines": [ + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "text", + "content": "Figure 2. Our differentiable graph-generator (DGG) takes input nodes " + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "text", + "content": " and generates an adjacency matrix " + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "text", + "content": ". It consists of: (1) Degree-estimator: generates samples of " + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "text", + "content": " for each node, (2) Edge-ranker: generates edge samples " + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "text", + "content": " for each node and (3) Top-k selector: takes " + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "text", + "content": " and edge samples " + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "text", + "content": " and selects top-k elements in a differentiable manner to output a final adjacency " + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 144, + 547, + 211 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "text", + "content": "reparametrization tricks: one for discrete variables [12] such that " + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "inline_equation", + "content": "Q_{\\theta}(A|X, k)" + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "text", + "content": " can generate differentiable graph samples " + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "text", + "content": ", and another for continuous variables [14] of " + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "inline_equation", + "content": "k'" + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "text", + "content": " drawn from " + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "inline_equation", + "content": "Q_{\\rho}(k|X)" + }, + { + "bbox": [ + 304, + 230, + 547, + 278 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 388, + 288, + 546, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 288, + 546, + 315 + ], + "spans": [ + { + "bbox": [ + 388, + 288, + 546, + 315 + ], + "type": "interline_equation", + "content": "P (Y | X) \\approx \\sum_ {A ^ {\\prime}} \\sum_ {k ^ {\\prime}} Q _ {\\phi} \\left(X, A ^ {\\prime}\\right), \\tag {4}", + "image_path": "dd52fb4cd39591affa14c3feca74e4f3d84c728d2390d25786d450fd6a40310c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 332, + 316, + 518, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 316, + 518, + 330 + ], + "spans": [ + { + "bbox": [ + 332, + 316, + 518, + 330 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 332, + 316, + 518, + 330 + ], + "type": "inline_equation", + "content": "A^{\\prime}\\sim Q_{\\theta}(A|X,k^{\\prime})" + }, + { + "bbox": [ + 332, + 316, + 518, + 330 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 332, + 316, + 518, + 330 + ], + "type": "inline_equation", + "content": "k^{\\prime}\\sim Q_{\\rho}(k|X)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 339, + 547, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 547, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 547, + 386 + ], + "type": "text", + "content": "As both the graph structure " + }, + { + "bbox": [ + 304, + 339, + 547, + 386 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 304, + 339, + 547, + 386 + ], + "type": "text", + "content": " and variable " + }, + { + "bbox": [ + 304, + 339, + 547, + 386 + ], + "type": "inline_equation", + "content": "k'" + }, + { + "bbox": [ + 304, + 339, + 547, + 386 + ], + "type": "text", + "content": " samplers are differentiable, our DGG module can be readily integrated into pipelines involving graph convolutions and jointly trained end-to-end." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 395, + 484, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 395, + 484, + 408 + ], + "spans": [ + { + "bbox": [ + 306, + 395, + 484, + 408 + ], + "type": "text", + "content": "3.1. Differentiable Graph Generation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "text", + "content": "Our differentiable graph-generator (DGG) takes a set of nodes " + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "inline_equation", + "content": "V = \\{v_{1},\\dots,v_{N}\\}" + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "text", + "content": "-dimensional features " + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N\\times d}" + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "text", + "content": " and generates a (potentially) asymmetric adjacency matrix " + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 304, + 414, + 547, + 497 + ], + "type": "text", + "content": ". This adjacency matrix can be used directly in any downstream graph convolution operation (see Module Instantiation below). As illustrated by Fig. 2, the DGG module consists of four components:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 498, + 547, + 713 + ], + "type": "list", + "angle": 0, + "index": 21, + "blocks": [ + { + "bbox": [ + 313, + 498, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 498, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 313, + 498, + 547, + 545 + ], + "type": "text", + "content": "1. Node encoding: this component projects the input node features " + }, + { + "bbox": [ + 313, + 498, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 313, + 498, + 547, + 545 + ], + "type": "text", + "content": " to a latent representation " + }, + { + "bbox": [ + 313, + 498, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}} \\in \\mathbb{R}^{N \\times d'}" + }, + { + "bbox": [ + 313, + 498, + 547, + 545 + ], + "type": "text", + "content": ", which forms the primary representation space of the model." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "type": "text", + "content": "2. Edge ranking: this takes the latent node features " + }, + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}}\\in \\mathbb{R}^{N\\times d^{\\prime}}" + }, + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "type": "text", + "content": " and generates a matrix representing a stochastic ordering of edges " + }, + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{E}\\in \\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "type": "text", + "content": " drawn from a learned distribution over the edge-probabilities " + }, + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "type": "inline_equation", + "content": "(A^{\\prime}\\sim Q_{\\theta}(A|X,k^{\\prime})" + }, + { + "bbox": [ + 313, + 546, + 547, + 605 + ], + "type": "text", + "content": " from Eq. 4)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "type": "text", + "content": "3. Degree estimation: this component estimates the number of neighbors each individual node is connected to. It takes as input the latent node features " + }, + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}}\\in \\mathbb{R}^{N\\times d^{\\prime}}" + }, + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "type": "text", + "content": " and generates random samples " + }, + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "type": "inline_equation", + "content": "k\\in \\mathbb{R}^N" + }, + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "type": "text", + "content": " drawn from a learned distribution over the node degree " + }, + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "type": "inline_equation", + "content": "(k^{\\prime}\\sim Q_{\\rho}(k|X)" + }, + { + "bbox": [ + 313, + 605, + 547, + 677 + ], + "type": "text", + "content": " from Eq. 4)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "type": "text", + "content": "4. Differentiable top-" + }, + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "type": "text", + "content": " edge selector: takes " + }, + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "type": "text", + "content": " and the edge-samples " + }, + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 313, + 677, + 547, + 713 + ], + "type": "text", + "content": " and performs a soft thresholding that probabilistically selects the most important elements," + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22543" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 66, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 66, + 72, + 287, + 95 + ], + "type": "text", + "content": "based on the output of the Edge-ranking to output an adjacency matrix " + }, + { + "bbox": [ + 66, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\in \\mathbb{R}^{N\\times N}" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 97, + 220, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 97, + 220, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 97, + 220, + 108 + ], + "type": "text", + "content": "We now explain these steps in more detail:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "text", + "content": "Node encoding We construct a single latent space from the input node features, and use it for edge ranking and degree estimation. We first map input node features " + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "text", + "content": " into latent features " + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}} \\in \\mathbb{R}^{N \\times d'}" + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "text", + "content": " using a multi-layer perceptron (MLP) " + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "inline_equation", + "content": "N_{\\phi}" + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "text", + "content": " with weights " + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}} = N_{\\phi}(\\mathbf{X})" + }, + { + "bbox": [ + 46, + 109, + 288, + 205 + ], + "type": "text", + "content": ". These latent features form the input for the rest of the DGG. Furthermore, they are output by the DGG and passed to the GCN downstream to prevent vanishing gradients." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "text", + "content": "Edge ranking The edge ranking returns an implicit distribution of edge orderings, from which we sample the neighborhood for each node. For each node " + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "text", + "content": ", it draws a set of scores " + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i = \\{e_{ij}\\}_{j}^N" + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "text", + "content": " quantifying its relevance to all nodes " + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "inline_equation", + "content": "v_{j} \\in V" + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "text", + "content": " including itself. To generate differentiable edge samples " + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 47, + 205, + 288, + 276 + ], + "type": "text", + "content": " we use the Gumbel-Softmax [12]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 277, + 288, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 288, + 313 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 288, + 313 + ], + "type": "text", + "content": "Before locally scoring each edge embedding " + }, + { + "bbox": [ + 47, + 277, + 288, + 313 + ], + "type": "inline_equation", + "content": "e_{ij} \\in \\mathbf{e}_i" + }, + { + "bbox": [ + 47, + 277, + 288, + 313 + ], + "type": "text", + "content": " for node " + }, + { + "bbox": [ + 47, + 277, + 288, + 313 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 47, + 277, + 288, + 313 + ], + "type": "text", + "content": ", we implement a global stage which constructs edge embeddings with both local and global dependencies:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "spans": [ + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "text", + "content": "1. Using latent node features " + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_i\\in \\hat{\\mathbf{X}}" + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "text", + "content": " , determine local edge embeddings " + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_{ij}\\in \\mathbb{R}^{d^{\\prime}}" + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "text", + "content": " by passing each pair of node features through an MLP " + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "inline_equation", + "content": "l_{\\phi}" + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "text", + "content": " .. " + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_{ij} = l_{\\phi}(\\hat{\\mathbf{x}}_i,\\hat{\\mathbf{x}}_j)" + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "text", + "content": " These embeddings now form a complete graph " + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "text", + "content": " over the nodes, with each edge attributed " + }, + { + "bbox": [ + 55, + 314, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_{ij}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "spans": [ + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": "2. As each edge embedding " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_{ij} \\in \\mathbf{C}" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": " is calculated independently of the others, we refine it to account for its dependencies to adjacent edges. We do this through edge-to-edge message passing. However, we avoid computing dependencies between all edges of the complete graph for two reasons: first, some edges may not have any common nodes, so passing messages between them could propagate irrelevant information, and secondly, it could be prohibitively expensive. To restrict message-passing between adjacent edges only, we first compute the adjoint graph " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": " of the complete graph " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": ". In the adjoint " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": ", each edge is associated with a node, and two nodes are connected if and only if their corresponding edges in " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": " have a node in common. The adjoint's adjacency " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "A^{\\mathcal{H}}" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": " can be calculated using its incidence matrix " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "A^{\\mathcal{H}} = L^{T}L - 2I" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": ". In the adjoint, each node embedding " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_i" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": " is then updated using an average of its neighboring nodes " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_j" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": " and passed through an MLP " + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "inline_equation", + "content": "h_\\phi" + }, + { + "bbox": [ + 54, + 374, + 289, + 590 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 117, + 600, + 288, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 600, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 117, + 600, + 288, + 628 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {c}} _ {i} ^ {\\prime} = \\sum_ {j \\in \\mathcal {N} (i)} h _ {\\phi} \\left(\\hat {\\mathbf {c}} _ {i} \\| \\mathbf {c} _ {i} - \\mathbf {c} _ {j}\\right) \\tag {5}", + "image_path": "e0ecf77d6ff752826d9e1920041cb9e1726f977167c4d2eb643b3ed6c1574698.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "text", + "content": "Having computed edge embeddings " + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{C} \\in \\mathbb{R}^{N \\times N \\times d'}" + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "text", + "content": " with global dependencies, we rank these edges for each node. Without loss of generality, we focus on a single node " + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "inline_equation", + "content": "v_i \\in V" + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "text", + "content": ", with latent features " + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_i \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "text", + "content": ". We implement the approximation function " + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "inline_equation", + "content": "Q_{\\theta}(A|X,k)" + }, + { + "bbox": [ + 47, + 628, + 288, + 689 + ], + "type": "text", + "content": " of the Edge-ranker as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 700, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 700, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 55, + 700, + 289, + 714 + ], + "type": "text", + "content": "1. Using edge embeddings " + }, + { + "bbox": [ + 55, + 700, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}_{ij} \\in \\mathbb{R}^{d'}" + }, + { + "bbox": [ + 55, + 700, + 289, + 714 + ], + "type": "text", + "content": ", calculate edge prob" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "type": "text", + "content": "abilities " + }, + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i\\in \\mathbb{R}^N" + }, + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "type": "text", + "content": " for node " + }, + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "type": "text", + "content": " using an MLP " + }, + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "type": "inline_equation", + "content": "m_{\\theta}" + }, + { + "bbox": [ + 325, + 72, + 523, + 84 + ], + "type": "text", + "content": " .." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 382, + 93, + 547, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 93, + 547, + 107 + ], + "spans": [ + { + "bbox": [ + 382, + 93, + 547, + 107 + ], + "type": "interline_equation", + "content": "\\mathbf {p} _ {i} = \\left\\{m _ {\\theta} \\left(\\hat {\\mathbf {c}} _ {i j}\\right) | \\forall j \\in N \\right\\}. \\tag {6}", + "image_path": "ee73f449d5cc0ea01a366e28bde1f9fa240d07bda23435fc015c15ab65c601a3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "spans": [ + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "type": "text", + "content": "Each element " + }, + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "type": "inline_equation", + "content": "p_{ij} \\in \\mathbf{p}_i" + }, + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "type": "text", + "content": " represents a similarity measure between the latent features of node " + }, + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "type": "inline_equation", + "content": "v_j" + }, + { + "bbox": [ + 324, + 115, + 547, + 150 + ], + "type": "text", + "content": ". In practice, any distance measure can be used here." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "type": "text", + "content": "2. Using Gumbel-Softmax over the edge probabilities " + }, + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i\\in \\mathbb{R}^N" + }, + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "type": "text", + "content": ", we generate differentiable samples " + }, + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i\\in \\mathbb{R}^N" + }, + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "type": "text", + "content": " with Gumbel noise " + }, + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 313, + 151, + 545, + 187 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 334, + 194, + 545, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 194, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 334, + 194, + 545, + 255 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {i} = \\left\\{\\frac {\\exp \\left(\\left(\\log \\left(p _ {i j}\\right) + g _ {i}\\right) + \\tau\\right)}{\\sum_ {j} \\exp \\left(\\left(\\log \\left(p _ {i j}\\right) + g _ {i}\\right) + \\tau\\right)} \\mid \\forall j \\in N \\right\\}, \\quad g _ {i} \\sim \\operatorname {G u m b e l} (0, 1) \\tag {7}", + "image_path": "75ccbbab61d960ac2897fc22bec3be910e8ed2141929352ac79f4359ee227938.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "spans": [ + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "content": " is a temperature hyperparameter controlling the interpolation between a discrete one-hot categorical distribution and a continuous categorical density. When " + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "inline_equation", + "content": "\\tau \\rightarrow 0" + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "content": ", the edge energies " + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "inline_equation", + "content": "e_{ij} \\in \\mathbf{e}_i" + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "content": " approach a degenerate distribution. The temperature " + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "content": " is important for inducing sparsity, but given the exponential function, this results in a single element in " + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "content": " given much more weighting than the rest, i.e., it approaches a one-hot argmax over " + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "content": ". As we want a variable number of edges to be given higher importance and others to be close to zero, we select a higher temperature and use the top-" + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 324, + 264, + 547, + 430 + ], + "type": "text", + "content": " selection procedure (detailed below) to induce sparsity. This additionally avoids the high-variance gradients induced by lower temperatures." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "type": "text", + "content": "Degree estimation A key limitation of existing graph generation methods [13, 15, 43] is their use of a fixed node degree " + }, + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "type": "text", + "content": " across the entire graph. This can be suboptimal as mentioned previously. In our approach, rather than fixing " + }, + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "type": "text", + "content": " for the entire graph, we sample it per node from a learned distribution. Focusing on a single node as before, the approximation function " + }, + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "type": "inline_equation", + "content": "Q_{\\rho}(k|X)" + }, + { + "bbox": [ + 304, + 431, + 547, + 525 + ], + "type": "text", + "content": " of the Degree-estimator works as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "content": "1. We approximate the distribution of latent node features " + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_i\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "content": " following a VAE-like formulation [14]. We encode its mean " + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\pmb {\\mu}_i\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\sigma_{i}\\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "content": " using two MLPs " + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "inline_equation", + "content": "M_{\\rho}" + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "inline_equation", + "content": "S_{\\rho}" + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "content": ", and then reparametrize with noise " + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "content": " to obtain latent variable " + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 526, + 547, + 586 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 364, + 594, + 545, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 594, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 364, + 594, + 545, + 614 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {i}, \\boldsymbol {\\sigma} _ {i} = M _ {\\rho} (\\hat {\\mathbf {x}} _ {i}), S _ {\\rho} (\\hat {\\mathbf {x}} _ {i}), \\tag {8}", + "image_path": "5bb1ff9cc872a91a356295298c110f96bba103fb17fb4456e4abc12bde77695d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 382, + 610, + 506, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 610, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 382, + 610, + 506, + 622 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {i} = \\boldsymbol {\\mu} _ {i} + \\epsilon_ {i} \\boldsymbol {\\sigma} _ {i}, \\epsilon_ {i} \\sim \\mathcal {N} (0, 1).", + "image_path": "fa3f5f3b6bc2b05ff07eed1cbe98d2d6463ff895d1442c18054256d308df32c2.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "spans": [ + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "text", + "content": "2. Finally, we concatenate each latent variable " + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "text", + "content": " with the L1-norm of the edge samples " + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_i = ||\\mathbf{e}_i||_1" + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "text", + "content": " and decode it into a scalar " + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "inline_equation", + "content": "k_{i}\\in \\mathbb{R}" + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "text", + "content": " with another MLP " + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "inline_equation", + "content": "D_{\\rho}" + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "text", + "content": " representing a continuous relaxation of the neighborhood size for node " + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 313, + 632, + 547, + 691 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 396, + 701, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 396, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 396, + 701, + 545, + 714 + ], + "type": "interline_equation", + "content": "k _ {i} = D _ {\\rho} \\left(\\mathbf {z} _ {i}\\right) + \\mathbf {h} _ {i}. \\tag {9}", + "image_path": "92f2a23380397405a0530d403cbd52dd83f0be4079b4d5be2af4fb1814075a3a.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "22544" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_i" + }, + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "type": "text", + "content": " is a summation of a node's edge probabilities, it can be understood as representing an initial estimate of the node degree which is then improved by combining with a second node representation " + }, + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "type": "text", + "content": " based entirely on the node's features. Using the edge samples to estimate the node degree links these representation spaces back to the primary latent space of node features " + }, + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}}" + }, + { + "bbox": [ + 66, + 72, + 288, + 156 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": "Top-" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " Edge-Selector Having sampled edge weights, and node degrees " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": ", this function selects the top-" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " edges for each node. The top-" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " operation, i.e. finding the indices corresponding to the " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " largest elements in a set of values, is a piecewise constant function and cannot be directly used in gradient-based optimization. Previous work [40] framed the top-" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " operation as an optimal transport problem, providing a smoothed top-" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " approximator. However, as their function is only defined for discrete values of " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " it cannot be optimized with gradient descent. As an alternative that is differentiable with respect to " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": ", we relax the discrete constraint on " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": ", and instead use it to control the " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": "-axis value of the inflection point on a smoothed-Heaviside function (Fig. 3). For a node " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "v_{i} \\in V" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": ", of smoothed degree " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k_{i} \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " and edges " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_{i} \\in \\mathbb{R}^{N}" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": ", our Top-" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " Edge Selector outputs an adjacency vector " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{i} \\in \\mathbb{R}^{N}" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " where the " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " largest elements from " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_{i}" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " are close to 1, and the rest close to 0. Focusing on a single node " + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 47, + 156, + 289, + 370 + ], + "type": "text", + "content": " as before, the implementation is as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 371, + 287, + 430 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "spans": [ + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "type": "text", + "content": "1. Draw 1D input points " + }, + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i = \\{1,\\dots,N\\}" + }, + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "type": "text", + "content": " is the number of nodes in " + }, + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 55, + 371, + 287, + 394 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 395, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 395, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 54, + 395, + 287, + 430 + ], + "type": "text", + "content": "2. Pass " + }, + { + "bbox": [ + 54, + 395, + 287, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 54, + 395, + 287, + 430 + ], + "type": "text", + "content": " through a hyperbolic tangent (tanh) which serves as a smooth approximation of the Heaviside function:" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 74, + 439, + 287, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 439, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 74, + 439, + 287, + 455 + ], + "type": "interline_equation", + "content": "\\mathbf {h} _ {i} = 1 - 0. 5 * \\left\\{1 + \\tanh \\left(\\lambda^ {- 1} d _ {i} - \\lambda^ {- 1} k _ {i}\\right) \\right\\}, \\tag {10}", + "image_path": "29f30a37b39371aa58a7d09f51087413add2e6332f704edb5e0b3878d9a1d5be.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "text", + "content": "here " + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\lambda > 0" + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "text", + "content": " is a temperature parameter controlling the gradient of the function's inflection point. As " + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\lambda \\to 0" + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "text", + "content": ", the smooth function approaches the Heaviside step function. The first-" + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "text", + "content": " values in " + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_i = \\{h_{ij}\\}_{j}^N" + }, + { + "bbox": [ + 66, + 462, + 287, + 521 + ], + "type": "text", + "content": " will now be closer to 1, while the rest closer to 0." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "content": "3. Finally, for each node " + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "content": " we sort its edge-energies " + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i = \\{e_{ij}\\}_{j}^{N}" + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "content": " in descending order, multiply by " + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_i = \\{h_{ij}\\}_{j}^{N}" + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "content": " and then restore the original order to obtain the final adjacency vector " + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i = \\{a_{ij}\\}_{j}^{N}" + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "content": ". Stacking " + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i" + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "content": " over all nodes " + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "inline_equation", + "content": "v_i \\in V" + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "content": " creates the final adjacency matrix " + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 55, + 522, + 287, + 592 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "text", + "content": "Symmetric adjacency matrix If the adjacency matrix " + }, + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "text", + "content": " must be symmetric, this can be enforced by replacing it with " + }, + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "inline_equation", + "content": "A_{sym}" + }, + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "text", + "content": " where: " + }, + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{sym} = (\\mathbf{A} + \\mathbf{A}^T) / 2" + }, + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "text", + "content": "Straight through Top-" + }, + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "text", + "content": " Edge Selector To make our final adjacency matrix " + }, + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "text", + "content": " discrete, we follow the trick used in the Straight-Through Gumbel Softmax [12]: we output the discretized version of " + }, + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 631, + 288, + 714 + ], + "type": "text", + "content": " in the forward pass and the continuous version in the backwards pass. For the discretized version in the forward pass, we replace the smooth-Heaviside function in Eq. 10 with a step function." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "Module Instantiation: The DGG module can be easily combined with any graph convolution operation. A typical graph convolution [16] is defined as follows: " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{X}' = \\hat{\\mathbf{D}}^{-1/2} \\hat{\\mathbf{A}} \\hat{\\mathbf{D}}^{-1/2} \\mathbf{X} \\Theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}} = \\mathbf{A} + \\mathbf{I}" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " denotes the adjacency matrix with inserted self-loops, " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{D}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " its diagonal degree matrix and " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " its weights. To use this graph convolution with the DGG, we simply use our module to generate the adjacency matrix " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 178, + 388, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 388, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 388, + 192 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 198, + 547, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 342 + ], + "type": "text", + "content": "We evaluate our DGG on node classification, point cloud classification and trajectory prediction. We chose these tasks as they demonstrate the wide applicability of our module: (1) graphs for node classification require models that can generate edge structures from noisy input graphs, (2) point cloud classification tasks have no input graph structures and (3) trajectory prediction additionally requires models which can handle a variable number of nodes per batch. We compare against state-of-the-art structure learning methods in each domain. As far as we know, our structure-learning approach is the only one that can be easily applied without modification to any GCN pipeline in such a range of tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 348, + 416, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 416, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 416, + 360 + ], + "type": "text", + "content": "4.1. Node classification" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 366, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 547, + 474 + ], + "type": "text", + "content": "Beginning with node classification, we conduct ablations examining the behavior of different parts of the DGG, followed by comparisons to other state-of-the-art structure learning approaches. In the supplementary we include experiments investigating the effect of the DGG on downstream models under the addition of noisy edges to input graphs. We perform these experiments under both transductive and inductive scenarios, as well as semi-supervised and fully-supervised settings." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 475, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 548, + 713 + ], + "type": "text", + "content": "Datasets In the transductive setting, we evaluate on three citation benchmark datasets Cora, Citeseer and Pubmed [26] introduced by [41]. In an inductive setting, we evaluate on Reddit [42] and PPI [11]. Further dataset details can be found in the supplementary. Baselines and Implementation As our DGG is a GCN-agnostic module that can be integrated alongside any graph convolution operation, we compare its performance to both other GCN-agnostic approaches and bespoke structure-learning architectures. To compare against other GCN-agnostic methods, we integrate our DGG into four representative GCN backbones: GCN [16], GraphSage [11], GAT [35] and GCNII [2]. On these backbones, we compare against other GCN-agnostic structure learning methods: DropEdge [29], NeuralSparse [43], PTDNet [21]. Then we compare against bespoke architectures IDGL [3], LDS [9], SLAPS [8], NodeFormer [37] and VGCN [7]. To make our comparison fair against these bespoke architectures which learn the structure specifically for node classification, we integrate our DGG into a GCN backbone that is comparable to the bespoke architecture in design. Please see the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22545" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 146, + 71, + 449, + 192 + ], + "blocks": [ + { + "bbox": [ + 146, + 71, + 449, + 192 + ], + "lines": [ + { + "bbox": [ + 146, + 71, + 449, + 192 + ], + "spans": [ + { + "bbox": [ + 146, + 71, + 449, + 192 + ], + "type": "image", + "image_path": "678a2bd19dc1970d2e5608459adbcd451c2e2fcdc004e529cc504652718eb851.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "lines": [ + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "text", + "content": "Figure 3. The differentiable Top-" + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "text", + "content": " Edge Selector. This component uses the node degree " + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "inline_equation", + "content": "k_{i}" + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "text", + "content": " output by the Degree Estimator to control the inflection point on a smooth-Heaviside function and uses it to select the top edges from " + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "text", + "content": " output by the Edge Ranker. This produces an adjacency vector " + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i" + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "text", + "content": " for each node, and stacking " + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i" + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "text", + "content": " across all nodes produces the final adjacency matrix " + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 195, + 547, + 229 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 248, + 219, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 219, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 219, + 260 + ], + "type": "text", + "content": "supplementary for implementation details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 261, + 290, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 290, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 290, + 499 + ], + "type": "text", + "content": "Training details A node classification model partitions the latent space of node embeddings into separate classes. However, when message-passing, there is one phenomenon of the input graph that can limit classification accuracy: two nodes with different classes but similar features and an edge connecting them. Classifying these nodes is challenging as their feature similarity can be compounded by passing messages between them. The goal of the DGG is to move such nodes apart in the latent space such that there is no edge and communication between them. However, traversing the loss landscape from the initial random initialization of the network to one where the model is able to discriminate between these nodes can take several iterations using only the downstream classification loss. To speed up training, we add an intermediate loss to further partition the latent space. We do this by supervising the adjacency matrix generated by the DGG to remove all edges between classes and only maintain those within a class. We then anneal this loss over the training cycle, eventually leaving only the downstream classification loss. We provide more details in the supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 515, + 122, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 122, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 122, + 526 + ], + "type": "text", + "content": "4.1.1 Ablations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "type": "text", + "content": "In Table 1, we explore the effect of disabling different components of our DGG module when integrated into a GCN [16] for node classification: 1. DGG without Degree Estimation and Differentiable Top-k Edge Selection — we remove the Degree Estimator and instead fix " + }, + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 533, + 288, + 665 + ], + "type": "text", + "content": " to select the top-k stochastically ordered edges. 2. DGG with deterministic Edge Ranking — we remove the noise in Eq. 7 of the Edge Ranker. 3. DGG with deterministic Degree Estimation — we remove the noise in Eq. 8 of the Degree Estimator. We perform these on Cora [41] and omit the annealed intermediate loss during training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Table 1 shows the benefit of learning a distribution over the node degree. When learning it deterministically, the accuracy decreases by " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": ". This becomes significantly worse when the node degree is fixed for the entire graph" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 266, + 545, + 318 + ], + "blocks": [ + { + "bbox": [ + 305, + 245, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 305, + 245, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 545, + 266 + ], + "type": "text", + "content": "Table 1. Ablation study. DGG integrated into a GCN for node classification on Cora [41]." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 266, + 545, + 318 + ], + "lines": [ + { + "bbox": [ + 307, + 266, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 307, + 266, + 545, + 318 + ], + "type": "table", + "html": "
ModelAccuracy
Fixed node degree, k = {1, 5, 10, 100}{49.7, 78.9, 55.0, 37.0}
With deterministic Edge Ranking and Degree Estimation82.4
With deterministic Edge Ranking82.7
With deterministic Degree Estimation82.8
DGG83.2
", + "image_path": "ccc582ffadd73620476b37cbc02c7e49ba0634eb9cdf77e5bc54976f604d57e7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "text", + "content": "rather than learned per node. Note also, the sensitivity with respect to choice of " + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "text", + "content": ". A fixed node degree of " + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "inline_equation", + "content": "k = 10" + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "text", + "content": " reduces accuracy by almost " + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "text", + "content": " vs a graph of 5. This is due to the graph convolution operation: as it has no adaptive weighting mechanism for a node's neighborhood, each of the neighbors is given the same weight. Naturally, this leads to information sharing between unrelated nodes, reducing the quality of node representation after message-passing. In contrast, by learning a distribution over the node degree we are able to select only the most relevant neighbors, even though these are then weighted equally in the graph convolution. Finally, the inclusion of noise in any of the DGG components does increase accuracy, but only by approximately " + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 329, + 547, + 508 + ], + "type": "text", + "content": " — demonstrating both its benefit and the robustness of the DGG without it." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 526, + 371, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 371, + 537 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 371, + 537 + ], + "type": "text", + "content": "4.1.2 Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "type": "text", + "content": "Comparison to GCN-agnostic modules In Table 2 we compare against GCN-agnostic structure learning methods. For fair comparison, we present two versions of our method: DGG-wl trained with the downstream loss only and DGG* trained with both the downstream and intermediate loss." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 713 + ], + "type": "text", + "content": "DGG improves performance across all baselines and datasets. Against other approaches, DGG-wl generally outperforms the state-of-the-art NeuralSparse and PTDNet-wl (both trained with only the downstream loss). This can be attributed to our method for modelling sparsity, which explicitly lets each node to select the size of its neighborhood based on the downstream training signal. This training signal helps partition the node representation space, while the estimated node-degree additionally prevents communication" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22546" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 124, + 286, + 331 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 288, + 123 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 288, + 123 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 288, + 123 + ], + "type": "text", + "content": "Table 2. Semi-supervised node classification compared to other architecture agnostic SOTA structure learning methods. We compare against prior methods reported in [21, 43, 2], using the official results where available. Those with ' -' have no official results or we ran into out-of-memory errors." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 124, + 286, + 331 + ], + "lines": [ + { + "bbox": [ + 49, + 124, + 286, + 331 + ], + "spans": [ + { + "bbox": [ + 49, + 124, + 286, + 331 + ], + "type": "table", + "html": "
BackboneMethodCoraCiteseerPubmedRedditPPI
GCNOriginal81.170.379.092.253.2
DropEdge80.972.278.596.154.8
NeuralSparse82.171.578.896.665.1
PTDNet-wl82.471.779.1-75.2
DGG-wl83.272.680.296.877.1
PTDNet-wl + low rank82.872.779.8-80.3
DGG*84.174.984.097.381.6
GraphSageOriginal79.267.676.793.861.8
NeuralSparse79.367.475.196.762.6
PTDNet-wl79.467.877.0-64.5
DGG-wl79.468.277.696.665.3
PTDNet-wl + low rank80.367.977.1-64.8
DGG*80.570.880.296.967.3
GATOriginal83.072.179.0-97.3
DropEdge83.270.977.9-85.1
NeuralSparse83.472.478.0-92.1
PTDNet-wl83.772.379.2-97.8
DGG-wl84.673.279.7-97.4
PTDNet-wl + low rank84.473.779.3-98.0
DGG*85.376.482.0-97.6
GCNIIOriginal85.373.280.2-99.5
DropEdge84.973.479.4-99.0
DGG-wl86.974.581.5-99.6
DGG*87.875.781.9-99.7
", + "image_path": "a66a0df4ba53012141d76bbc996dd5b4529d459de05ed9c6d5a0a752be2ea479.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 350, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 288, + 422 + ], + "type": "text", + "content": "between distant nodes. Although PTDNet-wl does this implicitly through its attention mechanism, discovering this sparse subgraph of the input graph is challenging given its complexity. NeuralSparse on the other hand selects " + }, + { + "bbox": [ + 46, + 350, + 288, + 422 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 350, + 288, + 422 + ], + "type": "text", + "content": " for its entire generated subgraph, which is both suboptimal and requires additional hyperparameter tuning." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 460, + 286, + 511 + ], + "blocks": [ + { + "bbox": [ + 47, + 430, + 287, + 460 + ], + "lines": [ + { + "bbox": [ + 47, + 430, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 287, + 460 + ], + "type": "text", + "content": "Table 3. Adjacency matrix constraints: our intermediate annealed loss vs. PTDNet's low rank regularizer [21] for semi-supervised node classification with a GCN backbone." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 460, + 286, + 511 + ], + "lines": [ + { + "bbox": [ + 48, + 460, + 286, + 511 + ], + "spans": [ + { + "bbox": [ + 48, + 460, + 286, + 511 + ], + "type": "table", + "html": "
MethodCoraCiteseerPubmedPPI
DGG-wl86.874.481.299.5
DGG-wl + low rank87.175.381.499.5
DGG-wl + int. loss (aka DGG*)87.775.881.999.7
DGG-wl + int. loss + low rank87.876.282.199.7
", + "image_path": "8d415e5272affed7c8fb788ee9bd0dbccb44c7db93d80f0ea18b19a2a584504a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 522, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 689 + ], + "type": "text", + "content": "Comparing methods which enforce additional constraints on the adjacency matrix, DGG* demonstrates larger accuracy gains than PTDNet*. PTDNet* regularizes its adjacency matrix to be of low-rank, as previous work [30] has shown that the rank of an adjacency matrix can reflect the number of clusters. This regularizer reasons about the graph's topology globally. While this may aid generalization, the accuracy difference may then be attributed to our intermediate loss providing stronger signals to discriminate between nodes with similar features but different classes (and therefore remove the edges between them). Furthermore, their regularizer uses the sum of the top-" + }, + { + "bbox": [ + 46, + 522, + 288, + 689 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 522, + 288, + 689 + ], + "type": "text", + "content": " singular values during training, where " + }, + { + "bbox": [ + 46, + 522, + 288, + 689 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 522, + 288, + 689 + ], + "type": "text", + "content": " again is a hyperparameter tuned to each dataset individually. Our method requires no additional parameters to be chosen." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 289, + 712 + ], + "type": "text", + "content": "Finally in Table 3 we compare the low-rank constraint of PTDNet with our intermediate annealed loss. Our interme" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 91, + 545, + 201 + ], + "blocks": [ + { + "bbox": [ + 305, + 69, + 547, + 90 + ], + "lines": [ + { + "bbox": [ + 305, + 69, + 547, + 90 + ], + "spans": [ + { + "bbox": [ + 305, + 69, + 547, + 90 + ], + "type": "text", + "content": "Table 4. Node classification results against bespoke SOTA architectures which learn the graph structure." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 91, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 307, + 91, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 307, + 91, + 545, + 201 + ], + "type": "table", + "html": "
ModelCoraCiteseer
Setting 1IDGL [3]84.574.1
originalDGG* + GAT85.476.4
Setting 2LDS [9]71.573.3
Input graph = noneSLAPS [8]74.273.1
train split = {train + 1/2 val}DGG* + GCN82.474.0
Setting 3NodeFormer [37]88.776.2
split = 0.5/0.25/0.25DGG* + GAT90.177.8
Setting 4VGCN [7]85.976.5
train split = {train + 1/2 val}DGG* + GAT87.677.1
", + "image_path": "fc8d0eff7aee23a7a36b1f1c6ae10554b38c248823abccbaa5f2ef2a0663255b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 243, + 545, + 338 + ], + "blocks": [ + { + "bbox": [ + 305, + 209, + 547, + 242 + ], + "lines": [ + { + "bbox": [ + 305, + 209, + 547, + 242 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 547, + 242 + ], + "type": "text", + "content": "Table 5. ADE/FDE on the ETH & UCY datasets using SocialSTGCNN (first table), and Stanford Drone Dataset (SDD) using DAGNet (second table). For DGM [13], " + }, + { + "bbox": [ + 305, + 209, + 547, + 242 + ], + "type": "inline_equation", + "content": "k = 2" + }, + { + "bbox": [ + 305, + 209, + 547, + 242 + ], + "type": "text", + "content": " for both datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 243, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 307, + 243, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 307, + 243, + 545, + 338 + ], + "type": "table", + "html": "
DatasetOriginalDGM [13] Gain (%)DGG Gain (%)
ADE↓FDE ↓ADE ↑FDE↑ADE ↑FDE ↑
ETH0.641.112.4%6.4%7.8%21.4%
Hotel0.490.8514.2%18.9%22.7%37.5%
Univ0.440.796.2%3.5%11.8%14.9%
Zara10.340.533.8%13.7%7.7%23.8%
Zara20.300.485.0%5.0%12.8%17.3%
Mean0.440.756.3%10.6%12.6%23.0%
SDD0.531.041.9%3.0%10.9%9.5%
", + "image_path": "ca0b9ed8f6cc9a6f399cbfc8a6c931c0f984e9b33038984abcaa2d6f33b4bed2.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 359, + 547, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 547, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 547, + 419 + ], + "type": "text", + "content": "diate loss ('DGG-wl + int. loss') outperforms the low-rank constraint ('DGG-wl + low rank'). However, using both constraints ('DGG-wl + int. loss + low rank') increases classification accuracy further, suggesting the edges removed by both methods are complementary." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 421, + 547, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 547, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 547, + 648 + ], + "type": "text", + "content": "Comparison with bespoke architectures In Table 4 we compare against bespoke architectures specifically designed for node classification. As each of these methods uses different experiment settings, we train our DGG-integrated architecture separately for each. See the supplementary for details on each setting and reasons for our choice of backbone. Our performance gains here can generally be attributed to factors: (1) our intermediate loss on the adjacency matrix and (2) our adjacency matrix factorizations where we learn the neighborhood for each node. Our intermediate loss particularly benefits from the experimental settings adopted by the other methods as they use larger training splits involving half the validation graph. Additionally, constructing the adjacency matrix by learning nodewise neighborhoods restricts the graph search space, making optimization easier. However, we note that some of these other methods are designed for node-classification on graphs which are orders of magnitude larger than Cora and Citeseer. In such cases, factorizing the adjacency per node, as we do, may be unfeasible." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 658, + 429, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 429, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 429, + 671 + ], + "type": "text", + "content": "4.2. Trajectory prediction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "We evaluate on trajectory prediction tasks as these have neither an input or ground truth graph structure, thus the ideal structure has to be generated entirely from the data. We" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22547" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 91, + 286, + 179 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 90 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 90 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 90 + ], + "type": "text", + "content": "Table 6. ADE/FDE metrics on the SportVU Basketball dataset using DAGNet. For DGM [13], " + }, + { + "bbox": [ + 47, + 69, + 287, + 90 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 47, + 69, + 287, + 90 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 91, + 286, + 179 + ], + "lines": [ + { + "bbox": [ + 47, + 91, + 286, + 179 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 286, + 179 + ], + "type": "table", + "html": "
SplitTeamOriginalDGM [13] Gain (%)DGG Gain (%)
ADEFDEADEFDEADEFDE
10-40ATK2.744.29-0.4%-0.2%6.7%5.1%
DEF2.092.97-0.5%-0.1%9.7%6.4%
20-30ATK2.033.980.1%0.1%7.2%8.2%
DEF1.533.070.2%0.3%21.4%19.1%
40-10ATK0.811.711.3%0.9%15.5%17.0%
DEF0.721.490.8%0.8%10.9%16.2%
Mean—1.652.920.3%0.3%11.9%12.0%
", + "image_path": "070ff4a41fec7a8bd509de208040856f81c528475a6353a6659b19468ebb5d99.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 183, + 288, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 183, + 288, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 288, + 243 + ], + "type": "text", + "content": "consider four datasets covering a range of scenarios from basketball to crowded urban environments. On each, we integrate our DGG into a SOTA GCN trajectory prediction pipeline and compare results to another task-agnostic structure learning approach, DGM [13]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 290, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 290, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 290, + 459 + ], + "type": "text", + "content": "Datasets We evaluate on four trajectory prediction benchmarks. 1. ETH [27] and UCY [18] — 5 subsets of widely used real-world pedestrian trajectories. 2. STATS SportVU [32] — multiple NBA seasons tracking trajectories of basketball players over a game. Stanford Drone Dataset (SDD) [28] — top-down scenes across multiple areas at Stanford University. Further details on these datasets can be found in the supplementary. Baselines and Implementation We integrate our DGG module into two state-of-the-art trajectory prediction pipelines: Social-STGCNN [22] and DAGNet [23]. Our DGG is placed within both networks to generate the adjacency matrix on the fly and forms part of its forward and backward pass. Please see the supplementary for implementation details. Evaluation metrics. Model performance is measured with Average Displacement Error (ADE) and Final Displacement Error (FDE). ADE measures the average Euclidean distance along the entire predicted trajectory, while the FDE is that of the last timestep only." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 459, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 288, + 628 + ], + "type": "text", + "content": "Results In Table 5, the integration of our DGG into Social-STGCNN reduces ADE/FDE compared to both the baseline and the integration of DGM. In Table 5 and 6 we demonstrate similar gains over DGM when integrated into DAGNet. First, this shows the benefit of inducing sparsity when message-passing over a distance weighted adjacency matrix like Social-STGCNN or even an attention-mechanism like DAGNet. The larger error reduction of our DGG compared to DGM may be attributed to DGM's use of a fixed node-degree " + }, + { + "bbox": [ + 46, + 459, + 288, + 628 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 459, + 288, + 628 + ], + "type": "text", + "content": " across its learned graph. While this can prevent the propagation of irrelevant information across the graph in some cases, in others it might limit the context available to certain nodes. We provide qualitative analysis in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 635, + 192, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 192, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 192, + 647 + ], + "type": "text", + "content": "4.3. Point Cloud Classification" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "We evaluate on another vision task of point cloud classification for models which use GCNs. This task differs from the previous two as predictions are made for the entire graph as opposed to node-wise. As with our trajectory prediction experiments, we integrate our DGG into SOTA classification" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 100, + 545, + 168 + ], + "blocks": [ + { + "bbox": [ + 305, + 68, + 545, + 101 + ], + "lines": [ + { + "bbox": [ + 305, + 68, + 545, + 101 + ], + "spans": [ + { + "bbox": [ + 305, + 68, + 545, + 101 + ], + "type": "text", + "content": "Table 7. Point Cloud classification on ModelNet40 with our module and DGM [13] integrated into two different point cloud labelling architectures." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 100, + 545, + 168 + ], + "lines": [ + { + "bbox": [ + 307, + 100, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 307, + 100, + 545, + 168 + ], + "type": "table", + "html": "
BaselineMethodMean degreeS.D. degreeAccuracy
ResGCN [19]Original9093.3
DGM [13]20093.5
DGG14.87.494.4
DGCNN [36]Original40092.9
DGM [13]20093.3
DGG19.35.293.8
", + "image_path": "8fa34207ace01cf1db1ba3524e9c1ff3e6583d4b21df988d6bb0f665b6128958.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 188, + 545, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 188, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 305, + 188, + 545, + 212 + ], + "type": "text", + "content": "architectures and compare against the other task-agnostic graph-learning module DGM [13]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 212, + 547, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 547, + 295 + ], + "type": "text", + "content": "Datasets We evaluate on ModelNet40 [39], consisting of CAD models for a variety of object categories. Baselines and Implementation We integrate our DGG into a SOTA ResGCN [19] and DGCNN [36]. Both models use a " + }, + { + "bbox": [ + 304, + 212, + 547, + 295 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 212, + 547, + 295 + ], + "type": "text", + "content": "-NN sampling scheme to construct its graph. We simply replace this sampler with our DGG and keep the rest of the network and training protocol the same." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 296, + 548, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 296, + 548, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 548, + 535 + ], + "type": "text", + "content": "Results Our results in Table 7 demonstrate the benefits of learning an adaptive neighborhood size across the latent graph. DGM [13] learns a fully-connected latent graph and then imposes a fixed node degree of " + }, + { + "bbox": [ + 304, + 296, + 548, + 535 + ], + "type": "inline_equation", + "content": "k = 20" + }, + { + "bbox": [ + 304, + 296, + 548, + 535 + ], + "type": "text", + "content": " across it (i.e. selecting the top 20 neighbors for each node). This marginally improves upon the baselines ResGCN [19] and DGCNN[36], which both also used fixed node-degrees " + }, + { + "bbox": [ + 304, + 296, + 548, + 535 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 296, + 548, + 535 + ], + "type": "text", + "content": ". In contrast, we learn a distribution over the node degree from which we sample each node's neighborhood size. As shown in Table 7, the node degree varies in our models with a standard deviation of around 5-7 across both baselines. Our accuracy gains over the baseline and DGM can be attributed to this variance in neighborhood sizes across the graph. These gains can be understood when viewing an input point cloud as a composition of object parts. Building semantic representations for different parts may naturally require varying amounts of contextual points. For instance, the wheels of a car might be identifiable with a smaller neighborhood than the car's body. This may suggest why an adaptive neighborhood size is helpful in this case." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 545, + 379, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 545, + 379, + 558 + ], + "spans": [ + { + "bbox": [ + 306, + 545, + 379, + 558 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 565, + 547, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 565, + 547, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 565, + 547, + 650 + ], + "type": "text", + "content": "We have presented a novel approach for learning graph topologies, and shown how it obtains state-of-the-art performance across multiple baselines and datasets for trajectory prediction, point cloud classification and node classification. The principal advantage of our approach is that it can be combined with any existing graph convolution layer, under the presence of noisy, incomplete or unavailable edge structures." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 658, + 409, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 409, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 409, + 671 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "This project was supported by the EPSRC project ROSSINI (EP/S016317/1) and studentship 2327211 (EP/T517616/1)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22548" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "type": "text", + "content": "[1] Michael M Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. 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PMLR, 2020." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22550" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_content_list.json b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..08d8d63e54009d8c27ff1e428d39631c89a9b781 --- /dev/null +++ b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_content_list.json @@ -0,0 +1,1884 @@ +[ + { + "type": "text", + "text": "Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification", + "text_level": 1, + "bbox": [ + 163, + 130, + 807, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Feng Liu, Minchul Kim, ZiAng Gu, Anil Jain, Xiaoming Liu \nDepartment of Computer Science and Engineering \nMichigan State University, East Lansing MI 48824", + "bbox": [ + 215, + 203, + 754, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{liufeng6, kimminc2, guziang, jain, liuxm}@msu.edu", + "bbox": [ + 215, + 256, + 754, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Long-Term Person Re-Identification (LT-ReID) has become increasingly crucial in computer vision and biometrics. In this work, we aim to extend LT-ReID beyond pedestrian recognition to include a wider range of real-world human activities while still accounting for cloth-changing scenarios over large time gaps. This setting poses additional challenges due to the geometric misalignment and appearance ambiguity caused by the diversity of human pose and clothing. To address these challenges, we propose a new approach 3DInvarReID for (i) disentangling identity from non-identity components (pose, clothing shape, and texture) of 3D clothed humans, and (ii) reconstructing accurate 3D clothed body shapes and learning discriminative features of naked body shapes for person ReID in a joint manner. To better evaluate our study of LT-ReID, we collect a real-world dataset called CCDA, which contains a wide variety of human activities and clothing changes. Experimentally, we show the superior performance of our approach for person ReID. Code is available at http://cvlab.cse.msu.edu/project-reid3dinvar.html.", + "bbox": [ + 75, + 340, + 473, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 676, + 209, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Person Re-Identification (ReID) aims to recognize and match a specific pedestrian in various locations and at different times [1, 26, 29, 57, 62]. This is a crucial task for various applications, including crime prevention, forensic identification and security monitoring [13, 63].", + "bbox": [ + 75, + 702, + 468, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most existing works [11, 12, 24, 25] in this field concentrate on the short-term scenarios, assuming that pedestrians' clothing remains unchanged. However, in this paper, we focus on a more challenging yet practical scenario of Long-Term Person Re-Identification (LT-ReID), where the objective is to recognize individuals over long time periods while taking into account variations in clothing and diverse human activities. For the first time, we extend person re", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/07bd8e7862043c6c2969e5be7cdaf7fd2193660a02924aacf26def1d87672441.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 514, + 308, + 877, + 419 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1ae17e6a7ef456b3aae5cbf9e2f1e4de74c78d3c7faea2a36d48d360d8b53411.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 511, + 421, + 622, + 496 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f0294bd1d03f091e258c4881f01841c2bea2a3961be47b2bb25180dfc78d6378.jpg", + "image_caption": [ + "(b)", + "Figure 1. Illustration of the differences between various person re-identification (ReID) settings. Both (a) conventional/short-term and (b) cloth-changing person ReID benchmarks often restrict subjects to walking or standing, limiting their applications in real-world scenarios. This paper expands on the long-term person re-identification (LT-ReID) setting by tackling a wider range of human activities, increasing its practicality." + ], + "image_footnote": [], + "bbox": [ + 640, + 421, + 750, + 496 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7a0d1cb22e0ece9d0b2e2393bcc59eae3c16e598bc62be6f05bebd1d951b3dec.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 767, + 421, + 875, + 496 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "identification beyond pedestrian recognition to encompass a wider range of human activities, such as identifying students playing tennis or soldiers crawling in the field (see Fig. 1). This setting poses new challenges due to the geometric misalignment and appearance ambiguity caused by the diversity of human poses and their clothing.", + "bbox": [ + 496, + 641, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, various approaches [14,18,20,23,27,46,56,59] have been proposed to investigate LT-ReID under clothing changes. They extract clothing-irrelevant features for robust person ReID by custom-designed architectures [19,20], training process [27], loss functions [14], and data augmentation [64]. However, these methods only attempt to mine texture-insensitive body-structural cues in 2D space while ignoring the prior knowledge that the human body is a 3D non-rigid object. A new line of research introduces 3D priors for LT-ReID by either lifting 2D images to a 3D space [67] or including 3D body reconstruction as an auxil", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19617", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "iary task [5]. However, without modeling the 3D clothing, the clothing-sensitive features can not be properly disentangled in either method. Moreover, none of the methods above handle body images with diverse activities.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given the numerous variations in body images, including body pose, clothing, and view angles, we posit that the most reliable identity cue for LT-ReID is the 3D naked (unclothed) body shape, if it can be accurately and discriminately estimated from a 2D body image. Obviously this is extremely challenging due to confounding factors and the lack of supervision, such as paired images and 3D naked body scans. However, taking inspiration from advancements in 3D feature learning for face recognition [32, 41], we propose a new algorithm, 3DInvarReID, to disentangle identity (naked body) from non-identity components (pose, clothing shape and texture) of 3D clothed humans. This innovative approach not only reconstructs accurate 3D clothed body shapes that faithfully represent the input 2D images, but it also simultaneously learns discriminative naked shape features that effectively enhance LT-ReID.", + "bbox": [ + 75, + 157, + 470, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An effective representation of the 3D shape and texture of the human body is a key component of such a learning-based process. To this end, we propose a joint two-layer neural implicit function to represent 3D humans, where identity, clothing shape, and texture components are disentangled into latent representations. Based on the composite model, we jointly learn a model fitting module to disentangle identity from non-identity components (body pose, clothing shape and texture) from 2D images. Modeling texture, along with a differentiable renderer enables us to compare the rendered image with the input image in a self-supervised manner. This allows the learning process to be supervised by both image reconstruction loss and identification loss, using a set of 2D images with identity labels only. Comprehensive experiments demonstrate the superiority of our method in diverse ReID benchmarks. Additionally, to advance the research in the field of LT-ReID, we collect a Cloth-Changing and Diverse Activities (CCDA) dataset (see Fig. 1). The CCDA dataset is specifically designed to evaluate the ReID of the person undergoing both human activities and changes in clothing.", + "bbox": [ + 75, + 406, + 468, + 723 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the contributions of this work include:", + "bbox": [ + 96, + 729, + 434, + 744 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "$\\diamond$ We propose a novel LT-ReID method, 3DInvarReID, to learn clothing/pose invariant 3D shape representation.", + "$\\diamond$ We devise a novel joint two-layer implicit model that fully models a textured 3D clothed human. Our approach includes a robust and discriminative fitting process that disentangles identity and non-identity features in reconstructing two-layer 3D body shapes from real-world images.", + "$\\diamond$ We achieve superior performance in both LT-ReID accuracy and 3D body shape reconstruction." + ], + "bbox": [ + 75, + 751, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/39f015873675a720d34a489c3e53bac675e2a2b46f3ec47e79be779539978082.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodEnd-to-End trainableModel textureDiscriminativeModel type
3D modeling methods
SCANimate [44]-XXuniversal
SMPLicit [10]-XXuniversal
Neural-GIF [49]-XXindividual
SNARF [7]-XXindividual
gDNA [6]-XXuniversal
3D fitting methods
PiFu [42]X✓X-
PiFuHD [43]XXX-
Arch [21]X✓X-
Arch++ [15]X✓X-
ICON [55]X✓X-
ClothWild [37]XXX-
PHORHUM [2]✓✓X-
3DInvarReID✓✓✓universal
", + "bbox": [ + 504, + 89, + 888, + 292 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Overview of the 3D clothed human modeling (top) and fitting (bottom) methods. Our method is the only one that models clothing texture and learns discriminative information compared to 3D modeling methods. Compared to 3D fitting methods, our end-to-end trainable pipeline enables disentangling identity-sensitive shape features from whole-body images.", + "bbox": [ + 498, + 300, + 890, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Prior Work", + "text_level": 1, + "bbox": [ + 500, + 411, + 622, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Person Re-identification. Person ReID aims to match a person across images captured by a distributed camera system. The majority of prior methods [11, 12, 24, 25, 28, 52, 58, 60] assume a short-term application scenario without clothing changes by the person. This limitation has generated a growing interest in long-term cloth-changing person ReID [14, 23, 27, 56]. Datasets such as Real28 [50], VC-Clothes [50], PRCC [56], LTCC [46], COCAS [59] and Celebrities-reID [18, 20] are collected to facilitate this research. These datasets, however, either ignore or only minimally consider human activities, assuming that subjects are pedestrians with a restricted set of activities, limiting their applicability in real-world scenarios. As a result, there is a noticeable discrepancy between published approaches and the real-world LT-ReID problem. In contrast to the focus on the clothing-change person ReID, our research takes a step further by addressing a more challenging and practical issue of person ReID that involves diverse human activities, which are not limited to walking.", + "bbox": [ + 496, + 441, + 890, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Clothed Human Modeling and Fitting. In early attempts [22, 34, 40], a clothed person was modeled as displacements over naked body meshes, obtained by SMPL [33]. However, the fixed mesh topology and bounded resolution approach limit geometric expressivity. Recently, neural implicit representations have been explored to model 3D body shapes due to their topological flexibility and resolution independence [6, 7, 10, 38, 44, 45, 49, 53]. However, as shown in Tab. 1, modeling texture in 3D remains a challenge. While these approaches provide rich geometric detail, insufficient attention has been paid", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19618", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e10db5972659fac7a0118d123b811cfc392e5b4f266031a77f77590c7393c236.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed joint learning framework for long-term person re-identification and 3D clothed body shape reconstruction. During the inference of ReID, the identity shape feature $\\mathbf{z}_{id}$ is utilized for matching." + ], + "image_footnote": [], + "bbox": [ + 107, + 85, + 861, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to the discriminativeness of the resulting body shapes. In contrast, we build a discriminative and textured 3D clothed human, serving the purpose of LT-ReID.", + "bbox": [ + 75, + 387, + 468, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These 3D clothed models can be naturally applied to monocular 3D reconstruction (2D-to-3D fitting). Generally, the input image is encoded as a latent vector, from which the generative model reconstructs the 3D shape [10, 30, 31, 37]. Alternatively, two-step pipelines [15, 21, 42, 43, 55] firstly recover 2.5D sketches (e.g., surface normal), and then infer a full 3D shape. A common limitation of these works is that they require 3D body scans for training, as they are trained on synthetic datasets derived from 3D scans and their rendered images. Furthermore, existing methods do not explicitly consider the discriminative ability of reconstructed 3D clothed body shapes. LVD [9] and SHAPY [8] introduce new discriminative fitting pipelines to reconstruct naked body shapes from images. However, without modeling 3D clothing, 2D image cues can not be fully exploited.", + "bbox": [ + 75, + 431, + 468, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a novel joint two-layer shape and texture representation of a 3D clothed human model, consisting of both shape and texture. Together with a model fitting module, our representation allows semi-supervised training from images without 3D labels. More importantly, guided by the completed 3D model and the discriminative 2D-to-3D fitting module, our approach disentangles identity features from identity-irrelevant features in 3D space for LT-ReID. Tab. 1 compares our method with prior works.", + "bbox": [ + 75, + 659, + 468, + 795 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 806, + 250, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 830, + 279, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A 3D clothed human model is described by three disentangled latent variables: identity shape, clothing shape and clothing texture. As shown in Fig. 2, these latent repre", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sentations can be sequentially decoded into canonical 3D shape and texture, respectively by three decoders. To enable self-supervised training on real images, we estimate these latent codes along with the body pose and camera projection parameters. In this work, we use an off-the-shelf method [36] as our PoseNet to predict pose and camera projection, while our image encoder focuses on identity disentanglement learning, i.e., the fitting module. These networks disentangle identity and non-identity components of 3D shapes and reconstruct the input body images via a differentiable render.", + "bbox": [ + 496, + 387, + 890, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, given a training set of $T$ images $\\{\\mathbf{I}_i\\}_{i=1}^T$ and the corresponding identity labels $\\{l_i\\}_{i=1}^T$ , the image encoder $\\mathcal{E}(\\mathbf{I}) : \\mathbf{I} \\to \\mathbf{z}_{id}, \\mathbf{z}_{cloth}, \\mathbf{z}_{tex}$ predicts the identity shape code of naked body $\\mathbf{z}_{id} \\in \\mathbb{R}^{L_{id}}$ , clothed shape code $\\mathbf{z}_{cloth} \\in \\mathbb{R}^{L_{cloth}}$ and texture code $\\mathbf{z}_{tex} \\in \\mathbb{R}^{L_{tex}}$ . Functions $\\mathcal{F}, \\mathcal{C}$ and $\\mathcal{T}$ decode the latent codes to identity shape, clothing shape and texture components, respectively. Additionally, PoseNet $\\mathcal{P}$ predicts the camera projection parameters $\\Omega$ and SMPL body pose $\\theta$ : $(\\Omega, \\theta) = \\mathcal{P}(\\mathbf{I})$ .", + "bbox": [ + 496, + 551, + 890, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mathematically, the learning objective is defined as:", + "bbox": [ + 517, + 689, + 862, + 704 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathcal {E}, \\mathcal {F}, \\mathcal {C}, \\mathcal {T}} {\\arg \\min } \\sum_ {i = 1} ^ {T} \\left(\\left| \\hat {\\mathbf {I}} _ {i} - \\mathbf {I} _ {i} \\right| _ {1} + \\mathcal {L} _ {c l a} (\\mathbf {z} _ {i d}, l _ {i})\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 710, + 890, + 751 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{cla}$ is the classification loss. $\\hat{\\mathbf{I}}$ is the rendered image. This objective enables us to jointly learn accurate 3D clothed shape and discriminative shape for the naked body.", + "bbox": [ + 496, + 758, + 890, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Joint Two-Layer Implicit Model", + "text_level": 1, + "bbox": [ + 500, + 813, + 782, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We jointly model 3D naked body shape, clothed shape and texture in a canonical space by implicit representations.", + "bbox": [ + 496, + 837, + 890, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Discriminative Body Shape Component. We represent the 3D naked body shape as the $\\tau = 0.5$ level set of the", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19619", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f28251ba6aba23315550902cca8f703d3b054397f99ae1f33d704e4360c6d755.jpg", + "image_caption": [ + "Figure 3. Joint two-layer implicit model. The naked body shape model $\\mathcal{F}$ and clothed body shape model $\\mathcal{C}$ take identity shape code $\\mathbf{z}_{id}$ , clothing shape code $\\mathbf{z}_{cloth}$ and a spatial point $\\mathbf{x}$ , and produces two occupancy values $o_1$ and $o_2$ . The texture model $\\mathcal{T}$ takes $\\mathbf{z}_{tex}$ and $\\mathbf{z}_{cloth}$ to estimate RGB color at $\\mathbf{x}$ . A 3D generator $\\mathcal{G}$ uses $\\mathbf{z}_{id}$ to produce a 3D feature volume, enabling hierarchical point-wise feature representation." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 465, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "occupancy function [35]:", + "bbox": [ + 76, + 335, + 248, + 353 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {i d} (\\mathbf {z} _ {i d}) = \\{\\mathbf {x} | \\mathcal {F} (\\mathbf {z} _ {i d}, \\mathbf {x}) = \\tau \\}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 358, + 468, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{F}$ predicts the occupancy value, $o_1$ for any point $\\mathbf{x}$ in the canonical space. Specifically,", + "bbox": [ + 76, + 381, + 468, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F}: \\mathbb {R} ^ {L _ {i d}} \\times \\mathbb {R} ^ {3} \\rightarrow (o _ {1}, \\mathbf {f}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 417, + 468, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{f} \\in \\mathbb{R}^{L_f}$ is a point-wise feature and will be utilized to predict clothing details.", + "bbox": [ + 75, + 440, + 468, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following [6], we make use of function $\\mathcal{F}$ , implemented via a Multi-Layer Perceptron (MLP), coupled with a 3D CNN-based generator $\\mathcal{G}$ to model 3D naked bodies. As shown in Fig. 3(a), the generator produces a 3D feature volume using $\\mathbf{z}_{id}$ as input. We then use trilinear interpolation to query continuous 3D points and feed the feature at $\\mathbf{x}$ to the MLP.", + "bbox": [ + 75, + 470, + 468, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Clothed Shape Component. Similarly, we also represent the clothed body shape as the $\\tau = 0.5$ level set function:", + "bbox": [ + 76, + 580, + 468, + 612 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {\\text {c l o t h}} \\left(\\mathbf {z} _ {\\text {c l o t h}}\\right) = \\{\\mathbf {x} | \\mathcal {C} \\left(\\mathbf {z} _ {\\text {c l o t h}}, \\mathbf {f}, \\mathbf {x}\\right) = \\tau \\}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 618, + 468, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{C}$ is implemented as a MLP:", + "bbox": [ + 76, + 640, + 313, + 656 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C}: \\mathbb {R} ^ {L _ {\\text {c l o t h}}} \\times \\mathbb {R} ^ {L _ {f}} \\times \\mathbb {R} ^ {3} \\rightarrow o _ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 661, + 468, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{C}$ outputs the occupancy value $o_2$ to represent the clothed shape information.", + "bbox": [ + 75, + 686, + 468, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Texture Component. We define a texture field as a mapping function $\\mathcal{T}$ from a point $\\mathbf{x}$ in the canonical space, texture latent $\\mathbf{z}_{\\text{tex}}$ and $\\mathbf{z}_{\\text{cloth}}$ to a RGB value $\\mathbf{c} \\in \\mathbb{R}^3$ :", + "bbox": [ + 75, + 719, + 468, + 765 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {T}: \\mathbb {R} ^ {L _ {\\text {t e x}}} \\times \\mathbb {R} ^ {L _ {\\text {c l o t h}}} \\times \\mathbb {R} ^ {3} \\rightarrow \\mathbf {c}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 770, + 468, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The design of our joint two-layer implicit model is inspired by the approach in [6]. However, as shown in Fig. 3, our model has two novel traits: 1) Instead of simply decomposing the 3D clothed human into coarse and fine models, we apply a two-layer implicit model to represent the naked body and clothing shapes. 2) We additionally model texture to form a complete 3D human model.", + "bbox": [ + 75, + 794, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1d99a1eaa2499273d01ce15c16977b6620f7ec525435f2d837e683f64e340ccc.jpg", + "image_caption": [ + "Figure 4. Neural blend skinning network. This module deforms the pose space to canonical space. Given a deformed point $\\mathbf{x}'$ , we compute its corresponding position $\\hat{\\mathbf{x}}$ in canonical space by iteratively finding the root of Eqn. 9." + ], + "image_footnote": [], + "bbox": [ + 524, + 90, + 864, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Neural Linear Blend Skinning Network", + "text_level": 1, + "bbox": [ + 498, + 285, + 841, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our joint two-layer implicit model is built within the canonical space. However, the 3D clothed human data, usually captured in various poses, introduces misalignments between this canonical space and the deformed counterpart. To predict the occupancy values $\\mathbf{o}_1$ , $\\mathbf{o}_2$ and the texture $\\mathbf{c}$ for a given observed point $\\mathbf{x}'$ within the deformed space, it is essential to first determine its canonical correspondence point $\\hat{\\mathbf{x}}$ . Once $\\mathbf{x}$ is identified, we can then compute $\\mathbf{o}_1$ , $\\mathbf{o}_2$ and $\\mathbf{c}$ using Eqns. 3, 5 and 6. The objective of this step is to find the canonical correspondence $\\hat{\\mathbf{x}}$ of any query point $\\mathbf{x}'$ . To achieve this goal, similar to [6, 7], we learn a linear blend skinning (LBS) [33] using neural networks in an unsupervised manner.", + "bbox": [ + 496, + 308, + 890, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Regressing Blend Weight. We follow [6, 7] which define the skinning field in canonical space conditioned on our identity latent code $\\mathbf{z}_{id}$ :", + "bbox": [ + 498, + 508, + 893, + 555 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {W}: \\mathbb {R} ^ {L _ {i d}} \\times \\mathbb {R} ^ {3} \\rightarrow \\mathbb {R} ^ {K}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 563, + 774, + 580 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\mathbf {z} _ {i d}, \\mathbf {x}\\right)\\rightarrow \\mathbf {w}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 669, + 583, + 890, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{w}$ is the point-wise blend weight of the canonical point $\\mathbf{x}$ . Then deformed point $\\mathbf{x}'$ is determined by the following convex combination:", + "bbox": [ + 496, + 611, + 893, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} ^ {\\prime} = \\mathbf {d} \\left(\\mathbf {z} _ {i d}, \\mathbf {x}, \\theta\\right) = \\sum_ {k = 1} ^ {K} \\mathbf {w} _ {k} \\mathbf {B} _ {k} \\mathbf {x}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 667, + 890, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{w}_k$ is $k$ -element in the vector $\\mathbf{w}$ , while $\\mathbf{B}_k$ denotes the $k$ -element from the set of bone transformation matrices $\\mathcal{B} = \\{\\mathbf{B}_k \\in \\mathbb{R}^{4 \\times 4}\\}_{k=1}^K$ . Both $\\mathbf{x}$ and $\\mathbf{x}'$ in Eqn. 8 are represented in homogeneous coordinates.", + "bbox": [ + 496, + 719, + 890, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Implicit Differentiable Skinning. An overview is illustrated in Fig. 4. While the goal is to determine $\\mathbf{x}' \\rightarrow \\hat{\\mathbf{x}}$ , we only have direct access to the mapping defined by Eqn. 8, which is not invertible. Following [6,7], the correspondence is calculated numerically by finding the root of the equation with Broyden's method [3]:", + "bbox": [ + 496, + 782, + 890, + 873 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} = \\{\\hat {\\mathbf {x}} | \\mathbf {d} (\\mathbf {z} _ {i d}, \\hat {\\mathbf {x}}, \\theta) - \\mathbf {x} ^ {\\prime} = \\mathbf {0} \\}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19620", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Implicit Rendering", + "text_level": 1, + "bbox": [ + 76, + 90, + 261, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During rendering, when 2D pixels are unprojected to 3D points, they are intrinsically mapped in the deformed 3D space. Given a pixel $p$ of a masked input image, we construct a ray $\\mathbf{x}' = \\{\\mathbf{c}_0 + t\\mathbf{v}|t\\geqslant 0\\}$ , where $\\mathbf{c}_0$ represents the camera's position and $\\mathbf{v}$ indicates the viewing direction based on the camera projection parameters $\\Omega$ . $t$ is the scalar distance along the ray. We then map the ray points to the canonical space, following Eqn. 9. The intersection point $\\hat{\\mathbf{x}}_p$ of the ray can be calculated by identifying the first change of clothed shape occupancy $o_2$ . Finally, the rendered color of the pixel $p$ is calculated via Eqn. 6.", + "bbox": [ + 75, + 114, + 473, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Semi-supervised Model Learning", + "text_level": 1, + "bbox": [ + 76, + 292, + 369, + 309 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While our model can perform self-supervised learning from real images without 3D labels, we first pre-train our joint implicit 3D model with 3D data in order to mitigate the inherent ambiguity.", + "bbox": [ + 75, + 316, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5.1 Supervised Pre-training 3D clothed Model", + "text_level": 1, + "bbox": [ + 76, + 400, + 426, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Data. We combine CAPE [34] (3,000 scans) and THuman2.0 [65] (526 scans) to train our joint two-layer implicit model. THuman2.0 consists of 526 texture clothed 3D scans of 105 subjects. Following [6], for each scan, we obtain its SMPL naked shape code. CAPE provides 148,584 pairs of scans under clothing and SMPL naked body with rich pose variations of 15 subjects. We randomly sample 3,000 scans for training. Formally, each training sample can be represented as SMPL pose $\\theta$ , identity label $l_{3D}$ , $n$ spatial points $\\mathbf{x}_i'$ , and their SDFs $o_1^i$ , $o_2^i$ , and color $\\mathbf{c}_i$ : $\\{\\theta, l_{3D}, \\{\\mathbf{x}_i', o_1^i, o_2^i, \\mathbf{c}_i\\}_{i=1}^n\\}$ . With the autodecoding technique [39], we assign trainable identity shape code, clothing shape code, and texture code to each training sample.", + "bbox": [ + 75, + 428, + 472, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss Function. We define the loss below for each sample:", + "bbox": [ + 76, + 628, + 468, + 645 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathcal {F}, \\mathcal {C}, \\mathcal {T}, \\mathbf {z} _ {i d}, \\mathbf {z} _ {c l o t h}, \\mathbf {z} _ {t e x}} {\\arg \\min } \\mathcal {L} _ {i d} + \\mathcal {L} _ {c l o t h} + \\mathcal {L} _ {t e x} + \\mathcal {L} _ {c l a} ^ {3 D} (\\mathbf {z} _ {i d}, l _ {3 D})\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 665, + 464, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i d} = \\sum_ {i = 0} ^ {n} B C E \\left(\\mathcal {F} \\left(\\mathbf {z} _ {i d}, \\hat {\\mathbf {x}} _ {i}\\right), o _ {1} ^ {i}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 695, + 468, + 712 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c l o t h}} = \\sum_ {i = 0} ^ {n} B C E \\left(\\mathcal {C} \\left(\\mathbf {z} _ {\\text {c l o t h}}, \\mathbf {f} _ {i}, \\hat {\\mathbf {x}} _ {i}\\right), o _ {2} ^ {i}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 715, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t e x} = \\sum_ {i = 0} ^ {n} \\left\\| \\mathcal {T} \\left(\\mathbf {z} _ {t e x}, \\mathbf {z} _ {\\text {c l o t h}}, \\hat {\\mathbf {x}} _ {i}\\right) - \\mathbf {c} _ {i} \\right\\| _ {2}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 734, + 468, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{cla}^{3D}(\\mathbf{z}_{id},l_{3D})$ is the cross-entropy classification loss. We additionally add auxiliary loss $\\mathcal{L}_W$ to train network $\\mathcal{W}$", + "bbox": [ + 76, + 766, + 468, + 797 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\arg \\min _ {\\mathcal {W}} \\mathcal {L} _ {W} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 222, + 819, + 468, + 834 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {W} = \\sum_ {k = 0} ^ {K} | | \\mathcal {W} (\\mathbf {z} _ {i d}, \\mathbf {J} _ {k}) - \\mathbf {w} _ {\\mathbf {J} _ {k}} | | _ {2}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 837, + 468, + 857 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{w}_{\\mathbf{J}_k}$ is the pre-computed ground truth skinning weights of SMPL joints location $\\mathbf{J}_k$", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7b47a5577bf922153fbee7520a8ef58b11b558883757a4c2522e0fca1d226f52.jpg", + "image_caption": [ + "Figure 5. Example images from CCDA, with one subject per row, showcasing the diversity of body poses, clothing styles and colors." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 887, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5.2 Self-supervised Joint Modeling and Fitting", + "text_level": 1, + "bbox": [ + 500, + 364, + 852, + 381 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a set of in-the-wild 2D images with body masks and identity labels $\\{\\mathbf{I}_i, \\mathbf{M}_i, l_i\\}_{i=1}^T$ , the self-supervised identity disentanglement loss is:", + "bbox": [ + 498, + 388, + 892, + 434 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathcal {E}, \\mathcal {T}} {\\arg \\min } \\sum_ {i = 1} ^ {T} \\mathcal {L} _ {s i l} + \\mathcal {L} _ {r g b} + \\mathcal {L} _ {c l a}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 436, + 890, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{rgb}$ is the photometric loss, $\\mathcal{L}_{sil}$ is silhouette loss and $\\mathcal{L}_{cla}$ is the classification loss. Specifically, we denote $\\mathbf{I}_p$ and $\\mathbf{M}_p$ as the RGB and silhouette values of pixel $p\\in P$ . Here, $P$ denotes the entire set of pixels in the input image $\\mathbf{I}$ . A subset of $P$ , represented as $P^{in}$ , corresponds to the pixels where an intersection between the rays and the body in the image has been detected. The photometric loss is defined as", + "bbox": [ + 498, + 470, + 892, + 577 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r g b} = \\frac {1}{| P |} \\sum_ {p \\in P ^ {i n}} \\left| \\mathbf {I} _ {p} - \\mathcal {T} \\left(\\mathcal {E} _ {t e x} (\\mathbf {I}), \\mathcal {E} _ {c l o t h} (\\mathbf {I}), \\hat {\\mathbf {x}} _ {p}\\right) \\right|, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 590, + 890, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the encoder $\\mathcal{E}$ estimates $\\mathbf{z}_{id} = \\mathcal{E}_{id}(\\mathbf{I})$ , $\\mathbf{z}_{cloth} = \\mathcal{E}_{cloth}(\\mathbf{I})$ and $\\mathbf{z}_{tex} = \\mathcal{E}_{tex}(\\mathbf{I})$ from image $\\mathbf{I}$ . $\\hat{\\mathbf{x}}$ is the intersection point (see Sec. 3.4).", + "bbox": [ + 498, + 637, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We further define the silhouette loss as", + "bbox": [ + 519, + 683, + 777, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s i l} = \\frac {1}{| P |} \\sum_ {p \\in P ^ {\\text {o u t}}} C E \\left(\\mathbf {M} _ {p}, \\hat {\\mathbf {M}} _ {p}\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 700, + 890, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{M}}$ is the masked rendering, $P^{out} = P - P^{in}$ represents the indices in the mini-batch for which there is no ray-geometry intersection or $\\mathbf{M}_p = 0$ , and $CE(\\cdot ,\\cdot)$ denotes the cross-entropy loss. We impose triplet loss and cross-entropy loss on the identity shape code $\\mathbf{z}_{id} = \\mathcal{E}_{id}(\\mathbf{I})$ as our classification loss $\\mathcal{L}_{cla}(\\mathbf{z}_{id},l)$ .", + "bbox": [ + 496, + 747, + 893, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Person ReID Inference", + "text_level": 1, + "bbox": [ + 500, + 847, + 710, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For person ReID inference, the encoder $\\mathcal{E}$ processes body images and extracts the identity shape features $\\mathbf{z}_{id}$ .", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19621", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Cosine similarity of $\\mathbf{z}_{id}$ is then used to determine if the two images belong to the same person. It is worth noting that, the inference of our ReID does not incorporate the 3D reconstruction module, making it highly efficient.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. CCDA Person ReID Dataset", + "text_level": 1, + "bbox": [ + 76, + 164, + 336, + 179 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We construct a new dataset with diverse human activities and clothing changes for evaluating LT-ReID. Specifically, we collect data for popular athletes in soccer, tennis, and basketball, and popular artists, such as fashion models and singers. We crawl whole body images of each subject on Google Image1 with athlete/artist names. We collect two sets of images per subject: 'challenging' and 'normal' body poses. As an example, for a basketball player, the 'challenging' set includes images of players' actions on the court, while the 'normal' set contains standing or walking poses. We then crop the body region from the original image via the detected bounding box and resize it to $256 \\times 128$ . Finally, the annotator verifies the identity of each image. In total, 1,555 images of 100 subjects are retained. For each subject, we randomly select one image from 'normal' images for the gallery set, while the remaining 1,455 images comprise the query set. Fig. 5 shows examples of images in the CCDA dataset.", + "bbox": [ + 75, + 188, + 470, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 469, + 282, + 486 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. Our training process includes two stages: 1) Networks $\\mathcal{F},\\mathcal{C},\\mathcal{T},\\mathcal{W}$ are pre-trained on 3D data. 2) $\\mathcal{E}$ and $\\mathcal{T}$ are trained or fine-tuned with real images. The encoder $\\mathcal{E}$ is implemented as a ResNet-50. Networks $\\mathcal{F},\\mathcal{C},\\mathcal{T}$ and $\\mathcal{W}$ are MLPs. In experiments, we set $L_{cloth} = L_{tex} = 512$ , $L_{id} = 4,096$ , $L_{f} = L_{h} = 256$ , $K = 24$ , $n = 200,000$ . We implement in Pytorch and use Adam optimizer in both stages.", + "bbox": [ + 75, + 494, + 468, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Person ReID", + "text_level": 1, + "bbox": [ + 76, + 623, + 212, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metric. For person ReID, we follow the standard retrieval accuracy metrics, namely the Cumulative Matching Characteristics (CMC) and mean average precision (mAP).", + "bbox": [ + 75, + 650, + 468, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline. We compare our method with eight SoTA person ReID methods: Two-Stream [66], MLFN [4], HACNN [26], Part-Aligned [47], PCB [48], TriNet [16], MGN [51], DG-Net [64], and five SoTA cloth-changing re-ID methods: ReIDCaps [20], 3DSL [5], RCSAnet [19], FSAM [17] and CAL [14].", + "bbox": [ + 75, + 699, + 468, + 789 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1.1 Results on Cloth-changing Person ReID datasets", + "text_level": 1, + "bbox": [ + 75, + 806, + 467, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We test on four popular cloth-changing ReID datasets: Celeb-reID/Celeb-reID-light [18, 20], PRCC [56], LTCC [46] and the recent CCVID dataset [14, 61].", + "bbox": [ + 75, + 834, + 467, + 880 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/89afd734a9f100650eaaeb59780cf92eb8dc6d48de559fd4378480dc47887074.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneCeleb-reIDCeleb-reID-light
mAPRank1mAPRank1
Two-Stream [66]ResNet-507.836.3--
MLFN [4]*6.041.46.310.6
HACNN [26]*9.547.611.516.2
Part-Aligned [47]GoogLeNet×26.419.4--
PCB [48]ResNet-508.237.1--
MGN [51]ResNet-5010.849.013.921.5
DG-Net [64]ResNet-5010.650.112.623.5
", + "bbox": [ + 504, + 89, + 888, + 193 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d2a1505e3da4d0922278e7f88114e032d95f0729b47abaaf31f1f3fa9ff44ad5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
cloth-changing person ReID methods
ReIDCaps- [20]DenseNet-1219.851.211.220.3
ReIDCaps [20]DenseNet-121×615.863.019.033.5
RCSAnet [19]DenseNet-121×211.955.616.729.5
CAL [14]ResNet-5013.759.218.533.6
3DInvarReIDResNet-5011.855.215.030.1
3DInvarReID#ResNet-5015.261.221.837.0
ReIDCaps+ \n3DInvarReID#-18.465.525.742.2
", + "bbox": [ + 504, + 194, + 888, + 299 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0ba4be9b3456b7c40b0ba6af8ef5ae404f737c5b997bb8fad39db906e9045cc2.jpg", + "table_caption": [ + "Table 2. Comparison with SoTA on Celeb-reID and Celeb-reID-light datasets (\\%). * indicates that the backbone is designed by the authors. The red number means the total number of models. 3DInvarReID#'s weights are initialized using the CAL model." + ], + "table_footnote": [], + "table_body": "
MethodBackboneLTCCPRCC
mAPRank1mAPRank1
HACNN [26]*9.321.6-21.8
PCB [48]ResNet-5010.023.538.741.8
3DSL [5]ResNet-50×214.831.2-51.3
FSAM [17]ResNet-5016.238.5-54.5
CAL [14]ResNet-5018.040.155.855.2
3DInvarReIDResNet-5016.737.852.551.6
CAL+3DInvarReID-18.940.957.256.5
CALResNet-502.83.820.331.6
3DInvarReIDResNet-502.85.120.134.6
3DInvarReID#ResNet-502.85.621.440.7
", + "bbox": [ + 514, + 380, + 879, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Comparison with SoTA cloth-changing person ReID methods on the LTCC and PRCC datasets $(\\%)$ Models highlighted in pink are trained on the Celeb-reID dataset. 3DInvarReID#'s weights are initialized using the CAL model.", + "bbox": [ + 498, + 551, + 890, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Celeb-reID and Celeb-reID-light. As reported in Tab. 2, our 3DInvarReID (Ours) outperforms all the general person re-ID baselines on both datasets. Considering methods using a single network, we also outperform the cloth-changing baseline, ReIDCaps- [20]. More importantly, to investigate the complementarity between our learned 3D shape features and existing 2D features, we fuse our method with cloth-changing baselines by simple summation at the score level. By fusing with ReIDCaps [20], our method improves the Rank1 accuracy on Celeb-reID from $63.0\\%$ to $65.5\\%$ and from $33.5\\%$ to $42.2\\%$ on Celeb-reID-light. These results clearly demonstrate that the 3D shape features learned from our method are both discriminative and complementary to the 2D features, indicating the effectiveness of our proposed approach for person ReID, particularly under cloth-changing scenarios.", + "bbox": [ + 496, + 638, + 890, + 878 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on LTCC, PRCC and CCVID. The compari-", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1All collected images are under Creative Commons licenses.", + "bbox": [ + 94, + 886, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19622", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e989bba30d648413438f2153e5cadce6456a6bbab91ab849666352497ade6787.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneGeneralCloth-changing
mAPRank1mAPRank1
TriNet [16]ResNet-5078.181.577.081.1
CAL [14]ResNet-5081.382.679.681.7
3DInvarReIDResNet-5066.170.865.470.2
CAL+3DInvarReID-82.683.981.384.3
", + "bbox": [ + 89, + 88, + 454, + 186 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2744793c3745b3c1cc1b8072136e8429d097bf9905b78dd2e783bb289bed4c8b.jpg", + "table_caption": [ + "Table 4. Comparison with SoTA methods on CCVID $(\\%)$" + ], + "table_footnote": [], + "table_body": "
MethodBackbonemAPRank1Rank5
ReLU caps [20]DenseNet-121×610.96.520.2
CAL [14]ResNet-5019.310.026.7
3DInvarReIDResNet-5021.711.130.5
", + "bbox": [ + 99, + 220, + 447, + 276 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "son of the LTCC, PRCC and CCVID datasets is shown in Tabs. 3 and 4. Similarly, by fusing the best baseline CAL [14], our method achieves additional improvements. For instance, when evaluated in the cloth-changing setting, our method achieves a significant improvement of $2.6\\%$ in Rank1 accuracy by fusing with CAL on the CCVID dataset. These findings highlight the effectiveness of 3DInvarReID, with the 3D shape features being shown to be both discriminative and complementary to 2D features. Our approach stands out for its superior performance compared to other 3D feature extraction methods for person ReID. This is particularly noteworthy in comparison to the 3DSL [5] (Tab. 3). Additionally, we assess our model under a cross-domain setting—that is, the model is trained with the Celeb-reID dataset and tested using the LTCC and PRCC datasets. Table 3 shows that our models outperform the baseline CAL, indicating a superior discriminative feature representation.", + "bbox": [ + 75, + 325, + 472, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1.2 Results on LT-ReID dataset (CCDA)", + "text_level": 1, + "bbox": [ + 76, + 604, + 383, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given that both our CCDA and Celeb-reID datasets are obtained from the Internet and share a similar image style, we choose trained models on Celeb-reID and evaluate them on CCDA. We choose the SoTA cloth-changing methods, ReIDCaps- [20] and CAL [14] as baselines. The results in Tab. 5 demonstrate that our 3DInvarReID outperforms the baselines, providing strong evidence of its effectiveness in handling person ReID with challenging body poses and cloth-changing variations.", + "bbox": [ + 75, + 628, + 468, + 765 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1.3 Results on Short-term Person ReID datasets", + "text_level": 1, + "bbox": [ + 76, + 785, + 439, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Despite our method is designed for LT-ReID, we additionally compare with SoTA methods on two conventional short-term ReID datasets: Market-1501 [62] and MSMT17 [54], in Tab. 6. By fusing with CAL [14], we observe an average improvement of $2.7\\%$ in Rank1 accuracy on both datasets, demonstrating the complementary nature", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b967882e12eb098066949f01f5b8a8a5598ca3edd14740f0ea6e8050f9e6af07.jpg", + "table_caption": [ + "Table 5. Comparison with SoTA methods on CCDA dataset $(\\%)$" + ], + "table_footnote": [], + "table_body": "
MethodBackboneMarket-1501MSMT17
mAPRank1mAPRank1
PCB [48]ResNet-5081.693.840.468.2
3DSL [5]ResNet-50×287.395.0--
FSAM [17]ResNet-5085.694.6--
CAL [14]ResNet-5087.594.757.379.7
3DInvarReIDResNet-5085.594.255.176.3
CAL+3DInvarReID-87.995.159.180.8
", + "bbox": [ + 513, + 88, + 877, + 205 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/303f12f976a700f594b752464ef1fb5a2e04cd23dc5f4bff748647f525159c0f.jpg", + "table_caption": [ + "Table 6. Comparison on short-term ReID datasets $(\\%)$" + ], + "table_footnote": [], + "table_body": "
LVD [9]SHAPY [8]Ours
CD-L20.6540.6320.610
", + "bbox": [ + 580, + 239, + 812, + 271 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/829cec7f3f798b5d33dd0145fa921f91d8505b2c55a519e587d48303c8cadf74.jpg", + "table_caption": [ + "Table 7. Comparison of 3D boy reconstruction on HBW." + ], + "table_footnote": [], + "table_body": "
Model TypemAPRank1Rank5
3DInvarReID17.536.356.4
3DInvarReID-w/o 3D14.628.448.3
3DInvarReID-w/o Pre-training15.129.350.7
3DInvarReID-w/o 3D clothing16.032.152.8
", + "bbox": [ + 524, + 306, + 869, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 8. Ablaton studies on CCDA dataset $(\\%)$", + "bbox": [ + 553, + 386, + 836, + 400 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of our 3D shape feature, even on short-term datasets.", + "bbox": [ + 500, + 424, + 846, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2.3D Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 449, + 679, + 463 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Most 3D body reconstruction methods focus more on pose estimation than shape estimation. Recently, SHAPY [8] releases a dataset (HBW) that contains ground-truth 3D body scans and the corresponding in-the-wild images, which enables us to test the accuracy of our reconstructed 3D naked body shapes. We thus evaluate our methods on the validation set of HBW, which contains 237 in-the-wild images of 10 subjects. Our baseline includes LVD [9] and SHAPY [8], which are recent pipelines for discriminative identity shape fitting. Following [9], we evaluate the reconstruction accuracy with Chamfer distance $(\\mathrm{CD} - L_2)$ , by uniformly sampling 10,000 points on both ground-truth and predicted meshes in the canonical space. As shown in Tab. 7, our method outperforms the two baselines. We also visualize 3D reconstructions in Fig. 6. Our reconstructions resemble the ground truth better than the baselines. These results demonstrate the superiority of the proposed method in reconstructing naked 3D body shapes. Fig. 7 shows qualitative comparisons with ICON [55] and ClothWild [37]. Our approach achieves comparable clothed 3D body reconstructions.", + "bbox": [ + 496, + 472, + 890, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 797, + 653, + 814 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, all models are trained on Celeb-reID and tested on the CCDA dataset.", + "bbox": [ + 500, + 821, + 890, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of the 3D module. We compare our full model with an ablated version that only incorporates the $\\mathcal{L}_{cla}$ loss in its training, disregarding 3D modules. The results in", + "bbox": [ + 500, + 854, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19623", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/116224ffaac5f58f3a788b784baaec84a9f9f9018ac4e7baa8e734afd02c6f35.jpg", + "image_caption": [ + "Figure 6. Qualitative comparisons with LVD [9] and SHAPY [8] on 3D naked body reconstruction. Our approach recovers more accurate 3D body shapes from the images." + ], + "image_footnote": [], + "bbox": [ + 99, + 89, + 455, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 8 show that our 3DInvarReID significantly improves the recognition accuracy, leading to a Rank1 accuracy increase from 28.4 to 36.3.", + "bbox": [ + 75, + 518, + 468, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Our Two-layer Implicit Model. Our primary goal is to disentangle the identity feature from non-identity features in 3D shape space. To evaluate the effectiveness of our 3D disentanglement module, we train a model (Oursw/o 3D clothing) by replacing our 3D body model with SMPL shape bases and omitting the modeling of the 3D clothing component and rendering layer. The results in Tab. 8 demonstrate the advantages of modeling clothing shape and texture for person ReID (Rank1: $32.1\\rightarrow 36.3$ ).", + "bbox": [ + 75, + 568, + 468, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Pre-training. Tab. 8 shows that removing the pre-training stage results in a lower Rank1 accuracy, with a score of 29.3 compared to our 36.3. This finding highlights the effectiveness of pre-training in addressing the inherent ambiguity of disentanglement.", + "bbox": [ + 75, + 708, + 468, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 76, + 799, + 204, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper tackles the challenging setting of long-term person ReID, which allows a wider range of real-world human activities and accounts for cloth-changing scenarios. To address this problem, we present a joint two-layer implicit representation to model textured 3D clothed humans", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7d64ea0e24c18426461c1c696af139bfd11aa935824c4b0a0d63014a409f1588.jpg", + "image_caption": [ + "Figure 7. Qualitative comparisons with ICON [55] and Cloth-Wild [37] on 3D clothed body reconstruction." + ], + "image_footnote": [], + "bbox": [ + 532, + 90, + 867, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "together with a discriminative fitting module, enabling us to disentangle identity and non-identity features for real-world images. We collect a new LT-ReID dataset, CCDA, with diverse human activities and clothing changes, facilitating future research on real-world scenarios. Experimental results demonstrate the effectiveness of our method in disentangling identity and non-identity features in 3D clothed body shapes, thereby contributing to LT-ReID.", + "bbox": [ + 496, + 439, + 892, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations & Potential Negative Impacts Impacts. Our work tackles the challenge of disentangling clothing and body shape in 3D shape representation. The clothing reconstruction task remains challenging as evidenced by the visual quality of the published models and our models. Our results show that the task of body-clothing disentangle-ment brings benefit in the recognition task, a finding which opens new possibilities to multi-task learning across 2D-3D modalities. Like most person ReID methods, one potential negative impact of our approach is that it could be used for unethical surveillance and invasion of privacy.", + "bbox": [ + 496, + 571, + 892, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2022-21102100004. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.", + "bbox": [ + 496, + 750, + 892, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19624", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ejaz Ahmed, Michael Jones, and Tim K Marks. An improved deep learning architecture for person re-identification. In CVPR, 2015. 1", + "[2] Thiemo Alldieck, Mihai Zanfir, and Cristian Sminchisescu. Photorealistic monocular 3D reconstruction of humans wearing clothing. In CVPR, 2022. 2", + "[3] Charles G Broyden. A class of methods for solving nonlinear simultaneous equations. 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Parameter-efficient person re-identification in the 3D space. arXiv preprint arXiv:2006.04569, 2020.1" + ], + "bbox": [ + 501, + 92, + 890, + 816 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19626", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_model.json b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..49dd569892072cdfff1c7cec0af8625955d0d531 --- /dev/null +++ b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_model.json @@ -0,0 +1,2651 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.164, + 0.131, + 0.808, + 0.177 + ], + "angle": 0, + "content": "Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.204, + 0.756, + 0.256 + ], + "angle": 0, + "content": "Feng Liu, Minchul Kim, ZiAng Gu, Anil Jain, Xiaoming Liu \nDepartment of Computer Science and Engineering \nMichigan State University, East Lansing MI 48824" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.257, + 0.756, + 0.275 + ], + "angle": 0, + "content": "{liufeng6, kimminc2, guziang, jain, liuxm}@msu.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.645 + ], + "angle": 0, + "content": "Long-Term Person Re-Identification (LT-ReID) has become increasingly crucial in computer vision and biometrics. In this work, we aim to extend LT-ReID beyond pedestrian recognition to include a wider range of real-world human activities while still accounting for cloth-changing scenarios over large time gaps. This setting poses additional challenges due to the geometric misalignment and appearance ambiguity caused by the diversity of human pose and clothing. To address these challenges, we propose a new approach 3DInvarReID for (i) disentangling identity from non-identity components (pose, clothing shape, and texture) of 3D clothed humans, and (ii) reconstructing accurate 3D clothed body shapes and learning discriminative features of naked body shapes for person ReID in a joint manner. To better evaluate our study of LT-ReID, we collect a real-world dataset called CCDA, which contains a wide variety of human activities and clothing changes. Experimentally, we show the superior performance of our approach for person ReID. Code is available at http://cvlab.cse.msu.edu/project-reid3dinvar.html." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.677, + 0.21, + 0.693 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Person Re-Identification (ReID) aims to recognize and match a specific pedestrian in various locations and at different times [1, 26, 29, 57, 62]. This is a crucial task for various applications, including crime prevention, forensic identification and security monitoring [13, 63]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Most existing works [11, 12, 24, 25] in this field concentrate on the short-term scenarios, assuming that pedestrians' clothing remains unchanged. However, in this paper, we focus on a more challenging yet practical scenario of Long-Term Person Re-Identification (LT-ReID), where the objective is to recognize individuals over long time periods while taking into account variations in clothing and diverse human activities. For the first time, we extend person re" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.309, + 0.878, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.422, + 0.623, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.499, + 0.572, + 0.51 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.422, + 0.75, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.499, + 0.7, + 0.51 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.769, + 0.422, + 0.877, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.81, + 0.499, + 0.826, + 0.51 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.515, + 0.895, + 0.613 + ], + "angle": 0, + "content": "Figure 1. Illustration of the differences between various person re-identification (ReID) settings. Both (a) conventional/short-term and (b) cloth-changing person ReID benchmarks often restrict subjects to walking or standing, limiting their applications in real-world scenarios. This paper expands on the long-term person re-identification (LT-ReID) setting by tackling a wider range of human activities, increasing its practicality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.894, + 0.734 + ], + "angle": 0, + "content": "identification beyond pedestrian recognition to encompass a wider range of human activities, such as identifying students playing tennis or soldiers crawling in the field (see Fig. 1). This setting poses new challenges due to the geometric misalignment and appearance ambiguity caused by the diversity of human poses and their clothing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recently, various approaches [14,18,20,23,27,46,56,59] have been proposed to investigate LT-ReID under clothing changes. They extract clothing-irrelevant features for robust person ReID by custom-designed architectures [19,20], training process [27], loss functions [14], and data augmentation [64]. However, these methods only attempt to mine texture-insensitive body-structural cues in 2D space while ignoring the prior knowledge that the human body is a 3D non-rigid object. A new line of research introduces 3D priors for LT-ReID by either lifting 2D images to a 3D space [67] or including 3D body reconstruction as an auxil" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19617" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.152 + ], + "angle": 0, + "content": "iary task [5]. However, without modeling the 3D clothing, the clothing-sensitive features can not be properly disentangled in either method. Moreover, none of the methods above handle body images with diverse activities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.159, + 0.471, + 0.4 + ], + "angle": 0, + "content": "Given the numerous variations in body images, including body pose, clothing, and view angles, we posit that the most reliable identity cue for LT-ReID is the 3D naked (unclothed) body shape, if it can be accurately and discriminately estimated from a 2D body image. Obviously this is extremely challenging due to confounding factors and the lack of supervision, such as paired images and 3D naked body scans. However, taking inspiration from advancements in 3D feature learning for face recognition [32, 41], we propose a new algorithm, 3DInvarReID, to disentangle identity (naked body) from non-identity components (pose, clothing shape and texture) of 3D clothed humans. This innovative approach not only reconstructs accurate 3D clothed body shapes that faithfully represent the input 2D images, but it also simultaneously learns discriminative naked shape features that effectively enhance LT-ReID." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.47, + 0.724 + ], + "angle": 0, + "content": "An effective representation of the 3D shape and texture of the human body is a key component of such a learning-based process. To this end, we propose a joint two-layer neural implicit function to represent 3D humans, where identity, clothing shape, and texture components are disentangled into latent representations. Based on the composite model, we jointly learn a model fitting module to disentangle identity from non-identity components (body pose, clothing shape and texture) from 2D images. Modeling texture, along with a differentiable renderer enables us to compare the rendered image with the input image in a self-supervised manner. This allows the learning process to be supervised by both image reconstruction loss and identification loss, using a set of 2D images with identity labels only. Comprehensive experiments demonstrate the superiority of our method in diverse ReID benchmarks. Additionally, to advance the research in the field of LT-ReID, we collect a Cloth-Changing and Diverse Activities (CCDA) dataset (see Fig. 1). The CCDA dataset is specifically designed to evaluate the ReID of the person undergoing both human activities and changes in clothing." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.731, + 0.436, + 0.745 + ], + "angle": 0, + "content": "In summary, the contributions of this work include:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.752, + 0.468, + 0.782 + ], + "angle": 0, + "content": "\\(\\diamond\\) We propose a novel LT-ReID method, 3DInvarReID, to learn clothing/pose invariant 3D shape representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.789, + 0.468, + 0.864 + ], + "angle": 0, + "content": "\\(\\diamond\\) We devise a novel joint two-layer implicit model that fully models a textured 3D clothed human. Our approach includes a robust and discriminative fitting process that disentangles identity and non-identity features in reconstructing two-layer 3D body shapes from real-world images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "\\(\\diamond\\) We achieve superior performance in both LT-ReID accuracy and 3D body shape reconstruction." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.752, + 0.468, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.09, + 0.89, + 0.294 + ], + "angle": 0, + "content": "
MethodEnd-to-End trainableModel textureDiscriminativeModel type
3D modeling methods
SCANimate [44]-XXuniversal
SMPLicit [10]-XXuniversal
Neural-GIF [49]-XXindividual
SNARF [7]-XXindividual
gDNA [6]-XXuniversal
3D fitting methods
PiFu [42]X✓X-
PiFuHD [43]XXX-
Arch [21]X✓X-
Arch++ [15]X✓X-
ICON [55]X✓X-
ClothWild [37]XXX-
PHORHUM [2]✓✓X-
3DInvarReID✓✓✓universal
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.301, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Table 1. Overview of the 3D clothed human modeling (top) and fitting (bottom) methods. Our method is the only one that models clothing texture and learns discriminative information compared to 3D modeling methods. Compared to 3D fitting methods, our end-to-end trainable pipeline enables disentangling identity-sensitive shape features from whole-body images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.412, + 0.623, + 0.427 + ], + "angle": 0, + "content": "2. Prior Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.892, + 0.73 + ], + "angle": 0, + "content": "Person Re-identification. Person ReID aims to match a person across images captured by a distributed camera system. The majority of prior methods [11, 12, 24, 25, 28, 52, 58, 60] assume a short-term application scenario without clothing changes by the person. This limitation has generated a growing interest in long-term cloth-changing person ReID [14, 23, 27, 56]. Datasets such as Real28 [50], VC-Clothes [50], PRCC [56], LTCC [46], COCAS [59] and Celebrities-reID [18, 20] are collected to facilitate this research. These datasets, however, either ignore or only minimally consider human activities, assuming that subjects are pedestrians with a restricted set of activities, limiting their applicability in real-world scenarios. As a result, there is a noticeable discrepancy between published approaches and the real-world LT-ReID problem. In contrast to the focus on the clothing-change person ReID, our research takes a step further by addressing a more challenging and practical issue of person ReID that involves diverse human activities, which are not limited to walking." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "3D Clothed Human Modeling and Fitting. In early attempts [22, 34, 40], a clothed person was modeled as displacements over naked body meshes, obtained by SMPL [33]. However, the fixed mesh topology and bounded resolution approach limit geometric expressivity. Recently, neural implicit representations have been explored to model 3D body shapes due to their topological flexibility and resolution independence [6, 7, 10, 38, 44, 45, 49, 53]. However, as shown in Tab. 1, modeling texture in 3D remains a challenge. While these approaches provide rich geometric detail, insufficient attention has been paid" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19618" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.087, + 0.862, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.335, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed joint learning framework for long-term person re-identification and 3D clothed body shape reconstruction. During the inference of ReID, the identity shape feature \\(\\mathbf{z}_{id}\\) is utilized for matching." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.47, + 0.432 + ], + "angle": 0, + "content": "to the discriminativeness of the resulting body shapes. In contrast, we build a discriminative and textured 3D clothed human, serving the purpose of LT-ReID." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.659 + ], + "angle": 0, + "content": "These 3D clothed models can be naturally applied to monocular 3D reconstruction (2D-to-3D fitting). Generally, the input image is encoded as a latent vector, from which the generative model reconstructs the 3D shape [10, 30, 31, 37]. Alternatively, two-step pipelines [15, 21, 42, 43, 55] firstly recover 2.5D sketches (e.g., surface normal), and then infer a full 3D shape. A common limitation of these works is that they require 3D body scans for training, as they are trained on synthetic datasets derived from 3D scans and their rendered images. Furthermore, existing methods do not explicitly consider the discriminative ability of reconstructed 3D clothed body shapes. LVD [9] and SHAPY [8] introduce new discriminative fitting pipelines to reconstruct naked body shapes from images. However, without modeling 3D clothing, 2D image cues can not be fully exploited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.796 + ], + "angle": 0, + "content": "We propose a novel joint two-layer shape and texture representation of a 3D clothed human model, consisting of both shape and texture. Together with a model fitting module, our representation allows semi-supervised training from images without 3D labels. More importantly, guided by the completed 3D model and the discriminative 2D-to-3D fitting module, our approach disentangles identity features from identity-irrelevant features in 3D space for LT-ReID. Tab. 1 compares our method with prior works." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.808, + 0.251, + 0.824 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.281, + 0.847 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "A 3D clothed human model is described by three disentangled latent variables: identity shape, clothing shape and clothing texture. As shown in Fig. 2, these latent repre" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.553 + ], + "angle": 0, + "content": "sentations can be sequentially decoded into canonical 3D shape and texture, respectively by three decoders. To enable self-supervised training on real images, we estimate these latent codes along with the body pose and camera projection parameters. In this work, we use an off-the-shelf method [36] as our PoseNet to predict pose and camera projection, while our image encoder focuses on identity disentanglement learning, i.e., the fitting module. These networks disentangle identity and non-identity components of 3D shapes and reconstruct the input body images via a differentiable render." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.689 + ], + "angle": 0, + "content": "Formally, given a training set of \\(T\\) images \\(\\{\\mathbf{I}_i\\}_{i=1}^T\\) and the corresponding identity labels \\(\\{l_i\\}_{i=1}^T\\), the image encoder \\(\\mathcal{E}(\\mathbf{I}) : \\mathbf{I} \\to \\mathbf{z}_{id}, \\mathbf{z}_{cloth}, \\mathbf{z}_{tex}\\) predicts the identity shape code of naked body \\(\\mathbf{z}_{id} \\in \\mathbb{R}^{L_{id}}\\), clothed shape code \\(\\mathbf{z}_{cloth} \\in \\mathbb{R}^{L_{cloth}}\\) and texture code \\(\\mathbf{z}_{tex} \\in \\mathbb{R}^{L_{tex}}\\). Functions \\(\\mathcal{F}, \\mathcal{C}\\) and \\(\\mathcal{T}\\) decode the latent codes to identity shape, clothing shape and texture components, respectively. Additionally, PoseNet \\(\\mathcal{P}\\) predicts the camera projection parameters \\(\\Omega\\) and SMPL body pose \\(\\theta\\): \\((\\Omega, \\theta) = \\mathcal{P}(\\mathbf{I})\\)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.69, + 0.863, + 0.705 + ], + "angle": 0, + "content": "Mathematically, the learning objective is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.712, + 0.892, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathcal {E}, \\mathcal {F}, \\mathcal {C}, \\mathcal {T}} {\\arg \\min } \\sum_ {i = 1} ^ {T} \\left(\\left| \\hat {\\mathbf {I}} _ {i} - \\mathbf {I} _ {i} \\right| _ {1} + \\mathcal {L} _ {c l a} (\\mathbf {z} _ {i d}, l _ {i})\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.76, + 0.892, + 0.807 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{cla}\\) is the classification loss. \\(\\hat{\\mathbf{I}}\\) is the rendered image. This objective enables us to jointly learn accurate 3D clothed shape and discriminative shape for the naked body." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.814, + 0.783, + 0.83 + ], + "angle": 0, + "content": "3.2. Joint Two-Layer Implicit Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.838, + 0.892, + 0.868 + ], + "angle": 0, + "content": "We jointly model 3D naked body shape, clothed shape and texture in a canonical space by implicit representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Discriminative Body Shape Component. We represent the 3D naked body shape as the \\(\\tau = 0.5\\) level set of the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19619" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.466, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.219, + 0.473, + 0.318 + ], + "angle": 0, + "content": "Figure 3. Joint two-layer implicit model. The naked body shape model \\(\\mathcal{F}\\) and clothed body shape model \\(\\mathcal{C}\\) take identity shape code \\(\\mathbf{z}_{id}\\), clothing shape code \\(\\mathbf{z}_{cloth}\\) and a spatial point \\(\\mathbf{x}\\), and produces two occupancy values \\(o_1\\) and \\(o_2\\). The texture model \\(\\mathcal{T}\\) takes \\(\\mathbf{z}_{tex}\\) and \\(\\mathbf{z}_{cloth}\\) to estimate RGB color at \\(\\mathbf{x}\\). A 3D generator \\(\\mathcal{G}\\) uses \\(\\mathbf{z}_{id}\\) to produce a 3D feature volume, enabling hierarchical point-wise feature representation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.249, + 0.354 + ], + "angle": 0, + "content": "occupancy function [35]:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.359, + 0.47, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {i d} (\\mathbf {z} _ {i d}) = \\{\\mathbf {x} | \\mathcal {F} (\\mathbf {z} _ {i d}, \\mathbf {x}) = \\tau \\}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.382, + 0.47, + 0.413 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}\\) predicts the occupancy value, \\(o_1\\) for any point \\(\\mathbf{x}\\) in the canonical space. Specifically," + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.418, + 0.469, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F}: \\mathbb {R} ^ {L _ {i d}} \\times \\mathbb {R} ^ {3} \\rightarrow (o _ {1}, \\mathbf {f}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.47, + 0.472 + ], + "angle": 0, + "content": "where \\(\\mathbf{f} \\in \\mathbb{R}^{L_f}\\) is a point-wise feature and will be utilized to predict clothing details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.47, + 0.576 + ], + "angle": 0, + "content": "Following [6], we make use of function \\(\\mathcal{F}\\), implemented via a Multi-Layer Perceptron (MLP), coupled with a 3D CNN-based generator \\(\\mathcal{G}\\) to model 3D naked bodies. As shown in Fig. 3(a), the generator produces a 3D feature volume using \\(\\mathbf{z}_{id}\\) as input. We then use trilinear interpolation to query continuous 3D points and feed the feature at \\(\\mathbf{x}\\) to the MLP." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.581, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Clothed Shape Component. Similarly, we also represent the clothed body shape as the \\(\\tau = 0.5\\) level set function:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.619, + 0.47, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {\\text {c l o t h}} \\left(\\mathbf {z} _ {\\text {c l o t h}}\\right) = \\{\\mathbf {x} | \\mathcal {C} \\left(\\mathbf {z} _ {\\text {c l o t h}}, \\mathbf {f}, \\mathbf {x}\\right) = \\tau \\}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.641, + 0.314, + 0.657 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}\\) is implemented as a MLP:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.662, + 0.469, + 0.68 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C}: \\mathbb {R} ^ {L _ {\\text {c l o t h}}} \\times \\mathbb {R} ^ {L _ {f}} \\times \\mathbb {R} ^ {3} \\rightarrow o _ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.716 + ], + "angle": 0, + "content": "\\(\\mathcal{C}\\) outputs the occupancy value \\(o_2\\) to represent the clothed shape information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.766 + ], + "angle": 0, + "content": "Texture Component. We define a texture field as a mapping function \\(\\mathcal{T}\\) from a point \\(\\mathbf{x}\\) in the canonical space, texture latent \\(\\mathbf{z}_{\\text{tex}}\\) and \\(\\mathbf{z}_{\\text{cloth}}\\) to a RGB value \\(\\mathbf{c} \\in \\mathbb{R}^3\\):" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.771, + 0.469, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\mathcal {T}: \\mathbb {R} ^ {L _ {\\text {t e x}}} \\times \\mathbb {R} ^ {L _ {\\text {c l o t h}}} \\times \\mathbb {R} ^ {3} \\rightarrow \\mathbf {c}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The design of our joint two-layer implicit model is inspired by the approach in [6]. However, as shown in Fig. 3, our model has two novel traits: 1) Instead of simply decomposing the 3D clothed human into coarse and fine models, we apply a two-layer implicit model to represent the naked body and clothing shapes. 2) We additionally model texture to form a complete 3D human model." + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.092, + 0.865, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.206, + 0.895, + 0.263 + ], + "angle": 0, + "content": "Figure 4. Neural blend skinning network. This module deforms the pose space to canonical space. Given a deformed point \\(\\mathbf{x}'\\), we compute its corresponding position \\(\\hat{\\mathbf{x}}\\) in canonical space by iteratively finding the root of Eqn. 9." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.286, + 0.842, + 0.303 + ], + "angle": 0, + "content": "3.3. Neural Linear Blend Skinning Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.892, + 0.505 + ], + "angle": 0, + "content": "Our joint two-layer implicit model is built within the canonical space. However, the 3D clothed human data, usually captured in various poses, introduces misalignments between this canonical space and the deformed counterpart. To predict the occupancy values \\(\\mathbf{o}_1\\), \\(\\mathbf{o}_2\\) and the texture \\(\\mathbf{c}\\) for a given observed point \\(\\mathbf{x}'\\) within the deformed space, it is essential to first determine its canonical correspondence point \\(\\hat{\\mathbf{x}}\\). Once \\(\\mathbf{x}\\) is identified, we can then compute \\(\\mathbf{o}_1\\), \\(\\mathbf{o}_2\\) and \\(\\mathbf{c}\\) using Eqns. 3, 5 and 6. The objective of this step is to find the canonical correspondence \\(\\hat{\\mathbf{x}}\\) of any query point \\(\\mathbf{x}'\\). To achieve this goal, similar to [6, 7], we learn a linear blend skinning (LBS) [33] using neural networks in an unsupervised manner." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.509, + 0.895, + 0.556 + ], + "angle": 0, + "content": "Regressing Blend Weight. We follow [6, 7] which define the skinning field in canonical space conditioned on our identity latent code \\(\\mathbf{z}_{id}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.564, + 0.775, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\mathcal {W}: \\mathbb {R} ^ {L _ {i d}} \\times \\mathbb {R} ^ {3} \\rightarrow \\mathbb {R} ^ {K}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.671, + 0.584, + 0.892, + 0.601 + ], + "angle": 0, + "content": "\\[\n\\left(\\mathbf {z} _ {i d}, \\mathbf {x}\\right)\\rightarrow \\mathbf {w}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.894, + 0.658 + ], + "angle": 0, + "content": "where \\(\\mathbf{w}\\) is the point-wise blend weight of the canonical point \\(\\mathbf{x}\\). Then deformed point \\(\\mathbf{x}'\\) is determined by the following convex combination:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.668, + 0.892, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} ^ {\\prime} = \\mathbf {d} \\left(\\mathbf {z} _ {i d}, \\mathbf {x}, \\theta\\right) = \\sum_ {k = 1} ^ {K} \\mathbf {w} _ {k} \\mathbf {B} _ {k} \\mathbf {x}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.78 + ], + "angle": 0, + "content": "where \\(\\mathbf{w}_k\\) is \\(k\\)-element in the vector \\(\\mathbf{w}\\), while \\(\\mathbf{B}_k\\) denotes the \\(k\\)-element from the set of bone transformation matrices \\(\\mathcal{B} = \\{\\mathbf{B}_k \\in \\mathbb{R}^{4 \\times 4}\\}_{k=1}^K\\). Both \\(\\mathbf{x}\\) and \\(\\mathbf{x}'\\) in Eqn. 8 are represented in homogeneous coordinates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.784, + 0.892, + 0.874 + ], + "angle": 0, + "content": "Implicit Differentiable Skinning. An overview is illustrated in Fig. 4. While the goal is to determine \\(\\mathbf{x}' \\rightarrow \\hat{\\mathbf{x}}\\), we only have direct access to the mapping defined by Eqn. 8, which is not invertible. Following [6,7], the correspondence is calculated numerically by finding the root of the equation with Broyden's method [3]:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} = \\{\\hat {\\mathbf {x}} | \\mathbf {d} (\\mathbf {z} _ {i d}, \\hat {\\mathbf {x}}, \\theta) - \\mathbf {x} ^ {\\prime} = \\mathbf {0} \\}. \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19620" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.262, + 0.108 + ], + "angle": 0, + "content": "3.4. Implicit Rendering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.474, + 0.283 + ], + "angle": 0, + "content": "During rendering, when 2D pixels are unprojected to 3D points, they are intrinsically mapped in the deformed 3D space. Given a pixel \\( p \\) of a masked input image, we construct a ray \\( \\mathbf{x}' = \\{\\mathbf{c}_0 + t\\mathbf{v}|t\\geqslant 0\\} \\), where \\( \\mathbf{c}_0 \\) represents the camera's position and \\( \\mathbf{v} \\) indicates the viewing direction based on the camera projection parameters \\( \\Omega \\). \\( t \\) is the scalar distance along the ray. We then map the ray points to the canonical space, following Eqn. 9. The intersection point \\( \\hat{\\mathbf{x}}_p \\) of the ray can be calculated by identifying the first change of clothed shape occupancy \\( o_2 \\). Finally, the rendered color of the pixel \\( p \\) is calculated via Eqn. 6." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.293, + 0.37, + 0.31 + ], + "angle": 0, + "content": "3.5. Semi-supervised Model Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.317, + 0.47, + 0.38 + ], + "angle": 0, + "content": "While our model can perform self-supervised learning from real images without 3D labels, we first pre-train our joint implicit 3D model with 3D data in order to mitigate the inherent ambiguity." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.401, + 0.427, + 0.417 + ], + "angle": 0, + "content": "3.5.1 Supervised Pre-training 3D clothed Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.473, + 0.627 + ], + "angle": 0, + "content": "Training Data. We combine CAPE [34] (3,000 scans) and THuman2.0 [65] (526 scans) to train our joint two-layer implicit model. THuman2.0 consists of 526 texture clothed 3D scans of 105 subjects. Following [6], for each scan, we obtain its SMPL naked shape code. CAPE provides 148,584 pairs of scans under clothing and SMPL naked body with rich pose variations of 15 subjects. We randomly sample 3,000 scans for training. Formally, each training sample can be represented as SMPL pose \\(\\theta\\), identity label \\(l_{3D}\\), \\(n\\) spatial points \\(\\mathbf{x}_i'\\), and their SDFs \\(o_1^i\\), \\(o_2^i\\), and color \\(\\mathbf{c}_i\\): \\(\\{\\theta, l_{3D}, \\{\\mathbf{x}_i', o_1^i, o_2^i, \\mathbf{c}_i\\}_{i=1}^n\\}\\). With the autodecoding technique [39], we assign trainable identity shape code, clothing shape code, and texture code to each training sample." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.47, + 0.646 + ], + "angle": 0, + "content": "Loss Function. We define the loss below for each sample:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.666, + 0.465, + 0.692 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathcal {F}, \\mathcal {C}, \\mathcal {T}, \\mathbf {z} _ {i d}, \\mathbf {z} _ {c l o t h}, \\mathbf {z} _ {t e x}} {\\arg \\min } \\mathcal {L} _ {i d} + \\mathcal {L} _ {c l o t h} + \\mathcal {L} _ {t e x} + \\mathcal {L} _ {c l a} ^ {3 D} (\\mathbf {z} _ {i d}, l _ {3 D})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.696, + 0.469, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i d} = \\sum_ {i = 0} ^ {n} B C E \\left(\\mathcal {F} \\left(\\mathbf {z} _ {i d}, \\hat {\\mathbf {x}} _ {i}\\right), o _ {1} ^ {i}\\right) \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.716, + 0.469, + 0.734 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c l o t h}} = \\sum_ {i = 0} ^ {n} B C E \\left(\\mathcal {C} \\left(\\mathbf {z} _ {\\text {c l o t h}}, \\mathbf {f} _ {i}, \\hat {\\mathbf {x}} _ {i}\\right), o _ {2} ^ {i}\\right) \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.736, + 0.469, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t e x} = \\sum_ {i = 0} ^ {n} \\left\\| \\mathcal {T} \\left(\\mathbf {z} _ {t e x}, \\mathbf {z} _ {\\text {c l o t h}}, \\hat {\\mathbf {x}} _ {i}\\right) - \\mathbf {c} _ {i} \\right\\| _ {2}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.767, + 0.469, + 0.798 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{cla}^{3D}(\\mathbf{z}_{id},l_{3D})\\) is the cross-entropy classification loss. We additionally add auxiliary loss \\(\\mathcal{L}_W\\) to train network \\(\\mathcal{W}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.223, + 0.82, + 0.469, + 0.835 + ], + "angle": 0, + "content": "\\[\n\\arg \\min _ {\\mathcal {W}} \\mathcal {L} _ {W} \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.838, + 0.469, + 0.858 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {W} = \\sum_ {k = 0} ^ {K} | | \\mathcal {W} (\\mathbf {z} _ {i d}, \\mathbf {J} _ {k}) - \\mathbf {w} _ {\\mathbf {J} _ {k}} | | _ {2}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{w}_{\\mathbf{J}_k}\\) is the pre-computed ground truth skinning weights of SMPL joints location \\(\\mathbf{J}_k\\)" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.091, + 0.888, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.318, + 0.892, + 0.347 + ], + "angle": 0, + "content": "Figure 5. Example images from CCDA, with one subject per row, showcasing the diversity of body poses, clothing styles and colors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.366, + 0.853, + 0.382 + ], + "angle": 0, + "content": "3.5.2 Self-supervised Joint Modeling and Fitting" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.389, + 0.893, + 0.435 + ], + "angle": 0, + "content": "Given a set of in-the-wild 2D images with body masks and identity labels \\(\\{\\mathbf{I}_i, \\mathbf{M}_i, l_i\\}_{i=1}^T\\), the self-supervised identity disentanglement loss is:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.437, + 0.892, + 0.464 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathcal {E}, \\mathcal {T}} {\\arg \\min } \\sum_ {i = 1} ^ {T} \\mathcal {L} _ {s i l} + \\mathcal {L} _ {r g b} + \\mathcal {L} _ {c l a}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.471, + 0.893, + 0.578 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{rgb}\\) is the photometric loss, \\(\\mathcal{L}_{sil}\\) is silhouette loss and \\(\\mathcal{L}_{cla}\\) is the classification loss. Specifically, we denote \\(\\mathbf{I}_p\\) and \\(\\mathbf{M}_p\\) as the RGB and silhouette values of pixel \\(p\\in P\\). Here, \\(P\\) denotes the entire set of pixels in the input image \\(\\mathbf{I}\\). A subset of \\(P\\), represented as \\(P^{in}\\), corresponds to the pixels where an intersection between the rays and the body in the image has been detected. The photometric loss is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.592, + 0.892, + 0.631 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r g b} = \\frac {1}{| P |} \\sum_ {p \\in P ^ {i n}} \\left| \\mathbf {I} _ {p} - \\mathcal {T} \\left(\\mathcal {E} _ {t e x} (\\mathbf {I}), \\mathcal {E} _ {c l o t h} (\\mathbf {I}), \\hat {\\mathbf {x}} _ {p}\\right) \\right|, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.638, + 0.892, + 0.682 + ], + "angle": 0, + "content": "where the encoder \\(\\mathcal{E}\\) estimates \\(\\mathbf{z}_{id} = \\mathcal{E}_{id}(\\mathbf{I})\\), \\(\\mathbf{z}_{cloth} = \\mathcal{E}_{cloth}(\\mathbf{I})\\) and \\(\\mathbf{z}_{tex} = \\mathcal{E}_{tex}(\\mathbf{I})\\) from image \\(\\mathbf{I}\\). \\(\\hat{\\mathbf{x}}\\) is the intersection point (see Sec. 3.4)." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.684, + 0.778, + 0.697 + ], + "angle": 0, + "content": "We further define the silhouette loss as" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.702, + 0.892, + 0.739 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s i l} = \\frac {1}{| P |} \\sum_ {p \\in P ^ {\\text {o u t}}} C E \\left(\\mathbf {M} _ {p}, \\hat {\\mathbf {M}} _ {p}\\right), \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.894, + 0.841 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{M}}\\) is the masked rendering, \\(P^{out} = P - P^{in}\\) represents the indices in the mini-batch for which there is no ray-geometry intersection or \\(\\mathbf{M}_p = 0\\), and \\(CE(\\cdot ,\\cdot)\\) denotes the cross-entropy loss. We impose triplet loss and cross-entropy loss on the identity shape code \\(\\mathbf{z}_{id} = \\mathcal{E}_{id}(\\mathbf{I})\\) as our classification loss \\(\\mathcal{L}_{cla}(\\mathbf{z}_{id},l)\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.712, + 0.862 + ], + "angle": 0, + "content": "3.6. Person ReID Inference" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "For person ReID inference, the encoder \\(\\mathcal{E}\\) processes body images and extracts the identity shape features \\(\\mathbf{z}_{id}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19621" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "The Cosine similarity of \\(\\mathbf{z}_{id}\\) is then used to determine if the two images belong to the same person. It is worth noting that, the inference of our ReID does not incorporate the 3D reconstruction module, making it highly efficient." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.165, + 0.338, + 0.18 + ], + "angle": 0, + "content": "4. CCDA Person ReID Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.189, + 0.471, + 0.461 + ], + "angle": 0, + "content": "We construct a new dataset with diverse human activities and clothing changes for evaluating LT-ReID. Specifically, we collect data for popular athletes in soccer, tennis, and basketball, and popular artists, such as fashion models and singers. We crawl whole body images of each subject on Google Image1 with athlete/artist names. We collect two sets of images per subject: 'challenging' and 'normal' body poses. As an example, for a basketball player, the 'challenging' set includes images of players' actions on the court, while the 'normal' set contains standing or walking poses. We then crop the body region from the original image via the detected bounding box and resize it to \\(256 \\times 128\\). Finally, the annotator verifies the identity of each image. In total, 1,555 images of 100 subjects are retained. For each subject, we randomly select one image from 'normal' images for the gallery set, while the remaining 1,455 images comprise the query set. Fig. 5 shows examples of images in the CCDA dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.47, + 0.283, + 0.487 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.47, + 0.618 + ], + "angle": 0, + "content": "Implementation Details. Our training process includes two stages: 1) Networks \\(\\mathcal{F},\\mathcal{C},\\mathcal{T},\\mathcal{W}\\) are pre-trained on 3D data. 2) \\(\\mathcal{E}\\) and \\(\\mathcal{T}\\) are trained or fine-tuned with real images. The encoder \\(\\mathcal{E}\\) is implemented as a ResNet-50. Networks \\(\\mathcal{F},\\mathcal{C},\\mathcal{T}\\) and \\(\\mathcal{W}\\) are MLPs. In experiments, we set \\(L_{cloth} = L_{tex} = 512\\), \\(L_{id} = 4,096\\), \\(L_{f} = L_{h} = 256\\), \\(K = 24\\), \\(n = 200,000\\). We implement in Pytorch and use Adam optimizer in both stages." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.624, + 0.214, + 0.639 + ], + "angle": 0, + "content": "5.1. Person ReID" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.651, + 0.47, + 0.697 + ], + "angle": 0, + "content": "Metric. For person ReID, we follow the standard retrieval accuracy metrics, namely the Cumulative Matching Characteristics (CMC) and mean average precision (mAP)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.47, + 0.79 + ], + "angle": 0, + "content": "Baseline. We compare our method with eight SoTA person ReID methods: Two-Stream [66], MLFN [4], HACNN [26], Part-Aligned [47], PCB [48], TriNet [16], MGN [51], DG-Net [64], and five SoTA cloth-changing re-ID methods: ReIDCaps [20], 3DSL [5], RCSAnet [19], FSAM [17] and CAL [14]." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.808, + 0.468, + 0.824 + ], + "angle": 0, + "content": "5.1.1 Results on Cloth-changing Person ReID datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.835, + 0.468, + 0.881 + ], + "angle": 0, + "content": "Datasets. We test on four popular cloth-changing ReID datasets: Celeb-reID/Celeb-reID-light [18, 20], PRCC [56], LTCC [46] and the recent CCVID dataset [14, 61]." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.09, + 0.89, + 0.194 + ], + "angle": 0, + "content": "
MethodBackboneCeleb-reIDCeleb-reID-light
mAPRank1mAPRank1
Two-Stream [66]ResNet-507.836.3--
MLFN [4]*6.041.46.310.6
HACNN [26]*9.547.611.516.2
Part-Aligned [47]GoogLeNet×26.419.4--
PCB [48]ResNet-508.237.1--
MGN [51]ResNet-5010.849.013.921.5
DG-Net [64]ResNet-5010.650.112.623.5
" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.195, + 0.889, + 0.3 + ], + "angle": 0, + "content": "
cloth-changing person ReID methods
ReIDCaps- [20]DenseNet-1219.851.211.220.3
ReIDCaps [20]DenseNet-121×615.863.019.033.5
RCSAnet [19]DenseNet-121×211.955.616.729.5
CAL [14]ResNet-5013.759.218.533.6
3DInvarReIDResNet-5011.855.215.030.1
3DInvarReID#ResNet-5015.261.221.837.0
ReIDCaps+ \n3DInvarReID#-18.465.525.742.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.309, + 0.892, + 0.366 + ], + "angle": 0, + "content": "Table 2. Comparison with SoTA on Celeb-reID and Celeb-reID-light datasets (\\%). * indicates that the backbone is designed by the authors. The red number means the total number of models. 3DInvarReID#'s weights are initialized using the CAL model." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.381, + 0.88, + 0.543 + ], + "angle": 0, + "content": "
MethodBackboneLTCCPRCC
mAPRank1mAPRank1
HACNN [26]*9.321.6-21.8
PCB [48]ResNet-5010.023.538.741.8
3DSL [5]ResNet-50×214.831.2-51.3
FSAM [17]ResNet-5016.238.5-54.5
CAL [14]ResNet-5018.040.155.855.2
3DInvarReIDResNet-5016.737.852.551.6
CAL+3DInvarReID-18.940.957.256.5
CALResNet-502.83.820.331.6
3DInvarReIDResNet-502.85.120.134.6
3DInvarReID#ResNet-502.85.621.440.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.553, + 0.892, + 0.61 + ], + "angle": 0, + "content": "Table 3. Comparison with SoTA cloth-changing person ReID methods on the LTCC and PRCC datasets \\((\\%)\\) Models highlighted in pink are trained on the Celeb-reID dataset. 3DInvarReID#'s weights are initialized using the CAL model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.88 + ], + "angle": 0, + "content": "Results on Celeb-reID and Celeb-reID-light. As reported in Tab. 2, our 3DInvarReID (Ours) outperforms all the general person re-ID baselines on both datasets. Considering methods using a single network, we also outperform the cloth-changing baseline, ReIDCaps- [20]. More importantly, to investigate the complementarity between our learned 3D shape features and existing 2D features, we fuse our method with cloth-changing baselines by simple summation at the score level. By fusing with ReIDCaps [20], our method improves the Rank1 accuracy on Celeb-reID from \\(63.0\\%\\) to \\(65.5\\%\\) and from \\(33.5\\%\\) to \\(42.2\\%\\) on Celeb-reID-light. These results clearly demonstrate that the 3D shape features learned from our method are both discriminative and complementary to the 2D features, indicating the effectiveness of our proposed approach for person ReID, particularly under cloth-changing scenarios." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Results on LTCC, PRCC and CCVID. The compari-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.468, + 0.9 + ], + "angle": 0, + "content": "1All collected images are under Creative Commons licenses." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19622" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.089, + 0.455, + 0.187 + ], + "angle": 0, + "content": "
MethodBackboneGeneralCloth-changing
mAPRank1mAPRank1
TriNet [16]ResNet-5078.181.577.081.1
CAL [14]ResNet-5081.382.679.681.7
3DInvarReIDResNet-5066.170.865.470.2
CAL+3DInvarReID-82.683.981.384.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.101, + 0.195, + 0.446, + 0.21 + ], + "angle": 0, + "content": "Table 4. Comparison with SoTA methods on CCVID \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.222, + 0.449, + 0.277 + ], + "angle": 0, + "content": "
MethodBackbonemAPRank1Rank5
ReLU caps [20]DenseNet-121×610.96.520.2
CAL [14]ResNet-5019.310.026.7
3DInvarReIDResNet-5021.711.130.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.286, + 0.461, + 0.302 + ], + "angle": 0, + "content": "Table 5. Comparison with SoTA methods on CCDA dataset \\((\\%)\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.327, + 0.473, + 0.584 + ], + "angle": 0, + "content": "son of the LTCC, PRCC and CCVID datasets is shown in Tabs. 3 and 4. Similarly, by fusing the best baseline CAL [14], our method achieves additional improvements. For instance, when evaluated in the cloth-changing setting, our method achieves a significant improvement of \\(2.6\\%\\) in Rank1 accuracy by fusing with CAL on the CCVID dataset. These findings highlight the effectiveness of 3DInvarReID, with the 3D shape features being shown to be both discriminative and complementary to 2D features. Our approach stands out for its superior performance compared to other 3D feature extraction methods for person ReID. This is particularly noteworthy in comparison to the 3DSL [5] (Tab. 3). Additionally, we assess our model under a cross-domain setting—that is, the model is trained with the Celeb-reID dataset and tested using the LTCC and PRCC datasets. Table 3 shows that our models outperform the baseline CAL, indicating a superior discriminative feature representation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.385, + 0.62 + ], + "angle": 0, + "content": "5.1.2 Results on LT-ReID dataset (CCDA)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.766 + ], + "angle": 0, + "content": "Given that both our CCDA and Celeb-reID datasets are obtained from the Internet and share a similar image style, we choose trained models on Celeb-reID and evaluate them on CCDA. We choose the SoTA cloth-changing methods, ReIDCaps- [20] and CAL [14] as baselines. The results in Tab. 5 demonstrate that our 3DInvarReID outperforms the baselines, providing strong evidence of its effectiveness in handling person ReID with challenging body poses and cloth-changing variations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.441, + 0.801 + ], + "angle": 0, + "content": "5.1.3 Results on Short-term Person ReID datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Despite our method is designed for LT-ReID, we additionally compare with SoTA methods on two conventional short-term ReID datasets: Market-1501 [62] and MSMT17 [54], in Tab. 6. By fusing with CAL [14], we observe an average improvement of \\(2.7\\%\\) in Rank1 accuracy on both datasets, demonstrating the complementary nature" + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.089, + 0.878, + 0.207 + ], + "angle": 0, + "content": "
MethodBackboneMarket-1501MSMT17
mAPRank1mAPRank1
PCB [48]ResNet-5081.693.840.468.2
3DSL [5]ResNet-50×287.395.0--
FSAM [17]ResNet-5085.694.6--
CAL [14]ResNet-5087.594.757.379.7
3DInvarReIDResNet-5085.594.255.176.3
CAL+3DInvarReID-87.995.159.180.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.533, + 0.216, + 0.859, + 0.23 + ], + "angle": 0, + "content": "Table 6. Comparison on short-term ReID datasets \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.581, + 0.241, + 0.813, + 0.272 + ], + "angle": 0, + "content": "
LVD [9]SHAPY [8]Ours
CD-L20.6540.6320.610
" + }, + { + "type": "table_caption", + "bbox": [ + 0.528, + 0.281, + 0.864, + 0.295 + ], + "angle": 0, + "content": "Table 7. Comparison of 3D boy reconstruction on HBW." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.307, + 0.87, + 0.378 + ], + "angle": 0, + "content": "
Model TypemAPRank1Rank5
3DInvarReID17.536.356.4
3DInvarReID-w/o 3D14.628.448.3
3DInvarReID-w/o Pre-training15.129.350.7
3DInvarReID-w/o 3D clothing16.032.152.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.555, + 0.387, + 0.838, + 0.401 + ], + "angle": 0, + "content": "Table 8. Ablaton studies on CCDA dataset \\((\\%)\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.425, + 0.848, + 0.44 + ], + "angle": 0, + "content": "of our 3D shape feature, even on short-term datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.681, + 0.464 + ], + "angle": 0, + "content": "5.2.3D Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.79 + ], + "angle": 0, + "content": "Most 3D body reconstruction methods focus more on pose estimation than shape estimation. Recently, SHAPY [8] releases a dataset (HBW) that contains ground-truth 3D body scans and the corresponding in-the-wild images, which enables us to test the accuracy of our reconstructed 3D naked body shapes. We thus evaluate our methods on the validation set of HBW, which contains 237 in-the-wild images of 10 subjects. Our baseline includes LVD [9] and SHAPY [8], which are recent pipelines for discriminative identity shape fitting. Following [9], we evaluate the reconstruction accuracy with Chamfer distance \\((\\mathrm{CD} - L_2)\\), by uniformly sampling 10,000 points on both ground-truth and predicted meshes in the canonical space. As shown in Tab. 7, our method outperforms the two baselines. We also visualize 3D reconstructions in Fig. 6. Our reconstructions resemble the ground truth better than the baselines. These results demonstrate the superiority of the proposed method in reconstructing naked 3D body shapes. Fig. 7 shows qualitative comparisons with ICON [55] and ClothWild [37]. Our approach achieves comparable clothed 3D body reconstructions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.655, + 0.815 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.822, + 0.892, + 0.852 + ], + "angle": 0, + "content": "In this section, all models are trained on Celeb-reID and tested on the CCDA dataset." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Effect of the 3D module. We compare our full model with an ablated version that only incorporates the \\(\\mathcal{L}_{cla}\\) loss in its training, disregarding 3D modules. The results in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19623" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.09, + 0.457, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.499 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparisons with LVD [9] and SHAPY [8] on 3D naked body reconstruction. Our approach recovers more accurate 3D body shapes from the images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.565 + ], + "angle": 0, + "content": "Tab. 8 show that our 3DInvarReID significantly improves the recognition accuracy, leading to a Rank1 accuracy increase from 28.4 to 36.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.706 + ], + "angle": 0, + "content": "Effect of Our Two-layer Implicit Model. Our primary goal is to disentangle the identity feature from non-identity features in 3D shape space. To evaluate the effectiveness of our 3D disentanglement module, we train a model (Oursw/o 3D clothing) by replacing our 3D body model with SMPL shape bases and omitting the modeling of the 3D clothing component and rendering layer. The results in Tab. 8 demonstrate the advantages of modeling clothing shape and texture for person ReID (Rank1: \\(32.1\\rightarrow 36.3\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Effect of Pre-training. Tab. 8 shows that removing the pre-training stage results in a lower Rank1 accuracy, with a score of 29.3 compared to our 36.3. This finding highlights the effectiveness of pre-training in addressing the inherent ambiguity of disentanglement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.205, + 0.815 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "This paper tackles the challenging setting of long-term person ReID, which allows a wider range of real-world human activities and accounts for cloth-changing scenarios. To address this problem, we present a joint two-layer implicit representation to model textured 3D clothed humans" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.091, + 0.868, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.369, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparisons with ICON [55] and Cloth-Wild [37] on 3D clothed body reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.893, + 0.562 + ], + "angle": 0, + "content": "together with a discriminative fitting module, enabling us to disentangle identity and non-identity features for real-world images. We collect a new LT-ReID dataset, CCDA, with diverse human activities and clothing changes, facilitating future research on real-world scenarios. Experimental results demonstrate the effectiveness of our method in disentangling identity and non-identity features in 3D clothed body shapes, thereby contributing to LT-ReID." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.893, + 0.74 + ], + "angle": 0, + "content": "Limitations & Potential Negative Impacts Impacts. Our work tackles the challenge of disentangling clothing and body shape in 3D shape representation. The clothing reconstruction task remains challenging as evidenced by the visual quality of the published models and our models. Our results show that the task of body-clothing disentangle-ment brings benefit in the recognition task, a finding which opens new possibilities to multi-task learning across 2D-3D modalities. Like most person ReID methods, one potential negative impact of our approach is that it could be used for unethical surveillance and invasion of privacy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Acknowledgments. This research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2022-21102100004. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19624" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Ejaz Ahmed, Michael Jones, and Tim K Marks. An improved deep learning architecture for person re-identification. In CVPR, 2015. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[2] Thiemo Alldieck, Mihai Zanfir, and Cristian Sminchisescu. Photorealistic monocular 3D reconstruction of humans wearing clothing. 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Parameter-efficient person re-identification in the 3D space. arXiv preprint arXiv:2006.04569, 2020.1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.817 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19626" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_origin.pdf b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5d0df152e0a0a0a1cd8b63064ac754cd540aecee --- /dev/null +++ b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/33efc350-232b-4a85-9272-b3026fb811bb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:44ca32569cf870593be499e9d8000ebf9242a3a98cf5ce02f4303d8c31ad9c34 +size 7097491 diff --git a/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/full.md b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ecefc80c97acd5201626be501f0cef3df89c143e --- /dev/null +++ b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/full.md @@ -0,0 +1,407 @@ +# Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification + +Feng Liu, Minchul Kim, ZiAng Gu, Anil Jain, Xiaoming Liu +Department of Computer Science and Engineering +Michigan State University, East Lansing MI 48824 + +{liufeng6, kimminc2, guziang, jain, liuxm}@msu.edu + +# Abstract + +Long-Term Person Re-Identification (LT-ReID) has become increasingly crucial in computer vision and biometrics. In this work, we aim to extend LT-ReID beyond pedestrian recognition to include a wider range of real-world human activities while still accounting for cloth-changing scenarios over large time gaps. This setting poses additional challenges due to the geometric misalignment and appearance ambiguity caused by the diversity of human pose and clothing. To address these challenges, we propose a new approach 3DInvarReID for (i) disentangling identity from non-identity components (pose, clothing shape, and texture) of 3D clothed humans, and (ii) reconstructing accurate 3D clothed body shapes and learning discriminative features of naked body shapes for person ReID in a joint manner. To better evaluate our study of LT-ReID, we collect a real-world dataset called CCDA, which contains a wide variety of human activities and clothing changes. Experimentally, we show the superior performance of our approach for person ReID. Code is available at http://cvlab.cse.msu.edu/project-reid3dinvar.html. + +# 1. Introduction + +Person Re-Identification (ReID) aims to recognize and match a specific pedestrian in various locations and at different times [1, 26, 29, 57, 62]. This is a crucial task for various applications, including crime prevention, forensic identification and security monitoring [13, 63]. + +Most existing works [11, 12, 24, 25] in this field concentrate on the short-term scenarios, assuming that pedestrians' clothing remains unchanged. However, in this paper, we focus on a more challenging yet practical scenario of Long-Term Person Re-Identification (LT-ReID), where the objective is to recognize individuals over long time periods while taking into account variations in clothing and diverse human activities. For the first time, we extend person re + +![](images/07bd8e7862043c6c2969e5be7cdaf7fd2193660a02924aacf26def1d87672441.jpg) + +![](images/1ae17e6a7ef456b3aae5cbf9e2f1e4de74c78d3c7faea2a36d48d360d8b53411.jpg) +(a) + +![](images/f0294bd1d03f091e258c4881f01841c2bea2a3961be47b2bb25180dfc78d6378.jpg) +(b) +Figure 1. Illustration of the differences between various person re-identification (ReID) settings. Both (a) conventional/short-term and (b) cloth-changing person ReID benchmarks often restrict subjects to walking or standing, limiting their applications in real-world scenarios. This paper expands on the long-term person re-identification (LT-ReID) setting by tackling a wider range of human activities, increasing its practicality. + +![](images/7a0d1cb22e0ece9d0b2e2393bcc59eae3c16e598bc62be6f05bebd1d951b3dec.jpg) +(c) + +identification beyond pedestrian recognition to encompass a wider range of human activities, such as identifying students playing tennis or soldiers crawling in the field (see Fig. 1). This setting poses new challenges due to the geometric misalignment and appearance ambiguity caused by the diversity of human poses and their clothing. + +Recently, various approaches [14,18,20,23,27,46,56,59] have been proposed to investigate LT-ReID under clothing changes. They extract clothing-irrelevant features for robust person ReID by custom-designed architectures [19,20], training process [27], loss functions [14], and data augmentation [64]. However, these methods only attempt to mine texture-insensitive body-structural cues in 2D space while ignoring the prior knowledge that the human body is a 3D non-rigid object. A new line of research introduces 3D priors for LT-ReID by either lifting 2D images to a 3D space [67] or including 3D body reconstruction as an auxil + +iary task [5]. However, without modeling the 3D clothing, the clothing-sensitive features can not be properly disentangled in either method. Moreover, none of the methods above handle body images with diverse activities. + +Given the numerous variations in body images, including body pose, clothing, and view angles, we posit that the most reliable identity cue for LT-ReID is the 3D naked (unclothed) body shape, if it can be accurately and discriminately estimated from a 2D body image. Obviously this is extremely challenging due to confounding factors and the lack of supervision, such as paired images and 3D naked body scans. However, taking inspiration from advancements in 3D feature learning for face recognition [32, 41], we propose a new algorithm, 3DInvarReID, to disentangle identity (naked body) from non-identity components (pose, clothing shape and texture) of 3D clothed humans. This innovative approach not only reconstructs accurate 3D clothed body shapes that faithfully represent the input 2D images, but it also simultaneously learns discriminative naked shape features that effectively enhance LT-ReID. + +An effective representation of the 3D shape and texture of the human body is a key component of such a learning-based process. To this end, we propose a joint two-layer neural implicit function to represent 3D humans, where identity, clothing shape, and texture components are disentangled into latent representations. Based on the composite model, we jointly learn a model fitting module to disentangle identity from non-identity components (body pose, clothing shape and texture) from 2D images. Modeling texture, along with a differentiable renderer enables us to compare the rendered image with the input image in a self-supervised manner. This allows the learning process to be supervised by both image reconstruction loss and identification loss, using a set of 2D images with identity labels only. Comprehensive experiments demonstrate the superiority of our method in diverse ReID benchmarks. Additionally, to advance the research in the field of LT-ReID, we collect a Cloth-Changing and Diverse Activities (CCDA) dataset (see Fig. 1). The CCDA dataset is specifically designed to evaluate the ReID of the person undergoing both human activities and changes in clothing. + +In summary, the contributions of this work include: + +$\diamond$ We propose a novel LT-ReID method, 3DInvarReID, to learn clothing/pose invariant 3D shape representation. +$\diamond$ We devise a novel joint two-layer implicit model that fully models a textured 3D clothed human. Our approach includes a robust and discriminative fitting process that disentangles identity and non-identity features in reconstructing two-layer 3D body shapes from real-world images. +$\diamond$ We achieve superior performance in both LT-ReID accuracy and 3D body shape reconstruction. + +
MethodEnd-to-End trainableModel textureDiscriminativeModel type
3D modeling methods
SCANimate [44]-XXuniversal
SMPLicit [10]-XXuniversal
Neural-GIF [49]-XXindividual
SNARF [7]-XXindividual
gDNA [6]-XXuniversal
3D fitting methods
PiFu [42]X✓X-
PiFuHD [43]XXX-
Arch [21]X✓X-
Arch++ [15]X✓X-
ICON [55]X✓X-
ClothWild [37]XXX-
PHORHUM [2]✓✓X-
3DInvarReID✓✓✓universal
+ +Table 1. Overview of the 3D clothed human modeling (top) and fitting (bottom) methods. Our method is the only one that models clothing texture and learns discriminative information compared to 3D modeling methods. Compared to 3D fitting methods, our end-to-end trainable pipeline enables disentangling identity-sensitive shape features from whole-body images. + +# 2. Prior Work + +Person Re-identification. Person ReID aims to match a person across images captured by a distributed camera system. The majority of prior methods [11, 12, 24, 25, 28, 52, 58, 60] assume a short-term application scenario without clothing changes by the person. This limitation has generated a growing interest in long-term cloth-changing person ReID [14, 23, 27, 56]. Datasets such as Real28 [50], VC-Clothes [50], PRCC [56], LTCC [46], COCAS [59] and Celebrities-reID [18, 20] are collected to facilitate this research. These datasets, however, either ignore or only minimally consider human activities, assuming that subjects are pedestrians with a restricted set of activities, limiting their applicability in real-world scenarios. As a result, there is a noticeable discrepancy between published approaches and the real-world LT-ReID problem. In contrast to the focus on the clothing-change person ReID, our research takes a step further by addressing a more challenging and practical issue of person ReID that involves diverse human activities, which are not limited to walking. + +3D Clothed Human Modeling and Fitting. In early attempts [22, 34, 40], a clothed person was modeled as displacements over naked body meshes, obtained by SMPL [33]. However, the fixed mesh topology and bounded resolution approach limit geometric expressivity. Recently, neural implicit representations have been explored to model 3D body shapes due to their topological flexibility and resolution independence [6, 7, 10, 38, 44, 45, 49, 53]. However, as shown in Tab. 1, modeling texture in 3D remains a challenge. While these approaches provide rich geometric detail, insufficient attention has been paid + +![](images/e10db5972659fac7a0118d123b811cfc392e5b4f266031a77f77590c7393c236.jpg) +Figure 2. Overview of the proposed joint learning framework for long-term person re-identification and 3D clothed body shape reconstruction. During the inference of ReID, the identity shape feature $\mathbf{z}_{id}$ is utilized for matching. + +to the discriminativeness of the resulting body shapes. In contrast, we build a discriminative and textured 3D clothed human, serving the purpose of LT-ReID. + +These 3D clothed models can be naturally applied to monocular 3D reconstruction (2D-to-3D fitting). Generally, the input image is encoded as a latent vector, from which the generative model reconstructs the 3D shape [10, 30, 31, 37]. Alternatively, two-step pipelines [15, 21, 42, 43, 55] firstly recover 2.5D sketches (e.g., surface normal), and then infer a full 3D shape. A common limitation of these works is that they require 3D body scans for training, as they are trained on synthetic datasets derived from 3D scans and their rendered images. Furthermore, existing methods do not explicitly consider the discriminative ability of reconstructed 3D clothed body shapes. LVD [9] and SHAPY [8] introduce new discriminative fitting pipelines to reconstruct naked body shapes from images. However, without modeling 3D clothing, 2D image cues can not be fully exploited. + +We propose a novel joint two-layer shape and texture representation of a 3D clothed human model, consisting of both shape and texture. Together with a model fitting module, our representation allows semi-supervised training from images without 3D labels. More importantly, guided by the completed 3D model and the discriminative 2D-to-3D fitting module, our approach disentangles identity features from identity-irrelevant features in 3D space for LT-ReID. Tab. 1 compares our method with prior works. + +# 3. Proposed Method + +# 3.1. Problem Formulation + +A 3D clothed human model is described by three disentangled latent variables: identity shape, clothing shape and clothing texture. As shown in Fig. 2, these latent repre + +sentations can be sequentially decoded into canonical 3D shape and texture, respectively by three decoders. To enable self-supervised training on real images, we estimate these latent codes along with the body pose and camera projection parameters. In this work, we use an off-the-shelf method [36] as our PoseNet to predict pose and camera projection, while our image encoder focuses on identity disentanglement learning, i.e., the fitting module. These networks disentangle identity and non-identity components of 3D shapes and reconstruct the input body images via a differentiable render. + +Formally, given a training set of $T$ images $\{\mathbf{I}_i\}_{i=1}^T$ and the corresponding identity labels $\{l_i\}_{i=1}^T$ , the image encoder $\mathcal{E}(\mathbf{I}) : \mathbf{I} \to \mathbf{z}_{id}, \mathbf{z}_{cloth}, \mathbf{z}_{tex}$ predicts the identity shape code of naked body $\mathbf{z}_{id} \in \mathbb{R}^{L_{id}}$ , clothed shape code $\mathbf{z}_{cloth} \in \mathbb{R}^{L_{cloth}}$ and texture code $\mathbf{z}_{tex} \in \mathbb{R}^{L_{tex}}$ . Functions $\mathcal{F}, \mathcal{C}$ and $\mathcal{T}$ decode the latent codes to identity shape, clothing shape and texture components, respectively. Additionally, PoseNet $\mathcal{P}$ predicts the camera projection parameters $\Omega$ and SMPL body pose $\theta$ : $(\Omega, \theta) = \mathcal{P}(\mathbf{I})$ . + +Mathematically, the learning objective is defined as: + +$$ +\underset {\mathcal {E}, \mathcal {F}, \mathcal {C}, \mathcal {T}} {\arg \min } \sum_ {i = 1} ^ {T} \left(\left| \hat {\mathbf {I}} _ {i} - \mathbf {I} _ {i} \right| _ {1} + \mathcal {L} _ {c l a} (\mathbf {z} _ {i d}, l _ {i})\right), \tag {1} +$$ + +where $\mathcal{L}_{cla}$ is the classification loss. $\hat{\mathbf{I}}$ is the rendered image. This objective enables us to jointly learn accurate 3D clothed shape and discriminative shape for the naked body. + +# 3.2. Joint Two-Layer Implicit Model + +We jointly model 3D naked body shape, clothed shape and texture in a canonical space by implicit representations. + +Discriminative Body Shape Component. We represent the 3D naked body shape as the $\tau = 0.5$ level set of the + +![](images/f28251ba6aba23315550902cca8f703d3b054397f99ae1f33d704e4360c6d755.jpg) +Figure 3. Joint two-layer implicit model. The naked body shape model $\mathcal{F}$ and clothed body shape model $\mathcal{C}$ take identity shape code $\mathbf{z}_{id}$ , clothing shape code $\mathbf{z}_{cloth}$ and a spatial point $\mathbf{x}$ , and produces two occupancy values $o_1$ and $o_2$ . The texture model $\mathcal{T}$ takes $\mathbf{z}_{tex}$ and $\mathbf{z}_{cloth}$ to estimate RGB color at $\mathbf{x}$ . A 3D generator $\mathcal{G}$ uses $\mathbf{z}_{id}$ to produce a 3D feature volume, enabling hierarchical point-wise feature representation. + +occupancy function [35]: + +$$ +\mathbf {S} _ {i d} (\mathbf {z} _ {i d}) = \{\mathbf {x} | \mathcal {F} (\mathbf {z} _ {i d}, \mathbf {x}) = \tau \}, \tag {2} +$$ + +where $\mathcal{F}$ predicts the occupancy value, $o_1$ for any point $\mathbf{x}$ in the canonical space. Specifically, + +$$ +\mathcal {F}: \mathbb {R} ^ {L _ {i d}} \times \mathbb {R} ^ {3} \rightarrow (o _ {1}, \mathbf {f}), \tag {3} +$$ + +where $\mathbf{f} \in \mathbb{R}^{L_f}$ is a point-wise feature and will be utilized to predict clothing details. + +Following [6], we make use of function $\mathcal{F}$ , implemented via a Multi-Layer Perceptron (MLP), coupled with a 3D CNN-based generator $\mathcal{G}$ to model 3D naked bodies. As shown in Fig. 3(a), the generator produces a 3D feature volume using $\mathbf{z}_{id}$ as input. We then use trilinear interpolation to query continuous 3D points and feed the feature at $\mathbf{x}$ to the MLP. + +Clothed Shape Component. Similarly, we also represent the clothed body shape as the $\tau = 0.5$ level set function: + +$$ +\mathbf {S} _ {\text {c l o t h}} \left(\mathbf {z} _ {\text {c l o t h}}\right) = \{\mathbf {x} | \mathcal {C} \left(\mathbf {z} _ {\text {c l o t h}}, \mathbf {f}, \mathbf {x}\right) = \tau \}, \tag {4} +$$ + +where $\mathcal{C}$ is implemented as a MLP: + +$$ +\mathcal {C}: \mathbb {R} ^ {L _ {\text {c l o t h}}} \times \mathbb {R} ^ {L _ {f}} \times \mathbb {R} ^ {3} \rightarrow o _ {2}. \tag {5} +$$ + +$\mathcal{C}$ outputs the occupancy value $o_2$ to represent the clothed shape information. + +Texture Component. We define a texture field as a mapping function $\mathcal{T}$ from a point $\mathbf{x}$ in the canonical space, texture latent $\mathbf{z}_{\text{tex}}$ and $\mathbf{z}_{\text{cloth}}$ to a RGB value $\mathbf{c} \in \mathbb{R}^3$ : + +$$ +\mathcal {T}: \mathbb {R} ^ {L _ {\text {t e x}}} \times \mathbb {R} ^ {L _ {\text {c l o t h}}} \times \mathbb {R} ^ {3} \rightarrow \mathbf {c}. \tag {6} +$$ + +The design of our joint two-layer implicit model is inspired by the approach in [6]. However, as shown in Fig. 3, our model has two novel traits: 1) Instead of simply decomposing the 3D clothed human into coarse and fine models, we apply a two-layer implicit model to represent the naked body and clothing shapes. 2) We additionally model texture to form a complete 3D human model. + +![](images/1d99a1eaa2499273d01ce15c16977b6620f7ec525435f2d837e683f64e340ccc.jpg) +Figure 4. Neural blend skinning network. This module deforms the pose space to canonical space. Given a deformed point $\mathbf{x}'$ , we compute its corresponding position $\hat{\mathbf{x}}$ in canonical space by iteratively finding the root of Eqn. 9. + +# 3.3. Neural Linear Blend Skinning Network + +Our joint two-layer implicit model is built within the canonical space. However, the 3D clothed human data, usually captured in various poses, introduces misalignments between this canonical space and the deformed counterpart. To predict the occupancy values $\mathbf{o}_1$ , $\mathbf{o}_2$ and the texture $\mathbf{c}$ for a given observed point $\mathbf{x}'$ within the deformed space, it is essential to first determine its canonical correspondence point $\hat{\mathbf{x}}$ . Once $\mathbf{x}$ is identified, we can then compute $\mathbf{o}_1$ , $\mathbf{o}_2$ and $\mathbf{c}$ using Eqns. 3, 5 and 6. The objective of this step is to find the canonical correspondence $\hat{\mathbf{x}}$ of any query point $\mathbf{x}'$ . To achieve this goal, similar to [6, 7], we learn a linear blend skinning (LBS) [33] using neural networks in an unsupervised manner. + +Regressing Blend Weight. We follow [6, 7] which define the skinning field in canonical space conditioned on our identity latent code $\mathbf{z}_{id}$ : + +$$ +\mathcal {W}: \mathbb {R} ^ {L _ {i d}} \times \mathbb {R} ^ {3} \rightarrow \mathbb {R} ^ {K} +$$ + +$$ +\left(\mathbf {z} _ {i d}, \mathbf {x}\right)\rightarrow \mathbf {w}, \tag {7} +$$ + +where $\mathbf{w}$ is the point-wise blend weight of the canonical point $\mathbf{x}$ . Then deformed point $\mathbf{x}'$ is determined by the following convex combination: + +$$ +\mathbf {x} ^ {\prime} = \mathbf {d} \left(\mathbf {z} _ {i d}, \mathbf {x}, \theta\right) = \sum_ {k = 1} ^ {K} \mathbf {w} _ {k} \mathbf {B} _ {k} \mathbf {x}, \tag {8} +$$ + +where $\mathbf{w}_k$ is $k$ -element in the vector $\mathbf{w}$ , while $\mathbf{B}_k$ denotes the $k$ -element from the set of bone transformation matrices $\mathcal{B} = \{\mathbf{B}_k \in \mathbb{R}^{4 \times 4}\}_{k=1}^K$ . Both $\mathbf{x}$ and $\mathbf{x}'$ in Eqn. 8 are represented in homogeneous coordinates. + +Implicit Differentiable Skinning. An overview is illustrated in Fig. 4. While the goal is to determine $\mathbf{x}' \rightarrow \hat{\mathbf{x}}$ , we only have direct access to the mapping defined by Eqn. 8, which is not invertible. Following [6,7], the correspondence is calculated numerically by finding the root of the equation with Broyden's method [3]: + +$$ +\hat {\mathbf {x}} = \{\hat {\mathbf {x}} | \mathbf {d} (\mathbf {z} _ {i d}, \hat {\mathbf {x}}, \theta) - \mathbf {x} ^ {\prime} = \mathbf {0} \}. \tag {9} +$$ + +# 3.4. Implicit Rendering + +During rendering, when 2D pixels are unprojected to 3D points, they are intrinsically mapped in the deformed 3D space. Given a pixel $p$ of a masked input image, we construct a ray $\mathbf{x}' = \{\mathbf{c}_0 + t\mathbf{v}|t\geqslant 0\}$ , where $\mathbf{c}_0$ represents the camera's position and $\mathbf{v}$ indicates the viewing direction based on the camera projection parameters $\Omega$ . $t$ is the scalar distance along the ray. We then map the ray points to the canonical space, following Eqn. 9. The intersection point $\hat{\mathbf{x}}_p$ of the ray can be calculated by identifying the first change of clothed shape occupancy $o_2$ . Finally, the rendered color of the pixel $p$ is calculated via Eqn. 6. + +# 3.5. Semi-supervised Model Learning + +While our model can perform self-supervised learning from real images without 3D labels, we first pre-train our joint implicit 3D model with 3D data in order to mitigate the inherent ambiguity. + +# 3.5.1 Supervised Pre-training 3D clothed Model + +Training Data. We combine CAPE [34] (3,000 scans) and THuman2.0 [65] (526 scans) to train our joint two-layer implicit model. THuman2.0 consists of 526 texture clothed 3D scans of 105 subjects. Following [6], for each scan, we obtain its SMPL naked shape code. CAPE provides 148,584 pairs of scans under clothing and SMPL naked body with rich pose variations of 15 subjects. We randomly sample 3,000 scans for training. Formally, each training sample can be represented as SMPL pose $\theta$ , identity label $l_{3D}$ , $n$ spatial points $\mathbf{x}_i'$ , and their SDFs $o_1^i$ , $o_2^i$ , and color $\mathbf{c}_i$ : $\{\theta, l_{3D}, \{\mathbf{x}_i', o_1^i, o_2^i, \mathbf{c}_i\}_{i=1}^n\}$ . With the autodecoding technique [39], we assign trainable identity shape code, clothing shape code, and texture code to each training sample. + +Loss Function. We define the loss below for each sample: + +$$ +\underset {\mathcal {F}, \mathcal {C}, \mathcal {T}, \mathbf {z} _ {i d}, \mathbf {z} _ {c l o t h}, \mathbf {z} _ {t e x}} {\arg \min } \mathcal {L} _ {i d} + \mathcal {L} _ {c l o t h} + \mathcal {L} _ {t e x} + \mathcal {L} _ {c l a} ^ {3 D} (\mathbf {z} _ {i d}, l _ {3 D}) +$$ + +$$ +\mathcal {L} _ {i d} = \sum_ {i = 0} ^ {n} B C E \left(\mathcal {F} \left(\mathbf {z} _ {i d}, \hat {\mathbf {x}} _ {i}\right), o _ {1} ^ {i}\right) \tag {10} +$$ + +$$ +\mathcal {L} _ {\text {c l o t h}} = \sum_ {i = 0} ^ {n} B C E \left(\mathcal {C} \left(\mathbf {z} _ {\text {c l o t h}}, \mathbf {f} _ {i}, \hat {\mathbf {x}} _ {i}\right), o _ {2} ^ {i}\right) \tag {11} +$$ + +$$ +\mathcal {L} _ {t e x} = \sum_ {i = 0} ^ {n} \left\| \mathcal {T} \left(\mathbf {z} _ {t e x}, \mathbf {z} _ {\text {c l o t h}}, \hat {\mathbf {x}} _ {i}\right) - \mathbf {c} _ {i} \right\| _ {2}, \tag {12} +$$ + +where $\mathcal{L}_{cla}^{3D}(\mathbf{z}_{id},l_{3D})$ is the cross-entropy classification loss. We additionally add auxiliary loss $\mathcal{L}_W$ to train network $\mathcal{W}$ + +$$ +\arg \min _ {\mathcal {W}} \mathcal {L} _ {W} \tag {13} +$$ + +$$ +\mathcal {L} _ {W} = \sum_ {k = 0} ^ {K} | | \mathcal {W} (\mathbf {z} _ {i d}, \mathbf {J} _ {k}) - \mathbf {w} _ {\mathbf {J} _ {k}} | | _ {2}, \tag {14} +$$ + +where $\mathbf{w}_{\mathbf{J}_k}$ is the pre-computed ground truth skinning weights of SMPL joints location $\mathbf{J}_k$ + +![](images/7b47a5577bf922153fbee7520a8ef58b11b558883757a4c2522e0fca1d226f52.jpg) +Figure 5. Example images from CCDA, with one subject per row, showcasing the diversity of body poses, clothing styles and colors. + +# 3.5.2 Self-supervised Joint Modeling and Fitting + +Given a set of in-the-wild 2D images with body masks and identity labels $\{\mathbf{I}_i, \mathbf{M}_i, l_i\}_{i=1}^T$ , the self-supervised identity disentanglement loss is: + +$$ +\underset {\mathcal {E}, \mathcal {T}} {\arg \min } \sum_ {i = 1} ^ {T} \mathcal {L} _ {s i l} + \mathcal {L} _ {r g b} + \mathcal {L} _ {c l a}, \tag {15} +$$ + +where $\mathcal{L}_{rgb}$ is the photometric loss, $\mathcal{L}_{sil}$ is silhouette loss and $\mathcal{L}_{cla}$ is the classification loss. Specifically, we denote $\mathbf{I}_p$ and $\mathbf{M}_p$ as the RGB and silhouette values of pixel $p\in P$ . Here, $P$ denotes the entire set of pixels in the input image $\mathbf{I}$ . A subset of $P$ , represented as $P^{in}$ , corresponds to the pixels where an intersection between the rays and the body in the image has been detected. The photometric loss is defined as + +$$ +\mathcal {L} _ {r g b} = \frac {1}{| P |} \sum_ {p \in P ^ {i n}} \left| \mathbf {I} _ {p} - \mathcal {T} \left(\mathcal {E} _ {t e x} (\mathbf {I}), \mathcal {E} _ {c l o t h} (\mathbf {I}), \hat {\mathbf {x}} _ {p}\right) \right|, \tag {16} +$$ + +where the encoder $\mathcal{E}$ estimates $\mathbf{z}_{id} = \mathcal{E}_{id}(\mathbf{I})$ , $\mathbf{z}_{cloth} = \mathcal{E}_{cloth}(\mathbf{I})$ and $\mathbf{z}_{tex} = \mathcal{E}_{tex}(\mathbf{I})$ from image $\mathbf{I}$ . $\hat{\mathbf{x}}$ is the intersection point (see Sec. 3.4). + +We further define the silhouette loss as + +$$ +\mathcal {L} _ {s i l} = \frac {1}{| P |} \sum_ {p \in P ^ {\text {o u t}}} C E \left(\mathbf {M} _ {p}, \hat {\mathbf {M}} _ {p}\right), \tag {17} +$$ + +where $\hat{\mathbf{M}}$ is the masked rendering, $P^{out} = P - P^{in}$ represents the indices in the mini-batch for which there is no ray-geometry intersection or $\mathbf{M}_p = 0$ , and $CE(\cdot ,\cdot)$ denotes the cross-entropy loss. We impose triplet loss and cross-entropy loss on the identity shape code $\mathbf{z}_{id} = \mathcal{E}_{id}(\mathbf{I})$ as our classification loss $\mathcal{L}_{cla}(\mathbf{z}_{id},l)$ . + +# 3.6. Person ReID Inference + +For person ReID inference, the encoder $\mathcal{E}$ processes body images and extracts the identity shape features $\mathbf{z}_{id}$ . + +The Cosine similarity of $\mathbf{z}_{id}$ is then used to determine if the two images belong to the same person. It is worth noting that, the inference of our ReID does not incorporate the 3D reconstruction module, making it highly efficient. + +# 4. CCDA Person ReID Dataset + +We construct a new dataset with diverse human activities and clothing changes for evaluating LT-ReID. Specifically, we collect data for popular athletes in soccer, tennis, and basketball, and popular artists, such as fashion models and singers. We crawl whole body images of each subject on Google Image1 with athlete/artist names. We collect two sets of images per subject: 'challenging' and 'normal' body poses. As an example, for a basketball player, the 'challenging' set includes images of players' actions on the court, while the 'normal' set contains standing or walking poses. We then crop the body region from the original image via the detected bounding box and resize it to $256 \times 128$ . Finally, the annotator verifies the identity of each image. In total, 1,555 images of 100 subjects are retained. For each subject, we randomly select one image from 'normal' images for the gallery set, while the remaining 1,455 images comprise the query set. Fig. 5 shows examples of images in the CCDA dataset. + +# 5. Experimental Results + +Implementation Details. Our training process includes two stages: 1) Networks $\mathcal{F},\mathcal{C},\mathcal{T},\mathcal{W}$ are pre-trained on 3D data. 2) $\mathcal{E}$ and $\mathcal{T}$ are trained or fine-tuned with real images. The encoder $\mathcal{E}$ is implemented as a ResNet-50. Networks $\mathcal{F},\mathcal{C},\mathcal{T}$ and $\mathcal{W}$ are MLPs. In experiments, we set $L_{cloth} = L_{tex} = 512$ , $L_{id} = 4,096$ , $L_{f} = L_{h} = 256$ , $K = 24$ , $n = 200,000$ . We implement in Pytorch and use Adam optimizer in both stages. + +# 5.1. Person ReID + +Metric. For person ReID, we follow the standard retrieval accuracy metrics, namely the Cumulative Matching Characteristics (CMC) and mean average precision (mAP). + +Baseline. We compare our method with eight SoTA person ReID methods: Two-Stream [66], MLFN [4], HACNN [26], Part-Aligned [47], PCB [48], TriNet [16], MGN [51], DG-Net [64], and five SoTA cloth-changing re-ID methods: ReIDCaps [20], 3DSL [5], RCSAnet [19], FSAM [17] and CAL [14]. + +# 5.1.1 Results on Cloth-changing Person ReID datasets + +Datasets. We test on four popular cloth-changing ReID datasets: Celeb-reID/Celeb-reID-light [18, 20], PRCC [56], LTCC [46] and the recent CCVID dataset [14, 61]. + +
MethodBackboneCeleb-reIDCeleb-reID-light
mAPRank1mAPRank1
Two-Stream [66]ResNet-507.836.3--
MLFN [4]*6.041.46.310.6
HACNN [26]*9.547.611.516.2
Part-Aligned [47]GoogLeNet×26.419.4--
PCB [48]ResNet-508.237.1--
MGN [51]ResNet-5010.849.013.921.5
DG-Net [64]ResNet-5010.650.112.623.5
+ +
cloth-changing person ReID methods
ReIDCaps- [20]DenseNet-1219.851.211.220.3
ReIDCaps [20]DenseNet-121×615.863.019.033.5
RCSAnet [19]DenseNet-121×211.955.616.729.5
CAL [14]ResNet-5013.759.218.533.6
3DInvarReIDResNet-5011.855.215.030.1
3DInvarReID#ResNet-5015.261.221.837.0
ReIDCaps+ +3DInvarReID#-18.465.525.742.2
+ +Table 2. Comparison with SoTA on Celeb-reID and Celeb-reID-light datasets (\%). * indicates that the backbone is designed by the authors. The red number means the total number of models. 3DInvarReID#'s weights are initialized using the CAL model. + +
MethodBackboneLTCCPRCC
mAPRank1mAPRank1
HACNN [26]*9.321.6-21.8
PCB [48]ResNet-5010.023.538.741.8
3DSL [5]ResNet-50×214.831.2-51.3
FSAM [17]ResNet-5016.238.5-54.5
CAL [14]ResNet-5018.040.155.855.2
3DInvarReIDResNet-5016.737.852.551.6
CAL+3DInvarReID-18.940.957.256.5
CALResNet-502.83.820.331.6
3DInvarReIDResNet-502.85.120.134.6
3DInvarReID#ResNet-502.85.621.440.7
+ +Table 3. Comparison with SoTA cloth-changing person ReID methods on the LTCC and PRCC datasets $(\%)$ Models highlighted in pink are trained on the Celeb-reID dataset. 3DInvarReID#'s weights are initialized using the CAL model. + +Results on Celeb-reID and Celeb-reID-light. As reported in Tab. 2, our 3DInvarReID (Ours) outperforms all the general person re-ID baselines on both datasets. Considering methods using a single network, we also outperform the cloth-changing baseline, ReIDCaps- [20]. More importantly, to investigate the complementarity between our learned 3D shape features and existing 2D features, we fuse our method with cloth-changing baselines by simple summation at the score level. By fusing with ReIDCaps [20], our method improves the Rank1 accuracy on Celeb-reID from $63.0\%$ to $65.5\%$ and from $33.5\%$ to $42.2\%$ on Celeb-reID-light. These results clearly demonstrate that the 3D shape features learned from our method are both discriminative and complementary to the 2D features, indicating the effectiveness of our proposed approach for person ReID, particularly under cloth-changing scenarios. + +Results on LTCC, PRCC and CCVID. The compari- + +
MethodBackboneGeneralCloth-changing
mAPRank1mAPRank1
TriNet [16]ResNet-5078.181.577.081.1
CAL [14]ResNet-5081.382.679.681.7
3DInvarReIDResNet-5066.170.865.470.2
CAL+3DInvarReID-82.683.981.384.3
+ +Table 4. Comparison with SoTA methods on CCVID $(\%)$ + +
MethodBackbonemAPRank1Rank5
ReLU caps [20]DenseNet-121×610.96.520.2
CAL [14]ResNet-5019.310.026.7
3DInvarReIDResNet-5021.711.130.5
+ +son of the LTCC, PRCC and CCVID datasets is shown in Tabs. 3 and 4. Similarly, by fusing the best baseline CAL [14], our method achieves additional improvements. For instance, when evaluated in the cloth-changing setting, our method achieves a significant improvement of $2.6\%$ in Rank1 accuracy by fusing with CAL on the CCVID dataset. These findings highlight the effectiveness of 3DInvarReID, with the 3D shape features being shown to be both discriminative and complementary to 2D features. Our approach stands out for its superior performance compared to other 3D feature extraction methods for person ReID. This is particularly noteworthy in comparison to the 3DSL [5] (Tab. 3). Additionally, we assess our model under a cross-domain setting—that is, the model is trained with the Celeb-reID dataset and tested using the LTCC and PRCC datasets. Table 3 shows that our models outperform the baseline CAL, indicating a superior discriminative feature representation. + +# 5.1.2 Results on LT-ReID dataset (CCDA) + +Given that both our CCDA and Celeb-reID datasets are obtained from the Internet and share a similar image style, we choose trained models on Celeb-reID and evaluate them on CCDA. We choose the SoTA cloth-changing methods, ReIDCaps- [20] and CAL [14] as baselines. The results in Tab. 5 demonstrate that our 3DInvarReID outperforms the baselines, providing strong evidence of its effectiveness in handling person ReID with challenging body poses and cloth-changing variations. + +# 5.1.3 Results on Short-term Person ReID datasets + +Despite our method is designed for LT-ReID, we additionally compare with SoTA methods on two conventional short-term ReID datasets: Market-1501 [62] and MSMT17 [54], in Tab. 6. By fusing with CAL [14], we observe an average improvement of $2.7\%$ in Rank1 accuracy on both datasets, demonstrating the complementary nature + +Table 5. Comparison with SoTA methods on CCDA dataset $(\%)$ + +
MethodBackboneMarket-1501MSMT17
mAPRank1mAPRank1
PCB [48]ResNet-5081.693.840.468.2
3DSL [5]ResNet-50×287.395.0--
FSAM [17]ResNet-5085.694.6--
CAL [14]ResNet-5087.594.757.379.7
3DInvarReIDResNet-5085.594.255.176.3
CAL+3DInvarReID-87.995.159.180.8
+ +Table 6. Comparison on short-term ReID datasets $(\%)$ + +
LVD [9]SHAPY [8]Ours
CD-L20.6540.6320.610
+ +Table 7. Comparison of 3D boy reconstruction on HBW. + +
Model TypemAPRank1Rank5
3DInvarReID17.536.356.4
3DInvarReID-w/o 3D14.628.448.3
3DInvarReID-w/o Pre-training15.129.350.7
3DInvarReID-w/o 3D clothing16.032.152.8
+ +Table 8. Ablaton studies on CCDA dataset $(\%)$ + +of our 3D shape feature, even on short-term datasets. + +# 5.2.3D Reconstruction + +Most 3D body reconstruction methods focus more on pose estimation than shape estimation. Recently, SHAPY [8] releases a dataset (HBW) that contains ground-truth 3D body scans and the corresponding in-the-wild images, which enables us to test the accuracy of our reconstructed 3D naked body shapes. We thus evaluate our methods on the validation set of HBW, which contains 237 in-the-wild images of 10 subjects. Our baseline includes LVD [9] and SHAPY [8], which are recent pipelines for discriminative identity shape fitting. Following [9], we evaluate the reconstruction accuracy with Chamfer distance $(\mathrm{CD} - L_2)$ , by uniformly sampling 10,000 points on both ground-truth and predicted meshes in the canonical space. As shown in Tab. 7, our method outperforms the two baselines. We also visualize 3D reconstructions in Fig. 6. Our reconstructions resemble the ground truth better than the baselines. These results demonstrate the superiority of the proposed method in reconstructing naked 3D body shapes. Fig. 7 shows qualitative comparisons with ICON [55] and ClothWild [37]. Our approach achieves comparable clothed 3D body reconstructions. + +# 5.3. Ablation Study + +In this section, all models are trained on Celeb-reID and tested on the CCDA dataset. + +Effect of the 3D module. We compare our full model with an ablated version that only incorporates the $\mathcal{L}_{cla}$ loss in its training, disregarding 3D modules. The results in + +![](images/116224ffaac5f58f3a788b784baaec84a9f9f9018ac4e7baa8e734afd02c6f35.jpg) +Figure 6. Qualitative comparisons with LVD [9] and SHAPY [8] on 3D naked body reconstruction. Our approach recovers more accurate 3D body shapes from the images. + +Tab. 8 show that our 3DInvarReID significantly improves the recognition accuracy, leading to a Rank1 accuracy increase from 28.4 to 36.3. + +Effect of Our Two-layer Implicit Model. Our primary goal is to disentangle the identity feature from non-identity features in 3D shape space. To evaluate the effectiveness of our 3D disentanglement module, we train a model (Oursw/o 3D clothing) by replacing our 3D body model with SMPL shape bases and omitting the modeling of the 3D clothing component and rendering layer. The results in Tab. 8 demonstrate the advantages of modeling clothing shape and texture for person ReID (Rank1: $32.1\rightarrow 36.3$ ). + +Effect of Pre-training. Tab. 8 shows that removing the pre-training stage results in a lower Rank1 accuracy, with a score of 29.3 compared to our 36.3. This finding highlights the effectiveness of pre-training in addressing the inherent ambiguity of disentanglement. + +# 6. Conclusions + +This paper tackles the challenging setting of long-term person ReID, which allows a wider range of real-world human activities and accounts for cloth-changing scenarios. To address this problem, we present a joint two-layer implicit representation to model textured 3D clothed humans + +![](images/7d64ea0e24c18426461c1c696af139bfd11aa935824c4b0a0d63014a409f1588.jpg) +Figure 7. Qualitative comparisons with ICON [55] and Cloth-Wild [37] on 3D clothed body reconstruction. + +together with a discriminative fitting module, enabling us to disentangle identity and non-identity features for real-world images. We collect a new LT-ReID dataset, CCDA, with diverse human activities and clothing changes, facilitating future research on real-world scenarios. Experimental results demonstrate the effectiveness of our method in disentangling identity and non-identity features in 3D clothed body shapes, thereby contributing to LT-ReID. + +Limitations & Potential Negative Impacts Impacts. Our work tackles the challenge of disentangling clothing and body shape in 3D shape representation. The clothing reconstruction task remains challenging as evidenced by the visual quality of the published models and our models. Our results show that the task of body-clothing disentangle-ment brings benefit in the recognition task, a finding which opens new possibilities to multi-task learning across 2D-3D modalities. Like most person ReID methods, one potential negative impact of our approach is that it could be used for unethical surveillance and invasion of privacy. + +Acknowledgments. This research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2022-21102100004. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. + +# References + +[1] Ejaz Ahmed, Michael Jones, and Tim K Marks. An improved deep learning architecture for person re-identification. In CVPR, 2015. 1 +[2] Thiemo Alldieck, Mihai Zanfir, and Cristian Sminchisescu. Photorealistic monocular 3D reconstruction of humans wearing clothing. In CVPR, 2022. 2 +[3] Charles G Broyden. A class of methods for solving nonlinear simultaneous equations. 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Parameter-efficient person re-identification in the 3D space. arXiv preprint arXiv:2006.04569, 2020.1 \ No newline at end of file diff --git a/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/images.zip b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..245ba8d2df756ee9689bc1d3997fb3e79da88bfa --- /dev/null +++ b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5d5a57bc1e91ab93bbf2d7c4cab2f6deae60666c468b72d8f13bf54d6052dc27 +size 649364 diff --git a/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/layout.json b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b8aadfc460b6a158469ffa6829ecaa4c87494eeb --- /dev/null +++ b/2023/Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification/layout.json @@ -0,0 +1,11084 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 100, + 103, + 494, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 103, + 494, + 140 + ], + "spans": [ + { + "bbox": [ + 100, + 103, + 494, + 140 + ], + "type": "text", + "content": "Learning Clothing and Pose Invariant 3D Shape Representation for Long-Term Person Re-Identification" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 132, + 161, + 462, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 161, + 462, + 202 + ], + "spans": [ + { + "bbox": [ + 132, + 161, + 462, + 202 + ], + "type": "text", + "content": "Feng Liu, Minchul Kim, ZiAng Gu, Anil Jain, Xiaoming Liu \nDepartment of Computer Science and Engineering \nMichigan State University, East Lansing MI 48824" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 132, + 203, + 462, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 203, + 462, + 217 + ], + "spans": [ + { + "bbox": [ + 132, + 203, + 462, + 217 + ], + "type": "text", + "content": "{liufeng6, kimminc2, guziang, jain, liuxm}@msu.edu" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 270, + 290, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 510 + ], + "type": "text", + "content": "Long-Term Person Re-Identification (LT-ReID) has become increasingly crucial in computer vision and biometrics. In this work, we aim to extend LT-ReID beyond pedestrian recognition to include a wider range of real-world human activities while still accounting for cloth-changing scenarios over large time gaps. This setting poses additional challenges due to the geometric misalignment and appearance ambiguity caused by the diversity of human pose and clothing. To address these challenges, we propose a new approach 3DInvarReID for (i) disentangling identity from non-identity components (pose, clothing shape, and texture) of 3D clothed humans, and (ii) reconstructing accurate 3D clothed body shapes and learning discriminative features of naked body shapes for person ReID in a joint manner. To better evaluate our study of LT-ReID, we collect a real-world dataset called CCDA, which contains a wide variety of human activities and clothing changes. Experimentally, we show the superior performance of our approach for person ReID. Code is available at http://cvlab.cse.msu.edu/project-reid3dinvar.html." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 556, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 617 + ], + "type": "text", + "content": "Person Re-Identification (ReID) aims to recognize and match a specific pedestrian in various locations and at different times [1, 26, 29, 57, 62]. This is a crucial task for various applications, including crime prevention, forensic identification and security monitoring [13, 63]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "Most existing works [11, 12, 24, 25] in this field concentrate on the short-term scenarios, assuming that pedestrians' clothing remains unchanged. However, in this paper, we focus on a more challenging yet practical scenario of Long-Term Person Re-Identification (LT-ReID), where the objective is to recognize individuals over long time periods while taking into account variations in clothing and diverse human activities. 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Illustration of the differences between various person re-identification (ReID) settings. Both (a) conventional/short-term and (b) cloth-changing person ReID benchmarks often restrict subjects to walking or standing, limiting their applications in real-world scenarios. This paper expands on the long-term person re-identification (LT-ReID) setting by tackling a wider range of human activities, increasing its practicality." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 470, + 334, + 536, + 393 + ], + "blocks": [ + { + "bbox": [ + 470, + 334, + 536, + 393 + ], + "lines": [ + { + "bbox": [ + 470, + 334, + 536, + 393 + ], + "spans": [ + { + "bbox": [ + 470, + 334, + 536, + 393 + ], + "type": "image", + "image_path": "7a0d1cb22e0ece9d0b2e2393bcc59eae3c16e598bc62be6f05bebd1d951b3dec.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 495, + 395, + 505, + 403 + ], + "lines": [ + { + "bbox": [ + 495, + 395, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 495, + 395, + 505, + 403 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 508, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 581 + ], + "type": "text", + "content": "identification beyond pedestrian recognition to encompass a wider range of human activities, such as identifying students playing tennis or soldiers crawling in the field (see Fig. 1). This setting poses new challenges due to the geometric misalignment and appearance ambiguity caused by the diversity of human poses and their clothing." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Recently, various approaches [14,18,20,23,27,46,56,59] have been proposed to investigate LT-ReID under clothing changes. They extract clothing-irrelevant features for robust person ReID by custom-designed architectures [19,20], training process [27], loss functions [14], and data augmentation [64]. However, these methods only attempt to mine texture-insensitive body-structural cues in 2D space while ignoring the prior knowledge that the human body is a 3D non-rigid object. A new line of research introduces 3D priors for LT-ReID by either lifting 2D images to a 3D space [67] or including 3D body reconstruction as an auxil" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19617" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "iary task [5]. However, without modeling the 3D clothing, the clothing-sensitive features can not be properly disentangled in either method. Moreover, none of the methods above handle body images with diverse activities." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 125, + 288, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 125, + 288, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 125, + 288, + 316 + ], + "type": "text", + "content": "Given the numerous variations in body images, including body pose, clothing, and view angles, we posit that the most reliable identity cue for LT-ReID is the 3D naked (unclothed) body shape, if it can be accurately and discriminately estimated from a 2D body image. Obviously this is extremely challenging due to confounding factors and the lack of supervision, such as paired images and 3D naked body scans. However, taking inspiration from advancements in 3D feature learning for face recognition [32, 41], we propose a new algorithm, 3DInvarReID, to disentangle identity (naked body) from non-identity components (pose, clothing shape and texture) of 3D clothed humans. This innovative approach not only reconstructs accurate 3D clothed body shapes that faithfully represent the input 2D images, but it also simultaneously learns discriminative naked shape features that effectively enhance LT-ReID." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 322, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 287, + 573 + ], + "type": "text", + "content": "An effective representation of the 3D shape and texture of the human body is a key component of such a learning-based process. To this end, we propose a joint two-layer neural implicit function to represent 3D humans, where identity, clothing shape, and texture components are disentangled into latent representations. Based on the composite model, we jointly learn a model fitting module to disentangle identity from non-identity components (body pose, clothing shape and texture) from 2D images. Modeling texture, along with a differentiable renderer enables us to compare the rendered image with the input image in a self-supervised manner. This allows the learning process to be supervised by both image reconstruction loss and identification loss, using a set of 2D images with identity labels only. Comprehensive experiments demonstrate the superiority of our method in diverse ReID benchmarks. Additionally, to advance the research in the field of LT-ReID, we collect a Cloth-Changing and Diverse Activities (CCDA) dataset (see Fig. 1). The CCDA dataset is specifically designed to evaluate the ReID of the person undergoing both human activities and changes in clothing." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 578, + 266, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 578, + 266, + 590 + ], + "spans": [ + { + "bbox": [ + 59, + 578, + 266, + 590 + ], + "type": "text", + "content": "In summary, the contributions of this work include:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 595, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 595, + 286, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 286, + 619 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 286, + 619 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 47, + 595, + 286, + 619 + ], + "type": "text", + "content": " We propose a novel LT-ReID method, 3DInvarReID, to learn clothing/pose invariant 3D shape representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 46, + 624, + 286, + 684 + ], + "type": "text", + "content": " We devise a novel joint two-layer implicit model that fully models a textured 3D clothed human. Our approach includes a robust and discriminative fitting process that disentangles identity and non-identity features in reconstructing two-layer 3D body shapes from real-world images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 712 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 46, + 689, + 286, + 712 + ], + "type": "text", + "content": " We achieve superior performance in both LT-ReID accuracy and 3D body shape reconstruction." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 309, + 71, + 544, + 232 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 544, + 232 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 544, + 232 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 544, + 232 + ], + "type": "table", + "html": "
MethodEnd-to-End trainableModel textureDiscriminativeModel type
3D modeling methods
SCANimate [44]-XXuniversal
SMPLicit [10]-XXuniversal
Neural-GIF [49]-XXindividual
SNARF [7]-XXindividual
gDNA [6]-XXuniversal
3D fitting methods
PiFu [42]X✓X-
PiFuHD [43]XXX-
Arch [21]X✓X-
Arch++ [15]X✓X-
ICON [55]X✓X-
ClothWild [37]XXX-
PHORHUM [2]✓✓X-
3DInvarReID✓✓✓universal
", + "image_path": "39f015873675a720d34a489c3e53bac675e2a2b46f3ec47e79be779539978082.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 238, + 545, + 304 + ], + "lines": [ + { + "bbox": [ + 305, + 238, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 305, + 238, + 545, + 304 + ], + "type": "text", + "content": "Table 1. Overview of the 3D clothed human modeling (top) and fitting (bottom) methods. Our method is the only one that models clothing texture and learns discriminative information compared to 3D modeling methods. Compared to 3D fitting methods, our end-to-end trainable pipeline enables disentangling identity-sensitive shape features from whole-body images." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 326, + 381, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 326, + 381, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 326, + 381, + 338 + ], + "type": "text", + "content": "2. Prior Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 350, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 578 + ], + "type": "text", + "content": "Person Re-identification. Person ReID aims to match a person across images captured by a distributed camera system. The majority of prior methods [11, 12, 24, 25, 28, 52, 58, 60] assume a short-term application scenario without clothing changes by the person. This limitation has generated a growing interest in long-term cloth-changing person ReID [14, 23, 27, 56]. Datasets such as Real28 [50], VC-Clothes [50], PRCC [56], LTCC [46], COCAS [59] and Celebrities-reID [18, 20] are collected to facilitate this research. These datasets, however, either ignore or only minimally consider human activities, assuming that subjects are pedestrians with a restricted set of activities, limiting their applicability in real-world scenarios. As a result, there is a noticeable discrepancy between published approaches and the real-world LT-ReID problem. In contrast to the focus on the clothing-change person ReID, our research takes a step further by addressing a more challenging and practical issue of person ReID that involves diverse human activities, which are not limited to walking." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "3D Clothed Human Modeling and Fitting. In early attempts [22, 34, 40], a clothed person was modeled as displacements over naked body meshes, obtained by SMPL [33]. However, the fixed mesh topology and bounded resolution approach limit geometric expressivity. Recently, neural implicit representations have been explored to model 3D body shapes due to their topological flexibility and resolution independence [6, 7, 10, 38, 44, 45, 49, 53]. However, as shown in Tab. 1, modeling texture in 3D remains a challenge. While these approaches provide rich geometric detail, insufficient attention has been paid" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19618" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 68, + 527, + 263 + ], + "blocks": [ + { + "bbox": [ + 66, + 68, + 527, + 263 + ], + "lines": [ + { + "bbox": [ + 66, + 68, + 527, + 263 + ], + "spans": [ + { + "bbox": [ + 66, + 68, + 527, + 263 + ], + "type": "image", + "image_path": "e10db5972659fac7a0118d123b811cfc392e5b4f266031a77f77590c7393c236.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 265, + 545, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 265, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 545, + 288 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed joint learning framework for long-term person re-identification and 3D clothed body shape reconstruction. During the inference of ReID, the identity shape feature " + }, + { + "bbox": [ + 46, + 265, + 545, + 288 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id}" + }, + { + "bbox": [ + 46, + 265, + 545, + 288 + ], + "type": "text", + "content": " is utilized for matching." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 307, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 287, + 342 + ], + "type": "text", + "content": "to the discriminativeness of the resulting body shapes. In contrast, we build a discriminative and textured 3D clothed human, serving the purpose of LT-ReID." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 342, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 521 + ], + "type": "text", + "content": "These 3D clothed models can be naturally applied to monocular 3D reconstruction (2D-to-3D fitting). Generally, the input image is encoded as a latent vector, from which the generative model reconstructs the 3D shape [10, 30, 31, 37]. Alternatively, two-step pipelines [15, 21, 42, 43, 55] firstly recover 2.5D sketches (e.g., surface normal), and then infer a full 3D shape. A common limitation of these works is that they require 3D body scans for training, as they are trained on synthetic datasets derived from 3D scans and their rendered images. Furthermore, existing methods do not explicitly consider the discriminative ability of reconstructed 3D clothed body shapes. LVD [9] and SHAPY [8] introduce new discriminative fitting pipelines to reconstruct naked body shapes from images. However, without modeling 3D clothing, 2D image cues can not be fully exploited." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 522, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 630 + ], + "type": "text", + "content": "We propose a novel joint two-layer shape and texture representation of a 3D clothed human model, consisting of both shape and texture. Together with a model fitting module, our representation allows semi-supervised training from images without 3D labels. More importantly, guided by the completed 3D model and the discriminative 2D-to-3D fitting module, our approach disentangles identity features from identity-irrelevant features in 3D space for LT-ReID. Tab. 1 compares our method with prior works." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 639, + 153, + 652 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 153, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 153, + 652 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 171, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 171, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 171, + 670 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "A 3D clothed human model is described by three disentangled latent variables: identity shape, clothing shape and clothing texture. As shown in Fig. 2, these latent repre" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 307, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 437 + ], + "type": "text", + "content": "sentations can be sequentially decoded into canonical 3D shape and texture, respectively by three decoders. To enable self-supervised training on real images, we estimate these latent codes along with the body pose and camera projection parameters. In this work, we use an off-the-shelf method [36] as our PoseNet to predict pose and camera projection, while our image encoder focuses on identity disentanglement learning, i.e., the fitting module. These networks disentangle identity and non-identity components of 3D shapes and reconstruct the input body images via a differentiable render." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": "Formally, given a training set of " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i\\}_{i=1}^T" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": " and the corresponding identity labels " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\{l_i\\}_{i=1}^T" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": ", the image encoder " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\mathbf{I}) : \\mathbf{I} \\to \\mathbf{z}_{id}, \\mathbf{z}_{cloth}, \\mathbf{z}_{tex}" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": " predicts the identity shape code of naked body " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id} \\in \\mathbb{R}^{L_{id}}" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": ", clothed shape code " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{cloth} \\in \\mathbb{R}^{L_{cloth}}" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": " and texture code " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{tex} \\in \\mathbb{R}^{L_{tex}}" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": ". Functions " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{F}, \\mathcal{C}" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": " decode the latent codes to identity shape, clothing shape and texture components, respectively. Additionally, PoseNet " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": " predicts the camera projection parameters " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": " and SMPL body pose " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "inline_equation", + "content": "(\\Omega, \\theta) = \\mathcal{P}(\\mathbf{I})" + }, + { + "bbox": [ + 304, + 437, + 545, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 546, + 528, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 546, + 528, + 558 + ], + "spans": [ + { + "bbox": [ + 317, + 546, + 528, + 558 + ], + "type": "text", + "content": "Mathematically, the learning objective is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 340, + 563, + 545, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 563, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 340, + 563, + 545, + 595 + ], + "type": "interline_equation", + "content": "\\underset {\\mathcal {E}, \\mathcal {F}, \\mathcal {C}, \\mathcal {T}} {\\arg \\min } \\sum_ {i = 1} ^ {T} \\left(\\left| \\hat {\\mathbf {I}} _ {i} - \\mathbf {I} _ {i} \\right| _ {1} + \\mathcal {L} _ {c l a} (\\mathbf {z} _ {i d}, l _ {i})\\right), \\tag {1}", + "image_path": "ae707f65cac7aa12a841a5633a88550cce2ef55ab3347867b94e2806529f1a07.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 601, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 601, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cla}" + }, + { + "bbox": [ + 304, + 601, + 545, + 639 + ], + "type": "text", + "content": " is the classification loss. " + }, + { + "bbox": [ + 304, + 601, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}" + }, + { + "bbox": [ + 304, + 601, + 545, + 639 + ], + "type": "text", + "content": " is the rendered image. This objective enables us to jointly learn accurate 3D clothed shape and discriminative shape for the naked body." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 644, + 479, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 644, + 479, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 479, + 657 + ], + "type": "text", + "content": "3.2. 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We represent the 3D naked body shape as the " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau = 0.5" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " level set of the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19619" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 285, + 167 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 285, + 167 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 285, + 167 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 285, + 167 + ], + "type": "image", + "image_path": "f28251ba6aba23315550902cca8f703d3b054397f99ae1f33d704e4360c6d755.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": "Figure 3. Joint two-layer implicit model. The naked body shape model " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " and clothed body shape model " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " take identity shape code " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": ", clothing shape code " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{cloth}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " and a spatial point " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": ", and produces two occupancy values " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "o_1" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "o_2" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": ". The texture model " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " takes " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{tex}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{cloth}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " to estimate RGB color at " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": ". A 3D generator " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " uses " + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id}" + }, + { + "bbox": [ + 46, + 173, + 289, + 251 + ], + "type": "text", + "content": " to produce a 3D feature volume, enabling hierarchical point-wise feature representation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 266, + 152, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 152, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 152, + 280 + ], + "type": "text", + "content": "occupancy function [35]:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 101, + 284, + 287, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 284, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 101, + 284, + 287, + 298 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {i d} (\\mathbf {z} _ {i d}) = \\{\\mathbf {x} | \\mathcal {F} (\\mathbf {z} _ {i d}, \\mathbf {x}) = \\tau \\}, \\tag {2}", + "image_path": "38d4a3b7838534838d790df2e45a3b85676a29809ed2c229b9a761c12d3334dc.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "type": "text", + "content": " predicts the occupancy value, " + }, + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "type": "inline_equation", + "content": "o_1" + }, + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "type": "text", + "content": " for any point " + }, + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 302, + 287, + 327 + ], + "type": "text", + "content": " in the canonical space. Specifically," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 113, + 331, + 287, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 331, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 113, + 331, + 287, + 345 + ], + "type": "interline_equation", + "content": "\\mathcal {F}: \\mathbb {R} ^ {L _ {i d}} \\times \\mathbb {R} ^ {3} \\rightarrow (o _ {1}, \\mathbf {f}), \\tag {3}", + "image_path": "ae2c2cc12461bbc72cbfe99f1f56e3e032f76ee482f70689b213734c376ed7b0.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{f} \\in \\mathbb{R}^{L_f}" + }, + { + "bbox": [ + 46, + 349, + 287, + 373 + ], + "type": "text", + "content": " is a point-wise feature and will be utilized to predict clothing details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": "Following [6], we make use of function " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": ", implemented via a Multi-Layer Perceptron (MLP), coupled with a 3D CNN-based generator " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " to model 3D naked bodies. As shown in Fig. 3(a), the generator produces a 3D feature volume using " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " as input. We then use trilinear interpolation to query continuous 3D points and feed the feature at " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " to the MLP." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 460, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 287, + 485 + ], + "type": "text", + "content": "Clothed Shape Component. Similarly, we also represent the clothed body shape as the " + }, + { + "bbox": [ + 47, + 460, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\tau = 0.5" + }, + { + "bbox": [ + 47, + 460, + 287, + 485 + ], + "type": "text", + "content": " level set function:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 82, + 490, + 287, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 490, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 82, + 490, + 287, + 504 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {\\text {c l o t h}} \\left(\\mathbf {z} _ {\\text {c l o t h}}\\right) = \\{\\mathbf {x} | \\mathcal {C} \\left(\\mathbf {z} _ {\\text {c l o t h}}, \\mathbf {f}, \\mathbf {x}\\right) = \\tau \\}, \\tag {4}", + "image_path": "73a675fec4c167f54a994001821afc38b5f61369369e643871a0d7acb7a20d42.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 507, + 192, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 507, + 192, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 507, + 192, + 520 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 507, + 192, + 520 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 47, + 507, + 192, + 520 + ], + "type": "text", + "content": " is implemented as a MLP:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 102, + 524, + 287, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 524, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 102, + 524, + 287, + 538 + ], + "type": "interline_equation", + "content": "\\mathcal {C}: \\mathbb {R} ^ {L _ {\\text {c l o t h}}} \\times \\mathbb {R} ^ {L _ {f}} \\times \\mathbb {R} ^ {3} \\rightarrow o _ {2}. \\tag {5}", + "image_path": "92c849cbc749ef2abb06094c315366b611eb5c25627aca208135bb2bd9b2e1ef.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 544, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 544, + 287, + 567 + ], + "type": "text", + "content": " outputs the occupancy value " + }, + { + "bbox": [ + 46, + 544, + 287, + 567 + ], + "type": "inline_equation", + "content": "o_2" + }, + { + "bbox": [ + 46, + 544, + 287, + 567 + ], + "type": "text", + "content": " to represent the clothed shape information." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "text", + "content": "Texture Component. We define a texture field as a mapping function " + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "text", + "content": " from a point " + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "text", + "content": " in the canonical space, texture latent " + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\text{tex}}" + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\text{cloth}}" + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "text", + "content": " to a RGB value " + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\mathbf{c} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 570, + 287, + 606 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 100, + 610, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 610, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 100, + 610, + 287, + 624 + ], + "type": "interline_equation", + "content": "\\mathcal {T}: \\mathbb {R} ^ {L _ {\\text {t e x}}} \\times \\mathbb {R} ^ {L _ {\\text {c l o t h}}} \\times \\mathbb {R} ^ {3} \\rightarrow \\mathbf {c}. \\tag {6}", + "image_path": "e37f55b8042b8784ebe195476c2132dcaa396283dd280977d411e3e3b8785cf4.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "content": "The design of our joint two-layer implicit model is inspired by the approach in [6]. However, as shown in Fig. 3, our model has two novel traits: 1) Instead of simply decomposing the 3D clothed human into coarse and fine models, we apply a two-layer implicit model to represent the naked body and clothing shapes. 2) We additionally model texture to form a complete 3D human model." + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 321, + 72, + 529, + 158 + ], + "blocks": [ + { + "bbox": [ + 321, + 72, + 529, + 158 + ], + "lines": [ + { + "bbox": [ + 321, + 72, + 529, + 158 + ], + "spans": [ + { + "bbox": [ + 321, + 72, + 529, + 158 + ], + "type": "image", + "image_path": "1d99a1eaa2499273d01ce15c16977b6620f7ec525435f2d837e683f64e340ccc.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 163, + 547, + 208 + ], + "lines": [ + { + "bbox": [ + 304, + 163, + 547, + 208 + ], + "spans": [ + { + "bbox": [ + 304, + 163, + 547, + 208 + ], + "type": "text", + "content": "Figure 4. Neural blend skinning network. This module deforms the pose space to canonical space. Given a deformed point " + }, + { + "bbox": [ + 304, + 163, + 547, + 208 + ], + "type": "inline_equation", + "content": "\\mathbf{x}'" + }, + { + "bbox": [ + 304, + 163, + 547, + 208 + ], + "type": "text", + "content": ", we compute its corresponding position " + }, + { + "bbox": [ + 304, + 163, + 547, + 208 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 163, + 547, + 208 + ], + "type": "text", + "content": " in canonical space by iteratively finding the root of Eqn. 9." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 226, + 515, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 226, + 515, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 226, + 515, + 239 + ], + "type": "text", + "content": "3.3. Neural Linear Blend Skinning Network" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": "Our joint two-layer implicit model is built within the canonical space. However, the 3D clothed human data, usually captured in various poses, introduces misalignments between this canonical space and the deformed counterpart. To predict the occupancy values " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_1" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_2" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": " and the texture " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": " for a given observed point " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{x}'" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": " within the deformed space, it is essential to first determine its canonical correspondence point " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": ". Once " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": " is identified, we can then compute " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_1" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_2" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": " using Eqns. 3, 5 and 6. The objective of this step is to find the canonical correspondence " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": " of any query point " + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{x}'" + }, + { + "bbox": [ + 304, + 244, + 545, + 399 + ], + "type": "text", + "content": ". To achieve this goal, similar to [6, 7], we learn a linear blend skinning (LBS) [33] using neural networks in an unsupervised manner." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 403, + 547, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 403, + 547, + 440 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 547, + 440 + ], + "type": "text", + "content": "Regressing Blend Weight. We follow [6, 7] which define the skinning field in canonical space conditioned on our identity latent code " + }, + { + "bbox": [ + 305, + 403, + 547, + 440 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id}" + }, + { + "bbox": [ + 305, + 403, + 547, + 440 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 376, + 446, + 474, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 446, + 474, + 460 + ], + "spans": [ + { + "bbox": [ + 376, + 446, + 474, + 460 + ], + "type": "interline_equation", + "content": "\\mathcal {W}: \\mathbb {R} ^ {L _ {i d}} \\times \\mathbb {R} ^ {3} \\rightarrow \\mathbb {R} ^ {K}", + "image_path": "9729bcf1958ab53c1248fb4fd56c1af373448c3fbeffee44f8c156c234799f16.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 410, + 462, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 410, + 462, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 410, + 462, + 545, + 475 + ], + "type": "interline_equation", + "content": "\\left(\\mathbf {z} _ {i d}, \\mathbf {x}\\right)\\rightarrow \\mathbf {w}, \\tag {7}", + "image_path": "6e2e4a46f8efc4813a96903db3641c76ef05ddbf4050702f0e87cb36a3fa40e3.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "type": "text", + "content": " is the point-wise blend weight of the canonical point " + }, + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "type": "text", + "content": ". Then deformed point " + }, + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{x}'" + }, + { + "bbox": [ + 304, + 484, + 547, + 521 + ], + "type": "text", + "content": " is determined by the following convex combination:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 357, + 529, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 529, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 357, + 529, + 545, + 563 + ], + "type": "interline_equation", + "content": "\\mathbf {x} ^ {\\prime} = \\mathbf {d} \\left(\\mathbf {z} _ {i d}, \\mathbf {x}, \\theta\\right) = \\sum_ {k = 1} ^ {K} \\mathbf {w} _ {k} \\mathbf {B} _ {k} \\mathbf {x}, \\tag {8}", + "image_path": "5384deed56ee6ec6e1fe6f683b6a272e7a6418921e758339b22bdb6677f60f34.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k" + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": "-element in the vector " + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_k" + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": "-element from the set of bone transformation matrices " + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{B} = \\{\\mathbf{B}_k \\in \\mathbb{R}^{4 \\times 4}\\}_{k=1}^K" + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": ". Both " + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{x}'" + }, + { + "bbox": [ + 304, + 570, + 545, + 617 + ], + "type": "text", + "content": " in Eqn. 8 are represented in homogeneous coordinates." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 620, + 545, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 620, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 545, + 692 + ], + "type": "text", + "content": "Implicit Differentiable Skinning. An overview is illustrated in Fig. 4. While the goal is to determine " + }, + { + "bbox": [ + 304, + 620, + 545, + 692 + ], + "type": "inline_equation", + "content": "\\mathbf{x}' \\rightarrow \\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 620, + 545, + 692 + ], + "type": "text", + "content": ", we only have direct access to the mapping defined by Eqn. 8, which is not invertible. Following [6,7], the correspondence is calculated numerically by finding the root of the equation with Broyden's method [3]:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 359, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 359, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} = \\{\\hat {\\mathbf {x}} | \\mathbf {d} (\\mathbf {z} _ {i d}, \\hat {\\mathbf {x}}, \\theta) - \\mathbf {x} ^ {\\prime} = \\mathbf {0} \\}. \\tag {9}", + "image_path": "9302cf6664cd0efe6b156394ea0510f0833842b77ff9090126515523cb5251e1.jpg" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19620" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 160, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 160, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 160, + 85 + ], + "type": "text", + "content": "3.4. Implicit Rendering" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": "During rendering, when 2D pixels are unprojected to 3D points, they are intrinsically mapped in the deformed 3D space. Given a pixel " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": " of a masked input image, we construct a ray " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "\\mathbf{x}' = \\{\\mathbf{c}_0 + t\\mathbf{v}|t\\geqslant 0\\}" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_0" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": " represents the camera's position and " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": " indicates the viewing direction based on the camera projection parameters " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": " is the scalar distance along the ray. We then map the ray points to the canonical space, following Eqn. 9. The intersection point " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_p" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": " of the ray can be calculated by identifying the first change of clothed shape occupancy " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "o_2" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": ". Finally, the rendered color of the pixel " + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 91, + 290, + 224 + ], + "type": "text", + "content": " is calculated via Eqn. 6." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 232, + 226, + 245 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 232, + 226, + 245 + ], + "spans": [ + { + "bbox": [ + 47, + 232, + 226, + 245 + ], + "type": "text", + "content": "3.5. Semi-supervised Model Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 251, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 300 + ], + "type": "text", + "content": "While our model can perform self-supervised learning from real images without 3D labels, we first pre-train our joint implicit 3D model with 3D data in order to mitigate the inherent ambiguity." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 317, + 261, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 261, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 261, + 330 + ], + "type": "text", + "content": "3.5.1 Supervised Pre-training 3D clothed Model" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": "Training Data. We combine CAPE [34] (3,000 scans) and THuman2.0 [65] (526 scans) to train our joint two-layer implicit model. THuman2.0 consists of 526 texture clothed 3D scans of 105 subjects. Following [6], for each scan, we obtain its SMPL naked shape code. CAPE provides 148,584 pairs of scans under clothing and SMPL naked body with rich pose variations of 15 subjects. We randomly sample 3,000 scans for training. Formally, each training sample can be represented as SMPL pose " + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": ", identity label " + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "inline_equation", + "content": "l_{3D}" + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": " spatial points " + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i'" + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": ", and their SDFs " + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "inline_equation", + "content": "o_1^i" + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "inline_equation", + "content": "o_2^i" + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": ", and color " + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i" + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "inline_equation", + "content": "\\{\\theta, l_{3D}, \\{\\mathbf{x}_i', o_1^i, o_2^i, \\mathbf{c}_i\\}_{i=1}^n\\}" + }, + { + "bbox": [ + 46, + 339, + 289, + 496 + ], + "type": "text", + "content": ". With the autodecoding technique [39], we assign trainable identity shape code, clothing shape code, and texture code to each training sample." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 498, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 511 + ], + "type": "text", + "content": "Loss Function. We define the loss below for each sample:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 527, + 284, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 527, + 284, + 548 + ], + "spans": [ + { + "bbox": [ + 51, + 527, + 284, + 548 + ], + "type": "interline_equation", + "content": "\\underset {\\mathcal {F}, \\mathcal {C}, \\mathcal {T}, \\mathbf {z} _ {i d}, \\mathbf {z} _ {c l o t h}, \\mathbf {z} _ {t e x}} {\\arg \\min } \\mathcal {L} _ {i d} + \\mathcal {L} _ {c l o t h} + \\mathcal {L} _ {t e x} + \\mathcal {L} _ {c l a} ^ {3 D} (\\mathbf {z} _ {i d}, l _ {3 D})", + "image_path": "fc899cc98101e1c345111bc75d2bf76c0ed9ac91594fe84b703e99fab2c866e4.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 96, + 551, + 287, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 551, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 96, + 551, + 287, + 564 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i d} = \\sum_ {i = 0} ^ {n} B C E \\left(\\mathcal {F} \\left(\\mathbf {z} _ {i d}, \\hat {\\mathbf {x}} _ {i}\\right), o _ {1} ^ {i}\\right) \\tag {10}", + "image_path": "aa434eb59dab62e226c18bcb15b2aa0f51dbd6097aafa69cb00c1ba431acb379.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 82, + 567, + 287, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 567, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 82, + 567, + 287, + 581 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c l o t h}} = \\sum_ {i = 0} ^ {n} B C E \\left(\\mathcal {C} \\left(\\mathbf {z} _ {\\text {c l o t h}}, \\mathbf {f} _ {i}, \\hat {\\mathbf {x}} _ {i}\\right), o _ {2} ^ {i}\\right) \\tag {11}", + "image_path": "93a04088895cd851200cf4ec4b066b20993021ebf7f7416a8e5fc205fb935e43.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 82, + 582, + 287, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 582, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 82, + 582, + 287, + 596 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t e x} = \\sum_ {i = 0} ^ {n} \\left\\| \\mathcal {T} \\left(\\mathbf {z} _ {t e x}, \\mathbf {z} _ {\\text {c l o t h}}, \\hat {\\mathbf {x}} _ {i}\\right) - \\mathbf {c} _ {i} \\right\\| _ {2}, \\tag {12}", + "image_path": "fc6541ddb6ba96bb931735494848645fcb1f21a556ad6966d4627cc136cb40f2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 607, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 607, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 607, + 287, + 632 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 607, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cla}^{3D}(\\mathbf{z}_{id},l_{3D})" + }, + { + "bbox": [ + 47, + 607, + 287, + 632 + ], + "type": "text", + "content": " is the cross-entropy classification loss. We additionally add auxiliary loss " + }, + { + "bbox": [ + 47, + 607, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_W" + }, + { + "bbox": [ + 47, + 607, + 287, + 632 + ], + "type": "text", + "content": " to train network " + }, + { + "bbox": [ + 47, + 607, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 136, + 649, + 287, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 649, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 136, + 649, + 287, + 661 + ], + "type": "interline_equation", + "content": "\\arg \\min _ {\\mathcal {W}} \\mathcal {L} _ {W} \\tag {13}", + "image_path": "32488b0564665a36c4111cadb07d701e33cc4f5c36a1e3fab3ea9cd0d79b3a05.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 91, + 663, + 287, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 663, + 287, + 679 + ], + "spans": [ + { + "bbox": [ + 91, + 663, + 287, + 679 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {W} = \\sum_ {k = 0} ^ {K} | | \\mathcal {W} (\\mathbf {z} _ {i d}, \\mathbf {J} _ {k}) - \\mathbf {w} _ {\\mathbf {J} _ {k}} | | _ {2}, \\tag {14}", + "image_path": "9b3f7bc997481ca2d14e23d1899c31760e9ee5cef052d880ff19b878c260ce2d.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{\\mathbf{J}_k}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " is the pre-computed ground truth skinning weights of SMPL joints location " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_k" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 543, + 248 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 543, + 248 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 543, + 248 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 543, + 248 + ], + "type": "image", + "image_path": "7b47a5577bf922153fbee7520a8ef58b11b558883757a4c2522e0fca1d226f52.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 251, + 545, + 274 + ], + "lines": [ + { + "bbox": [ + 306, + 251, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 545, + 274 + ], + "type": "text", + "content": "Figure 5. Example images from CCDA, with one subject per row, showcasing the diversity of body poses, clothing styles and colors." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 289, + 522, + 302 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 522, + 302 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 522, + 302 + ], + "type": "text", + "content": "3.5.2 Self-supervised Joint Modeling and Fitting" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 308, + 546, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 308, + 546, + 344 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 546, + 344 + ], + "type": "text", + "content": "Given a set of in-the-wild 2D images with body masks and identity labels " + }, + { + "bbox": [ + 305, + 308, + 546, + 344 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}_i, \\mathbf{M}_i, l_i\\}_{i=1}^T" + }, + { + "bbox": [ + 305, + 308, + 546, + 344 + ], + "type": "text", + "content": ", the self-supervised identity disentanglement loss is:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 354, + 346, + 545, + 367 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 346, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 354, + 346, + 545, + 367 + ], + "type": "interline_equation", + "content": "\\underset {\\mathcal {E}, \\mathcal {T}} {\\arg \\min } \\sum_ {i = 1} ^ {T} \\mathcal {L} _ {s i l} + \\mathcal {L} _ {r g b} + \\mathcal {L} _ {c l a}, \\tag {15}", + "image_path": "94ea76f34352f9204d2aa823f2eb8828163031ee567b19437432213e69963007.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "spans": [ + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rgb}" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": " is the photometric loss, " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sil}" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": " is silhouette loss and " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cla}" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": " is the classification loss. Specifically, we denote " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_p" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_p" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": " as the RGB and silhouette values of pixel " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "p\\in P" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": " denotes the entire set of pixels in the input image " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": ". A subset of " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": ", represented as " + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "inline_equation", + "content": "P^{in}" + }, + { + "bbox": [ + 305, + 373, + 546, + 457 + ], + "type": "text", + "content": ", corresponds to the pixels where an intersection between the rays and the body in the image has been detected. The photometric loss is defined as" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 468, + 545, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 468, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 313, + 468, + 545, + 499 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r g b} = \\frac {1}{| P |} \\sum_ {p \\in P ^ {i n}} \\left| \\mathbf {I} _ {p} - \\mathcal {T} \\left(\\mathcal {E} _ {t e x} (\\mathbf {I}), \\mathcal {E} _ {c l o t h} (\\mathbf {I}), \\hat {\\mathbf {x}} _ {p}\\right) \\right|, \\tag {16}", + "image_path": "36d5b5123bb6f5f39f39797bf5dbe424acb7c971bb0247096d063dc268c12693.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "text", + "content": "where the encoder " + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "text", + "content": " estimates " + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id} = \\mathcal{E}_{id}(\\mathbf{I})" + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{cloth} = \\mathcal{E}_{cloth}(\\mathbf{I})" + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{tex} = \\mathcal{E}_{tex}(\\mathbf{I})" + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "text", + "content": " from image " + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 305, + 505, + 545, + 540 + ], + "type": "text", + "content": " is the intersection point (see Sec. 3.4)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 318, + 541, + 476, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 541, + 476, + 552 + ], + "spans": [ + { + "bbox": [ + 318, + 541, + 476, + 552 + ], + "type": "text", + "content": "We further define the silhouette loss as" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 355, + 555, + 545, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 555, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 355, + 555, + 545, + 585 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s i l} = \\frac {1}{| P |} \\sum_ {p \\in P ^ {\\text {o u t}}} C E \\left(\\mathbf {M} _ {p}, \\hat {\\mathbf {M}} _ {p}\\right), \\tag {17}", + "image_path": "9429dcf491f65290cbc49757a6428e6de0de799c8805e9aed25f62ebf705db4f.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{M}}" + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "text", + "content": " is the masked rendering, " + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "inline_equation", + "content": "P^{out} = P - P^{in}" + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "text", + "content": " represents the indices in the mini-batch for which there is no ray-geometry intersection or " + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_p = 0" + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "inline_equation", + "content": "CE(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "text", + "content": " denotes the cross-entropy loss. We impose triplet loss and cross-entropy loss on the identity shape code " + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id} = \\mathcal{E}_{id}(\\mathbf{I})" + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "text", + "content": " as our classification loss " + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cla}(\\mathbf{z}_{id},l)" + }, + { + "bbox": [ + 304, + 592, + 547, + 666 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 671, + 435, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 435, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 435, + 682 + ], + "type": "text", + "content": "3.6. Person ReID Inference" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "For person ReID inference, the encoder " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " processes body images and extracts the identity shape features " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19621" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "The Cosine similarity of " + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{id}" + }, + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": " is then used to determine if the two images belong to the same person. It is worth noting that, the inference of our ReID does not incorporate the 3D reconstruction module, making it highly efficient." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 130, + 206, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 130, + 206, + 142 + ], + "spans": [ + { + "bbox": [ + 47, + 130, + 206, + 142 + ], + "type": "text", + "content": "4. CCDA Person ReID Dataset" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 149, + 288, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 149, + 288, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 149, + 288, + 365 + ], + "type": "text", + "content": "We construct a new dataset with diverse human activities and clothing changes for evaluating LT-ReID. Specifically, we collect data for popular athletes in soccer, tennis, and basketball, and popular artists, such as fashion models and singers. We crawl whole body images of each subject on Google Image1 with athlete/artist names. We collect two sets of images per subject: 'challenging' and 'normal' body poses. As an example, for a basketball player, the 'challenging' set includes images of players' actions on the court, while the 'normal' set contains standing or walking poses. We then crop the body region from the original image via the detected bounding box and resize it to " + }, + { + "bbox": [ + 46, + 149, + 288, + 365 + ], + "type": "inline_equation", + "content": "256 \\times 128" + }, + { + "bbox": [ + 46, + 149, + 288, + 365 + ], + "type": "text", + "content": ". Finally, the annotator verifies the identity of each image. In total, 1,555 images of 100 subjects are retained. For each subject, we randomly select one image from 'normal' images for the gallery set, while the remaining 1,455 images comprise the query set. Fig. 5 shows examples of images in the CCDA dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 372, + 173, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 372, + 173, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 173, + 385 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": "Implementation Details. Our training process includes two stages: 1) Networks " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\mathcal{F},\\mathcal{C},\\mathcal{T},\\mathcal{W}" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": " are pre-trained on 3D data. 2) " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": " are trained or fine-tuned with real images. The encoder " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": " is implemented as a ResNet-50. Networks " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\mathcal{F},\\mathcal{C},\\mathcal{T}" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": " are MLPs. In experiments, we set " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "L_{cloth} = L_{tex} = 512" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "L_{id} = 4,096" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "L_{f} = L_{h} = 256" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "K = 24" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "inline_equation", + "content": "n = 200,000" + }, + { + "bbox": [ + 46, + 392, + 287, + 489 + ], + "type": "text", + "content": ". We implement in Pytorch and use Adam optimizer in both stages." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 494, + 130, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 494, + 130, + 506 + ], + "spans": [ + { + "bbox": [ + 47, + 494, + 130, + 506 + ], + "type": "text", + "content": "5.1. Person ReID" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 515, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 515, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 515, + 287, + 552 + ], + "type": "text", + "content": "Metric. For person ReID, we follow the standard retrieval accuracy metrics, namely the Cumulative Matching Characteristics (CMC) and mean average precision (mAP)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 554, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 625 + ], + "type": "text", + "content": "Baseline. We compare our method with eight SoTA person ReID methods: Two-Stream [66], MLFN [4], HACNN [26], Part-Aligned [47], PCB [48], TriNet [16], MGN [51], DG-Net [64], and five SoTA cloth-changing re-ID methods: ReIDCaps [20], 3DSL [5], RCSAnet [19], FSAM [17] and CAL [14]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 639, + 286, + 652 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 286, + 652 + ], + "type": "text", + "content": "5.1.1 Results on Cloth-changing Person ReID datasets" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 661, + 286, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 661, + 286, + 697 + ], + "spans": [ + { + "bbox": [ + 46, + 661, + 286, + 697 + ], + "type": "text", + "content": "Datasets. We test on four popular cloth-changing ReID datasets: Celeb-reID/Celeb-reID-light [18, 20], PRCC [56], LTCC [46] and the recent CCVID dataset [14, 61]." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 309, + 71, + 544, + 153 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 544, + 153 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 544, + 153 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 544, + 153 + ], + "type": "table", + "html": "
MethodBackboneCeleb-reIDCeleb-reID-light
mAPRank1mAPRank1
Two-Stream [66]ResNet-507.836.3--
MLFN [4]*6.041.46.310.6
HACNN [26]*9.547.611.516.2
Part-Aligned [47]GoogLeNet×26.419.4--
PCB [48]ResNet-508.237.1--
MGN [51]ResNet-5010.849.013.921.5
DG-Net [64]ResNet-5010.650.112.623.5
", + "image_path": "89afd734a9f100650eaaeb59780cf92eb8dc6d48de559fd4378480dc47887074.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 309, + 154, + 544, + 237 + ], + "blocks": [ + { + "bbox": [ + 309, + 154, + 544, + 237 + ], + "lines": [ + { + "bbox": [ + 309, + 154, + 544, + 237 + ], + "spans": [ + { + "bbox": [ + 309, + 154, + 544, + 237 + ], + "type": "table", + "html": "
cloth-changing person ReID methods
ReIDCaps- [20]DenseNet-1219.851.211.220.3
ReIDCaps [20]DenseNet-121×615.863.019.033.5
RCSAnet [19]DenseNet-121×211.955.616.729.5
CAL [14]ResNet-5013.759.218.533.6
3DInvarReIDResNet-5011.855.215.030.1
3DInvarReID#ResNet-5015.261.221.837.0
ReIDCaps+ \n3DInvarReID#-18.465.525.742.2
", + "image_path": "d2a1505e3da4d0922278e7f88114e032d95f0729b47abaaf31f1f3fa9ff44ad5.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 315, + 301, + 538, + 430 + ], + "blocks": [ + { + "bbox": [ + 305, + 244, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 305, + 244, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 244, + 545, + 289 + ], + "type": "text", + "content": "Table 2. Comparison with SoTA on Celeb-reID and Celeb-reID-light datasets (\\%). * indicates that the backbone is designed by the authors. The red number means the total number of models. 3DInvarReID#'s weights are initialized using the CAL model." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 301, + 538, + 430 + ], + "lines": [ + { + "bbox": [ + 315, + 301, + 538, + 430 + ], + "spans": [ + { + "bbox": [ + 315, + 301, + 538, + 430 + ], + "type": "table", + "html": "
MethodBackboneLTCCPRCC
mAPRank1mAPRank1
HACNN [26]*9.321.6-21.8
PCB [48]ResNet-5010.023.538.741.8
3DSL [5]ResNet-50×214.831.2-51.3
FSAM [17]ResNet-5016.238.5-54.5
CAL [14]ResNet-5018.040.155.855.2
3DInvarReIDResNet-5016.737.852.551.6
CAL+3DInvarReID-18.940.957.256.5
CALResNet-502.83.820.331.6
3DInvarReIDResNet-502.85.120.134.6
3DInvarReID#ResNet-502.85.621.440.7
", + "image_path": "0ba4be9b3456b7c40b0ba6af8ef5ae404f737c5b997bb8fad39db906e9045cc2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 437, + 545, + 483 + ], + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 483 + ], + "type": "text", + "content": "Table 3. Comparison with SoTA cloth-changing person ReID methods on the LTCC and PRCC datasets " + }, + { + "bbox": [ + 305, + 437, + 545, + 483 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 437, + 545, + 483 + ], + "type": "text", + "content": " Models highlighted in pink are trained on the Celeb-reID dataset. 3DInvarReID#'s weights are initialized using the CAL model." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "content": "Results on Celeb-reID and Celeb-reID-light. As reported in Tab. 2, our 3DInvarReID (Ours) outperforms all the general person re-ID baselines on both datasets. Considering methods using a single network, we also outperform the cloth-changing baseline, ReIDCaps- [20]. More importantly, to investigate the complementarity between our learned 3D shape features and existing 2D features, we fuse our method with cloth-changing baselines by simple summation at the score level. By fusing with ReIDCaps [20], our method improves the Rank1 accuracy on Celeb-reID from " + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "inline_equation", + "content": "63.0\\%" + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "inline_equation", + "content": "65.5\\%" + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "content": " and from " + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "inline_equation", + "content": "33.5\\%" + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "inline_equation", + "content": "42.2\\%" + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "content": " on Celeb-reID-light. These results clearly demonstrate that the 3D shape features learned from our method are both discriminative and complementary to the 2D features, indicating the effectiveness of our proposed approach for person ReID, particularly under cloth-changing scenarios." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Results on LTCC, PRCC and CCVID. The compari-" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "text", + "content": "1All collected images are under Creative Commons licenses." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19622" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 278, + 148 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 278, + 148 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 278, + 148 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 278, + 148 + ], + "type": "table", + "html": "
MethodBackboneGeneralCloth-changing
mAPRank1mAPRank1
TriNet [16]ResNet-5078.181.577.081.1
CAL [14]ResNet-5081.382.679.681.7
3DInvarReIDResNet-5066.170.865.470.2
CAL+3DInvarReID-82.683.981.384.3
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MethodBackbonemAPRank1Rank5
ReLU caps [20]DenseNet-121×610.96.520.2
CAL [14]ResNet-5019.310.026.7
3DInvarReIDResNet-5021.711.130.5
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MethodBackboneMarket-1501MSMT17
mAPRank1mAPRank1
PCB [48]ResNet-5081.693.840.468.2
3DSL [5]ResNet-50×287.395.0--
FSAM [17]ResNet-5085.694.6--
CAL [14]ResNet-5087.594.757.379.7
3DInvarReIDResNet-5085.594.255.176.3
CAL+3DInvarReID-87.995.159.180.8
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LVD [9]SHAPY [8]Ours
CD-L20.6540.6320.610
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Model TypemAPRank1Rank5
3DInvarReID17.536.356.4
3DInvarReID-w/o 3D14.628.448.3
3DInvarReID-w/o Pre-training15.129.350.7
3DInvarReID-w/o 3D clothing16.032.152.8
", + "image_path": "829cec7f3f798b5d33dd0145fa921f91d8505b2c55a519e587d48303c8cadf74.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 339, + 306, + 512, + 317 + ], + "lines": [ + { + "bbox": [ + 339, + 306, + 512, + 317 + ], + "spans": [ + { + "bbox": [ + 339, + 306, + 512, + 317 + ], + "type": "text", + "content": "Table 8. Ablaton studies on CCDA dataset " + }, + { + "bbox": [ + 339, + 306, + 512, + 317 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 336, + 518, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 336, + 518, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 336, + 518, + 348 + ], + "type": "text", + "content": "of our 3D shape feature, even on short-term datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 356, + 416, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 416, + 367 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 416, + 367 + ], + "type": "text", + "content": "5.2.3D Reconstruction" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 374, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 625 + ], + "type": "text", + "content": "Most 3D body reconstruction methods focus more on pose estimation than shape estimation. Recently, SHAPY [8] releases a dataset (HBW) that contains ground-truth 3D body scans and the corresponding in-the-wild images, which enables us to test the accuracy of our reconstructed 3D naked body shapes. We thus evaluate our methods on the validation set of HBW, which contains 237 in-the-wild images of 10 subjects. Our baseline includes LVD [9] and SHAPY [8], which are recent pipelines for discriminative identity shape fitting. Following [9], we evaluate the reconstruction accuracy with Chamfer distance " + }, + { + "bbox": [ + 304, + 374, + 545, + 625 + ], + "type": "inline_equation", + "content": "(\\mathrm{CD} - L_2)" + }, + { + "bbox": [ + 304, + 374, + 545, + 625 + ], + "type": "text", + "content": ", by uniformly sampling 10,000 points on both ground-truth and predicted meshes in the canonical space. As shown in Tab. 7, our method outperforms the two baselines. We also visualize 3D reconstructions in Fig. 6. Our reconstructions resemble the ground truth better than the baselines. These results demonstrate the superiority of the proposed method in reconstructing naked 3D body shapes. Fig. 7 shows qualitative comparisons with ICON [55] and ClothWild [37]. Our approach achieves comparable clothed 3D body reconstructions." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 632, + 400, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 400, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 400, + 645 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 651, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 545, + 674 + ], + "type": "text", + "content": "In this section, all models are trained on Celeb-reID and tested on the CCDA dataset." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 546, + 713 + ], + "type": "text", + "content": "Effect of the 3D module. We compare our full model with an ablated version that only incorporates the " + }, + { + "bbox": [ + 306, + 677, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cla}" + }, + { + "bbox": [ + 306, + 677, + 546, + 713 + ], + "type": "text", + "content": " loss in its training, disregarding 3D modules. The results in" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19623" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 279, + 355 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 279, + 355 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 279, + 355 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 279, + 355 + ], + "type": "image", + "image_path": "116224ffaac5f58f3a788b784baaec84a9f9f9018ac4e7baa8e734afd02c6f35.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 360, + 287, + 395 + ], + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 395 + ], + "type": "text", + "content": "Figure 6. Qualitative comparisons with LVD [9] and SHAPY [8] on 3D naked body reconstruction. Our approach recovers more accurate 3D body shapes from the images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 411, + 287, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 447 + ], + "type": "text", + "content": "Tab. 8 show that our 3DInvarReID significantly improves the recognition accuracy, leading to a Rank1 accuracy increase from 28.4 to 36.3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 450, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 559 + ], + "type": "text", + "content": "Effect of Our Two-layer Implicit Model. Our primary goal is to disentangle the identity feature from non-identity features in 3D shape space. To evaluate the effectiveness of our 3D disentanglement module, we train a model (Oursw/o 3D clothing) by replacing our 3D body model with SMPL shape bases and omitting the modeling of the 3D clothing component and rendering layer. The results in Tab. 8 demonstrate the advantages of modeling clothing shape and texture for person ReID (Rank1: " + }, + { + "bbox": [ + 46, + 450, + 287, + 559 + ], + "type": "inline_equation", + "content": "32.1\\rightarrow 36.3" + }, + { + "bbox": [ + 46, + 450, + 287, + 559 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 561, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 622 + ], + "type": "text", + "content": "Effect of Pre-training. Tab. 8 shows that removing the pre-training stage results in a lower Rank1 accuracy, with a score of 29.3 compared to our 36.3. This finding highlights the effectiveness of pre-training in addressing the inherent ambiguity of disentanglement." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 633, + 125, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 125, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 125, + 645 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "This paper tackles the challenging setting of long-term person ReID, which allows a wider range of real-world human activities and accounts for cloth-changing scenarios. To address this problem, we present a joint two-layer implicit representation to model textured 3D clothed humans" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 326, + 72, + 531, + 284 + ], + "blocks": [ + { + "bbox": [ + 326, + 72, + 531, + 284 + ], + "lines": [ + { + "bbox": [ + 326, + 72, + 531, + 284 + ], + "spans": [ + { + "bbox": [ + 326, + 72, + 531, + 284 + ], + "type": "image", + "image_path": "7d64ea0e24c18426461c1c696af139bfd11aa935824c4b0a0d63014a409f1588.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 292, + 545, + 314 + ], + "lines": [ + { + "bbox": [ + 305, + 292, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 305, + 292, + 545, + 314 + ], + "type": "text", + "content": "Figure 7. Qualitative comparisons with ICON [55] and Cloth-Wild [37] on 3D clothed body reconstruction." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 348, + 546, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 546, + 445 + ], + "type": "text", + "content": "together with a discriminative fitting module, enabling us to disentangle identity and non-identity features for real-world images. We collect a new LT-ReID dataset, CCDA, with diverse human activities and clothing changes, facilitating future research on real-world scenarios. Experimental results demonstrate the effectiveness of our method in disentangling identity and non-identity features in 3D clothed body shapes, thereby contributing to LT-ReID." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 546, + 586 + ], + "type": "text", + "content": "Limitations & Potential Negative Impacts Impacts. Our work tackles the challenge of disentangling clothing and body shape in 3D shape representation. The clothing reconstruction task remains challenging as evidenced by the visual quality of the published models and our models. Our results show that the task of body-clothing disentangle-ment brings benefit in the recognition task, a finding which opens new possibilities to multi-task learning across 2D-3D modalities. Like most person ReID methods, one potential negative impact of our approach is that it could be used for unethical surveillance and invasion of privacy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 715 + ], + "type": "text", + "content": "Acknowledgments. This research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2022-21102100004. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. 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Parameter-efficient person re-identification in the 3D space. arXiv preprint arXiv:2006.04569, 2020.1" + } + ] + } + ], + "index": 33 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "19626" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Concise and Descriptive Attributes for Visual Recognition/eb8f500b-e381-4a8d-9629-e0fa391759b6_content_list.json b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/eb8f500b-e381-4a8d-9629-e0fa391759b6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e222251d08ba93bf5464aced957cf39e3776a0 --- /dev/null +++ b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/eb8f500b-e381-4a8d-9629-e0fa391759b6_content_list.json @@ -0,0 +1,1892 @@ +[ + { + "type": "text", + "text": "Learning Concise and Descriptive Attributes for Visual Recognition", + "text_level": 1, + "bbox": [ + 143, + 130, + 826, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "An Yan\\*, Yu Wang\\*, Yiwu Zhong\\*, Chengyu Dong, Zexue He, Yujie Lu, William Yang Wang, Jingbo Shang, Julian McAuley", + "bbox": [ + 205, + 178, + 764, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$\\diamond$ UC San Diego, $\\clubsuit$ University of Wisconsin-Madison, $\\clubsuit$ UC Santa Barbara", + "bbox": [ + 197, + 215, + 774, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{ayan, yuw164, cdong, zehe, jshang, jmcauley}@ucsd.edu", + "bbox": [ + 267, + 236, + 700, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{yujielu,william}@cs.ucsb.edu，yzhong52@wisc.edu", + "bbox": [ + 272, + 253, + 696, + 270 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 319, + 313, + 335 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advances in foundation models present new opportunities for interpretable visual recognition – one can first query Large Language Models (LLMs) to obtain a set of attributes that describe each class, then apply vision-language models to classify images via these attributes. Pioneering work shows that querying thousands of attributes can achieve performance competitive with image features. However, our further investigation on 8 datasets reveals that LLM-generated attributes in a large quantity perform almost the same as random words. This surprising finding suggests that significant noise may be present in these attributes. We hypothesize that there exist subsets of attributes that can maintain the classification performance with much smaller sizes, and propose a novel learning-to-search method to discover those concise sets of attributes. As a result, on the CUB dataset, our method achieves performance close to that of massive LLM-generated attributes (e.g., 10k attributes for CUB), yet using only 32 attributes in total to distinguish 200 bird species. Furthermore, our new paradigm demonstrates several additional benefits: higher interpretability and interactivity for humans, and the ability to summarize knowledge for a recognition task.", + "bbox": [ + 75, + 351, + 473, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 700, + 209, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Explaining black-box neural models is a critical research problem. For visual recognition, one line of research tries to classify objects with descriptions or attributes [12, 8, 39, 18, 22], which provide additional information beyond visual cues such as activation maps [41, 40]. However, they require in-depth human analysis and intensive annotation to obtain key attributes for a particular recognition task. Such a paradigm is costly and thus impractical to scale up when the number of classes and domains grows.", + "bbox": [ + 75, + 726, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The recent advance of foundation models creates new", + "bbox": [ + 96, + 863, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/378836f04f43311f916c3d656a3e79289956974f54269591503a2254a185b5c0.jpg", + "image_caption": [ + "Figure 1: Our proposed paradigm for visual recognition via learning a concise set of descriptive attributes." + ], + "image_footnote": [], + "bbox": [ + 504, + 304, + 890, + 414 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "opportunities for building interpretable visual recognition models, as demonstrated by the powerful capabilities of models such as GPT-3 and ChatGPT in encoding world knowledge [5, 32, 21]. One can query useful visual attributes from LLMs and classify images via these attributes by converting visual features from vision-language models (VLMs) (e.g., CLIP [36]) into attribute scores [56]. One recent work [52] shows that a large set of attributes from LLMs (e.g., 50 attributes per class) can achieve comparable performance to image features in a linear probing setting. However, two key observations motivate us to re-think this formulation: (1) A large number of attributes dramatically hurts the interpretability of a model. It is unrealistic to manually check thousands of attributes to fully understand model decisions. (2) We surprisingly find that when the number of attributes is large enough (e.g., the dimension of image features), random words drawn from the entire vocabulary can perform equally well as LLM-generated attributes. Moreover, reducing the number of random words by $25\\%$ can still attain competitive performance. This indicates that redundant and noisy information exists in the massive LLM-generated attributes.", + "bbox": [ + 496, + 474, + 892, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With our findings, we ask the research question: Can we learn a concise set of representative visual attributes in the form of natural language to explain how visual recognition works? For example, can we find a few representative attributes to distinguish 200 bird species? This is a nontrivial problem. Even for humans, it is not easy to summa", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* equal contributions.", + "bbox": [ + 101, + 887, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3090", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rize what are the representative visual attributes given many visual classes. To tackle this challenge, we propose a novel learning-to-search method, which uses image-level labels to guide the searching of discriminative attributes. Specifically, we train a learnable dictionary to approximate the embedding space of VLMs, and then find descriptive attributes in the latent text space via nearest neighbor search.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we propose a new paradigm for visual recognition (Figure 1), which seeks to learn a concise set of visual attributes in the form of natural language. Once learned, there are several benefits to our new paradigm: (1) Our discovered attributes are highly descriptive. On 8 visual recognition datasets, our model classifies images via these attributes and achieves comparable classification performance as image features, even if the number of attributes is much smaller than the dimension of image features. (2) The condensed sets of attributes enable strong interpretability for the model decision process through a few human-friendly text descriptions. (3) Additionally, our framework presents a natural language interface for humans to interact with. One can correct a wrong prediction during model inference, by perturbing the values of attribute scores where it made mistakes. (4) Lastly, these expressive attributes can be viewed as a concise form of knowledge to summarize useful features for a visual recognition task, without costly human effort.", + "bbox": [ + 75, + 198, + 470, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, our contributions are three-fold:", + "bbox": [ + 96, + 484, + 367, + 500 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Leveraging recent advances in foundation models, we propose a new paradigm for visual recognition by learning a concise set of attribute descriptions.", + "- To find these attributes, we propose a novel learning-to-search method which prunes the large attribute pool from large language models to a descriptive subset.", + "- We conduct extensive experiments across 8 visual recognition datasets to validate our recognition effectiveness and efficiency with additional benefits." + ], + "bbox": [ + 96, + 503, + 468, + 646 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Methodology", + "text_level": 1, + "bbox": [ + 76, + 662, + 210, + 680 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we introduce our key components for a new paradigm of visual recognition. It mainly consists of three modules: First, in Section 2.1, given an image domain, we query large language models to obtain a large set of visual attributes for the categories of a task. Second, we use a semantic transformation (Section 2.2) to project the image features into attribute features via a vision-language model, where each dimension in the new space corresponds to an attribute concept, and a higher value represents higher correlation between the image and the attribute. Finally, given the large space of attributes, we propose a novel learning-to-search method (Section 2.4) to efficiently prune the attributes into a much smaller subset to obtain a concise model for classification.", + "bbox": [ + 75, + 689, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Generating Attribute Concepts via LLMs", + "text_level": 1, + "bbox": [ + 500, + 90, + 854, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The first step of our framework is to obtain a set of appropriate attribute concepts. Given a dataset with different categories, (e.g., CUB with 200 bird classes), what are the distinctive visual attributes to recognize them? Manually labeling and designing these attribute concepts can be costly, and can not scale to large numbers of classes. Large Language Models (LLMs), such as GPT-3 [5] and ChatGPT, provide an alternative solution. We can view these language models as implicit knowledge bases with exceptional world knowledge on a variety of tasks and topics, which humans can easily interact with through natural language to query knowledge. To this end, prompt engineering, or the ability to ask good questions to language models, is still important. To effectively query knowledge from LLMs with regard to classifying images, we design two types of prompts.", + "bbox": [ + 496, + 114, + 890, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instance Prompting for Class-level Features. For each class $c$ in a given task, our first design choice is to query class-level information from LLMs. We prompt a language model with the instance prompt:", + "bbox": [ + 496, + 342, + 890, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Q: What are the useful visual features to distinguish $Y_{c}$ in a photo?", + "bbox": [ + 496, + 404, + 890, + 434 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $Y_{c}$ corresponds to the name of class $c$ in the form of natural language.", + "bbox": [ + 496, + 435, + 890, + 465 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Batch Prompting for Group-level Features. For certain datasets (e.g., CIFAR-100 and ImageNet), there is inherently a hierarchy that some categories belong to the same group. For example, in CIFAR-100, there is a superclass for every five categories. Hence, we propose batch prompting, where we ask the language model to reason about the distinctive visual features among a batch of categories:", + "bbox": [ + 496, + 465, + 890, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Q: Here are $N_{g}$ kinds of $Y_{g}$ : $\\{Y_{c_1}, Y_{c_2}, \\ldots, Y_{c_M}\\}$ . What are the useful visual features to distinguish them in a photo? where $N_{g}$ is the number of classes in a group $g$ , $Y_{g}$ is the name of the group, $Y_{c_i}$ corresponds to the name of each class $c_i$ in the form of natural language.", + "bbox": [ + 496, + 571, + 890, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We present more details regarding our prompt design, robustness check of different prompts, and examples of the generated attributes in Appendix A.", + "bbox": [ + 496, + 651, + 890, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Semantic Projection", + "text_level": 1, + "bbox": [ + 500, + 709, + 691, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "After obtaining a pool consisting of $N$ attribute concepts $\\mathcal{C} = \\{a_1, a_2, \\ldots, a_N\\}$ , the second challenge is how we can best leverage these attributes to build interpretable image classifiers. Recent advances of vision-language models such as CLIP bridge the gap between images and text, by pre-training models with large scale image-text pairs. Intuitively, converting from images to text is a discretization process that will unavoidably lose rich semantic information stored in an image.", + "bbox": [ + 496, + 733, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To better preserve information, we use a semantic projection that transforms a visual feature into an attribute", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3091", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ac43e802c7c5e152b759b209b27fcfd4a967c543c873967fac2c6e284e4dc87f.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 187, + 108, + 810, + 334 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/85c4349b51a989e82980283e1e8dba0cf300b0aac9f28acf03a708ecbd3f7d17.jpg", + "image_caption": [ + "(b)", + "Figure 2: The framework of our model. (a) Querying attributes from LLMs and finding a concise set of representative attributes; (b) An example using the attributes for interpretable visual recognition." + ], + "image_footnote": [], + "bbox": [ + 127, + 375, + 839, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "concept space. Given an image $I$ , we convert the D-dimensional image feature $\\mathbf{V} \\in \\mathbb{R}^{D}$ into an N-dimensional attribute concept vector $\\mathbf{A} \\in \\mathbb{R}^{N}$ :", + "bbox": [ + 75, + 527, + 468, + 574 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {V} = \\Theta_ {V} (I), \\mathbf {T} _ {i} = \\Theta_ {T} (a _ {i})\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 585, + 352, + 602 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} = \\cos (\\mathbf {V}, \\mathbf {T} _ {i}), i = 1, \\dots , N \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 604, + 468, + 621 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} = \\left(s _ {1}, \\dots , s _ {N}\\right) ^ {T}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 625, + 308, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\cos (\\cdot ,\\cdot)$ is the cosine similarity between two vectors, $s_i$ is the cosine similarity between two vectors. $\\Theta_V$ and $\\Theta_T$ are the visual and text encoder of a VLM. $\\mathbf{T}_i$ is the embedding of the $i$ -th attribute in the attribute concept pool, $i\\in \\{1,\\dots ,N\\}$ . A is the semantic vector of image $I$ .", + "bbox": [ + 76, + 655, + 468, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. The Hypothesis of Attribute Concept Space", + "text_level": 1, + "bbox": [ + 76, + 739, + 446, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Conceptually, our semantic projection resembles principal component analysis, where we aim to find a set of bases in the form of natural language, and by projecting the images into these bases we obtain a new attribute concept space where each dimension in the space corresponds to a visual attribute concept. However, the large bag of attribute concepts we obtained from large language models is not the optimal language basis. As of today, LLMs are models that noisily condense world knowledge from the web,", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and are not optimized for visual recognition or visual reasoning tasks. We hypothesize that there exist subsets of attributes that can still achieve high classification performance with a much smaller size. Intuitively, most attributes in the large attribute concept pool are irrelevant to classify a certain class. For example, attributes that describe dogs are less likely to be suitable attributes to recognize birds or cars. Practically, formatting a compact attribute set is also helpful for humans to interact with the model and understand its behavior better. A small number of attributes is much easier for diagnostic purposes and making decisions with these neural models, which is the ultimate goal of building interpretable models.", + "bbox": [ + 496, + 527, + 892, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.4. Task-Guided Attribute Concept Searching", + "text_level": 1, + "bbox": [ + 500, + 738, + 861, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finding an expressive set of language bases is nontrivial. The massive attributes from LLMs are noisy, and finding a few representative attributes for hundreds of classes in a task can be challenging and costly, even for human experts with domain knowledge. An exhaustive search is also impractical given the large text space.", + "bbox": [ + 496, + 763, + 890, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by dictionary learning and vector quantization techniques [43], we present a learning-to-search method that learns a dictionary to approximate an expressive sub", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3092", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "set of attributes given fixed $K$ . Specifically, we first define an embedding matrix $\\mathbf{E} \\in \\mathbb{R}^{K \\times D}$ , where $K$ is a $K$ -way categorical that equals the number of attributes, and $D$ is the dimensionality of embedding vectors $\\mathbf{V}$ and $\\mathbf{T}_i$ (i.e., the latent dimension of VLMs), where $\\mathbf{V}$ and $\\mathbf{T}_i$ is the image embedding and the $i$ -th attribute embedding shown in Eq.(1). Since our goal is to find $K$ attributes to be expressive, we propose a task-guided attribute concept searching method to optimize for a particular task. For visual recognition tasks, we use a classification head to project the dictionary into $K_C$ classes and guide the learning process with the categorical cross-entropy loss:", + "bbox": [ + 76, + 90, + 472, + 272 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c e} = - \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\sum_ {c = 1} ^ {K _ {C}} y _ {i, c} \\log \\left(p _ {i, c}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 284, + 468, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M$ is the number of images in a mini-batch, $y_{i,c}$ is the binary indicator of the $i$ -th image in the mini-batch belonging to class $c$ , and $p_{i,c}$ is the predicted probability of the $i$ -th image belonging to class $c$ .", + "bbox": [ + 76, + 335, + 468, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "But simply training with the guidance of the cross-entropy loss is suboptimal, as the embeddings $\\mathbf{E}$ are not in the same space of $\\mathbf{T}$ . Thus, we use the Mahalanobis distance as a constraint to encourage the embeddings to be optimized towards the latent space of vision-language models. Given a sampled probability distribution $\\mathbf{T}$ , the Mahalanobis distance of $\\mathbf{E}_j$ from $\\mathbf{T}$ is defined as", + "bbox": [ + 75, + 398, + 468, + 505 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {m a h} ^ {j} = \\sqrt {(\\mathbf {E} _ {j} - \\boldsymbol {\\mu}) \\mathbf {S} ^ {- 1} (\\mathbf {E} _ {j} - \\boldsymbol {\\mu})} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 517, + 468, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{\\mu} = (\\mu_{1},\\dots,\\mu_{D})$ is the mean vector and $\\mathbf{S}$ is the positive-definite covariance matrix of $\\mathbf{T}$ . Then the regularization term is defined as:", + "bbox": [ + 76, + 553, + 468, + 599 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m a h} ^ {j} = \\frac {1}{K} \\sum_ {j = 1} ^ {k} \\mathcal {D} _ {m a h} ^ {j} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 609, + 468, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall, our model is optimized with a mixture of two losses:", + "bbox": [ + 76, + 662, + 468, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {l o s s}} = \\mathcal {L} _ {\\text {c e}} + \\lambda \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {\\text {m a h}} ^ {j}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 691, + 468, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After training, we have the embedding matrix $\\mathbf{E}$ which will be used for searching the attributes from the attribute concept pool $\\mathcal{C}$ . Note that for $\\mathbf{E} \\in \\mathbb{R}^{K*D}$ , each row of $\\mathbf{E}$ is a $D$ -dimensional vector. We denote the $j$ -th row of $\\mathbf{E}$ as $\\mathbf{E}_j$ . We use greedy search as follows:", + "bbox": [ + 76, + 741, + 468, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf{T}_{j}^{*} = \\operatorname *{arg max}_{i\\in \\{1,\\dots ,N\\}}\\cos (\\mathbf{T}_{i},\\mathbf{E}_{j}),\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 829, + 369, + 854 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns. t. \\mathbf {T} _ {j} ^ {*} \\neq \\mathbf {T} _ {k} ^ {*}, \\forall 1 \\leq k < j, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 859, + 468, + 877 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $j$ is from 1 to $K$ ,", + "bbox": [ + 192, + 880, + 352, + 895 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As $j$ iterates from 1 to $K$ , we can find $K$ attribute embeddings $\\mathbf{T}_j^*, j \\in \\{1, \\dots, K\\}$ , which corresponds to $K$ expressive attribute concepts and are the condensed features containing the necessary knowledge for the task. With the selected attributes, we can calculate the semantic vector of each image as in Eq. (1), where each dimension of the vector is a similarity score between the image and an attribute. We evaluate the performance of these semantic vectors with linear probes, and the obtained linear model is used for inference and analysis.", + "bbox": [ + 500, + 90, + 890, + 242 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Experiments", + "text_level": 1, + "bbox": [ + 500, + 256, + 630, + 273 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 280, + 689, + 297 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Datasets We conduct our experiments on 8 different image classification datasets, including: CUB [44], CIFAR-10 and CIFAR-100 [24], Food-101 [4], Flower [31], Oxford-pets [33], Stanford-cars [23], Imagenet [9]. For Imagenet, it is not trivial to analyze all 1000 diverse classes. So we narrow the scope to 397 animal classes, with 509,230/19,850 samples for train/test. We denote this subset as Imagenet-Animals. For other datasets, most of them include images within a specific domain (CUB, Flower, Food, Oxford-pets, Stanford-cars), while CIFAR-10 and CIFAR-100 contain broader classes that lie across domains.", + "bbox": [ + 498, + 303, + 890, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Implementation Details Our method involves two stages of training. The first stage consists of task-guided learning of a dictionary $\\mathbf{E}$ to approximate CLIP text embeddings and using this dictionary to find $K$ attributes for visual recognition. For the Mahalanobis distance, the parameter $\\lambda$ is tuned with a grid search in $\\{1, 0.1, 0.01, 0.001, 0\\}$ . The second stage is one-layer linear probing to classify semantic vectors. The batchsize is set to 4,096 for all datasets except 32,768 on Imagenet-Animals for faster converging. We set the number of epochs to 5,000 epochs with early stopping. The learning rate is set to 0.01 in all experiments with an Adam optimizer [20]. Unless specified, we use GPT-3 and CLIP ViT-B/32 for all performance comparison.", + "bbox": [ + 498, + 489, + 890, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Baselines We compare with state-of-the-art works that leverage attributes either from human annotations or from LLMs. For a fair comparison, we use linear probes to evaluate all methods: (1) CompDL [56] builds semantic vectors using CLIP scores between human-designed attributes and images. (2) LaBO [52] is a recent work that builds semantic vectors with a large set of attributes from LLMs. (3) Human [44, 22]. Attribute labels for each image are annotated by humans. We compare with two versions: binary labels for each attribute, and calibrated labels with confidence scores given by annotators.", + "bbox": [ + 498, + 703, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To validate the effectiveness of learning-to-search, we explore other baselines: (1) K-means. Perform K-means", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3093", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/b6c1821c8e3d6648764beab22569ff1a36bf29a7f14bdc81630eef31b52309f4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsCUBCIFAR-10CIFAR-100Flower
K32200400810206410020032102204
LaBo-60.9362.61-78.1184.84-75.1076.94-80.9886.76
Ours60.2763.8864.0577.4780.0987.9973.3175.1277.2980.8887.2689.02
DatasetsFoodOxford_PetsStanfordCarsImagenet_Animals
K6410120216377464196392128397794
LaBo-79.9581.33-76.9184.33-72.3374.39-74.8875.49
Ours78.4180.2281.8576.2983.1585.9172.0774.5775.5674.4875.6975.83
", + "bbox": [ + 99, + 88, + 874, + 256 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0d51d6add56ba8671251b624eef2ea1131bacd22fc7b50f05c64cff23169c231.jpg", + "table_caption": [ + "Table 1: Comparison with state-of-the-art. LaBo is designed to use at least as many attributes as classes. We use “-” to denote non-applicability." + ], + "table_footnote": [], + "table_body": "
K (# of attributes)81632312
Human Binary [44]4.027.3110.1147.38
Human Calibration [22]3.757.159.7843.37
CompDL [56]12.6426.4128.6952.60
Ours31.6748.5560.2765.17
", + "bbox": [ + 78, + 320, + 468, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "clustering on CLIP attribute embeddings, then find $K$ attributes with nearest distance to each clustering center. Intuitively this can be a strong baseline, as $K$ attributes close to each center can be distinctive. (2) Uniform Sampling from the large attribute pool. (3) SVD. After obtaining the attribute embeddings $\\mathbf{T}$ , we run SVD decomposition of $\\mathbf{T}$ to get the top $K$ vectors and find attributes with the largest similarity with the $K$ important vectors. (4) Similarity. We calculate the average score of each attribute across all images and then find the $K$ attributes with the largest average scores. (5) Img Features. Black-box linear probing on latent image features with two linear layers and an intermediate dimension $K$ as a reference.", + "bbox": [ + 75, + 452, + 472, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Main Results", + "text_level": 1, + "bbox": [ + 76, + 662, + 217, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison with previous work We first compare our method with LaBo [52]. It is designed to use $M_{c}$ concepts per class with default number of 50, which corresponds to 10,000 attributes for CUB. For fair-comparison, we set $M_{c}$ as 1 and 2 in the experiments. As shown in Table 1, our method outperforms LaBo with the same number of attributes on both the full and few-shot setting. Furthermore, our method can achieve similar accuracy with only a smaller number of attributes (e.g., 32 attributes for CUB). These results suggest that our learned attributes are discriminative enough to classify the images, despite given much fewer attributes.", + "bbox": [ + 75, + 686, + 468, + 867 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We then further compare with human annotations from CUB. For $K < 312$ , we select attributes based on their", + "bbox": [ + 75, + 869, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8fa097bb07ae87b8730115ec4af4fec5b0f13685698b69d15d5b5e9f9ce646d6.jpg", + "image_caption": [ + "Figure 3: Performance comparison with random or similar words on CUB." + ], + "image_footnote": [], + "bbox": [ + 504, + 321, + 689, + 436 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2a388d00423951ce88c7fb94d0eabe8ba7f0a1bbd19e5229422d30b43147baf6.jpg", + "table_caption": [ + "Table 2: Comparison with human annotations on CUB." + ], + "table_footnote": [], + "table_body": "
Examples
Rboy champagne\nallied whose acrobat\neight centered lobby heads
Sred,gray,snow wings\norange wings\nlime,navy wings
Gsloping forehead\ndistinctive white throat\nbright red head and breast
", + "bbox": [ + 705, + 325, + 893, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 3: Examples from Random (R), Silimlar (S), GPT-3 (G) attributes", + "bbox": [ + 702, + 444, + 892, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "accumulated confidence score for all samples. As shown in Table 2, human annotated attributes are more noisy than CLIP similarities. With the same attributes, CLIP scores from CompDL build more expressive features. Furthermore, our LLM-suggested attributes significantly outperform human designs, e.g. by using 16 attributes we achieve similar performance as 312 attributes defined by humans.", + "bbox": [ + 496, + 522, + 890, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Large-scale attributes behave like random words We present our finding that LLM-generated attributes in a large quantity behave like random words. Specifically, we compare our method of using GPT-3 attributes with random or similar words. Here, we constructed random words by randomly choosing 1-5 words from the entire English vocabulary, and semantically similar words by combining 1-3 random colors with the noun \"wings\" as suffix. As shown in Figure 3, when $K = 512$ , random words perform as well as GPT-3 attributes in terms of classification accuracy. Even reducing $K$ from 512 to 256 does not significantly hurt its performance. But when $K$ is small (e.g., 64), the performance of random words drops dramatically. We conjecture that it is because text embeddings randomly drawn from CLIP are nearly orthogonal bases [45]. Given an image feature $\\in \\mathbb{R}^D$ , projection with a set of $K = D$ orthogonal bases can perfectly preserve its information. We further", + "bbox": [ + 496, + 643, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3094", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fe412a41bc515202f88dd7bb590eef00713b2f97f0242f99b8f921b1af8ec658.jpg", + "image_caption": [ + "(a) CUB" + ], + "image_footnote": [], + "bbox": [ + 81, + 97, + 277, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6ad23405e17905e449fbf11b5c675e834625759e29a37f55d3398b1876573a6c.jpg", + "image_caption": [ + "(b) CIFAR10" + ], + "image_footnote": [], + "bbox": [ + 292, + 98, + 480, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/264151bdc9862fba23eafb5a2eff21b65895a4226cae5945f727bc5a33b11eaa.jpg", + "image_caption": [ + "(c) CIFAR-100" + ], + "image_footnote": [], + "bbox": [ + 488, + 97, + 681, + 202 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/597ed152f2527c7746a8cfdcbf5f32cc899e3c510d554ed6f1995a870325fa12.jpg", + "image_caption": [ + "(d) Flower" + ], + "image_footnote": [], + "bbox": [ + 694, + 97, + 888, + 202 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9ba7b916a13745d677105e16138ff43081eb30ed8b65203084fd6b401402d880.jpg", + "image_caption": [ + "(e) Food" + ], + "image_footnote": [], + "bbox": [ + 89, + 233, + 284, + 339 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f5a025df1c61c1c4a064c9af410899bd68b21e5070a668f615be931215cc368c.jpg", + "image_caption": [ + "(f) Oxford_pets" + ], + "image_footnote": [], + "bbox": [ + 290, + 233, + 483, + 339 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f689137bc6edc6bcba9b58ee9234988c780b72303457a3ea8664ed0e48df253b.jpg", + "image_caption": [ + "(g) StanfordCars", + "Figure 4: Overall Performance on all datasets. X-axis: number of attributes, Y-axis: Accuracy $(\\%)$ , “(f)” means “full”, i.e., all attributes in the pool are used. Uniform refers to uniform sampling." + ], + "image_footnote": [], + "bbox": [ + 488, + 233, + 679, + 339 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cb8746e5d59efaefc70bb897c85f180abec40a2519e73ae51e513dc190b02f11.jpg", + "image_caption": [ + "(h) Imagenet_Animals" + ], + "image_footnote": [], + "bbox": [ + 686, + 233, + 879, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "explore how similar words (e.g., red wings, yellow wings) behave. Embeddings of similar words in a trained language model are not orthogonal bases hence the projection will lose information when $K$ is large (e.g., intuitively it is hard to classify 200 bird species using only the color combination of wings). But as $K$ gets smaller, since those similar words have close semantic meanings, they start to outperform random words. Overall, these findings motivate us to find a concise set of meaningful attributes while maintaining competitive performance.", + "bbox": [ + 75, + 431, + 472, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Number of attributes and selection methods Finally, we study performance change under different number of attributes in Figure 4. First, our method is competitive with image features when $K$ is large. Reducing number of attributes $K$ to the number of classes $C$ (e.g., 512 to 128 for CUB) does not significantly hurt performance, even for baseline methods. This validates our hypothesis that there is plenty of redundant information in the semantic space when the number of attributes is large (as used in LaBO [52]). It is possible to find a subset of expressive attributes for visual recognition. Second, we also consistently outperform other methods such as K-means clustering and uniform sampling, demonstrating the effectiveness of our task-guided searching method. Third, a heuristic design such as K-means performs similar as uniform selection. Note that though there is a performance gap between image features and using attributes, the gap can be minimized by using a stronger VLM, as the classification accuracy of attributes relies on the accurate estimation of the correlation between images and attributes (see more results in appendix D).", + "bbox": [ + 75, + 598, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/467452fb764c2881ff03caf1fb8264daf1175c5eb81d00982be9f90f50bc075a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsCUBCIFAR-100
K8163281632
GPT-331.6748.5560.2734.7752.2466.30
GPT-3-Imagenet30.8149.2960.4133.8051.0165.61
", + "bbox": [ + 501, + 429, + 893, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4: Ablation study w.r.t. different concept pools.", + "bbox": [ + 517, + 508, + 870, + 525 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 551, + 653, + 569 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Robustness to the attribute pool First, we aim to explore the effects of different initialized attribute concept pools generated by LLMs. On CUB and CIFAR-100, we compare two attribute pools, attributes generated from classes in each dataset, and attributes generated from the full set of ImageNet classes. As shown in Table 4, even with the large and noisy attributes from ImageNet, our method can still efficiently find a small number of representative attributes for a task, and obtains competitive classification performance.", + "bbox": [ + 496, + 575, + 890, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of learning-to-search Then, we discuss possible choices for selection out of the large attribute pool. Results are shown in Table 5 with the following observations: heuristic methods such as K-means and SVD are not optimal choices for identifying the most distinctive attributes. In fact, they are sometimes less effective than uniform sampling. This is likely because we need to identify the most distinguishing attributes for visual recognition, rather than the most diverse ones based on text embeddings. Overall, our method significantly outperforms other baseline selection methods, showing its efficacy.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3095", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a826748065530bd1bfb55babaa3471daa9d73754568fb309a4f3a4da614779ee.jpg", + "image_caption": [ + "are classified as Least Auklet because:" + ], + "image_footnote": [ + "overall yellowish coloration", + "- dark gray and white mottled feathers" + ], + "bbox": [ + 78, + 97, + 212, + 178 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bbdcdd38da6327f3ddb38a9f908dae72c4f163618af759518ffac00c6686112d.jpg", + "image_caption": [], + "image_footnote": [ + "- iridescent black body with blue and purple highlights", + "large, round eyes with an orange ring around them", + "- medium-sized sea bird with a white head and black cap", + "- bright yellow throat, breast, and flanks with black bars" + ], + "bbox": [ + 375, + 109, + 462, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/20d9f86a1f5cbd04c6d74999259b5ade9a23996bb554d33f14572064db37edc0.jpg", + "image_caption": [ + "Overall yellowish coloration" + ], + "image_footnote": [], + "bbox": [ + 78, + 183, + 215, + 263 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/09adffb4573c105878120c2af64efc0a0d3e52909ac35f637ac742c99eb54bfc.jpg", + "image_caption": [ + "(a) Least Auklet" + ], + "image_footnote": [], + "bbox": [ + 218, + 202, + 364, + 262 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b69f69bd3541a64981d41e3538f7c3ab6289b94b2baa5766794ff0ad52e5b78c.jpg", + "image_caption": [ + "Least Auklet (Correct)", + "Figure 5: Examples on interpretability and interactivity. (1) The upper half of each figure shows important attributes for two classes of birds. We choose 6 out of 32 attributes with highest importance scores, which are computed by multiplication between clip scores and weights in the linear probe, defined in Eq. (7). (2) The lower half of each figure demonstrates the intervention on the semantic vector (i.e., CLIP scores) to correct the prediction, we use $\\delta = 0.03$ for all interventions on clip scores as an empirical value. The array of 6 scores are of the same order as the attributes." + ], + "image_footnote": [], + "bbox": [ + 383, + 179, + 459, + 262 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bf6aaec7f318ba1b37c48285074d4687fe8797e713fd74fc70c1a9d9102c6e04.jpg", + "image_caption": [ + "are classified as yellow billed cuckoo because:" + ], + "image_footnote": [ + "gray and white streaked head, back, and chest", + "dark slate gray crown, back and", + "white throat and yellowish belly", + "pinkish red breast patch with white edges", + "white neck with a black collar and", + "chestnut red head and breast", + "- distinctive large white wing patches edged", + "in bold black stripes", + "brownish head with yellow supercilium" + ], + "bbox": [ + 468, + 97, + 604, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c243adc9dc2318ecd6b85ceaecd9b0ab3fee17b4ae8dd93604af1621f81ad9af.jpg", + "image_caption": [ + "White neck with a black collar and", + "chestnut red head and breast", + "[0.2782,0.2810,0.2334,0.2318,0.2242,0.2405] $\\Rightarrow$", + "Intervention", + "[ [0.2782, 0.2810, 0.2334, 0.2618, 0.2242, 0.2405] \\Rightarrow ]", + "(b) Yellow Billed Cuckoo" + ], + "image_footnote": [ + "(eyebrow) and white throat" + ], + "bbox": [ + 468, + 179, + 604, + 262 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a44b46ab4083441b22380cb1d15eee4e27667ea70c53f6127a8bb849133b80a8.jpg", + "image_caption": [ + "14.9", + "A", + "", + "117", + "-10.03", + "3", + "Mangrove cuckoo (Wrong)" + ], + "image_footnote": [], + "bbox": [ + 764, + 189, + 831, + 223 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa974fd77d0288a463394d90f636fde05b2d8da45332d90bc63802f3ab0fc6ab.jpg", + "image_caption": [ + "yellow billed cuckoo (Correct)" + ], + "image_footnote": [], + "bbox": [ + 764, + 224, + 831, + 260 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/53c04db1ac88bd2f6cb0cc3a8901edb9d1f902043e6679fb150c003553eba721.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsCUBCIFAR-100
K8163281632
K-means16.8321.0232.7625.3945.2664.41
Uniform7.0225.9840.5828.0747.1464.34
SVD6.5220.0235.8329.0650.0064.99
Similarity4.739.7218.0026.7545.6162.79
Ours31.6748.5560.2734.7752.2466.30
", + "bbox": [ + 78, + 404, + 468, + 522 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of regularization We compare the Mahalanobis distance (MAH) with two variations: (1) COS: For each vector $\\mathbf{E}_j$ and $\\mathbf{T}_i$ (of the $i$ -th attribute) in the concept pool, we computed averaged cosine distance as follows:", + "bbox": [ + 75, + 590, + 468, + 652 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c o s} = \\frac {1}{K ^ {2}} \\sum_ {j = 1} ^ {K} \\sum_ {i = 1} ^ {K} \\frac {\\mathbf {T} _ {i} ^ {\\top} \\mathbf {E} _ {j}}{| | \\mathbf {T} _ {i} | | | | \\mathbf {E} _ {j} | |}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 676, + 379, + 719 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(2) $CE$ : Learning with Eq. (2) only. Results are in Table 6. Overall, Mahalanobis distance is an effective constraint to encourage the dictionary $E$ to be close to the distribution of CLIP embeddings.", + "bbox": [ + 75, + 729, + 468, + 791 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.4. Analysis of Interpretability and Interactivity", + "text_level": 1, + "bbox": [ + 76, + 801, + 454, + 818 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform analysis and visualizations to show that:", + "bbox": [ + 75, + 825, + 424, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(1) Our learned attributes provide interpretability. As shown in Figure 5, the upper half presents the images in a class $c$ and high relevant attributes to recognize them. Specifically, we denote $\\mathbf{W} \\in \\mathbb{R}^{K_C * K}$ as the weight of the", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e8cb5f115d58cfa40817275fb0528db6434217c6787217b7bdf36200e2428f82.jpg", + "table_caption": [ + "Table 5: Ablation study w.r.t. different attribute selection strategies." + ], + "table_footnote": [], + "table_body": "
DatasetCUB
K8163264
MAH30.7647.8760.2764.25
COS28.9647.3558.2763.25
CE31.6748.5555.8860.73
DatasetCIFAR-100
K8163264
MAH34.7752.2465.9173.31
COS31.9851.1565.0272.80
CE32.4550.8366.2973.25
", + "bbox": [ + 568, + 404, + 823, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6: Ablation study w.r.t. different regularization.", + "bbox": [ + 517, + 580, + 870, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "FC layer in linear probing, where $K_{C}, K$ are the number of classes and attributes. Then for each image $i$ and its semantic vector $\\mathbf{A} \\in \\mathbb{R}^{K}$ , we multiply the corresponding score vector of image $i$ with the corresponding row of the FC layer $\\mathbf{W}_{c}$ to compute Importance Score $\\mathbf{IS} \\in \\mathbb{R}^{K}$ :", + "bbox": [ + 496, + 621, + 890, + 698 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I S} = \\mathbf {W} _ {c} \\otimes \\mathbf {A} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 708, + 890, + 723 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\otimes$ means element-wise multiplication. Then we present attributes with the top absolute values of IS averaged over all samples in a class from the test set, with blue/orange bars indicating the positive/negative importance. Higher absolute values denote greater significance. Since all CLIP scores are positive [16], the positivity or negativity of high IS signifies their relevance to the class.", + "bbox": [ + 496, + 734, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(2) Our concise set of attributes enables simple interactivity. As shown in the lower half of Figure 5, we can correct the model's wrong predictions during inference by changing only a single similarity score between an image", + "bbox": [ + 496, + 840, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3096", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/30ab7324d9b797f4e40184d89755342df4db6857406a402efcf77b6bd9db06ff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CUB· distinctive white throat\n· bright red head and breast\n· pinkish red breast patch with white edges\n· bright yellow, green and blue plumage\n· Red face with a black cap and bib\n· Short legs for perching on reeds\n· white and black spotted breast\n· sloping foreheadCIFAR10· antlers (in males)\n· pointed bow and stern\n· propellers or jet engines\n· moist slimy skin\n· long head with a mane and tail\n· landing gear\n· portholes along the hull\n· four wheels
CIFAR100· a seat for the rider\n· catkins (flowers) in spring\n· many windows in the façade\n· five pairs of walking legs\n· smooth oval shaped sepals\n· four-limbed primate\n· headboard and footboard\n· towers with conical roofsFlower· Shiny wax coating on the spathe\n· large, yellow or orange flower head\n· bright pink color\n· large, white petals with a yellow center\n· pink to purple colored petals with red lips\n· bright red and yellow petals\n· pink, white, or lavender flowers with five petals\n· deep purple or blue flowers
Food· elbow macaroni noodles\n· Shredded pork meat in the middle of the sandwich\n· large pieces of clams visible in the chowder\n· usually served in a warm wrap or burrito shell\n· sliced into thin wedges or cubes\n· thinly sliced raw fish\n· tender squid rings inside\n· a crisp, fried pastry dough exteriorOxford Pets· black and tan coloring\n· short coat of glossy black fur\n· Long legs and neck\n· Shade of red or wheaten color\n· large, round eyes\n· Pointed ears\n· white blaze on face and chest\n· greyish blue fur with silver tips
Imagenet Animals· male finches have a bright red breast\n· brownish-yellow fur\n· small, four-limbed canid\n· long, black, shiny body\n· the carapace is rough and bumpy\n· white spots on the crab's shell\n· English setters are bred in England\n· long, wire-haired coatStanford Cars· signature Lincoln split headlamps\n· large front grille with the signature BMW kidney shape\n· large size with a wheelbase of 149.4 inches\n· "4Runner" badge on the rear liftgate\n· signature SRT8 grille with crosshair pattern\n· Porsche logo on front grille and trunk lid\n· S6 badge on the trunk lid\n· unique HUMMER H2 logo on front grille
", + "bbox": [ + 78, + 88, + 890, + 452 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and the attribute that the CLIP model made a mistake on. This is a significant simplification compared with previous work [22] where they need to manipulate scores from a group of concepts for the CUB dataset. We present more user studies in appendix E.", + "bbox": [ + 75, + 505, + 470, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3.5. Visualization of Our Discovered Attributes", + "text_level": 1, + "bbox": [ + 76, + 590, + 441, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We show our learned descriptive attributes with $K = 8$ in Figure 6. Intuitively, we can observe these attributes are distinctive for each domain. Take birds recognition (CUB) as an example, the eight attributes covered most of the body parts of a bird (head, breast, legs, etc.). As we are condensing knowledge from hundreds of bird classes, each attribute broadly covers many categories. A bright red head and breast can be a noticeable visual attribute for many bird species, such as the Northern Cardinal and the Vermilion Flycatcher. Overall, explaining a domain with a few descriptive attributes is challenging, even for an expert with sufficient domain knowledge. But our model is able to automatically provide a level of knowledge to help humans understand how visual recognition works.", + "bbox": [ + 75, + 613, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We then present case studies on CIFAR-10 with 4 attributes and CLIP scores of 10 random images from each class in Figure 7. In general, each image is activated in an distinguishable way in the heat map. Some attributes can distinguish a few classes, for example, cat and dog have", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b8e7d25ac801a5fef5ea03e0fca45d515da4b6f9ea076ce89d132d6863e3494a.jpg", + "image_caption": [ + "Figure 6: A concise set of 8 descriptive attributes learned for each dataset with sampled images.", + "Figure 7: Case study on CIFAR-10. The numbers are CLIP similarity scores between each image and attributes." + ], + "image_footnote": [], + "bbox": [ + 501, + 503, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "higher activation on \"fur coat\" compared to automobile or truck. Thus \"fur coat\" may be an important feature to differentiate animals and vehicles.", + "bbox": [ + 498, + 708, + 890, + 752 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4. Related work", + "text_level": 1, + "bbox": [ + 500, + 768, + 635, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Interpretable Deep Learning Interpretability is a critical research problem for deep learning with black-box models [11, 34, 37, 38, 13, 2, 50]. Some works study model behavior and explore if deep models could encode concepts for understanding [19, 28, 49, 29]. For image classification, preliminary attempts aim to describe objects with attributes [12, 26, 25] or building concept bottleneck mod", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3097", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "els [22, 56, 55, 6]. These methods require in-depth human analysis and intensive labeling, which are impractical to scale to more classes and domains.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Recent works [30, 35, 52] tackle this problem by using GPT-3 as a knowledge base to query visual attributes or concepts. Specifically, [30, 35] generate descriptions with LLMs, and use them for knowledge-aware prompting for each class to improve zero-shot performance of CLIP [36]. For example, given the class name \"bee\", it will augment it with attributes such as \"A bee with black and yellow body\". Our work differs in that our goal is to learn representative attributes for visual recognition without using class names. LABO [52] extends the idea of concept bottleneck models by generating thousands of concepts from LLMs. Inspired by our finding that there is great redundancy in the large-scale attributes, we aim to learn a concise set of attributes that are initially generated from LLMs for each task, while maintaining the classification performance as possible. Concise attributes also enable stronger interpretability and interactivity, and can help humans to summarize critical knowledge for visual recognition in an automatic way.", + "bbox": [ + 75, + 136, + 472, + 409 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Foundation Models Recently, foundation models [3], which are pre-trained with a large amount of data and large model sizes, have revolutionized machine learning research and many fields. These models are shown to be adaptable to a wide range of downstream tasks for computer vision [15, 46, 58], natural language processing [10, 7, 57, 48] and cross-modal research [27, 42, 17, 14]. One direction is to train LLMs such as GPT3 [5] and ChatGPT with massive text to serve as a powerful knowledge base with high interactivity and beyond. Another direction is to build VLMs [36, 51, 54, 53, 1], which connect vision and language by pre-training with image-text pairs and learning a joint embedding space for both. In this work, we use LLMs as a knowledge base for querying visual related knowledge, and use VLMs to bridge vision and text, presenting a new paradigm for interpretable visual recognition in the era of foundation models.", + "bbox": [ + 75, + 425, + 472, + 681 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 694, + 191, + 709 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "There are many interesting topics to explore with our new paradigm. First, our framework is a plug-and-play model that can be readily applied to many other vision tasks, by simply changing the task-guided learning objective to a particular task, e.g., classification losses for object detection, video understanding, and 3D classification. Furthermore, a concise set of descriptive attributes enables interactivity for vision models and empowers human-machine cooperation in a user-friendly way through natural language interfaces. Lastly, we show the potential of summarizing knowledge for challenging vision tasks in the new era of LLMs, which could have broad impact for various domains.", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 90, + 619, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we propose a new paradigm for visual recognition that leverages a concise set of descriptive attributes. Motivated by our insightful finding that significant redundancy exists in massive LLMs-generated attributes, we design a simple yet effective searching method guided by image-level labels, to identify an informative subset. Our new paradigm is validated across 8 datasets to achieve strong classification accuracy with multiple benefits and broad impacts, including efficiency, interpretability, human interactivity, and knowledge summarization.", + "bbox": [ + 496, + 114, + 893, + 267 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 281, + 658, + 297 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We would like to sincerely thank the anonymous reviewers and chairs for their careful review of our work, with helpful and constructive suggestions to improve the paper.", + "bbox": [ + 496, + 306, + 893, + 353 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 366, + 596, + 381 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.144, + 0.131, + 0.828, + 0.154 + ], + "angle": 0, + "content": "Learning Concise and Descriptive Attributes for Visual Recognition" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.179, + 0.765, + 0.217 + ], + "angle": 0, + "content": "An Yan\\*, Yu Wang\\*, Yiwu Zhong\\*, Chengyu Dong, Zexue He, Yujie Lu, William Yang Wang, Jingbo Shang, Julian McAuley" + }, + { + "type": "text", + "bbox": [ + 0.198, + 0.217, + 0.776, + 0.235 + ], + "angle": 0, + "content": "\\(\\diamond\\)UC San Diego, \\(\\clubsuit\\)University of Wisconsin-Madison, \\(\\clubsuit\\)UC Santa Barbara" + }, + { + "type": "text", + "bbox": [ + 0.269, + 0.237, + 0.701, + 0.253 + ], + "angle": 0, + "content": "{ayan, yuw164, cdong, zehe, jshang, jmcauley}@ucsd.edu" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.255, + 0.697, + 0.271 + ], + "angle": 0, + "content": "{yujielu,william}@cs.ucsb.edu，yzhong52@wisc.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.32, + 0.314, + 0.336 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.474, + 0.685 + ], + "angle": 0, + "content": "Recent advances in foundation models present new opportunities for interpretable visual recognition – one can first query Large Language Models (LLMs) to obtain a set of attributes that describe each class, then apply vision-language models to classify images via these attributes. Pioneering work shows that querying thousands of attributes can achieve performance competitive with image features. However, our further investigation on 8 datasets reveals that LLM-generated attributes in a large quantity perform almost the same as random words. This surprising finding suggests that significant noise may be present in these attributes. We hypothesize that there exist subsets of attributes that can maintain the classification performance with much smaller sizes, and propose a novel learning-to-search method to discover those concise sets of attributes. As a result, on the CUB dataset, our method achieves performance close to that of massive LLM-generated attributes (e.g., 10k attributes for CUB), yet using only 32 attributes in total to distinguish 200 bird species. Furthermore, our new paradigm demonstrates several additional benefits: higher interpretability and interactivity for humans, and the ability to summarize knowledge for a recognition task." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.702, + 0.21, + 0.717 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.727, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Explaining black-box neural models is a critical research problem. For visual recognition, one line of research tries to classify objects with descriptions or attributes [12, 8, 39, 18, 22], which provide additional information beyond visual cues such as activation maps [41, 40]. However, they require in-depth human analysis and intensive annotation to obtain key attributes for a particular recognition task. Such a paradigm is costly and thus impractical to scale up when the number of classes and domains grows." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.864, + 0.469, + 0.879 + ], + "angle": 0, + "content": "The recent advance of foundation models creates new" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.305, + 0.891, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.427, + 0.893, + 0.457 + ], + "angle": 0, + "content": "Figure 1: Our proposed paradigm for visual recognition via learning a concise set of descriptive attributes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.893, + 0.809 + ], + "angle": 0, + "content": "opportunities for building interpretable visual recognition models, as demonstrated by the powerful capabilities of models such as GPT-3 and ChatGPT in encoding world knowledge [5, 32, 21]. One can query useful visual attributes from LLMs and classify images via these attributes by converting visual features from vision-language models (VLMs) (e.g., CLIP [36]) into attribute scores [56]. One recent work [52] shows that a large set of attributes from LLMs (e.g., 50 attributes per class) can achieve comparable performance to image features in a linear probing setting. However, two key observations motivate us to re-think this formulation: (1) A large number of attributes dramatically hurts the interpretability of a model. It is unrealistic to manually check thousands of attributes to fully understand model decisions. (2) We surprisingly find that when the number of attributes is large enough (e.g., the dimension of image features), random words drawn from the entire vocabulary can perform equally well as LLM-generated attributes. Moreover, reducing the number of random words by \\(25\\%\\) can still attain competitive performance. This indicates that redundant and noisy information exists in the massive LLM-generated attributes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.901 + ], + "angle": 0, + "content": "With our findings, we ask the research question: Can we learn a concise set of representative visual attributes in the form of natural language to explain how visual recognition works? For example, can we find a few representative attributes to distinguish 200 bird species? This is a nontrivial problem. Even for humans, it is not easy to summa" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.22, + 0.9 + ], + "angle": 0, + "content": "* equal contributions." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3090" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "rize what are the representative visual attributes given many visual classes. To tackle this challenge, we propose a novel learning-to-search method, which uses image-level labels to guide the searching of discriminative attributes. Specifically, we train a learnable dictionary to approximate the embedding space of VLMs, and then find descriptive attributes in the latent text space via nearest neighbor search." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.471, + 0.485 + ], + "angle": 0, + "content": "In summary, we propose a new paradigm for visual recognition (Figure 1), which seeks to learn a concise set of visual attributes in the form of natural language. Once learned, there are several benefits to our new paradigm: (1) Our discovered attributes are highly descriptive. On 8 visual recognition datasets, our model classifies images via these attributes and achieves comparable classification performance as image features, even if the number of attributes is much smaller than the dimension of image features. (2) The condensed sets of attributes enable strong interpretability for the model decision process through a few human-friendly text descriptions. (3) Additionally, our framework presents a natural language interface for humans to interact with. One can correct a wrong prediction during model inference, by perturbing the values of attribute scores where it made mistakes. (4) Lastly, these expressive attributes can be viewed as a concise form of knowledge to summarize useful features for a visual recognition task, without costly human effort." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.486, + 0.368, + 0.5 + ], + "angle": 0, + "content": "Overall, our contributions are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.504, + 0.469, + 0.549 + ], + "angle": 0, + "content": "- Leveraging recent advances in foundation models, we propose a new paradigm for visual recognition by learning a concise set of attribute descriptions." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.553, + 0.469, + 0.599 + ], + "angle": 0, + "content": "- To find these attributes, we propose a novel learning-to-search method which prunes the large attribute pool from large language models to a descriptive subset." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.602, + 0.469, + 0.647 + ], + "angle": 0, + "content": "- We conduct extensive experiments across 8 visual recognition datasets to validate our recognition effectiveness and efficiency with additional benefits." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.504, + 0.469, + 0.647 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.664, + 0.212, + 0.681 + ], + "angle": 0, + "content": "2. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.47, + 0.9 + ], + "angle": 0, + "content": "In this section, we introduce our key components for a new paradigm of visual recognition. It mainly consists of three modules: First, in Section 2.1, given an image domain, we query large language models to obtain a large set of visual attributes for the categories of a task. Second, we use a semantic transformation (Section 2.2) to project the image features into attribute features via a vision-language model, where each dimension in the new space corresponds to an attribute concept, and a higher value represents higher correlation between the image and the attribute. Finally, given the large space of attributes, we propose a novel learning-to-search method (Section 2.4) to efficiently prune the attributes into a much smaller subset to obtain a concise model for classification." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.855, + 0.108 + ], + "angle": 0, + "content": "2.1. Generating Attribute Concepts via LLMs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.342 + ], + "angle": 0, + "content": "The first step of our framework is to obtain a set of appropriate attribute concepts. Given a dataset with different categories, (e.g., CUB with 200 bird classes), what are the distinctive visual attributes to recognize them? Manually labeling and designing these attribute concepts can be costly, and can not scale to large numbers of classes. Large Language Models (LLMs), such as GPT-3 [5] and ChatGPT, provide an alternative solution. We can view these language models as implicit knowledge bases with exceptional world knowledge on a variety of tasks and topics, which humans can easily interact with through natural language to query knowledge. To this end, prompt engineering, or the ability to ask good questions to language models, is still important. To effectively query knowledge from LLMs with regard to classifying images, we design two types of prompts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.892, + 0.404 + ], + "angle": 0, + "content": "Instance Prompting for Class-level Features. For each class \\( c \\) in a given task, our first design choice is to query class-level information from LLMs. We prompt a language model with the instance prompt:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Q: What are the useful visual features to distinguish \\( Y_{c} \\) in a photo?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.892, + 0.466 + ], + "angle": 0, + "content": "where \\( Y_{c} \\) corresponds to the name of class \\( c \\) in the form of natural language." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.572 + ], + "angle": 0, + "content": "Batch Prompting for Group-level Features. For certain datasets (e.g., CIFAR-100 and ImageNet), there is inherently a hierarchy that some categories belong to the same group. For example, in CIFAR-100, there is a superclass for every five categories. Hence, we propose batch prompting, where we ask the language model to reason about the distinctive visual features among a batch of categories:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.573, + 0.892, + 0.651 + ], + "angle": 0, + "content": "Q: Here are \\(N_{g}\\) kinds of \\(Y_{g}\\): \\(\\{Y_{c_1}, Y_{c_2}, \\ldots, Y_{c_M}\\}\\). What are the useful visual features to distinguish them in a photo? where \\(N_{g}\\) is the number of classes in a group \\(g\\), \\(Y_{g}\\) is the name of the group, \\(Y_{c_i}\\) corresponds to the name of each class \\(c_i\\) in the form of natural language." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.698 + ], + "angle": 0, + "content": "We present more details regarding our prompt design, robustness check of different prompts, and examples of the generated attributes in Appendix A." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.692, + 0.726 + ], + "angle": 0, + "content": "2.2. Semantic Projection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.87 + ], + "angle": 0, + "content": "After obtaining a pool consisting of \\(N\\) attribute concepts \\(\\mathcal{C} = \\{a_1, a_2, \\ldots, a_N\\}\\), the second challenge is how we can best leverage these attributes to build interpretable image classifiers. Recent advances of vision-language models such as CLIP bridge the gap between images and text, by pre-training models with large scale image-text pairs. Intuitively, converting from images to text is a discretization process that will unavoidably lose rich semantic information stored in an image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To better preserve information, we use a semantic projection that transforms a visual feature into an attribute" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3091" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.109, + 0.196, + 0.124 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.188, + 0.109, + 0.812, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.355, + 0.143, + 0.37 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.129, + 0.376, + 0.841, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.471, + 0.893, + 0.503 + ], + "angle": 0, + "content": "Figure 2: The framework of our model. (a) Querying attributes from LLMs and finding a concise set of representative attributes; (b) An example using the attributes for interpretable visual recognition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.47, + 0.575 + ], + "angle": 0, + "content": "concept space. Given an image \\(I\\), we convert the D-dimensional image feature \\(\\mathbf{V} \\in \\mathbb{R}^{D}\\) into an N-dimensional attribute concept vector \\(\\mathbf{A} \\in \\mathbb{R}^{N}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.587, + 0.354, + 0.603 + ], + "angle": 0, + "content": "\\[\n\\mathbf {V} = \\Theta_ {V} (I), \\mathbf {T} _ {i} = \\Theta_ {T} (a _ {i})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.606, + 0.469, + 0.622 + ], + "angle": 0, + "content": "\\[\ns _ {i} = \\cos (\\mathbf {V}, \\mathbf {T} _ {i}), i = 1, \\dots , N \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.625, + 0.31, + 0.644 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} = \\left(s _ {1}, \\dots , s _ {N}\\right) ^ {T}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.656, + 0.47, + 0.732 + ], + "angle": 0, + "content": "where \\(\\cos (\\cdot ,\\cdot)\\) is the cosine similarity between two vectors, \\(s_i\\) is the cosine similarity between two vectors. \\(\\Theta_V\\) and \\(\\Theta_T\\) are the visual and text encoder of a VLM. \\(\\mathbf{T}_i\\) is the embedding of the \\(i\\)-th attribute in the attribute concept pool, \\(i\\in \\{1,\\dots ,N\\}\\). A is the semantic vector of image \\(I\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.447, + 0.759 + ], + "angle": 0, + "content": "2.3. The Hypothesis of Attribute Concept Space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Conceptually, our semantic projection resembles principal component analysis, where we aim to find a set of bases in the form of natural language, and by projecting the images into these bases we obtain a new attribute concept space where each dimension in the space corresponds to a visual attribute concept. However, the large bag of attribute concepts we obtained from large language models is not the optimal language basis. As of today, LLMs are models that noisily condense world knowledge from the web," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.893, + 0.726 + ], + "angle": 0, + "content": "and are not optimized for visual recognition or visual reasoning tasks. We hypothesize that there exist subsets of attributes that can still achieve high classification performance with a much smaller size. Intuitively, most attributes in the large attribute concept pool are irrelevant to classify a certain class. For example, attributes that describe dogs are less likely to be suitable attributes to recognize birds or cars. Practically, formatting a compact attribute set is also helpful for humans to interact with the model and understand its behavior better. A small number of attributes is much easier for diagnostic purposes and making decisions with these neural models, which is the ultimate goal of building interpretable models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.862, + 0.756 + ], + "angle": 0, + "content": "2.4. Task-Guided Attribute Concept Searching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Finding an expressive set of language bases is nontrivial. The massive attributes from LLMs are noisy, and finding a few representative attributes for hundreds of classes in a task can be challenging and costly, even for human experts with domain knowledge. An exhaustive search is also impractical given the large text space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Inspired by dictionary learning and vector quantization techniques [43], we present a learning-to-search method that learns a dictionary to approximate an expressive sub" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3092" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "set of attributes given fixed \\(K\\). Specifically, we first define an embedding matrix \\(\\mathbf{E} \\in \\mathbb{R}^{K \\times D}\\), where \\(K\\) is a \\(K\\)-way categorical that equals the number of attributes, and \\(D\\) is the dimensionality of embedding vectors \\(\\mathbf{V}\\) and \\(\\mathbf{T}_i\\) (i.e., the latent dimension of VLMs), where \\(\\mathbf{V}\\) and \\(\\mathbf{T}_i\\) is the image embedding and the \\(i\\)-th attribute embedding shown in Eq.(1). Since our goal is to find \\(K\\) attributes to be expressive, we propose a task-guided attribute concept searching method to optimize for a particular task. For visual recognition tasks, we use a classification head to project the dictionary into \\(K_C\\) classes and guide the learning process with the categorical cross-entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.285, + 0.47, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c e} = - \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\sum_ {c = 1} ^ {K _ {C}} y _ {i, c} \\log \\left(p _ {i, c}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.47, + 0.398 + ], + "angle": 0, + "content": "where \\( M \\) is the number of images in a mini-batch, \\( y_{i,c} \\) is the binary indicator of the \\( i \\)-th image in the mini-batch belonging to class \\( c \\), and \\( p_{i,c} \\) is the predicted probability of the \\( i \\)-th image belonging to class \\( c \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.47, + 0.506 + ], + "angle": 0, + "content": "But simply training with the guidance of the cross-entropy loss is suboptimal, as the embeddings \\(\\mathbf{E}\\) are not in the same space of \\(\\mathbf{T}\\). Thus, we use the Mahalanobis distance as a constraint to encourage the embeddings to be optimized towards the latent space of vision-language models. Given a sampled probability distribution \\(\\mathbf{T}\\), the Mahalanobis distance of \\(\\mathbf{E}_j\\) from \\(\\mathbf{T}\\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.518, + 0.47, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {m a h} ^ {j} = \\sqrt {(\\mathbf {E} _ {j} - \\boldsymbol {\\mu}) \\mathbf {S} ^ {- 1} (\\mathbf {E} _ {j} - \\boldsymbol {\\mu})} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.469, + 0.6 + ], + "angle": 0, + "content": "where \\(\\pmb{\\mu} = (\\mu_{1},\\dots,\\mu_{D})\\) is the mean vector and \\(\\mathbf{S}\\) is the positive-definite covariance matrix of \\(\\mathbf{T}\\). Then the regularization term is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.61, + 0.47, + 0.652 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m a h} ^ {j} = \\frac {1}{K} \\sum_ {j = 1} ^ {k} \\mathcal {D} _ {m a h} ^ {j} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.664, + 0.469, + 0.692 + ], + "angle": 0, + "content": "Overall, our model is optimized with a mixture of two losses:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.692, + 0.47, + 0.735 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {l o s s}} = \\mathcal {L} _ {\\text {c e}} + \\lambda \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {\\text {m a h}} ^ {j}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.742, + 0.469, + 0.817 + ], + "angle": 0, + "content": "After training, we have the embedding matrix \\(\\mathbf{E}\\) which will be used for searching the attributes from the attribute concept pool \\(\\mathcal{C}\\). Note that for \\(\\mathbf{E} \\in \\mathbb{R}^{K*D}\\), each row of \\(\\mathbf{E}\\) is a \\(D\\)-dimensional vector. We denote the \\(j\\)-th row of \\(\\mathbf{E}\\) as \\(\\mathbf{E}_j\\). We use greedy search as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.83, + 0.37, + 0.856 + ], + "angle": 0, + "content": "\\[\n\\mathbf{T}_{j}^{*} = \\operatorname *{arg max}_{i\\in \\{1,\\dots ,N\\}}\\cos (\\mathbf{T}_{i},\\mathbf{E}_{j}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.861, + 0.469, + 0.878 + ], + "angle": 0, + "content": "\\[\ns. t. \\mathbf {T} _ {j} ^ {*} \\neq \\mathbf {T} _ {k} ^ {*}, \\forall 1 \\leq k < j, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.881, + 0.353, + 0.896 + ], + "angle": 0, + "content": "where \\(j\\) is from 1 to \\(K\\)," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "As \\( j \\) iterates from 1 to \\( K \\), we can find \\( K \\) attribute embeddings \\( \\mathbf{T}_j^*, j \\in \\{1, \\dots, K\\} \\), which corresponds to \\( K \\) expressive attribute concepts and are the condensed features containing the necessary knowledge for the task. With the selected attributes, we can calculate the semantic vector of each image as in Eq. (1), where each dimension of the vector is a similarity score between the image and an attribute. We evaluate the performance of these semantic vectors with linear probes, and the obtained linear model is used for inference and analysis." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.257, + 0.632, + 0.274 + ], + "angle": 0, + "content": "3. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.281, + 0.691, + 0.298 + ], + "angle": 0, + "content": "3.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.304, + 0.892, + 0.47 + ], + "angle": 0, + "content": "Datasets We conduct our experiments on 8 different image classification datasets, including: CUB [44], CIFAR-10 and CIFAR-100 [24], Food-101 [4], Flower [31], Oxford-pets [33], Stanford-cars [23], Imagenet [9]. For Imagenet, it is not trivial to analyze all 1000 diverse classes. So we narrow the scope to 397 animal classes, with 509,230/19,850 samples for train/test. We denote this subset as Imagenet-Animals. For other datasets, most of them include images within a specific domain (CUB, Flower, Food, Oxford-pets, Stanford-cars), while CIFAR-10 and CIFAR-100 contain broader classes that lie across domains." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.687 + ], + "angle": 0, + "content": "Implementation Details Our method involves two stages of training. The first stage consists of task-guided learning of a dictionary \\(\\mathbf{E}\\) to approximate CLIP text embeddings and using this dictionary to find \\(K\\) attributes for visual recognition. For the Mahalanobis distance, the parameter \\(\\lambda\\) is tuned with a grid search in \\(\\{1, 0.1, 0.01, 0.001, 0\\}\\). The second stage is one-layer linear probing to classify semantic vectors. The batchsize is set to 4,096 for all datasets except 32,768 on Imagenet-Animals for faster converging. We set the number of epochs to 5,000 epochs with early stopping. The learning rate is set to 0.01 in all experiments with an Adam optimizer [20]. Unless specified, we use GPT-3 and CLIP ViT-B/32 for all performance comparison." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.704, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Baselines We compare with state-of-the-art works that leverage attributes either from human annotations or from LLMs. For a fair comparison, we use linear probes to evaluate all methods: (1) CompDL [56] builds semantic vectors using CLIP scores between human-designed attributes and images. (2) LaBO [52] is a recent work that builds semantic vectors with a large set of attributes from LLMs. (3) Human [44, 22]. Attribute labels for each image are annotated by humans. We compare with two versions: binary labels for each attribute, and calibrated labels with confidence scores given by annotators." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To validate the effectiveness of learning-to-search, we explore other baselines: (1) K-means. Perform K-means" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3093" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.875, + 0.257 + ], + "angle": 0, + "content": "
DatasetsCUBCIFAR-10CIFAR-100Flower
K32200400810206410020032102204
LaBo-60.9362.61-78.1184.84-75.1076.94-80.9886.76
Ours60.2763.8864.0577.4780.0987.9973.3175.1277.2980.8887.2689.02
DatasetsFoodOxford_PetsStanfordCarsImagenet_Animals
K6410120216377464196392128397794
LaBo-79.9581.33-76.9184.33-72.3374.39-74.8875.49
Ours78.4180.2281.8576.2983.1585.9172.0774.5775.5674.4875.6975.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.266, + 0.895, + 0.299 + ], + "angle": 0, + "content": "Table 1: Comparison with state-of-the-art. LaBo is designed to use at least as many attributes as classes. We use “-” to denote non-applicability." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.321, + 0.47, + 0.41 + ], + "angle": 0, + "content": "
K (# of attributes)81632312
Human Binary [44]4.027.3110.1147.38
Human Calibration [22]3.757.159.7843.37
CompDL [56]12.6426.4128.6952.60
Ours31.6748.5560.2765.17
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.421, + 0.456, + 0.435 + ], + "angle": 0, + "content": "Table 2: Comparison with human annotations on CUB." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.473, + 0.651 + ], + "angle": 0, + "content": "clustering on CLIP attribute embeddings, then find \\( K \\) attributes with nearest distance to each clustering center. Intuitively this can be a strong baseline, as \\( K \\) attributes close to each center can be distinctive. (2) Uniform Sampling from the large attribute pool. (3) SVD. After obtaining the attribute embeddings \\( \\mathbf{T} \\), we run SVD decomposition of \\( \\mathbf{T} \\) to get the top \\( K \\) vectors and find attributes with the largest similarity with the \\( K \\) important vectors. (4) Similarity. We calculate the average score of each attribute across all images and then find the \\( K \\) attributes with the largest average scores. (5) Img Features. Black-box linear probing on latent image features with two linear layers and an intermediate dimension \\( K \\) as a reference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.218, + 0.679 + ], + "angle": 0, + "content": "3.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Comparison with previous work We first compare our method with LaBo [52]. It is designed to use \\( M_{c} \\) concepts per class with default number of 50, which corresponds to 10,000 attributes for CUB. For fair-comparison, we set \\( M_{c} \\) as 1 and 2 in the experiments. As shown in Table 1, our method outperforms LaBo with the same number of attributes on both the full and few-shot setting. Furthermore, our method can achieve similar accuracy with only a smaller number of attributes (e.g., 32 attributes for CUB). These results suggest that our learned attributes are discriminative enough to classify the images, despite given much fewer attributes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We then further compare with human annotations from CUB. For \\( K < 312 \\), we select attributes based on their" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.323, + 0.69, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.45, + 0.692, + 0.494 + ], + "angle": 0, + "content": "Figure 3: Performance comparison with random or similar words on CUB." + }, + { + "type": "table", + "bbox": [ + 0.706, + 0.326, + 0.895, + 0.436 + ], + "angle": 0, + "content": "
Examples
Rboy champagne\nallied whose acrobat\neight centered lobby heads
Sred,gray,snow wings\norange wings\nlime,navy wings
Gsloping forehead\ndistinctive white throat\nbright red head and breast
" + }, + { + "type": "table_caption", + "bbox": [ + 0.704, + 0.445, + 0.893, + 0.49 + ], + "angle": 0, + "content": "Table 3: Examples from Random (R), Silimlar (S), GPT-3 (G) attributes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.63 + ], + "angle": 0, + "content": "accumulated confidence score for all samples. As shown in Table 2, human annotated attributes are more noisy than CLIP similarities. With the same attributes, CLIP scores from CompDL build more expressive features. Furthermore, our LLM-suggested attributes significantly outperform human designs, e.g. by using 16 attributes we achieve similar performance as 312 attributes defined by humans." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Large-scale attributes behave like random words We present our finding that LLM-generated attributes in a large quantity behave like random words. Specifically, we compare our method of using GPT-3 attributes with random or similar words. Here, we constructed random words by randomly choosing 1-5 words from the entire English vocabulary, and semantically similar words by combining 1-3 random colors with the noun \"wings\" as suffix. As shown in Figure 3, when \\( K = 512 \\), random words perform as well as GPT-3 attributes in terms of classification accuracy. Even reducing \\( K \\) from 512 to 256 does not significantly hurt its performance. But when \\( K \\) is small (e.g., 64), the performance of random words drops dramatically. We conjecture that it is because text embeddings randomly drawn from CLIP are nearly orthogonal bases [45]. Given an image feature \\( \\in \\mathbb{R}^D \\), projection with a set of \\( K = D \\) orthogonal bases can perfectly preserve its information. We further" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "3094" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.098, + 0.278, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.154, + 0.21, + 0.203, + 0.222 + ], + "angle": 0, + "content": "(a) CUB" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.099, + 0.481, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.349, + 0.21, + 0.424, + 0.222 + ], + "angle": 0, + "content": "(b) CIFAR10" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.098, + 0.682, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.543, + 0.21, + 0.627, + 0.222 + ], + "angle": 0, + "content": "(c) CIFAR-100" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.098, + 0.89, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.763, + 0.21, + 0.824, + 0.222 + ], + "angle": 0, + "content": "(d) Flower" + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.234, + 0.285, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.165, + 0.346, + 0.213, + 0.358 + ], + "angle": 0, + "content": "(e) Food" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.234, + 0.484, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.346, + 0.429, + 0.358 + ], + "angle": 0, + "content": "(f) Oxford_pets" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.234, + 0.681, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.346, + 0.632, + 0.358 + ], + "angle": 0, + "content": "(g) StanfordCars" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.234, + 0.88, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.346, + 0.843, + 0.358 + ], + "angle": 0, + "content": "(h) Imagenet_Animals" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.375, + 0.893, + 0.406 + ], + "angle": 0, + "content": "Figure 4: Overall Performance on all datasets. X-axis: number of attributes, Y-axis: Accuracy \\((\\%)\\), “(f)” means “full”, i.e., all attributes in the pool are used. Uniform refers to uniform sampling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.473, + 0.584 + ], + "angle": 0, + "content": "explore how similar words (e.g., red wings, yellow wings) behave. Embeddings of similar words in a trained language model are not orthogonal bases hence the projection will lose information when \\( K \\) is large (e.g., intuitively it is hard to classify 200 bird species using only the color combination of wings). But as \\( K \\) gets smaller, since those similar words have close semantic meanings, they start to outperform random words. Overall, these findings motivate us to find a concise set of meaningful attributes while maintaining competitive performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Number of attributes and selection methods Finally, we study performance change under different number of attributes in Figure 4. First, our method is competitive with image features when \\( K \\) is large. Reducing number of attributes \\( K \\) to the number of classes \\( C \\) (e.g., 512 to 128 for CUB) does not significantly hurt performance, even for baseline methods. This validates our hypothesis that there is plenty of redundant information in the semantic space when the number of attributes is large (as used in LaBO [52]). It is possible to find a subset of expressive attributes for visual recognition. Second, we also consistently outperform other methods such as K-means clustering and uniform sampling, demonstrating the effectiveness of our task-guided searching method. Third, a heuristic design such as K-means performs similar as uniform selection. Note that though there is a performance gap between image features and using attributes, the gap can be minimized by using a stronger VLM, as the classification accuracy of attributes relies on the accurate estimation of the correlation between images and attributes (see more results in appendix D)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.43, + 0.895, + 0.501 + ], + "angle": 0, + "content": "
DatasetsCUBCIFAR-100
K8163281632
GPT-331.6748.5560.2734.7752.2466.30
GPT-3-Imagenet30.8149.2960.4133.8051.0165.61
" + }, + { + "type": "table_caption", + "bbox": [ + 0.519, + 0.51, + 0.872, + 0.526 + ], + "angle": 0, + "content": "Table 4: Ablation study w.r.t. different concept pools." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.553, + 0.655, + 0.57 + ], + "angle": 0, + "content": "3.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.713 + ], + "angle": 0, + "content": "Robustness to the attribute pool First, we aim to explore the effects of different initialized attribute concept pools generated by LLMs. On CUB and CIFAR-100, we compare two attribute pools, attributes generated from classes in each dataset, and attributes generated from the full set of ImageNet classes. As shown in Table 4, even with the large and noisy attributes from ImageNet, our method can still efficiently find a small number of representative attributes for a task, and obtains competitive classification performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of learning-to-search Then, we discuss possible choices for selection out of the large attribute pool. Results are shown in Table 5 with the following observations: heuristic methods such as K-means and SVD are not optimal choices for identifying the most distinctive attributes. In fact, they are sometimes less effective than uniform sampling. This is likely because we need to identify the most distinguishing attributes for visual recognition, rather than the most diverse ones based on text embeddings. Overall, our method significantly outperforms other baseline selection methods, showing its efficacy." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3095" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.098, + 0.214, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.217, + 0.098, + 0.381, + 0.108 + ], + "angle": 0, + "content": "are classified as Least Auklet because:" + }, + { + "type": "image_footnote", + "bbox": [ + 0.22, + 0.111, + 0.379, + 0.119 + ], + "angle": 0, + "content": "- iridescent black body with blue and purple highlights" + }, + { + "type": "image_footnote", + "bbox": [ + 0.221, + 0.122, + 0.306, + 0.13 + ], + "angle": 0, + "content": "overall yellowish coloration" + }, + { + "type": "image_footnote", + "bbox": [ + 0.221, + 0.132, + 0.334, + 0.14 + ], + "angle": 0, + "content": "- dark gray and white mottled feathers" + }, + { + "type": "image_footnote", + "bbox": [ + 0.221, + 0.142, + 0.373, + 0.151 + ], + "angle": 0, + "content": "large, round eyes with an orange ring around them" + }, + { + "type": "image_footnote", + "bbox": [ + 0.221, + 0.156, + 0.385, + 0.164 + ], + "angle": 0, + "content": "- medium-sized sea bird with a white head and black cap" + }, + { + "type": "image_footnote", + "bbox": [ + 0.221, + 0.167, + 0.382, + 0.175 + ], + "angle": 0, + "content": "- bright yellow throat, breast, and flanks with black bars" + }, + { + "type": "list", + "bbox": [ + 0.22, + 0.111, + 0.385, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.111, + 0.464, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.184, + 0.216, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.219, + 0.188, + 0.3, + 0.196 + ], + "angle": 0, + "content": "Overall yellowish coloration" + }, + { + "type": "image", + "bbox": [ + 0.22, + 0.203, + 0.366, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.277, + 0.319, + 0.288 + ], + "angle": 0, + "content": "(a) Least Auklet" + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.18, + 0.46, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.388, + 0.264, + 0.453, + 0.269 + ], + "angle": 0, + "content": "Least Auklet (Correct)" + }, + { + "type": "image", + "bbox": [ + 0.469, + 0.098, + 0.605, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.47, + 0.18, + 0.605, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.098, + 0.806, + 0.108 + ], + "angle": 0, + "content": "are classified as yellow billed cuckoo because:" + }, + { + "type": "image_footnote", + "bbox": [ + 0.61, + 0.111, + 0.747, + 0.118 + ], + "angle": 0, + "content": "gray and white streaked head, back, and chest" + }, + { + "type": "image_footnote", + "bbox": [ + 0.611, + 0.119, + 0.709, + 0.126 + ], + "angle": 0, + "content": "dark slate gray crown, back and" + }, + { + "type": "image_footnote", + "bbox": [ + 0.611, + 0.127, + 0.708, + 0.133 + ], + "angle": 0, + "content": "white throat and yellowish belly" + }, + { + "type": "image_footnote", + "bbox": [ + 0.612, + 0.134, + 0.735, + 0.14 + ], + "angle": 0, + "content": "pinkish red breast patch with white edges" + }, + { + "type": "image_footnote", + "bbox": [ + 0.612, + 0.141, + 0.712, + 0.148 + ], + "angle": 0, + "content": "white neck with a black collar and" + }, + { + "type": "image_footnote", + "bbox": [ + 0.612, + 0.149, + 0.702, + 0.155 + ], + "angle": 0, + "content": "chestnut red head and breast" + }, + { + "type": "image_footnote", + "bbox": [ + 0.612, + 0.156, + 0.737, + 0.162 + ], + "angle": 0, + "content": "- distinctive large white wing patches edged" + }, + { + "type": "image_footnote", + "bbox": [ + 0.612, + 0.163, + 0.673, + 0.169 + ], + "angle": 0, + "content": "in bold black stripes" + }, + { + "type": "image_footnote", + "bbox": [ + 0.613, + 0.17, + 0.726, + 0.176 + ], + "angle": 0, + "content": "brownish head with yellow supercilium" + }, + { + "type": "image_footnote", + "bbox": [ + 0.613, + 0.177, + 0.694, + 0.183 + ], + "angle": 0, + "content": "(eyebrow) and white throat" + }, + { + "type": "image_caption", + "bbox": [ + 0.613, + 0.184, + 0.738, + 0.19 + ], + "angle": 0, + "content": "White neck with a black collar and" + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.191, + 0.725, + 0.197 + ], + "angle": 0, + "content": "chestnut red head and breast" + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.2, + 0.752, + 0.207 + ], + "angle": 0, + "content": "[0.2782,0.2810,0.2334,0.2318,0.2242,0.2405] \\(\\Rightarrow\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.618, + 0.221, + 0.675, + 0.228 + ], + "angle": 0, + "content": "Intervention" + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.241, + 0.752, + 0.248 + ], + "angle": 0, + "content": "\\[ [0.2782, 0.2810, 0.2334, 0.2618, 0.2242, 0.2405] \\Rightarrow \\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.111, + 0.84, + 0.118 + ], + "angle": 0, + "content": "14.9" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.12, + 0.835, + 0.127 + ], + "angle": 0, + "content": "A" + }, + { + "type": "image_caption", + "bbox": [ + 0.762, + 0.134, + 0.79, + 0.141 + ], + "angle": 0, + "content": "" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.142, + 0.829, + 0.149 + ], + "angle": 0, + "content": "117" + }, + { + "type": "image_caption", + "bbox": [ + 0.762, + 0.156, + 0.79, + 0.163 + ], + "angle": 0, + "content": "-10.03" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.164, + 0.824, + 0.172 + ], + "angle": 0, + "content": "3" + }, + { + "type": "image_caption", + "bbox": [ + 0.762, + 0.181, + 0.839, + 0.188 + ], + "angle": 0, + "content": "Mangrove cuckoo (Wrong)" + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.19, + 0.832, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.225, + 0.832, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.758, + 0.262, + 0.842, + 0.268 + ], + "angle": 0, + "content": "yellow billed cuckoo (Correct)" + }, + { + "type": "image_caption", + "bbox": [ + 0.592, + 0.276, + 0.731, + 0.288 + ], + "angle": 0, + "content": "(b) Yellow Billed Cuckoo" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.305, + 0.894, + 0.381 + ], + "angle": 0, + "content": "Figure 5: Examples on interpretability and interactivity. (1) The upper half of each figure shows important attributes for two classes of birds. We choose 6 out of 32 attributes with highest importance scores, which are computed by multiplication between clip scores and weights in the linear probe, defined in Eq. (7). (2) The lower half of each figure demonstrates the intervention on the semantic vector (i.e., CLIP scores) to correct the prediction, we use \\(\\delta = 0.03\\) for all interventions on clip scores as an empirical value. The array of 6 scores are of the same order as the attributes." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.405, + 0.47, + 0.523 + ], + "angle": 0, + "content": "
DatasetsCUBCIFAR-100
K8163281632
K-means16.8321.0232.7625.3945.2664.41
Uniform7.0225.9840.5828.0747.1464.34
SVD6.5220.0235.8329.0650.0064.99
Similarity4.739.7218.0026.7545.6162.79
Ours31.6748.5560.2734.7752.2466.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.565 + ], + "angle": 0, + "content": "Table 5: Ablation study w.r.t. different attribute selection strategies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.654 + ], + "angle": 0, + "content": "Effectiveness of regularization We compare the Mahalanobis distance (MAH) with two variations: (1) COS: For each vector \\(\\mathbf{E}_j\\) and \\(\\mathbf{T}_i\\) (of the \\(i\\)-th attribute) in the concept pool, we computed averaged cosine distance as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.677, + 0.38, + 0.72 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c o s} = \\frac {1}{K ^ {2}} \\sum_ {j = 1} ^ {K} \\sum_ {i = 1} ^ {K} \\frac {\\mathbf {T} _ {i} ^ {\\top} \\mathbf {E} _ {j}}{| | \\mathbf {T} _ {i} | | | | \\mathbf {E} _ {j} | |}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.47, + 0.792 + ], + "angle": 0, + "content": "(2) \\(CE\\): Learning with Eq. (2) only. Results are in Table 6. Overall, Mahalanobis distance is an effective constraint to encourage the dictionary \\(E\\) to be close to the distribution of CLIP embeddings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.455, + 0.819 + ], + "angle": 0, + "content": "3.4. Analysis of Interpretability and Interactivity" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.426, + 0.84 + ], + "angle": 0, + "content": "We perform analysis and visualizations to show that:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "(1) Our learned attributes provide interpretability. As shown in Figure 5, the upper half presents the images in a class \\( c \\) and high relevant attributes to recognize them. Specifically, we denote \\( \\mathbf{W} \\in \\mathbb{R}^{K_C * K} \\) as the weight of the" + }, + { + "type": "table", + "bbox": [ + 0.57, + 0.405, + 0.825, + 0.571 + ], + "angle": 0, + "content": "
DatasetCUB
K8163264
MAH30.7647.8760.2764.25
COS28.9647.3558.2763.25
CE31.6748.5555.8860.73
DatasetCIFAR-100
K8163264
MAH34.7752.2465.9173.31
COS31.9851.1565.0272.80
CE32.4550.8366.2973.25
" + }, + { + "type": "table_caption", + "bbox": [ + 0.519, + 0.582, + 0.871, + 0.597 + ], + "angle": 0, + "content": "Table 6: Ablation study w.r.t. different regularization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.699 + ], + "angle": 0, + "content": "FC layer in linear probing, where \\(K_{C}, K\\) are the number of classes and attributes. Then for each image \\(i\\) and its semantic vector \\(\\mathbf{A} \\in \\mathbb{R}^{K}\\), we multiply the corresponding score vector of image \\(i\\) with the corresponding row of the FC layer \\(\\mathbf{W}_{c}\\) to compute Importance Score \\(\\mathbf{IS} \\in \\mathbb{R}^{K}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.647, + 0.709, + 0.892, + 0.724 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I S} = \\mathbf {W} _ {c} \\otimes \\mathbf {A} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.84 + ], + "angle": 0, + "content": "where \\(\\otimes\\) means element-wise multiplication. Then we present attributes with the top absolute values of IS averaged over all samples in a class from the test set, with blue/orange bars indicating the positive/negative importance. Higher absolute values denote greater significance. Since all CLIP scores are positive [16], the positivity or negativity of high IS signifies their relevance to the class." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.902 + ], + "angle": 0, + "content": "(2) Our concise set of attributes enables simple interactivity. As shown in the lower half of Figure 5, we can correct the model's wrong predictions during inference by changing only a single similarity score between an image" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3096" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.891, + 0.453 + ], + "angle": 0, + "content": "
CUB· distinctive white throat\n· bright red head and breast\n· pinkish red breast patch with white edges\n· bright yellow, green and blue plumage\n· Red face with a black cap and bib\n· Short legs for perching on reeds\n· white and black spotted breast\n· sloping foreheadCIFAR10· antlers (in males)\n· pointed bow and stern\n· propellers or jet engines\n· moist slimy skin\n· long head with a mane and tail\n· landing gear\n· portholes along the hull\n· four wheels
CIFAR100· a seat for the rider\n· catkins (flowers) in spring\n· many windows in the façade\n· five pairs of walking legs\n· smooth oval shaped sepals\n· four-limbed primate\n· headboard and footboard\n· towers with conical roofsFlower· Shiny wax coating on the spathe\n· large, yellow or orange flower head\n· bright pink color\n· large, white petals with a yellow center\n· pink to purple colored petals with red lips\n· bright red and yellow petals\n· pink, white, or lavender flowers with five petals\n· deep purple or blue flowers
Food· elbow macaroni noodles\n· Shredded pork meat in the middle of the sandwich\n· large pieces of clams visible in the chowder\n· usually served in a warm wrap or burrito shell\n· sliced into thin wedges or cubes\n· thinly sliced raw fish\n· tender squid rings inside\n· a crisp, fried pastry dough exteriorOxford Pets· black and tan coloring\n· short coat of glossy black fur\n· Long legs and neck\n· Shade of red or wheaten color\n· large, round eyes\n· Pointed ears\n· white blaze on face and chest\n· greyish blue fur with silver tips
Imagenet Animals· male finches have a bright red breast\n· brownish-yellow fur\n· small, four-limbed canid\n· long, black, shiny body\n· the carapace is rough and bumpy\n· white spots on the crab's shell\n· English setters are bred in England\n· long, wire-haired coatStanford Cars· signature Lincoln split headlamps\n· large front grille with the signature BMW kidney shape\n· large size with a wheelbase of 149.4 inches\n· "4Runner" badge on the rear liftgate\n· signature SRT8 grille with crosshair pattern\n· Porsche logo on front grille and trunk lid\n· S6 badge on the trunk lid\n· unique HUMMER H2 logo on front grille
" + }, + { + "type": "image_caption", + "bbox": [ + 0.169, + 0.464, + 0.799, + 0.479 + ], + "angle": 0, + "content": "Figure 6: A concise set of 8 descriptive attributes learned for each dataset with sampled images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.471, + 0.582 + ], + "angle": 0, + "content": "and the attribute that the CLIP model made a mistake on. This is a significant simplification compared with previous work [22] where they need to manipulate scores from a group of concepts for the CUB dataset. We present more user studies in appendix E." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.591, + 0.442, + 0.606 + ], + "angle": 0, + "content": "3.5. Visualization of Our Discovered Attributes" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.825 + ], + "angle": 0, + "content": "We show our learned descriptive attributes with \\( K = 8 \\) in Figure 6. Intuitively, we can observe these attributes are distinctive for each domain. Take birds recognition (CUB) as an example, the eight attributes covered most of the body parts of a bird (head, breast, legs, etc.). As we are condensing knowledge from hundreds of bird classes, each attribute broadly covers many categories. A bright red head and breast can be a noticeable visual attribute for many bird species, such as the Northern Cardinal and the Vermilion Flycatcher. Overall, explaining a domain with a few descriptive attributes is challenging, even for an expert with sufficient domain knowledge. But our model is able to automatically provide a level of knowledge to help humans understand how visual recognition works." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We then present case studies on CIFAR-10 with 4 attributes and CLIP scores of 10 random images from each class in Figure 7. In general, each image is activated in an distinguishable way in the heat map. Some attributes can distinguish a few classes, for example, cat and dog have" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.504, + 0.892, + 0.635 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.649, + 0.892, + 0.681 + ], + "angle": 0, + "content": "Figure 7: Case study on CIFAR-10. The numbers are CLIP similarity scores between each image and attributes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.709, + 0.892, + 0.753 + ], + "angle": 0, + "content": "higher activation on \"fur coat\" compared to automobile or truck. Thus \"fur coat\" may be an important feature to differentiate animals and vehicles." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.637, + 0.785 + ], + "angle": 0, + "content": "4. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Interpretable Deep Learning Interpretability is a critical research problem for deep learning with black-box models [11, 34, 37, 38, 13, 2, 50]. Some works study model behavior and explore if deep models could encode concepts for understanding [19, 28, 49, 29]. For image classification, preliminary attempts aim to describe objects with attributes [12, 26, 25] or building concept bottleneck mod" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3097" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "els [22, 56, 55, 6]. These methods require in-depth human analysis and intensive labeling, which are impractical to scale to more classes and domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.473, + 0.41 + ], + "angle": 0, + "content": "Recent works [30, 35, 52] tackle this problem by using GPT-3 as a knowledge base to query visual attributes or concepts. Specifically, [30, 35] generate descriptions with LLMs, and use them for knowledge-aware prompting for each class to improve zero-shot performance of CLIP [36]. For example, given the class name \"bee\", it will augment it with attributes such as \"A bee with black and yellow body\". Our work differs in that our goal is to learn representative attributes for visual recognition without using class names. LABO [52] extends the idea of concept bottleneck models by generating thousands of concepts from LLMs. Inspired by our finding that there is great redundancy in the large-scale attributes, we aim to learn a concise set of attributes that are initially generated from LLMs for each task, while maintaining the classification performance as possible. Concise attributes also enable stronger interpretability and interactivity, and can help humans to summarize critical knowledge for visual recognition in an automatic way." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.473, + 0.683 + ], + "angle": 0, + "content": "Foundation Models Recently, foundation models [3], which are pre-trained with a large amount of data and large model sizes, have revolutionized machine learning research and many fields. These models are shown to be adaptable to a wide range of downstream tasks for computer vision [15, 46, 58], natural language processing [10, 7, 57, 48] and cross-modal research [27, 42, 17, 14]. One direction is to train LLMs such as GPT3 [5] and ChatGPT with massive text to serve as a powerful knowledge base with high interactivity and beyond. Another direction is to build VLMs [36, 51, 54, 53, 1], which connect vision and language by pre-training with image-text pairs and learning a joint embedding space for both. In this work, we use LLMs as a knowledge base for querying visual related knowledge, and use VLMs to bridge vision and text, presenting a new paradigm for interpretable visual recognition in the era of foundation models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.695, + 0.192, + 0.71 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "There are many interesting topics to explore with our new paradigm. First, our framework is a plug-and-play model that can be readily applied to many other vision tasks, by simply changing the task-guided learning objective to a particular task, e.g., classification losses for object detection, video understanding, and 3D classification. Furthermore, a concise set of descriptive attributes enables interactivity for vision models and empowers human-machine cooperation in a user-friendly way through natural language interfaces. Lastly, we show the potential of summarizing knowledge for challenging vision tasks in the new era of LLMs, which could have broad impact for various domains." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.62, + 0.106 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.268 + ], + "angle": 0, + "content": "In this work, we propose a new paradigm for visual recognition that leverages a concise set of descriptive attributes. Motivated by our insightful finding that significant redundancy exists in massive LLMs-generated attributes, we design a simple yet effective searching method guided by image-level labels, to identify an informative subset. Our new paradigm is validated across 8 datasets to achieve strong classification accuracy with multiple benefits and broad impacts, including efficiency, interpretability, human interactivity, and knowledge summarization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.282, + 0.66, + 0.298 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.307, + 0.894, + 0.354 + ], + "angle": 0, + "content": "We would like to sincerely thank the anonymous reviewers and chairs for their careful review of our work, with helpful and constructive suggestions to improve the paper." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.367, + 0.597, + 0.382 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.391, + 0.895, + 0.46 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01068, 2022.9" + }, + { + "type": "ref_text", + "bbox": [ + 0.503, + 0.46, + 0.892, + 0.514 + ], + "angle": 0, + "content": "[58] Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang Xie, Alan Yuille, and Tao Kong. ibot: Image bert pre-training with online tokenizer. arXiv preprint arXiv:2111.07832, 2021.9" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "3100" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Concise and Descriptive Attributes for Visual Recognition/eb8f500b-e381-4a8d-9629-e0fa391759b6_origin.pdf b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/eb8f500b-e381-4a8d-9629-e0fa391759b6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d487d94d6fb4f2de4b82814eaa677b7c4e0d1944 --- /dev/null +++ b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/eb8f500b-e381-4a8d-9629-e0fa391759b6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d93f881699f41e50e311c6c846a3c59c828bb96a724e5e23320e3d1de61f32ab +size 5595863 diff --git a/2023/Learning Concise and Descriptive Attributes for Visual Recognition/full.md b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fcbabd7d759d7c819fb706052e0f56cad8642325 --- /dev/null +++ b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/full.md @@ -0,0 +1,466 @@ +# Learning Concise and Descriptive Attributes for Visual Recognition + +An Yan\*, Yu Wang\*, Yiwu Zhong\*, Chengyu Dong, Zexue He, Yujie Lu, William Yang Wang, Jingbo Shang, Julian McAuley + +$\diamond$ UC San Diego, $\clubsuit$ University of Wisconsin-Madison, $\clubsuit$ UC Santa Barbara + +{ayan, yuw164, cdong, zehe, jshang, jmcauley}@ucsd.edu + +{yujielu,william}@cs.ucsb.edu，yzhong52@wisc.edu + +# Abstract + +Recent advances in foundation models present new opportunities for interpretable visual recognition – one can first query Large Language Models (LLMs) to obtain a set of attributes that describe each class, then apply vision-language models to classify images via these attributes. Pioneering work shows that querying thousands of attributes can achieve performance competitive with image features. However, our further investigation on 8 datasets reveals that LLM-generated attributes in a large quantity perform almost the same as random words. This surprising finding suggests that significant noise may be present in these attributes. We hypothesize that there exist subsets of attributes that can maintain the classification performance with much smaller sizes, and propose a novel learning-to-search method to discover those concise sets of attributes. As a result, on the CUB dataset, our method achieves performance close to that of massive LLM-generated attributes (e.g., 10k attributes for CUB), yet using only 32 attributes in total to distinguish 200 bird species. Furthermore, our new paradigm demonstrates several additional benefits: higher interpretability and interactivity for humans, and the ability to summarize knowledge for a recognition task. + +# 1. Introduction + +Explaining black-box neural models is a critical research problem. For visual recognition, one line of research tries to classify objects with descriptions or attributes [12, 8, 39, 18, 22], which provide additional information beyond visual cues such as activation maps [41, 40]. However, they require in-depth human analysis and intensive annotation to obtain key attributes for a particular recognition task. Such a paradigm is costly and thus impractical to scale up when the number of classes and domains grows. + +The recent advance of foundation models creates new + +![](images/378836f04f43311f916c3d656a3e79289956974f54269591503a2254a185b5c0.jpg) +Figure 1: Our proposed paradigm for visual recognition via learning a concise set of descriptive attributes. + +opportunities for building interpretable visual recognition models, as demonstrated by the powerful capabilities of models such as GPT-3 and ChatGPT in encoding world knowledge [5, 32, 21]. One can query useful visual attributes from LLMs and classify images via these attributes by converting visual features from vision-language models (VLMs) (e.g., CLIP [36]) into attribute scores [56]. One recent work [52] shows that a large set of attributes from LLMs (e.g., 50 attributes per class) can achieve comparable performance to image features in a linear probing setting. However, two key observations motivate us to re-think this formulation: (1) A large number of attributes dramatically hurts the interpretability of a model. It is unrealistic to manually check thousands of attributes to fully understand model decisions. (2) We surprisingly find that when the number of attributes is large enough (e.g., the dimension of image features), random words drawn from the entire vocabulary can perform equally well as LLM-generated attributes. Moreover, reducing the number of random words by $25\%$ can still attain competitive performance. This indicates that redundant and noisy information exists in the massive LLM-generated attributes. + +With our findings, we ask the research question: Can we learn a concise set of representative visual attributes in the form of natural language to explain how visual recognition works? For example, can we find a few representative attributes to distinguish 200 bird species? This is a nontrivial problem. Even for humans, it is not easy to summa + +rize what are the representative visual attributes given many visual classes. To tackle this challenge, we propose a novel learning-to-search method, which uses image-level labels to guide the searching of discriminative attributes. Specifically, we train a learnable dictionary to approximate the embedding space of VLMs, and then find descriptive attributes in the latent text space via nearest neighbor search. + +In summary, we propose a new paradigm for visual recognition (Figure 1), which seeks to learn a concise set of visual attributes in the form of natural language. Once learned, there are several benefits to our new paradigm: (1) Our discovered attributes are highly descriptive. On 8 visual recognition datasets, our model classifies images via these attributes and achieves comparable classification performance as image features, even if the number of attributes is much smaller than the dimension of image features. (2) The condensed sets of attributes enable strong interpretability for the model decision process through a few human-friendly text descriptions. (3) Additionally, our framework presents a natural language interface for humans to interact with. One can correct a wrong prediction during model inference, by perturbing the values of attribute scores where it made mistakes. (4) Lastly, these expressive attributes can be viewed as a concise form of knowledge to summarize useful features for a visual recognition task, without costly human effort. + +Overall, our contributions are three-fold: + +- Leveraging recent advances in foundation models, we propose a new paradigm for visual recognition by learning a concise set of attribute descriptions. +- To find these attributes, we propose a novel learning-to-search method which prunes the large attribute pool from large language models to a descriptive subset. +- We conduct extensive experiments across 8 visual recognition datasets to validate our recognition effectiveness and efficiency with additional benefits. + +# 2. Methodology + +In this section, we introduce our key components for a new paradigm of visual recognition. It mainly consists of three modules: First, in Section 2.1, given an image domain, we query large language models to obtain a large set of visual attributes for the categories of a task. Second, we use a semantic transformation (Section 2.2) to project the image features into attribute features via a vision-language model, where each dimension in the new space corresponds to an attribute concept, and a higher value represents higher correlation between the image and the attribute. Finally, given the large space of attributes, we propose a novel learning-to-search method (Section 2.4) to efficiently prune the attributes into a much smaller subset to obtain a concise model for classification. + +# 2.1. Generating Attribute Concepts via LLMs + +The first step of our framework is to obtain a set of appropriate attribute concepts. Given a dataset with different categories, (e.g., CUB with 200 bird classes), what are the distinctive visual attributes to recognize them? Manually labeling and designing these attribute concepts can be costly, and can not scale to large numbers of classes. Large Language Models (LLMs), such as GPT-3 [5] and ChatGPT, provide an alternative solution. We can view these language models as implicit knowledge bases with exceptional world knowledge on a variety of tasks and topics, which humans can easily interact with through natural language to query knowledge. To this end, prompt engineering, or the ability to ask good questions to language models, is still important. To effectively query knowledge from LLMs with regard to classifying images, we design two types of prompts. + +Instance Prompting for Class-level Features. For each class $c$ in a given task, our first design choice is to query class-level information from LLMs. We prompt a language model with the instance prompt: + +Q: What are the useful visual features to distinguish $Y_{c}$ in a photo? + +where $Y_{c}$ corresponds to the name of class $c$ in the form of natural language. + +Batch Prompting for Group-level Features. For certain datasets (e.g., CIFAR-100 and ImageNet), there is inherently a hierarchy that some categories belong to the same group. For example, in CIFAR-100, there is a superclass for every five categories. Hence, we propose batch prompting, where we ask the language model to reason about the distinctive visual features among a batch of categories: + +Q: Here are $N_{g}$ kinds of $Y_{g}$ : $\{Y_{c_1}, Y_{c_2}, \ldots, Y_{c_M}\}$ . What are the useful visual features to distinguish them in a photo? where $N_{g}$ is the number of classes in a group $g$ , $Y_{g}$ is the name of the group, $Y_{c_i}$ corresponds to the name of each class $c_i$ in the form of natural language. + +We present more details regarding our prompt design, robustness check of different prompts, and examples of the generated attributes in Appendix A. + +# 2.2. Semantic Projection + +After obtaining a pool consisting of $N$ attribute concepts $\mathcal{C} = \{a_1, a_2, \ldots, a_N\}$ , the second challenge is how we can best leverage these attributes to build interpretable image classifiers. Recent advances of vision-language models such as CLIP bridge the gap between images and text, by pre-training models with large scale image-text pairs. Intuitively, converting from images to text is a discretization process that will unavoidably lose rich semantic information stored in an image. + +To better preserve information, we use a semantic projection that transforms a visual feature into an attribute + +![](images/ac43e802c7c5e152b759b209b27fcfd4a967c543c873967fac2c6e284e4dc87f.jpg) +(a) + +![](images/85c4349b51a989e82980283e1e8dba0cf300b0aac9f28acf03a708ecbd3f7d17.jpg) +(b) +Figure 2: The framework of our model. (a) Querying attributes from LLMs and finding a concise set of representative attributes; (b) An example using the attributes for interpretable visual recognition. + +concept space. Given an image $I$ , we convert the D-dimensional image feature $\mathbf{V} \in \mathbb{R}^{D}$ into an N-dimensional attribute concept vector $\mathbf{A} \in \mathbb{R}^{N}$ : + +$$ +\mathbf {V} = \Theta_ {V} (I), \mathbf {T} _ {i} = \Theta_ {T} (a _ {i}) +$$ + +$$ +s _ {i} = \cos (\mathbf {V}, \mathbf {T} _ {i}), i = 1, \dots , N \tag {1} +$$ + +$$ +\mathbf {A} = \left(s _ {1}, \dots , s _ {N}\right) ^ {T} +$$ + +where $\cos (\cdot ,\cdot)$ is the cosine similarity between two vectors, $s_i$ is the cosine similarity between two vectors. $\Theta_V$ and $\Theta_T$ are the visual and text encoder of a VLM. $\mathbf{T}_i$ is the embedding of the $i$ -th attribute in the attribute concept pool, $i\in \{1,\dots ,N\}$ . A is the semantic vector of image $I$ . + +# 2.3. The Hypothesis of Attribute Concept Space + +Conceptually, our semantic projection resembles principal component analysis, where we aim to find a set of bases in the form of natural language, and by projecting the images into these bases we obtain a new attribute concept space where each dimension in the space corresponds to a visual attribute concept. However, the large bag of attribute concepts we obtained from large language models is not the optimal language basis. As of today, LLMs are models that noisily condense world knowledge from the web, + +and are not optimized for visual recognition or visual reasoning tasks. We hypothesize that there exist subsets of attributes that can still achieve high classification performance with a much smaller size. Intuitively, most attributes in the large attribute concept pool are irrelevant to classify a certain class. For example, attributes that describe dogs are less likely to be suitable attributes to recognize birds or cars. Practically, formatting a compact attribute set is also helpful for humans to interact with the model and understand its behavior better. A small number of attributes is much easier for diagnostic purposes and making decisions with these neural models, which is the ultimate goal of building interpretable models. + +# 2.4. Task-Guided Attribute Concept Searching + +Finding an expressive set of language bases is nontrivial. The massive attributes from LLMs are noisy, and finding a few representative attributes for hundreds of classes in a task can be challenging and costly, even for human experts with domain knowledge. An exhaustive search is also impractical given the large text space. + +Inspired by dictionary learning and vector quantization techniques [43], we present a learning-to-search method that learns a dictionary to approximate an expressive sub + +set of attributes given fixed $K$ . Specifically, we first define an embedding matrix $\mathbf{E} \in \mathbb{R}^{K \times D}$ , where $K$ is a $K$ -way categorical that equals the number of attributes, and $D$ is the dimensionality of embedding vectors $\mathbf{V}$ and $\mathbf{T}_i$ (i.e., the latent dimension of VLMs), where $\mathbf{V}$ and $\mathbf{T}_i$ is the image embedding and the $i$ -th attribute embedding shown in Eq.(1). Since our goal is to find $K$ attributes to be expressive, we propose a task-guided attribute concept searching method to optimize for a particular task. For visual recognition tasks, we use a classification head to project the dictionary into $K_C$ classes and guide the learning process with the categorical cross-entropy loss: + +$$ +\mathcal {L} _ {c e} = - \frac {1}{M} \sum_ {i = 1} ^ {M} \sum_ {c = 1} ^ {K _ {C}} y _ {i, c} \log \left(p _ {i, c}\right) \tag {2} +$$ + +where $M$ is the number of images in a mini-batch, $y_{i,c}$ is the binary indicator of the $i$ -th image in the mini-batch belonging to class $c$ , and $p_{i,c}$ is the predicted probability of the $i$ -th image belonging to class $c$ . + +But simply training with the guidance of the cross-entropy loss is suboptimal, as the embeddings $\mathbf{E}$ are not in the same space of $\mathbf{T}$ . Thus, we use the Mahalanobis distance as a constraint to encourage the embeddings to be optimized towards the latent space of vision-language models. Given a sampled probability distribution $\mathbf{T}$ , the Mahalanobis distance of $\mathbf{E}_j$ from $\mathbf{T}$ is defined as + +$$ +\mathcal {D} _ {m a h} ^ {j} = \sqrt {(\mathbf {E} _ {j} - \boldsymbol {\mu}) \mathbf {S} ^ {- 1} (\mathbf {E} _ {j} - \boldsymbol {\mu})} \tag {3} +$$ + +where $\pmb{\mu} = (\mu_{1},\dots,\mu_{D})$ is the mean vector and $\mathbf{S}$ is the positive-definite covariance matrix of $\mathbf{T}$ . Then the regularization term is defined as: + +$$ +\mathcal {L} _ {m a h} ^ {j} = \frac {1}{K} \sum_ {j = 1} ^ {k} \mathcal {D} _ {m a h} ^ {j} \tag {4} +$$ + +Overall, our model is optimized with a mixture of two losses: + +$$ +\mathcal {L} _ {\text {l o s s}} = \mathcal {L} _ {\text {c e}} + \lambda \sum_ {j = 1} ^ {K} \mathcal {L} _ {\text {m a h}} ^ {j}. \tag {5} +$$ + +After training, we have the embedding matrix $\mathbf{E}$ which will be used for searching the attributes from the attribute concept pool $\mathcal{C}$ . Note that for $\mathbf{E} \in \mathbb{R}^{K*D}$ , each row of $\mathbf{E}$ is a $D$ -dimensional vector. We denote the $j$ -th row of $\mathbf{E}$ as $\mathbf{E}_j$ . We use greedy search as follows: + +$$ +\mathbf{T}_{j}^{*} = \operatorname *{arg max}_{i\in \{1,\dots ,N\}}\cos (\mathbf{T}_{i},\mathbf{E}_{j}), +$$ + +$$ +s. t. \mathbf {T} _ {j} ^ {*} \neq \mathbf {T} _ {k} ^ {*}, \forall 1 \leq k < j, \tag {6} +$$ + +where $j$ is from 1 to $K$ , + +As $j$ iterates from 1 to $K$ , we can find $K$ attribute embeddings $\mathbf{T}_j^*, j \in \{1, \dots, K\}$ , which corresponds to $K$ expressive attribute concepts and are the condensed features containing the necessary knowledge for the task. With the selected attributes, we can calculate the semantic vector of each image as in Eq. (1), where each dimension of the vector is a similarity score between the image and an attribute. We evaluate the performance of these semantic vectors with linear probes, and the obtained linear model is used for inference and analysis. + +# 3. Experiments + +# 3.1. Experimental Setup + +Datasets We conduct our experiments on 8 different image classification datasets, including: CUB [44], CIFAR-10 and CIFAR-100 [24], Food-101 [4], Flower [31], Oxford-pets [33], Stanford-cars [23], Imagenet [9]. For Imagenet, it is not trivial to analyze all 1000 diverse classes. So we narrow the scope to 397 animal classes, with 509,230/19,850 samples for train/test. We denote this subset as Imagenet-Animals. For other datasets, most of them include images within a specific domain (CUB, Flower, Food, Oxford-pets, Stanford-cars), while CIFAR-10 and CIFAR-100 contain broader classes that lie across domains. + +Implementation Details Our method involves two stages of training. The first stage consists of task-guided learning of a dictionary $\mathbf{E}$ to approximate CLIP text embeddings and using this dictionary to find $K$ attributes for visual recognition. For the Mahalanobis distance, the parameter $\lambda$ is tuned with a grid search in $\{1, 0.1, 0.01, 0.001, 0\}$ . The second stage is one-layer linear probing to classify semantic vectors. The batchsize is set to 4,096 for all datasets except 32,768 on Imagenet-Animals for faster converging. We set the number of epochs to 5,000 epochs with early stopping. The learning rate is set to 0.01 in all experiments with an Adam optimizer [20]. Unless specified, we use GPT-3 and CLIP ViT-B/32 for all performance comparison. + +Baselines We compare with state-of-the-art works that leverage attributes either from human annotations or from LLMs. For a fair comparison, we use linear probes to evaluate all methods: (1) CompDL [56] builds semantic vectors using CLIP scores between human-designed attributes and images. (2) LaBO [52] is a recent work that builds semantic vectors with a large set of attributes from LLMs. (3) Human [44, 22]. Attribute labels for each image are annotated by humans. We compare with two versions: binary labels for each attribute, and calibrated labels with confidence scores given by annotators. + +To validate the effectiveness of learning-to-search, we explore other baselines: (1) K-means. Perform K-means + +
DatasetsCUBCIFAR-10CIFAR-100Flower
K32200400810206410020032102204
LaBo-60.9362.61-78.1184.84-75.1076.94-80.9886.76
Ours60.2763.8864.0577.4780.0987.9973.3175.1277.2980.8887.2689.02
DatasetsFoodOxford_PetsStanfordCarsImagenet_Animals
K6410120216377464196392128397794
LaBo-79.9581.33-76.9184.33-72.3374.39-74.8875.49
Ours78.4180.2281.8576.2983.1585.9172.0774.5775.5674.4875.6975.83
+ +Table 1: Comparison with state-of-the-art. LaBo is designed to use at least as many attributes as classes. We use “-” to denote non-applicability. + +
K (# of attributes)81632312
Human Binary [44]4.027.3110.1147.38
Human Calibration [22]3.757.159.7843.37
CompDL [56]12.6426.4128.6952.60
Ours31.6748.5560.2765.17
+ +clustering on CLIP attribute embeddings, then find $K$ attributes with nearest distance to each clustering center. Intuitively this can be a strong baseline, as $K$ attributes close to each center can be distinctive. (2) Uniform Sampling from the large attribute pool. (3) SVD. After obtaining the attribute embeddings $\mathbf{T}$ , we run SVD decomposition of $\mathbf{T}$ to get the top $K$ vectors and find attributes with the largest similarity with the $K$ important vectors. (4) Similarity. We calculate the average score of each attribute across all images and then find the $K$ attributes with the largest average scores. (5) Img Features. Black-box linear probing on latent image features with two linear layers and an intermediate dimension $K$ as a reference. + +# 3.2. Main Results + +Comparison with previous work We first compare our method with LaBo [52]. It is designed to use $M_{c}$ concepts per class with default number of 50, which corresponds to 10,000 attributes for CUB. For fair-comparison, we set $M_{c}$ as 1 and 2 in the experiments. As shown in Table 1, our method outperforms LaBo with the same number of attributes on both the full and few-shot setting. Furthermore, our method can achieve similar accuracy with only a smaller number of attributes (e.g., 32 attributes for CUB). These results suggest that our learned attributes are discriminative enough to classify the images, despite given much fewer attributes. + +We then further compare with human annotations from CUB. For $K < 312$ , we select attributes based on their + +![](images/8fa097bb07ae87b8730115ec4af4fec5b0f13685698b69d15d5b5e9f9ce646d6.jpg) +Figure 3: Performance comparison with random or similar words on CUB. + +Table 2: Comparison with human annotations on CUB. + +
Examples
Rboy champagne +allied whose acrobat +eight centered lobby heads
Sred,gray,snow wings +orange wings +lime,navy wings
Gsloping forehead +distinctive white throat +bright red head and breast
+ +Table 3: Examples from Random (R), Silimlar (S), GPT-3 (G) attributes + +accumulated confidence score for all samples. As shown in Table 2, human annotated attributes are more noisy than CLIP similarities. With the same attributes, CLIP scores from CompDL build more expressive features. Furthermore, our LLM-suggested attributes significantly outperform human designs, e.g. by using 16 attributes we achieve similar performance as 312 attributes defined by humans. + +Large-scale attributes behave like random words We present our finding that LLM-generated attributes in a large quantity behave like random words. Specifically, we compare our method of using GPT-3 attributes with random or similar words. Here, we constructed random words by randomly choosing 1-5 words from the entire English vocabulary, and semantically similar words by combining 1-3 random colors with the noun "wings" as suffix. As shown in Figure 3, when $K = 512$ , random words perform as well as GPT-3 attributes in terms of classification accuracy. Even reducing $K$ from 512 to 256 does not significantly hurt its performance. But when $K$ is small (e.g., 64), the performance of random words drops dramatically. We conjecture that it is because text embeddings randomly drawn from CLIP are nearly orthogonal bases [45]. Given an image feature $\in \mathbb{R}^D$ , projection with a set of $K = D$ orthogonal bases can perfectly preserve its information. We further + +![](images/fe412a41bc515202f88dd7bb590eef00713b2f97f0242f99b8f921b1af8ec658.jpg) +(a) CUB + +![](images/6ad23405e17905e449fbf11b5c675e834625759e29a37f55d3398b1876573a6c.jpg) +(b) CIFAR10 + +![](images/264151bdc9862fba23eafb5a2eff21b65895a4226cae5945f727bc5a33b11eaa.jpg) +(c) CIFAR-100 + +![](images/597ed152f2527c7746a8cfdcbf5f32cc899e3c510d554ed6f1995a870325fa12.jpg) +(d) Flower + +![](images/9ba7b916a13745d677105e16138ff43081eb30ed8b65203084fd6b401402d880.jpg) +(e) Food + +![](images/f5a025df1c61c1c4a064c9af410899bd68b21e5070a668f615be931215cc368c.jpg) +(f) Oxford_pets + +![](images/f689137bc6edc6bcba9b58ee9234988c780b72303457a3ea8664ed0e48df253b.jpg) +(g) StanfordCars +Figure 4: Overall Performance on all datasets. X-axis: number of attributes, Y-axis: Accuracy $(\%)$ , “(f)” means “full”, i.e., all attributes in the pool are used. Uniform refers to uniform sampling. + +![](images/cb8746e5d59efaefc70bb897c85f180abec40a2519e73ae51e513dc190b02f11.jpg) +(h) Imagenet_Animals + +explore how similar words (e.g., red wings, yellow wings) behave. Embeddings of similar words in a trained language model are not orthogonal bases hence the projection will lose information when $K$ is large (e.g., intuitively it is hard to classify 200 bird species using only the color combination of wings). But as $K$ gets smaller, since those similar words have close semantic meanings, they start to outperform random words. Overall, these findings motivate us to find a concise set of meaningful attributes while maintaining competitive performance. + +Number of attributes and selection methods Finally, we study performance change under different number of attributes in Figure 4. First, our method is competitive with image features when $K$ is large. Reducing number of attributes $K$ to the number of classes $C$ (e.g., 512 to 128 for CUB) does not significantly hurt performance, even for baseline methods. This validates our hypothesis that there is plenty of redundant information in the semantic space when the number of attributes is large (as used in LaBO [52]). It is possible to find a subset of expressive attributes for visual recognition. Second, we also consistently outperform other methods such as K-means clustering and uniform sampling, demonstrating the effectiveness of our task-guided searching method. Third, a heuristic design such as K-means performs similar as uniform selection. Note that though there is a performance gap between image features and using attributes, the gap can be minimized by using a stronger VLM, as the classification accuracy of attributes relies on the accurate estimation of the correlation between images and attributes (see more results in appendix D). + +
DatasetsCUBCIFAR-100
K8163281632
GPT-331.6748.5560.2734.7752.2466.30
GPT-3-Imagenet30.8149.2960.4133.8051.0165.61
+ +Table 4: Ablation study w.r.t. different concept pools. + +# 3.3. Ablation Study + +Robustness to the attribute pool First, we aim to explore the effects of different initialized attribute concept pools generated by LLMs. On CUB and CIFAR-100, we compare two attribute pools, attributes generated from classes in each dataset, and attributes generated from the full set of ImageNet classes. As shown in Table 4, even with the large and noisy attributes from ImageNet, our method can still efficiently find a small number of representative attributes for a task, and obtains competitive classification performance. + +Effectiveness of learning-to-search Then, we discuss possible choices for selection out of the large attribute pool. Results are shown in Table 5 with the following observations: heuristic methods such as K-means and SVD are not optimal choices for identifying the most distinctive attributes. In fact, they are sometimes less effective than uniform sampling. This is likely because we need to identify the most distinguishing attributes for visual recognition, rather than the most diverse ones based on text embeddings. Overall, our method significantly outperforms other baseline selection methods, showing its efficacy. + +are classified as Least Auklet because: +![](images/a826748065530bd1bfb55babaa3471daa9d73754568fb309a4f3a4da614779ee.jpg) +overall yellowish coloration +- dark gray and white mottled feathers + +![](images/bbdcdd38da6327f3ddb38a9f908dae72c4f163618af759518ffac00c6686112d.jpg) +- iridescent black body with blue and purple highlights +large, round eyes with an orange ring around them +- medium-sized sea bird with a white head and black cap +- bright yellow throat, breast, and flanks with black bars + +![](images/20d9f86a1f5cbd04c6d74999259b5ade9a23996bb554d33f14572064db37edc0.jpg) +Overall yellowish coloration + +![](images/09adffb4573c105878120c2af64efc0a0d3e52909ac35f637ac742c99eb54bfc.jpg) +(a) Least Auklet + +![](images/b69f69bd3541a64981d41e3538f7c3ab6289b94b2baa5766794ff0ad52e5b78c.jpg) +Least Auklet (Correct) +Figure 5: Examples on interpretability and interactivity. (1) The upper half of each figure shows important attributes for two classes of birds. We choose 6 out of 32 attributes with highest importance scores, which are computed by multiplication between clip scores and weights in the linear probe, defined in Eq. (7). (2) The lower half of each figure demonstrates the intervention on the semantic vector (i.e., CLIP scores) to correct the prediction, we use $\delta = 0.03$ for all interventions on clip scores as an empirical value. The array of 6 scores are of the same order as the attributes. + +are classified as yellow billed cuckoo because: +![](images/bf6aaec7f318ba1b37c48285074d4687fe8797e713fd74fc70c1a9d9102c6e04.jpg) +gray and white streaked head, back, and chest +dark slate gray crown, back and +white throat and yellowish belly +pinkish red breast patch with white edges +white neck with a black collar and +chestnut red head and breast +- distinctive large white wing patches edged +in bold black stripes +brownish head with yellow supercilium + +White neck with a black collar and +chestnut red head and breast +[0.2782,0.2810,0.2334,0.2318,0.2242,0.2405] $\Rightarrow$ +Intervention +[ [0.2782, 0.2810, 0.2334, 0.2618, 0.2242, 0.2405] \Rightarrow ] +(b) Yellow Billed Cuckoo +![](images/c243adc9dc2318ecd6b85ceaecd9b0ab3fee17b4ae8dd93604af1621f81ad9af.jpg) +(eyebrow) and white throat + +![](images/a44b46ab4083441b22380cb1d15eee4e27667ea70c53f6127a8bb849133b80a8.jpg) +14.9 +A + +117 +-10.03 +3 +Mangrove cuckoo (Wrong) + +![](images/fa974fd77d0288a463394d90f636fde05b2d8da45332d90bc63802f3ab0fc6ab.jpg) +yellow billed cuckoo (Correct) + +
DatasetsCUBCIFAR-100
K8163281632
K-means16.8321.0232.7625.3945.2664.41
Uniform7.0225.9840.5828.0747.1464.34
SVD6.5220.0235.8329.0650.0064.99
Similarity4.739.7218.0026.7545.6162.79
Ours31.6748.5560.2734.7752.2466.30
+ +Effectiveness of regularization We compare the Mahalanobis distance (MAH) with two variations: (1) COS: For each vector $\mathbf{E}_j$ and $\mathbf{T}_i$ (of the $i$ -th attribute) in the concept pool, we computed averaged cosine distance as follows: + +$$ +\mathcal {L} _ {c o s} = \frac {1}{K ^ {2}} \sum_ {j = 1} ^ {K} \sum_ {i = 1} ^ {K} \frac {\mathbf {T} _ {i} ^ {\top} \mathbf {E} _ {j}}{| | \mathbf {T} _ {i} | | | | \mathbf {E} _ {j} | |} +$$ + +(2) $CE$ : Learning with Eq. (2) only. Results are in Table 6. Overall, Mahalanobis distance is an effective constraint to encourage the dictionary $E$ to be close to the distribution of CLIP embeddings. + +# 3.4. Analysis of Interpretability and Interactivity + +We perform analysis and visualizations to show that: + +(1) Our learned attributes provide interpretability. As shown in Figure 5, the upper half presents the images in a class $c$ and high relevant attributes to recognize them. Specifically, we denote $\mathbf{W} \in \mathbb{R}^{K_C * K}$ as the weight of the + +Table 5: Ablation study w.r.t. different attribute selection strategies. + +
DatasetCUB
K8163264
MAH30.7647.8760.2764.25
COS28.9647.3558.2763.25
CE31.6748.5555.8860.73
DatasetCIFAR-100
K8163264
MAH34.7752.2465.9173.31
COS31.9851.1565.0272.80
CE32.4550.8366.2973.25
+ +Table 6: Ablation study w.r.t. different regularization. + +FC layer in linear probing, where $K_{C}, K$ are the number of classes and attributes. Then for each image $i$ and its semantic vector $\mathbf{A} \in \mathbb{R}^{K}$ , we multiply the corresponding score vector of image $i$ with the corresponding row of the FC layer $\mathbf{W}_{c}$ to compute Importance Score $\mathbf{IS} \in \mathbb{R}^{K}$ : + +$$ +\mathbf {I S} = \mathbf {W} _ {c} \otimes \mathbf {A} \tag {7} +$$ + +where $\otimes$ means element-wise multiplication. Then we present attributes with the top absolute values of IS averaged over all samples in a class from the test set, with blue/orange bars indicating the positive/negative importance. Higher absolute values denote greater significance. Since all CLIP scores are positive [16], the positivity or negativity of high IS signifies their relevance to the class. + +(2) Our concise set of attributes enables simple interactivity. As shown in the lower half of Figure 5, we can correct the model's wrong predictions during inference by changing only a single similarity score between an image + +
CUB· distinctive white throat +· bright red head and breast +· pinkish red breast patch with white edges +· bright yellow, green and blue plumage +· Red face with a black cap and bib +· Short legs for perching on reeds +· white and black spotted breast +· sloping foreheadCIFAR10· antlers (in males) +· pointed bow and stern +· propellers or jet engines +· moist slimy skin +· long head with a mane and tail +· landing gear +· portholes along the hull +· four wheels
CIFAR100· a seat for the rider +· catkins (flowers) in spring +· many windows in the façade +· five pairs of walking legs +· smooth oval shaped sepals +· four-limbed primate +· headboard and footboard +· towers with conical roofsFlower· Shiny wax coating on the spathe +· large, yellow or orange flower head +· bright pink color +· large, white petals with a yellow center +· pink to purple colored petals with red lips +· bright red and yellow petals +· pink, white, or lavender flowers with five petals +· deep purple or blue flowers
Food· elbow macaroni noodles +· Shredded pork meat in the middle of the sandwich +· large pieces of clams visible in the chowder +· usually served in a warm wrap or burrito shell +· sliced into thin wedges or cubes +· thinly sliced raw fish +· tender squid rings inside +· a crisp, fried pastry dough exteriorOxford Pets· black and tan coloring +· short coat of glossy black fur +· Long legs and neck +· Shade of red or wheaten color +· large, round eyes +· Pointed ears +· white blaze on face and chest +· greyish blue fur with silver tips
Imagenet Animals· male finches have a bright red breast +· brownish-yellow fur +· small, four-limbed canid +· long, black, shiny body +· the carapace is rough and bumpy +· white spots on the crab's shell +· English setters are bred in England +· long, wire-haired coatStanford Cars· signature Lincoln split headlamps +· large front grille with the signature BMW kidney shape +· large size with a wheelbase of 149.4 inches +· "4Runner" badge on the rear liftgate +· signature SRT8 grille with crosshair pattern +· Porsche logo on front grille and trunk lid +· S6 badge on the trunk lid +· unique HUMMER H2 logo on front grille
+ +and the attribute that the CLIP model made a mistake on. This is a significant simplification compared with previous work [22] where they need to manipulate scores from a group of concepts for the CUB dataset. We present more user studies in appendix E. + +# 3.5. Visualization of Our Discovered Attributes + +We show our learned descriptive attributes with $K = 8$ in Figure 6. Intuitively, we can observe these attributes are distinctive for each domain. Take birds recognition (CUB) as an example, the eight attributes covered most of the body parts of a bird (head, breast, legs, etc.). As we are condensing knowledge from hundreds of bird classes, each attribute broadly covers many categories. A bright red head and breast can be a noticeable visual attribute for many bird species, such as the Northern Cardinal and the Vermilion Flycatcher. Overall, explaining a domain with a few descriptive attributes is challenging, even for an expert with sufficient domain knowledge. But our model is able to automatically provide a level of knowledge to help humans understand how visual recognition works. + +We then present case studies on CIFAR-10 with 4 attributes and CLIP scores of 10 random images from each class in Figure 7. In general, each image is activated in an distinguishable way in the heat map. Some attributes can distinguish a few classes, for example, cat and dog have + +![](images/b8e7d25ac801a5fef5ea03e0fca45d515da4b6f9ea076ce89d132d6863e3494a.jpg) +Figure 6: A concise set of 8 descriptive attributes learned for each dataset with sampled images. +Figure 7: Case study on CIFAR-10. The numbers are CLIP similarity scores between each image and attributes. + +higher activation on "fur coat" compared to automobile or truck. Thus "fur coat" may be an important feature to differentiate animals and vehicles. + +# 4. Related work + +Interpretable Deep Learning Interpretability is a critical research problem for deep learning with black-box models [11, 34, 37, 38, 13, 2, 50]. Some works study model behavior and explore if deep models could encode concepts for understanding [19, 28, 49, 29]. For image classification, preliminary attempts aim to describe objects with attributes [12, 26, 25] or building concept bottleneck mod + +els [22, 56, 55, 6]. These methods require in-depth human analysis and intensive labeling, which are impractical to scale to more classes and domains. + +Recent works [30, 35, 52] tackle this problem by using GPT-3 as a knowledge base to query visual attributes or concepts. Specifically, [30, 35] generate descriptions with LLMs, and use them for knowledge-aware prompting for each class to improve zero-shot performance of CLIP [36]. For example, given the class name "bee", it will augment it with attributes such as "A bee with black and yellow body". Our work differs in that our goal is to learn representative attributes for visual recognition without using class names. LABO [52] extends the idea of concept bottleneck models by generating thousands of concepts from LLMs. Inspired by our finding that there is great redundancy in the large-scale attributes, we aim to learn a concise set of attributes that are initially generated from LLMs for each task, while maintaining the classification performance as possible. Concise attributes also enable stronger interpretability and interactivity, and can help humans to summarize critical knowledge for visual recognition in an automatic way. + +Foundation Models Recently, foundation models [3], which are pre-trained with a large amount of data and large model sizes, have revolutionized machine learning research and many fields. These models are shown to be adaptable to a wide range of downstream tasks for computer vision [15, 46, 58], natural language processing [10, 7, 57, 48] and cross-modal research [27, 42, 17, 14]. One direction is to train LLMs such as GPT3 [5] and ChatGPT with massive text to serve as a powerful knowledge base with high interactivity and beyond. Another direction is to build VLMs [36, 51, 54, 53, 1], which connect vision and language by pre-training with image-text pairs and learning a joint embedding space for both. In this work, we use LLMs as a knowledge base for querying visual related knowledge, and use VLMs to bridge vision and text, presenting a new paradigm for interpretable visual recognition in the era of foundation models. + +# 5. Discussion + +There are many interesting topics to explore with our new paradigm. First, our framework is a plug-and-play model that can be readily applied to many other vision tasks, by simply changing the task-guided learning objective to a particular task, e.g., classification losses for object detection, video understanding, and 3D classification. Furthermore, a concise set of descriptive attributes enables interactivity for vision models and empowers human-machine cooperation in a user-friendly way through natural language interfaces. Lastly, we show the potential of summarizing knowledge for challenging vision tasks in the new era of LLMs, which could have broad impact for various domains. + +# 6. Conclusion + +In this work, we propose a new paradigm for visual recognition that leverages a concise set of descriptive attributes. Motivated by our insightful finding that significant redundancy exists in massive LLMs-generated attributes, we design a simple yet effective searching method guided by image-level labels, to identify an informative subset. 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Visual clues: Bridging vision and language foundations for image paragraph captioning. arXiv preprint arXiv:2206.01843, 2022. 12 +[48] An Yan, Julian McAuley, Xing Lu, Jiang Du, Eric Y Chang, Amilcare Gentili, and Chun-Nan Hsu. Radbert: Adapting transformer-based language models to radiology. *Radiology: Artificial Intelligence*, 4(4):e210258, 2022. 9 +[49] An Yan, Xin Eric Wang, Tsu-Jui Fu, and William Yang Wang. L2c: Describing visual differences needs semantic understanding of individuals. arXiv preprint arXiv:2102.01860, 2021. 8 +[50] An Yan, Yali Wang, Zhifeng Li, and Yu Qiao. Pa3d: Pose-action 3d machine for video recognition. In Proceedings of the iee/cvf conference on computer vision and pattern recognition, pages 7922-7931, 2019. 8 +[51] Jianwei Yang, Chunyuan Li, Pengchuan Zhang, Bin Xiao, Ce Liu, Lu Yuan, and Jianfeng Gao. Unified contrastive learning in image-text-label space. 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CoRR, abs/2205.15480, 2022. 9 +[56] Tian Yun, Usha Bhalla, Ellie Pavlick, and Chen Sun. Do vision-language pretrained models learn primitive concepts? arXiv preprint arXiv:2203.17271, 2022. 1, 4, 5, 9 +[57] Susan Zhang, Stephen Roller, Naman Goyal, Mikel Artetxe, Moya Chen, Shuohui Chen, Christopher Dewan, Mona Diab, Xian Li, Xi Victoria Lin, et al. Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01068, 2022.9 +[58] Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang Xie, Alan Yuille, and Tao Kong. ibot: Image bert pre-training with online tokenizer. arXiv preprint arXiv:2111.07832, 2021.9 \ No newline at end of file diff --git a/2023/Learning Concise and Descriptive Attributes for Visual Recognition/images.zip b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..24871a95dda79a9747d80c41ea82b7519eccc4ae --- /dev/null +++ b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8f9217425e7d3c7167c6738ae87b980d5c1c49f088822bdbb8569b5a7c64accb +size 810142 diff --git a/2023/Learning Concise and Descriptive Attributes for Visual Recognition/layout.json b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ea2fe47e16e5119991a4bb3f8d6b832817fd7349 --- /dev/null +++ b/2023/Learning Concise and Descriptive Attributes for Visual Recognition/layout.json @@ -0,0 +1,11384 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "spans": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "type": "text", + "content": "Learning Concise and Descriptive Attributes for Visual Recognition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 126, + 141, + 468, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 141, + 468, + 171 + ], + "spans": [ + { + "bbox": [ + 126, + 141, + 468, + 171 + ], + "type": "text", + "content": "An Yan\\*, Yu Wang\\*, Yiwu Zhong\\*, Chengyu Dong, Zexue He, Yujie Lu, William Yang Wang, Jingbo Shang, Julian McAuley" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 121, + 171, + 474, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 171, + 474, + 186 + ], + "spans": [ + { + "bbox": [ + 121, + 171, + 474, + 186 + ], + "type": "inline_equation", + "content": "\\diamond" + }, + { + "bbox": [ + 121, + 171, + 474, + 186 + ], + "type": "text", + "content": "UC San Diego, " + }, + { + "bbox": [ + 121, + 171, + 474, + 186 + ], + "type": "inline_equation", + "content": "\\clubsuit" + }, + { + "bbox": [ + 121, + 171, + 474, + 186 + ], + "type": "text", + "content": "University of Wisconsin-Madison, " + }, + { + "bbox": [ + 121, + 171, + 474, + 186 + ], + "type": "inline_equation", + "content": "\\clubsuit" + }, + { + "bbox": [ + 121, + 171, + 474, + 186 + ], + "type": "text", + "content": "UC Santa Barbara" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 164, + 187, + 429, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 164, + 187, + 429, + 200 + ], + "spans": [ + { + "bbox": [ + 164, + 187, + 429, + 200 + ], + "type": "text", + "content": "{ayan, yuw164, cdong, zehe, jshang, jmcauley}@ucsd.edu" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 167, + 201, + 426, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 167, + 201, + 426, + 214 + ], + "spans": [ + { + "bbox": [ + 167, + 201, + 426, + 214 + ], + "type": "text", + "content": "{yujielu,william}@cs.ucsb.edu，yzhong52@wisc.edu" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 253, + 192, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 253, + 192, + 266 + ], + "spans": [ + { + "bbox": [ + 143, + 253, + 192, + 266 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 278, + 290, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 290, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 290, + 542 + ], + "type": "text", + "content": "Recent advances in foundation models present new opportunities for interpretable visual recognition – one can first query Large Language Models (LLMs) to obtain a set of attributes that describe each class, then apply vision-language models to classify images via these attributes. Pioneering work shows that querying thousands of attributes can achieve performance competitive with image features. However, our further investigation on 8 datasets reveals that LLM-generated attributes in a large quantity perform almost the same as random words. This surprising finding suggests that significant noise may be present in these attributes. We hypothesize that there exist subsets of attributes that can maintain the classification performance with much smaller sizes, and propose a novel learning-to-search method to discover those concise sets of attributes. As a result, on the CUB dataset, our method achieves performance close to that of massive LLM-generated attributes (e.g., 10k attributes for CUB), yet using only 32 attributes in total to distinguish 200 bird species. Furthermore, our new paradigm demonstrates several additional benefits: higher interpretability and interactivity for humans, and the ability to summarize knowledge for a recognition task." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 575, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 287, + 684 + ], + "type": "text", + "content": "Explaining black-box neural models is a critical research problem. For visual recognition, one line of research tries to classify objects with descriptions or attributes [12, 8, 39, 18, 22], which provide additional information beyond visual cues such as activation maps [41, 40]. However, they require in-depth human analysis and intensive annotation to obtain key attributes for a particular recognition task. 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One can query useful visual attributes from LLMs and classify images via these attributes by converting visual features from vision-language models (VLMs) (e.g., CLIP [36]) into attribute scores [56]. One recent work [52] shows that a large set of attributes from LLMs (e.g., 50 attributes per class) can achieve comparable performance to image features in a linear probing setting. However, two key observations motivate us to re-think this formulation: (1) A large number of attributes dramatically hurts the interpretability of a model. It is unrealistic to manually check thousands of attributes to fully understand model decisions. (2) We surprisingly find that when the number of attributes is large enough (e.g., the dimension of image features), random words drawn from the entire vocabulary can perform equally well as LLM-generated attributes. Moreover, reducing the number of random words by " + }, + { + "bbox": [ + 304, + 376, + 546, + 640 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 376, + 546, + 640 + ], + "type": "text", + "content": " can still attain competitive performance. This indicates that redundant and noisy information exists in the massive LLM-generated attributes." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "content": "With our findings, we ask the research question: Can we learn a concise set of representative visual attributes in the form of natural language to explain how visual recognition works? For example, can we find a few representative attributes to distinguish 200 bird species? This is a nontrivial problem. Even for humans, it is not easy to summa" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 134, + 712 + ], + "type": "text", + "content": "* equal contributions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3090" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "rize what are the representative visual attributes given many visual classes. To tackle this challenge, we propose a novel learning-to-search method, which uses image-level labels to guide the searching of discriminative attributes. Specifically, we train a learnable dictionary to approximate the embedding space of VLMs, and then find descriptive attributes in the latent text space via nearest neighbor search." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 288, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 288, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 288, + 384 + ], + "type": "text", + "content": "In summary, we propose a new paradigm for visual recognition (Figure 1), which seeks to learn a concise set of visual attributes in the form of natural language. Once learned, there are several benefits to our new paradigm: (1) Our discovered attributes are highly descriptive. On 8 visual recognition datasets, our model classifies images via these attributes and achieves comparable classification performance as image features, even if the number of attributes is much smaller than the dimension of image features. (2) The condensed sets of attributes enable strong interpretability for the model decision process through a few human-friendly text descriptions. (3) Additionally, our framework presents a natural language interface for humans to interact with. One can correct a wrong prediction during model inference, by perturbing the values of attribute scores where it made mistakes. (4) Lastly, these expressive attributes can be viewed as a concise form of knowledge to summarize useful features for a visual recognition task, without costly human effort." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 384, + 225, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 384, + 225, + 396 + ], + "spans": [ + { + "bbox": [ + 59, + 384, + 225, + 396 + ], + "type": "text", + "content": "Overall, our contributions are three-fold:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 399, + 287, + 512 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 399, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 399, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 59, + 399, + 287, + 434 + ], + "type": "text", + "content": "- Leveraging recent advances in foundation models, we propose a new paradigm for visual recognition by learning a concise set of attribute descriptions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 437, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 437, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 59, + 437, + 287, + 474 + ], + "type": "text", + "content": "- To find these attributes, we propose a novel learning-to-search method which prunes the large attribute pool from large language models to a descriptive subset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 476, + 287, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 476, + 287, + 512 + ], + "spans": [ + { + "bbox": [ + 59, + 476, + 287, + 512 + ], + "type": "text", + "content": "- We conduct extensive experiments across 8 visual recognition datasets to validate our recognition effectiveness and efficiency with additional benefits." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 525, + 129, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 129, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 129, + 539 + ], + "type": "text", + "content": "2. Methodology" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 546, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 287, + 712 + ], + "type": "text", + "content": "In this section, we introduce our key components for a new paradigm of visual recognition. It mainly consists of three modules: First, in Section 2.1, given an image domain, we query large language models to obtain a large set of visual attributes for the categories of a task. Second, we use a semantic transformation (Section 2.2) to project the image features into attribute features via a vision-language model, where each dimension in the new space corresponds to an attribute concept, and a higher value represents higher correlation between the image and the attribute. Finally, given the large space of attributes, we propose a novel learning-to-search method (Section 2.4) to efficiently prune the attributes into a much smaller subset to obtain a concise model for classification." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 523, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 523, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 523, + 85 + ], + "type": "text", + "content": "2.1. Generating Attribute Concepts via LLMs" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 91, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 270 + ], + "type": "text", + "content": "The first step of our framework is to obtain a set of appropriate attribute concepts. Given a dataset with different categories, (e.g., CUB with 200 bird classes), what are the distinctive visual attributes to recognize them? Manually labeling and designing these attribute concepts can be costly, and can not scale to large numbers of classes. Large Language Models (LLMs), such as GPT-3 [5] and ChatGPT, provide an alternative solution. We can view these language models as implicit knowledge bases with exceptional world knowledge on a variety of tasks and topics, which humans can easily interact with through natural language to query knowledge. To this end, prompt engineering, or the ability to ask good questions to language models, is still important. To effectively query knowledge from LLMs with regard to classifying images, we design two types of prompts." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 271, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 545, + 319 + ], + "type": "text", + "content": "Instance Prompting for Class-level Features. For each class " + }, + { + "bbox": [ + 304, + 271, + 545, + 319 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 271, + 545, + 319 + ], + "type": "text", + "content": " in a given task, our first design choice is to query class-level information from LLMs. We prompt a language model with the instance prompt:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 320, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 344 + ], + "type": "text", + "content": "Q: What are the useful visual features to distinguish " + }, + { + "bbox": [ + 304, + 320, + 545, + 344 + ], + "type": "inline_equation", + "content": "Y_{c}" + }, + { + "bbox": [ + 304, + 320, + 545, + 344 + ], + "type": "text", + "content": " in a photo?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "inline_equation", + "content": "Y_{c}" + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "text", + "content": " corresponds to the name of class " + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "text", + "content": " in the form of natural language." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 369, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 453 + ], + "type": "text", + "content": "Batch Prompting for Group-level Features. For certain datasets (e.g., CIFAR-100 and ImageNet), there is inherently a hierarchy that some categories belong to the same group. For example, in CIFAR-100, there is a superclass for every five categories. Hence, we propose batch prompting, where we ask the language model to reason about the distinctive visual features among a batch of categories:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": "Q: Here are " + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "inline_equation", + "content": "N_{g}" + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": " kinds of " + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "inline_equation", + "content": "Y_{g}" + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "inline_equation", + "content": "\\{Y_{c_1}, Y_{c_2}, \\ldots, Y_{c_M}\\}" + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": ". What are the useful visual features to distinguish them in a photo? where " + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "inline_equation", + "content": "N_{g}" + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": " is the number of classes in a group " + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "inline_equation", + "content": "Y_{g}" + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": " is the name of the group, " + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "inline_equation", + "content": "Y_{c_i}" + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": " corresponds to the name of each class " + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 304, + 453, + 545, + 515 + ], + "type": "text", + "content": " in the form of natural language." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 516, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 552 + ], + "type": "text", + "content": "We present more details regarding our prompt design, robustness check of different prompts, and examples of the generated attributes in Appendix A." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 562, + 423, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 423, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 423, + 574 + ], + "type": "text", + "content": "2.2. Semantic Projection" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "type": "text", + "content": "After obtaining a pool consisting of " + }, + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "type": "text", + "content": " attribute concepts " + }, + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = \\{a_1, a_2, \\ldots, a_N\\}" + }, + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "type": "text", + "content": ", the second challenge is how we can best leverage these attributes to build interpretable image classifiers. Recent advances of vision-language models such as CLIP bridge the gap between images and text, by pre-training models with large scale image-text pairs. Intuitively, converting from images to text is a discretization process that will unavoidably lose rich semantic information stored in an image." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "To better preserve information, we use a semantic projection that transforms a visual feature into an attribute" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3091" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 86, + 496, + 265 + ], + "blocks": [ + { + "bbox": [ + 107, + 86, + 119, + 98 + ], + "lines": [ + { + "bbox": [ + 107, + 86, + 119, + 98 + ], + "spans": [ + { + "bbox": [ + 107, + 86, + 119, + 98 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 115, + 86, + 496, + 265 + ], + "lines": [ + { + "bbox": [ + 115, + 86, + 496, + 265 + ], + "spans": [ + { + "bbox": [ + 115, + 86, + 496, + 265 + ], + "type": "image", + "image_path": "ac43e802c7c5e152b759b209b27fcfd4a967c543c873967fac2c6e284e4dc87f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 78, + 297, + 514, + 361 + ], + "blocks": [ + { + "bbox": [ + 76, + 281, + 87, + 293 + ], + "lines": [ + { + "bbox": [ + 76, + 281, + 87, + 293 + ], + "spans": [ + { + "bbox": [ + 76, + 281, + 87, + 293 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 78, + 297, + 514, + 361 + ], + "lines": [ + { + "bbox": [ + 78, + 297, + 514, + 361 + ], + "spans": [ + { + "bbox": [ + 78, + 297, + 514, + 361 + ], + "type": "image", + "image_path": "85c4349b51a989e82980283e1e8dba0cf300b0aac9f28acf03a708ecbd3f7d17.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 373, + 546, + 398 + ], + "lines": [ + { + "bbox": [ + 46, + 373, + 546, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 546, + 398 + ], + "type": "text", + "content": "Figure 2: The framework of our model. (a) Querying attributes from LLMs and finding a concise set of representative attributes; (b) An example using the attributes for interpretable visual recognition." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "type": "text", + "content": "concept space. Given an image " + }, + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "type": "text", + "content": ", we convert the D-dimensional image feature " + }, + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "type": "text", + "content": " into an N-dimensional attribute concept vector " + }, + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{N}" + }, + { + "bbox": [ + 46, + 418, + 287, + 455 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 464, + 216, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 464, + 216, + 477 + ], + "spans": [ + { + "bbox": [ + 107, + 464, + 216, + 477 + ], + "type": "interline_equation", + "content": "\\mathbf {V} = \\Theta_ {V} (I), \\mathbf {T} _ {i} = \\Theta_ {T} (a _ {i})", + "image_path": "f1327501fe93216d98e1e674424267cd0e81ff197e3d39c60872596d855517a8.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 479, + 287, + 492 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 479, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 107, + 479, + 287, + 492 + ], + "type": "interline_equation", + "content": "s _ {i} = \\cos (\\mathbf {V}, \\mathbf {T} _ {i}), i = 1, \\dots , N \\tag {1}", + "image_path": "51290a8f753b98b8a3ec876e410c570384ccf3bde4399ded6771bda615d8120c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 107, + 495, + 189, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 495, + 189, + 510 + ], + "spans": [ + { + "bbox": [ + 107, + 495, + 189, + 510 + ], + "type": "interline_equation", + "content": "\\mathbf {A} = \\left(s _ {1}, \\dots , s _ {N}\\right) ^ {T}", + "image_path": "8290238a3039a1683bc6de5afe5702ed65ef25e8b4fd46b125f8a197b5105e7c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\cos (\\cdot ,\\cdot)" + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": " is the cosine similarity between two vectors, " + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": " is the cosine similarity between two vectors. " + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\Theta_V" + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\Theta_T" + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": " are the visual and text encoder of a VLM. " + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i" + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": " is the embedding of the " + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": "-th attribute in the attribute concept pool, " + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "inline_equation", + "content": "i\\in \\{1,\\dots ,N\\}" + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": ". A is the semantic vector of image " + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 519, + 287, + 579 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 586, + 273, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 273, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 273, + 601 + ], + "type": "text", + "content": "2.3. The Hypothesis of Attribute Concept Space" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Conceptually, our semantic projection resembles principal component analysis, where we aim to find a set of bases in the form of natural language, and by projecting the images into these bases we obtain a new attribute concept space where each dimension in the space corresponds to a visual attribute concept. However, the large bag of attribute concepts we obtained from large language models is not the optimal language basis. As of today, LLMs are models that noisily condense world knowledge from the web," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 418, + 546, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 546, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 546, + 574 + ], + "type": "text", + "content": "and are not optimized for visual recognition or visual reasoning tasks. We hypothesize that there exist subsets of attributes that can still achieve high classification performance with a much smaller size. Intuitively, most attributes in the large attribute concept pool are irrelevant to classify a certain class. For example, attributes that describe dogs are less likely to be suitable attributes to recognize birds or cars. Practically, formatting a compact attribute set is also helpful for humans to interact with the model and understand its behavior better. A small number of attributes is much easier for diagnostic purposes and making decisions with these neural models, which is the ultimate goal of building interpretable models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 585, + 527, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 527, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 527, + 598 + ], + "type": "text", + "content": "2.4. Task-Guided Attribute Concept Searching" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": "Finding an expressive set of language bases is nontrivial. The massive attributes from LLMs are noisy, and finding a few representative attributes for hundreds of classes in a task can be challenging and costly, even for human experts with domain knowledge. An exhaustive search is also impractical given the large text space." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "Inspired by dictionary learning and vector quantization techniques [43], we present a learning-to-search method that learns a dictionary to approximate an expressive sub" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3092" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": "set of attributes given fixed " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": ". Specifically, we first define an embedding matrix " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{E} \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": "-way categorical that equals the number of attributes, and " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " is the dimensionality of embedding vectors " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " (i.e., the latent dimension of VLMs), where " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " is the image embedding and the " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": "-th attribute embedding shown in Eq.(1). Since our goal is to find " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " attributes to be expressive, we propose a task-guided attribute concept searching method to optimize for a particular task. For visual recognition tasks, we use a classification head to project the dictionary into " + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "K_C" + }, + { + "bbox": [ + 47, + 72, + 289, + 216 + ], + "type": "text", + "content": " classes and guide the learning process with the categorical cross-entropy loss:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 98, + 225, + 287, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 225, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 98, + 225, + 287, + 258 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c e} = - \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\sum_ {c = 1} ^ {K _ {C}} y _ {i, c} \\log \\left(p _ {i, c}\\right) \\tag {2}", + "image_path": "cc0ef3789d1d5defde9438c1c6deaaa79ab5d8b4d0c807abf67a7f2724c72abc.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "content": " is the number of images in a mini-batch, " + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "inline_equation", + "content": "y_{i,c}" + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "content": " is the binary indicator of the " + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "content": "-th image in the mini-batch belonging to class " + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "inline_equation", + "content": "p_{i,c}" + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "content": " is the predicted probability of the " + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "content": "-th image belonging to class " + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 266, + 287, + 315 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "text", + "content": "But simply training with the guidance of the cross-entropy loss is suboptimal, as the embeddings " + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "text", + "content": " are not in the same space of " + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "text", + "content": ". Thus, we use the Mahalanobis distance as a constraint to encourage the embeddings to be optimized towards the latent space of vision-language models. Given a sampled probability distribution " + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "text", + "content": ", the Mahalanobis distance of " + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_j" + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 316, + 287, + 400 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 95, + 410, + 287, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 410, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 95, + 410, + 287, + 430 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {m a h} ^ {j} = \\sqrt {(\\mathbf {E} _ {j} - \\boldsymbol {\\mu}) \\mathbf {S} ^ {- 1} (\\mathbf {E} _ {j} - \\boldsymbol {\\mu})} \\tag {3}", + "image_path": "251b330ac490ad17169fee110ca32a5bd5ef4b81895d70315ae8312bdecdbe27.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu} = (\\mu_{1},\\dots,\\mu_{D})" + }, + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "type": "text", + "content": " is the mean vector and " + }, + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "type": "text", + "content": " is the positive-definite covariance matrix of " + }, + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 47, + 438, + 287, + 475 + ], + "type": "text", + "content": ". Then the regularization term is defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 120, + 483, + 287, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 483, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 120, + 483, + 287, + 516 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m a h} ^ {j} = \\frac {1}{K} \\sum_ {j = 1} ^ {k} \\mathcal {D} _ {m a h} ^ {j} \\tag {4}", + "image_path": "f0d84f6ff6acbcaa3f657d8b386f0d849434c1f1e9293f269e63edf884bd22df.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 525, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 287, + 548 + ], + "type": "text", + "content": "Overall, our model is optimized with a mixture of two losses:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 110, + 548, + 287, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 548, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 110, + 548, + 287, + 582 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {l o s s}} = \\mathcal {L} _ {\\text {c e}} + \\lambda \\sum_ {j = 1} ^ {K} \\mathcal {L} _ {\\text {m a h}} ^ {j}. \\tag {5}", + "image_path": "dadf46726a1730b768dc961c250b4f63f1c5277afa5a0c622c821a84ed5d9652.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": "After training, we have the embedding matrix " + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": " which will be used for searching the attributes from the attribute concept pool " + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": ". Note that for " + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{E} \\in \\mathbb{R}^{K*D}" + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": ", each row of " + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": "-dimensional vector. We denote the " + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": "-th row of " + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_j" + }, + { + "bbox": [ + 47, + 587, + 287, + 647 + ], + "type": "text", + "content": ". We use greedy search as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 657, + 226, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 657, + 226, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 226, + 677 + ], + "type": "interline_equation", + "content": "\\mathbf{T}_{j}^{*} = \\operatorname *{arg max}_{i\\in \\{1,\\dots ,N\\}}\\cos (\\mathbf{T}_{i},\\mathbf{E}_{j}),", + "image_path": "d4e6fc5424ec910cc5adff3d6a235dc1cebc3cd5965a1f89c92343adb28965d5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 118, + 681, + 287, + 695 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 681, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 118, + 681, + 287, + 695 + ], + "type": "interline_equation", + "content": "s. t. \\mathbf {T} _ {j} ^ {*} \\neq \\mathbf {T} _ {k} ^ {*}, \\forall 1 \\leq k < j, \\tag {6}", + "image_path": "fcb64459682798ccc644b54b395d7aeaba77148b665cfdfb280f7b5bfd56e739.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 118, + 697, + 216, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 697, + 216, + 709 + ], + "spans": [ + { + "bbox": [ + 118, + 697, + 216, + 709 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 118, + 697, + 216, + 709 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 118, + 697, + 216, + 709 + ], + "type": "text", + "content": " is from 1 to " + }, + { + "bbox": [ + 118, + 697, + 216, + 709 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 118, + 697, + 216, + 709 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": "As " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " iterates from 1 to " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": ", we can find " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " attribute embeddings " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_j^*, j \\in \\{1, \\dots, K\\}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": ", which corresponds to " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " expressive attribute concepts and are the condensed features containing the necessary knowledge for the task. With the selected attributes, we can calculate the semantic vector of each image as in Eq. (1), where each dimension of the vector is a similarity score between the image and an attribute. We evaluate the performance of these semantic vectors with linear probes, and the obtained linear model is used for inference and analysis." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 203, + 386, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 203, + 386, + 217 + ], + "spans": [ + { + "bbox": [ + 306, + 203, + 386, + 217 + ], + "type": "text", + "content": "3. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 222, + 422, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 222, + 422, + 236 + ], + "spans": [ + { + "bbox": [ + 306, + 222, + 422, + 236 + ], + "type": "text", + "content": "3.1. Experimental Setup" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 240, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 240, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 545, + 372 + ], + "type": "text", + "content": "Datasets We conduct our experiments on 8 different image classification datasets, including: CUB [44], CIFAR-10 and CIFAR-100 [24], Food-101 [4], Flower [31], Oxford-pets [33], Stanford-cars [23], Imagenet [9]. For Imagenet, it is not trivial to analyze all 1000 diverse classes. So we narrow the scope to 397 animal classes, with 509,230/19,850 samples for train/test. We denote this subset as Imagenet-Animals. For other datasets, most of them include images within a specific domain (CUB, Flower, Food, Oxford-pets, Stanford-cars), while CIFAR-10 and CIFAR-100 contain broader classes that lie across domains." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "text", + "content": "Implementation Details Our method involves two stages of training. The first stage consists of task-guided learning of a dictionary " + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "text", + "content": " to approximate CLIP text embeddings and using this dictionary to find " + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "text", + "content": " attributes for visual recognition. For the Mahalanobis distance, the parameter " + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "text", + "content": " is tuned with a grid search in " + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\{1, 0.1, 0.01, 0.001, 0\\}" + }, + { + "bbox": [ + 305, + 388, + 545, + 544 + ], + "type": "text", + "content": ". The second stage is one-layer linear probing to classify semantic vectors. The batchsize is set to 4,096 for all datasets except 32,768 on Imagenet-Animals for faster converging. We set the number of epochs to 5,000 epochs with early stopping. The learning rate is set to 0.01 in all experiments with an Adam optimizer [20]. Unless specified, we use GPT-3 and CLIP ViT-B/32 for all performance comparison." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 557, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 557, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 305, + 557, + 545, + 689 + ], + "type": "text", + "content": "Baselines We compare with state-of-the-art works that leverage attributes either from human annotations or from LLMs. For a fair comparison, we use linear probes to evaluate all methods: (1) CompDL [56] builds semantic vectors using CLIP scores between human-designed attributes and images. (2) LaBO [52] is a recent work that builds semantic vectors with a large set of attributes from LLMs. (3) Human [44, 22]. Attribute labels for each image are annotated by humans. We compare with two versions: binary labels for each attribute, and calibrated labels with confidence scores given by annotators." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "To validate the effectiveness of learning-to-search, we explore other baselines: (1) K-means. Perform K-means" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3093" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 535, + 203 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 535, + 203 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 535, + 203 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 535, + 203 + ], + "type": "table", + "html": "
DatasetsCUBCIFAR-10CIFAR-100Flower
K32200400810206410020032102204
LaBo-60.9362.61-78.1184.84-75.1076.94-80.9886.76
Ours60.2763.8864.0577.4780.0987.9973.3175.1277.2980.8887.2689.02
DatasetsFoodOxford_PetsStanfordCarsImagenet_Animals
K6410120216377464196392128397794
LaBo-79.9581.33-76.9184.33-72.3374.39-74.8875.49
Ours78.4180.2281.8576.2983.1585.9172.0774.5775.5674.4875.6975.83
", + "image_path": "b6c1821c8e3d6648764beab22569ff1a36bf29a7f14bdc81630eef31b52309f4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 254, + 287, + 324 + ], + "blocks": [ + { + "bbox": [ + 46, + 210, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 210, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 547, + 236 + ], + "type": "text", + "content": "Table 1: Comparison with state-of-the-art. LaBo is designed to use at least as many attributes as classes. We use “-” to denote non-applicability." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 254, + 287, + 324 + ], + "lines": [ + { + "bbox": [ + 48, + 254, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 48, + 254, + 287, + 324 + ], + "type": "table", + "html": "
K (# of attributes)81632312
Human Binary [44]4.027.3110.1147.38
Human Calibration [22]3.757.159.7843.37
CompDL [56]12.6426.4128.6952.60
Ours31.6748.5560.2765.17
", + "image_path": "0d51d6add56ba8671251b624eef2ea1131bacd22fc7b50f05c64cff23169c231.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": "clustering on CLIP attribute embeddings, then find " + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": " attributes with nearest distance to each clustering center. Intuitively this can be a strong baseline, as " + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": " attributes close to each center can be distinctive. (2) Uniform Sampling from the large attribute pool. (3) SVD. After obtaining the attribute embeddings " + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": ", we run SVD decomposition of " + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": " to get the top " + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": " vectors and find attributes with the largest similarity with the " + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": " important vectors. (4) Similarity. We calculate the average score of each attribute across all images and then find the " + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": " attributes with the largest average scores. (5) Img Features. Black-box linear probing on latent image features with two linear layers and an intermediate dimension " + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 358, + 289, + 515 + ], + "type": "text", + "content": " as a reference." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 525, + 133, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 133, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 133, + 537 + ], + "type": "text", + "content": "3.2. Main Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "type": "text", + "content": "Comparison with previous work We first compare our method with LaBo [52]. It is designed to use " + }, + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "type": "inline_equation", + "content": "M_{c}" + }, + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "type": "text", + "content": " concepts per class with default number of 50, which corresponds to 10,000 attributes for CUB. For fair-comparison, we set " + }, + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "type": "inline_equation", + "content": "M_{c}" + }, + { + "bbox": [ + 46, + 544, + 287, + 687 + ], + "type": "text", + "content": " as 1 and 2 in the experiments. As shown in Table 1, our method outperforms LaBo with the same number of attributes on both the full and few-shot setting. Furthermore, our method can achieve similar accuracy with only a smaller number of attributes (e.g., 32 attributes for CUB). These results suggest that our learned attributes are discriminative enough to classify the images, despite given much fewer attributes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "content": "We then further compare with human annotations from CUB. For " + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "inline_equation", + "content": "K < 312" + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "content": ", we select attributes based on their" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 255, + 422, + 346 + ], + "blocks": [ + { + "bbox": [ + 309, + 255, + 422, + 346 + ], + "lines": [ + { + "bbox": [ + 309, + 255, + 422, + 346 + ], + "spans": [ + { + "bbox": [ + 309, + 255, + 422, + 346 + ], + "type": "image", + "image_path": "8fa097bb07ae87b8730115ec4af4fec5b0f13685698b69d15d5b5e9f9ce646d6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 356, + 423, + 391 + ], + "lines": [ + { + "bbox": [ + 306, + 356, + 423, + 391 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 423, + 391 + ], + "type": "text", + "content": "Figure 3: Performance comparison with random or similar words on CUB." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 432, + 258, + 547, + 345 + ], + "blocks": [ + { + "bbox": [ + 55, + 333, + 279, + 344 + ], + "lines": [ + { + "bbox": [ + 55, + 333, + 279, + 344 + ], + "spans": [ + { + "bbox": [ + 55, + 333, + 279, + 344 + ], + "type": "text", + "content": "Table 2: Comparison with human annotations on CUB." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 432, + 258, + 547, + 345 + ], + "lines": [ + { + "bbox": [ + 432, + 258, + 547, + 345 + ], + "spans": [ + { + "bbox": [ + 432, + 258, + 547, + 345 + ], + "type": "table", + "html": "
Examples
Rboy champagne\nallied whose acrobat\neight centered lobby heads
Sred,gray,snow wings\norange wings\nlime,navy wings
Gsloping forehead\ndistinctive white throat\nbright red head and breast
", + "image_path": "2a388d00423951ce88c7fb94d0eabe8ba7f0a1bbd19e5229422d30b43147baf6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 430, + 352, + 546, + 388 + ], + "lines": [ + { + "bbox": [ + 430, + 352, + 546, + 388 + ], + "spans": [ + { + "bbox": [ + 430, + 352, + 546, + 388 + ], + "type": "text", + "content": "Table 3: Examples from Random (R), Silimlar (S), GPT-3 (G) attributes" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 414, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 498 + ], + "type": "text", + "content": "accumulated confidence score for all samples. As shown in Table 2, human annotated attributes are more noisy than CLIP similarities. With the same attributes, CLIP scores from CompDL build more expressive features. Furthermore, our LLM-suggested attributes significantly outperform human designs, e.g. by using 16 attributes we achieve similar performance as 312 attributes defined by humans." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": "Large-scale attributes behave like random words We present our finding that LLM-generated attributes in a large quantity behave like random words. Specifically, we compare our method of using GPT-3 attributes with random or similar words. Here, we constructed random words by randomly choosing 1-5 words from the entire English vocabulary, and semantically similar words by combining 1-3 random colors with the noun \"wings\" as suffix. As shown in Figure 3, when " + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "inline_equation", + "content": "K = 512" + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": ", random words perform as well as GPT-3 attributes in terms of classification accuracy. Even reducing " + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": " from 512 to 256 does not significantly hurt its performance. But when " + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": " is small (e.g., 64), the performance of random words drops dramatically. We conjecture that it is because text embeddings randomly drawn from CLIP are nearly orthogonal bases [45]. Given an image feature " + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\in \\mathbb{R}^D" + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": ", projection with a set of " + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "inline_equation", + "content": "K = D" + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": " orthogonal bases can perfectly preserve its information. 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416, + 269 + ], + "blocks": [ + { + "bbox": [ + 299, + 185, + 416, + 269 + ], + "lines": [ + { + "bbox": [ + 299, + 185, + 416, + 269 + ], + "spans": [ + { + "bbox": [ + 299, + 185, + 416, + 269 + ], + "type": "image", + "image_path": "f689137bc6edc6bcba9b58ee9234988c780b72303457a3ea8664ed0e48df253b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 274, + 386, + 283 + ], + "lines": [ + { + "bbox": [ + 329, + 274, + 386, + 283 + ], + "spans": [ + { + "bbox": [ + 329, + 274, + 386, + 283 + ], + "type": "text", + "content": "(g) StanfordCars" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 297, + 546, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 297, + 546, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 546, + 321 + ], + "type": "text", + "content": "Figure 4: Overall Performance on all datasets. X-axis: number of attributes, Y-axis: Accuracy " + }, + { + "bbox": [ + 46, + 297, + 546, + 321 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 297, + 546, + 321 + ], + "type": "text", + "content": ", “(f)” means “full”, i.e., all attributes in the pool are used. Uniform refers to uniform sampling." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 420, + 185, + 538, + 269 + ], + "blocks": [ + { + "bbox": [ + 420, + 185, + 538, + 269 + ], + "lines": [ + { + "bbox": [ + 420, + 185, + 538, + 269 + ], + "spans": [ + { + "bbox": [ + 420, + 185, + 538, + 269 + ], + "type": "image", + "image_path": "cb8746e5d59efaefc70bb897c85f180abec40a2519e73ae51e513dc190b02f11.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 274, + 515, + 283 + ], + "lines": [ + { + "bbox": [ + 443, + 274, + 515, + 283 + ], + "spans": [ + { + "bbox": [ + 443, + 274, + 515, + 283 + ], + "type": "text", + "content": "(h) Imagenet_Animals" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 342, + 289, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 289, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 289, + 462 + ], + "type": "text", + "content": "explore how similar words (e.g., red wings, yellow wings) behave. Embeddings of similar words in a trained language model are not orthogonal bases hence the projection will lose information when " + }, + { + "bbox": [ + 46, + 342, + 289, + 462 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 342, + 289, + 462 + ], + "type": "text", + "content": " is large (e.g., intuitively it is hard to classify 200 bird species using only the color combination of wings). But as " + }, + { + "bbox": [ + 46, + 342, + 289, + 462 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 342, + 289, + 462 + ], + "type": "text", + "content": " gets smaller, since those similar words have close semantic meanings, they start to outperform random words. Overall, these findings motivate us to find a concise set of meaningful attributes while maintaining competitive performance." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": "Number of attributes and selection methods Finally, we study performance change under different number of attributes in Figure 4. First, our method is competitive with image features when " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " is large. Reducing number of attributes " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " to the number of classes " + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": " (e.g., 512 to 128 for CUB) does not significantly hurt performance, even for baseline methods. This validates our hypothesis that there is plenty of redundant information in the semantic space when the number of attributes is large (as used in LaBO [52]). It is possible to find a subset of expressive attributes for visual recognition. Second, we also consistently outperform other methods such as K-means clustering and uniform sampling, demonstrating the effectiveness of our task-guided searching method. Third, a heuristic design such as K-means performs similar as uniform selection. Note that though there is a performance gap between image features and using attributes, the gap can be minimized by using a stronger VLM, as the classification accuracy of attributes relies on the accurate estimation of the correlation between images and attributes (see more results in appendix D)." + } + ] + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 307, + 340, + 547, + 396 + ], + "blocks": [ + { + "bbox": [ + 307, + 340, + 547, + 396 + ], + "lines": [ + { + "bbox": [ + 307, + 340, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 307, + 340, + 547, + 396 + ], + "type": "table", + "html": "
DatasetsCUBCIFAR-100
K8163281632
GPT-331.6748.5560.2734.7752.2466.30
GPT-3-Imagenet30.8149.2960.4133.8051.0165.61
", + "image_path": "467452fb764c2881ff03caf1fb8264daf1175c5eb81d00982be9f90f50bc075a.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 317, + 403, + 533, + 416 + ], + "lines": [ + { + "bbox": [ + 317, + 403, + 533, + 416 + ], + "spans": [ + { + "bbox": [ + 317, + 403, + 533, + 416 + ], + "type": "text", + "content": "Table 4: Ablation study w.r.t. different concept pools." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 437, + 400, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 400, + 451 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 400, + 451 + ], + "type": "text", + "content": "3.3. Ablation Study" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 456, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 564 + ], + "type": "text", + "content": "Robustness to the attribute pool First, we aim to explore the effects of different initialized attribute concept pools generated by LLMs. On CUB and CIFAR-100, we compare two attribute pools, attributes generated from classes in each dataset, and attributes generated from the full set of ImageNet classes. As shown in Table 4, even with the large and noisy attributes from ImageNet, our method can still efficiently find a small number of representative attributes for a task, and obtains competitive classification performance." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of learning-to-search Then, we discuss possible choices for selection out of the large attribute pool. Results are shown in Table 5 with the following observations: heuristic methods such as K-means and SVD are not optimal choices for identifying the most distinctive attributes. In fact, they are sometimes less effective than uniform sampling. This is likely because we need to identify the most distinguishing attributes for visual recognition, rather than the most diverse ones based on text embeddings. 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(1) The upper half of each figure shows important attributes for two classes of birds. We choose 6 out of 32 attributes with highest importance scores, which are computed by multiplication between clip scores and weights in the linear probe, defined in Eq. (7). (2) The lower half of each figure demonstrates the intervention on the semantic vector (i.e., CLIP scores) to correct the prediction, we use " + }, + { + "bbox": [ + 45, + 241, + 547, + 301 + ], + "type": "inline_equation", + "content": "\\delta = 0.03" + }, + { + "bbox": [ + 45, + 241, + 547, + 301 + ], + "type": "text", + "content": " for all interventions on clip scores as an empirical value. 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DatasetsCUBCIFAR-100
K8163281632
K-means16.8321.0232.7625.3945.2664.41
Uniform7.0225.9840.5828.0747.1464.34
SVD6.5220.0235.8329.0650.0064.99
Similarity4.739.7218.0026.7545.6162.79
Ours31.6748.5560.2734.7752.2466.30
", + "image_path": "53c04db1ac88bd2f6cb0cc3a8901edb9d1f902043e6679fb150c003553eba721.jpg" + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "table_body" + } + ], + "index": 46 + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "content": "Effectiveness of regularization We compare the Mahalanobis distance (MAH) with two variations: (1) COS: For each vector " + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_j" + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i" + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "content": " (of the " + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "content": "-th attribute) in the concept pool, we computed averaged cosine distance as follows:" + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 102, + 536, + 232, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 536, + 232, + 570 + ], + "spans": [ + { + "bbox": [ + 102, + 536, + 232, + 570 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c o s} = \\frac {1}{K ^ {2}} \\sum_ {j = 1} ^ {K} \\sum_ {i = 1} ^ {K} \\frac {\\mathbf {T} _ {i} ^ {\\top} \\mathbf {E} _ {j}}{| | \\mathbf {T} _ {i} | | | | \\mathbf {E} _ {j} | |}", + "image_path": "bbe517ab53d252ac5ba94fc3e2b480bd14b7861fa960cd8842249fd4282f6227.jpg" + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": "(2) " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "CE" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": ": Learning with Eq. (2) only. Results are in Table 6. Overall, Mahalanobis distance is an effective constraint to encourage the dictionary " + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 578, + 287, + 627 + ], + "type": "text", + "content": " to be close to the distribution of CLIP embeddings." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 47, + 635, + 278, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 278, + 648 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 278, + 648 + ], + "type": "text", + "content": "3.4. Analysis of Interpretability and Interactivity" + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 46, + 654, + 260, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 260, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 260, + 665 + ], + "type": "text", + "content": "We perform analysis and visualizations to show that:" + } + ] + } + ], + "index": 52 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "(1) Our learned attributes provide interpretability. As shown in Figure 5, the upper half presents the images in a class " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " and high relevant attributes to recognize them. Specifically, we denote " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{K_C * K}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " as the weight of the" + } + ] + } + ], + "index": 53 + }, + { + "type": "table", + "bbox": [ + 348, + 320, + 504, + 452 + ], + "blocks": [ + { + "bbox": [ + 46, + 422, + 287, + 447 + ], + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 447 + ], + "type": "text", + "content": "Table 5: Ablation study w.r.t. different attribute selection strategies." + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 348, + 320, + 504, + 452 + ], + "lines": [ + { + "bbox": [ + 348, + 320, + 504, + 452 + ], + "spans": [ + { + "bbox": [ + 348, + 320, + 504, + 452 + ], + "type": "table", + "html": "
DatasetCUB
K8163264
MAH30.7647.8760.2764.25
COS28.9647.3558.2763.25
CE31.6748.5555.8860.73
DatasetCIFAR-100
K8163264
MAH34.7752.2465.9173.31
COS31.9851.1565.0272.80
CE32.4550.8366.2973.25
", + "image_path": "e8cb5f115d58cfa40817275fb0528db6434217c6787217b7bdf36200e2428f82.jpg" + } + ] + } + ], + "index": 54, + "angle": 0, + "type": "table_body" + } + ], + "index": 54 + }, + { + "bbox": [ + 317, + 460, + 533, + 472 + ], + "lines": [ + { + "bbox": [ + 317, + 460, + 533, + 472 + ], + "spans": [ + { + "bbox": [ + 317, + 460, + 533, + 472 + ], + "type": "text", + "content": "Table 6: Ablation study w.r.t. different regularization." + } + ] + } + ], + "index": 55, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "text", + "content": "FC layer in linear probing, where " + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "inline_equation", + "content": "K_{C}, K" + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "text", + "content": " are the number of classes and attributes. Then for each image " + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "text", + "content": " and its semantic vector " + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{K}" + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "text", + "content": ", we multiply the corresponding score vector of image " + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "text", + "content": " with the corresponding row of the FC layer " + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{c}" + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "text", + "content": " to compute Importance Score " + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\mathbf{IS} \\in \\mathbb{R}^{K}" + }, + { + "bbox": [ + 304, + 492, + 545, + 553 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 395, + 561, + 545, + 573 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 561, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 395, + 561, + 545, + 573 + ], + "type": "interline_equation", + "content": "\\mathbf {I S} = \\mathbf {W} _ {c} \\otimes \\mathbf {A} \\tag {7}", + "image_path": "2b477787292246bfc0c3b0f3a255ebb6691a36137b68706d489cfad54623641e.jpg" + } + ] + } + ], + "index": 57 + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "text", + "content": " means element-wise multiplication. Then we present attributes with the top absolute values of IS averaged over all samples in a class from the test set, with blue/orange bars indicating the positive/negative importance. Higher absolute values denote greater significance. Since all CLIP scores are positive [16], the positivity or negativity of high IS signifies their relevance to the class." + } + ] + } + ], + "index": 58 + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": "(2) Our concise set of attributes enables simple interactivity. As shown in the lower half of Figure 5, we can correct the model's wrong predictions during inference by changing only a single similarity score between an image" + } + ] + } + ], + "index": 59 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3096" + } + ] + } + ], + "index": 60 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 545, + 358 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 545, + 358 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 545, + 358 + ], + "type": "table", + "html": "
CUB· distinctive white throat\n· bright red head and breast\n· pinkish red breast patch with white edges\n· bright yellow, green and blue plumage\n· Red face with a black cap and bib\n· Short legs for perching on reeds\n· white and black spotted breast\n· sloping foreheadCIFAR10· antlers (in males)\n· pointed bow and stern\n· propellers or jet engines\n· moist slimy skin\n· long head with a mane and tail\n· landing gear\n· portholes along the hull\n· four wheels
CIFAR100· a seat for the rider\n· catkins (flowers) in spring\n· many windows in the façade\n· five pairs of walking legs\n· smooth oval shaped sepals\n· four-limbed primate\n· headboard and footboard\n· towers with conical roofsFlower· Shiny wax coating on the spathe\n· large, yellow or orange flower head\n· bright pink color\n· large, white petals with a yellow center\n· pink to purple colored petals with red lips\n· bright red and yellow petals\n· pink, white, or lavender flowers with five petals\n· deep purple or blue flowers
Food· elbow macaroni noodles\n· Shredded pork meat in the middle of the sandwich\n· large pieces of clams visible in the chowder\n· usually served in a warm wrap or burrito shell\n· sliced into thin wedges or cubes\n· thinly sliced raw fish\n· tender squid rings inside\n· a crisp, fried pastry dough exteriorOxford Pets· black and tan coloring\n· short coat of glossy black fur\n· Long legs and neck\n· Shade of red or wheaten color\n· large, round eyes\n· Pointed ears\n· white blaze on face and chest\n· greyish blue fur with silver tips
Imagenet Animals· male finches have a bright red breast\n· brownish-yellow fur\n· small, four-limbed canid\n· long, black, shiny body\n· the carapace is rough and bumpy\n· white spots on the crab's shell\n· English setters are bred in England\n· long, wire-haired coatStanford Cars· signature Lincoln split headlamps\n· large front grille with the signature BMW kidney shape\n· large size with a wheelbase of 149.4 inches\n· "4Runner" badge on the rear liftgate\n· signature SRT8 grille with crosshair pattern\n· Porsche logo on front grille and trunk lid\n· S6 badge on the trunk lid\n· unique HUMMER H2 logo on front grille
", + "image_path": "30ab7324d9b797f4e40184d89755342df4db6857406a402efcf77b6bd9db06ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 400, + 288, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 288, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 288, + 460 + ], + "type": "text", + "content": "and the attribute that the CLIP model made a mistake on. This is a significant simplification compared with previous work [22] where they need to manipulate scores from a group of concepts for the CUB dataset. We present more user studies in appendix E." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 468, + 270, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 270, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 270, + 479 + ], + "type": "text", + "content": "3.5. Visualization of Our Discovered Attributes" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 653 + ], + "type": "text", + "content": "We show our learned descriptive attributes with " + }, + { + "bbox": [ + 46, + 486, + 287, + 653 + ], + "type": "inline_equation", + "content": "K = 8" + }, + { + "bbox": [ + 46, + 486, + 287, + 653 + ], + "type": "text", + "content": " in Figure 6. Intuitively, we can observe these attributes are distinctive for each domain. Take birds recognition (CUB) as an example, the eight attributes covered most of the body parts of a bird (head, breast, legs, etc.). As we are condensing knowledge from hundreds of bird classes, each attribute broadly covers many categories. A bright red head and breast can be a noticeable visual attribute for many bird species, such as the Northern Cardinal and the Vermilion Flycatcher. Overall, explaining a domain with a few descriptive attributes is challenging, even for an expert with sufficient domain knowledge. But our model is able to automatically provide a level of knowledge to help humans understand how visual recognition works." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "We then present case studies on CIFAR-10 with 4 attributes and CLIP scores of 10 random images from each class in Figure 7. In general, each image is activated in an distinguishable way in the heat map. Some attributes can distinguish a few classes, for example, cat and dog have" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 399, + 545, + 502 + ], + "blocks": [ + { + "bbox": [ + 103, + 367, + 488, + 379 + ], + "lines": [ + { + "bbox": [ + 103, + 367, + 488, + 379 + ], + "spans": [ + { + "bbox": [ + 103, + 367, + 488, + 379 + ], + "type": "text", + "content": "Figure 6: A concise set of 8 descriptive attributes learned for each dataset with sampled images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 399, + 545, + 502 + ], + "lines": [ + { + "bbox": [ + 307, + 399, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 307, + 399, + 545, + 502 + ], + "type": "image", + "image_path": "b8e7d25ac801a5fef5ea03e0fca45d515da4b6f9ea076ce89d132d6863e3494a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 514, + 545, + 539 + ], + "lines": [ + { + "bbox": [ + 305, + 514, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 305, + 514, + 545, + 539 + ], + "type": "text", + "content": "Figure 7: Case study on CIFAR-10. The numbers are CLIP similarity scores between each image and attributes." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 561, + 545, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 561, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 305, + 561, + 545, + 596 + ], + "type": "text", + "content": "higher activation on \"fur coat\" compared to automobile or truck. Thus \"fur coat\" may be an important feature to differentiate animals and vehicles." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 609, + 389, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 389, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 389, + 621 + ], + "type": "text", + "content": "4. Related work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Interpretable Deep Learning Interpretability is a critical research problem for deep learning with black-box models [11, 34, 37, 38, 13, 2, 50]. Some works study model behavior and explore if deep models could encode concepts for understanding [19, 28, 49, 29]. For image classification, preliminary attempts aim to describe objects with attributes [12, 26, 25] or building concept bottleneck mod" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3097" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "els [22, 56, 55, 6]. These methods require in-depth human analysis and intensive labeling, which are impractical to scale to more classes and domains." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 289, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 289, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 289, + 324 + ], + "type": "text", + "content": "Recent works [30, 35, 52] tackle this problem by using GPT-3 as a knowledge base to query visual attributes or concepts. Specifically, [30, 35] generate descriptions with LLMs, and use them for knowledge-aware prompting for each class to improve zero-shot performance of CLIP [36]. For example, given the class name \"bee\", it will augment it with attributes such as \"A bee with black and yellow body\". Our work differs in that our goal is to learn representative attributes for visual recognition without using class names. LABO [52] extends the idea of concept bottleneck models by generating thousands of concepts from LLMs. Inspired by our finding that there is great redundancy in the large-scale attributes, we aim to learn a concise set of attributes that are initially generated from LLMs for each task, while maintaining the classification performance as possible. Concise attributes also enable stronger interpretability and interactivity, and can help humans to summarize critical knowledge for visual recognition in an automatic way." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 337, + 289, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 289, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 289, + 540 + ], + "type": "text", + "content": "Foundation Models Recently, foundation models [3], which are pre-trained with a large amount of data and large model sizes, have revolutionized machine learning research and many fields. These models are shown to be adaptable to a wide range of downstream tasks for computer vision [15, 46, 58], natural language processing [10, 7, 57, 48] and cross-modal research [27, 42, 17, 14]. One direction is to train LLMs such as GPT3 [5] and ChatGPT with massive text to serve as a powerful knowledge base with high interactivity and beyond. Another direction is to build VLMs [36, 51, 54, 53, 1], which connect vision and language by pre-training with image-text pairs and learning a joint embedding space for both. In this work, we use LLMs as a knowledge base for querying visual related knowledge, and use VLMs to bridge vision and text, presenting a new paradigm for interpretable visual recognition in the era of foundation models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 550, + 117, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 117, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 117, + 562 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "There are many interesting topics to explore with our new paradigm. First, our framework is a plug-and-play model that can be readily applied to many other vision tasks, by simply changing the task-guided learning objective to a particular task, e.g., classification losses for object detection, video understanding, and 3D classification. Furthermore, a concise set of descriptive attributes enables interactivity for vision models and empowers human-machine cooperation in a user-friendly way through natural language interfaces. Lastly, we show the potential of summarizing knowledge for challenging vision tasks in the new era of LLMs, which could have broad impact for various domains." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 379, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 379, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 379, + 83 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 91, + 547, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 212 + ], + "type": "text", + "content": "In this work, we propose a new paradigm for visual recognition that leverages a concise set of descriptive attributes. Motivated by our insightful finding that significant redundancy exists in massive LLMs-generated attributes, we design a simple yet effective searching method guided by image-level labels, to identify an informative subset. Our new paradigm is validated across 8 datasets to achieve strong classification accuracy with multiple benefits and broad impacts, including efficiency, interpretability, human interactivity, and knowledge summarization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 223, + 403, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 223, + 403, + 236 + ], + "spans": [ + { + "bbox": [ + 306, + 223, + 403, + 236 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 243, + 547, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 280 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 280 + ], + "type": "text", + "content": "We would like to sincerely thank the anonymous reviewers and chairs for their careful review of our work, with helpful and constructive suggestions to improve the paper." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 290, + 365, + 302 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 290, + 365, + 302 + ], + "spans": [ + { + "bbox": [ + 306, + 290, + 365, + 302 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 310, + 309, + 547, + 714 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 310, + 309, + 547, + 364 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 309, + 547, + 364 + ], + "spans": [ + { + "bbox": [ + 310, + 309, + 547, + 364 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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In this paper, we present Concordant Attention Learning (CAL), a novel framework that learns semantic-aligned representations for VI Re-ID. Specifically, we design the Target-aware Concordant Alignment paradigm, which allows target-aware attention adaptation when aligning heterogeneous samples (i.e., adaptive attention adjustment according to the target image being aligned). This is achieved by exploiting the discriminative clues from the modality counterpart and designing effective modality-agnostic correspondence searching strategies. To ensure semantic concordance during the cross-modal retrieval stage, we further propose MatchDistill, which matches the attention patterns across modalities and learns their underlying semantic correlations by bipartite-graph-based similarity modeling and cross-modal knowledge exchange. Extensive experiments on VI Re-ID benchmark datasets demonstrate the effectiveness and superiority of the proposed CAL.", + "bbox": [ + 76, + 342, + 473, + 676 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 707, + 209, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Person Re-identification (Re-ID) aims to associate person identities across non-overlapping cameras. It has gained increasing attention in recent years due to its practical applications in real-world surveillance systems. Conventional person Re-ID methods mainly focus on retrieving the same identity across visible (RGB) cameras [48, 29, 16, 23, 10]. Despite their remarkable success, they have limited applicability since visible cameras cannot capture discriminative information under poor-lighting conditions (e.g., at night). To improve the illumination robustness, infrared (IR) cameras are widely applied to cooperate with visible ones in", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d606ca4fac1a5800e24b1d535f9fcd07a13c330834ff54f8cc5c5ef01a8c0f05.jpg", + "image_caption": [ + "Figure 1. A high-level overview of typical local feature learning paradigms. (a) Splitting-based: The semantics of the hand-craft stripes are not always properly aligned. (b) Auxiliary-model-based: Pretrained auxiliary models are often error-prone due to the domain shifts (especially for infrared image). (c) Attention-based: Due to the inter-modal distribution gap, existing style-sensitive attention module with less descriptive learnable prototypes often fails to attend semantically consistent regions. (d) CAL (Ours): Our method can learn concordant attention by discriminative region mining, target-aware style-agnostic attention, and part-aligned knowledge exchange." + ], + "image_footnote": [], + "bbox": [ + 501, + 308, + 890, + 534 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "real-world surveillance systems. This increases the need to explore the Visible-Infrared Person Re-identification (VI Re-ID) problem, which aims to associate the person images taken by different spectrum cameras to achieve long-term person tracking in 24-hour surveillance systems.", + "bbox": [ + 496, + 715, + 893, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compared to traditional RGB-based re-identification, VI Re-ID is much more challenging due to the differences in spectral properties between visible and infrared images. This data heterogeneity can lead to severe misalignment in the feature space and large intra-class discrepancy, resulting in significant degradation in performance. In addition, similarly to RGB-based Re-ID tasks, VI Re-ID can also be", + "bbox": [ + 496, + 794, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11122", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "impacted by the changes in pose or background, resulting in increased difficulties.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent years have witnessed a surge of creative work on mitigating the modality gap for VI Re-ID [38, 43, 18, 44, 4, 20]. However, as most existing methods only consider learning global representations from the whole image, they fail to compare local details. In addition, owing to the shortcut learning characteristics [6], global-feature-based methods would tend to learn modality-specific shortcut patterns, making the learned features susceptible to concentrating on divergent regions in each modality and resulting in suboptimal performance. A seemingly straightforward solution is to learn semantic-aligned local features with either splitting-based [29, 8, 20], auxiliary-model-based methods [26, 19, 28, 1], or attention-base paradigms [18, 16, 33, 27] instead of the global ones. However, these methods also fail to achieve inter-modal semantic alignment, as demonstrated in Figure 1, and forcibly aligning these semantic-misaligned embeddings would inevitably injure the training process and compromise the performance.", + "bbox": [ + 75, + 122, + 472, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from these deep learning methods, human visual systems can naturally avoid the misalignment issue thanks to their target-aware comparison strategy. Considering the scenario of comparing two images of persons (referred to as \"base image\" and \"target image\", respectively), human vision systems would first identify multiple distinctive key regions (such as facial and clothing details) in the target image and then direct their attention to corresponding regions in the base image. In this manner, humans can always make perfect part-to-part comparisons since they are able to adaptively and accurately adjust their attention by referencing the key regions of the target image. This suggests that exploiting clues from the target image of the modality counterpart and exploring an effective cross-modal corresponding region-searching strategy can benefit in mitigating the inter-modal semantic misalignment issue.", + "bbox": [ + 75, + 393, + 472, + 636 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present Concordant Attention Learning (CAL), a novel framework that mimics the target-aware comparison behavior of human vision systems to learn semantic-aligned representations for VI Re-ID. Firstly, we devise the Target-aware Concordant Alignment (TCA) paradigm, which aims to exploit discriminative local clues from the target modality (i.e., the modality counterpart) when aligning heterogeneous embeddings. The proposed TCA consists of three components: (1) Discriminative Region Mining: identifying diverse and discriminative key regions from the feature maps of each training sample; (2) Target-aware Style-agnostic Attention Adapter: taking the selected key regions from the target modality as part queries, and applying target-aware refinement to adapt the feature attention and generate part-aligned embeddings;", + "bbox": [ + 75, + 637, + 472, + 864 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(3) Part-aligned Metric Learning: clustering or separating the part-aligned embeddings across modalities according to their identity labels. Even though this target-aware refinement scheme can mitigate the modality discrepancy by leveraging the clues from the target modality, it brings higher computational costs during inference. Because it needs to be carried out for all query-gallery pairs, and the gallery set is generally large. To this end, we further propose MatchDistill. First, we need to associate the generated part queries of different modalities to guarantee that the subsequent distillation is conducted on semantic-aligned features. This is achieved by modeling the correlations of their corresponding attention maps with bipartite graphs and conducting Cross-modal Query Matching (CQM) to find the optimal matches. After that, a dual-level knowledge distillation loss is designed to allow cross-modality knowledge exchange between the best-matched queries. This can facilitate the learning of underlying relationships between the visible and infrared modalities. After training with MatchDistill, each modality can learn knowledge from its modality counterpart, and no cross-modal interaction is needed during inference.", + "bbox": [ + 500, + 90, + 890, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overall, our contributions are summarized as follows:", + "bbox": [ + 517, + 425, + 874, + 439 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Concordant Attention Learning (CAL), a target-aware training paradigm that mimics human behavior and learns concordant attention to alleviate the inter-modal attention bias issue for VI Re-ID.", + "- To enable part-aligned metric learning, we present Target-aware Concordant Alignment (TCA), which leverages cross-modal clues and allows adaptive attention adjustment when aligning heterogeneous embeddings.", + "- We propose MatchDistill, which matches the attention patterns across modalities and learns their underlying semantic correlations by bipartite-graph-based similarity modeling and cross-modal knowledge exchange.", + "- Extensive experiments demonstrate that the proposed CAL archives state-of-the-art performance on both the SYSU-MM01 [38] and RegDB [25] datasets." + ], + "bbox": [ + 500, + 444, + 890, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 688, + 640, + 704 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visible-Infrared Person Re-ID. Visible-Infrared Person Re-ID (VI Re-ID) has drawn increasing attention in recent years [43, 17, 39, 12, 20]. Mainstream VI Re-ID paradigms focus on bridging the modality gap via designing metric learning constraints [45, 42, 40], normalizing feature statistics [14, 39, 13], synthesizing auxiliary training samples [34, 3, 49, 24], or developing modality-specific and modality-shared feature learning paradigms [5, 22, 30]. However, these methods only consider learning global representations from entire images without considering the local information of images, leading to limited expressiveness of learned features. A few works also attempt to learn local", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1Note that we use the term \"region\" and \"part\" interchangeably to denote the same thing.", + "bbox": [ + 75, + 875, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11123", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "features for VI Re-ID [8, 20, 41, 47] by splitting the feature maps into several hand-craft stripes. However, due to inaccurate detection boxes, pose variations, and occlusion, the hand-craft stripes are not always well-aligned, resulting in unsatisfactory performance.", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Local Feature Learning in Person Re-ID. Local feature learning is an important research direction for person re-identification since learning part aggregated features makes the model robust against misalignment [44]. It can be roughly divided into splitting-based methods, auxiliary-model-based methods, and attention-based methods. Splitting-based methods [29, 8, 20] focus on learning local features from horizontal-divided regions, which now serve as a strong part feature learning baseline. However, due to inaccurate detection boxes, pose variations, and occlusion, the semantics of the hand-craft stripes are not well aligned. The auxiliary-model-based methods [26, 19, 28, 1] often adopt off-the-shelf auxiliary human parsing or pose estimation networks to obtain semantically meaningful body parts. However, they require additional computational costs and are prone to noisy estimation, especially when the data distribution varies. The attention-based methods focus on exploiting attention mechanisms to localize discriminative human parts and have achieved great success [18, 16, 33, 27]. However, these methods cannot be directly applied to the cross-modality scenario of VI Re-ID due to the inter-modal semantic misalignment issue as discussed in Sec. 1.", + "bbox": [ + 75, + 169, + 472, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 527, + 212, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Intuition of Target-aware Alignment", + "text_level": 1, + "bbox": [ + 76, + 551, + 393, + 569 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\pmb{x}^k$ denote the training images of modality $k$ , where $k \\in \\{V, I\\}$ ( $V$ for visible modality and $I$ for infrared modality). The visible and infrared samples in the dataset are denoted by $\\mathcal{V} = \\{\\pmb{x}_j^V, y_j^V\\}_{j=0}^{N_v}$ and $\\mathcal{I} = \\{\\pmb{x}_j^I, y_j^I\\}_{j=0}^{N_i}$ , respectively, where $N_v$ and $N_i$ are the numbers of samples of each modality in the dataset, and $y_j^k$ is the corresponding identity label of the $j$ -th sample from modality $k$ . The goal of Visible-Infrared Person Re-identification is to match the person identities across modalities according to feature similarities. Therefore, it is essential to reduce the large intra-class variation between heterogeneous samples. Existing paradigms often attempt to reduce the cross-modal intra-class variation by directly optimizing", + "bbox": [ + 75, + 575, + 468, + 773 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {i, j} \\left[ \\mathbb {1} \\left(y _ {i} ^ {V} = y _ {j} ^ {I}\\right) \\cdot \\mathrm {d} \\left(f \\left(\\boldsymbol {x} _ {i} ^ {V}\\right), f \\left(\\boldsymbol {x} _ {j} ^ {I}\\right)\\right) \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 777, + 468, + 804 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f$ denotes the feature extractor, and $\\mathrm{d}(\\cdot, \\cdot)$ represents the distance between features. However, as discussed in Sec. 1, the attention misalignment issue could injure the training process and compromise performance. We thus endow the model with the ability to adaptively adjust the attention according to the target being compared to achieve", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "attention consensus. First, the Discriminative Region Mining (DRM) module, formulated as $\\gamma(\\cdot)$ , is introduced to disentangle the global features into diverse key body parts. We then devise the Target-aware Style-agnostic Attention Adapter (TSAA) to allow adaptive style-agnostic attention adjustment according to any given part queries regardless of the image styles. The feature extractor is then reformulated as $f(\\pmb{x},\\pmb{p})$ to represent the above dynamic attention adjustment process, where $\\pmb{p}$ denotes the given body parts. The objective function to reduce the cross-modal intra-class variation can then be defined as", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {i, j, k} \\left[ \\mathbb {1} \\left(y _ {i} ^ {V} = y _ {j} ^ {I}\\right) \\cdot \\mathrm {d} \\left(f \\left(\\boldsymbol {x} _ {i} ^ {V}, \\gamma \\left(\\boldsymbol {x} _ {j} ^ {I}\\right) _ {k}\\right), f \\left(\\boldsymbol {x} _ {j} ^ {I}, \\gamma \\left(\\boldsymbol {x} _ {j} ^ {I}\\right) _ {k}\\right)\\right) + \\right. \\tag {2} \\\\ \\mathbb {1} (y _ {i} ^ {I} = y _ {j} ^ {V}) \\cdot \\mathrm {d} \\big (f (\\pmb {x} _ {i} ^ {I}, \\gamma (\\pmb {x} _ {j} ^ {V}) _ {k}), f (\\pmb {x} _ {j} ^ {V}, \\gamma (\\pmb {x} _ {j} ^ {V}) _ {k}) \\big) \\Big ]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 267, + 890, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this manner, the embeddings being optimized can achieve semantic concordance since the same queries are used to guide feature attention (for instance, $f(\\pmb{x}_i^V, \\gamma(\\pmb{x}_j^I)_k)$ and $f(\\pmb{x}_j^I, \\gamma(\\pmb{x}_j^I)_k)$ correspond to the same semantic region since they are refined using the same part query $\\gamma(\\pmb{x}_j^I)_k$ ). This also allows cross-modal interaction to facilitate the learning of underline relationships between modalities. The overall pipeline is depicted in Figure 2, and more details will be introduced in the following subsections.", + "bbox": [ + 496, + 330, + 890, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Target-aware Concordant Alignment", + "text_level": 1, + "bbox": [ + 500, + 483, + 821, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Discriminative Region Mining", + "text_level": 1, + "bbox": [ + 500, + 508, + 764, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Discriminative Region Mining module aims to discover several diverse discriminative key regions from the feature maps $X \\in \\mathbb{R}^{C \\times H \\times W}$ derived from the backbone network, where $C$ , $H$ , and $W$ denote the number of channels, the height, and the width of the feature maps. Our DRM contains two stages: Part Scoring and Token Selection and Aggregation. The former aims to classify the tokens (i.e., the spatial vectors of $X$ ) into $N_{p}$ different parts, while the latter selects the top-k tokens for each part based on the scores and aggregates them to derive the part features $P$ .", + "bbox": [ + 496, + 534, + 890, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Part Scoring. To disentangle the feature maps into several diverse discriminative regions, we first develop a simple scorer network $\\gamma_{\\theta}$ to predict the scores of $N_{p}$ discriminative parts for each token in the feature maps. Here, $N_{p}$ is a hyperparameter representing the number of parts. Specifically, as illustrated in Figure 2, the feature maps $\\mathbf{X}$ are first passed through multiple max-pooling layers with different scales (i.e., $1 \\times 1$ for identity mapping, $3 \\times 3$ , and $5 \\times 5$ in this paper) to obtain features with different receptive fields. These features are then upsampled and concatenated along the channel dimension. Finally, the concatenated feature maps are fed into a point-wise convolutional layer with softmax activation along the spatial function to predict the scores of each part.", + "bbox": [ + 496, + 689, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11124", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/866656e8d8514b0175e3d4181602bac0fc6dcff9987b7a4feef6f11faffa2acf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 89, + 519, + 271 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ab90f2e02d2db4488c582fe72d83a857731f3f43cffcab11e5e902891d814068.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 90, + 888, + 271 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9f9bcc79bdb7cb081ddf330bf6c2061cb15ba5e58424e8f633a92d48679c59c5.jpg", + "image_caption": [ + "Figure 2. (a) The overall pipeline of the proposed Concordant Attention Learning (CAL), which consists of a deep CNN backbone, the Discriminative Region Mining (DRM), the Target-aware Style-agnostic Attention Adapter (TSAA), and the MatchDistill paradigm. Note that only half of the pipeline is depicted for clarity since the model is symmetric. (b) The pipeline of DRM. (c) The architecture of the proposed TSAA. (d) The pipeline of MatchDistill. Notations are introduced in Sec. 3." + ], + "image_footnote": [], + "bbox": [ + 78, + 275, + 890, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Token Selection and Aggregation. Given the scores predicted by $\\gamma_{\\theta}$ , we then select the tokens with top-k scores for each part and aggregate them by weighted averaging to derive the aggregated part features. Specifically, let $S \\in \\mathbb{R}^{(H \\cdot W) \\times N_p}$ denote the predicted score after the softmax layer produced by $\\gamma_{\\theta}$ , and let $T \\in \\mathbb{R}^{(H \\cdot W) \\times C}$ denote the flattened feature maps of $X$ . The token selection and aggregation process can be formulated as", + "bbox": [ + 75, + 455, + 468, + 577 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} = \\frac {\\hat {\\boldsymbol {S}} ^ {T} \\boldsymbol {T}}{\\sum_ {j} \\hat {\\boldsymbol {S}} _ {j}}, \\text {w h e r e} \\hat {\\boldsymbol {S}} = \\mathcal {T} (\\boldsymbol {S}, N _ {k}), N _ {k} = \\left[ \\alpha \\cdot \\frac {H \\cdot W}{N _ {p}} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 583, + 468, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{T}$ denotes the top-k operation; $\\hat{S} \\in \\mathbb{R}^{(H \\cdot W) \\times N_p}$ represents the selected regions, $N_k$ is the number of selected tokens, $\\alpha$ is a hyperparameter controlling the selection ratio, and $P \\in \\mathbb{R}^{N_p \\times C}$ represents the aggregated part features. There are two main advantages of selecting the top-k tokens instead of preserving all of them: (1) it helps filter out noisy tokens that could bring noisy clues to subsequent modules; (2) it can enhance the locality of the selected region and facilitate the learning of local representations.", + "bbox": [ + 75, + 632, + 468, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discriminability Constraint. To ensure the part features $P$ contains discriminative information, we design the discriminative constraint loss, which is formulated as", + "bbox": [ + 76, + 772, + 468, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i s} = - \\sum_ {i = 1} ^ {N _ {p}} \\log \\left(\\Phi_ {i} \\left(\\boldsymbol {P} _ {i}\\right) _ {y}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 823, + 468, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Phi_k$ denotes part-specific classifiers implemented with a simple fully connected layer with softmax activation, and $y$ is the label of the current sample.", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diversity Constraint. By training DRM with only Eq. (4), the model would tend to select several identical regions, resulting in suboptimal performance. This can be attributed to the shortcut learning characteristics [6] of deep learning systems that models attempt to find the simplest (but may be suboptimal) solution to solve a given task. To enhance the diversity of the selected regions, we further design the diversity constraint loss, which is defined as", + "bbox": [ + 496, + 455, + 890, + 577 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i v} = \\sum_ {i, j} \\operatorname {t r i u} \\left(\\hat {\\boldsymbol {S}} ^ {T} \\hat {\\boldsymbol {S}}, 1\\right) _ {i, j}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 589, + 890, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{triu}(\\cdot, 1)$ denotes the upper triangular part (excluding the diagonal) of the given matrix. This diversity constraint loss can be regarded as imposing an explicit penalty on the model when the selected key regions become too similar.", + "bbox": [ + 496, + 630, + 890, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 2, the DRM module is not shared across modalities. This can help to learn better modality-specific part prototypes and select more discriminative regions, leading to better performance. This design will be empirically validated in Sec. 4.", + "bbox": [ + 496, + 693, + 890, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Target-aware Style-agnostic Attention Adapter", + "text_level": 1, + "bbox": [ + 500, + 797, + 879, + 813 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve target-aware attention, it is important to properly localize relevant regions in the feature maps by taking the aggregated part features $P$ as the reference. A straightforward solution is to directly apply Scaled Dot-Product Attention [32] by taking $P$ as the part queries and the flattened", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11125", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "feature maps $T$ as the keys and the values, formulated as", + "bbox": [ + 76, + 90, + 452, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t n} (\\boldsymbol {T}; \\boldsymbol {P}) = \\operatorname {s o f t m a x} \\left(\\boldsymbol {P} \\boldsymbol {T} ^ {T} / \\sqrt {d}\\right) \\boldsymbol {T}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 111, + 468, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d$ is the feature dimension. However, this naive solution simply adopts dot product as the similarity metric, which could result in inaccurate attention scores. Because the features of different modalities suffer from large distributions shift, making them hard to be properly compared using a simple dot product operation. To this end, we design the Target-aware Style-agnostic Attention Adapter (TSAA), which includes a more reasonable similarity calculator. As shown in Figure 2 (b), we first apply Instance Normalization (IN) [31] to the part queries $P$ and each token of the feature maps $X$ , formulated as", + "bbox": [ + 75, + 140, + 468, + 306 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {I N} (\\boldsymbol {P}) = \\frac {\\boldsymbol {P} - \\mu (\\boldsymbol {T} _ {P})}{\\sigma (\\boldsymbol {T} _ {P})}, \\quad \\operatorname {I N} (\\boldsymbol {T}) = \\frac {\\boldsymbol {T} - \\mu (\\boldsymbol {T})}{\\sigma (\\boldsymbol {T})}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 311, + 468, + 344 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mu (\\cdot)$ and $\\sigma (\\cdot)$ denote calculating the instance-level mean and standard deviation; $T_{P}$ is the flattened feature maps that $P$ derives from (see Eq. (3)). The motivation of this design is that the modality gap between IR and RGB images can be interpreted as the large discrepancies in style, and IN has been proven to be effective in reducing the style variance [14, 39, 13]. After that, the normalized features are fed into multi-layer perceptrons (MLPs) to learn nonlinear projection and capture complex patterns of the features. We then calculate the inner product of the projected features after the MLPs and apply softmax function on the spatial dimension to derive the final similarity. We can then apply spatial attention by weighted averaging all tokens using the computed similarities. In addition, we also apply query-guided channel attention to emphasize important channels in the feature map and suppress less important ones, where scores of channel attention are generated by an MLP layer taking part queries as input. Formally, the TSAA module, denoted by $\\mathcal{A}(\\cdot ;\\cdot)$ , can be formulated as", + "bbox": [ + 75, + 348, + 470, + 636 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (\\boldsymbol {T}; \\boldsymbol {P}) = \\mathcal {S} (\\boldsymbol {T}, \\boldsymbol {P}) \\boldsymbol {T} \\otimes \\mathcal {M} (\\boldsymbol {P}; \\theta_ {3}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 642, + 468, + 659 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} (\\boldsymbol {T}, \\boldsymbol {P}) = \\operatorname {s o f t m a x} \\left(\\hat {\\boldsymbol {P}} \\hat {\\boldsymbol {T}} ^ {T} / \\sqrt {d}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 661, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {T}} = \\mathcal {M} (\\operatorname {I N} (\\boldsymbol {T}); \\theta_ {1}), \\quad \\hat {\\boldsymbol {P}} = \\mathcal {M} (\\operatorname {I N} (\\boldsymbol {P}); \\theta_ {2}), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 111, + 688, + 468, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{S}$ denotes the spatial similarity calculator, $\\otimes$ denotes channel-wise multiplication, and $\\mathcal{M}(\\cdot ;\\theta)$ denotes MLP with parameter $\\theta$ . The TSAA has two merits: (1) it allows style-agnostic attention adjustment based on any given part queries $P$ regardless of the image styles, making it easier to achieve attention consensus; (2) it can naturally bridge the gap between cross-modal samples by attending to relevant regions and emphasizing relevant channels.", + "bbox": [ + 75, + 708, + 468, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.3 Part-aligned Metric Learning", + "text_level": 1, + "bbox": [ + 76, + 845, + 338, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our part-aligned metric learning aims to reduce the cross-modal intra-class discrepancies between the part-aligned", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "features. As shown in Figure 2 (a), we first employ TSAA to perform cross-modal refinement since it can effectively bridge the gap between cross-modal samples as discussed in Sec. 3.2.2. The cross-modal refinement is defined as", + "bbox": [ + 496, + 90, + 890, + 150 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {f} _ {i} ^ {V, I} = \\mathcal {A} \\left(\\boldsymbol {T} _ {j} ^ {V}; \\boldsymbol {P} _ {i} ^ {I}\\right), \\quad \\boldsymbol {f} _ {i} ^ {I, V} = \\mathcal {A} \\left(\\boldsymbol {T} _ {j} ^ {I}; \\boldsymbol {P} _ {i} ^ {V}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 161, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{T}_j$ is randomly selected from the mini-batch and $y_{i}^{I} = y_{j}^{V}$ . $\\pmb{f}^{V,I}$ and $\\pmb{f}^{I,V}$ are called cross-refined features. Similarly, we also apply self-refinement using", + "bbox": [ + 498, + 191, + 890, + 239 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {f} _ {i} ^ {V, V} = \\mathcal {A} \\left(\\boldsymbol {T} _ {i} ^ {V}; \\boldsymbol {P} _ {i} ^ {V}\\right), \\quad \\boldsymbol {f} _ {i} ^ {I, I} = \\mathcal {A} \\left(\\boldsymbol {T} _ {i} ^ {I}; \\boldsymbol {P} _ {i} ^ {I}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 250, + 890, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to obtain the self-refined features. Since $\\pmb{f}_i^{V,I}$ and $\\pmb{f}_i^{I,I}$ are refined using the same query (i.e., $P_i^I$ ), they would attend to the same regions and can thus be regarded as part-aligned features. We then design the Part-aligned Center Loss (PCL) to enhance the discriminability of these semantically aligned embeddings. Let $c_j^k$ denotes the batch feature centroid of class $y_j^k$ in modality $k$ ( $k \\in \\{V, I\\}$ ) given by", + "bbox": [ + 496, + 276, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {c} _ {j} ^ {V} = \\frac {1}{| \\mathcal {S} (j) |} \\sum_ {i \\in \\mathcal {S} (j)} \\boldsymbol {f} _ {i} ^ {V, V}, \\quad \\boldsymbol {c} _ {j} ^ {I} = \\frac {1}{| \\mathcal {S} (j) |} \\sum_ {i \\in \\mathcal {S} (j)} \\boldsymbol {f} _ {i} ^ {I, I}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 396, + 890, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $S(j) = \\{i\\mid y_i = y_j\\}$ . Our PCL is then defined as", + "bbox": [ + 500, + 441, + 872, + 458 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {p c l} = \\sum_ {i, j} \\left[ \\mathrm {g} \\left(\\boldsymbol {f} _ {i} ^ {V I}, \\boldsymbol {c} _ {j} ^ {I}\\right) + \\mathrm {g} \\left(\\boldsymbol {f} _ {i} ^ {I V}, \\boldsymbol {c} _ {j} ^ {V}\\right) + \\right. \\tag {14} \\\\ \\left. \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {I}, \\boldsymbol {c} _ {j} ^ {V}\\right) + \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {I}, \\boldsymbol {c} _ {j} ^ {I}\\right) + \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {V}, \\boldsymbol {c} _ {j} ^ {V}\\right) \\right]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 469, + 890, + 515 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\mathrm{g}$ and $\\mathrm{s}$ aim to gather up intra-class features and separate inter-class features, respectively, formulated as", + "bbox": [ + 498, + 525, + 890, + 556 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathrm {g} (\\boldsymbol {f}, \\boldsymbol {c}) = \\left[ \\mathbb {1} \\left(y _ {(\\boldsymbol {f})} = y _ {(\\boldsymbol {c})}\\right) \\cdot \\| \\boldsymbol {f} - \\boldsymbol {c} \\| _ {2} \\right], \\\\ \\mathrm {s} \\left(\\boldsymbol {c} _ {i}, \\boldsymbol {c} _ {j}\\right) = \\left[ \\mathbb {1} \\left(y _ {\\left(\\boldsymbol {c} _ {i}\\right)} \\neq y _ {\\left(\\boldsymbol {c} _ {j}\\right)}\\right) \\cdot \\left[ \\sigma - \\| \\boldsymbol {c} _ {i} - \\boldsymbol {c} _ {j} \\| _ {2} \\right] _ {+} \\right], \\tag {15} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 561, + 890, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma$ is a marginal parameter adopted to avoid optimizing \"already correct\" centroid pairs; $[z]_{+} = \\max (z,0);y(\\cdot)$ denotes the label of the corresponding embedding/centroid.", + "bbox": [ + 498, + 609, + 890, + 656 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Cross-modal Knowledge Exchange", + "text_level": 1, + "bbox": [ + 500, + 665, + 803, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Even though the cross-refined embeddings yield smaller distribution gaps with respect to the target modality, it is infeasible to employ cross-refined embeddings for retrieval during the inference stage. Because the cross-modal refinement requires taking the part features $P$ (derived from DRM using the images of modality counterpart) as queries and applying query-guided attention using Eq. (10). This process need to be carried out for all query-gallery pairs, which brings high computational costs since gallery sets are generally large. To this end, we propose a novel solution called MatchDistill, which allows DRM to directly generate target-modality-like part features. This is achieved by associating the heterogeneous queries $P^V$ and $P^I$ with our Cross-modal Query Matching algorithm and propagating", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11126", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the modality-specific knowledge to the best-matched query of modality counterparts. For clarity, here we only take matching and propagating the knowledge from $P^I$ to $P^V$ as an example since MatchDistill has a symmetric pipeline. As shown in Figure 2, in MatchDistill, we first construct a complete bipartite graph $G(U, V, E)$ , where the vertices $U$ and $V$ represent $P^I$ and $P^V$ , respectively. Each edge in $E$ connects a vertex in $U$ to one in $V$ . The weights of the edges are the semantic similarities between queries, which are measured by the dot product of the attention mask calculated by Eq. (10), formulated as", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nw \\left(\\boldsymbol {E} _ {k _ {1}, k _ {2}} ^ {V}\\right) = \\langle \\mathcal {S} \\left(\\boldsymbol {X} ^ {V}, \\boldsymbol {P} _ {k _ {1}} ^ {I}\\right), \\mathcal {S} \\left(\\boldsymbol {X} ^ {V}, \\boldsymbol {P} _ {k _ {2}} ^ {V}\\right) \\rangle , \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 265, + 468, + 286 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $w(\\cdot)$ denotes the weight of the edge. The idea behind this is straightforward: if $P_{k1}$ and $P_{k2}$ represent the same semantic region, their attention masks should have a high level of similarity. This could help effectively model the semantic correlations of the heterogeneous part queries. The part query matching problem can then be formulated as", + "bbox": [ + 75, + 294, + 468, + 385 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\arg \\max _ {M \\subseteq E} \\sum_ {e \\in M} w (e), \\quad s. t. \\left| M \\right| = N _ {p} \\text {a n d} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 395, + 468, + 424 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\forall (u _ {1}, v _ {1}), (u _ {2}, v _ {2}) \\in M, u _ {1} \\neq u _ {2} \\text {a n d} v _ {1} \\neq v _ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 425, + 416, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $M$ represents the edges of the optimal match (meaning that $\\forall (u,v)\\in M$ , $P_u^V$ and $P_v^I$ represent the same semantic region). We solve this part query matching problem (Eq. (17)) with the Kuhn-Munkres assignment algorithm [15]. After that, the mutual knowledge propagation process can be performed between all $(u,v)\\in M$ pairs since they are semantically aligned. Specifically, the proposed knowledge distillation is conducted in two levels, i.e., the feature level and the logit level. For the feature level, we propose to align the similarity maps of the best-matched query pairs. This is equivalent to maximizing the weight of the optimal bipartite graph, formulated as", + "bbox": [ + 75, + 450, + 472, + 632 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {k d 1} = - \\sum_ {e \\in M} w (e). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 638, + 468, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the logit level, we constrain the consistency of their softmax classification distribution by", + "bbox": [ + 75, + 667, + 468, + 696 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {k d 2} = \\sum_ {(u, v) \\in \\boldsymbol {M}} \\mathcal {D} _ {k l} \\left(\\boldsymbol {p} _ {u} ^ {V, I} \\| \\boldsymbol {p} _ {v} ^ {V, V}\\right), \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 704, + 468, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\pmb{p}$ denotes the post-softmax classification probability, and $\\mathcal{D}_{kl}$ denotes Kullback-Leibler divergence. With the above cross-modal knowledgeable propagation, the self-refined features can also capture important information that can benefit cross-modal retrieval like the cross-refined ones. Therefore, there is no needs to perform cross-refinement during inference. In addition, by optimizing $\\mathcal{L}_{kd1}$ and $\\mathcal{L}_{kd2}$ , we observe that the optimal matches $M$ gradually get stabilized as the training progresses. This suggests that the optimal matches with the highest occurrence in the last training epoch, denoted as $\\hat{M}$ , can be used for test-time matching.", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Training and Inference", + "text_level": 1, + "bbox": [ + 500, + 90, + 714, + 106 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. The overall training objective is defined as", + "bbox": [ + 500, + 116, + 856, + 132 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {i d} + \\mathcal {L} _ {p c l} + \\lambda_ {1} \\mathcal {L} _ {k d 1} + \\lambda_ {2} \\mathcal {L} _ {k d 2} + \\lambda_ {3} \\mathcal {L} _ {d i s} + \\lambda_ {4} \\mathcal {L} _ {d i v}, \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 138, + 890, + 155 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{id}$ is the routinely used identity classification loss; $\\lambda_1, \\lambda_2, \\lambda_3$ , and $\\lambda_4$ are adopted to balance different losses.", + "bbox": [ + 500, + 161, + 890, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inference. During inference, we first reorder the learned prototypes of the DRM (i.e., the parameters of the pointwise convolutional layer in DRM) according to $\\hat{M}$ to ensure that the self-refined embeddings can be semantically aligned. After that, the summation of the cosine similarity of each part is then adopted as the comparison metric. Formally, the similarity between the $i^{th}$ visible and the $j^{th}$ infrared sample is given by $\\sum_{p} \\cos(\\boldsymbol{f}_{i,p}^{V,V}, \\boldsymbol{f}_{j,p}^{I,I})$ , where $\\cos$ denotes cosine similarity computation, and the subscript $p$ denotes indexing in the part dimension.", + "bbox": [ + 496, + 196, + 893, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 359, + 633, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 385, + 705, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. The proposed method is evaluated under the same protocols of existing work [20] on two widely-used VI Re-ID datasets, i.e., SYSU-MM01 [38] and RegDB [25].", + "bbox": [ + 496, + 411, + 890, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We adopt ResNet-50 [9] as the backbone network following existing work. At each training iteration, 8 identities are randomly sampled. For each identity, 4 visible and 4 infrared images are selected to form a mini-batch. The model is trained for 100 epochs in total on RTX 3090 GPUs with SGD optimizer. The learning rate linearly increased from 0.01 to 0.1 in the first 10 epochs. The cosine annealing strategy [21] is adopted in the remaining 90 epochs to decay the learning rate to $10^{-3}$ . The hyperparameters are decided by cross-validation. Specifically, we set $\\lambda_{1} = 1$ , $\\lambda_{2} = 1$ , $\\lambda_{3} = 0.1$ , $\\lambda_{4} = 0.1$ , $N_{p} = 4$ , $\\alpha = 0.6$ and $\\sigma = 0.6$ . All models are tested without using re-ranking algorithms or gallery set information for fair comparison.", + "bbox": [ + 496, + 458, + 890, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 500, + 662, + 867, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The comparison results on SYSU-MM01 and RegDB with state-of-the-art (SOTA) methods are shown in Table 1 and Table 2, respectively. It can be seen that the proposed CAL outperforms existing approaches by large margins on both datasets. Specifically, on the SYSU-MM01 dataset, our proposed method surpasses the state-of-the-art approaches [12, 20] on most of the evaluation metrics. As for the RegDB dataset, our method also achieves new state-of-the-art results. These experimental results verify the effectiveness and superiority of the proposed method.", + "bbox": [ + 496, + 686, + 890, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Analysis and Discussion", + "text_level": 1, + "bbox": [ + 500, + 844, + 720, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of TCA and MatchDistill. To verify the effectiveness of the two key components of CAL (i.e., TCA", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11127", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/44476c906e4d473766ff15aa9507eeab3739cc76061c78c52e3637827b1907df.jpg", + "table_caption": [ + "Table 1. Comparison with SOTA methods on the SYSU-MM01 dataset. †: Following previous work [43], for cm-SSFT [22] and CIFT [17], we report the performance when no extra auxiliary information of the gallery set is introduced for fair comparison." + ], + "table_footnote": [], + "table_body": "
MethodVenueAll-searchIndoor-Search
Single-ShotMulti-ShotSingle-ShotMulti-Shot
R1↑R10↑mAP↑R1↑R10↑mAP↑R1↑R10↑mAP↑R1↑R10↑mAP↑
Zero-Pad [38]ICCV 201714.8054.1215.9519.1361.4010.8920.5868.3826.9224.4375.8618.64
AGW [44]TPAMI 202247.5084.3947.65---54.1791.1462.97---
cm-SSFT†[22]CVPR 202047.70-54.1057.40-59.10------
NFS [2]CVPR 202156.9191.3455.4563.5194.4248.5662.7996.5369.7970.0397.7061.45
SMCL [36]ICCV 202167.3992.8761.7872.1590.6654.9368.8496.5575.5679.5795.3366.57
MCLNet [7]ICCV 202165.4093.3361.98---72.5696.9876.58---
MPMN [35]TMM 202148.9890.3362.4160.8888.7051.9064.8996.8576.4774.4292.9366.98
FMCNet [46]CVPR 202266.34-62.51---68.15-74.09---
CAJ [43]ICCV 202169.8895.7166.89---76.2697.8880.37---
CIFT†[17]ECCV 202271.77-67.6478.00-62.4678.65-82.1186.97-77.03
MPANet [39]CVPR 202170.5896.2168.2475.5897.9162.9176.7498.2180.9584.2299.6675.11
CMT [12]ECCV 202271.8896.4568.5780.2397.9163.1376.9097.6879.9184.8799.4174.11
MAUM [20]CVPR 202271.68-68.79---76.97-81.94---
CAL (Ours)-74.6696.4771.7377.0598.0164.8679.6998.9383.6886.9799.8378.51
", + "bbox": [ + 80, + 118, + 890, + 347 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1099f430a6c6079fe08e5f5213158edee077fd91cc6f8945dac47ee5ca6cd862.jpg", + "table_caption": [ + "Table 2. Comparison with SOTA methods under \"visible to infrared\" and \"infrared to visible\" modes on RegDB. †: see Table 1." + ], + "table_footnote": [], + "table_body": "
MethodVisible to InfraredInfrared to Visible
R1 ↑R10 ↑mAP ↑R1 ↑R10 ↑mAP ↑
Zero-Pad [38]17.7534.2118.9016.6334.6817.82
cm-SSFT†[22]65.40-65.6063.80-64.20
AGW [44]70.0586.2166.3775.9390.9369.49
NFS [2]80.5491.9672.1077.9590.4569.79
MCLNet [7]80.3192.7073.0775.9390.9369.49
CAJ [43]85.0395.4979.1484.7595.3377.82
SMCL [36]83.93-79.8383.05-78.57
MPANet [39]83.70-80.9082.80-80.70
MPMN [35]86.5696.8682.9184.6295.5179.49
FMCNet [46]89.12-84.4388.38-83.86
MAUM [20]87.87-85.0986.95-84.34
CIFT†[17]92.17-86.9690.12-84.81
CMT [12]95.1798.8287.3091.9797.9284.46
CAL (Ours)94.5199.7088.6793.6499.4687.61
", + "bbox": [ + 80, + 393, + 467, + 597 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and MatchDistill) and analyze their contribution to the overall performance, we conduct experiments on the more challenging SYSU-MM01 dataset. The experimental results are given in Table 3, where we adopt ResNet-50 as the baseline method. We can see that both TCA and MatchDistill are shown to be essential to the final performance and can significantly boost the performance of the baseline method. These findings demonstrate the effectiveness and importance of our proposed approach.", + "bbox": [ + 75, + 622, + 467, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on the DRM Module. To demonstrate the superiority of the design of DRM, we conduct experiments by removing the key components of DRM or replacing them with other alternatives. The experimental results are shown in Table 4 (top). We can see that all modifications can lead to performance degradation. Specifically, we can see that when training DRM without the diversity constraint $(\\mathcal{L}_{div})$ or discriminability constraint $(\\mathcal{L}_{dis})$ , the performance drops significantly, indicating that it is essential to", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "guarantee both the discriminability and diversity of the selected regions. When replacing the modality-specific DRM with the modality-shared one, a performance drop can also be observed. This is because the modality-shared DRM cannot learn modality-specific patterns, making it hard to discover discriminative modality-specific clues. It can also be observed that using learnable vectors instead of DRM produces poor performance since they are less descriptive than the part features generated by DRM. Horizontal Splitting (HS), which divides the feature maps into horizontal chunks, achieves slightly better results than learnable vectors since the chunks are more informative than learnable vectors. However, HS is still inferior to our DRM as handcrafted stripes cannot properly disentangle the feature maps into fine-grained discriminative body parts. We also study the impact of the number of regions generated and the parameter $N_{k}$ and $\\alpha$ in DRM. The experimental results are shown in Figure 3. The best performance is achieved when $N_{p} = 4$ and $\\alpha = 0.6$ .", + "bbox": [ + 496, + 366, + 890, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on the TSAA Module. To demonstrate the superiority of the TSAA design, we conduct experiments by replacing the spatial similarity calculation process (Eq. (9)) with the simple scaled dot-product operation and removing the query-guided channel attention mechanism. As shown in Table 4 (middle), the experimental results reveal significant drops in performance when adopting the scaled dot product as the similarity metric. This can be attributed to the style discrepancies between modalities, which make it difficult to effectively find the correlation between heterogeneous data with dot product. Our TSAA module, on the other hand, is adept at reducing style discrepancies between heterogeneous data when computing similarity scores. In addition, the experimental results also validate the effectiveness of our query-guided channel attention mechanism.", + "bbox": [ + 496, + 656, + 890, + 881 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on PCL. The PCL aligns the cross-modal em", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11128", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d192d45f56712d50b48210e5393d3472360de3778818d3c77c976fc4b1585503.jpg", + "table_caption": [ + "Table 3. Effectiveness of the proposed components on the SYSUMM01 dataset under the all-search single-shot mode." + ], + "table_footnote": [], + "table_body": "
BaselineTCAMatchDistillSYSU-MM01
R1↑R10↑mAP↑
✓57.8289.9156.40
✓✓70.1593.1267.40
✓✓✓74.6696.4771.73
", + "bbox": [ + 81, + 116, + 467, + 195 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a9e9f3c0316d1885a0e72ce4f9cae773cdb9b67b6bc923a19a3d1cb4daec2f48.jpg", + "table_caption": [ + "Table 4. Ablation study of DRM and TSAA on SYSU-MM01 under the all-search single-shot mode. Shared DRM: the weights of DRM are shared for both modalities. $LV$ : replacing the selected regions with $N_p$ learnable vectors. HS: Horizontal Split ( $n$ chunks). TSAA (SD): adopting scaled dot-product for similarity computation in TSAA. CA: the channel-wise attention in TSAA." + ], + "table_footnote": [], + "table_body": "
MethodSYSU-MM01
R1↑R10↑mAP ↑
DRM w/o L_div72.7695.7169.85
DRM w/o L_dis72.2395.3769.38
DRM → Shared DRM72.5794.9569.51
DRM → LV71.0794.0168.60
DRM → HS (n = 2)72.7095.5070.02
DRM → HS (n = 4)73.1595.7670.24
DRM → HS (n = 6)72.5794.9569.51
TSAA (SD)72.5794.9569.51
TSAA (SD) w/o CA70.5795.4767.77
w/o PCL66.9493.4264.32
PCL → Triplet loss [11]68.0993.2465.41
PCL → Center loss [37]71.4894.6069.13
PCL → ICA&CCA [7]69.5595.2170.01
CAL (Ours)74.6696.4771.73
", + "bbox": [ + 81, + 290, + 467, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "beddings that have consistent semantics. We conduct experiments by removing or replacing PCL with other alternatives, including the prevailing metric learning losses [11, 37] and the one [7] designed specifically for VI Re-ID. The experimental results reported in Table 4 (bottom) show that our PCL contributes largely to the final performance and surpasses other competitors. This is mainly owing to the superior design of PCL that consider reducing intra-class variation using the part-aligned embeddings.", + "bbox": [ + 75, + 549, + 468, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis on MatchDistill. We conduct ablation experiments to evaluate the contribution of the proposed Cross-modal Query Matching algorithm and the two knowledge distillation losses $(\\mathcal{L}_{kd1}$ and $\\mathcal{L}_{kd2})$ in MatchDistill. As shown in Table 5, the experimental results demonstrate the significant role they play in enhancing retrieval accuracy. When aligning the attention maps with $\\mathcal{L}_{kd1}$ and constraining the consistency of classification probability with $\\mathcal{L}_{kd2}$ , the performance boosts significantly, verifying the effectiveness of our knowledge exchange strategies. When incorporating our CQM, the accuracy can be further improved. This suggests that it is beneficial to ensure semantic consistency when conducting knowledge exchange by finding the best-matched part queries with our CQM algorithm.", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e52b8ba48855e236125ef46062507df9dc111c5781a894ec4fb32c2b0440050.jpg", + "image_caption": [ + "Figure 3. Parameter analysis of $N_{p}$ and $\\alpha$" + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 696, + 180 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d3882dd81a25206d1149786924800f8f4ebb93ea3e04a3c17c3a3248aa87bb5a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 88, + 885, + 180 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/88623aff9273c28a58b8639e4aafc57d78a5a5883eab2ae35bfe52451d804517.jpg", + "table_caption": [ + "Table 5. Effectiveness of each component of MatchDistill on the SYSU-MM01 dataset under the all-search single-shot mode." + ], + "table_footnote": [], + "table_body": "
Lkd1Lkd2CQMSYSU-MM01
R1↑R10↑mAP↑
70.1593.1267.40
✓72.7595.7169.86
✓72.2695.1668.50
✓✓73.6395.7970.61
✓✓✓74.6696.4771.73
", + "bbox": [ + 504, + 238, + 890, + 348 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8a22a19c9a5e43fa912354792fd3830caa7008a9d4188f11697b52178cfda6ec.jpg", + "image_caption": [ + "Figure 4. Qualitative analysis of the proposed DRM and TSAA." + ], + "image_footnote": [], + "bbox": [ + 501, + 353, + 684, + 508 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6b37ebd55b5c322f9b30a06605275334041e98bec4ff75cdd8b05eda49cb14c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 353, + 890, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Results. We visualize the regions selected by the DRM module in Figure 4. It can be seen that the DRM can select diverse and discriminative regions, which could serve as strong guidance for the subsequent TSAA module. We also visualize the attention scores generated by the TSAA in Figure 4. We can see that the proposed TSAA has a strong capability in searching the corresponding regions given the key regions selected by DRM.", + "bbox": [ + 496, + 544, + 890, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 679, + 617, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present the Concordant Attention Learning (CAL) framework, which learns concordant attention across the visible and infrared modalities and can effectively bridge the modality gap for VI Re-ID. We show that it is beneficial to design target-aware attention mechanisms to ensure attention concordance when aligning cross-modal samples. We also verify that exploiting cross-modal clues from the target modality and enabling cross-modal knowledge exchange in a match-and-distill manner can facilitate the learning of inter-modal correlations. Extensive experiments demonstrate the effectiveness and superiority of CAL over state-of-the-art methods, suggesting the potential of our approach for improving VI Re-ID research.", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11129", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 78, + 90, + 243, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by National Natural Science Foundation of China (No.62073004), Science and Technology Plan of Shenzhen (No.JCYJ20200109140410340), and Shenzhen Fundamental Research Program (No.GXWD20 201231165807007-20200807164903001).", + "bbox": [ + 76, + 116, + 468, + 191 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 209, + 173, + 224 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Guangyi Chen, Jiwen Lu, Ming Yang, and Jie Zhou. 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IEEE TCSVT, 32(3):1418-1430, Mar. 2022. 2" + ], + "bbox": [ + 503, + 92, + 890, + 487 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11131", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/f96bbbd7-1bf4-40cd-9545-e535cf6aa841_model.json b/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/f96bbbd7-1bf4-40cd-9545-e535cf6aa841_model.json new file mode 100644 index 0000000000000000000000000000000000000000..74b276b4b584bf7aad0f7dd8492a71f959207733 --- /dev/null +++ b/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/f96bbbd7-1bf4-40cd-9545-e535cf6aa841_model.json @@ -0,0 +1,2200 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.18, + 0.131, + 0.795, + 0.175 + ], + "angle": 0, + "content": "Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.202, + 0.778, + 0.221 + ], + "angle": 0, + "content": "Jianbing \\(\\mathrm{Wu}^{1,\\dagger}\\) Hong Liu\\(^{2,\\dagger,*}\\) Yuxin \\(\\mathrm{Su}^{3,\\dagger}\\) Wei Shi\\(^{4,\\dagger}\\) Hao Tang\\(^{5,\\ddagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.221, + 0.86, + 0.257 + ], + "angle": 0, + "content": "† Key Laboratory of Machine Perception, Shenzhen Graduate School, Peking University, China ‡ Computer Vision Lab, ETH Zürich, Switzerland" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.26, + 0.875, + 0.275 + ], + "angle": 0, + "content": "1,3{kimbing.ng, yuxinsu}@stu.pku.edu.cn 2,4{hongliu, pkusw}@pku.edu.cn hao.tang@vision.ee.ethz.ch" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.31, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.343, + 0.474, + 0.678 + ], + "angle": 0, + "content": "Owing to the large distribution gap between the heterogeneous data in Visible-Infrared Person Re-identification (VI Re-ID), we point out that existing paradigms often suffer from the inter-modal semantic misalignment issue and thus fail to align and compare local details properly. In this paper, we present Concordant Attention Learning (CAL), a novel framework that learns semantic-aligned representations for VI Re-ID. Specifically, we design the Target-aware Concordant Alignment paradigm, which allows target-aware attention adaptation when aligning heterogeneous samples (i.e., adaptive attention adjustment according to the target image being aligned). This is achieved by exploiting the discriminative clues from the modality counterpart and designing effective modality-agnostic correspondence searching strategies. To ensure semantic concordance during the cross-modal retrieval stage, we further propose MatchDistill, which matches the attention patterns across modalities and learns their underlying semantic correlations by bipartite-graph-based similarity modeling and cross-modal knowledge exchange. Extensive experiments on VI Re-ID benchmark datasets demonstrate the effectiveness and superiority of the proposed CAL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.708, + 0.21, + 0.723 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Person Re-identification (Re-ID) aims to associate person identities across non-overlapping cameras. It has gained increasing attention in recent years due to its practical applications in real-world surveillance systems. Conventional person Re-ID methods mainly focus on retrieving the same identity across visible (RGB) cameras [48, 29, 16, 23, 10]. Despite their remarkable success, they have limited applicability since visible cameras cannot capture discriminative information under poor-lighting conditions (e.g., at night). To improve the illumination robustness, infrared (IR) cameras are widely applied to cooperate with visible ones in" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.309, + 0.892, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.539, + 0.895, + 0.693 + ], + "angle": 0, + "content": "Figure 1. A high-level overview of typical local feature learning paradigms. (a) Splitting-based: The semantics of the hand-craft stripes are not always properly aligned. (b) Auxiliary-model-based: Pretrained auxiliary models are often error-prone due to the domain shifts (especially for infrared image). (c) Attention-based: Due to the inter-modal distribution gap, existing style-sensitive attention module with less descriptive learnable prototypes often fails to attend semantically consistent regions. (d) CAL (Ours): Our method can learn concordant attention by discriminative region mining, target-aware style-agnostic attention, and part-aligned knowledge exchange." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.894, + 0.793 + ], + "angle": 0, + "content": "real-world surveillance systems. This increases the need to explore the Visible-Infrared Person Re-identification (VI Re-ID) problem, which aims to associate the person images taken by different spectrum cameras to achieve long-term person tracking in 24-hour surveillance systems." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Compared to traditional RGB-based re-identification, VI Re-ID is much more challenging due to the differences in spectral properties between visible and infrared images. This data heterogeneity can lead to severe misalignment in the feature space and large intra-class discrepancy, resulting in significant degradation in performance. In addition, similarly to RGB-based Re-ID tasks, VI Re-ID can also be" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11122" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "impacted by the changes in pose or background, resulting in increased difficulties." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.123, + 0.473, + 0.394 + ], + "angle": 0, + "content": "Recent years have witnessed a surge of creative work on mitigating the modality gap for VI Re-ID [38, 43, 18, 44, 4, 20]. However, as most existing methods only consider learning global representations from the whole image, they fail to compare local details. In addition, owing to the shortcut learning characteristics [6], global-feature-based methods would tend to learn modality-specific shortcut patterns, making the learned features susceptible to concentrating on divergent regions in each modality and resulting in suboptimal performance. A seemingly straightforward solution is to learn semantic-aligned local features with either splitting-based [29, 8, 20], auxiliary-model-based methods [26, 19, 28, 1], or attention-base paradigms [18, 16, 33, 27] instead of the global ones. However, these methods also fail to achieve inter-modal semantic alignment, as demonstrated in Figure 1, and forcibly aligning these semantic-misaligned embeddings would inevitably injure the training process and compromise the performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.473, + 0.637 + ], + "angle": 0, + "content": "Different from these deep learning methods, human visual systems can naturally avoid the misalignment issue thanks to their target-aware comparison strategy. Considering the scenario of comparing two images of persons (referred to as \"base image\" and \"target image\", respectively), human vision systems would first identify multiple distinctive key regions (such as facial and clothing details) in the target image and then direct their attention to corresponding regions in the base image. In this manner, humans can always make perfect part-to-part comparisons since they are able to adaptively and accurately adjust their attention by referencing the key regions of the target image. This suggests that exploiting clues from the target image of the modality counterpart and exploring an effective cross-modal corresponding region-searching strategy can benefit in mitigating the inter-modal semantic misalignment issue." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.473, + 0.865 + ], + "angle": 0, + "content": "In this paper, we present Concordant Attention Learning (CAL), a novel framework that mimics the target-aware comparison behavior of human vision systems to learn semantic-aligned representations for VI Re-ID. Firstly, we devise the Target-aware Concordant Alignment (TCA) paradigm, which aims to exploit discriminative local clues from the target modality (i.e., the modality counterpart) when aligning heterogeneous embeddings. The proposed TCA consists of three components: (1) Discriminative Region Mining: identifying diverse and discriminative key regions from the feature maps of each training sample; (2) Target-aware Style-agnostic Attention Adapter: taking the selected key regions from the target modality as part queries, and applying target-aware refinement to adapt the feature attention and generate part-aligned embeddings;" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.424 + ], + "angle": 0, + "content": "(3) Part-aligned Metric Learning: clustering or separating the part-aligned embeddings across modalities according to their identity labels. Even though this target-aware refinement scheme can mitigate the modality discrepancy by leveraging the clues from the target modality, it brings higher computational costs during inference. Because it needs to be carried out for all query-gallery pairs, and the gallery set is generally large. To this end, we further propose MatchDistill. First, we need to associate the generated part queries of different modalities to guarantee that the subsequent distillation is conducted on semantic-aligned features. This is achieved by modeling the correlations of their corresponding attention maps with bipartite graphs and conducting Cross-modal Query Matching (CQM) to find the optimal matches. After that, a dual-level knowledge distillation loss is designed to allow cross-modality knowledge exchange between the best-matched queries. This can facilitate the learning of underlying relationships between the visible and infrared modalities. After training with MatchDistill, each modality can learn knowledge from its modality counterpart, and no cross-modal interaction is needed during inference." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.426, + 0.875, + 0.44 + ], + "angle": 0, + "content": "Overall, our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.445, + 0.892, + 0.503 + ], + "angle": 0, + "content": "- We propose Concordant Attention Learning (CAL), a target-aware training paradigm that mimics human behavior and learns concordant attention to alleviate the inter-modal attention bias issue for VI Re-ID." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.505, + 0.892, + 0.564 + ], + "angle": 0, + "content": "- To enable part-aligned metric learning, we present Target-aware Concordant Alignment (TCA), which leverages cross-modal clues and allows adaptive attention adjustment when aligning heterogeneous embeddings." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.565, + 0.892, + 0.624 + ], + "angle": 0, + "content": "- We propose MatchDistill, which matches the attention patterns across modalities and learns their underlying semantic correlations by bipartite-graph-based similarity modeling and cross-modal knowledge exchange." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.625, + 0.892, + 0.671 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that the proposed CAL archives state-of-the-art performance on both the SYSU-MM01 [38] and RegDB [25] datasets." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.445, + 0.892, + 0.671 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.689, + 0.642, + 0.705 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Visible-Infrared Person Re-ID. Visible-Infrared Person Re-ID (VI Re-ID) has drawn increasing attention in recent years [43, 17, 39, 12, 20]. Mainstream VI Re-ID paradigms focus on bridging the modality gap via designing metric learning constraints [45, 42, 40], normalizing feature statistics [14, 39, 13], synthesizing auxiliary training samples [34, 3, 49, 24], or developing modality-specific and modality-shared feature learning paradigms [5, 22, 30]. However, these methods only consider learning global representations from entire images without considering the local information of images, leading to limited expressiveness of learned features. A few works also attempt to learn local" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.901 + ], + "angle": 0, + "content": "1Note that we use the term \"region\" and \"part\" interchangeably to denote the same thing." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11123" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.471, + 0.168 + ], + "angle": 0, + "content": "features for VI Re-ID [8, 20, 41, 47] by splitting the feature maps into several hand-craft stripes. However, due to inaccurate detection boxes, pose variations, and occlusion, the hand-craft stripes are not always well-aligned, resulting in unsatisfactory performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.473, + 0.518 + ], + "angle": 0, + "content": "Local Feature Learning in Person Re-ID. Local feature learning is an important research direction for person re-identification since learning part aggregated features makes the model robust against misalignment [44]. It can be roughly divided into splitting-based methods, auxiliary-model-based methods, and attention-based methods. Splitting-based methods [29, 8, 20] focus on learning local features from horizontal-divided regions, which now serve as a strong part feature learning baseline. However, due to inaccurate detection boxes, pose variations, and occlusion, the semantics of the hand-craft stripes are not well aligned. The auxiliary-model-based methods [26, 19, 28, 1] often adopt off-the-shelf auxiliary human parsing or pose estimation networks to obtain semantically meaningful body parts. However, they require additional computational costs and are prone to noisy estimation, especially when the data distribution varies. The attention-based methods focus on exploiting attention mechanisms to localize discriminative human parts and have achieved great success [18, 16, 33, 27]. However, these methods cannot be directly applied to the cross-modality scenario of VI Re-ID due to the inter-modal semantic misalignment issue as discussed in Sec. 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.529, + 0.214, + 0.545 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.553, + 0.394, + 0.57 + ], + "angle": 0, + "content": "3.1. Intuition of Target-aware Alignment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.47, + 0.775 + ], + "angle": 0, + "content": "Let \\(\\pmb{x}^k\\) denote the training images of modality \\(k\\), where \\(k \\in \\{V, I\\}\\) (\\(V\\) for visible modality and \\(I\\) for infrared modality). The visible and infrared samples in the dataset are denoted by \\(\\mathcal{V} = \\{\\pmb{x}_j^V, y_j^V\\}_{j=0}^{N_v}\\) and \\(\\mathcal{I} = \\{\\pmb{x}_j^I, y_j^I\\}_{j=0}^{N_i}\\), respectively, where \\(N_v\\) and \\(N_i\\) are the numbers of samples of each modality in the dataset, and \\(y_j^k\\) is the corresponding identity label of the \\(j\\)-th sample from modality \\(k\\). The goal of Visible-Infrared Person Re-identification is to match the person identities across modalities according to feature similarities. Therefore, it is essential to reduce the large intra-class variation between heterogeneous samples. Existing paradigms often attempt to reduce the cross-modal intra-class variation by directly optimizing" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.779, + 0.47, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {i, j} \\left[ \\mathbb {1} \\left(y _ {i} ^ {V} = y _ {j} ^ {I}\\right) \\cdot \\mathrm {d} \\left(f \\left(\\boldsymbol {x} _ {i} ^ {V}\\right), f \\left(\\boldsymbol {x} _ {j} ^ {I}\\right)\\right) \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\( f \\) denotes the feature extractor, and \\( \\mathrm{d}(\\cdot, \\cdot) \\) represents the distance between features. However, as discussed in Sec. 1, the attention misalignment issue could injure the training process and compromise performance. We thus endow the model with the ability to adaptively adjust the attention according to the target being compared to achieve" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "attention consensus. First, the Discriminative Region Mining (DRM) module, formulated as \\(\\gamma(\\cdot)\\), is introduced to disentangle the global features into diverse key body parts. We then devise the Target-aware Style-agnostic Attention Adapter (TSAA) to allow adaptive style-agnostic attention adjustment according to any given part queries regardless of the image styles. The feature extractor is then reformulated as \\(f(\\pmb{x},\\pmb{p})\\) to represent the above dynamic attention adjustment process, where \\(\\pmb{p}\\) denotes the given body parts. The objective function to reduce the cross-modal intra-class variation can then be defined as" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.268, + 0.892, + 0.32 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {i, j, k} \\left[ \\mathbb {1} \\left(y _ {i} ^ {V} = y _ {j} ^ {I}\\right) \\cdot \\mathrm {d} \\left(f \\left(\\boldsymbol {x} _ {i} ^ {V}, \\gamma \\left(\\boldsymbol {x} _ {j} ^ {I}\\right) _ {k}\\right), f \\left(\\boldsymbol {x} _ {j} ^ {I}, \\gamma \\left(\\boldsymbol {x} _ {j} ^ {I}\\right) _ {k}\\right)\\right) + \\right. \\tag {2} \\\\ \\mathbb {1} (y _ {i} ^ {I} = y _ {j} ^ {V}) \\cdot \\mathrm {d} \\big (f (\\pmb {x} _ {i} ^ {I}, \\gamma (\\pmb {x} _ {j} ^ {V}) _ {k}), f (\\pmb {x} _ {j} ^ {V}, \\gamma (\\pmb {x} _ {j} ^ {V}) _ {k}) \\big) \\Big ]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.331, + 0.892, + 0.472 + ], + "angle": 0, + "content": "In this manner, the embeddings being optimized can achieve semantic concordance since the same queries are used to guide feature attention (for instance, \\( f(\\pmb{x}_i^V, \\gamma(\\pmb{x}_j^I)_k) \\) and \\( f(\\pmb{x}_j^I, \\gamma(\\pmb{x}_j^I)_k) \\) correspond to the same semantic region since they are refined using the same part query \\( \\gamma(\\pmb{x}_j^I)_k \\)). This also allows cross-modal interaction to facilitate the learning of underline relationships between modalities. The overall pipeline is depicted in Figure 2, and more details will be introduced in the following subsections." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.484, + 0.822, + 0.501 + ], + "angle": 0, + "content": "3.2. Target-aware Concordant Alignment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.509, + 0.766, + 0.525 + ], + "angle": 0, + "content": "3.2.1 Discriminative Region Mining" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.687 + ], + "angle": 0, + "content": "The Discriminative Region Mining module aims to discover several diverse discriminative key regions from the feature maps \\( X \\in \\mathbb{R}^{C \\times H \\times W} \\) derived from the backbone network, where \\( C \\), \\( H \\), and \\( W \\) denote the number of channels, the height, and the width of the feature maps. Our DRM contains two stages: Part Scoring and Token Selection and Aggregation. The former aims to classify the tokens (i.e., the spatial vectors of \\( X \\)) into \\( N_{p} \\) different parts, while the latter selects the top-k tokens for each part based on the scores and aggregates them to derive the part features \\( P \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Part Scoring. To disentangle the feature maps into several diverse discriminative regions, we first develop a simple scorer network \\(\\gamma_{\\theta}\\) to predict the scores of \\(N_{p}\\) discriminative parts for each token in the feature maps. Here, \\(N_{p}\\) is a hyperparameter representing the number of parts. Specifically, as illustrated in Figure 2, the feature maps \\(\\mathbf{X}\\) are first passed through multiple max-pooling layers with different scales (i.e., \\(1 \\times 1\\) for identity mapping, \\(3 \\times 3\\), and \\(5 \\times 5\\) in this paper) to obtain features with different receptive fields. These features are then upsampled and concatenated along the channel dimension. Finally, the concatenated feature maps are fed into a point-wise convolutional layer with softmax activation along the spatial function to predict the scores of each part." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11124" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.52, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.091, + 0.89, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.276, + 0.891, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.384, + 0.893, + 0.44 + ], + "angle": 0, + "content": "Figure 2. (a) The overall pipeline of the proposed Concordant Attention Learning (CAL), which consists of a deep CNN backbone, the Discriminative Region Mining (DRM), the Target-aware Style-agnostic Attention Adapter (TSAA), and the MatchDistill paradigm. Note that only half of the pipeline is depicted for clarity since the model is symmetric. (b) The pipeline of DRM. (c) The architecture of the proposed TSAA. (d) The pipeline of MatchDistill. Notations are introduced in Sec. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.47, + 0.578 + ], + "angle": 0, + "content": "Token Selection and Aggregation. Given the scores predicted by \\(\\gamma_{\\theta}\\), we then select the tokens with top-k scores for each part and aggregate them by weighted averaging to derive the aggregated part features. Specifically, let \\(S \\in \\mathbb{R}^{(H \\cdot W) \\times N_p}\\) denote the predicted score after the softmax layer produced by \\(\\gamma_{\\theta}\\), and let \\(T \\in \\mathbb{R}^{(H \\cdot W) \\times C}\\) denote the flattened feature maps of \\(X\\). The token selection and aggregation process can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.584, + 0.469, + 0.626 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} = \\frac {\\hat {\\boldsymbol {S}} ^ {T} \\boldsymbol {T}}{\\sum_ {j} \\hat {\\boldsymbol {S}} _ {j}}, \\text {w h e r e} \\hat {\\boldsymbol {S}} = \\mathcal {T} (\\boldsymbol {S}, N _ {k}), N _ {k} = \\left[ \\alpha \\cdot \\frac {H \\cdot W}{N _ {p}} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.469, + 0.77 + ], + "angle": 0, + "content": "where \\(\\mathcal{T}\\) denotes the top-k operation; \\(\\hat{S} \\in \\mathbb{R}^{(H \\cdot W) \\times N_p}\\) represents the selected regions, \\(N_k\\) is the number of selected tokens, \\(\\alpha\\) is a hyperparameter controlling the selection ratio, and \\(P \\in \\mathbb{R}^{N_p \\times C}\\) represents the aggregated part features. There are two main advantages of selecting the top-k tokens instead of preserving all of them: (1) it helps filter out noisy tokens that could bring noisy clues to subsequent modules; (2) it can enhance the locality of the selected region and facilitate the learning of local representations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.773, + 0.469, + 0.817 + ], + "angle": 0, + "content": "Discriminability Constraint. To ensure the part features \\( P \\) contains discriminative information, we design the discriminative constraint loss, which is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.824, + 0.469, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i s} = - \\sum_ {i = 1} ^ {N _ {p}} \\log \\left(\\Phi_ {i} \\left(\\boldsymbol {P} _ {i}\\right) _ {y}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\Phi_k\\) denotes part-specific classifiers implemented with a simple fully connected layer with softmax activation, and \\(y\\) is the label of the current sample." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.578 + ], + "angle": 0, + "content": "Diversity Constraint. By training DRM with only Eq. (4), the model would tend to select several identical regions, resulting in suboptimal performance. This can be attributed to the shortcut learning characteristics [6] of deep learning systems that models attempt to find the simplest (but may be suboptimal) solution to solve a given task. To enhance the diversity of the selected regions, we further design the diversity constraint loss, which is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.59, + 0.891, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i v} = \\sum_ {i, j} \\operatorname {t r i u} \\left(\\hat {\\boldsymbol {S}} ^ {T} \\hat {\\boldsymbol {S}}, 1\\right) _ {i, j}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.892, + 0.691 + ], + "angle": 0, + "content": "where \\(\\mathrm{triu}(\\cdot, 1)\\) denotes the upper triangular part (excluding the diagonal) of the given matrix. This diversity constraint loss can be regarded as imposing an explicit penalty on the model when the selected key regions become too similar." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.769 + ], + "angle": 0, + "content": "As shown in Figure 2, the DRM module is not shared across modalities. This can help to learn better modality-specific part prototypes and select more discriminative regions, leading to better performance. This design will be empirically validated in Sec. 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.798, + 0.88, + 0.814 + ], + "angle": 0, + "content": "3.2.2 Target-aware Style-agnostic Attention Adapter" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To achieve target-aware attention, it is important to properly localize relevant regions in the feature maps by taking the aggregated part features \\( P \\) as the reference. A straightforward solution is to directly apply Scaled Dot-Product Attention [32] by taking \\( P \\) as the part queries and the flattened" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11125" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.454, + 0.106 + ], + "angle": 0, + "content": "feature maps \\( T \\) as the keys and the values, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.112, + 0.47, + 0.137 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t n} (\\boldsymbol {T}; \\boldsymbol {P}) = \\operatorname {s o f t m a x} \\left(\\boldsymbol {P} \\boldsymbol {T} ^ {T} / \\sqrt {d}\\right) \\boldsymbol {T}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.141, + 0.47, + 0.307 + ], + "angle": 0, + "content": "where \\(d\\) is the feature dimension. However, this naive solution simply adopts dot product as the similarity metric, which could result in inaccurate attention scores. Because the features of different modalities suffer from large distributions shift, making them hard to be properly compared using a simple dot product operation. To this end, we design the Target-aware Style-agnostic Attention Adapter (TSAA), which includes a more reasonable similarity calculator. As shown in Figure 2 (b), we first apply Instance Normalization (IN) [31] to the part queries \\(P\\) and each token of the feature maps \\(X\\), formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.312, + 0.47, + 0.345 + ], + "angle": 0, + "content": "\\[\n\\operatorname {I N} (\\boldsymbol {P}) = \\frac {\\boldsymbol {P} - \\mu (\\boldsymbol {T} _ {P})}{\\sigma (\\boldsymbol {T} _ {P})}, \\quad \\operatorname {I N} (\\boldsymbol {T}) = \\frac {\\boldsymbol {T} - \\mu (\\boldsymbol {T})}{\\sigma (\\boldsymbol {T})}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.471, + 0.637 + ], + "angle": 0, + "content": "where \\(\\mu (\\cdot)\\) and \\(\\sigma (\\cdot)\\) denote calculating the instance-level mean and standard deviation; \\(T_{P}\\) is the flattened feature maps that \\(P\\) derives from (see Eq. (3)). The motivation of this design is that the modality gap between IR and RGB images can be interpreted as the large discrepancies in style, and IN has been proven to be effective in reducing the style variance [14, 39, 13]. After that, the normalized features are fed into multi-layer perceptrons (MLPs) to learn nonlinear projection and capture complex patterns of the features. We then calculate the inner product of the projected features after the MLPs and apply softmax function on the spatial dimension to derive the final similarity. We can then apply spatial attention by weighted averaging all tokens using the computed similarities. In addition, we also apply query-guided channel attention to emphasize important channels in the feature map and suppress less important ones, where scores of channel attention are generated by an MLP layer taking part queries as input. Formally, the TSAA module, denoted by \\(\\mathcal{A}(\\cdot ;\\cdot)\\), can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.643, + 0.469, + 0.66 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (\\boldsymbol {T}; \\boldsymbol {P}) = \\mathcal {S} (\\boldsymbol {T}, \\boldsymbol {P}) \\boldsymbol {T} \\otimes \\mathcal {M} (\\boldsymbol {P}; \\theta_ {3}), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.662, + 0.469, + 0.687 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} (\\boldsymbol {T}, \\boldsymbol {P}) = \\operatorname {s o f t m a x} \\left(\\hat {\\boldsymbol {P}} \\hat {\\boldsymbol {T}} ^ {T} / \\sqrt {d}\\right), \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.112, + 0.689, + 0.469, + 0.706 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {T}} = \\mathcal {M} (\\operatorname {I N} (\\boldsymbol {T}); \\theta_ {1}), \\quad \\hat {\\boldsymbol {P}} = \\mathcal {M} (\\operatorname {I N} (\\boldsymbol {P}); \\theta_ {2}), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.469, + 0.83 + ], + "angle": 0, + "content": "where \\(\\mathcal{S}\\) denotes the spatial similarity calculator, \\(\\otimes\\) denotes channel-wise multiplication, and \\(\\mathcal{M}(\\cdot ;\\theta)\\) denotes MLP with parameter \\(\\theta\\). The TSAA has two merits: (1) it allows style-agnostic attention adjustment based on any given part queries \\(P\\) regardless of the image styles, making it easier to achieve attention consensus; (2) it can naturally bridge the gap between cross-modal samples by attending to relevant regions and emphasizing relevant channels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.339, + 0.863 + ], + "angle": 0, + "content": "3.2.3 Part-aligned Metric Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Our part-aligned metric learning aims to reduce the cross-modal intra-class discrepancies between the part-aligned" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "features. As shown in Figure 2 (a), we first employ TSAA to perform cross-modal refinement since it can effectively bridge the gap between cross-modal samples as discussed in Sec. 3.2.2. The cross-modal refinement is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.162, + 0.892, + 0.183 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {f} _ {i} ^ {V, I} = \\mathcal {A} \\left(\\boldsymbol {T} _ {j} ^ {V}; \\boldsymbol {P} _ {i} ^ {I}\\right), \\quad \\boldsymbol {f} _ {i} ^ {I, V} = \\mathcal {A} \\left(\\boldsymbol {T} _ {j} ^ {I}; \\boldsymbol {P} _ {i} ^ {V}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.193, + 0.892, + 0.24 + ], + "angle": 0, + "content": "where \\(\\pmb{T}_j\\) is randomly selected from the mini-batch and \\(y_{i}^{I} = y_{j}^{V}\\) . \\(\\pmb{f}^{V,I}\\) and \\(\\pmb{f}^{I,V}\\) are called cross-refined features. Similarly, we also apply self-refinement using" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.25, + 0.892, + 0.27 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {f} _ {i} ^ {V, V} = \\mathcal {A} \\left(\\boldsymbol {T} _ {i} ^ {V}; \\boldsymbol {P} _ {i} ^ {V}\\right), \\quad \\boldsymbol {f} _ {i} ^ {I, I} = \\mathcal {A} \\left(\\boldsymbol {T} _ {i} ^ {I}; \\boldsymbol {P} _ {i} ^ {I}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.892, + 0.389 + ], + "angle": 0, + "content": "to obtain the self-refined features. Since \\( \\pmb{f}_i^{V,I} \\) and \\( \\pmb{f}_i^{I,I} \\) are refined using the same query (i.e., \\( P_i^I \\)), they would attend to the same regions and can thus be regarded as part-aligned features. We then design the Part-aligned Center Loss (PCL) to enhance the discriminability of these semantically aligned embeddings. Let \\( c_j^k \\) denotes the batch feature centroid of class \\( y_j^k \\) in modality \\( k \\) (\\( k \\in \\{V, I\\} \\)) given by" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.397, + 0.892, + 0.431 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {c} _ {j} ^ {V} = \\frac {1}{| \\mathcal {S} (j) |} \\sum_ {i \\in \\mathcal {S} (j)} \\boldsymbol {f} _ {i} ^ {V, V}, \\quad \\boldsymbol {c} _ {j} ^ {I} = \\frac {1}{| \\mathcal {S} (j) |} \\sum_ {i \\in \\mathcal {S} (j)} \\boldsymbol {f} _ {i} ^ {I, I}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.443, + 0.874, + 0.459 + ], + "angle": 0, + "content": "where \\(S(j) = \\{i\\mid y_i = y_j\\}\\). Our PCL is then defined as" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.47, + 0.892, + 0.516 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {p c l} = \\sum_ {i, j} \\left[ \\mathrm {g} \\left(\\boldsymbol {f} _ {i} ^ {V I}, \\boldsymbol {c} _ {j} ^ {I}\\right) + \\mathrm {g} \\left(\\boldsymbol {f} _ {i} ^ {I V}, \\boldsymbol {c} _ {j} ^ {V}\\right) + \\right. \\tag {14} \\\\ \\left. \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {I}, \\boldsymbol {c} _ {j} ^ {V}\\right) + \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {I}, \\boldsymbol {c} _ {j} ^ {I}\\right) + \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {V}, \\boldsymbol {c} _ {j} ^ {V}\\right) \\right]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.526, + 0.892, + 0.557 + ], + "angle": 0, + "content": "Here, \\( \\mathrm{g} \\) and \\( \\mathrm{s} \\) aim to gather up intra-class features and separate inter-class features, respectively, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.562, + 0.891, + 0.607 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathrm {g} (\\boldsymbol {f}, \\boldsymbol {c}) = \\left[ \\mathbb {1} \\left(y _ {(\\boldsymbol {f})} = y _ {(\\boldsymbol {c})}\\right) \\cdot \\| \\boldsymbol {f} - \\boldsymbol {c} \\| _ {2} \\right], \\\\ \\mathrm {s} \\left(\\boldsymbol {c} _ {i}, \\boldsymbol {c} _ {j}\\right) = \\left[ \\mathbb {1} \\left(y _ {\\left(\\boldsymbol {c} _ {i}\\right)} \\neq y _ {\\left(\\boldsymbol {c} _ {j}\\right)}\\right) \\cdot \\left[ \\sigma - \\| \\boldsymbol {c} _ {i} - \\boldsymbol {c} _ {j} \\| _ {2} \\right] _ {+} \\right], \\tag {15} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.611, + 0.892, + 0.657 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is a marginal parameter adopted to avoid optimizing \"already correct\" centroid pairs; \\([z]_{+} = \\max (z,0);y(\\cdot)\\) denotes the label of the corresponding embedding/centroid." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.804, + 0.683 + ], + "angle": 0, + "content": "3.3. Cross-modal Knowledge Exchange" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Even though the cross-refined embeddings yield smaller distribution gaps with respect to the target modality, it is infeasible to employ cross-refined embeddings for retrieval during the inference stage. Because the cross-modal refinement requires taking the part features \\( P \\) (derived from DRM using the images of modality counterpart) as queries and applying query-guided attention using Eq. (10). This process need to be carried out for all query-gallery pairs, which brings high computational costs since gallery sets are generally large. To this end, we propose a novel solution called MatchDistill, which allows DRM to directly generate target-modality-like part features. This is achieved by associating the heterogeneous queries \\( P^V \\) and \\( P^I \\) with our Cross-modal Query Matching algorithm and propagating" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11126" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "the modality-specific knowledge to the best-matched query of modality counterparts. For clarity, here we only take matching and propagating the knowledge from \\( P^I \\) to \\( P^V \\) as an example since MatchDistill has a symmetric pipeline. As shown in Figure 2, in MatchDistill, we first construct a complete bipartite graph \\( G(U, V, E) \\), where the vertices \\( U \\) and \\( V \\) represent \\( P^I \\) and \\( P^V \\), respectively. Each edge in \\( E \\) connects a vertex in \\( U \\) to one in \\( V \\). The weights of the edges are the semantic similarities between queries, which are measured by the dot product of the attention mask calculated by Eq. (10), formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.266, + 0.47, + 0.287 + ], + "angle": 0, + "content": "\\[\nw \\left(\\boldsymbol {E} _ {k _ {1}, k _ {2}} ^ {V}\\right) = \\langle \\mathcal {S} \\left(\\boldsymbol {X} ^ {V}, \\boldsymbol {P} _ {k _ {1}} ^ {I}\\right), \\mathcal {S} \\left(\\boldsymbol {X} ^ {V}, \\boldsymbol {P} _ {k _ {2}} ^ {V}\\right) \\rangle , \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.295, + 0.47, + 0.386 + ], + "angle": 0, + "content": "where \\( w(\\cdot) \\) denotes the weight of the edge. The idea behind this is straightforward: if \\( P_{k1} \\) and \\( P_{k2} \\) represent the same semantic region, their attention masks should have a high level of similarity. This could help effectively model the semantic correlations of the heterogeneous part queries. The part query matching problem can then be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.396, + 0.47, + 0.425 + ], + "angle": 0, + "content": "\\[\n\\arg \\max _ {M \\subseteq E} \\sum_ {e \\in M} w (e), \\quad s. t. \\left| M \\right| = N _ {p} \\text {a n d} \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.426, + 0.418, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\forall (u _ {1}, v _ {1}), (u _ {2}, v _ {2}) \\in M, u _ {1} \\neq u _ {2} \\text {a n d} v _ {1} \\neq v _ {2},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.473, + 0.633 + ], + "angle": 0, + "content": "where \\(M\\) represents the edges of the optimal match (meaning that \\(\\forall (u,v)\\in M\\), \\(P_u^V\\) and \\(P_v^I\\) represent the same semantic region). We solve this part query matching problem (Eq. (17)) with the Kuhn-Munkres assignment algorithm [15]. After that, the mutual knowledge propagation process can be performed between all \\((u,v)\\in M\\) pairs since they are semantically aligned. Specifically, the proposed knowledge distillation is conducted in two levels, i.e., the feature level and the logit level. For the feature level, we propose to align the similarity maps of the best-matched query pairs. This is equivalent to maximizing the weight of the optimal bipartite graph, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.639, + 0.47, + 0.663 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {k d 1} = - \\sum_ {e \\in M} w (e). \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.469, + 0.698 + ], + "angle": 0, + "content": "For the logit level, we constrain the consistency of their softmax classification distribution by" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.705, + 0.47, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {k d 2} = \\sum_ {(u, v) \\in \\boldsymbol {M}} \\mathcal {D} _ {k l} \\left(\\boldsymbol {p} _ {u} ^ {V, I} \\| \\boldsymbol {p} _ {v} ^ {V, V}\\right), \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\pmb{p}\\) denotes the post-softmax classification probability, and \\(\\mathcal{D}_{kl}\\) denotes Kullback-Leibler divergence. With the above cross-modal knowledgeable propagation, the self-refined features can also capture important information that can benefit cross-modal retrieval like the cross-refined ones. Therefore, there is no needs to perform cross-refinement during inference. In addition, by optimizing \\(\\mathcal{L}_{kd1}\\) and \\(\\mathcal{L}_{kd2}\\), we observe that the optimal matches \\(M\\) gradually get stabilized as the training progresses. This suggests that the optimal matches with the highest occurrence in the last training epoch, denoted as \\(\\hat{M}\\), can be used for test-time matching." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.715, + 0.107 + ], + "angle": 0, + "content": "3.4. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.117, + 0.857, + 0.133 + ], + "angle": 0, + "content": "Training. The overall training objective is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.139, + 0.892, + 0.156 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {i d} + \\mathcal {L} _ {p c l} + \\lambda_ {1} \\mathcal {L} _ {k d 1} + \\lambda_ {2} \\mathcal {L} _ {k d 2} + \\lambda_ {3} \\mathcal {L} _ {d i s} + \\lambda_ {4} \\mathcal {L} _ {d i v}, \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.162, + 0.892, + 0.193 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{id}\\) is the routinely used identity classification loss; \\(\\lambda_1, \\lambda_2, \\lambda_3\\), and \\(\\lambda_4\\) are adopted to balance different losses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Inference. During inference, we first reorder the learned prototypes of the DRM (i.e., the parameters of the pointwise convolutional layer in DRM) according to \\(\\hat{M}\\) to ensure that the self-refined embeddings can be semantically aligned. After that, the summation of the cosine similarity of each part is then adopted as the comparison metric. Formally, the similarity between the \\(i^{th}\\) visible and the \\(j^{th}\\) infrared sample is given by \\(\\sum_{p} \\cos(\\boldsymbol{f}_{i,p}^{V,V}, \\boldsymbol{f}_{j,p}^{I,I})\\), where \\(\\cos\\) denotes cosine similarity computation, and the subscript \\(p\\) denotes indexing in the part dimension." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.361, + 0.634, + 0.379 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.386, + 0.707, + 0.403 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.457 + ], + "angle": 0, + "content": "Datasets. The proposed method is evaluated under the same protocols of existing work [20] on two widely-used VI Re-ID datasets, i.e., SYSU-MM01 [38] and RegDB [25]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Implementation Details. We adopt ResNet-50 [9] as the backbone network following existing work. At each training iteration, 8 identities are randomly sampled. For each identity, 4 visible and 4 infrared images are selected to form a mini-batch. The model is trained for 100 epochs in total on RTX 3090 GPUs with SGD optimizer. The learning rate linearly increased from 0.01 to 0.1 in the first 10 epochs. The cosine annealing strategy [21] is adopted in the remaining 90 epochs to decay the learning rate to \\(10^{-3}\\). The hyperparameters are decided by cross-validation. Specifically, we set \\(\\lambda_{1} = 1\\), \\(\\lambda_{2} = 1\\), \\(\\lambda_{3} = 0.1\\), \\(\\lambda_{4} = 0.1\\), \\(N_{p} = 4\\), \\(\\alpha = 0.6\\) and \\(\\sigma = 0.6\\). All models are tested without using re-ranking algorithms or gallery set information for fair comparison." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.664, + 0.869, + 0.68 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.838 + ], + "angle": 0, + "content": "The comparison results on SYSU-MM01 and RegDB with state-of-the-art (SOTA) methods are shown in Table 1 and Table 2, respectively. It can be seen that the proposed CAL outperforms existing approaches by large margins on both datasets. Specifically, on the SYSU-MM01 dataset, our proposed method surpasses the state-of-the-art approaches [12, 20] on most of the evaluation metrics. As for the RegDB dataset, our method also achieves new state-of-the-art results. These experimental results verify the effectiveness and superiority of the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.721, + 0.861 + ], + "angle": 0, + "content": "4.3. Analysis and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of TCA and MatchDistill. To verify the effectiveness of the two key components of CAL (i.e., TCA" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11127" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.088, + 0.892, + 0.116 + ], + "angle": 0, + "content": "Table 1. Comparison with SOTA methods on the SYSU-MM01 dataset. †: Following previous work [43], for cm-SSFT [22] and CIFT [17], we report the performance when no extra auxiliary information of the gallery set is introduced for fair comparison." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.119, + 0.892, + 0.348 + ], + "angle": 0, + "content": "
MethodVenueAll-searchIndoor-Search
Single-ShotMulti-ShotSingle-ShotMulti-Shot
R1↑R10↑mAP↑R1↑R10↑mAP↑R1↑R10↑mAP↑R1↑R10↑mAP↑
Zero-Pad [38]ICCV 201714.8054.1215.9519.1361.4010.8920.5868.3826.9224.4375.8618.64
AGW [44]TPAMI 202247.5084.3947.65---54.1791.1462.97---
cm-SSFT†[22]CVPR 202047.70-54.1057.40-59.10------
NFS [2]CVPR 202156.9191.3455.4563.5194.4248.5662.7996.5369.7970.0397.7061.45
SMCL [36]ICCV 202167.3992.8761.7872.1590.6654.9368.8496.5575.5679.5795.3366.57
MCLNet [7]ICCV 202165.4093.3361.98---72.5696.9876.58---
MPMN [35]TMM 202148.9890.3362.4160.8888.7051.9064.8996.8576.4774.4292.9366.98
FMCNet [46]CVPR 202266.34-62.51---68.15-74.09---
CAJ [43]ICCV 202169.8895.7166.89---76.2697.8880.37---
CIFT†[17]ECCV 202271.77-67.6478.00-62.4678.65-82.1186.97-77.03
MPANet [39]CVPR 202170.5896.2168.2475.5897.9162.9176.7498.2180.9584.2299.6675.11
CMT [12]ECCV 202271.8896.4568.5780.2397.9163.1376.9097.6879.9184.8799.4174.11
MAUM [20]CVPR 202271.68-68.79---76.97-81.94---
CAL (Ours)-74.6696.4771.7377.0598.0164.8679.6998.9383.6886.9799.8378.51
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.363, + 0.468, + 0.391 + ], + "angle": 0, + "content": "Table 2. Comparison with SOTA methods under \"visible to infrared\" and \"infrared to visible\" modes on RegDB. †: see Table 1." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.394, + 0.468, + 0.598 + ], + "angle": 0, + "content": "
MethodVisible to InfraredInfrared to Visible
R1 ↑R10 ↑mAP ↑R1 ↑R10 ↑mAP ↑
Zero-Pad [38]17.7534.2118.9016.6334.6817.82
cm-SSFT†[22]65.40-65.6063.80-64.20
AGW [44]70.0586.2166.3775.9390.9369.49
NFS [2]80.5491.9672.1077.9590.4569.79
MCLNet [7]80.3192.7073.0775.9390.9369.49
CAJ [43]85.0395.4979.1484.7595.3377.82
SMCL [36]83.93-79.8383.05-78.57
MPANet [39]83.70-80.9082.80-80.70
MPMN [35]86.5696.8682.9184.6295.5179.49
FMCNet [46]89.12-84.4388.38-83.86
MAUM [20]87.87-85.0986.95-84.34
CIFT†[17]92.17-86.9690.12-84.81
CMT [12]95.1798.8287.3091.9797.9284.46
CAL (Ours)94.5199.7088.6793.6499.4687.61
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.468, + 0.759 + ], + "angle": 0, + "content": "and MatchDistill) and analyze their contribution to the overall performance, we conduct experiments on the more challenging SYSU-MM01 dataset. The experimental results are given in Table 3, where we adopt ResNet-50 as the baseline method. We can see that both TCA and MatchDistill are shown to be essential to the final performance and can significantly boost the performance of the baseline method. These findings demonstrate the effectiveness and importance of our proposed approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Analysis on the DRM Module. To demonstrate the superiority of the design of DRM, we conduct experiments by removing the key components of DRM or replacing them with other alternatives. The experimental results are shown in Table 4 (top). We can see that all modifications can lead to performance degradation. Specifically, we can see that when training DRM without the diversity constraint \\((\\mathcal{L}_{div})\\) or discriminability constraint \\((\\mathcal{L}_{dis})\\), the performance drops significantly, indicating that it is essential to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.892, + 0.653 + ], + "angle": 0, + "content": "guarantee both the discriminability and diversity of the selected regions. When replacing the modality-specific DRM with the modality-shared one, a performance drop can also be observed. This is because the modality-shared DRM cannot learn modality-specific patterns, making it hard to discover discriminative modality-specific clues. It can also be observed that using learnable vectors instead of DRM produces poor performance since they are less descriptive than the part features generated by DRM. Horizontal Splitting (HS), which divides the feature maps into horizontal chunks, achieves slightly better results than learnable vectors since the chunks are more informative than learnable vectors. However, HS is still inferior to our DRM as handcrafted stripes cannot properly disentangle the feature maps into fine-grained discriminative body parts. We also study the impact of the number of regions generated and the parameter \\( N_{k} \\) and \\( \\alpha \\) in DRM. The experimental results are shown in Figure 3. The best performance is achieved when \\( N_{p} = 4 \\) and \\( \\alpha = 0.6 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.882 + ], + "angle": 0, + "content": "Analysis on the TSAA Module. To demonstrate the superiority of the TSAA design, we conduct experiments by replacing the spatial similarity calculation process (Eq. (9)) with the simple scaled dot-product operation and removing the query-guided channel attention mechanism. As shown in Table 4 (middle), the experimental results reveal significant drops in performance when adopting the scaled dot product as the similarity metric. This can be attributed to the style discrepancies between modalities, which make it difficult to effectively find the correlation between heterogeneous data with dot product. Our TSAA module, on the other hand, is adept at reducing style discrepancies between heterogeneous data when computing similarity scores. In addition, the experimental results also validate the effectiveness of our query-guided channel attention mechanism." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Analysis on PCL. The PCL aligns the cross-modal em" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11128" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.088, + 0.47, + 0.116 + ], + "angle": 0, + "content": "Table 3. Effectiveness of the proposed components on the SYSUMM01 dataset under the all-search single-shot mode." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.117, + 0.468, + 0.196 + ], + "angle": 0, + "content": "
BaselineTCAMatchDistillSYSU-MM01
R1↑R10↑mAP↑
✓57.8289.9156.40
✓✓70.1593.1267.40
✓✓✓74.6696.4771.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.206, + 0.47, + 0.29 + ], + "angle": 0, + "content": "Table 4. Ablation study of DRM and TSAA on SYSU-MM01 under the all-search single-shot mode. Shared DRM: the weights of DRM are shared for both modalities. \\(LV\\): replacing the selected regions with \\(N_p\\) learnable vectors. HS: Horizontal Split (\\(n\\) chunks). TSAA (SD): adopting scaled dot-product for similarity computation in TSAA. CA: the channel-wise attention in TSAA." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.291, + 0.468, + 0.528 + ], + "angle": 0, + "content": "
MethodSYSU-MM01
R1↑R10↑mAP ↑
DRM w/o L_div72.7695.7169.85
DRM w/o L_dis72.2395.3769.38
DRM → Shared DRM72.5794.9569.51
DRM → LV71.0794.0168.60
DRM → HS (n = 2)72.7095.5070.02
DRM → HS (n = 4)73.1595.7670.24
DRM → HS (n = 6)72.5794.9569.51
TSAA (SD)72.5794.9569.51
TSAA (SD) w/o CA70.5795.4767.77
w/o PCL66.9493.4264.32
PCL → Triplet loss [11]68.0993.2465.41
PCL → Center loss [37]71.4894.6069.13
PCL → ICA&CCA [7]69.5595.2170.01
CAL (Ours)74.6696.4771.73
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.687 + ], + "angle": 0, + "content": "beddings that have consistent semantics. We conduct experiments by removing or replacing PCL with other alternatives, including the prevailing metric learning losses [11, 37] and the one [7] designed specifically for VI Re-ID. The experimental results reported in Table 4 (bottom) show that our PCL contributes largely to the final performance and surpasses other competitors. This is mainly owing to the superior design of PCL that consider reducing intra-class variation using the part-aligned embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Analysis on MatchDistill. We conduct ablation experiments to evaluate the contribution of the proposed Cross-modal Query Matching algorithm and the two knowledge distillation losses \\((\\mathcal{L}_{kd1}\\) and \\(\\mathcal{L}_{kd2})\\) in MatchDistill. As shown in Table 5, the experimental results demonstrate the significant role they play in enhancing retrieval accuracy. When aligning the attention maps with \\(\\mathcal{L}_{kd1}\\) and constraining the consistency of classification probability with \\(\\mathcal{L}_{kd2}\\), the performance boosts significantly, verifying the effectiveness of our knowledge exchange strategies. When incorporating our CQM, the accuracy can be further improved. This suggests that it is beneficial to ensure semantic consistency when conducting knowledge exchange by finding the best-matched part queries with our CQM algorithm." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.089, + 0.697, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.089, + 0.887, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.57, + 0.185, + 0.822, + 0.199 + ], + "angle": 0, + "content": "Figure 3. Parameter analysis of \\(N_{p}\\) and \\(\\alpha\\)" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.21, + 0.892, + 0.238 + ], + "angle": 0, + "content": "Table 5. Effectiveness of each component of MatchDistill on the SYSU-MM01 dataset under the all-search single-shot mode." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.239, + 0.891, + 0.349 + ], + "angle": 0, + "content": "
Lkd1Lkd2CQMSYSU-MM01
R1↑R10↑mAP↑
70.1593.1267.40
✓72.7595.7169.86
✓72.2695.1668.50
✓✓73.6395.7970.61
✓✓✓74.6696.4771.73
" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.354, + 0.685, + 0.51 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.354, + 0.892, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.515, + 0.88, + 0.529 + ], + "angle": 0, + "content": "Figure 4. Qualitative analysis of the proposed DRM and TSAA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.892, + 0.667 + ], + "angle": 0, + "content": "Qualitative Results. We visualize the regions selected by the DRM module in Figure 4. It can be seen that the DRM can select diverse and discriminative regions, which could serve as strong guidance for the subsequent TSAA module. We also visualize the attention scores generated by the TSAA in Figure 4. We can see that the proposed TSAA has a strong capability in searching the corresponding regions given the key regions selected by DRM." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.619, + 0.695 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present the Concordant Attention Learning (CAL) framework, which learns concordant attention across the visible and infrared modalities and can effectively bridge the modality gap for VI Re-ID. We show that it is beneficial to design target-aware attention mechanisms to ensure attention concordance when aligning cross-modal samples. We also verify that exploiting cross-modal clues from the target modality and enabling cross-modal knowledge exchange in a match-and-distill manner can facilitate the learning of inter-modal correlations. Extensive experiments demonstrate the effectiveness and superiority of CAL over state-of-the-art methods, suggesting the potential of our approach for improving VI Re-ID research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11129" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.091, + 0.245, + 0.108 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.117, + 0.47, + 0.192 + ], + "angle": 0, + "content": "This work is supported by National Natural Science Foundation of China (No.62073004), Science and Technology Plan of Shenzhen (No.JCYJ20200109140410340), and Shenzhen Fundamental Research Program (No.GXWD20 201231165807007-20200807164903001)." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.21, + 0.174, + 0.226 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.236, + 0.47, + 0.291 + ], + "angle": 0, + "content": "[1] Guangyi Chen, Jiwen Lu, Ming Yang, and Jie Zhou. 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IEEE TCSVT, 32(3):1418-1430, Mar. 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11131" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/f96bbbd7-1bf4-40cd-9545-e535cf6aa841_origin.pdf b/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/f96bbbd7-1bf4-40cd-9545-e535cf6aa841_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3d410a0b4ed27bf0c10293321d9ee57320a8996e --- /dev/null +++ b/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/f96bbbd7-1bf4-40cd-9545-e535cf6aa841_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e8ebbfb885f3cb250ae7bb23e1a02aab981918b29cdee3ed105744c9ab7359a9 +size 1353908 diff --git a/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/full.md b/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e3fa01e35c3066a43d29a6df8cd8b8d3c9121e61 --- /dev/null +++ b/2023/Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification/full.md @@ -0,0 +1,348 @@ +# Learning Concordant Attention via Target-aware Alignment for Visible-Infrared Person Re-identification + +Jianbing $\mathrm{Wu}^{1,\dagger}$ Hong Liu $^{2,\dagger,*}$ Yuxin $\mathrm{Su}^{3,\dagger}$ Wei Shi $^{4,\dagger}$ Hao Tang $^{5,\ddagger}$ + +† Key Laboratory of Machine Perception, Shenzhen Graduate School, Peking University, China ‡ Computer Vision Lab, ETH Zürich, Switzerland + +1,3{kimbing.ng, yuxinsu}@stu.pku.edu.cn 2,4{hongliu, pkusw}@pku.edu.cn hao.tang@vision.ee.ethz.ch + +# Abstract + +Owing to the large distribution gap between the heterogeneous data in Visible-Infrared Person Re-identification (VI Re-ID), we point out that existing paradigms often suffer from the inter-modal semantic misalignment issue and thus fail to align and compare local details properly. In this paper, we present Concordant Attention Learning (CAL), a novel framework that learns semantic-aligned representations for VI Re-ID. Specifically, we design the Target-aware Concordant Alignment paradigm, which allows target-aware attention adaptation when aligning heterogeneous samples (i.e., adaptive attention adjustment according to the target image being aligned). This is achieved by exploiting the discriminative clues from the modality counterpart and designing effective modality-agnostic correspondence searching strategies. To ensure semantic concordance during the cross-modal retrieval stage, we further propose MatchDistill, which matches the attention patterns across modalities and learns their underlying semantic correlations by bipartite-graph-based similarity modeling and cross-modal knowledge exchange. Extensive experiments on VI Re-ID benchmark datasets demonstrate the effectiveness and superiority of the proposed CAL. + +# 1. Introduction + +Person Re-identification (Re-ID) aims to associate person identities across non-overlapping cameras. It has gained increasing attention in recent years due to its practical applications in real-world surveillance systems. Conventional person Re-ID methods mainly focus on retrieving the same identity across visible (RGB) cameras [48, 29, 16, 23, 10]. Despite their remarkable success, they have limited applicability since visible cameras cannot capture discriminative information under poor-lighting conditions (e.g., at night). To improve the illumination robustness, infrared (IR) cameras are widely applied to cooperate with visible ones in + +![](images/d606ca4fac1a5800e24b1d535f9fcd07a13c330834ff54f8cc5c5ef01a8c0f05.jpg) +Figure 1. A high-level overview of typical local feature learning paradigms. (a) Splitting-based: The semantics of the hand-craft stripes are not always properly aligned. (b) Auxiliary-model-based: Pretrained auxiliary models are often error-prone due to the domain shifts (especially for infrared image). (c) Attention-based: Due to the inter-modal distribution gap, existing style-sensitive attention module with less descriptive learnable prototypes often fails to attend semantically consistent regions. (d) CAL (Ours): Our method can learn concordant attention by discriminative region mining, target-aware style-agnostic attention, and part-aligned knowledge exchange. + +real-world surveillance systems. This increases the need to explore the Visible-Infrared Person Re-identification (VI Re-ID) problem, which aims to associate the person images taken by different spectrum cameras to achieve long-term person tracking in 24-hour surveillance systems. + +Compared to traditional RGB-based re-identification, VI Re-ID is much more challenging due to the differences in spectral properties between visible and infrared images. This data heterogeneity can lead to severe misalignment in the feature space and large intra-class discrepancy, resulting in significant degradation in performance. In addition, similarly to RGB-based Re-ID tasks, VI Re-ID can also be + +impacted by the changes in pose or background, resulting in increased difficulties. + +Recent years have witnessed a surge of creative work on mitigating the modality gap for VI Re-ID [38, 43, 18, 44, 4, 20]. However, as most existing methods only consider learning global representations from the whole image, they fail to compare local details. In addition, owing to the shortcut learning characteristics [6], global-feature-based methods would tend to learn modality-specific shortcut patterns, making the learned features susceptible to concentrating on divergent regions in each modality and resulting in suboptimal performance. A seemingly straightforward solution is to learn semantic-aligned local features with either splitting-based [29, 8, 20], auxiliary-model-based methods [26, 19, 28, 1], or attention-base paradigms [18, 16, 33, 27] instead of the global ones. However, these methods also fail to achieve inter-modal semantic alignment, as demonstrated in Figure 1, and forcibly aligning these semantic-misaligned embeddings would inevitably injure the training process and compromise the performance. + +Different from these deep learning methods, human visual systems can naturally avoid the misalignment issue thanks to their target-aware comparison strategy. Considering the scenario of comparing two images of persons (referred to as "base image" and "target image", respectively), human vision systems would first identify multiple distinctive key regions (such as facial and clothing details) in the target image and then direct their attention to corresponding regions in the base image. In this manner, humans can always make perfect part-to-part comparisons since they are able to adaptively and accurately adjust their attention by referencing the key regions of the target image. This suggests that exploiting clues from the target image of the modality counterpart and exploring an effective cross-modal corresponding region-searching strategy can benefit in mitigating the inter-modal semantic misalignment issue. + +In this paper, we present Concordant Attention Learning (CAL), a novel framework that mimics the target-aware comparison behavior of human vision systems to learn semantic-aligned representations for VI Re-ID. Firstly, we devise the Target-aware Concordant Alignment (TCA) paradigm, which aims to exploit discriminative local clues from the target modality (i.e., the modality counterpart) when aligning heterogeneous embeddings. The proposed TCA consists of three components: (1) Discriminative Region Mining: identifying diverse and discriminative key regions from the feature maps of each training sample; (2) Target-aware Style-agnostic Attention Adapter: taking the selected key regions from the target modality as part queries, and applying target-aware refinement to adapt the feature attention and generate part-aligned embeddings; + +(3) Part-aligned Metric Learning: clustering or separating the part-aligned embeddings across modalities according to their identity labels. Even though this target-aware refinement scheme can mitigate the modality discrepancy by leveraging the clues from the target modality, it brings higher computational costs during inference. Because it needs to be carried out for all query-gallery pairs, and the gallery set is generally large. To this end, we further propose MatchDistill. First, we need to associate the generated part queries of different modalities to guarantee that the subsequent distillation is conducted on semantic-aligned features. This is achieved by modeling the correlations of their corresponding attention maps with bipartite graphs and conducting Cross-modal Query Matching (CQM) to find the optimal matches. After that, a dual-level knowledge distillation loss is designed to allow cross-modality knowledge exchange between the best-matched queries. This can facilitate the learning of underlying relationships between the visible and infrared modalities. After training with MatchDistill, each modality can learn knowledge from its modality counterpart, and no cross-modal interaction is needed during inference. + +Overall, our contributions are summarized as follows: + +- We propose Concordant Attention Learning (CAL), a target-aware training paradigm that mimics human behavior and learns concordant attention to alleviate the inter-modal attention bias issue for VI Re-ID. +- To enable part-aligned metric learning, we present Target-aware Concordant Alignment (TCA), which leverages cross-modal clues and allows adaptive attention adjustment when aligning heterogeneous embeddings. +- We propose MatchDistill, which matches the attention patterns across modalities and learns their underlying semantic correlations by bipartite-graph-based similarity modeling and cross-modal knowledge exchange. +- Extensive experiments demonstrate that the proposed CAL archives state-of-the-art performance on both the SYSU-MM01 [38] and RegDB [25] datasets. + +# 2. Related Work + +Visible-Infrared Person Re-ID. Visible-Infrared Person Re-ID (VI Re-ID) has drawn increasing attention in recent years [43, 17, 39, 12, 20]. Mainstream VI Re-ID paradigms focus on bridging the modality gap via designing metric learning constraints [45, 42, 40], normalizing feature statistics [14, 39, 13], synthesizing auxiliary training samples [34, 3, 49, 24], or developing modality-specific and modality-shared feature learning paradigms [5, 22, 30]. However, these methods only consider learning global representations from entire images without considering the local information of images, leading to limited expressiveness of learned features. A few works also attempt to learn local + +features for VI Re-ID [8, 20, 41, 47] by splitting the feature maps into several hand-craft stripes. However, due to inaccurate detection boxes, pose variations, and occlusion, the hand-craft stripes are not always well-aligned, resulting in unsatisfactory performance. + +Local Feature Learning in Person Re-ID. Local feature learning is an important research direction for person re-identification since learning part aggregated features makes the model robust against misalignment [44]. It can be roughly divided into splitting-based methods, auxiliary-model-based methods, and attention-based methods. Splitting-based methods [29, 8, 20] focus on learning local features from horizontal-divided regions, which now serve as a strong part feature learning baseline. However, due to inaccurate detection boxes, pose variations, and occlusion, the semantics of the hand-craft stripes are not well aligned. The auxiliary-model-based methods [26, 19, 28, 1] often adopt off-the-shelf auxiliary human parsing or pose estimation networks to obtain semantically meaningful body parts. However, they require additional computational costs and are prone to noisy estimation, especially when the data distribution varies. The attention-based methods focus on exploiting attention mechanisms to localize discriminative human parts and have achieved great success [18, 16, 33, 27]. However, these methods cannot be directly applied to the cross-modality scenario of VI Re-ID due to the inter-modal semantic misalignment issue as discussed in Sec. 1. + +# 3. Methodology + +# 3.1. Intuition of Target-aware Alignment + +Let $\pmb{x}^k$ denote the training images of modality $k$ , where $k \in \{V, I\}$ ( $V$ for visible modality and $I$ for infrared modality). The visible and infrared samples in the dataset are denoted by $\mathcal{V} = \{\pmb{x}_j^V, y_j^V\}_{j=0}^{N_v}$ and $\mathcal{I} = \{\pmb{x}_j^I, y_j^I\}_{j=0}^{N_i}$ , respectively, where $N_v$ and $N_i$ are the numbers of samples of each modality in the dataset, and $y_j^k$ is the corresponding identity label of the $j$ -th sample from modality $k$ . The goal of Visible-Infrared Person Re-identification is to match the person identities across modalities according to feature similarities. Therefore, it is essential to reduce the large intra-class variation between heterogeneous samples. Existing paradigms often attempt to reduce the cross-modal intra-class variation by directly optimizing + +$$ +\mathbb {E} _ {i, j} \left[ \mathbb {1} \left(y _ {i} ^ {V} = y _ {j} ^ {I}\right) \cdot \mathrm {d} \left(f \left(\boldsymbol {x} _ {i} ^ {V}\right), f \left(\boldsymbol {x} _ {j} ^ {I}\right)\right) \right], \tag {1} +$$ + +where $f$ denotes the feature extractor, and $\mathrm{d}(\cdot, \cdot)$ represents the distance between features. However, as discussed in Sec. 1, the attention misalignment issue could injure the training process and compromise performance. We thus endow the model with the ability to adaptively adjust the attention according to the target being compared to achieve + +attention consensus. First, the Discriminative Region Mining (DRM) module, formulated as $\gamma(\cdot)$ , is introduced to disentangle the global features into diverse key body parts. We then devise the Target-aware Style-agnostic Attention Adapter (TSAA) to allow adaptive style-agnostic attention adjustment according to any given part queries regardless of the image styles. The feature extractor is then reformulated as $f(\pmb{x},\pmb{p})$ to represent the above dynamic attention adjustment process, where $\pmb{p}$ denotes the given body parts. The objective function to reduce the cross-modal intra-class variation can then be defined as + +$$ +\begin{array}{l} \mathbb {E} _ {i, j, k} \left[ \mathbb {1} \left(y _ {i} ^ {V} = y _ {j} ^ {I}\right) \cdot \mathrm {d} \left(f \left(\boldsymbol {x} _ {i} ^ {V}, \gamma \left(\boldsymbol {x} _ {j} ^ {I}\right) _ {k}\right), f \left(\boldsymbol {x} _ {j} ^ {I}, \gamma \left(\boldsymbol {x} _ {j} ^ {I}\right) _ {k}\right)\right) + \right. \tag {2} \\ \mathbb {1} (y _ {i} ^ {I} = y _ {j} ^ {V}) \cdot \mathrm {d} \big (f (\pmb {x} _ {i} ^ {I}, \gamma (\pmb {x} _ {j} ^ {V}) _ {k}), f (\pmb {x} _ {j} ^ {V}, \gamma (\pmb {x} _ {j} ^ {V}) _ {k}) \big) \Big ]. \\ \end{array} +$$ + +In this manner, the embeddings being optimized can achieve semantic concordance since the same queries are used to guide feature attention (for instance, $f(\pmb{x}_i^V, \gamma(\pmb{x}_j^I)_k)$ and $f(\pmb{x}_j^I, \gamma(\pmb{x}_j^I)_k)$ correspond to the same semantic region since they are refined using the same part query $\gamma(\pmb{x}_j^I)_k$ ). This also allows cross-modal interaction to facilitate the learning of underline relationships between modalities. The overall pipeline is depicted in Figure 2, and more details will be introduced in the following subsections. + +# 3.2. Target-aware Concordant Alignment + +# 3.2.1 Discriminative Region Mining + +The Discriminative Region Mining module aims to discover several diverse discriminative key regions from the feature maps $X \in \mathbb{R}^{C \times H \times W}$ derived from the backbone network, where $C$ , $H$ , and $W$ denote the number of channels, the height, and the width of the feature maps. Our DRM contains two stages: Part Scoring and Token Selection and Aggregation. The former aims to classify the tokens (i.e., the spatial vectors of $X$ ) into $N_{p}$ different parts, while the latter selects the top-k tokens for each part based on the scores and aggregates them to derive the part features $P$ . + +Part Scoring. To disentangle the feature maps into several diverse discriminative regions, we first develop a simple scorer network $\gamma_{\theta}$ to predict the scores of $N_{p}$ discriminative parts for each token in the feature maps. Here, $N_{p}$ is a hyperparameter representing the number of parts. Specifically, as illustrated in Figure 2, the feature maps $\mathbf{X}$ are first passed through multiple max-pooling layers with different scales (i.e., $1 \times 1$ for identity mapping, $3 \times 3$ , and $5 \times 5$ in this paper) to obtain features with different receptive fields. These features are then upsampled and concatenated along the channel dimension. Finally, the concatenated feature maps are fed into a point-wise convolutional layer with softmax activation along the spatial function to predict the scores of each part. + +![](images/866656e8d8514b0175e3d4181602bac0fc6dcff9987b7a4feef6f11faffa2acf.jpg) + +![](images/ab90f2e02d2db4488c582fe72d83a857731f3f43cffcab11e5e902891d814068.jpg) + +![](images/9f9bcc79bdb7cb081ddf330bf6c2061cb15ba5e58424e8f633a92d48679c59c5.jpg) +Figure 2. (a) The overall pipeline of the proposed Concordant Attention Learning (CAL), which consists of a deep CNN backbone, the Discriminative Region Mining (DRM), the Target-aware Style-agnostic Attention Adapter (TSAA), and the MatchDistill paradigm. Note that only half of the pipeline is depicted for clarity since the model is symmetric. (b) The pipeline of DRM. (c) The architecture of the proposed TSAA. (d) The pipeline of MatchDistill. Notations are introduced in Sec. 3. + +Token Selection and Aggregation. Given the scores predicted by $\gamma_{\theta}$ , we then select the tokens with top-k scores for each part and aggregate them by weighted averaging to derive the aggregated part features. Specifically, let $S \in \mathbb{R}^{(H \cdot W) \times N_p}$ denote the predicted score after the softmax layer produced by $\gamma_{\theta}$ , and let $T \in \mathbb{R}^{(H \cdot W) \times C}$ denote the flattened feature maps of $X$ . The token selection and aggregation process can be formulated as + +$$ +\boldsymbol {P} = \frac {\hat {\boldsymbol {S}} ^ {T} \boldsymbol {T}}{\sum_ {j} \hat {\boldsymbol {S}} _ {j}}, \text {w h e r e} \hat {\boldsymbol {S}} = \mathcal {T} (\boldsymbol {S}, N _ {k}), N _ {k} = \left[ \alpha \cdot \frac {H \cdot W}{N _ {p}} \right], \tag {3} +$$ + +where $\mathcal{T}$ denotes the top-k operation; $\hat{S} \in \mathbb{R}^{(H \cdot W) \times N_p}$ represents the selected regions, $N_k$ is the number of selected tokens, $\alpha$ is a hyperparameter controlling the selection ratio, and $P \in \mathbb{R}^{N_p \times C}$ represents the aggregated part features. There are two main advantages of selecting the top-k tokens instead of preserving all of them: (1) it helps filter out noisy tokens that could bring noisy clues to subsequent modules; (2) it can enhance the locality of the selected region and facilitate the learning of local representations. + +Discriminability Constraint. To ensure the part features $P$ contains discriminative information, we design the discriminative constraint loss, which is formulated as + +$$ +\mathcal {L} _ {d i s} = - \sum_ {i = 1} ^ {N _ {p}} \log \left(\Phi_ {i} \left(\boldsymbol {P} _ {i}\right) _ {y}\right), \tag {4} +$$ + +where $\Phi_k$ denotes part-specific classifiers implemented with a simple fully connected layer with softmax activation, and $y$ is the label of the current sample. + +Diversity Constraint. By training DRM with only Eq. (4), the model would tend to select several identical regions, resulting in suboptimal performance. This can be attributed to the shortcut learning characteristics [6] of deep learning systems that models attempt to find the simplest (but may be suboptimal) solution to solve a given task. To enhance the diversity of the selected regions, we further design the diversity constraint loss, which is defined as + +$$ +\mathcal {L} _ {d i v} = \sum_ {i, j} \operatorname {t r i u} \left(\hat {\boldsymbol {S}} ^ {T} \hat {\boldsymbol {S}}, 1\right) _ {i, j}, \tag {5} +$$ + +where $\mathrm{triu}(\cdot, 1)$ denotes the upper triangular part (excluding the diagonal) of the given matrix. This diversity constraint loss can be regarded as imposing an explicit penalty on the model when the selected key regions become too similar. + +As shown in Figure 2, the DRM module is not shared across modalities. This can help to learn better modality-specific part prototypes and select more discriminative regions, leading to better performance. This design will be empirically validated in Sec. 4. + +# 3.2.2 Target-aware Style-agnostic Attention Adapter + +To achieve target-aware attention, it is important to properly localize relevant regions in the feature maps by taking the aggregated part features $P$ as the reference. A straightforward solution is to directly apply Scaled Dot-Product Attention [32] by taking $P$ as the part queries and the flattened + +feature maps $T$ as the keys and the values, formulated as + +$$ +\operatorname {A t t n} (\boldsymbol {T}; \boldsymbol {P}) = \operatorname {s o f t m a x} \left(\boldsymbol {P} \boldsymbol {T} ^ {T} / \sqrt {d}\right) \boldsymbol {T}, \tag {6} +$$ + +where $d$ is the feature dimension. However, this naive solution simply adopts dot product as the similarity metric, which could result in inaccurate attention scores. Because the features of different modalities suffer from large distributions shift, making them hard to be properly compared using a simple dot product operation. To this end, we design the Target-aware Style-agnostic Attention Adapter (TSAA), which includes a more reasonable similarity calculator. As shown in Figure 2 (b), we first apply Instance Normalization (IN) [31] to the part queries $P$ and each token of the feature maps $X$ , formulated as + +$$ +\operatorname {I N} (\boldsymbol {P}) = \frac {\boldsymbol {P} - \mu (\boldsymbol {T} _ {P})}{\sigma (\boldsymbol {T} _ {P})}, \quad \operatorname {I N} (\boldsymbol {T}) = \frac {\boldsymbol {T} - \mu (\boldsymbol {T})}{\sigma (\boldsymbol {T})}, \tag {7} +$$ + +where $\mu (\cdot)$ and $\sigma (\cdot)$ denote calculating the instance-level mean and standard deviation; $T_{P}$ is the flattened feature maps that $P$ derives from (see Eq. (3)). The motivation of this design is that the modality gap between IR and RGB images can be interpreted as the large discrepancies in style, and IN has been proven to be effective in reducing the style variance [14, 39, 13]. After that, the normalized features are fed into multi-layer perceptrons (MLPs) to learn nonlinear projection and capture complex patterns of the features. We then calculate the inner product of the projected features after the MLPs and apply softmax function on the spatial dimension to derive the final similarity. We can then apply spatial attention by weighted averaging all tokens using the computed similarities. In addition, we also apply query-guided channel attention to emphasize important channels in the feature map and suppress less important ones, where scores of channel attention are generated by an MLP layer taking part queries as input. Formally, the TSAA module, denoted by $\mathcal{A}(\cdot ;\cdot)$ , can be formulated as + +$$ +\mathcal {A} (\boldsymbol {T}; \boldsymbol {P}) = \mathcal {S} (\boldsymbol {T}, \boldsymbol {P}) \boldsymbol {T} \otimes \mathcal {M} (\boldsymbol {P}; \theta_ {3}), \tag {8} +$$ + +$$ +\mathcal {S} (\boldsymbol {T}, \boldsymbol {P}) = \operatorname {s o f t m a x} \left(\hat {\boldsymbol {P}} \hat {\boldsymbol {T}} ^ {T} / \sqrt {d}\right), \tag {9} +$$ + +$$ +\hat {\boldsymbol {T}} = \mathcal {M} (\operatorname {I N} (\boldsymbol {T}); \theta_ {1}), \quad \hat {\boldsymbol {P}} = \mathcal {M} (\operatorname {I N} (\boldsymbol {P}); \theta_ {2}), \tag {10} +$$ + +where $\mathcal{S}$ denotes the spatial similarity calculator, $\otimes$ denotes channel-wise multiplication, and $\mathcal{M}(\cdot ;\theta)$ denotes MLP with parameter $\theta$ . The TSAA has two merits: (1) it allows style-agnostic attention adjustment based on any given part queries $P$ regardless of the image styles, making it easier to achieve attention consensus; (2) it can naturally bridge the gap between cross-modal samples by attending to relevant regions and emphasizing relevant channels. + +# 3.2.3 Part-aligned Metric Learning + +Our part-aligned metric learning aims to reduce the cross-modal intra-class discrepancies between the part-aligned + +features. As shown in Figure 2 (a), we first employ TSAA to perform cross-modal refinement since it can effectively bridge the gap between cross-modal samples as discussed in Sec. 3.2.2. The cross-modal refinement is defined as + +$$ +\boldsymbol {f} _ {i} ^ {V, I} = \mathcal {A} \left(\boldsymbol {T} _ {j} ^ {V}; \boldsymbol {P} _ {i} ^ {I}\right), \quad \boldsymbol {f} _ {i} ^ {I, V} = \mathcal {A} \left(\boldsymbol {T} _ {j} ^ {I}; \boldsymbol {P} _ {i} ^ {V}\right), \tag {11} +$$ + +where $\pmb{T}_j$ is randomly selected from the mini-batch and $y_{i}^{I} = y_{j}^{V}$ . $\pmb{f}^{V,I}$ and $\pmb{f}^{I,V}$ are called cross-refined features. Similarly, we also apply self-refinement using + +$$ +\boldsymbol {f} _ {i} ^ {V, V} = \mathcal {A} \left(\boldsymbol {T} _ {i} ^ {V}; \boldsymbol {P} _ {i} ^ {V}\right), \quad \boldsymbol {f} _ {i} ^ {I, I} = \mathcal {A} \left(\boldsymbol {T} _ {i} ^ {I}; \boldsymbol {P} _ {i} ^ {I}\right), \tag {12} +$$ + +to obtain the self-refined features. Since $\pmb{f}_i^{V,I}$ and $\pmb{f}_i^{I,I}$ are refined using the same query (i.e., $P_i^I$ ), they would attend to the same regions and can thus be regarded as part-aligned features. We then design the Part-aligned Center Loss (PCL) to enhance the discriminability of these semantically aligned embeddings. Let $c_j^k$ denotes the batch feature centroid of class $y_j^k$ in modality $k$ ( $k \in \{V, I\}$ ) given by + +$$ +\boldsymbol {c} _ {j} ^ {V} = \frac {1}{| \mathcal {S} (j) |} \sum_ {i \in \mathcal {S} (j)} \boldsymbol {f} _ {i} ^ {V, V}, \quad \boldsymbol {c} _ {j} ^ {I} = \frac {1}{| \mathcal {S} (j) |} \sum_ {i \in \mathcal {S} (j)} \boldsymbol {f} _ {i} ^ {I, I}, \tag {13} +$$ + +where $S(j) = \{i\mid y_i = y_j\}$ . Our PCL is then defined as + +$$ +\begin{array}{l} \mathcal {L} _ {p c l} = \sum_ {i, j} \left[ \mathrm {g} \left(\boldsymbol {f} _ {i} ^ {V I}, \boldsymbol {c} _ {j} ^ {I}\right) + \mathrm {g} \left(\boldsymbol {f} _ {i} ^ {I V}, \boldsymbol {c} _ {j} ^ {V}\right) + \right. \tag {14} \\ \left. \mathbf {s} \left(\boldsymbol {c} _ {i} ^ {I}, \boldsymbol {c} _ {j} ^ {V}\right) + \mathbf {s} \left(\boldsymbol {c} _ {i} ^ {I}, \boldsymbol {c} _ {j} ^ {I}\right) + \mathbf {s} \left(\boldsymbol {c} _ {i} ^ {V}, \boldsymbol {c} _ {j} ^ {V}\right) \right]. \\ \end{array} +$$ + +Here, $\mathrm{g}$ and $\mathrm{s}$ aim to gather up intra-class features and separate inter-class features, respectively, formulated as + +$$ +\begin{array}{l} \mathrm {g} (\boldsymbol {f}, \boldsymbol {c}) = \left[ \mathbb {1} \left(y _ {(\boldsymbol {f})} = y _ {(\boldsymbol {c})}\right) \cdot \| \boldsymbol {f} - \boldsymbol {c} \| _ {2} \right], \\ \mathrm {s} \left(\boldsymbol {c} _ {i}, \boldsymbol {c} _ {j}\right) = \left[ \mathbb {1} \left(y _ {\left(\boldsymbol {c} _ {i}\right)} \neq y _ {\left(\boldsymbol {c} _ {j}\right)}\right) \cdot \left[ \sigma - \| \boldsymbol {c} _ {i} - \boldsymbol {c} _ {j} \| _ {2} \right] _ {+} \right], \tag {15} \\ \end{array} +$$ + +where $\sigma$ is a marginal parameter adopted to avoid optimizing "already correct" centroid pairs; $[z]_{+} = \max (z,0);y(\cdot)$ denotes the label of the corresponding embedding/centroid. + +# 3.3. Cross-modal Knowledge Exchange + +Even though the cross-refined embeddings yield smaller distribution gaps with respect to the target modality, it is infeasible to employ cross-refined embeddings for retrieval during the inference stage. Because the cross-modal refinement requires taking the part features $P$ (derived from DRM using the images of modality counterpart) as queries and applying query-guided attention using Eq. (10). This process need to be carried out for all query-gallery pairs, which brings high computational costs since gallery sets are generally large. To this end, we propose a novel solution called MatchDistill, which allows DRM to directly generate target-modality-like part features. This is achieved by associating the heterogeneous queries $P^V$ and $P^I$ with our Cross-modal Query Matching algorithm and propagating + +the modality-specific knowledge to the best-matched query of modality counterparts. For clarity, here we only take matching and propagating the knowledge from $P^I$ to $P^V$ as an example since MatchDistill has a symmetric pipeline. As shown in Figure 2, in MatchDistill, we first construct a complete bipartite graph $G(U, V, E)$ , where the vertices $U$ and $V$ represent $P^I$ and $P^V$ , respectively. Each edge in $E$ connects a vertex in $U$ to one in $V$ . The weights of the edges are the semantic similarities between queries, which are measured by the dot product of the attention mask calculated by Eq. (10), formulated as + +$$ +w \left(\boldsymbol {E} _ {k _ {1}, k _ {2}} ^ {V}\right) = \langle \mathcal {S} \left(\boldsymbol {X} ^ {V}, \boldsymbol {P} _ {k _ {1}} ^ {I}\right), \mathcal {S} \left(\boldsymbol {X} ^ {V}, \boldsymbol {P} _ {k _ {2}} ^ {V}\right) \rangle , \tag {16} +$$ + +where $w(\cdot)$ denotes the weight of the edge. The idea behind this is straightforward: if $P_{k1}$ and $P_{k2}$ represent the same semantic region, their attention masks should have a high level of similarity. This could help effectively model the semantic correlations of the heterogeneous part queries. The part query matching problem can then be formulated as + +$$ +\arg \max _ {M \subseteq E} \sum_ {e \in M} w (e), \quad s. t. \left| M \right| = N _ {p} \text {a n d} \tag {17} +$$ + +$$ +\forall (u _ {1}, v _ {1}), (u _ {2}, v _ {2}) \in M, u _ {1} \neq u _ {2} \text {a n d} v _ {1} \neq v _ {2}, +$$ + +where $M$ represents the edges of the optimal match (meaning that $\forall (u,v)\in M$ , $P_u^V$ and $P_v^I$ represent the same semantic region). We solve this part query matching problem (Eq. (17)) with the Kuhn-Munkres assignment algorithm [15]. After that, the mutual knowledge propagation process can be performed between all $(u,v)\in M$ pairs since they are semantically aligned. Specifically, the proposed knowledge distillation is conducted in two levels, i.e., the feature level and the logit level. For the feature level, we propose to align the similarity maps of the best-matched query pairs. This is equivalent to maximizing the weight of the optimal bipartite graph, formulated as + +$$ +\mathcal {L} _ {k d 1} = - \sum_ {e \in M} w (e). \tag {18} +$$ + +For the logit level, we constrain the consistency of their softmax classification distribution by + +$$ +\mathcal {L} _ {k d 2} = \sum_ {(u, v) \in \boldsymbol {M}} \mathcal {D} _ {k l} \left(\boldsymbol {p} _ {u} ^ {V, I} \| \boldsymbol {p} _ {v} ^ {V, V}\right), \tag {19} +$$ + +where $\pmb{p}$ denotes the post-softmax classification probability, and $\mathcal{D}_{kl}$ denotes Kullback-Leibler divergence. With the above cross-modal knowledgeable propagation, the self-refined features can also capture important information that can benefit cross-modal retrieval like the cross-refined ones. Therefore, there is no needs to perform cross-refinement during inference. In addition, by optimizing $\mathcal{L}_{kd1}$ and $\mathcal{L}_{kd2}$ , we observe that the optimal matches $M$ gradually get stabilized as the training progresses. This suggests that the optimal matches with the highest occurrence in the last training epoch, denoted as $\hat{M}$ , can be used for test-time matching. + +# 3.4. Training and Inference + +Training. The overall training objective is defined as + +$$ +\mathcal {L} = \mathcal {L} _ {i d} + \mathcal {L} _ {p c l} + \lambda_ {1} \mathcal {L} _ {k d 1} + \lambda_ {2} \mathcal {L} _ {k d 2} + \lambda_ {3} \mathcal {L} _ {d i s} + \lambda_ {4} \mathcal {L} _ {d i v}, \tag {20} +$$ + +where $\mathcal{L}_{id}$ is the routinely used identity classification loss; $\lambda_1, \lambda_2, \lambda_3$ , and $\lambda_4$ are adopted to balance different losses. + +Inference. During inference, we first reorder the learned prototypes of the DRM (i.e., the parameters of the pointwise convolutional layer in DRM) according to $\hat{M}$ to ensure that the self-refined embeddings can be semantically aligned. After that, the summation of the cosine similarity of each part is then adopted as the comparison metric. Formally, the similarity between the $i^{th}$ visible and the $j^{th}$ infrared sample is given by $\sum_{p} \cos(\boldsymbol{f}_{i,p}^{V,V}, \boldsymbol{f}_{j,p}^{I,I})$ , where $\cos$ denotes cosine similarity computation, and the subscript $p$ denotes indexing in the part dimension. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets. The proposed method is evaluated under the same protocols of existing work [20] on two widely-used VI Re-ID datasets, i.e., SYSU-MM01 [38] and RegDB [25]. + +Implementation Details. We adopt ResNet-50 [9] as the backbone network following existing work. At each training iteration, 8 identities are randomly sampled. For each identity, 4 visible and 4 infrared images are selected to form a mini-batch. The model is trained for 100 epochs in total on RTX 3090 GPUs with SGD optimizer. The learning rate linearly increased from 0.01 to 0.1 in the first 10 epochs. The cosine annealing strategy [21] is adopted in the remaining 90 epochs to decay the learning rate to $10^{-3}$ . The hyperparameters are decided by cross-validation. Specifically, we set $\lambda_{1} = 1$ , $\lambda_{2} = 1$ , $\lambda_{3} = 0.1$ , $\lambda_{4} = 0.1$ , $N_{p} = 4$ , $\alpha = 0.6$ and $\sigma = 0.6$ . All models are tested without using re-ranking algorithms or gallery set information for fair comparison. + +# 4.2. Comparison with State-of-the-Art Methods + +The comparison results on SYSU-MM01 and RegDB with state-of-the-art (SOTA) methods are shown in Table 1 and Table 2, respectively. It can be seen that the proposed CAL outperforms existing approaches by large margins on both datasets. Specifically, on the SYSU-MM01 dataset, our proposed method surpasses the state-of-the-art approaches [12, 20] on most of the evaluation metrics. As for the RegDB dataset, our method also achieves new state-of-the-art results. These experimental results verify the effectiveness and superiority of the proposed method. + +# 4.3. Analysis and Discussion + +Effectiveness of TCA and MatchDistill. To verify the effectiveness of the two key components of CAL (i.e., TCA + +Table 1. Comparison with SOTA methods on the SYSU-MM01 dataset. †: Following previous work [43], for cm-SSFT [22] and CIFT [17], we report the performance when no extra auxiliary information of the gallery set is introduced for fair comparison. + +
MethodVenueAll-searchIndoor-Search
Single-ShotMulti-ShotSingle-ShotMulti-Shot
R1↑R10↑mAP↑R1↑R10↑mAP↑R1↑R10↑mAP↑R1↑R10↑mAP↑
Zero-Pad [38]ICCV 201714.8054.1215.9519.1361.4010.8920.5868.3826.9224.4375.8618.64
AGW [44]TPAMI 202247.5084.3947.65---54.1791.1462.97---
cm-SSFT†[22]CVPR 202047.70-54.1057.40-59.10------
NFS [2]CVPR 202156.9191.3455.4563.5194.4248.5662.7996.5369.7970.0397.7061.45
SMCL [36]ICCV 202167.3992.8761.7872.1590.6654.9368.8496.5575.5679.5795.3366.57
MCLNet [7]ICCV 202165.4093.3361.98---72.5696.9876.58---
MPMN [35]TMM 202148.9890.3362.4160.8888.7051.9064.8996.8576.4774.4292.9366.98
FMCNet [46]CVPR 202266.34-62.51---68.15-74.09---
CAJ [43]ICCV 202169.8895.7166.89---76.2697.8880.37---
CIFT†[17]ECCV 202271.77-67.6478.00-62.4678.65-82.1186.97-77.03
MPANet [39]CVPR 202170.5896.2168.2475.5897.9162.9176.7498.2180.9584.2299.6675.11
CMT [12]ECCV 202271.8896.4568.5780.2397.9163.1376.9097.6879.9184.8799.4174.11
MAUM [20]CVPR 202271.68-68.79---76.97-81.94---
CAL (Ours)-74.6696.4771.7377.0598.0164.8679.6998.9383.6886.9799.8378.51
+ +Table 2. Comparison with SOTA methods under "visible to infrared" and "infrared to visible" modes on RegDB. †: see Table 1. + +
MethodVisible to InfraredInfrared to Visible
R1 ↑R10 ↑mAP ↑R1 ↑R10 ↑mAP ↑
Zero-Pad [38]17.7534.2118.9016.6334.6817.82
cm-SSFT†[22]65.40-65.6063.80-64.20
AGW [44]70.0586.2166.3775.9390.9369.49
NFS [2]80.5491.9672.1077.9590.4569.79
MCLNet [7]80.3192.7073.0775.9390.9369.49
CAJ [43]85.0395.4979.1484.7595.3377.82
SMCL [36]83.93-79.8383.05-78.57
MPANet [39]83.70-80.9082.80-80.70
MPMN [35]86.5696.8682.9184.6295.5179.49
FMCNet [46]89.12-84.4388.38-83.86
MAUM [20]87.87-85.0986.95-84.34
CIFT†[17]92.17-86.9690.12-84.81
CMT [12]95.1798.8287.3091.9797.9284.46
CAL (Ours)94.5199.7088.6793.6499.4687.61
+ +and MatchDistill) and analyze their contribution to the overall performance, we conduct experiments on the more challenging SYSU-MM01 dataset. The experimental results are given in Table 3, where we adopt ResNet-50 as the baseline method. We can see that both TCA and MatchDistill are shown to be essential to the final performance and can significantly boost the performance of the baseline method. These findings demonstrate the effectiveness and importance of our proposed approach. + +Analysis on the DRM Module. To demonstrate the superiority of the design of DRM, we conduct experiments by removing the key components of DRM or replacing them with other alternatives. The experimental results are shown in Table 4 (top). We can see that all modifications can lead to performance degradation. Specifically, we can see that when training DRM without the diversity constraint $(\mathcal{L}_{div})$ or discriminability constraint $(\mathcal{L}_{dis})$ , the performance drops significantly, indicating that it is essential to + +guarantee both the discriminability and diversity of the selected regions. When replacing the modality-specific DRM with the modality-shared one, a performance drop can also be observed. This is because the modality-shared DRM cannot learn modality-specific patterns, making it hard to discover discriminative modality-specific clues. It can also be observed that using learnable vectors instead of DRM produces poor performance since they are less descriptive than the part features generated by DRM. Horizontal Splitting (HS), which divides the feature maps into horizontal chunks, achieves slightly better results than learnable vectors since the chunks are more informative than learnable vectors. However, HS is still inferior to our DRM as handcrafted stripes cannot properly disentangle the feature maps into fine-grained discriminative body parts. We also study the impact of the number of regions generated and the parameter $N_{k}$ and $\alpha$ in DRM. The experimental results are shown in Figure 3. The best performance is achieved when $N_{p} = 4$ and $\alpha = 0.6$ . + +Analysis on the TSAA Module. To demonstrate the superiority of the TSAA design, we conduct experiments by replacing the spatial similarity calculation process (Eq. (9)) with the simple scaled dot-product operation and removing the query-guided channel attention mechanism. As shown in Table 4 (middle), the experimental results reveal significant drops in performance when adopting the scaled dot product as the similarity metric. This can be attributed to the style discrepancies between modalities, which make it difficult to effectively find the correlation between heterogeneous data with dot product. Our TSAA module, on the other hand, is adept at reducing style discrepancies between heterogeneous data when computing similarity scores. In addition, the experimental results also validate the effectiveness of our query-guided channel attention mechanism. + +Analysis on PCL. The PCL aligns the cross-modal em + +Table 3. Effectiveness of the proposed components on the SYSUMM01 dataset under the all-search single-shot mode. + +
BaselineTCAMatchDistillSYSU-MM01
R1↑R10↑mAP↑
✓57.8289.9156.40
✓✓70.1593.1267.40
✓✓✓74.6696.4771.73
+ +Table 4. Ablation study of DRM and TSAA on SYSU-MM01 under the all-search single-shot mode. Shared DRM: the weights of DRM are shared for both modalities. $LV$ : replacing the selected regions with $N_p$ learnable vectors. HS: Horizontal Split ( $n$ chunks). TSAA (SD): adopting scaled dot-product for similarity computation in TSAA. CA: the channel-wise attention in TSAA. + +
MethodSYSU-MM01
R1↑R10↑mAP ↑
DRM w/o L_div72.7695.7169.85
DRM w/o L_dis72.2395.3769.38
DRM → Shared DRM72.5794.9569.51
DRM → LV71.0794.0168.60
DRM → HS (n = 2)72.7095.5070.02
DRM → HS (n = 4)73.1595.7670.24
DRM → HS (n = 6)72.5794.9569.51
TSAA (SD)72.5794.9569.51
TSAA (SD) w/o CA70.5795.4767.77
w/o PCL66.9493.4264.32
PCL → Triplet loss [11]68.0993.2465.41
PCL → Center loss [37]71.4894.6069.13
PCL → ICA&CCA [7]69.5595.2170.01
CAL (Ours)74.6696.4771.73
+ +beddings that have consistent semantics. We conduct experiments by removing or replacing PCL with other alternatives, including the prevailing metric learning losses [11, 37] and the one [7] designed specifically for VI Re-ID. The experimental results reported in Table 4 (bottom) show that our PCL contributes largely to the final performance and surpasses other competitors. This is mainly owing to the superior design of PCL that consider reducing intra-class variation using the part-aligned embeddings. + +Analysis on MatchDistill. We conduct ablation experiments to evaluate the contribution of the proposed Cross-modal Query Matching algorithm and the two knowledge distillation losses $(\mathcal{L}_{kd1}$ and $\mathcal{L}_{kd2})$ in MatchDistill. As shown in Table 5, the experimental results demonstrate the significant role they play in enhancing retrieval accuracy. When aligning the attention maps with $\mathcal{L}_{kd1}$ and constraining the consistency of classification probability with $\mathcal{L}_{kd2}$ , the performance boosts significantly, verifying the effectiveness of our knowledge exchange strategies. When incorporating our CQM, the accuracy can be further improved. This suggests that it is beneficial to ensure semantic consistency when conducting knowledge exchange by finding the best-matched part queries with our CQM algorithm. + +![](images/8e52b8ba48855e236125ef46062507df9dc111c5781a894ec4fb32c2b0440050.jpg) +Figure 3. Parameter analysis of $N_{p}$ and $\alpha$ + +![](images/d3882dd81a25206d1149786924800f8f4ebb93ea3e04a3c17c3a3248aa87bb5a.jpg) + +Table 5. Effectiveness of each component of MatchDistill on the SYSU-MM01 dataset under the all-search single-shot mode. + +
Lkd1Lkd2CQMSYSU-MM01
R1↑R10↑mAP↑
70.1593.1267.40
✓72.7595.7169.86
✓72.2695.1668.50
✓✓73.6395.7970.61
✓✓✓74.6696.4771.73
+ +![](images/8a22a19c9a5e43fa912354792fd3830caa7008a9d4188f11697b52178cfda6ec.jpg) +Figure 4. Qualitative analysis of the proposed DRM and TSAA. + +![](images/6b37ebd55b5c322f9b30a06605275334041e98bec4ff75cdd8b05eda49cb14c2.jpg) + +Qualitative Results. We visualize the regions selected by the DRM module in Figure 4. It can be seen that the DRM can select diverse and discriminative regions, which could serve as strong guidance for the subsequent TSAA module. We also visualize the attention scores generated by the TSAA in Figure 4. We can see that the proposed TSAA has a strong capability in searching the corresponding regions given the key regions selected by DRM. + +# 5. Conclusion + +In this paper, we present the Concordant Attention Learning (CAL) framework, which learns concordant attention across the visible and infrared modalities and can effectively bridge the modality gap for VI Re-ID. We show that it is beneficial to design target-aware attention mechanisms to ensure attention concordance when aligning cross-modal samples. We also verify that exploiting cross-modal clues from the target modality and enabling cross-modal knowledge exchange in a match-and-distill manner can facilitate the learning of inter-modal correlations. Extensive experiments demonstrate the effectiveness and superiority of CAL over state-of-the-art methods, suggesting the potential of our approach for improving VI Re-ID research. + +# Acknowledgements + +This work is supported by National Natural Science Foundation of China (No.62073004), Science and Technology Plan of Shenzhen (No.JCYJ20200109140410340), and Shenzhen Fundamental Research Program (No.GXWD20 201231165807007-20200807164903001). + +# References + +[1] Guangyi Chen, Jiwen Lu, Ming Yang, and Jie Zhou. Spatial-Temporal Attention-Aware Learning for Video-Based Person Re-Identification. 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IEEE TIP, 30:1583-1595, 2021. 2 +[41] Mang Ye, Cuiqun Chen, Jianbing Shen, and Ling Shao. Dynamic Tri-Level Relation Mining with Attentive Graph for Visible Infrared Re-Identification. IEEE TIFS, 2021. 3 +[42] Mang Ye, Xiangyuan Lan, Zheng Wang, and Pong C Yuen. Bi-Directional Center-Constrained Top-Ranking for Visible + +Thermal Person Re-Identification. IEEE TIFS, 15:407-419, 2019. 2 +[43] Mang Ye, Weijian Ruan, Bo Du, and Mike Zheng Shou. Channel Augmented Joint Learning for Visible-Infrared Recognition. In ICCV, pages 13567-13576, 2021. 2, 7 +[44] Mang Ye, Jianbing Shen, Gaojie Lin, Tao Xiang, Ling Shao, and Steven C. H. Hoi. Deep Learning for Person Re-Identification: A Survey and Outlook. IEEE TPAMI, 44(6):2872–2893, June 2022. 2, 3, 7 +[45] Mang Ye, Zheng Wang, Xiangyuan Lan, and Pong C. Yuen. Visible Thermal Person Re-Identification via Dual-Constrained Top-Ranking. 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In this paper, we present Concordant Attention Learning (CAL), a novel framework that learns semantic-aligned representations for VI Re-ID. Specifically, we design the Target-aware Concordant Alignment paradigm, which allows target-aware attention adaptation when aligning heterogeneous samples (i.e., adaptive attention adjustment according to the target image being aligned). This is achieved by exploiting the discriminative clues from the modality counterpart and designing effective modality-agnostic correspondence searching strategies. To ensure semantic concordance during the cross-modal retrieval stage, we further propose MatchDistill, which matches the attention patterns across modalities and learns their underlying semantic correlations by bipartite-graph-based similarity modeling and cross-modal knowledge exchange. Extensive experiments on VI Re-ID benchmark datasets demonstrate the effectiveness and superiority of the proposed CAL." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 560, + 128, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 128, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 128, + 572 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "Person Re-identification (Re-ID) aims to associate person identities across non-overlapping cameras. It has gained increasing attention in recent years due to its practical applications in real-world surveillance systems. Conventional person Re-ID methods mainly focus on retrieving the same identity across visible (RGB) cameras [48, 29, 16, 23, 10]. Despite their remarkable success, they have limited applicability since visible cameras cannot capture discriminative information under poor-lighting conditions (e.g., at night). To improve the illumination robustness, infrared (IR) cameras are widely applied to cooperate with visible ones in" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 244, + 545, + 423 + ], + "blocks": [ + { + "bbox": [ + 307, + 244, + 545, + 423 + ], + "lines": [ + { + "bbox": [ + 307, + 244, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 307, + 244, + 545, + 423 + ], + "type": "image", + "image_path": "d606ca4fac1a5800e24b1d535f9fcd07a13c330834ff54f8cc5c5ef01a8c0f05.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 426, + 547, + 548 + ], + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 548 + ], + "type": "text", + "content": "Figure 1. A high-level overview of typical local feature learning paradigms. (a) Splitting-based: The semantics of the hand-craft stripes are not always properly aligned. (b) Auxiliary-model-based: Pretrained auxiliary models are often error-prone due to the domain shifts (especially for infrared image). (c) Attention-based: Due to the inter-modal distribution gap, existing style-sensitive attention module with less descriptive learnable prototypes often fails to attend semantically consistent regions. (d) CAL (Ours): Our method can learn concordant attention by discriminative region mining, target-aware style-agnostic attention, and part-aligned knowledge exchange." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 567, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 547, + 628 + ], + "type": "text", + "content": "real-world surveillance systems. This increases the need to explore the Visible-Infrared Person Re-identification (VI Re-ID) problem, which aims to associate the person images taken by different spectrum cameras to achieve long-term person tracking in 24-hour surveillance systems." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": "Compared to traditional RGB-based re-identification, VI Re-ID is much more challenging due to the differences in spectral properties between visible and infrared images. This data heterogeneity can lead to severe misalignment in the feature space and large intra-class discrepancy, resulting in significant degradation in performance. In addition, similarly to RGB-based Re-ID tasks, VI Re-ID can also be" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11122" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "impacted by the changes in pose or background, resulting in increased difficulties." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 97, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 97, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 97, + 289, + 312 + ], + "type": "text", + "content": "Recent years have witnessed a surge of creative work on mitigating the modality gap for VI Re-ID [38, 43, 18, 44, 4, 20]. However, as most existing methods only consider learning global representations from the whole image, they fail to compare local details. In addition, owing to the shortcut learning characteristics [6], global-feature-based methods would tend to learn modality-specific shortcut patterns, making the learned features susceptible to concentrating on divergent regions in each modality and resulting in suboptimal performance. A seemingly straightforward solution is to learn semantic-aligned local features with either splitting-based [29, 8, 20], auxiliary-model-based methods [26, 19, 28, 1], or attention-base paradigms [18, 16, 33, 27] instead of the global ones. However, these methods also fail to achieve inter-modal semantic alignment, as demonstrated in Figure 1, and forcibly aligning these semantic-misaligned embeddings would inevitably injure the training process and compromise the performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 312, + 289, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 289, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 289, + 504 + ], + "type": "text", + "content": "Different from these deep learning methods, human visual systems can naturally avoid the misalignment issue thanks to their target-aware comparison strategy. Considering the scenario of comparing two images of persons (referred to as \"base image\" and \"target image\", respectively), human vision systems would first identify multiple distinctive key regions (such as facial and clothing details) in the target image and then direct their attention to corresponding regions in the base image. In this manner, humans can always make perfect part-to-part comparisons since they are able to adaptively and accurately adjust their attention by referencing the key regions of the target image. This suggests that exploiting clues from the target image of the modality counterpart and exploring an effective cross-modal corresponding region-searching strategy can benefit in mitigating the inter-modal semantic misalignment issue." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 505, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 289, + 685 + ], + "type": "text", + "content": "In this paper, we present Concordant Attention Learning (CAL), a novel framework that mimics the target-aware comparison behavior of human vision systems to learn semantic-aligned representations for VI Re-ID. Firstly, we devise the Target-aware Concordant Alignment (TCA) paradigm, which aims to exploit discriminative local clues from the target modality (i.e., the modality counterpart) when aligning heterogeneous embeddings. The proposed TCA consists of three components: (1) Discriminative Region Mining: identifying diverse and discriminative key regions from the feature maps of each training sample; (2) Target-aware Style-agnostic Attention Adapter: taking the selected key regions from the target modality as part queries, and applying target-aware refinement to adapt the feature attention and generate part-aligned embeddings;" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 72, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 335 + ], + "type": "text", + "content": "(3) Part-aligned Metric Learning: clustering or separating the part-aligned embeddings across modalities according to their identity labels. Even though this target-aware refinement scheme can mitigate the modality discrepancy by leveraging the clues from the target modality, it brings higher computational costs during inference. Because it needs to be carried out for all query-gallery pairs, and the gallery set is generally large. To this end, we further propose MatchDistill. First, we need to associate the generated part queries of different modalities to guarantee that the subsequent distillation is conducted on semantic-aligned features. This is achieved by modeling the correlations of their corresponding attention maps with bipartite graphs and conducting Cross-modal Query Matching (CQM) to find the optimal matches. After that, a dual-level knowledge distillation loss is designed to allow cross-modality knowledge exchange between the best-matched queries. This can facilitate the learning of underlying relationships between the visible and infrared modalities. After training with MatchDistill, each modality can learn knowledge from its modality counterpart, and no cross-modal interaction is needed during inference." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 337, + 535, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 337, + 535, + 348 + ], + "spans": [ + { + "bbox": [ + 317, + 337, + 535, + 348 + ], + "type": "text", + "content": "Overall, our contributions are summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 352, + 545, + 531 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 352, + 545, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 352, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 352, + 545, + 398 + ], + "type": "text", + "content": "- We propose Concordant Attention Learning (CAL), a target-aware training paradigm that mimics human behavior and learns concordant attention to alleviate the inter-modal attention bias issue for VI Re-ID." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 399, + 545, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 545, + 446 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 545, + 446 + ], + "type": "text", + "content": "- To enable part-aligned metric learning, we present Target-aware Concordant Alignment (TCA), which leverages cross-modal clues and allows adaptive attention adjustment when aligning heterogeneous embeddings." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 447, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 447, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 306, + 447, + 545, + 494 + ], + "type": "text", + "content": "- We propose MatchDistill, which matches the attention patterns across modalities and learns their underlying semantic correlations by bipartite-graph-based similarity modeling and cross-modal knowledge exchange." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 495, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 545, + 531 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that the proposed CAL archives state-of-the-art performance on both the SYSU-MM01 [38] and RegDB [25] datasets." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 545, + 392, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 545, + 392, + 558 + ], + "spans": [ + { + "bbox": [ + 306, + 545, + 392, + 558 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Visible-Infrared Person Re-ID. Visible-Infrared Person Re-ID (VI Re-ID) has drawn increasing attention in recent years [43, 17, 39, 12, 20]. Mainstream VI Re-ID paradigms focus on bridging the modality gap via designing metric learning constraints [45, 42, 40], normalizing feature statistics [14, 39, 13], synthesizing auxiliary training samples [34, 3, 49, 24], or developing modality-specific and modality-shared feature learning paradigms [5, 22, 30]. However, these methods only consider learning global representations from entire images without considering the local information of images, leading to limited expressiveness of learned features. A few works also attempt to learn local" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "text", + "content": "1Note that we use the term \"region\" and \"part\" interchangeably to denote the same thing." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11123" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "features for VI Re-ID [8, 20, 41, 47] by splitting the feature maps into several hand-craft stripes. However, due to inaccurate detection boxes, pose variations, and occlusion, the hand-craft stripes are not always well-aligned, resulting in unsatisfactory performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 134, + 289, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 289, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 289, + 410 + ], + "type": "text", + "content": "Local Feature Learning in Person Re-ID. Local feature learning is an important research direction for person re-identification since learning part aggregated features makes the model robust against misalignment [44]. It can be roughly divided into splitting-based methods, auxiliary-model-based methods, and attention-based methods. Splitting-based methods [29, 8, 20] focus on learning local features from horizontal-divided regions, which now serve as a strong part feature learning baseline. However, due to inaccurate detection boxes, pose variations, and occlusion, the semantics of the hand-craft stripes are not well aligned. The auxiliary-model-based methods [26, 19, 28, 1] often adopt off-the-shelf auxiliary human parsing or pose estimation networks to obtain semantically meaningful body parts. However, they require additional computational costs and are prone to noisy estimation, especially when the data distribution varies. The attention-based methods focus on exploiting attention mechanisms to localize discriminative human parts and have achieved great success [18, 16, 33, 27]. However, these methods cannot be directly applied to the cross-modality scenario of VI Re-ID due to the inter-modal semantic misalignment issue as discussed in Sec. 1." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 418, + 130, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 130, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 130, + 431 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 437, + 241, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 241, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 241, + 451 + ], + "type": "text", + "content": "3.1. Intuition of Target-aware Alignment" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\pmb{x}^k" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": " denote the training images of modality " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "k \\in \\{V, I\\}" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": " for visible modality and " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": " for infrared modality). The visible and infrared samples in the dataset are denoted by " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{\\pmb{x}_j^V, y_j^V\\}_{j=0}^{N_v}" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\{\\pmb{x}_j^I, y_j^I\\}_{j=0}^{N_i}" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": ", respectively, where " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "N_v" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "N_i" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": " are the numbers of samples of each modality in the dataset, and " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "y_j^k" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": " is the corresponding identity label of the " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": "-th sample from modality " + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 456, + 287, + 613 + ], + "type": "text", + "content": ". The goal of Visible-Infrared Person Re-identification is to match the person identities across modalities according to feature similarities. Therefore, it is essential to reduce the large intra-class variation between heterogeneous samples. Existing paradigms often attempt to reduce the cross-modal intra-class variation by directly optimizing" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 88, + 616, + 287, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 616, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 88, + 616, + 287, + 637 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {i, j} \\left[ \\mathbb {1} \\left(y _ {i} ^ {V} = y _ {j} ^ {I}\\right) \\cdot \\mathrm {d} \\left(f \\left(\\boldsymbol {x} _ {i} ^ {V}\\right), f \\left(\\boldsymbol {x} _ {j} ^ {I}\\right)\\right) \\right], \\tag {1}", + "image_path": "375c836c99b49e4ec7b7e9a7e2d2772abe78ee7ad96e4d20d18474830a93da42.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " denotes the feature extractor, and " + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{d}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": " represents the distance between features. However, as discussed in Sec. 1, the attention misalignment issue could injure the training process and compromise performance. We thus endow the model with the ability to adaptively adjust the attention according to the target being compared to achieve" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "attention consensus. First, the Discriminative Region Mining (DRM) module, formulated as " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\gamma(\\cdot)" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": ", is introduced to disentangle the global features into diverse key body parts. We then devise the Target-aware Style-agnostic Attention Adapter (TSAA) to allow adaptive style-agnostic attention adjustment according to any given part queries regardless of the image styles. The feature extractor is then reformulated as " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "f(\\pmb{x},\\pmb{p})" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " to represent the above dynamic attention adjustment process, where " + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": " denotes the given body parts. The objective function to reduce the cross-modal intra-class variation can then be defined as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 311, + 212, + 545, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 212, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 311, + 212, + 545, + 253 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {i, j, k} \\left[ \\mathbb {1} \\left(y _ {i} ^ {V} = y _ {j} ^ {I}\\right) \\cdot \\mathrm {d} \\left(f \\left(\\boldsymbol {x} _ {i} ^ {V}, \\gamma \\left(\\boldsymbol {x} _ {j} ^ {I}\\right) _ {k}\\right), f \\left(\\boldsymbol {x} _ {j} ^ {I}, \\gamma \\left(\\boldsymbol {x} _ {j} ^ {I}\\right) _ {k}\\right)\\right) + \\right. \\tag {2} \\\\ \\mathbb {1} (y _ {i} ^ {I} = y _ {j} ^ {V}) \\cdot \\mathrm {d} \\big (f (\\pmb {x} _ {i} ^ {I}, \\gamma (\\pmb {x} _ {j} ^ {V}) _ {k}), f (\\pmb {x} _ {j} ^ {V}, \\gamma (\\pmb {x} _ {j} ^ {V}) _ {k}) \\big) \\Big ]. \\\\ \\end{array}", + "image_path": "0f79efa0bd4e5779d14ef9321ba587e1d4ad0e490b13168ea36c7de4159ed4f2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "type": "text", + "content": "In this manner, the embeddings being optimized can achieve semantic concordance since the same queries are used to guide feature attention (for instance, " + }, + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "type": "inline_equation", + "content": "f(\\pmb{x}_i^V, \\gamma(\\pmb{x}_j^I)_k)" + }, + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "type": "inline_equation", + "content": "f(\\pmb{x}_j^I, \\gamma(\\pmb{x}_j^I)_k)" + }, + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "type": "text", + "content": " correspond to the same semantic region since they are refined using the same part query " + }, + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\gamma(\\pmb{x}_j^I)_k" + }, + { + "bbox": [ + 304, + 262, + 545, + 373 + ], + "type": "text", + "content": "). This also allows cross-modal interaction to facilitate the learning of underline relationships between modalities. The overall pipeline is depicted in Figure 2, and more details will be introduced in the following subsections." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 383, + 503, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 383, + 503, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 383, + 503, + 396 + ], + "type": "text", + "content": "3.2. Target-aware Concordant Alignment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 403, + 468, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 468, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 468, + 415 + ], + "type": "text", + "content": "3.2.1 Discriminative Region Mining" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "content": "The Discriminative Region Mining module aims to discover several diverse discriminative key regions from the feature maps " + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{C \\times H \\times W}" + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "content": " derived from the backbone network, where " + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "content": " denote the number of channels, the height, and the width of the feature maps. Our DRM contains two stages: Part Scoring and Token Selection and Aggregation. The former aims to classify the tokens (i.e., the spatial vectors of " + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "content": ") into " + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "content": " different parts, while the latter selects the top-k tokens for each part based on the scores and aggregates them to derive the part features " + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 423, + 545, + 544 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": "Part Scoring. To disentangle the feature maps into several diverse discriminative regions, we first develop a simple scorer network " + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\gamma_{\\theta}" + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": " to predict the scores of " + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": " discriminative parts for each token in the feature maps. Here, " + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": " is a hyperparameter representing the number of parts. Specifically, as illustrated in Figure 2, the feature maps " + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": " are first passed through multiple max-pooling layers with different scales (i.e., " + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": " for identity mapping, " + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": " in this paper) to obtain features with different receptive fields. These features are then upsampled and concatenated along the channel dimension. Finally, the concatenated feature maps are fed into a point-wise convolutional layer with softmax activation along the spatial function to predict the scores of each part." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11124" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 318, + 215 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 318, + 215 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 318, + 215 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 318, + 215 + ], + "type": "image", + "image_path": "866656e8d8514b0175e3d4181602bac0fc6dcff9987b7a4feef6f11faffa2acf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 320, + 72, + 544, + 215 + ], + "blocks": [ + { + "bbox": [ + 320, + 72, + 544, + 215 + ], + "lines": [ + { + "bbox": [ + 320, + 72, + 544, + 215 + ], + "spans": [ + { + "bbox": [ + 320, + 72, + 544, + 215 + ], + "type": "image", + "image_path": "ab90f2e02d2db4488c582fe72d83a857731f3f43cffcab11e5e902891d814068.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 218, + 545, + 300 + ], + "blocks": [ + { + "bbox": [ + 48, + 218, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 48, + 218, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 48, + 218, + 545, + 300 + ], + "type": "image", + "image_path": "9f9bcc79bdb7cb081ddf330bf6c2061cb15ba5e58424e8f633a92d48679c59c5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 304, + 546, + 348 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 546, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 546, + 348 + ], + "type": "text", + "content": "Figure 2. (a) The overall pipeline of the proposed Concordant Attention Learning (CAL), which consists of a deep CNN backbone, the Discriminative Region Mining (DRM), the Target-aware Style-agnostic Attention Adapter (TSAA), and the MatchDistill paradigm. Note that only half of the pipeline is depicted for clarity since the model is symmetric. (b) The pipeline of DRM. (c) The architecture of the proposed TSAA. (d) The pipeline of MatchDistill. Notations are introduced in Sec. 3." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "text", + "content": "Token Selection and Aggregation. Given the scores predicted by " + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "inline_equation", + "content": "\\gamma_{\\theta}" + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "text", + "content": ", we then select the tokens with top-k scores for each part and aggregate them by weighted averaging to derive the aggregated part features. Specifically, let " + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{(H \\cdot W) \\times N_p}" + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "text", + "content": " denote the predicted score after the softmax layer produced by " + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "inline_equation", + "content": "\\gamma_{\\theta}" + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "text", + "content": ", and let " + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "inline_equation", + "content": "T \\in \\mathbb{R}^{(H \\cdot W) \\times C}" + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "text", + "content": " denote the flattened feature maps of " + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 361, + 287, + 457 + ], + "type": "text", + "content": ". The token selection and aggregation process can be formulated as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 462, + 287, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 462, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 53, + 462, + 287, + 495 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} = \\frac {\\hat {\\boldsymbol {S}} ^ {T} \\boldsymbol {T}}{\\sum_ {j} \\hat {\\boldsymbol {S}} _ {j}}, \\text {w h e r e} \\hat {\\boldsymbol {S}} = \\mathcal {T} (\\boldsymbol {S}, N _ {k}), N _ {k} = \\left[ \\alpha \\cdot \\frac {H \\cdot W}{N _ {p}} \\right], \\tag {3}", + "image_path": "bb73d4b34b920148ab3a5c23f2b0b1e6499e8d2a90d82ad96229a3e871196361.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " denotes the top-k operation; " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\hat{S} \\in \\mathbb{R}^{(H \\cdot W) \\times N_p}" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " represents the selected regions, " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "N_k" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " is the number of selected tokens, " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " is a hyperparameter controlling the selection ratio, and " + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "inline_equation", + "content": "P \\in \\mathbb{R}^{N_p \\times C}" + }, + { + "bbox": [ + 46, + 501, + 287, + 609 + ], + "type": "text", + "content": " represents the aggregated part features. There are two main advantages of selecting the top-k tokens instead of preserving all of them: (1) it helps filter out noisy tokens that could bring noisy clues to subsequent modules; (2) it can enhance the locality of the selected region and facilitate the learning of local representations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 612, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 612, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 612, + 287, + 647 + ], + "type": "text", + "content": "Discriminability Constraint. To ensure the part features " + }, + { + "bbox": [ + 47, + 612, + 287, + 647 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 612, + 287, + 647 + ], + "type": "text", + "content": " contains discriminative information, we design the discriminative constraint loss, which is formulated as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 100, + 652, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 652, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 100, + 652, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i s} = - \\sum_ {i = 1} ^ {N _ {p}} \\log \\left(\\Phi_ {i} \\left(\\boldsymbol {P} _ {i}\\right) _ {y}\\right), \\tag {4}", + "image_path": "41a2e38f74ae19d2c4d9867e7f23d203ee062e6e3be12345139f09d260f3aa96.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Phi_k" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " denotes part-specific classifiers implemented with a simple fully connected layer with softmax activation, and " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " is the label of the current sample." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 457 + ], + "type": "text", + "content": "Diversity Constraint. By training DRM with only Eq. (4), the model would tend to select several identical regions, resulting in suboptimal performance. This can be attributed to the shortcut learning characteristics [6] of deep learning systems that models attempt to find the simplest (but may be suboptimal) solution to solve a given task. To enhance the diversity of the selected regions, we further design the diversity constraint loss, which is defined as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 362, + 467, + 545, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 467, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 362, + 467, + 545, + 488 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i v} = \\sum_ {i, j} \\operatorname {t r i u} \\left(\\hat {\\boldsymbol {S}} ^ {T} \\hat {\\boldsymbol {S}}, 1\\right) _ {i, j}, \\tag {5}", + "image_path": "3f6c8d726f5ff8fa3e2add393b35f00c87ca84d25bcb421ded76fedad99c7df1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 499, + 545, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 499, + 545, + 547 + ], + "spans": [ + { + "bbox": [ + 304, + 499, + 545, + 547 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 499, + 545, + 547 + ], + "type": "inline_equation", + "content": "\\mathrm{triu}(\\cdot, 1)" + }, + { + "bbox": [ + 304, + 499, + 545, + 547 + ], + "type": "text", + "content": " denotes the upper triangular part (excluding the diagonal) of the given matrix. This diversity constraint loss can be regarded as imposing an explicit penalty on the model when the selected key regions become too similar." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 609 + ], + "type": "text", + "content": "As shown in Figure 2, the DRM module is not shared across modalities. This can help to learn better modality-specific part prototypes and select more discriminative regions, leading to better performance. This design will be empirically validated in Sec. 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 632, + 538, + 644 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 538, + 644 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 538, + 644 + ], + "type": "text", + "content": "3.2.2 Target-aware Style-agnostic Attention Adapter" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "To achieve target-aware attention, it is important to properly localize relevant regions in the feature maps by taking the aggregated part features " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " as the reference. A straightforward solution is to directly apply Scaled Dot-Product Attention [32] by taking " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " as the part queries and the flattened" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11125" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 277, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 277, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 277, + 83 + ], + "type": "text", + "content": "feature maps " + }, + { + "bbox": [ + 47, + 72, + 277, + 83 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 72, + 277, + 83 + ], + "type": "text", + "content": " as the keys and the values, formulated as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 83, + 88, + 287, + 108 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 88, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 83, + 88, + 287, + 108 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t n} (\\boldsymbol {T}; \\boldsymbol {P}) = \\operatorname {s o f t m a x} \\left(\\boldsymbol {P} \\boldsymbol {T} ^ {T} / \\sqrt {d}\\right) \\boldsymbol {T}, \\tag {6}", + "image_path": "4cb153536831e41511d9e436a272bdcc6e6a65556744edded2e68bda76465a88.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "type": "text", + "content": " is the feature dimension. However, this naive solution simply adopts dot product as the similarity metric, which could result in inaccurate attention scores. Because the features of different modalities suffer from large distributions shift, making them hard to be properly compared using a simple dot product operation. To this end, we design the Target-aware Style-agnostic Attention Adapter (TSAA), which includes a more reasonable similarity calculator. As shown in Figure 2 (b), we first apply Instance Normalization (IN) [31] to the part queries " + }, + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "type": "text", + "content": " and each token of the feature maps " + }, + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 111, + 287, + 243 + ], + "type": "text", + "content": ", formulated as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 63, + 247, + 287, + 273 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 247, + 287, + 273 + ], + "spans": [ + { + "bbox": [ + 63, + 247, + 287, + 273 + ], + "type": "interline_equation", + "content": "\\operatorname {I N} (\\boldsymbol {P}) = \\frac {\\boldsymbol {P} - \\mu (\\boldsymbol {T} _ {P})}{\\sigma (\\boldsymbol {T} _ {P})}, \\quad \\operatorname {I N} (\\boldsymbol {T}) = \\frac {\\boldsymbol {T} - \\mu (\\boldsymbol {T})}{\\sigma (\\boldsymbol {T})}, \\tag {7}", + "image_path": "49192871097a8e147e2837c0c8791e9cd19a51d1010026c39fa781e619fc4f70.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "inline_equation", + "content": "\\mu (\\cdot)" + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "text", + "content": " denote calculating the instance-level mean and standard deviation; " + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "inline_equation", + "content": "T_{P}" + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "text", + "content": " is the flattened feature maps that " + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "text", + "content": " derives from (see Eq. (3)). The motivation of this design is that the modality gap between IR and RGB images can be interpreted as the large discrepancies in style, and IN has been proven to be effective in reducing the style variance [14, 39, 13]. After that, the normalized features are fed into multi-layer perceptrons (MLPs) to learn nonlinear projection and capture complex patterns of the features. We then calculate the inner product of the projected features after the MLPs and apply softmax function on the spatial dimension to derive the final similarity. We can then apply spatial attention by weighted averaging all tokens using the computed similarities. In addition, we also apply query-guided channel attention to emphasize important channels in the feature map and suppress less important ones, where scores of channel attention are generated by an MLP layer taking part queries as input. Formally, the TSAA module, denoted by " + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(\\cdot ;\\cdot)" + }, + { + "bbox": [ + 46, + 276, + 288, + 504 + ], + "type": "text", + "content": ", can be formulated as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 87, + 509, + 287, + 522 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 509, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 87, + 509, + 287, + 522 + ], + "type": "interline_equation", + "content": "\\mathcal {A} (\\boldsymbol {T}; \\boldsymbol {P}) = \\mathcal {S} (\\boldsymbol {T}, \\boldsymbol {P}) \\boldsymbol {T} \\otimes \\mathcal {M} (\\boldsymbol {P}; \\theta_ {3}), \\tag {8}", + "image_path": "144b1c02f02c905364dd6f7e532ef530c1576abd71f2410a700a988727b26d6d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 93, + 524, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 524, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 93, + 524, + 287, + 544 + ], + "type": "interline_equation", + "content": "\\mathcal {S} (\\boldsymbol {T}, \\boldsymbol {P}) = \\operatorname {s o f t m a x} \\left(\\hat {\\boldsymbol {P}} \\hat {\\boldsymbol {T}} ^ {T} / \\sqrt {d}\\right), \\tag {9}", + "image_path": "24cd87ac33fd3c9de79fa8c7dd97e2563bb6f4e1b7e6bccbd6197c07b579fefa.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 545, + 287, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 545, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 68, + 545, + 287, + 559 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {T}} = \\mathcal {M} (\\operatorname {I N} (\\boldsymbol {T}); \\theta_ {1}), \\quad \\hat {\\boldsymbol {P}} = \\mathcal {M} (\\operatorname {I N} (\\boldsymbol {P}); \\theta_ {2}), \\tag {10}", + "image_path": "7c88c07c447c3c4b7a8aac72bdf0731ec6a2be2659c9bbd8a94970477dac05a6.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": " denotes the spatial similarity calculator, " + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": " denotes channel-wise multiplication, and " + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(\\cdot ;\\theta)" + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": " denotes MLP with parameter " + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": ". The TSAA has two merits: (1) it allows style-agnostic attention adjustment based on any given part queries " + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 561, + 287, + 657 + ], + "type": "text", + "content": " regardless of the image styles, making it easier to achieve attention consensus; (2) it can naturally bridge the gap between cross-modal samples by attending to relevant regions and emphasizing relevant channels." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 670, + 207, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 207, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 207, + 683 + ], + "type": "text", + "content": "3.2.3 Part-aligned Metric Learning" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "Our part-aligned metric learning aims to reduce the cross-modal intra-class discrepancies between the part-aligned" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "content": "features. As shown in Figure 2 (a), we first employ TSAA to perform cross-modal refinement since it can effectively bridge the gap between cross-modal samples as discussed in Sec. 3.2.2. The cross-modal refinement is defined as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 326, + 128, + 545, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 128, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 326, + 128, + 545, + 144 + ], + "type": "interline_equation", + "content": "\\boldsymbol {f} _ {i} ^ {V, I} = \\mathcal {A} \\left(\\boldsymbol {T} _ {j} ^ {V}; \\boldsymbol {P} _ {i} ^ {I}\\right), \\quad \\boldsymbol {f} _ {i} ^ {I, V} = \\mathcal {A} \\left(\\boldsymbol {T} _ {j} ^ {I}; \\boldsymbol {P} _ {i} ^ {V}\\right), \\tag {11}", + "image_path": "c085bba824399c81a82d10a574df3d08af7f2c732c62e5df8c585460b2c3e37f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\pmb{T}_j" + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "text", + "content": " is randomly selected from the mini-batch and " + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "inline_equation", + "content": "y_{i}^{I} = y_{j}^{V}" + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\pmb{f}^{V,I}" + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\pmb{f}^{I,V}" + }, + { + "bbox": [ + 305, + 152, + 545, + 190 + ], + "type": "text", + "content": " are called cross-refined features. Similarly, we also apply self-refinement using" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 326, + 198, + 545, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 198, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 326, + 198, + 545, + 213 + ], + "type": "interline_equation", + "content": "\\boldsymbol {f} _ {i} ^ {V, V} = \\mathcal {A} \\left(\\boldsymbol {T} _ {i} ^ {V}; \\boldsymbol {P} _ {i} ^ {V}\\right), \\quad \\boldsymbol {f} _ {i} ^ {I, I} = \\mathcal {A} \\left(\\boldsymbol {T} _ {i} ^ {I}; \\boldsymbol {P} _ {i} ^ {I}\\right), \\tag {12}", + "image_path": "5a531f002dafa5a251150843f82fd8cba913bb91d3748bb0793a23d4a88660f2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "content": "to obtain the self-refined features. Since " + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\pmb{f}_i^{V,I}" + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "inline_equation", + "content": "\\pmb{f}_i^{I,I}" + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "content": " are refined using the same query (i.e., " + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "inline_equation", + "content": "P_i^I" + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "content": "), they would attend to the same regions and can thus be regarded as part-aligned features. We then design the Part-aligned Center Loss (PCL) to enhance the discriminability of these semantically aligned embeddings. Let " + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "inline_equation", + "content": "c_j^k" + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "content": " denotes the batch feature centroid of class " + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "inline_equation", + "content": "y_j^k" + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "content": " in modality " + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "inline_equation", + "content": "k \\in \\{V, I\\}" + }, + { + "bbox": [ + 304, + 219, + 545, + 308 + ], + "type": "text", + "content": ") given by" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 324, + 314, + 545, + 341 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 314, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 324, + 314, + 545, + 341 + ], + "type": "interline_equation", + "content": "\\boldsymbol {c} _ {j} ^ {V} = \\frac {1}{| \\mathcal {S} (j) |} \\sum_ {i \\in \\mathcal {S} (j)} \\boldsymbol {f} _ {i} ^ {V, V}, \\quad \\boldsymbol {c} _ {j} ^ {I} = \\frac {1}{| \\mathcal {S} (j) |} \\sum_ {i \\in \\mathcal {S} (j)} \\boldsymbol {f} _ {i} ^ {I, I}, \\tag {13}", + "image_path": "0386f138ab6b821f1001fe96c0041d797c76abeab41d2e91ea8534de3f9355d1.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 350, + 534, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 534, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 534, + 363 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 350, + 534, + 363 + ], + "type": "inline_equation", + "content": "S(j) = \\{i\\mid y_i = y_j\\}" + }, + { + "bbox": [ + 306, + 350, + 534, + 363 + ], + "type": "text", + "content": ". Our PCL is then defined as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 372, + 545, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 372, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 317, + 372, + 545, + 408 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {p c l} = \\sum_ {i, j} \\left[ \\mathrm {g} \\left(\\boldsymbol {f} _ {i} ^ {V I}, \\boldsymbol {c} _ {j} ^ {I}\\right) + \\mathrm {g} \\left(\\boldsymbol {f} _ {i} ^ {I V}, \\boldsymbol {c} _ {j} ^ {V}\\right) + \\right. \\tag {14} \\\\ \\left. \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {I}, \\boldsymbol {c} _ {j} ^ {V}\\right) + \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {I}, \\boldsymbol {c} _ {j} ^ {I}\\right) + \\mathbf {s} \\left(\\boldsymbol {c} _ {i} ^ {V}, \\boldsymbol {c} _ {j} ^ {V}\\right) \\right]. \\\\ \\end{array}", + "image_path": "48fe81b7d0c4ed39fa567795dd561a3b9884235c315d43839ca5b80f936a0b3d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\mathrm{g}" + }, + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\mathrm{s}" + }, + { + "bbox": [ + 305, + 416, + 545, + 441 + ], + "type": "text", + "content": " aim to gather up intra-class features and separate inter-class features, respectively, formulated as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 315, + 445, + 545, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 445, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 315, + 445, + 545, + 480 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathrm {g} (\\boldsymbol {f}, \\boldsymbol {c}) = \\left[ \\mathbb {1} \\left(y _ {(\\boldsymbol {f})} = y _ {(\\boldsymbol {c})}\\right) \\cdot \\| \\boldsymbol {f} - \\boldsymbol {c} \\| _ {2} \\right], \\\\ \\mathrm {s} \\left(\\boldsymbol {c} _ {i}, \\boldsymbol {c} _ {j}\\right) = \\left[ \\mathbb {1} \\left(y _ {\\left(\\boldsymbol {c} _ {i}\\right)} \\neq y _ {\\left(\\boldsymbol {c} _ {j}\\right)}\\right) \\cdot \\left[ \\sigma - \\| \\boldsymbol {c} _ {i} - \\boldsymbol {c} _ {j} \\| _ {2} \\right] _ {+} \\right], \\tag {15} \\\\ \\end{array}", + "image_path": "c98b559b96eb6ff3b58057e080b8541304ff251ad5d208e36fd5c7a8f9a97313.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 483, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 483, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 305, + 483, + 545, + 520 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 483, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 483, + 545, + 520 + ], + "type": "text", + "content": " is a marginal parameter adopted to avoid optimizing \"already correct\" centroid pairs; " + }, + { + "bbox": [ + 305, + 483, + 545, + 520 + ], + "type": "inline_equation", + "content": "[z]_{+} = \\max (z,0);y(\\cdot)" + }, + { + "bbox": [ + 305, + 483, + 545, + 520 + ], + "type": "text", + "content": " denotes the label of the corresponding embedding/centroid." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 527, + 492, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 492, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 492, + 540 + ], + "type": "text", + "content": "3.3. Cross-modal Knowledge Exchange" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Even though the cross-refined embeddings yield smaller distribution gaps with respect to the target modality, it is infeasible to employ cross-refined embeddings for retrieval during the inference stage. Because the cross-modal refinement requires taking the part features " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " (derived from DRM using the images of modality counterpart) as queries and applying query-guided attention using Eq. (10). This process need to be carried out for all query-gallery pairs, which brings high computational costs since gallery sets are generally large. To this end, we propose a novel solution called MatchDistill, which allows DRM to directly generate target-modality-like part features. This is achieved by associating the heterogeneous queries " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "P^V" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "P^I" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " with our Cross-modal Query Matching algorithm and propagating" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11126" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "the modality-specific knowledge to the best-matched query of modality counterparts. For clarity, here we only take matching and propagating the knowledge from " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "P^I" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "P^V" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " as an example since MatchDistill has a symmetric pipeline. As shown in Figure 2, in MatchDistill, we first construct a complete bipartite graph " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "G(U, V, E)" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", where the vertices " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " represent " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "P^I" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "P^V" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", respectively. Each edge in " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " connects a vertex in " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " to one in " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ". The weights of the edges are the semantic similarities between queries, which are measured by the dot product of the attention mask calculated by Eq. (10), formulated as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 62, + 210, + 287, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 210, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 62, + 210, + 287, + 227 + ], + "type": "interline_equation", + "content": "w \\left(\\boldsymbol {E} _ {k _ {1}, k _ {2}} ^ {V}\\right) = \\langle \\mathcal {S} \\left(\\boldsymbol {X} ^ {V}, \\boldsymbol {P} _ {k _ {1}} ^ {I}\\right), \\mathcal {S} \\left(\\boldsymbol {X} ^ {V}, \\boldsymbol {P} _ {k _ {2}} ^ {V}\\right) \\rangle , \\tag {16}", + "image_path": "b8051baa72d42cc4ab883af3e2de0cc3a4f8e283724ca9ac019892b8387eafa3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "type": "inline_equation", + "content": "w(\\cdot)" + }, + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "type": "text", + "content": " denotes the weight of the edge. The idea behind this is straightforward: if " + }, + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "type": "inline_equation", + "content": "P_{k1}" + }, + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "type": "inline_equation", + "content": "P_{k2}" + }, + { + "bbox": [ + 46, + 233, + 287, + 305 + ], + "type": "text", + "content": " represent the same semantic region, their attention masks should have a high level of similarity. This could help effectively model the semantic correlations of the heterogeneous part queries. The part query matching problem can then be formulated as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 313, + 287, + 336 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 313, + 287, + 336 + ], + "spans": [ + { + "bbox": [ + 61, + 313, + 287, + 336 + ], + "type": "interline_equation", + "content": "\\arg \\max _ {M \\subseteq E} \\sum_ {e \\in M} w (e), \\quad s. t. \\left| M \\right| = N _ {p} \\text {a n d} \\tag {17}", + "image_path": "1c39161144d4ee5e3a0c09f44f12f6154f1b5074e6ccf41a14abe5fcd8d1bae8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 337, + 255, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 337, + 255, + 350 + ], + "spans": [ + { + "bbox": [ + 62, + 337, + 255, + 350 + ], + "type": "interline_equation", + "content": "\\forall (u _ {1}, v _ {1}), (u _ {2}, v _ {2}) \\in M, u _ {1} \\neq u _ {2} \\text {a n d} v _ {1} \\neq v _ {2},", + "image_path": "df96e89a959640520082b9bbbc23f36279c9bff8a2a34521ed5d9cd7c11a4796.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "content": " represents the edges of the optimal match (meaning that " + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "inline_equation", + "content": "\\forall (u,v)\\in M" + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "inline_equation", + "content": "P_u^V" + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "inline_equation", + "content": "P_v^I" + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "content": " represent the same semantic region). We solve this part query matching problem (Eq. (17)) with the Kuhn-Munkres assignment algorithm [15]. After that, the mutual knowledge propagation process can be performed between all " + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "inline_equation", + "content": "(u,v)\\in M" + }, + { + "bbox": [ + 46, + 357, + 289, + 501 + ], + "type": "text", + "content": " pairs since they are semantically aligned. Specifically, the proposed knowledge distillation is conducted in two levels, i.e., the feature level and the logit level. For the feature level, we propose to align the similarity maps of the best-matched query pairs. This is equivalent to maximizing the weight of the optimal bipartite graph, formulated as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 506, + 287, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 506, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 115, + 506, + 287, + 525 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {k d 1} = - \\sum_ {e \\in M} w (e). \\tag {18}", + "image_path": "3c9ec2fde8387148ddbd9125cf7f9c6c072735e134debf24da927ce19adaf138.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 529, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 552 + ], + "type": "text", + "content": "For the logit level, we constrain the consistency of their softmax classification distribution by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 558, + 287, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 558, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 86, + 558, + 287, + 578 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {k d 2} = \\sum_ {(u, v) \\in \\boldsymbol {M}} \\mathcal {D} _ {k l} \\left(\\boldsymbol {p} _ {u} ^ {V, I} \\| \\boldsymbol {p} _ {v} ^ {V, V}\\right), \\tag {19}", + "image_path": "feef2855c1470f14b44af6e3539e6fb1ed395cdeb8a7b6ecd5acffc6a2f592b1.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " denotes the post-softmax classification probability, and " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{kl}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " denotes Kullback-Leibler divergence. With the above cross-modal knowledgeable propagation, the self-refined features can also capture important information that can benefit cross-modal retrieval like the cross-refined ones. Therefore, there is no needs to perform cross-refinement during inference. In addition, by optimizing " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kd1}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kd2}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": ", we observe that the optimal matches " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " gradually get stabilized as the training progresses. This suggests that the optimal matches with the highest occurrence in the last training epoch, denoted as " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": ", can be used for test-time matching." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 437, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 437, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 437, + 84 + ], + "type": "text", + "content": "3.4. Training and Inference" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 92, + 524, + 105 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 92, + 524, + 105 + ], + "spans": [ + { + "bbox": [ + 306, + 92, + 524, + 105 + ], + "type": "text", + "content": "Training. The overall training objective is defined as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 311, + 110, + 545, + 123 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 110, + 545, + 123 + ], + "spans": [ + { + "bbox": [ + 311, + 110, + 545, + 123 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {i d} + \\mathcal {L} _ {p c l} + \\lambda_ {1} \\mathcal {L} _ {k d 1} + \\lambda_ {2} \\mathcal {L} _ {k d 2} + \\lambda_ {3} \\mathcal {L} _ {d i s} + \\lambda_ {4} \\mathcal {L} _ {d i v}, \\tag {20}", + "image_path": "9b1113f42aa3480d52d84adcdc6d47ac4417035dcd4c8d50dd41c38fd35e7662.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{id}" + }, + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "type": "text", + "content": " is the routinely used identity classification loss; " + }, + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3" + }, + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "type": "inline_equation", + "content": "\\lambda_4" + }, + { + "bbox": [ + 306, + 128, + 545, + 152 + ], + "type": "text", + "content": " are adopted to balance different losses." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "text", + "content": "Inference. During inference, we first reorder the learned prototypes of the DRM (i.e., the parameters of the pointwise convolutional layer in DRM) according to " + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "text", + "content": " to ensure that the self-refined embeddings can be semantically aligned. After that, the summation of the cosine similarity of each part is then adopted as the comparison metric. Formally, the similarity between the " + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "text", + "content": " visible and the " + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "inline_equation", + "content": "j^{th}" + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "text", + "content": " infrared sample is given by " + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\sum_{p} \\cos(\\boldsymbol{f}_{i,p}^{V,V}, \\boldsymbol{f}_{j,p}^{I,I})" + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\cos" + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "text", + "content": " denotes cosine similarity computation, and the subscript " + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 156, + 547, + 277 + ], + "type": "text", + "content": " denotes indexing in the part dimension." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 285, + 388, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 388, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 388, + 300 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 305, + 432, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 305, + 432, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 305, + 432, + 319 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 326, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 361 + ], + "type": "text", + "content": "Datasets. The proposed method is evaluated under the same protocols of existing work [20] on two widely-used VI Re-ID datasets, i.e., SYSU-MM01 [38] and RegDB [25]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": "Implementation Details. We adopt ResNet-50 [9] as the backbone network following existing work. At each training iteration, 8 identities are randomly sampled. For each identity, 4 visible and 4 infrared images are selected to form a mini-batch. The model is trained for 100 epochs in total on RTX 3090 GPUs with SGD optimizer. The learning rate linearly increased from 0.01 to 0.1 in the first 10 epochs. The cosine annealing strategy [21] is adopted in the remaining 90 epochs to decay the learning rate to " + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": ". The hyperparameters are decided by cross-validation. Specifically, we set " + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\lambda_{1} = 1" + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 1" + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\lambda_{3} = 0.1" + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\lambda_{4} = 0.1" + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "inline_equation", + "content": "N_{p} = 4" + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\alpha = 0.6" + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\sigma = 0.6" + }, + { + "bbox": [ + 304, + 363, + 545, + 519 + ], + "type": "text", + "content": ". All models are tested without using re-ranking algorithms or gallery set information for fair comparison." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 525, + 531, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 531, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 531, + 538 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-Art Methods" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 544, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 663 + ], + "type": "text", + "content": "The comparison results on SYSU-MM01 and RegDB with state-of-the-art (SOTA) methods are shown in Table 1 and Table 2, respectively. It can be seen that the proposed CAL outperforms existing approaches by large margins on both datasets. Specifically, on the SYSU-MM01 dataset, our proposed method surpasses the state-of-the-art approaches [12, 20] on most of the evaluation metrics. As for the RegDB dataset, our method also achieves new state-of-the-art results. These experimental results verify the effectiveness and superiority of the proposed method." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 669, + 441, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 441, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 441, + 681 + ], + "type": "text", + "content": "4.3. Analysis and Discussion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of TCA and MatchDistill. To verify the effectiveness of the two key components of CAL (i.e., TCA" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11127" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 94, + 545, + 275 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": "Table 1. Comparison with SOTA methods on the SYSU-MM01 dataset. †: Following previous work [43], for cm-SSFT [22] and CIFT [17], we report the performance when no extra auxiliary information of the gallery set is introduced for fair comparison." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 94, + 545, + 275 + ], + "lines": [ + { + "bbox": [ + 49, + 94, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 49, + 94, + 545, + 275 + ], + "type": "table", + "html": "
MethodVenueAll-searchIndoor-Search
Single-ShotMulti-ShotSingle-ShotMulti-Shot
R1↑R10↑mAP↑R1↑R10↑mAP↑R1↑R10↑mAP↑R1↑R10↑mAP↑
Zero-Pad [38]ICCV 201714.8054.1215.9519.1361.4010.8920.5868.3826.9224.4375.8618.64
AGW [44]TPAMI 202247.5084.3947.65---54.1791.1462.97---
cm-SSFT†[22]CVPR 202047.70-54.1057.40-59.10------
NFS [2]CVPR 202156.9191.3455.4563.5194.4248.5662.7996.5369.7970.0397.7061.45
SMCL [36]ICCV 202167.3992.8761.7872.1590.6654.9368.8496.5575.5679.5795.3366.57
MCLNet [7]ICCV 202165.4093.3361.98---72.5696.9876.58---
MPMN [35]TMM 202148.9890.3362.4160.8888.7051.9064.8996.8576.4774.4292.9366.98
FMCNet [46]CVPR 202266.34-62.51---68.15-74.09---
CAJ [43]ICCV 202169.8895.7166.89---76.2697.8880.37---
CIFT†[17]ECCV 202271.77-67.6478.00-62.4678.65-82.1186.97-77.03
MPANet [39]CVPR 202170.5896.2168.2475.5897.9162.9176.7498.2180.9584.2299.6675.11
CMT [12]ECCV 202271.8896.4568.5780.2397.9163.1376.9097.6879.9184.8799.4174.11
MAUM [20]CVPR 202271.68-68.79---76.97-81.94---
CAL (Ours)-74.6696.4771.7377.0598.0164.8679.6998.9383.6886.9799.8378.51
", + "image_path": "44476c906e4d473766ff15aa9507eeab3739cc76061c78c52e3637827b1907df.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 312, + 286, + 473 + ], + "blocks": [ + { + "bbox": [ + 47, + 287, + 286, + 309 + ], + "lines": [ + { + "bbox": [ + 47, + 287, + 286, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 287, + 286, + 309 + ], + "type": "text", + "content": "Table 2. Comparison with SOTA methods under \"visible to infrared\" and \"infrared to visible\" modes on RegDB. †: see Table 1." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 312, + 286, + 473 + ], + "lines": [ + { + "bbox": [ + 49, + 312, + 286, + 473 + ], + "spans": [ + { + "bbox": [ + 49, + 312, + 286, + 473 + ], + "type": "table", + "html": "
MethodVisible to InfraredInfrared to Visible
R1 ↑R10 ↑mAP ↑R1 ↑R10 ↑mAP ↑
Zero-Pad [38]17.7534.2118.9016.6334.6817.82
cm-SSFT†[22]65.40-65.6063.80-64.20
AGW [44]70.0586.2166.3775.9390.9369.49
NFS [2]80.5491.9672.1077.9590.4569.79
MCLNet [7]80.3192.7073.0775.9390.9369.49
CAJ [43]85.0395.4979.1484.7595.3377.82
SMCL [36]83.93-79.8383.05-78.57
MPANet [39]83.70-80.9082.80-80.70
MPMN [35]86.5696.8682.9184.6295.5179.49
FMCNet [46]89.12-84.4388.38-83.86
MAUM [20]87.87-85.0986.95-84.34
CIFT†[17]92.17-86.9690.12-84.81
CMT [12]95.1798.8287.3091.9797.9284.46
CAL (Ours)94.5199.7088.6793.6499.4687.61
", + "image_path": "1099f430a6c6079fe08e5f5213158edee077fd91cc6f8945dac47ee5ca6cd862.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 493, + 286, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 286, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 286, + 601 + ], + "type": "text", + "content": "and MatchDistill) and analyze their contribution to the overall performance, we conduct experiments on the more challenging SYSU-MM01 dataset. The experimental results are given in Table 3, where we adopt ResNet-50 as the baseline method. We can see that both TCA and MatchDistill are shown to be essential to the final performance and can significantly boost the performance of the baseline method. These findings demonstrate the effectiveness and importance of our proposed approach." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "Analysis on the DRM Module. To demonstrate the superiority of the design of DRM, we conduct experiments by removing the key components of DRM or replacing them with other alternatives. The experimental results are shown in Table 4 (top). We can see that all modifications can lead to performance degradation. Specifically, we can see that when training DRM without the diversity constraint " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{div})" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " or discriminability constraint " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{dis})" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": ", the performance drops significantly, indicating that it is essential to" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "text", + "content": "guarantee both the discriminability and diversity of the selected regions. When replacing the modality-specific DRM with the modality-shared one, a performance drop can also be observed. This is because the modality-shared DRM cannot learn modality-specific patterns, making it hard to discover discriminative modality-specific clues. It can also be observed that using learnable vectors instead of DRM produces poor performance since they are less descriptive than the part features generated by DRM. Horizontal Splitting (HS), which divides the feature maps into horizontal chunks, achieves slightly better results than learnable vectors since the chunks are more informative than learnable vectors. However, HS is still inferior to our DRM as handcrafted stripes cannot properly disentangle the feature maps into fine-grained discriminative body parts. We also study the impact of the number of regions generated and the parameter " + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "inline_equation", + "content": "N_{k}" + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "text", + "content": " in DRM. The experimental results are shown in Figure 3. The best performance is achieved when " + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "inline_equation", + "content": "N_{p} = 4" + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\alpha = 0.6" + }, + { + "bbox": [ + 304, + 290, + 545, + 517 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 520, + 545, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 698 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 698 + ], + "type": "text", + "content": "Analysis on the TSAA Module. To demonstrate the superiority of the TSAA design, we conduct experiments by replacing the spatial similarity calculation process (Eq. (9)) with the simple scaled dot-product operation and removing the query-guided channel attention mechanism. As shown in Table 4 (middle), the experimental results reveal significant drops in performance when adopting the scaled dot product as the similarity metric. This can be attributed to the style discrepancies between modalities, which make it difficult to effectively find the correlation between heterogeneous data with dot product. Our TSAA module, on the other hand, is adept at reducing style discrepancies between heterogeneous data when computing similarity scores. In addition, the experimental results also validate the effectiveness of our query-guided channel attention mechanism." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "Analysis on PCL. The PCL aligns the cross-modal em" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11128" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 92, + 286, + 155 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "type": "text", + "content": "Table 3. Effectiveness of the proposed components on the SYSUMM01 dataset under the all-search single-shot mode." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 92, + 286, + 155 + ], + "lines": [ + { + "bbox": [ + 50, + 92, + 286, + 155 + ], + "spans": [ + { + "bbox": [ + 50, + 92, + 286, + 155 + ], + "type": "table", + "html": "
BaselineTCAMatchDistillSYSU-MM01
R1↑R10↑mAP↑
✓57.8289.9156.40
✓✓70.1593.1267.40
✓✓✓74.6696.4771.73
", + "image_path": "d192d45f56712d50b48210e5393d3472360de3778818d3c77c976fc4b1585503.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 230, + 286, + 418 + ], + "blocks": [ + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "lines": [ + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "type": "text", + "content": "Table 4. Ablation study of DRM and TSAA on SYSU-MM01 under the all-search single-shot mode. Shared DRM: the weights of DRM are shared for both modalities. " + }, + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "type": "inline_equation", + "content": "LV" + }, + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "type": "text", + "content": ": replacing the selected regions with " + }, + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "type": "inline_equation", + "content": "N_p" + }, + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "type": "text", + "content": " learnable vectors. HS: Horizontal Split (" + }, + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 163, + 287, + 229 + ], + "type": "text", + "content": " chunks). TSAA (SD): adopting scaled dot-product for similarity computation in TSAA. CA: the channel-wise attention in TSAA." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 230, + 286, + 418 + ], + "lines": [ + { + "bbox": [ + 50, + 230, + 286, + 418 + ], + "spans": [ + { + "bbox": [ + 50, + 230, + 286, + 418 + ], + "type": "table", + "html": "
MethodSYSU-MM01
R1↑R10↑mAP ↑
DRM w/o L_div72.7695.7169.85
DRM w/o L_dis72.2395.3769.38
DRM → Shared DRM72.5794.9569.51
DRM → LV71.0794.0168.60
DRM → HS (n = 2)72.7095.5070.02
DRM → HS (n = 4)73.1595.7670.24
DRM → HS (n = 6)72.5794.9569.51
TSAA (SD)72.5794.9569.51
TSAA (SD) w/o CA70.5795.4767.77
w/o PCL66.9493.4264.32
PCL → Triplet loss [11]68.0993.2465.41
PCL → Center loss [37]71.4894.6069.13
PCL → ICA&CCA [7]69.5595.2170.01
CAL (Ours)74.6696.4771.73
", + "image_path": "a9e9f3c0316d1885a0e72ce4f9cae773cdb9b67b6bc923a19a3d1cb4daec2f48.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 435, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 544 + ], + "type": "text", + "content": "beddings that have consistent semantics. We conduct experiments by removing or replacing PCL with other alternatives, including the prevailing metric learning losses [11, 37] and the one [7] designed specifically for VI Re-ID. The experimental results reported in Table 4 (bottom) show that our PCL contributes largely to the final performance and surpasses other competitors. This is mainly owing to the superior design of PCL that consider reducing intra-class variation using the part-aligned embeddings." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "Analysis on MatchDistill. We conduct ablation experiments to evaluate the contribution of the proposed Cross-modal Query Matching algorithm and the two knowledge distillation losses " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{kd1}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kd2})" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " in MatchDistill. As shown in Table 5, the experimental results demonstrate the significant role they play in enhancing retrieval accuracy. When aligning the attention maps with " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kd1}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " and constraining the consistency of classification probability with " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kd2}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ", the performance boosts significantly, verifying the effectiveness of our knowledge exchange strategies. When incorporating our CQM, the accuracy can be further improved. This suggests that it is beneficial to ensure semantic consistency when conducting knowledge exchange by finding the best-matched part queries with our CQM algorithm." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 426, + 143 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 426, + 143 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 426, + 143 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 426, + 143 + ], + "type": "image", + "image_path": "8e52b8ba48855e236125ef46062507df9dc111c5781a894ec4fb32c2b0440050.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 348, + 146, + 503, + 157 + ], + "lines": [ + { + "bbox": [ + 348, + 146, + 503, + 157 + ], + "spans": [ + { + "bbox": [ + 348, + 146, + 503, + 157 + ], + "type": "text", + "content": "Figure 3. Parameter analysis of " + }, + { + "bbox": [ + 348, + 146, + 503, + 157 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 348, + 146, + 503, + 157 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 348, + 146, + 503, + 157 + ], + "type": "inline_equation", + "content": "\\alpha" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 426, + 70, + 542, + 143 + ], + "blocks": [ + { + "bbox": [ + 426, + 70, + 542, + 143 + ], + "lines": [ + { + "bbox": [ + 426, + 70, + 542, + 143 + ], + "spans": [ + { + "bbox": [ + 426, + 70, + 542, + 143 + ], + "type": "image", + "image_path": "d3882dd81a25206d1149786924800f8f4ebb93ea3e04a3c17c3a3248aa87bb5a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 189, + 545, + 276 + ], + "blocks": [ + { + "bbox": [ + 306, + 166, + 545, + 188 + ], + "lines": [ + { + "bbox": [ + 306, + 166, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 306, + 166, + 545, + 188 + ], + "type": "text", + "content": "Table 5. Effectiveness of each component of MatchDistill on the SYSU-MM01 dataset under the all-search single-shot mode." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 189, + 545, + 276 + ], + "lines": [ + { + "bbox": [ + 309, + 189, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 309, + 189, + 545, + 276 + ], + "type": "table", + "html": "
Lkd1Lkd2CQMSYSU-MM01
R1↑R10↑mAP↑
70.1593.1267.40
✓72.7595.7169.86
✓72.2695.1668.50
✓✓73.6395.7970.61
✓✓✓74.6696.4771.73
", + "image_path": "88623aff9273c28a58b8639e4aafc57d78a5a5883eab2ae35bfe52451d804517.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 280, + 419, + 403 + ], + "blocks": [ + { + "bbox": [ + 307, + 280, + 419, + 403 + ], + "lines": [ + { + "bbox": [ + 307, + 280, + 419, + 403 + ], + "spans": [ + { + "bbox": [ + 307, + 280, + 419, + 403 + ], + "type": "image", + "image_path": "8a22a19c9a5e43fa912354792fd3830caa7008a9d4188f11697b52178cfda6ec.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 407, + 538, + 418 + ], + "lines": [ + { + "bbox": [ + 306, + 407, + 538, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 538, + 418 + ], + "type": "text", + "content": "Figure 4. Qualitative analysis of the proposed DRM and TSAA." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 434, + 280, + 545, + 404 + ], + "blocks": [ + { + "bbox": [ + 434, + 280, + 545, + 404 + ], + "lines": [ + { + "bbox": [ + 434, + 280, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 434, + 280, + 545, + 404 + ], + "type": "image", + "image_path": "6b37ebd55b5c322f9b30a06605275334041e98bec4ff75cdd8b05eda49cb14c2.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 431, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 545, + 528 + ], + "type": "text", + "content": "Qualitative Results. We visualize the regions selected by the DRM module in Figure 4. It can be seen that the DRM can select diverse and discriminative regions, which could serve as strong guidance for the subsequent TSAA module. We also visualize the attention scores generated by the TSAA in Figure 4. We can see that the proposed TSAA has a strong capability in searching the corresponding regions given the key regions selected by DRM." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "In this paper, we present the Concordant Attention Learning (CAL) framework, which learns concordant attention across the visible and infrared modalities and can effectively bridge the modality gap for VI Re-ID. We show that it is beneficial to design target-aware attention mechanisms to ensure attention concordance when aligning cross-modal samples. We also verify that exploiting cross-modal clues from the target modality and enabling cross-modal knowledge exchange in a match-and-distill manner can facilitate the learning of inter-modal correlations. Extensive experiments demonstrate the effectiveness and superiority of CAL over state-of-the-art methods, suggesting the potential of our approach for improving VI Re-ID research." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11129" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 149, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 149, + 85 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 149, + 85 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 92, + 287, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 92, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 92, + 287, + 152 + ], + "type": "text", + "content": "This work is supported by National Natural Science Foundation of China (No.62073004), Science and Technology Plan of Shenzhen (No.JCYJ20200109140410340), and Shenzhen Fundamental Research Program (No.GXWD20 201231165807007-20200807164903001)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 166, + 106, + 178 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 166, + 106, + 178 + ], + "spans": [ + { + "bbox": [ + 48, + 166, + 106, + 178 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 186, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 186, + 287, + 230 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 186, + 287, + 230 + ], + "spans": [ + { + "bbox": [ + 53, + 186, + 287, + 230 + ], + "type": "text", + "content": "[1] Guangyi Chen, Jiwen Lu, Ming Yang, and Jie Zhou. 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IEEE TCSVT, 32(3):1418-1430, Mar. 2022. 2" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11131" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction/4c1481b1-79c6-4632-b011-bcc21d585466_content_list.json b/2023/Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction/4c1481b1-79c6-4632-b011-bcc21d585466_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..32f16909fdd816e71f76a9d266df02e6886a6ab1 --- /dev/null +++ b/2023/Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction/4c1481b1-79c6-4632-b011-bcc21d585466_content_list.json @@ -0,0 +1,1581 @@ +[ + { + "type": "text", + "text": "Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction", + "text_level": 1, + "bbox": [ + 192, + 130, + 777, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Su-Kai Chen $^{1,2}$ Hung-Lin Yen $^{1}$ Yu-Lun Liu $^{1}$ Min-Hung Chen $^{3}$ Hou-Ning Hu $^{2}$ Wen-Hsiao Peng $^{1}$ Yen-Yu Lin $^{1}$ $^{1}$ National Yang Ming Chiao Tung University $^{2}$ MediaTek Inc. $^{3}$ NVIDIA https://skchen1993.github.io/CEVR_web/", + "bbox": [ + 181, + 202, + 784, + 276 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d93458dad08349dd8ba925b5f67b07704529e40629336420bd9acf2e8c094ae7.jpg", + "image_caption": [ + "Figure 1: Single-image HDR reconstruction from continuous LDR stack. (a) Continuous Exposure Value Representation (CEVR) generates LDR images with continuous exposure values (EV) without corresponding ground truth during training. (b) Existing methods build LDR stacks only with EVs covered by training data, which brings less visible details for Debevec's method [11] to estimate an accurate inverse camera response function (CRF), resulting in artifacts on HDR results. (c) Our CEVR model enriches the LDR stack by including additional LDR images with continuous and dense EVs (red frames), allowing Debevec's method to predict a more precise inverse CRF and reconstruct more visually pleasing HDR images." + ], + "image_footnote": [], + "bbox": [ + 124, + 308, + 486, + 498 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0d11f861c2ea9ee7f9b74afcd48155da1ae0896a4a63e14c0066c08852676eac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 311, + 846, + 498 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 613, + 313, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning is commonly used to reconstruct HDR images from LDR images. LDR stack-based methods are used for single-image HDR reconstruction, generating an HDR image from a deep learning-generated LDR stack. However, current methods generate the stack with predetermined exposure values (EVs), which may limit the quality of HDR reconstruction. To address this, we propose the continuous exposure value representation (CEVR), which uses an implicit function to generate LDR images with arbitrary EVs, including those unseen during training. Our approach generates a continuous stack with more images containing diverse EVs, significantly improving HDR reconstruction. We use a cycle training strategy to supervise the model in generating continuous EV LDR images without corresponding ground truths. Our CEVR model outperforms existing methods, as demonstrated by experimental results.", + "bbox": [ + 73, + 641, + 470, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 613, + 630, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "High dynamic range (HDR) images can capture detailed appearances in regions with extreme lighting conditions, like sun and shadow. As conventional cameras only capture a limited dynamic range in real-world scenes, one approach to address this issue is to blend multiple LDR images with different exposures into a single HDR image. However, this method is limited to static scenes and may result in ghosting or blurring artifacts in dynamic scenes. Additionally, this method is not applicable when multiple images of the same scene are unavailable, such as an image on the internet.", + "bbox": [ + 496, + 641, + 890, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Another branch of methods, e.g., [12, 13, 23, 24, 26, 32, 43], takes a single LDR image as input to generate the HDR counterpart without suffering from misalignment, which is referred to as single-image HDR reconstruction. These approaches, e.g., [23, 24], are trained on particular datasets and build an LDR stack with a single LDR image to generate an HDR image using Debevec's method [11].", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12990", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/5e661398f3bd67b1934540560d855f1e85f2500b4d1335986292b267ee8db77a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
EV stack of real imagesPSNRPSNRHDR-VDP-2
RH's TMOKK's TMO
mσmσmσ
[-2, 0, 2]24.963.1823.522.7545.125.74
[-2, -1.3, 0, 1.3, 2]25.152.9823.713.1245.265.12
[-2, -1.3, -0.7, 0, 0.7, 1.3, 2]25.323.0123.923.0445.514.86
", + "bbox": [ + 78, + 89, + 467, + 166 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/411919c29c24e2ed655afa44a6dfbedc7733c4f7e9a6455fb65bd232135e8321.jpg", + "image_caption": [ + "[-2,0,2]" + ], + "image_footnote": [], + "bbox": [ + 81, + 169, + 176, + 277 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a67fde51315db7f407847a941eecb2ce5253aecc98df5b21dda545e4ef056d11.jpg", + "image_caption": [ + "[-2,-1.3,0,1.3,2]", + "[-2,-1.3,-0.7,0,0.7,1.3,2]" + ], + "image_footnote": [], + "bbox": [ + 176, + 169, + 274, + 277 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9a366616408ac8106c9df3567b35bab873b34203fa8fa4a5d416f5a9e10fb9c0.jpg", + "image_caption": [ + "Figure 2: Motivation. We observe that an LDR stack with dense EVs improves HDR reconstruction even with the same exposure range (from -2EV to +2EV). A list $[-2,0,2]$ means the stack contains three LDR images with -2, 0, and 2 EVs. An example of visual comparison is given." + ], + "image_footnote": [], + "bbox": [ + 274, + 169, + 370, + 277 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/93b80681d9d2606a41ca1bedf3f8aefffc5bbe4a6f57fe491b45ca8ffc08787d.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 372, + 169, + 467, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Using more LDR images with richer EVs improves HDR image quality, as demonstrated in Fig. 2 with different EV stack settings using Debevec's method on the real LDR images of the HDREye dataset [36]. We compare tone-mapping operators RH [39] and KK [20] and use HDR-VDP-2 to evaluate HDR quality. However, accessible datasets have predefined and quantized EVs and may not cover optimal values for HDR reconstruction, causing information loss.", + "bbox": [ + 75, + 396, + 467, + 530 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Previous studies [8, 35, 46] show the effectiveness of implicit neural representations in modeling continuous relationships, motivating our research. Inspired by the observation in Fig. 2, we address the issue of predefined, quantized EVs by leveraging an implicit neural function to model relationships between image appearance and continuous EVs. It turns out our method can generate LDR images with arbitrary EVs even if the corresponding ground truth is unavailable. More importantly, LDR stacks enriched by images with these continuous and dense EVs can reconstruct HDR images of better quality.", + "bbox": [ + 75, + 534, + 467, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, the proposed approach, continuous exposure value representation (CEVR), exploits an implicit neural function to generate LDR images with continuous exposure values, as shown in Fig. 1(a). Based on the flexibility of our CEVR model, we further develop two strategies, cycle training and continuous stack, to improve the quality of the LDR stack and the final HDR result.", + "bbox": [ + 75, + 702, + 467, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Cycle training utilizes CEVR to generate continuous EV images without relying on direct supervision from corresponding ground truths. We train the model using two continuous EVs that sum up to a predefined EV, with the proportion of these two continuous EVs randomly sampled. This strategy enforces the cycle consistency constraint, im", + "bbox": [ + 75, + 810, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "proving the model's ability to synthesize images with varying EVs and enhancing the quality of the LDR stack. We then use the enriched LDR stack containing seen and unseen EVs in training data for Debevec's method to produce more accurate inverse camera response functions (CRFs) and visually appealing tone-mapped images (Fig. 1(c)) compared to previous methods [23, 24] (Fig. 1(b)).", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Extensive evaluations demonstrate the effectiveness of our proposed continuous stack and cycle training on the VDS [23] and HDREye [36] datasets. Both quantitative and qualitative evaluations show that CEVR significantly outperforms existing methods. The following summarizes our three primary contributions:", + "bbox": [ + 496, + 198, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the CEVR approach, which can generate LDR images with continuous exposure values by modeling relationships between image appearances and exposure values.", + "- With the flexibility of the CEVR model, we design a training strategy, cycle training, to explore continuous EV information and enhance the quality of the estimated LDR stack.", + "- We propose the continuous stack, which consists of LDR images with continuous and dense exposure values and can improve the quality of final HDR images." + ], + "bbox": [ + 517, + 297, + 890, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 489, + 638, + 505 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-image HDR reconstruction. Modern cameras typically have limited dynamic ranges and cannot well capture all visible details of a scene with a wide range of illumination. To address this issue, one practical solution is to take multiple LDR images at different exposure levels and blend them into an HDR image. To this end, conventional methods such as [11,30] are developed to estimate the CRF [15], upon which multiple LDR images are converted into the radiance field of the scene and transformed into an HDR image. Recent methods, e.g., [17, 51], use CNNs for directly fusing LDR images and reconstructing their HDR counterpart. However, both conventional and CNN-based methods require multiple differently exposed images of a static scene. Furthermore, for working on dynamic scenes, additional mechanisms are needed to alleviate the misalignment problem and avoid blurring or ghosting artifacts [18,29,47]. However, misalignment itself is a complicated issue to resolve.", + "bbox": [ + 496, + 518, + 890, + 789 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Single-image HDR reconstruction. This task aims to reconstruct the HDR image using just one LDR input, also called inverse tone mapping [3-6], and can bypass the misalignment problem. Existing methods need to enlarge the dynamic range [1, 33, 40, 44] and restore the lost details. Generation techniques [14,25,55,56,58] for image synthesis are essential to methods of this category. Due to the", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12991", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "superior mapping power of CNNs [16, 45] and GAN [14], deep neural networks are widely adopted for HDR reconstruction.", + "bbox": [ + 75, + 90, + 468, + 133 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "One branch of research efforts [12,32,43,53,57] focuses on learning the mapping from the input LDR image to the HDR image. For example, Marnerides et al. [32] use CNNs to generate the HDR image based on an LDR input. To further improve the performance, Santos et al. [43] filter out the saturated regions in the LDR input and pretrain the deep network for an inpainting task. However, learning the LDR-to-HDR mapping is ill-posed since different LDR images can be mapped to the same HDR image [13].", + "bbox": [ + 75, + 137, + 467, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another branch of methods, e.g., [13, 19, 23, 24], aims to synthesize a stack of differently exposed LDR counterparts given an LDR image as input. Then, the conventional multi-image methods can be applied to the synthesized LDR stack to complete HDR reconstruction. For example, Endo et al. [13] use 3D convolutions, with exposure variation being one dimension, to learn the relationship between the LDR input and its counterparts with different exposure values. Their approach can generate the LDR stack directly. The LDR stack can be synthesized in a recursive manner [19,23,24]. For example, Lee et al. [24] use GAN to generate an image with relative exposure value change. The LDR stack is constructed by recursively using their model.", + "bbox": [ + 75, + 273, + 467, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Nevertheless, existing stack-based methods can only generate LDR images with predefined exposure values present in the training data. Inspired by the fact that the real-world captured images can have any EV value depending on different shutter settings instead of predefined ones, we present a method that can synthesize LDR images with continuous exposure values that are even unseen in the training data. Our method can generate an enriched and denser stack with which significantly better HDR results are achieved.", + "bbox": [ + 75, + 472, + 467, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Implicit neural representations. An implicit function space is a shared function space that contains the neural representation of different objects or images learned by a shared implicit function. It is commonly a latent space where a latent code is mapped to an image using an encoder-decoder structure [9,34,41,42,52]. This approach has been widely used in image super-resolution [8, 22], 3D shape, surface modeling [2,9,46], and view synthesis of 3D structures [35,37]. Methods using implicit functions have shown that the learned latent space can be continuous [8,10,35,38], allowing for exploring continuous relationships of exposure differences between images.", + "bbox": [ + 75, + 612, + 467, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "More and more radiance field reconstruction research aims to generalize the trained model across scenes unseen in training data. The methods in [7, 48, 54] propose advanced model architectures and training strategies, making the learned implicit function space achieve the generalization on unseen views. Our method, similar to [7, 48, 54], can generalize well to all images without fine-tuning.", + "bbox": [ + 75, + 795, + 467, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 498, + 90, + 607, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present our proposed Continuous Exposure Value Representation (CEVR) which generates LDR images with continuous EV. We provide an overview of our method in Section 3.1, followed by the architectural design in Section 3.2, which includes the implicit module and intensity transformation. Additionally, we propose two strategies, cycle training, and continuous stack, to further enhance the flexibility of CEVR, which are discussed in detail in Section 3.3 and 3.4, respectively.", + "bbox": [ + 496, + 114, + 890, + 251 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 258, + 609, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the observation in Fig. 2, we propose the CEVR model to generate an enriched and denser LDR stack for high-quality HDR reconstruction. Our model, shown in Fig. 3, utilizes a hierarchical U-Net structure (Fig. 3(a)) and incorporates the implicit neural representation into the design to predict LDR images with continuous EVs (Fig. 3(c)). To maintain accurate color and image structure while adjusting brightness, we introduce intensity transformation (Fig. 3(d)), which generates an adjustment map from each scale of the feature map. As the ground-truth LDR images with unseen exposure values are lacking, we train the model using unsupervised cycle training (Fig. 4), enabling our method to learn images with varying EVs and enhance the quality of the predicted LDR stack.", + "bbox": [ + 496, + 281, + 890, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Continuous Exposure Value Representation", + "text_level": 1, + "bbox": [ + 500, + 501, + 869, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We show our CEVR model in Fig. 3(a). Our CEVR model employs the hierarchical U-Net structure, where the encoder is a pre-trained VGG-Net and the decoder is a cascade of decoder blocks (Fig. 3(b)), each of which comprises an implicit module that compiles the feature map with an input EV step $s$ . Each decoder block is followed by an intensity transformation to adjust the intensity of input image at that scale. Specifically, the CEVR model $F$ takes an LDR image $I$ and the specified EV step $s$ as input and generates another LDR image $\\hat{I}_s$ , a counterpart of $I$ with the relative exposure value change $s$ , via", + "bbox": [ + 496, + 523, + 890, + 690 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {I} _ {s} = F (I, s). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 696, + 890, + 714 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Take the widely used VDS dataset [23] as an example. An LDR image with EV0 in this dataset can serve as $I$ . An LDR stack can be generated by applying our CEVR $F$ to $I$ and every EV step in $\\{s \\in \\mathbb{Z} | - 3 \\leq s \\leq 3\\}$ .", + "bbox": [ + 496, + 722, + 890, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Implicit module. To synthesize an LDR image conditioned on a continuous EV step $s$ even unseen in the training data, each decoder block in Fig. 3(b) has an associated, learnable implicit module $f_{\\theta}$ , which is built by MLPs and shown in Fig. 3(c). The implicit module $f_{\\theta}$ parameterized by $\\theta$ takes the form:", + "bbox": [ + 496, + 786, + 890, + 876 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {s} (p, q) = f _ {\\theta} ([ x (p, q), s ]), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 883, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12992", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d59f4d880cac398893b811a011f2a2d7c0ce4fe58c728a6c17d0b8e42f2d0ec7.jpg", + "image_caption": [ + "(a) CEVR network" + ], + "image_footnote": [], + "bbox": [ + 83, + 93, + 883, + 277 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/26ec1ab924208f4eba6280ef9439c4c0453cb11984e8a679bc1a48921e250eaf.jpg", + "image_caption": [ + "(b) Decoder block" + ], + "image_footnote": [], + "bbox": [ + 81, + 313, + 331, + 385 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/81c6570a730eaeadf20dbb79ba944437c9dde2522f5885652ce980efc3956c61.jpg", + "image_caption": [ + "(c) Implicit module", + "Figure 3: Proposed network architecture. (a) The proposed CEVR model takes an image $I$ and an EV step $s$ as input, and produces an LDR image $\\hat{I}_s$ with a relative exposure value change $s$ . It adopts the U-Net structure, where the encoder is a pre-trained VGG-Net, and the decoder is a cascade of decoder blocks. (b) Each decoder block comprises an implicit module to enable continuous EV representation learning, as shown in (c). (d) Following each decoder block, an intensity transformation module is learned to produce the $\\alpha$ and $\\beta$ maps for image brightness transformation." + ], + "image_footnote": [], + "bbox": [ + 357, + 313, + 607, + 385 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b812d92be0f417526f4b0afd5d4445bec19b2d059d8265885da40e9f135e55d4.jpg", + "image_caption": [ + "(d) Intensity transformation" + ], + "image_footnote": [], + "bbox": [ + 638, + 313, + 888, + 385 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x \\in \\mathbb{R}^{H \\times W \\times C}$ is the input feature map, $x(p,q) \\in \\mathbb{R}^C$ is the feature vector at location $(p,q)$ , and $[x(p,q),s] \\in \\mathbb{R}^{C + 1}$ refers to the concatenation of $x(p,q)$ and $s$ . The output feature map $x_{s}$ is generated by repeatedly applying the implicit module $f_{\\theta}$ to all $H \\times W$ locations of $x$ with the desired relative exposure value change $s$ .", + "bbox": [ + 75, + 513, + 468, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intensity transformation. In Fig. 3(a), our CEVR leverages U-Net to perform multi-scale synthesis to generate a better LDR image with a different EV. The input and output images, $I$ and $\\hat{I}_s$ , cover the same scene under different exposures. Thus, their content should not undergo significant changes. To preserve the image structure and allow the model to focus on the brightness changes for detail reconstruction at each scale, the proposed intensity transformation module in Fig. 3(d) takes the resized feature map from the decoder block as input and produces the $\\alpha$ and $\\beta$ maps. As shown in Fig. 3(a), the $\\alpha$ and $\\beta$ maps carry out affine brightness transformation at each scale. The output $\\hat{I}_s$ is synthesized through multi-scale transformations.", + "bbox": [ + 75, + 609, + 468, + 805 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reconstruction Loss. Suppose that we are given a training set of $N$ images $\\{I_n\\}_{n=1}^N$ with a set of $M$ EV steps $\\{s_m\\}_{m=1}^M$ . For each training image $I_n$ , its ground-truth LDR stack $\\{I_n^*(s_m)\\}_{m=1}^M$ is provided, where $I_n^*(s_m)$ is the counterpart of $I_n$ with the relative exposure value change $s_m$ . We train the CEVR model $F$ in Eq. (1) by minimizing", + "bbox": [ + 76, + 810, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the $L_{1}$ reconstruction loss:", + "bbox": [ + 500, + 515, + 679, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e c}} = \\sum_ {n = 1} ^ {N} \\sum_ {m = 1} ^ {M} \\| I _ {n} ^ {*} (s _ {m}) - F (I _ {n}, s _ {m}) \\| _ {1}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 539, + 890, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Cycle Training Strategy", + "text_level": 1, + "bbox": [ + 500, + 590, + 718, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Existing training datasets, such as the VDS dataset [23], provide the ground truth for a sparse set of predefined EV steps, e.g., $[-3, -2, \\dots, 3]$ . Inspired by the success of cycle consistency training in video frame interpolation [27] and to make our CEVR work well for synthesizing images with arbitrary EVs, we introduce the cycle training strategy to train the model with continuous EV steps without the corresponding ground-truth images. For each training image $I_{n}$ and each EV step $s_m$ covered by the training set, the cycle training strategy shown in Fig. 4, derives the CEVR model with two branches. The first branch takes $I_{n}$ and $s_m$ as input. Since the ground-truth image $I_{n}^{*}(s_{m})$ is available, the reconstruction loss $\\mathcal{L}_{\\mathrm{rec}}$ is used to supervise this branch.", + "bbox": [ + 496, + 613, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The second branch implements a two-step process. We randomly sample a real value $a \\in [0,1]$ for each image $I_{n}$ at each training iteration, and decompose the EV step $s_m$ into two sub-steps: $u = as_m$ and $\\nu = (1 - a)s_m$ , with $u + \\nu = s_m$ . Our CEVR model is applied twice with the two EV sub-steps, respectively. Although the ground truth for", + "bbox": [ + 496, + 810, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12993", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c4088f9482480235ec0b81fabddcd2ec6f7b55638b3c76753fc1e02694577609.jpg", + "image_caption": [ + "Figure 4: Cycle training. We derive the CEVR model in an unsupervised cycle training strategy without using the corresponding ground truth. In this way, our model exploits the cycle consistency constraint and learns more continuous information by varying the EV sub-step $u$ ." + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 467, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the randomly sampled sub-step $u$ is unavailable, we expect that the output of taking the two sub-steps should be similar to the ground truth $I_{n}^{*}(s_{m})$ because of $u + v = s_{m}$ . Thereby, we enforce the proposed cycle loss:", + "bbox": [ + 75, + 383, + 468, + 445 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c y c}} = \\sum_ {n = 1} ^ {N} \\sum_ {m = 1} ^ {M} \\| I _ {n} ^ {*} (s _ {m}) - F (F (I _ {n}, u), v) \\| _ {1}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 452, + 468, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The sub-step $u$ in Eq. (4) is randomly sampled for each training image with each covered EV step at each training iteration. It is used to simulate arbitrary EV step input to our CEVR model. To compensate for the lack of the ground truth of the intermediate output $F(I_{n},u)$ , the cycle loss $\\mathcal{L}_{\\mathrm{cyc}}$ in Eq. (4) offers indirect supervision, ensuring the continuity of our CEVR model with continuous EV steps.", + "bbox": [ + 75, + 501, + 468, + 607 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The objective function used to derive the proposed CEVR is defined by", + "bbox": [ + 75, + 607, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {r e c}} + \\lambda \\mathcal {L} _ {\\text {c y c}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 209, + 647, + 468, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we empirically set $\\lambda$ to 0.1 in our experiments.", + "bbox": [ + 76, + 672, + 429, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Continuous Stack", + "text_level": 1, + "bbox": [ + 76, + 696, + 250, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the inference phase, with the implicit module and the cycle training strategy, our CEVR model can generate high-quality LDR images with continuous EVs. The LDR stack containing more LDR images with various EVs can help Debevec's method [11] estimate a more accurate inverse CRF, as shown in Fig. 1(c), and improve the HDR image reconstruction, as shown in Fig. 2. Inspired by this observation, we proposed the continuous stack, which predicts additional LDR images with continuous EVs from our CEVR model. The predicted continuous and dense LDR stack further benefits the stack fusion process and enhances the final HDR quality, as shown in Fig. 1(c).", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d2482cbe4dc031d33aa169fad0098c6e0716ce8e25767fbdd7cf09256e4418d1.jpg", + "table_caption": [ + "Table 1: Quantitative comparison of the predicted LDR stacks on the VDS dataset [23]. CEVR outperforms existing approaches in estimating LDR stacks for all EVs. With cycle training, our method can generate high-quality LDR images even with large EV changes." + ], + "table_footnote": [], + "table_body": "
EVMethodPSNRSSIMMS-SSIM
mσmσmσ
+3Deep chain HDRI [23]28.182.770.9530.0650.9830.015
Deep recursive HDRI [24]28.972.920.9440.0440.9810.014
CEVR (Ours)34.343.460.9730.0210.9890.007
+2Deep chain HDRI [23]29.653.060.9590.0650.9860.016
Deep recursive HDRI [24]29.432.850.9520.0390.9860.010
CEVR (Ours)35.303.080.9810.0160.9930.004
+1Deep chain HDRI [23]31.903.430.9690.0390.9920.008
Deep recursive HDRI [24]32.022.850.9690.0260.9920.006
CEVR (Ours)37.642.960.9890.0090.9960.004
-1Deep chain HDRI [23]29.013.830.9350.0560.9800.017
Deep recursive HDRI [24]31.223.690.9510.0310.9860.090
CEVR (Ours)34.623.470.9800.0110.9920.005
-2Deep chain HDRI [23]26.724.540.9520.0290.9740.021
Deep recursive HDRI [24]31.083.070.9480.0410.9860.014
CEVR (Ours)33.894.340.9780.0170.9880.010
-3Deep chain HDRI [23]24.334.570.9190.0360.9480.037
Deep recursive HDRI [24]29.154.750.9100.0610.9660.025
CEVR (Ours)30.585.320.9540.0460.9720.032
", + "bbox": [ + 501, + 176, + 890, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 431, + 633, + 449 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 455, + 689, + 473 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We train our model using the training set of the VDS dataset [23], which contains image stacks of 48 scenes. The testing sets of the VDS and HDREye datasets [36], which contain 48 and 42 scenes respectively, serve as the testing sets for evaluations. The auto-bracketing feature of the camera produces seven photos with predefined exposure values for each scene in the VDS dataset (EV-3 to EV+3). We follow the common evaluation protocol [23, 24] and select the image with the zero exposure value, which is expected to have the most evenly distributed histogram, as the input to the model.", + "bbox": [ + 496, + 484, + 890, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training details. For training, we consider each training scene $n$ from the VDS dataset [23] and take the corresponding EV0 LDR image as input $I_{n}$ . We also take each EV step $s_m \\in \\{-3, -2, -1, 0, 1, 2, 3\\}$ into account. We feed $I_{n}$ and $s_m$ to the CEVR model and estimate the LDR image with EV $s_m$ for model training. Since the inverse CRF is usually asymmetrical, we train two different models with the same architecture to handle the increasing and decreasing exposure changes, respectively. For upsampling, we use bicubic upsampling, followed by a $3 \\times 3$ 2D convolution with stride 1 and padding 1. The model is trained for 1,250 epochs with Adam optimizer [21] and cosine annealing warmup with restarts as the scheduler. We use random rotation and flip to augment the data.", + "bbox": [ + 496, + 654, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. We employ PSNR, SSIM [49], and MS-SSIM [50] as the metrics for evaluating the qualities of", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12994", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/769aa35ddb79c50ab4a85e543c69f472e2cb47c40649ae0269327573bfecb2e5.jpg", + "image_caption": [ + "Figure 5: Qualitative comparison of LDR image predictions in the VDS dataset [23]. Our approach recovers more details compared to Deep recursive HDRI [24] in the EV-3 example. In the $\\mathrm{EV} + 3$ example, our approach generates LDR images with a color tone similar to the ground truth." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 465, + 241 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the predicted LDR stacks and HDR tone-mapped images. We also utilize HDR-VDP-2 [31], a metric based on the human visual system, to evaluate the quality of the reconstructed HDR images. We follow the setting of [23, 24], which sets a 24-inch monitor with a viewing distance of 0.5 meters, a peak contrast of 0.0025, and a gamma of 2.2 for measuring the HDR-VDP-2 metric.", + "bbox": [ + 75, + 327, + 467, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "HDR reconstruction and tone-mapping operators. Our approach uses Debevec's approach [11] to reconstruct HDR images with the predicted LDR stack and utilizes Reinhard's method [39] or Kim and Kautz's method [20] to tonemap the HDR images.", + "bbox": [ + 75, + 436, + 468, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison of LDR Stacks Prediction", + "text_level": 1, + "bbox": [ + 76, + 522, + 408, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative comparisons. The quantitative comparisons of the estimated LDR exposure stacks from the VDS dataset are shown in Tab. 1. The table shows that the proposed method performs favorably against existing methods at every exposure value. The output LDR image quality decreases as the exposure value gap increases because more extensive over- and under-exposed regions reconstruction are required, which makes the task more difficult. However, with our cycle training, our model can still generate high-quality LDR images in the cases of EV+3 and EV-3 by incorporating continuous and dense EV information into the training process. The continuous EV generation during training helps the model learn how to explicitly infer LDR images with arbitrary exposure values.", + "bbox": [ + 75, + 549, + 468, + 761 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative comparisons. With the cycle training, our method can generate a high-quality LDR image even with large EV changes. A detailed qualitative comparison is presented in Fig. 5. The first row of this figure shows that Deep recursive HDRI [24] often gets less accurate color tone in estimating the LDR images, which may further degrade the quality of the HDR images fused by the LDR stack. On the contrary, our method can better estimate the LDR images in all EVs with more accurate color tones. In addition, the", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4e45b539190586498fb2ff762a5205cd5323c12ae274858bd79fea967a84e75d.jpg", + "table_caption": [ + "Table 2: Quantitative comparison of HDR and TMO images. Two tone-mapping approaches, Reinhard's approach [39], and Kim and Kautz's approach [20], are denoted as RH's and KK's TMO." + ], + "table_footnote": [], + "table_body": "
DatasetMethodPSNRPSNRHDR-VDP-2
RH's TMOKK's TMO
mσmσmσ
VDSDrTMO [13]25.494.2821.364.5054.336.27
Deep chain HDRI [23]30.863.3624.544.0156.364.41
Deep recursive HDRI [24]32.992.8128.023.5057.154.35
Santos et al. [43]22.562.6818.233.5353.514.76
Liu et al. [26]30.893.2728.004.1156.976.15
CEVR (Ours)34.673.5030.044.4559.005.78
HDREyeDrTMO [13]23.683.2719.974.1146.675.81
Deep chain HDRI [23]25.772.4422.623.3949.805.97
Deep recursive HDRI [24]26.282.7024.262.9052.634.84
Santos et al. [43]19.892.4619.003.0649.975.44
Liu et al. [26]26.253.0824.673.5450.336.67
CEVR (Ours)26.543.1024.812.9153.154.91
", + "bbox": [ + 501, + 160, + 890, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "second row demonstrates that our method can estimate the LDR images without severe artifacts. More visual comparisons can be found in the supplementary material.", + "bbox": [ + 498, + 347, + 890, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison of HDR Image Prediction", + "text_level": 1, + "bbox": [ + 500, + 401, + 830, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method with five recent single-image HDR reconstruction methods, including Santos et al. [43], DrTMO [13], Deep chain HDRI [23], Deep recursive HDRI [24], and Liu et al. [26]. For Santos et al. [43], Deep recursive HDRI [24] and Liu et al. [26], we use their official implementations along with the released pre-trained model weight to generate all the quantitative and qualitative results on the VDS [23] and HDREye [36] datasets. For DrTMO [13] and Deep chain HDRI [23], we compare our results to the numbers reported in their papers. For HDR image prediction, our approach adopts the continuous stack strategy where the EV steps are enriched from $\\{-3, -2, \\dots, +3\\}$ to $\\{-3, -2.5, \\dots, +3\\}$ , and the images with the extra EV steps are also synthesized by using the proposed CEVR model.", + "bbox": [ + 496, + 425, + 890, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative evaluations. As shown in Tab. 2, our method performs favorably against the competing methods on the VDS dataset [23]. The HDRey dataset [36] serves as a blind test bed, our HDR prediction still achieves better qualities using the same tone-mapping operators. Our proposed cycle training makes the model explicitly learn the continuity as EV steps change, leading to better generalization on the unseen dataset, HDRey. With the continuous stack, more LDR images with various EVs are involved in the fusion process, which helps Debevec's approach [11] estimate a more accurate inverse CRF and generate HDR images with better qualities.", + "bbox": [ + 496, + 655, + 890, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative comparisons. To generate the tone-mapped images for visual comparisons, we first reconstruct HDR images by fusing the LDR stacks with Debevec's approach [11]. Then we use Reinhard's method [39] to gen", + "bbox": [ + 496, + 839, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12995", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4ef053b31807fde2c6621d220ecb0e9338af0839ceff9c3e601b58fa1350ca18.jpg", + "image_caption": [ + "Figure 6: Qualitative comparison of tone-mapped HDR images. We adopt Reinhard's method [39] to generate HDR images shown in the figure. Deep recursive HDRI [24] often suffers from erroneous color tones and artifacts. As shown in the figure, our method can better recover details when compared to Liu et al.'s method [26]. In most regions, our method reconstructs the tone-mapped images with more accurate high-frequency details, leading to visually pleasing results." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 421, + 440 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05c8cf6686e24dd533684cea42e596e2881b74dd43cbf5d58a5cce70edced964.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 437, + 88, + 866, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "erate HDR TMO images for all comleting methods. As Liu et al. [26] generate an HDR image directly, we apply Reinhard's tone-mapping operator [39] for tone-mapping the HDR images. Note that Liu et al. [26] do not train their method on the VDS dataset; hence we only compare the qualitative results with their method on the HDREye dataset, as shown in Fig. 6.", + "bbox": [ + 75, + 526, + 468, + 632 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 6, it can be observed that Deep recursive HDRI [24] often suffers from inaccurate color tone: the color of the building is inaccurate in the tone-mapped images, and artifacts are present in severely exposed regions. Liu et al. [26] directly estimate and reverse the whole camera pipeline to generate HDR images. It sometimes struggles with generating detailed textures and produces artifacts in severely exposed regions, e.g., the over-exposed window frame and sky in the daylight. With the intensity transformation, our model can preserve the image structure and generate the tone-mapped images with similar tones to the ground truth. It also produces fewer artifacts. More visual comparisons can be found in the supplementary material.", + "bbox": [ + 75, + 633, + 470, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 845, + 240, + 859 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In the following, we validate three design contributions to improving the quality of the LDR stack and HDR images.", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cabf71087322e790f25c7e7564fa7fb4bac029f43eb1936ed33a68abdf01f0ef.jpg", + "table_caption": [ + "Table 3: Ablation studies on the predicted LDR stack. Intensity transformation balances two distinct tasks: brightness adjustment and precise color tone generation while preserving the image structure. Cycle training provides the model with extra information about changing EVs. Both designs improve LDR stack quality." + ], + "table_footnote": [], + "table_body": "
Intensity transformation-✓✓
Cycle training--✓
PSNRPSNRPSNR
mσmσmσ
EV+331.954.2033.903.5734.343.46
EV+233.193.1634.893.1235.303.08
EV+135.092.5637.493.0737.642.96
EV-133.672.0634.432.5534.623.47
EV-232.533.3732.914.4133.894.34
EV-330.235.4730.355.8630.585.32
", + "bbox": [ + 500, + 626, + 890, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Intensity transformation. Learning to adjust image brightness while maintaining color tone accuracy and image structures can be challenging. The CEVR model, which directly outputs results from the U-net structure without using intensity transformation, can struggle to adjust brightness or produce inaccurate LDR images with artifacts, as shown in Fig. 7. The intensity transformation module can restrict", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12996", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9ba8547d3af91dac367943c636ade8bd47cf20b70900726e6ebccaadccc64dfa.jpg", + "table_caption": [ + "Table 4: Ablation studies on the reconstructed HDR images on the VDS dataset [23]. Intensity transformation and cycle training enhance the quality of LDR stacks, and continuous stack benefits the stack fusion process." + ], + "table_footnote": [], + "table_body": "
Intensity transformation-✓✓✓
Continuous stack--✓✓
Cycle training---✓
PSNR32.5234.2034.4734.67
", + "bbox": [ + 76, + 151, + 467, + 224 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9b165b71189518004c02a2f38ea268c920563bedda0322f41ecedd9c6bff16a2.jpg", + "image_caption": [ + "Figure 7: Ablation on intensity transformation. With intensity transformation, CEVR can adjust LDR image intensity while preserving the image structure and color tone." + ], + "image_footnote": [], + "bbox": [ + 76, + 227, + 464, + 385 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the model's capacity, producing LDR images with more accurate brightness, color tones, and structures. This design improves the quality of the LDR stack and HDR results, as demonstrated in Tab. 3 and Tab. 4.", + "bbox": [ + 75, + 454, + 468, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Cycle training. With cycle training, the model can be supervised on continuous EV steps without using the corresponding ground truth. It can learn how to change the exposure value continuously, which improves the quality and reduces the artifacts of the estimated LDR images, which also leads to better HDR quality, as shown in Fig. 8, Tab. 3 and Tab. 4. To further demonstrate the effectiveness of cycle training, we conducted the hold-out experiment, excluding EV-1 and +1 LDR images during training. Then, we used the model to estimate EV-1 and +1 LDR images for each scene and evaluated the PSNR. The table shows that our model can generate better LDR images with unseen EVs when the cycle training strategy is adopted.", + "bbox": [ + 75, + 518, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d6318f8ec802b11aa9be93f948517a8a32f70319e0e62810b0e90fe4e6ff52cd.jpg", + "table_caption": [ + "Table 5: Hold-out experiment. Hold-out experiment excludes EV-1 and +1 LDR images during training. With cycle training, the model generate better LDR images with unseen EVs (EV-1, +1)." + ], + "table_footnote": [], + "table_body": "
Cycle training×✓
EV-127.7533.77
EV+133.3736.96
", + "bbox": [ + 133, + 801, + 405, + 883 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aebf62d06684dc5f7fc450b280af29c3d6c7100c961334957cbe89be337057e4.jpg", + "image_caption": [ + "Figure 8: Ablation on cycle training for LDR and HDR images generation. With the cycle training, the model captures the finer granularity of \"EV changing\" and generates more accurate and visually pleasing LDR and HDR images." + ], + "image_footnote": [], + "bbox": [ + 500, + 90, + 890, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Continuous stack. Debevec's method [11] uses the LDR stack to recover response curves and reconstruct HDR images. A denser and continuous EV LDR stack helps produce an accurate inverse CRF, enhancing HDR quality. We compare two stack settings: \"predefined stack\" and \"continuous stack.\" The CEVR model estimates seven LDR images (EVs: -3, -2, -1, ..., +3) for the predefined stack, which is the setting used in existing methods, while the continuous stack has 13 LDR images with various EVs (-3, -2.5, -2, ..., +3). Tab. 4 and Fig. 1(b)(c) show that the tone-mapped image from the continuous stack has superior quality and is more visually pleasing. We can further validate the effectiveness of the continuous stack by visualizing the CRF of both the predefined stack and the continuous stack. As shown in Fig. 9, the denser EV setting can help generate a smoother CRF compared to the predefined EV setting. Additional analysis of the inverse CRF can be found in the supplementary material.", + "bbox": [ + 496, + 325, + 892, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Failure cases", + "text_level": 1, + "bbox": [ + 500, + 609, + 635, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although the proposed method performs favorably against other existing methods in quantitative and qualitative results, we do not explicitly design the module to address the over-exposed issue, which may make the CEVR model fail to generate reasonable content in large saturated regions, as shown in Fig. 10. It is a promising direction to take the emerging generative model designs, e.g. [28, 59], into account to address this issue.", + "bbox": [ + 496, + 633, + 890, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 768, + 617, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduce CEVR, a learning-based method that produces LDR EV stacks from continuous EV input. Our approach combines U-Net with implicit functions, and allows the network to generate LDR images with continuous EVs. We propose two strategies, including (1) cycle training for learning on continuous EV changes unseen in the training dataset and (2) continuous stack for improving LDR stack", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12997", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/15a25b9f267f666d06daad0753f417ffd2b6ce4b2a4b5e643ccf2d2182d6f779.jpg", + "image_caption": [ + "Figure 9: Analysis of the estimated inverse CRF. Continuous stack, adding additional LDR images with dense and continuous EVs, can help Debevec's method [11] generate more accurate inverse CRF and generate HDR images with better quality." + ], + "image_footnote": [], + "bbox": [ + 106, + 89, + 261, + 303 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/2e4ced7110a2af3793c322dcfc60571c2a446ffcdefd59241b4c3be08e4cadff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 266, + 90, + 436, + 301 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/f243004cc140a2bd9868d442871ace04b229c45f6d50064dc07823f149cb1667.jpg", + "image_caption": [ + "Figure 10: Failure case. Existing methods and our proposed method cannot generate reasonable content as the sky region is severely over-exposed." + ], + "image_footnote": [], + "bbox": [ + 76, + 402, + 184, + 488 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/8b379577cc7eb4fa3529ebc391fae22e41171f512022c2acbd96d2f3cc8aa0d2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 402, + 279, + 488 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/b05ecd9e17c10b9890e21ec5c20a8a87d13b402c711f9ad84d74ea070128cb1d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 402, + 370, + 488 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/011c035686162fafcd1e18f828c6a4378d6e2082a522845962d9eb10e2686be3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 402, + 467, + 488 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "fusion using additional images with dense and continuous EVs. Our approach with the two strategies greatly enhances LDR stack quality and improves HDR image results, as demonstrated through extensive quantitative and qualitative evaluations on two benchmark datasets.", + "bbox": [ + 76, + 559, + 468, + 633 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported in part by National Science and Technology Council (NSTC) under grants 111-2628-E-A49-025-MY3, 112-2221-E-A49-090-MY3, 111-2634-F-002-023, 111-2634-F-006-012, 110-2221-E-A49-065-MY3 and 111-2634-F-A49-010. This work was funded in part by MediaTek.", + "bbox": [ + 76, + 638, + 468, + 729 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 744, + 173, + 760 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ahmet Oğuz Akyüz, Roland Fleming, Bernhard E Riecke, Erik Reinhard, and Heinrich H Bulthoff. 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In ECCV, 2022. 8" + ], + "bbox": [ + 78, + 90, + 467, + 402 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "13000", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction/4c1481b1-79c6-4632-b011-bcc21d585466_model.json b/2023/Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction/4c1481b1-79c6-4632-b011-bcc21d585466_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fcaddd22775655c64e6e34db9f3de6406a4a3347 --- /dev/null +++ b/2023/Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction/4c1481b1-79c6-4632-b011-bcc21d585466_model.json @@ -0,0 +1,2356 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.194, + 0.131, + 0.778, + 0.177 + ], + "angle": 0, + "content": "Learning Continuous Exposure Value Representations for Single-Image HDR Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.203, + 0.785, + 0.277 + ], + "angle": 0, + "content": "Su-Kai Chen\\(^{1,2}\\) Hung-Lin Yen\\(^{1}\\) Yu-Lun Liu\\(^{1}\\) Min-Hung Chen\\(^{3}\\) Hou-Ning Hu\\(^{2}\\) Wen-Hsiao Peng\\(^{1}\\) Yen-Yu Lin\\(^{1}\\) \n\\(^{1}\\)National Yang Ming Chiao Tung University \\(^{2}\\)MediaTek Inc. \\(^{3}\\)NVIDIA https://skchen1993.github.io/CEVR_web/" + }, + { + "type": "image", + "bbox": [ + 0.125, + 0.309, + 0.487, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.312, + 0.847, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.51, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Figure 1: Single-image HDR reconstruction from continuous LDR stack. (a) Continuous Exposure Value Representation (CEVR) generates LDR images with continuous exposure values (EV) without corresponding ground truth during training. (b) Existing methods build LDR stacks only with EVs covered by training data, which brings less visible details for Debevec's method [11] to estimate an accurate inverse camera response function (CRF), resulting in artifacts on HDR results. (c) Our CEVR model enriches the LDR stack by including additional LDR images with continuous and dense EVs (red frames), allowing Debevec's method to predict a more precise inverse CRF and reconstruct more visually pleasing HDR images." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.614, + 0.314, + 0.63 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.642, + 0.471, + 0.884 + ], + "angle": 0, + "content": "Deep learning is commonly used to reconstruct HDR images from LDR images. LDR stack-based methods are used for single-image HDR reconstruction, generating an HDR image from a deep learning-generated LDR stack. However, current methods generate the stack with predetermined exposure values (EVs), which may limit the quality of HDR reconstruction. To address this, we propose the continuous exposure value representation (CEVR), which uses an implicit function to generate LDR images with arbitrary EVs, including those unseen during training. Our approach generates a continuous stack with more images containing diverse EVs, significantly improving HDR reconstruction. We use a cycle training strategy to supervise the model in generating continuous EV LDR images without corresponding ground truths. Our CEVR model outperforms existing methods, as demonstrated by experimental results." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.614, + 0.631, + 0.63 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.892, + 0.793 + ], + "angle": 0, + "content": "High dynamic range (HDR) images can capture detailed appearances in regions with extreme lighting conditions, like sun and shadow. As conventional cameras only capture a limited dynamic range in real-world scenes, one approach to address this issue is to blend multiple LDR images with different exposures into a single HDR image. However, this method is limited to static scenes and may result in ghosting or blurring artifacts in dynamic scenes. Additionally, this method is not applicable when multiple images of the same scene are unavailable, such as an image on the internet." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Another branch of methods, e.g., [12, 13, 23, 24, 26, 32, 43], takes a single LDR image as input to generate the HDR counterpart without suffering from misalignment, which is referred to as single-image HDR reconstruction. These approaches, e.g., [23, 24], are trained on particular datasets and build an LDR stack with a single LDR image to generate an HDR image using Debevec's method [11]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12990" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.09, + 0.468, + 0.167 + ], + "angle": 0, + "content": "
EV stack of real imagesPSNRPSNRHDR-VDP-2
RH's TMOKK's TMO
mσmσmσ
[-2, 0, 2]24.963.1823.522.7545.125.74
[-2, -1.3, 0, 1.3, 2]25.152.9823.713.1245.265.12
[-2, -1.3, -0.7, 0, 0.7, 1.3, 2]25.323.0123.923.0445.514.86
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.17, + 0.177, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.28, + 0.147, + 0.288 + ], + "angle": 0, + "content": "[-2,0,2]" + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.17, + 0.275, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.28, + 0.257, + 0.288 + ], + "angle": 0, + "content": "[-2,-1.3,0,1.3,2]" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.17, + 0.372, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.276, + 0.28, + 0.372, + 0.288 + ], + "angle": 0, + "content": "[-2,-1.3,-0.7,0,0.7,1.3,2]" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.17, + 0.468, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.394, + 0.28, + 0.446, + 0.288 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.301, + 0.47, + 0.378 + ], + "angle": 0, + "content": "Figure 2: Motivation. We observe that an LDR stack with dense EVs improves HDR reconstruction even with the same exposure range (from -2EV to +2EV). A list \\([-2,0,2]\\) means the stack contains three LDR images with -2, 0, and 2 EVs. An example of visual comparison is given." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.468, + 0.531 + ], + "angle": 0, + "content": "Using more LDR images with richer EVs improves HDR image quality, as demonstrated in Fig. 2 with different EV stack settings using Debevec's method on the real LDR images of the HDREye dataset [36]. We compare tone-mapping operators RH [39] and KK [20] and use HDR-VDP-2 to evaluate HDR quality. However, accessible datasets have predefined and quantized EVs and may not cover optimal values for HDR reconstruction, causing information loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.468, + 0.701 + ], + "angle": 0, + "content": "Previous studies [8, 35, 46] show the effectiveness of implicit neural representations in modeling continuous relationships, motivating our research. Inspired by the observation in Fig. 2, we address the issue of predefined, quantized EVs by leveraging an implicit neural function to model relationships between image appearance and continuous EVs. It turns out our method can generate LDR images with arbitrary EVs even if the corresponding ground truth is unavailable. More importantly, LDR stacks enriched by images with these continuous and dense EVs can reconstruct HDR images of better quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.468, + 0.807 + ], + "angle": 0, + "content": "Specifically, the proposed approach, continuous exposure value representation (CEVR), exploits an implicit neural function to generate LDR images with continuous exposure values, as shown in Fig. 1(a). Based on the flexibility of our CEVR model, we further develop two strategies, cycle training and continuous stack, to improve the quality of the LDR stack and the final HDR result." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Cycle training utilizes CEVR to generate continuous EV images without relying on direct supervision from corresponding ground truths. We train the model using two continuous EVs that sum up to a predefined EV, with the proportion of these two continuous EVs randomly sampled. This strategy enforces the cycle consistency constraint, im" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "proving the model's ability to synthesize images with varying EVs and enhancing the quality of the LDR stack. We then use the enriched LDR stack containing seen and unseen EVs in training data for Debevec's method to produce more accurate inverse camera response functions (CRFs) and visually appealing tone-mapped images (Fig. 1(c)) compared to previous methods [23, 24] (Fig. 1(b))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.892, + 0.288 + ], + "angle": 0, + "content": "Extensive evaluations demonstrate the effectiveness of our proposed continuous stack and cycle training on the VDS [23] and HDREye [36] datasets. Both quantitative and qualitative evaluations show that CEVR significantly outperforms existing methods. The following summarizes our three primary contributions:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.299, + 0.892, + 0.359 + ], + "angle": 0, + "content": "- We propose the CEVR approach, which can generate LDR images with continuous exposure values by modeling relationships between image appearances and exposure values." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.365, + 0.892, + 0.424 + ], + "angle": 0, + "content": "- With the flexibility of the CEVR model, we design a training strategy, cycle training, to explore continuous EV information and enhance the quality of the estimated LDR stack." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.431, + 0.892, + 0.476 + ], + "angle": 0, + "content": "- We propose the continuous stack, which consists of LDR images with continuous and dense exposure values and can improve the quality of final HDR images." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.299, + 0.892, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.491, + 0.64, + 0.506 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.79 + ], + "angle": 0, + "content": "Multi-image HDR reconstruction. Modern cameras typically have limited dynamic ranges and cannot well capture all visible details of a scene with a wide range of illumination. To address this issue, one practical solution is to take multiple LDR images at different exposure levels and blend them into an HDR image. To this end, conventional methods such as [11,30] are developed to estimate the CRF [15], upon which multiple LDR images are converted into the radiance field of the scene and transformed into an HDR image. Recent methods, e.g., [17, 51], use CNNs for directly fusing LDR images and reconstructing their HDR counterpart. However, both conventional and CNN-based methods require multiple differently exposed images of a static scene. Furthermore, for working on dynamic scenes, additional mechanisms are needed to alleviate the misalignment problem and avoid blurring or ghosting artifacts [18,29,47]. However, misalignment itself is a complicated issue to resolve." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Single-image HDR reconstruction. This task aims to reconstruct the HDR image using just one LDR input, also called inverse tone mapping [3-6], and can bypass the misalignment problem. Existing methods need to enlarge the dynamic range [1, 33, 40, 44] and restore the lost details. Generation techniques [14,25,55,56,58] for image synthesis are essential to methods of this category. Due to the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12991" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.135 + ], + "angle": 0, + "content": "superior mapping power of CNNs [16, 45] and GAN [14], deep neural networks are widely adopted for HDR reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.468, + 0.273 + ], + "angle": 0, + "content": "One branch of research efforts [12,32,43,53,57] focuses on learning the mapping from the input LDR image to the HDR image. For example, Marnerides et al. [32] use CNNs to generate the HDR image based on an LDR input. To further improve the performance, Santos et al. [43] filter out the saturated regions in the LDR input and pretrain the deep network for an inpainting task. However, learning the LDR-to-HDR mapping is ill-posed since different LDR images can be mapped to the same HDR image [13]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.468, + 0.472 + ], + "angle": 0, + "content": "Another branch of methods, e.g., [13, 19, 23, 24], aims to synthesize a stack of differently exposed LDR counterparts given an LDR image as input. Then, the conventional multi-image methods can be applied to the synthesized LDR stack to complete HDR reconstruction. For example, Endo et al. [13] use 3D convolutions, with exposure variation being one dimension, to learn the relationship between the LDR input and its counterparts with different exposure values. Their approach can generate the LDR stack directly. The LDR stack can be synthesized in a recursive manner [19,23,24]. For example, Lee et al. [24] use GAN to generate an image with relative exposure value change. The LDR stack is constructed by recursively using their model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.468, + 0.608 + ], + "angle": 0, + "content": "Nevertheless, existing stack-based methods can only generate LDR images with predefined exposure values present in the training data. Inspired by the fact that the real-world captured images can have any EV value depending on different shutter settings instead of predefined ones, we present a method that can synthesize LDR images with continuous exposure values that are even unseen in the training data. Our method can generate an enriched and denser stack with which significantly better HDR results are achieved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.468, + 0.794 + ], + "angle": 0, + "content": "Implicit neural representations. An implicit function space is a shared function space that contains the neural representation of different objects or images learned by a shared implicit function. It is commonly a latent space where a latent code is mapped to an image using an encoder-decoder structure [9,34,41,42,52]. This approach has been widely used in image super-resolution [8, 22], 3D shape, surface modeling [2,9,46], and view synthesis of 3D structures [35,37]. Methods using implicit functions have shown that the learned latent space can be continuous [8,10,35,38], allowing for exploring continuous relationships of exposure differences between images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.902 + ], + "angle": 0, + "content": "More and more radiance field reconstruction research aims to generalize the trained model across scenes unseen in training data. The methods in [7, 48, 54] propose advanced model architectures and training strategies, making the learned implicit function space achieve the generalization on unseen views. Our method, similar to [7, 48, 54], can generalize well to all images without fine-tuning." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.609, + 0.108 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.252 + ], + "angle": 0, + "content": "In this section, we present our proposed Continuous Exposure Value Representation (CEVR) which generates LDR images with continuous EV. We provide an overview of our method in Section 3.1, followed by the architectural design in Section 3.2, which includes the implicit module and intensity transformation. Additionally, we propose two strategies, cycle training, and continuous stack, to further enhance the flexibility of CEVR, which are discussed in detail in Section 3.3 and 3.4, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.26, + 0.61, + 0.274 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.493 + ], + "angle": 0, + "content": "Based on the observation in Fig. 2, we propose the CEVR model to generate an enriched and denser LDR stack for high-quality HDR reconstruction. Our model, shown in Fig. 3, utilizes a hierarchical U-Net structure (Fig. 3(a)) and incorporates the implicit neural representation into the design to predict LDR images with continuous EVs (Fig. 3(c)). To maintain accurate color and image structure while adjusting brightness, we introduce intensity transformation (Fig. 3(d)), which generates an adjustment map from each scale of the feature map. As the ground-truth LDR images with unseen exposure values are lacking, we train the model using unsupervised cycle training (Fig. 4), enabling our method to learn images with varying EVs and enhance the quality of the predicted LDR stack." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.502, + 0.87, + 0.518 + ], + "angle": 0, + "content": "3.2. Continuous Exposure Value Representation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.525, + 0.892, + 0.691 + ], + "angle": 0, + "content": "We show our CEVR model in Fig. 3(a). Our CEVR model employs the hierarchical U-Net structure, where the encoder is a pre-trained VGG-Net and the decoder is a cascade of decoder blocks (Fig. 3(b)), each of which comprises an implicit module that compiles the feature map with an input EV step \\( s \\). Each decoder block is followed by an intensity transformation to adjust the intensity of input image at that scale. Specifically, the CEVR model \\( F \\) takes an LDR image \\( I \\) and the specified EV step \\( s \\) as input and generates another LDR image \\( \\hat{I}_s \\), a counterpart of \\( I \\) with the relative exposure value change \\( s \\), via" + }, + { + "type": "equation", + "bbox": [ + 0.65, + 0.697, + 0.891, + 0.715 + ], + "angle": 0, + "content": "\\[\n\\hat {I} _ {s} = F (I, s). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.892, + 0.784 + ], + "angle": 0, + "content": "Take the widely used VDS dataset [23] as an example. An LDR image with EV0 in this dataset can serve as \\(I\\). An LDR stack can be generated by applying our CEVR \\(F\\) to \\(I\\) and every EV step in \\(\\{s \\in \\mathbb{Z} | - 3 \\leq s \\leq 3\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.787, + 0.892, + 0.877 + ], + "angle": 0, + "content": "Implicit module. To synthesize an LDR image conditioned on a continuous EV step \\(s\\) even unseen in the training data, each decoder block in Fig. 3(b) has an associated, learnable implicit module \\(f_{\\theta}\\), which is built by MLPs and shown in Fig. 3(c). The implicit module \\(f_{\\theta}\\) parameterized by \\(\\theta\\) takes the form:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.885, + 0.891, + 0.902 + ], + "angle": 0, + "content": "\\[\nx _ {s} (p, q) = f _ {\\theta} ([ x (p, q), s ]), \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12992" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.094, + 0.885, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.428, + 0.291, + 0.543, + 0.305 + ], + "angle": 0, + "content": "(a) CEVR network" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.314, + 0.332, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.151, + 0.4, + 0.262, + 0.413 + ], + "angle": 0, + "content": "(b) Decoder block" + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.314, + 0.609, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.425, + 0.4, + 0.542, + 0.413 + ], + "angle": 0, + "content": "(c) Implicit module" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.314, + 0.89, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.681, + 0.4, + 0.846, + 0.413 + ], + "angle": 0, + "content": "(d) Intensity transformation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.421, + 0.893, + 0.497 + ], + "angle": 0, + "content": "Figure 3: Proposed network architecture. (a) The proposed CEVR model takes an image \\(I\\) and an EV step \\(s\\) as input, and produces an LDR image \\(\\hat{I}_s\\) with a relative exposure value change \\(s\\). It adopts the U-Net structure, where the encoder is a pre-trained VGG-Net, and the decoder is a cascade of decoder blocks. (b) Each decoder block comprises an implicit module to enable continuous EV representation learning, as shown in (c). (d) Following each decoder block, an intensity transformation module is learned to produce the \\(\\alpha\\) and \\(\\beta\\) maps for image brightness transformation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.47, + 0.606 + ], + "angle": 0, + "content": "where \\( x \\in \\mathbb{R}^{H \\times W \\times C} \\) is the input feature map, \\( x(p,q) \\in \\mathbb{R}^C \\) is the feature vector at location \\( (p,q) \\), and \\( [x(p,q),s] \\in \\mathbb{R}^{C + 1} \\) refers to the concatenation of \\( x(p,q) \\) and \\( s \\). The output feature map \\( x_{s} \\) is generated by repeatedly applying the implicit module \\( f_{\\theta} \\) to all \\( H \\times W \\) locations of \\( x \\) with the desired relative exposure value change \\( s \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.47, + 0.806 + ], + "angle": 0, + "content": "Intensity transformation. In Fig. 3(a), our CEVR leverages U-Net to perform multi-scale synthesis to generate a better LDR image with a different EV. The input and output images, \\(I\\) and \\(\\hat{I}_s\\), cover the same scene under different exposures. Thus, their content should not undergo significant changes. To preserve the image structure and allow the model to focus on the brightness changes for detail reconstruction at each scale, the proposed intensity transformation module in Fig. 3(d) takes the resized feature map from the decoder block as input and produces the \\(\\alpha\\) and \\(\\beta\\) maps. As shown in Fig. 3(a), the \\(\\alpha\\) and \\(\\beta\\) maps carry out affine brightness transformation at each scale. The output \\(\\hat{I}_s\\) is synthesized through multi-scale transformations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Reconstruction Loss. Suppose that we are given a training set of \\(N\\) images \\(\\{I_n\\}_{n=1}^N\\) with a set of \\(M\\) EV steps \\(\\{s_m\\}_{m=1}^M\\). For each training image \\(I_n\\), its ground-truth LDR stack \\(\\{I_n^*(s_m)\\}_{m=1}^M\\) is provided, where \\(I_n^*(s_m)\\) is the counterpart of \\(I_n\\) with the relative exposure value change \\(s_m\\). We train the CEVR model \\(F\\) in Eq. (1) by minimizing" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.516, + 0.68, + 0.53 + ], + "angle": 0, + "content": "the \\(L_{1}\\) reconstruction loss:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.54, + 0.892, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e c}} = \\sum_ {n = 1} ^ {N} \\sum_ {m = 1} ^ {M} \\| I _ {n} ^ {*} (s _ {m}) - F (I _ {n}, s _ {m}) \\| _ {1}. \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.72, + 0.607 + ], + "angle": 0, + "content": "3.3. Cycle Training Strategy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Existing training datasets, such as the VDS dataset [23], provide the ground truth for a sparse set of predefined EV steps, e.g., \\([-3, -2, \\dots, 3]\\). Inspired by the success of cycle consistency training in video frame interpolation [27] and to make our CEVR work well for synthesizing images with arbitrary EVs, we introduce the cycle training strategy to train the model with continuous EV steps without the corresponding ground-truth images. For each training image \\( I_{n} \\) and each EV step \\( s_m \\) covered by the training set, the cycle training strategy shown in Fig. 4, derives the CEVR model with two branches. The first branch takes \\( I_{n} \\) and \\( s_m \\) as input. Since the ground-truth image \\( I_{n}^{*}(s_{m}) \\) is available, the reconstruction loss \\( \\mathcal{L}_{\\mathrm{rec}} \\) is used to supervise this branch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The second branch implements a two-step process. We randomly sample a real value \\(a \\in [0,1]\\) for each image \\(I_{n}\\) at each training iteration, and decompose the EV step \\(s_m\\) into two sub-steps: \\(u = as_m\\) and \\(\\nu = (1 - a)s_m\\), with \\(u + \\nu = s_m\\). Our CEVR model is applied twice with the two EV sub-steps, respectively. Although the ground truth for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12993" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.468, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.291, + 0.471, + 0.368 + ], + "angle": 0, + "content": "Figure 4: Cycle training. We derive the CEVR model in an unsupervised cycle training strategy without using the corresponding ground truth. In this way, our model exploits the cycle consistency constraint and learns more continuous information by varying the EV sub-step \\( u \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.446 + ], + "angle": 0, + "content": "the randomly sampled sub-step \\( u \\) is unavailable, we expect that the output of taking the two sub-steps should be similar to the ground truth \\( I_{n}^{*}(s_{m}) \\) because of \\( u + v = s_{m} \\). Thereby, we enforce the proposed cycle loss:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.453, + 0.47, + 0.495 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c y c}} = \\sum_ {n = 1} ^ {N} \\sum_ {m = 1} ^ {M} \\| I _ {n} ^ {*} (s _ {m}) - F (F (I _ {n}, u), v) \\| _ {1}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.47, + 0.608 + ], + "angle": 0, + "content": "The sub-step \\( u \\) in Eq. (4) is randomly sampled for each training image with each covered EV step at each training iteration. It is used to simulate arbitrary EV step input to our CEVR model. To compensate for the lack of the ground truth of the intermediate output \\( F(I_{n},u) \\), the cycle loss \\( \\mathcal{L}_{\\mathrm{cyc}} \\) in Eq. (4) offers indirect supervision, ensuring the continuity of our CEVR model with continuous EV steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.639 + ], + "angle": 0, + "content": "The objective function used to derive the proposed CEVR is defined by" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.648, + 0.47, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {r e c}} + \\lambda \\mathcal {L} _ {\\text {c y c}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.673, + 0.431, + 0.689 + ], + "angle": 0, + "content": "where we empirically set \\(\\lambda\\) to 0.1 in our experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.25, + 0.712 + ], + "angle": 0, + "content": "3.4. Continuous Stack" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In the inference phase, with the implicit module and the cycle training strategy, our CEVR model can generate high-quality LDR images with continuous EVs. The LDR stack containing more LDR images with various EVs can help Debevec's method [11] estimate a more accurate inverse CRF, as shown in Fig. 1(c), and improve the HDR image reconstruction, as shown in Fig. 2. Inspired by this observation, we proposed the continuous stack, which predicts additional LDR images with continuous EVs from our CEVR model. The predicted continuous and dense LDR stack further benefits the stack fusion process and enhances the final HDR quality, as shown in Fig. 1(c)." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.894, + 0.166 + ], + "angle": 0, + "content": "Table 1: Quantitative comparison of the predicted LDR stacks on the VDS dataset [23]. CEVR outperforms existing approaches in estimating LDR stacks for all EVs. With cycle training, our method can generate high-quality LDR images even with large EV changes." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.177, + 0.892, + 0.417 + ], + "angle": 0, + "content": "
EVMethodPSNRSSIMMS-SSIM
mσmσmσ
+3Deep chain HDRI [23]28.182.770.9530.0650.9830.015
Deep recursive HDRI [24]28.972.920.9440.0440.9810.014
CEVR (Ours)34.343.460.9730.0210.9890.007
+2Deep chain HDRI [23]29.653.060.9590.0650.9860.016
Deep recursive HDRI [24]29.432.850.9520.0390.9860.010
CEVR (Ours)35.303.080.9810.0160.9930.004
+1Deep chain HDRI [23]31.903.430.9690.0390.9920.008
Deep recursive HDRI [24]32.022.850.9690.0260.9920.006
CEVR (Ours)37.642.960.9890.0090.9960.004
-1Deep chain HDRI [23]29.013.830.9350.0560.9800.017
Deep recursive HDRI [24]31.223.690.9510.0310.9860.090
CEVR (Ours)34.623.470.9800.0110.9920.005
-2Deep chain HDRI [23]26.724.540.9520.0290.9740.021
Deep recursive HDRI [24]31.083.070.9480.0410.9860.014
CEVR (Ours)33.894.340.9780.0170.9880.010
-3Deep chain HDRI [23]24.334.570.9190.0360.9480.037
Deep recursive HDRI [24]29.154.750.9100.0610.9660.025
CEVR (Ours)30.585.320.9540.0460.9720.032
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.432, + 0.634, + 0.45 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.457, + 0.691, + 0.474 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.651 + ], + "angle": 0, + "content": "Datasets. We train our model using the training set of the VDS dataset [23], which contains image stacks of 48 scenes. The testing sets of the VDS and HDREye datasets [36], which contain 48 and 42 scenes respectively, serve as the testing sets for evaluations. The auto-bracketing feature of the camera produces seven photos with predefined exposure values for each scene in the VDS dataset (EV-3 to EV+3). We follow the common evaluation protocol [23, 24] and select the image with the zero exposure value, which is expected to have the most evenly distributed histogram, as the input to the model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Training details. For training, we consider each training scene \\( n \\) from the VDS dataset [23] and take the corresponding EV0 LDR image as input \\( I_{n} \\). We also take each EV step \\( s_m \\in \\{-3, -2, -1, 0, 1, 2, 3\\} \\) into account. We feed \\( I_{n} \\) and \\( s_m \\) to the CEVR model and estimate the LDR image with EV \\( s_m \\) for model training. Since the inverse CRF is usually asymmetrical, we train two different models with the same architecture to handle the increasing and decreasing exposure changes, respectively. For upsampling, we use bicubic upsampling, followed by a \\( 3 \\times 3 \\) 2D convolution with stride 1 and padding 1. The model is trained for 1,250 epochs with Adam optimizer [21] and cosine annealing warmup with restarts as the scheduler. We use random rotation and flip to augment the data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Evaluation metrics. We employ PSNR, SSIM [49], and MS-SSIM [50] as the metrics for evaluating the qualities of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12994" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.466, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.244, + 0.47, + 0.32 + ], + "angle": 0, + "content": "Figure 5: Qualitative comparison of LDR image predictions in the VDS dataset [23]. Our approach recovers more details compared to Deep recursive HDRI [24] in the EV-3 example. In the \\(\\mathrm{EV} + 3\\) example, our approach generates LDR images with a color tone similar to the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.468, + 0.435 + ], + "angle": 0, + "content": "the predicted LDR stacks and HDR tone-mapped images. We also utilize HDR-VDP-2 [31], a metric based on the human visual system, to evaluate the quality of the reconstructed HDR images. We follow the setting of [23, 24], which sets a 24-inch monitor with a viewing distance of 0.5 meters, a peak contrast of 0.0025, and a gamma of 2.2 for measuring the HDR-VDP-2 metric." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.469, + 0.514 + ], + "angle": 0, + "content": "HDR reconstruction and tone-mapping operators. Our approach uses Debevec's approach [11] to reconstruct HDR images with the predicted LDR stack and utilizes Reinhard's method [39] or Kim and Kautz's method [20] to tonemap the HDR images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.523, + 0.409, + 0.539 + ], + "angle": 0, + "content": "4.2. Comparison of LDR Stacks Prediction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.469, + 0.762 + ], + "angle": 0, + "content": "Quantitative comparisons. The quantitative comparisons of the estimated LDR exposure stacks from the VDS dataset are shown in Tab. 1. The table shows that the proposed method performs favorably against existing methods at every exposure value. The output LDR image quality decreases as the exposure value gap increases because more extensive over- and under-exposed regions reconstruction are required, which makes the task more difficult. However, with our cycle training, our model can still generate high-quality LDR images in the cases of EV+3 and EV-3 by incorporating continuous and dense EV information into the training process. The continuous EV generation during training helps the model learn how to explicitly infer LDR images with arbitrary exposure values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Qualitative comparisons. With the cycle training, our method can generate a high-quality LDR image even with large EV changes. A detailed qualitative comparison is presented in Fig. 5. The first row of this figure shows that Deep recursive HDRI [24] often gets less accurate color tone in estimating the LDR images, which may further degrade the quality of the HDR images fused by the LDR stack. On the contrary, our method can better estimate the LDR images in all EVs with more accurate color tones. In addition, the" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.15 + ], + "angle": 0, + "content": "Table 2: Quantitative comparison of HDR and TMO images. Two tone-mapping approaches, Reinhard's approach [39], and Kim and Kautz's approach [20], are denoted as RH's and KK's TMO." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.161, + 0.891, + 0.327 + ], + "angle": 0, + "content": "
DatasetMethodPSNRPSNRHDR-VDP-2
RH's TMOKK's TMO
mσmσmσ
VDSDrTMO [13]25.494.2821.364.5054.336.27
Deep chain HDRI [23]30.863.3624.544.0156.364.41
Deep recursive HDRI [24]32.992.8128.023.5057.154.35
Santos et al. [43]22.562.6818.233.5353.514.76
Liu et al. [26]30.893.2728.004.1156.976.15
CEVR (Ours)34.673.5030.044.4559.005.78
HDREyeDrTMO [13]23.683.2719.974.1146.675.81
Deep chain HDRI [23]25.772.4422.623.3949.805.97
Deep recursive HDRI [24]26.282.7024.262.9052.634.84
Santos et al. [43]19.892.4619.003.0649.975.44
Liu et al. [26]26.253.0824.673.5450.336.67
CEVR (Ours)26.543.1024.812.9153.154.91
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.348, + 0.892, + 0.395 + ], + "angle": 0, + "content": "second row demonstrates that our method can estimate the LDR images without severe artifacts. More visual comparisons can be found in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.402, + 0.831, + 0.419 + ], + "angle": 0, + "content": "4.3. Comparison of HDR Image Prediction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.892, + 0.653 + ], + "angle": 0, + "content": "We compare our method with five recent single-image HDR reconstruction methods, including Santos et al. [43], DrTMO [13], Deep chain HDRI [23], Deep recursive HDRI [24], and Liu et al. [26]. For Santos et al. [43], Deep recursive HDRI [24] and Liu et al. [26], we use their official implementations along with the released pre-trained model weight to generate all the quantitative and qualitative results on the VDS [23] and HDREye [36] datasets. For DrTMO [13] and Deep chain HDRI [23], we compare our results to the numbers reported in their papers. For HDR image prediction, our approach adopts the continuous stack strategy where the EV steps are enriched from \\(\\{-3, -2, \\dots, +3\\}\\) to \\(\\{-3, -2.5, \\dots, +3\\}\\), and the images with the extra EV steps are also synthesized by using the proposed CEVR model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Quantitative evaluations. As shown in Tab. 2, our method performs favorably against the competing methods on the VDS dataset [23]. The HDRey dataset [36] serves as a blind test bed, our HDR prediction still achieves better qualities using the same tone-mapping operators. Our proposed cycle training makes the model explicitly learn the continuity as EV steps change, leading to better generalization on the unseen dataset, HDRey. With the continuous stack, more LDR images with various EVs are involved in the fusion process, which helps Debevec's approach [11] estimate a more accurate inverse CRF and generate HDR images with better qualities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Qualitative comparisons. To generate the tone-mapped images for visual comparisons, we first reconstruct HDR images by fusing the LDR stacks with Debevec's approach [11]. Then we use Reinhard's method [39] to gen" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12995" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.422, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.438, + 0.089, + 0.867, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.447, + 0.895, + 0.509 + ], + "angle": 0, + "content": "Figure 6: Qualitative comparison of tone-mapped HDR images. We adopt Reinhard's method [39] to generate HDR images shown in the figure. Deep recursive HDRI [24] often suffers from erroneous color tones and artifacts. As shown in the figure, our method can better recover details when compared to Liu et al.'s method [26]. In most regions, our method reconstructs the tone-mapped images with more accurate high-frequency details, leading to visually pleasing results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.633 + ], + "angle": 0, + "content": "erate HDR TMO images for all comleting methods. As Liu et al. [26] generate an HDR image directly, we apply Reinhard's tone-mapping operator [39] for tone-mapping the HDR images. Note that Liu et al. [26] do not train their method on the VDS dataset; hence we only compare the qualitative results with their method on the HDREye dataset, as shown in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.471, + 0.834 + ], + "angle": 0, + "content": "In Fig. 6, it can be observed that Deep recursive HDRI [24] often suffers from inaccurate color tone: the color of the building is inaccurate in the tone-mapped images, and artifacts are present in severely exposed regions. Liu et al. [26] directly estimate and reverse the whole camera pipeline to generate HDR images. It sometimes struggles with generating detailed textures and produces artifacts in severely exposed regions, e.g., the over-exposed window frame and sky in the daylight. With the intensity transformation, our model can preserve the image structure and generate the tone-mapped images with similar tones to the ground truth. It also produces fewer artifacts. More visual comparisons can be found in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.846, + 0.241, + 0.86 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In the following, we validate three design contributions to improving the quality of the LDR stack and HDR images." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.525, + 0.892, + 0.617 + ], + "angle": 0, + "content": "Table 3: Ablation studies on the predicted LDR stack. Intensity transformation balances two distinct tasks: brightness adjustment and precise color tone generation while preserving the image structure. Cycle training provides the model with extra information about changing EVs. Both designs improve LDR stack quality." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.627, + 0.892, + 0.789 + ], + "angle": 0, + "content": "
Intensity transformation-✓✓
Cycle training--✓
PSNRPSNRPSNR
mσmσmσ
EV+331.954.2033.903.5734.343.46
EV+233.193.1634.893.1235.303.08
EV+135.092.5637.493.0737.642.96
EV-133.672.0634.432.5534.623.47
EV-232.533.3732.914.4133.894.34
EV-330.235.4730.355.8630.585.32
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Intensity transformation. Learning to adjust image brightness while maintaining color tone accuracy and image structures can be challenging. The CEVR model, which directly outputs results from the U-net structure without using intensity transformation, can struggle to adjust brightness or produce inaccurate LDR images with artifacts, as shown in Fig. 7. The intensity transformation module can restrict" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12996" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.15 + ], + "angle": 0, + "content": "Table 4: Ablation studies on the reconstructed HDR images on the VDS dataset [23]. Intensity transformation and cycle training enhance the quality of LDR stacks, and continuous stack benefits the stack fusion process." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.152, + 0.468, + 0.226 + ], + "angle": 0, + "content": "
Intensity transformation-✓✓✓
Continuous stack--✓✓
Cycle training---✓
PSNR32.5234.2034.4734.67
" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.228, + 0.465, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.393, + 0.47, + 0.439 + ], + "angle": 0, + "content": "Figure 7: Ablation on intensity transformation. With intensity transformation, CEVR can adjust LDR image intensity while preserving the image structure and color tone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.515 + ], + "angle": 0, + "content": "the model's capacity, producing LDR images with more accurate brightness, color tones, and structures. This design improves the quality of the LDR stack and HDR results, as demonstrated in Tab. 3 and Tab. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Cycle training. With cycle training, the model can be supervised on continuous EV steps without using the corresponding ground truth. It can learn how to change the exposure value continuously, which improves the quality and reduces the artifacts of the estimated LDR images, which also leads to better HDR quality, as shown in Fig. 8, Tab. 3 and Tab. 4. To further demonstrate the effectiveness of cycle training, we conducted the hold-out experiment, excluding EV-1 and +1 LDR images during training. Then, we used the model to estimate EV-1 and +1 LDR images for each scene and evaluated the PSNR. The table shows that our model can generate better LDR images with unseen EVs when the cycle training strategy is adopted." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.73, + 0.469, + 0.791 + ], + "angle": 0, + "content": "Table 5: Hold-out experiment. Hold-out experiment excludes EV-1 and +1 LDR images during training. With cycle training, the model generate better LDR images with unseen EVs (EV-1, +1)." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.803, + 0.406, + 0.884 + ], + "angle": 0, + "content": "
Cycle training×✓
EV-127.7533.77
EV+133.3736.96
" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.091, + 0.892, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.311 + ], + "angle": 0, + "content": "Figure 8: Ablation on cycle training for LDR and HDR images generation. With the cycle training, the model captures the finer granularity of \"EV changing\" and generates more accurate and visually pleasing LDR and HDR images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.893, + 0.6 + ], + "angle": 0, + "content": "Continuous stack. Debevec's method [11] uses the LDR stack to recover response curves and reconstruct HDR images. A denser and continuous EV LDR stack helps produce an accurate inverse CRF, enhancing HDR quality. We compare two stack settings: \"predefined stack\" and \"continuous stack.\" The CEVR model estimates seven LDR images (EVs: -3, -2, -1, ..., +3) for the predefined stack, which is the setting used in existing methods, while the continuous stack has 13 LDR images with various EVs (-3, -2.5, -2, ..., +3). Tab. 4 and Fig. 1(b)(c) show that the tone-mapped image from the continuous stack has superior quality and is more visually pleasing. We can further validate the effectiveness of the continuous stack by visualizing the CRF of both the predefined stack and the continuous stack. As shown in Fig. 9, the denser EV setting can help generate a smoother CRF compared to the predefined EV setting. Additional analysis of the inverse CRF can be found in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.61, + 0.636, + 0.625 + ], + "angle": 0, + "content": "4.5. Failure cases" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.754 + ], + "angle": 0, + "content": "Although the proposed method performs favorably against other existing methods in quantitative and qualitative results, we do not explicitly design the module to address the over-exposed issue, which may make the CEVR model fail to generate reasonable content in large saturated regions, as shown in Fig. 10. It is a promising direction to take the emerging generative model designs, e.g. [28, 59], into account to address this issue." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.619, + 0.785 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We introduce CEVR, a learning-based method that produces LDR EV stacks from continuous EV input. Our approach combines U-Net with implicit functions, and allows the network to generate LDR images with continuous EVs. We propose two strategies, including (1) cycle training for learning on continuous EV changes unseen in the training dataset and (2) continuous stack for improving LDR stack" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12997" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.09, + 0.262, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.267, + 0.091, + 0.437, + 0.303 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.318, + 0.471, + 0.395 + ], + "angle": 0, + "content": "Figure 9: Analysis of the estimated inverse CRF. Continuous stack, adding additional LDR images with dense and continuous EVs, can help Debevec's method [11] generate more accurate inverse CRF and generate HDR images with better quality." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.404, + 0.186, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.404, + 0.28, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.404, + 0.372, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.404, + 0.468, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.497, + 0.47, + 0.543 + ], + "angle": 0, + "content": "Figure 10: Failure case. Existing methods and our proposed method cannot generate reasonable content as the sky region is severely over-exposed." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.56, + 0.47, + 0.635 + ], + "angle": 0, + "content": "fusion using additional images with dense and continuous EVs. Our approach with the two strategies greatly enhances LDR stack quality and improves HDR image results, as demonstrated through extensive quantitative and qualitative evaluations on two benchmark datasets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.64, + 0.47, + 0.731 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported in part by National Science and Technology Council (NSTC) under grants 111-2628-E-A49-025-MY3, 112-2221-E-A49-090-MY3, 111-2634-F-002-023, 111-2634-F-006-012, 110-2221-E-A49-065-MY3 and 111-2634-F-A49-010. 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(a) Continuous Exposure Value Representation (CEVR) generates LDR images with continuous exposure values (EV) without corresponding ground truth during training. (b) Existing methods build LDR stacks only with EVs covered by training data, which brings less visible details for Debevec's method [11] to estimate an accurate inverse camera response function (CRF), resulting in artifacts on HDR results. (c) Our CEVR model enriches the LDR stack by including additional LDR images with continuous and dense EVs (red frames), allowing Debevec's method to predict a more precise inverse CRF and reconstruct more visually pleasing HDR images. + +![](images/0d11f861c2ea9ee7f9b74afcd48155da1ae0896a4a63e14c0066c08852676eac.jpg) + +# Abstract + +Deep learning is commonly used to reconstruct HDR images from LDR images. LDR stack-based methods are used for single-image HDR reconstruction, generating an HDR image from a deep learning-generated LDR stack. However, current methods generate the stack with predetermined exposure values (EVs), which may limit the quality of HDR reconstruction. To address this, we propose the continuous exposure value representation (CEVR), which uses an implicit function to generate LDR images with arbitrary EVs, including those unseen during training. Our approach generates a continuous stack with more images containing diverse EVs, significantly improving HDR reconstruction. We use a cycle training strategy to supervise the model in generating continuous EV LDR images without corresponding ground truths. Our CEVR model outperforms existing methods, as demonstrated by experimental results. + +# 1. Introduction + +High dynamic range (HDR) images can capture detailed appearances in regions with extreme lighting conditions, like sun and shadow. As conventional cameras only capture a limited dynamic range in real-world scenes, one approach to address this issue is to blend multiple LDR images with different exposures into a single HDR image. However, this method is limited to static scenes and may result in ghosting or blurring artifacts in dynamic scenes. Additionally, this method is not applicable when multiple images of the same scene are unavailable, such as an image on the internet. + +Another branch of methods, e.g., [12, 13, 23, 24, 26, 32, 43], takes a single LDR image as input to generate the HDR counterpart without suffering from misalignment, which is referred to as single-image HDR reconstruction. These approaches, e.g., [23, 24], are trained on particular datasets and build an LDR stack with a single LDR image to generate an HDR image using Debevec's method [11]. + +
EV stack of real imagesPSNRPSNRHDR-VDP-2
RH's TMOKK's TMO
mσmσmσ
[-2, 0, 2]24.963.1823.522.7545.125.74
[-2, -1.3, 0, 1.3, 2]25.152.9823.713.1245.265.12
[-2, -1.3, -0.7, 0, 0.7, 1.3, 2]25.323.0123.923.0445.514.86
+ +![](images/411919c29c24e2ed655afa44a6dfbedc7733c4f7e9a6455fb65bd232135e8321.jpg) +[-2,0,2] + +![](images/a67fde51315db7f407847a941eecb2ce5253aecc98df5b21dda545e4ef056d11.jpg) +[-2,-1.3,0,1.3,2] +[-2,-1.3,-0.7,0,0.7,1.3,2] + +![](images/9a366616408ac8106c9df3567b35bab873b34203fa8fa4a5d416f5a9e10fb9c0.jpg) +Figure 2: Motivation. We observe that an LDR stack with dense EVs improves HDR reconstruction even with the same exposure range (from -2EV to +2EV). A list $[-2,0,2]$ means the stack contains three LDR images with -2, 0, and 2 EVs. An example of visual comparison is given. + +![](images/93b80681d9d2606a41ca1bedf3f8aefffc5bbe4a6f57fe491b45ca8ffc08787d.jpg) +Ground Truth + +Using more LDR images with richer EVs improves HDR image quality, as demonstrated in Fig. 2 with different EV stack settings using Debevec's method on the real LDR images of the HDREye dataset [36]. We compare tone-mapping operators RH [39] and KK [20] and use HDR-VDP-2 to evaluate HDR quality. However, accessible datasets have predefined and quantized EVs and may not cover optimal values for HDR reconstruction, causing information loss. + +Previous studies [8, 35, 46] show the effectiveness of implicit neural representations in modeling continuous relationships, motivating our research. Inspired by the observation in Fig. 2, we address the issue of predefined, quantized EVs by leveraging an implicit neural function to model relationships between image appearance and continuous EVs. It turns out our method can generate LDR images with arbitrary EVs even if the corresponding ground truth is unavailable. More importantly, LDR stacks enriched by images with these continuous and dense EVs can reconstruct HDR images of better quality. + +Specifically, the proposed approach, continuous exposure value representation (CEVR), exploits an implicit neural function to generate LDR images with continuous exposure values, as shown in Fig. 1(a). Based on the flexibility of our CEVR model, we further develop two strategies, cycle training and continuous stack, to improve the quality of the LDR stack and the final HDR result. + +Cycle training utilizes CEVR to generate continuous EV images without relying on direct supervision from corresponding ground truths. We train the model using two continuous EVs that sum up to a predefined EV, with the proportion of these two continuous EVs randomly sampled. This strategy enforces the cycle consistency constraint, im + +proving the model's ability to synthesize images with varying EVs and enhancing the quality of the LDR stack. We then use the enriched LDR stack containing seen and unseen EVs in training data for Debevec's method to produce more accurate inverse camera response functions (CRFs) and visually appealing tone-mapped images (Fig. 1(c)) compared to previous methods [23, 24] (Fig. 1(b)). + +Extensive evaluations demonstrate the effectiveness of our proposed continuous stack and cycle training on the VDS [23] and HDREye [36] datasets. Both quantitative and qualitative evaluations show that CEVR significantly outperforms existing methods. The following summarizes our three primary contributions: + +- We propose the CEVR approach, which can generate LDR images with continuous exposure values by modeling relationships between image appearances and exposure values. +- With the flexibility of the CEVR model, we design a training strategy, cycle training, to explore continuous EV information and enhance the quality of the estimated LDR stack. +- We propose the continuous stack, which consists of LDR images with continuous and dense exposure values and can improve the quality of final HDR images. + +# 2. Related Work + +Multi-image HDR reconstruction. Modern cameras typically have limited dynamic ranges and cannot well capture all visible details of a scene with a wide range of illumination. To address this issue, one practical solution is to take multiple LDR images at different exposure levels and blend them into an HDR image. To this end, conventional methods such as [11,30] are developed to estimate the CRF [15], upon which multiple LDR images are converted into the radiance field of the scene and transformed into an HDR image. Recent methods, e.g., [17, 51], use CNNs for directly fusing LDR images and reconstructing their HDR counterpart. However, both conventional and CNN-based methods require multiple differently exposed images of a static scene. Furthermore, for working on dynamic scenes, additional mechanisms are needed to alleviate the misalignment problem and avoid blurring or ghosting artifacts [18,29,47]. However, misalignment itself is a complicated issue to resolve. + +Single-image HDR reconstruction. This task aims to reconstruct the HDR image using just one LDR input, also called inverse tone mapping [3-6], and can bypass the misalignment problem. Existing methods need to enlarge the dynamic range [1, 33, 40, 44] and restore the lost details. Generation techniques [14,25,55,56,58] for image synthesis are essential to methods of this category. Due to the + +superior mapping power of CNNs [16, 45] and GAN [14], deep neural networks are widely adopted for HDR reconstruction. + +One branch of research efforts [12,32,43,53,57] focuses on learning the mapping from the input LDR image to the HDR image. For example, Marnerides et al. [32] use CNNs to generate the HDR image based on an LDR input. To further improve the performance, Santos et al. [43] filter out the saturated regions in the LDR input and pretrain the deep network for an inpainting task. However, learning the LDR-to-HDR mapping is ill-posed since different LDR images can be mapped to the same HDR image [13]. + +Another branch of methods, e.g., [13, 19, 23, 24], aims to synthesize a stack of differently exposed LDR counterparts given an LDR image as input. Then, the conventional multi-image methods can be applied to the synthesized LDR stack to complete HDR reconstruction. For example, Endo et al. [13] use 3D convolutions, with exposure variation being one dimension, to learn the relationship between the LDR input and its counterparts with different exposure values. Their approach can generate the LDR stack directly. The LDR stack can be synthesized in a recursive manner [19,23,24]. For example, Lee et al. [24] use GAN to generate an image with relative exposure value change. The LDR stack is constructed by recursively using their model. + +Nevertheless, existing stack-based methods can only generate LDR images with predefined exposure values present in the training data. Inspired by the fact that the real-world captured images can have any EV value depending on different shutter settings instead of predefined ones, we present a method that can synthesize LDR images with continuous exposure values that are even unseen in the training data. Our method can generate an enriched and denser stack with which significantly better HDR results are achieved. + +Implicit neural representations. An implicit function space is a shared function space that contains the neural representation of different objects or images learned by a shared implicit function. It is commonly a latent space where a latent code is mapped to an image using an encoder-decoder structure [9,34,41,42,52]. This approach has been widely used in image super-resolution [8, 22], 3D shape, surface modeling [2,9,46], and view synthesis of 3D structures [35,37]. Methods using implicit functions have shown that the learned latent space can be continuous [8,10,35,38], allowing for exploring continuous relationships of exposure differences between images. + +More and more radiance field reconstruction research aims to generalize the trained model across scenes unseen in training data. The methods in [7, 48, 54] propose advanced model architectures and training strategies, making the learned implicit function space achieve the generalization on unseen views. Our method, similar to [7, 48, 54], can generalize well to all images without fine-tuning. + +# 3. Approach + +In this section, we present our proposed Continuous Exposure Value Representation (CEVR) which generates LDR images with continuous EV. We provide an overview of our method in Section 3.1, followed by the architectural design in Section 3.2, which includes the implicit module and intensity transformation. Additionally, we propose two strategies, cycle training, and continuous stack, to further enhance the flexibility of CEVR, which are discussed in detail in Section 3.3 and 3.4, respectively. + +# 3.1. Overview + +Based on the observation in Fig. 2, we propose the CEVR model to generate an enriched and denser LDR stack for high-quality HDR reconstruction. Our model, shown in Fig. 3, utilizes a hierarchical U-Net structure (Fig. 3(a)) and incorporates the implicit neural representation into the design to predict LDR images with continuous EVs (Fig. 3(c)). To maintain accurate color and image structure while adjusting brightness, we introduce intensity transformation (Fig. 3(d)), which generates an adjustment map from each scale of the feature map. As the ground-truth LDR images with unseen exposure values are lacking, we train the model using unsupervised cycle training (Fig. 4), enabling our method to learn images with varying EVs and enhance the quality of the predicted LDR stack. + +# 3.2. Continuous Exposure Value Representation + +We show our CEVR model in Fig. 3(a). Our CEVR model employs the hierarchical U-Net structure, where the encoder is a pre-trained VGG-Net and the decoder is a cascade of decoder blocks (Fig. 3(b)), each of which comprises an implicit module that compiles the feature map with an input EV step $s$ . Each decoder block is followed by an intensity transformation to adjust the intensity of input image at that scale. Specifically, the CEVR model $F$ takes an LDR image $I$ and the specified EV step $s$ as input and generates another LDR image $\hat{I}_s$ , a counterpart of $I$ with the relative exposure value change $s$ , via + +$$ +\hat {I} _ {s} = F (I, s). \tag {1} +$$ + +Take the widely used VDS dataset [23] as an example. An LDR image with EV0 in this dataset can serve as $I$ . An LDR stack can be generated by applying our CEVR $F$ to $I$ and every EV step in $\{s \in \mathbb{Z} | - 3 \leq s \leq 3\}$ . + +Implicit module. To synthesize an LDR image conditioned on a continuous EV step $s$ even unseen in the training data, each decoder block in Fig. 3(b) has an associated, learnable implicit module $f_{\theta}$ , which is built by MLPs and shown in Fig. 3(c). The implicit module $f_{\theta}$ parameterized by $\theta$ takes the form: + +$$ +x _ {s} (p, q) = f _ {\theta} ([ x (p, q), s ]), \tag {2} +$$ + +![](images/d59f4d880cac398893b811a011f2a2d7c0ce4fe58c728a6c17d0b8e42f2d0ec7.jpg) +(a) CEVR network + +![](images/26ec1ab924208f4eba6280ef9439c4c0453cb11984e8a679bc1a48921e250eaf.jpg) +(b) Decoder block + +![](images/81c6570a730eaeadf20dbb79ba944437c9dde2522f5885652ce980efc3956c61.jpg) +(c) Implicit module +Figure 3: Proposed network architecture. (a) The proposed CEVR model takes an image $I$ and an EV step $s$ as input, and produces an LDR image $\hat{I}_s$ with a relative exposure value change $s$ . It adopts the U-Net structure, where the encoder is a pre-trained VGG-Net, and the decoder is a cascade of decoder blocks. (b) Each decoder block comprises an implicit module to enable continuous EV representation learning, as shown in (c). (d) Following each decoder block, an intensity transformation module is learned to produce the $\alpha$ and $\beta$ maps for image brightness transformation. + +![](images/b812d92be0f417526f4b0afd5d4445bec19b2d059d8265885da40e9f135e55d4.jpg) +(d) Intensity transformation + +where $x \in \mathbb{R}^{H \times W \times C}$ is the input feature map, $x(p,q) \in \mathbb{R}^C$ is the feature vector at location $(p,q)$ , and $[x(p,q),s] \in \mathbb{R}^{C + 1}$ refers to the concatenation of $x(p,q)$ and $s$ . The output feature map $x_{s}$ is generated by repeatedly applying the implicit module $f_{\theta}$ to all $H \times W$ locations of $x$ with the desired relative exposure value change $s$ . + +Intensity transformation. In Fig. 3(a), our CEVR leverages U-Net to perform multi-scale synthesis to generate a better LDR image with a different EV. The input and output images, $I$ and $\hat{I}_s$ , cover the same scene under different exposures. Thus, their content should not undergo significant changes. To preserve the image structure and allow the model to focus on the brightness changes for detail reconstruction at each scale, the proposed intensity transformation module in Fig. 3(d) takes the resized feature map from the decoder block as input and produces the $\alpha$ and $\beta$ maps. As shown in Fig. 3(a), the $\alpha$ and $\beta$ maps carry out affine brightness transformation at each scale. The output $\hat{I}_s$ is synthesized through multi-scale transformations. + +Reconstruction Loss. Suppose that we are given a training set of $N$ images $\{I_n\}_{n=1}^N$ with a set of $M$ EV steps $\{s_m\}_{m=1}^M$ . For each training image $I_n$ , its ground-truth LDR stack $\{I_n^*(s_m)\}_{m=1}^M$ is provided, where $I_n^*(s_m)$ is the counterpart of $I_n$ with the relative exposure value change $s_m$ . We train the CEVR model $F$ in Eq. (1) by minimizing + +the $L_{1}$ reconstruction loss: + +$$ +\mathcal {L} _ {\text {r e c}} = \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {M} \| I _ {n} ^ {*} (s _ {m}) - F (I _ {n}, s _ {m}) \| _ {1}. \tag {3} +$$ + +# 3.3. Cycle Training Strategy + +Existing training datasets, such as the VDS dataset [23], provide the ground truth for a sparse set of predefined EV steps, e.g., $[-3, -2, \dots, 3]$ . Inspired by the success of cycle consistency training in video frame interpolation [27] and to make our CEVR work well for synthesizing images with arbitrary EVs, we introduce the cycle training strategy to train the model with continuous EV steps without the corresponding ground-truth images. For each training image $I_{n}$ and each EV step $s_m$ covered by the training set, the cycle training strategy shown in Fig. 4, derives the CEVR model with two branches. The first branch takes $I_{n}$ and $s_m$ as input. Since the ground-truth image $I_{n}^{*}(s_{m})$ is available, the reconstruction loss $\mathcal{L}_{\mathrm{rec}}$ is used to supervise this branch. + +The second branch implements a two-step process. We randomly sample a real value $a \in [0,1]$ for each image $I_{n}$ at each training iteration, and decompose the EV step $s_m$ into two sub-steps: $u = as_m$ and $\nu = (1 - a)s_m$ , with $u + \nu = s_m$ . Our CEVR model is applied twice with the two EV sub-steps, respectively. Although the ground truth for + +![](images/c4088f9482480235ec0b81fabddcd2ec6f7b55638b3c76753fc1e02694577609.jpg) +Figure 4: Cycle training. We derive the CEVR model in an unsupervised cycle training strategy without using the corresponding ground truth. In this way, our model exploits the cycle consistency constraint and learns more continuous information by varying the EV sub-step $u$ . + +the randomly sampled sub-step $u$ is unavailable, we expect that the output of taking the two sub-steps should be similar to the ground truth $I_{n}^{*}(s_{m})$ because of $u + v = s_{m}$ . Thereby, we enforce the proposed cycle loss: + +$$ +\mathcal {L} _ {\text {c y c}} = \sum_ {n = 1} ^ {N} \sum_ {m = 1} ^ {M} \| I _ {n} ^ {*} (s _ {m}) - F (F (I _ {n}, u), v) \| _ {1}. \tag {4} +$$ + +The sub-step $u$ in Eq. (4) is randomly sampled for each training image with each covered EV step at each training iteration. It is used to simulate arbitrary EV step input to our CEVR model. To compensate for the lack of the ground truth of the intermediate output $F(I_{n},u)$ , the cycle loss $\mathcal{L}_{\mathrm{cyc}}$ in Eq. (4) offers indirect supervision, ensuring the continuity of our CEVR model with continuous EV steps. + +The objective function used to derive the proposed CEVR is defined by + +$$ +\mathcal {L} = \mathcal {L} _ {\text {r e c}} + \lambda \mathcal {L} _ {\text {c y c}}, \tag {5} +$$ + +where we empirically set $\lambda$ to 0.1 in our experiments. + +# 3.4. Continuous Stack + +In the inference phase, with the implicit module and the cycle training strategy, our CEVR model can generate high-quality LDR images with continuous EVs. The LDR stack containing more LDR images with various EVs can help Debevec's method [11] estimate a more accurate inverse CRF, as shown in Fig. 1(c), and improve the HDR image reconstruction, as shown in Fig. 2. Inspired by this observation, we proposed the continuous stack, which predicts additional LDR images with continuous EVs from our CEVR model. The predicted continuous and dense LDR stack further benefits the stack fusion process and enhances the final HDR quality, as shown in Fig. 1(c). + +Table 1: Quantitative comparison of the predicted LDR stacks on the VDS dataset [23]. CEVR outperforms existing approaches in estimating LDR stacks for all EVs. With cycle training, our method can generate high-quality LDR images even with large EV changes. + +
EVMethodPSNRSSIMMS-SSIM
mσmσmσ
+3Deep chain HDRI [23]28.182.770.9530.0650.9830.015
Deep recursive HDRI [24]28.972.920.9440.0440.9810.014
CEVR (Ours)34.343.460.9730.0210.9890.007
+2Deep chain HDRI [23]29.653.060.9590.0650.9860.016
Deep recursive HDRI [24]29.432.850.9520.0390.9860.010
CEVR (Ours)35.303.080.9810.0160.9930.004
+1Deep chain HDRI [23]31.903.430.9690.0390.9920.008
Deep recursive HDRI [24]32.022.850.9690.0260.9920.006
CEVR (Ours)37.642.960.9890.0090.9960.004
-1Deep chain HDRI [23]29.013.830.9350.0560.9800.017
Deep recursive HDRI [24]31.223.690.9510.0310.9860.090
CEVR (Ours)34.623.470.9800.0110.9920.005
-2Deep chain HDRI [23]26.724.540.9520.0290.9740.021
Deep recursive HDRI [24]31.083.070.9480.0410.9860.014
CEVR (Ours)33.894.340.9780.0170.9880.010
-3Deep chain HDRI [23]24.334.570.9190.0360.9480.037
Deep recursive HDRI [24]29.154.750.9100.0610.9660.025
CEVR (Ours)30.585.320.9540.0460.9720.032
+ +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets. We train our model using the training set of the VDS dataset [23], which contains image stacks of 48 scenes. The testing sets of the VDS and HDREye datasets [36], which contain 48 and 42 scenes respectively, serve as the testing sets for evaluations. The auto-bracketing feature of the camera produces seven photos with predefined exposure values for each scene in the VDS dataset (EV-3 to EV+3). We follow the common evaluation protocol [23, 24] and select the image with the zero exposure value, which is expected to have the most evenly distributed histogram, as the input to the model. + +Training details. For training, we consider each training scene $n$ from the VDS dataset [23] and take the corresponding EV0 LDR image as input $I_{n}$ . We also take each EV step $s_m \in \{-3, -2, -1, 0, 1, 2, 3\}$ into account. We feed $I_{n}$ and $s_m$ to the CEVR model and estimate the LDR image with EV $s_m$ for model training. Since the inverse CRF is usually asymmetrical, we train two different models with the same architecture to handle the increasing and decreasing exposure changes, respectively. For upsampling, we use bicubic upsampling, followed by a $3 \times 3$ 2D convolution with stride 1 and padding 1. The model is trained for 1,250 epochs with Adam optimizer [21] and cosine annealing warmup with restarts as the scheduler. We use random rotation and flip to augment the data. + +Evaluation metrics. We employ PSNR, SSIM [49], and MS-SSIM [50] as the metrics for evaluating the qualities of + +![](images/769aa35ddb79c50ab4a85e543c69f472e2cb47c40649ae0269327573bfecb2e5.jpg) +Figure 5: Qualitative comparison of LDR image predictions in the VDS dataset [23]. Our approach recovers more details compared to Deep recursive HDRI [24] in the EV-3 example. In the $\mathrm{EV} + 3$ example, our approach generates LDR images with a color tone similar to the ground truth. + +the predicted LDR stacks and HDR tone-mapped images. We also utilize HDR-VDP-2 [31], a metric based on the human visual system, to evaluate the quality of the reconstructed HDR images. We follow the setting of [23, 24], which sets a 24-inch monitor with a viewing distance of 0.5 meters, a peak contrast of 0.0025, and a gamma of 2.2 for measuring the HDR-VDP-2 metric. + +HDR reconstruction and tone-mapping operators. Our approach uses Debevec's approach [11] to reconstruct HDR images with the predicted LDR stack and utilizes Reinhard's method [39] or Kim and Kautz's method [20] to tonemap the HDR images. + +# 4.2. Comparison of LDR Stacks Prediction + +Quantitative comparisons. The quantitative comparisons of the estimated LDR exposure stacks from the VDS dataset are shown in Tab. 1. The table shows that the proposed method performs favorably against existing methods at every exposure value. The output LDR image quality decreases as the exposure value gap increases because more extensive over- and under-exposed regions reconstruction are required, which makes the task more difficult. However, with our cycle training, our model can still generate high-quality LDR images in the cases of EV+3 and EV-3 by incorporating continuous and dense EV information into the training process. The continuous EV generation during training helps the model learn how to explicitly infer LDR images with arbitrary exposure values. + +Qualitative comparisons. With the cycle training, our method can generate a high-quality LDR image even with large EV changes. A detailed qualitative comparison is presented in Fig. 5. The first row of this figure shows that Deep recursive HDRI [24] often gets less accurate color tone in estimating the LDR images, which may further degrade the quality of the HDR images fused by the LDR stack. On the contrary, our method can better estimate the LDR images in all EVs with more accurate color tones. In addition, the + +Table 2: Quantitative comparison of HDR and TMO images. Two tone-mapping approaches, Reinhard's approach [39], and Kim and Kautz's approach [20], are denoted as RH's and KK's TMO. + +
DatasetMethodPSNRPSNRHDR-VDP-2
RH's TMOKK's TMO
mσmσmσ
VDSDrTMO [13]25.494.2821.364.5054.336.27
Deep chain HDRI [23]30.863.3624.544.0156.364.41
Deep recursive HDRI [24]32.992.8128.023.5057.154.35
Santos et al. [43]22.562.6818.233.5353.514.76
Liu et al. [26]30.893.2728.004.1156.976.15
CEVR (Ours)34.673.5030.044.4559.005.78
HDREyeDrTMO [13]23.683.2719.974.1146.675.81
Deep chain HDRI [23]25.772.4422.623.3949.805.97
Deep recursive HDRI [24]26.282.7024.262.9052.634.84
Santos et al. [43]19.892.4619.003.0649.975.44
Liu et al. [26]26.253.0824.673.5450.336.67
CEVR (Ours)26.543.1024.812.9153.154.91
+ +second row demonstrates that our method can estimate the LDR images without severe artifacts. More visual comparisons can be found in the supplementary material. + +# 4.3. Comparison of HDR Image Prediction + +We compare our method with five recent single-image HDR reconstruction methods, including Santos et al. [43], DrTMO [13], Deep chain HDRI [23], Deep recursive HDRI [24], and Liu et al. [26]. For Santos et al. [43], Deep recursive HDRI [24] and Liu et al. [26], we use their official implementations along with the released pre-trained model weight to generate all the quantitative and qualitative results on the VDS [23] and HDREye [36] datasets. For DrTMO [13] and Deep chain HDRI [23], we compare our results to the numbers reported in their papers. For HDR image prediction, our approach adopts the continuous stack strategy where the EV steps are enriched from $\{-3, -2, \dots, +3\}$ to $\{-3, -2.5, \dots, +3\}$ , and the images with the extra EV steps are also synthesized by using the proposed CEVR model. + +Quantitative evaluations. As shown in Tab. 2, our method performs favorably against the competing methods on the VDS dataset [23]. The HDRey dataset [36] serves as a blind test bed, our HDR prediction still achieves better qualities using the same tone-mapping operators. Our proposed cycle training makes the model explicitly learn the continuity as EV steps change, leading to better generalization on the unseen dataset, HDRey. With the continuous stack, more LDR images with various EVs are involved in the fusion process, which helps Debevec's approach [11] estimate a more accurate inverse CRF and generate HDR images with better qualities. + +Qualitative comparisons. To generate the tone-mapped images for visual comparisons, we first reconstruct HDR images by fusing the LDR stacks with Debevec's approach [11]. Then we use Reinhard's method [39] to gen + +![](images/4ef053b31807fde2c6621d220ecb0e9338af0839ceff9c3e601b58fa1350ca18.jpg) +Figure 6: Qualitative comparison of tone-mapped HDR images. We adopt Reinhard's method [39] to generate HDR images shown in the figure. Deep recursive HDRI [24] often suffers from erroneous color tones and artifacts. As shown in the figure, our method can better recover details when compared to Liu et al.'s method [26]. In most regions, our method reconstructs the tone-mapped images with more accurate high-frequency details, leading to visually pleasing results. + +![](images/05c8cf6686e24dd533684cea42e596e2881b74dd43cbf5d58a5cce70edced964.jpg) + +erate HDR TMO images for all comleting methods. As Liu et al. [26] generate an HDR image directly, we apply Reinhard's tone-mapping operator [39] for tone-mapping the HDR images. Note that Liu et al. [26] do not train their method on the VDS dataset; hence we only compare the qualitative results with their method on the HDREye dataset, as shown in Fig. 6. + +In Fig. 6, it can be observed that Deep recursive HDRI [24] often suffers from inaccurate color tone: the color of the building is inaccurate in the tone-mapped images, and artifacts are present in severely exposed regions. Liu et al. [26] directly estimate and reverse the whole camera pipeline to generate HDR images. It sometimes struggles with generating detailed textures and produces artifacts in severely exposed regions, e.g., the over-exposed window frame and sky in the daylight. With the intensity transformation, our model can preserve the image structure and generate the tone-mapped images with similar tones to the ground truth. It also produces fewer artifacts. More visual comparisons can be found in the supplementary material. + +# 4.4. Ablation Studies + +In the following, we validate three design contributions to improving the quality of the LDR stack and HDR images. + +Table 3: Ablation studies on the predicted LDR stack. Intensity transformation balances two distinct tasks: brightness adjustment and precise color tone generation while preserving the image structure. Cycle training provides the model with extra information about changing EVs. Both designs improve LDR stack quality. + +
Intensity transformation-✓✓
Cycle training--✓
PSNRPSNRPSNR
mσmσmσ
EV+331.954.2033.903.5734.343.46
EV+233.193.1634.893.1235.303.08
EV+135.092.5637.493.0737.642.96
EV-133.672.0634.432.5534.623.47
EV-232.533.3732.914.4133.894.34
EV-330.235.4730.355.8630.585.32
+ +Intensity transformation. Learning to adjust image brightness while maintaining color tone accuracy and image structures can be challenging. The CEVR model, which directly outputs results from the U-net structure without using intensity transformation, can struggle to adjust brightness or produce inaccurate LDR images with artifacts, as shown in Fig. 7. The intensity transformation module can restrict + +Table 4: Ablation studies on the reconstructed HDR images on the VDS dataset [23]. Intensity transformation and cycle training enhance the quality of LDR stacks, and continuous stack benefits the stack fusion process. + +
Intensity transformation-✓✓✓
Continuous stack--✓✓
Cycle training---✓
PSNR32.5234.2034.4734.67
+ +![](images/9b165b71189518004c02a2f38ea268c920563bedda0322f41ecedd9c6bff16a2.jpg) +Figure 7: Ablation on intensity transformation. With intensity transformation, CEVR can adjust LDR image intensity while preserving the image structure and color tone. + +the model's capacity, producing LDR images with more accurate brightness, color tones, and structures. This design improves the quality of the LDR stack and HDR results, as demonstrated in Tab. 3 and Tab. 4. + +Cycle training. With cycle training, the model can be supervised on continuous EV steps without using the corresponding ground truth. It can learn how to change the exposure value continuously, which improves the quality and reduces the artifacts of the estimated LDR images, which also leads to better HDR quality, as shown in Fig. 8, Tab. 3 and Tab. 4. To further demonstrate the effectiveness of cycle training, we conducted the hold-out experiment, excluding EV-1 and +1 LDR images during training. Then, we used the model to estimate EV-1 and +1 LDR images for each scene and evaluated the PSNR. The table shows that our model can generate better LDR images with unseen EVs when the cycle training strategy is adopted. + +Table 5: Hold-out experiment. Hold-out experiment excludes EV-1 and +1 LDR images during training. With cycle training, the model generate better LDR images with unseen EVs (EV-1, +1). + +
Cycle training×✓
EV-127.7533.77
EV+133.3736.96
+ +![](images/aebf62d06684dc5f7fc450b280af29c3d6c7100c961334957cbe89be337057e4.jpg) +Figure 8: Ablation on cycle training for LDR and HDR images generation. With the cycle training, the model captures the finer granularity of "EV changing" and generates more accurate and visually pleasing LDR and HDR images. + +Continuous stack. Debevec's method [11] uses the LDR stack to recover response curves and reconstruct HDR images. A denser and continuous EV LDR stack helps produce an accurate inverse CRF, enhancing HDR quality. We compare two stack settings: "predefined stack" and "continuous stack." The CEVR model estimates seven LDR images (EVs: -3, -2, -1, ..., +3) for the predefined stack, which is the setting used in existing methods, while the continuous stack has 13 LDR images with various EVs (-3, -2.5, -2, ..., +3). Tab. 4 and Fig. 1(b)(c) show that the tone-mapped image from the continuous stack has superior quality and is more visually pleasing. We can further validate the effectiveness of the continuous stack by visualizing the CRF of both the predefined stack and the continuous stack. As shown in Fig. 9, the denser EV setting can help generate a smoother CRF compared to the predefined EV setting. Additional analysis of the inverse CRF can be found in the supplementary material. + +# 4.5. Failure cases + +Although the proposed method performs favorably against other existing methods in quantitative and qualitative results, we do not explicitly design the module to address the over-exposed issue, which may make the CEVR model fail to generate reasonable content in large saturated regions, as shown in Fig. 10. It is a promising direction to take the emerging generative model designs, e.g. [28, 59], into account to address this issue. + +# 5. Conclusion + +We introduce CEVR, a learning-based method that produces LDR EV stacks from continuous EV input. Our approach combines U-Net with implicit functions, and allows the network to generate LDR images with continuous EVs. We propose two strategies, including (1) cycle training for learning on continuous EV changes unseen in the training dataset and (2) continuous stack for improving LDR stack + +![](images/15a25b9f267f666d06daad0753f417ffd2b6ce4b2a4b5e643ccf2d2182d6f779.jpg) +Figure 9: Analysis of the estimated inverse CRF. Continuous stack, adding additional LDR images with dense and continuous EVs, can help Debevec's method [11] generate more accurate inverse CRF and generate HDR images with better quality. + +![](images/2e4ced7110a2af3793c322dcfc60571c2a446ffcdefd59241b4c3be08e4cadff.jpg) + +![](images/f243004cc140a2bd9868d442871ace04b229c45f6d50064dc07823f149cb1667.jpg) +Figure 10: Failure case. Existing methods and our proposed method cannot generate reasonable content as the sky region is severely over-exposed. + +![](images/8b379577cc7eb4fa3529ebc391fae22e41171f512022c2acbd96d2f3cc8aa0d2.jpg) + +![](images/b05ecd9e17c10b9890e21ec5c20a8a87d13b402c711f9ad84d74ea070128cb1d.jpg) + +![](images/011c035686162fafcd1e18f828c6a4378d6e2082a522845962d9eb10e2686be3.jpg) + +fusion using additional images with dense and continuous EVs. Our approach with the two strategies greatly enhances LDR stack quality and improves HDR image results, as demonstrated through extensive quantitative and qualitative evaluations on two benchmark datasets. + +Acknowledgments. This work was supported in part by National Science and Technology Council (NSTC) under grants 111-2628-E-A49-025-MY3, 112-2221-E-A49-090-MY3, 111-2634-F-002-023, 111-2634-F-006-012, 110-2221-E-A49-065-MY3 and 111-2634-F-A49-010. 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(a) Continuous Exposure Value Representation (CEVR) generates LDR images with continuous exposure values (EV) without corresponding ground truth during training. (b) Existing methods build LDR stacks only with EVs covered by training data, which brings less visible details for Debevec's method [11] to estimate an accurate inverse camera response function (CRF), resulting in artifacts on HDR results. (c) Our CEVR model enriches the LDR stack by including additional LDR images with continuous and dense EVs (red frames), allowing Debevec's method to predict a more precise inverse CRF and reconstruct more visually pleasing HDR images." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 306, + 247, + 518, + 395 + ], + "blocks": [ + { + "bbox": [ + 306, + 247, + 518, + 395 + ], + "lines": [ + { + "bbox": [ + 306, + 247, + 518, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 518, + 395 + ], + "type": "image", + "image_path": "0d11f861c2ea9ee7f9b74afcd48155da1ae0896a4a63e14c0066c08852676eac.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 486, + 192, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 486, + 192, + 498 + ], + "spans": [ + { + "bbox": [ + 143, + 486, + 192, + 498 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 508, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 508, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 45, + 508, + 288, + 700 + ], + "type": "text", + "content": "Deep learning is commonly used to reconstruct HDR images from LDR images. LDR stack-based methods are used for single-image HDR reconstruction, generating an HDR image from a deep learning-generated LDR stack. However, current methods generate the stack with predetermined exposure values (EVs), which may limit the quality of HDR reconstruction. To address this, we propose the continuous exposure value representation (CEVR), which uses an implicit function to generate LDR images with arbitrary EVs, including those unseen during training. Our approach generates a continuous stack with more images containing diverse EVs, significantly improving HDR reconstruction. We use a cycle training strategy to supervise the model in generating continuous EV LDR images without corresponding ground truths. Our CEVR model outperforms existing methods, as demonstrated by experimental results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 486, + 386, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 486, + 386, + 498 + ], + "spans": [ + { + "bbox": [ + 307, + 486, + 386, + 498 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 508, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 545, + 628 + ], + "type": "text", + "content": "High dynamic range (HDR) images can capture detailed appearances in regions with extreme lighting conditions, like sun and shadow. As conventional cameras only capture a limited dynamic range in real-world scenes, one approach to address this issue is to blend multiple LDR images with different exposures into a single HDR image. However, this method is limited to static scenes and may result in ghosting or blurring artifacts in dynamic scenes. Additionally, this method is not applicable when multiple images of the same scene are unavailable, such as an image on the internet." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Another branch of methods, e.g., [12, 13, 23, 24, 26, 32, 43], takes a single LDR image as input to generate the HDR counterpart without suffering from misalignment, which is referred to as single-image HDR reconstruction. 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EV stack of real imagesPSNRPSNRHDR-VDP-2
RH's TMOKK's TMO
mσmσmσ
[-2, 0, 2]24.963.1823.522.7545.125.74
[-2, -1.3, 0, 1.3, 2]25.152.9823.713.1245.265.12
[-2, -1.3, -0.7, 0, 0.7, 1.3, 2]25.323.0123.923.0445.514.86
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We observe that an LDR stack with dense EVs improves HDR reconstruction even with the same exposure range (from -2EV to +2EV). A list " + }, + { + "bbox": [ + 46, + 238, + 287, + 299 + ], + "type": "inline_equation", + "content": "[-2,0,2]" + }, + { + "bbox": [ + 46, + 238, + 287, + 299 + ], + "type": "text", + "content": " means the stack contains three LDR images with -2, 0, and 2 EVs. An example of visual comparison is given." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 228, + 134, + 286, + 220 + ], + "blocks": [ + { + "bbox": [ + 228, + 134, + 286, + 220 + ], + "lines": [ + { + "bbox": [ + 228, + 134, + 286, + 220 + ], + "spans": [ + { + "bbox": [ + 228, + 134, + 286, + 220 + ], + "type": "image", + "image_path": "93b80681d9d2606a41ca1bedf3f8aefffc5bbe4a6f57fe491b45ca8ffc08787d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 241, + 221, + 272, + 228 + ], + "lines": [ + { + "bbox": [ + 241, + 221, + 272, + 228 + ], + "spans": [ + { + "bbox": [ + 241, + 221, + 272, + 228 + ], + "type": "text", + "content": "Ground Truth" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 314, + 286, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 286, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 286, + 420 + ], + "type": "text", + "content": "Using more LDR images with richer EVs improves HDR image quality, as demonstrated in Fig. 2 with different EV stack settings using Debevec's method on the real LDR images of the HDREye dataset [36]. We compare tone-mapping operators RH [39] and KK [20] and use HDR-VDP-2 to evaluate HDR quality. However, accessible datasets have predefined and quantized EVs and may not cover optimal values for HDR reconstruction, causing information loss." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 423, + 286, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 286, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 286, + 555 + ], + "type": "text", + "content": "Previous studies [8, 35, 46] show the effectiveness of implicit neural representations in modeling continuous relationships, motivating our research. Inspired by the observation in Fig. 2, we address the issue of predefined, quantized EVs by leveraging an implicit neural function to model relationships between image appearance and continuous EVs. It turns out our method can generate LDR images with arbitrary EVs even if the corresponding ground truth is unavailable. More importantly, LDR stacks enriched by images with these continuous and dense EVs can reconstruct HDR images of better quality." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 556, + 286, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 286, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 286, + 639 + ], + "type": "text", + "content": "Specifically, the proposed approach, continuous exposure value representation (CEVR), exploits an implicit neural function to generate LDR images with continuous exposure values, as shown in Fig. 1(a). Based on the flexibility of our CEVR model, we further develop two strategies, cycle training and continuous stack, to improve the quality of the LDR stack and the final HDR result." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": "Cycle training utilizes CEVR to generate continuous EV images without relying on direct supervision from corresponding ground truths. We train the model using two continuous EVs that sum up to a predefined EV, with the proportion of these two continuous EVs randomly sampled. This strategy enforces the cycle consistency constraint, im" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "proving the model's ability to synthesize images with varying EVs and enhancing the quality of the LDR stack. We then use the enriched LDR stack containing seen and unseen EVs in training data for Debevec's method to produce more accurate inverse camera response functions (CRFs) and visually appealing tone-mapped images (Fig. 1(c)) compared to previous methods [23, 24] (Fig. 1(b))." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 157, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 545, + 228 + ], + "type": "text", + "content": "Extensive evaluations demonstrate the effectiveness of our proposed continuous stack and cycle training on the VDS [23] and HDREye [36] datasets. Both quantitative and qualitative evaluations show that CEVR significantly outperforms existing methods. The following summarizes our three primary contributions:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 236, + 545, + 376 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 317, + 236, + 545, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 236, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 317, + 236, + 545, + 284 + ], + "type": "text", + "content": "- We propose the CEVR approach, which can generate LDR images with continuous exposure values by modeling relationships between image appearances and exposure values." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 289, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 289, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 317, + 289, + 545, + 335 + ], + "type": "text", + "content": "- With the flexibility of the CEVR model, we design a training strategy, cycle training, to explore continuous EV information and enhance the quality of the estimated LDR stack." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 341, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 341, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 317, + 341, + 545, + 376 + ], + "type": "text", + "content": "- We propose the continuous stack, which consists of LDR images with continuous and dense exposure values and can improve the quality of final HDR images." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 388, + 391, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 388, + 391, + 400 + ], + "spans": [ + { + "bbox": [ + 306, + 388, + 391, + 400 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 411, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 625 + ], + "type": "text", + "content": "Multi-image HDR reconstruction. Modern cameras typically have limited dynamic ranges and cannot well capture all visible details of a scene with a wide range of illumination. To address this issue, one practical solution is to take multiple LDR images at different exposure levels and blend them into an HDR image. To this end, conventional methods such as [11,30] are developed to estimate the CRF [15], upon which multiple LDR images are converted into the radiance field of the scene and transformed into an HDR image. Recent methods, e.g., [17, 51], use CNNs for directly fusing LDR images and reconstructing their HDR counterpart. However, both conventional and CNN-based methods require multiple differently exposed images of a static scene. Furthermore, for working on dynamic scenes, additional mechanisms are needed to alleviate the misalignment problem and avoid blurring or ghosting artifacts [18,29,47]. However, misalignment itself is a complicated issue to resolve." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Single-image HDR reconstruction. This task aims to reconstruct the HDR image using just one LDR input, also called inverse tone mapping [3-6], and can bypass the misalignment problem. Existing methods need to enlarge the dynamic range [1, 33, 40, 44] and restore the lost details. Generation techniques [14,25,55,56,58] for image synthesis are essential to methods of this category. Due to the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12991" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 106 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 106 + ], + "type": "text", + "content": "superior mapping power of CNNs [16, 45] and GAN [14], deep neural networks are widely adopted for HDR reconstruction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 286, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 286, + 216 + ], + "type": "text", + "content": "One branch of research efforts [12,32,43,53,57] focuses on learning the mapping from the input LDR image to the HDR image. For example, Marnerides et al. [32] use CNNs to generate the HDR image based on an LDR input. To further improve the performance, Santos et al. [43] filter out the saturated regions in the LDR input and pretrain the deep network for an inpainting task. However, learning the LDR-to-HDR mapping is ill-posed since different LDR images can be mapped to the same HDR image [13]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 217, + 286, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 286, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 286, + 373 + ], + "type": "text", + "content": "Another branch of methods, e.g., [13, 19, 23, 24], aims to synthesize a stack of differently exposed LDR counterparts given an LDR image as input. Then, the conventional multi-image methods can be applied to the synthesized LDR stack to complete HDR reconstruction. For example, Endo et al. [13] use 3D convolutions, with exposure variation being one dimension, to learn the relationship between the LDR input and its counterparts with different exposure values. Their approach can generate the LDR stack directly. The LDR stack can be synthesized in a recursive manner [19,23,24]. For example, Lee et al. [24] use GAN to generate an image with relative exposure value change. The LDR stack is constructed by recursively using their model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 374, + 286, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 286, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 286, + 481 + ], + "type": "text", + "content": "Nevertheless, existing stack-based methods can only generate LDR images with predefined exposure values present in the training data. Inspired by the fact that the real-world captured images can have any EV value depending on different shutter settings instead of predefined ones, we present a method that can synthesize LDR images with continuous exposure values that are even unseen in the training data. Our method can generate an enriched and denser stack with which significantly better HDR results are achieved." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 485, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 286, + 628 + ], + "type": "text", + "content": "Implicit neural representations. An implicit function space is a shared function space that contains the neural representation of different objects or images learned by a shared implicit function. It is commonly a latent space where a latent code is mapped to an image using an encoder-decoder structure [9,34,41,42,52]. This approach has been widely used in image super-resolution [8, 22], 3D shape, surface modeling [2,9,46], and view synthesis of 3D structures [35,37]. Methods using implicit functions have shown that the learned latent space can be continuous [8,10,35,38], allowing for exploring continuous relationships of exposure differences between images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 714 + ], + "type": "text", + "content": "More and more radiance field reconstruction research aims to generalize the trained model across scenes unseen in training data. The methods in [7, 48, 54] propose advanced model architectures and training strategies, making the learned implicit function space achieve the generalization on unseen views. Our method, similar to [7, 48, 54], can generalize well to all images without fine-tuning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 372, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 372, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 372, + 85 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 91, + 545, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 199 + ], + "type": "text", + "content": "In this section, we present our proposed Continuous Exposure Value Representation (CEVR) which generates LDR images with continuous EV. We provide an overview of our method in Section 3.1, followed by the architectural design in Section 3.2, which includes the implicit module and intensity transformation. Additionally, we propose two strategies, cycle training, and continuous stack, to further enhance the flexibility of CEVR, which are discussed in detail in Section 3.3 and 3.4, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 205, + 373, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 373, + 217 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 373, + 217 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 223, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 390 + ], + "type": "text", + "content": "Based on the observation in Fig. 2, we propose the CEVR model to generate an enriched and denser LDR stack for high-quality HDR reconstruction. Our model, shown in Fig. 3, utilizes a hierarchical U-Net structure (Fig. 3(a)) and incorporates the implicit neural representation into the design to predict LDR images with continuous EVs (Fig. 3(c)). To maintain accurate color and image structure while adjusting brightness, we introduce intensity transformation (Fig. 3(d)), which generates an adjustment map from each scale of the feature map. As the ground-truth LDR images with unseen exposure values are lacking, we train the model using unsupervised cycle training (Fig. 4), enabling our method to learn images with varying EVs and enhance the quality of the predicted LDR stack." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 397, + 532, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 397, + 532, + 410 + ], + "spans": [ + { + "bbox": [ + 306, + 397, + 532, + 410 + ], + "type": "text", + "content": "3.2. Continuous Exposure Value Representation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "content": "We show our CEVR model in Fig. 3(a). Our CEVR model employs the hierarchical U-Net structure, where the encoder is a pre-trained VGG-Net and the decoder is a cascade of decoder blocks (Fig. 3(b)), each of which comprises an implicit module that compiles the feature map with an input EV step " + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "content": ". Each decoder block is followed by an intensity transformation to adjust the intensity of input image at that scale. Specifically, the CEVR model " + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "content": " takes an LDR image " + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "content": " and the specified EV step " + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "content": " as input and generates another LDR image " + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "inline_equation", + "content": "\\hat{I}_s" + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "content": ", a counterpart of " + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "content": " with the relative exposure value change " + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 415, + 545, + 547 + ], + "type": "text", + "content": ", via" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 397, + 552, + 545, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 552, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 397, + 552, + 545, + 566 + ], + "type": "interline_equation", + "content": "\\hat {I} _ {s} = F (I, s). \\tag {1}", + "image_path": "b3afaa6f47e23b62299a3a8d06a92de22f9a37e5a03862802104e7af71c14a0e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "text", + "content": "Take the widely used VDS dataset [23] as an example. An LDR image with EV0 in this dataset can serve as " + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "text", + "content": ". An LDR stack can be generated by applying our CEVR " + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "text", + "content": " and every EV step in " + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "inline_equation", + "content": "\\{s \\in \\mathbb{Z} | - 3 \\leq s \\leq 3\\}" + }, + { + "bbox": [ + 304, + 572, + 545, + 620 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "text", + "content": "Implicit module. To synthesize an LDR image conditioned on a continuous EV step " + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "text", + "content": " even unseen in the training data, each decoder block in Fig. 3(b) has an associated, learnable implicit module " + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "text", + "content": ", which is built by MLPs and shown in Fig. 3(c). The implicit module " + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 623, + 545, + 694 + ], + "type": "text", + "content": " takes the form:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 370, + 700, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 700, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 370, + 700, + 545, + 714 + ], + "type": "interline_equation", + "content": "x _ {s} (p, q) = f _ {\\theta} ([ x (p, q), s ]), \\tag {2}", + "image_path": "58ba6773cac03d47434b2fb329f5ec216b7b02e887198a9052a834e5f39fa4ce.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12992" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 74, + 541, + 220 + ], + "blocks": [ + { + "bbox": [ + 51, + 74, + 541, + 220 + ], + "lines": [ + { + "bbox": [ + 51, + 74, + 541, + 220 + ], + "spans": [ + { + "bbox": [ + 51, + 74, + 541, + 220 + ], + "type": "image", + "image_path": "d59f4d880cac398893b811a011f2a2d7c0ce4fe58c728a6c17d0b8e42f2d0ec7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 261, + 230, + 332, + 241 + ], + "lines": [ + { + "bbox": [ + 261, + 230, + 332, + 241 + ], + "spans": [ + { + "bbox": [ + 261, + 230, + 332, + 241 + ], + "type": "text", + "content": "(a) CEVR network" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 248, + 203, + 305 + ], + "blocks": [ + { + "bbox": [ + 50, + 248, + 203, + 305 + ], + "lines": [ + { + "bbox": [ + 50, + 248, + 203, + 305 + ], + "spans": [ + { + "bbox": [ + 50, + 248, + 203, + 305 + ], + "type": "image", + "image_path": "26ec1ab924208f4eba6280ef9439c4c0453cb11984e8a679bc1a48921e250eaf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 92, + 316, + 160, + 327 + ], + "lines": [ + { + "bbox": [ + 92, + 316, + 160, + 327 + ], + "spans": [ + { + "bbox": [ + 92, + 316, + 160, + 327 + ], + "type": "text", + "content": "(b) Decoder block" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 219, + 248, + 372, + 305 + ], + "blocks": [ + { + "bbox": [ + 219, + 248, + 372, + 305 + ], + "lines": [ + { + "bbox": [ + 219, + 248, + 372, + 305 + ], + "spans": [ + { + "bbox": [ + 219, + 248, + 372, + 305 + ], + "type": "image", + "image_path": "81c6570a730eaeadf20dbb79ba944437c9dde2522f5885652ce980efc3956c61.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 260, + 316, + 331, + 327 + ], + "lines": [ + { + "bbox": [ + 260, + 316, + 331, + 327 + ], + "spans": [ + { + "bbox": [ + 260, + 316, + 331, + 327 + ], + "type": "text", + "content": "(c) Implicit module" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "lines": [ + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "text", + "content": "Figure 3: Proposed network architecture. (a) The proposed CEVR model takes an image " + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "text", + "content": " and an EV step " + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "text", + "content": " as input, and produces an LDR image " + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "inline_equation", + "content": "\\hat{I}_s" + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "text", + "content": " with a relative exposure value change " + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "text", + "content": ". It adopts the U-Net structure, where the encoder is a pre-trained VGG-Net, and the decoder is a cascade of decoder blocks. (b) Each decoder block comprises an implicit module to enable continuous EV representation learning, as shown in (c). (d) Following each decoder block, an intensity transformation module is learned to produce the " + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 333, + 546, + 393 + ], + "type": "text", + "content": " maps for image brightness transformation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 391, + 248, + 544, + 305 + ], + "blocks": [ + { + "bbox": [ + 391, + 248, + 544, + 305 + ], + "lines": [ + { + "bbox": [ + 391, + 248, + 544, + 305 + ], + "spans": [ + { + "bbox": [ + 391, + 248, + 544, + 305 + ], + "type": "image", + "image_path": "b812d92be0f417526f4b0afd5d4445bec19b2d059d8265885da40e9f135e55d4.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 416, + 316, + 517, + 327 + ], + "lines": [ + { + "bbox": [ + 416, + 316, + 517, + 327 + ], + "spans": [ + { + "bbox": [ + 416, + 316, + 517, + 327 + ], + "type": "text", + "content": "(d) Intensity transformation" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": " is the input feature map, " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "x(p,q) \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": " is the feature vector at location " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "(p,q)" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "[x(p,q),s] \\in \\mathbb{R}^{C + 1}" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": " refers to the concatenation of " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "x(p,q)" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": ". The output feature map " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "x_{s}" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": " is generated by repeatedly applying the implicit module " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": " to all " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": " locations of " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": " with the desired relative exposure value change " + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 407, + 287, + 479 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": "Intensity transformation. In Fig. 3(a), our CEVR leverages U-Net to perform multi-scale synthesis to generate a better LDR image with a different EV. The input and output images, " + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\hat{I}_s" + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": ", cover the same scene under different exposures. Thus, their content should not undergo significant changes. To preserve the image structure and allow the model to focus on the brightness changes for detail reconstruction at each scale, the proposed intensity transformation module in Fig. 3(d) takes the resized feature map from the decoder block as input and produces the " + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": " maps. As shown in Fig. 3(a), the " + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": " maps carry out affine brightness transformation at each scale. The output " + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\hat{I}_s" + }, + { + "bbox": [ + 46, + 483, + 287, + 638 + ], + "type": "text", + "content": " is synthesized through multi-scale transformations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": "Reconstruction Loss. Suppose that we are given a training set of " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{I_n\\}_{n=1}^N" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " with a set of " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " EV steps " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{s_m\\}_{m=1}^M" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": ". For each training image " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_n" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": ", its ground-truth LDR stack " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{I_n^*(s_m)\\}_{m=1}^M" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " is provided, where " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_n^*(s_m)" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " is the counterpart of " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_n" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " with the relative exposure value change " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "s_m" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": ". We train the CEVR model " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " in Eq. (1) by minimizing" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 408, + 416, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 408, + 416, + 419 + ], + "spans": [ + { + "bbox": [ + 306, + 408, + 416, + 419 + ], + "type": "text", + "content": "the " + }, + { + "bbox": [ + 306, + 408, + 416, + 419 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 306, + 408, + 416, + 419 + ], + "type": "text", + "content": " reconstruction loss:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 341, + 427, + 545, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 427, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 341, + 427, + 545, + 460 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e c}} = \\sum_ {n = 1} ^ {N} \\sum_ {m = 1} ^ {M} \\| I _ {n} ^ {*} (s _ {m}) - F (I _ {n}, s _ {m}) \\| _ {1}. \\tag {3}", + "image_path": "64430128a33e690d016bc97fdc20cf953d6c9f0504c52fb1ba23a57679b7f0f0.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 468, + 440, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 440, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 440, + 480 + ], + "type": "text", + "content": "3.3. Cycle Training Strategy" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": "Existing training datasets, such as the VDS dataset [23], provide the ground truth for a sparse set of predefined EV steps, e.g., " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "[-3, -2, \\dots, 3]" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": ". Inspired by the success of cycle consistency training in video frame interpolation [27] and to make our CEVR work well for synthesizing images with arbitrary EVs, we introduce the cycle training strategy to train the model with continuous EV steps without the corresponding ground-truth images. For each training image " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "I_{n}" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " and each EV step " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "s_m" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " covered by the training set, the cycle training strategy shown in Fig. 4, derives the CEVR model with two branches. The first branch takes " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "I_{n}" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "s_m" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " as input. Since the ground-truth image " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "I_{n}^{*}(s_{m})" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " is available, the reconstruction loss " + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 486, + 545, + 641 + ], + "type": "text", + "content": " is used to supervise this branch." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": "The second branch implements a two-step process. We randomly sample a real value " + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "inline_equation", + "content": "a \\in [0,1]" + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": " for each image " + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "inline_equation", + "content": "I_{n}" + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": " at each training iteration, and decompose the EV step " + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "inline_equation", + "content": "s_m" + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": " into two sub-steps: " + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "inline_equation", + "content": "u = as_m" + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\nu = (1 - a)s_m" + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "inline_equation", + "content": "u + \\nu = s_m" + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": ". Our CEVR model is applied twice with the two EV sub-steps, respectively. Although the ground truth for" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12993" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 286, + 223 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 223 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 223 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 223 + ], + "type": "image", + "image_path": "c4088f9482480235ec0b81fabddcd2ec6f7b55638b3c76753fc1e02694577609.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 230, + 288, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 230, + 288, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 288, + 291 + ], + "type": "text", + "content": "Figure 4: Cycle training. We derive the CEVR model in an unsupervised cycle training strategy without using the corresponding ground truth. In this way, our model exploits the cycle consistency constraint and learns more continuous information by varying the EV sub-step " + }, + { + "bbox": [ + 46, + 230, + 288, + 291 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 230, + 288, + 291 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "type": "text", + "content": "the randomly sampled sub-step " + }, + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "type": "text", + "content": " is unavailable, we expect that the output of taking the two sub-steps should be similar to the ground truth " + }, + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "type": "inline_equation", + "content": "I_{n}^{*}(s_{m})" + }, + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "type": "text", + "content": " because of " + }, + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "type": "inline_equation", + "content": "u + v = s_{m}" + }, + { + "bbox": [ + 46, + 304, + 287, + 353 + ], + "type": "text", + "content": ". Thereby, we enforce the proposed cycle loss:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 73, + 358, + 287, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 358, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 73, + 358, + 287, + 392 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c y c}} = \\sum_ {n = 1} ^ {N} \\sum_ {m = 1} ^ {M} \\| I _ {n} ^ {*} (s _ {m}) - F (F (I _ {n}, u), v) \\| _ {1}. \\tag {4}", + "image_path": "2661e6a2430b2171db1bc61129c5733d72178746039893d28e4e18f1f27c1a89.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "type": "text", + "content": "The sub-step " + }, + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "type": "text", + "content": " in Eq. (4) is randomly sampled for each training image with each covered EV step at each training iteration. It is used to simulate arbitrary EV step input to our CEVR model. To compensate for the lack of the ground truth of the intermediate output " + }, + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "type": "inline_equation", + "content": "F(I_{n},u)" + }, + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "type": "text", + "content": ", the cycle loss " + }, + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cyc}}" + }, + { + "bbox": [ + 46, + 397, + 287, + 481 + ], + "type": "text", + "content": " in Eq. (4) offers indirect supervision, ensuring the continuity of our CEVR model with continuous EV steps." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 481, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 506 + ], + "type": "text", + "content": "The objective function used to derive the proposed CEVR is defined by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 128, + 513, + 287, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 513, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 128, + 513, + 287, + 526 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {r e c}} + \\lambda \\mathcal {L} _ {\\text {c y c}}, \\tag {5}", + "image_path": "37022628a82b096ce3a41bf837e9700bc7b145f676ca934e3cd7e0fbbb113fd3.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 533, + 263, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 263, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 263, + 545 + ], + "type": "text", + "content": "where we empirically set " + }, + { + "bbox": [ + 47, + 533, + 263, + 545 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 533, + 263, + 545 + ], + "type": "text", + "content": " to 0.1 in our experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 552, + 153, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 153, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 153, + 563 + ], + "type": "text", + "content": "3.4. Continuous Stack" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "In the inference phase, with the implicit module and the cycle training strategy, our CEVR model can generate high-quality LDR images with continuous EVs. The LDR stack containing more LDR images with various EVs can help Debevec's method [11] estimate a more accurate inverse CRF, as shown in Fig. 1(c), and improve the HDR image reconstruction, as shown in Fig. 2. Inspired by this observation, we proposed the continuous stack, which predicts additional LDR images with continuous EVs from our CEVR model. The predicted continuous and dense LDR stack further benefits the stack fusion process and enhances the final HDR quality, as shown in Fig. 1(c)." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 140, + 545, + 330 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 547, + 131 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 131 + ], + "type": "text", + "content": "Table 1: Quantitative comparison of the predicted LDR stacks on the VDS dataset [23]. CEVR outperforms existing approaches in estimating LDR stacks for all EVs. With cycle training, our method can generate high-quality LDR images even with large EV changes." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 140, + 545, + 330 + ], + "lines": [ + { + "bbox": [ + 307, + 140, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 307, + 140, + 545, + 330 + ], + "type": "table", + "html": "
EVMethodPSNRSSIMMS-SSIM
mσmσmσ
+3Deep chain HDRI [23]28.182.770.9530.0650.9830.015
Deep recursive HDRI [24]28.972.920.9440.0440.9810.014
CEVR (Ours)34.343.460.9730.0210.9890.007
+2Deep chain HDRI [23]29.653.060.9590.0650.9860.016
Deep recursive HDRI [24]29.432.850.9520.0390.9860.010
CEVR (Ours)35.303.080.9810.0160.9930.004
+1Deep chain HDRI [23]31.903.430.9690.0390.9920.008
Deep recursive HDRI [24]32.022.850.9690.0260.9920.006
CEVR (Ours)37.642.960.9890.0090.9960.004
-1Deep chain HDRI [23]29.013.830.9350.0560.9800.017
Deep recursive HDRI [24]31.223.690.9510.0310.9860.090
CEVR (Ours)34.623.470.9800.0110.9920.005
-2Deep chain HDRI [23]26.724.540.9520.0290.9740.021
Deep recursive HDRI [24]31.083.070.9480.0410.9860.014
CEVR (Ours)33.894.340.9780.0170.9880.010
-3Deep chain HDRI [23]24.334.570.9190.0360.9480.037
Deep recursive HDRI [24]29.154.750.9100.0610.9660.025
CEVR (Ours)30.585.320.9540.0460.9720.032
", + "image_path": "d2482cbe4dc031d33aa169fad0098c6e0716ce8e25767fbdd7cf09256e4418d1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 342, + 388, + 356 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 342, + 388, + 356 + ], + "spans": [ + { + "bbox": [ + 306, + 342, + 388, + 356 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 361, + 422, + 375 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 422, + 375 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 422, + 375 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 384, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 515 + ], + "type": "text", + "content": "Datasets. We train our model using the training set of the VDS dataset [23], which contains image stacks of 48 scenes. The testing sets of the VDS and HDREye datasets [36], which contain 48 and 42 scenes respectively, serve as the testing sets for evaluations. The auto-bracketing feature of the camera produces seven photos with predefined exposure values for each scene in the VDS dataset (EV-3 to EV+3). We follow the common evaluation protocol [23, 24] and select the image with the zero exposure value, which is expected to have the most evenly distributed histogram, as the input to the model." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "content": "Training details. For training, we consider each training scene " + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "content": " from the VDS dataset [23] and take the corresponding EV0 LDR image as input " + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "inline_equation", + "content": "I_{n}" + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "content": ". We also take each EV step " + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "inline_equation", + "content": "s_m \\in \\{-3, -2, -1, 0, 1, 2, 3\\}" + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "content": " into account. We feed " + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "inline_equation", + "content": "I_{n}" + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "inline_equation", + "content": "s_m" + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "content": " to the CEVR model and estimate the LDR image with EV " + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "inline_equation", + "content": "s_m" + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "content": " for model training. Since the inverse CRF is usually asymmetrical, we train two different models with the same architecture to handle the increasing and decreasing exposure changes, respectively. For upsampling, we use bicubic upsampling, followed by a " + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 518, + 545, + 686 + ], + "type": "text", + "content": " 2D convolution with stride 1 and padding 1. The model is trained for 1,250 epochs with Adam optimizer [21] and cosine annealing warmup with restarts as the scheduler. We use random rotation and flip to augment the data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "Evaluation metrics. We employ PSNR, SSIM [49], and MS-SSIM [50] as the metrics for evaluating the qualities of" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12994" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 285, + 191 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 285, + 191 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 285, + 191 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 285, + 191 + ], + "type": "image", + "image_path": "769aa35ddb79c50ab4a85e543c69f472e2cb47c40649ae0269327573bfecb2e5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 193, + 287, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 193, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 287, + 253 + ], + "type": "text", + "content": "Figure 5: Qualitative comparison of LDR image predictions in the VDS dataset [23]. Our approach recovers more details compared to Deep recursive HDRI [24] in the EV-3 example. In the " + }, + { + "bbox": [ + 46, + 193, + 287, + 253 + ], + "type": "inline_equation", + "content": "\\mathrm{EV} + 3" + }, + { + "bbox": [ + 46, + 193, + 287, + 253 + ], + "type": "text", + "content": " example, our approach generates LDR images with a color tone similar to the ground truth." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 259, + 286, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 286, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 286, + 344 + ], + "type": "text", + "content": "the predicted LDR stacks and HDR tone-mapped images. We also utilize HDR-VDP-2 [31], a metric based on the human visual system, to evaluate the quality of the reconstructed HDR images. We follow the setting of [23, 24], which sets a 24-inch monitor with a viewing distance of 0.5 meters, a peak contrast of 0.0025, and a gamma of 2.2 for measuring the HDR-VDP-2 metric." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 407 + ], + "type": "text", + "content": "HDR reconstruction and tone-mapping operators. Our approach uses Debevec's approach [11] to reconstruct HDR images with the predicted LDR stack and utilizes Reinhard's method [39] or Kim and Kautz's method [20] to tonemap the HDR images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 414, + 250, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 414, + 250, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 414, + 250, + 426 + ], + "type": "text", + "content": "4.2. Comparison of LDR Stacks Prediction" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 435, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 603 + ], + "type": "text", + "content": "Quantitative comparisons. The quantitative comparisons of the estimated LDR exposure stacks from the VDS dataset are shown in Tab. 1. The table shows that the proposed method performs favorably against existing methods at every exposure value. The output LDR image quality decreases as the exposure value gap increases because more extensive over- and under-exposed regions reconstruction are required, which makes the task more difficult. However, with our cycle training, our model can still generate high-quality LDR images in the cases of EV+3 and EV-3 by incorporating continuous and dense EV information into the training process. The continuous EV generation during training helps the model learn how to explicitly infer LDR images with arbitrary exposure values." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Qualitative comparisons. With the cycle training, our method can generate a high-quality LDR image even with large EV changes. A detailed qualitative comparison is presented in Fig. 5. The first row of this figure shows that Deep recursive HDRI [24] often gets less accurate color tone in estimating the LDR images, which may further degrade the quality of the HDR images fused by the LDR stack. On the contrary, our method can better estimate the LDR images in all EVs with more accurate color tones. In addition, the" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 127, + 545, + 258 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 118 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 118 + ], + "type": "text", + "content": "Table 2: Quantitative comparison of HDR and TMO images. Two tone-mapping approaches, Reinhard's approach [39], and Kim and Kautz's approach [20], are denoted as RH's and KK's TMO." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 127, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 307, + 127, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 307, + 127, + 545, + 258 + ], + "type": "table", + "html": "
DatasetMethodPSNRPSNRHDR-VDP-2
RH's TMOKK's TMO
mσmσmσ
VDSDrTMO [13]25.494.2821.364.5054.336.27
Deep chain HDRI [23]30.863.3624.544.0156.364.41
Deep recursive HDRI [24]32.992.8128.023.5057.154.35
Santos et al. [43]22.562.6818.233.5353.514.76
Liu et al. [26]30.893.2728.004.1156.976.15
CEVR (Ours)34.673.5030.044.4559.005.78
HDREyeDrTMO [13]23.683.2719.974.1146.675.81
Deep chain HDRI [23]25.772.4422.623.3949.805.97
Deep recursive HDRI [24]26.282.7024.262.9052.634.84
Santos et al. [43]19.892.4619.003.0649.975.44
Liu et al. [26]26.253.0824.673.5450.336.67
CEVR (Ours)26.543.1024.812.9153.154.91
", + "image_path": "4e45b539190586498fb2ff762a5205cd5323c12ae274858bd79fea967a84e75d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 275, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 275, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 545, + 312 + ], + "type": "text", + "content": "second row demonstrates that our method can estimate the LDR images without severe artifacts. More visual comparisons can be found in the supplementary material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 318, + 508, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 318, + 508, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 318, + 508, + 331 + ], + "type": "text", + "content": "4.3. Comparison of HDR Image Prediction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 337, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 545, + 517 + ], + "type": "text", + "content": "We compare our method with five recent single-image HDR reconstruction methods, including Santos et al. [43], DrTMO [13], Deep chain HDRI [23], Deep recursive HDRI [24], and Liu et al. [26]. For Santos et al. [43], Deep recursive HDRI [24] and Liu et al. [26], we use their official implementations along with the released pre-trained model weight to generate all the quantitative and qualitative results on the VDS [23] and HDREye [36] datasets. For DrTMO [13] and Deep chain HDRI [23], we compare our results to the numbers reported in their papers. For HDR image prediction, our approach adopts the continuous stack strategy where the EV steps are enriched from " + }, + { + "bbox": [ + 304, + 337, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\{-3, -2, \\dots, +3\\}" + }, + { + "bbox": [ + 304, + 337, + 545, + 517 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 337, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\{-3, -2.5, \\dots, +3\\}" + }, + { + "bbox": [ + 304, + 337, + 545, + 517 + ], + "type": "text", + "content": ", and the images with the extra EV steps are also synthesized by using the proposed CEVR model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 519, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 662 + ], + "type": "text", + "content": "Quantitative evaluations. As shown in Tab. 2, our method performs favorably against the competing methods on the VDS dataset [23]. The HDRey dataset [36] serves as a blind test bed, our HDR prediction still achieves better qualities using the same tone-mapping operators. Our proposed cycle training makes the model explicitly learn the continuity as EV steps change, leading to better generalization on the unseen dataset, HDRey. With the continuous stack, more LDR images with various EVs are involved in the fusion process, which helps Debevec's approach [11] estimate a more accurate inverse CRF and generate HDR images with better qualities." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": "Qualitative comparisons. To generate the tone-mapped images for visual comparisons, we first reconstruct HDR images by fusing the LDR stacks with Debevec's approach [11]. Then we use Reinhard's method [39] to gen" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12995" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 258, + 349 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 258, + 349 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 258, + 349 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 258, + 349 + ], + "type": "image", + "image_path": "4ef053b31807fde2c6621d220ecb0e9338af0839ceff9c3e601b58fa1350ca18.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 354, + 547, + 403 + ], + "lines": [ + { + "bbox": [ + 46, + 354, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 547, + 403 + ], + "type": "text", + "content": "Figure 6: Qualitative comparison of tone-mapped HDR images. We adopt Reinhard's method [39] to generate HDR images shown in the figure. Deep recursive HDRI [24] often suffers from erroneous color tones and artifacts. As shown in the figure, our method can better recover details when compared to Liu et al.'s method [26]. In most regions, our method reconstructs the tone-mapped images with more accurate high-frequency details, leading to visually pleasing results." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 268, + 70, + 530, + 350 + ], + "blocks": [ + { + "bbox": [ + 268, + 70, + 530, + 350 + ], + "lines": [ + { + "bbox": [ + 268, + 70, + 530, + 350 + ], + "spans": [ + { + "bbox": [ + 268, + 70, + 530, + 350 + ], + "type": "image", + "image_path": "05c8cf6686e24dd533684cea42e596e2881b74dd43cbf5d58a5cce70edced964.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "content": "erate HDR TMO images for all comleting methods. As Liu et al. [26] generate an HDR image directly, we apply Reinhard's tone-mapping operator [39] for tone-mapping the HDR images. Note that Liu et al. [26] do not train their method on the VDS dataset; hence we only compare the qualitative results with their method on the HDREye dataset, as shown in Fig. 6." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 502, + 288, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 288, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 288, + 660 + ], + "type": "text", + "content": "In Fig. 6, it can be observed that Deep recursive HDRI [24] often suffers from inaccurate color tone: the color of the building is inaccurate in the tone-mapped images, and artifacts are present in severely exposed regions. Liu et al. [26] directly estimate and reverse the whole camera pipeline to generate HDR images. It sometimes struggles with generating detailed textures and produces artifacts in severely exposed regions, e.g., the over-exposed window frame and sky in the daylight. With the intensity transformation, our model can preserve the image structure and generate the tone-mapped images with similar tones to the ground truth. It also produces fewer artifacts. More visual comparisons can be found in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 147, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 147, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 147, + 681 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "In the following, we validate three design contributions to improving the quality of the LDR stack and HDR images." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 496, + 545, + 624 + ], + "blocks": [ + { + "bbox": [ + 304, + 415, + 545, + 488 + ], + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 488 + ], + "type": "text", + "content": "Table 3: Ablation studies on the predicted LDR stack. Intensity transformation balances two distinct tasks: brightness adjustment and precise color tone generation while preserving the image structure. Cycle training provides the model with extra information about changing EVs. Both designs improve LDR stack quality." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 496, + 545, + 624 + ], + "lines": [ + { + "bbox": [ + 306, + 496, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 496, + 545, + 624 + ], + "type": "table", + "html": "
Intensity transformation-✓✓
Cycle training--✓
PSNRPSNRPSNR
mσmσmσ
EV+331.954.2033.903.5734.343.46
EV+233.193.1634.893.1235.303.08
EV+135.092.5637.493.0737.642.96
EV-133.672.0634.432.5534.623.47
EV-232.533.3732.914.4133.894.34
EV-330.235.4730.355.8630.585.32
", + "image_path": "cabf71087322e790f25c7e7564fa7fb4bac029f43eb1936ed33a68abdf01f0ef.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Intensity transformation. Learning to adjust image brightness while maintaining color tone accuracy and image structures can be challenging. The CEVR model, which directly outputs results from the U-net structure without using intensity transformation, can struggle to adjust brightness or produce inaccurate LDR images with artifacts, as shown in Fig. 7. The intensity transformation module can restrict" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12996" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 120, + 286, + 178 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 118 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 118 + ], + "type": "text", + "content": "Table 4: Ablation studies on the reconstructed HDR images on the VDS dataset [23]. Intensity transformation and cycle training enhance the quality of LDR stacks, and continuous stack benefits the stack fusion process." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 120, + 286, + 178 + ], + "lines": [ + { + "bbox": [ + 47, + 120, + 286, + 178 + ], + "spans": [ + { + "bbox": [ + 47, + 120, + 286, + 178 + ], + "type": "table", + "html": "
Intensity transformation-✓✓✓
Continuous stack--✓✓
Cycle training---✓
PSNR32.5234.2034.4734.67
", + "image_path": "9ba8547d3af91dac367943c636ade8bd47cf20b70900726e6ebccaadccc64dfa.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 47, + 180, + 284, + 305 + ], + "blocks": [ + { + "bbox": [ + 47, + 180, + 284, + 305 + ], + "lines": [ + { + "bbox": [ + 47, + 180, + 284, + 305 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 284, + 305 + ], + "type": "image", + "image_path": "9b165b71189518004c02a2f38ea268c920563bedda0322f41ecedd9c6bff16a2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "lines": [ + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 287, + 347 + ], + "type": "text", + "content": "Figure 7: Ablation on intensity transformation. With intensity transformation, CEVR can adjust LDR image intensity while preserving the image structure and color tone." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 360, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 407 + ], + "type": "text", + "content": "the model's capacity, producing LDR images with more accurate brightness, color tones, and structures. This design improves the quality of the LDR stack and HDR results, as demonstrated in Tab. 3 and Tab. 4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 411, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 567 + ], + "type": "text", + "content": "Cycle training. With cycle training, the model can be supervised on continuous EV steps without using the corresponding ground truth. It can learn how to change the exposure value continuously, which improves the quality and reduces the artifacts of the estimated LDR images, which also leads to better HDR quality, as shown in Fig. 8, Tab. 3 and Tab. 4. To further demonstrate the effectiveness of cycle training, we conducted the hold-out experiment, excluding EV-1 and +1 LDR images during training. Then, we used the model to estimate EV-1 and +1 LDR images for each scene and evaluated the PSNR. The table shows that our model can generate better LDR images with unseen EVs when the cycle training strategy is adopted." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 82, + 635, + 248, + 700 + ], + "blocks": [ + { + "bbox": [ + 46, + 578, + 287, + 626 + ], + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 626 + ], + "type": "text", + "content": "Table 5: Hold-out experiment. Hold-out experiment excludes EV-1 and +1 LDR images during training. With cycle training, the model generate better LDR images with unseen EVs (EV-1, +1)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 82, + 635, + 248, + 700 + ], + "lines": [ + { + "bbox": [ + 82, + 635, + 248, + 700 + ], + "spans": [ + { + "bbox": [ + 82, + 635, + 248, + 700 + ], + "type": "table", + "html": "
Cycle training×✓
EV-127.7533.77
EV+133.3736.96
", + "image_path": "d6318f8ec802b11aa9be93f948517a8a32f70319e0e62810b0e90fe4e6ff52cd.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 72, + 545, + 194 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 545, + 194 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 194 + ], + "type": "image", + "image_path": "aebf62d06684dc5f7fc450b280af29c3d6c7100c961334957cbe89be337057e4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 198, + 545, + 246 + ], + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 246 + ], + "type": "text", + "content": "Figure 8: Ablation on cycle training for LDR and HDR images generation. With the cycle training, the model captures the finer granularity of \"EV changing\" and generates more accurate and visually pleasing LDR and HDR images." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 258, + 546, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 546, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 546, + 475 + ], + "type": "text", + "content": "Continuous stack. Debevec's method [11] uses the LDR stack to recover response curves and reconstruct HDR images. A denser and continuous EV LDR stack helps produce an accurate inverse CRF, enhancing HDR quality. We compare two stack settings: \"predefined stack\" and \"continuous stack.\" The CEVR model estimates seven LDR images (EVs: -3, -2, -1, ..., +3) for the predefined stack, which is the setting used in existing methods, while the continuous stack has 13 LDR images with various EVs (-3, -2.5, -2, ..., +3). Tab. 4 and Fig. 1(b)(c) show that the tone-mapped image from the continuous stack has superior quality and is more visually pleasing. We can further validate the effectiveness of the continuous stack by visualizing the CRF of both the predefined stack and the continuous stack. As shown in Fig. 9, the denser EV setting can help generate a smoother CRF compared to the predefined EV setting. Additional analysis of the inverse CRF can be found in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 483, + 389, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 389, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 389, + 495 + ], + "type": "text", + "content": "4.5. Failure cases" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 502, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 597 + ], + "type": "text", + "content": "Although the proposed method performs favorably against other existing methods in quantitative and qualitative results, we do not explicitly design the module to address the over-exposed issue, which may make the CEVR model fail to generate reasonable content in large saturated regions, as shown in Fig. 10. It is a promising direction to take the emerging generative model designs, e.g. [28, 59], into account to address this issue." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 609, + 378, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 378, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 378, + 621 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "We introduce CEVR, a learning-based method that produces LDR EV stacks from continuous EV input. Our approach combines U-Net with implicit functions, and allows the network to generate LDR images with continuous EVs. We propose two strategies, including (1) cycle training for learning on continuous EV changes unseen in the training dataset and (2) continuous stack for improving LDR stack" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12997" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 71, + 160, + 240 + ], + "blocks": [ + { + "bbox": [ + 65, + 71, + 160, + 240 + ], + "lines": [ + { + "bbox": [ + 65, + 71, + 160, + 240 + ], + "spans": [ + { + "bbox": [ + 65, + 71, + 160, + 240 + ], + "type": "image", + "image_path": "15a25b9f267f666d06daad0753f417ffd2b6ce4b2a4b5e643ccf2d2182d6f779.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 251, + 288, + 312 + ], + "lines": [ + { + "bbox": [ + 47, + 251, + 288, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 288, + 312 + ], + "type": "text", + "content": "Figure 9: Analysis of the estimated inverse CRF. Continuous stack, adding additional LDR images with dense and continuous EVs, can help Debevec's method [11] generate more accurate inverse CRF and generate HDR images with better quality." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 163, + 72, + 267, + 239 + ], + "blocks": [ + { + "bbox": [ + 163, + 72, + 267, + 239 + ], + "lines": [ + { + "bbox": [ + 163, + 72, + 267, + 239 + ], + "spans": [ + { + "bbox": [ + 163, + 72, + 267, + 239 + ], + "type": "image", + "image_path": "2e4ced7110a2af3793c322dcfc60571c2a446ffcdefd59241b4c3be08e4cadff.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 47, + 319, + 113, + 387 + ], + "blocks": [ + { + "bbox": [ + 47, + 319, + 113, + 387 + ], + "lines": [ + { + "bbox": [ + 47, + 319, + 113, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 113, + 387 + ], + "type": "image", + "image_path": "f243004cc140a2bd9868d442871ace04b229c45f6d50064dc07823f149cb1667.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 393, + 287, + 430 + ], + "lines": [ + { + "bbox": [ + 47, + 393, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 393, + 287, + 430 + ], + "type": "text", + "content": "Figure 10: Failure case. Existing methods and our proposed method cannot generate reasonable content as the sky region is severely over-exposed." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 114, + 319, + 171, + 387 + ], + "blocks": [ + { + "bbox": [ + 114, + 319, + 171, + 387 + ], + "lines": [ + { + "bbox": [ + 114, + 319, + 171, + 387 + ], + "spans": [ + { + "bbox": [ + 114, + 319, + 171, + 387 + ], + "type": "image", + "image_path": "8b379577cc7eb4fa3529ebc391fae22e41171f512022c2acbd96d2f3cc8aa0d2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 171, + 319, + 227, + 387 + ], + "blocks": [ + { + "bbox": [ + 171, + 319, + 227, + 387 + ], + "lines": [ + { + "bbox": [ + 171, + 319, + 227, + 387 + ], + "spans": [ + { + "bbox": [ + 171, + 319, + 227, + 387 + ], + "type": "image", + "image_path": "b05ecd9e17c10b9890e21ec5c20a8a87d13b402c711f9ad84d74ea070128cb1d.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 228, + 319, + 286, + 387 + ], + "blocks": [ + { + "bbox": [ + 228, + 319, + 286, + 387 + ], + "lines": [ + { + "bbox": [ + 228, + 319, + 286, + 387 + ], + "spans": [ + { + "bbox": [ + 228, + 319, + 286, + 387 + ], + "type": "image", + "image_path": "011c035686162fafcd1e18f828c6a4378d6e2082a522845962d9eb10e2686be3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 443, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 287, + 502 + ], + "type": "text", + "content": "fusion using additional images with dense and continuous EVs. Our approach with the two strategies greatly enhances LDR stack quality and improves HDR image results, as demonstrated through extensive quantitative and qualitative evaluations on two benchmark datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 506, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 287, + 578 + ], + "type": "text", + "content": "Acknowledgments. This work was supported in part by National Science and Technology Council (NSTC) under grants 111-2628-E-A49-025-MY3, 112-2221-E-A49-090-MY3, 111-2634-F-002-023, 111-2634-F-006-012, 110-2221-E-A49-065-MY3 and 111-2634-F-A49-010. 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To address the problem, we propose an innovative unsupervised method of Learning Correction Filter via Degradation-Adaptive Regression for Blind Single Image Super-Resolution. Highly inspired by the generalized sampling theory, our method aims to enhance the strength of off-the-shelf SR methods trained on known degradations and adapt to unknown complex degradations to generate improved results. Specifically, we first conduct degradation estimation for each local image region by learning the internal distribution in an unsupervised manner via GAN. Instead of assuming degradation are spatially invariant across the whole image, we learn correction filters to adjust degradations to known degradations in a spatially variant way by a novel linearly-assembled pixel degradation-adaptive regression module (DARM). DARM is lightweight and easy to optimize on a dictionary of multiple pre-defined filter bases. Extensive experiments on synthetic and real-world datasets verify the effectiveness of our method both qualitatively and quantitatively. Code can be available at: https://github.com/edbca/DARSR.", + "bbox": [ + 75, + 358, + 473, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 762, + 209, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Single image super-resolution (SISR) aims to recover a photo-realistic HR image from its LR counterpart. As a fundamental computer vision task, SISR has been widely used in various applications, such as enhancing the images' visual perception on high-resolution devices and improving the image quality for other vision tasks [7]. In recent years,", + "bbox": [ + 75, + 787, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e96fb24e240c4ce66d893ed3218e71b41156fe37ed4ca3c87e9e6c95b727be7b.jpg", + "image_caption": [ + "(a) Most degradation estimation strategies" + ], + "image_footnote": [], + "bbox": [ + 501, + 325, + 890, + 414 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/63ff87a910f583a2557a7cea54b24daa542fcdd2d4cde6bae75444e0515395f6.jpg", + "image_caption": [ + "(b) Our method", + "Figure 1. Illustration of most degradation estimation strategies for blindSR and our method. (a) Most methods assume degradations are spatially invariant and estimate a single degradation for the whole image. (b) Our method can learn correction filters to adjust the degradations to a known degradation in a spatially variant way." + ], + "image_footnote": [], + "bbox": [ + 501, + 426, + 890, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "a multiplicity of deep learning-based SISR methods have been proposed [33, 18, 25, 52, 51, 8, 29, 54] and achieved substantial performance improvement.", + "bbox": [ + 496, + 627, + 890, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Typically, training and testing LR images in existing SISR approaches are simulated from a large collection of HR images. As a pioneer work, Dong et al. [9] first introduced a three-layer convolutional neural network in SISR to learn LR-HR mapping. Zhang et al. [51] proposed a channel attention mechanism to build a deep model for SISR. Liang et al. [22] proposed a baseline model SwinIR for SISR based on the transformer mechanism. In these methods, the LR images are often generated by limited numbers of fixed degradations (e.g., Bicubic or blur-downscale). However, the degradation process in real-world scenarios is extremely complicated and unpredictable. Although existing methods [25, 51, 29, 21, 18, 8] have achieved promising performance, they often encounter severe performance drops when the degradation is not well covered in training.", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author (zhuxiaobin@ustb.edu.cn).", + "bbox": [ + 94, + 886, + 362, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12365", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, many works have attempted to address the challenging degradation adaptation problem by explicit or implicit degradation modeling in a blind or non-blind manner. SRMD [48] learns an SR model with training data covering a large set of degradation maps, which are modeled with blur kernel and noise. Following SRMD, UDVD [43] proposes a single unified dynamic network trained for various degradations to improve performance. However, in most practical applications, blur kernels are not available. They can hardly deal with the LR inputs with degradations out of their modeling scope. To tackle this problem, some methods [34, 35, 2, 11] estimate a blur kernel from each input LR image for adapting to complex degradations. IKC [12] proposes to correct kernel estimation in an iterative way to approach a satisfactory result gradually. ZSSR [34] learns degradation kernels of LR images via internal statistics for every image in a self-supervised manner. Pseudosupervision [53] combines the forward SR reconstruction path in CinCGAN [44] architecture with degradation learning to deal with the domain shift problem. In addition, Hussein et al. [14] proposed a correction filter strategy on the signal that is sampled by a certain basis can be reconstructed by a different basis, for modifying an LR input to match the SR model with a pre-defined degradation. These methods' generalization ability still greatly relies on the accuracy of degradation estimation or training data distribution. In addition, as shown in Fig. 1 (a), they assume degradations are spatially invariant and only estimate a single degradation for the whole image. Such an assumption is rarely applicable for real images whose regions (e.g., edges, corners) are discriminative for degradation estimation.", + "bbox": [ + 76, + 90, + 472, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To fully take advantage of the off-the-shelf superresolvers, we try to robustify the degradation of LR input without hurting useful information for efficiently adapting to practical applications. A brief illustration and comparison to the existing degradation estimation strategy for blindSR are presented in Fig. 1. Specifically, we propose an innovative unsupervised method of learning correction filter via a linearly-assembled pixel degradation-adaptive regression module (DARM) for correcting the LR image's degradation to the known one in a spatially variant way. Our DARM is highly lightweight and can be easily optimized over a dictionary of multiple pre-defined filter bases. In this way, our method can conduct correction filtering and help off-the-shelf SISR models to adapt to complex degradations on every testing image efficiently. In addition, we propose a degradation metric (DM) loss to learning to map the unquantifiable degradation in a metric space to guarantee the accuracy of degradation correction.", + "bbox": [ + 76, + 559, + 472, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are three-fold:", + "bbox": [ + 94, + 830, + 433, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose an innovative unsupervised strategy by learning correction filters for Blind Single Image Super-Resolution in a spatially variant way, greatly en", + "bbox": [ + 93, + 854, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "hancing the adapting ability of trained super-resolvers to unknown complex degradations.", + "bbox": [ + 529, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a lightweight degradation-adaptive regression module (DARM) that could accurately yet efficiently learn correction filters over a dictionary of multiple pre-defined filter bases.", + "- We propose a novel degradation metric (DM) loss via metric learning to map the unquantifiable degradation in a metric space to effectively improve the accuracy of degradation correction.", + "- Extensive experiments on synthetic datasets and real images verify that our method can consistently improve the performance of the off-the-shelf superresolvers both qualitatively and quantitatively." + ], + "bbox": [ + 516, + 128, + 890, + 325 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 338, + 640, + 354 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Predefined-Degradation based SR", + "text_level": 1, + "bbox": [ + 500, + 363, + 797, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dong et al. [9] firstly proposed a three consecutive convolutional neural network in SISR to learn a complex LR-HR mapping. Kim et al. [15] increased the depth of the network via a skip connection for stable training. To achieve promising performance, most methods adopt residual architecture [38, 52, 26]. EDSR [25] removes the batch normalization layer in a residual block and increasing the network depth. RCAN [51], SAN [8] and HAN [29] introduce the attention mechanism to draw more high-frequency information to further improve the performance. Furthermore, SwinIR [22], IPT [4], GRL [20] employ the transformer mechanism for constantly refreshing the state-of-the-art of SISR. However, these methods perform promisingly under a single degradation model (e.g., bicubic and blur-downscale degradation models); they tend to produce over-sharped or blurry results if the degradations present in the testing deviate from training.", + "bbox": [ + 496, + 386, + 890, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Degradation-Learning based SR", + "text_level": 1, + "bbox": [ + 500, + 650, + 784, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multiple degradation modeling based SR. By modeling multiple degradations, this type of method can produce good results for LR inputs covered by the training dataset. SRMD [48] proposes to directly concatenate an LR input image with its degradation map as a unified input to the SR model, thus allowing feature adaptation according to the specific degradation and covering multiple degradation types in a single model. DPSR [49] incorporates a super-resolution network into a MAP-based iterative optimization scheme which solves the HR image by minimizing objective functions. Similar to DPSR, USRNet [46] proposes an end-to-end trainable unfolding network that leverages both learning-based methods and model-based methods by unfolding the MAP inference via a half-quadratic splitting algorithm. Luo et al. [13] adopted an alternating optimization", + "bbox": [ + 496, + 672, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12366", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/207885a8c046b4dba7e9f0e989ee6be9558b1ba334655cec53be0afeec8d273a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 90, + 869, + 323 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0dfa40cd6bae6119b1e8bc06dee33afffc586c8bf29e00d32412ecf77f058eb8.jpg", + "image_caption": [ + "(a) Learning correction filter via Degradation-Adaptive Regression", + "(b) Degradation correction for input LR image via a traind SR model", + "Figure 2. Architecture of our method. (a) Illustration of the learning of correction filters. (b) Illustration of the degradation correction." + ], + "image_footnote": [], + "bbox": [ + 101, + 337, + 696, + 440 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ee6187886ddd3c70f391bc5da75bccf24e6795273bc95fa5f25052991ae9c88b.jpg", + "image_caption": [ + "x,y, x b Training data Discriminator" + ], + "image_footnote": [], + "bbox": [ + 700, + 349, + 723, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Degradation Generator", + "bbox": [ + 728, + 359, + 861, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sigmoid", + "bbox": [ + 736, + 373, + 815, + 387 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Element-wise product", + "bbox": [ + 728, + 388, + 857, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Element-wise sum", + "bbox": [ + 736, + 405, + 844, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DM Loss", + "bbox": [ + 700, + 428, + 759, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Degradation Metric loss", + "bbox": [ + 772, + 422, + 870, + 448 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "algorithm to estimate blur kernel and restore SR image in a single model. However, the performance of these methods still relies on accurate estimation of input kernel, which is challenging on arbitrary LR images.", + "bbox": [ + 75, + 497, + 468, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Degradation estimation based SR. Gu et al. [12] proposed a general framework for blind SR by using self-similarity to recover the blur kernel and the HR image jointly. KernelGAN [2] interprets the maximization of patch recurrence within a single image as a data distribution learning problem and generates downscaled LR images by learning the internal patch distribution of the testing LR image. Shocher et al. [34] proposed a zero-shot super-resolution (ZSSR) method which trains image-specific on the testing LR image to take the degradation parameters and estimate blur kernel for improving the performance. Afterward, Soh et al. [35] proposed to learn an image-specific degradation simulation network together with a zero-shot image-specific super-solution network which exploits the depth information of the image to extract an unpaired high/low resolution patch collection to train the network. Liang et al. [24] proposed a novel method to incorporate a flow-based kernel prior into the framework by learning an invertible mapping between the anisotropic Gaussian kernel distribution and a tractable latent distribution. While these methods consider degradation are spatially invariant and only estimate a single degradation for input image. Cornillere et al. [5] pro", + "bbox": [ + 75, + 568, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "posed a degradation-aware SR network to adapt spatially variant degradations. MANet [23] uses mutual affine convolution in their network for spatially variant kernel estimation. However, these methods greatly rely on the coverage of degradation modeling or training data distribution.", + "bbox": [ + 496, + 497, + 890, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Method", + "text_level": 1, + "bbox": [ + 500, + 585, + 630, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 611, + 638, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The SISR degradation model can be mathematically formulated as:", + "bbox": [ + 500, + 635, + 890, + 662 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx = (y \\otimes k) \\downarrow_ {s}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 665, + 890, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $y$ denotes the HR image; $x$ denotes the LR image; $k$ is the blur kernel; $\\otimes$ denotes convolution operator; $\\downarrow_{s}$ denotes sub-sampling operator with stride of $s$ . Note that Eq. 1 can be written as:", + "bbox": [ + 496, + 686, + 890, + 746 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx = D y, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 663, + 748, + 890, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $D$ represents degradation operator. As assumed by Hussein et al [14], the signal $y$ can be perfectly recovered from its samples $x$ by the operator $U(DU)^{-1}$ as:", + "bbox": [ + 496, + 770, + 890, + 816 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ny = U (D U) ^ {- 1} x = U (D U) ^ {- 1} D y, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 825, + 890, + 843 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $U$ is an upsampling operator which is the adjoint operator of $D$ . Eq. 3 indicates that the image $y$ resides in the linear subspace can be spanned by the known degradation.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12367", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Therefore, it can be perfectly recovered from the observations $x_{k}$ by applying the pseudo inverse of $U_{k}$ as:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny ^ {\\prime} = U _ {k} \\left(D _ {k} U _ {k}\\right) ^ {- 1} D _ {k} y = U _ {k} \\left(D _ {k} U _ {k}\\right) ^ {- 1} x _ {k}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 126, + 468, + 143 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $D_{k}$ denotes known degradation operation; $x_{k}$ denotes known degraded image; $U_{k}$ denotes a DNN super-resolver trained under the assumption of known degradation and it can handle the $x_{k}$ quite well with a learned prior.", + "bbox": [ + 75, + 148, + 468, + 209 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to the generalization of classical Whittaker-Shannon sampling theorem [17, 30, 32, 42], some works [3, 10, 39] consider that a signal sampled by a certain basis can be reconstructed by different basis. By combining a correction filter with a reconstruction kernel, a sampled signal can be reconstructed. The correction filter can transform the sampling coefficients associated with the sampling kernel to coefficients that fit the reconstruction kernel. Given a degraded LR image $x_{u}$ obtained by a unknown degradation $D_{u}$ , $x_{u} = D_{u}y$ . Then, the $y'$ can be reconstructed as:", + "bbox": [ + 75, + 210, + 468, + 361 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny ^ {\\prime} = U _ {k} C x _ {u} = U _ {k} C D _ {u} y, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 366, + 468, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C$ is a correction operator for $x_{u}$ . Combining Equation 4 and Eq. 5, we can find the expression of $C$ as follows:", + "bbox": [ + 76, + 388, + 468, + 419 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC = \\left(D _ {u} U _ {k}\\right) ^ {- 1} \\Rightarrow C D _ {u} = U _ {k} ^ {- 1}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 424, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The operator $C$ can be applied simply as a convolution with a correction filter. Following Eq. 6, we first conduct spatial-variant degradation estimation to model $D_{u}$ , which learns the spatially variant degradations in $x_{u}$ . Then, we use our DARM to learn the correction filters $C$ for correcting the degradations of $x_{u}$ to pre-defined degradation. Finally, we employ a trained $U_{k}$ to super-resolve the corrected image.", + "bbox": [ + 75, + 446, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our method mainly distinguishes from the work [14] in two respects: (1) The performance of the work [14] greatly relies on the accuracy of degradation estimation. In our method, we coherently combine degradation estimation with correction filter learning into a unified network, greatly improving the accuracy and adaptiveness; (2) The work [14] only considers the spatially invariant degradation situation, failing to adopt a correction filter to solve a natural image with complex degradations. In our method, we estimate degradations in a spatially variant way.", + "bbox": [ + 75, + 553, + 468, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overview", + "text_level": 1, + "bbox": [ + 76, + 710, + 187, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2 (a), we learn correction filters via DARM in an unsupervised manner. Then, as shown in Fig. 2 (b), we use learned correction filters to correct the degradation of the input LR image to the pre-defined degradation. Finally, an off-the-shelf super-resolver trained by known degradation is used for upsampling the degradation adapted LR image for SR. The learning of correction filters mainly consists of three components: generation of training data from input LR image, spatial-variant degradation estimation, and learning correction filters through proposed degradation adaptation regression module.", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1349fba85821b237496bfc8133f2104d099ca7ebd95d696faf03e2f741305c91.jpg", + "image_caption": [ + "Figure 3. Illustration of the generation of training data from the input LR image. $X = \\{x^{i}\\}$ , $Y = \\{y^{i}\\}$ , and $X_{b} = \\{x_{b}^{i}\\}$ are used to train our proposed degradation-adaptive regression module." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 893, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Generation of Training Data", + "text_level": 1, + "bbox": [ + 500, + 290, + 756, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the input LR image, our goal is to correct complex degradations of all regions to the degradation (e.g. bicubic) in the off-the-shelf super-resolver. As shown in Fig. 3, we first crop the input LR image to generate the patches $X = \\{x^{i}\\}$ where each patch $x^{i}$ has the degradation of the corresponding area and $X$ can cover the degradation of each region in the input LR image. Then, we crop the input LR image to generate the patches $Y = \\{y^{i}\\}$ , which aims to learn a downscaled image (e.g., by a factor of 2 or 4) such that its degradation is approximate to that of the patches $X$ (see Sec. 3.4). Finally, we use known downsampling operation to degrade patches $Y$ for generating patches $X_{b} = \\{x_{b}^{i}\\}$ of the same size with $x^{i}$ for degradation-adaptive regression learning. After obtaining training data $X$ , $X_{b}$ , and $Y$ , we will train our network to learn correction filters as shown in Fig. 2 (a).", + "bbox": [ + 496, + 314, + 890, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Spatial-Variant Degradation Estimation.", + "text_level": 1, + "bbox": [ + 500, + 568, + 846, + 584 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$X$ and $X_{b}$ are not paired, which leads to the correction filters are unable to be learned directly. Thus, we adopt the GAN-based method to learn $X_{c} = \\{x_{c}^{i}\\}$ with the same degradation as $X$ through a GAN. Specially, we employ a degradation generator $G$ and a discriminator $D$ , as shown in Fig. 2 (a). Different from KernelGAN [2] which only learns one global invariant degenerate kernel, we will learn spatially variant degradation for each local patch $x_{c}^{i}$ . In this way, we can learn $X_{c}$ to cover the degradation of each region for improving performance. In addition, we propose a novel degradation metric (DM) loss (see Sec. 3.6) to learn more accurate degradation in $x_{i}$ .", + "bbox": [ + 496, + 592, + 890, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Learning Correction Filters via DARM", + "text_level": 1, + "bbox": [ + 500, + 785, + 836, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2 (a), we adopt paired training data $X_{c}$ and $X_{b}$ to learn correction filters by training our DARM through L1 loss and DM loss. We also train our network on unpaired training data $X$ and $X_{b}$ by DM loss. The output of $X_{c}$ and $X$ through DARM can be expressed as $X_{b^{\\prime}} = \\{x_{b^{\\prime}}^{i}\\}$ and $X_{a} = \\{x_{a}^{i}\\}$ , respectively. Notably, our DARM learns a", + "bbox": [ + 498, + 809, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12368", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "correction filter for each input pixel.", + "bbox": [ + 76, + 90, + 316, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our key idea lies on the total probability theorem and the additivity of normal distribution. We can obtain the correction filter by combining multiple Gaussian filters. Specifically, a correction filter $F^i$ can be represented as a linear combination of a set of underlying base Gaussian filters:", + "bbox": [ + 75, + 106, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF ^ {i} = \\Phi^ {i} \\mathbb {D} = \\sum_ {j = 1} ^ {N} \\theta_ {j} ^ {i} f _ {j}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 191, + 468, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F = \\mathbb{R}^{HW \\times (k \\times k)}$ ( $k$ is the kernel size which is empirically set to 5 in our experiments) denotes the learned correction filters for each pixel in the input image of size $H \\times W$ ; $\\Phi = \\mathbb{R}^{HW \\times N}$ denotes the learned linear combination coefficients for each pixel; The dictionary $\\mathbb{D} = \\mathbb{R}^{N \\times (k \\times k)}$ consists of 72 Gaussian and difference of Gaussians (DoG) filters [19], which can help to increase the visibility of details accurately learn correction filters.", + "bbox": [ + 76, + 247, + 468, + 368 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the purpose of efficiency, we adopt a lightweight residual network for DARM via learning linear combination coefficients $\\Phi$ . It mainly consists of two residual channel attention blocks (RCAB) [51] to learn deep feature, the convolutional layers in the head to extract the shallow feature of the input image, and the final convolutional layers to generate combination coefficients.", + "bbox": [ + 75, + 369, + 468, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Loss Functions", + "text_level": 1, + "bbox": [ + 76, + 484, + 228, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adversarial loss. We adopt GAN-based method to learn spatially variant degradations of LR image. The adversarial loss for the degradation generator $G$ can be formulated as:", + "bbox": [ + 75, + 508, + 468, + 553 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {g a n} = \\mathbb {E} [ D (G (y ^ {i})) - 1 ] ^ {2} + \\mathcal {R}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 564, + 468, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{R}$ denotes the regularization term which applies realistic explicit priors [2]. The discriminator $D$ tries to distinguish degradations generated by $G$ from $x^i$ of input LR image and the constrain of $D$ can be formulated as:", + "bbox": [ + 75, + 593, + 468, + 654 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D} = \\mathbb {E} \\left[ D \\left(x ^ {i}\\right) - 1\\right) ^ {2} ] + \\mathbb {E} \\left[ D \\left(G \\left(y ^ {i}\\right)\\right) ^ {2} \\right]. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 664, + 468, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pixelwise loss. It is used to accelerate the convergence of DRAM. Besides, it can effectively compensate for the structural distortion caused by GAN. We use L1 loss to constrain the results generated by DASR and SR model. The mathematic formulation is:", + "bbox": [ + 75, + 694, + 468, + 768 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p i x} = \\left| \\left| x _ {b} ^ {i} - x _ {b ^ {\\prime}} ^ {i} \\right| \\right| _ {1} + \\left| \\left| y ^ {i} - S R \\left(x _ {b ^ {\\prime}} ^ {i}\\right) \\right| \\right| _ {1}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 781, + 468, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $SR(*)$ denotes an off-the-shelf super-resolver.", + "bbox": [ + 76, + 809, + 428, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Degradation metric loss. It is difficult to estimate complex degradations accurately via single adversarial learning in real-world scenarios. To overcome this problem, we propose a novel degradation metric (DM) loss which maps the complex degradation into a metric space for effective", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/485e6ebed9b107eda27615761f31f9adae26ebc2efa0944a47fb427e34603bd4.jpg", + "image_caption": [ + "Figure 4. Architecture of degradation score estimation module (DSEM), which mainly consist of three Resblocks [25], an average pooling layer, a sigmoid layer, and a full connection layer." + ], + "image_footnote": [], + "bbox": [ + 540, + 89, + 854, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "constraint. Specially, we use a degradation score estimation module (DSEM) to model the distance between target degradation and estimated degradation. We use $x^{i}$ and $x_{b}^{i}$ as anchor samples to train the metric space as shown in Fig. 4. The mathematical formulation is elaborated as:", + "bbox": [ + 498, + 267, + 890, + 340 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a c} = \\frac {1}{N} \\sum_ {i} ^ {N} \\left(\\left| \\left| S \\left(x _ {b} ^ {i}\\right) \\right| \\right| _ {2} ^ {2} + \\left| \\left| S \\left(x ^ {i}\\right) - 1 \\right| \\right| _ {2} ^ {2}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 349, + 890, + 392 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $S(*)$ denotes the degradation score estimation operation, which is implemented by DSEM. Then, we use DM loss from two parts, one is the result generated by downscale generator $G$ , and the other one is the result generated by DARM. The mathematical formulation is elaborated as:", + "bbox": [ + 498, + 404, + 890, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {d m l} = \\left| \\left| S \\left(x _ {b} ^ {i}\\right) - S \\left(x _ {b ^ {\\prime}} ^ {i}\\right) \\right| \\right| _ {2} ^ {2} + \\left| \\left| S \\left(x ^ {i}\\right) - S (G \\left(y ^ {i}\\right)) \\right| \\right| _ {2} ^ {2} \\\\ + \\left\\| S \\left(x ^ {i}\\right) - S \\left(x _ {a} ^ {i}\\right) \\right\\| _ {2} ^ {2}. \\tag {12} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 489, + 890, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Full objective. Mathematically, the total loss function for our method can be formulated as:", + "bbox": [ + 498, + 541, + 890, + 570 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {A l l} = \\mathcal {L} _ {g a n} + \\lambda_ {1} \\mathcal {L} _ {p i x} + \\lambda_ {2} \\mathcal {L} _ {d m l}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 583, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are two empirical hyper-parameters that are set to 2.5 and 0.5, respectively.", + "bbox": [ + 498, + 612, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 656, + 633, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 680, + 715, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments on real-world datasets (RealSRSet [47]) and synthetic datasets (NTIRE2017 [36] and NTIRE2018 [37]). The results are evaluated by the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) [41], and learned perceptual image patch similarity (LPIPS) [50]. PSNR and SSIM are evaluated on the Y channel of transformed YCbCr, while LPIPS is on RGB. We train our network by each iteration with 16 batches which consist of paired patches from the LR input. The patches $32 \\times 32$ and $128 \\times 128$ ( $x^i$ and $y^i$ in Fig. 3) are for scaling $\\times 4$ . The patches $64 \\times 64$ and $128 \\times 128$ are for scaling $\\times 2$ . The iteration number is set to 3,000, and the optimizer is the Adam [16] with $\\beta 1 = 0.9$ , $\\beta 2 = 0.999$ . The initial", + "bbox": [ + 498, + 704, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12369", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/75dbfffdcd55ea4c810bb0ed7b9f83af5e0386f1081ac4e65dd0b755f6a4a595.jpg", + "table_caption": [ + "Table 1. Quantitative results on NTIRE2017 [36] and NTIRE2018 [37] testing datasets for scaling factor $\\times 4$ . $\\uparrow$ denotes the larger the better. $\\downarrow$ denotes the smaller the better. Red color indicates the best performance, and blue color indicates the second best performance." + ], + "table_footnote": [], + "table_body": "
Methods2017Track22018Track22018Track32018Track4
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
SRGAN [18]22.990.58890.466918.990.45820.612719.750.47060.624119.500.46870.6150
SRFBN-s [21]23.070.60430.484518.870.48860.608519.780.50430.625119.510.50200.6112
KernelGAN [2] + ZSSR [34]22.490.58000.495118.430.54500.573919.750.57500.600019.360.57470.5774
BlindSR [5]21.610.54830.482018.350.40960.608819.310.42430.619218.900.41710.6102
IKC [12]22.280.57380.468318.720.54880.568619.810.57160.595019.420.57130.5723
SRGAN [18] + Correction Filter [14]20.980.57760.582118.730.55550.614119.070.55710.628818.950.56610.6147
SRFBN-s [21] + Correction Filter [14]20.980.58510.602318.740.56310.625519.100.56590.649918.980.57460.6313
USRNet [46]22.850.60290.511019.000.56410.570019.970.58250.601619.670.58530.5795
MANet [23]21.410.55790.491118.660.47440.609019.310.48330.628819.010.47620.6154
DIP-FKP [24]20.490.53360.505018.110.55280.578118.720.56090.608618.450.56050.5869
DASR [40]22.920.59680.478018.920.55790.569019.830.57480.592919.530.57820.5712
BSRDM [45]21.630.57970.558118.720.54830.594619.570.56570.612419.180.55960.6001
Ours + SRGAN [18]23.090.60170.463720.240.57410.608821.040.58450.617321.180.58870.6021
Ours + SRFBN-s [21]23.350.61260.506320.320.57870.622521.110.58590.629121.340.59480.6021
", + "bbox": [ + 78, + 114, + 893, + 363 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7c34ef47b07584f863171fa40dc0c8e11d6daaad85c74ff0181532295715282a.jpg", + "table_caption": [ + "Table 2. Quantitative results on NTIRE2017 Track2 [36] testing dataset for scaling factor $\\times 2$ ." + ], + "table_footnote": [], + "table_body": "
MethodsPSNR↑SSIM↑LPIPS↓
SRFBN-s [21]26.430.72460.3437
KernelGAN [2] + ZSSR [34]26.340.72880.3295
BlindSR [5]27.220.75390.3054
SRFBN-s [21] + Correction Filter [14]23.440.61250.3482
USRNet [46]26.520.73680.3710
MANet [23]27.920.78180.3086
DIP-FKP [24]26.290.74920.3188
DASR [40]26.380.72220.3335
BSRDM [45]26.650.73030.4432
Ours + SRFBN-s [21]27.990.78220.3513
", + "bbox": [ + 81, + 412, + 460, + 584 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f8479f53ad8147f4e13eedcb790c1d90f398c661abcbc7245b9c578a02ff1183.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 598, + 156, + 635 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2d9740a959ea1f83638e80aa3c357fbd91aaeb0b01d523e1518012f066b38049.jpg", + "image_caption": [ + "Figure 5. Illustration of degradation estimation for MANet [23] and DIP-FKP [24] on “ $0801 \\times 4m$ .png” in NTIRE2018 track2." + ], + "image_footnote": [], + "bbox": [ + 163, + 598, + 385, + 713 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7d771580c3225ee5b14bc79dd9814ce91c2233c62c2ccde5a6f3beab7f232a91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 598, + 468, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "learning rate is $10^{-3}$ which will be decayed by 0.5 after each 750 iterations. Data augmentation includes randomly rotating 90, 180, 270 degrees, and horizontally flipping. We implement experiments with PyTorch1.12.0 on an NVIDIA Geforce RTX 3090 GPU.", + "bbox": [ + 75, + 755, + 468, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experiments on Synthetic Datasets.", + "text_level": 1, + "bbox": [ + 76, + 845, + 383, + 862 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct experiments on four synthetic benchmarks: track2 of NTIRE2017 [36] and track2, track3, and track4", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of NTIRE2018 [37]. The degradations in these datasets are complex and unknown. Notably, the official uses same degradation operators within an image. But, as shown in Fig. 5, we use MANet [23] and DIP-FKP [24] to estimate the degradation of different regions in LR image, we find that the degradation of degraded image is spatially variant. We think that the given HR images are spatially variant degraded from the real HR ones due to camera acquisition in complex scenes, which make the LR images are spatially variant. We compare with unsupervised and supervised methods, including SRGAN [18], SRFBNs [21], KernelGAN [2], ZSSR [34], BlindSR [5], IKC [12], Correction_Filter [14], USRNet [46], DIP-FKP [24], MANet [23] and BSRDM [45].", + "bbox": [ + 496, + 388, + 890, + 599 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Quantitative Evaluation.", + "text_level": 1, + "bbox": [ + 500, + 619, + 723, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The detailed experimental results are listed in Tab. 1 and Tab. 2. Note that our method does not have a design module for denoising, so we employ CBM3D [6] to conduct on track2, track3, and track4 of NTIRE2018 datasets firstly. We also use the same operation for other methods without the ability of denoising for a fair comparison.", + "bbox": [ + 496, + 643, + 890, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparing with trained SR methods. As listed in Tab. 1 and Tab. 2, our method can improve the performance of SRGAN in all testing datasets on PSNR/SSIM/LPIPS. Our method also improves the performance of SRFBN-s in all testing datasets on PSNR/SSIM for scaling factor $\\times 2$ and $\\times 4$ . We noticed that our method did not improve the LPIPS values of SRFBN-s. This phenomenon often occurs in PSNR-Oriented methods (e.g., EDSR, RCAN). Our method can improve the performance of perceptual-driven methods (e.g., SRGAN, ESRGAN) in all indicators, including LPIPS. PSNR-Oriented methods focus on achiev-", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12370", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f1018431990cdb7671a7733bad961580dd6fa391446f1c546a3cec8344da028e.jpg", + "image_caption": [ + "Figure 6. Visual comparisons of different methods on 2017Track2 [36], 2018Track2 [37], and 2018Track4 [37]. Zoom in for best view." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 893, + 477 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ffbf38f8543376616977d37da786c8af2cd94c2ff2a38a8d60ee6677f55fb03c.jpg", + "image_caption": [ + "Figure 7. Visual comparisons of different method for $\\times 4$ on RealSRSet [47] dataset. Zoom in for best view." + ], + "image_footnote": [], + "bbox": [ + 78, + 507, + 890, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing high PSNR and tend to generate images with too smooth and lost details (More analysis in Supp. Materials). Although our method can effectively recover LR images, the characteristics of these methods still lead to LPIPS degradation. But in general, our method can consistently improve the performance of off-the-shelf super-resolvers.", + "bbox": [ + 75, + 710, + 470, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparing with Correction_Filter. As shown in Tab. 1 and Tab. 2, Correction_Filter failed to improve the performance of SRFBN-s and SRGAN. The performance of Correction_Filter greatly relies on the accuracy of degradation estimation. However, it is difficult to solve complex degradation by their iterative approximation strategies. Be-", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sides, they only considers the spatially invariant degradation, failing to tackle spatially ones (More comparison are in Supp. Materials). The experimental results show that our method is more effective than Correction_Filter.", + "bbox": [ + 496, + 710, + 893, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparing with spatially-variant SR methods. From Tab. 2, we can see that the performance of SRFBN-s is far lower than BlindSR and MANet in all indicators. While SRFBN-s equipped our method outperforms BlindSR and MANet by 0.77 dB/0.0283 and 0.07 dB/0.0004 in terms of PSNR/SSIM, respectively. In Tab. 1, our method can help SRGAN and SRFBN-s outperforms Blind and MANet on all testing datasets in terms of PSRN/SSIM. The experi", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12371", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "mental results verify that our method is superior in solving spatial-variant degradation.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparing with other blind methods. As listed in Tab. 1, Ours+SRFBN-s achieves the best SSIM and PSNR on all datasets. Ours+SRFBN-s outperforms BSRDM by 1.72 dB/0.0329 and 2.16 dB/0.0352 on 2017Track2 and 2018Track4 on PSNR/SSIM, respectively. Ours+SRFBN-s outperforms DASR by 1.4 dB/0.0208 and 1.81 dB/0.0166 on 2018Track2 and 2018Track4 on PSNR/SSIM, respectively. Tab. 2 also verify that our method outperforms other blind methods. We conclude that our method is effective and has strong degradation-adaptive ability.", + "bbox": [ + 75, + 119, + 470, + 272 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7320125b16f9f4c9adbedb85bf8d38300925d8e3e72de6944739499db000299d.jpg", + "image_caption": [ + "(a) Input LR image", + "Figure 8. Visual ablation study about DM loss." + ], + "image_footnote": [], + "bbox": [ + 81, + 286, + 207, + 434 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/230ec42adbd55eee88136bd9683ce6ac27d3cd63292d030f18e23a990ad23aa9.jpg", + "image_caption": [ + "(b) Corrected LR image", + "(without DM Loss)" + ], + "image_footnote": [], + "bbox": [ + 210, + 286, + 336, + 434 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8228e52d4edc6c8ec6e8eef9c82f579f74f187869528a6709c4fd59396dba844.jpg", + "image_caption": [ + "(c) Corrected LR image" + ], + "image_footnote": [], + "bbox": [ + 341, + 286, + 467, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2.2 Qualitative Evaluation.", + "text_level": 1, + "bbox": [ + 76, + 494, + 292, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 6 are representative visual results. As shown in Fig. 6 (a), our method can generate sharper and cleaner SR images, but most other methods generate details with blurry or artifacts. Although the SR images generated by BSRDM seem to be clear, they lose some important details. In Fig. 6 (b), Ours+SRFBN-s can correctly restore font textures, while most other methods will produce incorrect textures. Although BSRDM generates font texture with good visual effects, many distortions exist. In Fig. 6 (c), Ours+SRFBN-s recovers clear and natural details, while other methods are prone to generate detailed textures with visual aliasing and artifacts. Notably, our method can greatly improves the visual quality of SRFBNs, demonstrating our method's effectiveness.", + "bbox": [ + 75, + 520, + 468, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Experiments on Real-World Dataset.", + "text_level": 1, + "bbox": [ + 76, + 741, + 395, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also conduct experiments on RealSRSet [47] dataset. (Due to most images in RealSRSet are small size, we reduce the cropped image size in Sec 4.1.) As mentioned in [47, 45], current non-reference metrics (e.g., NIQE [28], NRQM [27], and PI [1]) are not consistent with the perceptual visual system. Therefore, we only compare visual results. Fig. 7 shows the visual results on two representative images. Apparently, Ours+SRFBN-s generates improved visual results than other methods. In the first examples in", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 7, most other methods tend to generate noises or artifacts. USRNet generated observable visual results but with too many white lines that should not exist. BSRDM generates unrealistic and discontinuous lines with some distortions. In the second example in Fig. 7, most other methods cannot finely deal with the hair and tend to produce unrealistic detailed textures with visual aliasing. In contrast, our Ours+SRFBN-s reconstructs clear and natural details.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/526f2883388679b9542c6b02f50f38d32506c31564834e202bf7d97a3d9ffa22.jpg", + "table_caption": [ + "Table 3. Ablation study of DM Loss on NTIRE2017 Track2 testing dataset for scaling factor $\\times 4$ ." + ], + "table_footnote": [], + "table_body": "
Method\\( \\mathcal{L}_{gan} \\)\\( \\mathcal{L}_{pix} \\)\\( \\mathcal{L}_{dml} \\)PSNR↑SSIM↑LPIPS↓
Ours+SRFBN-s✓16.240.37570.7231
Ours+SRFBN-s✓21.890.56240.6532
Ours+SRFBN-s✓✓22.060.57040.6430
Ours+SRFBN-s✓✓✓23.350.61260.5063
", + "bbox": [ + 501, + 247, + 887, + 328 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 354, + 651, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "About DM Loss. To verify the effectiveness of DM loss, we conduct experiments on the 2017Track2 dataset. As listed in Tab. 3, Ours+SRFBN-s outperforms Ours +SRFBN-s (without $\\mathcal{L}_{dml}$ ) on scale $\\times 4$ by $1.29\\mathrm{dB}$ on PSNR, 0.0423 on SISM, and 0.1367 on LPIPS, respectively. Besides, our DM loss can clearly improve the accuracy of degradation correction of corrected LR image (Fig. 8 (c)), compared with our model without DM loss (Fig. 8 (b)).", + "bbox": [ + 496, + 378, + 890, + 500 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9e800121584d17a785670883b42c66cafd8643170de26ae26ca13e1545420045.jpg", + "table_caption": [ + "Table 4. Ablation study of filter dictionary on NTIRE2017 Track2 testing dataset for scaling factor $\\times 4$ ." + ], + "table_footnote": [], + "table_body": "
Filter TypeNumberPSNR↑SSIM↑LPIPS↓
G + DoG [19]7223.350.61260.5063
RAISR [31]7222.120.53340.6430
Learned7222.440.53430.6266
G + DoG [19]2423.170.61140.5145
", + "bbox": [ + 501, + 537, + 890, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "About the base Filter Dictionary. We conducted experiments on the 2017Track2 dataset to verify the chosen of the base filter dictionary. We compare with RAISR filters [31] and filters directly learned by networks. As listed in Tab. 4, it is clear that 72 Gaussian and DoG combination achieves the best result. Tab. 4 also shows that the result with 72 basic filters is better than the dictionary with 24 basic filters. Besides, the filters size with $5 \\times 5$ for each pixel is sufficient to restore complex real-world images. Various kernel sizes definitely can enhance performance but introduce great computational costs.", + "bbox": [ + 496, + 635, + 890, + 801 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/235bf769e9c2e8865de8069ff84ece368e2207db103a83fd832d48207c58c576.jpg", + "table_caption": [ + "Table 5. Ablation study on trained SR with different degradations." + ], + "table_footnote": [], + "table_body": "
Method2018Track22018Track3
Ours + SRFBN-s(Bicubic)20.32/0.578721.11/05859
Ours + SRFBN-s(Gaussian)20.31/0.578721.11/0.5858
Ours + SRFBN-s(Lanczos)20.32/0.578721.13/0.5859
", + "bbox": [ + 501, + 825, + 890, + 897 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12372", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "About trained SR with different degradation. We choose two different degradations (Gaussian blur and Lanczos) to train SRFBN-s on DIV2K dataset for scaling factor $\\times 4$ , respectively. Tab. 5 lists the detailed results on NTIRE 2018 track2 and NTIRE 2018 track3. The results on the two degradation models are nearly consistent with bicubic degradation, which demonstrates that our method can adapt to any known degeneration in a trained model.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 226, + 194, + 242 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose a novel blind image superresolution method that corrects the degradations of an LR input to that of the training data in an off-the-shelf method. Specifically, we propose an innovative unsupervised method of learning correction filter via a linearly-assembled pixel DARM for correcting the LR image's degradation to the known one in a spatially variant way for each testing image. Besides, we propose a degradation metric loss to map the unquantifiable degradation to guarantee the accuracy of degradation correction. Extensive experiments verify the superior performance of our method both quantitatively and qualitatively.", + "bbox": [ + 75, + 251, + 472, + 434 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Acknowledge", + "text_level": 1, + "bbox": [ + 76, + 448, + 215, + 465 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The research is supported by National Key Research and Development Program of China (2020AAA0109700), National Science Fund for Distinguished Young Scholars(62125601), National Natural Science Foundation of China (62172035, 62076024, 62006018).", + "bbox": [ + 75, + 472, + 470, + 547 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 563, + 174, + 579 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 126-135, 2017. 8", + "[2] Sefi Bell-Kligler, Assaf Shocher, and Michal Irani. Blind super-resolution kernel estimation using an internal-gan. 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Pattern Recognition, 110:107619, 2021. 1" + ], + "bbox": [ + 78, + 90, + 468, + 768 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12375", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Correction Filter via Degradation-Adaptive Regression for Blind Single Image Super-Resolution/eaad2ba2-88cf-4d2a-a334-fd43747c9ca0_model.json b/2023/Learning Correction Filter via Degradation-Adaptive Regression for Blind Single Image Super-Resolution/eaad2ba2-88cf-4d2a-a334-fd43747c9ca0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b0c744fa9e00905a2a532ff1d4fe9650042fbf52 --- /dev/null +++ b/2023/Learning Correction Filter via Degradation-Adaptive Regression for Blind Single Image Super-Resolution/eaad2ba2-88cf-4d2a-a334-fd43747c9ca0_model.json @@ -0,0 +1,2510 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.111, + 0.13, + 0.861, + 0.177 + ], + "angle": 0, + "content": "Learning Correction Filter via Degradation-Adaptive Regression for Blind Single Image Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.203, + 0.794, + 0.24 + ], + "angle": 0, + "content": "Hongyang Zhou\\(^{1}\\), Xiaobin Zhu\\(^{1*}\\), Jianqing Zhu\\(^{2}\\), Zheng Han\\(^{1}\\), Shi-Xue Zhang\\(^{1}\\), Jingyan Qin\\(^{1}\\), Xu-Cheng Yin\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.24, + 0.856, + 0.293 + ], + "angle": 0, + "content": "1University Of Science and Technology Beijing, 2College of Engineering, Huaqiao University ilaopi@foxmail.com, zhuxiaobin@ustb.edu.cn, jqzhu@hqu.edu.cn, han970421@foxmail.com zhangshixue111@163.com, qinjingyanking@foxmail.com, xuchengyin@ustb.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.474, + 0.722 + ], + "angle": 0, + "content": "Although existing image deep learning super-resolution (SR) methods achieve promising performance on benchmark datasets, they still suffer from severe performance drops when the degradation of the low-resolution (LR) input is not covered in training. To address the problem, we propose an innovative unsupervised method of Learning Correction Filter via Degradation-Adaptive Regression for Blind Single Image Super-Resolution. Highly inspired by the generalized sampling theory, our method aims to enhance the strength of off-the-shelf SR methods trained on known degradations and adapt to unknown complex degradations to generate improved results. Specifically, we first conduct degradation estimation for each local image region by learning the internal distribution in an unsupervised manner via GAN. Instead of assuming degradation are spatially invariant across the whole image, we learn correction filters to adjust degradations to known degradations in a spatially variant way by a novel linearly-assembled pixel degradation-adaptive regression module (DARM). DARM is lightweight and easy to optimize on a dictionary of multiple pre-defined filter bases. Extensive experiments on synthetic and real-world datasets verify the effectiveness of our method both qualitatively and quantitatively. Code can be available at: https://github.com/edbca/DARSR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.763, + 0.21, + 0.78 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.789, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Single image super-resolution (SISR) aims to recover a photo-realistic HR image from its LR counterpart. As a fundamental computer vision task, SISR has been widely used in various applications, such as enhancing the images' visual perception on high-resolution devices and improving the image quality for other vision tasks [7]. In recent years," + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.327, + 0.892, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.577, + 0.415, + 0.798, + 0.427 + ], + "angle": 0, + "content": "(a) Most degradation estimation strategies" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.427, + 0.892, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.515, + 0.732, + 0.527 + ], + "angle": 0, + "content": "(b) Our method" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.53, + 0.894, + 0.6 + ], + "angle": 0, + "content": "Figure 1. Illustration of most degradation estimation strategies for blindSR and our method. (a) Most methods assume degradations are spatially invariant and estimate a single degradation for the whole image. (b) Our method can learn correction filters to adjust the degradations to a known degradation in a spatially variant way." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.673 + ], + "angle": 0, + "content": "a multiplicity of deep learning-based SISR methods have been proposed [33, 18, 25, 52, 51, 8, 29, 54] and achieved substantial performance improvement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Typically, training and testing LR images in existing SISR approaches are simulated from a large collection of HR images. As a pioneer work, Dong et al. [9] first introduced a three-layer convolutional neural network in SISR to learn LR-HR mapping. Zhang et al. [51] proposed a channel attention mechanism to build a deep model for SISR. Liang et al. [22] proposed a baseline model SwinIR for SISR based on the transformer mechanism. In these methods, the LR images are often generated by limited numbers of fixed degradations (e.g., Bicubic or blur-downscale). However, the degradation process in real-world scenarios is extremely complicated and unpredictable. Although existing methods [25, 51, 29, 21, 18, 8] have achieved promising performance, they often encounter severe performance drops when the degradation is not well covered in training." + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.364, + 0.9 + ], + "angle": 0, + "content": "* Corresponding author (zhuxiaobin@ustb.edu.cn)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12365" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.56 + ], + "angle": 0, + "content": "Recently, many works have attempted to address the challenging degradation adaptation problem by explicit or implicit degradation modeling in a blind or non-blind manner. SRMD [48] learns an SR model with training data covering a large set of degradation maps, which are modeled with blur kernel and noise. Following SRMD, UDVD [43] proposes a single unified dynamic network trained for various degradations to improve performance. However, in most practical applications, blur kernels are not available. They can hardly deal with the LR inputs with degradations out of their modeling scope. To tackle this problem, some methods [34, 35, 2, 11] estimate a blur kernel from each input LR image for adapting to complex degradations. IKC [12] proposes to correct kernel estimation in an iterative way to approach a satisfactory result gradually. ZSSR [34] learns degradation kernels of LR images via internal statistics for every image in a self-supervised manner. Pseudosupervision [53] combines the forward SR reconstruction path in CinCGAN [44] architecture with degradation learning to deal with the domain shift problem. In addition, Hussein et al. [14] proposed a correction filter strategy on the signal that is sampled by a certain basis can be reconstructed by a different basis, for modifying an LR input to match the SR model with a pre-defined degradation. These methods' generalization ability still greatly relies on the accuracy of degradation estimation or training data distribution. In addition, as shown in Fig. 1 (a), they assume degradations are spatially invariant and only estimate a single degradation for the whole image. Such an assumption is rarely applicable for real images whose regions (e.g., edges, corners) are discriminative for degradation estimation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.56, + 0.473, + 0.831 + ], + "angle": 0, + "content": "To fully take advantage of the off-the-shelf superresolvers, we try to robustify the degradation of LR input without hurting useful information for efficiently adapting to practical applications. A brief illustration and comparison to the existing degradation estimation strategy for blindSR are presented in Fig. 1. Specifically, we propose an innovative unsupervised method of learning correction filter via a linearly-assembled pixel degradation-adaptive regression module (DARM) for correcting the LR image's degradation to the known one in a spatially variant way. Our DARM is highly lightweight and can be easily optimized over a dictionary of multiple pre-defined filter bases. In this way, our method can conduct correction filtering and help off-the-shelf SISR models to adapt to complex degradations on every testing image efficiently. In addition, we propose a degradation metric (DM) loss to learning to map the unquantifiable degradation in a metric space to guarantee the accuracy of degradation correction." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.832, + 0.434, + 0.846 + ], + "angle": 0, + "content": "In summary, our main contributions are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "- We propose an innovative unsupervised strategy by learning correction filters for Blind Single Image Super-Resolution in a spatially variant way, greatly en" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "hancing the adapting ability of trained super-resolvers to unknown complex degradations." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.13, + 0.892, + 0.19 + ], + "angle": 0, + "content": "- We propose a lightweight degradation-adaptive regression module (DARM) that could accurately yet efficiently learn correction filters over a dictionary of multiple pre-defined filter bases." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.199, + 0.892, + 0.258 + ], + "angle": 0, + "content": "- We propose a novel degradation metric (DM) loss via metric learning to map the unquantifiable degradation in a metric space to effectively improve the accuracy of degradation correction." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.267, + 0.892, + 0.327 + ], + "angle": 0, + "content": "- Extensive experiments on synthetic datasets and real images verify that our method can consistently improve the performance of the off-the-shelf superresolvers both qualitatively and quantitatively." + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.13, + 0.892, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.339, + 0.642, + 0.355 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.364, + 0.798, + 0.38 + ], + "angle": 0, + "content": "2.1. Predefined-Degradation based SR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Dong et al. [9] firstly proposed a three consecutive convolutional neural network in SISR to learn a complex LR-HR mapping. Kim et al. [15] increased the depth of the network via a skip connection for stable training. To achieve promising performance, most methods adopt residual architecture [38, 52, 26]. EDSR [25] removes the batch normalization layer in a residual block and increasing the network depth. RCAN [51], SAN [8] and HAN [29] introduce the attention mechanism to draw more high-frequency information to further improve the performance. Furthermore, SwinIR [22], IPT [4], GRL [20] employ the transformer mechanism for constantly refreshing the state-of-the-art of SISR. However, these methods perform promisingly under a single degradation model (e.g., bicubic and blur-downscale degradation models); they tend to produce over-sharped or blurry results if the degradations present in the testing deviate from training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.785, + 0.667 + ], + "angle": 0, + "content": "2.2. Degradation-Learning based SR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Multiple degradation modeling based SR. By modeling multiple degradations, this type of method can produce good results for LR inputs covered by the training dataset. SRMD [48] proposes to directly concatenate an LR input image with its degradation map as a unified input to the SR model, thus allowing feature adaptation according to the specific degradation and covering multiple degradation types in a single model. DPSR [49] incorporates a super-resolution network into a MAP-based iterative optimization scheme which solves the HR image by minimizing objective functions. Similar to DPSR, USRNet [46] proposes an end-to-end trainable unfolding network that leverages both learning-based methods and model-based methods by unfolding the MAP inference via a half-quadratic splitting algorithm. Luo et al. [13] adopted an alternating optimization" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12366" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.092, + 0.87, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.287, + 0.325, + 0.673, + 0.338 + ], + "angle": 0, + "content": "(a) Learning correction filter via Degradation-Adaptive Regression" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.338, + 0.697, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.442, + 0.576, + 0.455 + ], + "angle": 0, + "content": "(b) Degradation correction for input LR image via a traind SR model" + }, + { + "type": "image_caption", + "bbox": [ + 0.7, + 0.327, + 0.865, + 0.358 + ], + "angle": 0, + "content": "x,y, x b Training data Discriminator" + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.35, + 0.725, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.729, + 0.361, + 0.862, + 0.372 + ], + "angle": 0, + "content": "Degradation Generator" + }, + { + "type": "text", + "bbox": [ + 0.738, + 0.374, + 0.816, + 0.388 + ], + "angle": 0, + "content": "Sigmoid" + }, + { + "type": "text", + "bbox": [ + 0.73, + 0.39, + 0.858, + 0.403 + ], + "angle": 0, + "content": "Element-wise product" + }, + { + "type": "text", + "bbox": [ + 0.737, + 0.406, + 0.845, + 0.419 + ], + "angle": 0, + "content": "Element-wise sum" + }, + { + "type": "text", + "bbox": [ + 0.701, + 0.429, + 0.76, + 0.442 + ], + "angle": 0, + "content": "DM Loss" + }, + { + "type": "text", + "bbox": [ + 0.773, + 0.423, + 0.872, + 0.449 + ], + "angle": 0, + "content": "Degradation Metric loss" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.459, + 0.867, + 0.473 + ], + "angle": 0, + "content": "Figure 2. Architecture of our method. (a) Illustration of the learning of correction filters. (b) Illustration of the degradation correction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.498, + 0.47, + 0.56 + ], + "angle": 0, + "content": "algorithm to estimate blur kernel and restore SR image in a single model. However, the performance of these methods still relies on accurate estimation of input kernel, which is challenging on arbitrary LR images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Degradation estimation based SR. Gu et al. [12] proposed a general framework for blind SR by using self-similarity to recover the blur kernel and the HR image jointly. KernelGAN [2] interprets the maximization of patch recurrence within a single image as a data distribution learning problem and generates downscaled LR images by learning the internal patch distribution of the testing LR image. Shocher et al. [34] proposed a zero-shot super-resolution (ZSSR) method which trains image-specific on the testing LR image to take the degradation parameters and estimate blur kernel for improving the performance. Afterward, Soh et al. [35] proposed to learn an image-specific degradation simulation network together with a zero-shot image-specific super-solution network which exploits the depth information of the image to extract an unpaired high/low resolution patch collection to train the network. Liang et al. [24] proposed a novel method to incorporate a flow-based kernel prior into the framework by learning an invertible mapping between the anisotropic Gaussian kernel distribution and a tractable latent distribution. While these methods consider degradation are spatially invariant and only estimate a single degradation for input image. Cornillere et al. [5] pro" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.575 + ], + "angle": 0, + "content": "posed a degradation-aware SR network to adapt spatially variant degradations. MANet [23] uses mutual affine convolution in their network for spatially variant kernel estimation. However, these methods greatly rely on the coverage of degradation modeling or training data distribution." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.587, + 0.631, + 0.603 + ], + "angle": 0, + "content": "3. Our Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.612, + 0.64, + 0.627 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.636, + 0.891, + 0.663 + ], + "angle": 0, + "content": "The SISR degradation model can be mathematically formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.666, + 0.891, + 0.681 + ], + "angle": 0, + "content": "\\[\nx = (y \\otimes k) \\downarrow_ {s}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.747 + ], + "angle": 0, + "content": "where \\(y\\) denotes the HR image; \\(x\\) denotes the LR image; \\(k\\) is the blur kernel; \\(\\otimes\\) denotes convolution operator; \\(\\downarrow_{s}\\) denotes sub-sampling operator with stride of \\(s\\). Note that Eq. 1 can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.665, + 0.749, + 0.891, + 0.763 + ], + "angle": 0, + "content": "\\[\nx = D y, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.771, + 0.892, + 0.817 + ], + "angle": 0, + "content": "where \\(D\\) represents degradation operator. As assumed by Hussein et al [14], the signal \\(y\\) can be perfectly recovered from its samples \\(x\\) by the operator \\(U(DU)^{-1}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.827, + 0.891, + 0.844 + ], + "angle": 0, + "content": "\\[\ny = U (D U) ^ {- 1} x = U (D U) ^ {- 1} D y, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( U \\) is an upsampling operator which is the adjoint operator of \\( D \\). Eq. 3 indicates that the image \\( y \\) resides in the linear subspace can be spanned by the known degradation." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12367" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "Therefore, it can be perfectly recovered from the observations \\( x_{k} \\) by applying the pseudo inverse of \\( U_{k} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.127, + 0.469, + 0.145 + ], + "angle": 0, + "content": "\\[\ny ^ {\\prime} = U _ {k} \\left(D _ {k} U _ {k}\\right) ^ {- 1} D _ {k} y = U _ {k} \\left(D _ {k} U _ {k}\\right) ^ {- 1} x _ {k}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.15, + 0.469, + 0.21 + ], + "angle": 0, + "content": "where \\(D_{k}\\) denotes known degradation operation; \\(x_{k}\\) denotes known degraded image; \\(U_{k}\\) denotes a DNN super-resolver trained under the assumption of known degradation and it can handle the \\(x_{k}\\) quite well with a learned prior." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.211, + 0.47, + 0.362 + ], + "angle": 0, + "content": "According to the generalization of classical Whittaker-Shannon sampling theorem [17, 30, 32, 42], some works [3, 10, 39] consider that a signal sampled by a certain basis can be reconstructed by different basis. By combining a correction filter with a reconstruction kernel, a sampled signal can be reconstructed. The correction filter can transform the sampling coefficients associated with the sampling kernel to coefficients that fit the reconstruction kernel. Given a degraded LR image \\( x_{u} \\) obtained by a unknown degradation \\( D_{u} \\), \\( x_{u} = D_{u}y \\). Then, the \\( y' \\) can be reconstructed as:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.367, + 0.469, + 0.385 + ], + "angle": 0, + "content": "\\[\ny ^ {\\prime} = U _ {k} C x _ {u} = U _ {k} C D _ {u} y, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.389, + 0.469, + 0.42 + ], + "angle": 0, + "content": "where \\(C\\) is a correction operator for \\(x_{u}\\). Combining Equation 4 and Eq. 5, we can find the expression of \\(C\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.425, + 0.469, + 0.443 + ], + "angle": 0, + "content": "\\[\nC = \\left(D _ {u} U _ {k}\\right) ^ {- 1} \\Rightarrow C D _ {u} = U _ {k} ^ {- 1}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.469, + 0.553 + ], + "angle": 0, + "content": "The operator \\(C\\) can be applied simply as a convolution with a correction filter. Following Eq. 6, we first conduct spatial-variant degradation estimation to model \\(D_{u}\\), which learns the spatially variant degradations in \\(x_{u}\\). Then, we use our DARM to learn the correction filters \\(C\\) for correcting the degradations of \\(x_{u}\\) to pre-defined degradation. Finally, we employ a trained \\(U_{k}\\) to super-resolve the corrected image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.469, + 0.706 + ], + "angle": 0, + "content": "Our method mainly distinguishes from the work [14] in two respects: (1) The performance of the work [14] greatly relies on the accuracy of degradation estimation. In our method, we coherently combine degradation estimation with correction filter learning into a unified network, greatly improving the accuracy and adaptiveness; (2) The work [14] only considers the spatially invariant degradation situation, failing to adopt a correction filter to solve a natural image with complex degradations. In our method, we estimate degradations in a spatially variant way." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.188, + 0.726 + ], + "angle": 0, + "content": "3.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 2 (a), we learn correction filters via DARM in an unsupervised manner. Then, as shown in Fig. 2 (b), we use learned correction filters to correct the degradation of the input LR image to the pre-defined degradation. Finally, an off-the-shelf super-resolver trained by known degradation is used for upsampling the degradation adapted LR image for SR. The learning of correction filters mainly consists of three components: generation of training data from input LR image, spatial-variant degradation estimation, and learning correction filters through proposed degradation adaptation regression module." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.091, + 0.895, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.223, + 0.894, + 0.266 + ], + "angle": 0, + "content": "Figure 3. Illustration of the generation of training data from the input LR image. \\( X = \\{x^{i}\\} \\), \\( Y = \\{y^{i}\\} \\), and \\( X_{b} = \\{x_{b}^{i}\\} \\) are used to train our proposed degradation-adaptive regression module." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.291, + 0.757, + 0.307 + ], + "angle": 0, + "content": "3.3. Generation of Training Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.315, + 0.892, + 0.557 + ], + "angle": 0, + "content": "Given the input LR image, our goal is to correct complex degradations of all regions to the degradation (e.g. bicubic) in the off-the-shelf super-resolver. As shown in Fig. 3, we first crop the input LR image to generate the patches \\( X = \\{x^{i}\\} \\) where each patch \\( x^{i} \\) has the degradation of the corresponding area and \\( X \\) can cover the degradation of each region in the input LR image. Then, we crop the input LR image to generate the patches \\( Y = \\{y^{i}\\} \\), which aims to learn a downscaled image (e.g., by a factor of 2 or 4) such that its degradation is approximate to that of the patches \\( X \\) (see Sec. 3.4). Finally, we use known downsampling operation to degrade patches \\( Y \\) for generating patches \\( X_{b} = \\{x_{b}^{i}\\} \\) of the same size with \\( x^{i} \\) for degradation-adaptive regression learning. After obtaining training data \\( X \\), \\( X_{b} \\), and \\( Y \\), we will train our network to learn correction filters as shown in Fig. 2 (a)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.569, + 0.848, + 0.585 + ], + "angle": 0, + "content": "3.4. Spatial-Variant Degradation Estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.775 + ], + "angle": 0, + "content": "\\(X\\) and \\(X_{b}\\) are not paired, which leads to the correction filters are unable to be learned directly. Thus, we adopt the GAN-based method to learn \\(X_{c} = \\{x_{c}^{i}\\}\\) with the same degradation as \\(X\\) through a GAN. Specially, we employ a degradation generator \\(G\\) and a discriminator \\(D\\), as shown in Fig. 2 (a). Different from KernelGAN [2] which only learns one global invariant degenerate kernel, we will learn spatially variant degradation for each local patch \\(x_{c}^{i}\\). In this way, we can learn \\(X_{c}\\) to cover the degradation of each region for improving performance. In addition, we propose a novel degradation metric (DM) loss (see Sec. 3.6) to learn more accurate degradation in \\(x_{i}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.837, + 0.802 + ], + "angle": 0, + "content": "3.5. Learning Correction Filters via DARM" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.81, + 0.894, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 2 (a), we adopt paired training data \\( X_{c} \\) and \\( X_{b} \\) to learn correction filters by training our DARM through L1 loss and DM loss. We also train our network on unpaired training data \\( X \\) and \\( X_{b} \\) by DM loss. The output of \\( X_{c} \\) and \\( X \\) through DARM can be expressed as \\( X_{b^{\\prime}} = \\{x_{b^{\\prime}}^{i}\\} \\) and \\( X_{a} = \\{x_{a}^{i}\\} \\), respectively. Notably, our DARM learns a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12368" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.318, + 0.106 + ], + "angle": 0, + "content": "correction filter for each input pixel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.469, + 0.182 + ], + "angle": 0, + "content": "Our key idea lies on the total probability theorem and the additivity of normal distribution. We can obtain the correction filter by combining multiple Gaussian filters. Specifically, a correction filter \\( F^i \\) can be represented as a linear combination of a set of underlying base Gaussian filters:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.193, + 0.47, + 0.236 + ], + "angle": 0, + "content": "\\[\nF ^ {i} = \\Phi^ {i} \\mathbb {D} = \\sum_ {j = 1} ^ {N} \\theta_ {j} ^ {i} f _ {j}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.248, + 0.469, + 0.369 + ], + "angle": 0, + "content": "where \\( F = \\mathbb{R}^{HW \\times (k \\times k)} \\) (\\( k \\) is the kernel size which is empirically set to 5 in our experiments) denotes the learned correction filters for each pixel in the input image of size \\( H \\times W \\); \\( \\Phi = \\mathbb{R}^{HW \\times N} \\) denotes the learned linear combination coefficients for each pixel; The dictionary \\( \\mathbb{D} = \\mathbb{R}^{N \\times (k \\times k)} \\) consists of 72 Gaussian and difference of Gaussians (DoG) filters [19], which can help to increase the visibility of details accurately learn correction filters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.469, + 0.476 + ], + "angle": 0, + "content": "For the purpose of efficiency, we adopt a lightweight residual network for DARM via learning linear combination coefficients \\(\\Phi\\). It mainly consists of two residual channel attention blocks (RCAB) [51] to learn deep feature, the convolutional layers in the head to extract the shallow feature of the input image, and the final convolutional layers to generate combination coefficients." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.23, + 0.5 + ], + "angle": 0, + "content": "3.6. Loss Functions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.469, + 0.554 + ], + "angle": 0, + "content": "Adversarial loss. We adopt GAN-based method to learn spatially variant degradations of LR image. The adversarial loss for the degradation generator \\(G\\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.565, + 0.469, + 0.583 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {g a n} = \\mathbb {E} [ D (G (y ^ {i})) - 1 ] ^ {2} + \\mathcal {R}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.469, + 0.655 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}\\) denotes the regularization term which applies realistic explicit priors [2]. The discriminator \\(D\\) tries to distinguish degradations generated by \\(G\\) from \\(x^i\\) of input LR image and the constrain of \\(D\\) can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.665, + 0.469, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D} = \\mathbb {E} \\left[ D \\left(x ^ {i}\\right) - 1\\right) ^ {2} ] + \\mathbb {E} \\left[ D \\left(G \\left(y ^ {i}\\right)\\right) ^ {2} \\right]. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.469, + 0.769 + ], + "angle": 0, + "content": "Pixelwise loss. It is used to accelerate the convergence of DRAM. Besides, it can effectively compensate for the structural distortion caused by GAN. We use L1 loss to constrain the results generated by DASR and SR model. The mathematic formulation is:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.782, + 0.469, + 0.8 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p i x} = \\left| \\left| x _ {b} ^ {i} - x _ {b ^ {\\prime}} ^ {i} \\right| \\right| _ {1} + \\left| \\left| y ^ {i} - S R \\left(x _ {b ^ {\\prime}} ^ {i}\\right) \\right| \\right| _ {1}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.81, + 0.429, + 0.825 + ], + "angle": 0, + "content": "where \\( SR(*) \\) denotes an off-the-shelf super-resolver." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Degradation metric loss. It is difficult to estimate complex degradations accurately via single adversarial learning in real-world scenarios. To overcome this problem, we propose a novel degradation metric (DM) loss which maps the complex degradation into a metric space for effective" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.09, + 0.855, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.2, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Figure 4. Architecture of degradation score estimation module (DSEM), which mainly consist of three Resblocks [25], an average pooling layer, a sigmoid layer, and a full connection layer." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.268, + 0.892, + 0.342 + ], + "angle": 0, + "content": "constraint. Specially, we use a degradation score estimation module (DSEM) to model the distance between target degradation and estimated degradation. We use \\( x^{i} \\) and \\( x_{b}^{i} \\) as anchor samples to train the metric space as shown in Fig. 4. The mathematical formulation is elaborated as:" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.351, + 0.892, + 0.393 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a c} = \\frac {1}{N} \\sum_ {i} ^ {N} \\left(\\left| \\left| S \\left(x _ {b} ^ {i}\\right) \\right| \\right| _ {2} ^ {2} + \\left| \\left| S \\left(x ^ {i}\\right) - 1 \\right| \\right| _ {2} ^ {2}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.405, + 0.892, + 0.48 + ], + "angle": 0, + "content": "where \\( S(*) \\) denotes the degradation score estimation operation, which is implemented by DSEM. Then, we use DM loss from two parts, one is the result generated by downscale generator \\( G \\), and the other one is the result generated by DARM. The mathematical formulation is elaborated as:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.491, + 0.891, + 0.53 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {d m l} = \\left| \\left| S \\left(x _ {b} ^ {i}\\right) - S \\left(x _ {b ^ {\\prime}} ^ {i}\\right) \\right| \\right| _ {2} ^ {2} + \\left| \\left| S \\left(x ^ {i}\\right) - S (G \\left(y ^ {i}\\right)) \\right| \\right| _ {2} ^ {2} \\\\ + \\left\\| S \\left(x ^ {i}\\right) - S \\left(x _ {a} ^ {i}\\right) \\right\\| _ {2} ^ {2}. \\tag {12} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.542, + 0.892, + 0.571 + ], + "angle": 0, + "content": "Full objective. Mathematically, the total loss function for our method can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.584, + 0.891, + 0.601 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {A l l} = \\mathcal {L} _ {g a n} + \\lambda_ {1} \\mathcal {L} _ {p i x} + \\lambda_ {2} \\mathcal {L} _ {d m l}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.613, + 0.892, + 0.643 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are two empirical hyper-parameters that are set to 2.5 and 0.5, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.657, + 0.634, + 0.674 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.717, + 0.697 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We conduct experiments on real-world datasets (RealSRSet [47]) and synthetic datasets (NTIRE2017 [36] and NTIRE2018 [37]). The results are evaluated by the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) [41], and learned perceptual image patch similarity (LPIPS) [50]. PSNR and SSIM are evaluated on the Y channel of transformed YCbCr, while LPIPS is on RGB. We train our network by each iteration with 16 batches which consist of paired patches from the LR input. The patches \\(32 \\times 32\\) and \\(128 \\times 128\\) (\\(x^i\\) and \\(y^i\\) in Fig. 3) are for scaling \\(\\times 4\\). The patches \\(64 \\times 64\\) and \\(128 \\times 128\\) are for scaling \\(\\times 2\\). The iteration number is set to 3,000, and the optimizer is the Adam [16] with \\(\\beta 1 = 0.9\\), \\(\\beta 2 = 0.999\\). The initial" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12369" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.891, + 0.115 + ], + "angle": 0, + "content": "Table 1. Quantitative results on NTIRE2017 [36] and NTIRE2018 [37] testing datasets for scaling factor \\(\\times 4\\). \\(\\uparrow\\) denotes the larger the better. \\(\\downarrow\\) denotes the smaller the better. Red color indicates the best performance, and blue color indicates the second best performance." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.115, + 0.894, + 0.364 + ], + "angle": 0, + "content": "
Methods2017Track22018Track22018Track32018Track4
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
SRGAN [18]22.990.58890.466918.990.45820.612719.750.47060.624119.500.46870.6150
SRFBN-s [21]23.070.60430.484518.870.48860.608519.780.50430.625119.510.50200.6112
KernelGAN [2] + ZSSR [34]22.490.58000.495118.430.54500.573919.750.57500.600019.360.57470.5774
BlindSR [5]21.610.54830.482018.350.40960.608819.310.42430.619218.900.41710.6102
IKC [12]22.280.57380.468318.720.54880.568619.810.57160.595019.420.57130.5723
SRGAN [18] + Correction Filter [14]20.980.57760.582118.730.55550.614119.070.55710.628818.950.56610.6147
SRFBN-s [21] + Correction Filter [14]20.980.58510.602318.740.56310.625519.100.56590.649918.980.57460.6313
USRNet [46]22.850.60290.511019.000.56410.570019.970.58250.601619.670.58530.5795
MANet [23]21.410.55790.491118.660.47440.609019.310.48330.628819.010.47620.6154
DIP-FKP [24]20.490.53360.505018.110.55280.578118.720.56090.608618.450.56050.5869
DASR [40]22.920.59680.478018.920.55790.569019.830.57480.592919.530.57820.5712
BSRDM [45]21.630.57970.558118.720.54830.594619.570.56570.612419.180.55960.6001
Ours + SRGAN [18]23.090.60170.463720.240.57410.608821.040.58450.617321.180.58870.6021
Ours + SRFBN-s [21]23.350.61260.506320.320.57870.622521.110.58590.629121.340.59480.6021
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.386, + 0.468, + 0.413 + ], + "angle": 0, + "content": "Table 2. Quantitative results on NTIRE2017 Track2 [36] testing dataset for scaling factor \\(\\times 2\\)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.414, + 0.462, + 0.585 + ], + "angle": 0, + "content": "
MethodsPSNR↑SSIM↑LPIPS↓
SRFBN-s [21]26.430.72460.3437
KernelGAN [2] + ZSSR [34]26.340.72880.3295
BlindSR [5]27.220.75390.3054
SRFBN-s [21] + Correction Filter [14]23.440.61250.3482
USRNet [46]26.520.73680.3710
MANet [23]27.920.78180.3086
DIP-FKP [24]26.290.74920.3188
DASR [40]26.380.72220.3335
BSRDM [45]26.650.73030.4432
Ours + SRFBN-s [21]27.990.78220.3513
" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.599, + 0.157, + 0.636 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.164, + 0.599, + 0.387, + 0.714 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.392, + 0.599, + 0.469, + 0.636 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.717, + 0.468, + 0.745 + ], + "angle": 0, + "content": "Figure 5. Illustration of degradation estimation for MANet [23] and DIP-FKP [24] on “\\(0801 \\times 4m\\) .png” in NTIRE2018 track2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.469, + 0.832 + ], + "angle": 0, + "content": "learning rate is \\(10^{-3}\\) which will be decayed by 0.5 after each 750 iterations. Data augmentation includes randomly rotating 90, 180, 270 degrees, and horizontally flipping. We implement experiments with PyTorch1.12.0 on an NVIDIA Geforce RTX 3090 GPU." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.846, + 0.385, + 0.863 + ], + "angle": 0, + "content": "4.2. Experiments on Synthetic Datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We conduct experiments on four synthetic benchmarks: track2 of NTIRE2017 [36] and track2, track3, and track4" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.892, + 0.601 + ], + "angle": 0, + "content": "of NTIRE2018 [37]. The degradations in these datasets are complex and unknown. Notably, the official uses same degradation operators within an image. But, as shown in Fig. 5, we use MANet [23] and DIP-FKP [24] to estimate the degradation of different regions in LR image, we find that the degradation of degraded image is spatially variant. We think that the given HR images are spatially variant degraded from the real HR ones due to camera acquisition in complex scenes, which make the LR images are spatially variant. We compare with unsupervised and supervised methods, including SRGAN [18], SRFBNs [21], KernelGAN [2], ZSSR [34], BlindSR [5], IKC [12], Correction_Filter [14], USRNet [46], DIP-FKP [24], MANet [23] and BSRDM [45]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.621, + 0.725, + 0.635 + ], + "angle": 0, + "content": "4.2.1 Quantitative Evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.734 + ], + "angle": 0, + "content": "The detailed experimental results are listed in Tab. 1 and Tab. 2. Note that our method does not have a design module for denoising, so we employ CBM3D [6] to conduct on track2, track3, and track4 of NTIRE2018 datasets firstly. We also use the same operation for other methods without the ability of denoising for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparing with trained SR methods. As listed in Tab. 1 and Tab. 2, our method can improve the performance of SRGAN in all testing datasets on PSNR/SSIM/LPIPS. Our method also improves the performance of SRFBN-s in all testing datasets on PSNR/SSIM for scaling factor \\(\\times 2\\) and \\(\\times 4\\). We noticed that our method did not improve the LPIPS values of SRFBN-s. This phenomenon often occurs in PSNR-Oriented methods (e.g., EDSR, RCAN). Our method can improve the performance of perceptual-driven methods (e.g., SRGAN, ESRGAN) in all indicators, including LPIPS. PSNR-Oriented methods focus on achiev-" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12370" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.895, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.482, + 0.877, + 0.499 + ], + "angle": 0, + "content": "Figure 6. Visual comparisons of different methods on 2017Track2 [36], 2018Track2 [37], and 2018Track4 [37]. Zoom in for best view." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.508, + 0.892, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.164, + 0.673, + 0.807, + 0.688 + ], + "angle": 0, + "content": "Figure 7. Visual comparisons of different method for \\(\\times 4\\) on RealSRSet [47] dataset. Zoom in for best view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.471, + 0.803 + ], + "angle": 0, + "content": "ing high PSNR and tend to generate images with too smooth and lost details (More analysis in Supp. Materials). Although our method can effectively recover LR images, the characteristics of these methods still lead to LPIPS degradation. But in general, our method can consistently improve the performance of off-the-shelf super-resolvers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Comparing with Correction_Filter. As shown in Tab. 1 and Tab. 2, Correction_Filter failed to improve the performance of SRFBN-s and SRGAN. The performance of Correction_Filter greatly relies on the accuracy of degradation estimation. However, it is difficult to solve complex degradation by their iterative approximation strategies. Be-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.712, + 0.894, + 0.773 + ], + "angle": 0, + "content": "sides, they only considers the spatially invariant degradation, failing to tackle spatially ones (More comparison are in Supp. Materials). The experimental results show that our method is more effective than Correction_Filter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Comparing with spatially-variant SR methods. From Tab. 2, we can see that the performance of SRFBN-s is far lower than BlindSR and MANet in all indicators. While SRFBN-s equipped our method outperforms BlindSR and MANet by 0.77 dB/0.0283 and 0.07 dB/0.0004 in terms of PSNR/SSIM, respectively. In Tab. 1, our method can help SRGAN and SRFBN-s outperforms Blind and MANet on all testing datasets in terms of PSRN/SSIM. The experi" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12371" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "mental results verify that our method is superior in solving spatial-variant degradation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.121, + 0.471, + 0.273 + ], + "angle": 0, + "content": "Comparing with other blind methods. As listed in Tab. 1, Ours+SRFBN-s achieves the best SSIM and PSNR on all datasets. Ours+SRFBN-s outperforms BSRDM by 1.72 dB/0.0329 and 2.16 dB/0.0352 on 2017Track2 and 2018Track4 on PSNR/SSIM, respectively. Ours+SRFBN-s outperforms DASR by 1.4 dB/0.0208 and 1.81 dB/0.0166 on 2018Track2 and 2018Track4 on PSNR/SSIM, respectively. Tab. 2 also verify that our method outperforms other blind methods. We conclude that our method is effective and has strong degradation-adaptive ability." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.287, + 0.209, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.435, + 0.197, + 0.446 + ], + "angle": 0, + "content": "(a) Input LR image" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.287, + 0.338, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.22, + 0.435, + 0.338, + 0.445 + ], + "angle": 0, + "content": "(b) Corrected LR image" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.287, + 0.468, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.346, + 0.435, + 0.465, + 0.445 + ], + "angle": 0, + "content": "(c) Corrected LR image" + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.446, + 0.329, + 0.456 + ], + "angle": 0, + "content": "(without DM Loss)" + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.46, + 0.412, + 0.474 + ], + "angle": 0, + "content": "Figure 8. Visual ablation study about DM loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.496, + 0.294, + 0.511 + ], + "angle": 0, + "content": "4.2.2 Qualitative Evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.47, + 0.732 + ], + "angle": 0, + "content": "Fig. 6 are representative visual results. As shown in Fig. 6 (a), our method can generate sharper and cleaner SR images, but most other methods generate details with blurry or artifacts. Although the SR images generated by BSRDM seem to be clear, they lose some important details. In Fig. 6 (b), Ours+SRFBN-s can correctly restore font textures, while most other methods will produce incorrect textures. Although BSRDM generates font texture with good visual effects, many distortions exist. In Fig. 6 (c), Ours+SRFBN-s recovers clear and natural details, while other methods are prone to generate detailed textures with visual aliasing and artifacts. Notably, our method can greatly improves the visual quality of SRFBNs, demonstrating our method's effectiveness." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.396, + 0.758 + ], + "angle": 0, + "content": "4.3. Experiments on Real-World Dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We also conduct experiments on RealSRSet [47] dataset. (Due to most images in RealSRSet are small size, we reduce the cropped image size in Sec 4.1.) As mentioned in [47, 45], current non-reference metrics (e.g., NIQE [28], NRQM [27], and PI [1]) are not consistent with the perceptual visual system. Therefore, we only compare visual results. Fig. 7 shows the visual results on two representative images. Apparently, Ours+SRFBN-s generates improved visual results than other methods. In the first examples in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "Fig. 7, most other methods tend to generate noises or artifacts. USRNet generated observable visual results but with too many white lines that should not exist. BSRDM generates unrealistic and discontinuous lines with some distortions. In the second example in Fig. 7, most other methods cannot finely deal with the hair and tend to produce unrealistic detailed textures with visual aliasing. In contrast, our Ours+SRFBN-s reconstructs clear and natural details." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.221, + 0.892, + 0.248 + ], + "angle": 0, + "content": "Table 3. Ablation study of DM Loss on NTIRE2017 Track2 testing dataset for scaling factor \\( \\times 4 \\) ." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.248, + 0.888, + 0.329 + ], + "angle": 0, + "content": "
Method\\( \\mathcal{L}_{gan} \\)\\( \\mathcal{L}_{pix} \\)\\( \\mathcal{L}_{dml} \\)PSNR↑SSIM↑LPIPS↓
Ours+SRFBN-s✓16.240.37570.7231
Ours+SRFBN-s✓21.890.56240.6532
Ours+SRFBN-s✓✓22.060.57040.6430
Ours+SRFBN-s✓✓✓23.350.61260.5063
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.356, + 0.653, + 0.372 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.501 + ], + "angle": 0, + "content": "About DM Loss. To verify the effectiveness of DM loss, we conduct experiments on the 2017Track2 dataset. As listed in Tab. 3, Ours+SRFBN-s outperforms Ours +SRFBN-s (without \\(\\mathcal{L}_{dml}\\)) on scale \\(\\times 4\\) by \\(1.29\\mathrm{dB}\\) on PSNR, 0.0423 on SISM, and 0.1367 on LPIPS, respectively. Besides, our DM loss can clearly improve the accuracy of degradation correction of corrected LR image (Fig. 8 (c)), compared with our model without DM loss (Fig. 8 (b))." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.511, + 0.892, + 0.539 + ], + "angle": 0, + "content": "Table 4. Ablation study of filter dictionary on NTIRE2017 Track2 testing dataset for scaling factor \\( \\times 4 \\) ." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.539, + 0.892, + 0.619 + ], + "angle": 0, + "content": "
Filter TypeNumberPSNR↑SSIM↑LPIPS↓
G + DoG [19]7223.350.61260.5063
RAISR [31]7222.120.53340.6430
Learned7222.440.53430.6266
G + DoG [19]2423.170.61140.5145
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.802 + ], + "angle": 0, + "content": "About the base Filter Dictionary. We conducted experiments on the 2017Track2 dataset to verify the chosen of the base filter dictionary. We compare with RAISR filters [31] and filters directly learned by networks. As listed in Tab. 4, it is clear that 72 Gaussian and DoG combination achieves the best result. Tab. 4 also shows that the result with 72 basic filters is better than the dictionary with 24 basic filters. Besides, the filters size with \\(5 \\times 5\\) for each pixel is sufficient to restore complex real-world images. Various kernel sizes definitely can enhance performance but introduce great computational costs." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.813, + 0.89, + 0.827 + ], + "angle": 0, + "content": "Table 5. Ablation study on trained SR with different degradations." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.827, + 0.892, + 0.898 + ], + "angle": 0, + "content": "
Method2018Track22018Track3
Ours + SRFBN-s(Bicubic)20.32/0.578721.11/05859
Ours + SRFBN-s(Gaussian)20.31/0.578721.11/0.5858
Ours + SRFBN-s(Lanczos)20.32/0.578721.13/0.5859
" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12372" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "About trained SR with different degradation. We choose two different degradations (Gaussian blur and Lanczos) to train SRFBN-s on DIV2K dataset for scaling factor \\(\\times 4\\), respectively. Tab. 5 lists the detailed results on NTIRE 2018 track2 and NTIRE 2018 track3. The results on the two degradation models are nearly consistent with bicubic degradation, which demonstrates that our method can adapt to any known degeneration in a trained model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.227, + 0.196, + 0.243 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.252, + 0.473, + 0.435 + ], + "angle": 0, + "content": "In this paper, we propose a novel blind image superresolution method that corrects the degradations of an LR input to that of the training data in an off-the-shelf method. Specifically, we propose an innovative unsupervised method of learning correction filter via a linearly-assembled pixel DARM for correcting the LR image's degradation to the known one in a spatially variant way for each testing image. Besides, we propose a degradation metric loss to map the unquantifiable degradation to guarantee the accuracy of degradation correction. Extensive experiments verify the superior performance of our method both quantitatively and qualitatively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.449, + 0.216, + 0.466 + ], + "angle": 0, + "content": "6. Acknowledge" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.472, + 0.549 + ], + "angle": 0, + "content": "The research is supported by National Key Research and Development Program of China (2020AAA0109700), National Science Fund for Distinguished Young Scholars(62125601), National Natural Science Foundation of China (62172035, 62076024, 62006018)." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.564, + 0.175, + 0.58 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.588, + 0.47, + 0.645 + ], + "angle": 0, + "content": "[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 126-135, 2017. 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.647, + 0.472, + 0.7 + ], + "angle": 0, + "content": "[2] Sefi Bell-Kligler, Assaf Shocher, and Michal Irani. 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To address the problem, we propose an innovative unsupervised method of Learning Correction Filter via Degradation-Adaptive Regression for Blind Single Image Super-Resolution. Highly inspired by the generalized sampling theory, our method aims to enhance the strength of off-the-shelf SR methods trained on known degradations and adapt to unknown complex degradations to generate improved results. Specifically, we first conduct degradation estimation for each local image region by learning the internal distribution in an unsupervised manner via GAN. Instead of assuming degradation are spatially invariant across the whole image, we learn correction filters to adjust degradations to known degradations in a spatially variant way by a novel linearly-assembled pixel degradation-adaptive regression module (DARM). DARM is lightweight and easy to optimize on a dictionary of multiple pre-defined filter bases. Extensive experiments on synthetic and real-world datasets verify the effectiveness of our method both qualitatively and quantitatively. Code can be available at: https://github.com/edbca/DARSR. + +# 1. Introduction + +Single image super-resolution (SISR) aims to recover a photo-realistic HR image from its LR counterpart. As a fundamental computer vision task, SISR has been widely used in various applications, such as enhancing the images' visual perception on high-resolution devices and improving the image quality for other vision tasks [7]. In recent years, + +![](images/e96fb24e240c4ce66d893ed3218e71b41156fe37ed4ca3c87e9e6c95b727be7b.jpg) +(a) Most degradation estimation strategies + +![](images/63ff87a910f583a2557a7cea54b24daa542fcdd2d4cde6bae75444e0515395f6.jpg) +(b) Our method +Figure 1. Illustration of most degradation estimation strategies for blindSR and our method. (a) Most methods assume degradations are spatially invariant and estimate a single degradation for the whole image. (b) Our method can learn correction filters to adjust the degradations to a known degradation in a spatially variant way. + +a multiplicity of deep learning-based SISR methods have been proposed [33, 18, 25, 52, 51, 8, 29, 54] and achieved substantial performance improvement. + +Typically, training and testing LR images in existing SISR approaches are simulated from a large collection of HR images. As a pioneer work, Dong et al. [9] first introduced a three-layer convolutional neural network in SISR to learn LR-HR mapping. Zhang et al. [51] proposed a channel attention mechanism to build a deep model for SISR. Liang et al. [22] proposed a baseline model SwinIR for SISR based on the transformer mechanism. In these methods, the LR images are often generated by limited numbers of fixed degradations (e.g., Bicubic or blur-downscale). However, the degradation process in real-world scenarios is extremely complicated and unpredictable. Although existing methods [25, 51, 29, 21, 18, 8] have achieved promising performance, they often encounter severe performance drops when the degradation is not well covered in training. + +Recently, many works have attempted to address the challenging degradation adaptation problem by explicit or implicit degradation modeling in a blind or non-blind manner. SRMD [48] learns an SR model with training data covering a large set of degradation maps, which are modeled with blur kernel and noise. Following SRMD, UDVD [43] proposes a single unified dynamic network trained for various degradations to improve performance. However, in most practical applications, blur kernels are not available. They can hardly deal with the LR inputs with degradations out of their modeling scope. To tackle this problem, some methods [34, 35, 2, 11] estimate a blur kernel from each input LR image for adapting to complex degradations. IKC [12] proposes to correct kernel estimation in an iterative way to approach a satisfactory result gradually. ZSSR [34] learns degradation kernels of LR images via internal statistics for every image in a self-supervised manner. Pseudosupervision [53] combines the forward SR reconstruction path in CinCGAN [44] architecture with degradation learning to deal with the domain shift problem. In addition, Hussein et al. [14] proposed a correction filter strategy on the signal that is sampled by a certain basis can be reconstructed by a different basis, for modifying an LR input to match the SR model with a pre-defined degradation. These methods' generalization ability still greatly relies on the accuracy of degradation estimation or training data distribution. In addition, as shown in Fig. 1 (a), they assume degradations are spatially invariant and only estimate a single degradation for the whole image. Such an assumption is rarely applicable for real images whose regions (e.g., edges, corners) are discriminative for degradation estimation. + +To fully take advantage of the off-the-shelf superresolvers, we try to robustify the degradation of LR input without hurting useful information for efficiently adapting to practical applications. A brief illustration and comparison to the existing degradation estimation strategy for blindSR are presented in Fig. 1. Specifically, we propose an innovative unsupervised method of learning correction filter via a linearly-assembled pixel degradation-adaptive regression module (DARM) for correcting the LR image's degradation to the known one in a spatially variant way. Our DARM is highly lightweight and can be easily optimized over a dictionary of multiple pre-defined filter bases. In this way, our method can conduct correction filtering and help off-the-shelf SISR models to adapt to complex degradations on every testing image efficiently. In addition, we propose a degradation metric (DM) loss to learning to map the unquantifiable degradation in a metric space to guarantee the accuracy of degradation correction. + +In summary, our main contributions are three-fold: + +- We propose an innovative unsupervised strategy by learning correction filters for Blind Single Image Super-Resolution in a spatially variant way, greatly en + +hancing the adapting ability of trained super-resolvers to unknown complex degradations. + +- We propose a lightweight degradation-adaptive regression module (DARM) that could accurately yet efficiently learn correction filters over a dictionary of multiple pre-defined filter bases. +- We propose a novel degradation metric (DM) loss via metric learning to map the unquantifiable degradation in a metric space to effectively improve the accuracy of degradation correction. +- Extensive experiments on synthetic datasets and real images verify that our method can consistently improve the performance of the off-the-shelf superresolvers both qualitatively and quantitatively. + +# 2. Related Work + +# 2.1. Predefined-Degradation based SR + +Dong et al. [9] firstly proposed a three consecutive convolutional neural network in SISR to learn a complex LR-HR mapping. Kim et al. [15] increased the depth of the network via a skip connection for stable training. To achieve promising performance, most methods adopt residual architecture [38, 52, 26]. EDSR [25] removes the batch normalization layer in a residual block and increasing the network depth. RCAN [51], SAN [8] and HAN [29] introduce the attention mechanism to draw more high-frequency information to further improve the performance. Furthermore, SwinIR [22], IPT [4], GRL [20] employ the transformer mechanism for constantly refreshing the state-of-the-art of SISR. However, these methods perform promisingly under a single degradation model (e.g., bicubic and blur-downscale degradation models); they tend to produce over-sharped or blurry results if the degradations present in the testing deviate from training. + +# 2.2. Degradation-Learning based SR + +Multiple degradation modeling based SR. By modeling multiple degradations, this type of method can produce good results for LR inputs covered by the training dataset. SRMD [48] proposes to directly concatenate an LR input image with its degradation map as a unified input to the SR model, thus allowing feature adaptation according to the specific degradation and covering multiple degradation types in a single model. DPSR [49] incorporates a super-resolution network into a MAP-based iterative optimization scheme which solves the HR image by minimizing objective functions. Similar to DPSR, USRNet [46] proposes an end-to-end trainable unfolding network that leverages both learning-based methods and model-based methods by unfolding the MAP inference via a half-quadratic splitting algorithm. Luo et al. [13] adopted an alternating optimization + +![](images/207885a8c046b4dba7e9f0e989ee6be9558b1ba334655cec53be0afeec8d273a.jpg) + +![](images/0dfa40cd6bae6119b1e8bc06dee33afffc586c8bf29e00d32412ecf77f058eb8.jpg) +(a) Learning correction filter via Degradation-Adaptive Regression +(b) Degradation correction for input LR image via a traind SR model +Figure 2. Architecture of our method. (a) Illustration of the learning of correction filters. (b) Illustration of the degradation correction. + +![](images/ee6187886ddd3c70f391bc5da75bccf24e6795273bc95fa5f25052991ae9c88b.jpg) +x,y, x b Training data Discriminator + +Degradation Generator + +Sigmoid + +Element-wise product + +Element-wise sum + +DM Loss + +Degradation Metric loss + +algorithm to estimate blur kernel and restore SR image in a single model. However, the performance of these methods still relies on accurate estimation of input kernel, which is challenging on arbitrary LR images. + +Degradation estimation based SR. Gu et al. [12] proposed a general framework for blind SR by using self-similarity to recover the blur kernel and the HR image jointly. KernelGAN [2] interprets the maximization of patch recurrence within a single image as a data distribution learning problem and generates downscaled LR images by learning the internal patch distribution of the testing LR image. Shocher et al. [34] proposed a zero-shot super-resolution (ZSSR) method which trains image-specific on the testing LR image to take the degradation parameters and estimate blur kernel for improving the performance. Afterward, Soh et al. [35] proposed to learn an image-specific degradation simulation network together with a zero-shot image-specific super-solution network which exploits the depth information of the image to extract an unpaired high/low resolution patch collection to train the network. Liang et al. [24] proposed a novel method to incorporate a flow-based kernel prior into the framework by learning an invertible mapping between the anisotropic Gaussian kernel distribution and a tractable latent distribution. While these methods consider degradation are spatially invariant and only estimate a single degradation for input image. Cornillere et al. [5] pro + +posed a degradation-aware SR network to adapt spatially variant degradations. MANet [23] uses mutual affine convolution in their network for spatially variant kernel estimation. However, these methods greatly rely on the coverage of degradation modeling or training data distribution. + +# 3. Our Method + +# 3.1. Preliminaries + +The SISR degradation model can be mathematically formulated as: + +$$ +x = (y \otimes k) \downarrow_ {s}, \tag {1} +$$ + +where $y$ denotes the HR image; $x$ denotes the LR image; $k$ is the blur kernel; $\otimes$ denotes convolution operator; $\downarrow_{s}$ denotes sub-sampling operator with stride of $s$ . Note that Eq. 1 can be written as: + +$$ +x = D y, \tag {2} +$$ + +where $D$ represents degradation operator. As assumed by Hussein et al [14], the signal $y$ can be perfectly recovered from its samples $x$ by the operator $U(DU)^{-1}$ as: + +$$ +y = U (D U) ^ {- 1} x = U (D U) ^ {- 1} D y, \tag {3} +$$ + +where $U$ is an upsampling operator which is the adjoint operator of $D$ . Eq. 3 indicates that the image $y$ resides in the linear subspace can be spanned by the known degradation. + +Therefore, it can be perfectly recovered from the observations $x_{k}$ by applying the pseudo inverse of $U_{k}$ as: + +$$ +y ^ {\prime} = U _ {k} \left(D _ {k} U _ {k}\right) ^ {- 1} D _ {k} y = U _ {k} \left(D _ {k} U _ {k}\right) ^ {- 1} x _ {k}, \tag {4} +$$ + +where $D_{k}$ denotes known degradation operation; $x_{k}$ denotes known degraded image; $U_{k}$ denotes a DNN super-resolver trained under the assumption of known degradation and it can handle the $x_{k}$ quite well with a learned prior. + +According to the generalization of classical Whittaker-Shannon sampling theorem [17, 30, 32, 42], some works [3, 10, 39] consider that a signal sampled by a certain basis can be reconstructed by different basis. By combining a correction filter with a reconstruction kernel, a sampled signal can be reconstructed. The correction filter can transform the sampling coefficients associated with the sampling kernel to coefficients that fit the reconstruction kernel. Given a degraded LR image $x_{u}$ obtained by a unknown degradation $D_{u}$ , $x_{u} = D_{u}y$ . Then, the $y'$ can be reconstructed as: + +$$ +y ^ {\prime} = U _ {k} C x _ {u} = U _ {k} C D _ {u} y, \tag {5} +$$ + +where $C$ is a correction operator for $x_{u}$ . Combining Equation 4 and Eq. 5, we can find the expression of $C$ as follows: + +$$ +C = \left(D _ {u} U _ {k}\right) ^ {- 1} \Rightarrow C D _ {u} = U _ {k} ^ {- 1}. \tag {6} +$$ + +The operator $C$ can be applied simply as a convolution with a correction filter. Following Eq. 6, we first conduct spatial-variant degradation estimation to model $D_{u}$ , which learns the spatially variant degradations in $x_{u}$ . Then, we use our DARM to learn the correction filters $C$ for correcting the degradations of $x_{u}$ to pre-defined degradation. Finally, we employ a trained $U_{k}$ to super-resolve the corrected image. + +Our method mainly distinguishes from the work [14] in two respects: (1) The performance of the work [14] greatly relies on the accuracy of degradation estimation. In our method, we coherently combine degradation estimation with correction filter learning into a unified network, greatly improving the accuracy and adaptiveness; (2) The work [14] only considers the spatially invariant degradation situation, failing to adopt a correction filter to solve a natural image with complex degradations. In our method, we estimate degradations in a spatially variant way. + +# 3.2. Overview + +As shown in Fig. 2 (a), we learn correction filters via DARM in an unsupervised manner. Then, as shown in Fig. 2 (b), we use learned correction filters to correct the degradation of the input LR image to the pre-defined degradation. Finally, an off-the-shelf super-resolver trained by known degradation is used for upsampling the degradation adapted LR image for SR. The learning of correction filters mainly consists of three components: generation of training data from input LR image, spatial-variant degradation estimation, and learning correction filters through proposed degradation adaptation regression module. + +![](images/1349fba85821b237496bfc8133f2104d099ca7ebd95d696faf03e2f741305c91.jpg) +Figure 3. Illustration of the generation of training data from the input LR image. $X = \{x^{i}\}$ , $Y = \{y^{i}\}$ , and $X_{b} = \{x_{b}^{i}\}$ are used to train our proposed degradation-adaptive regression module. + +# 3.3. Generation of Training Data + +Given the input LR image, our goal is to correct complex degradations of all regions to the degradation (e.g. bicubic) in the off-the-shelf super-resolver. As shown in Fig. 3, we first crop the input LR image to generate the patches $X = \{x^{i}\}$ where each patch $x^{i}$ has the degradation of the corresponding area and $X$ can cover the degradation of each region in the input LR image. Then, we crop the input LR image to generate the patches $Y = \{y^{i}\}$ , which aims to learn a downscaled image (e.g., by a factor of 2 or 4) such that its degradation is approximate to that of the patches $X$ (see Sec. 3.4). Finally, we use known downsampling operation to degrade patches $Y$ for generating patches $X_{b} = \{x_{b}^{i}\}$ of the same size with $x^{i}$ for degradation-adaptive regression learning. After obtaining training data $X$ , $X_{b}$ , and $Y$ , we will train our network to learn correction filters as shown in Fig. 2 (a). + +# 3.4. Spatial-Variant Degradation Estimation. + +$X$ and $X_{b}$ are not paired, which leads to the correction filters are unable to be learned directly. Thus, we adopt the GAN-based method to learn $X_{c} = \{x_{c}^{i}\}$ with the same degradation as $X$ through a GAN. Specially, we employ a degradation generator $G$ and a discriminator $D$ , as shown in Fig. 2 (a). Different from KernelGAN [2] which only learns one global invariant degenerate kernel, we will learn spatially variant degradation for each local patch $x_{c}^{i}$ . In this way, we can learn $X_{c}$ to cover the degradation of each region for improving performance. In addition, we propose a novel degradation metric (DM) loss (see Sec. 3.6) to learn more accurate degradation in $x_{i}$ . + +# 3.5. Learning Correction Filters via DARM + +As shown in Fig. 2 (a), we adopt paired training data $X_{c}$ and $X_{b}$ to learn correction filters by training our DARM through L1 loss and DM loss. We also train our network on unpaired training data $X$ and $X_{b}$ by DM loss. The output of $X_{c}$ and $X$ through DARM can be expressed as $X_{b^{\prime}} = \{x_{b^{\prime}}^{i}\}$ and $X_{a} = \{x_{a}^{i}\}$ , respectively. Notably, our DARM learns a + +correction filter for each input pixel. + +Our key idea lies on the total probability theorem and the additivity of normal distribution. We can obtain the correction filter by combining multiple Gaussian filters. Specifically, a correction filter $F^i$ can be represented as a linear combination of a set of underlying base Gaussian filters: + +$$ +F ^ {i} = \Phi^ {i} \mathbb {D} = \sum_ {j = 1} ^ {N} \theta_ {j} ^ {i} f _ {j}, \tag {7} +$$ + +where $F = \mathbb{R}^{HW \times (k \times k)}$ ( $k$ is the kernel size which is empirically set to 5 in our experiments) denotes the learned correction filters for each pixel in the input image of size $H \times W$ ; $\Phi = \mathbb{R}^{HW \times N}$ denotes the learned linear combination coefficients for each pixel; The dictionary $\mathbb{D} = \mathbb{R}^{N \times (k \times k)}$ consists of 72 Gaussian and difference of Gaussians (DoG) filters [19], which can help to increase the visibility of details accurately learn correction filters. + +For the purpose of efficiency, we adopt a lightweight residual network for DARM via learning linear combination coefficients $\Phi$ . It mainly consists of two residual channel attention blocks (RCAB) [51] to learn deep feature, the convolutional layers in the head to extract the shallow feature of the input image, and the final convolutional layers to generate combination coefficients. + +# 3.6. Loss Functions + +Adversarial loss. We adopt GAN-based method to learn spatially variant degradations of LR image. The adversarial loss for the degradation generator $G$ can be formulated as: + +$$ +\mathcal {L} _ {g a n} = \mathbb {E} [ D (G (y ^ {i})) - 1 ] ^ {2} + \mathcal {R}, \tag {8} +$$ + +where $\mathcal{R}$ denotes the regularization term which applies realistic explicit priors [2]. The discriminator $D$ tries to distinguish degradations generated by $G$ from $x^i$ of input LR image and the constrain of $D$ can be formulated as: + +$$ +\mathcal {L} _ {D} = \mathbb {E} \left[ D \left(x ^ {i}\right) - 1\right) ^ {2} ] + \mathbb {E} \left[ D \left(G \left(y ^ {i}\right)\right) ^ {2} \right]. \tag {9} +$$ + +Pixelwise loss. It is used to accelerate the convergence of DRAM. Besides, it can effectively compensate for the structural distortion caused by GAN. We use L1 loss to constrain the results generated by DASR and SR model. The mathematic formulation is: + +$$ +\mathcal {L} _ {p i x} = \left| \left| x _ {b} ^ {i} - x _ {b ^ {\prime}} ^ {i} \right| \right| _ {1} + \left| \left| y ^ {i} - S R \left(x _ {b ^ {\prime}} ^ {i}\right) \right| \right| _ {1}, \tag {10} +$$ + +where $SR(*)$ denotes an off-the-shelf super-resolver. + +Degradation metric loss. It is difficult to estimate complex degradations accurately via single adversarial learning in real-world scenarios. To overcome this problem, we propose a novel degradation metric (DM) loss which maps the complex degradation into a metric space for effective + +![](images/485e6ebed9b107eda27615761f31f9adae26ebc2efa0944a47fb427e34603bd4.jpg) +Figure 4. Architecture of degradation score estimation module (DSEM), which mainly consist of three Resblocks [25], an average pooling layer, a sigmoid layer, and a full connection layer. + +constraint. Specially, we use a degradation score estimation module (DSEM) to model the distance between target degradation and estimated degradation. We use $x^{i}$ and $x_{b}^{i}$ as anchor samples to train the metric space as shown in Fig. 4. The mathematical formulation is elaborated as: + +$$ +\mathcal {L} _ {a c} = \frac {1}{N} \sum_ {i} ^ {N} \left(\left| \left| S \left(x _ {b} ^ {i}\right) \right| \right| _ {2} ^ {2} + \left| \left| S \left(x ^ {i}\right) - 1 \right| \right| _ {2} ^ {2}\right), \tag {11} +$$ + +where $S(*)$ denotes the degradation score estimation operation, which is implemented by DSEM. Then, we use DM loss from two parts, one is the result generated by downscale generator $G$ , and the other one is the result generated by DARM. The mathematical formulation is elaborated as: + +$$ +\begin{array}{l} \mathcal {L} _ {d m l} = \left| \left| S \left(x _ {b} ^ {i}\right) - S \left(x _ {b ^ {\prime}} ^ {i}\right) \right| \right| _ {2} ^ {2} + \left| \left| S \left(x ^ {i}\right) - S (G \left(y ^ {i}\right)) \right| \right| _ {2} ^ {2} \\ + \left\| S \left(x ^ {i}\right) - S \left(x _ {a} ^ {i}\right) \right\| _ {2} ^ {2}. \tag {12} \\ \end{array} +$$ + +Full objective. Mathematically, the total loss function for our method can be formulated as: + +$$ +\mathcal {L} _ {A l l} = \mathcal {L} _ {g a n} + \lambda_ {1} \mathcal {L} _ {p i x} + \lambda_ {2} \mathcal {L} _ {d m l}, \tag {13} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are two empirical hyper-parameters that are set to 2.5 and 0.5, respectively. + +# 4. Experiments + +# 4.1. Implementation Details + +We conduct experiments on real-world datasets (RealSRSet [47]) and synthetic datasets (NTIRE2017 [36] and NTIRE2018 [37]). The results are evaluated by the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) [41], and learned perceptual image patch similarity (LPIPS) [50]. PSNR and SSIM are evaluated on the Y channel of transformed YCbCr, while LPIPS is on RGB. We train our network by each iteration with 16 batches which consist of paired patches from the LR input. The patches $32 \times 32$ and $128 \times 128$ ( $x^i$ and $y^i$ in Fig. 3) are for scaling $\times 4$ . The patches $64 \times 64$ and $128 \times 128$ are for scaling $\times 2$ . The iteration number is set to 3,000, and the optimizer is the Adam [16] with $\beta 1 = 0.9$ , $\beta 2 = 0.999$ . The initial + +Table 1. Quantitative results on NTIRE2017 [36] and NTIRE2018 [37] testing datasets for scaling factor $\times 4$ . $\uparrow$ denotes the larger the better. $\downarrow$ denotes the smaller the better. Red color indicates the best performance, and blue color indicates the second best performance. + +
Methods2017Track22018Track22018Track32018Track4
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
SRGAN [18]22.990.58890.466918.990.45820.612719.750.47060.624119.500.46870.6150
SRFBN-s [21]23.070.60430.484518.870.48860.608519.780.50430.625119.510.50200.6112
KernelGAN [2] + ZSSR [34]22.490.58000.495118.430.54500.573919.750.57500.600019.360.57470.5774
BlindSR [5]21.610.54830.482018.350.40960.608819.310.42430.619218.900.41710.6102
IKC [12]22.280.57380.468318.720.54880.568619.810.57160.595019.420.57130.5723
SRGAN [18] + Correction Filter [14]20.980.57760.582118.730.55550.614119.070.55710.628818.950.56610.6147
SRFBN-s [21] + Correction Filter [14]20.980.58510.602318.740.56310.625519.100.56590.649918.980.57460.6313
USRNet [46]22.850.60290.511019.000.56410.570019.970.58250.601619.670.58530.5795
MANet [23]21.410.55790.491118.660.47440.609019.310.48330.628819.010.47620.6154
DIP-FKP [24]20.490.53360.505018.110.55280.578118.720.56090.608618.450.56050.5869
DASR [40]22.920.59680.478018.920.55790.569019.830.57480.592919.530.57820.5712
BSRDM [45]21.630.57970.558118.720.54830.594619.570.56570.612419.180.55960.6001
Ours + SRGAN [18]23.090.60170.463720.240.57410.608821.040.58450.617321.180.58870.6021
Ours + SRFBN-s [21]23.350.61260.506320.320.57870.622521.110.58590.629121.340.59480.6021
+ +Table 2. Quantitative results on NTIRE2017 Track2 [36] testing dataset for scaling factor $\times 2$ . + +
MethodsPSNR↑SSIM↑LPIPS↓
SRFBN-s [21]26.430.72460.3437
KernelGAN [2] + ZSSR [34]26.340.72880.3295
BlindSR [5]27.220.75390.3054
SRFBN-s [21] + Correction Filter [14]23.440.61250.3482
USRNet [46]26.520.73680.3710
MANet [23]27.920.78180.3086
DIP-FKP [24]26.290.74920.3188
DASR [40]26.380.72220.3335
BSRDM [45]26.650.73030.4432
Ours + SRFBN-s [21]27.990.78220.3513
+ +![](images/f8479f53ad8147f4e13eedcb790c1d90f398c661abcbc7245b9c578a02ff1183.jpg) + +![](images/2d9740a959ea1f83638e80aa3c357fbd91aaeb0b01d523e1518012f066b38049.jpg) +Figure 5. Illustration of degradation estimation for MANet [23] and DIP-FKP [24] on “ $0801 \times 4m$ .png” in NTIRE2018 track2. + +![](images/7d771580c3225ee5b14bc79dd9814ce91c2233c62c2ccde5a6f3beab7f232a91.jpg) + +learning rate is $10^{-3}$ which will be decayed by 0.5 after each 750 iterations. Data augmentation includes randomly rotating 90, 180, 270 degrees, and horizontally flipping. We implement experiments with PyTorch1.12.0 on an NVIDIA Geforce RTX 3090 GPU. + +# 4.2. Experiments on Synthetic Datasets. + +We conduct experiments on four synthetic benchmarks: track2 of NTIRE2017 [36] and track2, track3, and track4 + +of NTIRE2018 [37]. The degradations in these datasets are complex and unknown. Notably, the official uses same degradation operators within an image. But, as shown in Fig. 5, we use MANet [23] and DIP-FKP [24] to estimate the degradation of different regions in LR image, we find that the degradation of degraded image is spatially variant. We think that the given HR images are spatially variant degraded from the real HR ones due to camera acquisition in complex scenes, which make the LR images are spatially variant. We compare with unsupervised and supervised methods, including SRGAN [18], SRFBNs [21], KernelGAN [2], ZSSR [34], BlindSR [5], IKC [12], Correction_Filter [14], USRNet [46], DIP-FKP [24], MANet [23] and BSRDM [45]. + +# 4.2.1 Quantitative Evaluation. + +The detailed experimental results are listed in Tab. 1 and Tab. 2. Note that our method does not have a design module for denoising, so we employ CBM3D [6] to conduct on track2, track3, and track4 of NTIRE2018 datasets firstly. We also use the same operation for other methods without the ability of denoising for a fair comparison. + +Comparing with trained SR methods. As listed in Tab. 1 and Tab. 2, our method can improve the performance of SRGAN in all testing datasets on PSNR/SSIM/LPIPS. Our method also improves the performance of SRFBN-s in all testing datasets on PSNR/SSIM for scaling factor $\times 2$ and $\times 4$ . We noticed that our method did not improve the LPIPS values of SRFBN-s. This phenomenon often occurs in PSNR-Oriented methods (e.g., EDSR, RCAN). Our method can improve the performance of perceptual-driven methods (e.g., SRGAN, ESRGAN) in all indicators, including LPIPS. PSNR-Oriented methods focus on achiev- + +![](images/f1018431990cdb7671a7733bad961580dd6fa391446f1c546a3cec8344da028e.jpg) +Figure 6. Visual comparisons of different methods on 2017Track2 [36], 2018Track2 [37], and 2018Track4 [37]. Zoom in for best view. + +![](images/ffbf38f8543376616977d37da786c8af2cd94c2ff2a38a8d60ee6677f55fb03c.jpg) +Figure 7. Visual comparisons of different method for $\times 4$ on RealSRSet [47] dataset. Zoom in for best view. + +ing high PSNR and tend to generate images with too smooth and lost details (More analysis in Supp. Materials). Although our method can effectively recover LR images, the characteristics of these methods still lead to LPIPS degradation. But in general, our method can consistently improve the performance of off-the-shelf super-resolvers. + +Comparing with Correction_Filter. As shown in Tab. 1 and Tab. 2, Correction_Filter failed to improve the performance of SRFBN-s and SRGAN. The performance of Correction_Filter greatly relies on the accuracy of degradation estimation. However, it is difficult to solve complex degradation by their iterative approximation strategies. Be- + +sides, they only considers the spatially invariant degradation, failing to tackle spatially ones (More comparison are in Supp. Materials). The experimental results show that our method is more effective than Correction_Filter. + +Comparing with spatially-variant SR methods. From Tab. 2, we can see that the performance of SRFBN-s is far lower than BlindSR and MANet in all indicators. While SRFBN-s equipped our method outperforms BlindSR and MANet by 0.77 dB/0.0283 and 0.07 dB/0.0004 in terms of PSNR/SSIM, respectively. In Tab. 1, our method can help SRGAN and SRFBN-s outperforms Blind and MANet on all testing datasets in terms of PSRN/SSIM. The experi + +mental results verify that our method is superior in solving spatial-variant degradation. + +Comparing with other blind methods. As listed in Tab. 1, Ours+SRFBN-s achieves the best SSIM and PSNR on all datasets. Ours+SRFBN-s outperforms BSRDM by 1.72 dB/0.0329 and 2.16 dB/0.0352 on 2017Track2 and 2018Track4 on PSNR/SSIM, respectively. Ours+SRFBN-s outperforms DASR by 1.4 dB/0.0208 and 1.81 dB/0.0166 on 2018Track2 and 2018Track4 on PSNR/SSIM, respectively. Tab. 2 also verify that our method outperforms other blind methods. We conclude that our method is effective and has strong degradation-adaptive ability. + +![](images/7320125b16f9f4c9adbedb85bf8d38300925d8e3e72de6944739499db000299d.jpg) +(a) Input LR image +Figure 8. Visual ablation study about DM loss. + +![](images/230ec42adbd55eee88136bd9683ce6ac27d3cd63292d030f18e23a990ad23aa9.jpg) +(b) Corrected LR image +(without DM Loss) + +![](images/8228e52d4edc6c8ec6e8eef9c82f579f74f187869528a6709c4fd59396dba844.jpg) +(c) Corrected LR image + +# 4.2.2 Qualitative Evaluation. + +Fig. 6 are representative visual results. As shown in Fig. 6 (a), our method can generate sharper and cleaner SR images, but most other methods generate details with blurry or artifacts. Although the SR images generated by BSRDM seem to be clear, they lose some important details. In Fig. 6 (b), Ours+SRFBN-s can correctly restore font textures, while most other methods will produce incorrect textures. Although BSRDM generates font texture with good visual effects, many distortions exist. In Fig. 6 (c), Ours+SRFBN-s recovers clear and natural details, while other methods are prone to generate detailed textures with visual aliasing and artifacts. Notably, our method can greatly improves the visual quality of SRFBNs, demonstrating our method's effectiveness. + +# 4.3. Experiments on Real-World Dataset. + +We also conduct experiments on RealSRSet [47] dataset. (Due to most images in RealSRSet are small size, we reduce the cropped image size in Sec 4.1.) As mentioned in [47, 45], current non-reference metrics (e.g., NIQE [28], NRQM [27], and PI [1]) are not consistent with the perceptual visual system. Therefore, we only compare visual results. Fig. 7 shows the visual results on two representative images. Apparently, Ours+SRFBN-s generates improved visual results than other methods. In the first examples in + +Fig. 7, most other methods tend to generate noises or artifacts. USRNet generated observable visual results but with too many white lines that should not exist. BSRDM generates unrealistic and discontinuous lines with some distortions. In the second example in Fig. 7, most other methods cannot finely deal with the hair and tend to produce unrealistic detailed textures with visual aliasing. In contrast, our Ours+SRFBN-s reconstructs clear and natural details. + +Table 3. Ablation study of DM Loss on NTIRE2017 Track2 testing dataset for scaling factor $\times 4$ . + +
Method\( \mathcal{L}_{gan} \)\( \mathcal{L}_{pix} \)\( \mathcal{L}_{dml} \)PSNR↑SSIM↑LPIPS↓
Ours+SRFBN-s✓16.240.37570.7231
Ours+SRFBN-s✓21.890.56240.6532
Ours+SRFBN-s✓✓22.060.57040.6430
Ours+SRFBN-s✓✓✓23.350.61260.5063
+ +# 4.4. Ablation Study + +About DM Loss. To verify the effectiveness of DM loss, we conduct experiments on the 2017Track2 dataset. As listed in Tab. 3, Ours+SRFBN-s outperforms Ours +SRFBN-s (without $\mathcal{L}_{dml}$ ) on scale $\times 4$ by $1.29\mathrm{dB}$ on PSNR, 0.0423 on SISM, and 0.1367 on LPIPS, respectively. Besides, our DM loss can clearly improve the accuracy of degradation correction of corrected LR image (Fig. 8 (c)), compared with our model without DM loss (Fig. 8 (b)). + +Table 4. Ablation study of filter dictionary on NTIRE2017 Track2 testing dataset for scaling factor $\times 4$ . + +
Filter TypeNumberPSNR↑SSIM↑LPIPS↓
G + DoG [19]7223.350.61260.5063
RAISR [31]7222.120.53340.6430
Learned7222.440.53430.6266
G + DoG [19]2423.170.61140.5145
+ +About the base Filter Dictionary. We conducted experiments on the 2017Track2 dataset to verify the chosen of the base filter dictionary. We compare with RAISR filters [31] and filters directly learned by networks. As listed in Tab. 4, it is clear that 72 Gaussian and DoG combination achieves the best result. Tab. 4 also shows that the result with 72 basic filters is better than the dictionary with 24 basic filters. Besides, the filters size with $5 \times 5$ for each pixel is sufficient to restore complex real-world images. Various kernel sizes definitely can enhance performance but introduce great computational costs. + +Table 5. Ablation study on trained SR with different degradations. + +
Method2018Track22018Track3
Ours + SRFBN-s(Bicubic)20.32/0.578721.11/05859
Ours + SRFBN-s(Gaussian)20.31/0.578721.11/0.5858
Ours + SRFBN-s(Lanczos)20.32/0.578721.13/0.5859
+ +About trained SR with different degradation. We choose two different degradations (Gaussian blur and Lanczos) to train SRFBN-s on DIV2K dataset for scaling factor $\times 4$ , respectively. Tab. 5 lists the detailed results on NTIRE 2018 track2 and NTIRE 2018 track3. The results on the two degradation models are nearly consistent with bicubic degradation, which demonstrates that our method can adapt to any known degeneration in a trained model. + +# 5. Conclusion + +In this paper, we propose a novel blind image superresolution method that corrects the degradations of an LR input to that of the training data in an off-the-shelf method. Specifically, we propose an innovative unsupervised method of learning correction filter via a linearly-assembled pixel DARM for correcting the LR image's degradation to the known one in a spatially variant way for each testing image. Besides, we propose a degradation metric loss to map the unquantifiable degradation to guarantee the accuracy of degradation correction. Extensive experiments verify the superior performance of our method both quantitatively and qualitatively. + +# 6. Acknowledge + +The research is supported by National Key Research and Development Program of China (2020AAA0109700), National Science Fund for Distinguished Young Scholars(62125601), National Natural Science Foundation of China (62172035, 62076024, 62006018). + +# References + +[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 126-135, 2017. 8 +[2] Sefi Bell-Kligler, Assaf Shocher, and Michal Irani. Blind super-resolution kernel estimation using an internal-gan. Advances in Neural Information Processing Systems, 32, 2019. 2, 3, 4, 5, 6 +[3] Paul Leo Butzer. 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To address the problem, we propose an innovative unsupervised method of Learning Correction Filter via Degradation-Adaptive Regression for Blind Single Image Super-Resolution. Highly inspired by the generalized sampling theory, our method aims to enhance the strength of off-the-shelf SR methods trained on known degradations and adapt to unknown complex degradations to generate improved results. Specifically, we first conduct degradation estimation for each local image region by learning the internal distribution in an unsupervised manner via GAN. Instead of assuming degradation are spatially invariant across the whole image, we learn correction filters to adjust degradations to known degradations in a spatially variant way by a novel linearly-assembled pixel degradation-adaptive regression module (DARM). DARM is lightweight and easy to optimize on a dictionary of multiple pre-defined filter bases. 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As a fundamental computer vision task, SISR has been widely used in various applications, such as enhancing the images' visual perception on high-resolution devices and improving the image quality for other vision tasks [7]. In recent years," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 258, + 545, + 328 + ], + "blocks": [ + { + "bbox": [ + 307, + 258, + 545, + 328 + ], + "lines": [ + { + "bbox": [ + 307, + 258, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 307, + 258, + 545, + 328 + ], + "type": "image", + "image_path": "e96fb24e240c4ce66d893ed3218e71b41156fe37ed4ca3c87e9e6c95b727be7b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 353, + 328, + 488, + 338 + ], + "lines": [ + { + "bbox": [ + 353, + 328, + 488, + 338 + ], + "spans": [ + { + "bbox": [ + 353, + 328, + 488, + 338 + ], + "type": "text", + "content": "(a) Most degradation estimation strategies" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 338, + 545, + 407 + ], + "blocks": [ + { + "bbox": [ + 307, + 338, + 545, + 407 + ], + "lines": [ + { + "bbox": [ + 307, + 338, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 307, + 338, + 545, + 407 + ], + "type": "image", + "image_path": "63ff87a910f583a2557a7cea54b24daa542fcdd2d4cde6bae75444e0515395f6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 396, + 407, + 447, + 417 + ], + "lines": [ + { + "bbox": [ + 396, + 407, + 447, + 417 + ], + "spans": [ + { + "bbox": [ + 396, + 407, + 447, + 417 + ], + "type": "text", + "content": "(b) Our method" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 419, + 547, + 475 + ], + "lines": [ + { + "bbox": [ + 305, + 419, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 419, + 547, + 475 + ], + "type": "text", + "content": "Figure 1. Illustration of most degradation estimation strategies for blindSR and our method. (a) Most methods assume degradations are spatially invariant and estimate a single degradation for the whole image. (b) Our method can learn correction filters to adjust the degradations to a known degradation in a spatially variant way." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "content": "a multiplicity of deep learning-based SISR methods have been proposed [33, 18, 25, 52, 51, 8, 29, 54] and achieved substantial performance improvement." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "Typically, training and testing LR images in existing SISR approaches are simulated from a large collection of HR images. As a pioneer work, Dong et al. [9] first introduced a three-layer convolutional neural network in SISR to learn LR-HR mapping. Zhang et al. [51] proposed a channel attention mechanism to build a deep model for SISR. Liang et al. [22] proposed a baseline model SwinIR for SISR based on the transformer mechanism. In these methods, the LR images are often generated by limited numbers of fixed degradations (e.g., Bicubic or blur-downscale). However, the degradation process in real-world scenarios is extremely complicated and unpredictable. Although existing methods [25, 51, 29, 21, 18, 8] have achieved promising performance, they often encounter severe performance drops when the degradation is not well covered in training." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 222, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 222, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 222, + 712 + ], + "type": "text", + "content": "* Corresponding author (zhuxiaobin@ustb.edu.cn)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12365" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 443 + ], + "type": "text", + "content": "Recently, many works have attempted to address the challenging degradation adaptation problem by explicit or implicit degradation modeling in a blind or non-blind manner. SRMD [48] learns an SR model with training data covering a large set of degradation maps, which are modeled with blur kernel and noise. Following SRMD, UDVD [43] proposes a single unified dynamic network trained for various degradations to improve performance. However, in most practical applications, blur kernels are not available. They can hardly deal with the LR inputs with degradations out of their modeling scope. To tackle this problem, some methods [34, 35, 2, 11] estimate a blur kernel from each input LR image for adapting to complex degradations. IKC [12] proposes to correct kernel estimation in an iterative way to approach a satisfactory result gradually. ZSSR [34] learns degradation kernels of LR images via internal statistics for every image in a self-supervised manner. Pseudosupervision [53] combines the forward SR reconstruction path in CinCGAN [44] architecture with degradation learning to deal with the domain shift problem. In addition, Hussein et al. [14] proposed a correction filter strategy on the signal that is sampled by a certain basis can be reconstructed by a different basis, for modifying an LR input to match the SR model with a pre-defined degradation. These methods' generalization ability still greatly relies on the accuracy of degradation estimation or training data distribution. In addition, as shown in Fig. 1 (a), they assume degradations are spatially invariant and only estimate a single degradation for the whole image. Such an assumption is rarely applicable for real images whose regions (e.g., edges, corners) are discriminative for degradation estimation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 443, + 289, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 289, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 289, + 658 + ], + "type": "text", + "content": "To fully take advantage of the off-the-shelf superresolvers, we try to robustify the degradation of LR input without hurting useful information for efficiently adapting to practical applications. A brief illustration and comparison to the existing degradation estimation strategy for blindSR are presented in Fig. 1. Specifically, we propose an innovative unsupervised method of learning correction filter via a linearly-assembled pixel degradation-adaptive regression module (DARM) for correcting the LR image's degradation to the known one in a spatially variant way. Our DARM is highly lightweight and can be easily optimized over a dictionary of multiple pre-defined filter bases. In this way, our method can conduct correction filtering and help off-the-shelf SISR models to adapt to complex degradations on every testing image efficiently. In addition, we propose a degradation metric (DM) loss to learning to map the unquantifiable degradation in a metric space to guarantee the accuracy of degradation correction." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 658, + 265, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 658, + 265, + 670 + ], + "spans": [ + { + "bbox": [ + 58, + 658, + 265, + 670 + ], + "type": "text", + "content": "In summary, our main contributions are three-fold:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 57, + 677, + 287, + 715 + ], + "type": "text", + "content": "- We propose an innovative unsupervised strategy by learning correction filters for Blind Single Image Super-Resolution in a spatially variant way, greatly en" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "type": "text", + "content": "hancing the adapting ability of trained super-resolvers to unknown complex degradations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 316, + 102, + 545, + 258 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 316, + 102, + 545, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 102, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 316, + 102, + 545, + 150 + ], + "type": "text", + "content": "- We propose a lightweight degradation-adaptive regression module (DARM) that could accurately yet efficiently learn correction filters over a dictionary of multiple pre-defined filter bases." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 316, + 157, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 157, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 316, + 157, + 545, + 204 + ], + "type": "text", + "content": "- We propose a novel degradation metric (DM) loss via metric learning to map the unquantifiable degradation in a metric space to effectively improve the accuracy of degradation correction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 316, + 211, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 211, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 316, + 211, + 545, + 258 + ], + "type": "text", + "content": "- Extensive experiments on synthetic datasets and real images verify that our method can consistently improve the performance of the off-the-shelf superresolvers both qualitatively and quantitatively." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 268, + 392, + 281 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 268, + 392, + 281 + ], + "spans": [ + { + "bbox": [ + 306, + 268, + 392, + 281 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 288, + 488, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 288, + 488, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 288, + 488, + 300 + ], + "type": "text", + "content": "2.1. Predefined-Degradation based SR" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 306, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 510 + ], + "type": "text", + "content": "Dong et al. [9] firstly proposed a three consecutive convolutional neural network in SISR to learn a complex LR-HR mapping. Kim et al. [15] increased the depth of the network via a skip connection for stable training. To achieve promising performance, most methods adopt residual architecture [38, 52, 26]. EDSR [25] removes the batch normalization layer in a residual block and increasing the network depth. RCAN [51], SAN [8] and HAN [29] introduce the attention mechanism to draw more high-frequency information to further improve the performance. Furthermore, SwinIR [22], IPT [4], GRL [20] employ the transformer mechanism for constantly refreshing the state-of-the-art of SISR. However, these methods perform promisingly under a single degradation model (e.g., bicubic and blur-downscale degradation models); they tend to produce over-sharped or blurry results if the degradations present in the testing deviate from training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 515, + 480, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 480, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 480, + 528 + ], + "type": "text", + "content": "2.2. Degradation-Learning based SR" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 533, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 714 + ], + "type": "text", + "content": "Multiple degradation modeling based SR. By modeling multiple degradations, this type of method can produce good results for LR inputs covered by the training dataset. SRMD [48] proposes to directly concatenate an LR input image with its degradation map as a unified input to the SR model, thus allowing feature adaptation according to the specific degradation and covering multiple degradation types in a single model. DPSR [49] incorporates a super-resolution network into a MAP-based iterative optimization scheme which solves the HR image by minimizing objective functions. Similar to DPSR, USRNet [46] proposes an end-to-end trainable unfolding network that leverages both learning-based methods and model-based methods by unfolding the MAP inference via a half-quadratic splitting algorithm. Luo et al. [13] adopted an alternating optimization" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12366" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 72, + 532, + 256 + ], + "blocks": [ + { + "bbox": [ + 62, + 72, + 532, + 256 + ], + "lines": [ + { + "bbox": [ + 62, + 72, + 532, + 256 + ], + "spans": [ + { + "bbox": [ + 62, + 72, + 532, + 256 + ], + "type": "image", + "image_path": "207885a8c046b4dba7e9f0e989ee6be9558b1ba334655cec53be0afeec8d273a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 62, + 267, + 426, + 349 + ], + "blocks": [ + { + "bbox": [ + 175, + 257, + 411, + 267 + ], + "lines": [ + { + "bbox": [ + 175, + 257, + 411, + 267 + ], + "spans": [ + { + "bbox": [ + 175, + 257, + 411, + 267 + ], + "type": "text", + "content": "(a) Learning correction filter via Degradation-Adaptive Regression" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 62, + 267, + 426, + 349 + ], + "lines": [ + { + "bbox": [ + 62, + 267, + 426, + 349 + ], + "spans": [ + { + "bbox": [ + 62, + 267, + 426, + 349 + ], + "type": "image", + "image_path": "0dfa40cd6bae6119b1e8bc06dee33afffc586c8bf29e00d32412ecf77f058eb8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 109, + 350, + 352, + 360 + ], + "lines": [ + { + "bbox": [ + 109, + 350, + 352, + 360 + ], + "spans": [ + { + "bbox": [ + 109, + 350, + 352, + 360 + ], + "type": "text", + "content": "(b) Degradation correction for input LR image via a traind SR model" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 363, + 530, + 374 + ], + "lines": [ + { + "bbox": [ + 47, + 363, + 530, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 363, + 530, + 374 + ], + "type": "text", + "content": "Figure 2. Architecture of our method. (a) Illustration of the learning of correction filters. (b) Illustration of the degradation correction." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 429, + 277, + 443, + 287 + ], + "blocks": [ + { + "bbox": [ + 428, + 258, + 529, + 283 + ], + "lines": [ + { + "bbox": [ + 428, + 258, + 529, + 283 + ], + "spans": [ + { + "bbox": [ + 428, + 258, + 529, + 283 + ], + "type": "text", + "content": "x,y, x b Training data Discriminator" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 429, + 277, + 443, + 287 + ], + "lines": [ + { + "bbox": [ + 429, + 277, + 443, + 287 + ], + "spans": [ + { + "bbox": [ + 429, + 277, + 443, + 287 + ], + "type": "image", + "image_path": "ee6187886ddd3c70f391bc5da75bccf24e6795273bc95fa5f25052991ae9c88b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 446, + 285, + 527, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 446, + 285, + 527, + 294 + ], + "spans": [ + { + "bbox": [ + 446, + 285, + 527, + 294 + ], + "type": "text", + "content": "Degradation Generator" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 451, + 296, + 499, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 451, + 296, + 499, + 307 + ], + "spans": [ + { + "bbox": [ + 451, + 296, + 499, + 307 + ], + "type": "text", + "content": "Sigmoid" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 446, + 308, + 525, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 446, + 308, + 525, + 319 + ], + "spans": [ + { + "bbox": [ + 446, + 308, + 525, + 319 + ], + "type": "text", + "content": "Element-wise product" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 451, + 321, + 517, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 451, + 321, + 517, + 331 + ], + "spans": [ + { + "bbox": [ + 451, + 321, + 517, + 331 + ], + "type": "text", + "content": "Element-wise sum" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 429, + 339, + 465, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 429, + 339, + 465, + 350 + ], + "spans": [ + { + "bbox": [ + 429, + 339, + 465, + 350 + ], + "type": "text", + "content": "DM Loss" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 473, + 335, + 533, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 473, + 335, + 533, + 355 + ], + "spans": [ + { + "bbox": [ + 473, + 335, + 533, + 355 + ], + "type": "text", + "content": "Degradation Metric loss" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 394, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 394, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 287, + 443 + ], + "type": "text", + "content": "algorithm to estimate blur kernel and restore SR image in a single model. However, the performance of these methods still relies on accurate estimation of input kernel, which is challenging on arbitrary LR images." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 289, + 715 + ], + "type": "text", + "content": "Degradation estimation based SR. Gu et al. [12] proposed a general framework for blind SR by using self-similarity to recover the blur kernel and the HR image jointly. KernelGAN [2] interprets the maximization of patch recurrence within a single image as a data distribution learning problem and generates downscaled LR images by learning the internal patch distribution of the testing LR image. Shocher et al. [34] proposed a zero-shot super-resolution (ZSSR) method which trains image-specific on the testing LR image to take the degradation parameters and estimate blur kernel for improving the performance. Afterward, Soh et al. [35] proposed to learn an image-specific degradation simulation network together with a zero-shot image-specific super-solution network which exploits the depth information of the image to extract an unpaired high/low resolution patch collection to train the network. Liang et al. [24] proposed a novel method to incorporate a flow-based kernel prior into the framework by learning an invertible mapping between the anisotropic Gaussian kernel distribution and a tractable latent distribution. While these methods consider degradation are spatially invariant and only estimate a single degradation for input image. Cornillere et al. [5] pro" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 394, + 545, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 455 + ], + "type": "text", + "content": "posed a degradation-aware SR network to adapt spatially variant degradations. MANet [23] uses mutual affine convolution in their network for spatially variant kernel estimation. However, these methods greatly rely on the coverage of degradation modeling or training data distribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 464, + 386, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 386, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 386, + 477 + ], + "type": "text", + "content": "3. Our Method" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 484, + 391, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 484, + 391, + 496 + ], + "spans": [ + { + "bbox": [ + 306, + 484, + 391, + 496 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 503, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 545, + 525 + ], + "type": "text", + "content": "The SISR degradation model can be mathematically formulated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 392, + 527, + 545, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 527, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 392, + 527, + 545, + 539 + ], + "type": "interline_equation", + "content": "x = (y \\otimes k) \\downarrow_ {s}, \\tag {1}", + "image_path": "ae5832c6ad9b180002fdeb962fbab9f86739049fa38430335916538279ef5adf.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "text", + "content": " denotes the HR image; " + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "text", + "content": " denotes the LR image; " + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "text", + "content": " is the blur kernel; " + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "text", + "content": " denotes convolution operator; " + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "inline_equation", + "content": "\\downarrow_{s}" + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "text", + "content": " denotes sub-sampling operator with stride of " + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 544, + 545, + 591 + ], + "type": "text", + "content": ". Note that Eq. 1 can be written as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 406, + 593, + 545, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 406, + 593, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 406, + 593, + 545, + 604 + ], + "type": "interline_equation", + "content": "x = D y, \\tag {2}", + "image_path": "4ba28308deb4a26f68cd4e6c9eadbe440a36cfcb7f89d56d87d00dea964827b8.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "text", + "content": " represents degradation operator. As assumed by Hussein et al [14], the signal " + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "text", + "content": " can be perfectly recovered from its samples " + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "text", + "content": " by the operator " + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "inline_equation", + "content": "U(DU)^{-1}" + }, + { + "bbox": [ + 304, + 610, + 545, + 647 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 353, + 654, + 545, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 654, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 353, + 654, + 545, + 668 + ], + "type": "interline_equation", + "content": "y = U (D U) ^ {- 1} x = U (D U) ^ {- 1} D y, \\tag {3}", + "image_path": "efd773db77386cd33d375609539e7fe9b6e43ddacccef2b7d3c4a715c73bbf7d.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " is an upsampling operator which is the adjoint operator of " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": ". Eq. 3 indicates that the image " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " resides in the linear subspace can be spanned by the known degradation." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "12367" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "Therefore, it can be perfectly recovered from the observations " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "x_{k}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " by applying the pseudo inverse of " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "U_{k}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 77, + 100, + 287, + 114 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 100, + 287, + 114 + ], + "spans": [ + { + "bbox": [ + 77, + 100, + 287, + 114 + ], + "type": "interline_equation", + "content": "y ^ {\\prime} = U _ {k} \\left(D _ {k} U _ {k}\\right) ^ {- 1} D _ {k} y = U _ {k} \\left(D _ {k} U _ {k}\\right) ^ {- 1} x _ {k}, \\tag {4}", + "image_path": "cd552b02a428918f5fb4fa3bc2968197633c9c8fdabc9ffa69a55c403ff497a7.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "spans": [ + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "inline_equation", + "content": "D_{k}" + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "text", + "content": " denotes known degradation operation; " + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "inline_equation", + "content": "x_{k}" + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "text", + "content": " denotes known degraded image; " + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "inline_equation", + "content": "U_{k}" + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "text", + "content": " denotes a DNN super-resolver trained under the assumption of known degradation and it can handle the " + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "inline_equation", + "content": "x_{k}" + }, + { + "bbox": [ + 46, + 118, + 287, + 166 + ], + "type": "text", + "content": " quite well with a learned prior." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "text", + "content": "According to the generalization of classical Whittaker-Shannon sampling theorem [17, 30, 32, 42], some works [3, 10, 39] consider that a signal sampled by a certain basis can be reconstructed by different basis. By combining a correction filter with a reconstruction kernel, a sampled signal can be reconstructed. The correction filter can transform the sampling coefficients associated with the sampling kernel to coefficients that fit the reconstruction kernel. Given a degraded LR image " + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "inline_equation", + "content": "x_{u}" + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "text", + "content": " obtained by a unknown degradation " + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "inline_equation", + "content": "D_{u}" + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "inline_equation", + "content": "x_{u} = D_{u}y" + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "text", + "content": ". Then, the " + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "inline_equation", + "content": "y'" + }, + { + "bbox": [ + 46, + 167, + 287, + 286 + ], + "type": "text", + "content": " can be reconstructed as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 111, + 290, + 287, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 290, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 111, + 290, + 287, + 304 + ], + "type": "interline_equation", + "content": "y ^ {\\prime} = U _ {k} C x _ {u} = U _ {k} C D _ {u} y, \\tag {5}", + "image_path": "d426adb16c726a7e63408d0dd8f80f8c6744f89ccb80f4183ec9bcf5da9d5896.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "type": "text", + "content": " is a correction operator for " + }, + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "type": "inline_equation", + "content": "x_{u}" + }, + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "type": "text", + "content": ". Combining Equation 4 and Eq. 5, we can find the expression of " + }, + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 308, + 287, + 332 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 97, + 336, + 287, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 336, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 97, + 336, + 287, + 350 + ], + "type": "interline_equation", + "content": "C = \\left(D _ {u} U _ {k}\\right) ^ {- 1} \\Rightarrow C D _ {u} = U _ {k} ^ {- 1}. \\tag {6}", + "image_path": "c0a0653260755c629db27fb9d52d01512df727b0cb2df73ab80a17a41b1777c6.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "content": "The operator " + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "content": " can be applied simply as a convolution with a correction filter. Following Eq. 6, we first conduct spatial-variant degradation estimation to model " + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "inline_equation", + "content": "D_{u}" + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "content": ", which learns the spatially variant degradations in " + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "inline_equation", + "content": "x_{u}" + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "content": ". Then, we use our DARM to learn the correction filters " + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "content": " for correcting the degradations of " + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "inline_equation", + "content": "x_{u}" + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "content": " to pre-defined degradation. Finally, we employ a trained " + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "inline_equation", + "content": "U_{k}" + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "content": " to super-resolve the corrected image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 438, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 559 + ], + "type": "text", + "content": "Our method mainly distinguishes from the work [14] in two respects: (1) The performance of the work [14] greatly relies on the accuracy of degradation estimation. In our method, we coherently combine degradation estimation with correction filter learning into a unified network, greatly improving the accuracy and adaptiveness; (2) The work [14] only considers the spatially invariant degradation situation, failing to adopt a correction filter to solve a natural image with complex degradations. In our method, we estimate degradations in a spatially variant way." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 563, + 115, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 115, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 115, + 574 + ], + "type": "text", + "content": "3.2. Overview" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "As shown in Fig. 2 (a), we learn correction filters via DARM in an unsupervised manner. Then, as shown in Fig. 2 (b), we use learned correction filters to correct the degradation of the input LR image to the pre-defined degradation. Finally, an off-the-shelf super-resolver trained by known degradation is used for upsampling the degradation adapted LR image for SR. The learning of correction filters mainly consists of three components: generation of training data from input LR image, spatial-variant degradation estimation, and learning correction filters through proposed degradation adaptation regression module." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 547, + 174 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 547, + 174 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 547, + 174 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 547, + 174 + ], + "type": "image", + "image_path": "1349fba85821b237496bfc8133f2104d099ca7ebd95d696faf03e2f741305c91.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "lines": [ + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "spans": [ + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "type": "text", + "content": "Figure 3. Illustration of the generation of training data from the input LR image. " + }, + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "type": "inline_equation", + "content": "X = \\{x^{i}\\}" + }, + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "type": "inline_equation", + "content": "Y = \\{y^{i}\\}" + }, + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "type": "inline_equation", + "content": "X_{b} = \\{x_{b}^{i}\\}" + }, + { + "bbox": [ + 305, + 176, + 547, + 210 + ], + "type": "text", + "content": " are used to train our proposed degradation-adaptive regression module." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 230, + 463, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 230, + 463, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 230, + 463, + 243 + ], + "type": "text", + "content": "3.3. Generation of Training Data" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": "Given the input LR image, our goal is to correct complex degradations of all regions to the degradation (e.g. bicubic) in the off-the-shelf super-resolver. As shown in Fig. 3, we first crop the input LR image to generate the patches " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "X = \\{x^{i}\\}" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": " where each patch " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "x^{i}" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": " has the degradation of the corresponding area and " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": " can cover the degradation of each region in the input LR image. Then, we crop the input LR image to generate the patches " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "Y = \\{y^{i}\\}" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": ", which aims to learn a downscaled image (e.g., by a factor of 2 or 4) such that its degradation is approximate to that of the patches " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": " (see Sec. 3.4). Finally, we use known downsampling operation to degrade patches " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": " for generating patches " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "X_{b} = \\{x_{b}^{i}\\}" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": " of the same size with " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "x^{i}" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": " for degradation-adaptive regression learning. After obtaining training data " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "X_{b}" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 249, + 545, + 441 + ], + "type": "text", + "content": ", we will train our network to learn correction filters as shown in Fig. 2 (a)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 450, + 518, + 463 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 450, + 518, + 463 + ], + "spans": [ + { + "bbox": [ + 306, + 450, + 518, + 463 + ], + "type": "text", + "content": "3.4. Spatial-Variant Degradation Estimation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "X_{b}" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": " are not paired, which leads to the correction filters are unable to be learned directly. Thus, we adopt the GAN-based method to learn " + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "X_{c} = \\{x_{c}^{i}\\}" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": " with the same degradation as " + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": " through a GAN. Specially, we employ a degradation generator " + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": " and a discriminator " + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": ", as shown in Fig. 2 (a). Different from KernelGAN [2] which only learns one global invariant degenerate kernel, we will learn spatially variant degradation for each local patch " + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "x_{c}^{i}" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": ". In this way, we can learn " + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "X_{c}" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": " to cover the degradation of each region for improving performance. In addition, we propose a novel degradation metric (DM) loss (see Sec. 3.6) to learn more accurate degradation in " + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 469, + 545, + 613 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 622, + 512, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 512, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 512, + 635 + ], + "type": "text", + "content": "3.5. Learning Correction Filters via DARM" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": "As shown in Fig. 2 (a), we adopt paired training data " + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "inline_equation", + "content": "X_{c}" + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "inline_equation", + "content": "X_{b}" + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": " to learn correction filters by training our DARM through L1 loss and DM loss. We also train our network on unpaired training data " + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "inline_equation", + "content": "X_{b}" + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": " by DM loss. The output of " + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "inline_equation", + "content": "X_{c}" + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": " through DARM can be expressed as " + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "inline_equation", + "content": "X_{b^{\\prime}} = \\{x_{b^{\\prime}}^{i}\\}" + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "inline_equation", + "content": "X_{a} = \\{x_{a}^{i}\\}" + }, + { + "bbox": [ + 305, + 641, + 547, + 714 + ], + "type": "text", + "content": ", respectively. Notably, our DARM learns a" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12368" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 194, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 194, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 194, + 83 + ], + "type": "text", + "content": "correction filter for each input pixel." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 287, + 144 + ], + "type": "text", + "content": "Our key idea lies on the total probability theorem and the additivity of normal distribution. We can obtain the correction filter by combining multiple Gaussian filters. Specifically, a correction filter " + }, + { + "bbox": [ + 46, + 84, + 287, + 144 + ], + "type": "inline_equation", + "content": "F^i" + }, + { + "bbox": [ + 46, + 84, + 287, + 144 + ], + "type": "text", + "content": " can be represented as a linear combination of a set of underlying base Gaussian filters:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 119, + 152, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 152, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 119, + 152, + 287, + 186 + ], + "type": "interline_equation", + "content": "F ^ {i} = \\Phi^ {i} \\mathbb {D} = \\sum_ {j = 1} ^ {N} \\theta_ {j} ^ {i} f _ {j}, \\tag {7}", + "image_path": "9309f6ed545a5653315e9e874ef004cb242d91cf47e88119c91412543c6c257c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "inline_equation", + "content": "F = \\mathbb{R}^{HW \\times (k \\times k)}" + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "text", + "content": " is the kernel size which is empirically set to 5 in our experiments) denotes the learned correction filters for each pixel in the input image of size " + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "inline_equation", + "content": "\\Phi = \\mathbb{R}^{HW \\times N}" + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "text", + "content": " denotes the learned linear combination coefficients for each pixel; The dictionary " + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "inline_equation", + "content": "\\mathbb{D} = \\mathbb{R}^{N \\times (k \\times k)}" + }, + { + "bbox": [ + 47, + 196, + 287, + 292 + ], + "type": "text", + "content": " consists of 72 Gaussian and difference of Gaussians (DoG) filters [19], which can help to increase the visibility of details accurately learn correction filters." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "type": "text", + "content": "For the purpose of efficiency, we adopt a lightweight residual network for DARM via learning linear combination coefficients " + }, + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "type": "text", + "content": ". It mainly consists of two residual channel attention blocks (RCAB) [51] to learn deep feature, the convolutional layers in the head to extract the shallow feature of the input image, and the final convolutional layers to generate combination coefficients." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 384, + 140, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 140, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 140, + 396 + ], + "type": "text", + "content": "3.6. Loss Functions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 403, + 287, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 438 + ], + "type": "text", + "content": "Adversarial loss. We adopt GAN-based method to learn spatially variant degradations of LR image. The adversarial loss for the degradation generator " + }, + { + "bbox": [ + 46, + 403, + 287, + 438 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 403, + 287, + 438 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 99, + 447, + 287, + 461 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 447, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 99, + 447, + 287, + 461 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {g a n} = \\mathbb {E} [ D (G (y ^ {i})) - 1 ] ^ {2} + \\mathcal {R}, \\tag {8}", + "image_path": "81157215b3efe9973a0d6d0a5c86a14d7090f38f9b9418131ad52296d352c43f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "text", + "content": " denotes the regularization term which applies realistic explicit priors [2]. The discriminator " + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "text", + "content": " tries to distinguish degradations generated by " + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "inline_equation", + "content": "x^i" + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "text", + "content": " of input LR image and the constrain of " + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 470, + 287, + 518 + ], + "type": "text", + "content": " can be formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 84, + 526, + 287, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 526, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 84, + 526, + 287, + 541 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D} = \\mathbb {E} \\left[ D \\left(x ^ {i}\\right) - 1\\right) ^ {2} ] + \\mathbb {E} \\left[ D \\left(G \\left(y ^ {i}\\right)\\right) ^ {2} \\right]. \\tag {9}", + "image_path": "6fb14fd02fdd140bd60e76dd402e6c62a228108ad475009036a94724e2db160b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 550, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 609 + ], + "type": "text", + "content": "Pixelwise loss. It is used to accelerate the convergence of DRAM. Besides, it can effectively compensate for the structural distortion caused by GAN. We use L1 loss to constrain the results generated by DASR and SR model. The mathematic formulation is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 81, + 619, + 287, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 619, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 81, + 619, + 287, + 633 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p i x} = \\left| \\left| x _ {b} ^ {i} - x _ {b ^ {\\prime}} ^ {i} \\right| \\right| _ {1} + \\left| \\left| y ^ {i} - S R \\left(x _ {b ^ {\\prime}} ^ {i}\\right) \\right| \\right| _ {1}, \\tag {10}", + "image_path": "430ac532b39a476d0688481d5d72e13687e976a5b6f0f01936b78ce5ccd8a890.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 641, + 262, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 262, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 262, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 641, + 262, + 653 + ], + "type": "inline_equation", + "content": "SR(*)" + }, + { + "bbox": [ + 47, + 641, + 262, + 653 + ], + "type": "text", + "content": " denotes an off-the-shelf super-resolver." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Degradation metric loss. It is difficult to estimate complex degradations accurately via single adversarial learning in real-world scenarios. To overcome this problem, we propose a novel degradation metric (DM) loss which maps the complex degradation into a metric space for effective" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 331, + 71, + 523, + 156 + ], + "blocks": [ + { + "bbox": [ + 331, + 71, + 523, + 156 + ], + "lines": [ + { + "bbox": [ + 331, + 71, + 523, + 156 + ], + "spans": [ + { + "bbox": [ + 331, + 71, + 523, + 156 + ], + "type": "image", + "image_path": "485e6ebed9b107eda27615761f31f9adae26ebc2efa0944a47fb427e34603bd4.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "type": "text", + "content": "Figure 4. Architecture of degradation score estimation module (DSEM), which mainly consist of three Resblocks [25], an average pooling layer, a sigmoid layer, and a full connection layer." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 212, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 212, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 212, + 545, + 270 + ], + "type": "text", + "content": "constraint. Specially, we use a degradation score estimation module (DSEM) to model the distance between target degradation and estimated degradation. We use " + }, + { + "bbox": [ + 305, + 212, + 545, + 270 + ], + "type": "inline_equation", + "content": "x^{i}" + }, + { + "bbox": [ + 305, + 212, + 545, + 270 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 212, + 545, + 270 + ], + "type": "inline_equation", + "content": "x_{b}^{i}" + }, + { + "bbox": [ + 305, + 212, + 545, + 270 + ], + "type": "text", + "content": " as anchor samples to train the metric space as shown in Fig. 4. The mathematical formulation is elaborated as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 328, + 277, + 545, + 311 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 277, + 545, + 311 + ], + "spans": [ + { + "bbox": [ + 328, + 277, + 545, + 311 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a c} = \\frac {1}{N} \\sum_ {i} ^ {N} \\left(\\left| \\left| S \\left(x _ {b} ^ {i}\\right) \\right| \\right| _ {2} ^ {2} + \\left| \\left| S \\left(x ^ {i}\\right) - 1 \\right| \\right| _ {2} ^ {2}\\right), \\tag {11}", + "image_path": "c57d8384d3f9c0e4b18a36d512b585a000e9c4ea93bbf61c5e2168d7c89d06cc.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 320, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 320, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 320, + 545, + 380 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 320, + 545, + 380 + ], + "type": "inline_equation", + "content": "S(*)" + }, + { + "bbox": [ + 305, + 320, + 545, + 380 + ], + "type": "text", + "content": " denotes the degradation score estimation operation, which is implemented by DSEM. Then, we use DM loss from two parts, one is the result generated by downscale generator " + }, + { + "bbox": [ + 305, + 320, + 545, + 380 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 320, + 545, + 380 + ], + "type": "text", + "content": ", and the other one is the result generated by DARM. The mathematical formulation is elaborated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 315, + 388, + 545, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 388, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 315, + 388, + 545, + 419 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {d m l} = \\left| \\left| S \\left(x _ {b} ^ {i}\\right) - S \\left(x _ {b ^ {\\prime}} ^ {i}\\right) \\right| \\right| _ {2} ^ {2} + \\left| \\left| S \\left(x ^ {i}\\right) - S (G \\left(y ^ {i}\\right)) \\right| \\right| _ {2} ^ {2} \\\\ + \\left\\| S \\left(x ^ {i}\\right) - S \\left(x _ {a} ^ {i}\\right) \\right\\| _ {2} ^ {2}. \\tag {12} \\\\ \\end{array}", + "image_path": "01ee32e9e04688a9c348116560364c934a6a6e6c3865fd75ae4cac90e29c6cef.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 429, + 545, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 429, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 305, + 429, + 545, + 452 + ], + "type": "text", + "content": "Full objective. Mathematically, the total loss function for our method can be formulated as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 354, + 462, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 462, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 354, + 462, + 545, + 475 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {A l l} = \\mathcal {L} _ {g a n} + \\lambda_ {1} \\mathcal {L} _ {p i x} + \\lambda_ {2} \\mathcal {L} _ {d m l}, \\tag {13}", + "image_path": "3e6d0bb9e52b2700ea52dc616bf45d8b044ef48631659d01b8e2d95951e5a18b.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 305, + 485, + 545, + 509 + ], + "type": "text", + "content": " are two empirical hyper-parameters that are set to 2.5 and 0.5, respectively." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 520, + 388, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 388, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 388, + 533 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 539, + 438, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 438, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 438, + 552 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": "We conduct experiments on real-world datasets (RealSRSet [47]) and synthetic datasets (NTIRE2017 [36] and NTIRE2018 [37]). The results are evaluated by the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) [41], and learned perceptual image patch similarity (LPIPS) [50]. PSNR and SSIM are evaluated on the Y channel of transformed YCbCr, while LPIPS is on RGB. We train our network by each iteration with 16 batches which consist of paired patches from the LR input. The patches " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "x^i" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "y^i" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": " in Fig. 3) are for scaling " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": ". The patches " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": " are for scaling " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": ". The iteration number is set to 3,000, and the optimizer is the Adam [16] with " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta 1 = 0.9" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta 2 = 0.999" + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": ". The initial" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12369" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 91, + 547, + 288 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": "Table 1. Quantitative results on NTIRE2017 [36] and NTIRE2018 [37] testing datasets for scaling factor " + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": " denotes the larger the better. " + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 47, + 69, + 545, + 91 + ], + "type": "text", + "content": " denotes the smaller the better. Red color indicates the best performance, and blue color indicates the second best performance." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 91, + 547, + 288 + ], + "lines": [ + { + "bbox": [ + 48, + 91, + 547, + 288 + ], + "spans": [ + { + "bbox": [ + 48, + 91, + 547, + 288 + ], + "type": "table", + "html": "
Methods2017Track22018Track22018Track32018Track4
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
SRGAN [18]22.990.58890.466918.990.45820.612719.750.47060.624119.500.46870.6150
SRFBN-s [21]23.070.60430.484518.870.48860.608519.780.50430.625119.510.50200.6112
KernelGAN [2] + ZSSR [34]22.490.58000.495118.430.54500.573919.750.57500.600019.360.57470.5774
BlindSR [5]21.610.54830.482018.350.40960.608819.310.42430.619218.900.41710.6102
IKC [12]22.280.57380.468318.720.54880.568619.810.57160.595019.420.57130.5723
SRGAN [18] + Correction Filter [14]20.980.57760.582118.730.55550.614119.070.55710.628818.950.56610.6147
SRFBN-s [21] + Correction Filter [14]20.980.58510.602318.740.56310.625519.100.56590.649918.980.57460.6313
USRNet [46]22.850.60290.511019.000.56410.570019.970.58250.601619.670.58530.5795
MANet [23]21.410.55790.491118.660.47440.609019.310.48330.628819.010.47620.6154
DIP-FKP [24]20.490.53360.505018.110.55280.578118.720.56090.608618.450.56050.5869
DASR [40]22.920.59680.478018.920.55790.569019.830.57480.592919.530.57820.5712
BSRDM [45]21.630.57970.558118.720.54830.594619.570.56570.612419.180.55960.6001
Ours + SRGAN [18]23.090.60170.463720.240.57410.608821.040.58450.617321.180.58870.6021
Ours + SRFBN-s [21]23.350.61260.506320.320.57870.622521.110.58590.629121.340.59480.6021
", + "image_path": "75dbfffdcd55ea4c810bb0ed7b9f83af5e0386f1081ac4e65dd0b755f6a4a595.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 327, + 282, + 463 + ], + "blocks": [ + { + "bbox": [ + 47, + 305, + 286, + 327 + ], + "lines": [ + { + "bbox": [ + 47, + 305, + 286, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 305, + 286, + 327 + ], + "type": "text", + "content": "Table 2. Quantitative results on NTIRE2017 Track2 [36] testing dataset for scaling factor " + }, + { + "bbox": [ + 47, + 305, + 286, + 327 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 47, + 305, + 286, + 327 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 327, + 282, + 463 + ], + "lines": [ + { + "bbox": [ + 50, + 327, + 282, + 463 + ], + "spans": [ + { + "bbox": [ + 50, + 327, + 282, + 463 + ], + "type": "table", + "html": "
MethodsPSNR↑SSIM↑LPIPS↓
SRFBN-s [21]26.430.72460.3437
KernelGAN [2] + ZSSR [34]26.340.72880.3295
BlindSR [5]27.220.75390.3054
SRFBN-s [21] + Correction Filter [14]23.440.61250.3482
USRNet [46]26.520.73680.3710
MANet [23]27.920.78180.3086
DIP-FKP [24]26.290.74920.3188
DASR [40]26.380.72220.3335
BSRDM [45]26.650.73030.4432
Ours + SRFBN-s [21]27.990.78220.3513
", + "image_path": "7c34ef47b07584f863171fa40dc0c8e11d6daaad85c74ff0181532295715282a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 49, + 474, + 96, + 503 + ], + "blocks": [ + { + "bbox": [ + 49, + 474, + 96, + 503 + ], + "lines": [ + { + "bbox": [ + 49, + 474, + 96, + 503 + ], + "spans": [ + { + "bbox": [ + 49, + 474, + 96, + 503 + ], + "type": "image", + "image_path": "f8479f53ad8147f4e13eedcb790c1d90f398c661abcbc7245b9c578a02ff1183.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 100, + 474, + 236, + 565 + ], + "blocks": [ + { + "bbox": [ + 100, + 474, + 236, + 565 + ], + "lines": [ + { + "bbox": [ + 100, + 474, + 236, + 565 + ], + "spans": [ + { + "bbox": [ + 100, + 474, + 236, + 565 + ], + "type": "image", + "image_path": "2d9740a959ea1f83638e80aa3c357fbd91aaeb0b01d523e1518012f066b38049.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 567, + 286, + 590 + ], + "lines": [ + { + "bbox": [ + 47, + 567, + 286, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 286, + 590 + ], + "type": "text", + "content": "Figure 5. Illustration of degradation estimation for MANet [23] and DIP-FKP [24] on “" + }, + { + "bbox": [ + 47, + 567, + 286, + 590 + ], + "type": "inline_equation", + "content": "0801 \\times 4m" + }, + { + "bbox": [ + 47, + 567, + 286, + 590 + ], + "type": "text", + "content": " .png” in NTIRE2018 track2." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 239, + 474, + 287, + 503 + ], + "blocks": [ + { + "bbox": [ + 239, + 474, + 287, + 503 + ], + "lines": [ + { + "bbox": [ + 239, + 474, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 239, + 474, + 287, + 503 + ], + "type": "image", + "image_path": "7d771580c3225ee5b14bc79dd9814ce91c2233c62c2ccde5a6f3beab7f232a91.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 598, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 658 + ], + "type": "text", + "content": "learning rate is " + }, + { + "bbox": [ + 46, + 598, + 287, + 658 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 46, + 598, + 287, + 658 + ], + "type": "text", + "content": " which will be decayed by 0.5 after each 750 iterations. Data augmentation includes randomly rotating 90, 180, 270 degrees, and horizontally flipping. We implement experiments with PyTorch1.12.0 on an NVIDIA Geforce RTX 3090 GPU." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 670, + 235, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 235, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 235, + 683 + ], + "type": "text", + "content": "4.2. Experiments on Synthetic Datasets." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "We conduct experiments on four synthetic benchmarks: track2 of NTIRE2017 [36] and track2, track3, and track4" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 308, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 475 + ], + "type": "text", + "content": "of NTIRE2018 [37]. The degradations in these datasets are complex and unknown. Notably, the official uses same degradation operators within an image. But, as shown in Fig. 5, we use MANet [23] and DIP-FKP [24] to estimate the degradation of different regions in LR image, we find that the degradation of degraded image is spatially variant. We think that the given HR images are spatially variant degraded from the real HR ones due to camera acquisition in complex scenes, which make the LR images are spatially variant. We compare with unsupervised and supervised methods, including SRGAN [18], SRFBNs [21], KernelGAN [2], ZSSR [34], BlindSR [5], IKC [12], Correction_Filter [14], USRNet [46], DIP-FKP [24], MANet [23] and BSRDM [45]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 491, + 443, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 443, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 443, + 502 + ], + "type": "text", + "content": "4.2.1 Quantitative Evaluation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 581 + ], + "type": "text", + "content": "The detailed experimental results are listed in Tab. 1 and Tab. 2. Note that our method does not have a design module for denoising, so we employ CBM3D [6] to conduct on track2, track3, and track4 of NTIRE2018 datasets firstly. We also use the same operation for other methods without the ability of denoising for a fair comparison." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Comparing with trained SR methods. As listed in Tab. 1 and Tab. 2, our method can improve the performance of SRGAN in all testing datasets on PSNR/SSIM/LPIPS. Our method also improves the performance of SRFBN-s in all testing datasets on PSNR/SSIM for scaling factor " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ". We noticed that our method did not improve the LPIPS values of SRFBN-s. This phenomenon often occurs in PSNR-Oriented methods (e.g., EDSR, RCAN). Our method can improve the performance of perceptual-driven methods (e.g., SRGAN, ESRGAN) in all indicators, including LPIPS. PSNR-Oriented methods focus on achiev-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "12370" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 547, + 378 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 547, + 378 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 547, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 547, + 378 + ], + "type": "image", + "image_path": "f1018431990cdb7671a7733bad961580dd6fa391446f1c546a3cec8344da028e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 381, + 536, + 395 + ], + "lines": [ + { + "bbox": [ + 47, + 381, + 536, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 536, + 395 + ], + "type": "text", + "content": "Figure 6. Visual comparisons of different methods on 2017Track2 [36], 2018Track2 [37], and 2018Track4 [37]. Zoom in for best view." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 402, + 545, + 529 + ], + "blocks": [ + { + "bbox": [ + 48, + 402, + 545, + 529 + ], + "lines": [ + { + "bbox": [ + 48, + 402, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 48, + 402, + 545, + 529 + ], + "type": "image", + "image_path": "ffbf38f8543376616977d37da786c8af2cd94c2ff2a38a8d60ee6677f55fb03c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 100, + 533, + 493, + 544 + ], + "lines": [ + { + "bbox": [ + 100, + 533, + 493, + 544 + ], + "spans": [ + { + "bbox": [ + 100, + 533, + 493, + 544 + ], + "type": "text", + "content": "Figure 7. Visual comparisons of different method for " + }, + { + "bbox": [ + 100, + 533, + 493, + 544 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 100, + 533, + 493, + 544 + ], + "type": "text", + "content": " on RealSRSet [47] dataset. Zoom in for best view." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 563, + 288, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 288, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 288, + 635 + ], + "type": "text", + "content": "ing high PSNR and tend to generate images with too smooth and lost details (More analysis in Supp. Materials). Although our method can effectively recover LR images, the characteristics of these methods still lead to LPIPS degradation. But in general, our method can consistently improve the performance of off-the-shelf super-resolvers." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Comparing with Correction_Filter. As shown in Tab. 1 and Tab. 2, Correction_Filter failed to improve the performance of SRFBN-s and SRGAN. The performance of Correction_Filter greatly relies on the accuracy of degradation estimation. However, it is difficult to solve complex degradation by their iterative approximation strategies. Be-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 563, + 547, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 547, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 547, + 612 + ], + "type": "text", + "content": "sides, they only considers the spatially invariant degradation, failing to tackle spatially ones (More comparison are in Supp. Materials). The experimental results show that our method is more effective than Correction_Filter." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Comparing with spatially-variant SR methods. From Tab. 2, we can see that the performance of SRFBN-s is far lower than BlindSR and MANet in all indicators. While SRFBN-s equipped our method outperforms BlindSR and MANet by 0.77 dB/0.0283 and 0.07 dB/0.0004 in terms of PSNR/SSIM, respectively. In Tab. 1, our method can help SRGAN and SRFBN-s outperforms Blind and MANet on all testing datasets in terms of PSRN/SSIM. The experi" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12371" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "mental results verify that our method is superior in solving spatial-variant degradation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 95, + 288, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 95, + 288, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 95, + 288, + 216 + ], + "type": "text", + "content": "Comparing with other blind methods. As listed in Tab. 1, Ours+SRFBN-s achieves the best SSIM and PSNR on all datasets. Ours+SRFBN-s outperforms BSRDM by 1.72 dB/0.0329 and 2.16 dB/0.0352 on 2017Track2 and 2018Track4 on PSNR/SSIM, respectively. Ours+SRFBN-s outperforms DASR by 1.4 dB/0.0208 and 1.81 dB/0.0166 on 2018Track2 and 2018Track4 on PSNR/SSIM, respectively. Tab. 2 also verify that our method outperforms other blind methods. We conclude that our method is effective and has strong degradation-adaptive ability." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 227, + 127, + 344 + ], + "blocks": [ + { + "bbox": [ + 50, + 227, + 127, + 344 + ], + "lines": [ + { + "bbox": [ + 50, + 227, + 127, + 344 + ], + "spans": [ + { + "bbox": [ + 50, + 227, + 127, + 344 + ], + "type": "image", + "image_path": "7320125b16f9f4c9adbedb85bf8d38300925d8e3e72de6944739499db000299d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 344, + 120, + 353 + ], + "lines": [ + { + "bbox": [ + 61, + 344, + 120, + 353 + ], + "spans": [ + { + "bbox": [ + 61, + 344, + 120, + 353 + ], + "type": "text", + "content": "(a) Input LR image" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 81, + 364, + 252, + 375 + ], + "lines": [ + { + "bbox": [ + 81, + 364, + 252, + 375 + ], + "spans": [ + { + "bbox": [ + 81, + 364, + 252, + 375 + ], + "type": "text", + "content": "Figure 8. Visual ablation study about DM loss." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 129, + 227, + 206, + 344 + ], + "blocks": [ + { + "bbox": [ + 129, + 227, + 206, + 344 + ], + "lines": [ + { + "bbox": [ + 129, + 227, + 206, + 344 + ], + "spans": [ + { + "bbox": [ + 129, + 227, + 206, + 344 + ], + "type": "image", + "image_path": "230ec42adbd55eee88136bd9683ce6ac27d3cd63292d030f18e23a990ad23aa9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 134, + 344, + 206, + 352 + ], + "lines": [ + { + "bbox": [ + 134, + 344, + 206, + 352 + ], + "spans": [ + { + "bbox": [ + 134, + 344, + 206, + 352 + ], + "type": "text", + "content": "(b) Corrected LR image" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 141, + 353, + 201, + 361 + ], + "lines": [ + { + "bbox": [ + 141, + 353, + 201, + 361 + ], + "spans": [ + { + "bbox": [ + 141, + 353, + 201, + 361 + ], + "type": "text", + "content": "(without DM Loss)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 209, + 227, + 286, + 344 + ], + "blocks": [ + { + "bbox": [ + 209, + 227, + 286, + 344 + ], + "lines": [ + { + "bbox": [ + 209, + 227, + 286, + 344 + ], + "spans": [ + { + "bbox": [ + 209, + 227, + 286, + 344 + ], + "type": "image", + "image_path": "8228e52d4edc6c8ec6e8eef9c82f579f74f187869528a6709c4fd59396dba844.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 211, + 344, + 284, + 352 + ], + "lines": [ + { + "bbox": [ + 211, + 344, + 284, + 352 + ], + "spans": [ + { + "bbox": [ + 211, + 344, + 284, + 352 + ], + "type": "text", + "content": "(c) Corrected LR image" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 392, + 179, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 179, + 404 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 179, + 404 + ], + "type": "text", + "content": "4.2.2 Qualitative Evaluation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 412, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 579 + ], + "type": "text", + "content": "Fig. 6 are representative visual results. As shown in Fig. 6 (a), our method can generate sharper and cleaner SR images, but most other methods generate details with blurry or artifacts. Although the SR images generated by BSRDM seem to be clear, they lose some important details. In Fig. 6 (b), Ours+SRFBN-s can correctly restore font textures, while most other methods will produce incorrect textures. Although BSRDM generates font texture with good visual effects, many distortions exist. In Fig. 6 (c), Ours+SRFBN-s recovers clear and natural details, while other methods are prone to generate detailed textures with visual aliasing and artifacts. Notably, our method can greatly improves the visual quality of SRFBNs, demonstrating our method's effectiveness." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 587, + 242, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 242, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 242, + 600 + ], + "type": "text", + "content": "4.3. Experiments on Real-World Dataset." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "We also conduct experiments on RealSRSet [47] dataset. (Due to most images in RealSRSet are small size, we reduce the cropped image size in Sec 4.1.) As mentioned in [47, 45], current non-reference metrics (e.g., NIQE [28], NRQM [27], and PI [1]) are not consistent with the perceptual visual system. Therefore, we only compare visual results. Fig. 7 shows the visual results on two representative images. Apparently, Ours+SRFBN-s generates improved visual results than other methods. In the first examples in" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "Fig. 7, most other methods tend to generate noises or artifacts. USRNet generated observable visual results but with too many white lines that should not exist. BSRDM generates unrealistic and discontinuous lines with some distortions. In the second example in Fig. 7, most other methods cannot finely deal with the hair and tend to produce unrealistic detailed textures with visual aliasing. In contrast, our Ours+SRFBN-s reconstructs clear and natural details." + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 307, + 196, + 543, + 260 + ], + "blocks": [ + { + "bbox": [ + 305, + 175, + 545, + 196 + ], + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 196 + ], + "type": "text", + "content": "Table 3. Ablation study of DM Loss on NTIRE2017 Track2 testing dataset for scaling factor " + }, + { + "bbox": [ + 305, + 175, + 545, + 196 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 305, + 175, + 545, + 196 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 196, + 543, + 260 + ], + "lines": [ + { + "bbox": [ + 307, + 196, + 543, + 260 + ], + "spans": [ + { + "bbox": [ + 307, + 196, + 543, + 260 + ], + "type": "table", + "html": "
Method\\( \\mathcal{L}_{gan} \\)\\( \\mathcal{L}_{pix} \\)\\( \\mathcal{L}_{dml} \\)PSNR↑SSIM↑LPIPS↓
Ours+SRFBN-s✓16.240.37570.7231
Ours+SRFBN-s✓21.890.56240.6532
Ours+SRFBN-s✓✓22.060.57040.6430
Ours+SRFBN-s✓✓✓23.350.61260.5063
", + "image_path": "526f2883388679b9542c6b02f50f38d32506c31564834e202bf7d97a3d9ffa22.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 281, + 399, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 399, + 294 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 399, + 294 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "type": "text", + "content": "About DM Loss. To verify the effectiveness of DM loss, we conduct experiments on the 2017Track2 dataset. As listed in Tab. 3, Ours+SRFBN-s outperforms Ours +SRFBN-s (without " + }, + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dml}" + }, + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "type": "text", + "content": ") on scale " + }, + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "1.29\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 300, + 545, + 396 + ], + "type": "text", + "content": " on PSNR, 0.0423 on SISM, and 0.1367 on LPIPS, respectively. Besides, our DM loss can clearly improve the accuracy of degradation correction of corrected LR image (Fig. 8 (c)), compared with our model without DM loss (Fig. 8 (b))." + } + ] + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 307, + 426, + 545, + 490 + ], + "blocks": [ + { + "bbox": [ + 305, + 404, + 545, + 426 + ], + "lines": [ + { + "bbox": [ + 305, + 404, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 404, + 545, + 426 + ], + "type": "text", + "content": "Table 4. Ablation study of filter dictionary on NTIRE2017 Track2 testing dataset for scaling factor " + }, + { + "bbox": [ + 305, + 404, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 305, + 404, + 545, + 426 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 426, + 545, + 490 + ], + "lines": [ + { + "bbox": [ + 307, + 426, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 307, + 426, + 545, + 490 + ], + "type": "table", + "html": "
Filter TypeNumberPSNR↑SSIM↑LPIPS↓
G + DoG [19]7223.350.61260.5063
RAISR [31]7222.120.53340.6430
Learned7222.440.53430.6266
G + DoG [19]2423.170.61140.5145
", + "image_path": "9e800121584d17a785670883b42c66cafd8643170de26ae26ca13e1545420045.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "type": "text", + "content": "About the base Filter Dictionary. We conducted experiments on the 2017Track2 dataset to verify the chosen of the base filter dictionary. We compare with RAISR filters [31] and filters directly learned by networks. As listed in Tab. 4, it is clear that 72 Gaussian and DoG combination achieves the best result. Tab. 4 also shows that the result with 72 basic filters is better than the dictionary with 24 basic filters. Besides, the filters size with " + }, + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 304, + 503, + 545, + 635 + ], + "type": "text", + "content": " for each pixel is sufficient to restore complex real-world images. Various kernel sizes definitely can enhance performance but introduce great computational costs." + } + ] + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 307, + 654, + 545, + 711 + ], + "blocks": [ + { + "bbox": [ + 306, + 643, + 544, + 654 + ], + "lines": [ + { + "bbox": [ + 306, + 643, + 544, + 654 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 544, + 654 + ], + "type": "text", + "content": "Table 5. Ablation study on trained SR with different degradations." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 654, + 545, + 711 + ], + "lines": [ + { + "bbox": [ + 307, + 654, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 307, + 654, + 545, + 711 + ], + "type": "table", + "html": "
Method2018Track22018Track3
Ours + SRFBN-s(Bicubic)20.32/0.578721.11/05859
Ours + SRFBN-s(Gaussian)20.31/0.578721.11/0.5858
Ours + SRFBN-s(Lanczos)20.32/0.578721.13/0.5859
", + "image_path": "235bf769e9c2e8865de8069ff84ece368e2207db103a83fd832d48207c58c576.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "table_body" + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12372" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "About trained SR with different degradation. We choose two different degradations (Gaussian blur and Lanczos) to train SRFBN-s on DIV2K dataset for scaling factor " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": ", respectively. Tab. 5 lists the detailed results on NTIRE 2018 track2 and NTIRE 2018 track3. The results on the two degradation models are nearly consistent with bicubic degradation, which demonstrates that our method can adapt to any known degeneration in a trained model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 179, + 119, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 179, + 119, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 179, + 119, + 192 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 199, + 289, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 199, + 289, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 289, + 344 + ], + "type": "text", + "content": "In this paper, we propose a novel blind image superresolution method that corrects the degradations of an LR input to that of the training data in an off-the-shelf method. Specifically, we propose an innovative unsupervised method of learning correction filter via a linearly-assembled pixel DARM for correcting the LR image's degradation to the known one in a spatially variant way for each testing image. Besides, we propose a degradation metric loss to map the unquantifiable degradation to guarantee the accuracy of degradation correction. Extensive experiments verify the superior performance of our method both quantitatively and qualitatively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 355, + 132, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 355, + 132, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 355, + 132, + 369 + ], + "type": "text", + "content": "6. Acknowledge" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 374, + 288, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 288, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 288, + 434 + ], + "type": "text", + "content": "The research is supported by National Key Research and Development Program of China (2020AAA0109700), National Science Fund for Distinguished Young Scholars(62125601), National Natural Science Foundation of China (62172035, 62076024, 62006018)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 446, + 107, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 446, + 107, + 459 + ], + "spans": [ + { + "bbox": [ + 48, + 446, + 107, + 459 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 465, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 465, + 287, + 510 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 465, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 53, + 465, + 287, + 510 + ], + "type": "text", + "content": "[1] Eirikur Agustsson and Radu Timofte. 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However, in more realistic scenarios, only minimal annotations are available for a new scene, which poses significant challenges to existing RVOS methods. With this in mind, we propose a simple yet effective model with a newly designed cross-modal affinity (CMA) module based on a Transformer architecture. The CMA module builds multimodal affinity with a few samples, thus quickly learning new semantic information, and enabling the model to adapt to different scenarios. Since the proposed method targets limited samples for new scenes, we generalize the problem as - few-shot referring video object segmentation (FS-RVOS). To foster research in this direction, we build up a new FS-RVOS benchmark based on currently available datasets. The benchmark covers a wide range and includes multiple situations, which can maximally simulate real-world scenarios. Extensive experiments show that our model adapts well to different scenarios with only a few samples, reaching state-of-the-art performance on the benchmark. On Mini-Ref-YouTube-VOS, our model achieves an average performance of 53.1 J and 54.8 F, which are $10\\%$ better than the baselines. Furthermore, we show impressive results of 77.7 J and 74.8 F on Mini-Ref-SAIL-VOS, which are significantly better than the baselines. Code is publicly available at https://github.com/hengliusky/Few_shot_RVOS.", + "bbox": [ + 75, + 358, + 473, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 796, + 209, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Referring video object segmentation (RVOS) aims to segment target objects described in natural language in", + "bbox": [ + 76, + 821, + 468, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/51c78b03dfa4f5896407f3be56632029b4e9182c5e1f088ab1e018a35182bfbe.jpg", + "image_caption": [ + "(a) Data distribution in RVOS" + ], + "image_footnote": [], + "bbox": [ + 501, + 323, + 687, + 393 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fffe53df1222bb9fdfd40c1597c476e240465d053f8c7d1489e8437b3463a70f.jpg", + "image_caption": [ + "(b) Data distribution in Few-shot RVOS" + ], + "image_footnote": [], + "bbox": [ + 696, + 323, + 887, + 393 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/04ceb22e28d922f20e90a16ee492e24a0fa73a6a57c4c9b3095190e5eea3a3a0.jpg", + "image_caption": [ + "Text: \"A dog standing in water\"", + "(c) Few-shot RVOS" + ], + "image_footnote": [], + "bbox": [ + 503, + 412, + 681, + 489 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2e700290fbc6d2afa0990fe98144ca1ffcef690df869fa65d5230ba891266d44.jpg", + "image_caption": [ + "Text: \"A dog walking along the shore\"", + "Figure 1: Comparison of Few-shot RVOS and RVOS and the setting of Few-shot RVOS. (a) The training and testing sets overlap in the RVOS. (b) Disjoint training and testing sets in the Few-shot RVOS. Different shapes represent different classes. (c) Few-shot RVOS segments the referred object of the same class as the support set in the video." + ], + "image_footnote": [], + "bbox": [ + 683, + 412, + 887, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "videos. In real-world scenarios, it has a wide range of applications, such as video editing [9] and human-computer interaction, so RVOS has attracted much attention from the research community. Unlike traditional semi-supervised video object segmentation [10], RVOS is more challenging because it not only lacks the ground-truth mask of the first frame of the video but also needs to interact with multimodal information of vision and language.", + "bbox": [ + 496, + 654, + 890, + 775 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The great success of various tasks based on deep learning benefits from sufficient labeled data. Detailed annotated masks and language descriptions in real-world RVOS tasks are relatively scarce. The researchers have to annotate each frame in the video in detail and provide a referring expression for the segmentation object. Therefore, obtaining high-quality labeled data requires a high cost. With the popularity of movies, YouTube videos, TikTok streaming videos,", + "bbox": [ + 496, + 779, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. This work was done when G. Li visited to Feng Zheng Lab in Southern University of Science and Technology. \n†Corresponding author.", + "bbox": [ + 76, + 862, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2684", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "etc., video data in various fields has shown explosive growth in this media age. The demand for processing diverse data has brought significant challenges. In order to handle diverse data, existing RVOS methods must rely on massive and diverse labeled data for training. But due to fixed and limited training classes, existing RVOS methods [1, 33] are essentially constrained to adapt to the highly dynamic and highly diverse data in the real world. On the other hand, if ones fine-tune existing RVOS methods on a few samples to adapt to real-world data, high-quality results are hard to be achieved because the labelled data is insufficient to support the model for learning the new semantics. Therefore, how to make the RVOS methods applicable to real-world diverse data with a lower cost is an urgent problem.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this problem, we propose the cross-modal affinity (CMA) module to build multimodal relationships in a few samples and learn new semantic information for diversified data. Specifically, given only a few annotated samples (language expressions and the referred object masks), we hierarchically fuse visual and text features in a cross-attention manner to obtain robust feature representations for a specific category. In this way, the model can handle enormous data in the same category more efficiently.", + "bbox": [ + 75, + 304, + 472, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Essentially, the proposed method targets limited samples. Therefore, we generalize the problem as Few-Shot Referring Video Object Segmentation (FS-RVOS). We show the setting of FS-RVOS and the difference from existing RVOS in Figure 1. Unlike RVOS, the training and testing sets' categories disjoint in the FS-RVOS. Given a few support video clips together with corresponding language descriptions and object masks, FS-RVOS aims at segmenting videos in the query set, as shown in Figure 1(c).", + "bbox": [ + 75, + 443, + 472, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The key to FS-RVOS lies in the support set utilization and understanding of vision-language information. To better leverage the information in the support set, two methods have been proposed based on the prototype and attention mechanisms. The prototype-based [21, 35] methods compress the features belonging to different classes to obtain prototypes. However, noise is easily generated during the process. In addition, the spatial structures are ignored, resulting in different degree of information loss. Another methods [37, 38, 39] employ the attention mechanism to encode foreground pixels from support features and aggregate them with query features. Although these methods achieve high-quality results in image and video domains, they are still under-explored in vision-language tasks.", + "bbox": [ + 75, + 580, + 472, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To better utilize vision-language inputs, we propose the cross-modal affinity module to build the multimodal relationships between samples in the support and query sets. Specifically, multimodal features within the support set and query set are first fused separately. The information among them is then aggregated, which effectively prevents query features from being biased by irrelevant features.", + "bbox": [ + 75, + 795, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since this is the first work exploring Few-shot RVOS, the existing datasets are not directly applicable. Therefore, we build up a new FS-RVOS benchmark based on Ref-YouTube-VOS [22], named Mini-Ref-YouTube-VOS. The new benchmark covers a wide range with a balanced number of high-quality videos in each category. To measure the model's generalization ability, we also build a dataset different from natural scenes based on a synthetic dataset SAIL-VOS [13], named Mini-Ref-SAIL-VOS. Since only videos and detailed annotated masks exist in the SAIL-VOS dataset, we add natural language descriptions corresponding to the segmentation targets for the dataset.", + "bbox": [ + 496, + 90, + 893, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this work are as follows.", + "bbox": [ + 517, + 273, + 857, + 287 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- For real-world limited samples, we propose a CrossModal Affinity (CMA) for building multimodal information affinity for referring video object segmentation.", + "- We explore a novel Few-shot RVOS problem, which learns new semantic information with limited samples and can adapt to diverse scenarios.", + "- We build up the first FS-RVOS benchmark, where we conduct comprehensive comparisons with existing methods, showing the superiority of the proposed model." + ], + "bbox": [ + 500, + 294, + 890, + 443 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 459, + 640, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Few-Shot Semantic Segmentation. Few-shot semantic segmentation, first proposed by Shaban et al. [23], aims to learn how to segment new categories of images through a few samples. Recent advances in few-shot semantic segmentation originate from the application of metric learning. Based on PrototypicalNet, Dong et al. [7] first employ the metric learning technique and apply cosine similarity between pixels and prototypes for prediction. In addition, PANet et al. [31] introduce prototype alignment regularization to simplify the framework. PFENet et al. [28] use prior knowledge from the pretrained backbone to find the regions of interest and the different designs of feature pyramid modules, and previous leverage mappings to achieve better segmentation performance.", + "bbox": [ + 496, + 492, + 890, + 702 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, the effectiveness of these few-shot segmentation methods depends mainly on the quality of the prototypes obtained from the support set. Fan et al. [8] address the critical intra-class appearance differences inherent in the few-shot segmentation problem by performing self-support matching with query features. Their strategy effectively captures the consistent underlying features of query objects to match query features. Tian et al. [27] propose a novel context-aware prototype learning method that leverages prior knowledge from support samples and dynamically enriches contextual information by using adaptive features. Motivated by the idea that using the base learner to identify confusing regions in the query image and further", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2685", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "refining the predictions of the meta-learner, BAM [15] establishes a new method for few-shot segmentation that does not focus on feature extraction or visual correspondence.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compared to image-based few-shot segmentation, few-shot video object segmentation works are relatively rare and remain in the early stage. The initial work [25], [3] mainly solves this problem through the attention mechanism. However, these methods do not consider temporal information. Thus, based on temporal transductive, the recent work [24] applies reasoning mechanisms and has achieved good results in cross-domain scenarios. In a word, all the above-mentioned few-shot segmentation methods are only for a single modality - image or video, and cannot handle segmentation under multimodal conditions (i.e., with linguistic referring expressions).", + "bbox": [ + 75, + 137, + 470, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Referring Video Object Segmentation. Gavrilyuk et al. [11] first introduce the RVOS task. They generate convolutional dynamic filters from textual representations and convolve them with visual features of different resolutions to obtain segmentation masks. To overcome the limitations of traditional dynamic convolution, Wang et al. [30] propose a context-modulated dynamic convolution operation for RVOS, where the kernel is generated from language sentences and surrounding contextual features. However, since the focus is only on video actors and actions, their approach only applies to a few object classes and action-oriented descriptions. Weak-Shot Semantic Segmentation (WSSS) [4, 42] focuses on the overall scene in the image, treating masks and text as the support set and text as the query set. However, in WSSS, the text is limited to single words or phrases indicating class names and directly mapped to labels for pixel-level classification.", + "bbox": [ + 75, + 325, + 468, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Khoreva et al. [14] propose a two-stage approach that first performs referring expressions grounding and then utilizes the predicted bounding boxes to guide pixel-wise segmentation. Seo et al. [22] also present a framework called URVOS, which first predicts the initial mask based on the image and then utilizes the predicted mask of the previous frame for RVOS by memorizing the attention module.", + "bbox": [ + 75, + 582, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most recent RVOS works employ cross-attention to interact visual images with linguistic information. LBDT [6] uses language as an intermediate bridge to connect temporal and spatial information and leverages cross-modal attention operations to aggregate language-related motion and appearance. MMVT [40] calculates the optical flow between frames and fuses it as motion information with text features and visual features. However, these frame-based spatial granularity multimodal fusion methods have limitations and tend to lead to mismatches between visual and linguistic information. Therefore, a recent piece of work [32, 40] explores a novel multi-level representation learning method and introduces dynamic semantic alignment to adaptively fuse the two modal information.", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformer [29] has been widely applied and achieved great success in many computer vision tasks, such as object detection [2, 43] and image segmentation [41, 5]. Since DETR [2] introduces a new query-based paradigm, the latest works [1, 33, 16] prefer to apply the DETR's framework for RVOS task. Specifically, they utilize Transformer structures to interact visual images with linguistic data. Because Transformer has a remarkable ability to mine non-local correlation, they are able to attain SOTA performance in accuracy and efficiency. Despite the relative effectiveness of current RVOS techniques, they are primarily restricted to regular supervised learning settings, which would not be able to deal with unseen scenes with few shots.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 500, + 300, + 598, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 324, + 609, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the setting of FS-RVOS, we have training and testing datasets $D_{train}$ and $D_{test}$ with disjoint category sets $C_{train}$ and $C_{test}$ , i.e., $C_{train} \\cap C_{test} = \\emptyset$ . Similar to few-shot learning tasks [26], episode training is adopted in this work, where $D_{train}$ and $D_{test}$ consist of several episodes. Each episode contains a support set $S$ and a query set $Q$ where the text-referred objects (target objects) from both sets belong to the same class. The support set has $K$ image-mask pairs $S = \\{x_k, m_k\\}_{k=1}^K$ and the corresponding referring expression with $L$ words $T_s = \\{t_i\\}_{i=1}^L$ , where $m_k$ is the ground-truth mask of the video frame $x_k$ . The query set $Q = \\{x_i^q\\}_{i=1}^N$ is a selection of consecutive frames from a video and the corresponding natural language description with $M$ words $T_q = \\{t_i\\}_{i=1}^M$ , $N$ is the number of frames. With the setting above, FS-RVOS encourages models to segment objects with the unseen class in a query set based on a few samples in the support set.", + "bbox": [ + 496, + 348, + 890, + 608 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 2, our framework mainly consists of a Feature Extraction module, a Cross-modal Affinity module (CMA), and a Mask Generation module. With the support and query data as input, the framework predicts object masks for the query data, under the guidance of the corresponding language expressions. Specifically, the vision and text encoders extract features for visual and textual inputs, respectively. Then, CMA fuses visual and textual features hierarchically. The fused features are used to build the relationship between the support set and the query set. The output features are finally fed to the Mask Generation module to get the final segmentation results.", + "bbox": [ + 496, + 609, + 890, + 790 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Feature Extraction", + "text_level": 1, + "bbox": [ + 500, + 799, + 681, + 814 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use a shared-weight visual encoder to extract multiscale features from each frame in the support set and query set, resulting in visual feature sequences $F_{vs} = \\{f_{vs}\\}_{vs=1}^{K}$ and $F_{vq} = \\{f_{vq}\\}_{vq=1}^{N}$ . For linguistic information, we use a Transformer-based text encoder [19] to extract text features", + "bbox": [ + 496, + 821, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2686", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/175a6b26cca735b38aae6825349ebb0e580a1356544d946b4b5fcc3082415177.jpg", + "image_caption": [ + "Figure 2: The overall pipeline of our framework. The feature encoder extracts visual and textual information from the support and query sets. Then, the Cross-modal Affinity module calculates the multimodal information affinity between the support set and the query set. Finally, the final segmentation result is obtained through Mask Generation." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$F_{ts} = \\{f_{ts}\\}_{ts=1}^{L}$ and $F_{tq} = \\{f_{tq}\\}_{tq=1}^{M}$ from the natural language descriptions $T_s$ and $T_q$ that correspond to the input support data and the query data.", + "bbox": [ + 76, + 439, + 470, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Cross-modal Affinity Construction", + "text_level": 1, + "bbox": [ + 76, + 505, + 380, + 522 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With a few samples in the support set, the goal of FS-RVOS is to efficiently leverage the given information and quickly adapt to relevant scenarios. Compared with conventional few-shot tasks, FS-RVOS not only builds the affinity between the support and query sets but also involves multimodal relationships between videos and referring expressions. Therefore, FS-RVOS is more challenging and requires specialized solutions for high-quality results.", + "bbox": [ + 75, + 532, + 468, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose the Cross-Modal Affinity (CMA) module to achieve this, as shown in Figure 3. We first perform crossattention fusion between the visual and textual features of support and query data, to obtain pixel-augmented multimodal features. Then, in order to aggregate beneficial information in support features, we build an affinity relationship between the support set and the query set.", + "bbox": [ + 75, + 655, + 470, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the diversity of referred objects and the drastic changes between video frames, it is a challenge to achieve the accurate location of the target only by visual information. Therefore, to obtain the accurate positioning of the segmentation target, we use language information as a supplement, which contains a specific description of the referred objects. To interact and align the visual features and text features, multi-head cross-attention (MCA) is proposed to fuse multimodal information, achieving two multi-scale", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "feature maps $F_{vs}^{\\prime} = \\{f_s^{\\prime}\\}_{s = 1}^{K}$ and $F_{vq}^{\\prime} = \\{f_q^{\\prime}\\}_{q = 1}^{N}$ :", + "bbox": [ + 498, + 88, + 834, + 109 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {v s} ^ {\\prime} = \\operatorname {M C A} \\left(f _ {v s}, f _ {t s}\\right), f _ {v q} ^ {\\prime} = \\operatorname {M C A} \\left(f _ {v q}, f _ {t q}\\right), \\quad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 117, + 893, + 138 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{vs}$ , $f_{vq}$ represent the visual features of support and query, $f_{ts}$ , $f_{tq}$ are their corresponding textual features. Here we calculate an affinity between textual features and visual features to filter out irrelevant visual information. Compared with concatenation, MCA suits our framework better since it can leverage the similarities between multimodal features for information complementation.", + "bbox": [ + 496, + 146, + 893, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The affinity between the support set and query set indicates the multimodal feature correlation among them, providing valuable clues for the segmentation of the query data. Although the objects to segment in the support and query sets belong to the same category, their visual properties usually have significant differences, such as appearance, pose, and scene. This means only a tiny part of the information in the support data is conducive to segmenting the query data, while other information will cause bad results. Therefore, we urgently need to solve the problem of computing the correct affinity relationship between multimodal information in the support and query sets.", + "bbox": [ + 496, + 252, + 890, + 433 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve this, we propose a self-affinity block to encode the query features and a cross-affinity block to enable the query features to focus on beneficial pixels in the support features. In particular, given the input query features, we utilize a convolution operation to map them as query $q_{q}$ , key $k_{q}$ , and value $v_{q}$ . We perform the same operation for the support features to map them to key $k_{s}$ and value $v_{s}$ . The input of the self-affinity block does not include the support features and mainly aggregates the context information of the query features for better segmentation.", + "bbox": [ + 496, + 433, + 892, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, we calculate the affinity map $A^Q = \\frac{q_q \\cdot (k_q)^{\\mathrm{T}}}{\\sqrt{d_{head}}}$ , where $d_{head}$ is the hidden dimension of the input sequences, and we assume all sequences have the same dimension 256 by default. Therefore, the query features after the self-affinity block are represented as:", + "bbox": [ + 496, + 583, + 893, + 664 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {s} = \\operatorname {S o f t m a x} \\left(A ^ {Q}\\right) v _ {q}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 674, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then feed the obtained query features to the cross-affinity block. The purpose of the cross-affinity block is to construct the cross-affinity relationship between the support features and the query features and aggregate the useful information. Our cross-affinity block can be formulated as:", + "bbox": [ + 496, + 700, + 893, + 777 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq u e r y _ {f e a t} = \\operatorname {S o f t m a x} \\left(\\frac {q _ {s} \\cdot \\left(k _ {s}\\right) ^ {\\mathrm {T}}}{\\sqrt {d _ {h e a d}}}\\right) v _ {s}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 787, + 890, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $q_{s}$ is the output of the self-affinity block. Through these two modules, query features enhance features by modeling contextual information and computing the correlation between support and query features, effectively avoiding the attention bias caused by irrelevant features.", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2687", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/474a3563cbe4faad7d046799fd570a34df91ba3f0e3ac0631ab5ec1c2cc3c202.jpg", + "image_caption": [ + "Figure 3: The architecture of the Cross-modal Affinity (CMA) module. We use multi-head cross-attention to fuse visual and text features to get more robust features. Self-affinity for modeling contextual information on query features and cross-affinity for aggregating beneficial information from support features." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 468, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Mask Generation", + "text_level": 1, + "bbox": [ + 76, + 385, + 246, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The goal of the Mask Generation module is to find the most relevant objects and decode the features step by step. To achieve this goal, the structure of Deformable-DETR [43] and feature pyramid [17] has been used in our work. We add the corresponding positional encoding to the feature sequence that aggregates beneficial information, which is then sent to the Transformer encoder. In the decoder part of Transformer, we introduce $N$ learnable anchor boxes as queries to represent the instances of each frame. These queries are replicated as decoder input for all frames and finally converted into instance embeddings by the decoder, resulting in $N_{q} = T \\times N$ predictions.", + "bbox": [ + 75, + 407, + 468, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the feature pyramid network, in order to gradually fuse multimodal features from different layers, the output of the Transformer encoder and the features from the vision encoder are stacked to form hierarchical features. We use $f_{v}^{l}$ to represent visual features at each level. First, we downsample the multi-scale visual features, and the time dimension remains unchanged. Then interact with visual and linguistic features in a cross-attention manner to enhance object pixel features, thereby facilitating mask prediction. The fused features are upsampled to restore the previous shape:", + "bbox": [ + 75, + 590, + 468, + 741 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC r o s s \\left(f _ {v} ^ {l}, f _ {t q}\\right) = \\operatorname {S o f t m a x} \\left(\\frac {f _ {v} ^ {l} \\cdot \\left(f _ {t q}\\right) ^ {\\mathrm {T}}}{\\sqrt {d _ {\\text {h e a d}}}}\\right) f _ {t q}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 750, + 468, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{tq}$ represents the text features corresponding to the query set. Finally, we pass the features of the last layer through a $3 \\times 3$ convolutional layer to get the final feature maps $F_{seg} = \\{f_{seg}^{t}\\}_{t=1}^{T}$ , where $f_{seg}^{t} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C}$ .", + "bbox": [ + 75, + 792, + 468, + 856 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Furthermore, we construct a set of auxiliary heads to obtain the final object mask across frames. The class head is used to calculate the confidence score $s_t$ . The score indi", + "bbox": [ + 75, + 856, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "cates whether the instance corresponds to the referred object and whether the object is visible in the current frame. The kernel head is implemented by three consecutive linear layers, which generate the parameters $W = \\{w_{t}\\}_{t=1}^{N_{q}}$ of the $N_{q}$ dynamic kernels. We use them as convolution filters on the feature maps, generating a series of segmentation masks.", + "bbox": [ + 496, + 90, + 890, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Loss Function", + "text_level": 1, + "bbox": [ + 500, + 191, + 643, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Mask Generation, we use $N$ learnable anchor boxes as queries and generate a set of $N_{q} = T \\times N$ prediction sequences. We denote the predicted sequence as $\\hat{y} = \\{\\hat{y}_i\\}_{i=1}^{N_q}$ and the prediction for the $i^{\\text{th}}$ instance is expressed as:", + "bbox": [ + 496, + 214, + 890, + 279 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {i} = \\left\\{\\hat {s} _ {i} ^ {t}, \\hat {m} _ {i} ^ {t} \\right\\} _ {t = 1} ^ {T}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 285, + 890, + 308 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{s}_i^t\\in \\mathbb{R}^1$ is a fractional score indicating whether the instance corresponds to the referred object. $\\hat{m}_i^t\\in \\mathbb{R}^{\\frac{H}{4}\\times \\frac{W}{4}}$ is the predicted binary segmentation mask. Similar to the previous methods [1, 33], we use dynamic convolution to generate the object mask. We get the final feature maps $f_{seg}^{t}$ through the feature pyramid network, and the mask prediction can be calculated by $\\hat{m}^t = \\left\\{w_t*f_{seg}^t\\right\\}$ .", + "bbox": [ + 496, + 316, + 890, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The sequence of ground-truth instances is denoted as $y = \\{s^t, m^t\\}_{t=1}^T$ , and $s^t$ is an one-hot value and equals 1 when the ground-truth instance is visible in the frame, and 0 otherwise. Our loss function is defined as:", + "bbox": [ + 496, + 425, + 890, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (y, \\hat {y} _ {i}) = \\lambda_ {c l s} \\mathcal {L} _ {c l s} (y, \\hat {y} _ {i}) + \\lambda_ {k e r n e l} \\mathcal {L} _ {k e r n e l} (y, \\hat {y} _ {i}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 494, + 890, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{cls}, \\lambda_{kernel}$ are hyperparameters to balance the loss. We use focal loss [18] (denoted as $\\mathcal{L}_{cls}$ ) to supervise the prediction of instance sequence reference results. $\\mathcal{L}_{kernel}$ is a combination of DICE loss [20] and the binary mask focal loss.", + "bbox": [ + 496, + 526, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Inference", + "text_level": 1, + "bbox": [ + 500, + 609, + 609, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the inference phase, we treat all input video frames as a whole and predict the mask trajectory for the entire video using only one forward pass. Given an input video and the corresponding linguistic expression, our model generates a sequence of $N$ instances. For each frame, we select the instance sequence with the highest confidence score as the final prediction, and its index can be expressed as:", + "bbox": [ + 496, + 633, + 890, + 739 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\bar {s} = \\arg \\max s _ {i}. \\tag {7} \\\\ i \\in \\{1, 2, \\dots , N \\} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 750, + 890, + 775 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final prediction $m = \\{s_t\\}_{t=1}^T$ for each frame is obtained from the mask candidate set $\\hat{m}^t$ with index $\\overline{s}$ .", + "bbox": [ + 496, + 786, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Benchmark", + "text_level": 1, + "bbox": [ + 500, + 830, + 622, + 844 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the existing RVOS datasets [22, 14, 34, 11] only target specific scenarios, the model cannot handle the diverse scenarios in the real world. Likewise, these datasets", + "bbox": [ + 496, + 854, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2688", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fc95c807c4f5d0914d457f4367feb471ebe29a82d69c66647db43d2aeee61614.jpg", + "image_caption": [ + "A man in a brown jacket is standing on the right" + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 885, + 167 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/131a5f661cec88b0ddc78dcaabd961a2821e393d0d6632cafc9494c973be2f7a.jpg", + "image_caption": [ + "A man in a gray coat standing on the right is saying something" + ], + "image_footnote": [], + "bbox": [ + 83, + 189, + 885, + 271 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9512643f130555d90df3f4470e02e062e7cfafb4620217e1afcd65c2be234811.jpg", + "image_caption": [ + "A brown dog is barking", + "Figure 4: Annotation examples of the Mini-Ref-SAIL-VOS dataset." + ], + "image_footnote": [], + "bbox": [ + 83, + 292, + 885, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "are not suitable for the few-shot RVOS problem. This is because the train/test/Validation sets of these datasets have class repetition and cannot be used to evaluate the generality of unseen classes.", + "bbox": [ + 75, + 426, + 467, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mini-Ref-YouTube-VOS. To match the FS-RVOS setting, we build up a new dataset called Mini-Ref-YouTube-VOS based on the Ref-YouTube-VOS dataset [22]. The data that can be directly obtained from the Ref-YouTube-VOS dataset contains 3,471 videos, 12,913 referring expressions, and annotated instances covering more than 60 categories. However, some videos in this dataset consist of multiple category instances. When preparing data for the few-shot setting, we cleaned up the dataset, i.e., removing such videos and keeping only those containing only one category instance, a total of 2387 videos were obtained.", + "bbox": [ + 75, + 496, + 467, + 661 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The video data in the dataset should be class-balanced, and the number of samples in each class should not vary too much to avoid overfitting any class. Therefore, we deal with the categories whose number of videos does not meet the requirements to ensure the class balance of the dataset. After the above screening, 1,668 videos were obtained, including 48 classes. To better show the model results, we adopt the cross-validation method to divide the dataset into four folds on average. Each fold contains 36 training and 12 test classes with disjoint categories.", + "bbox": [ + 75, + 664, + 467, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mini-Ref-SAIL-VOS. Most Mini-Ref-YouTube-VOS data involve natural scenes of a relatively homogeneous type and therefore do not represent the diversity of data in the real world. To better demonstrate the generalization of our model, we collect videos from SAIL-VOS [13] to", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "construct a new dataset Mini-Ref-SAIL-VOS. The SAIL-VOS dataset is a synthetic dataset collected from a video game GTA-V, aiming to foster semantic amodal segmentation research. In SAIL-VOS, each frame is accompanied by densely annotated, pixel-wise and amodal segmentation masks with semantic labels. Since the data is collected from the game, phenomena such as shot transition, segmentation target cross-frame, and target occlusion are inevitable, which brings challenges to the segmentation task.", + "bbox": [ + 496, + 426, + 890, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We reorganize the SAIL-VOS dataset to pick out samples suitable for the FS-RVOS setting. First, for videos with few frames for segmentation targets, we directly discard them. For the case where the segmentation target appears across frames, we manually delete the frames where the target does not appear in the middle to maintain the temporal continuity of the segmentation target. For phenomena such as object occlusion, we characterize it as a challenge and do not deliberately delete video frames with object occlusion. Following the above settings, we collected a dataset with 68 videos and 3 semantic categories.", + "bbox": [ + 496, + 565, + 890, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is worth noting that although there are accurate mask annotations in the SAIL-VOS dataset, natural language description corresponding to the segmentation target is not available. Thus, to adapt it to FS-RVOS, we employed expert annotators to provide referring expressions after data collection. Given a pair of videos for each annotator, the video frames are superimposed with corresponding masks to indicate the objects to be segmented. The annotators were then asked to provide a distinguishing statement with a word limit of 20 words. To ensure the quality of natural language annotations, all annotations are verified and cleaned", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2689", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/43183858f2a5ddd04d3f986a4cb8708d6d4f3dd097aeb7c72e1fcbc0710aaa50.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFold-1Fold-2Fold-3Fold-4Mean
JDANet [3]4733.538.54440.8
Ours59.545.350.457.353.1
FDANet [3]49.338.241.445.843.7
Ours60.848.951.358.154.8
", + "bbox": [ + 81, + 89, + 465, + 172 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/05d704f298d63f8ae6458567f25b9c4078bb139678c2f8b962bf032aef190c67.jpg", + "table_caption": [ + "Table 1: Quantitative results on Mini-Ref-YouTube-VOS. We added visual language fusion modules to DANet." + ], + "table_footnote": [], + "table_body": "
MethodFold-1Fold-2Fold-3Fold-4Mean
JDANet [3]54.347.630.930.640.9
Ours80.980.880.168.977.7
FDANet [3]54.148.435.23643.4
Ours77.17777.367.874.8
", + "bbox": [ + 81, + 222, + 465, + 308 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "up after the initial annotation. The target will not be used if the natural language description cannot clearly describe the target. As shown in Figure 4, we show the selected videos along with referring expressions.", + "bbox": [ + 75, + 352, + 468, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 426, + 209, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 450, + 294, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We adopt ResNet-50 [12] and RoBERTa-Base [19] as our vision and text encoders, respectively. During the training stage, the parameters of both encoders are frozen. In our experiments, we adopt a 5-shot setting. Specifically, we extract 5 consecutive frames and the corresponding referring expressions from a certain video of a class as a support set. The query set is composed of consecutive frames and corresponding referring expressions extracted from other videos belonging to the same class. We test each fold 5 times and report the average confidence of the results. Our model utilizes AdamW for optimization. The weight decay is $5 \\times 10^{-4}$ and the initial learning rate is $1 \\times 10^{-4}$ . To balance GPU memory efficiency, we downsample all video frames, with the shortest video frame size being 360 and the longest 640. The parameters of the loss function are set as $\\lambda_{cls} = 2$ , $\\lambda_{kernel} = 5$ . All methods for conducting experiments will be pre-processed and fine-tuned in the same way, i.e., pre-trained on Ref-COCO [36] dataset.", + "bbox": [ + 75, + 474, + 468, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following the settings of previous RVOS works, we use the region similarity $(\\mathcal{I})$ and the contour accuracy $(\\mathcal{F})$ to measure the model performance.", + "bbox": [ + 75, + 747, + 468, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Results", + "text_level": 1, + "bbox": [ + 76, + 801, + 171, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As a novel problem, no relevant works can be directly used for comparisons. Therefore, we choose DANet [3] as the baseline given we both focus on few-shot video segmentation. For a fair comparison, we add a visual-language fusion module to the Few-Shot VOS model.", + "bbox": [ + 75, + 824, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/80890ff27b7a805d02cd4a8e55a4863eada4566e6de8fdc1f9bcb7e02916f14e.jpg", + "table_caption": [ + "Table 2: Quantitative results on Mini-Ref-SAIL-VOS." + ], + "table_footnote": [], + "table_body": "
MethodJFJ&F
LBDT [6]27.5 / 42.436.2 / 37.331.6 / 39.6
ReferFormer [33]65.1 / 74.162.8 / 64.964.0 / 69.5
MTTR [1]66.5 / 69.764.9 / 68.165.7 / 68.9
Ours80.977.179
", + "bbox": [ + 506, + 89, + 883, + 176 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3ccff4b6b91fccfc764a372f22d9f304a4fce86fe6dcebd5c6fd15b9f5c9299a.jpg", + "table_caption": [ + "Table 3: Comparison with state-of-the-art methods from RVOS on the Mini-Ref-SAIL-VOS dataset to measure the model's generalization. Underlined scores are achieved after fine-tuning." + ], + "table_footnote": [], + "table_body": "
Self-affinityCross-affinityJ&F
--57.9
✓-59.2
✓✓60.2
", + "bbox": [ + 560, + 258, + 831, + 330 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4: Ablation studies that validate the effectiveness of each component in our CMA. The first result is obtained with our baseline.", + "bbox": [ + 498, + 340, + 893, + 386 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Mini-Ref-YouTube-VOS. We present the experimental results of our model on the Mini-Ref-YouTube-VOS dataset in Table 1. It can be observed that our method significantly outperforms DANet. Compared with previous methods, our method achieves a substantial increase in average performance, with an average improvement of more than $10\\%$ . The excellent performance demonstrates the superiority and robustness of our proposed method.", + "bbox": [ + 496, + 406, + 890, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Mini-Ref-SAIL-VOS. To evaluate the generalization of our model, we make further experiments and comparisons on the Mini-Ref-SAIL-VOS dataset. We do not perform new training on the Mini-Ref-SAIL-VOS dataset but directly test with the model trained on Mini-Ref-Youtube-VOS. Note that the videos in the Mini-Ref-SAIL-VOS dataset are from Game scenes, and they hold a noticeable domain different from the data in the Mini-Ref-Youtube-VOS dataset. In addition, the objects in some videos are occluded and these phenomena make this dataset somewhat challenging. We show the experimental results in Table 2. According to the Table, it is clear that our method achieves a significant improvement over the baseline.", + "bbox": [ + 496, + 536, + 890, + 732 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Moreover, we also make further comparisons with some state-of-the-art RVOS methods [6, 33, 1]. Here, we only show the results under Fold-1. To measure the RVOS model's generalization, we first directly test the trained RVOS models on the Mini-Ref-SAIL-VOS dataset. Since our few-shot learning task needs a few samples as support data, for a fair comparison, these RVOS models will be finetuned with a few samples. The corresponding results are shown in Table 3. From the table, it can be seen that although the fine-tuning of the existing models can lead to performance gains, there is still a big gap compared to our", + "bbox": [ + 496, + 734, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2690", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/abbc8c84edf7444b1c5876a957db1d2a9e28895b70aeb8dcab4eab629beaf73e.jpg", + "image_caption": [ + "(a)", + "a zebra to the left of another zebra", + "a zebra on the right side of the screen, eating grass" + ], + "image_footnote": [], + "bbox": [ + 116, + 88, + 885, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a5f015327f4a5f877837e8e31d12dedfdff432be38946d4c8e84fca097f7d6b8.jpg", + "image_caption": [ + "a bear walking towards another bear", + "a beer on the right hand side of another walking in their area." + ], + "image_footnote": [], + "bbox": [ + 116, + 178, + 885, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4c4a6dffdbdf34f15296d3602a351aeb37f6752321829b466f516fe15359512d.jpg", + "image_caption": [ + "a whale swimming on the left of another whale", + "a whale, swimming deeper into the ocean, on the right side of the screen" + ], + "image_footnote": [], + "bbox": [ + 116, + 268, + 885, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5285a9bbe7acf98c882acd3df7f45356b33fc90a3cf4d12e8a6814cb7b644f47.jpg", + "image_caption": [ + "(b)", + "A man in a red dress and a hat standing on the left is talking to someone" + ], + "image_footnote": [], + "bbox": [ + 116, + 359, + 885, + 436 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8b8004bcdb7452cc6c9f3697fe58eafc4946fc669dc3383d087738bac56c409d.jpg", + "image_caption": [ + "A black car parked on the side of the road", + "Figure 5: Qualitative results on (a) Mini-Ref-YouTube-VOS and (b) Mini-Ref-SAIL-VOS." + ], + "image_footnote": [], + "bbox": [ + 117, + 458, + 885, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "proposed approach. This is because our model effectively constructs the multimodal relationship between the support set and the query set so that it can quickly adapt to new scenarios by only using a few samples.", + "bbox": [ + 75, + 588, + 468, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 659, + 230, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we perform an ablation study on the Mini-Ref-YouTube-VOS dataset to evaluate the design and the robustness of the model. Unless otherwise stated, we only show results under Fold-1. Denoting $\\mathcal{I}\\&\\mathcal{F}$ as the average of $\\mathcal{I}$ and $\\mathcal{F}$ , we can use the indicator to show the performance of the model.", + "bbox": [ + 75, + 681, + 468, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Cross-modal Affinity. We perform ablation studies on the components of the CMA in Table 4. The results of the baseline are shown in the first line. As mentioned before, the baseline refers to directly concatenating the support features and query features into the Mask Generation to obtain the segmentation mask.", + "bbox": [ + 75, + 779, + 468, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "First, we only utilize the self-affinity block to establish contextual information between pixels to enhance query", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "features. At this time, support features are concatenated with the enhanced query features and then fed to the Mask Generation module. It can be seen that good results are achieved, indicating that the Transformer does work for modeling features and extracting contextual information. By adding the proposed cross-affinity block, the performance can be further improved by $1\\%$ . Such comparisons show that the cross-affinity block properly constructs the multimodal relationship between the support set and the query set, effectively avoiding the bias of the query features.", + "bbox": [ + 496, + 588, + 890, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Qualitative Results", + "text_level": 1, + "bbox": [ + 500, + 768, + 681, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The qualitative results of our model are presented in Figure 5. From the figure, It can be seen that the proposed model can segment the referred objects accurately in a variety of challenging situations. Furthermore, we also show the qualitative results on the Mini-Ref-SAIL-VOS dataset. In general, our model always achieves high-quality results even in the face of samples from different scenes.", + "bbox": [ + 496, + 799, + 890, + 904 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2691", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 90, + 194, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we propose CMA to learn multimodal affinity in a few samples to segment diverse data. Further, we generalize it as a few-shot RVOS problem. We validate our model on the newly constructed datasets - Mini-RefYouTube-VOS and Mini-Ref-SAIL-VOS and obtain state-of-the-art performance. We hope this work can cast a light on future FS-RVOS research.", + "bbox": [ + 75, + 114, + 468, + 220 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported in part by the National Key R&D Program of China (Grant No. 2022YFF1202903), the National Natural Science Foundation of China (Grant No. 61971004, 62122035), the Natural Science Foundation of Anhui Province, China (Grant No. 2008085MF190), and the Equipment Advanced Research Sharing Technology Project, China (Grant No. 80912020104).", + "bbox": [ + 75, + 227, + 472, + 348 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 76, + 363, + 174, + 378 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Adam Botach, Evgenii Zheltonozhskii, and Chaim Baskin. End-to-end referring video object segmentation with multimodal transformers. arXiv preprint arXiv:2111.14821, 2021. 2, 3, 5, 7", + "[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 3, 5" + ], + "bbox": [ + 503, + 92, + 890, + 612 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2693", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/a0fe2dc9-eb10-4dc5-8bfa-8f5f03212fc3_model.json b/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/a0fe2dc9-eb10-4dc5-8bfa-8f5f03212fc3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3a1679d494a1dfcf81d7dd1729c9de3f7ac6c26e --- /dev/null +++ b/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/a0fe2dc9-eb10-4dc5-8bfa-8f5f03212fc3_model.json @@ -0,0 +1,2266 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.119, + 0.13, + 0.853, + 0.177 + ], + "angle": 0, + "content": "Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples" + }, + { + "type": "text", + "bbox": [ + 0.15, + 0.203, + 0.82, + 0.258 + ], + "angle": 0, + "content": "Guanghui Li\\(^{1*}\\), Mingqi Gao\\(^{2,3*}\\), Heng Liu\\(^{1\\dagger}\\), Xiantong Zhen\\(^{4}\\), Feng Zheng\\(^{2\\dagger}\\) \n\\(^{1}\\) Anhui University of Technology, \\(^{2}\\) Southern University of Science and Technology, \\(^{3}\\) University of Warwick, \\(^{4}\\) United Imaging" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.26, + 0.802, + 0.293 + ], + "angle": 0, + "content": "guanghui.li1998@gmail.com, mingqi.gao@outlook.com, hengliusky@aliyun.com, zhenxt@gmail.com, f.zheng@ieee.org" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.474, + 0.768 + ], + "angle": 0, + "content": "Referring video object segmentation (RVOS), as a supervised learning task, relies on sufficient annotated data for a given scene. However, in more realistic scenarios, only minimal annotations are available for a new scene, which poses significant challenges to existing RVOS methods. With this in mind, we propose a simple yet effective model with a newly designed cross-modal affinity (CMA) module based on a Transformer architecture. The CMA module builds multimodal affinity with a few samples, thus quickly learning new semantic information, and enabling the model to adapt to different scenarios. Since the proposed method targets limited samples for new scenes, we generalize the problem as - few-shot referring video object segmentation (FS-RVOS). To foster research in this direction, we build up a new FS-RVOS benchmark based on currently available datasets. The benchmark covers a wide range and includes multiple situations, which can maximally simulate real-world scenarios. Extensive experiments show that our model adapts well to different scenarios with only a few samples, reaching state-of-the-art performance on the benchmark. On Mini-Ref-YouTube-VOS, our model achieves an average performance of 53.1 J and 54.8 F, which are \\(10\\%\\) better than the baselines. Furthermore, we show impressive results of 77.7 J and 74.8 F on Mini-Ref-SAIL-VOS, which are significantly better than the baselines. Code is publicly available at https://github.com/hengliusky/Few_shot_RVOS." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.797, + 0.21, + 0.812 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.823, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Referring video object segmentation (RVOS) aims to segment target objects described in natural language in" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.324, + 0.688, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.399, + 0.664, + 0.411 + ], + "angle": 0, + "content": "(a) Data distribution in RVOS" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.324, + 0.888, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.698, + 0.399, + 0.889, + 0.411 + ], + "angle": 0, + "content": "(b) Data distribution in Few-shot RVOS" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.414, + 0.683, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.492, + 0.668, + 0.502 + ], + "angle": 0, + "content": "Text: \"A dog standing in water\"" + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.414, + 0.888, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.714, + 0.492, + 0.885, + 0.502 + ], + "angle": 0, + "content": "Text: \"A dog walking along the shore\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.507, + 0.737, + 0.518 + ], + "angle": 0, + "content": "(c) Few-shot RVOS" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.529, + 0.895, + 0.621 + ], + "angle": 0, + "content": "Figure 1: Comparison of Few-shot RVOS and RVOS and the setting of Few-shot RVOS. (a) The training and testing sets overlap in the RVOS. (b) Disjoint training and testing sets in the Few-shot RVOS. Different shapes represent different classes. (c) Few-shot RVOS segments the referred object of the same class as the support set in the video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.776 + ], + "angle": 0, + "content": "videos. In real-world scenarios, it has a wide range of applications, such as video editing [9] and human-computer interaction, so RVOS has attracted much attention from the research community. Unlike traditional semi-supervised video object segmentation [10], RVOS is more challenging because it not only lacks the ground-truth mask of the first frame of the video but also needs to interact with multimodal information of vision and language." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.902 + ], + "angle": 0, + "content": "The great success of various tasks based on deep learning benefits from sufficient labeled data. Detailed annotated masks and language descriptions in real-world RVOS tasks are relatively scarce. The researchers have to annotate each frame in the video in detail and provide a referring expression for the segmentation object. Therefore, obtaining high-quality labeled data requires a high cost. With the popularity of movies, YouTube videos, TikTok streaming videos," + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.863, + 0.469, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution. This work was done when G. Li visited to Feng Zheng Lab in Southern University of Science and Technology. \n†Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2684" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "etc., video data in various fields has shown explosive growth in this media age. The demand for processing diverse data has brought significant challenges. In order to handle diverse data, existing RVOS methods must rely on massive and diverse labeled data for training. But due to fixed and limited training classes, existing RVOS methods [1, 33] are essentially constrained to adapt to the highly dynamic and highly diverse data in the real world. On the other hand, if ones fine-tune existing RVOS methods on a few samples to adapt to real-world data, high-quality results are hard to be achieved because the labelled data is insufficient to support the model for learning the new semantics. Therefore, how to make the RVOS methods applicable to real-world diverse data with a lower cost is an urgent problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.473, + 0.442 + ], + "angle": 0, + "content": "To address this problem, we propose the cross-modal affinity (CMA) module to build multimodal relationships in a few samples and learn new semantic information for diversified data. Specifically, given only a few annotated samples (language expressions and the referred object masks), we hierarchically fuse visual and text features in a cross-attention manner to obtain robust feature representations for a specific category. In this way, the model can handle enormous data in the same category more efficiently." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.473, + 0.581 + ], + "angle": 0, + "content": "Essentially, the proposed method targets limited samples. Therefore, we generalize the problem as Few-Shot Referring Video Object Segmentation (FS-RVOS). We show the setting of FS-RVOS and the difference from existing RVOS in Figure 1. Unlike RVOS, the training and testing sets' categories disjoint in the FS-RVOS. Given a few support video clips together with corresponding language descriptions and object masks, FS-RVOS aims at segmenting videos in the query set, as shown in Figure 1(c)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.473, + 0.794 + ], + "angle": 0, + "content": "The key to FS-RVOS lies in the support set utilization and understanding of vision-language information. To better leverage the information in the support set, two methods have been proposed based on the prototype and attention mechanisms. The prototype-based [21, 35] methods compress the features belonging to different classes to obtain prototypes. However, noise is easily generated during the process. In addition, the spatial structures are ignored, resulting in different degree of information loss. Another methods [37, 38, 39] employ the attention mechanism to encode foreground pixels from support features and aggregate them with query features. Although these methods achieve high-quality results in image and video domains, they are still under-explored in vision-language tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To better utilize vision-language inputs, we propose the cross-modal affinity module to build the multimodal relationships between samples in the support and query sets. Specifically, multimodal features within the support set and query set are first fused separately. The information among them is then aggregated, which effectively prevents query features from being biased by irrelevant features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.273 + ], + "angle": 0, + "content": "Since this is the first work exploring Few-shot RVOS, the existing datasets are not directly applicable. Therefore, we build up a new FS-RVOS benchmark based on Ref-YouTube-VOS [22], named Mini-Ref-YouTube-VOS. The new benchmark covers a wide range with a balanced number of high-quality videos in each category. To measure the model's generalization ability, we also build a dataset different from natural scenes based on a synthetic dataset SAIL-VOS [13], named Mini-Ref-SAIL-VOS. Since only videos and detailed annotated masks exist in the SAIL-VOS dataset, we add natural language descriptions corresponding to the segmentation targets for the dataset." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.274, + 0.858, + 0.288 + ], + "angle": 0, + "content": "The main contributions of this work are as follows." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.295, + 0.891, + 0.34 + ], + "angle": 0, + "content": "- For real-world limited samples, we propose a CrossModal Affinity (CMA) for building multimodal information affinity for referring video object segmentation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.346, + 0.892, + 0.391 + ], + "angle": 0, + "content": "- We explore a novel Few-shot RVOS problem, which learns new semantic information with limited samples and can adapt to diverse scenarios." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.398, + 0.892, + 0.444 + ], + "angle": 0, + "content": "- We build up the first FS-RVOS benchmark, where we conduct comprehensive comparisons with existing methods, showing the superiority of the proposed model." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.295, + 0.892, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.46, + 0.642, + 0.475 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.703 + ], + "angle": 0, + "content": "Few-Shot Semantic Segmentation. Few-shot semantic segmentation, first proposed by Shaban et al. [23], aims to learn how to segment new categories of images through a few samples. Recent advances in few-shot semantic segmentation originate from the application of metric learning. Based on PrototypicalNet, Dong et al. [7] first employ the metric learning technique and apply cosine similarity between pixels and prototypes for prediction. In addition, PANet et al. [31] introduce prototype alignment regularization to simplify the framework. PFENet et al. [28] use prior knowledge from the pretrained backbone to find the regions of interest and the different designs of feature pyramid modules, and previous leverage mappings to achieve better segmentation performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "However, the effectiveness of these few-shot segmentation methods depends mainly on the quality of the prototypes obtained from the support set. Fan et al. [8] address the critical intra-class appearance differences inherent in the few-shot segmentation problem by performing self-support matching with query features. Their strategy effectively captures the consistent underlying features of query objects to match query features. Tian et al. [27] propose a novel context-aware prototype learning method that leverages prior knowledge from support samples and dynamically enriches contextual information by using adaptive features. Motivated by the idea that using the base learner to identify confusing regions in the query image and further" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2685" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "refining the predictions of the meta-learner, BAM [15] establishes a new method for few-shot segmentation that does not focus on feature extraction or visual correspondence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.471, + 0.319 + ], + "angle": 0, + "content": "Compared to image-based few-shot segmentation, few-shot video object segmentation works are relatively rare and remain in the early stage. The initial work [25], [3] mainly solves this problem through the attention mechanism. However, these methods do not consider temporal information. Thus, based on temporal transductive, the recent work [24] applies reasoning mechanisms and has achieved good results in cross-domain scenarios. In a word, all the above-mentioned few-shot segmentation methods are only for a single modality - image or video, and cannot handle segmentation under multimodal conditions (i.e., with linguistic referring expressions)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Referring Video Object Segmentation. Gavrilyuk et al. [11] first introduce the RVOS task. They generate convolutional dynamic filters from textual representations and convolve them with visual features of different resolutions to obtain segmentation masks. To overcome the limitations of traditional dynamic convolution, Wang et al. [30] propose a context-modulated dynamic convolution operation for RVOS, where the kernel is generated from language sentences and surrounding contextual features. However, since the focus is only on video actors and actions, their approach only applies to a few object classes and action-oriented descriptions. Weak-Shot Semantic Segmentation (WSSS) [4, 42] focuses on the overall scene in the image, treating masks and text as the support set and text as the query set. However, in WSSS, the text is limited to single words or phrases indicating class names and directly mapped to labels for pixel-level classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Khoreva et al. [14] propose a two-stage approach that first performs referring expressions grounding and then utilizes the predicted bounding boxes to guide pixel-wise segmentation. Seo et al. [22] also present a framework called URVOS, which first predicts the initial mask based on the image and then utilizes the predicted mask of the previous frame for RVOS by memorizing the attention module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Most recent RVOS works employ cross-attention to interact visual images with linguistic information. LBDT [6] uses language as an intermediate bridge to connect temporal and spatial information and leverages cross-modal attention operations to aggregate language-related motion and appearance. MMVT [40] calculates the optical flow between frames and fuses it as motion information with text features and visual features. However, these frame-based spatial granularity multimodal fusion methods have limitations and tend to lead to mismatches between visual and linguistic information. Therefore, a recent piece of work [32, 40] explores a novel multi-level representation learning method and introduces dynamic semantic alignment to adaptively fuse the two modal information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "Transformer [29] has been widely applied and achieved great success in many computer vision tasks, such as object detection [2, 43] and image segmentation [41, 5]. Since DETR [2] introduces a new query-based paradigm, the latest works [1, 33, 16] prefer to apply the DETR's framework for RVOS task. Specifically, they utilize Transformer structures to interact visual images with linguistic data. Because Transformer has a remarkable ability to mine non-local correlation, they are able to attain SOTA performance in accuracy and efficiency. Despite the relative effectiveness of current RVOS techniques, they are primarily restricted to regular supervised learning settings, which would not be able to deal with unseen scenes with few shots." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.301, + 0.599, + 0.317 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.325, + 0.611, + 0.34 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.609 + ], + "angle": 0, + "content": "In the setting of FS-RVOS, we have training and testing datasets \\( D_{train} \\) and \\( D_{test} \\) with disjoint category sets \\( C_{train} \\) and \\( C_{test} \\), i.e., \\( C_{train} \\cap C_{test} = \\emptyset \\). Similar to few-shot learning tasks [26], episode training is adopted in this work, where \\( D_{train} \\) and \\( D_{test} \\) consist of several episodes. Each episode contains a support set \\( S \\) and a query set \\( Q \\) where the text-referred objects (target objects) from both sets belong to the same class. The support set has \\( K \\) image-mask pairs \\( S = \\{x_k, m_k\\}_{k=1}^K \\) and the corresponding referring expression with \\( L \\) words \\( T_s = \\{t_i\\}_{i=1}^L \\), where \\( m_k \\) is the ground-truth mask of the video frame \\( x_k \\). The query set \\( Q = \\{x_i^q\\}_{i=1}^N \\) is a selection of consecutive frames from a video and the corresponding natural language description with \\( M \\) words \\( T_q = \\{t_i\\}_{i=1}^M \\), \\( N \\) is the number of frames. With the setting above, FS-RVOS encourages models to segment objects with the unseen class in a query set based on a few samples in the support set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.791 + ], + "angle": 0, + "content": "As shown in Figure 2, our framework mainly consists of a Feature Extraction module, a Cross-modal Affinity module (CMA), and a Mask Generation module. With the support and query data as input, the framework predicts object masks for the query data, under the guidance of the corresponding language expressions. Specifically, the vision and text encoders extract features for visual and textual inputs, respectively. Then, CMA fuses visual and textual features hierarchically. The fused features are used to build the relationship between the support set and the query set. The output features are finally fed to the Mask Generation module to get the final segmentation results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.682, + 0.815 + ], + "angle": 0, + "content": "3.2. Feature Extraction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.823, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We use a shared-weight visual encoder to extract multiscale features from each frame in the support set and query set, resulting in visual feature sequences \\( F_{vs} = \\{f_{vs}\\}_{vs=1}^{K} \\) and \\( F_{vq} = \\{f_{vq}\\}_{vq=1}^{N} \\). For linguistic information, we use a Transformer-based text encoder [19] to extract text features" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2686" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.325, + 0.473, + 0.419 + ], + "angle": 0, + "content": "Figure 2: The overall pipeline of our framework. The feature encoder extracts visual and textual information from the support and query sets. Then, the Cross-modal Affinity module calculates the multimodal information affinity between the support set and the query set. Finally, the final segmentation result is obtained through Mask Generation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.44, + 0.472, + 0.489 + ], + "angle": 0, + "content": "\\(F_{ts} = \\{f_{ts}\\}_{ts=1}^{L}\\) and \\(F_{tq} = \\{f_{tq}\\}_{tq=1}^{M}\\) from the natural language descriptions \\(T_s\\) and \\(T_q\\) that correspond to the input support data and the query data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.506, + 0.382, + 0.523 + ], + "angle": 0, + "content": "3.3. Cross-modal Affinity Construction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.653 + ], + "angle": 0, + "content": "With a few samples in the support set, the goal of FS-RVOS is to efficiently leverage the given information and quickly adapt to relevant scenarios. Compared with conventional few-shot tasks, FS-RVOS not only builds the affinity between the support and query sets but also involves multimodal relationships between videos and referring expressions. Therefore, FS-RVOS is more challenging and requires specialized solutions for high-quality results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.471, + 0.763 + ], + "angle": 0, + "content": "We propose the Cross-Modal Affinity (CMA) module to achieve this, as shown in Figure 3. We first perform crossattention fusion between the visual and textual features of support and query data, to obtain pixel-augmented multimodal features. Then, in order to aggregate beneficial information in support features, we build an affinity relationship between the support set and the query set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Due to the diversity of referred objects and the drastic changes between video frames, it is a challenge to achieve the accurate location of the target only by visual information. Therefore, to obtain the accurate positioning of the segmentation target, we use language information as a supplement, which contains a specific description of the referred objects. To interact and align the visual features and text features, multi-head cross-attention (MCA) is proposed to fuse multimodal information, achieving two multi-scale" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.089, + 0.836, + 0.11 + ], + "angle": 0, + "content": "feature maps \\(F_{vs}^{\\prime} = \\{f_s^{\\prime}\\}_{s = 1}^{K}\\) and \\(F_{vq}^{\\prime} = \\{f_q^{\\prime}\\}_{q = 1}^{N}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.118, + 0.894, + 0.139 + ], + "angle": 0, + "content": "\\[\nf _ {v s} ^ {\\prime} = \\operatorname {M C A} \\left(f _ {v s}, f _ {t s}\\right), f _ {v q} ^ {\\prime} = \\operatorname {M C A} \\left(f _ {v q}, f _ {t q}\\right), \\quad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.147, + 0.894, + 0.252 + ], + "angle": 0, + "content": "where \\( f_{vs} \\), \\( f_{vq} \\) represent the visual features of support and query, \\( f_{ts} \\), \\( f_{tq} \\) are their corresponding textual features. Here we calculate an affinity between textual features and visual features to filter out irrelevant visual information. Compared with concatenation, MCA suits our framework better since it can leverage the similarities between multimodal features for information complementation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.253, + 0.892, + 0.434 + ], + "angle": 0, + "content": "The affinity between the support set and query set indicates the multimodal feature correlation among them, providing valuable clues for the segmentation of the query data. Although the objects to segment in the support and query sets belong to the same category, their visual properties usually have significant differences, such as appearance, pose, and scene. This means only a tiny part of the information in the support data is conducive to segmenting the query data, while other information will cause bad results. Therefore, we urgently need to solve the problem of computing the correct affinity relationship between multimodal information in the support and query sets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.893, + 0.584 + ], + "angle": 0, + "content": "To achieve this, we propose a self-affinity block to encode the query features and a cross-affinity block to enable the query features to focus on beneficial pixels in the support features. In particular, given the input query features, we utilize a convolution operation to map them as query \\( q_{q} \\), key \\( k_{q} \\), and value \\( v_{q} \\). We perform the same operation for the support features to map them to key \\( k_{s} \\) and value \\( v_{s} \\). The input of the self-affinity block does not include the support features and mainly aggregates the context information of the query features for better segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.894, + 0.665 + ], + "angle": 0, + "content": "First, we calculate the affinity map \\( A^Q = \\frac{q_q \\cdot (k_q)^{\\mathrm{T}}}{\\sqrt{d_{head}}} \\), where \\( d_{head} \\) is the hidden dimension of the input sequences, and we assume all sequences have the same dimension 256 by default. Therefore, the query features after the self-affinity block are represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.675, + 0.892, + 0.693 + ], + "angle": 0, + "content": "\\[\nq _ {s} = \\operatorname {S o f t m a x} \\left(A ^ {Q}\\right) v _ {q}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.894, + 0.779 + ], + "angle": 0, + "content": "We then feed the obtained query features to the cross-affinity block. The purpose of the cross-affinity block is to construct the cross-affinity relationship between the support features and the query features and aggregate the useful information. Our cross-affinity block can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.788, + 0.892, + 0.822 + ], + "angle": 0, + "content": "\\[\nq u e r y _ {f e a t} = \\operatorname {S o f t m a x} \\left(\\frac {q _ {s} \\cdot \\left(k _ {s}\\right) ^ {\\mathrm {T}}}{\\sqrt {d _ {h e a d}}}\\right) v _ {s}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "where \\( q_{s} \\) is the output of the self-affinity block. Through these two modules, query features enhance features by modeling contextual information and computing the correlation between support and query features, effectively avoiding the attention bias caused by irrelevant features." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2687" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.47, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.277, + 0.47, + 0.368 + ], + "angle": 0, + "content": "Figure 3: The architecture of the Cross-modal Affinity (CMA) module. We use multi-head cross-attention to fuse visual and text features to get more robust features. Self-affinity for modeling contextual information on query features and cross-affinity for aggregating beneficial information from support features." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.386, + 0.248, + 0.4 + ], + "angle": 0, + "content": "3.4. Mask Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.47, + 0.59 + ], + "angle": 0, + "content": "The goal of the Mask Generation module is to find the most relevant objects and decode the features step by step. To achieve this goal, the structure of Deformable-DETR [43] and feature pyramid [17] has been used in our work. We add the corresponding positional encoding to the feature sequence that aggregates beneficial information, which is then sent to the Transformer encoder. In the decoder part of Transformer, we introduce \\(N\\) learnable anchor boxes as queries to represent the instances of each frame. These queries are replicated as decoder input for all frames and finally converted into instance embeddings by the decoder, resulting in \\(N_{q} = T \\times N\\) predictions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.469, + 0.742 + ], + "angle": 0, + "content": "In the feature pyramid network, in order to gradually fuse multimodal features from different layers, the output of the Transformer encoder and the features from the vision encoder are stacked to form hierarchical features. We use \\( f_{v}^{l} \\) to represent visual features at each level. First, we downsample the multi-scale visual features, and the time dimension remains unchanged. Then interact with visual and linguistic features in a cross-attention manner to enhance object pixel features, thereby facilitating mask prediction. The fused features are upsampled to restore the previous shape:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.75, + 0.469, + 0.786 + ], + "angle": 0, + "content": "\\[\nC r o s s \\left(f _ {v} ^ {l}, f _ {t q}\\right) = \\operatorname {S o f t m a x} \\left(\\frac {f _ {v} ^ {l} \\cdot \\left(f _ {t q}\\right) ^ {\\mathrm {T}}}{\\sqrt {d _ {\\text {h e a d}}}}\\right) f _ {t q}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.469, + 0.857 + ], + "angle": 0, + "content": "where \\( f_{tq} \\) represents the text features corresponding to the query set. Finally, we pass the features of the last layer through a \\( 3 \\times 3 \\) convolutional layer to get the final feature maps \\( F_{seg} = \\{f_{seg}^{t}\\}_{t=1}^{T} \\), where \\( f_{seg}^{t} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.857, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Furthermore, we construct a set of auxiliary heads to obtain the final object mask across frames. The class head is used to calculate the confidence score \\( s_t \\). The score indi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.184 + ], + "angle": 0, + "content": "cates whether the instance corresponds to the referred object and whether the object is visible in the current frame. The kernel head is implemented by three consecutive linear layers, which generate the parameters \\( W = \\{w_{t}\\}_{t=1}^{N_{q}} \\) of the \\( N_{q} \\) dynamic kernels. We use them as convolution filters on the feature maps, generating a series of segmentation masks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.192, + 0.645, + 0.206 + ], + "angle": 0, + "content": "3.5. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.215, + 0.892, + 0.28 + ], + "angle": 0, + "content": "In Mask Generation, we use \\(N\\) learnable anchor boxes as queries and generate a set of \\(N_{q} = T \\times N\\) prediction sequences. We denote the predicted sequence as \\(\\hat{y} = \\{\\hat{y}_i\\}_{i=1}^{N_q}\\) and the prediction for the \\(i^{\\text{th}}\\) instance is expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.286, + 0.892, + 0.309 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {i} = \\left\\{\\hat {s} _ {i} ^ {t}, \\hat {m} _ {i} ^ {t} \\right\\} _ {t = 1} ^ {T}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.317, + 0.892, + 0.426 + ], + "angle": 0, + "content": "where \\(\\hat{s}_i^t\\in \\mathbb{R}^1\\) is a fractional score indicating whether the instance corresponds to the referred object. \\(\\hat{m}_i^t\\in \\mathbb{R}^{\\frac{H}{4}\\times \\frac{W}{4}}\\) is the predicted binary segmentation mask. Similar to the previous methods [1, 33], we use dynamic convolution to generate the object mask. We get the final feature maps \\(f_{seg}^{t}\\) through the feature pyramid network, and the mask prediction can be calculated by \\(\\hat{m}^t = \\left\\{w_t*f_{seg}^t\\right\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.892, + 0.486 + ], + "angle": 0, + "content": "The sequence of ground-truth instances is denoted as \\( y = \\{s^t, m^t\\}_{t=1}^T \\), and \\( s^t \\) is an one-hot value and equals 1 when the ground-truth instance is visible in the frame, and 0 otherwise. Our loss function is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.496, + 0.892, + 0.526 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (y, \\hat {y} _ {i}) = \\lambda_ {c l s} \\mathcal {L} _ {c l s} (y, \\hat {y} _ {i}) + \\lambda_ {k e r n e l} \\mathcal {L} _ {k e r n e l} (y, \\hat {y} _ {i}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.892, + 0.601 + ], + "angle": 0, + "content": "where \\(\\lambda_{cls}, \\lambda_{kernel}\\) are hyperparameters to balance the loss. We use focal loss [18] (denoted as \\(\\mathcal{L}_{cls}\\)) to supervise the prediction of instance sequence reference results. \\(\\mathcal{L}_{kernel}\\) is a combination of DICE loss [20] and the binary mask focal loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.611, + 0.61, + 0.625 + ], + "angle": 0, + "content": "3.6. Inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.74 + ], + "angle": 0, + "content": "In the inference phase, we treat all input video frames as a whole and predict the mask trajectory for the entire video using only one forward pass. Given an input video and the corresponding linguistic expression, our model generates a sequence of \\( N \\) instances. For each frame, we select the instance sequence with the highest confidence score as the final prediction, and its index can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.75, + 0.892, + 0.776 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\bar {s} = \\arg \\max s _ {i}. \\tag {7} \\\\ i \\in \\{1, 2, \\dots , N \\} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.787, + 0.891, + 0.817 + ], + "angle": 0, + "content": "The final prediction \\( m = \\{s_t\\}_{t=1}^T \\) for each frame is obtained from the mask candidate set \\( \\hat{m}^t \\) with index \\( \\overline{s} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.623, + 0.845 + ], + "angle": 0, + "content": "4. Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Since the existing RVOS datasets [22, 14, 34, 11] only target specific scenarios, the model cannot handle the diverse scenarios in the real world. Likewise, these datasets" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2688" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.887, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.17, + 0.408, + 0.185 + ], + "angle": 0, + "content": "A man in a brown jacket is standing on the right" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.19, + 0.887, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.273, + 0.502, + 0.288 + ], + "angle": 0, + "content": "A man in a gray coat standing on the right is saying something" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.293, + 0.887, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.376, + 0.248, + 0.391 + ], + "angle": 0, + "content": "A brown dog is barking" + }, + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.4, + 0.707, + 0.415 + ], + "angle": 0, + "content": "Figure 4: Annotation examples of the Mini-Ref-SAIL-VOS dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.468, + 0.486 + ], + "angle": 0, + "content": "are not suitable for the few-shot RVOS problem. This is because the train/test/Validation sets of these datasets have class repetition and cannot be used to evaluate the generality of unseen classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.468, + 0.662 + ], + "angle": 0, + "content": "Mini-Ref-YouTube-VOS. To match the FS-RVOS setting, we build up a new dataset called Mini-Ref-YouTube-VOS based on the Ref-YouTube-VOS dataset [22]. The data that can be directly obtained from the Ref-YouTube-VOS dataset contains 3,471 videos, 12,913 referring expressions, and annotated instances covering more than 60 categories. However, some videos in this dataset consist of multiple category instances. When preparing data for the few-shot setting, we cleaned up the dataset, i.e., removing such videos and keeping only those containing only one category instance, a total of 2387 videos were obtained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.665, + 0.468, + 0.816 + ], + "angle": 0, + "content": "The video data in the dataset should be class-balanced, and the number of samples in each class should not vary too much to avoid overfitting any class. Therefore, we deal with the categories whose number of videos does not meet the requirements to ensure the class balance of the dataset. After the above screening, 1,668 videos were obtained, including 48 classes. To better show the model results, we adopt the cross-validation method to divide the dataset into four folds on average. Each fold contains 36 training and 12 test classes with disjoint categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Mini-Ref-SAIL-VOS. Most Mini-Ref-YouTube-VOS data involve natural scenes of a relatively homogeneous type and therefore do not represent the diversity of data in the real world. To better demonstrate the generalization of our model, we collect videos from SAIL-VOS [13] to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.563 + ], + "angle": 0, + "content": "construct a new dataset Mini-Ref-SAIL-VOS. The SAIL-VOS dataset is a synthetic dataset collected from a video game GTA-V, aiming to foster semantic amodal segmentation research. In SAIL-VOS, each frame is accompanied by densely annotated, pixel-wise and amodal segmentation masks with semantic labels. Since the data is collected from the game, phenomena such as shot transition, segmentation target cross-frame, and target occlusion are inevitable, which brings challenges to the segmentation task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.732 + ], + "angle": 0, + "content": "We reorganize the SAIL-VOS dataset to pick out samples suitable for the FS-RVOS setting. First, for videos with few frames for segmentation targets, we directly discard them. For the case where the segmentation target appears across frames, we manually delete the frames where the target does not appear in the middle to maintain the temporal continuity of the segmentation target. For phenomena such as object occlusion, we characterize it as a challenge and do not deliberately delete video frames with object occlusion. Following the above settings, we collected a dataset with 68 videos and 3 semantic categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "It is worth noting that although there are accurate mask annotations in the SAIL-VOS dataset, natural language description corresponding to the segmentation target is not available. Thus, to adapt it to FS-RVOS, we employed expert annotators to provide referring expressions after data collection. Given a pair of videos for each annotator, the video frames are superimposed with corresponding masks to indicate the objects to be segmented. The annotators were then asked to provide a distinguishing statement with a word limit of 20 words. To ensure the quality of natural language annotations, all annotations are verified and cleaned" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2689" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.466, + 0.174 + ], + "angle": 0, + "content": "
MethodFold-1Fold-2Fold-3Fold-4Mean
JDANet [3]4733.538.54440.8
Ours59.545.350.457.353.1
FDANet [3]49.338.241.445.843.7
Ours60.848.951.358.154.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.185, + 0.468, + 0.216 + ], + "angle": 0, + "content": "Table 1: Quantitative results on Mini-Ref-YouTube-VOS. We added visual language fusion modules to DANet." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.223, + 0.466, + 0.309 + ], + "angle": 0, + "content": "
MethodFold-1Fold-2Fold-3Fold-4Mean
JDANet [3]54.347.630.930.640.9
Ours80.980.880.168.977.7
FDANet [3]54.148.435.23643.4
Ours77.17777.367.874.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.094, + 0.318, + 0.451, + 0.334 + ], + "angle": 0, + "content": "Table 2: Quantitative results on Mini-Ref-SAIL-VOS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.47, + 0.415 + ], + "angle": 0, + "content": "up after the initial annotation. The target will not be used if the natural language description cannot clearly describe the target. As shown in Figure 4, we show the selected videos along with referring expressions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.428, + 0.21, + 0.445 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.452, + 0.295, + 0.468 + ], + "angle": 0, + "content": "5.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.747 + ], + "angle": 0, + "content": "We adopt ResNet-50 [12] and RoBERTa-Base [19] as our vision and text encoders, respectively. During the training stage, the parameters of both encoders are frozen. In our experiments, we adopt a 5-shot setting. Specifically, we extract 5 consecutive frames and the corresponding referring expressions from a certain video of a class as a support set. The query set is composed of consecutive frames and corresponding referring expressions extracted from other videos belonging to the same class. We test each fold 5 times and report the average confidence of the results. Our model utilizes AdamW for optimization. The weight decay is \\(5 \\times 10^{-4}\\) and the initial learning rate is \\(1 \\times 10^{-4}\\). To balance GPU memory efficiency, we downsample all video frames, with the shortest video frame size being 360 and the longest 640. The parameters of the loss function are set as \\(\\lambda_{cls} = 2\\), \\(\\lambda_{kernel} = 5\\). All methods for conducting experiments will be pre-processed and fine-tuned in the same way, i.e., pre-trained on Ref-COCO [36] dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Following the settings of previous RVOS works, we use the region similarity \\((\\mathcal{I})\\) and the contour accuracy \\((\\mathcal{F})\\) to measure the model performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.172, + 0.817 + ], + "angle": 0, + "content": "5.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.9 + ], + "angle": 0, + "content": "As a novel problem, no relevant works can be directly used for comparisons. Therefore, we choose DANet [3] as the baseline given we both focus on few-shot video segmentation. For a fair comparison, we add a visual-language fusion module to the Few-Shot VOS model." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.09, + 0.885, + 0.178 + ], + "angle": 0, + "content": "
MethodJFJ&F
LBDT [6]27.5 / 42.436.2 / 37.331.6 / 39.6
ReferFormer [33]65.1 / 74.162.8 / 64.964.0 / 69.5
MTTR [1]66.5 / 69.764.9 / 68.165.7 / 68.9
Ours80.977.179
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.188, + 0.892, + 0.248 + ], + "angle": 0, + "content": "Table 3: Comparison with state-of-the-art methods from RVOS on the Mini-Ref-SAIL-VOS dataset to measure the model's generalization. Underlined scores are achieved after fine-tuning." + }, + { + "type": "table", + "bbox": [ + 0.561, + 0.26, + 0.832, + 0.332 + ], + "angle": 0, + "content": "
Self-affinityCross-affinityJ&F
--57.9
✓-59.2
✓✓60.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.342, + 0.894, + 0.387 + ], + "angle": 0, + "content": "Table 4: Ablation studies that validate the effectiveness of each component in our CMA. The first result is obtained with our baseline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.892, + 0.528 + ], + "angle": 0, + "content": "Mini-Ref-YouTube-VOS. We present the experimental results of our model on the Mini-Ref-YouTube-VOS dataset in Table 1. It can be observed that our method significantly outperforms DANet. Compared with previous methods, our method achieves a substantial increase in average performance, with an average improvement of more than \\(10\\%\\). The excellent performance demonstrates the superiority and robustness of our proposed method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.733 + ], + "angle": 0, + "content": "Mini-Ref-SAIL-VOS. To evaluate the generalization of our model, we make further experiments and comparisons on the Mini-Ref-SAIL-VOS dataset. We do not perform new training on the Mini-Ref-SAIL-VOS dataset but directly test with the model trained on Mini-Ref-Youtube-VOS. Note that the videos in the Mini-Ref-SAIL-VOS dataset are from Game scenes, and they hold a noticeable domain different from the data in the Mini-Ref-Youtube-VOS dataset. In addition, the objects in some videos are occluded and these phenomena make this dataset somewhat challenging. We show the experimental results in Table 2. According to the Table, it is clear that our method achieves a significant improvement over the baseline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Moreover, we also make further comparisons with some state-of-the-art RVOS methods [6, 33, 1]. Here, we only show the results under Fold-1. To measure the RVOS model's generalization, we first directly test the trained RVOS models on the Mini-Ref-SAIL-VOS dataset. Since our few-shot learning task needs a few samples as support data, for a fair comparison, these RVOS models will be finetuned with a few samples. The corresponding results are shown in Table 3. From the table, it can be seen that although the fine-tuning of the existing models can lead to performance gains, there is still a big gap compared to our" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2690" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.118, + 0.103, + 0.132 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.089, + 0.887, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.16, + 0.341, + 0.172 + ], + "angle": 0, + "content": "a zebra to the left of another zebra" + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.16, + 0.885, + 0.174 + ], + "angle": 0, + "content": "a zebra on the right side of the screen, eating grass" + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.179, + 0.887, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.251, + 0.354, + 0.264 + ], + "angle": 0, + "content": "a bear walking towards another bear" + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.251, + 0.885, + 0.265 + ], + "angle": 0, + "content": "a beer on the right hand side of another walking in their area." + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.27, + 0.887, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.342, + 0.421, + 0.354 + ], + "angle": 0, + "content": "a whale swimming on the left of another whale" + }, + { + "type": "image_caption", + "bbox": [ + 0.433, + 0.342, + 0.886, + 0.355 + ], + "angle": 0, + "content": "a whale, swimming deeper into the ocean, on the right side of the screen" + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.384, + 0.104, + 0.398 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.361, + 0.887, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.439, + 0.578, + 0.453 + ], + "angle": 0, + "content": "A man in a red dress and a hat standing on the left is talking to someone" + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.459, + 0.887, + 0.536 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.537, + 0.39, + 0.551 + ], + "angle": 0, + "content": "A black car parked on the side of the road" + }, + { + "type": "image_caption", + "bbox": [ + 0.186, + 0.561, + 0.782, + 0.575 + ], + "angle": 0, + "content": "Figure 5: Qualitative results on (a) Mini-Ref-YouTube-VOS and (b) Mini-Ref-SAIL-VOS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.589, + 0.47, + 0.65 + ], + "angle": 0, + "content": "proposed approach. This is because our model effectively constructs the multimodal relationship between the support set and the query set so that it can quickly adapt to new scenarios by only using a few samples." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.66, + 0.231, + 0.675 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.469, + 0.773 + ], + "angle": 0, + "content": "In this section, we perform an ablation study on the Mini-Ref-YouTube-VOS dataset to evaluate the design and the robustness of the model. Unless otherwise stated, we only show results under Fold-1. Denoting \\(\\mathcal{I}\\&\\mathcal{F}\\) as the average of \\(\\mathcal{I}\\) and \\(\\mathcal{F}\\), we can use the indicator to show the performance of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.869 + ], + "angle": 0, + "content": "Cross-modal Affinity. We perform ablation studies on the components of the CMA in Table 4. The results of the baseline are shown in the first line. As mentioned before, the baseline refers to directly concatenating the support features and query features into the Mask Generation to obtain the segmentation mask." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "First, we only utilize the self-affinity block to establish contextual information between pixels to enhance query" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.892, + 0.74 + ], + "angle": 0, + "content": "features. At this time, support features are concatenated with the enhanced query features and then fed to the Mask Generation module. It can be seen that good results are achieved, indicating that the Transformer does work for modeling features and extracting contextual information. By adding the proposed cross-affinity block, the performance can be further improved by \\(1\\%\\). Such comparisons show that the cross-affinity block properly constructs the multimodal relationship between the support set and the query set, effectively avoiding the bias of the query features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.683, + 0.785 + ], + "angle": 0, + "content": "5.4. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.8, + 0.892, + 0.905 + ], + "angle": 0, + "content": "The qualitative results of our model are presented in Figure 5. From the figure, It can be seen that the proposed model can segment the referred objects accurately in a variety of challenging situations. Furthermore, we also show the qualitative results on the Mini-Ref-SAIL-VOS dataset. In general, our model always achieves high-quality results even in the face of samples from different scenes." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2691" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.196, + 0.106 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.221 + ], + "angle": 0, + "content": "In this work, we propose CMA to learn multimodal affinity in a few samples to segment diverse data. Further, we generalize it as a few-shot RVOS problem. We validate our model on the newly constructed datasets - Mini-RefYouTube-VOS and Mini-Ref-SAIL-VOS and obtain state-of-the-art performance. We hope this work can cast a light on future FS-RVOS research." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.349 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported in part by the National Key R&D Program of China (Grant No. 2022YFF1202903), the National Natural Science Foundation of China (Grant No. 61971004, 62122035), the Natural Science Foundation of Anhui Province, China (Grant No. 2008085MF190), and the Equipment Advanced Research Sharing Technology Project, China (Grant No. 80912020104)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.364, + 0.175, + 0.38 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.389, + 0.47, + 0.444 + ], + "angle": 0, + "content": "[1] Adam Botach, Evgenii Zheltonozhskii, and Chaim Baskin. End-to-end referring video object segmentation with multimodal transformers. arXiv preprint arXiv:2111.14821, 2021. 2, 3, 5, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.446, + 0.472, + 0.516 + ], + "angle": 0, + "content": "[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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Deformable detr: Deformable transformers for end-to-end object detection. arXiv preprint arXiv:2010.04159, 2020. 3, 5" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.613 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.515, + 0.957 + ], + "angle": 0, + "content": "2693" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/a0fe2dc9-eb10-4dc5-8bfa-8f5f03212fc3_origin.pdf b/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/a0fe2dc9-eb10-4dc5-8bfa-8f5f03212fc3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7de03efd9bc1440e100d6df869f26d589debb2ef --- /dev/null +++ b/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/a0fe2dc9-eb10-4dc5-8bfa-8f5f03212fc3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:88a6cd32fa974ff39076a0c1ec75ddaf6f007525efeb59b175829d5f06f9958f +size 9323118 diff --git a/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/full.md b/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/full.md new file mode 100644 index 0000000000000000000000000000000000000000..45f69bae941f62a965bf4ff57562e74e58e52c75 --- /dev/null +++ b/2023/Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples/full.md @@ -0,0 +1,321 @@ +# Learning Cross-Modal Affinity for Referring Video Object Segmentation Targeting Limited Samples + +Guanghui Li $^{1*}$ , Mingqi Gao $^{2,3*}$ , Heng Liu $^{1\dagger}$ , Xiantong Zhen $^{4}$ , Feng Zheng $^{2\dagger}$ $^{1}$ Anhui University of Technology, $^{2}$ Southern University of Science and Technology, $^{3}$ University of Warwick, $^{4}$ United Imaging + +guanghui.li1998@gmail.com, mingqi.gao@outlook.com, hengliusky@aliyun.com, zhenxt@gmail.com, f.zheng@ieee.org + +# Abstract + +Referring video object segmentation (RVOS), as a supervised learning task, relies on sufficient annotated data for a given scene. However, in more realistic scenarios, only minimal annotations are available for a new scene, which poses significant challenges to existing RVOS methods. With this in mind, we propose a simple yet effective model with a newly designed cross-modal affinity (CMA) module based on a Transformer architecture. The CMA module builds multimodal affinity with a few samples, thus quickly learning new semantic information, and enabling the model to adapt to different scenarios. Since the proposed method targets limited samples for new scenes, we generalize the problem as - few-shot referring video object segmentation (FS-RVOS). To foster research in this direction, we build up a new FS-RVOS benchmark based on currently available datasets. The benchmark covers a wide range and includes multiple situations, which can maximally simulate real-world scenarios. Extensive experiments show that our model adapts well to different scenarios with only a few samples, reaching state-of-the-art performance on the benchmark. On Mini-Ref-YouTube-VOS, our model achieves an average performance of 53.1 J and 54.8 F, which are $10\%$ better than the baselines. Furthermore, we show impressive results of 77.7 J and 74.8 F on Mini-Ref-SAIL-VOS, which are significantly better than the baselines. Code is publicly available at https://github.com/hengliusky/Few_shot_RVOS. + +# 1. Introduction + +Referring video object segmentation (RVOS) aims to segment target objects described in natural language in + +![](images/51c78b03dfa4f5896407f3be56632029b4e9182c5e1f088ab1e018a35182bfbe.jpg) +(a) Data distribution in RVOS + +![](images/fffe53df1222bb9fdfd40c1597c476e240465d053f8c7d1489e8437b3463a70f.jpg) +(b) Data distribution in Few-shot RVOS + +![](images/04ceb22e28d922f20e90a16ee492e24a0fa73a6a57c4c9b3095190e5eea3a3a0.jpg) +Text: "A dog standing in water" +(c) Few-shot RVOS + +![](images/2e700290fbc6d2afa0990fe98144ca1ffcef690df869fa65d5230ba891266d44.jpg) +Text: "A dog walking along the shore" +Figure 1: Comparison of Few-shot RVOS and RVOS and the setting of Few-shot RVOS. (a) The training and testing sets overlap in the RVOS. (b) Disjoint training and testing sets in the Few-shot RVOS. Different shapes represent different classes. (c) Few-shot RVOS segments the referred object of the same class as the support set in the video. + +videos. In real-world scenarios, it has a wide range of applications, such as video editing [9] and human-computer interaction, so RVOS has attracted much attention from the research community. Unlike traditional semi-supervised video object segmentation [10], RVOS is more challenging because it not only lacks the ground-truth mask of the first frame of the video but also needs to interact with multimodal information of vision and language. + +The great success of various tasks based on deep learning benefits from sufficient labeled data. Detailed annotated masks and language descriptions in real-world RVOS tasks are relatively scarce. The researchers have to annotate each frame in the video in detail and provide a referring expression for the segmentation object. Therefore, obtaining high-quality labeled data requires a high cost. With the popularity of movies, YouTube videos, TikTok streaming videos, + +etc., video data in various fields has shown explosive growth in this media age. The demand for processing diverse data has brought significant challenges. In order to handle diverse data, existing RVOS methods must rely on massive and diverse labeled data for training. But due to fixed and limited training classes, existing RVOS methods [1, 33] are essentially constrained to adapt to the highly dynamic and highly diverse data in the real world. On the other hand, if ones fine-tune existing RVOS methods on a few samples to adapt to real-world data, high-quality results are hard to be achieved because the labelled data is insufficient to support the model for learning the new semantics. Therefore, how to make the RVOS methods applicable to real-world diverse data with a lower cost is an urgent problem. + +To address this problem, we propose the cross-modal affinity (CMA) module to build multimodal relationships in a few samples and learn new semantic information for diversified data. Specifically, given only a few annotated samples (language expressions and the referred object masks), we hierarchically fuse visual and text features in a cross-attention manner to obtain robust feature representations for a specific category. In this way, the model can handle enormous data in the same category more efficiently. + +Essentially, the proposed method targets limited samples. Therefore, we generalize the problem as Few-Shot Referring Video Object Segmentation (FS-RVOS). We show the setting of FS-RVOS and the difference from existing RVOS in Figure 1. Unlike RVOS, the training and testing sets' categories disjoint in the FS-RVOS. Given a few support video clips together with corresponding language descriptions and object masks, FS-RVOS aims at segmenting videos in the query set, as shown in Figure 1(c). + +The key to FS-RVOS lies in the support set utilization and understanding of vision-language information. To better leverage the information in the support set, two methods have been proposed based on the prototype and attention mechanisms. The prototype-based [21, 35] methods compress the features belonging to different classes to obtain prototypes. However, noise is easily generated during the process. In addition, the spatial structures are ignored, resulting in different degree of information loss. Another methods [37, 38, 39] employ the attention mechanism to encode foreground pixels from support features and aggregate them with query features. Although these methods achieve high-quality results in image and video domains, they are still under-explored in vision-language tasks. + +To better utilize vision-language inputs, we propose the cross-modal affinity module to build the multimodal relationships between samples in the support and query sets. Specifically, multimodal features within the support set and query set are first fused separately. The information among them is then aggregated, which effectively prevents query features from being biased by irrelevant features. + +Since this is the first work exploring Few-shot RVOS, the existing datasets are not directly applicable. Therefore, we build up a new FS-RVOS benchmark based on Ref-YouTube-VOS [22], named Mini-Ref-YouTube-VOS. The new benchmark covers a wide range with a balanced number of high-quality videos in each category. To measure the model's generalization ability, we also build a dataset different from natural scenes based on a synthetic dataset SAIL-VOS [13], named Mini-Ref-SAIL-VOS. Since only videos and detailed annotated masks exist in the SAIL-VOS dataset, we add natural language descriptions corresponding to the segmentation targets for the dataset. + +The main contributions of this work are as follows. + +- For real-world limited samples, we propose a CrossModal Affinity (CMA) for building multimodal information affinity for referring video object segmentation. +- We explore a novel Few-shot RVOS problem, which learns new semantic information with limited samples and can adapt to diverse scenarios. +- We build up the first FS-RVOS benchmark, where we conduct comprehensive comparisons with existing methods, showing the superiority of the proposed model. + +# 2. Related Work + +Few-Shot Semantic Segmentation. Few-shot semantic segmentation, first proposed by Shaban et al. [23], aims to learn how to segment new categories of images through a few samples. Recent advances in few-shot semantic segmentation originate from the application of metric learning. Based on PrototypicalNet, Dong et al. [7] first employ the metric learning technique and apply cosine similarity between pixels and prototypes for prediction. In addition, PANet et al. [31] introduce prototype alignment regularization to simplify the framework. PFENet et al. [28] use prior knowledge from the pretrained backbone to find the regions of interest and the different designs of feature pyramid modules, and previous leverage mappings to achieve better segmentation performance. + +However, the effectiveness of these few-shot segmentation methods depends mainly on the quality of the prototypes obtained from the support set. Fan et al. [8] address the critical intra-class appearance differences inherent in the few-shot segmentation problem by performing self-support matching with query features. Their strategy effectively captures the consistent underlying features of query objects to match query features. Tian et al. [27] propose a novel context-aware prototype learning method that leverages prior knowledge from support samples and dynamically enriches contextual information by using adaptive features. Motivated by the idea that using the base learner to identify confusing regions in the query image and further + +refining the predictions of the meta-learner, BAM [15] establishes a new method for few-shot segmentation that does not focus on feature extraction or visual correspondence. + +Compared to image-based few-shot segmentation, few-shot video object segmentation works are relatively rare and remain in the early stage. The initial work [25], [3] mainly solves this problem through the attention mechanism. However, these methods do not consider temporal information. Thus, based on temporal transductive, the recent work [24] applies reasoning mechanisms and has achieved good results in cross-domain scenarios. In a word, all the above-mentioned few-shot segmentation methods are only for a single modality - image or video, and cannot handle segmentation under multimodal conditions (i.e., with linguistic referring expressions). + +Referring Video Object Segmentation. Gavrilyuk et al. [11] first introduce the RVOS task. They generate convolutional dynamic filters from textual representations and convolve them with visual features of different resolutions to obtain segmentation masks. To overcome the limitations of traditional dynamic convolution, Wang et al. [30] propose a context-modulated dynamic convolution operation for RVOS, where the kernel is generated from language sentences and surrounding contextual features. However, since the focus is only on video actors and actions, their approach only applies to a few object classes and action-oriented descriptions. Weak-Shot Semantic Segmentation (WSSS) [4, 42] focuses on the overall scene in the image, treating masks and text as the support set and text as the query set. However, in WSSS, the text is limited to single words or phrases indicating class names and directly mapped to labels for pixel-level classification. + +Khoreva et al. [14] propose a two-stage approach that first performs referring expressions grounding and then utilizes the predicted bounding boxes to guide pixel-wise segmentation. Seo et al. [22] also present a framework called URVOS, which first predicts the initial mask based on the image and then utilizes the predicted mask of the previous frame for RVOS by memorizing the attention module. + +Most recent RVOS works employ cross-attention to interact visual images with linguistic information. LBDT [6] uses language as an intermediate bridge to connect temporal and spatial information and leverages cross-modal attention operations to aggregate language-related motion and appearance. MMVT [40] calculates the optical flow between frames and fuses it as motion information with text features and visual features. However, these frame-based spatial granularity multimodal fusion methods have limitations and tend to lead to mismatches between visual and linguistic information. Therefore, a recent piece of work [32, 40] explores a novel multi-level representation learning method and introduces dynamic semantic alignment to adaptively fuse the two modal information. + +Transformer [29] has been widely applied and achieved great success in many computer vision tasks, such as object detection [2, 43] and image segmentation [41, 5]. Since DETR [2] introduces a new query-based paradigm, the latest works [1, 33, 16] prefer to apply the DETR's framework for RVOS task. Specifically, they utilize Transformer structures to interact visual images with linguistic data. Because Transformer has a remarkable ability to mine non-local correlation, they are able to attain SOTA performance in accuracy and efficiency. Despite the relative effectiveness of current RVOS techniques, they are primarily restricted to regular supervised learning settings, which would not be able to deal with unseen scenes with few shots. + +# 3. Methods + +# 3.1. Overview + +In the setting of FS-RVOS, we have training and testing datasets $D_{train}$ and $D_{test}$ with disjoint category sets $C_{train}$ and $C_{test}$ , i.e., $C_{train} \cap C_{test} = \emptyset$ . Similar to few-shot learning tasks [26], episode training is adopted in this work, where $D_{train}$ and $D_{test}$ consist of several episodes. Each episode contains a support set $S$ and a query set $Q$ where the text-referred objects (target objects) from both sets belong to the same class. The support set has $K$ image-mask pairs $S = \{x_k, m_k\}_{k=1}^K$ and the corresponding referring expression with $L$ words $T_s = \{t_i\}_{i=1}^L$ , where $m_k$ is the ground-truth mask of the video frame $x_k$ . The query set $Q = \{x_i^q\}_{i=1}^N$ is a selection of consecutive frames from a video and the corresponding natural language description with $M$ words $T_q = \{t_i\}_{i=1}^M$ , $N$ is the number of frames. With the setting above, FS-RVOS encourages models to segment objects with the unseen class in a query set based on a few samples in the support set. + +As shown in Figure 2, our framework mainly consists of a Feature Extraction module, a Cross-modal Affinity module (CMA), and a Mask Generation module. With the support and query data as input, the framework predicts object masks for the query data, under the guidance of the corresponding language expressions. Specifically, the vision and text encoders extract features for visual and textual inputs, respectively. Then, CMA fuses visual and textual features hierarchically. The fused features are used to build the relationship between the support set and the query set. The output features are finally fed to the Mask Generation module to get the final segmentation results. + +# 3.2. Feature Extraction + +We use a shared-weight visual encoder to extract multiscale features from each frame in the support set and query set, resulting in visual feature sequences $F_{vs} = \{f_{vs}\}_{vs=1}^{K}$ and $F_{vq} = \{f_{vq}\}_{vq=1}^{N}$ . For linguistic information, we use a Transformer-based text encoder [19] to extract text features + +![](images/175a6b26cca735b38aae6825349ebb0e580a1356544d946b4b5fcc3082415177.jpg) +Figure 2: The overall pipeline of our framework. The feature encoder extracts visual and textual information from the support and query sets. Then, the Cross-modal Affinity module calculates the multimodal information affinity between the support set and the query set. Finally, the final segmentation result is obtained through Mask Generation. + +$F_{ts} = \{f_{ts}\}_{ts=1}^{L}$ and $F_{tq} = \{f_{tq}\}_{tq=1}^{M}$ from the natural language descriptions $T_s$ and $T_q$ that correspond to the input support data and the query data. + +# 3.3. Cross-modal Affinity Construction + +With a few samples in the support set, the goal of FS-RVOS is to efficiently leverage the given information and quickly adapt to relevant scenarios. Compared with conventional few-shot tasks, FS-RVOS not only builds the affinity between the support and query sets but also involves multimodal relationships between videos and referring expressions. Therefore, FS-RVOS is more challenging and requires specialized solutions for high-quality results. + +We propose the Cross-Modal Affinity (CMA) module to achieve this, as shown in Figure 3. We first perform crossattention fusion between the visual and textual features of support and query data, to obtain pixel-augmented multimodal features. Then, in order to aggregate beneficial information in support features, we build an affinity relationship between the support set and the query set. + +Due to the diversity of referred objects and the drastic changes between video frames, it is a challenge to achieve the accurate location of the target only by visual information. Therefore, to obtain the accurate positioning of the segmentation target, we use language information as a supplement, which contains a specific description of the referred objects. To interact and align the visual features and text features, multi-head cross-attention (MCA) is proposed to fuse multimodal information, achieving two multi-scale + +feature maps $F_{vs}^{\prime} = \{f_s^{\prime}\}_{s = 1}^{K}$ and $F_{vq}^{\prime} = \{f_q^{\prime}\}_{q = 1}^{N}$ : + +$$ +f _ {v s} ^ {\prime} = \operatorname {M C A} \left(f _ {v s}, f _ {t s}\right), f _ {v q} ^ {\prime} = \operatorname {M C A} \left(f _ {v q}, f _ {t q}\right), \quad (1) +$$ + +where $f_{vs}$ , $f_{vq}$ represent the visual features of support and query, $f_{ts}$ , $f_{tq}$ are their corresponding textual features. Here we calculate an affinity between textual features and visual features to filter out irrelevant visual information. Compared with concatenation, MCA suits our framework better since it can leverage the similarities between multimodal features for information complementation. + +The affinity between the support set and query set indicates the multimodal feature correlation among them, providing valuable clues for the segmentation of the query data. Although the objects to segment in the support and query sets belong to the same category, their visual properties usually have significant differences, such as appearance, pose, and scene. This means only a tiny part of the information in the support data is conducive to segmenting the query data, while other information will cause bad results. Therefore, we urgently need to solve the problem of computing the correct affinity relationship between multimodal information in the support and query sets. + +To achieve this, we propose a self-affinity block to encode the query features and a cross-affinity block to enable the query features to focus on beneficial pixels in the support features. In particular, given the input query features, we utilize a convolution operation to map them as query $q_{q}$ , key $k_{q}$ , and value $v_{q}$ . We perform the same operation for the support features to map them to key $k_{s}$ and value $v_{s}$ . The input of the self-affinity block does not include the support features and mainly aggregates the context information of the query features for better segmentation. + +First, we calculate the affinity map $A^Q = \frac{q_q \cdot (k_q)^{\mathrm{T}}}{\sqrt{d_{head}}}$ , where $d_{head}$ is the hidden dimension of the input sequences, and we assume all sequences have the same dimension 256 by default. Therefore, the query features after the self-affinity block are represented as: + +$$ +q _ {s} = \operatorname {S o f t m a x} \left(A ^ {Q}\right) v _ {q}. \tag {2} +$$ + +We then feed the obtained query features to the cross-affinity block. The purpose of the cross-affinity block is to construct the cross-affinity relationship between the support features and the query features and aggregate the useful information. Our cross-affinity block can be formulated as: + +$$ +q u e r y _ {f e a t} = \operatorname {S o f t m a x} \left(\frac {q _ {s} \cdot \left(k _ {s}\right) ^ {\mathrm {T}}}{\sqrt {d _ {h e a d}}}\right) v _ {s}, \tag {3} +$$ + +where $q_{s}$ is the output of the self-affinity block. Through these two modules, query features enhance features by modeling contextual information and computing the correlation between support and query features, effectively avoiding the attention bias caused by irrelevant features. + +![](images/474a3563cbe4faad7d046799fd570a34df91ba3f0e3ac0631ab5ec1c2cc3c202.jpg) +Figure 3: The architecture of the Cross-modal Affinity (CMA) module. We use multi-head cross-attention to fuse visual and text features to get more robust features. Self-affinity for modeling contextual information on query features and cross-affinity for aggregating beneficial information from support features. + +# 3.4. Mask Generation + +The goal of the Mask Generation module is to find the most relevant objects and decode the features step by step. To achieve this goal, the structure of Deformable-DETR [43] and feature pyramid [17] has been used in our work. We add the corresponding positional encoding to the feature sequence that aggregates beneficial information, which is then sent to the Transformer encoder. In the decoder part of Transformer, we introduce $N$ learnable anchor boxes as queries to represent the instances of each frame. These queries are replicated as decoder input for all frames and finally converted into instance embeddings by the decoder, resulting in $N_{q} = T \times N$ predictions. + +In the feature pyramid network, in order to gradually fuse multimodal features from different layers, the output of the Transformer encoder and the features from the vision encoder are stacked to form hierarchical features. We use $f_{v}^{l}$ to represent visual features at each level. First, we downsample the multi-scale visual features, and the time dimension remains unchanged. Then interact with visual and linguistic features in a cross-attention manner to enhance object pixel features, thereby facilitating mask prediction. The fused features are upsampled to restore the previous shape: + +$$ +C r o s s \left(f _ {v} ^ {l}, f _ {t q}\right) = \operatorname {S o f t m a x} \left(\frac {f _ {v} ^ {l} \cdot \left(f _ {t q}\right) ^ {\mathrm {T}}}{\sqrt {d _ {\text {h e a d}}}}\right) f _ {t q}, \tag {4} +$$ + +where $f_{tq}$ represents the text features corresponding to the query set. Finally, we pass the features of the last layer through a $3 \times 3$ convolutional layer to get the final feature maps $F_{seg} = \{f_{seg}^{t}\}_{t=1}^{T}$ , where $f_{seg}^{t} \in \mathbb{R}^{\frac{H}{4} \times \frac{W}{4} \times C}$ . + +Furthermore, we construct a set of auxiliary heads to obtain the final object mask across frames. The class head is used to calculate the confidence score $s_t$ . The score indi + +cates whether the instance corresponds to the referred object and whether the object is visible in the current frame. The kernel head is implemented by three consecutive linear layers, which generate the parameters $W = \{w_{t}\}_{t=1}^{N_{q}}$ of the $N_{q}$ dynamic kernels. We use them as convolution filters on the feature maps, generating a series of segmentation masks. + +# 3.5. Loss Function + +In Mask Generation, we use $N$ learnable anchor boxes as queries and generate a set of $N_{q} = T \times N$ prediction sequences. We denote the predicted sequence as $\hat{y} = \{\hat{y}_i\}_{i=1}^{N_q}$ and the prediction for the $i^{\text{th}}$ instance is expressed as: + +$$ +\hat {y} _ {i} = \left\{\hat {s} _ {i} ^ {t}, \hat {m} _ {i} ^ {t} \right\} _ {t = 1} ^ {T}, \tag {5} +$$ + +where $\hat{s}_i^t\in \mathbb{R}^1$ is a fractional score indicating whether the instance corresponds to the referred object. $\hat{m}_i^t\in \mathbb{R}^{\frac{H}{4}\times \frac{W}{4}}$ is the predicted binary segmentation mask. Similar to the previous methods [1, 33], we use dynamic convolution to generate the object mask. We get the final feature maps $f_{seg}^{t}$ through the feature pyramid network, and the mask prediction can be calculated by $\hat{m}^t = \left\{w_t*f_{seg}^t\right\}$ . + +The sequence of ground-truth instances is denoted as $y = \{s^t, m^t\}_{t=1}^T$ , and $s^t$ is an one-hot value and equals 1 when the ground-truth instance is visible in the frame, and 0 otherwise. Our loss function is defined as: + +$$ +\mathcal {L} (y, \hat {y} _ {i}) = \lambda_ {c l s} \mathcal {L} _ {c l s} (y, \hat {y} _ {i}) + \lambda_ {k e r n e l} \mathcal {L} _ {k e r n e l} (y, \hat {y} _ {i}), \tag {6} +$$ + +where $\lambda_{cls}, \lambda_{kernel}$ are hyperparameters to balance the loss. We use focal loss [18] (denoted as $\mathcal{L}_{cls}$ ) to supervise the prediction of instance sequence reference results. $\mathcal{L}_{kernel}$ is a combination of DICE loss [20] and the binary mask focal loss. + +# 3.6. Inference + +In the inference phase, we treat all input video frames as a whole and predict the mask trajectory for the entire video using only one forward pass. Given an input video and the corresponding linguistic expression, our model generates a sequence of $N$ instances. For each frame, we select the instance sequence with the highest confidence score as the final prediction, and its index can be expressed as: + +$$ +\begin{array}{l} \bar {s} = \arg \max s _ {i}. \tag {7} \\ i \in \{1, 2, \dots , N \} \\ \end{array} +$$ + +The final prediction $m = \{s_t\}_{t=1}^T$ for each frame is obtained from the mask candidate set $\hat{m}^t$ with index $\overline{s}$ . + +# 4. Benchmark + +Since the existing RVOS datasets [22, 14, 34, 11] only target specific scenarios, the model cannot handle the diverse scenarios in the real world. Likewise, these datasets + +![](images/fc95c807c4f5d0914d457f4367feb471ebe29a82d69c66647db43d2aeee61614.jpg) +A man in a brown jacket is standing on the right + +![](images/131a5f661cec88b0ddc78dcaabd961a2821e393d0d6632cafc9494c973be2f7a.jpg) +A man in a gray coat standing on the right is saying something + +![](images/9512643f130555d90df3f4470e02e062e7cfafb4620217e1afcd65c2be234811.jpg) +A brown dog is barking +Figure 4: Annotation examples of the Mini-Ref-SAIL-VOS dataset. + +are not suitable for the few-shot RVOS problem. This is because the train/test/Validation sets of these datasets have class repetition and cannot be used to evaluate the generality of unseen classes. + +Mini-Ref-YouTube-VOS. To match the FS-RVOS setting, we build up a new dataset called Mini-Ref-YouTube-VOS based on the Ref-YouTube-VOS dataset [22]. The data that can be directly obtained from the Ref-YouTube-VOS dataset contains 3,471 videos, 12,913 referring expressions, and annotated instances covering more than 60 categories. However, some videos in this dataset consist of multiple category instances. When preparing data for the few-shot setting, we cleaned up the dataset, i.e., removing such videos and keeping only those containing only one category instance, a total of 2387 videos were obtained. + +The video data in the dataset should be class-balanced, and the number of samples in each class should not vary too much to avoid overfitting any class. Therefore, we deal with the categories whose number of videos does not meet the requirements to ensure the class balance of the dataset. After the above screening, 1,668 videos were obtained, including 48 classes. To better show the model results, we adopt the cross-validation method to divide the dataset into four folds on average. Each fold contains 36 training and 12 test classes with disjoint categories. + +Mini-Ref-SAIL-VOS. Most Mini-Ref-YouTube-VOS data involve natural scenes of a relatively homogeneous type and therefore do not represent the diversity of data in the real world. To better demonstrate the generalization of our model, we collect videos from SAIL-VOS [13] to + +construct a new dataset Mini-Ref-SAIL-VOS. The SAIL-VOS dataset is a synthetic dataset collected from a video game GTA-V, aiming to foster semantic amodal segmentation research. In SAIL-VOS, each frame is accompanied by densely annotated, pixel-wise and amodal segmentation masks with semantic labels. Since the data is collected from the game, phenomena such as shot transition, segmentation target cross-frame, and target occlusion are inevitable, which brings challenges to the segmentation task. + +We reorganize the SAIL-VOS dataset to pick out samples suitable for the FS-RVOS setting. First, for videos with few frames for segmentation targets, we directly discard them. For the case where the segmentation target appears across frames, we manually delete the frames where the target does not appear in the middle to maintain the temporal continuity of the segmentation target. For phenomena such as object occlusion, we characterize it as a challenge and do not deliberately delete video frames with object occlusion. Following the above settings, we collected a dataset with 68 videos and 3 semantic categories. + +It is worth noting that although there are accurate mask annotations in the SAIL-VOS dataset, natural language description corresponding to the segmentation target is not available. Thus, to adapt it to FS-RVOS, we employed expert annotators to provide referring expressions after data collection. Given a pair of videos for each annotator, the video frames are superimposed with corresponding masks to indicate the objects to be segmented. The annotators were then asked to provide a distinguishing statement with a word limit of 20 words. To ensure the quality of natural language annotations, all annotations are verified and cleaned + +
MethodFold-1Fold-2Fold-3Fold-4Mean
JDANet [3]4733.538.54440.8
Ours59.545.350.457.353.1
FDANet [3]49.338.241.445.843.7
Ours60.848.951.358.154.8
+ +Table 1: Quantitative results on Mini-Ref-YouTube-VOS. We added visual language fusion modules to DANet. + +
MethodFold-1Fold-2Fold-3Fold-4Mean
JDANet [3]54.347.630.930.640.9
Ours80.980.880.168.977.7
FDANet [3]54.148.435.23643.4
Ours77.17777.367.874.8
+ +up after the initial annotation. The target will not be used if the natural language description cannot clearly describe the target. As shown in Figure 4, we show the selected videos along with referring expressions. + +# 5. Experiments + +# 5.1. Implementation Details + +We adopt ResNet-50 [12] and RoBERTa-Base [19] as our vision and text encoders, respectively. During the training stage, the parameters of both encoders are frozen. In our experiments, we adopt a 5-shot setting. Specifically, we extract 5 consecutive frames and the corresponding referring expressions from a certain video of a class as a support set. The query set is composed of consecutive frames and corresponding referring expressions extracted from other videos belonging to the same class. We test each fold 5 times and report the average confidence of the results. Our model utilizes AdamW for optimization. The weight decay is $5 \times 10^{-4}$ and the initial learning rate is $1 \times 10^{-4}$ . To balance GPU memory efficiency, we downsample all video frames, with the shortest video frame size being 360 and the longest 640. The parameters of the loss function are set as $\lambda_{cls} = 2$ , $\lambda_{kernel} = 5$ . All methods for conducting experiments will be pre-processed and fine-tuned in the same way, i.e., pre-trained on Ref-COCO [36] dataset. + +Following the settings of previous RVOS works, we use the region similarity $(\mathcal{I})$ and the contour accuracy $(\mathcal{F})$ to measure the model performance. + +# 5.2. Results + +As a novel problem, no relevant works can be directly used for comparisons. Therefore, we choose DANet [3] as the baseline given we both focus on few-shot video segmentation. For a fair comparison, we add a visual-language fusion module to the Few-Shot VOS model. + +Table 2: Quantitative results on Mini-Ref-SAIL-VOS. + +
MethodJFJ&F
LBDT [6]27.5 / 42.436.2 / 37.331.6 / 39.6
ReferFormer [33]65.1 / 74.162.8 / 64.964.0 / 69.5
MTTR [1]66.5 / 69.764.9 / 68.165.7 / 68.9
Ours80.977.179
+ +Table 3: Comparison with state-of-the-art methods from RVOS on the Mini-Ref-SAIL-VOS dataset to measure the model's generalization. Underlined scores are achieved after fine-tuning. + +
Self-affinityCross-affinityJ&F
--57.9
✓-59.2
✓✓60.2
+ +Table 4: Ablation studies that validate the effectiveness of each component in our CMA. The first result is obtained with our baseline. + +Mini-Ref-YouTube-VOS. We present the experimental results of our model on the Mini-Ref-YouTube-VOS dataset in Table 1. It can be observed that our method significantly outperforms DANet. Compared with previous methods, our method achieves a substantial increase in average performance, with an average improvement of more than $10\%$ . The excellent performance demonstrates the superiority and robustness of our proposed method. + +Mini-Ref-SAIL-VOS. To evaluate the generalization of our model, we make further experiments and comparisons on the Mini-Ref-SAIL-VOS dataset. We do not perform new training on the Mini-Ref-SAIL-VOS dataset but directly test with the model trained on Mini-Ref-Youtube-VOS. Note that the videos in the Mini-Ref-SAIL-VOS dataset are from Game scenes, and they hold a noticeable domain different from the data in the Mini-Ref-Youtube-VOS dataset. In addition, the objects in some videos are occluded and these phenomena make this dataset somewhat challenging. We show the experimental results in Table 2. According to the Table, it is clear that our method achieves a significant improvement over the baseline. + +Moreover, we also make further comparisons with some state-of-the-art RVOS methods [6, 33, 1]. Here, we only show the results under Fold-1. To measure the RVOS model's generalization, we first directly test the trained RVOS models on the Mini-Ref-SAIL-VOS dataset. Since our few-shot learning task needs a few samples as support data, for a fair comparison, these RVOS models will be finetuned with a few samples. The corresponding results are shown in Table 3. From the table, it can be seen that although the fine-tuning of the existing models can lead to performance gains, there is still a big gap compared to our + +![](images/abbc8c84edf7444b1c5876a957db1d2a9e28895b70aeb8dcab4eab629beaf73e.jpg) +(a) +a zebra to the left of another zebra +a zebra on the right side of the screen, eating grass + +![](images/a5f015327f4a5f877837e8e31d12dedfdff432be38946d4c8e84fca097f7d6b8.jpg) +a bear walking towards another bear +a beer on the right hand side of another walking in their area. + +![](images/4c4a6dffdbdf34f15296d3602a351aeb37f6752321829b466f516fe15359512d.jpg) +a whale swimming on the left of another whale +a whale, swimming deeper into the ocean, on the right side of the screen + +![](images/5285a9bbe7acf98c882acd3df7f45356b33fc90a3cf4d12e8a6814cb7b644f47.jpg) +(b) +A man in a red dress and a hat standing on the left is talking to someone + +![](images/8b8004bcdb7452cc6c9f3697fe58eafc4946fc669dc3383d087738bac56c409d.jpg) +A black car parked on the side of the road +Figure 5: Qualitative results on (a) Mini-Ref-YouTube-VOS and (b) Mini-Ref-SAIL-VOS. + +proposed approach. This is because our model effectively constructs the multimodal relationship between the support set and the query set so that it can quickly adapt to new scenarios by only using a few samples. + +# 5.3. Ablation Study + +In this section, we perform an ablation study on the Mini-Ref-YouTube-VOS dataset to evaluate the design and the robustness of the model. Unless otherwise stated, we only show results under Fold-1. Denoting $\mathcal{I}\&\mathcal{F}$ as the average of $\mathcal{I}$ and $\mathcal{F}$ , we can use the indicator to show the performance of the model. + +Cross-modal Affinity. We perform ablation studies on the components of the CMA in Table 4. The results of the baseline are shown in the first line. As mentioned before, the baseline refers to directly concatenating the support features and query features into the Mask Generation to obtain the segmentation mask. + +First, we only utilize the self-affinity block to establish contextual information between pixels to enhance query + +features. At this time, support features are concatenated with the enhanced query features and then fed to the Mask Generation module. It can be seen that good results are achieved, indicating that the Transformer does work for modeling features and extracting contextual information. By adding the proposed cross-affinity block, the performance can be further improved by $1\%$ . Such comparisons show that the cross-affinity block properly constructs the multimodal relationship between the support set and the query set, effectively avoiding the bias of the query features. + +# 5.4. Qualitative Results + +The qualitative results of our model are presented in Figure 5. From the figure, It can be seen that the proposed model can segment the referred objects accurately in a variety of challenging situations. Furthermore, we also show the qualitative results on the Mini-Ref-SAIL-VOS dataset. In general, our model always achieves high-quality results even in the face of samples from different scenes. + +# 6. Conclusion + +In this work, we propose CMA to learn multimodal affinity in a few samples to segment diverse data. Further, we generalize it as a few-shot RVOS problem. We validate our model on the newly constructed datasets - Mini-RefYouTube-VOS and Mini-Ref-SAIL-VOS and obtain state-of-the-art performance. We hope this work can cast a light on future FS-RVOS research. + +Acknowledgements. This work is supported in part by the National Key R&D Program of China (Grant No. 2022YFF1202903), the National Natural Science Foundation of China (Grant No. 61971004, 62122035), the Natural Science Foundation of Anhui Province, China (Grant No. 2008085MF190), and the Equipment Advanced Research Sharing Technology Project, China (Grant No. 80912020104). + +# References + +[1] Adam Botach, Evgenii Zheltonozhskii, and Chaim Baskin. End-to-end referring video object segmentation with multimodal transformers. arXiv preprint arXiv:2111.14821, 2021. 2, 3, 5, 7 +[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In European Conference on Computer Vision, pages 213-229. Springer, 2020. 3 +[3] Haoxin Chen, Hanjie Wu, Nanxuan Zhao, Sucheng Ren, and Shengfeng He. Delving deep into many-to-many attention for few-shot video object segmentation. 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However, in more realistic scenarios, only minimal annotations are available for a new scene, which poses significant challenges to existing RVOS methods. With this in mind, we propose a simple yet effective model with a newly designed cross-modal affinity (CMA) module based on a Transformer architecture. The CMA module builds multimodal affinity with a few samples, thus quickly learning new semantic information, and enabling the model to adapt to different scenarios. Since the proposed method targets limited samples for new scenes, we generalize the problem as - few-shot referring video object segmentation (FS-RVOS). To foster research in this direction, we build up a new FS-RVOS benchmark based on currently available datasets. The benchmark covers a wide range and includes multiple situations, which can maximally simulate real-world scenarios. Extensive experiments show that our model adapts well to different scenarios with only a few samples, reaching state-of-the-art performance on the benchmark. On Mini-Ref-YouTube-VOS, our model achieves an average performance of 53.1 J and 54.8 F, which are " + }, + { + "bbox": [ + 46, + 284, + 290, + 608 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 284, + 290, + 608 + ], + "type": "text", + "content": " better than the baselines. Furthermore, we show impressive results of 77.7 J and 74.8 F on Mini-Ref-SAIL-VOS, which are significantly better than the baselines. Code is publicly available at https://github.com/hengliusky/Few_shot_RVOS." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 651, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 287, + 676 + ], + "type": "text", + "content": "Referring video object segmentation (RVOS) aims to segment target objects described in natural language in" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 256, + 421, + 312 + ], + "blocks": [ + { + "bbox": [ + 307, + 256, + 421, + 312 + ], + "lines": [ + { + "bbox": [ + 307, + 256, + 421, + 312 + ], + "spans": [ + { + "bbox": [ + 307, + 256, + 421, + 312 + ], + "type": "image", + "image_path": "51c78b03dfa4f5896407f3be56632029b4e9182c5e1f088ab1e018a35182bfbe.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 316, + 406, + 325 + ], + "lines": [ + { + "bbox": [ + 318, + 316, + 406, + 325 + ], + "spans": [ + { + "bbox": [ + 318, + 316, + 406, + 325 + ], + "type": "text", + "content": "(a) Data distribution in RVOS" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 426, + 256, + 543, + 312 + ], + "blocks": [ + { + "bbox": [ + 426, + 256, + 543, + 312 + ], + "lines": [ + { + "bbox": [ + 426, + 256, + 543, + 312 + ], + "spans": [ + { + "bbox": [ + 426, + 256, + 543, + 312 + ], + "type": "image", + "image_path": "fffe53df1222bb9fdfd40c1597c476e240465d053f8c7d1489e8437b3463a70f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 427, + 316, + 544, + 325 + ], + "lines": [ + { + "bbox": [ + 427, + 316, + 544, + 325 + ], + "spans": [ + { + "bbox": [ + 427, + 316, + 544, + 325 + ], + "type": "text", + "content": "(b) Data distribution in Few-shot RVOS" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 308, + 327, + 417, + 388 + ], + "blocks": [ + { + "bbox": [ + 308, + 327, + 417, + 388 + ], + "lines": [ + { + "bbox": [ + 308, + 327, + 417, + 388 + ], + "spans": [ + { + "bbox": [ + 308, + 327, + 417, + 388 + ], + "type": "image", + "image_path": "04ceb22e28d922f20e90a16ee492e24a0fa73a6a57c4c9b3095190e5eea3a3a0.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 389, + 408, + 397 + ], + "lines": [ + { + "bbox": [ + 321, + 389, + 408, + 397 + ], + "spans": [ + { + "bbox": [ + 321, + 389, + 408, + 397 + ], + "type": "text", + "content": "Text: \"A dog standing in water\"" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 390, + 401, + 451, + 410 + ], + "lines": [ + { + "bbox": [ + 390, + 401, + 451, + 410 + ], + "spans": [ + { + "bbox": [ + 390, + 401, + 451, + 410 + ], + "type": "text", + "content": "(c) Few-shot RVOS" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 418, + 327, + 543, + 388 + ], + "blocks": [ + { + "bbox": [ + 418, + 327, + 543, + 388 + ], + "lines": [ + { + "bbox": [ + 418, + 327, + 543, + 388 + ], + "spans": [ + { + "bbox": [ + 418, + 327, + 543, + 388 + ], + "type": "image", + "image_path": "2e700290fbc6d2afa0990fe98144ca1ffcef690df869fa65d5230ba891266d44.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 436, + 389, + 541, + 397 + ], + "lines": [ + { + "bbox": [ + 436, + 389, + 541, + 397 + ], + "spans": [ + { + "bbox": [ + 436, + 389, + 541, + 397 + ], + "type": "text", + "content": "Text: \"A dog walking along the shore\"" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 418, + 547, + 491 + ], + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 491 + ], + "type": "text", + "content": "Figure 1: Comparison of Few-shot RVOS and RVOS and the setting of Few-shot RVOS. (a) The training and testing sets overlap in the RVOS. (b) Disjoint training and testing sets in the Few-shot RVOS. Different shapes represent different classes. (c) Few-shot RVOS segments the referred object of the same class as the support set in the video." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 614 + ], + "type": "text", + "content": "videos. In real-world scenarios, it has a wide range of applications, such as video editing [9] and human-computer interaction, so RVOS has attracted much attention from the research community. Unlike traditional semi-supervised video object segmentation [10], RVOS is more challenging because it not only lacks the ground-truth mask of the first frame of the video but also needs to interact with multimodal information of vision and language." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 617, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 714 + ], + "type": "text", + "content": "The great success of various tasks based on deep learning benefits from sufficient labeled data. Detailed annotated masks and language descriptions in real-world RVOS tasks are relatively scarce. The researchers have to annotate each frame in the video in detail and provide a referring expression for the segmentation object. Therefore, obtaining high-quality labeled data requires a high cost. With the popularity of movies, YouTube videos, TikTok streaming videos," + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "text", + "content": "*Equal contribution. This work was done when G. Li visited to Feng Zheng Lab in Southern University of Science and Technology. \n†Corresponding author." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2684" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "etc., video data in various fields has shown explosive growth in this media age. The demand for processing diverse data has brought significant challenges. In order to handle diverse data, existing RVOS methods must rely on massive and diverse labeled data for training. But due to fixed and limited training classes, existing RVOS methods [1, 33] are essentially constrained to adapt to the highly dynamic and highly diverse data in the real world. On the other hand, if ones fine-tune existing RVOS methods on a few samples to adapt to real-world data, high-quality results are hard to be achieved because the labelled data is insufficient to support the model for learning the new semantics. Therefore, how to make the RVOS methods applicable to real-world diverse data with a lower cost is an urgent problem." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 241, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 289, + 350 + ], + "type": "text", + "content": "To address this problem, we propose the cross-modal affinity (CMA) module to build multimodal relationships in a few samples and learn new semantic information for diversified data. Specifically, given only a few annotated samples (language expressions and the referred object masks), we hierarchically fuse visual and text features in a cross-attention manner to obtain robust feature representations for a specific category. In this way, the model can handle enormous data in the same category more efficiently." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 351, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 289, + 460 + ], + "type": "text", + "content": "Essentially, the proposed method targets limited samples. Therefore, we generalize the problem as Few-Shot Referring Video Object Segmentation (FS-RVOS). We show the setting of FS-RVOS and the difference from existing RVOS in Figure 1. Unlike RVOS, the training and testing sets' categories disjoint in the FS-RVOS. Given a few support video clips together with corresponding language descriptions and object masks, FS-RVOS aims at segmenting videos in the query set, as shown in Figure 1(c)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 460, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 289, + 628 + ], + "type": "text", + "content": "The key to FS-RVOS lies in the support set utilization and understanding of vision-language information. To better leverage the information in the support set, two methods have been proposed based on the prototype and attention mechanisms. The prototype-based [21, 35] methods compress the features belonging to different classes to obtain prototypes. However, noise is easily generated during the process. In addition, the spatial structures are ignored, resulting in different degree of information loss. Another methods [37, 38, 39] employ the attention mechanism to encode foreground pixels from support features and aggregate them with query features. Although these methods achieve high-quality results in image and video domains, they are still under-explored in vision-language tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "type": "text", + "content": "To better utilize vision-language inputs, we propose the cross-modal affinity module to build the multimodal relationships between samples in the support and query sets. Specifically, multimodal features within the support set and query set are first fused separately. The information among them is then aggregated, which effectively prevents query features from being biased by irrelevant features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": "Since this is the first work exploring Few-shot RVOS, the existing datasets are not directly applicable. Therefore, we build up a new FS-RVOS benchmark based on Ref-YouTube-VOS [22], named Mini-Ref-YouTube-VOS. The new benchmark covers a wide range with a balanced number of high-quality videos in each category. To measure the model's generalization ability, we also build a dataset different from natural scenes based on a synthetic dataset SAIL-VOS [13], named Mini-Ref-SAIL-VOS. Since only videos and detailed annotated masks exist in the SAIL-VOS dataset, we add natural language descriptions corresponding to the segmentation targets for the dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 217, + 525, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 217, + 525, + 228 + ], + "spans": [ + { + "bbox": [ + 317, + 217, + 525, + 228 + ], + "type": "text", + "content": "The main contributions of this work are as follows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 233, + 545, + 351 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 233, + 545, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 233, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 306, + 233, + 545, + 269 + ], + "type": "text", + "content": "- For real-world limited samples, we propose a CrossModal Affinity (CMA) for building multimodal information affinity for referring video object segmentation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 274, + 545, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 545, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 545, + 309 + ], + "type": "text", + "content": "- We explore a novel Few-shot RVOS problem, which learns new semantic information with limited samples and can adapt to diverse scenarios." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 315, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 315, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 306, + 315, + 545, + 351 + ], + "type": "text", + "content": "- We build up the first FS-RVOS benchmark, where we conduct comprehensive comparisons with existing methods, showing the superiority of the proposed model." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 364, + 392, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 364, + 392, + 376 + ], + "spans": [ + { + "bbox": [ + 306, + 364, + 392, + 376 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 390, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 556 + ], + "type": "text", + "content": "Few-Shot Semantic Segmentation. Few-shot semantic segmentation, first proposed by Shaban et al. [23], aims to learn how to segment new categories of images through a few samples. Recent advances in few-shot semantic segmentation originate from the application of metric learning. Based on PrototypicalNet, Dong et al. [7] first employ the metric learning technique and apply cosine similarity between pixels and prototypes for prediction. In addition, PANet et al. [31] introduce prototype alignment regularization to simplify the framework. PFENet et al. [28] use prior knowledge from the pretrained backbone to find the regions of interest and the different designs of feature pyramid modules, and previous leverage mappings to achieve better segmentation performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "However, the effectiveness of these few-shot segmentation methods depends mainly on the quality of the prototypes obtained from the support set. Fan et al. [8] address the critical intra-class appearance differences inherent in the few-shot segmentation problem by performing self-support matching with query features. Their strategy effectively captures the consistent underlying features of query objects to match query features. Tian et al. [27] propose a novel context-aware prototype learning method that leverages prior knowledge from support samples and dynamically enriches contextual information by using adaptive features. Motivated by the idea that using the base learner to identify confusing regions in the query image and further" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2685" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "refining the predictions of the meta-learner, BAM [15] establishes a new method for few-shot segmentation that does not focus on feature extraction or visual correspondence." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 288, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 288, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 288, + 252 + ], + "type": "text", + "content": "Compared to image-based few-shot segmentation, few-shot video object segmentation works are relatively rare and remain in the early stage. The initial work [25], [3] mainly solves this problem through the attention mechanism. However, these methods do not consider temporal information. Thus, based on temporal transductive, the recent work [24] applies reasoning mechanisms and has achieved good results in cross-domain scenarios. In a word, all the above-mentioned few-shot segmentation methods are only for a single modality - image or video, and cannot handle segmentation under multimodal conditions (i.e., with linguistic referring expressions)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 258, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 460 + ], + "type": "text", + "content": "Referring Video Object Segmentation. Gavrilyuk et al. [11] first introduce the RVOS task. They generate convolutional dynamic filters from textual representations and convolve them with visual features of different resolutions to obtain segmentation masks. To overcome the limitations of traditional dynamic convolution, Wang et al. [30] propose a context-modulated dynamic convolution operation for RVOS, where the kernel is generated from language sentences and surrounding contextual features. However, since the focus is only on video actors and actions, their approach only applies to a few object classes and action-oriented descriptions. Weak-Shot Semantic Segmentation (WSSS) [4, 42] focuses on the overall scene in the image, treating masks and text as the support set and text as the query set. However, in WSSS, the text is limited to single words or phrases indicating class names and directly mapped to labels for pixel-level classification." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": "Khoreva et al. [14] propose a two-stage approach that first performs referring expressions grounding and then utilizes the predicted bounding boxes to guide pixel-wise segmentation. Seo et al. [22] also present a framework called URVOS, which first predicts the initial mask based on the image and then utilizes the predicted mask of the previous frame for RVOS by memorizing the attention module." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "Most recent RVOS works employ cross-attention to interact visual images with linguistic information. LBDT [6] uses language as an intermediate bridge to connect temporal and spatial information and leverages cross-modal attention operations to aggregate language-related motion and appearance. MMVT [40] calculates the optical flow between frames and fuses it as motion information with text features and visual features. However, these frame-based spatial granularity multimodal fusion methods have limitations and tend to lead to mismatches between visual and linguistic information. Therefore, a recent piece of work [32, 40] explores a novel multi-level representation learning method and introduces dynamic semantic alignment to adaptively fuse the two modal information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "Transformer [29] has been widely applied and achieved great success in many computer vision tasks, such as object detection [2, 43] and image segmentation [41, 5]. Since DETR [2] introduces a new query-based paradigm, the latest works [1, 33, 16] prefer to apply the DETR's framework for RVOS task. Specifically, they utilize Transformer structures to interact visual images with linguistic data. Because Transformer has a remarkable ability to mine non-local correlation, they are able to attain SOTA performance in accuracy and efficiency. Despite the relative effectiveness of current RVOS techniques, they are primarily restricted to regular supervised learning settings, which would not be able to deal with unseen scenes with few shots." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 238, + 366, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 238, + 366, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 238, + 366, + 251 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 257, + 373, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 257, + 373, + 269 + ], + "spans": [ + { + "bbox": [ + 306, + 257, + 373, + 269 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": "In the setting of FS-RVOS, we have training and testing datasets " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "D_{train}" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "D_{test}" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " with disjoint category sets " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "C_{train}" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "C_{test}" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "C_{train} \\cap C_{test} = \\emptyset" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": ". Similar to few-shot learning tasks [26], episode training is adopted in this work, where " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "D_{train}" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "D_{test}" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " consist of several episodes. Each episode contains a support set " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " and a query set " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " where the text-referred objects (target objects) from both sets belong to the same class. The support set has " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " image-mask pairs " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "S = \\{x_k, m_k\\}_{k=1}^K" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " and the corresponding referring expression with " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " words " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "T_s = \\{t_i\\}_{i=1}^L" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "m_k" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " is the ground-truth mask of the video frame " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "x_k" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": ". The query set " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "Q = \\{x_i^q\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " is a selection of consecutive frames from a video and the corresponding natural language description with " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " words " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "T_q = \\{t_i\\}_{i=1}^M" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 276, + 545, + 482 + ], + "type": "text", + "content": " is the number of frames. With the setting above, FS-RVOS encourages models to segment objects with the unseen class in a query set based on a few samples in the support set." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 483, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 626 + ], + "type": "text", + "content": "As shown in Figure 2, our framework mainly consists of a Feature Extraction module, a Cross-modal Affinity module (CMA), and a Mask Generation module. With the support and query data as input, the framework predicts object masks for the query data, under the guidance of the corresponding language expressions. Specifically, the vision and text encoders extract features for visual and textual inputs, respectively. Then, CMA fuses visual and textual features hierarchically. The fused features are used to build the relationship between the support set and the query set. The output features are finally fed to the Mask Generation module to get the final segmentation results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 633, + 417, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 417, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 417, + 645 + ], + "type": "text", + "content": "3.2. Feature Extraction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 651, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 651, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 651, + 545, + 713 + ], + "type": "text", + "content": "We use a shared-weight visual encoder to extract multiscale features from each frame in the support set and query set, resulting in visual feature sequences " + }, + { + "bbox": [ + 304, + 651, + 545, + 713 + ], + "type": "inline_equation", + "content": "F_{vs} = \\{f_{vs}\\}_{vs=1}^{K}" + }, + { + "bbox": [ + 304, + 651, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 651, + 545, + 713 + ], + "type": "inline_equation", + "content": "F_{vq} = \\{f_{vq}\\}_{vq=1}^{N}" + }, + { + "bbox": [ + 304, + 651, + 545, + 713 + ], + "type": "text", + "content": ". For linguistic information, we use a Transformer-based text encoder [19] to extract text features" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2686" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 251 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 251 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 251 + ], + "type": "image", + "image_path": "175a6b26cca735b38aae6825349ebb0e580a1356544d946b4b5fcc3082415177.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 257, + 289, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 289, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 289, + 331 + ], + "type": "text", + "content": "Figure 2: The overall pipeline of our framework. The feature encoder extracts visual and textual information from the support and query sets. Then, the Cross-modal Affinity module calculates the multimodal information affinity between the support set and the query set. Finally, the final segmentation result is obtained through Mask Generation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "inline_equation", + "content": "F_{ts} = \\{f_{ts}\\}_{ts=1}^{L}" + }, + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "inline_equation", + "content": "F_{tq} = \\{f_{tq}\\}_{tq=1}^{M}" + }, + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "text", + "content": " from the natural language descriptions " + }, + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "inline_equation", + "content": "T_s" + }, + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "inline_equation", + "content": "T_q" + }, + { + "bbox": [ + 47, + 348, + 288, + 387 + ], + "type": "text", + "content": " that correspond to the input support data and the query data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 400, + 233, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 400, + 233, + 414 + ], + "spans": [ + { + "bbox": [ + 47, + 400, + 233, + 414 + ], + "type": "text", + "content": "3.3. Cross-modal Affinity Construction" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 422, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 517 + ], + "type": "text", + "content": "With a few samples in the support set, the goal of FS-RVOS is to efficiently leverage the given information and quickly adapt to relevant scenarios. Compared with conventional few-shot tasks, FS-RVOS not only builds the affinity between the support and query sets but also involves multimodal relationships between videos and referring expressions. Therefore, FS-RVOS is more challenging and requires specialized solutions for high-quality results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 519, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 288, + 604 + ], + "type": "text", + "content": "We propose the Cross-Modal Affinity (CMA) module to achieve this, as shown in Figure 3. We first perform crossattention fusion between the visual and textual features of support and query data, to obtain pixel-augmented multimodal features. Then, in order to aggregate beneficial information in support features, we build an affinity relationship between the support set and the query set." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Due to the diversity of referred objects and the drastic changes between video frames, it is a challenge to achieve the accurate location of the target only by visual information. Therefore, to obtain the accurate positioning of the segmentation target, we use language information as a supplement, which contains a specific description of the referred objects. To interact and align the visual features and text features, multi-head cross-attention (MCA) is proposed to fuse multimodal information, achieving two multi-scale" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 70, + 511, + 87 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 70, + 511, + 87 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 511, + 87 + ], + "type": "text", + "content": "feature maps " + }, + { + "bbox": [ + 305, + 70, + 511, + 87 + ], + "type": "inline_equation", + "content": "F_{vs}^{\\prime} = \\{f_s^{\\prime}\\}_{s = 1}^{K}" + }, + { + "bbox": [ + 305, + 70, + 511, + 87 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 70, + 511, + 87 + ], + "type": "inline_equation", + "content": "F_{vq}^{\\prime} = \\{f_q^{\\prime}\\}_{q = 1}^{N}" + }, + { + "bbox": [ + 305, + 70, + 511, + 87 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 331, + 93, + 547, + 110 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 93, + 547, + 110 + ], + "spans": [ + { + "bbox": [ + 331, + 93, + 547, + 110 + ], + "type": "interline_equation", + "content": "f _ {v s} ^ {\\prime} = \\operatorname {M C A} \\left(f _ {v s}, f _ {t s}\\right), f _ {v q} ^ {\\prime} = \\operatorname {M C A} \\left(f _ {v q}, f _ {t q}\\right), \\quad (1)", + "image_path": "7198764dbf76b67c3d072fd2df1316a576be27a0aae525daeacc889334f22731.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "spans": [ + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "inline_equation", + "content": "f_{vs}" + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "inline_equation", + "content": "f_{vq}" + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "text", + "content": " represent the visual features of support and query, " + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "inline_equation", + "content": "f_{ts}" + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "inline_equation", + "content": "f_{tq}" + }, + { + "bbox": [ + 304, + 116, + 547, + 199 + ], + "type": "text", + "content": " are their corresponding textual features. Here we calculate an affinity between textual features and visual features to filter out irrelevant visual information. Compared with concatenation, MCA suits our framework better since it can leverage the similarities between multimodal features for information complementation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 200, + 545, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 200, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 545, + 343 + ], + "type": "text", + "content": "The affinity between the support set and query set indicates the multimodal feature correlation among them, providing valuable clues for the segmentation of the query data. Although the objects to segment in the support and query sets belong to the same category, their visual properties usually have significant differences, such as appearance, pose, and scene. This means only a tiny part of the information in the support data is conducive to segmenting the query data, while other information will cause bad results. Therefore, we urgently need to solve the problem of computing the correct affinity relationship between multimodal information in the support and query sets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "text", + "content": "To achieve this, we propose a self-affinity block to encode the query features and a cross-affinity block to enable the query features to focus on beneficial pixels in the support features. In particular, given the input query features, we utilize a convolution operation to map them as query " + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "inline_equation", + "content": "q_{q}" + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "inline_equation", + "content": "k_{q}" + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "text", + "content": ", and value " + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "inline_equation", + "content": "v_{q}" + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "text", + "content": ". We perform the same operation for the support features to map them to key " + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "inline_equation", + "content": "k_{s}" + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "text", + "content": " and value " + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "inline_equation", + "content": "v_{s}" + }, + { + "bbox": [ + 304, + 343, + 546, + 462 + ], + "type": "text", + "content": ". The input of the self-affinity block does not include the support features and mainly aggregates the context information of the query features for better segmentation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 462, + 547, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 526 + ], + "type": "text", + "content": "First, we calculate the affinity map " + }, + { + "bbox": [ + 304, + 462, + 547, + 526 + ], + "type": "inline_equation", + "content": "A^Q = \\frac{q_q \\cdot (k_q)^{\\mathrm{T}}}{\\sqrt{d_{head}}}" + }, + { + "bbox": [ + 304, + 462, + 547, + 526 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 462, + 547, + 526 + ], + "type": "inline_equation", + "content": "d_{head}" + }, + { + "bbox": [ + 304, + 462, + 547, + 526 + ], + "type": "text", + "content": " is the hidden dimension of the input sequences, and we assume all sequences have the same dimension 256 by default. Therefore, the query features after the self-affinity block are represented as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 378, + 534, + 545, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 534, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 378, + 534, + 545, + 548 + ], + "type": "interline_equation", + "content": "q _ {s} = \\operatorname {S o f t m a x} \\left(A ^ {Q}\\right) v _ {q}. \\tag {2}", + "image_path": "c018c9126960fefaf6e9892a2544861a2a75ad69a28b0f2638189999b17af567.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 555, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 616 + ], + "type": "text", + "content": "We then feed the obtained query features to the cross-affinity block. The purpose of the cross-affinity block is to construct the cross-affinity relationship between the support features and the query features and aggregate the useful information. Our cross-affinity block can be formulated as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 349, + 624, + 545, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 624, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 349, + 624, + 545, + 651 + ], + "type": "interline_equation", + "content": "q u e r y _ {f e a t} = \\operatorname {S o f t m a x} \\left(\\frac {q _ {s} \\cdot \\left(k _ {s}\\right) ^ {\\mathrm {T}}}{\\sqrt {d _ {h e a d}}}\\right) v _ {s}, \\tag {3}", + "image_path": "1952aef8197beb8e9c7067eeca610886b205b229ce874432eec71fe619a10391.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "q_{s}" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": " is the output of the self-affinity block. Through these two modules, query features enhance features by modeling contextual information and computing the correlation between support and query features, effectively avoiding the attention bias caused by irrelevant features." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2687" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 287, + 210 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 287, + 210 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 287, + 210 + ], + "type": "image", + "image_path": "474a3563cbe4faad7d046799fd570a34df91ba3f0e3ac0631ab5ec1c2cc3c202.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 219, + 287, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 219, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 287, + 291 + ], + "type": "text", + "content": "Figure 3: The architecture of the Cross-modal Affinity (CMA) module. We use multi-head cross-attention to fuse visual and text features to get more robust features. Self-affinity for modeling contextual information on query features and cross-affinity for aggregating beneficial information from support features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 305, + 151, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 305, + 151, + 316 + ], + "spans": [ + { + "bbox": [ + 47, + 305, + 151, + 316 + ], + "type": "text", + "content": "3.4. Mask Generation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": "The goal of the Mask Generation module is to find the most relevant objects and decode the features step by step. To achieve this goal, the structure of Deformable-DETR [43] and feature pyramid [17] has been used in our work. We add the corresponding positional encoding to the feature sequence that aggregates beneficial information, which is then sent to the Transformer encoder. In the decoder part of Transformer, we introduce " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": " learnable anchor boxes as queries to represent the instances of each frame. These queries are replicated as decoder input for all frames and finally converted into instance embeddings by the decoder, resulting in " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "N_{q} = T \\times N" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": " predictions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 468, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 587 + ], + "type": "text", + "content": "In the feature pyramid network, in order to gradually fuse multimodal features from different layers, the output of the Transformer encoder and the features from the vision encoder are stacked to form hierarchical features. We use " + }, + { + "bbox": [ + 46, + 468, + 287, + 587 + ], + "type": "inline_equation", + "content": "f_{v}^{l}" + }, + { + "bbox": [ + 46, + 468, + 287, + 587 + ], + "type": "text", + "content": " to represent visual features at each level. First, we downsample the multi-scale visual features, and the time dimension remains unchanged. Then interact with visual and linguistic features in a cross-attention manner to enhance object pixel features, thereby facilitating mask prediction. The fused features are upsampled to restore the previous shape:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 78, + 594, + 287, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 594, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 78, + 594, + 287, + 622 + ], + "type": "interline_equation", + "content": "C r o s s \\left(f _ {v} ^ {l}, f _ {t q}\\right) = \\operatorname {S o f t m a x} \\left(\\frac {f _ {v} ^ {l} \\cdot \\left(f _ {t q}\\right) ^ {\\mathrm {T}}}{\\sqrt {d _ {\\text {h e a d}}}}\\right) f _ {t q}, \\tag {4}", + "image_path": "9ab32f28fa29e6b6d6f4622b4b5ee04202471df12b9c8f266aff5a0436822043.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "inline_equation", + "content": "f_{tq}" + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "text", + "content": " represents the text features corresponding to the query set. Finally, we pass the features of the last layer through a " + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "text", + "content": " convolutional layer to get the final feature maps " + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "inline_equation", + "content": "F_{seg} = \\{f_{seg}^{t}\\}_{t=1}^{T}" + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "inline_equation", + "content": "f_{seg}^{t} \\in \\mathbb{R}^{\\frac{H}{4} \\times \\frac{W}{4} \\times C}" + }, + { + "bbox": [ + 46, + 628, + 287, + 678 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 678, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 678, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 678, + 287, + 712 + ], + "type": "text", + "content": "Furthermore, we construct a set of auxiliary heads to obtain the final object mask across frames. The class head is used to calculate the confidence score " + }, + { + "bbox": [ + 46, + 678, + 287, + 712 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 46, + 678, + 287, + 712 + ], + "type": "text", + "content": ". The score indi" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "type": "text", + "content": "cates whether the instance corresponds to the referred object and whether the object is visible in the current frame. The kernel head is implemented by three consecutive linear layers, which generate the parameters " + }, + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "type": "inline_equation", + "content": "W = \\{w_{t}\\}_{t=1}^{N_{q}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "type": "inline_equation", + "content": "N_{q}" + }, + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "type": "text", + "content": " dynamic kernels. We use them as convolution filters on the feature maps, generating a series of segmentation masks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 152, + 394, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 152, + 394, + 163 + ], + "spans": [ + { + "bbox": [ + 306, + 152, + 394, + 163 + ], + "type": "text", + "content": "3.5. Loss Function" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "text", + "content": "In Mask Generation, we use " + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "text", + "content": " learnable anchor boxes as queries and generate a set of " + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "inline_equation", + "content": "N_{q} = T \\times N" + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "text", + "content": " prediction sequences. We denote the predicted sequence as " + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\hat{y} = \\{\\hat{y}_i\\}_{i=1}^{N_q}" + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "text", + "content": " and the prediction for the " + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "inline_equation", + "content": "i^{\\text{th}}" + }, + { + "bbox": [ + 304, + 170, + 545, + 221 + ], + "type": "text", + "content": " instance is expressed as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 386, + 226, + 545, + 244 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 226, + 545, + 244 + ], + "spans": [ + { + "bbox": [ + 386, + 226, + 545, + 244 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {i} = \\left\\{\\hat {s} _ {i} ^ {t}, \\hat {m} _ {i} ^ {t} \\right\\} _ {t = 1} ^ {T}, \\tag {5}", + "image_path": "3b03cfa915f58496f6ce93bf8ab3afaf9ce1da6a09d9bd9e5422f8ba84dd7c18.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\hat{s}_i^t\\in \\mathbb{R}^1" + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "text", + "content": " is a fractional score indicating whether the instance corresponds to the referred object. " + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\hat{m}_i^t\\in \\mathbb{R}^{\\frac{H}{4}\\times \\frac{W}{4}}" + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "text", + "content": " is the predicted binary segmentation mask. Similar to the previous methods [1, 33], we use dynamic convolution to generate the object mask. We get the final feature maps " + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "inline_equation", + "content": "f_{seg}^{t}" + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "text", + "content": " through the feature pyramid network, and the mask prediction can be calculated by " + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\hat{m}^t = \\left\\{w_t*f_{seg}^t\\right\\}" + }, + { + "bbox": [ + 304, + 251, + 545, + 337 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 337, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 545, + 384 + ], + "type": "text", + "content": "The sequence of ground-truth instances is denoted as " + }, + { + "bbox": [ + 304, + 337, + 545, + 384 + ], + "type": "inline_equation", + "content": "y = \\{s^t, m^t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 337, + 545, + 384 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 337, + 545, + 384 + ], + "type": "inline_equation", + "content": "s^t" + }, + { + "bbox": [ + 304, + 337, + 545, + 384 + ], + "type": "text", + "content": " is an one-hot value and equals 1 when the ground-truth instance is visible in the frame, and 0 otherwise. Our loss function is defined as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 392, + 545, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 392, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 315, + 392, + 545, + 416 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (y, \\hat {y} _ {i}) = \\lambda_ {c l s} \\mathcal {L} _ {c l s} (y, \\hat {y} _ {i}) + \\lambda_ {k e r n e l} \\mathcal {L} _ {k e r n e l} (y, \\hat {y} _ {i}), \\tag {6}", + "image_path": "38a384e15637af43ec9f8244489aa797d5200ce24acc18b8067ebbbdab588940.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\lambda_{cls}, \\lambda_{kernel}" + }, + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "type": "text", + "content": " are hyperparameters to balance the loss. We use focal loss [18] (denoted as " + }, + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "type": "text", + "content": ") to supervise the prediction of instance sequence reference results. " + }, + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kernel}" + }, + { + "bbox": [ + 304, + 417, + 545, + 475 + ], + "type": "text", + "content": " is a combination of DICE loss [20] and the binary mask focal loss." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 483, + 373, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 373, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 373, + 495 + ], + "type": "text", + "content": "3.6. Inference" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 502, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 586 + ], + "type": "text", + "content": "In the inference phase, we treat all input video frames as a whole and predict the mask trajectory for the entire video using only one forward pass. Given an input video and the corresponding linguistic expression, our model generates a sequence of " + }, + { + "bbox": [ + 304, + 502, + 545, + 586 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 502, + 545, + 586 + ], + "type": "text", + "content": " instances. For each frame, we select the instance sequence with the highest confidence score as the final prediction, and its index can be expressed as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 385, + 594, + 545, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 594, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 385, + 594, + 545, + 614 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\bar {s} = \\arg \\max s _ {i}. \\tag {7} \\\\ i \\in \\{1, 2, \\dots , N \\} \\\\ \\end{array}", + "image_path": "f2e5304da0a622d803a64799f102eb9417a150c1ffa70f17f398fc7eb71c72ec.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "type": "text", + "content": "The final prediction " + }, + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "type": "inline_equation", + "content": "m = \\{s_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "type": "text", + "content": " for each frame is obtained from the mask candidate set " + }, + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\hat{m}^t" + }, + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "type": "text", + "content": " with index " + }, + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\overline{s}" + }, + { + "bbox": [ + 304, + 623, + 545, + 647 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 658, + 381, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 381, + 669 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 381, + 669 + ], + "type": "text", + "content": "4. Benchmark" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "Since the existing RVOS datasets [22, 14, 34, 11] only target specific scenarios, the model cannot handle the diverse scenarios in the real world. Likewise, these datasets" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2688" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 542, + 133 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 542, + 133 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 542, + 133 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 542, + 133 + ], + "type": "image", + "image_path": "fc95c807c4f5d0914d457f4367feb471ebe29a82d69c66647db43d2aeee61614.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 134, + 249, + 146 + ], + "lines": [ + { + "bbox": [ + 54, + 134, + 249, + 146 + ], + "spans": [ + { + "bbox": [ + 54, + 134, + 249, + 146 + ], + "type": "text", + "content": "A man in a brown jacket is standing on the right" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 150, + 542, + 215 + ], + "blocks": [ + { + "bbox": [ + 51, + 150, + 542, + 215 + ], + "lines": [ + { + "bbox": [ + 51, + 150, + 542, + 215 + ], + "spans": [ + { + "bbox": [ + 51, + 150, + 542, + 215 + ], + "type": "image", + "image_path": "131a5f661cec88b0ddc78dcaabd961a2821e393d0d6632cafc9494c973be2f7a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 216, + 307, + 228 + ], + "lines": [ + { + "bbox": [ + 54, + 216, + 307, + 228 + ], + "spans": [ + { + "bbox": [ + 54, + 216, + 307, + 228 + ], + "type": "text", + "content": "A man in a gray coat standing on the right is saying something" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 51, + 232, + 542, + 297 + ], + "blocks": [ + { + "bbox": [ + 51, + 232, + 542, + 297 + ], + "lines": [ + { + "bbox": [ + 51, + 232, + 542, + 297 + ], + "spans": [ + { + "bbox": [ + 51, + 232, + 542, + 297 + ], + "type": "image", + "image_path": "9512643f130555d90df3f4470e02e062e7cfafb4620217e1afcd65c2be234811.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 297, + 151, + 309 + ], + "lines": [ + { + "bbox": [ + 55, + 297, + 151, + 309 + ], + "spans": [ + { + "bbox": [ + 55, + 297, + 151, + 309 + ], + "type": "text", + "content": "A brown dog is barking" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 159, + 316, + 432, + 328 + ], + "lines": [ + { + "bbox": [ + 159, + 316, + 432, + 328 + ], + "spans": [ + { + "bbox": [ + 159, + 316, + 432, + 328 + ], + "type": "text", + "content": "Figure 4: Annotation examples of the Mini-Ref-SAIL-VOS dataset." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 338, + 286, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 286, + 384 + ], + "type": "text", + "content": "are not suitable for the few-shot RVOS problem. This is because the train/test/Validation sets of these datasets have class repetition and cannot be used to evaluate the generality of unseen classes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 393, + 286, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 286, + 524 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 286, + 524 + ], + "type": "text", + "content": "Mini-Ref-YouTube-VOS. To match the FS-RVOS setting, we build up a new dataset called Mini-Ref-YouTube-VOS based on the Ref-YouTube-VOS dataset [22]. The data that can be directly obtained from the Ref-YouTube-VOS dataset contains 3,471 videos, 12,913 referring expressions, and annotated instances covering more than 60 categories. However, some videos in this dataset consist of multiple category instances. When preparing data for the few-shot setting, we cleaned up the dataset, i.e., removing such videos and keeping only those containing only one category instance, a total of 2387 videos were obtained." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 526, + 286, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 526, + 286, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 526, + 286, + 646 + ], + "type": "text", + "content": "The video data in the dataset should be class-balanced, and the number of samples in each class should not vary too much to avoid overfitting any class. Therefore, we deal with the categories whose number of videos does not meet the requirements to ensure the class balance of the dataset. After the above screening, 1,668 videos were obtained, including 48 classes. To better show the model results, we adopt the cross-validation method to divide the dataset into four folds on average. Each fold contains 36 training and 12 test classes with disjoint categories." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "Mini-Ref-SAIL-VOS. Most Mini-Ref-YouTube-VOS data involve natural scenes of a relatively homogeneous type and therefore do not represent the diversity of data in the real world. To better demonstrate the generalization of our model, we collect videos from SAIL-VOS [13] to" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 338, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 445 + ], + "type": "text", + "content": "construct a new dataset Mini-Ref-SAIL-VOS. The SAIL-VOS dataset is a synthetic dataset collected from a video game GTA-V, aiming to foster semantic amodal segmentation research. In SAIL-VOS, each frame is accompanied by densely annotated, pixel-wise and amodal segmentation masks with semantic labels. Since the data is collected from the game, phenomena such as shot transition, segmentation target cross-frame, and target occlusion are inevitable, which brings challenges to the segmentation task." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 448, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 579 + ], + "type": "text", + "content": "We reorganize the SAIL-VOS dataset to pick out samples suitable for the FS-RVOS setting. First, for videos with few frames for segmentation targets, we directly discard them. For the case where the segmentation target appears across frames, we manually delete the frames where the target does not appear in the middle to maintain the temporal continuity of the segmentation target. For phenomena such as object occlusion, we characterize it as a challenge and do not deliberately delete video frames with object occlusion. Following the above settings, we collected a dataset with 68 videos and 3 semantic categories." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "It is worth noting that although there are accurate mask annotations in the SAIL-VOS dataset, natural language description corresponding to the segmentation target is not available. Thus, to adapt it to FS-RVOS, we employed expert annotators to provide referring expressions after data collection. Given a pair of videos for each annotator, the video frames are superimposed with corresponding masks to indicate the objects to be segmented. The annotators were then asked to provide a distinguishing statement with a word limit of 20 words. To ensure the quality of natural language annotations, all annotations are verified and cleaned" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2689" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 71, + 285, + 137 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 285, + 137 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 285, + 137 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 285, + 137 + ], + "type": "table", + "html": "
MethodFold-1Fold-2Fold-3Fold-4Mean
JDANet [3]4733.538.54440.8
Ours59.545.350.457.353.1
FDANet [3]49.338.241.445.843.7
Ours60.848.951.358.154.8
", + "image_path": "43183858f2a5ddd04d3f986a4cb8708d6d4f3dd097aeb7c72e1fcbc0710aaa50.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 176, + 285, + 244 + ], + "blocks": [ + { + "bbox": [ + 47, + 146, + 286, + 171 + ], + "lines": [ + { + "bbox": [ + 47, + 146, + 286, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 146, + 286, + 171 + ], + "type": "text", + "content": "Table 1: Quantitative results on Mini-Ref-YouTube-VOS. We added visual language fusion modules to DANet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 176, + 285, + 244 + ], + "lines": [ + { + "bbox": [ + 50, + 176, + 285, + 244 + ], + "spans": [ + { + "bbox": [ + 50, + 176, + 285, + 244 + ], + "type": "table", + "html": "
MethodFold-1Fold-2Fold-3Fold-4Mean
JDANet [3]54.347.630.930.640.9
Ours80.980.880.168.977.7
FDANet [3]54.148.435.23643.4
Ours77.17777.367.874.8
", + "image_path": "05d704f298d63f8ae6458567f25b9c4078bb139678c2f8b962bf032aef190c67.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 279, + 287, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 287, + 328 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 287, + 328 + ], + "type": "text", + "content": "up after the initial annotation. The target will not be used if the natural language description cannot clearly describe the target. As shown in Figure 4, we show the selected videos along with referring expressions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 338, + 128, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 338, + 128, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 338, + 128, + 352 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 357, + 180, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 180, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 180, + 370 + ], + "type": "text", + "content": "5.1. Implementation Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "text", + "content": "We adopt ResNet-50 [12] and RoBERTa-Base [19] as our vision and text encoders, respectively. During the training stage, the parameters of both encoders are frozen. In our experiments, we adopt a 5-shot setting. Specifically, we extract 5 consecutive frames and the corresponding referring expressions from a certain video of a class as a support set. The query set is composed of consecutive frames and corresponding referring expressions extracted from other videos belonging to the same class. We test each fold 5 times and report the average confidence of the results. Our model utilizes AdamW for optimization. The weight decay is " + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "text", + "content": " and the initial learning rate is " + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "text", + "content": ". To balance GPU memory efficiency, we downsample all video frames, with the shortest video frame size being 360 and the longest 640. The parameters of the loss function are set as " + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\lambda_{cls} = 2" + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\lambda_{kernel} = 5" + }, + { + "bbox": [ + 46, + 376, + 287, + 591 + ], + "type": "text", + "content": ". All methods for conducting experiments will be pre-processed and fine-tuned in the same way, i.e., pre-trained on Ref-COCO [36] dataset." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 592, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 287, + 628 + ], + "type": "text", + "content": "Following the settings of previous RVOS works, we use the region similarity " + }, + { + "bbox": [ + 46, + 592, + 287, + 628 + ], + "type": "inline_equation", + "content": "(\\mathcal{I})" + }, + { + "bbox": [ + 46, + 592, + 287, + 628 + ], + "type": "text", + "content": " and the contour accuracy " + }, + { + "bbox": [ + 46, + 592, + 287, + 628 + ], + "type": "inline_equation", + "content": "(\\mathcal{F})" + }, + { + "bbox": [ + 46, + 592, + 287, + 628 + ], + "type": "text", + "content": " to measure the model performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 635, + 105, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 105, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 105, + 647 + ], + "type": "text", + "content": "5.2. Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "type": "text", + "content": "As a novel problem, no relevant works can be directly used for comparisons. Therefore, we choose DANet [3] as the baseline given we both focus on few-shot video segmentation. For a fair comparison, we add a visual-language fusion module to the Few-Shot VOS model." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 310, + 71, + 541, + 140 + ], + "blocks": [ + { + "bbox": [ + 57, + 251, + 276, + 264 + ], + "lines": [ + { + "bbox": [ + 57, + 251, + 276, + 264 + ], + "spans": [ + { + "bbox": [ + 57, + 251, + 276, + 264 + ], + "type": "text", + "content": "Table 2: Quantitative results on Mini-Ref-SAIL-VOS." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 71, + 541, + 140 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 541, + 140 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 541, + 140 + ], + "type": "table", + "html": "
MethodJFJ&F
LBDT [6]27.5 / 42.436.2 / 37.331.6 / 39.6
ReferFormer [33]65.1 / 74.162.8 / 64.964.0 / 69.5
MTTR [1]66.5 / 69.764.9 / 68.165.7 / 68.9
Ours80.977.179
", + "image_path": "80890ff27b7a805d02cd4a8e55a4863eada4566e6de8fdc1f9bcb7e02916f14e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 343, + 205, + 509, + 262 + ], + "blocks": [ + { + "bbox": [ + 305, + 148, + 545, + 196 + ], + "lines": [ + { + "bbox": [ + 305, + 148, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 545, + 196 + ], + "type": "text", + "content": "Table 3: Comparison with state-of-the-art methods from RVOS on the Mini-Ref-SAIL-VOS dataset to measure the model's generalization. Underlined scores are achieved after fine-tuning." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 343, + 205, + 509, + 262 + ], + "lines": [ + { + "bbox": [ + 343, + 205, + 509, + 262 + ], + "spans": [ + { + "bbox": [ + 343, + 205, + 509, + 262 + ], + "type": "table", + "html": "
Self-affinityCross-affinityJ&F
--57.9
✓-59.2
✓✓60.2
", + "image_path": "3ccff4b6b91fccfc764a372f22d9f304a4fce86fe6dcebd5c6fd15b9f5c9299a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 270, + 547, + 306 + ], + "lines": [ + { + "bbox": [ + 305, + 270, + 547, + 306 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 547, + 306 + ], + "type": "text", + "content": "Table 4: Ablation studies that validate the effectiveness of each component in our CMA. The first result is obtained with our baseline." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 322, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 545, + 418 + ], + "type": "text", + "content": "Mini-Ref-YouTube-VOS. We present the experimental results of our model on the Mini-Ref-YouTube-VOS dataset in Table 1. It can be observed that our method significantly outperforms DANet. Compared with previous methods, our method achieves a substantial increase in average performance, with an average improvement of more than " + }, + { + "bbox": [ + 304, + 322, + 545, + 418 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 322, + 545, + 418 + ], + "type": "text", + "content": ". The excellent performance demonstrates the superiority and robustness of our proposed method." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 425, + 545, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 580 + ], + "type": "text", + "content": "Mini-Ref-SAIL-VOS. To evaluate the generalization of our model, we make further experiments and comparisons on the Mini-Ref-SAIL-VOS dataset. We do not perform new training on the Mini-Ref-SAIL-VOS dataset but directly test with the model trained on Mini-Ref-Youtube-VOS. Note that the videos in the Mini-Ref-SAIL-VOS dataset are from Game scenes, and they hold a noticeable domain different from the data in the Mini-Ref-Youtube-VOS dataset. In addition, the objects in some videos are occluded and these phenomena make this dataset somewhat challenging. We show the experimental results in Table 2. According to the Table, it is clear that our method achieves a significant improvement over the baseline." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": "Moreover, we also make further comparisons with some state-of-the-art RVOS methods [6, 33, 1]. Here, we only show the results under Fold-1. To measure the RVOS model's generalization, we first directly test the trained RVOS models on the Mini-Ref-SAIL-VOS dataset. Since our few-shot learning task needs a few samples as support data, for a fair comparison, these RVOS models will be finetuned with a few samples. The corresponding results are shown in Table 3. 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"spans": [ + { + "bbox": [ + 75, + 347, + 353, + 358 + ], + "type": "text", + "content": "A man in a red dress and a hat standing on the left is talking to someone" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 72, + 363, + 542, + 424 + ], + "blocks": [ + { + "bbox": [ + 72, + 363, + 542, + 424 + ], + "lines": [ + { + "bbox": [ + 72, + 363, + 542, + 424 + ], + "spans": [ + { + "bbox": [ + 72, + 363, + 542, + 424 + ], + "type": "image", + "image_path": "8b8004bcdb7452cc6c9f3697fe58eafc4946fc669dc3383d087738bac56c409d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 76, + 425, + 238, + 436 + ], + "lines": [ + { + "bbox": [ + 76, + 425, + 238, + 436 + ], + "spans": [ + { + "bbox": [ + 76, + 425, + 238, + 436 + ], + "type": "text", + "content": "A black car parked on the side of the road" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 113, + 444, + 478, + 455 + ], + "lines": [ + { + "bbox": [ + 113, + 444, + 478, + 455 + ], + "spans": [ + { + "bbox": [ + 113, + 444, + 478, + 455 + ], + "type": "text", + "content": "Figure 5: Qualitative results on (a) Mini-Ref-YouTube-VOS and (b) Mini-Ref-SAIL-VOS." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 466, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 466, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 287, + 514 + ], + "type": "text", + "content": "proposed approach. This is because our model effectively constructs the multimodal relationship between the support set and the query set so that it can quickly adapt to new scenarios by only using a few samples." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 522, + 141, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 141, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 141, + 534 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "type": "text", + "content": "In this section, we perform an ablation study on the Mini-Ref-YouTube-VOS dataset to evaluate the design and the robustness of the model. Unless otherwise stated, we only show results under Fold-1. Denoting " + }, + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{I}\\&\\mathcal{F}" + }, + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "type": "text", + "content": " as the average of " + }, + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 540, + 287, + 612 + ], + "type": "text", + "content": ", we can use the indicator to show the performance of the model." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 617, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 688 + ], + "type": "text", + "content": "Cross-modal Affinity. We perform ablation studies on the components of the CMA in Table 4. The results of the baseline are shown in the first line. As mentioned before, the baseline refers to directly concatenating the support features and query features into the Mask Generation to obtain the segmentation mask." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "First, we only utilize the self-affinity block to establish contextual information between pixels to enhance query" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 466, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 545, + 586 + ], + "type": "text", + "content": "features. At this time, support features are concatenated with the enhanced query features and then fed to the Mask Generation module. It can be seen that good results are achieved, indicating that the Transformer does work for modeling features and extracting contextual information. By adding the proposed cross-affinity block, the performance can be further improved by " + }, + { + "bbox": [ + 304, + 466, + 545, + 586 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 466, + 545, + 586 + ], + "type": "text", + "content": ". Such comparisons show that the cross-affinity block properly constructs the multimodal relationship between the support set and the query set, effectively avoiding the bias of the query features." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 609, + 417, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 417, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 417, + 621 + ], + "type": "text", + "content": "5.4. Qualitative Results" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 633, + 545, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 633, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 304, + 633, + 545, + 716 + ], + "type": "text", + "content": "The qualitative results of our model are presented in Figure 5. From the figure, It can be seen that the proposed model can segment the referred objects accurately in a variety of challenging situations. Furthermore, we also show the qualitative results on the Mini-Ref-SAIL-VOS dataset. In general, our model always achieves high-quality results even in the face of samples from different scenes." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "2691" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 119, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 119, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 119, + 83 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "content": "In this work, we propose CMA to learn multimodal affinity in a few samples to segment diverse data. Further, we generalize it as a few-shot RVOS problem. We validate our model on the newly constructed datasets - Mini-RefYouTube-VOS and Mini-Ref-SAIL-VOS and obtain state-of-the-art performance. We hope this work can cast a light on future FS-RVOS research." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 180, + 289, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 276 + ], + "type": "text", + "content": "Acknowledgements. This work is supported in part by the National Key R&D Program of China (Grant No. 2022YFF1202903), the National Natural Science Foundation of China (Grant No. 61971004, 62122035), the Natural Science Foundation of Anhui Province, China (Grant No. 2008085MF190), and the Equipment Advanced Research Sharing Technology Project, China (Grant No. 80912020104)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 288, + 107, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 107, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 107, + 300 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 308, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 308, + 287, + 351 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 308, + 287, + 351 + ], + "spans": [ + { + "bbox": [ + 53, + 308, + 287, + 351 + ], + "type": "text", + "content": "[1] Adam Botach, Evgenii Zheltonozhskii, and Chaim Baskin. 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In this paper, we propose a sparsely supervised biomedical instance segmentation framework via cross-representation affinity consistency regularization. Specifically, we adopt two individual networks to enforce the perturbation consistency between an explicit affinity map and an implicit affinity map to capture both feature-level instance discrimination and pixel-level instance boundary structure. We then select the highly confident region of each affinity map as the pseudo label to supervise the other one for affinity consistency learning. To obtain the highly confident region, we propose a pseudo-label noise filtering scheme by integrating two entropy-based decision strategies. Extensive experiments on four biomedical datasets with sparse instance annotations show the state-of-the-art performance of our proposed framework. For the first time, we demonstrate the superiority of sparse instance-level supervision on 3D volumetric datasets, compared to common semi-supervision under the same annotation cost. Code is available at https://github.com/liuxy1103/CRAC.", + "bbox": [ + 76, + 348, + 473, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Biomedical instance segmentation aims to assign each image pixel to an instance, which plays an essential role in biomedical instance morphology and distribution analysis [36, 32]. Recently, deep-learning-based methods [22, 26, 48, 20, 15, 30, 6] have achieved state-of-the-art perfor", + "bbox": [ + 75, + 777, + 468, + 854 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/882dd8515faae5d7a3b99bd769557fef71340ee49b4c5e94514c7d87948650c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 323, + 629, + 434 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bc5e4692f357cbd5d7cb5762243b95ac7efb4d3571face524e6efb30cbbae756.jpg", + "image_caption": [ + "Figure 1. Comparison of instance annotation schemes in different supervision ways for the volumetric dataset. (a) Full supervision, where the whole volume is annotated. (b) Semi-supervision, where a subset of the whole volume is densely annotated. (c) sparse instance-level supervision, where a subset of instances of the whole volume is annotated." + ], + "image_footnote": [], + "bbox": [ + 635, + 316, + 756, + 436 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a7963f0e64cd1a3c2b2f114ae386e07ced5b9e92e3c7d344d9bbe3ab0f0e1635.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 316, + 888, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mance on biomedical instance segmentation with densely annotated images for fully-supervised training. However, it is expensive and laborious to obtain accurate and dense annotations.", + "bbox": [ + 498, + 547, + 892, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To alleviate the huge cost of manual annotations, many works [42, 13, 49, 37, 7] adopt the semi-supervised learning strategy to train an effective segmentation model with a small set of densely annotated images and a large set of unannotated images. However, in the field of biomedical instance segmentation, dense annotation is difficult to apply due to the crowded instances. Especially, for the 3D volumetric datasets (e.g., electron microscopy datasets), dense annotation within a small sub-volume usually damages the completeness of the instances along the axial direction. Meanwhile, in practice, domain experts tend to annotate instances one by one sparsely, rather than annotating all instances densely within a small sub-volume.", + "bbox": [ + 496, + 611, + 893, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we aim to deal with the task of biomedical instance segmentation with sparse instance annotations. This task is of utmost importance, as annotating a small subset of instances in a biomedical dataset not only saves the annotation cost but also conforms to annotation habits in the practical scenario. We illustrate different annotation", + "bbox": [ + 496, + 809, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was done during Xiaoyu Liu's internship at Institute of Artificial Intelligence, Hefei Comprehensive National Science Center. \n†Corresponding author: zwxiong@ustc.edu.cn.", + "bbox": [ + 75, + 862, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21107", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "schemes in Fig. 1 and focus on the comparison between common semi-supervision and sparse instance-level supervision. For a volumetric dataset, a few consecutive images are densely annotated for the semi-supervision in Fig. 1 (b), which generates many incomplete instances along the axial direction. Instead, a few instances are randomly annotated for the sparse instance-level supervision in Fig. 1 (c), which preserves complete 3D structure information of each instance under the same number of annotated voxels as the semi-supervision.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Actually, sparse instance-level supervision can be considered a special kind of semi-supervision at the region level. Thus, existing semi-supervised methods [42, 13, 49, 37, 7] can be readily adapted to the sparse instance-level supervision. As a pioneer work, SPOCO [46] imposes a consistency regularization scheme [42] in the unannotated regions of two embedding maps predicted in different augmented views. However, SPOCO adopts a metric learning [9]-based segmentation method to distinguish different instances in the feature space, whose performance heavily drops as the number of annotated instances decreases. On the other hand, the perturbation consistency used in SPOCO is relatively simple and cannot effectively exploit instance structure information in unannotated regions. In other words, there remains a large room to release the potential of the sparse instance-level supervision.", + "bbox": [ + 75, + 244, + 472, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared to metric learning, affinity-based instance segmentation methods [44, 43] are less sensitive to the number of annotated instances, since affinities encode instance boundary structure knowledge and are easier to be learned. Inspired by this kind of methods, we propose an effective biomedical instance segmentation framework with sparse instance annotations, which learns cross-representation affinity consistency. Specifically, our framework consists of two individual networks to predict two different representations, i.e., an embedding map and an implicit affinity map (IAM), respectively. We then calculate the similarity between pixel embeddings and convert the embedding map into an explicit affinity map (EAM). The IAM exploits the spatial structure information of instances, while the EAM exploits the semantic information of instances in the feature space. By building the perturbation consistency between the IAM and the EAM, we combine the advantages of two kinds of affinity modeling to capture both feature-level instance discrimination and pixel-level instance boundary structure. This perturbation consistency is different from the existing perturbation consistency between the same kinds of representations widely used in semi-supervised learning.", + "bbox": [ + 75, + 489, + 472, + 837 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our framework, we use the groundtruth affinity map generated from sparse instance annotations to supervise the two affinity maps in the annotated regions. Inspired by the cross pseudo supervision [7], we further propose an affin", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ity cross-supervision mechanism to facilitate affinity consistency learning on the unannotated regions. Specifically, we design a pseudo-label noise filtering scheme that integrates a heuristic decision strategy based on an adaptive threshold and a learning decision strategy based on a pretrained confident pixel selection network (CPSN), to select highly confident regions as pseudo labels from one affinity map to supervise the other.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our methods on four biomedical datasets with sparse instance annotations to demonstrate the state-of-the-art performance of our proposed framework, compared to three kinds of baselines: 1) the existing sparsely supervised method SPOCO, 2) advanced semi-supervised methods which are adapted to sparse instance-level supervision, and 3) original semi-supervised methods trained with dense annotation under the same annotation cost.", + "bbox": [ + 496, + 212, + 890, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are as follows:", + "bbox": [ + 519, + 334, + 823, + 349 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a sparsely supervised biomedical instance segmentation framework by enforcing the perturbation consistency between two kinds of affinity modeling.", + "- We propose an affinity cross-supervision mechanism with a pseudo-label noise filtering scheme integrating two decision strategies to select highly confident regions to facilitate affinity consistency learning.", + "- We conduct extensive experiments on four biomedical datasets with sparse instance annotations to demonstrate the state-of-the-art performance of our method.", + "- We demonstrate the general superiority of sparse instance-level supervision over semi-supervision on 3D volumetric datasets for the first time." + ], + "bbox": [ + 517, + 361, + 890, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 625, + 640, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Biomedical Instance Segmentation", + "text_level": 1, + "bbox": [ + 500, + 648, + 800, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The prevalent instance segmentation methods are mainly divided into two categories: proposal-based [12, 26, 3, 47] and proposal-free [5, 38, 27, 29, 28, 33]. The former is based on object detection to distinguish different instances, while the latter is based on instance-aware features and morphology properties, which is more suitable to complex and dense instances of biomedical datasets. Metric learning [9, 22] and affinity learning [11, 31] are two proposal-free representatives.", + "bbox": [ + 496, + 672, + 890, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Metric learning [9, 22, 20] uses a discriminative loss [9] to impose pixels belonging to different instances to be discriminative from each other in the feature space. However, as the number of instances decreases in the sparse instance-level supervision setting, it is difficult for the network to distinguish different instances in the feature space.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21108", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0a5f6d0e6f7d1d1c5fa1cbb99dafa976f10241e10b0b146f153ba293306eda9f.jpg", + "image_caption": [ + "Figure 2. The workflow of our proposed sparsely supervised biomedical instance segmentation framework. (a) The input image is fed into two networks $f(\\theta_1)$ and $f(\\theta_2)$ to predict an affinity map and an embedding map, respectively. The embedding map is then explicitly converted into an affinity map. (b) These two affinity maps are supervised by the affinity label on the annotated region. The unannotated region of the affinity label is highlighted in gray color. The white and black colors indicate the affinity value as 1 and 0. (c) The highly confident region with low entropy of each affinity map is selected by a confident pixel selection network (CPSN) to supervise the other on the unannotated region. The red color indicates the region of the affinity map with high entropy, which is not used for cross-supervision. (d) This diagram illustrates the training stage of the CPSN, in which the model is trained on the annotated region to predict regions with segmentation errors. These regions are then excluded from being used as pseudo labels to supervise the other affinity map. $\\odot$ and $\\oplus$ represent dot product and concatenation operations, respectively." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 895, + 295 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Affinity learning [2, 11, 31, 14] predicts pixel affinities that only encode spatial structure information between adjacent instances without ensuring the uniqueness of each instance in the feature space. Thus, the affinities are easy to be learned by the network and less affected by the number of instances. Even if there is only one annotated instance, this method can learn affinities between the unannotated region and the instance.", + "bbox": [ + 75, + 444, + 472, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Consistency Regularization", + "text_level": 1, + "bbox": [ + 76, + 577, + 323, + 593 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consistency regularization [1] plays a vital role in semisupervised learning. It enforces the consistency of predictions of unannotated data with various perturbations, by introducing a regularization loss function. The categories of perturbation are mainly divided into input perturbation [49, 25, 10], feature perturbation [37, 40], and network perturbation [7, 17]. Existing methods generally enforce the consistency between different perturbations of the same representation. Take an example of combining meanteacher [42] and the affinity-based segmentation method: both the teacher and student networks directly predict affinity maps that belong to the same representation. Different from existing consistency regularization methods, our proposed framework enforces consistency between two different representations from two kinds of affinity modeling.", + "bbox": [ + 75, + 601, + 468, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 844, + 284, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an input image $I$ with a size of $H\\times W$ , containing K instances (including background), $\\mathbf{M}$ of which are", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "annotated $(M\\ll K)$ . The image $I$ is divided into two pixel sets, i.e., an annotated pixel region $R^L$ and an unannotated pixel region $R^{U}$ . The unannotated region $R^{U}$ contains unannotated instances and background. Different from semi-supervised learning, our goal is to train a model to predict the accurate affinity map by leveraging both a few annotated instances in the annotated region $R^{L}$ and the unannotated region $R^{U}$ .", + "bbox": [ + 496, + 444, + 890, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before introducing our method, we clarify the definition of affinity. The affinity map $A = [a_{1}, a_{2}, \\ldots, a_{N}] \\in \\mathbb{R}^{N \\times H \\times W}$ describes whether the current pixel and adjacent pixels belong to the same instances or not, where $a_{n}(n = 1, 2, \\ldots, N)$ denotes the different adjacent relations between the current pixel and its $n$ order adjacent pixel. Given the segmentation groundtruth $y \\in \\mathbb{R}^{H \\times W}$ , a pixel affinity $a_{n,i} \\in a_{n}$ at the $i^{th}$ pixel of the image $I$ is formulated as", + "bbox": [ + 496, + 566, + 892, + 700 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\na _ {n, i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} y _ {i} \\neq y _ {i + n} \\\\ 1, & \\text {i f} y _ {i} = y _ {i + n}, \\end{array} \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 700, + 890, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $y_{i}$ and $y_{i + n}$ are the instance segmentation IDs of paired pixels $i$ and $i + n$ . 1 means that pixel $i$ and $i + n$ belong to one instance, while 0 means the opposite.", + "bbox": [ + 496, + 750, + 893, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Considering the segmentation groundtruth with sparse instance-level annotations, we regard the unannotated region (including the background) as an identical instance ID. The generated affinity label is divided into annotated region $R_{a}^{L}$ and unannotated region $R_{a}^{U}$ . If the pixel affinity $a_{n,i}$ is located in the annotated region $R_{a}^{L}$ , at least one of the pixels $i$ and $i + n$ is located in the annotation region $R^{L}$ , i.e.,", + "bbox": [ + 496, + 795, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21109", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$y_{i} \\in R^{L}$ or $y_{i + n} \\in R^{L}$ . Therefore, the annotated affinity region $R_{a}^{L}$ is slightly larger than the annotated segmentation region $R^{L}$ .", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Cross-Representation Affinity Consistency", + "text_level": 1, + "bbox": [ + 76, + 154, + 457, + 171 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce the proposed sparsely supervised biomedical instance segmentation framework. The input of our framework can be either 2D images or 3D volumes. Here we illustrate it using a 2D image example for easy visualization. As shown in Fig. 2, our framework consists of two main parts. The first part contains two parallel networks to build affinity perturbation by predicting different representations: IAM and EAM (detailed in 4.1). The second part contains an affinity cross-supervision mechanism by a pseudo-label noise filtering scheme to select the highly confident region of the two affinity maps to supervise each other for consistency learning (detailed in 4.2).", + "bbox": [ + 75, + 181, + 470, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Affinity Perturbation", + "text_level": 1, + "bbox": [ + 76, + 376, + 276, + 392 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unlike the common perturbation consistency strategy, we build the perturbation between two affinity representations predicted by two parallel networks. Following the existing affinity learning methods [11, 31], we adopt a network $f(\\theta_1)$ to directly predict an implicit affinity map $\\hat{A}^1 = [\\hat{a}_1^1, \\hat{a}_2^1, \\dots, \\hat{a}_N^1]$ . For accurate pixel affinities, the network $f(\\theta_1)$ focuses on the structure information of instance boundaries.", + "bbox": [ + 75, + 401, + 468, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In contrast to implicit learning, explicitly modeled affinity has been widely studied [22, 14] by calculating the pairwise relationships between pixel embeddings. Given the limited number of instances, we only impose local constraints on the adjacent instances instead of constraining all instances by a discriminative loss [9]. We adopt a network $f(\\theta_2)$ to predict an embedding map $E \\in \\mathbb{R}^{D \\times H \\times W}$ , where $D$ is the number of channels of the last layer of the network. Each pixel $i$ of the image $I$ is mapped into a pixel embedding vector $e_i \\in \\mathbb{R}^D$ , which is a D-dimensional feature representation. We then adopt a cosine distance to calculate the relationship between pixel embeddings and converted the embedding map into an explicit affinity map $\\hat{A}^2 = [\\hat{a}_1^2, \\hat{a}_2^2, \\dots, \\hat{a}_N^2]$ . The transformation from a paired of pixel embeddings to a pixel affinity $\\hat{a}_{n,i}^2$ is formulated as", + "bbox": [ + 75, + 523, + 468, + 751 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {a} _ {n, i} ^ {2} = \\frac {e _ {i} ^ {T} e _ {i + n}}{\\| e _ {i} \\| _ {2} \\| e _ {i + n} \\| _ {2}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 765, + 468, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The network $f(\\theta_2)$ pays more attention to extracting the semantic instance information to discriminate pixels belonging to different instances in the feature space.", + "bbox": [ + 75, + 814, + 468, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We adopt the MSE loss to supervise both $f(\\theta_1)$ and $f(\\theta_2)$ in the annotated region $R_a^L$ of the affinity label $A$ :", + "bbox": [ + 500, + 90, + 890, + 122 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {s} = L _ {s 1} + L _ {s 2} \\\\ = \\frac {1}{\\left| R _ {a} ^ {L} \\right|} \\sum_ {i \\in R _ {a} ^ {L}} \\sum_ {n = 1} ^ {N} \\left(\\left\\| \\hat {a} _ {n, i} ^ {1} - a _ {n, i} \\right\\| _ {2} + \\left\\| \\hat {a} _ {n, i} ^ {2} - a _ {n, i} \\right\\| _ {2}\\right), \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 133, + 908, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{s1}$ and $L_{s2}$ represent the loss functions for $f(\\theta_1)$ and $f(\\theta_2)$ , respectively.", + "bbox": [ + 498, + 196, + 890, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Affinity Cross-Supervision", + "text_level": 1, + "bbox": [ + 498, + 237, + 738, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to combine the advantages of the two kinds of affinity modeling, we propose an affinity cross-supervision mechanism to enforce the consistency between the IAM and the EAM. Since the two affinity maps may suffer from prediction errors during the initial training phase, we propose a pseudo-label noise filtering scheme by integrating two entropy-based decision strategies, i.e., adaptive threshold and prediction by a CPSN, to select highly confident pixel affinities to avoid the collapse of the consistency learning. For a pixel affinity $a_{n,i}$ , its entropy is computed by", + "bbox": [ + 496, + 261, + 890, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {n, i} = - a _ {n, i} \\log \\left(a _ {n, i}\\right) - (1 - a _ {n, i}) \\log \\left(1 - a _ {n, i}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 424, + 890, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Adaptive threshold. As a heuristic strategy, we can determine whether the pixel affinity is confident by the following indicator:", + "bbox": [ + 498, + 453, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {n, i} ^ {\\text {t h r e s}} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} h _ {n, i} < \\gamma_ {t} \\\\ 0, & \\text {o t h e r s ,} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 496, + 890, + 536 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{t}$ refers to the entropy threshold at the $t^{th}$ training iteration, which is the quantile of $h_{n,i}$ corresponding to $\\alpha_{t}$ to limit unreliable pixels with top $\\alpha_{t}$ entropy. 1 means the pixel affinity is confident with low entropy, while 0 means the opposite.", + "bbox": [ + 496, + 542, + 890, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the confident pixels gradually increase during the training procedure, $\\alpha_{t}$ is dynamically adjusted by a power function:", + "bbox": [ + 496, + 619, + 890, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {t} = \\alpha_ {0} (1 - t / T) ^ {p}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 664, + 890, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_0$ is the initial quantile and is set to $5\\%$ , $p$ is the power and is set as 1.5, $t$ is the current training iteration, and $T$ is total iterations.", + "bbox": [ + 496, + 688, + 890, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Confidence pixel selection network. Inspired by approaches that address pseudo label errors using auxiliary networks [35, 21], we employ a binary-classification network called CPSN to identify highly confident pixels, which is trained only using the annotated regions of the groundtruth error map, as shown in Fig. 2 (d). Specifically, we sample five segmentation models under different training iterations of $f(\\theta_{1})$ and $f(\\theta_{2})$ respectively, and add a certain rate of dropout to these models. We then use the prediction from these models to simulate various segmentation errors. Using this kind of simulation data, we train", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1We call it implicit affinity map to distinguish from the one explicitly calculated from the embedding map below.", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21110", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a robust CPSN to locate errors and generate highly confident pixels. We provide training details (including the loss $L_{CPSN}$ ) in the supplementary material.", + "bbox": [ + 76, + 90, + 468, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the input image $I$ , affinity map $A$ and affinity entropy map $H$ , the CPSN can predict a binary error map $B \\in \\mathbb{R}^{N \\times H \\times W}$ with the same size as $A$ :", + "bbox": [ + 76, + 136, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nB = \\operatorname {C P S N} (I \\oplus A \\oplus H), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 189, + 468, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\oplus$ is the concatenation operation.", + "bbox": [ + 76, + 214, + 341, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We then determine whether the pixel affinity is confident by the following indicator:", + "bbox": [ + 75, + 229, + 468, + 258 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {n, i} ^ {c p s n} = 1 - b _ {n, i}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 265, + 468, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $b_{n,i} \\in B$ is the pixel-level prediction of CPSN.", + "bbox": [ + 76, + 291, + 431, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pseudo-label noise filtering. We integrate the above two decision strategies to obtain more robust highly confident pixels, which is described by $\\delta_{n,i} = \\delta_{n,i}^{thres}\\delta_{n,i}^{cpsn}$ . After obtaining the confident pixels of the IAM (indicated by $\\delta_{n,i}^{1}$ ) and the EAM (indicated by $\\delta_{n,i}^{2}$ ), we utilize their confident pixels on the unannotated affinity region $R_{a}^{U}$ to cross-supervise each other. The consistency loss is formulated as", + "bbox": [ + 75, + 306, + 468, + 417 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {c} = L _ {c 1} + L _ {c 2} \\\\ = \\frac {1}{\\left| R _ {a} ^ {U} \\right|} \\sum_ {i \\in R _ {a} ^ {U}} \\sum_ {n = 1} ^ {N} \\left(\\left\\| \\hat {a} _ {n, i} ^ {1} - \\hat {a} _ {n, i} ^ {2} \\right\\| _ {2} \\delta_ {n, i} ^ {2} \\right. \\tag {9} \\\\ + \\left\\| \\hat {a} _ {n, i} ^ {2} - \\hat {a} _ {n, i} ^ {1} \\right\\| _ {2} \\delta_ {n, i} ^ {1}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 425, + 468, + 496 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{c1}$ and $L_{c2}$ represent the consistency loss functions for $f(\\theta_1)$ and $f(\\theta_2)$ .", + "bbox": [ + 76, + 502, + 468, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Overall Optimization", + "text_level": 1, + "bbox": [ + 76, + 540, + 277, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall objection function is the combination of losses on the annotated region and the unannotated region, which terms", + "bbox": [ + 76, + 564, + 468, + 607 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {s} + \\lambda L _ {c}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 609, + 468, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is the trade-off weight and is set to make the two loss value ranges comparable.", + "bbox": [ + 76, + 628, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following [14], we adopt the network $f(\\theta_2)$ to predict an explicit affinity map in the inference stage. The affinity map is converted into final instance segmentation results by different post-processing algorithms. The 3D results and 2D results are generated by Waterz [11] (50% quantile and 0.5 threshold) and Mutex [45] post-processing algorithms, respectively. Since affinities calculated by these two different normalization schemes (sigmoid vs cosine) belong to different intervals, we use a RELU function to map the output value into [0, 1], for Waterz post-processing algorithm.", + "bbox": [ + 75, + 659, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 821, + 209, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 76, + 847, + 274, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct evaluations on four representative biomedical datasets with corresponding commonly used metrics.", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "AC3. The AC3 dataset is a popular electron microscopy (EM) neuron dataset, imaged from the mouse somatosensory cortex at $3 \\times 3 \\times 29$ nm resolution. It is a subset of the Kasthuri [16] dataset, and contains 256 volumetric images ( $1024 \\times 1024$ ). We adopt the top 100 sections as the labeled set and sparsely select different numbers of neuron instances as the annotations. At the same time, the bottom 50 sections are adopted for evaluation. We adopt two widely used metrics in the field of EM image segmentation to quantitatively evaluate the result, i.e., Variation of Information (VOI) [34] and Adapted Rand Error (ARAND) [39]. The VOI is defined as a sum of another two metrics $VOI_{split}$ and $VOI_{merge}$ which indicate the split and merge errors, respectively. Note that smaller values of these metrics indicate better performance.", + "bbox": [ + 496, + 90, + 890, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CREMI-C. The CREMI dataset is from the CREMI challenge [8] for neuron segmentation in EM volumes. It is composed of three volumetric datasets (CREMI-A, CREMI-B, and CREMI-C) imaged from the adult drosophila brain at $4 \\times 4 \\times 40$ nm resolution. Each of the three datasets contains 125 images. Given that the neurites in CREMI-A and CREMI-C are mostly homogeneous in morphology, we evaluate our method on the CREMI-C dataset, which contains more challenging neuron types. We adopt the top 75 sections as the labeled set and the bottom 50 sections for evaluation. We adopt the same metrics used for the AC3 to evaluate the results on the CREMI-C dataset.", + "bbox": [ + 496, + 316, + 890, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CVPPP. The A1 sequence of the CVPPP [36] dataset contains leaves with complex shapes and severe occlusions, which is widely used to evaluate biomedical instance segmentation. We randomly sample 108 images for training and 20 images for testing, where each image is with a size of $530 \\times 500$ . We adopt the Symmetric Best Dice (SBD) and the absolute Difference in Counting $(|DiC|)$ metrics [36] to evaluate the quantitative result.", + "bbox": [ + 496, + 500, + 890, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BBBC039V1. The BBBC039V1 dataset [32] contains 200 fluorescence microscopy images with a resolution of $696 \\times 520$ pixels. The dataset focuses on the U2OS cells with various shape and density. Following the official data split, we use 100 images for training, 50 for validation, and the rest 50 for testing. We adopt four metrics for cell segmentation for quantitative evaluation, i.e., Aggregated Jaccard Index (AJI) [39], object-level F1 score (F1) [4], Panoptic Quality (PQ) [19], and pixel-level Dice score (Dice).", + "bbox": [ + 496, + 622, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 770, + 715, + 786 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt two different backbone networks, i.e., 3D U-Net [23] and 2D Residual U-Net for the 3D volumetric datasets (AC3, CREMI-C) and 2D datasets (CVPPP, BBBC039V1), respectively. Both the network $f(\\theta_{1})$ and $f(\\theta_{2})$ are based on the same backbone network but different in the last convolution layer. We train these networks using Adam optimizer [18] with $\\beta_{1} = 0.9$ and $\\beta_{2} = 0.999$ , a", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21111", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9c3cf3631cf107ad95a3c3f96fb7a10b30c31483bedbc9d773855f868e2456db.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsAC3CREMI-C
VOISplit ↓VOIMerge ↓VOI ↓ARAND ↓VOISplit ↓VOIMerge ↓VOI ↓ARAND ↓
Semi.Vanilla0.4225.4035.8250.9110.9292.1173.0460.580
PseudoL-hard [41]0.0895.9556.0440.9200.8631.4622.3250.311
PseudoL-soft [50]0.8513.7444.5950.8530.9500.8941.8440.230
MT [42]0.8632.0582.9210.5580.9161.0271.9430.211
π-model [25]0.8471.8672.7140.5620.9850.9181.9030.227
UA-MT [49]0.7201.8602.5800.4260.9780.8631.8410.227
SASSNet [24]1.1601.1802.3400.3240.9350.8141.7490.193
SSNS [13]0.7020.5271.2290.1200.9340.7751.7090.175
Sparse.SPOCO [46]1.6081.3492.9570.2361.8320.8962.7280.303
Vanilla0.9300.2371.1670.1111.6130.4512.0640.187
MT* [42]0.6990.4321.1320.0921.3750.5591.9340.173
UA-MT* [49]0.7850.2511.0360.0821.5020.3331.8350.155
CCT* [37]0.8590.2381.0970.0881.4250.4631.8880.173
CPS* [7]0.7180.2480.9660.0671.3840.3981.7820.158
Ours0.6420.2600.9030.0641.0320.5871.6200.153
", + "bbox": [ + 96, + 89, + 874, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison of segmentation results on AC3 and CREMI-C datasets using 5 densely annotated sections for semi-supervision and randomly annotated instances for sparse instance-level supervision. The number of annotated voxels is the same for the two settings. Vanilla refers to training models only using available groundtruth. The top right corner \\* indicates these methods are originally proposed in the semi-supervision but adapted into the sparse instance-level supervision. Note that we adopt the same backbone ResUnet [23] in all methods for a fair comparison. The best results and the second-best results are highlighted in bold and underlined.", + "bbox": [ + 75, + 325, + 890, + 396 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8d1bdac39117ed7cb187248f6c823d05ed433d52e39556cad583628a4c7b15dc.jpg", + "image_caption": [ + "Figure 3. 2D Visual comparison of different methods on AC3 and CREMI-C datasets. The first row and the second row of each dataset are the affinity map and the corresponding instance segmentation result. Red and blue boxes indicate merge and split errors, respectively." + ], + "image_footnote": [], + "bbox": [ + 76, + 406, + 890, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "learning rate of $1e - 4$ , and a batch size of 2 on one NVIDIA TitanXP GPU for 200K iterations.", + "bbox": [ + 75, + 744, + 467, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparison Methods", + "text_level": 1, + "bbox": [ + 76, + 785, + 279, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The evaluation of our method is performed against three kinds of baselines:", + "bbox": [ + 75, + 809, + 467, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(1) For the 3D volumetric datasets, the sparse instance-level supervision and the common semi-supervision contain different 3D structure information of instances in the axial direction. For a comprehensive evaluation, we compare", + "bbox": [ + 75, + 840, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "our proposed sparsely supervised method with a number of existing semi-supervised methods that are widely used for 3D datasets, including: PseudoL-hard [41], PseudoL-soft [50], mean-teacher (MT) [42], $\\pi$ -model [25], UAMT [49], SASSNet [24] and SSNS [13].", + "bbox": [ + 496, + 744, + 890, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(2) SPOCO [46] provides a baseline solution for the sparsely supervised segmentation task. We use the official code and configurations to reproduce the results on 2D datasets (CVPPP and BBBC039V1), and adapt this method to 3D datasets (AC3 and CREMI-C).", + "bbox": [ + 496, + 824, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21112", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4a06ad5c7604e4b54db385d891b3cde031e5af6048fb2305fd608789f705946c.jpg", + "image_caption": [ + "Figure 4. 3D Visual comparison of different methods on AC3 and CREMI-C datasets. Red and blue arrows indicate split and merge errors, respectively." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 324 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(3) We adapt a variety of advanced semi-supervised methods to the sparsely supervised segmentation task, including mean-teacher (MT) [42], uncertainty-aware mean teacher model(UA-MT) [49], cross-consistency training (CCT) [37] and cross pseudo supervision (CPS) [7].", + "bbox": [ + 75, + 388, + 468, + 465 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Results on 3D Datasets", + "text_level": 1, + "bbox": [ + 76, + 478, + 289, + 492 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We list an extensive quantitative comparison on the AC3 and the CREMI-C datasets in Table 1. We conduct the semi-supervised experiments with 5 densely annotated sections, and the sparsely supervised experiments with 23 and 33 randomly annotated instances for AC3 and CREMI-C datasets respectively. The number of annotated voxels is the same for the two settings. From the results in Table 1, we can observe that:", + "bbox": [ + 75, + 502, + 468, + 622 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) With the same number of annotated voxels, sparsely supervised methods perform better than corresponding semi-supervised methods by a large margin. Specifically, our results outperform the state-of-the-art semi-supervised results from SSNS [13] by $26.4\\%$ and $5.2\\%$ for the VOI metric on the AC3 and CREMI-C datasets.", + "(2) For the EM neuron segmentation datasets, the sparse instance annotations are not conducive to the training of SPOCO [46] based on metric learning. Therefore, SPOCO [46] does not perform well on these two datasets.", + "(3) Our method achieves better performance than other adapted methods in the sparse instance-level supervision setting. Specifically, We achieve $6.3\\%$ and $9.2\\%$ improvement from the key VOI metric on the AC3 and CREMI-C datasets, compared with the second-best method. It demonstrates the superiority of the proposed affinity consistency regularization." + ], + "bbox": [ + 75, + 625, + 468, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show 2D and 3D visual comparison results in Fig. 3", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/43e9583f5594c6a42e6fc9dd315d237be1d0b1f6ca051c9a81bda045de44ae20.jpg", + "image_caption": [ + "Figure 5. Comparison of different methods on the AC3 dataset under different annotation amounts converted into the number of sections for counting, where each section contains $1 \\times 10^{6}$ pixels." + ], + "image_footnote": [], + "bbox": [ + 506, + 386, + 883, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and Fig. 4, respectively. As can be seen, our proposed method predicts the affinity map with higher fidelity than other methods, which significantly reduces the split and merge errors. We also provide 3D visual comparison results in the supplementary material. As can be seen, our results contain fewer merge and split errors, and maintain the accuracy of neuron structures, compared with other methods.", + "bbox": [ + 496, + 640, + 890, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further compare different methods on the AC3 dataset under different numbers of annotated voxels. We convert the number of voxels to the number of sections for counting, where each section contains about $1 \\times 10^{6}$ voxels. The results are shown in Fig. 5. As more annotations are available, the performance gap between different methods gradually narrows, but the superiority of our method can still be observed. Especially, the state-of-the-art semi-supervised method SSNS performs worse than sparsely supervised methods under very limited annotations, due to the", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21113", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f6cf06fa9551f992ccde968cd7d417e4eda8032d19f438fbbfc3319fa5f25d4c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methods10% instances40% instances
SBD ↑|DiC| ↓SBD ↑|DiC| ↓
CPS [7] (semi)83.21.887.61.1
SPOCO [46]70.63.082.12.0
Vanilla69.86.078.01.9
MT* [42]78.51.484.31.3
UA-MT* [49]79.61.484.51.1
CCT* [37]78.81.983.91.6
CPS* [7]80.71.885.51.1
Ours83.61.186.60.8
", + "bbox": [ + 88, + 88, + 459, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f9a150eb8efc7c3c5e7a35657d8367799856ad96eaad5822d0b5d661e5fc1315.jpg", + "image_caption": [ + "Raw Image" + ], + "image_footnote": [], + "bbox": [ + 81, + 287, + 174, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c33d7e2f802677bdd954ebfcaab5877abef1055eddcab1addecd30e88ae15924.jpg", + "image_caption": [ + "MT*" + ], + "image_footnote": [], + "bbox": [ + 178, + 287, + 271, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a100951a106da68f7bb3db6e9ffa4e5a6d8fa847da1eac39de4eac77a849f05.jpg", + "image_caption": [ + "UAMT*" + ], + "image_footnote": [], + "bbox": [ + 274, + 287, + 367, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a71f3c9df7a7855541fa039f2add481cb04b081237d63697f73c1a998f29d736.jpg", + "image_caption": [ + "CCT*" + ], + "image_footnote": [], + "bbox": [ + 372, + 287, + 465, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/da79899e01d2720456a8ec9e3e866376dc4d8afc6c0cea9d3139f2477067315b.jpg", + "image_caption": [ + "SPOCO", + "Figure 6. Visual comparison of different methods on the CVPPP dataset with $40\\%$ instances. The segmentation errors are highlighted by white boxes." + ], + "image_footnote": [], + "bbox": [ + 81, + 366, + 174, + 429 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/21b1b5ea8e9206226ab3479924ac7ac85e0fe086f2d0cd21e73a359a7ec14265.jpg", + "image_caption": [ + "CPS*" + ], + "image_footnote": [], + "bbox": [ + 178, + 366, + 271, + 429 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ecf26c81624f0714b2771309fdc6b8e56cb389392ae8f928d97fd793bacb47cf.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 274, + 366, + 367, + 429 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dbda1af37a3b95a4387b06ef7740ddcd4ff3f3aaffea90435f812e7ca1cb1c00.jpg", + "image_caption": [ + "Groundtruth" + ], + "image_footnote": [], + "bbox": [ + 372, + 366, + 465, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "incomplete 3D structure information of instances.", + "bbox": [ + 76, + 520, + 405, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Results on 2D Datasets", + "text_level": 1, + "bbox": [ + 76, + 544, + 287, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further validate our method on two 2D datasets, i.e., CVPPP and BBBC039V1, and their quantitative results are shown in Table 2 and Table 3, respectively. Compared with other adapted methods in the sparse instance-level supervision setting, our method achieves the best performance on the CVPPP dataset with $10\\%$ and $40\\%$ annotated instances, and the BBBC039V1 dataset with $1\\%$ and $10\\%$ annotated instances. Visual results on these two datasets also illustrate the superior performance of our method with fewer segmentation errors, as shown in Fig. 6 and Fig. 7.", + "bbox": [ + 75, + 568, + 468, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although the sparse instance-level supervision and the common semi-supervision have no difference in the instance structure for 2D datasets, we also evaluate the semi-supervised setting (with the same annotated pixels) on these two datasets. Our proposed method performs better than the state-of-the-art semi-supervised method CPS [7], when the annotation amount is very limited. Meanwhile, our method significantly outperforms the existing sparely supervised method SPOCO in all experiments. As more annotation amount is available, the semi-supervised method has a better performance. Therefore, the sparse instance-level supervision is still a meaningful complement to the com", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7b073976d8992b92c9bf09d446b9153a089d90f5b388eed446a566987e4edf6b.jpg", + "table_caption": [ + "Table 2. Quantitative comparison results on the CVPPP dataset. Results in the first row are based on the semi-supervision setting." + ], + "table_footnote": [], + "table_body": "
MethodsAJI ↑Dice ↑F1 ↑PQ ↑
1% instancesCPS [7] (semi)0.81200.90330.95950.8168
SPOCO [46]0.68960.84780.84920.6933
Vanilla0.56310.64110.75700.4890
MT* [42]0.77160.82600.90180.7533
UA-MT* [49]0.80650.87380.94390.7928
CCT* [37]0.81130.91360.92950.7830
CPS* [7]0.83230.91850.94440.8153
Ours0.83030.93380.94420.8222
10% instancesCPS [7] (semi)0.83930.91890.95980.8437
SPOCO [46]0.74880.87460.92630.7503
Vanilla0.59850.71770.77090.5652
MT* [42]0.84160.91670.93380.8283
UA-MT* [49]0.84040.91180.93800.8314
CCT* [37]0.83090.92790.93270.7975
CPS* [7]0.84630.93660.94080.8174
Ours0.85450.94690.94500.8343
", + "bbox": [ + 501, + 88, + 890, + 332 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/479842fcf3f6091ceacf27448e70c335ae363e115cc8af74f313b08b97e6a7ed.jpg", + "image_caption": [ + "Raw Image" + ], + "image_footnote": [], + "bbox": [ + 504, + 359, + 599, + 414 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2b7ad6c196c6ca60b48667c3682def10831df07fae671a3aa7f05233b5c82c99.jpg", + "image_caption": [ + "MT*" + ], + "image_footnote": [], + "bbox": [ + 601, + 359, + 694, + 415 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b61f8bb29e42382f7d1780b06776a276a6e29b7acd7f8dcd548f54e897b3318d.jpg", + "image_caption": [ + "UAMT" + ], + "image_footnote": [], + "bbox": [ + 697, + 359, + 790, + 414 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f2d4925b5d5ffcebf1a0fd03a6e6859dd98a5ea56ea05af81af5fdb5ecadd30c.jpg", + "image_caption": [ + "CCT*" + ], + "image_footnote": [], + "bbox": [ + 794, + 359, + 887, + 414 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cfb40ba30b61f4b4bdbc8af932c9abed6ec011f218e8c5983407768a686f2dc9.jpg", + "image_caption": [ + "SPOCO", + "Figure 7. Visual comparison of different methods on the BBBC039V1 dataset with $10\\%$ instances." + ], + "image_footnote": [], + "bbox": [ + 504, + 425, + 599, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5260862763891f4c692a30f99c066dc57dcb065a0f90e34ae489e88d2e94acfd.jpg", + "image_caption": [ + "CPS*" + ], + "image_footnote": [], + "bbox": [ + 601, + 425, + 694, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d39497e4181406cafbe13ea8b2a11c48f90a420a1ea6fed4da718f8feb659ea9.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 697, + 425, + 790, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c4ed470c768b3ed962475ab162c50e1c8fbaec9f6e08947685e1aec1ee2112b0.jpg", + "image_caption": [ + "Groundtruth" + ], + "image_footnote": [], + "bbox": [ + 794, + 425, + 887, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mon semi-supervision when instances are so crowded that dense annotation is laborious and the amount of annotations is very limited, for the 2D datasets.", + "bbox": [ + 498, + 555, + 890, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 611, + 663, + 626 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ac909fd59584d4ff3788b9f083fdeb0adeef1b8868980c29f220275eb21f61ec.jpg", + "table_caption": [ + "Table 3. Quantitative comparison on the BBBC039V1 dataset." + ], + "table_footnote": [], + "table_body": "
Method15102050100
Vanilla2.2891.1670.9820.8710.7790.726
Ours1.2710.9030.8160.8070.7380.717
", + "bbox": [ + 501, + 646, + 890, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study on the annotation amount which is converted into the number of sections for counting, where each section contains about $1 \\times 10^{6}$ voxels. The key metric VOI is used to evaluate the results.", + "bbox": [ + 498, + 707, + 890, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct ablation studies on the impacts of each component of the proposed framework on the AC3 dataset.", + "bbox": [ + 498, + 779, + 888, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Annotation amounts. We conduct an ablation study to investigate the effects of different amounts of annotated instances. As shown in Table 4, our proposed method consistently outperforms the vanilla model trained only using available annotated instances. When the annotation amount is small (e.g., the number of annotated voxels is about a sec", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21114", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8f1d37088d121cd263d22b2f94c21375896766a4f35e7f7407eaf97a2d12ea05.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
f(θ1)f(θ2)cross-supervisionVOI ↓ARAND ↓
ThresholdCPSN
IAMIAM✓✓0.9260.074
EAMEAM✓✓0.9270.068
IAMEAMXX0.9160.068
IAMEAM✓X0.9060.068
IAMEAMX✓0.9090.067
IAMEAM✓✓0.9030.065
", + "bbox": [ + 91, + 88, + 457, + 224 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/c3a89c94499d21ea98138b347dc806f75ef5e7849528a3d48b39e9c8b8e76e5b.jpg", + "table_caption": [ + "Table 5. Ablation study on different components of the proposed affinity consistency regularization. IAM and EAM represent the different kinds of affinity modeling for the two networks $f(\\theta_{1})$ and $f(\\theta_{2})$ . 'Threshold' and 'CPSN' denote the two different strategies to select highly confident regions in cross-supervision." + ], + "table_footnote": [], + "table_body": "
MethodVOISplit ↓VOIMerge ↓VOI ↓ARAND ↓
Ours-f(θ1)0.7090.1980.9070.071
Ours-f(θ2)0.6870.2180.9030.065
", + "bbox": [ + 94, + 316, + 452, + 368 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/368550d4c08a72bdb1ecedeaf8b673bc21db4cf64282f7b1ccb5989e5d6c87ae.jpg", + "table_caption": [ + "Table 6. Ablation study on which affinity map used for inference." + ], + "table_footnote": [], + "table_body": "
α00.010.050.1
VOI↓/ ARAND ↓0.933 / 0.0750.903 / 0.0650.924 / 0.069
Dropout rate00.10.3
VOI↓/ ARAND ↓0.920 / 0.0660.903 / 0.0650.923 / 0.067
λ0.010.11
VOI↓/ ARAND ↓0.914 / 0.0660.903 / 0.0651.258 / 0.106
", + "bbox": [ + 94, + 401, + 450, + 518 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 7. Ablation study on key parameters of the proposed framework. VOI/ARAND are adopted as metrics.", + "bbox": [ + 76, + 527, + 467, + 555 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "tion), our method significantly improves the performance of the vanilla model. The performance gap narrows as more annotations are available.", + "bbox": [ + 76, + 582, + 468, + 626 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Affinity consistency regularization. As shown in Table 5, we conduct an ablation study on the proposed affinity consistency learning scheme. We compare different combinations of affinity modeling for the two networks $f(\\theta_{1})$ and $f(\\theta_{2})$ by directly enforcing their consistency. It can be observed that the combination of IAM and EAM achieves the best performance. Furthermore, we demonstrate the effectiveness of pseudo-label noise filtering with different decision strategies. Both strategies have been shown to improve performance, and their integration can obtain more robust highly confident regions and achieves the best performance. Moreover, We have compared our method with an equivalent implementation of [14] in Table 5, i.e., two network branches both use EAM. Our method achieves better performance.", + "bbox": [ + 75, + 628, + 467, + 851 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Affinity map used in the inference stage. The two affinity maps predicted by $f(\\theta_{1})$ and $f(\\theta_{2})$ have different performances, as shown in Table 6. The EAM predicted by", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "$f(\\theta_2)$ performs slightly better, so we adopt it in the inference stage.", + "bbox": [ + 498, + 90, + 888, + 119 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Ablation study on hyper-parameters. We conducted ablation experiments to evaluate the impact of key hyperparameters, of the proposed framework, as shown in Table 7. For the proposed pseudo-label noise filtering scheme, we test different values of hyper-parameters $\\alpha_0$ for adaptive threshold and different dropout rates used in the CPSN training. Also, we provide the ablation study on different loss weights $\\lambda$ .", + "bbox": [ + 496, + 121, + 890, + 242 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 258, + 617, + 272 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose an effective sparsely supervised biomedical instance segmentation framework via learning cross-representation affinity consistency. The proposed framework builds the perturbation consistency between an implicit affinity map and an explicit affinity map with an affinity cross-supervision mechanism. We conduct extensive experiments on 3D volumetric datasets and 2D datasets to demonstrate the superiority of our proposed framework over the existing sparsely supervised method. Meanwhile, for the first time, we validate that sparsely supervised methods can better utilize the 3D structure information of instances and perform better than semi-supervised methods for volumetric datasets.", + "bbox": [ + 496, + 282, + 890, + 479 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 492, + 658, + 508 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China under Grant 62021001.", + "bbox": [ + 500, + 513, + 888, + 542 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 559, + 594, + 574 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Philip Bachman, Ouais Alsharif, and Doina Precup. 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In ECCV, 2018. 6" + ], + "bbox": [ + 78, + 90, + 468, + 684 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21117", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/e6b0e920-39b7-4259-9938-916b268677a8_model.json b/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/e6b0e920-39b7-4259-9938-916b268677a8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0dee5a39675437300cabaf90283da6cf21cdf8f7 --- /dev/null +++ b/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/e6b0e920-39b7-4259-9938-916b268677a8_model.json @@ -0,0 +1,2697 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.188, + 0.131, + 0.784, + 0.177 + ], + "angle": 0, + "content": "Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.148, + 0.203, + 0.823, + 0.284 + ], + "angle": 0, + "content": "Xiaoyu Liu\\(^{1,\\ast}\\) Wei Huang\\(^{1}\\) Zhiwei Xiong\\(^{1,2,\\dagger}\\) \nShenglong Zhou\\(^{1}\\) Yuei Zhang\\(^{1,2}\\) Xuejin Chen\\(^{1,2}\\) Zheng-Jun Zha\\(^{1}\\) Feng Wu\\(^{1,2}\\) \n\\(^{1}\\)University of Science and Technology of China \n\\(^{2}\\)Institute of Artificial Intelligence, Hefei Comprehensive National Science Center" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.317, + 0.314, + 0.334 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.349, + 0.474, + 0.726 + ], + "angle": 0, + "content": "Sparse instance-level supervision has recently been explored to address insufficient annotation in biomedical instance segmentation, which is easier to annotate crowded instances and better preserves instance completeness for 3D volumetric datasets compared to common semi-supervision. In this paper, we propose a sparsely supervised biomedical instance segmentation framework via cross-representation affinity consistency regularization. Specifically, we adopt two individual networks to enforce the perturbation consistency between an explicit affinity map and an implicit affinity map to capture both feature-level instance discrimination and pixel-level instance boundary structure. We then select the highly confident region of each affinity map as the pseudo label to supervise the other one for affinity consistency learning. To obtain the highly confident region, we propose a pseudo-label noise filtering scheme by integrating two entropy-based decision strategies. Extensive experiments on four biomedical datasets with sparse instance annotations show the state-of-the-art performance of our proposed framework. For the first time, we demonstrate the superiority of sparse instance-level supervision on 3D volumetric datasets, compared to common semi-supervision under the same annotation cost. Code is available at https://github.com/liuxy1103/CRAC." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.754, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Biomedical instance segmentation aims to assign each image pixel to an instance, which plays an essential role in biomedical instance morphology and distribution analysis [36, 32]. Recently, deep-learning-based methods [22, 26, 48, 20, 15, 30, 6] have achieved state-of-the-art perfor" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.324, + 0.63, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.318, + 0.758, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.317, + 0.889, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.439, + 0.895, + 0.522 + ], + "angle": 0, + "content": "Figure 1. Comparison of instance annotation schemes in different supervision ways for the volumetric dataset. (a) Full supervision, where the whole volume is annotated. (b) Semi-supervision, where a subset of the whole volume is densely annotated. (c) sparse instance-level supervision, where a subset of instances of the whole volume is annotated." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.549, + 0.893, + 0.609 + ], + "angle": 0, + "content": "mance on biomedical instance segmentation with densely annotated images for fully-supervised training. However, it is expensive and laborious to obtain accurate and dense annotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.895, + 0.809 + ], + "angle": 0, + "content": "To alleviate the huge cost of manual annotations, many works [42, 13, 49, 37, 7] adopt the semi-supervised learning strategy to train an effective segmentation model with a small set of densely annotated images and a large set of unannotated images. However, in the field of biomedical instance segmentation, dense annotation is difficult to apply due to the crowded instances. Especially, for the 3D volumetric datasets (e.g., electron microscopy datasets), dense annotation within a small sub-volume usually damages the completeness of the instances along the axial direction. Meanwhile, in practice, domain experts tend to annotate instances one by one sparsely, rather than annotating all instances densely within a small sub-volume." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In this paper, we aim to deal with the task of biomedical instance segmentation with sparse instance annotations. This task is of utmost importance, as annotating a small subset of instances in a biomedical dataset not only saves the annotation cost but also conforms to annotation habits in the practical scenario. We illustrate different annotation" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.468, + 0.901 + ], + "angle": 0, + "content": "*This work was done during Xiaoyu Liu's internship at Institute of Artificial Intelligence, Hefei Comprehensive National Science Center. \n†Corresponding author: zwxiong@ustc.edu.cn." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21107" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "schemes in Fig. 1 and focus on the comparison between common semi-supervision and sparse instance-level supervision. For a volumetric dataset, a few consecutive images are densely annotated for the semi-supervision in Fig. 1 (b), which generates many incomplete instances along the axial direction. Instead, a few instances are randomly annotated for the sparse instance-level supervision in Fig. 1 (c), which preserves complete 3D structure information of each instance under the same number of annotated voxels as the semi-supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.473, + 0.488 + ], + "angle": 0, + "content": "Actually, sparse instance-level supervision can be considered a special kind of semi-supervision at the region level. Thus, existing semi-supervised methods [42, 13, 49, 37, 7] can be readily adapted to the sparse instance-level supervision. As a pioneer work, SPOCO [46] imposes a consistency regularization scheme [42] in the unannotated regions of two embedding maps predicted in different augmented views. However, SPOCO adopts a metric learning [9]-based segmentation method to distinguish different instances in the feature space, whose performance heavily drops as the number of annotated instances decreases. On the other hand, the perturbation consistency used in SPOCO is relatively simple and cannot effectively exploit instance structure information in unannotated regions. In other words, there remains a large room to release the potential of the sparse instance-level supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.473, + 0.838 + ], + "angle": 0, + "content": "Compared to metric learning, affinity-based instance segmentation methods [44, 43] are less sensitive to the number of annotated instances, since affinities encode instance boundary structure knowledge and are easier to be learned. Inspired by this kind of methods, we propose an effective biomedical instance segmentation framework with sparse instance annotations, which learns cross-representation affinity consistency. Specifically, our framework consists of two individual networks to predict two different representations, i.e., an embedding map and an implicit affinity map (IAM), respectively. We then calculate the similarity between pixel embeddings and convert the embedding map into an explicit affinity map (EAM). The IAM exploits the spatial structure information of instances, while the EAM exploits the semantic information of instances in the feature space. By building the perturbation consistency between the IAM and the EAM, we combine the advantages of two kinds of affinity modeling to capture both feature-level instance discrimination and pixel-level instance boundary structure. This perturbation consistency is different from the existing perturbation consistency between the same kinds of representations widely used in semi-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "In our framework, we use the groundtruth affinity map generated from sparse instance annotations to supervise the two affinity maps in the annotated regions. Inspired by the cross pseudo supervision [7], we further propose an affin" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "ity cross-supervision mechanism to facilitate affinity consistency learning on the unannotated regions. Specifically, we design a pseudo-label noise filtering scheme that integrates a heuristic decision strategy based on an adaptive threshold and a learning decision strategy based on a pretrained confident pixel selection network (CPSN), to select highly confident regions as pseudo labels from one affinity map to supervise the other." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.333 + ], + "angle": 0, + "content": "We evaluate our methods on four biomedical datasets with sparse instance annotations to demonstrate the state-of-the-art performance of our proposed framework, compared to three kinds of baselines: 1) the existing sparsely supervised method SPOCO, 2) advanced semi-supervised methods which are adapted to sparse instance-level supervision, and 3) original semi-supervised methods trained with dense annotation under the same annotation cost." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.335, + 0.825, + 0.35 + ], + "angle": 0, + "content": "The contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.362, + 0.892, + 0.408 + ], + "angle": 0, + "content": "- We propose a sparsely supervised biomedical instance segmentation framework by enforcing the perturbation consistency between two kinds of affinity modeling." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.42, + 0.892, + 0.481 + ], + "angle": 0, + "content": "- We propose an affinity cross-supervision mechanism with a pseudo-label noise filtering scheme integrating two decision strategies to select highly confident regions to facilitate affinity consistency learning." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.494, + 0.892, + 0.539 + ], + "angle": 0, + "content": "- We conduct extensive experiments on four biomedical datasets with sparse instance annotations to demonstrate the state-of-the-art performance of our method." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.552, + 0.892, + 0.596 + ], + "angle": 0, + "content": "- We demonstrate the general superiority of sparse instance-level supervision over semi-supervision on 3D volumetric datasets for the first time." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.362, + 0.892, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.642, + 0.64 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.802, + 0.667 + ], + "angle": 0, + "content": "2.1. Biomedical Instance Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.809 + ], + "angle": 0, + "content": "The prevalent instance segmentation methods are mainly divided into two categories: proposal-based [12, 26, 3, 47] and proposal-free [5, 38, 27, 29, 28, 33]. The former is based on object detection to distinguish different instances, while the latter is based on instance-aware features and morphology properties, which is more suitable to complex and dense instances of biomedical datasets. Metric learning [9, 22] and affinity learning [11, 31] are two proposal-free representatives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Metric learning [9, 22, 20] uses a discriminative loss [9] to impose pixels belonging to different instances to be discriminative from each other in the feature space. However, as the number of instances decreases in the sparse instance-level supervision setting, it is difficult for the network to distinguish different instances in the feature space." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21108" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.896, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.309, + 0.895, + 0.436 + ], + "angle": 0, + "content": "Figure 2. The workflow of our proposed sparsely supervised biomedical instance segmentation framework. (a) The input image is fed into two networks \\( f(\\theta_1) \\) and \\( f(\\theta_2) \\) to predict an affinity map and an embedding map, respectively. The embedding map is then explicitly converted into an affinity map. (b) These two affinity maps are supervised by the affinity label on the annotated region. The unannotated region of the affinity label is highlighted in gray color. The white and black colors indicate the affinity value as 1 and 0. (c) The highly confident region with low entropy of each affinity map is selected by a confident pixel selection network (CPSN) to supervise the other on the unannotated region. The red color indicates the region of the affinity map with high entropy, which is not used for cross-supervision. (d) This diagram illustrates the training stage of the CPSN, in which the model is trained on the annotated region to predict regions with segmentation errors. These regions are then excluded from being used as pseudo labels to supervise the other affinity map. \\( \\odot \\) and \\( \\oplus \\) represent dot product and concatenation operations, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.473, + 0.566 + ], + "angle": 0, + "content": "Affinity learning [2, 11, 31, 14] predicts pixel affinities that only encode spatial structure information between adjacent instances without ensuring the uniqueness of each instance in the feature space. Thus, the affinities are easy to be learned by the network and less affected by the number of instances. Even if there is only one annotated instance, this method can learn affinities between the unannotated region and the instance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.578, + 0.325, + 0.594 + ], + "angle": 0, + "content": "2.2. Consistency Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.47, + 0.83 + ], + "angle": 0, + "content": "Consistency regularization [1] plays a vital role in semisupervised learning. It enforces the consistency of predictions of unannotated data with various perturbations, by introducing a regularization loss function. The categories of perturbation are mainly divided into input perturbation [49, 25, 10], feature perturbation [37, 40], and network perturbation [7, 17]. Existing methods generally enforce the consistency between different perturbations of the same representation. Take an example of combining meanteacher [42] and the affinity-based segmentation method: both the teacher and student networks directly predict affinity maps that belong to the same representation. Different from existing consistency regularization methods, our proposed framework enforces consistency between two different representations from two kinds of affinity modeling." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.285, + 0.86 + ], + "angle": 0, + "content": "3. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Given an input image \\(I\\) with a size of \\(H\\times W\\), containing K instances (including background), \\(\\mathbf{M}\\) of which are" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.566 + ], + "angle": 0, + "content": "annotated \\((M\\ll K)\\). The image \\(I\\) is divided into two pixel sets, i.e., an annotated pixel region \\(R^L\\) and an unannotated pixel region \\(R^{U}\\). The unannotated region \\(R^{U}\\) contains unannotated instances and background. Different from semi-supervised learning, our goal is to train a model to predict the accurate affinity map by leveraging both a few annotated instances in the annotated region \\(R^{L}\\) and the unannotated region \\(R^{U}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.893, + 0.701 + ], + "angle": 0, + "content": "Before introducing our method, we clarify the definition of affinity. The affinity map \\( A = [a_{1}, a_{2}, \\ldots, a_{N}] \\in \\mathbb{R}^{N \\times H \\times W} \\) describes whether the current pixel and adjacent pixels belong to the same instances or not, where \\( a_{n}(n = 1, 2, \\ldots, N) \\) denotes the different adjacent relations between the current pixel and its \\( n \\) order adjacent pixel. Given the segmentation groundtruth \\( y \\in \\mathbb{R}^{H \\times W} \\), a pixel affinity \\( a_{n,i} \\in a_{n} \\) at the \\( i^{th} \\) pixel of the image \\( I \\) is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.701, + 0.892, + 0.742 + ], + "angle": 0, + "content": "\\[\na _ {n, i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} y _ {i} \\neq y _ {i + n} \\\\ 1, & \\text {i f} y _ {i} = y _ {i + n}, \\end{array} \\right. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.795 + ], + "angle": 0, + "content": "where \\( y_{i} \\) and \\( y_{i + n} \\) are the instance segmentation IDs of paired pixels \\( i \\) and \\( i + n \\). 1 means that pixel \\( i \\) and \\( i + n \\) belong to one instance, while 0 means the opposite." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Considering the segmentation groundtruth with sparse instance-level annotations, we regard the unannotated region (including the background) as an identical instance ID. The generated affinity label is divided into annotated region \\( R_{a}^{L} \\) and unannotated region \\( R_{a}^{U} \\). If the pixel affinity \\( a_{n,i} \\) is located in the annotated region \\( R_{a}^{L} \\), at least one of the pixels \\( i \\) and \\( i + n \\) is located in the annotation region \\( R^{L} \\), i.e.," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21109" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.136 + ], + "angle": 0, + "content": "\\(y_{i} \\in R^{L}\\) or \\(y_{i + n} \\in R^{L}\\). Therefore, the annotated affinity region \\(R_{a}^{L}\\) is slightly larger than the annotated segmentation region \\(R^{L}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.155, + 0.458, + 0.172 + ], + "angle": 0, + "content": "4. Cross-Representation Affinity Consistency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.182, + 0.471, + 0.364 + ], + "angle": 0, + "content": "In this section, we introduce the proposed sparsely supervised biomedical instance segmentation framework. The input of our framework can be either 2D images or 3D volumes. Here we illustrate it using a 2D image example for easy visualization. As shown in Fig. 2, our framework consists of two main parts. The first part contains two parallel networks to build affinity perturbation by predicting different representations: IAM and EAM (detailed in 4.1). The second part contains an affinity cross-supervision mechanism by a pseudo-label noise filtering scheme to select the highly confident region of the two affinity maps to supervise each other for consistency learning (detailed in 4.2)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.377, + 0.277, + 0.393 + ], + "angle": 0, + "content": "4.1. Affinity Perturbation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.469, + 0.52 + ], + "angle": 0, + "content": "Unlike the common perturbation consistency strategy, we build the perturbation between two affinity representations predicted by two parallel networks. Following the existing affinity learning methods [11, 31], we adopt a network \\( f(\\theta_1) \\) to directly predict an implicit affinity map \\( \\hat{A}^1 = [\\hat{a}_1^1, \\hat{a}_2^1, \\dots, \\hat{a}_N^1] \\). For accurate pixel affinities, the network \\( f(\\theta_1) \\) focuses on the structure information of instance boundaries." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.752 + ], + "angle": 0, + "content": "In contrast to implicit learning, explicitly modeled affinity has been widely studied [22, 14] by calculating the pairwise relationships between pixel embeddings. Given the limited number of instances, we only impose local constraints on the adjacent instances instead of constraining all instances by a discriminative loss [9]. We adopt a network \\( f(\\theta_2) \\) to predict an embedding map \\( E \\in \\mathbb{R}^{D \\times H \\times W} \\), where \\( D \\) is the number of channels of the last layer of the network. Each pixel \\( i \\) of the image \\( I \\) is mapped into a pixel embedding vector \\( e_i \\in \\mathbb{R}^D \\), which is a D-dimensional feature representation. We then adopt a cosine distance to calculate the relationship between pixel embeddings and converted the embedding map into an explicit affinity map \\( \\hat{A}^2 = [\\hat{a}_1^2, \\hat{a}_2^2, \\dots, \\hat{a}_N^2] \\). The transformation from a paired of pixel embeddings to a pixel affinity \\( \\hat{a}_{n,i}^2 \\) is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.766, + 0.469, + 0.802 + ], + "angle": 0, + "content": "\\[\n\\hat {a} _ {n, i} ^ {2} = \\frac {e _ {i} ^ {T} e _ {i + n}}{\\| e _ {i} \\| _ {2} \\| e _ {i + n} \\| _ {2}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.815, + 0.469, + 0.86 + ], + "angle": 0, + "content": "The network \\( f(\\theta_2) \\) pays more attention to extracting the semantic instance information to discriminate pixels belonging to different instances in the feature space." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "We adopt the MSE loss to supervise both \\( f(\\theta_1) \\) and \\( f(\\theta_2) \\) in the annotated region \\( R_a^L \\) of the affinity label \\( A \\):" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.135, + 0.909, + 0.197 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {s} = L _ {s 1} + L _ {s 2} \\\\ = \\frac {1}{\\left| R _ {a} ^ {L} \\right|} \\sum_ {i \\in R _ {a} ^ {L}} \\sum_ {n = 1} ^ {N} \\left(\\left\\| \\hat {a} _ {n, i} ^ {1} - a _ {n, i} \\right\\| _ {2} + \\left\\| \\hat {a} _ {n, i} ^ {2} - a _ {n, i} \\right\\| _ {2}\\right), \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.198, + 0.891, + 0.228 + ], + "angle": 0, + "content": "where \\(L_{s1}\\) and \\(L_{s2}\\) represent the loss functions for \\(f(\\theta_1)\\) and \\(f(\\theta_2)\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.238, + 0.74, + 0.254 + ], + "angle": 0, + "content": "4.2. Affinity Cross-Supervision" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.413 + ], + "angle": 0, + "content": "In order to combine the advantages of the two kinds of affinity modeling, we propose an affinity cross-supervision mechanism to enforce the consistency between the IAM and the EAM. Since the two affinity maps may suffer from prediction errors during the initial training phase, we propose a pseudo-label noise filtering scheme by integrating two entropy-based decision strategies, i.e., adaptive threshold and prediction by a CPSN, to select highly confident pixel affinities to avoid the collapse of the consistency learning. For a pixel affinity \\(a_{n,i}\\), its entropy is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.425, + 0.892, + 0.442 + ], + "angle": 0, + "content": "\\[\nh _ {n, i} = - a _ {n, i} \\log \\left(a _ {n, i}\\right) - (1 - a _ {n, i}) \\log \\left(1 - a _ {n, i}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.454, + 0.892, + 0.496 + ], + "angle": 0, + "content": "Adaptive threshold. As a heuristic strategy, we can determine whether the pixel affinity is confident by the following indicator:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.497, + 0.891, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\delta_ {n, i} ^ {\\text {t h r e s}} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} h _ {n, i} < \\gamma_ {t} \\\\ 0, & \\text {o t h e r s ,} \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.544, + 0.891, + 0.619 + ], + "angle": 0, + "content": "where \\(\\gamma_{t}\\) refers to the entropy threshold at the \\(t^{th}\\) training iteration, which is the quantile of \\(h_{n,i}\\) corresponding to \\(\\alpha_{t}\\) to limit unreliable pixels with top \\(\\alpha_{t}\\) entropy. 1 means the pixel affinity is confident with low entropy, while 0 means the opposite." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.663 + ], + "angle": 0, + "content": "Since the confident pixels gradually increase during the training procedure, \\(\\alpha_{t}\\) is dynamically adjusted by a power function:" + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.665, + 0.891, + 0.682 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {t} = \\alpha_ {0} (1 - t / T) ^ {p}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.891, + 0.734 + ], + "angle": 0, + "content": "where \\(\\alpha_0\\) is the initial quantile and is set to \\(5\\%\\), \\(p\\) is the power and is set as 1.5, \\(t\\) is the current training iteration, and \\(T\\) is total iterations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Confidence pixel selection network. Inspired by approaches that address pseudo label errors using auxiliary networks [35, 21], we employ a binary-classification network called CPSN to identify highly confident pixels, which is trained only using the annotated regions of the groundtruth error map, as shown in Fig. 2 (d). Specifically, we sample five segmentation models under different training iterations of \\( f(\\theta_{1}) \\) and \\( f(\\theta_{2}) \\) respectively, and add a certain rate of dropout to these models. We then use the prediction from these models to simulate various segmentation errors. Using this kind of simulation data, we train" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.901 + ], + "angle": 0, + "content": "1We call it implicit affinity map to distinguish from the one explicitly calculated from the embedding map below." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21110" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "a robust CPSN to locate errors and generate highly confident pixels. We provide training details (including the loss \\( L_{CPSN} \\)) in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.137, + 0.47, + 0.182 + ], + "angle": 0, + "content": "Given the input image \\(I\\), affinity map \\(A\\) and affinity entropy map \\(H\\), the CPSN can predict a binary error map \\(B \\in \\mathbb{R}^{N \\times H \\times W}\\) with the same size as \\(A\\):" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.19, + 0.469, + 0.207 + ], + "angle": 0, + "content": "\\[\nB = \\operatorname {C P S N} (I \\oplus A \\oplus H), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.215, + 0.342, + 0.229 + ], + "angle": 0, + "content": "where \\(\\oplus\\) is the concatenation operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.469, + 0.259 + ], + "angle": 0, + "content": "We then determine whether the pixel affinity is confident by the following indicator:" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.266, + 0.469, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\delta_ {n, i} ^ {c p s n} = 1 - b _ {n, i}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.292, + 0.432, + 0.307 + ], + "angle": 0, + "content": "where \\( b_{n,i} \\in B \\) is the pixel-level prediction of CPSN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.469, + 0.418 + ], + "angle": 0, + "content": "Pseudo-label noise filtering. We integrate the above two decision strategies to obtain more robust highly confident pixels, which is described by \\(\\delta_{n,i} = \\delta_{n,i}^{thres}\\delta_{n,i}^{cpsn}\\). After obtaining the confident pixels of the IAM (indicated by \\(\\delta_{n,i}^{1}\\)) and the EAM (indicated by \\(\\delta_{n,i}^{2}\\)), we utilize their confident pixels on the unannotated affinity region \\(R_{a}^{U}\\) to cross-supervise each other. The consistency loss is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.426, + 0.469, + 0.497 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {c} = L _ {c 1} + L _ {c 2} \\\\ = \\frac {1}{\\left| R _ {a} ^ {U} \\right|} \\sum_ {i \\in R _ {a} ^ {U}} \\sum_ {n = 1} ^ {N} \\left(\\left\\| \\hat {a} _ {n, i} ^ {1} - \\hat {a} _ {n, i} ^ {2} \\right\\| _ {2} \\delta_ {n, i} ^ {2} \\right. \\tag {9} \\\\ + \\left\\| \\hat {a} _ {n, i} ^ {2} - \\hat {a} _ {n, i} ^ {1} \\right\\| _ {2} \\delta_ {n, i} ^ {1}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.503, + 0.469, + 0.534 + ], + "angle": 0, + "content": "where \\(L_{c1}\\) and \\(L_{c2}\\) represent the consistency loss functions for \\(f(\\theta_1)\\) and \\(f(\\theta_2)\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.541, + 0.279, + 0.557 + ], + "angle": 0, + "content": "4.3. Overall Optimization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.565, + 0.47, + 0.608 + ], + "angle": 0, + "content": "The overall objection function is the combination of losses on the annotated region and the unannotated region, which terms" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.61, + 0.469, + 0.626 + ], + "angle": 0, + "content": "\\[\nL = L _ {s} + \\lambda L _ {c}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.469, + 0.659 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the trade-off weight and is set to make the two loss value ranges comparable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.812 + ], + "angle": 0, + "content": "Following [14], we adopt the network \\( f(\\theta_2) \\) to predict an explicit affinity map in the inference stage. The affinity map is converted into final instance segmentation results by different post-processing algorithms. The 3D results and 2D results are generated by Waterz [11] (50% quantile and 0.5 threshold) and Mutex [45] post-processing algorithms, respectively. Since affinities calculated by these two different normalization schemes (sigmoid vs cosine) belong to different intervals, we use a RELU function to map the output value into [0, 1], for Waterz post-processing algorithm." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.822, + 0.21, + 0.839 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.276, + 0.862 + ], + "angle": 0, + "content": "5.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We conduct evaluations on four representative biomedical datasets with corresponding commonly used metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.318 + ], + "angle": 0, + "content": "AC3. The AC3 dataset is a popular electron microscopy (EM) neuron dataset, imaged from the mouse somatosensory cortex at \\(3 \\times 3 \\times 29\\) nm resolution. It is a subset of the Kasthuri [16] dataset, and contains 256 volumetric images (\\(1024 \\times 1024\\)). We adopt the top 100 sections as the labeled set and sparsely select different numbers of neuron instances as the annotations. At the same time, the bottom 50 sections are adopted for evaluation. We adopt two widely used metrics in the field of EM image segmentation to quantitatively evaluate the result, i.e., Variation of Information (VOI) [34] and Adapted Rand Error (ARAND) [39]. The VOI is defined as a sum of another two metrics \\(VOI_{split}\\) and \\(VOI_{merge}\\) which indicate the split and merge errors, respectively. Note that smaller values of these metrics indicate better performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.892, + 0.499 + ], + "angle": 0, + "content": "CREMI-C. The CREMI dataset is from the CREMI challenge [8] for neuron segmentation in EM volumes. It is composed of three volumetric datasets (CREMI-A, CREMI-B, and CREMI-C) imaged from the adult drosophila brain at \\(4 \\times 4 \\times 40\\) nm resolution. Each of the three datasets contains 125 images. Given that the neurites in CREMI-A and CREMI-C are mostly homogeneous in morphology, we evaluate our method on the CREMI-C dataset, which contains more challenging neuron types. We adopt the top 75 sections as the labeled set and the bottom 50 sections for evaluation. We adopt the same metrics used for the AC3 to evaluate the results on the CREMI-C dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.892, + 0.622 + ], + "angle": 0, + "content": "CVPPP. The A1 sequence of the CVPPP [36] dataset contains leaves with complex shapes and severe occlusions, which is widely used to evaluate biomedical instance segmentation. We randomly sample 108 images for training and 20 images for testing, where each image is with a size of \\(530 \\times 500\\). We adopt the Symmetric Best Dice (SBD) and the absolute Difference in Counting \\((|DiC|)\\) metrics [36] to evaluate the quantitative result." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.759 + ], + "angle": 0, + "content": "BBBC039V1. The BBBC039V1 dataset [32] contains 200 fluorescence microscopy images with a resolution of \\(696 \\times 520\\) pixels. The dataset focuses on the U2OS cells with various shape and density. Following the official data split, we use 100 images for training, 50 for validation, and the rest 50 for testing. We adopt four metrics for cell segmentation for quantitative evaluation, i.e., Aggregated Jaccard Index (AJI) [39], object-level F1 score (F1) [4], Panoptic Quality (PQ) [19], and pixel-level Dice score (Dice)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.716, + 0.787 + ], + "angle": 0, + "content": "5.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We adopt two different backbone networks, i.e., 3D U-Net [23] and 2D Residual U-Net for the 3D volumetric datasets (AC3, CREMI-C) and 2D datasets (CVPPP, BBBC039V1), respectively. Both the network \\( f(\\theta_{1}) \\) and \\( f(\\theta_{2}) \\) are based on the same backbone network but different in the last convolution layer. We train these networks using Adam optimizer [18] with \\( \\beta_{1} = 0.9 \\) and \\( \\beta_{2} = 0.999 \\), a" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21111" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.098, + 0.09, + 0.875, + 0.317 + ], + "angle": 0, + "content": "
MethodsAC3CREMI-C
VOISplit ↓VOIMerge ↓VOI ↓ARAND ↓VOISplit ↓VOIMerge ↓VOI ↓ARAND ↓
Semi.Vanilla0.4225.4035.8250.9110.9292.1173.0460.580
PseudoL-hard [41]0.0895.9556.0440.9200.8631.4622.3250.311
PseudoL-soft [50]0.8513.7444.5950.8530.9500.8941.8440.230
MT [42]0.8632.0582.9210.5580.9161.0271.9430.211
π-model [25]0.8471.8672.7140.5620.9850.9181.9030.227
UA-MT [49]0.7201.8602.5800.4260.9780.8631.8410.227
SASSNet [24]1.1601.1802.3400.3240.9350.8141.7490.193
SSNS [13]0.7020.5271.2290.1200.9340.7751.7090.175
Sparse.SPOCO [46]1.6081.3492.9570.2361.8320.8962.7280.303
Vanilla0.9300.2371.1670.1111.6130.4512.0640.187
MT* [42]0.6990.4321.1320.0921.3750.5591.9340.173
UA-MT* [49]0.7850.2511.0360.0821.5020.3331.8350.155
CCT* [37]0.8590.2381.0970.0881.4250.4631.8880.173
CPS* [7]0.7180.2480.9660.0671.3840.3981.7820.158
Ours0.6420.2600.9030.0641.0320.5871.6200.153
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.327, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of segmentation results on AC3 and CREMI-C datasets using 5 densely annotated sections for semi-supervision and randomly annotated instances for sparse instance-level supervision. The number of annotated voxels is the same for the two settings. Vanilla refers to training models only using available groundtruth. The top right corner \\* indicates these methods are originally proposed in the semi-supervision but adapted into the sparse instance-level supervision. Note that we adopt the same backbone ResUnet [23] in all methods for a fair comparison. The best results and the second-best results are highlighted in bold and underlined." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.407, + 0.892, + 0.681 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.693, + 0.89, + 0.723 + ], + "angle": 0, + "content": "Figure 3. 2D Visual comparison of different methods on AC3 and CREMI-C datasets. The first row and the second row of each dataset are the affinity map and the corresponding instance segmentation result. Red and blue boxes indicate merge and split errors, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.468, + 0.775 + ], + "angle": 0, + "content": "learning rate of \\(1e - 4\\) , and a batch size of 2 on one NVIDIA TitanXP GPU for 200K iterations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.28, + 0.803 + ], + "angle": 0, + "content": "5.3. Comparison Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.468, + 0.839 + ], + "angle": 0, + "content": "The evaluation of our method is performed against three kinds of baselines:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.468, + 0.901 + ], + "angle": 0, + "content": "(1) For the 3D volumetric datasets, the sparse instance-level supervision and the common semi-supervision contain different 3D structure information of instances in the axial direction. For a comprehensive evaluation, we compare" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.746, + 0.892, + 0.822 + ], + "angle": 0, + "content": "our proposed sparsely supervised method with a number of existing semi-supervised methods that are widely used for 3D datasets, including: PseudoL-hard [41], PseudoL-soft [50], mean-teacher (MT) [42], \\(\\pi\\)-model [25], UAMT [49], SASSNet [24] and SSNS [13]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.9 + ], + "angle": 0, + "content": "(2) SPOCO [46] provides a baseline solution for the sparsely supervised segmentation task. We use the official code and configurations to reproduce the results on 2D datasets (CVPPP and BBBC039V1), and adapt this method to 3D datasets (AC3 and CREMI-C)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21112" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.336, + 0.893, + 0.366 + ], + "angle": 0, + "content": "Figure 4. 3D Visual comparison of different methods on AC3 and CREMI-C datasets. Red and blue arrows indicate split and merge errors, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.47, + 0.466 + ], + "angle": 0, + "content": "(3) We adapt a variety of advanced semi-supervised methods to the sparsely supervised segmentation task, including mean-teacher (MT) [42], uncertainty-aware mean teacher model(UA-MT) [49], cross-consistency training (CCT) [37] and cross pseudo supervision (CPS) [7]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.479, + 0.29, + 0.493 + ], + "angle": 0, + "content": "5.4. Results on 3D Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.469, + 0.623 + ], + "angle": 0, + "content": "We list an extensive quantitative comparison on the AC3 and the CREMI-C datasets in Table 1. We conduct the semi-supervised experiments with 5 densely annotated sections, and the sparsely supervised experiments with 23 and 33 randomly annotated instances for AC3 and CREMI-C datasets respectively. The number of annotated voxels is the same for the two settings. From the results in Table 1, we can observe that:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.469, + 0.715 + ], + "angle": 0, + "content": "(1) With the same number of annotated voxels, sparsely supervised methods perform better than corresponding semi-supervised methods by a large margin. Specifically, our results outperform the state-of-the-art semi-supervised results from SSNS [13] by \\(26.4\\%\\) and \\(5.2\\%\\) for the VOI metric on the AC3 and CREMI-C datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.777 + ], + "angle": 0, + "content": "(2) For the EM neuron segmentation datasets, the sparse instance annotations are not conducive to the training of SPOCO [46] based on metric learning. Therefore, SPOCO [46] does not perform well on these two datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.884 + ], + "angle": 0, + "content": "(3) Our method achieves better performance than other adapted methods in the sparse instance-level supervision setting. Specifically, We achieve \\(6.3\\%\\) and \\(9.2\\%\\) improvement from the key VOI metric on the AC3 and CREMI-C datasets, compared with the second-best method. It demonstrates the superiority of the proposed affinity consistency regularization." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.626, + 0.469, + 0.884 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We show 2D and 3D visual comparison results in Fig. 3" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.387, + 0.885, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.567, + 0.892, + 0.609 + ], + "angle": 0, + "content": "Figure 5. Comparison of different methods on the AC3 dataset under different annotation amounts converted into the number of sections for counting, where each section contains \\(1 \\times 10^{6}\\) pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.892, + 0.746 + ], + "angle": 0, + "content": "and Fig. 4, respectively. As can be seen, our proposed method predicts the affinity map with higher fidelity than other methods, which significantly reduces the split and merge errors. We also provide 3D visual comparison results in the supplementary material. As can be seen, our results contain fewer merge and split errors, and maintain the accuracy of neuron structures, compared with other methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "We further compare different methods on the AC3 dataset under different numbers of annotated voxels. We convert the number of voxels to the number of sections for counting, where each section contains about \\(1 \\times 10^{6}\\) voxels. The results are shown in Fig. 5. As more annotations are available, the performance gap between different methods gradually narrows, but the superiority of our method can still be observed. Especially, the state-of-the-art semi-supervised method SSNS performs worse than sparsely supervised methods under very limited annotations, due to the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21113" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.089, + 0.089, + 0.46, + 0.238 + ], + "angle": 0, + "content": "
Methods10% instances40% instances
SBD ↑|DiC| ↓SBD ↑|DiC| ↓
CPS [7] (semi)83.21.887.61.1
SPOCO [46]70.63.082.12.0
Vanilla69.86.078.01.9
MT* [42]78.51.484.31.3
UA-MT* [49]79.61.484.51.1
CCT* [37]78.81.983.91.6
CPS* [7]80.71.885.51.1
Ours83.61.186.60.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.248, + 0.468, + 0.276 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison results on the CVPPP dataset. Results in the first row are based on the semi-supervision setting." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.288, + 0.175, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.352, + 0.162, + 0.363 + ], + "angle": 0, + "content": "Raw Image" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.288, + 0.272, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.215, + 0.352, + 0.245, + 0.362 + ], + "angle": 0, + "content": "MT*" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.288, + 0.369, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.302, + 0.352, + 0.35, + 0.362 + ], + "angle": 0, + "content": "UAMT*" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.289, + 0.466, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.405, + 0.352, + 0.441, + 0.361 + ], + "angle": 0, + "content": "CCT*" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.367, + 0.175, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.43, + 0.151, + 0.44 + ], + "angle": 0, + "content": "SPOCO" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.367, + 0.272, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.214, + 0.43, + 0.246, + 0.44 + ], + "angle": 0, + "content": "CPS*" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.367, + 0.369, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.31, + 0.43, + 0.34, + 0.44 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.367, + 0.466, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.384, + 0.43, + 0.455, + 0.44 + ], + "angle": 0, + "content": "Groundtruth" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.455, + 0.469, + 0.496 + ], + "angle": 0, + "content": "Figure 6. Visual comparison of different methods on the CVPPP dataset with \\(40\\%\\) instances. The segmentation errors are highlighted by white boxes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.521, + 0.406, + 0.536 + ], + "angle": 0, + "content": "incomplete 3D structure information of instances." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.545, + 0.289, + 0.56 + ], + "angle": 0, + "content": "5.5. Results on 2D Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.719 + ], + "angle": 0, + "content": "We further validate our method on two 2D datasets, i.e., CVPPP and BBBC039V1, and their quantitative results are shown in Table 2 and Table 3, respectively. Compared with other adapted methods in the sparse instance-level supervision setting, our method achieves the best performance on the CVPPP dataset with \\(10\\%\\) and \\(40\\%\\) annotated instances, and the BBBC039V1 dataset with \\(1\\%\\) and \\(10\\%\\) annotated instances. Visual results on these two datasets also illustrate the superior performance of our method with fewer segmentation errors, as shown in Fig. 6 and Fig. 7." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Although the sparse instance-level supervision and the common semi-supervision have no difference in the instance structure for 2D datasets, we also evaluate the semi-supervised setting (with the same annotated pixels) on these two datasets. Our proposed method performs better than the state-of-the-art semi-supervised method CPS [7], when the annotation amount is very limited. Meanwhile, our method significantly outperforms the existing sparely supervised method SPOCO in all experiments. As more annotation amount is available, the semi-supervised method has a better performance. Therefore, the sparse instance-level supervision is still a meaningful complement to the com" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.333 + ], + "angle": 0, + "content": "
MethodsAJI ↑Dice ↑F1 ↑PQ ↑
1% instancesCPS [7] (semi)0.81200.90330.95950.8168
SPOCO [46]0.68960.84780.84920.6933
Vanilla0.56310.64110.75700.4890
MT* [42]0.77160.82600.90180.7533
UA-MT* [49]0.80650.87380.94390.7928
CCT* [37]0.81130.91360.92950.7830
CPS* [7]0.83230.91850.94440.8153
Ours0.83030.93380.94420.8222
10% instancesCPS [7] (semi)0.83930.91890.95980.8437
SPOCO [46]0.74880.87460.92630.7503
Vanilla0.59850.71770.77090.5652
MT* [42]0.84160.91670.93380.8283
UA-MT* [49]0.84040.91180.93800.8314
CCT* [37]0.83090.92790.93270.7975
CPS* [7]0.84630.93660.94080.8174
Ours0.85450.94690.94500.8343
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.343, + 0.871, + 0.356 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison on the BBBC039V1 dataset." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.36, + 0.6, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.415, + 0.582, + 0.424 + ], + "angle": 0, + "content": "Raw Image" + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.36, + 0.696, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.415, + 0.665, + 0.423 + ], + "angle": 0, + "content": "MT*" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.36, + 0.792, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.415, + 0.769, + 0.423 + ], + "angle": 0, + "content": "UAMT" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.36, + 0.888, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.415, + 0.859, + 0.423 + ], + "angle": 0, + "content": "CCT*" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.426, + 0.6, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.481, + 0.572, + 0.49 + ], + "angle": 0, + "content": "SPOCO" + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.426, + 0.696, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.637, + 0.481, + 0.664, + 0.49 + ], + "angle": 0, + "content": "CPS*" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.426, + 0.792, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.733, + 0.481, + 0.758, + 0.49 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.426, + 0.888, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.815, + 0.481, + 0.877, + 0.49 + ], + "angle": 0, + "content": "Groundtruth" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.504, + 0.892, + 0.532 + ], + "angle": 0, + "content": "Figure 7. Visual comparison of different methods on the BBBC039V1 dataset with \\(10\\%\\) instances." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.556, + 0.892, + 0.601 + ], + "angle": 0, + "content": "mon semi-supervision when instances are so crowded that dense annotation is laborious and the amount of annotations is very limited, for the 2D datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.612, + 0.665, + 0.627 + ], + "angle": 0, + "content": "5.6. Ablation Studies" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.647, + 0.892, + 0.699 + ], + "angle": 0, + "content": "
Method15102050100
Vanilla2.2891.1670.9820.8710.7790.726
Ours1.2710.9030.8160.8070.7380.717
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.708, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Table 4. Ablation study on the annotation amount which is converted into the number of sections for counting, where each section contains about \\(1 \\times 10^{6}\\) voxels. The key metric VOI is used to evaluate the results." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.78, + 0.89, + 0.81 + ], + "angle": 0, + "content": "We conduct ablation studies on the impacts of each component of the proposed framework on the AC3 dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Annotation amounts. We conduct an ablation study to investigate the effects of different amounts of annotated instances. As shown in Table 4, our proposed method consistently outperforms the vanilla model trained only using available annotated instances. When the annotation amount is small (e.g., the number of annotated voxels is about a sec" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21114" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.089, + 0.458, + 0.226 + ], + "angle": 0, + "content": "
f(θ1)f(θ2)cross-supervisionVOI ↓ARAND ↓
ThresholdCPSN
IAMIAM✓✓0.9260.074
EAMEAM✓✓0.9270.068
IAMEAMXX0.9160.068
IAMEAM✓X0.9060.068
IAMEAMX✓0.9090.067
IAMEAM✓✓0.9030.065
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.234, + 0.47, + 0.304 + ], + "angle": 0, + "content": "Table 5. Ablation study on different components of the proposed affinity consistency regularization. IAM and EAM represent the different kinds of affinity modeling for the two networks \\( f(\\theta_{1}) \\) and \\( f(\\theta_{2}) \\). 'Threshold' and 'CPSN' denote the two different strategies to select highly confident regions in cross-supervision." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.317, + 0.454, + 0.369 + ], + "angle": 0, + "content": "
MethodVOISplit ↓VOIMerge ↓VOI ↓ARAND ↓
Ours-f(θ1)0.7090.1980.9070.071
Ours-f(θ2)0.6870.2180.9030.065
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.378, + 0.465, + 0.393 + ], + "angle": 0, + "content": "Table 6. Ablation study on which affinity map used for inference." + }, + { + "type": "table", + "bbox": [ + 0.096, + 0.402, + 0.452, + 0.519 + ], + "angle": 0, + "content": "
α00.010.050.1
VOI↓/ ARAND ↓0.933 / 0.0750.903 / 0.0650.924 / 0.069
Dropout rate00.10.3
VOI↓/ ARAND ↓0.920 / 0.0660.903 / 0.0650.923 / 0.067
λ0.010.11
VOI↓/ ARAND ↓0.914 / 0.0660.903 / 0.0651.258 / 0.106
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.528, + 0.468, + 0.556 + ], + "angle": 0, + "content": "Table 7. Ablation study on key parameters of the proposed framework. VOI/ARAND are adopted as metrics." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.583, + 0.47, + 0.627 + ], + "angle": 0, + "content": "tion), our method significantly improves the performance of the vanilla model. The performance gap narrows as more annotations are available." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.468, + 0.852 + ], + "angle": 0, + "content": "Affinity consistency regularization. As shown in Table 5, we conduct an ablation study on the proposed affinity consistency learning scheme. We compare different combinations of affinity modeling for the two networks \\( f(\\theta_{1}) \\) and \\( f(\\theta_{2}) \\) by directly enforcing their consistency. It can be observed that the combination of IAM and EAM achieves the best performance. Furthermore, we demonstrate the effectiveness of pseudo-label noise filtering with different decision strategies. Both strategies have been shown to improve performance, and their integration can obtain more robust highly confident regions and achieves the best performance. Moreover, We have compared our method with an equivalent implementation of [14] in Table 5, i.e., two network branches both use EAM. Our method achieves better performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Affinity map used in the inference stage. The two affinity maps predicted by \\( f(\\theta_{1}) \\) and \\( f(\\theta_{2}) \\) have different performances, as shown in Table 6. The EAM predicted by" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.89, + 0.121 + ], + "angle": 0, + "content": "\\(f(\\theta_2)\\) performs slightly better, so we adopt it in the inference stage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.892, + 0.243 + ], + "angle": 0, + "content": "Ablation study on hyper-parameters. We conducted ablation experiments to evaluate the impact of key hyperparameters, of the proposed framework, as shown in Table 7. For the proposed pseudo-label noise filtering scheme, we test different values of hyper-parameters \\(\\alpha_0\\) for adaptive threshold and different dropout rates used in the CPSN training. Also, we provide the ablation study on different loss weights \\(\\lambda\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.259, + 0.618, + 0.273 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.892, + 0.48 + ], + "angle": 0, + "content": "In this paper, we propose an effective sparsely supervised biomedical instance segmentation framework via learning cross-representation affinity consistency. The proposed framework builds the perturbation consistency between an implicit affinity map and an explicit affinity map with an affinity cross-supervision mechanism. We conduct extensive experiments on 3D volumetric datasets and 2D datasets to demonstrate the superiority of our proposed framework over the existing sparsely supervised method. Meanwhile, for the first time, we validate that sparsely supervised methods can better utilize the 3D structure information of instances and perform better than semi-supervised methods for volumetric datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.493, + 0.66, + 0.509 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.515, + 0.89, + 0.544 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China under Grant 62021001." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.56, + 0.596, + 0.575 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.507, + 0.584, + 0.891, + 0.613 + ], + "angle": 0, + "content": "[1] Philip Bachman, Ouais Alsharif, and Doina Precup. 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In this paper, we propose a sparsely supervised biomedical instance segmentation framework via cross-representation affinity consistency regularization. Specifically, we adopt two individual networks to enforce the perturbation consistency between an explicit affinity map and an implicit affinity map to capture both feature-level instance discrimination and pixel-level instance boundary structure. We then select the highly confident region of each affinity map as the pseudo label to supervise the other one for affinity consistency learning. To obtain the highly confident region, we propose a pseudo-label noise filtering scheme by integrating two entropy-based decision strategies. Extensive experiments on four biomedical datasets with sparse instance annotations show the state-of-the-art performance of our proposed framework. For the first time, we demonstrate the superiority of sparse instance-level supervision on 3D volumetric datasets, compared to common semi-supervision under the same annotation cost. Code is available at https://github.com/liuxy1103/CRAC. + +# 1. Introduction + +Biomedical instance segmentation aims to assign each image pixel to an instance, which plays an essential role in biomedical instance morphology and distribution analysis [36, 32]. Recently, deep-learning-based methods [22, 26, 48, 20, 15, 30, 6] have achieved state-of-the-art perfor + +![](images/882dd8515faae5d7a3b99bd769557fef71340ee49b4c5e94514c7d87948650c1.jpg) + +![](images/bc5e4692f357cbd5d7cb5762243b95ac7efb4d3571face524e6efb30cbbae756.jpg) +Figure 1. Comparison of instance annotation schemes in different supervision ways for the volumetric dataset. (a) Full supervision, where the whole volume is annotated. (b) Semi-supervision, where a subset of the whole volume is densely annotated. (c) sparse instance-level supervision, where a subset of instances of the whole volume is annotated. + +![](images/a7963f0e64cd1a3c2b2f114ae386e07ced5b9e92e3c7d344d9bbe3ab0f0e1635.jpg) + +mance on biomedical instance segmentation with densely annotated images for fully-supervised training. However, it is expensive and laborious to obtain accurate and dense annotations. + +To alleviate the huge cost of manual annotations, many works [42, 13, 49, 37, 7] adopt the semi-supervised learning strategy to train an effective segmentation model with a small set of densely annotated images and a large set of unannotated images. However, in the field of biomedical instance segmentation, dense annotation is difficult to apply due to the crowded instances. Especially, for the 3D volumetric datasets (e.g., electron microscopy datasets), dense annotation within a small sub-volume usually damages the completeness of the instances along the axial direction. Meanwhile, in practice, domain experts tend to annotate instances one by one sparsely, rather than annotating all instances densely within a small sub-volume. + +In this paper, we aim to deal with the task of biomedical instance segmentation with sparse instance annotations. This task is of utmost importance, as annotating a small subset of instances in a biomedical dataset not only saves the annotation cost but also conforms to annotation habits in the practical scenario. We illustrate different annotation + +schemes in Fig. 1 and focus on the comparison between common semi-supervision and sparse instance-level supervision. For a volumetric dataset, a few consecutive images are densely annotated for the semi-supervision in Fig. 1 (b), which generates many incomplete instances along the axial direction. Instead, a few instances are randomly annotated for the sparse instance-level supervision in Fig. 1 (c), which preserves complete 3D structure information of each instance under the same number of annotated voxels as the semi-supervision. + +Actually, sparse instance-level supervision can be considered a special kind of semi-supervision at the region level. Thus, existing semi-supervised methods [42, 13, 49, 37, 7] can be readily adapted to the sparse instance-level supervision. As a pioneer work, SPOCO [46] imposes a consistency regularization scheme [42] in the unannotated regions of two embedding maps predicted in different augmented views. However, SPOCO adopts a metric learning [9]-based segmentation method to distinguish different instances in the feature space, whose performance heavily drops as the number of annotated instances decreases. On the other hand, the perturbation consistency used in SPOCO is relatively simple and cannot effectively exploit instance structure information in unannotated regions. In other words, there remains a large room to release the potential of the sparse instance-level supervision. + +Compared to metric learning, affinity-based instance segmentation methods [44, 43] are less sensitive to the number of annotated instances, since affinities encode instance boundary structure knowledge and are easier to be learned. Inspired by this kind of methods, we propose an effective biomedical instance segmentation framework with sparse instance annotations, which learns cross-representation affinity consistency. Specifically, our framework consists of two individual networks to predict two different representations, i.e., an embedding map and an implicit affinity map (IAM), respectively. We then calculate the similarity between pixel embeddings and convert the embedding map into an explicit affinity map (EAM). The IAM exploits the spatial structure information of instances, while the EAM exploits the semantic information of instances in the feature space. By building the perturbation consistency between the IAM and the EAM, we combine the advantages of two kinds of affinity modeling to capture both feature-level instance discrimination and pixel-level instance boundary structure. This perturbation consistency is different from the existing perturbation consistency between the same kinds of representations widely used in semi-supervised learning. + +In our framework, we use the groundtruth affinity map generated from sparse instance annotations to supervise the two affinity maps in the annotated regions. Inspired by the cross pseudo supervision [7], we further propose an affin + +ity cross-supervision mechanism to facilitate affinity consistency learning on the unannotated regions. Specifically, we design a pseudo-label noise filtering scheme that integrates a heuristic decision strategy based on an adaptive threshold and a learning decision strategy based on a pretrained confident pixel selection network (CPSN), to select highly confident regions as pseudo labels from one affinity map to supervise the other. + +We evaluate our methods on four biomedical datasets with sparse instance annotations to demonstrate the state-of-the-art performance of our proposed framework, compared to three kinds of baselines: 1) the existing sparsely supervised method SPOCO, 2) advanced semi-supervised methods which are adapted to sparse instance-level supervision, and 3) original semi-supervised methods trained with dense annotation under the same annotation cost. + +The contributions of this paper are as follows: + +- We propose a sparsely supervised biomedical instance segmentation framework by enforcing the perturbation consistency between two kinds of affinity modeling. +- We propose an affinity cross-supervision mechanism with a pseudo-label noise filtering scheme integrating two decision strategies to select highly confident regions to facilitate affinity consistency learning. +- We conduct extensive experiments on four biomedical datasets with sparse instance annotations to demonstrate the state-of-the-art performance of our method. +- We demonstrate the general superiority of sparse instance-level supervision over semi-supervision on 3D volumetric datasets for the first time. + +# 2. Related Work + +# 2.1. Biomedical Instance Segmentation + +The prevalent instance segmentation methods are mainly divided into two categories: proposal-based [12, 26, 3, 47] and proposal-free [5, 38, 27, 29, 28, 33]. The former is based on object detection to distinguish different instances, while the latter is based on instance-aware features and morphology properties, which is more suitable to complex and dense instances of biomedical datasets. Metric learning [9, 22] and affinity learning [11, 31] are two proposal-free representatives. + +Metric learning [9, 22, 20] uses a discriminative loss [9] to impose pixels belonging to different instances to be discriminative from each other in the feature space. However, as the number of instances decreases in the sparse instance-level supervision setting, it is difficult for the network to distinguish different instances in the feature space. + +![](images/0a5f6d0e6f7d1d1c5fa1cbb99dafa976f10241e10b0b146f153ba293306eda9f.jpg) +Figure 2. The workflow of our proposed sparsely supervised biomedical instance segmentation framework. (a) The input image is fed into two networks $f(\theta_1)$ and $f(\theta_2)$ to predict an affinity map and an embedding map, respectively. The embedding map is then explicitly converted into an affinity map. (b) These two affinity maps are supervised by the affinity label on the annotated region. The unannotated region of the affinity label is highlighted in gray color. The white and black colors indicate the affinity value as 1 and 0. (c) The highly confident region with low entropy of each affinity map is selected by a confident pixel selection network (CPSN) to supervise the other on the unannotated region. The red color indicates the region of the affinity map with high entropy, which is not used for cross-supervision. (d) This diagram illustrates the training stage of the CPSN, in which the model is trained on the annotated region to predict regions with segmentation errors. These regions are then excluded from being used as pseudo labels to supervise the other affinity map. $\odot$ and $\oplus$ represent dot product and concatenation operations, respectively. + +Affinity learning [2, 11, 31, 14] predicts pixel affinities that only encode spatial structure information between adjacent instances without ensuring the uniqueness of each instance in the feature space. Thus, the affinities are easy to be learned by the network and less affected by the number of instances. Even if there is only one annotated instance, this method can learn affinities between the unannotated region and the instance. + +# 2.2. Consistency Regularization + +Consistency regularization [1] plays a vital role in semisupervised learning. It enforces the consistency of predictions of unannotated data with various perturbations, by introducing a regularization loss function. The categories of perturbation are mainly divided into input perturbation [49, 25, 10], feature perturbation [37, 40], and network perturbation [7, 17]. Existing methods generally enforce the consistency between different perturbations of the same representation. Take an example of combining meanteacher [42] and the affinity-based segmentation method: both the teacher and student networks directly predict affinity maps that belong to the same representation. Different from existing consistency regularization methods, our proposed framework enforces consistency between two different representations from two kinds of affinity modeling. + +# 3. Problem Formulation + +Given an input image $I$ with a size of $H\times W$ , containing K instances (including background), $\mathbf{M}$ of which are + +annotated $(M\ll K)$ . The image $I$ is divided into two pixel sets, i.e., an annotated pixel region $R^L$ and an unannotated pixel region $R^{U}$ . The unannotated region $R^{U}$ contains unannotated instances and background. Different from semi-supervised learning, our goal is to train a model to predict the accurate affinity map by leveraging both a few annotated instances in the annotated region $R^{L}$ and the unannotated region $R^{U}$ . + +Before introducing our method, we clarify the definition of affinity. The affinity map $A = [a_{1}, a_{2}, \ldots, a_{N}] \in \mathbb{R}^{N \times H \times W}$ describes whether the current pixel and adjacent pixels belong to the same instances or not, where $a_{n}(n = 1, 2, \ldots, N)$ denotes the different adjacent relations between the current pixel and its $n$ order adjacent pixel. Given the segmentation groundtruth $y \in \mathbb{R}^{H \times W}$ , a pixel affinity $a_{n,i} \in a_{n}$ at the $i^{th}$ pixel of the image $I$ is formulated as + +$$ +a _ {n, i} = \left\{ \begin{array}{l l} 0, & \text {i f} y _ {i} \neq y _ {i + n} \\ 1, & \text {i f} y _ {i} = y _ {i + n}, \end{array} \right. \tag {1} +$$ + +where $y_{i}$ and $y_{i + n}$ are the instance segmentation IDs of paired pixels $i$ and $i + n$ . 1 means that pixel $i$ and $i + n$ belong to one instance, while 0 means the opposite. + +Considering the segmentation groundtruth with sparse instance-level annotations, we regard the unannotated region (including the background) as an identical instance ID. The generated affinity label is divided into annotated region $R_{a}^{L}$ and unannotated region $R_{a}^{U}$ . If the pixel affinity $a_{n,i}$ is located in the annotated region $R_{a}^{L}$ , at least one of the pixels $i$ and $i + n$ is located in the annotation region $R^{L}$ , i.e., + +$y_{i} \in R^{L}$ or $y_{i + n} \in R^{L}$ . Therefore, the annotated affinity region $R_{a}^{L}$ is slightly larger than the annotated segmentation region $R^{L}$ . + +# 4. Cross-Representation Affinity Consistency + +In this section, we introduce the proposed sparsely supervised biomedical instance segmentation framework. The input of our framework can be either 2D images or 3D volumes. Here we illustrate it using a 2D image example for easy visualization. As shown in Fig. 2, our framework consists of two main parts. The first part contains two parallel networks to build affinity perturbation by predicting different representations: IAM and EAM (detailed in 4.1). The second part contains an affinity cross-supervision mechanism by a pseudo-label noise filtering scheme to select the highly confident region of the two affinity maps to supervise each other for consistency learning (detailed in 4.2). + +# 4.1. Affinity Perturbation + +Unlike the common perturbation consistency strategy, we build the perturbation between two affinity representations predicted by two parallel networks. Following the existing affinity learning methods [11, 31], we adopt a network $f(\theta_1)$ to directly predict an implicit affinity map $\hat{A}^1 = [\hat{a}_1^1, \hat{a}_2^1, \dots, \hat{a}_N^1]$ . For accurate pixel affinities, the network $f(\theta_1)$ focuses on the structure information of instance boundaries. + +In contrast to implicit learning, explicitly modeled affinity has been widely studied [22, 14] by calculating the pairwise relationships between pixel embeddings. Given the limited number of instances, we only impose local constraints on the adjacent instances instead of constraining all instances by a discriminative loss [9]. We adopt a network $f(\theta_2)$ to predict an embedding map $E \in \mathbb{R}^{D \times H \times W}$ , where $D$ is the number of channels of the last layer of the network. Each pixel $i$ of the image $I$ is mapped into a pixel embedding vector $e_i \in \mathbb{R}^D$ , which is a D-dimensional feature representation. We then adopt a cosine distance to calculate the relationship between pixel embeddings and converted the embedding map into an explicit affinity map $\hat{A}^2 = [\hat{a}_1^2, \hat{a}_2^2, \dots, \hat{a}_N^2]$ . The transformation from a paired of pixel embeddings to a pixel affinity $\hat{a}_{n,i}^2$ is formulated as + +$$ +\hat {a} _ {n, i} ^ {2} = \frac {e _ {i} ^ {T} e _ {i + n}}{\| e _ {i} \| _ {2} \| e _ {i + n} \| _ {2}}. \tag {2} +$$ + +The network $f(\theta_2)$ pays more attention to extracting the semantic instance information to discriminate pixels belonging to different instances in the feature space. + +We adopt the MSE loss to supervise both $f(\theta_1)$ and $f(\theta_2)$ in the annotated region $R_a^L$ of the affinity label $A$ : + +$$ +\begin{array}{l} L _ {s} = L _ {s 1} + L _ {s 2} \\ = \frac {1}{\left| R _ {a} ^ {L} \right|} \sum_ {i \in R _ {a} ^ {L}} \sum_ {n = 1} ^ {N} \left(\left\| \hat {a} _ {n, i} ^ {1} - a _ {n, i} \right\| _ {2} + \left\| \hat {a} _ {n, i} ^ {2} - a _ {n, i} \right\| _ {2}\right), \tag {3} \\ \end{array} +$$ + +where $L_{s1}$ and $L_{s2}$ represent the loss functions for $f(\theta_1)$ and $f(\theta_2)$ , respectively. + +# 4.2. Affinity Cross-Supervision + +In order to combine the advantages of the two kinds of affinity modeling, we propose an affinity cross-supervision mechanism to enforce the consistency between the IAM and the EAM. Since the two affinity maps may suffer from prediction errors during the initial training phase, we propose a pseudo-label noise filtering scheme by integrating two entropy-based decision strategies, i.e., adaptive threshold and prediction by a CPSN, to select highly confident pixel affinities to avoid the collapse of the consistency learning. For a pixel affinity $a_{n,i}$ , its entropy is computed by + +$$ +h _ {n, i} = - a _ {n, i} \log \left(a _ {n, i}\right) - (1 - a _ {n, i}) \log \left(1 - a _ {n, i}\right). \tag {4} +$$ + +Adaptive threshold. As a heuristic strategy, we can determine whether the pixel affinity is confident by the following indicator: + +$$ +\delta_ {n, i} ^ {\text {t h r e s}} = \left\{ \begin{array}{l l} 1, & \text {i f} h _ {n, i} < \gamma_ {t} \\ 0, & \text {o t h e r s ,} \end{array} \right. \tag {5} +$$ + +where $\gamma_{t}$ refers to the entropy threshold at the $t^{th}$ training iteration, which is the quantile of $h_{n,i}$ corresponding to $\alpha_{t}$ to limit unreliable pixels with top $\alpha_{t}$ entropy. 1 means the pixel affinity is confident with low entropy, while 0 means the opposite. + +Since the confident pixels gradually increase during the training procedure, $\alpha_{t}$ is dynamically adjusted by a power function: + +$$ +\alpha_ {t} = \alpha_ {0} (1 - t / T) ^ {p}, \tag {6} +$$ + +where $\alpha_0$ is the initial quantile and is set to $5\%$ , $p$ is the power and is set as 1.5, $t$ is the current training iteration, and $T$ is total iterations. + +Confidence pixel selection network. Inspired by approaches that address pseudo label errors using auxiliary networks [35, 21], we employ a binary-classification network called CPSN to identify highly confident pixels, which is trained only using the annotated regions of the groundtruth error map, as shown in Fig. 2 (d). Specifically, we sample five segmentation models under different training iterations of $f(\theta_{1})$ and $f(\theta_{2})$ respectively, and add a certain rate of dropout to these models. We then use the prediction from these models to simulate various segmentation errors. Using this kind of simulation data, we train + +a robust CPSN to locate errors and generate highly confident pixels. We provide training details (including the loss $L_{CPSN}$ ) in the supplementary material. + +Given the input image $I$ , affinity map $A$ and affinity entropy map $H$ , the CPSN can predict a binary error map $B \in \mathbb{R}^{N \times H \times W}$ with the same size as $A$ : + +$$ +B = \operatorname {C P S N} (I \oplus A \oplus H), \tag {7} +$$ + +where $\oplus$ is the concatenation operation. + +We then determine whether the pixel affinity is confident by the following indicator: + +$$ +\delta_ {n, i} ^ {c p s n} = 1 - b _ {n, i}, \tag {8} +$$ + +where $b_{n,i} \in B$ is the pixel-level prediction of CPSN. + +Pseudo-label noise filtering. We integrate the above two decision strategies to obtain more robust highly confident pixels, which is described by $\delta_{n,i} = \delta_{n,i}^{thres}\delta_{n,i}^{cpsn}$ . After obtaining the confident pixels of the IAM (indicated by $\delta_{n,i}^{1}$ ) and the EAM (indicated by $\delta_{n,i}^{2}$ ), we utilize their confident pixels on the unannotated affinity region $R_{a}^{U}$ to cross-supervise each other. The consistency loss is formulated as + +$$ +\begin{array}{l} L _ {c} = L _ {c 1} + L _ {c 2} \\ = \frac {1}{\left| R _ {a} ^ {U} \right|} \sum_ {i \in R _ {a} ^ {U}} \sum_ {n = 1} ^ {N} \left(\left\| \hat {a} _ {n, i} ^ {1} - \hat {a} _ {n, i} ^ {2} \right\| _ {2} \delta_ {n, i} ^ {2} \right. \tag {9} \\ + \left\| \hat {a} _ {n, i} ^ {2} - \hat {a} _ {n, i} ^ {1} \right\| _ {2} \delta_ {n, i} ^ {1}), \\ \end{array} +$$ + +where $L_{c1}$ and $L_{c2}$ represent the consistency loss functions for $f(\theta_1)$ and $f(\theta_2)$ . + +# 4.3. Overall Optimization + +The overall objection function is the combination of losses on the annotated region and the unannotated region, which terms + +$$ +L = L _ {s} + \lambda L _ {c}, \tag {10} +$$ + +where $\lambda$ is the trade-off weight and is set to make the two loss value ranges comparable. + +Following [14], we adopt the network $f(\theta_2)$ to predict an explicit affinity map in the inference stage. The affinity map is converted into final instance segmentation results by different post-processing algorithms. The 3D results and 2D results are generated by Waterz [11] (50% quantile and 0.5 threshold) and Mutex [45] post-processing algorithms, respectively. Since affinities calculated by these two different normalization schemes (sigmoid vs cosine) belong to different intervals, we use a RELU function to map the output value into [0, 1], for Waterz post-processing algorithm. + +# 5. Experiments + +# 5.1. Datasets and Metrics + +We conduct evaluations on four representative biomedical datasets with corresponding commonly used metrics. + +AC3. The AC3 dataset is a popular electron microscopy (EM) neuron dataset, imaged from the mouse somatosensory cortex at $3 \times 3 \times 29$ nm resolution. It is a subset of the Kasthuri [16] dataset, and contains 256 volumetric images ( $1024 \times 1024$ ). We adopt the top 100 sections as the labeled set and sparsely select different numbers of neuron instances as the annotations. At the same time, the bottom 50 sections are adopted for evaluation. We adopt two widely used metrics in the field of EM image segmentation to quantitatively evaluate the result, i.e., Variation of Information (VOI) [34] and Adapted Rand Error (ARAND) [39]. The VOI is defined as a sum of another two metrics $VOI_{split}$ and $VOI_{merge}$ which indicate the split and merge errors, respectively. Note that smaller values of these metrics indicate better performance. + +CREMI-C. The CREMI dataset is from the CREMI challenge [8] for neuron segmentation in EM volumes. It is composed of three volumetric datasets (CREMI-A, CREMI-B, and CREMI-C) imaged from the adult drosophila brain at $4 \times 4 \times 40$ nm resolution. Each of the three datasets contains 125 images. Given that the neurites in CREMI-A and CREMI-C are mostly homogeneous in morphology, we evaluate our method on the CREMI-C dataset, which contains more challenging neuron types. We adopt the top 75 sections as the labeled set and the bottom 50 sections for evaluation. We adopt the same metrics used for the AC3 to evaluate the results on the CREMI-C dataset. + +CVPPP. The A1 sequence of the CVPPP [36] dataset contains leaves with complex shapes and severe occlusions, which is widely used to evaluate biomedical instance segmentation. We randomly sample 108 images for training and 20 images for testing, where each image is with a size of $530 \times 500$ . We adopt the Symmetric Best Dice (SBD) and the absolute Difference in Counting $(|DiC|)$ metrics [36] to evaluate the quantitative result. + +BBBC039V1. The BBBC039V1 dataset [32] contains 200 fluorescence microscopy images with a resolution of $696 \times 520$ pixels. The dataset focuses on the U2OS cells with various shape and density. Following the official data split, we use 100 images for training, 50 for validation, and the rest 50 for testing. We adopt four metrics for cell segmentation for quantitative evaluation, i.e., Aggregated Jaccard Index (AJI) [39], object-level F1 score (F1) [4], Panoptic Quality (PQ) [19], and pixel-level Dice score (Dice). + +# 5.2. Implementation Details + +We adopt two different backbone networks, i.e., 3D U-Net [23] and 2D Residual U-Net for the 3D volumetric datasets (AC3, CREMI-C) and 2D datasets (CVPPP, BBBC039V1), respectively. Both the network $f(\theta_{1})$ and $f(\theta_{2})$ are based on the same backbone network but different in the last convolution layer. We train these networks using Adam optimizer [18] with $\beta_{1} = 0.9$ and $\beta_{2} = 0.999$ , a + +
MethodsAC3CREMI-C
VOISplit ↓VOIMerge ↓VOI ↓ARAND ↓VOISplit ↓VOIMerge ↓VOI ↓ARAND ↓
Semi.Vanilla0.4225.4035.8250.9110.9292.1173.0460.580
PseudoL-hard [41]0.0895.9556.0440.9200.8631.4622.3250.311
PseudoL-soft [50]0.8513.7444.5950.8530.9500.8941.8440.230
MT [42]0.8632.0582.9210.5580.9161.0271.9430.211
π-model [25]0.8471.8672.7140.5620.9850.9181.9030.227
UA-MT [49]0.7201.8602.5800.4260.9780.8631.8410.227
SASSNet [24]1.1601.1802.3400.3240.9350.8141.7490.193
SSNS [13]0.7020.5271.2290.1200.9340.7751.7090.175
Sparse.SPOCO [46]1.6081.3492.9570.2361.8320.8962.7280.303
Vanilla0.9300.2371.1670.1111.6130.4512.0640.187
MT* [42]0.6990.4321.1320.0921.3750.5591.9340.173
UA-MT* [49]0.7850.2511.0360.0821.5020.3331.8350.155
CCT* [37]0.8590.2381.0970.0881.4250.4631.8880.173
CPS* [7]0.7180.2480.9660.0671.3840.3981.7820.158
Ours0.6420.2600.9030.0641.0320.5871.6200.153
+ +Table 1. Quantitative comparison of segmentation results on AC3 and CREMI-C datasets using 5 densely annotated sections for semi-supervision and randomly annotated instances for sparse instance-level supervision. The number of annotated voxels is the same for the two settings. Vanilla refers to training models only using available groundtruth. The top right corner \* indicates these methods are originally proposed in the semi-supervision but adapted into the sparse instance-level supervision. Note that we adopt the same backbone ResUnet [23] in all methods for a fair comparison. The best results and the second-best results are highlighted in bold and underlined. + +![](images/8d1bdac39117ed7cb187248f6c823d05ed433d52e39556cad583628a4c7b15dc.jpg) +Figure 3. 2D Visual comparison of different methods on AC3 and CREMI-C datasets. The first row and the second row of each dataset are the affinity map and the corresponding instance segmentation result. Red and blue boxes indicate merge and split errors, respectively. + +learning rate of $1e - 4$ , and a batch size of 2 on one NVIDIA TitanXP GPU for 200K iterations. + +# 5.3. Comparison Methods + +The evaluation of our method is performed against three kinds of baselines: + +(1) For the 3D volumetric datasets, the sparse instance-level supervision and the common semi-supervision contain different 3D structure information of instances in the axial direction. For a comprehensive evaluation, we compare + +our proposed sparsely supervised method with a number of existing semi-supervised methods that are widely used for 3D datasets, including: PseudoL-hard [41], PseudoL-soft [50], mean-teacher (MT) [42], $\pi$ -model [25], UAMT [49], SASSNet [24] and SSNS [13]. + +(2) SPOCO [46] provides a baseline solution for the sparsely supervised segmentation task. We use the official code and configurations to reproduce the results on 2D datasets (CVPPP and BBBC039V1), and adapt this method to 3D datasets (AC3 and CREMI-C). + +![](images/4a06ad5c7604e4b54db385d891b3cde031e5af6048fb2305fd608789f705946c.jpg) +Figure 4. 3D Visual comparison of different methods on AC3 and CREMI-C datasets. Red and blue arrows indicate split and merge errors, respectively. + +(3) We adapt a variety of advanced semi-supervised methods to the sparsely supervised segmentation task, including mean-teacher (MT) [42], uncertainty-aware mean teacher model(UA-MT) [49], cross-consistency training (CCT) [37] and cross pseudo supervision (CPS) [7]. + +# 5.4. Results on 3D Datasets + +We list an extensive quantitative comparison on the AC3 and the CREMI-C datasets in Table 1. We conduct the semi-supervised experiments with 5 densely annotated sections, and the sparsely supervised experiments with 23 and 33 randomly annotated instances for AC3 and CREMI-C datasets respectively. The number of annotated voxels is the same for the two settings. From the results in Table 1, we can observe that: + +(1) With the same number of annotated voxels, sparsely supervised methods perform better than corresponding semi-supervised methods by a large margin. Specifically, our results outperform the state-of-the-art semi-supervised results from SSNS [13] by $26.4\%$ and $5.2\%$ for the VOI metric on the AC3 and CREMI-C datasets. +(2) For the EM neuron segmentation datasets, the sparse instance annotations are not conducive to the training of SPOCO [46] based on metric learning. Therefore, SPOCO [46] does not perform well on these two datasets. +(3) Our method achieves better performance than other adapted methods in the sparse instance-level supervision setting. Specifically, We achieve $6.3\%$ and $9.2\%$ improvement from the key VOI metric on the AC3 and CREMI-C datasets, compared with the second-best method. It demonstrates the superiority of the proposed affinity consistency regularization. + +We show 2D and 3D visual comparison results in Fig. 3 + +![](images/43e9583f5594c6a42e6fc9dd315d237be1d0b1f6ca051c9a81bda045de44ae20.jpg) +Figure 5. Comparison of different methods on the AC3 dataset under different annotation amounts converted into the number of sections for counting, where each section contains $1 \times 10^{6}$ pixels. + +and Fig. 4, respectively. As can be seen, our proposed method predicts the affinity map with higher fidelity than other methods, which significantly reduces the split and merge errors. We also provide 3D visual comparison results in the supplementary material. As can be seen, our results contain fewer merge and split errors, and maintain the accuracy of neuron structures, compared with other methods. + +We further compare different methods on the AC3 dataset under different numbers of annotated voxels. We convert the number of voxels to the number of sections for counting, where each section contains about $1 \times 10^{6}$ voxels. The results are shown in Fig. 5. As more annotations are available, the performance gap between different methods gradually narrows, but the superiority of our method can still be observed. Especially, the state-of-the-art semi-supervised method SSNS performs worse than sparsely supervised methods under very limited annotations, due to the + +
Methods10% instances40% instances
SBD ↑|DiC| ↓SBD ↑|DiC| ↓
CPS [7] (semi)83.21.887.61.1
SPOCO [46]70.63.082.12.0
Vanilla69.86.078.01.9
MT* [42]78.51.484.31.3
UA-MT* [49]79.61.484.51.1
CCT* [37]78.81.983.91.6
CPS* [7]80.71.885.51.1
Ours83.61.186.60.8
+ +![](images/f9a150eb8efc7c3c5e7a35657d8367799856ad96eaad5822d0b5d661e5fc1315.jpg) +Raw Image + +![](images/c33d7e2f802677bdd954ebfcaab5877abef1055eddcab1addecd30e88ae15924.jpg) +MT* + +![](images/7a100951a106da68f7bb3db6e9ffa4e5a6d8fa847da1eac39de4eac77a849f05.jpg) +UAMT* + +![](images/a71f3c9df7a7855541fa039f2add481cb04b081237d63697f73c1a998f29d736.jpg) +CCT* + +![](images/da79899e01d2720456a8ec9e3e866376dc4d8afc6c0cea9d3139f2477067315b.jpg) +SPOCO +Figure 6. Visual comparison of different methods on the CVPPP dataset with $40\%$ instances. The segmentation errors are highlighted by white boxes. + +![](images/21b1b5ea8e9206226ab3479924ac7ac85e0fe086f2d0cd21e73a359a7ec14265.jpg) +CPS* + +![](images/ecf26c81624f0714b2771309fdc6b8e56cb389392ae8f928d97fd793bacb47cf.jpg) +Ours + +![](images/dbda1af37a3b95a4387b06ef7740ddcd4ff3f3aaffea90435f812e7ca1cb1c00.jpg) +Groundtruth + +incomplete 3D structure information of instances. + +# 5.5. Results on 2D Datasets + +We further validate our method on two 2D datasets, i.e., CVPPP and BBBC039V1, and their quantitative results are shown in Table 2 and Table 3, respectively. Compared with other adapted methods in the sparse instance-level supervision setting, our method achieves the best performance on the CVPPP dataset with $10\%$ and $40\%$ annotated instances, and the BBBC039V1 dataset with $1\%$ and $10\%$ annotated instances. Visual results on these two datasets also illustrate the superior performance of our method with fewer segmentation errors, as shown in Fig. 6 and Fig. 7. + +Although the sparse instance-level supervision and the common semi-supervision have no difference in the instance structure for 2D datasets, we also evaluate the semi-supervised setting (with the same annotated pixels) on these two datasets. Our proposed method performs better than the state-of-the-art semi-supervised method CPS [7], when the annotation amount is very limited. Meanwhile, our method significantly outperforms the existing sparely supervised method SPOCO in all experiments. As more annotation amount is available, the semi-supervised method has a better performance. Therefore, the sparse instance-level supervision is still a meaningful complement to the com + +Table 2. Quantitative comparison results on the CVPPP dataset. Results in the first row are based on the semi-supervision setting. + +
MethodsAJI ↑Dice ↑F1 ↑PQ ↑
1% instancesCPS [7] (semi)0.81200.90330.95950.8168
SPOCO [46]0.68960.84780.84920.6933
Vanilla0.56310.64110.75700.4890
MT* [42]0.77160.82600.90180.7533
UA-MT* [49]0.80650.87380.94390.7928
CCT* [37]0.81130.91360.92950.7830
CPS* [7]0.83230.91850.94440.8153
Ours0.83030.93380.94420.8222
10% instancesCPS [7] (semi)0.83930.91890.95980.8437
SPOCO [46]0.74880.87460.92630.7503
Vanilla0.59850.71770.77090.5652
MT* [42]0.84160.91670.93380.8283
UA-MT* [49]0.84040.91180.93800.8314
CCT* [37]0.83090.92790.93270.7975
CPS* [7]0.84630.93660.94080.8174
Ours0.85450.94690.94500.8343
+ +![](images/479842fcf3f6091ceacf27448e70c335ae363e115cc8af74f313b08b97e6a7ed.jpg) +Raw Image + +![](images/2b7ad6c196c6ca60b48667c3682def10831df07fae671a3aa7f05233b5c82c99.jpg) +MT* + +![](images/b61f8bb29e42382f7d1780b06776a276a6e29b7acd7f8dcd548f54e897b3318d.jpg) +UAMT + +![](images/f2d4925b5d5ffcebf1a0fd03a6e6859dd98a5ea56ea05af81af5fdb5ecadd30c.jpg) +CCT* + +![](images/cfb40ba30b61f4b4bdbc8af932c9abed6ec011f218e8c5983407768a686f2dc9.jpg) +SPOCO +Figure 7. Visual comparison of different methods on the BBBC039V1 dataset with $10\%$ instances. + +![](images/5260862763891f4c692a30f99c066dc57dcb065a0f90e34ae489e88d2e94acfd.jpg) +CPS* + +![](images/d39497e4181406cafbe13ea8b2a11c48f90a420a1ea6fed4da718f8feb659ea9.jpg) +Ours + +![](images/c4ed470c768b3ed962475ab162c50e1c8fbaec9f6e08947685e1aec1ee2112b0.jpg) +Groundtruth + +mon semi-supervision when instances are so crowded that dense annotation is laborious and the amount of annotations is very limited, for the 2D datasets. + +# 5.6. Ablation Studies + +Table 3. Quantitative comparison on the BBBC039V1 dataset. + +
Method15102050100
Vanilla2.2891.1670.9820.8710.7790.726
Ours1.2710.9030.8160.8070.7380.717
+ +Table 4. Ablation study on the annotation amount which is converted into the number of sections for counting, where each section contains about $1 \times 10^{6}$ voxels. The key metric VOI is used to evaluate the results. + +We conduct ablation studies on the impacts of each component of the proposed framework on the AC3 dataset. + +Annotation amounts. We conduct an ablation study to investigate the effects of different amounts of annotated instances. As shown in Table 4, our proposed method consistently outperforms the vanilla model trained only using available annotated instances. When the annotation amount is small (e.g., the number of annotated voxels is about a sec + +
f(θ1)f(θ2)cross-supervisionVOI ↓ARAND ↓
ThresholdCPSN
IAMIAM✓✓0.9260.074
EAMEAM✓✓0.9270.068
IAMEAMXX0.9160.068
IAMEAM✓X0.9060.068
IAMEAMX✓0.9090.067
IAMEAM✓✓0.9030.065
+ +Table 5. Ablation study on different components of the proposed affinity consistency regularization. IAM and EAM represent the different kinds of affinity modeling for the two networks $f(\theta_{1})$ and $f(\theta_{2})$ . 'Threshold' and 'CPSN' denote the two different strategies to select highly confident regions in cross-supervision. + +
MethodVOISplit ↓VOIMerge ↓VOI ↓ARAND ↓
Ours-f(θ1)0.7090.1980.9070.071
Ours-f(θ2)0.6870.2180.9030.065
+ +Table 6. Ablation study on which affinity map used for inference. + +
α00.010.050.1
VOI↓/ ARAND ↓0.933 / 0.0750.903 / 0.0650.924 / 0.069
Dropout rate00.10.3
VOI↓/ ARAND ↓0.920 / 0.0660.903 / 0.0650.923 / 0.067
λ0.010.11
VOI↓/ ARAND ↓0.914 / 0.0660.903 / 0.0651.258 / 0.106
+ +Table 7. Ablation study on key parameters of the proposed framework. VOI/ARAND are adopted as metrics. + +tion), our method significantly improves the performance of the vanilla model. The performance gap narrows as more annotations are available. + +Affinity consistency regularization. As shown in Table 5, we conduct an ablation study on the proposed affinity consistency learning scheme. We compare different combinations of affinity modeling for the two networks $f(\theta_{1})$ and $f(\theta_{2})$ by directly enforcing their consistency. It can be observed that the combination of IAM and EAM achieves the best performance. Furthermore, we demonstrate the effectiveness of pseudo-label noise filtering with different decision strategies. Both strategies have been shown to improve performance, and their integration can obtain more robust highly confident regions and achieves the best performance. Moreover, We have compared our method with an equivalent implementation of [14] in Table 5, i.e., two network branches both use EAM. Our method achieves better performance. + +Affinity map used in the inference stage. The two affinity maps predicted by $f(\theta_{1})$ and $f(\theta_{2})$ have different performances, as shown in Table 6. The EAM predicted by + +$f(\theta_2)$ performs slightly better, so we adopt it in the inference stage. + +Ablation study on hyper-parameters. We conducted ablation experiments to evaluate the impact of key hyperparameters, of the proposed framework, as shown in Table 7. For the proposed pseudo-label noise filtering scheme, we test different values of hyper-parameters $\alpha_0$ for adaptive threshold and different dropout rates used in the CPSN training. Also, we provide the ablation study on different loss weights $\lambda$ . + +# 6. Conclusion + +In this paper, we propose an effective sparsely supervised biomedical instance segmentation framework via learning cross-representation affinity consistency. The proposed framework builds the perturbation consistency between an implicit affinity map and an explicit affinity map with an affinity cross-supervision mechanism. We conduct extensive experiments on 3D volumetric datasets and 2D datasets to demonstrate the superiority of our proposed framework over the existing sparsely supervised method. Meanwhile, for the first time, we validate that sparsely supervised methods can better utilize the 3D structure information of instances and perform better than semi-supervised methods for volumetric datasets. + +# Acknowledgement + +This work was supported in part by the National Natural Science Foundation of China under Grant 62021001. + +# References + +[1] Philip Bachman, Ouais Alsharif, and Doina Precup. 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In ECCV, 2018. 6 \ No newline at end of file diff --git a/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/images.zip b/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ec0e3287715ad94a5620280b41413bdd06a31454 --- /dev/null +++ b/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2926257d9f4bf4847b4733a6f8b8ec7f5919b1d74b67d74144053db625616005 +size 817329 diff --git a/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/layout.json b/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..beaee8f65405a2bb0536c502ae5216ff824c2f19 --- /dev/null +++ b/2023/Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation/layout.json @@ -0,0 +1,11099 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 115, + 103, + 479, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 103, + 479, + 140 + ], + "spans": [ + { + "bbox": [ + 115, + 103, + 479, + 140 + ], + "type": "text", + "content": "Learning Cross-Representation Affinity Consistency for Sparsely Supervised Biomedical Instance Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "spans": [ + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": "Xiaoyu Liu" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1,\\ast}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": " Wei Huang" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": " Zhiwei Xiong" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1,2,\\dagger}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": " \nShenglong Zhou" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": " Yuei Zhang" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": " Xuejin Chen" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": " Zheng-Jun Zha" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": " Feng Wu" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": "University of Science and Technology of China \n" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 90, + 160, + 503, + 224 + ], + "type": "text", + "content": "Institute of Artificial Intelligence, Hefei Comprehensive National Science Center" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "spans": [ + { + "bbox": [ + 143, + 251, + 192, + 264 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 276, + 290, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 276, + 290, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 276, + 290, + 574 + ], + "type": "text", + "content": "Sparse instance-level supervision has recently been explored to address insufficient annotation in biomedical instance segmentation, which is easier to annotate crowded instances and better preserves instance completeness for 3D volumetric datasets compared to common semi-supervision. In this paper, we propose a sparsely supervised biomedical instance segmentation framework via cross-representation affinity consistency regularization. Specifically, we adopt two individual networks to enforce the perturbation consistency between an explicit affinity map and an implicit affinity map to capture both feature-level instance discrimination and pixel-level instance boundary structure. We then select the highly confident region of each affinity map as the pseudo label to supervise the other one for affinity consistency learning. To obtain the highly confident region, we propose a pseudo-label noise filtering scheme by integrating two entropy-based decision strategies. Extensive experiments on four biomedical datasets with sparse instance annotations show the state-of-the-art performance of our proposed framework. For the first time, we demonstrate the superiority of sparse instance-level supervision on 3D volumetric datasets, compared to common semi-supervision under the same annotation cost. Code is available at https://github.com/liuxy1103/CRAC." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 616, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 677 + ], + "type": "text", + "content": "Biomedical instance segmentation aims to assign each image pixel to an instance, which plays an essential role in biomedical instance morphology and distribution analysis [36, 32]. Recently, deep-learning-based methods [22, 26, 48, 20, 15, 30, 6] have achieved state-of-the-art perfor" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 256, + 385, + 344 + ], + "blocks": [ + { + "bbox": [ + 310, + 256, + 385, + 344 + ], + "lines": [ + { + "bbox": [ + 310, + 256, + 385, + 344 + ], + "spans": [ + { + "bbox": [ + 310, + 256, + 385, + 344 + ], + "type": "image", + "image_path": "882dd8515faae5d7a3b99bd769557fef71340ee49b4c5e94514c7d87948650c1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 389, + 251, + 463, + 346 + ], + "blocks": [ + { + "bbox": [ + 389, + 251, + 463, + 346 + ], + "lines": [ + { + "bbox": [ + 389, + 251, + 463, + 346 + ], + "spans": [ + { + "bbox": [ + 389, + 251, + 463, + 346 + ], + "type": "image", + "image_path": "bc5e4692f357cbd5d7cb5762243b95ac7efb4d3571face524e6efb30cbbae756.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 347, + 547, + 413 + ], + "lines": [ + { + "bbox": [ + 305, + 347, + 547, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 347, + 547, + 413 + ], + "type": "text", + "content": "Figure 1. Comparison of instance annotation schemes in different supervision ways for the volumetric dataset. (a) Full supervision, where the whole volume is annotated. (b) Semi-supervision, where a subset of the whole volume is densely annotated. (c) sparse instance-level supervision, where a subset of instances of the whole volume is annotated." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 466, + 251, + 544, + 346 + ], + "blocks": [ + { + "bbox": [ + 466, + 251, + 544, + 346 + ], + "lines": [ + { + "bbox": [ + 466, + 251, + 544, + 346 + ], + "spans": [ + { + "bbox": [ + 466, + 251, + 544, + 346 + ], + "type": "image", + "image_path": "a7963f0e64cd1a3c2b2f114ae386e07ced5b9e92e3c7d344d9bbe3ab0f0e1635.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 434, + 546, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 546, + 482 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 546, + 482 + ], + "type": "text", + "content": "mance on biomedical instance segmentation with densely annotated images for fully-supervised training. However, it is expensive and laborious to obtain accurate and dense annotations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 484, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 640 + ], + "type": "text", + "content": "To alleviate the huge cost of manual annotations, many works [42, 13, 49, 37, 7] adopt the semi-supervised learning strategy to train an effective segmentation model with a small set of densely annotated images and a large set of unannotated images. However, in the field of biomedical instance segmentation, dense annotation is difficult to apply due to the crowded instances. Especially, for the 3D volumetric datasets (e.g., electron microscopy datasets), dense annotation within a small sub-volume usually damages the completeness of the instances along the axial direction. Meanwhile, in practice, domain experts tend to annotate instances one by one sparsely, rather than annotating all instances densely within a small sub-volume." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": "In this paper, we aim to deal with the task of biomedical instance segmentation with sparse instance annotations. This task is of utmost importance, as annotating a small subset of instances in a biomedical dataset not only saves the annotation cost but also conforms to annotation habits in the practical scenario. We illustrate different annotation" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 683, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 286, + 713 + ], + "type": "text", + "content": "*This work was done during Xiaoyu Liu's internship at Institute of Artificial Intelligence, Hefei Comprehensive National Science Center. \n†Corresponding author: zwxiong@ustc.edu.cn." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21107" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "schemes in Fig. 1 and focus on the comparison between common semi-supervision and sparse instance-level supervision. For a volumetric dataset, a few consecutive images are densely annotated for the semi-supervision in Fig. 1 (b), which generates many incomplete instances along the axial direction. Instead, a few instances are randomly annotated for the sparse instance-level supervision in Fig. 1 (c), which preserves complete 3D structure information of each instance under the same number of annotated voxels as the semi-supervision." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 386 + ], + "type": "text", + "content": "Actually, sparse instance-level supervision can be considered a special kind of semi-supervision at the region level. Thus, existing semi-supervised methods [42, 13, 49, 37, 7] can be readily adapted to the sparse instance-level supervision. As a pioneer work, SPOCO [46] imposes a consistency regularization scheme [42] in the unannotated regions of two embedding maps predicted in different augmented views. However, SPOCO adopts a metric learning [9]-based segmentation method to distinguish different instances in the feature space, whose performance heavily drops as the number of annotated instances decreases. On the other hand, the perturbation consistency used in SPOCO is relatively simple and cannot effectively exploit instance structure information in unannotated regions. In other words, there remains a large room to release the potential of the sparse instance-level supervision." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 388, + 289, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 289, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 289, + 663 + ], + "type": "text", + "content": "Compared to metric learning, affinity-based instance segmentation methods [44, 43] are less sensitive to the number of annotated instances, since affinities encode instance boundary structure knowledge and are easier to be learned. Inspired by this kind of methods, we propose an effective biomedical instance segmentation framework with sparse instance annotations, which learns cross-representation affinity consistency. Specifically, our framework consists of two individual networks to predict two different representations, i.e., an embedding map and an implicit affinity map (IAM), respectively. We then calculate the similarity between pixel embeddings and convert the embedding map into an explicit affinity map (EAM). The IAM exploits the spatial structure information of instances, while the EAM exploits the semantic information of instances in the feature space. By building the perturbation consistency between the IAM and the EAM, we combine the advantages of two kinds of affinity modeling to capture both feature-level instance discrimination and pixel-level instance boundary structure. This perturbation consistency is different from the existing perturbation consistency between the same kinds of representations widely used in semi-supervised learning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "In our framework, we use the groundtruth affinity map generated from sparse instance annotations to supervise the two affinity maps in the annotated regions. Inspired by the cross pseudo supervision [7], we further propose an affin" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "ity cross-supervision mechanism to facilitate affinity consistency learning on the unannotated regions. Specifically, we design a pseudo-label noise filtering scheme that integrates a heuristic decision strategy based on an adaptive threshold and a learning decision strategy based on a pretrained confident pixel selection network (CPSN), to select highly confident regions as pseudo labels from one affinity map to supervise the other." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 168, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 263 + ], + "type": "text", + "content": "We evaluate our methods on four biomedical datasets with sparse instance annotations to demonstrate the state-of-the-art performance of our proposed framework, compared to three kinds of baselines: 1) the existing sparsely supervised method SPOCO, 2) advanced semi-supervised methods which are adapted to sparse instance-level supervision, and 3) original semi-supervised methods trained with dense annotation under the same annotation cost." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 265, + 504, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 265, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 318, + 265, + 504, + 277 + ], + "type": "text", + "content": "The contributions of this paper are as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 286, + 545, + 472 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 317, + 286, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 286, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 317, + 286, + 545, + 323 + ], + "type": "text", + "content": "- We propose a sparsely supervised biomedical instance segmentation framework by enforcing the perturbation consistency between two kinds of affinity modeling." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 332, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 332, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 332, + 545, + 380 + ], + "type": "text", + "content": "- We propose an affinity cross-supervision mechanism with a pseudo-label noise filtering scheme integrating two decision strategies to select highly confident regions to facilitate affinity consistency learning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 391, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 391, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 318, + 391, + 545, + 426 + ], + "type": "text", + "content": "- We conduct extensive experiments on four biomedical datasets with sparse instance annotations to demonstrate the state-of-the-art performance of our method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 318, + 437, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 437, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 318, + 437, + 545, + 472 + ], + "type": "text", + "content": "- We demonstrate the general superiority of sparse instance-level supervision over semi-supervision on 3D volumetric datasets for the first time." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 495, + 392, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 392, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 392, + 506 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 514, + 490, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 490, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 490, + 528 + ], + "type": "text", + "content": "2.1. Biomedical Instance Segmentation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 640 + ], + "type": "text", + "content": "The prevalent instance segmentation methods are mainly divided into two categories: proposal-based [12, 26, 3, 47] and proposal-free [5, 38, 27, 29, 28, 33]. The former is based on object detection to distinguish different instances, while the latter is based on instance-aware features and morphology properties, which is more suitable to complex and dense instances of biomedical datasets. Metric learning [9, 22] and affinity learning [11, 31] are two proposal-free representatives." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Metric learning [9, 22, 20] uses a discriminative loss [9] to impose pixels belonging to different instances to be discriminative from each other in the feature space. However, as the number of instances decreases in the sparse instance-level supervision setting, it is difficult for the network to distinguish different instances in the feature space." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21108" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 548, + 234 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 548, + 234 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 548, + 234 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 548, + 234 + ], + "type": "image", + "image_path": "0a5f6d0e6f7d1d1c5fa1cbb99dafa976f10241e10b0b146f153ba293306eda9f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "lines": [ + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "text", + "content": "Figure 2. The workflow of our proposed sparsely supervised biomedical instance segmentation framework. (a) The input image is fed into two networks " + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "inline_equation", + "content": "f(\\theta_1)" + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "inline_equation", + "content": "f(\\theta_2)" + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "text", + "content": " to predict an affinity map and an embedding map, respectively. The embedding map is then explicitly converted into an affinity map. (b) These two affinity maps are supervised by the affinity label on the annotated region. The unannotated region of the affinity label is highlighted in gray color. The white and black colors indicate the affinity value as 1 and 0. (c) The highly confident region with low entropy of each affinity map is selected by a confident pixel selection network (CPSN) to supervise the other on the unannotated region. The red color indicates the region of the affinity map with high entropy, which is not used for cross-supervision. (d) This diagram illustrates the training stage of the CPSN, in which the model is trained on the annotated region to predict regions with segmentation errors. These regions are then excluded from being used as pseudo labels to supervise the other affinity map. " + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 46, + 244, + 547, + 345 + ], + "type": "text", + "content": " represent dot product and concatenation operations, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 352, + 289, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 289, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 289, + 448 + ], + "type": "text", + "content": "Affinity learning [2, 11, 31, 14] predicts pixel affinities that only encode spatial structure information between adjacent instances without ensuring the uniqueness of each instance in the feature space. Thus, the affinities are easy to be learned by the network and less affected by the number of instances. Even if there is only one annotated instance, this method can learn affinities between the unannotated region and the instance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 457, + 198, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 198, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 198, + 470 + ], + "type": "text", + "content": "2.2. Consistency Regularization" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 476, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 287, + 657 + ], + "type": "text", + "content": "Consistency regularization [1] plays a vital role in semisupervised learning. It enforces the consistency of predictions of unannotated data with various perturbations, by introducing a regularization loss function. The categories of perturbation are mainly divided into input perturbation [49, 25, 10], feature perturbation [37, 40], and network perturbation [7, 17]. Existing methods generally enforce the consistency between different perturbations of the same representation. Take an example of combining meanteacher [42] and the affinity-based segmentation method: both the teacher and student networks directly predict affinity maps that belong to the same representation. Different from existing consistency regularization methods, our proposed framework enforces consistency between two different representations from two kinds of affinity modeling." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 669, + 174, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 174, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 174, + 681 + ], + "type": "text", + "content": "3. Problem Formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Given an input image " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " with a size of " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": ", containing K instances (including background), " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " of which are" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": "annotated " + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "inline_equation", + "content": "(M\\ll K)" + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": ". The image " + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": " is divided into two pixel sets, i.e., an annotated pixel region " + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "inline_equation", + "content": "R^L" + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": " and an unannotated pixel region " + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "inline_equation", + "content": "R^{U}" + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": ". The unannotated region " + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "inline_equation", + "content": "R^{U}" + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": " contains unannotated instances and background. Different from semi-supervised learning, our goal is to train a model to predict the accurate affinity map by leveraging both a few annotated instances in the annotated region " + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "inline_equation", + "content": "R^{L}" + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": " and the unannotated region " + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "inline_equation", + "content": "R^{U}" + }, + { + "bbox": [ + 304, + 352, + 545, + 448 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "content": "Before introducing our method, we clarify the definition of affinity. The affinity map " + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "inline_equation", + "content": "A = [a_{1}, a_{2}, \\ldots, a_{N}] \\in \\mathbb{R}^{N \\times H \\times W}" + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "content": " describes whether the current pixel and adjacent pixels belong to the same instances or not, where " + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "inline_equation", + "content": "a_{n}(n = 1, 2, \\ldots, N)" + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "content": " denotes the different adjacent relations between the current pixel and its " + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "content": " order adjacent pixel. Given the segmentation groundtruth " + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "content": ", a pixel affinity " + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "inline_equation", + "content": "a_{n,i} \\in a_{n}" + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "content": " pixel of the image " + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 449, + 546, + 555 + ], + "type": "text", + "content": " is formulated as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 364, + 555, + 545, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 555, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 364, + 555, + 545, + 587 + ], + "type": "interline_equation", + "content": "a _ {n, i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} y _ {i} \\neq y _ {i + n} \\\\ 1, & \\text {i f} y _ {i} = y _ {i + n}, \\end{array} \\right. \\tag {1}", + "image_path": "ac44fc6528ec5fb5a6efbad928dd953dd7167ab709f1ede6ac08f0197d9c2b8f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "inline_equation", + "content": "y_{i + n}" + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "text", + "content": " are the instance segmentation IDs of paired pixels " + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "inline_equation", + "content": "i + n" + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "text", + "content": ". 1 means that pixel " + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "inline_equation", + "content": "i + n" + }, + { + "bbox": [ + 304, + 594, + 547, + 629 + ], + "type": "text", + "content": " belong to one instance, while 0 means the opposite." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": "Considering the segmentation groundtruth with sparse instance-level annotations, we regard the unannotated region (including the background) as an identical instance ID. The generated affinity label is divided into annotated region " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "R_{a}^{L}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " and unannotated region " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "R_{a}^{U}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": ". If the pixel affinity " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "a_{n,i}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " is located in the annotated region " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "R_{a}^{L}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": ", at least one of the pixels " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "i + n" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " is located in the annotation region " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "R^{L}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21109" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "y_{i} \\in R^{L}" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "y_{i + n} \\in R^{L}" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": ". Therefore, the annotated affinity region " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "R_{a}^{L}" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": " is slightly larger than the annotated segmentation region " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "R^{L}" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 122, + 280, + 136 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 122, + 280, + 136 + ], + "spans": [ + { + "bbox": [ + 47, + 122, + 280, + 136 + ], + "type": "text", + "content": "4. Cross-Representation Affinity Consistency" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 144, + 288, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 288 + ], + "type": "text", + "content": "In this section, we introduce the proposed sparsely supervised biomedical instance segmentation framework. The input of our framework can be either 2D images or 3D volumes. Here we illustrate it using a 2D image example for easy visualization. As shown in Fig. 2, our framework consists of two main parts. The first part contains two parallel networks to build affinity perturbation by predicting different representations: IAM and EAM (detailed in 4.1). The second part contains an affinity cross-supervision mechanism by a pseudo-label noise filtering scheme to select the highly confident region of the two affinity maps to supervise each other for consistency learning (detailed in 4.2)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 298, + 169, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 298, + 169, + 311 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 169, + 311 + ], + "type": "text", + "content": "4.1. Affinity Perturbation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "type": "text", + "content": "Unlike the common perturbation consistency strategy, we build the perturbation between two affinity representations predicted by two parallel networks. Following the existing affinity learning methods [11, 31], we adopt a network " + }, + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "type": "inline_equation", + "content": "f(\\theta_1)" + }, + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "type": "text", + "content": " to directly predict an implicit affinity map " + }, + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "type": "inline_equation", + "content": "\\hat{A}^1 = [\\hat{a}_1^1, \\hat{a}_2^1, \\dots, \\hat{a}_N^1]" + }, + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "type": "text", + "content": ". For accurate pixel affinities, the network " + }, + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "type": "inline_equation", + "content": "f(\\theta_1)" + }, + { + "bbox": [ + 46, + 318, + 287, + 411 + ], + "type": "text", + "content": " focuses on the structure information of instance boundaries." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": "In contrast to implicit learning, explicitly modeled affinity has been widely studied [22, 14] by calculating the pairwise relationships between pixel embeddings. Given the limited number of instances, we only impose local constraints on the adjacent instances instead of constraining all instances by a discriminative loss [9]. We adopt a network " + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "inline_equation", + "content": "f(\\theta_2)" + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": " to predict an embedding map " + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "inline_equation", + "content": "E \\in \\mathbb{R}^{D \\times H \\times W}" + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": " is the number of channels of the last layer of the network. Each pixel " + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": " of the image " + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": " is mapped into a pixel embedding vector " + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "inline_equation", + "content": "e_i \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": ", which is a D-dimensional feature representation. We then adopt a cosine distance to calculate the relationship between pixel embeddings and converted the embedding map into an explicit affinity map " + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\hat{A}^2 = [\\hat{a}_1^2, \\hat{a}_2^2, \\dots, \\hat{a}_N^2]" + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": ". The transformation from a paired of pixel embeddings to a pixel affinity " + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\hat{a}_{n,i}^2" + }, + { + "bbox": [ + 46, + 415, + 287, + 595 + ], + "type": "text", + "content": " is formulated as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 119, + 606, + 287, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 606, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 119, + 606, + 287, + 635 + ], + "type": "interline_equation", + "content": "\\hat {a} _ {n, i} ^ {2} = \\frac {e _ {i} ^ {T} e _ {i + n}}{\\| e _ {i} \\| _ {2} \\| e _ {i + n} \\| _ {2}}. \\tag {2}", + "image_path": "fa4da93e7fc2ca5353cb0ca3c80c5d1963ca6e271140549021154730be9d9f11.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 645, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 645, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 645, + 287, + 681 + ], + "type": "text", + "content": "The network " + }, + { + "bbox": [ + 46, + 645, + 287, + 681 + ], + "type": "inline_equation", + "content": "f(\\theta_2)" + }, + { + "bbox": [ + 46, + 645, + 287, + 681 + ], + "type": "text", + "content": " pays more attention to extracting the semantic instance information to discriminate pixels belonging to different instances in the feature space." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": "We adopt the MSE loss to supervise both " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "f(\\theta_1)" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "f(\\theta_2)" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": " in the annotated region " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "R_a^L" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": " of the affinity label " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 106, + 556, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 106, + 556, + 156 + ], + "spans": [ + { + "bbox": [ + 306, + 106, + 556, + 156 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {s} = L _ {s 1} + L _ {s 2} \\\\ = \\frac {1}{\\left| R _ {a} ^ {L} \\right|} \\sum_ {i \\in R _ {a} ^ {L}} \\sum_ {n = 1} ^ {N} \\left(\\left\\| \\hat {a} _ {n, i} ^ {1} - a _ {n, i} \\right\\| _ {2} + \\left\\| \\hat {a} _ {n, i} ^ {2} - a _ {n, i} \\right\\| _ {2}\\right), \\tag {3} \\\\ \\end{array}", + "image_path": "b7324a1f44e2faae012c8fc8d39f55546402dadbc92862f1a83c2ff211651352.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "inline_equation", + "content": "L_{s1}" + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "inline_equation", + "content": "L_{s2}" + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "text", + "content": " represent the loss functions for " + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "inline_equation", + "content": "f(\\theta_1)" + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "inline_equation", + "content": "f(\\theta_2)" + }, + { + "bbox": [ + 305, + 156, + 545, + 180 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 188, + 452, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 188, + 452, + 201 + ], + "spans": [ + { + "bbox": [ + 305, + 188, + 452, + 201 + ], + "type": "text", + "content": "4.2. Affinity Cross-Supervision" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "content": "In order to combine the advantages of the two kinds of affinity modeling, we propose an affinity cross-supervision mechanism to enforce the consistency between the IAM and the EAM. Since the two affinity maps may suffer from prediction errors during the initial training phase, we propose a pseudo-label noise filtering scheme by integrating two entropy-based decision strategies, i.e., adaptive threshold and prediction by a CPSN, to select highly confident pixel affinities to avoid the collapse of the consistency learning. For a pixel affinity " + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "inline_equation", + "content": "a_{n,i}" + }, + { + "bbox": [ + 304, + 207, + 545, + 327 + ], + "type": "text", + "content": ", its entropy is computed by" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 314, + 336, + 545, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 336, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 314, + 336, + 545, + 350 + ], + "type": "interline_equation", + "content": "h _ {n, i} = - a _ {n, i} \\log \\left(a _ {n, i}\\right) - (1 - a _ {n, i}) \\log \\left(1 - a _ {n, i}\\right). \\tag {4}", + "image_path": "17212ecf011f6e8d8d686c09ac181df7568bc20044334841ceedfacff23f222b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 359, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 359, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 359, + 545, + 392 + ], + "type": "text", + "content": "Adaptive threshold. As a heuristic strategy, we can determine whether the pixel affinity is confident by the following indicator:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 365, + 393, + 545, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 393, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 365, + 393, + 545, + 425 + ], + "type": "interline_equation", + "content": "\\delta_ {n, i} ^ {\\text {t h r e s}} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} h _ {n, i} < \\gamma_ {t} \\\\ 0, & \\text {o t h e r s ,} \\end{array} \\right. \\tag {5}", + "image_path": "adcbdbbe8b57a794818c6b7bdd2ca4054ba2ba7a993b2956413de6d90ba5b0d1.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "text", + "content": " refers to the entropy threshold at the " + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "inline_equation", + "content": "t^{th}" + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "text", + "content": " training iteration, which is the quantile of " + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "inline_equation", + "content": "h_{n,i}" + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "text", + "content": " to limit unreliable pixels with top " + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 430, + 545, + 490 + ], + "type": "text", + "content": " entropy. 1 means the pixel affinity is confident with low entropy, while 0 means the opposite." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 491, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 525 + ], + "type": "text", + "content": "Since the confident pixels gradually increase during the training procedure, " + }, + { + "bbox": [ + 304, + 491, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 491, + 545, + 525 + ], + "type": "text", + "content": " is dynamically adjusted by a power function:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 381, + 526, + 545, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 526, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 381, + 526, + 545, + 540 + ], + "type": "interline_equation", + "content": "\\alpha_ {t} = \\alpha_ {0} (1 - t / T) ^ {p}, \\tag {6}", + "image_path": "8293273b68ee59fccbcb866e13f4e348019ade06a02360c422b00e53cc28bcf6.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\alpha_0" + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": " is the initial quantile and is set to " + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": " is the power and is set as 1.5, " + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": " is the current training iteration, and " + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 545, + 545, + 581 + ], + "type": "text", + "content": " is total iterations." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Confidence pixel selection network. Inspired by approaches that address pseudo label errors using auxiliary networks [35, 21], we employ a binary-classification network called CPSN to identify highly confident pixels, which is trained only using the annotated regions of the groundtruth error map, as shown in Fig. 2 (d). Specifically, we sample five segmentation models under different training iterations of " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "f(\\theta_{1})" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "f(\\theta_{2})" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " respectively, and add a certain rate of dropout to these models. We then use the prediction from these models to simulate various segmentation errors. Using this kind of simulation data, we train" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": "1We call it implicit affinity map to distinguish from the one explicitly calculated from the embedding map below." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21110" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "content": "a robust CPSN to locate errors and generate highly confident pixels. We provide training details (including the loss " + }, + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "L_{CPSN}" + }, + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "content": ") in the supplementary material." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "text", + "content": "Given the input image " + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "text", + "content": ", affinity map " + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "text", + "content": " and affinity entropy map " + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "text", + "content": ", the CPSN can predict a binary error map " + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "inline_equation", + "content": "B \\in \\mathbb{R}^{N \\times H \\times W}" + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "text", + "content": " with the same size as " + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 108, + 287, + 144 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 111, + 150, + 287, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 150, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 111, + 150, + 287, + 163 + ], + "type": "interline_equation", + "content": "B = \\operatorname {C P S N} (I \\oplus A \\oplus H), \\tag {7}", + "image_path": "42c62b41de3bb8748e11060a04d40b376b52a2eca0da1d44cd2e46932ea95f24.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 170, + 209, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 170, + 209, + 181 + ], + "spans": [ + { + "bbox": [ + 47, + 170, + 209, + 181 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 170, + 209, + 181 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 47, + 170, + 209, + 181 + ], + "type": "text", + "content": " is the concatenation operation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "content": "We then determine whether the pixel affinity is confident by the following indicator:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 129, + 210, + 287, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 210, + 287, + 225 + ], + "spans": [ + { + "bbox": [ + 129, + 210, + 287, + 225 + ], + "type": "interline_equation", + "content": "\\delta_ {n, i} ^ {c p s n} = 1 - b _ {n, i}, \\tag {8}", + "image_path": "c2d53053820c1e5fd31849200997c9ffb6d4dc8acca82ccd9e870f1937c37fec.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 231, + 264, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 231, + 264, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 231, + 264, + 243 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 231, + 264, + 243 + ], + "type": "inline_equation", + "content": "b_{n,i} \\in B" + }, + { + "bbox": [ + 47, + 231, + 264, + 243 + ], + "type": "text", + "content": " is the pixel-level prediction of CPSN." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "text", + "content": "Pseudo-label noise filtering. We integrate the above two decision strategies to obtain more robust highly confident pixels, which is described by " + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\delta_{n,i} = \\delta_{n,i}^{thres}\\delta_{n,i}^{cpsn}" + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "text", + "content": ". After obtaining the confident pixels of the IAM (indicated by " + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\delta_{n,i}^{1}" + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "text", + "content": ") and the EAM (indicated by " + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\delta_{n,i}^{2}" + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "text", + "content": "), we utilize their confident pixels on the unannotated affinity region " + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "inline_equation", + "content": "R_{a}^{U}" + }, + { + "bbox": [ + 46, + 243, + 287, + 331 + ], + "type": "text", + "content": " to cross-supervise each other. The consistency loss is formulated as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 337, + 287, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 337, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 61, + 337, + 287, + 393 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {c} = L _ {c 1} + L _ {c 2} \\\\ = \\frac {1}{\\left| R _ {a} ^ {U} \\right|} \\sum_ {i \\in R _ {a} ^ {U}} \\sum_ {n = 1} ^ {N} \\left(\\left\\| \\hat {a} _ {n, i} ^ {1} - \\hat {a} _ {n, i} ^ {2} \\right\\| _ {2} \\delta_ {n, i} ^ {2} \\right. \\tag {9} \\\\ + \\left\\| \\hat {a} _ {n, i} ^ {2} - \\hat {a} _ {n, i} ^ {1} \\right\\| _ {2} \\delta_ {n, i} ^ {1}), \\\\ \\end{array}", + "image_path": "fb75670cb208418950b394b5a6b542ec4d2d4948c7fa41e002c4a956b274fb50.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "inline_equation", + "content": "L_{c1}" + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "inline_equation", + "content": "L_{c2}" + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "text", + "content": " represent the consistency loss functions for " + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "inline_equation", + "content": "f(\\theta_1)" + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "inline_equation", + "content": "f(\\theta_2)" + }, + { + "bbox": [ + 47, + 398, + 287, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 428, + 170, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 428, + 170, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 428, + 170, + 441 + ], + "type": "text", + "content": "4.3. Overall Optimization" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 447, + 287, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 287, + 481 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 287, + 481 + ], + "type": "text", + "content": "The overall objection function is the combination of losses on the annotated region and the unannotated region, which terms" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 134, + 483, + 287, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 483, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 134, + 483, + 287, + 495 + ], + "type": "interline_equation", + "content": "L = L _ {s} + \\lambda L _ {c}, \\tag {10}", + "image_path": "1d9d57697d6892a4a2f02d13ad15a126554f81bb567b401022f13f99091ab9f8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 498, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 498, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 498, + 287, + 521 + ], + "type": "text", + "content": " is the trade-off weight and is set to make the two loss value ranges comparable." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 522, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 643 + ], + "type": "text", + "content": "Following [14], we adopt the network " + }, + { + "bbox": [ + 46, + 522, + 287, + 643 + ], + "type": "inline_equation", + "content": "f(\\theta_2)" + }, + { + "bbox": [ + 46, + 522, + 287, + 643 + ], + "type": "text", + "content": " to predict an explicit affinity map in the inference stage. The affinity map is converted into final instance segmentation results by different post-processing algorithms. The 3D results and 2D results are generated by Waterz [11] (50% quantile and 0.5 threshold) and Mutex [45] post-processing algorithms, respectively. Since affinities calculated by these two different normalization schemes (sigmoid vs cosine) belong to different intervals, we use a RELU function to map the output value into [0, 1], for Waterz post-processing algorithm." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 128, + 664 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 671, + 168, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 168, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 168, + 682 + ], + "type": "text", + "content": "5.1. Datasets and Metrics" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "We conduct evaluations on four representative biomedical datasets with corresponding commonly used metrics." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "AC3. The AC3 dataset is a popular electron microscopy (EM) neuron dataset, imaged from the mouse somatosensory cortex at " + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 29" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": " nm resolution. It is a subset of the Kasthuri [16] dataset, and contains 256 volumetric images (" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "). We adopt the top 100 sections as the labeled set and sparsely select different numbers of neuron instances as the annotations. At the same time, the bottom 50 sections are adopted for evaluation. We adopt two widely used metrics in the field of EM image segmentation to quantitatively evaluate the result, i.e., Variation of Information (VOI) [34] and Adapted Rand Error (ARAND) [39]. The VOI is defined as a sum of another two metrics " + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "VOI_{split}" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "VOI_{merge}" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": " which indicate the split and merge errors, respectively. Note that smaller values of these metrics indicate better performance." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 251, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 395 + ], + "type": "text", + "content": "CREMI-C. The CREMI dataset is from the CREMI challenge [8] for neuron segmentation in EM volumes. It is composed of three volumetric datasets (CREMI-A, CREMI-B, and CREMI-C) imaged from the adult drosophila brain at " + }, + { + "bbox": [ + 304, + 251, + 545, + 395 + ], + "type": "inline_equation", + "content": "4 \\times 4 \\times 40" + }, + { + "bbox": [ + 304, + 251, + 545, + 395 + ], + "type": "text", + "content": " nm resolution. Each of the three datasets contains 125 images. Given that the neurites in CREMI-A and CREMI-C are mostly homogeneous in morphology, we evaluate our method on the CREMI-C dataset, which contains more challenging neuron types. We adopt the top 75 sections as the labeled set and the bottom 50 sections for evaluation. We adopt the same metrics used for the AC3 to evaluate the results on the CREMI-C dataset." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 396, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 492 + ], + "type": "text", + "content": "CVPPP. The A1 sequence of the CVPPP [36] dataset contains leaves with complex shapes and severe occlusions, which is widely used to evaluate biomedical instance segmentation. We randomly sample 108 images for training and 20 images for testing, where each image is with a size of " + }, + { + "bbox": [ + 304, + 396, + 545, + 492 + ], + "type": "inline_equation", + "content": "530 \\times 500" + }, + { + "bbox": [ + 304, + 396, + 545, + 492 + ], + "type": "text", + "content": ". We adopt the Symmetric Best Dice (SBD) and the absolute Difference in Counting " + }, + { + "bbox": [ + 304, + 396, + 545, + 492 + ], + "type": "inline_equation", + "content": "(|DiC|)" + }, + { + "bbox": [ + 304, + 396, + 545, + 492 + ], + "type": "text", + "content": " metrics [36] to evaluate the quantitative result." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 493, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 601 + ], + "type": "text", + "content": "BBBC039V1. The BBBC039V1 dataset [32] contains 200 fluorescence microscopy images with a resolution of " + }, + { + "bbox": [ + 304, + 493, + 545, + 601 + ], + "type": "inline_equation", + "content": "696 \\times 520" + }, + { + "bbox": [ + 304, + 493, + 545, + 601 + ], + "type": "text", + "content": " pixels. The dataset focuses on the U2OS cells with various shape and density. Following the official data split, we use 100 images for training, 50 for validation, and the rest 50 for testing. We adopt four metrics for cell segmentation for quantitative evaluation, i.e., Aggregated Jaccard Index (AJI) [39], object-level F1 score (F1) [4], Panoptic Quality (PQ) [19], and pixel-level Dice score (Dice)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 610, + 438, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 438, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 438, + 623 + ], + "type": "text", + "content": "5.2. Implementation Details" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "We adopt two different backbone networks, i.e., 3D U-Net [23] and 2D Residual U-Net for the 3D volumetric datasets (AC3, CREMI-C) and 2D datasets (CVPPP, BBBC039V1), respectively. Both the network " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "f(\\theta_{1})" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "f(\\theta_{2})" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " are based on the same backbone network but different in the last convolution layer. We train these networks using Adam optimizer [18] with " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ", a" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21111" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 71, + 535, + 251 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 535, + 251 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 535, + 251 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 535, + 251 + ], + "type": "table", + "html": "
MethodsAC3CREMI-C
VOISplit ↓VOIMerge ↓VOI ↓ARAND ↓VOISplit ↓VOIMerge ↓VOI ↓ARAND ↓
Semi.Vanilla0.4225.4035.8250.9110.9292.1173.0460.580
PseudoL-hard [41]0.0895.9556.0440.9200.8631.4622.3250.311
PseudoL-soft [50]0.8513.7444.5950.8530.9500.8941.8440.230
MT [42]0.8632.0582.9210.5580.9161.0271.9430.211
π-model [25]0.8471.8672.7140.5620.9850.9181.9030.227
UA-MT [49]0.7201.8602.5800.4260.9780.8631.8410.227
SASSNet [24]1.1601.1802.3400.3240.9350.8141.7490.193
SSNS [13]0.7020.5271.2290.1200.9340.7751.7090.175
Sparse.SPOCO [46]1.6081.3492.9570.2361.8320.8962.7280.303
Vanilla0.9300.2371.1670.1111.6130.4512.0640.187
MT* [42]0.6990.4321.1320.0921.3750.5591.9340.173
UA-MT* [49]0.7850.2511.0360.0821.5020.3331.8350.155
CCT* [37]0.8590.2381.0970.0881.4250.4631.8880.173
CPS* [7]0.7180.2480.9660.0671.3840.3981.7820.158
Ours0.6420.2600.9030.0641.0320.5871.6200.153
", + "image_path": "9c3cf3631cf107ad95a3c3f96fb7a10b30c31483bedbc9d773855f868e2456db.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 258, + 545, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 545, + 314 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of segmentation results on AC3 and CREMI-C datasets using 5 densely annotated sections for semi-supervision and randomly annotated instances for sparse instance-level supervision. The number of annotated voxels is the same for the two settings. Vanilla refers to training models only using available groundtruth. The top right corner \\* indicates these methods are originally proposed in the semi-supervision but adapted into the sparse instance-level supervision. Note that we adopt the same backbone ResUnet [23] in all methods for a fair comparison. The best results and the second-best results are highlighted in bold and underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 47, + 322, + 545, + 539 + ], + "blocks": [ + { + "bbox": [ + 47, + 322, + 545, + 539 + ], + "lines": [ + { + "bbox": [ + 47, + 322, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 322, + 545, + 539 + ], + "type": "image", + "image_path": "8d1bdac39117ed7cb187248f6c823d05ed433d52e39556cad583628a4c7b15dc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 548, + 544, + 572 + ], + "lines": [ + { + "bbox": [ + 46, + 548, + 544, + 572 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 544, + 572 + ], + "type": "text", + "content": "Figure 3. 2D Visual comparison of different methods on AC3 and CREMI-C datasets. The first row and the second row of each dataset are the affinity map and the corresponding instance segmentation result. Red and blue boxes indicate merge and split errors, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 590, + 286, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 286, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 286, + 613 + ], + "type": "text", + "content": "learning rate of " + }, + { + "bbox": [ + 46, + 590, + 286, + 613 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 46, + 590, + 286, + 613 + ], + "type": "text", + "content": " , and a batch size of 2 on one NVIDIA TitanXP GPU for 200K iterations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 622, + 171, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 171, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 171, + 635 + ], + "type": "text", + "content": "5.3. Comparison Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 286, + 664 + ], + "type": "text", + "content": "The evaluation of our method is performed against three kinds of baselines:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 666, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 286, + 713 + ], + "type": "text", + "content": "(1) For the 3D volumetric datasets, the sparse instance-level supervision and the common semi-supervision contain different 3D structure information of instances in the axial direction. For a comprehensive evaluation, we compare" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 590, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 545, + 651 + ], + "type": "text", + "content": "our proposed sparsely supervised method with a number of existing semi-supervised methods that are widely used for 3D datasets, including: PseudoL-hard [41], PseudoL-soft [50], mean-teacher (MT) [42], " + }, + { + "bbox": [ + 304, + 590, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 590, + 545, + 651 + ], + "type": "text", + "content": "-model [25], UAMT [49], SASSNet [24] and SSNS [13]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "content": "(2) SPOCO [46] provides a baseline solution for the sparsely supervised segmentation task. We use the official code and configurations to reproduce the results on 2D datasets (CVPPP and BBBC039V1), and adapt this method to 3D datasets (AC3 and CREMI-C)." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21112" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 257 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 257 + ], + "type": "image", + "image_path": "4a06ad5c7604e4b54db385d891b3cde031e5af6048fb2305fd608789f705946c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 266, + 546, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 546, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 546, + 289 + ], + "type": "text", + "content": "Figure 4. 3D Visual comparison of different methods on AC3 and CREMI-C datasets. Red and blue arrows indicate split and merge errors, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 308, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 369 + ], + "type": "text", + "content": "(3) We adapt a variety of advanced semi-supervised methods to the sparsely supervised segmentation task, including mean-teacher (MT) [42], uncertainty-aware mean teacher model(UA-MT) [49], cross-consistency training (CCT) [37] and cross pseudo supervision (CPS) [7]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 379, + 177, + 390 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 379, + 177, + 390 + ], + "spans": [ + { + "bbox": [ + 47, + 379, + 177, + 390 + ], + "type": "text", + "content": "5.4. Results on 3D Datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 398, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 398, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 287, + 493 + ], + "type": "text", + "content": "We list an extensive quantitative comparison on the AC3 and the CREMI-C datasets in Table 1. We conduct the semi-supervised experiments with 5 densely annotated sections, and the sparsely supervised experiments with 23 and 33 randomly annotated instances for AC3 and CREMI-C datasets respectively. The number of annotated voxels is the same for the two settings. From the results in Table 1, we can observe that:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 495, + 287, + 700 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 46, + 495, + 287, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 566 + ], + "type": "text", + "content": "(1) With the same number of annotated voxels, sparsely supervised methods perform better than corresponding semi-supervised methods by a large margin. Specifically, our results outperform the state-of-the-art semi-supervised results from SSNS [13] by " + }, + { + "bbox": [ + 46, + 495, + 287, + 566 + ], + "type": "inline_equation", + "content": "26.4\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 566 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 495, + 287, + 566 + ], + "type": "inline_equation", + "content": "5.2\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 566 + ], + "type": "text", + "content": " for the VOI metric on the AC3 and CREMI-C datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 568, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 615 + ], + "type": "text", + "content": "(2) For the EM neuron segmentation datasets, the sparse instance annotations are not conducive to the training of SPOCO [46] based on metric learning. Therefore, SPOCO [46] does not perform well on these two datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "type": "text", + "content": "(3) Our method achieves better performance than other adapted methods in the sparse instance-level supervision setting. Specifically, We achieve " + }, + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "type": "inline_equation", + "content": "6.3\\%" + }, + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "type": "inline_equation", + "content": "9.2\\%" + }, + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "type": "text", + "content": " improvement from the key VOI metric on the AC3 and CREMI-C datasets, compared with the second-best method. It demonstrates the superiority of the proposed affinity consistency regularization." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "We show 2D and 3D visual comparison results in Fig. 3" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 306, + 541, + 441 + ], + "blocks": [ + { + "bbox": [ + 310, + 306, + 541, + 441 + ], + "lines": [ + { + "bbox": [ + 310, + 306, + 541, + 441 + ], + "spans": [ + { + "bbox": [ + 310, + 306, + 541, + 441 + ], + "type": "image", + "image_path": "43e9583f5594c6a42e6fc9dd315d237be1d0b1f6ca051c9a81bda045de44ae20.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 449, + 545, + 482 + ], + "lines": [ + { + "bbox": [ + 305, + 449, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 545, + 482 + ], + "type": "text", + "content": "Figure 5. Comparison of different methods on the AC3 dataset under different annotation amounts converted into the number of sections for counting, where each section contains " + }, + { + "bbox": [ + 305, + 449, + 545, + 482 + ], + "type": "inline_equation", + "content": "1 \\times 10^{6}" + }, + { + "bbox": [ + 305, + 449, + 545, + 482 + ], + "type": "text", + "content": " pixels." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 507, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 545, + 590 + ], + "type": "text", + "content": "and Fig. 4, respectively. As can be seen, our proposed method predicts the affinity map with higher fidelity than other methods, which significantly reduces the split and merge errors. We also provide 3D visual comparison results in the supplementary material. As can be seen, our results contain fewer merge and split errors, and maintain the accuracy of neuron structures, compared with other methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "We further compare different methods on the AC3 dataset under different numbers of annotated voxels. We convert the number of voxels to the number of sections for counting, where each section contains about " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{6}" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " voxels. The results are shown in Fig. 5. As more annotations are available, the performance gap between different methods gradually narrows, but the superiority of our method can still be observed. Especially, the state-of-the-art semi-supervised method SSNS performs worse than sparsely supervised methods under very limited annotations, due to the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21113" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 54, + 70, + 281, + 188 + ], + "blocks": [ + { + "bbox": [ + 54, + 70, + 281, + 188 + ], + "lines": [ + { + "bbox": [ + 54, + 70, + 281, + 188 + ], + "spans": [ + { + "bbox": [ + 54, + 70, + 281, + 188 + ], + "type": "table", + "html": "
Methods10% instances40% instances
SBD ↑|DiC| ↓SBD ↑|DiC| ↓
CPS [7] (semi)83.21.887.61.1
SPOCO [46]70.63.082.12.0
Vanilla69.86.078.01.9
MT* [42]78.51.484.31.3
UA-MT* [49]79.61.484.51.1
CCT* [37]78.81.983.91.6
CPS* [7]80.71.885.51.1
Ours83.61.186.60.8
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Visual comparison of different methods on the CVPPP dataset with " + }, + { + "bbox": [ + 47, + 360, + 287, + 392 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 47, + 360, + 287, + 392 + ], + "type": "text", + "content": " instances. The segmentation errors are highlighted by white boxes." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 109, + 290, + 166, + 340 + ], + "blocks": [ + { + "bbox": [ + 109, + 290, + 166, + 340 + ], + "lines": [ + { + "bbox": [ + 109, + 290, + 166, + 340 + ], + "spans": [ + { + "bbox": [ + 109, + 290, + 166, + 340 + ], + "type": "image", + "image_path": "21b1b5ea8e9206226ab3479924ac7ac85e0fe086f2d0cd21e73a359a7ec14265.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 130, + 340, + 150, + 348 + ], + "lines": [ + { + "bbox": [ + 130, + 340, + 150, + 348 + ], + "spans": [ + { + "bbox": [ + 130, + 340, + 150, + 348 + ], + "type": "text", + "content": "CPS*" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 168, + 290, + 225, + 340 + ], + "blocks": [ + { + "bbox": [ + 168, + 290, + 225, + 340 + ], + "lines": [ + { + "bbox": [ + 168, + 290, + 225, + 340 + ], + "spans": [ + { + "bbox": [ + 168, + 290, + 225, + 340 + ], + "type": "image", + "image_path": "ecf26c81624f0714b2771309fdc6b8e56cb389392ae8f928d97fd793bacb47cf.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 189, + 340, + 208, + 348 + ], + "lines": [ + { + "bbox": [ + 189, + 340, + 208, + 348 + ], + "spans": [ + { + "bbox": [ + 189, + 340, + 208, + 348 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 228, + 290, + 285, + 340 + ], + "blocks": [ + { + "bbox": [ + 228, + 290, + 285, + 340 + ], + "lines": [ + { + "bbox": [ + 228, + 290, + 285, + 340 + ], + "spans": [ + { + "bbox": [ + 228, + 290, + 285, + 340 + ], + "type": "image", + "image_path": "dbda1af37a3b95a4387b06ef7740ddcd4ff3f3aaffea90435f812e7ca1cb1c00.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 235, + 340, + 278, + 348 + ], + "lines": [ + { + "bbox": [ + 235, + 340, + 278, + 348 + ], + "spans": [ + { + "bbox": [ + 235, + 340, + 278, + 348 + ], + "type": "text", + "content": "Groundtruth" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 412, + 248, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 412, + 248, + 424 + ], + "spans": [ + { + "bbox": [ + 47, + 412, + 248, + 424 + ], + "type": "text", + "content": "incomplete 3D structure information of instances." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 431, + 176, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 176, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 176, + 443 + ], + "type": "text", + "content": "5.5. Results on 2D Datasets" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "content": "We further validate our method on two 2D datasets, i.e., CVPPP and BBBC039V1, and their quantitative results are shown in Table 2 and Table 3, respectively. Compared with other adapted methods in the sparse instance-level supervision setting, our method achieves the best performance on the CVPPP dataset with " + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "content": " annotated instances, and the BBBC039V1 dataset with " + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "content": " annotated instances. Visual results on these two datasets also illustrate the superior performance of our method with fewer segmentation errors, as shown in Fig. 6 and Fig. 7." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Although the sparse instance-level supervision and the common semi-supervision have no difference in the instance structure for 2D datasets, we also evaluate the semi-supervised setting (with the same annotated pixels) on these two datasets. Our proposed method performs better than the state-of-the-art semi-supervised method CPS [7], when the annotation amount is very limited. Meanwhile, our method significantly outperforms the existing sparely supervised method SPOCO in all experiments. As more annotation amount is available, the semi-supervised method has a better performance. Therefore, the sparse instance-level supervision is still a meaningful complement to the com" + } + ] + } + ], + "index": 22 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 263 + ], + "blocks": [ + { + "bbox": [ + 47, + 196, + 286, + 218 + ], + "lines": [ + { + "bbox": [ + 47, + 196, + 286, + 218 + ], + "spans": [ + { + "bbox": [ + 47, + 196, + 286, + 218 + ], + "type": "text", + "content": "Table 2. Quantitative comparison results on the CVPPP dataset. Results in the first row are based on the semi-supervision setting." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 70, + 545, + 263 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 263 + ], + "type": "table", + "html": "
MethodsAJI ↑Dice ↑F1 ↑PQ ↑
1% instancesCPS [7] (semi)0.81200.90330.95950.8168
SPOCO [46]0.68960.84780.84920.6933
Vanilla0.56310.64110.75700.4890
MT* [42]0.77160.82600.90180.7533
UA-MT* [49]0.80650.87380.94390.7928
CCT* [37]0.81130.91360.92950.7830
CPS* [7]0.83230.91850.94440.8153
Ours0.83030.93380.94420.8222
10% instancesCPS [7] (semi)0.83930.91890.95980.8437
SPOCO [46]0.74880.87460.92630.7503
Vanilla0.59850.71770.77090.5652
MT* [42]0.84160.91670.93380.8283
UA-MT* [49]0.84040.91180.93800.8314
CCT* [37]0.83090.92790.93270.7975
CPS* [7]0.84630.93660.94080.8174
Ours0.85450.94690.94500.8343
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Ablation Studies" + } + ] + } + ], + "index": 43 + }, + { + "type": "table", + "bbox": [ + 307, + 512, + 545, + 553 + ], + "blocks": [ + { + "bbox": [ + 306, + 271, + 533, + 281 + ], + "lines": [ + { + "bbox": [ + 306, + 271, + 533, + 281 + ], + "spans": [ + { + "bbox": [ + 306, + 271, + 533, + 281 + ], + "type": "text", + "content": "Table 3. Quantitative comparison on the BBBC039V1 dataset." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 512, + 545, + 553 + ], + "lines": [ + { + "bbox": [ + 307, + 512, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 307, + 512, + 545, + 553 + ], + "type": "table", + "html": "
Method15102050100
Vanilla2.2891.1670.9820.8710.7790.726
Ours1.2710.9030.8160.8070.7380.717
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f(θ1)f(θ2)cross-supervisionVOI ↓ARAND ↓
ThresholdCPSN
IAMIAM✓✓0.9260.074
EAMEAM✓✓0.9270.068
IAMEAMXX0.9160.068
IAMEAM✓X0.9060.068
IAMEAMX✓0.9090.067
IAMEAM✓✓0.9030.065
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MethodVOISplit ↓VOIMerge ↓VOI ↓ARAND ↓
Ours-f(θ1)0.7090.1980.9070.071
Ours-f(θ2)0.6870.2180.9030.065
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α00.010.050.1
VOI↓/ ARAND ↓0.933 / 0.0750.903 / 0.0650.924 / 0.069
Dropout rate00.10.3
VOI↓/ ARAND ↓0.920 / 0.0660.903 / 0.0650.923 / 0.067
λ0.010.11
VOI↓/ ARAND ↓0.914 / 0.0660.903 / 0.0651.258 / 0.106
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The performance gap narrows as more annotations are available." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 498, + 286, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 286, + 674 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 286, + 674 + ], + "type": "text", + "content": "Affinity consistency regularization. As shown in Table 5, we conduct an ablation study on the proposed affinity consistency learning scheme. We compare different combinations of affinity modeling for the two networks " + }, + { + "bbox": [ + 46, + 498, + 286, + 674 + ], + "type": "inline_equation", + "content": "f(\\theta_{1})" + }, + { + "bbox": [ + 46, + 498, + 286, + 674 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 286, + 674 + ], + "type": "inline_equation", + "content": "f(\\theta_{2})" + }, + { + "bbox": [ + 46, + 498, + 286, + 674 + ], + "type": "text", + "content": " by directly enforcing their consistency. It can be observed that the combination of IAM and EAM achieves the best performance. Furthermore, we demonstrate the effectiveness of pseudo-label noise filtering with different decision strategies. Both strategies have been shown to improve performance, and their integration can obtain more robust highly confident regions and achieves the best performance. Moreover, We have compared our method with an equivalent implementation of [14] in Table 5, i.e., two network branches both use EAM. Our method achieves better performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "Affinity map used in the inference stage. The two affinity maps predicted by " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "f(\\theta_{1})" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "f(\\theta_{2})" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " have different performances, as shown in Table 6. The EAM predicted by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "inline_equation", + "content": "f(\\theta_2)" + }, + { + "bbox": [ + 305, + 72, + 544, + 95 + ], + "type": "text", + "content": " performs slightly better, so we adopt it in the inference stage." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "type": "text", + "content": "Ablation study on hyper-parameters. We conducted ablation experiments to evaluate the impact of key hyperparameters, of the proposed framework, as shown in Table 7. For the proposed pseudo-label noise filtering scheme, we test different values of hyper-parameters " + }, + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\alpha_0" + }, + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "type": "text", + "content": " for adaptive threshold and different dropout rates used in the CPSN training. Also, we provide the ablation study on different loss weights " + }, + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 205, + 378, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 378, + 216 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 378, + 216 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 224, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 380 + ], + "type": "text", + "content": "In this paper, we propose an effective sparsely supervised biomedical instance segmentation framework via learning cross-representation affinity consistency. The proposed framework builds the perturbation consistency between an implicit affinity map and an explicit affinity map with an affinity cross-supervision mechanism. We conduct extensive experiments on 3D volumetric datasets and 2D datasets to demonstrate the superiority of our proposed framework over the existing sparsely supervised method. 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In this paper, we thoroughly explore the characteristics of animation videos and leverage the rich priors in real-world animation data for a more practical animation VSR model. In particular, we propose a multi-scale Vector-Quantized Degradation model for animation video Super-Resolution (VQD-SR) to decompose the local details from global structures and transfer the degradation priors in real-world animation videos to a learned vector-quantized codebook for degradation modeling. A rich-content Real Animation Low-quality (RAL) video dataset is collected for extracting the priors. We further propose a data enhancement strategy for high-resolution (HR) training videos based on our observation that existing HR videos are mostly collected from the Web which contains conspicuous compression artifacts. The proposed strategy is valid to lift the upper bound of animation VSR performance, regardless of the specific VSR model. Experimental results demonstrate the superiority of the proposed VQD-SR over state-of-the-art methods, through extensive quantitative and qualitative evaluations of the latest animation video super-resolution benchmark. The code and pre-trained models can be downloaded at https://github.com/researchmm/VQD-SR.", + "bbox": [ + 75, + 340, + 473, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Animation video super-resolution (VSR) [35], which is a subdiscipline of video super-resolution (VSR) [1, 2, 3, 19, 28, 37], aims to restore high-resolution (HR) videos from their low-resolution (LR) counterparts in animation domain. As a special type of visual art, animation video shows great", + "bbox": [ + 75, + 779, + 468, + 854 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b648bb4b0a308669630b744b7072bd28b420f33c98a7502a1b7edcefda12053a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 308, + 888, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0c361d45be249385c7744bd7051eb36015d0647a1a62470b8130dc50bf462825.jpg", + "image_caption": [ + "Figure 1. A comparison between our proposed VQD-SR and other SOTA VSR methods in real scenario. As indicated by the red dotted circles, our VQD-SR could restore more appealing details by considering the degradation priors in real animation videos. (\\* denotes fine-tune on animation videos)." + ], + "image_footnote": [], + "bbox": [ + 501, + 457, + 630, + 556 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/29a534dcd8374b41053e293d9c453b983be018fe36a1cf107e7625467f6821f3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 457, + 759, + 556 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dc1a260162d5f9d5223932387f0723ceb9fddce29fc1b608b0662a81bbe78ffa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 457, + 887, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "entertainment, cultural, educational and commercial values. However, most of them available on the Web are in limited resolutions and have visually unappealing artifacts due to the passing ages, lossy compression and transmission. Dedicated to real applications, animation VSR is a blind SR [21, 32, 46, 40, 43] task which is more challenging than conventional VSR tasks [1, 2, 14, 19, 28, 36], because of the complicated and agnostic real-world degradations. Thus, practical VSR methods for improving real-world LR animation videos are in highly demanded.", + "bbox": [ + 496, + 671, + 890, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Blind SR model for open-domain has long been the focus. As it's hard to collect LR-HR pairs in real scenarios, recent learning-based approaches try to model the real-world degradations from HR to LR, thus generating pseudo LR-HR pairs to train SR models. These approaches can", + "bbox": [ + 496, + 824, + 890, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was done while Zixi Tuo was a research intern at Microsoft Research Asia.", + "bbox": [ + 76, + 862, + 468, + 886 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13179", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "be roughly divided into two categories, explicit modeling and implicit modeling, with regard to the degradation procedures. Explicit modeling [9, 20, 32, 46] methods try to combine basic degradation operators like noise, blur and rescaling to imitate the real-world degradation pipeline. Instead, implicit modeling methods employ a neural network, which is usually in the manner of generative adversarial networks (GAN) [7], as an alternative to the combination of basic degradation operators. However, these general degradation methods designed for open-domain videos are not quite suitable for the animation domain as they ignore the intrinsic characteristics of the data. Directly adopting existing degradation models for open-domain to animation VSR would lead to unpleasant results (as shown in Fig. 1 a), even though they are fine-tuned on the animation videos.", + "bbox": [ + 80, + 90, + 467, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specific to animation VSR, AnimeSR [35] moves one step further to propose a learnable basic operator (LBO) with an \"input-rescaling\" strategy that considers the data characteristics and demonstrates their advantages over open-domain VSR methods. However, the proposed \"input-rescaling\" strategy of constructing pseudo HR-LR pairs for the LBO training requires human annotations, which prevents their method from scaling up to modeling various real-world degradations. In AnimeSR [35], only three LBOs are trained with three human-annotated videos respectively, leading to unappealing results (as shown in Fig. 1 b). Thus, how to effectively leverage large-scale real-world animation videos based on their data characteristics is still an open problem.", + "bbox": [ + 80, + 321, + 467, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a multi-scale Vector-Quantized Degradation model for animation video Super-Resolution (VQD-SR), which leverages the data characteristics of animation videos. We observe that different from open-domain videos with complex textures and irregular illumination conditions, animation videos are roughly composed of basic visual patterns like smooth color patches and clear lines which can be easily captured with high fidelity by vector-quantization (VQ) [5, 25, 29]. Such data characteristics could also be used for encoding and transferring degradation priors from low-quality animation videos and results in a degradation codebook. Given any clean LR animation frame, the degraded LR counterpart can be easily obtained by looking up the pre-trained degradation codebook. Specifically, a novel multi-scale VQGAN for degradation modeling is proposed to learn and transfer real-world degradation priors from a large-scale Real Animation Low-quality (RAL) video dataset collected from the Web. To improve the generalization ability of VQD-SR, we propose a two-stage training pipeline and a stochastic top-k VQ strategy to match up with the multi-scale VQGAN, yielding visually appealing results (as shown in Fig. 1 c).", + "bbox": [ + 80, + 535, + 467, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To further lift the upper bound of existing animation VSR methods, we propose an HR-SR strategy to enhance", + "bbox": [ + 80, + 869, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the quality of HR training videos for more ideal ground truths. This is motivated by our observations that existing HR animation videos are mostly collected from the Web which contains conspicuous compression artifacts and such artifacts could be easily reduced by existing SR methods. Our contributions are summarized as follows:", + "bbox": [ + 503, + 90, + 888, + 180 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We collect a large-scale real LR animation dataset, and conduct a comprehensive study on real animation data to thoroughly explore the challenges and data characteristics in animation VSR task.", + "bbox": [ + 521, + 183, + 888, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose a novel multi-scale VQ degradation model to transfer real-world degradation priors for synthesizing pseudo LR-HR training pairs. We further propose an HR-SR data enhancement strategy to improve the performance of existing VSR methods for animation.", + "bbox": [ + 521, + 243, + 888, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments demonstrate the effectiveness of our proposed methods which significantly improve the recent SOTA animation VSR method in both quantitative and qualitative comparisons.", + "bbox": [ + 521, + 319, + 888, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 503, + 396, + 638, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Video Super-Resolution", + "text_level": 1, + "bbox": [ + 503, + 422, + 715, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent years have witnessed a prosperity in deep learning based VSR methods [2, 3, 14, 24, 28, 31, 38]. Different from single-image super-resolution (SISR), the auxiliary temporal information is available in VSR for the restoration of inner-frame features. Sliding-window structure [28, 31, 38, 42] and recurrent structure [1, 2, 6, 12, 14] are two common paradigms in VSR to utilize the interframe information. However, it also faces challenges while taking the advantages. The degradations could be more complicated in videos and may accumulate along the time sequence [3, 37], causing the performance drop in real-world scenarios.", + "bbox": [ + 503, + 446, + 888, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There have been several attempts in blind-SR field to deal with real-world degradations, which could be categorized into explicit and implicit modeling. Explicit methods model the degradation as the effects of objective operators (or kernels). Methods like [9, 47] assume these degradations to be simple combinations of blur, noise and down-sampling kernels, therefore conducting conditional restoration based on the prediction of kernel parameters. Operators like JPEG/FFmpeg [20] for lossy compression, sinc filter [32] for ringing artifacts and strategies like high-order modeling [32], random shuffling [46], are further investigated in latest studies to simulate the real degradation pipeline and expand the synthesis space. However, these methods merely depend on predefined operators, and ignore to utilize the information contained in real data, thus there's still a gap between the synthesis LR and real LR data. Implicit methods [21, 22, 34, 44] discard the objective degradation operators, but learn the distribution of real data,", + "bbox": [ + 503, + 628, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13180", + "bbox": [ + 480, + 946, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "therefore realize the degradation by converting the HR input to fit the real LR distribution. Yet, the learned distribution space is uncontrollable, thus the degradation network may easily project unseen out-of-distribution samples to unpredictable suboptimal space causing annoying artifacts.", + "bbox": [ + 75, + 90, + 472, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Animation Video Processing", + "text_level": 1, + "bbox": [ + 76, + 176, + 331, + 194 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Animation is a type of visual art that is represented in a nonrealistic artistic style. A diversity of animation processing technologies based on deep learning have been developed these years, such as animation style transfer [4, 13, 30], animation video colorization [18, 27, 45], animation video generation [11] and animation video interpolation [26]. AnimeSR [35] is a recent study for real-world animation VSR tasks, which develops LBO to expand the basic degradation operators. In this paper, we take a further step to explore the characteristics of animation videos, and make special designs in consideration of these characteristics to improve the performance of real-world animation VSR.", + "bbox": [ + 75, + 200, + 472, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Vector-Quantized Codebook", + "text_level": 1, + "bbox": [ + 76, + 407, + 331, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vector-quantized(VQ) codebook was first proposed in VQ-VAE [29] to learn the discrete representation for images in latent space. Later, a hierarchical VQ-VAE-2 [25] is further proposed. To improve the perceptual quality, a discriminator and perceptual loss were added in VQGAN [5]. Recently in VQFR [10], a VQ-based face restoration method was also proposed. Although initially designed to avoid the \"posterior collapse\" issue of VAE or tokenizer input images for a more effective transformer modeling, we discover that the idea of VQ is naturally suitable for representing animation video frames and the form of codebook is capable to internalize the real degradation priors.", + "bbox": [ + 75, + 431, + 472, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 628, + 210, + 646 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first discuss the characteristics of real animation videos and the challenges for animation VSR task in Sec. 3.1. Based on the observations in Sec. 3.1, we introduce the proposed real-world animation degradation model in Sec. 3.2. Finally, we illustrate our HR training data enhancement strategy in Sec. 3.3.", + "bbox": [ + 75, + 654, + 468, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Real-World Degradation in Animation Videos", + "text_level": 1, + "bbox": [ + 76, + 756, + 465, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To thoroughly understand the characteristics of animation videos and the challenges in animation VSR task, we collect a Real Animation Low-quality (RAL) video dataset. RAL contains over 10K LR frames extracted from 441 real-world low-quality animation videos. To the best of our knowledge, RAL is the largest real-world low-quality video dataset in the animation domain. Example frames are shown in Fig. 2 (statistics of RAL can be found in the", + "bbox": [ + 75, + 780, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/de9e663f028e943d78215689fcd4fb172eaa7dbe3dafa367cd87813363aa29ce.jpg", + "image_caption": [ + "Figure 2. Samples of RAL and typical degradation phenomena in real-world LR animation videos. RAL is a real-world animation video dataset contains over 10K LR frames. Intermittent edges, aliasing edges, ringing artifacts and rainbow effects are four typical degradation phenomena in real-world animation videos." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 893, + 233 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "supplementary). To construct such a dataset, we first download numerous earlier animation videos from multiple video sites such as YouTube and Bilibili. Then we manually select videos according to their resolutions, quality, contents and styles. To ensure the dataset contains rich animation structures and degradation priors, we adopt a simple scene filtering procedure to remove the frames which have subtle motions by evaluating their average absolute differences, thus reducing the redundancy.", + "bbox": [ + 496, + 339, + 890, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Animation videos are roughly composed of smooth color patches and clear lines, while the latter ones usually play an important role in portraying objects and expressing visual semantics. In contrast to the fact that degradation losses for open domain videos are mainly about high-frequency textures, degradations for animation videos mostly happen around the edges which are more sensitive according to the human perceptual. Such degradations usually act as intermittent edges, aliasing edges, ringing artifacts, and rainbow effects, as shown in Fig. 2. These observations of the proposed RAL dataset inspire us that the key challenge in animation VSR is to restore visually natural and clear edges.", + "bbox": [ + 496, + 476, + 892, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Degradation modeling has been the focus of many previous blind-SR works. Because of the obvious differences between animation and natural style videos, degradation methods designed for natural videos cannot properly handle degradations in animation videos. As a result, these methods suffer from amplified artifacts causing phenomena like perturbation edges, bleeding edges and inaccurate colorization along edges, even though they are fine-tuned on the animation videos (as shown in Fig. 1 a).", + "bbox": [ + 496, + 657, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Vector-Quantized Degradation Modeling", + "text_level": 1, + "bbox": [ + 500, + 801, + 849, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instead of imitating the real-world degradation pipeline by simply combining and adjusting some predefined basic operators [32, 46], we propose to explore the data intrinsic characteristics further and utilize degradation priors of real-world animation videos. As illustrated in Sec. 3.1,", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13181", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5fcf775f84a2a2f016fd0a7bef3f148f6cf4fd6558de1773bca2ba28085e46c2.jpg", + "image_caption": [ + "Figure 3. The overview of VQD-SR for training the animation VSR model. (a) Vector-quantized degradation model is a multi-scale VQGAN which transfers the real-world degradations from the learned VQ codebook to clean LR video frames to synthesize pseudo LR videos for VSR training, with the stochastic top-k VQ strategy. (b) HR-SR enhancement strategy eliminates the artifacts in HR animation training videos with an existing SR model to generate more ideal ground truths for supervising the VSR results." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 893, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "animation videos are roughly composed of smooth color patches and clear lines. Compared to open-domain videos, which contain complex textures and irregular illumination conditions, it is possible to encode such animation video frames into a codebook of finite basic visual patterns (i.e., color patches and lines). More importantly, any animation video frame can be further decoded with corresponding patterns with high fidelity. If such a process is restricted to the real LR domain (e.g., the proposed RAL dataset), the degradation priors of real animation videos will be encapsulated into the aforementioned codebook simultaneously and could be further used for synthesizing pseudo LR data for the VSR training.", + "bbox": [ + 75, + 405, + 472, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "VQGAN [5] is a reconstruction network composed of an encoder $E$ , a decoder $G$ and a vector-quantized codebook $Z$ . Motivated by the perceptually rich codebook, we resort to VQGAN [5], trained on the proposed RAL dataset with rich degradations of animation videos, to realize the decomposition of low-quality frames and encapsulate degradation priors into a learned codebook. When given a clean LR frame, the real-world degradation priors can be transferred by replacing the original clean patches with the corresponding degraded versions by looking up the learned degradation codebook. In this section, we first introduce our modified multi-scale VQGAN, then illustrate the two-stage training pipeline, and finally use the trained model to synthesize pseudo LR-HR pairs in diverse levels of degradations by a stochastic top-k vector-quantization strategy.", + "bbox": [ + 75, + 607, + 468, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-Scale VQGAN. As discussed in Sec. 3.1, the degradations in animation videos mostly happen around the edges, which are fine-grained local details. A degradation model should be capable of processing these local details while", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "keeping the global structures (e.g., colors and shapes) at the same time. However, these two goals are usually conflicted with each other under the scope of the original single-scale VQGAN [5], as these two kinds of components are entangled together. Disentangling local details from global structures is a requisite for degradation modeling with VQGAN.", + "bbox": [ + 496, + 405, + 890, + 497 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The multi-scale design has been widely explored in low-level vision [23, 39] and achieved great success, especially in the image restoration task. Inspired by this, we propose a multi-scale VQGAN which contains three parallel encoding branches. As shown in Fig. 3 a, these three branches share a shallow feature extraction module but have independent deeper encoding modules with different compression factors $f$ (we choose $f = \\{8,4,2\\}$ for the top, middle and bottom branches respectively). Benefiting from our multi-scale design, image information of different levels could be effectively disentangled and learned by each encoding branch in one VQ-GAN model.", + "bbox": [ + 496, + 501, + 892, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Two-Stage Training Pipeline. However, it is non-trivial to achieve the feature disentanglement as we expected by directly training the proposed model from scratch. This is because the bottom branch with the smallest scale will dominate the model training since it provides the easiest way to model converge. We call this phenomenon \"short-cut\". Such a problem prevents the top and the middle branches from learning image information for different scales, and the learned image representations are still entangled with each other. To take full advantage of our multi-scale VQGAN, we propose a two-stage training pipeline. We first remove the middle and the bottom branches, and only train the top branch with the largest compression factor $f$ . In this stage, the top branch is forced to take effect and be re", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13182", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "sponsible to reconstruct the global structures. After the convergence of the top branch, we add the other two branches back to fine-tune the overall multi-scale VQGAN. In the second stage, the two new branches only need to recover the remaining smaller structures and fine-grained details, thus avoiding the \"short-cut\" problem.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stochastic Top-k VQ Strategy. After training our multiscale VQGAN on a real-world low-quality animation video dataset (e.g., the proposed RAL dataset in Sec. 3.1), the learned codebooks will contain rich degradation information and are capable of transferring such degradations into unseen animation data. Specifically, as shown in Fig. 3, the learned multi-scale VQGAN will be used as the degradation model to synthesize pseudo LR images from clean LR images for further VSR model training. Although the degradation priors in the codebooks are diverse, there is only one fixed degradation output for each input as the quantization process takes the nearest neighbor search strategy to reconstruct the input, leading to poor generalization capability of the final VSR model. To expand the degradation space and introduce more randomness during training, we adopt a stochastic top-k search strategy when looking up the codebook for the VQ process. More precisely, given the encoded output $\\hat{z} = E(x) \\in \\mathbb{R}^{h \\times w \\times n_z}$ from the input image $x$ , the former vector quantization methods search the nearest entry in the codebook $\\mathcal{Z} = \\{z_l\\}_{l=1}^L$ for each vector $\\hat{z}_{ij}$ in position $(i,j)$ to get the quantized output $z_q$ :", + "bbox": [ + 75, + 183, + 470, + 503 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {q} = q (\\hat {z}) := \\left(\\arg \\min _ {z _ {l} \\in \\mathcal {Z}} \\| \\hat {z} _ {i j} - z _ {l} \\|\\right) \\in \\mathbb {R} ^ {h \\times w \\times n _ {z}}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 513, + 468, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We expand the nearest search strategy to a stochastic topk search strategy. That is, we obtain the $k_{th}$ closest entry in the codebook for each vector $\\hat{z}_{ij}$ in position $(i,j)$ :", + "bbox": [ + 76, + 556, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {q} = q (\\hat {z}) := \\left(\\arg \\underset {z _ {l} \\in \\mathcal {Z}} {k _ {t h}} \\| \\hat {z} _ {i j} - z _ {l} \\|\\right) \\in \\mathbb {R} ^ {h \\times w \\times n _ {z}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 616, + 468, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each sample in every training iteration, the value of $k$ is randomly chosen from a predefined range $[1, K]$ and controls the level of degradation. We chose $K = 50$ in VQD-SR and the experiment of the choice of $K$ can be found in the supplementary.", + "bbox": [ + 75, + 657, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A key point here is that we adopt the stochastic top-k strategy only for the bottom branch while keeping the nearest neighbor search for the top and middle branches. This is because the larger-scale structures like colors and shapes are encoded in these two branches, and we do not want them to be changed when augmenting the local details for degradation. That is also the reason why we make a great effort to design the multi-scale VQGAN that encodes the different components in input images separately. The idea of stochastic top-k VQ strategy also corresponds with the fact that one HR image could have multiple degraded versions.", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. HR-SR Enhancement Strategy", + "text_level": 1, + "bbox": [ + 500, + 90, + 769, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "AVC [35] is the latest large-scale high-quality animation video dataset, specified for animation VSR tasks. As opposed to images that could be recorded in lossless format, most of the animation videos available on the Web all went through compression to reduce the network traffic. As demonstrated in Fig. 3 b, the HR animation video frames still suffered from the compression artifacts, and therefore are not completely ideal as the training ground truths. Based on this observation, we suggest enhancing the HR animation videos to further lift the upper bound for the existing animation VSR model. Since the contents of animation videos are relatively simple and the HR video frames are relatively clean, general pre-trained SR models (e.g., RealESRGAN [32]) could be used to reduce the artifacts while not contaminating image details. We thus enhance all the HR video frames in the AVC dataset by first applying an SR model, then downsampling to align the original sizes.", + "bbox": [ + 496, + 113, + 890, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Details", + "text_level": 1, + "bbox": [ + 500, + 380, + 661, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Degradation Model. In our multi-scale VQGAN, we set the compression factor $f$ to $\\{8,4,2\\}$ for the {top, middle, bottom} branch respectively and use 1024 codebook entries with 256 channels in total. The input images are randomly cropped to patches of $256 \\times 256$ . The training of our multiscale VQGAN is a two-stage procedure. We follow [5] to adopt Adam [16] optimizer with the base learning rate of $4.5 \\times 10^{-6}$ for both stages. The learning rate in top branch is decreased by 4 times in the second stage. We set the total batch size to 32 and 24 for the two stages, respectively. We only apply VQ loss $L_{vq}$ [29] and perceptual loss $L_{per}$ [48] in the first stage, while adding the adversarial loss $L_{adv}$ [5] in the second stage. The full objective function for encoder $E$ , decoder $G$ and hierarchical VQ codebook $Z$ is:", + "bbox": [ + 496, + 404, + 890, + 614 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL (E, G, Z) = L _ {v q} + L _ {p e r} + L _ {a d v}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 627, + 890, + 645 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which $L_{vq}$ is calculate by:", + "bbox": [ + 500, + 656, + 692, + 672 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {v q} = \\| x - \\hat {x} \\| + \\beta \\| s g [ E (x) _ {(s)} ] - z _ {q (s)} \\| _ {2} ^ {2} \\tag {4} \\\\ + \\left\\| s g \\left[ z _ {q (s)} \\right] - E (x) _ {(s)} \\right\\| _ {2} ^ {2}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 683, + 890, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where $x, \\hat{x}$ are the input and reconstructed images, $sg[\\cdot]$ denotes the stop-gradient operation, and $s \\in \\{t, m, b\\}$ means the top, middle or bottom branches. More implementation details can be found in the supplementary.", + "bbox": [ + 496, + 733, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Video Super-Resolution Model. We adopt the unidirectional recurrent network in AnimeSR [35] as the VSR model because of its efficiency, and further remove the SR feedback in the recurrent block to ensure a more stable training according to our observation that too many recurrent features would sometimes cause a collapse of GAN loss as the omitting of explicit alignment module. We train the", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13183", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VSR model in two stages. In the first stage, we pre-train the VSR model with $L1$ loss for 300K iterations, with batch size 16 and learning rate $10^{-4}$ . In the second stage, we further add perceptual loss [15] and GAN loss [17] to fine-tune the network for another 300K iterations, with batch size 16 and learning rate $5 \\times 10^{-5}$ . As the promotion of perceptual quality is mainly during the second stage, we only append our multi-scale VQGAN for more realistic degradations in the second stage to reduce the training cost while only adopting basic operators in the first stage.", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 257, + 209, + 275 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 76, + 282, + 274, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method and compare its performance with other SOTA SR methods on AVC [35], the latest proposed large-scale animation video clip dataset. AVC is composed of three subsets. The training set AVC-Train contains 553 high-quality clips, and the testing set AVCTest contains 30 high-quality clips. There is also a AVCRealLQ, which contains 46 real-world low-quality clips for evaluation. Each clip consists of 100 frames. We adopt MANIQA [41], the winner in NTIRE 2022 NR-IQA challenge [8], as the no-reference image quality evaluation metric, as it in the previous animation VSR work [35].", + "bbox": [ + 75, + 306, + 472, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparisons with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 483, + 447, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our VQD-SR with six SOTA SR methods. Among them, AnimeSR [35] and RealBasicVSR [3] are blind video super-resolution (VSR) methods. RealESRGAN [32] and BSRGAN [46] are blind single-image super-resolution (SISR) methods with explicit degradation modeling. We also conduct experiments on BasicVSR [1] and PDM [21] as two representative methods for none-blind VSR method and blind SISR with implicit degradation modeling. Apart from AnimeSR [35], for which we report the result in the original paper, all the others are general SR methods for open-domain images or videos. For fair comparisons, we fine-tune their officially released models on animation dataset AVC-Train.", + "bbox": [ + 75, + 507, + 468, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Comparison. As shown in Tab. 1, we evaluate all the methods on AVC-RealLQ [35] for quantitative comparisons. Among them, Real-ESRGAN [32] and BSRGAN [46] expand the former explicit degradation models by introducing high-order degradations and random shuffling respectively, which greatly improve the synthetic ability. And with the help of powerful SR backbone (RRDB-Net [33] with 16.70M parameters), their results are quite remarkable. Nonetheless, ignoring the intrinsic characteristics of animation data limits their performance when applied to animation domain. Although specialized for animation videos, AnimeSR [35] only utilizes a small number of real data (three human-annotated animation videos), which hin", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f6817ae803d25ff54049326c828096c12a462220cf97255fdcf384dbe057b2d8.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on AVC-RealLQ for $4 \\times$ animation VSR. \\* denotes fine-tune on animation dataset AVC-Train [35]. Bold text indicates the best performance." + ], + "table_footnote": [], + "table_body": "
MethodParams (M)Runtime (ms)MANIQA↑
BasicVSR* [1]6.291750.2829
PDM* [21]16.704380.2574
Real-ESRGAN* [32]16.704380.3825
BSRGAN* [46]16.704380.3836
RealBasicVSR*[3]6.292520.3504
AnimeSR [35]1.50260.3832
VQD-SR (Ours)1.47250.4096
", + "bbox": [ + 504, + 138, + 890, + 244 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2fd7a6a138fb5b257ddbe577dfedbaf5ca233cefccc1692ba0376c89b0fb35a6.jpg", + "image_caption": [ + "Figure 4. Results of User Study. The values on Y-axis represent the percentage of users that prefer VQD-SR over other approaches." + ], + "image_footnote": [], + "bbox": [ + 500, + 258, + 890, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ders the performance of VSR model in real scenarios. Different from them, our VQD-SR considers the intrinsic characteristics of animation videos and leverages the enormous degradation priors contained in rich-content real animation videos. VQD-SR also adopts the HR enhancement strategy for more effective SR supervision. Due to these advantages, VQD-SR achieves a result of 0.4096 and significantly outperforms the SOTA animation VSR model [35] by 0.0264 in MANIQA on AVC-RealLQ [35]. Meanwhile, as the removal of SR recurrent feedback in VSR model, the number of parameters in VQD-SR are further reduced to $1.47\\mathrm{M}$ with the runtime of $25~\\mathrm{ms}$ computed on a NVIDIA Tesla M40 GPU with the LR size of $180\\times 320$ , which demonstrates the superiority of our VQD-SR in real applications.", + "bbox": [ + 496, + 459, + 890, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Comparison. As shown in Fig. 5, we compare visual qualities of different approaches on real-world AVC-RealLQ video clips. It can be observed that VQD-SR greatly improves the visual quality, especially for the recovery of clear lines. Additionally, the results of VQD-SR are more visually natural with fewer artifacts in some intended scenarios (e.g., the out-focus background blur and smooth underwater scene in row 5-6), while most of the other methods suffer from over-sharp artifacts like irregular lines and patterns. More visual comparisons with original inputs for reference and result analysis are in the supplementary materials.", + "bbox": [ + 496, + 672, + 890, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also conduct a user study to further evaluate the visual quality of our approach. There are 20 subjects involved in this user study and 22080 votes are collected on AVC-", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13184", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/11dd21c861ce4353f53a73dfd05d4bcefad6fe3a75c245b9609afdae1cbee255.jpg", + "image_caption": [ + "```python\nanime_dance_level_0/739" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 246, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c0415e48810790aa84f1e2e0ab600f0cd3a8f5c1584814fd7820cc408dfa84e.jpg", + "image_caption": [ + "BasicVSR*" + ], + "image_footnote": [], + "bbox": [ + 246, + 88, + 428, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e1a6a443b3312fb7fcb463b8814b2d4e8f574a394249661a8f10ffc1f1738d17.jpg", + "image_caption": [ + "Real-ESRGAN*" + ], + "image_footnote": [], + "bbox": [ + 429, + 88, + 521, + 148 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+ }, + { + "type": "image", + "img_path": "images/061e9c7895d214848a1b6b7f0db566ea462e7bbef0fc2175667c11375b1a18b6.jpg", + "image_caption": [ + "go_player/95" + ], + "image_footnote": [], + "bbox": [ + 81, + 159, + 243, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/139920fce1f83b5764607af8a4494d4406136eee52d167057503fe33ebddd676.jpg", + "image_caption": [ + "BasicVSR*" + ], + "image_footnote": [], + "bbox": [ + 246, + 159, + 428, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fe0ddcd25e34e5f9d6a7b4a058a41718d78e98964776d38dc8bb55789695eb6d.jpg", + "image_caption": [ + "Real-ESRGAN*" + ], + "image_footnote": [], + "bbox": [ + 429, + 159, + 519, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5057af45eab411da61b3818814d44a5fe941f40f9b54eeaf8685b20b10985325.jpg", + "image_caption": [ + "BSRGAN*" + ], + "image_footnote": [], + "bbox": [ + 521, + 159, + 612, + 220 + ], + "page_idx": 6 + }, + { + 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+ "img_path": "images/cb7f9cc12cc1b0764015971d34e10cef56d81c19f41720ebc3b7f9c125d5926c.jpg", + "image_caption": [ + "AnimeSR" + ], + "image_footnote": [], + "bbox": [ + 707, + 231, + 795, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/22b1281bbe4ab3b1c66f9dab620bd98a5047344c442dcdacfd64e3d84f722910.jpg", + "image_caption": [ + "VQD-SR (Ours)" + ], + "image_footnote": [], + "bbox": [ + 797, + 231, + 888, + 292 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d920f03d035efdd6f6122b8d29954a5f9ef453d72909cc7b3ce8a05d35dd62c8.jpg", + "image_caption": [ + "mado_king/38" + ], + "image_footnote": [], + "bbox": [ + 81, + 304, + 243, + 364 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c83b055fd856da52be293318b6da4172e7a4b20ed89c99b2b140c7d6c724ca61.jpg", + "image_caption": [ + "BasicVSR*" + ], + "image_footnote": [], + "bbox": [ + 246, + 304, + 428, + 364 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": 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"images/8c5584107e0049ccf1c9f4ced69c716527ebbe7fdb569d8afbe4cfec3b8259f6.jpg", + "image_caption": [ + "hell girl/105", + "Figure 5. Qualitative comparisons on AVC-RealLQ [35] for $4 \\times$ scaling factor. $*$ denotes fine-tune on animation domain dataset. The frame name is shown at the bottom of each case. Our VQD-SR recovers visually natural and sharper lines with fewer artifacts (the first 4 rows) and is also capable to handle some intended scenarios with fewer over-sharp artifacts (row 5th with smooth background and clear foreground, row 6th in underwater scene). Zoom in to see better visualization." + ], + "image_footnote": [], + "bbox": [ + 81, + 450, + 243, + 510 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/decc0b4115d983b1dd34bb85907a0391e29860bce380ff3b4a51d4e16e6607bb.jpg", + "image_caption": [ + "BasicVSR*" + ], + "image_footnote": [], + "bbox": [ + 246, + 450, + 428, + 510 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/02ec84f07748f0187b3994bac72eaf6b9e8aba24751c18ea22af0b8be1cbe2dc.jpg", + "image_caption": [ + "Real-ESRGAN*" + ], + "image_footnote": [], + "bbox": [ + 429, + 450, + 519, + 510 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5172bd670aea5d64edc97573e40a634060f5c7715d77656b7eded508bf1da6c5.jpg", + "image_caption": [ + "BSRGAN*" + ], + "image_footnote": [], + "bbox": [ + 521, + 450, + 612, + 510 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/196f50dd5d21222eabe327a40a885f70d55c9a23dcc622c38754f4e36a95f814.jpg", + "image_caption": [ + "RealBasicVSR*" + ], + "image_footnote": [], + "bbox": [ + 614, + 450, + 705, + 510 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4e698f41f555235f89bdf5770f16b06c5c4aedda214d682916e8b7af5a1cd0e7.jpg", + "image_caption": [ + "AnimeSR" + ], + "image_footnote": [], + "bbox": [ + 707, + 450, + 795, + 510 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/810f3b5c709fa53465b424fcc420c8fc541a57c58fc02bc1a7a2dc123dce1686.jpg", + "image_caption": [ + "VQD-SR (Ours)" + ], + "image_footnote": [], + "bbox": [ + 797, + 450, + 888, + 510 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "RealLQ [35] with 46 video clips. For each comparison, we adopt an A-B test that provides the users with two images in random order which include one VQD-SR frame. Users are asked to select the one with higher visual quality. As shown in Fig. 4, comparing with the SR methods designed for open-domain, over $80\\%$ of users voted for our VQD-SR. By considering the data characteristic of animation, there are still over $65\\%$ users who prefer our method to AnimeSR [35].", + "bbox": [ + 75, + 618, + 467, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 768, + 225, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies on each significant component of our VQ degradation model and HR-SR enhancement strategy in VQD-SR.", + "bbox": [ + 75, + 792, + 467, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "VQ Degradation Model. In the ablation study of VQ degradation model design, we conduct all the experiments based on VQD-SR (base), which denotes a plain version of VQD-SR trained without HR-SR enhancement. As shown", + "bbox": [ + 75, + 839, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e38c4b60fd4419149f7b2af673704e39d5311c76cae6ae761b55d513c20c7650.jpg", + "image_caption": [ + "VQD-SR (base)" + ], + "image_footnote": [], + "bbox": [ + 501, + 614, + 581, + 666 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9bfe7786d0c171fa06e0f76b92d2a10b6894c51984922af5e281a30572af1954.jpg", + "image_caption": [ + "(a) BasicOP" + ], + "image_footnote": [], + "bbox": [ + 584, + 616, + 656, + 666 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/318504e6fb24b5d2812e43f1d200a368a81d963de6958f25386449f1622f6b66.jpg", + "image_caption": [ + "(b) Single Scale" + ], + "image_footnote": [], + "bbox": [ + 658, + 616, + 733, + 666 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/df80a32e9a329d8f9aaa2c72597474f1295d4e9a47ef59537101f8bfacca4694.jpg", + "image_caption": [ + "(c) Single Stage" + ], + "image_footnote": [], + "bbox": [ + 736, + 616, + 812, + 666 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bb11b9c6811fdbc1fa046a33c7b4723bac02857aab967a6d3036c1f42aa4a3d5.jpg", + "image_caption": [ + "(d) Top-1", + "Figure 6. Ablation study on VQ degradation model." + ], + "image_footnote": [], + "bbox": [ + 815, + 616, + 890, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "in Tab. 2 a, we first compare the degradation model which is simply composed of basic operators (blur, noise and FFmpeg) to our VQD-SR (base). With the help of real-world degradation priors contained in VQ codebook, the result can be improved from 0.3768 to 0.3857 in MANIQA. Referring to Fig. 6 a, VSR model trained with only basic operators fails to handle some real-world degradations, leading to artifacts around the edges. We further compare the structure and training strategy of VQ degradation model in Tab. 2 b and Tab. 2 c. As the global structures and local details are entangled together in single-scale VQ model and the", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13185", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3eb8edf58cd826d5441e5b3cfaaf5adaac7d6cd70c76e85cef6af102dace2060.jpg", + "table_caption": [ + "Table 2. Ablation study results of degradation models, structures of VQ degradation model, training pipelines of VQ degradation model and VQ codebook search strategies. The MANIQA scores are reported for comparisons." + ], + "table_footnote": [], + "table_body": "
MANIQA↑(a) Degradation Model
BasicOP-OnlyVQD-SR (base)
0.37680.3857
MANIQA↑(b) VQGAN Structure
Single-scaleVQD-SR (base)
0.34660.3857
MANIQA↑(c) Training Strategy
Single-stageVQD-SR (base)
0.34300.3857
MANIQA↑(d) Codebook Search
NearestVQD-SR (base)
0.37700.3857
", + "bbox": [ + 117, + 152, + 429, + 325 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/da28e6ac1a19b677e9c22d5d3121b812aadef8e1f9a44bc1259c35d33c2b84f3.jpg", + "table_caption": [ + "Table 3. Applying VQ degradation to widely used SR backbones. For each backbone, settings are consistent apart from degradation methods." + ], + "table_footnote": [], + "table_body": "
BackboneReal-ESRGAN*RealBasicVSR*AnimeSR
Params (M)16.76.31.5
Original degradation0.38250.35040.3832
VQ degradation0.39670.38490.3857
", + "bbox": [ + 81, + 378, + 465, + 430 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "multi-scale model trained in single-stage, the performances dropped by 0.0391 and 0.0427, respectively. As shown in Fig. 6 b and Fig. 6 c, some fine-grained details are missing. For VQ strategies, as shown in Tab. 2 d and Fig. 6 d, our stochastic top-k VQ strategy can improve MANIQA by 0.0087 compared with the original nearest neighbor search strategy, as the top-k VQ strategy enables multi-level degradations which improves the generalization ability of the trained animation model, leading to more appealing results.", + "bbox": [ + 75, + 459, + 467, + 594 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further illustrate the general applicability, we also apply our VQ degradation model to other SOTA SR backbones, Real-ESRGAN and RealBasicVSR, fine-tuned with animation data in the same setting. Referring to Tab. 3, SR models with VQ degradation achieve better results comparing with their original degradation methods, which indicates that the proposed VQ degradation is generally effective for animation SR models. It is noteworthy that the performance gains could be more significant for larger backbones. The visual examples in Fig. 7 also show the superiority of our VQ degradation method, especially to recover clear and visual natural lines which are the most import patterns deciding the visual quality of animation videos.", + "bbox": [ + 75, + 595, + 467, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "HR Enhancement. The training HR animation videos collected from the Web also contain artifacts which are not ideal for ground truths, hindering the performances of animation VSR models. We propose the HR-SR strategy to enhance the quality of HR animation videos for more effective training ground truths. We first compare three different HR enhancement models by experiments on VQD-SR (base).", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1eb1163edd9cc2da5f992492be466466a46478f9daf8dafca6598336f99336a5.jpg", + "image_caption": [ + "bhd and shs/30" + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 658, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ea8657d1d46a1f27755b3dcb46451e2ad86d58f3259c9e708b882a3aef2e1ab2.jpg", + "image_caption": [ + "Real-ESRGAN(VQ)\\*" + ], + "image_footnote": [], + "bbox": [ + 661, + 90, + 735, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c8e3faa3e7e35b96fc86946992ae756ead402e2dde3a7c27b24ee091c246a08c.jpg", + "image_caption": [ + "RealBasicVSR (VQ)*" + ], + "image_footnote": [], + "bbox": [ + 736, + 90, + 812, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/00235d79094e3e82498506024c20bc3e2450cf9cbc0b73582055597d4e0d98af.jpg", + "image_caption": [ + "AnimeSR (VQ)" + ], + "image_footnote": [], + "bbox": [ + 815, + 90, + 890, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b270e28040b9d1e5e7a70651882ef451ddbcf80eaba8611981d40a9871b9b380.jpg", + "image_caption": [ + "ccs/124" + ], + "image_footnote": [], + "bbox": [ + 503, + 210, + 656, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f1a80af2d2cc7fd210f592cc26e3d9c0346412fd2824b49c6503581af577217b.jpg", + "image_caption": [ + "Real-ESRGAN(VQ)*" + ], + "image_footnote": [], + "bbox": [ + 660, + 210, + 735, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/985c099ef590b55358926e9ba76e182732955876a9856603e90dd121251dc424.jpg", + "image_caption": [ + "RealBasicVSR (VQ)*" + ], + "image_footnote": [], + "bbox": [ + 736, + 210, + 812, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/598b0dbdd59f79e6b9261bbbf2c7dd53bd3d5de3d3362ae415415044651ba359.jpg", + "image_caption": [ + "```bash\nAnimeSR(VQ)" + ], + "image_footnote": [], + "bbox": [ + 815, + 210, + 890, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d7e6cfc54c4460eb7841454b91c6526073d0c9a4fb43836488899ef598a9c6e.jpg", + "image_caption": [ + "big_ear_tutu/105", + "Figure 7. Applying VQ degradation to widely used SR backbones. Settings are consistent apart from degradation methods. Models trained with VQ degradation could produce more clear and visual natural lines with fewer artifacts." + ], + "image_footnote": [], + "bbox": [ + 503, + 330, + 656, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4679650b4f7ffa3da7517e76191ca9e914c02f6ee5e8c25479f96fe44776700b.jpg", + "image_caption": [ + "Real-ESRGAN(VQ)*" + ], + "image_footnote": [], + "bbox": [ + 660, + 330, + 723, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3e28d4db9a7a5fc788f7b6f62ed802bdf886df975e4496aac6c03400820e41a9.jpg", + "image_caption": [ + "RealBasicVSR (VQ)*" + ], + "image_footnote": [], + "bbox": [ + 736, + 330, + 800, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/26b46579d5bf3a14df71f4c343065090874377aac3b07faa1222c6024b0be855.jpg", + "image_caption": [ + "AnimeSR (VQ)" + ], + "image_footnote": [], + "bbox": [ + 815, + 330, + 875, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The quantitative results are shown in Tab. 4. All three models improve the performance of animation VSR model, which verifies that the proposed HR-SR strategy is suitable for the training of animation VSR model, and improvements are not subject to the specific model for enhancement. However, as the SR process for data enhancement is conducted in HR domain, which takes a high demand on computing resources, we finally choose SISR model, Real-ESRGAN (S) [32] with relatively small model size. Visual examples of the enhanced HR frames can be found in Fig. 8.", + "bbox": [ + 496, + 565, + 890, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further utilize the enhanced HR animation videos processed by Real-ESRGAN(S) [32] to fine-tune different VSR models. Apart from the proposed VQD-SR, RealBasicVSR [3] is a blind VSR model designed for open-domain videos and AnimeSR [35] is an VSR model specified for animation domain. As shown in Tab. 5, with the help of HR enhancement, all three VSR models get improved, which illustrates that the proposed HR enhancement strategy is effective for animation VSR task, regardless of the specific VSR model. The visual results of RealBasicVSR+, AnimeSR+, and VQD-SR in Fig. 9 also verify the advantages of the HR-SR enhancement strategy for animation VSR.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13186", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ad7ea045d521303e2879be7bbd44cec5db77e17dd5e6b9498a105db3f394d645.jpg", + "table_caption": [ + "Table 4. Ablation study of different SR models for HR-SR enhancement. All three models improve the performance. We choose Real-ESRGAN (S) considering the computing cost." + ], + "table_footnote": [], + "table_body": "
Enhancement MethodMANIQA↑
No Enhancement0.3857
AnimeSR [35]0.4146
Real-ESRGAN (L) [32]0.4211
Real-ESRGAN (S) [32]0.4096
", + "bbox": [ + 135, + 138, + 411, + 220 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/ed346cd3a3822237a13dc86006c7aa8f2880965f8a0e59654524e9e95d49f35d.jpg", + "table_caption": [ + "Table 5. Ablation study of HR-SR enhancement for different animation VSR models on AVC-RealLQ. We report MANIQA for comparison." + ], + "table_footnote": [], + "table_body": "
MANIQA↑wo /HR-SRw /HR-SR
RealBasicVSR [3]0.35040.3855
AnimeSR [35]0.38320.4079
VQD-SR0.38570.4096
", + "bbox": [ + 119, + 285, + 426, + 347 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/288b23c9f96b2e5b320263d78fa05b0c9bcc369851be187288d3fa07711e1ab8.jpg", + "image_caption": [ + "Input HR" + ], + "image_footnote": [], + "bbox": [ + 78, + 359, + 173, + 424 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/8bd30a794c90e3775c6e9d5136f22e1d79a6e4d07d91431d1515f59e5267c835.jpg", + "image_caption": [ + "AnimeSR" + ], + "image_footnote": [], + "bbox": [ + 178, + 359, + 271, + 424 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/edc8cea2379ff6a1ea0d4eda18a3c55e69d4507100b117671f587a4f80e2f3fb.jpg", + "image_caption": [ + "Real-ESRGAN (L)" + ], + "image_footnote": [], + "bbox": [ + 274, + 359, + 369, + 424 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/cec83923fbacbef652e404c9c053d83114c4d18188df215f34b60c9d06d3765b.jpg", + "image_caption": [ + "Real-ESRGAN (S)" + ], + "image_footnote": [], + "bbox": [ + 372, + 359, + 467, + 424 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/3647eed832df0feac7de703f26776095b6911d835ac2055d7a48e45301cc6ff4.jpg", + "image_caption": [ + "Figure 8. Enhanced HR data with HR-SR strategy by different enhancement models." + ], + "image_footnote": [], + "bbox": [ + 78, + 436, + 173, + 508 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/9f21713189335e97c33931f2e9822afd863fc6596d85bc89dc2f67a5bd11bff6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 178, + 436, + 271, + 508 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/658b894565bb7e2e88c9ee65830f61d5756c2c8a1e802d1155fea4ec094cb267.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 436, + 369, + 508 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/741372d0a6ebb21a0ac3d0ba67e9552a2400f31913a3d0734745a7d035fdcd1e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 436, + 467, + 508 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Limitation and Discussion", + "text_level": 1, + "bbox": [ + 76, + 590, + 318, + 606 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this section, we visualize the failure cases of VQDSR in Fig. 10. Our VQD-SR is capable to restore sharper lines and suppress diverse artifacts in animation videos. However, in some extreme circumstances (e.g., severe lossy compressions, long passing ages), there still gets room for improvement, for example the remaining color distortions around edges. Nevertheless, comparing with other SOTA methods, our VQD-SR still achieves better performances.", + "bbox": [ + 75, + 616, + 467, + 736 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 753, + 194, + 768 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we thoroughly study the characteristics of animation videos and fully leverage the rich prior knowledge contained in real data for a more practical animation VSR model. To be specific, we propose a novel degradation model which utilize a multi-scale VQGAN, self-supervised on purely real low-quality animation data (RAL), to decompose animation frames and establish a codebook containing diverse real-world degradation priors. We also propose a", + "bbox": [ + 75, + 780, + 467, + 900 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/062a2d2d270777366b243426b3a6227d5f48c89b6dd65db42a3dbeb38b06cda8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 88, + 656, + 208 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/e216297b447cce1c3c142d04fefeba3acaaf1a61c5c84c3a405b8d68ca4cb137.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 658, + 89, + 733, + 208 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/7b06d098e2a4f4d29df1797906f7fe4fc421be0066a1809694ce56056739e420.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 89, + 810, + 208 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/1f08ec1d58913099cd82a957e3d29ce7a8b2905df3fcd2bf94e80769a13ed1b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 812, + 89, + 888, + 208 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/b1518647e25bc99910d9d18b21e77c620f659b7747e0b3b50a95d368a850606d.jpg", + "image_caption": [ + "Figure 9. Ablation study of HR-SR enhancement strategy for different VSR models. HR-SR enhancement is generally effective task, regardless of the specific VSR model." + ], + "image_footnote": [], + "bbox": [ + 501, + 210, + 656, + 332 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/848f4fbdaf33bee1c6b665c8874fe6d01a681fc3aa56510d2b220397f7a1b146.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 210, + 888, + 332 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/9511866f611eb8672b9a808e9c35377fdd79ba71a11d22e752b3927514b9265b.jpg", + "image_caption": [ + "tom_and_jerry/90" + ], + "image_footnote": [], + "bbox": [ + 503, + 411, + 658, + 523 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/860247ac53f6bbb948e7f41ec8cff0e7174f978c7fec47f19d88fed50f5cca45.jpg", + "image_caption": [ + "RealBasicVSR*" + ], + "image_footnote": [], + "bbox": [ + 661, + 411, + 736, + 521 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/5907f63ad63737f42ccb4618ded71d95e8fc6168e6573b2e29400752e60c3170.jpg", + "image_caption": [ + "AnimeSR" + ], + "image_footnote": [], + "bbox": [ + 736, + 411, + 813, + 521 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/963499b40c3825af8b39ee1b0bc36f8ca3b2738b02b61a34b790a9654e4824a1.jpg", + "image_caption": [ + "VQD-SR (Ours)" + ], + "image_footnote": [], + "bbox": [ + 815, + 411, + 890, + 521 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/bc2911550d49571cbd2cb24c31448a2e1cbd1f6cb24b77fe721c792d9aacd8e5.jpg", + "image_caption": [ + "doraemon/91" + ], + "image_footnote": [], + "bbox": [ + 504, + 531, + 658, + 646 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/5c6eeadd8ac8c455006ce98b5a207b2945afb4d646f97a0268d50bd118ab3111.jpg", + "image_caption": [ + "Figure 10. Failure cases when LR frames endure severe color distortions around edges." + ], + "image_footnote": [], + "bbox": [ + 661, + 531, + 736, + 648 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/6194893cdefff487dd2a60ce31ff9a7dfb4e24e484bfabe8c1dc7e7d22964405.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 531, + 813, + 648 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/c5f6de546fd183f28bd1a3f34bc41983f32fdc66e89eb6170fdb8b628e2df343.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 813, + 531, + 890, + 648 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "two-stage training pipeline and a stochastic top-k VQ strategy to match up with the VQ degradation model. We further propose to enhance the HR training videos to lift the performance ceiling for animation VSR tasks. Experiment results show the superiority of the proposed VQD-SR over existing SOTA models, as our methods could generate more effective LR-HR training pairs in view of the characteristics in real animation videos.", + "bbox": [ + 496, + 714, + 890, + 834 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported in part by the NSFC under Grant 62272380 and 62103317, the Science and Technology Program of Xi'an, China under Grant 21RGZN0017, and Microsoft Research Asia.", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "13187", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kelvin CK Chan, Xintao Wang, Ke Yu, Chao Dong, and Chen Change Loy. 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In CVPR, pages 586-595, 2018." + ], + "bbox": [ + 78, + 90, + 467, + 840 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "13189", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/8790a28a-4db4-4d06-856c-466efed197ec_model.json b/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/8790a28a-4db4-4d06-856c-466efed197ec_model.json new file mode 100644 index 0000000000000000000000000000000000000000..eee934cdbaca2a56625b6ee6b354cd94f5cf5221 --- /dev/null +++ b/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/8790a28a-4db4-4d06-856c-466efed197ec_model.json @@ -0,0 +1,3654 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.18, + 0.131, + 0.79, + 0.176 + ], + "angle": 0, + "content": "Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.203, + 0.756, + 0.222 + ], + "angle": 0, + "content": "Zixi Tuo\\*, Huan Yang†, Jianlong Fu², Yujie Dun¹, Xueming Qian¹,³" + }, + { + "type": "text", + "bbox": [ + 0.268, + 0.222, + 0.705, + 0.239 + ], + "angle": 0, + "content": "\\(^{1}\\)Xi'an Jiaotong University \\(^{2}\\)Microsoft Research Asia" + }, + { + "type": "text", + "bbox": [ + 0.205, + 0.239, + 0.767, + 0.257 + ], + "angle": 0, + "content": "3Shaanxi Yulan Jiuzhou Intelligent Optoelectronic Technology Co., Ltd" + }, + { + "type": "text", + "bbox": [ + 0.125, + 0.26, + 0.845, + 0.275 + ], + "angle": 0, + "content": "zixit99@gmail.com, {huayan, jianf}@microsoft.com, {dunyj, qianxm}@mail.xjtu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.75 + ], + "angle": 0, + "content": "Existing real-world video super-resolution (VSR) methods focus on designing a general degradation pipeline for open-domain videos while ignoring data intrinsic characteristics which strongly limit their performance when applying to some specific domains (e.g., animation videos). In this paper, we thoroughly explore the characteristics of animation videos and leverage the rich priors in real-world animation data for a more practical animation VSR model. In particular, we propose a multi-scale Vector-Quantized Degradation model for animation video Super-Resolution (VQD-SR) to decompose the local details from global structures and transfer the degradation priors in real-world animation videos to a learned vector-quantized codebook for degradation modeling. A rich-content Real Animation Low-quality (RAL) video dataset is collected for extracting the priors. We further propose a data enhancement strategy for high-resolution (HR) training videos based on our observation that existing HR videos are mostly collected from the Web which contains conspicuous compression artifacts. The proposed strategy is valid to lift the upper bound of animation VSR performance, regardless of the specific VSR model. Experimental results demonstrate the superiority of the proposed VQD-SR over state-of-the-art methods, through extensive quantitative and qualitative evaluations of the latest animation video super-resolution benchmark. The code and pre-trained models can be downloaded at https://github.com/researchmm/VQD-SR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Animation video super-resolution (VSR) [35], which is a subdiscipline of video super-resolution (VSR) [1, 2, 3, 19, 28, 37], aims to restore high-resolution (HR) videos from their low-resolution (LR) counterparts in animation domain. As a special type of visual art, animation video shows great" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.309, + 0.89, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.458, + 0.631, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.458, + 0.76, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.458, + 0.888, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.572, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Figure 1. A comparison between our proposed VQD-SR and other SOTA VSR methods in real scenario. As indicated by the red dotted circles, our VQD-SR could restore more appealing details by considering the degradation priors in real animation videos. (\\* denotes fine-tune on animation videos)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.824 + ], + "angle": 0, + "content": "entertainment, cultural, educational and commercial values. However, most of them available on the Web are in limited resolutions and have visually unappealing artifacts due to the passing ages, lossy compression and transmission. Dedicated to real applications, animation VSR is a blind SR [21, 32, 46, 40, 43] task which is more challenging than conventional VSR tasks [1, 2, 14, 19, 28, 36], because of the complicated and agnostic real-world degradations. Thus, practical VSR methods for improving real-world LR animation videos are in highly demanded." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Blind SR model for open-domain has long been the focus. As it's hard to collect LR-HR pairs in real scenarios, recent learning-based approaches try to model the real-world degradations from HR to LR, thus generating pseudo LR-HR pairs to train SR models. These approaches can" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.863, + 0.469, + 0.887 + ], + "angle": 0, + "content": "*This work was done while Zixi Tuo was a research intern at Microsoft Research Asia." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.863, + 0.469, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13179" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.317 + ], + "angle": 0, + "content": "be roughly divided into two categories, explicit modeling and implicit modeling, with regard to the degradation procedures. Explicit modeling [9, 20, 32, 46] methods try to combine basic degradation operators like noise, blur and rescaling to imitate the real-world degradation pipeline. Instead, implicit modeling methods employ a neural network, which is usually in the manner of generative adversarial networks (GAN) [7], as an alternative to the combination of basic degradation operators. However, these general degradation methods designed for open-domain videos are not quite suitable for the animation domain as they ignore the intrinsic characteristics of the data. Directly adopting existing degradation models for open-domain to animation VSR would lead to unpleasant results (as shown in Fig. 1 a), even though they are fine-tuned on the animation videos." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.322, + 0.468, + 0.532 + ], + "angle": 0, + "content": "Specific to animation VSR, AnimeSR [35] moves one step further to propose a learnable basic operator (LBO) with an \"input-rescaling\" strategy that considers the data characteristics and demonstrates their advantages over open-domain VSR methods. However, the proposed \"input-rescaling\" strategy of constructing pseudo HR-LR pairs for the LBO training requires human annotations, which prevents their method from scaling up to modeling various real-world degradations. In AnimeSR [35], only three LBOs are trained with three human-annotated videos respectively, leading to unappealing results (as shown in Fig. 1 b). Thus, how to effectively leverage large-scale real-world animation videos based on their data characteristics is still an open problem." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.536, + 0.468, + 0.867 + ], + "angle": 0, + "content": "In this paper, we propose a multi-scale Vector-Quantized Degradation model for animation video Super-Resolution (VQD-SR), which leverages the data characteristics of animation videos. We observe that different from open-domain videos with complex textures and irregular illumination conditions, animation videos are roughly composed of basic visual patterns like smooth color patches and clear lines which can be easily captured with high fidelity by vector-quantization (VQ) [5, 25, 29]. Such data characteristics could also be used for encoding and transferring degradation priors from low-quality animation videos and results in a degradation codebook. Given any clean LR animation frame, the degraded LR counterpart can be easily obtained by looking up the pre-trained degradation codebook. Specifically, a novel multi-scale VQGAN for degradation modeling is proposed to learn and transfer real-world degradation priors from a large-scale Real Animation Low-quality (RAL) video dataset collected from the Web. To improve the generalization ability of VQD-SR, we propose a two-stage training pipeline and a stochastic top-k VQ strategy to match up with the multi-scale VQGAN, yielding visually appealing results (as shown in Fig. 1 c)." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "To further lift the upper bound of existing animation VSR methods, we propose an HR-SR strategy to enhance" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.181 + ], + "angle": 0, + "content": "the quality of HR training videos for more ideal ground truths. This is motivated by our observations that existing HR animation videos are mostly collected from the Web which contains conspicuous compression artifacts and such artifacts could be easily reduced by existing SR methods. Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.184, + 0.89, + 0.242 + ], + "angle": 0, + "content": "- We collect a large-scale real LR animation dataset, and conduct a comprehensive study on real animation data to thoroughly explore the challenges and data characteristics in animation VSR task." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.244, + 0.89, + 0.318 + ], + "angle": 0, + "content": "- We propose a novel multi-scale VQ degradation model to transfer real-world degradation priors for synthesizing pseudo LR-HR training pairs. We further propose an HR-SR data enhancement strategy to improve the performance of existing VSR methods for animation." + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.32, + 0.89, + 0.379 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the effectiveness of our proposed methods which significantly improve the recent SOTA animation VSR method in both quantitative and qualitative comparisons." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.397, + 0.64, + 0.412 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.423, + 0.717, + 0.438 + ], + "angle": 0, + "content": "2.1. Video Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.448, + 0.89, + 0.627 + ], + "angle": 0, + "content": "Recent years have witnessed a prosperity in deep learning based VSR methods [2, 3, 14, 24, 28, 31, 38]. Different from single-image super-resolution (SISR), the auxiliary temporal information is available in VSR for the restoration of inner-frame features. Sliding-window structure [28, 31, 38, 42] and recurrent structure [1, 2, 6, 12, 14] are two common paradigms in VSR to utilize the interframe information. However, it also faces challenges while taking the advantages. The degradations could be more complicated in videos and may accumulate along the time sequence [3, 37], causing the performance drop in real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.63, + 0.89, + 0.9 + ], + "angle": 0, + "content": "There have been several attempts in blind-SR field to deal with real-world degradations, which could be categorized into explicit and implicit modeling. Explicit methods model the degradation as the effects of objective operators (or kernels). Methods like [9, 47] assume these degradations to be simple combinations of blur, noise and down-sampling kernels, therefore conducting conditional restoration based on the prediction of kernel parameters. Operators like JPEG/FFmpeg [20] for lossy compression, sinc filter [32] for ringing artifacts and strategies like high-order modeling [32], random shuffling [46], are further investigated in latest studies to simulate the real degradation pipeline and expand the synthesis space. However, these methods merely depend on predefined operators, and ignore to utilize the information contained in real data, thus there's still a gap between the synthesis LR and real LR data. Implicit methods [21, 22, 34, 44] discard the objective degradation operators, but learn the distribution of real data," + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13180" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.168 + ], + "angle": 0, + "content": "therefore realize the degradation by converting the HR input to fit the real LR distribution. Yet, the learned distribution space is uncontrollable, thus the degradation network may easily project unseen out-of-distribution samples to unpredictable suboptimal space causing annoying artifacts." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.178, + 0.332, + 0.195 + ], + "angle": 0, + "content": "2.2. Animation Video Processing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.202, + 0.473, + 0.398 + ], + "angle": 0, + "content": "Animation is a type of visual art that is represented in a nonrealistic artistic style. A diversity of animation processing technologies based on deep learning have been developed these years, such as animation style transfer [4, 13, 30], animation video colorization [18, 27, 45], animation video generation [11] and animation video interpolation [26]. AnimeSR [35] is a recent study for real-world animation VSR tasks, which develops LBO to expand the basic degradation operators. In this paper, we take a further step to explore the characteristics of animation videos, and make special designs in consideration of these characteristics to improve the performance of real-world animation VSR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.409, + 0.332, + 0.425 + ], + "angle": 0, + "content": "2.3. Vector-Quantized Codebook" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.473, + 0.614 + ], + "angle": 0, + "content": "Vector-quantized(VQ) codebook was first proposed in VQ-VAE [29] to learn the discrete representation for images in latent space. Later, a hierarchical VQ-VAE-2 [25] is further proposed. To improve the perceptual quality, a discriminator and perceptual loss were added in VQGAN [5]. Recently in VQFR [10], a VQ-based face restoration method was also proposed. Although initially designed to avoid the \"posterior collapse\" issue of VAE or tokenizer input images for a more effective transformer modeling, we discover that the idea of VQ is naturally suitable for representing animation video frames and the form of codebook is capable to internalize the real degradation priors." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.629, + 0.212, + 0.647 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.746 + ], + "angle": 0, + "content": "In this section, we first discuss the characteristics of real animation videos and the challenges for animation VSR task in Sec. 3.1. Based on the observations in Sec. 3.1, we introduce the proposed real-world animation degradation model in Sec. 3.2. Finally, we illustrate our HR training data enhancement strategy in Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.466, + 0.773 + ], + "angle": 0, + "content": "3.1. Real-World Degradation in Animation Videos" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To thoroughly understand the characteristics of animation videos and the challenges in animation VSR task, we collect a Real Animation Low-quality (RAL) video dataset. RAL contains over 10K LR frames extracted from 441 real-world low-quality animation videos. To the best of our knowledge, RAL is the largest real-world low-quality video dataset in the animation domain. Example frames are shown in Fig. 2 (statistics of RAL can be found in the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.895, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.246, + 0.892, + 0.316 + ], + "angle": 0, + "content": "Figure 2. Samples of RAL and typical degradation phenomena in real-world LR animation videos. RAL is a real-world animation video dataset contains over 10K LR frames. Intermittent edges, aliasing edges, ringing artifacts and rainbow effects are four typical degradation phenomena in real-world animation videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.892, + 0.476 + ], + "angle": 0, + "content": "supplementary). To construct such a dataset, we first download numerous earlier animation videos from multiple video sites such as YouTube and Bilibili. Then we manually select videos according to their resolutions, quality, contents and styles. To ensure the dataset contains rich animation structures and degradation priors, we adopt a simple scene filtering procedure to remove the frames which have subtle motions by evaluating their average absolute differences, thus reducing the redundancy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.893, + 0.657 + ], + "angle": 0, + "content": "Animation videos are roughly composed of smooth color patches and clear lines, while the latter ones usually play an important role in portraying objects and expressing visual semantics. In contrast to the fact that degradation losses for open domain videos are mainly about high-frequency textures, degradations for animation videos mostly happen around the edges which are more sensitive according to the human perceptual. Such degradations usually act as intermittent edges, aliasing edges, ringing artifacts, and rainbow effects, as shown in Fig. 2. These observations of the proposed RAL dataset inspire us that the key challenge in animation VSR is to restore visually natural and clear edges." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Degradation modeling has been the focus of many previous blind-SR works. Because of the obvious differences between animation and natural style videos, degradation methods designed for natural videos cannot properly handle degradations in animation videos. As a result, these methods suffer from amplified artifacts causing phenomena like perturbation edges, bleeding edges and inaccurate colorization along edges, even though they are fine-tuned on the animation videos (as shown in Fig. 1 a)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.85, + 0.818 + ], + "angle": 0, + "content": "3.2. Vector-Quantized Degradation Modeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Instead of imitating the real-world degradation pipeline by simply combining and adjusting some predefined basic operators [32, 46], we propose to explore the data intrinsic characteristics further and utilize degradation priors of real-world animation videos. As illustrated in Sec. 3.1," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13181" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.895, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.325, + 0.895, + 0.385 + ], + "angle": 0, + "content": "Figure 3. The overview of VQD-SR for training the animation VSR model. (a) Vector-quantized degradation model is a multi-scale VQGAN which transfers the real-world degradations from the learned VQ codebook to clean LR video frames to synthesize pseudo LR videos for VSR training, with the stochastic top-k VQ strategy. (b) HR-SR enhancement strategy eliminates the artifacts in HR animation training videos with an existing SR model to generate more ideal ground truths for supervising the VSR results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.473, + 0.603 + ], + "angle": 0, + "content": "animation videos are roughly composed of smooth color patches and clear lines. Compared to open-domain videos, which contain complex textures and irregular illumination conditions, it is possible to encode such animation video frames into a codebook of finite basic visual patterns (i.e., color patches and lines). More importantly, any animation video frame can be further decoded with corresponding patterns with high fidelity. If such a process is restricted to the real LR domain (e.g., the proposed RAL dataset), the degradation priors of real animation videos will be encapsulated into the aforementioned codebook simultaneously and could be further used for synthesizing pseudo LR data for the VSR training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.837 + ], + "angle": 0, + "content": "VQGAN [5] is a reconstruction network composed of an encoder \\( E \\), a decoder \\( G \\) and a vector-quantized codebook \\( Z \\). Motivated by the perceptually rich codebook, we resort to VQGAN [5], trained on the proposed RAL dataset with rich degradations of animation videos, to realize the decomposition of low-quality frames and encapsulate degradation priors into a learned codebook. When given a clean LR frame, the real-world degradation priors can be transferred by replacing the original clean patches with the corresponding degraded versions by looking up the learned degradation codebook. In this section, we first introduce our modified multi-scale VQGAN, then illustrate the two-stage training pipeline, and finally use the trained model to synthesize pseudo LR-HR pairs in diverse levels of degradations by a stochastic top-k vector-quantization strategy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Multi-Scale VQGAN. As discussed in Sec. 3.1, the degradations in animation videos mostly happen around the edges, which are fine-grained local details. A degradation model should be capable of processing these local details while" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.892, + 0.498 + ], + "angle": 0, + "content": "keeping the global structures (e.g., colors and shapes) at the same time. However, these two goals are usually conflicted with each other under the scope of the original single-scale VQGAN [5], as these two kinds of components are entangled together. Disentangling local details from global structures is a requisite for degradation modeling with VQGAN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.893, + 0.683 + ], + "angle": 0, + "content": "The multi-scale design has been widely explored in low-level vision [23, 39] and achieved great success, especially in the image restoration task. Inspired by this, we propose a multi-scale VQGAN which contains three parallel encoding branches. As shown in Fig. 3 a, these three branches share a shallow feature extraction module but have independent deeper encoding modules with different compression factors \\( f \\) (we choose \\( f = \\{8,4,2\\} \\) for the top, middle and bottom branches respectively). Benefiting from our multi-scale design, image information of different levels could be effectively disentangled and learned by each encoding branch in one VQ-GAN model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Two-Stage Training Pipeline. However, it is non-trivial to achieve the feature disentanglement as we expected by directly training the proposed model from scratch. This is because the bottom branch with the smallest scale will dominate the model training since it provides the easiest way to model converge. We call this phenomenon \"short-cut\". Such a problem prevents the top and the middle branches from learning image information for different scales, and the learned image representations are still entangled with each other. To take full advantage of our multi-scale VQGAN, we propose a two-stage training pipeline. We first remove the middle and the bottom branches, and only train the top branch with the largest compression factor \\( f \\). In this stage, the top branch is forced to take effect and be re" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13182" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "sponsible to reconstruct the global structures. After the convergence of the top branch, we add the other two branches back to fine-tune the overall multi-scale VQGAN. In the second stage, the two new branches only need to recover the remaining smaller structures and fine-grained details, thus avoiding the \"short-cut\" problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.184, + 0.471, + 0.504 + ], + "angle": 0, + "content": "Stochastic Top-k VQ Strategy. After training our multiscale VQGAN on a real-world low-quality animation video dataset (e.g., the proposed RAL dataset in Sec. 3.1), the learned codebooks will contain rich degradation information and are capable of transferring such degradations into unseen animation data. Specifically, as shown in Fig. 3, the learned multi-scale VQGAN will be used as the degradation model to synthesize pseudo LR images from clean LR images for further VSR model training. Although the degradation priors in the codebooks are diverse, there is only one fixed degradation output for each input as the quantization process takes the nearest neighbor search strategy to reconstruct the input, leading to poor generalization capability of the final VSR model. To expand the degradation space and introduce more randomness during training, we adopt a stochastic top-k search strategy when looking up the codebook for the VQ process. More precisely, given the encoded output \\(\\hat{z} = E(x) \\in \\mathbb{R}^{h \\times w \\times n_z}\\) from the input image \\(x\\), the former vector quantization methods search the nearest entry in the codebook \\(\\mathcal{Z} = \\{z_l\\}_{l=1}^L\\) for each vector \\(\\hat{z}_{ij}\\) in position \\((i,j)\\) to get the quantized output \\(z_q\\):" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.515, + 0.47, + 0.54 + ], + "angle": 0, + "content": "\\[\nz _ {q} = q (\\hat {z}) := \\left(\\arg \\min _ {z _ {l} \\in \\mathcal {Z}} \\| \\hat {z} _ {i j} - z _ {l} \\|\\right) \\in \\mathbb {R} ^ {h \\times w \\times n _ {z}}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.557, + 0.469, + 0.603 + ], + "angle": 0, + "content": "We expand the nearest search strategy to a stochastic topk search strategy. That is, we obtain the \\( k_{th} \\) closest entry in the codebook for each vector \\( \\hat{z}_{ij} \\) in position \\( (i,j) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.617, + 0.47, + 0.643 + ], + "angle": 0, + "content": "\\[\nz _ {q} = q (\\hat {z}) := \\left(\\arg \\underset {z _ {l} \\in \\mathcal {Z}} {k _ {t h}} \\| \\hat {z} _ {i j} - z _ {l} \\|\\right) \\in \\mathbb {R} ^ {h \\times w \\times n _ {z}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.734 + ], + "angle": 0, + "content": "For each sample in every training iteration, the value of \\( k \\) is randomly chosen from a predefined range \\( [1, K] \\) and controls the level of degradation. We chose \\( K = 50 \\) in VQD-SR and the experiment of the choice of \\( K \\) can be found in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.901 + ], + "angle": 0, + "content": "A key point here is that we adopt the stochastic top-k strategy only for the bottom branch while keeping the nearest neighbor search for the top and middle branches. This is because the larger-scale structures like colors and shapes are encoded in these two branches, and we do not want them to be changed when augmenting the local details for degradation. That is also the reason why we make a great effort to design the multi-scale VQGAN that encodes the different components in input images separately. The idea of stochastic top-k VQ strategy also corresponds with the fact that one HR image could have multiple degraded versions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.771, + 0.108 + ], + "angle": 0, + "content": "3.3. HR-SR Enhancement Strategy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.372 + ], + "angle": 0, + "content": "AVC [35] is the latest large-scale high-quality animation video dataset, specified for animation VSR tasks. As opposed to images that could be recorded in lossless format, most of the animation videos available on the Web all went through compression to reduce the network traffic. As demonstrated in Fig. 3 b, the HR animation video frames still suffered from the compression artifacts, and therefore are not completely ideal as the training ground truths. Based on this observation, we suggest enhancing the HR animation videos to further lift the upper bound for the existing animation VSR model. Since the contents of animation videos are relatively simple and the HR video frames are relatively clean, general pre-trained SR models (e.g., RealESRGAN [32]) could be used to reduce the artifacts while not contaminating image details. We thus enhance all the HR video frames in the AVC dataset by first applying an SR model, then downsampling to align the original sizes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.381, + 0.662, + 0.397 + ], + "angle": 0, + "content": "3.4. Training Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.892, + 0.616 + ], + "angle": 0, + "content": "Degradation Model. In our multi-scale VQGAN, we set the compression factor \\( f \\) to \\(\\{8,4,2\\}\\) for the {top, middle, bottom} branch respectively and use 1024 codebook entries with 256 channels in total. The input images are randomly cropped to patches of \\( 256 \\times 256 \\). The training of our multiscale VQGAN is a two-stage procedure. We follow [5] to adopt Adam [16] optimizer with the base learning rate of \\( 4.5 \\times 10^{-6} \\) for both stages. The learning rate in top branch is decreased by 4 times in the second stage. We set the total batch size to 32 and 24 for the two stages, respectively. We only apply VQ loss \\( L_{vq} \\) [29] and perceptual loss \\( L_{per} \\) [48] in the first stage, while adding the adversarial loss \\( L_{adv} \\) [5] in the second stage. The full objective function for encoder \\( E \\), decoder \\( G \\) and hierarchical VQ codebook \\( Z \\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.628, + 0.892, + 0.646 + ], + "angle": 0, + "content": "\\[\nL (E, G, Z) = L _ {v q} + L _ {p e r} + L _ {a d v}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.657, + 0.694, + 0.673 + ], + "angle": 0, + "content": "in which \\( L_{vq} \\) is calculate by:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.684, + 0.892, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {v q} = \\| x - \\hat {x} \\| + \\beta \\| s g [ E (x) _ {(s)} ] - z _ {q (s)} \\| _ {2} ^ {2} \\tag {4} \\\\ + \\left\\| s g \\left[ z _ {q (s)} \\right] - E (x) _ {(s)} \\right\\| _ {2} ^ {2}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Where \\( x, \\hat{x} \\) are the input and reconstructed images, \\( sg[\\cdot] \\) denotes the stop-gradient operation, and \\( s \\in \\{t, m, b\\} \\) means the top, middle or bottom branches. More implementation details can be found in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Video Super-Resolution Model. We adopt the unidirectional recurrent network in AnimeSR [35] as the VSR model because of its efficiency, and further remove the SR feedback in the recurrent block to ensure a more stable training according to our observation that too many recurrent features would sometimes cause a collapse of GAN loss as the omitting of explicit alignment module. We train the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13183" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "VSR model in two stages. In the first stage, we pre-train the VSR model with \\( L1 \\) loss for 300K iterations, with batch size 16 and learning rate \\( 10^{-4} \\). In the second stage, we further add perceptual loss [15] and GAN loss [17] to fine-tune the network for another 300K iterations, with batch size 16 and learning rate \\( 5 \\times 10^{-5} \\). As the promotion of perceptual quality is mainly during the second stage, we only append our multi-scale VQGAN for more realistic degradations in the second stage to reduce the training cost while only adopting basic operators in the first stage." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.258, + 0.21, + 0.276 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.283, + 0.276, + 0.298 + ], + "angle": 0, + "content": "4.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.473, + 0.475 + ], + "angle": 0, + "content": "We evaluate our method and compare its performance with other SOTA SR methods on AVC [35], the latest proposed large-scale animation video clip dataset. AVC is composed of three subsets. The training set AVC-Train contains 553 high-quality clips, and the testing set AVCTest contains 30 high-quality clips. There is also a AVCRealLQ, which contains 46 real-world low-quality clips for evaluation. Each clip consists of 100 frames. We adopt MANIQA [41], the winner in NTIRE 2022 NR-IQA challenge [8], as the no-reference image quality evaluation metric, as it in the previous animation VSR work [35]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.484, + 0.449, + 0.5 + ], + "angle": 0, + "content": "4.2. Comparisons with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.703 + ], + "angle": 0, + "content": "We compare our VQD-SR with six SOTA SR methods. Among them, AnimeSR [35] and RealBasicVSR [3] are blind video super-resolution (VSR) methods. RealESRGAN [32] and BSRGAN [46] are blind single-image super-resolution (SISR) methods with explicit degradation modeling. We also conduct experiments on BasicVSR [1] and PDM [21] as two representative methods for none-blind VSR method and blind SISR with implicit degradation modeling. Apart from AnimeSR [35], for which we report the result in the original paper, all the others are general SR methods for open-domain images or videos. For fair comparisons, we fine-tune their officially released models on animation dataset AVC-Train." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Quantitative Comparison. As shown in Tab. 1, we evaluate all the methods on AVC-RealLQ [35] for quantitative comparisons. Among them, Real-ESRGAN [32] and BSRGAN [46] expand the former explicit degradation models by introducing high-order degradations and random shuffling respectively, which greatly improve the synthetic ability. And with the help of powerful SR backbone (RRDB-Net [33] with 16.70M parameters), their results are quite remarkable. Nonetheless, ignoring the intrinsic characteristics of animation data limits their performance when applied to animation domain. Although specialized for animation videos, AnimeSR [35] only utilizes a small number of real data (three human-annotated animation videos), which hin" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.088, + 0.892, + 0.13 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on AVC-RealLQ for \\(4 \\times\\) animation VSR. \\* denotes fine-tune on animation dataset AVC-Train [35]. Bold text indicates the best performance." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.139, + 0.892, + 0.246 + ], + "angle": 0, + "content": "
MethodParams (M)Runtime (ms)MANIQA↑
BasicVSR* [1]6.291750.2829
PDM* [21]16.704380.2574
Real-ESRGAN* [32]16.704380.3825
BSRGAN* [46]16.704380.3836
RealBasicVSR*[3]6.292520.3504
AnimeSR [35]1.50260.3832
VQD-SR (Ours)1.47250.4096
" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.26, + 0.892, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.404, + 0.892, + 0.434 + ], + "angle": 0, + "content": "Figure 4. Results of User Study. The values on Y-axis represent the percentage of users that prefer VQD-SR over other approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.672 + ], + "angle": 0, + "content": "ders the performance of VSR model in real scenarios. Different from them, our VQD-SR considers the intrinsic characteristics of animation videos and leverages the enormous degradation priors contained in rich-content real animation videos. VQD-SR also adopts the HR enhancement strategy for more effective SR supervision. Due to these advantages, VQD-SR achieves a result of 0.4096 and significantly outperforms the SOTA animation VSR model [35] by 0.0264 in MANIQA on AVC-RealLQ [35]. Meanwhile, as the removal of SR recurrent feedback in VSR model, the number of parameters in VQD-SR are further reduced to \\(1.47\\mathrm{M}\\) with the runtime of \\(25~\\mathrm{ms}\\) computed on a NVIDIA Tesla M40 GPU with the LR size of \\(180\\times 320\\), which demonstrates the superiority of our VQD-SR in real applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.853 + ], + "angle": 0, + "content": "Qualitative Comparison. As shown in Fig. 5, we compare visual qualities of different approaches on real-world AVC-RealLQ video clips. It can be observed that VQD-SR greatly improves the visual quality, especially for the recovery of clear lines. Additionally, the results of VQD-SR are more visually natural with fewer artifacts in some intended scenarios (e.g., the out-focus background blur and smooth underwater scene in row 5-6), while most of the other methods suffer from over-sharp artifacts like irregular lines and patterns. More visual comparisons with original inputs for reference and result analysis are in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We also conduct a user study to further evaluate the visual quality of our approach. There are 20 subjects involved in this user study and 22080 votes are collected on AVC-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13184" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.247, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.15, + 0.231, + 0.159 + ], + "angle": 0, + "content": "```python\nanime_dance_level_0/739" + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.089, + 0.429, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.264, + 0.15, + 0.321, + 0.159 + ], + "angle": 0, + "content": "BasicVSR*" + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.089, + 0.522, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.436, + 0.15, + 0.516, + 0.159 + ], + "angle": 0, + "content": "Real-ESRGAN*" + }, + { + "type": "image", + "bbox": [ + 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"content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.222, + 0.196, + 0.231 + ], + "angle": 0, + "content": "go_player/95" + }, + { + "type": "image", + "bbox": [ + 0.247, + 0.16, + 0.429, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.263, + 0.221, + 0.32, + 0.23 + ], + "angle": 0, + "content": "BasicVSR*" + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.16, + 0.521, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.434, + 0.221, + 0.515, + 0.23 + ], + "angle": 0, + "content": "Real-ESRGAN*" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.16, + 0.614, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.221, + 0.593, + 0.23 + ], + "angle": 0, + "content": "BSRGAN*" + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.16, + 0.706, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.221, + 0.698, + 0.23 + ], + "angle": 0, + "content": "RealBasicVSR*" + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.16, + 0.797, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.726, + 0.221, + 0.776, + 0.23 + ], + "angle": 0, + "content": "AnimeSR" + }, + { + "type": "image", + "bbox": [ + 0.798, + 0.16, + 0.889, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.221, + 0.885, + 0.231 + ], + "angle": 0, + "content": "VQD-SR (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.232, + 0.245, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.293, + 0.215, + 0.302 + ], + "angle": 0, + "content": "crayon_shinchan/30" + }, + { + "type": "image", + "bbox": [ + 0.247, + 0.232, + 0.429, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 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"angle": 0, + "content": "AnimeSR" + }, + { + "type": "image", + "bbox": [ + 0.798, + 0.232, + 0.889, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.802, + 0.293, + 0.885, + 0.302 + ], + "angle": 0, + "content": "VQD-SR (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.305, + 0.245, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.366, + 0.2, + 0.375 + ], + "angle": 0, + "content": "mado_king/38" + }, + { + "type": "image", + "bbox": [ + 0.247, + 0.305, + 0.429, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.366, + 0.321, + 0.374 + ], + "angle": 0, + "content": "BasicVSR*" + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.305, + 0.521, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.437, + 0.366, + 0.516, + 0.374 + ], + "angle": 0, + "content": "Real-ESRGAN*" + 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"angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.62, + 0.442, + 0.699, + 0.45 + ], + "angle": 0, + "content": "RealBasicVSR*" + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.381, + 0.797, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.728, + 0.442, + 0.776, + 0.45 + ], + "angle": 0, + "content": "AnimeSR" + }, + { + "type": "image", + "bbox": [ + 0.798, + 0.381, + 0.889, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.803, + 0.441, + 0.885, + 0.45 + ], + "angle": 0, + "content": "VQD-SR (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.452, + 0.245, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.512, + 0.195, + 0.521 + ], + "angle": 0, + "content": "hell girl/105" + }, + { + "type": "image", + "bbox": [ + 0.247, + 0.452, + 0.429, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.512, + 0.321, + 0.521 + ], + "angle": 0, + "content": "BasicVSR*" + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.452, + 0.521, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.437, + 0.512, + 0.515, + 0.52 + ], + "angle": 0, + "content": "Real-ESRGAN*" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.452, + 0.614, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.512, + 0.594, + 0.52 + ], + "angle": 0, + "content": "BSRGAN*" + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.452, + 0.706, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.62, + 0.512, + 0.699, + 0.52 + ], + "angle": 0, + "content": "RealBasicVSR*" + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.452, + 0.797, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.728, + 0.512, + 0.776, + 0.52 + ], + "angle": 0, + "content": "AnimeSR" + }, + { + "type": "image", + "bbox": [ + 0.798, + 0.452, + 0.889, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.803, + 0.512, + 0.885, + 0.521 + ], + "angle": 0, + "content": "VQD-SR (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.526, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparisons on AVC-RealLQ [35] for \\(4 \\times\\) scaling factor. \\(*\\) denotes fine-tune on animation domain dataset. The frame name is shown at the bottom of each case. Our VQD-SR recovers visually natural and sharper lines with fewer artifacts (the first 4 rows) and is also capable to handle some intended scenarios with fewer over-sharp artifacts (row 5th with smooth background and clear foreground, row 6th in underwater scene). Zoom in to see better visualization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.468, + 0.754 + ], + "angle": 0, + "content": "RealLQ [35] with 46 video clips. For each comparison, we adopt an A-B test that provides the users with two images in random order which include one VQD-SR frame. Users are asked to select the one with higher visual quality. As shown in Fig. 4, comparing with the SR methods designed for open-domain, over \\(80\\%\\) of users voted for our VQD-SR. By considering the data characteristic of animation, there are still over \\(65\\%\\) users who prefer our method to AnimeSR [35]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.227, + 0.786 + ], + "angle": 0, + "content": "4.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.468, + 0.839 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies on each significant component of our VQ degradation model and HR-SR enhancement strategy in VQD-SR." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.9 + ], + "angle": 0, + "content": "VQ Degradation Model. In the ablation study of VQ degradation model design, we conduct all the experiments based on VQD-SR (base), which denotes a plain version of VQD-SR trained without HR-SR enhancement. As shown" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.616, + 0.583, + 0.667 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.668, + 0.576, + 0.677 + ], + "angle": 0, + "content": "VQD-SR (base)" + }, + { + "type": "image", + "bbox": [ + 0.585, + 0.617, + 0.658, + 0.667 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.593, + 0.668, + 0.644, + 0.676 + ], + "angle": 0, + "content": "(a) BasicOP" + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.617, + 0.735, + 0.667 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.664, + 0.668, + 0.733, + 0.676 + ], + "angle": 0, + "content": "(b) Single Scale" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.617, + 0.813, + 0.667 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.739, + 0.668, + 0.808, + 0.676 + ], + "angle": 0, + "content": "(c) Single Stage" + }, + { + "type": "image", + "bbox": [ + 0.816, + 0.617, + 0.892, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.668, + 0.872, + 0.676 + ], + "angle": 0, + "content": "(d) Top-1" + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.695, + 0.85, + 0.708 + ], + "angle": 0, + "content": "Figure 6. Ablation study on VQ degradation model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "in Tab. 2 a, we first compare the degradation model which is simply composed of basic operators (blur, noise and FFmpeg) to our VQD-SR (base). With the help of real-world degradation priors contained in VQ codebook, the result can be improved from 0.3768 to 0.3857 in MANIQA. Referring to Fig. 6 a, VSR model trained with only basic operators fails to handle some real-world degradations, leading to artifacts around the edges. We further compare the structure and training strategy of VQ degradation model in Tab. 2 b and Tab. 2 c. As the global structures and local details are entangled together in single-scale VQ model and the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13185" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.471, + 0.143 + ], + "angle": 0, + "content": "Table 2. Ablation study results of degradation models, structures of VQ degradation model, training pipelines of VQ degradation model and VQ codebook search strategies. The MANIQA scores are reported for comparisons." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.153, + 0.431, + 0.327 + ], + "angle": 0, + "content": "
MANIQA↑(a) Degradation Model
BasicOP-OnlyVQD-SR (base)
0.37680.3857
MANIQA↑(b) VQGAN Structure
Single-scaleVQD-SR (base)
0.34660.3857
MANIQA↑(c) Training Strategy
Single-stageVQD-SR (base)
0.34300.3857
MANIQA↑(d) Codebook Search
NearestVQD-SR (base)
0.37700.3857
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.341, + 0.468, + 0.379 + ], + "angle": 0, + "content": "Table 3. Applying VQ degradation to widely used SR backbones. For each backbone, settings are consistent apart from degradation methods." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.38, + 0.466, + 0.431 + ], + "angle": 0, + "content": "
BackboneReal-ESRGAN*RealBasicVSR*AnimeSR
Params (M)16.76.31.5
Original degradation0.38250.35040.3832
VQ degradation0.39670.38490.3857
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.468, + 0.595 + ], + "angle": 0, + "content": "multi-scale model trained in single-stage, the performances dropped by 0.0391 and 0.0427, respectively. As shown in Fig. 6 b and Fig. 6 c, some fine-grained details are missing. For VQ strategies, as shown in Tab. 2 d and Fig. 6 d, our stochastic top-k VQ strategy can improve MANIQA by 0.0087 compared with the original nearest neighbor search strategy, as the top-k VQ strategy enables multi-level degradations which improves the generalization ability of the trained animation model, leading to more appealing results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.468, + 0.793 + ], + "angle": 0, + "content": "To further illustrate the general applicability, we also apply our VQ degradation model to other SOTA SR backbones, Real-ESRGAN and RealBasicVSR, fine-tuned with animation data in the same setting. Referring to Tab. 3, SR models with VQ degradation achieve better results comparing with their original degradation methods, which indicates that the proposed VQ degradation is generally effective for animation SR models. It is noteworthy that the performance gains could be more significant for larger backbones. The visual examples in Fig. 7 also show the superiority of our VQ degradation method, especially to recover clear and visual natural lines which are the most import patterns deciding the visual quality of animation videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "HR Enhancement. The training HR animation videos collected from the Web also contain artifacts which are not ideal for ground truths, hindering the performances of animation VSR models. We propose the HR-SR strategy to enhance the quality of HR animation videos for more effective training ground truths. We first compare three different HR enhancement models by experiments on VQD-SR (base)." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.659, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.552, + 0.201, + 0.61, + 0.207 + ], + "angle": 0, + "content": "bhd and shs/30" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.091, + 0.736, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.666, + 0.201, + 0.735, + 0.207 + ], + "angle": 0, + "content": "Real-ESRGAN(VQ)\\*" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.091, + 0.813, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.201, + 0.812, + 0.207 + ], + "angle": 0, + "content": "RealBasicVSR (VQ)*" + }, + { + "type": "image", + "bbox": [ + 0.816, + 0.091, + 0.891, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.201, + 0.879, + 0.207 + ], + "angle": 0, + "content": "AnimeSR (VQ)" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.212, + 0.658, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.322, + 0.594, + 0.328 + ], + "angle": 0, + "content": "ccs/124" + }, + { + "type": "image", + "bbox": [ + 0.661, + 0.212, + 0.736, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.322, + 0.734, + 0.328 + ], + "angle": 0, + "content": "Real-ESRGAN(VQ)*" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.212, + 0.813, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.322, + 0.812, + 0.328 + ], + "angle": 0, + "content": "RealBasicVSR (VQ)*" + }, + { + "type": "image", + "bbox": [ + 0.816, + 0.212, + 0.891, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.322, + 0.879, + 0.328 + ], + "angle": 0, + "content": "```bash\nAnimeSR(VQ)" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.332, + 0.658, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.443, + 0.609, + 0.45 + ], + "angle": 0, + "content": "big_ear_tutu/105" + }, + { + "type": "image", + "bbox": [ + 0.661, + 0.332, + 0.724, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.666, + 0.443, + 0.733, + 0.45 + ], + "angle": 0, + "content": "Real-ESRGAN(VQ)*" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.332, + 0.801, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.443, + 0.81, + 0.45 + ], + "angle": 0, + "content": "RealBasicVSR (VQ)*" + }, + { + "type": "image", + "bbox": [ + 0.816, + 0.332, + 0.876, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.443, + 0.878, + 0.45 + ], + "angle": 0, + "content": "AnimeSR (VQ)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.467, + 0.891, + 0.522 + ], + "angle": 0, + "content": "Figure 7. Applying VQ degradation to widely used SR backbones. Settings are consistent apart from degradation methods. Models trained with VQ degradation could produce more clear and visual natural lines with fewer artifacts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.717 + ], + "angle": 0, + "content": "The quantitative results are shown in Tab. 4. All three models improve the performance of animation VSR model, which verifies that the proposed HR-SR strategy is suitable for the training of animation VSR model, and improvements are not subject to the specific model for enhancement. However, as the SR process for data enhancement is conducted in HR domain, which takes a high demand on computing resources, we finally choose SISR model, Real-ESRGAN (S) [32] with relatively small model size. Visual examples of the enhanced HR frames can be found in Fig. 8." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We further utilize the enhanced HR animation videos processed by Real-ESRGAN(S) [32] to fine-tune different VSR models. Apart from the proposed VQD-SR, RealBasicVSR [3] is a blind VSR model designed for open-domain videos and AnimeSR [35] is an VSR model specified for animation domain. As shown in Tab. 5, with the help of HR enhancement, all three VSR models get improved, which illustrates that the proposed HR enhancement strategy is effective for animation VSR task, regardless of the specific VSR model. The visual results of RealBasicVSR+, AnimeSR+, and VQD-SR in Fig. 9 also verify the advantages of the HR-SR enhancement strategy for animation VSR." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13186" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.088, + 0.47, + 0.13 + ], + "angle": 0, + "content": "Table 4. Ablation study of different SR models for HR-SR enhancement. All three models improve the performance. We choose Real-ESRGAN (S) considering the computing cost." + }, + { + "type": "table", + "bbox": [ + 0.137, + 0.14, + 0.413, + 0.221 + ], + "angle": 0, + "content": "
Enhancement MethodMANIQA↑
No Enhancement0.3857
AnimeSR [35]0.4146
Real-ESRGAN (L) [32]0.4211
Real-ESRGAN (S) [32]0.4096
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.234, + 0.468, + 0.276 + ], + "angle": 0, + "content": "Table 5. Ablation study of HR-SR enhancement for different animation VSR models on AVC-RealLQ. We report MANIQA for comparison." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.286, + 0.428, + 0.348 + ], + "angle": 0, + "content": "
MANIQA↑wo /HR-SRw /HR-SR
RealBasicVSR [3]0.35040.3855
AnimeSR [35]0.38320.4079
VQD-SR0.38570.4096
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.361, + 0.174, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.425, + 0.15, + 0.434 + ], + "angle": 0, + "content": "Input HR" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.361, + 0.272, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.425, + 0.247, + 0.434 + ], + "angle": 0, + "content": "AnimeSR" + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.361, + 0.37, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.425, + 0.365, + 0.434 + ], + "angle": 0, + "content": "Real-ESRGAN (L)" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.361, + 0.468, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.425, + 0.462, + 0.435 + ], + "angle": 0, + "content": "Real-ESRGAN (S)" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.437, + 0.174, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.437, + 0.272, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.437, + 0.37, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.437, + 0.468, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.526, + 0.468, + 0.553 + ], + "angle": 0, + "content": "Figure 8. Enhanced HR data with HR-SR strategy by different enhancement models." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.591, + 0.32, + 0.607 + ], + "angle": 0, + "content": "5. Limitation and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.468, + 0.737 + ], + "angle": 0, + "content": "In this section, we visualize the failure cases of VQDSR in Fig. 10. Our VQD-SR is capable to restore sharper lines and suppress diverse artifacts in animation videos. However, in some extreme circumstances (e.g., severe lossy compressions, long passing ages), there still gets room for improvement, for example the remaining color distortions around edges. Nevertheless, comparing with other SOTA methods, our VQD-SR still achieves better performances." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.754, + 0.195, + 0.769 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In this paper, we thoroughly study the characteristics of animation videos and fully leverage the rich prior knowledge contained in real data for a more practical animation VSR model. To be specific, we propose a novel degradation model which utilize a multi-scale VQGAN, self-supervised on purely real low-quality animation data (RAL), to decompose animation frames and establish a codebook containing diverse real-world degradation priors. We also propose a" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.657, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.659, + 0.09, + 0.735, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.09, + 0.812, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.813, + 0.09, + 0.89, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.212, + 0.657, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.211, + 0.89, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.348, + 0.892, + 0.39 + ], + "angle": 0, + "content": "Figure 9. Ablation study of HR-SR enhancement strategy for different VSR models. HR-SR enhancement is generally effective task, regardless of the specific VSR model." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.412, + 0.66, + 0.524 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.521, + 0.613, + 0.53 + ], + "angle": 0, + "content": "tom_and_jerry/90" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.412, + 0.738, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.521, + 0.73, + 0.529 + ], + "angle": 0, + "content": "RealBasicVSR*" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.412, + 0.815, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.759, + 0.521, + 0.796, + 0.529 + ], + "angle": 0, + "content": "AnimeSR" + }, + { + "type": "image", + "bbox": [ + 0.816, + 0.412, + 0.892, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.824, + 0.521, + 0.882, + 0.529 + ], + "angle": 0, + "content": "VQD-SR (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.532, + 0.66, + 0.647 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.641, + 0.607, + 0.649 + ], + "angle": 0, + "content": "doraemon/91" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.532, + 0.738, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.532, + 0.814, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.815, + 0.532, + 0.891, + 0.649 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.653, + 0.89, + 0.681 + ], + "angle": 0, + "content": "Figure 10. Failure cases when LR frames endure severe color distortions around edges." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.835 + ], + "angle": 0, + "content": "two-stage training pipeline and a stochastic top-k VQ strategy to match up with the VQ degradation model. We further propose to enhance the HR training videos to lift the performance ceiling for animation VSR tasks. Experiment results show the superiority of the proposed VQD-SR over existing SOTA models, as our methods could generate more effective LR-HR training pairs in view of the characteristics in real animation videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported in part by the NSFC under Grant 62272380 and 62103317, the Science and Technology Program of Xi'an, China under Grant 21RGZN0017, and Microsoft Research Asia." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13187" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Kelvin CK Chan, Xintao Wang, Ke Yu, Chao Dong, and Chen Change Loy. BasicVSR: The search for essential components in video super-resolution and beyond. In CVPR, pages 4947-4956, 2021." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.226 + ], + "angle": 0, + "content": "[2] Kelvin CK Chan, Shangchen Zhou, Xiangyu Xu, and Chen Change Loy. BasicVSR++: Improving video superresolution with enhanced propagation and alignment. 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In CVPR, pages 586-595, 2018." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.841 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "13189" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/8790a28a-4db4-4d06-856c-466efed197ec_origin.pdf b/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/8790a28a-4db4-4d06-856c-466efed197ec_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..af8619a86e8b8258305d863ca36594d2360115aa --- /dev/null +++ b/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/8790a28a-4db4-4d06-856c-466efed197ec_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:984e6b0f90c208a814374da14e3f9fe25963d9d517e58c4e4f6e4103b46cdab6 +size 3445797 diff --git a/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/full.md b/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f8cc1099de23ae26b5914f2a83a0f0e8cfa8f90a --- /dev/null +++ b/2023/Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution/full.md @@ -0,0 +1,507 @@ +# Learning Data-Driven Vector-Quantized Degradation Model for Animation Video Super-Resolution + +Zixi Tuo\*, Huan Yang†, Jianlong Fu², Yujie Dun¹, Xueming Qian¹,³ + +$^{1}$ Xi'an Jiaotong University $^{2}$ Microsoft Research Asia + +3Shaanxi Yulan Jiuzhou Intelligent Optoelectronic Technology Co., Ltd + +zixit99@gmail.com, {huayan, jianf}@microsoft.com, {dunyj, qianxm}@mail.xjtu.edu.cn + +# Abstract + +Existing real-world video super-resolution (VSR) methods focus on designing a general degradation pipeline for open-domain videos while ignoring data intrinsic characteristics which strongly limit their performance when applying to some specific domains (e.g., animation videos). In this paper, we thoroughly explore the characteristics of animation videos and leverage the rich priors in real-world animation data for a more practical animation VSR model. In particular, we propose a multi-scale Vector-Quantized Degradation model for animation video Super-Resolution (VQD-SR) to decompose the local details from global structures and transfer the degradation priors in real-world animation videos to a learned vector-quantized codebook for degradation modeling. A rich-content Real Animation Low-quality (RAL) video dataset is collected for extracting the priors. We further propose a data enhancement strategy for high-resolution (HR) training videos based on our observation that existing HR videos are mostly collected from the Web which contains conspicuous compression artifacts. The proposed strategy is valid to lift the upper bound of animation VSR performance, regardless of the specific VSR model. Experimental results demonstrate the superiority of the proposed VQD-SR over state-of-the-art methods, through extensive quantitative and qualitative evaluations of the latest animation video super-resolution benchmark. The code and pre-trained models can be downloaded at https://github.com/researchmm/VQD-SR. + +# 1. Introduction + +Animation video super-resolution (VSR) [35], which is a subdiscipline of video super-resolution (VSR) [1, 2, 3, 19, 28, 37], aims to restore high-resolution (HR) videos from their low-resolution (LR) counterparts in animation domain. As a special type of visual art, animation video shows great + +![](images/b648bb4b0a308669630b744b7072bd28b420f33c98a7502a1b7edcefda12053a.jpg) + +![](images/0c361d45be249385c7744bd7051eb36015d0647a1a62470b8130dc50bf462825.jpg) +Figure 1. A comparison between our proposed VQD-SR and other SOTA VSR methods in real scenario. As indicated by the red dotted circles, our VQD-SR could restore more appealing details by considering the degradation priors in real animation videos. (\* denotes fine-tune on animation videos). + +![](images/29a534dcd8374b41053e293d9c453b983be018fe36a1cf107e7625467f6821f3.jpg) + +![](images/dc1a260162d5f9d5223932387f0723ceb9fddce29fc1b608b0662a81bbe78ffa.jpg) + +entertainment, cultural, educational and commercial values. However, most of them available on the Web are in limited resolutions and have visually unappealing artifacts due to the passing ages, lossy compression and transmission. Dedicated to real applications, animation VSR is a blind SR [21, 32, 46, 40, 43] task which is more challenging than conventional VSR tasks [1, 2, 14, 19, 28, 36], because of the complicated and agnostic real-world degradations. Thus, practical VSR methods for improving real-world LR animation videos are in highly demanded. + +Blind SR model for open-domain has long been the focus. As it's hard to collect LR-HR pairs in real scenarios, recent learning-based approaches try to model the real-world degradations from HR to LR, thus generating pseudo LR-HR pairs to train SR models. These approaches can + +be roughly divided into two categories, explicit modeling and implicit modeling, with regard to the degradation procedures. Explicit modeling [9, 20, 32, 46] methods try to combine basic degradation operators like noise, blur and rescaling to imitate the real-world degradation pipeline. Instead, implicit modeling methods employ a neural network, which is usually in the manner of generative adversarial networks (GAN) [7], as an alternative to the combination of basic degradation operators. However, these general degradation methods designed for open-domain videos are not quite suitable for the animation domain as they ignore the intrinsic characteristics of the data. Directly adopting existing degradation models for open-domain to animation VSR would lead to unpleasant results (as shown in Fig. 1 a), even though they are fine-tuned on the animation videos. + +Specific to animation VSR, AnimeSR [35] moves one step further to propose a learnable basic operator (LBO) with an "input-rescaling" strategy that considers the data characteristics and demonstrates their advantages over open-domain VSR methods. However, the proposed "input-rescaling" strategy of constructing pseudo HR-LR pairs for the LBO training requires human annotations, which prevents their method from scaling up to modeling various real-world degradations. In AnimeSR [35], only three LBOs are trained with three human-annotated videos respectively, leading to unappealing results (as shown in Fig. 1 b). Thus, how to effectively leverage large-scale real-world animation videos based on their data characteristics is still an open problem. + +In this paper, we propose a multi-scale Vector-Quantized Degradation model for animation video Super-Resolution (VQD-SR), which leverages the data characteristics of animation videos. We observe that different from open-domain videos with complex textures and irregular illumination conditions, animation videos are roughly composed of basic visual patterns like smooth color patches and clear lines which can be easily captured with high fidelity by vector-quantization (VQ) [5, 25, 29]. Such data characteristics could also be used for encoding and transferring degradation priors from low-quality animation videos and results in a degradation codebook. Given any clean LR animation frame, the degraded LR counterpart can be easily obtained by looking up the pre-trained degradation codebook. Specifically, a novel multi-scale VQGAN for degradation modeling is proposed to learn and transfer real-world degradation priors from a large-scale Real Animation Low-quality (RAL) video dataset collected from the Web. To improve the generalization ability of VQD-SR, we propose a two-stage training pipeline and a stochastic top-k VQ strategy to match up with the multi-scale VQGAN, yielding visually appealing results (as shown in Fig. 1 c). + +To further lift the upper bound of existing animation VSR methods, we propose an HR-SR strategy to enhance + +the quality of HR training videos for more ideal ground truths. This is motivated by our observations that existing HR animation videos are mostly collected from the Web which contains conspicuous compression artifacts and such artifacts could be easily reduced by existing SR methods. Our contributions are summarized as follows: + +- We collect a large-scale real LR animation dataset, and conduct a comprehensive study on real animation data to thoroughly explore the challenges and data characteristics in animation VSR task. + +- We propose a novel multi-scale VQ degradation model to transfer real-world degradation priors for synthesizing pseudo LR-HR training pairs. We further propose an HR-SR data enhancement strategy to improve the performance of existing VSR methods for animation. + +- Extensive experiments demonstrate the effectiveness of our proposed methods which significantly improve the recent SOTA animation VSR method in both quantitative and qualitative comparisons. + +# 2. Related Work + +# 2.1. Video Super-Resolution + +Recent years have witnessed a prosperity in deep learning based VSR methods [2, 3, 14, 24, 28, 31, 38]. Different from single-image super-resolution (SISR), the auxiliary temporal information is available in VSR for the restoration of inner-frame features. Sliding-window structure [28, 31, 38, 42] and recurrent structure [1, 2, 6, 12, 14] are two common paradigms in VSR to utilize the interframe information. However, it also faces challenges while taking the advantages. The degradations could be more complicated in videos and may accumulate along the time sequence [3, 37], causing the performance drop in real-world scenarios. + +There have been several attempts in blind-SR field to deal with real-world degradations, which could be categorized into explicit and implicit modeling. Explicit methods model the degradation as the effects of objective operators (or kernels). Methods like [9, 47] assume these degradations to be simple combinations of blur, noise and down-sampling kernels, therefore conducting conditional restoration based on the prediction of kernel parameters. Operators like JPEG/FFmpeg [20] for lossy compression, sinc filter [32] for ringing artifacts and strategies like high-order modeling [32], random shuffling [46], are further investigated in latest studies to simulate the real degradation pipeline and expand the synthesis space. However, these methods merely depend on predefined operators, and ignore to utilize the information contained in real data, thus there's still a gap between the synthesis LR and real LR data. Implicit methods [21, 22, 34, 44] discard the objective degradation operators, but learn the distribution of real data, + +therefore realize the degradation by converting the HR input to fit the real LR distribution. Yet, the learned distribution space is uncontrollable, thus the degradation network may easily project unseen out-of-distribution samples to unpredictable suboptimal space causing annoying artifacts. + +# 2.2. Animation Video Processing + +Animation is a type of visual art that is represented in a nonrealistic artistic style. A diversity of animation processing technologies based on deep learning have been developed these years, such as animation style transfer [4, 13, 30], animation video colorization [18, 27, 45], animation video generation [11] and animation video interpolation [26]. AnimeSR [35] is a recent study for real-world animation VSR tasks, which develops LBO to expand the basic degradation operators. In this paper, we take a further step to explore the characteristics of animation videos, and make special designs in consideration of these characteristics to improve the performance of real-world animation VSR. + +# 2.3. Vector-Quantized Codebook + +Vector-quantized(VQ) codebook was first proposed in VQ-VAE [29] to learn the discrete representation for images in latent space. Later, a hierarchical VQ-VAE-2 [25] is further proposed. To improve the perceptual quality, a discriminator and perceptual loss were added in VQGAN [5]. Recently in VQFR [10], a VQ-based face restoration method was also proposed. Although initially designed to avoid the "posterior collapse" issue of VAE or tokenizer input images for a more effective transformer modeling, we discover that the idea of VQ is naturally suitable for representing animation video frames and the form of codebook is capable to internalize the real degradation priors. + +# 3. Methodology + +In this section, we first discuss the characteristics of real animation videos and the challenges for animation VSR task in Sec. 3.1. Based on the observations in Sec. 3.1, we introduce the proposed real-world animation degradation model in Sec. 3.2. Finally, we illustrate our HR training data enhancement strategy in Sec. 3.3. + +# 3.1. Real-World Degradation in Animation Videos + +To thoroughly understand the characteristics of animation videos and the challenges in animation VSR task, we collect a Real Animation Low-quality (RAL) video dataset. RAL contains over 10K LR frames extracted from 441 real-world low-quality animation videos. To the best of our knowledge, RAL is the largest real-world low-quality video dataset in the animation domain. Example frames are shown in Fig. 2 (statistics of RAL can be found in the + +![](images/de9e663f028e943d78215689fcd4fb172eaa7dbe3dafa367cd87813363aa29ce.jpg) +Figure 2. Samples of RAL and typical degradation phenomena in real-world LR animation videos. RAL is a real-world animation video dataset contains over 10K LR frames. Intermittent edges, aliasing edges, ringing artifacts and rainbow effects are four typical degradation phenomena in real-world animation videos. + +supplementary). To construct such a dataset, we first download numerous earlier animation videos from multiple video sites such as YouTube and Bilibili. Then we manually select videos according to their resolutions, quality, contents and styles. To ensure the dataset contains rich animation structures and degradation priors, we adopt a simple scene filtering procedure to remove the frames which have subtle motions by evaluating their average absolute differences, thus reducing the redundancy. + +Animation videos are roughly composed of smooth color patches and clear lines, while the latter ones usually play an important role in portraying objects and expressing visual semantics. In contrast to the fact that degradation losses for open domain videos are mainly about high-frequency textures, degradations for animation videos mostly happen around the edges which are more sensitive according to the human perceptual. Such degradations usually act as intermittent edges, aliasing edges, ringing artifacts, and rainbow effects, as shown in Fig. 2. These observations of the proposed RAL dataset inspire us that the key challenge in animation VSR is to restore visually natural and clear edges. + +Degradation modeling has been the focus of many previous blind-SR works. Because of the obvious differences between animation and natural style videos, degradation methods designed for natural videos cannot properly handle degradations in animation videos. As a result, these methods suffer from amplified artifacts causing phenomena like perturbation edges, bleeding edges and inaccurate colorization along edges, even though they are fine-tuned on the animation videos (as shown in Fig. 1 a). + +# 3.2. Vector-Quantized Degradation Modeling + +Instead of imitating the real-world degradation pipeline by simply combining and adjusting some predefined basic operators [32, 46], we propose to explore the data intrinsic characteristics further and utilize degradation priors of real-world animation videos. As illustrated in Sec. 3.1, + +![](images/5fcf775f84a2a2f016fd0a7bef3f148f6cf4fd6558de1773bca2ba28085e46c2.jpg) +Figure 3. The overview of VQD-SR for training the animation VSR model. (a) Vector-quantized degradation model is a multi-scale VQGAN which transfers the real-world degradations from the learned VQ codebook to clean LR video frames to synthesize pseudo LR videos for VSR training, with the stochastic top-k VQ strategy. (b) HR-SR enhancement strategy eliminates the artifacts in HR animation training videos with an existing SR model to generate more ideal ground truths for supervising the VSR results. + +animation videos are roughly composed of smooth color patches and clear lines. Compared to open-domain videos, which contain complex textures and irregular illumination conditions, it is possible to encode such animation video frames into a codebook of finite basic visual patterns (i.e., color patches and lines). More importantly, any animation video frame can be further decoded with corresponding patterns with high fidelity. If such a process is restricted to the real LR domain (e.g., the proposed RAL dataset), the degradation priors of real animation videos will be encapsulated into the aforementioned codebook simultaneously and could be further used for synthesizing pseudo LR data for the VSR training. + +VQGAN [5] is a reconstruction network composed of an encoder $E$ , a decoder $G$ and a vector-quantized codebook $Z$ . Motivated by the perceptually rich codebook, we resort to VQGAN [5], trained on the proposed RAL dataset with rich degradations of animation videos, to realize the decomposition of low-quality frames and encapsulate degradation priors into a learned codebook. When given a clean LR frame, the real-world degradation priors can be transferred by replacing the original clean patches with the corresponding degraded versions by looking up the learned degradation codebook. In this section, we first introduce our modified multi-scale VQGAN, then illustrate the two-stage training pipeline, and finally use the trained model to synthesize pseudo LR-HR pairs in diverse levels of degradations by a stochastic top-k vector-quantization strategy. + +Multi-Scale VQGAN. As discussed in Sec. 3.1, the degradations in animation videos mostly happen around the edges, which are fine-grained local details. A degradation model should be capable of processing these local details while + +keeping the global structures (e.g., colors and shapes) at the same time. However, these two goals are usually conflicted with each other under the scope of the original single-scale VQGAN [5], as these two kinds of components are entangled together. Disentangling local details from global structures is a requisite for degradation modeling with VQGAN. + +The multi-scale design has been widely explored in low-level vision [23, 39] and achieved great success, especially in the image restoration task. Inspired by this, we propose a multi-scale VQGAN which contains three parallel encoding branches. As shown in Fig. 3 a, these three branches share a shallow feature extraction module but have independent deeper encoding modules with different compression factors $f$ (we choose $f = \{8,4,2\}$ for the top, middle and bottom branches respectively). Benefiting from our multi-scale design, image information of different levels could be effectively disentangled and learned by each encoding branch in one VQ-GAN model. + +Two-Stage Training Pipeline. However, it is non-trivial to achieve the feature disentanglement as we expected by directly training the proposed model from scratch. This is because the bottom branch with the smallest scale will dominate the model training since it provides the easiest way to model converge. We call this phenomenon "short-cut". Such a problem prevents the top and the middle branches from learning image information for different scales, and the learned image representations are still entangled with each other. To take full advantage of our multi-scale VQGAN, we propose a two-stage training pipeline. We first remove the middle and the bottom branches, and only train the top branch with the largest compression factor $f$ . In this stage, the top branch is forced to take effect and be re + +sponsible to reconstruct the global structures. After the convergence of the top branch, we add the other two branches back to fine-tune the overall multi-scale VQGAN. In the second stage, the two new branches only need to recover the remaining smaller structures and fine-grained details, thus avoiding the "short-cut" problem. + +Stochastic Top-k VQ Strategy. After training our multiscale VQGAN on a real-world low-quality animation video dataset (e.g., the proposed RAL dataset in Sec. 3.1), the learned codebooks will contain rich degradation information and are capable of transferring such degradations into unseen animation data. Specifically, as shown in Fig. 3, the learned multi-scale VQGAN will be used as the degradation model to synthesize pseudo LR images from clean LR images for further VSR model training. Although the degradation priors in the codebooks are diverse, there is only one fixed degradation output for each input as the quantization process takes the nearest neighbor search strategy to reconstruct the input, leading to poor generalization capability of the final VSR model. To expand the degradation space and introduce more randomness during training, we adopt a stochastic top-k search strategy when looking up the codebook for the VQ process. More precisely, given the encoded output $\hat{z} = E(x) \in \mathbb{R}^{h \times w \times n_z}$ from the input image $x$ , the former vector quantization methods search the nearest entry in the codebook $\mathcal{Z} = \{z_l\}_{l=1}^L$ for each vector $\hat{z}_{ij}$ in position $(i,j)$ to get the quantized output $z_q$ : + +$$ +z _ {q} = q (\hat {z}) := \left(\arg \min _ {z _ {l} \in \mathcal {Z}} \| \hat {z} _ {i j} - z _ {l} \|\right) \in \mathbb {R} ^ {h \times w \times n _ {z}}. \tag {1} +$$ + +We expand the nearest search strategy to a stochastic topk search strategy. That is, we obtain the $k_{th}$ closest entry in the codebook for each vector $\hat{z}_{ij}$ in position $(i,j)$ : + +$$ +z _ {q} = q (\hat {z}) := \left(\arg \underset {z _ {l} \in \mathcal {Z}} {k _ {t h}} \| \hat {z} _ {i j} - z _ {l} \|\right) \in \mathbb {R} ^ {h \times w \times n _ {z}}. \tag {2} +$$ + +For each sample in every training iteration, the value of $k$ is randomly chosen from a predefined range $[1, K]$ and controls the level of degradation. We chose $K = 50$ in VQD-SR and the experiment of the choice of $K$ can be found in the supplementary. + +A key point here is that we adopt the stochastic top-k strategy only for the bottom branch while keeping the nearest neighbor search for the top and middle branches. This is because the larger-scale structures like colors and shapes are encoded in these two branches, and we do not want them to be changed when augmenting the local details for degradation. That is also the reason why we make a great effort to design the multi-scale VQGAN that encodes the different components in input images separately. The idea of stochastic top-k VQ strategy also corresponds with the fact that one HR image could have multiple degraded versions. + +# 3.3. HR-SR Enhancement Strategy + +AVC [35] is the latest large-scale high-quality animation video dataset, specified for animation VSR tasks. As opposed to images that could be recorded in lossless format, most of the animation videos available on the Web all went through compression to reduce the network traffic. As demonstrated in Fig. 3 b, the HR animation video frames still suffered from the compression artifacts, and therefore are not completely ideal as the training ground truths. Based on this observation, we suggest enhancing the HR animation videos to further lift the upper bound for the existing animation VSR model. Since the contents of animation videos are relatively simple and the HR video frames are relatively clean, general pre-trained SR models (e.g., RealESRGAN [32]) could be used to reduce the artifacts while not contaminating image details. We thus enhance all the HR video frames in the AVC dataset by first applying an SR model, then downsampling to align the original sizes. + +# 3.4. Training Details + +Degradation Model. In our multi-scale VQGAN, we set the compression factor $f$ to $\{8,4,2\}$ for the {top, middle, bottom} branch respectively and use 1024 codebook entries with 256 channels in total. The input images are randomly cropped to patches of $256 \times 256$ . The training of our multiscale VQGAN is a two-stage procedure. We follow [5] to adopt Adam [16] optimizer with the base learning rate of $4.5 \times 10^{-6}$ for both stages. The learning rate in top branch is decreased by 4 times in the second stage. We set the total batch size to 32 and 24 for the two stages, respectively. We only apply VQ loss $L_{vq}$ [29] and perceptual loss $L_{per}$ [48] in the first stage, while adding the adversarial loss $L_{adv}$ [5] in the second stage. The full objective function for encoder $E$ , decoder $G$ and hierarchical VQ codebook $Z$ is: + +$$ +L (E, G, Z) = L _ {v q} + L _ {p e r} + L _ {a d v}, \tag {3} +$$ + +in which $L_{vq}$ is calculate by: + +$$ +\begin{array}{l} L _ {v q} = \| x - \hat {x} \| + \beta \| s g [ E (x) _ {(s)} ] - z _ {q (s)} \| _ {2} ^ {2} \tag {4} \\ + \left\| s g \left[ z _ {q (s)} \right] - E (x) _ {(s)} \right\| _ {2} ^ {2}. \\ \end{array} +$$ + +Where $x, \hat{x}$ are the input and reconstructed images, $sg[\cdot]$ denotes the stop-gradient operation, and $s \in \{t, m, b\}$ means the top, middle or bottom branches. More implementation details can be found in the supplementary. + +Video Super-Resolution Model. We adopt the unidirectional recurrent network in AnimeSR [35] as the VSR model because of its efficiency, and further remove the SR feedback in the recurrent block to ensure a more stable training according to our observation that too many recurrent features would sometimes cause a collapse of GAN loss as the omitting of explicit alignment module. We train the + +VSR model in two stages. In the first stage, we pre-train the VSR model with $L1$ loss for 300K iterations, with batch size 16 and learning rate $10^{-4}$ . In the second stage, we further add perceptual loss [15] and GAN loss [17] to fine-tune the network for another 300K iterations, with batch size 16 and learning rate $5 \times 10^{-5}$ . As the promotion of perceptual quality is mainly during the second stage, we only append our multi-scale VQGAN for more realistic degradations in the second stage to reduce the training cost while only adopting basic operators in the first stage. + +# 4. Experiments + +# 4.1. Datasets and Metrics + +We evaluate our method and compare its performance with other SOTA SR methods on AVC [35], the latest proposed large-scale animation video clip dataset. AVC is composed of three subsets. The training set AVC-Train contains 553 high-quality clips, and the testing set AVCTest contains 30 high-quality clips. There is also a AVCRealLQ, which contains 46 real-world low-quality clips for evaluation. Each clip consists of 100 frames. We adopt MANIQA [41], the winner in NTIRE 2022 NR-IQA challenge [8], as the no-reference image quality evaluation metric, as it in the previous animation VSR work [35]. + +# 4.2. Comparisons with State-of-the-art Methods + +We compare our VQD-SR with six SOTA SR methods. Among them, AnimeSR [35] and RealBasicVSR [3] are blind video super-resolution (VSR) methods. RealESRGAN [32] and BSRGAN [46] are blind single-image super-resolution (SISR) methods with explicit degradation modeling. We also conduct experiments on BasicVSR [1] and PDM [21] as two representative methods for none-blind VSR method and blind SISR with implicit degradation modeling. Apart from AnimeSR [35], for which we report the result in the original paper, all the others are general SR methods for open-domain images or videos. For fair comparisons, we fine-tune their officially released models on animation dataset AVC-Train. + +Quantitative Comparison. As shown in Tab. 1, we evaluate all the methods on AVC-RealLQ [35] for quantitative comparisons. Among them, Real-ESRGAN [32] and BSRGAN [46] expand the former explicit degradation models by introducing high-order degradations and random shuffling respectively, which greatly improve the synthetic ability. And with the help of powerful SR backbone (RRDB-Net [33] with 16.70M parameters), their results are quite remarkable. Nonetheless, ignoring the intrinsic characteristics of animation data limits their performance when applied to animation domain. Although specialized for animation videos, AnimeSR [35] only utilizes a small number of real data (three human-annotated animation videos), which hin + +Table 1. Quantitative comparison on AVC-RealLQ for $4 \times$ animation VSR. \* denotes fine-tune on animation dataset AVC-Train [35]. Bold text indicates the best performance. + +
MethodParams (M)Runtime (ms)MANIQA↑
BasicVSR* [1]6.291750.2829
PDM* [21]16.704380.2574
Real-ESRGAN* [32]16.704380.3825
BSRGAN* [46]16.704380.3836
RealBasicVSR*[3]6.292520.3504
AnimeSR [35]1.50260.3832
VQD-SR (Ours)1.47250.4096
+ +![](images/2fd7a6a138fb5b257ddbe577dfedbaf5ca233cefccc1692ba0376c89b0fb35a6.jpg) +Figure 4. Results of User Study. The values on Y-axis represent the percentage of users that prefer VQD-SR over other approaches. + +ders the performance of VSR model in real scenarios. Different from them, our VQD-SR considers the intrinsic characteristics of animation videos and leverages the enormous degradation priors contained in rich-content real animation videos. VQD-SR also adopts the HR enhancement strategy for more effective SR supervision. Due to these advantages, VQD-SR achieves a result of 0.4096 and significantly outperforms the SOTA animation VSR model [35] by 0.0264 in MANIQA on AVC-RealLQ [35]. Meanwhile, as the removal of SR recurrent feedback in VSR model, the number of parameters in VQD-SR are further reduced to $1.47\mathrm{M}$ with the runtime of $25~\mathrm{ms}$ computed on a NVIDIA Tesla M40 GPU with the LR size of $180\times 320$ , which demonstrates the superiority of our VQD-SR in real applications. + +Qualitative Comparison. As shown in Fig. 5, we compare visual qualities of different approaches on real-world AVC-RealLQ video clips. It can be observed that VQD-SR greatly improves the visual quality, especially for the recovery of clear lines. Additionally, the results of VQD-SR are more visually natural with fewer artifacts in some intended scenarios (e.g., the out-focus background blur and smooth underwater scene in row 5-6), while most of the other methods suffer from over-sharp artifacts like irregular lines and patterns. More visual comparisons with original inputs for reference and result analysis are in the supplementary materials. + +We also conduct a user study to further evaluate the visual quality of our approach. There are 20 subjects involved in this user study and 22080 votes are collected on AVC- + +![](images/11dd21c861ce4353f53a73dfd05d4bcefad6fe3a75c245b9609afdae1cbee255.jpg) +```python +anime_dance_level_0/739 + +![](images/2c0415e48810790aa84f1e2e0ab600f0cd3a8f5c1584814fd7820cc408dfa84e.jpg) +BasicVSR* + +![](images/e1a6a443b3312fb7fcb463b8814b2d4e8f574a394249661a8f10ffc1f1738d17.jpg) +Real-ESRGAN* + +![](images/e10b791c09bf71227b7cf84998c528912f30d3c369106585a06f86c74dcdbff8.jpg) +BSRGAN* + +![](images/1305fafaf90b70a48ceffd1f95f827a5f89c670a0d055eb9d20b02b0dc2998c2.jpg) +RealBasicVSR* + +![](images/ac7085bf5439f7f4ba6ebc8dd08ce3289fcbe0576d16ef17b8800b8f60ba66c3.jpg) +AnimeSR + +![](images/f7052839a146a21c48fca15d4895e6234a1b12cca05669d78a3d0d372fb5e60b.jpg) +VQD-SR (Ours) + +![](images/061e9c7895d214848a1b6b7f0db566ea462e7bbef0fc2175667c11375b1a18b6.jpg) +go_player/95 + +![](images/139920fce1f83b5764607af8a4494d4406136eee52d167057503fe33ebddd676.jpg) +BasicVSR* + +![](images/fe0ddcd25e34e5f9d6a7b4a058a41718d78e98964776d38dc8bb55789695eb6d.jpg) +Real-ESRGAN* + +![](images/5057af45eab411da61b3818814d44a5fe941f40f9b54eeaf8685b20b10985325.jpg) +BSRGAN* + +![](images/9cabf5fe2fb156906df426cc4286a1297dcbff1ef5f9d79c9bfab1f9204c5466.jpg) +RealBasicVSR* + +![](images/e3df7907f7df024fc30d1ed1f8d41a5c03fd9b93700db3f7a9341bbbc43e3ad1.jpg) +AnimeSR + +![](images/3fe6493a47622cad9be62b80a6a203f4be45e38138a6961acb5f255154858453.jpg) +VQD-SR (Ours) + +![](images/d34e4aa9a1acadfd7cd64047832ea1dabac6f7cb6dba6fd4825941330278c23b.jpg) +crayon_shinchan/30 + +![](images/f08ed6587b41a8e657baf329debc908b081b95f51e002f36eae9f716cbe1d883.jpg) +BasicVSR* + +![](images/6f40b2a0d20a4f6f1bfe45d76ddf3f1be29697b92eafb2ebee2659f82fe8755c.jpg) +Real-ESRGAN + +![](images/381b458a0a2b178ed669cad9fa4d63d7fcd0d1a2e18cf85449494eb8dbbeb54b.jpg) +BSRGAN* + +![](images/d41835e26cee118ecca3c86b199f3c6856553a64cfafd44bb3c61c5a5f02af0d.jpg) +RealBasicVSR* + +![](images/cb7f9cc12cc1b0764015971d34e10cef56d81c19f41720ebc3b7f9c125d5926c.jpg) +AnimeSR + +![](images/22b1281bbe4ab3b1c66f9dab620bd98a5047344c442dcdacfd64e3d84f722910.jpg) +VQD-SR (Ours) + +![](images/d920f03d035efdd6f6122b8d29954a5f9ef453d72909cc7b3ce8a05d35dd62c8.jpg) +mado_king/38 + +![](images/c83b055fd856da52be293318b6da4172e7a4b20ed89c99b2b140c7d6c724ca61.jpg) +BasicVSR* + +![](images/3a087ccefe44052bc163e5858cc015eecedea9716b938c481008e480b098b781.jpg) +Real-ESRGAN* + +![](images/1759948aead972342d40f2100af25532d994ead0a3aedec84f612727be8d4e52.jpg) +BSRGAN* + +![](images/3f43869d742a30b98e008939b41e7d2e60809ffe31e57bb0be23d8ec421e6513.jpg) +RealBasicVSR* + +![](images/65d86ebf02240b2e76efc24e5e62ea3c19bba5dfd76cef1c2ccde2c29cd9e86d.jpg) +AnimeSR + +![](images/7c33d00bc41051835717574d69b63bf8651492a5879ba4609ac74b02033470e3.jpg) +VQD-SR (Ours) + +![](images/3f08f15afffd96ec6365791c68702713a08ac813880c707e3312727e29ae8959.jpg) +transformers/90 + +![](images/913bfd5a8b0465ccaf808b0d855a3f8c7a4f79b8129b7511b526919a69c1ad79.jpg) +BasicVSR* + +![](images/0a4596fb414704ab7d9b56f1ef223e7fea6c53898f0e5f9e2ae914d21aff76e4.jpg) +Real-ESRGAN* + +![](images/49c9c742fb458061d86fb845fac1fc678c0cde17feae324efc941f30b20e00c0.jpg) +BSRGAN* + +![](images/ae778c23f3f592a1b77aa5947b52888f1dc827e29c9bd04d3f2051a6ed7c336d.jpg) +RealBasicVSR* + +![](images/8ef2c512d1f638cc5568e873efb2a274ef982cc1b405bba789df0a5ef0e077a1.jpg) +AnimeSR + +![](images/dd588571b5511c0efec4caecda0784980c78158be8b6cfcac32114d94ef093d6.jpg) +VQD-SR (Ours) + +![](images/8c5584107e0049ccf1c9f4ced69c716527ebbe7fdb569d8afbe4cfec3b8259f6.jpg) +hell girl/105 +Figure 5. Qualitative comparisons on AVC-RealLQ [35] for $4 \times$ scaling factor. $*$ denotes fine-tune on animation domain dataset. The frame name is shown at the bottom of each case. Our VQD-SR recovers visually natural and sharper lines with fewer artifacts (the first 4 rows) and is also capable to handle some intended scenarios with fewer over-sharp artifacts (row 5th with smooth background and clear foreground, row 6th in underwater scene). Zoom in to see better visualization. + +![](images/decc0b4115d983b1dd34bb85907a0391e29860bce380ff3b4a51d4e16e6607bb.jpg) +BasicVSR* + +![](images/02ec84f07748f0187b3994bac72eaf6b9e8aba24751c18ea22af0b8be1cbe2dc.jpg) +Real-ESRGAN* + +![](images/5172bd670aea5d64edc97573e40a634060f5c7715d77656b7eded508bf1da6c5.jpg) +BSRGAN* + +![](images/196f50dd5d21222eabe327a40a885f70d55c9a23dcc622c38754f4e36a95f814.jpg) +RealBasicVSR* + +![](images/4e698f41f555235f89bdf5770f16b06c5c4aedda214d682916e8b7af5a1cd0e7.jpg) +AnimeSR + +![](images/810f3b5c709fa53465b424fcc420c8fc541a57c58fc02bc1a7a2dc123dce1686.jpg) +VQD-SR (Ours) + +RealLQ [35] with 46 video clips. For each comparison, we adopt an A-B test that provides the users with two images in random order which include one VQD-SR frame. Users are asked to select the one with higher visual quality. As shown in Fig. 4, comparing with the SR methods designed for open-domain, over $80\%$ of users voted for our VQD-SR. By considering the data characteristic of animation, there are still over $65\%$ users who prefer our method to AnimeSR [35]. + +# 4.3. Ablation study + +In this section, we conduct ablation studies on each significant component of our VQ degradation model and HR-SR enhancement strategy in VQD-SR. + +VQ Degradation Model. In the ablation study of VQ degradation model design, we conduct all the experiments based on VQD-SR (base), which denotes a plain version of VQD-SR trained without HR-SR enhancement. As shown + +![](images/e38c4b60fd4419149f7b2af673704e39d5311c76cae6ae761b55d513c20c7650.jpg) +VQD-SR (base) + +![](images/9bfe7786d0c171fa06e0f76b92d2a10b6894c51984922af5e281a30572af1954.jpg) +(a) BasicOP + +![](images/318504e6fb24b5d2812e43f1d200a368a81d963de6958f25386449f1622f6b66.jpg) +(b) Single Scale + +![](images/df80a32e9a329d8f9aaa2c72597474f1295d4e9a47ef59537101f8bfacca4694.jpg) +(c) Single Stage + +![](images/bb11b9c6811fdbc1fa046a33c7b4723bac02857aab967a6d3036c1f42aa4a3d5.jpg) +(d) Top-1 +Figure 6. Ablation study on VQ degradation model. + +in Tab. 2 a, we first compare the degradation model which is simply composed of basic operators (blur, noise and FFmpeg) to our VQD-SR (base). With the help of real-world degradation priors contained in VQ codebook, the result can be improved from 0.3768 to 0.3857 in MANIQA. Referring to Fig. 6 a, VSR model trained with only basic operators fails to handle some real-world degradations, leading to artifacts around the edges. We further compare the structure and training strategy of VQ degradation model in Tab. 2 b and Tab. 2 c. As the global structures and local details are entangled together in single-scale VQ model and the + +Table 2. Ablation study results of degradation models, structures of VQ degradation model, training pipelines of VQ degradation model and VQ codebook search strategies. The MANIQA scores are reported for comparisons. + +
MANIQA↑(a) Degradation Model
BasicOP-OnlyVQD-SR (base)
0.37680.3857
MANIQA↑(b) VQGAN Structure
Single-scaleVQD-SR (base)
0.34660.3857
MANIQA↑(c) Training Strategy
Single-stageVQD-SR (base)
0.34300.3857
MANIQA↑(d) Codebook Search
NearestVQD-SR (base)
0.37700.3857
+ +Table 3. Applying VQ degradation to widely used SR backbones. For each backbone, settings are consistent apart from degradation methods. + +
BackboneReal-ESRGAN*RealBasicVSR*AnimeSR
Params (M)16.76.31.5
Original degradation0.38250.35040.3832
VQ degradation0.39670.38490.3857
+ +multi-scale model trained in single-stage, the performances dropped by 0.0391 and 0.0427, respectively. As shown in Fig. 6 b and Fig. 6 c, some fine-grained details are missing. For VQ strategies, as shown in Tab. 2 d and Fig. 6 d, our stochastic top-k VQ strategy can improve MANIQA by 0.0087 compared with the original nearest neighbor search strategy, as the top-k VQ strategy enables multi-level degradations which improves the generalization ability of the trained animation model, leading to more appealing results. + +To further illustrate the general applicability, we also apply our VQ degradation model to other SOTA SR backbones, Real-ESRGAN and RealBasicVSR, fine-tuned with animation data in the same setting. Referring to Tab. 3, SR models with VQ degradation achieve better results comparing with their original degradation methods, which indicates that the proposed VQ degradation is generally effective for animation SR models. It is noteworthy that the performance gains could be more significant for larger backbones. The visual examples in Fig. 7 also show the superiority of our VQ degradation method, especially to recover clear and visual natural lines which are the most import patterns deciding the visual quality of animation videos. + +HR Enhancement. The training HR animation videos collected from the Web also contain artifacts which are not ideal for ground truths, hindering the performances of animation VSR models. We propose the HR-SR strategy to enhance the quality of HR animation videos for more effective training ground truths. We first compare three different HR enhancement models by experiments on VQD-SR (base). + +![](images/1eb1163edd9cc2da5f992492be466466a46478f9daf8dafca6598336f99336a5.jpg) +bhd and shs/30 + +![](images/ea8657d1d46a1f27755b3dcb46451e2ad86d58f3259c9e708b882a3aef2e1ab2.jpg) +Real-ESRGAN(VQ)\* + +![](images/c8e3faa3e7e35b96fc86946992ae756ead402e2dde3a7c27b24ee091c246a08c.jpg) +RealBasicVSR (VQ)* + +![](images/00235d79094e3e82498506024c20bc3e2450cf9cbc0b73582055597d4e0d98af.jpg) +AnimeSR (VQ) + +![](images/b270e28040b9d1e5e7a70651882ef451ddbcf80eaba8611981d40a9871b9b380.jpg) +ccs/124 + +![](images/f1a80af2d2cc7fd210f592cc26e3d9c0346412fd2824b49c6503581af577217b.jpg) +Real-ESRGAN(VQ)* + +![](images/985c099ef590b55358926e9ba76e182732955876a9856603e90dd121251dc424.jpg) +RealBasicVSR (VQ)* + +![](images/598b0dbdd59f79e6b9261bbbf2c7dd53bd3d5de3d3362ae415415044651ba359.jpg) +```bash +AnimeSR(VQ) + +![](images/0d7e6cfc54c4460eb7841454b91c6526073d0c9a4fb43836488899ef598a9c6e.jpg) +big_ear_tutu/105 +Figure 7. Applying VQ degradation to widely used SR backbones. Settings are consistent apart from degradation methods. Models trained with VQ degradation could produce more clear and visual natural lines with fewer artifacts. + +![](images/4679650b4f7ffa3da7517e76191ca9e914c02f6ee5e8c25479f96fe44776700b.jpg) +Real-ESRGAN(VQ)* + +![](images/3e28d4db9a7a5fc788f7b6f62ed802bdf886df975e4496aac6c03400820e41a9.jpg) +RealBasicVSR (VQ)* + +![](images/26b46579d5bf3a14df71f4c343065090874377aac3b07faa1222c6024b0be855.jpg) +AnimeSR (VQ) + +The quantitative results are shown in Tab. 4. All three models improve the performance of animation VSR model, which verifies that the proposed HR-SR strategy is suitable for the training of animation VSR model, and improvements are not subject to the specific model for enhancement. However, as the SR process for data enhancement is conducted in HR domain, which takes a high demand on computing resources, we finally choose SISR model, Real-ESRGAN (S) [32] with relatively small model size. Visual examples of the enhanced HR frames can be found in Fig. 8. + +We further utilize the enhanced HR animation videos processed by Real-ESRGAN(S) [32] to fine-tune different VSR models. Apart from the proposed VQD-SR, RealBasicVSR [3] is a blind VSR model designed for open-domain videos and AnimeSR [35] is an VSR model specified for animation domain. As shown in Tab. 5, with the help of HR enhancement, all three VSR models get improved, which illustrates that the proposed HR enhancement strategy is effective for animation VSR task, regardless of the specific VSR model. The visual results of RealBasicVSR+, AnimeSR+, and VQD-SR in Fig. 9 also verify the advantages of the HR-SR enhancement strategy for animation VSR. + +Table 4. Ablation study of different SR models for HR-SR enhancement. All three models improve the performance. We choose Real-ESRGAN (S) considering the computing cost. + +
Enhancement MethodMANIQA↑
No Enhancement0.3857
AnimeSR [35]0.4146
Real-ESRGAN (L) [32]0.4211
Real-ESRGAN (S) [32]0.4096
+ +Table 5. Ablation study of HR-SR enhancement for different animation VSR models on AVC-RealLQ. We report MANIQA for comparison. + +
MANIQA↑wo /HR-SRw /HR-SR
RealBasicVSR [3]0.35040.3855
AnimeSR [35]0.38320.4079
VQD-SR0.38570.4096
+ +![](images/288b23c9f96b2e5b320263d78fa05b0c9bcc369851be187288d3fa07711e1ab8.jpg) +Input HR + +![](images/8bd30a794c90e3775c6e9d5136f22e1d79a6e4d07d91431d1515f59e5267c835.jpg) +AnimeSR + +![](images/edc8cea2379ff6a1ea0d4eda18a3c55e69d4507100b117671f587a4f80e2f3fb.jpg) +Real-ESRGAN (L) + +![](images/cec83923fbacbef652e404c9c053d83114c4d18188df215f34b60c9d06d3765b.jpg) +Real-ESRGAN (S) + +![](images/3647eed832df0feac7de703f26776095b6911d835ac2055d7a48e45301cc6ff4.jpg) +Figure 8. Enhanced HR data with HR-SR strategy by different enhancement models. + +![](images/9f21713189335e97c33931f2e9822afd863fc6596d85bc89dc2f67a5bd11bff6.jpg) + +![](images/658b894565bb7e2e88c9ee65830f61d5756c2c8a1e802d1155fea4ec094cb267.jpg) + +![](images/741372d0a6ebb21a0ac3d0ba67e9552a2400f31913a3d0734745a7d035fdcd1e.jpg) + +# 5. Limitation and Discussion + +In this section, we visualize the failure cases of VQDSR in Fig. 10. Our VQD-SR is capable to restore sharper lines and suppress diverse artifacts in animation videos. However, in some extreme circumstances (e.g., severe lossy compressions, long passing ages), there still gets room for improvement, for example the remaining color distortions around edges. Nevertheless, comparing with other SOTA methods, our VQD-SR still achieves better performances. + +# 6. Conclusion + +In this paper, we thoroughly study the characteristics of animation videos and fully leverage the rich prior knowledge contained in real data for a more practical animation VSR model. To be specific, we propose a novel degradation model which utilize a multi-scale VQGAN, self-supervised on purely real low-quality animation data (RAL), to decompose animation frames and establish a codebook containing diverse real-world degradation priors. We also propose a + +![](images/062a2d2d270777366b243426b3a6227d5f48c89b6dd65db42a3dbeb38b06cda8.jpg) + +![](images/e216297b447cce1c3c142d04fefeba3acaaf1a61c5c84c3a405b8d68ca4cb137.jpg) + +![](images/7b06d098e2a4f4d29df1797906f7fe4fc421be0066a1809694ce56056739e420.jpg) + +![](images/1f08ec1d58913099cd82a957e3d29ce7a8b2905df3fcd2bf94e80769a13ed1b4.jpg) + +![](images/b1518647e25bc99910d9d18b21e77c620f659b7747e0b3b50a95d368a850606d.jpg) +Figure 9. Ablation study of HR-SR enhancement strategy for different VSR models. HR-SR enhancement is generally effective task, regardless of the specific VSR model. + +![](images/848f4fbdaf33bee1c6b665c8874fe6d01a681fc3aa56510d2b220397f7a1b146.jpg) + +![](images/9511866f611eb8672b9a808e9c35377fdd79ba71a11d22e752b3927514b9265b.jpg) +tom_and_jerry/90 + +![](images/860247ac53f6bbb948e7f41ec8cff0e7174f978c7fec47f19d88fed50f5cca45.jpg) +RealBasicVSR* + +![](images/5907f63ad63737f42ccb4618ded71d95e8fc6168e6573b2e29400752e60c3170.jpg) +AnimeSR + +![](images/963499b40c3825af8b39ee1b0bc36f8ca3b2738b02b61a34b790a9654e4824a1.jpg) +VQD-SR (Ours) + +![](images/bc2911550d49571cbd2cb24c31448a2e1cbd1f6cb24b77fe721c792d9aacd8e5.jpg) +doraemon/91 + +![](images/5c6eeadd8ac8c455006ce98b5a207b2945afb4d646f97a0268d50bd118ab3111.jpg) +Figure 10. Failure cases when LR frames endure severe color distortions around edges. + +![](images/6194893cdefff487dd2a60ce31ff9a7dfb4e24e484bfabe8c1dc7e7d22964405.jpg) + +![](images/c5f6de546fd183f28bd1a3f34bc41983f32fdc66e89eb6170fdb8b628e2df343.jpg) + +two-stage training pipeline and a stochastic top-k VQ strategy to match up with the VQ degradation model. We further propose to enhance the HR training videos to lift the performance ceiling for animation VSR tasks. Experiment results show the superiority of the proposed VQD-SR over existing SOTA models, as our methods could generate more effective LR-HR training pairs in view of the characteristics in real animation videos. + +Acknowledgement. This work was supported in part by the NSFC under Grant 62272380 and 62103317, the Science and Technology Program of Xi'an, China under Grant 21RGZN0017, and Microsoft Research Asia. + +# References + +[1] Kelvin CK Chan, Xintao Wang, Ke Yu, Chao Dong, and Chen Change Loy. 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In this paper, we thoroughly explore the characteristics of animation videos and leverage the rich priors in real-world animation data for a more practical animation VSR model. In particular, we propose a multi-scale Vector-Quantized Degradation model for animation video Super-Resolution (VQD-SR) to decompose the local details from global structures and transfer the degradation priors in real-world animation videos to a learned vector-quantized codebook for degradation modeling. A rich-content Real Animation Low-quality (RAL) video dataset is collected for extracting the priors. We further propose a data enhancement strategy for high-resolution (HR) training videos based on our observation that existing HR videos are mostly collected from the Web which contains conspicuous compression artifacts. The proposed strategy is valid to lift the upper bound of animation VSR performance, regardless of the specific VSR model. 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Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": "Animation video super-resolution (VSR) [35], which is a subdiscipline of video super-resolution (VSR) [1, 2, 3, 19, 28, 37], aims to restore high-resolution (HR) videos from their low-resolution (LR) counterparts in animation domain. 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A comparison between our proposed VQD-SR and other SOTA VSR methods in real scenario. As indicated by the red dotted circles, our VQD-SR could restore more appealing details by considering the degradation priors in real animation videos. (\\* denotes fine-tune on animation videos)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 386, + 362, + 465, + 441 + ], + "blocks": [ + { + "bbox": [ + 386, + 362, + 465, + 441 + ], + "lines": [ + { + "bbox": [ + 386, + 362, + 465, + 441 + ], + "spans": [ + { + "bbox": [ + 386, + 362, + 465, + 441 + ], + "type": "image", + "image_path": "29a534dcd8374b41053e293d9c453b983be018fe36a1cf107e7625467f6821f3.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 465, + 362, + 543, + 441 + ], + "blocks": [ + { + "bbox": [ + 465, + 362, + 543, + 441 + ], + "lines": [ + { + "bbox": [ + 465, + 362, + 543, + 441 + ], + "spans": [ + { + "bbox": [ + 465, + 362, + 543, + 441 + ], + "type": "image", + "image_path": "dc1a260162d5f9d5223932387f0723ceb9fddce29fc1b608b0662a81bbe78ffa.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 652 + ], + "type": "text", + "content": "entertainment, cultural, educational and commercial values. However, most of them available on the Web are in limited resolutions and have visually unappealing artifacts due to the passing ages, lossy compression and transmission. Dedicated to real applications, animation VSR is a blind SR [21, 32, 46, 40, 43] task which is more challenging than conventional VSR tasks [1, 2, 14, 19, 28, 36], because of the complicated and agnostic real-world degradations. Thus, practical VSR methods for improving real-world LR animation videos are in highly demanded." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": "Blind SR model for open-domain has long been the focus. As it's hard to collect LR-HR pairs in real scenarios, recent learning-based approaches try to model the real-world degradations from HR to LR, thus generating pseudo LR-HR pairs to train SR models. These approaches can" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 683, + 287, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 287, + 702 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 287, + 702 + ], + "type": "text", + "content": "*This work was done while Zixi Tuo was a research intern at Microsoft Research Asia." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13179" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 251 + ], + "type": "text", + "content": "be roughly divided into two categories, explicit modeling and implicit modeling, with regard to the degradation procedures. Explicit modeling [9, 20, 32, 46] methods try to combine basic degradation operators like noise, blur and rescaling to imitate the real-world degradation pipeline. Instead, implicit modeling methods employ a neural network, which is usually in the manner of generative adversarial networks (GAN) [7], as an alternative to the combination of basic degradation operators. However, these general degradation methods designed for open-domain videos are not quite suitable for the animation domain as they ignore the intrinsic characteristics of the data. Directly adopting existing degradation models for open-domain to animation VSR would lead to unpleasant results (as shown in Fig. 1 a), even though they are fine-tuned on the animation videos." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 255, + 286, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 255, + 286, + 421 + ], + "spans": [ + { + "bbox": [ + 49, + 255, + 286, + 421 + ], + "type": "text", + "content": "Specific to animation VSR, AnimeSR [35] moves one step further to propose a learnable basic operator (LBO) with an \"input-rescaling\" strategy that considers the data characteristics and demonstrates their advantages over open-domain VSR methods. However, the proposed \"input-rescaling\" strategy of constructing pseudo HR-LR pairs for the LBO training requires human annotations, which prevents their method from scaling up to modeling various real-world degradations. In AnimeSR [35], only three LBOs are trained with three human-annotated videos respectively, leading to unappealing results (as shown in Fig. 1 b). Thus, how to effectively leverage large-scale real-world animation videos based on their data characteristics is still an open problem." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 424, + 286, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 424, + 286, + 686 + ], + "spans": [ + { + "bbox": [ + 49, + 424, + 286, + 686 + ], + "type": "text", + "content": "In this paper, we propose a multi-scale Vector-Quantized Degradation model for animation video Super-Resolution (VQD-SR), which leverages the data characteristics of animation videos. We observe that different from open-domain videos with complex textures and irregular illumination conditions, animation videos are roughly composed of basic visual patterns like smooth color patches and clear lines which can be easily captured with high fidelity by vector-quantization (VQ) [5, 25, 29]. Such data characteristics could also be used for encoding and transferring degradation priors from low-quality animation videos and results in a degradation codebook. Given any clean LR animation frame, the degraded LR counterpart can be easily obtained by looking up the pre-trained degradation codebook. Specifically, a novel multi-scale VQGAN for degradation modeling is proposed to learn and transfer real-world degradation priors from a large-scale Real Animation Low-quality (RAL) video dataset collected from the Web. To improve the generalization ability of VQD-SR, we propose a two-stage training pipeline and a stochastic top-k VQ strategy to match up with the multi-scale VQGAN, yielding visually appealing results (as shown in Fig. 1 c)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 689, + 286, + 712 + ], + "type": "text", + "content": "To further lift the upper bound of existing animation VSR methods, we propose an HR-SR strategy to enhance" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 72, + 544, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 143 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 143 + ], + "type": "text", + "content": "the quality of HR training videos for more ideal ground truths. This is motivated by our observations that existing HR animation videos are mostly collected from the Web which contains conspicuous compression artifacts and such artifacts could be easily reduced by existing SR methods. Our contributions are summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 319, + 145, + 544, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 145, + 544, + 191 + ], + "spans": [ + { + "bbox": [ + 319, + 145, + 544, + 191 + ], + "type": "text", + "content": "- We collect a large-scale real LR animation dataset, and conduct a comprehensive study on real animation data to thoroughly explore the challenges and data characteristics in animation VSR task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 319, + 193, + 544, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 193, + 544, + 251 + ], + "spans": [ + { + "bbox": [ + 319, + 193, + 544, + 251 + ], + "type": "text", + "content": "- We propose a novel multi-scale VQ degradation model to transfer real-world degradation priors for synthesizing pseudo LR-HR training pairs. We further propose an HR-SR data enhancement strategy to improve the performance of existing VSR methods for animation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 319, + 253, + 544, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 253, + 544, + 300 + ], + "spans": [ + { + "bbox": [ + 319, + 253, + 544, + 300 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the effectiveness of our proposed methods which significantly improve the recent SOTA animation VSR method in both quantitative and qualitative comparisons." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 314, + 391, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 314, + 391, + 326 + ], + "spans": [ + { + "bbox": [ + 308, + 314, + 391, + 326 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 335, + 438, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 335, + 438, + 346 + ], + "spans": [ + { + "bbox": [ + 308, + 335, + 438, + 346 + ], + "type": "text", + "content": "2.1. Video Super-Resolution" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 354, + 544, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 354, + 544, + 496 + ], + "spans": [ + { + "bbox": [ + 308, + 354, + 544, + 496 + ], + "type": "text", + "content": "Recent years have witnessed a prosperity in deep learning based VSR methods [2, 3, 14, 24, 28, 31, 38]. Different from single-image super-resolution (SISR), the auxiliary temporal information is available in VSR for the restoration of inner-frame features. Sliding-window structure [28, 31, 38, 42] and recurrent structure [1, 2, 6, 12, 14] are two common paradigms in VSR to utilize the interframe information. However, it also faces challenges while taking the advantages. The degradations could be more complicated in videos and may accumulate along the time sequence [3, 37], causing the performance drop in real-world scenarios." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 498, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 498, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 498, + 544, + 712 + ], + "type": "text", + "content": "There have been several attempts in blind-SR field to deal with real-world degradations, which could be categorized into explicit and implicit modeling. Explicit methods model the degradation as the effects of objective operators (or kernels). Methods like [9, 47] assume these degradations to be simple combinations of blur, noise and down-sampling kernels, therefore conducting conditional restoration based on the prediction of kernel parameters. Operators like JPEG/FFmpeg [20] for lossy compression, sinc filter [32] for ringing artifacts and strategies like high-order modeling [32], random shuffling [46], are further investigated in latest studies to simulate the real degradation pipeline and expand the synthesis space. However, these methods merely depend on predefined operators, and ignore to utilize the information contained in real data, thus there's still a gap between the synthesis LR and real LR data. Implicit methods [21, 22, 34, 44] discard the objective degradation operators, but learn the distribution of real data," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "text", + "content": "13180" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": "therefore realize the degradation by converting the HR input to fit the real LR distribution. Yet, the learned distribution space is uncontrollable, thus the degradation network may easily project unseen out-of-distribution samples to unpredictable suboptimal space causing annoying artifacts." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 140, + 203, + 154 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 203, + 154 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 203, + 154 + ], + "type": "text", + "content": "2.2. Animation Video Processing" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 159, + 289, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 159, + 289, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 289, + 315 + ], + "type": "text", + "content": "Animation is a type of visual art that is represented in a nonrealistic artistic style. A diversity of animation processing technologies based on deep learning have been developed these years, such as animation style transfer [4, 13, 30], animation video colorization [18, 27, 45], animation video generation [11] and animation video interpolation [26]. AnimeSR [35] is a recent study for real-world animation VSR tasks, which develops LBO to expand the basic degradation operators. In this paper, we take a further step to explore the characteristics of animation videos, and make special designs in consideration of these characteristics to improve the performance of real-world animation VSR." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 203, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 203, + 336 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 203, + 336 + ], + "type": "text", + "content": "2.3. Vector-Quantized Codebook" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 289, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 289, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 289, + 486 + ], + "type": "text", + "content": "Vector-quantized(VQ) codebook was first proposed in VQ-VAE [29] to learn the discrete representation for images in latent space. Later, a hierarchical VQ-VAE-2 [25] is further proposed. To improve the perceptual quality, a discriminator and perceptual loss were added in VQGAN [5]. Recently in VQFR [10], a VQ-based face restoration method was also proposed. Although initially designed to avoid the \"posterior collapse\" issue of VAE or tokenizer input images for a more effective transformer modeling, we discover that the idea of VQ is naturally suitable for representing animation video frames and the form of codebook is capable to internalize the real degradation priors." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 498, + 129, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 129, + 512 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 129, + 512 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": "In this section, we first discuss the characteristics of real animation videos and the challenges for animation VSR task in Sec. 3.1. Based on the observations in Sec. 3.1, we introduce the proposed real-world animation degradation model in Sec. 3.2. Finally, we illustrate our HR training data enhancement strategy in Sec. 3.3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 599, + 285, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 285, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 285, + 612 + ], + "type": "text", + "content": "3.1. Real-World Degradation in Animation Videos" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "type": "text", + "content": "To thoroughly understand the characteristics of animation videos and the challenges in animation VSR task, we collect a Real Animation Low-quality (RAL) video dataset. RAL contains over 10K LR frames extracted from 441 real-world low-quality animation videos. To the best of our knowledge, RAL is the largest real-world low-quality video dataset in the animation domain. Example frames are shown in Fig. 2 (statistics of RAL can be found in the" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 547, + 185 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 547, + 185 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 547, + 185 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 547, + 185 + ], + "type": "image", + "image_path": "de9e663f028e943d78215689fcd4fb172eaa7dbe3dafa367cd87813363aa29ce.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 194, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 250 + ], + "type": "text", + "content": "Figure 2. Samples of RAL and typical degradation phenomena in real-world LR animation videos. RAL is a real-world animation video dataset contains over 10K LR frames. Intermittent edges, aliasing edges, ringing artifacts and rainbow effects are four typical degradation phenomena in real-world animation videos." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 269, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 545, + 376 + ], + "type": "text", + "content": "supplementary). To construct such a dataset, we first download numerous earlier animation videos from multiple video sites such as YouTube and Bilibili. Then we manually select videos according to their resolutions, quality, contents and styles. To ensure the dataset contains rich animation structures and degradation priors, we adopt a simple scene filtering procedure to remove the frames which have subtle motions by evaluating their average absolute differences, thus reducing the redundancy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 546, + 520 + ], + "type": "text", + "content": "Animation videos are roughly composed of smooth color patches and clear lines, while the latter ones usually play an important role in portraying objects and expressing visual semantics. In contrast to the fact that degradation losses for open domain videos are mainly about high-frequency textures, degradations for animation videos mostly happen around the edges which are more sensitive according to the human perceptual. Such degradations usually act as intermittent edges, aliasing edges, ringing artifacts, and rainbow effects, as shown in Fig. 2. These observations of the proposed RAL dataset inspire us that the key challenge in animation VSR is to restore visually natural and clear edges." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": "Degradation modeling has been the focus of many previous blind-SR works. Because of the obvious differences between animation and natural style videos, degradation methods designed for natural videos cannot properly handle degradations in animation videos. As a result, these methods suffer from amplified artifacts causing phenomena like perturbation edges, bleeding edges and inaccurate colorization along edges, even though they are fine-tuned on the animation videos (as shown in Fig. 1 a)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 635, + 520, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 520, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 520, + 647 + ], + "type": "text", + "content": "3.2. Vector-Quantized Degradation Modeling" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Instead of imitating the real-world degradation pipeline by simply combining and adjusting some predefined basic operators [32, 46], we propose to explore the data intrinsic characteristics further and utilize degradation priors of real-world animation videos. As illustrated in Sec. 3.1," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13181" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 547, + 247 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 547, + 247 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 547, + 247 + ], + "type": "image", + "image_path": "5fcf775f84a2a2f016fd0a7bef3f148f6cf4fd6558de1773bca2ba28085e46c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 257, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 547, + 304 + ], + "type": "text", + "content": "Figure 3. The overview of VQD-SR for training the animation VSR model. (a) Vector-quantized degradation model is a multi-scale VQGAN which transfers the real-world degradations from the learned VQ codebook to clean LR video frames to synthesize pseudo LR videos for VSR training, with the stochastic top-k VQ strategy. (b) HR-SR enhancement strategy eliminates the artifacts in HR animation training videos with an existing SR model to generate more ideal ground truths for supervising the VSR results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 321, + 289, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 289, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 289, + 477 + ], + "type": "text", + "content": "animation videos are roughly composed of smooth color patches and clear lines. Compared to open-domain videos, which contain complex textures and irregular illumination conditions, it is possible to encode such animation video frames into a codebook of finite basic visual patterns (i.e., color patches and lines). More importantly, any animation video frame can be further decoded with corresponding patterns with high fidelity. If such a process is restricted to the real LR domain (e.g., the proposed RAL dataset), the degradation priors of real animation videos will be encapsulated into the aforementioned codebook simultaneously and could be further used for synthesizing pseudo LR data for the VSR training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "type": "text", + "content": "VQGAN [5] is a reconstruction network composed of an encoder " + }, + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "type": "text", + "content": ", a decoder " + }, + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "type": "text", + "content": " and a vector-quantized codebook " + }, + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 481, + 287, + 662 + ], + "type": "text", + "content": ". Motivated by the perceptually rich codebook, we resort to VQGAN [5], trained on the proposed RAL dataset with rich degradations of animation videos, to realize the decomposition of low-quality frames and encapsulate degradation priors into a learned codebook. When given a clean LR frame, the real-world degradation priors can be transferred by replacing the original clean patches with the corresponding degraded versions by looking up the learned degradation codebook. In this section, we first introduce our modified multi-scale VQGAN, then illustrate the two-stage training pipeline, and finally use the trained model to synthesize pseudo LR-HR pairs in diverse levels of degradations by a stochastic top-k vector-quantization strategy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Multi-Scale VQGAN. As discussed in Sec. 3.1, the degradations in animation videos mostly happen around the edges, which are fine-grained local details. A degradation model should be capable of processing these local details while" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 321, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 545, + 394 + ], + "type": "text", + "content": "keeping the global structures (e.g., colors and shapes) at the same time. However, these two goals are usually conflicted with each other under the scope of the original single-scale VQGAN [5], as these two kinds of components are entangled together. Disentangling local details from global structures is a requisite for degradation modeling with VQGAN." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 397, + 546, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 546, + 540 + ], + "type": "text", + "content": "The multi-scale design has been widely explored in low-level vision [23, 39] and achieved great success, especially in the image restoration task. Inspired by this, we propose a multi-scale VQGAN which contains three parallel encoding branches. As shown in Fig. 3 a, these three branches share a shallow feature extraction module but have independent deeper encoding modules with different compression factors " + }, + { + "bbox": [ + 304, + 397, + 546, + 540 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 397, + 546, + 540 + ], + "type": "text", + "content": " (we choose " + }, + { + "bbox": [ + 304, + 397, + 546, + 540 + ], + "type": "inline_equation", + "content": "f = \\{8,4,2\\}" + }, + { + "bbox": [ + 304, + 397, + 546, + 540 + ], + "type": "text", + "content": " for the top, middle and bottom branches respectively). Benefiting from our multi-scale design, image information of different levels could be effectively disentangled and learned by each encoding branch in one VQ-GAN model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": "Two-Stage Training Pipeline. However, it is non-trivial to achieve the feature disentanglement as we expected by directly training the proposed model from scratch. This is because the bottom branch with the smallest scale will dominate the model training since it provides the easiest way to model converge. We call this phenomenon \"short-cut\". Such a problem prevents the top and the middle branches from learning image information for different scales, and the learned image representations are still entangled with each other. To take full advantage of our multi-scale VQGAN, we propose a two-stage training pipeline. We first remove the middle and the bottom branches, and only train the top branch with the largest compression factor " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": ". In this stage, the top branch is forced to take effect and be re" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13182" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "sponsible to reconstruct the global structures. After the convergence of the top branch, we add the other two branches back to fine-tune the overall multi-scale VQGAN. In the second stage, the two new branches only need to recover the remaining smaller structures and fine-grained details, thus avoiding the \"short-cut\" problem." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "text", + "content": "Stochastic Top-k VQ Strategy. After training our multiscale VQGAN on a real-world low-quality animation video dataset (e.g., the proposed RAL dataset in Sec. 3.1), the learned codebooks will contain rich degradation information and are capable of transferring such degradations into unseen animation data. Specifically, as shown in Fig. 3, the learned multi-scale VQGAN will be used as the degradation model to synthesize pseudo LR images from clean LR images for further VSR model training. Although the degradation priors in the codebooks are diverse, there is only one fixed degradation output for each input as the quantization process takes the nearest neighbor search strategy to reconstruct the input, leading to poor generalization capability of the final VSR model. To expand the degradation space and introduce more randomness during training, we adopt a stochastic top-k search strategy when looking up the codebook for the VQ process. More precisely, given the encoded output " + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "inline_equation", + "content": "\\hat{z} = E(x) \\in \\mathbb{R}^{h \\times w \\times n_z}" + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "text", + "content": " from the input image " + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "text", + "content": ", the former vector quantization methods search the nearest entry in the codebook " + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{Z} = \\{z_l\\}_{l=1}^L" + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "text", + "content": " for each vector " + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "inline_equation", + "content": "\\hat{z}_{ij}" + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "text", + "content": " in position " + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "text", + "content": " to get the quantized output " + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "inline_equation", + "content": "z_q" + }, + { + "bbox": [ + 46, + 145, + 288, + 399 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 60, + 407, + 287, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 407, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 60, + 407, + 287, + 427 + ], + "type": "interline_equation", + "content": "z _ {q} = q (\\hat {z}) := \\left(\\arg \\min _ {z _ {l} \\in \\mathcal {Z}} \\| \\hat {z} _ {i j} - z _ {l} \\|\\right) \\in \\mathbb {R} ^ {h \\times w \\times n _ {z}}. \\tag {1}", + "image_path": "4337eab372df4977a8d08d6f272476576215d482510d76339de5bc1941ac62ac.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "type": "text", + "content": "We expand the nearest search strategy to a stochastic topk search strategy. That is, we obtain the " + }, + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "type": "inline_equation", + "content": "k_{th}" + }, + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "type": "text", + "content": " closest entry in the codebook for each vector " + }, + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\hat{z}_{ij}" + }, + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "type": "text", + "content": " in position " + }, + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 47, + 441, + 287, + 477 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 488, + 287, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 488, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 59, + 488, + 287, + 509 + ], + "type": "interline_equation", + "content": "z _ {q} = q (\\hat {z}) := \\left(\\arg \\underset {z _ {l} \\in \\mathcal {Z}} {k _ {t h}} \\| \\hat {z} _ {i j} - z _ {l} \\|\\right) \\in \\mathbb {R} ^ {h \\times w \\times n _ {z}}. \\tag {2}", + "image_path": "aa61e1f7f0d7a897ccae7dd5a5286892efbe8bc6087f81c43c5ccbfd48fa6102.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "content": "For each sample in every training iteration, the value of " + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "content": " is randomly chosen from a predefined range " + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "inline_equation", + "content": "[1, K]" + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "content": " and controls the level of degradation. We chose " + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "inline_equation", + "content": "K = 50" + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "content": " in VQD-SR and the experiment of the choice of " + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "content": " can be found in the supplementary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "A key point here is that we adopt the stochastic top-k strategy only for the bottom branch while keeping the nearest neighbor search for the top and middle branches. This is because the larger-scale structures like colors and shapes are encoded in these two branches, and we do not want them to be changed when augmenting the local details for degradation. That is also the reason why we make a great effort to design the multi-scale VQGAN that encodes the different components in input images separately. The idea of stochastic top-k VQ strategy also corresponds with the fact that one HR image could have multiple degraded versions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 471, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 471, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 471, + 85 + ], + "type": "text", + "content": "3.3. HR-SR Enhancement Strategy" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 90, + 545, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 294 + ], + "type": "text", + "content": "AVC [35] is the latest large-scale high-quality animation video dataset, specified for animation VSR tasks. As opposed to images that could be recorded in lossless format, most of the animation videos available on the Web all went through compression to reduce the network traffic. As demonstrated in Fig. 3 b, the HR animation video frames still suffered from the compression artifacts, and therefore are not completely ideal as the training ground truths. Based on this observation, we suggest enhancing the HR animation videos to further lift the upper bound for the existing animation VSR model. Since the contents of animation videos are relatively simple and the HR video frames are relatively clean, general pre-trained SR models (e.g., RealESRGAN [32]) could be used to reduce the artifacts while not contaminating image details. We thus enhance all the HR video frames in the AVC dataset by first applying an SR model, then downsampling to align the original sizes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 301, + 405, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 301, + 405, + 314 + ], + "spans": [ + { + "bbox": [ + 306, + 301, + 405, + 314 + ], + "type": "text", + "content": "3.4. Training Details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": "Degradation Model. In our multi-scale VQGAN, we set the compression factor " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "\\{8,4,2\\}" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": " for the {top, middle, bottom} branch respectively and use 1024 codebook entries with 256 channels in total. The input images are randomly cropped to patches of " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": ". The training of our multiscale VQGAN is a two-stage procedure. We follow [5] to adopt Adam [16] optimizer with the base learning rate of " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "4.5 \\times 10^{-6}" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": " for both stages. The learning rate in top branch is decreased by 4 times in the second stage. We set the total batch size to 32 and 24 for the two stages, respectively. We only apply VQ loss " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "L_{vq}" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": " [29] and perceptual loss " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "L_{per}" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": " [48] in the first stage, while adding the adversarial loss " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "L_{adv}" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": " [5] in the second stage. The full objective function for encoder " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": ", decoder " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": " and hierarchical VQ codebook " + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 320, + 545, + 487 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 351, + 497, + 545, + 511 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 497, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 351, + 497, + 545, + 511 + ], + "type": "interline_equation", + "content": "L (E, G, Z) = L _ {v q} + L _ {p e r} + L _ {a d v}, \\tag {3}", + "image_path": "24aea2cc1114b56bde5acaac62cae413a09de03b03fc4d629d208527d26e9eea.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 520, + 424, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 424, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 424, + 533 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 306, + 520, + 424, + 533 + ], + "type": "inline_equation", + "content": "L_{vq}" + }, + { + "bbox": [ + 306, + 520, + 424, + 533 + ], + "type": "text", + "content": " is calculate by:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 338, + 541, + 545, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 541, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 338, + 541, + 545, + 572 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {v q} = \\| x - \\hat {x} \\| + \\beta \\| s g [ E (x) _ {(s)} ] - z _ {q (s)} \\| _ {2} ^ {2} \\tag {4} \\\\ + \\left\\| s g \\left[ z _ {q (s)} \\right] - E (x) _ {(s)} \\right\\| _ {2} ^ {2}. \\\\ \\end{array}", + "image_path": "d4388b379d7523c7c0adbfd5dcdcdafe406724e2c6905a1f57db7b3f82af98b6.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "type": "inline_equation", + "content": "x, \\hat{x}" + }, + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "type": "text", + "content": " are the input and reconstructed images, " + }, + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "type": "inline_equation", + "content": "sg[\\cdot]" + }, + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "type": "text", + "content": " denotes the stop-gradient operation, and " + }, + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "type": "inline_equation", + "content": "s \\in \\{t, m, b\\}" + }, + { + "bbox": [ + 304, + 581, + 545, + 629 + ], + "type": "text", + "content": " means the top, middle or bottom branches. More implementation details can be found in the supplementary." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Video Super-Resolution Model. We adopt the unidirectional recurrent network in AnimeSR [35] as the VSR model because of its efficiency, and further remove the SR feedback in the recurrent block to ensure a more stable training according to our observation that too many recurrent features would sometimes cause a collapse of GAN loss as the omitting of explicit alignment module. We train the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13183" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": "VSR model in two stages. In the first stage, we pre-train the VSR model with " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "L1" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " loss for 300K iterations, with batch size 16 and learning rate " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ". In the second stage, we further add perceptual loss [15] and GAN loss [17] to fine-tune the network for another 300K iterations, with batch size 16 and learning rate " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-5}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ". As the promotion of perceptual quality is mainly during the second stage, we only append our multi-scale VQGAN for more realistic degradations in the second stage to reduce the training cost while only adopting basic operators in the first stage." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 204, + 128, + 218 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 204, + 128, + 218 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 128, + 218 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 224, + 168, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 168, + 236 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 168, + 236 + ], + "type": "text", + "content": "4.1. Datasets and Metrics" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 289, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 289, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 289, + 376 + ], + "type": "text", + "content": "We evaluate our method and compare its performance with other SOTA SR methods on AVC [35], the latest proposed large-scale animation video clip dataset. AVC is composed of three subsets. The training set AVC-Train contains 553 high-quality clips, and the testing set AVCTest contains 30 high-quality clips. There is also a AVCRealLQ, which contains 46 real-world low-quality clips for evaluation. Each clip consists of 100 frames. We adopt MANIQA [41], the winner in NTIRE 2022 NR-IQA challenge [8], as the no-reference image quality evaluation metric, as it in the previous animation VSR work [35]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 383, + 274, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 274, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 274, + 396 + ], + "type": "text", + "content": "4.2. Comparisons with State-of-the-art Methods" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 402, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 556 + ], + "type": "text", + "content": "We compare our VQD-SR with six SOTA SR methods. Among them, AnimeSR [35] and RealBasicVSR [3] are blind video super-resolution (VSR) methods. RealESRGAN [32] and BSRGAN [46] are blind single-image super-resolution (SISR) methods with explicit degradation modeling. We also conduct experiments on BasicVSR [1] and PDM [21] as two representative methods for none-blind VSR method and blind SISR with implicit degradation modeling. Apart from AnimeSR [35], for which we report the result in the original paper, all the others are general SR methods for open-domain images or videos. For fair comparisons, we fine-tune their officially released models on animation dataset AVC-Train." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "Quantitative Comparison. As shown in Tab. 1, we evaluate all the methods on AVC-RealLQ [35] for quantitative comparisons. Among them, Real-ESRGAN [32] and BSRGAN [46] expand the former explicit degradation models by introducing high-order degradations and random shuffling respectively, which greatly improve the synthetic ability. And with the help of powerful SR backbone (RRDB-Net [33] with 16.70M parameters), their results are quite remarkable. Nonetheless, ignoring the intrinsic characteristics of animation data limits their performance when applied to animation domain. Although specialized for animation videos, AnimeSR [35] only utilizes a small number of real data (three human-annotated animation videos), which hin" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 110, + 545, + 194 + ], + "blocks": [ + { + "bbox": [ + 305, + 69, + 545, + 102 + ], + "lines": [ + { + "bbox": [ + 305, + 69, + 545, + 102 + ], + "spans": [ + { + "bbox": [ + 305, + 69, + 545, + 102 + ], + "type": "text", + "content": "Table 1. Quantitative comparison on AVC-RealLQ for " + }, + { + "bbox": [ + 305, + 69, + 545, + 102 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 305, + 69, + 545, + 102 + ], + "type": "text", + "content": " animation VSR. \\* denotes fine-tune on animation dataset AVC-Train [35]. Bold text indicates the best performance." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 110, + 545, + 194 + ], + "lines": [ + { + "bbox": [ + 309, + 110, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 309, + 110, + 545, + 194 + ], + "type": "table", + "html": "
MethodParams (M)Runtime (ms)MANIQA↑
BasicVSR* [1]6.291750.2829
PDM* [21]16.704380.2574
Real-ESRGAN* [32]16.704380.3825
BSRGAN* [46]16.704380.3836
RealBasicVSR*[3]6.292520.3504
AnimeSR [35]1.50260.3832
VQD-SR (Ours)1.47250.4096
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The values on Y-axis represent the percentage of users that prefer VQD-SR over other approaches." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "type": "text", + "content": "ders the performance of VSR model in real scenarios. Different from them, our VQD-SR considers the intrinsic characteristics of animation videos and leverages the enormous degradation priors contained in rich-content real animation videos. VQD-SR also adopts the HR enhancement strategy for more effective SR supervision. Due to these advantages, VQD-SR achieves a result of 0.4096 and significantly outperforms the SOTA animation VSR model [35] by 0.0264 in MANIQA on AVC-RealLQ [35]. Meanwhile, as the removal of SR recurrent feedback in VSR model, the number of parameters in VQD-SR are further reduced to " + }, + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "type": "inline_equation", + "content": "1.47\\mathrm{M}" + }, + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "type": "text", + "content": " with the runtime of " + }, + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "type": "inline_equation", + "content": "25~\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "type": "text", + "content": " computed on a NVIDIA Tesla M40 GPU with the LR size of " + }, + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "type": "inline_equation", + "content": "180\\times 320" + }, + { + "bbox": [ + 304, + 364, + 545, + 532 + ], + "type": "text", + "content": ", which demonstrates the superiority of our VQD-SR in real applications." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 675 + ], + "type": "text", + "content": "Qualitative Comparison. As shown in Fig. 5, we compare visual qualities of different approaches on real-world AVC-RealLQ video clips. It can be observed that VQD-SR greatly improves the visual quality, especially for the recovery of clear lines. Additionally, the results of VQD-SR are more visually natural with fewer artifacts in some intended scenarios (e.g., the out-focus background blur and smooth underwater scene in row 5-6), while most of the other methods suffer from over-sharp artifacts like irregular lines and patterns. More visual comparisons with original inputs for reference and result analysis are in the supplementary materials." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "We also conduct a user study to further evaluate the visual quality of our approach. 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Qualitative comparisons on AVC-RealLQ [35] for " + }, + { + "bbox": [ + 46, + 416, + 545, + 460 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 416, + 545, + 460 + ], + "type": "text", + "content": " scaling factor. " + }, + { + "bbox": [ + 46, + 416, + 545, + 460 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 46, + 416, + 545, + 460 + ], + "type": "text", + "content": " denotes fine-tune on animation domain dataset. The frame name is shown at the bottom of each case. Our VQD-SR recovers visually natural and sharper lines with fewer artifacts (the first 4 rows) and is also capable to handle some intended scenarios with fewer over-sharp artifacts (row 5th with smooth background and clear foreground, row 6th in underwater scene). 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For each comparison, we adopt an A-B test that provides the users with two images in random order which include one VQD-SR frame. Users are asked to select the one with higher visual quality. As shown in Fig. 4, comparing with the SR methods designed for open-domain, over " + }, + { + "bbox": [ + 46, + 490, + 286, + 597 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 490, + 286, + 597 + ], + "type": "text", + "content": " of users voted for our VQD-SR. By considering the data characteristic of animation, there are still over " + }, + { + "bbox": [ + 46, + 490, + 286, + 597 + ], + "type": "inline_equation", + "content": "65\\%" + }, + { + "bbox": [ + 46, + 490, + 286, + 597 + ], + "type": "text", + "content": " users who prefer our method to AnimeSR [35]." + } + ] + } + ], + "index": 85 + }, + { + "bbox": [ + 47, + 609, + 138, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 138, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 138, + 622 + ], + "type": "text", + "content": "4.3. Ablation study" + } + ] + } + ], + "index": 86 + }, + { + "bbox": [ + 46, + 628, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 286, + 664 + ], + "type": "text", + "content": "In this section, we conduct ablation studies on each significant component of our VQ degradation model and HR-SR enhancement strategy in VQD-SR." + } + ] + } + ], + "index": 87 + }, + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "type": "text", + "content": "VQ Degradation Model. In the ablation study of VQ degradation model design, we conduct all the experiments based on VQD-SR (base), which denotes a plain version of VQD-SR trained without HR-SR enhancement. As shown" + } + ] + } + ], + "index": 88 + }, + { + "type": "image", + "bbox": [ + 307, + 487, + 356, + 528 + ], + "blocks": [ + { + "bbox": [ + 307, + 487, + 356, + 528 + ], + "lines": [ + { + "bbox": [ + 307, + 487, + 356, + 528 + ], + "spans": [ + { + "bbox": [ + 307, + 487, + 356, + 528 + ], + "type": "image", + "image_path": "e38c4b60fd4419149f7b2af673704e39d5311c76cae6ae761b55d513c20c7650.jpg" + } + ] + } + ], + "index": 89, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 529, + 352, + 536 + ], + "lines": [ + { + "bbox": [ + 310, + 529, + 352, + 536 + ], + "spans": [ + { + "bbox": [ + 310, + 529, + 352, + 536 + ], + "type": "text", + "content": "VQD-SR (base)" + } + ] + } + ], + "index": 90, + "angle": 0, + "type": "image_caption" + } + ], + "index": 89 + }, + { + "type": "image", + "bbox": [ + 358, + 488, + 402, + 528 + ], + "blocks": [ + { + "bbox": [ + 358, + 488, + 402, + 528 + ], + "lines": [ + { + "bbox": [ + 358, + 488, + 402, + 528 + ], + "spans": [ + { + "bbox": [ + 358, + 488, + 402, + 528 + ], + "type": "image", + "image_path": "9bfe7786d0c171fa06e0f76b92d2a10b6894c51984922af5e281a30572af1954.jpg" + } + ] + } + ], + "index": 91, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 362, + 529, + 394, + 535 + ], + "lines": [ + { + "bbox": [ + 362, + 529, + 394, + 535 + ], + "spans": [ + { + "bbox": [ + 362, + 529, + 394, + 535 + ], + "type": "text", + "content": "(a) BasicOP" + } + ] + } + ], + "index": 92, + "angle": 0, + "type": "image_caption" + } + ], + "index": 91 + }, + { + "type": "image", + "bbox": [ + 403, + 488, + 449, + 528 + ], + "blocks": [ + { + "bbox": [ + 403, + 488, + 449, + 528 + ], + "lines": [ + { + "bbox": [ + 403, + 488, + 449, + 528 + ], + "spans": [ + { + "bbox": [ + 403, + 488, + 449, + 528 + ], + "type": "image", + "image_path": "318504e6fb24b5d2812e43f1d200a368a81d963de6958f25386449f1622f6b66.jpg" + } + ] + } + ], + "index": 93, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 406, + 529, + 448, + 535 + ], + "lines": [ + { + "bbox": [ + 406, + 529, + 448, + 535 + ], + "spans": [ + { + "bbox": [ + 406, + 529, + 448, + 535 + ], + "type": "text", + "content": "(b) Single Scale" + } + ] + } + ], + "index": 94, + "angle": 0, + "type": "image_caption" + } + ], + "index": 93 + }, + { + "type": "image", + "bbox": [ + 451, + 488, + 497, + 528 + ], + "blocks": [ + { + "bbox": [ + 451, + 488, + 497, + 528 + ], + "lines": [ + { + "bbox": [ + 451, + 488, + 497, + 528 + ], + "spans": [ + { + "bbox": [ + 451, + 488, + 497, + 528 + ], + "type": "image", + "image_path": "df80a32e9a329d8f9aaa2c72597474f1295d4e9a47ef59537101f8bfacca4694.jpg" + } + ] + } + ], + "index": 95, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 452, + 529, + 494, + 535 + ], + "lines": [ + { + "bbox": [ + 452, + 529, + 494, + 535 + ], + "spans": [ + { + "bbox": [ + 452, + 529, + 494, + 535 + ], + "type": "text", + "content": "(c) Single Stage" + } + ] + } + ], + "index": 96, + "angle": 0, + "type": "image_caption" + } + ], + "index": 95 + }, + { + "type": "image", + "bbox": [ + 499, + 488, + 545, + 529 + ], + "blocks": [ + { + "bbox": [ + 499, + 488, + 545, + 529 + ], + "lines": [ + { + "bbox": [ + 499, + 488, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 499, + 488, + 545, + 529 + ], + "type": "image", + "image_path": "bb11b9c6811fdbc1fa046a33c7b4723bac02857aab967a6d3036c1f42aa4a3d5.jpg" + } + ] + } + ], + "index": 97, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 509, + 529, + 533, + 535 + ], + "lines": [ + { + "bbox": [ + 509, + 529, + 533, + 535 + ], + "spans": [ + { + "bbox": [ + 509, + 529, + 533, + 535 + ], + "type": "text", + "content": "(d) Top-1" + } + ] + } + ], + "index": 98, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 331, + 550, + 520, + 560 + ], + "lines": [ + { + "bbox": [ + 331, + 550, + 520, + 560 + ], + "spans": [ + { + "bbox": [ + 331, + 550, + 520, + 560 + ], + "type": "text", + "content": "Figure 6. Ablation study on VQ degradation model." + } + ] + } + ], + "index": 99, + "angle": 0, + "type": "image_caption" + } + ], + "index": 97 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "in Tab. 2 a, we first compare the degradation model which is simply composed of basic operators (blur, noise and FFmpeg) to our VQD-SR (base). With the help of real-world degradation priors contained in VQ codebook, the result can be improved from 0.3768 to 0.3857 in MANIQA. Referring to Fig. 6 a, VSR model trained with only basic operators fails to handle some real-world degradations, leading to artifacts around the edges. We further compare the structure and training strategy of VQ degradation model in Tab. 2 b and Tab. 2 c. As the global structures and local details are entangled together in single-scale VQ model and the" + } + ] + } + ], + "index": 100 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "13185" + } + ] + } + ], + "index": 101 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 72, + 121, + 263, + 258 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 288, + 113 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 288, + 113 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 288, + 113 + ], + "type": "text", + "content": "Table 2. Ablation study results of degradation models, structures of VQ degradation model, training pipelines of VQ degradation model and VQ codebook search strategies. The MANIQA scores are reported for comparisons." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 121, + 263, + 258 + ], + "lines": [ + { + "bbox": [ + 72, + 121, + 263, + 258 + ], + "spans": [ + { + "bbox": [ + 72, + 121, + 263, + 258 + ], + "type": "table", + "html": "
MANIQA↑(a) Degradation Model
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MANIQA↑(b) VQGAN Structure
Single-scaleVQD-SR (base)
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MANIQA↑(c) Training Strategy
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MANIQA↑(d) Codebook Search
NearestVQD-SR (base)
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", + "image_path": "3eb8edf58cd826d5441e5b3cfaaf5adaac7d6cd70c76e85cef6af102dace2060.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 300, + 285, + 341 + ], + "blocks": [ + { + "bbox": [ + 47, + 270, + 286, + 300 + ], + "lines": [ + { + "bbox": [ + 47, + 270, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 286, + 300 + ], + "type": "text", + "content": "Table 3. Applying VQ degradation to widely used SR backbones. For each backbone, settings are consistent apart from degradation methods." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 300, + 285, + 341 + ], + "lines": [ + { + "bbox": [ + 50, + 300, + 285, + 341 + ], + "spans": [ + { + "bbox": [ + 50, + 300, + 285, + 341 + ], + "type": "table", + "html": "
BackboneReal-ESRGAN*RealBasicVSR*AnimeSR
Params (M)16.76.31.5
Original degradation0.38250.35040.3832
VQ degradation0.39670.38490.3857
", + "image_path": "da28e6ac1a19b677e9c22d5d3121b812aadef8e1f9a44bc1259c35d33c2b84f3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 364, + 286, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 286, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 286, + 471 + ], + "type": "text", + "content": "multi-scale model trained in single-stage, the performances dropped by 0.0391 and 0.0427, respectively. As shown in Fig. 6 b and Fig. 6 c, some fine-grained details are missing. For VQ strategies, as shown in Tab. 2 d and Fig. 6 d, our stochastic top-k VQ strategy can improve MANIQA by 0.0087 compared with the original nearest neighbor search strategy, as the top-k VQ strategy enables multi-level degradations which improves the generalization ability of the trained animation model, leading to more appealing results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 472, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 286, + 628 + ], + "type": "text", + "content": "To further illustrate the general applicability, we also apply our VQ degradation model to other SOTA SR backbones, Real-ESRGAN and RealBasicVSR, fine-tuned with animation data in the same setting. Referring to Tab. 3, SR models with VQ degradation achieve better results comparing with their original degradation methods, which indicates that the proposed VQ degradation is generally effective for animation SR models. It is noteworthy that the performance gains could be more significant for larger backbones. The visual examples in Fig. 7 also show the superiority of our VQ degradation method, especially to recover clear and visual natural lines which are the most import patterns deciding the visual quality of animation videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "HR Enhancement. The training HR animation videos collected from the Web also contain artifacts which are not ideal for ground truths, hindering the performances of animation VSR models. We propose the HR-SR strategy to enhance the quality of HR animation videos for more effective training ground truths. 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"```bash\nAnimeSR(VQ)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 308, + 262, + 402, + 350 + ], + "blocks": [ + { + "bbox": [ + 308, + 262, + 402, + 350 + ], + "lines": [ + { + "bbox": [ + 308, + 262, + 402, + 350 + ], + "spans": [ + { + "bbox": [ + 308, + 262, + 402, + 350 + ], + "type": "image", + "image_path": "0d7e6cfc54c4460eb7841454b91c6526073d0c9a4fb43836488899ef598a9c6e.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 350, + 372, + 356 + ], + "lines": [ + { + "bbox": [ + 337, + 350, + 372, + 356 + ], + "spans": [ + { + "bbox": [ + 337, + 350, + 372, + 356 + ], + "type": "text", + "content": "big_ear_tutu/105" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 369, + 545, + 413 + ], + "lines": [ + { + "bbox": [ + 306, + 369, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 306, + 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Applying VQ degradation to widely used SR backbones. Settings are consistent apart from degradation methods. Models trained with VQ degradation could produce more clear and visual natural lines with fewer artifacts." + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 404, + 262, + 443, + 350 + ], + "blocks": [ + { + "bbox": [ + 404, + 262, + 443, + 350 + ], + "lines": [ + { + "bbox": [ + 404, + 262, + 443, + 350 + ], + "spans": [ + { + "bbox": [ + 404, + 262, + 443, + 350 + ], + "type": "image", + "image_path": "4679650b4f7ffa3da7517e76191ca9e914c02f6ee5e8c25479f96fe44776700b.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 407, + 350, + 448, + 356 + ], + "lines": [ + { + "bbox": [ + 407, + 350, + 448, + 356 + ], + "spans": [ + { + "bbox": [ + 407, + 350, + 448, + 356 + ], + "type": "text", + "content": "Real-ESRGAN(VQ)*" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 451, + 262, + 490, + 350 + ], + "blocks": [ + { + "bbox": [ + 451, + 262, + 490, + 350 + ], + "lines": [ + { + "bbox": [ + 451, + 262, + 490, + 350 + ], + "spans": [ + { + "bbox": [ + 451, + 262, + 490, + 350 + ], + "type": "image", + "image_path": "3e28d4db9a7a5fc788f7b6f62ed802bdf886df975e4496aac6c03400820e41a9.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 453, + 350, + 495, + 356 + ], + "lines": [ + { + "bbox": [ + 453, + 350, + 495, + 356 + ], + "spans": [ + { + "bbox": [ + 453, + 350, + 495, + 356 + ], + "type": "text", + "content": "RealBasicVSR (VQ)*" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 499, + 262, + 536, + 350 + ], + "blocks": [ + { + "bbox": [ + 499, + 262, + 536, + 350 + ], + "lines": [ + { + "bbox": [ + 499, + 262, + 536, + 350 + ], + "spans": [ + { + "bbox": [ + 499, + 262, + 536, + 350 + ], + "type": "image", + "image_path": "26b46579d5bf3a14df71f4c343065090874377aac3b07faa1222c6024b0be855.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 506, + 350, + 537, + 356 + ], + "lines": [ + { + "bbox": [ + 506, + 350, + 537, + 356 + ], + "spans": [ + { + "bbox": [ + 506, + 350, + 537, + 356 + ], + "type": "text", + "content": "AnimeSR (VQ)" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 448, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 567 + ], + "type": "text", + "content": "The quantitative results are shown in Tab. 4. All three models improve the performance of animation VSR model, which verifies that the proposed HR-SR strategy is suitable for the training of animation VSR model, and improvements are not subject to the specific model for enhancement. However, as the SR process for data enhancement is conducted in HR domain, which takes a high demand on computing resources, we finally choose SISR model, Real-ESRGAN (S) [32] with relatively small model size. Visual examples of the enhanced HR frames can be found in Fig. 8." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "We further utilize the enhanced HR animation videos processed by Real-ESRGAN(S) [32] to fine-tune different VSR models. Apart from the proposed VQD-SR, RealBasicVSR [3] is a blind VSR model designed for open-domain videos and AnimeSR [35] is an VSR model specified for animation domain. As shown in Tab. 5, with the help of HR enhancement, all three VSR models get improved, which illustrates that the proposed HR enhancement strategy is effective for animation VSR task, regardless of the specific VSR model. The visual results of RealBasicVSR+, AnimeSR+, and VQD-SR in Fig. 9 also verify the advantages of the HR-SR enhancement strategy for animation VSR." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13186" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 110, + 252, + 175 + ], + "blocks": [ + { + "bbox": [ + 46, + 69, + 287, + 102 + ], + "lines": [ + { + "bbox": [ + 46, + 69, + 287, + 102 + ], + "spans": [ + { + "bbox": [ + 46, + 69, + 287, + 102 + ], + "type": "text", + "content": "Table 4. Ablation study of different SR models for HR-SR enhancement. All three models improve the performance. We choose Real-ESRGAN (S) considering the computing cost." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 110, + 252, + 175 + ], + "lines": [ + { + "bbox": [ + 83, + 110, + 252, + 175 + ], + "spans": [ + { + "bbox": [ + 83, + 110, + 252, + 175 + ], + "type": "table", + "html": "
Enhancement MethodMANIQA↑
No Enhancement0.3857
AnimeSR [35]0.4146
Real-ESRGAN (L) [32]0.4211
Real-ESRGAN (S) [32]0.4096
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MANIQA↑wo /HR-SRw /HR-SR
RealBasicVSR [3]0.35040.3855
AnimeSR [35]0.38320.4079
VQD-SR0.38570.4096
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Enhanced HR data with HR-SR strategy by different enhancement models." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 109, + 346, + 166, + 403 + ], + "blocks": [ + { + "bbox": [ + 109, + 346, + 166, + 403 + ], + "lines": [ + { + "bbox": [ + 109, + 346, + 166, + 403 + ], + "spans": [ + { + "bbox": [ + 109, + 346, + 166, + 403 + ], + "type": "image", + "image_path": "9f21713189335e97c33931f2e9822afd863fc6596d85bc89dc2f67a5bd11bff6.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 168, + 346, + 226, + 403 + ], + "blocks": [ + { + "bbox": [ + 168, + 346, + 226, + 403 + ], + "lines": [ + { + "bbox": [ + 168, + 346, + 226, + 403 + ], + "spans": [ + { + "bbox": [ + 168, + 346, + 226, + 403 + ], + "type": "image", + "image_path": "658b894565bb7e2e88c9ee65830f61d5756c2c8a1e802d1155fea4ec094cb267.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 228, + 346, + 286, + 403 + ], + "blocks": [ + { + "bbox": [ + 228, + 346, + 286, + 403 + ], + "lines": [ + { + "bbox": [ + 228, + 346, + 286, + 403 + ], + "spans": [ + { + "bbox": [ + 228, + 346, + 286, + 403 + ], + "type": "image", + "image_path": "741372d0a6ebb21a0ac3d0ba67e9552a2400f31913a3d0734745a7d035fdcd1e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 468, + 195, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 195, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 195, + 480 + ], + "type": "text", + "content": "5. Limitation and Discussion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 488, + 286, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 286, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 286, + 583 + ], + "type": "text", + "content": "In this section, we visualize the failure cases of VQDSR in Fig. 10. Our VQD-SR is capable to restore sharper lines and suppress diverse artifacts in animation videos. However, in some extreme circumstances (e.g., severe lossy compressions, long passing ages), there still gets room for improvement, for example the remaining color distortions around edges. Nevertheless, comparing with other SOTA methods, our VQD-SR still achieves better performances." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 119, + 609 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 618, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 286, + 713 + ], + "type": "text", + "content": "In this paper, we thoroughly study the characteristics of animation videos and fully leverage the rich prior knowledge contained in real data for a more practical animation VSR model. To be specific, we propose a novel degradation model which utilize a multi-scale VQGAN, self-supervised on purely real low-quality animation data (RAL), to decompose animation frames and establish a codebook containing diverse real-world degradation priors. 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Failure cases when LR frames endure severe color distortions around edges." + } + ] + } + ], + "index": 41, + "angle": 0, + "type": "image_caption" + } + ], + "index": 38 + }, + { + "type": "image", + "bbox": [ + 451, + 421, + 498, + 514 + ], + "blocks": [ + { + "bbox": [ + 451, + 421, + 498, + 514 + ], + "lines": [ + { + "bbox": [ + 451, + 421, + 498, + 514 + ], + "spans": [ + { + "bbox": [ + 451, + 421, + 498, + 514 + ], + "type": "image", + "image_path": "6194893cdefff487dd2a60ce31ff9a7dfb4e24e484bfabe8c1dc7e7d22964405.jpg" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_body" + } + ], + "index": 39 + }, + { + "type": "image", + "bbox": [ + 498, + 421, + 545, + 514 + ], + "blocks": [ + { + "bbox": [ + 498, + 421, + 545, + 514 + ], + "lines": [ + { + "bbox": [ + 498, + 421, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 498, + 421, + 545, + 514 + ], + "type": "image", + "image_path": "c5f6de546fd183f28bd1a3f34bc41983f32fdc66e89eb6170fdb8b628e2df343.jpg" + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "image_body" + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 566, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 661 + ], + "type": "text", + "content": "two-stage training pipeline and a stochastic top-k VQ strategy to match up with the VQ degradation model. We further propose to enhance the HR training videos to lift the performance ceiling for animation VSR tasks. Experiment results show the superiority of the proposed VQD-SR over existing SOTA models, as our methods could generate more effective LR-HR training pairs in view of the characteristics in real animation videos." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement. This work was supported in part by the NSFC under Grant 62272380 and 62103317, the Science and Technology Program of Xi'an, China under Grant 21RGZN0017, and Microsoft Research Asia." + } + ] + } + ], + "index": 43 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13187" + } + ] + } + ], + "index": 44 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Kelvin CK Chan, Xintao Wang, Ke Yu, Chao Dong, and Chen Change Loy. 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In CVPR, pages 586-595, 2018." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "13189" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_content_list.json b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..aa0e022c8c53b69fc340422e46cdee942c546f0b --- /dev/null +++ b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_content_list.json @@ -0,0 +1,1538 @@ +[ + { + "type": "text", + "text": "Learning Depth Estimation for Transparent and Mirror Surfaces", + "text_level": 1, + "bbox": [ + 155, + 130, + 815, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Alex Costanzino* Pierluigi Zama Ramirez* Matteo Poggi* Fabio Tosi Stefano Mattoccia Luigi Di Stefano CVLAB, Department of Computer Science and Engineering (DISI) University of Bologna, Italy {alex.costanzino, pierluigi.zama, m.poggi, fabio.tosi5}@unibo.it https://cvlab-unibo.github.io/Depth4ToM/", + "bbox": [ + 179, + 180, + 789, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 321, + 313, + 337 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inferring the depth of transparent or mirror (ToM) surfaces represents a hard challenge for either sensors, algorithms, or deep networks. We propose a simple pipeline for learning to estimate depth properly for such surfaces with neural networks, without requiring any ground-truth annotation. We unveil how to obtain reliable pseudo labels by in-painting ToM objects in images and processing them with a monocular depth estimation model. These labels can be used to fine-tune existing monocular or stereo networks, to let them learn how to deal with ToM surfaces. Experimental results on the Booster dataset show the dramatic improvements enabled by our remarkably simple proposal.", + "bbox": [ + 75, + 353, + 473, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 564, + 209, + 579 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In our daily lives, we often interact with several objects of various appearances. Among them are those made of transparent or mirror surfaces (ToM), ranging from the glass windows of buildings to the reflective surfaces of cars and appliances. These might represent a hard challenge for an autonomous agent leveraging computer vision to operate in unknown environments. Specifically, among the many tasks involved in Spatial AI, accurately estimating depth information on these surfaces remains a challenging problem for both computer vision algorithms and deep networks [64], yet necessary for proper interaction with the environment in robotic, autonomous navigation, picking, and other application fields. This difficulty arises because ToM surfaces introduce misleading visual information about scene geometry, which makes depth estimation challenging not only for computer vision systems but even for humans - e.g., we might not distinguish the presence of a glass door in front of us due to its transparency. On the one hand, the definition of depth itself might appear ambiguous in such cases:", + "bbox": [ + 75, + 589, + 472, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/79a25101617001da4b54d1adbb56f190054b0effd3e78fe1a25140d97a60f4d9.jpg", + "image_caption": [ + "Figure 1. Depth estimation on ToM surfaces. Two examples for both monocular (top) and stereo (bottom) images. In the central column, the depth/disparity maps predicted by DPT [37] and CREStereo [22] original weights. In the rightmost column, the depth/disparity maps predicted by the models after being finetuned by our strategy without exploiting any ground-truth depth." + ], + "image_footnote": [], + "bbox": [ + 506, + 321, + 890, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "is depth the distance to the scene behind the glass door or to the door itself? Nonetheless, from a practical point of view, we argue that the actual definition depends on the task itself - e.g., a mobile robot should definitely be aware of the presence of the glass door. On the other hand, as humans can deal with this through experience, depth sensing techniques based on deep learning, e.g., monocular [38, 37] or stereo [26, 22] networks, hold the potential to address this challenge given sufficient training data [64].", + "bbox": [ + 496, + 744, + 893, + 882 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unfortunately, light reflection and refraction over ToM", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* These authors contributed equally to this work.", + "bbox": [ + 94, + 886, + 352, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9244", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "surfaces violate also the working principles of most active depth sensors, such as Time-of-Flight (ToF) cameras or devices projecting structured-light patterns. This has two practical consequences: i) it makes active sensors unsuited to deal with ToM objects in real-world applications, and ii) prevents the use of these sensors for collecting and annotating data to train deep neural networks to deal with ToM objects. As evidence of this, very few datasets featuring transparent objects provide ground-truth depth annotations, which have been obtained through very intensive human intervention [64], graphical engines [40], or based on the availability of CAD models [5] for ToM objects.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In short, accurately perceiving the presence (and depth) of ToM objects represents an open challenge for both sensing technologies and deep learning frameworks. Purposely, this paper proposes a simple yet effective strategy for obtaining training data and, thereby, dramatically boosting the accuracy of learning-based depth estimation frameworks dealing with ToM surfaces. Driven by the observation that ToM objects alone are responsible for misleading recent monocular networks [38, 37], which would otherwise generalize well to most unseen environments, we argue that replacing them with equivalent, yet opaque objects would allow restoring an environment layout in which such networks could accurately estimate the depth of the scene. To this end, we mask ToM objects in images by in-painting them with arbitrary uniform colors. Then, we employ a monocular depth network to generate a virtual depth map out of the modified image. By repeating this process on a variety of images featuring ToM objects, we can easily and effectively annotate a dataset and then use it to train the same monocular network used to distill labels, which will now process the not-in-painted images. As a result, the trained monocular network will learn to handle ToM objects, producing consistent depth even in their presence.", + "bbox": [ + 75, + 273, + 472, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be resumed as follows:", + "bbox": [ + 96, + 619, + 434, + 633 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a simple yet very effective strategy to deal with ToM objects. We trick a monocular depth estimation network by replacing ToM objects with virtually textured ones, inducing it to hallucinate their depths.", + "- We introduce a processing pipeline for fine-tuning a monocular depth estimation network to deal with ToM objects. Our pipeline exploits the network itself to generate virtual depth annotations and requires only segmentation masks delineating ToM objects – either human-made or predicted by other networks [54, 60] – thus getting rid of the need for any depth annotations.", + "- We show how our strategy can be extended to other depth estimation settings, such as stereo matching. Our experiments on the Booster dataset [64] prove how monocular and stereo networks dramatically improve" + ], + "bbox": [ + 94, + 650, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "their prediction on ToM objects after being fine-tuned according to our methodology.", + "bbox": [ + 531, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fig. 1 highlights some specific regions where monocular (top) and stereo (bottom) models struggle (middle column), and how they learn to handle ToM surfaces thanks to our strategy (rightmost column).", + "bbox": [ + 498, + 135, + 893, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 209, + 640, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Monocular Depth Estimation. Early methods used CNNs for pixel-level regression [10, 11]. More recent approaches such as AdaBins [2], DPT [37], and MiDaS [38] use adaptive bins and vision transformers for depth regression and leverage large-scale depth training by mixing multiple datasets. Self-supervised methods use view synthesis for image reconstruction, where predicted depth is combined with known or estimated camera pose to establish correspondences between adjacent images, exploiting either stereo pairs [10, 11] or monocular videos [70, 12]. Recent works aim to improve the robustness of the photometric loss based on SSIM and L1 [68] by incorporating photometric uncertainty [57, 35], feature descriptors [66, 44, 46], 3D geometric constraints [29], proxy supervision [52, 49], optical flow [62, 50], or adversarial losses [1, 34]. Others propose architecture changes as in [69, 14, 33, 18, 13]. Except for some works that address non-Lambertian depth estimation using depth completion approaches and sparse depth measurements from active sensors [8, 40], to the best of our knowledge, we are not aware of any previous single-view depth estimation network that can handle ToM surfaces.", + "bbox": [ + 496, + 234, + 890, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Stereo Matching. Traditional algorithms [42] utilize handcrafted features to estimate a disparity map [63, 17, 59, 58, 24, 47, 21, 3]. Then, deep learning methods replaced traditional matching cost computation, as demonstrated in [65], and, eventually, end-to-end approaches became the most effective solution for disparity estimation. These networks can be mainly categorized into 2D and 3D architectures, with the former adopting an encoder-decoder design [30, 32, 25, 39, 45, 56, 61, 48] and the latter building a feature cost volume from extracted features on the image pair [19, 4, 20, 67, 6, 7, 9, 55, 51, 16, 43]. A thorough review of these works can be found in [36]. Recent papers exploit iterative refinement paradigms [26, 22] or rely on Vision Transformers [23, 15]. However, due to its inherently ill-posed nature, dealing with non-Lambertian surfaces, such as ToM objects, remains a very challenging problem for any kind of existing stereo approach.", + "bbox": [ + 496, + 553, + 890, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Non-Lambertian Object Perception. Due to the relevance of dealing with ToM objects, some recent datasets focus on them. Trans10K [54] and MSD [60] consist of over 10 000 and 4 000 real in-the-wild images of transparent objects and mirrors, respectively. Both datasets provide manually annotated segmentations of ToM materials, though", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9245", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1e48d3d06a414270dd05b8d107c99780406abbdc24166552fb20384a735562cd.jpg", + "image_caption": [ + "Figure 2. Monocular Distillation pipeline. Given an RGB and a segmentation mask, we in-paint pixels belonging to transparent and mirror surfaces with a random uniform color and process these augmented images with a pre-trained monocular network. The obtained virtual depths are aggregated to obtain a pseudo-labeled dataset for fine-tuning the network itself." + ], + "image_footnote": [], + "bbox": [ + 83, + 98, + 883, + 262 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "none of them provide depth labels. Others provide depth annotations: ClearPose [5] includes over 350 000 labeled real-world RGB-D frames of 63 household objects. ClearGrasp [40] consists of over 50 000 synthetic RGB-D images of transparent objects, as well as real-world test benchmark with 286 RGB-D images. In addition, Booster [64] focuses on stereo matching, providing high-resolution depth labels and stereo pairs acquired in indoor scenes with specular and transparent surfaces. TOD [28] contains 15 transparent objects, labeled with relevant 3D keypoints, comprising 48 000 stereo and RGBD images. StereOBJ-1M [27] also deals with stereo vision, but focuses on pose estimation for ToM objects and do not provide depth ground truths. Obtaining depth labels for these kinds of datasets is expensive, challenging, and time-consuming since it requires either CAD models for ToM objects [5], painting such objects in the scene [40, 64, 28] or relies on a complex multi-camera setup [53]. In contrast, our proposal effectively sidesteps these challenges, by demonstrating that monocular and stereo networks can learn to deal with these objects in the absence of depth annotations.", + "bbox": [ + 75, + 335, + 472, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 676, + 169, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to generate depth annotations for images featuring ToM objects in a cheap and scalable manner. This allows for training deep networks to properly estimate their depth as the distance of the closest surface in front of the camera, rather than the distance of the scene content refracted/reflected through it. Our strategy is simple yet dramatically effective and relies on the availability of recent pre-trained monocular depth estimation models [38, 37], which are capable of strong generalization across a variety of scenes though struggling to deal with ToM surfaces. Based on the above state of affairs, we argue that ToM objects are often the sole elements harming the reliability of recent pre-trained monocular depth estimation networks.", + "bbox": [ + 75, + 704, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Therefore, by virtually replacing these objects with textured artifacts that resemble their very same shapes, the monocular model may be possibly tricked and induced into estimating the depth of an opaque object, ideally placed at the very same spot in the scene. This methodology can be realized by delineating ToM objects, through manual annotations or a segmentation network, masking them from the image and then in-painting virtual textures within the masked areas. On the one hand, since a proper detection of ToM objects is crucial to our methodology, manual labeling indisputably results in the most accurate choice, though it comes with significant annotation costs. On the other hand, relying on a segmentation network would alleviate this cost: one would need some initial human annotations for training, but this would then allow to segment a large number of images for free. Unfortunately, the overall effectiveness of our methodology would be inevitably affected by the accuracy of the trained segmentation model. However, we reckon that annotating images with segmentation masks requires, definitely, a vastly lower effort compared to depth annotation [64, 27]. Hence, we settled on exploring both the aforementioned approaches.", + "bbox": [ + 496, + 335, + 893, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The reader may argue that, as a consequence of our intuition, training a depth network to deal with ToM objects might be unnecessary - indeed, it would be sufficient to segment and in-paint such objects at deployment time before estimating depth. However, we retort that such a methodology would rely heavily on the actual accuracy of the model trained to segment ToM objects, which is not granted to generalize. Moreover, it would add non-negligible computational cost - i.e., the inference by a second network. On the contrary, an offline training or fine-tuning procedure allows for exploiting human-made annotation - if available - and, potentially, enable the trained network to learn how to properly estimate depth on ToM surfaces and to get rid of the second network, as well as design advanced strategies for other depth estimation frameworks, e.g. deep stereo net", + "bbox": [ + 496, + 674, + 895, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9246", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4ca76e917f36f197530d00e16d0984c0317b82ea3ea2a2432409db7039db4654.jpg", + "image_caption": [ + "Figure 3. Virtual depth generation alternatives. From left to right: RGB, ground-truth segmentation, DPT predictions on the RGB image, on the gray-masked input, and the median of five predictions on images masked with random colors." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 486, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "works. Our experiments will highlight that the former strategy results ineffective, while we achieve a large boost in accuracy by fine-tuning depth models with our approach.", + "bbox": [ + 75, + 268, + 468, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the remainder, we describe our methodology to deal with ToM objects. Given a dataset of images $\\mathcal{I}$ , our pipeline sketched in Fig. 2 builds as follows: i) surface labeling, ii) in-painting and distillation, and iii) fine-tuning of the depth network on virtual labels. Additionally, we show how it can be revised to fine-tune also deep stereo networks.", + "bbox": [ + 75, + 316, + 468, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Surface Labeling. For any image $I_k \\in \\mathcal{I}$ , we produce a segmentation mask $M_k$ classifying each pixel $p$ as", + "bbox": [ + 76, + 406, + 468, + 438 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {k} (p) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} I _ {k} (p) \\in \\operatorname {T o M} \\text {s u r f a c e s} \\\\ 0 & \\text {O t h e r w i s e} \\end{array} \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 450, + 468, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "by labeling pixels as either 1 or 0 if they belong to a ToM surface or not, respectively. Such a segmentation mask can be obtained either through manual annotation or by means of a segmentation network $\\Theta$ as $M_{k} = \\Theta (I_{k})$ .", + "bbox": [ + 75, + 497, + 468, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In-painting and Distillation. Given an image $I_{k}$ and its corresponding segmentation mask $M_{k}$ , we generated an augmented image $\\tilde{I}_{k}$ applying an in-painting operation to replace the pixels belonging to ToM objects with a color $c$ :", + "bbox": [ + 75, + 559, + 468, + 619 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {I} _ {k} (p) = \\left\\{ \\begin{array}{l l} c & \\text {i f} M _ {k} (p) = 1 \\\\ I _ {k} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 632, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, a virtual depth $\\tilde{D}_k$ for image $I_{k}$ is obtained by forwarding $\\tilde{I}_k$ to a monocular depth network $\\Psi$ as $\\tilde{D}_k = \\Psi (\\tilde{I}_k)$ . Colors are randomly sampled for every single frame $I_{k}$ . However, depending on the image content, certain colors might result ineffective and increase the scene ambiguity - e.g., by in-painting white pixels into a transparent object located in front of a white wall. To discourage these occurrences, we sample a set of $N$ custom colors $c_{i}, i\\in [0,N - 1]$ , and in-paint $I_{k}$ using each of these custom colors, so as to generate a set of $N$ augmented images $\\tilde{I}_k^i$ . Then, we obtain the final, Virtual Depth $\\tilde{D}_k$ by computing the per-pixel median between the $N$ depth maps", + "bbox": [ + 75, + 683, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {D} _ {k} ^ {*} = \\operatorname {m e d} \\left\\{\\Psi \\left(\\tilde {I} _ {k} ^ {i}\\right), i \\in [ 0, N - 1 ] \\right\\} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 878, + 468, + 905 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d554cea05e9314f1d45dee436a2bf0bcc6a884a55218bcee99b84867a0c0d7a3.jpg", + "image_caption": [ + "Figure 4. Stereo Distillation pipeline. Given a stereo pair and a segmentation mask for the left image, we merge predictions from a pre-trained stereo network with virtual depths obtained by a monocular network with our strategy. We merge the monocular or stereo maps, by taking values belonging to either ToM or other surfaces from mono or stereo, respectively. These final merged depth labels are used to fine-tune the original stereo network." + ], + "image_footnote": [], + "bbox": [ + 506, + 95, + 880, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As depicted in Fig. 3, in some cases, the in-painted color might be similar to the background – e.g., the transparent object disappears when a single gray mask is used – while it is visible by aggregating multi-color in-painting.", + "bbox": [ + 496, + 459, + 890, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fine-Tuning on Virtual Labels. The steps outlined so far allow for labeling a dataset $\\mathcal{I}$ with virtual depth labels that are not influenced by the ambiguities of ToM objects. Then, our newly annotated dataset can be used to train or fine-tune a depth estimation network, thereby enabling it to handle the aforementioned difficult objects robustly. Specifically, during training, the original images $I_{k}$ are forwarded to the network, and the predicted depth $\\hat{D}_k$ is optimized with respect to the distilled virtual ground-truth map $\\tilde{D}_k^*$ obtained from in-painted images. This simple pipeline can dramatically improve the accuracy of monocular depth estimation networks when dealing with ToM objects, as we will show in our experiments.", + "bbox": [ + 496, + 521, + 892, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Extension to Deep Stereo. Our pipeline can be adapted to fine-tune deep stereo models as well, as shown in Fig. 4. Again, we argue that state-of-the-art stereo architectures [26, 22] already expose outstanding generalization capabilities while struggling with ToM objects, due to the task of matching pixels belonging to non-Lambertian surfaces being inherently ambiguous. Consequently, we exploit a monocular depth estimation network to obtain virtual depth annotations solely for these objects. Given a dataset $S$ consisting of stereo pairs $(L_k,R_k)$ , we distill virtual depth labels $\\tilde{D}_k^*$ from $L_{k}$ and triangulate them into disparities $\\tilde{d}_k^*$ according to extrinsic parameters of the stereo rig. Then,", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9247", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/3dac301a6c1676fcaa5b3104761462e5e9907afe1e09d68df8e172ef277f4354.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Virtual depth distillation by varying $N$ . Results on Booster train set at quarter resolution. All networks use the official weights [37, 38] without further training. Different masking strategies are applied to the RGB input image. Best results in bold." + ], + "table_body": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllVirtual Depth N=196.0893.2387.6875.2349.2683.880.07112.03
AllVirtual Depth N=596.0493.5187.9375.7049.3682.980.07110.52
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMVirtual Depth N=194.1191.9984.1268.4041.1776.690.0986.46
ToMVirtual Depth N=593.8791.6483.6668.7643.6576.650.0886.01
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherVirtual Depth N=195.6292.5086.7774.6348.7688.300.07116.78
OtherVirtual Depth N=595.6692.9387.3175.4249.0686.490.07114.48
", + "bbox": [ + 83, + 88, + 553, + 208 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e33f1d0bbdf7c9bad97ae9208e6f8b92e5a942b190d8708b72da6dc5b3baad7b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
97.5995.8892.0682.7560.1464.990.0585.96
98.4396.7492.8683.4260.1862.460.0582.06
92.7788.7780.9862.4637.70113.140.10136.28
96.0093.6788.8875.7945.2665.580.0778.24
98.9497.1992.2477.5245.9757.190.0666.86
97.1094.8490.0879.7657.3173.190.0695.63
97.6395.9692.0983.1161.0166.100.0587.37
98.2996.5092.5783.5160.9064.170.0584.06
", + "bbox": [ + 566, + 88, + 901, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we predict a Base disparity map $d_{k}$ by forwarding $(L_{k}, R_{k})$ to the stereo network we aim to fine-tune. Eventually, we replace the disparities for ToM objects with those from $d_{k}$ according to $M_{k}$ , this latter produced over $L_{k}$ this time. Formally, this operation namely Merging, is defined as:", + "bbox": [ + 75, + 260, + 468, + 335 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd _ {k} (p) = \\left\\{ \\begin{array}{l l} d _ {k} (p) & \\text {i f} M _ {k} (p) = 0 \\\\ \\alpha_ {k} \\hat {d} _ {k} ^ {*} (p) + \\beta_ {k} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 347, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $\\alpha_{k},\\beta_{k}$ being scale and shift factors, as monocular predictions are up to an unknown scale factor. Following [38], $\\alpha_{k},\\beta_{k}$ are estimated through Least Square Estimation (LSE) regression over $d_{k}$ for pixels not belonging to any ToM object, i.e., having $M_{k}(p) = 0$ ..", + "bbox": [ + 76, + 393, + 470, + 472 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\alpha_ {k}, \\beta_ {k}\\right) = \\arg \\min _ {\\alpha , \\beta} \\sum_ {p \\mid M _ {k} (p) = 0} \\left(\\alpha \\hat {d} _ {k} ^ {*} (p) + \\beta - d _ {k} (p)\\right) ^ {2} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 494, + 468, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 558, + 287, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We employ MiDaS [38] and DPT [37] as our monocular networks using the official pretrained weights, given their excellent in-the-wild generalization performance. To fine-tune them, we iterate for 20 epochs with batch size 8 and a learning rate of $10^{-7}$ with exponential decay with gamma 0.95. We use random color and brightness and random horizontal flip augmentations. We pad/crop and resize images to match the pre-training resolution, i.e., 384 pixels for the long or short side, preserving aspect ratio with mirror pad or square crop, for MiDaS or DPT, respectively. We normalize images as the original networks do. Regarding stereo networks, we employ RAFT [26] and CREStereo [22], using the official pre-trained weights, since they achieve the top rankings in the Middlebury dataset [41] among published methods. To fine-tune them, we run 20 epochs, with batch size 2, fixed learning rate $10^{-5}$ . Following [64], we randomly resize images to half or quarter of the original dataset resolution, randomly crop to $456 \\times 884$ and $448 \\times 880$ for RAFT and CREStereo respectively, and further randomly scale images and disparities by a factor $\\in [0.9, 1.1]$ . We assume", + "bbox": [ + 75, + 583, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "22 and 10 iterations during training for RAFT-Stereo and CREStereo, respectively. During testing, we run 32 and 20 iterations. When creating virtual labels with our masking strategy, we fix the random seed of color sampling to 0.", + "bbox": [ + 496, + 260, + 890, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Among the datasets, we selected Trans10K [54], MSD[60], and Booster[64] as they focus on ToM surfaces and contain images acquired in many realistic environments. Trans10K contains 5003, 1003, 4431 images for the training, validation, and test set, respectively, featuring common transparent objects and stuff. It provides segmentation masks with pixels categorized into 12 different classes that we collapse into 2 - ToM (classes 1 to 11) or not. MSD contains 3066, and 958 images and binary segmentation masks for the training and test set, respectively, featuring mirrors. Booster contains 228, and 191 images for training and testing, respectively. The dataset provides disparity and segmentation maps for the training set, where the segmentation maps are categorized into 4 classes, which we group into 2 - classes 2-3 into \"ToM\" category, classes 0-1 into \"Other\" materials. We fine-tune on Trans10K and MSD for monocular models and on the Booster training split for stereo networks, without using any depth ground truths.", + "bbox": [ + 496, + 323, + 892, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Protocol. We evaluate the accuracy of the monocular networks using several metrics, including absolute error relative to the ground-truth value (ABS Rel.), the percentage of pixels having the maximum between the prediction/ground-truth and ground-truth/prediction ratios lower than a threshold $(\\delta_{i}$ , with $i$ being 1.05, 1.10, 1.15, 1.20, and 1.25), the mean absolute error (MAE) and Root Mean Squared Error (RMSE). Additionally, we evaluate stereo networks using the metrics defined in Booster [64], i.e. bad-2, bad-4, bad-6, bad-8, MAE, RMSE. Results are reported on all valid pixels (All) or for those belonging to either ToM or other objects, in order to assess the impact of our strategy on the different kinds of surfaces. For any metrics considered for stereo networks, the lower, the better - annotated with $\\downarrow$ in tables. The same applies to metrics used for monocular networks except for $\\delta_{i}$ , resulting in the higher, the better - with $\\uparrow$ being reported in tables. As the predictions by monocular networks are up to an unknown scale factor, we rescale them according to the LSE criterion [38] defined in Eq. 5, using all valid pixels here. Monocu", + "bbox": [ + 496, + 598, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9248", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6ae66fde484b492e27f296adc28b8322ea2278cc923b3f84ad11ecf0e5847c4c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllFt. Base94.0991.2885.2973.5549.1493.340.07124.54
AllFt. Virtual Depth95.0792.3186.3975.2050.5788.830.07118.23
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMFt. Base86.3082.9672.8461.0437.91126.710.12145.69
ToMFt. Virtual Depth91.8189.1281.6870.7547.8593.660.09104.80
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherFt. Base94.2791.4985.8773.7749.3892.480.07122.46
OtherFt. Virtual Depth95.3392.5386.8075.4350.4689.170.07119.58
", + "bbox": [ + 83, + 89, + 545, + 208 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8d771560c23393aaaae8351f258176f886460a097ac2b825802279bccadc01dd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
96.8394.6090.1479.4656.8976.000.06100.98
97.9996.6593.5583.9460.4664.930.0585.93
92.7788.7780.9862.4637.70113.140.10136.28
92.6989.4981.1263.6237.95118.840.11141.27
96.6895.9692.2379.9654.6770.680.0683.06
97.1094.8490.0879.7657.3173.190.0695.63
97.1595.0290.9780.7758.0572.450.0694.07
98.0796.6493.5284.3061.1964.700.0585.57
", + "bbox": [ + 560, + 89, + 893, + 208 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b10117560bd8708331ee7e559cc23fe39779ac5bc0e18acd550782cd48fdddda.jpg", + "table_caption": [ + "Table 2. Monocular networks fine-tuning - ground-truth segmentation. Training on all MSD and Trans10K, results on the Booster train set at quarter resolution. All models start from the official weights [37, 38]. Best results in bold." + ], + "table_footnote": [], + "table_body": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllVirtual Depth (Proxy)91.7887.5279.5766.0042.21105.670.09140.00
AllFt. Virtual Depth (GT)94.9992.1286.3274.9949.9188.630.07117.40
AllFt. Virtual Depth (Proxy)95.0092.1786.4875.4650.2488.100.07117.10
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMVirtual Depth (Proxy)86.3779.3569.9154.8432.31112.920.12124.10
ToMFt. Virtual Depth (GT)91.8589.9383.2570.6347.5592.050.09103.54
ToMFt. Virtual Depth (Proxy)91.1288.3681.1869.1545.0296.330.09107.59
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherVirtual Depth (Proxy)91.8087.4779.4165.8641.95108.090.09143.64
OtherFt. Virtual Depth (GT)95.2792.3086.6075.4349.9588.810.07118.48
OtherFt. Virtual Depth (Proxy)95.2792.4286.8476.0250.4888.070.07117.99
", + "bbox": [ + 84, + 247, + 552, + 383 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/776d6c890258df9a6d8466861b02d3c238266cf790319a0a10f2f68891699e42.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
93.2389.4381.9868.0643.6298.090.08128.36
98.0996.8593.9183.5058.7465.520.0586.41
98.1196.6893.4883.0058.1366.430.0587.18
92.7788.7780.9862.4637.70113.140.10136.28
89.7585.2675.1756.5731.75110.740.11123.28
96.9596.2693.2781.8455.4967.950.0680.88
96.8296.0592.5780.6253.7470.670.0683.44
97.1094.8490.0879.7657.3173.190.0695.63
93.2289.3982.0768.3043.8898.640.08129.48
98.1996.8593.8583.7058.9365.650.0586.30
98.2096.6793.3583.2058.4066.510.0587.06
", + "bbox": [ + 566, + 247, + 883, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Monocular networks fine-tuning - ground-truth vs proxy segmentation. Training on only the test set of MSD and Trans10K, results on the Booster train set at quarter resolution. All models start from the official weights [37, 38]. Best results in bold.", + "bbox": [ + 76, + 383, + 888, + 410 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0a9137aeff420bddf91763e0d75a359c19bcf9865ace3e32d8c151875ffbebfb.jpg", + "image_caption": [ + "RGB" + ], + "image_footnote": [], + "bbox": [ + 83, + 448, + 205, + 521 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c07ce1a4198a82e0ba1be3e3d0ef51edbb726cf5103d5f87629c7803d39ea2f1.jpg", + "image_caption": [ + "Mask GT" + ], + "image_footnote": [], + "bbox": [ + 210, + 448, + 334, + 521 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d20a9e8b8ce28f04359856c836a0928cc945e18fa840f0b9303f95bedccf2bc1.jpg", + "image_caption": [ + "Mask Proxy" + ], + "image_footnote": [], + "bbox": [ + 336, + 448, + 462, + 521 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0833e3dccf361f1390126863b8d0f6619501bc9f63a42996ba087c8870ac2821.jpg", + "image_caption": [ + "Base" + ], + "image_footnote": [], + "bbox": [ + 83, + 545, + 209, + 619 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/62220939b84220a1456ebf746e3a9c50b220eb393fd0a383f9afa8a176bb528d.jpg", + "image_caption": [ + "Virtual Depth (GT)" + ], + "image_footnote": [], + "bbox": [ + 210, + 545, + 334, + 619 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/db0ed78cb42f28433d23063f5f007b4ac46f016cd560578662bc334725674d45.jpg", + "image_caption": [ + "Virtual Depth (Proxy)", + "Figure 5. Virtual Depth Qualitatives - GT vs Proxy. From left to right - Top: RGB, ground-truth and proxy segmentations; Bottom: prediction with DPT on the RGB image prediction with DPT on the median of five predictions by in-painting with either the ground truth or semantic proxy masks on Booster." + ], + "image_footnote": [], + "bbox": [ + 336, + 545, + 462, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "lar networks are evaluated on the Booster training set, while stereo models are evaluated on the Booster test set.", + "bbox": [ + 75, + 717, + 468, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 763, + 207, + 780 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we report the outcome of our findings concerning both monocular and stereo depth estimation.", + "bbox": [ + 75, + 789, + 468, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Monocular Depth Estimation.", + "text_level": 1, + "bbox": [ + 76, + 830, + 341, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Number of In-Paintings. We investigate the quality of the virtual depth labels by varying $N$ . When using $N = 1$ we generate a single in-painted image that is forwarded to", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the monocular network, while with $N = 5$ we generate virtual depths from 5 masked images with different colors which are then aggregated by selecting the pixel-wise depth median. In Tab. 1, we report the accuracy of depth maps produced by the two strategies, together with those of the Base architectures, i.e. without applying any inpainting strategy. Firstly, with both MiDaS and DPT, both in-painting strategies obtain virtual depths that are much more accurate for ToM regions w.r.t. the Base architecture. Secondly, $N = 5$ maps yield slightly better results in most metrics, especially when looking at DPT performance. We ascribe it to the higher robustness of the second strategy. For the remaining experiments, we fix $N = 5$ as we did not observe any further improvement with larger values.", + "bbox": [ + 496, + 436, + 890, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fine-tuning Results (GT Segmentation). In Tab. 2, we report results on the Booster train set, obtained after fine-tuning MiDaS and DPT on all available data from Trans10K and MSD. In the Base row, we report the results of the network using the officially released weights without any further training, and we compare with those in row Ft. Virtual Depth, i.e., the results of our method. We notice that the accuracy on All pixels is improved with our approach. In particular, we achieve a significant boost in performances for ToM surfaces, of 4.37, 5.72, 8.97, 11.12 and $11.57\\%$ , $28.67\\mathrm{mm}$ , $0.03\\%$ , $35.51\\mathrm{mm}$ for MiDaS [38], and 3.91, 7.19, 11.25, 16.8 and $16.97\\%$ , $42.46\\mathrm{mm}$ , $0.04\\%$ , $53.255\\mathrm{mm}$ for DPT[38] in the $\\delta_{1.25}$ , $\\delta_{1.20}$ , $\\delta_{1.15}$ , $\\delta_{1.10}$ , $\\delta_{1.05}$ , MAE, Abs.Rel, and RMSE, respectively. We highlight that, after fine-tuning, the accuracy on ToM is only slightly worse than on Other. Moreover, class Other metrics are also slightly", + "bbox": [ + 496, + 659, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9249", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e33b3031ad8c00d1167b8cf5fd821fab848aaa39af1a5255bbb23bb7e45c99ce.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CategoryMethod
AllBase
AllFt. Virtual Depth
", + "bbox": [ + 84, + 89, + 205, + 136 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/acb5e70459fb439335f74fc3867191afee0090f4ee5d807de8095331aa72a91c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MiDaS [37]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓(mm)
91.6887.1379.1764.7739.0427.170.0940.16
90.3885.8977.9763.7438.5729.400.0944.37
", + "bbox": [ + 210, + 89, + 537, + 137 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ad7abbeb23e3b50061cc71df0cb7eaf6b29ee3f84a2c8d57382337120ec1c548.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓(mm)
91.7887.6180.4467.4242.6026.420.0940.10
90.9786.7479.5666.4542.1227.720.0942.56
", + "bbox": [ + 555, + 89, + 883, + 137 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/027ece8e49fa9eee0a08b3312f5a605275540d97fb3009a700c77f3cb5cf61b9.jpg", + "table_caption": [ + "Table 4. Monocular networks fine-tuning - results on NYU-V2 [31]. After training on MSD and Trans10K, both MiDaS and DPT show a negligible drop in accuracy on non-ToM surfaces of existing datasets." + ], + "table_footnote": [], + "table_body": "
CategoryMethod
AllBase
AllFt. Base
AllFt. Virtual Depth
AllFt. Merged
ToMBase
ToMFt. Base
ToMFt. Virtual Depth
ToMFt. Merged
OtherBase
OtherFt. Base
OtherFt. Virtual Depth
OtherFt. Merged
", + "bbox": [ + 89, + 176, + 259, + 354 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/68cbd83e43e902e132d089e1d67b118ee118ad7aa056fec6b92eb063b6d4f68f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RAFT-Stereo [26]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
17.4213.4911.5910.114.078.63
18.4414.0412.0210.494.338.92
16.8112.349.988.092.606.04
14.689.637.355.571.954.58
56.7744.3838.4333.3113.4516.56
58.5644.4038.0232.9913.8316.47
57.0942.8934.7027.618.4710.75
47.5430.5622.8316.615.837.43
8.485.744.523.831.583.79
9.226.234.914.161.713.99
7.975.033.813.151.193.20
7.144.082.872.220.962.63
", + "bbox": [ + 272, + 176, + 571, + 354 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3fcf70201d1c152dd1fda3de036b2d6c99d4956478eb4a7b291d712febd47424.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CREStereo [22]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
15.1310.708.917.573.157.40
14.6510.148.396.972.866.64
18.8514.3512.4210.875.119.83
10.866.134.413.131.513.64
51.8337.8832.8628.1912.4215.60
49.4534.4929.0024.2410.2513.01
49.7035.4529.8424.7911.9913.94
36.9620.7915.3810.675.046.73
8.114.833.502.781.142.77
7.024.203.152.531.002.56
11.458.247.036.302.735.45
5.272.731.821.340.681.70
", + "bbox": [ + 586, + 178, + 883, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Stereo networks fine-tuning - ground truth segmentation. Results on Booster test set at quarter resolution. All models start from the official weights [26, 22] and are fine-tuned according to different strategies. Best results in bold.", + "bbox": [ + 75, + 356, + 888, + 382 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "better, probably because of the enhanced features extracted by the network, which has a better understanding of the scene context. Finally, we have reported in Ft. Base the fine-tuning results obtained by self-training the networks on their own predictions without any in-painting strategy. As expected, without the appropriate virtual depth labels, the networks cannot effectively learn from the new dataset, yielding results comparable to the Base architecture. Experiments on additional datasets are in the supplement.", + "bbox": [ + 75, + 407, + 468, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fine-tuning Results (Proxy Segmentation). Even though obtaining semantic labels is cheaper than collecting depth ground truths, using the predictions of a segmentation network as proxy semantic annotations would accelerate the dataset collection process. Thus, we investigate the impact of replacing manually annotated masks in our pipeline with the predictions of Trans2Seg[54] and MirrorNet[60], pretrained on the training set of Trans10K and MSD, respectively, on the unseen test set of each dataset. We use weights made available by the authors. For a fair comparison, we also re-train again the models exploiting GT segmentations only on the test sets of the two datasets. Tab. 3 highlights that both models, using either GT - Ft. Virtual Depth (GT) - or proxy segmentations - Ft. Virtual Depth (Proxy), achieve much more accurate results compared to the Base network. Interestingly, the two networks yield comparable results in the class Other, while the one using GTs is slightly better than the other in the class ToM, yet still comparable. Finally, in row Virtual Depth (Proxy), we report the results of our in-painting methodology (i.e., without fine-tuning) but coloring pixels according to the proxy segmentations. We note that performances are even worse than the Base method. Indeed, the segmentation network struggles to gen", + "bbox": [ + 75, + 553, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0d084d59dddd09c24bd7b5cede67c7d0e700432dc1909b23c5cca51502c77976.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison - disparity virtual labels. On top: left RGB image, ground truth segmentation mask, and virtual disparities by CREstereo processing masked stereo pairs. At bottom: depth by DPT on the in-painted left image, disparities by CREstereo, and their final merged labels." + ], + "image_footnote": [], + "bbox": [ + 506, + 407, + 888, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "eralize to the Booster dataset, making the depth model incapable of estimating the correct values, e.g., due to some overextended in-painted ToM areas, as shown in Fig. 5. Yet, depth networks, fine-tuned on the test set of MSD and Trans10K (row Ft. Virtual Depth (Proxy)), generalize properly on Booster.", + "bbox": [ + 496, + 688, + 890, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance on non-ToM surfaces. To prove the effectiveness of the fine-tuned models on scenes with only a few ToM surfaces, we test the MiDaS and DPT trained over our proxy labels on the NYU-V2 dataset [31], reporting the results in Tab. 4. We notice only negligible drops in performances – the strictest metric $\\delta_{1.05}$ drops by less than $0.5\\%$ , which we consider a small price to pay for the large improvement on ToM surfaces observed before.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9250", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8fe06e6f93fd38a10e10960203d16b557899852d06ca88a7a20f6f6df13a6b64.jpg", + "table_caption": [], + "table_footnote": [ + "Table 6. Stereo networks fine-tuning - ground truth vs proxy segmentation. Results on Booster test set at quarter resolution. All models start from the official weights [26, 22] and are fine-tuned according to different strategies. Best results in bold." + ], + "table_body": "
CategoryMethod
AllBase
AllFt. Merged (Proxy)
AllFt. Merged (GT)
ToMBase
ToMFt. Merged (Proxy)
ToMFt. Merged (GT)
OtherBase
OtherFt. Merged (Proxy)
OtherFt. Merged (GT)
", + "bbox": [ + 89, + 97, + 269, + 236 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/32bd4c82f089675ab8f62609c0603c58d8c8ef8265afde023c4b706cad833a8a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RAFT-Stereo [26]
bad-2bad-4bad-6bad-8MAERMSE
↓(%)↓(%)↓(%)↓(%)↓(px)↓(px)
17.4213.4911.5910.114.078.63
19.5613.5310.538.282.515.37
14.689.637.355.571.954.58
56.7744.3838.4333.3113.4516.56
51.8535.3227.1720.886.568.04
47.5430.5522.8116.625.837.43
8.485.744.523.831.583.79
11.957.365.314.151.413.41
7.144.082.872.220.962.63
", + "bbox": [ + 284, + 89, + 581, + 236 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d04c5db2c38fe3a007aea1c7b7b71821b519df1b497f556cb5c25b815d67f92a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CREStereo [22]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
15.1310.708.917.573.157.40
12.607.425.243.641.413.33
10.866.134.413.131.513.64
51.8337.8832.8628.1912.4215.60
40.8523.6616.8311.104.185.61
36.9620.7915.3810.675.046.73
8.114.833.502.781.142.77
6.563.692.531.880.822.02
5.272.731.821.340.681.70
", + "bbox": [ + 596, + 89, + 893, + 236 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Stereo Depth Estimation", + "text_level": 1, + "bbox": [ + 76, + 287, + 302, + 303 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Virtual Disparity Generation Alternatives. We inquire about two main alternatives to generate virtual disparities: i) Virtual Disparity: masking both left and right images according to material segmentation masks – as materials annotations are provided for the left image only, we warp it over the right image according to ground-truth disparity – and then processing the two with the stereo network we are going to fine-tune similar to Monocular networks, ii) Merged: merging disparity labels produced by the stereo model itself with those generated by original DPT weights [37], as detailed in Eq. 4. Although the former might appear as the natural extension of our proposal from the monocular to the stereo case, we will demonstrate its ineffectiveness.", + "bbox": [ + 75, + 311, + 468, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fine-tuning Results (GT Segmentation). Tab. 5 collects the results obtained by fine-tuning RAFT-Stereo and CREStereo through our technique. From top to bottom, we report the results achieved by the original models (Base) as well as the instances fine-tuned on their own predictions (Ft. Base) or on pseudo labels obtained according to the two strategies (Ft. Virtual Depth, Ft. Merged).", + "bbox": [ + 75, + 507, + 468, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Not surprisingly, fine-tuning the networks on their own predictions is harmful (RAFT-Stereo) or scarcely effective (CREStereo). Applying the first of the two strategies sketched before yields just a negligible improvement over the original models on ToM classes. This evidence confirms that our pipeline designed for the monocular case cannot naively be extended to the stereo case by in-painting the two images since masking ToM objects with constant colors does not ease matching – on the contrary, it introduces textureless regions, which are likely to be labeled as planar surfaces by stereo models. Conversely, the second strategy consistently improves the predictions with both RAFT-Stereo and CREStereo. In particular, the former achieves 9.23, 13.83, 15.62, and $16.69\\%$ absolute reductions on bad-2, bad-4, bad-6, and bad-8, respectively, as well 7.62 and 9.13 reductions on MAE and RMSE on ToM regions. CREStereo obtains 14.93, 17.13, 17.48, and $17.54\\%$ on bad metrics, and 7.40 and 8.91 reductions on MAE and RMSE. Moreover, the accuracy over Other pixels is also improved,", + "bbox": [ + 75, + 613, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/574afd3295b26598ee735ee5b02b6c831ebf4af07779bb16e192e10195708765.jpg", + "image_caption": [ + "Figure 7. Stereo depth merging with GT or Proxy semantic labels. From left to right: RGB left image, ground-truth semantic mask, proxy semantic mask, prediction by CREstereo on the RGB images, and the final merged labels using either the GT or Proxy segmentation masks." + ], + "image_footnote": [], + "bbox": [ + 506, + 287, + 888, + 469 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "although with minor margins. Fig. 6 provides a qualitative comparison between the labels obtained by the two strategies. The former produces a planar surface for the mirror completely misaligned with respect to the wall, whereas the latter combines the virtual depth labels from DPT on masked images with disparity labels at best.", + "bbox": [ + 496, + 566, + 890, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fine-tuning Results (Proxy Segmentation). Finally, we replace the manually annotated segmentation masks with those predicted by Trans2Seg and MirrorNet and then distill virtual disparities for fine-tuning both stereo networks. As pointed out before, both Trans2Seg and MirrorNet have not been trained on Booster. Thus, Merging produces significant differences with respect to the use of manually annotated masks, as shown in Fig. 7. Nevertheless, Tab. 6 shows that our pipeline improves the performance of both RAFT-Stereo and CREStereo on ToM objects, even in the case of extremely noisy proxy semantic annotations. More precisely, CREStereo seems to benefit more from the Proxy segmentation configuration than RAFT-Stereo. Indeed, on the one hand, we can notice how RAFT-Stereo improves on ToM regions at the expense of accuracy on other pixels when using Proxy segmentations. This yields,", + "bbox": [ + 496, + 659, + 892, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9251", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1850abc761b52af9a14804be7c77ce8e368b448deb28d61a1f9e0711688475b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 88, + 888, + 320 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/4a34e05f893757dbd0cfb17051f26aa6ddcbdb374e65a0d60a2841d7d71e3647.jpg", + "image_caption": [ + "Figure 8. Qualitative post fine-tuning results. Examples of predictions by MiDaS and DPT (top), RAFT-Stereo and CREStereo (bottom). For each model, we show results achieved by the original model and by fine-tuned instances using proxy or GT segmentation masks." + ], + "image_footnote": [], + "bbox": [ + 84, + 335, + 888, + 566 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "on All pixels, an increase in the bad-2 and bad-4 error rates, whereas bad-6, bad-8, MAE, and RMSE remain lower. On the other hand, CREStereo seems capable of exploiting fine-tuning much better, yielding more accurate results on any metric with both Proxy or GT masks. This outcome proves that our pipeline is effective for fine-tuning stereo models even without manually annotated masks. Nonetheless, segmenting images through human labeling unleashes its full potential, whose cost is much lower compared to that that would be required to annotate depths.", + "bbox": [ + 75, + 619, + 472, + 772 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 784, + 261, + 800 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To conclude, Fig. 8 shows the effect of the fine-tuning carried out according to our proposal, with two examples for monocular (top) and stereo (bottom) networks from the Booster train and test sets respectively. We highlight how MiDaS, DPT, RAFT-Stereo, and CREStereo learn to deal with ToM surfaces either when relying on proxy segmenta", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "tion masks provided by neural networks or accurately annotated by humans. More qualitative examples are reported in the supplementary material.", + "bbox": [ + 498, + 619, + 890, + 666 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 724, + 617, + 739 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We have proposed an effective methodology for training depth estimation networks to deal with transparent and mirror surfaces. By in-painting these surfaces on RGB images, we can quickly annotate a dataset with virtual depth labels, that can be used to fine-tune both monocular and stereo networks, with outstanding results. A promising future direction would be to extend our technique to instance segmentation masks to get better virtual depth maps in the presence of multiple ToM objects in the same scene.", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9252", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Filippo Aleotti, Fabio Tosi, Matteo Poggi, and Stefano Mattoccia. Generative adversarial networks for unsupervised monocular depth prediction. In Proceedings of the European Conference on Computer Vision (ECCV) Workshops, pages 0–0, 2018. 2", + "[2] Shariq Farooq Bhat, Ibrahim Alhashim, and Peter Wonka. Adabins: Depth estimation using adaptive bins. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1851-1858, 2017. 2" + ], + "bbox": [ + 501, + 92, + 893, + 642 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "9255", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_model.json b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ef36eb870c0e9ebba873943d641a932fdd281223 --- /dev/null +++ b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_model.json @@ -0,0 +1,2391 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.156, + 0.131, + 0.816, + 0.154 + ], + "angle": 0, + "content": "Learning Depth Estimation for Transparent and Mirror Surfaces" + }, + { + "type": "text", + "bbox": [ + 0.18, + 0.181, + 0.79, + 0.288 + ], + "angle": 0, + "content": "Alex Costanzino* Pierluigi Zama Ramirez* Matteo Poggi* Fabio Tosi Stefano Mattoccia Luigi Di Stefano CVLAB, Department of Computer Science and Engineering (DISI) University of Bologna, Italy {alex.costanzino, pierluigi.zama, m.poggi, fabio.tosi5}@unibo.it https://cvlab-unibo.github.io/Depth4ToM/" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.338 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.474, + 0.537 + ], + "angle": 0, + "content": "Inferring the depth of transparent or mirror (ToM) surfaces represents a hard challenge for either sensors, algorithms, or deep networks. We propose a simple pipeline for learning to estimate depth properly for such surfaces with neural networks, without requiring any ground-truth annotation. We unveil how to obtain reliable pseudo labels by in-painting ToM objects in images and processing them with a monocular depth estimation model. These labels can be used to fine-tune existing monocular or stereo networks, to let them learn how to deal with ToM surfaces. Experimental results on the Booster dataset show the dramatic improvements enabled by our remarkably simple proposal." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.565, + 0.21, + 0.58 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.473, + 0.879 + ], + "angle": 0, + "content": "In our daily lives, we often interact with several objects of various appearances. Among them are those made of transparent or mirror surfaces (ToM), ranging from the glass windows of buildings to the reflective surfaces of cars and appliances. These might represent a hard challenge for an autonomous agent leveraging computer vision to operate in unknown environments. Specifically, among the many tasks involved in Spatial AI, accurately estimating depth information on these surfaces remains a challenging problem for both computer vision algorithms and deep networks [64], yet necessary for proper interaction with the environment in robotic, autonomous navigation, picking, and other application fields. This difficulty arises because ToM surfaces introduce misleading visual information about scene geometry, which makes depth estimation challenging not only for computer vision systems but even for humans - e.g., we might not distinguish the presence of a glass door in front of us due to its transparency. On the one hand, the definition of depth itself might appear ambiguous in such cases:" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.323, + 0.892, + 0.629 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.631, + 0.895, + 0.716 + ], + "angle": 0, + "content": "Figure 1. Depth estimation on ToM surfaces. Two examples for both monocular (top) and stereo (bottom) images. In the central column, the depth/disparity maps predicted by DPT [37] and CREStereo [22] original weights. In the rightmost column, the depth/disparity maps predicted by the models after being finetuned by our strategy without exploiting any ground-truth depth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.746, + 0.895, + 0.883 + ], + "angle": 0, + "content": "is depth the distance to the scene behind the glass door or to the door itself? Nonetheless, from a practical point of view, we argue that the actual definition depends on the task itself - e.g., a mobile robot should definitely be aware of the presence of the glass door. On the other hand, as humans can deal with this through experience, depth sensing techniques based on deep learning, e.g., monocular [38, 37] or stereo [26, 22] networks, hold the potential to address this challenge given sufficient training data [64]." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Unfortunately, light reflection and refraction over ToM" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.353, + 0.9 + ], + "angle": 0, + "content": "* These authors contributed equally to this work." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9244" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.272 + ], + "angle": 0, + "content": "surfaces violate also the working principles of most active depth sensors, such as Time-of-Flight (ToF) cameras or devices projecting structured-light patterns. This has two practical consequences: i) it makes active sensors unsuited to deal with ToM objects in real-world applications, and ii) prevents the use of these sensors for collecting and annotating data to train deep neural networks to deal with ToM objects. As evidence of this, very few datasets featuring transparent objects provide ground-truth depth annotations, which have been obtained through very intensive human intervention [64], graphical engines [40], or based on the availability of CAD models [5] for ToM objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.473, + 0.621 + ], + "angle": 0, + "content": "In short, accurately perceiving the presence (and depth) of ToM objects represents an open challenge for both sensing technologies and deep learning frameworks. Purposely, this paper proposes a simple yet effective strategy for obtaining training data and, thereby, dramatically boosting the accuracy of learning-based depth estimation frameworks dealing with ToM surfaces. Driven by the observation that ToM objects alone are responsible for misleading recent monocular networks [38, 37], which would otherwise generalize well to most unseen environments, we argue that replacing them with equivalent, yet opaque objects would allow restoring an environment layout in which such networks could accurately estimate the depth of the scene. To this end, we mask ToM objects in images by in-painting them with arbitrary uniform colors. Then, we employ a monocular depth network to generate a virtual depth map out of the modified image. By repeating this process on a variety of images featuring ToM objects, we can easily and effectively annotate a dataset and then use it to train the same monocular network used to distill labels, which will now process the not-in-painted images. As a result, the trained monocular network will learn to handle ToM objects, producing consistent depth even in their presence." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.621, + 0.435, + 0.635 + ], + "angle": 0, + "content": "Our main contributions can be resumed as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.651, + 0.47, + 0.711 + ], + "angle": 0, + "content": "- We propose a simple yet very effective strategy to deal with ToM objects. We trick a monocular depth estimation network by replacing ToM objects with virtually textured ones, inducing it to hallucinate their depths." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.723, + 0.47, + 0.829 + ], + "angle": 0, + "content": "- We introduce a processing pipeline for fine-tuning a monocular depth estimation network to deal with ToM objects. Our pipeline exploits the network itself to generate virtual depth annotations and requires only segmentation masks delineating ToM objects – either human-made or predicted by other networks [54, 60] – thus getting rid of the need for any depth annotations." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- We show how our strategy can be extended to other depth estimation settings, such as stereo matching. Our experiments on the Booster dataset [64] prove how monocular and stereo networks dramatically improve" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.651, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "their prediction on ToM objects after being fine-tuned according to our methodology." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.136, + 0.894, + 0.197 + ], + "angle": 0, + "content": "Fig. 1 highlights some specific regions where monocular (top) and stereo (bottom) models struggle (middle column), and how they learn to handle ToM surfaces thanks to our strategy (rightmost column)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.21, + 0.642, + 0.226 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.236, + 0.892, + 0.552 + ], + "angle": 0, + "content": "Monocular Depth Estimation. Early methods used CNNs for pixel-level regression [10, 11]. More recent approaches such as AdaBins [2], DPT [37], and MiDaS [38] use adaptive bins and vision transformers for depth regression and leverage large-scale depth training by mixing multiple datasets. Self-supervised methods use view synthesis for image reconstruction, where predicted depth is combined with known or estimated camera pose to establish correspondences between adjacent images, exploiting either stereo pairs [10, 11] or monocular videos [70, 12]. Recent works aim to improve the robustness of the photometric loss based on SSIM and L1 [68] by incorporating photometric uncertainty [57, 35], feature descriptors [66, 44, 46], 3D geometric constraints [29], proxy supervision [52, 49], optical flow [62, 50], or adversarial losses [1, 34]. Others propose architecture changes as in [69, 14, 33, 18, 13]. Except for some works that address non-Lambertian depth estimation using depth completion approaches and sparse depth measurements from active sensors [8, 40], to the best of our knowledge, we are not aware of any previous single-view depth estimation network that can handle ToM surfaces." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Stereo Matching. Traditional algorithms [42] utilize handcrafted features to estimate a disparity map [63, 17, 59, 58, 24, 47, 21, 3]. Then, deep learning methods replaced traditional matching cost computation, as demonstrated in [65], and, eventually, end-to-end approaches became the most effective solution for disparity estimation. These networks can be mainly categorized into 2D and 3D architectures, with the former adopting an encoder-decoder design [30, 32, 25, 39, 45, 56, 61, 48] and the latter building a feature cost volume from extracted features on the image pair [19, 4, 20, 67, 6, 7, 9, 55, 51, 16, 43]. A thorough review of these works can be found in [36]. Recent papers exploit iterative refinement paradigms [26, 22] or rely on Vision Transformers [23, 15]. However, due to its inherently ill-posed nature, dealing with non-Lambertian surfaces, such as ToM objects, remains a very challenging problem for any kind of existing stereo approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Non-Lambertian Object Perception. Due to the relevance of dealing with ToM objects, some recent datasets focus on them. Trans10K [54] and MSD [60] consist of over 10 000 and 4 000 real in-the-wild images of transparent objects and mirrors, respectively. Both datasets provide manually annotated segmentations of ToM materials, though" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9245" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.099, + 0.885, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.27, + 0.895, + 0.313 + ], + "angle": 0, + "content": "Figure 2. Monocular Distillation pipeline. Given an RGB and a segmentation mask, we in-paint pixels belonging to transparent and mirror surfaces with a random uniform color and process these augmented images with a pre-trained monocular network. The obtained virtual depths are aggregated to obtain a pseudo-labeled dataset for fine-tuning the network itself." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.473, + 0.655 + ], + "angle": 0, + "content": "none of them provide depth labels. Others provide depth annotations: ClearPose [5] includes over 350 000 labeled real-world RGB-D frames of 63 household objects. ClearGrasp [40] consists of over 50 000 synthetic RGB-D images of transparent objects, as well as real-world test benchmark with 286 RGB-D images. In addition, Booster [64] focuses on stereo matching, providing high-resolution depth labels and stereo pairs acquired in indoor scenes with specular and transparent surfaces. TOD [28] contains 15 transparent objects, labeled with relevant 3D keypoints, comprising 48 000 stereo and RGBD images. StereOBJ-1M [27] also deals with stereo vision, but focuses on pose estimation for ToM objects and do not provide depth ground truths. Obtaining depth labels for these kinds of datasets is expensive, challenging, and time-consuming since it requires either CAD models for ToM objects [5], painting such objects in the scene [40, 64, 28] or relies on a complex multi-camera setup [53]. In contrast, our proposal effectively sidesteps these challenges, by demonstrating that monocular and stereo networks can learn to deal with these objects in the absence of depth annotations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.677, + 0.17, + 0.693 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our goal is to generate depth annotations for images featuring ToM objects in a cheap and scalable manner. This allows for training deep networks to properly estimate their depth as the distance of the closest surface in front of the camera, rather than the distance of the scene content refracted/reflected through it. Our strategy is simple yet dramatically effective and relies on the availability of recent pre-trained monocular depth estimation models [38, 37], which are capable of strong generalization across a variety of scenes though struggling to deal with ToM surfaces. Based on the above state of affairs, we argue that ToM objects are often the sole elements harming the reliability of recent pre-trained monocular depth estimation networks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.895, + 0.67 + ], + "angle": 0, + "content": "Therefore, by virtually replacing these objects with textured artifacts that resemble their very same shapes, the monocular model may be possibly tricked and induced into estimating the depth of an opaque object, ideally placed at the very same spot in the scene. This methodology can be realized by delineating ToM objects, through manual annotations or a segmentation network, masking them from the image and then in-painting virtual textures within the masked areas. On the one hand, since a proper detection of ToM objects is crucial to our methodology, manual labeling indisputably results in the most accurate choice, though it comes with significant annotation costs. On the other hand, relying on a segmentation network would alleviate this cost: one would need some initial human annotations for training, but this would then allow to segment a large number of images for free. Unfortunately, the overall effectiveness of our methodology would be inevitably affected by the accuracy of the trained segmentation model. However, we reckon that annotating images with segmentation masks requires, definitely, a vastly lower effort compared to depth annotation [64, 27]. Hence, we settled on exploring both the aforementioned approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.896, + 0.903 + ], + "angle": 0, + "content": "The reader may argue that, as a consequence of our intuition, training a depth network to deal with ToM objects might be unnecessary - indeed, it would be sufficient to segment and in-paint such objects at deployment time before estimating depth. However, we retort that such a methodology would rely heavily on the actual accuracy of the model trained to segment ToM objects, which is not granted to generalize. Moreover, it would add non-negligible computational cost - i.e., the inference by a second network. On the contrary, an offline training or fine-tuning procedure allows for exploiting human-made annotation - if available - and, potentially, enable the trained network to learn how to properly estimate depth on ToM surfaces and to get rid of the second network, as well as design advanced strategies for other depth estimation frameworks, e.g. deep stereo net" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "9246" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.487, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.189, + 0.47, + 0.245 + ], + "angle": 0, + "content": "Figure 3. Virtual depth generation alternatives. From left to right: RGB, ground-truth segmentation, DPT predictions on the RGB image, on the gray-masked input, and the median of five predictions on images masked with random colors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.27, + 0.469, + 0.316 + ], + "angle": 0, + "content": "works. Our experiments will highlight that the former strategy results ineffective, while we achieve a large boost in accuracy by fine-tuning depth models with our approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.317, + 0.469, + 0.407 + ], + "angle": 0, + "content": "In the remainder, we describe our methodology to deal with ToM objects. Given a dataset of images \\(\\mathcal{I}\\), our pipeline sketched in Fig. 2 builds as follows: i) surface labeling, ii) in-painting and distillation, and iii) fine-tuning of the depth network on virtual labels. Additionally, we show how it can be revised to fine-tune also deep stereo networks." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.407, + 0.469, + 0.439 + ], + "angle": 0, + "content": "Surface Labeling. For any image \\( I_k \\in \\mathcal{I} \\), we produce a segmentation mask \\( M_k \\) classifying each pixel \\( p \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.451, + 0.469, + 0.492 + ], + "angle": 0, + "content": "\\[\nM _ {k} (p) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} I _ {k} (p) \\in \\operatorname {T o M} \\text {s u r f a c e s} \\\\ 0 & \\text {O t h e r w i s e} \\end{array} \\right. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.498, + 0.469, + 0.559 + ], + "angle": 0, + "content": "by labeling pixels as either 1 or 0 if they belong to a ToM surface or not, respectively. Such a segmentation mask can be obtained either through manual annotation or by means of a segmentation network \\(\\Theta\\) as \\(M_{k} = \\Theta (I_{k})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.469, + 0.621 + ], + "angle": 0, + "content": "In-painting and Distillation. Given an image \\( I_{k} \\) and its corresponding segmentation mask \\( M_{k} \\), we generated an augmented image \\( \\tilde{I}_{k} \\) applying an in-painting operation to replace the pixels belonging to ToM objects with a color \\( c \\):" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.633, + 0.469, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\tilde {I} _ {k} (p) = \\left\\{ \\begin{array}{l l} c & \\text {i f} M _ {k} (p) = 1 \\\\ I _ {k} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Then, a virtual depth \\(\\tilde{D}_k\\) for image \\(I_{k}\\) is obtained by forwarding \\(\\tilde{I}_k\\) to a monocular depth network \\(\\Psi\\) as \\(\\tilde{D}_k = \\Psi (\\tilde{I}_k)\\). Colors are randomly sampled for every single frame \\(I_{k}\\). However, depending on the image content, certain colors might result ineffective and increase the scene ambiguity - e.g., by in-painting white pixels into a transparent object located in front of a white wall. To discourage these occurrences, we sample a set of \\(N\\) custom colors \\(c_{i}, i\\in [0,N - 1]\\), and in-paint \\(I_{k}\\) using each of these custom colors, so as to generate a set of \\(N\\) augmented images \\(\\tilde{I}_k^i\\). Then, we obtain the final, Virtual Depth \\(\\tilde{D}_k\\) by computing the per-pixel median between the \\(N\\) depth maps" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.879, + 0.469, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\tilde {D} _ {k} ^ {*} = \\operatorname {m e d} \\left\\{\\Psi \\left(\\tilde {I} _ {k} ^ {i}\\right), i \\in [ 0, N - 1 ] \\right\\} \\tag {3}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.096, + 0.882, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.336, + 0.892, + 0.433 + ], + "angle": 0, + "content": "Figure 4. Stereo Distillation pipeline. Given a stereo pair and a segmentation mask for the left image, we merge predictions from a pre-trained stereo network with virtual depths obtained by a monocular network with our strategy. We merge the monocular or stereo maps, by taking values belonging to either ToM or other surfaces from mono or stereo, respectively. These final merged depth labels are used to fine-tune the original stereo network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.521 + ], + "angle": 0, + "content": "As depicted in Fig. 3, in some cases, the in-painted color might be similar to the background – e.g., the transparent object disappears when a single gray mask is used – while it is visible by aggregating multi-color in-painting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.893, + 0.718 + ], + "angle": 0, + "content": "Fine-Tuning on Virtual Labels. The steps outlined so far allow for labeling a dataset \\(\\mathcal{I}\\) with virtual depth labels that are not influenced by the ambiguities of ToM objects. Then, our newly annotated dataset can be used to train or fine-tune a depth estimation network, thereby enabling it to handle the aforementioned difficult objects robustly. Specifically, during training, the original images \\(I_{k}\\) are forwarded to the network, and the predicted depth \\(\\hat{D}_k\\) is optimized with respect to the distilled virtual ground-truth map \\(\\tilde{D}_k^*\\) obtained from in-painted images. This simple pipeline can dramatically improve the accuracy of monocular depth estimation networks when dealing with ToM objects, as we will show in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Extension to Deep Stereo. Our pipeline can be adapted to fine-tune deep stereo models as well, as shown in Fig. 4. Again, we argue that state-of-the-art stereo architectures [26, 22] already expose outstanding generalization capabilities while struggling with ToM objects, due to the task of matching pixels belonging to non-Lambertian surfaces being inherently ambiguous. Consequently, we exploit a monocular depth estimation network to obtain virtual depth annotations solely for these objects. Given a dataset \\(S\\) consisting of stereo pairs \\((L_k,R_k)\\), we distill virtual depth labels \\(\\tilde{D}_k^*\\) from \\(L_{k}\\) and triangulate them into disparities \\(\\tilde{d}_k^*\\) according to extrinsic parameters of the stereo rig. Then," + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9247" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.554, + 0.209 + ], + "angle": 0, + "content": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllVirtual Depth N=196.0893.2387.6875.2349.2683.880.07112.03
AllVirtual Depth N=596.0493.5187.9375.7049.3682.980.07110.52
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMVirtual Depth N=194.1191.9984.1268.4041.1776.690.0986.46
ToMVirtual Depth N=593.8791.6483.6668.7643.6576.650.0886.01
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherVirtual Depth N=195.6292.5086.7774.6348.7688.300.07116.78
OtherVirtual Depth N=595.6692.9387.3175.4249.0686.490.07114.48
" + }, + { + "type": "table", + "bbox": [ + 0.568, + 0.089, + 0.902, + 0.21 + ], + "angle": 0, + "content": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
97.5995.8892.0682.7560.1464.990.0585.96
98.4396.7492.8683.4260.1862.460.0582.06
92.7788.7780.9862.4637.70113.140.10136.28
96.0093.6788.8875.7945.2665.580.0778.24
98.9497.1992.2477.5245.9757.190.0666.86
97.1094.8490.0879.7657.3173.190.0695.63
97.6395.9692.0983.1161.0166.100.0587.37
98.2996.5092.5783.5160.9064.170.0584.06
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.209, + 0.892, + 0.236 + ], + "angle": 0, + "content": "Table 1. Virtual depth distillation by varying \\( N \\) . Results on Booster train set at quarter resolution. All networks use the official weights [37, 38] without further training. Different masking strategies are applied to the RGB input image. Best results in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.47, + 0.337 + ], + "angle": 0, + "content": "we predict a Base disparity map \\( d_{k} \\) by forwarding \\( (L_{k}, R_{k}) \\) to the stereo network we aim to fine-tune. Eventually, we replace the disparities for ToM objects with those from \\( d_{k} \\) according to \\( M_{k} \\), this latter produced over \\( L_{k} \\) this time. Formally, this operation namely Merging, is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.348, + 0.47, + 0.389 + ], + "angle": 0, + "content": "\\[\nd _ {k} (p) = \\left\\{ \\begin{array}{l l} d _ {k} (p) & \\text {i f} M _ {k} (p) = 0 \\\\ \\alpha_ {k} \\hat {d} _ {k} ^ {*} (p) + \\beta_ {k} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.395, + 0.471, + 0.473 + ], + "angle": 0, + "content": "with \\(\\alpha_{k},\\beta_{k}\\) being scale and shift factors, as monocular predictions are up to an unknown scale factor. Following [38], \\(\\alpha_{k},\\beta_{k}\\) are estimated through Least Square Estimation (LSE) regression over \\(d_{k}\\) for pixels not belonging to any ToM object, i.e., having \\(M_{k}(p) = 0\\) .." + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.495, + 0.47, + 0.533 + ], + "angle": 0, + "content": "\\[\n\\left(\\alpha_ {k}, \\beta_ {k}\\right) = \\arg \\min _ {\\alpha , \\beta} \\sum_ {p \\mid M _ {k} (p) = 0} \\left(\\alpha \\hat {d} _ {k} ^ {*} (p) + \\beta - d _ {k} (p)\\right) ^ {2} \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.289, + 0.576 + ], + "angle": 0, + "content": "4. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Implementation Details. We employ MiDaS [38] and DPT [37] as our monocular networks using the official pretrained weights, given their excellent in-the-wild generalization performance. To fine-tune them, we iterate for 20 epochs with batch size 8 and a learning rate of \\(10^{-7}\\) with exponential decay with gamma 0.95. We use random color and brightness and random horizontal flip augmentations. We pad/crop and resize images to match the pre-training resolution, i.e., 384 pixels for the long or short side, preserving aspect ratio with mirror pad or square crop, for MiDaS or DPT, respectively. We normalize images as the original networks do. Regarding stereo networks, we employ RAFT [26] and CREStereo [22], using the official pre-trained weights, since they achieve the top rankings in the Middlebury dataset [41] among published methods. To fine-tune them, we run 20 epochs, with batch size 2, fixed learning rate \\(10^{-5}\\). Following [64], we randomly resize images to half or quarter of the original dataset resolution, randomly crop to \\(456 \\times 884\\) and \\(448 \\times 880\\) for RAFT and CREStereo respectively, and further randomly scale images and disparities by a factor \\(\\in [0.9, 1.1]\\). We assume" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.892, + 0.322 + ], + "angle": 0, + "content": "22 and 10 iterations during training for RAFT-Stereo and CREStereo, respectively. During testing, we run 32 and 20 iterations. When creating virtual labels with our masking strategy, we fix the random seed of color sampling to 0." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.893, + 0.597 + ], + "angle": 0, + "content": "Datasets. Among the datasets, we selected Trans10K [54], MSD[60], and Booster[64] as they focus on ToM surfaces and contain images acquired in many realistic environments. Trans10K contains 5003, 1003, 4431 images for the training, validation, and test set, respectively, featuring common transparent objects and stuff. It provides segmentation masks with pixels categorized into 12 different classes that we collapse into 2 - ToM (classes 1 to 11) or not. MSD contains 3066, and 958 images and binary segmentation masks for the training and test set, respectively, featuring mirrors. Booster contains 228, and 191 images for training and testing, respectively. The dataset provides disparity and segmentation maps for the training set, where the segmentation maps are categorized into 4 classes, which we group into 2 - classes 2-3 into \"ToM\" category, classes 0-1 into \"Other\" materials. We fine-tune on Trans10K and MSD for monocular models and on the Booster training split for stereo networks, without using any depth ground truths." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Evaluation Protocol. We evaluate the accuracy of the monocular networks using several metrics, including absolute error relative to the ground-truth value (ABS Rel.), the percentage of pixels having the maximum between the prediction/ground-truth and ground-truth/prediction ratios lower than a threshold \\((\\delta_{i}\\), with \\(i\\) being 1.05, 1.10, 1.15, 1.20, and 1.25), the mean absolute error (MAE) and Root Mean Squared Error (RMSE). Additionally, we evaluate stereo networks using the metrics defined in Booster [64], i.e. bad-2, bad-4, bad-6, bad-8, MAE, RMSE. Results are reported on all valid pixels (All) or for those belonging to either ToM or other objects, in order to assess the impact of our strategy on the different kinds of surfaces. For any metrics considered for stereo networks, the lower, the better - annotated with \\(\\downarrow\\) in tables. The same applies to metrics used for monocular networks except for \\(\\delta_{i}\\), resulting in the higher, the better - with \\(\\uparrow\\) being reported in tables. As the predictions by monocular networks are up to an unknown scale factor, we rescale them according to the LSE criterion [38] defined in Eq. 5, using all valid pixels here. Monocu" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9248" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.09, + 0.546, + 0.209 + ], + "angle": 0, + "content": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllFt. Base94.0991.2885.2973.5549.1493.340.07124.54
AllFt. Virtual Depth95.0792.3186.3975.2050.5788.830.07118.23
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMFt. Base86.3082.9672.8461.0437.91126.710.12145.69
ToMFt. Virtual Depth91.8189.1281.6870.7547.8593.660.09104.80
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherFt. Base94.2791.4985.8773.7749.3892.480.07122.46
OtherFt. Virtual Depth95.3392.5386.8075.4350.4689.170.07119.58
" + }, + { + "type": "table", + "bbox": [ + 0.562, + 0.09, + 0.895, + 0.209 + ], + "angle": 0, + "content": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
96.8394.6090.1479.4656.8976.000.06100.98
97.9996.6593.5583.9460.4664.930.0585.93
92.7788.7780.9862.4637.70113.140.10136.28
92.6989.4981.1263.6237.95118.840.11141.27
96.6895.9692.2379.9654.6770.680.0683.06
97.1094.8490.0879.7657.3173.190.0695.63
97.1595.0290.9780.7758.0572.450.0694.07
98.0796.6493.5284.3061.1964.700.0585.57
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.209, + 0.891, + 0.234 + ], + "angle": 0, + "content": "Table 2. Monocular networks fine-tuning - ground-truth segmentation. Training on all MSD and Trans10K, results on the Booster train set at quarter resolution. All models start from the official weights [37, 38]. Best results in bold." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.248, + 0.553, + 0.384 + ], + "angle": 0, + "content": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllVirtual Depth (Proxy)91.7887.5279.5766.0042.21105.670.09140.00
AllFt. Virtual Depth (GT)94.9992.1286.3274.9949.9188.630.07117.40
AllFt. Virtual Depth (Proxy)95.0092.1786.4875.4650.2488.100.07117.10
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMVirtual Depth (Proxy)86.3779.3569.9154.8432.31112.920.12124.10
ToMFt. Virtual Depth (GT)91.8589.9383.2570.6347.5592.050.09103.54
ToMFt. Virtual Depth (Proxy)91.1288.3681.1869.1545.0296.330.09107.59
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherVirtual Depth (Proxy)91.8087.4779.4165.8641.95108.090.09143.64
OtherFt. Virtual Depth (GT)95.2792.3086.6075.4349.9588.810.07118.48
OtherFt. Virtual Depth (Proxy)95.2792.4286.8476.0250.4888.070.07117.99
" + }, + { + "type": "table", + "bbox": [ + 0.567, + 0.248, + 0.884, + 0.384 + ], + "angle": 0, + "content": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
93.2389.4381.9868.0643.6298.090.08128.36
98.0996.8593.9183.5058.7465.520.0586.41
98.1196.6893.4883.0058.1366.430.0587.18
92.7788.7780.9862.4637.70113.140.10136.28
89.7585.2675.1756.5731.75110.740.11123.28
96.9596.2693.2781.8455.4967.950.0680.88
96.8296.0592.5780.6253.7470.670.0683.44
97.1094.8490.0879.7657.3173.190.0695.63
93.2289.3982.0768.3043.8898.640.08129.48
98.1996.8593.8583.7058.9365.650.0586.30
98.2096.6793.3583.2058.4066.510.0587.06
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.385, + 0.89, + 0.411 + ], + "angle": 0, + "content": "Table 3. Monocular networks fine-tuning - ground-truth vs proxy segmentation. Training on only the test set of MSD and Trans10K, results on the Booster train set at quarter resolution. All models start from the official weights [37, 38]. Best results in bold." + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.439, + 0.16, + 0.447 + ], + "angle": 0, + "content": "RGB" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.449, + 0.206, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.251, + 0.439, + 0.297, + 0.447 + ], + "angle": 0, + "content": "Mask GT" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.449, + 0.336, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.439, + 0.43, + 0.448 + ], + "angle": 0, + "content": "Mask Proxy" + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.449, + 0.464, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.535, + 0.159, + 0.544 + ], + "angle": 0, + "content": "Base" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.546, + 0.21, + 0.62 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.535, + 0.32, + 0.545 + ], + "angle": 0, + "content": "Virtual Depth (GT)" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.546, + 0.336, + 0.62 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.349, + 0.535, + 0.452, + 0.545 + ], + "angle": 0, + "content": "Virtual Depth (Proxy)" + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.546, + 0.463, + 0.62 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.622, + 0.469, + 0.691 + ], + "angle": 0, + "content": "Figure 5. Virtual Depth Qualitatives - GT vs Proxy. From left to right - Top: RGB, ground-truth and proxy segmentations; Bottom: prediction with DPT on the RGB image prediction with DPT on the median of five predictions by in-painting with either the ground truth or semantic proxy masks on Booster." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.747 + ], + "angle": 0, + "content": "lar networks are evaluated on the Booster training set, while stereo models are evaluated on the Booster test set." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.764, + 0.209, + 0.781 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.79, + 0.469, + 0.82 + ], + "angle": 0, + "content": "In this section, we report the outcome of our findings concerning both monocular and stereo depth estimation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.342, + 0.848 + ], + "angle": 0, + "content": "5.1. Monocular Depth Estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Number of In-Paintings. We investigate the quality of the virtual depth labels by varying \\( N \\). When using \\( N = 1 \\) we generate a single in-painted image that is forwarded to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.892, + 0.649 + ], + "angle": 0, + "content": "the monocular network, while with \\( N = 5 \\) we generate virtual depths from 5 masked images with different colors which are then aggregated by selecting the pixel-wise depth median. In Tab. 1, we report the accuracy of depth maps produced by the two strategies, together with those of the Base architectures, i.e. without applying any inpainting strategy. Firstly, with both MiDaS and DPT, both in-painting strategies obtain virtual depths that are much more accurate for ToM regions w.r.t. the Base architecture. Secondly, \\( N = 5 \\) maps yield slightly better results in most metrics, especially when looking at DPT performance. We ascribe it to the higher robustness of the second strategy. For the remaining experiments, we fix \\( N = 5 \\) as we did not observe any further improvement with larger values." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Fine-tuning Results (GT Segmentation). In Tab. 2, we report results on the Booster train set, obtained after fine-tuning MiDaS and DPT on all available data from Trans10K and MSD. In the Base row, we report the results of the network using the officially released weights without any further training, and we compare with those in row Ft. Virtual Depth, i.e., the results of our method. We notice that the accuracy on All pixels is improved with our approach. In particular, we achieve a significant boost in performances for ToM surfaces, of 4.37, 5.72, 8.97, 11.12 and \\(11.57\\%\\), \\(28.67\\mathrm{mm}\\), \\(0.03\\%\\), \\(35.51\\mathrm{mm}\\) for MiDaS [38], and 3.91, 7.19, 11.25, 16.8 and \\(16.97\\%\\), \\(42.46\\mathrm{mm}\\), \\(0.04\\%\\), \\(53.255\\mathrm{mm}\\) for DPT[38] in the \\(\\delta_{1.25}\\), \\(\\delta_{1.20}\\), \\(\\delta_{1.15}\\), \\(\\delta_{1.10}\\), \\(\\delta_{1.05}\\), MAE, Abs.Rel, and RMSE, respectively. We highlight that, after fine-tuning, the accuracy on ToM is only slightly worse than on Other. Moreover, class Other metrics are also slightly" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9249" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.09, + 0.206, + 0.137 + ], + "angle": 0, + "content": "
CategoryMethod
AllBase
AllFt. Virtual Depth
" + }, + { + "type": "table", + "bbox": [ + 0.211, + 0.09, + 0.538, + 0.138 + ], + "angle": 0, + "content": "
MiDaS [37]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓(mm)
91.6887.1379.1764.7739.0427.170.0940.16
90.3885.8977.9763.7438.5729.400.0944.37
" + }, + { + "type": "table", + "bbox": [ + 0.556, + 0.09, + 0.885, + 0.138 + ], + "angle": 0, + "content": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓(mm)
91.7887.6180.4467.4242.6026.420.0940.10
90.9786.7479.5666.4542.1227.720.0942.56
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.139, + 0.89, + 0.166 + ], + "angle": 0, + "content": "Table 4. Monocular networks fine-tuning - results on NYU-V2 [31]. After training on MSD and Trans10K, both MiDaS and DPT show a negligible drop in accuracy on non-ToM surfaces of existing datasets." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.178, + 0.26, + 0.356 + ], + "angle": 0, + "content": "
CategoryMethod
AllBase
AllFt. Base
AllFt. Virtual Depth
AllFt. Merged
ToMBase
ToMFt. Base
ToMFt. Virtual Depth
ToMFt. Merged
OtherBase
OtherFt. Base
OtherFt. Virtual Depth
OtherFt. Merged
" + }, + { + "type": "table", + "bbox": [ + 0.274, + 0.178, + 0.572, + 0.356 + ], + "angle": 0, + "content": "
RAFT-Stereo [26]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
17.4213.4911.5910.114.078.63
18.4414.0412.0210.494.338.92
16.8112.349.988.092.606.04
14.689.637.355.571.954.58
56.7744.3838.4333.3113.4516.56
58.5644.4038.0232.9913.8316.47
57.0942.8934.7027.618.4710.75
47.5430.5622.8316.615.837.43
8.485.744.523.831.583.79
9.226.234.914.161.713.99
7.975.033.813.151.193.20
7.144.082.872.220.962.63
" + }, + { + "type": "table", + "bbox": [ + 0.587, + 0.179, + 0.885, + 0.356 + ], + "angle": 0, + "content": "
CREStereo [22]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
15.1310.708.917.573.157.40
14.6510.148.396.972.866.64
18.8514.3512.4210.875.119.83
10.866.134.413.131.513.64
51.8337.8832.8628.1912.4215.60
49.4534.4929.0024.2410.2513.01
49.7035.4529.8424.7911.9913.94
36.9620.7915.3810.675.046.73
8.114.833.502.781.142.77
7.024.203.152.531.002.56
11.458.247.036.302.735.45
5.272.731.821.340.681.70
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.357, + 0.89, + 0.383 + ], + "angle": 0, + "content": "Table 5. Stereo networks fine-tuning - ground truth segmentation. Results on Booster test set at quarter resolution. All models start from the official weights [26, 22] and are fine-tuned according to different strategies. Best results in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.469, + 0.545 + ], + "angle": 0, + "content": "better, probably because of the enhanced features extracted by the network, which has a better understanding of the scene context. Finally, we have reported in Ft. Base the fine-tuning results obtained by self-training the networks on their own predictions without any in-painting strategy. As expected, without the appropriate virtual depth labels, the networks cannot effectively learn from the new dataset, yielding results comparable to the Base architecture. Experiments on additional datasets are in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Fine-tuning Results (Proxy Segmentation). Even though obtaining semantic labels is cheaper than collecting depth ground truths, using the predictions of a segmentation network as proxy semantic annotations would accelerate the dataset collection process. Thus, we investigate the impact of replacing manually annotated masks in our pipeline with the predictions of Trans2Seg[54] and MirrorNet[60], pretrained on the training set of Trans10K and MSD, respectively, on the unseen test set of each dataset. We use weights made available by the authors. For a fair comparison, we also re-train again the models exploiting GT segmentations only on the test sets of the two datasets. Tab. 3 highlights that both models, using either GT - Ft. Virtual Depth (GT) - or proxy segmentations - Ft. Virtual Depth (Proxy), achieve much more accurate results compared to the Base network. Interestingly, the two networks yield comparable results in the class Other, while the one using GTs is slightly better than the other in the class ToM, yet still comparable. Finally, in row Virtual Depth (Proxy), we report the results of our in-painting methodology (i.e., without fine-tuning) but coloring pixels according to the proxy segmentations. We note that performances are even worse than the Base method. Indeed, the segmentation network struggles to gen" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.409, + 0.889, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.592, + 0.892, + 0.661 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison - disparity virtual labels. On top: left RGB image, ground truth segmentation mask, and virtual disparities by CREstereo processing masked stereo pairs. At bottom: depth by DPT on the in-painted left image, disparities by CREstereo, and their final merged labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.891, + 0.779 + ], + "angle": 0, + "content": "eralize to the Booster dataset, making the depth model incapable of estimating the correct values, e.g., due to some overextended in-painted ToM areas, as shown in Fig. 5. Yet, depth networks, fine-tuned on the test set of MSD and Trans10K (row Ft. Virtual Depth (Proxy)), generalize properly on Booster." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Performance on non-ToM surfaces. To prove the effectiveness of the fine-tuned models on scenes with only a few ToM surfaces, we test the MiDaS and DPT trained over our proxy labels on the NYU-V2 dataset [31], reporting the results in Tab. 4. We notice only negligible drops in performances – the strictest metric \\(\\delta_{1.05}\\) drops by less than \\(0.5\\%\\), which we consider a small price to pay for the large improvement on ToM surfaces observed before." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9250" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.091, + 0.098, + 0.27, + 0.237 + ], + "angle": 0, + "content": "
CategoryMethod
AllBase
AllFt. Merged (Proxy)
AllFt. Merged (GT)
ToMBase
ToMFt. Merged (Proxy)
ToMFt. Merged (GT)
OtherBase
OtherFt. Merged (Proxy)
OtherFt. Merged (GT)
" + }, + { + "type": "table", + "bbox": [ + 0.285, + 0.09, + 0.583, + 0.237 + ], + "angle": 0, + "content": "
RAFT-Stereo [26]
bad-2bad-4bad-6bad-8MAERMSE
↓(%)↓(%)↓(%)↓(%)↓(px)↓(px)
17.4213.4911.5910.114.078.63
19.5613.5310.538.282.515.37
14.689.637.355.571.954.58
56.7744.3838.4333.3113.4516.56
51.8535.3227.1720.886.568.04
47.5430.5522.8116.625.837.43
8.485.744.523.831.583.79
11.957.365.314.151.413.41
7.144.082.872.220.962.63
" + }, + { + "type": "table", + "bbox": [ + 0.598, + 0.09, + 0.895, + 0.237 + ], + "angle": 0, + "content": "
CREStereo [22]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
15.1310.708.917.573.157.40
12.607.425.243.641.413.33
10.866.134.413.131.513.64
51.8337.8832.8628.1912.4215.60
40.8523.6616.8311.104.185.61
36.9620.7915.3810.675.046.73
8.114.833.502.781.142.77
6.563.692.531.880.822.02
5.272.731.821.340.681.70
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.237, + 0.892, + 0.264 + ], + "angle": 0, + "content": "Table 6. Stereo networks fine-tuning - ground truth vs proxy segmentation. Results on Booster test set at quarter resolution. All models start from the official weights [26, 22] and are fine-tuned according to different strategies. Best results in bold." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.288, + 0.303, + 0.304 + ], + "angle": 0, + "content": "5.2. Stereo Depth Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.47, + 0.506 + ], + "angle": 0, + "content": "Virtual Disparity Generation Alternatives. We inquire about two main alternatives to generate virtual disparities: i) Virtual Disparity: masking both left and right images according to material segmentation masks – as materials annotations are provided for the left image only, we warp it over the right image according to ground-truth disparity – and then processing the two with the stereo network we are going to fine-tune similar to Monocular networks, ii) Merged: merging disparity labels produced by the stereo model itself with those generated by original DPT weights [37], as detailed in Eq. 4. Although the former might appear as the natural extension of our proposal from the monocular to the stereo case, we will demonstrate its ineffectiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.614 + ], + "angle": 0, + "content": "Fine-tuning Results (GT Segmentation). Tab. 5 collects the results obtained by fine-tuning RAFT-Stereo and CREStereo through our technique. From top to bottom, we report the results achieved by the original models (Base) as well as the instances fine-tuned on their own predictions (Ft. Base) or on pseudo labels obtained according to the two strategies (Ft. Virtual Depth, Ft. Merged)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Not surprisingly, fine-tuning the networks on their own predictions is harmful (RAFT-Stereo) or scarcely effective (CREStereo). Applying the first of the two strategies sketched before yields just a negligible improvement over the original models on ToM classes. This evidence confirms that our pipeline designed for the monocular case cannot naively be extended to the stereo case by in-painting the two images since masking ToM objects with constant colors does not ease matching – on the contrary, it introduces textureless regions, which are likely to be labeled as planar surfaces by stereo models. Conversely, the second strategy consistently improves the predictions with both RAFT-Stereo and CREStereo. In particular, the former achieves 9.23, 13.83, 15.62, and \\(16.69\\%\\) absolute reductions on bad-2, bad-4, bad-6, and bad-8, respectively, as well 7.62 and 9.13 reductions on MAE and RMSE on ToM regions. CREStereo obtains 14.93, 17.13, 17.48, and \\(17.54\\%\\) on bad metrics, and 7.40 and 8.91 reductions on MAE and RMSE. Moreover, the accuracy over Other pixels is also improved," + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.288, + 0.889, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.473, + 0.892, + 0.542 + ], + "angle": 0, + "content": "Figure 7. Stereo depth merging with GT or Proxy semantic labels. From left to right: RGB left image, ground-truth semantic mask, proxy semantic mask, prediction by CREstereo on the RGB images, and the final merged labels using either the GT or Proxy segmentation masks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.659 + ], + "angle": 0, + "content": "although with minor margins. Fig. 6 provides a qualitative comparison between the labels obtained by the two strategies. The former produces a planar surface for the mirror completely misaligned with respect to the wall, whereas the latter combines the virtual depth labels from DPT on masked images with disparity labels at best." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Fine-tuning Results (Proxy Segmentation). Finally, we replace the manually annotated segmentation masks with those predicted by Trans2Seg and MirrorNet and then distill virtual disparities for fine-tuning both stereo networks. As pointed out before, both Trans2Seg and MirrorNet have not been trained on Booster. Thus, Merging produces significant differences with respect to the use of manually annotated masks, as shown in Fig. 7. Nevertheless, Tab. 6 shows that our pipeline improves the performance of both RAFT-Stereo and CREStereo on ToM objects, even in the case of extremely noisy proxy semantic annotations. More precisely, CREStereo seems to benefit more from the Proxy segmentation configuration than RAFT-Stereo. Indeed, on the one hand, we can notice how RAFT-Stereo improves on ToM regions at the expense of accuracy on other pixels when using Proxy segmentations. This yields," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9251" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.889, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.336, + 0.889, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.568, + 0.891, + 0.596 + ], + "angle": 0, + "content": "Figure 8. Qualitative post fine-tuning results. Examples of predictions by MiDaS and DPT (top), RAFT-Stereo and CREStereo (bottom). For each model, we show results achieved by the original model and by fine-tuned instances using proxy or GT segmentation masks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.473, + 0.773 + ], + "angle": 0, + "content": "on All pixels, an increase in the bad-2 and bad-4 error rates, whereas bad-6, bad-8, MAE, and RMSE remain lower. On the other hand, CREStereo seems capable of exploiting fine-tuning much better, yielding more accurate results on any metric with both Proxy or GT masks. This outcome proves that our pipeline is effective for fine-tuning stereo models even without manually annotated masks. Nonetheless, segmenting images through human labeling unleashes its full potential, whose cost is much lower compared to that that would be required to annotate depths." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.262, + 0.801 + ], + "angle": 0, + "content": "5.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To conclude, Fig. 8 shows the effect of the fine-tuning carried out according to our proposal, with two examples for monocular (top) and stereo (bottom) networks from the Booster train and test sets respectively. We highlight how MiDaS, DPT, RAFT-Stereo, and CREStereo learn to deal with ToM surfaces either when relying on proxy segmenta" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.62, + 0.892, + 0.667 + ], + "angle": 0, + "content": "tion masks provided by neural networks or accurately annotated by humans. More qualitative examples are reported in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.619, + 0.74 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We have proposed an effective methodology for training depth estimation networks to deal with transparent and mirror surfaces. By in-painting these surfaces on RGB images, we can quickly annotate a dataset with virtual depth labels, that can be used to fine-tune both monocular and stereo networks, with outstanding results. A promising future direction would be to extend our technique to instance segmentation masks to get better virtual depth maps in the presence of multiple ToM objects in the same scene." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9252" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Filippo Aleotti, Fabio Tosi, Matteo Poggi, and Stefano Mattoccia. Generative adversarial networks for unsupervised monocular depth prediction. In Proceedings of the European Conference on Computer Vision (ECCV) Workshops, pages 0–0, 2018. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.185, + 0.472, + 0.242 + ], + "angle": 0, + "content": "[2] Shariq Farooq Bhat, Ibrahim Alhashim, and Peter Wonka. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1851-1858, 2017. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.643 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9255" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_origin.pdf b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2717d60fd1e42fbf20395655f2b513c085fa6d68 --- /dev/null +++ b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/4e49b9b1-7456-432b-aaae-0da1220f3a37_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4c063fad323969f320dc685025298a4076c2fbe37989268bb0f136a33b453a75 +size 11858748 diff --git a/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/full.md b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7357aade0c997ec82f57e0c7633b87855b6695a3 --- /dev/null +++ b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/full.md @@ -0,0 +1,311 @@ +# Learning Depth Estimation for Transparent and Mirror Surfaces + +Alex Costanzino* Pierluigi Zama Ramirez* Matteo Poggi* Fabio Tosi Stefano Mattoccia Luigi Di Stefano CVLAB, Department of Computer Science and Engineering (DISI) University of Bologna, Italy {alex.costanzino, pierluigi.zama, m.poggi, fabio.tosi5}@unibo.it https://cvlab-unibo.github.io/Depth4ToM/ + +# Abstract + +Inferring the depth of transparent or mirror (ToM) surfaces represents a hard challenge for either sensors, algorithms, or deep networks. We propose a simple pipeline for learning to estimate depth properly for such surfaces with neural networks, without requiring any ground-truth annotation. We unveil how to obtain reliable pseudo labels by in-painting ToM objects in images and processing them with a monocular depth estimation model. These labels can be used to fine-tune existing monocular or stereo networks, to let them learn how to deal with ToM surfaces. Experimental results on the Booster dataset show the dramatic improvements enabled by our remarkably simple proposal. + +# 1. Introduction + +In our daily lives, we often interact with several objects of various appearances. Among them are those made of transparent or mirror surfaces (ToM), ranging from the glass windows of buildings to the reflective surfaces of cars and appliances. These might represent a hard challenge for an autonomous agent leveraging computer vision to operate in unknown environments. Specifically, among the many tasks involved in Spatial AI, accurately estimating depth information on these surfaces remains a challenging problem for both computer vision algorithms and deep networks [64], yet necessary for proper interaction with the environment in robotic, autonomous navigation, picking, and other application fields. This difficulty arises because ToM surfaces introduce misleading visual information about scene geometry, which makes depth estimation challenging not only for computer vision systems but even for humans - e.g., we might not distinguish the presence of a glass door in front of us due to its transparency. On the one hand, the definition of depth itself might appear ambiguous in such cases: + +![](images/79a25101617001da4b54d1adbb56f190054b0effd3e78fe1a25140d97a60f4d9.jpg) +Figure 1. Depth estimation on ToM surfaces. Two examples for both monocular (top) and stereo (bottom) images. In the central column, the depth/disparity maps predicted by DPT [37] and CREStereo [22] original weights. In the rightmost column, the depth/disparity maps predicted by the models after being finetuned by our strategy without exploiting any ground-truth depth. + +is depth the distance to the scene behind the glass door or to the door itself? Nonetheless, from a practical point of view, we argue that the actual definition depends on the task itself - e.g., a mobile robot should definitely be aware of the presence of the glass door. On the other hand, as humans can deal with this through experience, depth sensing techniques based on deep learning, e.g., monocular [38, 37] or stereo [26, 22] networks, hold the potential to address this challenge given sufficient training data [64]. + +Unfortunately, light reflection and refraction over ToM + +surfaces violate also the working principles of most active depth sensors, such as Time-of-Flight (ToF) cameras or devices projecting structured-light patterns. This has two practical consequences: i) it makes active sensors unsuited to deal with ToM objects in real-world applications, and ii) prevents the use of these sensors for collecting and annotating data to train deep neural networks to deal with ToM objects. As evidence of this, very few datasets featuring transparent objects provide ground-truth depth annotations, which have been obtained through very intensive human intervention [64], graphical engines [40], or based on the availability of CAD models [5] for ToM objects. + +In short, accurately perceiving the presence (and depth) of ToM objects represents an open challenge for both sensing technologies and deep learning frameworks. Purposely, this paper proposes a simple yet effective strategy for obtaining training data and, thereby, dramatically boosting the accuracy of learning-based depth estimation frameworks dealing with ToM surfaces. Driven by the observation that ToM objects alone are responsible for misleading recent monocular networks [38, 37], which would otherwise generalize well to most unseen environments, we argue that replacing them with equivalent, yet opaque objects would allow restoring an environment layout in which such networks could accurately estimate the depth of the scene. To this end, we mask ToM objects in images by in-painting them with arbitrary uniform colors. Then, we employ a monocular depth network to generate a virtual depth map out of the modified image. By repeating this process on a variety of images featuring ToM objects, we can easily and effectively annotate a dataset and then use it to train the same monocular network used to distill labels, which will now process the not-in-painted images. As a result, the trained monocular network will learn to handle ToM objects, producing consistent depth even in their presence. + +Our main contributions can be resumed as follows: + +- We propose a simple yet very effective strategy to deal with ToM objects. We trick a monocular depth estimation network by replacing ToM objects with virtually textured ones, inducing it to hallucinate their depths. +- We introduce a processing pipeline for fine-tuning a monocular depth estimation network to deal with ToM objects. Our pipeline exploits the network itself to generate virtual depth annotations and requires only segmentation masks delineating ToM objects – either human-made or predicted by other networks [54, 60] – thus getting rid of the need for any depth annotations. +- We show how our strategy can be extended to other depth estimation settings, such as stereo matching. Our experiments on the Booster dataset [64] prove how monocular and stereo networks dramatically improve + +their prediction on ToM objects after being fine-tuned according to our methodology. + +Fig. 1 highlights some specific regions where monocular (top) and stereo (bottom) models struggle (middle column), and how they learn to handle ToM surfaces thanks to our strategy (rightmost column). + +# 2. Related Work + +Monocular Depth Estimation. Early methods used CNNs for pixel-level regression [10, 11]. More recent approaches such as AdaBins [2], DPT [37], and MiDaS [38] use adaptive bins and vision transformers for depth regression and leverage large-scale depth training by mixing multiple datasets. Self-supervised methods use view synthesis for image reconstruction, where predicted depth is combined with known or estimated camera pose to establish correspondences between adjacent images, exploiting either stereo pairs [10, 11] or monocular videos [70, 12]. Recent works aim to improve the robustness of the photometric loss based on SSIM and L1 [68] by incorporating photometric uncertainty [57, 35], feature descriptors [66, 44, 46], 3D geometric constraints [29], proxy supervision [52, 49], optical flow [62, 50], or adversarial losses [1, 34]. Others propose architecture changes as in [69, 14, 33, 18, 13]. Except for some works that address non-Lambertian depth estimation using depth completion approaches and sparse depth measurements from active sensors [8, 40], to the best of our knowledge, we are not aware of any previous single-view depth estimation network that can handle ToM surfaces. + +Stereo Matching. Traditional algorithms [42] utilize handcrafted features to estimate a disparity map [63, 17, 59, 58, 24, 47, 21, 3]. Then, deep learning methods replaced traditional matching cost computation, as demonstrated in [65], and, eventually, end-to-end approaches became the most effective solution for disparity estimation. These networks can be mainly categorized into 2D and 3D architectures, with the former adopting an encoder-decoder design [30, 32, 25, 39, 45, 56, 61, 48] and the latter building a feature cost volume from extracted features on the image pair [19, 4, 20, 67, 6, 7, 9, 55, 51, 16, 43]. A thorough review of these works can be found in [36]. Recent papers exploit iterative refinement paradigms [26, 22] or rely on Vision Transformers [23, 15]. However, due to its inherently ill-posed nature, dealing with non-Lambertian surfaces, such as ToM objects, remains a very challenging problem for any kind of existing stereo approach. + +Non-Lambertian Object Perception. Due to the relevance of dealing with ToM objects, some recent datasets focus on them. Trans10K [54] and MSD [60] consist of over 10 000 and 4 000 real in-the-wild images of transparent objects and mirrors, respectively. Both datasets provide manually annotated segmentations of ToM materials, though + +![](images/1e48d3d06a414270dd05b8d107c99780406abbdc24166552fb20384a735562cd.jpg) +Figure 2. Monocular Distillation pipeline. Given an RGB and a segmentation mask, we in-paint pixels belonging to transparent and mirror surfaces with a random uniform color and process these augmented images with a pre-trained monocular network. The obtained virtual depths are aggregated to obtain a pseudo-labeled dataset for fine-tuning the network itself. + +none of them provide depth labels. Others provide depth annotations: ClearPose [5] includes over 350 000 labeled real-world RGB-D frames of 63 household objects. ClearGrasp [40] consists of over 50 000 synthetic RGB-D images of transparent objects, as well as real-world test benchmark with 286 RGB-D images. In addition, Booster [64] focuses on stereo matching, providing high-resolution depth labels and stereo pairs acquired in indoor scenes with specular and transparent surfaces. TOD [28] contains 15 transparent objects, labeled with relevant 3D keypoints, comprising 48 000 stereo and RGBD images. StereOBJ-1M [27] also deals with stereo vision, but focuses on pose estimation for ToM objects and do not provide depth ground truths. Obtaining depth labels for these kinds of datasets is expensive, challenging, and time-consuming since it requires either CAD models for ToM objects [5], painting such objects in the scene [40, 64, 28] or relies on a complex multi-camera setup [53]. In contrast, our proposal effectively sidesteps these challenges, by demonstrating that monocular and stereo networks can learn to deal with these objects in the absence of depth annotations. + +# 3. Method + +Our goal is to generate depth annotations for images featuring ToM objects in a cheap and scalable manner. This allows for training deep networks to properly estimate their depth as the distance of the closest surface in front of the camera, rather than the distance of the scene content refracted/reflected through it. Our strategy is simple yet dramatically effective and relies on the availability of recent pre-trained monocular depth estimation models [38, 37], which are capable of strong generalization across a variety of scenes though struggling to deal with ToM surfaces. Based on the above state of affairs, we argue that ToM objects are often the sole elements harming the reliability of recent pre-trained monocular depth estimation networks. + +Therefore, by virtually replacing these objects with textured artifacts that resemble their very same shapes, the monocular model may be possibly tricked and induced into estimating the depth of an opaque object, ideally placed at the very same spot in the scene. This methodology can be realized by delineating ToM objects, through manual annotations or a segmentation network, masking them from the image and then in-painting virtual textures within the masked areas. On the one hand, since a proper detection of ToM objects is crucial to our methodology, manual labeling indisputably results in the most accurate choice, though it comes with significant annotation costs. On the other hand, relying on a segmentation network would alleviate this cost: one would need some initial human annotations for training, but this would then allow to segment a large number of images for free. Unfortunately, the overall effectiveness of our methodology would be inevitably affected by the accuracy of the trained segmentation model. However, we reckon that annotating images with segmentation masks requires, definitely, a vastly lower effort compared to depth annotation [64, 27]. Hence, we settled on exploring both the aforementioned approaches. + +The reader may argue that, as a consequence of our intuition, training a depth network to deal with ToM objects might be unnecessary - indeed, it would be sufficient to segment and in-paint such objects at deployment time before estimating depth. However, we retort that such a methodology would rely heavily on the actual accuracy of the model trained to segment ToM objects, which is not granted to generalize. Moreover, it would add non-negligible computational cost - i.e., the inference by a second network. On the contrary, an offline training or fine-tuning procedure allows for exploiting human-made annotation - if available - and, potentially, enable the trained network to learn how to properly estimate depth on ToM surfaces and to get rid of the second network, as well as design advanced strategies for other depth estimation frameworks, e.g. deep stereo net + +![](images/4ca76e917f36f197530d00e16d0984c0317b82ea3ea2a2432409db7039db4654.jpg) +Figure 3. Virtual depth generation alternatives. From left to right: RGB, ground-truth segmentation, DPT predictions on the RGB image, on the gray-masked input, and the median of five predictions on images masked with random colors. + +works. Our experiments will highlight that the former strategy results ineffective, while we achieve a large boost in accuracy by fine-tuning depth models with our approach. + +In the remainder, we describe our methodology to deal with ToM objects. Given a dataset of images $\mathcal{I}$ , our pipeline sketched in Fig. 2 builds as follows: i) surface labeling, ii) in-painting and distillation, and iii) fine-tuning of the depth network on virtual labels. Additionally, we show how it can be revised to fine-tune also deep stereo networks. + +Surface Labeling. For any image $I_k \in \mathcal{I}$ , we produce a segmentation mask $M_k$ classifying each pixel $p$ as + +$$ +M _ {k} (p) = \left\{ \begin{array}{l l} 1 & \text {i f} I _ {k} (p) \in \operatorname {T o M} \text {s u r f a c e s} \\ 0 & \text {O t h e r w i s e} \end{array} \right. \tag {1} +$$ + +by labeling pixels as either 1 or 0 if they belong to a ToM surface or not, respectively. Such a segmentation mask can be obtained either through manual annotation or by means of a segmentation network $\Theta$ as $M_{k} = \Theta (I_{k})$ . + +In-painting and Distillation. Given an image $I_{k}$ and its corresponding segmentation mask $M_{k}$ , we generated an augmented image $\tilde{I}_{k}$ applying an in-painting operation to replace the pixels belonging to ToM objects with a color $c$ : + +$$ +\tilde {I} _ {k} (p) = \left\{ \begin{array}{l l} c & \text {i f} M _ {k} (p) = 1 \\ I _ {k} & \text {o t h e r w i s e} \end{array} \right. \tag {2} +$$ + +Then, a virtual depth $\tilde{D}_k$ for image $I_{k}$ is obtained by forwarding $\tilde{I}_k$ to a monocular depth network $\Psi$ as $\tilde{D}_k = \Psi (\tilde{I}_k)$ . Colors are randomly sampled for every single frame $I_{k}$ . However, depending on the image content, certain colors might result ineffective and increase the scene ambiguity - e.g., by in-painting white pixels into a transparent object located in front of a white wall. To discourage these occurrences, we sample a set of $N$ custom colors $c_{i}, i\in [0,N - 1]$ , and in-paint $I_{k}$ using each of these custom colors, so as to generate a set of $N$ augmented images $\tilde{I}_k^i$ . Then, we obtain the final, Virtual Depth $\tilde{D}_k$ by computing the per-pixel median between the $N$ depth maps + +$$ +\tilde {D} _ {k} ^ {*} = \operatorname {m e d} \left\{\Psi \left(\tilde {I} _ {k} ^ {i}\right), i \in [ 0, N - 1 ] \right\} \tag {3} +$$ + +![](images/d554cea05e9314f1d45dee436a2bf0bcc6a884a55218bcee99b84867a0c0d7a3.jpg) +Figure 4. Stereo Distillation pipeline. Given a stereo pair and a segmentation mask for the left image, we merge predictions from a pre-trained stereo network with virtual depths obtained by a monocular network with our strategy. We merge the monocular or stereo maps, by taking values belonging to either ToM or other surfaces from mono or stereo, respectively. These final merged depth labels are used to fine-tune the original stereo network. + +As depicted in Fig. 3, in some cases, the in-painted color might be similar to the background – e.g., the transparent object disappears when a single gray mask is used – while it is visible by aggregating multi-color in-painting. + +Fine-Tuning on Virtual Labels. The steps outlined so far allow for labeling a dataset $\mathcal{I}$ with virtual depth labels that are not influenced by the ambiguities of ToM objects. Then, our newly annotated dataset can be used to train or fine-tune a depth estimation network, thereby enabling it to handle the aforementioned difficult objects robustly. Specifically, during training, the original images $I_{k}$ are forwarded to the network, and the predicted depth $\hat{D}_k$ is optimized with respect to the distilled virtual ground-truth map $\tilde{D}_k^*$ obtained from in-painted images. This simple pipeline can dramatically improve the accuracy of monocular depth estimation networks when dealing with ToM objects, as we will show in our experiments. + +Extension to Deep Stereo. Our pipeline can be adapted to fine-tune deep stereo models as well, as shown in Fig. 4. Again, we argue that state-of-the-art stereo architectures [26, 22] already expose outstanding generalization capabilities while struggling with ToM objects, due to the task of matching pixels belonging to non-Lambertian surfaces being inherently ambiguous. Consequently, we exploit a monocular depth estimation network to obtain virtual depth annotations solely for these objects. Given a dataset $S$ consisting of stereo pairs $(L_k,R_k)$ , we distill virtual depth labels $\tilde{D}_k^*$ from $L_{k}$ and triangulate them into disparities $\tilde{d}_k^*$ according to extrinsic parameters of the stereo rig. Then, + +
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllVirtual Depth N=196.0893.2387.6875.2349.2683.880.07112.03
AllVirtual Depth N=596.0493.5187.9375.7049.3682.980.07110.52
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMVirtual Depth N=194.1191.9984.1268.4041.1776.690.0986.46
ToMVirtual Depth N=593.8791.6483.6668.7643.6576.650.0886.01
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherVirtual Depth N=195.6292.5086.7774.6348.7688.300.07116.78
OtherVirtual Depth N=595.6692.9387.3175.4249.0686.490.07114.48
+ +Table 1. Virtual depth distillation by varying $N$ . Results on Booster train set at quarter resolution. All networks use the official weights [37, 38] without further training. Different masking strategies are applied to the RGB input image. Best results in bold. + +
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
97.5995.8892.0682.7560.1464.990.0585.96
98.4396.7492.8683.4260.1862.460.0582.06
92.7788.7780.9862.4637.70113.140.10136.28
96.0093.6788.8875.7945.2665.580.0778.24
98.9497.1992.2477.5245.9757.190.0666.86
97.1094.8490.0879.7657.3173.190.0695.63
97.6395.9692.0983.1161.0166.100.0587.37
98.2996.5092.5783.5160.9064.170.0584.06
+ +we predict a Base disparity map $d_{k}$ by forwarding $(L_{k}, R_{k})$ to the stereo network we aim to fine-tune. Eventually, we replace the disparities for ToM objects with those from $d_{k}$ according to $M_{k}$ , this latter produced over $L_{k}$ this time. Formally, this operation namely Merging, is defined as: + +$$ +d _ {k} (p) = \left\{ \begin{array}{l l} d _ {k} (p) & \text {i f} M _ {k} (p) = 0 \\ \alpha_ {k} \hat {d} _ {k} ^ {*} (p) + \beta_ {k} & \text {o t h e r w i s e} \end{array} \right. \tag {4} +$$ + +with $\alpha_{k},\beta_{k}$ being scale and shift factors, as monocular predictions are up to an unknown scale factor. Following [38], $\alpha_{k},\beta_{k}$ are estimated through Least Square Estimation (LSE) regression over $d_{k}$ for pixels not belonging to any ToM object, i.e., having $M_{k}(p) = 0$ .. + +$$ +\left(\alpha_ {k}, \beta_ {k}\right) = \arg \min _ {\alpha , \beta} \sum_ {p \mid M _ {k} (p) = 0} \left(\alpha \hat {d} _ {k} ^ {*} (p) + \beta - d _ {k} (p)\right) ^ {2} \tag {5} +$$ + +# 4. Experimental Settings + +Implementation Details. We employ MiDaS [38] and DPT [37] as our monocular networks using the official pretrained weights, given their excellent in-the-wild generalization performance. To fine-tune them, we iterate for 20 epochs with batch size 8 and a learning rate of $10^{-7}$ with exponential decay with gamma 0.95. We use random color and brightness and random horizontal flip augmentations. We pad/crop and resize images to match the pre-training resolution, i.e., 384 pixels for the long or short side, preserving aspect ratio with mirror pad or square crop, for MiDaS or DPT, respectively. We normalize images as the original networks do. Regarding stereo networks, we employ RAFT [26] and CREStereo [22], using the official pre-trained weights, since they achieve the top rankings in the Middlebury dataset [41] among published methods. To fine-tune them, we run 20 epochs, with batch size 2, fixed learning rate $10^{-5}$ . Following [64], we randomly resize images to half or quarter of the original dataset resolution, randomly crop to $456 \times 884$ and $448 \times 880$ for RAFT and CREStereo respectively, and further randomly scale images and disparities by a factor $\in [0.9, 1.1]$ . We assume + +22 and 10 iterations during training for RAFT-Stereo and CREStereo, respectively. During testing, we run 32 and 20 iterations. When creating virtual labels with our masking strategy, we fix the random seed of color sampling to 0. + +Datasets. Among the datasets, we selected Trans10K [54], MSD[60], and Booster[64] as they focus on ToM surfaces and contain images acquired in many realistic environments. Trans10K contains 5003, 1003, 4431 images for the training, validation, and test set, respectively, featuring common transparent objects and stuff. It provides segmentation masks with pixels categorized into 12 different classes that we collapse into 2 - ToM (classes 1 to 11) or not. MSD contains 3066, and 958 images and binary segmentation masks for the training and test set, respectively, featuring mirrors. Booster contains 228, and 191 images for training and testing, respectively. The dataset provides disparity and segmentation maps for the training set, where the segmentation maps are categorized into 4 classes, which we group into 2 - classes 2-3 into "ToM" category, classes 0-1 into "Other" materials. We fine-tune on Trans10K and MSD for monocular models and on the Booster training split for stereo networks, without using any depth ground truths. + +Evaluation Protocol. We evaluate the accuracy of the monocular networks using several metrics, including absolute error relative to the ground-truth value (ABS Rel.), the percentage of pixels having the maximum between the prediction/ground-truth and ground-truth/prediction ratios lower than a threshold $(\delta_{i}$ , with $i$ being 1.05, 1.10, 1.15, 1.20, and 1.25), the mean absolute error (MAE) and Root Mean Squared Error (RMSE). Additionally, we evaluate stereo networks using the metrics defined in Booster [64], i.e. bad-2, bad-4, bad-6, bad-8, MAE, RMSE. Results are reported on all valid pixels (All) or for those belonging to either ToM or other objects, in order to assess the impact of our strategy on the different kinds of surfaces. For any metrics considered for stereo networks, the lower, the better - annotated with $\downarrow$ in tables. The same applies to metrics used for monocular networks except for $\delta_{i}$ , resulting in the higher, the better - with $\uparrow$ being reported in tables. As the predictions by monocular networks are up to an unknown scale factor, we rescale them according to the LSE criterion [38] defined in Eq. 5, using all valid pixels here. Monocu + +
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllFt. Base94.0991.2885.2973.5549.1493.340.07124.54
AllFt. Virtual Depth95.0792.3186.3975.2050.5788.830.07118.23
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMFt. Base86.3082.9672.8461.0437.91126.710.12145.69
ToMFt. Virtual Depth91.8189.1281.6870.7547.8593.660.09104.80
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherFt. Base94.2791.4985.8773.7749.3892.480.07122.46
OtherFt. Virtual Depth95.3392.5386.8075.4350.4689.170.07119.58
+ +
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
96.8394.6090.1479.4656.8976.000.06100.98
97.9996.6593.5583.9460.4664.930.0585.93
92.7788.7780.9862.4637.70113.140.10136.28
92.6989.4981.1263.6237.95118.840.11141.27
96.6895.9692.2379.9654.6770.680.0683.06
97.1094.8490.0879.7657.3173.190.0695.63
97.1595.0290.9780.7758.0572.450.0694.07
98.0796.6493.5284.3061.1964.700.0585.57
+ +Table 2. Monocular networks fine-tuning - ground-truth segmentation. Training on all MSD and Trans10K, results on the Booster train set at quarter resolution. All models start from the official weights [37, 38]. Best results in bold. + +
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllVirtual Depth (Proxy)91.7887.5279.5766.0042.21105.670.09140.00
AllFt. Virtual Depth (GT)94.9992.1286.3274.9949.9188.630.07117.40
AllFt. Virtual Depth (Proxy)95.0092.1786.4875.4650.2488.100.07117.10
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMVirtual Depth (Proxy)86.3779.3569.9154.8432.31112.920.12124.10
ToMFt. Virtual Depth (GT)91.8589.9383.2570.6347.5592.050.09103.54
ToMFt. Virtual Depth (Proxy)91.1288.3681.1869.1545.0296.330.09107.59
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherVirtual Depth (Proxy)91.8087.4779.4165.8641.95108.090.09143.64
OtherFt. Virtual Depth (GT)95.2792.3086.6075.4349.9588.810.07118.48
OtherFt. Virtual Depth (Proxy)95.2792.4286.8476.0250.4888.070.07117.99
+ +
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
93.2389.4381.9868.0643.6298.090.08128.36
98.0996.8593.9183.5058.7465.520.0586.41
98.1196.6893.4883.0058.1366.430.0587.18
92.7788.7780.9862.4637.70113.140.10136.28
89.7585.2675.1756.5731.75110.740.11123.28
96.9596.2693.2781.8455.4967.950.0680.88
96.8296.0592.5780.6253.7470.670.0683.44
97.1094.8490.0879.7657.3173.190.0695.63
93.2289.3982.0768.3043.8898.640.08129.48
98.1996.8593.8583.7058.9365.650.0586.30
98.2096.6793.3583.2058.4066.510.0587.06
+ +Table 3. Monocular networks fine-tuning - ground-truth vs proxy segmentation. Training on only the test set of MSD and Trans10K, results on the Booster train set at quarter resolution. All models start from the official weights [37, 38]. Best results in bold. + +![](images/0a9137aeff420bddf91763e0d75a359c19bcf9865ace3e32d8c151875ffbebfb.jpg) +RGB + +![](images/c07ce1a4198a82e0ba1be3e3d0ef51edbb726cf5103d5f87629c7803d39ea2f1.jpg) +Mask GT + +![](images/d20a9e8b8ce28f04359856c836a0928cc945e18fa840f0b9303f95bedccf2bc1.jpg) +Mask Proxy + +![](images/0833e3dccf361f1390126863b8d0f6619501bc9f63a42996ba087c8870ac2821.jpg) +Base + +![](images/62220939b84220a1456ebf746e3a9c50b220eb393fd0a383f9afa8a176bb528d.jpg) +Virtual Depth (GT) + +![](images/db0ed78cb42f28433d23063f5f007b4ac46f016cd560578662bc334725674d45.jpg) +Virtual Depth (Proxy) +Figure 5. Virtual Depth Qualitatives - GT vs Proxy. From left to right - Top: RGB, ground-truth and proxy segmentations; Bottom: prediction with DPT on the RGB image prediction with DPT on the median of five predictions by in-painting with either the ground truth or semantic proxy masks on Booster. + +lar networks are evaluated on the Booster training set, while stereo models are evaluated on the Booster test set. + +# 5. Experiments + +In this section, we report the outcome of our findings concerning both monocular and stereo depth estimation. + +# 5.1. Monocular Depth Estimation. + +Number of In-Paintings. We investigate the quality of the virtual depth labels by varying $N$ . When using $N = 1$ we generate a single in-painted image that is forwarded to + +the monocular network, while with $N = 5$ we generate virtual depths from 5 masked images with different colors which are then aggregated by selecting the pixel-wise depth median. In Tab. 1, we report the accuracy of depth maps produced by the two strategies, together with those of the Base architectures, i.e. without applying any inpainting strategy. Firstly, with both MiDaS and DPT, both in-painting strategies obtain virtual depths that are much more accurate for ToM regions w.r.t. the Base architecture. Secondly, $N = 5$ maps yield slightly better results in most metrics, especially when looking at DPT performance. We ascribe it to the higher robustness of the second strategy. For the remaining experiments, we fix $N = 5$ as we did not observe any further improvement with larger values. + +Fine-tuning Results (GT Segmentation). In Tab. 2, we report results on the Booster train set, obtained after fine-tuning MiDaS and DPT on all available data from Trans10K and MSD. In the Base row, we report the results of the network using the officially released weights without any further training, and we compare with those in row Ft. Virtual Depth, i.e., the results of our method. We notice that the accuracy on All pixels is improved with our approach. In particular, we achieve a significant boost in performances for ToM surfaces, of 4.37, 5.72, 8.97, 11.12 and $11.57\%$ , $28.67\mathrm{mm}$ , $0.03\%$ , $35.51\mathrm{mm}$ for MiDaS [38], and 3.91, 7.19, 11.25, 16.8 and $16.97\%$ , $42.46\mathrm{mm}$ , $0.04\%$ , $53.255\mathrm{mm}$ for DPT[38] in the $\delta_{1.25}$ , $\delta_{1.20}$ , $\delta_{1.15}$ , $\delta_{1.10}$ , $\delta_{1.05}$ , MAE, Abs.Rel, and RMSE, respectively. We highlight that, after fine-tuning, the accuracy on ToM is only slightly worse than on Other. Moreover, class Other metrics are also slightly + +
CategoryMethod
AllBase
AllFt. Virtual Depth
+ +
MiDaS [37]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓(mm)
91.6887.1379.1764.7739.0427.170.0940.16
90.3885.8977.9763.7438.5729.400.0944.37
+ +
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓(mm)
91.7887.6180.4467.4242.6026.420.0940.10
90.9786.7479.5666.4542.1227.720.0942.56
+ +Table 4. Monocular networks fine-tuning - results on NYU-V2 [31]. After training on MSD and Trans10K, both MiDaS and DPT show a negligible drop in accuracy on non-ToM surfaces of existing datasets. + +
CategoryMethod
AllBase
AllFt. Base
AllFt. Virtual Depth
AllFt. Merged
ToMBase
ToMFt. Base
ToMFt. Virtual Depth
ToMFt. Merged
OtherBase
OtherFt. Base
OtherFt. Virtual Depth
OtherFt. Merged
+ +
RAFT-Stereo [26]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
17.4213.4911.5910.114.078.63
18.4414.0412.0210.494.338.92
16.8112.349.988.092.606.04
14.689.637.355.571.954.58
56.7744.3838.4333.3113.4516.56
58.5644.4038.0232.9913.8316.47
57.0942.8934.7027.618.4710.75
47.5430.5622.8316.615.837.43
8.485.744.523.831.583.79
9.226.234.914.161.713.99
7.975.033.813.151.193.20
7.144.082.872.220.962.63
+ +
CREStereo [22]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
15.1310.708.917.573.157.40
14.6510.148.396.972.866.64
18.8514.3512.4210.875.119.83
10.866.134.413.131.513.64
51.8337.8832.8628.1912.4215.60
49.4534.4929.0024.2410.2513.01
49.7035.4529.8424.7911.9913.94
36.9620.7915.3810.675.046.73
8.114.833.502.781.142.77
7.024.203.152.531.002.56
11.458.247.036.302.735.45
5.272.731.821.340.681.70
+ +Table 5. Stereo networks fine-tuning - ground truth segmentation. Results on Booster test set at quarter resolution. All models start from the official weights [26, 22] and are fine-tuned according to different strategies. Best results in bold. + +better, probably because of the enhanced features extracted by the network, which has a better understanding of the scene context. Finally, we have reported in Ft. Base the fine-tuning results obtained by self-training the networks on their own predictions without any in-painting strategy. As expected, without the appropriate virtual depth labels, the networks cannot effectively learn from the new dataset, yielding results comparable to the Base architecture. Experiments on additional datasets are in the supplement. + +Fine-tuning Results (Proxy Segmentation). Even though obtaining semantic labels is cheaper than collecting depth ground truths, using the predictions of a segmentation network as proxy semantic annotations would accelerate the dataset collection process. Thus, we investigate the impact of replacing manually annotated masks in our pipeline with the predictions of Trans2Seg[54] and MirrorNet[60], pretrained on the training set of Trans10K and MSD, respectively, on the unseen test set of each dataset. We use weights made available by the authors. For a fair comparison, we also re-train again the models exploiting GT segmentations only on the test sets of the two datasets. Tab. 3 highlights that both models, using either GT - Ft. Virtual Depth (GT) - or proxy segmentations - Ft. Virtual Depth (Proxy), achieve much more accurate results compared to the Base network. Interestingly, the two networks yield comparable results in the class Other, while the one using GTs is slightly better than the other in the class ToM, yet still comparable. Finally, in row Virtual Depth (Proxy), we report the results of our in-painting methodology (i.e., without fine-tuning) but coloring pixels according to the proxy segmentations. We note that performances are even worse than the Base method. Indeed, the segmentation network struggles to gen + +![](images/0d084d59dddd09c24bd7b5cede67c7d0e700432dc1909b23c5cca51502c77976.jpg) +Figure 6. Qualitative comparison - disparity virtual labels. On top: left RGB image, ground truth segmentation mask, and virtual disparities by CREstereo processing masked stereo pairs. At bottom: depth by DPT on the in-painted left image, disparities by CREstereo, and their final merged labels. + +eralize to the Booster dataset, making the depth model incapable of estimating the correct values, e.g., due to some overextended in-painted ToM areas, as shown in Fig. 5. Yet, depth networks, fine-tuned on the test set of MSD and Trans10K (row Ft. Virtual Depth (Proxy)), generalize properly on Booster. + +Performance on non-ToM surfaces. To prove the effectiveness of the fine-tuned models on scenes with only a few ToM surfaces, we test the MiDaS and DPT trained over our proxy labels on the NYU-V2 dataset [31], reporting the results in Tab. 4. We notice only negligible drops in performances – the strictest metric $\delta_{1.05}$ drops by less than $0.5\%$ , which we consider a small price to pay for the large improvement on ToM surfaces observed before. + +
CategoryMethod
AllBase
AllFt. Merged (Proxy)
AllFt. Merged (GT)
ToMBase
ToMFt. Merged (Proxy)
ToMFt. Merged (GT)
OtherBase
OtherFt. Merged (Proxy)
OtherFt. Merged (GT)
+ +Table 6. Stereo networks fine-tuning - ground truth vs proxy segmentation. Results on Booster test set at quarter resolution. All models start from the official weights [26, 22] and are fine-tuned according to different strategies. Best results in bold. + +
RAFT-Stereo [26]
bad-2bad-4bad-6bad-8MAERMSE
↓(%)↓(%)↓(%)↓(%)↓(px)↓(px)
17.4213.4911.5910.114.078.63
19.5613.5310.538.282.515.37
14.689.637.355.571.954.58
56.7744.3838.4333.3113.4516.56
51.8535.3227.1720.886.568.04
47.5430.5522.8116.625.837.43
8.485.744.523.831.583.79
11.957.365.314.151.413.41
7.144.082.872.220.962.63
+ +
CREStereo [22]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
15.1310.708.917.573.157.40
12.607.425.243.641.413.33
10.866.134.413.131.513.64
51.8337.8832.8628.1912.4215.60
40.8523.6616.8311.104.185.61
36.9620.7915.3810.675.046.73
8.114.833.502.781.142.77
6.563.692.531.880.822.02
5.272.731.821.340.681.70
+ +# 5.2. Stereo Depth Estimation + +Virtual Disparity Generation Alternatives. We inquire about two main alternatives to generate virtual disparities: i) Virtual Disparity: masking both left and right images according to material segmentation masks – as materials annotations are provided for the left image only, we warp it over the right image according to ground-truth disparity – and then processing the two with the stereo network we are going to fine-tune similar to Monocular networks, ii) Merged: merging disparity labels produced by the stereo model itself with those generated by original DPT weights [37], as detailed in Eq. 4. Although the former might appear as the natural extension of our proposal from the monocular to the stereo case, we will demonstrate its ineffectiveness. + +Fine-tuning Results (GT Segmentation). Tab. 5 collects the results obtained by fine-tuning RAFT-Stereo and CREStereo through our technique. From top to bottom, we report the results achieved by the original models (Base) as well as the instances fine-tuned on their own predictions (Ft. Base) or on pseudo labels obtained according to the two strategies (Ft. Virtual Depth, Ft. Merged). + +Not surprisingly, fine-tuning the networks on their own predictions is harmful (RAFT-Stereo) or scarcely effective (CREStereo). Applying the first of the two strategies sketched before yields just a negligible improvement over the original models on ToM classes. This evidence confirms that our pipeline designed for the monocular case cannot naively be extended to the stereo case by in-painting the two images since masking ToM objects with constant colors does not ease matching – on the contrary, it introduces textureless regions, which are likely to be labeled as planar surfaces by stereo models. Conversely, the second strategy consistently improves the predictions with both RAFT-Stereo and CREStereo. In particular, the former achieves 9.23, 13.83, 15.62, and $16.69\%$ absolute reductions on bad-2, bad-4, bad-6, and bad-8, respectively, as well 7.62 and 9.13 reductions on MAE and RMSE on ToM regions. CREStereo obtains 14.93, 17.13, 17.48, and $17.54\%$ on bad metrics, and 7.40 and 8.91 reductions on MAE and RMSE. Moreover, the accuracy over Other pixels is also improved, + +![](images/574afd3295b26598ee735ee5b02b6c831ebf4af07779bb16e192e10195708765.jpg) +Figure 7. Stereo depth merging with GT or Proxy semantic labels. From left to right: RGB left image, ground-truth semantic mask, proxy semantic mask, prediction by CREstereo on the RGB images, and the final merged labels using either the GT or Proxy segmentation masks. + +although with minor margins. Fig. 6 provides a qualitative comparison between the labels obtained by the two strategies. The former produces a planar surface for the mirror completely misaligned with respect to the wall, whereas the latter combines the virtual depth labels from DPT on masked images with disparity labels at best. + +Fine-tuning Results (Proxy Segmentation). Finally, we replace the manually annotated segmentation masks with those predicted by Trans2Seg and MirrorNet and then distill virtual disparities for fine-tuning both stereo networks. As pointed out before, both Trans2Seg and MirrorNet have not been trained on Booster. Thus, Merging produces significant differences with respect to the use of manually annotated masks, as shown in Fig. 7. Nevertheless, Tab. 6 shows that our pipeline improves the performance of both RAFT-Stereo and CREStereo on ToM objects, even in the case of extremely noisy proxy semantic annotations. More precisely, CREStereo seems to benefit more from the Proxy segmentation configuration than RAFT-Stereo. Indeed, on the one hand, we can notice how RAFT-Stereo improves on ToM regions at the expense of accuracy on other pixels when using Proxy segmentations. This yields, + +![](images/1850abc761b52af9a14804be7c77ce8e368b448deb28d61a1f9e0711688475b2.jpg) + +![](images/4a34e05f893757dbd0cfb17051f26aa6ddcbdb374e65a0d60a2841d7d71e3647.jpg) +Figure 8. Qualitative post fine-tuning results. Examples of predictions by MiDaS and DPT (top), RAFT-Stereo and CREStereo (bottom). For each model, we show results achieved by the original model and by fine-tuned instances using proxy or GT segmentation masks. + +on All pixels, an increase in the bad-2 and bad-4 error rates, whereas bad-6, bad-8, MAE, and RMSE remain lower. On the other hand, CREStereo seems capable of exploiting fine-tuning much better, yielding more accurate results on any metric with both Proxy or GT masks. This outcome proves that our pipeline is effective for fine-tuning stereo models even without manually annotated masks. Nonetheless, segmenting images through human labeling unleashes its full potential, whose cost is much lower compared to that that would be required to annotate depths. + +# 5.3. Qualitative Results + +To conclude, Fig. 8 shows the effect of the fine-tuning carried out according to our proposal, with two examples for monocular (top) and stereo (bottom) networks from the Booster train and test sets respectively. We highlight how MiDaS, DPT, RAFT-Stereo, and CREStereo learn to deal with ToM surfaces either when relying on proxy segmenta + +tion masks provided by neural networks or accurately annotated by humans. More qualitative examples are reported in the supplementary material. + +# 6. Conclusion + +We have proposed an effective methodology for training depth estimation networks to deal with transparent and mirror surfaces. 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Open challenges in deep stereo: the booster dataset. In Proceedings of the IEEE conference on computer vision and pattern recognition, 2022. CVPR. 1, 2, 3, 5 +[65] Jure Zbontar, Yann LeCun, et al. Stereo matching by training a convolutional neural network to compare image patches. J. Mach. Learn. Res., 17(1):2287-2318, 2016. 2 +[66] Huangying Zhan, Ravi Garg, Chamara Saroj Weerasekera, Kejie Li, Harsh Agarwal, and Ian Reid. Unsupervised learning of monocular depth estimation and visual odometry with deep feature reconstruction. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 340-349, 2018. 2 +[67] Feihu Zhang, Victor Prisacariu, Ruigang Yang, and Philip HS Torr. GA-Net: Guided aggregation net for end-to-end stereo matching. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019. 2 +[68] Chaoqiang Zhao, Qiyu Sun, Chongzhen Zhang, Yang Tang, and Feng Qian. Monocular depth estimation based on deep learning: An overview. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1851-1858, 2017. 2 \ No newline at end of file diff --git a/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/images.zip b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1314ebe36768b2f6716859ab6d0faa680e8c7f98 --- /dev/null +++ b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b82e8b70a44cab8d4f234575860e70caa24365d314c3794c8462d861a5338178 +size 850707 diff --git a/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/layout.json b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..10c9b4884e10f25235c0b74669c47c384f2badee --- /dev/null +++ b/2023/Learning Depth Estimation for Transparent and Mirror Surfaces/layout.json @@ -0,0 +1,8948 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 95, + 103, + 499, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 103, + 499, + 121 + ], + "spans": [ + { + "bbox": [ + 95, + 103, + 499, + 121 + ], + "type": "text", + "content": "Learning Depth Estimation for Transparent and Mirror Surfaces" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 110, + 143, + 483, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 143, + 483, + 228 + ], + "spans": [ + { + "bbox": [ + 110, + 143, + 483, + 228 + ], + "type": "text", + "content": "Alex Costanzino* Pierluigi Zama Ramirez* Matteo Poggi* Fabio Tosi Stefano Mattoccia Luigi Di Stefano CVLAB, Department of Computer Science and Engineering (DISI) University of Bologna, Italy {alex.costanzino, pierluigi.zama, m.poggi, fabio.tosi5}@unibo.it https://cvlab-unibo.github.io/Depth4ToM/" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 255, + 192, + 267 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 255, + 192, + 267 + ], + "spans": [ + { + "bbox": [ + 143, + 255, + 192, + 267 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 280, + 290, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 280, + 290, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 290, + 425 + ], + "type": "text", + "content": "Inferring the depth of transparent or mirror (ToM) surfaces represents a hard challenge for either sensors, algorithms, or deep networks. We propose a simple pipeline for learning to estimate depth properly for such surfaces with neural networks, without requiring any ground-truth annotation. We unveil how to obtain reliable pseudo labels by in-painting ToM objects in images and processing them with a monocular depth estimation model. These labels can be used to fine-tune existing monocular or stereo networks, to let them learn how to deal with ToM surfaces. Experimental results on the Booster dataset show the dramatic improvements enabled by our remarkably simple proposal." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 447, + 128, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 128, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 128, + 459 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 467, + 289, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 289, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 289, + 696 + ], + "type": "text", + "content": "In our daily lives, we often interact with several objects of various appearances. Among them are those made of transparent or mirror surfaces (ToM), ranging from the glass windows of buildings to the reflective surfaces of cars and appliances. These might represent a hard challenge for an autonomous agent leveraging computer vision to operate in unknown environments. Specifically, among the many tasks involved in Spatial AI, accurately estimating depth information on these surfaces remains a challenging problem for both computer vision algorithms and deep networks [64], yet necessary for proper interaction with the environment in robotic, autonomous navigation, picking, and other application fields. This difficulty arises because ToM surfaces introduce misleading visual information about scene geometry, which makes depth estimation challenging not only for computer vision systems but even for humans - e.g., we might not distinguish the presence of a glass door in front of us due to its transparency. On the one hand, the definition of depth itself might appear ambiguous in such cases:" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 255, + 545, + 498 + ], + "blocks": [ + { + "bbox": [ + 310, + 255, + 545, + 498 + ], + "lines": [ + { + "bbox": [ + 310, + 255, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 310, + 255, + 545, + 498 + ], + "type": "image", + "image_path": "79a25101617001da4b54d1adbb56f190054b0effd3e78fe1a25140d97a60f4d9.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 499, + 547, + 567 + ], + "lines": [ + { + "bbox": [ + 304, + 499, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 499, + 547, + 567 + ], + "type": "text", + "content": "Figure 1. Depth estimation on ToM surfaces. Two examples for both monocular (top) and stereo (bottom) images. In the central column, the depth/disparity maps predicted by DPT [37] and CREStereo [22] original weights. In the rightmost column, the depth/disparity maps predicted by the models after being finetuned by our strategy without exploiting any ground-truth depth." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 590, + 547, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 547, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 547, + 699 + ], + "type": "text", + "content": "is depth the distance to the scene behind the glass door or to the door itself? Nonetheless, from a practical point of view, we argue that the actual definition depends on the task itself - e.g., a mobile robot should definitely be aware of the presence of the glass door. On the other hand, as humans can deal with this through experience, depth sensing techniques based on deep learning, e.g., monocular [38, 37] or stereo [26, 22] networks, hold the potential to address this challenge given sufficient training data [64]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "Unfortunately, light reflection and refraction over ToM" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 216, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 216, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 216, + 712 + ], + "type": "text", + "content": "* These authors contributed equally to this work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9244" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "surfaces violate also the working principles of most active depth sensors, such as Time-of-Flight (ToF) cameras or devices projecting structured-light patterns. This has two practical consequences: i) it makes active sensors unsuited to deal with ToM objects in real-world applications, and ii) prevents the use of these sensors for collecting and annotating data to train deep neural networks to deal with ToM objects. As evidence of this, very few datasets featuring transparent objects provide ground-truth depth annotations, which have been obtained through very intensive human intervention [64], graphical engines [40], or based on the availability of CAD models [5] for ToM objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 289, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 491 + ], + "type": "text", + "content": "In short, accurately perceiving the presence (and depth) of ToM objects represents an open challenge for both sensing technologies and deep learning frameworks. Purposely, this paper proposes a simple yet effective strategy for obtaining training data and, thereby, dramatically boosting the accuracy of learning-based depth estimation frameworks dealing with ToM surfaces. Driven by the observation that ToM objects alone are responsible for misleading recent monocular networks [38, 37], which would otherwise generalize well to most unseen environments, we argue that replacing them with equivalent, yet opaque objects would allow restoring an environment layout in which such networks could accurately estimate the depth of the scene. To this end, we mask ToM objects in images by in-painting them with arbitrary uniform colors. Then, we employ a monocular depth network to generate a virtual depth map out of the modified image. By repeating this process on a variety of images featuring ToM objects, we can easily and effectively annotate a dataset and then use it to train the same monocular network used to distill labels, which will now process the not-in-painted images. As a result, the trained monocular network will learn to handle ToM objects, producing consistent depth even in their presence." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 491, + 266, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 491, + 266, + 502 + ], + "spans": [ + { + "bbox": [ + 59, + 491, + 266, + 502 + ], + "type": "text", + "content": "Our main contributions can be resumed as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 515, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 515, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 515, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 59, + 515, + 287, + 563 + ], + "type": "text", + "content": "- We propose a simple yet very effective strategy to deal with ToM objects. We trick a monocular depth estimation network by replacing ToM objects with virtually textured ones, inducing it to hallucinate their depths." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 572, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 572, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 58, + 572, + 287, + 656 + ], + "type": "text", + "content": "- We introduce a processing pipeline for fine-tuning a monocular depth estimation network to deal with ToM objects. Our pipeline exploits the network itself to generate virtual depth annotations and requires only segmentation masks delineating ToM objects – either human-made or predicted by other networks [54, 60] – thus getting rid of the need for any depth annotations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 665, + 288, + 714 + ], + "type": "text", + "content": "- We show how our strategy can be extended to other depth estimation settings, such as stereo matching. Our experiments on the Booster dataset [64] prove how monocular and stereo networks dramatically improve" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "content": "their prediction on ToM objects after being fine-tuned according to our methodology." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 107, + 547, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 107, + 547, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 107, + 547, + 156 + ], + "type": "text", + "content": "Fig. 1 highlights some specific regions where monocular (top) and stereo (bottom) models struggle (middle column), and how they learn to handle ToM surfaces thanks to our strategy (rightmost column)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 166, + 392, + 178 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 166, + 392, + 178 + ], + "spans": [ + { + "bbox": [ + 306, + 166, + 392, + 178 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 186, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 545, + 437 + ], + "type": "text", + "content": "Monocular Depth Estimation. Early methods used CNNs for pixel-level regression [10, 11]. More recent approaches such as AdaBins [2], DPT [37], and MiDaS [38] use adaptive bins and vision transformers for depth regression and leverage large-scale depth training by mixing multiple datasets. Self-supervised methods use view synthesis for image reconstruction, where predicted depth is combined with known or estimated camera pose to establish correspondences between adjacent images, exploiting either stereo pairs [10, 11] or monocular videos [70, 12]. Recent works aim to improve the robustness of the photometric loss based on SSIM and L1 [68] by incorporating photometric uncertainty [57, 35], feature descriptors [66, 44, 46], 3D geometric constraints [29], proxy supervision [52, 49], optical flow [62, 50], or adversarial losses [1, 34]. Others propose architecture changes as in [69, 14, 33, 18, 13]. Except for some works that address non-Lambertian depth estimation using depth completion approaches and sparse depth measurements from active sensors [8, 40], to the best of our knowledge, we are not aware of any previous single-view depth estimation network that can handle ToM surfaces." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 438, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 641 + ], + "type": "text", + "content": "Stereo Matching. Traditional algorithms [42] utilize handcrafted features to estimate a disparity map [63, 17, 59, 58, 24, 47, 21, 3]. Then, deep learning methods replaced traditional matching cost computation, as demonstrated in [65], and, eventually, end-to-end approaches became the most effective solution for disparity estimation. These networks can be mainly categorized into 2D and 3D architectures, with the former adopting an encoder-decoder design [30, 32, 25, 39, 45, 56, 61, 48] and the latter building a feature cost volume from extracted features on the image pair [19, 4, 20, 67, 6, 7, 9, 55, 51, 16, 43]. A thorough review of these works can be found in [36]. Recent papers exploit iterative refinement paradigms [26, 22] or rely on Vision Transformers [23, 15]. However, due to its inherently ill-posed nature, dealing with non-Lambertian surfaces, such as ToM objects, remains a very challenging problem for any kind of existing stereo approach." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Non-Lambertian Object Perception. Due to the relevance of dealing with ToM objects, some recent datasets focus on them. Trans10K [54] and MSD [60] consist of over 10 000 and 4 000 real in-the-wild images of transparent objects and mirrors, respectively. Both datasets provide manually annotated segmentations of ToM materials, though" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9245" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 78, + 541, + 208 + ], + "blocks": [ + { + "bbox": [ + 51, + 78, + 541, + 208 + ], + "lines": [ + { + "bbox": [ + 51, + 78, + 541, + 208 + ], + "spans": [ + { + "bbox": [ + 51, + 78, + 541, + 208 + ], + "type": "image", + "image_path": "1e48d3d06a414270dd05b8d107c99780406abbdc24166552fb20384a735562cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 547, + 247 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 547, + 247 + ], + "type": "text", + "content": "Figure 2. Monocular Distillation pipeline. Given an RGB and a segmentation mask, we in-paint pixels belonging to transparent and mirror surfaces with a random uniform color and process these augmented images with a pre-trained monocular network. The obtained virtual depths are aggregated to obtain a pseudo-labeled dataset for fine-tuning the network itself." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "type": "text", + "content": "none of them provide depth labels. Others provide depth annotations: ClearPose [5] includes over 350 000 labeled real-world RGB-D frames of 63 household objects. ClearGrasp [40] consists of over 50 000 synthetic RGB-D images of transparent objects, as well as real-world test benchmark with 286 RGB-D images. In addition, Booster [64] focuses on stereo matching, providing high-resolution depth labels and stereo pairs acquired in indoor scenes with specular and transparent surfaces. TOD [28] contains 15 transparent objects, labeled with relevant 3D keypoints, comprising 48 000 stereo and RGBD images. StereOBJ-1M [27] also deals with stereo vision, but focuses on pose estimation for ToM objects and do not provide depth ground truths. Obtaining depth labels for these kinds of datasets is expensive, challenging, and time-consuming since it requires either CAD models for ToM objects [5], painting such objects in the scene [40, 64, 28] or relies on a complex multi-camera setup [53]. In contrast, our proposal effectively sidesteps these challenges, by demonstrating that monocular and stereo networks can learn to deal with these objects in the absence of depth annotations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "Our goal is to generate depth annotations for images featuring ToM objects in a cheap and scalable manner. This allows for training deep networks to properly estimate their depth as the distance of the closest surface in front of the camera, rather than the distance of the scene content refracted/reflected through it. Our strategy is simple yet dramatically effective and relies on the availability of recent pre-trained monocular depth estimation models [38, 37], which are capable of strong generalization across a variety of scenes though struggling to deal with ToM surfaces. Based on the above state of affairs, we argue that ToM objects are often the sole elements harming the reliability of recent pre-trained monocular depth estimation networks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 266, + 547, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 547, + 530 + ], + "type": "text", + "content": "Therefore, by virtually replacing these objects with textured artifacts that resemble their very same shapes, the monocular model may be possibly tricked and induced into estimating the depth of an opaque object, ideally placed at the very same spot in the scene. This methodology can be realized by delineating ToM objects, through manual annotations or a segmentation network, masking them from the image and then in-painting virtual textures within the masked areas. On the one hand, since a proper detection of ToM objects is crucial to our methodology, manual labeling indisputably results in the most accurate choice, though it comes with significant annotation costs. On the other hand, relying on a segmentation network would alleviate this cost: one would need some initial human annotations for training, but this would then allow to segment a large number of images for free. Unfortunately, the overall effectiveness of our methodology would be inevitably affected by the accuracy of the trained segmentation model. However, we reckon that annotating images with segmentation masks requires, definitely, a vastly lower effort compared to depth annotation [64, 27]. Hence, we settled on exploring both the aforementioned approaches." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "content": "The reader may argue that, as a consequence of our intuition, training a depth network to deal with ToM objects might be unnecessary - indeed, it would be sufficient to segment and in-paint such objects at deployment time before estimating depth. However, we retort that such a methodology would rely heavily on the actual accuracy of the model trained to segment ToM objects, which is not granted to generalize. Moreover, it would add non-negligible computational cost - i.e., the inference by a second network. On the contrary, an offline training or fine-tuning procedure allows for exploiting human-made annotation - if available - and, potentially, enable the trained network to learn how to properly estimate depth on ToM surfaces and to get rid of the second network, as well as design advanced strategies for other depth estimation frameworks, e.g. deep stereo net" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "9246" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 298, + 148 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 298, + 148 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 298, + 148 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 298, + 148 + ], + "type": "image", + "image_path": "4ca76e917f36f197530d00e16d0984c0317b82ea3ea2a2432409db7039db4654.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 149, + 287, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 149, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 149, + 287, + 194 + ], + "type": "text", + "content": "Figure 3. Virtual depth generation alternatives. From left to right: RGB, ground-truth segmentation, DPT predictions on the RGB image, on the gray-masked input, and the median of five predictions on images masked with random colors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 213, + 287, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 250 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 250 + ], + "type": "text", + "content": "works. Our experiments will highlight that the former strategy results ineffective, while we achieve a large boost in accuracy by fine-tuning depth models with our approach." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 251, + 287, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 322 + ], + "type": "text", + "content": "In the remainder, we describe our methodology to deal with ToM objects. Given a dataset of images " + }, + { + "bbox": [ + 46, + 251, + 287, + 322 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 251, + 287, + 322 + ], + "type": "text", + "content": ", our pipeline sketched in Fig. 2 builds as follows: i) surface labeling, ii) in-painting and distillation, and iii) fine-tuning of the depth network on virtual labels. Additionally, we show how it can be revised to fine-tune also deep stereo networks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "type": "text", + "content": "Surface Labeling. For any image " + }, + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "type": "inline_equation", + "content": "I_k \\in \\mathcal{I}" + }, + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "type": "text", + "content": ", we produce a segmentation mask " + }, + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "type": "inline_equation", + "content": "M_k" + }, + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "type": "text", + "content": " classifying each pixel " + }, + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 322, + 287, + 347 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 83, + 357, + 287, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 357, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 83, + 357, + 287, + 389 + ], + "type": "interline_equation", + "content": "M _ {k} (p) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} I _ {k} (p) \\in \\operatorname {T o M} \\text {s u r f a c e s} \\\\ 0 & \\text {O t h e r w i s e} \\end{array} \\right. \\tag {1}", + "image_path": "b6fb18c10bf46174586750f15a5fa7ba8c5ac09adb5c10238b68277513815354.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 394, + 287, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 394, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 287, + 442 + ], + "type": "text", + "content": "by labeling pixels as either 1 or 0 if they belong to a ToM surface or not, respectively. Such a segmentation mask can be obtained either through manual annotation or by means of a segmentation network " + }, + { + "bbox": [ + 46, + 394, + 287, + 442 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 394, + 287, + 442 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 394, + 287, + 442 + ], + "type": "inline_equation", + "content": "M_{k} = \\Theta (I_{k})" + }, + { + "bbox": [ + 46, + 394, + 287, + 442 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "text", + "content": "In-painting and Distillation. Given an image " + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "inline_equation", + "content": "I_{k}" + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "text", + "content": " and its corresponding segmentation mask " + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "inline_equation", + "content": "M_{k}" + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "text", + "content": ", we generated an augmented image " + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\tilde{I}_{k}" + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "text", + "content": " applying an in-painting operation to replace the pixels belonging to ToM objects with a color " + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 443, + 287, + 491 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 501, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 501, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 287, + 533 + ], + "type": "interline_equation", + "content": "\\tilde {I} _ {k} (p) = \\left\\{ \\begin{array}{l l} c & \\text {i f} M _ {k} (p) = 1 \\\\ I _ {k} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}", + "image_path": "02a17890095bb8354a5f427ce754489404d4760f87cc50a5deacc578e59f5194.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": "Then, a virtual depth " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\tilde{D}_k" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " for image " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "I_{k}" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " is obtained by forwarding " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\tilde{I}_k" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " to a monocular depth network " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\tilde{D}_k = \\Psi (\\tilde{I}_k)" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": ". Colors are randomly sampled for every single frame " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "I_{k}" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": ". However, depending on the image content, certain colors might result ineffective and increase the scene ambiguity - e.g., by in-painting white pixels into a transparent object located in front of a white wall. To discourage these occurrences, we sample a set of " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " custom colors " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "c_{i}, i\\in [0,N - 1]" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": ", and in-paint " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "I_{k}" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " using each of these custom colors, so as to generate a set of " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " augmented images " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\tilde{I}_k^i" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": ". Then, we obtain the final, Virtual Depth " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\tilde{D}_k" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " by computing the per-pixel median between the " + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 541, + 287, + 686 + ], + "type": "text", + "content": " depth maps" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 94, + 696, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 696, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 94, + 696, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\tilde {D} _ {k} ^ {*} = \\operatorname {m e d} \\left\\{\\Psi \\left(\\tilde {I} _ {k} ^ {i}\\right), i \\in [ 0, N - 1 ] \\right\\} \\tag {3}", + "image_path": "56bd475ca516bdea4775114c98393902e1361e99823a12f3e2ff8760ded3c743.jpg" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 76, + 539, + 258 + ], + "blocks": [ + { + "bbox": [ + 310, + 76, + 539, + 258 + ], + "lines": [ + { + "bbox": [ + 310, + 76, + 539, + 258 + ], + "spans": [ + { + "bbox": [ + 310, + 76, + 539, + 258 + ], + "type": "image", + "image_path": "d554cea05e9314f1d45dee436a2bf0bcc6a884a55218bcee99b84867a0c0d7a3.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 266, + 545, + 342 + ], + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 342 + ], + "type": "text", + "content": "Figure 4. Stereo Distillation pipeline. Given a stereo pair and a segmentation mask for the left image, we merge predictions from a pre-trained stereo network with virtual depths obtained by a monocular network with our strategy. We merge the monocular or stereo maps, by taking values belonging to either ToM or other surfaces from mono or stereo, respectively. These final merged depth labels are used to fine-tune the original stereo network." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 364, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 412 + ], + "type": "text", + "content": "As depicted in Fig. 3, in some cases, the in-painted color might be similar to the background – e.g., the transparent object disappears when a single gray mask is used – while it is visible by aggregating multi-color in-painting." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "text", + "content": "Fine-Tuning on Virtual Labels. The steps outlined so far allow for labeling a dataset " + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "text", + "content": " with virtual depth labels that are not influenced by the ambiguities of ToM objects. Then, our newly annotated dataset can be used to train or fine-tune a depth estimation network, thereby enabling it to handle the aforementioned difficult objects robustly. Specifically, during training, the original images " + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "inline_equation", + "content": "I_{k}" + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "text", + "content": " are forwarded to the network, and the predicted depth " + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "inline_equation", + "content": "\\hat{D}_k" + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "text", + "content": " is optimized with respect to the distilled virtual ground-truth map " + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "inline_equation", + "content": "\\tilde{D}_k^*" + }, + { + "bbox": [ + 304, + 413, + 546, + 568 + ], + "type": "text", + "content": " obtained from in-painted images. This simple pipeline can dramatically improve the accuracy of monocular depth estimation networks when dealing with ToM objects, as we will show in our experiments." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Extension to Deep Stereo. Our pipeline can be adapted to fine-tune deep stereo models as well, as shown in Fig. 4. Again, we argue that state-of-the-art stereo architectures [26, 22] already expose outstanding generalization capabilities while struggling with ToM objects, due to the task of matching pixels belonging to non-Lambertian surfaces being inherently ambiguous. Consequently, we exploit a monocular depth estimation network to obtain virtual depth annotations solely for these objects. Given a dataset " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " consisting of stereo pairs " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "(L_k,R_k)" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ", we distill virtual depth labels " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{D}_k^*" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "L_{k}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " and triangulate them into disparities " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{d}_k^*" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " according to extrinsic parameters of the stereo rig. Then," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9247" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 339, + 165 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 339, + 165 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 339, + 165 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 339, + 165 + ], + "type": "table", + "html": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllVirtual Depth N=196.0893.2387.6875.2349.2683.880.07112.03
AllVirtual Depth N=596.0493.5187.9375.7049.3682.980.07110.52
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMVirtual Depth N=194.1191.9984.1268.4041.1776.690.0986.46
ToMVirtual Depth N=593.8791.6483.6668.7643.6576.650.0886.01
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherVirtual Depth N=195.6292.5086.7774.6348.7688.300.07116.78
OtherVirtual Depth N=595.6692.9387.3175.4249.0686.490.07114.48
", + "image_path": "3dac301a6c1676fcaa5b3104761462e5e9907afe1e09d68df8e172ef277f4354.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 165, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 47, + 165, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 545, + 186 + ], + "type": "text", + "content": "Table 1. Virtual depth distillation by varying " + }, + { + "bbox": [ + 47, + 165, + 545, + 186 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 165, + 545, + 186 + ], + "type": "text", + "content": " . Results on Booster train set at quarter resolution. All networks use the official weights [37, 38] without further training. Different masking strategies are applied to the RGB input image. Best results in bold." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 347, + 70, + 552, + 166 + ], + "blocks": [ + { + "bbox": [ + 347, + 70, + 552, + 166 + ], + "lines": [ + { + "bbox": [ + 347, + 70, + 552, + 166 + ], + "spans": [ + { + "bbox": [ + 347, + 70, + 552, + 166 + ], + "type": "table", + "html": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
97.5995.8892.0682.7560.1464.990.0585.96
98.4396.7492.8683.4260.1862.460.0582.06
92.7788.7780.9862.4637.70113.140.10136.28
96.0093.6788.8875.7945.2665.580.0778.24
98.9497.1992.2477.5245.9757.190.0666.86
97.1094.8490.0879.7657.3173.190.0695.63
97.6395.9692.0983.1161.0166.100.0587.37
98.2996.5092.5783.5160.9064.170.0584.06
", + "image_path": "e33f1d0bbdf7c9bad97ae9208e6f8b92e5a942b190d8708b72da6dc5b3baad7b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "text", + "content": "we predict a Base disparity map " + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "inline_equation", + "content": "d_{k}" + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "text", + "content": " by forwarding " + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "inline_equation", + "content": "(L_{k}, R_{k})" + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "text", + "content": " to the stereo network we aim to fine-tune. Eventually, we replace the disparities for ToM objects with those from " + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "inline_equation", + "content": "d_{k}" + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "text", + "content": " according to " + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "inline_equation", + "content": "M_{k}" + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "text", + "content": ", this latter produced over " + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "inline_equation", + "content": "L_{k}" + }, + { + "bbox": [ + 46, + 206, + 287, + 266 + ], + "type": "text", + "content": " this time. Formally, this operation namely Merging, is defined as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 81, + 275, + 287, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 275, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 81, + 275, + 287, + 308 + ], + "type": "interline_equation", + "content": "d _ {k} (p) = \\left\\{ \\begin{array}{l l} d _ {k} (p) & \\text {i f} M _ {k} (p) = 0 \\\\ \\alpha_ {k} \\hat {d} _ {k} ^ {*} (p) + \\beta_ {k} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}", + "image_path": "4f9cedcc3bc5c28947dd3d52da34e2e3cd1fb7970b7e2e7c12a7dea7de1e1b70.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\alpha_{k},\\beta_{k}" + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "text", + "content": " being scale and shift factors, as monocular predictions are up to an unknown scale factor. Following [38], " + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\alpha_{k},\\beta_{k}" + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "text", + "content": " are estimated through Least Square Estimation (LSE) regression over " + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "inline_equation", + "content": "d_{k}" + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "text", + "content": " for pixels not belonging to any ToM object, i.e., having " + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "inline_equation", + "content": "M_{k}(p) = 0" + }, + { + "bbox": [ + 47, + 312, + 288, + 374 + ], + "type": "text", + "content": " .." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 392, + 287, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 392, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 52, + 392, + 287, + 422 + ], + "type": "interline_equation", + "content": "\\left(\\alpha_ {k}, \\beta_ {k}\\right) = \\arg \\min _ {\\alpha , \\beta} \\sum_ {p \\mid M _ {k} (p) = 0} \\left(\\alpha \\hat {d} _ {k} ^ {*} (p) + \\beta - d _ {k} (p)\\right) ^ {2} \\tag {5}", + "image_path": "b57fdb98f0341ad59e03e97e322b279a0e0c27f3a7eaf48850045b722d68a704.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 442, + 176, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 176, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 176, + 456 + ], + "type": "text", + "content": "4. Experimental Settings" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": "Implementation Details. We employ MiDaS [38] and DPT [37] as our monocular networks using the official pretrained weights, given their excellent in-the-wild generalization performance. To fine-tune them, we iterate for 20 epochs with batch size 8 and a learning rate of " + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "inline_equation", + "content": "10^{-7}" + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": " with exponential decay with gamma 0.95. We use random color and brightness and random horizontal flip augmentations. We pad/crop and resize images to match the pre-training resolution, i.e., 384 pixels for the long or short side, preserving aspect ratio with mirror pad or square crop, for MiDaS or DPT, respectively. We normalize images as the original networks do. Regarding stereo networks, we employ RAFT [26] and CREStereo [22], using the official pre-trained weights, since they achieve the top rankings in the Middlebury dataset [41] among published methods. To fine-tune them, we run 20 epochs, with batch size 2, fixed learning rate " + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": ". Following [64], we randomly resize images to half or quarter of the original dataset resolution, randomly crop to " + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "inline_equation", + "content": "456 \\times 884" + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "inline_equation", + "content": "448 \\times 880" + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": " for RAFT and CREStereo respectively, and further randomly scale images and disparities by a factor " + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\in [0.9, 1.1]" + }, + { + "bbox": [ + 46, + 462, + 288, + 715 + ], + "type": "text", + "content": ". We assume" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 206, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 545, + 255 + ], + "type": "text", + "content": "22 and 10 iterations during training for RAFT-Stereo and CREStereo, respectively. During testing, we run 32 and 20 iterations. When creating virtual labels with our masking strategy, we fix the random seed of color sampling to 0." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "text", + "content": "Datasets. Among the datasets, we selected Trans10K [54], MSD[60], and Booster[64] as they focus on ToM surfaces and contain images acquired in many realistic environments. Trans10K contains 5003, 1003, 4431 images for the training, validation, and test set, respectively, featuring common transparent objects and stuff. It provides segmentation masks with pixels categorized into 12 different classes that we collapse into 2 - ToM (classes 1 to 11) or not. MSD contains 3066, and 958 images and binary segmentation masks for the training and test set, respectively, featuring mirrors. Booster contains 228, and 191 images for training and testing, respectively. The dataset provides disparity and segmentation maps for the training set, where the segmentation maps are categorized into 4 classes, which we group into 2 - classes 2-3 into \"ToM\" category, classes 0-1 into \"Other\" materials. We fine-tune on Trans10K and MSD for monocular models and on the Booster training split for stereo networks, without using any depth ground truths." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "content": "Evaluation Protocol. We evaluate the accuracy of the monocular networks using several metrics, including absolute error relative to the ground-truth value (ABS Rel.), the percentage of pixels having the maximum between the prediction/ground-truth and ground-truth/prediction ratios lower than a threshold " + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "inline_equation", + "content": "(\\delta_{i}" + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "content": " being 1.05, 1.10, 1.15, 1.20, and 1.25), the mean absolute error (MAE) and Root Mean Squared Error (RMSE). Additionally, we evaluate stereo networks using the metrics defined in Booster [64], i.e. bad-2, bad-4, bad-6, bad-8, MAE, RMSE. Results are reported on all valid pixels (All) or for those belonging to either ToM or other objects, in order to assess the impact of our strategy on the different kinds of surfaces. For any metrics considered for stereo networks, the lower, the better - annotated with " + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "content": " in tables. The same applies to metrics used for monocular networks except for " + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\delta_{i}" + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "content": ", resulting in the higher, the better - with " + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "content": " being reported in tables. As the predictions by monocular networks are up to an unknown scale factor, we rescale them according to the LSE criterion [38] defined in Eq. 5, using all valid pixels here. Monocu" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9248" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 71, + 334, + 165 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 334, + 165 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 334, + 165 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 334, + 165 + ], + "type": "table", + "html": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllFt. Base94.0991.2885.2973.5549.1493.340.07124.54
AllFt. Virtual Depth95.0792.3186.3975.2050.5788.830.07118.23
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMFt. Base86.3082.9672.8461.0437.91126.710.12145.69
ToMFt. Virtual Depth91.8189.1281.6870.7547.8593.660.09104.80
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherFt. Base94.2791.4985.8773.7749.3892.480.07122.46
OtherFt. Virtual Depth95.3392.5386.8075.4350.4689.170.07119.58
", + "image_path": "6ae66fde484b492e27f296adc28b8322ea2278cc923b3f84ad11ecf0e5847c4c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 343, + 71, + 547, + 165 + ], + "blocks": [ + { + "bbox": [ + 343, + 71, + 547, + 165 + ], + "lines": [ + { + "bbox": [ + 343, + 71, + 547, + 165 + ], + "spans": [ + { + "bbox": [ + 343, + 71, + 547, + 165 + ], + "type": "table", + "html": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
96.8394.6090.1479.4656.8976.000.06100.98
97.9996.6593.5583.9460.4664.930.0585.93
92.7788.7780.9862.4637.70113.140.10136.28
92.6989.4981.1263.6237.95118.840.11141.27
96.6895.9692.2379.9654.6770.680.0683.06
97.1094.8490.0879.7657.3173.190.0695.63
97.1595.0290.9780.7758.0572.450.0694.07
98.0796.6493.5284.3061.1964.700.0585.57
", + "image_path": "8d771560c23393aaaae8351f258176f886460a097ac2b825802279bccadc01dd.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 196, + 338, + 304 + ], + "blocks": [ + { + "bbox": [ + 47, + 165, + 545, + 185 + ], + "lines": [ + { + "bbox": [ + 47, + 165, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 545, + 185 + ], + "type": "text", + "content": "Table 2. Monocular networks fine-tuning - ground-truth segmentation. Training on all MSD and Trans10K, results on the Booster train set at quarter resolution. All models start from the official weights [37, 38]. Best results in bold." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 196, + 338, + 304 + ], + "lines": [ + { + "bbox": [ + 52, + 196, + 338, + 304 + ], + "spans": [ + { + "bbox": [ + 52, + 196, + 338, + 304 + ], + "type": "table", + "html": "
CategoryMethodMiDaS [37]
δ < 1.25↑ (%)δ < 1.20↑ (%)δ < 1.15↑ (%)δ < 1.10↑ (%)δ < 1.05↑ (%)MAE↓ (mm)Abs. Rel↓RMSE↓ (mm)
AllBase94.5691.7285.6874.0050.1290.820.07120.51
AllVirtual Depth (Proxy)91.7887.5279.5766.0042.21105.670.09140.00
AllFt. Virtual Depth (GT)94.9992.1286.3274.9949.9188.630.07117.40
AllFt. Virtual Depth (Proxy)95.0092.1786.4875.4650.2488.100.07117.10
ToMBase87.4483.4072.7159.6336.28122.330.12140.31
ToMVirtual Depth (Proxy)86.3779.3569.9154.8432.31112.920.12124.10
ToMFt. Virtual Depth (GT)91.8589.9383.2570.6347.5592.050.09103.54
ToMFt. Virtual Depth (Proxy)91.1288.3681.1869.1545.0296.330.09107.59
OtherBase94.5791.8185.9974.0150.2891.080.07119.86
OtherVirtual Depth (Proxy)91.8087.4779.4165.8641.95108.090.09143.64
OtherFt. Virtual Depth (GT)95.2792.3086.6075.4349.9588.810.07118.48
OtherFt. Virtual Depth (Proxy)95.2792.4286.8476.0250.4888.070.07117.99
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DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓↓ (mm)
96.7994.4589.7179.0056.2675.350.06100.68
93.2389.4381.9868.0643.6298.090.08128.36
98.0996.8593.9183.5058.7465.520.0586.41
98.1196.6893.4883.0058.1366.430.0587.18
92.7788.7780.9862.4637.70113.140.10136.28
89.7585.2675.1756.5731.75110.740.11123.28
96.9596.2693.2781.8455.4967.950.0680.88
96.8296.0592.5780.6253.7470.670.0683.44
97.1094.8490.0879.7657.3173.190.0695.63
93.2289.3982.0768.3043.8898.640.08129.48
98.1996.8593.8583.7058.9365.650.0586.30
98.2096.6793.3583.2058.4066.510.0587.06
", + "image_path": "776d6c890258df9a6d8466861b02d3c238266cf790319a0a10f2f68891699e42.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 304, + 544, + 325 + ], + "lines": [ + { + "bbox": [ + 47, + 304, + 544, + 325 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 544, + 325 + ], + "type": "text", + "content": "Table 3. Monocular networks fine-tuning - ground-truth vs proxy segmentation. Training on only the test set of MSD and Trans10K, results on the Booster train set at quarter resolution. All models start from the official weights [37, 38]. Best results in bold." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 51, + 355, + 126, + 413 + ], + "blocks": [ + { + "bbox": [ + 82, + 347, + 97, + 354 + ], + "lines": [ + { + "bbox": [ + 82, + 347, + 97, + 354 + ], + "spans": [ + { + "bbox": [ + 82, + 347, + 97, + 354 + ], + "type": "text", + "content": "RGB" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 355, + 126, + 413 + ], + "lines": [ + { + "bbox": [ + 51, + 355, + 126, + 413 + ], + "spans": [ + { + "bbox": [ + 51, + 355, + 126, + 413 + ], + "type": "image", + "image_path": "0a9137aeff420bddf91763e0d75a359c19bcf9865ace3e32d8c151875ffbebfb.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 129, + 355, + 205, + 413 + ], + "blocks": [ + { + "bbox": [ + 153, + 347, + 181, + 354 + ], + "lines": [ + { + "bbox": [ + 153, + 347, + 181, + 354 + ], + "spans": [ + { + "bbox": [ + 153, + 347, + 181, + 354 + ], + "type": "text", + "content": "Mask GT" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 129, + 355, + 205, + 413 + ], + "lines": [ + { + "bbox": [ + 129, + 355, + 205, + 413 + ], + "spans": [ + { + "bbox": [ + 129, + 355, + 205, + 413 + ], + "type": "image", + "image_path": "c07ce1a4198a82e0ba1be3e3d0ef51edbb726cf5103d5f87629c7803d39ea2f1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 206, + 355, + 283, + 413 + ], + "blocks": [ + { + "bbox": [ + 227, + 347, + 263, + 354 + ], + "lines": [ + { + "bbox": [ + 227, + 347, + 263, + 354 + ], + "spans": [ + { + "bbox": [ + 227, + 347, + 263, + 354 + ], + "type": "text", + "content": "Mask Proxy" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 206, + 355, + 283, + 413 + ], + "lines": [ + { + "bbox": [ + 206, + 355, + 283, + 413 + ], + "spans": [ + { + "bbox": [ + 206, + 355, + 283, + 413 + ], + "type": "image", + "image_path": "d20a9e8b8ce28f04359856c836a0928cc945e18fa840f0b9303f95bedccf2bc1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 51, + 432, + 128, + 491 + ], + "blocks": [ + { + "bbox": [ + 82, + 423, + 97, + 430 + ], + "lines": [ + { + "bbox": [ + 82, + 423, + 97, + 430 + ], + "spans": [ + { + "bbox": [ + 82, + 423, + 97, + 430 + ], + "type": "text", + "content": "Base" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 432, + 128, + 491 + ], + "lines": [ + { + "bbox": [ + 51, + 432, + 128, + 491 + ], + "spans": [ + { + "bbox": [ + 51, + 432, + 128, + 491 + ], + "type": "image", + "image_path": "0833e3dccf361f1390126863b8d0f6619501bc9f63a42996ba087c8870ac2821.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 129, + 432, + 205, + 491 + ], + "blocks": [ + { + "bbox": [ + 139, + 423, + 195, + 431 + ], + "lines": [ + { + "bbox": [ + 139, + 423, + 195, + 431 + ], + "spans": [ + { + "bbox": [ + 139, + 423, + 195, + 431 + ], + "type": "text", + "content": "Virtual Depth (GT)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 129, + 432, + 205, + 491 + ], + "lines": [ + { + "bbox": [ + 129, + 432, + 205, + 491 + ], + "spans": [ + { + "bbox": [ + 129, + 432, + 205, + 491 + ], + "type": "image", + "image_path": "62220939b84220a1456ebf746e3a9c50b220eb393fd0a383f9afa8a176bb528d.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 206, + 432, + 283, + 491 + ], + "blocks": [ + { + "bbox": [ + 213, + 423, + 276, + 431 + ], + "lines": [ + { + "bbox": [ + 213, + 423, + 276, + 431 + ], + "spans": [ + { + "bbox": [ + 213, + 423, + 276, + 431 + ], + "type": "text", + "content": "Virtual Depth (Proxy)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 206, + 432, + 283, + 491 + ], + "lines": [ + { + "bbox": [ + 206, + 432, + 283, + 491 + ], + "spans": [ + { + "bbox": [ + 206, + 432, + 283, + 491 + ], + "type": "image", + "image_path": "db0ed78cb42f28433d23063f5f007b4ac46f016cd560578662bc334725674d45.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 492, + 287, + 547 + ], + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 547 + ], + "type": "text", + "content": "Figure 5. Virtual Depth Qualitatives - GT vs Proxy. From left to right - Top: RGB, ground-truth and proxy segmentations; Bottom: prediction with DPT on the RGB image prediction with DPT on the median of five predictions by in-painting with either the ground truth or semantic proxy masks on Booster." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 568, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 591 + ], + "type": "text", + "content": "lar networks are evaluated on the Booster training set, while stereo models are evaluated on the Booster test set." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 605, + 127, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 127, + 618 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 127, + 618 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 625, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 625, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 625, + 287, + 649 + ], + "type": "text", + "content": "In this section, we report the outcome of our findings concerning both monocular and stereo depth estimation." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 658, + 209, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 209, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 209, + 671 + ], + "type": "text", + "content": "5.1. Monocular Depth Estimation." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Number of In-Paintings. We investigate the quality of the virtual depth labels by varying " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": ". When using " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "N = 1" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " we generate a single in-painted image that is forwarded to" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "type": "text", + "content": "the monocular network, while with " + }, + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "type": "text", + "content": " we generate virtual depths from 5 masked images with different colors which are then aggregated by selecting the pixel-wise depth median. In Tab. 1, we report the accuracy of depth maps produced by the two strategies, together with those of the Base architectures, i.e. without applying any inpainting strategy. Firstly, with both MiDaS and DPT, both in-painting strategies obtain virtual depths that are much more accurate for ToM regions w.r.t. the Base architecture. Secondly, " + }, + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "type": "text", + "content": " maps yield slightly better results in most metrics, especially when looking at DPT performance. We ascribe it to the higher robustness of the second strategy. For the remaining experiments, we fix " + }, + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 304, + 346, + 545, + 514 + ], + "type": "text", + "content": " as we did not observe any further improvement with larger values." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": "Fine-tuning Results (GT Segmentation). In Tab. 2, we report results on the Booster train set, obtained after fine-tuning MiDaS and DPT on all available data from Trans10K and MSD. In the Base row, we report the results of the network using the officially released weights without any further training, and we compare with those in row Ft. Virtual Depth, i.e., the results of our method. We notice that the accuracy on All pixels is improved with our approach. In particular, we achieve a significant boost in performances for ToM surfaces, of 4.37, 5.72, 8.97, 11.12 and " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "11.57\\%" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "28.67\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "0.03\\%" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "35.51\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " for MiDaS [38], and 3.91, 7.19, 11.25, 16.8 and " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "16.97\\%" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "42.46\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "0.04\\%" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "53.255\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " for DPT[38] in the " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{1.25}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{1.20}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{1.15}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{1.10}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{1.05}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", MAE, Abs.Rel, and RMSE, respectively. We highlight that, after fine-tuning, the accuracy on ToM is only slightly worse than on Other. Moreover, class Other metrics are also slightly" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9249" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 71, + 126, + 108 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 126, + 108 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 126, + 108 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 126, + 108 + ], + "type": "table", + "html": "
CategoryMethod
AllBase
AllFt. Virtual Depth
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MiDaS [37]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓(mm)
91.6887.1379.1764.7739.0427.170.0940.16
90.3885.8977.9763.7438.5729.400.0944.37
", + "image_path": "acb5e70459fb439335f74fc3867191afee0090f4ee5d807de8095331aa72a91c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 340, + 71, + 541, + 109 + ], + "blocks": [ + { + "bbox": [ + 340, + 71, + 541, + 109 + ], + "lines": [ + { + "bbox": [ + 340, + 71, + 541, + 109 + ], + "spans": [ + { + "bbox": [ + 340, + 71, + 541, + 109 + ], + "type": "table", + "html": "
DPT [38]
δ < 1.25δ < 1.20δ < 1.15δ < 1.10δ < 1.05MAEAbs. RelRMSE
↑ (%)↑ (%)↑ (%)↑ (%)↑ (%)↓ (mm)↓(mm)
91.7887.6180.4467.4242.6026.420.0940.10
90.9786.7479.5666.4542.1227.720.0942.56
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CategoryMethod
AllBase
AllFt. Base
AllFt. Virtual Depth
AllFt. Merged
ToMBase
ToMFt. Base
ToMFt. Virtual Depth
ToMFt. Merged
OtherBase
OtherFt. Base
OtherFt. Virtual Depth
OtherFt. Merged
", + "image_path": "027ece8e49fa9eee0a08b3312f5a605275540d97fb3009a700c77f3cb5cf61b9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 167, + 140, + 350, + 281 + ], + "blocks": [ + { + "bbox": [ + 167, + 140, + 350, + 281 + ], + "lines": [ + { + "bbox": [ + 167, + 140, + 350, + 281 + ], + "spans": [ + { + "bbox": [ + 167, + 140, + 350, + 281 + ], + "type": "table", + "html": "
RAFT-Stereo [26]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
17.4213.4911.5910.114.078.63
18.4414.0412.0210.494.338.92
16.8112.349.988.092.606.04
14.689.637.355.571.954.58
56.7744.3838.4333.3113.4516.56
58.5644.4038.0232.9913.8316.47
57.0942.8934.7027.618.4710.75
47.5430.5622.8316.615.837.43
8.485.744.523.831.583.79
9.226.234.914.161.713.99
7.975.033.813.151.193.20
7.144.082.872.220.962.63
", + "image_path": "68cbd83e43e902e132d089e1d67b118ee118ad7aa056fec6b92eb063b6d4f68f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 359, + 141, + 541, + 281 + ], + "blocks": [ + { + "bbox": [ + 359, + 141, + 541, + 281 + ], + "lines": [ + { + "bbox": [ + 359, + 141, + 541, + 281 + ], + "spans": [ + { + "bbox": [ + 359, + 141, + 541, + 281 + ], + "type": "table", + "html": "
CREStereo [22]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
15.1310.708.917.573.157.40
14.6510.148.396.972.866.64
18.8514.3512.4210.875.119.83
10.866.134.413.131.513.64
51.8337.8832.8628.1912.4215.60
49.4534.4929.0024.2410.2513.01
49.7035.4529.8424.7911.9913.94
36.9620.7915.3810.675.046.73
8.114.833.502.781.142.77
7.024.203.152.531.002.56
11.458.247.036.302.735.45
5.272.731.821.340.681.70
", + "image_path": "3fcf70201d1c152dd1fda3de036b2d6c99d4956478eb4a7b291d712febd47424.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 282, + 544, + 303 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 544, + 303 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 544, + 303 + ], + "type": "text", + "content": "Table 5. Stereo networks fine-tuning - ground truth segmentation. Results on Booster test set at quarter resolution. All models start from the official weights [26, 22] and are fine-tuned according to different strategies. Best results in bold." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 323, + 287, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 431 + ], + "type": "text", + "content": "better, probably because of the enhanced features extracted by the network, which has a better understanding of the scene context. Finally, we have reported in Ft. Base the fine-tuning results obtained by self-training the networks on their own predictions without any in-painting strategy. As expected, without the appropriate virtual depth labels, the networks cannot effectively learn from the new dataset, yielding results comparable to the Base architecture. Experiments on additional datasets are in the supplement." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 438, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 715 + ], + "type": "text", + "content": "Fine-tuning Results (Proxy Segmentation). Even though obtaining semantic labels is cheaper than collecting depth ground truths, using the predictions of a segmentation network as proxy semantic annotations would accelerate the dataset collection process. Thus, we investigate the impact of replacing manually annotated masks in our pipeline with the predictions of Trans2Seg[54] and MirrorNet[60], pretrained on the training set of Trans10K and MSD, respectively, on the unseen test set of each dataset. We use weights made available by the authors. For a fair comparison, we also re-train again the models exploiting GT segmentations only on the test sets of the two datasets. Tab. 3 highlights that both models, using either GT - Ft. Virtual Depth (GT) - or proxy segmentations - Ft. Virtual Depth (Proxy), achieve much more accurate results compared to the Base network. Interestingly, the two networks yield comparable results in the class Other, while the one using GTs is slightly better than the other in the class ToM, yet still comparable. Finally, in row Virtual Depth (Proxy), we report the results of our in-painting methodology (i.e., without fine-tuning) but coloring pixels according to the proxy segmentations. We note that performances are even worse than the Base method. Indeed, the segmentation network struggles to gen" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 323, + 544, + 467 + ], + "blocks": [ + { + "bbox": [ + 310, + 323, + 544, + 467 + ], + "lines": [ + { + "bbox": [ + 310, + 323, + 544, + 467 + ], + "spans": [ + { + "bbox": [ + 310, + 323, + 544, + 467 + ], + "type": "image", + "image_path": "0d084d59dddd09c24bd7b5cede67c7d0e700432dc1909b23c5cca51502c77976.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 468, + 545, + 523 + ], + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 523 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison - disparity virtual labels. On top: left RGB image, ground truth segmentation mask, and virtual disparities by CREstereo processing masked stereo pairs. At bottom: depth by DPT on the in-painted left image, disparities by CREstereo, and their final merged labels." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 616 + ], + "type": "text", + "content": "eralize to the Booster dataset, making the depth model incapable of estimating the correct values, e.g., due to some overextended in-painted ToM areas, as shown in Fig. 5. Yet, depth networks, fine-tuned on the test set of MSD and Trans10K (row Ft. Virtual Depth (Proxy)), generalize properly on Booster." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Performance on non-ToM surfaces. To prove the effectiveness of the fine-tuned models on scenes with only a few ToM surfaces, we test the MiDaS and DPT trained over our proxy labels on the NYU-V2 dataset [31], reporting the results in Tab. 4. We notice only negligible drops in performances – the strictest metric " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\delta_{1.05}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " drops by less than " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ", which we consider a small price to pay for the large improvement on ToM surfaces observed before." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9250" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 77, + 165, + 187 + ], + "blocks": [ + { + "bbox": [ + 55, + 77, + 165, + 187 + ], + "lines": [ + { + "bbox": [ + 55, + 77, + 165, + 187 + ], + "spans": [ + { + "bbox": [ + 55, + 77, + 165, + 187 + ], + "type": "table", + "html": "
CategoryMethod
AllBase
AllFt. Merged (Proxy)
AllFt. Merged (GT)
ToMBase
ToMFt. Merged (Proxy)
ToMFt. Merged (GT)
OtherBase
OtherFt. Merged (Proxy)
OtherFt. Merged (GT)
", + "image_path": "8fe06e6f93fd38a10e10960203d16b557899852d06ca88a7a20f6f6df13a6b64.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 187, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 545, + 209 + ], + "type": "text", + "content": "Table 6. Stereo networks fine-tuning - ground truth vs proxy segmentation. Results on Booster test set at quarter resolution. All models start from the official weights [26, 22] and are fine-tuned according to different strategies. Best results in bold." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 174, + 71, + 356, + 187 + ], + "blocks": [ + { + "bbox": [ + 174, + 71, + 356, + 187 + ], + "lines": [ + { + "bbox": [ + 174, + 71, + 356, + 187 + ], + "spans": [ + { + "bbox": [ + 174, + 71, + 356, + 187 + ], + "type": "table", + "html": "
RAFT-Stereo [26]
bad-2bad-4bad-6bad-8MAERMSE
↓(%)↓(%)↓(%)↓(%)↓(px)↓(px)
17.4213.4911.5910.114.078.63
19.5613.5310.538.282.515.37
14.689.637.355.571.954.58
56.7744.3838.4333.3113.4516.56
51.8535.3227.1720.886.568.04
47.5430.5522.8116.625.837.43
8.485.744.523.831.583.79
11.957.365.314.151.413.41
7.144.082.872.220.962.63
", + "image_path": "32bd4c82f089675ab8f62609c0603c58d8c8ef8265afde023c4b706cad833a8a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 365, + 71, + 547, + 187 + ], + "blocks": [ + { + "bbox": [ + 365, + 71, + 547, + 187 + ], + "lines": [ + { + "bbox": [ + 365, + 71, + 547, + 187 + ], + "spans": [ + { + "bbox": [ + 365, + 71, + 547, + 187 + ], + "type": "table", + "html": "
CREStereo [22]
bad-2bad-4bad-6bad-8MAERMSE
↓ (%)↓ (%)↓ (%)↓ (%)↓ (px)↓ (px)
15.1310.708.917.573.157.40
12.607.425.243.641.413.33
10.866.134.413.131.513.64
51.8337.8832.8628.1912.4215.60
40.8523.6616.8311.104.185.61
36.9620.7915.3810.675.046.73
8.114.833.502.781.142.77
6.563.692.531.880.822.02
5.272.731.821.340.681.70
", + "image_path": "d04c5db2c38fe3a007aea1c7b7b71821b519df1b497f556cb5c25b815d67f92a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 228, + 185, + 240 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 185, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 185, + 240 + ], + "type": "text", + "content": "5.2. Stereo Depth Estimation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 247, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 400 + ], + "type": "text", + "content": "Virtual Disparity Generation Alternatives. We inquire about two main alternatives to generate virtual disparities: i) Virtual Disparity: masking both left and right images according to material segmentation masks – as materials annotations are provided for the left image only, we warp it over the right image according to ground-truth disparity – and then processing the two with the stereo network we are going to fine-tune similar to Monocular networks, ii) Merged: merging disparity labels produced by the stereo model itself with those generated by original DPT weights [37], as detailed in Eq. 4. Although the former might appear as the natural extension of our proposal from the monocular to the stereo case, we will demonstrate its ineffectiveness." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 402, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 486 + ], + "type": "text", + "content": "Fine-tuning Results (GT Segmentation). Tab. 5 collects the results obtained by fine-tuning RAFT-Stereo and CREStereo through our technique. From top to bottom, we report the results achieved by the original models (Base) as well as the instances fine-tuned on their own predictions (Ft. Base) or on pseudo labels obtained according to the two strategies (Ft. Virtual Depth, Ft. Merged)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": "Not surprisingly, fine-tuning the networks on their own predictions is harmful (RAFT-Stereo) or scarcely effective (CREStereo). Applying the first of the two strategies sketched before yields just a negligible improvement over the original models on ToM classes. This evidence confirms that our pipeline designed for the monocular case cannot naively be extended to the stereo case by in-painting the two images since masking ToM objects with constant colors does not ease matching – on the contrary, it introduces textureless regions, which are likely to be labeled as planar surfaces by stereo models. Conversely, the second strategy consistently improves the predictions with both RAFT-Stereo and CREStereo. In particular, the former achieves 9.23, 13.83, 15.62, and " + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "inline_equation", + "content": "16.69\\%" + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": " absolute reductions on bad-2, bad-4, bad-6, and bad-8, respectively, as well 7.62 and 9.13 reductions on MAE and RMSE on ToM regions. CREStereo obtains 14.93, 17.13, 17.48, and " + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "inline_equation", + "content": "17.54\\%" + }, + { + "bbox": [ + 46, + 486, + 288, + 714 + ], + "type": "text", + "content": " on bad metrics, and 7.40 and 8.91 reductions on MAE and RMSE. Moreover, the accuracy over Other pixels is also improved," + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 228, + 544, + 372 + ], + "blocks": [ + { + "bbox": [ + 310, + 228, + 544, + 372 + ], + "lines": [ + { + "bbox": [ + 310, + 228, + 544, + 372 + ], + "spans": [ + { + "bbox": [ + 310, + 228, + 544, + 372 + ], + "type": "image", + "image_path": "574afd3295b26598ee735ee5b02b6c831ebf4af07779bb16e192e10195708765.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 374, + 545, + 429 + ], + "lines": [ + { + "bbox": [ + 305, + 374, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 305, + 374, + 545, + 429 + ], + "type": "text", + "content": "Figure 7. Stereo depth merging with GT or Proxy semantic labels. From left to right: RGB left image, ground-truth semantic mask, proxy semantic mask, prediction by CREstereo on the RGB images, and the final merged labels using either the GT or Proxy segmentation masks." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 521 + ], + "type": "text", + "content": "although with minor margins. Fig. 6 provides a qualitative comparison between the labels obtained by the two strategies. The former produces a planar surface for the mirror completely misaligned with respect to the wall, whereas the latter combines the virtual depth labels from DPT on masked images with disparity labels at best." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "type": "text", + "content": "Fine-tuning Results (Proxy Segmentation). Finally, we replace the manually annotated segmentation masks with those predicted by Trans2Seg and MirrorNet and then distill virtual disparities for fine-tuning both stereo networks. As pointed out before, both Trans2Seg and MirrorNet have not been trained on Booster. Thus, Merging produces significant differences with respect to the use of manually annotated masks, as shown in Fig. 7. Nevertheless, Tab. 6 shows that our pipeline improves the performance of both RAFT-Stereo and CREStereo on ToM objects, even in the case of extremely noisy proxy semantic annotations. More precisely, CREStereo seems to benefit more from the Proxy segmentation configuration than RAFT-Stereo. Indeed, on the one hand, we can notice how RAFT-Stereo improves on ToM regions at the expense of accuracy on other pixels when using Proxy segmentations. This yields," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "9251" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 544, + 254 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 544, + 254 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 544, + 254 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 544, + 254 + ], + "type": "image", + "image_path": "1850abc761b52af9a14804be7c77ce8e368b448deb28d61a1f9e0711688475b2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 266, + 544, + 449 + ], + "blocks": [ + { + "bbox": [ + 52, + 266, + 544, + 449 + ], + "lines": [ + { + "bbox": [ + 52, + 266, + 544, + 449 + ], + "spans": [ + { + "bbox": [ + 52, + 266, + 544, + 449 + ], + "type": "image", + "image_path": "4a34e05f893757dbd0cfb17051f26aa6ddcbdb374e65a0d60a2841d7d71e3647.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 449, + 545, + 472 + ], + "lines": [ + { + "bbox": [ + 46, + 449, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 545, + 472 + ], + "type": "text", + "content": "Figure 8. Qualitative post fine-tuning results. Examples of predictions by MiDaS and DPT (top), RAFT-Stereo and CREStereo (bottom). For each model, we show results achieved by the original model and by fine-tuned instances using proxy or GT segmentation masks." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 491, + 289, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 289, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 289, + 612 + ], + "type": "text", + "content": "on All pixels, an increase in the bad-2 and bad-4 error rates, whereas bad-6, bad-8, MAE, and RMSE remain lower. On the other hand, CREStereo seems capable of exploiting fine-tuning much better, yielding more accurate results on any metric with both Proxy or GT masks. This outcome proves that our pipeline is effective for fine-tuning stereo models even without manually annotated masks. Nonetheless, segmenting images through human labeling unleashes its full potential, whose cost is much lower compared to that that would be required to annotate depths." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 621, + 160, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 160, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 160, + 634 + ], + "type": "text", + "content": "5.3. Qualitative Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "To conclude, Fig. 8 shows the effect of the fine-tuning carried out according to our proposal, with two examples for monocular (top) and stereo (bottom) networks from the Booster train and test sets respectively. We highlight how MiDaS, DPT, RAFT-Stereo, and CREStereo learn to deal with ToM surfaces either when relying on proxy segmenta" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 491, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 545, + 528 + ], + "type": "text", + "content": "tion masks provided by neural networks or accurately annotated by humans. More qualitative examples are reported in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 574, + 378, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 378, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 378, + 586 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "We have proposed an effective methodology for training depth estimation networks to deal with transparent and mirror surfaces. By in-painting these surfaces on RGB images, we can quickly annotate a dataset with virtual depth labels, that can be used to fine-tune both monocular and stereo networks, with outstanding results. A promising future direction would be to extend our technique to instance segmentation masks to get better virtual depth maps in the presence of multiple ToM objects in the same scene." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9252" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Filippo Aleotti, Fabio Tosi, Matteo Poggi, and Stefano Mattoccia. 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To tackle this problem, recent studies have advocated feature learning methods that aim to learn distinctive representations to match the pixels, especially in a self-supervised fashion. Unfortunately, these methods have difficulties for tiny or even single-pixel visual targets. Pixel-wise video correspondences were traditionally related to optical flows, which however lead to deterministic correspondences and lack robustness on real-world videos. We address the problem of learning features for establishing pixel-wise correspondences. Motivated by optical flows as well as the self-supervised feature learning, we propose to use not only labeled synthetic videos but also unlabeled real-world videos for learning fine-grained representations in a holistic framework. We adopt an adversarial learning scheme to enhance the generalization ability of the learned features. Moreover, we design a coarse-to-fine framework to pursue high computational efficiency. Our experimental results on a series of correspondence-based tasks demonstrate that the proposed method outperforms state-of-the-art rivals in both accuracy and efficiency.", + "bbox": [ + 75, + 333, + 473, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 666, + 208, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One of the most fundamental problems in computer vision is learning visual correspondences across space and time, which has many applications such as 3D reconstruction, physical understanding, and dynamic object modeling. Due to the factors such as viewpoint change, distractors, and deformations, this task is extremely challenging and can be roughly divided into three categories accord", + "bbox": [ + 75, + 690, + 468, + 788 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This work was supported by the Natural Science Foundation of China under Grants 62022075 and 62036005, and by the Fundamental Research Funds for the Central Universities under Grant WK349000006. This work was also supported by the advanced computing resources provided by the Supercomputing Center of USTC. (Corresponding author: Dong Liu.)", + "bbox": [ + 75, + 798, + 470, + 866 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e46fc9c6515f46f39d67c68a14c5f995b5c8bb7bd968d9b1d6dc2d144cd009da.jpg", + "image_caption": [ + "Figure 1: We illustrate video correspondences with different granularities, including object-wise, group-wise, and pixel-wise. In this paper, we concentrate on learning fine-grained features to address the pixel-wise video correspondences." + ], + "image_footnote": [], + "bbox": [ + 500, + 302, + 894, + 442 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing to the granularity: the first one is object-wise correspondences that exist between coarsely localized bounding boxes [36, 39] along the video; the second one is groupwise correspondences, indicating the mapping at group-level, and usually applied to downstream tasks like video object segmentation [5, 25]; the third one is pixel-wise correspondences, which describe the pixel-level relation between video frames with the finest granularity.", + "bbox": [ + 497, + 505, + 890, + 618 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning dense representations from videos is one approach to finding the correspondences. Researchers have been exploring different self-supervised methods for learning generalizable representations using unlabeled videos collected in the real world [16,20,23,24,41,45]. For example, Wang et al. [41] propose using an object-level cycle-consistency across time (i.e., forward-backward tracking) as a supervision signal. Jabri et al. [16] further enhance it by combining cycles of time with the similarities between path-level representations. Inspired by contrastive learning, Xu et al. [45] try to learn spatial and temporal representation through a frame-wise contrastive loss, while Li et al. [23] propose a spatial-then-temporal pretext task to learn better spatiotemporal features. Despite obtaining promising outcomes, current research has predominantly emphasized performing object-level or patch-level similarity learning, making it difficult to accurately recognize pixel-wise differences with the learned features. As a result, there is an in", + "bbox": [ + 497, + 618, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 253, + 48, + 789, + 86 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9632", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "creasing necessity for learning fine-grained representations in order to tackle this problem.", + "bbox": [ + 75, + 125, + 467, + 153 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "At the same time, there is another line of work approaching video correspondences by deterministically predicting the displacement of each pixel, which is known as optical flow estimation. Early studies used optimization methods to estimate the motion between two frames [4]. In recent years, approaches use synthetic data with supervised learning for flow estimation [8, 26], using a coarse-to-fine pyramid framework to improve the accuracy [33]. RAFT [34] further devises an iterative optimization algorithm to come up with the result of high-resolution flow fields through iterative updates, which show a superior ability to find fine-grained correspondences. However, in real scenarios, there are often appearance variants, illumination changes, and deformations between video frames, which leads to the lack of robustness on real-world videos for the optical flow model supervised by labeled synthetic videos.", + "bbox": [ + 75, + 155, + 467, + 376 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we explore how to learn fine-grained representations to meet the needs of pixel-wise video correspondences. To this end, we first investigate how to leverage synthetic data for fine-grained feature learning. Specifically, given a query pixel, the supervision in synthetic videos only supplies the one-to-one mapping, i.e., a motion vector, representing the deterministic correspondence of the pixel to another pixel in the next frame. Nevertheless, the pixel-wise features evolve slowly over space and time, which indicates a soft distribution of the correspondences. We find directly utilizing the synthetic supervision as hard labels results in inferior representations, and the learned features are unable to recognize the pixel-wise differences across different spatial locations and periods of time. To address the issue, we propose to use an external pre-trained 2D encoder to derive soft supervision for optimization based on the flow.", + "bbox": [ + 75, + 378, + 467, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, we incorporate self-supervised feature learning on unlabeled real data in the overall training to alleviate the generalization issues in real scenes, which consists of two carefully designed components. Firstly, inspired by the temporal consistency assumption [3], we learn temporal persistent features via self-supervised reconstructive learning, where each query pixel can be reconstructed by leveraging the information in adjacent frames. Besides, given the synthetic and real data, we perform adversarial training by introducing Gradient Reverse Layer [9] with a discriminator for the learned correspondences. We observe such designs can further enhance learned fine-grained features.", + "bbox": [ + 75, + 600, + 467, + 767 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Though already getting impressive results, we find it takes more time to get the results of the dense matching between fine-grained features. Thus, we make another step to devise a coarse-to-fine framework to address the problem. We put the complex feature matching on the coarse-grained feature map and then get the fine-grained results through a learnable up-sampling layer. As a result, we achieve a", + "bbox": [ + 75, + 769, + 467, + 865 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "good balance of performance and efficiency. In summary, the main contribution of this work lies in:", + "bbox": [ + 499, + 125, + 890, + 152 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We address the problem of establishing pixel-wise video correspondences via a feature learning approach.", + "- We propose an effective method of learning fine-grained features from both synthetic and unlabeled videos, followed by a carefully designed framework to address the issue of efficiency.", + "- We validate our method in a series of correspondence-based tasks. Experiment results indicate consistent improvement over state-of-the-art methods." + ], + "bbox": [ + 500, + 163, + 889, + 305 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 499, + 318, + 636, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Representation learning for video correspondences. Recent researches center around learning dense representations without labels in a self-supervised way for video correspondences, which occurs in two distinct directions: reconstruct-based [20, 21, 23, 24, 38, 40] and cycle-consistency-based techniques [16, 41, 49]. In the works of the first type, the query pixel is reconstructed from the adjacent frames based on the temporal consistency assumption, while the works of the second type execute forward-backward tracking to reduce cycle inconsistency. Furthermore, VFS [45] proposes to learn representations through frame-wise contrastive loss. SFC [13] proposes a two-stream architecture to learn semantic and fine-grained features through two different models. Despite the progress made in learning representations for video correspondences, accurately recognizing pixel-wise distinctions over space and time remains challenging.", + "bbox": [ + 497, + 340, + 890, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Optical flow estimation for video correspondences. Recently, the classic optical flow estimation problem of predicting per-pixel motion between two frames has been explored using synthetic graphics data for supervised training [8, 26]. FlowNet [8] was one of the first deep learning methods to tackle end-to-end optical flow learning. This research inspired a multitude of other methods, such as FlowNet2.0 [15], DCFlow [44], SpyNet [30], PwC-Net [33], and LiteFlowNet3 [14]. Most of these methods employ cost volumes for finding pixel matching. RAFT [34] stands out from the rest due to its multi-scale correlation volumes and iterative flow refinements, whilst achieving superior performance, and is also a precursor to many successive works. However, learning a deterministic model with synthetic computer graphics data limits generalization ability and robustness on real videos.", + "bbox": [ + 497, + 576, + 890, + 796 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised domain adaptation with self-supervised learning. Recently, there has been a surge in approaches to reduce the distribution discrepancy between real and synthetic data by leveraging unsupervised domain adaptation [9, 19, 28, 35, 42, 48]. An effective way to", + "bbox": [ + 497, + 796, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9633", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/bba51a297b61be3c08f62c60202a29053e2d99f3657afce5298bb11aa2bec209.jpg", + "image_caption": [ + "(a) Learning with synthetic videos", + "Figure 2: Overview of the framework for fine-grained feature learning. We facilitate fine-grained feature learning by integrating self-supervised learning on unlabeled videos into supervised learning with labeled synthetic videos. For learning with synthetic data $\\mathcal{D}_S$ , we devise a soft labeling module to convert the hard labels indicated by the motion vectors to soft labels. To learn more generalizable features, we leverage free supervision from unlabeled videos $\\mathcal{D}_{\\mathcal{T}}$ with the objective of frame reconstruction. Furthermore, an adversarial loss (along with Gradient Reverse Layer and a discriminator) is proposed to encourage domain invariant representations. The whole framework is jointly optimized in an end-to-end manner with the proposed objective functions." + ], + "image_footnote": [], + "bbox": [ + 139, + 137, + 828, + 334 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "realize it is through adversarial training. Recent studies execute adversarial training by learning a domain classifier (the discriminator) to distinguish the learned features from different distributions, utilizing adversarial loss to increase domain confusion. Meanwhile, self-supervised learning obtains impressive performance and shows good generalizing ability by designing different pretext tasks [11, 41, 43, 45] with unlabeled data, which motivates us to combine supervised learning and self-supervised learning to encourage consistent representations for both domains as well as improved results for downstream tasks.", + "bbox": [ + 75, + 428, + 473, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 77, + 591, + 184, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We address the problem of estimating the pixel-wise correspondences between a pair of video frames, which can be realized by learning fine-grained features for matching. Our goal is to learn a fine-grained feature space $\\phi$ with the encoder $\\theta$ by designing different learning objective functions for the probabilistic mapping.", + "bbox": [ + 75, + 614, + 468, + 695 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Probabilistic mapping. Given a pair of video frames $I_1, I_2 \\in \\mathbb{R}^{h \\times w \\times 3}$ , for all pixels in $I_1$ , we aim to predict the probabilistic mapping $P_{1 \\to 2} \\in \\mathbb{R}^{H \\times W \\times (2r + 1)^2}$ and $P_{1 \\to 2}(\\cdot | i) \\in \\mathbb{R}^{(2r + 1)^2}$ gives the probability that $i$ is mapped to $j$ in frame $I_2$ within a limited range $r$ , considering the nature of temporal coherence in the video. The $i, j \\in \\mathbb{R}^2$ indicate the 2D pixel location. $P_{1 \\to 2}(\\cdot | i) \\in \\mathbb{R}^{(2r + 1)^2}$ thus encodes the entire discrete conditional probability distribution of where $i$ is mapped in frame $I_2$ . The probabilistic mapping can be achieved by calculating the feature similarities using the learned fine-grained features. More specifically, we first extract the dense features $F_1, F_2 \\in$", + "bbox": [ + 75, + 695, + 470, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbb{R}^{H\\times W\\times C}$ . Then the discrete probabilistic map can be obtained by computing the local correlation w.r.t. each key $j$ in $I_{2}$ within a local window for each query $i$ ,", + "bbox": [ + 497, + 427, + 890, + 469 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP _ {1 \\rightarrow 2} (j | i) = \\frac {\\exp \\left(F _ {1} (i) \\cdot F _ {2} (j) / \\tau\\right)}{\\sum_ {n} \\exp \\left(F _ {1} (i) \\cdot F _ {2} (n) / \\tau\\right)}, i \\in \\{1,.., H W \\}, j, n \\in \\mathcal {K} (i), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 499, + 478, + 900, + 514 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{K}(i)$ is the index set in the local window with a limited range of $r$ centered at $i$ , and $\\tau$ is the temperature. The result of the probabilistic mapping is further post-processed and directly applied to various downstream tasks.", + "bbox": [ + 497, + 515, + 892, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Fine-Grained Feature Learning", + "text_level": 1, + "bbox": [ + 499, + 586, + 779, + 600 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We design the learning objective functions for probabilistic mapping with both synthetic and real-world videos. The overview of the framework is shown in Figure 2.", + "bbox": [ + 497, + 609, + 890, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning with synthetic videos. Labeled synthetic videos are often used as supervision for learning the optical flows in recent studies [8,34]. Given a pair of rendered video frames $I_1^s, I_2^s$ , the synthetic data $\\mathcal{D}_S$ provides pixelwise motion vector, i.e., optical flow $G_{1\\rightarrow 2}$ . A valid question then emerges as how to learn features using such deterministic correspondences? Indeed, we believe the deterministic correspondences are hard to obtain for real-world videos, thus we argue the necessity to convert them into soft (probabilistic) ones. We devise the following variants:", + "bbox": [ + 497, + 653, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(i) Dirac distribution: As shown in Figure 3 (a), we can directly convert the motion vector to a dirac distribution $\\delta (\\cdot |i)$ in order to describe the ground truth mapping. Then, the learning objective function defined as Kullback-Leibler divergence between $P_{1\\rightarrow 2}^{s}(\\cdot |i)$ and $\\delta (\\cdot |i)$ . The $P_{1 - > 2}^{s}$ stands", + "bbox": [ + 497, + 796, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9634", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bc2a06a2cc2db348f2d241dc610fa5ca42109622ef28dd21601b81c088aa6161.jpg", + "image_caption": [ + "Figure 3: Illustration of the probabilistic map. For $i$ in $I_1^s$ , we visualize the probability value of the mapping from $i$ to the locations in $I_2^s$ within a limited range." + ], + "image_footnote": [], + "bbox": [ + 82, + 124, + 460, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for the correlation calculated by Eq. (1) with synthetic data:", + "bbox": [ + 75, + 273, + 467, + 286 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {K L - v l}} = \\sum_ {i} D _ {K L} (\\delta (\\cdot | i) \\| P _ {1 \\rightarrow 2} ^ {s} (\\cdot | i)). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 139, + 296, + 468, + 326 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(ii) Gaussian distribution: However, the feature of the query pixel $i$ varies smoothly over space and time, which indicates a soft distribution of the potential location in the next frame. As shown in Figure 3 (a), the dirac distribution does not provide the feature learning with any knowledge of relative probability in the background, making it hard to learn the features with the ability to tell the fine-grained differences with synthetic videos. Thus, we devise to generate the probabilistic map with gaussian distribution, which introduces a soft distribution centered at the ground truth coordinate:", + "bbox": [ + 75, + 328, + 468, + 465 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {N} (j | i, \\mu , \\sigma^ {2}) = \\frac {1}{\\sqrt {2 \\pi} \\sigma_ {u}} e ^ {- \\frac {\\left(u _ {j} - \\mu_ {t} ^ {u}\\right) ^ {2}}{2 \\sigma_ {u} ^ {2}}} \\cdot \\frac {1}{\\sqrt {2 \\pi} \\sigma_ {v}} e ^ {- \\frac {\\left(v _ {j} - \\mu_ {t} ^ {v}\\right) ^ {2}}{2 \\sigma_ {v} ^ {2}}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 82, + 471, + 468, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu = (\\mu_i^u,\\mu_i^v)$ represents the 2D coordinate of ground truth in the $I_2^s$ for pixel $i$ , and $(u_{j},v_{j})$ indicates the 2D coordinate of $j$ . Then the loss can be devised as:", + "bbox": [ + 75, + 516, + 468, + 557 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {K L - v 2}} = \\sum_ {i} D _ {K L} \\left(\\mathcal {N} (\\cdot | i, \\mu , \\sigma^ {2}) \\| P _ {1 \\rightarrow 2} (\\cdot | i)\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 115, + 576, + 468, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(iii) Soft-labeling: The gaussian prior only considers the euclidean distance of coordinates, which shows limited capability of modeling the complicated distributions. We believe the synthetic supervision already provides valuable temporal cues ( $i$ in $I_1^s$ move to $j$ in $I_2^s$ ), and the soft distribution over space can be approached by computing the self-similarities for $j$ using the pre-trained 2D visual encoder $\\theta_{self}$ which can produce spatially-discriminative features. As shown in Figure 3 (c), for the $i$ in $I_1^s$ that moves to $j$ , we get the feature of the query $i$ (denoted as $\\overline{F}_q$ ) at the location $j$ in $\\overline{F}_2$ ( $\\overline{F}_2$ is the feature map of $I_2^s$ computed by $\\theta_{self}$ ). Then we can compute the feature similarities $S_{1\\rightarrow 2}(\\cdot |i)$ between $\\overline{F}_q$ and $\\{\\overline{F}_2(k)|k\\in \\mathcal{K}(i)\\}$ , where $\\mathcal{K}(i)$ is the index set in the local window centered at $i$ . The $S_{1\\rightarrow 2}(\\cdot |i)$ are further normalized (by softmax) to obtain the discrete probability distribution $P_{1\\rightarrow 2}(\\cdot |i)$ :", + "bbox": [ + 75, + 610, + 468, + 832 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {K L - v 3}} = \\sum_ {i} D _ {K L} \\left(P _ {1 \\rightarrow 2} (\\cdot | i) \\| P _ {1 \\rightarrow 2} ^ {s} (\\cdot | i)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 840, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Table 4, we find soft labeling works well when only pre-training $\\theta_{\\text{self}}$ on synthetic data $\\mathcal{D}_{\\mathcal{S}}$ with $\\mathcal{L}_{\\mathrm{rec}}$ (Eq. (8)), and leveraging more strong 2D encoder would contribute to better performance. The comparisons between different loss functions will be discussed in the experiments, and the $\\mathcal{L}_{\\mathrm{KL - v3}}$ is used as the default loss.", + "bbox": [ + 497, + 125, + 890, + 207 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning with unlabeled videos. Meanwhile, we observe in real scenarios, there are apparent differences with synthetic videos in appearance variants, illumination changes and deformations, leading to notable changes in the distribution, where the learned features on synthetic videos show unsatisfied generalization ability. Inspired by recent studies [16, 41], we try to improve the learned fine-grained features by introducing self-supervised feature learning into the framework. As observed in the bottom of Figure 1, the pixel repetition encourages us to learn the fine-grained features by reconstructive learning, where each pixel in the $I_1^t$ can be reconstructed by leveraging the information of $I_2^t$ with a limited range. To achieve this, the video frames $I_1^t, I_2^t$ are firstly projected into pixel embeddings $F_1^t, F_2^t$ by the encoder $\\theta$ . For each query $i$ in $I_1^t$ , we calculate the probabilistic map $P_{1\\rightarrow 2}^t$ with Eq. (1). Then the query $i$ in $I_1^t$ can be reconstructed by a weighted sum of pixels in $\\mathcal{K}(i)$ :", + "bbox": [ + 497, + 210, + 890, + 444 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {1} ^ {\\text {r e c}} (i) = \\sum_ {j \\in \\mathcal {K} (i)} P _ {1 \\rightarrow 2} ^ {t} (j | i) I _ {2} ^ {t} (j). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 588, + 454, + 890, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then the reconstruction loss for self-supervised training is defined as $L_{1}$ distance between $I_1^{rec}$ and $I_1^t$ . Training with such self-supervision leads to temporal persistent features that generalize well in real scenarios.", + "bbox": [ + 497, + 494, + 890, + 548 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the pixel repetition does not hold for pixels that become occluded. Thus, we exclude occluded pixels from the reconstruction loss to avoid learning incorrect features. We follow the forward-backward consistency assumption to detect the occluded pixels. which is defined in Eq. (7) as the occlusion flag $O_{1\\rightarrow 2}$ to be 1 whenever the constraint is violated, and 0 otherwise:", + "bbox": [ + 497, + 549, + 890, + 646 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nO _ {1 \\rightarrow 2} (i) = \\mathbb {1} \\left(\\underset {i} {\\arg \\max } P _ {2 \\rightarrow 1} ^ {t} \\left(i \\mid \\underset {j} {\\arg \\max } P _ {1 \\rightarrow 2} ^ {t} (j \\mid i)\\right) = i\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 505, + 653, + 890, + 692 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The loss for reconstructive learning is defined as follows:", + "bbox": [ + 499, + 693, + 877, + 707 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e c}} = \\sum_ {i} O _ {1 \\rightarrow 2} (i) \\cdot \\left\\| I _ {1} ^ {\\text {r e c}} (i) - I _ {1} ^ {t} (i) \\right\\| _ {1}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 718, + 890, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Adversarial training. We further improve the fine-grained features by leveraging the technique in recent works of unsupervised domain adaptation, which aims to bridge the gap caused by the domain shift between the synthetic videos $\\mathcal{D}_S$ and real videos $\\mathcal{D}_{\\mathcal{T}}$ via adversarial training. An effective way to approach this problem consists in introducing the network a Gradient Reversal Layer (GRL). We additionally train a discriminator $\\theta_{D}$ to identify whether the", + "bbox": [ + 497, + 755, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9635", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cb6b891b9ea7d8de9c1f0ff74d573e49bb0e50dea06e647cec26c4c97c831b24.jpg", + "image_caption": [ + "Figure 4: Illustration of the coarse-to-fine framework for efficient probabilistic mapping. We first obtain coarse-grained matching and then upsample it to get the fine-grained result." + ], + "image_footnote": [], + "bbox": [ + 78, + 123, + 472, + 180 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "probabilistic map comes from synthetic or real videos:", + "bbox": [ + 75, + 233, + 436, + 247 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {a d v}} = \\mathbb {E} _ {P ^ {t} \\in P _ {\\mathcal {T}}} [ \\log (D (P ^ {t})) ] + \\mathbb {E} _ {P ^ {s} \\in P _ {\\mathcal {S}}} [ \\log (1 - D (P ^ {s})) ], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 75, + 254, + 468, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and then we reverse the gradient direction during the backward pass in back-propagation when updating the parameters of the encoder $\\theta$ with $\\mathcal{L}_{\\mathrm{adv}}$ :", + "bbox": [ + 75, + 282, + 468, + 324 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta \\leftarrow \\theta + \\lambda \\frac {\\partial \\mathcal {L} _ {\\mathrm {a d v}}}{\\partial \\theta}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 203, + 332, + 468, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The GRL allows to train the discriminator and the encoder at the same time, and the adversarial training helps to learn domain invariant patterns.", + "bbox": [ + 75, + 363, + 468, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall training objective. The overall training objective for learning fine-grained features is formulated as a multi-task loss, which is written as $\\mathcal{L} = \\mathcal{L}_{\\mathrm{KL}} + \\mathcal{L}_{\\mathrm{rec}} + \\mathcal{L}_{\\mathrm{adv}}$ where we empirically treat each loss equally.", + "bbox": [ + 75, + 404, + 468, + 461 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Efficient Fine-grained Probabilistic Mapping", + "text_level": 1, + "bbox": [ + 77, + 467, + 457, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To get the fine-grained probabilistic map, i.e., $P_{1\\rightarrow 2}\\in \\mathbb{R}^{H\\times W\\times (2r + 1)^2}$ , we need to compute the similarities w.r.t. all key pixels in the local window centered at every query pixel, which is computationally costly. In this section, we devise a coarse-to-fine framework. The overview of the framework can be found in Figure 4, where we first compute the correlation at coarse-grained features and then up-sample it to get fine-grained probabilistic maps.", + "bbox": [ + 75, + 489, + 468, + 600 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Self-attention and Cross-attention Layers. More specifically, we first extract the coarse feature maps $F_{1}^{\\downarrow}, F_{2}^{\\downarrow} \\in \\mathbb{R}^{H/4 \\times W/4 \\times C}$ , and we further enhance the coarse features by introducing the self-attention and cross-attention layers with positional encoding. Then, we obtain the coarse-grained probabilistic map $P_{1 \\rightarrow 2} \\downarrow \\in \\mathbb{R}^{H/4 \\times W/4 \\times (2r\\downarrow + 1)^{2}}$ by Eq (1).", + "bbox": [ + 75, + 600, + 468, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Up-sampling. We devise an up-sampling layer to obtain fine-grained probabilistic map $P_{1\\rightarrow 2}\\in \\mathbb{R}^{H\\times W\\times (2r + 1)^2}$ which can be simply done by leveraging pixel-shuffle or convolution layer with bilinear interpolation.", + "bbox": [ + 75, + 699, + 468, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More details of the architecture are included in the supplementary material. We train the coarse-to-fine framework in a distillation manner on $\\mathcal{D}_{\\mathcal{T}}$ , with the same objective function as $\\mathcal{L}_{\\mathrm{KL}}$ . The supervisions for $P_{1\\rightarrow 2}$ are obtained by computing the probabilistic map using pre-trained encoder in Sec. 3.1. Without losing much performance, we find such a design helps to get rid of the complicated fine-grained feature matching and exhibit higher efficiency.", + "bbox": [ + 75, + 755, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 499, + 124, + 631, + 138 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We verify the effectiveness of our method in a series of correspondence-based tasks. We will first introduce implementation and evaluation details, and report the performance comparison with baselines. Finally, we perform detailed ablation studies for each component of our method.", + "bbox": [ + 497, + 150, + 890, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 499, + 239, + 715, + 254 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Backbone. We exploit the encoder $\\theta$ with ResNet-18 [12]. We reduce the stride up to layer $\\mathrm{res}_4$ to get features at $1/2$ of the original image dimension for training. In our coarse-to-fine framework, we increase the stride of the encoder to 8 for coarse-grained feature matching.", + "bbox": [ + 497, + 263, + 890, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training details. The training is conducted on the train set of synthetic dataset FlyingThings [26] and YouTube-VOS [46] collected in real-world. The FlyingThings/YouTube-VOS contains $40\\mathrm{k} / 3.5\\mathrm{k}$ videos for training. For both datasets, we sample pair of frames which are resized into $256\\times 256$ and converted to Lab color space with channel-wise dropout as the information bottleneck [20]. The local range $r$ in the probabilistic map is set to $24 / 6$ for the fine-grained features $(\\frac{h}{2}\\times \\frac{w}{2}$ (stride=2)) or coarse-grained features $(\\frac{h}{8}\\times \\frac{w}{8}$ (stride=8)). We first train an encoder using reconstruction loss (Eq. (8)) with a batchsize of 32 for 30 epochs on FlyingThings [26], which is further utilized as $\\theta_{self}$ in soft labeling. Then the final model $\\theta$ is jointly trained for 30 epochs with proposed three losses, with a batchsize of 16 for each dataset. When training with synthetic optical flow, we filter out the points that are out of the local range or occluded by forward-backward checking. The $\\tau$ is set to 1. We use Adam as the optimizer, and the initial learning rate is set to 1e-3 with a cosine (half-period) learning rate schedule for each stage. We include more training details in the supplementary.", + "bbox": [ + 497, + 336, + 892, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation. An important problem is how to evaluate the quality of the learned fine-grained features for pixel-wise video correspondences. Following the previous works [16,41,45], without any fine-tuning, we directly leverage the pre-trained encoder $\\theta$ to extract features $F_{i}, F_{j}$ with a spatial resolution of $\\frac{h}{s} \\times \\frac{w}{s}$ (the $s$ represents the stride of the encoder) for the pair of frames $I_{i}, I_{j}$ , which are later used to compute the probabilistic map $P_{i \\rightarrow j}$ by Eq (1). Based on the probabilistic map $P_{i \\rightarrow j}$ , we follow the recurrent inference strategy inference strategies of recent studies [16,41,45] to propagate the target points or semantic labels of the first frame, as well as previous predictions, to the current frame $I_{t}$ . We evaluate the point tracking on three popular benchmarks including BADJA [2], JHMDB [18], TAP-Vid-DAVIS [7] and TAP-Vid-Kinetics [7], and the evaluation of video object segmentation is conducted on the widely used dataset DAVIS-2017 [29].", + "bbox": [ + 497, + 631, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9636", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ecf8503885b5ce8652e1dd2daea872faf1d5d75fdbdd577fba74e38fc918c463.jpg", + "table_caption": [ + "Table 1: Quantitative results for point tracking on different datasets. The frame per second (FPS) results of getting pixelwise correspondences between a pair of video frames are measured on a single GTX-3090 at the resolution of $480 \\times 640$ . The * indicates our coarse-to-fine framework. The - indicates the unavailable result due to the unavailable pre-trained model." + ], + "table_footnote": [], + "table_body": "
MethodBackboneStrideFPSBADJAJHMDBTAP-DAVISTAP-Kinetics
PCK@0.1↑PCK@0.1↑<δxavg-p↑<δxavg-p↑
TimeCycle [41]ResNet-5082841.157.327.128.6
UVC [24]ResNet-18814248.258.629.025.2
CRW [16]ResNet-18814250.959.332.525.4
VFS [45]ResNet-18814251.960.531.928.8
CLSC [31]ResNet-188142-61.7--
SFC [13]ResNet-18 + ResNet-5082753.861.937.231.1
MAST [20]ResNet-1843355.762.442.533.2
LIIR [22]ResNet-18433-60.7--
Ours*ResNet-1883456.864.648.043.8
ImageNet Pre. [12]ResNet-182857.561.551.344.5
UVC [24]ResNet-182856.765.152.741.8
CRW [16]ResNet-182855.961.443.237.1
VFS [45]ResNet-182858.161.051.444.9
SFC [13]ResNet-182861.565.953.943.6
MAST [20]ResNet-182863.063.153.842.7
OursResNet-182867.266.859.848.8
", + "bbox": [ + 166, + 169, + 806, + 376 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results for Point Tracking", + "text_level": 1, + "bbox": [ + 75, + 385, + 315, + 401 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We firstly make comparisons for point tracking since it requires the finest granularity of the learned features. The main comparators of our method are the works aim to learn good representations for matching, e.g., TimeCycle [41], UVC [24], CRW [16], VFS [45], SFC [13], and MAST [20]. We also include the model pre-trained on ImageNet [6] with human annotations. These works share a similar evaluation protocol as we mentioned in 4.1.", + "bbox": [ + 75, + 408, + 470, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While previous works test the pixel-wise correspondences on JHMDB [18] that only provides the human keypoint annotations. We additionally include BADJA [2], TAP-Vid-DAVIS [7] and TAP-Vid-Kinetics [7]. We propagate the points of the first frame to other frames and evaluate the results using the annotations of each dataset. We notice some works are trained and evaluated with the coarse-grained features (e.g., the features at 1/8 of the original image dimension). For these methods, we use our coarse-to-fine framework that also executes coarse-grained feature matching for comparisons. Meanwhile, for better comparisons, we follow the studies in [16,45] to further reduce the stride $s$ of the encoder to 2, in order to get more fine-grained results for CRW, VFS, SFC and MAST. We also provide the FPS of computing the pixel-wise correspondences between two frames for feature-matching-based methods, which can be done by first taking the index of the maximum value in $P_{1\\rightarrow 2}(\\cdot |i)$ for each $i$ and then applying up-sampling to get full-resolution results. More details about the evaluation are included in the supplementary material.", + "bbox": [ + 75, + 519, + 468, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on BADJA/JHMDB. We adopt the standard PCK [47] of all visible points (not compute PCK for each video then take average) as the evaluation metric. Each point is considered correct if it is within a distance of $0.1\\sqrt{A}$ from the ground truth, where $A$ is the distance be", + "bbox": [ + 75, + 796, + 470, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tween keypoints (for JHMDB) or the area of the ground-truth segmentation mask on the frame (for BADJA). In Table 1, our method achieves $67.2\\% / 66.8\\%$ , surpassing all state-of-the-art methods. Besides, our method with the coarse-to-fine design still makes the absolute improvements by $1.1\\%$ and $2.2\\%$ compared with MAST, and shows better efficiency compared with SFC [13] that uses the two-stream network to find the correspondences. More remarkably, our efficient framework even surpasses part of the methods using more fine-grained features for inference.", + "bbox": [ + 497, + 385, + 890, + 524 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on TAP-Vid. TAP-Vid is a newly developed benchmark composed of long-term videos in real-world with accurate human annotations of point tracks. We test on the whole set of TAP-Vid-DAVIS and the test set of TAP-Vid-Kinetics. We adopt the setting of \"first fashion\" in [7], which tracks only into the future. The average position accuracy over all visible points $(< \\delta_{avg-p}^{x})$ is adopted as the metric. The learned fine-grained features obtain $59.8\\% / 48.8\\%$ on TAP-Vid-DAVIS/TAP-Vid-Kinetics, leading apparent improvements over state-of-the-arts by $5.9\\% / 3.9\\%$ . Moreover, the proposed coarse-to-fine framework gets $48.0\\% / 43.8\\%$ , surpassing MAST by $5.5\\% / 10.6\\%$ .", + "bbox": [ + 497, + 529, + 892, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons with task-specific methods. Besides, we notice there are some recent methods specifically designed for point tracking, like RAFT [34], PIPs [10], TAPNet [7], and Thin-Slicing Net [32] even trained with human annotations. Here we also present the performance comparisons with them in Table 2. It's worth noting that, to align the evaluation with these methods, except JHMDB, we first compute the $< \\delta_{avg-p}^{x}$ or PCK for each video to obtain video-level results, and the final results are obtained by taking the average over all videos. Without any specific designs, our performance even surpasses these methods by $7.4\\% / 7.5\\% / 0.2\\%$ on BADJA/TAP-DAVIS/TAP-Kinetics.", + "bbox": [ + 497, + 700, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9637", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/63693f9b4c2b6b0fe8af4c0a6ef33d4baec674c4cf1b55cb7670bfca7829017f.jpg", + "image_caption": [ + "$1^{st}$ frame with target" + ], + "image_footnote": [], + "bbox": [ + 117, + 124, + 262, + 451 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c3b3f39ca9443ce7a15af9176ef87f5e2b4677c64895d8efa1d9b43cb4cf002d.jpg", + "image_caption": [ + "VFS" + ], + "image_footnote": [], + "bbox": [ + 263, + 124, + 408, + 451 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8da4cc658d11c65d46cda28d85b9421fedca55094da20aef7e3ebbcd939fb826.jpg", + "image_caption": [ + "MAST" + ], + "image_footnote": [], + "bbox": [ + 410, + 124, + 554, + 451 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a3792b42b1ebc6c7f2aaf7ba33b98653555b1f364bc9190277e2af7f6ed03f6e.jpg", + "image_caption": [ + "RAFT" + ], + "image_footnote": [], + "bbox": [ + 557, + 124, + 700, + 451 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/56ca515c545cf458a4f2ff892511cf6c36418b442caaba0248b73d794b7e9dc2.jpg", + "image_caption": [ + "Ours", + "Figure 5: Qualitative results for point tracking. Given the target pixel in the first frame, we visualize the estimated trajectory with a pink-to-yellow colormap (pink/yellow indicates the start/end of the video clip). We visualize sparse ground-truth labels with cyan cross marks. Please refer to the video in the supplementary for better animations. (Zoom in for best view)" + ], + "image_footnote": [], + "bbox": [ + 702, + 124, + 845, + 451 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/59098e5984a44a7dbbd882c1aaf0bc0cc19a60f1de308ad1e49150b128b02e9d.jpg", + "table_caption": [ + "Table 2: Comparisons with methods specifically designed for point tracking. “‡” means we align the evaluation protocol with each method for fair comparisons." + ], + "table_footnote": [], + "table_body": "
MethodBADJAJHMDBTAP-DAVISTAP-Kinetics
PCK@0.2↑PCK@0.1↑<δxavg↑<δxavg↑
RAFT [34]45.666.442.144.3
PIPs [10]62.3-55.348.2
TAPNet [7]-62.348.654.4
Thin-Slicing Net [32]-68.7--
Ours‡69.766.862.854.6
", + "bbox": [ + 85, + 564, + 468, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 5 shows some visualization results of the point tracking on TAP-Vid-DAVIS. Given the target in the first frame, we visualize the estimated trajectory with a pink-to-yellow map. Compared with VFS, MAST and RAFT, our approach can output more smooth and accurate trajectories close to the sparse visualized ground truth, even facing dramatic appearance changes and deformation.", + "bbox": [ + 75, + 652, + 468, + 749 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Results for Video Object Segmentation", + "text_level": 1, + "bbox": [ + 75, + 760, + 410, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next, we evaluate methods with semi-supervised video object segmentation. We use the mean of region similarity $\\mathcal{I}_m$ , mean of contour accuracy $\\mathcal{F}_m$ and their average $\\mathcal{J} \\& \\mathcal{F}_m$ as the evaluation metrics. In Table 3, our method still leads the performance. More remarkably, our method even outperforms some task-specific fully-supervised algo", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c3692d0053e51876246e1be956ed591403333d250e61046a04156d4b68fe4688.jpg", + "table_caption": [ + "Table 3: Quantitative results for video object segmentation on $\\mathbf{DAVIS}_{17}$ [29]. \"Sup.\" means using human annotations for training." + ], + "table_footnote": [], + "table_body": "
MethodSup.BackboneDAVIS17
J&Fm↑Jm↑Fm↑
TimeCycle [41]ResNet-5040.741.939.4
UVC [24]ResNet-1859.557.761.3
MAST [20]ResNet-1865.563.367.6
CRW [16]ResNet-1867.664.870.2
JSTG [49]ResNet-1868.765.871.6
VFS [45]ResNet-5068.966.571.3
DUL [1]ResNet-1869.367.171.6
MAMP [27]ResNet-1869.768.371.2
CLTC [17]ResNet-1870.367.972.6
CLSC [31]ResNet-1870.567.473.6
SFC [13]ResNet-18 + ResNet-5071.268.374.0
LIIR [22]ResNet-1872.169.774.5
OursResNet-1872.470.574.4
OSVOS-S [25]✓VGG-1668.064.771.3
FEELVOS [37]✓Xception-6571.569.174.0
", + "bbox": [ + 510, + 567, + 890, + 752 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "rithms [25,37]. Here we select several representative videos for inference, and give the visualization results in Figure 6, our method produces tight boundaries around the object areas, and obtains more fine-grained results, especially for small objects. For example, in the first column of Figure 6, the tiny arm of the human can still be segmented, which further demonstrates the advantages of learning fine-grained features for video correspondences. However, we", + "bbox": [ + 497, + 755, + 892, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9638", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ce43baff0c7d9458c25d5e9a2c25edb606ce5502bf5bed6eb55f3b8fca109a2.jpg", + "image_caption": [ + "Figure 6: Qualitative results for video object segmentation. Given the semantic mask in the first frame, we show the propagation results on the target frame. (Zoom in for best view)" + ], + "image_footnote": [], + "bbox": [ + 80, + 122, + 467, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "find that fine-grained features may hinder object-centric feature learning since it may rely more on low-level patterns (e.g., texture, color, etc), which degrades the performance in video object segmentation to some extent. We regard it as our future work.", + "bbox": [ + 75, + 429, + 468, + 497 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 77, + 511, + 228, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We perform ablation study with point tracking on the TAP-Vid-DAVIS [7] dataset.", + "bbox": [ + 75, + 533, + 468, + 560 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Learning with synthetic videos. We study the effect of three different ways as defined in Eq. (2), Eq. (4) and Eq. (5) for learning the fine-grained features with synthetic videos. Table 4 shows the performance comparisons across the three kinds of objective functions. As indicated by the results, the loss $\\mathcal{L}_{\\mathrm{KL - v1}}$ using dirac distribution to generate the labels performs badly. We think the deterministic labels were given on synthetic videos, resulting in the learned features not being robust enough on real-world videos. Besides, we find introducing the gaussian distribution in $\\mathcal{L}_{\\mathrm{KL - v2}}$ results in performance degradation. The performance drops a lot when progressively increasing the variance, which may be attributed to the inability of gaussian distribution to approach the real probabilistic distribution since it is extremely complicated. Expectedly, the proposed soft labeling boosts up the performance from $42.6\\%$ to $55.8\\%$ when only pre-training the $\\theta_{self}$ with Eq. (8). Moreover, we also try another 2D encoder pre-trained with the contrastive loss $\\mathcal{L}_{\\mathrm{nce}}$ [11] on ImageNet [6], which has a stronger ability to capture the spatially discriminative features. The results are further improved to $57.5\\%$ , which motivates us to leverage a more powerful 2D feature extractor", + "bbox": [ + 75, + 562, + 470, + 866 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/067f9ff5f1206a77eaefaf08b2e8a74ead78a094d2eaf5f4788b4d2c91b0d13b.jpg", + "table_caption": [ + "Table 4: Ablation study for $\\mathcal{L}_{\\mathrm{KL}}$ . The $\\sigma/\\theta_{\\text{self}}$ represents the variance / encoder used in $\\mathcal{L}_{\\mathrm{KL - v2}} / \\mathcal{L}_{\\mathrm{KL - v3}}$ ." + ], + "table_footnote": [], + "table_body": "
Obj. FunctionHyper-param.TAP-Vid-DAVIS < δxavg↑
(σu, σv)θself
LKL-v1--42.6
LKL-v2(1,1)-41.9
(3,3)-33.8
(6,6)-29.7
LKL-v3-w. Lrec55.8
-w. Lnce [11]57.5
", + "bbox": [ + 532, + 153, + 858, + 250 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d758550de50b815d85743449c08ce9d93f26635ddf945e8dbae47a8f5c61b036.jpg", + "table_caption": [ + "Table 5: Ablation study for training objective functions. FT: FlyingThings [26]. YTV: YouTube-VOS [46]." + ], + "table_footnote": [], + "table_body": "
\\( {\\mathcal{L}}_{\\mathrm{{KL}}} \\)\\( {\\mathcal{L}}_{\\text{rec }} \\)\\( {\\mathcal{L}}_{\\text{adv }} \\)Training DataTAP-Vid-DAVIS < \\( {\\delta }_{avg}^{x} \\uparrow \\)
✓FT55.8
✓YTV56.4
✓FT + YTV56.7
✓✓FT + YTV59.2
✓✓✓FT + YTV59.8
", + "bbox": [ + 537, + 290, + 855, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "for obtaining the soft labels. We regard it as future work.", + "bbox": [ + 497, + 393, + 875, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different training objective functions. We examine how different objective functions impact the overall performance, which is shown in Table 5. The $\\mathcal{L}_{\\mathrm{KL}}$ , $\\mathcal{L}_{\\mathrm{rec}}$ and $\\mathcal{L}_{\\mathrm{adv}}$ denotes the losses defined in Eq. (5), Eq. (8) and Eq. (9). Surprisingly, we find the model trained on unlabeled real-world videos with $\\mathcal{L}_{\\mathrm{rec}}$ obtains a better result, which indicates better generalization of self-supervised feature learning. By leveraging both $\\mathcal{L}_{\\mathrm{KL}}$ and $\\mathcal{L}_{\\mathrm{rec}}$ with synthetic and real-world videos, the performance is further improved to $59.2\\%$ . As expected, executing $\\mathcal{L}_{\\mathrm{adv}}$ to address the domain mismatch improves performance by $0.6\\%$ . By fusing three losses, the performance reaches $59.8\\%$ . The results consistently indicate that incorporating self-supervised and adversarial training with unlabeled data exhibits a performance boost against the model only trained with synthetic data.", + "bbox": [ + 497, + 409, + 890, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 499, + 631, + 626, + 646 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we address pixel-wise video correspondences by learning fine-grained features. We propose to use not only labeled synthetic videos but also unlabeled real-world videos for feature learning. We first study how to take advantage of synthetic supervision for feature learning, and we find directly utilizing the motion vector results in degradation for the learned features. Thus, we propose soft labeling to address the issue. To improve the generalization, we introduce self-supervised reconstructive learning into the overall training and further enhance the features by leveraging adversarial training. Moreover, we propose a coarse-to-fine framework to alleviate the problem of computational efficiency. Extensive experiments on the downstream tasks validate the effectiveness of the proposed feature learning method and our efficient design.", + "bbox": [ + 497, + 659, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9639", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nikita Araslanov, Simone Schaub-Meyer, and Stefan Roth. Dense unsupervised learning for video segmentation. 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Modelling neighbor relation in joint space-time graph for video correspondence learning. In ICCV, pages 9960–9969, 2021." + ], + "bbox": [ + 78, + 125, + 467, + 789 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "9641", + "bbox": [ + 468, + 887, + 499, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/fd6b6adc-a24b-4ea2-b63f-ac1670224d69_model.json b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/fd6b6adc-a24b-4ea2-b63f-ac1670224d69_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3cdf754647e4cce4e7a2309768612e872adff3 --- /dev/null +++ b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/fd6b6adc-a24b-4ea2-b63f-ac1670224d69_model.json @@ -0,0 +1,2090 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.087 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.162, + 0.843, + 0.183 + ], + "angle": 0, + "content": "Learning Fine-Grained Features for Pixel-wise Video Correspondences" + }, + { + "type": "text", + "bbox": [ + 0.31, + 0.209, + 0.659, + 0.225 + ], + "angle": 0, + "content": "Rui Li Shenglong Zhou Dong Liu" + }, + { + "type": "text", + "bbox": [ + 0.242, + 0.226, + 0.728, + 0.241 + ], + "angle": 0, + "content": "University of Science and Technology of China, Hefei, China" + }, + { + "type": "text", + "bbox": [ + 0.239, + 0.243, + 0.732, + 0.257 + ], + "angle": 0, + "content": "{1iruid,slzhou96}@mail.ustc.edu.cn，dongeliu@ustc.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.324, + 0.26, + 0.646, + 0.272 + ], + "angle": 0, + "content": "https://github.com/qianduoduolr/FGVC" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.474, + 0.64 + ], + "angle": 0, + "content": "Video analysis tasks rely heavily on identifying the pixels from different frames that correspond to the same visual target. To tackle this problem, recent studies have advocated feature learning methods that aim to learn distinctive representations to match the pixels, especially in a self-supervised fashion. Unfortunately, these methods have difficulties for tiny or even single-pixel visual targets. Pixel-wise video correspondences were traditionally related to optical flows, which however lead to deterministic correspondences and lack robustness on real-world videos. We address the problem of learning features for establishing pixel-wise correspondences. Motivated by optical flows as well as the self-supervised feature learning, we propose to use not only labeled synthetic videos but also unlabeled real-world videos for learning fine-grained representations in a holistic framework. We adopt an adversarial learning scheme to enhance the generalization ability of the learned features. Moreover, we design a coarse-to-fine framework to pursue high computational efficiency. Our experimental results on a series of correspondence-based tasks demonstrate that the proposed method outperforms state-of-the-art rivals in both accuracy and efficiency." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.667, + 0.21, + 0.682 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.691, + 0.47, + 0.789 + ], + "angle": 0, + "content": "One of the most fundamental problems in computer vision is learning visual correspondences across space and time, which has many applications such as 3D reconstruction, physical understanding, and dynamic object modeling. Due to the factors such as viewpoint change, distractors, and deformations, this task is extremely challenging and can be roughly divided into three categories accord" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.799, + 0.471, + 0.867 + ], + "angle": 0, + "content": "This work was supported by the Natural Science Foundation of China under Grants 62022075 and 62036005, and by the Fundamental Research Funds for the Central Universities under Grant WK349000006. This work was also supported by the advanced computing resources provided by the Supercomputing Center of USTC. (Corresponding author: Dong Liu.)" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.303, + 0.895, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.447, + 0.893, + 0.498 + ], + "angle": 0, + "content": "Figure 1: We illustrate video correspondences with different granularities, including object-wise, group-wise, and pixel-wise. In this paper, we concentrate on learning fine-grained features to address the pixel-wise video correspondences." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.619 + ], + "angle": 0, + "content": "ing to the granularity: the first one is object-wise correspondences that exist between coarsely localized bounding boxes [36, 39] along the video; the second one is groupwise correspondences, indicating the mapping at group-level, and usually applied to downstream tasks like video object segmentation [5, 25]; the third one is pixel-wise correspondences, which describe the pixel-level relation between video frames with the finest granularity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.893, + 0.867 + ], + "angle": 0, + "content": "Learning dense representations from videos is one approach to finding the correspondences. Researchers have been exploring different self-supervised methods for learning generalizable representations using unlabeled videos collected in the real world [16,20,23,24,41,45]. For example, Wang et al. [41] propose using an object-level cycle-consistency across time (i.e., forward-backward tracking) as a supervision signal. Jabri et al. [16] further enhance it by combining cycles of time with the similarities between path-level representations. Inspired by contrastive learning, Xu et al. [45] try to learn spatial and temporal representation through a frame-wise contrastive loss, while Li et al. [23] propose a spatial-then-temporal pretext task to learn better spatiotemporal features. Despite obtaining promising outcomes, current research has predominantly emphasized performing object-level or patch-level similarity learning, making it difficult to accurately recognize pixel-wise differences with the learned features. As a result, there is an in" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "9632" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.127, + 0.468, + 0.154 + ], + "angle": 0, + "content": "creasing necessity for learning fine-grained representations in order to tackle this problem." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.156, + 0.468, + 0.377 + ], + "angle": 0, + "content": "At the same time, there is another line of work approaching video correspondences by deterministically predicting the displacement of each pixel, which is known as optical flow estimation. Early studies used optimization methods to estimate the motion between two frames [4]. In recent years, approaches use synthetic data with supervised learning for flow estimation [8, 26], using a coarse-to-fine pyramid framework to improve the accuracy [33]. RAFT [34] further devises an iterative optimization algorithm to come up with the result of high-resolution flow fields through iterative updates, which show a superior ability to find fine-grained correspondences. However, in real scenarios, there are often appearance variants, illumination changes, and deformations between video frames, which leads to the lack of robustness on real-world videos for the optical flow model supervised by labeled synthetic videos." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.468, + 0.6 + ], + "angle": 0, + "content": "In this paper, we explore how to learn fine-grained representations to meet the needs of pixel-wise video correspondences. To this end, we first investigate how to leverage synthetic data for fine-grained feature learning. Specifically, given a query pixel, the supervision in synthetic videos only supplies the one-to-one mapping, i.e., a motion vector, representing the deterministic correspondence of the pixel to another pixel in the next frame. Nevertheless, the pixel-wise features evolve slowly over space and time, which indicates a soft distribution of the correspondences. We find directly utilizing the synthetic supervision as hard labels results in inferior representations, and the learned features are unable to recognize the pixel-wise differences across different spatial locations and periods of time. To address the issue, we propose to use an external pre-trained 2D encoder to derive soft supervision for optimization based on the flow." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.602, + 0.468, + 0.768 + ], + "angle": 0, + "content": "Furthermore, we incorporate self-supervised feature learning on unlabeled real data in the overall training to alleviate the generalization issues in real scenes, which consists of two carefully designed components. Firstly, inspired by the temporal consistency assumption [3], we learn temporal persistent features via self-supervised reconstructive learning, where each query pixel can be reconstructed by leveraging the information in adjacent frames. Besides, given the synthetic and real data, we perform adversarial training by introducing Gradient Reverse Layer [9] with a discriminator for the learned correspondences. We observe such designs can further enhance learned fine-grained features." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.77, + 0.468, + 0.866 + ], + "angle": 0, + "content": "Though already getting impressive results, we find it takes more time to get the results of the dense matching between fine-grained features. Thus, we make another step to devise a coarse-to-fine framework to address the problem. We put the complex feature matching on the coarse-grained feature map and then get the fine-grained results through a learnable up-sampling layer. As a result, we achieve a" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.127, + 0.892, + 0.153 + ], + "angle": 0, + "content": "good balance of performance and efficiency. In summary, the main contribution of this work lies in:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.165, + 0.89, + 0.192 + ], + "angle": 0, + "content": "- We address the problem of establishing pixel-wise video correspondences via a feature learning approach." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.202, + 0.89, + 0.257 + ], + "angle": 0, + "content": "- We propose an effective method of learning fine-grained features from both synthetic and unlabeled videos, followed by a carefully designed framework to address the issue of efficiency." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.266, + 0.89, + 0.306 + ], + "angle": 0, + "content": "- We validate our method in a series of correspondence-based tasks. Experiment results indicate consistent improvement over state-of-the-art methods." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.165, + 0.89, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.319, + 0.637, + 0.333 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Representation learning for video correspondences. Recent researches center around learning dense representations without labels in a self-supervised way for video correspondences, which occurs in two distinct directions: reconstruct-based [20, 21, 23, 24, 38, 40] and cycle-consistency-based techniques [16, 41, 49]. In the works of the first type, the query pixel is reconstructed from the adjacent frames based on the temporal consistency assumption, while the works of the second type execute forward-backward tracking to reduce cycle inconsistency. Furthermore, VFS [45] proposes to learn representations through frame-wise contrastive loss. SFC [13] proposes a two-stream architecture to learn semantic and fine-grained features through two different models. Despite the progress made in learning representations for video correspondences, accurately recognizing pixel-wise distinctions over space and time remains challenging." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.797 + ], + "angle": 0, + "content": "Optical flow estimation for video correspondences. Recently, the classic optical flow estimation problem of predicting per-pixel motion between two frames has been explored using synthetic graphics data for supervised training [8, 26]. FlowNet [8] was one of the first deep learning methods to tackle end-to-end optical flow learning. This research inspired a multitude of other methods, such as FlowNet2.0 [15], DCFlow [44], SpyNet [30], PwC-Net [33], and LiteFlowNet3 [14]. Most of these methods employ cost volumes for finding pixel matching. RAFT [34] stands out from the rest due to its multi-scale correlation volumes and iterative flow refinements, whilst achieving superior performance, and is also a precursor to many successive works. However, learning a deterministic model with synthetic computer graphics data limits generalization ability and robustness on real videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Unsupervised domain adaptation with self-supervised learning. Recently, there has been a surge in approaches to reduce the distribution discrepancy between real and synthetic data by leveraging unsupervised domain adaptation [9, 19, 28, 35, 42, 48]. An effective way to" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "9633" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.125, + 0.346, + 0.138 + ], + "angle": 0, + "content": "(a) Learning with synthetic videos" + }, + { + "type": "image", + "bbox": [ + 0.141, + 0.138, + 0.829, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.347, + 0.892, + 0.424 + ], + "angle": 0, + "content": "Figure 2: Overview of the framework for fine-grained feature learning. We facilitate fine-grained feature learning by integrating self-supervised learning on unlabeled videos into supervised learning with labeled synthetic videos. For learning with synthetic data \\(\\mathcal{D}_S\\), we devise a soft labeling module to convert the hard labels indicated by the motion vectors to soft labels. To learn more generalizable features, we leverage free supervision from unlabeled videos \\(\\mathcal{D}_{\\mathcal{T}}\\) with the objective of frame reconstruction. Furthermore, an adversarial loss (along with Gradient Reverse Layer and a discriminator) is proposed to encourage domain invariant representations. The whole framework is jointly optimized in an end-to-end manner with the proposed objective functions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.474, + 0.581 + ], + "angle": 0, + "content": "realize it is through adversarial training. Recent studies execute adversarial training by learning a domain classifier (the discriminator) to distinguish the learned features from different distributions, utilizing adversarial loss to increase domain confusion. Meanwhile, self-supervised learning obtains impressive performance and shows good generalizing ability by designing different pretext tasks [11, 41, 43, 45] with unlabeled data, which motivates us to combine supervised learning and self-supervised learning to encourage consistent representations for both domains as well as improved results for downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.592, + 0.185, + 0.607 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.47, + 0.697 + ], + "angle": 0, + "content": "We address the problem of estimating the pixel-wise correspondences between a pair of video frames, which can be realized by learning fine-grained features for matching. Our goal is to learn a fine-grained feature space \\(\\phi\\) with the encoder \\(\\theta\\) by designing different learning objective functions for the probabilistic mapping." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Probabilistic mapping. Given a pair of video frames \\( I_1, I_2 \\in \\mathbb{R}^{h \\times w \\times 3} \\), for all pixels in \\( I_1 \\), we aim to predict the probabilistic mapping \\( P_{1 \\to 2} \\in \\mathbb{R}^{H \\times W \\times (2r + 1)^2} \\) and \\( P_{1 \\to 2}(\\cdot | i) \\in \\mathbb{R}^{(2r + 1)^2} \\) gives the probability that \\( i \\) is mapped to \\( j \\) in frame \\( I_2 \\) within a limited range \\( r \\), considering the nature of temporal coherence in the video. The \\( i, j \\in \\mathbb{R}^2 \\) indicate the 2D pixel location. \\( P_{1 \\to 2}(\\cdot | i) \\in \\mathbb{R}^{(2r + 1)^2} \\) thus encodes the entire discrete conditional probability distribution of where \\( i \\) is mapped in frame \\( I_2 \\). The probabilistic mapping can be achieved by calculating the feature similarities using the learned fine-grained features. More specifically, we first extract the dense features \\( F_1, F_2 \\in \\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.428, + 0.892, + 0.47 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^{H\\times W\\times C}\\). Then the discrete probabilistic map can be obtained by computing the local correlation w.r.t. each key \\(j\\) in \\(I_{2}\\) within a local window for each query \\(i\\)," + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.479, + 0.901, + 0.515 + ], + "angle": 0, + "content": "\\[\nP _ {1 \\rightarrow 2} (j | i) = \\frac {\\exp \\left(F _ {1} (i) \\cdot F _ {2} (j) / \\tau\\right)}{\\sum_ {n} \\exp \\left(F _ {1} (i) \\cdot F _ {2} (n) / \\tau\\right)}, i \\in \\{1,.., H W \\}, j, n \\in \\mathcal {K} (i), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.516, + 0.893, + 0.571 + ], + "angle": 0, + "content": "where \\(\\mathcal{K}(i)\\) is the index set in the local window with a limited range of \\(r\\) centered at \\(i\\), and \\(\\tau\\) is the temperature. The result of the probabilistic mapping is further post-processed and directly applied to various downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.587, + 0.78, + 0.602 + ], + "angle": 0, + "content": "3.1. Fine-Grained Feature Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.891, + 0.652 + ], + "angle": 0, + "content": "We design the learning objective functions for probabilistic mapping with both synthetic and real-world videos. The overview of the framework is shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Learning with synthetic videos. Labeled synthetic videos are often used as supervision for learning the optical flows in recent studies [8,34]. Given a pair of rendered video frames \\( I_1^s, I_2^s \\), the synthetic data \\( \\mathcal{D}_S \\) provides pixelwise motion vector, i.e., optical flow \\( G_{1\\rightarrow 2} \\). A valid question then emerges as how to learn features using such deterministic correspondences? Indeed, we believe the deterministic correspondences are hard to obtain for real-world videos, thus we argue the necessity to convert them into soft (probabilistic) ones. We devise the following variants:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.868 + ], + "angle": 0, + "content": "(i) Dirac distribution: As shown in Figure 3 (a), we can directly convert the motion vector to a dirac distribution \\(\\delta (\\cdot |i)\\) in order to describe the ground truth mapping. Then, the learning objective function defined as Kullback-Leibler divergence between \\(P_{1\\rightarrow 2}^{s}(\\cdot |i)\\) and \\(\\delta (\\cdot |i)\\). The \\(P_{1 - > 2}^{s}\\) stands" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "9634" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.125, + 0.462, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.233, + 0.47, + 0.271 + ], + "angle": 0, + "content": "Figure 3: Illustration of the probabilistic map. For \\( i \\) in \\( I_1^s \\), we visualize the probability value of the mapping from \\( i \\) to the locations in \\( I_2^s \\) within a limited range." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.274, + 0.468, + 0.287 + ], + "angle": 0, + "content": "for the correlation calculated by Eq. (1) with synthetic data:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.298, + 0.469, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {K L - v l}} = \\sum_ {i} D _ {K L} (\\delta (\\cdot | i) \\| P _ {1 \\rightarrow 2} ^ {s} (\\cdot | i)). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.33, + 0.469, + 0.466 + ], + "angle": 0, + "content": "(ii) Gaussian distribution: However, the feature of the query pixel \\( i \\) varies smoothly over space and time, which indicates a soft distribution of the potential location in the next frame. As shown in Figure 3 (a), the dirac distribution does not provide the feature learning with any knowledge of relative probability in the background, making it hard to learn the features with the ability to tell the fine-grained differences with synthetic videos. Thus, we devise to generate the probabilistic map with gaussian distribution, which introduces a soft distribution centered at the ground truth coordinate:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.472, + 0.469, + 0.516 + ], + "angle": 0, + "content": "\\[\n\\mathcal {N} (j | i, \\mu , \\sigma^ {2}) = \\frac {1}{\\sqrt {2 \\pi} \\sigma_ {u}} e ^ {- \\frac {\\left(u _ {j} - \\mu_ {t} ^ {u}\\right) ^ {2}}{2 \\sigma_ {u} ^ {2}}} \\cdot \\frac {1}{\\sqrt {2 \\pi} \\sigma_ {v}} e ^ {- \\frac {\\left(v _ {j} - \\mu_ {t} ^ {v}\\right) ^ {2}}{2 \\sigma_ {v} ^ {2}}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.517, + 0.469, + 0.558 + ], + "angle": 0, + "content": "where \\(\\mu = (\\mu_i^u,\\mu_i^v)\\) represents the 2D coordinate of ground truth in the \\(I_2^s\\) for pixel \\(i\\), and \\((u_{j},v_{j})\\) indicates the 2D coordinate of \\(j\\). Then the loss can be devised as:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.577, + 0.469, + 0.605 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {K L - v 2}} = \\sum_ {i} D _ {K L} \\left(\\mathcal {N} (\\cdot | i, \\mu , \\sigma^ {2}) \\| P _ {1 \\rightarrow 2} (\\cdot | i)\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.611, + 0.469, + 0.833 + ], + "angle": 0, + "content": "(iii) Soft-labeling: The gaussian prior only considers the euclidean distance of coordinates, which shows limited capability of modeling the complicated distributions. We believe the synthetic supervision already provides valuable temporal cues (\\(i\\) in \\(I_1^s\\) move to \\(j\\) in \\(I_2^s\\)), and the soft distribution over space can be approached by computing the self-similarities for \\(j\\) using the pre-trained 2D visual encoder \\(\\theta_{self}\\) which can produce spatially-discriminative features. As shown in Figure 3 (c), for the \\(i\\) in \\(I_1^s\\) that moves to \\(j\\), we get the feature of the query \\(i\\) (denoted as \\(\\overline{F}_q\\)) at the location \\(j\\) in \\(\\overline{F}_2\\) (\\(\\overline{F}_2\\) is the feature map of \\(I_2^s\\) computed by \\(\\theta_{self}\\)). Then we can compute the feature similarities \\(S_{1\\rightarrow 2}(\\cdot |i)\\) between \\(\\overline{F}_q\\) and \\(\\{\\overline{F}_2(k)|k\\in \\mathcal{K}(i)\\}\\), where \\(\\mathcal{K}(i)\\) is the index set in the local window centered at \\(i\\). The \\(S_{1\\rightarrow 2}(\\cdot |i)\\) are further normalized (by softmax) to obtain the discrete probability distribution \\(P_{1\\rightarrow 2}(\\cdot |i)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.841, + 0.469, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {K L - v 3}} = \\sum_ {i} D _ {K L} \\left(P _ {1 \\rightarrow 2} (\\cdot | i) \\| P _ {1 \\rightarrow 2} ^ {s} (\\cdot | i)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.892, + 0.209 + ], + "angle": 0, + "content": "In Table 4, we find soft labeling works well when only pre-training \\(\\theta_{\\text{self}}\\) on synthetic data \\(\\mathcal{D}_{\\mathcal{S}}\\) with \\(\\mathcal{L}_{\\mathrm{rec}}\\) (Eq. (8)), and leveraging more strong 2D encoder would contribute to better performance. The comparisons between different loss functions will be discussed in the experiments, and the \\(\\mathcal{L}_{\\mathrm{KL - v3}}\\) is used as the default loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.211, + 0.892, + 0.445 + ], + "angle": 0, + "content": "Learning with unlabeled videos. Meanwhile, we observe in real scenarios, there are apparent differences with synthetic videos in appearance variants, illumination changes and deformations, leading to notable changes in the distribution, where the learned features on synthetic videos show unsatisfied generalization ability. Inspired by recent studies [16, 41], we try to improve the learned fine-grained features by introducing self-supervised feature learning into the framework. As observed in the bottom of Figure 1, the pixel repetition encourages us to learn the fine-grained features by reconstructive learning, where each pixel in the \\( I_1^t \\) can be reconstructed by leveraging the information of \\( I_2^t \\) with a limited range. To achieve this, the video frames \\( I_1^t, I_2^t \\) are firstly projected into pixel embeddings \\( F_1^t, F_2^t \\) by the encoder \\( \\theta \\). For each query \\( i \\) in \\( I_1^t \\), we calculate the probabilistic map \\( P_{1\\rightarrow 2}^t \\) with Eq. (1). Then the query \\( i \\) in \\( I_1^t \\) can be reconstructed by a weighted sum of pixels in \\( \\mathcal{K}(i) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.589, + 0.456, + 0.891, + 0.485 + ], + "angle": 0, + "content": "\\[\nI _ {1} ^ {\\text {r e c}} (i) = \\sum_ {j \\in \\mathcal {K} (i)} P _ {1 \\rightarrow 2} ^ {t} (j | i) I _ {2} ^ {t} (j). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.495, + 0.891, + 0.549 + ], + "angle": 0, + "content": "Then the reconstruction loss for self-supervised training is defined as \\( L_{1} \\) distance between \\( I_1^{rec} \\) and \\( I_1^t \\). Training with such self-supervision leads to temporal persistent features that generalize well in real scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.647 + ], + "angle": 0, + "content": "However, the pixel repetition does not hold for pixels that become occluded. Thus, we exclude occluded pixels from the reconstruction loss to avoid learning incorrect features. We follow the forward-backward consistency assumption to detect the occluded pixels. which is defined in Eq. (7) as the occlusion flag \\(O_{1\\rightarrow 2}\\) to be 1 whenever the constraint is violated, and 0 otherwise:" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.654, + 0.891, + 0.693 + ], + "angle": 0, + "content": "\\[\nO _ {1 \\rightarrow 2} (i) = \\mathbb {1} \\left(\\underset {i} {\\arg \\max } P _ {2 \\rightarrow 1} ^ {t} \\left(i \\mid \\underset {j} {\\arg \\max } P _ {1 \\rightarrow 2} ^ {t} (j \\mid i)\\right) = i\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.694, + 0.878, + 0.708 + ], + "angle": 0, + "content": "The loss for reconstructive learning is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.719, + 0.891, + 0.744 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e c}} = \\sum_ {i} O _ {1 \\rightarrow 2} (i) \\cdot \\left\\| I _ {1} ^ {\\text {r e c}} (i) - I _ {1} ^ {t} (i) \\right\\| _ {1}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Adversarial training. We further improve the fine-grained features by leveraging the technique in recent works of unsupervised domain adaptation, which aims to bridge the gap caused by the domain shift between the synthetic videos \\(\\mathcal{D}_S\\) and real videos \\(\\mathcal{D}_{\\mathcal{T}}\\) via adversarial training. An effective way to approach this problem consists in introducing the network a Gradient Reversal Layer (GRL). We additionally train a discriminator \\(\\theta_{D}\\) to identify whether the" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.501, + 0.898 + ], + "angle": 0, + "content": "9635" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.124, + 0.473, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.191, + 0.47, + 0.231 + ], + "angle": 0, + "content": "Figure 4: Illustration of the coarse-to-fine framework for efficient probabilistic mapping. We first obtain coarse-grained matching and then upsample it to get the fine-grained result." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.234, + 0.438, + 0.248 + ], + "angle": 0, + "content": "probabilistic map comes from synthetic or real videos:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.255, + 0.469, + 0.282 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {a d v}} = \\mathbb {E} _ {P ^ {t} \\in P _ {\\mathcal {T}}} [ \\log (D (P ^ {t})) ] + \\mathbb {E} _ {P ^ {s} \\in P _ {\\mathcal {S}}} [ \\log (1 - D (P ^ {s})) ], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.283, + 0.469, + 0.325 + ], + "angle": 0, + "content": "and then we reverse the gradient direction during the backward pass in back-propagation when updating the parameters of the encoder \\(\\theta\\) with \\(\\mathcal{L}_{\\mathrm{adv}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.333, + 0.469, + 0.36 + ], + "angle": 0, + "content": "\\[\n\\theta \\leftarrow \\theta + \\lambda \\frac {\\partial \\mathcal {L} _ {\\mathrm {a d v}}}{\\partial \\theta}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.469, + 0.405 + ], + "angle": 0, + "content": "The GRL allows to train the discriminator and the encoder at the same time, and the adversarial training helps to learn domain invariant patterns." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.406, + 0.469, + 0.462 + ], + "angle": 0, + "content": "Overall training objective. The overall training objective for learning fine-grained features is formulated as a multi-task loss, which is written as \\(\\mathcal{L} = \\mathcal{L}_{\\mathrm{KL}} + \\mathcal{L}_{\\mathrm{rec}} + \\mathcal{L}_{\\mathrm{adv}}\\) where we empirically treat each loss equally." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.469, + 0.458, + 0.485 + ], + "angle": 0, + "content": "3.2. Efficient Fine-grained Probabilistic Mapping" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.49, + 0.469, + 0.601 + ], + "angle": 0, + "content": "To get the fine-grained probabilistic map, i.e., \\(P_{1\\rightarrow 2}\\in \\mathbb{R}^{H\\times W\\times (2r + 1)^2}\\), we need to compute the similarities w.r.t. all key pixels in the local window centered at every query pixel, which is computationally costly. In this section, we devise a coarse-to-fine framework. The overview of the framework can be found in Figure 4, where we first compute the correlation at coarse-grained features and then up-sample it to get fine-grained probabilistic maps." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.602, + 0.469, + 0.699 + ], + "angle": 0, + "content": "Self-attention and Cross-attention Layers. More specifically, we first extract the coarse feature maps \\(F_{1}^{\\downarrow}, F_{2}^{\\downarrow} \\in \\mathbb{R}^{H/4 \\times W/4 \\times C}\\), and we further enhance the coarse features by introducing the self-attention and cross-attention layers with positional encoding. Then, we obtain the coarse-grained probabilistic map \\(P_{1 \\rightarrow 2} \\downarrow \\in \\mathbb{R}^{H/4 \\times W/4 \\times (2r\\downarrow + 1)^{2}}\\) by Eq (1)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.7, + 0.469, + 0.756 + ], + "angle": 0, + "content": "Up-sampling. We devise an up-sampling layer to obtain fine-grained probabilistic map \\(P_{1\\rightarrow 2}\\in \\mathbb{R}^{H\\times W\\times (2r + 1)^2}\\) which can be simply done by leveraging pixel-shuffle or convolution layer with bilinear interpolation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.469, + 0.867 + ], + "angle": 0, + "content": "More details of the architecture are included in the supplementary material. We train the coarse-to-fine framework in a distillation manner on \\(\\mathcal{D}_{\\mathcal{T}}\\), with the same objective function as \\(\\mathcal{L}_{\\mathrm{KL}}\\). The supervisions for \\(P_{1\\rightarrow 2}\\) are obtained by computing the probabilistic map using pre-trained encoder in Sec. 3.1. Without losing much performance, we find such a design helps to get rid of the complicated fine-grained feature matching and exhibit higher efficiency." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.125, + 0.632, + 0.14 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.892, + 0.221 + ], + "angle": 0, + "content": "We verify the effectiveness of our method in a series of correspondence-based tasks. We will first introduce implementation and evaluation details, and report the performance comparison with baselines. Finally, we perform detailed ablation studies for each component of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.24, + 0.716, + 0.255 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.264, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Backbone. We exploit the encoder \\(\\theta\\) with ResNet-18 [12]. We reduce the stride up to layer \\(\\mathrm{res}_4\\) to get features at \\(1/2\\) of the original image dimension for training. In our coarse-to-fine framework, we increase the stride of the encoder to 8 for coarse-grained feature matching." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.893, + 0.629 + ], + "angle": 0, + "content": "Training details. The training is conducted on the train set of synthetic dataset FlyingThings [26] and YouTube-VOS [46] collected in real-world. The FlyingThings/YouTube-VOS contains \\(40\\mathrm{k} / 3.5\\mathrm{k}\\) videos for training. For both datasets, we sample pair of frames which are resized into \\(256\\times 256\\) and converted to Lab color space with channel-wise dropout as the information bottleneck [20]. The local range \\(r\\) in the probabilistic map is set to \\(24 / 6\\) for the fine-grained features \\((\\frac{h}{2}\\times \\frac{w}{2}\\) (stride=2)) or coarse-grained features \\((\\frac{h}{8}\\times \\frac{w}{8}\\) (stride=8)). We first train an encoder using reconstruction loss (Eq. (8)) with a batchsize of 32 for 30 epochs on FlyingThings [26], which is further utilized as \\(\\theta_{self}\\) in soft labeling. Then the final model \\(\\theta\\) is jointly trained for 30 epochs with proposed three losses, with a batchsize of 16 for each dataset. When training with synthetic optical flow, we filter out the points that are out of the local range or occluded by forward-backward checking. The \\(\\tau\\) is set to 1. We use Adam as the optimizer, and the initial learning rate is set to 1e-3 with a cosine (half-period) learning rate schedule for each stage. We include more training details in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Evaluation. An important problem is how to evaluate the quality of the learned fine-grained features for pixel-wise video correspondences. Following the previous works [16,41,45], without any fine-tuning, we directly leverage the pre-trained encoder \\(\\theta\\) to extract features \\(F_{i}, F_{j}\\) with a spatial resolution of \\(\\frac{h}{s} \\times \\frac{w}{s}\\) (the \\(s\\) represents the stride of the encoder) for the pair of frames \\(I_{i}, I_{j}\\), which are later used to compute the probabilistic map \\(P_{i \\rightarrow j}\\) by Eq (1). Based on the probabilistic map \\(P_{i \\rightarrow j}\\), we follow the recurrent inference strategy inference strategies of recent studies [16,41,45] to propagate the target points or semantic labels of the first frame, as well as previous predictions, to the current frame \\(I_{t}\\). We evaluate the point tracking on three popular benchmarks including BADJA [2], JHMDB [18], TAP-Vid-DAVIS [7] and TAP-Vid-Kinetics [7], and the evaluation of video object segmentation is conducted on the widely used dataset DAVIS-2017 [29]." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "9636" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.124, + 0.894, + 0.166 + ], + "angle": 0, + "content": "Table 1: Quantitative results for point tracking on different datasets. The frame per second (FPS) results of getting pixelwise correspondences between a pair of video frames are measured on a single GTX-3090 at the resolution of \\(480 \\times 640\\). The * indicates our coarse-to-fine framework. The - indicates the unavailable result due to the unavailable pre-trained model." + }, + { + "type": "table", + "bbox": [ + 0.168, + 0.171, + 0.807, + 0.377 + ], + "angle": 0, + "content": "
MethodBackboneStrideFPSBADJAJHMDBTAP-DAVISTAP-Kinetics
PCK@0.1↑PCK@0.1↑<δxavg-p↑<δxavg-p↑
TimeCycle [41]ResNet-5082841.157.327.128.6
UVC [24]ResNet-18814248.258.629.025.2
CRW [16]ResNet-18814250.959.332.525.4
VFS [45]ResNet-18814251.960.531.928.8
CLSC [31]ResNet-188142-61.7--
SFC [13]ResNet-18 + ResNet-5082753.861.937.231.1
MAST [20]ResNet-1843355.762.442.533.2
LIIR [22]ResNet-18433-60.7--
Ours*ResNet-1883456.864.648.043.8
ImageNet Pre. [12]ResNet-182857.561.551.344.5
UVC [24]ResNet-182856.765.152.741.8
CRW [16]ResNet-182855.961.443.237.1
VFS [45]ResNet-182858.161.051.444.9
SFC [13]ResNet-182861.565.953.943.6
MAST [20]ResNet-182863.063.153.842.7
OursResNet-182867.266.859.848.8
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.386, + 0.317, + 0.402 + ], + "angle": 0, + "content": "4.2. Results for Point Tracking" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.471, + 0.519 + ], + "angle": 0, + "content": "We firstly make comparisons for point tracking since it requires the finest granularity of the learned features. The main comparators of our method are the works aim to learn good representations for matching, e.g., TimeCycle [41], UVC [24], CRW [16], VFS [45], SFC [13], and MAST [20]. We also include the model pre-trained on ImageNet [6] with human annotations. These works share a similar evaluation protocol as we mentioned in 4.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.797 + ], + "angle": 0, + "content": "While previous works test the pixel-wise correspondences on JHMDB [18] that only provides the human keypoint annotations. We additionally include BADJA [2], TAP-Vid-DAVIS [7] and TAP-Vid-Kinetics [7]. We propagate the points of the first frame to other frames and evaluate the results using the annotations of each dataset. We notice some works are trained and evaluated with the coarse-grained features (e.g., the features at 1/8 of the original image dimension). For these methods, we use our coarse-to-fine framework that also executes coarse-grained feature matching for comparisons. Meanwhile, for better comparisons, we follow the studies in [16,45] to further reduce the stride \\(s\\) of the encoder to 2, in order to get more fine-grained results for CRW, VFS, SFC and MAST. We also provide the FPS of computing the pixel-wise correspondences between two frames for feature-matching-based methods, which can be done by first taking the index of the maximum value in \\(P_{1\\rightarrow 2}(\\cdot |i)\\) for each \\(i\\) and then applying up-sampling to get full-resolution results. More details about the evaluation are included in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Results on BADJA/JHMDB. We adopt the standard PCK [47] of all visible points (not compute PCK for each video then take average) as the evaluation metric. Each point is considered correct if it is within a distance of \\(0.1\\sqrt{A}\\) from the ground truth, where \\(A\\) is the distance be" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.386, + 0.892, + 0.526 + ], + "angle": 0, + "content": "tween keypoints (for JHMDB) or the area of the ground-truth segmentation mask on the frame (for BADJA). In Table 1, our method achieves \\(67.2\\% / 66.8\\%\\), surpassing all state-of-the-art methods. Besides, our method with the coarse-to-fine design still makes the absolute improvements by \\(1.1\\%\\) and \\(2.2\\%\\) compared with MAST, and shows better efficiency compared with SFC [13] that uses the two-stream network to find the correspondences. More remarkably, our efficient framework even surpasses part of the methods using more fine-grained features for inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.893, + 0.697 + ], + "angle": 0, + "content": "Results on TAP-Vid. TAP-Vid is a newly developed benchmark composed of long-term videos in real-world with accurate human annotations of point tracks. We test on the whole set of TAP-Vid-DAVIS and the test set of TAP-Vid-Kinetics. We adopt the setting of \"first fashion\" in [7], which tracks only into the future. The average position accuracy over all visible points \\((< \\delta_{avg-p}^{x})\\) is adopted as the metric. The learned fine-grained features obtain \\(59.8\\% / 48.8\\%\\) on TAP-Vid-DAVIS/TAP-Vid-Kinetics, leading apparent improvements over state-of-the-arts by \\(5.9\\% / 3.9\\%\\). Moreover, the proposed coarse-to-fine framework gets \\(48.0\\% / 43.8\\%\\), surpassing MAST by \\(5.5\\% / 10.6\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Comparisons with task-specific methods. Besides, we notice there are some recent methods specifically designed for point tracking, like RAFT [34], PIPs [10], TAPNet [7], and Thin-Slicing Net [32] even trained with human annotations. Here we also present the performance comparisons with them in Table 2. It's worth noting that, to align the evaluation with these methods, except JHMDB, we first compute the \\(< \\delta_{avg-p}^{x}\\) or PCK for each video to obtain video-level results, and the final results are obtained by taking the average over all videos. Without any specific designs, our performance even surpasses these methods by \\(7.4\\% / 7.5\\% / 0.2\\%\\) on BADJA/TAP-DAVIS/TAP-Kinetics." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "9637" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.125, + 0.263, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.455, + 0.258, + 0.468 + ], + "angle": 0, + "content": "\\(1^{st}\\) frame with target" + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.125, + 0.409, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.456, + 0.349, + 0.467 + ], + "angle": 0, + "content": "VFS" + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.125, + 0.555, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.464, + 0.456, + 0.502, + 0.467 + ], + "angle": 0, + "content": "MAST" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.125, + 0.701, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.612, + 0.456, + 0.645, + 0.467 + ], + "angle": 0, + "content": "RAFT" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.125, + 0.847, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.759, + 0.456, + 0.79, + 0.467 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.471, + 0.893, + 0.51 + ], + "angle": 0, + "content": "Figure 5: Qualitative results for point tracking. Given the target pixel in the first frame, we visualize the estimated trajectory with a pink-to-yellow colormap (pink/yellow indicates the start/end of the video clip). We visualize sparse ground-truth labels with cyan cross marks. Please refer to the video in the supplementary for better animations. (Zoom in for best view)" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.561 + ], + "angle": 0, + "content": "Table 2: Comparisons with methods specifically designed for point tracking. “‡” means we align the evaluation protocol with each method for fair comparisons." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.565, + 0.469, + 0.643 + ], + "angle": 0, + "content": "
MethodBADJAJHMDBTAP-DAVISTAP-Kinetics
PCK@0.2↑PCK@0.1↑<δxavg↑<δxavg↑
RAFT [34]45.666.442.144.3
PIPs [10]62.3-55.348.2
TAPNet [7]-62.348.654.4
Thin-Slicing Net [32]-68.7--
Ours‡69.766.862.854.6
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.653, + 0.47, + 0.75 + ], + "angle": 0, + "content": "Figure 5 shows some visualization results of the point tracking on TAP-Vid-DAVIS. Given the target in the first frame, we visualize the estimated trajectory with a pink-to-yellow map. Compared with VFS, MAST and RAFT, our approach can output more smooth and accurate trajectories close to the sparse visualized ground truth, even facing dramatic appearance changes and deformation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.761, + 0.411, + 0.777 + ], + "angle": 0, + "content": "4.3. Results for Video Object Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Next, we evaluate methods with semi-supervised video object segmentation. We use the mean of region similarity \\(\\mathcal{I}_m\\), mean of contour accuracy \\(\\mathcal{F}_m\\) and their average \\(\\mathcal{J} \\& \\mathcal{F}_m\\) as the evaluation metrics. In Table 3, our method still leads the performance. More remarkably, our method even outperforms some task-specific fully-supervised algo" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.519, + 0.892, + 0.561 + ], + "angle": 0, + "content": "Table 3: Quantitative results for video object segmentation on \\(\\mathbf{DAVIS}_{17}\\) [29]. \"Sup.\" means using human annotations for training." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.568, + 0.892, + 0.753 + ], + "angle": 0, + "content": "
MethodSup.BackboneDAVIS17
J&Fm↑Jm↑Fm↑
TimeCycle [41]ResNet-5040.741.939.4
UVC [24]ResNet-1859.557.761.3
MAST [20]ResNet-1865.563.367.6
CRW [16]ResNet-1867.664.870.2
JSTG [49]ResNet-1868.765.871.6
VFS [45]ResNet-5068.966.571.3
DUL [1]ResNet-1869.367.171.6
MAMP [27]ResNet-1869.768.371.2
CLTC [17]ResNet-1870.367.972.6
CLSC [31]ResNet-1870.567.473.6
SFC [13]ResNet-18 + ResNet-5071.268.374.0
LIIR [22]ResNet-1872.169.774.5
OursResNet-1872.470.574.4
OSVOS-S [25]✓VGG-1668.064.771.3
FEELVOS [37]✓Xception-6571.569.174.0
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.893, + 0.868 + ], + "angle": 0, + "content": "rithms [25,37]. Here we select several representative videos for inference, and give the visualization results in Figure 6, our method produces tight boundaries around the object areas, and obtains more fine-grained results, especially for small objects. For example, in the first column of Figure 6, the tiny arm of the human can still be segmented, which further demonstrates the advantages of learning fine-grained features for video correspondences. However, we" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "9638" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.123, + 0.468, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.379, + 0.47, + 0.419 + ], + "angle": 0, + "content": "Figure 6: Qualitative results for video object segmentation. Given the semantic mask in the first frame, we show the propagation results on the target frame. (Zoom in for best view)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.43, + 0.47, + 0.498 + ], + "angle": 0, + "content": "find that fine-grained features may hinder object-centric feature learning since it may rely more on low-level patterns (e.g., texture, color, etc), which degrades the performance in video object segmentation to some extent. We regard it as our future work." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.512, + 0.23, + 0.527 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.534, + 0.47, + 0.561 + ], + "angle": 0, + "content": "We perform ablation study with point tracking on the TAP-Vid-DAVIS [7] dataset." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.563, + 0.471, + 0.867 + ], + "angle": 0, + "content": "Learning with synthetic videos. We study the effect of three different ways as defined in Eq. (2), Eq. (4) and Eq. (5) for learning the fine-grained features with synthetic videos. Table 4 shows the performance comparisons across the three kinds of objective functions. As indicated by the results, the loss \\(\\mathcal{L}_{\\mathrm{KL - v1}}\\) using dirac distribution to generate the labels performs badly. We think the deterministic labels were given on synthetic videos, resulting in the learned features not being robust enough on real-world videos. Besides, we find introducing the gaussian distribution in \\(\\mathcal{L}_{\\mathrm{KL - v2}}\\) results in performance degradation. The performance drops a lot when progressively increasing the variance, which may be attributed to the inability of gaussian distribution to approach the real probabilistic distribution since it is extremely complicated. Expectedly, the proposed soft labeling boosts up the performance from \\(42.6\\%\\) to \\(55.8\\%\\) when only pre-training the \\(\\theta_{self}\\) with Eq. (8). Moreover, we also try another 2D encoder pre-trained with the contrastive loss \\(\\mathcal{L}_{\\mathrm{nce}}\\) [11] on ImageNet [6], which has a stronger ability to capture the spatially discriminative features. The results are further improved to \\(57.5\\%\\), which motivates us to leverage a more powerful 2D feature extractor" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.124, + 0.892, + 0.15 + ], + "angle": 0, + "content": "Table 4: Ablation study for \\(\\mathcal{L}_{\\mathrm{KL}}\\). The \\(\\sigma/\\theta_{\\text{self}}\\) represents the variance / encoder used in \\(\\mathcal{L}_{\\mathrm{KL - v2}} / \\mathcal{L}_{\\mathrm{KL - v3}}\\)." + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.154, + 0.86, + 0.251 + ], + "angle": 0, + "content": "
Obj. FunctionHyper-param.TAP-Vid-DAVIS < δxavg↑
(σu, σv)θself
LKL-v1--42.6
LKL-v2(1,1)-41.9
(3,3)-33.8
(6,6)-29.7
LKL-v3-w. Lrec55.8
-w. Lnce [11]57.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.262, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Table 5: Ablation study for training objective functions. FT: FlyingThings [26]. YTV: YouTube-VOS [46]." + }, + { + "type": "table", + "bbox": [ + 0.538, + 0.292, + 0.857, + 0.384 + ], + "angle": 0, + "content": "
\\( {\\mathcal{L}}_{\\mathrm{{KL}}} \\)\\( {\\mathcal{L}}_{\\text{rec }} \\)\\( {\\mathcal{L}}_{\\text{adv }} \\)Training DataTAP-Vid-DAVIS < \\( {\\delta }_{avg}^{x} \\uparrow \\)
✓FT55.8
✓YTV56.4
✓FT + YTV56.7
✓✓FT + YTV59.2
✓✓✓FT + YTV59.8
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.394, + 0.876, + 0.408 + ], + "angle": 0, + "content": "for obtaining the soft labels. We regard it as future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.619 + ], + "angle": 0, + "content": "Different training objective functions. We examine how different objective functions impact the overall performance, which is shown in Table 5. The \\(\\mathcal{L}_{\\mathrm{KL}}\\), \\(\\mathcal{L}_{\\mathrm{rec}}\\) and \\(\\mathcal{L}_{\\mathrm{adv}}\\) denotes the losses defined in Eq. (5), Eq. (8) and Eq. (9). Surprisingly, we find the model trained on unlabeled real-world videos with \\(\\mathcal{L}_{\\mathrm{rec}}\\) obtains a better result, which indicates better generalization of self-supervised feature learning. By leveraging both \\(\\mathcal{L}_{\\mathrm{KL}}\\) and \\(\\mathcal{L}_{\\mathrm{rec}}\\) with synthetic and real-world videos, the performance is further improved to \\(59.2\\%\\). As expected, executing \\(\\mathcal{L}_{\\mathrm{adv}}\\) to address the domain mismatch improves performance by \\(0.6\\%\\). By fusing three losses, the performance reaches \\(59.8\\%\\). The results consistently indicate that incorporating self-supervised and adversarial training with unlabeled data exhibits a performance boost against the model only trained with synthetic data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.628, + 0.647 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.867 + ], + "angle": 0, + "content": "In this paper, we address pixel-wise video correspondences by learning fine-grained features. We propose to use not only labeled synthetic videos but also unlabeled real-world videos for feature learning. We first study how to take advantage of synthetic supervision for feature learning, and we find directly utilizing the motion vector results in degradation for the learned features. Thus, we propose soft labeling to address the issue. To improve the generalization, we introduce self-supervised reconstructive learning into the overall training and further enhance the features by leveraging adversarial training. Moreover, we propose a coarse-to-fine framework to alleviate the problem of computational efficiency. Extensive experiments on the downstream tasks validate the effectiveness of the proposed feature learning method and our efficient design." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "9639" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.173, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.469, + 0.186 + ], + "angle": 0, + "content": "[1] Nikita Araslanov, Simone Schaub-Meyer, and Stefan Roth. Dense unsupervised learning for video segmentation. In NeurIPS, pages 25308-25319, 2021." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.469, + 0.236 + ], + "angle": 0, + "content": "[2] Benjamin Biggs, Thomas Roddick, Andrew Fitzgibbon, and Roberto Cipolla. Creatures great and small: Recovering the shape and motion of animals from video. 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In ICCV, pages 9960–9969, 2021." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.127, + 0.468, + 0.79 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.888, + 0.5, + 0.898 + ], + "angle": 0, + "content": "9641" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/fd6b6adc-a24b-4ea2-b63f-ac1670224d69_origin.pdf b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/fd6b6adc-a24b-4ea2-b63f-ac1670224d69_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..36a08640fb78a02a3e5cdc63000344919bdcfddb --- /dev/null +++ b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/fd6b6adc-a24b-4ea2-b63f-ac1670224d69_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4595aaa8e749dc18335ab2972fb287a1a34ab4314d3d14856232c74fabf54f6d +size 3430528 diff --git a/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/full.md b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/full.md new file mode 100644 index 0000000000000000000000000000000000000000..758cf595c2be2df6c0dfadf99ad57308bdbba43b --- /dev/null +++ b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/full.md @@ -0,0 +1,302 @@ +# Learning Fine-Grained Features for Pixel-wise Video Correspondences + +Rui Li Shenglong Zhou Dong Liu + +University of Science and Technology of China, Hefei, China + +{1iruid,slzhou96}@mail.ustc.edu.cn，dongeliu@ustc.edu.cn + +https://github.com/qianduoduolr/FGVC + +# Abstract + +Video analysis tasks rely heavily on identifying the pixels from different frames that correspond to the same visual target. To tackle this problem, recent studies have advocated feature learning methods that aim to learn distinctive representations to match the pixels, especially in a self-supervised fashion. Unfortunately, these methods have difficulties for tiny or even single-pixel visual targets. Pixel-wise video correspondences were traditionally related to optical flows, which however lead to deterministic correspondences and lack robustness on real-world videos. We address the problem of learning features for establishing pixel-wise correspondences. Motivated by optical flows as well as the self-supervised feature learning, we propose to use not only labeled synthetic videos but also unlabeled real-world videos for learning fine-grained representations in a holistic framework. We adopt an adversarial learning scheme to enhance the generalization ability of the learned features. Moreover, we design a coarse-to-fine framework to pursue high computational efficiency. Our experimental results on a series of correspondence-based tasks demonstrate that the proposed method outperforms state-of-the-art rivals in both accuracy and efficiency. + +# 1. Introduction + +One of the most fundamental problems in computer vision is learning visual correspondences across space and time, which has many applications such as 3D reconstruction, physical understanding, and dynamic object modeling. Due to the factors such as viewpoint change, distractors, and deformations, this task is extremely challenging and can be roughly divided into three categories accord + +This work was supported by the Natural Science Foundation of China under Grants 62022075 and 62036005, and by the Fundamental Research Funds for the Central Universities under Grant WK349000006. This work was also supported by the advanced computing resources provided by the Supercomputing Center of USTC. (Corresponding author: Dong Liu.) + +![](images/e46fc9c6515f46f39d67c68a14c5f995b5c8bb7bd968d9b1d6dc2d144cd009da.jpg) +Figure 1: We illustrate video correspondences with different granularities, including object-wise, group-wise, and pixel-wise. In this paper, we concentrate on learning fine-grained features to address the pixel-wise video correspondences. + +ing to the granularity: the first one is object-wise correspondences that exist between coarsely localized bounding boxes [36, 39] along the video; the second one is groupwise correspondences, indicating the mapping at group-level, and usually applied to downstream tasks like video object segmentation [5, 25]; the third one is pixel-wise correspondences, which describe the pixel-level relation between video frames with the finest granularity. + +Learning dense representations from videos is one approach to finding the correspondences. Researchers have been exploring different self-supervised methods for learning generalizable representations using unlabeled videos collected in the real world [16,20,23,24,41,45]. For example, Wang et al. [41] propose using an object-level cycle-consistency across time (i.e., forward-backward tracking) as a supervision signal. Jabri et al. [16] further enhance it by combining cycles of time with the similarities between path-level representations. Inspired by contrastive learning, Xu et al. [45] try to learn spatial and temporal representation through a frame-wise contrastive loss, while Li et al. [23] propose a spatial-then-temporal pretext task to learn better spatiotemporal features. Despite obtaining promising outcomes, current research has predominantly emphasized performing object-level or patch-level similarity learning, making it difficult to accurately recognize pixel-wise differences with the learned features. As a result, there is an in + +creasing necessity for learning fine-grained representations in order to tackle this problem. + +At the same time, there is another line of work approaching video correspondences by deterministically predicting the displacement of each pixel, which is known as optical flow estimation. Early studies used optimization methods to estimate the motion between two frames [4]. In recent years, approaches use synthetic data with supervised learning for flow estimation [8, 26], using a coarse-to-fine pyramid framework to improve the accuracy [33]. RAFT [34] further devises an iterative optimization algorithm to come up with the result of high-resolution flow fields through iterative updates, which show a superior ability to find fine-grained correspondences. However, in real scenarios, there are often appearance variants, illumination changes, and deformations between video frames, which leads to the lack of robustness on real-world videos for the optical flow model supervised by labeled synthetic videos. + +In this paper, we explore how to learn fine-grained representations to meet the needs of pixel-wise video correspondences. To this end, we first investigate how to leverage synthetic data for fine-grained feature learning. Specifically, given a query pixel, the supervision in synthetic videos only supplies the one-to-one mapping, i.e., a motion vector, representing the deterministic correspondence of the pixel to another pixel in the next frame. Nevertheless, the pixel-wise features evolve slowly over space and time, which indicates a soft distribution of the correspondences. We find directly utilizing the synthetic supervision as hard labels results in inferior representations, and the learned features are unable to recognize the pixel-wise differences across different spatial locations and periods of time. To address the issue, we propose to use an external pre-trained 2D encoder to derive soft supervision for optimization based on the flow. + +Furthermore, we incorporate self-supervised feature learning on unlabeled real data in the overall training to alleviate the generalization issues in real scenes, which consists of two carefully designed components. Firstly, inspired by the temporal consistency assumption [3], we learn temporal persistent features via self-supervised reconstructive learning, where each query pixel can be reconstructed by leveraging the information in adjacent frames. Besides, given the synthetic and real data, we perform adversarial training by introducing Gradient Reverse Layer [9] with a discriminator for the learned correspondences. We observe such designs can further enhance learned fine-grained features. + +Though already getting impressive results, we find it takes more time to get the results of the dense matching between fine-grained features. Thus, we make another step to devise a coarse-to-fine framework to address the problem. We put the complex feature matching on the coarse-grained feature map and then get the fine-grained results through a learnable up-sampling layer. As a result, we achieve a + +good balance of performance and efficiency. In summary, the main contribution of this work lies in: + +- We address the problem of establishing pixel-wise video correspondences via a feature learning approach. +- We propose an effective method of learning fine-grained features from both synthetic and unlabeled videos, followed by a carefully designed framework to address the issue of efficiency. +- We validate our method in a series of correspondence-based tasks. Experiment results indicate consistent improvement over state-of-the-art methods. + +# 2. Related work + +Representation learning for video correspondences. Recent researches center around learning dense representations without labels in a self-supervised way for video correspondences, which occurs in two distinct directions: reconstruct-based [20, 21, 23, 24, 38, 40] and cycle-consistency-based techniques [16, 41, 49]. In the works of the first type, the query pixel is reconstructed from the adjacent frames based on the temporal consistency assumption, while the works of the second type execute forward-backward tracking to reduce cycle inconsistency. Furthermore, VFS [45] proposes to learn representations through frame-wise contrastive loss. SFC [13] proposes a two-stream architecture to learn semantic and fine-grained features through two different models. Despite the progress made in learning representations for video correspondences, accurately recognizing pixel-wise distinctions over space and time remains challenging. + +Optical flow estimation for video correspondences. Recently, the classic optical flow estimation problem of predicting per-pixel motion between two frames has been explored using synthetic graphics data for supervised training [8, 26]. FlowNet [8] was one of the first deep learning methods to tackle end-to-end optical flow learning. This research inspired a multitude of other methods, such as FlowNet2.0 [15], DCFlow [44], SpyNet [30], PwC-Net [33], and LiteFlowNet3 [14]. Most of these methods employ cost volumes for finding pixel matching. RAFT [34] stands out from the rest due to its multi-scale correlation volumes and iterative flow refinements, whilst achieving superior performance, and is also a precursor to many successive works. However, learning a deterministic model with synthetic computer graphics data limits generalization ability and robustness on real videos. + +Unsupervised domain adaptation with self-supervised learning. Recently, there has been a surge in approaches to reduce the distribution discrepancy between real and synthetic data by leveraging unsupervised domain adaptation [9, 19, 28, 35, 42, 48]. An effective way to + +![](images/bba51a297b61be3c08f62c60202a29053e2d99f3657afce5298bb11aa2bec209.jpg) +(a) Learning with synthetic videos +Figure 2: Overview of the framework for fine-grained feature learning. We facilitate fine-grained feature learning by integrating self-supervised learning on unlabeled videos into supervised learning with labeled synthetic videos. For learning with synthetic data $\mathcal{D}_S$ , we devise a soft labeling module to convert the hard labels indicated by the motion vectors to soft labels. To learn more generalizable features, we leverage free supervision from unlabeled videos $\mathcal{D}_{\mathcal{T}}$ with the objective of frame reconstruction. Furthermore, an adversarial loss (along with Gradient Reverse Layer and a discriminator) is proposed to encourage domain invariant representations. The whole framework is jointly optimized in an end-to-end manner with the proposed objective functions. + +realize it is through adversarial training. Recent studies execute adversarial training by learning a domain classifier (the discriminator) to distinguish the learned features from different distributions, utilizing adversarial loss to increase domain confusion. Meanwhile, self-supervised learning obtains impressive performance and shows good generalizing ability by designing different pretext tasks [11, 41, 43, 45] with unlabeled data, which motivates us to combine supervised learning and self-supervised learning to encourage consistent representations for both domains as well as improved results for downstream tasks. + +# 3. Approach + +We address the problem of estimating the pixel-wise correspondences between a pair of video frames, which can be realized by learning fine-grained features for matching. Our goal is to learn a fine-grained feature space $\phi$ with the encoder $\theta$ by designing different learning objective functions for the probabilistic mapping. + +Probabilistic mapping. Given a pair of video frames $I_1, I_2 \in \mathbb{R}^{h \times w \times 3}$ , for all pixels in $I_1$ , we aim to predict the probabilistic mapping $P_{1 \to 2} \in \mathbb{R}^{H \times W \times (2r + 1)^2}$ and $P_{1 \to 2}(\cdot | i) \in \mathbb{R}^{(2r + 1)^2}$ gives the probability that $i$ is mapped to $j$ in frame $I_2$ within a limited range $r$ , considering the nature of temporal coherence in the video. The $i, j \in \mathbb{R}^2$ indicate the 2D pixel location. $P_{1 \to 2}(\cdot | i) \in \mathbb{R}^{(2r + 1)^2}$ thus encodes the entire discrete conditional probability distribution of where $i$ is mapped in frame $I_2$ . The probabilistic mapping can be achieved by calculating the feature similarities using the learned fine-grained features. More specifically, we first extract the dense features $F_1, F_2 \in$ + +$\mathbb{R}^{H\times W\times C}$ . Then the discrete probabilistic map can be obtained by computing the local correlation w.r.t. each key $j$ in $I_{2}$ within a local window for each query $i$ , + +$$ +P _ {1 \rightarrow 2} (j | i) = \frac {\exp \left(F _ {1} (i) \cdot F _ {2} (j) / \tau\right)}{\sum_ {n} \exp \left(F _ {1} (i) \cdot F _ {2} (n) / \tau\right)}, i \in \{1,.., H W \}, j, n \in \mathcal {K} (i), \tag {1} +$$ + +where $\mathcal{K}(i)$ is the index set in the local window with a limited range of $r$ centered at $i$ , and $\tau$ is the temperature. The result of the probabilistic mapping is further post-processed and directly applied to various downstream tasks. + +# 3.1. Fine-Grained Feature Learning + +We design the learning objective functions for probabilistic mapping with both synthetic and real-world videos. The overview of the framework is shown in Figure 2. + +Learning with synthetic videos. Labeled synthetic videos are often used as supervision for learning the optical flows in recent studies [8,34]. Given a pair of rendered video frames $I_1^s, I_2^s$ , the synthetic data $\mathcal{D}_S$ provides pixelwise motion vector, i.e., optical flow $G_{1\rightarrow 2}$ . A valid question then emerges as how to learn features using such deterministic correspondences? Indeed, we believe the deterministic correspondences are hard to obtain for real-world videos, thus we argue the necessity to convert them into soft (probabilistic) ones. We devise the following variants: + +(i) Dirac distribution: As shown in Figure 3 (a), we can directly convert the motion vector to a dirac distribution $\delta (\cdot |i)$ in order to describe the ground truth mapping. Then, the learning objective function defined as Kullback-Leibler divergence between $P_{1\rightarrow 2}^{s}(\cdot |i)$ and $\delta (\cdot |i)$ . The $P_{1 - > 2}^{s}$ stands + +![](images/bc2a06a2cc2db348f2d241dc610fa5ca42109622ef28dd21601b81c088aa6161.jpg) +Figure 3: Illustration of the probabilistic map. For $i$ in $I_1^s$ , we visualize the probability value of the mapping from $i$ to the locations in $I_2^s$ within a limited range. + +for the correlation calculated by Eq. (1) with synthetic data: + +$$ +\mathcal {L} _ {\mathrm {K L - v l}} = \sum_ {i} D _ {K L} (\delta (\cdot | i) \| P _ {1 \rightarrow 2} ^ {s} (\cdot | i)). \tag {2} +$$ + +(ii) Gaussian distribution: However, the feature of the query pixel $i$ varies smoothly over space and time, which indicates a soft distribution of the potential location in the next frame. As shown in Figure 3 (a), the dirac distribution does not provide the feature learning with any knowledge of relative probability in the background, making it hard to learn the features with the ability to tell the fine-grained differences with synthetic videos. Thus, we devise to generate the probabilistic map with gaussian distribution, which introduces a soft distribution centered at the ground truth coordinate: + +$$ +\mathcal {N} (j | i, \mu , \sigma^ {2}) = \frac {1}{\sqrt {2 \pi} \sigma_ {u}} e ^ {- \frac {\left(u _ {j} - \mu_ {t} ^ {u}\right) ^ {2}}{2 \sigma_ {u} ^ {2}}} \cdot \frac {1}{\sqrt {2 \pi} \sigma_ {v}} e ^ {- \frac {\left(v _ {j} - \mu_ {t} ^ {v}\right) ^ {2}}{2 \sigma_ {v} ^ {2}}}, \tag {3} +$$ + +where $\mu = (\mu_i^u,\mu_i^v)$ represents the 2D coordinate of ground truth in the $I_2^s$ for pixel $i$ , and $(u_{j},v_{j})$ indicates the 2D coordinate of $j$ . Then the loss can be devised as: + +$$ +\mathcal {L} _ {\mathrm {K L - v 2}} = \sum_ {i} D _ {K L} \left(\mathcal {N} (\cdot | i, \mu , \sigma^ {2}) \| P _ {1 \rightarrow 2} (\cdot | i)\right). \tag {4} +$$ + +(iii) Soft-labeling: The gaussian prior only considers the euclidean distance of coordinates, which shows limited capability of modeling the complicated distributions. We believe the synthetic supervision already provides valuable temporal cues ( $i$ in $I_1^s$ move to $j$ in $I_2^s$ ), and the soft distribution over space can be approached by computing the self-similarities for $j$ using the pre-trained 2D visual encoder $\theta_{self}$ which can produce spatially-discriminative features. As shown in Figure 3 (c), for the $i$ in $I_1^s$ that moves to $j$ , we get the feature of the query $i$ (denoted as $\overline{F}_q$ ) at the location $j$ in $\overline{F}_2$ ( $\overline{F}_2$ is the feature map of $I_2^s$ computed by $\theta_{self}$ ). Then we can compute the feature similarities $S_{1\rightarrow 2}(\cdot |i)$ between $\overline{F}_q$ and $\{\overline{F}_2(k)|k\in \mathcal{K}(i)\}$ , where $\mathcal{K}(i)$ is the index set in the local window centered at $i$ . The $S_{1\rightarrow 2}(\cdot |i)$ are further normalized (by softmax) to obtain the discrete probability distribution $P_{1\rightarrow 2}(\cdot |i)$ : + +$$ +\mathcal {L} _ {\mathrm {K L - v 3}} = \sum_ {i} D _ {K L} \left(P _ {1 \rightarrow 2} (\cdot | i) \| P _ {1 \rightarrow 2} ^ {s} (\cdot | i)\right). \tag {5} +$$ + +In Table 4, we find soft labeling works well when only pre-training $\theta_{\text{self}}$ on synthetic data $\mathcal{D}_{\mathcal{S}}$ with $\mathcal{L}_{\mathrm{rec}}$ (Eq. (8)), and leveraging more strong 2D encoder would contribute to better performance. The comparisons between different loss functions will be discussed in the experiments, and the $\mathcal{L}_{\mathrm{KL - v3}}$ is used as the default loss. + +Learning with unlabeled videos. Meanwhile, we observe in real scenarios, there are apparent differences with synthetic videos in appearance variants, illumination changes and deformations, leading to notable changes in the distribution, where the learned features on synthetic videos show unsatisfied generalization ability. Inspired by recent studies [16, 41], we try to improve the learned fine-grained features by introducing self-supervised feature learning into the framework. As observed in the bottom of Figure 1, the pixel repetition encourages us to learn the fine-grained features by reconstructive learning, where each pixel in the $I_1^t$ can be reconstructed by leveraging the information of $I_2^t$ with a limited range. To achieve this, the video frames $I_1^t, I_2^t$ are firstly projected into pixel embeddings $F_1^t, F_2^t$ by the encoder $\theta$ . For each query $i$ in $I_1^t$ , we calculate the probabilistic map $P_{1\rightarrow 2}^t$ with Eq. (1). Then the query $i$ in $I_1^t$ can be reconstructed by a weighted sum of pixels in $\mathcal{K}(i)$ : + +$$ +I _ {1} ^ {\text {r e c}} (i) = \sum_ {j \in \mathcal {K} (i)} P _ {1 \rightarrow 2} ^ {t} (j | i) I _ {2} ^ {t} (j). \tag {6} +$$ + +Then the reconstruction loss for self-supervised training is defined as $L_{1}$ distance between $I_1^{rec}$ and $I_1^t$ . Training with such self-supervision leads to temporal persistent features that generalize well in real scenarios. + +However, the pixel repetition does not hold for pixels that become occluded. Thus, we exclude occluded pixels from the reconstruction loss to avoid learning incorrect features. We follow the forward-backward consistency assumption to detect the occluded pixels. which is defined in Eq. (7) as the occlusion flag $O_{1\rightarrow 2}$ to be 1 whenever the constraint is violated, and 0 otherwise: + +$$ +O _ {1 \rightarrow 2} (i) = \mathbb {1} \left(\underset {i} {\arg \max } P _ {2 \rightarrow 1} ^ {t} \left(i \mid \underset {j} {\arg \max } P _ {1 \rightarrow 2} ^ {t} (j \mid i)\right) = i\right). \tag {7} +$$ + +The loss for reconstructive learning is defined as follows: + +$$ +\mathcal {L} _ {\text {r e c}} = \sum_ {i} O _ {1 \rightarrow 2} (i) \cdot \left\| I _ {1} ^ {\text {r e c}} (i) - I _ {1} ^ {t} (i) \right\| _ {1}. \tag {8} +$$ + +Adversarial training. We further improve the fine-grained features by leveraging the technique in recent works of unsupervised domain adaptation, which aims to bridge the gap caused by the domain shift between the synthetic videos $\mathcal{D}_S$ and real videos $\mathcal{D}_{\mathcal{T}}$ via adversarial training. An effective way to approach this problem consists in introducing the network a Gradient Reversal Layer (GRL). We additionally train a discriminator $\theta_{D}$ to identify whether the + +![](images/cb6b891b9ea7d8de9c1f0ff74d573e49bb0e50dea06e647cec26c4c97c831b24.jpg) +Figure 4: Illustration of the coarse-to-fine framework for efficient probabilistic mapping. We first obtain coarse-grained matching and then upsample it to get the fine-grained result. + +probabilistic map comes from synthetic or real videos: + +$$ +\mathcal {L} _ {\mathrm {a d v}} = \mathbb {E} _ {P ^ {t} \in P _ {\mathcal {T}}} [ \log (D (P ^ {t})) ] + \mathbb {E} _ {P ^ {s} \in P _ {\mathcal {S}}} [ \log (1 - D (P ^ {s})) ], \tag {9} +$$ + +and then we reverse the gradient direction during the backward pass in back-propagation when updating the parameters of the encoder $\theta$ with $\mathcal{L}_{\mathrm{adv}}$ : + +$$ +\theta \leftarrow \theta + \lambda \frac {\partial \mathcal {L} _ {\mathrm {a d v}}}{\partial \theta}. \tag {10} +$$ + +The GRL allows to train the discriminator and the encoder at the same time, and the adversarial training helps to learn domain invariant patterns. + +Overall training objective. The overall training objective for learning fine-grained features is formulated as a multi-task loss, which is written as $\mathcal{L} = \mathcal{L}_{\mathrm{KL}} + \mathcal{L}_{\mathrm{rec}} + \mathcal{L}_{\mathrm{adv}}$ where we empirically treat each loss equally. + +# 3.2. Efficient Fine-grained Probabilistic Mapping + +To get the fine-grained probabilistic map, i.e., $P_{1\rightarrow 2}\in \mathbb{R}^{H\times W\times (2r + 1)^2}$ , we need to compute the similarities w.r.t. all key pixels in the local window centered at every query pixel, which is computationally costly. In this section, we devise a coarse-to-fine framework. The overview of the framework can be found in Figure 4, where we first compute the correlation at coarse-grained features and then up-sample it to get fine-grained probabilistic maps. + +Self-attention and Cross-attention Layers. More specifically, we first extract the coarse feature maps $F_{1}^{\downarrow}, F_{2}^{\downarrow} \in \mathbb{R}^{H/4 \times W/4 \times C}$ , and we further enhance the coarse features by introducing the self-attention and cross-attention layers with positional encoding. Then, we obtain the coarse-grained probabilistic map $P_{1 \rightarrow 2} \downarrow \in \mathbb{R}^{H/4 \times W/4 \times (2r\downarrow + 1)^{2}}$ by Eq (1). + +Up-sampling. We devise an up-sampling layer to obtain fine-grained probabilistic map $P_{1\rightarrow 2}\in \mathbb{R}^{H\times W\times (2r + 1)^2}$ which can be simply done by leveraging pixel-shuffle or convolution layer with bilinear interpolation. + +More details of the architecture are included in the supplementary material. We train the coarse-to-fine framework in a distillation manner on $\mathcal{D}_{\mathcal{T}}$ , with the same objective function as $\mathcal{L}_{\mathrm{KL}}$ . The supervisions for $P_{1\rightarrow 2}$ are obtained by computing the probabilistic map using pre-trained encoder in Sec. 3.1. Without losing much performance, we find such a design helps to get rid of the complicated fine-grained feature matching and exhibit higher efficiency. + +# 4. Experiments + +We verify the effectiveness of our method in a series of correspondence-based tasks. We will first introduce implementation and evaluation details, and report the performance comparison with baselines. Finally, we perform detailed ablation studies for each component of our method. + +# 4.1. Implementation Details + +Backbone. We exploit the encoder $\theta$ with ResNet-18 [12]. We reduce the stride up to layer $\mathrm{res}_4$ to get features at $1/2$ of the original image dimension for training. In our coarse-to-fine framework, we increase the stride of the encoder to 8 for coarse-grained feature matching. + +Training details. The training is conducted on the train set of synthetic dataset FlyingThings [26] and YouTube-VOS [46] collected in real-world. The FlyingThings/YouTube-VOS contains $40\mathrm{k} / 3.5\mathrm{k}$ videos for training. For both datasets, we sample pair of frames which are resized into $256\times 256$ and converted to Lab color space with channel-wise dropout as the information bottleneck [20]. The local range $r$ in the probabilistic map is set to $24 / 6$ for the fine-grained features $(\frac{h}{2}\times \frac{w}{2}$ (stride=2)) or coarse-grained features $(\frac{h}{8}\times \frac{w}{8}$ (stride=8)). We first train an encoder using reconstruction loss (Eq. (8)) with a batchsize of 32 for 30 epochs on FlyingThings [26], which is further utilized as $\theta_{self}$ in soft labeling. Then the final model $\theta$ is jointly trained for 30 epochs with proposed three losses, with a batchsize of 16 for each dataset. When training with synthetic optical flow, we filter out the points that are out of the local range or occluded by forward-backward checking. The $\tau$ is set to 1. We use Adam as the optimizer, and the initial learning rate is set to 1e-3 with a cosine (half-period) learning rate schedule for each stage. We include more training details in the supplementary. + +Evaluation. An important problem is how to evaluate the quality of the learned fine-grained features for pixel-wise video correspondences. Following the previous works [16,41,45], without any fine-tuning, we directly leverage the pre-trained encoder $\theta$ to extract features $F_{i}, F_{j}$ with a spatial resolution of $\frac{h}{s} \times \frac{w}{s}$ (the $s$ represents the stride of the encoder) for the pair of frames $I_{i}, I_{j}$ , which are later used to compute the probabilistic map $P_{i \rightarrow j}$ by Eq (1). Based on the probabilistic map $P_{i \rightarrow j}$ , we follow the recurrent inference strategy inference strategies of recent studies [16,41,45] to propagate the target points or semantic labels of the first frame, as well as previous predictions, to the current frame $I_{t}$ . We evaluate the point tracking on three popular benchmarks including BADJA [2], JHMDB [18], TAP-Vid-DAVIS [7] and TAP-Vid-Kinetics [7], and the evaluation of video object segmentation is conducted on the widely used dataset DAVIS-2017 [29]. + +Table 1: Quantitative results for point tracking on different datasets. The frame per second (FPS) results of getting pixelwise correspondences between a pair of video frames are measured on a single GTX-3090 at the resolution of $480 \times 640$ . The * indicates our coarse-to-fine framework. The - indicates the unavailable result due to the unavailable pre-trained model. + +
MethodBackboneStrideFPSBADJAJHMDBTAP-DAVISTAP-Kinetics
PCK@0.1↑PCK@0.1↑<δxavg-p↑<δxavg-p↑
TimeCycle [41]ResNet-5082841.157.327.128.6
UVC [24]ResNet-18814248.258.629.025.2
CRW [16]ResNet-18814250.959.332.525.4
VFS [45]ResNet-18814251.960.531.928.8
CLSC [31]ResNet-188142-61.7--
SFC [13]ResNet-18 + ResNet-5082753.861.937.231.1
MAST [20]ResNet-1843355.762.442.533.2
LIIR [22]ResNet-18433-60.7--
Ours*ResNet-1883456.864.648.043.8
ImageNet Pre. [12]ResNet-182857.561.551.344.5
UVC [24]ResNet-182856.765.152.741.8
CRW [16]ResNet-182855.961.443.237.1
VFS [45]ResNet-182858.161.051.444.9
SFC [13]ResNet-182861.565.953.943.6
MAST [20]ResNet-182863.063.153.842.7
OursResNet-182867.266.859.848.8
+ +# 4.2. Results for Point Tracking + +We firstly make comparisons for point tracking since it requires the finest granularity of the learned features. The main comparators of our method are the works aim to learn good representations for matching, e.g., TimeCycle [41], UVC [24], CRW [16], VFS [45], SFC [13], and MAST [20]. We also include the model pre-trained on ImageNet [6] with human annotations. These works share a similar evaluation protocol as we mentioned in 4.1. + +While previous works test the pixel-wise correspondences on JHMDB [18] that only provides the human keypoint annotations. We additionally include BADJA [2], TAP-Vid-DAVIS [7] and TAP-Vid-Kinetics [7]. We propagate the points of the first frame to other frames and evaluate the results using the annotations of each dataset. We notice some works are trained and evaluated with the coarse-grained features (e.g., the features at 1/8 of the original image dimension). For these methods, we use our coarse-to-fine framework that also executes coarse-grained feature matching for comparisons. Meanwhile, for better comparisons, we follow the studies in [16,45] to further reduce the stride $s$ of the encoder to 2, in order to get more fine-grained results for CRW, VFS, SFC and MAST. We also provide the FPS of computing the pixel-wise correspondences between two frames for feature-matching-based methods, which can be done by first taking the index of the maximum value in $P_{1\rightarrow 2}(\cdot |i)$ for each $i$ and then applying up-sampling to get full-resolution results. More details about the evaluation are included in the supplementary material. + +Results on BADJA/JHMDB. We adopt the standard PCK [47] of all visible points (not compute PCK for each video then take average) as the evaluation metric. Each point is considered correct if it is within a distance of $0.1\sqrt{A}$ from the ground truth, where $A$ is the distance be + +tween keypoints (for JHMDB) or the area of the ground-truth segmentation mask on the frame (for BADJA). In Table 1, our method achieves $67.2\% / 66.8\%$ , surpassing all state-of-the-art methods. Besides, our method with the coarse-to-fine design still makes the absolute improvements by $1.1\%$ and $2.2\%$ compared with MAST, and shows better efficiency compared with SFC [13] that uses the two-stream network to find the correspondences. More remarkably, our efficient framework even surpasses part of the methods using more fine-grained features for inference. + +Results on TAP-Vid. TAP-Vid is a newly developed benchmark composed of long-term videos in real-world with accurate human annotations of point tracks. We test on the whole set of TAP-Vid-DAVIS and the test set of TAP-Vid-Kinetics. We adopt the setting of "first fashion" in [7], which tracks only into the future. The average position accuracy over all visible points $(< \delta_{avg-p}^{x})$ is adopted as the metric. The learned fine-grained features obtain $59.8\% / 48.8\%$ on TAP-Vid-DAVIS/TAP-Vid-Kinetics, leading apparent improvements over state-of-the-arts by $5.9\% / 3.9\%$ . Moreover, the proposed coarse-to-fine framework gets $48.0\% / 43.8\%$ , surpassing MAST by $5.5\% / 10.6\%$ . + +Comparisons with task-specific methods. Besides, we notice there are some recent methods specifically designed for point tracking, like RAFT [34], PIPs [10], TAPNet [7], and Thin-Slicing Net [32] even trained with human annotations. Here we also present the performance comparisons with them in Table 2. It's worth noting that, to align the evaluation with these methods, except JHMDB, we first compute the $< \delta_{avg-p}^{x}$ or PCK for each video to obtain video-level results, and the final results are obtained by taking the average over all videos. Without any specific designs, our performance even surpasses these methods by $7.4\% / 7.5\% / 0.2\%$ on BADJA/TAP-DAVIS/TAP-Kinetics. + +![](images/63693f9b4c2b6b0fe8af4c0a6ef33d4baec674c4cf1b55cb7670bfca7829017f.jpg) +$1^{st}$ frame with target + +![](images/c3b3f39ca9443ce7a15af9176ef87f5e2b4677c64895d8efa1d9b43cb4cf002d.jpg) +VFS + +![](images/8da4cc658d11c65d46cda28d85b9421fedca55094da20aef7e3ebbcd939fb826.jpg) +MAST + +![](images/a3792b42b1ebc6c7f2aaf7ba33b98653555b1f364bc9190277e2af7f6ed03f6e.jpg) +RAFT + +![](images/56ca515c545cf458a4f2ff892511cf6c36418b442caaba0248b73d794b7e9dc2.jpg) +Ours +Figure 5: Qualitative results for point tracking. Given the target pixel in the first frame, we visualize the estimated trajectory with a pink-to-yellow colormap (pink/yellow indicates the start/end of the video clip). We visualize sparse ground-truth labels with cyan cross marks. Please refer to the video in the supplementary for better animations. (Zoom in for best view) + +Table 2: Comparisons with methods specifically designed for point tracking. “‡” means we align the evaluation protocol with each method for fair comparisons. + +
MethodBADJAJHMDBTAP-DAVISTAP-Kinetics
PCK@0.2↑PCK@0.1↑<δxavg↑<δxavg↑
RAFT [34]45.666.442.144.3
PIPs [10]62.3-55.348.2
TAPNet [7]-62.348.654.4
Thin-Slicing Net [32]-68.7--
Ours‡69.766.862.854.6
+ +Figure 5 shows some visualization results of the point tracking on TAP-Vid-DAVIS. Given the target in the first frame, we visualize the estimated trajectory with a pink-to-yellow map. Compared with VFS, MAST and RAFT, our approach can output more smooth and accurate trajectories close to the sparse visualized ground truth, even facing dramatic appearance changes and deformation. + +# 4.3. Results for Video Object Segmentation + +Next, we evaluate methods with semi-supervised video object segmentation. We use the mean of region similarity $\mathcal{I}_m$ , mean of contour accuracy $\mathcal{F}_m$ and their average $\mathcal{J} \& \mathcal{F}_m$ as the evaluation metrics. In Table 3, our method still leads the performance. More remarkably, our method even outperforms some task-specific fully-supervised algo + +Table 3: Quantitative results for video object segmentation on $\mathbf{DAVIS}_{17}$ [29]. "Sup." means using human annotations for training. + +
MethodSup.BackboneDAVIS17
J&Fm↑Jm↑Fm↑
TimeCycle [41]ResNet-5040.741.939.4
UVC [24]ResNet-1859.557.761.3
MAST [20]ResNet-1865.563.367.6
CRW [16]ResNet-1867.664.870.2
JSTG [49]ResNet-1868.765.871.6
VFS [45]ResNet-5068.966.571.3
DUL [1]ResNet-1869.367.171.6
MAMP [27]ResNet-1869.768.371.2
CLTC [17]ResNet-1870.367.972.6
CLSC [31]ResNet-1870.567.473.6
SFC [13]ResNet-18 + ResNet-5071.268.374.0
LIIR [22]ResNet-1872.169.774.5
OursResNet-1872.470.574.4
OSVOS-S [25]✓VGG-1668.064.771.3
FEELVOS [37]✓Xception-6571.569.174.0
+ +rithms [25,37]. Here we select several representative videos for inference, and give the visualization results in Figure 6, our method produces tight boundaries around the object areas, and obtains more fine-grained results, especially for small objects. For example, in the first column of Figure 6, the tiny arm of the human can still be segmented, which further demonstrates the advantages of learning fine-grained features for video correspondences. However, we + +![](images/5ce43baff0c7d9458c25d5e9a2c25edb606ce5502bf5bed6eb55f3b8fca109a2.jpg) +Figure 6: Qualitative results for video object segmentation. Given the semantic mask in the first frame, we show the propagation results on the target frame. (Zoom in for best view) + +find that fine-grained features may hinder object-centric feature learning since it may rely more on low-level patterns (e.g., texture, color, etc), which degrades the performance in video object segmentation to some extent. We regard it as our future work. + +# 4.4. Ablation Study + +We perform ablation study with point tracking on the TAP-Vid-DAVIS [7] dataset. + +Learning with synthetic videos. We study the effect of three different ways as defined in Eq. (2), Eq. (4) and Eq. (5) for learning the fine-grained features with synthetic videos. Table 4 shows the performance comparisons across the three kinds of objective functions. As indicated by the results, the loss $\mathcal{L}_{\mathrm{KL - v1}}$ using dirac distribution to generate the labels performs badly. We think the deterministic labels were given on synthetic videos, resulting in the learned features not being robust enough on real-world videos. Besides, we find introducing the gaussian distribution in $\mathcal{L}_{\mathrm{KL - v2}}$ results in performance degradation. The performance drops a lot when progressively increasing the variance, which may be attributed to the inability of gaussian distribution to approach the real probabilistic distribution since it is extremely complicated. Expectedly, the proposed soft labeling boosts up the performance from $42.6\%$ to $55.8\%$ when only pre-training the $\theta_{self}$ with Eq. (8). Moreover, we also try another 2D encoder pre-trained with the contrastive loss $\mathcal{L}_{\mathrm{nce}}$ [11] on ImageNet [6], which has a stronger ability to capture the spatially discriminative features. The results are further improved to $57.5\%$ , which motivates us to leverage a more powerful 2D feature extractor + +Table 4: Ablation study for $\mathcal{L}_{\mathrm{KL}}$ . The $\sigma/\theta_{\text{self}}$ represents the variance / encoder used in $\mathcal{L}_{\mathrm{KL - v2}} / \mathcal{L}_{\mathrm{KL - v3}}$ . + +
Obj. FunctionHyper-param.TAP-Vid-DAVIS < δxavg↑
(σu, σv)θself
LKL-v1--42.6
LKL-v2(1,1)-41.9
(3,3)-33.8
(6,6)-29.7
LKL-v3-w. Lrec55.8
-w. Lnce [11]57.5
+ +Table 5: Ablation study for training objective functions. FT: FlyingThings [26]. YTV: YouTube-VOS [46]. + +
\( {\mathcal{L}}_{\mathrm{{KL}}} \)\( {\mathcal{L}}_{\text{rec }} \)\( {\mathcal{L}}_{\text{adv }} \)Training DataTAP-Vid-DAVIS < \( {\delta }_{avg}^{x} \uparrow \)
✓FT55.8
✓YTV56.4
✓FT + YTV56.7
✓✓FT + YTV59.2
✓✓✓FT + YTV59.8
+ +for obtaining the soft labels. We regard it as future work. + +Different training objective functions. We examine how different objective functions impact the overall performance, which is shown in Table 5. The $\mathcal{L}_{\mathrm{KL}}$ , $\mathcal{L}_{\mathrm{rec}}$ and $\mathcal{L}_{\mathrm{adv}}$ denotes the losses defined in Eq. (5), Eq. (8) and Eq. (9). Surprisingly, we find the model trained on unlabeled real-world videos with $\mathcal{L}_{\mathrm{rec}}$ obtains a better result, which indicates better generalization of self-supervised feature learning. By leveraging both $\mathcal{L}_{\mathrm{KL}}$ and $\mathcal{L}_{\mathrm{rec}}$ with synthetic and real-world videos, the performance is further improved to $59.2\%$ . As expected, executing $\mathcal{L}_{\mathrm{adv}}$ to address the domain mismatch improves performance by $0.6\%$ . By fusing three losses, the performance reaches $59.8\%$ . The results consistently indicate that incorporating self-supervised and adversarial training with unlabeled data exhibits a performance boost against the model only trained with synthetic data. + +# 5. Conclusions + +In this paper, we address pixel-wise video correspondences by learning fine-grained features. We propose to use not only labeled synthetic videos but also unlabeled real-world videos for feature learning. We first study how to take advantage of synthetic supervision for feature learning, and we find directly utilizing the motion vector results in degradation for the learned features. Thus, we propose soft labeling to address the issue. To improve the generalization, we introduce self-supervised reconstructive learning into the overall training and further enhance the features by leveraging adversarial training. Moreover, we propose a coarse-to-fine framework to alleviate the problem of computational efficiency. 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In ICCV, pages 9960–9969, 2021. \ No newline at end of file diff --git a/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/images.zip b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..55e7d8ac492f8f02a3385f1088cb567830d6fb58 --- /dev/null +++ b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d6f29c33d79c192bd7f8bd59b7e9b2c8689ffc2e8289d98821875f8d50ea6d6e +size 655633 diff --git a/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/layout.json b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6ee60ce4d73d1e8f57864118aaf6d9b4fdb10d7c --- /dev/null +++ b/2023/Learning Fine-Grained Features for Pixel-Wise Video Correspondences/layout.json @@ -0,0 +1,9569 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 76, + 136, + 501, + 154 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 136, + 501, + 154 + ], + "spans": [ + { + "bbox": [ + 76, + 136, + 501, + 154 + ], + "type": "text", + "content": "Learning Fine-Grained Features for Pixel-wise Video Correspondences" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 184, + 175, + 392, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 184, + 175, + 392, + 189 + ], + "spans": [ + { + "bbox": [ + 184, + 175, + 392, + 189 + ], + "type": "text", + "content": "Rui Li Shenglong Zhou Dong Liu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 190, + 433, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 190, + 433, + 202 + ], + "spans": [ + { + "bbox": [ + 143, + 190, + 433, + 202 + ], + "type": "text", + "content": "University of Science and Technology of China, Hefei, China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 142, + 204, + 435, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 142, + 204, + 435, + 216 + ], + "spans": [ + { + "bbox": [ + 142, + 204, + 435, + 216 + ], + "type": "text", + "content": "{1iruid,slzhou96}@mail.ustc.edu.cn，dongeliu@ustc.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 192, + 218, + 384, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 192, + 218, + 384, + 229 + ], + "spans": [ + { + "bbox": [ + 192, + 218, + 384, + 229 + ], + "type": "text", + "content": "https://github.com/qianduoduolr/FGVC" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 139, + 256, + 186, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 256, + 186, + 269 + ], + "spans": [ + { + "bbox": [ + 139, + 256, + 186, + 269 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 281, + 282, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 281, + 282, + 538 + ], + "spans": [ + { + "bbox": [ + 45, + 281, + 282, + 538 + ], + "type": "text", + "content": "Video analysis tasks rely heavily on identifying the pixels from different frames that correspond to the same visual target. To tackle this problem, recent studies have advocated feature learning methods that aim to learn distinctive representations to match the pixels, especially in a self-supervised fashion. Unfortunately, these methods have difficulties for tiny or even single-pixel visual targets. Pixel-wise video correspondences were traditionally related to optical flows, which however lead to deterministic correspondences and lack robustness on real-world videos. We address the problem of learning features for establishing pixel-wise correspondences. Motivated by optical flows as well as the self-supervised feature learning, we propose to use not only labeled synthetic videos but also unlabeled real-world videos for learning fine-grained representations in a holistic framework. We adopt an adversarial learning scheme to enhance the generalization ability of the learned features. Moreover, we design a coarse-to-fine framework to pursue high computational efficiency. Our experimental results on a series of correspondence-based tasks demonstrate that the proposed method outperforms state-of-the-art rivals in both accuracy and efficiency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 561, + 124, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 124, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 124, + 574 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 581, + 279, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 581, + 279, + 664 + ], + "spans": [ + { + "bbox": [ + 45, + 581, + 279, + 664 + ], + "type": "text", + "content": "One of the most fundamental problems in computer vision is learning visual correspondences across space and time, which has many applications such as 3D reconstruction, physical understanding, and dynamic object modeling. Due to the factors such as viewpoint change, distractors, and deformations, this task is extremely challenging and can be roughly divided into three categories accord" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 672, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 672, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 672, + 280, + 730 + ], + "type": "text", + "content": "This work was supported by the Natural Science Foundation of China under Grants 62022075 and 62036005, and by the Fundamental Research Funds for the Central Universities under Grant WK349000006. This work was also supported by the advanced computing resources provided by the Supercomputing Center of USTC. (Corresponding author: Dong Liu.)" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 298, + 255, + 532, + 373 + ], + "blocks": [ + { + "bbox": [ + 298, + 255, + 532, + 373 + ], + "lines": [ + { + "bbox": [ + 298, + 255, + 532, + 373 + ], + "spans": [ + { + "bbox": [ + 298, + 255, + 532, + 373 + ], + "type": "image", + "image_path": "e46fc9c6515f46f39d67c68a14c5f995b5c8bb7bd968d9b1d6dc2d144cd009da.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 376, + 531, + 419 + ], + "lines": [ + { + "bbox": [ + 296, + 376, + 531, + 419 + ], + "spans": [ + { + "bbox": [ + 296, + 376, + 531, + 419 + ], + "type": "text", + "content": "Figure 1: We illustrate video correspondences with different granularities, including object-wise, group-wise, and pixel-wise. In this paper, we concentrate on learning fine-grained features to address the pixel-wise video correspondences." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 426, + 530, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 426, + 530, + 521 + ], + "spans": [ + { + "bbox": [ + 296, + 426, + 530, + 521 + ], + "type": "text", + "content": "ing to the granularity: the first one is object-wise correspondences that exist between coarsely localized bounding boxes [36, 39] along the video; the second one is groupwise correspondences, indicating the mapping at group-level, and usually applied to downstream tasks like video object segmentation [5, 25]; the third one is pixel-wise correspondences, which describe the pixel-level relation between video frames with the finest granularity." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 521, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 521, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 521, + 531, + 730 + ], + "type": "text", + "content": "Learning dense representations from videos is one approach to finding the correspondences. Researchers have been exploring different self-supervised methods for learning generalizable representations using unlabeled videos collected in the real world [16,20,23,24,41,45]. For example, Wang et al. [41] propose using an object-level cycle-consistency across time (i.e., forward-backward tracking) as a supervision signal. Jabri et al. [16] further enhance it by combining cycles of time with the similarities between path-level representations. Inspired by contrastive learning, Xu et al. [45] try to learn spatial and temporal representation through a frame-wise contrastive loss, while Li et al. [23] propose a spatial-then-temporal pretext task to learn better spatiotemporal features. Despite obtaining promising outcomes, current research has predominantly emphasized performing object-level or patch-level similarity learning, making it difficult to accurately recognize pixel-wise differences with the learned features. As a result, there is an in" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 151, + 41, + 470, + 73 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 41, + 470, + 73 + ], + "spans": [ + { + "bbox": [ + 151, + 41, + 470, + 73 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "9632" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 278, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 278, + 129 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 278, + 129 + ], + "type": "text", + "content": "creasing necessity for learning fine-grained representations in order to tackle this problem." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 131, + 278, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 131, + 278, + 317 + ], + "spans": [ + { + "bbox": [ + 45, + 131, + 278, + 317 + ], + "type": "text", + "content": "At the same time, there is another line of work approaching video correspondences by deterministically predicting the displacement of each pixel, which is known as optical flow estimation. Early studies used optimization methods to estimate the motion between two frames [4]. In recent years, approaches use synthetic data with supervised learning for flow estimation [8, 26], using a coarse-to-fine pyramid framework to improve the accuracy [33]. RAFT [34] further devises an iterative optimization algorithm to come up with the result of high-resolution flow fields through iterative updates, which show a superior ability to find fine-grained correspondences. However, in real scenarios, there are often appearance variants, illumination changes, and deformations between video frames, which leads to the lack of robustness on real-world videos for the optical flow model supervised by labeled synthetic videos." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 319, + 278, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 319, + 278, + 505 + ], + "spans": [ + { + "bbox": [ + 45, + 319, + 278, + 505 + ], + "type": "text", + "content": "In this paper, we explore how to learn fine-grained representations to meet the needs of pixel-wise video correspondences. To this end, we first investigate how to leverage synthetic data for fine-grained feature learning. Specifically, given a query pixel, the supervision in synthetic videos only supplies the one-to-one mapping, i.e., a motion vector, representing the deterministic correspondence of the pixel to another pixel in the next frame. Nevertheless, the pixel-wise features evolve slowly over space and time, which indicates a soft distribution of the correspondences. We find directly utilizing the synthetic supervision as hard labels results in inferior representations, and the learned features are unable to recognize the pixel-wise differences across different spatial locations and periods of time. To address the issue, we propose to use an external pre-trained 2D encoder to derive soft supervision for optimization based on the flow." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 506, + 278, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 506, + 278, + 646 + ], + "spans": [ + { + "bbox": [ + 45, + 506, + 278, + 646 + ], + "type": "text", + "content": "Furthermore, we incorporate self-supervised feature learning on unlabeled real data in the overall training to alleviate the generalization issues in real scenes, which consists of two carefully designed components. Firstly, inspired by the temporal consistency assumption [3], we learn temporal persistent features via self-supervised reconstructive learning, where each query pixel can be reconstructed by leveraging the information in adjacent frames. Besides, given the synthetic and real data, we perform adversarial training by introducing Gradient Reverse Layer [9] with a discriminator for the learned correspondences. We observe such designs can further enhance learned fine-grained features." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 648, + 278, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 278, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 278, + 729 + ], + "type": "text", + "content": "Though already getting impressive results, we find it takes more time to get the results of the dense matching between fine-grained features. Thus, we make another step to devise a coarse-to-fine framework to address the problem. We put the complex feature matching on the coarse-grained feature map and then get the fine-grained results through a learnable up-sampling layer. As a result, we achieve a" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 297, + 106, + 530, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 106, + 530, + 128 + ], + "spans": [ + { + "bbox": [ + 297, + 106, + 530, + 128 + ], + "type": "text", + "content": "good balance of performance and efficiency. In summary, the main contribution of this work lies in:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 298, + 138, + 529, + 257 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 298, + 138, + 529, + 161 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 138, + 529, + 161 + ], + "spans": [ + { + "bbox": [ + 298, + 138, + 529, + 161 + ], + "type": "text", + "content": "- We address the problem of establishing pixel-wise video correspondences via a feature learning approach." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 298, + 170, + 529, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 170, + 529, + 216 + ], + "spans": [ + { + "bbox": [ + 298, + 170, + 529, + 216 + ], + "type": "text", + "content": "- We propose an effective method of learning fine-grained features from both synthetic and unlabeled videos, followed by a carefully designed framework to address the issue of efficiency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 298, + 223, + 529, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 223, + 529, + 257 + ], + "spans": [ + { + "bbox": [ + 298, + 223, + 529, + 257 + ], + "type": "text", + "content": "- We validate our method in a series of correspondence-based tasks. Experiment results indicate consistent improvement over state-of-the-art methods." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 297, + 268, + 379, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 268, + 379, + 280 + ], + "spans": [ + { + "bbox": [ + 297, + 268, + 379, + 280 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 287, + 530, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 287, + 530, + 484 + ], + "spans": [ + { + "bbox": [ + 296, + 287, + 530, + 484 + ], + "type": "text", + "content": "Representation learning for video correspondences. Recent researches center around learning dense representations without labels in a self-supervised way for video correspondences, which occurs in two distinct directions: reconstruct-based [20, 21, 23, 24, 38, 40] and cycle-consistency-based techniques [16, 41, 49]. In the works of the first type, the query pixel is reconstructed from the adjacent frames based on the temporal consistency assumption, while the works of the second type execute forward-backward tracking to reduce cycle inconsistency. Furthermore, VFS [45] proposes to learn representations through frame-wise contrastive loss. SFC [13] proposes a two-stream architecture to learn semantic and fine-grained features through two different models. Despite the progress made in learning representations for video correspondences, accurately recognizing pixel-wise distinctions over space and time remains challenging." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 485, + 530, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 485, + 530, + 671 + ], + "spans": [ + { + "bbox": [ + 296, + 485, + 530, + 671 + ], + "type": "text", + "content": "Optical flow estimation for video correspondences. Recently, the classic optical flow estimation problem of predicting per-pixel motion between two frames has been explored using synthetic graphics data for supervised training [8, 26]. FlowNet [8] was one of the first deep learning methods to tackle end-to-end optical flow learning. This research inspired a multitude of other methods, such as FlowNet2.0 [15], DCFlow [44], SpyNet [30], PwC-Net [33], and LiteFlowNet3 [14]. Most of these methods employ cost volumes for finding pixel matching. RAFT [34] stands out from the rest due to its multi-scale correlation volumes and iterative flow refinements, whilst achieving superior performance, and is also a precursor to many successive works. However, learning a deterministic model with synthetic computer graphics data limits generalization ability and robustness on real videos." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": "Unsupervised domain adaptation with self-supervised learning. Recently, there has been a surge in approaches to reduce the distribution discrepancy between real and synthetic data by leveraging unsupervised domain adaptation [9, 19, 28, 35, 42, 48]. An effective way to" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "9633" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 116, + 493, + 282 + ], + "blocks": [ + { + "bbox": [ + 83, + 105, + 205, + 116 + ], + "lines": [ + { + "bbox": [ + 83, + 105, + 205, + 116 + ], + "spans": [ + { + "bbox": [ + 83, + 105, + 205, + 116 + ], + "type": "text", + "content": "(a) Learning with synthetic videos" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 83, + 116, + 493, + 282 + ], + "lines": [ + { + "bbox": [ + 83, + 116, + 493, + 282 + ], + "spans": [ + { + "bbox": [ + 83, + 116, + 493, + 282 + ], + "type": "image", + "image_path": "bba51a297b61be3c08f62c60202a29053e2d99f3657afce5298bb11aa2bec209.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 292, + 530, + 357 + ], + "lines": [ + { + "bbox": [ + 45, + 292, + 530, + 357 + ], + "spans": [ + { + "bbox": [ + 45, + 292, + 530, + 357 + ], + "type": "text", + "content": "Figure 2: Overview of the framework for fine-grained feature learning. We facilitate fine-grained feature learning by integrating self-supervised learning on unlabeled videos into supervised learning with labeled synthetic videos. For learning with synthetic data " + }, + { + "bbox": [ + 45, + 292, + 530, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 45, + 292, + 530, + 357 + ], + "type": "text", + "content": ", we devise a soft labeling module to convert the hard labels indicated by the motion vectors to soft labels. To learn more generalizable features, we leverage free supervision from unlabeled videos " + }, + { + "bbox": [ + 45, + 292, + 530, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathcal{T}}" + }, + { + "bbox": [ + 45, + 292, + 530, + 357 + ], + "type": "text", + "content": " with the objective of frame reconstruction. Furthermore, an adversarial loss (along with Gradient Reverse Layer and a discriminator) is proposed to encourage domain invariant representations. The whole framework is jointly optimized in an end-to-end manner with the proposed objective functions." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 361, + 282, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 361, + 282, + 489 + ], + "spans": [ + { + "bbox": [ + 45, + 361, + 282, + 489 + ], + "type": "text", + "content": "realize it is through adversarial training. Recent studies execute adversarial training by learning a domain classifier (the discriminator) to distinguish the learned features from different distributions, utilizing adversarial loss to increase domain confusion. Meanwhile, self-supervised learning obtains impressive performance and shows good generalizing ability by designing different pretext tasks [11, 41, 43, 45] with unlabeled data, which motivates us to combine supervised learning and self-supervised learning to encourage consistent representations for both domains as well as improved results for downstream tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 110, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 110, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 110, + 511 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 517, + 279, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 517, + 279, + 586 + ], + "spans": [ + { + "bbox": [ + 45, + 517, + 279, + 586 + ], + "type": "text", + "content": "We address the problem of estimating the pixel-wise correspondences between a pair of video frames, which can be realized by learning fine-grained features for matching. Our goal is to learn a fine-grained feature space " + }, + { + "bbox": [ + 45, + 517, + 279, + 586 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 45, + 517, + 279, + 586 + ], + "type": "text", + "content": " with the encoder " + }, + { + "bbox": [ + 45, + 517, + 279, + 586 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 517, + 279, + 586 + ], + "type": "text", + "content": " by designing different learning objective functions for the probabilistic mapping." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": "Probabilistic mapping. Given a pair of video frames " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "I_1, I_2 \\in \\mathbb{R}^{h \\times w \\times 3}" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": ", for all pixels in " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "I_1" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": ", we aim to predict the probabilistic mapping " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "P_{1 \\to 2} \\in \\mathbb{R}^{H \\times W \\times (2r + 1)^2}" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "P_{1 \\to 2}(\\cdot | i) \\in \\mathbb{R}^{(2r + 1)^2}" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": " gives the probability that " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": " is mapped to " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": " in frame " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "I_2" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": " within a limited range " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": ", considering the nature of temporal coherence in the video. The " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "i, j \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": " indicate the 2D pixel location. " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "P_{1 \\to 2}(\\cdot | i) \\in \\mathbb{R}^{(2r + 1)^2}" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": " thus encodes the entire discrete conditional probability distribution of where " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": " is mapped in frame " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "I_2" + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "text", + "content": ". The probabilistic mapping can be achieved by calculating the feature similarities using the learned fine-grained features. More specifically, we first extract the dense features " + }, + { + "bbox": [ + 45, + 586, + 280, + 730 + ], + "type": "inline_equation", + "content": "F_1, F_2 \\in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "spans": [ + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "text", + "content": ". Then the discrete probabilistic map can be obtained by computing the local correlation w.r.t. each key " + }, + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "inline_equation", + "content": "I_{2}" + }, + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "text", + "content": " within a local window for each query " + }, + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 360, + 530, + 395 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 297, + 403, + 536, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 403, + 536, + 433 + ], + "spans": [ + { + "bbox": [ + 297, + 403, + 536, + 433 + ], + "type": "interline_equation", + "content": "P _ {1 \\rightarrow 2} (j | i) = \\frac {\\exp \\left(F _ {1} (i) \\cdot F _ {2} (j) / \\tau\\right)}{\\sum_ {n} \\exp \\left(F _ {1} (i) \\cdot F _ {2} (n) / \\tau\\right)}, i \\in \\{1,.., H W \\}, j, n \\in \\mathcal {K} (i), \\tag {1}", + "image_path": "f976a406e3a530d2eee6d74e7202e0638e1889c28649b4983774645e342b3e6c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "spans": [ + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "inline_equation", + "content": "\\mathcal{K}(i)" + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "text", + "content": " is the index set in the local window with a limited range of " + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "text", + "content": " centered at " + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 296, + 434, + 531, + 480 + ], + "type": "text", + "content": " is the temperature. The result of the probabilistic mapping is further post-processed and directly applied to various downstream tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 494, + 464, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 494, + 464, + 506 + ], + "spans": [ + { + "bbox": [ + 297, + 494, + 464, + 506 + ], + "type": "text", + "content": "3.1. Fine-Grained Feature Learning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 513, + 530, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 513, + 530, + 548 + ], + "spans": [ + { + "bbox": [ + 296, + 513, + 530, + 548 + ], + "type": "text", + "content": "We design the learning objective functions for probabilistic mapping with both synthetic and real-world videos. The overview of the framework is shown in Figure 2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "spans": [ + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "type": "text", + "content": "Learning with synthetic videos. Labeled synthetic videos are often used as supervision for learning the optical flows in recent studies [8,34]. Given a pair of rendered video frames " + }, + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "type": "inline_equation", + "content": "I_1^s, I_2^s" + }, + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "type": "text", + "content": ", the synthetic data " + }, + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "type": "text", + "content": " provides pixelwise motion vector, i.e., optical flow " + }, + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "type": "inline_equation", + "content": "G_{1\\rightarrow 2}" + }, + { + "bbox": [ + 296, + 550, + 530, + 667 + ], + "type": "text", + "content": ". A valid question then emerges as how to learn features using such deterministic correspondences? Indeed, we believe the deterministic correspondences are hard to obtain for real-world videos, thus we argue the necessity to convert them into soft (probabilistic) ones. We devise the following variants:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": "(i) Dirac distribution: As shown in Figure 3 (a), we can directly convert the motion vector to a dirac distribution " + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\delta (\\cdot |i)" + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": " in order to describe the ground truth mapping. Then, the learning objective function defined as Kullback-Leibler divergence between " + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "inline_equation", + "content": "P_{1\\rightarrow 2}^{s}(\\cdot |i)" + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\delta (\\cdot |i)" + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "inline_equation", + "content": "P_{1 - > 2}^{s}" + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": " stands" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "9634" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 105, + 274, + 193 + ], + "blocks": [ + { + "bbox": [ + 49, + 105, + 274, + 193 + ], + "lines": [ + { + "bbox": [ + 49, + 105, + 274, + 193 + ], + "spans": [ + { + "bbox": [ + 49, + 105, + 274, + 193 + ], + "type": "image", + "image_path": "bc2a06a2cc2db348f2d241dc610fa5ca42109622ef28dd21601b81c088aa6161.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "lines": [ + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "spans": [ + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "text", + "content": "Figure 3: Illustration of the probabilistic map. For " + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "inline_equation", + "content": "I_1^s" + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "text", + "content": ", we visualize the probability value of the mapping from " + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "text", + "content": " to the locations in " + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "inline_equation", + "content": "I_2^s" + }, + { + "bbox": [ + 45, + 196, + 279, + 228 + ], + "type": "text", + "content": " within a limited range." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 230, + 278, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 230, + 278, + 241 + ], + "spans": [ + { + "bbox": [ + 45, + 230, + 278, + 241 + ], + "type": "text", + "content": "for the correlation calculated by Eq. (1) with synthetic data:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 83, + 250, + 279, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 250, + 279, + 275 + ], + "spans": [ + { + "bbox": [ + 83, + 250, + 279, + 275 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {K L - v l}} = \\sum_ {i} D _ {K L} (\\delta (\\cdot | i) \\| P _ {1 \\rightarrow 2} ^ {s} (\\cdot | i)). \\tag {2}", + "image_path": "b75d3655765fcf0a2839e9f908c8734a1d50d929211769a751d902362c14310f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 277, + 279, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 277, + 279, + 392 + ], + "spans": [ + { + "bbox": [ + 45, + 277, + 279, + 392 + ], + "type": "text", + "content": "(ii) Gaussian distribution: However, the feature of the query pixel " + }, + { + "bbox": [ + 45, + 277, + 279, + 392 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 277, + 279, + 392 + ], + "type": "text", + "content": " varies smoothly over space and time, which indicates a soft distribution of the potential location in the next frame. As shown in Figure 3 (a), the dirac distribution does not provide the feature learning with any knowledge of relative probability in the background, making it hard to learn the features with the ability to tell the fine-grained differences with synthetic videos. Thus, we devise to generate the probabilistic map with gaussian distribution, which introduces a soft distribution centered at the ground truth coordinate:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 397, + 279, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 397, + 279, + 434 + ], + "spans": [ + { + "bbox": [ + 49, + 397, + 279, + 434 + ], + "type": "interline_equation", + "content": "\\mathcal {N} (j | i, \\mu , \\sigma^ {2}) = \\frac {1}{\\sqrt {2 \\pi} \\sigma_ {u}} e ^ {- \\frac {\\left(u _ {j} - \\mu_ {t} ^ {u}\\right) ^ {2}}{2 \\sigma_ {u} ^ {2}}} \\cdot \\frac {1}{\\sqrt {2 \\pi} \\sigma_ {v}} e ^ {- \\frac {\\left(v _ {j} - \\mu_ {t} ^ {v}\\right) ^ {2}}{2 \\sigma_ {v} ^ {2}}}, \\tag {3}", + "image_path": "c566aeed9899b835522604a117ee4acd5436a626af031519b96081a32f9511f1.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "spans": [ + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "inline_equation", + "content": "\\mu = (\\mu_i^u,\\mu_i^v)" + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "text", + "content": " represents the 2D coordinate of ground truth in the " + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "inline_equation", + "content": "I_2^s" + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "text", + "content": " for pixel " + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "inline_equation", + "content": "(u_{j},v_{j})" + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "text", + "content": " indicates the 2D coordinate of " + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 435, + 279, + 469 + ], + "type": "text", + "content": ". Then the loss can be devised as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 485, + 279, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 485, + 279, + 509 + ], + "spans": [ + { + "bbox": [ + 69, + 485, + 279, + 509 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {K L - v 2}} = \\sum_ {i} D _ {K L} \\left(\\mathcal {N} (\\cdot | i, \\mu , \\sigma^ {2}) \\| P _ {1 \\rightarrow 2} (\\cdot | i)\\right). \\tag {4}", + "image_path": "c22c0d6c37d4685fe8cfe27bf53abe00ac8c48a93da840a64a07b97382c75ccd.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "spans": [ + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": "(iii) Soft-labeling: The gaussian prior only considers the euclidean distance of coordinates, which shows limited capability of modeling the complicated distributions. We believe the synthetic supervision already provides valuable temporal cues (" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "I_1^s" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " move to " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "I_2^s" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": "), and the soft distribution over space can be approached by computing the self-similarities for " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " using the pre-trained 2D visual encoder " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "\\theta_{self}" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " which can produce spatially-discriminative features. As shown in Figure 3 (c), for the " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "I_1^s" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " that moves to " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": ", we get the feature of the query " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " (denoted as " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "\\overline{F}_q" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": ") at the location " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "\\overline{F}_2" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "\\overline{F}_2" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " is the feature map of " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "I_2^s" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " computed by " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "\\theta_{self}" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": "). Then we can compute the feature similarities " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "S_{1\\rightarrow 2}(\\cdot |i)" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "\\overline{F}_q" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "\\{\\overline{F}_2(k)|k\\in \\mathcal{K}(i)\\}" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "\\mathcal{K}(i)" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " is the index set in the local window centered at " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "S_{1\\rightarrow 2}(\\cdot |i)" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": " are further normalized (by softmax) to obtain the discrete probability distribution " + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "inline_equation", + "content": "P_{1\\rightarrow 2}(\\cdot |i)" + }, + { + "bbox": [ + 45, + 514, + 279, + 701 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 74, + 708, + 279, + 732 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 708, + 279, + 732 + ], + "spans": [ + { + "bbox": [ + 74, + 708, + 279, + 732 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {K L - v 3}} = \\sum_ {i} D _ {K L} \\left(P _ {1 \\rightarrow 2} (\\cdot | i) \\| P _ {1 \\rightarrow 2} ^ {s} (\\cdot | i)\\right). \\tag {5}", + "image_path": "5585c487fa226cac546f2f2999dc8f4e1eac0036e2a78350c3e809b5fdb06a05.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": "In Table 4, we find soft labeling works well when only pre-training " + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "inline_equation", + "content": "\\theta_{\\text{self}}" + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": " on synthetic data " + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathcal{S}}" + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}" + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": " (Eq. (8)), and leveraging more strong 2D encoder would contribute to better performance. The comparisons between different loss functions will be discussed in the experiments, and the " + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL - v3}}" + }, + { + "bbox": [ + 296, + 106, + 530, + 175 + ], + "type": "text", + "content": " is used as the default loss." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "spans": [ + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": "Learning with unlabeled videos. Meanwhile, we observe in real scenarios, there are apparent differences with synthetic videos in appearance variants, illumination changes and deformations, leading to notable changes in the distribution, where the learned features on synthetic videos show unsatisfied generalization ability. Inspired by recent studies [16, 41], we try to improve the learned fine-grained features by introducing self-supervised feature learning into the framework. As observed in the bottom of Figure 1, the pixel repetition encourages us to learn the fine-grained features by reconstructive learning, where each pixel in the " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "I_1^t" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": " can be reconstructed by leveraging the information of " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "I_2^t" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": " with a limited range. To achieve this, the video frames " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "I_1^t, I_2^t" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": " are firstly projected into pixel embeddings " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "F_1^t, F_2^t" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": " by the encoder " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": ". For each query " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "I_1^t" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": ", we calculate the probabilistic map " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "P_{1\\rightarrow 2}^t" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": " with Eq. (1). Then the query " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "I_1^t" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": " can be reconstructed by a weighted sum of pixels in " + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "inline_equation", + "content": "\\mathcal{K}(i)" + }, + { + "bbox": [ + 296, + 177, + 530, + 374 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 350, + 383, + 530, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 383, + 530, + 408 + ], + "spans": [ + { + "bbox": [ + 350, + 383, + 530, + 408 + ], + "type": "interline_equation", + "content": "I _ {1} ^ {\\text {r e c}} (i) = \\sum_ {j \\in \\mathcal {K} (i)} P _ {1 \\rightarrow 2} ^ {t} (j | i) I _ {2} ^ {t} (j). \\tag {6}", + "image_path": "1fe049e4ac00e34a7bf89d9d8393d2cfda4ed8bff1f1fffbdcb2a53f3c0f4584.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "spans": [ + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "type": "text", + "content": "Then the reconstruction loss for self-supervised training is defined as " + }, + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "type": "text", + "content": " distance between " + }, + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "type": "inline_equation", + "content": "I_1^{rec}" + }, + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "type": "inline_equation", + "content": "I_1^t" + }, + { + "bbox": [ + 296, + 416, + 530, + 462 + ], + "type": "text", + "content": ". Training with such self-supervision leads to temporal persistent features that generalize well in real scenarios." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 463, + 530, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 463, + 530, + 544 + ], + "spans": [ + { + "bbox": [ + 296, + 463, + 530, + 544 + ], + "type": "text", + "content": "However, the pixel repetition does not hold for pixels that become occluded. Thus, we exclude occluded pixels from the reconstruction loss to avoid learning incorrect features. We follow the forward-backward consistency assumption to detect the occluded pixels. which is defined in Eq. (7) as the occlusion flag " + }, + { + "bbox": [ + 296, + 463, + 530, + 544 + ], + "type": "inline_equation", + "content": "O_{1\\rightarrow 2}" + }, + { + "bbox": [ + 296, + 463, + 530, + 544 + ], + "type": "text", + "content": " to be 1 whenever the constraint is violated, and 0 otherwise:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 301, + 550, + 530, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 550, + 530, + 583 + ], + "spans": [ + { + "bbox": [ + 301, + 550, + 530, + 583 + ], + "type": "interline_equation", + "content": "O _ {1 \\rightarrow 2} (i) = \\mathbb {1} \\left(\\underset {i} {\\arg \\max } P _ {2 \\rightarrow 1} ^ {t} \\left(i \\mid \\underset {j} {\\arg \\max } P _ {1 \\rightarrow 2} ^ {t} (j \\mid i)\\right) = i\\right). \\tag {7}", + "image_path": "c2da230b47203672fd997629548a9a90dce58ecabed54430a01c2c4d1b0e24f6.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 584, + 522, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 584, + 522, + 596 + ], + "spans": [ + { + "bbox": [ + 297, + 584, + 522, + 596 + ], + "type": "text", + "content": "The loss for reconstructive learning is defined as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 335, + 605, + 530, + 626 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 605, + 530, + 626 + ], + "spans": [ + { + "bbox": [ + 335, + 605, + 530, + 626 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e c}} = \\sum_ {i} O _ {1 \\rightarrow 2} (i) \\cdot \\left\\| I _ {1} ^ {\\text {r e c}} (i) - I _ {1} ^ {t} (i) \\right\\| _ {1}. \\tag {8}", + "image_path": "357480bf7bed852b85b0825cee2648037566e49b4c4deda21516c18bd0df6f00.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": "Adversarial training. We further improve the fine-grained features by leveraging the technique in recent works of unsupervised domain adaptation, which aims to bridge the gap caused by the domain shift between the synthetic videos " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " and real videos " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathcal{T}}" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " via adversarial training. An effective way to approach this problem consists in introducing the network a Gradient Reversal Layer (GRL). We additionally train a discriminator " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\theta_{D}" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " to identify whether the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "9635" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 104, + 281, + 152 + ], + "blocks": [ + { + "bbox": [ + 47, + 104, + 281, + 152 + ], + "lines": [ + { + "bbox": [ + 47, + 104, + 281, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 104, + 281, + 152 + ], + "type": "image", + "image_path": "cb6b891b9ea7d8de9c1f0ff74d573e49bb0e50dea06e647cec26c4c97c831b24.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 160, + 279, + 194 + ], + "lines": [ + { + "bbox": [ + 45, + 160, + 279, + 194 + ], + "spans": [ + { + "bbox": [ + 45, + 160, + 279, + 194 + ], + "type": "text", + "content": "Figure 4: Illustration of the coarse-to-fine framework for efficient probabilistic mapping. We first obtain coarse-grained matching and then upsample it to get the fine-grained result." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 197, + 260, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 197, + 260, + 208 + ], + "spans": [ + { + "bbox": [ + 45, + 197, + 260, + 208 + ], + "type": "text", + "content": "probabilistic map comes from synthetic or real videos:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 214, + 279, + 237 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 214, + 279, + 237 + ], + "spans": [ + { + "bbox": [ + 45, + 214, + 279, + 237 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {a d v}} = \\mathbb {E} _ {P ^ {t} \\in P _ {\\mathcal {T}}} [ \\log (D (P ^ {t})) ] + \\mathbb {E} _ {P ^ {s} \\in P _ {\\mathcal {S}}} [ \\log (1 - D (P ^ {s})) ], \\tag {9}", + "image_path": "7b6644fe8ed74ec69107d07f6634a6f75e6b03027b2b04b60533f05af24945fd.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 238, + 279, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 238, + 279, + 273 + ], + "spans": [ + { + "bbox": [ + 45, + 238, + 279, + 273 + ], + "type": "text", + "content": "and then we reverse the gradient direction during the backward pass in back-propagation when updating the parameters of the encoder " + }, + { + "bbox": [ + 45, + 238, + 279, + 273 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 238, + 279, + 273 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 45, + 238, + 279, + 273 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{adv}}" + }, + { + "bbox": [ + 45, + 238, + 279, + 273 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 121, + 280, + 279, + 303 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 280, + 279, + 303 + ], + "spans": [ + { + "bbox": [ + 121, + 280, + 279, + 303 + ], + "type": "interline_equation", + "content": "\\theta \\leftarrow \\theta + \\lambda \\frac {\\partial \\mathcal {L} _ {\\mathrm {a d v}}}{\\partial \\theta}. \\tag {10}", + "image_path": "d19aaca5c2a2917313a61a8a0dd9ad28f52966016b41612e4a9b9548fc530155.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 306, + 279, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 306, + 279, + 341 + ], + "spans": [ + { + "bbox": [ + 45, + 306, + 279, + 341 + ], + "type": "text", + "content": "The GRL allows to train the discriminator and the encoder at the same time, and the adversarial training helps to learn domain invariant patterns." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 341, + 279, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 341, + 279, + 389 + ], + "spans": [ + { + "bbox": [ + 45, + 341, + 279, + 389 + ], + "type": "text", + "content": "Overall training objective. The overall training objective for learning fine-grained features is formulated as a multi-task loss, which is written as " + }, + { + "bbox": [ + 45, + 341, + 279, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_{\\mathrm{KL}} + \\mathcal{L}_{\\mathrm{rec}} + \\mathcal{L}_{\\mathrm{adv}}" + }, + { + "bbox": [ + 45, + 341, + 279, + 389 + ], + "type": "text", + "content": " where we empirically treat each loss equally." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 394, + 272, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 394, + 272, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 272, + 408 + ], + "type": "text", + "content": "3.2. Efficient Fine-grained Probabilistic Mapping" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 412, + 279, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 412, + 279, + 506 + ], + "spans": [ + { + "bbox": [ + 45, + 412, + 279, + 506 + ], + "type": "text", + "content": "To get the fine-grained probabilistic map, i.e., " + }, + { + "bbox": [ + 45, + 412, + 279, + 506 + ], + "type": "inline_equation", + "content": "P_{1\\rightarrow 2}\\in \\mathbb{R}^{H\\times W\\times (2r + 1)^2}" + }, + { + "bbox": [ + 45, + 412, + 279, + 506 + ], + "type": "text", + "content": ", we need to compute the similarities w.r.t. all key pixels in the local window centered at every query pixel, which is computationally costly. In this section, we devise a coarse-to-fine framework. The overview of the framework can be found in Figure 4, where we first compute the correlation at coarse-grained features and then up-sample it to get fine-grained probabilistic maps." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 506, + 279, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 506, + 279, + 588 + ], + "spans": [ + { + "bbox": [ + 45, + 506, + 279, + 588 + ], + "type": "text", + "content": "Self-attention and Cross-attention Layers. More specifically, we first extract the coarse feature maps " + }, + { + "bbox": [ + 45, + 506, + 279, + 588 + ], + "type": "inline_equation", + "content": "F_{1}^{\\downarrow}, F_{2}^{\\downarrow} \\in \\mathbb{R}^{H/4 \\times W/4 \\times C}" + }, + { + "bbox": [ + 45, + 506, + 279, + 588 + ], + "type": "text", + "content": ", and we further enhance the coarse features by introducing the self-attention and cross-attention layers with positional encoding. Then, we obtain the coarse-grained probabilistic map " + }, + { + "bbox": [ + 45, + 506, + 279, + 588 + ], + "type": "inline_equation", + "content": "P_{1 \\rightarrow 2} \\downarrow \\in \\mathbb{R}^{H/4 \\times W/4 \\times (2r\\downarrow + 1)^{2}}" + }, + { + "bbox": [ + 45, + 506, + 279, + 588 + ], + "type": "text", + "content": " by Eq (1)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "spans": [ + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": "Up-sampling. We devise an up-sampling layer to obtain fine-grained probabilistic map " + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "inline_equation", + "content": "P_{1\\rightarrow 2}\\in \\mathbb{R}^{H\\times W\\times (2r + 1)^2}" + }, + { + "bbox": [ + 45, + 589, + 279, + 636 + ], + "type": "text", + "content": " which can be simply done by leveraging pixel-shuffle or convolution layer with bilinear interpolation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": "More details of the architecture are included in the supplementary material. We train the coarse-to-fine framework in a distillation manner on " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathcal{T}}" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ", with the same objective function as " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL}}" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": ". The supervisions for " + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "inline_equation", + "content": "P_{1\\rightarrow 2}" + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": " are obtained by computing the probabilistic map using pre-trained encoder in Sec. 3.1. Without losing much performance, we find such a design helps to get rid of the complicated fine-grained feature matching and exhibit higher efficiency." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 105, + 376, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 105, + 376, + 117 + ], + "spans": [ + { + "bbox": [ + 297, + 105, + 376, + 117 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 127, + 530, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 127, + 530, + 186 + ], + "spans": [ + { + "bbox": [ + 296, + 127, + 530, + 186 + ], + "type": "text", + "content": "We verify the effectiveness of our method in a series of correspondence-based tasks. We will first introduce implementation and evaluation details, and report the performance comparison with baselines. Finally, we perform detailed ablation studies for each component of our method." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 202, + 426, + 214 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 202, + 426, + 214 + ], + "spans": [ + { + "bbox": [ + 297, + 202, + 426, + 214 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "spans": [ + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "type": "text", + "content": "Backbone. We exploit the encoder " + }, + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "type": "text", + "content": " with ResNet-18 [12]. We reduce the stride up to layer " + }, + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "type": "inline_equation", + "content": "\\mathrm{res}_4" + }, + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "type": "text", + "content": " to get features at " + }, + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 296, + 222, + 530, + 281 + ], + "type": "text", + "content": " of the original image dimension for training. In our coarse-to-fine framework, we increase the stride of the encoder to 8 for coarse-grained feature matching." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "spans": [ + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": "Training details. The training is conducted on the train set of synthetic dataset FlyingThings [26] and YouTube-VOS [46] collected in real-world. The FlyingThings/YouTube-VOS contains " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "40\\mathrm{k} / 3.5\\mathrm{k}" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " videos for training. For both datasets, we sample pair of frames which are resized into " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "256\\times 256" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " and converted to Lab color space with channel-wise dropout as the information bottleneck [20]. The local range " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " in the probabilistic map is set to " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "24 / 6" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " for the fine-grained features " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "(\\frac{h}{2}\\times \\frac{w}{2}" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " (stride=2)) or coarse-grained features " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "(\\frac{h}{8}\\times \\frac{w}{8}" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " (stride=8)). We first train an encoder using reconstruction loss (Eq. (8)) with a batchsize of 32 for 30 epochs on FlyingThings [26], which is further utilized as " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "\\theta_{self}" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " in soft labeling. Then the final model " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " is jointly trained for 30 epochs with proposed three losses, with a batchsize of 16 for each dataset. When training with synthetic optical flow, we filter out the points that are out of the local range or occluded by forward-backward checking. The " + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 296, + 283, + 531, + 529 + ], + "type": "text", + "content": " is set to 1. We use Adam as the optimizer, and the initial learning rate is set to 1e-3 with a cosine (half-period) learning rate schedule for each stage. We include more training details in the supplementary." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": "Evaluation. An important problem is how to evaluate the quality of the learned fine-grained features for pixel-wise video correspondences. Following the previous works [16,41,45], without any fine-tuning, we directly leverage the pre-trained encoder " + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": " to extract features " + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "inline_equation", + "content": "F_{i}, F_{j}" + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": " with a spatial resolution of " + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\frac{h}{s} \\times \\frac{w}{s}" + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": " (the " + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": " represents the stride of the encoder) for the pair of frames " + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "inline_equation", + "content": "I_{i}, I_{j}" + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": ", which are later used to compute the probabilistic map " + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "inline_equation", + "content": "P_{i \\rightarrow j}" + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": " by Eq (1). Based on the probabilistic map " + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "inline_equation", + "content": "P_{i \\rightarrow j}" + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": ", we follow the recurrent inference strategy inference strategies of recent studies [16,41,45] to propagate the target points or semantic labels of the first frame, as well as previous predictions, to the current frame " + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 296, + 532, + 530, + 730 + ], + "type": "text", + "content": ". We evaluate the point tracking on three popular benchmarks including BADJA [2], JHMDB [18], TAP-Vid-DAVIS [7] and TAP-Vid-Kinetics [7], and the evaluation of video object segmentation is conducted on the widely used dataset DAVIS-2017 [29]." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "9636" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 99, + 143, + 480, + 317 + ], + "blocks": [ + { + "bbox": [ + 45, + 104, + 531, + 139 + ], + "lines": [ + { + "bbox": [ + 45, + 104, + 531, + 139 + ], + "spans": [ + { + "bbox": [ + 45, + 104, + 531, + 139 + ], + "type": "text", + "content": "Table 1: Quantitative results for point tracking on different datasets. The frame per second (FPS) results of getting pixelwise correspondences between a pair of video frames are measured on a single GTX-3090 at the resolution of " + }, + { + "bbox": [ + 45, + 104, + 531, + 139 + ], + "type": "inline_equation", + "content": "480 \\times 640" + }, + { + "bbox": [ + 45, + 104, + 531, + 139 + ], + "type": "text", + "content": ". The * indicates our coarse-to-fine framework. The - indicates the unavailable result due to the unavailable pre-trained model." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 99, + 143, + 480, + 317 + ], + "lines": [ + { + "bbox": [ + 99, + 143, + 480, + 317 + ], + "spans": [ + { + "bbox": [ + 99, + 143, + 480, + 317 + ], + "type": "table", + "html": "
MethodBackboneStrideFPSBADJAJHMDBTAP-DAVISTAP-Kinetics
PCK@0.1↑PCK@0.1↑<δxavg-p↑<δxavg-p↑
TimeCycle [41]ResNet-5082841.157.327.128.6
UVC [24]ResNet-18814248.258.629.025.2
CRW [16]ResNet-18814250.959.332.525.4
VFS [45]ResNet-18814251.960.531.928.8
CLSC [31]ResNet-188142-61.7--
SFC [13]ResNet-18 + ResNet-5082753.861.937.231.1
MAST [20]ResNet-1843355.762.442.533.2
LIIR [22]ResNet-18433-60.7--
Ours*ResNet-1883456.864.648.043.8
ImageNet Pre. [12]ResNet-182857.561.551.344.5
UVC [24]ResNet-182856.765.152.741.8
CRW [16]ResNet-182855.961.443.237.1
VFS [45]ResNet-182858.161.051.444.9
SFC [13]ResNet-182861.565.953.943.6
MAST [20]ResNet-182863.063.153.842.7
OursResNet-182867.266.859.848.8
", + "image_path": "ecf8503885b5ce8652e1dd2daea872faf1d5d75fdbdd577fba74e38fc918c463.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 325, + 188, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 325, + 188, + 338 + ], + "spans": [ + { + "bbox": [ + 45, + 325, + 188, + 338 + ], + "type": "text", + "content": "4.2. Results for Point Tracking" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 344, + 280, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 344, + 280, + 436 + ], + "spans": [ + { + "bbox": [ + 45, + 344, + 280, + 436 + ], + "type": "text", + "content": "We firstly make comparisons for point tracking since it requires the finest granularity of the learned features. The main comparators of our method are the works aim to learn good representations for matching, e.g., TimeCycle [41], UVC [24], CRW [16], VFS [45], SFC [13], and MAST [20]. We also include the model pre-trained on ImageNet [6] with human annotations. These works share a similar evaluation protocol as we mentioned in 4.1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "spans": [ + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "type": "text", + "content": "While previous works test the pixel-wise correspondences on JHMDB [18] that only provides the human keypoint annotations. We additionally include BADJA [2], TAP-Vid-DAVIS [7] and TAP-Vid-Kinetics [7]. We propagate the points of the first frame to other frames and evaluate the results using the annotations of each dataset. We notice some works are trained and evaluated with the coarse-grained features (e.g., the features at 1/8 of the original image dimension). For these methods, we use our coarse-to-fine framework that also executes coarse-grained feature matching for comparisons. Meanwhile, for better comparisons, we follow the studies in [16,45] to further reduce the stride " + }, + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "type": "text", + "content": " of the encoder to 2, in order to get more fine-grained results for CRW, VFS, SFC and MAST. We also provide the FPS of computing the pixel-wise correspondences between two frames for feature-matching-based methods, which can be done by first taking the index of the maximum value in " + }, + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "type": "inline_equation", + "content": "P_{1\\rightarrow 2}(\\cdot |i)" + }, + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "type": "text", + "content": " for each " + }, + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 437, + 279, + 671 + ], + "type": "text", + "content": " and then applying up-sampling to get full-resolution results. More details about the evaluation are included in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": "Results on BADJA/JHMDB. We adopt the standard PCK [47] of all visible points (not compute PCK for each video then take average) as the evaluation metric. Each point is considered correct if it is within a distance of " + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "inline_equation", + "content": "0.1\\sqrt{A}" + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": " from the ground truth, where " + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": " is the distance be" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "spans": [ + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "type": "text", + "content": "tween keypoints (for JHMDB) or the area of the ground-truth segmentation mask on the frame (for BADJA). In Table 1, our method achieves " + }, + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "type": "inline_equation", + "content": "67.2\\% / 66.8\\%" + }, + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "type": "text", + "content": ", surpassing all state-of-the-art methods. Besides, our method with the coarse-to-fine design still makes the absolute improvements by " + }, + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 296, + 325, + 530, + 442 + ], + "type": "text", + "content": " compared with MAST, and shows better efficiency compared with SFC [13] that uses the two-stream network to find the correspondences. More remarkably, our efficient framework even surpasses part of the methods using more fine-grained features for inference." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "spans": [ + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "text", + "content": "Results on TAP-Vid. TAP-Vid is a newly developed benchmark composed of long-term videos in real-world with accurate human annotations of point tracks. We test on the whole set of TAP-Vid-DAVIS and the test set of TAP-Vid-Kinetics. We adopt the setting of \"first fashion\" in [7], which tracks only into the future. The average position accuracy over all visible points " + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "inline_equation", + "content": "(< \\delta_{avg-p}^{x})" + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "text", + "content": " is adopted as the metric. The learned fine-grained features obtain " + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "inline_equation", + "content": "59.8\\% / 48.8\\%" + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "text", + "content": " on TAP-Vid-DAVIS/TAP-Vid-Kinetics, leading apparent improvements over state-of-the-arts by " + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "inline_equation", + "content": "5.9\\% / 3.9\\%" + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "text", + "content": ". Moreover, the proposed coarse-to-fine framework gets " + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "inline_equation", + "content": "48.0\\% / 43.8\\%" + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "text", + "content": ", surpassing MAST by " + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "inline_equation", + "content": "5.5\\% / 10.6\\%" + }, + { + "bbox": [ + 296, + 446, + 531, + 586 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": "Comparisons with task-specific methods. Besides, we notice there are some recent methods specifically designed for point tracking, like RAFT [34], PIPs [10], TAPNet [7], and Thin-Slicing Net [32] even trained with human annotations. Here we also present the performance comparisons with them in Table 2. It's worth noting that, to align the evaluation with these methods, except JHMDB, we first compute the " + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "inline_equation", + "content": "< \\delta_{avg-p}^{x}" + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": " or PCK for each video to obtain video-level results, and the final results are obtained by taking the average over all videos. Without any specific designs, our performance even surpasses these methods by " + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "inline_equation", + "content": "7.4\\% / 7.5\\% / 0.2\\%" + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": " on BADJA/TAP-DAVIS/TAP-Kinetics." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "9637" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 105, + 156, + 380 + ], + "blocks": [ + { + "bbox": [ + 70, + 105, + 156, + 380 + ], + "lines": [ + { + "bbox": [ + 70, + 105, + 156, + 380 + ], + "spans": [ + { + "bbox": [ + 70, + 105, + 156, + 380 + ], + "type": "image", + "image_path": "63693f9b4c2b6b0fe8af4c0a6ef33d4baec674c4cf1b55cb7670bfca7829017f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 76, + 383, + 153, + 394 + ], + "lines": [ + { + "bbox": [ + 76, + 383, + 153, + 394 + ], + "spans": [ + { + "bbox": [ + 76, + 383, + 153, + 394 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 76, + 383, + 153, + 394 + ], + "type": "text", + "content": " frame with target" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 157, + 105, + 243, + 380 + ], + "blocks": [ + { + "bbox": [ + 157, + 105, + 243, + 380 + ], + "lines": [ + { + "bbox": [ + 157, + 105, + 243, + 380 + ], + "spans": [ + { + "bbox": [ + 157, + 105, + 243, + 380 + ], + "type": "image", + "image_path": "c3b3f39ca9443ce7a15af9176ef87f5e2b4677c64895d8efa1d9b43cb4cf002d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 192, + 383, + 207, + 393 + ], + "lines": [ + { + "bbox": [ + 192, + 383, + 207, + 393 + ], + "spans": [ + { + "bbox": [ + 192, + 383, + 207, + 393 + ], + "type": "text", + "content": "VFS" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 244, + 105, + 330, + 380 + ], + "blocks": [ + { + "bbox": [ + 244, + 105, + 330, + 380 + ], + "lines": [ + { + "bbox": [ + 244, + 105, + 330, + 380 + ], + "spans": [ + { + "bbox": [ + 244, + 105, + 330, + 380 + ], + "type": "image", + "image_path": "8da4cc658d11c65d46cda28d85b9421fedca55094da20aef7e3ebbcd939fb826.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 276, + 383, + 298, + 393 + ], + "lines": [ + { + "bbox": [ + 276, + 383, + 298, + 393 + ], + "spans": [ + { + "bbox": [ + 276, + 383, + 298, + 393 + ], + "type": "text", + "content": "MAST" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 332, + 105, + 417, + 380 + ], + "blocks": [ + { + "bbox": [ + 332, + 105, + 417, + 380 + ], + "lines": [ + { + "bbox": [ + 332, + 105, + 417, + 380 + ], + "spans": [ + { + "bbox": [ + 332, + 105, + 417, + 380 + ], + "type": "image", + "image_path": "a3792b42b1ebc6c7f2aaf7ba33b98653555b1f364bc9190277e2af7f6ed03f6e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 364, + 383, + 383, + 393 + ], + "lines": [ + { + "bbox": [ + 364, + 383, + 383, + 393 + ], + "spans": [ + { + "bbox": [ + 364, + 383, + 383, + 393 + ], + "type": "text", + "content": "RAFT" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 418, + 105, + 503, + 380 + ], + "blocks": [ + { + "bbox": [ + 418, + 105, + 503, + 380 + ], + "lines": [ + { + "bbox": [ + 418, + 105, + 503, + 380 + ], + "spans": [ + { + "bbox": [ + 418, + 105, + 503, + 380 + ], + "type": "image", + "image_path": "56ca515c545cf458a4f2ff892511cf6c36418b442caaba0248b73d794b7e9dc2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 451, + 383, + 470, + 393 + ], + "lines": [ + { + "bbox": [ + 451, + 383, + 470, + 393 + ], + "spans": [ + { + "bbox": [ + 451, + 383, + 470, + 393 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 396, + 531, + 429 + ], + "lines": [ + { + "bbox": [ + 45, + 396, + 531, + 429 + ], + "spans": [ + { + "bbox": [ + 45, + 396, + 531, + 429 + ], + "type": "text", + "content": "Figure 5: Qualitative results for point tracking. Given the target pixel in the first frame, we visualize the estimated trajectory with a pink-to-yellow colormap (pink/yellow indicates the start/end of the video clip). We visualize sparse ground-truth labels with cyan cross marks. Please refer to the video in the supplementary for better animations. (Zoom in for best view)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 51, + 475, + 279, + 541 + ], + "blocks": [ + { + "bbox": [ + 45, + 436, + 279, + 472 + ], + "lines": [ + { + "bbox": [ + 45, + 436, + 279, + 472 + ], + "spans": [ + { + "bbox": [ + 45, + 436, + 279, + 472 + ], + "type": "text", + "content": "Table 2: Comparisons with methods specifically designed for point tracking. “‡” means we align the evaluation protocol with each method for fair comparisons." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 475, + 279, + 541 + ], + "lines": [ + { + "bbox": [ + 51, + 475, + 279, + 541 + ], + "spans": [ + { + "bbox": [ + 51, + 475, + 279, + 541 + ], + "type": "table", + "html": "
MethodBADJAJHMDBTAP-DAVISTAP-Kinetics
PCK@0.2↑PCK@0.1↑<δxavg↑<δxavg↑
RAFT [34]45.666.442.144.3
PIPs [10]62.3-55.348.2
TAPNet [7]-62.348.654.4
Thin-Slicing Net [32]-68.7--
Ours‡69.766.862.854.6
", + "image_path": "59098e5984a44a7dbbd882c1aaf0bc0cc19a60f1de308ad1e49150b128b02e9d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 549, + 279, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 549, + 279, + 631 + ], + "spans": [ + { + "bbox": [ + 45, + 549, + 279, + 631 + ], + "type": "text", + "content": "Figure 5 shows some visualization results of the point tracking on TAP-Vid-DAVIS. Given the target in the first frame, we visualize the estimated trajectory with a pink-to-yellow map. Compared with VFS, MAST and RAFT, our approach can output more smooth and accurate trajectories close to the sparse visualized ground truth, even facing dramatic appearance changes and deformation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 45, + 640, + 244, + 654 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 640, + 244, + 654 + ], + "spans": [ + { + "bbox": [ + 45, + 640, + 244, + 654 + ], + "type": "text", + "content": "4.3. Results for Video Object Segmentation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "Next, we evaluate methods with semi-supervised video object segmentation. We use the mean of region similarity " + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_m" + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": ", mean of contour accuracy " + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_m" + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": " and their average " + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{J} \\& \\mathcal{F}_m" + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": " as the evaluation metrics. In Table 3, our method still leads the performance. More remarkably, our method even outperforms some task-specific fully-supervised algo" + } + ] + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 304, + 478, + 530, + 634 + ], + "blocks": [ + { + "bbox": [ + 296, + 436, + 530, + 472 + ], + "lines": [ + { + "bbox": [ + 296, + 436, + 530, + 472 + ], + "spans": [ + { + "bbox": [ + 296, + 436, + 530, + 472 + ], + "type": "text", + "content": "Table 3: Quantitative results for video object segmentation on " + }, + { + "bbox": [ + 296, + 436, + 530, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{DAVIS}_{17}" + }, + { + "bbox": [ + 296, + 436, + 530, + 472 + ], + "type": "text", + "content": " [29]. \"Sup.\" means using human annotations for training." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 304, + 478, + 530, + 634 + ], + "lines": [ + { + "bbox": [ + 304, + 478, + 530, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 478, + 530, + 634 + ], + "type": "table", + "html": "
MethodSup.BackboneDAVIS17
J&Fm↑Jm↑Fm↑
TimeCycle [41]ResNet-5040.741.939.4
UVC [24]ResNet-1859.557.761.3
MAST [20]ResNet-1865.563.367.6
CRW [16]ResNet-1867.664.870.2
JSTG [49]ResNet-1868.765.871.6
VFS [45]ResNet-5068.966.571.3
DUL [1]ResNet-1869.367.171.6
MAMP [27]ResNet-1869.768.371.2
CLTC [17]ResNet-1870.367.972.6
CLSC [31]ResNet-1870.567.473.6
SFC [13]ResNet-18 + ResNet-5071.268.374.0
LIIR [22]ResNet-1872.169.774.5
OursResNet-1872.470.574.4
OSVOS-S [25]✓VGG-1668.064.771.3
FEELVOS [37]✓Xception-6571.569.174.0
", + "image_path": "c3692d0053e51876246e1be956ed591403333d250e61046a04156d4b68fe4688.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 636, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 531, + 730 + ], + "type": "text", + "content": "rithms [25,37]. Here we select several representative videos for inference, and give the visualization results in Figure 6, our method produces tight boundaries around the object areas, and obtains more fine-grained results, especially for small objects. For example, in the first column of Figure 6, the tiny arm of the human can still be segmented, which further demonstrates the advantages of learning fine-grained features for video correspondences. However, we" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "9638" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 103, + 278, + 311 + ], + "blocks": [ + { + "bbox": [ + 48, + 103, + 278, + 311 + ], + "lines": [ + { + "bbox": [ + 48, + 103, + 278, + 311 + ], + "spans": [ + { + "bbox": [ + 48, + 103, + 278, + 311 + ], + "type": "image", + "image_path": "5ce43baff0c7d9458c25d5e9a2c25edb606ce5502bf5bed6eb55f3b8fca109a2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 319, + 279, + 352 + ], + "lines": [ + { + "bbox": [ + 45, + 319, + 279, + 352 + ], + "spans": [ + { + "bbox": [ + 45, + 319, + 279, + 352 + ], + "type": "text", + "content": "Figure 6: Qualitative results for video object segmentation. Given the semantic mask in the first frame, we show the propagation results on the target frame. (Zoom in for best view)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 362, + 279, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 362, + 279, + 419 + ], + "spans": [ + { + "bbox": [ + 45, + 362, + 279, + 419 + ], + "type": "text", + "content": "find that fine-grained features may hinder object-centric feature learning since it may rely more on low-level patterns (e.g., texture, color, etc), which degrades the performance in video object segmentation to some extent. We regard it as our future work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 431, + 136, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 136, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 136, + 443 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 449, + 279, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 449, + 279, + 472 + ], + "spans": [ + { + "bbox": [ + 45, + 449, + 279, + 472 + ], + "type": "text", + "content": "We perform ablation study with point tracking on the TAP-Vid-DAVIS [7] dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "content": "Learning with synthetic videos. We study the effect of three different ways as defined in Eq. (2), Eq. (4) and Eq. (5) for learning the fine-grained features with synthetic videos. Table 4 shows the performance comparisons across the three kinds of objective functions. As indicated by the results, the loss " + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL - v1}}" + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "content": " using dirac distribution to generate the labels performs badly. We think the deterministic labels were given on synthetic videos, resulting in the learned features not being robust enough on real-world videos. Besides, we find introducing the gaussian distribution in " + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL - v2}}" + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "content": " results in performance degradation. The performance drops a lot when progressively increasing the variance, which may be attributed to the inability of gaussian distribution to approach the real probabilistic distribution since it is extremely complicated. Expectedly, the proposed soft labeling boosts up the performance from " + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "inline_equation", + "content": "42.6\\%" + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "inline_equation", + "content": "55.8\\%" + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "content": " when only pre-training the " + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "inline_equation", + "content": "\\theta_{self}" + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "content": " with Eq. (8). Moreover, we also try another 2D encoder pre-trained with the contrastive loss " + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{nce}}" + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "content": " [11] on ImageNet [6], which has a stronger ability to capture the spatially discriminative features. The results are further improved to " + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "inline_equation", + "content": "57.5\\%" + }, + { + "bbox": [ + 45, + 474, + 280, + 730 + ], + "type": "text", + "content": ", which motivates us to leverage a more powerful 2D feature extractor" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 317, + 129, + 511, + 211 + ], + "blocks": [ + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "lines": [ + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "spans": [ + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "type": "text", + "content": "Table 4: Ablation study for " + }, + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL}}" + }, + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "type": "inline_equation", + "content": "\\sigma/\\theta_{\\text{self}}" + }, + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "type": "text", + "content": " represents the variance / encoder used in " + }, + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL - v2}} / \\mathcal{L}_{\\mathrm{KL - v3}}" + }, + { + "bbox": [ + 296, + 104, + 530, + 126 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 129, + 511, + 211 + ], + "lines": [ + { + "bbox": [ + 317, + 129, + 511, + 211 + ], + "spans": [ + { + "bbox": [ + 317, + 129, + 511, + 211 + ], + "type": "table", + "html": "
Obj. FunctionHyper-param.TAP-Vid-DAVIS < δxavg↑
(σu, σv)θself
LKL-v1--42.6
LKL-v2(1,1)-41.9
(3,3)-33.8
(6,6)-29.7
LKL-v3-w. Lrec55.8
-w. Lnce [11]57.5
", + "image_path": "067f9ff5f1206a77eaefaf08b2e8a74ead78a094d2eaf5f4788b4d2c91b0d13b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 320, + 245, + 509, + 323 + ], + "blocks": [ + { + "bbox": [ + 296, + 220, + 530, + 243 + ], + "lines": [ + { + "bbox": [ + 296, + 220, + 530, + 243 + ], + "spans": [ + { + "bbox": [ + 296, + 220, + 530, + 243 + ], + "type": "text", + "content": "Table 5: Ablation study for training objective functions. FT: FlyingThings [26]. YTV: YouTube-VOS [46]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 245, + 509, + 323 + ], + "lines": [ + { + "bbox": [ + 320, + 245, + 509, + 323 + ], + "spans": [ + { + "bbox": [ + 320, + 245, + 509, + 323 + ], + "type": "table", + "html": "
\\( {\\mathcal{L}}_{\\mathrm{{KL}}} \\)\\( {\\mathcal{L}}_{\\text{rec }} \\)\\( {\\mathcal{L}}_{\\text{adv }} \\)Training DataTAP-Vid-DAVIS < \\( {\\delta }_{avg}^{x} \\uparrow \\)
✓FT55.8
✓YTV56.4
✓FT + YTV56.7
✓✓FT + YTV59.2
✓✓✓FT + YTV59.8
", + "image_path": "d758550de50b815d85743449c08ce9d93f26635ddf945e8dbae47a8f5c61b036.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 331, + 521, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 331, + 521, + 343 + ], + "spans": [ + { + "bbox": [ + 296, + 331, + 521, + 343 + ], + "type": "text", + "content": "for obtaining the soft labels. We regard it as future work." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "spans": [ + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": "Different training objective functions. We examine how different objective functions impact the overall performance, which is shown in Table 5. The " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL}}" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{adv}}" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": " denotes the losses defined in Eq. (5), Eq. (8) and Eq. (9). Surprisingly, we find the model trained on unlabeled real-world videos with " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": " obtains a better result, which indicates better generalization of self-supervised feature learning. By leveraging both " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{KL}}" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": " with synthetic and real-world videos, the performance is further improved to " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "59.2\\%" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": ". As expected, executing " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{adv}}" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": " to address the domain mismatch improves performance by " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": ". By fusing three losses, the performance reaches " + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "inline_equation", + "content": "59.8\\%" + }, + { + "bbox": [ + 296, + 345, + 530, + 521 + ], + "type": "text", + "content": ". The results consistently indicate that incorporating self-supervised and adversarial training with unlabeled data exhibits a performance boost against the model only trained with synthetic data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 532, + 373, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 532, + 373, + 544 + ], + "spans": [ + { + "bbox": [ + 297, + 532, + 373, + 544 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 555, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 555, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 555, + 530, + 730 + ], + "type": "text", + "content": "In this paper, we address pixel-wise video correspondences by learning fine-grained features. We propose to use not only labeled synthetic videos but also unlabeled real-world videos for feature learning. We first study how to take advantage of synthetic supervision for feature learning, and we find directly utilizing the motion vector results in degradation for the learned features. Thus, we propose soft labeling to address the issue. To improve the generalization, we introduce self-supervised reconstructive learning into the overall training and further enhance the features by leveraging adversarial training. Moreover, we propose a coarse-to-fine framework to alleviate the problem of computational efficiency. Extensive experiments on the downstream tasks validate the effectiveness of the proposed feature learning method and our efficient design." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "9639" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 279, + 729 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 156 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 156 + ], + "type": "text", + "content": "[1] Nikita Araslanov, Simone Schaub-Meyer, and Stefan Roth. 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Difficulties come from complex states and dynamics, diverse configurations and high-dimensional action space of deformable objects. Besides, the manipulation tasks usually require multiple steps to accomplish, and greedy policies may easily lead to local optimal states. Existing studies usually tackle this problem using reinforcement learning or imitating expert demonstrations, with limitations in modeling complex states or requiring hand-crafted expert policies. In this paper, we study deformable object manipulation using dense visual affordance, with generalization towards diverse states, and propose a novel kind of foresightful dense affordance, which avoids local optima by estimating states' values for long-term manipulation. We propose a framework for learning this representation, with novel designs such as multi-stage stable learning and efficient self-supervised data collection without experts. Experiments demonstrate the superiority of our proposed foresightful dense affordance. Project page: https://hyperplane-lab.github.io/DeformableAffordance", + "bbox": [ + 75, + 321, + 473, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 662, + 209, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Many kinds of deformable objects, such as ropes and fabrics, exist everywhere in our daily life. Perceiving and manipulating deformable objects plays a significant role and paves the way for future home-assistant robots.", + "bbox": [ + 75, + 683, + 468, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unlike rigid or articulated objects, due to the complex dynamics, high-dimensional and nearly infinite degrees of freedom, large action space, and severe self-occlusion, deformable objects pose much more challenges to manipulate. Moreover, unlike tasks for rigid objects (like grasping) or articulated objects (like pushing a door) that require one or only a few steps to accomplish, deformable object manipulation tasks usually require many steps to accomplish,", + "bbox": [ + 75, + 744, + 470, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/892d46690a37f5eb77b336411c0f25725f3c35ef69de2ba7ba9a9cf59297b913.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 297, + 651, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8b702a90502fac6221cc4396597b88531cbd27435c9e6ab92197b36cfda18de7.jpg", + "image_caption": [ + "0.382 0.320" + ], + "image_footnote": [], + "bbox": [ + 656, + 299, + 732, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/49bbab9debe74f6e59bcbfa58359f5410261c52b16728c27b65091fe62ee0035.jpg", + "image_caption": [ + "0.557", + "Pick Point", + "- Place Point", + "Coverage" + ], + "image_footnote": [], + "bbox": [ + 738, + 299, + 823, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/aa99dd6357db2247c410eb2f433090cb6717d1e475e5d76576353c0c6a5e8af3.jpg", + "image_caption": [ + "Local Optimal State", + "Figure 1. Deformable Object Manipulation has many difficulties. 1) It requires multiple steps to complete. 2) Most actions can hardly facilitate tasks, for the exceptionally complex states and dynamics. 3) Many local optimal states are temporarily closer to the target, but making following actions harder to coordinate for the whole task. We propose to learn Foresightful Dense Visual Affordance aware of future actions to avoid local optima for deformable object manipulation, with real-world implementations." + ], + "image_footnote": [], + "bbox": [ + 511, + 455, + 867, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "laying much focus on relationships and influences between actions in a sequence, as an action leading to local optimal states may not eventually complete the task.", + "bbox": [ + 496, + 715, + 892, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Specifically, as shown in Figure 1, unfolding crumpled cloth requires a sequence of actions (pick-and-place). Because of the exceptionally complex states and dynamics, and large action space, most actions fail to facilitate the task. Moreover, although some cloth in local optimal states temporarily have larger coverage areas than others, following actions face difficulties in smoothly completing the task.", + "bbox": [ + 496, + 762, + 893, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Proposed by Gibson [8] and aimed at providing indicative information for agents to execute actions (e.g., el", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution, order determined by coin flip.", + "bbox": [ + 94, + 875, + 364, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10947", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "emetary actions such as picking and pulling) and thus facilitating downstream tasks, visual affordance is arousing much attention in vision and robotics. Recent works have demonstrated its efficiency in a large range of tasks like grasping [25, 28, 3, 16, 15, 42], manipulating articulated objects [26, 36, 33, 5] and assisting robots in a scene [29, 30, 9]. Among them, point-level dense affordance [36, 26, 27, 33] learns whether an action on each point of the object could facilitate the task. Compared with Reinforcement Learning (RL) approaches, dense affordance is stably supervised and has better generalization ability towards objects with diverse shapes.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The above dense affordance is suitable for representing deformable objects with complex states, capable of indicating whether diverse actions could help complete the task.", + "bbox": [ + 75, + 272, + 468, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While most previous works only study dense affordance for short-term manipulation on rigid [43] or articulated objects [26, 36], to tackle the local optima problem in multi-step manipulation, we move a step towards equipping dense affordance with foresightfulness for future states.", + "bbox": [ + 75, + 316, + 468, + 391 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by Dynamic Programming with Bellman Equation [1] and Q-Learning [34], estimating a state's 'value' (expected return in the long term, instead of only the current performance) for future actions to coordinate and eventually complete the task will help avoid local optimal states and boost the smoothness and quickness of multi-step manipulation. Dense affordance is suitable for such 'value' estimation, because such 'value' requires understanding and aggregating a large number of diverse following actions on complex states and their corresponding results.", + "bbox": [ + 75, + 393, + 468, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With such state 'value's (instead of only the current performance) in supervisions, dense affordance would gain foresightfulness for the future.", + "bbox": [ + 75, + 544, + 468, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose to learn dense visual affordance for manipulating deformable objects, and further estimate state 'value's by aggregating such affordance to avoid local optima and smoothly accomplish multi-step tasks. As shown in Figure 1 (Down), the task can be accomplished smoothly using our proposed dense affordance in the real world. To learn such representations, we propose a novel framework generic to diverse tasks with many novel designs, such as the stage-by-stage stable training and Fold to Unfold efficient multi-stage data collection. Thus the proposed affordance could be learned stably, efficiently, and self-supervisedly without hand-crafted policies for different tasks. Experiments on representative benchmark tasks demonstrate our framework's impressive performance.", + "bbox": [ + 73, + 589, + 468, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are:", + "bbox": [ + 96, + 804, + 326, + 818 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose to use dense visual affordance for manipulating deformable objects with complex states and dynamics, using such representation to estimate state 'value's for future actions to avoid local optima and smoothly accomplish multi-step manipulation tasks;", + "bbox": [ + 94, + 821, + 468, + 897 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a self-supervised framework with novel designs such as multi-stage training and efficient data collection to learn the proposed affordance stably;", + "- Qualitative and quantitative results on representative benchmarks and real-world experiments demonstrate the superiority of our proposed dense visual affordance and learning framework for deformable objects." + ], + "bbox": [ + 517, + 90, + 890, + 198 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 220, + 640, + 234 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deformable Object Manipulation", + "text_level": 1, + "bbox": [ + 500, + 239, + 790, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deformable object manipulation is a typical and significant kind of task in robotic manipulation [4, 17, 2]. Compared to rigid or articulated objects, the manipulation of deformable objects is challenging for its high complexity, described in the Introduction Section. Typical methods utilize Reinforcement Learning (RL) or Imitation Learning. RL methods take object states [13] or visual information [37, 20] as policy input. Imitation based methods [41, 31, 19] imitate human-designed expert policy or human demonstrations for each task. Vision-based methods [6, 14] use visual feedback or correspondence to perform manipulations. Flow-based methods [32, 35] learn forward dynamics for manipulation, requiring much time in planning. Besides, a series of works [12, 21, 39, 38, 22] develop differentiable environments for diverse tasks and tackle these tasks by optimization. Different from above methods, our work builds a bridge between perception and manipulation, taking advantage of the generalization ability of affordance and estimating state 'value' for efficient planning.", + "bbox": [ + 496, + 263, + 890, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Visual Affordance for Robotic Manipulation", + "text_level": 1, + "bbox": [ + 500, + 561, + 874, + 577 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual affordance [8] indicates possible ways for robots to interact with and complete tasks. Many recent works learn affordance for grasping [25, 28, 3, 16, 15, 42], articulated object manipulation [26, 36, 33, 5, 7], object-object interaction [27], collaboration [43] and interaction in a scene [29, 30, 9]. Among them, point-level dense affordance [26, 36, 43, 33] learns per-point representations of objects, which is more sensitive to local geometries and easier to generalize to different objects. Most tasks can be achieved in a single step (e.g., grasping, pulling drawers), with the learned affordance only containing actionable information for single-step manipulation. However, deformable objects with complex states and dynamics require many steps to manipulate. We move a step towards proposing dense affordance for deformable objects, which not only indicates complex states and dynamics but also takes the subsequent actions of a certain state into consideration for long-term tasks to avoid local optima. FlingBot [10] learns affordance for unfolding cloth by flinging, while our proposed affordance uses pick-and-place which is more generic for large action space and diverse tasks.", + "bbox": [ + 496, + 585, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10948", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 89, + 284, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we describe how we formulate learning policy for multi-step deformable object manipulation into learning policies for picking and placing.", + "bbox": [ + 76, + 109, + 468, + 155 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following benchmarks DeformableRavens [31] and SoftGym [23], the problem is formulated as learning a policy $\\pi$ to output robot action $a_{t}$ , given the visual observation $o_{t}$ (denoted as $o$ ) at time $t$ . We use pick-and-place as the action, i.e., $a_{t} = (a_{pick}, a_{place})$ , with $a_{pick}$ and $a_{place}$ denoting picking and placing poses. Explained in [31], the selector can fulfill the tasks without rotation, so $a_{pick}$ and $a_{place}$ are denoted as picking point $p_{pick}$ and placing point $p_{place}$ .", + "bbox": [ + 75, + 156, + 470, + 277 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The composite of $p_{pick}$ and $p_{place}$ makes up a large combinatorial action space hard for a network to learn directly and simultaneously. For the underlying nature that $p_{place}$ highly depends on $p_{pick}$ , we follow [37] and disentangle learning the composite of $p_{pick}$ and $p_{place}$ into respectively learning $p_{pick}$ and $p_{place|p_{pick}}$ (denoted as $p_{place}$ ).", + "bbox": [ + 75, + 277, + 468, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Therefore, we formulate the problem into learning picking and placing policies. In Method Section 4, we describe how we learn the policies using foresightful dense visual affordance with each state's 'value' to avoid local optima.", + "bbox": [ + 75, + 369, + 468, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 436, + 166, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 463, + 187, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Shown in Figure 2, our framework is composed of two main parts: (1) we propose to use dense affordance to represent policy (4.2), estimate state 'value' using dense affordance and incorporate 'value' into dense affordance to avoid local optima for multi-step manipulation (4.3), break the picking-placing dependency cycle and stably learn affordance stage by stage (4.4); (2) to tackle the difficulty in collecting multi-stage and successful interactions, we propose a method (named Fold to Unfold) generic to many tasks to efficiently collect data in the reversed task completion order (e.g., collecting unfolding data by folding cloth) (4.5). Besides, we propose Integrated Systematic Training to further integrate the proposed affordance into a whole system (4.6). Finally, we describe network architectures and losses (4.7).", + "bbox": [ + 75, + 479, + 468, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Dense Visual Affordance Representing Policy", + "text_level": 1, + "bbox": [ + 76, + 696, + 460, + 713 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section introduces how to use dense visual affordance to represent manipulation policy. For simplicity, we first discuss affordance for a greedy policy.", + "bbox": [ + 75, + 717, + 468, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Described in Section 3, we formulate the problem into learning picking and placing policies, i.e., the picking point $p_{pick}$ and placing point $p_{place}$ given the observation $o$ (with the size of $m \\times n$ points). As the action space is all points on the object for picking, and all points in the space for placing, it comes naturally to use per-point score map $A_{o}^{pick}$ (size $m \\times n$ ) indicating how picking each point will facilitate the task, and dense placing affordance map $A_{o|p_{pick}}^{place}$ (size $m \\times n$ ) indicating how placing the picking point $p_{pick}$ on", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/497af368c9425e59601868bc8966758080da72368628910cc10f3e07b0de35a5.jpg", + "image_caption": [ + "Stage-1 Data Collection Multi-stage Training" + ], + "image_footnote": [], + "bbox": [ + 501, + 107, + 883, + 220 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/957947f01947c1496668e31533c85d687557cb99714a829b640bc577a3fcb977.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 220, + 883, + 333 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5f9da6c34624fb49b9ee6eb3da226318d2173bce7ec91b1da93318c586ac12da.jpg", + "image_caption": [ + "Figure 2. Our proposed framework learns dense picking and placing affordance for deformable object manipulation (e.g., Unfolding Cloth). We collect multi-stage interaction data efficiently (Left) and learn proposed affordance stably in a multi-stage schema (Right) in the reversed task accomplishment order, from states close to the target to complex states." + ], + "image_footnote": [], + "bbox": [ + 500, + 333, + 883, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "each point will facilitate the task. Following previous dense affordance studies [26, 36, 43], we notify such task-specific per-point score maps as task-specific dense affordance (denoted as affordance for simplicity). Demonstrated in above studies, such dense affordance performs well in extracting diverse geometric information and generalizes well to unseen visual states, which is significant in representing and manipulating deformable objects with complicated states.", + "bbox": [ + 496, + 549, + 890, + 670 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An intuitive greedy way to supervise $A_{o|p_{pick}}^{place}$ is directly using the distance between the target $T$ and the new object state $o'$ after picking $p_{pick}$ and placing on $p_{place}$ in $o$ . For example, we use $1 - dist(o, T)$ , i.e., the cloth coverage area, to supervise $A_{o|p_{pick}}^{place}$ for unfolding. So we can estimate placing affordance score $g_{o, p_{place}|p_{pick}}^{place}$ on $p_{place}$ as (Figure 3, Middle, temporarily dismiss 'value' in Figure):", + "bbox": [ + 496, + 670, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ng _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = 1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 789, + 890, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a picking point $p_{pick}$ , the placing policy will select $p_{place}$ with the highest affordance, so the picking affordance score $g_{0,pick}^{pick}$ on $p_{pick}$ can be estimated using the affordance score of the best placing point (Figure 3, Left):", + "bbox": [ + 496, + 813, + 890, + 873 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ng _ {o, p _ {p i c k}} ^ {p i c k} = \\max _ {i} g _ {o, p _ {i} | p _ {p i c k}} ^ {\\text {p l a c e}}, i \\in \\{1,,.., m \\times n \\} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 878, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10949", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use two networks $\\mathcal{M}_{pick}$ and $\\mathcal{M}_{place}$ to respectively learn $A_{o}^{pick}$ and $A_{o|p_{pick}}^{place}$ (architectures in Section 4.7).", + "bbox": [ + 76, + 90, + 468, + 127 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0b770f79a78927c7c90db6efbd028a6c23d21f9ba7e2fdf243270ac14b89bb38.jpg", + "image_caption": [ + "Figure 3. Learning placing and picking affordance with state 'value's for the future. Left to Right: The bottom black arrow indicates the manipulation (inference) order. Right to Left: Arrow flows show dependencies among placing affordance, picking affordance and 'value's. Given observation $o$ , we select 3 picking points $p_1$ , $p_2$ , $p_3$ , and show how to supervise corresponding placing affordance $A_{o|p_1}^{place}$ , $A_{o|p_2}^{place}$ , $A_{o|p_3}^{place}$ , and how to supervise $A_{o}^{pick}$ on $p_1$ , $p_2$ , $p_3$ using computed corresponding placing affordance." + ], + "image_footnote": [], + "bbox": [ + 84, + 137, + 450, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During inference, in each step, the greedy policy first selects $p_{pick}$ with the highest affordance score in $A_o^{pick}$ given $o$ , and then selects $p_{place}$ with the highest affordance score in $A_{o|p_{pick}}^{place}$ given $o$ and $p_{pick}$ , resulting in the temporary best state after the pick-and-place action.", + "bbox": [ + 76, + 473, + 468, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Estimating State Values and Learning Foresightful Affordance", + "text_level": 1, + "bbox": [ + 76, + 556, + 468, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 4, for multi-step manipulation, only evaluating the direct distance between the current state and the target (greedy method described above) may result in many local optimal states that are temporarily closer to target but harder for future actions to complete the whole task.", + "bbox": [ + 75, + 592, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dynamic Programming (DP) [1] and Q-Learning [34] tackle this local optima problem by estimating the 'value' of a state that indicates whether a state is beneficial to the task in the long term (instead of the current performance). Inspired by them, we can add such state 'value' (formally formulated in Equation 4) to the estimation of $A_{o|p_{pick}}^{place}$ :", + "bbox": [ + 75, + 667, + 470, + 763 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ng _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = \\alpha \\times \\operatorname {v a l u e} _ {o ^ {\\prime}} + \\beta \\times (1 - \\operatorname {d i s t} (o ^ {\\prime}, T)) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 768, + 473, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha +\\beta = 1$", + "bbox": [ + 310, + 792, + 442, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With such $A_{o|p_{pick}}^{place}$ that is foresightful for long-term tasks, $A_{o}^{pick}$ , which is the aggregation of $A_{o|p_{pick}}^{place}$ , will therefore get such foresightfulness spontaneously.", + "bbox": [ + 75, + 816, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Estimating the 'value' in a state requires understanding all possible actions and their corresponding future results,", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a575a90d01a30e068e125fd5704cf82992ad53784a3a116dd4db963725457a03.jpg", + "image_caption": [ + "Figure 4. Local Optima v.s. Global Optima. Many local optimal states are temporarily closer to target (e.g., having larger coverage area in unfolding task), but making future actions hard to coordinate to accomplish the whole task. We propose to use 'value' to indicate whether a state is suitable for future actions, with which the policy can avoid those local optimal states in multi-step tasks." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and then selecting the best for the estimation. As $A_{o}^{pick}$ estimates the action result on each point, state 'value' can be estimated by selecting the $p_{pick}$ with the highest score in $A_{o}^{pick}$ (Figure 3, Left):", + "bbox": [ + 498, + 393, + 890, + 455 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nv a l u e _ {o} = \\max _ {i} g _ {o, p _ {i}} ^ {\\text {p i c k}}, i \\in \\{1,.., m \\times n \\} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 458, + 890, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As $value_{o}$ could be estimated by $A_{o}^{pick}$ , $A_{o|p_{pick}}^{place}$ could be reformulated using both $A_{o}^{pick}$ and the direct distance:", + "bbox": [ + 498, + 486, + 890, + 522 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ng _ {o, p _ {\\text {p l a c e}} | p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = \\alpha \\times \\max _ {i} g _ {o ^ {\\prime}, p _ {i}} ^ {\\text {p i c k}}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 523, + 784, + 546 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n+ \\beta \\times (1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right)) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 663, + 547, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha +\\beta = 1$", + "bbox": [ + 658, + 570, + 787, + 584 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Break the Cycle and Cut into Stages: Learning Foresightful Affordance Stably Stage by Stage", + "text_level": 1, + "bbox": [ + 500, + 585, + 888, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above-formulated picking and placing affordance forms a chicken-egg dependency cycle: picking affordance is dependent on placing affordance, while placing affordance is dependent on picking affordance.", + "bbox": [ + 498, + 619, + 890, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To break the dependency cycle, states close to the target (e.g., cloth almost fully unfolded) become the key. As the task is almost accomplished in these states, their values and direct distances to the target are nearly the same. So for an interaction where the ending state $o'$ is close to the target, we directly use their distances to the target (instead of both distances and 'value's) to supervise the corresponding placing affordance of the starting state $o$ :", + "bbox": [ + 496, + 681, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ng _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = 1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 806, + 890, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "when $dist(o', T)$ is close to 0 i.e., the last step", + "bbox": [ + 521, + 832, + 849, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to Equations 2, 5 and 6, the proposed picking and placing affordance could be estimated without the dependency cycle. As the dependency cycle breaks in states", + "bbox": [ + 498, + 854, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10950", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "close to the target, we learn dense affordance from these simple states to more complex states (reversed order of inference) shown in Figure 2 (Right). Specifically, we divide learning procedure into multiple stages. In the first stage, we learn affordance for states that can reach states close to the target within one step, using the direct distances of the following states as supervisions. In the $i$ -th $(i > 1)$ stage, we learn affordance for states that can reach states in the $(i-1)$ -th stage in one step, using both the direct distances and the 'value's of states in the $(i-1)$ -th stage as supervisions. In each stage, we first train $\\mathcal{M}_{\\text{place}}$ using stable 'value's provided from the trained $\\mathcal{M}_{\\text{pick}}$ in the previous stage, and then train $\\mathcal{M}_{\\text{pick}}$ with stable supervisions (max of placing affordance) provided from the trained $\\mathcal{M}_{\\text{place}}$ in this stage.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this way, during the whole training, $A_{o|p_{pick}}^{place}$ and $A_{o}^{pick}$ both have stable supervisions from the former stage, and can provide stable supervisions for the latter stage.", + "bbox": [ + 75, + 303, + 468, + 351 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This stage-by-stage learning schema empowers our method with superiority over RL methods. Although RL also estimates states and actions using Bellman Equation, it simultaneously estimates and updates values across all states (offline RL) or trajectories of states (online RL), which is difficult to efficiently and stably learn the values, as RL struggles in iteratively updating state 'value's, especially when considering the prohibitively large state and action space of deformable objects. In contrast, like other dense affordance works [26, 43, 36], we stably learn affordance with 'value' using supervised learning, with stable supervisions provided in the previous training stage. Experiments demonstrate our superiority over RL in Section 5.4.", + "bbox": [ + 75, + 352, + 472, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5. Fold to Unfold: Efficient Multi-stage Data Collection for Learning Foresightful Affordance", + "text_level": 1, + "bbox": [ + 76, + 559, + 468, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The above-described training schema requires multi-stage data for training. Specifically, in the first stage, the starting states are one-step to states close to the target. In the $i$ -th $(i > 1)$ stage, the starting states are one-step to states in the $(i-1)$ -th stage. Each starting state's actions and corresponding ending states should be diverse, as we need to learn the affordance representing dense distributions.", + "bbox": [ + 75, + 598, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, due to the complexity of states and dynamics, data collection methods used by previous dense affordance works (random policies [26, 27] or state-based RL [36, 43]) could hardly collect such data. On the other hand, designing expert policies [31] or hand-crafting demonstrations are difficult and time-consuming for different tasks.", + "bbox": [ + 75, + 704, + 468, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, we propose a novel self-supervised method, named Fold to Unfold, using reversed actions of tasks to efficiently collect multi-stage data. This method is generic to many kinds of deformable object manipulation tasks, with no need for human-designed expert policies or annotations.", + "bbox": [ + 75, + 794, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to the training procedure, we collect data from states close to the target, to more complex states.", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cb1ec1709a51636d0da2a6cbeb3d4408525cccf8cc7c971e3364bb9fbe1965b2.jpg", + "image_caption": [ + "Figure 5. Fold to Unfold collection in simulator and real world." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 874, + 140 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, as shown in Figure 5, from a state $o_i$ in stage $i$ , we select a picking point $p_{pick}$ , put it on a placing point $p_{place}$ and get $o_{i+1}$ . Then, from $o_{i+1}$ , we execute the reversed action, pick $p_{place}$ , place on $p_{pick}$ and get $o_i'$ . If $o_i'$ is similar to $o_i$ , we choose $o_{i+1}$ as a starting state in stage $i+1$ , and sample diverse actions on $o_{i+1}$ with different corresponding results to train dense affordance in the $(i+1)$ -th stage (shown in Figure 2).", + "bbox": [ + 496, + 176, + 890, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through a few stages of data collection, object states become complex and diverse, empowering trained affordance networks with generalization towards diverse novel states.", + "bbox": [ + 496, + 297, + 890, + 343 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that, although reversed actions cannot fully recover previous states, i.e., $o_i'$ are not the same as $o_i$ , chances are that $o_i'$ and $o_i$ are similar, and thus this method still greatly improves sample efficiency. Also, proposed affordance is not dependent on this data collection method, as it can be trained on data collected by any method.", + "bbox": [ + 496, + 344, + 890, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.6. Integrated Systematic Training", + "text_level": 1, + "bbox": [ + 500, + 443, + 774, + 459 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although above designs and training procedure enable affordance learning for multi-step tasks, $\\mathcal{M}_{pick}$ and $\\mathcal{M}_{place}$ are trained using only offline collected data in different stages, not considering the actual execution performance of the policies provided by the two modules. During actual manipulation procedures, the policy is the composite policy of $\\mathcal{M}_{pick}$ and $\\mathcal{M}_{place}$ , and pick-and-place actions are executed one by one sequentially as a whole system. Therefore, we propose the Integrated Systematic Training (IST) procedure to adapt $\\mathcal{M}_{pick}$ and $\\mathcal{M}_{place}$ using online data.", + "bbox": [ + 496, + 463, + 890, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this procedure, with offline trained $\\mathcal{M}_{\\text{place}}$ and $\\mathcal{M}_{\\text{pick}}$ , we randomly sample object initial states, use $\\mathcal{M}_{\\text{place}}$ and $\\mathcal{M}_{\\text{pick}}$ as the policy to select $p_{\\text{pick}}$ and $p_{\\text{place}}$ , execute pick-and-place step by step, and use actual results to simultaneously update $\\mathcal{M}_{\\text{place}}$ and $\\mathcal{M}_{\\text{pick}}$ . Through this procedure, the two modules are constantly adapted by consecutively online-sampled and actually-executed data, and thus are gradually integrated into a whole system.", + "bbox": [ + 496, + 616, + 890, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.7. Network Architectures and Loss Function", + "text_level": 1, + "bbox": [ + 500, + 744, + 856, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For architectures of $\\mathcal{M}_{pick}$ and $\\mathcal{M}_{place}$ , we use Fully Convolutional Networks (FCNs) [24] same in Transporter [41, 31] with extra skip-connections as backbone perpoint feature extractor. For $\\mathcal{M}_{pick}$ , we directly use $p_{pick}$ feature to predict picking affordance score on $p_{pick}$ . For $\\mathcal{M}_{place}$ , we use feature concatenation of $p_{pick}$ and $p_{place}$ to predict placing affordance score on $p_{place}$ . To train both $\\mathcal{M}_{pick}$ and $\\mathcal{M}_{place}$ , we use Mean Absolute Error (MAE) between predictions and ground truth as the loss function.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10951", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 106 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Tasks, Settings and Metrics", + "text_level": 1, + "bbox": [ + 76, + 114, + 323, + 130 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tasks. To demonstrate the superiority of our framework, we select 2 representative tasks from DeformableRavens benchmark: (1) cable-ring: manipulating a ring to a given green circle, (2) cable-ring-nottarget: manipulating a ring to any circle, as well as 2 representative tasks from SoftGym: (3) SpreadCloth: spreading crumpled cloth to be flat, (4) RopeConfiguration: manipulating a rope from a random pose to a target pose (we use the shape 'S' as the target). Among them, the first two are relatively easier. They can be accomplished without considering future actions and states, and we conduct them to show our dense affordance's superiority over methods imitating expert demonstrations. The last two are much harder and would be better accomplished considering future actions and states to avoid local optima.", + "bbox": [ + 76, + 137, + 468, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. For all tasks, in both training and testing, we set different random seeds for each episode, producing unseen and diverse initial poses of objects. To compare the generalization ability between our proposed dense affordance and imitation-based methods, for cables in DeformableRavens, we directly test the model trained on cables with 32 beads over novel cable configurations with 24, 28 or 36 beads.", + "bbox": [ + 76, + 349, + 468, + 453 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. For cable-ring and cable-ring-notarget, we follow DeformableRavens and use the manipulation successful rate as the metric. For SpreadCloth and RopeConfiguration, we follow SoftGym and use the normalized score as the metric. For all tasks, higher scores indicate better performance.", + "bbox": [ + 76, + 454, + 468, + 529 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Baselines", + "text_level": 1, + "bbox": [ + 76, + 536, + 184, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For two cable-ring related tasks, we compare our method with baselines with or without expert demonstrations:", + "bbox": [ + 76, + 560, + 468, + 589 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Transporter [41, 31] is commonly used for robotic manipulation by learning visual correlation for picking and placing points. In DeformableRavens [31] it is trained by cloning expert demonstrations and achieves SOTA performance over relevant tasks.", + "- GT-State receives ground truth (GT) pose of the target object, and regresses $p_{pick}$ and $p_{place}$ with MLP.", + "- GT-State 2-Step first regresses $p_{pick}$ and then $p_{place}$ using $p_{pick}$ and GT pose concatenation, both via MLP." + ], + "bbox": [ + 94, + 589, + 468, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For SpreadCloth and RopeConfiguration, as object states and dynamics are too complex and the tasks are too difficult to hand-engineer expert policies, we compare our method with baselines focused on multi-step planning:", + "bbox": [ + 76, + 739, + 468, + 799 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- CURL-SAC [18] that uses a model-free RL approach with contrastive unsupervised representations.", + "- $\\mathbf{DrQ}[40]$ applies augmentation, regularization to RL.", + "- PlaNet [11] learns state space dynamics for planning.", + "- MVP [37] learns pick-and-place policy with model-free RL designed for deformbale object manipulation." + ], + "bbox": [ + 94, + 800, + 468, + 893 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Qualitative Results and Analysis", + "text_level": 1, + "bbox": [ + 500, + 90, + 784, + 106 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9db4217d99372e08885f33ed3dbca7249a70e0e9addf08c3e170698a15875aec.jpg", + "image_caption": [ + "Figure 6. Example action sequences for cable-ring, cable-ring-nottarget, SpreadCloth and RopeConfiguration. White point denotes picking and black point denotes placing." + ], + "image_footnote": [], + "bbox": [ + 501, + 119, + 880, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 6 shows examples of manipulation trajectories for diverse tasks using our proposed affordance. It is worth mentioning that, in the second state of SpreadCloth (Row 3), though it is intuitive to place the picking point (white) to the top-left position, the model places it to the bottom-right position (black), as the corresponding next state has low coverage but high 'value', requiring only one following pick-and-place action to almost fully unfold the cloth.", + "bbox": [ + 498, + 400, + 890, + 521 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0a78697860ce08f90fe17d4b4e107a1f9f0172ba7b64d08c612b41b3f57f2819.jpg", + "image_caption": [ + "Figure 7. Picking and placing affordance. Each row contains two (picking affordance, observation with $p_{pick}$ , placing affordance) tuples for a task. $p_{pick}$ is selected by picking affordance. Higher color temperature means higher affordance." + ], + "image_footnote": [], + "bbox": [ + 504, + 535, + 890, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 7 visualizes picking and placing affordance, clearly showing that the learned affordance represents deformable objects with complex states and dynamics and facilitates selecting picking and placing points for manipulation. Figure 8 visualizes 'value's of states.", + "bbox": [ + 498, + 824, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10952", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0bf082f810e775cd5289fbe1311d0187385a7a7cb29ead914c6b6db5e1fe65d4.jpg", + "image_caption": [ + "Figure 8. Visualization of 'value' shows that some states with closer distances to the target (e.g., larger area) may not have higher 'value', as these states are hard for future actions to fulfill the task." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 450, + 200 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4312f57a41c7bd677239333724a8659783e68c1a08d3107d2e9cb8b325cddf7b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodcable-ringcable-ring-notarget
GT-State0.05.0
GT-State 2-Step0.01.7
Transporter68.370.0
Ours81.795.0
", + "bbox": [ + 112, + 258, + 433, + 368 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7bdb535b9b53040143b6032b821cd4773d843a0ef44f414ad275e0113571aace.jpg", + "table_caption": [ + "Table 1. Quantitative results in DeformableRavens." + ], + "table_footnote": [], + "table_body": "
MethodSpreadClothRopeConfiguration
CURL-SAC0.1950.348
PlaNet0.3870.236
DrQ0.2750.154
MVP0.3720.258
Ours0.7580.529
", + "bbox": [ + 117, + 391, + 429, + 525 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Quantitative Results and Analysis", + "text_level": 1, + "bbox": [ + 76, + 547, + 374, + 564 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Shown in Table 1, our method outperforms all baselines in DeformableRavens. For GT State and GT State 2-Step, GT states can only provide part of the necessary information, and it is difficult to acquire the precise GT states of deformable objects in the real world. For Transporter that learns visual correlation for the matching between picking and placing points, although it directly clones successful demonstrations from hand-crafted expert policies, we outperform it for two possible reasons: 1) dense affordance is more suitable for deformable objects as it represents the results of diverse actions on complex states, while visual correlation in Transporter is suitable for matching like assembling-kits; 2) training on and cloning expert demonstrations will limit the model's generalization toward diverse situations for inference. To further evaluate the generalization ability of dense affordance, we produce different novel object configurations, using 24, 28, and 36 as the bead number instead of the initial 32. Our method's slighter performance decrease in Table 3 also demonstrates its generalization ability. Besides, expert policies need elaborate hand-engineering for different tasks, while our method can apply to diverse tasks without large modifications.", + "bbox": [ + 75, + 568, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 shows our framework outperforms all baselines in SoftGym. As described in 4.4, compared with those RL methods, our framework learns representations of complex states for multi-step manipulation in a stable way.", + "bbox": [ + 496, + 90, + 890, + 152 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/adc1d708535a9d4b147fb738c315a66507d15d69b18dd8cb2a82dc3cb67843bc.jpg", + "table_caption": [ + "Table 2. Quantitative results in SoftGym." + ], + "table_footnote": [], + "table_body": "
Task configurationscable-ring 24 / 28 / 36cable-ring-notarget 24 / 28 / 36
Transporter33.3 / 58.3 / 32.760.0 / 71.7 / 31.7
Ours61.6 / 86.7 / 58.381.7 / 96.7 / 78.3
", + "bbox": [ + 517, + 162, + 874, + 244 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Ablation Studies and Analysis", + "text_level": 1, + "bbox": [ + 500, + 295, + 766, + 311 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate necessities of our framework's different components, we conduct ablation experiments by comparing our method with: 1) Ours RandPick: our method with the picking policy replaced by a random policy; 2) Ours ExpertPick: our method with the picking policy replaced by Transporter's expert; 3) Ours w/o IST: our method without Integrated Systematic Training (IST);", + "bbox": [ + 496, + 315, + 890, + 420 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For SpreadCloth and RopeConfiguration that require strongly related sequential actions, we additionally compare 1) ablated versions using different stages of data, 2) Ours only dist directly and greedily trained on all collected data instead of stage-by-stage considering 'value's.", + "bbox": [ + 496, + 421, + 890, + 496 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8bd5eb4a33c25cfb0ae5a28259a03c123526b6660547157ce4337e317fd0507c.jpg", + "table_caption": [ + "Table 3. Manipulation scores on novel configurations in DeformableRaves showing our method's generalization capability." + ], + "table_footnote": [], + "table_body": "
Methodcable-ringcable-ring-notarget
Ours RandPick11.758.3
Ours ExpertPick76.741.7
Ours w/o IST78.391.7
Ours81.795.0
", + "bbox": [ + 517, + 508, + 872, + 621 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0d577c3fe00afb8ab97d05ead979b981f9f8b12cc7046bb7833d1c76334f6596.jpg", + "table_caption": [ + "Table 4. Ablation studies in DeformableRavens." + ], + "table_footnote": [], + "table_body": "
Methodstage1stage2stage3stage4stage5
Ours RandPick0.2410.2110.3040.1850.190
Ours w/o IST0.5260.5860.6210.6240.612
Ours only dist0.7010.7010.7010.7010.701
Ours0.5890.6950.7520.7540.758
", + "bbox": [ + 511, + 650, + 879, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Ablation studies in SpreadCloth.", + "bbox": [ + 568, + 762, + 821, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5 and 6 show that, a series of steps of data empowers affordance with generalization to diverse states.", + "bbox": [ + 496, + 780, + 888, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4, 5 and 6 show quantitative results of ablation experiments. Ours RandPick and Ours ExpertPick show that, with the same placing affordance, our proposed picking affordance helps the framework perform the best.", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ours only dist in Table 5 and 6 show that, directly training on all the diverse data without estimating state 'value'", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10953", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1f72d7c0438e0054b0827368797d865ebf195c64ae2b99ac771c80c42cf756a2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodstage1stage2stage3stage4stage5
Ours RandPick0.3290.3020.3320.3340.322
Ours w/o IST0.3590.4180.4370.4790.474
Ours only dist0.4600.4600.4600.4600.460
Ours0.4410.5030.5180.5270.529
", + "bbox": [ + 88, + 88, + 459, + 200 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "limits the performance compared with our proposed framework. Besides, as shown in Figure 9, Ours only dist will propose actions leading to local optimal states, while our foresightful affordance will help to avoid that.", + "bbox": [ + 76, + 218, + 468, + 279 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ours w/o IST in Table 4, 5 and 6, and adjusted affordance and 'value's in Figure 10 demonstrate IST helps integrating picking and placing modules into a whole, generating more precise perception of affordance and 'value's.", + "bbox": [ + 76, + 279, + 468, + 340 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6ec8f8fd88edfa70e425414dc64e22dce7afb8e223273d2ea9d6f647d9eedd55.jpg", + "image_caption": [ + "Figure 9. Placing affordance trained using 'value' supervision (red) and only using the greedy direct distance (blue)." + ], + "image_footnote": [], + "bbox": [ + 84, + 353, + 467, + 559 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f750f63d33004b583be939382322d1b7fa8067cbe965e26c00001c401a1ee6c.jpg", + "image_caption": [ + "Figure 10. Picking and placing affordance before (middle) and after (right) IST of the observation (left). White: pick point." + ], + "image_footnote": [], + "bbox": [ + 78, + 612, + 140, + 660 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b765bf39c7f617e59f30ca3c062f4c032f05b820c94f1646ea71624083aee0e8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 143, + 618, + 256, + 654 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e636a61295d19ba3f2990508f6db10cf33583b5844ac321671cc3746daa1aba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 611, + 334, + 659 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1bda6bfffd93bb6675d50a91c868618c68ca10c728feb7b33e41f6f1a877575b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 612, + 398, + 657 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b7784fad5e2c57fd54d35a17b311fe3a443f0d782ed2811e060d34bd94fb134e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 408, + 612, + 467, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Real-world Experiments", + "text_level": 1, + "bbox": [ + 76, + 710, + 302, + 727 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To bridge the sim2real gap and implement our method in the real world, similar to [37, 10], we use domain randomization to train affordance models in simulation and fine-tune them in real world. Specifically, we collect real-world data using Fold to Unfold, fine-tune trained-in-simulation $\\mathcal{M}_{pick}$ and $\\mathcal{M}_{place}$ stage by stage using the collected data.", + "bbox": [ + 76, + 734, + 468, + 825 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For evaluations, we randomly lift and drop the objects for five times to get the initial state, and then run the models for ten pick-and-place actions to perform the tasks. The manipulation score is the average normalized score (computed the same as in SoftGym) of sixty trajectories.", + "bbox": [ + 76, + 825, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Shown in Figure 11, given real-world observations with textures and physics different from objects in simulation, our method predicts reasonable picking and placing affordance and selects actions for tasks.", + "bbox": [ + 498, + 90, + 890, + 150 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We use MVP [37] for comparison, as (1) it also uses pick-and-place as action primitive, thus could do both cloth and rope tasks, and (2) provides real-world experiments. Table 7 shows performance comparison, explained in 5.4.", + "bbox": [ + 498, + 152, + 890, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "See the supplementary for more implementation details.", + "bbox": [ + 517, + 214, + 888, + 229 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bb3ffa4e19d97350d294a7cf95b4027270a8839a45f0dc745bacb89d6ba2f89e.jpg", + "table_caption": [ + "Table 6. Ablation studies in RopeConfiguration." + ], + "table_footnote": [], + "table_body": "
MethodSpreadClothRopeConfiguration
MVP0.3070.227
Ours0.6830.461
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Manipulation scores in the real world.", + "bbox": [ + 555, + 315, + 834, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d190040a272ec96773a234ad26b6e957cfb1d9fd3429ff8bcb936d84299e9d06.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 349, + 625, + 477 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6736b7fa185168fcb193522a2f6b6dca1eae3ea15b5cdcb48848b75d9376a8cf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 349, + 689, + 477 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/38724ec8ee12581fe816e0a3e16d10350cdf2fb5ef345a896a89cacd7c175fe3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 349, + 756, + 477 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e4388c8415535ba82f58e6f6d9b8e53d4ade5ffb813da6ac8caf78fed396fc6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 349, + 823, + 477 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cd5f6011880b68ff978d298c62b245c13f87a7d12961b625b100c15cb02707af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 826, + 349, + 888, + 478 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f2cc5a9946095642b921b2ab803d2eb0323a4915a34a0191f0c8b50b1f627c9.jpg", + "image_caption": [ + "Figure 11. Real-world pick-place actions guided by affordance." + ], + "image_footnote": [], + "bbox": [ + 503, + 481, + 625, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32e1d534763bc2aa043f3f97c470d6233a14f7ee96dbd9924cdd2cf37dddafc2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 481, + 689, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/53dec26d712a30941ace7abf7a10fc26340440f12ac7f85f7bcb3a66c2680c91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 481, + 756, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0cac705322bdb16167be05a7bd74b9a1ed32a18a257b9058d1db2667c2875cae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 481, + 821, + 611 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4059d4cf036cf01104104c42c4e230f3d573ad105d860edf744cf84772b3a9cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 826, + 489, + 888, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 643, + 617, + 660 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose to use dense visual affordance for manipulating deformable objects with complex states and dynamics. For tasks that require a series of strongly related actions, we further empower the proposed affordance with the awareness of a certain action's influence on subsequent actions. We propose a self-supervised framework with novel designs to efficiently collect multi-stage interaction data and stably learn this representation. Experiments on representative tasks and in the real world show the superiority of our proposed dense affordance and the learning framework.", + "bbox": [ + 496, + 667, + 890, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 824, + 669, + 840 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Natural Science Foundation of China (No. 62136001). We thank Qianxu Yang and Haoran Lu for assisting real-world experiments, Mingdong Wu and Hongcheng Wang for discussions.", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10954", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Richard Bellman. Dynamic programming. science, 153(3731):34-37, 1966. 2, 4", + "[2] Aude Billard and Danica Kragic. Trends and challenges in robot manipulation. 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International Conference on Learning Representations (ICLR), 2023. 2, 3, 5" + ], + "bbox": [ + 501, + 90, + 893, + 287 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10956", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/b7d619c9-c5f2-438e-896d-a2c31b01ebe0_model.json b/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/b7d619c9-c5f2-438e-896d-a2c31b01ebe0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..756774e6188e691bed31e3041b28d6ca291dae6f --- /dev/null +++ b/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/b7d619c9-c5f2-438e-896d-a2c31b01ebe0_model.json @@ -0,0 +1,2739 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.247, + 0.131, + 0.726, + 0.177 + ], + "angle": 0, + "content": "Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.266, + 0.203, + 0.71, + 0.221 + ], + "angle": 0, + "content": "Ruihai Wu\\(^{1,3,4*}\\) Chuanruo Ning\\(^{2,1*}\\) Hao Dong\\(^{1,3,4\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.228, + 0.221, + 0.739, + 0.239 + ], + "angle": 0, + "content": "\\(^{1}\\)CFCS, School of CS, PKU \\(^{2}\\)School of EECS, PKU \\(^{3}\\)BAAI" + }, + { + "type": "text", + "bbox": [ + 0.143, + 0.239, + 0.823, + 0.257 + ], + "angle": 0, + "content": "\\(^{4}\\)National Key Laboratory for Multimedia Information Processing, School of CS, PKU" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.474, + 0.643 + ], + "angle": 0, + "content": "Understanding and manipulating deformable objects (e.g., ropes and fabrics) is an essential yet challenging task with broad applications. Difficulties come from complex states and dynamics, diverse configurations and high-dimensional action space of deformable objects. Besides, the manipulation tasks usually require multiple steps to accomplish, and greedy policies may easily lead to local optimal states. Existing studies usually tackle this problem using reinforcement learning or imitating expert demonstrations, with limitations in modeling complex states or requiring hand-crafted expert policies. In this paper, we study deformable object manipulation using dense visual affordance, with generalization towards diverse states, and propose a novel kind of foresightful dense affordance, which avoids local optima by estimating states' values for long-term manipulation. We propose a framework for learning this representation, with novel designs such as multi-stage stable learning and efficient self-supervised data collection without experts. Experiments demonstrate the superiority of our proposed foresightful dense affordance. Project page: https://hyperplane-lab.github.io/DeformableAffordance" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.664, + 0.21, + 0.68 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.47, + 0.745 + ], + "angle": 0, + "content": "Many kinds of deformable objects, such as ropes and fabrics, exist everywhere in our daily life. Perceiving and manipulating deformable objects plays a significant role and paves the way for future home-assistant robots." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.745, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Unlike rigid or articulated objects, due to the complex dynamics, high-dimensional and nearly infinite degrees of freedom, large action space, and severe self-occlusion, deformable objects pose much more challenges to manipulate. Moreover, unlike tasks for rigid objects (like grasping) or articulated objects (like pushing a door) that require one or only a few steps to accomplish, deformable object manipulation tasks usually require many steps to accomplish," + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.299, + 0.653, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.3, + 0.733, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.66, + 0.381, + 0.728, + 0.391 + ], + "angle": 0, + "content": "0.382 0.320" + }, + { + "type": "image", + "bbox": [ + 0.74, + 0.3, + 0.824, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.745, + 0.381, + 0.778, + 0.391 + ], + "angle": 0, + "content": "0.557" + }, + { + "type": "image_caption", + "bbox": [ + 0.833, + 0.312, + 0.877, + 0.336 + ], + "angle": 0, + "content": "Pick Point" + }, + { + "type": "image_caption", + "bbox": [ + 0.833, + 0.35, + 0.879, + 0.372 + ], + "angle": 0, + "content": "- Place Point" + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.381, + 0.884, + 0.391 + ], + "angle": 0, + "content": "Coverage" + }, + { + "type": "image_caption", + "bbox": [ + 0.839, + 0.401, + 0.879, + 0.435 + ], + "angle": 0, + "content": "Local Optimal State" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.457, + 0.868, + 0.577 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.588, + 0.895, + 0.701 + ], + "angle": 0, + "content": "Figure 1. Deformable Object Manipulation has many difficulties. 1) It requires multiple steps to complete. 2) Most actions can hardly facilitate tasks, for the exceptionally complex states and dynamics. 3) Many local optimal states are temporarily closer to the target, but making following actions harder to coordinate for the whole task. We propose to learn Foresightful Dense Visual Affordance aware of future actions to avoid local optima for deformable object manipulation, with real-world implementations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.893, + 0.763 + ], + "angle": 0, + "content": "laying much focus on relationships and influences between actions in a sequence, as an action leading to local optimal states may not eventually complete the task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.895, + 0.87 + ], + "angle": 0, + "content": "Specifically, as shown in Figure 1, unfolding crumpled cloth requires a sequence of actions (pick-and-place). Because of the exceptionally complex states and dynamics, and large action space, most actions fail to facilitate the task. Moreover, although some cloth in local optimal states temporarily have larger coverage areas than others, following actions face difficulties in smoothly completing the task." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Proposed by Gibson [8] and aimed at providing indicative information for agents to execute actions (e.g., el" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.875, + 0.365, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution, order determined by coin flip." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.095, + 0.875, + 0.365, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10947" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.272 + ], + "angle": 0, + "content": "emetary actions such as picking and pulling) and thus facilitating downstream tasks, visual affordance is arousing much attention in vision and robotics. Recent works have demonstrated its efficiency in a large range of tasks like grasping [25, 28, 3, 16, 15, 42], manipulating articulated objects [26, 36, 33, 5] and assisting robots in a scene [29, 30, 9]. Among them, point-level dense affordance [36, 26, 27, 33] learns whether an action on each point of the object could facilitate the task. Compared with Reinforcement Learning (RL) approaches, dense affordance is stably supervised and has better generalization ability towards objects with diverse shapes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.47, + 0.318 + ], + "angle": 0, + "content": "The above dense affordance is suitable for representing deformable objects with complex states, capable of indicating whether diverse actions could help complete the task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.469, + 0.392 + ], + "angle": 0, + "content": "While most previous works only study dense affordance for short-term manipulation on rigid [43] or articulated objects [26, 36], to tackle the local optima problem in multi-step manipulation, we move a step towards equipping dense affordance with foresightfulness for future states." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.47, + 0.544 + ], + "angle": 0, + "content": "Inspired by Dynamic Programming with Bellman Equation [1] and Q-Learning [34], estimating a state's 'value' (expected return in the long term, instead of only the current performance) for future actions to coordinate and eventually complete the task will help avoid local optimal states and boost the smoothness and quickness of multi-step manipulation. Dense affordance is suitable for such 'value' estimation, because such 'value' requires understanding and aggregating a large number of diverse following actions on complex states and their corresponding results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.469, + 0.589 + ], + "angle": 0, + "content": "With such state 'value's (instead of only the current performance) in supervisions, dense affordance would gain foresightfulness for the future." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.59, + 0.469, + 0.801 + ], + "angle": 0, + "content": "We propose to learn dense visual affordance for manipulating deformable objects, and further estimate state 'value's by aggregating such affordance to avoid local optima and smoothly accomplish multi-step tasks. As shown in Figure 1 (Down), the task can be accomplished smoothly using our proposed dense affordance in the real world. To learn such representations, we propose a novel framework generic to diverse tasks with many novel designs, such as the stage-by-stage stable training and Fold to Unfold efficient multi-stage data collection. Thus the proposed affordance could be learned stably, efficiently, and self-supervisedly without hand-crafted policies for different tasks. Experiments on representative benchmark tasks demonstrate our framework's impressive performance." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.805, + 0.327, + 0.819 + ], + "angle": 0, + "content": "In summary, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.822, + 0.469, + 0.898 + ], + "angle": 0, + "content": "- We propose to use dense visual affordance for manipulating deformable objects with complex states and dynamics, using such representation to estimate state 'value's for future actions to avoid local optima and smoothly accomplish multi-step manipulation tasks;" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.891, + 0.136 + ], + "angle": 0, + "content": "- We propose a self-supervised framework with novel designs such as multi-stage training and efficient data collection to learn the proposed affordance stably;" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.139, + 0.891, + 0.199 + ], + "angle": 0, + "content": "- Qualitative and quantitative results on representative benchmarks and real-world experiments demonstrate the superiority of our proposed dense visual affordance and learning framework for deformable objects." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.092, + 0.891, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.221, + 0.642, + 0.236 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.241, + 0.792, + 0.257 + ], + "angle": 0, + "content": "2.1. Deformable Object Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.264, + 0.892, + 0.552 + ], + "angle": 0, + "content": "Deformable object manipulation is a typical and significant kind of task in robotic manipulation [4, 17, 2]. Compared to rigid or articulated objects, the manipulation of deformable objects is challenging for its high complexity, described in the Introduction Section. Typical methods utilize Reinforcement Learning (RL) or Imitation Learning. RL methods take object states [13] or visual information [37, 20] as policy input. Imitation based methods [41, 31, 19] imitate human-designed expert policy or human demonstrations for each task. Vision-based methods [6, 14] use visual feedback or correspondence to perform manipulations. Flow-based methods [32, 35] learn forward dynamics for manipulation, requiring much time in planning. Besides, a series of works [12, 21, 39, 38, 22] develop differentiable environments for diverse tasks and tackle these tasks by optimization. Different from above methods, our work builds a bridge between perception and manipulation, taking advantage of the generalization ability of affordance and estimating state 'value' for efficient planning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.563, + 0.875, + 0.578 + ], + "angle": 0, + "content": "2.2. Visual Affordance for Robotic Manipulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Visual affordance [8] indicates possible ways for robots to interact with and complete tasks. Many recent works learn affordance for grasping [25, 28, 3, 16, 15, 42], articulated object manipulation [26, 36, 33, 5, 7], object-object interaction [27], collaboration [43] and interaction in a scene [29, 30, 9]. Among them, point-level dense affordance [26, 36, 43, 33] learns per-point representations of objects, which is more sensitive to local geometries and easier to generalize to different objects. Most tasks can be achieved in a single step (e.g., grasping, pulling drawers), with the learned affordance only containing actionable information for single-step manipulation. However, deformable objects with complex states and dynamics require many steps to manipulate. We move a step towards proposing dense affordance for deformable objects, which not only indicates complex states and dynamics but also takes the subsequent actions of a certain state into consideration for long-term tasks to avoid local optima. FlingBot [10] learns affordance for unfolding cloth by flinging, while our proposed affordance uses pick-and-place which is more generic for large action space and diverse tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10948" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.285, + 0.106 + ], + "angle": 0, + "content": "3. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.111, + 0.47, + 0.156 + ], + "angle": 0, + "content": "In this section, we describe how we formulate learning policy for multi-step deformable object manipulation into learning policies for picking and placing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.157, + 0.471, + 0.278 + ], + "angle": 0, + "content": "Following benchmarks DeformableRavens [31] and SoftGym [23], the problem is formulated as learning a policy \\(\\pi\\) to output robot action \\(a_{t}\\), given the visual observation \\(o_{t}\\) (denoted as \\(o\\)) at time \\(t\\). We use pick-and-place as the action, i.e., \\(a_{t} = (a_{pick}, a_{place})\\), with \\(a_{pick}\\) and \\(a_{place}\\) denoting picking and placing poses. Explained in [31], the selector can fulfill the tasks without rotation, so \\(a_{pick}\\) and \\(a_{place}\\) are denoted as picking point \\(p_{pick}\\) and placing point \\(p_{place}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.279, + 0.469, + 0.37 + ], + "angle": 0, + "content": "The composite of \\( p_{pick} \\) and \\( p_{place} \\) makes up a large combinatorial action space hard for a network to learn directly and simultaneously. For the underlying nature that \\( p_{place} \\) highly depends on \\( p_{pick} \\), we follow [37] and disentangle learning the composite of \\( p_{pick} \\) and \\( p_{place} \\) into respectively learning \\( p_{pick} \\) and \\( p_{place|p_{pick}} \\) (denoted as \\( p_{place} \\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.47, + 0.43 + ], + "angle": 0, + "content": "Therefore, we formulate the problem into learning picking and placing policies. In Method Section 4, we describe how we learn the policies using foresightful dense visual affordance with each state's 'value' to avoid local optima." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.438, + 0.168, + 0.453 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.464, + 0.188, + 0.478 + ], + "angle": 0, + "content": "4.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.47, + 0.692 + ], + "angle": 0, + "content": "Shown in Figure 2, our framework is composed of two main parts: (1) we propose to use dense affordance to represent policy (4.2), estimate state 'value' using dense affordance and incorporate 'value' into dense affordance to avoid local optima for multi-step manipulation (4.3), break the picking-placing dependency cycle and stably learn affordance stage by stage (4.4); (2) to tackle the difficulty in collecting multi-stage and successful interactions, we propose a method (named Fold to Unfold) generic to many tasks to efficiently collect data in the reversed task completion order (e.g., collecting unfolding data by folding cloth) (4.5). Besides, we propose Integrated Systematic Training to further integrate the proposed affordance into a whole system (4.6). Finally, we describe network architectures and losses (4.7)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.698, + 0.462, + 0.714 + ], + "angle": 0, + "content": "4.2. Dense Visual Affordance Representing Policy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.763 + ], + "angle": 0, + "content": "This section introduces how to use dense visual affordance to represent manipulation policy. For simplicity, we first discuss affordance for a greedy policy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Described in Section 3, we formulate the problem into learning picking and placing policies, i.e., the picking point \\( p_{pick} \\) and placing point \\( p_{place} \\) given the observation \\( o \\) (with the size of \\( m \\times n \\) points). As the action space is all points on the object for picking, and all points in the space for placing, it comes naturally to use per-point score map \\( A_{o}^{pick} \\) (size \\( m \\times n \\)) indicating how picking each point will facilitate the task, and dense placing affordance map \\( A_{o|p_{pick}}^{place} \\) (size \\( m \\times n \\)) indicating how placing the picking point \\( p_{pick} \\) on" + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.091, + 0.885, + 0.108 + ], + "angle": 0, + "content": "Stage-1 Data Collection Multi-stage Training" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.108, + 0.885, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.222, + 0.885, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.334, + 0.885, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.452, + 0.894, + 0.537 + ], + "angle": 0, + "content": "Figure 2. Our proposed framework learns dense picking and placing affordance for deformable object manipulation (e.g., Unfolding Cloth). We collect multi-stage interaction data efficiently (Left) and learn proposed affordance stably in a multi-stage schema (Right) in the reversed task accomplishment order, from states close to the target to complex states." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.671 + ], + "angle": 0, + "content": "each point will facilitate the task. Following previous dense affordance studies [26, 36, 43], we notify such task-specific per-point score maps as task-specific dense affordance (denoted as affordance for simplicity). Demonstrated in above studies, such dense affordance performs well in extracting diverse geometric information and generalizes well to unseen visual states, which is significant in representing and manipulating deformable objects with complicated states." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.788 + ], + "angle": 0, + "content": "An intuitive greedy way to supervise \\( A_{o|p_{pick}}^{place} \\) is directly using the distance between the target \\( T \\) and the new object state \\( o' \\) after picking \\( p_{pick} \\) and placing on \\( p_{place} \\) in \\( o \\). For example, we use \\( 1 - dist(o, T) \\), i.e., the cloth coverage area, to supervise \\( A_{o|p_{pick}}^{place} \\) for unfolding. So we can estimate placing affordance score \\( g_{o, p_{place}|p_{pick}}^{place} \\) on \\( p_{place} \\) as (Figure 3, Middle, temporarily dismiss 'value' in Figure):" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.79, + 0.892, + 0.812 + ], + "angle": 0, + "content": "\\[\ng _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = 1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.814, + 0.892, + 0.874 + ], + "angle": 0, + "content": "Given a picking point \\( p_{pick} \\), the placing policy will select \\( p_{place} \\) with the highest affordance, so the picking affordance score \\( g_{0,pick}^{pick} \\) on \\( p_{pick} \\) can be estimated using the affordance score of the best placing point (Figure 3, Left):" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.88, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\ng _ {o, p _ {p i c k}} ^ {p i c k} = \\max _ {i} g _ {o, p _ {i} | p _ {p i c k}} ^ {\\text {p l a c e}}, i \\in \\{1,,.., m \\times n \\} \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10949" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.47, + 0.128 + ], + "angle": 0, + "content": "We use two networks \\(\\mathcal{M}_{pick}\\) and \\(\\mathcal{M}_{place}\\) to respectively learn \\(A_{o}^{pick}\\) and \\(A_{o|p_{pick}}^{place}\\) (architectures in Section 4.7)." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.138, + 0.451, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.359, + 0.47, + 0.472 + ], + "angle": 0, + "content": "Figure 3. Learning placing and picking affordance with state 'value's for the future. Left to Right: The bottom black arrow indicates the manipulation (inference) order. Right to Left: Arrow flows show dependencies among placing affordance, picking affordance and 'value's. Given observation \\( o \\), we select 3 picking points \\( p_1 \\), \\( p_2 \\), \\( p_3 \\), and show how to supervise corresponding placing affordance \\( A_{o|p_1}^{place} \\), \\( A_{o|p_2}^{place} \\), \\( A_{o|p_3}^{place} \\), and how to supervise \\( A_{o}^{pick} \\) on \\( p_1 \\), \\( p_2 \\), \\( p_3 \\) using computed corresponding placing affordance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.47, + 0.554 + ], + "angle": 0, + "content": "During inference, in each step, the greedy policy first selects \\( p_{pick} \\) with the highest affordance score in \\( A_o^{pick} \\) given \\( o \\), and then selects \\( p_{place} \\) with the highest affordance score in \\( A_{o|p_{pick}}^{place} \\) given \\( o \\) and \\( p_{pick} \\), resulting in the temporary best state after the pick-and-place action." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.558, + 0.47, + 0.589 + ], + "angle": 0, + "content": "4.3. Estimating State Values and Learning Foresightful Affordance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.669 + ], + "angle": 0, + "content": "As shown in Figure 4, for multi-step manipulation, only evaluating the direct distance between the current state and the target (greedy method described above) may result in many local optimal states that are temporarily closer to target but harder for future actions to complete the whole task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.471, + 0.764 + ], + "angle": 0, + "content": "Dynamic Programming (DP) [1] and Q-Learning [34] tackle this local optima problem by estimating the 'value' of a state that indicates whether a state is beneficial to the task in the long term (instead of the current performance). Inspired by them, we can add such state 'value' (formally formulated in Equation 4) to the estimation of \\( A_{o|p_{pick}}^{place} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.77, + 0.475, + 0.793 + ], + "angle": 0, + "content": "\\[\ng _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = \\alpha \\times \\operatorname {v a l u e} _ {o ^ {\\prime}} + \\beta \\times (1 - \\operatorname {d i s t} (o ^ {\\prime}, T)) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.794, + 0.443, + 0.808 + ], + "angle": 0, + "content": "where \\(\\alpha +\\beta = 1\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.817, + 0.469, + 0.871 + ], + "angle": 0, + "content": "With such \\( A_{o|p_{pick}}^{place} \\) that is foresightful for long-term tasks, \\( A_{o}^{pick} \\), which is the aggregation of \\( A_{o|p_{pick}}^{place} \\), will therefore get such foresightfulness spontaneously." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Estimating the 'value' in a state requires understanding all possible actions and their corresponding future results," + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.304, + 0.892, + 0.389 + ], + "angle": 0, + "content": "Figure 4. Local Optima v.s. Global Optima. Many local optimal states are temporarily closer to target (e.g., having larger coverage area in unfolding task), but making future actions hard to coordinate to accomplish the whole task. We propose to use 'value' to indicate whether a state is suitable for future actions, with which the policy can avoid those local optimal states in multi-step tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.395, + 0.892, + 0.457 + ], + "angle": 0, + "content": "and then selecting the best for the estimation. As \\( A_{o}^{pick} \\) estimates the action result on each point, state 'value' can be estimated by selecting the \\( p_{pick} \\) with the highest score in \\( A_{o}^{pick} \\) (Figure 3, Left):" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.459, + 0.892, + 0.482 + ], + "angle": 0, + "content": "\\[\nv a l u e _ {o} = \\max _ {i} g _ {o, p _ {i}} ^ {\\text {p i c k}}, i \\in \\{1,.., m \\times n \\} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.487, + 0.892, + 0.523 + ], + "angle": 0, + "content": "As \\(value_{o}\\) could be estimated by \\(A_{o}^{pick}\\), \\(A_{o|p_{pick}}^{place}\\) could be reformulated using both \\(A_{o}^{pick}\\) and the direct distance:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.524, + 0.785, + 0.547 + ], + "angle": 0, + "content": "\\[\ng _ {o, p _ {\\text {p l a c e}} | p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = \\alpha \\times \\max _ {i} g _ {o ^ {\\prime}, p _ {i}} ^ {\\text {p i c k}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.664, + 0.548, + 0.892, + 0.567 + ], + "angle": 0, + "content": "\\[\n+ \\beta \\times (1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right)) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.66, + 0.571, + 0.789, + 0.585 + ], + "angle": 0, + "content": "where \\(\\alpha +\\beta = 1\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.587, + 0.89, + 0.618 + ], + "angle": 0, + "content": "4.4. Break the Cycle and Cut into Stages: Learning Foresightful Affordance Stably Stage by Stage" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.621, + 0.892, + 0.681 + ], + "angle": 0, + "content": "The above-formulated picking and placing affordance forms a chicken-egg dependency cycle: picking affordance is dependent on placing affordance, while placing affordance is dependent on picking affordance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.682, + 0.892, + 0.803 + ], + "angle": 0, + "content": "To break the dependency cycle, states close to the target (e.g., cloth almost fully unfolded) become the key. As the task is almost accomplished in these states, their values and direct distances to the target are nearly the same. So for an interaction where the ending state \\( o' \\) is close to the target, we directly use their distances to the target (instead of both distances and 'value's) to supervise the corresponding placing affordance of the starting state \\( o \\):" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.808, + 0.892, + 0.836 + ], + "angle": 0, + "content": "\\[\ng _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = 1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.522, + 0.833, + 0.85, + 0.849 + ], + "angle": 0, + "content": "when \\(dist(o', T)\\) is close to 0 i.e., the last step" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "According to Equations 2, 5 and 6, the proposed picking and placing affordance could be estimated without the dependency cycle. As the dependency cycle breaks in states" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10950" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "close to the target, we learn dense affordance from these simple states to more complex states (reversed order of inference) shown in Figure 2 (Right). Specifically, we divide learning procedure into multiple stages. In the first stage, we learn affordance for states that can reach states close to the target within one step, using the direct distances of the following states as supervisions. In the \\(i\\)-th \\((i > 1)\\) stage, we learn affordance for states that can reach states in the \\((i-1)\\)-th stage in one step, using both the direct distances and the 'value's of states in the \\((i-1)\\)-th stage as supervisions. In each stage, we first train \\(\\mathcal{M}_{\\text{place}}\\) using stable 'value's provided from the trained \\(\\mathcal{M}_{\\text{pick}}\\) in the previous stage, and then train \\(\\mathcal{M}_{\\text{pick}}\\) with stable supervisions (max of placing affordance) provided from the trained \\(\\mathcal{M}_{\\text{place}}\\) in this stage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.47, + 0.352 + ], + "angle": 0, + "content": "In this way, during the whole training, \\( A_{o|p_{pick}}^{place} \\) and \\( A_{o}^{pick} \\) both have stable supervisions from the former stage, and can provide stable supervisions for the latter stage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.473, + 0.549 + ], + "angle": 0, + "content": "This stage-by-stage learning schema empowers our method with superiority over RL methods. Although RL also estimates states and actions using Bellman Equation, it simultaneously estimates and updates values across all states (offline RL) or trajectories of states (online RL), which is difficult to efficiently and stably learn the values, as RL struggles in iteratively updating state 'value's, especially when considering the prohibitively large state and action space of deformable objects. In contrast, like other dense affordance works [26, 43, 36], we stably learn affordance with 'value' using supervised learning, with stable supervisions provided in the previous training stage. Experiments demonstrate our superiority over RL in Section 5.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.56, + 0.47, + 0.59 + ], + "angle": 0, + "content": "4.5. Fold to Unfold: Efficient Multi-stage Data Collection for Learning Foresightful Affordance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.704 + ], + "angle": 0, + "content": "The above-described training schema requires multi-stage data for training. Specifically, in the first stage, the starting states are one-step to states close to the target. In the \\(i\\)-th \\((i > 1)\\) stage, the starting states are one-step to states in the \\((i-1)\\)-th stage. Each starting state's actions and corresponding ending states should be diverse, as we need to learn the affordance representing dense distributions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.795 + ], + "angle": 0, + "content": "However, due to the complexity of states and dynamics, data collection methods used by previous dense affordance works (random policies [26, 27] or state-based RL [36, 43]) could hardly collect such data. On the other hand, designing expert policies [31] or hand-crafting demonstrations are difficult and time-consuming for different tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.871 + ], + "angle": 0, + "content": "Therefore, we propose a novel self-supervised method, named Fold to Unfold, using reversed actions of tasks to efficiently collect multi-stage data. This method is generic to many kinds of deformable object manipulation tasks, with no need for human-designed expert policies or annotations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Similar to the training procedure, we collect data from states close to the target, to more complex states." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.092, + 0.875, + 0.141 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.147, + 0.875, + 0.161 + ], + "angle": 0, + "content": "Figure 5. Fold to Unfold collection in simulator and real world." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.177, + 0.892, + 0.298 + ], + "angle": 0, + "content": "Specifically, as shown in Figure 5, from a state \\( o_i \\) in stage \\( i \\), we select a picking point \\( p_{pick} \\), put it on a placing point \\( p_{place} \\) and get \\( o_{i+1} \\). Then, from \\( o_{i+1} \\), we execute the reversed action, pick \\( p_{place} \\), place on \\( p_{pick} \\) and get \\( o_i' \\). If \\( o_i' \\) is similar to \\( o_i \\), we choose \\( o_{i+1} \\) as a starting state in stage \\( i+1 \\), and sample diverse actions on \\( o_{i+1} \\) with different corresponding results to train dense affordance in the \\( (i+1) \\)-th stage (shown in Figure 2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.892, + 0.344 + ], + "angle": 0, + "content": "Through a few stages of data collection, object states become complex and diverse, empowering trained affordance networks with generalization towards diverse novel states." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Note that, although reversed actions cannot fully recover previous states, i.e., \\( o_i' \\) are not the same as \\( o_i \\), chances are that \\( o_i' \\) and \\( o_i \\) are similar, and thus this method still greatly improves sample efficiency. Also, proposed affordance is not dependent on this data collection method, as it can be trained on data collected by any method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.444, + 0.776, + 0.46 + ], + "angle": 0, + "content": "4.6. Integrated Systematic Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.892, + 0.617 + ], + "angle": 0, + "content": "Although above designs and training procedure enable affordance learning for multi-step tasks, \\(\\mathcal{M}_{pick}\\) and \\(\\mathcal{M}_{place}\\) are trained using only offline collected data in different stages, not considering the actual execution performance of the policies provided by the two modules. During actual manipulation procedures, the policy is the composite policy of \\(\\mathcal{M}_{pick}\\) and \\(\\mathcal{M}_{place}\\), and pick-and-place actions are executed one by one sequentially as a whole system. Therefore, we propose the Integrated Systematic Training (IST) procedure to adapt \\(\\mathcal{M}_{pick}\\) and \\(\\mathcal{M}_{place}\\) using online data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.617, + 0.892, + 0.737 + ], + "angle": 0, + "content": "In this procedure, with offline trained \\(\\mathcal{M}_{\\text{place}}\\) and \\(\\mathcal{M}_{\\text{pick}}\\), we randomly sample object initial states, use \\(\\mathcal{M}_{\\text{place}}\\) and \\(\\mathcal{M}_{\\text{pick}}\\) as the policy to select \\(p_{\\text{pick}}\\) and \\(p_{\\text{place}}\\), execute pick-and-place step by step, and use actual results to simultaneously update \\(\\mathcal{M}_{\\text{place}}\\) and \\(\\mathcal{M}_{\\text{pick}}\\). Through this procedure, the two modules are constantly adapted by consecutively online-sampled and actually-executed data, and thus are gradually integrated into a whole system." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.745, + 0.857, + 0.76 + ], + "angle": 0, + "content": "4.7. Network Architectures and Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For architectures of \\(\\mathcal{M}_{pick}\\) and \\(\\mathcal{M}_{place}\\), we use Fully Convolutional Networks (FCNs) [24] same in Transporter [41, 31] with extra skip-connections as backbone perpoint feature extractor. For \\(\\mathcal{M}_{pick}\\), we directly use \\(p_{pick}\\) feature to predict picking affordance score on \\(p_{pick}\\). For \\(\\mathcal{M}_{place}\\), we use feature concatenation of \\(p_{pick}\\) and \\(p_{place}\\) to predict placing affordance score on \\(p_{place}\\). To train both \\(\\mathcal{M}_{pick}\\) and \\(\\mathcal{M}_{place}\\), we use Mean Absolute Error (MAE) between predictions and ground truth as the loss function." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10951" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.21, + 0.107 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.325, + 0.131 + ], + "angle": 0, + "content": "5.1. Tasks, Settings and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.138, + 0.47, + 0.349 + ], + "angle": 0, + "content": "Tasks. To demonstrate the superiority of our framework, we select 2 representative tasks from DeformableRavens benchmark: (1) cable-ring: manipulating a ring to a given green circle, (2) cable-ring-nottarget: manipulating a ring to any circle, as well as 2 representative tasks from SoftGym: (3) SpreadCloth: spreading crumpled cloth to be flat, (4) RopeConfiguration: manipulating a rope from a random pose to a target pose (we use the shape 'S' as the target). Among them, the first two are relatively easier. They can be accomplished without considering future actions and states, and we conduct them to show our dense affordance's superiority over methods imitating expert demonstrations. The last two are much harder and would be better accomplished considering future actions and states to avoid local optima." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.35, + 0.47, + 0.454 + ], + "angle": 0, + "content": "Settings. For all tasks, in both training and testing, we set different random seeds for each episode, producing unseen and diverse initial poses of objects. To compare the generalization ability between our proposed dense affordance and imitation-based methods, for cables in DeformableRavens, we directly test the model trained on cables with 32 beads over novel cable configurations with 24, 28 or 36 beads." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.455, + 0.469, + 0.53 + ], + "angle": 0, + "content": "Metrics. For cable-ring and cable-ring-notarget, we follow DeformableRavens and use the manipulation successful rate as the metric. For SpreadCloth and RopeConfiguration, we follow SoftGym and use the normalized score as the metric. For all tasks, higher scores indicate better performance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.537, + 0.185, + 0.552 + ], + "angle": 0, + "content": "5.2. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.561, + 0.47, + 0.59 + ], + "angle": 0, + "content": "For two cable-ring related tasks, we compare our method with baselines with or without expert demonstrations:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.59, + 0.47, + 0.665 + ], + "angle": 0, + "content": "- Transporter [41, 31] is commonly used for robotic manipulation by learning visual correlation for picking and placing points. In DeformableRavens [31] it is trained by cloning expert demonstrations and achieves SOTA performance over relevant tasks." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.669, + 0.47, + 0.701 + ], + "angle": 0, + "content": "- GT-State receives ground truth (GT) pose of the target object, and regresses \\( p_{pick} \\) and \\( p_{place} \\) with MLP." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.705, + 0.469, + 0.736 + ], + "angle": 0, + "content": "- GT-State 2-Step first regresses \\( p_{pick} \\) and then \\( p_{place} \\) using \\( p_{pick} \\) and GT pose concatenation, both via MLP." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.59, + 0.47, + 0.736 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.741, + 0.469, + 0.8 + ], + "angle": 0, + "content": "For SpreadCloth and RopeConfiguration, as object states and dynamics are too complex and the tasks are too difficult to hand-engineer expert policies, we compare our method with baselines focused on multi-step planning:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.801, + 0.469, + 0.831 + ], + "angle": 0, + "content": "- CURL-SAC [18] that uses a model-free RL approach with contrastive unsupervised representations." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.832, + 0.461, + 0.848 + ], + "angle": 0, + "content": "- \\(\\mathbf{DrQ}[40]\\) applies augmentation, regularization to RL." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.848, + 0.463, + 0.863 + ], + "angle": 0, + "content": "- PlaNet [11] learns state space dynamics for planning." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.864, + 0.468, + 0.894 + ], + "angle": 0, + "content": "- MVP [37] learns pick-and-place policy with model-free RL designed for deformbale object manipulation." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.801, + 0.469, + 0.894 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.785, + 0.107 + ], + "angle": 0, + "content": "5.3. Qualitative Results and Analysis" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.121, + 0.882, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.354, + 0.892, + 0.396 + ], + "angle": 0, + "content": "Figure 6. Example action sequences for cable-ring, cable-ring-nottarget, SpreadCloth and RopeConfiguration. White point denotes picking and black point denotes placing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.401, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Figure 6 shows examples of manipulation trajectories for diverse tasks using our proposed affordance. It is worth mentioning that, in the second state of SpreadCloth (Row 3), though it is intuitive to place the picking point (white) to the top-left position, the model places it to the bottom-right position (black), as the corresponding next state has low coverage but high 'value', requiring only one following pick-and-place action to almost fully unfold the cloth." + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.536, + 0.891, + 0.754 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.757, + 0.892, + 0.813 + ], + "angle": 0, + "content": "Figure 7. Picking and placing affordance. Each row contains two (picking affordance, observation with \\( p_{pick} \\), placing affordance) tuples for a task. \\( p_{pick} \\) is selected by picking affordance. Higher color temperature means higher affordance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Figure 7 visualizes picking and placing affordance, clearly showing that the learned affordance represents deformable objects with complex states and dynamics and facilitates selecting picking and placing points for manipulation. Figure 8 visualizes 'value's of states." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10952" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.452, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.203, + 0.47, + 0.245 + ], + "angle": 0, + "content": "Figure 8. Visualization of 'value' shows that some states with closer distances to the target (e.g., larger area) may not have higher 'value', as these states are hard for future actions to fulfill the task." + }, + { + "type": "table", + "bbox": [ + 0.113, + 0.259, + 0.434, + 0.369 + ], + "angle": 0, + "content": "
Methodcable-ringcable-ring-notarget
GT-State0.05.0
GT-State 2-Step0.01.7
Transporter68.370.0
Ours81.795.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.117, + 0.371, + 0.432, + 0.385 + ], + "angle": 0, + "content": "Table 1. Quantitative results in DeformableRavens." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.392, + 0.43, + 0.526 + ], + "angle": 0, + "content": "
MethodSpreadClothRopeConfiguration
CURL-SAC0.1950.348
PlaNet0.3870.236
DrQ0.2750.154
MVP0.3720.258
Ours0.7580.529
" + }, + { + "type": "table_caption", + "bbox": [ + 0.145, + 0.526, + 0.4, + 0.539 + ], + "angle": 0, + "content": "Table 2. Quantitative results in SoftGym." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.548, + 0.375, + 0.565 + ], + "angle": 0, + "content": "5.4. Quantitative Results and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Shown in Table 1, our method outperforms all baselines in DeformableRavens. For GT State and GT State 2-Step, GT states can only provide part of the necessary information, and it is difficult to acquire the precise GT states of deformable objects in the real world. For Transporter that learns visual correlation for the matching between picking and placing points, although it directly clones successful demonstrations from hand-crafted expert policies, we outperform it for two possible reasons: 1) dense affordance is more suitable for deformable objects as it represents the results of diverse actions on complex states, while visual correlation in Transporter is suitable for matching like assembling-kits; 2) training on and cloning expert demonstrations will limit the model's generalization toward diverse situations for inference. To further evaluate the generalization ability of dense affordance, we produce different novel object configurations, using 24, 28, and 36 as the bead number instead of the initial 32. Our method's slighter performance decrease in Table 3 also demonstrates its generalization ability. Besides, expert policies need elaborate hand-engineering for different tasks, while our method can apply to diverse tasks without large modifications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.153 + ], + "angle": 0, + "content": "Table 2 shows our framework outperforms all baselines in SoftGym. As described in 4.4, compared with those RL methods, our framework learns representations of complex states for multi-step manipulation in a stable way." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.164, + 0.875, + 0.245 + ], + "angle": 0, + "content": "
Task configurationscable-ring 24 / 28 / 36cable-ring-notarget 24 / 28 / 36
Transporter33.3 / 58.3 / 32.760.0 / 71.7 / 31.7
Ours61.6 / 86.7 / 58.381.7 / 96.7 / 78.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.248, + 0.892, + 0.276 + ], + "angle": 0, + "content": "Table 3. Manipulation scores on novel configurations in DeformableRaves showing our method's generalization capability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.296, + 0.767, + 0.312 + ], + "angle": 0, + "content": "5.5. Ablation Studies and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.892, + 0.421 + ], + "angle": 0, + "content": "To demonstrate necessities of our framework's different components, we conduct ablation experiments by comparing our method with: 1) Ours RandPick: our method with the picking policy replaced by a random policy; 2) Ours ExpertPick: our method with the picking policy replaced by Transporter's expert; 3) Ours w/o IST: our method without Integrated Systematic Training (IST);" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.497 + ], + "angle": 0, + "content": "For SpreadCloth and RopeConfiguration that require strongly related sequential actions, we additionally compare 1) ablated versions using different stages of data, 2) Ours only dist directly and greedily trained on all collected data instead of stage-by-stage considering 'value's." + }, + { + "type": "table", + "bbox": [ + 0.519, + 0.509, + 0.874, + 0.622 + ], + "angle": 0, + "content": "
Methodcable-ringcable-ring-notarget
Ours RandPick11.758.3
Ours ExpertPick76.741.7
Ours w/o IST78.391.7
Ours81.795.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.55, + 0.622, + 0.842, + 0.635 + ], + "angle": 0, + "content": "Table 4. Ablation studies in DeformableRavens." + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.651, + 0.88, + 0.763 + ], + "angle": 0, + "content": "
Methodstage1stage2stage3stage4stage5
Ours RandPick0.2410.2110.3040.1850.190
Ours w/o IST0.5260.5860.6210.6240.612
Ours only dist0.7010.7010.7010.7010.701
Ours0.5890.6950.7520.7540.758
" + }, + { + "type": "table_caption", + "bbox": [ + 0.569, + 0.763, + 0.822, + 0.776 + ], + "angle": 0, + "content": "Table 5. Ablation studies in SpreadCloth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.89, + 0.81 + ], + "angle": 0, + "content": "Table 5 and 6 show that, a series of steps of data empowers affordance with generalization to diverse states." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Table 4, 5 and 6 show quantitative results of ablation experiments. Ours RandPick and Ours ExpertPick show that, with the same placing affordance, our proposed picking affordance helps the framework perform the best." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Ours only dist in Table 5 and 6 show that, directly training on all the diverse data without estimating state 'value'" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10953" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.089, + 0.089, + 0.46, + 0.202 + ], + "angle": 0, + "content": "
Methodstage1stage2stage3stage4stage5
Ours RandPick0.3290.3020.3320.3340.322
Ours w/o IST0.3590.4180.4370.4790.474
Ours only dist0.4600.4600.4600.4600.460
Ours0.4410.5030.5180.5270.529
" + }, + { + "type": "table_caption", + "bbox": [ + 0.127, + 0.201, + 0.419, + 0.215 + ], + "angle": 0, + "content": "Table 6. Ablation studies in RopeConfiguration." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.219, + 0.469, + 0.28 + ], + "angle": 0, + "content": "limits the performance compared with our proposed framework. Besides, as shown in Figure 9, Ours only dist will propose actions leading to local optimal states, while our foresightful affordance will help to avoid that." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.28, + 0.469, + 0.341 + ], + "angle": 0, + "content": "Ours w/o IST in Table 4, 5 and 6, and adjusted affordance and 'value's in Figure 10 demonstrate IST helps integrating picking and placing modules into a whole, generating more precise perception of affordance and 'value's." + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.354, + 0.468, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.565, + 0.469, + 0.594 + ], + "angle": 0, + "content": "Figure 9. Placing affordance trained using 'value' supervision (red) and only using the greedy direct distance (blue)." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.613, + 0.141, + 0.661 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.144, + 0.619, + 0.258, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.273, + 0.612, + 0.335, + 0.66 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.613, + 0.4, + 0.659 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.409, + 0.613, + 0.468, + 0.659 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.672, + 0.469, + 0.702 + ], + "angle": 0, + "content": "Figure 10. Picking and placing affordance before (middle) and after (right) IST of the observation (left). White: pick point." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.711, + 0.303, + 0.728 + ], + "angle": 0, + "content": "5.6. Real-world Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.469, + 0.826 + ], + "angle": 0, + "content": "To bridge the sim2real gap and implement our method in the real world, similar to [37, 10], we use domain randomization to train affordance models in simulation and fine-tune them in real world. Specifically, we collect real-world data using Fold to Unfold, fine-tune trained-in-simulation \\(\\mathcal{M}_{pick}\\) and \\(\\mathcal{M}_{place}\\) stage by stage using the collected data." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For evaluations, we randomly lift and drop the objects for five times to get the initial state, and then run the models for ten pick-and-place actions to perform the tasks. The manipulation score is the average normalized score (computed the same as in SoftGym) of sixty trajectories." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "Shown in Figure 11, given real-world observations with textures and physics different from objects in simulation, our method predicts reasonable picking and placing affordance and selects actions for tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.153, + 0.892, + 0.213 + ], + "angle": 0, + "content": "We use MVP [37] for comparison, as (1) it also uses pick-and-place as action primitive, thus could do both cloth and rope tasks, and (2) provides real-world experiments. Table 7 shows performance comparison, explained in 5.4." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.215, + 0.889, + 0.23 + ], + "angle": 0, + "content": "See the supplementary for more implementation details." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.244, + 0.852, + 0.315 + ], + "angle": 0, + "content": "
MethodSpreadClothRopeConfiguration
MVP0.3070.227
Ours0.6830.461
" + }, + { + "type": "table_caption", + "bbox": [ + 0.557, + 0.316, + 0.835, + 0.33 + ], + "angle": 0, + "content": "Table 7. Manipulation scores in the real world." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.35, + 0.626, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.35, + 0.691, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.35, + 0.758, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.35, + 0.824, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.827, + 0.35, + 0.889, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.482, + 0.626, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.482, + 0.691, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.482, + 0.758, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.482, + 0.822, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.827, + 0.49, + 0.889, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.617, + 0.875, + 0.632 + ], + "angle": 0, + "content": "Figure 11. Real-world pick-place actions guided by affordance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.645, + 0.619, + 0.661 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.892, + 0.82 + ], + "angle": 0, + "content": "We propose to use dense visual affordance for manipulating deformable objects with complex states and dynamics. For tasks that require a series of strongly related actions, we further empower the proposed affordance with the awareness of a certain action's influence on subsequent actions. We propose a self-supervised framework with novel designs to efficiently collect multi-stage interaction data and stably learn this representation. Experiments on representative tasks and in the real world show the superiority of our proposed dense affordance and the learning framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.825, + 0.671, + 0.841 + ], + "angle": 0, + "content": "7. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by National Natural Science Foundation of China (No. 62136001). We thank Qianxu Yang and Haoran Lu for assisting real-world experiments, Mingdong Wu and Hongcheng Wang for discussions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10954" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Richard Bellman. Dynamic programming. science, 153(3731):34-37, 1966. 2, 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.146, + 0.468, + 0.172 + ], + "angle": 0, + "content": "[2] Aude Billard and Danica Kragic. Trends and challenges in robot manipulation. 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International Conference on Learning Representations (ICLR), 2023. 2, 3, 5" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.894, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10956" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/b7d619c9-c5f2-438e-896d-a2c31b01ebe0_origin.pdf b/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/b7d619c9-c5f2-438e-896d-a2c31b01ebe0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cb282f866f338c9f130cd4243ab5b0c335b54693 --- /dev/null +++ b/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/b7d619c9-c5f2-438e-896d-a2c31b01ebe0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ca9666c7e24cdf638c8d63d47b6f055afd078c2f53641fad49d8894d0e73cb14 +size 9776143 diff --git a/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/full.md b/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e6f01e55d811dc7c716678b7473570f243fec7a1 --- /dev/null +++ b/2023/Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation/full.md @@ -0,0 +1,399 @@ +# Learning Foresightful Dense Visual Affordance for Deformable Object Manipulation + +Ruihai Wu $^{1,3,4*}$ Chuanruo Ning $^{2,1*}$ Hao Dong $^{1,3,4\dagger}$ + +$^{1}$ CFCS, School of CS, PKU $^{2}$ School of EECS, PKU $^{3}$ BAAI + +$^{4}$ National Key Laboratory for Multimedia Information Processing, School of CS, PKU + +# Abstract + +Understanding and manipulating deformable objects (e.g., ropes and fabrics) is an essential yet challenging task with broad applications. Difficulties come from complex states and dynamics, diverse configurations and high-dimensional action space of deformable objects. Besides, the manipulation tasks usually require multiple steps to accomplish, and greedy policies may easily lead to local optimal states. Existing studies usually tackle this problem using reinforcement learning or imitating expert demonstrations, with limitations in modeling complex states or requiring hand-crafted expert policies. In this paper, we study deformable object manipulation using dense visual affordance, with generalization towards diverse states, and propose a novel kind of foresightful dense affordance, which avoids local optima by estimating states' values for long-term manipulation. We propose a framework for learning this representation, with novel designs such as multi-stage stable learning and efficient self-supervised data collection without experts. Experiments demonstrate the superiority of our proposed foresightful dense affordance. Project page: https://hyperplane-lab.github.io/DeformableAffordance + +# 1. Introduction + +Many kinds of deformable objects, such as ropes and fabrics, exist everywhere in our daily life. Perceiving and manipulating deformable objects plays a significant role and paves the way for future home-assistant robots. + +Unlike rigid or articulated objects, due to the complex dynamics, high-dimensional and nearly infinite degrees of freedom, large action space, and severe self-occlusion, deformable objects pose much more challenges to manipulate. Moreover, unlike tasks for rigid objects (like grasping) or articulated objects (like pushing a door) that require one or only a few steps to accomplish, deformable object manipulation tasks usually require many steps to accomplish, + +![](images/892d46690a37f5eb77b336411c0f25725f3c35ef69de2ba7ba9a9cf59297b913.jpg) + +![](images/8b702a90502fac6221cc4396597b88531cbd27435c9e6ab92197b36cfda18de7.jpg) +0.382 0.320 + +![](images/49bbab9debe74f6e59bcbfa58359f5410261c52b16728c27b65091fe62ee0035.jpg) +0.557 +Pick Point +- Place Point +Coverage + +![](images/aa99dd6357db2247c410eb2f433090cb6717d1e475e5d76576353c0c6a5e8af3.jpg) +Local Optimal State +Figure 1. Deformable Object Manipulation has many difficulties. 1) It requires multiple steps to complete. 2) Most actions can hardly facilitate tasks, for the exceptionally complex states and dynamics. 3) Many local optimal states are temporarily closer to the target, but making following actions harder to coordinate for the whole task. We propose to learn Foresightful Dense Visual Affordance aware of future actions to avoid local optima for deformable object manipulation, with real-world implementations. + +laying much focus on relationships and influences between actions in a sequence, as an action leading to local optimal states may not eventually complete the task. + +Specifically, as shown in Figure 1, unfolding crumpled cloth requires a sequence of actions (pick-and-place). Because of the exceptionally complex states and dynamics, and large action space, most actions fail to facilitate the task. Moreover, although some cloth in local optimal states temporarily have larger coverage areas than others, following actions face difficulties in smoothly completing the task. + +Proposed by Gibson [8] and aimed at providing indicative information for agents to execute actions (e.g., el + +emetary actions such as picking and pulling) and thus facilitating downstream tasks, visual affordance is arousing much attention in vision and robotics. Recent works have demonstrated its efficiency in a large range of tasks like grasping [25, 28, 3, 16, 15, 42], manipulating articulated objects [26, 36, 33, 5] and assisting robots in a scene [29, 30, 9]. Among them, point-level dense affordance [36, 26, 27, 33] learns whether an action on each point of the object could facilitate the task. Compared with Reinforcement Learning (RL) approaches, dense affordance is stably supervised and has better generalization ability towards objects with diverse shapes. + +The above dense affordance is suitable for representing deformable objects with complex states, capable of indicating whether diverse actions could help complete the task. + +While most previous works only study dense affordance for short-term manipulation on rigid [43] or articulated objects [26, 36], to tackle the local optima problem in multi-step manipulation, we move a step towards equipping dense affordance with foresightfulness for future states. + +Inspired by Dynamic Programming with Bellman Equation [1] and Q-Learning [34], estimating a state's 'value' (expected return in the long term, instead of only the current performance) for future actions to coordinate and eventually complete the task will help avoid local optimal states and boost the smoothness and quickness of multi-step manipulation. Dense affordance is suitable for such 'value' estimation, because such 'value' requires understanding and aggregating a large number of diverse following actions on complex states and their corresponding results. + +With such state 'value's (instead of only the current performance) in supervisions, dense affordance would gain foresightfulness for the future. + +We propose to learn dense visual affordance for manipulating deformable objects, and further estimate state 'value's by aggregating such affordance to avoid local optima and smoothly accomplish multi-step tasks. As shown in Figure 1 (Down), the task can be accomplished smoothly using our proposed dense affordance in the real world. To learn such representations, we propose a novel framework generic to diverse tasks with many novel designs, such as the stage-by-stage stable training and Fold to Unfold efficient multi-stage data collection. Thus the proposed affordance could be learned stably, efficiently, and self-supervisedly without hand-crafted policies for different tasks. Experiments on representative benchmark tasks demonstrate our framework's impressive performance. + +In summary, our contributions are: + +- We propose to use dense visual affordance for manipulating deformable objects with complex states and dynamics, using such representation to estimate state 'value's for future actions to avoid local optima and smoothly accomplish multi-step manipulation tasks; + +- We propose a self-supervised framework with novel designs such as multi-stage training and efficient data collection to learn the proposed affordance stably; +- Qualitative and quantitative results on representative benchmarks and real-world experiments demonstrate the superiority of our proposed dense visual affordance and learning framework for deformable objects. + +# 2. Related Work + +# 2.1. Deformable Object Manipulation + +Deformable object manipulation is a typical and significant kind of task in robotic manipulation [4, 17, 2]. Compared to rigid or articulated objects, the manipulation of deformable objects is challenging for its high complexity, described in the Introduction Section. Typical methods utilize Reinforcement Learning (RL) or Imitation Learning. RL methods take object states [13] or visual information [37, 20] as policy input. Imitation based methods [41, 31, 19] imitate human-designed expert policy or human demonstrations for each task. Vision-based methods [6, 14] use visual feedback or correspondence to perform manipulations. Flow-based methods [32, 35] learn forward dynamics for manipulation, requiring much time in planning. Besides, a series of works [12, 21, 39, 38, 22] develop differentiable environments for diverse tasks and tackle these tasks by optimization. Different from above methods, our work builds a bridge between perception and manipulation, taking advantage of the generalization ability of affordance and estimating state 'value' for efficient planning. + +# 2.2. Visual Affordance for Robotic Manipulation + +Visual affordance [8] indicates possible ways for robots to interact with and complete tasks. Many recent works learn affordance for grasping [25, 28, 3, 16, 15, 42], articulated object manipulation [26, 36, 33, 5, 7], object-object interaction [27], collaboration [43] and interaction in a scene [29, 30, 9]. Among them, point-level dense affordance [26, 36, 43, 33] learns per-point representations of objects, which is more sensitive to local geometries and easier to generalize to different objects. Most tasks can be achieved in a single step (e.g., grasping, pulling drawers), with the learned affordance only containing actionable information for single-step manipulation. However, deformable objects with complex states and dynamics require many steps to manipulate. We move a step towards proposing dense affordance for deformable objects, which not only indicates complex states and dynamics but also takes the subsequent actions of a certain state into consideration for long-term tasks to avoid local optima. FlingBot [10] learns affordance for unfolding cloth by flinging, while our proposed affordance uses pick-and-place which is more generic for large action space and diverse tasks. + +# 3. Problem Formulation + +In this section, we describe how we formulate learning policy for multi-step deformable object manipulation into learning policies for picking and placing. + +Following benchmarks DeformableRavens [31] and SoftGym [23], the problem is formulated as learning a policy $\pi$ to output robot action $a_{t}$ , given the visual observation $o_{t}$ (denoted as $o$ ) at time $t$ . We use pick-and-place as the action, i.e., $a_{t} = (a_{pick}, a_{place})$ , with $a_{pick}$ and $a_{place}$ denoting picking and placing poses. Explained in [31], the selector can fulfill the tasks without rotation, so $a_{pick}$ and $a_{place}$ are denoted as picking point $p_{pick}$ and placing point $p_{place}$ . + +The composite of $p_{pick}$ and $p_{place}$ makes up a large combinatorial action space hard for a network to learn directly and simultaneously. For the underlying nature that $p_{place}$ highly depends on $p_{pick}$ , we follow [37] and disentangle learning the composite of $p_{pick}$ and $p_{place}$ into respectively learning $p_{pick}$ and $p_{place|p_{pick}}$ (denoted as $p_{place}$ ). + +Therefore, we formulate the problem into learning picking and placing policies. In Method Section 4, we describe how we learn the policies using foresightful dense visual affordance with each state's 'value' to avoid local optima. + +# 4. Method + +# 4.1. Overview + +Shown in Figure 2, our framework is composed of two main parts: (1) we propose to use dense affordance to represent policy (4.2), estimate state 'value' using dense affordance and incorporate 'value' into dense affordance to avoid local optima for multi-step manipulation (4.3), break the picking-placing dependency cycle and stably learn affordance stage by stage (4.4); (2) to tackle the difficulty in collecting multi-stage and successful interactions, we propose a method (named Fold to Unfold) generic to many tasks to efficiently collect data in the reversed task completion order (e.g., collecting unfolding data by folding cloth) (4.5). Besides, we propose Integrated Systematic Training to further integrate the proposed affordance into a whole system (4.6). Finally, we describe network architectures and losses (4.7). + +# 4.2. Dense Visual Affordance Representing Policy + +This section introduces how to use dense visual affordance to represent manipulation policy. For simplicity, we first discuss affordance for a greedy policy. + +Described in Section 3, we formulate the problem into learning picking and placing policies, i.e., the picking point $p_{pick}$ and placing point $p_{place}$ given the observation $o$ (with the size of $m \times n$ points). As the action space is all points on the object for picking, and all points in the space for placing, it comes naturally to use per-point score map $A_{o}^{pick}$ (size $m \times n$ ) indicating how picking each point will facilitate the task, and dense placing affordance map $A_{o|p_{pick}}^{place}$ (size $m \times n$ ) indicating how placing the picking point $p_{pick}$ on + +![](images/497af368c9425e59601868bc8966758080da72368628910cc10f3e07b0de35a5.jpg) +Stage-1 Data Collection Multi-stage Training + +![](images/957947f01947c1496668e31533c85d687557cb99714a829b640bc577a3fcb977.jpg) + +![](images/5f9da6c34624fb49b9ee6eb3da226318d2173bce7ec91b1da93318c586ac12da.jpg) +Figure 2. Our proposed framework learns dense picking and placing affordance for deformable object manipulation (e.g., Unfolding Cloth). We collect multi-stage interaction data efficiently (Left) and learn proposed affordance stably in a multi-stage schema (Right) in the reversed task accomplishment order, from states close to the target to complex states. + +each point will facilitate the task. Following previous dense affordance studies [26, 36, 43], we notify such task-specific per-point score maps as task-specific dense affordance (denoted as affordance for simplicity). Demonstrated in above studies, such dense affordance performs well in extracting diverse geometric information and generalizes well to unseen visual states, which is significant in representing and manipulating deformable objects with complicated states. + +An intuitive greedy way to supervise $A_{o|p_{pick}}^{place}$ is directly using the distance between the target $T$ and the new object state $o'$ after picking $p_{pick}$ and placing on $p_{place}$ in $o$ . For example, we use $1 - dist(o, T)$ , i.e., the cloth coverage area, to supervise $A_{o|p_{pick}}^{place}$ for unfolding. So we can estimate placing affordance score $g_{o, p_{place}|p_{pick}}^{place}$ on $p_{place}$ as (Figure 3, Middle, temporarily dismiss 'value' in Figure): + +$$ +g _ {o, p _ {\text {p l a c e}} \mid p _ {\text {p i c k}}} ^ {\text {p l a c e}} = 1 - \operatorname {d i s t} \left(o ^ {\prime}, T\right) \tag {1} +$$ + +Given a picking point $p_{pick}$ , the placing policy will select $p_{place}$ with the highest affordance, so the picking affordance score $g_{0,pick}^{pick}$ on $p_{pick}$ can be estimated using the affordance score of the best placing point (Figure 3, Left): + +$$ +g _ {o, p _ {p i c k}} ^ {p i c k} = \max _ {i} g _ {o, p _ {i} | p _ {p i c k}} ^ {\text {p l a c e}}, i \in \{1,,.., m \times n \} \tag {2} +$$ + +We use two networks $\mathcal{M}_{pick}$ and $\mathcal{M}_{place}$ to respectively learn $A_{o}^{pick}$ and $A_{o|p_{pick}}^{place}$ (architectures in Section 4.7). + +![](images/0b770f79a78927c7c90db6efbd028a6c23d21f9ba7e2fdf243270ac14b89bb38.jpg) +Figure 3. Learning placing and picking affordance with state 'value's for the future. Left to Right: The bottom black arrow indicates the manipulation (inference) order. Right to Left: Arrow flows show dependencies among placing affordance, picking affordance and 'value's. Given observation $o$ , we select 3 picking points $p_1$ , $p_2$ , $p_3$ , and show how to supervise corresponding placing affordance $A_{o|p_1}^{place}$ , $A_{o|p_2}^{place}$ , $A_{o|p_3}^{place}$ , and how to supervise $A_{o}^{pick}$ on $p_1$ , $p_2$ , $p_3$ using computed corresponding placing affordance. + +During inference, in each step, the greedy policy first selects $p_{pick}$ with the highest affordance score in $A_o^{pick}$ given $o$ , and then selects $p_{place}$ with the highest affordance score in $A_{o|p_{pick}}^{place}$ given $o$ and $p_{pick}$ , resulting in the temporary best state after the pick-and-place action. + +# 4.3. Estimating State Values and Learning Foresightful Affordance + +As shown in Figure 4, for multi-step manipulation, only evaluating the direct distance between the current state and the target (greedy method described above) may result in many local optimal states that are temporarily closer to target but harder for future actions to complete the whole task. + +Dynamic Programming (DP) [1] and Q-Learning [34] tackle this local optima problem by estimating the 'value' of a state that indicates whether a state is beneficial to the task in the long term (instead of the current performance). Inspired by them, we can add such state 'value' (formally formulated in Equation 4) to the estimation of $A_{o|p_{pick}}^{place}$ : + +$$ +g _ {o, p _ {\text {p l a c e}} \mid p _ {\text {p i c k}}} ^ {\text {p l a c e}} = \alpha \times \operatorname {v a l u e} _ {o ^ {\prime}} + \beta \times (1 - \operatorname {d i s t} (o ^ {\prime}, T)) \tag {3} +$$ + +where $\alpha +\beta = 1$ + +With such $A_{o|p_{pick}}^{place}$ that is foresightful for long-term tasks, $A_{o}^{pick}$ , which is the aggregation of $A_{o|p_{pick}}^{place}$ , will therefore get such foresightfulness spontaneously. + +Estimating the 'value' in a state requires understanding all possible actions and their corresponding future results, + +![](images/a575a90d01a30e068e125fd5704cf82992ad53784a3a116dd4db963725457a03.jpg) +Figure 4. Local Optima v.s. Global Optima. Many local optimal states are temporarily closer to target (e.g., having larger coverage area in unfolding task), but making future actions hard to coordinate to accomplish the whole task. We propose to use 'value' to indicate whether a state is suitable for future actions, with which the policy can avoid those local optimal states in multi-step tasks. + +and then selecting the best for the estimation. As $A_{o}^{pick}$ estimates the action result on each point, state 'value' can be estimated by selecting the $p_{pick}$ with the highest score in $A_{o}^{pick}$ (Figure 3, Left): + +$$ +v a l u e _ {o} = \max _ {i} g _ {o, p _ {i}} ^ {\text {p i c k}}, i \in \{1,.., m \times n \} \tag {4} +$$ + +As $value_{o}$ could be estimated by $A_{o}^{pick}$ , $A_{o|p_{pick}}^{place}$ could be reformulated using both $A_{o}^{pick}$ and the direct distance: + +$$ +g _ {o, p _ {\text {p l a c e}} | p _ {\text {p i c k}}} ^ {\text {p l a c e}} = \alpha \times \max _ {i} g _ {o ^ {\prime}, p _ {i}} ^ {\text {p i c k}} +$$ + +$$ ++ \beta \times (1 - \operatorname {d i s t} \left(o ^ {\prime}, T\right)) \tag {5} +$$ + +where $\alpha +\beta = 1$ + +# 4.4. Break the Cycle and Cut into Stages: Learning Foresightful Affordance Stably Stage by Stage + +The above-formulated picking and placing affordance forms a chicken-egg dependency cycle: picking affordance is dependent on placing affordance, while placing affordance is dependent on picking affordance. + +To break the dependency cycle, states close to the target (e.g., cloth almost fully unfolded) become the key. As the task is almost accomplished in these states, their values and direct distances to the target are nearly the same. So for an interaction where the ending state $o'$ is close to the target, we directly use their distances to the target (instead of both distances and 'value's) to supervise the corresponding placing affordance of the starting state $o$ : + +$$ +g _ {o, p _ {\text {p l a c e}} \mid p _ {\text {p i c k}}} ^ {\text {p l a c e}} = 1 - \operatorname {d i s t} \left(o ^ {\prime}, T\right) \tag {6} +$$ + +when $dist(o', T)$ is close to 0 i.e., the last step + +According to Equations 2, 5 and 6, the proposed picking and placing affordance could be estimated without the dependency cycle. As the dependency cycle breaks in states + +close to the target, we learn dense affordance from these simple states to more complex states (reversed order of inference) shown in Figure 2 (Right). Specifically, we divide learning procedure into multiple stages. In the first stage, we learn affordance for states that can reach states close to the target within one step, using the direct distances of the following states as supervisions. In the $i$ -th $(i > 1)$ stage, we learn affordance for states that can reach states in the $(i-1)$ -th stage in one step, using both the direct distances and the 'value's of states in the $(i-1)$ -th stage as supervisions. In each stage, we first train $\mathcal{M}_{\text{place}}$ using stable 'value's provided from the trained $\mathcal{M}_{\text{pick}}$ in the previous stage, and then train $\mathcal{M}_{\text{pick}}$ with stable supervisions (max of placing affordance) provided from the trained $\mathcal{M}_{\text{place}}$ in this stage. + +In this way, during the whole training, $A_{o|p_{pick}}^{place}$ and $A_{o}^{pick}$ both have stable supervisions from the former stage, and can provide stable supervisions for the latter stage. + +This stage-by-stage learning schema empowers our method with superiority over RL methods. Although RL also estimates states and actions using Bellman Equation, it simultaneously estimates and updates values across all states (offline RL) or trajectories of states (online RL), which is difficult to efficiently and stably learn the values, as RL struggles in iteratively updating state 'value's, especially when considering the prohibitively large state and action space of deformable objects. In contrast, like other dense affordance works [26, 43, 36], we stably learn affordance with 'value' using supervised learning, with stable supervisions provided in the previous training stage. Experiments demonstrate our superiority over RL in Section 5.4. + +# 4.5. Fold to Unfold: Efficient Multi-stage Data Collection for Learning Foresightful Affordance + +The above-described training schema requires multi-stage data for training. Specifically, in the first stage, the starting states are one-step to states close to the target. In the $i$ -th $(i > 1)$ stage, the starting states are one-step to states in the $(i-1)$ -th stage. Each starting state's actions and corresponding ending states should be diverse, as we need to learn the affordance representing dense distributions. + +However, due to the complexity of states and dynamics, data collection methods used by previous dense affordance works (random policies [26, 27] or state-based RL [36, 43]) could hardly collect such data. On the other hand, designing expert policies [31] or hand-crafting demonstrations are difficult and time-consuming for different tasks. + +Therefore, we propose a novel self-supervised method, named Fold to Unfold, using reversed actions of tasks to efficiently collect multi-stage data. This method is generic to many kinds of deformable object manipulation tasks, with no need for human-designed expert policies or annotations. + +Similar to the training procedure, we collect data from states close to the target, to more complex states. + +![](images/cb1ec1709a51636d0da2a6cbeb3d4408525cccf8cc7c971e3364bb9fbe1965b2.jpg) +Figure 5. Fold to Unfold collection in simulator and real world. + +Specifically, as shown in Figure 5, from a state $o_i$ in stage $i$ , we select a picking point $p_{pick}$ , put it on a placing point $p_{place}$ and get $o_{i+1}$ . Then, from $o_{i+1}$ , we execute the reversed action, pick $p_{place}$ , place on $p_{pick}$ and get $o_i'$ . If $o_i'$ is similar to $o_i$ , we choose $o_{i+1}$ as a starting state in stage $i+1$ , and sample diverse actions on $o_{i+1}$ with different corresponding results to train dense affordance in the $(i+1)$ -th stage (shown in Figure 2). + +Through a few stages of data collection, object states become complex and diverse, empowering trained affordance networks with generalization towards diverse novel states. + +Note that, although reversed actions cannot fully recover previous states, i.e., $o_i'$ are not the same as $o_i$ , chances are that $o_i'$ and $o_i$ are similar, and thus this method still greatly improves sample efficiency. Also, proposed affordance is not dependent on this data collection method, as it can be trained on data collected by any method. + +# 4.6. Integrated Systematic Training + +Although above designs and training procedure enable affordance learning for multi-step tasks, $\mathcal{M}_{pick}$ and $\mathcal{M}_{place}$ are trained using only offline collected data in different stages, not considering the actual execution performance of the policies provided by the two modules. During actual manipulation procedures, the policy is the composite policy of $\mathcal{M}_{pick}$ and $\mathcal{M}_{place}$ , and pick-and-place actions are executed one by one sequentially as a whole system. Therefore, we propose the Integrated Systematic Training (IST) procedure to adapt $\mathcal{M}_{pick}$ and $\mathcal{M}_{place}$ using online data. + +In this procedure, with offline trained $\mathcal{M}_{\text{place}}$ and $\mathcal{M}_{\text{pick}}$ , we randomly sample object initial states, use $\mathcal{M}_{\text{place}}$ and $\mathcal{M}_{\text{pick}}$ as the policy to select $p_{\text{pick}}$ and $p_{\text{place}}$ , execute pick-and-place step by step, and use actual results to simultaneously update $\mathcal{M}_{\text{place}}$ and $\mathcal{M}_{\text{pick}}$ . Through this procedure, the two modules are constantly adapted by consecutively online-sampled and actually-executed data, and thus are gradually integrated into a whole system. + +# 4.7. Network Architectures and Loss Function + +For architectures of $\mathcal{M}_{pick}$ and $\mathcal{M}_{place}$ , we use Fully Convolutional Networks (FCNs) [24] same in Transporter [41, 31] with extra skip-connections as backbone perpoint feature extractor. For $\mathcal{M}_{pick}$ , we directly use $p_{pick}$ feature to predict picking affordance score on $p_{pick}$ . For $\mathcal{M}_{place}$ , we use feature concatenation of $p_{pick}$ and $p_{place}$ to predict placing affordance score on $p_{place}$ . To train both $\mathcal{M}_{pick}$ and $\mathcal{M}_{place}$ , we use Mean Absolute Error (MAE) between predictions and ground truth as the loss function. + +# 5. Experiments + +# 5.1. Tasks, Settings and Metrics + +Tasks. To demonstrate the superiority of our framework, we select 2 representative tasks from DeformableRavens benchmark: (1) cable-ring: manipulating a ring to a given green circle, (2) cable-ring-nottarget: manipulating a ring to any circle, as well as 2 representative tasks from SoftGym: (3) SpreadCloth: spreading crumpled cloth to be flat, (4) RopeConfiguration: manipulating a rope from a random pose to a target pose (we use the shape 'S' as the target). Among them, the first two are relatively easier. They can be accomplished without considering future actions and states, and we conduct them to show our dense affordance's superiority over methods imitating expert demonstrations. The last two are much harder and would be better accomplished considering future actions and states to avoid local optima. + +Settings. For all tasks, in both training and testing, we set different random seeds for each episode, producing unseen and diverse initial poses of objects. To compare the generalization ability between our proposed dense affordance and imitation-based methods, for cables in DeformableRavens, we directly test the model trained on cables with 32 beads over novel cable configurations with 24, 28 or 36 beads. + +Metrics. For cable-ring and cable-ring-notarget, we follow DeformableRavens and use the manipulation successful rate as the metric. For SpreadCloth and RopeConfiguration, we follow SoftGym and use the normalized score as the metric. For all tasks, higher scores indicate better performance. + +# 5.2. Baselines + +For two cable-ring related tasks, we compare our method with baselines with or without expert demonstrations: + +- Transporter [41, 31] is commonly used for robotic manipulation by learning visual correlation for picking and placing points. In DeformableRavens [31] it is trained by cloning expert demonstrations and achieves SOTA performance over relevant tasks. +- GT-State receives ground truth (GT) pose of the target object, and regresses $p_{pick}$ and $p_{place}$ with MLP. +- GT-State 2-Step first regresses $p_{pick}$ and then $p_{place}$ using $p_{pick}$ and GT pose concatenation, both via MLP. + +For SpreadCloth and RopeConfiguration, as object states and dynamics are too complex and the tasks are too difficult to hand-engineer expert policies, we compare our method with baselines focused on multi-step planning: + +- CURL-SAC [18] that uses a model-free RL approach with contrastive unsupervised representations. +- $\mathbf{DrQ}[40]$ applies augmentation, regularization to RL. +- PlaNet [11] learns state space dynamics for planning. +- MVP [37] learns pick-and-place policy with model-free RL designed for deformbale object manipulation. + +# 5.3. Qualitative Results and Analysis + +![](images/9db4217d99372e08885f33ed3dbca7249a70e0e9addf08c3e170698a15875aec.jpg) +Figure 6. Example action sequences for cable-ring, cable-ring-nottarget, SpreadCloth and RopeConfiguration. White point denotes picking and black point denotes placing. + +Figure 6 shows examples of manipulation trajectories for diverse tasks using our proposed affordance. It is worth mentioning that, in the second state of SpreadCloth (Row 3), though it is intuitive to place the picking point (white) to the top-left position, the model places it to the bottom-right position (black), as the corresponding next state has low coverage but high 'value', requiring only one following pick-and-place action to almost fully unfold the cloth. + +![](images/0a78697860ce08f90fe17d4b4e107a1f9f0172ba7b64d08c612b41b3f57f2819.jpg) +Figure 7. Picking and placing affordance. Each row contains two (picking affordance, observation with $p_{pick}$ , placing affordance) tuples for a task. $p_{pick}$ is selected by picking affordance. Higher color temperature means higher affordance. + +Figure 7 visualizes picking and placing affordance, clearly showing that the learned affordance represents deformable objects with complex states and dynamics and facilitates selecting picking and placing points for manipulation. Figure 8 visualizes 'value's of states. + +![](images/0bf082f810e775cd5289fbe1311d0187385a7a7cb29ead914c6b6db5e1fe65d4.jpg) +Figure 8. Visualization of 'value' shows that some states with closer distances to the target (e.g., larger area) may not have higher 'value', as these states are hard for future actions to fulfill the task. + +
Methodcable-ringcable-ring-notarget
GT-State0.05.0
GT-State 2-Step0.01.7
Transporter68.370.0
Ours81.795.0
+ +Table 1. Quantitative results in DeformableRavens. + +
MethodSpreadClothRopeConfiguration
CURL-SAC0.1950.348
PlaNet0.3870.236
DrQ0.2750.154
MVP0.3720.258
Ours0.7580.529
+ +# 5.4. Quantitative Results and Analysis + +Shown in Table 1, our method outperforms all baselines in DeformableRavens. For GT State and GT State 2-Step, GT states can only provide part of the necessary information, and it is difficult to acquire the precise GT states of deformable objects in the real world. For Transporter that learns visual correlation for the matching between picking and placing points, although it directly clones successful demonstrations from hand-crafted expert policies, we outperform it for two possible reasons: 1) dense affordance is more suitable for deformable objects as it represents the results of diverse actions on complex states, while visual correlation in Transporter is suitable for matching like assembling-kits; 2) training on and cloning expert demonstrations will limit the model's generalization toward diverse situations for inference. To further evaluate the generalization ability of dense affordance, we produce different novel object configurations, using 24, 28, and 36 as the bead number instead of the initial 32. Our method's slighter performance decrease in Table 3 also demonstrates its generalization ability. Besides, expert policies need elaborate hand-engineering for different tasks, while our method can apply to diverse tasks without large modifications. + +Table 2 shows our framework outperforms all baselines in SoftGym. As described in 4.4, compared with those RL methods, our framework learns representations of complex states for multi-step manipulation in a stable way. + +Table 2. Quantitative results in SoftGym. + +
Task configurationscable-ring 24 / 28 / 36cable-ring-notarget 24 / 28 / 36
Transporter33.3 / 58.3 / 32.760.0 / 71.7 / 31.7
Ours61.6 / 86.7 / 58.381.7 / 96.7 / 78.3
+ +# 5.5. Ablation Studies and Analysis + +To demonstrate necessities of our framework's different components, we conduct ablation experiments by comparing our method with: 1) Ours RandPick: our method with the picking policy replaced by a random policy; 2) Ours ExpertPick: our method with the picking policy replaced by Transporter's expert; 3) Ours w/o IST: our method without Integrated Systematic Training (IST); + +For SpreadCloth and RopeConfiguration that require strongly related sequential actions, we additionally compare 1) ablated versions using different stages of data, 2) Ours only dist directly and greedily trained on all collected data instead of stage-by-stage considering 'value's. + +Table 3. Manipulation scores on novel configurations in DeformableRaves showing our method's generalization capability. + +
Methodcable-ringcable-ring-notarget
Ours RandPick11.758.3
Ours ExpertPick76.741.7
Ours w/o IST78.391.7
Ours81.795.0
+ +Table 4. Ablation studies in DeformableRavens. + +
Methodstage1stage2stage3stage4stage5
Ours RandPick0.2410.2110.3040.1850.190
Ours w/o IST0.5260.5860.6210.6240.612
Ours only dist0.7010.7010.7010.7010.701
Ours0.5890.6950.7520.7540.758
+ +Table 5. Ablation studies in SpreadCloth. + +Table 5 and 6 show that, a series of steps of data empowers affordance with generalization to diverse states. + +Table 4, 5 and 6 show quantitative results of ablation experiments. Ours RandPick and Ours ExpertPick show that, with the same placing affordance, our proposed picking affordance helps the framework perform the best. + +Ours only dist in Table 5 and 6 show that, directly training on all the diverse data without estimating state 'value' + +
Methodstage1stage2stage3stage4stage5
Ours RandPick0.3290.3020.3320.3340.322
Ours w/o IST0.3590.4180.4370.4790.474
Ours only dist0.4600.4600.4600.4600.460
Ours0.4410.5030.5180.5270.529
+ +limits the performance compared with our proposed framework. Besides, as shown in Figure 9, Ours only dist will propose actions leading to local optimal states, while our foresightful affordance will help to avoid that. + +Ours w/o IST in Table 4, 5 and 6, and adjusted affordance and 'value's in Figure 10 demonstrate IST helps integrating picking and placing modules into a whole, generating more precise perception of affordance and 'value's. + +![](images/6ec8f8fd88edfa70e425414dc64e22dce7afb8e223273d2ea9d6f647d9eedd55.jpg) +Figure 9. Placing affordance trained using 'value' supervision (red) and only using the greedy direct distance (blue). + +![](images/5f750f63d33004b583be939382322d1b7fa8067cbe965e26c00001c401a1ee6c.jpg) +Figure 10. Picking and placing affordance before (middle) and after (right) IST of the observation (left). White: pick point. + +![](images/b765bf39c7f617e59f30ca3c062f4c032f05b820c94f1646ea71624083aee0e8.jpg) + +![](images/6e636a61295d19ba3f2990508f6db10cf33583b5844ac321671cc3746daa1aba.jpg) + +![](images/1bda6bfffd93bb6675d50a91c868618c68ca10c728feb7b33e41f6f1a877575b.jpg) + +![](images/b7784fad5e2c57fd54d35a17b311fe3a443f0d782ed2811e060d34bd94fb134e.jpg) + +# 5.6. Real-world Experiments + +To bridge the sim2real gap and implement our method in the real world, similar to [37, 10], we use domain randomization to train affordance models in simulation and fine-tune them in real world. Specifically, we collect real-world data using Fold to Unfold, fine-tune trained-in-simulation $\mathcal{M}_{pick}$ and $\mathcal{M}_{place}$ stage by stage using the collected data. + +For evaluations, we randomly lift and drop the objects for five times to get the initial state, and then run the models for ten pick-and-place actions to perform the tasks. The manipulation score is the average normalized score (computed the same as in SoftGym) of sixty trajectories. + +Shown in Figure 11, given real-world observations with textures and physics different from objects in simulation, our method predicts reasonable picking and placing affordance and selects actions for tasks. + +We use MVP [37] for comparison, as (1) it also uses pick-and-place as action primitive, thus could do both cloth and rope tasks, and (2) provides real-world experiments. Table 7 shows performance comparison, explained in 5.4. + +See the supplementary for more implementation details. + +Table 6. Ablation studies in RopeConfiguration. + +
MethodSpreadClothRopeConfiguration
MVP0.3070.227
Ours0.6830.461
+ +Table 7. Manipulation scores in the real world. + +![](images/d190040a272ec96773a234ad26b6e957cfb1d9fd3429ff8bcb936d84299e9d06.jpg) + +![](images/6736b7fa185168fcb193522a2f6b6dca1eae3ea15b5cdcb48848b75d9376a8cf.jpg) + +![](images/38724ec8ee12581fe816e0a3e16d10350cdf2fb5ef345a896a89cacd7c175fe3.jpg) + +![](images/8e4388c8415535ba82f58e6f6d9b8e53d4ade5ffb813da6ac8caf78fed396fc6.jpg) + +![](images/cd5f6011880b68ff978d298c62b245c13f87a7d12961b625b100c15cb02707af.jpg) + +![](images/3f2cc5a9946095642b921b2ab803d2eb0323a4915a34a0191f0c8b50b1f627c9.jpg) +Figure 11. Real-world pick-place actions guided by affordance. + +![](images/32e1d534763bc2aa043f3f97c470d6233a14f7ee96dbd9924cdd2cf37dddafc2.jpg) + +![](images/53dec26d712a30941ace7abf7a10fc26340440f12ac7f85f7bcb3a66c2680c91.jpg) + +![](images/0cac705322bdb16167be05a7bd74b9a1ed32a18a257b9058d1db2667c2875cae.jpg) + +![](images/4059d4cf036cf01104104c42c4e230f3d573ad105d860edf744cf84772b3a9cc.jpg) + +# 6. Conclusion + +We propose to use dense visual affordance for manipulating deformable objects with complex states and dynamics. For tasks that require a series of strongly related actions, we further empower the proposed affordance with the awareness of a certain action's influence on subsequent actions. We propose a self-supervised framework with novel designs to efficiently collect multi-stage interaction data and stably learn this representation. Experiments on representative tasks and in the real world show the superiority of our proposed dense affordance and the learning framework. + +# 7. Acknowledgment + +This work was supported by National Natural Science Foundation of China (No. 62136001). We thank Qianxu Yang and Haoran Lu for assisting real-world experiments, Mingdong Wu and Hongcheng Wang for discussions. + +# References + +[1] Richard Bellman. Dynamic programming. science, 153(3731):34-37, 1966. 2, 4 +[2] Aude Billard and Danica Kragic. 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Difficulties come from complex states and dynamics, diverse configurations and high-dimensional action space of deformable objects. Besides, the manipulation tasks usually require multiple steps to accomplish, and greedy policies may easily lead to local optimal states. Existing studies usually tackle this problem using reinforcement learning or imitating expert demonstrations, with limitations in modeling complex states or requiring hand-crafted expert policies. In this paper, we study deformable object manipulation using dense visual affordance, with generalization towards diverse states, and propose a novel kind of foresightful dense affordance, which avoids local optima by estimating states' values for long-term manipulation. We propose a framework for learning this representation, with novel designs such as multi-stage stable learning and efficient self-supervised data collection without experts. Experiments demonstrate the superiority of our proposed foresightful dense affordance. Project page: https://hyperplane-lab.github.io/DeformableAffordance" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 541, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 287, + 590 + ], + "type": "text", + "content": "Many kinds of deformable objects, such as ropes and fabrics, exist everywhere in our daily life. Perceiving and manipulating deformable objects plays a significant role and paves the way for future home-assistant robots." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 590, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 288, + 687 + ], + "type": "text", + "content": "Unlike rigid or articulated objects, due to the complex dynamics, high-dimensional and nearly infinite degrees of freedom, large action space, and severe self-occlusion, deformable objects pose much more challenges to manipulate. 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Deformable Object Manipulation has many difficulties. 1) It requires multiple steps to complete. 2) Most actions can hardly facilitate tasks, for the exceptionally complex states and dynamics. 3) Many local optimal states are temporarily closer to the target, but making following actions harder to coordinate for the whole task. We propose to learn Foresightful Dense Visual Affordance aware of future actions to avoid local optima for deformable object manipulation, with real-world implementations." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 567, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 546, + 604 + ], + "type": "text", + "content": "laying much focus on relationships and influences between actions in a sequence, as an action leading to local optimal states may not eventually complete the task." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 604, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 547, + 689 + ], + "type": "text", + "content": "Specifically, as shown in Figure 1, unfolding crumpled cloth requires a sequence of actions (pick-and-place). Because of the exceptionally complex states and dynamics, and large action space, most actions fail to facilitate the task. Moreover, although some cloth in local optimal states temporarily have larger coverage areas than others, following actions face difficulties in smoothly completing the task." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Proposed by Gibson [8] and aimed at providing indicative information for agents to execute actions (e.g., el" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 223, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 223, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 223, + 703 + ], + "type": "text", + "content": "*Equal contribution, order determined by coin flip." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10947" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "emetary actions such as picking and pulling) and thus facilitating downstream tasks, visual affordance is arousing much attention in vision and robotics. Recent works have demonstrated its efficiency in a large range of tasks like grasping [25, 28, 3, 16, 15, 42], manipulating articulated objects [26, 36, 33, 5] and assisting robots in a scene [29, 30, 9]. Among them, point-level dense affordance [36, 26, 27, 33] learns whether an action on each point of the object could facilitate the task. Compared with Reinforcement Learning (RL) approaches, dense affordance is stably supervised and has better generalization ability towards objects with diverse shapes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 287, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 251 + ], + "type": "text", + "content": "The above dense affordance is suitable for representing deformable objects with complex states, capable of indicating whether diverse actions could help complete the task." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 251, + 287, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 310 + ], + "type": "text", + "content": "While most previous works only study dense affordance for short-term manipulation on rigid [43] or articulated objects [26, 36], to tackle the local optima problem in multi-step manipulation, we move a step towards equipping dense affordance with foresightfulness for future states." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 312, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 430 + ], + "type": "text", + "content": "Inspired by Dynamic Programming with Bellman Equation [1] and Q-Learning [34], estimating a state's 'value' (expected return in the long term, instead of only the current performance) for future actions to coordinate and eventually complete the task will help avoid local optimal states and boost the smoothness and quickness of multi-step manipulation. Dense affordance is suitable for such 'value' estimation, because such 'value' requires understanding and aggregating a large number of diverse following actions on complex states and their corresponding results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 431, + 287, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 287, + 466 + ], + "type": "text", + "content": "With such state 'value's (instead of only the current performance) in supervisions, dense affordance would gain foresightfulness for the future." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 467, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 467, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 45, + 467, + 287, + 634 + ], + "type": "text", + "content": "We propose to learn dense visual affordance for manipulating deformable objects, and further estimate state 'value's by aggregating such affordance to avoid local optima and smoothly accomplish multi-step tasks. As shown in Figure 1 (Down), the task can be accomplished smoothly using our proposed dense affordance in the real world. To learn such representations, we propose a novel framework generic to diverse tasks with many novel designs, such as the stage-by-stage stable training and Fold to Unfold efficient multi-stage data collection. Thus the proposed affordance could be learned stably, efficiently, and self-supervisedly without hand-crafted policies for different tasks. Experiments on representative benchmark tasks demonstrate our framework's impressive performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 637, + 200, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 637, + 200, + 648 + ], + "spans": [ + { + "bbox": [ + 59, + 637, + 200, + 648 + ], + "type": "text", + "content": "In summary, our contributions are:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 651, + 287, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 651, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 58, + 651, + 287, + 711 + ], + "type": "text", + "content": "- We propose to use dense visual affordance for manipulating deformable objects with complex states and dynamics, using such representation to estimate state 'value's for future actions to avoid local optima and smoothly accomplish multi-step manipulation tasks;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 72, + 545, + 157 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 107 + ], + "type": "text", + "content": "- We propose a self-supervised framework with novel designs such as multi-stage training and efficient data collection to learn the proposed affordance stably;" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 110, + 545, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 110, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 317, + 110, + 545, + 157 + ], + "type": "text", + "content": "- Qualitative and quantitative results on representative benchmarks and real-world experiments demonstrate the superiority of our proposed dense visual affordance and learning framework for deformable objects." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 175, + 392, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 175, + 392, + 186 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 392, + 186 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 190, + 484, + 203 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 190, + 484, + 203 + ], + "spans": [ + { + "bbox": [ + 306, + 190, + 484, + 203 + ], + "type": "text", + "content": "2.1. Deformable Object Manipulation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 209, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 437 + ], + "type": "text", + "content": "Deformable object manipulation is a typical and significant kind of task in robotic manipulation [4, 17, 2]. Compared to rigid or articulated objects, the manipulation of deformable objects is challenging for its high complexity, described in the Introduction Section. Typical methods utilize Reinforcement Learning (RL) or Imitation Learning. RL methods take object states [13] or visual information [37, 20] as policy input. Imitation based methods [41, 31, 19] imitate human-designed expert policy or human demonstrations for each task. Vision-based methods [6, 14] use visual feedback or correspondence to perform manipulations. Flow-based methods [32, 35] learn forward dynamics for manipulation, requiring much time in planning. Besides, a series of works [12, 21, 39, 38, 22] develop differentiable environments for diverse tasks and tackle these tasks by optimization. Different from above methods, our work builds a bridge between perception and manipulation, taking advantage of the generalization ability of affordance and estimating state 'value' for efficient planning." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 445, + 535, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 535, + 457 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 535, + 457 + ], + "type": "text", + "content": "2.2. Visual Affordance for Robotic Manipulation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 464, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 545, + 715 + ], + "type": "text", + "content": "Visual affordance [8] indicates possible ways for robots to interact with and complete tasks. Many recent works learn affordance for grasping [25, 28, 3, 16, 15, 42], articulated object manipulation [26, 36, 33, 5, 7], object-object interaction [27], collaboration [43] and interaction in a scene [29, 30, 9]. Among them, point-level dense affordance [26, 36, 43, 33] learns per-point representations of objects, which is more sensitive to local geometries and easier to generalize to different objects. Most tasks can be achieved in a single step (e.g., grasping, pulling drawers), with the learned affordance only containing actionable information for single-step manipulation. However, deformable objects with complex states and dynamics require many steps to manipulate. We move a step towards proposing dense affordance for deformable objects, which not only indicates complex states and dynamics but also takes the subsequent actions of a certain state into consideration for long-term tasks to avoid local optima. FlingBot [10] learns affordance for unfolding cloth by flinging, while our proposed affordance uses pick-and-place which is more generic for large action space and diverse tasks." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10948" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 174, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 174, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 174, + 83 + ], + "type": "text", + "content": "3. Problem Formulation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 87, + 287, + 123 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 87, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 47, + 87, + 287, + 123 + ], + "type": "text", + "content": "In this section, we describe how we formulate learning policy for multi-step deformable object manipulation into learning policies for picking and placing." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": "Following benchmarks DeformableRavens [31] and SoftGym [23], the problem is formulated as learning a policy " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": " to output robot action " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "a_{t}" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": ", given the visual observation " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "o_{t}" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": " (denoted as " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": ") at time " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": ". We use pick-and-place as the action, i.e., " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "a_{t} = (a_{pick}, a_{place})" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "a_{pick}" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "a_{place}" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": " denoting picking and placing poses. Explained in [31], the selector can fulfill the tasks without rotation, so " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "a_{pick}" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "a_{place}" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": " are denoted as picking point " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": " and placing point " + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 46, + 124, + 288, + 220 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": "The composite of " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " makes up a large combinatorial action space hard for a network to learn directly and simultaneously. For the underlying nature that " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " highly depends on " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": ", we follow [37] and disentangle learning the composite of " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " into respectively learning " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{place|p_{pick}}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": " (denoted as " + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 46, + 220, + 287, + 293 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 293, + 287, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 340 + ], + "type": "text", + "content": "Therefore, we formulate the problem into learning picking and placing policies. In Method Section 4, we describe how we learn the policies using foresightful dense visual affordance with each state's 'value' to avoid local optima." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 346, + 102, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 102, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 102, + 358 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 367, + 115, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 367, + 115, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 367, + 115, + 378 + ], + "type": "text", + "content": "4.1. Overview" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 380, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 548 + ], + "type": "text", + "content": "Shown in Figure 2, our framework is composed of two main parts: (1) we propose to use dense affordance to represent policy (4.2), estimate state 'value' using dense affordance and incorporate 'value' into dense affordance to avoid local optima for multi-step manipulation (4.3), break the picking-placing dependency cycle and stably learn affordance stage by stage (4.4); (2) to tackle the difficulty in collecting multi-stage and successful interactions, we propose a method (named Fold to Unfold) generic to many tasks to efficiently collect data in the reversed task completion order (e.g., collecting unfolding data by folding cloth) (4.5). Besides, we propose Integrated Systematic Training to further integrate the proposed affordance into a whole system (4.6). Finally, we describe network architectures and losses (4.7)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 552, + 282, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 282, + 565 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 282, + 565 + ], + "type": "text", + "content": "4.2. Dense Visual Affordance Representing Policy" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 568, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 604 + ], + "type": "text", + "content": "This section introduces how to use dense visual affordance to represent manipulation policy. For simplicity, we first discuss affordance for a greedy policy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Described in Section 3, we formulate the problem into learning picking and placing policies, i.e., the picking point " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " and placing point " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " given the observation " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " (with the size of " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "m \\times n" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " points). As the action space is all points on the object for picking, and all points in the space for placing, it comes naturally to use per-point score map " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " (size " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "m \\times n" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ") indicating how picking each point will facilitate the task, and dense placing affordance map " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " (size " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "m \\times n" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ") indicating how placing the picking point " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " on" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 85, + 541, + 175 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 541, + 85 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 541, + 85 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 541, + 85 + ], + "type": "text", + "content": "Stage-1 Data Collection Multi-stage Training" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 85, + 541, + 175 + ], + "lines": [ + { + "bbox": [ + 307, + 85, + 541, + 175 + ], + "spans": [ + { + "bbox": [ + 307, + 85, + 541, + 175 + ], + "type": "image", + "image_path": "497af368c9425e59601868bc8966758080da72368628910cc10f3e07b0de35a5.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 306, + 175, + 541, + 264 + ], + "blocks": [ + { + "bbox": [ + 306, + 175, + 541, + 264 + ], + "lines": [ + { + "bbox": [ + 306, + 175, + 541, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 541, + 264 + ], + "type": "image", + "image_path": "957947f01947c1496668e31533c85d687557cb99714a829b640bc577a3fcb977.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 306, + 264, + 541, + 356 + ], + "blocks": [ + { + "bbox": [ + 306, + 264, + 541, + 356 + ], + "lines": [ + { + "bbox": [ + 306, + 264, + 541, + 356 + ], + "spans": [ + { + "bbox": [ + 306, + 264, + 541, + 356 + ], + "type": "image", + "image_path": "5f9da6c34624fb49b9ee6eb3da226318d2173bce7ec91b1da93318c586ac12da.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 357, + 547, + 425 + ], + "lines": [ + { + "bbox": [ + 304, + 357, + 547, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 547, + 425 + ], + "type": "text", + "content": "Figure 2. Our proposed framework learns dense picking and placing affordance for deformable object manipulation (e.g., Unfolding Cloth). We collect multi-stage interaction data efficiently (Left) and learn proposed affordance stably in a multi-stage schema (Right) in the reversed task accomplishment order, from states close to the target to complex states." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 435, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 531 + ], + "type": "text", + "content": "each point will facilitate the task. Following previous dense affordance studies [26, 36, 43], we notify such task-specific per-point score maps as task-specific dense affordance (denoted as affordance for simplicity). Demonstrated in above studies, such dense affordance performs well in extracting diverse geometric information and generalizes well to unseen visual states, which is significant in representing and manipulating deformable objects with complicated states." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": "An intuitive greedy way to supervise " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": " is directly using the distance between the target " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": " and the new object state " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "o'" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": " after picking " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": " and placing on " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": ". For example, we use " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "1 - dist(o, T)" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": ", i.e., the cloth coverage area, to supervise " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": " for unfolding. So we can estimate placing affordance score " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "g_{o, p_{place}|p_{pick}}^{place}" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 304, + 531, + 545, + 624 + ], + "type": "text", + "content": " as (Figure 3, Middle, temporarily dismiss 'value' in Figure):" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 357, + 625, + 545, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 625, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 357, + 625, + 545, + 643 + ], + "type": "interline_equation", + "content": "g _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = 1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right) \\tag {1}", + "image_path": 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545, + 692 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 304, + 644, + 545, + 692 + ], + "type": "text", + "content": " can be estimated using the affordance score of the best placing point (Figure 3, Left):" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 331, + 696, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 696, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 331, + 696, + 545, + 715 + ], + "type": "interline_equation", + "content": "g _ {o, p _ {p i c k}} ^ {p i c k} = \\max _ {i} g _ {o, p _ {i} | p _ {p i c k}} ^ {\\text {p l a c e}}, i \\in \\{1,,.., m \\times n \\} \\tag {2}", + "image_path": "9c6108ca1b900dc0a5bad6cebb8172f6fbd7e9e0c8b1a3e90750b017056f4d7d.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10949" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "text", + "content": "We use two networks " + }, + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{pick}" + }, + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{place}" + }, + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "text", + "content": " to respectively learn " + }, + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 47, + 72, + 287, + 101 + ], + "type": "text", + "content": " (architectures in Section 4.7)." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 109, + 276, + 281 + ], + "blocks": [ + { + "bbox": [ + 52, + 109, + 276, + 281 + ], + "lines": [ + { + "bbox": [ + 52, + 109, + 276, + 281 + ], + "spans": [ + { + "bbox": [ + 52, + 109, + 276, + 281 + ], + "type": "image", + "image_path": "0b770f79a78927c7c90db6efbd028a6c23d21f9ba7e2fdf243270ac14b89bb38.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": "Figure 3. Learning placing and picking affordance with state 'value's for the future. Left to Right: The bottom black arrow indicates the manipulation (inference) order. Right to Left: Arrow flows show dependencies among placing affordance, picking affordance and 'value's. Given observation " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", we select 3 picking points " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "p_2" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "p_3" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", and show how to supervise corresponding placing affordance " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "A_{o|p_1}^{place}" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "A_{o|p_2}^{place}" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "A_{o|p_3}^{place}" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", and how to supervise " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "p_2" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "inline_equation", + "content": "p_3" + }, + { + "bbox": [ + 46, + 284, + 287, + 373 + ], + "type": "text", + "content": " using computed corresponding placing affordance." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "content": "During inference, in each step, the greedy policy first selects " + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "content": " with the highest affordance score in " + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "inline_equation", + "content": "A_o^{pick}" + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "content": ", and then selects " + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "content": " with the highest affordance score in " + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 47, + 375, + 287, + 438 + ], + "type": "text", + "content": ", resulting in the temporary best state after the pick-and-place action." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 441, + 287, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 287, + 466 + ], + "type": "text", + "content": "4.3. Estimating State Values and Learning Foresightful Affordance" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 529 + ], + "type": "text", + "content": "As shown in Figure 4, for multi-step manipulation, only evaluating the direct distance between the current state and the target (greedy method described above) may result in many local optimal states that are temporarily closer to target but harder for future actions to complete the whole task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 529, + 288, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 288, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 288, + 605 + ], + "type": "text", + "content": "Dynamic Programming (DP) [1] and Q-Learning [34] tackle this local optima problem by estimating the 'value' of a state that indicates whether a state is beneficial to the task in the long term (instead of the current performance). Inspired by them, we can add such state 'value' (formally formulated in Equation 4) to the estimation of " + }, + { + "bbox": [ + 46, + 529, + 288, + 605 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 46, + 529, + 288, + 605 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 609, + 290, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 290, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 290, + 628 + ], + "type": "interline_equation", + "content": "g _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = \\alpha \\times \\operatorname {v a l u e} _ {o ^ {\\prime}} + \\beta \\times (1 - \\operatorname {d i s t} (o ^ {\\prime}, T)) \\tag {3}", + "image_path": "2c764d371b3c06fb0b5500115d9e7b2c836b08df7fc50e3495211a3df1488029.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 190, + 628, + 271, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 190, + 628, + 271, + 639 + ], + "spans": [ + { + "bbox": [ + 190, + 628, + 271, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 190, + 628, + 271, + 639 + ], + "type": "inline_equation", + "content": "\\alpha +\\beta = 1" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "type": "text", + "content": "With such " + }, + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "type": "text", + "content": " that is foresightful for long-term tasks, " + }, + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "type": "text", + "content": ", which is the aggregation of " + }, + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 46, + 647, + 287, + 689 + ], + "type": "text", + "content": ", will therefore get such foresightfulness spontaneously." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Estimating the 'value' in a state requires understanding all possible actions and their corresponding future results," + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 545, + 239 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 545, + 239 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 239 + ], + "type": "image", + "image_path": "a575a90d01a30e068e125fd5704cf82992ad53784a3a116dd4db963725457a03.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 240, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 305, + 240, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 545, + 308 + ], + "type": "text", + "content": "Figure 4. Local Optima v.s. Global Optima. Many local optimal states are temporarily closer to target (e.g., having larger coverage area in unfolding task), but making future actions hard to coordinate to accomplish the whole task. We propose to use 'value' to indicate whether a state is suitable for future actions, with which the policy can avoid those local optimal states in multi-step tasks." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "type": "text", + "content": "and then selecting the best for the estimation. As " + }, + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "type": "text", + "content": " estimates the action result on each point, state 'value' can be estimated by selecting the " + }, + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "type": "text", + "content": " with the highest score in " + }, + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 305, + 312, + 545, + 361 + ], + "type": "text", + "content": " (Figure 3, Left):" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 343, + 363, + 545, + 381 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 363, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 343, + 363, + 545, + 381 + ], + "type": "interline_equation", + "content": "v a l u e _ {o} = \\max _ {i} g _ {o, p _ {i}} ^ {\\text {p i c k}}, i \\in \\{1,.., m \\times n \\} \\tag {4}", + "image_path": "4c98387ff7b65808f2db734d4fb3de4e4546129782899a46655265b19f0f271a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "text", + "content": "As " + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "inline_equation", + "content": "value_{o}" + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "text", + "content": " could be estimated by " + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "text", + "content": " could be reformulated using both " + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 305, + 385, + 545, + 414 + ], + "type": "text", + "content": " and the direct distance:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 347, + 415, + 480, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 415, + 480, + 433 + ], + "spans": [ + { + "bbox": [ + 347, + 415, + 480, + 433 + ], + "type": "interline_equation", + "content": "g _ {o, p _ {\\text {p l a c e}} | p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = \\alpha \\times \\max _ {i} g _ {o ^ {\\prime}, p _ {i}} ^ {\\text {p i c k}}", + "image_path": "6be9253fe10f2a074149e3c4e008b856709d87aa292e2b11f984eac8573f0078.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 406, + 434, + 545, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 406, + 434, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 406, + 434, + 545, + 449 + ], + "type": "interline_equation", + "content": "+ \\beta \\times (1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right)) \\tag {5}", + "image_path": "e875e4628518b6f9d4b153c3144624434f23bb2ad1a19a4767a0d5beb3a39752.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 403, + 452, + 482, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 403, + 452, + 482, + 463 + ], + "spans": [ + { + "bbox": [ + 403, + 452, + 482, + 463 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 403, + 452, + 482, + 463 + ], + "type": "inline_equation", + "content": "\\alpha +\\beta = 1" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 464, + 544, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 544, + 489 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 544, + 489 + ], + "type": "text", + "content": "4.4. Break the Cycle and Cut into Stages: Learning Foresightful Affordance Stably Stage by Stage" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 491, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 545, + 539 + ], + "type": "text", + "content": "The above-formulated picking and placing affordance forms a chicken-egg dependency cycle: picking affordance is dependent on placing affordance, while placing affordance is dependent on picking affordance." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "text", + "content": "To break the dependency cycle, states close to the target (e.g., cloth almost fully unfolded) become the key. As the task is almost accomplished in these states, their values and direct distances to the target are nearly the same. So for an interaction where the ending state " + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "inline_equation", + "content": "o'" + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "text", + "content": " is close to the target, we directly use their distances to the target (instead of both distances and 'value's) to supervise the corresponding placing affordance of the starting state " + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 304, + 540, + 545, + 635 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 319, + 639, + 545, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 639, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 319, + 639, + 545, + 662 + ], + "type": "interline_equation", + "content": "g _ {o, p _ {\\text {p l a c e}} \\mid p _ {\\text {p i c k}}} ^ {\\text {p l a c e}} = 1 - \\operatorname {d i s t} \\left(o ^ {\\prime}, T\\right) \\tag {6}", + "image_path": "bc825b7733f8188b5aa920ee92921600a2b9d973e915d3aaf61009e0785a741b.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 319, + 659, + 520, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 659, + 520, + 672 + ], + "spans": [ + { + "bbox": [ + 319, + 659, + 520, + 672 + ], + "type": "text", + "content": "when " + }, + { + "bbox": [ + 319, + 659, + 520, + 672 + ], + "type": "inline_equation", + "content": "dist(o', T)" + }, + { + "bbox": [ + 319, + 659, + 520, + 672 + ], + "type": "text", + "content": " is close to 0 i.e., the last step" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": "According to Equations 2, 5 and 6, the proposed picking and placing affordance could be estimated without the dependency cycle. As the dependency cycle breaks in states" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10950" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "close to the target, we learn dense affordance from these simple states to more complex states (reversed order of inference) shown in Figure 2 (Right). Specifically, we divide learning procedure into multiple stages. In the first stage, we learn affordance for states that can reach states close to the target within one step, using the direct distances of the following states as supervisions. In the " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "-th " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "(i > 1)" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " stage, we learn affordance for states that can reach states in the " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "(i-1)" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "-th stage in one step, using both the direct distances and the 'value's of states in the " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "(i-1)" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "-th stage as supervisions. In each stage, we first train " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{place}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " using stable 'value's provided from the trained " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{pick}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " in the previous stage, and then train " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{pick}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " with stable supervisions (max of placing affordance) provided from the trained " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{place}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " in this stage." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 240, + 287, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 287, + 278 + ], + "type": "text", + "content": "In this way, during the whole training, " + }, + { + "bbox": [ + 46, + 240, + 287, + 278 + ], + "type": "inline_equation", + "content": "A_{o|p_{pick}}^{place}" + }, + { + "bbox": [ + 46, + 240, + 287, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 240, + 287, + 278 + ], + "type": "inline_equation", + "content": "A_{o}^{pick}" + }, + { + "bbox": [ + 46, + 240, + 287, + 278 + ], + "type": "text", + "content": " both have stable supervisions from the former stage, and can provide stable supervisions for the latter stage." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 279, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 289, + 434 + ], + "type": "text", + "content": "This stage-by-stage learning schema empowers our method with superiority over RL methods. Although RL also estimates states and actions using Bellman Equation, it simultaneously estimates and updates values across all states (offline RL) or trajectories of states (online RL), which is difficult to efficiently and stably learn the values, as RL struggles in iteratively updating state 'value's, especially when considering the prohibitively large state and action space of deformable objects. In contrast, like other dense affordance works [26, 43, 36], we stably learn affordance with 'value' using supervised learning, with stable supervisions provided in the previous training stage. Experiments demonstrate our superiority over RL in Section 5.4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 443, + 287, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 287, + 467 + ], + "type": "text", + "content": "4.5. Fold to Unfold: Efficient Multi-stage Data Collection for Learning Foresightful Affordance" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "content": "The above-described training schema requires multi-stage data for training. Specifically, in the first stage, the starting states are one-step to states close to the target. In the " + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "content": "-th " + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "inline_equation", + "content": "(i > 1)" + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "content": " stage, the starting states are one-step to states in the " + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "inline_equation", + "content": "(i-1)" + }, + { + "bbox": [ + 46, + 474, + 287, + 557 + ], + "type": "text", + "content": "-th stage. Each starting state's actions and corresponding ending states should be diverse, as we need to learn the affordance representing dense distributions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "content": "However, due to the complexity of states and dynamics, data collection methods used by previous dense affordance works (random policies [26, 27] or state-based RL [36, 43]) could hardly collect such data. On the other hand, designing expert policies [31] or hand-crafting demonstrations are difficult and time-consuming for different tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 689 + ], + "type": "text", + "content": "Therefore, we propose a novel self-supervised method, named Fold to Unfold, using reversed actions of tasks to efficiently collect multi-stage data. This method is generic to many kinds of deformable object manipulation tasks, with no need for human-designed expert policies or annotations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Similar to the training procedure, we collect data from states close to the target, to more complex states." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 535, + 111 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 535, + 111 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 535, + 111 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 535, + 111 + ], + "type": "image", + "image_path": "cb1ec1709a51636d0da2a6cbeb3d4408525cccf8cc7c971e3364bb9fbe1965b2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 116, + 535, + 127 + ], + "lines": [ + { + "bbox": [ + 306, + 116, + 535, + 127 + ], + "spans": [ + { + "bbox": [ + 306, + 116, + 535, + 127 + ], + "type": "text", + "content": "Figure 5. Fold to Unfold collection in simulator and real world." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": "Specifically, as shown in Figure 5, from a state " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": " in stage " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": ", we select a picking point " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": ", put it on a placing point " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": " and get " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "o_{i+1}" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": ". Then, from " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "o_{i+1}" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": ", we execute the reversed action, pick " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": ", place on " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": " and get " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "o_i'" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "o_i'" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": " is similar to " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": ", we choose " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "o_{i+1}" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": " as a starting state in stage " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "i+1" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": ", and sample diverse actions on " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "o_{i+1}" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": " with different corresponding results to train dense affordance in the " + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "inline_equation", + "content": "(i+1)" + }, + { + "bbox": [ + 304, + 140, + 545, + 236 + ], + "type": "text", + "content": "-th stage (shown in Figure 2)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 236, + 545, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 272 + ], + "type": "text", + "content": "Through a few stages of data collection, object states become complex and diverse, empowering trained affordance networks with generalization towards diverse novel states." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": "Note that, although reversed actions cannot fully recover previous states, i.e., " + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "inline_equation", + "content": "o_i'" + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": " are not the same as " + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": ", chances are that " + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "inline_equation", + "content": "o_i'" + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 304, + 273, + 545, + 344 + ], + "type": "text", + "content": " are similar, and thus this method still greatly improves sample efficiency. Also, proposed affordance is not dependent on this data collection method, as it can be trained on data collected by any method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 351, + 474, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 351, + 474, + 364 + ], + "spans": [ + { + "bbox": [ + 306, + 351, + 474, + 364 + ], + "type": "text", + "content": "4.6. Integrated Systematic Training" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "text", + "content": "Although above designs and training procedure enable affordance learning for multi-step tasks, " + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{pick}" + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{place}" + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "text", + "content": " are trained using only offline collected data in different stages, not considering the actual execution performance of the policies provided by the two modules. During actual manipulation procedures, the policy is the composite policy of " + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{pick}" + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{place}" + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "text", + "content": ", and pick-and-place actions are executed one by one sequentially as a whole system. Therefore, we propose the Integrated Systematic Training (IST) procedure to adapt " + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{pick}" + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{place}" + }, + { + "bbox": [ + 304, + 367, + 545, + 488 + ], + "type": "text", + "content": " using online data." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": "In this procedure, with offline trained " + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{place}}" + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{pick}}" + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": ", we randomly sample object initial states, use " + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{place}}" + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{pick}}" + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": " as the policy to select " + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "inline_equation", + "content": "p_{\\text{pick}}" + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "inline_equation", + "content": "p_{\\text{place}}" + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": ", execute pick-and-place step by step, and use actual results to simultaneously update " + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{place}}" + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\text{pick}}" + }, + { + "bbox": [ + 304, + 488, + 545, + 583 + ], + "type": "text", + "content": ". Through this procedure, the two modules are constantly adapted by consecutively online-sampled and actually-executed data, and thus are gradually integrated into a whole system." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 590, + 524, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 590, + 524, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 590, + 524, + 601 + ], + "type": "text", + "content": "4.7. Network Architectures and Loss Function" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "For architectures of " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{pick}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{place}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", we use Fully Convolutional Networks (FCNs) [24] same in Transporter [41, 31] with extra skip-connections as backbone perpoint feature extractor. For " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{pick}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", we directly use " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " feature to predict picking affordance score on " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{place}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", we use feature concatenation of " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " to predict placing affordance score on " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". To train both " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{pick}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{place}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", we use Mean Absolute Error (MAE) between predictions and ground truth as the loss function." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10951" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 84 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 198, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 198, + 103 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 198, + 103 + ], + "type": "text", + "content": "5.1. Tasks, Settings and Metrics" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 109, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 109, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 109, + 287, + 276 + ], + "type": "text", + "content": "Tasks. To demonstrate the superiority of our framework, we select 2 representative tasks from DeformableRavens benchmark: (1) cable-ring: manipulating a ring to a given green circle, (2) cable-ring-nottarget: manipulating a ring to any circle, as well as 2 representative tasks from SoftGym: (3) SpreadCloth: spreading crumpled cloth to be flat, (4) RopeConfiguration: manipulating a rope from a random pose to a target pose (we use the shape 'S' as the target). Among them, the first two are relatively easier. They can be accomplished without considering future actions and states, and we conduct them to show our dense affordance's superiority over methods imitating expert demonstrations. The last two are much harder and would be better accomplished considering future actions and states to avoid local optima." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 277, + 287, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 287, + 359 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 287, + 359 + ], + "type": "text", + "content": "Settings. For all tasks, in both training and testing, we set different random seeds for each episode, producing unseen and diverse initial poses of objects. To compare the generalization ability between our proposed dense affordance and imitation-based methods, for cables in DeformableRavens, we directly test the model trained on cables with 32 beads over novel cable configurations with 24, 28 or 36 beads." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 360, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 287, + 419 + ], + "type": "text", + "content": "Metrics. For cable-ring and cable-ring-notarget, we follow DeformableRavens and use the manipulation successful rate as the metric. For SpreadCloth and RopeConfiguration, we follow SoftGym and use the normalized score as the metric. For all tasks, higher scores indicate better performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 425, + 113, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 425, + 113, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 425, + 113, + 437 + ], + "type": "text", + "content": "5.2. Baselines" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 444, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 444, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 444, + 287, + 467 + ], + "type": "text", + "content": "For two cable-ring related tasks, we compare our method with baselines with or without expert demonstrations:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 467, + 287, + 582 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 58, + 467, + 287, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 467, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 58, + 467, + 287, + 526 + ], + "type": "text", + "content": "- Transporter [41, 31] is commonly used for robotic manipulation by learning visual correlation for picking and placing points. In DeformableRavens [31] it is trained by cloning expert demonstrations and achieves SOTA performance over relevant tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 529, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 529, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 58, + 529, + 287, + 555 + ], + "type": "text", + "content": "- GT-State receives ground truth (GT) pose of the target object, and regresses " + }, + { + "bbox": [ + 58, + 529, + 287, + 555 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 58, + 529, + 287, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 58, + 529, + 287, + 555 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 58, + 529, + 287, + 555 + ], + "type": "text", + "content": " with MLP." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "type": "text", + "content": "- GT-State 2-Step first regresses " + }, + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "type": "text", + "content": " and then " + }, + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "type": "inline_equation", + "content": "p_{place}" + }, + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 58, + 558, + 287, + 582 + ], + "type": "text", + "content": " and GT pose concatenation, both via MLP." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 586, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 287, + 633 + ], + "type": "text", + "content": "For SpreadCloth and RopeConfiguration, as object states and dynamics are too complex and the tasks are too difficult to hand-engineer expert policies, we compare our method with baselines focused on multi-step planning:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 58, + 634, + 287, + 708 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 58, + 634, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 634, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 58, + 634, + 287, + 658 + ], + "type": "text", + "content": "- CURL-SAC [18] that uses a model-free RL approach with contrastive unsupervised representations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 58, + 658, + 282, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 658, + 282, + 671 + ], + "spans": [ + { + "bbox": [ + 58, + 658, + 282, + 671 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 58, + 658, + 282, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{DrQ}[40]" + }, + { + "bbox": [ + 58, + 658, + 282, + 671 + ], + "type": "text", + "content": " applies augmentation, regularization to RL." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 58, + 671, + 283, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 671, + 283, + 683 + ], + "spans": [ + { + "bbox": [ + 58, + 671, + 283, + 683 + ], + "type": "text", + "content": "- PlaNet [11] learns state space dynamics for planning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 58, + 684, + 286, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 684, + 286, + 708 + ], + "spans": [ + { + "bbox": [ + 58, + 684, + 286, + 708 + ], + "type": "text", + "content": "- MVP [37] learns pick-and-place policy with model-free RL designed for deformbale object manipulation." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 72, + 480, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 480, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 480, + 84 + ], + "type": "text", + "content": "5.3. Qualitative Results and Analysis" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 307, + 95, + 539, + 277 + ], + "blocks": [ + { + "bbox": [ + 307, + 95, + 539, + 277 + ], + "lines": [ + { + "bbox": [ + 307, + 95, + 539, + 277 + ], + "spans": [ + { + "bbox": [ + 307, + 95, + 539, + 277 + ], + "type": "image", + "image_path": "9db4217d99372e08885f33ed3dbca7249a70e0e9addf08c3e170698a15875aec.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 280, + 545, + 313 + ], + "lines": [ + { + "bbox": [ + 305, + 280, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 305, + 280, + 545, + 313 + ], + "type": "text", + "content": "Figure 6. Example action sequences for cable-ring, cable-ring-nottarget, SpreadCloth and RopeConfiguration. White point denotes picking and black point denotes placing." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 317, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 317, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 317, + 545, + 413 + ], + "type": "text", + "content": "Figure 6 shows examples of manipulation trajectories for diverse tasks using our proposed affordance. It is worth mentioning that, in the second state of SpreadCloth (Row 3), though it is intuitive to place the picking point (white) to the top-left position, the model places it to the bottom-right position (black), as the corresponding next state has low coverage but high 'value', requiring only one following pick-and-place action to almost fully unfold the cloth." + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 309, + 424, + 545, + 597 + ], + "blocks": [ + { + "bbox": [ + 309, + 424, + 545, + 597 + ], + "lines": [ + { + "bbox": [ + 309, + 424, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 309, + 424, + 545, + 597 + ], + "type": "image", + "image_path": "0a78697860ce08f90fe17d4b4e107a1f9f0172ba7b64d08c612b41b3f57f2819.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 599, + 545, + 643 + ], + "lines": [ + { + "bbox": [ + 305, + 599, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 545, + 643 + ], + "type": "text", + "content": "Figure 7. Picking and placing affordance. Each row contains two (picking affordance, observation with " + }, + { + "bbox": [ + 305, + 599, + 545, + 643 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 305, + 599, + 545, + 643 + ], + "type": "text", + "content": ", placing affordance) tuples for a task. " + }, + { + "bbox": [ + 305, + 599, + 545, + 643 + ], + "type": "inline_equation", + "content": "p_{pick}" + }, + { + "bbox": [ + 305, + 599, + 545, + 643 + ], + "type": "text", + "content": " is selected by picking affordance. Higher color temperature means higher affordance." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": "Figure 7 visualizes picking and placing affordance, clearly showing that the learned affordance represents deformable objects with complex states and dynamics and facilitates selecting picking and placing points for manipulation. Figure 8 visualizes 'value's of states." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10952" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 276, + 159 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 276, + 159 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 276, + 159 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 276, + 159 + ], + "type": "image", + "image_path": "0bf082f810e775cd5289fbe1311d0187385a7a7cb29ead914c6b6db5e1fe65d4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 160, + 287, + 194 + ], + "lines": [ + { + "bbox": [ + 47, + 160, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 160, + 287, + 194 + ], + "type": "text", + "content": "Figure 8. Visualization of 'value' shows that some states with closer distances to the target (e.g., larger area) may not have higher 'value', as these states are hard for future actions to fulfill the task." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 69, + 205, + 265, + 292 + ], + "blocks": [ + { + "bbox": [ + 69, + 205, + 265, + 292 + ], + "lines": [ + { + "bbox": [ + 69, + 205, + 265, + 292 + ], + "spans": [ + { + "bbox": [ + 69, + 205, + 265, + 292 + ], + "type": "table", + "html": "
Methodcable-ringcable-ring-notarget
GT-State0.05.0
GT-State 2-Step0.01.7
Transporter68.370.0
Ours81.795.0
", + "image_path": "4312f57a41c7bd677239333724a8659783e68c1a08d3107d2e9cb8b325cddf7b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 72, + 310, + 263, + 416 + ], + "blocks": [ + { + "bbox": [ + 71, + 293, + 264, + 304 + ], + "lines": [ + { + "bbox": [ + 71, + 293, + 264, + 304 + ], + "spans": [ + { + "bbox": [ + 71, + 293, + 264, + 304 + ], + "type": "text", + "content": "Table 1. Quantitative results in DeformableRavens." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 310, + 263, + 416 + ], + "lines": [ + { + "bbox": [ + 72, + 310, + 263, + 416 + ], + "spans": [ + { + "bbox": [ + 72, + 310, + 263, + 416 + ], + "type": "table", + "html": "
MethodSpreadClothRopeConfiguration
CURL-SAC0.1950.348
PlaNet0.3870.236
DrQ0.2750.154
MVP0.3720.258
Ours0.7580.529
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Task configurationscable-ring 24 / 28 / 36cable-ring-notarget 24 / 28 / 36
Transporter33.3 / 58.3 / 32.760.0 / 71.7 / 31.7
Ours61.6 / 86.7 / 58.381.7 / 96.7 / 78.3
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Methodcable-ringcable-ring-notarget
Ours RandPick11.758.3
Ours ExpertPick76.741.7
Ours w/o IST78.391.7
Ours81.795.0
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Methodstage1stage2stage3stage4stage5
Ours RandPick0.2410.2110.3040.1850.190
Ours w/o IST0.5260.5860.6210.6240.612
Ours only dist0.7010.7010.7010.7010.701
Ours0.5890.6950.7520.7540.758
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Methodstage1stage2stage3stage4stage5
Ours RandPick0.3290.3020.3320.3340.322
Ours w/o IST0.3590.4180.4370.4790.474
Ours only dist0.4600.4600.4600.4600.460
Ours0.4410.5030.5180.5270.529
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Besides, as shown in Figure 9, Ours only dist will propose actions leading to local optimal states, while our foresightful affordance will help to avoid that." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 221, + 287, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 287, + 270 + ], + "type": "text", + "content": "Ours w/o IST in Table 4, 5 and 6, and adjusted affordance and 'value's in Figure 10 demonstrate IST helps integrating picking and placing modules into a whole, generating more precise perception of affordance and 'value's." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 52, + 280, + 286, + 443 + ], + "blocks": [ + { + "bbox": [ + 52, + 280, + 286, + 443 + ], + "lines": [ + { + "bbox": [ + 52, + 280, + 286, + 443 + ], + "spans": [ + { + "bbox": [ + 52, + 280, + 286, + 443 + ], + "type": "image", + "image_path": "6ec8f8fd88edfa70e425414dc64e22dce7afb8e223273d2ea9d6f647d9eedd55.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 447, + 287, + 470 + ], + "lines": [ + { + "bbox": [ + 47, + 447, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 287, + 470 + ], + "type": "text", + "content": "Figure 9. Placing affordance trained using 'value' supervision (red) and only using the greedy direct distance (blue)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 48, + 485, + 86, + 523 + ], + "blocks": [ + { + "bbox": [ + 48, + 485, + 86, + 523 + ], + "lines": [ + { + "bbox": [ + 48, + 485, + 86, + 523 + ], + "spans": [ + { + "bbox": [ + 48, + 485, + 86, + 523 + ], + "type": "image", + "image_path": "5f750f63d33004b583be939382322d1b7fa8067cbe965e26c00001c401a1ee6c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 532, + 287, + 555 + ], + "lines": [ + { + "bbox": [ + 47, + 532, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 287, + 555 + ], + "type": "text", + "content": "Figure 10. Picking and placing affordance before (middle) and after (right) IST of the observation (left). White: pick point." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 88, + 490, + 157, + 518 + ], + "blocks": [ + { + "bbox": [ + 88, + 490, + 157, + 518 + ], + "lines": [ + { + "bbox": [ + 88, + 490, + 157, + 518 + ], + "spans": [ + { + "bbox": [ + 88, + 490, + 157, + 518 + ], + "type": "image", + "image_path": "b765bf39c7f617e59f30ca3c062f4c032f05b820c94f1646ea71624083aee0e8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 167, + 484, + 205, + 522 + ], + "blocks": [ + { + "bbox": [ + 167, + 484, + 205, + 522 + ], + "lines": [ + { + "bbox": [ + 167, + 484, + 205, + 522 + ], + "spans": [ + { + "bbox": [ + 167, + 484, + 205, + 522 + ], + "type": "image", + "image_path": "6e636a61295d19ba3f2990508f6db10cf33583b5844ac321671cc3746daa1aba.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 207, + 485, + 244, + 521 + ], + "blocks": [ + { + "bbox": [ + 207, + 485, + 244, + 521 + ], + "lines": [ + { + "bbox": [ + 207, + 485, + 244, + 521 + ], + "spans": [ + { + "bbox": [ + 207, + 485, + 244, + 521 + ], + "type": "image", + "image_path": "1bda6bfffd93bb6675d50a91c868618c68ca10c728feb7b33e41f6f1a877575b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 250, + 485, + 286, + 521 + ], + "blocks": [ + { + "bbox": [ + 250, + 485, + 286, + 521 + ], + "lines": [ + { + "bbox": [ + 250, + 485, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 250, + 485, + 286, + 521 + ], + "type": "image", + "image_path": "b7784fad5e2c57fd54d35a17b311fe3a443f0d782ed2811e060d34bd94fb134e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 563, + 185, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 185, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 185, + 576 + ], + "type": "text", + "content": "5.6. Real-world Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 582, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 654 + ], + "type": "text", + "content": "To bridge the sim2real gap and implement our method in the real world, similar to [37, 10], we use domain randomization to train affordance models in simulation and fine-tune them in real world. Specifically, we collect real-world data using Fold to Unfold, fine-tune trained-in-simulation " + }, + { + "bbox": [ + 47, + 582, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{pick}" + }, + { + "bbox": [ + 47, + 582, + 287, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 582, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{place}" + }, + { + "bbox": [ + 47, + 582, + 287, + 654 + ], + "type": "text", + "content": " stage by stage using the collected data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "content": "For evaluations, we randomly lift and drop the objects for five times to get the initial state, and then run the models for ten pick-and-place actions to perform the tasks. The manipulation score is the average normalized score (computed the same as in SoftGym) of sixty trajectories." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 119 + ], + "type": "text", + "content": "Shown in Figure 11, given real-world observations with textures and physics different from objects in simulation, our method predicts reasonable picking and placing affordance and selects actions for tasks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 121, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 121, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 305, + 121, + 545, + 168 + ], + "type": "text", + "content": "We use MVP [37] for comparison, as (1) it also uses pick-and-place as action primitive, thus could do both cloth and rope tasks, and (2) provides real-world experiments. Table 7 shows performance comparison, explained in 5.4." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 170, + 544, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 170, + 544, + 182 + ], + "spans": [ + { + "bbox": [ + 317, + 170, + 544, + 182 + ], + "type": "text", + "content": "See the supplementary for more implementation details." + } + ] + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 331, + 193, + 521, + 249 + ], + "blocks": [ + { + "bbox": [ + 77, + 159, + 256, + 170 + ], + "lines": [ + { + "bbox": [ + 77, + 159, + 256, + 170 + ], + "spans": [ + { + "bbox": [ + 77, + 159, + 256, + 170 + ], + "type": "text", + "content": "Table 6. Ablation studies in RopeConfiguration." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 193, + 521, + 249 + ], + "lines": [ + { + "bbox": [ + 331, + 193, + 521, + 249 + ], + "spans": [ + { + "bbox": [ + 331, + 193, + 521, + 249 + ], + "type": "table", + "html": "
MethodSpreadClothRopeConfiguration
MVP0.3070.227
Ours0.6830.461
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Manipulation scores in the real world." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 308, + 277, + 383, + 378 + ], + "blocks": [ + { + "bbox": [ + 308, + 277, + 383, + 378 + ], + "lines": [ + { + "bbox": [ + 308, + 277, + 383, + 378 + ], + "spans": [ + { + "bbox": [ + 308, + 277, + 383, + 378 + ], + "type": "image", + "image_path": "d190040a272ec96773a234ad26b6e957cfb1d9fd3429ff8bcb936d84299e9d06.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 385, + 277, + 422, + 378 + ], + "blocks": [ + { + "bbox": [ + 385, + 277, + 422, + 378 + ], + "lines": [ + { + "bbox": [ + 385, + 277, + 422, + 378 + ], + "spans": [ + { + "bbox": [ + 385, + 277, + 422, + 378 + ], + "type": "image", + "image_path": "6736b7fa185168fcb193522a2f6b6dca1eae3ea15b5cdcb48848b75d9376a8cf.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 425, + 277, + 463, + 378 + ], + "blocks": [ + { + "bbox": [ + 425, + 277, + 463, + 378 + ], + "lines": [ + { + "bbox": [ + 425, + 277, + 463, + 378 + ], + "spans": [ + { + "bbox": [ + 425, + 277, + 463, + 378 + ], + "type": "image", + "image_path": "38724ec8ee12581fe816e0a3e16d10350cdf2fb5ef345a896a89cacd7c175fe3.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 467, + 277, + 504, + 378 + ], + "blocks": [ + { + "bbox": [ + 467, + 277, + 504, + 378 + ], + "lines": [ + { + "bbox": [ + 467, + 277, + 504, + 378 + ], + "spans": [ + { + "bbox": [ + 467, + 277, + 504, + 378 + ], + "type": "image", + "image_path": "8e4388c8415535ba82f58e6f6d9b8e53d4ade5ffb813da6ac8caf78fed396fc6.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 506, + 277, + 544, + 379 + ], + "blocks": [ + { + "bbox": [ + 506, + 277, + 544, + 379 + ], + "lines": [ + { + "bbox": [ + 506, + 277, + 544, + 379 + ], + "spans": [ + { + "bbox": [ + 506, + 277, + 544, + 379 + ], + "type": "image", + "image_path": "cd5f6011880b68ff978d298c62b245c13f87a7d12961b625b100c15cb02707af.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 308, + 381, + 383, + 484 + ], + "blocks": [ + { + "bbox": [ + 308, + 381, + 383, + 484 + ], + "lines": [ + { + "bbox": [ + 308, + 381, + 383, + 484 + ], + "spans": [ + { + "bbox": [ + 308, + 381, + 383, + 484 + ], + "type": "image", + "image_path": "3f2cc5a9946095642b921b2ab803d2eb0323a4915a34a0191f0c8b50b1f627c9.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 488, + 535, + 500 + ], + "lines": [ + { + "bbox": [ + 306, + 488, + 535, + 500 + ], + "spans": [ + { + "bbox": [ + 306, + 488, + 535, + 500 + ], + "type": "text", + "content": "Figure 11. Real-world pick-place actions guided by affordance." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 385, + 381, + 422, + 484 + ], + "blocks": [ + { + "bbox": [ + 385, + 381, + 422, + 484 + ], + "lines": [ + { + "bbox": [ + 385, + 381, + 422, + 484 + ], + "spans": [ + { + "bbox": [ + 385, + 381, + 422, + 484 + ], + "type": "image", + "image_path": "32e1d534763bc2aa043f3f97c470d6233a14f7ee96dbd9924cdd2cf37dddafc2.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 425, + 381, + 463, + 484 + ], + "blocks": [ + { + "bbox": [ + 425, + 381, + 463, + 484 + ], + "lines": [ + { + "bbox": [ + 425, + 381, + 463, + 484 + ], + "spans": [ + { + "bbox": [ + 425, + 381, + 463, + 484 + ], + "type": "image", + "image_path": "53dec26d712a30941ace7abf7a10fc26340440f12ac7f85f7bcb3a66c2680c91.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 467, + 381, + 503, + 484 + ], + "blocks": [ + { + "bbox": [ + 467, + 381, + 503, + 484 + ], + "lines": [ + { + "bbox": [ + 467, + 381, + 503, + 484 + ], + "spans": [ + { + "bbox": [ + 467, + 381, + 503, + 484 + ], + "type": "image", + "image_path": "0cac705322bdb16167be05a7bd74b9a1ed32a18a257b9058d1db2667c2875cae.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 506, + 388, + 544, + 473 + ], + "blocks": [ + { + "bbox": [ + 506, + 388, + 544, + 473 + ], + "lines": [ + { + "bbox": [ + 506, + 388, + 544, + 473 + ], + "spans": [ + { + "bbox": [ + 506, + 388, + 544, + 473 + ], + "type": "image", + "image_path": "4059d4cf036cf01104104c42c4e230f3d573ad105d860edf744cf84772b3a9cc.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 510, + 378, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 378, + 523 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 378, + 523 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 529, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 649 + ], + "type": "text", + "content": "We propose to use dense visual affordance for manipulating deformable objects with complex states and dynamics. For tasks that require a series of strongly related actions, we further empower the proposed affordance with the awareness of a certain action's influence on subsequent actions. We propose a self-supervised framework with novel designs to efficiently collect multi-stage interaction data and stably learn this representation. Experiments on representative tasks and in the real world show the superiority of our proposed dense affordance and the learning framework." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 653, + 410, + 666 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 653, + 410, + 666 + ], + "spans": [ + { + "bbox": [ + 306, + 653, + 410, + 666 + ], + "type": "text", + "content": "7. Acknowledgment" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by National Natural Science Foundation of China (No. 62136001). We thank Qianxu Yang and Haoran Lu for assisting real-world experiments, Mingdong Wu and Hongcheng Wang for discussions." + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10954" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Richard Bellman. 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Existing works have demonstrated the possibility of applying deep CNNs to exploit features that distinguish similar classes. However, CNNs suffer from problems including frequency bias and loss of detailed local information, which restricts the performance of recognizing fine-grained categories. To address the challenge, we propose a novel texture branch as complimentary to the CNN branch for feature extraction. We innovatively utilize Gabor filters as a powerful extractor to exploit texture features, motivated by the capability of Gabor filters in effectively capturing multi-frequency features and detailed local information. We implement several designs to enhance the effectiveness of Gabor filters, including imposing constraints on parameter values and developing a learning method to determine the optimal parameters. Moreover, we introduce a statistical feature extractor to utilize informative statistical information from the signals captured by Gabor filters, and a gate selection mechanism to enable efficient computation by only considering qualified regions as input for texture extraction. Through the integration of features from the Gabor-filter-based texture branch and CNN-based semantic branch, we achieve comprehensive information extraction. We demonstrate the efficacy of our method on multiple datasets, including CUB-200-2011, NA-bird, Stanford Dogs, and GTOS-mobile. State-of-the-art performance is achieved using our approach.", + "bbox": [ + 76, + 306, + 473, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 724, + 209, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recognizing fine-grained categories (e.g., different flower types or bird species) is challenging due to the subtle differences in their visual appearance. Recently, deep neural network technology [17, 8, 31, 57, 52, 12] has made remarkable advancement, allowing for significant progress in extracting deep class-discriminative features for fine-grained recognition [10, 38, 41, 23, 3, 56]. For example, [54] develops a graph-based module to extract cross-class relationship features. [13, 26] use bilinear pooling to ex", + "bbox": [ + 76, + 742, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ploit high-order features from different networks. [55, 38] leverage multi-scale information to enhance feature effectiveness. The success of these methods highlights the crucial role of extracting powerful features in distinguishing fine-grained categories.", + "bbox": [ + 500, + 287, + 892, + 363 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To exploit class-discriminative features, previous methods [38, 41, 23, 3, 56] have primarily relied on convolutional neural networks (CNNs) as the model backbone. CNNs have achieved significant success in many computer vision tasks. However, due to the following limitations, they may not be sufficient for capturing comprehensive information in fine-grained recognition. First, deep CNNs generally extract information with high receptive fields and resolution-reduced feature maps, leading to the loss of local detailed information that is critical for fine-grained recognition. Second, as discussed in [33, 45, 46], due to the regularity of the commonly used activation [45] and loss functions [33], CNNs prioritize learning low-frequency components while ignoring high-frequency components. This bias is detrimental to fine-grained classification, as the ignored high-frequency information, such as ripples and spots in bird feathers, can be important in distinguishing between similar classes. Considering these limitations of CNNs, we suggest that a more powerful feature extractor is required, which should be able to capture local detailed information and multi-frequency comprehensive features that are lost by CNNs but crucial for fine-grained recognition.", + "bbox": [ + 496, + 367, + 893, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Witnessing the challenge, in this work, we introduce a novel branch that extracts texture features as complimentary to the vanilla CNN features to facilitate fine-grained recognition. We employ Gabor filters as the texture extractor in the novel branch. The Gabor filter is a windowed Fourier transform that combines a sinusoidal signal with a Gaussian wave. It is widely used in image processing for extracting low-level texture features [30, 35, 29, 1, 40]. The motivations of using Gabor filters in fine-grained recognition can be illustrated in two-folds. (1) First, Gabor filters are effective in capturing local-detailed information. Previous research [5, 6] has found that Gabor functions are similar to the receptive field profiles in the mammalian cortical sim", + "bbox": [ + 496, + 703, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 887, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1621", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ple cells. This indicates that Gabor filters can perform the similar function as cortical cells to capture effective and locally detailed texture information, which is critical for recognizing confusing samples. (2) Second, Gabor filters can extract sufficient high-frequency information. A Gabor filter contains a parameter that directly controls the frequency of the extracted information. It is therefore possible to exploit sufficient high-frequency components by constraining the parameters of some filters into a high-value range, overcoming the frequency-bias limitations of traditional CNNs. Benefiting from these advantages, our introduction of Gabor filters enables texture features to be extracted as an effective supplement to the typical CNN features for improving fine-grained recognition.", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Utilizing Gabor filters in an effective manner is nontrivial. Previous methods with Gabor filters generally rely on hand-crafted designs for filter parameter setting, which cannot guarantee to be optimal. To overcome this limitation, we propose an approach to automatically learn parameters in a supervised manner, in which a value constraint strategy is used to stabilize the learning and enhance high-frequency information extraction. To extract effective information with Gabor filters, we further propose a statistical feature extractor to capture texture features from the Gabor response maps. We also introduce a gate mechanism that selects a limited number of appropriate regions as inputs to the texture branch, thereby reducing computational costs and avoiding information redundancy. These careful designs allow Gabor filters to benefit fine-grained recognition in an effective and efficient manner.", + "bbox": [ + 75, + 301, + 472, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To the best of our knowledge, our work pioneers to learn texture features using Gabor filters in the task of fine-grained recognition. We perform extensive experiments on four datasets, which demonstrate the effectiveness of our method. Benefiting from the powerful texture features from the Gabor filters, our network can leverage the informative and comprehensive information for recognition, resulting in state-of-the-art (SOTA) performance on all datasets. To summarize, our contributions are as follows. (1) First, we pioneer learning Gabor filters in fine-grained recognition. The texture features extracted from Gabor filters serve as an effective supplement to the vanilla CNN features, significantly improving recognition performance. (2) Second, to enhance model effectiveness and efficiency, we implement several key designs based on Gabor filters, including the parameter learning method, a powerful Gabor feature extractor and a region selection gate. (3) Third, extensive experiments demonstrate the effectiveness of our method with state-of-the-art (SOTA) performance achieved on four datasets.", + "bbox": [ + 75, + 544, + 472, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 852, + 218, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fine-Grained Recognition. The goal of fine-grained recognition is to classify classes that are visually similar.", + "bbox": [ + 75, + 869, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent methods for the task can be categorized into two major types: feature-encoding methods [13, 49, 26, 9, 10, 38, 41, 23, 3, 56] and localization methods [20, 43, 2, 21, 44, 7, 36, 11]. Feature-encoding methods emphasize on extracting effective features for the better classification results. For example, some methods [13, 49, 26] use bilinear pooling to obtain informative high-level features. Other works [9, 10] use feature constraints to enhance feature effectiveness. [38, 41, 23, 3] extract multi-level features to get comprehensive information. [54] exploits cross-class relationships to capture class-discriminative features. Localization methods emphasize on selecting the most effective regions to capture features. [20, 43, 2] use extra annotations such as bounding boxes and key points to promote the localization ability of the network. [21, 44, 7, 36] select informative regions through activation maps. Different from these works, our method innovatively learns Gabor filter to effectively capture texture information. Additionally, the region selection gate in our method can be end-to-end trained without the need for additional annotation, giving it a unique advantage.", + "bbox": [ + 496, + 90, + 893, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gabor Filters. The Gabor filter is an effective tool for extracting texture features, which makes it widely used in various computer vision applications such as face recognition [30, 35, 29], vehicle verification [1], object detection [42, 22, 39] and gait recognition [40]. Recently, some works [18, 32, 50, 53] introduce Gabor filters into deep neural networks. However, these approaches have suffered from problems like unstable training, frequency bias and high computation costs, leading to low effectiveness and efficiency. Our method addresses the challenges faced by previous approaches through our careful designs, making Gabor filters to be effectively applied in fine-grained recognition.", + "bbox": [ + 496, + 407, + 893, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 498, + 595, + 591, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Overall Structure", + "text_level": 1, + "bbox": [ + 498, + 613, + 671, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fig. 1 provides an overview of our approach. A semantic branch takes the entire image as input and generates a semantic feature $\\mathbf{M}$ through a vanilla CNN. Using intermediate features from the semantic branch, a gate mechanism selects impactful regions from the image. After that, each of the selected regions $i$ is zoomed into the size $S\\times S$ and fed into a texture branch to produce a texture feature $\\mathbf{T}_i$ . The texture branch comprises $N$ learnable Gabor filters followed by a statistical feature extractor that performs the following two-step workflow. First, each learnable Gabor filter is convolved with the input region to generate an intensity map $\\mathbf{I}$ . In this way, for all the $N$ learnable Gabor filters, a set of maps $\\{\\mathbf{I}^n\\}_{n = 1}^N$ are generated. Next, the statistical feature extractor processes each $\\mathbf{I}^n\\in \\{\\mathbf{I}^n\\}_{n = 1}^N$ through a Learnable Histogram Operator (LHO) and then passes the resulting $\\{\\mathbf{S}^n\\}_{n = 1}^N$ through a Filter Correlation Module (FCM) to generate the texture feature $\\mathbf{T}$ . Finally, the semantic feature $\\mathbf{M}$ and texture features $\\{\\mathbf{T}_i\\}$ from all", + "bbox": [ + 496, + 628, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1622", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0afe748d92d2a42160efab0bcb719fa755426e889fd3ed2164d5f48f437657f3.jpg", + "image_caption": [ + "Figure 1. Overall structure of our network. The semantic branch produces a semantic feature $\\mathbf{M}$ for the input image. The region selection gate selects impactful regions from a set of pre-defined region proposals. The texture branch generates a texture feature $\\mathbf{T}$ for each of the selected regions that is zoomed into the size $S \\times S$ . Finally, semantic feature $\\mathbf{M}$ and texture features $\\mathbf{T}$ from all selected regions are added for prediction. Note that, for simplicity of illustration, the figure only presents three region proposals for an image. In actual practice, the region proposals follow the same setting as RCNN [15], comprising multiple regions with different positions and scales." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 893, + 265 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "selected regions are added and fed into a fully connected layer to obtain the prediction.", + "bbox": [ + 75, + 363, + 468, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The subsequent sections are arranged as follows. In Sec. 3.2, we provide an introduction to Gabor filters, which are the key to our method to capture texture information. In Sec. 3.3, we illustrate the strategy to train our Gabor filters in a stable and effective manner. In Sec. 3.4, we elaborate on the statistical feature extractor that exploits informative statistical information from the output of Gabor filters. In Sec. 3.5, we introduce the gate mechanism that selects impactful regions into the texture branch for texture extraction.", + "bbox": [ + 75, + 393, + 468, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Gabor Filter", + "text_level": 1, + "bbox": [ + 76, + 530, + 210, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Gabor filter is a widely-used feature extractor in traditional image processing, owing to its biological relevance and powerful texture extraction ability. It has optimal joint localization in both spatial and frequency domains, which makes it possible to be effectively applied in both spatial- and frequency-wise analysis. In the spatial domain, a Gabor Filter is mathematically defined as follows:", + "bbox": [ + 75, + 546, + 468, + 650 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} g (x, y) = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} \\exp \\left\\{- \\frac {1}{2} \\left(\\frac {\\widetilde {x} ^ {2}}{\\sigma_ {x} ^ {2}} + \\frac {\\widetilde {y} ^ {2}}{\\sigma_ {y} ^ {2}}\\right) \\right\\} \\exp [ 2 \\pi j W \\widetilde {x} ]. (1) \\\\ \\left\\{ \\begin{array}{l} \\widetilde {x} = x \\cos \\theta + y \\sin \\theta \\\\ \\widetilde {y} = - x \\sin \\theta + y \\cos \\theta \\end{array} \\right. (2) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 75, + 659, + 468, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This representation can be regarded as a windowed Fourier transform, i.e., a Gaussian kernel function modulated by a sinusoidal plane wave. Specifically, $[\\sigma_x,\\sigma_y]$ defines the scale of the Gabor filter, and it can determine the effective size of a pixel's neighborhood where weighted summation occurs. $\\theta$ defines the orientation of the filter. $W$ denotes the radial frequency of the sinusoid. These four parameters $\\{\\sigma_x,\\sigma_y,\\theta ,W\\}$ can fully define a Gabor filter. By altering the parameters, different filters can be generated to capture different signal components.", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Learnable Gabor Filter Parameters", + "text_level": 1, + "bbox": [ + 498, + 362, + 808, + 377 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An effective Gabor filter requires the appropriate combination of parameters to match a given task. Previous works [40, 30, 42] have generally used a hand-crafted approach for parameter selection, relying on heuristic rules to inform manual parameter settings. However, this kind of handcrafted approach is highly dependent on the expertise of the individual and cannot guarantee effectiveness for the task at hand. To address this limitation, we propose an alternative method that automatically learns the optimal parameters in a supervised manner, ensuring that the parameter combination can better fit the task. However, learning the parameters presents significant challenges. Firstly, during experimentation, erratic loss fluctuations are observed in the training process, indicating a lack of training stability (see the experimental section for details). Secondly, the features extracted by the trained network exhibit a substantial bias towards low-frequency information. The high-frequency information, on the other hand, occupies only a small fraction of all features. Specifically, only $6\\%$ of the trained Gabor filters have a frequency parameter $W$ higher than 0.5. This tendency is mainly due to the regularity of commonly used activation and loss functions in deep learning (refer to [45, 33] for details), which is detrimental since the high-frequency information can be vital for fine-grained recognition.", + "bbox": [ + 496, + 386, + 890, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To ensure training stability and filter effectiveness, we propose two solutions to tackle the above problems. To address the first challenge, we propose constraining parameter values into a valid range, which is theoretically derived to avoid potential problems such as frequency aliasing that could hinder training stability. To address the second challenge, we propose a dual-range strategy to further regularize the frequency parameter $W$ , ensuring that sufficient high-frequency components can be extracted. These solutions enable our Gabor filters to be learned in a stable and ef", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1623", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "fective manner. A detailed illustration of these solutions is presented in the subsequent sections.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning Parameters under Constraints. We first introduce a novel parameter value constraint to enhance the stability of model training. Our approach is motivated by the analysis that training instability could be attributed to the mismatch between image properties and the ideal application scenario of Gabor filters. Specifically, Gabor filters are mathematically defined for infinite length signals [37]; the digital image signals, on the other hand, are finite in both spatial and frequency domains due to the limited length of image width and sampling frequency. As a result, directly applying Gabor filters to finite-length images may cause mathematical deficiency and distortion, leading to frequency aliasing and other issues that can impair model training [39]. To address this problem, we propose to concentrate most of the Gabor filter energy within the finite signal zone. This ensures that only a small amount of filter energy spills over the finite signal, minimizing the negative effects of using infinite-length-defined filters on finite-length images. Such a constraint could be implemented by limiting the value ranges of filter parameters, which determine the effective zone and energy concentration area of a Gabor filter. Specifically, according to the properties of Gabor filters and images mentioned above, we first derive $[0,\\pi ],\\left[\\frac{5}{2\\pi(1 - 2W)},\\frac{S}{5}\\right],\\left[\\frac{5}{2\\pi},\\frac{S}{5}\\right]$ and $[0,\\frac{2\\pi S - 25}{4\\pi S} ]$ to be the valid ranges for parameters $\\theta ,\\sigma_{x},\\sigma_{y}$ and $W$ respectively (please refer to supplementary materials for a detailed derivation of these valid ranges). Next, we propose a constraint function to ensure each parameter to fall within its valid range. Specifically for a parameter $p$ with lower bound $l_{p}$ and upper bound $u_{p}$ , we propose to obtain $p$ through a learnable parameter $\\mathbf{p}$ as follows:", + "bbox": [ + 75, + 121, + 472, + 592 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np = l _ {p} + \\left(u _ {p} - l _ {p}\\right) \\mathrm {S i g m o i d} (\\mathbf {p}) = \\frac {u _ {p} + l _ {p} e ^ {- \\mathbf {p}}}{1 + e ^ {- \\mathbf {p}}}. (3)\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 601, + 468, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The parameter $\\mathbf{p}$ can be learned to have any value ranging from $-\\infty$ to $+\\infty$ . By applying Eq. 3, parameter $p$ can be guaranteed to fall within its valid range $[l_p, u_p]$ . By doing so, parameter values are constrained to enhance the stability of training.", + "bbox": [ + 75, + 641, + 468, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "High Frequency Enhancement. To address the frequency bias problem and improve high-frequency information extraction, we further propose a dual-constraint strategy for the frequency parameter $W$ . Specifically, we constrain half of Gabor filters to only exploit high-frequency components, making the network to capture sufficient high-frequency information for facilitating fine-grained recognition. This is enabled by setting two value intervals for $W$ : $[0, \\frac{2\\pi S - 25}{8\\pi S}]$ and $[\\frac{2\\pi S - 25}{8\\pi S}, \\frac{2\\pi S - 25}{4\\pi S}]$ , which are equally divided from the valid range $[0, \\frac{2\\pi S - 25}{4\\pi S}]$ of the frequency parameter. Let $N$ be the total number of Gabor filters to be learned. Using the method in Eq. 3, we constrain $W$ of $N / 2$ fil", + "bbox": [ + 75, + 715, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/dd8d486a1acb36dc61fa34752fa98a2fb5991ff7d779f974f8ad06fdf6773ff2.jpg", + "image_caption": [ + "Figure 2. The structure of Learnable Histogram Operator (LHO)." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 893, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ters to fall between $[0, \\frac{2\\pi S - 25}{8\\pi S}]$ and the other $N/2$ filters to fall between $\\left[\\frac{2\\pi S - 25}{8\\pi S}, \\frac{2\\pi S - 25}{4\\pi S}\\right]$ , such that they serve as the low-frequency expert and high-frequency expert respectively. This strategy enhances the extraction ability of high-frequency information, alleviating the frequency bias problem in traditional DNNs where high-frequency features are difficult to extract.", + "bbox": [ + 496, + 247, + 893, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Statistical Feature Extractor", + "text_level": 1, + "bbox": [ + 498, + 364, + 756, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above method enables Gabor filters to be trained stably and effectively in a deep learning framework. These filters can capture texture signals from an input image. In the next step, we target at extracting effective features from these filters to facilitate fine-grained recognition. From the perspective of digital image processing, texture can be represented by the statistical properties of feature maps [16]. Based on this principle, in some previous research [40, 4, 1], textures were exploited by extracting hand-crafted statistics such as variance, contrast and smoothness from the output of Gabor filters. However, these statistics have limited effectiveness because they are hand-crafted designed. In this work, we step further and take advantage of deep learning to extract deep statistical features that are more comprehensive and effective. Specifically, we propose a novel statistical feature extractor that contains a Learnable Histogram Operator (LHO) followed by a Filer Correlation Module (FCM). In the following sections, we provide a detailed illustration of QCO and FCM respectively.", + "bbox": [ + 496, + 387, + 890, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learnable Histogram Operator. We first employ a Learnable Histogram Operator (LHO) to exploit statistical information, which is improved from [58]. Fig. 2 illustrates the structure of LHO. LHO receives the output from each Gabor filter as input and produces a statistical feature $\\mathbf{S} \\in \\mathbb{R}^{C}$ , where $C$ refers to the channel number. Let $\\mathbf{I} \\in \\mathbb{R}^{S \\times S}$ be the intensity map generated by convolving a Gabor filter with the processed image, where $S$ refers to image size. LHO first defines $M$ levels by equally dividing the minimal and maximal values for intensities of all pixels. Specifically, the $m$ -th level $\\mathbf{L}^{m}$ is computed as:", + "bbox": [ + 496, + 674, + 890, + 840 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {L} ^ {m} = \\min (\\mathbf {I}) + \\frac {\\max (\\mathbf {I}) - \\min (\\mathbf {I})}{M} \\cdot m \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 847, + 890, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, each pixel $\\mathbf{I}^{i,j}$ on $\\mathbf{I}$ is quantized to a vector $\\mathbf{V}^{i,j} \\in$", + "bbox": [ + 498, + 883, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1624", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbb{R}^M$ . Concretely, let $I$ be the interval between adjacent levels $(I = \\mathbf{L}^{m + 1} - \\mathbf{L}^m)$ , the $m$ -th channel $\\mathbf{V}^{i,j,m}$ on $\\mathbf{V}^{i,j}$ is computed as follows:", + "bbox": [ + 76, + 90, + 468, + 135 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {V} ^ {i, j, m} = \\left\\{ \\begin{array}{l l} 1 - \\left| \\mathbf {L} ^ {m} - \\mathbf {I} ^ {i, j} \\right| & \\text {i f} \\left| \\mathbf {L} ^ {m} - \\mathbf {I} ^ {i, j} \\right| < \\frac {I}{2} \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 145, + 468, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this way, $\\mathbf{I}$ is quantized to $\\mathbf{V} \\in \\mathbb{R}^{S \\times S \\times M}$ . Note a spire-shaped function is used for quantization instead of a binary one to ensure that the operation is differentiable. After the quantization, the number of pixels that fall into each level is counted and normalized to obtain a counting feature $\\mathbf{C} \\in \\mathbb{R}^M$ . Specifically, $\\mathbf{C}^m$ for the $m$ -th level is computed as:", + "bbox": [ + 76, + 205, + 468, + 297 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} ^ {m} = \\frac {\\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i , j , m}}{\\sum_ {m = 1} ^ {M} \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i , j , m}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 306, + 468, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We concatenate $\\mathbf{C}^m$ with $\\mathbf{L}^m$ , and obtain the feature $\\mathbf{F}^m$ for the $m$ -th quantization level as follows:", + "bbox": [ + 76, + 353, + 467, + 383 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} ^ {m} = \\phi (\\operatorname {C A T} \\left(\\mathbf {C} ^ {m}, \\mathbf {L} ^ {m}\\right)) + \\mathbf {P} ^ {m}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 393, + 468, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi$ refers to a linear layer. $\\mathbf{P}^m\\in \\mathbb{R}^C$ encodes the position information for pixels quantized to the $m$ -th level, which is computed as the weighted sum of position features from all pixels as follows:", + "bbox": [ + 76, + 421, + 468, + 482 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} ^ {m} = \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i, j, m} \\mathrm {P E} (i, j), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 493, + 468, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where PE refers to the position encoding operation as in vit [8]. Finally, the statistical texture $\\mathbf{S}$ is produced by correlating features from different levels:", + "bbox": [ + 76, + 545, + 468, + 590 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} = \\operatorname {A v g} \\left(\\operatorname {M H A} \\left(\\left\\{\\mathbf {F} ^ {m} \\right\\} _ {m = 1} ^ {M}\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 599, + 468, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where MHA denotes a multi-head attention and Avg refers to the average over all levels. Using LHO has two advantages. Firstly, it can be considered as a way to extract deep features from a differentiable and learnable histogram, which can produce effective and appropriate statistical features that can benefit the task [16, 58]. Secondly, conventional statistical features are typically pixel-relationship-invariant. For example, rearranging pixel positions does not alter the mean and variance values. In contrast, our method is pixel-relationship-aware as it encodes $\\mathbf{P}^m$ that represents the position information of pixels quantized to each level, which provides additional information that can be useful for fine-grained recognition. These advantages enable the extracted features from LHO to be effective in facilitating fine-grained recognition.", + "bbox": [ + 76, + 628, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Filter Correlation Module. The proposed LHO can produce a statistical feature from the output of each Gabor filter, resulting in a set of features $\\{\\mathbf{S}^n\\}_{n=1}^N$ for all filters. We", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "further propose a Filter Correlation Module (FCM) to aggregate statistical information from all Gabor filters as follows:", + "bbox": [ + 498, + 90, + 890, + 133 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {T} = \\operatorname {A v g} \\left(\\operatorname {M H A} \\left(\\left\\{\\mathbf {S} ^ {n} + \\phi \\left(\\sigma_ {x} ^ {n}, \\sigma_ {y} ^ {n}, \\theta^ {n}, W ^ {n}\\right) \\right\\} _ {n = 1} ^ {N}\\right)\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 145, + 890, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in which $\\mathbf{S}^n$ refers to the statistical feature for the $n$ -th Gabor filter. $\\phi(\\sigma_x^n, \\sigma_y^n, \\theta^n, W^n)$ uses a linear layer to encode filter parameter information, which can indicate the type of texture extracted by the Gabor filter. Eq. 10 exploits the correlations among different texture components from different Gabor filters, generating a powerful feature with long-range correlations that can facilitate fine-grained recognition.", + "bbox": [ + 498, + 184, + 890, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Region Selection Gate", + "text_level": 1, + "bbox": [ + 500, + 301, + 705, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through the methods outlined above, we can build a powerful feature extractor that captures texture information using Gabor filters. As a common practice used by previous methods, the extractor can generate features in an image-based [40] manner or a patch-based manner [39]. Image-based methods directly feed the whole image into the extractor, which might lead to the blurring of local detailed information. Patch-based methods address the problem by equally dividing the image into several patches and extracting a feature from each patch. However, it is computationally expensive as each image position must be processed by the feature extractor. Intuitively, the texture information in different regions of an image is not equally important. For example, some regions may contain critical textures for recognition, such as feather of the bird, while others may be less informative, consisting of background textures such as sky, road and lawn. Therefore, extracting textures from all positions is redundant and computationally inefficient, which can impede recognition accuracy and slow down algorithmic speed. To address the issue, we propose a novel approach to solely extract textures from informative regions that are automatically selected from a gate mechanism. More specifically, the gate mechanism for region selection involves three steps. Firstly, we introduce a shallow FPN block that takes the intermediate features of the CNN-based semantic branch as inputs and generates a feature map $F$ . Please refer to supplementary materials for a detailed description for the structure of this block. Since features from the CNN branch have a high receptive field and contain rich semantic information, $F$ can identify key parts of an image and assist in selecting class-discriminative regions in appropriate positions. Secondly, we introduce a set of regions proposals, denoted as $\\{\\mathcal{R}^k\\}_{k=1}^K$ , which is the same as that in RCNN [15], comprising regions with different scales and positions. For each region $\\mathcal{R}^k$ , a feature vector $f^k$ is generated by performing an RoI pooling on the corresponding region of the feature map $F$ . This feature vector is then fed into a linear layer to generate a score $s^k$ .", + "bbox": [ + 498, + 325, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1625", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lastly, regions that require texture extraction are selected based on their scores. This mechanism enables only the regions that contain class-discriminative information to be selected for texture extraction, thereby reducing computation costs and avoiding information redundancy.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To reduce computation for capturing texture features, we expect 'hard' selections instead of the 'soft' attention scores to be generated so that only a limited number of regions need texture extraction. However, such a hard selection may prohibit the gradients to be back-propagated to the earlier layers in optimization. To address this issue, we employ the Improved Semantic Hashing [24, 25] for region selection. In training, to encourage more decision space to be explored randomly, we add a standard Gaussian noise $\\epsilon$ to $s^k$ , resulting in the noise-injected score $\\hat{s}^k$ . Then two vectors are generated as follows:", + "bbox": [ + 75, + 167, + 470, + 332 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nc ^ {k} = \\sigma^ {\\prime} (\\hat {s} ^ {k}); d ^ {k} = \\mathbb {1} (\\hat {s} ^ {k} > 0), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 342, + 468, + 362 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\sigma^{\\prime}$ refers to the saturating Sigmoid function:", + "bbox": [ + 76, + 371, + 413, + 386 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma^ {\\prime} (\\hat {s} ^ {k}) = \\max (0, \\min (1, 1. 2 \\sigma (\\hat {s} ^ {k}) - 0. 1)), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 396, + 468, + 416 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\sigma$ denotes the original Sigmoid function. In this way, $d^{k}$ is a binarized discrete feature with value $\\{0,1\\}$ , which is used for making the selection decision. $c^{k}$ is a continuously differentiable vector that can be used to approximate gradients in back-propagation, whose details are presented in supplementary materials.", + "bbox": [ + 75, + 425, + 468, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Discussion with Previous Methods. Note that the proposed region gate mechanism differs from other key part localization methods used for fine-grained recognition. Unlike existing methods, our method can be trained end-to-end and generate hard decisions without the need for extra annotations. These properties enable our method to be highly effective and practical for region selection. Conversely, existing key part localization techniques have several limitations. For example, some methods [20, 43] require extra annotations such as bounding box and key points for joint training; [14] uses an indifferentiable selection process, making the network unable to be trained end-to-end; other methods [7, 21] typically produce soft attention rather than hard decisions, which cannot reduce computation costs. Our approach can be more practical and effective benefiting from our careful designs.", + "bbox": [ + 75, + 516, + 468, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.6. Optimization", + "text_level": 1, + "bbox": [ + 76, + 758, + 215, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proposed network is optimized by the following loss function:", + "bbox": [ + 75, + 782, + 468, + 810 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = L _ {c e} (p, l) + \\lambda \\sum_ {k = 1} ^ {K} d ^ {k}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 809, + 468, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $L_{ce}$ denotes the cross-entropy loss. $p$ and $l$ are the prediction logits and ground truth label. $d^{k}$ denotes the binarized discrete decision as in Eq. 11. The second item", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/db3f00c3977cbbff87a3a4435074d129482b4cf7e876751d62c54d6ea9c29b4b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5084.5
ResNet101 [17]ResNet10185.5
DenseNet161 [19]DenseNet16185.5
PC-Dense161 [9]DenseNet16186.9
NTSNet [48]ResNet5087.5
Cross-X [34]ResNet5087.7
DCL [3]ResNet5087.8
S3N [7]ResNet5088.5
iSQRT-COV [27]ResNet10188.7
GaRD [54]ResNet5089.6
APINet [59]DenseNet16190.0
OursResNet5090.8
OursResNet10191.3
OursDenseNet16191.5
", + "bbox": [ + 509, + 88, + 890, + 284 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Comparison results on CUB-200-2011 dataset.", + "bbox": [ + 527, + 284, + 857, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in Eq. 13 encourages fewer regions to be selected, thus avoiding the redundant information and reducing computation costs. $\\lambda$ is a hyper-parameter to control the trade-off between the two loss items.", + "bbox": [ + 498, + 308, + 890, + 369 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 377, + 632, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 402, + 715, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following [59], we adopt different networks as the semantic branch, including ResNet50, ResNet101 and DenseNet161. We use SGD as the optimizer with the momentum of 0.9. The initial learning rate is set to 1e-4, which decays by 0.1 for every 20 epochs (overall 100 epochs). Batch size is 16 for all datasets. Following previous works [54, 28], we use random cropping of $448 \\times 448$ in training and center crop at inference. We apply the commonly-used data augmentation strategies for training, including random scaling, left-right flipping and random cropping. $S$ indicating the size of regions that are zoomed in is set to 112. $N$ indicating the number of learnable Gabor filters is set to 128. $M$ indicating the number of quantization levels in QCO is set to 8. $\\lambda$ in Eq. 13 is set to 0.2. Experiments are conducted on 2 NVIDIA Titan V100 GPUs.", + "bbox": [ + 498, + 426, + 890, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art", + "text_level": 1, + "bbox": [ + 500, + 665, + 792, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method on four datasets, including three fine-grained datasets CUB-200-2011, NA-bird, Stanford Dogs and a terrain recognition dataset GTOS-mobile. The comparison results on these datasets are presented in Tables 1, 2, 3, and 4, respectively. Our method achieves the best performance when using DenseNet161 as the semantic branch, reaching accuracy scores of 91.5, 90.4, 92.1 and 87.5, outperforming the second-best method by 1.5, 2.3, 1.8 and 4.8, respectively. It is worth noting that even when using ResNet50, the least effective backbone among the three, our method remains superior to all other compared methods. This highlights the high effectiveness of our method. The advantage of our method is especially significant on the challenging terrain dataset GTOS-mobile. This is due to our", + "bbox": [ + 498, + 689, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1626", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/429412cd0a4619d96b1fa2ce2b917fd9ab4fcfb099f97c238b05192548a7c8b8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5082.2
ResNet101 [17]ResNet10182.9
DenseNet161 [19]DenseNet16183.1
Cross-X [34]ResNet5086.4
GaRD [54]ResNet5088.0
APINet [59]DensetNet10188.1
OursResNet5089.5
OursResNet10190.0
OursDenseNet16190.4
", + "bbox": [ + 96, + 89, + 344, + 218 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c7d34e9b836b7178544265363622612d530cec1b20e8447f0d1a828f232fea83.jpg", + "table_caption": [ + "Table 2. Comparison results on NA-bird dataset." + ], + "table_footnote": [], + "table_body": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5080.1
ResNet101 [17]ResNet10180.6
DenseNet161 [19]DenseNet16180.9
PC-Dense161 [9]DenseNet16182.8
Cross-X [34]ResNet5088.9
APINet [59]ResNet10190.3
OursResNet5091.0
OursResNet10191.7
OursDenseNet16192.1
", + "bbox": [ + 361, + 89, + 609, + 219 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/68e9b7720f574bb7bc7c4ece552834d4ba36fef1b33aaeb9989569b4cbcbc89a.jpg", + "table_caption": [ + "Table 3. Comparison results on Stanford Dogs dataset." + ], + "table_footnote": [], + "table_body": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5069.4
ResNet101 [17]ResNet10172.0
DenseNet161 [19]DenseNet16172.9
B-CNN [28]ResNet5075.8
Deep-TEN [51]ResNet5076.1
DEP [47]ResNet5082.7
OursResNet5086.4
OursResNet10187.0
OursDenseNet16187.5
", + "bbox": [ + 625, + 88, + 874, + 219 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3ad2681e43f9315ae928e58614a39f61ebe32c0cd5eed90ac3ac3766012813eb.jpg", + "table_caption": [ + "Table 4. Comparison results on GTOS-mobile dataset." + ], + "table_footnote": [], + "table_body": "
MethodAccuracyFlops(G)Params(M)
Baseline (ResNet50)84.516.2624.69
+ TB & RSG90.820.7232.41
+ TB (image-based manner)89.036.8829.82
+ TB (patch-based manner)89.937.0429.82
", + "bbox": [ + 81, + 268, + 467, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "method's ability to extract texture features, which are essential for the classification of visually-similar and closely-related terrain classes.", + "bbox": [ + 76, + 385, + 467, + 429 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 439, + 228, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform ablation study to verify the effectiveness of our designs. Experiments in this part are conducted on CUB-200-2011 dataset with ResNet50 as the semantic branch. Due to paper length limitation, more ablation study results are presented in supplementary materials.", + "bbox": [ + 76, + 462, + 468, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation of Different Components. As shown in Fig. 1, in addition to the basic CNN-based semantic branch, our method consists of two key components: a Gabor-filter-based texture branch (TB) and a region selection gate (RSG). We conduct experiments to validate the effect of these components and present the results in Table. 5, which includes the validation accuracy, computation costs and parameter numbers of different settings. We set the network that only has a ResNet50 semantic branch to be the baseline. Our method with adding both texture branch & region selection gate increases accuracy from 84.5 to 90.8. When the region selection gate is removed, extracting textures by feeding the whole image into texture branch (image-based manner) reduces accuracy to 89.0 and increases computation by $78\\%$ ; equally dividing image into $8 \\times 8$ patches and getting a feature from each patch (patch-based manner) reduces accuracy to 89.0 and increases computation by $79\\%$ . The results demonstrate that the region selection gate can reduce computation and improve performance.", + "bbox": [ + 76, + 537, + 468, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation of Learnable Gabor Filters. Results in this part are presented in Table. 6. (1) First, we validate the effectiveness of Gabor filters. Replacing all Gabor filters by the $3 \\times 3$ convolution layers decreases accuracy by 4.9. This indicates that the improvement does not simply come from", + "bbox": [ + 76, + 825, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/79c4a54fcef3e51f81f6d15bb77e1719d80ed95c75b06111baa77bfed1df0e05.jpg", + "table_caption": [ + "Table 5. Ablation results of different components in our method. TB and RSG refer to the texture branch and region selection gate, respectively." + ], + "table_footnote": [], + "table_body": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours replacing Gabor filters with conv85.920.0332.95
Ours w/o parameter learning86.520.7232.41
Ours w/o parameter value constraints75.420.4032.41
Ours w/o high frequency enhancement88.120.4032.41
", + "bbox": [ + 500, + 268, + 890, + 352 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Ablation results of learnable Gabor filters.", + "bbox": [ + 544, + 352, + 844, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "an increase in the number of parameters, but from the effectiveness of using Gabor filters for texture extraction. (2) Second, we evaluate the effectiveness of learning Gabor filter parameters in a supervised manner. We replace the learnable parameters with the manually set ones, where the setting rules are the same as [40]. This reduces accuracy by 4.3, showing the effectiveness of supervised learning. (3) Third, we verify the necessity of using parameter value constraints. In Fig. 3, we present the loss curves and validation accuracy curves for methods w/ and w/o using value constraints. Using value constraints results in a smoother loss decline curve and accuracy improvement curve. In contrast, free training causes violent loss and accuracy fluctuations, especially at the beginning stage of training, indicating that the training process is unstable. Compared to free training, using value constraints significantly improves validation accuracy by 15.4. (4) Last, we evaluate the high frequency enhancement strategy by setting two constraints for frequency parameter $W$ . Without the strategy and directly constraining $W$ into its valid range reduces accuracy by 2.7. Results demonstrate the effectiveness of our designs for the learnable Gabor filter parameters. Also note, using the proposed learning methods requires no extra parameters and only increases computation very slightly.", + "bbox": [ + 496, + 383, + 890, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation of Statistical Feature Extractor. We propose a statistical feature extractor to leverage texture information from the output of Gabor filters. The extractor consists of two parts: a Learnable Histogram Operator (LHO) and a Filter Correlation Module (FCM). We conduct experiments to validate the effect of these components and present the results in Table 7. Removing LHO and FCM reduces accuracy from 90.8 to 87.0 and 89.2 respectively. Also note that, both LHO and FCM are lightweight, only requiring extra parameters of 4.26M and 3.56M, increasing flops by", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1627", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bf6ae535852da6a1dcdd7c64b18b1eea0527101f1ccae213b2d3631a0c90ea3c.jpg", + "image_caption": [ + "(a) Loss Curves" + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 261, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b351441b6dfa7ae12b45b924a280075ac904eb290b5476753da49e8ebe784df4.jpg", + "image_caption": [ + "(b) Accuracy Curves", + "Figure 3. Loss curves (a) and accuracy curves (b) in different settings. Blue and orange lines indicate curves for training Gabor filters w/ and w/o using parameter value constraints, respectively." + ], + "image_footnote": [], + "bbox": [ + 261, + 95, + 439, + 181 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/67972098cfd8d6057dc05916ca3809bdcf860ecb58324c673a26089ca0ce6890.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours w/o LHO87.018.0328.25
Ours w/o FCM89.219.5528.85
", + "bbox": [ + 81, + 250, + 468, + 308 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$15\\%$ and $6\\%$ respectively. Results show the high effectiveness and efficiency of LHO and FCM.", + "bbox": [ + 76, + 330, + 467, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation of LHO. In Table. 8, we further evaluate the designs in LHO. First, we replace LHO with a hand-crafted statistical feature composed of mean, variance, maximum and minimum values, which reduces accuracy by 2.9. This demonstrates that LHO can produce statistical features that are more effective than hand-crafted ones widely used by previous methods. Next, we remove position information $\\mathbf{P}^m$ in Eq. 7 and multi-head attention in Eq. 9, which reduces accuracy by 1.5 and 2.1 respectively, showing the importance of encoding position features and correlating different levels in LHO. Finally, we move LHO from texture branch to CNN-based semantic branch. This reduces accuracy by 4.6, showing that the effectiveness of LHO relies on Gabor filters to extract texture-related signals.", + "bbox": [ + 75, + 361, + 468, + 573 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Visualization", + "text_level": 1, + "bbox": [ + 76, + 584, + 212, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Fig. 4, we provide a visualization of the outputs obtained from learned Gabor filters. More specifically, Fig. 4 (c) and Fig. 4 (d) show the average output of all high-frequency and low-frequency Gabor filters, respectively. As can be observed, the high-frequency filters primarily capture information of undulating areas such as speckles and ripples, whereas the low-frequency filters primarily capture information related to smooth changing areas. Both these two kinds of information are critical for recognition. By exploiting sufficient and balanced multi-frequency features through the carefully-designed learnable Gabor filters, our method can leverage comprehensive information for effective fine-grained recognition. Due to space limitation, more visualization results are presented in supplementary.", + "bbox": [ + 75, + 608, + 468, + 820 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Discussion of Computation and Parameter", + "text_level": 1, + "bbox": [ + 76, + 830, + 439, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Compared to the ResNet50 baseline, our method only increases computation and parameter usage slightly. Specifically, on CUB-200-2011 dataset, ResNet50 consumes", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ba6445037c1dc92259f4bf6f798dcd8024b90e93da4191a6c15cbcd72746e386.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 93, + 614, + 150 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/74c34d6ccfbd2aef9561cec30d558a45974f90da9e01cef6a545c74a2e2cfc5a.jpg", + "image_caption": [ + "(a) Image", + "Figure 4. Visualization of Gabor filters. (a), (b), (c) and (d) present the original images, the selected regions, average output of all high-frequency and low-frequency Gabor filters, respectively." + ], + "image_footnote": [], + "bbox": [ + 517, + 150, + 614, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b4de533b1dc2e946bb7f2255b0059b4aba494dac5e9404578de4945f51194eab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 95, + 700, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/42b275e5eec7ef8305390bb74e780a97e1eab92c5f17916d56b3f43a3283a102.jpg", + "image_caption": [ + "(b) Region", + "(c) High-W Filters" + ], + "image_footnote": [], + "bbox": [ + 630, + 150, + 782, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/26ca61c2fcd32aa9c29556f4a9cef283f37a8eda80a925da8da2c31bed412e04.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 95, + 782, + 148 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 712, + 150, + 782, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51140dae4b5ecba74b885c9ebcec3e8ec52038466912431c72748573acc4bc7f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 792, + 95, + 864, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e291067c22ed8beb39fa6e2b994b57b24f760f8514b560868c7aabc38270a716.jpg", + "image_caption": [ + "(d) Low-W Filters" + ], + "image_footnote": [], + "bbox": [ + 792, + 150, + 864, + 205 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8d9668f5aef3f1d28cd2e14e6730ae302cb507a68e08102f245d63efeee25d37.jpg", + "table_caption": [ + "Table 7. Ablation results of statistical feature extractor." + ], + "table_footnote": [ + "Table 8. Ablation results of LHO. HSF refers to a hand-crafted statistical feature composed of mean, variance, maximum and minimum values. MHA denotes multi-head attention. TB denotes texture branch." + ], + "table_body": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours w/o LHO w/ HSF87.918.1628.25
Ours w/o Pm in Eq. 789.318.5030.93
Ours w/o MHA in Eq.988.719.4929.73
Ours w/o LHO in TB w/ LHO in CNN86.222.8532.90
", + "bbox": [ + 501, + 275, + 890, + 348 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "16.26G flops of computation, requiring 24.69M parameters, reaching accuracy of 84.5. Our method consumes 20.72G flops of computation, requiring 32.41M parameters, reaching accuracy of 90.8. Compared to ResNet50, our method can improve accuracy significantly (+6.3) with only increasing computation and parameter usage by $27\\%$ and $31\\%$ respectively. This demonstrates the high effectiveness and high efficiency of our method with outstanding performance and reasonable computation costs.", + "bbox": [ + 498, + 422, + 890, + 558 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 583, + 617, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents a novel network that extracts texture features to facilitate fine-grained recognition using Gabor filters. We make the Gabor filter parameters to be automatically learned in a stable and effective manner through our carefully-designed value constraint strategies. We also propose a statistical feature extractor and a region selection gate, allowing informative and effective Gabor texture features to be extracted with very few extra computation costs. Our method is effective, as shown by the extensive experiments with state-of-the-art (SOTA) performance.", + "bbox": [ + 496, + 607, + 890, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-08-006), Singapore Ministry of Education (MOE) AcRF Tier 2 under Grant MOE-T2EP20222-0009, the National Research Foundation Singapore through AI Singapore Programme under Grant AISG-100E-2020-065, and SUTD SKI Project under Grant SKI 2021_02_06.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1628", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jon Arrospide and Luis Salgado. 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In Proceedings of the AAAI conference on artificial intelligence, volume 34, pages 13130-13137, 2020. 6, 7" + ], + "bbox": [ + 78, + 90, + 468, + 429 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1631", + "bbox": [ + 483, + 945, + 513, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Gabor Texture Features for Fine-Grained Recognition/6ca3f851-37f0-49f5-a456-09ea4b08c273_model.json b/2023/Learning Gabor Texture Features for Fine-Grained Recognition/6ca3f851-37f0-49f5-a456-09ea4b08c273_model.json new file mode 100644 index 0000000000000000000000000000000000000000..84264d7450b19c52d77f7532df7cb61ab25cff46 --- /dev/null +++ b/2023/Learning Gabor Texture Features for Fine-Grained Recognition/6ca3f851-37f0-49f5-a456-09ea4b08c273_model.json @@ -0,0 +1,2323 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.163, + 0.131, + 0.809, + 0.154 + ], + "angle": 0, + "content": "Learning Gabor Texture Features for Fine-Grained Recognition" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.18, + 0.905, + 0.218 + ], + "angle": 0, + "content": "Lanyun Zhu\\(^{1}\\) Tianrun Chen\\(^{2}\\) Jianxiong Yin\\(^{3}\\) Simon See\\(^{3}\\) Jun Liu\\(^{1*}\\) \nSingapore University of Technology and Design\\(^{1}\\) Zhejiang University\\(^{2}\\) NVIDIA AI Tech Centre\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.22, + 0.739, + 0.234 + ], + "angle": 0, + "content": "lanyun.zhu@mymail.sutd.edu.sg tianrun.chen@zju.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.237, + 0.721, + 0.252 + ], + "angle": 0, + "content": "{jianxiongy, ssee}@nvidia.com jun-liu@sutd.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.308, + 0.474, + 0.718 + ], + "angle": 0, + "content": "Extracting and using class-discriminative features is critical for fine-grained recognition. Existing works have demonstrated the possibility of applying deep CNNs to exploit features that distinguish similar classes. However, CNNs suffer from problems including frequency bias and loss of detailed local information, which restricts the performance of recognizing fine-grained categories. To address the challenge, we propose a novel texture branch as complimentary to the CNN branch for feature extraction. We innovatively utilize Gabor filters as a powerful extractor to exploit texture features, motivated by the capability of Gabor filters in effectively capturing multi-frequency features and detailed local information. We implement several designs to enhance the effectiveness of Gabor filters, including imposing constraints on parameter values and developing a learning method to determine the optimal parameters. Moreover, we introduce a statistical feature extractor to utilize informative statistical information from the signals captured by Gabor filters, and a gate selection mechanism to enable efficient computation by only considering qualified regions as input for texture extraction. Through the integration of features from the Gabor-filter-based texture branch and CNN-based semantic branch, we achieve comprehensive information extraction. We demonstrate the efficacy of our method on multiple datasets, including CUB-200-2011, NA-bird, Stanford Dogs, and GTOS-mobile. State-of-the-art performance is achieved using our approach." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.726, + 0.21, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.743, + 0.471, + 0.88 + ], + "angle": 0, + "content": "Recognizing fine-grained categories (e.g., different flower types or bird species) is challenging due to the subtle differences in their visual appearance. Recently, deep neural network technology [17, 8, 31, 57, 52, 12] has made remarkable advancement, allowing for significant progress in extracting deep class-discriminative features for fine-grained recognition [10, 38, 41, 23, 3, 56]. For example, [54] develops a graph-based module to extract cross-class relationship features. [13, 26] use bilinear pooling to ex" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.288, + 0.893, + 0.364 + ], + "angle": 0, + "content": "ploit high-order features from different networks. [55, 38] leverage multi-scale information to enhance feature effectiveness. The success of these methods highlights the crucial role of extracting powerful features in distinguishing fine-grained categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.895, + 0.701 + ], + "angle": 0, + "content": "To exploit class-discriminative features, previous methods [38, 41, 23, 3, 56] have primarily relied on convolutional neural networks (CNNs) as the model backbone. CNNs have achieved significant success in many computer vision tasks. However, due to the following limitations, they may not be sufficient for capturing comprehensive information in fine-grained recognition. First, deep CNNs generally extract information with high receptive fields and resolution-reduced feature maps, leading to the loss of local detailed information that is critical for fine-grained recognition. Second, as discussed in [33, 45, 46], due to the regularity of the commonly used activation [45] and loss functions [33], CNNs prioritize learning low-frequency components while ignoring high-frequency components. This bias is detrimental to fine-grained classification, as the ignored high-frequency information, such as ripples and spots in bird feathers, can be important in distinguishing between similar classes. Considering these limitations of CNNs, we suggest that a more powerful feature extractor is required, which should be able to capture local detailed information and multi-frequency comprehensive features that are lost by CNNs but crucial for fine-grained recognition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Witnessing the challenge, in this work, we introduce a novel branch that extracts texture features as complimentary to the vanilla CNN features to facilitate fine-grained recognition. We employ Gabor filters as the texture extractor in the novel branch. The Gabor filter is a windowed Fourier transform that combines a sinusoidal signal with a Gaussian wave. It is widely used in image processing for extracting low-level texture features [30, 35, 29, 1, 40]. The motivations of using Gabor filters in fine-grained recognition can be illustrated in two-folds. (1) First, Gabor filters are effective in capturing local-detailed information. Previous research [5, 6] has found that Gabor functions are similar to the receptive field profiles in the mammalian cortical sim" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1621" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "ple cells. This indicates that Gabor filters can perform the similar function as cortical cells to capture effective and locally detailed texture information, which is critical for recognizing confusing samples. (2) Second, Gabor filters can extract sufficient high-frequency information. A Gabor filter contains a parameter that directly controls the frequency of the extracted information. It is therefore possible to exploit sufficient high-frequency components by constraining the parameters of some filters into a high-value range, overcoming the frequency-bias limitations of traditional CNNs. Benefiting from these advantages, our introduction of Gabor filters enables texture features to be extracted as an effective supplement to the typical CNN features for improving fine-grained recognition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.544 + ], + "angle": 0, + "content": "Utilizing Gabor filters in an effective manner is nontrivial. Previous methods with Gabor filters generally rely on hand-crafted designs for filter parameter setting, which cannot guarantee to be optimal. To overcome this limitation, we propose an approach to automatically learn parameters in a supervised manner, in which a value constraint strategy is used to stabilize the learning and enhance high-frequency information extraction. To extract effective information with Gabor filters, we further propose a statistical feature extractor to capture texture features from the Gabor response maps. We also introduce a gate mechanism that selects a limited number of appropriate regions as inputs to the texture branch, thereby reducing computational costs and avoiding information redundancy. These careful designs allow Gabor filters to benefit fine-grained recognition in an effective and efficient manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.473, + 0.846 + ], + "angle": 0, + "content": "To the best of our knowledge, our work pioneers to learn texture features using Gabor filters in the task of fine-grained recognition. We perform extensive experiments on four datasets, which demonstrate the effectiveness of our method. Benefiting from the powerful texture features from the Gabor filters, our network can leverage the informative and comprehensive information for recognition, resulting in state-of-the-art (SOTA) performance on all datasets. To summarize, our contributions are as follows. (1) First, we pioneer learning Gabor filters in fine-grained recognition. The texture features extracted from Gabor filters serve as an effective supplement to the vanilla CNN features, significantly improving recognition performance. (2) Second, to enhance model effectiveness and efficiency, we implement several key designs based on Gabor filters, including the parameter learning method, a powerful Gabor feature extractor and a region selection gate. (3) Third, extensive experiments demonstrate the effectiveness of our method with state-of-the-art (SOTA) performance achieved on four datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.853, + 0.22, + 0.868 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Fine-Grained Recognition. The goal of fine-grained recognition is to classify classes that are visually similar." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.409 + ], + "angle": 0, + "content": "Recent methods for the task can be categorized into two major types: feature-encoding methods [13, 49, 26, 9, 10, 38, 41, 23, 3, 56] and localization methods [20, 43, 2, 21, 44, 7, 36, 11]. Feature-encoding methods emphasize on extracting effective features for the better classification results. For example, some methods [13, 49, 26] use bilinear pooling to obtain informative high-level features. Other works [9, 10] use feature constraints to enhance feature effectiveness. [38, 41, 23, 3] extract multi-level features to get comprehensive information. [54] exploits cross-class relationships to capture class-discriminative features. Localization methods emphasize on selecting the most effective regions to capture features. [20, 43, 2] use extra annotations such as bounding boxes and key points to promote the localization ability of the network. [21, 44, 7, 36] select informative regions through activation maps. Different from these works, our method innovatively learns Gabor filter to effectively capture texture information. Additionally, the region selection gate in our method can be end-to-end trained without the need for additional annotation, giving it a unique advantage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.895, + 0.591 + ], + "angle": 0, + "content": "Gabor Filters. The Gabor filter is an effective tool for extracting texture features, which makes it widely used in various computer vision applications such as face recognition [30, 35, 29], vehicle verification [1], object detection [42, 22, 39] and gait recognition [40]. Recently, some works [18, 32, 50, 53] introduce Gabor filters into deep neural networks. However, these approaches have suffered from problems like unstable training, frequency bias and high computation costs, leading to low effectiveness and efficiency. Our method addresses the challenges faced by previous approaches through our careful designs, making Gabor filters to be effectively applied in fine-grained recognition." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.597, + 0.593, + 0.611 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.614, + 0.673, + 0.628 + ], + "angle": 0, + "content": "3.1. Overall Structure" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Fig. 1 provides an overview of our approach. A semantic branch takes the entire image as input and generates a semantic feature \\(\\mathbf{M}\\) through a vanilla CNN. Using intermediate features from the semantic branch, a gate mechanism selects impactful regions from the image. After that, each of the selected regions \\(i\\) is zoomed into the size \\(S\\times S\\) and fed into a texture branch to produce a texture feature \\(\\mathbf{T}_i\\). The texture branch comprises \\(N\\) learnable Gabor filters followed by a statistical feature extractor that performs the following two-step workflow. First, each learnable Gabor filter is convolved with the input region to generate an intensity map \\(\\mathbf{I}\\). In this way, for all the \\(N\\) learnable Gabor filters, a set of maps \\(\\{\\mathbf{I}^n\\}_{n = 1}^N\\) are generated. Next, the statistical feature extractor processes each \\(\\mathbf{I}^n\\in \\{\\mathbf{I}^n\\}_{n = 1}^N\\) through a Learnable Histogram Operator (LHO) and then passes the resulting \\(\\{\\mathbf{S}^n\\}_{n = 1}^N\\) through a Filter Correlation Module (FCM) to generate the texture feature \\(\\mathbf{T}\\). Finally, the semantic feature \\(\\mathbf{M}\\) and texture features \\(\\{\\mathbf{T}_i\\}\\) from all" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1622" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.269, + 0.895, + 0.34 + ], + "angle": 0, + "content": "Figure 1. Overall structure of our network. The semantic branch produces a semantic feature \\(\\mathbf{M}\\) for the input image. The region selection gate selects impactful regions from a set of pre-defined region proposals. The texture branch generates a texture feature \\(\\mathbf{T}\\) for each of the selected regions that is zoomed into the size \\(S \\times S\\). Finally, semantic feature \\(\\mathbf{M}\\) and texture features \\(\\mathbf{T}\\) from all selected regions are added for prediction. Note that, for simplicity of illustration, the figure only presents three region proposals for an image. In actual practice, the region proposals follow the same setting as RCNN [15], comprising multiple regions with different positions and scales." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.47, + 0.394 + ], + "angle": 0, + "content": "selected regions are added and fed into a fully connected layer to obtain the prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.47, + 0.53 + ], + "angle": 0, + "content": "The subsequent sections are arranged as follows. In Sec. 3.2, we provide an introduction to Gabor filters, which are the key to our method to capture texture information. In Sec. 3.3, we illustrate the strategy to train our Gabor filters in a stable and effective manner. In Sec. 3.4, we elaborate on the statistical feature extractor that exploits informative statistical information from the output of Gabor filters. In Sec. 3.5, we introduce the gate mechanism that selects impactful regions into the texture branch for texture extraction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.212, + 0.545 + ], + "angle": 0, + "content": "3.2. Gabor Filter" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.651 + ], + "angle": 0, + "content": "The Gabor filter is a widely-used feature extractor in traditional image processing, owing to its biological relevance and powerful texture extraction ability. It has optimal joint localization in both spatial and frequency domains, which makes it possible to be effectively applied in both spatial- and frequency-wise analysis. In the spatial domain, a Gabor Filter is mathematically defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.746 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} g (x, y) = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} \\exp \\left\\{- \\frac {1}{2} \\left(\\frac {\\widetilde {x} ^ {2}}{\\sigma_ {x} ^ {2}} + \\frac {\\widetilde {y} ^ {2}}{\\sigma_ {y} ^ {2}}\\right) \\right\\} \\exp [ 2 \\pi j W \\widetilde {x} ]. (1) \\\\ \\left\\{ \\begin{array}{l} \\widetilde {x} = x \\cos \\theta + y \\sin \\theta \\\\ \\widetilde {y} = - x \\sin \\theta + y \\cos \\theta \\end{array} \\right. (2) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "This representation can be regarded as a windowed Fourier transform, i.e., a Gaussian kernel function modulated by a sinusoidal plane wave. Specifically, \\([\\sigma_x,\\sigma_y]\\) defines the scale of the Gabor filter, and it can determine the effective size of a pixel's neighborhood where weighted summation occurs. \\(\\theta\\) defines the orientation of the filter. \\(W\\) denotes the radial frequency of the sinusoid. These four parameters \\(\\{\\sigma_x,\\sigma_y,\\theta ,W\\}\\) can fully define a Gabor filter. By altering the parameters, different filters can be generated to capture different signal components." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.363, + 0.81, + 0.378 + ], + "angle": 0, + "content": "3.3. Learnable Gabor Filter Parameters" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.749 + ], + "angle": 0, + "content": "An effective Gabor filter requires the appropriate combination of parameters to match a given task. Previous works [40, 30, 42] have generally used a hand-crafted approach for parameter selection, relying on heuristic rules to inform manual parameter settings. However, this kind of handcrafted approach is highly dependent on the expertise of the individual and cannot guarantee effectiveness for the task at hand. To address this limitation, we propose an alternative method that automatically learns the optimal parameters in a supervised manner, ensuring that the parameter combination can better fit the task. However, learning the parameters presents significant challenges. Firstly, during experimentation, erratic loss fluctuations are observed in the training process, indicating a lack of training stability (see the experimental section for details). Secondly, the features extracted by the trained network exhibit a substantial bias towards low-frequency information. The high-frequency information, on the other hand, occupies only a small fraction of all features. Specifically, only \\(6\\%\\) of the trained Gabor filters have a frequency parameter \\(W\\) higher than 0.5. This tendency is mainly due to the regularity of commonly used activation and loss functions in deep learning (refer to [45, 33] for details), which is detrimental since the high-frequency information can be vital for fine-grained recognition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To ensure training stability and filter effectiveness, we propose two solutions to tackle the above problems. To address the first challenge, we propose constraining parameter values into a valid range, which is theoretically derived to avoid potential problems such as frequency aliasing that could hinder training stability. To address the second challenge, we propose a dual-range strategy to further regularize the frequency parameter \\( W \\), ensuring that sufficient high-frequency components can be extracted. These solutions enable our Gabor filters to be learned in a stable and ef" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1623" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "fective manner. A detailed illustration of these solutions is presented in the subsequent sections." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.473, + 0.593 + ], + "angle": 0, + "content": "Learning Parameters under Constraints. We first introduce a novel parameter value constraint to enhance the stability of model training. Our approach is motivated by the analysis that training instability could be attributed to the mismatch between image properties and the ideal application scenario of Gabor filters. Specifically, Gabor filters are mathematically defined for infinite length signals [37]; the digital image signals, on the other hand, are finite in both spatial and frequency domains due to the limited length of image width and sampling frequency. As a result, directly applying Gabor filters to finite-length images may cause mathematical deficiency and distortion, leading to frequency aliasing and other issues that can impair model training [39]. To address this problem, we propose to concentrate most of the Gabor filter energy within the finite signal zone. This ensures that only a small amount of filter energy spills over the finite signal, minimizing the negative effects of using infinite-length-defined filters on finite-length images. Such a constraint could be implemented by limiting the value ranges of filter parameters, which determine the effective zone and energy concentration area of a Gabor filter. Specifically, according to the properties of Gabor filters and images mentioned above, we first derive \\([0,\\pi ],\\left[\\frac{5}{2\\pi(1 - 2W)},\\frac{S}{5}\\right],\\left[\\frac{5}{2\\pi},\\frac{S}{5}\\right]\\) and \\([0,\\frac{2\\pi S - 25}{4\\pi S} ]\\) to be the valid ranges for parameters \\(\\theta ,\\sigma_{x},\\sigma_{y}\\) and \\(W\\) respectively (please refer to supplementary materials for a detailed derivation of these valid ranges). Next, we propose a constraint function to ensure each parameter to fall within its valid range. Specifically for a parameter \\(p\\) with lower bound \\(l_{p}\\) and upper bound \\(u_{p}\\), we propose to obtain \\(p\\) through a learnable parameter \\(\\mathbf{p}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.602, + 0.47, + 0.634 + ], + "angle": 0, + "content": "\\[\np = l _ {p} + \\left(u _ {p} - l _ {p}\\right) \\mathrm {S i g m o i d} (\\mathbf {p}) = \\frac {u _ {p} + l _ {p} e ^ {- \\mathbf {p}}}{1 + e ^ {- \\mathbf {p}}}. (3)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.717 + ], + "angle": 0, + "content": "The parameter \\(\\mathbf{p}\\) can be learned to have any value ranging from \\(-\\infty\\) to \\(+\\infty\\). By applying Eq. 3, parameter \\(p\\) can be guaranteed to fall within its valid range \\([l_p, u_p]\\). By doing so, parameter values are constrained to enhance the stability of training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.471, + 0.902 + ], + "angle": 0, + "content": "High Frequency Enhancement. To address the frequency bias problem and improve high-frequency information extraction, we further propose a dual-constraint strategy for the frequency parameter \\( W \\). Specifically, we constrain half of Gabor filters to only exploit high-frequency components, making the network to capture sufficient high-frequency information for facilitating fine-grained recognition. This is enabled by setting two value intervals for \\( W \\): \\([0, \\frac{2\\pi S - 25}{8\\pi S}]\\) and \\([\\frac{2\\pi S - 25}{8\\pi S}, \\frac{2\\pi S - 25}{4\\pi S}]\\), which are equally divided from the valid range \\([0, \\frac{2\\pi S - 25}{4\\pi S}]\\) of the frequency parameter. Let \\( N \\) be the total number of Gabor filters to be learned. Using the method in Eq. 3, we constrain \\( W \\) of \\( N / 2 \\) fil" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.089, + 0.895, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.224, + 0.887, + 0.239 + ], + "angle": 0, + "content": "Figure 2. The structure of Learnable Histogram Operator (LHO)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.248, + 0.894, + 0.356 + ], + "angle": 0, + "content": "ters to fall between \\([0, \\frac{2\\pi S - 25}{8\\pi S}]\\) and the other \\(N/2\\) filters to fall between \\(\\left[\\frac{2\\pi S - 25}{8\\pi S}, \\frac{2\\pi S - 25}{4\\pi S}\\right]\\), such that they serve as the low-frequency expert and high-frequency expert respectively. This strategy enhances the extraction ability of high-frequency information, alleviating the frequency bias problem in traditional DNNs where high-frequency features are difficult to extract." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.365, + 0.757, + 0.38 + ], + "angle": 0, + "content": "3.4. Statistical Feature Extractor" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.675 + ], + "angle": 0, + "content": "The above method enables Gabor filters to be trained stably and effectively in a deep learning framework. These filters can capture texture signals from an input image. In the next step, we target at extracting effective features from these filters to facilitate fine-grained recognition. From the perspective of digital image processing, texture can be represented by the statistical properties of feature maps [16]. Based on this principle, in some previous research [40, 4, 1], textures were exploited by extracting hand-crafted statistics such as variance, contrast and smoothness from the output of Gabor filters. However, these statistics have limited effectiveness because they are hand-crafted designed. In this work, we step further and take advantage of deep learning to extract deep statistical features that are more comprehensive and effective. Specifically, we propose a novel statistical feature extractor that contains a Learnable Histogram Operator (LHO) followed by a Filer Correlation Module (FCM). In the following sections, we provide a detailed illustration of QCO and FCM respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.842 + ], + "angle": 0, + "content": "Learnable Histogram Operator. We first employ a Learnable Histogram Operator (LHO) to exploit statistical information, which is improved from [58]. Fig. 2 illustrates the structure of LHO. LHO receives the output from each Gabor filter as input and produces a statistical feature \\(\\mathbf{S} \\in \\mathbb{R}^{C}\\), where \\(C\\) refers to the channel number. Let \\(\\mathbf{I} \\in \\mathbb{R}^{S \\times S}\\) be the intensity map generated by convolving a Gabor filter with the processed image, where \\(S\\) refers to image size. LHO first defines \\(M\\) levels by equally dividing the minimal and maximal values for intensities of all pixels. Specifically, the \\(m\\)-th level \\(\\mathbf{L}^{m}\\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.848, + 0.892, + 0.879 + ], + "angle": 0, + "content": "\\[\n\\mathbf {L} ^ {m} = \\min (\\mathbf {I}) + \\frac {\\max (\\mathbf {I}) - \\min (\\mathbf {I})}{M} \\cdot m \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.885, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Next, each pixel \\(\\mathbf{I}^{i,j}\\) on \\(\\mathbf{I}\\) is quantized to a vector \\(\\mathbf{V}^{i,j} \\in\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1624" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.136 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^M\\). Concretely, let \\(I\\) be the interval between adjacent levels \\((I = \\mathbf{L}^{m + 1} - \\mathbf{L}^m)\\), the \\(m\\)-th channel \\(\\mathbf{V}^{i,j,m}\\) on \\(\\mathbf{V}^{i,j}\\) is computed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.146, + 0.469, + 0.196 + ], + "angle": 0, + "content": "\\[\n\\mathbf {V} ^ {i, j, m} = \\left\\{ \\begin{array}{l l} 1 - \\left| \\mathbf {L} ^ {m} - \\mathbf {I} ^ {i, j} \\right| & \\text {i f} \\left| \\mathbf {L} ^ {m} - \\mathbf {I} ^ {i, j} \\right| < \\frac {I}{2} \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.206, + 0.469, + 0.298 + ], + "angle": 0, + "content": "In this way, \\(\\mathbf{I}\\) is quantized to \\(\\mathbf{V} \\in \\mathbb{R}^{S \\times S \\times M}\\). Note a spire-shaped function is used for quantization instead of a binary one to ensure that the operation is differentiable. After the quantization, the number of pixels that fall into each level is counted and normalized to obtain a counting feature \\(\\mathbf{C} \\in \\mathbb{R}^M\\). Specifically, \\(\\mathbf{C}^m\\) for the \\(m\\)-th level is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.307, + 0.469, + 0.35 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} ^ {m} = \\frac {\\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i , j , m}}{\\sum_ {m = 1} ^ {M} \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i , j , m}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.354, + 0.468, + 0.385 + ], + "angle": 0, + "content": "We concatenate \\(\\mathbf{C}^m\\) with \\(\\mathbf{L}^m\\), and obtain the feature \\(\\mathbf{F}^m\\) for the \\(m\\)-th quantization level as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.395, + 0.469, + 0.413 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} ^ {m} = \\phi (\\operatorname {C A T} \\left(\\mathbf {C} ^ {m}, \\mathbf {L} ^ {m}\\right)) + \\mathbf {P} ^ {m}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.422, + 0.469, + 0.483 + ], + "angle": 0, + "content": "where \\(\\phi\\) refers to a linear layer. \\(\\mathbf{P}^m\\in \\mathbb{R}^C\\) encodes the position information for pixels quantized to the \\(m\\)-th level, which is computed as the weighted sum of position features from all pixels as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.494, + 0.469, + 0.536 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} ^ {m} = \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i, j, m} \\mathrm {P E} (i, j), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.546, + 0.469, + 0.591 + ], + "angle": 0, + "content": "where PE refers to the position encoding operation as in vit [8]. Finally, the statistical texture \\(\\mathbf{S}\\) is produced by correlating features from different levels:" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.601, + 0.469, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} = \\operatorname {A v g} \\left(\\operatorname {M H A} \\left(\\left\\{\\mathbf {F} ^ {m} \\right\\} _ {m = 1} ^ {M}\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.629, + 0.469, + 0.855 + ], + "angle": 0, + "content": "where MHA denotes a multi-head attention and Avg refers to the average over all levels. Using LHO has two advantages. Firstly, it can be considered as a way to extract deep features from a differentiable and learnable histogram, which can produce effective and appropriate statistical features that can benefit the task [16, 58]. Secondly, conventional statistical features are typically pixel-relationship-invariant. For example, rearranging pixel positions does not alter the mean and variance values. In contrast, our method is pixel-relationship-aware as it encodes \\(\\mathbf{P}^m\\) that represents the position information of pixels quantized to each level, which provides additional information that can be useful for fine-grained recognition. These advantages enable the extracted features from LHO to be effective in facilitating fine-grained recognition." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Filter Correlation Module. The proposed LHO can produce a statistical feature from the output of each Gabor filter, resulting in a set of features \\(\\{\\mathbf{S}^n\\}_{n=1}^N\\) for all filters. We" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.135 + ], + "angle": 0, + "content": "further propose a Filter Correlation Module (FCM) to aggregate statistical information from all Gabor filters as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.146, + 0.892, + 0.184 + ], + "angle": 0, + "content": "\\[\n\\mathbf {T} = \\operatorname {A v g} \\left(\\operatorname {M H A} \\left(\\left\\{\\mathbf {S} ^ {n} + \\phi \\left(\\sigma_ {x} ^ {n}, \\sigma_ {y} ^ {n}, \\theta^ {n}, W ^ {n}\\right) \\right\\} _ {n = 1} ^ {N}\\right)\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.185, + 0.892, + 0.291 + ], + "angle": 0, + "content": "in which \\(\\mathbf{S}^n\\) refers to the statistical feature for the \\(n\\)-th Gabor filter. \\(\\phi(\\sigma_x^n, \\sigma_y^n, \\theta^n, W^n)\\) uses a linear layer to encode filter parameter information, which can indicate the type of texture extracted by the Gabor filter. Eq. 10 exploits the correlations among different texture components from different Gabor filters, generating a powerful feature with long-range correlations that can facilitate fine-grained recognition." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.303, + 0.706, + 0.318 + ], + "angle": 0, + "content": "3.5. Region Selection Gate" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.327, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Through the methods outlined above, we can build a powerful feature extractor that captures texture information using Gabor filters. As a common practice used by previous methods, the extractor can generate features in an image-based [40] manner or a patch-based manner [39]. Image-based methods directly feed the whole image into the extractor, which might lead to the blurring of local detailed information. Patch-based methods address the problem by equally dividing the image into several patches and extracting a feature from each patch. However, it is computationally expensive as each image position must be processed by the feature extractor. Intuitively, the texture information in different regions of an image is not equally important. For example, some regions may contain critical textures for recognition, such as feather of the bird, while others may be less informative, consisting of background textures such as sky, road and lawn. Therefore, extracting textures from all positions is redundant and computationally inefficient, which can impede recognition accuracy and slow down algorithmic speed. To address the issue, we propose a novel approach to solely extract textures from informative regions that are automatically selected from a gate mechanism. More specifically, the gate mechanism for region selection involves three steps. Firstly, we introduce a shallow FPN block that takes the intermediate features of the CNN-based semantic branch as inputs and generates a feature map \\(F\\). Please refer to supplementary materials for a detailed description for the structure of this block. Since features from the CNN branch have a high receptive field and contain rich semantic information, \\(F\\) can identify key parts of an image and assist in selecting class-discriminative regions in appropriate positions. Secondly, we introduce a set of regions proposals, denoted as \\(\\{\\mathcal{R}^k\\}_{k=1}^K\\), which is the same as that in RCNN [15], comprising regions with different scales and positions. For each region \\(\\mathcal{R}^k\\), a feature vector \\(f^k\\) is generated by performing an RoI pooling on the corresponding region of the feature map \\(F\\). This feature vector is then fed into a linear layer to generate a score \\(s^k\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1625" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "Lastly, regions that require texture extraction are selected based on their scores. This mechanism enables only the regions that contain class-discriminative information to be selected for texture extraction, thereby reducing computation costs and avoiding information redundancy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.471, + 0.333 + ], + "angle": 0, + "content": "To reduce computation for capturing texture features, we expect 'hard' selections instead of the 'soft' attention scores to be generated so that only a limited number of regions need texture extraction. However, such a hard selection may prohibit the gradients to be back-propagated to the earlier layers in optimization. To address this issue, we employ the Improved Semantic Hashing [24, 25] for region selection. In training, to encourage more decision space to be explored randomly, we add a standard Gaussian noise \\(\\epsilon\\) to \\(s^k\\), resulting in the noise-injected score \\(\\hat{s}^k\\). Then two vectors are generated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.343, + 0.469, + 0.363 + ], + "angle": 0, + "content": "\\[\nc ^ {k} = \\sigma^ {\\prime} (\\hat {s} ^ {k}); d ^ {k} = \\mathbb {1} (\\hat {s} ^ {k} > 0), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.372, + 0.414, + 0.387 + ], + "angle": 0, + "content": "where \\(\\sigma^{\\prime}\\) refers to the saturating Sigmoid function:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.397, + 0.47, + 0.417 + ], + "angle": 0, + "content": "\\[\n\\sigma^ {\\prime} (\\hat {s} ^ {k}) = \\max (0, \\min (1, 1. 2 \\sigma (\\hat {s} ^ {k}) - 0. 1)), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.469, + 0.516 + ], + "angle": 0, + "content": "where \\(\\sigma\\) denotes the original Sigmoid function. In this way, \\(d^{k}\\) is a binarized discrete feature with value \\(\\{0,1\\}\\), which is used for making the selection decision. \\(c^{k}\\) is a continuously differentiable vector that can be used to approximate gradients in back-propagation, whose details are presented in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.469, + 0.758 + ], + "angle": 0, + "content": "Discussion with Previous Methods. Note that the proposed region gate mechanism differs from other key part localization methods used for fine-grained recognition. Unlike existing methods, our method can be trained end-to-end and generate hard decisions without the need for extra annotations. These properties enable our method to be highly effective and practical for region selection. Conversely, existing key part localization techniques have several limitations. For example, some methods [20, 43] require extra annotations such as bounding box and key points for joint training; [14] uses an indifferentiable selection process, making the network unable to be trained end-to-end; other methods [7, 21] typically produce soft attention rather than hard decisions, which cannot reduce computation costs. Our approach can be more practical and effective benefiting from our careful designs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.759, + 0.216, + 0.775 + ], + "angle": 0, + "content": "3.6. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.783, + 0.469, + 0.811 + ], + "angle": 0, + "content": "The proposed network is optimized by the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.81, + 0.469, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = L _ {c e} (p, l) + \\lambda \\sum_ {k = 1} ^ {K} d ^ {k}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\( L_{ce} \\) denotes the cross-entropy loss. \\( p \\) and \\( l \\) are the prediction logits and ground truth label. \\( d^{k} \\) denotes the binarized discrete decision as in Eq. 11. The second item" + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.089, + 0.892, + 0.285 + ], + "angle": 0, + "content": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5084.5
ResNet101 [17]ResNet10185.5
DenseNet161 [19]DenseNet16185.5
PC-Dense161 [9]DenseNet16186.9
NTSNet [48]ResNet5087.5
Cross-X [34]ResNet5087.7
DCL [3]ResNet5087.8
S3N [7]ResNet5088.5
iSQRT-COV [27]ResNet10188.7
GaRD [54]ResNet5089.6
APINet [59]DenseNet16190.0
OursResNet5090.8
OursResNet10191.3
OursDenseNet16191.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.528, + 0.285, + 0.858, + 0.298 + ], + "angle": 0, + "content": "Table 1. Comparison results on CUB-200-2011 dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.309, + 0.892, + 0.37 + ], + "angle": 0, + "content": "in Eq. 13 encourages fewer regions to be selected, thus avoiding the redundant information and reducing computation costs. \\(\\lambda\\) is a hyper-parameter to control the trade-off between the two loss items." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.378, + 0.633, + 0.396 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.403, + 0.717, + 0.42 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.428, + 0.892, + 0.653 + ], + "angle": 0, + "content": "Following [59], we adopt different networks as the semantic branch, including ResNet50, ResNet101 and DenseNet161. We use SGD as the optimizer with the momentum of 0.9. The initial learning rate is set to 1e-4, which decays by 0.1 for every 20 epochs (overall 100 epochs). Batch size is 16 for all datasets. Following previous works [54, 28], we use random cropping of \\(448 \\times 448\\) in training and center crop at inference. We apply the commonly-used data augmentation strategies for training, including random scaling, left-right flipping and random cropping. \\(S\\) indicating the size of regions that are zoomed in is set to 112. \\(N\\) indicating the number of learnable Gabor filters is set to 128. \\(M\\) indicating the number of quantization levels in QCO is set to 8. \\(\\lambda\\) in Eq. 13 is set to 0.2. Experiments are conducted on 2 NVIDIA Titan V100 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.794, + 0.682 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.69, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We evaluate our method on four datasets, including three fine-grained datasets CUB-200-2011, NA-bird, Stanford Dogs and a terrain recognition dataset GTOS-mobile. The comparison results on these datasets are presented in Tables 1, 2, 3, and 4, respectively. Our method achieves the best performance when using DenseNet161 as the semantic branch, reaching accuracy scores of 91.5, 90.4, 92.1 and 87.5, outperforming the second-best method by 1.5, 2.3, 1.8 and 4.8, respectively. It is worth noting that even when using ResNet50, the least effective backbone among the three, our method remains superior to all other compared methods. This highlights the high effectiveness of our method. The advantage of our method is especially significant on the challenging terrain dataset GTOS-mobile. This is due to our" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1626" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.09, + 0.345, + 0.219 + ], + "angle": 0, + "content": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5082.2
ResNet101 [17]ResNet10182.9
DenseNet161 [19]DenseNet16183.1
Cross-X [34]ResNet5086.4
GaRD [54]ResNet5088.0
APINet [59]DensetNet10188.1
OursResNet5089.5
OursResNet10190.0
OursDenseNet16190.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.096, + 0.22, + 0.345, + 0.246 + ], + "angle": 0, + "content": "Table 2. Comparison results on NA-bird dataset." + }, + { + "type": "table", + "bbox": [ + 0.362, + 0.09, + 0.61, + 0.22 + ], + "angle": 0, + "content": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5080.1
ResNet101 [17]ResNet10180.6
DenseNet161 [19]DenseNet16180.9
PC-Dense161 [9]DenseNet16182.8
Cross-X [34]ResNet5088.9
APINet [59]ResNet10190.3
OursResNet5091.0
OursResNet10191.7
OursDenseNet16192.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.362, + 0.221, + 0.609, + 0.247 + ], + "angle": 0, + "content": "Table 3. Comparison results on Stanford Dogs dataset." + }, + { + "type": "table", + "bbox": [ + 0.627, + 0.089, + 0.875, + 0.22 + ], + "angle": 0, + "content": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5069.4
ResNet101 [17]ResNet10172.0
DenseNet161 [19]DenseNet16172.9
B-CNN [28]ResNet5075.8
Deep-TEN [51]ResNet5076.1
DEP [47]ResNet5082.7
OursResNet5086.4
OursResNet10187.0
OursDenseNet16187.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.627, + 0.221, + 0.875, + 0.246 + ], + "angle": 0, + "content": "Table 4. Comparison results on GTOS-mobile dataset." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.27, + 0.468, + 0.337 + ], + "angle": 0, + "content": "
MethodAccuracyFlops(G)Params(M)
Baseline (ResNet50)84.516.2624.69
+ TB & RSG90.820.7232.41
+ TB (image-based manner)89.036.8829.82
+ TB (patch-based manner)89.937.0429.82
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.337, + 0.468, + 0.377 + ], + "angle": 0, + "content": "Table 5. Ablation results of different components in our method. TB and RSG refer to the texture branch and region selection gate, respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.386, + 0.468, + 0.43 + ], + "angle": 0, + "content": "method's ability to extract texture features, which are essential for the classification of visually-similar and closely-related terrain classes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.44, + 0.23, + 0.456 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.463, + 0.469, + 0.538 + ], + "angle": 0, + "content": "We perform ablation study to verify the effectiveness of our designs. Experiments in this part are conducted on CUB-200-2011 dataset with ResNet50 as the semantic branch. Due to paper length limitation, more ablation study results are presented in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.539, + 0.469, + 0.825 + ], + "angle": 0, + "content": "Ablation of Different Components. As shown in Fig. 1, in addition to the basic CNN-based semantic branch, our method consists of two key components: a Gabor-filter-based texture branch (TB) and a region selection gate (RSG). We conduct experiments to validate the effect of these components and present the results in Table. 5, which includes the validation accuracy, computation costs and parameter numbers of different settings. We set the network that only has a ResNet50 semantic branch to be the baseline. Our method with adding both texture branch & region selection gate increases accuracy from 84.5 to 90.8. When the region selection gate is removed, extracting textures by feeding the whole image into texture branch (image-based manner) reduces accuracy to 89.0 and increases computation by \\(78\\%\\); equally dividing image into \\(8 \\times 8\\) patches and getting a feature from each patch (patch-based manner) reduces accuracy to 89.0 and increases computation by \\(79\\%\\). The results demonstrate that the region selection gate can reduce computation and improve performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Ablation of Learnable Gabor Filters. Results in this part are presented in Table. 6. (1) First, we validate the effectiveness of Gabor filters. Replacing all Gabor filters by the \\(3 \\times 3\\) convolution layers decreases accuracy by 4.9. This indicates that the improvement does not simply come from" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.27, + 0.892, + 0.353 + ], + "angle": 0, + "content": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours replacing Gabor filters with conv85.920.0332.95
Ours w/o parameter learning86.520.7232.41
Ours w/o parameter value constraints75.420.4032.41
Ours w/o high frequency enhancement88.120.4032.41
" + }, + { + "type": "table_caption", + "bbox": [ + 0.545, + 0.353, + 0.846, + 0.365 + ], + "angle": 0, + "content": "Table 6. Ablation results of learnable Gabor filters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.748 + ], + "angle": 0, + "content": "an increase in the number of parameters, but from the effectiveness of using Gabor filters for texture extraction. (2) Second, we evaluate the effectiveness of learning Gabor filter parameters in a supervised manner. We replace the learnable parameters with the manually set ones, where the setting rules are the same as [40]. This reduces accuracy by 4.3, showing the effectiveness of supervised learning. (3) Third, we verify the necessity of using parameter value constraints. In Fig. 3, we present the loss curves and validation accuracy curves for methods w/ and w/o using value constraints. Using value constraints results in a smoother loss decline curve and accuracy improvement curve. In contrast, free training causes violent loss and accuracy fluctuations, especially at the beginning stage of training, indicating that the training process is unstable. Compared to free training, using value constraints significantly improves validation accuracy by 15.4. (4) Last, we evaluate the high frequency enhancement strategy by setting two constraints for frequency parameter \\( W \\). Without the strategy and directly constraining \\( W \\) into its valid range reduces accuracy by 2.7. Results demonstrate the effectiveness of our designs for the learnable Gabor filter parameters. Also note, using the proposed learning methods requires no extra parameters and only increases computation very slightly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Ablation of Statistical Feature Extractor. We propose a statistical feature extractor to leverage texture information from the output of Gabor filters. The extractor consists of two parts: a Learnable Histogram Operator (LHO) and a Filter Correlation Module (FCM). We conduct experiments to validate the effect of these components and present the results in Table 7. Removing LHO and FCM reduces accuracy from 90.8 to 87.0 and 89.2 respectively. Also note that, both LHO and FCM are lightweight, only requiring extra parameters of 4.26M and 3.56M, increasing flops by" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1627" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.262, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.189, + 0.214, + 0.2 + ], + "angle": 0, + "content": "(a) Loss Curves" + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.096, + 0.44, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.291, + 0.188, + 0.404, + 0.201 + ], + "angle": 0, + "content": "(b) Accuracy Curves" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.205, + 0.47, + 0.247 + ], + "angle": 0, + "content": "Figure 3. Loss curves (a) and accuracy curves (b) in different settings. Blue and orange lines indicate curves for training Gabor filters w/ and w/o using parameter value constraints, respectively." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.25, + 0.469, + 0.309 + ], + "angle": 0, + "content": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours w/o LHO87.018.0328.25
Ours w/o FCM89.219.5528.85
" + }, + { + "type": "table_caption", + "bbox": [ + 0.108, + 0.31, + 0.434, + 0.321 + ], + "angle": 0, + "content": "Table 7. Ablation results of statistical feature extractor." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.331, + 0.468, + 0.361 + ], + "angle": 0, + "content": "\\(15\\%\\) and \\(6\\%\\) respectively. Results show the high effectiveness and efficiency of LHO and FCM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.47, + 0.574 + ], + "angle": 0, + "content": "Ablation of LHO. In Table. 8, we further evaluate the designs in LHO. First, we replace LHO with a hand-crafted statistical feature composed of mean, variance, maximum and minimum values, which reduces accuracy by 2.9. This demonstrates that LHO can produce statistical features that are more effective than hand-crafted ones widely used by previous methods. Next, we remove position information \\(\\mathbf{P}^m\\) in Eq. 7 and multi-head attention in Eq. 9, which reduces accuracy by 1.5 and 2.1 respectively, showing the importance of encoding position features and correlating different levels in LHO. Finally, we move LHO from texture branch to CNN-based semantic branch. This reduces accuracy by 4.6, showing that the effectiveness of LHO relies on Gabor filters to extract texture-related signals." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.585, + 0.214, + 0.6 + ], + "angle": 0, + "content": "4.4. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.47, + 0.821 + ], + "angle": 0, + "content": "In Fig. 4, we provide a visualization of the outputs obtained from learned Gabor filters. More specifically, Fig. 4 (c) and Fig. 4 (d) show the average output of all high-frequency and low-frequency Gabor filters, respectively. As can be observed, the high-frequency filters primarily capture information of undulating areas such as speckles and ripples, whereas the low-frequency filters primarily capture information related to smooth changing areas. Both these two kinds of information are critical for recognition. By exploiting sufficient and balanced multi-frequency features through the carefully-designed learnable Gabor filters, our method can leverage comprehensive information for effective fine-grained recognition. Due to space limitation, more visualization results are presented in supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.44, + 0.848 + ], + "angle": 0, + "content": "4.5. Discussion of Computation and Parameter" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Compared to the ResNet50 baseline, our method only increases computation and parameter usage slightly. Specifically, on CUB-200-2011 dataset, ResNet50 consumes" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.094, + 0.616, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.151, + 0.615, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.543, + 0.207, + 0.585, + 0.218 + ], + "angle": 0, + "content": "(a) Image" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.096, + 0.702, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.151, + 0.783, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.206, + 0.687, + 0.216 + ], + "angle": 0, + "content": "(b) Region" + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.096, + 0.783, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.151, + 0.783, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.71, + 0.206, + 0.783, + 0.216 + ], + "angle": 0, + "content": "(c) High-W Filters" + }, + { + "type": "image", + "bbox": [ + 0.794, + 0.096, + 0.865, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.794, + 0.151, + 0.865, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.206, + 0.865, + 0.216 + ], + "angle": 0, + "content": "(d) Low-W Filters" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.221, + 0.892, + 0.263 + ], + "angle": 0, + "content": "Figure 4. Visualization of Gabor filters. (a), (b), (c) and (d) present the original images, the selected regions, average output of all high-frequency and low-frequency Gabor filters, respectively." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.276, + 0.892, + 0.349 + ], + "angle": 0, + "content": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours w/o LHO w/ HSF87.918.1628.25
Ours w/o Pm in Eq. 789.318.5030.93
Ours w/o MHA in Eq.988.719.4929.73
Ours w/o LHO in TB w/ LHO in CNN86.222.8532.90
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.5, + 0.349, + 0.892, + 0.402 + ], + "angle": 0, + "content": "Table 8. Ablation results of LHO. HSF refers to a hand-crafted statistical feature composed of mean, variance, maximum and minimum values. MHA denotes multi-head attention. TB denotes texture branch." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.423, + 0.892, + 0.559 + ], + "angle": 0, + "content": "16.26G flops of computation, requiring 24.69M parameters, reaching accuracy of 84.5. Our method consumes 20.72G flops of computation, requiring 32.41M parameters, reaching accuracy of 90.8. Compared to ResNet50, our method can improve accuracy significantly (+6.3) with only increasing computation and parameter usage by \\(27\\%\\) and \\(31\\%\\) respectively. This demonstrates the high effectiveness and high efficiency of our method with outstanding performance and reasonable computation costs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.584, + 0.619, + 0.6 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.76 + ], + "angle": 0, + "content": "This paper presents a novel network that extracts texture features to facilitate fine-grained recognition using Gabor filters. We make the Gabor filter parameters to be automatically learned in a stable and effective manner through our carefully-designed value constraint strategies. We also propose a statistical feature extractor and a region selection gate, allowing informative and effective Gabor texture features to be extracted with very few extra computation costs. Our method is effective, as shown by the extensive experiments with state-of-the-art (SOTA) performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-08-006), Singapore Ministry of Education (MOE) AcRF Tier 2 under Grant MOE-T2EP20222-0009, the National Research Foundation Singapore through AI Singapore Programme under Grant AISG-100E-2020-065, and SUTD SKI Project under Grant SKI 2021_02_06." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1628" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Jon Arrospide and Luis Salgado. 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Existing works have demonstrated the possibility of applying deep CNNs to exploit features that distinguish similar classes. However, CNNs suffer from problems including frequency bias and loss of detailed local information, which restricts the performance of recognizing fine-grained categories. To address the challenge, we propose a novel texture branch as complimentary to the CNN branch for feature extraction. We innovatively utilize Gabor filters as a powerful extractor to exploit texture features, motivated by the capability of Gabor filters in effectively capturing multi-frequency features and detailed local information. We implement several designs to enhance the effectiveness of Gabor filters, including imposing constraints on parameter values and developing a learning method to determine the optimal parameters. Moreover, we introduce a statistical feature extractor to utilize informative statistical information from the signals captured by Gabor filters, and a gate selection mechanism to enable efficient computation by only considering qualified regions as input for texture extraction. Through the integration of features from the Gabor-filter-based texture branch and CNN-based semantic branch, we achieve comprehensive information extraction. We demonstrate the efficacy of our method on multiple datasets, including CUB-200-2011, NA-bird, Stanford Dogs, and GTOS-mobile. State-of-the-art performance is achieved using our approach. + +# 1. Introduction + +Recognizing fine-grained categories (e.g., different flower types or bird species) is challenging due to the subtle differences in their visual appearance. Recently, deep neural network technology [17, 8, 31, 57, 52, 12] has made remarkable advancement, allowing for significant progress in extracting deep class-discriminative features for fine-grained recognition [10, 38, 41, 23, 3, 56]. For example, [54] develops a graph-based module to extract cross-class relationship features. [13, 26] use bilinear pooling to ex + +ploit high-order features from different networks. [55, 38] leverage multi-scale information to enhance feature effectiveness. The success of these methods highlights the crucial role of extracting powerful features in distinguishing fine-grained categories. + +To exploit class-discriminative features, previous methods [38, 41, 23, 3, 56] have primarily relied on convolutional neural networks (CNNs) as the model backbone. CNNs have achieved significant success in many computer vision tasks. However, due to the following limitations, they may not be sufficient for capturing comprehensive information in fine-grained recognition. First, deep CNNs generally extract information with high receptive fields and resolution-reduced feature maps, leading to the loss of local detailed information that is critical for fine-grained recognition. Second, as discussed in [33, 45, 46], due to the regularity of the commonly used activation [45] and loss functions [33], CNNs prioritize learning low-frequency components while ignoring high-frequency components. This bias is detrimental to fine-grained classification, as the ignored high-frequency information, such as ripples and spots in bird feathers, can be important in distinguishing between similar classes. Considering these limitations of CNNs, we suggest that a more powerful feature extractor is required, which should be able to capture local detailed information and multi-frequency comprehensive features that are lost by CNNs but crucial for fine-grained recognition. + +Witnessing the challenge, in this work, we introduce a novel branch that extracts texture features as complimentary to the vanilla CNN features to facilitate fine-grained recognition. We employ Gabor filters as the texture extractor in the novel branch. The Gabor filter is a windowed Fourier transform that combines a sinusoidal signal with a Gaussian wave. It is widely used in image processing for extracting low-level texture features [30, 35, 29, 1, 40]. The motivations of using Gabor filters in fine-grained recognition can be illustrated in two-folds. (1) First, Gabor filters are effective in capturing local-detailed information. Previous research [5, 6] has found that Gabor functions are similar to the receptive field profiles in the mammalian cortical sim + +ple cells. This indicates that Gabor filters can perform the similar function as cortical cells to capture effective and locally detailed texture information, which is critical for recognizing confusing samples. (2) Second, Gabor filters can extract sufficient high-frequency information. A Gabor filter contains a parameter that directly controls the frequency of the extracted information. It is therefore possible to exploit sufficient high-frequency components by constraining the parameters of some filters into a high-value range, overcoming the frequency-bias limitations of traditional CNNs. Benefiting from these advantages, our introduction of Gabor filters enables texture features to be extracted as an effective supplement to the typical CNN features for improving fine-grained recognition. + +Utilizing Gabor filters in an effective manner is nontrivial. Previous methods with Gabor filters generally rely on hand-crafted designs for filter parameter setting, which cannot guarantee to be optimal. To overcome this limitation, we propose an approach to automatically learn parameters in a supervised manner, in which a value constraint strategy is used to stabilize the learning and enhance high-frequency information extraction. To extract effective information with Gabor filters, we further propose a statistical feature extractor to capture texture features from the Gabor response maps. We also introduce a gate mechanism that selects a limited number of appropriate regions as inputs to the texture branch, thereby reducing computational costs and avoiding information redundancy. These careful designs allow Gabor filters to benefit fine-grained recognition in an effective and efficient manner. + +To the best of our knowledge, our work pioneers to learn texture features using Gabor filters in the task of fine-grained recognition. We perform extensive experiments on four datasets, which demonstrate the effectiveness of our method. Benefiting from the powerful texture features from the Gabor filters, our network can leverage the informative and comprehensive information for recognition, resulting in state-of-the-art (SOTA) performance on all datasets. To summarize, our contributions are as follows. (1) First, we pioneer learning Gabor filters in fine-grained recognition. The texture features extracted from Gabor filters serve as an effective supplement to the vanilla CNN features, significantly improving recognition performance. (2) Second, to enhance model effectiveness and efficiency, we implement several key designs based on Gabor filters, including the parameter learning method, a powerful Gabor feature extractor and a region selection gate. (3) Third, extensive experiments demonstrate the effectiveness of our method with state-of-the-art (SOTA) performance achieved on four datasets. + +# 2. Related Work + +Fine-Grained Recognition. The goal of fine-grained recognition is to classify classes that are visually similar. + +Recent methods for the task can be categorized into two major types: feature-encoding methods [13, 49, 26, 9, 10, 38, 41, 23, 3, 56] and localization methods [20, 43, 2, 21, 44, 7, 36, 11]. Feature-encoding methods emphasize on extracting effective features for the better classification results. For example, some methods [13, 49, 26] use bilinear pooling to obtain informative high-level features. Other works [9, 10] use feature constraints to enhance feature effectiveness. [38, 41, 23, 3] extract multi-level features to get comprehensive information. [54] exploits cross-class relationships to capture class-discriminative features. Localization methods emphasize on selecting the most effective regions to capture features. [20, 43, 2] use extra annotations such as bounding boxes and key points to promote the localization ability of the network. [21, 44, 7, 36] select informative regions through activation maps. Different from these works, our method innovatively learns Gabor filter to effectively capture texture information. Additionally, the region selection gate in our method can be end-to-end trained without the need for additional annotation, giving it a unique advantage. + +Gabor Filters. The Gabor filter is an effective tool for extracting texture features, which makes it widely used in various computer vision applications such as face recognition [30, 35, 29], vehicle verification [1], object detection [42, 22, 39] and gait recognition [40]. Recently, some works [18, 32, 50, 53] introduce Gabor filters into deep neural networks. However, these approaches have suffered from problems like unstable training, frequency bias and high computation costs, leading to low effectiveness and efficiency. Our method addresses the challenges faced by previous approaches through our careful designs, making Gabor filters to be effectively applied in fine-grained recognition. + +# 3. Method + +# 3.1. Overall Structure + +Fig. 1 provides an overview of our approach. A semantic branch takes the entire image as input and generates a semantic feature $\mathbf{M}$ through a vanilla CNN. Using intermediate features from the semantic branch, a gate mechanism selects impactful regions from the image. After that, each of the selected regions $i$ is zoomed into the size $S\times S$ and fed into a texture branch to produce a texture feature $\mathbf{T}_i$ . The texture branch comprises $N$ learnable Gabor filters followed by a statistical feature extractor that performs the following two-step workflow. First, each learnable Gabor filter is convolved with the input region to generate an intensity map $\mathbf{I}$ . In this way, for all the $N$ learnable Gabor filters, a set of maps $\{\mathbf{I}^n\}_{n = 1}^N$ are generated. Next, the statistical feature extractor processes each $\mathbf{I}^n\in \{\mathbf{I}^n\}_{n = 1}^N$ through a Learnable Histogram Operator (LHO) and then passes the resulting $\{\mathbf{S}^n\}_{n = 1}^N$ through a Filter Correlation Module (FCM) to generate the texture feature $\mathbf{T}$ . Finally, the semantic feature $\mathbf{M}$ and texture features $\{\mathbf{T}_i\}$ from all + +![](images/0afe748d92d2a42160efab0bcb719fa755426e889fd3ed2164d5f48f437657f3.jpg) +Figure 1. Overall structure of our network. The semantic branch produces a semantic feature $\mathbf{M}$ for the input image. The region selection gate selects impactful regions from a set of pre-defined region proposals. The texture branch generates a texture feature $\mathbf{T}$ for each of the selected regions that is zoomed into the size $S \times S$ . Finally, semantic feature $\mathbf{M}$ and texture features $\mathbf{T}$ from all selected regions are added for prediction. Note that, for simplicity of illustration, the figure only presents three region proposals for an image. In actual practice, the region proposals follow the same setting as RCNN [15], comprising multiple regions with different positions and scales. + +selected regions are added and fed into a fully connected layer to obtain the prediction. + +The subsequent sections are arranged as follows. In Sec. 3.2, we provide an introduction to Gabor filters, which are the key to our method to capture texture information. In Sec. 3.3, we illustrate the strategy to train our Gabor filters in a stable and effective manner. In Sec. 3.4, we elaborate on the statistical feature extractor that exploits informative statistical information from the output of Gabor filters. In Sec. 3.5, we introduce the gate mechanism that selects impactful regions into the texture branch for texture extraction. + +# 3.2. Gabor Filter + +The Gabor filter is a widely-used feature extractor in traditional image processing, owing to its biological relevance and powerful texture extraction ability. It has optimal joint localization in both spatial and frequency domains, which makes it possible to be effectively applied in both spatial- and frequency-wise analysis. In the spatial domain, a Gabor Filter is mathematically defined as follows: + +$$ +\begin{array}{l} g (x, y) = \frac {1}{2 \pi \sigma_ {x} \sigma_ {y}} \exp \left\{- \frac {1}{2} \left(\frac {\widetilde {x} ^ {2}}{\sigma_ {x} ^ {2}} + \frac {\widetilde {y} ^ {2}}{\sigma_ {y} ^ {2}}\right) \right\} \exp [ 2 \pi j W \widetilde {x} ]. (1) \\ \left\{ \begin{array}{l} \widetilde {x} = x \cos \theta + y \sin \theta \\ \widetilde {y} = - x \sin \theta + y \cos \theta \end{array} \right. (2) \\ \end{array} +$$ + +This representation can be regarded as a windowed Fourier transform, i.e., a Gaussian kernel function modulated by a sinusoidal plane wave. Specifically, $[\sigma_x,\sigma_y]$ defines the scale of the Gabor filter, and it can determine the effective size of a pixel's neighborhood where weighted summation occurs. $\theta$ defines the orientation of the filter. $W$ denotes the radial frequency of the sinusoid. These four parameters $\{\sigma_x,\sigma_y,\theta ,W\}$ can fully define a Gabor filter. By altering the parameters, different filters can be generated to capture different signal components. + +# 3.3. Learnable Gabor Filter Parameters + +An effective Gabor filter requires the appropriate combination of parameters to match a given task. Previous works [40, 30, 42] have generally used a hand-crafted approach for parameter selection, relying on heuristic rules to inform manual parameter settings. However, this kind of handcrafted approach is highly dependent on the expertise of the individual and cannot guarantee effectiveness for the task at hand. To address this limitation, we propose an alternative method that automatically learns the optimal parameters in a supervised manner, ensuring that the parameter combination can better fit the task. However, learning the parameters presents significant challenges. Firstly, during experimentation, erratic loss fluctuations are observed in the training process, indicating a lack of training stability (see the experimental section for details). Secondly, the features extracted by the trained network exhibit a substantial bias towards low-frequency information. The high-frequency information, on the other hand, occupies only a small fraction of all features. Specifically, only $6\%$ of the trained Gabor filters have a frequency parameter $W$ higher than 0.5. This tendency is mainly due to the regularity of commonly used activation and loss functions in deep learning (refer to [45, 33] for details), which is detrimental since the high-frequency information can be vital for fine-grained recognition. + +To ensure training stability and filter effectiveness, we propose two solutions to tackle the above problems. To address the first challenge, we propose constraining parameter values into a valid range, which is theoretically derived to avoid potential problems such as frequency aliasing that could hinder training stability. To address the second challenge, we propose a dual-range strategy to further regularize the frequency parameter $W$ , ensuring that sufficient high-frequency components can be extracted. These solutions enable our Gabor filters to be learned in a stable and ef + +fective manner. A detailed illustration of these solutions is presented in the subsequent sections. + +Learning Parameters under Constraints. We first introduce a novel parameter value constraint to enhance the stability of model training. Our approach is motivated by the analysis that training instability could be attributed to the mismatch between image properties and the ideal application scenario of Gabor filters. Specifically, Gabor filters are mathematically defined for infinite length signals [37]; the digital image signals, on the other hand, are finite in both spatial and frequency domains due to the limited length of image width and sampling frequency. As a result, directly applying Gabor filters to finite-length images may cause mathematical deficiency and distortion, leading to frequency aliasing and other issues that can impair model training [39]. To address this problem, we propose to concentrate most of the Gabor filter energy within the finite signal zone. This ensures that only a small amount of filter energy spills over the finite signal, minimizing the negative effects of using infinite-length-defined filters on finite-length images. Such a constraint could be implemented by limiting the value ranges of filter parameters, which determine the effective zone and energy concentration area of a Gabor filter. Specifically, according to the properties of Gabor filters and images mentioned above, we first derive $[0,\pi ],\left[\frac{5}{2\pi(1 - 2W)},\frac{S}{5}\right],\left[\frac{5}{2\pi},\frac{S}{5}\right]$ and $[0,\frac{2\pi S - 25}{4\pi S} ]$ to be the valid ranges for parameters $\theta ,\sigma_{x},\sigma_{y}$ and $W$ respectively (please refer to supplementary materials for a detailed derivation of these valid ranges). Next, we propose a constraint function to ensure each parameter to fall within its valid range. Specifically for a parameter $p$ with lower bound $l_{p}$ and upper bound $u_{p}$ , we propose to obtain $p$ through a learnable parameter $\mathbf{p}$ as follows: + +$$ +p = l _ {p} + \left(u _ {p} - l _ {p}\right) \mathrm {S i g m o i d} (\mathbf {p}) = \frac {u _ {p} + l _ {p} e ^ {- \mathbf {p}}}{1 + e ^ {- \mathbf {p}}}. (3) +$$ + +The parameter $\mathbf{p}$ can be learned to have any value ranging from $-\infty$ to $+\infty$ . By applying Eq. 3, parameter $p$ can be guaranteed to fall within its valid range $[l_p, u_p]$ . By doing so, parameter values are constrained to enhance the stability of training. + +High Frequency Enhancement. To address the frequency bias problem and improve high-frequency information extraction, we further propose a dual-constraint strategy for the frequency parameter $W$ . Specifically, we constrain half of Gabor filters to only exploit high-frequency components, making the network to capture sufficient high-frequency information for facilitating fine-grained recognition. This is enabled by setting two value intervals for $W$ : $[0, \frac{2\pi S - 25}{8\pi S}]$ and $[\frac{2\pi S - 25}{8\pi S}, \frac{2\pi S - 25}{4\pi S}]$ , which are equally divided from the valid range $[0, \frac{2\pi S - 25}{4\pi S}]$ of the frequency parameter. Let $N$ be the total number of Gabor filters to be learned. Using the method in Eq. 3, we constrain $W$ of $N / 2$ fil + +![](images/dd8d486a1acb36dc61fa34752fa98a2fb5991ff7d779f974f8ad06fdf6773ff2.jpg) +Figure 2. The structure of Learnable Histogram Operator (LHO). + +ters to fall between $[0, \frac{2\pi S - 25}{8\pi S}]$ and the other $N/2$ filters to fall between $\left[\frac{2\pi S - 25}{8\pi S}, \frac{2\pi S - 25}{4\pi S}\right]$ , such that they serve as the low-frequency expert and high-frequency expert respectively. This strategy enhances the extraction ability of high-frequency information, alleviating the frequency bias problem in traditional DNNs where high-frequency features are difficult to extract. + +# 3.4. Statistical Feature Extractor + +The above method enables Gabor filters to be trained stably and effectively in a deep learning framework. These filters can capture texture signals from an input image. In the next step, we target at extracting effective features from these filters to facilitate fine-grained recognition. From the perspective of digital image processing, texture can be represented by the statistical properties of feature maps [16]. Based on this principle, in some previous research [40, 4, 1], textures were exploited by extracting hand-crafted statistics such as variance, contrast and smoothness from the output of Gabor filters. However, these statistics have limited effectiveness because they are hand-crafted designed. In this work, we step further and take advantage of deep learning to extract deep statistical features that are more comprehensive and effective. Specifically, we propose a novel statistical feature extractor that contains a Learnable Histogram Operator (LHO) followed by a Filer Correlation Module (FCM). In the following sections, we provide a detailed illustration of QCO and FCM respectively. + +Learnable Histogram Operator. We first employ a Learnable Histogram Operator (LHO) to exploit statistical information, which is improved from [58]. Fig. 2 illustrates the structure of LHO. LHO receives the output from each Gabor filter as input and produces a statistical feature $\mathbf{S} \in \mathbb{R}^{C}$ , where $C$ refers to the channel number. Let $\mathbf{I} \in \mathbb{R}^{S \times S}$ be the intensity map generated by convolving a Gabor filter with the processed image, where $S$ refers to image size. LHO first defines $M$ levels by equally dividing the minimal and maximal values for intensities of all pixels. Specifically, the $m$ -th level $\mathbf{L}^{m}$ is computed as: + +$$ +\mathbf {L} ^ {m} = \min (\mathbf {I}) + \frac {\max (\mathbf {I}) - \min (\mathbf {I})}{M} \cdot m \tag {4} +$$ + +Next, each pixel $\mathbf{I}^{i,j}$ on $\mathbf{I}$ is quantized to a vector $\mathbf{V}^{i,j} \in$ + +$\mathbb{R}^M$ . Concretely, let $I$ be the interval between adjacent levels $(I = \mathbf{L}^{m + 1} - \mathbf{L}^m)$ , the $m$ -th channel $\mathbf{V}^{i,j,m}$ on $\mathbf{V}^{i,j}$ is computed as follows: + +$$ +\mathbf {V} ^ {i, j, m} = \left\{ \begin{array}{l l} 1 - \left| \mathbf {L} ^ {m} - \mathbf {I} ^ {i, j} \right| & \text {i f} \left| \mathbf {L} ^ {m} - \mathbf {I} ^ {i, j} \right| < \frac {I}{2} \\ 0 & \text {e l s e} \end{array} \right. \tag {5} +$$ + +In this way, $\mathbf{I}$ is quantized to $\mathbf{V} \in \mathbb{R}^{S \times S \times M}$ . Note a spire-shaped function is used for quantization instead of a binary one to ensure that the operation is differentiable. After the quantization, the number of pixels that fall into each level is counted and normalized to obtain a counting feature $\mathbf{C} \in \mathbb{R}^M$ . Specifically, $\mathbf{C}^m$ for the $m$ -th level is computed as: + +$$ +\mathbf {C} ^ {m} = \frac {\sum_ {i = 1} ^ {S} \sum_ {j = 1} ^ {S} \mathbf {V} ^ {i , j , m}}{\sum_ {m = 1} ^ {M} \sum_ {i = 1} ^ {S} \sum_ {j = 1} ^ {S} \mathbf {V} ^ {i , j , m}}. \tag {6} +$$ + +We concatenate $\mathbf{C}^m$ with $\mathbf{L}^m$ , and obtain the feature $\mathbf{F}^m$ for the $m$ -th quantization level as follows: + +$$ +\mathbf {F} ^ {m} = \phi (\operatorname {C A T} \left(\mathbf {C} ^ {m}, \mathbf {L} ^ {m}\right)) + \mathbf {P} ^ {m}, \tag {7} +$$ + +where $\phi$ refers to a linear layer. $\mathbf{P}^m\in \mathbb{R}^C$ encodes the position information for pixels quantized to the $m$ -th level, which is computed as the weighted sum of position features from all pixels as follows: + +$$ +\mathbf {P} ^ {m} = \sum_ {i = 1} ^ {S} \sum_ {j = 1} ^ {S} \mathbf {V} ^ {i, j, m} \mathrm {P E} (i, j), \tag {8} +$$ + +where PE refers to the position encoding operation as in vit [8]. Finally, the statistical texture $\mathbf{S}$ is produced by correlating features from different levels: + +$$ +\mathbf {S} = \operatorname {A v g} \left(\operatorname {M H A} \left(\left\{\mathbf {F} ^ {m} \right\} _ {m = 1} ^ {M}\right)\right), \tag {9} +$$ + +where MHA denotes a multi-head attention and Avg refers to the average over all levels. Using LHO has two advantages. Firstly, it can be considered as a way to extract deep features from a differentiable and learnable histogram, which can produce effective and appropriate statistical features that can benefit the task [16, 58]. Secondly, conventional statistical features are typically pixel-relationship-invariant. For example, rearranging pixel positions does not alter the mean and variance values. In contrast, our method is pixel-relationship-aware as it encodes $\mathbf{P}^m$ that represents the position information of pixels quantized to each level, which provides additional information that can be useful for fine-grained recognition. These advantages enable the extracted features from LHO to be effective in facilitating fine-grained recognition. + +Filter Correlation Module. The proposed LHO can produce a statistical feature from the output of each Gabor filter, resulting in a set of features $\{\mathbf{S}^n\}_{n=1}^N$ for all filters. We + +further propose a Filter Correlation Module (FCM) to aggregate statistical information from all Gabor filters as follows: + +$$ +\mathbf {T} = \operatorname {A v g} \left(\operatorname {M H A} \left(\left\{\mathbf {S} ^ {n} + \phi \left(\sigma_ {x} ^ {n}, \sigma_ {y} ^ {n}, \theta^ {n}, W ^ {n}\right) \right\} _ {n = 1} ^ {N}\right)\right), \tag {10} +$$ + +in which $\mathbf{S}^n$ refers to the statistical feature for the $n$ -th Gabor filter. $\phi(\sigma_x^n, \sigma_y^n, \theta^n, W^n)$ uses a linear layer to encode filter parameter information, which can indicate the type of texture extracted by the Gabor filter. Eq. 10 exploits the correlations among different texture components from different Gabor filters, generating a powerful feature with long-range correlations that can facilitate fine-grained recognition. + +# 3.5. Region Selection Gate + +Through the methods outlined above, we can build a powerful feature extractor that captures texture information using Gabor filters. As a common practice used by previous methods, the extractor can generate features in an image-based [40] manner or a patch-based manner [39]. Image-based methods directly feed the whole image into the extractor, which might lead to the blurring of local detailed information. Patch-based methods address the problem by equally dividing the image into several patches and extracting a feature from each patch. However, it is computationally expensive as each image position must be processed by the feature extractor. Intuitively, the texture information in different regions of an image is not equally important. For example, some regions may contain critical textures for recognition, such as feather of the bird, while others may be less informative, consisting of background textures such as sky, road and lawn. Therefore, extracting textures from all positions is redundant and computationally inefficient, which can impede recognition accuracy and slow down algorithmic speed. To address the issue, we propose a novel approach to solely extract textures from informative regions that are automatically selected from a gate mechanism. More specifically, the gate mechanism for region selection involves three steps. Firstly, we introduce a shallow FPN block that takes the intermediate features of the CNN-based semantic branch as inputs and generates a feature map $F$ . Please refer to supplementary materials for a detailed description for the structure of this block. Since features from the CNN branch have a high receptive field and contain rich semantic information, $F$ can identify key parts of an image and assist in selecting class-discriminative regions in appropriate positions. Secondly, we introduce a set of regions proposals, denoted as $\{\mathcal{R}^k\}_{k=1}^K$ , which is the same as that in RCNN [15], comprising regions with different scales and positions. For each region $\mathcal{R}^k$ , a feature vector $f^k$ is generated by performing an RoI pooling on the corresponding region of the feature map $F$ . This feature vector is then fed into a linear layer to generate a score $s^k$ . + +Lastly, regions that require texture extraction are selected based on their scores. This mechanism enables only the regions that contain class-discriminative information to be selected for texture extraction, thereby reducing computation costs and avoiding information redundancy. + +To reduce computation for capturing texture features, we expect 'hard' selections instead of the 'soft' attention scores to be generated so that only a limited number of regions need texture extraction. However, such a hard selection may prohibit the gradients to be back-propagated to the earlier layers in optimization. To address this issue, we employ the Improved Semantic Hashing [24, 25] for region selection. In training, to encourage more decision space to be explored randomly, we add a standard Gaussian noise $\epsilon$ to $s^k$ , resulting in the noise-injected score $\hat{s}^k$ . Then two vectors are generated as follows: + +$$ +c ^ {k} = \sigma^ {\prime} (\hat {s} ^ {k}); d ^ {k} = \mathbb {1} (\hat {s} ^ {k} > 0), \tag {11} +$$ + +where $\sigma^{\prime}$ refers to the saturating Sigmoid function: + +$$ +\sigma^ {\prime} (\hat {s} ^ {k}) = \max (0, \min (1, 1. 2 \sigma (\hat {s} ^ {k}) - 0. 1)), \tag {12} +$$ + +where $\sigma$ denotes the original Sigmoid function. In this way, $d^{k}$ is a binarized discrete feature with value $\{0,1\}$ , which is used for making the selection decision. $c^{k}$ is a continuously differentiable vector that can be used to approximate gradients in back-propagation, whose details are presented in supplementary materials. + +Discussion with Previous Methods. Note that the proposed region gate mechanism differs from other key part localization methods used for fine-grained recognition. Unlike existing methods, our method can be trained end-to-end and generate hard decisions without the need for extra annotations. These properties enable our method to be highly effective and practical for region selection. Conversely, existing key part localization techniques have several limitations. For example, some methods [20, 43] require extra annotations such as bounding box and key points for joint training; [14] uses an indifferentiable selection process, making the network unable to be trained end-to-end; other methods [7, 21] typically produce soft attention rather than hard decisions, which cannot reduce computation costs. Our approach can be more practical and effective benefiting from our careful designs. + +# 3.6. Optimization + +The proposed network is optimized by the following loss function: + +$$ +\mathcal {L} = L _ {c e} (p, l) + \lambda \sum_ {k = 1} ^ {K} d ^ {k}, \tag {13} +$$ + +where $L_{ce}$ denotes the cross-entropy loss. $p$ and $l$ are the prediction logits and ground truth label. $d^{k}$ denotes the binarized discrete decision as in Eq. 11. The second item + +
MethodBackboneAccuracy
ResNet50 [17]ResNet5084.5
ResNet101 [17]ResNet10185.5
DenseNet161 [19]DenseNet16185.5
PC-Dense161 [9]DenseNet16186.9
NTSNet [48]ResNet5087.5
Cross-X [34]ResNet5087.7
DCL [3]ResNet5087.8
S3N [7]ResNet5088.5
iSQRT-COV [27]ResNet10188.7
GaRD [54]ResNet5089.6
APINet [59]DenseNet16190.0
OursResNet5090.8
OursResNet10191.3
OursDenseNet16191.5
+ +Table 1. Comparison results on CUB-200-2011 dataset. + +in Eq. 13 encourages fewer regions to be selected, thus avoiding the redundant information and reducing computation costs. $\lambda$ is a hyper-parameter to control the trade-off between the two loss items. + +# 4. Experiments + +# 4.1. Implementation Details + +Following [59], we adopt different networks as the semantic branch, including ResNet50, ResNet101 and DenseNet161. We use SGD as the optimizer with the momentum of 0.9. The initial learning rate is set to 1e-4, which decays by 0.1 for every 20 epochs (overall 100 epochs). Batch size is 16 for all datasets. Following previous works [54, 28], we use random cropping of $448 \times 448$ in training and center crop at inference. We apply the commonly-used data augmentation strategies for training, including random scaling, left-right flipping and random cropping. $S$ indicating the size of regions that are zoomed in is set to 112. $N$ indicating the number of learnable Gabor filters is set to 128. $M$ indicating the number of quantization levels in QCO is set to 8. $\lambda$ in Eq. 13 is set to 0.2. Experiments are conducted on 2 NVIDIA Titan V100 GPUs. + +# 4.2. Comparison with State-of-the-art + +We evaluate our method on four datasets, including three fine-grained datasets CUB-200-2011, NA-bird, Stanford Dogs and a terrain recognition dataset GTOS-mobile. The comparison results on these datasets are presented in Tables 1, 2, 3, and 4, respectively. Our method achieves the best performance when using DenseNet161 as the semantic branch, reaching accuracy scores of 91.5, 90.4, 92.1 and 87.5, outperforming the second-best method by 1.5, 2.3, 1.8 and 4.8, respectively. It is worth noting that even when using ResNet50, the least effective backbone among the three, our method remains superior to all other compared methods. This highlights the high effectiveness of our method. The advantage of our method is especially significant on the challenging terrain dataset GTOS-mobile. This is due to our + +
MethodBackboneAccuracy
ResNet50 [17]ResNet5082.2
ResNet101 [17]ResNet10182.9
DenseNet161 [19]DenseNet16183.1
Cross-X [34]ResNet5086.4
GaRD [54]ResNet5088.0
APINet [59]DensetNet10188.1
OursResNet5089.5
OursResNet10190.0
OursDenseNet16190.4
+ +Table 2. Comparison results on NA-bird dataset. + +
MethodBackboneAccuracy
ResNet50 [17]ResNet5080.1
ResNet101 [17]ResNet10180.6
DenseNet161 [19]DenseNet16180.9
PC-Dense161 [9]DenseNet16182.8
Cross-X [34]ResNet5088.9
APINet [59]ResNet10190.3
OursResNet5091.0
OursResNet10191.7
OursDenseNet16192.1
+ +Table 3. Comparison results on Stanford Dogs dataset. + +
MethodBackboneAccuracy
ResNet50 [17]ResNet5069.4
ResNet101 [17]ResNet10172.0
DenseNet161 [19]DenseNet16172.9
B-CNN [28]ResNet5075.8
Deep-TEN [51]ResNet5076.1
DEP [47]ResNet5082.7
OursResNet5086.4
OursResNet10187.0
OursDenseNet16187.5
+ +Table 4. Comparison results on GTOS-mobile dataset. + +
MethodAccuracyFlops(G)Params(M)
Baseline (ResNet50)84.516.2624.69
+ TB & RSG90.820.7232.41
+ TB (image-based manner)89.036.8829.82
+ TB (patch-based manner)89.937.0429.82
+ +method's ability to extract texture features, which are essential for the classification of visually-similar and closely-related terrain classes. + +# 4.3. Ablation Study + +We perform ablation study to verify the effectiveness of our designs. Experiments in this part are conducted on CUB-200-2011 dataset with ResNet50 as the semantic branch. Due to paper length limitation, more ablation study results are presented in supplementary materials. + +Ablation of Different Components. As shown in Fig. 1, in addition to the basic CNN-based semantic branch, our method consists of two key components: a Gabor-filter-based texture branch (TB) and a region selection gate (RSG). We conduct experiments to validate the effect of these components and present the results in Table. 5, which includes the validation accuracy, computation costs and parameter numbers of different settings. We set the network that only has a ResNet50 semantic branch to be the baseline. Our method with adding both texture branch & region selection gate increases accuracy from 84.5 to 90.8. When the region selection gate is removed, extracting textures by feeding the whole image into texture branch (image-based manner) reduces accuracy to 89.0 and increases computation by $78\%$ ; equally dividing image into $8 \times 8$ patches and getting a feature from each patch (patch-based manner) reduces accuracy to 89.0 and increases computation by $79\%$ . The results demonstrate that the region selection gate can reduce computation and improve performance. + +Ablation of Learnable Gabor Filters. Results in this part are presented in Table. 6. (1) First, we validate the effectiveness of Gabor filters. Replacing all Gabor filters by the $3 \times 3$ convolution layers decreases accuracy by 4.9. This indicates that the improvement does not simply come from + +Table 5. Ablation results of different components in our method. TB and RSG refer to the texture branch and region selection gate, respectively. + +
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours replacing Gabor filters with conv85.920.0332.95
Ours w/o parameter learning86.520.7232.41
Ours w/o parameter value constraints75.420.4032.41
Ours w/o high frequency enhancement88.120.4032.41
+ +Table 6. Ablation results of learnable Gabor filters. + +an increase in the number of parameters, but from the effectiveness of using Gabor filters for texture extraction. (2) Second, we evaluate the effectiveness of learning Gabor filter parameters in a supervised manner. We replace the learnable parameters with the manually set ones, where the setting rules are the same as [40]. This reduces accuracy by 4.3, showing the effectiveness of supervised learning. (3) Third, we verify the necessity of using parameter value constraints. In Fig. 3, we present the loss curves and validation accuracy curves for methods w/ and w/o using value constraints. Using value constraints results in a smoother loss decline curve and accuracy improvement curve. In contrast, free training causes violent loss and accuracy fluctuations, especially at the beginning stage of training, indicating that the training process is unstable. Compared to free training, using value constraints significantly improves validation accuracy by 15.4. (4) Last, we evaluate the high frequency enhancement strategy by setting two constraints for frequency parameter $W$ . Without the strategy and directly constraining $W$ into its valid range reduces accuracy by 2.7. Results demonstrate the effectiveness of our designs for the learnable Gabor filter parameters. Also note, using the proposed learning methods requires no extra parameters and only increases computation very slightly. + +Ablation of Statistical Feature Extractor. We propose a statistical feature extractor to leverage texture information from the output of Gabor filters. The extractor consists of two parts: a Learnable Histogram Operator (LHO) and a Filter Correlation Module (FCM). We conduct experiments to validate the effect of these components and present the results in Table 7. Removing LHO and FCM reduces accuracy from 90.8 to 87.0 and 89.2 respectively. Also note that, both LHO and FCM are lightweight, only requiring extra parameters of 4.26M and 3.56M, increasing flops by + +![](images/bf6ae535852da6a1dcdd7c64b18b1eea0527101f1ccae213b2d3631a0c90ea3c.jpg) +(a) Loss Curves + +![](images/b351441b6dfa7ae12b45b924a280075ac904eb290b5476753da49e8ebe784df4.jpg) +(b) Accuracy Curves +Figure 3. Loss curves (a) and accuracy curves (b) in different settings. Blue and orange lines indicate curves for training Gabor filters w/ and w/o using parameter value constraints, respectively. + +
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours w/o LHO87.018.0328.25
Ours w/o FCM89.219.5528.85
+ +$15\%$ and $6\%$ respectively. Results show the high effectiveness and efficiency of LHO and FCM. + +Ablation of LHO. In Table. 8, we further evaluate the designs in LHO. First, we replace LHO with a hand-crafted statistical feature composed of mean, variance, maximum and minimum values, which reduces accuracy by 2.9. This demonstrates that LHO can produce statistical features that are more effective than hand-crafted ones widely used by previous methods. Next, we remove position information $\mathbf{P}^m$ in Eq. 7 and multi-head attention in Eq. 9, which reduces accuracy by 1.5 and 2.1 respectively, showing the importance of encoding position features and correlating different levels in LHO. Finally, we move LHO from texture branch to CNN-based semantic branch. This reduces accuracy by 4.6, showing that the effectiveness of LHO relies on Gabor filters to extract texture-related signals. + +# 4.4. Visualization + +In Fig. 4, we provide a visualization of the outputs obtained from learned Gabor filters. More specifically, Fig. 4 (c) and Fig. 4 (d) show the average output of all high-frequency and low-frequency Gabor filters, respectively. As can be observed, the high-frequency filters primarily capture information of undulating areas such as speckles and ripples, whereas the low-frequency filters primarily capture information related to smooth changing areas. Both these two kinds of information are critical for recognition. By exploiting sufficient and balanced multi-frequency features through the carefully-designed learnable Gabor filters, our method can leverage comprehensive information for effective fine-grained recognition. Due to space limitation, more visualization results are presented in supplementary. + +# 4.5. Discussion of Computation and Parameter + +Compared to the ResNet50 baseline, our method only increases computation and parameter usage slightly. Specifically, on CUB-200-2011 dataset, ResNet50 consumes + +![](images/ba6445037c1dc92259f4bf6f798dcd8024b90e93da4191a6c15cbcd72746e386.jpg) + +![](images/74c34d6ccfbd2aef9561cec30d558a45974f90da9e01cef6a545c74a2e2cfc5a.jpg) +(a) Image +Figure 4. Visualization of Gabor filters. (a), (b), (c) and (d) present the original images, the selected regions, average output of all high-frequency and low-frequency Gabor filters, respectively. + +![](images/b4de533b1dc2e946bb7f2255b0059b4aba494dac5e9404578de4945f51194eab.jpg) + +![](images/42b275e5eec7ef8305390bb74e780a97e1eab92c5f17916d56b3f43a3283a102.jpg) +(b) Region +(c) High-W Filters + +![](images/26ca61c2fcd32aa9c29556f4a9cef283f37a8eda80a925da8da2c31bed412e04.jpg) + +![](images/51140dae4b5ecba74b885c9ebcec3e8ec52038466912431c72748573acc4bc7f.jpg) + +![](images/e291067c22ed8beb39fa6e2b994b57b24f760f8514b560868c7aabc38270a716.jpg) +(d) Low-W Filters + +Table 7. Ablation results of statistical feature extractor. + +
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours w/o LHO w/ HSF87.918.1628.25
Ours w/o Pm in Eq. 789.318.5030.93
Ours w/o MHA in Eq.988.719.4929.73
Ours w/o LHO in TB w/ LHO in CNN86.222.8532.90
+ +Table 8. Ablation results of LHO. HSF refers to a hand-crafted statistical feature composed of mean, variance, maximum and minimum values. MHA denotes multi-head attention. TB denotes texture branch. + +16.26G flops of computation, requiring 24.69M parameters, reaching accuracy of 84.5. Our method consumes 20.72G flops of computation, requiring 32.41M parameters, reaching accuracy of 90.8. Compared to ResNet50, our method can improve accuracy significantly (+6.3) with only increasing computation and parameter usage by $27\%$ and $31\%$ respectively. This demonstrates the high effectiveness and high efficiency of our method with outstanding performance and reasonable computation costs. + +# 5. Conclusion + +This paper presents a novel network that extracts texture features to facilitate fine-grained recognition using Gabor filters. We make the Gabor filter parameters to be automatically learned in a stable and effective manner through our carefully-designed value constraint strategies. We also propose a statistical feature extractor and a region selection gate, allowing informative and effective Gabor texture features to be extracted with very few extra computation costs. Our method is effective, as shown by the extensive experiments with state-of-the-art (SOTA) performance. + +Acknowledgement This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-08-006), Singapore Ministry of Education (MOE) AcRF Tier 2 under Grant MOE-T2EP20222-0009, the National Research Foundation Singapore through AI Singapore Programme under Grant AISG-100E-2020-065, and SUTD SKI Project under Grant SKI 2021_02_06. + +# References + +[1] Jon Arrospide and Luis Salgado. Log-gabor filters for image-based vehicle verification. 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Existing works have demonstrated the possibility of applying deep CNNs to exploit features that distinguish similar classes. However, CNNs suffer from problems including frequency bias and loss of detailed local information, which restricts the performance of recognizing fine-grained categories. To address the challenge, we propose a novel texture branch as complimentary to the CNN branch for feature extraction. We innovatively utilize Gabor filters as a powerful extractor to exploit texture features, motivated by the capability of Gabor filters in effectively capturing multi-frequency features and detailed local information. We implement several designs to enhance the effectiveness of Gabor filters, including imposing constraints on parameter values and developing a learning method to determine the optimal parameters. Moreover, we introduce a statistical feature extractor to utilize informative statistical information from the signals captured by Gabor filters, and a gate selection mechanism to enable efficient computation by only considering qualified regions as input for texture extraction. Through the integration of features from the Gabor-filter-based texture branch and CNN-based semantic branch, we achieve comprehensive information extraction. We demonstrate the efficacy of our method on multiple datasets, including CUB-200-2011, NA-bird, Stanford Dogs, and GTOS-mobile. State-of-the-art performance is achieved using our approach." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 588, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 288, + 696 + ], + "type": "text", + "content": "Recognizing fine-grained categories (e.g., different flower types or bird species) is challenging due to the subtle differences in their visual appearance. Recently, deep neural network technology [17, 8, 31, 57, 52, 12] has made remarkable advancement, allowing for significant progress in extracting deep class-discriminative features for fine-grained recognition [10, 38, 41, 23, 3, 56]. For example, [54] develops a graph-based module to extract cross-class relationship features. [13, 26] use bilinear pooling to ex" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 228, + 546, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 546, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 546, + 288 + ], + "type": "text", + "content": "ploit high-order features from different networks. [55, 38] leverage multi-scale information to enhance feature effectiveness. The success of these methods highlights the crucial role of extracting powerful features in distinguishing fine-grained categories." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 291, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 547, + 555 + ], + "type": "text", + "content": "To exploit class-discriminative features, previous methods [38, 41, 23, 3, 56] have primarily relied on convolutional neural networks (CNNs) as the model backbone. CNNs have achieved significant success in many computer vision tasks. However, due to the following limitations, they may not be sufficient for capturing comprehensive information in fine-grained recognition. First, deep CNNs generally extract information with high receptive fields and resolution-reduced feature maps, leading to the loss of local detailed information that is critical for fine-grained recognition. Second, as discussed in [33, 45, 46], due to the regularity of the commonly used activation [45] and loss functions [33], CNNs prioritize learning low-frequency components while ignoring high-frequency components. This bias is detrimental to fine-grained classification, as the ignored high-frequency information, such as ripples and spots in bird feathers, can be important in distinguishing between similar classes. Considering these limitations of CNNs, we suggest that a more powerful feature extractor is required, which should be able to capture local detailed information and multi-frequency comprehensive features that are lost by CNNs but crucial for fine-grained recognition." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "type": "text", + "content": "Witnessing the challenge, in this work, we introduce a novel branch that extracts texture features as complimentary to the vanilla CNN features to facilitate fine-grained recognition. We employ Gabor filters as the texture extractor in the novel branch. The Gabor filter is a windowed Fourier transform that combines a sinusoidal signal with a Gaussian wave. It is widely used in image processing for extracting low-level texture features [30, 35, 29, 1, 40]. The motivations of using Gabor filters in fine-grained recognition can be illustrated in two-folds. (1) First, Gabor filters are effective in capturing local-detailed information. Previous research [5, 6] has found that Gabor functions are similar to the receptive field profiles in the mammalian cortical sim" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1621" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "ple cells. This indicates that Gabor filters can perform the similar function as cortical cells to capture effective and locally detailed texture information, which is critical for recognizing confusing samples. (2) Second, Gabor filters can extract sufficient high-frequency information. A Gabor filter contains a parameter that directly controls the frequency of the extracted information. It is therefore possible to exploit sufficient high-frequency components by constraining the parameters of some filters into a high-value range, overcoming the frequency-bias limitations of traditional CNNs. Benefiting from these advantages, our introduction of Gabor filters enables texture features to be extracted as an effective supplement to the typical CNN features for improving fine-grained recognition." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 430 + ], + "type": "text", + "content": "Utilizing Gabor filters in an effective manner is nontrivial. Previous methods with Gabor filters generally rely on hand-crafted designs for filter parameter setting, which cannot guarantee to be optimal. To overcome this limitation, we propose an approach to automatically learn parameters in a supervised manner, in which a value constraint strategy is used to stabilize the learning and enhance high-frequency information extraction. To extract effective information with Gabor filters, we further propose a statistical feature extractor to capture texture features from the Gabor response maps. We also introduce a gate mechanism that selects a limited number of appropriate regions as inputs to the texture branch, thereby reducing computational costs and avoiding information redundancy. These careful designs allow Gabor filters to benefit fine-grained recognition in an effective and efficient manner." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 431, + 289, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 289, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 289, + 670 + ], + "type": "text", + "content": "To the best of our knowledge, our work pioneers to learn texture features using Gabor filters in the task of fine-grained recognition. We perform extensive experiments on four datasets, which demonstrate the effectiveness of our method. Benefiting from the powerful texture features from the Gabor filters, our network can leverage the informative and comprehensive information for recognition, resulting in state-of-the-art (SOTA) performance on all datasets. To summarize, our contributions are as follows. (1) First, we pioneer learning Gabor filters in fine-grained recognition. The texture features extracted from Gabor filters serve as an effective supplement to the vanilla CNN features, significantly improving recognition performance. (2) Second, to enhance model effectiveness and efficiency, we implement several key designs based on Gabor filters, including the parameter learning method, a powerful Gabor feature extractor and a region selection gate. (3) Third, extensive experiments demonstrate the effectiveness of our method with state-of-the-art (SOTA) performance achieved on four datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 675, + 134, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 675, + 134, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 675, + 134, + 687 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": "Fine-Grained Recognition. The goal of fine-grained recognition is to classify classes that are visually similar." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "type": "text", + "content": "Recent methods for the task can be categorized into two major types: feature-encoding methods [13, 49, 26, 9, 10, 38, 41, 23, 3, 56] and localization methods [20, 43, 2, 21, 44, 7, 36, 11]. Feature-encoding methods emphasize on extracting effective features for the better classification results. For example, some methods [13, 49, 26] use bilinear pooling to obtain informative high-level features. Other works [9, 10] use feature constraints to enhance feature effectiveness. [38, 41, 23, 3] extract multi-level features to get comprehensive information. [54] exploits cross-class relationships to capture class-discriminative features. Localization methods emphasize on selecting the most effective regions to capture features. [20, 43, 2] use extra annotations such as bounding boxes and key points to promote the localization ability of the network. [21, 44, 7, 36] select informative regions through activation maps. Different from these works, our method innovatively learns Gabor filter to effectively capture texture information. Additionally, the region selection gate in our method can be end-to-end trained without the need for additional annotation, giving it a unique advantage." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 323, + 547, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 547, + 468 + ], + "type": "text", + "content": "Gabor Filters. The Gabor filter is an effective tool for extracting texture features, which makes it widely used in various computer vision applications such as face recognition [30, 35, 29], vehicle verification [1], object detection [42, 22, 39] and gait recognition [40]. Recently, some works [18, 32, 50, 53] introduce Gabor filters into deep neural networks. However, these approaches have suffered from problems like unstable training, frequency bias and high computation costs, leading to low effectiveness and efficiency. Our method addresses the challenges faced by previous approaches through our careful designs, making Gabor filters to be effectively applied in fine-grained recognition." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 472, + 362, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 362, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 362, + 483 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 486, + 411, + 497 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 411, + 497 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 411, + 497 + ], + "type": "text", + "content": "3.1. Overall Structure" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": "Fig. 1 provides an overview of our approach. A semantic branch takes the entire image as input and generates a semantic feature " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " through a vanilla CNN. Using intermediate features from the semantic branch, a gate mechanism selects impactful regions from the image. After that, each of the selected regions " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " is zoomed into the size " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "S\\times S" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " and fed into a texture branch to produce a texture feature " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": ". The texture branch comprises " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " learnable Gabor filters followed by a statistical feature extractor that performs the following two-step workflow. First, each learnable Gabor filter is convolved with the input region to generate an intensity map " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": ". In this way, for all the " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " learnable Gabor filters, a set of maps " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{I}^n\\}_{n = 1}^N" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " are generated. Next, the statistical feature extractor processes each " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^n\\in \\{\\mathbf{I}^n\\}_{n = 1}^N" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " through a Learnable Histogram Operator (LHO) and then passes the resulting " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}^n\\}_{n = 1}^N" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " through a Filter Correlation Module (FCM) to generate the texture feature " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": ". Finally, the semantic feature " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " and texture features " + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{T}_i\\}" + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": " from all" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1622" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 547, + 210 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 210 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 210 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 210 + ], + "type": "image", + "image_path": "0afe748d92d2a42160efab0bcb719fa755426e889fd3ed2164d5f48f437657f3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "text", + "content": "Figure 1. Overall structure of our network. The semantic branch produces a semantic feature " + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "text", + "content": " for the input image. The region selection gate selects impactful regions from a set of pre-defined region proposals. The texture branch generates a texture feature " + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "text", + "content": " for each of the selected regions that is zoomed into the size " + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "inline_equation", + "content": "S \\times S" + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "text", + "content": ". Finally, semantic feature " + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "text", + "content": " and texture features " + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 213, + 547, + 269 + ], + "type": "text", + "content": " from all selected regions are added for prediction. Note that, for simplicity of illustration, the figure only presents three region proposals for an image. In actual practice, the region proposals follow the same setting as RCNN [15], comprising multiple regions with different positions and scales." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 287, + 312 + ], + "type": "text", + "content": "selected regions are added and fed into a fully connected layer to obtain the prediction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 312, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 419 + ], + "type": "text", + "content": "The subsequent sections are arranged as follows. In Sec. 3.2, we provide an introduction to Gabor filters, which are the key to our method to capture texture information. In Sec. 3.3, we illustrate the strategy to train our Gabor filters in a stable and effective manner. In Sec. 3.4, we elaborate on the statistical feature extractor that exploits informative statistical information from the output of Gabor filters. In Sec. 3.5, we introduce the gate mechanism that selects impactful regions into the texture branch for texture extraction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 420, + 129, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 129, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 129, + 431 + ], + "type": "text", + "content": "3.2. Gabor Filter" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 433, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 433, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 287, + 515 + ], + "type": "text", + "content": "The Gabor filter is a widely-used feature extractor in traditional image processing, owing to its biological relevance and powerful texture extraction ability. It has optimal joint localization in both spatial and frequency domains, which makes it possible to be effectively applied in both spatial- and frequency-wise analysis. In the spatial domain, a Gabor Filter is mathematically defined as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 522, + 287, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 590 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} g (x, y) = \\frac {1}{2 \\pi \\sigma_ {x} \\sigma_ {y}} \\exp \\left\\{- \\frac {1}{2} \\left(\\frac {\\widetilde {x} ^ {2}}{\\sigma_ {x} ^ {2}} + \\frac {\\widetilde {y} ^ {2}}{\\sigma_ {y} ^ {2}}\\right) \\right\\} \\exp [ 2 \\pi j W \\widetilde {x} ]. (1) \\\\ \\left\\{ \\begin{array}{l} \\widetilde {x} = x \\cos \\theta + y \\sin \\theta \\\\ \\widetilde {y} = - x \\sin \\theta + y \\cos \\theta \\end{array} \\right. (2) \\\\ \\end{array}", + "image_path": "7da00c33c39beb6a7f5b6f8cd8eff5f2e54f15f37e6e769e5ca5a42c33c9d2be.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "This representation can be regarded as a windowed Fourier transform, i.e., a Gaussian kernel function modulated by a sinusoidal plane wave. Specifically, " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "[\\sigma_x,\\sigma_y]" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " defines the scale of the Gabor filter, and it can determine the effective size of a pixel's neighborhood where weighted summation occurs. " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " defines the orientation of the filter. " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " denotes the radial frequency of the sinusoid. These four parameters " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{\\sigma_x,\\sigma_y,\\theta ,W\\}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " can fully define a Gabor filter. By altering the parameters, different filters can be generated to capture different signal components." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 287, + 495, + 299 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 287, + 495, + 299 + ], + "spans": [ + { + "bbox": [ + 305, + 287, + 495, + 299 + ], + "type": "text", + "content": "3.3. Learnable Gabor Filter Parameters" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 306, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 593 + ], + "type": "text", + "content": "An effective Gabor filter requires the appropriate combination of parameters to match a given task. Previous works [40, 30, 42] have generally used a hand-crafted approach for parameter selection, relying on heuristic rules to inform manual parameter settings. However, this kind of handcrafted approach is highly dependent on the expertise of the individual and cannot guarantee effectiveness for the task at hand. To address this limitation, we propose an alternative method that automatically learns the optimal parameters in a supervised manner, ensuring that the parameter combination can better fit the task. However, learning the parameters presents significant challenges. Firstly, during experimentation, erratic loss fluctuations are observed in the training process, indicating a lack of training stability (see the experimental section for details). Secondly, the features extracted by the trained network exhibit a substantial bias towards low-frequency information. The high-frequency information, on the other hand, occupies only a small fraction of all features. Specifically, only " + }, + { + "bbox": [ + 304, + 306, + 545, + 593 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 304, + 306, + 545, + 593 + ], + "type": "text", + "content": " of the trained Gabor filters have a frequency parameter " + }, + { + "bbox": [ + 304, + 306, + 545, + 593 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 306, + 545, + 593 + ], + "type": "text", + "content": " higher than 0.5. This tendency is mainly due to the regularity of commonly used activation and loss functions in deep learning (refer to [45, 33] for details), which is detrimental since the high-frequency information can be vital for fine-grained recognition." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "To ensure training stability and filter effectiveness, we propose two solutions to tackle the above problems. To address the first challenge, we propose constraining parameter values into a valid range, which is theoretically derived to avoid potential problems such as frequency aliasing that could hinder training stability. To address the second challenge, we propose a dual-range strategy to further regularize the frequency parameter " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ", ensuring that sufficient high-frequency components can be extracted. These solutions enable our Gabor filters to be learned in a stable and ef" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1623" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "fective manner. A detailed illustration of these solutions is presented in the subsequent sections." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": "Learning Parameters under Constraints. We first introduce a novel parameter value constraint to enhance the stability of model training. Our approach is motivated by the analysis that training instability could be attributed to the mismatch between image properties and the ideal application scenario of Gabor filters. Specifically, Gabor filters are mathematically defined for infinite length signals [37]; the digital image signals, on the other hand, are finite in both spatial and frequency domains due to the limited length of image width and sampling frequency. As a result, directly applying Gabor filters to finite-length images may cause mathematical deficiency and distortion, leading to frequency aliasing and other issues that can impair model training [39]. To address this problem, we propose to concentrate most of the Gabor filter energy within the finite signal zone. This ensures that only a small amount of filter energy spills over the finite signal, minimizing the negative effects of using infinite-length-defined filters on finite-length images. Such a constraint could be implemented by limiting the value ranges of filter parameters, which determine the effective zone and energy concentration area of a Gabor filter. Specifically, according to the properties of Gabor filters and images mentioned above, we first derive " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "[0,\\pi ],\\left[\\frac{5}{2\\pi(1 - 2W)},\\frac{S}{5}\\right],\\left[\\frac{5}{2\\pi},\\frac{S}{5}\\right]" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "[0,\\frac{2\\pi S - 25}{4\\pi S} ]" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": " to be the valid ranges for parameters " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "\\theta ,\\sigma_{x},\\sigma_{y}" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": " respectively (please refer to supplementary materials for a detailed derivation of these valid ranges). Next, we propose a constraint function to ensure each parameter to fall within its valid range. Specifically for a parameter " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": " with lower bound " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "l_{p}" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": " and upper bound " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "u_{p}" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": ", we propose to obtain " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": " through a learnable parameter " + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 96, + 289, + 469 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 476, + 287, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 476, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 62, + 476, + 287, + 502 + ], + "type": "interline_equation", + "content": "p = l _ {p} + \\left(u _ {p} - l _ {p}\\right) \\mathrm {S i g m o i d} (\\mathbf {p}) = \\frac {u _ {p} + l _ {p} e ^ {- \\mathbf {p}}}{1 + e ^ {- \\mathbf {p}}}. (3)", + "image_path": "52cd2a7ef07d124e58043c4efd374fdd5ce3a898cc28f9241e242b25d065dc27.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "text", + "content": "The parameter " + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "text", + "content": " can be learned to have any value ranging from " + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "inline_equation", + "content": "-\\infty" + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "inline_equation", + "content": "+\\infty" + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "text", + "content": ". By applying Eq. 3, parameter " + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "text", + "content": " can be guaranteed to fall within its valid range " + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "inline_equation", + "content": "[l_p, u_p]" + }, + { + "bbox": [ + 46, + 508, + 287, + 567 + ], + "type": "text", + "content": ". By doing so, parameter values are constrained to enhance the stability of training." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": "High Frequency Enhancement. To address the frequency bias problem and improve high-frequency information extraction, we further propose a dual-constraint strategy for the frequency parameter " + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": ". Specifically, we constrain half of Gabor filters to only exploit high-frequency components, making the network to capture sufficient high-frequency information for facilitating fine-grained recognition. This is enabled by setting two value intervals for " + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "inline_equation", + "content": "[0, \\frac{2\\pi S - 25}{8\\pi S}]" + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "inline_equation", + "content": "[\\frac{2\\pi S - 25}{8\\pi S}, \\frac{2\\pi S - 25}{4\\pi S}]" + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": ", which are equally divided from the valid range " + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "inline_equation", + "content": "[0, \\frac{2\\pi S - 25}{4\\pi S}]" + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": " of the frequency parameter. Let " + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": " be the total number of Gabor filters to be learned. Using the method in Eq. 3, we constrain " + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "inline_equation", + "content": "N / 2" + }, + { + "bbox": [ + 46, + 567, + 288, + 714 + ], + "type": "text", + "content": " fil" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 547, + 175 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 547, + 175 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 547, + 175 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 547, + 175 + ], + "type": "image", + "image_path": "dd8d486a1acb36dc61fa34752fa98a2fb5991ff7d779f974f8ad06fdf6773ff2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 177, + 542, + 189 + ], + "lines": [ + { + "bbox": [ + 305, + 177, + 542, + 189 + ], + "spans": [ + { + "bbox": [ + 305, + 177, + 542, + 189 + ], + "type": "text", + "content": "Figure 2. The structure of Learnable Histogram Operator (LHO)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "type": "text", + "content": "ters to fall between " + }, + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "type": "inline_equation", + "content": "[0, \\frac{2\\pi S - 25}{8\\pi S}]" + }, + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "type": "text", + "content": " and the other " + }, + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "type": "inline_equation", + "content": "N/2" + }, + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "type": "text", + "content": " filters to fall between " + }, + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "type": "inline_equation", + "content": "\\left[\\frac{2\\pi S - 25}{8\\pi S}, \\frac{2\\pi S - 25}{4\\pi S}\\right]" + }, + { + "bbox": [ + 304, + 196, + 547, + 281 + ], + "type": "text", + "content": ", such that they serve as the low-frequency expert and high-frequency expert respectively. This strategy enhances the extraction ability of high-frequency information, alleviating the frequency bias problem in traditional DNNs where high-frequency features are difficult to extract." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 289, + 463, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 463, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 463, + 300 + ], + "type": "text", + "content": "3.4. Statistical Feature Extractor" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 307, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 534 + ], + "type": "text", + "content": "The above method enables Gabor filters to be trained stably and effectively in a deep learning framework. These filters can capture texture signals from an input image. In the next step, we target at extracting effective features from these filters to facilitate fine-grained recognition. From the perspective of digital image processing, texture can be represented by the statistical properties of feature maps [16]. Based on this principle, in some previous research [40, 4, 1], textures were exploited by extracting hand-crafted statistics such as variance, contrast and smoothness from the output of Gabor filters. However, these statistics have limited effectiveness because they are hand-crafted designed. In this work, we step further and take advantage of deep learning to extract deep statistical features that are more comprehensive and effective. Specifically, we propose a novel statistical feature extractor that contains a Learnable Histogram Operator (LHO) followed by a Filer Correlation Module (FCM). In the following sections, we provide a detailed illustration of QCO and FCM respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "content": "Learnable Histogram Operator. We first employ a Learnable Histogram Operator (LHO) to exploit statistical information, which is improved from [58]. Fig. 2 illustrates the structure of LHO. LHO receives the output from each Gabor filter as input and produces a statistical feature " + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{S} \\in \\mathbb{R}^{C}" + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "content": " refers to the channel number. Let " + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{S \\times S}" + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "content": " be the intensity map generated by convolving a Gabor filter with the processed image, where " + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "content": " refers to image size. LHO first defines " + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "content": " levels by equally dividing the minimal and maximal values for intensities of all pixels. Specifically, the " + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "content": "-th level " + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{L}^{m}" + }, + { + "bbox": [ + 304, + 534, + 545, + 666 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 341, + 671, + 545, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 671, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 341, + 671, + 545, + 696 + ], + "type": "interline_equation", + "content": "\\mathbf {L} ^ {m} = \\min (\\mathbf {I}) + \\frac {\\max (\\mathbf {I}) - \\min (\\mathbf {I})}{M} \\cdot m \\tag {4}", + "image_path": "c842ff11083eead20f6dd0182d104d26de6baa259489e46c9b193bfbf2bf6df0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 700, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 700, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 700, + 545, + 714 + ], + "type": "text", + "content": "Next, each pixel " + }, + { + "bbox": [ + 305, + 700, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^{i,j}" + }, + { + "bbox": [ + 305, + 700, + 545, + 714 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 305, + 700, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 305, + 700, + 545, + 714 + ], + "type": "text", + "content": " is quantized to a vector " + }, + { + "bbox": [ + 305, + 700, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{i,j} \\in" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1624" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^M" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": ". Concretely, let " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " be the interval between adjacent levels " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "(I = \\mathbf{L}^{m + 1} - \\mathbf{L}^m)" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": "-th channel " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{i,j,m}" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{i,j}" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " is computed as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 115, + 287, + 155 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 115, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 61, + 115, + 287, + 155 + ], + "type": "interline_equation", + "content": "\\mathbf {V} ^ {i, j, m} = \\left\\{ \\begin{array}{l l} 1 - \\left| \\mathbf {L} ^ {m} - \\mathbf {I} ^ {i, j} \\right| & \\text {i f} \\left| \\mathbf {L} ^ {m} - \\mathbf {I} ^ {i, j} \\right| < \\frac {I}{2} \\\\ 0 & \\text {e l s e} \\end{array} \\right. \\tag {5}", + "image_path": "e5973fad9c7867514646d1677e6f5499b6f9483deff5ab4ebbbd2230cf216192.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "text", + "content": "In this way, " + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "text", + "content": " is quantized to " + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{S \\times S \\times M}" + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "text", + "content": ". Note a spire-shaped function is used for quantization instead of a binary one to ensure that the operation is differentiable. After the quantization, the number of pixels that fall into each level is counted and normalized to obtain a counting feature " + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{C} \\in \\mathbb{R}^M" + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^m" + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 163, + 287, + 236 + ], + "type": "text", + "content": "-th level is computed as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 93, + 243, + 287, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 243, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 93, + 243, + 287, + 277 + ], + "type": "interline_equation", + "content": "\\mathbf {C} ^ {m} = \\frac {\\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i , j , m}}{\\sum_ {m = 1} ^ {M} \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i , j , m}}. \\tag {6}", + "image_path": "b0404e44435677333e01605d0fea224e01905dbb3db5ba93f839f6feb274a708.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "text", + "content": "We concatenate " + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{C}^m" + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{L}^m" + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "text", + "content": ", and obtain the feature " + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^m" + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 280, + 286, + 304 + ], + "type": "text", + "content": "-th quantization level as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 312, + 287, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 312, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 96, + 312, + 287, + 327 + ], + "type": "interline_equation", + "content": "\\mathbf {F} ^ {m} = \\phi (\\operatorname {C A T} \\left(\\mathbf {C} ^ {m}, \\mathbf {L} ^ {m}\\right)) + \\mathbf {P} ^ {m}, \\tag {7}", + "image_path": "4612d3c37f1e3847617081deb9638fb13a748bb4918a7a3b2c18e74c1761b1f2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "type": "text", + "content": " refers to a linear layer. " + }, + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^m\\in \\mathbb{R}^C" + }, + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "type": "text", + "content": " encodes the position information for pixels quantized to the " + }, + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 334, + 287, + 382 + ], + "type": "text", + "content": "-th level, which is computed as the weighted sum of position features from all pixels as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 101, + 391, + 287, + 424 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 391, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 101, + 391, + 287, + 424 + ], + "type": "interline_equation", + "content": "\\mathbf {P} ^ {m} = \\sum_ {i = 1} ^ {S} \\sum_ {j = 1} ^ {S} \\mathbf {V} ^ {i, j, m} \\mathrm {P E} (i, j), \\tag {8}", + "image_path": "37e150348ebd268acf387cb755ac99c2bab4b5fc54e53ba1e1d8b73c3511632c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 432, + 287, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 287, + 468 + ], + "type": "text", + "content": "where PE refers to the position encoding operation as in vit [8]. Finally, the statistical texture " + }, + { + "bbox": [ + 47, + 432, + 287, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 47, + 432, + 287, + 468 + ], + "type": "text", + "content": " is produced by correlating features from different levels:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 100, + 475, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 475, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 100, + 475, + 287, + 491 + ], + "type": "interline_equation", + "content": "\\mathbf {S} = \\operatorname {A v g} \\left(\\operatorname {M H A} \\left(\\left\\{\\mathbf {F} ^ {m} \\right\\} _ {m = 1} ^ {M}\\right)\\right), \\tag {9}", + "image_path": "f3e3bedb81af189da0f4eaa4a7eec7dcffbddc6d32e97442fc657190b38a845a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 498, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 677 + ], + "type": "text", + "content": "where MHA denotes a multi-head attention and Avg refers to the average over all levels. Using LHO has two advantages. Firstly, it can be considered as a way to extract deep features from a differentiable and learnable histogram, which can produce effective and appropriate statistical features that can benefit the task [16, 58]. Secondly, conventional statistical features are typically pixel-relationship-invariant. For example, rearranging pixel positions does not alter the mean and variance values. In contrast, our method is pixel-relationship-aware as it encodes " + }, + { + "bbox": [ + 47, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^m" + }, + { + "bbox": [ + 47, + 498, + 287, + 677 + ], + "type": "text", + "content": " that represents the position information of pixels quantized to each level, which provides additional information that can be useful for fine-grained recognition. These advantages enable the extracted features from LHO to be effective in facilitating fine-grained recognition." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "Filter Correlation Module. The proposed LHO can produce a statistical feature from the output of each Gabor filter, resulting in a set of features " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}^n\\}_{n=1}^N" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " for all filters. We" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 106 + ], + "type": "text", + "content": "further propose a Filter Correlation Module (FCM) to aggregate statistical information from all Gabor filters as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 115, + 545, + 145 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 115, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 311, + 115, + 545, + 145 + ], + "type": "interline_equation", + "content": "\\mathbf {T} = \\operatorname {A v g} \\left(\\operatorname {M H A} \\left(\\left\\{\\mathbf {S} ^ {n} + \\phi \\left(\\sigma_ {x} ^ {n}, \\sigma_ {y} ^ {n}, \\theta^ {n}, W ^ {n}\\right) \\right\\} _ {n = 1} ^ {N}\\right)\\right), \\tag {10}", + "image_path": "77938b01885d81943738e8e08d36ca5362fbe1a2f389ffd8eafeb018212c2018.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^n" + }, + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "type": "text", + "content": " refers to the statistical feature for the " + }, + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "type": "text", + "content": "-th Gabor filter. " + }, + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "type": "inline_equation", + "content": "\\phi(\\sigma_x^n, \\sigma_y^n, \\theta^n, W^n)" + }, + { + "bbox": [ + 305, + 146, + 545, + 230 + ], + "type": "text", + "content": " uses a linear layer to encode filter parameter information, which can indicate the type of texture extracted by the Gabor filter. Eq. 10 exploits the correlations among different texture components from different Gabor filters, generating a powerful feature with long-range correlations that can facilitate fine-grained recognition." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 239, + 432, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 432, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 432, + 251 + ], + "type": "text", + "content": "3.5. Region Selection Gate" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "content": "Through the methods outlined above, we can build a powerful feature extractor that captures texture information using Gabor filters. As a common practice used by previous methods, the extractor can generate features in an image-based [40] manner or a patch-based manner [39]. Image-based methods directly feed the whole image into the extractor, which might lead to the blurring of local detailed information. Patch-based methods address the problem by equally dividing the image into several patches and extracting a feature from each patch. However, it is computationally expensive as each image position must be processed by the feature extractor. Intuitively, the texture information in different regions of an image is not equally important. For example, some regions may contain critical textures for recognition, such as feather of the bird, while others may be less informative, consisting of background textures such as sky, road and lawn. Therefore, extracting textures from all positions is redundant and computationally inefficient, which can impede recognition accuracy and slow down algorithmic speed. To address the issue, we propose a novel approach to solely extract textures from informative regions that are automatically selected from a gate mechanism. More specifically, the gate mechanism for region selection involves three steps. Firstly, we introduce a shallow FPN block that takes the intermediate features of the CNN-based semantic branch as inputs and generates a feature map " + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "content": ". Please refer to supplementary materials for a detailed description for the structure of this block. Since features from the CNN branch have a high receptive field and contain rich semantic information, " + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "content": " can identify key parts of an image and assist in selecting class-discriminative regions in appropriate positions. Secondly, we introduce a set of regions proposals, denoted as " + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{R}^k\\}_{k=1}^K" + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "content": ", which is the same as that in RCNN [15], comprising regions with different scales and positions. For each region " + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{R}^k" + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "content": ", a feature vector " + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "inline_equation", + "content": "f^k" + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "content": " is generated by performing an RoI pooling on the corresponding region of the feature map " + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "content": ". This feature vector is then fed into a linear layer to generate a score " + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "inline_equation", + "content": "s^k" + }, + { + "bbox": [ + 305, + 258, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1625" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "Lastly, regions that require texture extraction are selected based on their scores. This mechanism enables only the regions that contain class-discriminative information to be selected for texture extraction, thereby reducing computation costs and avoiding information redundancy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "type": "text", + "content": "To reduce computation for capturing texture features, we expect 'hard' selections instead of the 'soft' attention scores to be generated so that only a limited number of regions need texture extraction. However, such a hard selection may prohibit the gradients to be back-propagated to the earlier layers in optimization. To address this issue, we employ the Improved Semantic Hashing [24, 25] for region selection. In training, to encourage more decision space to be explored randomly, we add a standard Gaussian noise " + }, + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "type": "inline_equation", + "content": "s^k" + }, + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "type": "text", + "content": ", resulting in the noise-injected score " + }, + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "type": "inline_equation", + "content": "\\hat{s}^k" + }, + { + "bbox": [ + 46, + 133, + 288, + 263 + ], + "type": "text", + "content": ". Then two vectors are generated as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 98, + 271, + 287, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 271, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 98, + 271, + 287, + 287 + ], + "type": "interline_equation", + "content": "c ^ {k} = \\sigma^ {\\prime} (\\hat {s} ^ {k}); d ^ {k} = \\mathbb {1} (\\hat {s} ^ {k} > 0), \\tag {11}", + "image_path": "5bd54707a453948ae00e383c6077bd64e47b8ed3898a221394b381eaab04b1b5.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 294, + 253, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 294, + 253, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 294, + 253, + 306 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 294, + 253, + 306 + ], + "type": "inline_equation", + "content": "\\sigma^{\\prime}" + }, + { + "bbox": [ + 47, + 294, + 253, + 306 + ], + "type": "text", + "content": " refers to the saturating Sigmoid function:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 63, + 314, + 287, + 330 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 314, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 63, + 314, + 287, + 330 + ], + "type": "interline_equation", + "content": "\\sigma^ {\\prime} (\\hat {s} ^ {k}) = \\max (0, \\min (1, 1. 2 \\sigma (\\hat {s} ^ {k}) - 0. 1)), \\tag {12}", + "image_path": "d9475b5e08e33f323581790ebe4d3a13cc72db45f5e90ab0b3c264a28fab8449.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "text", + "content": " denotes the original Sigmoid function. In this way, " + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "inline_equation", + "content": "d^{k}" + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "text", + "content": " is a binarized discrete feature with value " + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "inline_equation", + "content": "\\{0,1\\}" + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "text", + "content": ", which is used for making the selection decision. " + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "inline_equation", + "content": "c^{k}" + }, + { + "bbox": [ + 46, + 337, + 287, + 408 + ], + "type": "text", + "content": " is a continuously differentiable vector that can be used to approximate gradients in back-propagation, whose details are presented in supplementary materials." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 409, + 287, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 600 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 600 + ], + "type": "text", + "content": "Discussion with Previous Methods. Note that the proposed region gate mechanism differs from other key part localization methods used for fine-grained recognition. Unlike existing methods, our method can be trained end-to-end and generate hard decisions without the need for extra annotations. These properties enable our method to be highly effective and practical for region selection. Conversely, existing key part localization techniques have several limitations. For example, some methods [20, 43] require extra annotations such as bounding box and key points for joint training; [14] uses an indifferentiable selection process, making the network unable to be trained end-to-end; other methods [7, 21] typically produce soft attention rather than hard decisions, which cannot reduce computation costs. Our approach can be more practical and effective benefiting from our careful designs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 601, + 132, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 132, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 132, + 613 + ], + "type": "text", + "content": "3.6. Optimization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 620, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 620, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 620, + 287, + 642 + ], + "type": "text", + "content": "The proposed network is optimized by the following loss function:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 112, + 641, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 641, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 112, + 641, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = L _ {c e} (p, l) + \\lambda \\sum_ {k = 1} ^ {K} d ^ {k}, \\tag {13}", + "image_path": "e51ca3e65dc73f9c5362a58ac55590f83c080b01299a703dd76b7839f7e13404.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "L_{ce}" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " denotes the cross-entropy loss. " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " are the prediction logits and ground truth label. " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "d^{k}" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " denotes the binarized discrete decision as in Eq. 11. The second item" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 312, + 70, + 545, + 225 + ], + "blocks": [ + { + "bbox": [ + 312, + 70, + 545, + 225 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 545, + 225 + ], + "type": "table", + "html": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5084.5
ResNet101 [17]ResNet10185.5
DenseNet161 [19]DenseNet16185.5
PC-Dense161 [9]DenseNet16186.9
NTSNet [48]ResNet5087.5
Cross-X [34]ResNet5087.7
DCL [3]ResNet5087.8
S3N [7]ResNet5088.5
iSQRT-COV [27]ResNet10188.7
GaRD [54]ResNet5089.6
APINet [59]DenseNet16190.0
OursResNet5090.8
OursResNet10191.3
OursDenseNet16191.5
", + "image_path": "db3f00c3977cbbff87a3a4435074d129482b4cf7e876751d62c54d6ea9c29b4b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 323, + 225, + 525, + 236 + ], + "lines": [ + { + "bbox": [ + 323, + 225, + 525, + 236 + ], + "spans": [ + { + "bbox": [ + 323, + 225, + 525, + 236 + ], + "type": "text", + "content": "Table 1. Comparison results on CUB-200-2011 dataset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 244, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 244, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 305, + 244, + 545, + 293 + ], + "type": "text", + "content": "in Eq. 13 encourages fewer regions to be selected, thus avoiding the redundant information and reducing computation costs. " + }, + { + "bbox": [ + 305, + 244, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 244, + 545, + 293 + ], + "type": "text", + "content": " is a hyper-parameter to control the trade-off between the two loss items." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 299, + 387, + 313 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 299, + 387, + 313 + ], + "spans": [ + { + "bbox": [ + 306, + 299, + 387, + 313 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 319, + 438, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 319, + 438, + 332 + ], + "spans": [ + { + "bbox": [ + 306, + 319, + 438, + 332 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "text", + "content": "Following [59], we adopt different networks as the semantic branch, including ResNet50, ResNet101 and DenseNet161. We use SGD as the optimizer with the momentum of 0.9. The initial learning rate is set to 1e-4, which decays by 0.1 for every 20 epochs (overall 100 epochs). Batch size is 16 for all datasets. Following previous works [54, 28], we use random cropping of " + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "inline_equation", + "content": "448 \\times 448" + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "text", + "content": " in training and center crop at inference. We apply the commonly-used data augmentation strategies for training, including random scaling, left-right flipping and random cropping. " + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "text", + "content": " indicating the size of regions that are zoomed in is set to 112. " + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "text", + "content": " indicating the number of learnable Gabor filters is set to 128. " + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "text", + "content": " indicating the number of quantization levels in QCO is set to 8. " + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 338, + 545, + 517 + ], + "type": "text", + "content": " in Eq. 13 is set to 0.2. Experiments are conducted on 2 NVIDIA Titan V100 GPUs." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 527, + 485, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 485, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 485, + 540 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 546, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 546, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 546, + 545, + 713 + ], + "type": "text", + "content": "We evaluate our method on four datasets, including three fine-grained datasets CUB-200-2011, NA-bird, Stanford Dogs and a terrain recognition dataset GTOS-mobile. The comparison results on these datasets are presented in Tables 1, 2, 3, and 4, respectively. Our method achieves the best performance when using DenseNet161 as the semantic branch, reaching accuracy scores of 91.5, 90.4, 92.1 and 87.5, outperforming the second-best method by 1.5, 2.3, 1.8 and 4.8, respectively. It is worth noting that even when using ResNet50, the least effective backbone among the three, our method remains superior to all other compared methods. This highlights the high effectiveness of our method. The advantage of our method is especially significant on the challenging terrain dataset GTOS-mobile. This is due to our" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1626" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 71, + 211, + 173 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 211, + 173 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 211, + 173 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 211, + 173 + ], + "type": "table", + "html": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5082.2
ResNet101 [17]ResNet10182.9
DenseNet161 [19]DenseNet16183.1
Cross-X [34]ResNet5086.4
GaRD [54]ResNet5088.0
APINet [59]DensetNet10188.1
OursResNet5089.5
OursResNet10190.0
OursDenseNet16190.4
", + "image_path": "429412cd0a4619d96b1fa2ce2b917fd9ab4fcfb099f97c238b05192548a7c8b8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 221, + 71, + 373, + 174 + ], + "blocks": [ + { + "bbox": [ + 58, + 174, + 211, + 194 + ], + "lines": [ + { + "bbox": [ + 58, + 174, + 211, + 194 + ], + "spans": [ + { + "bbox": [ + 58, + 174, + 211, + 194 + ], + "type": "text", + "content": "Table 2. Comparison results on NA-bird dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 221, + 71, + 373, + 174 + ], + "lines": [ + { + "bbox": [ + 221, + 71, + 373, + 174 + ], + "spans": [ + { + "bbox": [ + 221, + 71, + 373, + 174 + ], + "type": "table", + "html": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5080.1
ResNet101 [17]ResNet10180.6
DenseNet161 [19]DenseNet16180.9
PC-Dense161 [9]DenseNet16182.8
Cross-X [34]ResNet5088.9
APINet [59]ResNet10190.3
OursResNet5091.0
OursResNet10191.7
OursDenseNet16192.1
", + "image_path": "c7d34e9b836b7178544265363622612d530cec1b20e8447f0d1a828f232fea83.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 383, + 70, + 535, + 174 + ], + "blocks": [ + { + "bbox": [ + 221, + 175, + 372, + 195 + ], + "lines": [ + { + "bbox": [ + 221, + 175, + 372, + 195 + ], + "spans": [ + { + "bbox": [ + 221, + 175, + 372, + 195 + ], + "type": "text", + "content": "Table 3. Comparison results on Stanford Dogs dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 383, + 70, + 535, + 174 + ], + "lines": [ + { + "bbox": [ + 383, + 70, + 535, + 174 + ], + "spans": [ + { + "bbox": [ + 383, + 70, + 535, + 174 + ], + "type": "table", + "html": "
MethodBackboneAccuracy
ResNet50 [17]ResNet5069.4
ResNet101 [17]ResNet10172.0
DenseNet161 [19]DenseNet16172.9
B-CNN [28]ResNet5075.8
Deep-TEN [51]ResNet5076.1
DEP [47]ResNet5082.7
OursResNet5086.4
OursResNet10187.0
OursDenseNet16187.5
", + "image_path": "68e9b7720f574bb7bc7c4ece552834d4ba36fef1b33aaeb9989569b4cbcbc89a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 50, + 213, + 286, + 266 + ], + "blocks": [ + { + "bbox": [ + 383, + 175, + 535, + 194 + ], + "lines": [ + { + "bbox": [ + 383, + 175, + 535, + 194 + ], + "spans": [ + { + "bbox": [ + 383, + 175, + 535, + 194 + ], + "type": "text", + "content": "Table 4. Comparison results on GTOS-mobile dataset." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 213, + 286, + 266 + ], + "lines": [ + { + "bbox": [ + 50, + 213, + 286, + 266 + ], + "spans": [ + { + "bbox": [ + 50, + 213, + 286, + 266 + ], + "type": "table", + "html": "
MethodAccuracyFlops(G)Params(M)
Baseline (ResNet50)84.516.2624.69
+ TB & RSG90.820.7232.41
+ TB (image-based manner)89.036.8829.82
+ TB (patch-based manner)89.937.0429.82
", + "image_path": "3ad2681e43f9315ae928e58614a39f61ebe32c0cd5eed90ac3ac3766012813eb.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 305, + 286, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 305, + 286, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 305, + 286, + 340 + ], + "type": "text", + "content": "method's ability to extract texture features, which are essential for the classification of visually-similar and closely-related terrain classes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 348, + 140, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 140, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 140, + 361 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 366, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 287, + 426 + ], + "type": "text", + "content": "We perform ablation study to verify the effectiveness of our designs. Experiments in this part are conducted on CUB-200-2011 dataset with ResNet50 as the semantic branch. Due to paper length limitation, more ablation study results are presented in supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "type": "text", + "content": "Ablation of Different Components. As shown in Fig. 1, in addition to the basic CNN-based semantic branch, our method consists of two key components: a Gabor-filter-based texture branch (TB) and a region selection gate (RSG). We conduct experiments to validate the effect of these components and present the results in Table. 5, which includes the validation accuracy, computation costs and parameter numbers of different settings. We set the network that only has a ResNet50 semantic branch to be the baseline. Our method with adding both texture branch & region selection gate increases accuracy from 84.5 to 90.8. When the region selection gate is removed, extracting textures by feeding the whole image into texture branch (image-based manner) reduces accuracy to 89.0 and increases computation by " + }, + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "type": "inline_equation", + "content": "78\\%" + }, + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "type": "text", + "content": "; equally dividing image into " + }, + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "type": "text", + "content": " patches and getting a feature from each patch (patch-based manner) reduces accuracy to 89.0 and increases computation by " + }, + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "type": "inline_equation", + "content": "79\\%" + }, + { + "bbox": [ + 47, + 426, + 287, + 653 + ], + "type": "text", + "content": ". The results demonstrate that the region selection gate can reduce computation and improve performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "content": "Ablation of Learnable Gabor Filters. Results in this part are presented in Table. 6. (1) First, we validate the effectiveness of Gabor filters. Replacing all Gabor filters by the " + }, + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "content": " convolution layers decreases accuracy by 4.9. This indicates that the improvement does not simply come from" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 306, + 213, + 545, + 279 + ], + "blocks": [ + { + "bbox": [ + 47, + 266, + 286, + 298 + ], + "lines": [ + { + "bbox": [ + 47, + 266, + 286, + 298 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 286, + 298 + ], + "type": "text", + "content": "Table 5. Ablation results of different components in our method. TB and RSG refer to the texture branch and region selection gate, respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 213, + 545, + 279 + ], + "lines": [ + { + "bbox": [ + 306, + 213, + 545, + 279 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 545, + 279 + ], + "type": "table", + "html": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours replacing Gabor filters with conv85.920.0332.95
Ours w/o parameter learning86.520.7232.41
Ours w/o parameter value constraints75.420.4032.41
Ours w/o high frequency enhancement88.120.4032.41
", + "image_path": "79c4a54fcef3e51f81f6d15bb77e1719d80ed95c75b06111baa77bfed1df0e05.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 333, + 279, + 517, + 289 + ], + "lines": [ + { + "bbox": [ + 333, + 279, + 517, + 289 + ], + "spans": [ + { + "bbox": [ + 333, + 279, + 517, + 289 + ], + "type": "text", + "content": "Table 6. Ablation results of learnable Gabor filters." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 304, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 592 + ], + "type": "text", + "content": "an increase in the number of parameters, but from the effectiveness of using Gabor filters for texture extraction. (2) Second, we evaluate the effectiveness of learning Gabor filter parameters in a supervised manner. We replace the learnable parameters with the manually set ones, where the setting rules are the same as [40]. This reduces accuracy by 4.3, showing the effectiveness of supervised learning. (3) Third, we verify the necessity of using parameter value constraints. In Fig. 3, we present the loss curves and validation accuracy curves for methods w/ and w/o using value constraints. Using value constraints results in a smoother loss decline curve and accuracy improvement curve. In contrast, free training causes violent loss and accuracy fluctuations, especially at the beginning stage of training, indicating that the training process is unstable. Compared to free training, using value constraints significantly improves validation accuracy by 15.4. (4) Last, we evaluate the high frequency enhancement strategy by setting two constraints for frequency parameter " + }, + { + "bbox": [ + 304, + 304, + 545, + 592 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 304, + 545, + 592 + ], + "type": "text", + "content": ". Without the strategy and directly constraining " + }, + { + "bbox": [ + 304, + 304, + 545, + 592 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 304, + 545, + 592 + ], + "type": "text", + "content": " into its valid range reduces accuracy by 2.7. Results demonstrate the effectiveness of our designs for the learnable Gabor filter parameters. Also note, using the proposed learning methods requires no extra parameters and only increases computation very slightly." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "Ablation of Statistical Feature Extractor. We propose a statistical feature extractor to leverage texture information from the output of Gabor filters. The extractor consists of two parts: a Learnable Histogram Operator (LHO) and a Filter Correlation Module (FCM). We conduct experiments to validate the effect of these components and present the results in Table 7. Removing LHO and FCM reduces accuracy from 90.8 to 87.0 and 89.2 respectively. Also note that, both LHO and FCM are lightweight, only requiring extra parameters of 4.26M and 3.56M, increasing flops by" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1627" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 160, + 145 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 160, + 145 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 160, + 145 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 160, + 145 + ], + "type": "image", + "image_path": "bf6ae535852da6a1dcdd7c64b18b1eea0527101f1ccae213b2d3631a0c90ea3c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 77, + 149, + 130, + 158 + ], + "lines": [ + { + "bbox": [ + 77, + 149, + 130, + 158 + ], + "spans": [ + { + "bbox": [ + 77, + 149, + 130, + 158 + ], + "type": "text", + "content": "(a) Loss Curves" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 160, + 76, + 269, + 144 + ], + "blocks": [ + { + "bbox": [ + 160, + 76, + 269, + 144 + ], + "lines": [ + { + "bbox": [ + 160, + 76, + 269, + 144 + ], + "spans": [ + { + "bbox": [ + 160, + 76, + 269, + 144 + ], + "type": "image", + "image_path": "b351441b6dfa7ae12b45b924a280075ac904eb290b5476753da49e8ebe784df4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 178, + 148, + 247, + 159 + ], + "lines": [ + { + "bbox": [ + 178, + 148, + 247, + 159 + ], + "spans": [ + { + "bbox": [ + 178, + 148, + 247, + 159 + ], + "type": "text", + "content": "(b) Accuracy Curves" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 162, + 287, + 195 + ], + "lines": [ + { + "bbox": [ + 47, + 162, + 287, + 195 + ], + "spans": [ + { + "bbox": [ + 47, + 162, + 287, + 195 + ], + "type": "text", + "content": "Figure 3. Loss curves (a) and accuracy curves (b) in different settings. Blue and orange lines indicate curves for training Gabor filters w/ and w/o using parameter value constraints, respectively." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 50, + 198, + 287, + 244 + ], + "blocks": [ + { + "bbox": [ + 50, + 198, + 287, + 244 + ], + "lines": [ + { + "bbox": [ + 50, + 198, + 287, + 244 + ], + "spans": [ + { + "bbox": [ + 50, + 198, + 287, + 244 + ], + "type": "table", + "html": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours w/o LHO87.018.0328.25
Ours w/o FCM89.219.5528.85
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Results show the high effectiveness and efficiency of LHO and FCM." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 286, + 287, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 287, + 454 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 287, + 454 + ], + "type": "text", + "content": "Ablation of LHO. In Table. 8, we further evaluate the designs in LHO. First, we replace LHO with a hand-crafted statistical feature composed of mean, variance, maximum and minimum values, which reduces accuracy by 2.9. This demonstrates that LHO can produce statistical features that are more effective than hand-crafted ones widely used by previous methods. Next, we remove position information " + }, + { + "bbox": [ + 46, + 286, + 287, + 454 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^m" + }, + { + "bbox": [ + 46, + 286, + 287, + 454 + ], + "type": "text", + "content": " in Eq. 7 and multi-head attention in Eq. 9, which reduces accuracy by 1.5 and 2.1 respectively, showing the importance of encoding position features and correlating different levels in LHO. Finally, we move LHO from texture branch to CNN-based semantic branch. This reduces accuracy by 4.6, showing that the effectiveness of LHO relies on Gabor filters to extract texture-related signals." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 463, + 130, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 130, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 130, + 475 + ], + "type": "text", + "content": "4.4. Visualization" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 482, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 287, + 650 + ], + "type": "text", + "content": "In Fig. 4, we provide a visualization of the outputs obtained from learned Gabor filters. More specifically, Fig. 4 (c) and Fig. 4 (d) show the average output of all high-frequency and low-frequency Gabor filters, respectively. As can be observed, the high-frequency filters primarily capture information of undulating areas such as speckles and ripples, whereas the low-frequency filters primarily capture information related to smooth changing areas. Both these two kinds of information are critical for recognition. By exploiting sufficient and balanced multi-frequency features through the carefully-designed learnable Gabor filters, our method can leverage comprehensive information for effective fine-grained recognition. Due to space limitation, more visualization results are presented in supplementary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 658, + 269, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 269, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 269, + 671 + ], + "type": "text", + "content": "4.5. Discussion of Computation and Parameter" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Compared to the ResNet50 baseline, our method only increases computation and parameter usage slightly. Specifically, on CUB-200-2011 dataset, ResNet50 consumes" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 317, + 74, + 376, + 119 + ], + "blocks": [ + { + "bbox": [ + 317, + 74, + 376, + 119 + ], + "lines": [ + { + "bbox": [ + 317, + 74, + 376, + 119 + ], + "spans": [ + { + "bbox": [ + 317, + 74, + 376, + 119 + ], + "type": "image", + "image_path": "ba6445037c1dc92259f4bf6f798dcd8024b90e93da4191a6c15cbcd72746e386.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 317, + 119, + 376, + 163 + ], + "blocks": [ + { + "bbox": [ + 317, + 119, + 376, + 163 + ], + "lines": [ + { + "bbox": [ + 317, + 119, + 376, + 163 + ], + "spans": [ + { + "bbox": [ + 317, + 119, + 376, + 163 + ], + "type": "image", + "image_path": "74c34d6ccfbd2aef9561cec30d558a45974f90da9e01cef6a545c74a2e2cfc5a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 332, + 163, + 358, + 172 + ], + "lines": [ + { + "bbox": [ + 332, + 163, + 358, + 172 + ], + "spans": [ + { + "bbox": [ + 332, + 163, + 358, + 172 + ], + "type": "text", + "content": "(a) Image" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 175, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 306, + 175, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 545, + 208 + ], + "type": "text", + "content": "Figure 4. 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(a), (b), (c) and (d) present the original images, the selected regions, average output of all high-frequency and low-frequency Gabor filters, respectively." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 386, + 76, + 429, + 118 + ], + "blocks": [ + { + "bbox": [ + 386, + 76, + 429, + 118 + ], + "lines": [ + { + "bbox": [ + 386, + 76, + 429, + 118 + ], + "spans": [ + { + "bbox": [ + 386, + 76, + 429, + 118 + ], + "type": "image", + "image_path": "b4de533b1dc2e946bb7f2255b0059b4aba494dac5e9404578de4945f51194eab.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 386, + 119, + 479, + 163 + ], + "blocks": [ + { + "bbox": [ + 386, + 119, + 479, + 163 + ], + "lines": [ + { + "bbox": [ + 386, + 119, + 479, + 163 + ], + "spans": [ + { + "bbox": [ + 386, + 119, + 479, + 163 + ], + "type": "image", + "image_path": "42b275e5eec7ef8305390bb74e780a97e1eab92c5f17916d56b3f43a3283a102.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 163, + 420, + 171 + ], + "lines": [ + { + "bbox": [ + 392, + 163, + 420, + 171 + ], + "spans": [ + { + "bbox": [ + 392, + 163, + 420, + 171 + ], + "type": "text", + "content": "(b) Region" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 434, + 163, + 479, + 171 + ], + "lines": [ + { + "bbox": [ + 434, + 163, + 479, + 171 + ], + "spans": [ + { + "bbox": [ + 434, + 163, + 479, + 171 + ], + "type": "text", + "content": "(c) High-W Filters" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 436, + 76, + 479, + 118 + ], + "blocks": [ + { + "bbox": [ + 436, + 76, + 479, + 118 + ], + "lines": [ + { + "bbox": [ + 436, + 76, + 479, + 118 + ], + "spans": [ + { + "bbox": [ + 436, + 76, + 479, + 118 + ], + "type": "image", + "image_path": "26ca61c2fcd32aa9c29556f4a9cef283f37a8eda80a925da8da2c31bed412e04.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 436, + 119, + 479, + 163 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 436, + 119, + 479, + 163 + ], + "spans": [ + { + "bbox": [ + 436, + 119, + 479, + 163 + ], + "type": "image", + "image_path": "ac327de946a0b58826dcfaae7b78ec9d59ed2c281502e030db105d4fa3ba9de4.jpg" + } + ] + } + ], + "index": 20, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 485, + 76, + 529, + 118 + ], + "blocks": [ + { + "bbox": [ + 485, + 76, + 529, + 118 + ], + "lines": [ + { + "bbox": [ + 485, + 76, + 529, + 118 + ], + "spans": [ + { + "bbox": [ + 485, + 76, + 529, + 118 + ], + "type": "image", + "image_path": "51140dae4b5ecba74b885c9ebcec3e8ec52038466912431c72748573acc4bc7f.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 485, + 119, + 529, + 163 + ], + "blocks": [ + { + "bbox": [ + 485, + 119, + 529, + 163 + ], + "lines": [ + { + "bbox": [ + 485, + 119, + 529, + 163 + ], + "spans": [ + { + "bbox": [ + 485, + 119, + 529, + 163 + ], + "type": "image", + "image_path": "e291067c22ed8beb39fa6e2b994b57b24f760f8514b560868c7aabc38270a716.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 484, + 163, + 529, + 171 + ], + "lines": [ + { + "bbox": [ + 484, + 163, + 529, + 171 + ], + "spans": [ + { + "bbox": [ + 484, + 163, + 529, + 171 + ], + "type": "text", + "content": "(d) Low-W Filters" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "table", + "bbox": [ + 307, + 218, + 545, + 276 + ], + "blocks": [ + { + "bbox": [ + 66, + 245, + 265, + 254 + ], + "lines": [ + { + "bbox": [ + 66, + 245, + 265, + 254 + ], + "spans": [ + { + "bbox": [ + 66, + 245, + 265, + 254 + ], + "type": "text", + "content": "Table 7. Ablation results of statistical feature extractor." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 218, + 545, + 276 + ], + "lines": [ + { + "bbox": [ + 307, + 218, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 307, + 218, + 545, + 276 + ], + "type": "table", + "html": "
MethodAccuracyFlops(G)Params(M)
Ours90.820.7232.41
Ours w/o LHO w/ HSF87.918.1628.25
Ours w/o Pm in Eq. 789.318.5030.93
Ours w/o MHA in Eq.988.719.4929.73
Ours w/o LHO in TB w/ LHO in CNN86.222.8532.90
", + "image_path": "8d9668f5aef3f1d28cd2e14e6730ae302cb507a68e08102f245d63efeee25d37.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 306, + 276, + 545, + 318 + ], + "lines": [ + { + "bbox": [ + 306, + 276, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 306, + 276, + 545, + 318 + ], + "type": "text", + "content": "Table 8. Ablation results of LHO. HSF refers to a hand-crafted statistical feature composed of mean, variance, maximum and minimum values. MHA denotes multi-head attention. TB denotes texture branch." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 335, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 442 + ], + "type": "text", + "content": "16.26G flops of computation, requiring 24.69M parameters, reaching accuracy of 84.5. Our method consumes 20.72G flops of computation, requiring 32.41M parameters, reaching accuracy of 90.8. Compared to ResNet50, our method can improve accuracy significantly (+6.3) with only increasing computation and parameter usage by " + }, + { + "bbox": [ + 305, + 335, + 545, + 442 + ], + "type": "inline_equation", + "content": "27\\%" + }, + { + "bbox": [ + 305, + 335, + 545, + 442 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 335, + 545, + 442 + ], + "type": "inline_equation", + "content": "31\\%" + }, + { + "bbox": [ + 305, + 335, + 545, + 442 + ], + "type": "text", + "content": " respectively. This demonstrates the high effectiveness and high efficiency of our method with outstanding performance and reasonable computation costs." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 462, + 378, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 462, + 378, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 462, + 378, + 475 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 601 + ], + "type": "text", + "content": "This paper presents a novel network that extracts texture features to facilitate fine-grained recognition using Gabor filters. We make the Gabor filter parameters to be automatically learned in a stable and effective manner through our carefully-designed value constraint strategies. We also propose a statistical feature extractor and a region selection gate, allowing informative and effective Gabor texture features to be extracted with very few extra computation costs. Our method is effective, as shown by the extensive experiments with state-of-the-art (SOTA) performance." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-08-006), Singapore Ministry of Education (MOE) AcRF Tier 2 under Grant MOE-T2EP20222-0009, the National Research Foundation Singapore through AI Singapore Programme under Grant AISG-100E-2020-065, and SUTD SKI Project under Grant SKI 2021_02_06." + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1628" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Jon Arrospide and Luis Salgado. 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Existing methods employ local color transformation or region matching between foreground and background, which neglects powerful proximity prior and independently distinguishes fore-/back-ground as a whole part for harmonization. As a result, they still show a limited performance across varied foreground objects and scenes. To address this issue, we propose a novel Global-aware Kernel Network (GKNet) to harmonize local regions with comprehensive consideration of long-distance background references. Specifically, GKNet includes two parts, i.e., harmony kernel prediction and harmony kernel modulation branches. The former includes a Long-distance Reference Extractor (LRE) to obtain long-distance context and Kernel Prediction Blocks (KPB) to predict multi-level harmony kernels by fusing global information with local features. To achieve this goal, a novel Selective Correlation Fusion (SCF) module is proposed to better select relevant long-distance background references for local harmonization. The latter employs the predicted kernels to harmonize foreground regions with local and global awareness. Abundant experiments demonstrate the superiority of our method for image harmonization over state-of-the-art methods, e.g., achieving 39.53dB PSNR that surpasses the best counterpart by $+0.78dB \\uparrow$ ; decreasing fMSE/MSE by $11.5\\% \\downarrow / 6.7\\% \\downarrow$ compared with the SoTA method. Code will be available at here.", + "bbox": [ + 76, + 337, + 472, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 790, + 209, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image composition aims to synthesize foreground objects from one image into another, which is a common task in image editing. However, human eyes could clearly dis", + "bbox": [ + 75, + 816, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/18b0644d2601a9662414b3be2857663babf630b02ba2ffd049b7ae58df022ef8.jpg", + "image_caption": [ + "(a) Local-translation" + ], + "image_footnote": [], + "bbox": [ + 506, + 301, + 625, + 396 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/58db1f95237660e64235570f4c861c51bb3efba4d1070191792f14cb09d227b4.jpg", + "image_caption": [ + "(b) Region-matching" + ], + "image_footnote": [], + "bbox": [ + 633, + 301, + 754, + 396 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5d109600587945610c59bd0b9f0fd0b0af5a977e5bed7c4f559ec9083f2a00b8.jpg", + "image_caption": [ + "(c) Ours", + "Figure 1. Comparison of background reference methods in harmonization. Blue/Red region represent foreground/background, respectively, and white/red arrows refer to interaction/injection, respectively. (a) Local-translation methods reference nearby pixels. (b) Region-matching methods transfer reference with a unified view of fore-/back-ground region. (c) Our method interacts long-distance reference and injects it with short-distance consideration." + ], + "image_footnote": [], + "bbox": [ + 759, + 301, + 880, + 396 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tinguish synthetic images due to the visual inconsistency between foreground and background in composited images. In attempting to solve the photo-unrealistic problem, image harmonization is proposed to adjust the foreground objects based on the illumination and color tone in background environment, which plays an important role in image editing.", + "bbox": [ + 496, + 537, + 890, + 627 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Traditional image harmonization approaches are mainly based on low-level feature matching, which is only effective for specific scenes. Recently, numerous learning-based methods have achieved remarkable progress by addressing image harmonization as a generation task. Existing learning-based methods could be categorized from two angles, i.e., local-translation and region-matching. 1) The former employs a convolutional encoder-decoder to learn a foreground pixel-to-pixel translation [41, 8]. But a shallow CNN only captures limited surrounding background. As shown in Figure 1a, these approaches harmonize the current pixel with local references, which is insufficient for harmonization as inner foreground pixels could not attach background reference. Besides, related long-distance references are effective in some cases. 2) The latter region matching methods [29, 7] distinguish foreground and background regions as two styles or domains. As shown in Figure 1b, they tackle harmonization as a matching problem with a", + "bbox": [ + 496, + 628, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 875, + 207, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7535", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/126e8e65b587f58e3ebc19c83ecd57db234022d67b2ef5922e2871ffa7cffed1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 88, + 184, + 157 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3e8f0dd3e242b97e4e005be6e0b910d7e4cde5fe3edfab21a56329345d56c8e6.jpg", + "image_caption": [ + "Mask" + ], + "image_footnote": [], + "bbox": [ + 96, + 159, + 184, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5dcd8194484156588d0d3d1b131b7b79cf3e06e62344f96f5629aa780a33a480.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 90, + 274, + 157 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d497e4e99c43ef9861bce0724ec0993d966eac7a1940f23ec78d5fea7b3cd9dc.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 186, + 159, + 276, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2129599f4d0178d627aec0f6f50b1c8aabc821597aec715f72507013e947e802.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 90, + 364, + 157 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d2a1e7d66aad9544f5a005892ef82bb7619e6a00069d4977633fdd4843ba533f.jpg", + "image_caption": [ + "RainNet[7]" + ], + "image_footnote": [], + "bbox": [ + 277, + 159, + 364, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4a61754991603c4af3c2c8e7a40e68e81198b29e1d47e63f16d0b8898d69d18f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 90, + 454, + 157 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e8e3181544cdcda97f2a29799480e67ce129346e35e970bfb03b8184478ba255.jpg", + "image_caption": [ + "$\\mathrm{iS}^2\\mathrm{AM}[38]$" + ], + "image_footnote": [], + "bbox": [ + 367, + 159, + 454, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f7943e25f12f8712fc5f5ce8d3bbd56629d77a25c52d5859f7826a53b67f44ae.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 455, + 90, + 544, + 157 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/39c20972af67b4b2dd6ea3ab993291a6fb1d18773be9376e504def293283f183.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 455, + 159, + 545, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9a18663b0eecb52818d0e045a7820aa26152321ffe1a805b4512bd1b25f3cdb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 545, + 90, + 633, + 157 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d48040413b025fc1001af5170d458372e916a35665a3158ae185cfce6dc4abb9.jpg", + "image_caption": [ + "Real(GT)" + ], + "image_footnote": [], + "bbox": [ + 545, + 159, + 633, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1ec33eaddb2c5db32dd9643c980dac71dc5a8fcfa4ed471630eab05b038e7a23.jpg", + "image_caption": [ + "Figure 2. Left: Two challenging samples in image harmonization. Mask in column one and Red boxes represents the foreground. Right: Performance comparison with SOTA methods in terms of PSNR and model size. The circle size represents the floating-point number." + ], + "image_footnote": [], + "bbox": [ + 640, + 89, + 879, + 228 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "unified view of these two regions by statistics components or discriminators. Though these approaches harmonize images with a broader reference range, they totally neglect the spatial variations in two regions. Hang et al. [17] begin to notice this problem and add attention-based references in region matching method [29]. But they still separate two regions independently and harmonize foreground by unified matching without considering foreground spatial variations.", + "bbox": [ + 75, + 309, + 467, + 430 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To further illustrate existing problems, we provide two common harmonization cases in Figure 2. In the first case, a small foreground object appears in the background with obvious color changes. The region-matching method RainNet [7] provides a poor color correction result while the local method iS²AM [38] could tackle this case well, which indicates that the unified view of background will blend the overall complex color conditions. In the second case, related long-distance references exist in the background, while the local method could only attach insufficient adjacent information. Region-matching method RainNet could obtain whole background blue tone by matching, but it still excessively harmonizes the house due to the unified view. These two cases indicate that local reference is insufficient, but region-matching methods could not model long-distance reference well and will cause unbalanced harmonization problems by rough matching.", + "bbox": [ + 75, + 431, + 467, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To solve this problem, we rethink essential proximity priors in image harmonization, i.e., when we paste an object into background, the color or light is related to location and will be influenced by its neighboring first. Moreover, the effective long-distance information in background changes with pasted locations, which requires us to learn adaptive references for each part. Inspired by this observation, we propose a novel Global-aware Kernel Network (GKNet) to integrate local harmony modulation and long-distance background references, including harmony kernel prediction and harmony kernel modulation. For harmony kernel prediction, we propose a novel global-aware kernel prediction method including Long-distance Reference Extractor (LRE) to obtain long-distance references and Ker-", + "bbox": [ + 75, + 689, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "nel Prediction Blocks (KPB) to predict multi-level adaptive kernels with selected long-distance references by Selective Correlation Fusion (SCF). For kernel modulation, we propose to model local harmony operation by predicted global-aware kernels and multi-level features. Focusing on features in kernel region, kernel modulation is significant in alleviating unbalanced region-matching errors in complex scenes.", + "bbox": [ + 496, + 309, + 890, + 415 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, we make following contributions:", + "bbox": [ + 517, + 415, + 843, + 430 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- With the observation of proximity prior and long-distance references in image harmonization task, we design GKNet to model global-local interaction by learning global-aware harmony kernel, including harmony kernel prediction and harmony kernel modulation.", + "- For harmony kernel prediction, we propose a kernel prediction branch combined with LRE to model global information and multiple KPB to learn adaptive harmony kernels. For better global references, we design SCF to select relevant long-distance references for local harmonization. For harmony kernel modulation, we propose the method to harmonize local regions in multi-level decoder layers with predicted kernels.", + "- Extensive experiments demonstrate the superior performance of our methods in both quantitative and qualitative results, noting that our method achieves state-of-the-art results on iHarmony4 datasets." + ], + "bbox": [ + 500, + 436, + 890, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 715, + 635, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image Harmonization", + "text_level": 1, + "bbox": [ + 500, + 741, + 705, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional image harmonization works have focused on finding a better method for low-level appearances matching between foreground and background regions in images, which includes color statistics [36, 35, 45], gradient information [20, 34, 40], and multi-scale statistical features [39, 25]. However, traditional methods could only be effective in specific scenes. With the advanced generative ability of deep learning, Tsai et al. [41] firstly propose a learning-based encoder-decoder network assisted by", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7536", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/01d3f1749a8e2c43b19366b9a8d177ffaa464a09fa00df3ece36ce22c385a035.jpg", + "image_caption": [ + "Figure 3. The overview of our proposed GKNet, which consists of harmony kernel prediction branch and harmony kernel modulation branch. As shown in gray box, the harmony kernel prediction branch is combined with a Long-term Reference Extractor (LRE) and multi-level Kernel Prediction Blocks (KPB). As shown in yellow box, we propose Selective Correlation Fusion (SCF) module in KPB for better long-distance references. Given a composited image $I_{c}$ with corresponding foreground mask $\\mathbf{M}$ , we extract deep features $\\mathbf{F}_E^l$ from encoder $\\phi_E$ . Then, harmony kernel prediction branch utilizes the deepest feature map and $\\{\\mathbf{F}_E^l\\}$ to predict multi-level dynamic harmony kernels $\\{\\mathbf{K}^l\\}$ increasingly. The predicted global-aware kernels are employed for harmony kernel modulation in decoder $\\phi_D$ ." + ], + "image_footnote": [], + "bbox": [ + 89, + 85, + 880, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a semantic branch. In observation that semantic information is effective in image harmonization, Soffliuk et al. [38] also add additional pre-train semantic model to baseline DIH [41] and $\\mathbf{S}^2\\mathbf{A}\\mathbf{M}$ [8]. Inspired by domain transfer, Cong et al. [7] adopt a verification discriminator to distinguish foreground and background domains. Similarly, Ling et al. [29] also treat the composited image as two independent parts and apply style transfer idea to match mean-variance statistics. To focus on harmonize foreground region, some methods add attention mechanisms. Cun et al. [8] add a spatial-separated attention module. Guo et al. [15] for the first time introduce Transformer architecture to image harmonization. Hang et al. [17] add background attention calculation to the style transfer block [29], and they also incorporated the idea of contrast learning. Besides, Guo et al. [16] decompose image into reflectance and illumination by autoencoder for separate harmonization based on Retinex theory. Some high-resolution methods [24, 44] frame image harmonization as an image-level problem to learn white-box arguments. However, the above methods neglect spatial proximity prior and could not model long-distance references well. Instead in this paper, we design", + "bbox": [ + 75, + 565, + 472, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a better local modulation method combined with selected long-distance references to alleviate this problem.", + "bbox": [ + 498, + 565, + 890, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Dynamic Filtering in Image Editing", + "text_level": 1, + "bbox": [ + 500, + 604, + 812, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The input-dependent dynamic filtering first proposed by Jia [21] et al. aims to learn position-specific filters on pixel inputs and apply the generated kernels to another input, which has been widely used in numerous vision tasks [33, 23, 46, 9]. This method also shows effectiveness in image editing tasks, such as denoising [1, 32, 42], shadow removing [13], deraining [14], image inpainting [26], and blur synthesis [2]. However, most above methods apply dynamic filtering at image-level filter prediction and utilization. We propose to learn a multi-level global-aware kernel with long-term context references for harmonization.", + "bbox": [ + 496, + 627, + 893, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Feature Fusion", + "text_level": 1, + "bbox": [ + 500, + 801, + 653, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature fusion is to combine features from different layers or branches, which is an omnipresent part of modern neural networks and has been studied extensively. Most previous works [18, 37, 28] for feature fusion focus on the pathways structure design, applying two linear classic", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7537", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "methods of summation or concatenation. Recently, benefit from the successful use of Transformer in computer vision [4, 11, 31, 50, 49, 48, 3, 4, 12, 43, 22, 30, 15], some works [19, 27, 52, 10, 47, 51, 5] apply attention mechanism to present nonlinear approaches for feature fusion. As global information is significant in image harmonization, we design a dynamic weighted fusion method to effectively fuse long-distance reference into kernel prediction.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 223, + 168, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a composited image $I_{c}$ with its corresponding binary mask $\\mathbf{M}$ indicating the region to be harmonized, our goal is to learn a network $\\mathrm{G}$ that outputs harmonized image $I_{h}$ , which could be formulated as $I_{h} = G(I_{c}, M)$ . To make this composited image $I_{c}$ look natural, we train our model $\\mathrm{G}$ to adjust the foreground region $I_{f}$ in a supervised manner with paired real image $I$ . In this paper, we also define the background region as $I_{b}$ , and then the composition process could be formulated as $I_{c} = I_{f} \\cdot M + (1 - M) \\cdot I_{b}$ , where $\\cdot$ denotes element-wise multiplication.", + "bbox": [ + 75, + 250, + 472, + 401 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Overview of Our Network", + "text_level": 1, + "bbox": [ + 76, + 407, + 313, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 3, we design a novel network architecture for image harmonization tasks to allow our network to pay attention to short-distance and long-distance information simultaneously. Following the standard designs in image harmonization works [8, 38, 29] we use simple U-Net [37] with attention blocks [8] as the basic structure. We also take composited RGB image $I_{c} \\in \\mathbb{R}^{3 \\times H \\times W}$ concatenated with foreground region mask $\\mathbf{M} \\in \\mathbb{R}^{1 \\times H \\times W}$ as input.", + "bbox": [ + 75, + 431, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivated by proximity prior in image harmonization, we propose Global-aware Kernel Network (GKNet) to learn global-aware harmony kernel for image harmonization, which consists of two branches, harmony kernel prediction and harmony kernel modulation. Firstly, as long-distance reference is crucial for harmonization task, we design global-aware kernel prediction branch to predict harmony kernel with context modeling, which contains a transformer-based Long-term Reference Extractor (LRE) to extract global reference and Kernel Prediction Block (KPB) to predict harmony kernels. In order to incorporate relevant long-term references for local harmonization, a novel Selective Correlation Fusion (SCF) is proposed to select more effective references in backgrounds. Secondly, we design a multi-level harmony kernel modulation in decoder layers to employ the predicted global-aware kernels. The mechanism between global-aware harmony kernel prediction and harmony kernel modulation finally achieves local-global interaction for image harmonization.", + "bbox": [ + 75, + 551, + 472, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Harmony Kernel Prediction", + "text_level": 1, + "bbox": [ + 76, + 847, + 328, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by recent works in image editing [1, 14, 32], we propose to apply dynamic kernels to force the current pixel", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "harmonized with surrounding regions adaptively. This approach effectively makes up for the lack of consideration of proximity prior in previous harmonization works. However, basic dynamic kernels for image editing tasks such as denoising and deraining are applied with a fixed size at image-level. To predict more proper adaptive kernels for image harmonization, we analyze the following: 1) Global modeling is necessary for image harmonization as long-distance references may appear in the background. Hence, we design a novel global-aware harmony kernel prediction branch with LRE to extract global information and KPB to predict global-aware kernels with fusion module SCF. 2) Fixed-size kernels applied at image-level could not handle the scale problem well. e.g. The pixels inside the large foreground mask can hardly obtain any real background information, while predicting large kernels will bring high computation costs and breaks the intention of proximity prior. Besides, image-level dynamic kernels pay more attention to detailed structure, while in image harmonization we also need to adapt multiple scene variations to harmonize foregrounds at semantic level. In order to adapt to multi-scene and multiscale problems, we propose to predict kernels in multi-level structures.", + "bbox": [ + 496, + 90, + 893, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Long-distance Reference Extractor. In order to obtain long-term context, we employ 1-transformer layers [11] as our global information extractor. We feed the deepest feature map $\\mathbf{F}_E^1$ from CNN encoder into transformer layers. With the down-sampling feature map in low-resolution of $(\\frac{w}{r},\\frac{h}{r})$ , we treat each pixel as a token to generate embeddings. With the multi-head attention mechanism, we obtain global interactive feature $\\mathbf{F}_{global}\\in \\mathbb{R}^{C\\times HW}$ after 1-transformer layers. After reshaping and post-convolution layer, we obtain the long-term reference feature $\\mathbf{F}_{LR}$ .", + "bbox": [ + 496, + 453, + 893, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Kernel Prediction Block. To adapt diverse foreground scales and background scenarios, we apply our local operation kernel modulation in multiple decoder levels. Nevertheless, deep-level features contain more semantic information, and shallow features contain more details, we need to predict corresponding adaptive kernels for different level harmony kernel modulation. Thus, our designed global-aware harmony kernel prediction branch is in a multi-level structure to increasingly predict a series of kernels.", + "bbox": [ + 496, + 619, + 893, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Figure 3, we show our proposed KPB structure from predicting kernels to harmony kernel modulation operation. The operation in $l$ th KPBlock can be formulated as", + "bbox": [ + 496, + 755, + 890, + 800 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {K} ^ {l}, \\mathbf {F} _ {K P B} ^ {l} = K P B l o c k \\left(\\mathbf {F} _ {E} ^ {l}, \\mathbf {F} _ {K P B} ^ {l - 1}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 810, + 890, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where KPBlock $(\\cdot)$ is the KPBlock to predict $\\mathbf{K}^l$ . For each KPB, we take $\\mathbf{F}_{KP B}^{l-1} \\in \\mathbb{R}^{C_l \\times H_l \\times W_l}$ transferred from $(l-1)$ th KPB (For the deepest KPB, we input $\\mathbf{F}_{LR}$ ) and the $l$ th encoder layer feature $\\mathbf{F}_E^l$ as input (We denote $\\mathbf{F}_E^1$ as the deepest", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7538", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/440d5d4af20767d9b5227c920aa3704e9cdf4cf33eefd2930098bb5459379e23.jpg", + "image_caption": [ + "Figure 4. Schematic diagram of SCF. The module takes the (1-1)th layer feature $\\mathbf{F}_{KPB}^{l-1}$ and encoder feature $\\mathbf{F}_E^l$ as input and outputs the correlation-aware fusion feature $\\hat{\\mathbf{F}}_{KPB}^l$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "layer in encoder), which outputs feature $\\mathbf{F}_{KPB}^{l}$ for next KP-Block and the global-aware kernels $\\mathbf{K}^{l} = \\mathrm{Conv}(\\mathbf{F}_{KPB}^{l})$ after post-convolutions.", + "bbox": [ + 76, + 357, + 468, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Selective Correlation Fusion. Long-distance reference $\\mathbf{F}_{LR}$ obtained from LRE is then injected into the deepest KPBlock to model global information for local harmonization. The standard way of feature fusion, like concatenation or addition, equally treats low-level and high-level features. To efficiently model long-term information for local harmonization, we propose SCF to select relevant global information by interacting encoder features $\\mathbf{F}_E$ and long-distance references based on channel-wise attention mechanism.", + "bbox": [ + 75, + 417, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, as shown in Figure 4, we take the $(l - 1)$ th layer feature $\\mathbf{F}_{KPB}^{l - 1}\\in \\mathbb{R}^{C_{l - 1}\\times H_{l - 1}\\times W_{l - 1}}$ and the $l$ th encoder feature $\\mathbf{F}_E^l\\in \\mathbb{R}^{C_l\\times H_l\\times W_l}$ as input and extract attention vector $\\alpha_{KPB},\\alpha_E\\in \\mathbb{R}^{C_l}$ by $3\\times 3$ convolutions and MLP. Subsequently, the attention vector is divided into n groups with length m as $\\tilde{\\alpha}_{KPB},\\tilde{\\alpha}_E\\in \\mathbb{R}^{n\\times m}$ . Thus, the channel-wise attention relation $\\mathbf{A}\\in \\mathbb{R}^{n\\times n}$ can be calculated by matrix product", + "bbox": [ + 76, + 553, + 468, + 660 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} = \\tilde {\\alpha} _ {K P B} \\odot \\tilde {\\alpha} _ {E} ^ {T}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 667, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After that, we calculate the selective factor $\\overline{\\alpha}_{KPB},\\overline{\\alpha}_E\\in$ $\\mathbb{R}^{C_l}$ through $N\\times N$ convolutions with splitting. Then, we obtain the selective attention weights $S^l\\in \\{S_E^l,S_{KPB}^{l - 1}\\}$ for each features by $\\alpha \\in \\{\\alpha_{KPB},\\alpha_E\\}$ and $\\overline{\\alpha}\\in \\{\\overline{\\alpha}_{KPB},\\overline{\\alpha}_E\\}$ , which can be formulated as", + "bbox": [ + 76, + 695, + 468, + 768 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS ^ {l} = \\sigma (\\alpha + b \\cdot F C (\\bar {\\alpha})), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 777, + 468, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{b}$ is a learnable parameter, $\\sigma$ is sigmoid function. Based on the attention weight vector, then the shallow and deep information are interacted as follows:", + "bbox": [ + 76, + 805, + 468, + 849 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {F}} _ {K P B} ^ {l} = S _ {E} ^ {l} \\cdot \\operatorname {C o n v} \\left(\\mathbf {F} _ {E} ^ {l}\\right) + \\text {U p s a m p l e} \\left(S _ {K P B} ^ {l - 1} \\cdot \\operatorname {C o n v} \\left(\\mathbf {F} _ {K P B} ^ {l - 1}\\right)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 857, + 468, + 877 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\cdot$ denotes to element-wise multiplication.", + "bbox": [ + 76, + 885, + 390, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Harmony Kernel Modulation", + "text_level": 1, + "bbox": [ + 500, + 90, + 761, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The global-aware adaptive kernel obtained from the harmony kernel prediction branch is then utilized in harmony kernel modulation. In this section, we illustrate the regional harmony operation method kernel modulation in decoder layers, which converts the previous overall treatment of background and foreground into a local reference. As mentioned in Section 3.2, we apply multi-level kernel modulation in decoder layer to adapt scales and scenario variation problem. Figure 3 shows our proposed kernel modulation in $l$ th decoder layers, which could be formulated as", + "bbox": [ + 496, + 113, + 890, + 263 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {F}} _ {D} ^ {l} = \\mathbf {F} _ {D} ^ {l} \\otimes \\mathbf {K} ^ {l}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 268, + 890, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\oplus$ denotes the harmony kernel modulation, $\\mathbf{F}_D^l\\in$ $\\mathbb{R}^{C\\times H\\times W}$ is the deep feature extracted from the $l$ th layer in decoder, and the $\\hat{\\mathbf{F}}_{\\mathbf{D}}^{l}\\in \\mathbb{R}^{C\\times H\\times W}$ is its corresponding harmony kernel modulation result feature in the $l$ th layer. The tensor $\\mathbf{K}^l\\in \\mathbb{R}^{C\\times N^2\\times H\\times W}$ represents the kernels with size of $N$ for harmony kernel modulation in the $l$ th feature layer, which we obtain from KPB. For the kernel modulation in each pixel, we can expand the above equation as", + "bbox": [ + 496, + 294, + 892, + 415 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {F}} _ {D} ^ {l} [ \\mathbf {p} ] = \\sum_ {\\mathbf {q} \\in \\mathcal {N} _ {p}} \\mathbf {K} _ {p} ^ {l} [ \\mathbf {p} - \\mathbf {q} ] \\mathbf {F} _ {D} ^ {l} [ \\mathbf {q} ], \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 421, + 890, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{p}$ and $\\mathbf{q}$ are the coordinates of pixels in the image, $\\mathbf{K}_p^l$ is the kernel for filtering the element $\\mathbf{p}$ of $\\mathbf{F}_D^l$ via its surrounding elements, i.e., $\\mathcal{N}_p$ . As we illustrate in Eq. 5, $\\mathbf{K}^l$ contains all element-wise kernels, i.e., $\\mathbf{K}_p^l \\in \\mathbb{R}^{C \\times N \\times N}$ for filtering operations. After the kernel modulation in decoder layers, we finally obtain the harmonization result. In this paper, we define the U-Net decoder layer as $\\phi_D(\\cdot)$ , then we can formulate our harmonization process with kernel modulation as $\\hat{I}_h = \\phi_D^L (\\dots \\phi_D^1 (\\mathbf{F}_D^1\\otimes \\mathbf{K}^1))\\cdot M + (1 - M)\\cdot I_c$ .", + "bbox": [ + 496, + 460, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Objective function", + "text_level": 1, + "bbox": [ + 500, + 604, + 679, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the training phase, we only employ foreground-normalized MSE loss as our objective function. Compared with normal MSE loss, it reduces the impact of copying background area:", + "bbox": [ + 496, + 628, + 890, + 689 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} = \\frac {\\sum_ {h , w} \\left\\| \\hat {I} - I \\right\\| _ {2} ^ {2}}{\\max \\left\\{A _ {\\min } , \\sum_ {h , w} M _ {h , w} \\right\\}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 694, + 890, + 760 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $A_{min}$ is a hyperparameter to keep the loss function stable as there might be some too small foreground objects. In this paper, we set $A_{min} = 100$ as suggested in [38].", + "bbox": [ + 496, + 765, + 890, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 821, + 633, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 845, + 717, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct the image harmonization experiment at resolution $256 \\times 256$ on the benchmark dataset iHarmony4 [7].", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7539", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/39065f71897d790683bd3643b0da016d85173eea41cffeb5bcd14c0c7050ab01.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons across four sub-datasets of iHarmony4 [7]. ↑ indicates the higher the better, and ↓ indicates the lower the better. We compute fMSE for better reflection on harmonization tasks. Best results are in bold and the suboptimal results are in underline." + ], + "table_footnote": [], + "table_body": "
MethodHCOCOHAdobe5kHFlickrHday2nightALL
PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓
Composite33.9469.37996.5928.16345.542051.6128.32264.351574.3734.01109.651409.9831.63172.471376.42
DIH [41]34.6951.85798.9932.2892.65593.0329.55163.381099.1334.6282.341129.4033.4176.77773.18
S2AM [8]35.4741.07542.0633.7763.40404.6230.03143.45785.6535.6950.87835.0634.3559.67594.67
DoveNet [7]35.8336.72551.0134.3452.32380.3930.21133.14827.0335.2751.951075.7134.7652.33532.62
IIH [16]37.1624.92416.3835.2043.02284.2131.34105.13716.6035.9655.53797.0435.9038.71400.29
RAINNnet [29]37.0829.52501.1736.2243.35317.3531.64110.59688.4034.8357.40916.4836.1240.29469.60
iDIH-HRNet [38]39.1616.48266.1938.0821.88173.9633.1369.67443.6537.7240.59590.9738.1924.44264.96
D-HT [15]38.7616.89299.3036.8838.53265.1133.1374.51515.4537.1053.01704.4237.5530.30320.78
Harmonizer [24]38.7717.34298.4237.6421.89170.0533.6364.81434.0637.5633.14542.0737.8424.26280.51
DCCF [44]39.7214.55267.7938.2420.20171.0133.7266.20440.8438.1851.40629.6738.6022.64265.41
SCS-Co [17]39.8813.58245.5438.2921.01165.4834.2255.83393.7237.8341.75606.8038.7521.33248.86
Ours40.3212.95222.3139.9717.84138.2234.4557.58372.9038.4742.76546.0639.5319.90220.44
", + "bbox": [ + 80, + 128, + 893, + 303 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0d866ebe000c36fc921e749a553e83efaa2494d7579752c9ede1331fe74538b3.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons on different ratios of foreground based on iHarmony4 by MSE and fMSE metrics. The best results are in bold and the suboptimal results are in underline." + ], + "table_footnote": [], + "table_body": "
MethodVenue0%~5%5%~15%15%~100%
MSE↓fMSE↓MSE↓fMSE↓MSE↓fMSE↓
DIHCVPR'1718.92799.1764.23725.86228.86768.89
S2AMTIP'2015.09623.1148.33540.54117.62592.83
DoveNetCVPR'2014.03591.8844.90504.42152.07505.82
RainNetCVPR'2111.66550.3832.05378.69117.41389.80
iS2AMWACV'216.73294.7618.03204.6963.02207.82
GKNetOurs5.36244.0617.46200.3457.31188.75
", + "bbox": [ + 80, + 366, + 468, + 472 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The initial learning rate is set to $10^{-4}$ , and the models are trained for 120 epochs with a batch size of 16 on four 2080Ti GPUs. For optimizer, we adopt an Adam optimizer with $\\beta_{1} = 0.9, \\beta_{2} = 0.999$ and $\\epsilon = 10^{-8}$ . It takes about two days for training. Our proposed model is implemented by PyTorch, and more detailed network architectures could be found in the supplementary file.", + "bbox": [ + 75, + 486, + 468, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 76, + 604, + 274, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. To evaluate our proposed method for image harmonization, we conduct our experiments on the benchmark dataset iHarmony4 [7], which consists of 4 sub-datasets: HCOCO, HAdobe5K, HFlickr, and Hday2night, including 73147 pairs of synthesized composite images with their corresponding foreground mask and ground truth image.", + "bbox": [ + 75, + 628, + 468, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. Following the standard setups in image harmonization, we use the peak signal-to-noise ratio (PSNR) and Mean Squared Error (MSE) as evaluation metrics. Furthermore, it is more accurate to only calculate the difference in the foreground region with the metric foreground MSE (fMSE) introduced by [38]. The metric MSE is calculated for the whole image, while there is no changes for pixels in the background region in harmonization task. Without considering the foreground ratio, the average MSE and PSNR results of the dataset will be more responsive to the performance of large-scale targets. In this paper, we argue that fMSE is more suitable for harmonization task.", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with SOTAs", + "text_level": 1, + "bbox": [ + 498, + 314, + 728, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative comparison. As results shown in Table 1, we compare our method with other state-of-the-art image harmonization methods on iHarmony4 [7]. Following [7, 38], we also evaluate the model performance on different ratios of foreground by splitting the test images into three groups, i.e., $0\\% \\sim 5\\%$ , $5\\% \\sim 15\\%$ , and $15\\% \\sim 100\\%$ . We provide these results in Table 2. Observing the quantitative experiment results above, we can summarize the following conclusions: 1) Our method achieves SOTA results of all evaluation metrics on average iharmony4 datasets. More specifically, our method achieves $0.78\\mathrm{dB}\\uparrow$ improvement in PSNR, $1.43\\downarrow$ in MSE, and $28.42\\downarrow$ in fMSE compared with suboptimal methods. 2) Our method obtains the best fMSE scores on all sub-datasets, meaning that the foreground regions generated by our method are more natural and closer to real images. 3) As shown in Table 2, our model performs well on each foreground ratio, especially on $0\\% \\sim 5\\%$ , which indicates that our method has a strong ability to handle variable foreground scales. It also proves that our proposed global-aware adaptive kernel could process global-to-local impact with excellence.", + "bbox": [ + 496, + 338, + 890, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative comparison. We further provide qualitative results on iHarmony4 datasets in Figure 5. It could be observed that our GKNet generates more visually coherent images of the foreground and background than composited images, which are also closer to ground truth. 1) The first two rows of examples show that our method can effectively handle the small object harmonization problem in complex scenes with proximity prior consideration. 2) The last two row examples show that our regional modulation with multi-level structure performs well in large foreground cases, which handles a wide range of enormous contrast. For more detailed descriptions, please refer to the caption in Figure 5. In contrast, our method presents more photorealistic results. More visual comparison results on iHarmony4 datasets could be seen in supplementary materials.", + "bbox": [ + 496, + 657, + 890, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons on Real Datasets. 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Qualitative comparisons with SOTA methods on iHarmony4 [7]. Mask in column one and Red box in Input represents the foreground. Case 1: The background color shows spatial variation, while only our method captures practical color reference by predicted kernel and local harmony modulation. Case 2: The harmony result obtained by our method is better in the detailed structure like duckweed center due to target harmony kernels for each foreground part. Case 3 & 4: For large foregrounds, our approach could also achieve better results, which preserves more original details and is closer to ground truth." + ], + "image_footnote": [], + "bbox": [ + 109, + 459, + 235, + 527 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e189c02824a96cbe39e6550271286545d4037a4a557373b54802a21804f28fd6.jpg", + "image_caption": [ + "Mask" + ], + "image_footnote": [], + "bbox": [ + 111, + 527, + 235, + 590 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fda5e40261ee860e95f80fe971d58e0a31e26f156325902ed8ec75638152910a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 235, + 459, + 359, + 527 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f18198fd01a574b469e9356d42ac8b56acccb04740ce40239eb2d4cf732b4373.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 236, + 527, + 359, + 590 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/98a8745f1ac17a11e538750e287d681d461e9056e9f12ebcdea67c040357d247.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 459, + 486, + 527 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1333f811a8d75ec905214fb106ffadd0268e0496b307c73a7e176885487a6fb0.jpg", + "image_caption": [ + "RainNet [29]" + ], + "image_footnote": [], + "bbox": [ + 361, + 527, + 486, + 590 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9cd1f7ccb04c1ff068b1a3bba8daa9d7200ec7de472aff782d3a786ee52d448d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 459, + 612, + 527 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0c06e123d88f8d4bf1d9a412d85ea575c6c7d376432c214f498d4503d76b99f3.jpg", + "image_caption": [ + "iDIH-HRNet [38]", + "Figure 6. Qualitative comparisons with SOTA methods on real composite images [41]. Mask in column one and Red box in Input represents the foregrounds. Case 1: Comparing the results on the dogs, our method achieves more natural results over the sunset background. Case 2: Our result dims the foreground person based on background dim light, which achieves a more natural effect." + ], + "image_footnote": [], + "bbox": [ + 486, + 527, + 611, + 590 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e16a835e09f1c0120b1807b9a7b9b6d7df0432f5c9cbcbbcf47544281126023.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 612, + 459, + 736, + 527 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8f91f9cc8def8c8f92926d61cfc6d4e2e338913917945b785e626a0e929d51b6.jpg", + "image_caption": [ + "DoveNet [7]" + ], + "image_footnote": [], + "bbox": [ + 612, + 527, + 736, + 590 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/488de7ab53bdd093467a296ad45960758c2ed465ca75a1a6ec49a75c1efd4dd7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 459, + 862, + 527 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0d47297f164a21dfac4a1d2c8d9e725b817912eeffce39071b9b8c5ba8248465.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 738, + 527, + 862, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "real composition datasets [41] can be seen in Figure 6. For real composition cases, evaluation metrics are impossible to calculate as there are no ground truth images. Hence, we only show qualitative results and human study results here. More visual comparison results on real datasets could be seen in supplementary materials.", + "bbox": [ + 75, + 675, + 468, + 765 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4c7248f3797f24f7aa56f9b270bbb10625b23c0023235b2040d1e78cb6146e5a.jpg", + "table_caption": [ + "Table 3. B-T scores comparison on real composite images." + ], + "table_footnote": [], + "table_body": "
MethodCompositeDoveNet[7]RainNet[29]iDIH-HRNet[38]Ours
B-T Score ↑0.4160.6860.9721.5321.944
", + "bbox": [ + 86, + 804, + 457, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following [7, 6, 16, 17], we conduct our human study by inviting 50 volunteers to compare 24750 pairwise results. The pairwise results are obtained from 99 real composited images, with 25 results for each pair of different methods on", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "average. We also use the Bradley-Terry model (B-T model) to calculate the global ranking score. Our method achieves the best results as shown in Table 3.", + "bbox": [ + 498, + 675, + 890, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 738, + 663, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of network components. We further conduct quantitative experiments to verify the effectiveness of components in GKNet. Note that modules in GKNet have dependencies, we can only show gradually added ablation studies. As the results in Table 4, our full model obtains the highest performance on all metrics when KPB, LRE, and SCF work together. Table 4 also illustrates the effectiveness of each component. Moreover, to further illustrate our global-local interaction method for harmonization, we show", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7541", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bc08647a1ec3ee01fd13664012965cc3849c8cd91f2b176a15b9851644a6f4d4.jpg", + "table_caption": [ + "Table 4. Quantitative ablation study of our approach with different components on iHarmony4[7]" + ], + "table_footnote": [], + "table_body": "
BaselineKPBLRESCFMSE ↓PSNR ↑fMSE ↓
✓✗✗✗27.2737.83280.56
✓✓✗✗21.4238.68235.72
✓✓✓✗20.5039.30229.63
✓✓✓✓19.9039.53220.44
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Qualitative ablation study of our approach. Red boxes in input image mark foreground." + ], + "image_footnote": [], + "bbox": [ + 341, + 268, + 403, + 316 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c27b19a32c1d41b04c6021e48f4f0dec815973fdd010f935b2dcd9b388612ab0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 406, + 218, + 468, + 267 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2f85e00f514f004335f67c79a03689f9e4ba86f911c09d94828cdd549b978563.jpg", + "image_caption": [ + "Full Model" + ], + "image_footnote": [], + "bbox": [ + 406, + 268, + 468, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "qualitative results in Figure 7. Compared with the baseline, the model with only local KPB outputs stronger local modeling results but loses global view. After introducing LRE, global awareness of the background is enhanced. But it is evident that color is overcorrected in the second row. After adding SCF, we effectively correct the deviation by selecting relevant references in background, and the final result is closer to real image.", + "bbox": [ + 75, + 387, + 468, + 508 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f190d800eb3ed7cea56f4451a291ff338220507ff613afa0f893451f6a3d8f59.jpg", + "image_caption": [ + "Figure 8. The cluster visual results of adaptive harmony kernels. e.g., in flower case, structure information like petal margin is displayed, which proves that kernels are predicted to adapt local harmonization specifically." + ], + "image_footnote": [], + "bbox": [ + 84, + 518, + 468, + 659 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Interpretability of Global-aware Harmony Kernel. To further illustrate the effectiveness of the adaptive harmony kernels, we cluster the per-pixel adaptive harmony kernels predicted from KPB by K-means. As shown in Figure 8, the clusters show strong spatial structure, which indicates that our predicted dynamic kernel can make the structural adjustment to harmonize the foreground. Moreover, in some cases, the change of kernel classes is related to the object mask. This exhibits that our harmony kernels are predicted dynamically to deal with visual inconsistency in different spatial locations (e.g. fore-/background or edges).", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/17c1ea4edaec58b734fecaa9c07b5045e2339560c376c9d9c256014c175524a1.jpg", + "image_caption": [ + "(a) Mask" + ], + "image_footnote": [], + "bbox": [ + 509, + 88, + 571, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/66a2b5bb4d01fdccef935d2110b3bcb610164c93f001066cf619cdc4ed270a06.jpg", + "image_caption": [ + "(b) Comp" + ], + "image_footnote": [], + "bbox": [ + 573, + 88, + 637, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a0f1d38a812309877073c3b97c7188dc41e9723d06610b01ee3a2fbe949afc5b.jpg", + "image_caption": [ + "(c) Feature map with channel attention weight" + ], + "image_footnote": [], + "bbox": [ + 637, + 88, + 697, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(c", + "bbox": [ + 643, + 186, + 653, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/af4d206aca83d4aebc2c62243ab1bb3a8daae06ca5584598e5cf95459abb3aeb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 88, + 759, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e13c1346577d118804a494b63cda97e8f51ff4157aba1633a09972d8449ab83f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 88, + 825, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9b9bdc8e1176f5e9d290bd6f341f5f02e91cf52b20a73ad09472fc345973c9fb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 826, + 89, + 888, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cecb2bf9c6b69c1ec88a73f83e0d744a684d3d60298031e78d2ee1e1095def8e.jpg", + "image_caption": [ + "Figure 9. Feature maps in SCF. Red number in upper right corner of feature map represents channel-wise attention weights.", + "Figure 10. Cross-attention from example point (10,10). We show four attention maps for different heads, which proves LRE can match model related long-distance references." + ], + "image_footnote": [], + "bbox": [ + 522, + 241, + 870, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Interpretability of LRE and SCF Module. We visualize the attention mechanism in LRE and SCF for interpreting global-local interaction. In Figure 9, we visualize feature maps in decoder layers to illustrate our channel-wise attention module SCF. Visual feature maps with attention weights show that harmony kernels are predicted with more attention on related background area and less attention on irrelevant background area or foreground. In Figure 10, we visualize the attention maps of LRE, focusing on an example point in foreground. As the long-distance information in predicted harmony kernels is brought by LRE, the visualized attention maps in different heads indicate two points: 1) The kernels for local operation have a global perceptive field with long-distance information. 2) Different heads pay attention to different reference parts, i.e. relevant background reference, foreground content, overall tone, etc.", + "bbox": [ + 500, + 438, + 890, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 694, + 617, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes an effective network GKNet to learn global-aware harmony kernels for image harmonization, including harmony kernel prediction and harmony kernel modulation branches. For harmony kernel prediction, we propose LRE to extract long-term references and KPB to predict global-aware kernels. To better fuse long-term context, we design SCF to select relevant references. For harmony kernel modulation, we employ the predicted kernels for harmonization with location awareness. Extensive experiments demonstrate that our proposed algorithm outperforms the state-of-the-art algorithms on the iHarmony4 dataset and real image composition datasets.", + "bbox": [ + 500, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7542", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by a Grant from The National Natural Science Foundation of China (No. 2021YFB2012300).", + "bbox": [ + 76, + 90, + 472, + 137 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 150, + 174, + 166 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Steve Bako, Thijs Vogels, Brian McWilliams, Mark Meyer, Jan Novák, Alex Harvill, Pradeep Sen, Tony Derose, and Fabrice Rousselle. Kernel-predicting convolutional networks for denoising monte carlo renderings. ACM Trans. Graph., 36(4):97-1, 2017. 3, 4", + "[2] Tim Brooks and Jonathan T Barron. Learning to synthesize motion blur. In CVPR, pages 6840-6848, 2019. 3", + "[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In ECCV, pages 213-229. 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In ECCV, pages 269-284, 2018. 4" + ], + "bbox": [ + 501, + 92, + 890, + 544 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7544", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Global-aware Kernel for Image Harmonization/edcde37a-d026-4b0d-9a7a-a8c99e117c7b_model.json b/2023/Learning Global-aware Kernel for Image Harmonization/edcde37a-d026-4b0d-9a7a-a8c99e117c7b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..de309143e6b559c813e1373e6f80661bb747dbb5 --- /dev/null +++ b/2023/Learning Global-aware Kernel for Image Harmonization/edcde37a-d026-4b0d-9a7a-a8c99e117c7b_model.json @@ -0,0 +1,3146 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.197, + 0.131, + 0.773, + 0.154 + ], + "angle": 0, + "content": "Learning Global-aware Kernel for Image Harmonization" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.18, + 0.732, + 0.218 + ], + "angle": 0, + "content": "Xintian Shen\\(^{1*}\\) Jiangning Zhang\\(^{2*}\\) Jun Chen\\(^{1}\\) Shipeng Bai\\(^{1}\\) Yue Han\\(^{1}\\) Yabiao Wang\\(^{2}\\) Chengjie Wang\\(^{2,3}\\) Yong Liu\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.218, + 0.791, + 0.27 + ], + "angle": 0, + "content": "\\(^{1}\\)APRIL Lab, Zhejiang University \\(^{2}\\)Youtu Lab, Tencent \\(^{3}\\)Shanghai Jiao Tong University [22132133, 186368, junc, shipengbai, 22132041]@zju.edu.cn, [caseywang, jasoncjwang]@tencent.com, yongliu@iipc.zju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.304, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.338, + 0.473, + 0.761 + ], + "angle": 0, + "content": "Image harmonization aims to solve the visual inconsistency problem in composited images by adaptively adjusting the foreground pixels with the background as references. Existing methods employ local color transformation or region matching between foreground and background, which neglects powerful proximity prior and independently distinguishes fore-/back-ground as a whole part for harmonization. As a result, they still show a limited performance across varied foreground objects and scenes. To address this issue, we propose a novel Global-aware Kernel Network (GKNet) to harmonize local regions with comprehensive consideration of long-distance background references. Specifically, GKNet includes two parts, i.e., harmony kernel prediction and harmony kernel modulation branches. The former includes a Long-distance Reference Extractor (LRE) to obtain long-distance context and Kernel Prediction Blocks (KPB) to predict multi-level harmony kernels by fusing global information with local features. To achieve this goal, a novel Selective Correlation Fusion (SCF) module is proposed to better select relevant long-distance background references for local harmonization. The latter employs the predicted kernels to harmonize foreground regions with local and global awareness. Abundant experiments demonstrate the superiority of our method for image harmonization over state-of-the-art methods, e.g., achieving 39.53dB PSNR that surpasses the best counterpart by \\(+0.78dB \\uparrow\\); decreasing fMSE/MSE by \\(11.5\\% \\downarrow / 6.7\\% \\downarrow\\) compared with the SoTA method. Code will be available at here." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.791, + 0.21, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.817, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Image composition aims to synthesize foreground objects from one image into another, which is a common task in image editing. However, human eyes could clearly dis" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.303, + 0.627, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.399, + 0.624, + 0.411 + ], + "angle": 0, + "content": "(a) Local-translation" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.303, + 0.755, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.399, + 0.753, + 0.412 + ], + "angle": 0, + "content": "(b) Region-matching" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.303, + 0.882, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.802, + 0.399, + 0.848, + 0.411 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.423, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Figure 1. Comparison of background reference methods in harmonization. Blue/Red region represent foreground/background, respectively, and white/red arrows refer to interaction/injection, respectively. (a) Local-translation methods reference nearby pixels. (b) Region-matching methods transfer reference with a unified view of fore-/back-ground region. (c) Our method interacts long-distance reference and injects it with short-distance consideration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.628 + ], + "angle": 0, + "content": "tinguish synthetic images due to the visual inconsistency between foreground and background in composited images. In attempting to solve the photo-unrealistic problem, image harmonization is proposed to adjust the foreground objects based on the illumination and color tone in background environment, which plays an important role in image editing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Traditional image harmonization approaches are mainly based on low-level feature matching, which is only effective for specific scenes. Recently, numerous learning-based methods have achieved remarkable progress by addressing image harmonization as a generation task. Existing learning-based methods could be categorized from two angles, i.e., local-translation and region-matching. 1) The former employs a convolutional encoder-decoder to learn a foreground pixel-to-pixel translation [41, 8]. But a shallow CNN only captures limited surrounding background. As shown in Figure 1a, these approaches harmonize the current pixel with local references, which is insufficient for harmonization as inner foreground pixels could not attach background reference. Besides, related long-distance references are effective in some cases. 2) The latter region matching methods [29, 7] distinguish foreground and background regions as two styles or domains. As shown in Figure 1b, they tackle harmonization as a matching problem with a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.208, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.222, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7535" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.089, + 0.186, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.16, + 0.186, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.23, + 0.154, + 0.24 + ], + "angle": 0, + "content": "Mask" + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.091, + 0.276, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.16, + 0.277, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.23, + 0.243, + 0.24 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.091, + 0.366, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.16, + 0.366, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.296, + 0.23, + 0.344, + 0.24 + ], + "angle": 0, + "content": "RainNet[7]" + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.091, + 0.455, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.16, + 0.455, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.23, + 0.434, + 0.241 + ], + "angle": 0, + "content": "\\(\\mathrm{iS}^2\\mathrm{AM}[38]\\)" + }, + { + "type": "image", + "bbox": [ + 0.457, + 0.091, + 0.545, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.457, + 0.16, + 0.546, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.488, + 0.23, + 0.511, + 0.24 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.091, + 0.635, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.16, + 0.635, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.23, + 0.611, + 0.24 + ], + "angle": 0, + "content": "Real(GT)" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.09, + 0.88, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.892, + 0.283 + ], + "angle": 0, + "content": "Figure 2. Left: Two challenging samples in image harmonization. Mask in column one and Red boxes represents the foreground. Right: Performance comparison with SOTA methods in terms of PSNR and model size. The circle size represents the floating-point number." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.468, + 0.431 + ], + "angle": 0, + "content": "unified view of these two regions by statistics components or discriminators. Though these approaches harmonize images with a broader reference range, they totally neglect the spatial variations in two regions. Hang et al. [17] begin to notice this problem and add attention-based references in region matching method [29]. But they still separate two regions independently and harmonize foreground by unified matching without considering foreground spatial variations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.468, + 0.688 + ], + "angle": 0, + "content": "To further illustrate existing problems, we provide two common harmonization cases in Figure 2. In the first case, a small foreground object appears in the background with obvious color changes. The region-matching method RainNet [7] provides a poor color correction result while the local method iS²AM [38] could tackle this case well, which indicates that the unified view of background will blend the overall complex color conditions. In the second case, related long-distance references exist in the background, while the local method could only attach insufficient adjacent information. Region-matching method RainNet could obtain whole background blue tone by matching, but it still excessively harmonizes the house due to the unified view. These two cases indicate that local reference is insufficient, but region-matching methods could not model long-distance reference well and will cause unbalanced harmonization problems by rough matching." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To solve this problem, we rethink essential proximity priors in image harmonization, i.e., when we paste an object into background, the color or light is related to location and will be influenced by its neighboring first. Moreover, the effective long-distance information in background changes with pasted locations, which requires us to learn adaptive references for each part. Inspired by this observation, we propose a novel Global-aware Kernel Network (GKNet) to integrate local harmony modulation and long-distance background references, including harmony kernel prediction and harmony kernel modulation. For harmony kernel prediction, we propose a novel global-aware kernel prediction method including Long-distance Reference Extractor (LRE) to obtain long-distance references and Ker-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.416 + ], + "angle": 0, + "content": "nel Prediction Blocks (KPB) to predict multi-level adaptive kernels with selected long-distance references by Selective Correlation Fusion (SCF). For kernel modulation, we propose to model local harmony operation by predicted global-aware kernels and multi-level features. Focusing on features in kernel region, kernel modulation is significant in alleviating unbalanced region-matching errors in complex scenes." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.416, + 0.844, + 0.431 + ], + "angle": 0, + "content": "To summarize, we make following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.437, + 0.892, + 0.512 + ], + "angle": 0, + "content": "- With the observation of proximity prior and long-distance references in image harmonization task, we design GKNet to model global-local interaction by learning global-aware harmony kernel, including harmony kernel prediction and harmony kernel modulation." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.517, + 0.892, + 0.637 + ], + "angle": 0, + "content": "- For harmony kernel prediction, we propose a kernel prediction branch combined with LRE to model global information and multiple KPB to learn adaptive harmony kernels. For better global references, we design SCF to select relevant long-distance references for local harmonization. For harmony kernel modulation, we propose the method to harmonize local regions in multi-level decoder layers with predicted kernels." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.642, + 0.892, + 0.702 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the superior performance of our methods in both quantitative and qualitative results, noting that our method achieves state-of-the-art results on iHarmony4 datasets." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.437, + 0.892, + 0.702 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.717, + 0.637, + 0.732 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.706, + 0.758 + ], + "angle": 0, + "content": "2.1. Image Harmonization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Traditional image harmonization works have focused on finding a better method for low-level appearances matching between foreground and background regions in images, which includes color statistics [36, 35, 45], gradient information [20, 34, 40], and multi-scale statistical features [39, 25]. However, traditional methods could only be effective in specific scenes. With the advanced generative ability of deep learning, Tsai et al. [41] firstly propose a learning-based encoder-decoder network assisted by" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7536" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.087, + 0.881, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.455, + 0.896, + 0.542 + ], + "angle": 0, + "content": "Figure 3. The overview of our proposed GKNet, which consists of harmony kernel prediction branch and harmony kernel modulation branch. As shown in gray box, the harmony kernel prediction branch is combined with a Long-term Reference Extractor (LRE) and multi-level Kernel Prediction Blocks (KPB). As shown in yellow box, we propose Selective Correlation Fusion (SCF) module in KPB for better long-distance references. Given a composited image \\( I_{c} \\) with corresponding foreground mask \\( \\mathbf{M} \\), we extract deep features \\( \\mathbf{F}_E^l \\) from encoder \\( \\phi_E \\). Then, harmony kernel prediction branch utilizes the deepest feature map and \\( \\{\\mathbf{F}_E^l\\} \\) to predict multi-level dynamic harmony kernels \\( \\{\\mathbf{K}^l\\} \\) increasingly. The predicted global-aware kernels are employed for harmony kernel modulation in decoder \\( \\phi_D \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.473, + 0.899 + ], + "angle": 0, + "content": "a semantic branch. In observation that semantic information is effective in image harmonization, Soffliuk et al. [38] also add additional pre-train semantic model to baseline DIH [41] and \\(\\mathbf{S}^2\\mathbf{A}\\mathbf{M}\\) [8]. Inspired by domain transfer, Cong et al. [7] adopt a verification discriminator to distinguish foreground and background domains. Similarly, Ling et al. [29] also treat the composited image as two independent parts and apply style transfer idea to match mean-variance statistics. To focus on harmonize foreground region, some methods add attention mechanisms. Cun et al. [8] add a spatial-separated attention module. Guo et al. [15] for the first time introduce Transformer architecture to image harmonization. Hang et al. [17] add background attention calculation to the style transfer block [29], and they also incorporated the idea of contrast learning. Besides, Guo et al. [16] decompose image into reflectance and illumination by autoencoder for separate harmonization based on Retinex theory. Some high-resolution methods [24, 44] frame image harmonization as an image-level problem to learn white-box arguments. However, the above methods neglect spatial proximity prior and could not model long-distance references well. Instead in this paper, we design" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.566, + 0.892, + 0.597 + ], + "angle": 0, + "content": "a better local modulation method combined with selected long-distance references to alleviate this problem." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.605, + 0.813, + 0.621 + ], + "angle": 0, + "content": "2.2. Dynamic Filtering in Image Editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.794 + ], + "angle": 0, + "content": "The input-dependent dynamic filtering first proposed by Jia [21] et al. aims to learn position-specific filters on pixel inputs and apply the generated kernels to another input, which has been widely used in numerous vision tasks [33, 23, 46, 9]. This method also shows effectiveness in image editing tasks, such as denoising [1, 32, 42], shadow removing [13], deraining [14], image inpainting [26], and blur synthesis [2]. However, most above methods apply dynamic filtering at image-level filter prediction and utilization. We propose to learn a multi-level global-aware kernel with long-term context references for harmonization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.655, + 0.817 + ], + "angle": 0, + "content": "2.3. Feature Fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Feature fusion is to combine features from different layers or branches, which is an omnipresent part of modern neural networks and has been studied extensively. Most previous works [18, 37, 28] for feature fusion focus on the pathways structure design, applying two linear classic" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "7537" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "methods of summation or concatenation. Recently, benefit from the successful use of Transformer in computer vision [4, 11, 31, 50, 49, 48, 3, 4, 12, 43, 22, 30, 15], some works [19, 27, 52, 10, 47, 51, 5] apply attention mechanism to present nonlinear approaches for feature fusion. As global information is significant in image harmonization, we design a dynamic weighted fusion method to effectively fuse long-distance reference into kernel prediction." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.224, + 0.169, + 0.24 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.25, + 0.473, + 0.402 + ], + "angle": 0, + "content": "Given a composited image \\( I_{c} \\) with its corresponding binary mask \\( \\mathbf{M} \\) indicating the region to be harmonized, our goal is to learn a network \\( \\mathrm{G} \\) that outputs harmonized image \\( I_{h} \\), which could be formulated as \\( I_{h} = G(I_{c}, M) \\). To make this composited image \\( I_{c} \\) look natural, we train our model \\( \\mathrm{G} \\) to adjust the foreground region \\( I_{f} \\) in a supervised manner with paired real image \\( I \\). In this paper, we also define the background region as \\( I_{b} \\), and then the composition process could be formulated as \\( I_{c} = I_{f} \\cdot M + (1 - M) \\cdot I_{b} \\), where \\( \\cdot \\) denotes element-wise multiplication." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.409, + 0.315, + 0.423 + ], + "angle": 0, + "content": "3.1. Overview of Our Network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.47, + 0.553 + ], + "angle": 0, + "content": "As shown in Figure 3, we design a novel network architecture for image harmonization tasks to allow our network to pay attention to short-distance and long-distance information simultaneously. Following the standard designs in image harmonization works [8, 38, 29] we use simple U-Net [37] with attention blocks [8] as the basic structure. We also take composited RGB image \\( I_{c} \\in \\mathbb{R}^{3 \\times H \\times W} \\) concatenated with foreground region mask \\( \\mathbf{M} \\in \\mathbb{R}^{1 \\times H \\times W} \\) as input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.473, + 0.84 + ], + "angle": 0, + "content": "Motivated by proximity prior in image harmonization, we propose Global-aware Kernel Network (GKNet) to learn global-aware harmony kernel for image harmonization, which consists of two branches, harmony kernel prediction and harmony kernel modulation. Firstly, as long-distance reference is crucial for harmonization task, we design global-aware kernel prediction branch to predict harmony kernel with context modeling, which contains a transformer-based Long-term Reference Extractor (LRE) to extract global reference and Kernel Prediction Block (KPB) to predict harmony kernels. In order to incorporate relevant long-term references for local harmonization, a novel Selective Correlation Fusion (SCF) is proposed to select more effective references in backgrounds. Secondly, we design a multi-level harmony kernel modulation in decoder layers to employ the predicted global-aware kernels. The mechanism between global-aware harmony kernel prediction and harmony kernel modulation finally achieves local-global interaction for image harmonization." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.329, + 0.864 + ], + "angle": 0, + "content": "3.2. Harmony Kernel Prediction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Inspired by recent works in image editing [1, 14, 32], we propose to apply dynamic kernels to force the current pixel" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.439 + ], + "angle": 0, + "content": "harmonized with surrounding regions adaptively. This approach effectively makes up for the lack of consideration of proximity prior in previous harmonization works. However, basic dynamic kernels for image editing tasks such as denoising and deraining are applied with a fixed size at image-level. To predict more proper adaptive kernels for image harmonization, we analyze the following: 1) Global modeling is necessary for image harmonization as long-distance references may appear in the background. Hence, we design a novel global-aware harmony kernel prediction branch with LRE to extract global information and KPB to predict global-aware kernels with fusion module SCF. 2) Fixed-size kernels applied at image-level could not handle the scale problem well. e.g. The pixels inside the large foreground mask can hardly obtain any real background information, while predicting large kernels will bring high computation costs and breaks the intention of proximity prior. Besides, image-level dynamic kernels pay more attention to detailed structure, while in image harmonization we also need to adapt multiple scene variations to harmonize foregrounds at semantic level. In order to adapt to multi-scene and multiscale problems, we propose to predict kernels in multi-level structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.895, + 0.606 + ], + "angle": 0, + "content": "Long-distance Reference Extractor. In order to obtain long-term context, we employ 1-transformer layers [11] as our global information extractor. We feed the deepest feature map \\(\\mathbf{F}_E^1\\) from CNN encoder into transformer layers. With the down-sampling feature map in low-resolution of \\((\\frac{w}{r},\\frac{h}{r})\\), we treat each pixel as a token to generate embeddings. With the multi-head attention mechanism, we obtain global interactive feature \\(\\mathbf{F}_{global}\\in \\mathbb{R}^{C\\times HW}\\) after 1-transformer layers. After reshaping and post-convolution layer, we obtain the long-term reference feature \\(\\mathbf{F}_{LR}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.894, + 0.756 + ], + "angle": 0, + "content": "Kernel Prediction Block. To adapt diverse foreground scales and background scenarios, we apply our local operation kernel modulation in multiple decoder levels. Nevertheless, deep-level features contain more semantic information, and shallow features contain more details, we need to predict corresponding adaptive kernels for different level harmony kernel modulation. Thus, our designed global-aware harmony kernel prediction branch is in a multi-level structure to increasingly predict a series of kernels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.801 + ], + "angle": 0, + "content": "In Figure 3, we show our proposed KPB structure from predicting kernels to harmony kernel modulation operation. The operation in \\( l \\)th KPBlock can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.811, + 0.891, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\mathbf {K} ^ {l}, \\mathbf {F} _ {K P B} ^ {l} = K P B l o c k \\left(\\mathbf {F} _ {E} ^ {l}, \\mathbf {F} _ {K P B} ^ {l - 1}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where KPBlock \\((\\cdot)\\) is the KPBlock to predict \\(\\mathbf{K}^l\\). For each KPB, we take \\(\\mathbf{F}_{KP B}^{l-1} \\in \\mathbb{R}^{C_l \\times H_l \\times W_l}\\) transferred from \\((l-1)\\)th KPB (For the deepest KPB, we input \\(\\mathbf{F}_{LR}\\)) and the \\(l\\)th encoder layer feature \\(\\mathbf{F}_E^l\\) as input (We denote \\(\\mathbf{F}_E^1\\) as the deepest" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7538" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.304, + 0.471, + 0.348 + ], + "angle": 0, + "content": "Figure 4. Schematic diagram of SCF. The module takes the (1-1)th layer feature \\(\\mathbf{F}_{KPB}^{l-1}\\) and encoder feature \\(\\mathbf{F}_E^l\\) as input and outputs the correlation-aware fusion feature \\(\\hat{\\mathbf{F}}_{KPB}^l\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.358, + 0.47, + 0.404 + ], + "angle": 0, + "content": "layer in encoder), which outputs feature \\(\\mathbf{F}_{KPB}^{l}\\) for next KP-Block and the global-aware kernels \\(\\mathbf{K}^{l} = \\mathrm{Conv}(\\mathbf{F}_{KPB}^{l})\\) after post-convolutions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.553 + ], + "angle": 0, + "content": "Selective Correlation Fusion. Long-distance reference \\(\\mathbf{F}_{LR}\\) obtained from LRE is then injected into the deepest KPBlock to model global information for local harmonization. The standard way of feature fusion, like concatenation or addition, equally treats low-level and high-level features. To efficiently model long-term information for local harmonization, we propose SCF to select relevant global information by interacting encoder features \\(\\mathbf{F}_E\\) and long-distance references based on channel-wise attention mechanism." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.47, + 0.661 + ], + "angle": 0, + "content": "Specifically, as shown in Figure 4, we take the \\((l - 1)\\)th layer feature \\(\\mathbf{F}_{KPB}^{l - 1}\\in \\mathbb{R}^{C_{l - 1}\\times H_{l - 1}\\times W_{l - 1}}\\) and the \\(l\\)th encoder feature \\(\\mathbf{F}_E^l\\in \\mathbb{R}^{C_l\\times H_l\\times W_l}\\) as input and extract attention vector \\(\\alpha_{KPB},\\alpha_E\\in \\mathbb{R}^{C_l}\\) by \\(3\\times 3\\) convolutions and MLP. Subsequently, the attention vector is divided into n groups with length m as \\(\\tilde{\\alpha}_{KPB},\\tilde{\\alpha}_E\\in \\mathbb{R}^{n\\times m}\\). Thus, the channel-wise attention relation \\(\\mathbf{A}\\in \\mathbb{R}^{n\\times n}\\) can be calculated by matrix product" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.668, + 0.469, + 0.687 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} = \\tilde {\\alpha} _ {K P B} \\odot \\tilde {\\alpha} _ {E} ^ {T}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.696, + 0.47, + 0.77 + ], + "angle": 0, + "content": "After that, we calculate the selective factor \\(\\overline{\\alpha}_{KPB},\\overline{\\alpha}_E\\in\\) \\(\\mathbb{R}^{C_l}\\) through \\(N\\times N\\) convolutions with splitting. Then, we obtain the selective attention weights \\(S^l\\in \\{S_E^l,S_{KPB}^{l - 1}\\}\\) for each features by \\(\\alpha \\in \\{\\alpha_{KPB},\\alpha_E\\}\\) and \\(\\overline{\\alpha}\\in \\{\\overline{\\alpha}_{KPB},\\overline{\\alpha}_E\\}\\), which can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.779, + 0.469, + 0.797 + ], + "angle": 0, + "content": "\\[\nS ^ {l} = \\sigma (\\alpha + b \\cdot F C (\\bar {\\alpha})), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.806, + 0.469, + 0.851 + ], + "angle": 0, + "content": "where \\( \\mathbf{b} \\) is a learnable parameter, \\( \\sigma \\) is sigmoid function. Based on the attention weight vector, then the shallow and deep information are interacted as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.858, + 0.469, + 0.878 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {F}} _ {K P B} ^ {l} = S _ {E} ^ {l} \\cdot \\operatorname {C o n v} \\left(\\mathbf {F} _ {E} ^ {l}\\right) + \\text {U p s a m p l e} \\left(S _ {K P B} ^ {l - 1} \\cdot \\operatorname {C o n v} \\left(\\mathbf {F} _ {K P B} ^ {l - 1}\\right)\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.392, + 0.901 + ], + "angle": 0, + "content": "where \\(\\cdot\\) denotes to element-wise multiplication." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.763, + 0.107 + ], + "angle": 0, + "content": "3.3. Harmony Kernel Modulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.265 + ], + "angle": 0, + "content": "The global-aware adaptive kernel obtained from the harmony kernel prediction branch is then utilized in harmony kernel modulation. In this section, we illustrate the regional harmony operation method kernel modulation in decoder layers, which converts the previous overall treatment of background and foreground into a local reference. As mentioned in Section 3.2, we apply multi-level kernel modulation in decoder layer to adapt scales and scenario variation problem. Figure 3 shows our proposed kernel modulation in \\( l \\)th decoder layers, which could be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.644, + 0.27, + 0.892, + 0.29 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {F}} _ {D} ^ {l} = \\mathbf {F} _ {D} ^ {l} \\otimes \\mathbf {K} ^ {l}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.893, + 0.416 + ], + "angle": 0, + "content": "where \\(\\oplus\\) denotes the harmony kernel modulation, \\(\\mathbf{F}_D^l\\in\\) \\(\\mathbb{R}^{C\\times H\\times W}\\) is the deep feature extracted from the \\(l\\)th layer in decoder, and the \\(\\hat{\\mathbf{F}}_{\\mathbf{D}}^{l}\\in \\mathbb{R}^{C\\times H\\times W}\\) is its corresponding harmony kernel modulation result feature in the \\(l\\)th layer. The tensor \\(\\mathbf{K}^l\\in \\mathbb{R}^{C\\times N^2\\times H\\times W}\\) represents the kernels with size of \\(N\\) for harmony kernel modulation in the \\(l\\)th feature layer, which we obtain from KPB. For the kernel modulation in each pixel, we can expand the above equation as" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.422, + 0.892, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {F}} _ {D} ^ {l} [ \\mathbf {p} ] = \\sum_ {\\mathbf {q} \\in \\mathcal {N} _ {p}} \\mathbf {K} _ {p} ^ {l} [ \\mathbf {p} - \\mathbf {q} ] \\mathbf {F} _ {D} ^ {l} [ \\mathbf {q} ], \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.601 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}\\) and \\(\\mathbf{q}\\) are the coordinates of pixels in the image, \\(\\mathbf{K}_p^l\\) is the kernel for filtering the element \\(\\mathbf{p}\\) of \\(\\mathbf{F}_D^l\\) via its surrounding elements, i.e., \\(\\mathcal{N}_p\\). As we illustrate in Eq. 5, \\(\\mathbf{K}^l\\) contains all element-wise kernels, i.e., \\(\\mathbf{K}_p^l \\in \\mathbb{R}^{C \\times N \\times N}\\) for filtering operations. After the kernel modulation in decoder layers, we finally obtain the harmonization result. In this paper, we define the U-Net decoder layer as \\(\\phi_D(\\cdot)\\), then we can formulate our harmonization process with kernel modulation as \\(\\hat{I}_h = \\phi_D^L (\\dots \\phi_D^1 (\\mathbf{F}_D^1\\otimes \\mathbf{K}^1))\\cdot M + (1 - M)\\cdot I_c\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.68, + 0.622 + ], + "angle": 0, + "content": "3.4. Objective function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.69 + ], + "angle": 0, + "content": "In the training phase, we only employ foreground-normalized MSE loss as our objective function. Compared with normal MSE loss, it reduces the impact of copying background area:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.695, + 0.892, + 0.761 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} = \\frac {\\sum_ {h , w} \\left\\| \\hat {I} - I \\right\\| _ {2} ^ {2}}{\\max \\left\\{A _ {\\min } , \\sum_ {h , w} M _ {h , w} \\right\\}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.892, + 0.812 + ], + "angle": 0, + "content": "where \\( A_{min} \\) is a hyperparameter to keep the loss function stable as there might be some too small foreground objects. In this paper, we set \\( A_{min} = 100 \\) as suggested in [38]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.823, + 0.634, + 0.839 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.718, + 0.864 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We conduct the image harmonization experiment at resolution \\(256 \\times 256\\) on the benchmark dataset iHarmony4 [7]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7539" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons across four sub-datasets of iHarmony4 [7]. ↑ indicates the higher the better, and ↓ indicates the lower the better. We compute fMSE for better reflection on harmonization tasks. Best results are in bold and the suboptimal results are in underline." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.129, + 0.894, + 0.304 + ], + "angle": 0, + "content": "
MethodHCOCOHAdobe5kHFlickrHday2nightALL
PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓
Composite33.9469.37996.5928.16345.542051.6128.32264.351574.3734.01109.651409.9831.63172.471376.42
DIH [41]34.6951.85798.9932.2892.65593.0329.55163.381099.1334.6282.341129.4033.4176.77773.18
S2AM [8]35.4741.07542.0633.7763.40404.6230.03143.45785.6535.6950.87835.0634.3559.67594.67
DoveNet [7]35.8336.72551.0134.3452.32380.3930.21133.14827.0335.2751.951075.7134.7652.33532.62
IIH [16]37.1624.92416.3835.2043.02284.2131.34105.13716.6035.9655.53797.0435.9038.71400.29
RAINNnet [29]37.0829.52501.1736.2243.35317.3531.64110.59688.4034.8357.40916.4836.1240.29469.60
iDIH-HRNet [38]39.1616.48266.1938.0821.88173.9633.1369.67443.6537.7240.59590.9738.1924.44264.96
D-HT [15]38.7616.89299.3036.8838.53265.1133.1374.51515.4537.1053.01704.4237.5530.30320.78
Harmonizer [24]38.7717.34298.4237.6421.89170.0533.6364.81434.0637.5633.14542.0737.8424.26280.51
DCCF [44]39.7214.55267.7938.2420.20171.0133.7266.20440.8438.1851.40629.6738.6022.64265.41
SCS-Co [17]39.8813.58245.5438.2921.01165.4834.2255.83393.7237.8341.75606.8038.7521.33248.86
Ours40.3212.95222.3139.9717.84138.2234.4557.58372.9038.4742.76546.0639.5319.90220.44
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.314, + 0.47, + 0.356 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on different ratios of foreground based on iHarmony4 by MSE and fMSE metrics. The best results are in bold and the suboptimal results are in underline." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.367, + 0.47, + 0.473 + ], + "angle": 0, + "content": "
MethodVenue0%~5%5%~15%15%~100%
MSE↓fMSE↓MSE↓fMSE↓MSE↓fMSE↓
DIHCVPR'1718.92799.1764.23725.86228.86768.89
S2AMTIP'2015.09623.1148.33540.54117.62592.83
DoveNetCVPR'2014.03591.8844.90504.42152.07505.82
RainNetCVPR'2111.66550.3832.05378.69117.41389.80
iS2AMWACV'216.73294.7618.03204.6963.02207.82
GKNetOurs5.36244.0617.46200.3457.31188.75
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.47, + 0.593 + ], + "angle": 0, + "content": "The initial learning rate is set to \\(10^{-4}\\), and the models are trained for 120 epochs with a batch size of 16 on four 2080Ti GPUs. For optimizer, we adopt an Adam optimizer with \\(\\beta_{1} = 0.9, \\beta_{2} = 0.999\\) and \\(\\epsilon = 10^{-8}\\). It takes about two days for training. Our proposed model is implemented by PyTorch, and more detailed network architectures could be found in the supplementary file." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.276, + 0.619 + ], + "angle": 0, + "content": "4.2. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.719 + ], + "angle": 0, + "content": "Datasets. To evaluate our proposed method for image harmonization, we conduct our experiments on the benchmark dataset iHarmony4 [7], which consists of 4 sub-datasets: HCOCO, HAdobe5K, HFlickr, and Hday2night, including 73147 pairs of synthesized composite images with their corresponding foreground mask and ground truth image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics. Following the standard setups in image harmonization, we use the peak signal-to-noise ratio (PSNR) and Mean Squared Error (MSE) as evaluation metrics. Furthermore, it is more accurate to only calculate the difference in the foreground region with the metric foreground MSE (fMSE) introduced by [38]. The metric MSE is calculated for the whole image, while there is no changes for pixels in the background region in harmonization task. Without considering the foreground ratio, the average MSE and PSNR results of the dataset will be more responsive to the performance of large-scale targets. In this paper, we argue that fMSE is more suitable for harmonization task." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.315, + 0.729, + 0.332 + ], + "angle": 0, + "content": "4.3. Comparison with SOTAs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Quantitative comparison. As results shown in Table 1, we compare our method with other state-of-the-art image harmonization methods on iHarmony4 [7]. Following [7, 38], we also evaluate the model performance on different ratios of foreground by splitting the test images into three groups, i.e., \\(0\\% \\sim 5\\%\\), \\(5\\% \\sim 15\\%\\), and \\(15\\% \\sim 100\\%\\). We provide these results in Table 2. Observing the quantitative experiment results above, we can summarize the following conclusions: 1) Our method achieves SOTA results of all evaluation metrics on average iharmony4 datasets. More specifically, our method achieves \\(0.78\\mathrm{dB}\\uparrow\\) improvement in PSNR, \\(1.43\\downarrow\\) in MSE, and \\(28.42\\downarrow\\) in fMSE compared with suboptimal methods. 2) Our method obtains the best fMSE scores on all sub-datasets, meaning that the foreground regions generated by our method are more natural and closer to real images. 3) As shown in Table 2, our model performs well on each foreground ratio, especially on \\(0\\% \\sim 5\\%\\), which indicates that our method has a strong ability to handle variable foreground scales. It also proves that our proposed global-aware adaptive kernel could process global-to-local impact with excellence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.884 + ], + "angle": 0, + "content": "Qualitative comparison. We further provide qualitative results on iHarmony4 datasets in Figure 5. It could be observed that our GKNet generates more visually coherent images of the foreground and background than composited images, which are also closer to ground truth. 1) The first two rows of examples show that our method can effectively handle the small object harmonization problem in complex scenes with proximity prior consideration. 2) The last two row examples show that our regional modulation with multi-level structure performs well in large foreground cases, which handles a wide range of enormous contrast. For more detailed descriptions, please refer to the caption in Figure 5. In contrast, our method presents more photorealistic results. More visual comparison results on iHarmony4 datasets could be seen in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Comparisons on Real Datasets. Experiments results on" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7540" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.105, + 0.089, + 0.212, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.089, + 0.323, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.324, + 0.089, + 0.432, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.433, + 0.089, + 0.541, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.089, + 0.651, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.089, + 0.76, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.089, + 0.869, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.153, + 0.212, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.153, + 0.323, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.324, + 0.153, + 0.432, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.433, + 0.153, + 0.541, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.153, + 0.651, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.153, + 0.759, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.153, + 0.869, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.209, + 0.212, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.209, + 0.323, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.324, + 0.209, + 0.432, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.433, + 0.209, + 0.541, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.21, + 0.651, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.21, + 0.759, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.21, + 0.869, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.267, + 0.212, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.352, + 0.174, + 0.364 + ], + "angle": 0, + "content": "Mask" + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.267, + 0.323, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.251, + 0.352, + 0.282, + 0.364 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.324, + 0.267, + 0.432, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.34, + 0.352, + 0.411, + 0.365 + ], + "angle": 0, + "content": "RainNet [29]" + }, + { + "type": "image", + "bbox": [ + 0.434, + 0.267, + 0.542, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.456, + 0.352, + 0.515, + 0.364 + ], + "angle": 0, + "content": "D-HT [15]" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.267, + 0.651, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.352, + 0.64, + 0.364 + ], + "angle": 0, + "content": "Harmonizer [24]" + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.267, + 0.759, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.69, + 0.352, + 0.719, + 0.363 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.267, + 0.869, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.352, + 0.84, + 0.364 + ], + "angle": 0, + "content": "Real(GT)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.377, + 0.894, + 0.447 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparisons with SOTA methods on iHarmony4 [7]. Mask in column one and Red box in Input represents the foreground. Case 1: The background color shows spatial variation, while only our method captures practical color reference by predicted kernel and local harmony modulation. Case 2: The harmony result obtained by our method is better in the detailed structure like duckweed center due to target harmony kernels for each foreground part. Case 3 & 4: For large foregrounds, our approach could also achieve better results, which preserves more original details and is closer to ground truth." + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.46, + 0.236, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.528, + 0.236, + 0.592 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.595, + 0.188, + 0.607 + ], + "angle": 0, + "content": "Mask" + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.46, + 0.361, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.237, + 0.528, + 0.361, + 0.592 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.595, + 0.313, + 0.607 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.46, + 0.487, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.528, + 0.487, + 0.592 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.387, + 0.595, + 0.458, + 0.607 + ], + "angle": 0, + "content": "RainNet [29]" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.46, + 0.613, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.528, + 0.612, + 0.592 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.595, + 0.596, + 0.607 + ], + "angle": 0, + "content": "iDIH-HRNet [38]" + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.46, + 0.738, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.528, + 0.738, + 0.592 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.595, + 0.708, + 0.607 + ], + "angle": 0, + "content": "DoveNet [7]" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.46, + 0.864, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.739, + 0.528, + 0.863, + 0.592 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.595, + 0.814, + 0.606 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.62, + 0.893, + 0.662 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparisons with SOTA methods on real composite images [41]. Mask in column one and Red box in Input represents the foregrounds. Case 1: Comparing the results on the dogs, our method achieves more natural results over the sunset background. Case 2: Our result dims the foreground person based on background dim light, which achieves a more natural effect." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.676, + 0.47, + 0.766 + ], + "angle": 0, + "content": "real composition datasets [41] can be seen in Figure 6. For real composition cases, evaluation metrics are impossible to calculate as there are no ground truth images. Hence, we only show qualitative results and human study results here. More visual comparison results on real datasets could be seen in supplementary materials." + }, + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.781, + 0.447, + 0.795 + ], + "angle": 0, + "content": "Table 3. B-T scores comparison on real composite images." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.805, + 0.458, + 0.838 + ], + "angle": 0, + "content": "
MethodCompositeDoveNet[7]RainNet[29]iDIH-HRNet[38]Ours
B-T Score ↑0.4160.6860.9721.5321.944
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Following [7, 6, 16, 17], we conduct our human study by inviting 50 volunteers to compare 24750 pairwise results. The pairwise results are obtained from 99 real composited images, with 25 results for each pair of different methods on" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.676, + 0.892, + 0.721 + ], + "angle": 0, + "content": "average. We also use the Bradley-Terry model (B-T model) to calculate the global ranking score. Our method achieves the best results as shown in Table 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.665, + 0.754 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of network components. We further conduct quantitative experiments to verify the effectiveness of components in GKNet. Note that modules in GKNet have dependencies, we can only show gradually added ablation studies. As the results in Table 4, our full model obtains the highest performance on all metrics when KPB, LRE, and SCF work together. Table 4 also illustrates the effectiveness of each component. Moreover, to further illustrate our global-local interaction method for harmonization, we show" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7541" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 4. Quantitative ablation study of our approach with different components on iHarmony4[7]" + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.129, + 0.46, + 0.209 + ], + "angle": 0, + "content": "
BaselineKPBLRESCFMSE ↓PSNR ↑fMSE ↓
✓✗✗✗27.2737.83280.56
✓✓✗✗21.4238.68235.72
✓✓✓✗20.5039.30229.63
✓✓✓✓19.9039.53220.44
" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.219, + 0.149, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.269, + 0.149, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.319, + 0.129, + 0.329 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.219, + 0.213, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.269, + 0.213, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.319, + 0.187, + 0.329 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.219, + 0.277, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.269, + 0.277, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.319, + 0.264, + 0.329 + ], + "angle": 0, + "content": "Baseline" + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.219, + 0.34, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.269, + 0.34, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.297, + 0.319, + 0.318, + 0.329 + ], + "angle": 0, + "content": "KPB" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.219, + 0.404, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.269, + 0.404, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.319, + 0.382, + 0.329 + ], + "angle": 0, + "content": "LRE" + }, + { + "type": "image", + "bbox": [ + 0.407, + 0.219, + 0.469, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.407, + 0.269, + 0.469, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.411, + 0.319, + 0.461, + 0.329 + ], + "angle": 0, + "content": "Full Model" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.342, + 0.469, + 0.37 + ], + "angle": 0, + "content": "Figure 7. Qualitative ablation study of our approach. Red boxes in input image mark foreground." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.388, + 0.47, + 0.51 + ], + "angle": 0, + "content": "qualitative results in Figure 7. Compared with the baseline, the model with only local KPB outputs stronger local modeling results but loses global view. After introducing LRE, global awareness of the background is enhanced. But it is evident that color is overcorrected in the second row. After adding SCF, we effectively correct the deviation by selecting relevant references in background, and the final result is closer to real image." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.52, + 0.469, + 0.66 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.67, + 0.47, + 0.726 + ], + "angle": 0, + "content": "Figure 8. The cluster visual results of adaptive harmony kernels. e.g., in flower case, structure information like petal margin is displayed, which proves that kernels are predicted to adapt local harmonization specifically." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Interpretability of Global-aware Harmony Kernel. To further illustrate the effectiveness of the adaptive harmony kernels, we cluster the per-pixel adaptive harmony kernels predicted from KPB by K-means. As shown in Figure 8, the clusters show strong spatial structure, which indicates that our predicted dynamic kernel can make the structural adjustment to harmonize the foreground. Moreover, in some cases, the change of kernel classes is related to the object mask. This exhibits that our harmony kernels are predicted dynamically to deal with visual inconsistency in different spatial locations (e.g. fore-/background or edges)." + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.089, + 0.573, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.186, + 0.564, + 0.198 + ], + "angle": 0, + "content": "(a) Mask" + }, + { + "type": "image", + "bbox": [ + 0.575, + 0.089, + 0.638, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.578, + 0.187, + 0.629, + 0.198 + ], + "angle": 0, + "content": "(b) Comp" + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.089, + 0.699, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.645, + 0.187, + 0.655, + 0.198 + ], + "angle": 0, + "content": "(c" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.089, + 0.761, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.089, + 0.826, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.828, + 0.09, + 0.889, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.645, + 0.187, + 0.879, + 0.199 + ], + "angle": 0, + "content": "(c) Feature map with channel attention weight" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.211, + 0.892, + 0.239 + ], + "angle": 0, + "content": "Figure 9. Feature maps in SCF. Red number in upper right corner of feature map represents channel-wise attention weights." + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.242, + 0.872, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.384, + 0.892, + 0.425 + ], + "angle": 0, + "content": "Figure 10. Cross-attention from example point (10,10). We show four attention maps for different heads, which proves LRE can match model related long-distance references." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.439, + 0.892, + 0.681 + ], + "angle": 0, + "content": "Interpretability of LRE and SCF Module. We visualize the attention mechanism in LRE and SCF for interpreting global-local interaction. In Figure 9, we visualize feature maps in decoder layers to illustrate our channel-wise attention module SCF. Visual feature maps with attention weights show that harmony kernels are predicted with more attention on related background area and less attention on irrelevant background area or foreground. In Figure 10, we visualize the attention maps of LRE, focusing on an example point in foreground. As the long-distance information in predicted harmony kernels is brought by LRE, the visualized attention maps in different heads indicate two points: 1) The kernels for local operation have a global perceptive field with long-distance information. 2) Different heads pay attention to different reference parts, i.e. relevant background reference, foreground content, overall tone, etc." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.695, + 0.619, + 0.71 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This paper proposes an effective network GKNet to learn global-aware harmony kernels for image harmonization, including harmony kernel prediction and harmony kernel modulation branches. For harmony kernel prediction, we propose LRE to extract long-term references and KPB to predict global-aware kernels. To better fuse long-term context, we design SCF to select relevant references. For harmony kernel modulation, we employ the predicted kernels for harmonization with location awareness. Extensive experiments demonstrate that our proposed algorithm outperforms the state-of-the-art algorithms on the iHarmony4 dataset and real image composition datasets." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7542" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.473, + 0.138 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by a Grant from The National Natural Science Foundation of China (No. 2021YFB2012300)." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.151, + 0.175, + 0.167 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.177, + 0.47, + 0.245 + ], + "angle": 0, + "content": "[1] Steve Bako, Thijs Vogels, Brian McWilliams, Mark Meyer, Jan Novák, Alex Harvill, Pradeep Sen, Tony Derose, and Fabrice Rousselle. Kernel-predicting convolutional networks for denoising monte carlo renderings. ACM Trans. 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Existing methods employ local color transformation or region matching between foreground and background, which neglects powerful proximity prior and independently distinguishes fore-/back-ground as a whole part for harmonization. As a result, they still show a limited performance across varied foreground objects and scenes. To address this issue, we propose a novel Global-aware Kernel Network (GKNet) to harmonize local regions with comprehensive consideration of long-distance background references. Specifically, GKNet includes two parts, i.e., harmony kernel prediction and harmony kernel modulation branches. The former includes a Long-distance Reference Extractor (LRE) to obtain long-distance context and Kernel Prediction Blocks (KPB) to predict multi-level harmony kernels by fusing global information with local features. To achieve this goal, a novel Selective Correlation Fusion (SCF) module is proposed to better select relevant long-distance background references for local harmonization. The latter employs the predicted kernels to harmonize foreground regions with local and global awareness. Abundant experiments demonstrate the superiority of our method for image harmonization over state-of-the-art methods, e.g., achieving 39.53dB PSNR that surpasses the best counterpart by $+0.78dB \uparrow$ ; decreasing fMSE/MSE by $11.5\% \downarrow / 6.7\% \downarrow$ compared with the SoTA method. Code will be available at here. + +# 1. Introduction + +Image composition aims to synthesize foreground objects from one image into another, which is a common task in image editing. However, human eyes could clearly dis + +![](images/18b0644d2601a9662414b3be2857663babf630b02ba2ffd049b7ae58df022ef8.jpg) +(a) Local-translation + +![](images/58db1f95237660e64235570f4c861c51bb3efba4d1070191792f14cb09d227b4.jpg) +(b) Region-matching + +![](images/5d109600587945610c59bd0b9f0fd0b0af5a977e5bed7c4f559ec9083f2a00b8.jpg) +(c) Ours +Figure 1. Comparison of background reference methods in harmonization. Blue/Red region represent foreground/background, respectively, and white/red arrows refer to interaction/injection, respectively. (a) Local-translation methods reference nearby pixels. (b) Region-matching methods transfer reference with a unified view of fore-/back-ground region. (c) Our method interacts long-distance reference and injects it with short-distance consideration. + +tinguish synthetic images due to the visual inconsistency between foreground and background in composited images. In attempting to solve the photo-unrealistic problem, image harmonization is proposed to adjust the foreground objects based on the illumination and color tone in background environment, which plays an important role in image editing. + +Traditional image harmonization approaches are mainly based on low-level feature matching, which is only effective for specific scenes. Recently, numerous learning-based methods have achieved remarkable progress by addressing image harmonization as a generation task. Existing learning-based methods could be categorized from two angles, i.e., local-translation and region-matching. 1) The former employs a convolutional encoder-decoder to learn a foreground pixel-to-pixel translation [41, 8]. But a shallow CNN only captures limited surrounding background. As shown in Figure 1a, these approaches harmonize the current pixel with local references, which is insufficient for harmonization as inner foreground pixels could not attach background reference. Besides, related long-distance references are effective in some cases. 2) The latter region matching methods [29, 7] distinguish foreground and background regions as two styles or domains. As shown in Figure 1b, they tackle harmonization as a matching problem with a + +![](images/126e8e65b587f58e3ebc19c83ecd57db234022d67b2ef5922e2871ffa7cffed1.jpg) + +![](images/3e8f0dd3e242b97e4e005be6e0b910d7e4cde5fe3edfab21a56329345d56c8e6.jpg) +Mask + +![](images/5dcd8194484156588d0d3d1b131b7b79cf3e06e62344f96f5629aa780a33a480.jpg) + +![](images/d497e4e99c43ef9861bce0724ec0993d966eac7a1940f23ec78d5fea7b3cd9dc.jpg) +Input + +![](images/2129599f4d0178d627aec0f6f50b1c8aabc821597aec715f72507013e947e802.jpg) + +![](images/d2a1e7d66aad9544f5a005892ef82bb7619e6a00069d4977633fdd4843ba533f.jpg) +RainNet[7] + +![](images/4a61754991603c4af3c2c8e7a40e68e81198b29e1d47e63f16d0b8898d69d18f.jpg) + +![](images/e8e3181544cdcda97f2a29799480e67ce129346e35e970bfb03b8184478ba255.jpg) +$\mathrm{iS}^2\mathrm{AM}[38]$ + +![](images/f7943e25f12f8712fc5f5ce8d3bbd56629d77a25c52d5859f7826a53b67f44ae.jpg) + +![](images/39c20972af67b4b2dd6ea3ab993291a6fb1d18773be9376e504def293283f183.jpg) +Ours + +![](images/9a18663b0eecb52818d0e045a7820aa26152321ffe1a805b4512bd1b25f3cdb3.jpg) + +![](images/d48040413b025fc1001af5170d458372e916a35665a3158ae185cfce6dc4abb9.jpg) +Real(GT) + +![](images/1ec33eaddb2c5db32dd9643c980dac71dc5a8fcfa4ed471630eab05b038e7a23.jpg) +Figure 2. Left: Two challenging samples in image harmonization. Mask in column one and Red boxes represents the foreground. Right: Performance comparison with SOTA methods in terms of PSNR and model size. The circle size represents the floating-point number. + +unified view of these two regions by statistics components or discriminators. Though these approaches harmonize images with a broader reference range, they totally neglect the spatial variations in two regions. Hang et al. [17] begin to notice this problem and add attention-based references in region matching method [29]. But they still separate two regions independently and harmonize foreground by unified matching without considering foreground spatial variations. + +To further illustrate existing problems, we provide two common harmonization cases in Figure 2. In the first case, a small foreground object appears in the background with obvious color changes. The region-matching method RainNet [7] provides a poor color correction result while the local method iS²AM [38] could tackle this case well, which indicates that the unified view of background will blend the overall complex color conditions. In the second case, related long-distance references exist in the background, while the local method could only attach insufficient adjacent information. Region-matching method RainNet could obtain whole background blue tone by matching, but it still excessively harmonizes the house due to the unified view. These two cases indicate that local reference is insufficient, but region-matching methods could not model long-distance reference well and will cause unbalanced harmonization problems by rough matching. + +To solve this problem, we rethink essential proximity priors in image harmonization, i.e., when we paste an object into background, the color or light is related to location and will be influenced by its neighboring first. Moreover, the effective long-distance information in background changes with pasted locations, which requires us to learn adaptive references for each part. Inspired by this observation, we propose a novel Global-aware Kernel Network (GKNet) to integrate local harmony modulation and long-distance background references, including harmony kernel prediction and harmony kernel modulation. For harmony kernel prediction, we propose a novel global-aware kernel prediction method including Long-distance Reference Extractor (LRE) to obtain long-distance references and Ker- + +nel Prediction Blocks (KPB) to predict multi-level adaptive kernels with selected long-distance references by Selective Correlation Fusion (SCF). For kernel modulation, we propose to model local harmony operation by predicted global-aware kernels and multi-level features. Focusing on features in kernel region, kernel modulation is significant in alleviating unbalanced region-matching errors in complex scenes. + +To summarize, we make following contributions: + +- With the observation of proximity prior and long-distance references in image harmonization task, we design GKNet to model global-local interaction by learning global-aware harmony kernel, including harmony kernel prediction and harmony kernel modulation. +- For harmony kernel prediction, we propose a kernel prediction branch combined with LRE to model global information and multiple KPB to learn adaptive harmony kernels. For better global references, we design SCF to select relevant long-distance references for local harmonization. For harmony kernel modulation, we propose the method to harmonize local regions in multi-level decoder layers with predicted kernels. +- Extensive experiments demonstrate the superior performance of our methods in both quantitative and qualitative results, noting that our method achieves state-of-the-art results on iHarmony4 datasets. + +# 2. Related work + +# 2.1. Image Harmonization + +Traditional image harmonization works have focused on finding a better method for low-level appearances matching between foreground and background regions in images, which includes color statistics [36, 35, 45], gradient information [20, 34, 40], and multi-scale statistical features [39, 25]. However, traditional methods could only be effective in specific scenes. With the advanced generative ability of deep learning, Tsai et al. [41] firstly propose a learning-based encoder-decoder network assisted by + +![](images/01d3f1749a8e2c43b19366b9a8d177ffaa464a09fa00df3ece36ce22c385a035.jpg) +Figure 3. The overview of our proposed GKNet, which consists of harmony kernel prediction branch and harmony kernel modulation branch. As shown in gray box, the harmony kernel prediction branch is combined with a Long-term Reference Extractor (LRE) and multi-level Kernel Prediction Blocks (KPB). As shown in yellow box, we propose Selective Correlation Fusion (SCF) module in KPB for better long-distance references. Given a composited image $I_{c}$ with corresponding foreground mask $\mathbf{M}$ , we extract deep features $\mathbf{F}_E^l$ from encoder $\phi_E$ . Then, harmony kernel prediction branch utilizes the deepest feature map and $\{\mathbf{F}_E^l\}$ to predict multi-level dynamic harmony kernels $\{\mathbf{K}^l\}$ increasingly. The predicted global-aware kernels are employed for harmony kernel modulation in decoder $\phi_D$ . + +a semantic branch. In observation that semantic information is effective in image harmonization, Soffliuk et al. [38] also add additional pre-train semantic model to baseline DIH [41] and $\mathbf{S}^2\mathbf{A}\mathbf{M}$ [8]. Inspired by domain transfer, Cong et al. [7] adopt a verification discriminator to distinguish foreground and background domains. Similarly, Ling et al. [29] also treat the composited image as two independent parts and apply style transfer idea to match mean-variance statistics. To focus on harmonize foreground region, some methods add attention mechanisms. Cun et al. [8] add a spatial-separated attention module. Guo et al. [15] for the first time introduce Transformer architecture to image harmonization. Hang et al. [17] add background attention calculation to the style transfer block [29], and they also incorporated the idea of contrast learning. Besides, Guo et al. [16] decompose image into reflectance and illumination by autoencoder for separate harmonization based on Retinex theory. Some high-resolution methods [24, 44] frame image harmonization as an image-level problem to learn white-box arguments. However, the above methods neglect spatial proximity prior and could not model long-distance references well. Instead in this paper, we design + +a better local modulation method combined with selected long-distance references to alleviate this problem. + +# 2.2. Dynamic Filtering in Image Editing + +The input-dependent dynamic filtering first proposed by Jia [21] et al. aims to learn position-specific filters on pixel inputs and apply the generated kernels to another input, which has been widely used in numerous vision tasks [33, 23, 46, 9]. This method also shows effectiveness in image editing tasks, such as denoising [1, 32, 42], shadow removing [13], deraining [14], image inpainting [26], and blur synthesis [2]. However, most above methods apply dynamic filtering at image-level filter prediction and utilization. We propose to learn a multi-level global-aware kernel with long-term context references for harmonization. + +# 2.3. Feature Fusion + +Feature fusion is to combine features from different layers or branches, which is an omnipresent part of modern neural networks and has been studied extensively. Most previous works [18, 37, 28] for feature fusion focus on the pathways structure design, applying two linear classic + +methods of summation or concatenation. Recently, benefit from the successful use of Transformer in computer vision [4, 11, 31, 50, 49, 48, 3, 4, 12, 43, 22, 30, 15], some works [19, 27, 52, 10, 47, 51, 5] apply attention mechanism to present nonlinear approaches for feature fusion. As global information is significant in image harmonization, we design a dynamic weighted fusion method to effectively fuse long-distance reference into kernel prediction. + +# 3. Method + +Given a composited image $I_{c}$ with its corresponding binary mask $\mathbf{M}$ indicating the region to be harmonized, our goal is to learn a network $\mathrm{G}$ that outputs harmonized image $I_{h}$ , which could be formulated as $I_{h} = G(I_{c}, M)$ . To make this composited image $I_{c}$ look natural, we train our model $\mathrm{G}$ to adjust the foreground region $I_{f}$ in a supervised manner with paired real image $I$ . In this paper, we also define the background region as $I_{b}$ , and then the composition process could be formulated as $I_{c} = I_{f} \cdot M + (1 - M) \cdot I_{b}$ , where $\cdot$ denotes element-wise multiplication. + +# 3.1. Overview of Our Network + +As shown in Figure 3, we design a novel network architecture for image harmonization tasks to allow our network to pay attention to short-distance and long-distance information simultaneously. Following the standard designs in image harmonization works [8, 38, 29] we use simple U-Net [37] with attention blocks [8] as the basic structure. We also take composited RGB image $I_{c} \in \mathbb{R}^{3 \times H \times W}$ concatenated with foreground region mask $\mathbf{M} \in \mathbb{R}^{1 \times H \times W}$ as input. + +Motivated by proximity prior in image harmonization, we propose Global-aware Kernel Network (GKNet) to learn global-aware harmony kernel for image harmonization, which consists of two branches, harmony kernel prediction and harmony kernel modulation. Firstly, as long-distance reference is crucial for harmonization task, we design global-aware kernel prediction branch to predict harmony kernel with context modeling, which contains a transformer-based Long-term Reference Extractor (LRE) to extract global reference and Kernel Prediction Block (KPB) to predict harmony kernels. In order to incorporate relevant long-term references for local harmonization, a novel Selective Correlation Fusion (SCF) is proposed to select more effective references in backgrounds. Secondly, we design a multi-level harmony kernel modulation in decoder layers to employ the predicted global-aware kernels. The mechanism between global-aware harmony kernel prediction and harmony kernel modulation finally achieves local-global interaction for image harmonization. + +# 3.2. Harmony Kernel Prediction + +Inspired by recent works in image editing [1, 14, 32], we propose to apply dynamic kernels to force the current pixel + +harmonized with surrounding regions adaptively. This approach effectively makes up for the lack of consideration of proximity prior in previous harmonization works. However, basic dynamic kernels for image editing tasks such as denoising and deraining are applied with a fixed size at image-level. To predict more proper adaptive kernels for image harmonization, we analyze the following: 1) Global modeling is necessary for image harmonization as long-distance references may appear in the background. Hence, we design a novel global-aware harmony kernel prediction branch with LRE to extract global information and KPB to predict global-aware kernels with fusion module SCF. 2) Fixed-size kernels applied at image-level could not handle the scale problem well. e.g. The pixels inside the large foreground mask can hardly obtain any real background information, while predicting large kernels will bring high computation costs and breaks the intention of proximity prior. Besides, image-level dynamic kernels pay more attention to detailed structure, while in image harmonization we also need to adapt multiple scene variations to harmonize foregrounds at semantic level. In order to adapt to multi-scene and multiscale problems, we propose to predict kernels in multi-level structures. + +Long-distance Reference Extractor. In order to obtain long-term context, we employ 1-transformer layers [11] as our global information extractor. We feed the deepest feature map $\mathbf{F}_E^1$ from CNN encoder into transformer layers. With the down-sampling feature map in low-resolution of $(\frac{w}{r},\frac{h}{r})$ , we treat each pixel as a token to generate embeddings. With the multi-head attention mechanism, we obtain global interactive feature $\mathbf{F}_{global}\in \mathbb{R}^{C\times HW}$ after 1-transformer layers. After reshaping and post-convolution layer, we obtain the long-term reference feature $\mathbf{F}_{LR}$ . + +Kernel Prediction Block. To adapt diverse foreground scales and background scenarios, we apply our local operation kernel modulation in multiple decoder levels. Nevertheless, deep-level features contain more semantic information, and shallow features contain more details, we need to predict corresponding adaptive kernels for different level harmony kernel modulation. Thus, our designed global-aware harmony kernel prediction branch is in a multi-level structure to increasingly predict a series of kernels. + +In Figure 3, we show our proposed KPB structure from predicting kernels to harmony kernel modulation operation. The operation in $l$ th KPBlock can be formulated as + +$$ +\mathbf {K} ^ {l}, \mathbf {F} _ {K P B} ^ {l} = K P B l o c k \left(\mathbf {F} _ {E} ^ {l}, \mathbf {F} _ {K P B} ^ {l - 1}\right), \tag {1} +$$ + +where KPBlock $(\cdot)$ is the KPBlock to predict $\mathbf{K}^l$ . For each KPB, we take $\mathbf{F}_{KP B}^{l-1} \in \mathbb{R}^{C_l \times H_l \times W_l}$ transferred from $(l-1)$ th KPB (For the deepest KPB, we input $\mathbf{F}_{LR}$ ) and the $l$ th encoder layer feature $\mathbf{F}_E^l$ as input (We denote $\mathbf{F}_E^1$ as the deepest + +![](images/440d5d4af20767d9b5227c920aa3704e9cdf4cf33eefd2930098bb5459379e23.jpg) +Figure 4. Schematic diagram of SCF. The module takes the (1-1)th layer feature $\mathbf{F}_{KPB}^{l-1}$ and encoder feature $\mathbf{F}_E^l$ as input and outputs the correlation-aware fusion feature $\hat{\mathbf{F}}_{KPB}^l$ . + +layer in encoder), which outputs feature $\mathbf{F}_{KPB}^{l}$ for next KP-Block and the global-aware kernels $\mathbf{K}^{l} = \mathrm{Conv}(\mathbf{F}_{KPB}^{l})$ after post-convolutions. + +Selective Correlation Fusion. Long-distance reference $\mathbf{F}_{LR}$ obtained from LRE is then injected into the deepest KPBlock to model global information for local harmonization. The standard way of feature fusion, like concatenation or addition, equally treats low-level and high-level features. To efficiently model long-term information for local harmonization, we propose SCF to select relevant global information by interacting encoder features $\mathbf{F}_E$ and long-distance references based on channel-wise attention mechanism. + +Specifically, as shown in Figure 4, we take the $(l - 1)$ th layer feature $\mathbf{F}_{KPB}^{l - 1}\in \mathbb{R}^{C_{l - 1}\times H_{l - 1}\times W_{l - 1}}$ and the $l$ th encoder feature $\mathbf{F}_E^l\in \mathbb{R}^{C_l\times H_l\times W_l}$ as input and extract attention vector $\alpha_{KPB},\alpha_E\in \mathbb{R}^{C_l}$ by $3\times 3$ convolutions and MLP. Subsequently, the attention vector is divided into n groups with length m as $\tilde{\alpha}_{KPB},\tilde{\alpha}_E\in \mathbb{R}^{n\times m}$ . Thus, the channel-wise attention relation $\mathbf{A}\in \mathbb{R}^{n\times n}$ can be calculated by matrix product + +$$ +\mathbf {A} = \tilde {\alpha} _ {K P B} \odot \tilde {\alpha} _ {E} ^ {T}. \tag {2} +$$ + +After that, we calculate the selective factor $\overline{\alpha}_{KPB},\overline{\alpha}_E\in$ $\mathbb{R}^{C_l}$ through $N\times N$ convolutions with splitting. Then, we obtain the selective attention weights $S^l\in \{S_E^l,S_{KPB}^{l - 1}\}$ for each features by $\alpha \in \{\alpha_{KPB},\alpha_E\}$ and $\overline{\alpha}\in \{\overline{\alpha}_{KPB},\overline{\alpha}_E\}$ , which can be formulated as + +$$ +S ^ {l} = \sigma (\alpha + b \cdot F C (\bar {\alpha})), \tag {3} +$$ + +where $\mathbf{b}$ is a learnable parameter, $\sigma$ is sigmoid function. Based on the attention weight vector, then the shallow and deep information are interacted as follows: + +$$ +\hat {\mathbf {F}} _ {K P B} ^ {l} = S _ {E} ^ {l} \cdot \operatorname {C o n v} \left(\mathbf {F} _ {E} ^ {l}\right) + \text {U p s a m p l e} \left(S _ {K P B} ^ {l - 1} \cdot \operatorname {C o n v} \left(\mathbf {F} _ {K P B} ^ {l - 1}\right)\right), \tag {4} +$$ + +where $\cdot$ denotes to element-wise multiplication. + +# 3.3. Harmony Kernel Modulation + +The global-aware adaptive kernel obtained from the harmony kernel prediction branch is then utilized in harmony kernel modulation. In this section, we illustrate the regional harmony operation method kernel modulation in decoder layers, which converts the previous overall treatment of background and foreground into a local reference. As mentioned in Section 3.2, we apply multi-level kernel modulation in decoder layer to adapt scales and scenario variation problem. Figure 3 shows our proposed kernel modulation in $l$ th decoder layers, which could be formulated as + +$$ +\hat {\mathbf {F}} _ {D} ^ {l} = \mathbf {F} _ {D} ^ {l} \otimes \mathbf {K} ^ {l}, \tag {5} +$$ + +where $\oplus$ denotes the harmony kernel modulation, $\mathbf{F}_D^l\in$ $\mathbb{R}^{C\times H\times W}$ is the deep feature extracted from the $l$ th layer in decoder, and the $\hat{\mathbf{F}}_{\mathbf{D}}^{l}\in \mathbb{R}^{C\times H\times W}$ is its corresponding harmony kernel modulation result feature in the $l$ th layer. The tensor $\mathbf{K}^l\in \mathbb{R}^{C\times N^2\times H\times W}$ represents the kernels with size of $N$ for harmony kernel modulation in the $l$ th feature layer, which we obtain from KPB. For the kernel modulation in each pixel, we can expand the above equation as + +$$ +\hat {\mathbf {F}} _ {D} ^ {l} [ \mathbf {p} ] = \sum_ {\mathbf {q} \in \mathcal {N} _ {p}} \mathbf {K} _ {p} ^ {l} [ \mathbf {p} - \mathbf {q} ] \mathbf {F} _ {D} ^ {l} [ \mathbf {q} ], \tag {6} +$$ + +where $\mathbf{p}$ and $\mathbf{q}$ are the coordinates of pixels in the image, $\mathbf{K}_p^l$ is the kernel for filtering the element $\mathbf{p}$ of $\mathbf{F}_D^l$ via its surrounding elements, i.e., $\mathcal{N}_p$ . As we illustrate in Eq. 5, $\mathbf{K}^l$ contains all element-wise kernels, i.e., $\mathbf{K}_p^l \in \mathbb{R}^{C \times N \times N}$ for filtering operations. After the kernel modulation in decoder layers, we finally obtain the harmonization result. In this paper, we define the U-Net decoder layer as $\phi_D(\cdot)$ , then we can formulate our harmonization process with kernel modulation as $\hat{I}_h = \phi_D^L (\dots \phi_D^1 (\mathbf{F}_D^1\otimes \mathbf{K}^1))\cdot M + (1 - M)\cdot I_c$ . + +# 3.4. Objective function + +In the training phase, we only employ foreground-normalized MSE loss as our objective function. Compared with normal MSE loss, it reduces the impact of copying background area: + +$$ +\mathcal {L} _ {r e c} = \frac {\sum_ {h , w} \left\| \hat {I} - I \right\| _ {2} ^ {2}}{\max \left\{A _ {\min } , \sum_ {h , w} M _ {h , w} \right\}}, \tag {7} +$$ + +where $A_{min}$ is a hyperparameter to keep the loss function stable as there might be some too small foreground objects. In this paper, we set $A_{min} = 100$ as suggested in [38]. + +# 4. Experiments + +# 4.1. Implementation Details + +We conduct the image harmonization experiment at resolution $256 \times 256$ on the benchmark dataset iHarmony4 [7]. + +Table 1. Quantitative comparisons across four sub-datasets of iHarmony4 [7]. ↑ indicates the higher the better, and ↓ indicates the lower the better. We compute fMSE for better reflection on harmonization tasks. Best results are in bold and the suboptimal results are in underline. + +
MethodHCOCOHAdobe5kHFlickrHday2nightALL
PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓
Composite33.9469.37996.5928.16345.542051.6128.32264.351574.3734.01109.651409.9831.63172.471376.42
DIH [41]34.6951.85798.9932.2892.65593.0329.55163.381099.1334.6282.341129.4033.4176.77773.18
S2AM [8]35.4741.07542.0633.7763.40404.6230.03143.45785.6535.6950.87835.0634.3559.67594.67
DoveNet [7]35.8336.72551.0134.3452.32380.3930.21133.14827.0335.2751.951075.7134.7652.33532.62
IIH [16]37.1624.92416.3835.2043.02284.2131.34105.13716.6035.9655.53797.0435.9038.71400.29
RAINNnet [29]37.0829.52501.1736.2243.35317.3531.64110.59688.4034.8357.40916.4836.1240.29469.60
iDIH-HRNet [38]39.1616.48266.1938.0821.88173.9633.1369.67443.6537.7240.59590.9738.1924.44264.96
D-HT [15]38.7616.89299.3036.8838.53265.1133.1374.51515.4537.1053.01704.4237.5530.30320.78
Harmonizer [24]38.7717.34298.4237.6421.89170.0533.6364.81434.0637.5633.14542.0737.8424.26280.51
DCCF [44]39.7214.55267.7938.2420.20171.0133.7266.20440.8438.1851.40629.6738.6022.64265.41
SCS-Co [17]39.8813.58245.5438.2921.01165.4834.2255.83393.7237.8341.75606.8038.7521.33248.86
Ours40.3212.95222.3139.9717.84138.2234.4557.58372.9038.4742.76546.0639.5319.90220.44
+ +Table 2. Quantitative comparisons on different ratios of foreground based on iHarmony4 by MSE and fMSE metrics. The best results are in bold and the suboptimal results are in underline. + +
MethodVenue0%~5%5%~15%15%~100%
MSE↓fMSE↓MSE↓fMSE↓MSE↓fMSE↓
DIHCVPR'1718.92799.1764.23725.86228.86768.89
S2AMTIP'2015.09623.1148.33540.54117.62592.83
DoveNetCVPR'2014.03591.8844.90504.42152.07505.82
RainNetCVPR'2111.66550.3832.05378.69117.41389.80
iS2AMWACV'216.73294.7618.03204.6963.02207.82
GKNetOurs5.36244.0617.46200.3457.31188.75
+ +The initial learning rate is set to $10^{-4}$ , and the models are trained for 120 epochs with a batch size of 16 on four 2080Ti GPUs. For optimizer, we adopt an Adam optimizer with $\beta_{1} = 0.9, \beta_{2} = 0.999$ and $\epsilon = 10^{-8}$ . It takes about two days for training. Our proposed model is implemented by PyTorch, and more detailed network architectures could be found in the supplementary file. + +# 4.2. Datasets and Metrics + +Datasets. To evaluate our proposed method for image harmonization, we conduct our experiments on the benchmark dataset iHarmony4 [7], which consists of 4 sub-datasets: HCOCO, HAdobe5K, HFlickr, and Hday2night, including 73147 pairs of synthesized composite images with their corresponding foreground mask and ground truth image. + +Evaluation Metrics. Following the standard setups in image harmonization, we use the peak signal-to-noise ratio (PSNR) and Mean Squared Error (MSE) as evaluation metrics. Furthermore, it is more accurate to only calculate the difference in the foreground region with the metric foreground MSE (fMSE) introduced by [38]. The metric MSE is calculated for the whole image, while there is no changes for pixels in the background region in harmonization task. Without considering the foreground ratio, the average MSE and PSNR results of the dataset will be more responsive to the performance of large-scale targets. In this paper, we argue that fMSE is more suitable for harmonization task. + +# 4.3. Comparison with SOTAs + +Quantitative comparison. As results shown in Table 1, we compare our method with other state-of-the-art image harmonization methods on iHarmony4 [7]. Following [7, 38], we also evaluate the model performance on different ratios of foreground by splitting the test images into three groups, i.e., $0\% \sim 5\%$ , $5\% \sim 15\%$ , and $15\% \sim 100\%$ . We provide these results in Table 2. Observing the quantitative experiment results above, we can summarize the following conclusions: 1) Our method achieves SOTA results of all evaluation metrics on average iharmony4 datasets. More specifically, our method achieves $0.78\mathrm{dB}\uparrow$ improvement in PSNR, $1.43\downarrow$ in MSE, and $28.42\downarrow$ in fMSE compared with suboptimal methods. 2) Our method obtains the best fMSE scores on all sub-datasets, meaning that the foreground regions generated by our method are more natural and closer to real images. 3) As shown in Table 2, our model performs well on each foreground ratio, especially on $0\% \sim 5\%$ , which indicates that our method has a strong ability to handle variable foreground scales. It also proves that our proposed global-aware adaptive kernel could process global-to-local impact with excellence. + +Qualitative comparison. We further provide qualitative results on iHarmony4 datasets in Figure 5. It could be observed that our GKNet generates more visually coherent images of the foreground and background than composited images, which are also closer to ground truth. 1) The first two rows of examples show that our method can effectively handle the small object harmonization problem in complex scenes with proximity prior consideration. 2) The last two row examples show that our regional modulation with multi-level structure performs well in large foreground cases, which handles a wide range of enormous contrast. For more detailed descriptions, please refer to the caption in Figure 5. In contrast, our method presents more photorealistic results. More visual comparison results on iHarmony4 datasets could be seen in supplementary materials. + +Comparisons on Real Datasets. Experiments results on + +![](images/5562084d79c04136b4c32f29f9ef4577ddfd093a4cfec5211c4ac375fa8c69e3.jpg) + +![](images/c6f4f558a07eae3b8ea026d01679043f8e756bf965053d1ebf8ee7164646e164.jpg) + +![](images/90d238a2ceaf73457219af3e617973782f540b9e2065e59eca3bcaf157d0dd41.jpg) + +![](images/5208bb64d2ca16677665271eb51d3870c304132920bf17a1d1fa757da67102f8.jpg) + +![](images/8fcdb0ff918bb8a7897d43621b63bfa63006188450235a0a7564a8d3e49359ac.jpg) + +![](images/c1ff4b6f51e1309d17343a4b6604a7019bc6fa6f7623176fa5abe5e20e7083f5.jpg) + +![](images/7d3d168a12ac6fbd99d85940b433418b77daa7b08d403ddcd1395c2bbbfffd6a.jpg) + +![](images/962becbc27fcde7833a79c463b8e11155696313a0453e139e503fd149e2bfa76.jpg) + +![](images/c1597deb69a99032ad247178a1590393c9c0cebd8f06214fb08987c0081751fb.jpg) + +![](images/4d4d85e304bb30b94615060afc5615af2de7b3d1f5cde99583e23ab0f4d33e71.jpg) + +![](images/8458b816f1d67fd401991760bcbdbf5c278dbefec23b95a6859b7ec8f7b314a5.jpg) + +![](images/0d6590d9f27e4ade140b80c1370cd619ab0a49093940daa97899d48c09f778eb.jpg) + +![](images/941b0766a544219fa0339f7db96f56bcb3dcd56c31f50b38fd975db772011974.jpg) + +![](images/9e10cc63580a4d3ce8001d894f7640621107d3420c0a472b2580928d36055d15.jpg) + +![](images/fbfc138e3652fbf46821a169d575e43e4b4e1f8ab0d43fd3527fc6be2c5119ec.jpg) + +![](images/517c8e4f9d2644693ec2fb1d019d542a9dfa671b7fb551947d5cea6a50fdb846.jpg) + +![](images/646af3203846d214ed5329171f88202310cbfd81f075fcea2cf7dc9e5c73a550.jpg) + +![](images/771191118f7baf77de0e5d750884bed2d146fd070eb495085fb722443c243d2b.jpg) + +![](images/179915a7b08df2053441e0fa07da7ee01db951671a60e828e456b7ad93fb5dae.jpg) + +![](images/68aede6bef8c67462b0e2734421cdb6c05b75b3d2b386bec116b276907a14011.jpg) + +![](images/783a7b9cdd63b432145f835ea84949aaa201915b297e857b920b18e018c74b5a.jpg) + +![](images/194b66820e3d1f1f78a68ac05f6367c391b664b7ee6cda5e17905aa84fca5ee6.jpg) +Mask + +![](images/4fc4f0ee91c94460bdaf70dd71a011836d23389c8c14309c63235e6998b3260e.jpg) +Input + +![](images/ec36806cfd0312165c9fcbdbe43a4a88ae575944e4161d91a65286f2211a8ff8.jpg) +RainNet [29] + +![](images/65323b2bade496807e2e9ac2ce5f5dda85ba6e79dbc45b5d380116527bfe5926.jpg) +D-HT [15] + +![](images/81a5d9fe9c9fd32e128198c927eb5480e1fa2a512e2c6d76dec53f64c8f676f1.jpg) +Harmonizer [24] + +![](images/157d44c2bf032efac5cb9478b3ffaaa95df841b258bc38a734ba360b1968ef04.jpg) +Ours + +![](images/a0468a61b6e7d74fc3d805c96760282efb3e7e8a2f2e6bffb40eb37021fbd384.jpg) +Real(GT) + +![](images/1cb92b74e3a36e4bde3e22135b9cd1165f917968b1f710e3f09071f4f55d6a77.jpg) +Figure 5. Qualitative comparisons with SOTA methods on iHarmony4 [7]. Mask in column one and Red box in Input represents the foreground. Case 1: The background color shows spatial variation, while only our method captures practical color reference by predicted kernel and local harmony modulation. Case 2: The harmony result obtained by our method is better in the detailed structure like duckweed center due to target harmony kernels for each foreground part. Case 3 & 4: For large foregrounds, our approach could also achieve better results, which preserves more original details and is closer to ground truth. + +![](images/e189c02824a96cbe39e6550271286545d4037a4a557373b54802a21804f28fd6.jpg) +Mask + +![](images/fda5e40261ee860e95f80fe971d58e0a31e26f156325902ed8ec75638152910a.jpg) + +![](images/f18198fd01a574b469e9356d42ac8b56acccb04740ce40239eb2d4cf732b4373.jpg) +Input + +![](images/98a8745f1ac17a11e538750e287d681d461e9056e9f12ebcdea67c040357d247.jpg) + +![](images/1333f811a8d75ec905214fb106ffadd0268e0496b307c73a7e176885487a6fb0.jpg) +RainNet [29] + +![](images/9cd1f7ccb04c1ff068b1a3bba8daa9d7200ec7de472aff782d3a786ee52d448d.jpg) + +![](images/0c06e123d88f8d4bf1d9a412d85ea575c6c7d376432c214f498d4503d76b99f3.jpg) +iDIH-HRNet [38] +Figure 6. Qualitative comparisons with SOTA methods on real composite images [41]. Mask in column one and Red box in Input represents the foregrounds. Case 1: Comparing the results on the dogs, our method achieves more natural results over the sunset background. Case 2: Our result dims the foreground person based on background dim light, which achieves a more natural effect. + +![](images/0e16a835e09f1c0120b1807b9a7b9b6d7df0432f5c9cbcbbcf47544281126023.jpg) + +![](images/8f91f9cc8def8c8f92926d61cfc6d4e2e338913917945b785e626a0e929d51b6.jpg) +DoveNet [7] + +![](images/488de7ab53bdd093467a296ad45960758c2ed465ca75a1a6ec49a75c1efd4dd7.jpg) + +![](images/0d47297f164a21dfac4a1d2c8d9e725b817912eeffce39071b9b8c5ba8248465.jpg) +Ours + +real composition datasets [41] can be seen in Figure 6. For real composition cases, evaluation metrics are impossible to calculate as there are no ground truth images. Hence, we only show qualitative results and human study results here. More visual comparison results on real datasets could be seen in supplementary materials. + +Table 3. B-T scores comparison on real composite images. + +
MethodCompositeDoveNet[7]RainNet[29]iDIH-HRNet[38]Ours
B-T Score ↑0.4160.6860.9721.5321.944
+ +Following [7, 6, 16, 17], we conduct our human study by inviting 50 volunteers to compare 24750 pairwise results. The pairwise results are obtained from 99 real composited images, with 25 results for each pair of different methods on + +average. We also use the Bradley-Terry model (B-T model) to calculate the global ranking score. Our method achieves the best results as shown in Table 3. + +# 4.4. Ablation Studies + +Effectiveness of network components. We further conduct quantitative experiments to verify the effectiveness of components in GKNet. Note that modules in GKNet have dependencies, we can only show gradually added ablation studies. As the results in Table 4, our full model obtains the highest performance on all metrics when KPB, LRE, and SCF work together. Table 4 also illustrates the effectiveness of each component. Moreover, to further illustrate our global-local interaction method for harmonization, we show + +Table 4. Quantitative ablation study of our approach with different components on iHarmony4[7] + +
BaselineKPBLRESCFMSE ↓PSNR ↑fMSE ↓
✓✗✗✗27.2737.83280.56
✓✓✗✗21.4238.68235.72
✓✓✓✗20.5039.30229.63
✓✓✓✓19.9039.53220.44
+ +![](images/3e7d5075eb2db76e5b54a10765f317d95df929feb77d5cd1de57308c5ace0b18.jpg) + +![](images/bad7e5d703d4fe67b9064a89908977f605f9af835b24e2b8856d7c1613607d2c.jpg) +Input + +![](images/cfd8370fe6af2918d0868647434baccd841904d8d77ba3e9f4c9949db4cc98d5.jpg) + +![](images/20ef5c6b49c4ce0039cdf634c71b34f09e6aaf7eb15ad52fb4777ef6ab19ca9a.jpg) +GT + +![](images/99dd57e3688269833ca404994c4e4ddabe5ce9cec25da8b3fb2abe62efce1a04.jpg) + +![](images/0b596e44cdb72f2bf0c8dbe153ed361f903821f42d940dc93542b928f0e01114.jpg) +Baseline + +![](images/7fcbcfc1f43f86f9243ece16cd74418e72f21169098e42fb5fb41f24d26ed922.jpg) + +![](images/d84fa9ffb66dc21da263ef70b3a1a31c87e1c0209cb87d6ec5aa458d6b564ebf.jpg) +KPB + +![](images/c92de0bf653fb6cf0bfb67c2ac9928b5fd1bc7fac4bf75ee2933a6e192cd3f26.jpg) + +![](images/4b3fc776dbd81a6e9500f359c585cf53815c02203b0a0f1bd95eb6f867fe6932.jpg) +LRE +Figure 7. Qualitative ablation study of our approach. Red boxes in input image mark foreground. + +![](images/c27b19a32c1d41b04c6021e48f4f0dec815973fdd010f935b2dcd9b388612ab0.jpg) + +![](images/2f85e00f514f004335f67c79a03689f9e4ba86f911c09d94828cdd549b978563.jpg) +Full Model + +qualitative results in Figure 7. Compared with the baseline, the model with only local KPB outputs stronger local modeling results but loses global view. After introducing LRE, global awareness of the background is enhanced. But it is evident that color is overcorrected in the second row. After adding SCF, we effectively correct the deviation by selecting relevant references in background, and the final result is closer to real image. + +![](images/f190d800eb3ed7cea56f4451a291ff338220507ff613afa0f893451f6a3d8f59.jpg) +Figure 8. The cluster visual results of adaptive harmony kernels. e.g., in flower case, structure information like petal margin is displayed, which proves that kernels are predicted to adapt local harmonization specifically. + +Interpretability of Global-aware Harmony Kernel. To further illustrate the effectiveness of the adaptive harmony kernels, we cluster the per-pixel adaptive harmony kernels predicted from KPB by K-means. As shown in Figure 8, the clusters show strong spatial structure, which indicates that our predicted dynamic kernel can make the structural adjustment to harmonize the foreground. Moreover, in some cases, the change of kernel classes is related to the object mask. This exhibits that our harmony kernels are predicted dynamically to deal with visual inconsistency in different spatial locations (e.g. fore-/background or edges). + +![](images/17c1ea4edaec58b734fecaa9c07b5045e2339560c376c9d9c256014c175524a1.jpg) +(a) Mask + +![](images/66a2b5bb4d01fdccef935d2110b3bcb610164c93f001066cf619cdc4ed270a06.jpg) +(b) Comp + +![](images/a0f1d38a812309877073c3b97c7188dc41e9723d06610b01ee3a2fbe949afc5b.jpg) +(c) Feature map with channel attention weight + +(c + +![](images/af4d206aca83d4aebc2c62243ab1bb3a8daae06ca5584598e5cf95459abb3aeb.jpg) + +![](images/e13c1346577d118804a494b63cda97e8f51ff4157aba1633a09972d8449ab83f.jpg) + +![](images/9b9bdc8e1176f5e9d290bd6f341f5f02e91cf52b20a73ad09472fc345973c9fb.jpg) + +![](images/cecb2bf9c6b69c1ec88a73f83e0d744a684d3d60298031e78d2ee1e1095def8e.jpg) +Figure 9. Feature maps in SCF. Red number in upper right corner of feature map represents channel-wise attention weights. +Figure 10. Cross-attention from example point (10,10). We show four attention maps for different heads, which proves LRE can match model related long-distance references. + +Interpretability of LRE and SCF Module. We visualize the attention mechanism in LRE and SCF for interpreting global-local interaction. In Figure 9, we visualize feature maps in decoder layers to illustrate our channel-wise attention module SCF. Visual feature maps with attention weights show that harmony kernels are predicted with more attention on related background area and less attention on irrelevant background area or foreground. In Figure 10, we visualize the attention maps of LRE, focusing on an example point in foreground. As the long-distance information in predicted harmony kernels is brought by LRE, the visualized attention maps in different heads indicate two points: 1) The kernels for local operation have a global perceptive field with long-distance information. 2) Different heads pay attention to different reference parts, i.e. relevant background reference, foreground content, overall tone, etc. + +# 5. Conclusion + +This paper proposes an effective network GKNet to learn global-aware harmony kernels for image harmonization, including harmony kernel prediction and harmony kernel modulation branches. For harmony kernel prediction, we propose LRE to extract long-term references and KPB to predict global-aware kernels. To better fuse long-term context, we design SCF to select relevant references. For harmony kernel modulation, we employ the predicted kernels for harmonization with location awareness. Extensive experiments demonstrate that our proposed algorithm outperforms the state-of-the-art algorithms on the iHarmony4 dataset and real image composition datasets. + +Acknowledgements. This work was supported by a Grant from The National Natural Science Foundation of China (No. 2021YFB2012300). + +# References + +[1] Steve Bako, Thijs Vogels, Brian McWilliams, Mark Meyer, Jan Novák, Alex Harvill, Pradeep Sen, Tony Derose, and Fabrice Rousselle. Kernel-predicting convolutional networks for denoising monte carlo renderings. ACM Trans. Graph., 36(4):97-1, 2017. 3, 4 +[2] Tim Brooks and Jonathan T Barron. Learning to synthesize motion blur. In CVPR, pages 6840-6848, 2019. 3 +[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In ECCV, pages 213-229. Springer, 2020. 4 +[4] Mark Chen, Alec Radford, Rewon Child, Jeffrey Wu, Heewoo Jun, David Luan, and Ilya Sutskever. 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Existing methods employ local color transformation or region matching between foreground and background, which neglects powerful proximity prior and independently distinguishes fore-/back-ground as a whole part for harmonization. As a result, they still show a limited performance across varied foreground objects and scenes. To address this issue, we propose a novel Global-aware Kernel Network (GKNet) to harmonize local regions with comprehensive consideration of long-distance background references. Specifically, GKNet includes two parts, i.e., harmony kernel prediction and harmony kernel modulation branches. The former includes a Long-distance Reference Extractor (LRE) to obtain long-distance context and Kernel Prediction Blocks (KPB) to predict multi-level harmony kernels by fusing global information with local features. To achieve this goal, a novel Selective Correlation Fusion (SCF) module is proposed to better select relevant long-distance background references for local harmonization. The latter employs the predicted kernels to harmonize foreground regions with local and global awareness. Abundant experiments demonstrate the superiority of our method for image harmonization over state-of-the-art methods, e.g., achieving 39.53dB PSNR that surpasses the best counterpart by " + }, + { + "bbox": [ + 47, + 267, + 289, + 602 + ], + "type": "inline_equation", + "content": "+0.78dB \\uparrow" + }, + { + "bbox": [ + 47, + 267, + 289, + 602 + ], + "type": "text", + "content": "; decreasing fMSE/MSE by " + }, + { + "bbox": [ + 47, + 267, + 289, + 602 + ], + "type": "inline_equation", + "content": "11.5\\% \\downarrow / 6.7\\% \\downarrow" + }, + { + "bbox": [ + 47, + 267, + 289, + 602 + ], + "type": "text", + "content": " compared with the SoTA method. Code will be available at here." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 647, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 287, + 684 + ], + "type": "text", + "content": "Image composition aims to synthesize foreground objects from one image into another, which is a common task in image editing. 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Comparison of background reference methods in harmonization. Blue/Red region represent foreground/background, respectively, and white/red arrows refer to interaction/injection, respectively. (a) Local-translation methods reference nearby pixels. (b) Region-matching methods transfer reference with a unified view of fore-/back-ground region. (c) Our method interacts long-distance reference and injects it with short-distance consideration." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 426, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 497 + ], + "type": "text", + "content": "tinguish synthetic images due to the visual inconsistency between foreground and background in composited images. 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"image_body" + }, + { + "bbox": [ + 347, + 182, + 373, + 190 + ], + "lines": [ + { + "bbox": [ + 347, + 182, + 373, + 190 + ], + "spans": [ + { + "bbox": [ + 347, + 182, + 373, + 190 + ], + "type": "text", + "content": "Real(GT)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 392, + 71, + 538, + 181 + ], + "blocks": [ + { + "bbox": [ + 392, + 71, + 538, + 181 + ], + "lines": [ + { + "bbox": [ + 392, + 71, + 538, + 181 + ], + "spans": [ + { + "bbox": [ + 392, + 71, + 538, + 181 + ], + "type": "image", + "image_path": "1ec33eaddb2c5db32dd9643c980dac71dc5a8fcfa4ed471630eab05b038e7a23.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 545, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 545, + 224 + ], + "type": "text", + "content": "Figure 2. Left: Two challenging samples in image harmonization. Mask in column one and Red boxes represents the foreground. Right: Performance comparison with SOTA methods in terms of PSNR and model size. The circle size represents the floating-point number." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 245, + 286, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 286, + 341 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 286, + 341 + ], + "type": "text", + "content": "unified view of these two regions by statistics components or discriminators. Though these approaches harmonize images with a broader reference range, they totally neglect the spatial variations in two regions. Hang et al. [17] begin to notice this problem and add attention-based references in region matching method [29]. But they still separate two regions independently and harmonize foreground by unified matching without considering foreground spatial variations." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 342, + 286, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 286, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 286, + 544 + ], + "type": "text", + "content": "To further illustrate existing problems, we provide two common harmonization cases in Figure 2. In the first case, a small foreground object appears in the background with obvious color changes. The region-matching method RainNet [7] provides a poor color correction result while the local method iS²AM [38] could tackle this case well, which indicates that the unified view of background will blend the overall complex color conditions. In the second case, related long-distance references exist in the background, while the local method could only attach insufficient adjacent information. Region-matching method RainNet could obtain whole background blue tone by matching, but it still excessively harmonizes the house due to the unified view. These two cases indicate that local reference is insufficient, but region-matching methods could not model long-distance reference well and will cause unbalanced harmonization problems by rough matching." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 546, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 286, + 713 + ], + "type": "text", + "content": "To solve this problem, we rethink essential proximity priors in image harmonization, i.e., when we paste an object into background, the color or light is related to location and will be influenced by its neighboring first. Moreover, the effective long-distance information in background changes with pasted locations, which requires us to learn adaptive references for each part. Inspired by this observation, we propose a novel Global-aware Kernel Network (GKNet) to integrate local harmony modulation and long-distance background references, including harmony kernel prediction and harmony kernel modulation. For harmony kernel prediction, we propose a novel global-aware kernel prediction method including Long-distance Reference Extractor (LRE) to obtain long-distance references and Ker-" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 245, + 545, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 329 + ], + "type": "text", + "content": "nel Prediction Blocks (KPB) to predict multi-level adaptive kernels with selected long-distance references by Selective Correlation Fusion (SCF). For kernel modulation, we propose to model local harmony operation by predicted global-aware kernels and multi-level features. Focusing on features in kernel region, kernel modulation is significant in alleviating unbalanced region-matching errors in complex scenes." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 317, + 329, + 516, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 329, + 516, + 341 + ], + "spans": [ + { + "bbox": [ + 317, + 329, + 516, + 341 + ], + "type": "text", + "content": "To summarize, we make following contributions:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 346, + 545, + 555 + ], + "type": "list", + "angle": 0, + "index": 28, + "blocks": [ + { + "bbox": [ + 306, + 346, + 545, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 545, + 405 + ], + "type": "text", + "content": "- With the observation of proximity prior and long-distance references in image harmonization task, we design GKNet to model global-local interaction by learning global-aware harmony kernel, including harmony kernel prediction and harmony kernel modulation." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 409, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 409, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 409, + 545, + 504 + ], + "type": "text", + "content": "- For harmony kernel prediction, we propose a kernel prediction branch combined with LRE to model global information and multiple KPB to learn adaptive harmony kernels. For better global references, we design SCF to select relevant long-distance references for local harmonization. For harmony kernel modulation, we propose the method to harmonize local regions in multi-level decoder layers with predicted kernels." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 508, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 545, + 555 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the superior performance of our methods in both quantitative and qualitative results, noting that our method achieves state-of-the-art results on iHarmony4 datasets." + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 567, + 389, + 579 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 567, + 389, + 579 + ], + "spans": [ + { + "bbox": [ + 306, + 567, + 389, + 579 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 587, + 432, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 432, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 432, + 600 + ], + "type": "text", + "content": "2.1. Image Harmonization" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "Traditional image harmonization works have focused on finding a better method for low-level appearances matching between foreground and background regions in images, which includes color statistics [36, 35, 45], gradient information [20, 34, 40], and multi-scale statistical features [39, 25]. However, traditional methods could only be effective in specific scenes. With the advanced generative ability of deep learning, Tsai et al. [41] firstly propose a learning-based encoder-decoder network assisted by" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7536" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 68, + 539, + 350 + ], + "blocks": [ + { + "bbox": [ + 55, + 68, + 539, + 350 + ], + "lines": [ + { + "bbox": [ + 55, + 68, + 539, + 350 + ], + "spans": [ + { + "bbox": [ + 55, + 68, + 539, + 350 + ], + "type": "image", + "image_path": "01d3f1749a8e2c43b19366b9a8d177ffaa464a09fa00df3ece36ce22c385a035.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "lines": [ + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "text", + "content": "Figure 3. The overview of our proposed GKNet, which consists of harmony kernel prediction branch and harmony kernel modulation branch. As shown in gray box, the harmony kernel prediction branch is combined with a Long-term Reference Extractor (LRE) and multi-level Kernel Prediction Blocks (KPB). As shown in yellow box, we propose Selective Correlation Fusion (SCF) module in KPB for better long-distance references. Given a composited image " + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "text", + "content": " with corresponding foreground mask " + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "text", + "content": ", we extract deep features " + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_E^l" + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "text", + "content": " from encoder " + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "inline_equation", + "content": "\\phi_E" + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "text", + "content": ". Then, harmony kernel prediction branch utilizes the deepest feature map and " + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_E^l\\}" + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "text", + "content": " to predict multi-level dynamic harmony kernels " + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{K}^l\\}" + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "text", + "content": " increasingly. The predicted global-aware kernels are employed for harmony kernel modulation in decoder " + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "inline_equation", + "content": "\\phi_D" + }, + { + "bbox": [ + 46, + 360, + 548, + 429 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 448, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 289, + 712 + ], + "type": "text", + "content": "a semantic branch. In observation that semantic information is effective in image harmonization, Soffliuk et al. [38] also add additional pre-train semantic model to baseline DIH [41] and " + }, + { + "bbox": [ + 46, + 448, + 289, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^2\\mathbf{A}\\mathbf{M}" + }, + { + "bbox": [ + 46, + 448, + 289, + 712 + ], + "type": "text", + "content": " [8]. Inspired by domain transfer, Cong et al. [7] adopt a verification discriminator to distinguish foreground and background domains. Similarly, Ling et al. [29] also treat the composited image as two independent parts and apply style transfer idea to match mean-variance statistics. To focus on harmonize foreground region, some methods add attention mechanisms. Cun et al. [8] add a spatial-separated attention module. Guo et al. [15] for the first time introduce Transformer architecture to image harmonization. Hang et al. [17] add background attention calculation to the style transfer block [29], and they also incorporated the idea of contrast learning. Besides, Guo et al. [16] decompose image into reflectance and illumination by autoencoder for separate harmonization based on Retinex theory. Some high-resolution methods [24, 44] frame image harmonization as an image-level problem to learn white-box arguments. However, the above methods neglect spatial proximity prior and could not model long-distance references well. Instead in this paper, we design" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 448, + 545, + 472 + ], + "type": "text", + "content": "a better local modulation method combined with selected long-distance references to alleviate this problem." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 479, + 497, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 497, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 497, + 491 + ], + "type": "text", + "content": "2.2. Dynamic Filtering in Image Editing" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 497, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 628 + ], + "type": "text", + "content": "The input-dependent dynamic filtering first proposed by Jia [21] et al. aims to learn position-specific filters on pixel inputs and apply the generated kernels to another input, which has been widely used in numerous vision tasks [33, 23, 46, 9]. This method also shows effectiveness in image editing tasks, such as denoising [1, 32, 42], shadow removing [13], deraining [14], image inpainting [26], and blur synthesis [2]. However, most above methods apply dynamic filtering at image-level filter prediction and utilization. We propose to learn a multi-level global-aware kernel with long-term context references for harmonization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 635, + 400, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 400, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 400, + 647 + ], + "type": "text", + "content": "2.3. Feature Fusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Feature fusion is to combine features from different layers or branches, which is an omnipresent part of modern neural networks and has been studied extensively. Most previous works [18, 37, 28] for feature fusion focus on the pathways structure design, applying two linear classic" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "7537" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "methods of summation or concatenation. Recently, benefit from the successful use of Transformer in computer vision [4, 11, 31, 50, 49, 48, 3, 4, 12, 43, 22, 30, 15], some works [19, 27, 52, 10, 47, 51, 5] apply attention mechanism to present nonlinear approaches for feature fusion. As global information is significant in image harmonization, we design a dynamic weighted fusion method to effectively fuse long-distance reference into kernel prediction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 177, + 103, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 177, + 103, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 177, + 103, + 190 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": "Given a composited image " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": " with its corresponding binary mask " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": " indicating the region to be harmonized, our goal is to learn a network " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "\\mathrm{G}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": " that outputs harmonized image " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "I_{h}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": ", which could be formulated as " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "I_{h} = G(I_{c}, M)" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": ". To make this composited image " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": " look natural, we train our model " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "\\mathrm{G}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": " to adjust the foreground region " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "I_{f}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": " in a supervised manner with paired real image " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": ". In this paper, we also define the background region as " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "I_{b}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": ", and then the composition process could be formulated as " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "I_{c} = I_{f} \\cdot M + (1 - M) \\cdot I_{b}" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 46, + 198, + 289, + 318 + ], + "type": "text", + "content": " denotes element-wise multiplication." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 192, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 192, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 192, + 335 + ], + "type": "text", + "content": "3.1. Overview of Our Network" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 437 + ], + "type": "text", + "content": "As shown in Figure 3, we design a novel network architecture for image harmonization tasks to allow our network to pay attention to short-distance and long-distance information simultaneously. Following the standard designs in image harmonization works [8, 38, 29] we use simple U-Net [37] with attention blocks [8] as the basic structure. We also take composited RGB image " + }, + { + "bbox": [ + 46, + 342, + 287, + 437 + ], + "type": "inline_equation", + "content": "I_{c} \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 46, + 342, + 287, + 437 + ], + "type": "text", + "content": " concatenated with foreground region mask " + }, + { + "bbox": [ + 46, + 342, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\mathbb{R}^{1 \\times H \\times W}" + }, + { + "bbox": [ + 46, + 342, + 287, + 437 + ], + "type": "text", + "content": " as input." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 437, + 289, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 289, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 289, + 665 + ], + "type": "text", + "content": "Motivated by proximity prior in image harmonization, we propose Global-aware Kernel Network (GKNet) to learn global-aware harmony kernel for image harmonization, which consists of two branches, harmony kernel prediction and harmony kernel modulation. Firstly, as long-distance reference is crucial for harmonization task, we design global-aware kernel prediction branch to predict harmony kernel with context modeling, which contains a transformer-based Long-term Reference Extractor (LRE) to extract global reference and Kernel Prediction Block (KPB) to predict harmony kernels. In order to incorporate relevant long-term references for local harmonization, a novel Selective Correlation Fusion (SCF) is proposed to select more effective references in backgrounds. Secondly, we design a multi-level harmony kernel modulation in decoder layers to employ the predicted global-aware kernels. The mechanism between global-aware harmony kernel prediction and harmony kernel modulation finally achieves local-global interaction for image harmonization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 671, + 201, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 201, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 201, + 684 + ], + "type": "text", + "content": "3.2. Harmony Kernel Prediction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Inspired by recent works in image editing [1, 14, 32], we propose to apply dynamic kernels to force the current pixel" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 347 + ], + "type": "text", + "content": "harmonized with surrounding regions adaptively. This approach effectively makes up for the lack of consideration of proximity prior in previous harmonization works. However, basic dynamic kernels for image editing tasks such as denoising and deraining are applied with a fixed size at image-level. To predict more proper adaptive kernels for image harmonization, we analyze the following: 1) Global modeling is necessary for image harmonization as long-distance references may appear in the background. Hence, we design a novel global-aware harmony kernel prediction branch with LRE to extract global information and KPB to predict global-aware kernels with fusion module SCF. 2) Fixed-size kernels applied at image-level could not handle the scale problem well. e.g. The pixels inside the large foreground mask can hardly obtain any real background information, while predicting large kernels will bring high computation costs and breaks the intention of proximity prior. Besides, image-level dynamic kernels pay more attention to detailed structure, while in image harmonization we also need to adapt multiple scene variations to harmonize foregrounds at semantic level. In order to adapt to multi-scene and multiscale problems, we propose to predict kernels in multi-level structures." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "content": "Long-distance Reference Extractor. In order to obtain long-term context, we employ 1-transformer layers [11] as our global information extractor. We feed the deepest feature map " + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_E^1" + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "content": " from CNN encoder into transformer layers. With the down-sampling feature map in low-resolution of " + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "inline_equation", + "content": "(\\frac{w}{r},\\frac{h}{r})" + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "content": ", we treat each pixel as a token to generate embeddings. With the multi-head attention mechanism, we obtain global interactive feature " + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{global}\\in \\mathbb{R}^{C\\times HW}" + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "content": " after 1-transformer layers. After reshaping and post-convolution layer, we obtain the long-term reference feature " + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{LR}" + }, + { + "bbox": [ + 304, + 359, + 547, + 479 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 491, + 547, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 598 + ], + "type": "text", + "content": "Kernel Prediction Block. To adapt diverse foreground scales and background scenarios, we apply our local operation kernel modulation in multiple decoder levels. Nevertheless, deep-level features contain more semantic information, and shallow features contain more details, we need to predict corresponding adaptive kernels for different level harmony kernel modulation. Thus, our designed global-aware harmony kernel prediction branch is in a multi-level structure to increasingly predict a series of kernels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 598, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 598, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 598, + 545, + 634 + ], + "type": "text", + "content": "In Figure 3, we show our proposed KPB structure from predicting kernels to harmony kernel modulation operation. The operation in " + }, + { + "bbox": [ + 304, + 598, + 545, + 634 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 598, + 545, + 634 + ], + "type": "text", + "content": "th KPBlock can be formulated as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 359, + 642, + 545, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 642, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 359, + 642, + 545, + 657 + ], + "type": "interline_equation", + "content": "\\mathbf {K} ^ {l}, \\mathbf {F} _ {K P B} ^ {l} = K P B l o c k \\left(\\mathbf {F} _ {E} ^ {l}, \\mathbf {F} _ {K P B} ^ {l - 1}\\right), \\tag {1}", + "image_path": "e707a54405d33bf0201f30d8ef50db560087f4e1619eb636dfd8f5f5d2da3c6a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "where KPBlock " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " is the KPBlock to predict " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{K}^l" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": ". For each KPB, we take " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{KP B}^{l-1} \\in \\mathbb{R}^{C_l \\times H_l \\times W_l}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " transferred from " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "(l-1)" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "th KPB (For the deepest KPB, we input " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{LR}" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": ") and the " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "th encoder layer feature " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_E^l" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " as input (We denote " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_E^1" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " as the deepest" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7538" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 230 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 230 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 230 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 230 + ], + "type": "image", + "image_path": "440d5d4af20767d9b5227c920aa3704e9cdf4cf33eefd2930098bb5459379e23.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "lines": [ + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "type": "text", + "content": "Figure 4. Schematic diagram of SCF. The module takes the (1-1)th layer feature " + }, + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{KPB}^{l-1}" + }, + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "type": "text", + "content": " and encoder feature " + }, + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_E^l" + }, + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "type": "text", + "content": " as input and outputs the correlation-aware fusion feature " + }, + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{KPB}^l" + }, + { + "bbox": [ + 47, + 240, + 288, + 275 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 283, + 287, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 283, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 283, + 287, + 319 + ], + "type": "text", + "content": "layer in encoder), which outputs feature " + }, + { + "bbox": [ + 47, + 283, + 287, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{KPB}^{l}" + }, + { + "bbox": [ + 47, + 283, + 287, + 319 + ], + "type": "text", + "content": " for next KP-Block and the global-aware kernels " + }, + { + "bbox": [ + 47, + 283, + 287, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{K}^{l} = \\mathrm{Conv}(\\mathbf{F}_{KPB}^{l})" + }, + { + "bbox": [ + 47, + 283, + 287, + 319 + ], + "type": "text", + "content": " after post-convolutions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": "Selective Correlation Fusion. Long-distance reference " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{LR}" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " obtained from LRE is then injected into the deepest KPBlock to model global information for local harmonization. The standard way of feature fusion, like concatenation or addition, equally treats low-level and high-level features. To efficiently model long-term information for local harmonization, we propose SCF to select relevant global information by interacting encoder features " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_E" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " and long-distance references based on channel-wise attention mechanism." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": "Specifically, as shown in Figure 4, we take the " + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "inline_equation", + "content": "(l - 1)" + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": "th layer feature " + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{KPB}^{l - 1}\\in \\mathbb{R}^{C_{l - 1}\\times H_{l - 1}\\times W_{l - 1}}" + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": "th encoder feature " + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_E^l\\in \\mathbb{R}^{C_l\\times H_l\\times W_l}" + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": " as input and extract attention vector " + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\alpha_{KPB},\\alpha_E\\in \\mathbb{R}^{C_l}" + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": " convolutions and MLP. Subsequently, the attention vector is divided into n groups with length m as " + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\tilde{\\alpha}_{KPB},\\tilde{\\alpha}_E\\in \\mathbb{R}^{n\\times m}" + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": ". Thus, the channel-wise attention relation " + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\in \\mathbb{R}^{n\\times n}" + }, + { + "bbox": [ + 47, + 438, + 287, + 523 + ], + "type": "text", + "content": " can be calculated by matrix product" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 133, + 529, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 529, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 133, + 529, + 287, + 544 + ], + "type": "interline_equation", + "content": "\\mathbf {A} = \\tilde {\\alpha} _ {K P B} \\odot \\tilde {\\alpha} _ {E} ^ {T}. \\tag {2}", + "image_path": "9f1776707ef197330caadb8d19bafd478d31c3ca056d30eb04cd7efd646be48d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "text", + "content": "After that, we calculate the selective factor " + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}_{KPB},\\overline{\\alpha}_E\\in" + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{C_l}" + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "text", + "content": " through " + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "inline_equation", + "content": "N\\times N" + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "text", + "content": " convolutions with splitting. Then, we obtain the selective attention weights " + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "inline_equation", + "content": "S^l\\in \\{S_E^l,S_{KPB}^{l - 1}\\}" + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "text", + "content": " for each features by " + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\{\\alpha_{KPB},\\alpha_E\\}" + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}\\in \\{\\overline{\\alpha}_{KPB},\\overline{\\alpha}_E\\}" + }, + { + "bbox": [ + 47, + 551, + 287, + 609 + ], + "type": "text", + "content": ", which can be formulated as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 119, + 616, + 287, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 616, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 119, + 616, + 287, + 631 + ], + "type": "interline_equation", + "content": "S ^ {l} = \\sigma (\\alpha + b \\cdot F C (\\bar {\\alpha})), \\tag {3}", + "image_path": "2400fedf499917018717ddda3ad54e69fd2eaa6012f84ce3e6c518e5242f3961.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 638, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 638, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 638, + 287, + 673 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 638, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{b}" + }, + { + "bbox": [ + 47, + 638, + 287, + 673 + ], + "type": "text", + "content": " is a learnable parameter, " + }, + { + "bbox": [ + 47, + 638, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 638, + 287, + 673 + ], + "type": "text", + "content": " is sigmoid function. Based on the attention weight vector, then the shallow and deep information are interacted as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 51, + 679, + 287, + 695 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 679, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 51, + 679, + 287, + 695 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {F}} _ {K P B} ^ {l} = S _ {E} ^ {l} \\cdot \\operatorname {C o n v} \\left(\\mathbf {F} _ {E} ^ {l}\\right) + \\text {U p s a m p l e} \\left(S _ {K P B} ^ {l - 1} \\cdot \\operatorname {C o n v} \\left(\\mathbf {F} _ {K P B} ^ {l - 1}\\right)\\right), \\tag {4}", + "image_path": "e0e26316affaa563407b829ad9864b1b18ed89db8bd8aa9ffd98e996ece89e66.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 701, + 239, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 239, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 239, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 701, + 239, + 713 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 47, + 701, + 239, + 713 + ], + "type": "text", + "content": " denotes to element-wise multiplication." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 466, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 466, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 466, + 84 + ], + "type": "text", + "content": "3.3. Harmony Kernel Modulation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 90, + 545, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 209 + ], + "type": "text", + "content": "The global-aware adaptive kernel obtained from the harmony kernel prediction branch is then utilized in harmony kernel modulation. In this section, we illustrate the regional harmony operation method kernel modulation in decoder layers, which converts the previous overall treatment of background and foreground into a local reference. As mentioned in Section 3.2, we apply multi-level kernel modulation in decoder layer to adapt scales and scenario variation problem. Figure 3 shows our proposed kernel modulation in " + }, + { + "bbox": [ + 304, + 90, + 545, + 209 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 90, + 545, + 209 + ], + "type": "text", + "content": "th decoder layers, which could be formulated as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 394, + 213, + 545, + 229 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 213, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 394, + 213, + 545, + 229 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {F}} _ {D} ^ {l} = \\mathbf {F} _ {D} ^ {l} \\otimes \\mathbf {K} ^ {l}, \\tag {5}", + "image_path": "ef84e1ace021af70356c3b656dfb84e0f0401987d73ca55aad44dce5e8f5f8ce.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": " denotes the harmony kernel modulation, " + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_D^l\\in" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{C\\times H\\times W}" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": " is the deep feature extracted from the " + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": "th layer in decoder, and the " + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{F}}_{\\mathbf{D}}^{l}\\in \\mathbb{R}^{C\\times H\\times W}" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": " is its corresponding harmony kernel modulation result feature in the " + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": "th layer. The tensor " + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "\\mathbf{K}^l\\in \\mathbb{R}^{C\\times N^2\\times H\\times W}" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": " represents the kernels with size of " + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": " for harmony kernel modulation in the " + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 233, + 546, + 329 + ], + "type": "text", + "content": "th feature layer, which we obtain from KPB. For the kernel modulation in each pixel, we can expand the above equation as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 363, + 334, + 545, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 334, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 363, + 334, + 545, + 360 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {F}} _ {D} ^ {l} [ \\mathbf {p} ] = \\sum_ {\\mathbf {q} \\in \\mathcal {N} _ {p}} \\mathbf {K} _ {p} ^ {l} [ \\mathbf {p} - \\mathbf {q} ] \\mathbf {F} _ {D} ^ {l} [ \\mathbf {q} ], \\tag {6}", + "image_path": "8e26410e0639dbdf3ed12ae4739348a03657a0bf44964d6f9f3276171ebe2bc1.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": " are the coordinates of pixels in the image, " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_p^l" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": " is the kernel for filtering the element " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_D^l" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": " via its surrounding elements, i.e., " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_p" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": ". As we illustrate in Eq. 5, " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{K}^l" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": " contains all element-wise kernels, i.e., " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_p^l \\in \\mathbb{R}^{C \\times N \\times N}" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": " for filtering operations. After the kernel modulation in decoder layers, we finally obtain the harmonization result. In this paper, we define the U-Net decoder layer as " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\phi_D(\\cdot)" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": ", then we can formulate our harmonization process with kernel modulation as " + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "inline_equation", + "content": "\\hat{I}_h = \\phi_D^L (\\dots \\phi_D^1 (\\mathbf{F}_D^1\\otimes \\mathbf{K}^1))\\cdot M + (1 - M)\\cdot I_c" + }, + { + "bbox": [ + 304, + 365, + 545, + 475 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 479, + 416, + 492 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 416, + 492 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 416, + 492 + ], + "type": "text", + "content": "3.4. Objective function" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 498, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 546 + ], + "type": "text", + "content": "In the training phase, we only employ foreground-normalized MSE loss as our objective function. Compared with normal MSE loss, it reduces the impact of copying background area:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 366, + 550, + 545, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 550, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 366, + 550, + 545, + 602 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} = \\frac {\\sum_ {h , w} \\left\\| \\hat {I} - I \\right\\| _ {2} ^ {2}}{\\max \\left\\{A _ {\\min } , \\sum_ {h , w} M _ {h , w} \\right\\}}, \\tag {7}", + "image_path": "a70970deb3d8e85c59fa3a14267bf316b0405caf76a801ff1e7d439a23c0bfa8.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 606, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 545, + 643 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 606, + 545, + 643 + ], + "type": "inline_equation", + "content": "A_{min}" + }, + { + "bbox": [ + 304, + 606, + 545, + 643 + ], + "type": "text", + "content": " is a hyperparameter to keep the loss function stable as there might be some too small foreground objects. In this paper, we set " + }, + { + "bbox": [ + 304, + 606, + 545, + 643 + ], + "type": "inline_equation", + "content": "A_{min} = 100" + }, + { + "bbox": [ + 304, + 606, + 545, + 643 + ], + "type": "text", + "content": " as suggested in [38]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 651, + 388, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 388, + 664 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 388, + 664 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 670, + 439, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 439, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 439, + 684 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "We conduct the image harmonization experiment at resolution " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " on the benchmark dataset iHarmony4 [7]." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7539" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 102, + 547, + 240 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons across four sub-datasets of iHarmony4 [7]. ↑ indicates the higher the better, and ↓ indicates the lower the better. We compute fMSE for better reflection on harmonization tasks. Best results are in bold and the suboptimal results are in underline." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 102, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 49, + 102, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 49, + 102, + 547, + 240 + ], + "type": "table", + "html": "
MethodHCOCOHAdobe5kHFlickrHday2nightALL
PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓PSNR↑MSE↓fMSE↓
Composite33.9469.37996.5928.16345.542051.6128.32264.351574.3734.01109.651409.9831.63172.471376.42
DIH [41]34.6951.85798.9932.2892.65593.0329.55163.381099.1334.6282.341129.4033.4176.77773.18
S2AM [8]35.4741.07542.0633.7763.40404.6230.03143.45785.6535.6950.87835.0634.3559.67594.67
DoveNet [7]35.8336.72551.0134.3452.32380.3930.21133.14827.0335.2751.951075.7134.7652.33532.62
IIH [16]37.1624.92416.3835.2043.02284.2131.34105.13716.6035.9655.53797.0435.9038.71400.29
RAINNnet [29]37.0829.52501.1736.2243.35317.3531.64110.59688.4034.8357.40916.4836.1240.29469.60
iDIH-HRNet [38]39.1616.48266.1938.0821.88173.9633.1369.67443.6537.7240.59590.9738.1924.44264.96
D-HT [15]38.7616.89299.3036.8838.53265.1133.1374.51515.4537.1053.01704.4237.5530.30320.78
Harmonizer [24]38.7717.34298.4237.6421.89170.0533.6364.81434.0637.5633.14542.0737.8424.26280.51
DCCF [44]39.7214.55267.7938.2420.20171.0133.7266.20440.8438.1851.40629.6738.6022.64265.41
SCS-Co [17]39.8813.58245.5438.2921.01165.4834.2255.83393.7237.8341.75606.8038.7521.33248.86
Ours40.3212.95222.3139.9717.84138.2234.4557.58372.9038.4742.76546.0639.5319.90220.44
", + "image_path": "39065f71897d790683bd3643b0da016d85173eea41cffeb5bcd14c0c7050ab01.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 290, + 287, + 374 + ], + "blocks": [ + { + "bbox": [ + 47, + 248, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 248, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 248, + 287, + 281 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on different ratios of foreground based on iHarmony4 by MSE and fMSE metrics. The best results are in bold and the suboptimal results are in underline." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 290, + 287, + 374 + ], + "lines": [ + { + "bbox": [ + 49, + 290, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 49, + 290, + 287, + 374 + ], + "type": "table", + "html": "
MethodVenue0%~5%5%~15%15%~100%
MSE↓fMSE↓MSE↓fMSE↓MSE↓fMSE↓
DIHCVPR'1718.92799.1764.23725.86228.86768.89
S2AMTIP'2015.09623.1148.33540.54117.62592.83
DoveNetCVPR'2014.03591.8844.90504.42152.07505.82
RainNetCVPR'2111.66550.3832.05378.69117.41389.80
iS2AMWACV'216.73294.7618.03204.6963.02207.82
GKNetOurs5.36244.0617.46200.3457.31188.75
", + "image_path": "0d866ebe000c36fc921e749a553e83efaa2494d7579752c9ede1331fe74538b3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "type": "text", + "content": "The initial learning rate is set to " + }, + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "type": "text", + "content": ", and the models are trained for 120 epochs with a batch size of 16 on four 2080Ti GPUs. For optimizer, we adopt an Adam optimizer with " + }, + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9, \\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\epsilon = 10^{-8}" + }, + { + "bbox": [ + 46, + 385, + 287, + 469 + ], + "type": "text", + "content": ". It takes about two days for training. Our proposed model is implemented by PyTorch, and more detailed network architectures could be found in the supplementary file." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 479, + 168, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 168, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 168, + 490 + ], + "type": "text", + "content": "4.2. Datasets and Metrics" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 569 + ], + "type": "text", + "content": "Datasets. To evaluate our proposed method for image harmonization, we conduct our experiments on the benchmark dataset iHarmony4 [7], which consists of 4 sub-datasets: HCOCO, HAdobe5K, HFlickr, and Hday2night, including 73147 pairs of synthesized composite images with their corresponding foreground mask and ground truth image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Evaluation Metrics. Following the standard setups in image harmonization, we use the peak signal-to-noise ratio (PSNR) and Mean Squared Error (MSE) as evaluation metrics. Furthermore, it is more accurate to only calculate the difference in the foreground region with the metric foreground MSE (fMSE) introduced by [38]. The metric MSE is calculated for the whole image, while there is no changes for pixels in the background region in harmonization task. Without considering the foreground ratio, the average MSE and PSNR results of the dataset will be more responsive to the performance of large-scale targets. In this paper, we argue that fMSE is more suitable for harmonization task." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 249, + 446, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 249, + 446, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 249, + 446, + 262 + ], + "type": "text", + "content": "4.3. Comparison with SOTAs" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "content": "Quantitative comparison. As results shown in Table 1, we compare our method with other state-of-the-art image harmonization methods on iHarmony4 [7]. Following [7, 38], we also evaluate the model performance on different ratios of foreground by splitting the test images into three groups, i.e., " + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "inline_equation", + "content": "0\\% \\sim 5\\%" + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "inline_equation", + "content": "5\\% \\sim 15\\%" + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "inline_equation", + "content": "15\\% \\sim 100\\%" + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "content": ". We provide these results in Table 2. Observing the quantitative experiment results above, we can summarize the following conclusions: 1) Our method achieves SOTA results of all evaluation metrics on average iharmony4 datasets. More specifically, our method achieves " + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "inline_equation", + "content": "0.78\\mathrm{dB}\\uparrow" + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "content": " improvement in PSNR, " + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "inline_equation", + "content": "1.43\\downarrow" + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "content": " in MSE, and " + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "inline_equation", + "content": "28.42\\downarrow" + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "content": " in fMSE compared with suboptimal methods. 2) Our method obtains the best fMSE scores on all sub-datasets, meaning that the foreground regions generated by our method are more natural and closer to real images. 3) As shown in Table 2, our model performs well on each foreground ratio, especially on " + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "inline_equation", + "content": "0\\% \\sim 5\\%" + }, + { + "bbox": [ + 304, + 268, + 545, + 519 + ], + "type": "text", + "content": ", which indicates that our method has a strong ability to handle variable foreground scales. It also proves that our proposed global-aware adaptive kernel could process global-to-local impact with excellence." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 521, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 700 + ], + "type": "text", + "content": "Qualitative comparison. We further provide qualitative results on iHarmony4 datasets in Figure 5. It could be observed that our GKNet generates more visually coherent images of the foreground and background than composited images, which are also closer to ground truth. 1) The first two rows of examples show that our method can effectively handle the small object harmonization problem in complex scenes with proximity prior consideration. 2) The last two row examples show that our regional modulation with multi-level structure performs well in large foreground cases, which handles a wide range of enormous contrast. For more detailed descriptions, please refer to the caption in Figure 5. In contrast, our method presents more photorealistic results. More visual comparison results on iHarmony4 datasets could be seen in supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Comparisons on Real Datasets. 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Qualitative comparisons with SOTA methods on iHarmony4 [7]. Mask in column one and Red box in Input represents the foreground. Case 1: The background color shows spatial variation, while only our method captures practical color reference by predicted kernel and local harmony modulation. Case 2: The harmony result obtained by our method is better in the detailed structure like duckweed center due to target harmony kernels for each foreground part. 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Qualitative comparisons with SOTA methods on real composite images [41]. Mask in column one and Red box in Input represents the foregrounds. Case 1: Comparing the results on the dogs, our method achieves more natural results over the sunset background. 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For real composition cases, evaluation metrics are impossible to calculate as there are no ground truth images. Hence, we only show qualitative results and human study results here. More visual comparison results on real datasets could be seen in supplementary materials." + } + ] + } + ], + "index": 55 + }, + { + "type": "table", + "bbox": [ + 53, + 637, + 280, + 663 + ], + "blocks": [ + { + "bbox": [ + 59, + 618, + 273, + 629 + ], + "lines": [ + { + "bbox": [ + 59, + 618, + 273, + 629 + ], + "spans": [ + { + "bbox": [ + 59, + 618, + 273, + 629 + ], + "type": "text", + "content": "Table 3. B-T scores comparison on real composite images." + } + ] + } + ], + "index": 56, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 637, + 280, + 663 + ], + "lines": [ + { + "bbox": [ + 53, + 637, + 280, + 663 + ], + "spans": [ + { + "bbox": [ + 53, + 637, + 280, + 663 + ], + "type": "table", + "html": "
MethodCompositeDoveNet[7]RainNet[29]iDIH-HRNet[38]Ours
B-T Score ↑0.4160.6860.9721.5321.944
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BaselineKPBLRESCFMSE ↓PSNR ↑fMSE ↓
✓✗✗✗27.2737.83280.56
✓✓✗✗21.4238.68235.72
✓✓✓✗20.5039.30229.63
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"content": "LRE" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 270, + 287, + 293 + ], + "lines": [ + { + "bbox": [ + 47, + 270, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 287, + 293 + ], + "type": "text", + "content": "Figure 7. Qualitative ablation study of our approach. Red boxes in input image mark foreground." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 249, + 173, + 287, + 212 + ], + "blocks": [ + { + "bbox": [ + 249, + 173, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 249, + 173, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 249, + 173, + 287, + 212 + ], + "type": "image", + "image_path": "c27b19a32c1d41b04c6021e48f4f0dec815973fdd010f935b2dcd9b388612ab0.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 249, + 213, + 287, + 251 + ], + "blocks": [ + { + "bbox": [ + 249, + 213, + 287, + 251 + ], + "lines": [ + { + "bbox": [ + 249, + 213, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 249, + 213, + 287, + 251 + ], + "type": "image", + "image_path": "2f85e00f514f004335f67c79a03689f9e4ba86f911c09d94828cdd549b978563.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 251, + 252, + 282, + 260 + ], + "lines": [ + { + "bbox": [ + 251, + 252, + 282, + 260 + ], + "spans": [ + { + "bbox": [ + 251, + 252, + 282, + 260 + ], + "type": "text", + "content": "Full Model" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 307, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 307, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 307, + 287, + 403 + ], + "type": "text", + "content": "qualitative results in Figure 7. Compared with the baseline, the model with only local KPB outputs stronger local modeling results but loses global view. After introducing LRE, global awareness of the background is enhanced. But it is evident that color is overcorrected in the second row. After adding SCF, we effectively correct the deviation by selecting relevant references in background, and the final result is closer to real image." + } + ] + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 52, + 411, + 287, + 522 + ], + "blocks": [ + { + "bbox": [ + 52, + 411, + 287, + 522 + ], + "lines": [ + { + "bbox": [ + 52, + 411, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 52, + 411, + 287, + 522 + ], + "type": "image", + "image_path": "f190d800eb3ed7cea56f4451a291ff338220507ff613afa0f893451f6a3d8f59.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 530, + 287, + 574 + ], + "lines": [ + { + "bbox": [ + 46, + 530, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 287, + 574 + ], + "type": "text", + "content": "Figure 8. The cluster visual results of adaptive harmony kernels. e.g., in flower case, structure information like petal margin is displayed, which proves that kernels are predicted to adapt local harmonization specifically." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "Interpretability of Global-aware Harmony Kernel. To further illustrate the effectiveness of the adaptive harmony kernels, we cluster the per-pixel adaptive harmony kernels predicted from KPB by K-means. As shown in Figure 8, the clusters show strong spatial structure, which indicates that our predicted dynamic kernel can make the structural adjustment to harmonize the foreground. Moreover, in some cases, the change of kernel classes is related to the object mask. This exhibits that our harmony kernels are predicted dynamically to deal with visual inconsistency in different spatial locations (e.g. fore-/background or edges)." + } + ] + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 312, + 70, + 350, + 145 + ], + "blocks": [ + { + "bbox": [ + 312, + 70, + 350, + 145 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 350, + 145 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 350, + 145 + ], + "type": "image", + "image_path": "17c1ea4edaec58b734fecaa9c07b5045e2339560c376c9d9c256014c175524a1.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 147, + 345, + 156 + ], + "lines": [ + { + "bbox": [ + 315, + 147, + 345, + 156 + ], + "spans": [ + { + "bbox": [ + 315, + 147, + 345, + 156 + ], + "type": "text", + "content": "(a) Mask" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 351, + 70, + 390, + 148 + ], + "blocks": [ + { + "bbox": [ + 351, + 70, + 390, + 148 + ], + "lines": [ + { + "bbox": [ + 351, + 70, + 390, + 148 + ], + "spans": [ + { + "bbox": [ + 351, + 70, + 390, + 148 + ], + "type": "image", + "image_path": "66a2b5bb4d01fdccef935d2110b3bcb610164c93f001066cf619cdc4ed270a06.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 353, + 148, + 384, + 156 + ], + "lines": [ + { + "bbox": [ + 353, + 148, + 384, + 156 + ], + "spans": [ + { + "bbox": [ + 353, + 148, + 384, + 156 + ], + "type": "text", + "content": "(b) Comp" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 390, + 70, + 427, + 148 + ], + "blocks": [ + { + "bbox": [ + 390, + 70, + 427, + 148 + ], + "lines": [ + { + "bbox": [ + 390, + 70, + 427, + 148 + ], + "spans": [ + { + "bbox": [ + 390, + 70, + 427, + 148 + ], + "type": "image", + "image_path": "a0f1d38a812309877073c3b97c7188dc41e9723d06610b01ee3a2fbe949afc5b.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 394, + 148, + 537, + 157 + ], + "lines": [ + { + "bbox": [ + 394, + 148, + 537, + 157 + ], + "spans": [ + { + "bbox": [ + 394, + 148, + 537, + 157 + ], + "type": "text", + "content": "(c) Feature map with channel attention weight" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "bbox": [ + 394, + 148, + 400, + 156 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 148, + 400, + 156 + ], + "spans": [ + { + "bbox": [ + 394, + 148, + 400, + 156 + ], + "type": "text", + "content": "(c" + } + ] + } + ], + "index": 30, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 427, + 70, + 465, + 147 + ], + "blocks": [ + { + "bbox": [ + 427, + 70, + 465, + 147 + ], + "lines": [ + { + "bbox": [ + 427, + 70, + 465, + 147 + ], + "spans": [ + { + "bbox": [ + 427, + 70, + 465, + 147 + ], + "type": "image", + "image_path": "af4d206aca83d4aebc2c62243ab1bb3a8daae06ca5584598e5cf95459abb3aeb.jpg" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_body" + } + ], + "index": 31 + }, + { + "type": "image", + "bbox": [ + 467, + 70, + 505, + 147 + ], + "blocks": [ + { + "bbox": [ + 467, + 70, + 505, + 147 + ], + "lines": [ + { + "bbox": [ + 467, + 70, + 505, + 147 + ], + "spans": [ + { + "bbox": [ + 467, + 70, + 505, + 147 + ], + "type": "image", + "image_path": "e13c1346577d118804a494b63cda97e8f51ff4157aba1633a09972d8449ab83f.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 506, + 71, + 544, + 147 + ], + "blocks": [ + { + "bbox": [ + 506, + 71, + 544, + 147 + ], + "lines": [ + { + "bbox": [ + 506, + 71, + 544, + 147 + ], + "spans": [ + { + "bbox": [ + 506, + 71, + 544, + 147 + ], + "type": "image", + "image_path": "9b9bdc8e1176f5e9d290bd6f341f5f02e91cf52b20a73ad09472fc345973c9fb.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_body" + } + ], + "index": 33 + }, + { + "type": "image", + "bbox": [ + 320, + 191, + 533, + 294 + ], + "blocks": [ + { + "bbox": [ + 306, + 167, + 545, + 189 + ], + "lines": [ + { + "bbox": [ + 306, + 167, + 545, + 189 + ], + "spans": [ + { + "bbox": [ + 306, + 167, + 545, + 189 + ], + "type": "text", + "content": "Figure 9. Feature maps in SCF. Red number in upper right corner of feature map represents channel-wise attention weights." + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 320, + 191, + 533, + 294 + ], + "lines": [ + { + "bbox": [ + 320, + 191, + 533, + 294 + ], + "spans": [ + { + "bbox": [ + 320, + 191, + 533, + 294 + ], + "type": "image", + "image_path": "cecb2bf9c6b69c1ec88a73f83e0d744a684d3d60298031e78d2ee1e1095def8e.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 304, + 545, + 336 + ], + "lines": [ + { + "bbox": [ + 306, + 304, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 545, + 336 + ], + "type": "text", + "content": "Figure 10. Cross-attention from example point (10,10). We show four attention maps for different heads, which proves LRE can match model related long-distance references." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 347, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 347, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 347, + 545, + 539 + ], + "type": "text", + "content": "Interpretability of LRE and SCF Module. We visualize the attention mechanism in LRE and SCF for interpreting global-local interaction. In Figure 9, we visualize feature maps in decoder layers to illustrate our channel-wise attention module SCF. Visual feature maps with attention weights show that harmony kernels are predicted with more attention on related background area and less attention on irrelevant background area or foreground. In Figure 10, we visualize the attention maps of LRE, focusing on an example point in foreground. As the long-distance information in predicted harmony kernels is brought by LRE, the visualized attention maps in different heads indicate two points: 1) The kernels for local operation have a global perceptive field with long-distance information. 2) Different heads pay attention to different reference parts, i.e. relevant background reference, foreground content, overall tone, etc." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 306, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 570, + 545, + 713 + ], + "type": "text", + "content": "This paper proposes an effective network GKNet to learn global-aware harmony kernels for image harmonization, including harmony kernel prediction and harmony kernel modulation branches. For harmony kernel prediction, we propose LRE to extract long-term references and KPB to predict global-aware kernels. To better fuse long-term context, we design SCF to select relevant references. For harmony kernel modulation, we employ the predicted kernels for harmonization with location awareness. Extensive experiments demonstrate that our proposed algorithm outperforms the state-of-the-art algorithms on the iHarmony4 dataset and real image composition datasets." + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7542" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "content": "Acknowledgements. 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In ECCV, pages 269-284, 2018. 4" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7544" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_content_list.json b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b093a5c33b80b73450624aafd30d7d3683b89125 --- /dev/null +++ b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_content_list.json @@ -0,0 +1,2166 @@ +[ + { + "type": "text", + "text": "Learning Hierarchical Features with Joint Latent Space Energy-Based Prior", + "text_level": 1, + "bbox": [ + 99, + 130, + 870, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiali Cui $^{1}$ , Ying Nian Wu $^{2}$ , Tian Han $^{1}$ \\\n $^{1}$ Department of Computer Science, Stevens Institute of Technology\\\n $^{2}$ Department of Statistics, University of California, Los Angeles\\\n{jcui7,than6}@stevens.edu, ywu@stat.ucla.edu", + "bbox": [ + 218, + 179, + 750, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper studies the fundamental problem of multilayer generator models in learning hierarchical representations. The multi-layer generator model that consists of multiple layers of latent variables organized in a top-down architecture tends to learn multiple levels of data abstraction. However, such multi-layer latent variables are typically parameterized to be Gaussian, which can be less informative in capturing complex abstractions, resulting in limited success in hierarchical representation learning. On the other hand, the energy-based (EBM) prior is known to be expressive in capturing the data regularities, but it often lacks the hierarchical structure to capture different levels of hierarchical representations. In this paper, we propose a joint latent space EBM prior model with multi-layer latent variables for effective hierarchical representation learning. We develop a variational joint learning scheme that seamlessly integrates an inference model for efficient inference. Our experiments demonstrate that the proposed joint EBM prior is effective and expressive in capturing hierarchical representations and modelling data distribution.", + "bbox": [ + 75, + 318, + 473, + 621 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 652, + 209, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, deep generative models have achieved remarkable success in generating high-quality images [36, 31], texts [40, 13], and videos [28, 35]. However, learning generative models that incorporate hierarchical structures still remains a challenge. Such hierarchical generative models can play a critical role in enabling explainable artificial intelligence, thus representing an important area of ongoing research.", + "bbox": [ + 75, + 679, + 468, + 800 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To tackle this challenge, various methods of learning hierarchical representations have been explored [30, 42, 21, 3, 30]. These methods learn generative models with multiple layers of latent variables organized in a top-down ar", + "bbox": [ + 75, + 801, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "chitecture, which have shown the capability of learning increasingly abstract representations (e.g., general structures, classes) at the top layers while capturing low-level data features (e.g., colors, background) at the bottom layers. In general, one could categorize these methods into two classes: (i) conditional hierarchy and (ii) architectural hierarchy.", + "bbox": [ + 500, + 287, + 890, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The conditional hierarchies [30, 12, 25, 21, 3] employ stacked generative models layered on top of one another and assume conditional Gaussian distributions at different layers, while the architectural hierarchies [42, 20] instead leverage network architecture to place high-level representations at the top layers of latent variables and low-level representations at the bottom layers. However, they typically assume conditional Gaussian distribution or isotropic Gaussian as the prior, which could have limited expressivity [26]. Learning a more expressive and informative prior model for multiple layers of latent variables is thus needed.", + "bbox": [ + 496, + 380, + 892, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The energy-based models (EBMs) [19, 39, 7, 24, 26, 4], on the other hand, are shown to be expressive and proved to be powerful in capturing data regularities. Notably, [26] studies the EBM in the latent space, where the energy function is considered as a correction of the non-informative prior and tilts the non-informative prior to a more expressive prior distribution. The low dimensionality of the latent space makes EBM more effective in capturing regularities in the data. However, prior methods often rely on expensive MCMC methods for posterior sampling of the latent variables, and more importantly, the latent variables are not hierarchically organized, making it difficult to capture data variations at different levels.", + "bbox": [ + 496, + 550, + 893, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose to combine the strengths of latent space EBM and the multi-layer generator model for effective hierarchical representation learning. In particular, we build the EBM on the latent variables across different layers of the generator model, where the latent variables at different layers are concatenated and modelled jointly. The latent variables at different layers capture different levels of information from the data via the hierarchy of the generative model, and their inter-relations are further tightened up and better captured through EBM in joint latent space.", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Our project page is available at https://jcui1224.github.io/hierarchical-representation-ebm-proj/.", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2218", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning the EBM in the latent space can be challenging since it usually requires MCMC sampling for both the prior and posterior distributions of the latent variables. The prior sampling is efficient with the low dimensionality of the latent space and the lightweight network of the energy function, while the MCMC sampling of posterior distribution requires the backward propagation of generation network, which is usually heavy and thus renders inefficient inference. To ensure efficient inference, we introduce an inference model and develop a joint training scheme to efficiently and effectively learn the latent space EBM and multi-layer generator model. In particular, the inference model aims to approximate the exact posterior of the multi-layer latent variables while also serving to extract levels of data variations through the deep feed-forward inference network to facilitate hierarchical learning.", + "bbox": [ + 75, + 90, + 472, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions: 1) We propose the joint EBM prior model for hierarchical generator models with multiple layers of latent variables; 2) We develop a variational training scheme for efficient learning and inference; 3) We provide strong empirical results on hierarchical learning and image modeling, as well as various ablation studies to illustrate the effectiveness of the proposed model.", + "bbox": [ + 75, + 333, + 468, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background", + "text_level": 1, + "bbox": [ + 76, + 453, + 205, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we present the background of multi-layer generator models and the latent space EBM, which will serve as the foundation of the proposed model.", + "bbox": [ + 75, + 479, + 468, + 523 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Multi-layer generator models", + "text_level": 1, + "bbox": [ + 76, + 535, + 339, + 550 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Let $\\mathbf{x} \\in \\mathbb{R}^D$ represent the high-dimensional observed examples, and $\\mathbf{z} \\in \\mathbb{R}^d$ denote the low-dimensional latent variables. The multi-layer generator model [30, 36, 21] consists of multiple layers of latent variables that are organized in a top-down hierarchical structure and modelled to be conditionally dependent on its upper layer, i.e., $p_{\\theta}(\\mathbf{z}) = \\prod_{i=1}^{L-1} p_{\\theta_i}(\\mathbf{z}_i | \\mathbf{z}_{i+1}) p_0(\\mathbf{z}_L)$ , where $p_{\\theta_i}(\\mathbf{z}_i | \\mathbf{z}_{i+1}) \\sim \\mathcal{N}(\\mu_{\\theta_i}(\\mathbf{z}_{i+1}), \\sigma_{\\theta_i}(\\mathbf{z}_{i+1}))$ and $p_0(\\mathbf{z}_L) \\sim \\mathcal{N}(0, I)$ . Although such a modelling strategy has seen significant improvement in data density estimation, it can be less effective in learning hierarchical representations.", + "bbox": [ + 75, + 558, + 468, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To demonstrate, we train BIVA [21] on MNIST with 6 layers of latent variables and conduct hierarchical sampling by generating latent variables via the repamaramization trick, i.e., $\\mathbf{z}_i = \\mu_{\\theta_i}(\\mathbf{z}_{i + 1}) + \\sigma_{\\theta_i}(\\mathbf{z}_{i + 1})\\cdot \\epsilon_i$ where $\\epsilon_{i}$ is the added Gaussian noise. Specifically, the latent variables are generated by randomly sampling $\\epsilon_{i}$ for the $i$ -th layer, while fixing $\\epsilon_{j\\neq i}$ for other layers, and the corresponding image synthesis should deliver the variation of representation learned by $\\mathbf{z}_i$ . We show the results in Fig. 1, where the major semantic variation is only captured by the top layer", + "bbox": [ + 75, + 724, + 468, + 876 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of the latent variables, suggesting an ineffective hierarchical representation learned (compare with our model shown in Fig. 5).", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6f930224014083ecd13826e158c27fb2ce417d91e8e94836098ed0504bb9e331.jpg", + "image_caption": [ + "Figure 1. Visualization of hierarchical representations on BIVA. Left: sampling $\\epsilon_{1},\\epsilon_{2}$ for bottom layers. Middle: sampling $\\epsilon_{3},\\epsilon_{4}$ for middle layers. Right: sampling $\\epsilon_{5},\\epsilon_{6}$ for top layers." + ], + "image_footnote": [], + "bbox": [ + 527, + 146, + 640, + 232 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b58084dafd71d4b841e184de98769797bff9e0e917e8df57c3b0a79f3150c26e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 640, + 146, + 751, + 232 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/560d7740960843b959c50fb268c573692d2e62ebb53d4628ce4dd10449fefe3b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 751, + 147, + 864, + 232 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Latent space EBM", + "text_level": 1, + "bbox": [ + 500, + 285, + 679, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The energy-based models (EBMs) [7, 6, 24, 8, 38] present a flexible and appealing way for data modelling and are known for being expressive and powerful in capturing data regularities. Albeit their expressivity, learning the EBM on high-dimensional $\\mathbf{x}$ -space can be challenging since the energy function needs to support the entire data space. As such, another line of works [26, 1, 37] seek to build EBM on low-dimensional $\\mathbf{z}$ -space with the probability density defined as", + "bbox": [ + 496, + 308, + 890, + 444 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} (\\mathbf {z}) = \\frac {1}{\\mathbb {Z} (\\theta)} \\exp \\left[ f _ {\\theta} (\\mathbf {z}) \\right] p _ {0} (\\mathbf {z}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 450, + 890, + 482 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, with a single-layer non-hierarchical $\\mathbf{z}$ -space, it is typically infeasible to capture the data abstraction of different levels. To see this, we pick up the digit classes '0', '1', and '2' of the MNIST dataset, on which we train LEBM [26] with the latent dimension set to be 2. We show in Fig. 2 that changing the value of each latent unit could lead to a mixed variations in digit shape and class (compare to our proposed method in Fig. 6).", + "bbox": [ + 496, + 487, + 890, + 608 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3f61d13b300cf47d325a220a38d7e525400835b8561d0b4dcad7b2d5b719d9e6.jpg", + "image_caption": [ + "Figure 2. Visualization for latent space EBM [26] by changing each unit of 2-dimensional z. Left: changing the first unit. Right: changing the second unit. Top: the value of each unit, where the orange color indicates the first unit and the blue color indicates the second unit." + ], + "image_footnote": [], + "bbox": [ + 517, + 609, + 874, + 674 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 768, + 633, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we study a joint latent space EBM prior where latent variables are partitioned into multiple groups but modelled jointly for hierarchical representation learning. To ensure efficient inference, we introduce an inference model to approximate the generator posterior and develop a variational joint training scheme in which each model can be trained efficiently and effectively.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1 https://github.com/vlievin/biva-pytorch", + "bbox": [ + 94, + 886, + 308, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2219", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Latent variable generative model", + "text_level": 1, + "bbox": [ + 76, + 90, + 366, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A latent variable generative model (i.e., generator model) can be specified using joint distribution:", + "bbox": [ + 76, + 114, + 468, + 143 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\beta , \\alpha} (\\mathbf {x}, \\mathbf {z}) = p _ {\\beta} (\\mathbf {x} | \\mathbf {z}) p _ {\\alpha} (\\mathbf {z}) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 156, + 468, + 172 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which consists of the generation model $p_{\\beta}(\\mathbf{x}|\\mathbf{z})$ and the prior model $p_{\\alpha}(\\mathbf{z})$ .", + "bbox": [ + 76, + 184, + 468, + 213 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Joint latent space EBM: The prior model $p_{\\alpha}(\\mathbf{z})$ is usually assumed to be single-layer, which can be infeasible for learning hierarchical representations (see Sec. 2.2). In this work, we propose a joint latent space EBM prior, where latent variables are separated into multiple groups, i.e., $\\mathbf{z} = [\\mathbf{z}_1,\\mathbf{z}_2,\\dots ,\\mathbf{z}_L]$ , and our EBM prior model is defined as", + "bbox": [ + 76, + 215, + 468, + 319 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\alpha} (\\mathbf {z}) = \\frac {1}{\\mathbb {Z} (\\alpha)} \\exp \\left[ f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\right] p _ {0} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 329, + 468, + 361 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $[.]$ refers to the concatenation. $f_{\\alpha}(.)$ is the negative energy function that can be parameterized by a small multilayer perceptron with the parameters $\\alpha, p_0([\\dots])$ is a reference distribution assumed to be a unit Gaussian, and $\\mathbb{Z}(\\alpha)$ is the normalizing constant or partition function. Such a prior model can be considered as an energy-based refinement of the non-informative reference distribution, thus the relationship between different groups of latent codes can be well captured via the energy function $f_{\\alpha}([\\mathbf{z}_1,\\ldots ,\\mathbf{z}_L])]$ .", + "bbox": [ + 76, + 371, + 468, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For notation simplicity, we denote $\\mathbf{z} = [\\mathbf{z}_1,\\dots ,\\mathbf{z}_L]$ in subsequent discussions.", + "bbox": [ + 76, + 508, + 468, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generation Model. The generation model is defined as", + "bbox": [ + 76, + 537, + 446, + 551 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\beta} (\\mathbf {x} \\mid \\mathbf {z}) \\sim \\mathcal {N} \\left(g _ {\\beta} (\\mathbf {z}), \\sigma^ {2} I _ {D}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 564, + 468, + 582 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which models the observed data using top-down generator network $g_{\\beta}(\\mathbf{z})$ with additive Gaussian noise, i.e., $\\mathbf{x} = g_{\\beta}(\\mathbf{z}) + \\epsilon, \\epsilon \\sim \\mathcal{N}(0, \\sigma^2 I_D)$ . To facilitate the hierarchical representation learning with multi-layer latent variables, we consider multi-layer hierarchical generator network $g_{\\beta} (= \\{g_1, g_2, \\ldots, g_L\\})$ that is designed to explain the observation $\\mathbf{x}$ by integrating data representation from the above layers, i.e.,", + "bbox": [ + 76, + 594, + 468, + 715 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh _ {L} = g _ {L} (\\mathbf {z} _ {L})\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 727, + 230, + 742 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh _ {i} = g _ {i} \\left(\\left[ \\mathbf {z} _ {i}, h _ {i + 1} \\right]\\right), i = 1, 2, \\dots , L - 1 \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 744, + 468, + 762 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} \\sim \\mathcal {N} (h _ {1}, \\sigma^ {2} I _ {D})\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 765, + 261, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $\\mathbf{z}_L$ is at the top layer, and $g_{i}$ is a shallow network that decodes latent code $\\mathbf{z}_i$ while integrating features from the upper layer.", + "bbox": [ + 76, + 794, + 468, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Joint EBM prior vs. independent Gaussian prior: With such a multi-layer hierarchical generation model, it is also tempting to consider learning with the unit Gaussian prior, i.e., $p(\\mathbf{z}) \\sim \\mathcal{N}(0, I_d)$ . Such a prior choice is adopted in", + "bbox": [ + 76, + 840, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/14cdd146837521465e947bedad9458928b9cf3801129e918fb48c085b47db360.jpg", + "image_caption": [ + "Figure 3. The illustration of the proposed joint EBM prior model (Left). Red lines indicate the modelling of intra-layer relation, and blue lines indicate inter-layer relation. Compared to the Gaussian prior model and single-layer LEBM, our prior model is expressive and effective in learning hierarchical representations." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 890, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[42, 20] and has seen some success in learning hierarchical features. However, the independent Gaussian prior does not account for the relations between levels of representations and can be less expressive in capturing complex data features. The proposed EBM prior is expressive and can couple the latent variables across different layers within a joint modelling framework.", + "bbox": [ + 498, + 337, + 890, + 444 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our model is illustrated in the left panel of Fig. 3.", + "bbox": [ + 517, + 459, + 848, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Variational learning scheme", + "text_level": 1, + "bbox": [ + 500, + 482, + 750, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Suppose we have observed examples $(\\mathbf{x}_i, i = 1, \\dots, n)$ that come from (true) data distribution $p_{\\mathrm{data}}(\\mathbf{x})$ and denote $\\theta = (\\beta, \\alpha)$ that collects all parameters from the generator model. Learning the generator model can be done by maximizing the log-likelihood of all observed examples as", + "bbox": [ + 498, + 506, + 890, + 580 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {i = 1} ^ {n} \\log p _ {\\theta} (\\mathbf {x} _ {i}) = \\sum_ {i = 1} ^ {n} \\log \\int p _ {\\alpha} (\\mathbf {z}) p _ {\\beta} (\\mathbf {x} _ {i} | \\mathbf {z}) d \\mathbf {z} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 590, + 890, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When $n$ becomes sufficiently large, maximizing the above log-likelihood is equivalent to minimizing the Kullback-Leibler (KL) divergence between the model distribution and data distribution, i.e., $\\min_{\\theta} D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x}))$ .", + "bbox": [ + 498, + 638, + 890, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, directly maximizing Eq. 6 can be challenging, as the inference of generator posterior (by chain rule, $p_{\\theta}(\\mathbf{z}|\\mathbf{x}) = p_{\\theta}(\\mathbf{x},\\mathbf{z}) / p_{\\theta}(\\mathbf{x}))$ is typically intractable. To tackle the challenge, we employ an inference model $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ with a separate set of parameters $\\phi$ to approximate the generator posterior.", + "bbox": [ + 498, + 699, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inference model: The inference model maps from data space to latent space and is typically assumed to be Gaussian distributed,", + "bbox": [ + 498, + 789, + 890, + 833 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\sim \\mathcal {N} \\left(\\mu_ {\\phi} (\\mathbf {x}), V _ {\\phi} (\\mathbf {x})\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 843, + 890, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mu_{\\phi}(\\mathbf{x})$ and $V_{\\phi}(\\mathbf{x})$ are the d-dimensional mean vector and diagonal covariance matrix. To match with the hierar", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2220", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "chical generator model and facilitate the hierarchical representation learning, we consider the multi-layer inference model defined as", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr _ {1} = h _ {1} (\\mathbf {x})\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 148, + 251, + 164 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i} = h _ {i} \\left(r _ {i - 1}\\right) i = 2, 3, \\dots , L \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 166, + 468, + 181 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {i} \\sim \\mathcal {N} (\\mu_ {i} (r _ {i}), V _ {i} (r _ {i}))\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 185, + 328, + 202 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_L$ is the inferred latent code at the top layer and $\\mathbf{z}_1$ is the inferred bottom layer latent code. Each latent code $\\mathbf{z}_i$ can be inferred and sampled through reparametrization trick [17] using $\\mathbf{z}_i = \\mu_i(r_i) + V_i(r_i)^{1/2}\\epsilon$ where $\\epsilon \\sim \\mathcal{N}(0, I_{d_i})$ , with $d_i$ being the dimensionality of $z_i$ .", + "bbox": [ + 76, + 212, + 467, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Variational learning: We show that the proposed generator model and the inference model can be naturally unified and jointly trained within a variational learning scheme.", + "bbox": [ + 75, + 287, + 468, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we can define two joint densities, one for generator model density, i.e., $p_{\\theta}(\\mathbf{x}, \\mathbf{z}) = p_{\\alpha}(\\mathbf{z})p_{\\beta}(\\mathbf{x}|\\mathbf{z})$ , and one for data density, i.e., $q_{\\phi}(\\mathbf{x}, \\mathbf{z}) = p_{\\mathrm{data}}(\\mathbf{x})q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ . We propose joint learning through KL minimization, and we denote the objective to be $L(\\theta, \\phi)$ , i.e.,", + "bbox": [ + 75, + 333, + 468, + 409 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\min _ {\\phi} L (\\theta , \\phi) = \\min _ {\\theta} \\min _ {\\phi} D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {x}, \\mathbf {z}) | | p _ {\\theta} (\\mathbf {x}, \\mathbf {z})\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 419, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the generator model density is learned to match the true joint data density and capture extracted hierarchical features.", + "bbox": [ + 75, + 452, + 468, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning $p_{\\alpha}(\\mathbf{z})$ : With this joint KL minimization, the prior model can be learned with the gradient $-\\nabla_{\\alpha}L(\\theta ,\\phi)$", + "bbox": [ + 76, + 497, + 468, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} | \\mathbf {x})} [ \\nabla_ {\\alpha} f _ {\\alpha} ([ \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} ]) ] -\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 539, + 418, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {p _ {\\alpha} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right)} \\left[ \\nabla_ {\\alpha} f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\right] \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 559, + 468, + 577 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning $p_{\\beta}(\\mathbf{x}|\\mathbf{z})$ : The generation model can be learned with the gradient $-\\nabla_{\\beta}L(\\theta ,\\phi)$ computed as", + "bbox": [ + 76, + 585, + 468, + 617 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {q _ {\\phi} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\mid \\mathbf {x}\\right)} \\left[ \\nabla_ {\\beta} \\log p _ {\\beta} \\left(\\mathbf {x} \\mid \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right) \\right] \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 627, + 468, + 645 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ : The inference model can be learned by computing the gradient $-\\nabla_{\\phi}L(\\theta ,\\phi)$ as", + "bbox": [ + 75, + 654, + 468, + 685 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\phi} \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} | \\mathbf {x})} [ \\log p _ {\\beta} (\\mathbf {x} | \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}) ] - \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 696, + 468, + 713 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\phi} D _ {\\mathrm {K L}} \\left(q _ {\\phi} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\mid \\mathbf {x}\\right) \\mid \\mid p _ {\\alpha} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 717, + 437, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We provide further theoretical understanding in Sec. 3.4.", + "bbox": [ + 96, + 743, + 467, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Prior sampling", + "text_level": 1, + "bbox": [ + 76, + 768, + 228, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training the proposed joint EBM prior model requires sampling $\\mathbf{z}_1, \\mathbf{z}_2, \\ldots, \\mathbf{z}_L$ from the proposed EBM prior (see Eq. 10). To do so, we can use Langevin dynamic [22].", + "bbox": [ + 76, + 790, + 468, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For arbitrary target distribution $p(\\mathbf{z})$ , the Langevin dynamic iterates:", + "bbox": [ + 76, + 835, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {t + 1} = \\mathbf {z} _ {t} + \\frac {s ^ {2}}{2} \\nabla_ {\\mathbf {z}} \\log p (\\mathbf {z} _ {t}) + s \\epsilon_ {t} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 873, + 468, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t$ indexes the time step of Langevin dynamics. $s$ is the step size and $\\epsilon_t\\sim \\mathcal{N}(0,I_d)$ . We run the noise-initialized Langevin dynamics for $K$ steps. Noted that as $s\\to 0$ , and $K\\rightarrow \\infty$ , the distribution of $\\mathbf{z}_t$ will converge to the target $p(\\mathbf{z})$ regardless of the initial distribution of $\\mathbf{z}_0$ [22].", + "bbox": [ + 498, + 90, + 890, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, for prior sampling, we use the prior distribution $p_{\\alpha}(\\mathbf{z})$ as our target distribution, and the gradient $\\nabla_{\\mathbf{z}}\\log p_{\\alpha}(\\mathbf{z})$ is computed as:", + "bbox": [ + 498, + 167, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\mathbf {z}} f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) + \\nabla_ {\\mathbf {z}} \\log p _ {0} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 222, + 890, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Langevin dynamics for prior sampling can be efficient due to the low-dimensional latent space and the lightweight network structure for the energy function.", + "bbox": [ + 498, + 250, + 890, + 295 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overall procedure is summarized in Algorithm 1.", + "bbox": [ + 519, + 310, + 870, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Learning latent EBM prior for hierarchical generator model", + "bbox": [ + 500, + 339, + 890, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: Training iterations $T$ , observed training examples $\\{x_{i}\\}_{i = 1}^{n}$ , batch size $m$ , network parameters $\\alpha, \\beta, \\phi$ , learning rate $\\eta_{\\alpha}, \\eta_{\\beta}, \\eta_{\\phi}$ , Langevin steps $K$ , Langevin step size $s$ ,", + "bbox": [ + 514, + 371, + 890, + 430 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $t = 0$ and $\\theta = (\\alpha, \\beta)$ ;", + "bbox": [ + 516, + 431, + 689, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "repeat", + "bbox": [ + 517, + 448, + 565, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prior sampling for $\\{z_i^{-}\\}_{i = 1}^m$ using Eq. 13 and Eq. 14 with $K$ and $s$ .", + "bbox": [ + 532, + 462, + 890, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference sampling for $\\{z_i^+\\}_{i=1}^m$ using Eq. 8 with $\\{x_i\\}_{i=1}^m$ and reparametrization.", + "bbox": [ + 532, + 491, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learn joint EBM prior: Given $\\{z_i^-, z_i^+\\}_{i=1}^m$ , update $\\alpha = \\alpha - \\eta_\\alpha \\nabla_\\alpha L(\\theta, \\phi)$ using Eq. 10 with $\\eta_\\alpha$", + "bbox": [ + 532, + 522, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learn generation model:Given $\\{x_{i},z_{i}^{+}\\}_{i = 1}^{m}$ update $\\beta = \\beta -\\eta_{\\beta}\\nabla_{\\beta}L(\\theta ,\\phi)$ using Eq. 11 with $\\eta_{\\beta}$", + "bbox": [ + 532, + 553, + 890, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learn inference model: Given $\\{x_{i},z_{i}^{+}\\}_{i = 1}^{m}$ update $\\phi = \\phi -\\eta_{\\phi}\\nabla_{\\phi}L(\\theta ,\\phi)$ using Eq. 12 with $\\eta_{\\phi}$", + "bbox": [ + 532, + 583, + 890, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $t = t + 1$", + "bbox": [ + 532, + 614, + 629, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "until $t = T$", + "bbox": [ + 517, + 628, + 596, + 641 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Theoretical understanding", + "text_level": 1, + "bbox": [ + 500, + 670, + 748, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Divergence perturbation and ELBO. The KL joint minimization (Eq. 9) can be viewed as a surrogate of the MLE objective with the KL perturbation term,", + "bbox": [ + 498, + 693, + 890, + 738 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {x}, \\mathbf {z}) | | p _ {\\theta} (\\mathbf {x}, \\mathbf {z})\\right) \\\\ = D _ {\\mathrm {K L}} \\left(p _ {\\text {d a t a}} (\\mathbf {x}) | | p _ {\\theta} (\\mathbf {x})\\right) + D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) | | p _ {\\theta} (\\mathbf {z} | \\mathbf {x})\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 750, + 880, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x}))$ is the MLE loss function, and the perturbation term $D_{\\mathrm{KL}}(q_{\\phi}(\\mathbf{z}|\\mathbf{x})||p_{\\theta}(\\mathbf{z}|\\mathbf{x}))$ measures the KL-divergence between inference distribution and generator posterior. The inference $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ is learned to match the posterior distribution of the generator without expensive posterior sampling. In fact, such KL minimization in the joint space is equivalent to evidence lower bound", + "bbox": [ + 498, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2221", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(ELBO). To see this, noted that $D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x})) = -H(p_{\\mathrm{data}}(\\mathbf{x})) - \\mathbb{E}_{p_{\\mathrm{data}}}[\\log p_{\\theta}(\\mathbf{x})]$ where $H(p_{\\mathrm{data}}(\\mathbf{x}))$ is the entropy of the empirical data distribution and can be treated as constant $C \\equiv -H(p_{\\mathrm{data}}(\\mathbf{x}))$ w.r.t model parameters $\\theta$ . Then $L(\\theta, \\phi)$ is computed as", + "bbox": [ + 76, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} - \\mathbb {E} _ {p _ {\\mathrm {d a t a}}} [ \\log p _ {\\theta} (\\mathbf {x}) ] + D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p _ {\\theta} (\\mathbf {z} | \\mathbf {x})\\right) + C \\\\ = \\mathbb {E} _ {p _ {\\mathrm {d a t a}}} \\left[ \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left(\\log \\frac {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})}\\right) - \\log p _ {\\theta} (\\mathbf {x}) \\right] + C \\\\ = \\mathbb {E} _ {p _ {\\text {d a t a}}} [ - \\operatorname {E L B O} (\\mathbf {x}; \\theta , \\phi) ] + C \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 176, + 464, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 256, + 122, + 268 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {E L B O} (\\mathbf {x}; \\theta , \\phi) = \\log p _ {\\theta} (\\mathbf {x}) - \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log \\frac {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\right] \\\\ = \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log \\frac {p _ {\\theta} (\\mathbf {x} , \\mathbf {z})}{q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\right] \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 276, + 460, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and is referred to as evidence lower bound (ELBO) in the literature [17]. Noted that the prior model (i.e., $p_{\\theta}(\\mathbf{x}, \\mathbf{z}) = p_{\\beta}(\\mathbf{x}|\\mathbf{z})p_{\\alpha}(\\mathbf{z})$ ) is now parameterized to be our joint EBM prior. Minimizing Eq. 9 is equivalent to maximizing the evidence lower bound of the log-likelihood.", + "bbox": [ + 76, + 352, + 468, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Short run sampling and divergence perturbation. The learning of the energy-based model in Eq. 10 requires MCMC sampling from $p_{\\alpha}(\\mathbf{z})$ . We adopt the short-run Langevin dynamics (Eq. 13) with fixed $K$ steps to sample from prior $p_{\\alpha}(\\mathbf{z})$ for efficient computation. Such prior sampling amounts to approximates the objective $L(\\theta, \\phi)$ in Eq. 9 with yet another KL perturbation term, i.e.,", + "bbox": [ + 76, + 429, + 468, + 534 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {L} (\\theta , \\phi) = L (\\theta , \\phi) - D _ {\\mathrm {K L}} \\left(\\tilde {p} _ {\\alpha^ {(t)}} (\\mathbf {z}) | p _ {\\alpha} (\\mathbf {z})\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 542, + 398, + 560 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde{p}_{\\alpha^{(t)}}(\\mathbf{z})$ refers to the distribution of latent codes after $K$ steps of Langevin dynamics (Eq. 13) in the $t$ -th iteration of the learning. The corresponding learning gradient for the prior model is thus", + "bbox": [ + 76, + 569, + 468, + 630 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n- \\nabla_ {\\alpha} \\tilde {L} (\\theta , \\phi) = \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} [ \\nabla_ {\\alpha} f _ {\\alpha} (\\mathbf {z}) ] - \\mathbb {E} _ {\\tilde {p} _ {\\alpha (t)} (\\mathbf {z})} [ \\nabla_ {\\alpha} f _ {\\alpha} (\\mathbf {z}) ]\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 638, + 462, + 659 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When $K$ is sufficiently large, the perturbation term $D_{\\mathrm{KL}}(\\tilde{p}_{\\alpha^{(t)}}(\\mathbf{z})|p_{\\alpha}(\\mathbf{z})) \\to 0$ . The update rule for the energy-based prior model (also Eq. 10) can be interpreted as self-adversarial learning. The prior model $p_{\\alpha}(\\mathbf{z})$ serves as both generator and discriminator if we compare it to GAN (generative adversarial networks) [11]. In contrast to GAN, our learning follows MLE with divergence perturbations, which in general does not suffer from issues such as mode collapsing and instability, as it does not involve competition between two separate models. The energy-based model can thus be seen as its own adversary or its own critic.", + "bbox": [ + 76, + 666, + 468, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Related Work", + "text_level": 1, + "bbox": [ + 76, + 844, + 218, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generator model. The generator model has a top-down network that maps the low-dimensional latent code to the", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "observed data space. VAEs [17, 27, 33, 32] proposes variational learning by introducing an approximation of the true intractable posterior, which allows a tractable bound on log-likelihood to be maximized. Another line of work [14, 25] trains the generator model without inference model by using Langevin dynamics for generator posterior sampling. We follow the former approach and use the inference model for efficient training.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generator model with informative prior. The majority of the existing generator models assume that the latent code follows a simple and known prior distribution, such as isotropic Gaussian distribution. Such assumption may render an ineffective generator as observed in [34, 5]. Our work utilizes the informative and expressive energy-based prior in the joint space of latent variables and is related to the line of previous research on introducing flexible prior distributions. For example, [34] parameterizes the prior based on the posterior inference model. [5, 9] adopt a two-stage approach which first trains a latent variable model with simple prior and then trains a separate prior model (e.g., VAE or Gaussian mixture model) to match the aggregated posterior distribution.", + "bbox": [ + 496, + 229, + 890, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generator model with hierarchical structures. The generator models that consist of multi-layers of latent variables are recently attracting attention for hierarchical learning. [29, 2, 21, 3, 36] stack generative models on top of each other and assume conditional Gaussian distributions at different layers. However, as shown in Sec. 2.1, the bottom layer could act as a single generative model and absorb most features, leading to ineffective representation learning. [42, 20] propose to learn hierarchical features with unit Gaussian prior by adapting the generator into multiple layers. However, the latent variables at different layers are distributed independently a priori and are only loosely connected. Instead, we propose a joint EBM prior that could tightly couple and jointly model latent variables at different layers and show superior results through joint training.", + "bbox": [ + 496, + 459, + 890, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hierarchical generator model with informative prior. Recent advances [4, 1] have started exploring learning informative prior for multi-layer generator models. JEBM [4] and NCP-VAE [1] build latent space EBM on hierarchical generator models and showcase the capability of improving the generation quality. However, these models consider the conditional hierarchical models, which can be limited in learning effective hierarchical representations (see Sec. 2.1). This work studies hierarchical representation learning by introducing a novel framework where latent space EBM can be jointly trained with the architectural hierarchical models to capture complex representations of different levels.", + "bbox": [ + 496, + 704, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2222", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/28aa96ea11f0bd66327f1e7ad14b7336d8aa695525725a593f26e8b45abf6c80.jpg", + "image_caption": [ + "Figure 4. Hierarchical sampling on SVHN. Left: The latent code at bottom layer $(z_{1})$ represents the background light and shading. Center-left: the latent code at second bottom layer $(z_{2})$ represents the color schemes. Center-right: the latent code at second top layer $(z_{3})$ encodes the shape variations of the same digit. Right: the latent code at top layer $(z_{4})$ captures the digit identity and the general structure." + ], + "image_footnote": [], + "bbox": [ + 99, + 87, + 285, + 231 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7bd785344120ff2ed24d0957cfd19aae53ecac0fd868af25b60c269b8ae36af3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 87, + 480, + 232 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b6d465a1360f41482ed6cb3017f029550671c905dd1a0b440b4ab18026572489.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 88, + 676, + 232 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/05d3c4ad017755d67b5cf20cf477c158d536e7e2c4a95e42763a502eaf1d8e48.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 88, + 870, + 232 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e57bab778a351865d9a6b1143aadccd8a3edd709edb5fbb9bc108968be96d06d.jpg", + "image_caption": [ + "Figure 5. Hierarchical sampling on MNIST. Left: The latent code at bottom layer $(z_{1})$ indicates the stroke width. Center: the latent code at second layer $(z_{2})$ encodes geometric changes among similar digits. Right: the latent code at top layer $(z_{3})$ learns the digit identity and general structure." + ], + "image_footnote": [], + "bbox": [ + 98, + 299, + 447, + 386 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 484, + 209, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of our method, we conduct the following experiments: 1) hierarchical representation learning, 2) analysis of latent space, 3) image modelling, and 4) robustness. For a better understanding of the proposed method, we perform the disentanglement learning experiment, various ablation studies, and an analysis of parameter complexity.", + "bbox": [ + 75, + 512, + 468, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Hierarchical Representation Learning", + "text_level": 1, + "bbox": [ + 76, + 631, + 406, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first demonstrate the capability of our model in hierarchical representation learning by experiments of hierarchical sampling and latent classifier.", + "bbox": [ + 75, + 656, + 468, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hierarchical sampling. With partitioned latent variables and the hierarchical structure of generator, the latent variables at higher layers should capture semantic features, while the lower layers should capture low-level features. We train our model on MNIST using the same setting as in Sec. 2.2 with only '0', '1', and '2' digit classes available and the latent dimension set to 2. In Fig. 6, by changing the $\\mathbf{z}_1$ (at the bottom layer), our model can successfully deliver the variations in shape (low-level features), and changing the $\\mathbf{z}_2$ (at the top layer) leads to the variations in digit class (high-level features). This indicates a successfully learned hierarchical representation.", + "bbox": [ + 75, + 702, + 468, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Further, we train our model on MNIST with all digit", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8170f2bf23bded18b493feb09312a19064ca06767907ff2a449f4ef560b07d1b.jpg", + "image_caption": [ + "Figure 6. Visualization for our model by changing each unit of 2-dimensional z. Left: changing the first unit. Right: changing the second unit. Top: the value of each unit, where the orange color indicates the first unit and the blue color indicates the second unit." + ], + "image_footnote": [], + "bbox": [ + 506, + 301, + 885, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "classes and the more challenging SVHN dataset, and we generate the images by sampling (using Eq. 13) the latent code of one layer while keeping other layers fixed. The results shown in Fig. 4 and Fig. 5 also demonstrate the hierarchical representation learned by our model.", + "bbox": [ + 496, + 450, + 890, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Latent Classifier. We next show that our model can achieve better performance in hierarchical representation learning. Note that the inference model $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ should be learned to approximate the true posterior $p_{\\theta}(\\mathbf{z}|\\mathbf{x})$ of the generator, which integrates both the hierarchical inductive bias and the energy-based refinement. Therefore, to measure the learned hierarchical features, we learn classifiers on the inferred latent codes at different layers to predict the label of the data and measure the testing classification accuracy. The latent codes that carry rich high-level semantic features should achieve higher classification accuracy.", + "bbox": [ + 496, + 527, + 892, + 694 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5535d4bda11581333e5e2edb7f219e01833c3b34c8d3ffdd5e0b3add89af315b.jpg", + "table_caption": [ + "Table 1. Testing accuracy of inferred latent codes at each layer. We denote $(\\downarrow)$ for the layer that has unexpectedly lower accuracy." + ], + "table_footnote": [], + "table_body": "
L=1L=2L=3L=4
MNISTOurs32.60%58.32%67.64%-
VLAE35.69%57.86%52.08% (↓)-
Fashion-MNISTOurs39.27%44.81%84.27%-
VLAE52.43%35.65% (↓)83.24%-
SVHNOurs21.00%25.29%30.58%86.63%
VLAE22.59%26.97%56.70%52.14% (↓)
", + "bbox": [ + 511, + 734, + 877, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In practice, we first train our model on standard benchmarks, such as MNIST, Fashion-MNIST, and SVHN. Then, we train classifiers on the inferred latent codes at each layer. We consider VLAE [42] as our baseline model, which", + "bbox": [ + 498, + 840, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2223", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "learns a structural latent space with standard Gaussian prior. We show comparison results in Tab. 1, where our learned inference model $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ extracts varying levels of semantic features for different layers of latent codes. The top layer carries the most significant features, and the bottom layer carries the least. The baseline model that assumes Gaussian prior, however, extracted mixed semantic features across different layers. For fair comparisons, we use the same generation and inference structure as the baseline model2. The structure of the classifier contains two linear layers with a hidden dimension set to 256 and uses ReLU activation function. The classifier has softmax as its output layer. We do not employ drop-out and normalization strategies.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Image Modelling", + "text_level": 1, + "bbox": [ + 76, + 303, + 243, + 319 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we evaluate our model in image modelling by measuring the quality of generated and reconstructed images. We consider the baseline models that assume Gaussian prior, such as Alternating Back-propagation (ABP) [14], Ladder-VAE (LVAE) [30], BIVA [21], Short-run MCMC (SRI) [25], and VLAE [42], as well as generator models with informative prior, such as RAE [9], Two-stages VAE (2s-VAE) [5], NCP-VAE [1], Multi-NCP [37] and LEBM [26]. To make fair comparisons, we follow the protocol in [26].", + "bbox": [ + 75, + 329, + 468, + 481 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6bd2ca58c795b8f67a904a1ce18f0daf30ed7b97902f5606c2f9c6b3c0bf4a88.jpg", + "table_caption": [ + "Table 2. Testing reconstruction by MSE, and generation evaluation by FID on SVHN and CelebA-64." + ], + "table_footnote": [], + "table_body": "
ModelSVHNCelebA-64
MSE (↓)FID (↓)MSE (↓)FID (↓)
ABP-49.71-51.50
LVAE0.01439.260.02853.40
BIVA0.01031.650.01033.58
SRI0.01135.230.01136.84
VLAE0.01643.950.01044.05
2s-VAE0.01942.810.02144.40
RAE0.01440.020.01840.95
NCP-VAE0.02033.230.02142.07
Multi-NCP0.00426.190.00935.38
LEBM0.00829.440.01337.87
Ours0.00824.160.00432.15
", + "bbox": [ + 88, + 523, + 454, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Synthesis: We use Fréchet Inception Distance (FID) [16] to quantitatively evaluate the sample quality. In Tab. 2, it can be seen that our model obtains superior generation quality compared to the baseline models.", + "bbox": [ + 75, + 747, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Reconstructions: To evaluate the accuracy of our inference model, we compute mean square error (MSE) [26, 24] for testing reconstruction. As shown in Tab. 2, the proposed model leads to more accurate and faithful reconstructions.", + "bbox": [ + 75, + 810, + 468, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Analysis of Latent Space", + "text_level": 1, + "bbox": [ + 500, + 90, + 725, + 107 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of toy data. To illustrate the expressivity of the proposed EBM prior, we train our model on MNIST (using the same setting as shown in Fig. 2 and Fig. 6) and set the latent dimension for both $\\mathbf{z}_1$ and $\\mathbf{z}_2$ to 2 for better visualization. We visualized the Langevin transition of the prior sampling in Fig. 7, which shows that the latent codes at the top layer $(\\mathbf{z}_2)$ can effectively capture the multi-modal posterior, where using a Gaussian prior might be infeasible.", + "bbox": [ + 496, + 113, + 893, + 234 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b6f2688896c2d327233d4cbb8bfc623f5dd77ea71d379c914381d2de88bddf4c.jpg", + "image_caption": [ + "Figure 7. Visualization of the latent codes sampled from our EBM prior (Top row: $\\mathbf{z}_2$ ). Blue, Orange color indicate prior and posterior, respectively." + ], + "image_footnote": [], + "bbox": [ + 522, + 247, + 869, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Langevin trajectory. We explore the energy landscape of the learned prior $p_{\\alpha}(\\mathbf{z})$ via transition of Langevin dynamics initialized from $p_0(\\mathbf{z})$ towards $p_{\\alpha}(\\mathbf{z})$ on CelebA-64. If the EBM is well-learned, the energy prior should render local modes of the energy function, and traversing these local modes should present diverse, realistic image synthesis and steady-state energy scores. Existing EBMs often suffer from oversaturated synthesis via the challenging long-run Langevin dynamic (see oversaturated example in Fig.3 in [23]). We thereby test our model with 2500 Langevin steps, which is much longer than the 40 steps used in training. Fig. 8 shows the image synthesis and energy profile, where our EBM prior model does not exhibit the oversaturated phenomenon and successfully delivers diverse and realistic synthesis with steady-state energy.", + "bbox": [ + 496, + 416, + 892, + 643 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1eb3ae9ea9567caeea7d87a28a4d630ab6d92dffe3cb485d94faeda323dddfca.jpg", + "image_caption": [ + "Figure 8. Transition of Markov chains initialized from $p_0(\\mathbf{z})$ towards $p_{\\alpha}(\\mathbf{z})$ for 2500 steps. Top: Trajectory in the CelebA-64 data space for every 100 steps. Bottom: Energy profile over time." + ], + "image_footnote": [], + "bbox": [ + 501, + 655, + 888, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Robustness", + "text_level": 1, + "bbox": [ + 500, + 816, + 624, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we examine the robustness of our model in adversarial attack and outlier detection.", + "bbox": [ + 496, + 839, + 890, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Adversarial robustness. For adversarial robustness, we consider the latent attack [10], which is shown to be a", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "$^{2}$ https://github.com/ermongroup/Variational-Ladder-Autoencoder", + "bbox": [ + 93, + 886, + 441, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2224", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "strong attack for the generative model with latent variables, and it allows us to attack the latent codes at different layers. Specifically, let $\\mathbf{x}_t$ be the target and $\\mathbf{x}_o$ be the original image. The attack aims to create the distorted image $\\tilde{\\mathbf{x}} = \\mathbf{x}_o + \\epsilon$ such that its learned inference distribution $q_{\\phi}(\\mathbf{z}|\\tilde{\\mathbf{x}})$ is close to the inference $q_{\\phi}(\\mathbf{z}|\\mathbf{x}_t)$ on target images under KL-divergence (Eq. 5 in [10]).", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3e58d6bcfc7e2d9d796bc45b5616d9811133f7901841cf46f44c746623274646.jpg", + "image_caption": [ + "Figure 9. Adversarial latent attack on different layers. The leftmost figure indicates the bottom layer, and the rightmost figure indicates the top layer. 1st col: original image. 2nd col: target image. 3rd col: adversarial example. 4th col: reconstruction of adversarial example." + ], + "image_footnote": [], + "bbox": [ + 94, + 207, + 450, + 227 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We illustrate the adversarial attack on different layers in Fig. 9. The learned inference model $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ carries different levels of semantics for different layers. The adversarial example created by attacking latent codes at the bottom layer only perturbs the data along low-level features direction from the target image; hence, the model can be robust and have faithful reconstruction from adversarial examples. The adversarial example coming from the top-layer attack can distort the original data along a high-level semantic direction from the target image, thus, the reconstruction from the adversarial example can be substantially different from the original data, indicating a successful attack.", + "bbox": [ + 75, + 305, + 468, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Anomaly detection. We also evaluate the model on anomaly detection. If the model is well-learned, the inference model $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ should form an informative latent space that separates anomalies from the normal data. Following the protocols in [18, 26], we take latent samples from the learned inference model and use the unnormalized log-posterior $\\log p_{\\theta}(\\mathbf{x},\\mathbf{z})$ as our decision function to detect anomaly on MNIST. Only one digit class is held-out as an anomaly in training, while both normal and anomalous data are used for testing. We compare baseline models such as BiGAN- $\\sigma$ [41], MEG [18], LEBM [26], HVAE and VAE using area under the precision-recall curve (AUPRC). The results of baseline models are provided by [26], and we use $L^{>0}$ [15] as the decision function for HVAE model. Tab. 3 shows the result.", + "bbox": [ + 75, + 486, + 470, + 712 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f23050755c2b025490ed16534866d337b833f453cde3f9ceaf1b31470bedefaf.jpg", + "table_caption": [ + "Table 3. AUPRC scores for unsupervised anomaly detection on MNIST. Following the protocol of [26], we average the results over last 10 epochs to account for variance." + ], + "table_footnote": [], + "table_body": "
hold-out digit14579
VAE0.0630.3370.3250.1480.104
HVAE0.494 ± 0.0040.920 ± 0.0040.913 ± 0.0030.680 ± 0.0060.791 ± 0.008
MEG0.281 ± 0.0350.401 ± 0.0610.402 ± 0.0620.290 ± 0.0400.342 ± 0.034
BiGAN-σ0.287 ± 0.0230.443 ± 0.0290.514 ± 0.0290.347 ± 0.0170.307 ± 0.028
Latent EBM0.336 ± 0.0080.630 ± 0.0170.619 ± 0.0130.463 ± 0.0090.413 ± 0.010
Ours0.722 ± 0.0100.949 ± 0.0020.980 ± 0.0010.941 ± 0.0030.935 ± 0.003
", + "bbox": [ + 78, + 760, + 468, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 847, + 240, + 862 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The proposed expressive prior model enables complex data representations to be effectively captured, which in turn", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "improves the expressivity of the whole model in generating high-quality synthesis. To better understand the influence of the proposed method, we conduct ablation studies, including 1) MCMC steps, 2) complexity of EBM, and 3) other image datasets.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "MCMC steps: We examine the influence of steps of short-run MCMC for prior sampling. Tab. 4 shows that increasing steps could result in a better quality of generation. Increasing the step number from 15 to 60 could result in a significant improvement in synthesis quality, while exhibiting only minor influence when increased beyond 60.", + "bbox": [ + 496, + 167, + 890, + 257 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9ff20a8be7abe68f74470e082ff248865c2e7ca8b3d5274f9a228b8508b09706.jpg", + "table_caption": [ + "Table 4. Varying $k$ (steps number) of our model on CelebA-64." + ], + "table_footnote": [], + "table_body": "
k=15k=30k=60k=150k=300
FID56.4239.8932.1531.2030.78
", + "bbox": [ + 540, + 279, + 846, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Complexity of EBM: We further examine the influence of model parameters of EBM. The energy function is parameterized by a 2-layer perceptron. We fix the number of layers and increase the hidden units of EBM. As shown in Tab. 5, increasing the hidden units of EBM results in better performance.", + "bbox": [ + 496, + 320, + 890, + 409 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/24e90ca774416da3a6a7db20179803d631cf1717df7239398c9a1886b49f1eed.jpg", + "table_caption": [ + "Table 5. Increasing hidden units (denoted as nef) of EBM." + ], + "table_footnote": [], + "table_body": "
nefnef=0nef=10nef=20nef=50nef=100
FID43.9541.7233.1030.4224.16
", + "bbox": [ + 514, + 430, + 877, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Other image datasets: We test the scalability of our model on high-resolution image dataset, such as CelebA-128. We show the image synthesis in Fig. 10.", + "bbox": [ + 496, + 463, + 890, + 508 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/659522c8b7fddbc0a6ae09b6413bfc1945c66abb14f3b692c2484dd7583f4046.jpg", + "image_caption": [ + "Figure 10. Generated image synthesis on CelebA-128" + ], + "image_footnote": [], + "bbox": [ + 504, + 518, + 887, + 570 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also train our model on CIFAR-10 (32x32) and report the FID score for generation quality in Tab. 6, in which our model performs well compared to baseline models.", + "bbox": [ + 496, + 594, + 890, + 640 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/364bee638a88f6768cbfbdc7aba23d81bd1c202f43a763a82a8e30e257d84e47.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Table 6. FID on CIFAR-10
Ours2s-VAERAENCP-VAEMulti-NCPLEBM
63.4272.9074.1678.0665.0170.15
", + "bbox": [ + 540, + 648, + 846, + 685 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 709, + 617, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose to build a joint latent space EBM with hierarchical structures for better hierarchical representation learning. Our joint EBM prior is expressive in modelling the inter-layer relation among multiple layers of latent variables, which in turn enables different levels of data representations to be effectively captured. We develop an efficient variational learning scheme and conduct various experiments to demonstrate the capability of our model in hierarchical representation learning and image modelling. For future work, we shall explore learning the hierarchical representations from other domains, such as videos and texts.", + "bbox": [ + 496, + 733, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2225", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jyoti Aneja, Alex Schwing, Jan Kautz, and Arash Vahdat. A contrastive learning approach for training variational autoencoder priors. Advances in neural information processing systems, 34:480-493, 2021. 2, 5, 7", + "[2] Philip Bachman. An architecture for deep, hierarchical generative models. Advances in Neural Information Processing Systems, 29, 2016. 5", + "[3] Rewon Child. 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Learning hierarchical features from generative models. arXiv preprint arXiv:1702.08396, 2017. 1, 3, 5, 6, 7" + ], + "bbox": [ + 78, + 92, + 468, + 784 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2227", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_model.json b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ce14853d7ff1aa45f84ff476714334a61aeb9743 --- /dev/null +++ b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_model.json @@ -0,0 +1,2662 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.101, + 0.131, + 0.872, + 0.153 + ], + "angle": 0, + "content": "Learning Hierarchical Features with Joint Latent Space Energy-Based Prior" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.18, + 0.751, + 0.253 + ], + "angle": 0, + "content": "Jiali Cui\\(^{1}\\), Ying Nian Wu\\(^{2}\\), Tian Han\\(^{1}\\)\\\n\\(^{1}\\)Department of Computer Science, Stevens Institute of Technology\\\n\\(^{2}\\)Department of Statistics, University of California, Los Angeles\\\n{jcui7,than6}@stevens.edu, ywu@stat.ucla.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.622 + ], + "angle": 0, + "content": "This paper studies the fundamental problem of multilayer generator models in learning hierarchical representations. The multi-layer generator model that consists of multiple layers of latent variables organized in a top-down architecture tends to learn multiple levels of data abstraction. However, such multi-layer latent variables are typically parameterized to be Gaussian, which can be less informative in capturing complex abstractions, resulting in limited success in hierarchical representation learning. On the other hand, the energy-based (EBM) prior is known to be expressive in capturing the data regularities, but it often lacks the hierarchical structure to capture different levels of hierarchical representations. In this paper, we propose a joint latent space EBM prior model with multi-layer latent variables for effective hierarchical representation learning. We develop a variational joint learning scheme that seamlessly integrates an inference model for efficient inference. Our experiments demonstrate that the proposed joint EBM prior is effective and expressive in capturing hierarchical representations and modelling data distribution." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.654, + 0.21, + 0.67 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.68, + 0.47, + 0.801 + ], + "angle": 0, + "content": "In recent years, deep generative models have achieved remarkable success in generating high-quality images [36, 31], texts [40, 13], and videos [28, 35]. However, learning generative models that incorporate hierarchical structures still remains a challenge. Such hierarchical generative models can play a critical role in enabling explainable artificial intelligence, thus representing an important area of ongoing research." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.802, + 0.47, + 0.864 + ], + "angle": 0, + "content": "To tackle this challenge, various methods of learning hierarchical representations have been explored [30, 42, 21, 3, 30]. These methods learn generative models with multiple layers of latent variables organized in a top-down ar" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.288, + 0.892, + 0.379 + ], + "angle": 0, + "content": "chitecture, which have shown the capability of learning increasingly abstract representations (e.g., general structures, classes) at the top layers while capturing low-level data features (e.g., colors, background) at the bottom layers. In general, one could categorize these methods into two classes: (i) conditional hierarchy and (ii) architectural hierarchy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.893, + 0.548 + ], + "angle": 0, + "content": "The conditional hierarchies [30, 12, 25, 21, 3] employ stacked generative models layered on top of one another and assume conditional Gaussian distributions at different layers, while the architectural hierarchies [42, 20] instead leverage network architecture to place high-level representations at the top layers of latent variables and low-level representations at the bottom layers. However, they typically assume conditional Gaussian distribution or isotropic Gaussian as the prior, which could have limited expressivity [26]. Learning a more expressive and informative prior model for multiple layers of latent variables is thus needed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.895, + 0.746 + ], + "angle": 0, + "content": "The energy-based models (EBMs) [19, 39, 7, 24, 26, 4], on the other hand, are shown to be expressive and proved to be powerful in capturing data regularities. Notably, [26] studies the EBM in the latent space, where the energy function is considered as a correction of the non-informative prior and tilts the non-informative prior to a more expressive prior distribution. The low dimensionality of the latent space makes EBM more effective in capturing regularities in the data. However, prior methods often rely on expensive MCMC methods for posterior sampling of the latent variables, and more importantly, the latent variables are not hierarchically organized, making it difficult to capture data variations at different levels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In this paper, we propose to combine the strengths of latent space EBM and the multi-layer generator model for effective hierarchical representation learning. In particular, we build the EBM on the latent variables across different layers of the generator model, where the latent variables at different layers are concatenated and modelled jointly. The latent variables at different layers capture different levels of information from the data via the hierarchy of the generative model, and their inter-relations are further tightened up and better captured through EBM in joint latent space." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.876, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Our project page is available at https://jcui1224.github.io/hierarchical-representation-ebm-proj/." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2218" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.332 + ], + "angle": 0, + "content": "Learning the EBM in the latent space can be challenging since it usually requires MCMC sampling for both the prior and posterior distributions of the latent variables. The prior sampling is efficient with the low dimensionality of the latent space and the lightweight network of the energy function, while the MCMC sampling of posterior distribution requires the backward propagation of generation network, which is usually heavy and thus renders inefficient inference. To ensure efficient inference, we introduce an inference model and develop a joint training scheme to efficiently and effectively learn the latent space EBM and multi-layer generator model. In particular, the inference model aims to approximate the exact posterior of the multi-layer latent variables while also serving to extract levels of data variations through the deep feed-forward inference network to facilitate hierarchical learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.44 + ], + "angle": 0, + "content": "Contributions: 1) We propose the joint EBM prior model for hierarchical generator models with multiple layers of latent variables; 2) We develop a variational training scheme for efficient learning and inference; 3) We provide strong empirical results on hierarchical learning and image modeling, as well as various ablation studies to illustrate the effectiveness of the proposed model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.454, + 0.206, + 0.47 + ], + "angle": 0, + "content": "2. Background" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.47, + 0.525 + ], + "angle": 0, + "content": "In this section, we present the background of multi-layer generator models and the latent space EBM, which will serve as the foundation of the proposed model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.536, + 0.34, + 0.551 + ], + "angle": 0, + "content": "2.1. Multi-layer generator models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.47, + 0.725 + ], + "angle": 0, + "content": "Let \\(\\mathbf{x} \\in \\mathbb{R}^D\\) represent the high-dimensional observed examples, and \\(\\mathbf{z} \\in \\mathbb{R}^d\\) denote the low-dimensional latent variables. The multi-layer generator model [30, 36, 21] consists of multiple layers of latent variables that are organized in a top-down hierarchical structure and modelled to be conditionally dependent on its upper layer, i.e., \\(p_{\\theta}(\\mathbf{z}) = \\prod_{i=1}^{L-1} p_{\\theta_i}(\\mathbf{z}_i | \\mathbf{z}_{i+1}) p_0(\\mathbf{z}_L)\\), where \\(p_{\\theta_i}(\\mathbf{z}_i | \\mathbf{z}_{i+1}) \\sim \\mathcal{N}(\\mu_{\\theta_i}(\\mathbf{z}_{i+1}), \\sigma_{\\theta_i}(\\mathbf{z}_{i+1}))\\) and \\(p_0(\\mathbf{z}_L) \\sim \\mathcal{N}(0, I)\\). Although such a modelling strategy has seen significant improvement in data density estimation, it can be less effective in learning hierarchical representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.877 + ], + "angle": 0, + "content": "To demonstrate, we train BIVA [21] on MNIST with 6 layers of latent variables and conduct hierarchical sampling by generating latent variables via the repamaramization trick, i.e., \\(\\mathbf{z}_i = \\mu_{\\theta_i}(\\mathbf{z}_{i + 1}) + \\sigma_{\\theta_i}(\\mathbf{z}_{i + 1})\\cdot \\epsilon_i\\) where \\(\\epsilon_{i}\\) is the added Gaussian noise. Specifically, the latent variables are generated by randomly sampling \\(\\epsilon_{i}\\) for the \\(i\\)-th layer, while fixing \\(\\epsilon_{j\\neq i}\\) for other layers, and the corresponding image synthesis should deliver the variation of representation learned by \\(\\mathbf{z}_i\\). We show the results in Fig. 1, where the major semantic variation is only captured by the top layer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "of the latent variables, suggesting an ineffective hierarchical representation learned (compare with our model shown in Fig. 5)." + }, + { + "type": "image", + "bbox": [ + 0.528, + 0.147, + 0.642, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.147, + 0.753, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.148, + 0.865, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.236, + 0.892, + 0.278 + ], + "angle": 0, + "content": "Figure 1. Visualization of hierarchical representations on BIVA. Left: sampling \\(\\epsilon_{1},\\epsilon_{2}\\) for bottom layers. Middle: sampling \\(\\epsilon_{3},\\epsilon_{4}\\) for middle layers. Right: sampling \\(\\epsilon_{5},\\epsilon_{6}\\) for top layers." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.286, + 0.68, + 0.302 + ], + "angle": 0, + "content": "2.2. Latent space EBM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.892, + 0.445 + ], + "angle": 0, + "content": "The energy-based models (EBMs) [7, 6, 24, 8, 38] present a flexible and appealing way for data modelling and are known for being expressive and powerful in capturing data regularities. Albeit their expressivity, learning the EBM on high-dimensional \\(\\mathbf{x}\\)-space can be challenging since the energy function needs to support the entire data space. As such, another line of works [26, 1, 37] seek to build EBM on low-dimensional \\(\\mathbf{z}\\)-space with the probability density defined as" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.451, + 0.892, + 0.483 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} (\\mathbf {z}) = \\frac {1}{\\mathbb {Z} (\\theta)} \\exp \\left[ f _ {\\theta} (\\mathbf {z}) \\right] p _ {0} (\\mathbf {z}) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.609 + ], + "angle": 0, + "content": "However, with a single-layer non-hierarchical \\(\\mathbf{z}\\)-space, it is typically infeasible to capture the data abstraction of different levels. To see this, we pick up the digit classes '0', '1', and '2' of the MNIST dataset, on which we train LEBM [26] with the latent dimension set to be 2. We show in Fig. 2 that changing the value of each latent unit could lead to a mixed variations in digit shape and class (compare to our proposed method in Fig. 6)." + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.611, + 0.875, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.678, + 0.892, + 0.747 + ], + "angle": 0, + "content": "Figure 2. Visualization for latent space EBM [26] by changing each unit of 2-dimensional z. Left: changing the first unit. Right: changing the second unit. Top: the value of each unit, where the orange color indicates the first unit and the blue color indicates the second unit." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.635, + 0.788 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we study a joint latent space EBM prior where latent variables are partitioned into multiple groups but modelled jointly for hierarchical representation learning. To ensure efficient inference, we introduce an inference model to approximate the generator posterior and develop a variational joint training scheme in which each model can be trained efficiently and effectively." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.31, + 0.901 + ], + "angle": 0, + "content": "1 https://github.com/vlievin/biva-pytorch" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2219" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.367, + 0.108 + ], + "angle": 0, + "content": "3.1. Latent variable generative model" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.115, + 0.47, + 0.145 + ], + "angle": 0, + "content": "A latent variable generative model (i.e., generator model) can be specified using joint distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.157, + 0.469, + 0.174 + ], + "angle": 0, + "content": "\\[\np _ {\\beta , \\alpha} (\\mathbf {x}, \\mathbf {z}) = p _ {\\beta} (\\mathbf {x} | \\mathbf {z}) p _ {\\alpha} (\\mathbf {z}) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.185, + 0.469, + 0.214 + ], + "angle": 0, + "content": "which consists of the generation model \\(p_{\\beta}(\\mathbf{x}|\\mathbf{z})\\) and the prior model \\(p_{\\alpha}(\\mathbf{z})\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.216, + 0.469, + 0.32 + ], + "angle": 0, + "content": "Joint latent space EBM: The prior model \\(p_{\\alpha}(\\mathbf{z})\\) is usually assumed to be single-layer, which can be infeasible for learning hierarchical representations (see Sec. 2.2). In this work, we propose a joint latent space EBM prior, where latent variables are separated into multiple groups, i.e., \\(\\mathbf{z} = [\\mathbf{z}_1,\\mathbf{z}_2,\\dots ,\\mathbf{z}_L]\\), and our EBM prior model is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.33, + 0.469, + 0.362 + ], + "angle": 0, + "content": "\\[\np _ {\\alpha} (\\mathbf {z}) = \\frac {1}{\\mathbb {Z} (\\alpha)} \\exp \\left[ f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\right] p _ {0} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.372, + 0.469, + 0.508 + ], + "angle": 0, + "content": "where \\([.]\\) refers to the concatenation. \\(f_{\\alpha}(.)\\) is the negative energy function that can be parameterized by a small multilayer perceptron with the parameters \\(\\alpha, p_0([\\dots])\\) is a reference distribution assumed to be a unit Gaussian, and \\(\\mathbb{Z}(\\alpha)\\) is the normalizing constant or partition function. Such a prior model can be considered as an energy-based refinement of the non-informative reference distribution, thus the relationship between different groups of latent codes can be well captured via the energy function \\(f_{\\alpha}([\\mathbf{z}_1,\\ldots ,\\mathbf{z}_L])]\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.509, + 0.469, + 0.537 + ], + "angle": 0, + "content": "For notation simplicity, we denote \\(\\mathbf{z} = [\\mathbf{z}_1,\\dots ,\\mathbf{z}_L]\\) in subsequent discussions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.539, + 0.447, + 0.553 + ], + "angle": 0, + "content": "Generation Model. The generation model is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.565, + 0.469, + 0.583 + ], + "angle": 0, + "content": "\\[\np _ {\\beta} (\\mathbf {x} \\mid \\mathbf {z}) \\sim \\mathcal {N} \\left(g _ {\\beta} (\\mathbf {z}), \\sigma^ {2} I _ {D}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.595, + 0.469, + 0.716 + ], + "angle": 0, + "content": "which models the observed data using top-down generator network \\( g_{\\beta}(\\mathbf{z}) \\) with additive Gaussian noise, i.e., \\( \\mathbf{x} = g_{\\beta}(\\mathbf{z}) + \\epsilon, \\epsilon \\sim \\mathcal{N}(0, \\sigma^2 I_D) \\). To facilitate the hierarchical representation learning with multi-layer latent variables, we consider multi-layer hierarchical generator network \\( g_{\\beta} (= \\{g_1, g_2, \\ldots, g_L\\}) \\) that is designed to explain the observation \\( \\mathbf{x} \\) by integrating data representation from the above layers, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.728, + 0.232, + 0.743 + ], + "angle": 0, + "content": "\\[\nh _ {L} = g _ {L} (\\mathbf {z} _ {L})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.746, + 0.469, + 0.763 + ], + "angle": 0, + "content": "\\[\nh _ {i} = g _ {i} \\left(\\left[ \\mathbf {z} _ {i}, h _ {i + 1} \\right]\\right), i = 1, 2, \\dots , L - 1 \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.766, + 0.262, + 0.783 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} \\sim \\mathcal {N} (h _ {1}, \\sigma^ {2} I _ {D})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.469, + 0.84 + ], + "angle": 0, + "content": "in which \\(\\mathbf{z}_L\\) is at the top layer, and \\(g_{i}\\) is a shallow network that decodes latent code \\(\\mathbf{z}_i\\) while integrating features from the upper layer." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Joint EBM prior vs. independent Gaussian prior: With such a multi-layer hierarchical generation model, it is also tempting to consider learning with the unit Gaussian prior, i.e., \\( p(\\mathbf{z}) \\sim \\mathcal{N}(0, I_d) \\). Such a prior choice is adopted in" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.891, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.246, + 0.892, + 0.316 + ], + "angle": 0, + "content": "Figure 3. The illustration of the proposed joint EBM prior model (Left). Red lines indicate the modelling of intra-layer relation, and blue lines indicate inter-layer relation. Compared to the Gaussian prior model and single-layer LEBM, our prior model is expressive and effective in learning hierarchical representations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.338, + 0.892, + 0.445 + ], + "angle": 0, + "content": "[42, 20] and has seen some success in learning hierarchical features. However, the independent Gaussian prior does not account for the relations between levels of representations and can be less expressive in capturing complex data features. The proposed EBM prior is expressive and can couple the latent variables across different layers within a joint modelling framework." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.46, + 0.849, + 0.475 + ], + "angle": 0, + "content": "Our model is illustrated in the left panel of Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.483, + 0.751, + 0.499 + ], + "angle": 0, + "content": "3.2. Variational learning scheme" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.892, + 0.582 + ], + "angle": 0, + "content": "Suppose we have observed examples \\((\\mathbf{x}_i, i = 1, \\dots, n)\\) that come from (true) data distribution \\(p_{\\mathrm{data}}(\\mathbf{x})\\) and denote \\(\\theta = (\\beta, \\alpha)\\) that collects all parameters from the generator model. Learning the generator model can be done by maximizing the log-likelihood of all observed examples as" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.591, + 0.891, + 0.63 + ], + "angle": 0, + "content": "\\[\n\\sum_ {i = 1} ^ {n} \\log p _ {\\theta} (\\mathbf {x} _ {i}) = \\sum_ {i = 1} ^ {n} \\log \\int p _ {\\alpha} (\\mathbf {z}) p _ {\\beta} (\\mathbf {x} _ {i} | \\mathbf {z}) d \\mathbf {z} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.639, + 0.892, + 0.699 + ], + "angle": 0, + "content": "When \\( n \\) becomes sufficiently large, maximizing the above log-likelihood is equivalent to minimizing the Kullback-Leibler (KL) divergence between the model distribution and data distribution, i.e., \\( \\min_{\\theta} D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x})) \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.7, + 0.892, + 0.789 + ], + "angle": 0, + "content": "However, directly maximizing Eq. 6 can be challenging, as the inference of generator posterior (by chain rule, \\( p_{\\theta}(\\mathbf{z}|\\mathbf{x}) = p_{\\theta}(\\mathbf{x},\\mathbf{z}) / p_{\\theta}(\\mathbf{x})) \\) is typically intractable. To tackle the challenge, we employ an inference model \\( q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\) with a separate set of parameters \\( \\phi \\) to approximate the generator posterior." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.79, + 0.892, + 0.834 + ], + "angle": 0, + "content": "Inference model: The inference model maps from data space to latent space and is typically assumed to be Gaussian distributed," + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.844, + 0.891, + 0.862 + ], + "angle": 0, + "content": "\\[\nq _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\sim \\mathcal {N} \\left(\\mu_ {\\phi} (\\mathbf {x}), V _ {\\phi} (\\mathbf {x})\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mu_{\\phi}(\\mathbf{x})\\) and \\(V_{\\phi}(\\mathbf{x})\\) are the d-dimensional mean vector and diagonal covariance matrix. To match with the hierar" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2220" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "chical generator model and facilitate the hierarchical representation learning, we consider the multi-layer inference model defined as" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.149, + 0.252, + 0.165 + ], + "angle": 0, + "content": "\\[\nr _ {1} = h _ {1} (\\mathbf {x})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.167, + 0.469, + 0.183 + ], + "angle": 0, + "content": "\\[\nr _ {i} = h _ {i} \\left(r _ {i - 1}\\right) i = 2, 3, \\dots , L \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.186, + 0.329, + 0.203 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {i} \\sim \\mathcal {N} (\\mu_ {i} (r _ {i}), V _ {i} (r _ {i}))\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.213, + 0.468, + 0.288 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_L\\) is the inferred latent code at the top layer and \\(\\mathbf{z}_1\\) is the inferred bottom layer latent code. Each latent code \\(\\mathbf{z}_i\\) can be inferred and sampled through reparametrization trick [17] using \\(\\mathbf{z}_i = \\mu_i(r_i) + V_i(r_i)^{1/2}\\epsilon\\) where \\(\\epsilon \\sim \\mathcal{N}(0, I_{d_i})\\), with \\(d_i\\) being the dimensionality of \\(z_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.469, + 0.334 + ], + "angle": 0, + "content": "Variational learning: We show that the proposed generator model and the inference model can be naturally unified and jointly trained within a variational learning scheme." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.469, + 0.41 + ], + "angle": 0, + "content": "Specifically, we can define two joint densities, one for generator model density, i.e., \\( p_{\\theta}(\\mathbf{x}, \\mathbf{z}) = p_{\\alpha}(\\mathbf{z})p_{\\beta}(\\mathbf{x}|\\mathbf{z}) \\), and one for data density, i.e., \\( q_{\\phi}(\\mathbf{x}, \\mathbf{z}) = p_{\\mathrm{data}}(\\mathbf{x})q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\). We propose joint learning through KL minimization, and we denote the objective to be \\( L(\\theta, \\phi) \\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.42, + 0.469, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\min _ {\\phi} L (\\theta , \\phi) = \\min _ {\\theta} \\min _ {\\phi} D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {x}, \\mathbf {z}) | | p _ {\\theta} (\\mathbf {x}, \\mathbf {z})\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.469, + 0.496 + ], + "angle": 0, + "content": "where the generator model density is learned to match the true joint data density and capture extracted hierarchical features." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.498, + 0.469, + 0.53 + ], + "angle": 0, + "content": "Learning \\(p_{\\alpha}(\\mathbf{z})\\) : With this joint KL minimization, the prior model can be learned with the gradient \\(-\\nabla_{\\alpha}L(\\theta ,\\phi)\\)" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.54, + 0.419, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} | \\mathbf {x})} [ \\nabla_ {\\alpha} f _ {\\alpha} ([ \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} ]) ] -\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.56, + 0.469, + 0.578 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {p _ {\\alpha} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right)} \\left[ \\nabla_ {\\alpha} f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\right] \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.587, + 0.469, + 0.618 + ], + "angle": 0, + "content": "Learning \\(p_{\\beta}(\\mathbf{x}|\\mathbf{z})\\) : The generation model can be learned with the gradient \\(-\\nabla_{\\beta}L(\\theta ,\\phi)\\) computed as" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.628, + 0.469, + 0.646 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {q _ {\\phi} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\mid \\mathbf {x}\\right)} \\left[ \\nabla_ {\\beta} \\log p _ {\\beta} \\left(\\mathbf {x} \\mid \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right) \\right] \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.469, + 0.686 + ], + "angle": 0, + "content": "Learning \\(q_{\\phi}(\\mathbf{z}|\\mathbf{x})\\) : The inference model can be learned by computing the gradient \\(-\\nabla_{\\phi}L(\\theta ,\\phi)\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.697, + 0.469, + 0.714 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\phi} \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} | \\mathbf {x})} [ \\log p _ {\\beta} (\\mathbf {x} | \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}) ] - \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.718, + 0.438, + 0.734 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\phi} D _ {\\mathrm {K L}} \\left(q _ {\\phi} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\mid \\mathbf {x}\\right) \\mid \\mid p _ {\\alpha} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right)\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.744, + 0.468, + 0.759 + ], + "angle": 0, + "content": "We provide further theoretical understanding in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.769, + 0.229, + 0.785 + ], + "angle": 0, + "content": "3.3. Prior sampling" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.791, + 0.469, + 0.837 + ], + "angle": 0, + "content": "Training the proposed joint EBM prior model requires sampling \\(\\mathbf{z}_1, \\mathbf{z}_2, \\ldots, \\mathbf{z}_L\\) from the proposed EBM prior (see Eq. 10). To do so, we can use Langevin dynamic [22]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.837, + 0.469, + 0.866 + ], + "angle": 0, + "content": "For arbitrary target distribution \\(p(\\mathbf{z})\\), the Langevin dynamic iterates:" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.874, + 0.469, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {t + 1} = \\mathbf {z} _ {t} + \\frac {s ^ {2}}{2} \\nabla_ {\\mathbf {z}} \\log p (\\mathbf {z} _ {t}) + s \\epsilon_ {t} \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "where \\(t\\) indexes the time step of Langevin dynamics. \\(s\\) is the step size and \\(\\epsilon_t\\sim \\mathcal{N}(0,I_d)\\). We run the noise-initialized Langevin dynamics for \\(K\\) steps. Noted that as \\(s\\to 0\\), and \\(K\\rightarrow \\infty\\), the distribution of \\(\\mathbf{z}_t\\) will converge to the target \\(p(\\mathbf{z})\\) regardless of the initial distribution of \\(\\mathbf{z}_0\\) [22]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.168, + 0.892, + 0.213 + ], + "angle": 0, + "content": "Specifically, for prior sampling, we use the prior distribution \\( p_{\\alpha}(\\mathbf{z}) \\) as our target distribution, and the gradient \\( \\nabla_{\\mathbf{z}}\\log p_{\\alpha}(\\mathbf{z}) \\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.223, + 0.892, + 0.241 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\mathbf {z}} f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) + \\nabla_ {\\mathbf {z}} \\log p _ {0} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.296 + ], + "angle": 0, + "content": "The Langevin dynamics for prior sampling can be efficient due to the low-dimensional latent space and the lightweight network structure for the energy function." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.311, + 0.871, + 0.326 + ], + "angle": 0, + "content": "The overall procedure is summarized in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.34, + 0.892, + 0.37 + ], + "angle": 0, + "content": "Algorithm 1 Learning latent EBM prior for hierarchical generator model" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.372, + 0.892, + 0.431 + ], + "angle": 0, + "content": "Input: Training iterations \\(T\\), observed training examples \\(\\{x_{i}\\}_{i = 1}^{n}\\), batch size \\(m\\), network parameters \\(\\alpha, \\beta, \\phi\\), learning rate \\(\\eta_{\\alpha}, \\eta_{\\beta}, \\eta_{\\phi}\\), Langevin steps \\(K\\), Langevin step size \\(s\\)," + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.433, + 0.69, + 0.448 + ], + "angle": 0, + "content": "Let \\(t = 0\\) and \\(\\theta = (\\alpha, \\beta)\\);" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.449, + 0.566, + 0.461 + ], + "angle": 0, + "content": "repeat" + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.463, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Prior sampling for \\(\\{z_i^{-}\\}_{i = 1}^m\\) using Eq. 13 and Eq. 14 with \\(K\\) and \\(s\\)." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.492, + 0.891, + 0.522 + ], + "angle": 0, + "content": "Inference sampling for \\(\\{z_i^+\\}_{i=1}^m\\) using Eq. 8 with \\(\\{x_i\\}_{i=1}^m\\) and reparametrization." + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.523, + 0.891, + 0.553 + ], + "angle": 0, + "content": "Learn joint EBM prior: Given \\(\\{z_i^-, z_i^+\\}_{i=1}^m\\), update \\(\\alpha = \\alpha - \\eta_\\alpha \\nabla_\\alpha L(\\theta, \\phi)\\) using Eq. 10 with \\(\\eta_\\alpha\\)" + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.554, + 0.891, + 0.583 + ], + "angle": 0, + "content": "Learn generation model:Given \\(\\{x_{i},z_{i}^{+}\\}_{i = 1}^{m}\\) update \\(\\beta = \\beta -\\eta_{\\beta}\\nabla_{\\beta}L(\\theta ,\\phi)\\) using Eq. 11 with \\(\\eta_{\\beta}\\)" + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.584, + 0.891, + 0.614 + ], + "angle": 0, + "content": "Learn inference model: Given \\(\\{x_{i},z_{i}^{+}\\}_{i = 1}^{m}\\) update \\(\\phi = \\phi -\\eta_{\\phi}\\nabla_{\\phi}L(\\theta ,\\phi)\\) using Eq. 12 with \\(\\eta_{\\phi}\\)" + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.615, + 0.63, + 0.627 + ], + "angle": 0, + "content": "Let \\( t = t + 1 \\)" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.629, + 0.597, + 0.642 + ], + "angle": 0, + "content": "until \\(t = T\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.671, + 0.749, + 0.687 + ], + "angle": 0, + "content": "3.4. Theoretical understanding" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.694, + 0.892, + 0.739 + ], + "angle": 0, + "content": "Divergence perturbation and ELBO. The KL joint minimization (Eq. 9) can be viewed as a surrogate of the MLE objective with the KL perturbation term," + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.75, + 0.882, + 0.785 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {x}, \\mathbf {z}) | | p _ {\\theta} (\\mathbf {x}, \\mathbf {z})\\right) \\\\ = D _ {\\mathrm {K L}} \\left(p _ {\\text {d a t a}} (\\mathbf {x}) | | p _ {\\theta} (\\mathbf {x})\\right) + D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) | | p _ {\\theta} (\\mathbf {z} | \\mathbf {x})\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x}))\\) is the MLE loss function, and the perturbation term \\(D_{\\mathrm{KL}}(q_{\\phi}(\\mathbf{z}|\\mathbf{x})||p_{\\theta}(\\mathbf{z}|\\mathbf{x}))\\) measures the KL-divergence between inference distribution and generator posterior. The inference \\(q_{\\phi}(\\mathbf{z}|\\mathbf{x})\\) is learned to match the posterior distribution of the generator without expensive posterior sampling. In fact, such KL minimization in the joint space is equivalent to evidence lower bound" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2221" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.168 + ], + "angle": 0, + "content": "(ELBO). To see this, noted that \\( D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x})) = -H(p_{\\mathrm{data}}(\\mathbf{x})) - \\mathbb{E}_{p_{\\mathrm{data}}}[\\log p_{\\theta}(\\mathbf{x})] \\) where \\( H(p_{\\mathrm{data}}(\\mathbf{x})) \\) is the entropy of the empirical data distribution and can be treated as constant \\( C \\equiv -H(p_{\\mathrm{data}}(\\mathbf{x})) \\) w.r.t model parameters \\( \\theta \\). Then \\( L(\\theta, \\phi) \\) is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.177, + 0.465, + 0.248 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} - \\mathbb {E} _ {p _ {\\mathrm {d a t a}}} [ \\log p _ {\\theta} (\\mathbf {x}) ] + D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p _ {\\theta} (\\mathbf {z} | \\mathbf {x})\\right) + C \\\\ = \\mathbb {E} _ {p _ {\\mathrm {d a t a}}} \\left[ \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left(\\log \\frac {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})}\\right) - \\log p _ {\\theta} (\\mathbf {x}) \\right] + C \\\\ = \\mathbb {E} _ {p _ {\\text {d a t a}}} [ - \\operatorname {E L B O} (\\mathbf {x}; \\theta , \\phi) ] + C \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.257, + 0.124, + 0.27 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.277, + 0.462, + 0.346 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {E L B O} (\\mathbf {x}; \\theta , \\phi) = \\log p _ {\\theta} (\\mathbf {x}) - \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log \\frac {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\right] \\\\ = \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log \\frac {p _ {\\theta} (\\mathbf {x} , \\mathbf {z})}{q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\right] \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.353, + 0.469, + 0.429 + ], + "angle": 0, + "content": "and is referred to as evidence lower bound (ELBO) in the literature [17]. Noted that the prior model (i.e., \\( p_{\\theta}(\\mathbf{x}, \\mathbf{z}) = p_{\\beta}(\\mathbf{x}|\\mathbf{z})p_{\\alpha}(\\mathbf{z}) \\)) is now parameterized to be our joint EBM prior. Minimizing Eq. 9 is equivalent to maximizing the evidence lower bound of the log-likelihood." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.43, + 0.469, + 0.535 + ], + "angle": 0, + "content": "Short run sampling and divergence perturbation. The learning of the energy-based model in Eq. 10 requires MCMC sampling from \\( p_{\\alpha}(\\mathbf{z}) \\). We adopt the short-run Langevin dynamics (Eq. 13) with fixed \\( K \\) steps to sample from prior \\( p_{\\alpha}(\\mathbf{z}) \\) for efficient computation. Such prior sampling amounts to approximates the objective \\( L(\\theta, \\phi) \\) in Eq. 9 with yet another KL perturbation term, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.543, + 0.399, + 0.561 + ], + "angle": 0, + "content": "\\[\n\\tilde {L} (\\theta , \\phi) = L (\\theta , \\phi) - D _ {\\mathrm {K L}} \\left(\\tilde {p} _ {\\alpha^ {(t)}} (\\mathbf {z}) | p _ {\\alpha} (\\mathbf {z})\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.57, + 0.469, + 0.631 + ], + "angle": 0, + "content": "where \\(\\tilde{p}_{\\alpha^{(t)}}(\\mathbf{z})\\) refers to the distribution of latent codes after \\(K\\) steps of Langevin dynamics (Eq. 13) in the \\(t\\)-th iteration of the learning. The corresponding learning gradient for the prior model is thus" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.64, + 0.464, + 0.66 + ], + "angle": 0, + "content": "\\[\n- \\nabla_ {\\alpha} \\tilde {L} (\\theta , \\phi) = \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} [ \\nabla_ {\\alpha} f _ {\\alpha} (\\mathbf {z}) ] - \\mathbb {E} _ {\\tilde {p} _ {\\alpha (t)} (\\mathbf {z})} [ \\nabla_ {\\alpha} f _ {\\alpha} (\\mathbf {z}) ]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.667, + 0.469, + 0.833 + ], + "angle": 0, + "content": "When \\(K\\) is sufficiently large, the perturbation term \\(D_{\\mathrm{KL}}(\\tilde{p}_{\\alpha^{(t)}}(\\mathbf{z})|p_{\\alpha}(\\mathbf{z})) \\to 0\\). The update rule for the energy-based prior model (also Eq. 10) can be interpreted as self-adversarial learning. The prior model \\(p_{\\alpha}(\\mathbf{z})\\) serves as both generator and discriminator if we compare it to GAN (generative adversarial networks) [11]. In contrast to GAN, our learning follows MLE with divergence perturbations, which in general does not suffer from issues such as mode collapsing and instability, as it does not involve competition between two separate models. The energy-based model can thus be seen as its own adversary or its own critic." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.219, + 0.86 + ], + "angle": 0, + "content": "4. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Generator model. The generator model has a top-down network that maps the low-dimensional latent code to the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "observed data space. VAEs [17, 27, 33, 32] proposes variational learning by introducing an approximation of the true intractable posterior, which allows a tractable bound on log-likelihood to be maximized. Another line of work [14, 25] trains the generator model without inference model by using Langevin dynamics for generator posterior sampling. We follow the former approach and use the inference model for efficient training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.231, + 0.892, + 0.441 + ], + "angle": 0, + "content": "Generator model with informative prior. The majority of the existing generator models assume that the latent code follows a simple and known prior distribution, such as isotropic Gaussian distribution. Such assumption may render an ineffective generator as observed in [34, 5]. Our work utilizes the informative and expressive energy-based prior in the joint space of latent variables and is related to the line of previous research on introducing flexible prior distributions. For example, [34] parameterizes the prior based on the posterior inference model. [5, 9] adopt a two-stage approach which first trains a latent variable model with simple prior and then trains a separate prior model (e.g., VAE or Gaussian mixture model) to match the aggregated posterior distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.688 + ], + "angle": 0, + "content": "Generator model with hierarchical structures. The generator models that consist of multi-layers of latent variables are recently attracting attention for hierarchical learning. [29, 2, 21, 3, 36] stack generative models on top of each other and assume conditional Gaussian distributions at different layers. However, as shown in Sec. 2.1, the bottom layer could act as a single generative model and absorb most features, leading to ineffective representation learning. [42, 20] propose to learn hierarchical features with unit Gaussian prior by adapting the generator into multiple layers. However, the latent variables at different layers are distributed independently a priori and are only loosely connected. Instead, we propose a joint EBM prior that could tightly couple and jointly model latent variables at different layers and show superior results through joint training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Hierarchical generator model with informative prior. Recent advances [4, 1] have started exploring learning informative prior for multi-layer generator models. JEBM [4] and NCP-VAE [1] build latent space EBM on hierarchical generator models and showcase the capability of improving the generation quality. However, these models consider the conditional hierarchical models, which can be limited in learning effective hierarchical representations (see Sec. 2.1). This work studies hierarchical representation learning by introducing a novel framework where latent space EBM can be jointly trained with the architectural hierarchical models to capture complex representations of different levels." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2222" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.088, + 0.287, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.088, + 0.481, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.089, + 0.678, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.089, + 0.871, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.894, + 0.278 + ], + "angle": 0, + "content": "Figure 4. Hierarchical sampling on SVHN. Left: The latent code at bottom layer \\((z_{1})\\) represents the background light and shading. Center-left: the latent code at second bottom layer \\((z_{2})\\) represents the color schemes. Center-right: the latent code at second top layer \\((z_{3})\\) encodes the shape variations of the same digit. Right: the latent code at top layer \\((z_{4})\\) captures the digit identity and the general structure." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.3, + 0.449, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.39, + 0.471, + 0.46 + ], + "angle": 0, + "content": "Figure 5. Hierarchical sampling on MNIST. Left: The latent code at bottom layer \\((z_{1})\\) indicates the stroke width. Center: the latent code at second layer \\((z_{2})\\) encodes geometric changes among similar digits. Right: the latent code at top layer \\((z_{3})\\) learns the digit identity and general structure." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.486, + 0.21, + 0.503 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.47, + 0.618 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of our method, we conduct the following experiments: 1) hierarchical representation learning, 2) analysis of latent space, 3) image modelling, and 4) robustness. For a better understanding of the proposed method, we perform the disentanglement learning experiment, various ablation studies, and an analysis of parameter complexity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.632, + 0.407, + 0.649 + ], + "angle": 0, + "content": "5.1. Hierarchical Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.469, + 0.701 + ], + "angle": 0, + "content": "We first demonstrate the capability of our model in hierarchical representation learning by experiments of hierarchical sampling and latent classifier." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.884 + ], + "angle": 0, + "content": "Hierarchical sampling. With partitioned latent variables and the hierarchical structure of generator, the latent variables at higher layers should capture semantic features, while the lower layers should capture low-level features. We train our model on MNIST using the same setting as in Sec. 2.2 with only '0', '1', and '2' digit classes available and the latent dimension set to 2. In Fig. 6, by changing the \\( \\mathbf{z}_1 \\) (at the bottom layer), our model can successfully deliver the variations in shape (low-level features), and changing the \\( \\mathbf{z}_2 \\) (at the top layer) leads to the variations in digit class (high-level features). This indicates a successfully learned hierarchical representation." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Further, we train our model on MNIST with all digit" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.302, + 0.886, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.373, + 0.892, + 0.428 + ], + "angle": 0, + "content": "Figure 6. Visualization for our model by changing each unit of 2-dimensional z. Left: changing the first unit. Right: changing the second unit. Top: the value of each unit, where the orange color indicates the first unit and the blue color indicates the second unit." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.892, + 0.528 + ], + "angle": 0, + "content": "classes and the more challenging SVHN dataset, and we generate the images by sampling (using Eq. 13) the latent code of one layer while keeping other layers fixed. The results shown in Fig. 4 and Fig. 5 also demonstrate the hierarchical representation learned by our model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.893, + 0.695 + ], + "angle": 0, + "content": "Latent Classifier. We next show that our model can achieve better performance in hierarchical representation learning. Note that the inference model \\( q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\) should be learned to approximate the true posterior \\( p_{\\theta}(\\mathbf{z}|\\mathbf{x}) \\) of the generator, which integrates both the hierarchical inductive bias and the energy-based refinement. Therefore, to measure the learned hierarchical features, we learn classifiers on the inferred latent codes at different layers to predict the label of the data and measure the testing classification accuracy. The latent codes that carry rich high-level semantic features should achieve higher classification accuracy." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.707, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Table 1. Testing accuracy of inferred latent codes at each layer. We denote \\((\\downarrow)\\) for the layer that has unexpectedly lower accuracy." + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.735, + 0.878, + 0.825 + ], + "angle": 0, + "content": "
L=1L=2L=3L=4
MNISTOurs32.60%58.32%67.64%-
VLAE35.69%57.86%52.08% (↓)-
Fashion-MNISTOurs39.27%44.81%84.27%-
VLAE52.43%35.65% (↓)83.24%-
SVHNOurs21.00%25.29%30.58%86.63%
VLAE22.59%26.97%56.70%52.14% (↓)
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In practice, we first train our model on standard benchmarks, such as MNIST, Fashion-MNIST, and SVHN. Then, we train classifiers on the inferred latent codes at each layer. We consider VLAE [42] as our baseline model, which" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2223" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.289 + ], + "angle": 0, + "content": "learns a structural latent space with standard Gaussian prior. We show comparison results in Tab. 1, where our learned inference model \\( q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\) extracts varying levels of semantic features for different layers of latent codes. The top layer carries the most significant features, and the bottom layer carries the least. The baseline model that assumes Gaussian prior, however, extracted mixed semantic features across different layers. For fair comparisons, we use the same generation and inference structure as the baseline model2. The structure of the classifier contains two linear layers with a hidden dimension set to 256 and uses ReLU activation function. The classifier has softmax as its output layer. We do not employ drop-out and normalization strategies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.304, + 0.245, + 0.32 + ], + "angle": 0, + "content": "5.2. Image Modelling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.482 + ], + "angle": 0, + "content": "In this section, we evaluate our model in image modelling by measuring the quality of generated and reconstructed images. We consider the baseline models that assume Gaussian prior, such as Alternating Back-propagation (ABP) [14], Ladder-VAE (LVAE) [30], BIVA [21], Short-run MCMC (SRI) [25], and VLAE [42], as well as generator models with informative prior, such as RAE [9], Two-stages VAE (2s-VAE) [5], NCP-VAE [1], Multi-NCP [37] and LEBM [26]. To make fair comparisons, we follow the protocol in [26]." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.497, + 0.469, + 0.524 + ], + "angle": 0, + "content": "Table 2. Testing reconstruction by MSE, and generation evaluation by FID on SVHN and CelebA-64." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.524, + 0.455, + 0.729 + ], + "angle": 0, + "content": "
ModelSVHNCelebA-64
MSE (↓)FID (↓)MSE (↓)FID (↓)
ABP-49.71-51.50
LVAE0.01439.260.02853.40
BIVA0.01031.650.01033.58
SRI0.01135.230.01136.84
VLAE0.01643.950.01044.05
2s-VAE0.01942.810.02144.40
RAE0.01440.020.01840.95
NCP-VAE0.02033.230.02142.07
Multi-NCP0.00426.190.00935.38
LEBM0.00829.440.01337.87
Ours0.00824.160.00432.15
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Synthesis: We use Fréchet Inception Distance (FID) [16] to quantitatively evaluate the sample quality. In Tab. 2, it can be seen that our model obtains superior generation quality compared to the baseline models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.871 + ], + "angle": 0, + "content": "Reconstructions: To evaluate the accuracy of our inference model, we compute mean square error (MSE) [26, 24] for testing reconstruction. As shown in Tab. 2, the proposed model leads to more accurate and faithful reconstructions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.727, + 0.108 + ], + "angle": 0, + "content": "5.3. Analysis of Latent Space" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.894, + 0.236 + ], + "angle": 0, + "content": "Visualization of toy data. To illustrate the expressivity of the proposed EBM prior, we train our model on MNIST (using the same setting as shown in Fig. 2 and Fig. 6) and set the latent dimension for both \\(\\mathbf{z}_1\\) and \\(\\mathbf{z}_2\\) to 2 for better visualization. We visualized the Langevin transition of the prior sampling in Fig. 7, which shows that the latent codes at the top layer \\((\\mathbf{z}_2)\\) can effectively capture the multi-modal posterior, where using a Gaussian prior might be infeasible." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.248, + 0.87, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.36, + 0.892, + 0.403 + ], + "angle": 0, + "content": "Figure 7. Visualization of the latent codes sampled from our EBM prior (Top row: \\(\\mathbf{z}_2\\)). Blue, Orange color indicate prior and posterior, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.893, + 0.644 + ], + "angle": 0, + "content": "Langevin trajectory. We explore the energy landscape of the learned prior \\( p_{\\alpha}(\\mathbf{z}) \\) via transition of Langevin dynamics initialized from \\( p_0(\\mathbf{z}) \\) towards \\( p_{\\alpha}(\\mathbf{z}) \\) on CelebA-64. If the EBM is well-learned, the energy prior should render local modes of the energy function, and traversing these local modes should present diverse, realistic image synthesis and steady-state energy scores. Existing EBMs often suffer from oversaturated synthesis via the challenging long-run Langevin dynamic (see oversaturated example in Fig.3 in [23]). We thereby test our model with 2500 Langevin steps, which is much longer than the 40 steps used in training. Fig. 8 shows the image synthesis and energy profile, where our EBM prior model does not exhibit the oversaturated phenomenon and successfully delivers diverse and realistic synthesis with steady-state energy." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.656, + 0.89, + 0.748 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Figure 8. Transition of Markov chains initialized from \\( p_0(\\mathbf{z}) \\) towards \\( p_{\\alpha}(\\mathbf{z}) \\) for 2500 steps. Top: Trajectory in the CelebA-64 data space for every 100 steps. Bottom: Energy profile over time." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.625, + 0.832 + ], + "angle": 0, + "content": "5.4. Robustness" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.87 + ], + "angle": 0, + "content": "In this section, we examine the robustness of our model in adversarial attack and outlier detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Adversarial robustness. For adversarial robustness, we consider the latent attack [10], which is shown to be a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.887, + 0.442, + 0.901 + ], + "angle": 0, + "content": "\\(^{2}\\)https://github.com/ermongroup/Variational-Ladder-Autoencoder" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2224" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "strong attack for the generative model with latent variables, and it allows us to attack the latent codes at different layers. Specifically, let \\(\\mathbf{x}_t\\) be the target and \\(\\mathbf{x}_o\\) be the original image. The attack aims to create the distorted image \\(\\tilde{\\mathbf{x}} = \\mathbf{x}_o + \\epsilon\\) such that its learned inference distribution \\(q_{\\phi}(\\mathbf{z}|\\tilde{\\mathbf{x}})\\) is close to the inference \\(q_{\\phi}(\\mathbf{z}|\\mathbf{x}_t)\\) on target images under KL-divergence (Eq. 5 in [10])." + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.208, + 0.452, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.47, + 0.3 + ], + "angle": 0, + "content": "Figure 9. Adversarial latent attack on different layers. The leftmost figure indicates the bottom layer, and the rightmost figure indicates the top layer. 1st col: original image. 2nd col: target image. 3rd col: adversarial example. 4th col: reconstruction of adversarial example." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.47, + 0.487 + ], + "angle": 0, + "content": "We illustrate the adversarial attack on different layers in Fig. 9. The learned inference model \\( q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\) carries different levels of semantics for different layers. The adversarial example created by attacking latent codes at the bottom layer only perturbs the data along low-level features direction from the target image; hence, the model can be robust and have faithful reconstruction from adversarial examples. The adversarial example coming from the top-layer attack can distort the original data along a high-level semantic direction from the target image, thus, the reconstruction from the adversarial example can be substantially different from the original data, indicating a successful attack." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.471, + 0.713 + ], + "angle": 0, + "content": "Anomaly detection. We also evaluate the model on anomaly detection. If the model is well-learned, the inference model \\( q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\) should form an informative latent space that separates anomalies from the normal data. Following the protocols in [18, 26], we take latent samples from the learned inference model and use the unnormalized log-posterior \\( \\log p_{\\theta}(\\mathbf{x},\\mathbf{z}) \\) as our decision function to detect anomaly on MNIST. Only one digit class is held-out as an anomaly in training, while both normal and anomalous data are used for testing. We compare baseline models such as BiGAN-\\( \\sigma \\) [41], MEG [18], LEBM [26], HVAE and VAE using area under the precision-recall curve (AUPRC). The results of baseline models are provided by [26], and we use \\( L^{>0} \\) [15] as the decision function for HVAE model. Tab. 3 shows the result." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.761 + ], + "angle": 0, + "content": "Table 3. AUPRC scores for unsupervised anomaly detection on MNIST. Following the protocol of [26], we average the results over last 10 epochs to account for variance." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.761, + 0.469, + 0.824 + ], + "angle": 0, + "content": "
hold-out digit14579
VAE0.0630.3370.3250.1480.104
HVAE0.494 ± 0.0040.920 ± 0.0040.913 ± 0.0030.680 ± 0.0060.791 ± 0.008
MEG0.281 ± 0.0350.401 ± 0.0610.402 ± 0.0620.290 ± 0.0400.342 ± 0.034
BiGAN-σ0.287 ± 0.0230.443 ± 0.0290.514 ± 0.0290.347 ± 0.0170.307 ± 0.028
Latent EBM0.336 ± 0.0080.630 ± 0.0170.619 ± 0.0130.463 ± 0.0090.413 ± 0.010
Ours0.722 ± 0.0100.949 ± 0.0020.980 ± 0.0010.941 ± 0.0030.935 ± 0.003
" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.241, + 0.863 + ], + "angle": 0, + "content": "5.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The proposed expressive prior model enables complex data representations to be effectively captured, which in turn" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "improves the expressivity of the whole model in generating high-quality synthesis. To better understand the influence of the proposed method, we conduct ablation studies, including 1) MCMC steps, 2) complexity of EBM, and 3) other image datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.258 + ], + "angle": 0, + "content": "MCMC steps: We examine the influence of steps of short-run MCMC for prior sampling. Tab. 4 shows that increasing steps could result in a better quality of generation. Increasing the step number from 15 to 60 could result in a significant improvement in synthesis quality, while exhibiting only minor influence when increased beyond 60." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.267, + 0.874, + 0.28 + ], + "angle": 0, + "content": "Table 4. Varying \\( k \\) (steps number) of our model on CelebA-64." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.28, + 0.848, + 0.308 + ], + "angle": 0, + "content": "
k=15k=30k=60k=150k=300
FID56.4239.8932.1531.2030.78
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Complexity of EBM: We further examine the influence of model parameters of EBM. The energy function is parameterized by a 2-layer perceptron. We fix the number of layers and increase the hidden units of EBM. As shown in Tab. 5, increasing the hidden units of EBM results in better performance." + }, + { + "type": "table_caption", + "bbox": [ + 0.522, + 0.418, + 0.869, + 0.431 + ], + "angle": 0, + "content": "Table 5. Increasing hidden units (denoted as nef) of EBM." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.431, + 0.879, + 0.459 + ], + "angle": 0, + "content": "
nefnef=0nef=10nef=20nef=50nef=100
FID43.9541.7233.1030.4224.16
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.892, + 0.509 + ], + "angle": 0, + "content": "Other image datasets: We test the scalability of our model on high-resolution image dataset, such as CelebA-128. We show the image synthesis in Fig. 10." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.519, + 0.888, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.575, + 0.856, + 0.588 + ], + "angle": 0, + "content": "Figure 10. Generated image synthesis on CelebA-128" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.641 + ], + "angle": 0, + "content": "We also train our model on CIFAR-10 (32x32) and report the FID score for generation quality in Tab. 6, in which our model performs well compared to baseline models." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.649, + 0.848, + 0.686 + ], + "angle": 0, + "content": "
Table 6. FID on CIFAR-10
Ours2s-VAERAENCP-VAEMulti-NCPLEBM
63.4272.9074.1678.0665.0170.15
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.619, + 0.725 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In this paper, we propose to build a joint latent space EBM with hierarchical structures for better hierarchical representation learning. Our joint EBM prior is expressive in modelling the inter-layer relation among multiple layers of latent variables, which in turn enables different levels of data representations to be effectively captured. We develop an efficient variational learning scheme and conduct various experiments to demonstrate the capability of our model in hierarchical representation learning and image modelling. For future work, we shall explore learning the hierarchical representations from other domains, such as videos and texts." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2225" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Jyoti Aneja, Alex Schwing, Jan Kautz, and Arash Vahdat. A contrastive learning approach for training variational autoencoder priors. Advances in neural information processing systems, 34:480-493, 2021. 2, 5, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.47, + 0.214 + ], + "angle": 0, + "content": "[2] Philip Bachman. An architecture for deep, hierarchical generative models. 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Learning hierarchical features from generative models. arXiv preprint arXiv:1702.08396, 2017. 1, 3, 5, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.093, + 0.469, + 0.785 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2227" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_origin.pdf b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5609de0df4f051b5ca659c170177cac3b7cf4237 --- /dev/null +++ b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/240d7938-e848-4274-a9c2-b84ff0fe9ab2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ddc1c420bcaf23101931c5038fa492403fb528230e5779551dcdbf8b946880f1 +size 1706942 diff --git a/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/full.md b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8cda152a3020d1a5b112565fdb07612fa1a9d861 --- /dev/null +++ b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/full.md @@ -0,0 +1,445 @@ +# Learning Hierarchical Features with Joint Latent Space Energy-Based Prior + +Jiali Cui $^{1}$ , Ying Nian Wu $^{2}$ , Tian Han $^{1}$ \ + $^{1}$ Department of Computer Science, Stevens Institute of Technology\ + $^{2}$ Department of Statistics, University of California, Los Angeles\ +{jcui7,than6}@stevens.edu, ywu@stat.ucla.edu + +# Abstract + +This paper studies the fundamental problem of multilayer generator models in learning hierarchical representations. The multi-layer generator model that consists of multiple layers of latent variables organized in a top-down architecture tends to learn multiple levels of data abstraction. However, such multi-layer latent variables are typically parameterized to be Gaussian, which can be less informative in capturing complex abstractions, resulting in limited success in hierarchical representation learning. On the other hand, the energy-based (EBM) prior is known to be expressive in capturing the data regularities, but it often lacks the hierarchical structure to capture different levels of hierarchical representations. In this paper, we propose a joint latent space EBM prior model with multi-layer latent variables for effective hierarchical representation learning. We develop a variational joint learning scheme that seamlessly integrates an inference model for efficient inference. Our experiments demonstrate that the proposed joint EBM prior is effective and expressive in capturing hierarchical representations and modelling data distribution. + +# 1. Introduction + +In recent years, deep generative models have achieved remarkable success in generating high-quality images [36, 31], texts [40, 13], and videos [28, 35]. However, learning generative models that incorporate hierarchical structures still remains a challenge. Such hierarchical generative models can play a critical role in enabling explainable artificial intelligence, thus representing an important area of ongoing research. + +To tackle this challenge, various methods of learning hierarchical representations have been explored [30, 42, 21, 3, 30]. These methods learn generative models with multiple layers of latent variables organized in a top-down ar + +chitecture, which have shown the capability of learning increasingly abstract representations (e.g., general structures, classes) at the top layers while capturing low-level data features (e.g., colors, background) at the bottom layers. In general, one could categorize these methods into two classes: (i) conditional hierarchy and (ii) architectural hierarchy. + +The conditional hierarchies [30, 12, 25, 21, 3] employ stacked generative models layered on top of one another and assume conditional Gaussian distributions at different layers, while the architectural hierarchies [42, 20] instead leverage network architecture to place high-level representations at the top layers of latent variables and low-level representations at the bottom layers. However, they typically assume conditional Gaussian distribution or isotropic Gaussian as the prior, which could have limited expressivity [26]. Learning a more expressive and informative prior model for multiple layers of latent variables is thus needed. + +The energy-based models (EBMs) [19, 39, 7, 24, 26, 4], on the other hand, are shown to be expressive and proved to be powerful in capturing data regularities. Notably, [26] studies the EBM in the latent space, where the energy function is considered as a correction of the non-informative prior and tilts the non-informative prior to a more expressive prior distribution. The low dimensionality of the latent space makes EBM more effective in capturing regularities in the data. However, prior methods often rely on expensive MCMC methods for posterior sampling of the latent variables, and more importantly, the latent variables are not hierarchically organized, making it difficult to capture data variations at different levels. + +In this paper, we propose to combine the strengths of latent space EBM and the multi-layer generator model for effective hierarchical representation learning. In particular, we build the EBM on the latent variables across different layers of the generator model, where the latent variables at different layers are concatenated and modelled jointly. The latent variables at different layers capture different levels of information from the data via the hierarchy of the generative model, and their inter-relations are further tightened up and better captured through EBM in joint latent space. + +Learning the EBM in the latent space can be challenging since it usually requires MCMC sampling for both the prior and posterior distributions of the latent variables. The prior sampling is efficient with the low dimensionality of the latent space and the lightweight network of the energy function, while the MCMC sampling of posterior distribution requires the backward propagation of generation network, which is usually heavy and thus renders inefficient inference. To ensure efficient inference, we introduce an inference model and develop a joint training scheme to efficiently and effectively learn the latent space EBM and multi-layer generator model. In particular, the inference model aims to approximate the exact posterior of the multi-layer latent variables while also serving to extract levels of data variations through the deep feed-forward inference network to facilitate hierarchical learning. + +Contributions: 1) We propose the joint EBM prior model for hierarchical generator models with multiple layers of latent variables; 2) We develop a variational training scheme for efficient learning and inference; 3) We provide strong empirical results on hierarchical learning and image modeling, as well as various ablation studies to illustrate the effectiveness of the proposed model. + +# 2. Background + +In this section, we present the background of multi-layer generator models and the latent space EBM, which will serve as the foundation of the proposed model. + +# 2.1. Multi-layer generator models + +Let $\mathbf{x} \in \mathbb{R}^D$ represent the high-dimensional observed examples, and $\mathbf{z} \in \mathbb{R}^d$ denote the low-dimensional latent variables. The multi-layer generator model [30, 36, 21] consists of multiple layers of latent variables that are organized in a top-down hierarchical structure and modelled to be conditionally dependent on its upper layer, i.e., $p_{\theta}(\mathbf{z}) = \prod_{i=1}^{L-1} p_{\theta_i}(\mathbf{z}_i | \mathbf{z}_{i+1}) p_0(\mathbf{z}_L)$ , where $p_{\theta_i}(\mathbf{z}_i | \mathbf{z}_{i+1}) \sim \mathcal{N}(\mu_{\theta_i}(\mathbf{z}_{i+1}), \sigma_{\theta_i}(\mathbf{z}_{i+1}))$ and $p_0(\mathbf{z}_L) \sim \mathcal{N}(0, I)$ . Although such a modelling strategy has seen significant improvement in data density estimation, it can be less effective in learning hierarchical representations. + +To demonstrate, we train BIVA [21] on MNIST with 6 layers of latent variables and conduct hierarchical sampling by generating latent variables via the repamaramization trick, i.e., $\mathbf{z}_i = \mu_{\theta_i}(\mathbf{z}_{i + 1}) + \sigma_{\theta_i}(\mathbf{z}_{i + 1})\cdot \epsilon_i$ where $\epsilon_{i}$ is the added Gaussian noise. Specifically, the latent variables are generated by randomly sampling $\epsilon_{i}$ for the $i$ -th layer, while fixing $\epsilon_{j\neq i}$ for other layers, and the corresponding image synthesis should deliver the variation of representation learned by $\mathbf{z}_i$ . We show the results in Fig. 1, where the major semantic variation is only captured by the top layer + +of the latent variables, suggesting an ineffective hierarchical representation learned (compare with our model shown in Fig. 5). + +![](images/6f930224014083ecd13826e158c27fb2ce417d91e8e94836098ed0504bb9e331.jpg) +Figure 1. Visualization of hierarchical representations on BIVA. Left: sampling $\epsilon_{1},\epsilon_{2}$ for bottom layers. Middle: sampling $\epsilon_{3},\epsilon_{4}$ for middle layers. Right: sampling $\epsilon_{5},\epsilon_{6}$ for top layers. + +![](images/b58084dafd71d4b841e184de98769797bff9e0e917e8df57c3b0a79f3150c26e.jpg) + +![](images/560d7740960843b959c50fb268c573692d2e62ebb53d4628ce4dd10449fefe3b.jpg) + +# 2.2. Latent space EBM + +The energy-based models (EBMs) [7, 6, 24, 8, 38] present a flexible and appealing way for data modelling and are known for being expressive and powerful in capturing data regularities. Albeit their expressivity, learning the EBM on high-dimensional $\mathbf{x}$ -space can be challenging since the energy function needs to support the entire data space. As such, another line of works [26, 1, 37] seek to build EBM on low-dimensional $\mathbf{z}$ -space with the probability density defined as + +$$ +p _ {\theta} (\mathbf {z}) = \frac {1}{\mathbb {Z} (\theta)} \exp \left[ f _ {\theta} (\mathbf {z}) \right] p _ {0} (\mathbf {z}) \tag {1} +$$ + +However, with a single-layer non-hierarchical $\mathbf{z}$ -space, it is typically infeasible to capture the data abstraction of different levels. To see this, we pick up the digit classes '0', '1', and '2' of the MNIST dataset, on which we train LEBM [26] with the latent dimension set to be 2. We show in Fig. 2 that changing the value of each latent unit could lead to a mixed variations in digit shape and class (compare to our proposed method in Fig. 6). + +![](images/3f61d13b300cf47d325a220a38d7e525400835b8561d0b4dcad7b2d5b719d9e6.jpg) +Figure 2. Visualization for latent space EBM [26] by changing each unit of 2-dimensional z. Left: changing the first unit. Right: changing the second unit. Top: the value of each unit, where the orange color indicates the first unit and the blue color indicates the second unit. + +# 3. Methodology + +In this paper, we study a joint latent space EBM prior where latent variables are partitioned into multiple groups but modelled jointly for hierarchical representation learning. To ensure efficient inference, we introduce an inference model to approximate the generator posterior and develop a variational joint training scheme in which each model can be trained efficiently and effectively. + +# 3.1. Latent variable generative model + +A latent variable generative model (i.e., generator model) can be specified using joint distribution: + +$$ +p _ {\beta , \alpha} (\mathbf {x}, \mathbf {z}) = p _ {\beta} (\mathbf {x} | \mathbf {z}) p _ {\alpha} (\mathbf {z}) \tag {2} +$$ + +which consists of the generation model $p_{\beta}(\mathbf{x}|\mathbf{z})$ and the prior model $p_{\alpha}(\mathbf{z})$ . + +Joint latent space EBM: The prior model $p_{\alpha}(\mathbf{z})$ is usually assumed to be single-layer, which can be infeasible for learning hierarchical representations (see Sec. 2.2). In this work, we propose a joint latent space EBM prior, where latent variables are separated into multiple groups, i.e., $\mathbf{z} = [\mathbf{z}_1,\mathbf{z}_2,\dots ,\mathbf{z}_L]$ , and our EBM prior model is defined as + +$$ +p _ {\alpha} (\mathbf {z}) = \frac {1}{\mathbb {Z} (\alpha)} \exp \left[ f _ {\alpha} \left(\left[ \mathbf {z} _ {1}, \dots , \mathbf {z} _ {L} \right]\right) \right] p _ {0} \left(\left[ \mathbf {z} _ {1}, \dots , \mathbf {z} _ {L} \right]\right) \tag {3} +$$ + +where $[.]$ refers to the concatenation. $f_{\alpha}(.)$ is the negative energy function that can be parameterized by a small multilayer perceptron with the parameters $\alpha, p_0([\dots])$ is a reference distribution assumed to be a unit Gaussian, and $\mathbb{Z}(\alpha)$ is the normalizing constant or partition function. Such a prior model can be considered as an energy-based refinement of the non-informative reference distribution, thus the relationship between different groups of latent codes can be well captured via the energy function $f_{\alpha}([\mathbf{z}_1,\ldots ,\mathbf{z}_L])]$ . + +For notation simplicity, we denote $\mathbf{z} = [\mathbf{z}_1,\dots ,\mathbf{z}_L]$ in subsequent discussions. + +Generation Model. The generation model is defined as + +$$ +p _ {\beta} (\mathbf {x} \mid \mathbf {z}) \sim \mathcal {N} \left(g _ {\beta} (\mathbf {z}), \sigma^ {2} I _ {D}\right) \tag {4} +$$ + +which models the observed data using top-down generator network $g_{\beta}(\mathbf{z})$ with additive Gaussian noise, i.e., $\mathbf{x} = g_{\beta}(\mathbf{z}) + \epsilon, \epsilon \sim \mathcal{N}(0, \sigma^2 I_D)$ . To facilitate the hierarchical representation learning with multi-layer latent variables, we consider multi-layer hierarchical generator network $g_{\beta} (= \{g_1, g_2, \ldots, g_L\})$ that is designed to explain the observation $\mathbf{x}$ by integrating data representation from the above layers, i.e., + +$$ +h _ {L} = g _ {L} (\mathbf {z} _ {L}) +$$ + +$$ +h _ {i} = g _ {i} \left(\left[ \mathbf {z} _ {i}, h _ {i + 1} \right]\right), i = 1, 2, \dots , L - 1 \tag {5} +$$ + +$$ +\mathbf {x} \sim \mathcal {N} (h _ {1}, \sigma^ {2} I _ {D}) +$$ + +in which $\mathbf{z}_L$ is at the top layer, and $g_{i}$ is a shallow network that decodes latent code $\mathbf{z}_i$ while integrating features from the upper layer. + +Joint EBM prior vs. independent Gaussian prior: With such a multi-layer hierarchical generation model, it is also tempting to consider learning with the unit Gaussian prior, i.e., $p(\mathbf{z}) \sim \mathcal{N}(0, I_d)$ . Such a prior choice is adopted in + +![](images/14cdd146837521465e947bedad9458928b9cf3801129e918fb48c085b47db360.jpg) +Figure 3. The illustration of the proposed joint EBM prior model (Left). Red lines indicate the modelling of intra-layer relation, and blue lines indicate inter-layer relation. Compared to the Gaussian prior model and single-layer LEBM, our prior model is expressive and effective in learning hierarchical representations. + +[42, 20] and has seen some success in learning hierarchical features. However, the independent Gaussian prior does not account for the relations between levels of representations and can be less expressive in capturing complex data features. The proposed EBM prior is expressive and can couple the latent variables across different layers within a joint modelling framework. + +Our model is illustrated in the left panel of Fig. 3. + +# 3.2. Variational learning scheme + +Suppose we have observed examples $(\mathbf{x}_i, i = 1, \dots, n)$ that come from (true) data distribution $p_{\mathrm{data}}(\mathbf{x})$ and denote $\theta = (\beta, \alpha)$ that collects all parameters from the generator model. Learning the generator model can be done by maximizing the log-likelihood of all observed examples as + +$$ +\sum_ {i = 1} ^ {n} \log p _ {\theta} (\mathbf {x} _ {i}) = \sum_ {i = 1} ^ {n} \log \int p _ {\alpha} (\mathbf {z}) p _ {\beta} (\mathbf {x} _ {i} | \mathbf {z}) d \mathbf {z} \tag {6} +$$ + +When $n$ becomes sufficiently large, maximizing the above log-likelihood is equivalent to minimizing the Kullback-Leibler (KL) divergence between the model distribution and data distribution, i.e., $\min_{\theta} D_{\mathrm{KL}}(p_{\mathrm{data}}(\mathbf{x})||p_{\theta}(\mathbf{x}))$ . + +However, directly maximizing Eq. 6 can be challenging, as the inference of generator posterior (by chain rule, $p_{\theta}(\mathbf{z}|\mathbf{x}) = p_{\theta}(\mathbf{x},\mathbf{z}) / p_{\theta}(\mathbf{x}))$ is typically intractable. To tackle the challenge, we employ an inference model $q_{\phi}(\mathbf{z}|\mathbf{x})$ with a separate set of parameters $\phi$ to approximate the generator posterior. + +Inference model: The inference model maps from data space to latent space and is typically assumed to be Gaussian distributed, + +$$ +q _ {\phi} (\mathbf {z} | \mathbf {x}) \sim \mathcal {N} \left(\mu_ {\phi} (\mathbf {x}), V _ {\phi} (\mathbf {x})\right) \tag {7} +$$ + +where $\mu_{\phi}(\mathbf{x})$ and $V_{\phi}(\mathbf{x})$ are the d-dimensional mean vector and diagonal covariance matrix. To match with the hierar + +chical generator model and facilitate the hierarchical representation learning, we consider the multi-layer inference model defined as + +$$ +r _ {1} = h _ {1} (\mathbf {x}) +$$ + +$$ +r _ {i} = h _ {i} \left(r _ {i - 1}\right) i = 2, 3, \dots , L \tag {8} +$$ + +$$ +\mathbf {z} _ {i} \sim \mathcal {N} (\mu_ {i} (r _ {i}), V _ {i} (r _ {i})) +$$ + +where $\mathbf{z}_L$ is the inferred latent code at the top layer and $\mathbf{z}_1$ is the inferred bottom layer latent code. Each latent code $\mathbf{z}_i$ can be inferred and sampled through reparametrization trick [17] using $\mathbf{z}_i = \mu_i(r_i) + V_i(r_i)^{1/2}\epsilon$ where $\epsilon \sim \mathcal{N}(0, I_{d_i})$ , with $d_i$ being the dimensionality of $z_i$ . + +Variational learning: We show that the proposed generator model and the inference model can be naturally unified and jointly trained within a variational learning scheme. + +Specifically, we can define two joint densities, one for generator model density, i.e., $p_{\theta}(\mathbf{x}, \mathbf{z}) = p_{\alpha}(\mathbf{z})p_{\beta}(\mathbf{x}|\mathbf{z})$ , and one for data density, i.e., $q_{\phi}(\mathbf{x}, \mathbf{z}) = p_{\mathrm{data}}(\mathbf{x})q_{\phi}(\mathbf{z}|\mathbf{x})$ . We propose joint learning through KL minimization, and we denote the objective to be $L(\theta, \phi)$ , i.e., + +$$ +\min _ {\theta} \min _ {\phi} L (\theta , \phi) = \min _ {\theta} \min _ {\phi} D _ {\mathrm {K L}} \left(q _ {\phi} (\mathbf {x}, \mathbf {z}) | | p _ {\theta} (\mathbf {x}, \mathbf {z})\right) \tag {9} +$$ + +where the generator model density is learned to match the true joint data density and capture extracted hierarchical features. + +Learning $p_{\alpha}(\mathbf{z})$ : With this joint KL minimization, the prior model can be learned with the gradient $-\nabla_{\alpha}L(\theta ,\phi)$ + +$$ +\mathbb {E} _ {q _ {\phi} (\mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L} | \mathbf {x})} [ \nabla_ {\alpha} f _ {\alpha} ([ \mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L} ]) ] - +$$ + +$$ +\mathbb {E} _ {p _ {\alpha} \left(\mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L}\right)} \left[ \nabla_ {\alpha} f _ {\alpha} \left(\left[ \mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L} \right]\right) \right] \tag {10} +$$ + +Learning $p_{\beta}(\mathbf{x}|\mathbf{z})$ : The generation model can be learned with the gradient $-\nabla_{\beta}L(\theta ,\phi)$ computed as + +$$ +\mathbb {E} _ {q _ {\phi} \left(\mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L} \mid \mathbf {x}\right)} \left[ \nabla_ {\beta} \log p _ {\beta} \left(\mathbf {x} \mid \mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L}\right) \right] \tag {11} +$$ + +Learning $q_{\phi}(\mathbf{z}|\mathbf{x})$ : The inference model can be learned by computing the gradient $-\nabla_{\phi}L(\theta ,\phi)$ as + +$$ +\nabla_ {\phi} \mathbb {E} _ {q _ {\phi} (\mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L} | \mathbf {x})} [ \log p _ {\beta} (\mathbf {x} | \mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L}) ] - \tag {12} +$$ + +$$ +\nabla_ {\phi} D _ {\mathrm {K L}} \left(q _ {\phi} \left(\mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L} \mid \mathbf {x}\right) \mid \mid p _ {\alpha} \left(\mathbf {z} _ {1}, \mathbf {z} _ {2}, \dots , \mathbf {z} _ {L}\right)\right) +$$ + +We provide further theoretical understanding in Sec. 3.4. + +# 3.3. Prior sampling + +Training the proposed joint EBM prior model requires sampling $\mathbf{z}_1, \mathbf{z}_2, \ldots, \mathbf{z}_L$ from the proposed EBM prior (see Eq. 10). To do so, we can use Langevin dynamic [22]. + +For arbitrary target distribution $p(\mathbf{z})$ , the Langevin dynamic iterates: + +$$ +\mathbf {z} _ {t + 1} = \mathbf {z} _ {t} + \frac {s ^ {2}}{2} \nabla_ {\mathbf {z}} \log p (\mathbf {z} _ {t}) + s \epsilon_ {t} \tag {13} +$$ + +where $t$ indexes the time step of Langevin dynamics. $s$ is the step size and $\epsilon_t\sim \mathcal{N}(0,I_d)$ . We run the noise-initialized Langevin dynamics for $K$ steps. Noted that as $s\to 0$ , and $K\rightarrow \infty$ , the distribution of $\mathbf{z}_t$ will converge to the target $p(\mathbf{z})$ regardless of the initial distribution of $\mathbf{z}_0$ [22]. + +Specifically, for prior sampling, we use the prior distribution $p_{\alpha}(\mathbf{z})$ as our target distribution, and the gradient $\nabla_{\mathbf{z}}\log p_{\alpha}(\mathbf{z})$ is computed as: + +$$ +\nabla_ {\mathbf {z}} f _ {\alpha} \left(\left[ \mathbf {z} _ {1}, \dots , \mathbf {z} _ {L} \right]\right) + \nabla_ {\mathbf {z}} \log p _ {0} \left(\left[ \mathbf {z} _ {1}, \dots , \mathbf {z} _ {L} \right]\right) \tag {14} +$$ + +The Langevin dynamics for prior sampling can be efficient due to the low-dimensional latent space and the lightweight network structure for the energy function. + +The overall procedure is summarized in Algorithm 1. + +Algorithm 1 Learning latent EBM prior for hierarchical generator model + +Input: Training iterations $T$ , observed training examples $\{x_{i}\}_{i = 1}^{n}$ , batch size $m$ , network parameters $\alpha, \beta, \phi$ , learning rate $\eta_{\alpha}, \eta_{\beta}, \eta_{\phi}$ , Langevin steps $K$ , Langevin step size $s$ , + +Let $t = 0$ and $\theta = (\alpha, \beta)$ ; + +repeat + +Prior sampling for $\{z_i^{-}\}_{i = 1}^m$ using Eq. 13 and Eq. 14 with $K$ and $s$ . + +Inference sampling for $\{z_i^+\}_{i=1}^m$ using Eq. 8 with $\{x_i\}_{i=1}^m$ and reparametrization. + +Learn joint EBM prior: Given $\{z_i^-, z_i^+\}_{i=1}^m$ , update $\alpha = \alpha - \eta_\alpha \nabla_\alpha L(\theta, \phi)$ using Eq. 10 with $\eta_\alpha$ + +Learn generation model:Given $\{x_{i},z_{i}^{+}\}_{i = 1}^{m}$ update $\beta = \beta -\eta_{\beta}\nabla_{\beta}L(\theta ,\phi)$ using Eq. 11 with $\eta_{\beta}$ + +Learn inference model: Given $\{x_{i},z_{i}^{+}\}_{i = 1}^{m}$ update $\phi = \phi -\eta_{\phi}\nabla_{\phi}L(\theta ,\phi)$ using Eq. 12 with $\eta_{\phi}$ + +Let $t = t + 1$ + +until $t = T$ + +# 3.4. Theoretical understanding + +Divergence perturbation and ELBO. The KL joint minimization (Eq. 9) can be viewed as a surrogate of the MLE objective with the KL perturbation term, + +$$ +\begin{array}{l} D _ {\mathrm {K L}} \left(q _ {\phi} (\mathbf {x}, \mathbf {z}) | | p _ {\theta} (\mathbf {x}, \mathbf {z})\right) \\ = D _ {\mathrm {K L}} \left(p _ {\text {d a t a}} (\mathbf {x}) | | p _ {\theta} (\mathbf {x})\right) + D _ {\mathrm {K L}} \left(q _ {\phi} (\mathbf {z} | \mathbf {x}) | | p _ {\theta} (\mathbf {z} | \mathbf {x})\right) \\ \end{array} +$$ + +where $D_{\mathrm{KL}}(p_{\mathrm{data}}(\mathbf{x})||p_{\theta}(\mathbf{x}))$ is the MLE loss function, and the perturbation term $D_{\mathrm{KL}}(q_{\phi}(\mathbf{z}|\mathbf{x})||p_{\theta}(\mathbf{z}|\mathbf{x}))$ measures the KL-divergence between inference distribution and generator posterior. The inference $q_{\phi}(\mathbf{z}|\mathbf{x})$ is learned to match the posterior distribution of the generator without expensive posterior sampling. In fact, such KL minimization in the joint space is equivalent to evidence lower bound + +(ELBO). To see this, noted that $D_{\mathrm{KL}}(p_{\mathrm{data}}(\mathbf{x})||p_{\theta}(\mathbf{x})) = -H(p_{\mathrm{data}}(\mathbf{x})) - \mathbb{E}_{p_{\mathrm{data}}}[\log p_{\theta}(\mathbf{x})]$ where $H(p_{\mathrm{data}}(\mathbf{x}))$ is the entropy of the empirical data distribution and can be treated as constant $C \equiv -H(p_{\mathrm{data}}(\mathbf{x}))$ w.r.t model parameters $\theta$ . Then $L(\theta, \phi)$ is computed as + +$$ +\begin{array}{l} - \mathbb {E} _ {p _ {\mathrm {d a t a}}} [ \log p _ {\theta} (\mathbf {x}) ] + D _ {\mathrm {K L}} \left(q _ {\phi} (\mathbf {z} | \mathbf {x}) \| p _ {\theta} (\mathbf {z} | \mathbf {x})\right) + C \\ = \mathbb {E} _ {p _ {\mathrm {d a t a}}} \left[ \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left(\log \frac {q _ {\phi} (\mathbf {z} | \mathbf {x})}{p _ {\theta} (\mathbf {z} | \mathbf {x})}\right) - \log p _ {\theta} (\mathbf {x}) \right] + C \\ = \mathbb {E} _ {p _ {\text {d a t a}}} [ - \operatorname {E L B O} (\mathbf {x}; \theta , \phi) ] + C \\ \end{array} +$$ + +where + +$$ +\begin{array}{l} \operatorname {E L B O} (\mathbf {x}; \theta , \phi) = \log p _ {\theta} (\mathbf {x}) - \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \log \frac {q _ {\phi} (\mathbf {z} | \mathbf {x})}{p _ {\theta} (\mathbf {z} | \mathbf {x})} \right] \\ = \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} \left[ \log \frac {p _ {\theta} (\mathbf {x} , \mathbf {z})}{q _ {\phi} (\mathbf {z} | \mathbf {x})} \right] \\ \end{array} +$$ + +and is referred to as evidence lower bound (ELBO) in the literature [17]. Noted that the prior model (i.e., $p_{\theta}(\mathbf{x}, \mathbf{z}) = p_{\beta}(\mathbf{x}|\mathbf{z})p_{\alpha}(\mathbf{z})$ ) is now parameterized to be our joint EBM prior. Minimizing Eq. 9 is equivalent to maximizing the evidence lower bound of the log-likelihood. + +Short run sampling and divergence perturbation. The learning of the energy-based model in Eq. 10 requires MCMC sampling from $p_{\alpha}(\mathbf{z})$ . We adopt the short-run Langevin dynamics (Eq. 13) with fixed $K$ steps to sample from prior $p_{\alpha}(\mathbf{z})$ for efficient computation. Such prior sampling amounts to approximates the objective $L(\theta, \phi)$ in Eq. 9 with yet another KL perturbation term, i.e., + +$$ +\tilde {L} (\theta , \phi) = L (\theta , \phi) - D _ {\mathrm {K L}} \left(\tilde {p} _ {\alpha^ {(t)}} (\mathbf {z}) | p _ {\alpha} (\mathbf {z})\right) +$$ + +where $\tilde{p}_{\alpha^{(t)}}(\mathbf{z})$ refers to the distribution of latent codes after $K$ steps of Langevin dynamics (Eq. 13) in the $t$ -th iteration of the learning. The corresponding learning gradient for the prior model is thus + +$$ +- \nabla_ {\alpha} \tilde {L} (\theta , \phi) = \mathbb {E} _ {q _ {\phi} (\mathbf {z} | \mathbf {x})} [ \nabla_ {\alpha} f _ {\alpha} (\mathbf {z}) ] - \mathbb {E} _ {\tilde {p} _ {\alpha (t)} (\mathbf {z})} [ \nabla_ {\alpha} f _ {\alpha} (\mathbf {z}) ] +$$ + +When $K$ is sufficiently large, the perturbation term $D_{\mathrm{KL}}(\tilde{p}_{\alpha^{(t)}}(\mathbf{z})|p_{\alpha}(\mathbf{z})) \to 0$ . The update rule for the energy-based prior model (also Eq. 10) can be interpreted as self-adversarial learning. The prior model $p_{\alpha}(\mathbf{z})$ serves as both generator and discriminator if we compare it to GAN (generative adversarial networks) [11]. In contrast to GAN, our learning follows MLE with divergence perturbations, which in general does not suffer from issues such as mode collapsing and instability, as it does not involve competition between two separate models. The energy-based model can thus be seen as its own adversary or its own critic. + +# 4. Related Work + +Generator model. The generator model has a top-down network that maps the low-dimensional latent code to the + +observed data space. VAEs [17, 27, 33, 32] proposes variational learning by introducing an approximation of the true intractable posterior, which allows a tractable bound on log-likelihood to be maximized. Another line of work [14, 25] trains the generator model without inference model by using Langevin dynamics for generator posterior sampling. We follow the former approach and use the inference model for efficient training. + +Generator model with informative prior. The majority of the existing generator models assume that the latent code follows a simple and known prior distribution, such as isotropic Gaussian distribution. Such assumption may render an ineffective generator as observed in [34, 5]. Our work utilizes the informative and expressive energy-based prior in the joint space of latent variables and is related to the line of previous research on introducing flexible prior distributions. For example, [34] parameterizes the prior based on the posterior inference model. [5, 9] adopt a two-stage approach which first trains a latent variable model with simple prior and then trains a separate prior model (e.g., VAE or Gaussian mixture model) to match the aggregated posterior distribution. + +Generator model with hierarchical structures. The generator models that consist of multi-layers of latent variables are recently attracting attention for hierarchical learning. [29, 2, 21, 3, 36] stack generative models on top of each other and assume conditional Gaussian distributions at different layers. However, as shown in Sec. 2.1, the bottom layer could act as a single generative model and absorb most features, leading to ineffective representation learning. [42, 20] propose to learn hierarchical features with unit Gaussian prior by adapting the generator into multiple layers. However, the latent variables at different layers are distributed independently a priori and are only loosely connected. Instead, we propose a joint EBM prior that could tightly couple and jointly model latent variables at different layers and show superior results through joint training. + +Hierarchical generator model with informative prior. Recent advances [4, 1] have started exploring learning informative prior for multi-layer generator models. JEBM [4] and NCP-VAE [1] build latent space EBM on hierarchical generator models and showcase the capability of improving the generation quality. However, these models consider the conditional hierarchical models, which can be limited in learning effective hierarchical representations (see Sec. 2.1). This work studies hierarchical representation learning by introducing a novel framework where latent space EBM can be jointly trained with the architectural hierarchical models to capture complex representations of different levels. + +![](images/28aa96ea11f0bd66327f1e7ad14b7336d8aa695525725a593f26e8b45abf6c80.jpg) +Figure 4. Hierarchical sampling on SVHN. Left: The latent code at bottom layer $(z_{1})$ represents the background light and shading. Center-left: the latent code at second bottom layer $(z_{2})$ represents the color schemes. Center-right: the latent code at second top layer $(z_{3})$ encodes the shape variations of the same digit. Right: the latent code at top layer $(z_{4})$ captures the digit identity and the general structure. + +![](images/7bd785344120ff2ed24d0957cfd19aae53ecac0fd868af25b60c269b8ae36af3.jpg) + +![](images/b6d465a1360f41482ed6cb3017f029550671c905dd1a0b440b4ab18026572489.jpg) + +![](images/05d3c4ad017755d67b5cf20cf477c158d536e7e2c4a95e42763a502eaf1d8e48.jpg) + +![](images/e57bab778a351865d9a6b1143aadccd8a3edd709edb5fbb9bc108968be96d06d.jpg) +Figure 5. Hierarchical sampling on MNIST. Left: The latent code at bottom layer $(z_{1})$ indicates the stroke width. Center: the latent code at second layer $(z_{2})$ encodes geometric changes among similar digits. Right: the latent code at top layer $(z_{3})$ learns the digit identity and general structure. + +# 5. Experiments + +To demonstrate the effectiveness of our method, we conduct the following experiments: 1) hierarchical representation learning, 2) analysis of latent space, 3) image modelling, and 4) robustness. For a better understanding of the proposed method, we perform the disentanglement learning experiment, various ablation studies, and an analysis of parameter complexity. + +# 5.1. Hierarchical Representation Learning + +We first demonstrate the capability of our model in hierarchical representation learning by experiments of hierarchical sampling and latent classifier. + +Hierarchical sampling. With partitioned latent variables and the hierarchical structure of generator, the latent variables at higher layers should capture semantic features, while the lower layers should capture low-level features. We train our model on MNIST using the same setting as in Sec. 2.2 with only '0', '1', and '2' digit classes available and the latent dimension set to 2. In Fig. 6, by changing the $\mathbf{z}_1$ (at the bottom layer), our model can successfully deliver the variations in shape (low-level features), and changing the $\mathbf{z}_2$ (at the top layer) leads to the variations in digit class (high-level features). This indicates a successfully learned hierarchical representation. + +Further, we train our model on MNIST with all digit + +![](images/8170f2bf23bded18b493feb09312a19064ca06767907ff2a449f4ef560b07d1b.jpg) +Figure 6. Visualization for our model by changing each unit of 2-dimensional z. Left: changing the first unit. Right: changing the second unit. Top: the value of each unit, where the orange color indicates the first unit and the blue color indicates the second unit. + +classes and the more challenging SVHN dataset, and we generate the images by sampling (using Eq. 13) the latent code of one layer while keeping other layers fixed. The results shown in Fig. 4 and Fig. 5 also demonstrate the hierarchical representation learned by our model. + +Latent Classifier. We next show that our model can achieve better performance in hierarchical representation learning. Note that the inference model $q_{\phi}(\mathbf{z}|\mathbf{x})$ should be learned to approximate the true posterior $p_{\theta}(\mathbf{z}|\mathbf{x})$ of the generator, which integrates both the hierarchical inductive bias and the energy-based refinement. Therefore, to measure the learned hierarchical features, we learn classifiers on the inferred latent codes at different layers to predict the label of the data and measure the testing classification accuracy. The latent codes that carry rich high-level semantic features should achieve higher classification accuracy. + +Table 1. Testing accuracy of inferred latent codes at each layer. We denote $(\downarrow)$ for the layer that has unexpectedly lower accuracy. + +
L=1L=2L=3L=4
MNISTOurs32.60%58.32%67.64%-
VLAE35.69%57.86%52.08% (↓)-
Fashion-MNISTOurs39.27%44.81%84.27%-
VLAE52.43%35.65% (↓)83.24%-
SVHNOurs21.00%25.29%30.58%86.63%
VLAE22.59%26.97%56.70%52.14% (↓)
+ +In practice, we first train our model on standard benchmarks, such as MNIST, Fashion-MNIST, and SVHN. Then, we train classifiers on the inferred latent codes at each layer. We consider VLAE [42] as our baseline model, which + +learns a structural latent space with standard Gaussian prior. We show comparison results in Tab. 1, where our learned inference model $q_{\phi}(\mathbf{z}|\mathbf{x})$ extracts varying levels of semantic features for different layers of latent codes. The top layer carries the most significant features, and the bottom layer carries the least. The baseline model that assumes Gaussian prior, however, extracted mixed semantic features across different layers. For fair comparisons, we use the same generation and inference structure as the baseline model2. The structure of the classifier contains two linear layers with a hidden dimension set to 256 and uses ReLU activation function. The classifier has softmax as its output layer. We do not employ drop-out and normalization strategies. + +# 5.2. Image Modelling + +In this section, we evaluate our model in image modelling by measuring the quality of generated and reconstructed images. We consider the baseline models that assume Gaussian prior, such as Alternating Back-propagation (ABP) [14], Ladder-VAE (LVAE) [30], BIVA [21], Short-run MCMC (SRI) [25], and VLAE [42], as well as generator models with informative prior, such as RAE [9], Two-stages VAE (2s-VAE) [5], NCP-VAE [1], Multi-NCP [37] and LEBM [26]. To make fair comparisons, we follow the protocol in [26]. + +Table 2. Testing reconstruction by MSE, and generation evaluation by FID on SVHN and CelebA-64. + +
ModelSVHNCelebA-64
MSE (↓)FID (↓)MSE (↓)FID (↓)
ABP-49.71-51.50
LVAE0.01439.260.02853.40
BIVA0.01031.650.01033.58
SRI0.01135.230.01136.84
VLAE0.01643.950.01044.05
2s-VAE0.01942.810.02144.40
RAE0.01440.020.01840.95
NCP-VAE0.02033.230.02142.07
Multi-NCP0.00426.190.00935.38
LEBM0.00829.440.01337.87
Ours0.00824.160.00432.15
+ +Synthesis: We use Fréchet Inception Distance (FID) [16] to quantitatively evaluate the sample quality. In Tab. 2, it can be seen that our model obtains superior generation quality compared to the baseline models. + +Reconstructions: To evaluate the accuracy of our inference model, we compute mean square error (MSE) [26, 24] for testing reconstruction. As shown in Tab. 2, the proposed model leads to more accurate and faithful reconstructions. + +# 5.3. Analysis of Latent Space + +Visualization of toy data. To illustrate the expressivity of the proposed EBM prior, we train our model on MNIST (using the same setting as shown in Fig. 2 and Fig. 6) and set the latent dimension for both $\mathbf{z}_1$ and $\mathbf{z}_2$ to 2 for better visualization. We visualized the Langevin transition of the prior sampling in Fig. 7, which shows that the latent codes at the top layer $(\mathbf{z}_2)$ can effectively capture the multi-modal posterior, where using a Gaussian prior might be infeasible. + +![](images/b6f2688896c2d327233d4cbb8bfc623f5dd77ea71d379c914381d2de88bddf4c.jpg) +Figure 7. Visualization of the latent codes sampled from our EBM prior (Top row: $\mathbf{z}_2$ ). Blue, Orange color indicate prior and posterior, respectively. + +Langevin trajectory. We explore the energy landscape of the learned prior $p_{\alpha}(\mathbf{z})$ via transition of Langevin dynamics initialized from $p_0(\mathbf{z})$ towards $p_{\alpha}(\mathbf{z})$ on CelebA-64. If the EBM is well-learned, the energy prior should render local modes of the energy function, and traversing these local modes should present diverse, realistic image synthesis and steady-state energy scores. Existing EBMs often suffer from oversaturated synthesis via the challenging long-run Langevin dynamic (see oversaturated example in Fig.3 in [23]). We thereby test our model with 2500 Langevin steps, which is much longer than the 40 steps used in training. Fig. 8 shows the image synthesis and energy profile, where our EBM prior model does not exhibit the oversaturated phenomenon and successfully delivers diverse and realistic synthesis with steady-state energy. + +![](images/1eb3ae9ea9567caeea7d87a28a4d630ab6d92dffe3cb485d94faeda323dddfca.jpg) +Figure 8. Transition of Markov chains initialized from $p_0(\mathbf{z})$ towards $p_{\alpha}(\mathbf{z})$ for 2500 steps. Top: Trajectory in the CelebA-64 data space for every 100 steps. Bottom: Energy profile over time. + +# 5.4. Robustness + +In this section, we examine the robustness of our model in adversarial attack and outlier detection. + +Adversarial robustness. For adversarial robustness, we consider the latent attack [10], which is shown to be a + +strong attack for the generative model with latent variables, and it allows us to attack the latent codes at different layers. Specifically, let $\mathbf{x}_t$ be the target and $\mathbf{x}_o$ be the original image. The attack aims to create the distorted image $\tilde{\mathbf{x}} = \mathbf{x}_o + \epsilon$ such that its learned inference distribution $q_{\phi}(\mathbf{z}|\tilde{\mathbf{x}})$ is close to the inference $q_{\phi}(\mathbf{z}|\mathbf{x}_t)$ on target images under KL-divergence (Eq. 5 in [10]). + +![](images/3e58d6bcfc7e2d9d796bc45b5616d9811133f7901841cf46f44c746623274646.jpg) +Figure 9. Adversarial latent attack on different layers. The leftmost figure indicates the bottom layer, and the rightmost figure indicates the top layer. 1st col: original image. 2nd col: target image. 3rd col: adversarial example. 4th col: reconstruction of adversarial example. + +We illustrate the adversarial attack on different layers in Fig. 9. The learned inference model $q_{\phi}(\mathbf{z}|\mathbf{x})$ carries different levels of semantics for different layers. The adversarial example created by attacking latent codes at the bottom layer only perturbs the data along low-level features direction from the target image; hence, the model can be robust and have faithful reconstruction from adversarial examples. The adversarial example coming from the top-layer attack can distort the original data along a high-level semantic direction from the target image, thus, the reconstruction from the adversarial example can be substantially different from the original data, indicating a successful attack. + +Anomaly detection. We also evaluate the model on anomaly detection. If the model is well-learned, the inference model $q_{\phi}(\mathbf{z}|\mathbf{x})$ should form an informative latent space that separates anomalies from the normal data. Following the protocols in [18, 26], we take latent samples from the learned inference model and use the unnormalized log-posterior $\log p_{\theta}(\mathbf{x},\mathbf{z})$ as our decision function to detect anomaly on MNIST. Only one digit class is held-out as an anomaly in training, while both normal and anomalous data are used for testing. We compare baseline models such as BiGAN- $\sigma$ [41], MEG [18], LEBM [26], HVAE and VAE using area under the precision-recall curve (AUPRC). The results of baseline models are provided by [26], and we use $L^{>0}$ [15] as the decision function for HVAE model. Tab. 3 shows the result. + +Table 3. AUPRC scores for unsupervised anomaly detection on MNIST. Following the protocol of [26], we average the results over last 10 epochs to account for variance. + +
hold-out digit14579
VAE0.0630.3370.3250.1480.104
HVAE0.494 ± 0.0040.920 ± 0.0040.913 ± 0.0030.680 ± 0.0060.791 ± 0.008
MEG0.281 ± 0.0350.401 ± 0.0610.402 ± 0.0620.290 ± 0.0400.342 ± 0.034
BiGAN-σ0.287 ± 0.0230.443 ± 0.0290.514 ± 0.0290.347 ± 0.0170.307 ± 0.028
Latent EBM0.336 ± 0.0080.630 ± 0.0170.619 ± 0.0130.463 ± 0.0090.413 ± 0.010
Ours0.722 ± 0.0100.949 ± 0.0020.980 ± 0.0010.941 ± 0.0030.935 ± 0.003
+ +# 5.5. Ablation Studies + +The proposed expressive prior model enables complex data representations to be effectively captured, which in turn + +improves the expressivity of the whole model in generating high-quality synthesis. To better understand the influence of the proposed method, we conduct ablation studies, including 1) MCMC steps, 2) complexity of EBM, and 3) other image datasets. + +MCMC steps: We examine the influence of steps of short-run MCMC for prior sampling. Tab. 4 shows that increasing steps could result in a better quality of generation. Increasing the step number from 15 to 60 could result in a significant improvement in synthesis quality, while exhibiting only minor influence when increased beyond 60. + +Table 4. Varying $k$ (steps number) of our model on CelebA-64. + +
k=15k=30k=60k=150k=300
FID56.4239.8932.1531.2030.78
+ +Complexity of EBM: We further examine the influence of model parameters of EBM. The energy function is parameterized by a 2-layer perceptron. We fix the number of layers and increase the hidden units of EBM. As shown in Tab. 5, increasing the hidden units of EBM results in better performance. + +Table 5. Increasing hidden units (denoted as nef) of EBM. + +
nefnef=0nef=10nef=20nef=50nef=100
FID43.9541.7233.1030.4224.16
+ +Other image datasets: We test the scalability of our model on high-resolution image dataset, such as CelebA-128. We show the image synthesis in Fig. 10. + +![](images/659522c8b7fddbc0a6ae09b6413bfc1945c66abb14f3b692c2484dd7583f4046.jpg) +Figure 10. Generated image synthesis on CelebA-128 + +We also train our model on CIFAR-10 (32x32) and report the FID score for generation quality in Tab. 6, in which our model performs well compared to baseline models. + +
Table 6. FID on CIFAR-10
Ours2s-VAERAENCP-VAEMulti-NCPLEBM
63.4272.9074.1678.0665.0170.15
+ +# 6. Conclusion + +In this paper, we propose to build a joint latent space EBM with hierarchical structures for better hierarchical representation learning. Our joint EBM prior is expressive in modelling the inter-layer relation among multiple layers of latent variables, which in turn enables different levels of data representations to be effectively captured. We develop an efficient variational learning scheme and conduct various experiments to demonstrate the capability of our model in hierarchical representation learning and image modelling. For future work, we shall explore learning the hierarchical representations from other domains, such as videos and texts. + +# References + +[1] Jyoti Aneja, Alex Schwing, Jan Kautz, and Arash Vahdat. A contrastive learning approach for training variational autoencoder priors. Advances in neural information processing systems, 34:480-493, 2021. 2, 5, 7 +[2] Philip Bachman. An architecture for deep, hierarchical generative models. 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Handbook of markov chain monte carlo, 2(11):2, 2011. 4 +[23] Erik Nijkamp, Mitch Hill, Tian Han, Song-Chun Zhu, and Ying Nian Wu. On the anatomy of mcmc-based maximum likelihood learning of energy-based models. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 5272-5280, 2020. 7 +[24] Erik Nijkamp, Mitch Hill, Song-Chun Zhu, and Ying Nian Wu. Learning non-convergent non-persistent short-run mcmc toward energy-based model. Advances in Neural Information Processing Systems, 32, 2019. 1, 2, 7 +[25] Erik Nijkamp, Bo Pang, Tian Han, Linqi Zhou, Song-Chun Zhu, and Ying Nian Wu. Learning multi-layer latent variable model via variational optimization of short run mcmc for approximate inference. In European Conference on Computer Vision, pages 361-378. Springer, 2020. 1, 5, 7 +[26] Bo Pang, Tian Han, Erik Nijkamp, Song-Chun Zhu, and Ying Nian Wu. Learning latent space energy-based prior model. 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Mocogan: Decomposing motion and content for video generation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2018. 1 +[36] Arash Vahdat and Jan Kautz. Nvae: A deep hierarchical variational autoencoder. Advances in Neural Information Processing Systems, 33:19667-19679, 2020. 1, 2, 5 +[37] Zhisheng Xiao and Tian Han. Adaptive multi-stage density ratio estimation for learning latent space energy-based model. In Alice H. Oh, Alekh Agarwal, Danielle Belgrave, and Kyunghyun Cho, editors, Advances in Neural Information Processing Systems, 2022. 2, 7 +[38] Zhisheng Xiao, Karsten Kreis, Jan Kautz, and Arash Vahdat. Vaebm: A symbiosis between variational autoencoders and energy-based models. arXiv preprint arXiv:2010.00654, 2020. 2 +[39] Jianwen Xie, Yang Lu, Song-Chun Zhu, and Yingnian Wu. A theory of generative convnet. In International Conference on Machine Learning, pages 2635-2644. 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Learning hierarchical features from generative models. arXiv preprint arXiv:1702.08396, 2017. 1, 3, 5, 6, 7 \ No newline at end of file diff --git a/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/images.zip b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a5a3a568c6f652b777a535f92d7d00448fd7f5ed --- /dev/null +++ b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5d11a639a35633feaf4b6552b2c6bdc035aec3713e2532ef2b6ffa37a3fefd88 +size 547350 diff --git a/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/layout.json b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..11e6ece4214fce7dda0e5903987b62198876a48f --- /dev/null +++ b/2023/Learning Hierarchical Features with Joint Latent Space Energy-Based Prior/layout.json @@ -0,0 +1,11332 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 61, + 103, + 533, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 103, + 533, + 121 + ], + "spans": [ + { + "bbox": [ + 61, + 103, + 533, + 121 + ], + "type": "text", + "content": "Learning Hierarchical Features with Joint Latent Space Energy-Based Prior" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "spans": [ + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "text", + "content": "Jiali Cui" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "text", + "content": ", Ying Nian Wu" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "text", + "content": ", Tian Han" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "text", + "content": "\\\n" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "text", + "content": "Department of Computer Science, Stevens Institute of Technology\\\n" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 134, + 142, + 459, + 200 + ], + "type": "text", + "content": "Department of Statistics, University of California, Los Angeles\\\n{jcui7,than6}@stevens.edu, ywu@stat.ucla.edu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 252, + 290, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 492 + ], + "type": "text", + "content": "This paper studies the fundamental problem of multilayer generator models in learning hierarchical representations. The multi-layer generator model that consists of multiple layers of latent variables organized in a top-down architecture tends to learn multiple levels of data abstraction. However, such multi-layer latent variables are typically parameterized to be Gaussian, which can be less informative in capturing complex abstractions, resulting in limited success in hierarchical representation learning. On the other hand, the energy-based (EBM) prior is known to be expressive in capturing the data regularities, but it often lacks the hierarchical structure to capture different levels of hierarchical representations. In this paper, we propose a joint latent space EBM prior model with multi-layer latent variables for effective hierarchical representation learning. We develop a variational joint learning scheme that seamlessly integrates an inference model for efficient inference. Our experiments demonstrate that the proposed joint EBM prior is effective and expressive in capturing hierarchical representations and modelling data distribution." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 517, + 128, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 517, + 128, + 530 + ], + "spans": [ + { + "bbox": [ + 47, + 517, + 128, + 530 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 538, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 538, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 46, + 538, + 287, + 634 + ], + "type": "text", + "content": "In recent years, deep generative models have achieved remarkable success in generating high-quality images [36, 31], texts [40, 13], and videos [28, 35]. However, learning generative models that incorporate hierarchical structures still remains a challenge. Such hierarchical generative models can play a critical role in enabling explainable artificial intelligence, thus representing an important area of ongoing research." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 635, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 684 + ], + "type": "text", + "content": "To tackle this challenge, various methods of learning hierarchical representations have been explored [30, 42, 21, 3, 30]. These methods learn generative models with multiple layers of latent variables organized in a top-down ar" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 228, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 545, + 300 + ], + "type": "text", + "content": "chitecture, which have shown the capability of learning increasingly abstract representations (e.g., general structures, classes) at the top layers while capturing low-level data features (e.g., colors, background) at the bottom layers. In general, one could categorize these methods into two classes: (i) conditional hierarchy and (ii) architectural hierarchy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 301, + 546, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 546, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 546, + 434 + ], + "type": "text", + "content": "The conditional hierarchies [30, 12, 25, 21, 3] employ stacked generative models layered on top of one another and assume conditional Gaussian distributions at different layers, while the architectural hierarchies [42, 20] instead leverage network architecture to place high-level representations at the top layers of latent variables and low-level representations at the bottom layers. However, they typically assume conditional Gaussian distribution or isotropic Gaussian as the prior, which could have limited expressivity [26]. Learning a more expressive and informative prior model for multiple layers of latent variables is thus needed." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 436, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 547, + 590 + ], + "type": "text", + "content": "The energy-based models (EBMs) [19, 39, 7, 24, 26, 4], on the other hand, are shown to be expressive and proved to be powerful in capturing data regularities. Notably, [26] studies the EBM in the latent space, where the energy function is considered as a correction of the non-informative prior and tilts the non-informative prior to a more expressive prior distribution. The low dimensionality of the latent space makes EBM more effective in capturing regularities in the data. However, prior methods often rely on expensive MCMC methods for posterior sampling of the latent variables, and more importantly, the latent variables are not hierarchically organized, making it difficult to capture data variations at different levels." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "In this paper, we propose to combine the strengths of latent space EBM and the multi-layer generator model for effective hierarchical representation learning. In particular, we build the EBM on the latent variables across different layers of the generator model, where the latent variables at different layers are concatenated and modelled jointly. The latent variables at different layers capture different levels of information from the data via the hierarchy of the generative model, and their inter-relations are further tightened up and better captured through EBM in joint latent space." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "Our project page is available at https://jcui1224.github.io/hierarchical-representation-ebm-proj/." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2218" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "type": "text", + "content": "Learning the EBM in the latent space can be challenging since it usually requires MCMC sampling for both the prior and posterior distributions of the latent variables. The prior sampling is efficient with the low dimensionality of the latent space and the lightweight network of the energy function, while the MCMC sampling of posterior distribution requires the backward propagation of generation network, which is usually heavy and thus renders inefficient inference. To ensure efficient inference, we introduce an inference model and develop a joint training scheme to efficiently and effectively learn the latent space EBM and multi-layer generator model. In particular, the inference model aims to approximate the exact posterior of the multi-layer latent variables while also serving to extract levels of data variations through the deep feed-forward inference network to facilitate hierarchical learning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 348 + ], + "type": "text", + "content": "Contributions: 1) We propose the joint EBM prior model for hierarchical generator models with multiple layers of latent variables; 2) We develop a variational training scheme for efficient learning and inference; 3) We provide strong empirical results on hierarchical learning and image modeling, as well as various ablation studies to illustrate the effectiveness of the proposed model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 359, + 126, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 359, + 126, + 372 + ], + "spans": [ + { + "bbox": [ + 47, + 359, + 126, + 372 + ], + "type": "text", + "content": "2. Background" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 380, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 415 + ], + "type": "text", + "content": "In this section, we present the background of multi-layer generator models and the latent space EBM, which will serve as the foundation of the proposed model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 424, + 208, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 424, + 208, + 436 + ], + "spans": [ + { + "bbox": [ + 47, + 424, + 208, + 436 + ], + "type": "text", + "content": "2.1. Multi-layer generator models" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "text", + "content": " represent the high-dimensional observed examples, and " + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "text", + "content": " denote the low-dimensional latent variables. The multi-layer generator model [30, 36, 21] consists of multiple layers of latent variables that are organized in a top-down hierarchical structure and modelled to be conditionally dependent on its upper layer, i.e., " + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}) = \\prod_{i=1}^{L-1} p_{\\theta_i}(\\mathbf{z}_i | \\mathbf{z}_{i+1}) p_0(\\mathbf{z}_L)" + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "inline_equation", + "content": "p_{\\theta_i}(\\mathbf{z}_i | \\mathbf{z}_{i+1}) \\sim \\mathcal{N}(\\mu_{\\theta_i}(\\mathbf{z}_{i+1}), \\sigma_{\\theta_i}(\\mathbf{z}_{i+1}))" + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "inline_equation", + "content": "p_0(\\mathbf{z}_L) \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 46, + 442, + 287, + 574 + ], + "type": "text", + "content": ". Although such a modelling strategy has seen significant improvement in data density estimation, it can be less effective in learning hierarchical representations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": "To demonstrate, we train BIVA [21] on MNIST with 6 layers of latent variables and conduct hierarchical sampling by generating latent variables via the repamaramization trick, i.e., " + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i = \\mu_{\\theta_i}(\\mathbf{z}_{i + 1}) + \\sigma_{\\theta_i}(\\mathbf{z}_{i + 1})\\cdot \\epsilon_i" + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\epsilon_{i}" + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": " is the added Gaussian noise. Specifically, the latent variables are generated by randomly sampling " + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\epsilon_{i}" + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": "-th layer, while fixing " + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\epsilon_{j\\neq i}" + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": " for other layers, and the corresponding image synthesis should deliver the variation of representation learned by " + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": ". We show the results in Fig. 1, where the major semantic variation is only captured by the top layer" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "of the latent variables, suggesting an ineffective hierarchical representation learned (compare with our model shown in Fig. 5)." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 323, + 116, + 392, + 184 + ], + "blocks": [ + { + "bbox": [ + 323, + 116, + 392, + 184 + ], + "lines": [ + { + "bbox": [ + 323, + 116, + 392, + 184 + ], + "spans": [ + { + "bbox": [ + 323, + 116, + 392, + 184 + ], + "type": "image", + "image_path": "6f930224014083ecd13826e158c27fb2ce417d91e8e94836098ed0504bb9e331.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "type": "text", + "content": "Figure 1. Visualization of hierarchical representations on BIVA. Left: sampling " + }, + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\epsilon_{1},\\epsilon_{2}" + }, + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "type": "text", + "content": " for bottom layers. Middle: sampling " + }, + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\epsilon_{3},\\epsilon_{4}" + }, + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "type": "text", + "content": " for middle layers. Right: sampling " + }, + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\epsilon_{5},\\epsilon_{6}" + }, + { + "bbox": [ + 304, + 186, + 545, + 220 + ], + "type": "text", + "content": " for top layers." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 392, + 116, + 460, + 184 + ], + "blocks": [ + { + "bbox": [ + 392, + 116, + 460, + 184 + ], + "lines": [ + { + "bbox": [ + 392, + 116, + 460, + 184 + ], + "spans": [ + { + "bbox": [ + 392, + 116, + 460, + 184 + ], + "type": "image", + "image_path": "b58084dafd71d4b841e184de98769797bff9e0e917e8df57c3b0a79f3150c26e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 460, + 117, + 529, + 184 + ], + "blocks": [ + { + "bbox": [ + 460, + 117, + 529, + 184 + ], + "lines": [ + { + "bbox": [ + 460, + 117, + 529, + 184 + ], + "spans": [ + { + "bbox": [ + 460, + 117, + 529, + 184 + ], + "type": "image", + "image_path": "560d7740960843b959c50fb268c573692d2e62ebb53d4628ce4dd10449fefe3b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 226, + 416, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 226, + 416, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 226, + 416, + 239 + ], + "type": "text", + "content": "2.2. Latent space EBM" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 244, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 545, + 352 + ], + "type": "text", + "content": "The energy-based models (EBMs) [7, 6, 24, 8, 38] present a flexible and appealing way for data modelling and are known for being expressive and powerful in capturing data regularities. Albeit their expressivity, learning the EBM on high-dimensional " + }, + { + "bbox": [ + 304, + 244, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 244, + 545, + 352 + ], + "type": "text", + "content": "-space can be challenging since the energy function needs to support the entire data space. As such, another line of works [26, 1, 37] seek to build EBM on low-dimensional " + }, + { + "bbox": [ + 304, + 244, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 244, + 545, + 352 + ], + "type": "text", + "content": "-space with the probability density defined as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 350, + 357, + 545, + 382 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 357, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 350, + 357, + 545, + 382 + ], + "type": "interline_equation", + "content": "p _ {\\theta} (\\mathbf {z}) = \\frac {1}{\\mathbb {Z} (\\theta)} \\exp \\left[ f _ {\\theta} (\\mathbf {z}) \\right] p _ {0} (\\mathbf {z}) \\tag {1}", + "image_path": "0e3b96a382d9661e9baf4a8324a98d08f541558716a42352026596cafa6d3caf.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 386, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 482 + ], + "type": "text", + "content": "However, with a single-layer non-hierarchical " + }, + { + "bbox": [ + 304, + 386, + 545, + 482 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 386, + 545, + 482 + ], + "type": "text", + "content": "-space, it is typically infeasible to capture the data abstraction of different levels. To see this, we pick up the digit classes '0', '1', and '2' of the MNIST dataset, on which we train LEBM [26] with the latent dimension set to be 2. We show in Fig. 2 that changing the value of each latent unit could lead to a mixed variations in digit shape and class (compare to our proposed method in Fig. 6)." + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 317, + 483, + 535, + 534 + ], + "blocks": [ + { + "bbox": [ + 317, + 483, + 535, + 534 + ], + "lines": [ + { + "bbox": [ + 317, + 483, + 535, + 534 + ], + "spans": [ + { + "bbox": [ + 317, + 483, + 535, + 534 + ], + "type": "image", + "image_path": "3f61d13b300cf47d325a220a38d7e525400835b8561d0b4dcad7b2d5b719d9e6.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 536, + 545, + 591 + ], + "lines": [ + { + "bbox": [ + 304, + 536, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 545, + 591 + ], + "type": "text", + "content": "Figure 2. Visualization for latent space EBM [26] by changing each unit of 2-dimensional z. Left: changing the first unit. Right: changing the second unit. Top: the value of each unit, where the orange color indicates the first unit and the blue color indicates the second unit." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 609, + 388, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 388, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 388, + 624 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we study a joint latent space EBM prior where latent variables are partitioned into multiple groups but modelled jointly for hierarchical representation learning. To ensure efficient inference, we introduce an inference model to approximate the generator posterior and develop a variational joint training scheme in which each model can be trained efficiently and effectively." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 189, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 189, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 189, + 713 + ], + "type": "text", + "content": "1 https://github.com/vlievin/biva-pytorch" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2219" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "text", + "content": "3.1. Latent variable generative model" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 114 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 114 + ], + "type": "text", + "content": "A latent variable generative model (i.e., generator model) can be specified using joint distribution:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 110, + 124, + 287, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 124, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 110, + 124, + 287, + 137 + ], + "type": "interline_equation", + "content": "p _ {\\beta , \\alpha} (\\mathbf {x}, \\mathbf {z}) = p _ {\\beta} (\\mathbf {x} | \\mathbf {z}) p _ {\\alpha} (\\mathbf {z}) \\tag {2}", + "image_path": "59d28ac0590055bc0efb1b6230afcf8c9000c577f7120ed3f4466f4480715ecb.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 146, + 287, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 146, + 287, + 169 + ], + "spans": [ + { + "bbox": [ + 47, + 146, + 287, + 169 + ], + "type": "text", + "content": "which consists of the generation model " + }, + { + "bbox": [ + 47, + 146, + 287, + 169 + ], + "type": "inline_equation", + "content": "p_{\\beta}(\\mathbf{x}|\\mathbf{z})" + }, + { + "bbox": [ + 47, + 146, + 287, + 169 + ], + "type": "text", + "content": " and the prior model " + }, + { + "bbox": [ + 47, + 146, + 287, + 169 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 146, + 287, + 169 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 171, + 287, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 171, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 287, + 253 + ], + "type": "text", + "content": "Joint latent space EBM: The prior model " + }, + { + "bbox": [ + 47, + 171, + 287, + 253 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 171, + 287, + 253 + ], + "type": "text", + "content": " is usually assumed to be single-layer, which can be infeasible for learning hierarchical representations (see Sec. 2.2). In this work, we propose a joint latent space EBM prior, where latent variables are separated into multiple groups, i.e., " + }, + { + "bbox": [ + 47, + 171, + 287, + 253 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = [\\mathbf{z}_1,\\mathbf{z}_2,\\dots ,\\mathbf{z}_L]" + }, + { + "bbox": [ + 47, + 171, + 287, + 253 + ], + "type": "text", + "content": ", and our EBM prior model is defined as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 261, + 287, + 286 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 261, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 52, + 261, + 287, + 286 + ], + "type": "interline_equation", + "content": "p _ {\\alpha} (\\mathbf {z}) = \\frac {1}{\\mathbb {Z} (\\alpha)} \\exp \\left[ f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\right] p _ {0} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\tag {3}", + "image_path": "b63118820e49e2bbc625ef34c8c18dcb32154e51c8542cebfdc4d46231319e6f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "inline_equation", + "content": "[.]" + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "text", + "content": " refers to the concatenation. " + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "inline_equation", + "content": "f_{\\alpha}(.)" + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "text", + "content": " is the negative energy function that can be parameterized by a small multilayer perceptron with the parameters " + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "inline_equation", + "content": "\\alpha, p_0([\\dots])" + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "text", + "content": " is a reference distribution assumed to be a unit Gaussian, and " + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "inline_equation", + "content": "\\mathbb{Z}(\\alpha)" + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "text", + "content": " is the normalizing constant or partition function. Such a prior model can be considered as an energy-based refinement of the non-informative reference distribution, thus the relationship between different groups of latent codes can be well captured via the energy function " + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "inline_equation", + "content": "f_{\\alpha}([\\mathbf{z}_1,\\ldots ,\\mathbf{z}_L])]" + }, + { + "bbox": [ + 47, + 294, + 287, + 402 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 403, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 287, + 425 + ], + "type": "text", + "content": "For notation simplicity, we denote " + }, + { + "bbox": [ + 47, + 403, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = [\\mathbf{z}_1,\\dots ,\\mathbf{z}_L]" + }, + { + "bbox": [ + 47, + 403, + 287, + 425 + ], + "type": "text", + "content": " in subsequent discussions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 426, + 273, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 273, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 273, + 437 + ], + "type": "text", + "content": "Generation Model. The generation model is defined as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 108, + 447, + 287, + 461 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 447, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 108, + 447, + 287, + 461 + ], + "type": "interline_equation", + "content": "p _ {\\beta} (\\mathbf {x} \\mid \\mathbf {z}) \\sim \\mathcal {N} \\left(g _ {\\beta} (\\mathbf {z}), \\sigma^ {2} I _ {D}\\right) \\tag {4}", + "image_path": "138458aba778796a448cfb322da002a2e60b913cf0c02f95c89ee8a5ce9a7ea4.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "text", + "content": "which models the observed data using top-down generator network " + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "inline_equation", + "content": "g_{\\beta}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "text", + "content": " with additive Gaussian noise, i.e., " + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = g_{\\beta}(\\mathbf{z}) + \\epsilon, \\epsilon \\sim \\mathcal{N}(0, \\sigma^2 I_D)" + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "text", + "content": ". To facilitate the hierarchical representation learning with multi-layer latent variables, we consider multi-layer hierarchical generator network " + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "inline_equation", + "content": "g_{\\beta} (= \\{g_1, g_2, \\ldots, g_L\\})" + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "text", + "content": " that is designed to explain the observation " + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 471, + 287, + 567 + ], + "type": "text", + "content": " by integrating data representation from the above layers, i.e.," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 83, + 576, + 141, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 576, + 141, + 588 + ], + "spans": [ + { + "bbox": [ + 83, + 576, + 141, + 588 + ], + "type": "interline_equation", + "content": "h _ {L} = g _ {L} (\\mathbf {z} _ {L})", + "image_path": "a83bd5fc1a70e9aa39e86b69ad43a4dcd065e8e87e234e5c798746c2d2d29e51.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 85, + 590, + 287, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 590, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 85, + 590, + 287, + 604 + ], + "type": "interline_equation", + "content": "h _ {i} = g _ {i} \\left(\\left[ \\mathbf {z} _ {i}, h _ {i + 1} \\right]\\right), i = 1, 2, \\dots , L - 1 \\tag {5}", + "image_path": "b7620df84e99f6eb42580d0b13785748ff4f807ace6412c2cda92c37bf29aee8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 85, + 606, + 160, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 606, + 160, + 620 + ], + "spans": [ + { + "bbox": [ + 85, + 606, + 160, + 620 + ], + "type": "interline_equation", + "content": "\\mathbf {x} \\sim \\mathcal {N} (h _ {1}, \\sigma^ {2} I _ {D})", + "image_path": "93888390f42b967ac695b04458f419955c5cb0cf36efa77b7fe2f72e9c4cba1c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_L" + }, + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "type": "text", + "content": " is at the top layer, and " + }, + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "type": "inline_equation", + "content": "g_{i}" + }, + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "type": "text", + "content": " is a shallow network that decodes latent code " + }, + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 47, + 629, + 287, + 665 + ], + "type": "text", + "content": " while integrating features from the upper layer." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "text", + "content": "Joint EBM prior vs. independent Gaussian prior: With such a multi-layer hierarchical generation model, it is also tempting to consider learning with the unit Gaussian prior, i.e., " + }, + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "inline_equation", + "content": "p(\\mathbf{z}) \\sim \\mathcal{N}(0, I_d)" + }, + { + "bbox": [ + 47, + 666, + 287, + 713 + ], + "type": "text", + "content": ". Such a prior choice is adopted in" + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 545, + 191 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 545, + 191 + ], + "type": "image", + "image_path": "14cdd146837521465e947bedad9458928b9cf3801129e918fb48c085b47db360.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 194, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 305, + 194, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 194, + 545, + 250 + ], + "type": "text", + "content": "Figure 3. The illustration of the proposed joint EBM prior model (Left). Red lines indicate the modelling of intra-layer relation, and blue lines indicate inter-layer relation. Compared to the Gaussian prior model and single-layer LEBM, our prior model is expressive and effective in learning hierarchical representations." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 267, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 267, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 545, + 352 + ], + "type": "text", + "content": "[42, 20] and has seen some success in learning hierarchical features. However, the independent Gaussian prior does not account for the relations between levels of representations and can be less expressive in capturing complex data features. The proposed EBM prior is expressive and can couple the latent variables across different layers within a joint modelling framework." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 317, + 364, + 519, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 364, + 519, + 376 + ], + "spans": [ + { + "bbox": [ + 317, + 364, + 519, + 376 + ], + "type": "text", + "content": "Our model is illustrated in the left panel of Fig. 3." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 382, + 459, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 382, + 459, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 382, + 459, + 395 + ], + "type": "text", + "content": "3.2. Variational learning scheme" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "type": "text", + "content": "Suppose we have observed examples " + }, + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_i, i = 1, \\dots, n)" + }, + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "type": "text", + "content": " that come from (true) data distribution " + }, + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "type": "text", + "content": " and denote " + }, + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "type": "inline_equation", + "content": "\\theta = (\\beta, \\alpha)" + }, + { + "bbox": [ + 305, + 401, + 545, + 460 + ], + "type": "text", + "content": " that collects all parameters from the generator model. Learning the generator model can be done by maximizing the log-likelihood of all observed examples as" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 322, + 468, + 545, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 468, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 322, + 468, + 545, + 498 + ], + "type": "interline_equation", + "content": "\\sum_ {i = 1} ^ {n} \\log p _ {\\theta} (\\mathbf {x} _ {i}) = \\sum_ {i = 1} ^ {n} \\log \\int p _ {\\alpha} (\\mathbf {z}) p _ {\\beta} (\\mathbf {x} _ {i} | \\mathbf {z}) d \\mathbf {z} \\tag {6}", + "image_path": "9a7779f690589335c9bff9e33f3ed1e9e731c9e5a863f119f8511cdee30a8148.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 506, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 506, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 305, + 506, + 545, + 553 + ], + "type": "text", + "content": "When " + }, + { + "bbox": [ + 305, + 506, + 545, + 553 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 506, + 545, + 553 + ], + "type": "text", + "content": " becomes sufficiently large, maximizing the above log-likelihood is equivalent to minimizing the Kullback-Leibler (KL) divergence between the model distribution and data distribution, i.e., " + }, + { + "bbox": [ + 305, + 506, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\min_{\\theta} D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x}))" + }, + { + "bbox": [ + 305, + 506, + 545, + 553 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "type": "text", + "content": "However, directly maximizing Eq. 6 can be challenging, as the inference of generator posterior (by chain rule, " + }, + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}|\\mathbf{x}) = p_{\\theta}(\\mathbf{x},\\mathbf{z}) / p_{\\theta}(\\mathbf{x}))" + }, + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "type": "text", + "content": " is typically intractable. To tackle the challenge, we employ an inference model " + }, + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "type": "text", + "content": " with a separate set of parameters " + }, + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 554, + 545, + 624 + ], + "type": "text", + "content": " to approximate the generator posterior." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 625, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 625, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 305, + 625, + 545, + 660 + ], + "type": "text", + "content": "Inference model: The inference model maps from data space to latent space and is typically assumed to be Gaussian distributed," + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 365, + 668, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 668, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 365, + 668, + 545, + 682 + ], + "type": "interline_equation", + "content": "q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\sim \\mathcal {N} \\left(\\mu_ {\\phi} (\\mathbf {x}), V _ {\\phi} (\\mathbf {x})\\right) \\tag {7}", + "image_path": "d5caa8a00222d1bc7e66a54fbce32f8a626bfc3764e5608f097d6b504e50d742.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mu_{\\phi}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "V_{\\phi}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " are the d-dimensional mean vector and diagonal covariance matrix. To match with the hierar" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2220" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "chical generator model and facilitate the hierarchical representation learning, we consider the multi-layer inference model defined as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 118, + 154, + 130 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 118, + 154, + 130 + ], + "spans": [ + { + "bbox": [ + 104, + 118, + 154, + 130 + ], + "type": "interline_equation", + "content": "r _ {1} = h _ {1} (\\mathbf {x})", + "image_path": "3a59b6223a590184f46b59c9d7a88e7f253a32a6145f85d961044876a4c49421.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 132, + 287, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 132, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 287, + 144 + ], + "type": "interline_equation", + "content": "r _ {i} = h _ {i} \\left(r _ {i - 1}\\right) i = 2, 3, \\dots , L \\tag {8}", + "image_path": "d83b99544ec399044d255695edc8d4028be45cc1732a9ab87dea475d42b99559.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 147, + 201, + 160 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 147, + 201, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 201, + 160 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {i} \\sim \\mathcal {N} (\\mu_ {i} (r _ {i}), V _ {i} (r _ {i}))", + "image_path": "19bb2cba0d332c93d87bfcd286f341389ddbac7cd170e1fc5e109860787bcce6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_L" + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "content": " is the inferred latent code at the top layer and " + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_1" + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "content": " is the inferred bottom layer latent code. Each latent code " + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "content": " can be inferred and sampled through reparametrization trick [17] using " + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i = \\mu_i(r_i) + V_i(r_i)^{1/2}\\epsilon" + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0, I_{d_i})" + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "content": " being the dimensionality of " + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "inline_equation", + "content": "z_i" + }, + { + "bbox": [ + 47, + 168, + 286, + 228 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 228, + 287, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 287, + 264 + ], + "type": "text", + "content": "Variational learning: We show that the proposed generator model and the inference model can be naturally unified and jointly trained within a variational learning scheme." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "type": "text", + "content": "Specifically, we can define two joint densities, one for generator model density, i.e., " + }, + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}, \\mathbf{z}) = p_{\\alpha}(\\mathbf{z})p_{\\beta}(\\mathbf{x}|\\mathbf{z})" + }, + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "type": "text", + "content": ", and one for data density, i.e., " + }, + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{x}, \\mathbf{z}) = p_{\\mathrm{data}}(\\mathbf{x})q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "type": "text", + "content": ". We propose joint learning through KL minimization, and we denote the objective to be " + }, + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "type": "inline_equation", + "content": "L(\\theta, \\phi)" + }, + { + "bbox": [ + 46, + 264, + 287, + 324 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 332, + 287, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 287, + 350 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\min _ {\\phi} L (\\theta , \\phi) = \\min _ {\\theta} \\min _ {\\phi} D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {x}, \\mathbf {z}) | | p _ {\\theta} (\\mathbf {x}, \\mathbf {z})\\right) \\tag {9}", + "image_path": "98834eb5d6a2535381e58be36846040555be9d818f583315779aa191509d074f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 358, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 287, + 392 + ], + "type": "text", + "content": "where the generator model density is learned to match the true joint data density and capture extracted hierarchical features." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 394, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 287, + 419 + ], + "type": "text", + "content": "Learning " + }, + { + "bbox": [ + 47, + 394, + 287, + 419 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 394, + 287, + 419 + ], + "type": "text", + "content": " : With this joint KL minimization, the prior model can be learned with the gradient " + }, + { + "bbox": [ + 47, + 394, + 287, + 419 + ], + "type": "inline_equation", + "content": "-\\nabla_{\\alpha}L(\\theta ,\\phi)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 77, + 427, + 256, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 427, + 256, + 441 + ], + "spans": [ + { + "bbox": [ + 77, + 427, + 256, + 441 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} | \\mathbf {x})} [ \\nabla_ {\\alpha} f _ {\\alpha} ([ \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} ]) ] -", + "image_path": "2c66eb2d9b6181da8323cbb86002589bc94fb36663e814b8aaa69739f2725924.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 78, + 443, + 287, + 457 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 443, + 287, + 457 + ], + "spans": [ + { + "bbox": [ + 78, + 443, + 287, + 457 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {p _ {\\alpha} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right)} \\left[ \\nabla_ {\\alpha} f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\right] \\tag {10}", + "image_path": "44ac7dc21fcbd11ed8b2532ad7962b73a2e58d8299f353aa1cf7e120b93da155.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 464, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 287, + 489 + ], + "type": "text", + "content": "Learning " + }, + { + "bbox": [ + 47, + 464, + 287, + 489 + ], + "type": "inline_equation", + "content": "p_{\\beta}(\\mathbf{x}|\\mathbf{z})" + }, + { + "bbox": [ + 47, + 464, + 287, + 489 + ], + "type": "text", + "content": " : The generation model can be learned with the gradient " + }, + { + "bbox": [ + 47, + 464, + 287, + 489 + ], + "type": "inline_equation", + "content": "-\\nabla_{\\beta}L(\\theta ,\\phi)" + }, + { + "bbox": [ + 47, + 464, + 287, + 489 + ], + "type": "text", + "content": " computed as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 63, + 497, + 287, + 511 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 497, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 63, + 497, + 287, + 511 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {q _ {\\phi} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\mid \\mathbf {x}\\right)} \\left[ \\nabla_ {\\beta} \\log p _ {\\beta} \\left(\\mathbf {x} \\mid \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right) \\right] \\tag {11}", + "image_path": "5643de0b1de794f0d84662e7e8e1c1313c065d707e5f3979f05f803dd6b86dd5.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 518, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 543 + ], + "type": "text", + "content": "Learning " + }, + { + "bbox": [ + 46, + 518, + 287, + 543 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 46, + 518, + 287, + 543 + ], + "type": "text", + "content": " : The inference model can be learned by computing the gradient " + }, + { + "bbox": [ + 46, + 518, + 287, + 543 + ], + "type": "inline_equation", + "content": "-\\nabla_{\\phi}L(\\theta ,\\phi)" + }, + { + "bbox": [ + 46, + 518, + 287, + 543 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 60, + 552, + 287, + 565 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 552, + 287, + 565 + ], + "spans": [ + { + "bbox": [ + 60, + 552, + 287, + 565 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\phi} \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} | \\mathbf {x})} [ \\log p _ {\\beta} (\\mathbf {x} | \\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}) ] - \\tag {12}", + "image_path": "9ee8dc77a1c822917134e04c8315863c51bc8f58140422d12987198ab62a6135.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 60, + 568, + 268, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 568, + 268, + 581 + ], + "spans": [ + { + "bbox": [ + 60, + 568, + 268, + 581 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\phi} D _ {\\mathrm {K L}} \\left(q _ {\\phi} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L} \\mid \\mathbf {x}\\right) \\mid \\mid p _ {\\alpha} \\left(\\mathbf {z} _ {1}, \\mathbf {z} _ {2}, \\dots , \\mathbf {z} _ {L}\\right)\\right)", + "image_path": "f809e1f0b8e7f952fa410d0aa0162a7079d4b68119dde411de43f6244a6b82ec.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 59, + 589, + 286, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 589, + 286, + 601 + ], + "spans": [ + { + "bbox": [ + 59, + 589, + 286, + 601 + ], + "type": "text", + "content": "We provide further theoretical understanding in Sec. 3.4." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 609, + 140, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 140, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 140, + 621 + ], + "type": "text", + "content": "3.3. Prior sampling" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 626, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 287, + 662 + ], + "type": "text", + "content": "Training the proposed joint EBM prior model requires sampling " + }, + { + "bbox": [ + 47, + 626, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_1, \\mathbf{z}_2, \\ldots, \\mathbf{z}_L" + }, + { + "bbox": [ + 47, + 626, + 287, + 662 + ], + "type": "text", + "content": " from the proposed EBM prior (see Eq. 10). To do so, we can use Langevin dynamic [22]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 662, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 662, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 662, + 287, + 685 + ], + "type": "text", + "content": "For arbitrary target distribution " + }, + { + "bbox": [ + 47, + 662, + 287, + 685 + ], + "type": "inline_equation", + "content": "p(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 662, + 287, + 685 + ], + "type": "text", + "content": ", the Langevin dynamic iterates:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 94, + 692, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 692, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 94, + 692, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {t + 1} = \\mathbf {z} _ {t} + \\frac {s ^ {2}}{2} \\nabla_ {\\mathbf {z}} \\log p (\\mathbf {z} _ {t}) + s \\epsilon_ {t} \\tag {13}", + "image_path": "bc09eb788c7fef915262593f342382b40c130c871bb3d491b0f343f1c195c016.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": " indexes the time step of Langevin dynamics. " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": " is the step size and " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "\\epsilon_t\\sim \\mathcal{N}(0,I_d)" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": ". We run the noise-initialized Langevin dynamics for " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": " steps. Noted that as " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "s\\to 0" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "K\\rightarrow \\infty" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": ", the distribution of " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": " will converge to the target " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "p(\\mathbf{z})" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": " regardless of the initial distribution of " + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 305, + 72, + 545, + 132 + ], + "type": "text", + "content": " [22]." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 133, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 133, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 305, + 133, + 545, + 168 + ], + "type": "text", + "content": "Specifically, for prior sampling, we use the prior distribution " + }, + { + "bbox": [ + 305, + 133, + 545, + 168 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 305, + 133, + 545, + 168 + ], + "type": "text", + "content": " as our target distribution, and the gradient " + }, + { + "bbox": [ + 305, + 133, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{z}}\\log p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 305, + 133, + 545, + 168 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 321, + 176, + 545, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 176, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 321, + 176, + 545, + 190 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\mathbf {z}} f _ {\\alpha} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) + \\nabla_ {\\mathbf {z}} \\log p _ {0} \\left(\\left[ \\mathbf {z} _ {1}, \\dots , \\mathbf {z} _ {L} \\right]\\right) \\tag {14}", + "image_path": "7941b67c8887e1a2dabe464b0cadb1d68995adf9ac2177b13fc7c9f922e52a27.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 198, + 545, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 234 + ], + "type": "text", + "content": "The Langevin dynamics for prior sampling can be efficient due to the low-dimensional latent space and the lightweight network structure for the energy function." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 318, + 246, + 533, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 246, + 533, + 258 + ], + "spans": [ + { + "bbox": [ + 318, + 246, + 533, + 258 + ], + "type": "text", + "content": "The overall procedure is summarized in Algorithm 1." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 269, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 269, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 306, + 269, + 545, + 293 + ], + "type": "text", + "content": "Algorithm 1 Learning latent EBM prior for hierarchical generator model" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "content": "Input: Training iterations " + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "content": ", observed training examples " + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\{x_{i}\\}_{i = 1}^{n}" + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "content": ", batch size " + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "content": ", network parameters " + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta, \\phi" + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "content": ", learning rate " + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\eta_{\\alpha}, \\eta_{\\beta}, \\eta_{\\phi}" + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "content": ", Langevin steps " + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "content": ", Langevin step size " + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 315, + 294, + 545, + 341 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 316, + 342, + 422, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 342, + 422, + 354 + ], + "spans": [ + { + "bbox": [ + 316, + 342, + 422, + 354 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 316, + 342, + 422, + 354 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 316, + 342, + 422, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 316, + 342, + 422, + 354 + ], + "type": "inline_equation", + "content": "\\theta = (\\alpha, \\beta)" + }, + { + "bbox": [ + 316, + 342, + 422, + 354 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 317, + 355, + 346, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 355, + 346, + 365 + ], + "spans": [ + { + "bbox": [ + 317, + 355, + 346, + 365 + ], + "type": "text", + "content": "repeat" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "type": "text", + "content": "Prior sampling for " + }, + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\{z_i^{-}\\}_{i = 1}^m" + }, + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "type": "text", + "content": " using Eq. 13 and Eq. 14 with " + }, + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 326, + 366, + 545, + 388 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 326, + 389, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 389, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 326, + 389, + 545, + 413 + ], + "type": "text", + "content": "Inference sampling for " + }, + { + "bbox": [ + 326, + 389, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\{z_i^+\\}_{i=1}^m" + }, + { + "bbox": [ + 326, + 389, + 545, + 413 + ], + "type": "text", + "content": " using Eq. 8 with " + }, + { + "bbox": [ + 326, + 389, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\{x_i\\}_{i=1}^m" + }, + { + "bbox": [ + 326, + 389, + 545, + 413 + ], + "type": "text", + "content": " and reparametrization." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 326, + 414, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 414, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 326, + 414, + 545, + 437 + ], + "type": "text", + "content": "Learn joint EBM prior: Given " + }, + { + "bbox": [ + 326, + 414, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\{z_i^-, z_i^+\\}_{i=1}^m" + }, + { + "bbox": [ + 326, + 414, + 545, + 437 + ], + "type": "text", + "content": ", update " + }, + { + "bbox": [ + 326, + 414, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\alpha = \\alpha - \\eta_\\alpha \\nabla_\\alpha L(\\theta, \\phi)" + }, + { + "bbox": [ + 326, + 414, + 545, + 437 + ], + "type": "text", + "content": " using Eq. 10 with " + }, + { + "bbox": [ + 326, + 414, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\eta_\\alpha" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 326, + 438, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 438, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 326, + 438, + 545, + 461 + ], + "type": "text", + "content": "Learn generation model:Given " + }, + { + "bbox": [ + 326, + 438, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\{x_{i},z_{i}^{+}\\}_{i = 1}^{m}" + }, + { + "bbox": [ + 326, + 438, + 545, + 461 + ], + "type": "text", + "content": " update " + }, + { + "bbox": [ + 326, + 438, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\beta = \\beta -\\eta_{\\beta}\\nabla_{\\beta}L(\\theta ,\\phi)" + }, + { + "bbox": [ + 326, + 438, + 545, + 461 + ], + "type": "text", + "content": " using Eq. 11 with " + }, + { + "bbox": [ + 326, + 438, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\eta_{\\beta}" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 326, + 462, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 462, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 326, + 462, + 545, + 486 + ], + "type": "text", + "content": "Learn inference model: Given " + }, + { + "bbox": [ + 326, + 462, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\{x_{i},z_{i}^{+}\\}_{i = 1}^{m}" + }, + { + "bbox": [ + 326, + 462, + 545, + 486 + ], + "type": "text", + "content": " update " + }, + { + "bbox": [ + 326, + 462, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\phi = \\phi -\\eta_{\\phi}\\nabla_{\\phi}L(\\theta ,\\phi)" + }, + { + "bbox": [ + 326, + 462, + 545, + 486 + ], + "type": "text", + "content": " using Eq. 12 with " + }, + { + "bbox": [ + 326, + 462, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\eta_{\\phi}" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 326, + 487, + 385, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 487, + 385, + 496 + ], + "spans": [ + { + "bbox": [ + 326, + 487, + 385, + 496 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 326, + 487, + 385, + 496 + ], + "type": "inline_equation", + "content": "t = t + 1" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 317, + 498, + 365, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 498, + 365, + 508 + ], + "spans": [ + { + "bbox": [ + 317, + 498, + 365, + 508 + ], + "type": "text", + "content": "until " + }, + { + "bbox": [ + 317, + 498, + 365, + 508 + ], + "type": "inline_equation", + "content": "t = T" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 531, + 458, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 531, + 458, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 531, + 458, + 544 + ], + "type": "text", + "content": "3.4. Theoretical understanding" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 305, + 549, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 549, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 305, + 549, + 545, + 585 + ], + "type": "text", + "content": "Divergence perturbation and ELBO. The KL joint minimization (Eq. 9) can be viewed as a surrogate of the MLE objective with the KL perturbation term," + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 322, + 594, + 539, + 621 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 594, + 539, + 621 + ], + "spans": [ + { + "bbox": [ + 322, + 594, + 539, + 621 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {x}, \\mathbf {z}) | | p _ {\\theta} (\\mathbf {x}, \\mathbf {z})\\right) \\\\ = D _ {\\mathrm {K L}} \\left(p _ {\\text {d a t a}} (\\mathbf {x}) | | p _ {\\theta} (\\mathbf {x})\\right) + D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) | | p _ {\\theta} (\\mathbf {z} | \\mathbf {x})\\right) \\\\ \\end{array}", + "image_path": "28cfd89bbaede680d55daeb027258a1fca3c05aefcbde9e973c14e7e51230d46.jpg" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x}))" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " is the MLE loss function, and the perturbation term " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}(q_{\\phi}(\\mathbf{z}|\\mathbf{x})||p_{\\theta}(\\mathbf{z}|\\mathbf{x}))" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " measures the KL-divergence between inference distribution and generator posterior. The inference " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " is learned to match the posterior distribution of the generator without expensive posterior sampling. In fact, such KL minimization in the joint space is equivalent to evidence lower bound" + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "2221" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": "(ELBO). To see this, noted that " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}(p_{\\mathrm{data}}(\\mathbf{x})||p_{\\theta}(\\mathbf{x})) = -H(p_{\\mathrm{data}}(\\mathbf{x})) - \\mathbb{E}_{p_{\\mathrm{data}}}[\\log p_{\\theta}(\\mathbf{x})]" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "H(p_{\\mathrm{data}}(\\mathbf{x}))" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " is the entropy of the empirical data distribution and can be treated as constant " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "C \\equiv -H(p_{\\mathrm{data}}(\\mathbf{x}))" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " w.r.t model parameters " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": ". Then " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "L(\\theta, \\phi)" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " is computed as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 140, + 284, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 140, + 284, + 196 + ], + "spans": [ + { + "bbox": [ + 61, + 140, + 284, + 196 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} - \\mathbb {E} _ {p _ {\\mathrm {d a t a}}} [ \\log p _ {\\theta} (\\mathbf {x}) ] + D _ {\\mathrm {K L}} \\left(q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p _ {\\theta} (\\mathbf {z} | \\mathbf {x})\\right) + C \\\\ = \\mathbb {E} _ {p _ {\\mathrm {d a t a}}} \\left[ \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left(\\log \\frac {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})}\\right) - \\log p _ {\\theta} (\\mathbf {x}) \\right] + C \\\\ = \\mathbb {E} _ {p _ {\\text {d a t a}}} [ - \\operatorname {E L B O} (\\mathbf {x}; \\theta , \\phi) ] + C \\\\ \\end{array}", + "image_path": "029bad25b089aabba07d25b2920117d1d4c965a95fe995bff35a61853f0a65d5.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 203, + 75, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 203, + 75, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 203, + 75, + 213 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 219, + 282, + 274 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 219, + 282, + 274 + ], + "spans": [ + { + "bbox": [ + 49, + 219, + 282, + 274 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {E L B O} (\\mathbf {x}; \\theta , \\phi) = \\log p _ {\\theta} (\\mathbf {x}) - \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log \\frac {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\right] \\\\ = \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\left[ \\log \\frac {p _ {\\theta} (\\mathbf {x} , \\mathbf {z})}{q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\right] \\\\ \\end{array}", + "image_path": "f3c213f8c8c137c556f6a472d4c5b654459000299cb9aa717c3e17c8a43d3e72.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 279, + 287, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 287, + 339 + ], + "type": "text", + "content": "and is referred to as evidence lower bound (ELBO) in the literature [17]. Noted that the prior model (i.e., " + }, + { + "bbox": [ + 47, + 279, + 287, + 339 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}, \\mathbf{z}) = p_{\\beta}(\\mathbf{x}|\\mathbf{z})p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 279, + 287, + 339 + ], + "type": "text", + "content": ") is now parameterized to be our joint EBM prior. Minimizing Eq. 9 is equivalent to maximizing the evidence lower bound of the log-likelihood." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "text", + "content": "Short run sampling and divergence perturbation. The learning of the energy-based model in Eq. 10 requires MCMC sampling from " + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "text", + "content": ". We adopt the short-run Langevin dynamics (Eq. 13) with fixed " + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "text", + "content": " steps to sample from prior " + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "text", + "content": " for efficient computation. Such prior sampling amounts to approximates the objective " + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "inline_equation", + "content": "L(\\theta, \\phi)" + }, + { + "bbox": [ + 47, + 340, + 287, + 423 + ], + "type": "text", + "content": " in Eq. 9 with yet another KL perturbation term, i.e.," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 70, + 430, + 244, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 430, + 244, + 444 + ], + "spans": [ + { + "bbox": [ + 70, + 430, + 244, + 444 + ], + "type": "interline_equation", + "content": "\\tilde {L} (\\theta , \\phi) = L (\\theta , \\phi) - D _ {\\mathrm {K L}} \\left(\\tilde {p} _ {\\alpha^ {(t)}} (\\mathbf {z}) | p _ {\\alpha} (\\mathbf {z})\\right)", + "image_path": "4c1ffc3aa53aeaaf7f8e83c2ab2bf027137b0073c112d583d6cae95afa81adad.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\tilde{p}_{\\alpha^{(t)}}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "type": "text", + "content": " refers to the distribution of latent codes after " + }, + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "type": "text", + "content": " steps of Langevin dynamics (Eq. 13) in the " + }, + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 451, + 287, + 499 + ], + "type": "text", + "content": "-th iteration of the learning. The corresponding learning gradient for the prior model is thus" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 506, + 283, + 522 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 506, + 283, + 522 + ], + "spans": [ + { + "bbox": [ + 52, + 506, + 283, + 522 + ], + "type": "interline_equation", + "content": "- \\nabla_ {\\alpha} \\tilde {L} (\\theta , \\phi) = \\mathbb {E} _ {q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} [ \\nabla_ {\\alpha} f _ {\\alpha} (\\mathbf {z}) ] - \\mathbb {E} _ {\\tilde {p} _ {\\alpha (t)} (\\mathbf {z})} [ \\nabla_ {\\alpha} f _ {\\alpha} (\\mathbf {z}) ]", + "image_path": "cbce7b910db116bda3c7d71fe1bb906cd72b3e1277f64b1db9354ce8f3047ca9.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "type": "text", + "content": "When " + }, + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "type": "text", + "content": " is sufficiently large, the perturbation term " + }, + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}(\\tilde{p}_{\\alpha^{(t)}}(\\mathbf{z})|p_{\\alpha}(\\mathbf{z})) \\to 0" + }, + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "type": "text", + "content": ". The update rule for the energy-based prior model (also Eq. 10) can be interpreted as self-adversarial learning. The prior model " + }, + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 528, + 287, + 659 + ], + "type": "text", + "content": " serves as both generator and discriminator if we compare it to GAN (generative adversarial networks) [11]. In contrast to GAN, our learning follows MLE with divergence perturbations, which in general does not suffer from issues such as mode collapsing and instability, as it does not involve competition between two separate models. The energy-based model can thus be seen as its own adversary or its own critic." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "text", + "content": "4. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Generator model. The generator model has a top-down network that maps the low-dimensional latent code to the" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "observed data space. VAEs [17, 27, 33, 32] proposes variational learning by introducing an approximation of the true intractable posterior, which allows a tractable bound on log-likelihood to be maximized. Another line of work [14, 25] trains the generator model without inference model by using Langevin dynamics for generator posterior sampling. We follow the former approach and use the inference model for efficient training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 182, + 545, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 349 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 349 + ], + "type": "text", + "content": "Generator model with informative prior. The majority of the existing generator models assume that the latent code follows a simple and known prior distribution, such as isotropic Gaussian distribution. Such assumption may render an ineffective generator as observed in [34, 5]. Our work utilizes the informative and expressive energy-based prior in the joint space of latent variables and is related to the line of previous research on introducing flexible prior distributions. For example, [34] parameterizes the prior based on the posterior inference model. [5, 9] adopt a two-stage approach which first trains a latent variable model with simple prior and then trains a separate prior model (e.g., VAE or Gaussian mixture model) to match the aggregated posterior distribution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 364, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 544 + ], + "type": "text", + "content": "Generator model with hierarchical structures. The generator models that consist of multi-layers of latent variables are recently attracting attention for hierarchical learning. [29, 2, 21, 3, 36] stack generative models on top of each other and assume conditional Gaussian distributions at different layers. However, as shown in Sec. 2.1, the bottom layer could act as a single generative model and absorb most features, leading to ineffective representation learning. [42, 20] propose to learn hierarchical features with unit Gaussian prior by adapting the generator into multiple layers. However, the latent variables at different layers are distributed independently a priori and are only loosely connected. Instead, we propose a joint EBM prior that could tightly couple and jointly model latent variables at different layers and show superior results through joint training." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": "Hierarchical generator model with informative prior. Recent advances [4, 1] have started exploring learning informative prior for multi-layer generator models. JEBM [4] and NCP-VAE [1] build latent space EBM on hierarchical generator models and showcase the capability of improving the generation quality. However, these models consider the conditional hierarchical models, which can be limited in learning effective hierarchical representations (see Sec. 2.1). This work studies hierarchical representation learning by introducing a novel framework where latent space EBM can be jointly trained with the architectural hierarchical models to capture complex representations of different levels." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2222" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 69, + 175, + 183 + ], + "blocks": [ + { + "bbox": [ + 61, + 69, + 175, + 183 + ], + "lines": [ + { + "bbox": [ + 61, + 69, + 175, + 183 + ], + "spans": [ + { + "bbox": [ + 61, + 69, + 175, + 183 + ], + "type": "image", + "image_path": "28aa96ea11f0bd66327f1e7ad14b7336d8aa695525725a593f26e8b45abf6c80.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": "Figure 4. Hierarchical sampling on SVHN. Left: The latent code at bottom layer " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "(z_{1})" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " represents the background light and shading. Center-left: the latent code at second bottom layer " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "(z_{2})" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " represents the color schemes. Center-right: the latent code at second top layer " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "(z_{3})" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " encodes the shape variations of the same digit. Right: the latent code at top layer " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "(z_{4})" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " captures the digit identity and the general structure." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 179, + 69, + 294, + 184 + ], + "blocks": [ + { + "bbox": [ + 179, + 69, + 294, + 184 + ], + "lines": [ + { + "bbox": [ + 179, + 69, + 294, + 184 + ], + "spans": [ + { + "bbox": [ + 179, + 69, + 294, + 184 + ], + "type": "image", + "image_path": "7bd785344120ff2ed24d0957cfd19aae53ecac0fd868af25b60c269b8ae36af3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 299, + 70, + 414, + 184 + ], + "blocks": [ + { + "bbox": [ + 299, + 70, + 414, + 184 + ], + "lines": [ + { + "bbox": [ + 299, + 70, + 414, + 184 + ], + "spans": [ + { + "bbox": [ + 299, + 70, + 414, + 184 + ], + "type": "image", + "image_path": "b6d465a1360f41482ed6cb3017f029550671c905dd1a0b440b4ab18026572489.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 419, + 70, + 533, + 184 + ], + "blocks": [ + { + "bbox": [ + 419, + 70, + 533, + 184 + ], + "lines": [ + { + "bbox": [ + 419, + 70, + 533, + 184 + ], + "spans": [ + { + "bbox": [ + 419, + 70, + 533, + 184 + ], + "type": "image", + "image_path": "05d3c4ad017755d67b5cf20cf477c158d536e7e2c4a95e42763a502eaf1d8e48.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 60, + 237, + 274, + 306 + ], + "blocks": [ + { + "bbox": [ + 60, + 237, + 274, + 306 + ], + "lines": [ + { + "bbox": [ + 60, + 237, + 274, + 306 + ], + "spans": [ + { + "bbox": [ + 60, + 237, + 274, + 306 + ], + "type": "image", + "image_path": "e57bab778a351865d9a6b1143aadccd8a3edd709edb5fbb9bc108968be96d06d.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "lines": [ + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "type": "text", + "content": "Figure 5. Hierarchical sampling on MNIST. Left: The latent code at bottom layer " + }, + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "type": "inline_equation", + "content": "(z_{1})" + }, + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "type": "text", + "content": " indicates the stroke width. Center: the latent code at second layer " + }, + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "type": "inline_equation", + "content": "(z_{2})" + }, + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "type": "text", + "content": " encodes geometric changes among similar digits. Right: the latent code at top layer " + }, + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "type": "inline_equation", + "content": "(z_{3})" + }, + { + "bbox": [ + 46, + 308, + 288, + 364 + ], + "type": "text", + "content": " learns the digit identity and general structure." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 384, + 128, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 128, + 398 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 128, + 398 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 406, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 489 + ], + "type": "text", + "content": "To demonstrate the effectiveness of our method, we conduct the following experiments: 1) hierarchical representation learning, 2) analysis of latent space, 3) image modelling, and 4) robustness. For a better understanding of the proposed method, we perform the disentanglement learning experiment, various ablation studies, and an analysis of parameter complexity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 500, + 249, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 500, + 249, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 500, + 249, + 514 + ], + "type": "text", + "content": "5.1. Hierarchical Representation Learning" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 520, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 555 + ], + "type": "text", + "content": "We first demonstrate the capability of our model in hierarchical representation learning by experiments of hierarchical sampling and latent classifier." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "content": "Hierarchical sampling. With partitioned latent variables and the hierarchical structure of generator, the latent variables at higher layers should capture semantic features, while the lower layers should capture low-level features. We train our model on MNIST using the same setting as in Sec. 2.2 with only '0', '1', and '2' digit classes available and the latent dimension set to 2. In Fig. 6, by changing the " + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_1" + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "content": " (at the bottom layer), our model can successfully deliver the variations in shape (low-level features), and changing the " + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_2" + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "content": " (at the top layer) leads to the variations in digit class (high-level features). This indicates a successfully learned hierarchical representation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Further, we train our model on MNIST with all digit" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 239, + 542, + 292 + ], + "blocks": [ + { + "bbox": [ + 310, + 239, + 542, + 292 + ], + "lines": [ + { + "bbox": [ + 310, + 239, + 542, + 292 + ], + "spans": [ + { + "bbox": [ + 310, + 239, + 542, + 292 + ], + "type": "image", + "image_path": "8170f2bf23bded18b493feb09312a19064ca06767907ff2a449f4ef560b07d1b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 295, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 305, + 295, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 295, + 545, + 338 + ], + "type": "text", + "content": "Figure 6. Visualization for our model by changing each unit of 2-dimensional z. Left: changing the first unit. Right: changing the second unit. Top: the value of each unit, where the orange color indicates the first unit and the blue color indicates the second unit." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 357, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 545, + 418 + ], + "type": "text", + "content": "classes and the more challenging SVHN dataset, and we generate the images by sampling (using Eq. 13) the latent code of one layer while keeping other layers fixed. The results shown in Fig. 4 and Fig. 5 also demonstrate the hierarchical representation learned by our model." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 418, + 546, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 546, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 546, + 550 + ], + "type": "text", + "content": "Latent Classifier. We next show that our model can achieve better performance in hierarchical representation learning. Note that the inference model " + }, + { + "bbox": [ + 304, + 418, + 546, + 550 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 304, + 418, + 546, + 550 + ], + "type": "text", + "content": " should be learned to approximate the true posterior " + }, + { + "bbox": [ + 304, + 418, + 546, + 550 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 304, + 418, + 546, + 550 + ], + "type": "text", + "content": " of the generator, which integrates both the hierarchical inductive bias and the energy-based refinement. Therefore, to measure the learned hierarchical features, we learn classifiers on the inferred latent codes at different layers to predict the label of the data and measure the testing classification accuracy. The latent codes that carry rich high-level semantic features should achieve higher classification accuracy." + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 313, + 582, + 537, + 653 + ], + "blocks": [ + { + "bbox": [ + 305, + 559, + 545, + 581 + ], + "lines": [ + { + "bbox": [ + 305, + 559, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 305, + 559, + 545, + 581 + ], + "type": "text", + "content": "Table 1. Testing accuracy of inferred latent codes at each layer. We denote " + }, + { + "bbox": [ + 305, + 559, + 545, + 581 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 305, + 559, + 545, + 581 + ], + "type": "text", + "content": " for the layer that has unexpectedly lower accuracy." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 582, + 537, + 653 + ], + "lines": [ + { + "bbox": [ + 313, + 582, + 537, + 653 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 537, + 653 + ], + "type": "table", + "html": "
L=1L=2L=3L=4
MNISTOurs32.60%58.32%67.64%-
VLAE35.69%57.86%52.08% (↓)-
Fashion-MNISTOurs39.27%44.81%84.27%-
VLAE52.43%35.65% (↓)83.24%-
SVHNOurs21.00%25.29%30.58%86.63%
VLAE22.59%26.97%56.70%52.14% (↓)
", + "image_path": "5535d4bda11581333e5e2edb7f219e01833c3b34c8d3ffdd5e0b3add89af315b.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "content": "In practice, we first train our model on standard benchmarks, such as MNIST, Fashion-MNIST, and SVHN. Then, we train classifiers on the inferred latent codes at each layer. We consider VLAE [42] as our baseline model, which" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2223" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "learns a structural latent space with standard Gaussian prior. We show comparison results in Tab. 1, where our learned inference model " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " extracts varying levels of semantic features for different layers of latent codes. The top layer carries the most significant features, and the bottom layer carries the least. The baseline model that assumes Gaussian prior, however, extracted mixed semantic features across different layers. For fair comparisons, we use the same generation and inference structure as the baseline model2. The structure of the classifier contains two linear layers with a hidden dimension set to 256 and uses ReLU activation function. The classifier has softmax as its output layer. We do not employ drop-out and normalization strategies." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 240, + 149, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 149, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 149, + 253 + ], + "type": "text", + "content": "5.2. Image Modelling" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 261, + 287, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 381 + ], + "type": "text", + "content": "In this section, we evaluate our model in image modelling by measuring the quality of generated and reconstructed images. We consider the baseline models that assume Gaussian prior, such as Alternating Back-propagation (ABP) [14], Ladder-VAE (LVAE) [30], BIVA [21], Short-run MCMC (SRI) [25], and VLAE [42], as well as generator models with informative prior, such as RAE [9], Two-stages VAE (2s-VAE) [5], NCP-VAE [1], Multi-NCP [37] and LEBM [26]. To make fair comparisons, we follow the protocol in [26]." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 54, + 415, + 278, + 577 + ], + "blocks": [ + { + "bbox": [ + 47, + 393, + 287, + 415 + ], + "lines": [ + { + "bbox": [ + 47, + 393, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 393, + 287, + 415 + ], + "type": "text", + "content": "Table 2. Testing reconstruction by MSE, and generation evaluation by FID on SVHN and CelebA-64." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 54, + 415, + 278, + 577 + ], + "lines": [ + { + "bbox": [ + 54, + 415, + 278, + 577 + ], + "spans": [ + { + "bbox": [ + 54, + 415, + 278, + 577 + ], + "type": "table", + "html": "
ModelSVHNCelebA-64
MSE (↓)FID (↓)MSE (↓)FID (↓)
ABP-49.71-51.50
LVAE0.01439.260.02853.40
BIVA0.01031.650.01033.58
SRI0.01135.230.01136.84
VLAE0.01643.950.01044.05
2s-VAE0.01942.810.02144.40
RAE0.01440.020.01840.95
NCP-VAE0.02033.230.02142.07
Multi-NCP0.00426.190.00935.38
LEBM0.00829.440.01337.87
Ours0.00824.160.00432.15
", + "image_path": "6bd2ca58c795b8f67a904a1ce18f0daf30ed7b97902f5606c2f9c6b3c0bf4a88.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 592, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 287, + 640 + ], + "type": "text", + "content": "Synthesis: We use Fréchet Inception Distance (FID) [16] to quantitatively evaluate the sample quality. In Tab. 2, it can be seen that our model obtains superior generation quality compared to the baseline models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": "Reconstructions: To evaluate the accuracy of our inference model, we compute mean square error (MSE) [26, 24] for testing reconstruction. As shown in Tab. 2, the proposed model leads to more accurate and faithful reconstructions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 444, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 444, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 444, + 85 + ], + "type": "text", + "content": "5.3. Analysis of Latent Space" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "type": "text", + "content": "Visualization of toy data. To illustrate the expressivity of the proposed EBM prior, we train our model on MNIST (using the same setting as shown in Fig. 2 and Fig. 6) and set the latent dimension for both " + }, + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_1" + }, + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_2" + }, + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "type": "text", + "content": " to 2 for better visualization. We visualized the Langevin transition of the prior sampling in Fig. 7, which shows that the latent codes at the top layer " + }, + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "type": "inline_equation", + "content": "(\\mathbf{z}_2)" + }, + { + "bbox": [ + 304, + 90, + 547, + 186 + ], + "type": "text", + "content": " can effectively capture the multi-modal posterior, where using a Gaussian prior might be infeasible." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 320, + 196, + 532, + 281 + ], + "blocks": [ + { + "bbox": [ + 320, + 196, + 532, + 281 + ], + "lines": [ + { + "bbox": [ + 320, + 196, + 532, + 281 + ], + "spans": [ + { + "bbox": [ + 320, + 196, + 532, + 281 + ], + "type": "image", + "image_path": "b6f2688896c2d327233d4cbb8bfc623f5dd77ea71d379c914381d2de88bddf4c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 285, + 545, + 319 + ], + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 319 + ], + "type": "text", + "content": "Figure 7. Visualization of the latent codes sampled from our EBM prior (Top row: " + }, + { + "bbox": [ + 304, + 285, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_2" + }, + { + "bbox": [ + 304, + 285, + 545, + 319 + ], + "type": "text", + "content": "). Blue, Orange color indicate prior and posterior, respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "type": "text", + "content": "Langevin trajectory. We explore the energy landscape of the learned prior " + }, + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "type": "text", + "content": " via transition of Langevin dynamics initialized from " + }, + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "type": "inline_equation", + "content": "p_0(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "type": "text", + "content": " towards " + }, + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 330, + 546, + 510 + ], + "type": "text", + "content": " on CelebA-64. If the EBM is well-learned, the energy prior should render local modes of the energy function, and traversing these local modes should present diverse, realistic image synthesis and steady-state energy scores. Existing EBMs often suffer from oversaturated synthesis via the challenging long-run Langevin dynamic (see oversaturated example in Fig.3 in [23]). We thereby test our model with 2500 Langevin steps, which is much longer than the 40 steps used in training. Fig. 8 shows the image synthesis and energy profile, where our EBM prior model does not exhibit the oversaturated phenomenon and successfully delivers diverse and realistic synthesis with steady-state energy." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 519, + 544, + 592 + ], + "blocks": [ + { + "bbox": [ + 307, + 519, + 544, + 592 + ], + "lines": [ + { + "bbox": [ + 307, + 519, + 544, + 592 + ], + "spans": [ + { + "bbox": [ + 307, + 519, + 544, + 592 + ], + "type": "image", + "image_path": "1eb3ae9ea9567caeea7d87a28a4d630ab6d92dffe3cb485d94faeda323dddfca.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 594, + 545, + 628 + ], + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 628 + ], + "type": "text", + "content": "Figure 8. Transition of Markov chains initialized from " + }, + { + "bbox": [ + 304, + 594, + 545, + 628 + ], + "type": "inline_equation", + "content": "p_0(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 594, + 545, + 628 + ], + "type": "text", + "content": " towards " + }, + { + "bbox": [ + 304, + 594, + 545, + 628 + ], + "type": "inline_equation", + "content": "p_{\\alpha}(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 594, + 545, + 628 + ], + "type": "text", + "content": " for 2500 steps. Top: Trajectory in the CelebA-64 data space for every 100 steps. Bottom: Energy profile over time." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 647, + 382, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 382, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 382, + 658 + ], + "type": "text", + "content": "5.4. Robustness" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 689 + ], + "type": "text", + "content": "In this section, we examine the robustness of our model in adversarial attack and outlier detection." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "Adversarial robustness. For adversarial robustness, we consider the latent attack [10], which is shown to be a" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 702, + 270, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 702, + 270, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 702, + 270, + 713 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 57, + 702, + 270, + 713 + ], + "type": "text", + "content": "https://github.com/ermongroup/Variational-Ladder-Autoencoder" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2224" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "strong attack for the generative model with latent variables, and it allows us to attack the latent codes at different layers. Specifically, let " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " be the target and " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_o" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " be the original image. The attack aims to create the distorted image " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{x}} = \\mathbf{x}_o + \\epsilon" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " such that its learned inference distribution " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\tilde{\\mathbf{x}})" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " is close to the inference " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x}_t)" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " on target images under KL-divergence (Eq. 5 in [10])." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 164, + 276, + 180 + ], + "blocks": [ + { + "bbox": [ + 58, + 164, + 276, + 180 + ], + "lines": [ + { + "bbox": [ + 58, + 164, + 276, + 180 + ], + "spans": [ + { + "bbox": [ + 58, + 164, + 276, + 180 + ], + "type": "image", + "image_path": "3e58d6bcfc7e2d9d796bc45b5616d9811133f7901841cf46f44c746623274646.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 287, + 237 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 237 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 237 + ], + "type": "text", + "content": "Figure 9. Adversarial latent attack on different layers. The leftmost figure indicates the bottom layer, and the rightmost figure indicates the top layer. 1st col: original image. 2nd col: target image. 3rd col: adversarial example. 4th col: reconstruction of adversarial example." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 242, + 287, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 287, + 385 + ], + "type": "text", + "content": "We illustrate the adversarial attack on different layers in Fig. 9. The learned inference model " + }, + { + "bbox": [ + 46, + 242, + 287, + 385 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 46, + 242, + 287, + 385 + ], + "type": "text", + "content": " carries different levels of semantics for different layers. The adversarial example created by attacking latent codes at the bottom layer only perturbs the data along low-level features direction from the target image; hence, the model can be robust and have faithful reconstruction from adversarial examples. The adversarial example coming from the top-layer attack can distort the original data along a high-level semantic direction from the target image, thus, the reconstruction from the adversarial example can be substantially different from the original data, indicating a successful attack." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "text", + "content": "Anomaly detection. We also evaluate the model on anomaly detection. If the model is well-learned, the inference model " + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "text", + "content": " should form an informative latent space that separates anomalies from the normal data. Following the protocols in [18, 26], we take latent samples from the learned inference model and use the unnormalized log-posterior " + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "inline_equation", + "content": "\\log p_{\\theta}(\\mathbf{x},\\mathbf{z})" + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "text", + "content": " as our decision function to detect anomaly on MNIST. Only one digit class is held-out as an anomaly in training, while both normal and anomalous data are used for testing. We compare baseline models such as BiGAN-" + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "text", + "content": " [41], MEG [18], LEBM [26], HVAE and VAE using area under the precision-recall curve (AUPRC). The results of baseline models are provided by [26], and we use " + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "inline_equation", + "content": "L^{>0}" + }, + { + "bbox": [ + 46, + 385, + 288, + 564 + ], + "type": "text", + "content": " [15] as the decision function for HVAE model. Tab. 3 shows the result." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 602, + 287, + 652 + ], + "blocks": [ + { + "bbox": [ + 46, + 570, + 287, + 602 + ], + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 602 + ], + "type": "text", + "content": "Table 3. AUPRC scores for unsupervised anomaly detection on MNIST. Following the protocol of [26], we average the results over last 10 epochs to account for variance." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 602, + 287, + 652 + ], + "lines": [ + { + "bbox": [ + 48, + 602, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 48, + 602, + 287, + 652 + ], + "type": "table", + "html": "
hold-out digit14579
VAE0.0630.3370.3250.1480.104
HVAE0.494 ± 0.0040.920 ± 0.0040.913 ± 0.0030.680 ± 0.0060.791 ± 0.008
MEG0.281 ± 0.0350.401 ± 0.0610.402 ± 0.0620.290 ± 0.0400.342 ± 0.034
BiGAN-σ0.287 ± 0.0230.443 ± 0.0290.514 ± 0.0290.347 ± 0.0170.307 ± 0.028
Latent EBM0.336 ± 0.0080.630 ± 0.0170.619 ± 0.0130.463 ± 0.0090.413 ± 0.010
Ours0.722 ± 0.0100.949 ± 0.0020.980 ± 0.0010.941 ± 0.0030.935 ± 0.003
", + "image_path": "f23050755c2b025490ed16534866d337b833f453cde3f9ceaf1b31470bedefaf.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 147, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 147, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 147, + 683 + ], + "type": "text", + "content": "5.5. Ablation Studies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The proposed expressive prior model enables complex data representations to be effectively captured, which in turn" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "improves the expressivity of the whole model in generating high-quality synthesis. To better understand the influence of the proposed method, we conduct ablation studies, including 1) MCMC steps, 2) complexity of EBM, and 3) other image datasets." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 133, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 204 + ], + "type": "text", + "content": "MCMC steps: We examine the influence of steps of short-run MCMC for prior sampling. Tab. 4 shows that increasing steps could result in a better quality of generation. Increasing the step number from 15 to 60 could result in a significant improvement in synthesis quality, while exhibiting only minor influence when increased beyond 60." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 331, + 221, + 518, + 243 + ], + "blocks": [ + { + "bbox": [ + 306, + 211, + 534, + 221 + ], + "lines": [ + { + "bbox": [ + 306, + 211, + 534, + 221 + ], + "spans": [ + { + "bbox": [ + 306, + 211, + 534, + 221 + ], + "type": "text", + "content": "Table 4. Varying " + }, + { + "bbox": [ + 306, + 211, + 534, + 221 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 211, + 534, + 221 + ], + "type": "text", + "content": " (steps number) of our model on CelebA-64." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 221, + 518, + 243 + ], + "lines": [ + { + "bbox": [ + 331, + 221, + 518, + 243 + ], + "spans": [ + { + "bbox": [ + 331, + 221, + 518, + 243 + ], + "type": "table", + "html": "
k=15k=30k=60k=150k=300
FID56.4239.8932.1531.2030.78
", + "image_path": "9ff20a8be7abe68f74470e082ff248865c2e7ca8b3d5274f9a228b8508b09706.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 254, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 324 + ], + "type": "text", + "content": "Complexity of EBM: We further examine the influence of model parameters of EBM. The energy function is parameterized by a 2-layer perceptron. We fix the number of layers and increase the hidden units of EBM. As shown in Tab. 5, increasing the hidden units of EBM results in better performance." + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 315, + 341, + 537, + 363 + ], + "blocks": [ + { + "bbox": [ + 319, + 331, + 531, + 341 + ], + "lines": [ + { + "bbox": [ + 319, + 331, + 531, + 341 + ], + "spans": [ + { + "bbox": [ + 319, + 331, + 531, + 341 + ], + "type": "text", + "content": "Table 5. Increasing hidden units (denoted as nef) of EBM." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 341, + 537, + 363 + ], + "lines": [ + { + "bbox": [ + 315, + 341, + 537, + 363 + ], + "spans": [ + { + "bbox": [ + 315, + 341, + 537, + 363 + ], + "type": "table", + "html": "
nefnef=0nef=10nef=20nef=50nef=100
FID43.9541.7233.1030.4224.16
", + "image_path": "24e90ca774416da3a6a7db20179803d631cf1717df7239398c9a1886b49f1eed.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 367, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 403 + ], + "type": "text", + "content": "Other image datasets: We test the scalability of our model on high-resolution image dataset, such as CelebA-128. We show the image synthesis in Fig. 10." + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 309, + 411, + 543, + 452 + ], + "blocks": [ + { + "bbox": [ + 309, + 411, + 543, + 452 + ], + "lines": [ + { + "bbox": [ + 309, + 411, + 543, + 452 + ], + "spans": [ + { + "bbox": [ + 309, + 411, + 543, + 452 + ], + "type": "image", + "image_path": "659522c8b7fddbc0a6ae09b6413bfc1945c66abb14f3b692c2484dd7583f4046.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 455, + 523, + 465 + ], + "lines": [ + { + "bbox": [ + 328, + 455, + 523, + 465 + ], + "spans": [ + { + "bbox": [ + 328, + 455, + 523, + 465 + ], + "type": "text", + "content": "Figure 10. Generated image synthesis on CelebA-128" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 507 + ], + "type": "text", + "content": "We also train our model on CIFAR-10 (32x32) and report the FID score for generation quality in Tab. 6, in which our model performs well compared to baseline models." + } + ] + } + ], + "index": 19 + }, + { + "type": "table", + "bbox": [ + 331, + 514, + 518, + 543 + ], + "blocks": [ + { + "bbox": [ + 331, + 514, + 518, + 543 + ], + "lines": [ + { + "bbox": [ + 331, + 514, + 518, + 543 + ], + "spans": [ + { + "bbox": [ + 331, + 514, + 518, + 543 + ], + "type": "table", + "html": "
Table 6. FID on CIFAR-10
Ours2s-VAERAENCP-VAEMulti-NCPLEBM
63.4272.9074.1678.0665.0170.15
", + "image_path": "364bee638a88f6768cbfbdc7aba23d81bd1c202f43a763a82a8e30e257d84e47.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 562, + 378, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 378, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 378, + 574 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 581, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 712 + ], + "type": "text", + "content": "In this paper, we propose to build a joint latent space EBM with hierarchical structures for better hierarchical representation learning. Our joint EBM prior is expressive in modelling the inter-layer relation among multiple layers of latent variables, which in turn enables different levels of data representations to be effectively captured. We develop an efficient variational learning scheme and conduct various experiments to demonstrate the capability of our model in hierarchical representation learning and image modelling. For future work, we shall explore learning the hierarchical representations from other domains, such as videos and texts." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2225" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Jyoti Aneja, Alex Schwing, Jan Kautz, and Arash Vahdat. 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Learning hierarchical features from generative models. arXiv preprint arXiv:1702.08396, 2017. 1, 3, 5, 6, 7" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2227" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Human Dynamics in Autonomous Driving Scenarios/cdd5a67c-1587-4c07-9231-ae20be13d8d8_content_list.json b/2023/Learning Human Dynamics in Autonomous Driving Scenarios/cdd5a67c-1587-4c07-9231-ae20be13d8d8_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..165f7e949bdafc57364c52dddf085098cc2faaf5 --- /dev/null +++ b/2023/Learning Human Dynamics in Autonomous Driving Scenarios/cdd5a67c-1587-4c07-9231-ae20be13d8d8_content_list.json @@ -0,0 +1,1437 @@ +[ + { + "type": "text", + "text": "Learning Human Dynamics in Autonomous Driving Scenarios", + "text_level": 1, + "bbox": [ + 171, + 130, + 799, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jingbo Wang $^{1,2}$ Ye Yuan $^{1}$ Zhengyi Luo $^{1,3}$ Kevin Xie $^{1,4}$ Dahua Lin $^{2}$ Umar Iqbal $^{1}$ Sanja Fidler $^{1,4,5}$ Sameh Khamis $^{1}$", + "bbox": [ + 148, + 178, + 816, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ NVIDIA $^{2}$ The Chinese University of Hong Kong $^{3}$ Carnegie Mellon University", + "bbox": [ + 215, + 217, + 754, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ University of Toronto $^{5}$ Vector Institute", + "bbox": [ + 349, + 234, + 620, + 250 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b4f3f2f425c270ee3504c220cc4d52930ca9aac78280e0ca9ed911a52a3387ff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 98, + 285, + 870, + 381 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b6ee55ee16e268871a7861fa4bfb1736bb55730101fadad97eca7bbe2b09dca5.jpg", + "image_caption": [ + "Figure 1: We compare our method against GLAMR [67], the state-of-the-art method for global human motion mesh recovery. The output of GLAMR (left) suffers from various physical implausibilities, such as floating, sliding, or terrain penetration. Our method (right) yields a clear improvement." + ], + "image_footnote": [], + "bbox": [ + 99, + 382, + 870, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 633, + 313, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Simulation has emerged as an indispensable tool for scaling and accelerating the development of self-driving systems. A critical aspect of this is simulating realistic and diverse human behavior and intent. In this work, we propose a holistic framework for learning physically plausible human dynamics from real driving scenarios, narrowing the gap between real and simulated human behavior in safety-critical applications. We show that state-of-the-art methods underperform in driving scenarios where video data is recorded from moving vehicles, and humans are frequently partially or fully occluded. Furthermore, existing methods often disregard the global scene where humans are situated, resulting in various motion artifacts like foot sliding, floating, or ground penetration. To address this challenge, we propose an approach that incorporates physics with a rein", + "bbox": [ + 75, + 672, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "forcement learning-based motion controller to learn human dynamics for driving scenarios. Our framework can simulate physically plausible human dynamics that accurately match observed human motions and infill motions for occluded body parts, while improving the physical plausibility of the entire motion sequence. Experiments on the challenging Waymo Open Dataset show that our method outperforms state-of-the-art motion capture approaches significantly in recovering high-quality, physically plausible, and scene-aware human dynamics.", + "bbox": [ + 496, + 635, + 893, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 797, + 632, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Self-driving systems have come a long way in recent years. One major advancement that directly impacted these systems is the widespread adoption of simulation. While considerable attention was given to simulating traffic and other vehicles (e.g., TrafficSim [59], GeoSim [3],", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20796", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "STRIVE [51]), simulating pedestrian motion and behavior received less attention in the literature. In this work, we argue that understanding human behavior and intent is a critical step towards realistic simulation, which in turn is key to the safety of autonomous vehicles (AVs) in real-world settings. The first step towards this goal is capturing physically plausible human dynamics of entire motion sequences in driving scenarios.", + "bbox": [ + 80, + 90, + 467, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contrary to human motion in indoor scenes [12], motion captured in AV scenarios presents several challenges. These challenges include camera motion, long-term partial or full occlusions, scale variability, and complex interactions with the real-world environment. State-of-the-art (SOTA) approaches [69, 68, 70, 46, 34, 66, 35] for learning human dynamics in indoor scenarios tend to focus on enhancing physical plausibility for visible frames, neglecting several of these obstacles, such as long-term motion occlusions and the interplay between humans and terrains. As a result, it is challenging to directly apply these approaches to complex AV scenarios. Although recent works [67, 49] have demonstrated progress in infilling missing motions, there are significant limitations to using these methods for learning physically plausible human dynamics in AV scenarios, as shown in Figure 1. Firstly, these methods consider only physiologically inspired kinematics constraints such as joint limits, and do not model the physical plausibility of the pose in relation to the environment, such as when an object is floating. Secondly, these motion generation models are usually trained on indoor datasets, and the domain gap between indoor and driving scenarios renders them incapable of infilling missing motions in a plausible way.", + "bbox": [ + 80, + 217, + 467, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present a novel holistic framework to learn human dynamics in such challenging AV scenarios. Our proposed framework distinguishes itself from prior works by its ability to generate physically plausibility motions for long-term partially or fully missing body parts, thus addressing an important limitation in the SOTA approaches to learn human dynamics. Firstly, we integrate off-the-shelf motion capturing (e.g., KAMA [13]) and scene reconstruction (e.g., Possion Surface Reconstruction [17]) methods to recover observed motions of visible humans and recover the terrain mesh as well. Before learning human dynamics from the captured motions, we fix the missing terrains by the observed motion trajectories, as well as filter out frames with low-confidence estimation caused by partial occlusion, to guarantee the simulation framework is based on reasonable visual observation. Next, we track the captured motion on the reconstructed terrains by generating infilling motions for the missing frames while enforcing the physical plausibility of the captured motions (e.g. penetration free against the ground). In contrast to GLAMR [67], which infills a few missing frames together using the pretrained transformer-based model, our method generated the", + "bbox": [ + 80, + 569, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "motions in a stepwise fashion using a local motion controller, similar to [28, 62]. This controller-style motion generation reduces foot sliding over long-term occlusions. We demonstrate the adaptability of our approach by showing that, even though it is trained on indoor motion data, it can generalize to in-the-wild driving scenarios by placing physical constraints on the human-scene interactions. Specifically, we first train the conditional variational autoencoder [18] (cVAE) as the local motion generator whose latent space is the action space of movement. We then train a high-level controller to sample this latent space to perform infilling. Although all the motion generation models and physics-aware imitators are trained on an indoor dataset with flat ground, our method can easily adapt these models to uneven terrains in driving scenarios. Finally, we use an additional joint optimization, based on the physics-based imitator and generated motion, to match the video evidence (e.g., 2D keypoints with high confidence) not utilized in the previous stage. In summary, our framework is capable of learning physically plausible human dynamics for entire motion sequences in driving scenarios through visual observations.", + "bbox": [ + 503, + 90, + 888, + 421 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions as follows: 1) We propose the first framework for learning physically plausible human dynamics in driving scenarios, which is capable of generating physically plausible motions for partially or fully missing body parts. 2) We adapt a reinforcement learning-based motion generation framework trained only on indoor motion data, but can generalize to in-the-wild driving scenarios, infilling physically-plausible motion for occluded frames. 3) We achieve a significant improvement in motion quality over our motion capture framework to learn human dynamics, especially on partially or fully occluded frames.", + "bbox": [ + 503, + 422, + 888, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 503, + 603, + 645, + 618 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Kinematics-based Motion Capture: In recent times, the research community has focused on advancing the task of estimating 3D human keypoints directly to capture human motion, leading to impressive outcomes [6, 38, 40, 61, 44, 39, 1, 23]. Alternatively, several works have proposed adopting parametric human models, such as SMPL and SMPL-X [32, 42], as templates to capture human physiological motions [43, 15, 60, 2, 11, 58]. While some methods encourage the estimated motion to match observations during training [15, 53, 8] or fit the SMPL body through post-optimization [14, 22, 57], others predict SMPL parameters based on accurate keypoints [5] and apply inverse kinematics to transform the keypoint skeleton into the parametric body space [13, 26] to enable better keypoint localization.", + "bbox": [ + 503, + 628, + 888, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent works have also recognized the importance of exploiting temporal information to improve motion consistency [4, 19, 16, 33]. To this end, some methods, such as VIBE [20] and humor [49], employ a variational auto", + "bbox": [ + 503, + 840, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20797", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f565cc322cfc1e5a9757c681e17df370c7b5df34c96781f92a1f8cf7860c1fc2.jpg", + "image_caption": [ + "Figure 2: System Overview. Our approach processes each pedestrian mesh sequence in a stage-wise fashion. We first estimate motions for visible frames $\\widehat{Q}$ using an off-the-shelf motion capture method. We also reconstruct the ground terrain $G$ in preparation for the physics-based stages (Details in Section 3.1). The physics-aware motion tracking (Section 3.2) infills the motion $\\widehat{Q}$ for the occluded frames, as well as adapts the previously reconstructed motion to the reconstructed ground. In the last stage (Section 3.3), we optimize the entire motion $\\widehat{Q}$ to closely match the evidence from a 2D keypoint-based system to produce the final motion $\\overline{Q}$ ." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 883, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "encoder (VAE) to learn motion priors on large-scale motion datasets like AMASS [36] to enhance the robustness of the system. Similarly, GLAMR [67] introduces a transformer-based cVAE model that leverages a data-driven approach to smooth out captured motions and infill occluded frames. Nevertheless, the lack of consideration for the dynamics attributes of human motions, particularly in complex AV scenarios, may induce undesirable physical artifacts, such as foot sliding and ground penetrations.", + "bbox": [ + 75, + 337, + 472, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dynamics-based Motion Capture: To ameliorate the physical artifacts associated with capturing human motion sequences, recent works have sought to leverage the physics attributes of human dynamics. These methods can be broadly classified into two categories. The first category entails post-optimization during test time [50, 56, 63, 7] on both trajectories and body poses by leveraging physics forces and human motion dynamics equations to optimize physical metrics or characteristics. The second category involves reinforcement learning (RL) and motion imitation [69, 68, 70, 46, 34, 66, 35], with the focus on capturing human motion first, followed by utilizing RL and carefully-designed policies to imitate the captured motions in a simulator environment, enforcing physical plausibility. Unfortunately, training RL-based models on each motion sequence are time-consuming, necessitating the development of regression-based approaches to directly estimate physical attributes and then update the captured motions to reduce the computational time. Several recent works [55, 71, 25] have taken this approach. However, many of these works assume that the character is walking on flat ground or without long-term occlusions and missing frames. Differently, this work aims to tackle these challenges of learning human dynamics in complex AV scenarios.", + "bbox": [ + 75, + 476, + 472, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Occlusion-aware Motion Capture: Most of the existing works for human motion capturing assume the target human is fully visible in the image, and thus limit the robustness for the strong and long-term occluded human motions. Several", + "bbox": [ + 76, + 839, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "recent works [49, 72, 9, 52, 21] try to address this problem but still can not handle the long-term occlusions, especially when the person of interest is obstructed completely. GLAMR [67] is the first work to solve this problem by infilling the missing motions using a transformer-based cVAE model. While this is a promising direction with many successful applications, the domain gap between their training dataset and the captured outdoor motions is large enough to limit its applicability in a complex outdoor environment.", + "bbox": [ + 496, + 337, + 893, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motion Control: Our framework relies on a key component known as the motion controller, a long-standing research topic in computer graphics and robotics [65, 24, 41]. Recent character control works follow a reinforcement learning-based pipeline [31, 29, 47, 45, 30, 69] to generate physical motions using either reference motion or motion prediction [10, 28, 62]. Similar to [62], our work employs a motion controller, in conjunction with a physics module, to generate physically plausible motions using a cVAE model. However, we diverge from past research by using the motion controller to recover human motion sequences in a complex outdoor environment, from being solely trained on indoor datasets. Our approach is the first to use motion controllers for this task of motion recovery, generating a more physically plausible representation of human behavior in complex driving environments.", + "bbox": [ + 496, + 474, + 895, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 737, + 591, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our framework takes as input a monocular video sequence $I = (I_1, \\dots, I_M)$ with $M$ frames captured by a fast-moving vehicle camera. Our goal is to obtain physically plausible human dynamics $\\{Q^i\\}_{i=1}^N$ for both visible and occluded frames of $N$ entire motion sequences in the world coordinate system. Each person's motion $Q$ is defined as $(T, R, \\Theta)$ comprising the root translation $T = (\\tau_s, \\dots, \\tau_e)$ , root rotation $R = (r_s, \\dots, r_e)$ , and body motions $\\Theta = (\\theta_s, \\dots, \\theta_e)$ from the first frame $s$ to the last frame $e$ . We", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20798", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a876f3800bb3101cb5e86e10b1c26e59275e4f561524d14c75140882d478bf78.jpg", + "image_caption": [ + "Figure 3: Terrain Preparation. As shown in this figure, we first convert the reconstructed mesh to height map and extend this height map without valid LIDAR scanning for motions. At last, we convert the processed height map to mesh for the following physics-aware stages." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 450, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "employ the SMPL [32] model's definition for the root translation $\\tau_{t} \\in R^{3}$ , root orientation $r_{t} \\in R^{3}$ , and body pose $\\theta_{t} \\in R^{23 \\times 3}$ . To simulate the human dynamics captured from the real world, e.g. avoiding human-scene collisions, we also follow the definition of SMPL to estimate the body shape parameter $b_{i} \\in R^{10}$ for each motion sequence $i$ for meshes of characters in the simulator.", + "bbox": [ + 75, + 378, + 468, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our holistic framework (Figure 2) comprises three main stages. In Stage-I (Section 3.1), we prepare the initial observation, such as motion $\\widehat{Q}$ in visible frames and reconstructed terrain of the ground $G$ , for the following physics-aware steps. In Stage-II (Section 3.2), we employ a novel physics-aware tracking framework to address occlusion issues with $\\widehat{Q}$ and adapt visible motions to reconstructed terrains with plausibly physical attributes, resulting in the occlusion-free motion $\\widehat{Q}$ . In Stage-III (Section 3.3), we apply our physics-based optimization to the generated motion $\\widehat{Q}$ to ensure consistency between the generated motions and observations. More details as in the following sections.", + "bbox": [ + 75, + 484, + 470, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Stage I: Motion and Terrain Preparation", + "text_level": 1, + "bbox": [ + 76, + 676, + 426, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our physics-aware framework, we initiate physics-based simulation by computing initial kinematic human motions and reconstructing terrains. However, captured motions often have occlusions by cars and pedestrians in AV scenarios, leading to low-quality poses unsuitable for physics-based reasoning. Thus, we filter out occluded frames using 2D pose confidence scores and leverage physics-based priors to infill occluded frames later.", + "bbox": [ + 75, + 703, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also emphasize terrain reconstruction, an essential component of our framework. We use Poisson Surface Reconstruction [17] to reconstruct the terrain mesh from point clouds obtained from LIDAR on vehicles. However, point cloud densities are subject to occlusions and camera motion,", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "leading to holes and uneven surfaces on the mesh. To obtain a well-formed mesh for simulation, we use a two-step approach of converting the reconstructed mesh to a height map and then infilling and expanding the height map to cover the entire range of human motions captured, as shown in Figure 3. By doing so, we significantly enhance the mesh quality, enabling accurate physics-based simulations of human agents interacting with the environment. We perform these two steps on all motions and terrains utilized in our experiments to ensure reliable and accurate simulations.", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Stage II: Physics-Aware Motion Tracking", + "text_level": 1, + "bbox": [ + 498, + 253, + 854, + 270 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we will simulate physics-plausible human motion based on the processed observations from the first stage. In this section, we simulate physically plausible human motion based on the observations processed in the first stage. Our simulation aims to track the entire motion sequence on the reconstructed terrains, focusing on two aspects: 1) infilling physics-plausible human motions $\\{\\widehat{Q}_{t_1 + 1},\\ldots \\widehat{Q}_{t_2 - 1}\\}$ for occluded/missing frames between two visible frames $(\\widetilde{Q}_{t_1},\\widetilde{Q}_{t_2})$ ; 2) ensuring that the infilled entire human motion sequence $\\widehat{Q}$ can walk on the terrain with correct foot contact.", + "bbox": [ + 496, + 277, + 890, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While previous state-of-the-art [67] attempts to infill missing frames using a transformer-based cVAE, as shown in Figure 1, low-quality motions persist due to the domain gap between indoor motion data and outdoor pedestrian data in busy city scenes. To address this issue, we design a hierarchical control framework that is capable of generating motions in different scenarios. This framework mainly consists of a high-level latent-space controller and a lower-level generative motion transition model. Specifically, our framework begins with a low-level generative motion transition model that can provide plausible human motion based on sparse input. Inspired by [28, 62], we develop a controllable latent space that will serve as the action space of our high-level motion controller. Our high-level motion controller can then sample latent codes based on terrain, input video observations, and past states. In contrast to [67], our framework can generate plausible motions for occluded frames by fine-tuning our controller on each video. We then apply a physics-aware humanoid controller that imitates the generated motion in a physics simulator on the reconstructed terrain, to ensure the accurate physics attributes of the entire generated motion.", + "bbox": [ + 496, + 446, + 892, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Framework", + "text_level": 1, + "bbox": [ + 500, + 800, + 635, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overview: Within our physics-aware motion tracking framework, we identify three critical components: the motion model $\\pi_{M}$ , the physics-aware motion imitator $\\pi_{D}$ , and the high-level controller $\\pi_{C}$ , as depicted in Figure 4. The motion model $\\pi_{M}$ employs a generative transition model to", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20799", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/59c8285d71fff5fb0b873d3b5d5c84b1492e0a26c392a8bf0793c2636495a84e.jpg", + "image_caption": [ + "Figure 4: Motion Tracking Framework. At time step $t$ , our high-level controller predicts the latent code for the motion model $\\pi_{M}$ and the residuals for the occluded motion at $t + 1$ . Next, the physics-aware imitator $\\pi_{D}$ updates this prediction to ensure the physical plausibility of the generated motion. If the initial motion is visible at $t + 1$ , our high-level controller will directly use this captured motion rather than predict the latent code and generate motions by $\\pi_{M}$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 472, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "compute the next pose using the previous pose and a latent code. Meanwhile, the physics-aware motion imitator $\\pi_{D}$ takes either an occluded frame pose generated by $\\pi_{M}$ or a visible frame pose directly observed as input, thereby controlling a virtual character to mimic the motion in a physics simulator. For visible frames, we circumvent the use of $\\pi_{M}$ and provide the observed pose directly to $\\pi_{D}$ . When dealing with occluded frames, we call upon the high-level controller $\\pi_{C}$ to generate the latent code required by $\\pi_{M}$ in order to control the motion of the virtual character and infill coherent motions between visible frames. To accomplish this infilling, we train $\\pi_{C}$ to address the motion tracking task, which involves two objectives. The first goal requires driving the virtual character to reach the same position as $\\widetilde{Q}_{t_2}$ at time $t_2$ , starting from $\\widetilde{Q}_{t_1}$ , while ensuring the character attains a similar pose to $\\widetilde{Q}_{t_2}$ . The second objective entails maintaining compatibility with the underlying terrain $G$ .", + "bbox": [ + 75, + 381, + 472, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motion Transition Model: We follow one of the state-of-the-art local motion transition models [49] as $\\pi_{M}$ and use a pre-trained model from the official implementation. To infill occluded motions between two visible frames from $\\widetilde{Q}_{t_1}$ to $\\widetilde{Q}_{t_2}$ , the initial observation of model is $\\widetilde{S}_{t_1} = (\\widetilde{\\tau}_{t_1},\\widetilde{r}_{t_1},\\widetilde{\\theta}_{t_1},\\widetilde{j}_{t_1},\\widetilde{\\tau}_{t_1},\\widetilde{r}_{t_1},\\widetilde{j}_{t_1})$ , corresponding to the root translation, root orientation, body pose, joint position, the velocity of translation, velocity of rotation, and the velocity of joints respectively. The motion $\\widehat{S}_{t_1 + 1}^g = (\\widehat{\\tau}_{t_1 + 1}^g,\\widehat{r}_{t_1 + 1}^g,\\widehat{\\theta}_{t_1 + 1}^g,\\widehat{j}_{t_1 + 1}^g,\\widehat{\\tau}_{t_1 + 1}^g,\\widehat{r}_{t_1 + 1}^g,\\widehat{j}_{t_1 + 1}^g)$ for the occluded frame $t_1 + 1$ can be generated by sampling latent code $z_{t_1}$ . With this model, we can generate $t_2 - t_1 - 1$ step motions step by step for motion infilling.", + "bbox": [ + 75, + 645, + 472, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Physics-Based Motion Imitator: Our physics-based motion imitator $\\pi_{D}$ adapts the output motions of the generation module to the reconstructed terrains $G$ . Following [45, 69,", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "[70], this model drives a simulated humanoid to imitate the target pose, producing a physically valid motion sequence through the simulation process. As shown in Figure 4, the input of this imitator is the motion $\\widehat{S}_{t+1}^g$ of the motion generation model, as well as the motion simulated in the previous time step $\\widehat{S}_t$ . In practice, we adjust the height of $\\widehat{S}_{t+1}^g$ to remove floating and penetration to the reconstructed terrain $G$ . Our $\\pi_D$ predicts the target joint angle as $a_{t+1}$ for the physics simulator. Similar to [69, 70], we use the proportional derivative controllers (PD) on each non-root joint to produce joint torques $\\widehat{\\mathcal{T}}_{t+1}$ and obtain the physics-plausible motion $\\widehat{S}_{t+1} = (\\widehat{\\tau}_{t+1}, \\widehat{r}_{t+1}, \\widehat{\\theta}_{t+1}, \\widehat{j}_{t+1}, \\widehat{\\dot{\\tau}}_{t+1}, \\widehat{\\dot{r}}_{t+1}, \\widehat{\\dot{j}}_{t+1})$ by the simulator upon the reconstructed terrain $G$ .", + "bbox": [ + 496, + 90, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "High-level Controller: The goal of our high-level controller is to compute latent codes that can drive $\\pi_{M}$ from time step $t$ to $t + 1$ . For the visible frame at $t + 1$ , the motion $\\widetilde{G}_{t + 1}$ is adapted to the reconstructed terrain $G$ by first adjusting the height, and the high-level controller directly uses the adjusted captured motion as the imitation target for $\\pi_{D}$ , rather than predicting latent codes for $\\pi_{M}$ . For the occluded frame, our high-level controller samples specific latent code $z_{t + 1}$ for $\\pi_{M}$ . Basically, to ensure reaching the same position of $\\widetilde{Q}_{t_2}$ at $t_2$ from $\\widetilde{Q}_{t_1}$ , we formulate this reaching problem as a trajectory following task, which can guide the character to reach $\\widetilde{Q}_{t_2}$ at $t_2$ step-by-step and drive the character to a pose similar to $\\widetilde{Q}_{t_2}$ . We directly interpolate the root translation of $(\\widetilde{\\tau}_{t_1},\\widetilde{\\tau}_{t_2})$ as the following trajectory $\\{x_t\\}$ for these missing frames. For each time step $t\\in (t_1,t_2)$ , the input of the high-level controller consists of the generated motion state $\\widehat{S}_t^g$ , the simulated motion $\\widehat{S}_t$ , the future trajectories $x$ , the reconstructed terrain $G$ , and the target motion $\\widetilde{Q}_{t_2}$ . In addition to the latent code $z_{t + 1}$ , our high-level controller additionally predicts $z_{t + 1}^r$ as residuals of the motion generated at $t + 1$ , since the motion generation model $\\pi_{M}$ is only trained on indoor motions on flat ground and may have trouble producing motions on uneven terrains. In practice, $z_{t + 1}^r$ consists of root translation, root orientation, and character body pose. Thus, for the missing frame, the motion at $t + 1$ can be generated as follows:", + "bbox": [ + 496, + 292, + 892, + 690 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t + 1} ^ {g}, z _ {t + 1} ^ {r} = \\pi_ {C} \\left(\\widehat {S} _ {t} ^ {g}, \\widehat {S} _ {t}, x, G, \\widetilde {Q} _ {t _ {2}}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 699, + 890, + 719 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {S} _ {t + 1} ^ {g} = \\pi_ {M} \\left(\\widehat {S} _ {t} ^ {g}, z _ {t + 1} ^ {g}\\right) + z _ {t + 1} ^ {r}, \\widehat {a} _ {t + 1} = \\pi_ {D} \\left(\\widehat {S} _ {t}, \\widehat {S} _ {t + 1} ^ {g}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 753, + 890, + 773 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {S} _ {t + 1} = \\operatorname {S i m} \\left(\\widehat {S} _ {t}, \\widehat {\\mathcal {T}} _ {t + 1}\\right) = \\operatorname {S i m} \\left(\\widehat {S} _ {t}, \\mathrm {P D} \\left(\\widehat {S} _ {t}, \\widehat {a} _ {t + 1}\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 809, + 890, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Training Strategy", + "text_level": 1, + "bbox": [ + 500, + 845, + 678, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We follow [28] to train this high-level controller using the standard reinforcement learning algorithm [54]. Notice that", + "bbox": [ + 498, + 869, + 892, + 901 + ], + "page_idx": 4 + }, + { + "type": "footer", + "text": "20800", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\pi_{M}$ is pre-trained and frozen during this process. The reward for training is as follows:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nr = w _ {p} \\cdot r _ {p} + w _ {i} \\cdot r _ {i}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 133, + 468, + 148 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The reward for the trajectory following task is as", + "bbox": [ + 76, + 157, + 400, + 174 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nr _ {p} = \\exp \\left(- \\alpha_ {p} \\left(\\| \\hat {r} _ {p} ^ {x y} - x _ {p} ^ {x y} \\|\\right)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 183, + 468, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\widehat{r}_p^{xy}$ and $x_p^{xy}$ are the $xy$ coordinates of the translation of physics state $\\widehat{S}_t$ and the interpolated trajectory at time step $t$ . The infilling reward encourages the motion model to generate a similar motion as $\\widetilde{S}_{t_2}$ when the character is near to $t_2$ :", + "bbox": [ + 75, + 209, + 468, + 286 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i} = \\gamma_ {i} \\cdot \\exp \\left(- \\alpha_ {i} \\left(\\| \\widehat {S} _ {t} - \\widetilde {S} _ {t _ {2}} \\|\\right)\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 286, + 468, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The weights $(w_{p}, w_{i})$ and $(\\alpha_{t}, \\alpha_{i})$ can be adjusted to fit different scenarios. The $\\gamma_{i}$ is equal to 1 if $t \\in (t_{2} - 15, t_{2})$ . Otherwise, we set this $\\gamma_{i}$ as 0 and thus the task is only trajectory following.", + "bbox": [ + 75, + 309, + 468, + 369 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training such a high-level controller from scratch for different scenarios is time-consuming (more than 12 hours on a single V100 GPU by IsaacGym [37] for 1000 iterations). To mitigate the time cost and obtain a more robust controller for different environments (e.g., trajectories and terrains), we propose a pre-training and fine-tuning strategy for our high-level controller. We generate diverse uneven terrains and driving trajectories meant to simulate a range of scenarios in the simulator, followed by training the high-level controller on these synthetic environments for our designated tasks. For infilling ending motion, we sample from various motions in the AMASS [36] while performing motion-matching tasks. Leveraging the pre-trained high-level controller on synthetic data, the convergence of fine-tuning on real data is significantly faster, as illustrated in Figure 6. We present additional information about our pre-training strategy in our supplementary materials.", + "bbox": [ + 75, + 369, + 468, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Stage III: Physics-aware Motion Optimization", + "text_level": 1, + "bbox": [ + 76, + 635, + 467, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After we obtain the physics plausible and occlusion-free human motions $\\widehat{Q}$ in Section 3.2, the motion may not align with the image evidence such as 2D keypoints perfectly. Additionally, in Section 3.1, we have filtered out the whole body for some partially occluded motions, even if they have several high-confidence estimated keypoints. For these frames, our physics-aware motion tracking in Section 3.2 always obtains motions by motion generation and thus causes misalignment to the video observation.", + "bbox": [ + 75, + 659, + 468, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To close these gaps, in this section, we propose a physics-aware motion optimization method to further optimize $\\widehat{Q}$ . This stage mainly consists of two components. The first is a new physics-aware imitator $\\pi_K$ similar as $\\pi_D$ in Section 3.2, to maintain physics plausibility while matching video evidence. Additionally, we introduce residual parameters $\\{\\delta R_i\\}_{i=1}^T$ for the target motion $\\widehat{Q}$ of the imitator", + "bbox": [ + 75, + 795, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "at each time step. During optimization, the imitation target $\\widehat{Q}_{t + 1}$ is adjusted by $\\delta R_{t + 1}$ and thus encourages the imitator to predict a consistent motion $\\bar{a}_{t + 1}$ with video observation. In practice, we introduce these residual parameters to the root orientation and body pose of characters in the simulator. After training, the updated target motion is defined as:", + "bbox": [ + 498, + 90, + 890, + 181 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {r} _ {t + 1} ^ {u} = \\widehat {r} _ {t + 1} + \\delta R _ {t + 1} ^ {r}, \\widehat {\\theta} _ {t + 1} ^ {u} = \\widehat {\\theta} _ {t + 1} + \\delta R _ {t + 1} ^ {\\theta}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 193, + 890, + 213 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {S} _ {t _ {1} + 1} ^ {u} = \\left(\\widehat {\\tau} _ {t + 1}, \\widehat {r} _ {t + 1} ^ {u}, \\widehat {\\theta} _ {t + 1} ^ {u}, \\widehat {j} _ {t + 1}, \\widehat {\\dot {\\tau}} _ {t + 1}, \\widehat {r} _ {t + 1}, \\widehat {\\dot {j}} _ {t + 1}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 239, + 890, + 262 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on this adapted target motion, we first use the imitator $\\pi_{K}$ to predict the target joint angle as $\\overline{a}_{t + 1}$ for the physics simulator and produce joint torques $\\overline{\\mathcal{T}}_{t + 1}$ to obtain the final result $\\overline{Q}_{t + 1}$ , similar as $\\pi_{D}$ .", + "bbox": [ + 498, + 270, + 890, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During optimizing, we fine-tune this pre-trained imitator and these residual parameters for each motion sequence. To encourage consistency between observation and output motion, we use the following reward function:", + "bbox": [ + 498, + 330, + 890, + 391 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nr _ {p r o j} = \\exp \\left(- \\alpha_ {p} \\sum \\left(\\| \\Pi (\\bar {j} _ {t}) - \\tilde {j} _ {t} ^ {2 D} \\| \\times \\tilde {c} _ {t}\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 401, + 890, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\Pi$ is the projection function from world to image space, $\\widetilde{j}_t^{2D}$ is the estimated 2D pose at time step $t$ , as well as $\\widetilde{c}_t$ is the corresponding confidence score. Besides, we still use the similar reward function $r_{im}$ as [69, 70] used for motion imitation to encourage correct physics attributes for the motions with residuals. The final reward is as follows:", + "bbox": [ + 498, + 431, + 890, + 522 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nr = r _ {p r o j} \\cdot w _ {p} + r _ {i m} \\cdot w _ {i m}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 534, + 890, + 550 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $(w_{p},w_{im})$ and $(\\alpha_{p},\\alpha_{im})$ can be adjusted to fit different scenarios.", + "bbox": [ + 498, + 560, + 888, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 603, + 632, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset: We conduct our experiments on the Waymo Open Dataset [73], currently the largest dataset recorded for autonomous driving scenarios featuring point clouds representing the surrounding terrain and sparsely annotated 3D keypoints. To evaluate the effectiveness of our proposed method, we curate a subset of 20 sequences from the training and validation sets, each containing various scenarios, and incorporating more than 30 different pedestrian 3D keypoint annotations, as well as high-quality terrain reconstructions. The Waymo Open Dataset captures data at a $10\\mathrm{Hz}$ frame rate using a camera installed on the vehicle. As we require a $30\\mathrm{Hz}$ frame rate in our physics simulator, we up-sample the captured motions using linear interpolation.", + "bbox": [ + 496, + 628, + 890, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metric: We use both kinematics-based and physics-based metrics for evaluation. Firstly, to quantify the generated motions from our framework, we report the motion FID, a standard metric for evaluating motion fidelity [27, 48]. Besides, to demonstrate the reconstruction accuracy, we use", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "footer", + "text": "20801", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4a47a3dd71cc761de336683cb0880f2e7415e6f4d21806fc110c3792319c3d65.jpg", + "table_caption": [ + "Table 1: Baseline Comparison. We compare against several different baselines on the following metrics. GLAMR* means use the same physics-aware imitator as our framework after GLAMR. Our method achieves the significantly better result on FID, PAMPJPE on frames with occlusion (Occ), and physics-based metrics (GP, FS, FL)." + ], + "table_footnote": [], + "table_body": "
MethodFID ↓ (All)PA-MPJE ↓ (Occ)PA-MPJE ↓ (All)GP ↓ (All)FS ↓ (All)FL ↓ (All)Accel (All)
KAMA4.6297.5275.0682.2049.2778.89-
GLAMR4.1791.7474.3481.4246.3378.23154.14
GLAMR*4.2893.4476.3417.3438.3415.38138.44
Ours1.9686.0274.2212.627.4413.25105.48
", + "bbox": [ + 76, + 172, + 478, + 231 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0fc4247a36785547897ad10fa4fe92dae88f5c4672d1cc5f2de9aa006fe4b3c9.jpg", + "table_caption": [ + "Table 2: Ablation studies on the physics-aware imitator. Although we have adapted the generated motion to the ground during training, the physics-aware motion imitator still can improve the motion quality on these physics attributes. Our* means the result without post-optimization." + ], + "table_footnote": [], + "table_body": "
MethodGP ↓FS ↓FL ↓Accel
Without πD16.8210.8423.02114.48
Ours*12.927.0514.08108.59
", + "bbox": [ + 107, + 309, + 434, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the Procrustes-aligned mean per-joint position error (PA-MPJPE) and 2D localization error (2D-LE) for the generated human dynamics motion. For the physical attributes, we follow the metrics to measure jitter, foot sliding, ground penetration, and floating as in [70, 25]. The jitter is estimated by computing the acceleration (Accel). The foot sliding (FS) is estimated by finding the body mesh vertices that contact the ground in two adjacent frames and then computing their moving distance. The ground penetration (GP) is computed as the average distance between the ground and the mesh vertices below the ground. For floating (FL), we compute the distance between the ground and the nearest vertex of mesh to the ground. The unit for these metrics are millimeters (mm), except for Accel (mm/frame $^2$ ).", + "bbox": [ + 75, + 361, + 468, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 584, + 294, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Section 3.2 and Section 3.3, we follow the methodology outlined in RFC [69] to train our physics-aware motion imitator. This imitator is trained on the flat ground using the AMASS [36] dataset and IsaacGym [37]. We model the SMPL agent in this simulator following [35]. In Section 3.2, we use the official motion generation model put forth by HuMOR [49] as our motion model $\\pi_{M}$ . Regarding our high-level controller, we pre-train this model on synthetic environments for 5000 iterations before fine-tuning it in real-world environments. For motion infilling, we optimize the result for 2000 iterations with our physics-aware motion optimization. Finally, to ensure the accuracy of our optimization, we leverage VITPose [64] to extract precise 2D keypoints in the last stage of our framework.", + "bbox": [ + 75, + 608, + 468, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Evaluation", + "text_level": 1, + "bbox": [ + 76, + 830, + 197, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines: We conduct our method based on KAMA [13], a strong human motion captured method for visible motions. To evaluate the quality of the generated motion", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8f3efcf7139e05243fb5a9067db5a4d5455c1e8faac5da883232e6e3946c5763.jpg", + "table_caption": [ + "Table 3: Ablation studies on post optimization. We compare the infilling results with and without the post-optimization after physics-aware motion tracking." + ], + "table_footnote": [], + "table_body": "
Method2D-LE ↓(All)PA-MPJPE ↓(Occ)PA-MPJPE ↓(All)GP ↓(All)FS ↓(All)FL ↓(All)Accel (All)
Without Opt26.4189.8475.4812.927.0514.08108.59
With Opt17.3786.0274.2212.627.4413.25105.48
", + "bbox": [ + 501, + 131, + 893, + 170 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "by our method, we compare it with the state-of-the-art method [67], which is designed to generate missing parts for the entire motion sequence. As [67], we also compare with methods using linear interpolation for the infilling of the missing frames. For fair comparisons, we adapt all the methods and experiments by using the ground-truth camera extrinsic and intrinsic parameters provided by the Waymo Open Dataset.", + "bbox": [ + 496, + 180, + 890, + 300 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Results: We show our results in Table 1 to show the quality of generated motions. To begin with, we evaluate the quality of the motion sequences generated by our method and compare them with our baselines using the FID metric. Our approach produces the best performance with substantial improvements in this regard. Furthermore, our method exhibits the best result in the PA-MPJPE metric, particularly a notable reduction in the frames with occlusion. Regarding physics-based metrics, our method continues to outperform all baselines. However, we still encounter minor foot penetration issues while quantifying the physics attributes due to errors in the transformation between the height map and mesh, as well as in the character's SMPL model within the simulator. Despite utilizing GLAMR and the physics imitator cooperatively to facilitate better physics attribute outcomes, the infilling capability of GLAMR still influences the performance of kinematics metrics, FL, and Accel. This points to the considerable complexity involved in designing our controller-based physics-aware framework to address this problem. In summary, our approach possesses the potential to achieve high-quality human dynamics learning based on visual observations.", + "bbox": [ + 496, + 301, + 892, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results: We demonstrate the qualitative results in Figure 5. We compare against the GLAMR [67], which is the state-of-the-art method to infill captured motions. We find that our method achieves better results on the physical attributes of human motion. More comparison videos are in our supplementary material.", + "bbox": [ + 496, + 635, + 890, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 738, + 663, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Pre-training for High-level Controller: Firstly, we compare the performance of our method without the pre-training step on synthetic terrains and trajectories. As shown in Figure 6, the high-level controller based on the pre-trained model converges faster significantly. More comparisons of this pre-training are in our supplementary materials.", + "bbox": [ + 496, + 763, + 890, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Physics-based Motion Tracker: Then, we compare with the motion without our physics-aware imitator in Table 2. Although we adapt generated motion to the ground during", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20802", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d73664152e63197544f6bfb0fe73fbbc62ad6e2a207204afac8382707134831.jpg", + "image_caption": [ + "Figure 5: Qualitative Comparison. We compare our method with the state-of-the-art method [67] for global human motion mesh recovery in this figure. Under this comparison, our method mitigates the artifacts on physics attributes of the whole motion sequence significantly." + ], + "image_footnote": [], + "bbox": [ + 119, + 87, + 849, + 369 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f7efcea1eb6cc567e129c6a880825b87e8a2ff17c31940ab97900e63fb9e83f9.jpg", + "image_caption": [ + "Figure 6: Convergence Results. We compare the time cost of training the high-level controller on the Waymo Open Dataset with and without the pre-training on synthetic data. We show that the high-level controller converges much faster and achieves a better reward with the pre-training." + ], + "image_footnote": [], + "bbox": [ + 78, + 417, + 272, + 532 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/140bfefd3b922a9da077c8c9e9054d4809c385053af10cb2ee0c327ea13cbd3a.jpg", + "image_caption": [ + "Figure 7: Effect of physics-aware post-optimization. We demonstrate the effect of our physics-aware post-optimization in this figure. Following this optimization, generated motions from the previous stages end up better matched and aligned with the video evidence." + ], + "image_footnote": [], + "bbox": [ + 274, + 417, + 470, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "training, the physics-aware imitator still improves the performance on physics attributes of generated motion. More qualitative comparisons of different design choices are in our supplementary materials.", + "bbox": [ + 75, + 617, + 468, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Physics-based Post Optimization: Finally, we conduct a comparison of our method's performance without the post-optimization step outlined in Section 3.3. As indicated in Table 3, the inclusion of post-time optimization notably enhances the accuracy of matching 2D/3D observations and improves some physical attributes of the entire motion sequence. In addition, we demonstrate the effects of this stage by comparing the results with and without post-optimization in Figure 7.", + "bbox": [ + 75, + 678, + 470, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Limitations", + "text_level": 1, + "bbox": [ + 76, + 829, + 333, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents a holistic framework for learning physically-plausible human dynamics motion of entire sequences in AV scenarios. Our approach stands out from", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7c8e0c86c8e0d87896b5e33ccf97fb5d68f6d64a26c200b7d2bdf0f24855d9db.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 417, + 893, + 539 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "prior work by generating motion sequences not only for visible frames but also for frames with occlusions or missing data. The generated motion sequences are constrained by physics and thus are suitable for downstream simulation tasks in AV scenarios. Our methodology begins with processing reconstructed terrains using LIDAR and recovering visible motions with off-the-shelf components. We then use a reinforcement learning-based motion controller within a physically-constrained environment to infill the motions. Finally, we propose a physics-aware post-optimization stage that utilizes keypoint observations to optimize the entire motion sequence. Our approach outperforms previous methods, particularly in terms of entire sequence motion quality and physical attributes, in several challenging AV scenarios. Although our results meet the necessary quality for simulation tasks, a limitation we aim to address in the future is the ability to optimize body shapes estimated by MoCap with our physics-aware framework.", + "bbox": [ + 496, + 628, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20803", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. Scape: shape completion and animation of people. In ACM SIGGRAPH 2005 Papers, pages 408-416. 2005. 2", + "[2] Anurag Arnab, Carl Doersch, and Andrew Zisserman. Exploiting temporal context for 3d human pose estimation in the wild. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.131, + 0.8, + 0.154 + ], + "angle": 0, + "content": "Learning Human Dynamics in Autonomous Driving Scenarios" + }, + { + "type": "text", + "bbox": [ + 0.15, + 0.179, + 0.817, + 0.217 + ], + "angle": 0, + "content": "Jingbo Wang\\(^{1,2}\\) Ye Yuan\\(^{1}\\) Zhengyi Luo\\(^{1,3}\\) Kevin Xie\\(^{1,4}\\) Dahua Lin\\(^{2}\\) Umar Iqbal\\(^{1}\\) Sanja Fidler\\(^{1,4,5}\\) Sameh Khamis\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.218, + 0.755, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\)NVIDIA \\(^{2}\\)The Chinese University of Hong Kong \\(^{3}\\)Carnegie Mellon University" + }, + { + "type": "text", + "bbox": [ + 0.35, + 0.235, + 0.621, + 0.251 + ], + "angle": 0, + "content": "\\(^{4}\\)University of Toronto \\(^{5}\\)Vector Institute" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.286, + 0.871, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.383, + 0.871, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.592, + 0.893, + 0.634 + ], + "angle": 0, + "content": "Figure 1: We compare our method against GLAMR [67], the state-of-the-art method for global human motion mesh recovery. The output of GLAMR (left) suffers from various physical implausibilities, such as floating, sliding, or terrain penetration. Our method (right) yields a clear improvement." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.635, + 0.314, + 0.65 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Simulation has emerged as an indispensable tool for scaling and accelerating the development of self-driving systems. A critical aspect of this is simulating realistic and diverse human behavior and intent. In this work, we propose a holistic framework for learning physically plausible human dynamics from real driving scenarios, narrowing the gap between real and simulated human behavior in safety-critical applications. We show that state-of-the-art methods underperform in driving scenarios where video data is recorded from moving vehicles, and humans are frequently partially or fully occluded. Furthermore, existing methods often disregard the global scene where humans are situated, resulting in various motion artifacts like foot sliding, floating, or ground penetration. To address this challenge, we propose an approach that incorporates physics with a rein" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.895, + 0.788 + ], + "angle": 0, + "content": "forcement learning-based motion controller to learn human dynamics for driving scenarios. Our framework can simulate physically plausible human dynamics that accurately match observed human motions and infill motions for occluded body parts, while improving the physical plausibility of the entire motion sequence. Experiments on the challenging Waymo Open Dataset show that our method outperforms state-of-the-art motion capture approaches significantly in recovering high-quality, physically plausible, and scene-aware human dynamics." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.798, + 0.633, + 0.813 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Self-driving systems have come a long way in recent years. One major advancement that directly impacted these systems is the widespread adoption of simulation. While considerable attention was given to simulating traffic and other vehicles (e.g., TrafficSim [59], GeoSim [3]," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20796" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.091, + 0.468, + 0.211 + ], + "angle": 0, + "content": "STRIVE [51]), simulating pedestrian motion and behavior received less attention in the literature. In this work, we argue that understanding human behavior and intent is a critical step towards realistic simulation, which in turn is key to the safety of autonomous vehicles (AVs) in real-world settings. The first step towards this goal is capturing physically plausible human dynamics of entire motion sequences in driving scenarios." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.218, + 0.468, + 0.563 + ], + "angle": 0, + "content": "Contrary to human motion in indoor scenes [12], motion captured in AV scenarios presents several challenges. These challenges include camera motion, long-term partial or full occlusions, scale variability, and complex interactions with the real-world environment. State-of-the-art (SOTA) approaches [69, 68, 70, 46, 34, 66, 35] for learning human dynamics in indoor scenarios tend to focus on enhancing physical plausibility for visible frames, neglecting several of these obstacles, such as long-term motion occlusions and the interplay between humans and terrains. As a result, it is challenging to directly apply these approaches to complex AV scenarios. Although recent works [67, 49] have demonstrated progress in infilling missing motions, there are significant limitations to using these methods for learning physically plausible human dynamics in AV scenarios, as shown in Figure 1. Firstly, these methods consider only physiologically inspired kinematics constraints such as joint limits, and do not model the physical plausibility of the pose in relation to the environment, such as when an object is floating. Secondly, these motion generation models are usually trained on indoor datasets, and the domain gap between indoor and driving scenarios renders them incapable of infilling missing motions in a plausible way." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.57, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In this paper, we present a novel holistic framework to learn human dynamics in such challenging AV scenarios. Our proposed framework distinguishes itself from prior works by its ability to generate physically plausibility motions for long-term partially or fully missing body parts, thus addressing an important limitation in the SOTA approaches to learn human dynamics. Firstly, we integrate off-the-shelf motion capturing (e.g., KAMA [13]) and scene reconstruction (e.g., Possion Surface Reconstruction [17]) methods to recover observed motions of visible humans and recover the terrain mesh as well. Before learning human dynamics from the captured motions, we fix the missing terrains by the observed motion trajectories, as well as filter out frames with low-confidence estimation caused by partial occlusion, to guarantee the simulation framework is based on reasonable visual observation. Next, we track the captured motion on the reconstructed terrains by generating infilling motions for the missing frames while enforcing the physical plausibility of the captured motions (e.g. penetration free against the ground). In contrast to GLAMR [67], which infills a few missing frames together using the pretrained transformer-based model, our method generated the" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.422 + ], + "angle": 0, + "content": "motions in a stepwise fashion using a local motion controller, similar to [28, 62]. This controller-style motion generation reduces foot sliding over long-term occlusions. We demonstrate the adaptability of our approach by showing that, even though it is trained on indoor motion data, it can generalize to in-the-wild driving scenarios by placing physical constraints on the human-scene interactions. Specifically, we first train the conditional variational autoencoder [18] (cVAE) as the local motion generator whose latent space is the action space of movement. We then train a high-level controller to sample this latent space to perform infilling. Although all the motion generation models and physics-aware imitators are trained on an indoor dataset with flat ground, our method can easily adapt these models to uneven terrains in driving scenarios. Finally, we use an additional joint optimization, based on the physics-based imitator and generated motion, to match the video evidence (e.g., 2D keypoints with high confidence) not utilized in the previous stage. In summary, our framework is capable of learning physically plausible human dynamics for entire motion sequences in driving scenarios through visual observations." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.424, + 0.89, + 0.59 + ], + "angle": 0, + "content": "We summarize our contributions as follows: 1) We propose the first framework for learning physically plausible human dynamics in driving scenarios, which is capable of generating physically plausible motions for partially or fully missing body parts. 2) We adapt a reinforcement learning-based motion generation framework trained only on indoor motion data, but can generalize to in-the-wild driving scenarios, infilling physically-plausible motion for occluded frames. 3) We achieve a significant improvement in motion quality over our motion capture framework to learn human dynamics, especially on partially or fully occluded frames." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.604, + 0.647, + 0.619 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.629, + 0.89, + 0.84 + ], + "angle": 0, + "content": "Kinematics-based Motion Capture: In recent times, the research community has focused on advancing the task of estimating 3D human keypoints directly to capture human motion, leading to impressive outcomes [6, 38, 40, 61, 44, 39, 1, 23]. Alternatively, several works have proposed adopting parametric human models, such as SMPL and SMPL-X [32, 42], as templates to capture human physiological motions [43, 15, 60, 2, 11, 58]. While some methods encourage the estimated motion to match observations during training [15, 53, 8] or fit the SMPL body through post-optimization [14, 22, 57], others predict SMPL parameters based on accurate keypoints [5] and apply inverse kinematics to transform the keypoint skeleton into the parametric body space [13, 26] to enable better keypoint localization." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.841, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Recent works have also recognized the importance of exploiting temporal information to improve motion consistency [4, 19, 16, 33]. To this end, some methods, such as VIBE [20] and humor [49], employ a variational auto" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20797" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.885, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.896, + 0.331 + ], + "angle": 0, + "content": "Figure 2: System Overview. Our approach processes each pedestrian mesh sequence in a stage-wise fashion. We first estimate motions for visible frames \\(\\widehat{Q}\\) using an off-the-shelf motion capture method. We also reconstruct the ground terrain \\(G\\) in preparation for the physics-based stages (Details in Section 3.1). The physics-aware motion tracking (Section 3.2) infills the motion \\(\\widehat{Q}\\) for the occluded frames, as well as adapts the previously reconstructed motion to the reconstructed ground. In the last stage (Section 3.3), we optimize the entire motion \\(\\widehat{Q}\\) to closely match the evidence from a 2D keypoint-based system to produce the final motion \\(\\overline{Q}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.473, + 0.475 + ], + "angle": 0, + "content": "encoder (VAE) to learn motion priors on large-scale motion datasets like AMASS [36] to enhance the robustness of the system. Similarly, GLAMR [67] introduces a transformer-based cVAE model that leverages a data-driven approach to smooth out captured motions and infill occluded frames. Nevertheless, the lack of consideration for the dynamics attributes of human motions, particularly in complex AV scenarios, may induce undesirable physical artifacts, such as foot sliding and ground penetrations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.473, + 0.839 + ], + "angle": 0, + "content": "Dynamics-based Motion Capture: To ameliorate the physical artifacts associated with capturing human motion sequences, recent works have sought to leverage the physics attributes of human dynamics. These methods can be broadly classified into two categories. The first category entails post-optimization during test time [50, 56, 63, 7] on both trajectories and body poses by leveraging physics forces and human motion dynamics equations to optimize physical metrics or characteristics. The second category involves reinforcement learning (RL) and motion imitation [69, 68, 70, 46, 34, 66, 35], with the focus on capturing human motion first, followed by utilizing RL and carefully-designed policies to imitate the captured motions in a simulator environment, enforcing physical plausibility. Unfortunately, training RL-based models on each motion sequence are time-consuming, necessitating the development of regression-based approaches to directly estimate physical attributes and then update the captured motions to reduce the computational time. Several recent works [55, 71, 25] have taken this approach. However, many of these works assume that the character is walking on flat ground or without long-term occlusions and missing frames. Differently, this work aims to tackle these challenges of learning human dynamics in complex AV scenarios." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Occlusion-aware Motion Capture: Most of the existing works for human motion capturing assume the target human is fully visible in the image, and thus limit the robustness for the strong and long-term occluded human motions. Several" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.895, + 0.475 + ], + "angle": 0, + "content": "recent works [49, 72, 9, 52, 21] try to address this problem but still can not handle the long-term occlusions, especially when the person of interest is obstructed completely. GLAMR [67] is the first work to solve this problem by infilling the missing motions using a transformer-based cVAE model. While this is a promising direction with many successful applications, the domain gap between their training dataset and the captured outdoor motions is large enough to limit its applicability in a complex outdoor environment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.896, + 0.719 + ], + "angle": 0, + "content": "Motion Control: Our framework relies on a key component known as the motion controller, a long-standing research topic in computer graphics and robotics [65, 24, 41]. Recent character control works follow a reinforcement learning-based pipeline [31, 29, 47, 45, 30, 69] to generate physical motions using either reference motion or motion prediction [10, 28, 62]. Similar to [62], our work employs a motion controller, in conjunction with a physics module, to generate physically plausible motions using a cVAE model. However, we diverge from past research by using the motion controller to recover human motion sequences in a complex outdoor environment, from being solely trained on indoor datasets. Our approach is the first to use motion controllers for this task of motion recovery, generating a more physically plausible representation of human behavior in complex driving environments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.738, + 0.593, + 0.753 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Our framework takes as input a monocular video sequence \\(I = (I_1, \\dots, I_M)\\) with \\(M\\) frames captured by a fast-moving vehicle camera. Our goal is to obtain physically plausible human dynamics \\(\\{Q^i\\}_{i=1}^N\\) for both visible and occluded frames of \\(N\\) entire motion sequences in the world coordinate system. Each person's motion \\(Q\\) is defined as \\((T, R, \\Theta)\\) comprising the root translation \\(T = (\\tau_s, \\dots, \\tau_e)\\), root rotation \\(R = (r_s, \\dots, r_e)\\), and body motions \\(\\Theta = (\\theta_s, \\dots, \\theta_e)\\) from the first frame \\(s\\) to the last frame \\(e\\). We" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20798" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.451, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.47, + 0.37 + ], + "angle": 0, + "content": "Figure 3: Terrain Preparation. As shown in this figure, we first convert the reconstructed mesh to height map and extend this height map without valid LIDAR scanning for motions. At last, we convert the processed height map to mesh for the following physics-aware stages." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.483 + ], + "angle": 0, + "content": "employ the SMPL [32] model's definition for the root translation \\(\\tau_{t} \\in R^{3}\\), root orientation \\(r_{t} \\in R^{3}\\), and body pose \\(\\theta_{t} \\in R^{23 \\times 3}\\). To simulate the human dynamics captured from the real world, e.g. avoiding human-scene collisions, we also follow the definition of SMPL to estimate the body shape parameter \\(b_{i} \\in R^{10}\\) for each motion sequence \\(i\\) for meshes of characters in the simulator." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.471, + 0.668 + ], + "angle": 0, + "content": "Our holistic framework (Figure 2) comprises three main stages. In Stage-I (Section 3.1), we prepare the initial observation, such as motion \\(\\widehat{Q}\\) in visible frames and reconstructed terrain of the ground \\(G\\), for the following physics-aware steps. In Stage-II (Section 3.2), we employ a novel physics-aware tracking framework to address occlusion issues with \\(\\widehat{Q}\\) and adapt visible motions to reconstructed terrains with plausibly physical attributes, resulting in the occlusion-free motion \\(\\widehat{Q}\\). In Stage-III (Section 3.3), we apply our physics-based optimization to the generated motion \\(\\widehat{Q}\\) to ensure consistency between the generated motions and observations. More details as in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.678, + 0.427, + 0.695 + ], + "angle": 0, + "content": "3.1. Stage I: Motion and Terrain Preparation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.825 + ], + "angle": 0, + "content": "In our physics-aware framework, we initiate physics-based simulation by computing initial kinematic human motions and reconstructing terrains. However, captured motions often have occlusions by cars and pedestrians in AV scenarios, leading to low-quality poses unsuitable for physics-based reasoning. Thus, we filter out occluded frames using 2D pose confidence scores and leverage physics-based priors to infill occluded frames later." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We also emphasize terrain reconstruction, an essential component of our framework. We use Poisson Surface Reconstruction [17] to reconstruct the terrain mesh from point clouds obtained from LIDAR on vehicles. However, point cloud densities are subject to occlusions and camera motion," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "leading to holes and uneven surfaces on the mesh. To obtain a well-formed mesh for simulation, we use a two-step approach of converting the reconstructed mesh to a height map and then infilling and expanding the height map to cover the entire range of human motions captured, as shown in Figure 3. By doing so, we significantly enhance the mesh quality, enabling accurate physics-based simulations of human agents interacting with the environment. We perform these two steps on all motions and terrains utilized in our experiments to ensure reliable and accurate simulations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.254, + 0.855, + 0.271 + ], + "angle": 0, + "content": "3.2. Stage II: Physics-Aware Motion Tracking" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.446 + ], + "angle": 0, + "content": "In this section, we will simulate physics-plausible human motion based on the processed observations from the first stage. In this section, we simulate physically plausible human motion based on the observations processed in the first stage. Our simulation aims to track the entire motion sequence on the reconstructed terrains, focusing on two aspects: 1) infilling physics-plausible human motions \\(\\{\\widehat{Q}_{t_1 + 1},\\ldots \\widehat{Q}_{t_2 - 1}\\}\\) for occluded/missing frames between two visible frames \\((\\widetilde{Q}_{t_1},\\widetilde{Q}_{t_2})\\) ; 2) ensuring that the infilled entire human motion sequence \\(\\widehat{Q}\\) can walk on the terrain with correct foot contact." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.893, + 0.78 + ], + "angle": 0, + "content": "While previous state-of-the-art [67] attempts to infill missing frames using a transformer-based cVAE, as shown in Figure 1, low-quality motions persist due to the domain gap between indoor motion data and outdoor pedestrian data in busy city scenes. To address this issue, we design a hierarchical control framework that is capable of generating motions in different scenarios. This framework mainly consists of a high-level latent-space controller and a lower-level generative motion transition model. Specifically, our framework begins with a low-level generative motion transition model that can provide plausible human motion based on sparse input. Inspired by [28, 62], we develop a controllable latent space that will serve as the action space of our high-level motion controller. Our high-level motion controller can then sample latent codes based on terrain, input video observations, and past states. In contrast to [67], our framework can generate plausible motions for occluded frames by fine-tuning our controller on each video. We then apply a physics-aware humanoid controller that imitates the generated motion in a physics simulator on the reconstructed terrain, to ensure the accurate physics attributes of the entire generated motion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.637, + 0.815 + ], + "angle": 0, + "content": "3.2.1 Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Overview: Within our physics-aware motion tracking framework, we identify three critical components: the motion model \\(\\pi_{M}\\), the physics-aware motion imitator \\(\\pi_{D}\\), and the high-level controller \\(\\pi_{C}\\), as depicted in Figure 4. The motion model \\(\\pi_{M}\\) employs a generative transition model to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20799" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.473, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.473, + 0.368 + ], + "angle": 0, + "content": "Figure 4: Motion Tracking Framework. At time step \\( t \\), our high-level controller predicts the latent code for the motion model \\( \\pi_{M} \\) and the residuals for the occluded motion at \\( t + 1 \\). Next, the physics-aware imitator \\( \\pi_{D} \\) updates this prediction to ensure the physical plausibility of the generated motion. If the initial motion is visible at \\( t + 1 \\), our high-level controller will directly use this captured motion rather than predict the latent code and generate motions by \\( \\pi_{M} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.473, + 0.643 + ], + "angle": 0, + "content": "compute the next pose using the previous pose and a latent code. Meanwhile, the physics-aware motion imitator \\(\\pi_{D}\\) takes either an occluded frame pose generated by \\(\\pi_{M}\\) or a visible frame pose directly observed as input, thereby controlling a virtual character to mimic the motion in a physics simulator. For visible frames, we circumvent the use of \\(\\pi_{M}\\) and provide the observed pose directly to \\(\\pi_{D}\\). When dealing with occluded frames, we call upon the high-level controller \\(\\pi_{C}\\) to generate the latent code required by \\(\\pi_{M}\\) in order to control the motion of the virtual character and infill coherent motions between visible frames. To accomplish this infilling, we train \\(\\pi_{C}\\) to address the motion tracking task, which involves two objectives. The first goal requires driving the virtual character to reach the same position as \\(\\widetilde{Q}_{t_2}\\) at time \\(t_2\\), starting from \\(\\widetilde{Q}_{t_1}\\), while ensuring the character attains a similar pose to \\(\\widetilde{Q}_{t_2}\\). The second objective entails maintaining compatibility with the underlying terrain \\(G\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.646, + 0.473, + 0.853 + ], + "angle": 0, + "content": "Motion Transition Model: We follow one of the state-of-the-art local motion transition models [49] as \\(\\pi_{M}\\) and use a pre-trained model from the official implementation. To infill occluded motions between two visible frames from \\(\\widetilde{Q}_{t_1}\\) to \\(\\widetilde{Q}_{t_2}\\), the initial observation of model is \\(\\widetilde{S}_{t_1} = (\\widetilde{\\tau}_{t_1},\\widetilde{r}_{t_1},\\widetilde{\\theta}_{t_1},\\widetilde{j}_{t_1},\\widetilde{\\tau}_{t_1},\\widetilde{r}_{t_1},\\widetilde{j}_{t_1})\\), corresponding to the root translation, root orientation, body pose, joint position, the velocity of translation, velocity of rotation, and the velocity of joints respectively. The motion \\(\\widehat{S}_{t_1 + 1}^g = (\\widehat{\\tau}_{t_1 + 1}^g,\\widehat{r}_{t_1 + 1}^g,\\widehat{\\theta}_{t_1 + 1}^g,\\widehat{j}_{t_1 + 1}^g,\\widehat{\\tau}_{t_1 + 1}^g,\\widehat{r}_{t_1 + 1}^g,\\widehat{j}_{t_1 + 1}^g)\\) for the occluded frame \\(t_1 + 1\\) can be generated by sampling latent code \\(z_{t_1}\\). With this model, we can generate \\(t_2 - t_1 - 1\\) step motions step by step for motion infilling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Physics-Based Motion Imitator: Our physics-based motion imitator \\(\\pi_{D}\\) adapts the output motions of the generation module to the reconstructed terrains \\(G\\). Following [45, 69," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.293 + ], + "angle": 0, + "content": "[70], this model drives a simulated humanoid to imitate the target pose, producing a physically valid motion sequence through the simulation process. As shown in Figure 4, the input of this imitator is the motion \\(\\widehat{S}_{t+1}^g\\) of the motion generation model, as well as the motion simulated in the previous time step \\(\\widehat{S}_t\\). In practice, we adjust the height of \\(\\widehat{S}_{t+1}^g\\) to remove floating and penetration to the reconstructed terrain \\(G\\). Our \\(\\pi_D\\) predicts the target joint angle as \\(a_{t+1}\\) for the physics simulator. Similar to [69, 70], we use the proportional derivative controllers (PD) on each non-root joint to produce joint torques \\(\\widehat{\\mathcal{T}}_{t+1}\\) and obtain the physics-plausible motion \\(\\widehat{S}_{t+1} = (\\widehat{\\tau}_{t+1}, \\widehat{r}_{t+1}, \\widehat{\\theta}_{t+1}, \\widehat{j}_{t+1}, \\widehat{\\dot{\\tau}}_{t+1}, \\widehat{\\dot{r}}_{t+1}, \\widehat{\\dot{j}}_{t+1})\\) by the simulator upon the reconstructed terrain \\(G\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.893, + 0.691 + ], + "angle": 0, + "content": "High-level Controller: The goal of our high-level controller is to compute latent codes that can drive \\(\\pi_{M}\\) from time step \\(t\\) to \\(t + 1\\). For the visible frame at \\(t + 1\\), the motion \\(\\widetilde{G}_{t + 1}\\) is adapted to the reconstructed terrain \\(G\\) by first adjusting the height, and the high-level controller directly uses the adjusted captured motion as the imitation target for \\(\\pi_{D}\\), rather than predicting latent codes for \\(\\pi_{M}\\). For the occluded frame, our high-level controller samples specific latent code \\(z_{t + 1}\\) for \\(\\pi_{M}\\). Basically, to ensure reaching the same position of \\(\\widetilde{Q}_{t_2}\\) at \\(t_2\\) from \\(\\widetilde{Q}_{t_1}\\), we formulate this reaching problem as a trajectory following task, which can guide the character to reach \\(\\widetilde{Q}_{t_2}\\) at \\(t_2\\) step-by-step and drive the character to a pose similar to \\(\\widetilde{Q}_{t_2}\\). We directly interpolate the root translation of \\((\\widetilde{\\tau}_{t_1},\\widetilde{\\tau}_{t_2})\\) as the following trajectory \\(\\{x_t\\}\\) for these missing frames. For each time step \\(t\\in (t_1,t_2)\\), the input of the high-level controller consists of the generated motion state \\(\\widehat{S}_t^g\\), the simulated motion \\(\\widehat{S}_t\\), the future trajectories \\(x\\), the reconstructed terrain \\(G\\), and the target motion \\(\\widetilde{Q}_{t_2}\\). In addition to the latent code \\(z_{t + 1}\\), our high-level controller additionally predicts \\(z_{t + 1}^r\\) as residuals of the motion generated at \\(t + 1\\), since the motion generation model \\(\\pi_{M}\\) is only trained on indoor motions on flat ground and may have trouble producing motions on uneven terrains. In practice, \\(z_{t + 1}^r\\) consists of root translation, root orientation, and character body pose. Thus, for the missing frame, the motion at \\(t + 1\\) can be generated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.7, + 0.892, + 0.72 + ], + "angle": 0, + "content": "\\[\nz _ {t + 1} ^ {g}, z _ {t + 1} ^ {r} = \\pi_ {C} \\left(\\widehat {S} _ {t} ^ {g}, \\widehat {S} _ {t}, x, G, \\widetilde {Q} _ {t _ {2}}\\right) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.755, + 0.892, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\widehat {S} _ {t + 1} ^ {g} = \\pi_ {M} \\left(\\widehat {S} _ {t} ^ {g}, z _ {t + 1} ^ {g}\\right) + z _ {t + 1} ^ {r}, \\widehat {a} _ {t + 1} = \\pi_ {D} \\left(\\widehat {S} _ {t}, \\widehat {S} _ {t + 1} ^ {g}\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.81, + 0.892, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\widehat {S} _ {t + 1} = \\operatorname {S i m} \\left(\\widehat {S} _ {t}, \\widehat {\\mathcal {T}} _ {t + 1}\\right) = \\operatorname {S i m} \\left(\\widehat {S} _ {t}, \\mathrm {P D} \\left(\\widehat {S} _ {t}, \\widehat {a} _ {t + 1}\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.679, + 0.864 + ], + "angle": 0, + "content": "3.2.2 Training Strategy" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "We follow [28] to train this high-level controller using the standard reinforcement learning algorithm [54]. Notice that" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20800" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "\\(\\pi_{M}\\) is pre-trained and frozen during this process. The reward for training is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.134, + 0.47, + 0.15 + ], + "angle": 0, + "content": "\\[\nr = w _ {p} \\cdot r _ {p} + w _ {i} \\cdot r _ {i}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.159, + 0.401, + 0.175 + ], + "angle": 0, + "content": "The reward for the trajectory following task is as" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.184, + 0.469, + 0.202 + ], + "angle": 0, + "content": "\\[\nr _ {p} = \\exp \\left(- \\alpha_ {p} \\left(\\| \\hat {r} _ {p} ^ {x y} - x _ {p} ^ {x y} \\|\\right)\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.21, + 0.469, + 0.287 + ], + "angle": 0, + "content": "where \\(\\widehat{r}_p^{xy}\\) and \\(x_p^{xy}\\) are the \\(xy\\) coordinates of the translation of physics state \\(\\widehat{S}_t\\) and the interpolated trajectory at time step \\(t\\). The infilling reward encourages the motion model to generate a similar motion as \\(\\widetilde{S}_{t_2}\\) when the character is near to \\(t_2\\):" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.287, + 0.469, + 0.306 + ], + "angle": 0, + "content": "\\[\nr _ {i} = \\gamma_ {i} \\cdot \\exp \\left(- \\alpha_ {i} \\left(\\| \\widehat {S} _ {t} - \\widetilde {S} _ {t _ {2}} \\|\\right)\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.469, + 0.37 + ], + "angle": 0, + "content": "The weights \\((w_{p}, w_{i})\\) and \\((\\alpha_{t}, \\alpha_{i})\\) can be adjusted to fit different scenarios. The \\(\\gamma_{i}\\) is equal to 1 if \\(t \\in (t_{2} - 15, t_{2})\\). Otherwise, we set this \\(\\gamma_{i}\\) as 0 and thus the task is only trajectory following." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.47, + 0.628 + ], + "angle": 0, + "content": "Training such a high-level controller from scratch for different scenarios is time-consuming (more than 12 hours on a single V100 GPU by IsaacGym [37] for 1000 iterations). To mitigate the time cost and obtain a more robust controller for different environments (e.g., trajectories and terrains), we propose a pre-training and fine-tuning strategy for our high-level controller. We generate diverse uneven terrains and driving trajectories meant to simulate a range of scenarios in the simulator, followed by training the high-level controller on these synthetic environments for our designated tasks. For infilling ending motion, we sample from various motions in the AMASS [36] while performing motion-matching tasks. Leveraging the pre-trained high-level controller on synthetic data, the convergence of fine-tuning on real data is significantly faster, as illustrated in Figure 6. We present additional information about our pre-training strategy in our supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.468, + 0.653 + ], + "angle": 0, + "content": "3.3. Stage III: Physics-aware Motion Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.795 + ], + "angle": 0, + "content": "After we obtain the physics plausible and occlusion-free human motions \\(\\widehat{Q}\\) in Section 3.2, the motion may not align with the image evidence such as 2D keypoints perfectly. Additionally, in Section 3.1, we have filtered out the whole body for some partially occluded motions, even if they have several high-confidence estimated keypoints. For these frames, our physics-aware motion tracking in Section 3.2 always obtains motions by motion generation and thus causes misalignment to the video observation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.902 + ], + "angle": 0, + "content": "To close these gaps, in this section, we propose a physics-aware motion optimization method to further optimize \\(\\widehat{Q}\\). This stage mainly consists of two components. The first is a new physics-aware imitator \\(\\pi_K\\) similar as \\(\\pi_D\\) in Section 3.2, to maintain physics plausibility while matching video evidence. Additionally, we introduce residual parameters \\(\\{\\delta R_i\\}_{i=1}^T\\) for the target motion \\(\\widehat{Q}\\) of the imitator" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "at each time step. During optimization, the imitation target \\(\\widehat{Q}_{t + 1}\\) is adjusted by \\(\\delta R_{t + 1}\\) and thus encourages the imitator to predict a consistent motion \\(\\bar{a}_{t + 1}\\) with video observation. In practice, we introduce these residual parameters to the root orientation and body pose of characters in the simulator. After training, the updated target motion is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.194, + 0.892, + 0.214 + ], + "angle": 0, + "content": "\\[\n\\widehat {r} _ {t + 1} ^ {u} = \\widehat {r} _ {t + 1} + \\delta R _ {t + 1} ^ {r}, \\widehat {\\theta} _ {t + 1} ^ {u} = \\widehat {\\theta} _ {t + 1} + \\delta R _ {t + 1} ^ {\\theta}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.24, + 0.892, + 0.263 + ], + "angle": 0, + "content": "\\[\n\\widehat {S} _ {t _ {1} + 1} ^ {u} = \\left(\\widehat {\\tau} _ {t + 1}, \\widehat {r} _ {t + 1} ^ {u}, \\widehat {\\theta} _ {t + 1} ^ {u}, \\widehat {j} _ {t + 1}, \\widehat {\\dot {\\tau}} _ {t + 1}, \\widehat {r} _ {t + 1}, \\widehat {\\dot {j}} _ {t + 1}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.271, + 0.892, + 0.331 + ], + "angle": 0, + "content": "Based on this adapted target motion, we first use the imitator \\(\\pi_{K}\\) to predict the target joint angle as \\(\\overline{a}_{t + 1}\\) for the physics simulator and produce joint torques \\(\\overline{\\mathcal{T}}_{t + 1}\\) to obtain the final result \\(\\overline{Q}_{t + 1}\\), similar as \\(\\pi_{D}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.892, + 0.392 + ], + "angle": 0, + "content": "During optimizing, we fine-tune this pre-trained imitator and these residual parameters for each motion sequence. To encourage consistency between observation and output motion, we use the following reward function:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.402, + 0.892, + 0.424 + ], + "angle": 0, + "content": "\\[\nr _ {p r o j} = \\exp \\left(- \\alpha_ {p} \\sum \\left(\\| \\Pi (\\bar {j} _ {t}) - \\tilde {j} _ {t} ^ {2 D} \\| \\times \\tilde {c} _ {t}\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.433, + 0.892, + 0.523 + ], + "angle": 0, + "content": "where \\(\\Pi\\) is the projection function from world to image space, \\(\\widetilde{j}_t^{2D}\\) is the estimated 2D pose at time step \\(t\\), as well as \\(\\widetilde{c}_t\\) is the corresponding confidence score. Besides, we still use the similar reward function \\(r_{im}\\) as [69, 70] used for motion imitation to encourage correct physics attributes for the motions with residuals. The final reward is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.535, + 0.892, + 0.551 + ], + "angle": 0, + "content": "\\[\nr = r _ {p r o j} \\cdot w _ {p} + r _ {i m} \\cdot w _ {i m}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.561, + 0.89, + 0.59 + ], + "angle": 0, + "content": "where \\((w_{p},w_{im})\\) and \\((\\alpha_{p},\\alpha_{im})\\) can be adjusted to fit different scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.633, + 0.621 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Dataset: We conduct our experiments on the Waymo Open Dataset [73], currently the largest dataset recorded for autonomous driving scenarios featuring point clouds representing the surrounding terrain and sparsely annotated 3D keypoints. To evaluate the effectiveness of our proposed method, we curate a subset of 20 sequences from the training and validation sets, each containing various scenarios, and incorporating more than 30 different pedestrian 3D keypoint annotations, as well as high-quality terrain reconstructions. The Waymo Open Dataset captures data at a \\(10\\mathrm{Hz}\\) frame rate using a camera installed on the vehicle. As we require a \\(30\\mathrm{Hz}\\) frame rate in our physics simulator, we up-sample the captured motions using linear interpolation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Metric: We use both kinematics-based and physics-based metrics for evaluation. Firstly, to quantify the generated motions from our framework, we report the motion FID, a standard metric for evaluating motion fidelity [27, 48]. Besides, to demonstrate the reconstruction accuracy, we use" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20801" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.173 + ], + "angle": 0, + "content": "Table 1: Baseline Comparison. We compare against several different baselines on the following metrics. GLAMR* means use the same physics-aware imitator as our framework after GLAMR. Our method achieves the significantly better result on FID, PAMPJPE on frames with occlusion (Occ), and physics-based metrics (GP, FS, FL)." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.174, + 0.48, + 0.232 + ], + "angle": 0, + "content": "
MethodFID ↓ (All)PA-MPJE ↓ (Occ)PA-MPJE ↓ (All)GP ↓ (All)FS ↓ (All)FL ↓ (All)Accel (All)
KAMA4.6297.5275.0682.2049.2778.89-
GLAMR4.1791.7474.3481.4246.3378.23154.14
GLAMR*4.2893.4476.3417.3438.3415.38138.44
Ours1.9686.0274.2212.627.4413.25105.48
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.236, + 0.472, + 0.307 + ], + "angle": 0, + "content": "Table 2: Ablation studies on the physics-aware imitator. Although we have adapted the generated motion to the ground during training, the physics-aware motion imitator still can improve the motion quality on these physics attributes. Our* means the result without post-optimization." + }, + { + "type": "table", + "bbox": [ + 0.109, + 0.31, + 0.436, + 0.354 + ], + "angle": 0, + "content": "
MethodGP ↓FS ↓FL ↓Accel
Without πD16.8210.8423.02114.48
Ours*12.927.0514.08108.59
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.47, + 0.573 + ], + "angle": 0, + "content": "the Procrustes-aligned mean per-joint position error (PA-MPJPE) and 2D localization error (2D-LE) for the generated human dynamics motion. For the physical attributes, we follow the metrics to measure jitter, foot sliding, ground penetration, and floating as in [70, 25]. The jitter is estimated by computing the acceleration (Accel). The foot sliding (FS) is estimated by finding the body mesh vertices that contact the ground in two adjacent frames and then computing their moving distance. The ground penetration (GP) is computed as the average distance between the ground and the mesh vertices below the ground. For floating (FL), we compute the distance between the ground and the nearest vertex of mesh to the ground. The unit for these metrics are millimeters (mm), except for Accel (mm/frame\\(^2\\))." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.585, + 0.295, + 0.601 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.47, + 0.82 + ], + "angle": 0, + "content": "In Section 3.2 and Section 3.3, we follow the methodology outlined in RFC [69] to train our physics-aware motion imitator. This imitator is trained on the flat ground using the AMASS [36] dataset and IsaacGym [37]. We model the SMPL agent in this simulator following [35]. In Section 3.2, we use the official motion generation model put forth by HuMOR [49] as our motion model \\(\\pi_{M}\\). Regarding our high-level controller, we pre-train this model on synthetic environments for 5000 iterations before fine-tuning it in real-world environments. For motion infilling, we optimize the result for 2000 iterations with our physics-aware motion optimization. Finally, to ensure the accuracy of our optimization, we leverage VITPose [64] to extract precise 2D keypoints in the last stage of our framework." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.199, + 0.847 + ], + "angle": 0, + "content": "4.2. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Baselines: We conduct our method based on KAMA [13], a strong human motion captured method for visible motions. To evaluate the quality of the generated motion" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.131 + ], + "angle": 0, + "content": "Table 3: Ablation studies on post optimization. We compare the infilling results with and without the post-optimization after physics-aware motion tracking." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.132, + 0.895, + 0.171 + ], + "angle": 0, + "content": "
Method2D-LE ↓(All)PA-MPJPE ↓(Occ)PA-MPJPE ↓(All)GP ↓(All)FS ↓(All)FL ↓(All)Accel (All)
Without Opt26.4189.8475.4812.927.0514.08108.59
With Opt17.3786.0274.2212.627.4413.25105.48
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.181, + 0.892, + 0.301 + ], + "angle": 0, + "content": "by our method, we compare it with the state-of-the-art method [67], which is designed to generate missing parts for the entire motion sequence. As [67], we also compare with methods using linear interpolation for the infilling of the missing frames. For fair comparisons, we adapt all the methods and experiments by using the ground-truth camera extrinsic and intrinsic parameters provided by the Waymo Open Dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.893, + 0.634 + ], + "angle": 0, + "content": "Quantitative Results: We show our results in Table 1 to show the quality of generated motions. To begin with, we evaluate the quality of the motion sequences generated by our method and compare them with our baselines using the FID metric. Our approach produces the best performance with substantial improvements in this regard. Furthermore, our method exhibits the best result in the PA-MPJPE metric, particularly a notable reduction in the frames with occlusion. Regarding physics-based metrics, our method continues to outperform all baselines. However, we still encounter minor foot penetration issues while quantifying the physics attributes due to errors in the transformation between the height map and mesh, as well as in the character's SMPL model within the simulator. Despite utilizing GLAMR and the physics imitator cooperatively to facilitate better physics attribute outcomes, the infilling capability of GLAMR still influences the performance of kinematics metrics, FL, and Accel. This points to the considerable complexity involved in designing our controller-based physics-aware framework to address this problem. In summary, our approach possesses the potential to achieve high-quality human dynamics learning based on visual observations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.727 + ], + "angle": 0, + "content": "Qualitative Results: We demonstrate the qualitative results in Figure 5. We compare against the GLAMR [67], which is the state-of-the-art method to infill captured motions. We find that our method achieves better results on the physical attributes of human motion. More comparison videos are in our supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.665, + 0.754 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Pre-training for High-level Controller: Firstly, we compare the performance of our method without the pre-training step on synthetic terrains and trajectories. As shown in Figure 6, the high-level controller based on the pre-trained model converges faster significantly. More comparisons of this pre-training are in our supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Physics-based Motion Tracker: Then, we compare with the motion without our physics-aware imitator in Table 2. Although we adapt generated motion to the ground during" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20802" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.088, + 0.851, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.384, + 0.895, + 0.414 + ], + "angle": 0, + "content": "Figure 5: Qualitative Comparison. We compare our method with the state-of-the-art method [67] for global human motion mesh recovery in this figure. Under this comparison, our method mitigates the artifacts on physics attributes of the whole motion sequence significantly." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.418, + 0.273, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.418, + 0.472, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.539, + 0.472, + 0.609 + ], + "angle": 0, + "content": "Figure 6: Convergence Results. We compare the time cost of training the high-level controller on the Waymo Open Dataset with and without the pre-training on synthetic data. We show that the high-level controller converges much faster and achieves a better reward with the pre-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.47, + 0.678 + ], + "angle": 0, + "content": "training, the physics-aware imitator still improves the performance on physics attributes of generated motion. More qualitative comparisons of different design choices are in our supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.471, + 0.816 + ], + "angle": 0, + "content": "Physics-based Post Optimization: Finally, we conduct a comparison of our method's performance without the post-optimization step outlined in Section 3.3. As indicated in Table 3, the inclusion of post-time optimization notably enhances the accuracy of matching 2D/3D observations and improves some physical attributes of the entire motion sequence. In addition, we demonstrate the effects of this stage by comparing the results with and without post-optimization in Figure 7." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.334, + 0.847 + ], + "angle": 0, + "content": "5. Conclusion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "This paper presents a holistic framework for learning physically-plausible human dynamics motion of entire sequences in AV scenarios. Our approach stands out from" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.419, + 0.895, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.55, + 0.895, + 0.62 + ], + "angle": 0, + "content": "Figure 7: Effect of physics-aware post-optimization. We demonstrate the effect of our physics-aware post-optimization in this figure. Following this optimization, generated motions from the previous stages end up better matched and aligned with the video evidence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.903 + ], + "angle": 0, + "content": "prior work by generating motion sequences not only for visible frames but also for frames with occlusions or missing data. The generated motion sequences are constrained by physics and thus are suitable for downstream simulation tasks in AV scenarios. Our methodology begins with processing reconstructed terrains using LIDAR and recovering visible motions with off-the-shelf components. We then use a reinforcement learning-based motion controller within a physically-constrained environment to infill the motions. Finally, we propose a physics-aware post-optimization stage that utilizes keypoint observations to optimize the entire motion sequence. Our approach outperforms previous methods, particularly in terms of entire sequence motion quality and physical attributes, in several challenging AV scenarios. Although our results meet the necessary quality for simulation tasks, a limitation we aim to address in the future is the ability to optimize body shapes estimated by MoCap with our physics-aware framework." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20803" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. Scape: shape completion and animation of people. 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In CVPR, 2022. 6" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20806" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Human Dynamics in Autonomous Driving Scenarios/cdd5a67c-1587-4c07-9231-ae20be13d8d8_origin.pdf b/2023/Learning Human Dynamics in Autonomous Driving Scenarios/cdd5a67c-1587-4c07-9231-ae20be13d8d8_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..38872a85a8e5f69e0172a987d5f582508d3529f2 --- /dev/null +++ b/2023/Learning Human Dynamics in Autonomous Driving Scenarios/cdd5a67c-1587-4c07-9231-ae20be13d8d8_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:60f0b801ae84bc1f4eed9adaa8e8f1a59a8303f66bcb35b83eee62d72e4b959e +size 7514416 diff --git a/2023/Learning Human Dynamics in Autonomous Driving Scenarios/full.md b/2023/Learning Human Dynamics in Autonomous Driving Scenarios/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b01446285a19fce6717399baf2e91ed918dcbd5f --- /dev/null +++ b/2023/Learning Human Dynamics in Autonomous Driving Scenarios/full.md @@ -0,0 +1,309 @@ +# Learning Human Dynamics in Autonomous Driving Scenarios + +Jingbo Wang $^{1,2}$ Ye Yuan $^{1}$ Zhengyi Luo $^{1,3}$ Kevin Xie $^{1,4}$ Dahua Lin $^{2}$ Umar Iqbal $^{1}$ Sanja Fidler $^{1,4,5}$ Sameh Khamis $^{1}$ + +$^{1}$ NVIDIA $^{2}$ The Chinese University of Hong Kong $^{3}$ Carnegie Mellon University + +$^{4}$ University of Toronto $^{5}$ Vector Institute + +![](images/b4f3f2f425c270ee3504c220cc4d52930ca9aac78280e0ca9ed911a52a3387ff.jpg) + +![](images/b6ee55ee16e268871a7861fa4bfb1736bb55730101fadad97eca7bbe2b09dca5.jpg) +Figure 1: We compare our method against GLAMR [67], the state-of-the-art method for global human motion mesh recovery. The output of GLAMR (left) suffers from various physical implausibilities, such as floating, sliding, or terrain penetration. Our method (right) yields a clear improvement. + +# Abstract + +Simulation has emerged as an indispensable tool for scaling and accelerating the development of self-driving systems. A critical aspect of this is simulating realistic and diverse human behavior and intent. In this work, we propose a holistic framework for learning physically plausible human dynamics from real driving scenarios, narrowing the gap between real and simulated human behavior in safety-critical applications. We show that state-of-the-art methods underperform in driving scenarios where video data is recorded from moving vehicles, and humans are frequently partially or fully occluded. Furthermore, existing methods often disregard the global scene where humans are situated, resulting in various motion artifacts like foot sliding, floating, or ground penetration. To address this challenge, we propose an approach that incorporates physics with a rein + +forcement learning-based motion controller to learn human dynamics for driving scenarios. Our framework can simulate physically plausible human dynamics that accurately match observed human motions and infill motions for occluded body parts, while improving the physical plausibility of the entire motion sequence. Experiments on the challenging Waymo Open Dataset show that our method outperforms state-of-the-art motion capture approaches significantly in recovering high-quality, physically plausible, and scene-aware human dynamics. + +# 1. Introduction + +Self-driving systems have come a long way in recent years. One major advancement that directly impacted these systems is the widespread adoption of simulation. While considerable attention was given to simulating traffic and other vehicles (e.g., TrafficSim [59], GeoSim [3], + +STRIVE [51]), simulating pedestrian motion and behavior received less attention in the literature. In this work, we argue that understanding human behavior and intent is a critical step towards realistic simulation, which in turn is key to the safety of autonomous vehicles (AVs) in real-world settings. The first step towards this goal is capturing physically plausible human dynamics of entire motion sequences in driving scenarios. + +Contrary to human motion in indoor scenes [12], motion captured in AV scenarios presents several challenges. These challenges include camera motion, long-term partial or full occlusions, scale variability, and complex interactions with the real-world environment. State-of-the-art (SOTA) approaches [69, 68, 70, 46, 34, 66, 35] for learning human dynamics in indoor scenarios tend to focus on enhancing physical plausibility for visible frames, neglecting several of these obstacles, such as long-term motion occlusions and the interplay between humans and terrains. As a result, it is challenging to directly apply these approaches to complex AV scenarios. Although recent works [67, 49] have demonstrated progress in infilling missing motions, there are significant limitations to using these methods for learning physically plausible human dynamics in AV scenarios, as shown in Figure 1. Firstly, these methods consider only physiologically inspired kinematics constraints such as joint limits, and do not model the physical plausibility of the pose in relation to the environment, such as when an object is floating. Secondly, these motion generation models are usually trained on indoor datasets, and the domain gap between indoor and driving scenarios renders them incapable of infilling missing motions in a plausible way. + +In this paper, we present a novel holistic framework to learn human dynamics in such challenging AV scenarios. Our proposed framework distinguishes itself from prior works by its ability to generate physically plausibility motions for long-term partially or fully missing body parts, thus addressing an important limitation in the SOTA approaches to learn human dynamics. Firstly, we integrate off-the-shelf motion capturing (e.g., KAMA [13]) and scene reconstruction (e.g., Possion Surface Reconstruction [17]) methods to recover observed motions of visible humans and recover the terrain mesh as well. Before learning human dynamics from the captured motions, we fix the missing terrains by the observed motion trajectories, as well as filter out frames with low-confidence estimation caused by partial occlusion, to guarantee the simulation framework is based on reasonable visual observation. Next, we track the captured motion on the reconstructed terrains by generating infilling motions for the missing frames while enforcing the physical plausibility of the captured motions (e.g. penetration free against the ground). In contrast to GLAMR [67], which infills a few missing frames together using the pretrained transformer-based model, our method generated the + +motions in a stepwise fashion using a local motion controller, similar to [28, 62]. This controller-style motion generation reduces foot sliding over long-term occlusions. We demonstrate the adaptability of our approach by showing that, even though it is trained on indoor motion data, it can generalize to in-the-wild driving scenarios by placing physical constraints on the human-scene interactions. Specifically, we first train the conditional variational autoencoder [18] (cVAE) as the local motion generator whose latent space is the action space of movement. We then train a high-level controller to sample this latent space to perform infilling. Although all the motion generation models and physics-aware imitators are trained on an indoor dataset with flat ground, our method can easily adapt these models to uneven terrains in driving scenarios. Finally, we use an additional joint optimization, based on the physics-based imitator and generated motion, to match the video evidence (e.g., 2D keypoints with high confidence) not utilized in the previous stage. In summary, our framework is capable of learning physically plausible human dynamics for entire motion sequences in driving scenarios through visual observations. + +We summarize our contributions as follows: 1) We propose the first framework for learning physically plausible human dynamics in driving scenarios, which is capable of generating physically plausible motions for partially or fully missing body parts. 2) We adapt a reinforcement learning-based motion generation framework trained only on indoor motion data, but can generalize to in-the-wild driving scenarios, infilling physically-plausible motion for occluded frames. 3) We achieve a significant improvement in motion quality over our motion capture framework to learn human dynamics, especially on partially or fully occluded frames. + +# 2. Related Works + +Kinematics-based Motion Capture: In recent times, the research community has focused on advancing the task of estimating 3D human keypoints directly to capture human motion, leading to impressive outcomes [6, 38, 40, 61, 44, 39, 1, 23]. Alternatively, several works have proposed adopting parametric human models, such as SMPL and SMPL-X [32, 42], as templates to capture human physiological motions [43, 15, 60, 2, 11, 58]. While some methods encourage the estimated motion to match observations during training [15, 53, 8] or fit the SMPL body through post-optimization [14, 22, 57], others predict SMPL parameters based on accurate keypoints [5] and apply inverse kinematics to transform the keypoint skeleton into the parametric body space [13, 26] to enable better keypoint localization. + +Recent works have also recognized the importance of exploiting temporal information to improve motion consistency [4, 19, 16, 33]. To this end, some methods, such as VIBE [20] and humor [49], employ a variational auto + +![](images/f565cc322cfc1e5a9757c681e17df370c7b5df34c96781f92a1f8cf7860c1fc2.jpg) +Figure 2: System Overview. Our approach processes each pedestrian mesh sequence in a stage-wise fashion. We first estimate motions for visible frames $\widehat{Q}$ using an off-the-shelf motion capture method. We also reconstruct the ground terrain $G$ in preparation for the physics-based stages (Details in Section 3.1). The physics-aware motion tracking (Section 3.2) infills the motion $\widehat{Q}$ for the occluded frames, as well as adapts the previously reconstructed motion to the reconstructed ground. In the last stage (Section 3.3), we optimize the entire motion $\widehat{Q}$ to closely match the evidence from a 2D keypoint-based system to produce the final motion $\overline{Q}$ . + +encoder (VAE) to learn motion priors on large-scale motion datasets like AMASS [36] to enhance the robustness of the system. Similarly, GLAMR [67] introduces a transformer-based cVAE model that leverages a data-driven approach to smooth out captured motions and infill occluded frames. Nevertheless, the lack of consideration for the dynamics attributes of human motions, particularly in complex AV scenarios, may induce undesirable physical artifacts, such as foot sliding and ground penetrations. + +Dynamics-based Motion Capture: To ameliorate the physical artifacts associated with capturing human motion sequences, recent works have sought to leverage the physics attributes of human dynamics. These methods can be broadly classified into two categories. The first category entails post-optimization during test time [50, 56, 63, 7] on both trajectories and body poses by leveraging physics forces and human motion dynamics equations to optimize physical metrics or characteristics. The second category involves reinforcement learning (RL) and motion imitation [69, 68, 70, 46, 34, 66, 35], with the focus on capturing human motion first, followed by utilizing RL and carefully-designed policies to imitate the captured motions in a simulator environment, enforcing physical plausibility. Unfortunately, training RL-based models on each motion sequence are time-consuming, necessitating the development of regression-based approaches to directly estimate physical attributes and then update the captured motions to reduce the computational time. Several recent works [55, 71, 25] have taken this approach. However, many of these works assume that the character is walking on flat ground or without long-term occlusions and missing frames. Differently, this work aims to tackle these challenges of learning human dynamics in complex AV scenarios. + +Occlusion-aware Motion Capture: Most of the existing works for human motion capturing assume the target human is fully visible in the image, and thus limit the robustness for the strong and long-term occluded human motions. Several + +recent works [49, 72, 9, 52, 21] try to address this problem but still can not handle the long-term occlusions, especially when the person of interest is obstructed completely. GLAMR [67] is the first work to solve this problem by infilling the missing motions using a transformer-based cVAE model. While this is a promising direction with many successful applications, the domain gap between their training dataset and the captured outdoor motions is large enough to limit its applicability in a complex outdoor environment. + +Motion Control: Our framework relies on a key component known as the motion controller, a long-standing research topic in computer graphics and robotics [65, 24, 41]. Recent character control works follow a reinforcement learning-based pipeline [31, 29, 47, 45, 30, 69] to generate physical motions using either reference motion or motion prediction [10, 28, 62]. Similar to [62], our work employs a motion controller, in conjunction with a physics module, to generate physically plausible motions using a cVAE model. However, we diverge from past research by using the motion controller to recover human motion sequences in a complex outdoor environment, from being solely trained on indoor datasets. Our approach is the first to use motion controllers for this task of motion recovery, generating a more physically plausible representation of human behavior in complex driving environments. + +# 3. Method + +Our framework takes as input a monocular video sequence $I = (I_1, \dots, I_M)$ with $M$ frames captured by a fast-moving vehicle camera. Our goal is to obtain physically plausible human dynamics $\{Q^i\}_{i=1}^N$ for both visible and occluded frames of $N$ entire motion sequences in the world coordinate system. Each person's motion $Q$ is defined as $(T, R, \Theta)$ comprising the root translation $T = (\tau_s, \dots, \tau_e)$ , root rotation $R = (r_s, \dots, r_e)$ , and body motions $\Theta = (\theta_s, \dots, \theta_e)$ from the first frame $s$ to the last frame $e$ . We + +![](images/a876f3800bb3101cb5e86e10b1c26e59275e4f561524d14c75140882d478bf78.jpg) +Figure 3: Terrain Preparation. As shown in this figure, we first convert the reconstructed mesh to height map and extend this height map without valid LIDAR scanning for motions. At last, we convert the processed height map to mesh for the following physics-aware stages. + +employ the SMPL [32] model's definition for the root translation $\tau_{t} \in R^{3}$ , root orientation $r_{t} \in R^{3}$ , and body pose $\theta_{t} \in R^{23 \times 3}$ . To simulate the human dynamics captured from the real world, e.g. avoiding human-scene collisions, we also follow the definition of SMPL to estimate the body shape parameter $b_{i} \in R^{10}$ for each motion sequence $i$ for meshes of characters in the simulator. + +Our holistic framework (Figure 2) comprises three main stages. In Stage-I (Section 3.1), we prepare the initial observation, such as motion $\widehat{Q}$ in visible frames and reconstructed terrain of the ground $G$ , for the following physics-aware steps. In Stage-II (Section 3.2), we employ a novel physics-aware tracking framework to address occlusion issues with $\widehat{Q}$ and adapt visible motions to reconstructed terrains with plausibly physical attributes, resulting in the occlusion-free motion $\widehat{Q}$ . In Stage-III (Section 3.3), we apply our physics-based optimization to the generated motion $\widehat{Q}$ to ensure consistency between the generated motions and observations. More details as in the following sections. + +# 3.1. Stage I: Motion and Terrain Preparation + +In our physics-aware framework, we initiate physics-based simulation by computing initial kinematic human motions and reconstructing terrains. However, captured motions often have occlusions by cars and pedestrians in AV scenarios, leading to low-quality poses unsuitable for physics-based reasoning. Thus, we filter out occluded frames using 2D pose confidence scores and leverage physics-based priors to infill occluded frames later. + +We also emphasize terrain reconstruction, an essential component of our framework. We use Poisson Surface Reconstruction [17] to reconstruct the terrain mesh from point clouds obtained from LIDAR on vehicles. However, point cloud densities are subject to occlusions and camera motion, + +leading to holes and uneven surfaces on the mesh. To obtain a well-formed mesh for simulation, we use a two-step approach of converting the reconstructed mesh to a height map and then infilling and expanding the height map to cover the entire range of human motions captured, as shown in Figure 3. By doing so, we significantly enhance the mesh quality, enabling accurate physics-based simulations of human agents interacting with the environment. We perform these two steps on all motions and terrains utilized in our experiments to ensure reliable and accurate simulations. + +# 3.2. Stage II: Physics-Aware Motion Tracking + +In this section, we will simulate physics-plausible human motion based on the processed observations from the first stage. In this section, we simulate physically plausible human motion based on the observations processed in the first stage. Our simulation aims to track the entire motion sequence on the reconstructed terrains, focusing on two aspects: 1) infilling physics-plausible human motions $\{\widehat{Q}_{t_1 + 1},\ldots \widehat{Q}_{t_2 - 1}\}$ for occluded/missing frames between two visible frames $(\widetilde{Q}_{t_1},\widetilde{Q}_{t_2})$ ; 2) ensuring that the infilled entire human motion sequence $\widehat{Q}$ can walk on the terrain with correct foot contact. + +While previous state-of-the-art [67] attempts to infill missing frames using a transformer-based cVAE, as shown in Figure 1, low-quality motions persist due to the domain gap between indoor motion data and outdoor pedestrian data in busy city scenes. To address this issue, we design a hierarchical control framework that is capable of generating motions in different scenarios. This framework mainly consists of a high-level latent-space controller and a lower-level generative motion transition model. Specifically, our framework begins with a low-level generative motion transition model that can provide plausible human motion based on sparse input. Inspired by [28, 62], we develop a controllable latent space that will serve as the action space of our high-level motion controller. Our high-level motion controller can then sample latent codes based on terrain, input video observations, and past states. In contrast to [67], our framework can generate plausible motions for occluded frames by fine-tuning our controller on each video. We then apply a physics-aware humanoid controller that imitates the generated motion in a physics simulator on the reconstructed terrain, to ensure the accurate physics attributes of the entire generated motion. + +# 3.2.1 Framework + +Overview: Within our physics-aware motion tracking framework, we identify three critical components: the motion model $\pi_{M}$ , the physics-aware motion imitator $\pi_{D}$ , and the high-level controller $\pi_{C}$ , as depicted in Figure 4. The motion model $\pi_{M}$ employs a generative transition model to + +![](images/59c8285d71fff5fb0b873d3b5d5c84b1492e0a26c392a8bf0793c2636495a84e.jpg) +Figure 4: Motion Tracking Framework. At time step $t$ , our high-level controller predicts the latent code for the motion model $\pi_{M}$ and the residuals for the occluded motion at $t + 1$ . Next, the physics-aware imitator $\pi_{D}$ updates this prediction to ensure the physical plausibility of the generated motion. If the initial motion is visible at $t + 1$ , our high-level controller will directly use this captured motion rather than predict the latent code and generate motions by $\pi_{M}$ . + +compute the next pose using the previous pose and a latent code. Meanwhile, the physics-aware motion imitator $\pi_{D}$ takes either an occluded frame pose generated by $\pi_{M}$ or a visible frame pose directly observed as input, thereby controlling a virtual character to mimic the motion in a physics simulator. For visible frames, we circumvent the use of $\pi_{M}$ and provide the observed pose directly to $\pi_{D}$ . When dealing with occluded frames, we call upon the high-level controller $\pi_{C}$ to generate the latent code required by $\pi_{M}$ in order to control the motion of the virtual character and infill coherent motions between visible frames. To accomplish this infilling, we train $\pi_{C}$ to address the motion tracking task, which involves two objectives. The first goal requires driving the virtual character to reach the same position as $\widetilde{Q}_{t_2}$ at time $t_2$ , starting from $\widetilde{Q}_{t_1}$ , while ensuring the character attains a similar pose to $\widetilde{Q}_{t_2}$ . The second objective entails maintaining compatibility with the underlying terrain $G$ . + +Motion Transition Model: We follow one of the state-of-the-art local motion transition models [49] as $\pi_{M}$ and use a pre-trained model from the official implementation. To infill occluded motions between two visible frames from $\widetilde{Q}_{t_1}$ to $\widetilde{Q}_{t_2}$ , the initial observation of model is $\widetilde{S}_{t_1} = (\widetilde{\tau}_{t_1},\widetilde{r}_{t_1},\widetilde{\theta}_{t_1},\widetilde{j}_{t_1},\widetilde{\tau}_{t_1},\widetilde{r}_{t_1},\widetilde{j}_{t_1})$ , corresponding to the root translation, root orientation, body pose, joint position, the velocity of translation, velocity of rotation, and the velocity of joints respectively. The motion $\widehat{S}_{t_1 + 1}^g = (\widehat{\tau}_{t_1 + 1}^g,\widehat{r}_{t_1 + 1}^g,\widehat{\theta}_{t_1 + 1}^g,\widehat{j}_{t_1 + 1}^g,\widehat{\tau}_{t_1 + 1}^g,\widehat{r}_{t_1 + 1}^g,\widehat{j}_{t_1 + 1}^g)$ for the occluded frame $t_1 + 1$ can be generated by sampling latent code $z_{t_1}$ . With this model, we can generate $t_2 - t_1 - 1$ step motions step by step for motion infilling. + +Physics-Based Motion Imitator: Our physics-based motion imitator $\pi_{D}$ adapts the output motions of the generation module to the reconstructed terrains $G$ . Following [45, 69, + +[70], this model drives a simulated humanoid to imitate the target pose, producing a physically valid motion sequence through the simulation process. As shown in Figure 4, the input of this imitator is the motion $\widehat{S}_{t+1}^g$ of the motion generation model, as well as the motion simulated in the previous time step $\widehat{S}_t$ . In practice, we adjust the height of $\widehat{S}_{t+1}^g$ to remove floating and penetration to the reconstructed terrain $G$ . Our $\pi_D$ predicts the target joint angle as $a_{t+1}$ for the physics simulator. Similar to [69, 70], we use the proportional derivative controllers (PD) on each non-root joint to produce joint torques $\widehat{\mathcal{T}}_{t+1}$ and obtain the physics-plausible motion $\widehat{S}_{t+1} = (\widehat{\tau}_{t+1}, \widehat{r}_{t+1}, \widehat{\theta}_{t+1}, \widehat{j}_{t+1}, \widehat{\dot{\tau}}_{t+1}, \widehat{\dot{r}}_{t+1}, \widehat{\dot{j}}_{t+1})$ by the simulator upon the reconstructed terrain $G$ . + +High-level Controller: The goal of our high-level controller is to compute latent codes that can drive $\pi_{M}$ from time step $t$ to $t + 1$ . For the visible frame at $t + 1$ , the motion $\widetilde{G}_{t + 1}$ is adapted to the reconstructed terrain $G$ by first adjusting the height, and the high-level controller directly uses the adjusted captured motion as the imitation target for $\pi_{D}$ , rather than predicting latent codes for $\pi_{M}$ . For the occluded frame, our high-level controller samples specific latent code $z_{t + 1}$ for $\pi_{M}$ . Basically, to ensure reaching the same position of $\widetilde{Q}_{t_2}$ at $t_2$ from $\widetilde{Q}_{t_1}$ , we formulate this reaching problem as a trajectory following task, which can guide the character to reach $\widetilde{Q}_{t_2}$ at $t_2$ step-by-step and drive the character to a pose similar to $\widetilde{Q}_{t_2}$ . We directly interpolate the root translation of $(\widetilde{\tau}_{t_1},\widetilde{\tau}_{t_2})$ as the following trajectory $\{x_t\}$ for these missing frames. For each time step $t\in (t_1,t_2)$ , the input of the high-level controller consists of the generated motion state $\widehat{S}_t^g$ , the simulated motion $\widehat{S}_t$ , the future trajectories $x$ , the reconstructed terrain $G$ , and the target motion $\widetilde{Q}_{t_2}$ . In addition to the latent code $z_{t + 1}$ , our high-level controller additionally predicts $z_{t + 1}^r$ as residuals of the motion generated at $t + 1$ , since the motion generation model $\pi_{M}$ is only trained on indoor motions on flat ground and may have trouble producing motions on uneven terrains. In practice, $z_{t + 1}^r$ consists of root translation, root orientation, and character body pose. Thus, for the missing frame, the motion at $t + 1$ can be generated as follows: + +$$ +z _ {t + 1} ^ {g}, z _ {t + 1} ^ {r} = \pi_ {C} \left(\widehat {S} _ {t} ^ {g}, \widehat {S} _ {t}, x, G, \widetilde {Q} _ {t _ {2}}\right) \tag {1} +$$ + +$$ +\widehat {S} _ {t + 1} ^ {g} = \pi_ {M} \left(\widehat {S} _ {t} ^ {g}, z _ {t + 1} ^ {g}\right) + z _ {t + 1} ^ {r}, \widehat {a} _ {t + 1} = \pi_ {D} \left(\widehat {S} _ {t}, \widehat {S} _ {t + 1} ^ {g}\right) \tag {2} +$$ + +$$ +\widehat {S} _ {t + 1} = \operatorname {S i m} \left(\widehat {S} _ {t}, \widehat {\mathcal {T}} _ {t + 1}\right) = \operatorname {S i m} \left(\widehat {S} _ {t}, \mathrm {P D} \left(\widehat {S} _ {t}, \widehat {a} _ {t + 1}\right)\right) \tag {3} +$$ + +# 3.2.2 Training Strategy + +We follow [28] to train this high-level controller using the standard reinforcement learning algorithm [54]. Notice that + +$\pi_{M}$ is pre-trained and frozen during this process. The reward for training is as follows: + +$$ +r = w _ {p} \cdot r _ {p} + w _ {i} \cdot r _ {i}. \tag {4} +$$ + +The reward for the trajectory following task is as + +$$ +r _ {p} = \exp \left(- \alpha_ {p} \left(\| \hat {r} _ {p} ^ {x y} - x _ {p} ^ {x y} \|\right)\right), \tag {5} +$$ + +where $\widehat{r}_p^{xy}$ and $x_p^{xy}$ are the $xy$ coordinates of the translation of physics state $\widehat{S}_t$ and the interpolated trajectory at time step $t$ . The infilling reward encourages the motion model to generate a similar motion as $\widetilde{S}_{t_2}$ when the character is near to $t_2$ : + +$$ +r _ {i} = \gamma_ {i} \cdot \exp \left(- \alpha_ {i} \left(\| \widehat {S} _ {t} - \widetilde {S} _ {t _ {2}} \|\right)\right). \tag {6} +$$ + +The weights $(w_{p}, w_{i})$ and $(\alpha_{t}, \alpha_{i})$ can be adjusted to fit different scenarios. The $\gamma_{i}$ is equal to 1 if $t \in (t_{2} - 15, t_{2})$ . Otherwise, we set this $\gamma_{i}$ as 0 and thus the task is only trajectory following. + +Training such a high-level controller from scratch for different scenarios is time-consuming (more than 12 hours on a single V100 GPU by IsaacGym [37] for 1000 iterations). To mitigate the time cost and obtain a more robust controller for different environments (e.g., trajectories and terrains), we propose a pre-training and fine-tuning strategy for our high-level controller. We generate diverse uneven terrains and driving trajectories meant to simulate a range of scenarios in the simulator, followed by training the high-level controller on these synthetic environments for our designated tasks. For infilling ending motion, we sample from various motions in the AMASS [36] while performing motion-matching tasks. Leveraging the pre-trained high-level controller on synthetic data, the convergence of fine-tuning on real data is significantly faster, as illustrated in Figure 6. We present additional information about our pre-training strategy in our supplementary materials. + +# 3.3. Stage III: Physics-aware Motion Optimization + +After we obtain the physics plausible and occlusion-free human motions $\widehat{Q}$ in Section 3.2, the motion may not align with the image evidence such as 2D keypoints perfectly. Additionally, in Section 3.1, we have filtered out the whole body for some partially occluded motions, even if they have several high-confidence estimated keypoints. For these frames, our physics-aware motion tracking in Section 3.2 always obtains motions by motion generation and thus causes misalignment to the video observation. + +To close these gaps, in this section, we propose a physics-aware motion optimization method to further optimize $\widehat{Q}$ . This stage mainly consists of two components. The first is a new physics-aware imitator $\pi_K$ similar as $\pi_D$ in Section 3.2, to maintain physics plausibility while matching video evidence. Additionally, we introduce residual parameters $\{\delta R_i\}_{i=1}^T$ for the target motion $\widehat{Q}$ of the imitator + +at each time step. During optimization, the imitation target $\widehat{Q}_{t + 1}$ is adjusted by $\delta R_{t + 1}$ and thus encourages the imitator to predict a consistent motion $\bar{a}_{t + 1}$ with video observation. In practice, we introduce these residual parameters to the root orientation and body pose of characters in the simulator. After training, the updated target motion is defined as: + +$$ +\widehat {r} _ {t + 1} ^ {u} = \widehat {r} _ {t + 1} + \delta R _ {t + 1} ^ {r}, \widehat {\theta} _ {t + 1} ^ {u} = \widehat {\theta} _ {t + 1} + \delta R _ {t + 1} ^ {\theta}, \tag {7} +$$ + +$$ +\widehat {S} _ {t _ {1} + 1} ^ {u} = \left(\widehat {\tau} _ {t + 1}, \widehat {r} _ {t + 1} ^ {u}, \widehat {\theta} _ {t + 1} ^ {u}, \widehat {j} _ {t + 1}, \widehat {\dot {\tau}} _ {t + 1}, \widehat {r} _ {t + 1}, \widehat {\dot {j}} _ {t + 1}\right). \tag {8} +$$ + +Based on this adapted target motion, we first use the imitator $\pi_{K}$ to predict the target joint angle as $\overline{a}_{t + 1}$ for the physics simulator and produce joint torques $\overline{\mathcal{T}}_{t + 1}$ to obtain the final result $\overline{Q}_{t + 1}$ , similar as $\pi_{D}$ . + +During optimizing, we fine-tune this pre-trained imitator and these residual parameters for each motion sequence. To encourage consistency between observation and output motion, we use the following reward function: + +$$ +r _ {p r o j} = \exp \left(- \alpha_ {p} \sum \left(\| \Pi (\bar {j} _ {t}) - \tilde {j} _ {t} ^ {2 D} \| \times \tilde {c} _ {t}\right)\right), \tag {9} +$$ + +where $\Pi$ is the projection function from world to image space, $\widetilde{j}_t^{2D}$ is the estimated 2D pose at time step $t$ , as well as $\widetilde{c}_t$ is the corresponding confidence score. Besides, we still use the similar reward function $r_{im}$ as [69, 70] used for motion imitation to encourage correct physics attributes for the motions with residuals. The final reward is as follows: + +$$ +r = r _ {p r o j} \cdot w _ {p} + r _ {i m} \cdot w _ {i m}. \tag {10} +$$ + +where $(w_{p},w_{im})$ and $(\alpha_{p},\alpha_{im})$ can be adjusted to fit different scenarios. + +# 4. Experiments + +Dataset: We conduct our experiments on the Waymo Open Dataset [73], currently the largest dataset recorded for autonomous driving scenarios featuring point clouds representing the surrounding terrain and sparsely annotated 3D keypoints. To evaluate the effectiveness of our proposed method, we curate a subset of 20 sequences from the training and validation sets, each containing various scenarios, and incorporating more than 30 different pedestrian 3D keypoint annotations, as well as high-quality terrain reconstructions. The Waymo Open Dataset captures data at a $10\mathrm{Hz}$ frame rate using a camera installed on the vehicle. As we require a $30\mathrm{Hz}$ frame rate in our physics simulator, we up-sample the captured motions using linear interpolation. + +Metric: We use both kinematics-based and physics-based metrics for evaluation. Firstly, to quantify the generated motions from our framework, we report the motion FID, a standard metric for evaluating motion fidelity [27, 48]. Besides, to demonstrate the reconstruction accuracy, we use + +Table 1: Baseline Comparison. We compare against several different baselines on the following metrics. GLAMR* means use the same physics-aware imitator as our framework after GLAMR. Our method achieves the significantly better result on FID, PAMPJPE on frames with occlusion (Occ), and physics-based metrics (GP, FS, FL). + +
MethodFID ↓ (All)PA-MPJE ↓ (Occ)PA-MPJE ↓ (All)GP ↓ (All)FS ↓ (All)FL ↓ (All)Accel (All)
KAMA4.6297.5275.0682.2049.2778.89-
GLAMR4.1791.7474.3481.4246.3378.23154.14
GLAMR*4.2893.4476.3417.3438.3415.38138.44
Ours1.9686.0274.2212.627.4413.25105.48
+ +Table 2: Ablation studies on the physics-aware imitator. Although we have adapted the generated motion to the ground during training, the physics-aware motion imitator still can improve the motion quality on these physics attributes. Our* means the result without post-optimization. + +
MethodGP ↓FS ↓FL ↓Accel
Without πD16.8210.8423.02114.48
Ours*12.927.0514.08108.59
+ +the Procrustes-aligned mean per-joint position error (PA-MPJPE) and 2D localization error (2D-LE) for the generated human dynamics motion. For the physical attributes, we follow the metrics to measure jitter, foot sliding, ground penetration, and floating as in [70, 25]. The jitter is estimated by computing the acceleration (Accel). The foot sliding (FS) is estimated by finding the body mesh vertices that contact the ground in two adjacent frames and then computing their moving distance. The ground penetration (GP) is computed as the average distance between the ground and the mesh vertices below the ground. For floating (FL), we compute the distance between the ground and the nearest vertex of mesh to the ground. The unit for these metrics are millimeters (mm), except for Accel (mm/frame $^2$ ). + +# 4.1. Implementation Details + +In Section 3.2 and Section 3.3, we follow the methodology outlined in RFC [69] to train our physics-aware motion imitator. This imitator is trained on the flat ground using the AMASS [36] dataset and IsaacGym [37]. We model the SMPL agent in this simulator following [35]. In Section 3.2, we use the official motion generation model put forth by HuMOR [49] as our motion model $\pi_{M}$ . Regarding our high-level controller, we pre-train this model on synthetic environments for 5000 iterations before fine-tuning it in real-world environments. For motion infilling, we optimize the result for 2000 iterations with our physics-aware motion optimization. Finally, to ensure the accuracy of our optimization, we leverage VITPose [64] to extract precise 2D keypoints in the last stage of our framework. + +# 4.2. Evaluation + +Baselines: We conduct our method based on KAMA [13], a strong human motion captured method for visible motions. To evaluate the quality of the generated motion + +Table 3: Ablation studies on post optimization. We compare the infilling results with and without the post-optimization after physics-aware motion tracking. + +
Method2D-LE ↓(All)PA-MPJPE ↓(Occ)PA-MPJPE ↓(All)GP ↓(All)FS ↓(All)FL ↓(All)Accel (All)
Without Opt26.4189.8475.4812.927.0514.08108.59
With Opt17.3786.0274.2212.627.4413.25105.48
+ +by our method, we compare it with the state-of-the-art method [67], which is designed to generate missing parts for the entire motion sequence. As [67], we also compare with methods using linear interpolation for the infilling of the missing frames. For fair comparisons, we adapt all the methods and experiments by using the ground-truth camera extrinsic and intrinsic parameters provided by the Waymo Open Dataset. + +Quantitative Results: We show our results in Table 1 to show the quality of generated motions. To begin with, we evaluate the quality of the motion sequences generated by our method and compare them with our baselines using the FID metric. Our approach produces the best performance with substantial improvements in this regard. Furthermore, our method exhibits the best result in the PA-MPJPE metric, particularly a notable reduction in the frames with occlusion. Regarding physics-based metrics, our method continues to outperform all baselines. However, we still encounter minor foot penetration issues while quantifying the physics attributes due to errors in the transformation between the height map and mesh, as well as in the character's SMPL model within the simulator. Despite utilizing GLAMR and the physics imitator cooperatively to facilitate better physics attribute outcomes, the infilling capability of GLAMR still influences the performance of kinematics metrics, FL, and Accel. This points to the considerable complexity involved in designing our controller-based physics-aware framework to address this problem. In summary, our approach possesses the potential to achieve high-quality human dynamics learning based on visual observations. + +Qualitative Results: We demonstrate the qualitative results in Figure 5. We compare against the GLAMR [67], which is the state-of-the-art method to infill captured motions. We find that our method achieves better results on the physical attributes of human motion. More comparison videos are in our supplementary material. + +# 4.3. Ablation Studies + +Pre-training for High-level Controller: Firstly, we compare the performance of our method without the pre-training step on synthetic terrains and trajectories. As shown in Figure 6, the high-level controller based on the pre-trained model converges faster significantly. More comparisons of this pre-training are in our supplementary materials. + +Physics-based Motion Tracker: Then, we compare with the motion without our physics-aware imitator in Table 2. Although we adapt generated motion to the ground during + +![](images/6d73664152e63197544f6bfb0fe73fbbc62ad6e2a207204afac8382707134831.jpg) +Figure 5: Qualitative Comparison. We compare our method with the state-of-the-art method [67] for global human motion mesh recovery in this figure. Under this comparison, our method mitigates the artifacts on physics attributes of the whole motion sequence significantly. + +![](images/f7efcea1eb6cc567e129c6a880825b87e8a2ff17c31940ab97900e63fb9e83f9.jpg) +Figure 6: Convergence Results. We compare the time cost of training the high-level controller on the Waymo Open Dataset with and without the pre-training on synthetic data. We show that the high-level controller converges much faster and achieves a better reward with the pre-training. + +![](images/140bfefd3b922a9da077c8c9e9054d4809c385053af10cb2ee0c327ea13cbd3a.jpg) +Figure 7: Effect of physics-aware post-optimization. We demonstrate the effect of our physics-aware post-optimization in this figure. Following this optimization, generated motions from the previous stages end up better matched and aligned with the video evidence. + +training, the physics-aware imitator still improves the performance on physics attributes of generated motion. More qualitative comparisons of different design choices are in our supplementary materials. + +Physics-based Post Optimization: Finally, we conduct a comparison of our method's performance without the post-optimization step outlined in Section 3.3. As indicated in Table 3, the inclusion of post-time optimization notably enhances the accuracy of matching 2D/3D observations and improves some physical attributes of the entire motion sequence. In addition, we demonstrate the effects of this stage by comparing the results with and without post-optimization in Figure 7. + +# 5. Conclusion and Limitations + +This paper presents a holistic framework for learning physically-plausible human dynamics motion of entire sequences in AV scenarios. Our approach stands out from + +![](images/7c8e0c86c8e0d87896b5e33ccf97fb5d68f6d64a26c200b7d2bdf0f24855d9db.jpg) + +prior work by generating motion sequences not only for visible frames but also for frames with occlusions or missing data. The generated motion sequences are constrained by physics and thus are suitable for downstream simulation tasks in AV scenarios. Our methodology begins with processing reconstructed terrains using LIDAR and recovering visible motions with off-the-shelf components. We then use a reinforcement learning-based motion controller within a physically-constrained environment to infill the motions. Finally, we propose a physics-aware post-optimization stage that utilizes keypoint observations to optimize the entire motion sequence. Our approach outperforms previous methods, particularly in terms of entire sequence motion quality and physical attributes, in several challenging AV scenarios. 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The output of GLAMR (left) suffers from various physical implausibilities, such as floating, sliding, or terrain penetration. Our method (right) yields a clear improvement." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 502, + 192, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 502, + 192, + 514 + ], + "spans": [ + { + "bbox": [ + 143, + 502, + 192, + 514 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 533, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 289, + 715 + ], + "type": "text", + "content": "Simulation has emerged as an indispensable tool for scaling and accelerating the development of self-driving systems. A critical aspect of this is simulating realistic and diverse human behavior and intent. In this work, we propose a holistic framework for learning physically plausible human dynamics from real driving scenarios, narrowing the gap between real and simulated human behavior in safety-critical applications. We show that state-of-the-art methods underperform in driving scenarios where video data is recorded from moving vehicles, and humans are frequently partially or fully occluded. Furthermore, existing methods often disregard the global scene where humans are situated, resulting in various motion artifacts like foot sliding, floating, or ground penetration. To address this challenge, we propose an approach that incorporates physics with a rein" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 503, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 547, + 624 + ], + "type": "text", + "content": "forcement learning-based motion controller to learn human dynamics for driving scenarios. Our framework can simulate physically plausible human dynamics that accurately match observed human motions and infill motions for occluded body parts, while improving the physical plausibility of the entire motion sequence. Experiments on the challenging Waymo Open Dataset show that our method outperforms state-of-the-art motion capture approaches significantly in recovering high-quality, physically plausible, and scene-aware human dynamics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 632, + 387, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 387, + 643 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 387, + 643 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Self-driving systems have come a long way in recent years. One major advancement that directly impacted these systems is the widespread adoption of simulation. While considerable attention was given to simulating traffic and other vehicles (e.g., TrafficSim [59], GeoSim [3]," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20796" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 167 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 167 + ], + "type": "text", + "content": "STRIVE [51]), simulating pedestrian motion and behavior received less attention in the literature. In this work, we argue that understanding human behavior and intent is a critical step towards realistic simulation, which in turn is key to the safety of autonomous vehicles (AVs) in real-world settings. The first step towards this goal is capturing physically plausible human dynamics of entire motion sequences in driving scenarios." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 172, + 286, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 172, + 286, + 445 + ], + "spans": [ + { + "bbox": [ + 49, + 172, + 286, + 445 + ], + "type": "text", + "content": "Contrary to human motion in indoor scenes [12], motion captured in AV scenarios presents several challenges. These challenges include camera motion, long-term partial or full occlusions, scale variability, and complex interactions with the real-world environment. State-of-the-art (SOTA) approaches [69, 68, 70, 46, 34, 66, 35] for learning human dynamics in indoor scenarios tend to focus on enhancing physical plausibility for visible frames, neglecting several of these obstacles, such as long-term motion occlusions and the interplay between humans and terrains. As a result, it is challenging to directly apply these approaches to complex AV scenarios. Although recent works [67, 49] have demonstrated progress in infilling missing motions, there are significant limitations to using these methods for learning physically plausible human dynamics in AV scenarios, as shown in Figure 1. Firstly, these methods consider only physiologically inspired kinematics constraints such as joint limits, and do not model the physical plausibility of the pose in relation to the environment, such as when an object is floating. Secondly, these motion generation models are usually trained on indoor datasets, and the domain gap between indoor and driving scenarios renders them incapable of infilling missing motions in a plausible way." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 451, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 451, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 451, + 286, + 712 + ], + "type": "text", + "content": "In this paper, we present a novel holistic framework to learn human dynamics in such challenging AV scenarios. Our proposed framework distinguishes itself from prior works by its ability to generate physically plausibility motions for long-term partially or fully missing body parts, thus addressing an important limitation in the SOTA approaches to learn human dynamics. Firstly, we integrate off-the-shelf motion capturing (e.g., KAMA [13]) and scene reconstruction (e.g., Possion Surface Reconstruction [17]) methods to recover observed motions of visible humans and recover the terrain mesh as well. Before learning human dynamics from the captured motions, we fix the missing terrains by the observed motion trajectories, as well as filter out frames with low-confidence estimation caused by partial occlusion, to guarantee the simulation framework is based on reasonable visual observation. Next, we track the captured motion on the reconstructed terrains by generating infilling motions for the missing frames while enforcing the physical plausibility of the captured motions (e.g. penetration free against the ground). In contrast to GLAMR [67], which infills a few missing frames together using the pretrained transformer-based model, our method generated the" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 308, + 72, + 544, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 334 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 334 + ], + "type": "text", + "content": "motions in a stepwise fashion using a local motion controller, similar to [28, 62]. This controller-style motion generation reduces foot sliding over long-term occlusions. We demonstrate the adaptability of our approach by showing that, even though it is trained on indoor motion data, it can generalize to in-the-wild driving scenarios by placing physical constraints on the human-scene interactions. Specifically, we first train the conditional variational autoencoder [18] (cVAE) as the local motion generator whose latent space is the action space of movement. We then train a high-level controller to sample this latent space to perform infilling. Although all the motion generation models and physics-aware imitators are trained on an indoor dataset with flat ground, our method can easily adapt these models to uneven terrains in driving scenarios. Finally, we use an additional joint optimization, based on the physics-based imitator and generated motion, to match the video evidence (e.g., 2D keypoints with high confidence) not utilized in the previous stage. In summary, our framework is capable of learning physically plausible human dynamics for entire motion sequences in driving scenarios through visual observations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 335, + 544, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 335, + 544, + 467 + ], + "spans": [ + { + "bbox": [ + 308, + 335, + 544, + 467 + ], + "type": "text", + "content": "We summarize our contributions as follows: 1) We propose the first framework for learning physically plausible human dynamics in driving scenarios, which is capable of generating physically plausible motions for partially or fully missing body parts. 2) We adapt a reinforcement learning-based motion generation framework trained only on indoor motion data, but can generalize to in-the-wild driving scenarios, infilling physically-plausible motion for occluded frames. 3) We achieve a significant improvement in motion quality over our motion capture framework to learn human dynamics, especially on partially or fully occluded frames." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 478, + 395, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 478, + 395, + 490 + ], + "spans": [ + { + "bbox": [ + 308, + 478, + 395, + 490 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 498, + 544, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 498, + 544, + 665 + ], + "spans": [ + { + "bbox": [ + 308, + 498, + 544, + 665 + ], + "type": "text", + "content": "Kinematics-based Motion Capture: In recent times, the research community has focused on advancing the task of estimating 3D human keypoints directly to capture human motion, leading to impressive outcomes [6, 38, 40, 61, 44, 39, 1, 23]. Alternatively, several works have proposed adopting parametric human models, such as SMPL and SMPL-X [32, 42], as templates to capture human physiological motions [43, 15, 60, 2, 11, 58]. While some methods encourage the estimated motion to match observations during training [15, 53, 8] or fit the SMPL body through post-optimization [14, 22, 57], others predict SMPL parameters based on accurate keypoints [5] and apply inverse kinematics to transform the keypoint skeleton into the parametric body space [13, 26] to enable better keypoint localization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 666, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 666, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 666, + 544, + 712 + ], + "type": "text", + "content": "Recent works have also recognized the importance of exploiting temporal information to improve motion consistency [4, 19, 16, 33]. To this end, some methods, such as VIBE [20] and humor [49], employ a variational auto" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "20797" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 541, + 196 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 541, + 196 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 541, + 196 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 541, + 196 + ], + "type": "image", + "image_path": "f565cc322cfc1e5a9757c681e17df370c7b5df34c96781f92a1f8cf7860c1fc2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "text", + "content": "Figure 2: System Overview. Our approach processes each pedestrian mesh sequence in a stage-wise fashion. We first estimate motions for visible frames " + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "text", + "content": " using an off-the-shelf motion capture method. We also reconstruct the ground terrain " + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "text", + "content": " in preparation for the physics-based stages (Details in Section 3.1). The physics-aware motion tracking (Section 3.2) infills the motion " + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "text", + "content": " for the occluded frames, as well as adapts the previously reconstructed motion to the reconstructed ground. In the last stage (Section 3.3), we optimize the entire motion " + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "text", + "content": " to closely match the evidence from a 2D keypoint-based system to produce the final motion " + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\overline{Q}" + }, + { + "bbox": [ + 46, + 205, + 548, + 262 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 267, + 289, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 289, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 289, + 376 + ], + "type": "text", + "content": "encoder (VAE) to learn motion priors on large-scale motion datasets like AMASS [36] to enhance the robustness of the system. Similarly, GLAMR [67] introduces a transformer-based cVAE model that leverages a data-driven approach to smooth out captured motions and infill occluded frames. Nevertheless, the lack of consideration for the dynamics attributes of human motions, particularly in complex AV scenarios, may induce undesirable physical artifacts, such as foot sliding and ground penetrations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": "Dynamics-based Motion Capture: To ameliorate the physical artifacts associated with capturing human motion sequences, recent works have sought to leverage the physics attributes of human dynamics. These methods can be broadly classified into two categories. The first category entails post-optimization during test time [50, 56, 63, 7] on both trajectories and body poses by leveraging physics forces and human motion dynamics equations to optimize physical metrics or characteristics. The second category involves reinforcement learning (RL) and motion imitation [69, 68, 70, 46, 34, 66, 35], with the focus on capturing human motion first, followed by utilizing RL and carefully-designed policies to imitate the captured motions in a simulator environment, enforcing physical plausibility. Unfortunately, training RL-based models on each motion sequence are time-consuming, necessitating the development of regression-based approaches to directly estimate physical attributes and then update the captured motions to reduce the computational time. Several recent works [55, 71, 25] have taken this approach. However, many of these works assume that the character is walking on flat ground or without long-term occlusions and missing frames. Differently, this work aims to tackle these challenges of learning human dynamics in complex AV scenarios." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": "Occlusion-aware Motion Capture: Most of the existing works for human motion capturing assume the target human is fully visible in the image, and thus limit the robustness for the strong and long-term occluded human motions. Several" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 267, + 547, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 547, + 376 + ], + "type": "text", + "content": "recent works [49, 72, 9, 52, 21] try to address this problem but still can not handle the long-term occlusions, especially when the person of interest is obstructed completely. GLAMR [67] is the first work to solve this problem by infilling the missing motions using a transformer-based cVAE model. While this is a promising direction with many successful applications, the domain gap between their training dataset and the captured outdoor motions is large enough to limit its applicability in a complex outdoor environment." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 376, + 548, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 548, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 548, + 569 + ], + "type": "text", + "content": "Motion Control: Our framework relies on a key component known as the motion controller, a long-standing research topic in computer graphics and robotics [65, 24, 41]. Recent character control works follow a reinforcement learning-based pipeline [31, 29, 47, 45, 30, 69] to generate physical motions using either reference motion or motion prediction [10, 28, 62]. Similar to [62], our work employs a motion controller, in conjunction with a physics module, to generate physically plausible motions using a cVAE model. However, we diverge from past research by using the motion controller to recover human motion sequences in a complex outdoor environment, from being solely trained on indoor datasets. Our approach is the first to use motion controllers for this task of motion recovery, generating a more physically plausible representation of human behavior in complex driving environments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 584, + 362, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 584, + 362, + 596 + ], + "spans": [ + { + "bbox": [ + 306, + 584, + 362, + 596 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Our framework takes as input a monocular video sequence " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "I = (I_1, \\dots, I_M)" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " frames captured by a fast-moving vehicle camera. Our goal is to obtain physically plausible human dynamics " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{Q^i\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " for both visible and occluded frames of " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " entire motion sequences in the world coordinate system. Each person's motion " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " is defined as " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "(T, R, \\Theta)" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " comprising the root translation " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "T = (\\tau_s, \\dots, \\tau_e)" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": ", root rotation " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "R = (r_s, \\dots, r_e)" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": ", and body motions " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\Theta = (\\theta_s, \\dots, \\theta_e)" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " from the first frame " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " to the last frame " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": ". We" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20798" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 276, + 228 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 276, + 228 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 276, + 228 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 276, + 228 + ], + "type": "image", + "image_path": "a876f3800bb3101cb5e86e10b1c26e59275e4f561524d14c75140882d478bf78.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 287, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 293 + ], + "type": "text", + "content": "Figure 3: Terrain Preparation. As shown in this figure, we first convert the reconstructed mesh to height map and extend this height map without valid LIDAR scanning for motions. At last, we convert the processed height map to mesh for the following physics-aware stages." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "text", + "content": "employ the SMPL [32] model's definition for the root translation " + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "inline_equation", + "content": "\\tau_{t} \\in R^{3}" + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "text", + "content": ", root orientation " + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "inline_equation", + "content": "r_{t} \\in R^{3}" + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "text", + "content": ", and body pose " + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "inline_equation", + "content": "\\theta_{t} \\in R^{23 \\times 3}" + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "text", + "content": ". To simulate the human dynamics captured from the real world, e.g. avoiding human-scene collisions, we also follow the definition of SMPL to estimate the body shape parameter " + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "inline_equation", + "content": "b_{i} \\in R^{10}" + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "text", + "content": " for each motion sequence " + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 300, + 287, + 382 + ], + "type": "text", + "content": " for meshes of characters in the simulator." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "text", + "content": "Our holistic framework (Figure 2) comprises three main stages. In Stage-I (Section 3.1), we prepare the initial observation, such as motion " + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "text", + "content": " in visible frames and reconstructed terrain of the ground " + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "text", + "content": ", for the following physics-aware steps. In Stage-II (Section 3.2), we employ a novel physics-aware tracking framework to address occlusion issues with " + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "text", + "content": " and adapt visible motions to reconstructed terrains with plausibly physical attributes, resulting in the occlusion-free motion " + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "text", + "content": ". In Stage-III (Section 3.3), we apply our physics-based optimization to the generated motion " + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 384, + 288, + 529 + ], + "type": "text", + "content": " to ensure consistency between the generated motions and observations. More details as in the following sections." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 536, + 261, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 261, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 261, + 550 + ], + "type": "text", + "content": "3.1. Stage I: Motion and Terrain Preparation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 557, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 653 + ], + "type": "text", + "content": "In our physics-aware framework, we initiate physics-based simulation by computing initial kinematic human motions and reconstructing terrains. However, captured motions often have occlusions by cars and pedestrians in AV scenarios, leading to low-quality poses unsuitable for physics-based reasoning. Thus, we filter out occluded frames using 2D pose confidence scores and leverage physics-based priors to infill occluded frames later." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "We also emphasize terrain reconstruction, an essential component of our framework. We use Poisson Surface Reconstruction [17] to reconstruct the terrain mesh from point clouds obtained from LIDAR on vehicles. However, point cloud densities are subject to occlusions and camera motion," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "leading to holes and uneven surfaces on the mesh. To obtain a well-formed mesh for simulation, we use a two-step approach of converting the reconstructed mesh to a height map and then infilling and expanding the height map to cover the entire range of human motions captured, as shown in Figure 3. By doing so, we significantly enhance the mesh quality, enabling accurate physics-based simulations of human agents interacting with the environment. We perform these two steps on all motions and terrains utilized in our experiments to ensure reliable and accurate simulations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 201, + 523, + 214 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 201, + 523, + 214 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 523, + 214 + ], + "type": "text", + "content": "3.2. Stage II: Physics-Aware Motion Tracking" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "type": "text", + "content": "In this section, we will simulate physics-plausible human motion based on the processed observations from the first stage. In this section, we simulate physically plausible human motion based on the observations processed in the first stage. Our simulation aims to track the entire motion sequence on the reconstructed terrains, focusing on two aspects: 1) infilling physics-plausible human motions " + }, + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\{\\widehat{Q}_{t_1 + 1},\\ldots \\widehat{Q}_{t_2 - 1}\\}" + }, + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "type": "text", + "content": " for occluded/missing frames between two visible frames " + }, + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "type": "inline_equation", + "content": "(\\widetilde{Q}_{t_1},\\widetilde{Q}_{t_2})" + }, + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "type": "text", + "content": " ; 2) ensuring that the infilled entire human motion sequence " + }, + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 304, + 220, + 545, + 353 + ], + "type": "text", + "content": " can walk on the terrain with correct foot contact." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 354, + 546, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 546, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 546, + 617 + ], + "type": "text", + "content": "While previous state-of-the-art [67] attempts to infill missing frames using a transformer-based cVAE, as shown in Figure 1, low-quality motions persist due to the domain gap between indoor motion data and outdoor pedestrian data in busy city scenes. To address this issue, we design a hierarchical control framework that is capable of generating motions in different scenarios. This framework mainly consists of a high-level latent-space controller and a lower-level generative motion transition model. Specifically, our framework begins with a low-level generative motion transition model that can provide plausible human motion based on sparse input. Inspired by [28, 62], we develop a controllable latent space that will serve as the action space of our high-level motion controller. Our high-level motion controller can then sample latent codes based on terrain, input video observations, and past states. In contrast to [67], our framework can generate plausible motions for occluded frames by fine-tuning our controller on each video. We then apply a physics-aware humanoid controller that imitates the generated motion in a physics simulator on the reconstructed terrain, to ensure the accurate physics attributes of the entire generated motion." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 634, + 389, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 389, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 389, + 645 + ], + "type": "text", + "content": "3.2.1 Framework" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Overview: Within our physics-aware motion tracking framework, we identify three critical components: the motion model " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": ", the physics-aware motion imitator " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\pi_{D}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": ", and the high-level controller " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\pi_{C}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": ", as depicted in Figure 4. The motion model " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " employs a generative transition model to" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20799" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 289, + 194 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 289, + 194 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 289, + 194 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 289, + 194 + ], + "type": "image", + "image_path": "59c8285d71fff5fb0b873d3b5d5c84b1492e0a26c392a8bf0793c2636495a84e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "text", + "content": "Figure 4: Motion Tracking Framework. At time step " + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "text", + "content": ", our high-level controller predicts the latent code for the motion model " + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "text", + "content": " and the residuals for the occluded motion at " + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "text", + "content": ". Next, the physics-aware imitator " + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "inline_equation", + "content": "\\pi_{D}" + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "text", + "content": " updates this prediction to ensure the physical plausibility of the generated motion. If the initial motion is visible at " + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "text", + "content": ", our high-level controller will directly use this captured motion rather than predict the latent code and generate motions by " + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 46, + 201, + 289, + 291 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": "compute the next pose using the previous pose and a latent code. Meanwhile, the physics-aware motion imitator " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\pi_{D}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": " takes either an occluded frame pose generated by " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": " or a visible frame pose directly observed as input, thereby controlling a virtual character to mimic the motion in a physics simulator. For visible frames, we circumvent the use of " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": " and provide the observed pose directly to " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\pi_{D}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": ". When dealing with occluded frames, we call upon the high-level controller " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\pi_{C}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": " to generate the latent code required by " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": " in order to control the motion of the virtual character and infill coherent motions between visible frames. To accomplish this infilling, we train " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\pi_{C}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": " to address the motion tracking task, which involves two objectives. The first goal requires driving the virtual character to reach the same position as " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_2}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": ", starting from " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_1}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": ", while ensuring the character attains a similar pose to " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_2}" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": ". The second objective entails maintaining compatibility with the underlying terrain " + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 302, + 289, + 509 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": "Motion Transition Model: We follow one of the state-of-the-art local motion transition models [49] as " + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": " and use a pre-trained model from the official implementation. To infill occluded motions between two visible frames from " + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_1}" + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_2}" + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": ", the initial observation of model is " + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "inline_equation", + "content": "\\widetilde{S}_{t_1} = (\\widetilde{\\tau}_{t_1},\\widetilde{r}_{t_1},\\widetilde{\\theta}_{t_1},\\widetilde{j}_{t_1},\\widetilde{\\tau}_{t_1},\\widetilde{r}_{t_1},\\widetilde{j}_{t_1})" + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": ", corresponding to the root translation, root orientation, body pose, joint position, the velocity of translation, velocity of rotation, and the velocity of joints respectively. The motion " + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "inline_equation", + "content": "\\widehat{S}_{t_1 + 1}^g = (\\widehat{\\tau}_{t_1 + 1}^g,\\widehat{r}_{t_1 + 1}^g,\\widehat{\\theta}_{t_1 + 1}^g,\\widehat{j}_{t_1 + 1}^g,\\widehat{\\tau}_{t_1 + 1}^g,\\widehat{r}_{t_1 + 1}^g,\\widehat{j}_{t_1 + 1}^g)" + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": " for the occluded frame " + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "inline_equation", + "content": "t_1 + 1" + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": " can be generated by sampling latent code " + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "inline_equation", + "content": "z_{t_1}" + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": ". With this model, we can generate " + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "inline_equation", + "content": "t_2 - t_1 - 1" + }, + { + "bbox": [ + 46, + 511, + 289, + 675 + ], + "type": "text", + "content": " step motions step by step for motion infilling." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "Physics-Based Motion Imitator: Our physics-based motion imitator " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\pi_{D}" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": " adapts the output motions of the generation module to the reconstructed terrains " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": ". Following [45, 69," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": "[70], this model drives a simulated humanoid to imitate the target pose, producing a physically valid motion sequence through the simulation process. As shown in Figure 4, the input of this imitator is the motion " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\widehat{S}_{t+1}^g" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": " of the motion generation model, as well as the motion simulated in the previous time step " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\widehat{S}_t" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": ". In practice, we adjust the height of " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\widehat{S}_{t+1}^g" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": " to remove floating and penetration to the reconstructed terrain " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": ". Our " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\pi_D" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": " predicts the target joint angle as " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "a_{t+1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": " for the physics simulator. Similar to [69, 70], we use the proportional derivative controllers (PD) on each non-root joint to produce joint torques " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{T}}_{t+1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": " and obtain the physics-plausible motion " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\widehat{S}_{t+1} = (\\widehat{\\tau}_{t+1}, \\widehat{r}_{t+1}, \\widehat{\\theta}_{t+1}, \\widehat{j}_{t+1}, \\widehat{\\dot{\\tau}}_{t+1}, \\widehat{\\dot{r}}_{t+1}, \\widehat{\\dot{j}}_{t+1})" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": " by the simulator upon the reconstructed terrain " + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 72, + 545, + 232 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": "High-level Controller: The goal of our high-level controller is to compute latent codes that can drive " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " from time step " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ". For the visible frame at " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", the motion " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\widetilde{G}_{t + 1}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " is adapted to the reconstructed terrain " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " by first adjusting the height, and the high-level controller directly uses the adjusted captured motion as the imitation target for " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\pi_{D}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", rather than predicting latent codes for " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ". For the occluded frame, our high-level controller samples specific latent code " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "z_{t + 1}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ". Basically, to ensure reaching the same position of " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_2}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_1}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", we formulate this reaching problem as a trajectory following task, which can guide the character to reach " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_2}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " step-by-step and drive the character to a pose similar to " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_2}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ". We directly interpolate the root translation of " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "(\\widetilde{\\tau}_{t_1},\\widetilde{\\tau}_{t_2})" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " as the following trajectory " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\{x_t\\}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " for these missing frames. For each time step " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "t\\in (t_1,t_2)" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", the input of the high-level controller consists of the generated motion state " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\widehat{S}_t^g" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", the simulated motion " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\widehat{S}_t" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", the future trajectories " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", the reconstructed terrain " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", and the target motion " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\widetilde{Q}_{t_2}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ". In addition to the latent code " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "z_{t + 1}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", our high-level controller additionally predicts " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "z_{t + 1}^r" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " as residuals of the motion generated at " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": ", since the motion generation model " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " is only trained on indoor motions on flat ground and may have trouble producing motions on uneven terrains. In practice, " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "z_{t + 1}^r" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " consists of root translation, root orientation, and character body pose. Thus, for the missing frame, the motion at " + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 304, + 232, + 546, + 547 + ], + "type": "text", + "content": " can be generated as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 353, + 554, + 545, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 554, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 353, + 554, + 545, + 570 + ], + "type": "interline_equation", + "content": "z _ {t + 1} ^ {g}, z _ {t + 1} ^ {r} = \\pi_ {C} \\left(\\widehat {S} _ {t} ^ {g}, \\widehat {S} _ {t}, x, G, \\widetilde {Q} _ {t _ {2}}\\right) \\tag {1}", + "image_path": "a71fe01200e350c918265af5abfc5d20000523bc9ce54d9ae9c2b32cb333d346.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 597, + 545, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 597, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 312, + 597, + 545, + 613 + ], + "type": "interline_equation", + "content": "\\widehat {S} _ {t + 1} ^ {g} = \\pi_ {M} \\left(\\widehat {S} _ {t} ^ {g}, z _ {t + 1} ^ {g}\\right) + z _ {t + 1} ^ {r}, \\widehat {a} _ {t + 1} = \\pi_ {D} \\left(\\widehat {S} _ {t}, \\widehat {S} _ {t + 1} ^ {g}\\right) \\tag {2}", + "image_path": "4168dda7e3f241c99baf4196883300e68ab1180db895e053fd326beaf4a204da.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 641, + 545, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 641, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 318, + 641, + 545, + 657 + ], + "type": "interline_equation", + "content": "\\widehat {S} _ {t + 1} = \\operatorname {S i m} \\left(\\widehat {S} _ {t}, \\widehat {\\mathcal {T}} _ {t + 1}\\right) = \\operatorname {S i m} \\left(\\widehat {S} _ {t}, \\mathrm {P D} \\left(\\widehat {S} _ {t}, \\widehat {a} _ {t + 1}\\right)\\right) \\tag {3}", + "image_path": "91a881edd5e00af7d2a34ea26eca1ccfe5fca07b209da1ce370c81e195087363.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 670, + 415, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 415, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 415, + 684 + ], + "type": "text", + "content": "3.2.2 Training Strategy" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": "We follow [28] to train this high-level controller using the standard reinforcement learning algorithm [54]. Notice that" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20800" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " is pre-trained and frozen during this process. The reward for training is as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 122, + 106, + 287, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 106, + 287, + 118 + ], + "spans": [ + { + "bbox": [ + 122, + 106, + 287, + 118 + ], + "type": "interline_equation", + "content": "r = w _ {p} \\cdot r _ {p} + w _ {i} \\cdot r _ {i}. \\tag {4}", + "image_path": "b9f203e1d76e4cb40d650074ff654565fef0bf2b25a6d642f029479e1d3c4b02.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 125, + 245, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 125, + 245, + 138 + ], + "spans": [ + { + "bbox": [ + 47, + 125, + 245, + 138 + ], + "type": "text", + "content": "The reward for the trajectory following task is as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 102, + 145, + 287, + 159 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 145, + 287, + 159 + ], + "spans": [ + { + "bbox": [ + 102, + 145, + 287, + 159 + ], + "type": "interline_equation", + "content": "r _ {p} = \\exp \\left(- \\alpha_ {p} \\left(\\| \\hat {r} _ {p} ^ {x y} - x _ {p} ^ {x y} \\|\\right)\\right), \\tag {5}", + "image_path": "89b4fa0452b3ac3d2653e2f70ddb14aacfe3955f55c55d811f42116416c54e4c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "inline_equation", + "content": "\\widehat{r}_p^{xy}" + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "inline_equation", + "content": "x_p^{xy}" + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "inline_equation", + "content": "xy" + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "content": " coordinates of the translation of physics state " + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "inline_equation", + "content": "\\widehat{S}_t" + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "content": " and the interpolated trajectory at time step " + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "content": ". The infilling reward encourages the motion model to generate a similar motion as " + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "inline_equation", + "content": "\\widetilde{S}_{t_2}" + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "content": " when the character is near to " + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "inline_equation", + "content": "t_2" + }, + { + "bbox": [ + 46, + 166, + 287, + 227 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 99, + 227, + 287, + 242 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 227, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 99, + 227, + 287, + 242 + ], + "type": "interline_equation", + "content": "r _ {i} = \\gamma_ {i} \\cdot \\exp \\left(- \\alpha_ {i} \\left(\\| \\widehat {S} _ {t} - \\widetilde {S} _ {t _ {2}} \\|\\right)\\right). \\tag {6}", + "image_path": "5de52dcc42d226baa8cd9af1a91487cd1d2416ac3f2620fb4a195c2b8bdc033f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "text", + "content": "The weights " + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "inline_equation", + "content": "(w_{p}, w_{i})" + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "inline_equation", + "content": "(\\alpha_{t}, \\alpha_{i})" + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "text", + "content": " can be adjusted to fit different scenarios. The " + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "inline_equation", + "content": "\\gamma_{i}" + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "text", + "content": " is equal to 1 if " + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "inline_equation", + "content": "t \\in (t_{2} - 15, t_{2})" + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "text", + "content": ". Otherwise, we set this " + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "inline_equation", + "content": "\\gamma_{i}" + }, + { + "bbox": [ + 46, + 245, + 287, + 293 + ], + "type": "text", + "content": " as 0 and thus the task is only trajectory following." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 293, + 287, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 497 + ], + "type": "text", + "content": "Training such a high-level controller from scratch for different scenarios is time-consuming (more than 12 hours on a single V100 GPU by IsaacGym [37] for 1000 iterations). To mitigate the time cost and obtain a more robust controller for different environments (e.g., trajectories and terrains), we propose a pre-training and fine-tuning strategy for our high-level controller. We generate diverse uneven terrains and driving trajectories meant to simulate a range of scenarios in the simulator, followed by training the high-level controller on these synthetic environments for our designated tasks. For infilling ending motion, we sample from various motions in the AMASS [36] while performing motion-matching tasks. Leveraging the pre-trained high-level controller on synthetic data, the convergence of fine-tuning on real data is significantly faster, as illustrated in Figure 6. We present additional information about our pre-training strategy in our supplementary materials." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 503, + 286, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 286, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 286, + 517 + ], + "type": "text", + "content": "3.3. Stage III: Physics-aware Motion Optimization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": "After we obtain the physics plausible and occlusion-free human motions " + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": " in Section 3.2, the motion may not align with the image evidence such as 2D keypoints perfectly. Additionally, in Section 3.1, we have filtered out the whole body for some partially occluded motions, even if they have several high-confidence estimated keypoints. For these frames, our physics-aware motion tracking in Section 3.2 always obtains motions by motion generation and thus causes misalignment to the video observation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": "To close these gaps, in this section, we propose a physics-aware motion optimization method to further optimize " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": ". This stage mainly consists of two components. The first is a new physics-aware imitator " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pi_K" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": " similar as " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pi_D" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": " in Section 3.2, to maintain physics plausibility while matching video evidence. Additionally, we introduce residual parameters " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\{\\delta R_i\\}_{i=1}^T" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": " for the target motion " + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{Q}" + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": " of the imitator" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": "at each time step. During optimization, the imitation target " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\widehat{Q}_{t + 1}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " is adjusted by " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\delta R_{t + 1}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " and thus encourages the imitator to predict a consistent motion " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\bar{a}_{t + 1}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " with video observation. In practice, we introduce these residual parameters to the root orientation and body pose of characters in the simulator. After training, the updated target motion is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 332, + 153, + 545, + 169 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 153, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 332, + 153, + 545, + 169 + ], + "type": "interline_equation", + "content": "\\widehat {r} _ {t + 1} ^ {u} = \\widehat {r} _ {t + 1} + \\delta R _ {t + 1} ^ {r}, \\widehat {\\theta} _ {t + 1} ^ {u} = \\widehat {\\theta} _ {t + 1} + \\delta R _ {t + 1} ^ {\\theta}, \\tag {7}", + "image_path": "ec2b4924cc313d341022450329a8aa27562d7d5a88c549508d7aec977bc05aa8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 190, + 545, + 208 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 190, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 317, + 190, + 545, + 208 + ], + "type": "interline_equation", + "content": "\\widehat {S} _ {t _ {1} + 1} ^ {u} = \\left(\\widehat {\\tau} _ {t + 1}, \\widehat {r} _ {t + 1} ^ {u}, \\widehat {\\theta} _ {t + 1} ^ {u}, \\widehat {j} _ {t + 1}, \\widehat {\\dot {\\tau}} _ {t + 1}, \\widehat {r} _ {t + 1}, \\widehat {\\dot {j}} _ {t + 1}\\right). \\tag {8}", + "image_path": "239a766073f818807f1fd75a6b657605214cc43a14cdf614f15cc51cc7a4ef87.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "text", + "content": "Based on this adapted target motion, we first use the imitator " + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "inline_equation", + "content": "\\pi_{K}" + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "text", + "content": " to predict the target joint angle as " + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "inline_equation", + "content": "\\overline{a}_{t + 1}" + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "text", + "content": " for the physics simulator and produce joint torques " + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{T}}_{t + 1}" + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "text", + "content": " to obtain the final result " + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "inline_equation", + "content": "\\overline{Q}_{t + 1}" + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "text", + "content": ", similar as " + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "inline_equation", + "content": "\\pi_{D}" + }, + { + "bbox": [ + 305, + 214, + 545, + 262 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 262, + 545, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 310 + ], + "type": "text", + "content": "During optimizing, we fine-tune this pre-trained imitator and these residual parameters for each motion sequence. To encourage consistency between observation and output motion, we use the following reward function:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 332, + 318, + 545, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 318, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 332, + 318, + 545, + 335 + ], + "type": "interline_equation", + "content": "r _ {p r o j} = \\exp \\left(- \\alpha_ {p} \\sum \\left(\\| \\Pi (\\bar {j} _ {t}) - \\tilde {j} _ {t} ^ {2 D} \\| \\times \\tilde {c} _ {t}\\right)\\right), \\tag {9}", + "image_path": "d2eca69843d2a2838c69a3bcf3f4c72224d83d38d14d3a8ea0dfe196a7150b09.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": " is the projection function from world to image space, " + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "inline_equation", + "content": "\\widetilde{j}_t^{2D}" + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": " is the estimated 2D pose at time step " + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": ", as well as " + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "inline_equation", + "content": "\\widetilde{c}_t" + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": " is the corresponding confidence score. Besides, we still use the similar reward function " + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "inline_equation", + "content": "r_{im}" + }, + { + "bbox": [ + 305, + 342, + 545, + 414 + ], + "type": "text", + "content": " as [69, 70] used for motion imitation to encourage correct physics attributes for the motions with residuals. The final reward is as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 367, + 423, + 545, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 423, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 367, + 423, + 545, + 436 + ], + "type": "interline_equation", + "content": "r = r _ {p r o j} \\cdot w _ {p} + r _ {i m} \\cdot w _ {i m}. \\tag {10}", + "image_path": "6faf6f61c39968520736fad1c5f452e11ba138f11d2bbf7f7f28340d70ac0670.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 444, + 544, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 444, + 544, + 467 + ], + "spans": [ + { + "bbox": [ + 305, + 444, + 544, + 467 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 444, + 544, + 467 + ], + "type": "inline_equation", + "content": "(w_{p},w_{im})" + }, + { + "bbox": [ + 305, + 444, + 544, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 444, + 544, + 467 + ], + "type": "inline_equation", + "content": "(\\alpha_{p},\\alpha_{im})" + }, + { + "bbox": [ + 305, + 444, + 544, + 467 + ], + "type": "text", + "content": " can be adjusted to fit different scenarios." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 478, + 387, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 387, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 387, + 491 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 498, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 653 + ], + "type": "text", + "content": "Dataset: We conduct our experiments on the Waymo Open Dataset [73], currently the largest dataset recorded for autonomous driving scenarios featuring point clouds representing the surrounding terrain and sparsely annotated 3D keypoints. To evaluate the effectiveness of our proposed method, we curate a subset of 20 sequences from the training and validation sets, each containing various scenarios, and incorporating more than 30 different pedestrian 3D keypoint annotations, as well as high-quality terrain reconstructions. The Waymo Open Dataset captures data at a " + }, + { + "bbox": [ + 304, + 498, + 545, + 653 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 498, + 545, + 653 + ], + "type": "text", + "content": " frame rate using a camera installed on the vehicle. As we require a " + }, + { + "bbox": [ + 304, + 498, + 545, + 653 + ], + "type": "inline_equation", + "content": "30\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 498, + 545, + 653 + ], + "type": "text", + "content": " frame rate in our physics simulator, we up-sample the captured motions using linear interpolation." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "Metric: We use both kinematics-based and physics-based metrics for evaluation. Firstly, to quantify the generated motions from our framework, we report the motion FID, a standard metric for evaluating motion fidelity [27, 48]. Besides, to demonstrate the reconstruction accuracy, we use" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20801" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 137, + 293, + 183 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 137 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 137 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 137 + ], + "type": "text", + "content": "Table 1: Baseline Comparison. We compare against several different baselines on the following metrics. GLAMR* means use the same physics-aware imitator as our framework after GLAMR. Our method achieves the significantly better result on FID, PAMPJPE on frames with occlusion (Occ), and physics-based metrics (GP, FS, FL)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 137, + 293, + 183 + ], + "lines": [ + { + "bbox": [ + 47, + 137, + 293, + 183 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 293, + 183 + ], + "type": "table", + "html": "
MethodFID ↓ (All)PA-MPJE ↓ (Occ)PA-MPJE ↓ (All)GP ↓ (All)FS ↓ (All)FL ↓ (All)Accel (All)
KAMA4.6297.5275.0682.2049.2778.89-
GLAMR4.1791.7474.3481.4246.3378.23154.14
GLAMR*4.2893.4476.3417.3438.3415.38138.44
Ours1.9686.0274.2212.627.4413.25105.48
", + "image_path": "4a47a3dd71cc761de336683cb0880f2e7415e6f4d21806fc110c3792319c3d65.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 66, + 245, + 266, + 280 + ], + "blocks": [ + { + "bbox": [ + 47, + 186, + 288, + 243 + ], + "lines": [ + { + "bbox": [ + 47, + 186, + 288, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 288, + 243 + ], + "type": "text", + "content": "Table 2: Ablation studies on the physics-aware imitator. Although we have adapted the generated motion to the ground during training, the physics-aware motion imitator still can improve the motion quality on these physics attributes. Our* means the result without post-optimization." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 245, + 266, + 280 + ], + "lines": [ + { + "bbox": [ + 66, + 245, + 266, + 280 + ], + "spans": [ + { + "bbox": [ + 66, + 245, + 266, + 280 + ], + "type": "table", + "html": "
MethodGP ↓FS ↓FL ↓Accel
Without πD16.8210.8423.02114.48
Ours*12.927.0514.08108.59
", + "image_path": "0fc4247a36785547897ad10fa4fe92dae88f5c4672d1cc5f2de9aa006fe4b3c9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 286, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 287, + 453 + ], + "type": "text", + "content": "the Procrustes-aligned mean per-joint position error (PA-MPJPE) and 2D localization error (2D-LE) for the generated human dynamics motion. For the physical attributes, we follow the metrics to measure jitter, foot sliding, ground penetration, and floating as in [70, 25]. The jitter is estimated by computing the acceleration (Accel). The foot sliding (FS) is estimated by finding the body mesh vertices that contact the ground in two adjacent frames and then computing their moving distance. The ground penetration (GP) is computed as the average distance between the ground and the mesh vertices below the ground. For floating (FL), we compute the distance between the ground and the nearest vertex of mesh to the ground. The unit for these metrics are millimeters (mm), except for Accel (mm/frame" + }, + { + "bbox": [ + 46, + 286, + 287, + 453 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 286, + 287, + 453 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 463, + 180, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 180, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 180, + 475 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 482, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 287, + 649 + ], + "type": "text", + "content": "In Section 3.2 and Section 3.3, we follow the methodology outlined in RFC [69] to train our physics-aware motion imitator. This imitator is trained on the flat ground using the AMASS [36] dataset and IsaacGym [37]. We model the SMPL agent in this simulator following [35]. In Section 3.2, we use the official motion generation model put forth by HuMOR [49] as our motion model " + }, + { + "bbox": [ + 46, + 482, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\pi_{M}" + }, + { + "bbox": [ + 46, + 482, + 287, + 649 + ], + "type": "text", + "content": ". Regarding our high-level controller, we pre-train this model on synthetic environments for 5000 iterations before fine-tuning it in real-world environments. For motion infilling, we optimize the result for 2000 iterations with our physics-aware motion optimization. Finally, to ensure the accuracy of our optimization, we leverage VITPose [64] to extract precise 2D keypoints in the last stage of our framework." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 658, + 121, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 121, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 121, + 670 + ], + "type": "text", + "content": "4.2. Evaluation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "Baselines: We conduct our method based on KAMA [13], a strong human motion captured method for visible motions. To evaluate the quality of the generated motion" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 104, + 547, + 135 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 103 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 103 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 103 + ], + "type": "text", + "content": "Table 3: Ablation studies on post optimization. We compare the infilling results with and without the post-optimization after physics-aware motion tracking." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 104, + 547, + 135 + ], + "lines": [ + { + "bbox": [ + 307, + 104, + 547, + 135 + ], + "spans": [ + { + "bbox": [ + 307, + 104, + 547, + 135 + ], + "type": "table", + "html": "
Method2D-LE ↓(All)PA-MPJPE ↓(Occ)PA-MPJPE ↓(All)GP ↓(All)FS ↓(All)FL ↓(All)Accel (All)
Without Opt26.4189.8475.4812.927.0514.08108.59
With Opt17.3786.0274.2212.627.4413.25105.48
", + "image_path": "8f3efcf7139e05243fb5a9067db5a4d5455c1e8faac5da883232e6e3946c5763.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 143, + 545, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 143, + 545, + 238 + ], + "spans": [ + { + "bbox": [ + 304, + 143, + 545, + 238 + ], + "type": "text", + "content": "by our method, we compare it with the state-of-the-art method [67], which is designed to generate missing parts for the entire motion sequence. As [67], we also compare with methods using linear interpolation for the infilling of the missing frames. For fair comparisons, we adapt all the methods and experiments by using the ground-truth camera extrinsic and intrinsic parameters provided by the Waymo Open Dataset." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 239, + 546, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 546, + 502 + ], + "type": "text", + "content": "Quantitative Results: We show our results in Table 1 to show the quality of generated motions. To begin with, we evaluate the quality of the motion sequences generated by our method and compare them with our baselines using the FID metric. Our approach produces the best performance with substantial improvements in this regard. Furthermore, our method exhibits the best result in the PA-MPJPE metric, particularly a notable reduction in the frames with occlusion. Regarding physics-based metrics, our method continues to outperform all baselines. However, we still encounter minor foot penetration issues while quantifying the physics attributes due to errors in the transformation between the height map and mesh, as well as in the character's SMPL model within the simulator. Despite utilizing GLAMR and the physics imitator cooperatively to facilitate better physics attribute outcomes, the infilling capability of GLAMR still influences the performance of kinematics metrics, FL, and Accel. This points to the considerable complexity involved in designing our controller-based physics-aware framework to address this problem. In summary, our approach possesses the potential to achieve high-quality human dynamics learning based on visual observations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 575 + ], + "type": "text", + "content": "Qualitative Results: We demonstrate the qualitative results in Figure 5. We compare against the GLAMR [67], which is the state-of-the-art method to infill captured motions. We find that our method achieves better results on the physical attributes of human motion. More comparison videos are in our supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 585, + 406, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 406, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 406, + 597 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": "Pre-training for High-level Controller: Firstly, we compare the performance of our method without the pre-training step on synthetic terrains and trajectories. As shown in Figure 6, the high-level controller based on the pre-trained model converges faster significantly. More comparisons of this pre-training are in our supplementary materials." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "Physics-based Motion Tracker: Then, we compare with the motion without our physics-aware imitator in Table 2. Although we adapt generated motion to the ground during" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20802" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 69, + 520, + 293 + ], + "blocks": [ + { + "bbox": [ + 73, + 69, + 520, + 293 + ], + "lines": [ + { + "bbox": [ + 73, + 69, + 520, + 293 + ], + "spans": [ + { + "bbox": [ + 73, + 69, + 520, + 293 + ], + "type": "image", + "image_path": "6d73664152e63197544f6bfb0fe73fbbc62ad6e2a207204afac8382707134831.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 304, + 547, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 547, + 327 + ], + "type": "text", + "content": "Figure 5: Qualitative Comparison. We compare our method with the state-of-the-art method [67] for global human motion mesh recovery in this figure. Under this comparison, our method mitigates the artifacts on physics attributes of the whole motion sequence significantly." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 331, + 167, + 422 + ], + "blocks": [ + { + "bbox": [ + 48, + 331, + 167, + 422 + ], + "lines": [ + { + "bbox": [ + 48, + 331, + 167, + 422 + ], + "spans": [ + { + "bbox": [ + 48, + 331, + 167, + 422 + ], + "type": "image", + "image_path": "f7efcea1eb6cc567e129c6a880825b87e8a2ff17c31940ab97900e63fb9e83f9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 426, + 288, + 482 + ], + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 482 + ], + "type": "text", + "content": "Figure 6: Convergence Results. We compare the time cost of training the high-level controller on the Waymo Open Dataset with and without the pre-training on synthetic data. We show that the high-level controller converges much faster and achieves a better reward with the pre-training." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 331, + 288, + 420 + ], + "blocks": [ + { + "bbox": [ + 168, + 331, + 288, + 420 + ], + "lines": [ + { + "bbox": [ + 168, + 331, + 288, + 420 + ], + "spans": [ + { + "bbox": [ + 168, + 331, + 288, + 420 + ], + "type": "image", + "image_path": "140bfefd3b922a9da077c8c9e9054d4809c385053af10cb2ee0c327ea13cbd3a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 435, + 547, + 491 + ], + "lines": [ + { + "bbox": [ + 304, + 435, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 547, + 491 + ], + "type": "text", + "content": "Figure 7: Effect of physics-aware post-optimization. We demonstrate the effect of our physics-aware post-optimization in this figure. Following this optimization, generated motions from the previous stages end up better matched and aligned with the video evidence." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 489, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 489, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 287, + 536 + ], + "type": "text", + "content": "training, the physics-aware imitator still improves the performance on physics attributes of generated motion. More qualitative comparisons of different design choices are in our supplementary materials." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 537, + 288, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 288, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 288, + 646 + ], + "type": "text", + "content": "Physics-based Post Optimization: Finally, we conduct a comparison of our method's performance without the post-optimization step outlined in Section 3.3. As indicated in Table 3, the inclusion of post-time optimization notably enhances the accuracy of matching 2D/3D observations and improves some physical attributes of the entire motion sequence. In addition, we demonstrate the effects of this stage by comparing the results with and without post-optimization in Figure 7." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 657, + 204, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 204, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 204, + 670 + ], + "type": "text", + "content": "5. Conclusion and Limitations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "This paper presents a holistic framework for learning physically-plausible human dynamics motion of entire sequences in AV scenarios. Our approach stands out from" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 331, + 547, + 427 + ], + "blocks": [ + { + "bbox": [ + 308, + 331, + 547, + 427 + ], + "lines": [ + { + "bbox": [ + 308, + 331, + 547, + 427 + ], + "spans": [ + { + "bbox": [ + 308, + 331, + 547, + 427 + ], + "type": "image", + "image_path": "7c8e0c86c8e0d87896b5e33ccf97fb5d68f6d64a26c200b7d2bdf0f24855d9db.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": "prior work by generating motion sequences not only for visible frames but also for frames with occlusions or missing data. The generated motion sequences are constrained by physics and thus are suitable for downstream simulation tasks in AV scenarios. Our methodology begins with processing reconstructed terrains using LIDAR and recovering visible motions with off-the-shelf components. We then use a reinforcement learning-based motion controller within a physically-constrained environment to infill the motions. Finally, we propose a physics-aware post-optimization stage that utilizes keypoint observations to optimize the entire motion sequence. Our approach outperforms previous methods, particularly in terms of entire sequence motion quality and physical attributes, in several challenging AV scenarios. 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Multi-modal 3d human pose" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 326, + 73, + 544, + 94 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 73, + 544, + 94 + ], + "spans": [ + { + "bbox": [ + 326, + 73, + 544, + 94 + ], + "type": "text", + "content": "estimation with 2d weak supervision in autonomous driving. In CVPR, 2022. 6" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "20806" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/6803bdfe-c2d2-4fd6-a5a5-6f813d705eb4_content_list.json b/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/6803bdfe-c2d2-4fd6-a5a5-6f813d705eb4_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..dc7ce5273212329311c9646aa5c9b8e98d1095e3 --- /dev/null +++ b/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/6803bdfe-c2d2-4fd6-a5a5-6f813d705eb4_content_list.json @@ -0,0 +1,1658 @@ +[ + { + "type": "text", + "text": "Learning Human-Human Interactions in Images from Weak Textual Supervision", + "text_level": 1, + "bbox": [ + 78, + 130, + 893, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Morris Alper and Hadar Averbuch-Elor \nTel Aviv University", + "bbox": [ + 326, + 181, + 643, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 313, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Interactions between humans are diverse and context-dependent, but previous works have treated them as categorical, disregarding the heavy tail of possible interactions. We propose a new paradigm of learning human-human interactions as free text from a single still image, allowing for flexibility in modeling the unlimited space of situations and relationships between people. To overcome the absence of data labelled specifically for this task, we use knowledge distillation applied to synthetic caption data produced by a large language model without explicit supervision. We show that the pseudo-labels produced by this procedure can be used to train a captioning model to effectively understand human-human interactions in images, as measured by a variety of metrics that measure textual and semantic faithfulness and factual groundedness of our predictions. We further show that our approach outperforms SOTA image captioning and situation recognition models on this task. We will release1 our code and pseudo-labels along with Waldo and Wenda, a manually-curated test set for still image human-human interaction understanding.", + "bbox": [ + 73, + 282, + 473, + 585 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 613, + 209, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"No man is an island entire of itself.\" -John Donne", + "bbox": [ + 98, + 638, + 467, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Humans are social beings. As such, interactions among people are ubiquitous and diverse, affected by various factors including social context and cultural norms. Reasoning about these interactions is crucial for gaining a holistic understanding of visual scenes depicting people. However, in spite of significant progress in analyzing isolated human actions [29, 73, 79] and relationships between entities and objects [27, 83], far less attention has been devoted towards an automatic understanding of human-human interactions (HHI). This is despite the importance of this task for applications such as interactive robotics, social behaviour understanding, and captioning systems for the visually impaired.", + "bbox": [ + 75, + 669, + 468, + 849 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There are a number of factors that make the analysis of", + "bbox": [ + 94, + 849, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2eac0157c983513215b61bf41bf231e330d30fbffcbeaf99486c5a912655fdc5.jpg", + "image_caption": [ + "Figure 1. How would you describe the interactions depicted in these images? There are unlimited possible interactions between people which cannot be easily described by a fixed set of categories or actions. Context plays a crucial role, as in the left image where the clothing and cake in the background help to interpret the depicted interaction. Moreover, interactions may be involve participants at a physical distance as in the image on the right. To model the heavy tail of possible interactions, we propose to learn HHI as free text (see below2 for predictions using our method)." + ], + "image_footnote": [], + "bbox": [ + 501, + 250, + 697, + 349 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/de08acd4f4451fa863f88dd9e3fb1c5c7f150966362ce2b95071bfc54958c150.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 250, + 890, + 349 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "HHI difficult. The space of possible interactions between people is vast and requires understanding social context and physically non-local relationships, as illustrated in Figure 1. In addition, images depicting HHI may have multiple interpretations, some of which may be simultaneously correct. For example, the image on the left might depict \"celebrating a wedding\" as well as \"dancing\". Contextual cues such as the cake in the background of the image provide additional information that hints at the depicted HHI.", + "bbox": [ + 496, + 502, + 890, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior works targeting HHI understanding focus on a small fixed number of interactions; representative works include [63, 65, 43, 30], all of whose models are trained to recognize no more than ten interaction classes. In this work, we are interested in modeling the heavy tail of possible HHI to better understand the rich variety of ways in which people interact. To this aim, we propose to model HHI understanding as free text generation; since HHI are not confined to a fixed set of categories or even to a syntactic class such as verbs, HHI as free text enables the expression of an infinite variety of possible interactions. Furthermore, in contrast to previous works that frequently rely on extra context such as video data [60], we use a single image with no additional information (during inference), making our method more widely applicable. We focus on what Stergiou and", + "bbox": [ + 496, + 638, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "2A model fine-tuned on our pseudo-labels yields \"dancing\" and \"having a picnic\".", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1via our project page https://learning-interactions. github.io", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2887", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Poppe [60] term dyadic interactions—pairwise interactions between two people. Our goal is to identify the most salient dyadic interaction given an image of two or more people interacting.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One of the primary challenges to modeling HHI is a scarcity of labelled data for this particular task. There are only a handful of relatively small datasets specific to HHI, and larger video datasets for action recognition are lacking in coverage of interactions (see Table 1). To better model the heavy tail of possible HHI, we leverage the abundance of high-quality images of people and associated textual captions available on the Internet. In particular, we use the Who's Waldo dataset [13] that contains 270K image_caption pairs from Wikimedia Commons depicting people captured in a broad range of situations. Unlike many other image captioning datasets, Who's Waldo focuses on human-centric situations which are described using real-world captioned Internet data, and thus is more relevant to HHI understanding. However, it is extremely challenging to learn HHI from raw Internet captions directly, due to significant noise introduced by clutter and irrelevant details. To overcome this, we infer interactions from the original captions by applying knowledge distillation to synthetic data generated by a large language model, without explicit supervision. This approach allows for creating accurate pseudolabels that provide textual descriptions of the HHI depicted in the images. We will release these pseudo-labels along with a manually annotated test set containing 1K image-interaction pairs from diverse Internet images which we name Waldo and Wenda, a new benchmark for our paradigm of HHI understanding as free text on still images, capturing the heavy tail of human-human interactions.", + "bbox": [ + 75, + 152, + 472, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate the utility of these pseudo-labels for learning HHI from images by training captioning models and using them as targets for a language modelling objective. We provide qualitative and quantitative analysis on the Waldo and Wenda test set; in addition, we evaluate this method on a larger scale by applying it to verb prediction on the imSitu situation recognition dataset [75], which we filter to select for images relevant to HHI.", + "bbox": [ + 75, + 574, + 468, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Because we predict HHI as free text rather than categorically as in previous works, we propose a set of evaluation metrics chosen to measure important aspects of predicted HHI quality, namely textual similarity, factual groundedness, and verb similarity. Our evaluation shows that our HHI pseudo-labels allow for generating meaningful HHI free text descriptions from images, as measured by these metrics. We also show that learning on these pseudo-labels captures HHI substantially more effectively than either using existing SOTA image captioning models as-is or than training on interactions extracted with naive syntactic parsing. Explicitly stated, our key contributions are:", + "bbox": [ + 75, + 696, + 470, + 876 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- A new paradigm and benchmark for HHI understand", + "bbox": [ + 94, + 885, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing from images—i.e., predicting interactions as free text—allowing to better understand the vast variety of ways in which people interact.", + "bbox": [ + 529, + 90, + 890, + 137 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A method for isolating HHI from noisy Internet captions using knowledge distillation applied to a large language model, and a set of pseudo-labels generated by this method.", + "- An evaluation framework with metrics that capture HHI understanding, and results demonstrating that training image captioning models on these pseudolabels can allow for modeling the heavy tail of possible HHI across various situations and configurations more effectively than SOTA image captioning and situation recognition models." + ], + "bbox": [ + 517, + 148, + 890, + 328 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 345, + 640, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human action recognition. Human actions span a range from simple to complex. These include simple actions (\"running\"), human-object interactions (\"dribbling a ball\"), human-human interactions (\"shaking hands\"), and group actions (\"gathering\"). Because of the dynamic nature of actions, a large portion of work on action recognition uses video data [62, 64, 6, 82, 68]. Other approaches use other modalities such as depth or skeleton data [76, 48, 73]. Among video-based approaches, some use shallow approaches separating feature representation of action videos and classification of these features, while others use end-to-end trainable networks (see [29, 79] for detailed surveys). Works on human-object interactions (HOI) may use separate modules such as human and object detectors and relation modules [8, 20, 16], pose and gaze estimation [35, 66, 71], or graph neural networks applied to scene graphs [49, 72, 81, 36]. One line of recent work on HOI uses end-to-end models, frequently with transformer architectures [61, 83, 10, 27, 9]. In our work, we aim to predict the most salient interaction between the pictured individuals in an end-to-end manner from still image data alone.", + "bbox": [ + 496, + 371, + 890, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "HHIs are a subset of human actions which pose particular challenges to automatic recognition, due to non-locality, context dependency, and ambiguity. A number of works have explicitly tackled HHI recognition, as surveyed by Stergiou and Poppe [60]. As with general action recognition, these approaches most commonly use video data as input [43, 19, 67, 58, 34]. However, a few works have tackled the more challenging task of HHI recognition in still images. Some of these use classical computer vision methods to estimate human locations and poses in photos for predicting HHI [74, 7, 1]. Xiong et al. [70] use a CNN architecture with human, face, and object detection features for event recognition. These works all treat HHI as categorical, predicting them from a small set of predefined interaction", + "bbox": [ + 496, + 689, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2888", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "classes. In contrast, we use free text to describe HHIs allowing for more flexibility than categorical recognition.", + "bbox": [ + 76, + 90, + 468, + 122 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "HHI datasets. Most existing datasets of HHI or with subsets representing HHI classes only include a small number of interaction categories. The majority consist of video data, either curated [54, 77, 19, 22] or YouTube-based [59, 42, 80].", + "bbox": [ + 75, + 141, + 468, + 218 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "There are few image datasets dedicated to human actions, of which HHI are a subset. Ronchi and Perona [53] introduce the Visual Verbnet dataset consisting of images with dense verb annotations. Yatskar et al. [75] introduce the imSitu dataset for image situation recognition, involving recognizing the action portrayed in a still image (often with a human participant or participants) as well as predicting semantic roles for observed entities. In both cases the labels are selected from a fixed set of categories—single verbs in the case of imSitu, verbs or phrases containing verbs (e.g. \"shake hands\") for Visual Verbnet. Other image datasets such as Visual Genome [31] contain labeled entities, objects and their relationships, but focus more on general objects rather people and their interactions.", + "bbox": [ + 75, + 220, + 470, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "See Table 1 for a comparison of the most related datasets with our proposed HHI dataset. Unlike prior datasets, ours represents HHI as free text and not as fixed categories.", + "bbox": [ + 76, + 436, + 468, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In-context learning with large language models (LLMs). The recent explosive growth in size and NLP benchmark performance of LLMs has led to their use as foundation models for use on downstream tasks [3]. Models such as GPT-3 show an emergent in-context learning property, whereby they may solve new tasks when prompted with only a few examples of a new task, or even just with a task description, without any parameter updates [5, 14]. The output of such models may then be used as supervised training data for conventional model fine-tuning. The idea of training on data generated using in-context learning to create a large training data set has been successfully applied to achieve state-of-the-art results on the SuperGLUE NLP benchmark by Wang et al. [69]. In our case, we use this data to perform sequence-level knowledge distillation – transferring the knowledge exhibited by such a large model into a smaller model by training on its output sequences [28, 21].", + "bbox": [ + 75, + 503, + 468, + 761 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The use of LLM-generated synthetic data for multimodal learning has been explored by Brooks et al. [4], who use caption pairs generated by GPT-3 as auxiliary data for training a conditional diffusion model to perform image editing. Their method uses hundreds of manually labelled pairs of texts as training data; however, our pseudo-labelling method uses no explicit supervision, instead using syntactic parsing to generate automatic seeds for our synthetic data generation pipeline.", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/0bf4cccf47f7a1242816db526e5fcc409ea92938645ad7b52ca9e2b0a16855cd.jpg", + "table_caption": [], + "table_footnote": [ + "*The number of HHI classes for Visual Verbnet includes verbs in the communication, contact and social categories, which sometimes mark solo actions or human-object interactions. The imSitu dataset contains a total of 504 verbs. We estimate the number of HHI interactions using an automatic methodology detailed in Section 5. Our free text pseudo-labels are limited to the types of interactions available in Who's Waldo.", + "Table 1. Comparison of HHI datasets. Prior datasets usually capture video data and target a small number of interaction classes. Several datasets focus on human actions, some of which include HHI. We denote the number of video/image samples with #Seq, and the number of HHI classes with #HHI Classes (values are taken from Stergiou and Poppe [60] where relevant). In our work, we devise a technique for generating HHI pseudo-labels for Who's Waldo [13], a dataset containing real-world image-caption pairs, allowing for modeling the heavy tail of HHI." + ], + "table_body": "
Dataset#Seq#HHI Classes
Curated videos
UT-Interaction [54]606
TV Human Interaction [45]3004
Hollywood2 [39]36694
ShakeFive2 [19]1535
SBU Kinect [77]3008
AVA [22]~57.6k13
NTU RGB+D (120) [56, 37]~114k26
YouTube-based videos
Kinetics [26, 59]~500k11
Moments in Time [42]~800k32
HACS [80]~50k23
Still images
imSitu [75]126k50*
Visual Verbnet [53]10k52*
Who's Waldo [13] (w/ our labels)127k∞* (free text)
", + "bbox": [ + 500, + 88, + 893, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. LLM-Based HHI Inference from Captions", + "text_level": 1, + "bbox": [ + 500, + 587, + 879, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To model the heavy tail of possible HHI using free text, leverage weak supervision in the form of image captions. We turn to Who's Waldo [13], a dataset containing image-caption pairs depicting human-centric scenes scraped from Wikipedia Commons (with names masked using their suggested [NAME] token). As illustrated in Figure 2, the mentions of the depicted HHI are embedded in detailed textual captions, and do not directly correspond to syntactic structures such as verbs in the text. For instance, the first depicted caption is long and the only relevant detail is the phrase \"gets at [sic] high five\"; the last depicted caption contains no verb (while the noun phrase \"Ski Tour\" hints at the relevant interaction). These captions are thus inadequate for training an HHI understanding model directly, as a captioning model fine-tuned on them mainly learns to attend to details that are irrelevant for our task (as shown in Section 5.3). We therefore present a large language model (LLM)-based abstractive text summarization technique that produces clean interaction texts from the original Internet", + "bbox": [ + 496, + 613, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2889", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0264c0e65d32c54228af045f6c3be92d674fa855d082b6d8574fd80f0f4a6eb1.jpg", + "image_caption": [ + "Hospital Corpsman 1st Class [NAME], U.S. Fleet Forces Sea Soldier of the Year, gets at high five from Master Chief Petty Officer of the Navy (MCPON) [NAME] during a Navy Exchange meet and greet at the Navy Memorial. [NAME] will be meritoriously promoted to chief petty officer.", + "Parsing-based: $[\\star]$ getting five from $[\\star]$", + "Final: [ $\\star$ ] getting a high five from [ $\\star$ ]", + "Figure 2. HHI distilled from raw Internet captions alongside their corresponding images. On top we show several images and captions from the Who's Waldo dataset [13], with $[\\star]$ denoting masked named person entities. Our syntactic parsing approach allows for extracting an initial partial set of interactions (first row). We refine and enlarge this initial set using our abstractive summarization model which yields our final HHI pseudo-labels (second row). While the original captions possibly contain many additional details or no verb-based interaction at all (for example, see the rightmost image), our abstractive HHI pseudo-labels succeed in describing HHI visible in the associated images." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 269, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/791780bdb663735002de5f19acc5cb4fd6e6f37ffde6744f49c2db4b4fa6489e.jpg", + "image_caption": [ + "$[\\star ]$ and $[\\star ]$ playing", + "[ $\\star$ ] playing doublebass with [ $\\star$ ]", + "[NAME] and [NAME] playing as doublebass-duo in Club w71, 2018." + ], + "image_footnote": [], + "bbox": [ + 411, + 89, + 599, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/99789bbfeb267b78dc47586ab9ca7fbee0e941f1bdbc0da67c7ec586852b3910.jpg", + "image_caption": [ + "[ $\\star$ ] skiing with [ $\\star$ ]", + "[NAME], \n[NAME] and \n[NAME], 2017 \nSki Tour \nCanada, Quebec City." + ], + "image_footnote": [], + "bbox": [ + 669, + 89, + 823, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "captions, without explicit supervision.", + "bbox": [ + 76, + 329, + 328, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our unsupervised pseudo-labelling approach operates in three stages, illustrated in Figure 3: (1) We extract syntactic parsing-based interactions from captions from the Who's Waldo dataset, as well as constructing new synthetic interaction texts. (2) We prompt an LLM using the interaction-caption pairs from Who's Waldo along with the new interactions. The output synthetic captions are filtered using a pretrained natural language inference (NLI) model and various textual heuristics, to select for those that correspond to the new interactions. (3) We train an abstractive summarization model on these synthetic caption-interaction pairs; this model learns to output HHI from noisy Internet captions. As seen in Figure 2, these interaction pseudo-labels accurately describe the HHI visible in their associated images. Below, we provide more details for each stage (Sections 3.1-3.3). We then present Waldo and Wenda, our manually-curated HHI test set, in addition to statistics and an ethical discussion (Section 3.4).", + "bbox": [ + 75, + 345, + 468, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Constructing interaction texts", + "text_level": 1, + "bbox": [ + 76, + 632, + 341, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first define a rule-based approach for extracting interactions via syntactic parsing. Specifically, we extract the first verb in the caption with a [NAME] subject along with its direct objects and the heads of its prepositional arguments. This roughly corresponds to an interaction, although it may sound unnatural. This is also limited to captions containing verb phrases. We apply this procedure to captions from Who's Waldo to obtain corresponding parsing-based interactions.", + "bbox": [ + 75, + 657, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also construct new synthetic interactions by first applying this parsing procedure to scraped texts of news articles from the CC-News dataset [23] (from Commoncrawl, containing text without image data), and then using the output interaction texts to prompt the large (1.3B-parameter) language model GPT-Neo [2, 17], which produces a set of diverse and more natural-sounding interactions.", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Synthetic caption data generation", + "text_level": 1, + "bbox": [ + 500, + 328, + 792, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using the caption–interaction pairs from Who’s Waldo and the new synthetic interactions as seeds, we generate synthetic caption–interaction pairs using in-context learning with GPT-Neo. This allows us to create a larger and more diverse set of caption–interaction pairs than by using caption–interaction pairs directly from Who’s Waldo. These pairs serve as the teacher model outputs used for knowledge distillation in the following section.", + "bbox": [ + 496, + 351, + 890, + 472 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At each step, the language model is shown a prompt beginning with multiple randomly-selected examples of caption–interaction pairs from Who’s Waldo. This provides context for the model to understand the task at hand–associating interactions with captions that contain them. We use ten examples in each prompt to balance between the providing sufficient context with computational considerations. The prompt ends with a new desired interaction, and the language model proceeds to generate a caption corresponding to this interaction. We filter these results using a pretrained NLI model and various textual heuristics detailed further in the supplementary material, ensuring that the output caption logically is properly formatted and logically entails the corresponding interaction.", + "bbox": [ + 496, + 474, + 892, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Knowledge distillation for summarization", + "text_level": 1, + "bbox": [ + 500, + 695, + 854, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using the synthetic data generated in the previous stage, we fine-tune a smaller (220M-parameter) student T5 model, a sequence-to-sequence transformer network whose pretraining tasks include text summarization [52]. We use the synthetic captions (with the task prefix \"summarize:\") as input and the synthetic interactions of the target text for fine-tuning. Empirically, we find that our fine-tuned student model is able to summarize captions and output valid interactions even when the caption does not contain a verb or has a syntactic structure that the syntactic parsing-based method could not process.", + "bbox": [ + 496, + 719, + 890, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We apply this model to the captions in the Who's Waldo", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2890", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7302b9ae82a6b3c9229501a79a33518b605625b14d1727d799933d88cf145af4.jpg", + "image_caption": [ + "Synthetic caption generation with teacher LM and NLI filtering" + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 450, + 172 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4c857e58a313763fb53c5694bfc6bf76f9b7895c2c7c114f6801726083071d35.jpg", + "image_caption": [ + "Figure 3. LLM-Based HHI Extraction from Captions. We generate synthetic interaction-caption pairs via in-context learning (left), use them to fine-tune a summarization model (center), and then use this model to producing HHI pseudo-labels for captions in Who's Waldo (right), as detailed in Section 3. Captions are shown in red boxes, interaction texts in blue, and synthetic texts in italic letters. $\\mathrm{LM_T}$ and $\\mathrm{LM_S}$ indicate teacher and student language models respectively." + ], + "image_footnote": [], + "bbox": [ + 483, + 113, + 674, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c103438fadcaeacfdcabf9fc49f0ff266e1e2a0d7fea79fdba7ab85e4686e8a5.jpg", + "image_caption": [ + "Fine-tuning student LM", + "Pseudo-label inference" + ], + "image_footnote": [], + "bbox": [ + 692, + 113, + 883, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "dataset to create pseudo-labels representing interactions as free text. See Figure 2 for examples of such pseudo-labels.", + "bbox": [ + 75, + 284, + 468, + 314 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Our HHI dataset", + "text_level": 1, + "bbox": [ + 76, + 324, + 243, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Using our learned abstractive summarization model, we may generate interaction pseudo-labels from Who's Waldo captions. Out of the $\\sim 270k$ samples in Who's Waldo, we use only those $\\sim 130k$ containing at least two human face detections, using the detections provided by Cui et al. [13]. We filter out duplicate and near-duplicate images, those with high similarity to test set images, and samples with pseudo-labels that do not pass a few simple text-based filtering rules, including enforcing the format of [NAME], followed by a present continuous verb (\"-ing\"), and including another [NAME] token. We are left with $\\sim 126k$ images with pseudo-labels in total, which we hereby refer to as pHHI.", + "bbox": [ + 75, + 348, + 468, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Waldo and Wenda Benchmark. We also create Waldo and $Wenda^3$ , an HHI test set containing 1K manually curated image–interaction text pairs. In order to test generalization to HHI understanding across a wide variety of natural images, we include data from three sources: (1) 300 images from Who's Waldo, (2) 300 images from COCO Captions [11], (3) 400 images from Conceptual Captions [57]. The images are selected from the validation and test splits of the relevant datasets. As the distribution of HHI in natural photographs is highly imbalanced—for instance, images in captioning datasets often display people standing side by side and posing for photographs—we curate this test set to represent a wide variety of interactions and to reflect performance on the long tail of uncommon HHI. Examples of images from Waldo and Wenda can be seen in Figures 1, 2, and 4.", + "bbox": [ + 75, + 553, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset Statistics. Overall, our pHHI training dataset contains 126,696 pairs of images and pseudo-labels. These labels contain 1,263 unique verbs and 16,136 unique interactions. The majority of the images (59.3%) only contain two", + "bbox": [ + 75, + 804, + 468, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "detected people, with less than $5\\%$ of the images containing more than six detected people. The Waldo and Wenda test set contains 1,000 images along with their manually written ground truth HHI labels. These include 238 unique verbs and 575 unique interaction labels.", + "bbox": [ + 500, + 282, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ethical considerations. Our dataset inherits a diverse representation of people (ages, ethnicities, geographic etc.) from the Who's Waldo dataset [13]. Furthermore, we use their provided name masking to mitigate biases (e.g., gender biases). We verify that all manually-curated test samples are neutral in nature and do not contain lurid or negative material. We perform similar verification on external test data, as described in Section 5, to avoid exposure to harmful or offensive behaviors. Furthermore, our pseudo-labels and test set will only be made available for academic purposes.", + "bbox": [ + 498, + 366, + 892, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Learning HHI from Still Images", + "text_level": 1, + "bbox": [ + 500, + 532, + 794, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the previous section, we demonstrated how we can obtain free text HHI pseudo-labels from the Internet captions of the Who's Waldo dataset [13]. We proceed to show how we use these to supervise learning HHI from still images via the paradigm of image captioning.", + "bbox": [ + 498, + 556, + 890, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Models considered", + "text_level": 1, + "bbox": [ + 500, + 643, + 679, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining a set of images and pseudo-labels, we consider the task of HHI in the framework of image captioning. Given (image, pseudo-label) pair $(I,L)$ , we train an encoder-decoder network $M$ to maximize the predicted conditional likelihood of $L$ using a cross-entropy loss. During inference, we use autoregressive beam search decoding to generate text token by token, given $I$ as input.", + "bbox": [ + 496, + 666, + 890, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to evaluate the utility of transfer learning from general image captioning to our HHI understanding setting, we evaluate two choices for the model $M$ :", + "bbox": [ + 498, + 772, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(1) Vanilla encoder-decoder (EncDec). In this setting, we fine-tune a simple encoder-decoder model. We use the image encoder of pretrained CLIP-ViT [50], with its pooled embedding output followed by a single linear projection layer to match the hidden dimension of the decoder. For", + "bbox": [ + 498, + 824, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "3Wenda appears in the Where's Waldo? book series as Waldo's girlfriend.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2891", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d96ec9a4a7948b99e6c0c91b996a5d8ce789a9f94ffe2ad4da7c6dd3916b232c.jpg", + "image_caption": [ + "CLIPCap person, left, and person, (CC) right, receive a standing ovation for their service." + ], + "image_footnote": [], + "bbox": [ + 140, + 88, + 316, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1eb2564bad6011d9eb1ad35691c1f46e22fcda6d2a4ec96fbe0c6f924c355b86.jpg", + "image_caption": [ + "friday night rivals was for high school vs game!", + "EncDec $[\\star ]$ administering the oath (pHHI) to $[\\star ]$", + "$[\\star]$ coaching $[\\star]$", + "$[\\star]$ huddling with $[\\star]$" + ], + "image_footnote": [], + "bbox": [ + 321, + 88, + 501, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0e726725b148d80f78a2e66421fa63ad0dbecaf47235dbf660a47e61ace02e86.jpg", + "image_caption": [ + "wallpaper with a concert and a well dressed person entitled pop artist.", + "$[\\star]$ dancing with $[\\star]$" + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 678, + 193 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4779a3c0c4239da7b401d0fb93e225ec5190100b2672e06178c3cc2ebc45734c.jpg", + "image_caption": [ + "person, left, shakes hands with person, daughter of person, during a ribbon cutting ceremony.", + "$[\\star ]$ performing with $[\\star ]$", + "$[\\star]$ cutting the ribbon with $[\\star]$", + "$[\\star]$ cutting a ribbon with $[\\star]$", + "Figure 4. Results on the Waldo and Wenda test set. We compare results obtained by a baseline, our vanilla encoder-decoder technique (trained on our pHHI data), and the ground truth labels in Waldo and Wenda, with $[\\star]$ denoting [NAME] tokens that represent person entities. As illustrated above, our method generates text describing the HHI depicted in the image, without attending to other irrelevant details. In comparison, the SOTA captioning model CLIPCap used as-is may not output an interaction at all (middle two images). We also observe that our model predicts HHI that may require both a verb and other arguments to adequately understand (leftmost and rightmost images)." + ], + "image_footnote": [], + "bbox": [ + 681, + 88, + 887, + 195 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the decoder we use pretrained GPT-2 [51] with a causal language modelling head and cross-attention over the encoder output. Consistent with previous works on fine-tuning vision-and-language models [38, 41, 78], we freeze the weights of the image encoder as we fine-tune it on our pHHI data. By considering this model that was not previously trained on image captioning, we aim to evaluate the extent to which our pHHI aid in learning to understand the semantics of HHI in images (rather than simply cueing a captioning model to the correct surface form of HHI labels).", + "bbox": [ + 75, + 412, + 468, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(2) Fine-tuned captioner. The second approach we consider is to apply transfer learning to a SOTA captioning model by fine-tuning it on our pHHI data. Because the Conceptual Captions (CC) dataset is more people-centric than COCO and thus closer to our use case, we pick CLIPCap [41] pretrained on CC as the base model for fine-tuning. Consistent with CLIPCap's training method, we freeze its image encoder and fine-tune the model on our pHHI data.", + "bbox": [ + 75, + 570, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Training and Decoding", + "text_level": 1, + "bbox": [ + 76, + 700, + 290, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For all models, we use cross-entropy loss and consistent hyperparameter settings. For each model, we decode using beam search with 32 beams. We report metric values for the top 1, 5, and 8 beams.", + "bbox": [ + 75, + 724, + 468, + 785 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Evaluation", + "text_level": 1, + "bbox": [ + 76, + 799, + 192, + 814 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Test Datasets", + "text_level": 1, + "bbox": [ + 76, + 823, + 215, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our models on the following datasets:", + "bbox": [ + 96, + 847, + 428, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Waldo and Wenda. As detailed in Section 3.4, this consists of 1,000 images with manually-written ground truth labels.", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Examples of ground truth labels along with model predictions can be seen in Figure 4. We report metric values averaged over the three data sources (Who's Waldo, Conceptual Captions, COCO) of Waldo and Wenda in Table 2. We also show a breakdown of data source in Table 3.", + "bbox": [ + 496, + 412, + 892, + 487 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "imSitu-HHI. We use an 8,021-sample subset of the imSitu [75] situation recognition benchmark, which we refer to as imSitu-HHI, to perform a large-scale evaluation of our models. Although imSitu does not contain free text HHI labels, it does contain categorical verb labels which can be used for comparison. Additionally, as the majority of images in imSitu do not depict HHI, we first filter for relevant samples as follows: We use person detections from YoloV5 [15] to select for images containing at least two humans. We further filter to select only samples with semantic frames containing at least two human participants. Finally, due to the noisy nature of this filtering, we only use verbs supported by at least 100 images in this filtered subset, as these verbs are most likely to describe HHI. We use these verb labels as the ground truth and evaluate predictions with the verb similarity metric as described below.", + "bbox": [ + 496, + 492, + 892, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Baseline comparisons", + "text_level": 1, + "bbox": [ + 500, + 741, + 700, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our approach to two types of SOTA model of that do not use our pHHI data as baselines:", + "bbox": [ + 496, + 763, + 890, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(1) Pretrained captioner. The first baseline approach that we test is the use of a SOTA model that has already been pretrained for image captioning. We test the recent captioning models ExpansionNet v2 (ENv2) [25] and CLIP-Cap [41]. We use these captioners as-is and evaluate our metrics on their outputs with beam search decoding. CLIP-Cap is available with pretrained weights for both COCO [11]", + "bbox": [ + 496, + 795, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2892", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and Conceptual Captions (CC) [57], and thus we test both models. ENv2 only uses COCO weights.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(2) Pretrained situation recognition model. We provide a comparison to the results of the CoFormer model [12] for grounded situation recognition with pretrained weights. Unlike weakly-supervised models trained on our pseudolabels, which were generated from natural captions, CoFormer is supervised by training on the manually-labelled SWiG dataset [47], an extension of imSitu which includes grounding information for arguments that are visible in the accompanying images, and the model predicts the relevant verb, arguments, and grounding information given an image. We evaluate CoFormer by using its predicted verb, discarding semantic frame and grounding predictions since these semantic arguments do not directly map to the text of a human-human interaction string. See the supplementary material for details on how we insert its verb predictions into text prompts for metric calculations.", + "bbox": [ + 75, + 121, + 470, + 363 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablations", + "text_level": 1, + "bbox": [ + 76, + 373, + 187, + 387 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In order to ablate the effect of our pseudo-labelling, we also report results of a captioning model fine-tuned on the entire text of the captions provided in Who's Waldo (listed in 2 and 4 under training data as \"WW\"). In the supplementary material we also provide a detailed comparison with results when training directly on the syntactic parsing-based seeds described in Section 3.1.", + "bbox": [ + 75, + 397, + 468, + 502 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Metrics", + "text_level": 1, + "bbox": [ + 76, + 512, + 171, + 527 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A number of metrics have been proposed for natural language generation tasks, measuring various aspects of text quality [24, 18]. As no prior works (to the best of our knowledge) predict HHI as free text, we propose a set of metrics that evaluate various relevant aspects of generated text:", + "bbox": [ + 75, + 536, + 468, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Textual similarity. We use the BLEURT [55] metric to measure similarity to the ground truth interaction. This is a learned metric for text generation which measures similarity between the text output by a model and the reference text. Because our test set is relatively small and the reference texts are short, this better reflects textual similarity than ngram-based metrics such as BLEU [44] which have high variance and must be averaged over large datasets, as is shown in detail in the supplementary material.", + "bbox": [ + 75, + 635, + 468, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Factual groundedness. A key property of generated text is whether it is consistent or contradictory with respect to the ground truth (such as a source document in the case of summarization, or a reference caption in the case of image captioning) [32]. This may be quantified by using the scores output by a natural language inference (NLI) model, in order to measure the degree of factual groundedness or hallucination in generated text [40, 33]. For example, given", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6c359d34860ef4980534d51f905969a1f0d445e4ac209e17a1262f4806a8a386.jpg", + "table_caption": [], + "table_footnote": [ + "*Evaluated by using the best of two prompt templates for each item, as described in the supplementary material.", + "Table 2. Results on Waldo and Wenda. The listed metrics are BLEURT (BL) and NLI scores $(p_e, p_c)$ and verb embedding similarity (sim). CC+WW/pHHI indicates models that were initialized with pretrained CC weights and subsequently fine-tuned on Who's Waldo captions or on pHHI respectively. Best results are in bold, and second best are underlined. Results are aggregated across the three data sources of Waldo and Wenda. For models using beam search, we report results for top 1, 5, and 8 beams." + ], + "table_body": "
MethodTrain DataBL↑pe↑pc↓sim↑
Results@1
CoFormerSWiG0.41*0.33*0.28*0.35
ENv2COCO0.270.250.330.41
CLIPCapCOCO0.280.340.370.42
CLIPCapCC0.270.180.380.35
CLIPCapCC+WW0.260.160.400.17
EncDecpHHI0.380.300.370.41
CLIPCapCC+pHHI0.420.410.320.46
Results@5
ENv2COCO0.310.390.190.46
CLIPCapCOCO0.310.470.240.46
CLIPCapCC0.330.320.200.47
CLIPCapCC+WW0.330.290.240.27
EncDecpHHI0.510.610.090.59
CLIPCapCC+pHHI0.570.710.070.65
Results@8
ENv2COCO0.320.430.170.48
CLIPCapCOCO0.320.500.210.46
CLIPCapCC0.350.360.160.49
CLIPCapCC+WW0.350.330.210.31
EncDecpHHI0.540.650.190.65
CLIPCapCC+pHHI0.590.760.040.69
", + "bbox": [ + 501, + 88, + 888, + 448 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "an image with ground truth label [NAME] sitting next to [NAME], the prediction [NAME] standing with [NAME] logically contradicts the reference label and thus is a factual hallucination. To measure this, we use scores $(p_e, p_c)$ from a pretrained NLI model to estimate the factual groundedness of the predicted text, where $p_e$ is the probability of entailment and $p_c$ is the probability of contradiction. We treat the image caption from Waldo and Wenda as the premise and the model's prediction as the hypothesis for NLI inference. For test items sourced from COCO Captions, in which images correspond to multiple reference captions, we use the first reference as the premise for this calculation.", + "bbox": [ + 498, + 613, + 890, + 795 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Verb similarity. We calculate the average cosine similarity of the predicted and ground truth verbs in GloVe [46] embedding space. The motivation for this metric is that a prediction may be valid or nearly valid even if it is not identical to the ground truth label as long as the semantic distance between the verbs is small (e.g. \"hugging\" vs. \"embracing\").", + "bbox": [ + 496, + 809, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2893", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cb034aa140e3bf0c7593f9396a968706b4680281fb3072bf682fb0bd447baca5.jpg", + "table_caption": [], + "table_footnote": [ + "*Evaluated by using the best of two prompt templates for each item, as described in the supplementary material.", + "Table 3. Results on Waldo and Wenda split by data source - Who's Waldo (WW), Conceptual Captions (CC), and COCO Captions. For models using beam search, we report results for top 1, 5, and 8 beams." + ], + "table_body": "
MethodTrain DataWWCCCOCO
BL↑pe↑pc↓sim↑BL↑pe↑pc↓sim↑BL↑pe↑pc↓sim↑
Results@1
CoFormerSWiG0.40*0.29*0.35*0.340.45*0.40*0.43*0.380.37*0.30*0.33*0.33
Env2COCO0.240.200.280.380.260.200.450.410.310.360.260.45
CLIPCapCOCO0.270.370.350.390.260.260.430.430.310.380.330.44
CLIPCapCC0.300.240.420.360.250.180.380.400.260.110.340.30
CLIPCapCC+WW0.280.120.590.270.260.210.340.150.230.150.280.10
EncDecpHHI0.410.380.300.420.380.300.440.420.340.220.360.38
CLIPCapCC+pHHI0.420.380.330.450.440.440.330.470.400.400.300.47
Results@5
Env2COCO0.280.300.170.420.300.320.280.460.350.550.120.51
CLIPCapCOCO0.310.500.210.420.290.380.280.460.340.520.230.49
CLIPCapCC0.360.410.230.460.300.310.230.500.320.230.140.43
CLIPCapCC+WW0.330.200.500.330.340.370.130.280.330.310.090.20
EncDecpHHI0.550.610.110.630.510.650.100.590.460.560.070.56
CLIPCapCC+pHHI0.570.640.100.640.600.750.060.680.530.740.050.63
Results@8
Env2COCO0.290.340.150.420.310.350.250.480.360.590.100.53
Env2COCO0.320.530.180.430.300.410.250.470.350.550.210.50
CLIPCapCC0.380.470.170.480.320.350.190.530.340.260.110.45
CLIPCapCC+WW0.340.220.480.350.360.420.100.330.350.340.060.25
EncDecpHHI0.600.690.060.690.550.720.050.640.500.660.040.61
CLIPCapCC+pHHI0.600.700.070.680.630.810.030.720.550.780.030.67
", + "bbox": [ + 89, + 88, + 877, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate this on free text predictions, we either select the first non-[NAME] word in the output (for models trained on pHHI) or extract its first verb using a syntactic parsing model. If syntactic parsing does not yield a verb, the zero vector is used as the given embedding.", + "bbox": [ + 78, + 534, + 468, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Results and Discussion", + "text_level": 1, + "bbox": [ + 78, + 619, + 285, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For Waldo and Wenda, we report all of the metrics described above. For imSitu-HHI, we only use the verb similarity metric since the ground truth label is a single verb. We report average similarity over all samples in imSitu-HHI as well as displaying averages for the most-supported verbs. See Tables 2-4 for quantitative results, and see Figure 4 for a visual comparison on Waldo and Wenda. Note that we do not include CoFormer in the table of imSitu-HHI results since it was trained directly on some of these items; see the supplementary material for analysis of CoFormer on indistribution and out-of-distribution images in imSitu-HHI.", + "bbox": [ + 78, + 643, + 468, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Overall we see that training on our pseudo-labels improves performance on our benchmarks. In Tables 2 and 3, showing results on Waldo and Wenda, the best-performing model by all metrics is CLIPCap fine-tuned with our pseudo-labels. This holds across data sources, as seen in Table 3, showing that this improvement general-", + "bbox": [ + 78, + 810, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "izes to images beyond those originating in the Who's Waldo dataset. This model is also the best-performing on average and across a majority of verb categories on imSitu-HHI as seen in Table 4. Qualitative comparison shows that the captioning models used as-is output text that is far from the ground truth HHI labels, containing many irrelevant details and not necessarily describing an interaction. This can be seen in Figure 4, where the CLIPCap (CC) captions contain many hallucinated, non-factual details.", + "bbox": [ + 501, + 534, + 890, + 669 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While transfer learning with pretrained CLIPCap yields the best results, we also observe that the vanilla Encoder-Decoder fine-tuned on our pseudo-labels also performs well, achieving the second-best BLEURT score on Waldo and Wenda and second-best verbal similarity metrics overall and across many verb categories on imSitu-HHI. We infer that our pseudo-labels do impart semantic knowledge of HHI beyond simply cueing existing captioning models to the surface form of HHI labels. Nevertheless, CLIPCap fine-tuned on pHHI does generalize better across the data from all sources in Waldo and Wenda and to imSitu-HHI which is entirely out-of-distribution for this model.", + "bbox": [ + 501, + 672, + 890, + 852 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also note that the metrics improve dramatically for both datasets when considering 5 or 8 beams. This is consistent with the fact that beam search using models fine-tuned", + "bbox": [ + 503, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2894", + "bbox": [ + 483, + 946, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/22cbd1c7521062af0b282104a46f6c757c35378a9d23d85f3e3c1421c4a6c1a8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Average sim.socializingdistributingteachingcommunicatinginterviewinglecturingtrainingprovidinginstructinggivingpushinghelpingaskingcoachingtalking
Results@1
ENv2COCO0.220.190.070.220.210.280.190.250.260.110.450.380.290.440.280.28
CLIPCapCOCO0.230.180.070.260.240.290.170.260.240.100.440.360.250.460.300.63
CLIPCapCC0.270.160.250.370.260.210.230.280.350.160.460.310.370.380.260.53
CLIPCapCC+WW0.090.020.080.120.050.300.080.100.090.060.250.070.090.110.050.08
EncDecpHHI0.280.190.210.340.270.230.240.350.380.170.600.360.340.460.760.64
CLIPCapCC+pHHI0.320.210.250.560.330.270.300.430.440.190.660.380.440.460.650.70
Results@5
ENv2COCO0.260.210.100.260.230.300.210.270.310.130.490.450.350.490.330.31
CLIPCapCOCO0.250.190.090.290.260.310.200.270.260.120.470.410.290.480.320.66
CLIPCapCC0.350.210.300.480.330.280.310.370.430.210.560.420.480.470.310.64
CLIPCapCC+WW0.180.050.150.220.140.600.160.170.220.110.460.150.210.220.150.24
EncDecpHHI0.400.300.350.490.410.390.330.510.510.230.790.470.490.570.920.86
CLIPCapCC+pHHI0.440.290.350.850.440.410.400.560.560.270.880.480.560.580.860.92
Results@8
ENv2COCO0.280.220.120.270.240.300.210.280.320.130.510.470.370.500.350.34
CLIPCapCOCO0.260.200.100.310.270.310.210.280.260.120.480.430.310.490.320.67
CLIPCapCC0.370.230.310.510.340.310.320.400.450.220.590.450.510.490.320.70
CLIPCapCC+WW0.210.060.160.250.160.620.160.200.240.120.510.200.230.260.180.32
EncDecpHHI0.440.330.380.550.440.420.340.540.560.250.850.490.560.590.940.91
CLIPCapCC+pHHI0.470.330.370.900.460.410.430.600.590.290.920.500.590.610.910.96
", + "bbox": [ + 76, + 87, + 893, + 489 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 4. Results on imSitu-HHI. In addition to the average verb embedding similarity between predicted verbs and the ground truth verb, we also present mean similarities for the most common 15 verbs in imSitu-HHI. Best results are in bold, and second best are underlined. For models using beam search, we report results for top 1, 5, and 8 beams.", + "bbox": [ + 76, + 494, + 890, + 537 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "on pHHI outputs a list of diverse candidate interactions, allowing a more directed search in the space of HHI descriptors, while beam search applied to captioning models as-is tends to produce many slight variations of the same long caption.", + "bbox": [ + 75, + 561, + 470, + 638 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 659, + 194, + 674 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We present a new framework for learning to understand human-human interactions in still images using weak supervision from textual captions. We demonstrate the use of knowledge distillation applied to a large language model without explicit supervision to produce pseudo-labels that can serve as targets for predicting interactions as free text. We show that training on these pseudo-labels enables HHI understanding beyond that of SOTA captioning and situation recognition models, and we provide the Waldo and Wenda as a new benchmark for this task.", + "bbox": [ + 75, + 686, + 468, + 837 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "There are various avenues for future research to extend our work. One possible direction is the incorporation of visual grounding into HHI understanding. We predict the most salient interaction in an image, which we assume to", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "be the interaction the one that is described or suggested in its accompanying caption. It remains to localize the participants, including generalizing to group interactions where more than two participants are visible. Another important aspect that remains to be explored is the hierarchical nature of interactions. For example, the generic HHI label \"meeting\" is valid for almost every image, while \"shaking hands\" is more specific and valid for a subset of those images. Further research could extend our results to hierarchical prediction of multiple HHI labels for a single image.", + "bbox": [ + 496, + 561, + 890, + 712 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Finally, we note the importance of style-content disentanglement in HHI prediction, which our work does not explicitly consider. Scene cues in images can be important for correctly identifying HHI, as illustrated in Figure 1, but also may be misleading. For instance, an image of soldiers in uniform is more likely to depict \"saluting\", but HHI is only valid if the image actually contains a salute. Future work on disentangling style and content shows promise for improving the robustness of HHI understanding models.", + "bbox": [ + 496, + 713, + 890, + 849 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. We thank Ron Mokady for providing helpful feedback. This work was supported by a research gift from Meta and the Alon fellowship.", + "bbox": [ + 496, + 854, + 890, + 902 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "2895", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Stanislaw Antol, C Lawrence Zitnick, and Devi Parikh. Zero-shot learning via visual abstraction. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part IV 13, pages 401-416. Springer, 2014.", + "[2] Sid Black, Gao Leo, Phil Wang, Connor Leahy, and Stella Biderman. GPT-Neo: Large Scale Autoregressive Language Modeling with Mesh-Tensorflow, Mar. 2021. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18123-18133, 2022.", + "[79] Hong-Bo Zhang, Yi-Xiang Zhang, Bineng Zhong, Qing Lei, Lijie Yang, Ji-Xiang Du, and Duan-Sheng Chen. A comprehensive survey of vision-based human action recognition methods. Sensors, 19(5):1005, 2019.", + "[80] Hang Zhao, Antonio Torralba, Lorenzo Torresani, and Zhicheng Yan. Hacs: Human action clips and segments dataset for recognition and temporal localization. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 8668-8678, 2019." + ], + "bbox": [ + 501, + 92, + 890, + 900 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "2898", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 11 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[81] Penghao Zhou and Mingmin Chi. Relation parsing neural network for human-object interaction detection. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 843-851, 2019.", + "[82] Yi Zhu, Xinyu Li, Chunhui Liu, Mohammadreza Zolfaghari, Yuanjun Xiong, Chongruo Wu, Zhi Zhang, Joseph Tighe, R Manmatha, and Mu Li. A comprehensive study of deep video action recognition. arXiv preprint arXiv:2012.06567, 2020.", + "[83] Cheng Zou, Bohan Wang, Yue Hu, Junqi Liu, Qian Wu, Yu Zhao, Boxun Li, Chenguang Zhang, Chi Zhang, Yichen Wei, et al. End-to-end human object interaction detection with hoi transformer. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11825-11834, 2021." + ], + "bbox": [ + 78, + 90, + 468, + 287 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "2899", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/6803bdfe-c2d2-4fd6-a5a5-6f813d705eb4_model.json b/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/6803bdfe-c2d2-4fd6-a5a5-6f813d705eb4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bba3d8d30d30fc497c1780a2ec5d59ce2db49e4b --- /dev/null +++ b/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/6803bdfe-c2d2-4fd6-a5a5-6f813d705eb4_model.json @@ -0,0 +1,2811 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.131, + 0.895, + 0.155 + ], + "angle": 0, + "content": "Learning Human-Human Interactions in Images from Weak Textual Supervision" + }, + { + "type": "text", + "bbox": [ + 0.328, + 0.182, + 0.644, + 0.218 + ], + "angle": 0, + "content": "Morris Alper and Hadar Averbuch-Elor \nTel Aviv University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.269 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.283, + 0.474, + 0.587 + ], + "angle": 0, + "content": "Interactions between humans are diverse and context-dependent, but previous works have treated them as categorical, disregarding the heavy tail of possible interactions. We propose a new paradigm of learning human-human interactions as free text from a single still image, allowing for flexibility in modeling the unlimited space of situations and relationships between people. To overcome the absence of data labelled specifically for this task, we use knowledge distillation applied to synthetic caption data produced by a large language model without explicit supervision. We show that the pseudo-labels produced by this procedure can be used to train a captioning model to effectively understand human-human interactions in images, as measured by a variety of metrics that measure textual and semantic faithfulness and factual groundedness of our predictions. We further show that our approach outperforms SOTA image captioning and situation recognition models on this task. We will release1 our code and pseudo-labels along with Waldo and Wenda, a manually-curated test set for still image human-human interaction understanding." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.614, + 0.21, + 0.63 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.639, + 0.468, + 0.656 + ], + "angle": 0, + "content": "\"No man is an island entire of itself.\" -John Donne" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.47, + 0.851 + ], + "angle": 0, + "content": "Humans are social beings. As such, interactions among people are ubiquitous and diverse, affected by various factors including social context and cultural norms. Reasoning about these interactions is crucial for gaining a holistic understanding of visual scenes depicting people. However, in spite of significant progress in analyzing isolated human actions [29, 73, 79] and relationships between entities and objects [27, 83], far less attention has been devoted towards an automatic understanding of human-human interactions (HHI). This is despite the importance of this task for applications such as interactive robotics, social behaviour understanding, and captioning systems for the visually impaired." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.851, + 0.47, + 0.867 + ], + "angle": 0, + "content": "There are a number of factors that make the analysis of" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.25, + 0.698, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.25, + 0.892, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.354, + 0.895, + 0.48 + ], + "angle": 0, + "content": "Figure 1. How would you describe the interactions depicted in these images? There are unlimited possible interactions between people which cannot be easily described by a fixed set of categories or actions. Context plays a crucial role, as in the left image where the clothing and cake in the background help to interpret the depicted interaction. Moreover, interactions may be involve participants at a physical distance as in the image on the right. To model the heavy tail of possible interactions, we propose to learn HHI as free text (see below2 for predictions using our method)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.639 + ], + "angle": 0, + "content": "HHI difficult. The space of possible interactions between people is vast and requires understanding social context and physically non-local relationships, as illustrated in Figure 1. In addition, images depicting HHI may have multiple interpretations, some of which may be simultaneously correct. For example, the image on the left might depict \"celebrating a wedding\" as well as \"dancing\". Contextual cues such as the cake in the background of the image provide additional information that hints at the depicted HHI." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.893, + 0.867 + ], + "angle": 0, + "content": "Prior works targeting HHI understanding focus on a small fixed number of interactions; representative works include [63, 65, 43, 30], all of whose models are trained to recognize no more than ten interaction classes. In this work, we are interested in modeling the heavy tail of possible HHI to better understand the rich variety of ways in which people interact. To this aim, we propose to model HHI understanding as free text generation; since HHI are not confined to a fixed set of categories or even to a syntactic class such as verbs, HHI as free text enables the expression of an infinite variety of possible interactions. Furthermore, in contrast to previous works that frequently rely on extra context such as video data [60], we use a single image with no additional information (during inference), making our method more widely applicable. We focus on what Stergiou and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2A model fine-tuned on our pseudo-labels yields \"dancing\" and \"having a picnic\"." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "1via our project page https://learning-interactions. github.io" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2887" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "Poppe [60] term dyadic interactions—pairwise interactions between two people. Our goal is to identify the most salient dyadic interaction given an image of two or more people interacting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.473, + 0.573 + ], + "angle": 0, + "content": "One of the primary challenges to modeling HHI is a scarcity of labelled data for this particular task. There are only a handful of relatively small datasets specific to HHI, and larger video datasets for action recognition are lacking in coverage of interactions (see Table 1). To better model the heavy tail of possible HHI, we leverage the abundance of high-quality images of people and associated textual captions available on the Internet. In particular, we use the Who's Waldo dataset [13] that contains 270K image_caption pairs from Wikimedia Commons depicting people captured in a broad range of situations. Unlike many other image captioning datasets, Who's Waldo focuses on human-centric situations which are described using real-world captioned Internet data, and thus is more relevant to HHI understanding. However, it is extremely challenging to learn HHI from raw Internet captions directly, due to significant noise introduced by clutter and irrelevant details. To overcome this, we infer interactions from the original captions by applying knowledge distillation to synthetic data generated by a large language model, without explicit supervision. This approach allows for creating accurate pseudolabels that provide textual descriptions of the HHI depicted in the images. We will release these pseudo-labels along with a manually annotated test set containing 1K image-interaction pairs from diverse Internet images which we name Waldo and Wenda, a new benchmark for our paradigm of HHI understanding as free text on still images, capturing the heavy tail of human-human interactions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.47, + 0.695 + ], + "angle": 0, + "content": "We demonstrate the utility of these pseudo-labels for learning HHI from images by training captioning models and using them as targets for a language modelling objective. We provide qualitative and quantitative analysis on the Waldo and Wenda test set; in addition, we evaluate this method on a larger scale by applying it to verb prediction on the imSitu situation recognition dataset [75], which we filter to select for images relevant to HHI." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.471, + 0.877 + ], + "angle": 0, + "content": "Because we predict HHI as free text rather than categorically as in previous works, we propose a set of evaluation metrics chosen to measure important aspects of predicted HHI quality, namely textual similarity, factual groundedness, and verb similarity. Our evaluation shows that our HHI pseudo-labels allow for generating meaningful HHI free text descriptions from images, as measured by these metrics. We also show that learning on these pseudo-labels captures HHI substantially more effectively than either using existing SOTA image captioning models as-is or than training on interactions extracted with naive syntactic parsing. Explicitly stated, our key contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "- A new paradigm and benchmark for HHI understand" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "ing from images—i.e., predicting interactions as free text—allowing to better understand the vast variety of ways in which people interact." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.15, + 0.892, + 0.21 + ], + "angle": 0, + "content": "- A method for isolating HHI from noisy Internet captions using knowledge distillation applied to a large language model, and a set of pseudo-labels generated by this method." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.224, + 0.892, + 0.329 + ], + "angle": 0, + "content": "- An evaluation framework with metrics that capture HHI understanding, and results demonstrating that training image captioning models on these pseudolabels can allow for modeling the heavy tail of possible HHI across various situations and configurations more effectively than SOTA image captioning and situation recognition models." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.15, + 0.892, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.346, + 0.642, + 0.362 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.688 + ], + "angle": 0, + "content": "Human action recognition. Human actions span a range from simple to complex. These include simple actions (\"running\"), human-object interactions (\"dribbling a ball\"), human-human interactions (\"shaking hands\"), and group actions (\"gathering\"). Because of the dynamic nature of actions, a large portion of work on action recognition uses video data [62, 64, 6, 82, 68]. Other approaches use other modalities such as depth or skeleton data [76, 48, 73]. Among video-based approaches, some use shallow approaches separating feature representation of action videos and classification of these features, while others use end-to-end trainable networks (see [29, 79] for detailed surveys). Works on human-object interactions (HOI) may use separate modules such as human and object detectors and relation modules [8, 20, 16], pose and gaze estimation [35, 66, 71], or graph neural networks applied to scene graphs [49, 72, 81, 36]. One line of recent work on HOI uses end-to-end models, frequently with transformer architectures [61, 83, 10, 27, 9]. In our work, we aim to predict the most salient interaction between the pictured individuals in an end-to-end manner from still image data alone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.901 + ], + "angle": 0, + "content": "HHIs are a subset of human actions which pose particular challenges to automatic recognition, due to non-locality, context dependency, and ambiguity. A number of works have explicitly tackled HHI recognition, as surveyed by Stergiou and Poppe [60]. As with general action recognition, these approaches most commonly use video data as input [43, 19, 67, 58, 34]. However, a few works have tackled the more challenging task of HHI recognition in still images. Some of these use classical computer vision methods to estimate human locations and poses in photos for predicting HHI [74, 7, 1]. Xiong et al. [70] use a CNN architecture with human, face, and object detection features for event recognition. These works all treat HHI as categorical, predicting them from a small set of predefined interaction" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2888" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "classes. In contrast, we use free text to describe HHIs allowing for more flexibility than categorical recognition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.142, + 0.47, + 0.219 + ], + "angle": 0, + "content": "HHI datasets. Most existing datasets of HHI or with subsets representing HHI classes only include a small number of interaction categories. The majority consist of video data, either curated [54, 77, 19, 22] or YouTube-based [59, 42, 80]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.222, + 0.471, + 0.435 + ], + "angle": 0, + "content": "There are few image datasets dedicated to human actions, of which HHI are a subset. Ronchi and Perona [53] introduce the Visual Verbnet dataset consisting of images with dense verb annotations. Yatskar et al. [75] introduce the imSitu dataset for image situation recognition, involving recognizing the action portrayed in a still image (often with a human participant or participants) as well as predicting semantic roles for observed entities. In both cases the labels are selected from a fixed set of categories—single verbs in the case of imSitu, verbs or phrases containing verbs (e.g. \"shake hands\") for Visual Verbnet. Other image datasets such as Visual Genome [31] contain labeled entities, objects and their relationships, but focus more on general objects rather people and their interactions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.438, + 0.47, + 0.485 + ], + "angle": 0, + "content": "See Table 1 for a comparison of the most related datasets with our proposed HHI dataset. Unlike prior datasets, ours represents HHI as free text and not as fixed categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.762 + ], + "angle": 0, + "content": "In-context learning with large language models (LLMs). The recent explosive growth in size and NLP benchmark performance of LLMs has led to their use as foundation models for use on downstream tasks [3]. Models such as GPT-3 show an emergent in-context learning property, whereby they may solve new tasks when prompted with only a few examples of a new task, or even just with a task description, without any parameter updates [5, 14]. The output of such models may then be used as supervised training data for conventional model fine-tuning. The idea of training on data generated using in-context learning to create a large training data set has been successfully applied to achieve state-of-the-art results on the SuperGLUE NLP benchmark by Wang et al. [69]. In our case, we use this data to perform sequence-level knowledge distillation – transferring the knowledge exhibited by such a large model into a smaller model by training on its output sequences [28, 21]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The use of LLM-generated synthetic data for multimodal learning has been explored by Brooks et al. [4], who use caption pairs generated by GPT-3 as auxiliary data for training a conditional diffusion model to perform image editing. Their method uses hundreds of manually labelled pairs of texts as training data; however, our pseudo-labelling method uses no explicit supervision, instead using syntactic parsing to generate automatic seeds for our synthetic data generation pipeline." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.895, + 0.361 + ], + "angle": 0, + "content": "
Dataset#Seq#HHI Classes
Curated videos
UT-Interaction [54]606
TV Human Interaction [45]3004
Hollywood2 [39]36694
ShakeFive2 [19]1535
SBU Kinect [77]3008
AVA [22]~57.6k13
NTU RGB+D (120) [56, 37]~114k26
YouTube-based videos
Kinetics [26, 59]~500k11
Moments in Time [42]~800k32
HACS [80]~50k23
Still images
imSitu [75]126k50*
Visual Verbnet [53]10k52*
Who's Waldo [13] (w/ our labels)127k∞* (free text)
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.362, + 0.89, + 0.435 + ], + "angle": 0, + "content": "*The number of HHI classes for Visual Verbnet includes verbs in the communication, contact and social categories, which sometimes mark solo actions or human-object interactions. The imSitu dataset contains a total of 504 verbs. We estimate the number of HHI interactions using an automatic methodology detailed in Section 5. Our free text pseudo-labels are limited to the types of interactions available in Who's Waldo." + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.438, + 0.893, + 0.565 + ], + "angle": 0, + "content": "Table 1. Comparison of HHI datasets. Prior datasets usually capture video data and target a small number of interaction classes. Several datasets focus on human actions, some of which include HHI. We denote the number of video/image samples with #Seq, and the number of HHI classes with #HHI Classes (values are taken from Stergiou and Poppe [60] where relevant). In our work, we devise a technique for generating HHI pseudo-labels for Who's Waldo [13], a dataset containing real-world image-caption pairs, allowing for modeling the heavy tail of HHI." + }, + { + "type": "list", + "bbox": [ + 0.499, + 0.362, + 0.893, + 0.565 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.588, + 0.88, + 0.607 + ], + "angle": 0, + "content": "3. LLM-Based HHI Inference from Captions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To model the heavy tail of possible HHI using free text, leverage weak supervision in the form of image captions. We turn to Who's Waldo [13], a dataset containing image-caption pairs depicting human-centric scenes scraped from Wikipedia Commons (with names masked using their suggested [NAME] token). As illustrated in Figure 2, the mentions of the depicted HHI are embedded in detailed textual captions, and do not directly correspond to syntactic structures such as verbs in the text. For instance, the first depicted caption is long and the only relevant detail is the phrase \"gets at [sic] high five\"; the last depicted caption contains no verb (while the noun phrase \"Ski Tour\" hints at the relevant interaction). These captions are thus inadequate for training an HHI understanding model directly, as a captioning model fine-tuned on them mainly learns to attend to details that are irrelevant for our task (as shown in Section 5.3). We therefore present a large language model (LLM)-based abstractive text summarization technique that produces clean interaction texts from the original Internet" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2889" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.27, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.27, + 0.09, + 0.401, + 0.187 + ], + "angle": 0, + "content": "Hospital Corpsman 1st Class [NAME], U.S. Fleet Forces Sea Soldier of the Year, gets at high five from Master Chief Petty Officer of the Navy (MCPON) [NAME] during a Navy Exchange meet and greet at the Navy Memorial. [NAME] will be meritoriously promoted to chief petty officer." + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.192, + 0.327, + 0.204 + ], + "angle": 0, + "content": "Parsing-based: \\([\\star]\\) getting five from \\([\\star]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.206, + 0.367, + 0.218 + ], + "angle": 0, + "content": "Final: [ \\(\\star\\) ] getting a high five from [ \\(\\star\\) ]" + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.09, + 0.601, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.415, + 0.192, + 0.543, + 0.205 + ], + "angle": 0, + "content": "\\([\\star ]\\) and \\([\\star ]\\) playing" + }, + { + "type": "image_caption", + "bbox": [ + 0.415, + 0.206, + 0.613, + 0.218 + ], + "angle": 0, + "content": "[ \\(\\star\\) ] playing doublebass with [ \\(\\star\\) ]" + }, + { + "type": "image_caption", + "bbox": [ + 0.603, + 0.091, + 0.661, + 0.138 + ], + "angle": 0, + "content": "[NAME] and [NAME] playing as doublebass-duo in Club w71, 2018." + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.09, + 0.824, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.192, + 0.797, + 0.218 + ], + "angle": 0, + "content": "[ \\(\\star\\) ] skiing with [ \\(\\star\\) ]" + }, + { + "type": "image_caption", + "bbox": [ + 0.822, + 0.091, + 0.886, + 0.138 + ], + "angle": 0, + "content": "[NAME], \n[NAME] and \n[NAME], 2017 \nSki Tour \nCanada, Quebec City." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.221, + 0.894, + 0.304 + ], + "angle": 0, + "content": "Figure 2. HHI distilled from raw Internet captions alongside their corresponding images. On top we show several images and captions from the Who's Waldo dataset [13], with \\([\\star]\\) denoting masked named person entities. Our syntactic parsing approach allows for extracting an initial partial set of interactions (first row). We refine and enlarge this initial set using our abstractive summarization model which yields our final HHI pseudo-labels (second row). While the original captions possibly contain many additional details or no verb-based interaction at all (for example, see the rightmost image), our abstractive HHI pseudo-labels succeed in describing HHI visible in the associated images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.33, + 0.33, + 0.344 + ], + "angle": 0, + "content": "captions, without explicit supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.47, + 0.618 + ], + "angle": 0, + "content": "Our unsupervised pseudo-labelling approach operates in three stages, illustrated in Figure 3: (1) We extract syntactic parsing-based interactions from captions from the Who's Waldo dataset, as well as constructing new synthetic interaction texts. (2) We prompt an LLM using the interaction-caption pairs from Who's Waldo along with the new interactions. The output synthetic captions are filtered using a pretrained natural language inference (NLI) model and various textual heuristics, to select for those that correspond to the new interactions. (3) We train an abstractive summarization model on these synthetic caption-interaction pairs; this model learns to output HHI from noisy Internet captions. As seen in Figure 2, these interaction pseudo-labels accurately describe the HHI visible in their associated images. Below, we provide more details for each stage (Sections 3.1-3.3). We then present Waldo and Wenda, our manually-curated HHI test set, in addition to statistics and an ethical discussion (Section 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.633, + 0.343, + 0.648 + ], + "angle": 0, + "content": "3.1. Constructing interaction texts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.793 + ], + "angle": 0, + "content": "We first define a rule-based approach for extracting interactions via syntactic parsing. Specifically, we extract the first verb in the caption with a [NAME] subject along with its direct objects and the heads of its prepositional arguments. This roughly corresponds to an interaction, although it may sound unnatural. This is also limited to captions containing verb phrases. We apply this procedure to captions from Who's Waldo to obtain corresponding parsing-based interactions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We also construct new synthetic interactions by first applying this parsing procedure to scraped texts of news articles from the CC-News dataset [23] (from Commoncrawl, containing text without image data), and then using the output interaction texts to prompt the large (1.3B-parameter) language model GPT-Neo [2, 17], which produces a set of diverse and more natural-sounding interactions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.329, + 0.794, + 0.345 + ], + "angle": 0, + "content": "3.2. Synthetic caption data generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.473 + ], + "angle": 0, + "content": "Using the caption–interaction pairs from Who’s Waldo and the new synthetic interactions as seeds, we generate synthetic caption–interaction pairs using in-context learning with GPT-Neo. This allows us to create a larger and more diverse set of caption–interaction pairs than by using caption–interaction pairs directly from Who’s Waldo. These pairs serve as the teacher model outputs used for knowledge distillation in the following section." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.893, + 0.685 + ], + "angle": 0, + "content": "At each step, the language model is shown a prompt beginning with multiple randomly-selected examples of caption–interaction pairs from Who’s Waldo. This provides context for the model to understand the task at hand–associating interactions with captions that contain them. We use ten examples in each prompt to balance between the providing sufficient context with computational considerations. The prompt ends with a new desired interaction, and the language model proceeds to generate a caption corresponding to this interaction. We filter these results using a pretrained NLI model and various textual heuristics detailed further in the supplementary material, ensuring that the output caption logically is properly formatted and logically entails the corresponding interaction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.855, + 0.712 + ], + "angle": 0, + "content": "3.3. Knowledge distillation for summarization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.885 + ], + "angle": 0, + "content": "Using the synthetic data generated in the previous stage, we fine-tune a smaller (220M-parameter) student T5 model, a sequence-to-sequence transformer network whose pretraining tasks include text summarization [52]. We use the synthetic captions (with the task prefix \"summarize:\") as input and the synthetic interactions of the target text for fine-tuning. Empirically, we find that our fine-tuned student model is able to summarize captions and output valid interactions even when the caption does not contain a verb or has a syntactic structure that the syntactic parsing-based method could not process." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We apply this model to the captions in the Who's Waldo" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2890" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.452, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.18, + 0.466, + 0.194 + ], + "angle": 0, + "content": "Synthetic caption generation with teacher LM and NLI filtering" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.114, + 0.675, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.509, + 0.18, + 0.653, + 0.194 + ], + "angle": 0, + "content": "Fine-tuning student LM" + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.114, + 0.885, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.18, + 0.854, + 0.193 + ], + "angle": 0, + "content": "Pseudo-label inference" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.203, + 0.894, + 0.26 + ], + "angle": 0, + "content": "Figure 3. LLM-Based HHI Extraction from Captions. We generate synthetic interaction-caption pairs via in-context learning (left), use them to fine-tune a summarization model (center), and then use this model to producing HHI pseudo-labels for captions in Who's Waldo (right), as detailed in Section 3. Captions are shown in red boxes, interaction texts in blue, and synthetic texts in italic letters. \\(\\mathrm{LM_T}\\) and \\(\\mathrm{LM_S}\\) indicate teacher and student language models respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.469, + 0.315 + ], + "angle": 0, + "content": "dataset to create pseudo-labels representing interactions as free text. See Figure 2 for examples of such pseudo-labels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.325, + 0.245, + 0.34 + ], + "angle": 0, + "content": "3.4. Our HHI dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.546 + ], + "angle": 0, + "content": "Using our learned abstractive summarization model, we may generate interaction pseudo-labels from Who's Waldo captions. Out of the \\(\\sim 270k\\) samples in Who's Waldo, we use only those \\(\\sim 130k\\) containing at least two human face detections, using the detections provided by Cui et al. [13]. We filter out duplicate and near-duplicate images, those with high similarity to test set images, and samples with pseudo-labels that do not pass a few simple text-based filtering rules, including enforcing the format of [NAME], followed by a present continuous verb (\"-ing\"), and including another [NAME] token. We are left with \\(\\sim 126k\\) images with pseudo-labels in total, which we hereby refer to as pHHI." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.794 + ], + "angle": 0, + "content": "The Waldo and Wenda Benchmark. We also create Waldo and \\(Wenda^3\\), an HHI test set containing 1K manually curated image–interaction text pairs. In order to test generalization to HHI understanding across a wide variety of natural images, we include data from three sources: (1) 300 images from Who's Waldo, (2) 300 images from COCO Captions [11], (3) 400 images from Conceptual Captions [57]. The images are selected from the validation and test splits of the relevant datasets. As the distribution of HHI in natural photographs is highly imbalanced—for instance, images in captioning datasets often display people standing side by side and posing for photographs—we curate this test set to represent a wide variety of interactions and to reflect performance on the long tail of uncommon HHI. Examples of images from Waldo and Wenda can be seen in Figures 1, 2, and 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.805, + 0.469, + 0.866 + ], + "angle": 0, + "content": "Dataset Statistics. Overall, our pHHI training dataset contains 126,696 pairs of images and pseudo-labels. These labels contain 1,263 unique verbs and 16,136 unique interactions. The majority of the images (59.3%) only contain two" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.284, + 0.892, + 0.36 + ], + "angle": 0, + "content": "detected people, with less than \\(5\\%\\) of the images containing more than six detected people. The Waldo and Wenda test set contains 1,000 images along with their manually written ground truth HHI labels. These include 238 unique verbs and 575 unique interaction labels." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.367, + 0.893, + 0.519 + ], + "angle": 0, + "content": "Ethical considerations. Our dataset inherits a diverse representation of people (ages, ethnicities, geographic etc.) from the Who's Waldo dataset [13]. Furthermore, we use their provided name masking to mitigate biases (e.g., gender biases). We verify that all manually-curated test samples are neutral in nature and do not contain lurid or negative material. We perform similar verification on external test data, as described in Section 5, to avoid exposure to harmful or offensive behaviors. Furthermore, our pseudo-labels and test set will only be made available for academic purposes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.533, + 0.795, + 0.55 + ], + "angle": 0, + "content": "4. Learning HHI from Still Images" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.558, + 0.892, + 0.635 + ], + "angle": 0, + "content": "In the previous section, we demonstrated how we can obtain free text HHI pseudo-labels from the Internet captions of the Who's Waldo dataset [13]. We proceed to show how we use these to supervise learning HHI from still images via the paradigm of image captioning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.644, + 0.681, + 0.658 + ], + "angle": 0, + "content": "4.1. Models considered" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.892, + 0.772 + ], + "angle": 0, + "content": "After obtaining a set of images and pseudo-labels, we consider the task of HHI in the framework of image captioning. Given (image, pseudo-label) pair \\((I,L)\\), we train an encoder-decoder network \\(M\\) to maximize the predicted conditional likelihood of \\(L\\) using a cross-entropy loss. During inference, we use autoregressive beam search decoding to generate text token by token, given \\(I\\) as input." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.773, + 0.892, + 0.817 + ], + "angle": 0, + "content": "In order to evaluate the utility of transfer learning from general image captioning to our HHI understanding setting, we evaluate two choices for the model \\(M\\):" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.893, + 0.901 + ], + "angle": 0, + "content": "(1) Vanilla encoder-decoder (EncDec). In this setting, we fine-tune a simple encoder-decoder model. We use the image encoder of pretrained CLIP-ViT [50], with its pooled embedding output followed by a single linear projection layer to match the hidden dimension of the decoder. For" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.9 + ], + "angle": 0, + "content": "3Wenda appears in the Where's Waldo? book series as Waldo's girlfriend." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2891" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.089, + 0.317, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.197, + 0.287, + 0.238 + ], + "angle": 0, + "content": "CLIPCap person, left, and person, (CC) right, receive a standing ovation for their service." + }, + { + "type": "image", + "bbox": [ + 0.322, + 0.089, + 0.503, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.197, + 0.478, + 0.225 + ], + "angle": 0, + "content": "friday night rivals was for high school vs game!" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.679, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.509, + 0.197, + 0.663, + 0.238 + ], + "angle": 0, + "content": "wallpaper with a concert and a well dressed person entitled pop artist." + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.089, + 0.888, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.197, + 0.886, + 0.239 + ], + "angle": 0, + "content": "person, left, shakes hands with person, daughter of person, during a ribbon cutting ceremony." + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.245, + 0.665, + 0.26 + ], + "angle": 0, + "content": "\\([\\star ]\\) performing with \\([\\star ]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.245, + 0.878, + 0.26 + ], + "angle": 0, + "content": "\\([\\star]\\) cutting the ribbon with \\([\\star]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.245, + 0.305, + 0.274 + ], + "angle": 0, + "content": "EncDec \\([\\star ]\\) administering the oath (pHHI) to \\([\\star ]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.326, + 0.245, + 0.436, + 0.259 + ], + "angle": 0, + "content": "\\([\\star]\\) coaching \\([\\star]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.284, + 0.465, + 0.298 + ], + "angle": 0, + "content": "\\([\\star]\\) huddling with \\([\\star]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.284, + 0.646, + 0.298 + ], + "angle": 0, + "content": "\\([\\star]\\) dancing with \\([\\star]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.284, + 0.867, + 0.298 + ], + "angle": 0, + "content": "\\([\\star]\\) cutting a ribbon with \\([\\star]\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.304, + 0.894, + 0.388 + ], + "angle": 0, + "content": "Figure 4. Results on the Waldo and Wenda test set. We compare results obtained by a baseline, our vanilla encoder-decoder technique (trained on our pHHI data), and the ground truth labels in Waldo and Wenda, with \\([\\star]\\) denoting [NAME] tokens that represent person entities. As illustrated above, our method generates text describing the HHI depicted in the image, without attending to other irrelevant details. In comparison, the SOTA captioning model CLIPCap used as-is may not output an interaction at all (middle two images). We also observe that our model predicts HHI that may require both a verb and other arguments to adequately understand (leftmost and rightmost images)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.47, + 0.563 + ], + "angle": 0, + "content": "the decoder we use pretrained GPT-2 [51] with a causal language modelling head and cross-attention over the encoder output. Consistent with previous works on fine-tuning vision-and-language models [38, 41, 78], we freeze the weights of the image encoder as we fine-tune it on our pHHI data. By considering this model that was not previously trained on image captioning, we aim to evaluate the extent to which our pHHI aid in learning to understand the semantics of HHI in images (rather than simply cueing a captioning model to the correct surface form of HHI labels)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.47, + 0.693 + ], + "angle": 0, + "content": "(2) Fine-tuned captioner. The second approach we consider is to apply transfer learning to a SOTA captioning model by fine-tuning it on our pHHI data. Because the Conceptual Captions (CC) dataset is more people-centric than COCO and thus closer to our use case, we pick CLIPCap [41] pretrained on CC as the base model for fine-tuning. Consistent with CLIPCap's training method, we freeze its image encoder and fine-tune the model on our pHHI data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.702, + 0.291, + 0.719 + ], + "angle": 0, + "content": "4.2. Training and Decoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.786 + ], + "angle": 0, + "content": "For all models, we use cross-entropy loss and consistent hyperparameter settings. For each model, we decode using beam search with 32 beams. We report metric values for the top 1, 5, and 8 beams." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.194, + 0.815 + ], + "angle": 0, + "content": "5. Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.824, + 0.216, + 0.839 + ], + "angle": 0, + "content": "5.1. Test Datasets" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.848, + 0.429, + 0.864 + ], + "angle": 0, + "content": "We evaluate our models on the following datasets:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Waldo and Wenda. As detailed in Section 3.4, this consists of 1,000 images with manually-written ground truth labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.893, + 0.488 + ], + "angle": 0, + "content": "Examples of ground truth labels along with model predictions can be seen in Figure 4. We report metric values averaged over the three data sources (Who's Waldo, Conceptual Captions, COCO) of Waldo and Wenda in Table 2. We also show a breakdown of data source in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.893, + 0.735 + ], + "angle": 0, + "content": "imSitu-HHI. We use an 8,021-sample subset of the imSitu [75] situation recognition benchmark, which we refer to as imSitu-HHI, to perform a large-scale evaluation of our models. Although imSitu does not contain free text HHI labels, it does contain categorical verb labels which can be used for comparison. Additionally, as the majority of images in imSitu do not depict HHI, we first filter for relevant samples as follows: We use person detections from YoloV5 [15] to select for images containing at least two humans. We further filter to select only samples with semantic frames containing at least two human participants. Finally, due to the noisy nature of this filtering, we only use verbs supported by at least 100 images in this filtered subset, as these verbs are most likely to describe HHI. We use these verb labels as the ground truth and evaluate predictions with the verb similarity metric as described below." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.702, + 0.759 + ], + "angle": 0, + "content": "5.2. Baseline comparisons" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.795 + ], + "angle": 0, + "content": "We compare our approach to two types of SOTA model of that do not use our pHHI data as baselines:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.893, + 0.901 + ], + "angle": 0, + "content": "(1) Pretrained captioner. The first baseline approach that we test is the use of a SOTA model that has already been pretrained for image captioning. We test the recent captioning models ExpansionNet v2 (ENv2) [25] and CLIP-Cap [41]. We use these captioners as-is and evaluate our metrics on their outputs with beam search decoding. CLIP-Cap is available with pretrained weights for both COCO [11]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2892" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "and Conceptual Captions (CC) [57], and thus we test both models. ENv2 only uses COCO weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.471, + 0.364 + ], + "angle": 0, + "content": "(2) Pretrained situation recognition model. We provide a comparison to the results of the CoFormer model [12] for grounded situation recognition with pretrained weights. Unlike weakly-supervised models trained on our pseudolabels, which were generated from natural captions, CoFormer is supervised by training on the manually-labelled SWiG dataset [47], an extension of imSitu which includes grounding information for arguments that are visible in the accompanying images, and the model predicts the relevant verb, arguments, and grounding information given an image. We evaluate CoFormer by using its predicted verb, discarding semantic frame and grounding predictions since these semantic arguments do not directly map to the text of a human-human interaction string. See the supplementary material for details on how we insert its verb predictions into text prompts for metric calculations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.374, + 0.188, + 0.388 + ], + "angle": 0, + "content": "5.3. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.47, + 0.503 + ], + "angle": 0, + "content": "In order to ablate the effect of our pseudo-labelling, we also report results of a captioning model fine-tuned on the entire text of the captions provided in Who's Waldo (listed in 2 and 4 under training data as \"WW\"). In the supplementary material we also provide a detailed comparison with results when training directly on the syntactic parsing-based seeds described in Section 3.1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.513, + 0.173, + 0.528 + ], + "angle": 0, + "content": "5.4. Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.627 + ], + "angle": 0, + "content": "A number of metrics have been proposed for natural language generation tasks, measuring various aspects of text quality [24, 18]. As no prior works (to the best of our knowledge) predict HHI as free text, we propose a set of metrics that evaluate various relevant aspects of generated text:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Textual similarity. We use the BLEURT [55] metric to measure similarity to the ground truth interaction. This is a learned metric for text generation which measures similarity between the text output by a model and the reference text. Because our test set is relatively small and the reference texts are short, this better reflects textual similarity than ngram-based metrics such as BLEU [44] which have high variance and must be averaged over large datasets, as is shown in detail in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Factual groundedness. A key property of generated text is whether it is consistent or contradictory with respect to the ground truth (such as a source document in the case of summarization, or a reference caption in the case of image captioning) [32]. This may be quantified by using the scores output by a natural language inference (NLI) model, in order to measure the degree of factual groundedness or hallucination in generated text [40, 33]. For example, given" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.089, + 0.89, + 0.449 + ], + "angle": 0, + "content": "
MethodTrain DataBL↑pe↑pc↓sim↑
Results@1
CoFormerSWiG0.41*0.33*0.28*0.35
ENv2COCO0.270.250.330.41
CLIPCapCOCO0.280.340.370.42
CLIPCapCC0.270.180.380.35
CLIPCapCC+WW0.260.160.400.17
EncDecpHHI0.380.300.370.41
CLIPCapCC+pHHI0.420.410.320.46
Results@5
ENv2COCO0.310.390.190.46
CLIPCapCOCO0.310.470.240.46
CLIPCapCC0.330.320.200.47
CLIPCapCC+WW0.330.290.240.27
EncDecpHHI0.510.610.090.59
CLIPCapCC+pHHI0.570.710.070.65
Results@8
ENv2COCO0.320.430.170.48
CLIPCapCOCO0.320.500.210.46
CLIPCapCC0.350.360.160.49
CLIPCapCC+WW0.350.330.210.31
EncDecpHHI0.540.650.190.65
CLIPCapCC+pHHI0.590.760.040.69
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.5, + 0.453, + 0.878, + 0.478 + ], + "angle": 0, + "content": "*Evaluated by using the best of two prompt templates for each item, as described in the supplementary material." + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.483, + 0.892, + 0.595 + ], + "angle": 0, + "content": "Table 2. Results on Waldo and Wenda. The listed metrics are BLEURT (BL) and NLI scores \\((p_e, p_c)\\) and verb embedding similarity (sim). CC+WW/pHHI indicates models that were initialized with pretrained CC weights and subsequently fine-tuned on Who's Waldo captions or on pHHI respectively. Best results are in bold, and second best are underlined. Results are aggregated across the three data sources of Waldo and Wenda. For models using beam search, we report results for top 1, 5, and 8 beams." + }, + { + "type": "list", + "bbox": [ + 0.499, + 0.453, + 0.892, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.614, + 0.892, + 0.796 + ], + "angle": 0, + "content": "an image with ground truth label [NAME] sitting next to [NAME], the prediction [NAME] standing with [NAME] logically contradicts the reference label and thus is a factual hallucination. To measure this, we use scores \\((p_e, p_c)\\) from a pretrained NLI model to estimate the factual groundedness of the predicted text, where \\(p_e\\) is the probability of entailment and \\(p_c\\) is the probability of contradiction. We treat the image caption from Waldo and Wenda as the premise and the model's prediction as the hypothesis for NLI inference. For test items sourced from COCO Captions, in which images correspond to multiple reference captions, we use the first reference as the premise for this calculation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Verb similarity. We calculate the average cosine similarity of the predicted and ground truth verbs in GloVe [46] embedding space. The motivation for this metric is that a prediction may be valid or nearly valid even if it is not identical to the ground truth label as long as the semantic distance between the verbs is small (e.g. \"hugging\" vs. \"embracing\")." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2893" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.091, + 0.089, + 0.878, + 0.469 + ], + "angle": 0, + "content": "
MethodTrain DataWWCCCOCO
BL↑pe↑pc↓sim↑BL↑pe↑pc↓sim↑BL↑pe↑pc↓sim↑
Results@1
CoFormerSWiG0.40*0.29*0.35*0.340.45*0.40*0.43*0.380.37*0.30*0.33*0.33
Env2COCO0.240.200.280.380.260.200.450.410.310.360.260.45
CLIPCapCOCO0.270.370.350.390.260.260.430.430.310.380.330.44
CLIPCapCC0.300.240.420.360.250.180.380.400.260.110.340.30
CLIPCapCC+WW0.280.120.590.270.260.210.340.150.230.150.280.10
EncDecpHHI0.410.380.300.420.380.300.440.420.340.220.360.38
CLIPCapCC+pHHI0.420.380.330.450.440.440.330.470.400.400.300.47
Results@5
Env2COCO0.280.300.170.420.300.320.280.460.350.550.120.51
CLIPCapCOCO0.310.500.210.420.290.380.280.460.340.520.230.49
CLIPCapCC0.360.410.230.460.300.310.230.500.320.230.140.43
CLIPCapCC+WW0.330.200.500.330.340.370.130.280.330.310.090.20
EncDecpHHI0.550.610.110.630.510.650.100.590.460.560.070.56
CLIPCapCC+pHHI0.570.640.100.640.600.750.060.680.530.740.050.63
Results@8
Env2COCO0.290.340.150.420.310.350.250.480.360.590.100.53
Env2COCO0.320.530.180.430.300.410.250.470.350.550.210.50
CLIPCapCC0.380.470.170.480.320.350.190.530.340.260.110.45
CLIPCapCC+WW0.340.220.480.350.360.420.100.330.350.340.060.25
EncDecpHHI0.600.690.060.690.550.720.050.640.500.660.040.61
CLIPCapCC+pHHI0.600.700.070.680.630.810.030.720.550.780.030.67
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.08, + 0.473, + 0.667, + 0.486 + ], + "angle": 0, + "content": "*Evaluated by using the best of two prompt templates for each item, as described in the supplementary material." + }, + { + "type": "table_footnote", + "bbox": [ + 0.08, + 0.492, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Table 3. Results on Waldo and Wenda split by data source - Who's Waldo (WW), Conceptual Captions (CC), and COCO Captions. For models using beam search, we report results for top 1, 5, and 8 beams." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.473, + 0.892, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.535, + 0.469, + 0.61 + ], + "angle": 0, + "content": "To evaluate this on free text predictions, we either select the first non-[NAME] word in the output (for models trained on pHHI) or extract its first verb using a syntactic parsing model. If syntactic parsing does not yield a verb, the zero vector is used as the given embedding." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.621, + 0.287, + 0.635 + ], + "angle": 0, + "content": "5.5. Results and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.644, + 0.469, + 0.81 + ], + "angle": 0, + "content": "For Waldo and Wenda, we report all of the metrics described above. For imSitu-HHI, we only use the verb similarity metric since the ground truth label is a single verb. We report average similarity over all samples in imSitu-HHI as well as displaying averages for the most-supported verbs. See Tables 2-4 for quantitative results, and see Figure 4 for a visual comparison on Waldo and Wenda. Note that we do not include CoFormer in the table of imSitu-HHI results since it was trained directly on some of these items; see the supplementary material for analysis of CoFormer on indistribution and out-of-distribution images in imSitu-HHI." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Overall we see that training on our pseudo-labels improves performance on our benchmarks. In Tables 2 and 3, showing results on Waldo and Wenda, the best-performing model by all metrics is CLIPCap fine-tuned with our pseudo-labels. This holds across data sources, as seen in Table 3, showing that this improvement general-" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.535, + 0.891, + 0.67 + ], + "angle": 0, + "content": "izes to images beyond those originating in the Who's Waldo dataset. This model is also the best-performing on average and across a majority of verb categories on imSitu-HHI as seen in Table 4. Qualitative comparison shows that the captioning models used as-is output text that is far from the ground truth HHI labels, containing many irrelevant details and not necessarily describing an interaction. This can be seen in Figure 4, where the CLIPCap (CC) captions contain many hallucinated, non-factual details." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.673, + 0.891, + 0.853 + ], + "angle": 0, + "content": "While transfer learning with pretrained CLIPCap yields the best results, we also observe that the vanilla Encoder-Decoder fine-tuned on our pseudo-labels also performs well, achieving the second-best BLEURT score on Waldo and Wenda and second-best verbal similarity metrics overall and across many verb categories on imSitu-HHI. We infer that our pseudo-labels do impart semantic knowledge of HHI beyond simply cueing existing captioning models to the surface form of HHI labels. Nevertheless, CLIPCap fine-tuned on pHHI does generalize better across the data from all sources in Waldo and Wenda and to imSitu-HHI which is entirely out-of-distribution for this model." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.856, + 0.891, + 0.9 + ], + "angle": 0, + "content": "We also note that the metrics improve dramatically for both datasets when considering 5 or 8 beams. This is consistent with the fact that beam search using models fine-tuned" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.947, + 0.515, + 0.957 + ], + "angle": 0, + "content": "2894" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.088, + 0.895, + 0.491 + ], + "angle": 0, + "content": "
Average sim.socializingdistributingteachingcommunicatinginterviewinglecturingtrainingprovidinginstructinggivingpushinghelpingaskingcoachingtalking
Results@1
ENv2COCO0.220.190.070.220.210.280.190.250.260.110.450.380.290.440.280.28
CLIPCapCOCO0.230.180.070.260.240.290.170.260.240.100.440.360.250.460.300.63
CLIPCapCC0.270.160.250.370.260.210.230.280.350.160.460.310.370.380.260.53
CLIPCapCC+WW0.090.020.080.120.050.300.080.100.090.060.250.070.090.110.050.08
EncDecpHHI0.280.190.210.340.270.230.240.350.380.170.600.360.340.460.760.64
CLIPCapCC+pHHI0.320.210.250.560.330.270.300.430.440.190.660.380.440.460.650.70
Results@5
ENv2COCO0.260.210.100.260.230.300.210.270.310.130.490.450.350.490.330.31
CLIPCapCOCO0.250.190.090.290.260.310.200.270.260.120.470.410.290.480.320.66
CLIPCapCC0.350.210.300.480.330.280.310.370.430.210.560.420.480.470.310.64
CLIPCapCC+WW0.180.050.150.220.140.600.160.170.220.110.460.150.210.220.150.24
EncDecpHHI0.400.300.350.490.410.390.330.510.510.230.790.470.490.570.920.86
CLIPCapCC+pHHI0.440.290.350.850.440.410.400.560.560.270.880.480.560.580.860.92
Results@8
ENv2COCO0.280.220.120.270.240.300.210.280.320.130.510.470.370.500.350.34
CLIPCapCOCO0.260.200.100.310.270.310.210.280.260.120.480.430.310.490.320.67
CLIPCapCC0.370.230.310.510.340.310.320.400.450.220.590.450.510.490.320.70
CLIPCapCC+WW0.210.060.160.250.160.620.160.200.240.120.510.200.230.260.180.32
EncDecpHHI0.440.330.380.550.440.420.340.540.560.250.850.490.560.590.940.91
CLIPCapCC+pHHI0.470.330.370.900.460.410.430.600.590.290.920.500.590.610.910.96
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.495, + 0.892, + 0.539 + ], + "angle": 0, + "content": "Table 4. Results on imSitu-HHI. In addition to the average verb embedding similarity between predicted verbs and the ground truth verb, we also present mean similarities for the most common 15 verbs in imSitu-HHI. Best results are in bold, and second best are underlined. For models using beam search, we report results for top 1, 5, and 8 beams." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.471, + 0.64 + ], + "angle": 0, + "content": "on pHHI outputs a list of diverse candidate interactions, allowing a more directed search in the space of HHI descriptors, while beam search applied to captioning models as-is tends to produce many slight variations of the same long caption." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.66, + 0.196, + 0.675 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.838 + ], + "angle": 0, + "content": "We present a new framework for learning to understand human-human interactions in still images using weak supervision from textual captions. We demonstrate the use of knowledge distillation applied to a large language model without explicit supervision to produce pseudo-labels that can serve as targets for predicting interactions as free text. We show that training on these pseudo-labels enables HHI understanding beyond that of SOTA captioning and situation recognition models, and we provide the Waldo and Wenda as a new benchmark for this task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "There are various avenues for future research to extend our work. One possible direction is the incorporation of visual grounding into HHI understanding. We predict the most salient interaction in an image, which we assume to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.713 + ], + "angle": 0, + "content": "be the interaction the one that is described or suggested in its accompanying caption. It remains to localize the participants, including generalizing to group interactions where more than two participants are visible. Another important aspect that remains to be explored is the hierarchical nature of interactions. For example, the generic HHI label \"meeting\" is valid for almost every image, while \"shaking hands\" is more specific and valid for a subset of those images. Further research could extend our results to hierarchical prediction of multiple HHI labels for a single image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.892, + 0.851 + ], + "angle": 0, + "content": "Finally, we note the importance of style-content disentanglement in HHI prediction, which our work does not explicitly consider. Scene cues in images can be important for correctly identifying HHI, as illustrated in Figure 1, but also may be misleading. For instance, an image of soldiers in uniform is more likely to depict \"saluting\", but HHI is only valid if the image actually contains a salute. Future work on disentangling style and content shows promise for improving the robustness of HHI understanding models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. We thank Ron Mokady for providing helpful feedback. This work was supported by a research gift from Meta and the Alon fellowship." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2895" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Stanislaw Antol, C Lawrence Zitnick, and Devi Parikh. Zero-shot learning via visual abstraction. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part IV 13, pages 401-416. Springer, 2014." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.186, + 0.472, + 0.24 + ], + "angle": 0, + "content": "[2] Sid Black, Gao Leo, Phil Wang, Connor Leahy, and Stella Biderman. GPT-Neo: Large Scale Autoregressive Language Modeling with Mesh-Tensorflow, Mar. 2021. 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We propose a new paradigm of learning human-human interactions as free text from a single still image, allowing for flexibility in modeling the unlimited space of situations and relationships between people. To overcome the absence of data labelled specifically for this task, we use knowledge distillation applied to synthetic caption data produced by a large language model without explicit supervision. We show that the pseudo-labels produced by this procedure can be used to train a captioning model to effectively understand human-human interactions in images, as measured by a variety of metrics that measure textual and semantic faithfulness and factual groundedness of our predictions. We further show that our approach outperforms SOTA image captioning and situation recognition models on this task. We will release1 our code and pseudo-labels along with Waldo and Wenda, a manually-curated test set for still image human-human interaction understanding. + +# 1. Introduction + +"No man is an island entire of itself." -John Donne + +Humans are social beings. As such, interactions among people are ubiquitous and diverse, affected by various factors including social context and cultural norms. Reasoning about these interactions is crucial for gaining a holistic understanding of visual scenes depicting people. However, in spite of significant progress in analyzing isolated human actions [29, 73, 79] and relationships between entities and objects [27, 83], far less attention has been devoted towards an automatic understanding of human-human interactions (HHI). This is despite the importance of this task for applications such as interactive robotics, social behaviour understanding, and captioning systems for the visually impaired. + +There are a number of factors that make the analysis of + +![](images/2eac0157c983513215b61bf41bf231e330d30fbffcbeaf99486c5a912655fdc5.jpg) +Figure 1. How would you describe the interactions depicted in these images? There are unlimited possible interactions between people which cannot be easily described by a fixed set of categories or actions. Context plays a crucial role, as in the left image where the clothing and cake in the background help to interpret the depicted interaction. Moreover, interactions may be involve participants at a physical distance as in the image on the right. To model the heavy tail of possible interactions, we propose to learn HHI as free text (see below2 for predictions using our method). + +![](images/de08acd4f4451fa863f88dd9e3fb1c5c7f150966362ce2b95071bfc54958c150.jpg) + +HHI difficult. The space of possible interactions between people is vast and requires understanding social context and physically non-local relationships, as illustrated in Figure 1. In addition, images depicting HHI may have multiple interpretations, some of which may be simultaneously correct. For example, the image on the left might depict "celebrating a wedding" as well as "dancing". Contextual cues such as the cake in the background of the image provide additional information that hints at the depicted HHI. + +Prior works targeting HHI understanding focus on a small fixed number of interactions; representative works include [63, 65, 43, 30], all of whose models are trained to recognize no more than ten interaction classes. In this work, we are interested in modeling the heavy tail of possible HHI to better understand the rich variety of ways in which people interact. To this aim, we propose to model HHI understanding as free text generation; since HHI are not confined to a fixed set of categories or even to a syntactic class such as verbs, HHI as free text enables the expression of an infinite variety of possible interactions. Furthermore, in contrast to previous works that frequently rely on extra context such as video data [60], we use a single image with no additional information (during inference), making our method more widely applicable. We focus on what Stergiou and + +Poppe [60] term dyadic interactions—pairwise interactions between two people. Our goal is to identify the most salient dyadic interaction given an image of two or more people interacting. + +One of the primary challenges to modeling HHI is a scarcity of labelled data for this particular task. There are only a handful of relatively small datasets specific to HHI, and larger video datasets for action recognition are lacking in coverage of interactions (see Table 1). To better model the heavy tail of possible HHI, we leverage the abundance of high-quality images of people and associated textual captions available on the Internet. In particular, we use the Who's Waldo dataset [13] that contains 270K image_caption pairs from Wikimedia Commons depicting people captured in a broad range of situations. Unlike many other image captioning datasets, Who's Waldo focuses on human-centric situations which are described using real-world captioned Internet data, and thus is more relevant to HHI understanding. However, it is extremely challenging to learn HHI from raw Internet captions directly, due to significant noise introduced by clutter and irrelevant details. To overcome this, we infer interactions from the original captions by applying knowledge distillation to synthetic data generated by a large language model, without explicit supervision. This approach allows for creating accurate pseudolabels that provide textual descriptions of the HHI depicted in the images. We will release these pseudo-labels along with a manually annotated test set containing 1K image-interaction pairs from diverse Internet images which we name Waldo and Wenda, a new benchmark for our paradigm of HHI understanding as free text on still images, capturing the heavy tail of human-human interactions. + +We demonstrate the utility of these pseudo-labels for learning HHI from images by training captioning models and using them as targets for a language modelling objective. We provide qualitative and quantitative analysis on the Waldo and Wenda test set; in addition, we evaluate this method on a larger scale by applying it to verb prediction on the imSitu situation recognition dataset [75], which we filter to select for images relevant to HHI. + +Because we predict HHI as free text rather than categorically as in previous works, we propose a set of evaluation metrics chosen to measure important aspects of predicted HHI quality, namely textual similarity, factual groundedness, and verb similarity. Our evaluation shows that our HHI pseudo-labels allow for generating meaningful HHI free text descriptions from images, as measured by these metrics. We also show that learning on these pseudo-labels captures HHI substantially more effectively than either using existing SOTA image captioning models as-is or than training on interactions extracted with naive syntactic parsing. Explicitly stated, our key contributions are: + +- A new paradigm and benchmark for HHI understand + +ing from images—i.e., predicting interactions as free text—allowing to better understand the vast variety of ways in which people interact. + +- A method for isolating HHI from noisy Internet captions using knowledge distillation applied to a large language model, and a set of pseudo-labels generated by this method. +- An evaluation framework with metrics that capture HHI understanding, and results demonstrating that training image captioning models on these pseudolabels can allow for modeling the heavy tail of possible HHI across various situations and configurations more effectively than SOTA image captioning and situation recognition models. + +# 2. Related Work + +Human action recognition. Human actions span a range from simple to complex. These include simple actions ("running"), human-object interactions ("dribbling a ball"), human-human interactions ("shaking hands"), and group actions ("gathering"). Because of the dynamic nature of actions, a large portion of work on action recognition uses video data [62, 64, 6, 82, 68]. Other approaches use other modalities such as depth or skeleton data [76, 48, 73]. Among video-based approaches, some use shallow approaches separating feature representation of action videos and classification of these features, while others use end-to-end trainable networks (see [29, 79] for detailed surveys). Works on human-object interactions (HOI) may use separate modules such as human and object detectors and relation modules [8, 20, 16], pose and gaze estimation [35, 66, 71], or graph neural networks applied to scene graphs [49, 72, 81, 36]. One line of recent work on HOI uses end-to-end models, frequently with transformer architectures [61, 83, 10, 27, 9]. In our work, we aim to predict the most salient interaction between the pictured individuals in an end-to-end manner from still image data alone. + +HHIs are a subset of human actions which pose particular challenges to automatic recognition, due to non-locality, context dependency, and ambiguity. A number of works have explicitly tackled HHI recognition, as surveyed by Stergiou and Poppe [60]. As with general action recognition, these approaches most commonly use video data as input [43, 19, 67, 58, 34]. However, a few works have tackled the more challenging task of HHI recognition in still images. Some of these use classical computer vision methods to estimate human locations and poses in photos for predicting HHI [74, 7, 1]. Xiong et al. [70] use a CNN architecture with human, face, and object detection features for event recognition. These works all treat HHI as categorical, predicting them from a small set of predefined interaction + +classes. In contrast, we use free text to describe HHIs allowing for more flexibility than categorical recognition. + +HHI datasets. Most existing datasets of HHI or with subsets representing HHI classes only include a small number of interaction categories. The majority consist of video data, either curated [54, 77, 19, 22] or YouTube-based [59, 42, 80]. + +There are few image datasets dedicated to human actions, of which HHI are a subset. Ronchi and Perona [53] introduce the Visual Verbnet dataset consisting of images with dense verb annotations. Yatskar et al. [75] introduce the imSitu dataset for image situation recognition, involving recognizing the action portrayed in a still image (often with a human participant or participants) as well as predicting semantic roles for observed entities. In both cases the labels are selected from a fixed set of categories—single verbs in the case of imSitu, verbs or phrases containing verbs (e.g. "shake hands") for Visual Verbnet. Other image datasets such as Visual Genome [31] contain labeled entities, objects and their relationships, but focus more on general objects rather people and their interactions. + +See Table 1 for a comparison of the most related datasets with our proposed HHI dataset. Unlike prior datasets, ours represents HHI as free text and not as fixed categories. + +In-context learning with large language models (LLMs). The recent explosive growth in size and NLP benchmark performance of LLMs has led to their use as foundation models for use on downstream tasks [3]. Models such as GPT-3 show an emergent in-context learning property, whereby they may solve new tasks when prompted with only a few examples of a new task, or even just with a task description, without any parameter updates [5, 14]. The output of such models may then be used as supervised training data for conventional model fine-tuning. The idea of training on data generated using in-context learning to create a large training data set has been successfully applied to achieve state-of-the-art results on the SuperGLUE NLP benchmark by Wang et al. [69]. In our case, we use this data to perform sequence-level knowledge distillation – transferring the knowledge exhibited by such a large model into a smaller model by training on its output sequences [28, 21]. + +The use of LLM-generated synthetic data for multimodal learning has been explored by Brooks et al. [4], who use caption pairs generated by GPT-3 as auxiliary data for training a conditional diffusion model to perform image editing. Their method uses hundreds of manually labelled pairs of texts as training data; however, our pseudo-labelling method uses no explicit supervision, instead using syntactic parsing to generate automatic seeds for our synthetic data generation pipeline. + +
Dataset#Seq#HHI Classes
Curated videos
UT-Interaction [54]606
TV Human Interaction [45]3004
Hollywood2 [39]36694
ShakeFive2 [19]1535
SBU Kinect [77]3008
AVA [22]~57.6k13
NTU RGB+D (120) [56, 37]~114k26
YouTube-based videos
Kinetics [26, 59]~500k11
Moments in Time [42]~800k32
HACS [80]~50k23
Still images
imSitu [75]126k50*
Visual Verbnet [53]10k52*
Who's Waldo [13] (w/ our labels)127k∞* (free text)
+ +*The number of HHI classes for Visual Verbnet includes verbs in the communication, contact and social categories, which sometimes mark solo actions or human-object interactions. The imSitu dataset contains a total of 504 verbs. We estimate the number of HHI interactions using an automatic methodology detailed in Section 5. Our free text pseudo-labels are limited to the types of interactions available in Who's Waldo. +Table 1. Comparison of HHI datasets. Prior datasets usually capture video data and target a small number of interaction classes. Several datasets focus on human actions, some of which include HHI. We denote the number of video/image samples with #Seq, and the number of HHI classes with #HHI Classes (values are taken from Stergiou and Poppe [60] where relevant). In our work, we devise a technique for generating HHI pseudo-labels for Who's Waldo [13], a dataset containing real-world image-caption pairs, allowing for modeling the heavy tail of HHI. + +# 3. LLM-Based HHI Inference from Captions + +To model the heavy tail of possible HHI using free text, leverage weak supervision in the form of image captions. We turn to Who's Waldo [13], a dataset containing image-caption pairs depicting human-centric scenes scraped from Wikipedia Commons (with names masked using their suggested [NAME] token). As illustrated in Figure 2, the mentions of the depicted HHI are embedded in detailed textual captions, and do not directly correspond to syntactic structures such as verbs in the text. For instance, the first depicted caption is long and the only relevant detail is the phrase "gets at [sic] high five"; the last depicted caption contains no verb (while the noun phrase "Ski Tour" hints at the relevant interaction). These captions are thus inadequate for training an HHI understanding model directly, as a captioning model fine-tuned on them mainly learns to attend to details that are irrelevant for our task (as shown in Section 5.3). We therefore present a large language model (LLM)-based abstractive text summarization technique that produces clean interaction texts from the original Internet + +![](images/0264c0e65d32c54228af045f6c3be92d674fa855d082b6d8574fd80f0f4a6eb1.jpg) +Hospital Corpsman 1st Class [NAME], U.S. Fleet Forces Sea Soldier of the Year, gets at high five from Master Chief Petty Officer of the Navy (MCPON) [NAME] during a Navy Exchange meet and greet at the Navy Memorial. [NAME] will be meritoriously promoted to chief petty officer. +Parsing-based: $[\star]$ getting five from $[\star]$ +Final: [ $\star$ ] getting a high five from [ $\star$ ] +Figure 2. HHI distilled from raw Internet captions alongside their corresponding images. On top we show several images and captions from the Who's Waldo dataset [13], with $[\star]$ denoting masked named person entities. Our syntactic parsing approach allows for extracting an initial partial set of interactions (first row). We refine and enlarge this initial set using our abstractive summarization model which yields our final HHI pseudo-labels (second row). While the original captions possibly contain many additional details or no verb-based interaction at all (for example, see the rightmost image), our abstractive HHI pseudo-labels succeed in describing HHI visible in the associated images. + +![](images/791780bdb663735002de5f19acc5cb4fd6e6f37ffde6744f49c2db4b4fa6489e.jpg) +$[\star ]$ and $[\star ]$ playing +[ $\star$ ] playing doublebass with [ $\star$ ] +[NAME] and [NAME] playing as doublebass-duo in Club w71, 2018. + +![](images/99789bbfeb267b78dc47586ab9ca7fbee0e941f1bdbc0da67c7ec586852b3910.jpg) +[ $\star$ ] skiing with [ $\star$ ] +[NAME], +[NAME] and +[NAME], 2017 +Ski Tour +Canada, Quebec City. + +captions, without explicit supervision. + +Our unsupervised pseudo-labelling approach operates in three stages, illustrated in Figure 3: (1) We extract syntactic parsing-based interactions from captions from the Who's Waldo dataset, as well as constructing new synthetic interaction texts. (2) We prompt an LLM using the interaction-caption pairs from Who's Waldo along with the new interactions. The output synthetic captions are filtered using a pretrained natural language inference (NLI) model and various textual heuristics, to select for those that correspond to the new interactions. (3) We train an abstractive summarization model on these synthetic caption-interaction pairs; this model learns to output HHI from noisy Internet captions. As seen in Figure 2, these interaction pseudo-labels accurately describe the HHI visible in their associated images. Below, we provide more details for each stage (Sections 3.1-3.3). We then present Waldo and Wenda, our manually-curated HHI test set, in addition to statistics and an ethical discussion (Section 3.4). + +# 3.1. Constructing interaction texts + +We first define a rule-based approach for extracting interactions via syntactic parsing. Specifically, we extract the first verb in the caption with a [NAME] subject along with its direct objects and the heads of its prepositional arguments. This roughly corresponds to an interaction, although it may sound unnatural. This is also limited to captions containing verb phrases. We apply this procedure to captions from Who's Waldo to obtain corresponding parsing-based interactions. + +We also construct new synthetic interactions by first applying this parsing procedure to scraped texts of news articles from the CC-News dataset [23] (from Commoncrawl, containing text without image data), and then using the output interaction texts to prompt the large (1.3B-parameter) language model GPT-Neo [2, 17], which produces a set of diverse and more natural-sounding interactions. + +# 3.2. Synthetic caption data generation + +Using the caption–interaction pairs from Who’s Waldo and the new synthetic interactions as seeds, we generate synthetic caption–interaction pairs using in-context learning with GPT-Neo. This allows us to create a larger and more diverse set of caption–interaction pairs than by using caption–interaction pairs directly from Who’s Waldo. These pairs serve as the teacher model outputs used for knowledge distillation in the following section. + +At each step, the language model is shown a prompt beginning with multiple randomly-selected examples of caption–interaction pairs from Who’s Waldo. This provides context for the model to understand the task at hand–associating interactions with captions that contain them. We use ten examples in each prompt to balance between the providing sufficient context with computational considerations. The prompt ends with a new desired interaction, and the language model proceeds to generate a caption corresponding to this interaction. We filter these results using a pretrained NLI model and various textual heuristics detailed further in the supplementary material, ensuring that the output caption logically is properly formatted and logically entails the corresponding interaction. + +# 3.3. Knowledge distillation for summarization + +Using the synthetic data generated in the previous stage, we fine-tune a smaller (220M-parameter) student T5 model, a sequence-to-sequence transformer network whose pretraining tasks include text summarization [52]. We use the synthetic captions (with the task prefix "summarize:") as input and the synthetic interactions of the target text for fine-tuning. Empirically, we find that our fine-tuned student model is able to summarize captions and output valid interactions even when the caption does not contain a verb or has a syntactic structure that the syntactic parsing-based method could not process. + +We apply this model to the captions in the Who's Waldo + +![](images/7302b9ae82a6b3c9229501a79a33518b605625b14d1727d799933d88cf145af4.jpg) +Synthetic caption generation with teacher LM and NLI filtering + +![](images/4c857e58a313763fb53c5694bfc6bf76f9b7895c2c7c114f6801726083071d35.jpg) +Figure 3. LLM-Based HHI Extraction from Captions. We generate synthetic interaction-caption pairs via in-context learning (left), use them to fine-tune a summarization model (center), and then use this model to producing HHI pseudo-labels for captions in Who's Waldo (right), as detailed in Section 3. Captions are shown in red boxes, interaction texts in blue, and synthetic texts in italic letters. $\mathrm{LM_T}$ and $\mathrm{LM_S}$ indicate teacher and student language models respectively. + +![](images/c103438fadcaeacfdcabf9fc49f0ff266e1e2a0d7fea79fdba7ab85e4686e8a5.jpg) +Fine-tuning student LM +Pseudo-label inference + +dataset to create pseudo-labels representing interactions as free text. See Figure 2 for examples of such pseudo-labels. + +# 3.4. Our HHI dataset + +Using our learned abstractive summarization model, we may generate interaction pseudo-labels from Who's Waldo captions. Out of the $\sim 270k$ samples in Who's Waldo, we use only those $\sim 130k$ containing at least two human face detections, using the detections provided by Cui et al. [13]. We filter out duplicate and near-duplicate images, those with high similarity to test set images, and samples with pseudo-labels that do not pass a few simple text-based filtering rules, including enforcing the format of [NAME], followed by a present continuous verb ("-ing"), and including another [NAME] token. We are left with $\sim 126k$ images with pseudo-labels in total, which we hereby refer to as pHHI. + +The Waldo and Wenda Benchmark. We also create Waldo and $Wenda^3$ , an HHI test set containing 1K manually curated image–interaction text pairs. In order to test generalization to HHI understanding across a wide variety of natural images, we include data from three sources: (1) 300 images from Who's Waldo, (2) 300 images from COCO Captions [11], (3) 400 images from Conceptual Captions [57]. The images are selected from the validation and test splits of the relevant datasets. As the distribution of HHI in natural photographs is highly imbalanced—for instance, images in captioning datasets often display people standing side by side and posing for photographs—we curate this test set to represent a wide variety of interactions and to reflect performance on the long tail of uncommon HHI. Examples of images from Waldo and Wenda can be seen in Figures 1, 2, and 4. + +Dataset Statistics. Overall, our pHHI training dataset contains 126,696 pairs of images and pseudo-labels. These labels contain 1,263 unique verbs and 16,136 unique interactions. The majority of the images (59.3%) only contain two + +detected people, with less than $5\%$ of the images containing more than six detected people. The Waldo and Wenda test set contains 1,000 images along with their manually written ground truth HHI labels. These include 238 unique verbs and 575 unique interaction labels. + +Ethical considerations. Our dataset inherits a diverse representation of people (ages, ethnicities, geographic etc.) from the Who's Waldo dataset [13]. Furthermore, we use their provided name masking to mitigate biases (e.g., gender biases). We verify that all manually-curated test samples are neutral in nature and do not contain lurid or negative material. We perform similar verification on external test data, as described in Section 5, to avoid exposure to harmful or offensive behaviors. Furthermore, our pseudo-labels and test set will only be made available for academic purposes. + +# 4. Learning HHI from Still Images + +In the previous section, we demonstrated how we can obtain free text HHI pseudo-labels from the Internet captions of the Who's Waldo dataset [13]. We proceed to show how we use these to supervise learning HHI from still images via the paradigm of image captioning. + +# 4.1. Models considered + +After obtaining a set of images and pseudo-labels, we consider the task of HHI in the framework of image captioning. Given (image, pseudo-label) pair $(I,L)$ , we train an encoder-decoder network $M$ to maximize the predicted conditional likelihood of $L$ using a cross-entropy loss. During inference, we use autoregressive beam search decoding to generate text token by token, given $I$ as input. + +In order to evaluate the utility of transfer learning from general image captioning to our HHI understanding setting, we evaluate two choices for the model $M$ : + +(1) Vanilla encoder-decoder (EncDec). In this setting, we fine-tune a simple encoder-decoder model. We use the image encoder of pretrained CLIP-ViT [50], with its pooled embedding output followed by a single linear projection layer to match the hidden dimension of the decoder. For + +![](images/d96ec9a4a7948b99e6c0c91b996a5d8ce789a9f94ffe2ad4da7c6dd3916b232c.jpg) +CLIPCap person, left, and person, (CC) right, receive a standing ovation for their service. + +![](images/1eb2564bad6011d9eb1ad35691c1f46e22fcda6d2a4ec96fbe0c6f924c355b86.jpg) +friday night rivals was for high school vs game! +EncDec $[\star ]$ administering the oath (pHHI) to $[\star ]$ +$[\star]$ coaching $[\star]$ +$[\star]$ huddling with $[\star]$ + +![](images/0e726725b148d80f78a2e66421fa63ad0dbecaf47235dbf660a47e61ace02e86.jpg) +wallpaper with a concert and a well dressed person entitled pop artist. +$[\star]$ dancing with $[\star]$ + +![](images/4779a3c0c4239da7b401d0fb93e225ec5190100b2672e06178c3cc2ebc45734c.jpg) +person, left, shakes hands with person, daughter of person, during a ribbon cutting ceremony. +$[\star ]$ performing with $[\star ]$ +$[\star]$ cutting the ribbon with $[\star]$ +$[\star]$ cutting a ribbon with $[\star]$ +Figure 4. Results on the Waldo and Wenda test set. We compare results obtained by a baseline, our vanilla encoder-decoder technique (trained on our pHHI data), and the ground truth labels in Waldo and Wenda, with $[\star]$ denoting [NAME] tokens that represent person entities. As illustrated above, our method generates text describing the HHI depicted in the image, without attending to other irrelevant details. In comparison, the SOTA captioning model CLIPCap used as-is may not output an interaction at all (middle two images). We also observe that our model predicts HHI that may require both a verb and other arguments to adequately understand (leftmost and rightmost images). + +the decoder we use pretrained GPT-2 [51] with a causal language modelling head and cross-attention over the encoder output. Consistent with previous works on fine-tuning vision-and-language models [38, 41, 78], we freeze the weights of the image encoder as we fine-tune it on our pHHI data. By considering this model that was not previously trained on image captioning, we aim to evaluate the extent to which our pHHI aid in learning to understand the semantics of HHI in images (rather than simply cueing a captioning model to the correct surface form of HHI labels). + +(2) Fine-tuned captioner. The second approach we consider is to apply transfer learning to a SOTA captioning model by fine-tuning it on our pHHI data. Because the Conceptual Captions (CC) dataset is more people-centric than COCO and thus closer to our use case, we pick CLIPCap [41] pretrained on CC as the base model for fine-tuning. Consistent with CLIPCap's training method, we freeze its image encoder and fine-tune the model on our pHHI data. + +# 4.2. Training and Decoding + +For all models, we use cross-entropy loss and consistent hyperparameter settings. For each model, we decode using beam search with 32 beams. We report metric values for the top 1, 5, and 8 beams. + +# 5. Evaluation + +# 5.1. Test Datasets + +We evaluate our models on the following datasets: + +Waldo and Wenda. As detailed in Section 3.4, this consists of 1,000 images with manually-written ground truth labels. + +Examples of ground truth labels along with model predictions can be seen in Figure 4. We report metric values averaged over the three data sources (Who's Waldo, Conceptual Captions, COCO) of Waldo and Wenda in Table 2. We also show a breakdown of data source in Table 3. + +imSitu-HHI. We use an 8,021-sample subset of the imSitu [75] situation recognition benchmark, which we refer to as imSitu-HHI, to perform a large-scale evaluation of our models. Although imSitu does not contain free text HHI labels, it does contain categorical verb labels which can be used for comparison. Additionally, as the majority of images in imSitu do not depict HHI, we first filter for relevant samples as follows: We use person detections from YoloV5 [15] to select for images containing at least two humans. We further filter to select only samples with semantic frames containing at least two human participants. Finally, due to the noisy nature of this filtering, we only use verbs supported by at least 100 images in this filtered subset, as these verbs are most likely to describe HHI. We use these verb labels as the ground truth and evaluate predictions with the verb similarity metric as described below. + +# 5.2. Baseline comparisons + +We compare our approach to two types of SOTA model of that do not use our pHHI data as baselines: + +(1) Pretrained captioner. The first baseline approach that we test is the use of a SOTA model that has already been pretrained for image captioning. We test the recent captioning models ExpansionNet v2 (ENv2) [25] and CLIP-Cap [41]. We use these captioners as-is and evaluate our metrics on their outputs with beam search decoding. CLIP-Cap is available with pretrained weights for both COCO [11] + +and Conceptual Captions (CC) [57], and thus we test both models. ENv2 only uses COCO weights. + +(2) Pretrained situation recognition model. We provide a comparison to the results of the CoFormer model [12] for grounded situation recognition with pretrained weights. Unlike weakly-supervised models trained on our pseudolabels, which were generated from natural captions, CoFormer is supervised by training on the manually-labelled SWiG dataset [47], an extension of imSitu which includes grounding information for arguments that are visible in the accompanying images, and the model predicts the relevant verb, arguments, and grounding information given an image. We evaluate CoFormer by using its predicted verb, discarding semantic frame and grounding predictions since these semantic arguments do not directly map to the text of a human-human interaction string. See the supplementary material for details on how we insert its verb predictions into text prompts for metric calculations. + +# 5.3. Ablations + +In order to ablate the effect of our pseudo-labelling, we also report results of a captioning model fine-tuned on the entire text of the captions provided in Who's Waldo (listed in 2 and 4 under training data as "WW"). In the supplementary material we also provide a detailed comparison with results when training directly on the syntactic parsing-based seeds described in Section 3.1. + +# 5.4. Metrics + +A number of metrics have been proposed for natural language generation tasks, measuring various aspects of text quality [24, 18]. As no prior works (to the best of our knowledge) predict HHI as free text, we propose a set of metrics that evaluate various relevant aspects of generated text: + +Textual similarity. We use the BLEURT [55] metric to measure similarity to the ground truth interaction. This is a learned metric for text generation which measures similarity between the text output by a model and the reference text. Because our test set is relatively small and the reference texts are short, this better reflects textual similarity than ngram-based metrics such as BLEU [44] which have high variance and must be averaged over large datasets, as is shown in detail in the supplementary material. + +Factual groundedness. A key property of generated text is whether it is consistent or contradictory with respect to the ground truth (such as a source document in the case of summarization, or a reference caption in the case of image captioning) [32]. This may be quantified by using the scores output by a natural language inference (NLI) model, in order to measure the degree of factual groundedness or hallucination in generated text [40, 33]. For example, given + +
MethodTrain DataBL↑pe↑pc↓sim↑
Results@1
CoFormerSWiG0.41*0.33*0.28*0.35
ENv2COCO0.270.250.330.41
CLIPCapCOCO0.280.340.370.42
CLIPCapCC0.270.180.380.35
CLIPCapCC+WW0.260.160.400.17
EncDecpHHI0.380.300.370.41
CLIPCapCC+pHHI0.420.410.320.46
Results@5
ENv2COCO0.310.390.190.46
CLIPCapCOCO0.310.470.240.46
CLIPCapCC0.330.320.200.47
CLIPCapCC+WW0.330.290.240.27
EncDecpHHI0.510.610.090.59
CLIPCapCC+pHHI0.570.710.070.65
Results@8
ENv2COCO0.320.430.170.48
CLIPCapCOCO0.320.500.210.46
CLIPCapCC0.350.360.160.49
CLIPCapCC+WW0.350.330.210.31
EncDecpHHI0.540.650.190.65
CLIPCapCC+pHHI0.590.760.040.69
+ +*Evaluated by using the best of two prompt templates for each item, as described in the supplementary material. +Table 2. Results on Waldo and Wenda. The listed metrics are BLEURT (BL) and NLI scores $(p_e, p_c)$ and verb embedding similarity (sim). CC+WW/pHHI indicates models that were initialized with pretrained CC weights and subsequently fine-tuned on Who's Waldo captions or on pHHI respectively. Best results are in bold, and second best are underlined. Results are aggregated across the three data sources of Waldo and Wenda. For models using beam search, we report results for top 1, 5, and 8 beams. + +an image with ground truth label [NAME] sitting next to [NAME], the prediction [NAME] standing with [NAME] logically contradicts the reference label and thus is a factual hallucination. To measure this, we use scores $(p_e, p_c)$ from a pretrained NLI model to estimate the factual groundedness of the predicted text, where $p_e$ is the probability of entailment and $p_c$ is the probability of contradiction. We treat the image caption from Waldo and Wenda as the premise and the model's prediction as the hypothesis for NLI inference. For test items sourced from COCO Captions, in which images correspond to multiple reference captions, we use the first reference as the premise for this calculation. + +Verb similarity. We calculate the average cosine similarity of the predicted and ground truth verbs in GloVe [46] embedding space. The motivation for this metric is that a prediction may be valid or nearly valid even if it is not identical to the ground truth label as long as the semantic distance between the verbs is small (e.g. "hugging" vs. "embracing"). + +
MethodTrain DataWWCCCOCO
BL↑pe↑pc↓sim↑BL↑pe↑pc↓sim↑BL↑pe↑pc↓sim↑
Results@1
CoFormerSWiG0.40*0.29*0.35*0.340.45*0.40*0.43*0.380.37*0.30*0.33*0.33
Env2COCO0.240.200.280.380.260.200.450.410.310.360.260.45
CLIPCapCOCO0.270.370.350.390.260.260.430.430.310.380.330.44
CLIPCapCC0.300.240.420.360.250.180.380.400.260.110.340.30
CLIPCapCC+WW0.280.120.590.270.260.210.340.150.230.150.280.10
EncDecpHHI0.410.380.300.420.380.300.440.420.340.220.360.38
CLIPCapCC+pHHI0.420.380.330.450.440.440.330.470.400.400.300.47
Results@5
Env2COCO0.280.300.170.420.300.320.280.460.350.550.120.51
CLIPCapCOCO0.310.500.210.420.290.380.280.460.340.520.230.49
CLIPCapCC0.360.410.230.460.300.310.230.500.320.230.140.43
CLIPCapCC+WW0.330.200.500.330.340.370.130.280.330.310.090.20
EncDecpHHI0.550.610.110.630.510.650.100.590.460.560.070.56
CLIPCapCC+pHHI0.570.640.100.640.600.750.060.680.530.740.050.63
Results@8
Env2COCO0.290.340.150.420.310.350.250.480.360.590.100.53
Env2COCO0.320.530.180.430.300.410.250.470.350.550.210.50
CLIPCapCC0.380.470.170.480.320.350.190.530.340.260.110.45
CLIPCapCC+WW0.340.220.480.350.360.420.100.330.350.340.060.25
EncDecpHHI0.600.690.060.690.550.720.050.640.500.660.040.61
CLIPCapCC+pHHI0.600.700.070.680.630.810.030.720.550.780.030.67
+ +*Evaluated by using the best of two prompt templates for each item, as described in the supplementary material. +Table 3. Results on Waldo and Wenda split by data source - Who's Waldo (WW), Conceptual Captions (CC), and COCO Captions. For models using beam search, we report results for top 1, 5, and 8 beams. + +To evaluate this on free text predictions, we either select the first non-[NAME] word in the output (for models trained on pHHI) or extract its first verb using a syntactic parsing model. If syntactic parsing does not yield a verb, the zero vector is used as the given embedding. + +# 5.5. Results and Discussion + +For Waldo and Wenda, we report all of the metrics described above. For imSitu-HHI, we only use the verb similarity metric since the ground truth label is a single verb. We report average similarity over all samples in imSitu-HHI as well as displaying averages for the most-supported verbs. See Tables 2-4 for quantitative results, and see Figure 4 for a visual comparison on Waldo and Wenda. Note that we do not include CoFormer in the table of imSitu-HHI results since it was trained directly on some of these items; see the supplementary material for analysis of CoFormer on indistribution and out-of-distribution images in imSitu-HHI. + +Overall we see that training on our pseudo-labels improves performance on our benchmarks. In Tables 2 and 3, showing results on Waldo and Wenda, the best-performing model by all metrics is CLIPCap fine-tuned with our pseudo-labels. This holds across data sources, as seen in Table 3, showing that this improvement general- + +izes to images beyond those originating in the Who's Waldo dataset. This model is also the best-performing on average and across a majority of verb categories on imSitu-HHI as seen in Table 4. Qualitative comparison shows that the captioning models used as-is output text that is far from the ground truth HHI labels, containing many irrelevant details and not necessarily describing an interaction. This can be seen in Figure 4, where the CLIPCap (CC) captions contain many hallucinated, non-factual details. + +While transfer learning with pretrained CLIPCap yields the best results, we also observe that the vanilla Encoder-Decoder fine-tuned on our pseudo-labels also performs well, achieving the second-best BLEURT score on Waldo and Wenda and second-best verbal similarity metrics overall and across many verb categories on imSitu-HHI. We infer that our pseudo-labels do impart semantic knowledge of HHI beyond simply cueing existing captioning models to the surface form of HHI labels. Nevertheless, CLIPCap fine-tuned on pHHI does generalize better across the data from all sources in Waldo and Wenda and to imSitu-HHI which is entirely out-of-distribution for this model. + +We also note that the metrics improve dramatically for both datasets when considering 5 or 8 beams. This is consistent with the fact that beam search using models fine-tuned + +
Average sim.socializingdistributingteachingcommunicatinginterviewinglecturingtrainingprovidinginstructinggivingpushinghelpingaskingcoachingtalking
Results@1
ENv2COCO0.220.190.070.220.210.280.190.250.260.110.450.380.290.440.280.28
CLIPCapCOCO0.230.180.070.260.240.290.170.260.240.100.440.360.250.460.300.63
CLIPCapCC0.270.160.250.370.260.210.230.280.350.160.460.310.370.380.260.53
CLIPCapCC+WW0.090.020.080.120.050.300.080.100.090.060.250.070.090.110.050.08
EncDecpHHI0.280.190.210.340.270.230.240.350.380.170.600.360.340.460.760.64
CLIPCapCC+pHHI0.320.210.250.560.330.270.300.430.440.190.660.380.440.460.650.70
Results@5
ENv2COCO0.260.210.100.260.230.300.210.270.310.130.490.450.350.490.330.31
CLIPCapCOCO0.250.190.090.290.260.310.200.270.260.120.470.410.290.480.320.66
CLIPCapCC0.350.210.300.480.330.280.310.370.430.210.560.420.480.470.310.64
CLIPCapCC+WW0.180.050.150.220.140.600.160.170.220.110.460.150.210.220.150.24
EncDecpHHI0.400.300.350.490.410.390.330.510.510.230.790.470.490.570.920.86
CLIPCapCC+pHHI0.440.290.350.850.440.410.400.560.560.270.880.480.560.580.860.92
Results@8
ENv2COCO0.280.220.120.270.240.300.210.280.320.130.510.470.370.500.350.34
CLIPCapCOCO0.260.200.100.310.270.310.210.280.260.120.480.430.310.490.320.67
CLIPCapCC0.370.230.310.510.340.310.320.400.450.220.590.450.510.490.320.70
CLIPCapCC+WW0.210.060.160.250.160.620.160.200.240.120.510.200.230.260.180.32
EncDecpHHI0.440.330.380.550.440.420.340.540.560.250.850.490.560.590.940.91
CLIPCapCC+pHHI0.470.330.370.900.460.410.430.600.590.290.920.500.590.610.910.96
+ +Table 4. Results on imSitu-HHI. In addition to the average verb embedding similarity between predicted verbs and the ground truth verb, we also present mean similarities for the most common 15 verbs in imSitu-HHI. Best results are in bold, and second best are underlined. For models using beam search, we report results for top 1, 5, and 8 beams. + +on pHHI outputs a list of diverse candidate interactions, allowing a more directed search in the space of HHI descriptors, while beam search applied to captioning models as-is tends to produce many slight variations of the same long caption. + +# 6. Conclusion + +We present a new framework for learning to understand human-human interactions in still images using weak supervision from textual captions. We demonstrate the use of knowledge distillation applied to a large language model without explicit supervision to produce pseudo-labels that can serve as targets for predicting interactions as free text. We show that training on these pseudo-labels enables HHI understanding beyond that of SOTA captioning and situation recognition models, and we provide the Waldo and Wenda as a new benchmark for this task. + +There are various avenues for future research to extend our work. One possible direction is the incorporation of visual grounding into HHI understanding. We predict the most salient interaction in an image, which we assume to + +be the interaction the one that is described or suggested in its accompanying caption. It remains to localize the participants, including generalizing to group interactions where more than two participants are visible. Another important aspect that remains to be explored is the hierarchical nature of interactions. For example, the generic HHI label "meeting" is valid for almost every image, while "shaking hands" is more specific and valid for a subset of those images. Further research could extend our results to hierarchical prediction of multiple HHI labels for a single image. + +Finally, we note the importance of style-content disentanglement in HHI prediction, which our work does not explicitly consider. Scene cues in images can be important for correctly identifying HHI, as illustrated in Figure 1, but also may be misleading. For instance, an image of soldiers in uniform is more likely to depict "saluting", but HHI is only valid if the image actually contains a salute. Future work on disentangling style and content shows promise for improving the robustness of HHI understanding models. + +Acknowledgements. We thank Ron Mokady for providing helpful feedback. This work was supported by a research gift from Meta and the Alon fellowship. + +# References + +[1] Stanislaw Antol, C Lawrence Zitnick, and Devi Parikh. Zero-shot learning via visual abstraction. 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A comprehensive study of deep video action recognition. arXiv preprint arXiv:2012.06567, 2020. +[83] Cheng Zou, Bohan Wang, Yue Hu, Junqi Liu, Qian Wu, Yu Zhao, Boxun Li, Chenguang Zhang, Chi Zhang, Yichen Wei, et al. End-to-end human object interaction detection with hoi transformer. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11825-11834, 2021. \ No newline at end of file diff --git a/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/images.zip b/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..30ecf8ac777ef758cb716a1ad57cba1ead3e9c3b --- /dev/null +++ b/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:771931039146e266b5a44d49e2bc5a5d62da10290fcb47cd8163a1703e5b4edb +size 720880 diff --git a/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/layout.json b/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b585bdc0f72b614afc6a02f3003ca5dfb70af8d1 --- /dev/null +++ b/2023/Learning Human-Human Interactions in Images from Weak Textual Supervision/layout.json @@ -0,0 +1,9133 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 48, + 103, + 547, + 122 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 103, + 547, + 122 + ], + "spans": [ + { + "bbox": [ + 48, + 103, + 547, + 122 + ], + "type": "text", + "content": "Learning Human-Human Interactions in Images from Weak Textual Supervision" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 200, + 144, + 394, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 200, + 144, + 394, + 172 + ], + "spans": [ + { + "bbox": [ + 200, + 144, + 394, + 172 + ], + "type": "text", + "content": "Morris Alper and Hadar Averbuch-Elor \nTel Aviv University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 199, + 192, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 199, + 192, + 213 + ], + "spans": [ + { + "bbox": [ + 143, + 199, + 192, + 213 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 224, + 290, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 224, + 290, + 464 + ], + "spans": [ + { + "bbox": [ + 45, + 224, + 290, + 464 + ], + "type": "text", + "content": "Interactions between humans are diverse and context-dependent, but previous works have treated them as categorical, disregarding the heavy tail of possible interactions. We propose a new paradigm of learning human-human interactions as free text from a single still image, allowing for flexibility in modeling the unlimited space of situations and relationships between people. To overcome the absence of data labelled specifically for this task, we use knowledge distillation applied to synthetic caption data produced by a large language model without explicit supervision. We show that the pseudo-labels produced by this procedure can be used to train a captioning model to effectively understand human-human interactions in images, as measured by a variety of metrics that measure textual and semantic faithfulness and factual groundedness of our predictions. We further show that our approach outperforms SOTA image captioning and situation recognition models on this task. We will release1 our code and pseudo-labels along with Waldo and Wenda, a manually-curated test set for still image human-human interaction understanding." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 486, + 128, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 128, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 128, + 498 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 60, + 506, + 286, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 506, + 286, + 519 + ], + "spans": [ + { + "bbox": [ + 60, + 506, + 286, + 519 + ], + "type": "text", + "content": "\"No man is an island entire of itself.\" -John Donne" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 530, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 287, + 673 + ], + "type": "text", + "content": "Humans are social beings. As such, interactions among people are ubiquitous and diverse, affected by various factors including social context and cultural norms. Reasoning about these interactions is crucial for gaining a holistic understanding of visual scenes depicting people. However, in spite of significant progress in analyzing isolated human actions [29, 73, 79] and relationships between entities and objects [27, 83], far less attention has been devoted towards an automatic understanding of human-human interactions (HHI). This is despite the importance of this task for applications such as interactive robotics, social behaviour understanding, and captioning systems for the visually impaired." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 673, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 673, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 58, + 673, + 287, + 686 + ], + "type": "text", + "content": "There are a number of factors that make the analysis of" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 198, + 427, + 277 + ], + "blocks": [ + { + "bbox": [ + 307, + 198, + 427, + 277 + ], + "lines": [ + { + "bbox": [ + 307, + 198, + 427, + 277 + ], + "spans": [ + { + "bbox": [ + 307, + 198, + 427, + 277 + ], + "type": "image", + "image_path": "2eac0157c983513215b61bf41bf231e330d30fbffcbeaf99486c5a912655fdc5.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 280, + 547, + 380 + ], + "lines": [ + { + "bbox": [ + 305, + 280, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 280, + 547, + 380 + ], + "type": "text", + "content": "Figure 1. How would you describe the interactions depicted in these images? There are unlimited possible interactions between people which cannot be easily described by a fixed set of categories or actions. Context plays a crucial role, as in the left image where the clothing and cake in the background help to interpret the depicted interaction. Moreover, interactions may be involve participants at a physical distance as in the image on the right. To model the heavy tail of possible interactions, we propose to learn HHI as free text (see below2 for predictions using our method)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 429, + 198, + 545, + 277 + ], + "blocks": [ + { + "bbox": [ + 429, + 198, + 545, + 277 + ], + "lines": [ + { + "bbox": [ + 429, + 198, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 429, + 198, + 545, + 277 + ], + "type": "image", + "image_path": "de08acd4f4451fa863f88dd9e3fb1c5c7f150966362ce2b95071bfc54958c150.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 398, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 506 + ], + "type": "text", + "content": "HHI difficult. The space of possible interactions between people is vast and requires understanding social context and physically non-local relationships, as illustrated in Figure 1. In addition, images depicting HHI may have multiple interpretations, some of which may be simultaneously correct. For example, the image on the left might depict \"celebrating a wedding\" as well as \"dancing\". Contextual cues such as the cake in the background of the image provide additional information that hints at the depicted HHI." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 506, + 546, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 546, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 546, + 686 + ], + "type": "text", + "content": "Prior works targeting HHI understanding focus on a small fixed number of interactions; representative works include [63, 65, 43, 30], all of whose models are trained to recognize no more than ten interaction classes. In this work, we are interested in modeling the heavy tail of possible HHI to better understand the rich variety of ways in which people interact. To this aim, we propose to model HHI understanding as free text generation; since HHI are not confined to a fixed set of categories or even to a syntactic class such as verbs, HHI as free text enables the expression of an infinite variety of possible interactions. Furthermore, in contrast to previous works that frequently rely on extra context such as video data [60], we use a single image with no additional information (during inference), making our method more widely applicable. We focus on what Stergiou and" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "2A model fine-tuned on our pseudo-labels yields \"dancing\" and \"having a picnic\"." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "1via our project page https://learning-interactions. github.io" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2887" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "Poppe [60] term dyadic interactions—pairwise interactions between two people. Our goal is to identify the most salient dyadic interaction given an image of two or more people interacting." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 289, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 289, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 289, + 453 + ], + "type": "text", + "content": "One of the primary challenges to modeling HHI is a scarcity of labelled data for this particular task. There are only a handful of relatively small datasets specific to HHI, and larger video datasets for action recognition are lacking in coverage of interactions (see Table 1). To better model the heavy tail of possible HHI, we leverage the abundance of high-quality images of people and associated textual captions available on the Internet. In particular, we use the Who's Waldo dataset [13] that contains 270K image_caption pairs from Wikimedia Commons depicting people captured in a broad range of situations. Unlike many other image captioning datasets, Who's Waldo focuses on human-centric situations which are described using real-world captioned Internet data, and thus is more relevant to HHI understanding. However, it is extremely challenging to learn HHI from raw Internet captions directly, due to significant noise introduced by clutter and irrelevant details. To overcome this, we infer interactions from the original captions by applying knowledge distillation to synthetic data generated by a large language model, without explicit supervision. This approach allows for creating accurate pseudolabels that provide textual descriptions of the HHI depicted in the images. We will release these pseudo-labels along with a manually annotated test set containing 1K image-interaction pairs from diverse Internet images which we name Waldo and Wenda, a new benchmark for our paradigm of HHI understanding as free text on still images, capturing the heavy tail of human-human interactions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 455, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 550 + ], + "type": "text", + "content": "We demonstrate the utility of these pseudo-labels for learning HHI from images by training captioning models and using them as targets for a language modelling objective. We provide qualitative and quantitative analysis on the Waldo and Wenda test set; in addition, we evaluate this method on a larger scale by applying it to verb prediction on the imSitu situation recognition dataset [75], which we filter to select for images relevant to HHI." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 694 + ], + "type": "text", + "content": "Because we predict HHI as free text rather than categorically as in previous works, we propose a set of evaluation metrics chosen to measure important aspects of predicted HHI quality, namely textual similarity, factual groundedness, and verb similarity. Our evaluation shows that our HHI pseudo-labels allow for generating meaningful HHI free text descriptions from images, as measured by these metrics. We also show that learning on these pseudo-labels captures HHI substantially more effectively than either using existing SOTA image captioning models as-is or than training on interactions extracted with naive syntactic parsing. Explicitly stated, our key contributions are:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 701, + 287, + 713 + ], + "type": "text", + "content": "- A new paradigm and benchmark for HHI understand" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 324, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 109 + ], + "type": "text", + "content": "ing from images—i.e., predicting interactions as free text—allowing to better understand the vast variety of ways in which people interact." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 118, + 545, + 260 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 118, + 545, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 118, + 545, + 166 + ], + "spans": [ + { + "bbox": [ + 317, + 118, + 545, + 166 + ], + "type": "text", + "content": "- A method for isolating HHI from noisy Internet captions using knowledge distillation applied to a large language model, and a set of pseudo-labels generated by this method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 177, + 545, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 177, + 545, + 260 + ], + "spans": [ + { + "bbox": [ + 317, + 177, + 545, + 260 + ], + "type": "text", + "content": "- An evaluation framework with metrics that capture HHI understanding, and results demonstrating that training image captioning models on these pseudolabels can allow for modeling the heavy tail of possible HHI across various situations and configurations more effectively than SOTA image captioning and situation recognition models." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 274, + 392, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 392, + 286 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 392, + 286 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 294, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 544 + ], + "type": "text", + "content": "Human action recognition. Human actions span a range from simple to complex. These include simple actions (\"running\"), human-object interactions (\"dribbling a ball\"), human-human interactions (\"shaking hands\"), and group actions (\"gathering\"). Because of the dynamic nature of actions, a large portion of work on action recognition uses video data [62, 64, 6, 82, 68]. Other approaches use other modalities such as depth or skeleton data [76, 48, 73]. Among video-based approaches, some use shallow approaches separating feature representation of action videos and classification of these features, while others use end-to-end trainable networks (see [29, 79] for detailed surveys). Works on human-object interactions (HOI) may use separate modules such as human and object detectors and relation modules [8, 20, 16], pose and gaze estimation [35, 66, 71], or graph neural networks applied to scene graphs [49, 72, 81, 36]. One line of recent work on HOI uses end-to-end models, frequently with transformer architectures [61, 83, 10, 27, 9]. In our work, we aim to predict the most salient interaction between the pictured individuals in an end-to-end manner from still image data alone." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 713 + ], + "type": "text", + "content": "HHIs are a subset of human actions which pose particular challenges to automatic recognition, due to non-locality, context dependency, and ambiguity. A number of works have explicitly tackled HHI recognition, as surveyed by Stergiou and Poppe [60]. As with general action recognition, these approaches most commonly use video data as input [43, 19, 67, 58, 34]. However, a few works have tackled the more challenging task of HHI recognition in still images. Some of these use classical computer vision methods to estimate human locations and poses in photos for predicting HHI [74, 7, 1]. Xiong et al. [70] use a CNN architecture with human, face, and object detection features for event recognition. These works all treat HHI as categorical, predicting them from a small set of predefined interaction" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2888" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": "classes. In contrast, we use free text to describe HHIs allowing for more flexibility than categorical recognition." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 112, + 287, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 112, + 287, + 173 + ], + "spans": [ + { + "bbox": [ + 46, + 112, + 287, + 173 + ], + "type": "text", + "content": "HHI datasets. Most existing datasets of HHI or with subsets representing HHI classes only include a small number of interaction categories. The majority consist of video data, either curated [54, 77, 19, 22] or YouTube-based [59, 42, 80]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 175, + 288, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 288, + 344 + ], + "type": "text", + "content": "There are few image datasets dedicated to human actions, of which HHI are a subset. Ronchi and Perona [53] introduce the Visual Verbnet dataset consisting of images with dense verb annotations. Yatskar et al. [75] introduce the imSitu dataset for image situation recognition, involving recognizing the action portrayed in a still image (often with a human participant or participants) as well as predicting semantic roles for observed entities. In both cases the labels are selected from a fixed set of categories—single verbs in the case of imSitu, verbs or phrases containing verbs (e.g. \"shake hands\") for Visual Verbnet. Other image datasets such as Visual Genome [31] contain labeled entities, objects and their relationships, but focus more on general objects rather people and their interactions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 346, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 384 + ], + "type": "text", + "content": "See Table 1 for a comparison of the most related datasets with our proposed HHI dataset. Unlike prior datasets, ours represents HHI as free text and not as fixed categories." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 399, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 603 + ], + "type": "text", + "content": "In-context learning with large language models (LLMs). The recent explosive growth in size and NLP benchmark performance of LLMs has led to their use as foundation models for use on downstream tasks [3]. Models such as GPT-3 show an emergent in-context learning property, whereby they may solve new tasks when prompted with only a few examples of a new task, or even just with a task description, without any parameter updates [5, 14]. The output of such models may then be used as supervised training data for conventional model fine-tuning. The idea of training on data generated using in-context learning to create a large training data set has been successfully applied to achieve state-of-the-art results on the SuperGLUE NLP benchmark by Wang et al. [69]. In our case, we use this data to perform sequence-level knowledge distillation – transferring the knowledge exhibited by such a large model into a smaller model by training on its output sequences [28, 21]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "The use of LLM-generated synthetic data for multimodal learning has been explored by Brooks et al. [4], who use caption pairs generated by GPT-3 as auxiliary data for training a conditional diffusion model to perform image editing. Their method uses hundreds of manually labelled pairs of texts as training data; however, our pseudo-labelling method uses no explicit supervision, instead using syntactic parsing to generate automatic seeds for our synthetic data generation pipeline." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 547, + 285 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 547, + 285 + ], + "type": "table", + "html": "
Dataset#Seq#HHI Classes
Curated videos
UT-Interaction [54]606
TV Human Interaction [45]3004
Hollywood2 [39]36694
ShakeFive2 [19]1535
SBU Kinect [77]3008
AVA [22]~57.6k13
NTU RGB+D (120) [56, 37]~114k26
YouTube-based videos
Kinetics [26, 59]~500k11
Moments in Time [42]~800k32
HACS [80]~50k23
Still images
imSitu [75]126k50*
Visual Verbnet [53]10k52*
Who's Waldo [13] (w/ our labels)127k∞* (free text)
", + "image_path": "0bf4cccf47f7a1242816db526e5fcc409ea92938645ad7b52ca9e2b0a16855cd.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 286, + 544, + 344 + ], + "lines": [ + { + "bbox": [ + 305, + 286, + 544, + 344 + ], + "spans": [ + { + "bbox": [ + 305, + 286, + 544, + 344 + ], + "type": "text", + "content": "*The number of HHI classes for Visual Verbnet includes verbs in the communication, contact and social categories, which sometimes mark solo actions or human-object interactions. The imSitu dataset contains a total of 504 verbs. We estimate the number of HHI interactions using an automatic methodology detailed in Section 5. Our free text pseudo-labels are limited to the types of interactions available in Who's Waldo." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 305, + 346, + 546, + 447 + ], + "lines": [ + { + "bbox": [ + 305, + 346, + 546, + 447 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 546, + 447 + ], + "type": "text", + "content": "Table 1. Comparison of HHI datasets. Prior datasets usually capture video data and target a small number of interaction classes. Several datasets focus on human actions, some of which include HHI. We denote the number of video/image samples with #Seq, and the number of HHI classes with #HHI Classes (values are taken from Stergiou and Poppe [60] where relevant). In our work, we devise a technique for generating HHI pseudo-labels for Who's Waldo [13], a dataset containing real-world image-caption pairs, allowing for modeling the heavy tail of HHI." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 465, + 538, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 538, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 538, + 480 + ], + "type": "text", + "content": "3. LLM-Based HHI Inference from Captions" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 486, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 715 + ], + "type": "text", + "content": "To model the heavy tail of possible HHI using free text, leverage weak supervision in the form of image captions. We turn to Who's Waldo [13], a dataset containing image-caption pairs depicting human-centric scenes scraped from Wikipedia Commons (with names masked using their suggested [NAME] token). As illustrated in Figure 2, the mentions of the depicted HHI are embedded in detailed textual captions, and do not directly correspond to syntactic structures such as verbs in the text. For instance, the first depicted caption is long and the only relevant detail is the phrase \"gets at [sic] high five\"; the last depicted caption contains no verb (while the noun phrase \"Ski Tour\" hints at the relevant interaction). These captions are thus inadequate for training an HHI understanding model directly, as a captioning model fine-tuned on them mainly learns to attend to details that are irrelevant for our task (as shown in Section 5.3). We therefore present a large language model (LLM)-based abstractive text summarization technique that produces clean interaction texts from the original Internet" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2889" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 165, + 148 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 165, + 148 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 165, + 148 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 165, + 148 + ], + "type": "image", + "image_path": "0264c0e65d32c54228af045f6c3be92d674fa855d082b6d8574fd80f0f4a6eb1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 165, + 71, + 245, + 148 + ], + "lines": [ + { + "bbox": [ + 165, + 71, + 245, + 148 + ], + "spans": [ + { + "bbox": [ + 165, + 71, + 245, + 148 + ], + "type": "text", + "content": "Hospital Corpsman 1st Class [NAME], U.S. Fleet Forces Sea Soldier of the Year, gets at high five from Master Chief Petty Officer of the Navy (MCPON) [NAME] during a Navy Exchange meet and greet at the Navy Memorial. [NAME] will be meritoriously promoted to chief petty officer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 152, + 200, + 161 + ], + "lines": [ + { + "bbox": [ + 49, + 152, + 200, + 161 + ], + "spans": [ + { + "bbox": [ + 49, + 152, + 200, + 161 + ], + "type": "text", + "content": "Parsing-based: " + }, + { + "bbox": [ + 49, + 152, + 200, + 161 + ], + "type": "inline_equation", + "content": "[\\star]" + }, + { + "bbox": [ + 49, + 152, + 200, + 161 + ], + "type": "text", + "content": " getting five from " + }, + { + "bbox": [ + 49, + 152, + 200, + 161 + ], + "type": "inline_equation", + "content": "[\\star]" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 163, + 224, + 172 + ], + "lines": [ + { + "bbox": [ + 49, + 163, + 224, + 172 + ], + "spans": [ + { + "bbox": [ + 49, + 163, + 224, + 172 + ], + "type": "text", + "content": "Final: [ " + }, + { + "bbox": [ + 49, + 163, + 224, + 172 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 49, + 163, + 224, + 172 + ], + "type": "text", + "content": " ] getting a high five from [ " + }, + { + "bbox": [ + 49, + 163, + 224, + 172 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 49, + 163, + 224, + 172 + ], + "type": "text", + "content": " ]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 175, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 547, + 240 + ], + "type": "text", + "content": "Figure 2. HHI distilled from raw Internet captions alongside their corresponding images. On top we show several images and captions from the Who's Waldo dataset [13], with " + }, + { + "bbox": [ + 46, + 175, + 547, + 240 + ], + "type": "inline_equation", + "content": "[\\star]" + }, + { + "bbox": [ + 46, + 175, + 547, + 240 + ], + "type": "text", + "content": " denoting masked named person entities. Our syntactic parsing approach allows for extracting an initial partial set of interactions (first row). We refine and enlarge this initial set using our abstractive summarization model which yields our final HHI pseudo-labels (second row). While the original captions possibly contain many additional details or no verb-based interaction at all (for example, see the rightmost image), our abstractive HHI pseudo-labels succeed in describing HHI visible in the associated images." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 252, + 71, + 367, + 148 + ], + "blocks": [ + { + "bbox": [ + 252, + 71, + 367, + 148 + ], + "lines": [ + { + "bbox": [ + 252, + 71, + 367, + 148 + ], + "spans": [ + { + "bbox": [ + 252, + 71, + 367, + 148 + ], + "type": "image", + "image_path": "791780bdb663735002de5f19acc5cb4fd6e6f37ffde6744f49c2db4b4fa6489e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 253, + 152, + 332, + 162 + ], + "lines": [ + { + "bbox": [ + 253, + 152, + 332, + 162 + ], + "spans": [ + { + "bbox": [ + 253, + 152, + 332, + 162 + ], + "type": "inline_equation", + "content": "[\\star ]" + }, + { + "bbox": [ + 253, + 152, + 332, + 162 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 253, + 152, + 332, + 162 + ], + "type": "inline_equation", + "content": "[\\star ]" + }, + { + "bbox": [ + 253, + 152, + 332, + 162 + ], + "type": "text", + "content": " playing" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 253, + 163, + 375, + 172 + ], + "lines": [ + { + "bbox": [ + 253, + 163, + 375, + 172 + ], + "spans": [ + { + "bbox": [ + 253, + 163, + 375, + 172 + ], + "type": "text", + "content": "[ " + }, + { + "bbox": [ + 253, + 163, + 375, + 172 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 253, + 163, + 375, + 172 + ], + "type": "text", + "content": " ] playing doublebass with [ " + }, + { + "bbox": [ + 253, + 163, + 375, + 172 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 253, + 163, + 375, + 172 + ], + "type": "text", + "content": " ]" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 369, + 72, + 404, + 109 + ], + "lines": [ + { + "bbox": [ + 369, + 72, + 404, + 109 + ], + "spans": [ + { + "bbox": [ + 369, + 72, + 404, + 109 + ], + "type": "text", + "content": "[NAME] and [NAME] playing as doublebass-duo in Club w71, 2018." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 410, + 71, + 504, + 148 + ], + "blocks": [ + { + "bbox": [ + 410, + 71, + 504, + 148 + ], + "lines": [ + { + "bbox": [ + 410, + 71, + 504, + 148 + ], + "spans": [ + { + "bbox": [ + 410, + 71, + 504, + 148 + ], + "type": "image", + "image_path": "99789bbfeb267b78dc47586ab9ca7fbee0e941f1bdbc0da67c7ec586852b3910.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 152, + 487, + 172 + ], + "lines": [ + { + "bbox": [ + 411, + 152, + 487, + 172 + ], + "spans": [ + { + "bbox": [ + 411, + 152, + 487, + 172 + ], + "type": "text", + "content": "[ " + }, + { + "bbox": [ + 411, + 152, + 487, + 172 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 411, + 152, + 487, + 172 + ], + "type": "text", + "content": " ] skiing with [ " + }, + { + "bbox": [ + 411, + 152, + 487, + 172 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 411, + 152, + 487, + 172 + ], + "type": "text", + "content": " ]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 503, + 72, + 542, + 109 + ], + "lines": [ + { + "bbox": [ + 503, + 72, + 542, + 109 + ], + "spans": [ + { + "bbox": [ + 503, + 72, + 542, + 109 + ], + "type": "text", + "content": "[NAME], \n[NAME] and \n[NAME], 2017 \nSki Tour \nCanada, Quebec City." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 261, + 201, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 201, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 201, + 272 + ], + "type": "text", + "content": "captions, without explicit supervision." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 274, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 287, + 489 + ], + "type": "text", + "content": "Our unsupervised pseudo-labelling approach operates in three stages, illustrated in Figure 3: (1) We extract syntactic parsing-based interactions from captions from the Who's Waldo dataset, as well as constructing new synthetic interaction texts. (2) We prompt an LLM using the interaction-caption pairs from Who's Waldo along with the new interactions. The output synthetic captions are filtered using a pretrained natural language inference (NLI) model and various textual heuristics, to select for those that correspond to the new interactions. (3) We train an abstractive summarization model on these synthetic caption-interaction pairs; this model learns to output HHI from noisy Internet captions. As seen in Figure 2, these interaction pseudo-labels accurately describe the HHI visible in their associated images. Below, we provide more details for each stage (Sections 3.1-3.3). We then present Waldo and Wenda, our manually-curated HHI test set, in addition to statistics and an ethical discussion (Section 3.4)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 501, + 209, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 209, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 209, + 513 + ], + "type": "text", + "content": "3.1. Constructing interaction texts" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": "We first define a rule-based approach for extracting interactions via syntactic parsing. Specifically, we extract the first verb in the caption with a [NAME] subject along with its direct objects and the heads of its prepositional arguments. This roughly corresponds to an interaction, although it may sound unnatural. This is also limited to captions containing verb phrases. We apply this procedure to captions from Who's Waldo to obtain corresponding parsing-based interactions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "We also construct new synthetic interactions by first applying this parsing procedure to scraped texts of news articles from the CC-News dataset [23] (from Commoncrawl, containing text without image data), and then using the output interaction texts to prompt the large (1.3B-parameter) language model GPT-Neo [2, 17], which produces a set of diverse and more natural-sounding interactions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 260, + 485, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 260, + 485, + 273 + ], + "spans": [ + { + "bbox": [ + 306, + 260, + 485, + 273 + ], + "type": "text", + "content": "3.2. Synthetic caption data generation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 278, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 374 + ], + "type": "text", + "content": "Using the caption–interaction pairs from Who’s Waldo and the new synthetic interactions as seeds, we generate synthetic caption–interaction pairs using in-context learning with GPT-Neo. This allows us to create a larger and more diverse set of caption–interaction pairs than by using caption–interaction pairs directly from Who’s Waldo. These pairs serve as the teacher model outputs used for knowledge distillation in the following section." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 376, + 546, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 542 + ], + "type": "text", + "content": "At each step, the language model is shown a prompt beginning with multiple randomly-selected examples of caption–interaction pairs from Who’s Waldo. This provides context for the model to understand the task at hand–associating interactions with captions that contain them. We use ten examples in each prompt to balance between the providing sufficient context with computational considerations. The prompt ends with a new desired interaction, and the language model proceeds to generate a caption corresponding to this interaction. We filter these results using a pretrained NLI model and various textual heuristics detailed further in the supplementary material, ensuring that the output caption logically is properly formatted and logically entails the corresponding interaction." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 551, + 523, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 523, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 523, + 563 + ], + "type": "text", + "content": "3.3. Knowledge distillation for summarization" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": "Using the synthetic data generated in the previous stage, we fine-tune a smaller (220M-parameter) student T5 model, a sequence-to-sequence transformer network whose pretraining tasks include text summarization [52]. We use the synthetic captions (with the task prefix \"summarize:\") as input and the synthetic interactions of the target text for fine-tuning. Empirically, we find that our fine-tuned student model is able to summarize captions and output valid interactions even when the caption does not contain a verb or has a syntactic structure that the syntactic parsing-based method could not process." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "We apply this model to the captions in the Who's Waldo" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "2890" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 276, + 137 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 276, + 137 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 276, + 137 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 276, + 137 + ], + "type": "image", + "image_path": "7302b9ae82a6b3c9229501a79a33518b605625b14d1727d799933d88cf145af4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 142, + 285, + 153 + ], + "lines": [ + { + "bbox": [ + 55, + 142, + 285, + 153 + ], + "spans": [ + { + "bbox": [ + 55, + 142, + 285, + 153 + ], + "type": "text", + "content": "Synthetic caption generation with teacher LM and NLI filtering" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 90, + 413, + 133 + ], + "blocks": [ + { + "bbox": [ + 296, + 90, + 413, + 133 + ], + "lines": [ + { + "bbox": [ + 296, + 90, + 413, + 133 + ], + "spans": [ + { + "bbox": [ + 296, + 90, + 413, + 133 + ], + "type": "image", + "image_path": "4c857e58a313763fb53c5694bfc6bf76f9b7895c2c7c114f6801726083071d35.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 160, + 547, + 205 + ], + "lines": [ + { + "bbox": [ + 46, + 160, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 547, + 205 + ], + "type": "text", + "content": "Figure 3. LLM-Based HHI Extraction from Captions. We generate synthetic interaction-caption pairs via in-context learning (left), use them to fine-tune a summarization model (center), and then use this model to producing HHI pseudo-labels for captions in Who's Waldo (right), as detailed in Section 3. Captions are shown in red boxes, interaction texts in blue, and synthetic texts in italic letters. " + }, + { + "bbox": [ + 46, + 160, + 547, + 205 + ], + "type": "inline_equation", + "content": "\\mathrm{LM_T}" + }, + { + "bbox": [ + 46, + 160, + 547, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 160, + 547, + 205 + ], + "type": "inline_equation", + "content": "\\mathrm{LM_S}" + }, + { + "bbox": [ + 46, + 160, + 547, + 205 + ], + "type": "text", + "content": " indicate teacher and student language models respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 424, + 90, + 541, + 133 + ], + "blocks": [ + { + "bbox": [ + 311, + 142, + 399, + 153 + ], + "lines": [ + { + "bbox": [ + 311, + 142, + 399, + 153 + ], + "spans": [ + { + "bbox": [ + 311, + 142, + 399, + 153 + ], + "type": "text", + "content": "Fine-tuning student LM" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 424, + 90, + 541, + 133 + ], + "lines": [ + { + "bbox": [ + 424, + 90, + 541, + 133 + ], + "spans": [ + { + "bbox": [ + 424, + 90, + 541, + 133 + ], + "type": "image", + "image_path": "c103438fadcaeacfdcabf9fc49f0ff266e1e2a0d7fea79fdba7ab85e4686e8a5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 439, + 142, + 522, + 152 + ], + "lines": [ + { + "bbox": [ + 439, + 142, + 522, + 152 + ], + "spans": [ + { + "bbox": [ + 439, + 142, + 522, + 152 + ], + "type": "text", + "content": "Pseudo-label inference" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 225, + 287, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 287, + 249 + ], + "type": "text", + "content": "dataset to create pseudo-labels representing interactions as free text. See Figure 2 for examples of such pseudo-labels." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 257, + 149, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 257, + 149, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 257, + 149, + 269 + ], + "type": "text", + "content": "3.4. Our HHI dataset" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "content": "Using our learned abstractive summarization model, we may generate interaction pseudo-labels from Who's Waldo captions. Out of the " + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\sim 270k" + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "content": " samples in Who's Waldo, we use only those " + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\sim 130k" + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "content": " containing at least two human face detections, using the detections provided by Cui et al. [13]. We filter out duplicate and near-duplicate images, those with high similarity to test set images, and samples with pseudo-labels that do not pass a few simple text-based filtering rules, including enforcing the format of [NAME], followed by a present continuous verb (\"-ing\"), and including another [NAME] token. We are left with " + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\sim 126k" + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "content": " images with pseudo-labels in total, which we hereby refer to as pHHI." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 438, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 628 + ], + "type": "text", + "content": "The Waldo and Wenda Benchmark. We also create Waldo and " + }, + { + "bbox": [ + 46, + 438, + 287, + 628 + ], + "type": "inline_equation", + "content": "Wenda^3" + }, + { + "bbox": [ + 46, + 438, + 287, + 628 + ], + "type": "text", + "content": ", an HHI test set containing 1K manually curated image–interaction text pairs. In order to test generalization to HHI understanding across a wide variety of natural images, we include data from three sources: (1) 300 images from Who's Waldo, (2) 300 images from COCO Captions [11], (3) 400 images from Conceptual Captions [57]. The images are selected from the validation and test splits of the relevant datasets. As the distribution of HHI in natural photographs is highly imbalanced—for instance, images in captioning datasets often display people standing side by side and posing for photographs—we curate this test set to represent a wide variety of interactions and to reflect performance on the long tail of uncommon HHI. Examples of images from Waldo and Wenda can be seen in Figures 1, 2, and 4." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 637, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 637, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 637, + 287, + 685 + ], + "type": "text", + "content": "Dataset Statistics. Overall, our pHHI training dataset contains 126,696 pairs of images and pseudo-labels. These labels contain 1,263 unique verbs and 16,136 unique interactions. The majority of the images (59.3%) only contain two" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 224, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 224, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 545, + 285 + ], + "type": "text", + "content": "detected people, with less than " + }, + { + "bbox": [ + 306, + 224, + 545, + 285 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 306, + 224, + 545, + 285 + ], + "type": "text", + "content": " of the images containing more than six detected people. The Waldo and Wenda test set contains 1,000 images along with their manually written ground truth HHI labels. These include 238 unique verbs and 575 unique interaction labels." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 290, + 546, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 290, + 546, + 411 + ], + "spans": [ + { + "bbox": [ + 305, + 290, + 546, + 411 + ], + "type": "text", + "content": "Ethical considerations. Our dataset inherits a diverse representation of people (ages, ethnicities, geographic etc.) from the Who's Waldo dataset [13]. Furthermore, we use their provided name masking to mitigate biases (e.g., gender biases). We verify that all manually-curated test samples are neutral in nature and do not contain lurid or negative material. We perform similar verification on external test data, as described in Section 5, to avoid exposure to harmful or offensive behaviors. Furthermore, our pseudo-labels and test set will only be made available for academic purposes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 422, + 486, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 486, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 486, + 435 + ], + "type": "text", + "content": "4. Learning HHI from Still Images" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 545, + 502 + ], + "type": "text", + "content": "In the previous section, we demonstrated how we can obtain free text HHI pseudo-labels from the Internet captions of the Who's Waldo dataset [13]. We proceed to show how we use these to supervise learning HHI from still images via the paradigm of image captioning." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 510, + 416, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 510, + 416, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 510, + 416, + 521 + ], + "type": "text", + "content": "4.1. Models considered" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "text", + "content": "After obtaining a set of images and pseudo-labels, we consider the task of HHI in the framework of image captioning. Given (image, pseudo-label) pair " + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "inline_equation", + "content": "(I,L)" + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "text", + "content": ", we train an encoder-decoder network " + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "text", + "content": " to maximize the predicted conditional likelihood of " + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "text", + "content": " using a cross-entropy loss. During inference, we use autoregressive beam search decoding to generate text token by token, given " + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 528, + 545, + 611 + ], + "type": "text", + "content": " as input." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 612, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 612, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 612, + 545, + 647 + ], + "type": "text", + "content": "In order to evaluate the utility of transfer learning from general image captioning to our HHI understanding setting, we evaluate two choices for the model " + }, + { + "bbox": [ + 305, + 612, + 545, + 647 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 612, + 545, + 647 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 653, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 546, + 713 + ], + "type": "text", + "content": "(1) Vanilla encoder-decoder (EncDec). In this setting, we fine-tune a simple encoder-decoder model. We use the image encoder of pretrained CLIP-ViT [50], with its pooled embedding output followed by a single linear projection layer to match the hidden dimension of the decoder. For" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "3Wenda appears in the Where's Waldo? book series as Waldo's girlfriend." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2891" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 70, + 194, + 153 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 194, + 153 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 194, + 153 + ], + "spans": [ + { + "bbox": [ + 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person, during a ribbon cutting ceremony." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 312, + 194, + 406, + 205 + ], + "lines": [ + { + "bbox": [ + 312, + 194, + 406, + 205 + ], + "spans": [ + { + "bbox": [ + 312, + 194, + 406, + 205 + ], + "type": "inline_equation", + "content": "[\\star ]" + }, + { + "bbox": [ + 312, + 194, + 406, + 205 + ], + "type": "text", + "content": " performing with " + }, + { + "bbox": [ + 312, + 194, + 406, + 205 + ], + "type": "inline_equation", + "content": "[\\star ]" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 420, + 194, + 537, + 205 + ], + "lines": [ + { + "bbox": [ + 420, + 194, + 537, + 205 + ], + "spans": [ + { + "bbox": [ + 420, + 194, + 537, + 205 + ], + "type": "inline_equation", + "content": "[\\star]" + }, + { + "bbox": [ + 420, + 194, + 537, + 205 + ], + "type": "text", + "content": " cutting the ribbon with " + }, + { + "bbox": [ + 420, + 194, + 537, + 205 + ], + "type": "inline_equation", + "content": "[\\star]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 420, + 224, + 530, + 236 + ], + "lines": [ + { + "bbox": [ + 420, + 224, + 530, + 236 + ], + "spans": [ + { + "bbox": [ + 420, + 224, + 530, + 236 + ], + "type": "inline_equation", + "content": "[\\star]" + }, + { + "bbox": [ + 420, + 224, + 530, + 236 + ], + "type": "text", + "content": " cutting a ribbon with " + }, + { + "bbox": [ + 420, + 224, + 530, + 236 + ], + "type": "inline_equation", + "content": "[\\star]" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 240, + 547, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 547, + 307 + ], + "type": "text", + "content": "Figure 4. Results on the Waldo and Wenda test set. We compare results obtained by a baseline, our vanilla encoder-decoder technique (trained on our pHHI data), and the ground truth labels in Waldo and Wenda, with " + }, + { + "bbox": [ + 46, + 240, + 547, + 307 + ], + "type": "inline_equation", + "content": "[\\star]" + }, + { + "bbox": [ + 46, + 240, + 547, + 307 + ], + "type": "text", + "content": " denoting [NAME] tokens that represent person entities. As illustrated above, our method generates text describing the HHI depicted in the image, without attending to other irrelevant details. In comparison, the SOTA captioning model CLIPCap used as-is may not output an interaction at all (middle two images). We also observe that our model predicts HHI that may require both a verb and other arguments to adequately understand (leftmost and rightmost images)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 327, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 445 + ], + "type": "text", + "content": "the decoder we use pretrained GPT-2 [51] with a causal language modelling head and cross-attention over the encoder output. Consistent with previous works on fine-tuning vision-and-language models [38, 41, 78], we freeze the weights of the image encoder as we fine-tune it on our pHHI data. By considering this model that was not previously trained on image captioning, we aim to evaluate the extent to which our pHHI aid in learning to understand the semantics of HHI in images (rather than simply cueing a captioning model to the correct surface form of HHI labels)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 452, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 548 + ], + "type": "text", + "content": "(2) Fine-tuned captioner. The second approach we consider is to apply transfer learning to a SOTA captioning model by fine-tuning it on our pHHI data. Because the Conceptual Captions (CC) dataset is more people-centric than COCO and thus closer to our use case, we pick CLIPCap [41] pretrained on CC as the base model for fine-tuning. Consistent with CLIPCap's training method, we freeze its image encoder and fine-tune the model on our pHHI data." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 555, + 178, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 178, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 178, + 569 + ], + "type": "text", + "content": "4.2. Training and Decoding" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 574, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 622 + ], + "type": "text", + "content": "For all models, we use cross-entropy loss and consistent hyperparameter settings. For each model, we decode using beam search with 32 beams. We report metric values for the top 1, 5, and 8 beams." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 633, + 118, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 118, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 118, + 645 + ], + "type": "text", + "content": "5. Evaluation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 47, + 652, + 132, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 652, + 132, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 652, + 132, + 664 + ], + "type": "text", + "content": "5.1. Test Datasets" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 59, + 671, + 262, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 671, + 262, + 684 + ], + "spans": [ + { + "bbox": [ + 59, + 671, + 262, + 684 + ], + "type": "text", + "content": "We evaluate our models on the following datasets:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Waldo and Wenda. As detailed in Section 3.4, this consists of 1,000 images with manually-written ground truth labels." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 327, + 546, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 546, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 546, + 386 + ], + "type": "text", + "content": "Examples of ground truth labels along with model predictions can be seen in Figure 4. We report metric values averaged over the three data sources (Who's Waldo, Conceptual Captions, COCO) of Waldo and Wenda in Table 2. We also show a breakdown of data source in Table 3." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 390, + 546, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 546, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 546, + 582 + ], + "type": "text", + "content": "imSitu-HHI. We use an 8,021-sample subset of the imSitu [75] situation recognition benchmark, which we refer to as imSitu-HHI, to perform a large-scale evaluation of our models. Although imSitu does not contain free text HHI labels, it does contain categorical verb labels which can be used for comparison. Additionally, as the majority of images in imSitu do not depict HHI, we first filter for relevant samples as follows: We use person detections from YoloV5 [15] to select for images containing at least two humans. We further filter to select only samples with semantic frames containing at least two human participants. Finally, due to the noisy nature of this filtering, we only use verbs supported by at least 100 images in this filtered subset, as these verbs are most likely to describe HHI. We use these verb labels as the ground truth and evaluate predictions with the verb similarity metric as described below." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 587, + 429, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 429, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 429, + 601 + ], + "type": "text", + "content": "5.2. Baseline comparisons" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "type": "text", + "content": "We compare our approach to two types of SOTA model of that do not use our pHHI data as baselines:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "type": "text", + "content": "(1) Pretrained captioner. The first baseline approach that we test is the use of a SOTA model that has already been pretrained for image captioning. We test the recent captioning models ExpansionNet v2 (ENv2) [25] and CLIP-Cap [41]. We use these captioners as-is and evaluate our metrics on their outputs with beam search decoding. CLIP-Cap is available with pretrained weights for both COCO [11]" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2892" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "and Conceptual Captions (CC) [57], and thus we test both models. ENv2 only uses COCO weights." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 288, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 288, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 288, + 288 + ], + "type": "text", + "content": "(2) Pretrained situation recognition model. We provide a comparison to the results of the CoFormer model [12] for grounded situation recognition with pretrained weights. Unlike weakly-supervised models trained on our pseudolabels, which were generated from natural captions, CoFormer is supervised by training on the manually-labelled SWiG dataset [47], an extension of imSitu which includes grounding information for arguments that are visible in the accompanying images, and the model predicts the relevant verb, arguments, and grounding information given an image. We evaluate CoFormer by using its predicted verb, discarding semantic frame and grounding predictions since these semantic arguments do not directly map to the text of a human-human interaction string. See the supplementary material for details on how we insert its verb predictions into text prompts for metric calculations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 296, + 115, + 307 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 296, + 115, + 307 + ], + "spans": [ + { + "bbox": [ + 47, + 296, + 115, + 307 + ], + "type": "text", + "content": "5.3. Ablations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 315, + 287, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 287, + 398 + ], + "type": "text", + "content": "In order to ablate the effect of our pseudo-labelling, we also report results of a captioning model fine-tuned on the entire text of the captions provided in Who's Waldo (listed in 2 and 4 under training data as \"WW\"). In the supplementary material we also provide a detailed comparison with results when training directly on the syntactic parsing-based seeds described in Section 3.1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 406, + 105, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 105, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 105, + 418 + ], + "type": "text", + "content": "5.4. Metrics" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 425, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 496 + ], + "type": "text", + "content": "A number of metrics have been proposed for natural language generation tasks, measuring various aspects of text quality [24, 18]. As no prior works (to the best of our knowledge) predict HHI as free text, we propose a set of metrics that evaluate various relevant aspects of generated text:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 503, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 612 + ], + "type": "text", + "content": "Textual similarity. We use the BLEURT [55] metric to measure similarity to the ground truth interaction. This is a learned metric for text generation which measures similarity between the text output by a model and the reference text. Because our test set is relatively small and the reference texts are short, this better reflects textual similarity than ngram-based metrics such as BLEU [44] which have high variance and must be averaged over large datasets, as is shown in detail in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "Factual groundedness. A key property of generated text is whether it is consistent or contradictory with respect to the ground truth (such as a source document in the case of summarization, or a reference caption in the case of image captioning) [32]. This may be quantified by using the scores output by a natural language inference (NLI) model, in order to measure the degree of factual groundedness or hallucination in generated text [40, 33]. For example, given" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 544, + 355 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 544, + 355 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 544, + 355 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 544, + 355 + ], + "type": "table", + "html": "
MethodTrain DataBL↑pe↑pc↓sim↑
Results@1
CoFormerSWiG0.41*0.33*0.28*0.35
ENv2COCO0.270.250.330.41
CLIPCapCOCO0.280.340.370.42
CLIPCapCC0.270.180.380.35
CLIPCapCC+WW0.260.160.400.17
EncDecpHHI0.380.300.370.41
CLIPCapCC+pHHI0.420.410.320.46
Results@5
ENv2COCO0.310.390.190.46
CLIPCapCOCO0.310.470.240.46
CLIPCapCC0.330.320.200.47
CLIPCapCC+WW0.330.290.240.27
EncDecpHHI0.510.610.090.59
CLIPCapCC+pHHI0.570.710.070.65
Results@8
ENv2COCO0.320.430.170.48
CLIPCapCOCO0.320.500.210.46
CLIPCapCC0.350.360.160.49
CLIPCapCC+WW0.350.330.210.31
EncDecpHHI0.540.650.190.65
CLIPCapCC+pHHI0.590.760.040.69
", + "image_path": "6c359d34860ef4980534d51f905969a1f0d445e4ac209e17a1262f4806a8a386.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 306, + 358, + 537, + 378 + ], + "lines": [ + { + "bbox": [ + 306, + 358, + 537, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 537, + 378 + ], + "type": "text", + "content": "*Evaluated by using the best of two prompt templates for each item, as described in the supplementary material." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 305, + 382, + 545, + 471 + ], + "lines": [ + { + "bbox": [ + 305, + 382, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 305, + 382, + 545, + 471 + ], + "type": "text", + "content": "Table 2. Results on Waldo and Wenda. The listed metrics are BLEURT (BL) and NLI scores " + }, + { + "bbox": [ + 305, + 382, + 545, + 471 + ], + "type": "inline_equation", + "content": "(p_e, p_c)" + }, + { + "bbox": [ + 305, + 382, + 545, + 471 + ], + "type": "text", + "content": " and verb embedding similarity (sim). CC+WW/pHHI indicates models that were initialized with pretrained CC weights and subsequently fine-tuned on Who's Waldo captions or on pHHI respectively. Best results are in bold, and second best are underlined. Results are aggregated across the three data sources of Waldo and Wenda. For models using beam search, we report results for top 1, 5, and 8 beams." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "type": "text", + "content": "an image with ground truth label [NAME] sitting next to [NAME], the prediction [NAME] standing with [NAME] logically contradicts the reference label and thus is a factual hallucination. To measure this, we use scores " + }, + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "type": "inline_equation", + "content": "(p_e, p_c)" + }, + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "type": "text", + "content": " from a pretrained NLI model to estimate the factual groundedness of the predicted text, where " + }, + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "type": "inline_equation", + "content": "p_e" + }, + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "type": "text", + "content": " is the probability of entailment and " + }, + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "type": "inline_equation", + "content": "p_c" + }, + { + "bbox": [ + 305, + 486, + 545, + 630 + ], + "type": "text", + "content": " is the probability of contradiction. We treat the image caption from Waldo and Wenda as the premise and the model's prediction as the hypothesis for NLI inference. For test items sourced from COCO Captions, in which images correspond to multiple reference captions, we use the first reference as the premise for this calculation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": "Verb similarity. We calculate the average cosine similarity of the predicted and ground truth verbs in GloVe [46] embedding space. The motivation for this metric is that a prediction may be valid or nearly valid even if it is not identical to the ground truth label as long as the semantic distance between the verbs is small (e.g. \"hugging\" vs. \"embracing\")." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2893" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 537, + 371 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 537, + 371 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 537, + 371 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 537, + 371 + ], + "type": "table", + "html": "
MethodTrain DataWWCCCOCO
BL↑pe↑pc↓sim↑BL↑pe↑pc↓sim↑BL↑pe↑pc↓sim↑
Results@1
CoFormerSWiG0.40*0.29*0.35*0.340.45*0.40*0.43*0.380.37*0.30*0.33*0.33
Env2COCO0.240.200.280.380.260.200.450.410.310.360.260.45
CLIPCapCOCO0.270.370.350.390.260.260.430.430.310.380.330.44
CLIPCapCC0.300.240.420.360.250.180.380.400.260.110.340.30
CLIPCapCC+WW0.280.120.590.270.260.210.340.150.230.150.280.10
EncDecpHHI0.410.380.300.420.380.300.440.420.340.220.360.38
CLIPCapCC+pHHI0.420.380.330.450.440.440.330.470.400.400.300.47
Results@5
Env2COCO0.280.300.170.420.300.320.280.460.350.550.120.51
CLIPCapCOCO0.310.500.210.420.290.380.280.460.340.520.230.49
CLIPCapCC0.360.410.230.460.300.310.230.500.320.230.140.43
CLIPCapCC+WW0.330.200.500.330.340.370.130.280.330.310.090.20
EncDecpHHI0.550.610.110.630.510.650.100.590.460.560.070.56
CLIPCapCC+pHHI0.570.640.100.640.600.750.060.680.530.740.050.63
Results@8
Env2COCO0.290.340.150.420.310.350.250.480.360.590.100.53
Env2COCO0.320.530.180.430.300.410.250.470.350.550.210.50
CLIPCapCC0.380.470.170.480.320.350.190.530.340.260.110.45
CLIPCapCC+WW0.340.220.480.350.360.420.100.330.350.340.060.25
EncDecpHHI0.600.690.060.690.550.720.050.640.500.660.040.61
CLIPCapCC+pHHI0.600.700.070.680.630.810.030.720.550.780.030.67
", + "image_path": "cb034aa140e3bf0c7593f9396a968706b4680281fb3072bf682fb0bd447baca5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 48, + 374, + 408, + 384 + ], + "lines": [ + { + "bbox": [ + 48, + 374, + 408, + 384 + ], + "spans": [ + { + "bbox": [ + 48, + 374, + 408, + 384 + ], + "type": "text", + "content": "*Evaluated by using the best of two prompt templates for each item, as described in the supplementary material." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 48, + 389, + 545, + 411 + ], + "lines": [ + { + "bbox": [ + 48, + 389, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 48, + 389, + 545, + 411 + ], + "type": "text", + "content": "Table 3. Results on Waldo and Wenda split by data source - Who's Waldo (WW), Conceptual Captions (CC), and COCO Captions. For models using beam search, we report results for top 1, 5, and 8 beams." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 423, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 423, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 48, + 423, + 287, + 483 + ], + "type": "text", + "content": "To evaluate this on free text predictions, we either select the first non-[NAME] word in the output (for models trained on pHHI) or extract its first verb using a syntactic parsing model. If syntactic parsing does not yield a verb, the zero vector is used as the given embedding." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 491, + 175, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 491, + 175, + 502 + ], + "spans": [ + { + "bbox": [ + 48, + 491, + 175, + 502 + ], + "type": "text", + "content": "5.5. Results and Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 510, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 510, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 48, + 510, + 287, + 641 + ], + "type": "text", + "content": "For Waldo and Wenda, we report all of the metrics described above. For imSitu-HHI, we only use the verb similarity metric since the ground truth label is a single verb. We report average similarity over all samples in imSitu-HHI as well as displaying averages for the most-supported verbs. See Tables 2-4 for quantitative results, and see Figure 4 for a visual comparison on Waldo and Wenda. Note that we do not include CoFormer in the table of imSitu-HHI results since it was trained directly on some of these items; see the supplementary material for analysis of CoFormer on indistribution and out-of-distribution images in imSitu-HHI." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 48, + 642, + 287, + 713 + ], + "type": "text", + "content": "Overall we see that training on our pseudo-labels improves performance on our benchmarks. In Tables 2 and 3, showing results on Waldo and Wenda, the best-performing model by all metrics is CLIPCap fine-tuned with our pseudo-labels. This holds across data sources, as seen in Table 3, showing that this improvement general-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 423, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 423, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 307, + 423, + 545, + 530 + ], + "type": "text", + "content": "izes to images beyond those originating in the Who's Waldo dataset. This model is also the best-performing on average and across a majority of verb categories on imSitu-HHI as seen in Table 4. Qualitative comparison shows that the captioning models used as-is output text that is far from the ground truth HHI labels, containing many irrelevant details and not necessarily describing an interaction. This can be seen in Figure 4, where the CLIPCap (CC) captions contain many hallucinated, non-factual details." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 533, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 533, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 307, + 533, + 545, + 675 + ], + "type": "text", + "content": "While transfer learning with pretrained CLIPCap yields the best results, we also observe that the vanilla Encoder-Decoder fine-tuned on our pseudo-labels also performs well, achieving the second-best BLEURT score on Waldo and Wenda and second-best verbal similarity metrics overall and across many verb categories on imSitu-HHI. We infer that our pseudo-labels do impart semantic knowledge of HHI beyond simply cueing existing captioning models to the surface form of HHI labels. Nevertheless, CLIPCap fine-tuned on pHHI does generalize better across the data from all sources in Waldo and Wenda and to imSitu-HHI which is entirely out-of-distribution for this model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 677, + 545, + 712 + ], + "type": "text", + "content": "We also note that the metrics improve dramatically for both datasets when considering 5 or 8 beams. This is consistent with the fact that beam search using models fine-tuned" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 757 + ], + "type": "text", + "content": "2894" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 69, + 547, + 388 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 547, + 388 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 547, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 547, + 388 + ], + "type": "table", + "html": "
Average sim.socializingdistributingteachingcommunicatinginterviewinglecturingtrainingprovidinginstructinggivingpushinghelpingaskingcoachingtalking
Results@1
ENv2COCO0.220.190.070.220.210.280.190.250.260.110.450.380.290.440.280.28
CLIPCapCOCO0.230.180.070.260.240.290.170.260.240.100.440.360.250.460.300.63
CLIPCapCC0.270.160.250.370.260.210.230.280.350.160.460.310.370.380.260.53
CLIPCapCC+WW0.090.020.080.120.050.300.080.100.090.060.250.070.090.110.050.08
EncDecpHHI0.280.190.210.340.270.230.240.350.380.170.600.360.340.460.760.64
CLIPCapCC+pHHI0.320.210.250.560.330.270.300.430.440.190.660.380.440.460.650.70
Results@5
ENv2COCO0.260.210.100.260.230.300.210.270.310.130.490.450.350.490.330.31
CLIPCapCOCO0.250.190.090.290.260.310.200.270.260.120.470.410.290.480.320.66
CLIPCapCC0.350.210.300.480.330.280.310.370.430.210.560.420.480.470.310.64
CLIPCapCC+WW0.180.050.150.220.140.600.160.170.220.110.460.150.210.220.150.24
EncDecpHHI0.400.300.350.490.410.390.330.510.510.230.790.470.490.570.920.86
CLIPCapCC+pHHI0.440.290.350.850.440.410.400.560.560.270.880.480.560.580.860.92
Results@8
ENv2COCO0.280.220.120.270.240.300.210.280.320.130.510.470.370.500.350.34
CLIPCapCOCO0.260.200.100.310.270.310.210.280.260.120.480.430.310.490.320.67
CLIPCapCC0.370.230.310.510.340.310.320.400.450.220.590.450.510.490.320.70
CLIPCapCC+WW0.210.060.160.250.160.620.160.200.240.120.510.200.230.260.180.32
EncDecpHHI0.440.330.380.550.440.420.340.540.560.250.850.490.560.590.940.91
CLIPCapCC+pHHI0.470.330.370.900.460.410.430.600.590.290.920.500.590.610.910.96
", + "image_path": "22cbd1c7521062af0b282104a46f6c757c35378a9d23d85f3e3c1421c4a6c1a8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 392, + 545, + 426 + ], + "lines": [ + { + "bbox": [ + 47, + 392, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 545, + 426 + ], + "type": "text", + "content": "Table 4. Results on imSitu-HHI. In addition to the average verb embedding similarity between predicted verbs and the ground truth verb, we also present mean similarities for the most common 15 verbs in imSitu-HHI. Best results are in bold, and second best are underlined. For models using beam search, we report results for top 1, 5, and 8 beams." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 445, + 288, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 288, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 288, + 506 + ], + "type": "text", + "content": "on pHHI outputs a list of diverse candidate interactions, allowing a more directed search in the space of HHI descriptors, while beam search applied to captioning models as-is tends to produce many slight variations of the same long caption." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 522, + 119, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 119, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 119, + 534 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 544, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 663 + ], + "type": "text", + "content": "We present a new framework for learning to understand human-human interactions in still images using weak supervision from textual captions. We demonstrate the use of knowledge distillation applied to a large language model without explicit supervision to produce pseudo-labels that can serve as targets for predicting interactions as free text. We show that training on these pseudo-labels enables HHI understanding beyond that of SOTA captioning and situation recognition models, and we provide the Waldo and Wenda as a new benchmark for this task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "There are various avenues for future research to extend our work. One possible direction is the incorporation of visual grounding into HHI understanding. We predict the most salient interaction in an image, which we assume to" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "type": "text", + "content": "be the interaction the one that is described or suggested in its accompanying caption. It remains to localize the participants, including generalizing to group interactions where more than two participants are visible. Another important aspect that remains to be explored is the hierarchical nature of interactions. For example, the generic HHI label \"meeting\" is valid for almost every image, while \"shaking hands\" is more specific and valid for a subset of those images. Further research could extend our results to hierarchical prediction of multiple HHI labels for a single image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 565, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 565, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 565, + 545, + 673 + ], + "type": "text", + "content": "Finally, we note the importance of style-content disentanglement in HHI prediction, which our work does not explicitly consider. Scene cues in images can be important for correctly identifying HHI, as illustrated in Figure 1, but also may be misleading. For instance, an image of soldiers in uniform is more likely to depict \"saluting\", but HHI is only valid if the image actually contains a salute. Future work on disentangling style and content shows promise for improving the robustness of HHI understanding models." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": "Acknowledgements. We thank Ron Mokady for providing helpful feedback. This work was supported by a research gift from Meta and the Alon fellowship." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "2895" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Stanislaw Antol, C Lawrence Zitnick, and Devi Parikh. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11825-11834, 2021." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "text", + "content": "2899" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_content_list.json b/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..443fa0f14f9e94e517683fbfe44f4ea0126a2d87 --- /dev/null +++ b/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_content_list.json @@ -0,0 +1,1798 @@ +[ + { + "type": "text", + "text": "Learning Image Harmonization in the Linear Color Space", + "text_level": 1, + "bbox": [ + 191, + 130, + 779, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ke Xu, Gerhard Petrus Hancke, Rynson W.H. Lau \nCity University of Hong Kong", + "bbox": [ + 274, + 181, + 694, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{kkangwing, gp.hancke, rynson.lau}@cityu.edu.hk", + "bbox": [ + 276, + 219, + 692, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Harmonizing cut-and-paste images into perceptually realistic ones is challenging, as it requires a full understanding of the discrepancies between the background of the target image and the inserted object. Existing methods mainly adjust the appearances of the inserted object via pixel-level manipulations. They are not effective in correcting color discrepancy caused by different scene illuminations and the image formation processes. We note that image colors are essentially camera ISP projection of the scene radiance. If we can trace the image colors back to the radiance field, we may be able to model the scene illumination and harmonize the discrepancy better. In this paper, we propose a novel neural approach to harmonize the image colors in a camera-independent color space, in which color values are proportional to the scene radiance. To this end, we propose a novel image unprocessing module to estimate an intermediate high dynamic range version of the object to be inserted. We then propose a novel color harmonization module that harmonizes the colors of the inserted object by querying the estimated scene radiance and re-rendering the harmonized object in the output color space. Extensive experiments demonstrate that our method outperforms the state-of-the-art approaches.", + "bbox": [ + 76, + 301, + 473, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 662, + 209, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image compositing is a common process in vision and graphics. It is a technique to render a novel image by inserting a target object from the source image onto a target image. However, humans can easily identify this cut-and-paste (or composite) image as a synthetic one due to its color [7] and texture inconsistencies [31, 63]. Hence, there is a line of research to develop algorithms to harmonize cut-and-paste images to produce visually realistic output images.", + "bbox": [ + 75, + 689, + 468, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing image harmonization methods typically fall into two categories, i.e., non-deep learning-based methods [42, 10, 47, 58, 63] and deep learning-based methods [48, 13, 8, 12, 33, 21, 27, 20]. Non-deep learning based methods try to manipulate low-level image statistics (e.g., textures [47] and colors [42, 63, 58]) of the inserted ob", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f85ad6aa87af3675c826ba9f5fcff3dc6dcfb3ef13b2725491cb133eaeb19fb2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 267, + 633, + 342 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6fb0621fb08c6fce764943a3cc6d2bcf934610d955d4a3b0a84f1efa93fcf3ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 267, + 758, + 342 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5819487f83eed624bd07b7c491cd99856602fcbbabcf64a51e312b9e6ae393bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 267, + 885, + 342 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ea02a3bb8ed9838e180898a437efc31c64a708990b5705402bce512e80dfa564.jpg", + "image_caption": [ + "(a) Input" + ], + "image_footnote": [], + "bbox": [ + 506, + 358, + 633, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ae9da93e95a9e1c60b92a1524acec14201e0597e958aa6162ca8a34d118c3a8d.jpg", + "image_caption": [ + "(b) IIH [21]" + ], + "image_footnote": [], + "bbox": [ + 635, + 358, + 758, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2ac4531abb925b297e9808aa35fe0cfaf1ab476c71675026b4b32b2883088d2f.jpg", + "image_caption": [ + "(c) CDT [11]" + ], + "image_footnote": [], + "bbox": [ + 759, + 358, + 885, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/95751c73fd1a12e148a54b628abfc732048c0d99e3381dae1979c847948df52b.jpg", + "image_caption": [ + "(d) WBH [29]" + ], + "image_footnote": [], + "bbox": [ + 506, + 449, + 633, + 523 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c0199ba1b6ab2392cb404bfa2e2b21ed74f3af843e67e99a59e02fac2e8d2181.jpg", + "image_caption": [ + "(e) Ours" + ], + "image_footnote": [], + "bbox": [ + 635, + 449, + 758, + 523 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8ff7878fa73cf0c84e86c755a098b677b01aaaaa35b0d238c50633f446e797a3.jpg", + "image_caption": [ + "(f) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 759, + 449, + 885, + 523 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f5b381a2c2bbd8368f75b9e6bd14fa0d60cdbb59cb962d31ad3e4dcc30619f2f.jpg", + "image_caption": [ + "(g) Input", + "(j) WBH [29]", + "Figure 1. Harmonization results on the iHarmony4 dataset [12]. Existing harmonization methods tend to produce dull (b-d) or inconsistent (h-j) colors. Our method traces back to and harmonizes the colors in an intermediate linear color space, resulting in more realistic composite images as shown in (e) and (k)." + ], + "image_footnote": [], + "bbox": [ + 506, + 540, + 633, + 614 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/85c5ed936f4bed5e921f5a132c574cef7547829283b4a1bbea70d5f676c0f02d.jpg", + "image_caption": [ + "(h) IIH [21]", + "(k) Ours" + ], + "image_footnote": [], + "bbox": [ + 635, + 540, + 758, + 614 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/579de76c75f0dddcb81d50d7df09e58c1db2f09e7378f25ce28793bfa5477f9c.jpg", + "image_caption": [ + "(i)CDT [11]", + "(1) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 759, + 540, + 885, + 614 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ject, to match with those of the background. These methods often produce unrealistic images of inconsistent colors/textures when the hand-crafted features fail to represent the foreground/background. In contrast, deep learning based methods offer strong capability of modelling region appearances to facilitate harmonization. Some methods explore different priors (e.g., semantics [48], and gradient/color consistency [8, 53]) to constrain the harmonization process. Some other methods [12, 33, 21] may formulate the image harmonization process as a foreground-background transfer learning task.", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12570", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite their success, existing harmonization methods may still produce pale (Figure 1(b-d)) or inconsistent colors (Figure 1(h-j)) across the foreground and background regions, resulting in visually unpleasant images. We note that all these methods model the color harmonization process in the camera output sRGB (i.e., low dynamic range) color space. However, object colors in an image are determined not only by their material reflectance and scene illumination, but also by the black-box imaging pipeline (ISP) of the camera. Due to the non-linear operations (e.g., tone mapping) within the ISP, pixel intensities of camera output sRGB images are not proportional to the scene radiance, making them unreliable for use in estimating the scene illumination for color harmonization.", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this problem, we propose in this paper a novel approach to harmonize a cut-and-paste image (captured in low dynamic range) in the high dynamic range domain. Our key idea is to harmonize the scene illumination discrepancies in an intermediate (high dynamic range) color space, in which the scene illumination is proportional to the original scene radiance. To this end, we propose a novel neural network that first converts the source image (containing the target object) into an intermediate high dynamic range domain, then performs the harmonization process, and finally converts the harmonized image back to the low dynamic range sRGB space. To avoid exhaustive modeling of camera-dependent operations, we propose a novel image unprocessing module to estimate a high dynamic range version of the input image in the linear camera-independent CIE XYZ color space. We formulate this image unprocessing process as a diffusion process. We propose a novel color harmonization method that models image colors in the estimated linear color space to produce the final harmonized results. As shown in Figure 1(e,k), our method is able to produce more visually pleasing results. We conduct extensive experiments to demonstrate that our method outperforms state-of-the-art harmonization approaches.", + "bbox": [ + 75, + 301, + 472, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, this paper has three main contributions:", + "bbox": [ + 96, + 651, + 442, + 666 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel neural approach for image harmonization that performs the color harmonization process in the linear color space, allowing object color modeling based on faithful scene radiance.", + "- Our approach includes two novel modules: (1) a novel image unprocessing module to convert the source image (of the target object) into a version in the high dynamic range linear color space, and (2) a novel color harmonization module to harmonize object colors by querying scene radiance information and re-render the harmonized objects in the output color space.", + "- Extensive experiments show that the proposed method outperforms state-of-the-art harmonization methods." + ], + "bbox": [ + 94, + 680, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Harmonization aims to adjust the appearance of the foreground object so that it is compatible with the new composite background. Traditional methods [42, 10, 31, 47, 58, 63] typically rely on adjusting the appearance of the foreground to match with the color statistics of the background. Sunkavalli et al. [47] propose to first transfer the visual appearance of the target image to the source image via image histogram matching, and then use alpha blending to produce the composite image. Xue et al. [58] suggest to match zones of the (instead complete) histogram is more effective, and propose the zone selection classifier for matching. Reinhard et al. [42] propose a color transfer method to match the global color statistics between the source and target images. Lalonde and Efros [31] divide the source and target images into corresponding cluster pairs, and perform the color transfer [42] for each cluster pair locally.", + "bbox": [ + 496, + 114, + 893, + 356 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, many deep methods are proposed for image harmonization. Zhu et al. [63] propose to train a CNN classifier to distinguish between real and composite images, and use the learned model to adjust the brightness and contrast model for image composition. Tsai et al. [48] present the first end-to-end CNN-based harmonization method to leverage the semantic information of a scene parsing branch to help boost the performance of the harmonization branch. Cun and Pun [13] propose to use spatial attention modules to learn regional appearance changes for harmonization. Chen and Mae [8] propose a GAN-based method to harmonize images with geometric and color consistency constraints. Wu et al. [53] propose a GAN-based method to explore both gradient and color constraints for image harmonization. Cong et al. [12] construct a large-scale dataset, iHarmony4, and propose a domain verification discriminator to guide the generator to translate the foreground object to the background domain. Ling et al. [33] formulate the image harmonization task as a style transfer problem, and propose the region-aware adaptive instance normalization module to model the background style and apply it to the foreground. Guo et al. [21] propose to decompose the composite image into reflectance and illumination, and harmonize the two via material consistency and light transfer. Self-supervised learning and transformers have also been applied to image harmonization in [27] and [20], respectively. Methods are also proposed for high-resolution image harmonization [11, 32, 29, 57], multiple objects harmonization [44] and interactive portrait harmonization [49].", + "bbox": [ + 496, + 357, + 893, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unlike existing methods that harmonize colors in the low dynamic range image domain, we propose to model and harmonize these object colors by tracing back to the high dynamic range scene radiance field.", + "bbox": [ + 496, + 795, + 893, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Enhancement aims to produce visually pleasing images with vivid colors and details from low-quality input images of over- or under-exposures. Some meth", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12571", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/dc931499e6e50c72e15c95c3bbfa3b0670d34fc174c284c4fa25a7f440ee5550.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed method. Given an input composite image, we first convert it into an intermediate linear color space via the image unprocessing process. The Color Harmonization process then harmonizes the foreground colors in the feature domain, and renders the harmonized colors to produce an output sRGB image with the guidance of the background preserving process." + ], + "image_footnote": [], + "bbox": [ + 102, + 90, + 861, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ods [19, 17, 5, 51, 45, 36, 54] rely on the retinax theory to decompose the input image into reflectance and illumination layers, and enhance the illumination layer. Cai et al. [6] separately model illuminance and detail layers from multi-exposed images to enhance an under-exposed image. Xu et al. [56] decompose and enhance under-exposed images based on frequency information. Moran et al. [38] learn a set of local parametric filters for image enhancement. Some methods directly learn an image-to-image mapping using high dynamic range information [18, 59, 46] or adversarial learning [25, 9, 26, 43]. Mahmoud et al. [2] propose a coarse-to-fine network to learn color and detail enhancement for addressing over- or under-exposure. Recently, Wang et al. [50] build a local color distributions pyramid with a dual-illumination estimation method to handle images of both over-/under-exposures.", + "bbox": [ + 75, + 337, + 472, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While sharing some similarities with image harmonization methods, e.g., pixel-wise curve modeling and retina-based image decomposition, image enhancement methods do not model the discrepancy between source and target scenes. Directly enhancing composite images with image enhancement methods tends to amplify scene discrepancies.", + "bbox": [ + 75, + 580, + 470, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 686, + 250, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose to harmonize cut-and-paste object colors by tracing back them to the scene radiance field. To this end, we propose an image unprocessing method to transfer the input composite image into a linear high dynamic range color space, and a harmonization method to re-render the target object colors by querying the scene radiance information. Figure 2 shows the whole harmonization process.", + "bbox": [ + 75, + 713, + 468, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Image Unprocessing", + "text_level": 1, + "bbox": [ + 76, + 830, + 272, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Converting camera output sRGB images back to camera raw images, i.e., image unprocessing [60, 39, 40, 3, 55, 41], requires a systematic modelling of the ISP operations. Ex-", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "isting methods are typically sensor-specific, requiring additional camera information to convert each image. We note that most camera ISPs typically apply a set of camera-variant linear operations (e.g., white balance) to convert CCD data into a camera-independent color space, and then apply another set of non-linear operations (e.g., quantization and local enhancement) to render images [28]. Hence, converting the sRGB images back into the intermediate camera-independent color space has two advantages for harmonization. First, colors in this intermediate space response to the scene radiance linearly, which helps recover scene discrepancy for harmonization. Second, it avoids the need to model camera-dependent operations (e.g., camera response curves selection [16] or estimation [46]). We formulate a generative diffusion model to address this dynamic range expansion problem of image unprocessing. Although single-image reverse tone mapping is challenging (as it needs to generate missing info in the over-/underexposed regions), learning such image unprocessing in our task is feasible, as images to be harmonized are typically captured with proper exposures.", + "bbox": [ + 496, + 337, + 893, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Model Formulation. A diffusion model has a forward diffusion process and a reverse denoising process (used for generation). Given a distribution $q(x_0)$ , the forward diffusion process $q$ is a Markovian noisig process [23], which gradually adds noise to $x_0$ to obtain $x_{1:T}$ . Specifically, at each step $t$ , the diffusion process adds random Gaussian noise with a $\\beta_t$ -controlled variance:", + "bbox": [ + 496, + 672, + 893, + 780 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {1: T} \\mid x _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(x _ {t} \\mid x _ {t - 1}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 792, + 890, + 834 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq (x _ {t} | x _ {t - 1}) = \\mathcal {N} \\left(x _ {t}; \\sqrt {1 - \\beta_ {t}} x _ {t - 1}, \\beta_ {t} \\mathbb {I}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 837, + 890, + 857 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\beta_{t} \\in (0,1), t = 1, \\dots, T$ . With the reparameterization trick [30], we sample $x_{t}$ from each time step $t$ in a closed", + "bbox": [ + 496, + 869, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12572", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5c9df94b7360647e13cc5d15a81864cba294f34512345aaa45f2ae8aec0bf0e4.jpg", + "image_caption": [ + "Figure 3. The feature harmonization process. Given the concatenated linear foreground and background features $f = [F_{f}, F_{b}]$ , it first uses an SE block [24] to adjust the attention for each channel to be the same, and then propagates channel consistency to the spatial domain to produce harmonized foreground features $f_{h}$ ." + ], + "image_footnote": [], + "bbox": [ + 122, + 92, + 851, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "form: $x_{t} = \\sqrt{\\bar{\\alpha}_{t}} x_{0} + \\sqrt{1 - \\bar{\\alpha}_{t}}\\epsilon ,\\epsilon \\sim \\mathcal{N}(0,\\mathbb{I})$", + "bbox": [ + 76, + 362, + 382, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbb {I}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 388, + 468, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = 1 - \\beta_{t}$ and $\\bar{\\alpha}_{t} = \\prod_{i = 1}^{t}\\alpha_{i}$ . In this way, we directly derive $x_{t}$ from $q(x_{t}|x_{0})$ without repeatedly applying the Markovian process $q$ and calculating $q(x_{t}|x_{t - 1})$ .", + "bbox": [ + 76, + 416, + 468, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We formulate image unprocessing as a reverse denoising process (i.e., generation process) that is conditioned on the sRGB input image $I_{in}$ . We compute $x_0$ (i.e., the linear color image $I_l$ ) via the reverse diffusion process $p_\\theta(x_{t-1}|x_t)$ parameterized by $\\theta$ with a random Gaussian distribution, i.e., $x_T \\sim \\mathcal{N}(0,\\mathbb{I})$ , as:", + "bbox": [ + 76, + 463, + 468, + 553 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(x _ {0: T} \\mid I _ {i n}\\right) = p \\left(x _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}, I _ {i n}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 564, + 468, + 606 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}, I _ {i n}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, I _ {i n}, t\\right), \\sum_ {\\theta} \\left(x _ {t}, I _ {i n}, t\\right)\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 616, + 468, + 646 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unlike previous methods that are conditioned on the class labels [14] or shape latents [35], we condition the diffusion process on the sRGB image $I_{in}$ pixel-wisely.", + "bbox": [ + 76, + 647, + 468, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model Architecture. Our image unprocessing model adopts a fully convolutional encoder-decoder network [34], as shown in Figure 2(left). Given the sampled noise with the sRGB image as the condition, we encode them into a low dimensional latent representation, which is then decoded to reconstruct the linear color image. We leverage the generation ability of reversing the denoising process to expand the dynamic range, and use the encoder-decoder architecture to perform image unprocessing. To facilitate the learning process, we add a skip connection directly from the input image to the output. Instead of learning to generate the linear color image of the whole dynamic range, the image unprocessing network only needs to generate the difference between", + "bbox": [ + 76, + 703, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the input and the output, resulting in a fast reverse diffusion process. We train this network from scratch and use batch normalization and GELU activation for all the convolutional layers. We use the weighted variational bound [23] to optimize this model.", + "bbox": [ + 496, + 362, + 890, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Harmonization and Rendering", + "text_level": 1, + "bbox": [ + 500, + 469, + 772, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose a harmonization module to harmonize the colors of the target object by querying background radiance information and re-render the harmonized image in the sRGB space.", + "bbox": [ + 496, + 500, + 890, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Harmonization in Linear Space. As shown in Figure 2(right), given the reconstructed linear color image $I_{l}$ we first separately obtain foreground and background features (i.e., $F_{f}$ and $F_{b}$ ) via two separate encoders and the foreground mask $M$ , as $F_{f} = \\text{Enc}_{f}(I_{l} * M)$ and $F_{b} = \\text{Enc}_{b}(I_{l} * (1 - M))$ . Our goal is to harmonize the foreground features $F_{f}$ based on $F_{b}$ to obtain $\\hat{F}_{f}$ , and then render the harmonized foreground features $\\hat{F}_{f}$ into the sRGB space $\\hat{F}_{f} \\rightarrow \\hat{I}_{f}$ conditioned on the rendering process of $F_{b} \\rightarrow I_{b}$ . To this end, we harmonize the concatenated features $f = [F_{f}, F_{b}]$ in both channel and spatial dimensions. We implement the channel harmonization by using the squeeze-and-excitation operation [24] to assign consistent attention for each channel of $f = [F_{f}, F_{b}]$ . As the reweighed features are computed channel-wisely according to both foreground and background representations, the consistent attention indicates that these representations are harmonized to be consistent as well. We then propagate channel harmonization to the spatial domain via the bilat-", + "bbox": [ + 496, + 609, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12573", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/db618b9a860c212475127789a542c6ba3c7ce0fe783feb7fe16f94b771740a59.jpg", + "image_caption": [ + "(a) Input", + "(b) IIH [21]", + "(c) CDT [11]", + "(d) WBH [29]", + "(e) Ours", + "(f) Ground Truth", + "Figure 4. Visual comparison on composite images with humans. The proposed method is able to harmonize the colors in the cut-and-paste regions and produce realistic images compared with the state-of-the-art methods." + ], + "image_footnote": [], + "bbox": [ + 89, + 85, + 883, + 433 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "eral propagation activation functions:", + "bbox": [ + 76, + 489, + 323, + 505 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny _ {i} ^ {s} = \\frac {1}{C (f)} \\sum_ {j \\in s} g (\\| j - i \\|) f _ {j}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 525, + 468, + 563 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny _ {i} ^ {r} = \\frac {1}{C (f)} \\sum_ {j \\in v} h \\left(f _ {i}, f _ {j}\\right) f _ {j}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 565, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny _ {i} = c \\left(y _ {i} ^ {s}, y _ {i} ^ {r}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 604, + 468, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{i}$ is the feature channel at position $i$ of the input features $f$ . $f_{j}$ is a neighboring feature channel around $i$ at position $j$ . $y_{i}^{s}$ and $y_{i}^{r}$ are the features after spatial and range similarity measurements. The normalization factor is set to $C(f) = N$ , where $N$ is the number of positions in $f$ . $c$ represents the pixel-wise summation and a linear transformation of $y_{i}^{s}$ and $y_{i}^{r}$ via a $1 \\times 1$ convolutional layer. The bilateral propagation extends the consistency of feature channels to both spatial and range dimensions. In spatial propagation, we set the neighboring region $s$ to be of the same spatial resolution as the input features for global propagation. A Gaussian function $g(\\cdot)$ [52] is used to compute the spatial contributions from neighboring background features. In range propagation, we measure the similarity between features $f_{i}$ and $f_{j}$ via $h(\\cdot)$ within a neighboring region $v$ around $i$ . The size of $v$ is set to $3 \\times 3$ . The range similarity is computed via the pairwise function $h(\\cdot)$ with a", + "bbox": [ + 75, + 643, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "dot product operation:", + "bbox": [ + 500, + 489, + 650, + 503 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nh \\left(f _ {i}, f _ {j}\\right) = \\left(f _ {i}\\right) ^ {T} \\left(f _ {j}\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 513, + 890, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this way, the bilateral propagation process harmonizes the foreground colors by considering both global continuity via $y_{i}^{s}$ and local consistency via $y_{i}^{r}$ . Figure 3 shows the feature harmonization process.", + "bbox": [ + 496, + 541, + 890, + 601 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our bilateral propagation is close in spirit to the nonlocal block [52], in that for each $i$ , $\\frac{1}{C(f)}\\sum g(f_i,f_j)$ computes the softmax scores along dimension $j$ . The main difference is the regions of propagation. The non-local block uses feature channels from all positions to generate $y_{i}$ and the similarity is only measured between $f_{i}$ and $f_{j}$ . In contrast, our method considers channel similarity, long-range and neighboring spatial correlations between $f_{i}$ and $f_{j}$ for feature harmonization. During the long-range correlation modeling, we query the global scene radiance information using region $s$ of the original background features (i.e., before the channel-wise harmonization), while during the neighboring correlation modeling, we query the local scene information using the background features after channelwise adjustment. The foreground colors are then set to be consistent to the background both globally and locally.", + "bbox": [ + 496, + 602, + 892, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Background Preserving Guided Rendering. After the harmonization process in the linear embedding space, we assign a decoder to re-project the harmonized linear image", + "bbox": [ + 496, + 854, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12574", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/12a30c7e42593860ecc2f1aa4d50b923fd62db57577e3bef32362c1a92f7448b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 88, + 222, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c17d9e06c4f407f4449283dd347eee6d44e48496a7f4d72dec8913b03f48af10.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 222, + 88, + 352, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d3b5f0571314a43748ffd0529ab1078e27fe81f0b758f4d4e70618e7be624638.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 88, + 483, + 162 + ], + "page_idx": 5 + }, + { + "type": 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+ "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ead985a81d31ee7846d4cf8b74a9371f3e46b4c2afc91c2aa4e1b1c8cf344445.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 251, + 746, + 327 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/692fd09a30041e7239536c11819460f0efd0f9843ceab04b325aaf61bff71837.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 251, + 879, + 327 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b8c3e3c11cb5922d5054b9aa19fbfb404e6334542812b0b512a4d22bf6c50aa4.jpg", + "image_caption": [ + "(a) Input" + ], + "image_footnote": [], + "bbox": [ + 89, + 328, + 222, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8923dcc21fc00eac2d607d8b228b81f053b1a2177bc7e43e0f023c8aa9c3b6a1.jpg", + "image_caption": [ + "(b) IIH [21]" + ], + "image_footnote": [], + "bbox": [ + 222, + 328, + 352, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1c102ab7e5eee265300cea57572b39ccb64954789e6c89cdfe663cd5f925dbe5.jpg", + "image_caption": [ + "(c) CDT [11]" + ], + "image_footnote": [], + "bbox": [ + 352, + 328, + 483, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/15dcc1d2fd4c725509209bc82e766b12b818bc35ef96907d751cf99257c581b4.jpg", + "image_caption": [ + "(d) WBH [29]", + "Figure 5. Visual comparison on composite images with general objects. The proposed method is able to harmonize the colors in the cut-and-paste regions and produce more realistic images compared with the state-of-the-art methods." + ], + "image_footnote": [], + "bbox": [ + 483, + 328, + 614, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e15c6a4873adc5e3bb134de217426663539dd5fddd610c60eebf7ba7e415d980.jpg", + "image_caption": [ + "(e) Ours" + ], + "image_footnote": [], + "bbox": [ + 614, + 328, + 746, + 412 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/18d03eeda0430e3d259f60137735f86a1f615b94db256cdf9a8302990c5130b6.jpg", + "image_caption": [ + "(f) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 746, + 328, + 879, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "back to the sRGB space. To avoid further artifacts produced during the foreground rendering process, we leverage the identity property of the background rendering process (i.e., the background should remain identical after the color-metric conversion, harmonization and rendering processes) as the guidance. Since our encoder of the image unprocessing and the color rendering decoder are symmetric, we add a foreground feature consistency constraint to guide the rendering process. In our implementation, we add an $L_{1}$ and a Cosine similarity terms to align the foreground features in magnitude and directions, of the image unprocessing encoder and the Color Harmonization decoder (Figure 2 right). We follow previous methods to produce the final harmonized image $I_{h}$ as:", + "bbox": [ + 75, + 474, + 472, + 686 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nI _ {o u t} = I _ {o} \\times M + I _ {i n} \\times (1 - M), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 700, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $I_{o}$ is the decoder output of the Color Harmonization process. We use standard $L_{1}$ loss to optimize this model.", + "bbox": [ + 76, + 729, + 468, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 770, + 292, + 786 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We have implemented the proposed model under Pytorch, and tested it on a PC with an i7 4GHz CPU and a GTX4090 GPU. The network parameters are initialized using the truncated normal initializer. For loss minimization, we adopt the AdamW optimizer. We first train the image unprocessing network on the Adobe5K dataset [4] for 300 epochs with an initial learning rate of $1e^{-4}$ , which is di", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "vided by 2 every 75 epochs. We then freeze the image unprocessing network and train the Color Harmonization network on the iHarmony4 dataset [12] for 75 epochs, with an initial learning rate of $1e^{-4}$ , which is divided by 10 at the 30th epoch. T in Eq. 1 is empirically set to 4000. It takes around 50 hours to train our model and 0.87s for testing a $256 \\times 256$ image (3.78s for a $1024 \\times 1280$ image).", + "bbox": [ + 496, + 474, + 890, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Results", + "text_level": 1, + "bbox": [ + 500, + 601, + 584, + 616 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Methods. We compare our method to 7 latest state-of-the-art deep harmonization methods: Dove [12], $\\mathbf{S}^2\\mathrm{AM}$ [13], IIH [21], IHT [20], CDT [11], WBH [29] and SCSCo [22]. Since SCSCo [22] does not provide code and results, we directly copy their performances reported in their paper for references. For other methods, we use either the pre-trained models released by their authors or their released results for evaluation. Among them, $\\mathbf{S}^2\\mathrm{AM}$ [13] and WBH [29] learn either implicit mapping curves or explicit filters to adjust the appearances of the foreground objects; Dove [12] and SCSCo [22] perform harmonization based on style transfer learning. IIH [21] is retina-based. It harmonizes the foreground objects in the intermediate illumination layer. CDT [11] and IHT [20] model the harmonization process with pixel-to-pixel mapping while an additional color-to-color mapping is used in CDT [11]. We compare our method to these methods to demonstrate the effectiveness of harmonizing foreground objects in the in", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12575", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/397a19a0a9f55cb746b1e5bff9ca2ef73ae31fe6c9bfa8dfb823e6775c1225cb.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Quantitative comparison between the proposed method and state-of-the-art deep harmonization methods on the iHarmony4 dataset [12] at ${256} \\times {256}$ image resolution. It shows that the proposed method outperforms existing image harmonization methods. Best performances are marked in bold." + ], + "table_body": "
DatasetsMetricsS2AM [13]Dove [12]IIH [21]IHT [20]CDT [11]WBH [29]SCSCo [22]Ours
HAdobe5KPSNR↑33.7734.3435.2036.1038.2437.6438.2938.93
MSE↓63.4052.3243.0247.9620.6221.8921.0120.11
fMSE↓404.62380.39284.21321.14-170.05165.48154.82
HFlickrPSNR↑30.0329.7531.3432.3733.5533.6334.2234.76
MSE↓143.45145.21105.1388.4168.6164.8155.8354.20
fMSE↓785.65827.03716.60617.26-434.06393.72386.12
HCOCOPSNR↑35.4735.8337.1637.8739.1538.7739.8839.94
MSE↓41.0736.7224.9220.9916.2517.3413.5811.27
fMSE↓542.06551.01416.38377.11-298.42245.54217.55
Hday2nightPSNR↑34.5035.5335.9636.3837.9537.5637.8338.42
MSE↓76.6156.9255.5358.1436.7233.1441.7539.79
fMSE↓989.071075.71797.04823.68-542.07606.80587.44
AveragePSNR↑34.3534.7535.9036.7138.2337.8438.7539.36
MSE↓59.6752.3638.7137.0723.7524.2621.3320.77
fMSE↓594.67532.62400.29395.66-280.51248.86238.19
", + "bbox": [ + 107, + 88, + 861, + 314 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "intermediate linear color space.", + "bbox": [ + 75, + 393, + 274, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition, to verify whether our image unprocessing module produces faithful linear images, we perform an internal analysis and compare it to 4 representative state-of-the-art deep networks, including Unprocess [3], HDRCNN [15], CycleISP [61], and CIE-XYZNet [1]. Among them, Unprocess [3] is a systematic pipeline that converts sRGB images to raw images via a sequence of reverse ISP operations. HDRCNN [15] uses an encoder-decoder network to convert sRGB images into the HDR domain. CycleISP [61] and CIE-XYZNet [1] learn cycle mappings (sRGB-to-raw and raw-to-sRGB).", + "bbox": [ + 75, + 410, + 470, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation Datasets and Metrics. We follow existing methods to evaluate the harmonization performance by using the Mean Square Error (MSE), foreground MSE (fMSE) and Peak Signal-to-Noise Ratio (PSNR), on the iHarmony4 dataset [12]. When internally analyzing the proposed image unprocessing module on the Adobe5K dataset [4], in addition to the PSNR metric, we also use the widely adopted HDR-VDP-2 [37] metric to measure the image quality based on human perceptions.", + "bbox": [ + 75, + 579, + 468, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Comparing to State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 722, + 415, + 738 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare the proposed method with state-of-the-art image harmonization methods on the standard benchmarks.", + "bbox": [ + 75, + 744, + 468, + 776 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual Comparison. Figure 4 shows visual comparison where the cut-and-paste regions contain humans. While the latest methods are effective in adjusting the brightness of the foreground targets to fit the background illumination conditions, they are not able to produce visually pleasing colors, as shown in Figure 4(b-d). In contrast, our method is able to render realistic colors in the cut-and-paste regions, as shown in Figure 4(e). Figure 5 shows some ex", + "bbox": [ + 75, + 780, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "amples where the cut-and-paste regions contain general objects. While existing methods may produce pale colors Figure 5(b,c) or color artifacts Figure 5(d). In contrast, our method produces foreground colors that are more realistic and consistent with the background, as shown in Figure 5(e).", + "bbox": [ + 496, + 393, + 890, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Comparison. In addition to the visual evaluation, we also provide quantitative comparison between the proposed method and existing harmonization methods. We first follow existing methods to evaluate the harmonization performance on images of resolution $256 \\times 256$ in the iHarmony4 benchmark [12]. Table 1 shows the results. We can see that the proposed method outperforms existing methods on all evaluation metrics under all subsets of iHarmony4. Table 2 shows additional comparisons at the original image resolution. Note that CDT [11] only releases their low-resolution results. The comparison shows that our method can handle images of higher resolutions.", + "bbox": [ + 496, + 488, + 892, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Internal Analysis", + "text_level": 1, + "bbox": [ + 500, + 680, + 668, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As our method first converts the input composite image into the intermediate linear color space via the image unprocessing process, we demonstrate its effectiveness in producing faithful colors in the high dynamic range domain. We evaluate it on the CIE xyz version of the Adobe 5K dataset using the PSNR and HDR-VDP2 metrics. The HDR-VDP2 metric produces a Q score for each test image via a Mean-Oinion-score metric. The Q score indicates the degree of image quality degradation. Table 3 reports the average PSNR and Q score on the test set. The results show that the proposed image unprocessing process can produce more faithful images due to its generation ability.", + "bbox": [ + 496, + 704, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We now perform ablation studies on our network de", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12576", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4342b8af1e0ceeaa8234267fa1b53cf4104afe05bad9b8e31b6603d132fd663f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsMetricsIHT [20]WBH [29]Ours
HAdobe5KPSNR↑33.6337.8038.42
MSE↓56.9024.3723.76
HFlickrPSNR↑29.5933.3733.97
MSE↓135.4969.1961.70
HCOCOPSNR↑34.1937.6938.22
MSE↓44.9520.9320.08
Hday2nightPSNR↑35.7137.1537.64
MSE↓63.2637.2830.11
AveragePSNR↑33.5437.2337.92
MSE↓58.8927.6223.90
", + "bbox": [ + 81, + 88, + 472, + 263 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/763b70e20f73f5eab9a12134369ac03555df378bcbbc34e61482b54d8212713a.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons on the iHarmony4 dataset [12] at the original resolution. It shows that our method outperforms all existing image harmonization methods. Best performances are marked in bold." + ], + "table_footnote": [], + "table_body": "
MethodsPSNR↑Q score↑
Unprocess [3]22.1950.33
HDRCNN [15]27.7455.61
CycleISP [61]28.2954.74
CIE-XYZNet [1]29.6656.08
CycleGAN [64]27.6456.17
Ours30.3458.14
", + "bbox": [ + 140, + 335, + 406, + 448 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/197a38611f1be91a6019e4d3ee755450922334265c2a626e21fd9f1e4a6f4503.jpg", + "table_caption": [ + "Table 3. Internal Analysis. We quantitatively compare the converted linear images with existing representative methods using PSNR and Q score. Best performances are marked in bold." + ], + "table_footnote": [], + "table_body": "
MethodsPSNR↑MSE↓
w/o CC37.7924.26
DP→CP38.2823.60
w/o FH38.1023.94
w/o BP39.1721.10
Single Encoder39.0222.28
w/o SE Block38.4723.79
w/o Spatial Attention38.1923.57
Ours39.3620.77
", + "bbox": [ + 135, + 498, + 413, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation Study of network design on iHarmony4 at ${256} \\times$ 256 image resolution. Best performances are marked in bold.", + "bbox": [ + 76, + 638, + 467, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sign. We follow previous methods to perform it on the iHarmony4 dataset. In particular, we investigate the following ablated network architectures: (1) we remove the image unprocessing process and directly train a Color Harmonization network (denoted as “ $w/o$ CC”); (2) we replace the diffusion process of the image unprocessing with a standard convolution process (denoted as “ $\\mathrm{DP} \\rightarrow \\mathrm{CP}$ ”); (3) we remove the Feature Harmonization from the Color Harmonization process (denoted as “ $w/o$ FH”); (4) we remove the Background Preserving of the Color Rendering process (denoted as “ $w/o$ BP”); (5) we use a single encoder in the Color Harmonization network (“denoted as Single Encoder”); (6) we remove the SE block from the feature harmonization", + "bbox": [ + 75, + 703, + 472, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "process (\"denoted as $w / o$ SE Block\"); and (7) we remove the spatial attention from the feature harmonization process (\"denoted as $w / o$ Spatial Attention\"). Table 4 reports the performance. It shows that our designs of image unprocessing, Feature Harmonization and background preserving are able to improve the image harmonization performances. We have tried to train DoveNet [12] from scratch in linear space and it yields slightly better results (PSNR:34.94 (+0.19)) but fine-tuning using their pre-trained model degrades the performance (PSNR:33.18 (-1.57)). This is due to the discrepancy between linear and non-linear images, which demonstrates that it is necessary to design a specific image unprocessing model for harmonization. We have also tried ControlNet [62] for harmonization, which, however, does not perform well (PSNR/MAE: 14.36/109.40). As image harmonization requires the harmonized images to be photorealistic, directly using the diffusion-based model may generate visually pleasing but fake image details.", + "bbox": [ + 496, + 90, + 893, + 364 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1597dead988c9552610b87641f4054f8e22964cd90f0d367750aa13f8d544a79.jpg", + "image_caption": [ + "(a) Input" + ], + "image_footnote": [], + "bbox": [ + 506, + 376, + 633, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f83b7d23d2c203f36ab766daf86b289de85a9bdbb6889afe8b5a2a5ab2a0945.jpg", + "image_caption": [ + "(b) Ours" + ], + "image_footnote": [], + "bbox": [ + 635, + 376, + 758, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a52b29b3e0684a7a6be133d910d6fc6e459811998a34e62fbf95538f3b01d8de.jpg", + "image_caption": [ + "(c) Ground Truth", + "Figure 6. Our method may fail to harmonize the color tones of the inserted target when the new background does not provide sufficient scene illumination information." + ], + "image_footnote": [], + "bbox": [ + 759, + 376, + 885, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 556, + 617, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents a novel image harmonization method that performs the color harmonization process in the linear color space. Our method includes a novel image unprocessing process to convert the cut-and-paste image into the high dynamic range linear color space, and a novel color harmonization process to harmonize object colors by querying background radiance information. We have conducted extensive experiments on the benchmark datasets to analyze the properties of the proposed method, and shown that it outperforms the state-of-the-art harmonization methods.", + "bbox": [ + 496, + 582, + 890, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method does have limitations. It may fail when the background does not contain sufficient scene illumination information. Figure 6 shows such an example, in which the background is completely dark and our method fails to harmonize the color tones of the foreground.", + "bbox": [ + 496, + 734, + 890, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This project was partially supported by a GRF grant from the Research Grants Council of Hong Kong (Project No. CityU 11205620), by City University of Hong Kong (9678131), and by the Research Grants Council of the Hong Kong Special Administrative Region, China (CityU 11214620).", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12577", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mahmoud Afifi, Abdelrahman Abdelhamed, Abdullah Abuolaim, Abhijith Punnappurath, and Michael S Brown. Cie xyz net: Unprocessing images for low-level computer vision tasks. IEEE TPAMI, 2021. 7, 8", + "[2] Mahmoud Afifi, Konstantinos G Derpanis, Bjorn Ommer, and Michael S Brown. Learning multi-scale photo exposure correction. 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In ICCV, 2017. 8" + ], + "bbox": [ + 501, + 92, + 890, + 445 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12579", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_model.json b/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4d08f11b721261b82c5edf03b0a4e348033dc7df --- /dev/null +++ b/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_model.json @@ -0,0 +1,2695 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.192, + 0.131, + 0.78, + 0.154 + ], + "angle": 0, + "content": "Learning Image Harmonization in the Linear Color Space" + }, + { + "type": "text", + "bbox": [ + 0.276, + 0.182, + 0.696, + 0.218 + ], + "angle": 0, + "content": "Ke Xu, Gerhard Petrus Hancke, Rynson W.H. Lau \nCity University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.277, + 0.22, + 0.694, + 0.234 + ], + "angle": 0, + "content": "{kkangwing, gp.hancke, rynson.lau}@cityu.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.474, + 0.65 + ], + "angle": 0, + "content": "Harmonizing cut-and-paste images into perceptually realistic ones is challenging, as it requires a full understanding of the discrepancies between the background of the target image and the inserted object. Existing methods mainly adjust the appearances of the inserted object via pixel-level manipulations. They are not effective in correcting color discrepancy caused by different scene illuminations and the image formation processes. We note that image colors are essentially camera ISP projection of the scene radiance. If we can trace the image colors back to the radiance field, we may be able to model the scene illumination and harmonize the discrepancy better. In this paper, we propose a novel neural approach to harmonize the image colors in a camera-independent color space, in which color values are proportional to the scene radiance. To this end, we propose a novel image unprocessing module to estimate an intermediate high dynamic range version of the object to be inserted. We then propose a novel color harmonization module that harmonizes the colors of the inserted object by querying the estimated scene radiance and re-rendering the harmonized object in the output color space. Extensive experiments demonstrate that our method outperforms the state-of-the-art approaches." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.664, + 0.21, + 0.68 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Image compositing is a common process in vision and graphics. It is a technique to render a novel image by inserting a target object from the source image onto a target image. However, humans can easily identify this cut-and-paste (or composite) image as a synthetic one due to its color [7] and texture inconsistencies [31, 63]. Hence, there is a line of research to develop algorithms to harmonize cut-and-paste images to produce visually realistic output images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Existing image harmonization methods typically fall into two categories, i.e., non-deep learning-based methods [42, 10, 47, 58, 63] and deep learning-based methods [48, 13, 8, 12, 33, 21, 27, 20]. Non-deep learning based methods try to manipulate low-level image statistics (e.g., textures [47] and colors [42, 63, 58]) of the inserted ob" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.268, + 0.635, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.548, + 0.346, + 0.596, + 0.359 + ], + "angle": 0, + "content": "(a) Input" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.268, + 0.759, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.346, + 0.728, + 0.359 + ], + "angle": 0, + "content": "(b) IIH [21]" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.268, + 0.886, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.346, + 0.858, + 0.359 + ], + "angle": 0, + "content": "(c) CDT [11]" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.359, + 0.635, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.437, + 0.61, + 0.449 + ], + "angle": 0, + "content": "(d) WBH [29]" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.359, + 0.759, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.674, + 0.438, + 0.72, + 0.449 + ], + "angle": 0, + "content": "(e) Ours" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.359, + 0.886, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.777, + 0.438, + 0.866, + 0.449 + ], + "angle": 0, + "content": "(f) Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.45, + 0.635, + 0.524 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.548, + 0.528, + 0.596, + 0.541 + ], + "angle": 0, + "content": "(g) Input" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.45, + 0.759, + 0.524 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.528, + 0.728, + 0.54 + ], + "angle": 0, + "content": "(h) IIH [21]" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.45, + 0.886, + 0.524 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.787, + 0.528, + 0.857, + 0.54 + ], + "angle": 0, + "content": "(i)CDT [11]" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.541, + 0.635, + 0.615 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.619, + 0.609, + 0.632 + ], + "angle": 0, + "content": "(j) WBH [29]" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.541, + 0.759, + 0.615 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.674, + 0.619, + 0.72, + 0.63 + ], + "angle": 0, + "content": "(k) Ours" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.541, + 0.886, + 0.615 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.777, + 0.619, + 0.866, + 0.631 + ], + "angle": 0, + "content": "(1) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.637, + 0.894, + 0.707 + ], + "angle": 0, + "content": "Figure 1. Harmonization results on the iHarmony4 dataset [12]. Existing harmonization methods tend to produce dull (b-d) or inconsistent (h-j) colors. Our method traces back to and harmonizes the colors in an intermediate linear color space, resulting in more realistic composite images as shown in (e) and (k)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.903 + ], + "angle": 0, + "content": "ject, to match with those of the background. These methods often produce unrealistic images of inconsistent colors/textures when the hand-crafted features fail to represent the foreground/background. In contrast, deep learning based methods offer strong capability of modelling region appearances to facilitate harmonization. Some methods explore different priors (e.g., semantics [48], and gradient/color consistency [8, 53]) to constrain the harmonization process. Some other methods [12, 33, 21] may formulate the image harmonization process as a foreground-background transfer learning task." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12570" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "Despite their success, existing harmonization methods may still produce pale (Figure 1(b-d)) or inconsistent colors (Figure 1(h-j)) across the foreground and background regions, resulting in visually unpleasant images. We note that all these methods model the color harmonization process in the camera output sRGB (i.e., low dynamic range) color space. However, object colors in an image are determined not only by their material reflectance and scene illumination, but also by the black-box imaging pipeline (ISP) of the camera. Due to the non-linear operations (e.g., tone mapping) within the ISP, pixel intensities of camera output sRGB images are not proportional to the scene radiance, making them unreliable for use in estimating the scene illumination for color harmonization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.651 + ], + "angle": 0, + "content": "To address this problem, we propose in this paper a novel approach to harmonize a cut-and-paste image (captured in low dynamic range) in the high dynamic range domain. Our key idea is to harmonize the scene illumination discrepancies in an intermediate (high dynamic range) color space, in which the scene illumination is proportional to the original scene radiance. To this end, we propose a novel neural network that first converts the source image (containing the target object) into an intermediate high dynamic range domain, then performs the harmonization process, and finally converts the harmonized image back to the low dynamic range sRGB space. To avoid exhaustive modeling of camera-dependent operations, we propose a novel image unprocessing module to estimate a high dynamic range version of the input image in the linear camera-independent CIE XYZ color space. We formulate this image unprocessing process as a diffusion process. We propose a novel color harmonization method that models image colors in the estimated linear color space to produce the final harmonized results. As shown in Figure 1(e,k), our method is able to produce more visually pleasing results. We conduct extensive experiments to demonstrate that our method outperforms state-of-the-art harmonization approaches." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.652, + 0.444, + 0.667 + ], + "angle": 0, + "content": "In summary, this paper has three main contributions:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.681, + 0.47, + 0.742 + ], + "angle": 0, + "content": "- We propose a novel neural approach for image harmonization that performs the color harmonization process in the linear color space, allowing object color modeling based on faithful scene radiance." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.753, + 0.47, + 0.86 + ], + "angle": 0, + "content": "- Our approach includes two novel modules: (1) a novel image unprocessing module to convert the source image (of the target object) into a version in the high dynamic range linear color space, and (2) a novel color harmonization module to harmonize object colors by querying scene radiance information and re-render the harmonized objects in the output color space." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- Extensive experiments show that the proposed method outperforms state-of-the-art harmonization methods." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.681, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.107 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.357 + ], + "angle": 0, + "content": "Image Harmonization aims to adjust the appearance of the foreground object so that it is compatible with the new composite background. Traditional methods [42, 10, 31, 47, 58, 63] typically rely on adjusting the appearance of the foreground to match with the color statistics of the background. Sunkavalli et al. [47] propose to first transfer the visual appearance of the target image to the source image via image histogram matching, and then use alpha blending to produce the composite image. Xue et al. [58] suggest to match zones of the (instead complete) histogram is more effective, and propose the zone selection classifier for matching. Reinhard et al. [42] propose a color transfer method to match the global color statistics between the source and target images. Lalonde and Efros [31] divide the source and target images into corresponding cluster pairs, and perform the color transfer [42] for each cluster pair locally." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.358, + 0.895, + 0.794 + ], + "angle": 0, + "content": "In recent years, many deep methods are proposed for image harmonization. Zhu et al. [63] propose to train a CNN classifier to distinguish between real and composite images, and use the learned model to adjust the brightness and contrast model for image composition. Tsai et al. [48] present the first end-to-end CNN-based harmonization method to leverage the semantic information of a scene parsing branch to help boost the performance of the harmonization branch. Cun and Pun [13] propose to use spatial attention modules to learn regional appearance changes for harmonization. Chen and Mae [8] propose a GAN-based method to harmonize images with geometric and color consistency constraints. Wu et al. [53] propose a GAN-based method to explore both gradient and color constraints for image harmonization. Cong et al. [12] construct a large-scale dataset, iHarmony4, and propose a domain verification discriminator to guide the generator to translate the foreground object to the background domain. Ling et al. [33] formulate the image harmonization task as a style transfer problem, and propose the region-aware adaptive instance normalization module to model the background style and apply it to the foreground. Guo et al. [21] propose to decompose the composite image into reflectance and illumination, and harmonize the two via material consistency and light transfer. Self-supervised learning and transformers have also been applied to image harmonization in [27] and [20], respectively. Methods are also proposed for high-resolution image harmonization [11, 32, 29, 57], multiple objects harmonization [44] and interactive portrait harmonization [49]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.856 + ], + "angle": 0, + "content": "Unlike existing methods that harmonize colors in the low dynamic range image domain, we propose to model and harmonize these object colors by tracing back to the high dynamic range scene radiance field." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Image Enhancement aims to produce visually pleasing images with vivid colors and details from low-quality input images of over- or under-exposures. Some meth" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12571" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.092, + 0.862, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.282, + 0.895, + 0.327 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed method. Given an input composite image, we first convert it into an intermediate linear color space via the image unprocessing process. The Color Harmonization process then harmonizes the foreground colors in the feature domain, and renders the harmonized colors to produce an output sRGB image with the guidance of the background preserving process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.473, + 0.581 + ], + "angle": 0, + "content": "ods [19, 17, 5, 51, 45, 36, 54] rely on the retinax theory to decompose the input image into reflectance and illumination layers, and enhance the illumination layer. Cai et al. [6] separately model illuminance and detail layers from multi-exposed images to enhance an under-exposed image. Xu et al. [56] decompose and enhance under-exposed images based on frequency information. Moran et al. [38] learn a set of local parametric filters for image enhancement. Some methods directly learn an image-to-image mapping using high dynamic range information [18, 59, 46] or adversarial learning [25, 9, 26, 43]. Mahmoud et al. [2] propose a coarse-to-fine network to learn color and detail enhancement for addressing over- or under-exposure. Recently, Wang et al. [50] build a local color distributions pyramid with a dual-illumination estimation method to handle images of both over-/under-exposures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.472, + 0.673 + ], + "angle": 0, + "content": "While sharing some similarities with image harmonization methods, e.g., pixel-wise curve modeling and retina-based image decomposition, image enhancement methods do not model the discrepancy between source and target scenes. Directly enhancing composite images with image enhancement methods tends to amplify scene discrepancies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.687, + 0.251, + 0.705 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.47, + 0.82 + ], + "angle": 0, + "content": "We propose to harmonize cut-and-paste object colors by tracing back them to the scene radiance field. To this end, we propose an image unprocessing method to transfer the input composite image into a linear high dynamic range color space, and a harmonization method to re-render the target object colors by querying the scene radiance information. Figure 2 shows the whole harmonization process." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.273, + 0.849 + ], + "angle": 0, + "content": "3.1. Image Unprocessing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Converting camera output sRGB images back to camera raw images, i.e., image unprocessing [60, 39, 40, 3, 55, 41], requires a systematic modelling of the ISP operations. Ex-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.895, + 0.657 + ], + "angle": 0, + "content": "isting methods are typically sensor-specific, requiring additional camera information to convert each image. We note that most camera ISPs typically apply a set of camera-variant linear operations (e.g., white balance) to convert CCD data into a camera-independent color space, and then apply another set of non-linear operations (e.g., quantization and local enhancement) to render images [28]. Hence, converting the sRGB images back into the intermediate camera-independent color space has two advantages for harmonization. First, colors in this intermediate space response to the scene radiance linearly, which helps recover scene discrepancy for harmonization. Second, it avoids the need to model camera-dependent operations (e.g., camera response curves selection [16] or estimation [46]). We formulate a generative diffusion model to address this dynamic range expansion problem of image unprocessing. Although single-image reverse tone mapping is challenging (as it needs to generate missing info in the over-/underexposed regions), learning such image unprocessing in our task is feasible, as images to be harmonized are typically captured with proper exposures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.895, + 0.781 + ], + "angle": 0, + "content": "Model Formulation. A diffusion model has a forward diffusion process and a reverse denoising process (used for generation). Given a distribution \\( q(x_0) \\), the forward diffusion process \\( q \\) is a Markovian noisig process [23], which gradually adds noise to \\( x_0 \\) to obtain \\( x_{1:T} \\). Specifically, at each step \\( t \\), the diffusion process adds random Gaussian noise with a \\( \\beta_t \\)-controlled variance:" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.794, + 0.892, + 0.835 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {1: T} \\mid x _ {0}\\right) = \\prod_ {t = 1} ^ {T} q \\left(x _ {t} \\mid x _ {t - 1}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.838, + 0.892, + 0.858 + ], + "angle": 0, + "content": "\\[\nq (x _ {t} | x _ {t - 1}) = \\mathcal {N} \\left(x _ {t}; \\sqrt {1 - \\beta_ {t}} x _ {t - 1}, \\beta_ {t} \\mathbb {I}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(\\beta_{t} \\in (0,1), t = 1, \\dots, T\\). With the reparameterization trick [30], we sample \\(x_{t}\\) from each time step \\(t\\) in a closed" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "12572" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.093, + 0.852, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.895, + 0.34 + ], + "angle": 0, + "content": "Figure 3. The feature harmonization process. Given the concatenated linear foreground and background features \\( f = [F_{f}, F_{b}] \\), it first uses an SE block [24] to adjust the attention for each channel to be the same, and then propagates channel consistency to the spatial domain to produce harmonized foreground features \\( f_{h} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.363, + 0.383, + 0.38 + ], + "angle": 0, + "content": "form: \\(x_{t} = \\sqrt{\\bar{\\alpha}_{t}} x_{0} + \\sqrt{1 - \\bar{\\alpha}_{t}}\\epsilon ,\\epsilon \\sim \\mathcal{N}(0,\\mathbb{I})\\)" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.389, + 0.47, + 0.408 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbb {I}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.417, + 0.469, + 0.464 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = 1 - \\beta_{t}\\) and \\(\\bar{\\alpha}_{t} = \\prod_{i = 1}^{t}\\alpha_{i}\\). In this way, we directly derive \\(x_{t}\\) from \\(q(x_{t}|x_{0})\\) without repeatedly applying the Markovian process \\(q\\) and calculating \\(q(x_{t}|x_{t - 1})\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.464, + 0.47, + 0.554 + ], + "angle": 0, + "content": "We formulate image unprocessing as a reverse denoising process (i.e., generation process) that is conditioned on the sRGB input image \\(I_{in}\\). We compute \\(x_0\\) (i.e., the linear color image \\(I_l\\)) via the reverse diffusion process \\(p_\\theta(x_{t-1}|x_t)\\) parameterized by \\(\\theta\\) with a random Gaussian distribution, i.e., \\(x_T \\sim \\mathcal{N}(0,\\mathbb{I})\\), as:" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.565, + 0.469, + 0.607 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(x _ {0: T} \\mid I _ {i n}\\right) = p \\left(x _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}, I _ {i n}\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.617, + 0.469, + 0.647 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}, I _ {i n}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, I _ {i n}, t\\right), \\sum_ {\\theta} \\left(x _ {t}, I _ {i n}, t\\right)\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.469, + 0.693 + ], + "angle": 0, + "content": "Unlike previous methods that are conditioned on the class labels [14] or shape latents [35], we condition the diffusion process on the sRGB image \\( I_{in} \\) pixel-wisely." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.704, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Model Architecture. Our image unprocessing model adopts a fully convolutional encoder-decoder network [34], as shown in Figure 2(left). Given the sampled noise with the sRGB image as the condition, we encode them into a low dimensional latent representation, which is then decoded to reconstruct the linear color image. We leverage the generation ability of reversing the denoising process to expand the dynamic range, and use the encoder-decoder architecture to perform image unprocessing. To facilitate the learning process, we add a skip connection directly from the input image to the output. Instead of learning to generate the linear color image of the whole dynamic range, the image unprocessing network only needs to generate the difference between" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.363, + 0.892, + 0.44 + ], + "angle": 0, + "content": "the input and the output, resulting in a fast reverse diffusion process. We train this network from scratch and use batch normalization and GELU activation for all the convolutional layers. We use the weighted variational bound [23] to optimize this model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.47, + 0.773, + 0.487 + ], + "angle": 0, + "content": "3.2. Harmonization and Rendering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.892, + 0.562 + ], + "angle": 0, + "content": "We propose a harmonization module to harmonize the colors of the target object by querying background radiance information and re-render the harmonized image in the sRGB space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Harmonization in Linear Space. As shown in Figure 2(right), given the reconstructed linear color image \\(I_{l}\\) we first separately obtain foreground and background features (i.e., \\(F_{f}\\) and \\(F_{b}\\)) via two separate encoders and the foreground mask \\(M\\), as \\(F_{f} = \\text{Enc}_{f}(I_{l} * M)\\) and \\(F_{b} = \\text{Enc}_{b}(I_{l} * (1 - M))\\). Our goal is to harmonize the foreground features \\(F_{f}\\) based on \\(F_{b}\\) to obtain \\(\\hat{F}_{f}\\), and then render the harmonized foreground features \\(\\hat{F}_{f}\\) into the sRGB space \\(\\hat{F}_{f} \\rightarrow \\hat{I}_{f}\\) conditioned on the rendering process of \\(F_{b} \\rightarrow I_{b}\\). To this end, we harmonize the concatenated features \\(f = [F_{f}, F_{b}]\\) in both channel and spatial dimensions. We implement the channel harmonization by using the squeeze-and-excitation operation [24] to assign consistent attention for each channel of \\(f = [F_{f}, F_{b}]\\). As the reweighed features are computed channel-wisely according to both foreground and background representations, the consistent attention indicates that these representations are harmonized to be consistent as well. We then propagate channel harmonization to the spatial domain via the bilat-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12573" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.087, + 0.885, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.437, + 0.182, + 0.45 + ], + "angle": 0, + "content": "(a) Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.257, + 0.437, + 0.321, + 0.45 + ], + "angle": 0, + "content": "(b) IIH [21]" + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.437, + 0.455, + 0.45 + ], + "angle": 0, + "content": "(c) CDT [11]" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.437, + 0.589, + 0.45 + ], + "angle": 0, + "content": "(d) WBH [29]" + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.437, + 0.705, + 0.449 + ], + "angle": 0, + "content": "(e) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.768, + 0.437, + 0.858, + 0.449 + ], + "angle": 0, + "content": "(f) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.452, + 0.892, + 0.479 + ], + "angle": 0, + "content": "Figure 4. Visual comparison on composite images with humans. The proposed method is able to harmonize the colors in the cut-and-paste regions and produce realistic images compared with the state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.49, + 0.325, + 0.506 + ], + "angle": 0, + "content": "eral propagation activation functions:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.526, + 0.469, + 0.564 + ], + "angle": 0, + "content": "\\[\ny _ {i} ^ {s} = \\frac {1}{C (f)} \\sum_ {j \\in s} g (\\| j - i \\|) f _ {j}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.566, + 0.469, + 0.603 + ], + "angle": 0, + "content": "\\[\ny _ {i} ^ {r} = \\frac {1}{C (f)} \\sum_ {j \\in v} h \\left(f _ {i}, f _ {j}\\right) f _ {j}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.605, + 0.469, + 0.623 + ], + "angle": 0, + "content": "\\[\ny _ {i} = c \\left(y _ {i} ^ {s}, y _ {i} ^ {r}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.473, + 0.902 + ], + "angle": 0, + "content": "where \\( f_{i} \\) is the feature channel at position \\( i \\) of the input features \\( f \\). \\( f_{j} \\) is a neighboring feature channel around \\( i \\) at position \\( j \\). \\( y_{i}^{s} \\) and \\( y_{i}^{r} \\) are the features after spatial and range similarity measurements. The normalization factor is set to \\( C(f) = N \\), where \\( N \\) is the number of positions in \\( f \\). \\( c \\) represents the pixel-wise summation and a linear transformation of \\( y_{i}^{s} \\) and \\( y_{i}^{r} \\) via a \\( 1 \\times 1 \\) convolutional layer. The bilateral propagation extends the consistency of feature channels to both spatial and range dimensions. In spatial propagation, we set the neighboring region \\( s \\) to be of the same spatial resolution as the input features for global propagation. A Gaussian function \\( g(\\cdot) \\) [52] is used to compute the spatial contributions from neighboring background features. In range propagation, we measure the similarity between features \\( f_{i} \\) and \\( f_{j} \\) via \\( h(\\cdot) \\) within a neighboring region \\( v \\) around \\( i \\). The size of \\( v \\) is set to \\( 3 \\times 3 \\). The range similarity is computed via the pairwise function \\( h(\\cdot) \\) with a" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.491, + 0.651, + 0.505 + ], + "angle": 0, + "content": "dot product operation:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.514, + 0.891, + 0.532 + ], + "angle": 0, + "content": "\\[\nh \\left(f _ {i}, f _ {j}\\right) = \\left(f _ {i}\\right) ^ {T} \\left(f _ {j}\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.602 + ], + "angle": 0, + "content": "In this way, the bilateral propagation process harmonizes the foreground colors by considering both global continuity via \\( y_{i}^{s} \\) and local consistency via \\( y_{i}^{r} \\). Figure 3 shows the feature harmonization process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.893, + 0.846 + ], + "angle": 0, + "content": "Our bilateral propagation is close in spirit to the nonlocal block [52], in that for each \\(i\\), \\(\\frac{1}{C(f)}\\sum g(f_i,f_j)\\) computes the softmax scores along dimension \\(j\\). The main difference is the regions of propagation. The non-local block uses feature channels from all positions to generate \\(y_{i}\\) and the similarity is only measured between \\(f_{i}\\) and \\(f_{j}\\). In contrast, our method considers channel similarity, long-range and neighboring spatial correlations between \\(f_{i}\\) and \\(f_{j}\\) for feature harmonization. During the long-range correlation modeling, we query the global scene radiance information using region \\(s\\) of the original background features (i.e., before the channel-wise harmonization), while during the neighboring correlation modeling, we query the local scene information using the background features after channelwise adjustment. The foreground colors are then set to be consistent to the background both globally and locally." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Background Preserving Guided Rendering. After the harmonization process in the linear embedding space, we assign a decoder to re-project the harmonized linear image" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12574" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.089, + 0.223, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.089, + 0.354, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.089, + 0.485, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.089, + 0.616, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.089, + 0.747, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.089, + 0.88, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.165, + 0.223, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.165, + 0.354, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.165, + 0.485, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.165, + 0.616, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.165, + 0.747, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.165, + 0.88, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.252, + 0.223, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.252, + 0.354, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.252, + 0.485, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.252, + 0.616, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.252, + 0.747, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.252, + 0.88, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.329, + 0.223, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.329, + 0.354, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.329, + 0.485, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.329, + 0.616, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.616, + 0.329, + 0.747, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.329, + 0.88, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.419, + 0.182, + 0.431 + ], + "angle": 0, + "content": "(a) Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.257, + 0.418, + 0.321, + 0.431 + ], + "angle": 0, + "content": "(b) IIH [21]" + }, + { + "type": "image_caption", + "bbox": [ + 0.384, + 0.418, + 0.455, + 0.431 + ], + "angle": 0, + "content": "(c) CDT [11]" + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.419, + 0.589, + 0.431 + ], + "angle": 0, + "content": "(d) WBH [29]" + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.419, + 0.705, + 0.43 + ], + "angle": 0, + "content": "(e) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.768, + 0.419, + 0.858, + 0.43 + ], + "angle": 0, + "content": "(f) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.433, + 0.892, + 0.461 + ], + "angle": 0, + "content": "Figure 5. Visual comparison on composite images with general objects. The proposed method is able to harmonize the colors in the cut-and-paste regions and produce more realistic images compared with the state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.473, + 0.687 + ], + "angle": 0, + "content": "back to the sRGB space. To avoid further artifacts produced during the foreground rendering process, we leverage the identity property of the background rendering process (i.e., the background should remain identical after the color-metric conversion, harmonization and rendering processes) as the guidance. Since our encoder of the image unprocessing and the color rendering decoder are symmetric, we add a foreground feature consistency constraint to guide the rendering process. In our implementation, we add an \\( L_{1} \\) and a Cosine similarity terms to align the foreground features in magnitude and directions, of the image unprocessing encoder and the Color Harmonization decoder (Figure 2 right). We follow previous methods to produce the final harmonized image \\( I_{h} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.701, + 0.469, + 0.717 + ], + "angle": 0, + "content": "\\[\nI _ {o u t} = I _ {o} \\times M + I _ {i n} \\times (1 - M), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.73, + 0.47, + 0.76 + ], + "angle": 0, + "content": "where \\( I_{o} \\) is the decoder output of the Color Harmonization process. We use standard \\( L_{1} \\) loss to optimize this model." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.771, + 0.294, + 0.787 + ], + "angle": 0, + "content": "3.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We have implemented the proposed model under Pytorch, and tested it on a PC with an i7 4GHz CPU and a GTX4090 GPU. The network parameters are initialized using the truncated normal initializer. For loss minimization, we adopt the AdamW optimizer. We first train the image unprocessing network on the Adobe5K dataset [4] for 300 epochs with an initial learning rate of \\(1e^{-4}\\), which is di" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.581 + ], + "angle": 0, + "content": "vided by 2 every 75 epochs. We then freeze the image unprocessing network and train the Color Harmonization network on the iHarmony4 dataset [12] for 75 epochs, with an initial learning rate of \\(1e^{-4}\\), which is divided by 10 at the 30th epoch. T in Eq. 1 is empirically set to 4000. It takes around 50 hours to train our model and 0.87s for testing a \\(256 \\times 256\\) image (3.78s for a \\(1024 \\times 1280\\) image)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.602, + 0.586, + 0.617 + ], + "angle": 0, + "content": "4. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Evaluation Methods. We compare our method to 7 latest state-of-the-art deep harmonization methods: Dove [12], \\(\\mathbf{S}^2\\mathrm{AM}\\) [13], IIH [21], IHT [20], CDT [11], WBH [29] and SCSCo [22]. Since SCSCo [22] does not provide code and results, we directly copy their performances reported in their paper for references. For other methods, we use either the pre-trained models released by their authors or their released results for evaluation. Among them, \\(\\mathbf{S}^2\\mathrm{AM}\\) [13] and WBH [29] learn either implicit mapping curves or explicit filters to adjust the appearances of the foreground objects; Dove [12] and SCSCo [22] perform harmonization based on style transfer learning. IIH [21] is retina-based. It harmonizes the foreground objects in the intermediate illumination layer. CDT [11] and IHT [20] model the harmonization process with pixel-to-pixel mapping while an additional color-to-color mapping is used in CDT [11]. We compare our method to these methods to demonstrate the effectiveness of harmonizing foreground objects in the in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12575" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.109, + 0.089, + 0.862, + 0.315 + ], + "angle": 0, + "content": "
DatasetsMetricsS2AM [13]Dove [12]IIH [21]IHT [20]CDT [11]WBH [29]SCSCo [22]Ours
HAdobe5KPSNR↑33.7734.3435.2036.1038.2437.6438.2938.93
MSE↓63.4052.3243.0247.9620.6221.8921.0120.11
fMSE↓404.62380.39284.21321.14-170.05165.48154.82
HFlickrPSNR↑30.0329.7531.3432.3733.5533.6334.2234.76
MSE↓143.45145.21105.1388.4168.6164.8155.8354.20
fMSE↓785.65827.03716.60617.26-434.06393.72386.12
HCOCOPSNR↑35.4735.8337.1637.8739.1538.7739.8839.94
MSE↓41.0736.7224.9220.9916.2517.3413.5811.27
fMSE↓542.06551.01416.38377.11-298.42245.54217.55
Hday2nightPSNR↑34.5035.5335.9636.3837.9537.5637.8338.42
MSE↓76.6156.9255.5358.1436.7233.1441.7539.79
fMSE↓989.071075.71797.04823.68-542.07606.80587.44
AveragePSNR↑34.3534.7535.9036.7138.2337.8438.7539.36
MSE↓59.6752.3638.7137.0723.7524.2621.3320.77
fMSE↓594.67532.62400.29395.66-280.51248.86238.19
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.316, + 0.894, + 0.358 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison between the proposed method and state-of-the-art deep harmonization methods on the iHarmony4 dataset [12] at \\( {256} \\times {256} \\) image resolution. It shows that the proposed method outperforms existing image harmonization methods. Best performances are marked in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.275, + 0.41 + ], + "angle": 0, + "content": "intermediate linear color space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.471, + 0.576 + ], + "angle": 0, + "content": "In addition, to verify whether our image unprocessing module produces faithful linear images, we perform an internal analysis and compare it to 4 representative state-of-the-art deep networks, including Unprocess [3], HDRCNN [15], CycleISP [61], and CIE-XYZNet [1]. Among them, Unprocess [3] is a systematic pipeline that converts sRGB images to raw images via a sequence of reverse ISP operations. HDRCNN [15] uses an encoder-decoder network to convert sRGB images into the HDR domain. CycleISP [61] and CIE-XYZNet [1] learn cycle mappings (sRGB-to-raw and raw-to-sRGB)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Evaluation Datasets and Metrics. We follow existing methods to evaluate the harmonization performance by using the Mean Square Error (MSE), foreground MSE (fMSE) and Peak Signal-to-Noise Ratio (PSNR), on the iHarmony4 dataset [12]. When internally analyzing the proposed image unprocessing module on the Adobe5K dataset [4], in addition to the PSNR metric, we also use the widely adopted HDR-VDP-2 [37] metric to measure the image quality based on human perceptions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.416, + 0.739 + ], + "angle": 0, + "content": "4.1. Comparing to State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.469, + 0.777 + ], + "angle": 0, + "content": "We compare the proposed method with state-of-the-art image harmonization methods on the standard benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Visual Comparison. Figure 4 shows visual comparison where the cut-and-paste regions contain humans. While the latest methods are effective in adjusting the brightness of the foreground targets to fit the background illumination conditions, they are not able to produce visually pleasing colors, as shown in Figure 4(b-d). In contrast, our method is able to render realistic colors in the cut-and-paste regions, as shown in Figure 4(e). Figure 5 shows some ex" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.485 + ], + "angle": 0, + "content": "amples where the cut-and-paste regions contain general objects. While existing methods may produce pale colors Figure 5(b,c) or color artifacts Figure 5(d). In contrast, our method produces foreground colors that are more realistic and consistent with the background, as shown in Figure 5(e)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.893, + 0.672 + ], + "angle": 0, + "content": "Quantitative Comparison. In addition to the visual evaluation, we also provide quantitative comparison between the proposed method and existing harmonization methods. We first follow existing methods to evaluate the harmonization performance on images of resolution \\(256 \\times 256\\) in the iHarmony4 benchmark [12]. Table 1 shows the results. We can see that the proposed method outperforms existing methods on all evaluation metrics under all subsets of iHarmony4. Table 2 shows additional comparisons at the original image resolution. Note that CDT [11] only releases their low-resolution results. The comparison shows that our method can handle images of higher resolutions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.669, + 0.697 + ], + "angle": 0, + "content": "4.2. Internal Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.885 + ], + "angle": 0, + "content": "As our method first converts the input composite image into the intermediate linear color space via the image unprocessing process, we demonstrate its effectiveness in producing faithful colors in the high dynamic range domain. We evaluate it on the CIE xyz version of the Adobe 5K dataset using the PSNR and HDR-VDP2 metrics. The HDR-VDP2 metric produces a Q score for each test image via a Mean-Oinion-score metric. The Q score indicates the degree of image quality degradation. Table 3 reports the average PSNR and Q score on the test set. The results show that the proposed image unprocessing process can produce more faithful images due to its generation ability." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We now perform ablation studies on our network de" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12576" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.473, + 0.264 + ], + "angle": 0, + "content": "
DatasetsMetricsIHT [20]WBH [29]Ours
HAdobe5KPSNR↑33.6337.8038.42
MSE↓56.9024.3723.76
HFlickrPSNR↑29.5933.3733.97
MSE↓135.4969.1961.70
HCOCOPSNR↑34.1937.6938.22
MSE↓44.9520.9320.08
Hday2nightPSNR↑35.7137.1537.64
MSE↓63.2637.2830.11
AveragePSNR↑33.5437.2337.92
MSE↓58.8927.6223.90
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.265, + 0.47, + 0.318 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on the iHarmony4 dataset [12] at the original resolution. It shows that our method outperforms all existing image harmonization methods. Best performances are marked in bold." + }, + { + "type": "table", + "bbox": [ + 0.141, + 0.337, + 0.408, + 0.449 + ], + "angle": 0, + "content": "
MethodsPSNR↑Q score↑
Unprocess [3]22.1950.33
HDRCNN [15]27.7455.61
CycleISP [61]28.2954.74
CIE-XYZNet [1]29.6656.08
CycleGAN [64]27.6456.17
Ours30.3458.14
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.45, + 0.47, + 0.492 + ], + "angle": 0, + "content": "Table 3. Internal Analysis. We quantitatively compare the converted linear images with existing representative methods using PSNR and Q score. Best performances are marked in bold." + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.499, + 0.415, + 0.639 + ], + "angle": 0, + "content": "
MethodsPSNR↑MSE↓
w/o CC37.7924.26
DP→CP38.2823.60
w/o FH38.1023.94
w/o BP39.1721.10
Single Encoder39.0222.28
w/o SE Block38.4723.79
w/o Spatial Attention38.1923.57
Ours39.3620.77
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.64, + 0.468, + 0.668 + ], + "angle": 0, + "content": "Table 4. Ablation Study of network design on iHarmony4 at \\( {256} \\times \\) 256 image resolution. Best performances are marked in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.473, + 0.901 + ], + "angle": 0, + "content": "sign. We follow previous methods to perform it on the iHarmony4 dataset. In particular, we investigate the following ablated network architectures: (1) we remove the image unprocessing process and directly train a Color Harmonization network (denoted as “\\(w/o\\) CC”); (2) we replace the diffusion process of the image unprocessing with a standard convolution process (denoted as “\\(\\mathrm{DP} \\rightarrow \\mathrm{CP}\\)”); (3) we remove the Feature Harmonization from the Color Harmonization process (denoted as “\\(w/o\\) FH”); (4) we remove the Background Preserving of the Color Rendering process (denoted as “\\(w/o\\) BP”); (5) we use a single encoder in the Color Harmonization network (“denoted as Single Encoder”); (6) we remove the SE block from the feature harmonization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.895, + 0.365 + ], + "angle": 0, + "content": "process (\"denoted as \\( w / o \\) SE Block\"); and (7) we remove the spatial attention from the feature harmonization process (\"denoted as \\( w / o \\) Spatial Attention\"). Table 4 reports the performance. It shows that our designs of image unprocessing, Feature Harmonization and background preserving are able to improve the image harmonization performances. We have tried to train DoveNet [12] from scratch in linear space and it yields slightly better results (PSNR:34.94 (+0.19)) but fine-tuning using their pre-trained model degrades the performance (PSNR:33.18 (-1.57)). This is due to the discrepancy between linear and non-linear images, which demonstrates that it is necessary to design a specific image unprocessing model for harmonization. We have also tried ControlNet [62] for harmonization, which, however, does not perform well (PSNR/MAE: 14.36/109.40). As image harmonization requires the harmonized images to be photorealistic, directly using the diffusion-based model may generate visually pleasing but fake image details." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.377, + 0.635, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.547, + 0.484, + 0.596, + 0.497 + ], + "angle": 0, + "content": "(a) Input" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.377, + 0.759, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.484, + 0.72, + 0.496 + ], + "angle": 0, + "content": "(b) Ours" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.377, + 0.886, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.776, + 0.484, + 0.868, + 0.496 + ], + "angle": 0, + "content": "(c) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.54 + ], + "angle": 0, + "content": "Figure 6. Our method may fail to harmonize the color tones of the inserted target when the new background does not provide sufficient scene illumination information." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.557, + 0.619, + 0.573 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.734 + ], + "angle": 0, + "content": "This paper presents a novel image harmonization method that performs the color harmonization process in the linear color space. Our method includes a novel image unprocessing process to convert the cut-and-paste image into the high dynamic range linear color space, and a novel color harmonization process to harmonize object colors by querying background radiance information. We have conducted extensive experiments on the benchmark datasets to analyze the properties of the proposed method, and shown that it outperforms the state-of-the-art harmonization methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Our method does have limitations. It may fail when the background does not contain sufficient scene illumination information. Figure 6 shows such an example, in which the background is completely dark and our method fails to harmonize the color tones of the foreground." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This project was partially supported by a GRF grant from the Research Grants Council of Hong Kong (Project No. CityU 11205620), by City University of Hong Kong (9678131), and by the Research Grants Council of the Hong Kong Special Administrative Region, China (CityU 11214620)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12577" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Mahmoud Afifi, Abdelrahman Abdelhamed, Abdullah Abuolaim, Abhijith Punnappurath, and Michael S Brown. Cie xyz net: Unprocessing images for low-level computer vision tasks. 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In ICCV, 2017. 8" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12579" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_origin.pdf b/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a26686f2d7605f629e261f7bbbee735df176a985 --- /dev/null +++ b/2023/Learning Image Harmonization in the Linear Color Space/be202573-b803-48c5-8b87-29cda14139c4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8605846b711d390b8300f8418cf2e417fb08e9d0d54d93499226477078e519e0 +size 3231347 diff --git a/2023/Learning Image Harmonization in the Linear Color Space/full.md b/2023/Learning Image Harmonization in the Linear Color Space/full.md new file mode 100644 index 0000000000000000000000000000000000000000..effcb486e47416eded839d7e25754f624468ea5e --- /dev/null +++ b/2023/Learning Image Harmonization in the Linear Color Space/full.md @@ -0,0 +1,377 @@ +# Learning Image Harmonization in the Linear Color Space + +Ke Xu, Gerhard Petrus Hancke, Rynson W.H. Lau +City University of Hong Kong + +{kkangwing, gp.hancke, rynson.lau}@cityu.edu.hk + +# Abstract + +Harmonizing cut-and-paste images into perceptually realistic ones is challenging, as it requires a full understanding of the discrepancies between the background of the target image and the inserted object. Existing methods mainly adjust the appearances of the inserted object via pixel-level manipulations. They are not effective in correcting color discrepancy caused by different scene illuminations and the image formation processes. We note that image colors are essentially camera ISP projection of the scene radiance. If we can trace the image colors back to the radiance field, we may be able to model the scene illumination and harmonize the discrepancy better. In this paper, we propose a novel neural approach to harmonize the image colors in a camera-independent color space, in which color values are proportional to the scene radiance. To this end, we propose a novel image unprocessing module to estimate an intermediate high dynamic range version of the object to be inserted. We then propose a novel color harmonization module that harmonizes the colors of the inserted object by querying the estimated scene radiance and re-rendering the harmonized object in the output color space. Extensive experiments demonstrate that our method outperforms the state-of-the-art approaches. + +# 1. Introduction + +Image compositing is a common process in vision and graphics. It is a technique to render a novel image by inserting a target object from the source image onto a target image. However, humans can easily identify this cut-and-paste (or composite) image as a synthetic one due to its color [7] and texture inconsistencies [31, 63]. Hence, there is a line of research to develop algorithms to harmonize cut-and-paste images to produce visually realistic output images. + +Existing image harmonization methods typically fall into two categories, i.e., non-deep learning-based methods [42, 10, 47, 58, 63] and deep learning-based methods [48, 13, 8, 12, 33, 21, 27, 20]. Non-deep learning based methods try to manipulate low-level image statistics (e.g., textures [47] and colors [42, 63, 58]) of the inserted ob + +![](images/f85ad6aa87af3675c826ba9f5fcff3dc6dcfb3ef13b2725491cb133eaeb19fb2.jpg) + +![](images/6fb0621fb08c6fce764943a3cc6d2bcf934610d955d4a3b0a84f1efa93fcf3ce.jpg) + +![](images/5819487f83eed624bd07b7c491cd99856602fcbbabcf64a51e312b9e6ae393bd.jpg) + +![](images/ea02a3bb8ed9838e180898a437efc31c64a708990b5705402bce512e80dfa564.jpg) +(a) Input + +![](images/ae9da93e95a9e1c60b92a1524acec14201e0597e958aa6162ca8a34d118c3a8d.jpg) +(b) IIH [21] + +![](images/2ac4531abb925b297e9808aa35fe0cfaf1ab476c71675026b4b32b2883088d2f.jpg) +(c) CDT [11] + +![](images/95751c73fd1a12e148a54b628abfc732048c0d99e3381dae1979c847948df52b.jpg) +(d) WBH [29] + +![](images/c0199ba1b6ab2392cb404bfa2e2b21ed74f3af843e67e99a59e02fac2e8d2181.jpg) +(e) Ours + +![](images/8ff7878fa73cf0c84e86c755a098b677b01aaaaa35b0d238c50633f446e797a3.jpg) +(f) Ground Truth + +![](images/f5b381a2c2bbd8368f75b9e6bd14fa0d60cdbb59cb962d31ad3e4dcc30619f2f.jpg) +(g) Input +(j) WBH [29] +Figure 1. Harmonization results on the iHarmony4 dataset [12]. Existing harmonization methods tend to produce dull (b-d) or inconsistent (h-j) colors. Our method traces back to and harmonizes the colors in an intermediate linear color space, resulting in more realistic composite images as shown in (e) and (k). + +![](images/85c5ed936f4bed5e921f5a132c574cef7547829283b4a1bbea70d5f676c0f02d.jpg) +(h) IIH [21] +(k) Ours + +![](images/579de76c75f0dddcb81d50d7df09e58c1db2f09e7378f25ce28793bfa5477f9c.jpg) +(i)CDT [11] +(1) Ground Truth + +ject, to match with those of the background. These methods often produce unrealistic images of inconsistent colors/textures when the hand-crafted features fail to represent the foreground/background. In contrast, deep learning based methods offer strong capability of modelling region appearances to facilitate harmonization. Some methods explore different priors (e.g., semantics [48], and gradient/color consistency [8, 53]) to constrain the harmonization process. Some other methods [12, 33, 21] may formulate the image harmonization process as a foreground-background transfer learning task. + +Despite their success, existing harmonization methods may still produce pale (Figure 1(b-d)) or inconsistent colors (Figure 1(h-j)) across the foreground and background regions, resulting in visually unpleasant images. We note that all these methods model the color harmonization process in the camera output sRGB (i.e., low dynamic range) color space. However, object colors in an image are determined not only by their material reflectance and scene illumination, but also by the black-box imaging pipeline (ISP) of the camera. Due to the non-linear operations (e.g., tone mapping) within the ISP, pixel intensities of camera output sRGB images are not proportional to the scene radiance, making them unreliable for use in estimating the scene illumination for color harmonization. + +To address this problem, we propose in this paper a novel approach to harmonize a cut-and-paste image (captured in low dynamic range) in the high dynamic range domain. Our key idea is to harmonize the scene illumination discrepancies in an intermediate (high dynamic range) color space, in which the scene illumination is proportional to the original scene radiance. To this end, we propose a novel neural network that first converts the source image (containing the target object) into an intermediate high dynamic range domain, then performs the harmonization process, and finally converts the harmonized image back to the low dynamic range sRGB space. To avoid exhaustive modeling of camera-dependent operations, we propose a novel image unprocessing module to estimate a high dynamic range version of the input image in the linear camera-independent CIE XYZ color space. We formulate this image unprocessing process as a diffusion process. We propose a novel color harmonization method that models image colors in the estimated linear color space to produce the final harmonized results. As shown in Figure 1(e,k), our method is able to produce more visually pleasing results. We conduct extensive experiments to demonstrate that our method outperforms state-of-the-art harmonization approaches. + +In summary, this paper has three main contributions: + +- We propose a novel neural approach for image harmonization that performs the color harmonization process in the linear color space, allowing object color modeling based on faithful scene radiance. +- Our approach includes two novel modules: (1) a novel image unprocessing module to convert the source image (of the target object) into a version in the high dynamic range linear color space, and (2) a novel color harmonization module to harmonize object colors by querying scene radiance information and re-render the harmonized objects in the output color space. +- Extensive experiments show that the proposed method outperforms state-of-the-art harmonization methods. + +# 2. Related Work + +Image Harmonization aims to adjust the appearance of the foreground object so that it is compatible with the new composite background. Traditional methods [42, 10, 31, 47, 58, 63] typically rely on adjusting the appearance of the foreground to match with the color statistics of the background. Sunkavalli et al. [47] propose to first transfer the visual appearance of the target image to the source image via image histogram matching, and then use alpha blending to produce the composite image. Xue et al. [58] suggest to match zones of the (instead complete) histogram is more effective, and propose the zone selection classifier for matching. Reinhard et al. [42] propose a color transfer method to match the global color statistics between the source and target images. Lalonde and Efros [31] divide the source and target images into corresponding cluster pairs, and perform the color transfer [42] for each cluster pair locally. + +In recent years, many deep methods are proposed for image harmonization. Zhu et al. [63] propose to train a CNN classifier to distinguish between real and composite images, and use the learned model to adjust the brightness and contrast model for image composition. Tsai et al. [48] present the first end-to-end CNN-based harmonization method to leverage the semantic information of a scene parsing branch to help boost the performance of the harmonization branch. Cun and Pun [13] propose to use spatial attention modules to learn regional appearance changes for harmonization. Chen and Mae [8] propose a GAN-based method to harmonize images with geometric and color consistency constraints. Wu et al. [53] propose a GAN-based method to explore both gradient and color constraints for image harmonization. Cong et al. [12] construct a large-scale dataset, iHarmony4, and propose a domain verification discriminator to guide the generator to translate the foreground object to the background domain. Ling et al. [33] formulate the image harmonization task as a style transfer problem, and propose the region-aware adaptive instance normalization module to model the background style and apply it to the foreground. Guo et al. [21] propose to decompose the composite image into reflectance and illumination, and harmonize the two via material consistency and light transfer. Self-supervised learning and transformers have also been applied to image harmonization in [27] and [20], respectively. Methods are also proposed for high-resolution image harmonization [11, 32, 29, 57], multiple objects harmonization [44] and interactive portrait harmonization [49]. + +Unlike existing methods that harmonize colors in the low dynamic range image domain, we propose to model and harmonize these object colors by tracing back to the high dynamic range scene radiance field. + +Image Enhancement aims to produce visually pleasing images with vivid colors and details from low-quality input images of over- or under-exposures. Some meth + +![](images/dc931499e6e50c72e15c95c3bbfa3b0670d34fc174c284c4fa25a7f440ee5550.jpg) +Figure 2. Overview of the proposed method. Given an input composite image, we first convert it into an intermediate linear color space via the image unprocessing process. The Color Harmonization process then harmonizes the foreground colors in the feature domain, and renders the harmonized colors to produce an output sRGB image with the guidance of the background preserving process. + +ods [19, 17, 5, 51, 45, 36, 54] rely on the retinax theory to decompose the input image into reflectance and illumination layers, and enhance the illumination layer. Cai et al. [6] separately model illuminance and detail layers from multi-exposed images to enhance an under-exposed image. Xu et al. [56] decompose and enhance under-exposed images based on frequency information. Moran et al. [38] learn a set of local parametric filters for image enhancement. Some methods directly learn an image-to-image mapping using high dynamic range information [18, 59, 46] or adversarial learning [25, 9, 26, 43]. Mahmoud et al. [2] propose a coarse-to-fine network to learn color and detail enhancement for addressing over- or under-exposure. Recently, Wang et al. [50] build a local color distributions pyramid with a dual-illumination estimation method to handle images of both over-/under-exposures. + +While sharing some similarities with image harmonization methods, e.g., pixel-wise curve modeling and retina-based image decomposition, image enhancement methods do not model the discrepancy between source and target scenes. Directly enhancing composite images with image enhancement methods tends to amplify scene discrepancies. + +# 3. Proposed Method + +We propose to harmonize cut-and-paste object colors by tracing back them to the scene radiance field. To this end, we propose an image unprocessing method to transfer the input composite image into a linear high dynamic range color space, and a harmonization method to re-render the target object colors by querying the scene radiance information. Figure 2 shows the whole harmonization process. + +# 3.1. Image Unprocessing + +Converting camera output sRGB images back to camera raw images, i.e., image unprocessing [60, 39, 40, 3, 55, 41], requires a systematic modelling of the ISP operations. Ex- + +isting methods are typically sensor-specific, requiring additional camera information to convert each image. We note that most camera ISPs typically apply a set of camera-variant linear operations (e.g., white balance) to convert CCD data into a camera-independent color space, and then apply another set of non-linear operations (e.g., quantization and local enhancement) to render images [28]. Hence, converting the sRGB images back into the intermediate camera-independent color space has two advantages for harmonization. First, colors in this intermediate space response to the scene radiance linearly, which helps recover scene discrepancy for harmonization. Second, it avoids the need to model camera-dependent operations (e.g., camera response curves selection [16] or estimation [46]). We formulate a generative diffusion model to address this dynamic range expansion problem of image unprocessing. Although single-image reverse tone mapping is challenging (as it needs to generate missing info in the over-/underexposed regions), learning such image unprocessing in our task is feasible, as images to be harmonized are typically captured with proper exposures. + +Model Formulation. A diffusion model has a forward diffusion process and a reverse denoising process (used for generation). Given a distribution $q(x_0)$ , the forward diffusion process $q$ is a Markovian noisig process [23], which gradually adds noise to $x_0$ to obtain $x_{1:T}$ . Specifically, at each step $t$ , the diffusion process adds random Gaussian noise with a $\beta_t$ -controlled variance: + +$$ +q \left(x _ {1: T} \mid x _ {0}\right) = \prod_ {t = 1} ^ {T} q \left(x _ {t} \mid x _ {t - 1}\right), \tag {1} +$$ + +$$ +q (x _ {t} | x _ {t - 1}) = \mathcal {N} \left(x _ {t}; \sqrt {1 - \beta_ {t}} x _ {t - 1}, \beta_ {t} \mathbb {I}\right), \tag {2} +$$ + +where $\beta_{t} \in (0,1), t = 1, \dots, T$ . With the reparameterization trick [30], we sample $x_{t}$ from each time step $t$ in a closed + +![](images/5c9df94b7360647e13cc5d15a81864cba294f34512345aaa45f2ae8aec0bf0e4.jpg) +Figure 3. The feature harmonization process. Given the concatenated linear foreground and background features $f = [F_{f}, F_{b}]$ , it first uses an SE block [24] to adjust the attention for each channel to be the same, and then propagates channel consistency to the spatial domain to produce harmonized foreground features $f_{h}$ . + +form: $x_{t} = \sqrt{\bar{\alpha}_{t}} x_{0} + \sqrt{1 - \bar{\alpha}_{t}}\epsilon ,\epsilon \sim \mathcal{N}(0,\mathbb{I})$ + +$$ +q \left(x _ {t} \mid x _ {0}\right) = \mathcal {N} \left(x _ {t}; \sqrt {\bar {\alpha} _ {t}} x _ {0}, (1 - \bar {\alpha} _ {t}) \mathbb {I}\right), \tag {3} +$$ + +where $\alpha_{t} = 1 - \beta_{t}$ and $\bar{\alpha}_{t} = \prod_{i = 1}^{t}\alpha_{i}$ . In this way, we directly derive $x_{t}$ from $q(x_{t}|x_{0})$ without repeatedly applying the Markovian process $q$ and calculating $q(x_{t}|x_{t - 1})$ . + +We formulate image unprocessing as a reverse denoising process (i.e., generation process) that is conditioned on the sRGB input image $I_{in}$ . We compute $x_0$ (i.e., the linear color image $I_l$ ) via the reverse diffusion process $p_\theta(x_{t-1}|x_t)$ parameterized by $\theta$ with a random Gaussian distribution, i.e., $x_T \sim \mathcal{N}(0,\mathbb{I})$ , as: + +$$ +p _ {\theta} \left(x _ {0: T} \mid I _ {i n}\right) = p \left(x _ {T}\right) \prod_ {t = 1} ^ {T} p _ {\theta} \left(x _ {t - 1} \mid x _ {t}, I _ {i n}\right), \tag {4} +$$ + +$$ +p _ {\theta} \left(x _ {t - 1} \mid x _ {t}, I _ {i n}\right) = \mathcal {N} \left(x _ {t - 1}; \mu_ {\theta} \left(x _ {t}, I _ {i n}, t\right), \sum_ {\theta} \left(x _ {t}, I _ {i n}, t\right)\right). \tag {5} +$$ + +Unlike previous methods that are conditioned on the class labels [14] or shape latents [35], we condition the diffusion process on the sRGB image $I_{in}$ pixel-wisely. + +Model Architecture. Our image unprocessing model adopts a fully convolutional encoder-decoder network [34], as shown in Figure 2(left). Given the sampled noise with the sRGB image as the condition, we encode them into a low dimensional latent representation, which is then decoded to reconstruct the linear color image. We leverage the generation ability of reversing the denoising process to expand the dynamic range, and use the encoder-decoder architecture to perform image unprocessing. To facilitate the learning process, we add a skip connection directly from the input image to the output. Instead of learning to generate the linear color image of the whole dynamic range, the image unprocessing network only needs to generate the difference between + +the input and the output, resulting in a fast reverse diffusion process. We train this network from scratch and use batch normalization and GELU activation for all the convolutional layers. We use the weighted variational bound [23] to optimize this model. + +# 3.2. Harmonization and Rendering + +We propose a harmonization module to harmonize the colors of the target object by querying background radiance information and re-render the harmonized image in the sRGB space. + +Harmonization in Linear Space. As shown in Figure 2(right), given the reconstructed linear color image $I_{l}$ we first separately obtain foreground and background features (i.e., $F_{f}$ and $F_{b}$ ) via two separate encoders and the foreground mask $M$ , as $F_{f} = \text{Enc}_{f}(I_{l} * M)$ and $F_{b} = \text{Enc}_{b}(I_{l} * (1 - M))$ . Our goal is to harmonize the foreground features $F_{f}$ based on $F_{b}$ to obtain $\hat{F}_{f}$ , and then render the harmonized foreground features $\hat{F}_{f}$ into the sRGB space $\hat{F}_{f} \rightarrow \hat{I}_{f}$ conditioned on the rendering process of $F_{b} \rightarrow I_{b}$ . To this end, we harmonize the concatenated features $f = [F_{f}, F_{b}]$ in both channel and spatial dimensions. We implement the channel harmonization by using the squeeze-and-excitation operation [24] to assign consistent attention for each channel of $f = [F_{f}, F_{b}]$ . As the reweighed features are computed channel-wisely according to both foreground and background representations, the consistent attention indicates that these representations are harmonized to be consistent as well. We then propagate channel harmonization to the spatial domain via the bilat- + +![](images/db618b9a860c212475127789a542c6ba3c7ce0fe783feb7fe16f94b771740a59.jpg) +(a) Input +(b) IIH [21] +(c) CDT [11] +(d) WBH [29] +(e) Ours +(f) Ground Truth +Figure 4. Visual comparison on composite images with humans. The proposed method is able to harmonize the colors in the cut-and-paste regions and produce realistic images compared with the state-of-the-art methods. + +eral propagation activation functions: + +$$ +y _ {i} ^ {s} = \frac {1}{C (f)} \sum_ {j \in s} g (\| j - i \|) f _ {j}, \tag {6} +$$ + +$$ +y _ {i} ^ {r} = \frac {1}{C (f)} \sum_ {j \in v} h \left(f _ {i}, f _ {j}\right) f _ {j}, \tag {7} +$$ + +$$ +y _ {i} = c \left(y _ {i} ^ {s}, y _ {i} ^ {r}\right), \tag {8} +$$ + +where $f_{i}$ is the feature channel at position $i$ of the input features $f$ . $f_{j}$ is a neighboring feature channel around $i$ at position $j$ . $y_{i}^{s}$ and $y_{i}^{r}$ are the features after spatial and range similarity measurements. The normalization factor is set to $C(f) = N$ , where $N$ is the number of positions in $f$ . $c$ represents the pixel-wise summation and a linear transformation of $y_{i}^{s}$ and $y_{i}^{r}$ via a $1 \times 1$ convolutional layer. The bilateral propagation extends the consistency of feature channels to both spatial and range dimensions. In spatial propagation, we set the neighboring region $s$ to be of the same spatial resolution as the input features for global propagation. A Gaussian function $g(\cdot)$ [52] is used to compute the spatial contributions from neighboring background features. In range propagation, we measure the similarity between features $f_{i}$ and $f_{j}$ via $h(\cdot)$ within a neighboring region $v$ around $i$ . The size of $v$ is set to $3 \times 3$ . The range similarity is computed via the pairwise function $h(\cdot)$ with a + +dot product operation: + +$$ +h \left(f _ {i}, f _ {j}\right) = \left(f _ {i}\right) ^ {T} \left(f _ {j}\right). \tag {9} +$$ + +In this way, the bilateral propagation process harmonizes the foreground colors by considering both global continuity via $y_{i}^{s}$ and local consistency via $y_{i}^{r}$ . Figure 3 shows the feature harmonization process. + +Our bilateral propagation is close in spirit to the nonlocal block [52], in that for each $i$ , $\frac{1}{C(f)}\sum g(f_i,f_j)$ computes the softmax scores along dimension $j$ . The main difference is the regions of propagation. The non-local block uses feature channels from all positions to generate $y_{i}$ and the similarity is only measured between $f_{i}$ and $f_{j}$ . In contrast, our method considers channel similarity, long-range and neighboring spatial correlations between $f_{i}$ and $f_{j}$ for feature harmonization. During the long-range correlation modeling, we query the global scene radiance information using region $s$ of the original background features (i.e., before the channel-wise harmonization), while during the neighboring correlation modeling, we query the local scene information using the background features after channelwise adjustment. The foreground colors are then set to be consistent to the background both globally and locally. + +Background Preserving Guided Rendering. After the harmonization process in the linear embedding space, we assign a decoder to re-project the harmonized linear image + +![](images/12a30c7e42593860ecc2f1aa4d50b923fd62db57577e3bef32362c1a92f7448b.jpg) + +![](images/c17d9e06c4f407f4449283dd347eee6d44e48496a7f4d72dec8913b03f48af10.jpg) + +![](images/d3b5f0571314a43748ffd0529ab1078e27fe81f0b758f4d4e70618e7be624638.jpg) + +![](images/02f5d629497a7fa9a2f5db9f98019b57eb6f81d38f29dbb3b66ffa32aa800bb4.jpg) + +![](images/9729738102014cdc996f4e2b05c3ce397beac8e9e4fa74314ac8b64915362d14.jpg) + +![](images/6b74406cc7b10bc1c831c64ccf83ef80410b1acef4d9d2c0bf1658915fc5adbb.jpg) + +![](images/207368a7659620b52ce3fcf32896ff38a98505a30a2da6be7150985851fbce30.jpg) + +![](images/4545c77cb1f571f7b79baa03f91a5f74447157d9d866378bf59fa6f3d3c2a8c5.jpg) + +![](images/d1720b8206c9629c9a4f58117379fc0f6b0073b7126a89dff6654d146a8fdebe.jpg) + +![](images/551ff2246f1b811ed7b68ecfcdf8d3e105b450272fa1b0f89ad2105e5ca1028f.jpg) + +![](images/4281b9684dcef657ac27b34cde44064fa3e332f8eb8be88c4b63368c2bb98947.jpg) + +![](images/7c2699bd5995427813f33eaf9898ffe49b7393c541065f2d1f7614fe5945a394.jpg) + +![](images/73372cd4eaac07374a42f85436b3f97043ac31abba26bdfe91d710421e127f03.jpg) + +![](images/7b02aabdc1bfcb577a55e0563a0075ead4c808098b9270b4e0c20d786c367f3a.jpg) + +![](images/5a1641976c030215bae5de4f31d2161f6ebe85123e6fbea221ed7b530694c2c2.jpg) + +![](images/50cd2439446b8eff776dd927146706da10a0f766bd7fc6450a188e6ddadfbd47.jpg) + +![](images/ead985a81d31ee7846d4cf8b74a9371f3e46b4c2afc91c2aa4e1b1c8cf344445.jpg) + +![](images/692fd09a30041e7239536c11819460f0efd0f9843ceab04b325aaf61bff71837.jpg) + +![](images/b8c3e3c11cb5922d5054b9aa19fbfb404e6334542812b0b512a4d22bf6c50aa4.jpg) +(a) Input + +![](images/8923dcc21fc00eac2d607d8b228b81f053b1a2177bc7e43e0f023c8aa9c3b6a1.jpg) +(b) IIH [21] + +![](images/1c102ab7e5eee265300cea57572b39ccb64954789e6c89cdfe663cd5f925dbe5.jpg) +(c) CDT [11] + +![](images/15dcc1d2fd4c725509209bc82e766b12b818bc35ef96907d751cf99257c581b4.jpg) +(d) WBH [29] +Figure 5. Visual comparison on composite images with general objects. The proposed method is able to harmonize the colors in the cut-and-paste regions and produce more realistic images compared with the state-of-the-art methods. + +![](images/e15c6a4873adc5e3bb134de217426663539dd5fddd610c60eebf7ba7e415d980.jpg) +(e) Ours + +![](images/18d03eeda0430e3d259f60137735f86a1f615b94db256cdf9a8302990c5130b6.jpg) +(f) Ground Truth + +back to the sRGB space. To avoid further artifacts produced during the foreground rendering process, we leverage the identity property of the background rendering process (i.e., the background should remain identical after the color-metric conversion, harmonization and rendering processes) as the guidance. Since our encoder of the image unprocessing and the color rendering decoder are symmetric, we add a foreground feature consistency constraint to guide the rendering process. In our implementation, we add an $L_{1}$ and a Cosine similarity terms to align the foreground features in magnitude and directions, of the image unprocessing encoder and the Color Harmonization decoder (Figure 2 right). We follow previous methods to produce the final harmonized image $I_{h}$ as: + +$$ +I _ {o u t} = I _ {o} \times M + I _ {i n} \times (1 - M), \tag {10} +$$ + +where $I_{o}$ is the decoder output of the Color Harmonization process. We use standard $L_{1}$ loss to optimize this model. + +# 3.3. Implementation Details + +We have implemented the proposed model under Pytorch, and tested it on a PC with an i7 4GHz CPU and a GTX4090 GPU. The network parameters are initialized using the truncated normal initializer. For loss minimization, we adopt the AdamW optimizer. We first train the image unprocessing network on the Adobe5K dataset [4] for 300 epochs with an initial learning rate of $1e^{-4}$ , which is di + +vided by 2 every 75 epochs. We then freeze the image unprocessing network and train the Color Harmonization network on the iHarmony4 dataset [12] for 75 epochs, with an initial learning rate of $1e^{-4}$ , which is divided by 10 at the 30th epoch. T in Eq. 1 is empirically set to 4000. It takes around 50 hours to train our model and 0.87s for testing a $256 \times 256$ image (3.78s for a $1024 \times 1280$ image). + +# 4. Results + +Evaluation Methods. We compare our method to 7 latest state-of-the-art deep harmonization methods: Dove [12], $\mathbf{S}^2\mathrm{AM}$ [13], IIH [21], IHT [20], CDT [11], WBH [29] and SCSCo [22]. Since SCSCo [22] does not provide code and results, we directly copy their performances reported in their paper for references. For other methods, we use either the pre-trained models released by their authors or their released results for evaluation. Among them, $\mathbf{S}^2\mathrm{AM}$ [13] and WBH [29] learn either implicit mapping curves or explicit filters to adjust the appearances of the foreground objects; Dove [12] and SCSCo [22] perform harmonization based on style transfer learning. IIH [21] is retina-based. It harmonizes the foreground objects in the intermediate illumination layer. CDT [11] and IHT [20] model the harmonization process with pixel-to-pixel mapping while an additional color-to-color mapping is used in CDT [11]. We compare our method to these methods to demonstrate the effectiveness of harmonizing foreground objects in the in + +
DatasetsMetricsS2AM [13]Dove [12]IIH [21]IHT [20]CDT [11]WBH [29]SCSCo [22]Ours
HAdobe5KPSNR↑33.7734.3435.2036.1038.2437.6438.2938.93
MSE↓63.4052.3243.0247.9620.6221.8921.0120.11
fMSE↓404.62380.39284.21321.14-170.05165.48154.82
HFlickrPSNR↑30.0329.7531.3432.3733.5533.6334.2234.76
MSE↓143.45145.21105.1388.4168.6164.8155.8354.20
fMSE↓785.65827.03716.60617.26-434.06393.72386.12
HCOCOPSNR↑35.4735.8337.1637.8739.1538.7739.8839.94
MSE↓41.0736.7224.9220.9916.2517.3413.5811.27
fMSE↓542.06551.01416.38377.11-298.42245.54217.55
Hday2nightPSNR↑34.5035.5335.9636.3837.9537.5637.8338.42
MSE↓76.6156.9255.5358.1436.7233.1441.7539.79
fMSE↓989.071075.71797.04823.68-542.07606.80587.44
AveragePSNR↑34.3534.7535.9036.7138.2337.8438.7539.36
MSE↓59.6752.3638.7137.0723.7524.2621.3320.77
fMSE↓594.67532.62400.29395.66-280.51248.86238.19
+ +Table 1. Quantitative comparison between the proposed method and state-of-the-art deep harmonization methods on the iHarmony4 dataset [12] at ${256} \times {256}$ image resolution. It shows that the proposed method outperforms existing image harmonization methods. Best performances are marked in bold. + +intermediate linear color space. + +In addition, to verify whether our image unprocessing module produces faithful linear images, we perform an internal analysis and compare it to 4 representative state-of-the-art deep networks, including Unprocess [3], HDRCNN [15], CycleISP [61], and CIE-XYZNet [1]. Among them, Unprocess [3] is a systematic pipeline that converts sRGB images to raw images via a sequence of reverse ISP operations. HDRCNN [15] uses an encoder-decoder network to convert sRGB images into the HDR domain. CycleISP [61] and CIE-XYZNet [1] learn cycle mappings (sRGB-to-raw and raw-to-sRGB). + +Evaluation Datasets and Metrics. We follow existing methods to evaluate the harmonization performance by using the Mean Square Error (MSE), foreground MSE (fMSE) and Peak Signal-to-Noise Ratio (PSNR), on the iHarmony4 dataset [12]. When internally analyzing the proposed image unprocessing module on the Adobe5K dataset [4], in addition to the PSNR metric, we also use the widely adopted HDR-VDP-2 [37] metric to measure the image quality based on human perceptions. + +# 4.1. Comparing to State-of-the-art Methods + +We compare the proposed method with state-of-the-art image harmonization methods on the standard benchmarks. + +Visual Comparison. Figure 4 shows visual comparison where the cut-and-paste regions contain humans. While the latest methods are effective in adjusting the brightness of the foreground targets to fit the background illumination conditions, they are not able to produce visually pleasing colors, as shown in Figure 4(b-d). In contrast, our method is able to render realistic colors in the cut-and-paste regions, as shown in Figure 4(e). Figure 5 shows some ex + +amples where the cut-and-paste regions contain general objects. While existing methods may produce pale colors Figure 5(b,c) or color artifacts Figure 5(d). In contrast, our method produces foreground colors that are more realistic and consistent with the background, as shown in Figure 5(e). + +Quantitative Comparison. In addition to the visual evaluation, we also provide quantitative comparison between the proposed method and existing harmonization methods. We first follow existing methods to evaluate the harmonization performance on images of resolution $256 \times 256$ in the iHarmony4 benchmark [12]. Table 1 shows the results. We can see that the proposed method outperforms existing methods on all evaluation metrics under all subsets of iHarmony4. Table 2 shows additional comparisons at the original image resolution. Note that CDT [11] only releases their low-resolution results. The comparison shows that our method can handle images of higher resolutions. + +# 4.2. Internal Analysis + +As our method first converts the input composite image into the intermediate linear color space via the image unprocessing process, we demonstrate its effectiveness in producing faithful colors in the high dynamic range domain. We evaluate it on the CIE xyz version of the Adobe 5K dataset using the PSNR and HDR-VDP2 metrics. The HDR-VDP2 metric produces a Q score for each test image via a Mean-Oinion-score metric. The Q score indicates the degree of image quality degradation. Table 3 reports the average PSNR and Q score on the test set. The results show that the proposed image unprocessing process can produce more faithful images due to its generation ability. + +We now perform ablation studies on our network de + +
DatasetsMetricsIHT [20]WBH [29]Ours
HAdobe5KPSNR↑33.6337.8038.42
MSE↓56.9024.3723.76
HFlickrPSNR↑29.5933.3733.97
MSE↓135.4969.1961.70
HCOCOPSNR↑34.1937.6938.22
MSE↓44.9520.9320.08
Hday2nightPSNR↑35.7137.1537.64
MSE↓63.2637.2830.11
AveragePSNR↑33.5437.2337.92
MSE↓58.8927.6223.90
+ +Table 2. Quantitative comparisons on the iHarmony4 dataset [12] at the original resolution. It shows that our method outperforms all existing image harmonization methods. Best performances are marked in bold. + +
MethodsPSNR↑Q score↑
Unprocess [3]22.1950.33
HDRCNN [15]27.7455.61
CycleISP [61]28.2954.74
CIE-XYZNet [1]29.6656.08
CycleGAN [64]27.6456.17
Ours30.3458.14
+ +Table 3. Internal Analysis. We quantitatively compare the converted linear images with existing representative methods using PSNR and Q score. Best performances are marked in bold. + +
MethodsPSNR↑MSE↓
w/o CC37.7924.26
DP→CP38.2823.60
w/o FH38.1023.94
w/o BP39.1721.10
Single Encoder39.0222.28
w/o SE Block38.4723.79
w/o Spatial Attention38.1923.57
Ours39.3620.77
+ +Table 4. Ablation Study of network design on iHarmony4 at ${256} \times$ 256 image resolution. Best performances are marked in bold. + +sign. We follow previous methods to perform it on the iHarmony4 dataset. In particular, we investigate the following ablated network architectures: (1) we remove the image unprocessing process and directly train a Color Harmonization network (denoted as “ $w/o$ CC”); (2) we replace the diffusion process of the image unprocessing with a standard convolution process (denoted as “ $\mathrm{DP} \rightarrow \mathrm{CP}$ ”); (3) we remove the Feature Harmonization from the Color Harmonization process (denoted as “ $w/o$ FH”); (4) we remove the Background Preserving of the Color Rendering process (denoted as “ $w/o$ BP”); (5) we use a single encoder in the Color Harmonization network (“denoted as Single Encoder”); (6) we remove the SE block from the feature harmonization + +process ("denoted as $w / o$ SE Block"); and (7) we remove the spatial attention from the feature harmonization process ("denoted as $w / o$ Spatial Attention"). Table 4 reports the performance. It shows that our designs of image unprocessing, Feature Harmonization and background preserving are able to improve the image harmonization performances. We have tried to train DoveNet [12] from scratch in linear space and it yields slightly better results (PSNR:34.94 (+0.19)) but fine-tuning using their pre-trained model degrades the performance (PSNR:33.18 (-1.57)). This is due to the discrepancy between linear and non-linear images, which demonstrates that it is necessary to design a specific image unprocessing model for harmonization. We have also tried ControlNet [62] for harmonization, which, however, does not perform well (PSNR/MAE: 14.36/109.40). As image harmonization requires the harmonized images to be photorealistic, directly using the diffusion-based model may generate visually pleasing but fake image details. + +![](images/1597dead988c9552610b87641f4054f8e22964cd90f0d367750aa13f8d544a79.jpg) +(a) Input + +![](images/3f83b7d23d2c203f36ab766daf86b289de85a9bdbb6889afe8b5a2a5ab2a0945.jpg) +(b) Ours + +![](images/a52b29b3e0684a7a6be133d910d6fc6e459811998a34e62fbf95538f3b01d8de.jpg) +(c) Ground Truth +Figure 6. Our method may fail to harmonize the color tones of the inserted target when the new background does not provide sufficient scene illumination information. + +# 5. Conclusion + +This paper presents a novel image harmonization method that performs the color harmonization process in the linear color space. Our method includes a novel image unprocessing process to convert the cut-and-paste image into the high dynamic range linear color space, and a novel color harmonization process to harmonize object colors by querying background radiance information. We have conducted extensive experiments on the benchmark datasets to analyze the properties of the proposed method, and shown that it outperforms the state-of-the-art harmonization methods. + +Our method does have limitations. It may fail when the background does not contain sufficient scene illumination information. Figure 6 shows such an example, in which the background is completely dark and our method fails to harmonize the color tones of the foreground. + +Acknowledgement. This project was partially supported by a GRF grant from the Research Grants Council of Hong Kong (Project No. CityU 11205620), by City University of Hong Kong (9678131), and by the Research Grants Council of the Hong Kong Special Administrative Region, China (CityU 11214620). + +# References + +[1] Mahmoud Afifi, Abdelrahman Abdelhamed, Abdullah Abuolaim, Abhijith Punnappurath, and Michael S Brown. Cie xyz net: Unprocessing images for low-level computer vision tasks. IEEE TPAMI, 2021. 7, 8 +[2] Mahmoud Afifi, Konstantinos G Derpanis, Bjorn Ommer, and Michael S Brown. Learning multi-scale photo exposure correction. In CVPR, 2021. 3 +[3] Tim Brooks, Ben Mildenhall, Tianfan Xue, Jiawen Chen, Dillon Sharlet, and Jonathan T Barron. Unprocessing images for learned raw denoising. In CVPR, 2019. 3, 7, 8 +[4] Vladimir Bychkovsky, Sylvain Paris, Eric Chan, and Fredo Durand. Learning photographic global tonal adjustment with a database of input/output image pairs. 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In ICCV, 2017. 8 \ No newline at end of file diff --git a/2023/Learning Image Harmonization in the Linear Color Space/images.zip b/2023/Learning Image Harmonization in the Linear Color Space/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e8e92a98868f6079ab74213aa04d4d70168adf35 --- /dev/null +++ b/2023/Learning Image Harmonization in the Linear Color Space/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5c6ebb138391a7eb1e9af1648badc5967c8ae22423356212ad9939b94ed8aa78 +size 818621 diff --git a/2023/Learning Image Harmonization in the Linear Color Space/layout.json b/2023/Learning Image Harmonization in the Linear Color Space/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..93519fce43a3ceba30d5a1e62aba2507e1c4d133 --- /dev/null +++ b/2023/Learning Image Harmonization in the Linear Color Space/layout.json @@ -0,0 +1,10476 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 117, + 103, + 477, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 103, + 477, + 121 + ], + "spans": [ + { + "bbox": [ + 117, + 103, + 477, + 121 + ], + "type": "text", + "content": "Learning Image Harmonization in the Linear Color Space" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 168, + 144, + 425, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 144, + 425, + 172 + ], + "spans": [ + { + "bbox": [ + 168, + 144, + 425, + 172 + ], + "type": "text", + "content": "Ke Xu, Gerhard Petrus Hancke, Rynson W.H. Lau \nCity University of Hong Kong" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 169, + 174, + 424, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 169, + 174, + 424, + 185 + ], + "spans": [ + { + "bbox": [ + 169, + 174, + 424, + 185 + ], + "type": "text", + "content": "{kkangwing, gp.hancke, rynson.lau}@cityu.edu.hk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 239, + 290, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 290, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 290, + 514 + ], + "type": "text", + "content": "Harmonizing cut-and-paste images into perceptually realistic ones is challenging, as it requires a full understanding of the discrepancies between the background of the target image and the inserted object. Existing methods mainly adjust the appearances of the inserted object via pixel-level manipulations. They are not effective in correcting color discrepancy caused by different scene illuminations and the image formation processes. We note that image colors are essentially camera ISP projection of the scene radiance. If we can trace the image colors back to the radiance field, we may be able to model the scene illumination and harmonize the discrepancy better. In this paper, we propose a novel neural approach to harmonize the image colors in a camera-independent color space, in which color values are proportional to the scene radiance. To this end, we propose a novel image unprocessing module to estimate an intermediate high dynamic range version of the object to be inserted. We then propose a novel color harmonization module that harmonizes the colors of the inserted object by querying the estimated scene radiance and re-rendering the harmonized object in the output color space. Extensive experiments demonstrate that our method outperforms the state-of-the-art approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 525, + 128, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 525, + 128, + 538 + ], + "spans": [ + { + "bbox": [ + 48, + 525, + 128, + 538 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 546, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 287, + 641 + ], + "type": "text", + "content": "Image compositing is a common process in vision and graphics. It is a technique to render a novel image by inserting a target object from the source image onto a target image. However, humans can easily identify this cut-and-paste (or composite) image as a synthetic one due to its color [7] and texture inconsistencies [31, 63]. Hence, there is a line of research to develop algorithms to harmonize cut-and-paste images to produce visually realistic output images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Existing image harmonization methods typically fall into two categories, i.e., non-deep learning-based methods [42, 10, 47, 58, 63] and deep learning-based methods [48, 13, 8, 12, 33, 21, 27, 20]. 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Harmonization results on the iHarmony4 dataset [12]. Existing harmonization methods tend to produce dull (b-d) or inconsistent (h-j) colors. Our method traces back to and harmonizes the colors in an intermediate linear color space, resulting in more realistic composite images as shown in (e) and (k)." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 389, + 428, + 464, + 487 + ], + "blocks": [ + { + "bbox": [ + 406, + 418, + 445, + 427 + ], + "lines": [ + { + "bbox": [ + 406, + 418, + 445, + 427 + ], + "spans": [ + { + "bbox": [ + 406, + 418, + 445, + 427 + ], + "type": "text", + "content": "(h) IIH [21]" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 389, + 428, + 464, + 487 + ], + "lines": [ + { + "bbox": [ + 389, + 428, + 464, + 487 + ], + "spans": [ + { + "bbox": [ + 389, + 428, + 464, + 487 + ], + "type": "image", + "image_path": "85c5ed936f4bed5e921f5a132c574cef7547829283b4a1bbea70d5f676c0f02d.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 412, + 490, + 440, + 498 + ], + "lines": [ + { + "bbox": [ + 412, + 490, + 440, + 498 + ], + "spans": [ + { + "bbox": [ + 412, + 490, + 440, + 498 + ], + "type": "text", + "content": "(k) Ours" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 465, + 428, + 542, + 487 + ], + "blocks": [ + { + "bbox": [ + 481, + 418, + 524, + 427 + ], + "lines": [ + { + "bbox": [ + 481, + 418, + 524, + 427 + ], + "spans": [ + { + "bbox": [ + 481, + 418, + 524, + 427 + ], + "type": "text", + "content": "(i)CDT [11]" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 465, + 428, + 542, + 487 + ], + "lines": [ + { + "bbox": [ + 465, + 428, + 542, + 487 + ], + "spans": [ + { + "bbox": [ + 465, + 428, + 542, + 487 + ], + "type": "image", + "image_path": "579de76c75f0dddcb81d50d7df09e58c1db2f09e7378f25ce28793bfa5477f9c.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 475, + 490, + 529, + 499 + ], + "lines": [ + { + "bbox": [ + 475, + 490, + 529, + 499 + ], + "spans": [ + { + "bbox": [ + 475, + 490, + 529, + 499 + ], + "type": "text", + "content": "(1) Ground Truth" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "ject, to match with those of the background. These methods often produce unrealistic images of inconsistent colors/textures when the hand-crafted features fail to represent the foreground/background. In contrast, deep learning based methods offer strong capability of modelling region appearances to facilitate harmonization. Some methods explore different priors (e.g., semantics [48], and gradient/color consistency [8, 53]) to constrain the harmonization process. Some other methods [12, 33, 21] may formulate the image harmonization process as a foreground-background transfer learning task." + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12570" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "Despite their success, existing harmonization methods may still produce pale (Figure 1(b-d)) or inconsistent colors (Figure 1(h-j)) across the foreground and background regions, resulting in visually unpleasant images. We note that all these methods model the color harmonization process in the camera output sRGB (i.e., low dynamic range) color space. However, object colors in an image are determined not only by their material reflectance and scene illumination, but also by the black-box imaging pipeline (ISP) of the camera. Due to the non-linear operations (e.g., tone mapping) within the ISP, pixel intensities of camera output sRGB images are not proportional to the scene radiance, making them unreliable for use in estimating the scene illumination for color harmonization." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 515 + ], + "type": "text", + "content": "To address this problem, we propose in this paper a novel approach to harmonize a cut-and-paste image (captured in low dynamic range) in the high dynamic range domain. Our key idea is to harmonize the scene illumination discrepancies in an intermediate (high dynamic range) color space, in which the scene illumination is proportional to the original scene radiance. To this end, we propose a novel neural network that first converts the source image (containing the target object) into an intermediate high dynamic range domain, then performs the harmonization process, and finally converts the harmonized image back to the low dynamic range sRGB space. To avoid exhaustive modeling of camera-dependent operations, we propose a novel image unprocessing module to estimate a high dynamic range version of the input image in the linear camera-independent CIE XYZ color space. We formulate this image unprocessing process as a diffusion process. We propose a novel color harmonization method that models image colors in the estimated linear color space to produce the final harmonized results. As shown in Figure 1(e,k), our method is able to produce more visually pleasing results. We conduct extensive experiments to demonstrate that our method outperforms state-of-the-art harmonization approaches." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 516, + 271, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 516, + 271, + 528 + ], + "spans": [ + { + "bbox": [ + 59, + 516, + 271, + 528 + ], + "type": "text", + "content": "In summary, this paper has three main contributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 539, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 539, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 539, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 58, + 539, + 287, + 587 + ], + "type": "text", + "content": "- We propose a novel neural approach for image harmonization that performs the color harmonization process in the linear color space, allowing object color modeling based on faithful scene radiance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 596, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 596, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 58, + 596, + 287, + 681 + ], + "type": "text", + "content": "- Our approach includes two novel modules: (1) a novel image unprocessing module to convert the source image (of the target object) into a version in the high dynamic range linear color space, and (2) a novel color harmonization module to harmonize object colors by querying scene radiance information and re-render the harmonized objects in the output color space." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "content": "- Extensive experiments show that the proposed method outperforms state-of-the-art harmonization methods." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 547, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 282 + ], + "type": "text", + "content": "Image Harmonization aims to adjust the appearance of the foreground object so that it is compatible with the new composite background. Traditional methods [42, 10, 31, 47, 58, 63] typically rely on adjusting the appearance of the foreground to match with the color statistics of the background. Sunkavalli et al. [47] propose to first transfer the visual appearance of the target image to the source image via image histogram matching, and then use alpha blending to produce the composite image. Xue et al. [58] suggest to match zones of the (instead complete) histogram is more effective, and propose the zone selection classifier for matching. Reinhard et al. [42] propose a color transfer method to match the global color statistics between the source and target images. Lalonde and Efros [31] divide the source and target images into corresponding cluster pairs, and perform the color transfer [42] for each cluster pair locally." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 283, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 283, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 547, + 628 + ], + "type": "text", + "content": "In recent years, many deep methods are proposed for image harmonization. Zhu et al. [63] propose to train a CNN classifier to distinguish between real and composite images, and use the learned model to adjust the brightness and contrast model for image composition. Tsai et al. [48] present the first end-to-end CNN-based harmonization method to leverage the semantic information of a scene parsing branch to help boost the performance of the harmonization branch. Cun and Pun [13] propose to use spatial attention modules to learn regional appearance changes for harmonization. Chen and Mae [8] propose a GAN-based method to harmonize images with geometric and color consistency constraints. Wu et al. [53] propose a GAN-based method to explore both gradient and color constraints for image harmonization. Cong et al. [12] construct a large-scale dataset, iHarmony4, and propose a domain verification discriminator to guide the generator to translate the foreground object to the background domain. Ling et al. [33] formulate the image harmonization task as a style transfer problem, and propose the region-aware adaptive instance normalization module to model the background style and apply it to the foreground. Guo et al. [21] propose to decompose the composite image into reflectance and illumination, and harmonize the two via material consistency and light transfer. Self-supervised learning and transformers have also been applied to image harmonization in [27] and [20], respectively. Methods are also proposed for high-resolution image harmonization [11, 32, 29, 57], multiple objects harmonization [44] and interactive portrait harmonization [49]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 630, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 677 + ], + "type": "text", + "content": "Unlike existing methods that harmonize colors in the low dynamic range image domain, we propose to model and harmonize these object colors by tracing back to the high dynamic range scene radiance field." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Image Enhancement aims to produce visually pleasing images with vivid colors and details from low-quality input images of over- or under-exposures. Some meth" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12571" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 72, + 527, + 223 + ], + "blocks": [ + { + "bbox": [ + 63, + 72, + 527, + 223 + ], + "lines": [ + { + "bbox": [ + 63, + 72, + 527, + 223 + ], + "spans": [ + { + "bbox": [ + 63, + 72, + 527, + 223 + ], + "type": "image", + "image_path": "dc931499e6e50c72e15c95c3bbfa3b0670d34fc174c284c4fa25a7f440ee5550.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 223, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 223, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 547, + 258 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed method. Given an input composite image, we first convert it into an intermediate linear color space via the image unprocessing process. The Color Harmonization process then harmonizes the foreground colors in the feature domain, and renders the harmonized colors to produce an output sRGB image with the guidance of the background preserving process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 267, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 289, + 460 + ], + "type": "text", + "content": "ods [19, 17, 5, 51, 45, 36, 54] rely on the retinax theory to decompose the input image into reflectance and illumination layers, and enhance the illumination layer. Cai et al. [6] separately model illuminance and detail layers from multi-exposed images to enhance an under-exposed image. Xu et al. [56] decompose and enhance under-exposed images based on frequency information. Moran et al. [38] learn a set of local parametric filters for image enhancement. Some methods directly learn an image-to-image mapping using high dynamic range information [18, 59, 46] or adversarial learning [25, 9, 26, 43]. Mahmoud et al. [2] propose a coarse-to-fine network to learn color and detail enhancement for addressing over- or under-exposure. Recently, Wang et al. [50] build a local color distributions pyramid with a dual-illumination estimation method to handle images of both over-/under-exposures." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 460, + 288, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 288, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 288, + 533 + ], + "type": "text", + "content": "While sharing some similarities with image harmonization methods, e.g., pixel-wise curve modeling and retina-based image decomposition, image enhancement methods do not model the discrepancy between source and target scenes. Directly enhancing composite images with image enhancement methods tends to amplify scene discrepancies." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 544, + 153, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 153, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 153, + 558 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "type": "text", + "content": "We propose to harmonize cut-and-paste object colors by tracing back them to the scene radiance field. To this end, we propose an image unprocessing method to transfer the input composite image into a linear high dynamic range color space, and a harmonization method to re-render the target object colors by querying the scene radiance information. Figure 2 shows the whole harmonization process." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 167, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 167, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 167, + 672 + ], + "type": "text", + "content": "3.1. Image Unprocessing" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Converting camera output sRGB images back to camera raw images, i.e., image unprocessing [60, 39, 40, 3, 55, 41], requires a systematic modelling of the ISP operations. Ex-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 267, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 547, + 520 + ], + "type": "text", + "content": "isting methods are typically sensor-specific, requiring additional camera information to convert each image. We note that most camera ISPs typically apply a set of camera-variant linear operations (e.g., white balance) to convert CCD data into a camera-independent color space, and then apply another set of non-linear operations (e.g., quantization and local enhancement) to render images [28]. Hence, converting the sRGB images back into the intermediate camera-independent color space has two advantages for harmonization. First, colors in this intermediate space response to the scene radiance linearly, which helps recover scene discrepancy for harmonization. Second, it avoids the need to model camera-dependent operations (e.g., camera response curves selection [16] or estimation [46]). We formulate a generative diffusion model to address this dynamic range expansion problem of image unprocessing. Although single-image reverse tone mapping is challenging (as it needs to generate missing info in the over-/underexposed regions), learning such image unprocessing in our task is feasible, as images to be harmonized are typically captured with proper exposures." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "text", + "content": "Model Formulation. A diffusion model has a forward diffusion process and a reverse denoising process (used for generation). Given a distribution " + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "inline_equation", + "content": "q(x_0)" + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "text", + "content": ", the forward diffusion process " + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "text", + "content": " is a Markovian noisig process [23], which gradually adds noise to " + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "inline_equation", + "content": "x_{1:T}" + }, + { + "bbox": [ + 304, + 533, + 547, + 618 + ], + "type": "text", + "content": ". 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The feature harmonization process. Given the concatenated linear foreground and background features " + }, + { + "bbox": [ + 46, + 234, + 547, + 269 + ], + "type": "inline_equation", + "content": "f = [F_{f}, F_{b}]" + }, + { + "bbox": [ + 46, + 234, + 547, + 269 + ], + "type": "text", + "content": ", it first uses an SE block [24] to adjust the attention for each channel to be the same, and then propagates channel consistency to the spatial domain to produce harmonized foreground features " + }, + { + "bbox": [ + 46, + 234, + 547, + 269 + ], + "type": "inline_equation", + "content": "f_{h}" + }, + { + "bbox": [ + 46, + 234, + 547, + 269 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 287, + 234, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 287, + 234, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 287, + 234, + 300 + ], + "type": "text", + "content": "form: " + }, + { + "bbox": [ + 47, + 287, + 234, + 300 + ], + "type": "inline_equation", + "content": "x_{t} = \\sqrt{\\bar{\\alpha}_{t}} x_{0} + \\sqrt{1 - \\bar{\\alpha}_{t}}\\epsilon ,\\epsilon \\sim \\mathcal{N}(0,\\mathbb{I})" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 88, + 308, + 287, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 308, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 88, + 308, + 287, + 323 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t} \\mid x _ {0}\\right) = \\mathcal {N} \\left(x _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbb {I}\\right), \\tag {3}", + "image_path": "6397c7fd0fb5c1b95289974f24778720bbf144d28196a1b6c9799c0b1a744d8b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} = \\prod_{i = 1}^{t}\\alpha_{i}" + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "text", + "content": ". In this way, we directly derive " + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "inline_equation", + "content": "q(x_{t}|x_{0})" + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "text", + "content": " without repeatedly applying the Markovian process " + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "text", + "content": " and calculating " + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "inline_equation", + "content": "q(x_{t}|x_{t - 1})" + }, + { + "bbox": [ + 47, + 330, + 287, + 367 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "spans": [ + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "text", + "content": "We formulate image unprocessing as a reverse denoising process (i.e., generation process) that is conditioned on the sRGB input image " + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "inline_equation", + "content": "I_{in}" + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "text", + "content": ". We compute " + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "text", + "content": " (i.e., the linear color image " + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "inline_equation", + "content": "I_l" + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "text", + "content": ") via the reverse diffusion process " + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "inline_equation", + "content": "p_\\theta(x_{t-1}|x_t)" + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "text", + "content": " with a random Gaussian distribution, i.e., " + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "inline_equation", + "content": "x_T \\sim \\mathcal{N}(0,\\mathbb{I})" + }, + { + "bbox": [ + 47, + 367, + 287, + 438 + ], + "type": "text", + "content": ", as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 77, + 447, + 287, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 447, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 77, + 447, + 287, + 480 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(x _ {0: T} \\mid I _ {i n}\\right) = p \\left(x _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}, I _ {i n}\\right), \\tag {4}", + "image_path": "b4cef13114e0dae5225171df87ab6a81986c51d0c69ee0c2c744f2821efe7555.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 488, + 287, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 488, + 287, + 512 + ], + "spans": [ + { + "bbox": [ + 47, + 488, + 287, + 512 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}, I _ {i n}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, I _ {i n}, t\\right), \\sum_ {\\theta} \\left(x _ {t}, I _ {i n}, t\\right)\\right). \\tag {5}", + "image_path": "74e9e6ea32438eac8679368ea4564727b009bab649bbed11357c52750cbbe931.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 513, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 287, + 548 + ], + "type": "text", + "content": "Unlike previous methods that are conditioned on the class labels [14] or shape latents [35], we condition the diffusion process on the sRGB image " + }, + { + "bbox": [ + 47, + 513, + 287, + 548 + ], + "type": "inline_equation", + "content": "I_{in}" + }, + { + "bbox": [ + 47, + 513, + 287, + 548 + ], + "type": "text", + "content": " pixel-wisely." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 557, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 557, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 557, + 287, + 713 + ], + "type": "text", + "content": "Model Architecture. Our image unprocessing model adopts a fully convolutional encoder-decoder network [34], as shown in Figure 2(left). Given the sampled noise with the sRGB image as the condition, we encode them into a low dimensional latent representation, which is then decoded to reconstruct the linear color image. We leverage the generation ability of reversing the denoising process to expand the dynamic range, and use the encoder-decoder architecture to perform image unprocessing. To facilitate the learning process, we add a skip connection directly from the input image to the output. Instead of learning to generate the linear color image of the whole dynamic range, the image unprocessing network only needs to generate the difference between" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 287, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 287, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 287, + 545, + 348 + ], + "type": "text", + "content": "the input and the output, resulting in a fast reverse diffusion process. We train this network from scratch and use batch normalization and GELU activation for all the convolutional layers. We use the weighted variational bound [23] to optimize this model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 372, + 473, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 372, + 473, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 372, + 473, + 385 + ], + "type": "text", + "content": "3.2. Harmonization and Rendering" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 396, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 445 + ], + "type": "text", + "content": "We propose a harmonization module to harmonize the colors of the target object by querying background radiance information and re-render the harmonized image in the sRGB space." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": "Harmonization in Linear Space. As shown in Figure 2(right), given the reconstructed linear color image " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "I_{l}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": " we first separately obtain foreground and background features (i.e., " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{f}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{b}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": ") via two separate encoders and the foreground mask " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": ", as " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{f} = \\text{Enc}_{f}(I_{l} * M)" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{b} = \\text{Enc}_{b}(I_{l} * (1 - M))" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": ". Our goal is to harmonize the foreground features " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{f}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{b}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\hat{F}_{f}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": ", and then render the harmonized foreground features " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\hat{F}_{f}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": " into the sRGB space " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\hat{F}_{f} \\rightarrow \\hat{I}_{f}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": " conditioned on the rendering process of " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{b} \\rightarrow I_{b}" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": ". To this end, we harmonize the concatenated features " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "f = [F_{f}, F_{b}]" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": " in both channel and spatial dimensions. We implement the channel harmonization by using the squeeze-and-excitation operation [24] to assign consistent attention for each channel of " + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "inline_equation", + "content": "f = [F_{f}, F_{b}]" + }, + { + "bbox": [ + 304, + 483, + 546, + 713 + ], + "type": "text", + "content": ". As the reweighed features are computed channel-wisely according to both foreground and background representations, the consistent attention indicates that these representations are harmonized to be consistent as well. We then propagate channel harmonization to the spatial domain via the bilat-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12573" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 68, + 541, + 343 + ], + "blocks": [ + { + "bbox": [ + 55, + 68, + 541, + 343 + ], + "lines": [ + { + "bbox": [ + 55, + 68, + 541, + 343 + ], + "spans": [ + { + "bbox": [ + 55, + 68, + 541, + 343 + ], + "type": "image", + "image_path": "db618b9a860c212475127789a542c6ba3c7ce0fe783feb7fe16f94b771740a59.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 82, + 346, + 111, + 356 + ], + "lines": [ + { + "bbox": [ + 82, + 346, + 111, + 356 + ], + "spans": [ + { + "bbox": [ + 82, + 346, + 111, + 356 + ], + "type": "text", + "content": "(a) Input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 157, + 346, + 196, + 356 + ], + "lines": [ + { + "bbox": [ + 157, + 346, + 196, + 356 + ], + "spans": [ + { + "bbox": [ + 157, + 346, + 196, + 356 + ], + "type": "text", + "content": "(b) IIH [21]" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 235, + 346, + 278, + 356 + ], + "lines": [ + { + "bbox": [ + 235, + 346, + 278, + 356 + ], + "spans": [ + { + "bbox": [ + 235, + 346, + 278, + 356 + ], + "type": "text", + "content": "(c) CDT [11]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 313, + 346, + 360, + 356 + ], + "lines": [ + { + "bbox": [ + 313, + 346, + 360, + 356 + ], + "spans": [ + { + "bbox": [ + 313, + 346, + 360, + 356 + ], + "type": "text", + "content": "(d) WBH [29]" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 403, + 346, + 431, + 355 + ], + "lines": [ + { + "bbox": [ + 403, + 346, + 431, + 355 + ], + "spans": [ + { + "bbox": [ + 403, + 346, + 431, + 355 + ], + "type": "text", + "content": "(e) Ours" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 470, + 346, + 525, + 355 + ], + "lines": [ + { + "bbox": [ + 470, + 346, + 525, + 355 + ], + "spans": [ + { + "bbox": [ + 470, + 346, + 525, + 355 + ], + "type": "text", + "content": "(f) Ground Truth" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 357, + 545, + 379 + ], + "lines": [ + { + "bbox": [ + 46, + 357, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 545, + 379 + ], + "type": "text", + "content": "Figure 4. Visual comparison on composite images with humans. The proposed method is able to harmonize the colors in the cut-and-paste regions and produce realistic images compared with the state-of-the-art methods." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 388, + 198, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 198, + 400 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 198, + 400 + ], + "type": "text", + "content": "eral propagation activation functions:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 97, + 416, + 287, + 446 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 416, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 97, + 416, + 287, + 446 + ], + "type": "interline_equation", + "content": "y _ {i} ^ {s} = \\frac {1}{C (f)} \\sum_ {j \\in s} g (\\| j - i \\|) f _ {j}, \\tag {6}", + "image_path": "4345ba014ff0768de2400803ad81093e5ffbf95b943186b967710da3a61865fa.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 97, + 448, + 287, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 448, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 97, + 448, + 287, + 477 + ], + "type": "interline_equation", + "content": "y _ {i} ^ {r} = \\frac {1}{C (f)} \\sum_ {j \\in v} h \\left(f _ {i}, f _ {j}\\right) f _ {j}, \\tag {7}", + "image_path": "8963b010df45710bc8785eaf60001c84d1a6b96b12cc7680ac780624eeff12c9.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 99, + 479, + 287, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 479, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 99, + 479, + 287, + 493 + ], + "type": "interline_equation", + "content": "y _ {i} = c \\left(y _ {i} ^ {s}, y _ {i} ^ {r}\\right), \\tag {8}", + "image_path": "7eb83d38b0fb8a29315b7600f0ab1598962fbba6a0a1e08d0d01ea3c86e6dc54.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " is the feature channel at position " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " of the input features " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": ". 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The normalization factor is set to " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "C(f) = N" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " is the number of positions in " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": ". 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In spatial propagation, we set the neighboring region " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " to be of the same spatial resolution as the input features for global propagation. A Gaussian function " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " [52] is used to compute the spatial contributions from neighboring background features. 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The size of " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": ". The range similarity is computed via the pairwise function " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " with a" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 388, + 398, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 388, + 398, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 388, + 398, + 399 + ], + "type": "text", + "content": "dot product operation:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 378, + 407, + 545, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 407, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 378, + 407, + 545, + 421 + ], + "type": "interline_equation", + "content": "h \\left(f _ {i}, f _ {j}\\right) = \\left(f _ {i}\\right) ^ {T} \\left(f _ {j}\\right). \\tag {9}", + "image_path": "4d62fb2c9b35cc20178d81bfa467eb916f81131e81a33b0e95a54570a3f9c26a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "type": "text", + "content": "In this way, the bilateral propagation process harmonizes the foreground colors by considering both global continuity via " + }, + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "type": "inline_equation", + "content": "y_{i}^{s}" + }, + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "type": "text", + "content": " and local consistency via " + }, + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "type": "inline_equation", + "content": "y_{i}^{r}" + }, + { + "bbox": [ + 304, + 429, + 545, + 476 + ], + "type": "text", + "content": ". Figure 3 shows the feature harmonization process." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "text", + "content": "Our bilateral propagation is close in spirit to the nonlocal block [52], in that for each " + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "inline_equation", + "content": "\\frac{1}{C(f)}\\sum g(f_i,f_j)" + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "text", + "content": " computes the softmax scores along dimension " + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "text", + "content": ". The main difference is the regions of propagation. The non-local block uses feature channels from all positions to generate " + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "text", + "content": " and the similarity is only measured between " + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "inline_equation", + "content": "f_{j}" + }, + { + "bbox": [ + 304, + 477, + 546, + 670 + ], + "type": "text", + "content": ". 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Visual comparison on composite images with general objects. The proposed method is able to harmonize the colors in the cut-and-paste regions and produce more realistic images compared with the state-of-the-art methods." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 376, + 260, + 457, + 327 + ], + "blocks": [ + { + "bbox": [ + 376, + 260, + 457, + 327 + ], + "lines": [ + { + "bbox": [ + 376, + 260, + 457, + 327 + ], + "spans": [ + { + "bbox": [ + 376, + 260, + 457, + 327 + ], + "type": "image", + "image_path": "e15c6a4873adc5e3bb134de217426663539dd5fddd610c60eebf7ba7e415d980.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 403, + 331, + 431, + 340 + ], + "lines": [ + { + "bbox": [ + 403, + 331, + 431, + 340 + ], + "spans": [ + { + "bbox": [ + 403, + 331, + 431, + 340 + ], + "type": "text", + "content": "(e) Ours" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 457, + 260, + 538, + 327 + ], + "blocks": [ + { + "bbox": [ + 457, + 260, + 538, + 327 + ], + "lines": [ + { + "bbox": [ + 457, + 260, + 538, + 327 + ], + "spans": [ + { + "bbox": [ + 457, + 260, + 538, + 327 + ], + "type": "image", + "image_path": "18d03eeda0430e3d259f60137735f86a1f615b94db256cdf9a8302990c5130b6.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 470, + 331, + 525, + 340 + ], + "lines": [ + { + "bbox": [ + 470, + 331, + 525, + 340 + ], + "spans": [ + { + "bbox": [ + 470, + 331, + 525, + 340 + ], + "type": "text", + "content": "(f) Ground Truth" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 376, + 289, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 289, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 289, + 544 + ], + "type": "text", + "content": "back to the sRGB space. To avoid further artifacts produced during the foreground rendering process, we leverage the identity property of the background rendering process (i.e., the background should remain identical after the color-metric conversion, harmonization and rendering processes) as the guidance. Since our encoder of the image unprocessing and the color rendering decoder are symmetric, we add a foreground feature consistency constraint to guide the rendering process. In our implementation, we add an " + }, + { + "bbox": [ + 46, + 376, + 289, + 544 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 376, + 289, + 544 + ], + "type": "text", + "content": " and a Cosine similarity terms to align the foreground features in magnitude and directions, of the image unprocessing encoder and the Color Harmonization decoder (Figure 2 right). We follow previous methods to produce the final harmonized image " + }, + { + "bbox": [ + 46, + 376, + 289, + 544 + ], + "type": "inline_equation", + "content": "I_{h}" + }, + { + "bbox": [ + 46, + 376, + 289, + 544 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 96, + 555, + 287, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 555, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 96, + 555, + 287, + 567 + ], + "type": "interline_equation", + "content": "I _ {o u t} = I _ {o} \\times M + I _ {i n} \\times (1 - M), \\tag {10}", + "image_path": "60dd598e4735eb57b034e3046eafa6d9569a39bd77921f6f4b488df1b6fc349f.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "text", + "content": " is the decoder output of the Color Harmonization process. We use standard " + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "text", + "content": " loss to optimize this model." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 47, + 610, + 179, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 179, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 179, + 623 + ], + "type": "text", + "content": "3.3. Implementation Details" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "We have implemented the proposed model under Pytorch, and tested it on a PC with an i7 4GHz CPU and a GTX4090 GPU. The network parameters are initialized using the truncated normal initializer. For loss minimization, we adopt the AdamW optimizer. We first train the image unprocessing network on the Adobe5K dataset [4] for 300 epochs with an initial learning rate of " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ", which is di" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "text", + "content": "vided by 2 every 75 epochs. We then freeze the image unprocessing network and train the Color Harmonization network on the iHarmony4 dataset [12] for 75 epochs, with an initial learning rate of " + }, + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "text", + "content": ", which is divided by 10 at the 30th epoch. T in Eq. 1 is empirically set to 4000. It takes around 50 hours to train our model and 0.87s for testing a " + }, + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "text", + "content": " image (3.78s for a " + }, + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "inline_equation", + "content": "1024 \\times 1280" + }, + { + "bbox": [ + 304, + 376, + 545, + 460 + ], + "type": "text", + "content": " image)." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 476, + 358, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 476, + 358, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 476, + 358, + 488 + ], + "type": "text", + "content": "4. Results" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "Evaluation Methods. We compare our method to 7 latest state-of-the-art deep harmonization methods: Dove [12], " + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^2\\mathrm{AM}" + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": " [13], IIH [21], IHT [20], CDT [11], WBH [29] and SCSCo [22]. Since SCSCo [22] does not provide code and results, we directly copy their performances reported in their paper for references. For other methods, we use either the pre-trained models released by their authors or their released results for evaluation. Among them, " + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^2\\mathrm{AM}" + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": " [13] and WBH [29] learn either implicit mapping curves or explicit filters to adjust the appearances of the foreground objects; Dove [12] and SCSCo [22] perform harmonization based on style transfer learning. IIH [21] is retina-based. It harmonizes the foreground objects in the intermediate illumination layer. CDT [11] and IHT [20] model the harmonization process with pixel-to-pixel mapping while an additional color-to-color mapping is used in CDT [11]. We compare our method to these methods to demonstrate the effectiveness of harmonizing foreground objects in the in" + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12575" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 70, + 527, + 249 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 527, + 249 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 527, + 249 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 527, + 249 + ], + "type": "table", + "html": "
DatasetsMetricsS2AM [13]Dove [12]IIH [21]IHT [20]CDT [11]WBH [29]SCSCo [22]Ours
HAdobe5KPSNR↑33.7734.3435.2036.1038.2437.6438.2938.93
MSE↓63.4052.3243.0247.9620.6221.8921.0120.11
fMSE↓404.62380.39284.21321.14-170.05165.48154.82
HFlickrPSNR↑30.0329.7531.3432.3733.5533.6334.2234.76
MSE↓143.45145.21105.1388.4168.6164.8155.8354.20
fMSE↓785.65827.03716.60617.26-434.06393.72386.12
HCOCOPSNR↑35.4735.8337.1637.8739.1538.7739.8839.94
MSE↓41.0736.7224.9220.9916.2517.3413.5811.27
fMSE↓542.06551.01416.38377.11-298.42245.54217.55
Hday2nightPSNR↑34.5035.5335.9636.3837.9537.5637.8338.42
MSE↓76.6156.9255.5358.1436.7233.1441.7539.79
fMSE↓989.071075.71797.04823.68-542.07606.80587.44
AveragePSNR↑34.3534.7535.9036.7138.2337.8438.7539.36
MSE↓59.6752.3638.7137.0723.7524.2621.3320.77
fMSE↓594.67532.62400.29395.66-280.51248.86238.19
", + "image_path": "397a19a0a9f55cb746b1e5bff9ca2ef73ae31fe6c9bfa8dfb823e6775c1225cb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 250, + 547, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 250, + 547, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 547, + 283 + ], + "type": "text", + "content": "Table 1. Quantitative comparison between the proposed method and state-of-the-art deep harmonization methods on the iHarmony4 dataset [12] at " + }, + { + "bbox": [ + 46, + 250, + 547, + 283 + ], + "type": "inline_equation", + "content": "{256} \\times {256}" + }, + { + "bbox": [ + 46, + 250, + 547, + 283 + ], + "type": "text", + "content": " image resolution. It shows that the proposed method outperforms existing image harmonization methods. Best performances are marked in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 312, + 168, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 168, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 168, + 324 + ], + "type": "text", + "content": "intermediate linear color space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 325, + 288, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 288, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 288, + 456 + ], + "type": "text", + "content": "In addition, to verify whether our image unprocessing module produces faithful linear images, we perform an internal analysis and compare it to 4 representative state-of-the-art deep networks, including Unprocess [3], HDRCNN [15], CycleISP [61], and CIE-XYZNet [1]. Among them, Unprocess [3] is a systematic pipeline that converts sRGB images to raw images via a sequence of reverse ISP operations. HDRCNN [15] uses an encoder-decoder network to convert sRGB images into the HDR domain. CycleISP [61] and CIE-XYZNet [1] learn cycle mappings (sRGB-to-raw and raw-to-sRGB)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 459, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 567 + ], + "type": "text", + "content": "Evaluation Datasets and Metrics. We follow existing methods to evaluate the harmonization performance by using the Mean Square Error (MSE), foreground MSE (fMSE) and Peak Signal-to-Noise Ratio (PSNR), on the iHarmony4 dataset [12]. When internally analyzing the proposed image unprocessing module on the Adobe5K dataset [4], in addition to the PSNR metric, we also use the widely adopted HDR-VDP-2 [37] metric to measure the image quality based on human perceptions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 572, + 254, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 254, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 254, + 585 + ], + "type": "text", + "content": "4.1. Comparing to State-of-the-art Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 590, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 615 + ], + "type": "text", + "content": "We compare the proposed method with state-of-the-art image harmonization methods on the standard benchmarks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "content": "Visual Comparison. Figure 4 shows visual comparison where the cut-and-paste regions contain humans. While the latest methods are effective in adjusting the brightness of the foreground targets to fit the background illumination conditions, they are not able to produce visually pleasing colors, as shown in Figure 4(b-d). In contrast, our method is able to render realistic colors in the cut-and-paste regions, as shown in Figure 4(e). Figure 5 shows some ex" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 312, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 384 + ], + "type": "text", + "content": "amples where the cut-and-paste regions contain general objects. While existing methods may produce pale colors Figure 5(b,c) or color artifacts Figure 5(d). In contrast, our method produces foreground colors that are more realistic and consistent with the background, as shown in Figure 5(e)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 387, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 546, + 532 + ], + "type": "text", + "content": "Quantitative Comparison. In addition to the visual evaluation, we also provide quantitative comparison between the proposed method and existing harmonization methods. We first follow existing methods to evaluate the harmonization performance on images of resolution " + }, + { + "bbox": [ + 304, + 387, + 546, + 532 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 387, + 546, + 532 + ], + "type": "text", + "content": " in the iHarmony4 benchmark [12]. Table 1 shows the results. We can see that the proposed method outperforms existing methods on all evaluation metrics under all subsets of iHarmony4. Table 2 shows additional comparisons at the original image resolution. Note that CDT [11] only releases their low-resolution results. The comparison shows that our method can handle images of higher resolutions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 539, + 409, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 409, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 409, + 552 + ], + "type": "text", + "content": "4.2. Internal Analysis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 558, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 700 + ], + "type": "text", + "content": "As our method first converts the input composite image into the intermediate linear color space via the image unprocessing process, we demonstrate its effectiveness in producing faithful colors in the high dynamic range domain. We evaluate it on the CIE xyz version of the Adobe 5K dataset using the PSNR and HDR-VDP2 metrics. The HDR-VDP2 metric produces a Q score for each test image via a Mean-Oinion-score metric. The Q score indicates the degree of image quality degradation. Table 3 reports the average PSNR and Q score on the test set. The results show that the proposed image unprocessing process can produce more faithful images due to its generation ability." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "We now perform ablation studies on our network de" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12576" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 289, + 209 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 289, + 209 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 289, + 209 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 289, + 209 + ], + "type": "table", + "html": "
DatasetsMetricsIHT [20]WBH [29]Ours
HAdobe5KPSNR↑33.6337.8038.42
MSE↓56.9024.3723.76
HFlickrPSNR↑29.5933.3733.97
MSE↓135.4969.1961.70
HCOCOPSNR↑34.1937.6938.22
MSE↓44.9520.9320.08
Hday2nightPSNR↑35.7137.1537.64
MSE↓63.2637.2830.11
AveragePSNR↑33.5437.2337.92
MSE↓58.8927.6223.90
", + "image_path": "4342b8af1e0ceeaa8234267fa1b53cf4104afe05bad9b8e31b6603d132fd663f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 86, + 266, + 249, + 355 + ], + "blocks": [ + { + "bbox": [ + 47, + 209, + 287, + 251 + ], + "lines": [ + { + "bbox": [ + 47, + 209, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 287, + 251 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on the iHarmony4 dataset [12] at the original resolution. It shows that our method outperforms all existing image harmonization methods. Best performances are marked in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 266, + 249, + 355 + ], + "lines": [ + { + "bbox": [ + 86, + 266, + 249, + 355 + ], + "spans": [ + { + "bbox": [ + 86, + 266, + 249, + 355 + ], + "type": "table", + "html": "
MethodsPSNR↑Q score↑
Unprocess [3]22.1950.33
HDRCNN [15]27.7455.61
CycleISP [61]28.2954.74
CIE-XYZNet [1]29.6656.08
CycleGAN [64]27.6456.17
Ours30.3458.14
", + "image_path": "763b70e20f73f5eab9a12134369ac03555df378bcbbc34e61482b54d8212713a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 83, + 395, + 253, + 506 + ], + "blocks": [ + { + "bbox": [ + 47, + 356, + 287, + 389 + ], + "lines": [ + { + "bbox": [ + 47, + 356, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 287, + 389 + ], + "type": "text", + "content": "Table 3. Internal Analysis. We quantitatively compare the converted linear images with existing representative methods using PSNR and Q score. Best performances are marked in bold." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 395, + 253, + 506 + ], + "lines": [ + { + "bbox": [ + 83, + 395, + 253, + 506 + ], + "spans": [ + { + "bbox": [ + 83, + 395, + 253, + 506 + ], + "type": "table", + "html": "
MethodsPSNR↑MSE↓
w/o CC37.7924.26
DP→CP38.2823.60
w/o FH38.1023.94
w/o BP39.1721.10
Single Encoder39.0222.28
w/o SE Block38.4723.79
w/o Spatial Attention38.1923.57
Ours39.3620.77
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Best performances are marked in bold." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "text", + "content": "sign. We follow previous methods to perform it on the iHarmony4 dataset. In particular, we investigate the following ablated network architectures: (1) we remove the image unprocessing process and directly train a Color Harmonization network (denoted as “" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "text", + "content": " CC”); (2) we replace the diffusion process of the image unprocessing with a standard convolution process (denoted as “" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{DP} \\rightarrow \\mathrm{CP}" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "text", + "content": "”); (3) we remove the Feature Harmonization from the Color Harmonization process (denoted as “" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "text", + "content": " FH”); (4) we remove the Background Preserving of the Color Rendering process (denoted as “" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 46, + 557, + 289, + 713 + ], + "type": "text", + "content": " BP”); (5) we use a single encoder in the Color Harmonization network (“denoted as Single Encoder”); (6) we remove the SE block from the feature harmonization" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "type": "text", + "content": "process (\"denoted as " + }, + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "type": "text", + "content": " SE Block\"); and (7) we remove the spatial attention from the feature harmonization process (\"denoted as " + }, + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "type": "inline_equation", + "content": "w / o" + }, + { + "bbox": [ + 304, + 72, + 547, + 289 + ], + "type": "text", + "content": " Spatial Attention\"). Table 4 reports the performance. It shows that our designs of image unprocessing, Feature Harmonization and background preserving are able to improve the image harmonization performances. We have tried to train DoveNet [12] from scratch in linear space and it yields slightly better results (PSNR:34.94 (+0.19)) but fine-tuning using their pre-trained model degrades the performance (PSNR:33.18 (-1.57)). This is due to the discrepancy between linear and non-linear images, which demonstrates that it is necessary to design a specific image unprocessing model for harmonization. We have also tried ControlNet [62] for harmonization, which, however, does not perform well (PSNR/MAE: 14.36/109.40). As image harmonization requires the harmonized images to be photorealistic, directly using the diffusion-based model may generate visually pleasing but fake image details." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 298, + 388, + 380 + ], + "blocks": [ + { + "bbox": [ + 310, + 298, + 388, + 380 + ], + "lines": [ + { + "bbox": [ + 310, + 298, + 388, + 380 + ], + "spans": [ + { + "bbox": [ + 310, + 298, + 388, + 380 + ], + "type": "image", + "image_path": "1597dead988c9552610b87641f4054f8e22964cd90f0d367750aa13f8d544a79.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 334, + 383, + 364, + 393 + ], + "lines": [ + { + "bbox": [ + 334, + 383, + 364, + 393 + ], + "spans": [ + { + "bbox": [ + 334, + 383, + 364, + 393 + ], + "type": "text", + "content": "(a) Input" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 389, + 298, + 464, + 380 + ], + "blocks": [ + { + "bbox": [ + 389, + 298, + 464, + 380 + ], + "lines": [ + { + "bbox": [ + 389, + 298, + 464, + 380 + ], + "spans": [ + { + "bbox": [ + 389, + 298, + 464, + 380 + ], + "type": "image", + "image_path": "3f83b7d23d2c203f36ab766daf86b289de85a9bdbb6889afe8b5a2a5ab2a0945.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 383, + 440, + 392 + ], + "lines": [ + { + "bbox": [ + 411, + 383, + 440, + 392 + ], + "spans": [ + { + "bbox": [ + 411, + 383, + 440, + 392 + ], + "type": "text", + "content": "(b) Ours" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 465, + 298, + 542, + 380 + ], + "blocks": [ + { + "bbox": [ + 465, + 298, + 542, + 380 + ], + "lines": [ + { + "bbox": [ + 465, + 298, + 542, + 380 + ], + "spans": [ + { + "bbox": [ + 465, + 298, + 542, + 380 + ], + "type": "image", + "image_path": "a52b29b3e0684a7a6be133d910d6fc6e459811998a34e62fbf95538f3b01d8de.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 474, + 383, + 531, + 392 + ], + "lines": [ + { + "bbox": [ + 474, + 383, + 531, + 392 + ], + "spans": [ + { + "bbox": [ + 474, + 383, + 531, + 392 + ], + "type": "text", + "content": "(c) Ground Truth" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 395, + 545, + 427 + ], + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 427 + ], + "type": "text", + "content": "Figure 6. Our method may fail to harmonize the color tones of the inserted target when the new background does not provide sufficient scene illumination information." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 581 + ], + "type": "text", + "content": "This paper presents a novel image harmonization method that performs the color harmonization process in the linear color space. Our method includes a novel image unprocessing process to convert the cut-and-paste image into the high dynamic range linear color space, and a novel color harmonization process to harmonize object colors by querying background radiance information. We have conducted extensive experiments on the benchmark datasets to analyze the properties of the proposed method, and shown that it outperforms the state-of-the-art harmonization methods." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 641 + ], + "type": "text", + "content": "Our method does have limitations. It may fail when the background does not contain sufficient scene illumination information. Figure 6 shows such an example, in which the background is completely dark and our method fails to harmonize the color tones of the foreground." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgement. This project was partially supported by a GRF grant from the Research Grants Council of Hong Kong (Project No. CityU 11205620), by City University of Hong Kong (9678131), and by the Research Grants Council of the Hong Kong Special Administrative Region, China (CityU 11214620)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12577" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Mahmoud Afifi, Abdelrahman Abdelhamed, Abdullah Abuolaim, Abhijith Punnappurath, and Michael S Brown. 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For a number of image reconstruction and restoration tasks (e.g., super-resolution and inpainting), the proposed AdaCode achieved significantly better performance than latest prior work, such as VQGAN[7] and VQGAN with our merged basis codebooks (referred to as VQGAN-aux) for reconstruction; KX-Net[9], Real-ESRGAN[42] and FeMaSR[3] for super-resolution; GPEN[52], MAT[19] and our trained FeMaSR[3] for image inpainting. (Zoom in for best view)" + ], + "image_footnote": [], + "bbox": [ + 83, + 250, + 890, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 688, + 313, + 704 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent work on discrete generative priors, in the form of codebooks, has shown exciting performance for image reconstruction and restoration, as the discrete prior space spanned by the codebooks increases the robustness against diverse image degradations. Nevertheless, these methods require separate training of codebooks for different image categories, which limits their use to specific image categories only (e.g. face, architecture, etc.), and fail to handle arbitrary natural images. In this paper, we propose", + "bbox": [ + 75, + 720, + 470, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "AdaCode for learning image-adaptive codebooks for class-agnostic image restoration. Instead of learning a single codebook for each image category, we learn a set of basis codebooks. Given an input image, AdaCode learns a weight map with and computes a weighted combination of these basis codebooks for adaptive image restoration. Intuitively, AdaCode is a more flexible and expressive discrete generative prior than previous work. Experimental results demonstrate that AdaCode achieves state-of-the-art performance on image reconstruction and restoration tasks, including image super-resolution and inpainting. Codes are released at https://github.com/kechun1/AdaCode.", + "bbox": [ + 496, + 689, + 893, + 869 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*kechun@cs.washington.edu \nWork done during an internship at SenseBrain.", + "bbox": [ + 76, + 875, + 326, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5373", + "bbox": [ + 482, + 924, + 514, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 80, + 89, + 207, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, discrete generative priors (in the form of codebooks) [39, 7] have shown impressive performance for image synthesis [7, 11, 45, 61], exhibiting reduced mode collapse and more stable training. These learned codebooks essentially provide strong priors for compressing and reconstructing natural images, even in the presence of severe degradation. Nevertheless, these methods have a common limitation. The codebooks need to be learned separately for each image category (e.g., face, architecture), which restricts their applicability to arbitrary natural images [7, 45, 61]. Although FeMaSR [3] attempted to learn a single general codebook for all image categories, the expressiveness of the codebook is limited by the complexity of natural images. For example, as shown in Fig. 1, an image often includes textural and structural contents from multiple categories (e.g., face, man-made structural edges, repetitive texture, natural texture). It is challenging to rely on a single universal codebook to capture all. Prior work such as VQGAN [7] and FeMaSR [3] often introduce noticeable artifacts for image reconstruction and restoration.", + "bbox": [ + 80, + 114, + 467, + 415 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0b55270adc827965d9334d2ce43303ea54ac474dd7798218d2e856731b191dac.jpg", + "image_caption": [ + "Figure 2: Intuition of AdaCode vs a single codebook. Top: Prior work VQGAN[7] uses a single codebook as the learned representation in the discrete latent space, which may not fully capture complex visual patterns. Bottom: AdaCode learns multiple basis codebooks, each representing a different discretization of the latent space corresponding to different visual appearances. For an input image, its latent representation is a weighted linear combination of the codes from these codebooks. AdaCode thus is a more flexible representation for class-agnostic image restoration." + ], + "image_footnote": [], + "bbox": [ + 76, + 441, + 468, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Is it possible to learn a class-agnostic discrete generative prior for image reconstruction and restoration? Inspired", + "bbox": [ + 80, + 869, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "by a recent work [55], we propose AdaCode, which learns image-adaptive codebooks for class-agnostic image reconstruction and restoration. Instead of learning a single codebook for all categories of images, we learn a set of basis codebooks. For a given input image, AdaCode learns a weight map that determines the contribution of each basis codebook to the final representation. Intuitively, this design allows AdaCode to learn a more flexible and expressive discrete generative prior than previous work, as demonstrated in Fig. 2. In contrast to VQGAN [7] and FeMaSR [3], which utilize a single partition for the latent space and assign each image feature an exclusive discrete representation, AdaCode learns various partitions to the latent space from different perspectives – each corresponding to the learning of one of the basis codebooks. The discrete generative prior for an arbitrary image is a weighted linear combination derived from these basis codebooks, resulting in a more flexible and expressive representation. As depicted in Fig. 1, AdaCode outperforms previous work in various image restoration tasks, effectively preserving scene structure and texture.", + "bbox": [ + 501, + 90, + 890, + 406 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluated AdaCode on both image reconstruction and image restoration tasks (i.e., super-resolution and image inpainting). Across multiple benchmark datasets, AdaCode achieved state-of-the-art performance, while maintaining a comparable codebook size and computational cost.", + "bbox": [ + 503, + 411, + 890, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 503, + 507, + 638, + 523 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Representation Dictionary Learning Learning representation dictionaries in visual understanding has demonstrated its great power in image restoration tasks such as super-resolution [51, 62], denoising [59], and image inpainting [8, 36]. Using DNNs, VQVAE [39] first introduces a generative autoencoder model that learns discrete latent representations, also known as \"codebook\". The following VQGAN [7] employs perceptual and adversarial loss to train the visual codebook, resulting in better image generation quality with a relatively small codebook size. The representation dictionary-based generative model has inspired various impressive image generation work [11, 61, 53, 3, 45], as well as our AdaCode.", + "bbox": [ + 503, + 535, + 890, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The use of dictionaries is not limited to image restoration. Referred as lookup tables (LUTs), the dictionaries are also applied to optimize color transforms [55, 23, 49, 50]. In 3D-LUT [55], multiple LUTs are learned to serve as the bases of the LUT space. And a CNN is trained to predict weights to fuse the bases into an image-adaptive LUT. Inspired by 3D LUT, we leverage the discrete codebooks from VQGAN as the bases of the image latent space to build our image-adaptive codebook, AdaCode. Such design allows our method to fully and flexibly exploit the latent codes to represent diverse and complex natural images.", + "bbox": [ + 503, + 734, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5374", + "bbox": [ + 483, + 925, + 514, + 936 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4feafae5fd7df9622c925e0c00d46483863cb75b6531f85a6341358841d1b3f9.jpg", + "image_caption": [ + "Figure 3: The framework of the proposed AdaCode method. The training of AdaCode incorporates three stages: Class-specific Codebook Pretraining, AdaCode Representation Learning, and Restoration via AdaCode. The lock icon indicates that the codebooks $Z_{1,\\dots,K}$ are fixed in Stage II&III, and the decoder $G$ is fixed in Stage III. See Section 3 for more details." + ], + "image_footnote": [], + "bbox": [ + 80, + 87, + 883, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DNN-based Image Restoration DNN has been widely used for image restoration tasks, i.e. single image super-resolution (SISR) and image inpainting. In the field of super-resolution (SR), recent studies focus on recovering low-resolution input images with unknown degradation types, which is more relevant to real-world scenarios. They restore the images either by learning the degradation representations [33, 21, 41, 42, 57, 9], or by training unified generative networks with LR-HR pairs [16, 46, 32]. Some studies introduce additional image priors, such as latent representations [27, 2, 30] and discrete codebooks [7, 61, 3], to address unrealistic textures or over-smoothed areas commonly observed in GAN-based methods. However, a single partition of the latent space is often insufficient to model the intricate patterns in natural images, resulting in specific textures being generated regardless of the image content.", + "bbox": [ + 75, + 401, + 472, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the case of image inpainting, researchers often leverage deep generative models to fill missing image regions with plausible content [31, 25, 44, 56, 5]. Some approaches incorporate additional discriminators [35], partial or gated convolutions [24, 54], semantic texture or context [28, 48, 34, 13, 38, 15], or transformers [19, 6, 26, 40] to enhance the quality of inpainted results. However, these methods often require separate experiments for different image patterns, i.e. natural scenes, faces, etc., due to the significant variations among them.", + "bbox": [ + 75, + 651, + 468, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Both SR and inpainting methods face the challenge of effectively modeling complex visual patterns with a single model or codebook. In our proposed approach, AdaCode, we address this challenge by leveraging adaptive codebooks, enabling realistic and robust restoration results for general images.", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 400, + 635, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Building upon VQGAN [7], we introduce an additional degree of freedom to the codebook and construct an adaptive codebook (AdaCode) to model the intricate high-resolution natural image patterns. We summarize the AdaCode model in Fig.3. Our method's overall training consists of three sequential stages. In the first stage (Sec 3.1), we divide our HQ dataset into multiple semantic subsets and train a class-specific VQGAN [7] on each subset. In the second stage, using the fixed pretrained class-specific codebooks as bases, we leverage a transformer block to generate weight maps and train the AdaCode through the self-reconstruction task (Sec 3.2). In the last stage (Sec 3.3), we employ the AdaCode with fixed codebooks and fixed image decoder to address downstream restoration tasks, e.g. Super-Resolution and Image Inpainting. The details of each stage are discussed in the following sections.", + "bbox": [ + 496, + 426, + 890, + 670 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Codebook Pretraining (Stage I)", + "text_level": 1, + "bbox": [ + 498, + 680, + 777, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diversify Basis Codebooks To enhance the expressiveness of AdaCode, we aim to diversify the basis codebooks. Rather than applying various initializations as 3D-LUT [55], we achieve codebook divergence by training them on different HR subsets of our dataset. To accomplish this, we utilize an off-the-shelf SegFormer model [47] to perform semantic segmentation with 150 classes from the ADE20K dataset [60]. Each HR patch is labeled according to the semantic class with the largest area. We then group the 150 classes into 5 super-classes: Architectures, Indoor objects, Natural scenes, Street views, Portraits, and obtain the 5 semantic HR subsets accordingly. It is worth noting that the separation of subsets is not rigorous and each subset may", + "bbox": [ + 496, + 703, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5375", + "bbox": [ + 482, + 924, + 514, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/384e670cd4f183f44f844cb354d1e5a1b5b30b76aeda97c748a057d059600330.jpg", + "image_caption": [ + "Figure 4: Visualization of the learned codes for different categories of visual appearance. We randomly sample 10 code entries from each codebook and visualize them by projecting a tiled $4 \\times 4$ feature map onto a $32 \\times 32$ texture patch using the corresponding decoder. As expected, the codes from different categories exhibit distinct features." + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 460, + 213 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "contain semantic contexts from other subsets, as most images contain multiple semantics. More details regarding the clustering of the 150 classes can be found in the Appendix. This approach not only diversifies the codebooks but also provides various ways to partition the latent feature space. We randomly visualize some code samples in Fig. 4.", + "bbox": [ + 75, + 342, + 472, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning Basis Codebooks Given a HQ subset of class $k$ , we train a quantized autoencoder to learn the class-specific basis codebook. As shown in Fig. 3, the input HR patch $y \\in \\mathbb{R}^{H \\times W \\times 3}$ is first passed through the encoder $E$ to generate the embedding $\\hat{z} = E(y) \\in \\mathbb{R}^{h \\times w \\times n_z}$ . Following VQVAE [39] and VQGAN [7], each entry $\\hat{z}_i \\in \\mathbb{R}^{n_z}$ in $\\hat{z}$ is replaced with its nearest code in the learnable codebook $Z_k \\in \\mathbb{R}^{N \\times n_z}$ to construct the quantized embedding $z_{q_k}$ :", + "bbox": [ + 76, + 450, + 472, + 574 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {q _ {k}} = \\underset {c \\in \\{0, \\dots , N - 1 \\}} {\\arg \\min } | | \\hat {z} - Z _ {k, c} | | \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 580, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{N}$ is the number of codes in the corresponding codebook, $z_{q_k}$ denotes the quantized representation using $Z_{k}$ , and $Z_{k,c}$ represent the $c$ -th entry in codebook $Z_{k}$ . After the feature quantization, the decoder $G$ reconstructs the HR patch $\\hat{y}$ using $z_{q_k}$ :", + "bbox": [ + 75, + 618, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = G \\left(z _ {q _ {k}}\\right) \\approx y \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 704, + 468, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The adversarial learning scheme is employed to train the encoder $E$ , codebook $Z$ , and decoder $G$ with the discriminator $D$ . The detailed architectures of $E$ , $D$ , and $G$ are provided in the Appendix.", + "bbox": [ + 76, + 731, + 470, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training Objective To train the quantized autoencoder, we adopt 3 image-level losses: L1 loss $\\mathcal{L}_1$ , perceptual loss $\\mathcal{L}_{per}$ [17], and adversarial loss $\\mathcal{L}_{adv}$ [10], which are calculated using $\\hat{y}$ and $y$ .", + "bbox": [ + 76, + 809, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the quantization in Eqn. 1 is non-differentiable, we adopt the straight-through gradient estimator in [39, 7],", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which directly copies the gradients from decoder $G$ to encoder $E$ , enabling back-propagation and allowing end-to-end training using the code-level loss function $\\mathcal{L}_{VQ}$ :", + "bbox": [ + 496, + 90, + 892, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {V Q} (E, G, Z _ {k}) = | | s g [ \\hat {z} ] - z _ {q} | | _ {2} ^ {2} + \\beta \\cdot | | \\hat {z} - s g [ z _ {q} ] | | _ {2} ^ {2} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 143, + 892, + 162 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $sg[\\cdot]$ denotes the stop-gradient operation and $\\beta = 0.25$ is a hyper-parameter to control the update frequency of the codebook.", + "bbox": [ + 496, + 169, + 890, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further reinforce the semantics in the latent codebook and improve the texture restoration [43], we incorporate a VGG19-based regularization term $\\mathcal{L}_{sem}$ into the codebook training process, following the approach in [3].:", + "bbox": [ + 496, + 215, + 892, + 277 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s e m} = \\left| \\left| C O N V (\\hat {z}) - \\Phi \\left(y _ {k} ^ {\\prime}\\right) \\right| \\right| _ {2} ^ {2} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 284, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Phi$ denotes the feature extractor of VGG19 [37], and $CONV$ denotes a single convolutional layer to match the dimension of $\\hat{z}$ and $\\Phi(y_k')$ .", + "bbox": [ + 496, + 310, + 890, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the above image-level and code-level losses, we can summarize the training objective in Stage I as:", + "bbox": [ + 496, + 356, + 890, + 386 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s t a g e 1}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {V Q} + \\lambda \\cdot \\mathcal {L} _ {\\text {s e m}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 395, + 890, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the loss weight $\\lambda$ is set to 0.1.", + "bbox": [ + 496, + 420, + 743, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. AdaCode Representation Learning (Stage II)", + "text_level": 1, + "bbox": [ + 498, + 443, + 879, + 459 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the pretrained class-specific basis codebooks $Z_{k}, k \\in \\{1, \\dots, K\\}$ , the latent feature space can be partitioned into non-overlapping cells in $K$ different ways. Specifically, for a given input HR patch $y$ , $K$ quantized representations can be generated. Each distinct quantized representation $z_{q_k}$ obtains its code token from its corresponding semantic codebook. To combine the discrete representation $z_{q_{1}, \\dots, K}$ into the AdaCode representation $z$ , we employ a weight predictor module, which generates a $K$ -channel weight map $w \\in \\mathbb{R}^{h \\times w \\times K}$ , as illustrated in Fig. 3 and Fig. 5. The weight predictor module consists of four residual swim transformer blocks (RSTBs) [20] and a convolution layer to match the channels of weight map and $K$ . $z$ is computed following Eqn. 6. Finally, the adaptive feature $z$ is reconstructed to HR patch $\\hat{y}$ via the decoder $G$ .", + "bbox": [ + 496, + 465, + 890, + 693 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz = \\sum_ {i} w _ {i} \\times z _ {q _ {i}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 700, + 890, + 732 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To efficiently train AdaCode and maintain a comparable number of parameters in the codebooks to VQGAN [7] and FeMaSR [3], which both set the codebook dimension to be $1024 \\times 512$ , we set each of our class-specific codebooks to be $256 \\times 256$ or $512 \\times 256$ . These codebooks are fixed during the training of stage II while the rest of the model, i.e. the encoder $E$ , the weight predictor, the decoder $G$ , and the discriminator $D$ , are trained using the objective in Eqn. 7. Each term in this equation is defined in Sec. 3.1.", + "bbox": [ + 496, + 739, + 892, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s t a g e 2}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {V Q} (E, G) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 885, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5376", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4c778202d09786f4bd59eb347c9514e5ad8d7a2d9994243c9f77899c987e6434.jpg", + "image_caption": [ + "Figure 5: An example showing the learned weight maps. The input image contains multiple semantically-meaningful content (e.g. pyramid, person, animal, sky) which cannot be well represented with a single codebook. Instead, AdaCode uses multiple basis codebooks and weight maps for discrete representations. As shown, the weight maps correlate to the semantics to some extent." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 459, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Restoration via AdaCode (Stage III)", + "text_level": 1, + "bbox": [ + 76, + 400, + 390, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the powerful decoder $G$ , various image restoration tasks can be turned into a feature refinement problem through AdaCode scheme. From the perspective of latent space partition, each representation of the degraded input $x$ is pulled towards its nearest HR code entry, allowing for the information loss in $x$ to be relatively compensated. In comparison to the quantized representation $z_{q}$ using only one general codebook, the combination of $z_{q_{1},\\ldots ,K}$ with the weight map can be considered as adding an offset to $z_{q}$ . The offset helps to alleviate the discontinuity among the discrete codes, which is demonstrated in our ablation study. To further showcase the effectiveness of AdaCode, we train our model on two ill-posed problems, i.e. Single Image SuperResolution and Image Inpainting.", + "bbox": [ + 75, + 426, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In super-resolution and image inpainting tasks, the mapping between the input and the HR output has more than one solutions. Despite the benefits of the AdaCode scheme, restoring damaged content or missing details remains challenging given the uncertain degradations and the diversity of natural images. To better account for the degradation and improve the gradient flow, we adopt the encoder design in [3] which utilizes a feature extraction module and a residual shortcut module during stage III.", + "bbox": [ + 75, + 641, + 468, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thanks to the excellent reconstruction model in stage II, given a Degraded-HR image pair, we can obtain the groundtruth representation $z_{gt}$ via the fixed model. Since the decoder $G$ is fixed in this stage, the restoration problem can be formulated as minimizing the distance between HR feature $z_{gt}$ and degraded feature $z$ . To achieve this, we use a code-level loss that includes the InfoNCE loss in [29] and the style loss in [17]. Following the design as SimCLR[4],", + "bbox": [ + 75, + 779, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "given a degraded image feature $z$ , we use the HR feature $z_{gt}$ as the positive sample, while other $z_{gt}$ and $z$ from different source images in the same batch are treated as the negative samples. The code-level loss is defined as follows.", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {c o d e}} = \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {g t}, z\\right) + \\mathcal {L} _ {\\text {s t y l e}} \\left(z _ {g t}, z\\right) \\tag {8} \\\\ + \\beta \\cdot | | \\hat {z} - s g [ z _ {g t} ] | | _ {2} ^ {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 162, + 890, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "And the overall loss is summarized as:", + "bbox": [ + 500, + 208, + 754, + 222 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s t a g e 3}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {\\text {c o d e}} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 234, + 890, + 251 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 263, + 630, + 279 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets Our training dataset includes images from DIV2K train set [1], Flickr2K [22], DIV8K train set [12], and 10,000 face images from FFHQ [18]. We generate the training patches by cropping images into non-overlapping patches at $512 \\times 512$ resolution (face images in FFHQ are randomly resized with scale factors between [0.5, 1.0] before cropping). We adopt the same degradation model as BSRGAN [57] to generate LR patches. The final training dataset consists of 198,061 patches.", + "bbox": [ + 496, + 287, + 890, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the test stage, we evaluate the reconstruction task on OST dataset [43], which contains 300 images with rich textures. For super-resolution, we evaluate the performance on five classical benchmarks, i.e. Set5, Set14, BSD100, Urban100, and Manga109, with $\\times 2$ and $\\times 4$ scales. For image inpainting, we apply a publicly available script [52] to randomly draw irregular polyline masks and generate masked images. The inpainting performance is evaluated on the validation sets of DIV2K [1] and DIV8K [12].", + "bbox": [ + 496, + 424, + 890, + 560 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics For reconstruction, we adopt PSNR and SSIM as the evaluation metrics. For super-resolution, we employ an additional well-known perceptual score, LPIPS [58]. For image inpainting task, we use PSNR, LPIPS and a widely-used non-reference metric, FID [14].", + "bbox": [ + 496, + 577, + 890, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details According to the size of each semantic dataset, we empirically set the codebook bases sizes to be $\\{512, 256, 512, 256, 256\\} \\times 256$ for Architectures, Indoor Objects, Natural Scenes, Street Views, and Portraits. For all stages, we represent the input image as a $32 \\times 32$ code sequence. We train each stage for $350k$ iterations with an Adam optimizer and a batch size of 32. The learning rates for the generator and discriminator are fixed as 1e-4 and 4e-4 separately. Our method is implemented with PyTorch and trained with 4 NVIDIA Tesla V100 GPUs.", + "bbox": [ + 496, + 671, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Expressiveness of AdaCode", + "text_level": 1, + "bbox": [ + 500, + 832, + 746, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The key design in our work is to leverage the class-specific basis codebooks to construct an adaptive codebook, which supports more expressiveness even with a smaller", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5377", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2b7385bf74cd3ce9a2efb549c721dfdb99d6a270f55e502d62bde0bce15bc942.jpg", + "image_caption": [ + "Figure 6: Qualitative comparisons on image reconstruction task. Various scenes and semantics, i.e. text, plants, buildings, streets, and faces, are covered in these examples. Benefited from the adaptive codebook, our AdaCode is able to reconstruct images with higher quality and fidelity. (Zoom in for best view)" + ], + "image_footnote": [], + "bbox": [ + 109, + 94, + 851, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "codebook size. To verify our method's superiority, we evaluate the reconstruction performances using three codebook and model settings: (1) VQGAN [7] with its single general codebook. (2) VQGAN with a merged codebook concatenating all the basis codebooks, referred to as VQGAN-aux. (3) AdaCode with our adaptive codebook. The three approaches are trained with the same dataset (see Section. 4) to guarantee a fair comparison.", + "bbox": [ + 75, + 549, + 472, + 672 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/55889f84cdcaab8869c097a5f9732579294d67c7b3198dcb8eb882f0a24adfc9.jpg", + "table_caption": [ + "Table 1: Quantitative comparison of reconstruction performance. PSNR/SSIM↑: the higher, the better." + ], + "table_footnote": [], + "table_body": "
MethodOverall Codebook SizePerformance
PSNRSSIM
VQGAN[3]1024 × 51221.35570.5664
VQGAN-aux1792 × 25621.92190.6030
AdaCode (Ours)1792 × 25625.76290.7705
", + "bbox": [ + 86, + 724, + 460, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Table. 1, our AdaCode obtains overwhelming reconstruction results with a comparable or smaller codebook size. The gap between (1) and (2) certifies that training class-specific codebooks helps the codes to capture more image textures, while the great improvement between", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(2) and (3) justifies the expressiveness facilitated by our adaptive codebook design. Fig. 6 shows multiple scenarios, including plants, buildings, streets, portraits, and text which has distinct patterns but does not have a corresponding codebook in our experiments. AdaCode achieves exceedingly excellent results in all semantic cases, producing realistic and fidelitous reconstruction results.", + "bbox": [ + 496, + 549, + 893, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Benchmarking Image Restoration Results", + "text_level": 1, + "bbox": [ + 498, + 669, + 857, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Super-Resolution We compare AdaCode with state-of-the-art models for Image Super-Resolution, including KX-Net[9], Real-ESRGAN [42], and FeMaSR[3]. Specifically, KX-Net iteratively learns the degradation kernels from the LR images; Real-ESRGAN learns super-resolution using pure synthetic data with high-order degradation model; FeMaSR utilizes a single perceptually rich codebook to restore the images. We use the original codes and weights from each method's official public repository to conduct comparisons, as shown in Table. 2 and Fig. 7.", + "bbox": [ + 496, + 693, + 890, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image Inpainting We compare AdaCode with state-of-the-art inpainting methods GPEN [52] and MAT [19]. To", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5378", + "bbox": [ + 482, + 924, + 514, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e3e76863bc465173fce08c5b7a5e0d5e8738dbd0f0cb0dd089c35c54f00f7f37.jpg", + "image_caption": [ + "Figure 7: Qualitative comparisons on super-resolution task with $\\times 2$ and $\\times 4$ upscale factor. AdaCode restores LR with realistic and faithful details, while the competitive work either fails to deblur the LR, i.e. KX-Net [9], or generates artifacts or over-smooth areas, i.e. Real-ESRGAN [42] and FeMaSR [3]. See Appendix for more results. (Zoom in for best view)", + "Table 2: Quantitative comparison with state-of-the-art SISR methods. PSNR/SSIM↑: the higher, the better; LPIPS↓: the lower, the better. The best and second best performance are marked in red and blue." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 885, + 310 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/99c5df1469513a68bea6e35229789308b06d0e0703cae503d0a13e103faa5ea6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodScaleSet5Set14BSDS100Urban100Manga109
PSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPS
FeMaSRx227.5130.82500.105425.4040.75650.129224.9070.72600.144922.7130.75730.110221.5840.69380.2270
KX-Netx227.8370.88840.085925.9290.82910.130125.8180.80920.173422.6750.80160.097219.5610.50490.5312
Real-ESRGANx230.0320.89300.105127.0190.83790.138226.6700.79160.152623.5770.81150.097620.8150.68170.3056
Oursx229.2130.84440.084426.2490.77020.117926.0380.75290.137423.6630.78940.100922.0230.70290.2150
FeMaSRx424.0390.74520.150022.7240.63540.204521.9570.58190.251720.5090.64260.198318.1310.57570.3449
KX-Netx421.9220.70500.208021.1820.61260.304421.7080.57680.397218.6030.55760.270418.1810.53230.6909
Real-ESRGANx425.2630.76650.171024.1000.70040.233823.7760.62610.281921.3510.66250.214018.2220.59170.4091
Oursx425.8680.77310.150524.1580.66620.203123.1290.60410.248521.4460.65680.200718.1450.56640.3425
", + "bbox": [ + 78, + 421, + 926, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "conduct a fair comparison, we retrain MAT on our training dataset as discussed in Section. 4. Moreover, we train FeMaSR [3] for this task to demonstrate the effectiveness of our adaptive codebooks over the single codebook in FeMaSR. As shown in Table. 3, AdaCode achieves state-of-the-art performance on various metrics. Qualitative comparisons in Fig. 8 also illustrate that AdaCode consistently produce high-quality inpainting results across a wide range of scenes with a single model.", + "bbox": [ + 75, + 606, + 470, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 755, + 230, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We investigate AdaCode's expressiveness given a various number of basis codebooks. We fix the five basis codebooks trained in Stage I and train Stage II with various combinations of basis codebooks. We adopt PSNR and SSIM to evaluate the expressiveness on the reconstruction task. Fig. 9 empirically shows that the adaptive codebook benefits from the bases in a large extent. Meanwhile, it also indicates that our basis codebooks are \"non-multicollinear\"", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3dd7e7667bfbd1d4fb8afc35d99e007d5be350f8d78a082bec3ccb9c751fb930.jpg", + "table_caption": [ + "Table 3: Quantitative comparison with state-of-the-art inpainting methods. PSNR↑: the higher, the better; LPIPS/FID↓: the lower, the better. The best and second best performance are marked in red and blue." + ], + "table_footnote": [], + "table_body": "
MethodDIV2KDIV8KAll
PSNRLPIPSPSNRLPIPSFID
GPEN29.1290.093331.1910.07033.0924
FeMaSR29.7900.058132.2330.04161.6741
MAT30.1240.067632.3350.04061.2385
Ours30.11510.051632.7010.03721.1657
", + "bbox": [ + 526, + 676, + 867, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "even if the semantic sub-datasets have overlapping patches.", + "bbox": [ + 500, + 810, + 888, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Conclusion and Limitation", + "text_level": 1, + "bbox": [ + 500, + 843, + 750, + 859 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this work, we propose AdaCode, a novel approach for class-agnostic image reconstruction and restoration. In par", + "bbox": [ + 500, + 869, + 892, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5379", + "bbox": [ + 480, + 924, + 514, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f13fd9c00a3dcd3b7f55e7243723ad335daa1d71154e2b5936e0381aaffdad86.jpg", + "image_caption": [ + "Figure 8: Qualitative comparisons on image inpainting task. The first two rows demonstrate the inpainting results of face images, while the last two rows show the recovered results of place images. See Appendix for more results." + ], + "image_footnote": [], + "bbox": [ + 76, + 95, + 893, + 530 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/620eec168f790eab59940137f30f9577125c71996dc0f2f6607def8da89dd76a.jpg", + "image_caption": [ + "Figure 9: Ablation Study. PSNR and SSIM score of reconstructed results with varying number of basis codebooks. See supplementary for more result images." + ], + "image_footnote": [], + "bbox": [ + 86, + 593, + 459, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ticular, we train a set of class-specific basis codebooks and learn a weight map to construct an image-adaptive codebook for better image representation. Unlike previous methods that use a general codebook to represent images, our image-adaptive codebook is more flexible and suited for natural images. Extensive comparisons on image reconstruction, super-resolution, and image inpainting tasks validate our method's superiority.", + "bbox": [ + 496, + 597, + 890, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our work is a first step towards class-agnostic generative prior for arbitrary images. It has several limitations we plan to explore in future work. First, it is yet unclear how many basis codebooks and how many code entries in each codebook we need. Stage I is trained separately from Stage II&III, which may be suboptimal. Second, we do not yet incorporate high-level explicit semantic information such as semantic segmentation into the framework, which may be also useful for general image restoration tasks. Finally, it would be interesting to extend AdaCode for high-dimensional visual appearance, such as videos and multispectral images.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5380", + "bbox": [ + 482, + 924, + 514, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson and Radu Timofte. NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2017.", + "[2] Kelvin C.K. Chan, Xintao Wang, Xiangyu Xu, Jinwei Gu, and Chen Change Loy. GLEAN: Generative Latent Bank for Large-Factor Image Super-Resolution. 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IEEE Transactions on Multimedia (MM), 16(8):2178–2190, 2014." + ], + "bbox": [ + 78, + 90, + 468, + 810 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "5383", + "bbox": [ + 482, + 925, + 514, + 936 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/4f85f017-28ce-47a6-a95c-6487947424f7_model.json b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/4f85f017-28ce-47a6-a95c-6487947424f7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ccaa2b4df502690f0c9ed499e72b67ac0d9d3c53 --- /dev/null +++ b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/4f85f017-28ce-47a6-a95c-6487947424f7_model.json @@ -0,0 +1,2015 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.104, + 0.131, + 0.867, + 0.154 + ], + "angle": 0, + "content": "Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.18, + 0.724, + 0.199 + ], + "angle": 0, + "content": "Kechun Liu\\(^{1,3*}\\) Yitong Jiang\\(^{2}\\) Inchang Choi\\(^{3}\\) Jinwei Gu\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.199, + 0.815, + 0.218 + ], + "angle": 0, + "content": "1 University of Washington 2 The Chinese University of Hong Kong 3 SenseBrain" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.251, + 0.892, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.6, + 0.894, + 0.677 + ], + "angle": 0, + "content": "Figure 1: We propose an image-adaptive codebook learning method, named AdaCode, for class-agnostic image restoration. For a number of image reconstruction and restoration tasks (e.g., super-resolution and inpainting), the proposed AdaCode achieved significantly better performance than latest prior work, such as VQGAN[7] and VQGAN with our merged basis codebooks (referred to as VQGAN-aux) for reconstruction; KX-Net[9], Real-ESRGAN[42] and FeMaSR[3] for super-resolution; GPEN[52], MAT[19] and our trained FeMaSR[3] for image inpainting. (Zoom in for best view)" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.689, + 0.314, + 0.705 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.471, + 0.859 + ], + "angle": 0, + "content": "Recent work on discrete generative priors, in the form of codebooks, has shown exciting performance for image reconstruction and restoration, as the discrete prior space spanned by the codebooks increases the robustness against diverse image degradations. Nevertheless, these methods require separate training of codebooks for different image categories, which limits their use to specific image categories only (e.g. face, architecture, etc.), and fail to handle arbitrary natural images. In this paper, we propose" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.871 + ], + "angle": 0, + "content": "AdaCode for learning image-adaptive codebooks for class-agnostic image restoration. Instead of learning a single codebook for each image category, we learn a set of basis codebooks. Given an input image, AdaCode learns a weight map with and computes a weighted combination of these basis codebooks for adaptive image restoration. Intuitively, AdaCode is a more flexible and expressive discrete generative prior than previous work. Experimental results demonstrate that AdaCode achieves state-of-the-art performance on image reconstruction and restoration tasks, including image super-resolution and inpainting. Codes are released at https://github.com/kechun1/AdaCode." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.876, + 0.327, + 0.901 + ], + "angle": 0, + "content": "*kechun@cs.washington.edu \nWork done during an internship at SenseBrain." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "5373" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.09, + 0.208, + 0.106 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.115, + 0.468, + 0.416 + ], + "angle": 0, + "content": "In recent years, discrete generative priors (in the form of codebooks) [39, 7] have shown impressive performance for image synthesis [7, 11, 45, 61], exhibiting reduced mode collapse and more stable training. These learned codebooks essentially provide strong priors for compressing and reconstructing natural images, even in the presence of severe degradation. Nevertheless, these methods have a common limitation. The codebooks need to be learned separately for each image category (e.g., face, architecture), which restricts their applicability to arbitrary natural images [7, 45, 61]. Although FeMaSR [3] attempted to learn a single general codebook for all image categories, the expressiveness of the codebook is limited by the complexity of natural images. For example, as shown in Fig. 1, an image often includes textural and structural contents from multiple categories (e.g., face, man-made structural edges, repetitive texture, natural texture). It is challenging to rely on a single universal codebook to capture all. Prior work such as VQGAN [7] and FeMaSR [3] often introduce noticeable artifacts for image reconstruction and restoration." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.443, + 0.47, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.7, + 0.47, + 0.852 + ], + "angle": 0, + "content": "Figure 2: Intuition of AdaCode vs a single codebook. Top: Prior work VQGAN[7] uses a single codebook as the learned representation in the discrete latent space, which may not fully capture complex visual patterns. Bottom: AdaCode learns multiple basis codebooks, each representing a different discretization of the latent space corresponding to different visual appearances. For an input image, its latent representation is a weighted linear combination of the codes from these codebooks. AdaCode thus is a more flexible representation for class-agnostic image restoration." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Is it possible to learn a class-agnostic discrete generative prior for image reconstruction and restoration? Inspired" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.092, + 0.891, + 0.407 + ], + "angle": 0, + "content": "by a recent work [55], we propose AdaCode, which learns image-adaptive codebooks for class-agnostic image reconstruction and restoration. Instead of learning a single codebook for all categories of images, we learn a set of basis codebooks. For a given input image, AdaCode learns a weight map that determines the contribution of each basis codebook to the final representation. Intuitively, this design allows AdaCode to learn a more flexible and expressive discrete generative prior than previous work, as demonstrated in Fig. 2. In contrast to VQGAN [7] and FeMaSR [3], which utilize a single partition for the latent space and assign each image feature an exclusive discrete representation, AdaCode learns various partitions to the latent space from different perspectives – each corresponding to the learning of one of the basis codebooks. The discrete generative prior for an arbitrary image is a weighted linear combination derived from these basis codebooks, resulting in a more flexible and expressive representation. As depicted in Fig. 1, AdaCode outperforms previous work in various image restoration tasks, effectively preserving scene structure and texture." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.412, + 0.891, + 0.486 + ], + "angle": 0, + "content": "We evaluated AdaCode on both image reconstruction and image restoration tasks (i.e., super-resolution and image inpainting). Across multiple benchmark datasets, AdaCode achieved state-of-the-art performance, while maintaining a comparable codebook size and computational cost." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.508, + 0.64, + 0.524 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.536, + 0.891, + 0.732 + ], + "angle": 0, + "content": "Visual Representation Dictionary Learning Learning representation dictionaries in visual understanding has demonstrated its great power in image restoration tasks such as super-resolution [51, 62], denoising [59], and image inpainting [8, 36]. Using DNNs, VQVAE [39] first introduces a generative autoencoder model that learns discrete latent representations, also known as \"codebook\". The following VQGAN [7] employs perceptual and adversarial loss to train the visual codebook, resulting in better image generation quality with a relatively small codebook size. The representation dictionary-based generative model has inspired various impressive image generation work [11, 61, 53, 3, 45], as well as our AdaCode." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.735, + 0.891, + 0.9 + ], + "angle": 0, + "content": "The use of dictionaries is not limited to image restoration. Referred as lookup tables (LUTs), the dictionaries are also applied to optimize color transforms [55, 23, 49, 50]. In 3D-LUT [55], multiple LUTs are learned to serve as the bases of the LUT space. And a CNN is trained to predict weights to fuse the bases into an image-adaptive LUT. Inspired by 3D LUT, we leverage the discrete codebooks from VQGAN as the bases of the image latent space to build our image-adaptive codebook, AdaCode. Such design allows our method to fully and flexibly exploit the latent codes to represent diverse and complex natural images." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.926, + 0.515, + 0.937 + ], + "angle": 0, + "content": "5374" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.088, + 0.885, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.33, + 0.895, + 0.378 + ], + "angle": 0, + "content": "Figure 3: The framework of the proposed AdaCode method. The training of AdaCode incorporates three stages: Class-specific Codebook Pretraining, AdaCode Representation Learning, and Restoration via AdaCode. The lock icon indicates that the codebooks \\( Z_{1,\\dots,K} \\) are fixed in Stage II&III, and the decoder \\( G \\) is fixed in Stage III. See Section 3 for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.473, + 0.645 + ], + "angle": 0, + "content": "DNN-based Image Restoration DNN has been widely used for image restoration tasks, i.e. single image super-resolution (SISR) and image inpainting. In the field of super-resolution (SR), recent studies focus on recovering low-resolution input images with unknown degradation types, which is more relevant to real-world scenarios. They restore the images either by learning the degradation representations [33, 21, 41, 42, 57, 9], or by training unified generative networks with LR-HR pairs [16, 46, 32]. Some studies introduce additional image priors, such as latent representations [27, 2, 30] and discrete codebooks [7, 61, 3], to address unrealistic textures or over-smoothed areas commonly observed in GAN-based methods. However, a single partition of the latent space is often insufficient to model the intricate patterns in natural images, resulting in specific textures being generated regardless of the image content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.47, + 0.803 + ], + "angle": 0, + "content": "In the case of image inpainting, researchers often leverage deep generative models to fill missing image regions with plausible content [31, 25, 44, 56, 5]. Some approaches incorporate additional discriminators [35], partial or gated convolutions [24, 54], semantic texture or context [28, 48, 34, 13, 38, 15], or transformers [19, 6, 26, 40] to enhance the quality of inpainted results. However, these methods often require separate experiments for different image patterns, i.e. natural scenes, faces, etc., due to the significant variations among them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Both SR and inpainting methods face the challenge of effectively modeling complex visual patterns with a single model or codebook. In our proposed approach, AdaCode, we address this challenge by leveraging adaptive codebooks, enabling realistic and robust restoration results for general images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.401, + 0.637, + 0.419 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.671 + ], + "angle": 0, + "content": "Building upon VQGAN [7], we introduce an additional degree of freedom to the codebook and construct an adaptive codebook (AdaCode) to model the intricate high-resolution natural image patterns. We summarize the AdaCode model in Fig.3. Our method's overall training consists of three sequential stages. In the first stage (Sec 3.1), we divide our HQ dataset into multiple semantic subsets and train a class-specific VQGAN [7] on each subset. In the second stage, using the fixed pretrained class-specific codebooks as bases, we leverage a transformer block to generate weight maps and train the AdaCode through the self-reconstruction task (Sec 3.2). In the last stage (Sec 3.3), we employ the AdaCode with fixed codebooks and fixed image decoder to address downstream restoration tasks, e.g. Super-Resolution and Image Inpainting. The details of each stage are discussed in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.681, + 0.779, + 0.698 + ], + "angle": 0, + "content": "3.1. Codebook Pretraining (Stage I)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Diversify Basis Codebooks To enhance the expressiveness of AdaCode, we aim to diversify the basis codebooks. Rather than applying various initializations as 3D-LUT [55], we achieve codebook divergence by training them on different HR subsets of our dataset. To accomplish this, we utilize an off-the-shelf SegFormer model [47] to perform semantic segmentation with 150 classes from the ADE20K dataset [60]. Each HR patch is labeled according to the semantic class with the largest area. We then group the 150 classes into 5 super-classes: Architectures, Indoor objects, Natural scenes, Street views, Portraits, and obtain the 5 semantic HR subsets accordingly. It is worth noting that the separation of subsets is not rigorous and each subset may" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "5375" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.088, + 0.462, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.226, + 0.473, + 0.318 + ], + "angle": 0, + "content": "Figure 4: Visualization of the learned codes for different categories of visual appearance. We randomly sample 10 code entries from each codebook and visualize them by projecting a tiled \\(4 \\times 4\\) feature map onto a \\(32 \\times 32\\) texture patch using the corresponding decoder. As expected, the codes from different categories exhibit distinct features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.473, + 0.435 + ], + "angle": 0, + "content": "contain semantic contexts from other subsets, as most images contain multiple semantics. More details regarding the clustering of the 150 classes can be found in the Appendix. This approach not only diversifies the codebooks but also provides various ways to partition the latent feature space. We randomly visualize some code samples in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.451, + 0.473, + 0.575 + ], + "angle": 0, + "content": "Learning Basis Codebooks Given a HQ subset of class \\(k\\), we train a quantized autoencoder to learn the class-specific basis codebook. As shown in Fig. 3, the input HR patch \\(y \\in \\mathbb{R}^{H \\times W \\times 3}\\) is first passed through the encoder \\(E\\) to generate the embedding \\(\\hat{z} = E(y) \\in \\mathbb{R}^{h \\times w \\times n_z}\\). Following VQVAE [39] and VQGAN [7], each entry \\(\\hat{z}_i \\in \\mathbb{R}^{n_z}\\) in \\(\\hat{z}\\) is replaced with its nearest code in the learnable codebook \\(Z_k \\in \\mathbb{R}^{N \\times n_z}\\) to construct the quantized embedding \\(z_{q_k}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.582, + 0.47, + 0.61 + ], + "angle": 0, + "content": "\\[\nz _ {q _ {k}} = \\underset {c \\in \\{0, \\dots , N - 1 \\}} {\\arg \\min } | | \\hat {z} - Z _ {k, c} | | \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.697 + ], + "angle": 0, + "content": "where \\( \\mathbf{N} \\) is the number of codes in the corresponding codebook, \\( z_{q_k} \\) denotes the quantized representation using \\( Z_{k} \\), and \\( Z_{k,c} \\) represent the \\( c \\)-th entry in codebook \\( Z_{k} \\). After the feature quantization, the decoder \\( G \\) reconstructs the HR patch \\( \\hat{y} \\) using \\( z_{q_k} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.216, + 0.705, + 0.47, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = G \\left(z _ {q _ {k}}\\right) \\approx y \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.732, + 0.471, + 0.793 + ], + "angle": 0, + "content": "The adversarial learning scheme is employed to train the encoder \\( E \\), codebook \\( Z \\), and decoder \\( G \\) with the discriminator \\( D \\). The detailed architectures of \\( E \\), \\( D \\), and \\( G \\) are provided in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.81, + 0.47, + 0.871 + ], + "angle": 0, + "content": "Training Objective To train the quantized autoencoder, we adopt 3 image-level losses: L1 loss \\(\\mathcal{L}_1\\), perceptual loss \\(\\mathcal{L}_{per}\\) [17], and adversarial loss \\(\\mathcal{L}_{adv}\\) [10], which are calculated using \\(\\hat{y}\\) and \\(y\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Since the quantization in Eqn. 1 is non-differentiable, we adopt the straight-through gradient estimator in [39, 7]," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.138 + ], + "angle": 0, + "content": "which directly copies the gradients from decoder \\(G\\) to encoder \\(E\\), enabling back-propagation and allowing end-to-end training using the code-level loss function \\(\\mathcal{L}_{VQ}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.145, + 0.893, + 0.164 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {V Q} (E, G, Z _ {k}) = | | s g [ \\hat {z} ] - z _ {q} | | _ {2} ^ {2} + \\beta \\cdot | | \\hat {z} - s g [ z _ {q} ] | | _ {2} ^ {2} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.17, + 0.892, + 0.215 + ], + "angle": 0, + "content": "where \\( sg[\\cdot] \\) denotes the stop-gradient operation and \\( \\beta = 0.25 \\) is a hyper-parameter to control the update frequency of the codebook." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.217, + 0.893, + 0.278 + ], + "angle": 0, + "content": "To further reinforce the semantics in the latent codebook and improve the texture restoration [43], we incorporate a VGG19-based regularization term \\(\\mathcal{L}_{sem}\\) into the codebook training process, following the approach in [3].:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.285, + 0.892, + 0.303 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s e m} = \\left| \\left| C O N V (\\hat {z}) - \\Phi \\left(y _ {k} ^ {\\prime}\\right) \\right| \\right| _ {2} ^ {2} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.892, + 0.356 + ], + "angle": 0, + "content": "where \\(\\Phi\\) denotes the feature extractor of VGG19 [37], and \\(CONV\\) denotes a single convolutional layer to match the dimension of \\(\\hat{z}\\) and \\(\\Phi(y_k')\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.387 + ], + "angle": 0, + "content": "With the above image-level and code-level losses, we can summarize the training objective in Stage I as:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.396, + 0.892, + 0.413 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s t a g e 1}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {V Q} + \\lambda \\cdot \\mathcal {L} _ {\\text {s e m}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.744, + 0.435 + ], + "angle": 0, + "content": "where the loss weight \\(\\lambda\\) is set to 0.1." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.444, + 0.88, + 0.46 + ], + "angle": 0, + "content": "3.2. AdaCode Representation Learning (Stage II)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.694 + ], + "angle": 0, + "content": "Given the pretrained class-specific basis codebooks \\( Z_{k}, k \\in \\{1, \\dots, K\\} \\), the latent feature space can be partitioned into non-overlapping cells in \\( K \\) different ways. Specifically, for a given input HR patch \\( y \\), \\( K \\) quantized representations can be generated. Each distinct quantized representation \\( z_{q_k} \\) obtains its code token from its corresponding semantic codebook. To combine the discrete representation \\( z_{q_{1}, \\dots, K} \\) into the AdaCode representation \\( z \\), we employ a weight predictor module, which generates a \\( K \\)-channel weight map \\( w \\in \\mathbb{R}^{h \\times w \\times K} \\), as illustrated in Fig. 3 and Fig. 5. The weight predictor module consists of four residual swim transformer blocks (RSTBs) [20] and a convolution layer to match the channels of weight map and \\( K \\). \\( z \\) is computed following Eqn. 6. Finally, the adaptive feature \\( z \\) is reconstructed to HR patch \\( \\hat{y} \\) via the decoder \\( G \\)." + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.702, + 0.892, + 0.733 + ], + "angle": 0, + "content": "\\[\nz = \\sum_ {i} w _ {i} \\times z _ {q _ {i}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.74, + 0.893, + 0.877 + ], + "angle": 0, + "content": "To efficiently train AdaCode and maintain a comparable number of parameters in the codebooks to VQGAN [7] and FeMaSR [3], which both set the codebook dimension to be \\(1024 \\times 512\\), we set each of our class-specific codebooks to be \\(256 \\times 256\\) or \\(512 \\times 256\\). These codebooks are fixed during the training of stage II while the rest of the model, i.e. the encoder \\(E\\), the weight predictor, the decoder \\(G\\), and the discriminator \\(D\\), are trained using the objective in Eqn. 7. Each term in this equation is defined in Sec. 3.1." + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.886, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s t a g e 2}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {V Q} (E, G) \\tag {7}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "5376" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.46, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.47, + 0.368 + ], + "angle": 0, + "content": "Figure 5: An example showing the learned weight maps. The input image contains multiple semantically-meaningful content (e.g. pyramid, person, animal, sky) which cannot be well represented with a single codebook. Instead, AdaCode uses multiple basis codebooks and weight maps for discrete representations. As shown, the weight maps correlate to the semantics to some extent." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.401, + 0.391, + 0.417 + ], + "angle": 0, + "content": "3.3. Restoration via AdaCode (Stage III)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.469, + 0.639 + ], + "angle": 0, + "content": "With the powerful decoder \\( G \\), various image restoration tasks can be turned into a feature refinement problem through AdaCode scheme. From the perspective of latent space partition, each representation of the degraded input \\( x \\) is pulled towards its nearest HR code entry, allowing for the information loss in \\( x \\) to be relatively compensated. In comparison to the quantized representation \\( z_{q} \\) using only one general codebook, the combination of \\( z_{q_{1},\\ldots ,K} \\) with the weight map can be considered as adding an offset to \\( z_{q} \\). The offset helps to alleviate the discontinuity among the discrete codes, which is demonstrated in our ablation study. To further showcase the effectiveness of AdaCode, we train our model on two ill-posed problems, i.e. Single Image SuperResolution and Image Inpainting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.469, + 0.778 + ], + "angle": 0, + "content": "In super-resolution and image inpainting tasks, the mapping between the input and the HR output has more than one solutions. Despite the benefits of the AdaCode scheme, restoring damaged content or missing details remains challenging given the uncertain degradations and the diversity of natural images. To better account for the degradation and improve the gradient flow, we adopt the encoder design in [3] which utilizes a feature extraction module and a residual shortcut module during stage III." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Thanks to the excellent reconstruction model in stage II, given a Degraded-HR image pair, we can obtain the groundtruth representation \\( z_{gt} \\) via the fixed model. Since the decoder \\( G \\) is fixed in this stage, the restoration problem can be formulated as minimizing the distance between HR feature \\( z_{gt} \\) and degraded feature \\( z \\). To achieve this, we use a code-level loss that includes the InfoNCE loss in [29] and the style loss in [17]. Following the design as SimCLR[4]," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "given a degraded image feature \\( z \\), we use the HR feature \\( z_{gt} \\) as the positive sample, while other \\( z_{gt} \\) and \\( z \\) from different source images in the same batch are treated as the negative samples. The code-level loss is defined as follows." + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.163, + 0.892, + 0.201 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {c o d e}} = \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {g t}, z\\right) + \\mathcal {L} _ {\\text {s t y l e}} \\left(z _ {g t}, z\\right) \\tag {8} \\\\ + \\beta \\cdot | | \\hat {z} - s g [ z _ {g t} ] | | _ {2} ^ {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.209, + 0.756, + 0.223 + ], + "angle": 0, + "content": "And the overall loss is summarized as:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.236, + 0.892, + 0.252 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s t a g e 3}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {\\text {c o d e}} \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.264, + 0.632, + 0.28 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.424 + ], + "angle": 0, + "content": "Datasets Our training dataset includes images from DIV2K train set [1], Flickr2K [22], DIV8K train set [12], and 10,000 face images from FFHQ [18]. We generate the training patches by cropping images into non-overlapping patches at \\(512 \\times 512\\) resolution (face images in FFHQ are randomly resized with scale factors between [0.5, 1.0] before cropping). We adopt the same degradation model as BSRGAN [57] to generate LR patches. The final training dataset consists of 198,061 patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.892, + 0.561 + ], + "angle": 0, + "content": "In the test stage, we evaluate the reconstruction task on OST dataset [43], which contains 300 images with rich textures. For super-resolution, we evaluate the performance on five classical benchmarks, i.e. Set5, Set14, BSD100, Urban100, and Manga109, with \\(\\times 2\\) and \\(\\times 4\\) scales. For image inpainting, we apply a publicly available script [52] to randomly draw irregular polyline masks and generate masked images. The inpainting performance is evaluated on the validation sets of DIV2K [1] and DIV8K [12]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.891, + 0.655 + ], + "angle": 0, + "content": "Evaluation Metrics For reconstruction, we adopt PSNR and SSIM as the evaluation metrics. For super-resolution, we employ an additional well-known perceptual score, LPIPS [58]. For image inpainting task, we use PSNR, LPIPS and a widely-used non-reference metric, FID [14]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Implementation Details According to the size of each semantic dataset, we empirically set the codebook bases sizes to be \\(\\{512, 256, 512, 256, 256\\} \\times 256\\) for Architectures, Indoor Objects, Natural Scenes, Street Views, and Portraits. For all stages, we represent the input image as a \\(32 \\times 32\\) code sequence. We train each stage for \\(350k\\) iterations with an Adam optimizer and a batch size of 32. The learning rates for the generator and discriminator are fixed as 1e-4 and 4e-4 separately. Our method is implemented with PyTorch and trained with 4 NVIDIA Tesla V100 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.747, + 0.848 + ], + "angle": 0, + "content": "4.1. Expressiveness of AdaCode" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The key design in our work is to leverage the class-specific basis codebooks to construct an adaptive codebook, which supports more expressiveness even with a smaller" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "5377" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.111, + 0.095, + 0.852, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.483, + 0.895, + 0.531 + ], + "angle": 0, + "content": "Figure 6: Qualitative comparisons on image reconstruction task. Various scenes and semantics, i.e. text, plants, buildings, streets, and faces, are covered in these examples. Benefited from the adaptive codebook, our AdaCode is able to reconstruct images with higher quality and fidelity. (Zoom in for best view)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.473, + 0.673 + ], + "angle": 0, + "content": "codebook size. To verify our method's superiority, we evaluate the reconstruction performances using three codebook and model settings: (1) VQGAN [7] with its single general codebook. (2) VQGAN with a merged codebook concatenating all the basis codebooks, referred to as VQGAN-aux. (3) AdaCode with our adaptive codebook. The three approaches are trained with the same dataset (see Section. 4) to guarantee a fair comparison." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.683, + 0.47, + 0.714 + ], + "angle": 0, + "content": "Table 1: Quantitative comparison of reconstruction performance. PSNR/SSIM↑: the higher, the better." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.725, + 0.462, + 0.814 + ], + "angle": 0, + "content": "
MethodOverall Codebook SizePerformance
PSNRSSIM
VQGAN[3]1024 × 51221.35570.5664
VQGAN-aux1792 × 25621.92190.6030
AdaCode (Ours)1792 × 25625.76290.7705
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As shown in Table. 1, our AdaCode obtains overwhelming reconstruction results with a comparable or smaller codebook size. The gap between (1) and (2) certifies that training class-specific codebooks helps the codes to capture more image textures, while the great improvement between" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.895, + 0.657 + ], + "angle": 0, + "content": "(2) and (3) justifies the expressiveness facilitated by our adaptive codebook design. Fig. 6 shows multiple scenarios, including plants, buildings, streets, portraits, and text which has distinct patterns but does not have a corresponding codebook in our experiments. AdaCode achieves exceedingly excellent results in all semantic cases, producing realistic and fidelitous reconstruction results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.67, + 0.859, + 0.687 + ], + "angle": 0, + "content": "4.2. Benchmarking Image Restoration Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.846 + ], + "angle": 0, + "content": "Super-Resolution We compare AdaCode with state-of-the-art models for Image Super-Resolution, including KX-Net[9], Real-ESRGAN [42], and FeMaSR[3]. Specifically, KX-Net iteratively learns the degradation kernels from the LR images; Real-ESRGAN learns super-resolution using pure synthetic data with high-order degradation model; FeMaSR utilizes a single perceptually rich codebook to restore the images. We use the original codes and weights from each method's official public repository to conduct comparisons, as shown in Table. 2 and Fig. 7." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Image Inpainting We compare AdaCode with state-of-the-art inpainting methods GPEN [52] and MAT [19]. To" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "5378" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.887, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.319, + 0.895, + 0.368 + ], + "angle": 0, + "content": "Figure 7: Qualitative comparisons on super-resolution task with \\(\\times 2\\) and \\(\\times 4\\) upscale factor. AdaCode restores LR with realistic and faithful details, while the competitive work either fails to deblur the LR, i.e. KX-Net [9], or generates artifacts or over-smooth areas, i.e. Real-ESRGAN [42] and FeMaSR [3]. See Appendix for more results. (Zoom in for best view)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.38, + 0.893, + 0.41 + ], + "angle": 0, + "content": "Table 2: Quantitative comparison with state-of-the-art SISR methods. PSNR/SSIM↑: the higher, the better; LPIPS↓: the lower, the better. The best and second best performance are marked in red and blue." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.422, + 0.928, + 0.582 + ], + "angle": 0, + "content": "
MethodScaleSet5Set14BSDS100Urban100Manga109
PSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPS
FeMaSRx227.5130.82500.105425.4040.75650.129224.9070.72600.144922.7130.75730.110221.5840.69380.2270
KX-Netx227.8370.88840.085925.9290.82910.130125.8180.80920.173422.6750.80160.097219.5610.50490.5312
Real-ESRGANx230.0320.89300.105127.0190.83790.138226.6700.79160.152623.5770.81150.097620.8150.68170.3056
Oursx229.2130.84440.084426.2490.77020.117926.0380.75290.137423.6630.78940.100922.0230.70290.2150
FeMaSRx424.0390.74520.150022.7240.63540.204521.9570.58190.251720.5090.64260.198318.1310.57570.3449
KX-Netx421.9220.70500.208021.1820.61260.304421.7080.57680.397218.6030.55760.270418.1810.53230.6909
Real-ESRGANx425.2630.76650.171024.1000.70040.233823.7760.62610.281921.3510.66250.214018.2220.59170.4091
Oursx425.8680.77310.150524.1580.66620.203123.1290.60410.248521.4460.65680.200718.1450.56640.3425
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.471, + 0.743 + ], + "angle": 0, + "content": "conduct a fair comparison, we retrain MAT on our training dataset as discussed in Section. 4. Moreover, we train FeMaSR [3] for this task to demonstrate the effectiveness of our adaptive codebooks over the single codebook in FeMaSR. As shown in Table. 3, AdaCode achieves state-of-the-art performance on various metrics. Qualitative comparisons in Fig. 8 also illustrate that AdaCode consistently produce high-quality inpainting results across a wide range of scenes with a single model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.231, + 0.772 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We investigate AdaCode's expressiveness given a various number of basis codebooks. We fix the five basis codebooks trained in Stage I and train Stage II with various combinations of basis codebooks. We adopt PSNR and SSIM to evaluate the expressiveness on the reconstruction task. Fig. 9 empirically shows that the adaptive codebook benefits from the bases in a large extent. Meanwhile, it also indicates that our basis codebooks are \"non-multicollinear\"" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.605, + 0.895, + 0.665 + ], + "angle": 0, + "content": "Table 3: Quantitative comparison with state-of-the-art inpainting methods. PSNR↑: the higher, the better; LPIPS/FID↓: the lower, the better. The best and second best performance are marked in red and blue." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.677, + 0.868, + 0.783 + ], + "angle": 0, + "content": "
MethodDIV2KDIV8KAll
PSNRLPIPSPSNRLPIPSFID
GPEN29.1290.093331.1910.07033.0924
FeMaSR29.7900.058132.2330.04161.6741
MAT30.1240.067632.3350.04061.2385
Ours30.11510.051632.7010.03721.1657
" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.811, + 0.89, + 0.827 + ], + "angle": 0, + "content": "even if the semantic sub-datasets have overlapping patches." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.844, + 0.75, + 0.86 + ], + "angle": 0, + "content": "5. Conclusion and Limitation" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.903 + ], + "angle": 0, + "content": "In this work, we propose AdaCode, a novel approach for class-agnostic image reconstruction and restoration. In par" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.925, + 0.516, + 0.937 + ], + "angle": 0, + "content": "5379" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.097, + 0.895, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.54, + 0.893, + 0.571 + ], + "angle": 0, + "content": "Figure 8: Qualitative comparisons on image inpainting task. The first two rows demonstrate the inpainting results of face images, while the last two rows show the recovered results of place images. See Appendix for more results." + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.594, + 0.46, + 0.794 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.804, + 0.47, + 0.851 + ], + "angle": 0, + "content": "Figure 9: Ablation Study. PSNR and SSIM score of reconstructed results with varying number of basis codebooks. See supplementary for more result images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.719 + ], + "angle": 0, + "content": "ticular, we train a set of class-specific basis codebooks and learn a weight map to construct an image-adaptive codebook for better image representation. Unlike previous methods that use a general codebook to represent images, our image-adaptive codebook is more flexible and suited for natural images. Extensive comparisons on image reconstruction, super-resolution, and image inpainting tasks validate our method's superiority." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Our work is a first step towards class-agnostic generative prior for arbitrary images. It has several limitations we plan to explore in future work. First, it is yet unclear how many basis codebooks and how many code entries in each codebook we need. Stage I is trained separately from Stage II&III, which may be suboptimal. Second, we do not yet incorporate high-level explicit semantic information such as semantic segmentation into the framework, which may be also useful for general image restoration tasks. 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IEEE Transactions on Multimedia (MM), 16(8):2178–2190, 2014." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.811 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.926, + 0.515, + 0.937 + ], + "angle": 0, + "content": "5383" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/4f85f017-28ce-47a6-a95c-6487947424f7_origin.pdf b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/4f85f017-28ce-47a6-a95c-6487947424f7_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c42e4c6c939aa4e19585c79c434f4bd6312571b7 --- /dev/null +++ b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/4f85f017-28ce-47a6-a95c-6487947424f7_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c720122bcbbe76d17156887d8cb8343a80f9837aacf998ccfcefa26d2645fe49 +size 5784490 diff --git a/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/full.md b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0731a72f47096d946718fc496e640952b33f24c2 --- /dev/null +++ b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/full.md @@ -0,0 +1,271 @@ +# Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration + +Kechun Liu $^{1,3*}$ Yitong Jiang $^{2}$ Inchang Choi $^{3}$ Jinwei Gu $^{2}$ + +1 University of Washington 2 The Chinese University of Hong Kong 3 SenseBrain + +![](images/93be916efe1e5a676ec09fd10ee89a3729cb5a94b1e5512debeebd6736fedd93.jpg) +Figure 1: We propose an image-adaptive codebook learning method, named AdaCode, for class-agnostic image restoration. For a number of image reconstruction and restoration tasks (e.g., super-resolution and inpainting), the proposed AdaCode achieved significantly better performance than latest prior work, such as VQGAN[7] and VQGAN with our merged basis codebooks (referred to as VQGAN-aux) for reconstruction; KX-Net[9], Real-ESRGAN[42] and FeMaSR[3] for super-resolution; GPEN[52], MAT[19] and our trained FeMaSR[3] for image inpainting. (Zoom in for best view) + +# Abstract + +Recent work on discrete generative priors, in the form of codebooks, has shown exciting performance for image reconstruction and restoration, as the discrete prior space spanned by the codebooks increases the robustness against diverse image degradations. Nevertheless, these methods require separate training of codebooks for different image categories, which limits their use to specific image categories only (e.g. face, architecture, etc.), and fail to handle arbitrary natural images. In this paper, we propose + +AdaCode for learning image-adaptive codebooks for class-agnostic image restoration. Instead of learning a single codebook for each image category, we learn a set of basis codebooks. Given an input image, AdaCode learns a weight map with and computes a weighted combination of these basis codebooks for adaptive image restoration. Intuitively, AdaCode is a more flexible and expressive discrete generative prior than previous work. Experimental results demonstrate that AdaCode achieves state-of-the-art performance on image reconstruction and restoration tasks, including image super-resolution and inpainting. Codes are released at https://github.com/kechun1/AdaCode. + +# 1. Introduction + +In recent years, discrete generative priors (in the form of codebooks) [39, 7] have shown impressive performance for image synthesis [7, 11, 45, 61], exhibiting reduced mode collapse and more stable training. These learned codebooks essentially provide strong priors for compressing and reconstructing natural images, even in the presence of severe degradation. Nevertheless, these methods have a common limitation. The codebooks need to be learned separately for each image category (e.g., face, architecture), which restricts their applicability to arbitrary natural images [7, 45, 61]. Although FeMaSR [3] attempted to learn a single general codebook for all image categories, the expressiveness of the codebook is limited by the complexity of natural images. For example, as shown in Fig. 1, an image often includes textural and structural contents from multiple categories (e.g., face, man-made structural edges, repetitive texture, natural texture). It is challenging to rely on a single universal codebook to capture all. Prior work such as VQGAN [7] and FeMaSR [3] often introduce noticeable artifacts for image reconstruction and restoration. + +![](images/0b55270adc827965d9334d2ce43303ea54ac474dd7798218d2e856731b191dac.jpg) +Figure 2: Intuition of AdaCode vs a single codebook. Top: Prior work VQGAN[7] uses a single codebook as the learned representation in the discrete latent space, which may not fully capture complex visual patterns. Bottom: AdaCode learns multiple basis codebooks, each representing a different discretization of the latent space corresponding to different visual appearances. For an input image, its latent representation is a weighted linear combination of the codes from these codebooks. AdaCode thus is a more flexible representation for class-agnostic image restoration. + +Is it possible to learn a class-agnostic discrete generative prior for image reconstruction and restoration? Inspired + +by a recent work [55], we propose AdaCode, which learns image-adaptive codebooks for class-agnostic image reconstruction and restoration. Instead of learning a single codebook for all categories of images, we learn a set of basis codebooks. For a given input image, AdaCode learns a weight map that determines the contribution of each basis codebook to the final representation. Intuitively, this design allows AdaCode to learn a more flexible and expressive discrete generative prior than previous work, as demonstrated in Fig. 2. In contrast to VQGAN [7] and FeMaSR [3], which utilize a single partition for the latent space and assign each image feature an exclusive discrete representation, AdaCode learns various partitions to the latent space from different perspectives – each corresponding to the learning of one of the basis codebooks. The discrete generative prior for an arbitrary image is a weighted linear combination derived from these basis codebooks, resulting in a more flexible and expressive representation. As depicted in Fig. 1, AdaCode outperforms previous work in various image restoration tasks, effectively preserving scene structure and texture. + +We evaluated AdaCode on both image reconstruction and image restoration tasks (i.e., super-resolution and image inpainting). Across multiple benchmark datasets, AdaCode achieved state-of-the-art performance, while maintaining a comparable codebook size and computational cost. + +# 2. Related Work + +Visual Representation Dictionary Learning Learning representation dictionaries in visual understanding has demonstrated its great power in image restoration tasks such as super-resolution [51, 62], denoising [59], and image inpainting [8, 36]. Using DNNs, VQVAE [39] first introduces a generative autoencoder model that learns discrete latent representations, also known as "codebook". The following VQGAN [7] employs perceptual and adversarial loss to train the visual codebook, resulting in better image generation quality with a relatively small codebook size. The representation dictionary-based generative model has inspired various impressive image generation work [11, 61, 53, 3, 45], as well as our AdaCode. + +The use of dictionaries is not limited to image restoration. Referred as lookup tables (LUTs), the dictionaries are also applied to optimize color transforms [55, 23, 49, 50]. In 3D-LUT [55], multiple LUTs are learned to serve as the bases of the LUT space. And a CNN is trained to predict weights to fuse the bases into an image-adaptive LUT. Inspired by 3D LUT, we leverage the discrete codebooks from VQGAN as the bases of the image latent space to build our image-adaptive codebook, AdaCode. Such design allows our method to fully and flexibly exploit the latent codes to represent diverse and complex natural images. + +![](images/4feafae5fd7df9622c925e0c00d46483863cb75b6531f85a6341358841d1b3f9.jpg) +Figure 3: The framework of the proposed AdaCode method. The training of AdaCode incorporates three stages: Class-specific Codebook Pretraining, AdaCode Representation Learning, and Restoration via AdaCode. The lock icon indicates that the codebooks $Z_{1,\dots,K}$ are fixed in Stage II&III, and the decoder $G$ is fixed in Stage III. See Section 3 for more details. + +DNN-based Image Restoration DNN has been widely used for image restoration tasks, i.e. single image super-resolution (SISR) and image inpainting. In the field of super-resolution (SR), recent studies focus on recovering low-resolution input images with unknown degradation types, which is more relevant to real-world scenarios. They restore the images either by learning the degradation representations [33, 21, 41, 42, 57, 9], or by training unified generative networks with LR-HR pairs [16, 46, 32]. Some studies introduce additional image priors, such as latent representations [27, 2, 30] and discrete codebooks [7, 61, 3], to address unrealistic textures or over-smoothed areas commonly observed in GAN-based methods. However, a single partition of the latent space is often insufficient to model the intricate patterns in natural images, resulting in specific textures being generated regardless of the image content. + +In the case of image inpainting, researchers often leverage deep generative models to fill missing image regions with plausible content [31, 25, 44, 56, 5]. Some approaches incorporate additional discriminators [35], partial or gated convolutions [24, 54], semantic texture or context [28, 48, 34, 13, 38, 15], or transformers [19, 6, 26, 40] to enhance the quality of inpainted results. However, these methods often require separate experiments for different image patterns, i.e. natural scenes, faces, etc., due to the significant variations among them. + +Both SR and inpainting methods face the challenge of effectively modeling complex visual patterns with a single model or codebook. In our proposed approach, AdaCode, we address this challenge by leveraging adaptive codebooks, enabling realistic and robust restoration results for general images. + +# 3. Methodology + +Building upon VQGAN [7], we introduce an additional degree of freedom to the codebook and construct an adaptive codebook (AdaCode) to model the intricate high-resolution natural image patterns. We summarize the AdaCode model in Fig.3. Our method's overall training consists of three sequential stages. In the first stage (Sec 3.1), we divide our HQ dataset into multiple semantic subsets and train a class-specific VQGAN [7] on each subset. In the second stage, using the fixed pretrained class-specific codebooks as bases, we leverage a transformer block to generate weight maps and train the AdaCode through the self-reconstruction task (Sec 3.2). In the last stage (Sec 3.3), we employ the AdaCode with fixed codebooks and fixed image decoder to address downstream restoration tasks, e.g. Super-Resolution and Image Inpainting. The details of each stage are discussed in the following sections. + +# 3.1. Codebook Pretraining (Stage I) + +Diversify Basis Codebooks To enhance the expressiveness of AdaCode, we aim to diversify the basis codebooks. Rather than applying various initializations as 3D-LUT [55], we achieve codebook divergence by training them on different HR subsets of our dataset. To accomplish this, we utilize an off-the-shelf SegFormer model [47] to perform semantic segmentation with 150 classes from the ADE20K dataset [60]. Each HR patch is labeled according to the semantic class with the largest area. We then group the 150 classes into 5 super-classes: Architectures, Indoor objects, Natural scenes, Street views, Portraits, and obtain the 5 semantic HR subsets accordingly. It is worth noting that the separation of subsets is not rigorous and each subset may + +![](images/384e670cd4f183f44f844cb354d1e5a1b5b30b76aeda97c748a057d059600330.jpg) +Figure 4: Visualization of the learned codes for different categories of visual appearance. We randomly sample 10 code entries from each codebook and visualize them by projecting a tiled $4 \times 4$ feature map onto a $32 \times 32$ texture patch using the corresponding decoder. As expected, the codes from different categories exhibit distinct features. + +contain semantic contexts from other subsets, as most images contain multiple semantics. More details regarding the clustering of the 150 classes can be found in the Appendix. This approach not only diversifies the codebooks but also provides various ways to partition the latent feature space. We randomly visualize some code samples in Fig. 4. + +Learning Basis Codebooks Given a HQ subset of class $k$ , we train a quantized autoencoder to learn the class-specific basis codebook. As shown in Fig. 3, the input HR patch $y \in \mathbb{R}^{H \times W \times 3}$ is first passed through the encoder $E$ to generate the embedding $\hat{z} = E(y) \in \mathbb{R}^{h \times w \times n_z}$ . Following VQVAE [39] and VQGAN [7], each entry $\hat{z}_i \in \mathbb{R}^{n_z}$ in $\hat{z}$ is replaced with its nearest code in the learnable codebook $Z_k \in \mathbb{R}^{N \times n_z}$ to construct the quantized embedding $z_{q_k}$ : + +$$ +z _ {q _ {k}} = \underset {c \in \{0, \dots , N - 1 \}} {\arg \min } | | \hat {z} - Z _ {k, c} | | \tag {1} +$$ + +where $\mathbf{N}$ is the number of codes in the corresponding codebook, $z_{q_k}$ denotes the quantized representation using $Z_{k}$ , and $Z_{k,c}$ represent the $c$ -th entry in codebook $Z_{k}$ . After the feature quantization, the decoder $G$ reconstructs the HR patch $\hat{y}$ using $z_{q_k}$ : + +$$ +\hat {y} = G \left(z _ {q _ {k}}\right) \approx y \tag {2} +$$ + +The adversarial learning scheme is employed to train the encoder $E$ , codebook $Z$ , and decoder $G$ with the discriminator $D$ . The detailed architectures of $E$ , $D$ , and $G$ are provided in the Appendix. + +Training Objective To train the quantized autoencoder, we adopt 3 image-level losses: L1 loss $\mathcal{L}_1$ , perceptual loss $\mathcal{L}_{per}$ [17], and adversarial loss $\mathcal{L}_{adv}$ [10], which are calculated using $\hat{y}$ and $y$ . + +Since the quantization in Eqn. 1 is non-differentiable, we adopt the straight-through gradient estimator in [39, 7], + +which directly copies the gradients from decoder $G$ to encoder $E$ , enabling back-propagation and allowing end-to-end training using the code-level loss function $\mathcal{L}_{VQ}$ : + +$$ +\mathcal {L} _ {V Q} (E, G, Z _ {k}) = | | s g [ \hat {z} ] - z _ {q} | | _ {2} ^ {2} + \beta \cdot | | \hat {z} - s g [ z _ {q} ] | | _ {2} ^ {2} \tag {3} +$$ + +where $sg[\cdot]$ denotes the stop-gradient operation and $\beta = 0.25$ is a hyper-parameter to control the update frequency of the codebook. + +To further reinforce the semantics in the latent codebook and improve the texture restoration [43], we incorporate a VGG19-based regularization term $\mathcal{L}_{sem}$ into the codebook training process, following the approach in [3].: + +$$ +\mathcal {L} _ {s e m} = \left| \left| C O N V (\hat {z}) - \Phi \left(y _ {k} ^ {\prime}\right) \right| \right| _ {2} ^ {2} \tag {4} +$$ + +where $\Phi$ denotes the feature extractor of VGG19 [37], and $CONV$ denotes a single convolutional layer to match the dimension of $\hat{z}$ and $\Phi(y_k')$ . + +With the above image-level and code-level losses, we can summarize the training objective in Stage I as: + +$$ +\mathcal {L} _ {\text {s t a g e 1}} = \mathcal {L} _ {1} + \mathcal {L} _ {\text {p e r}} + \lambda \cdot \mathcal {L} _ {\text {a d v}} + \mathcal {L} _ {V Q} + \lambda \cdot \mathcal {L} _ {\text {s e m}} \tag {5} +$$ + +where the loss weight $\lambda$ is set to 0.1. + +# 3.2. AdaCode Representation Learning (Stage II) + +Given the pretrained class-specific basis codebooks $Z_{k}, k \in \{1, \dots, K\}$ , the latent feature space can be partitioned into non-overlapping cells in $K$ different ways. Specifically, for a given input HR patch $y$ , $K$ quantized representations can be generated. Each distinct quantized representation $z_{q_k}$ obtains its code token from its corresponding semantic codebook. To combine the discrete representation $z_{q_{1}, \dots, K}$ into the AdaCode representation $z$ , we employ a weight predictor module, which generates a $K$ -channel weight map $w \in \mathbb{R}^{h \times w \times K}$ , as illustrated in Fig. 3 and Fig. 5. The weight predictor module consists of four residual swim transformer blocks (RSTBs) [20] and a convolution layer to match the channels of weight map and $K$ . $z$ is computed following Eqn. 6. Finally, the adaptive feature $z$ is reconstructed to HR patch $\hat{y}$ via the decoder $G$ . + +$$ +z = \sum_ {i} w _ {i} \times z _ {q _ {i}} \tag {6} +$$ + +To efficiently train AdaCode and maintain a comparable number of parameters in the codebooks to VQGAN [7] and FeMaSR [3], which both set the codebook dimension to be $1024 \times 512$ , we set each of our class-specific codebooks to be $256 \times 256$ or $512 \times 256$ . These codebooks are fixed during the training of stage II while the rest of the model, i.e. the encoder $E$ , the weight predictor, the decoder $G$ , and the discriminator $D$ , are trained using the objective in Eqn. 7. Each term in this equation is defined in Sec. 3.1. + +$$ +\mathcal {L} _ {\text {s t a g e 2}} = \mathcal {L} _ {1} + \mathcal {L} _ {\text {p e r}} + \lambda \cdot \mathcal {L} _ {\text {a d v}} + \mathcal {L} _ {V Q} (E, G) \tag {7} +$$ + +![](images/4c778202d09786f4bd59eb347c9514e5ad8d7a2d9994243c9f77899c987e6434.jpg) +Figure 5: An example showing the learned weight maps. The input image contains multiple semantically-meaningful content (e.g. pyramid, person, animal, sky) which cannot be well represented with a single codebook. Instead, AdaCode uses multiple basis codebooks and weight maps for discrete representations. As shown, the weight maps correlate to the semantics to some extent. + +# 3.3. Restoration via AdaCode (Stage III) + +With the powerful decoder $G$ , various image restoration tasks can be turned into a feature refinement problem through AdaCode scheme. From the perspective of latent space partition, each representation of the degraded input $x$ is pulled towards its nearest HR code entry, allowing for the information loss in $x$ to be relatively compensated. In comparison to the quantized representation $z_{q}$ using only one general codebook, the combination of $z_{q_{1},\ldots ,K}$ with the weight map can be considered as adding an offset to $z_{q}$ . The offset helps to alleviate the discontinuity among the discrete codes, which is demonstrated in our ablation study. To further showcase the effectiveness of AdaCode, we train our model on two ill-posed problems, i.e. Single Image SuperResolution and Image Inpainting. + +In super-resolution and image inpainting tasks, the mapping between the input and the HR output has more than one solutions. Despite the benefits of the AdaCode scheme, restoring damaged content or missing details remains challenging given the uncertain degradations and the diversity of natural images. To better account for the degradation and improve the gradient flow, we adopt the encoder design in [3] which utilizes a feature extraction module and a residual shortcut module during stage III. + +Thanks to the excellent reconstruction model in stage II, given a Degraded-HR image pair, we can obtain the groundtruth representation $z_{gt}$ via the fixed model. Since the decoder $G$ is fixed in this stage, the restoration problem can be formulated as minimizing the distance between HR feature $z_{gt}$ and degraded feature $z$ . To achieve this, we use a code-level loss that includes the InfoNCE loss in [29] and the style loss in [17]. Following the design as SimCLR[4], + +given a degraded image feature $z$ , we use the HR feature $z_{gt}$ as the positive sample, while other $z_{gt}$ and $z$ from different source images in the same batch are treated as the negative samples. The code-level loss is defined as follows. + +$$ +\begin{array}{l} \mathcal {L} _ {\text {c o d e}} = \mathcal {L} _ {\text {I n f o N C E}} \left(z _ {g t}, z\right) + \mathcal {L} _ {\text {s t y l e}} \left(z _ {g t}, z\right) \tag {8} \\ + \beta \cdot | | \hat {z} - s g [ z _ {g t} ] | | _ {2} ^ {2} \\ \end{array} +$$ + +And the overall loss is summarized as: + +$$ +\mathcal {L} _ {\text {s t a g e 3}} = \mathcal {L} _ {1} + \mathcal {L} _ {\text {p e r}} + \lambda \cdot \mathcal {L} _ {\text {a d v}} + \mathcal {L} _ {\text {c o d e}} \tag {9} +$$ + +# 4. Experiments + +Datasets Our training dataset includes images from DIV2K train set [1], Flickr2K [22], DIV8K train set [12], and 10,000 face images from FFHQ [18]. We generate the training patches by cropping images into non-overlapping patches at $512 \times 512$ resolution (face images in FFHQ are randomly resized with scale factors between [0.5, 1.0] before cropping). We adopt the same degradation model as BSRGAN [57] to generate LR patches. The final training dataset consists of 198,061 patches. + +In the test stage, we evaluate the reconstruction task on OST dataset [43], which contains 300 images with rich textures. For super-resolution, we evaluate the performance on five classical benchmarks, i.e. Set5, Set14, BSD100, Urban100, and Manga109, with $\times 2$ and $\times 4$ scales. For image inpainting, we apply a publicly available script [52] to randomly draw irregular polyline masks and generate masked images. The inpainting performance is evaluated on the validation sets of DIV2K [1] and DIV8K [12]. + +Evaluation Metrics For reconstruction, we adopt PSNR and SSIM as the evaluation metrics. For super-resolution, we employ an additional well-known perceptual score, LPIPS [58]. For image inpainting task, we use PSNR, LPIPS and a widely-used non-reference metric, FID [14]. + +Implementation Details According to the size of each semantic dataset, we empirically set the codebook bases sizes to be $\{512, 256, 512, 256, 256\} \times 256$ for Architectures, Indoor Objects, Natural Scenes, Street Views, and Portraits. For all stages, we represent the input image as a $32 \times 32$ code sequence. We train each stage for $350k$ iterations with an Adam optimizer and a batch size of 32. The learning rates for the generator and discriminator are fixed as 1e-4 and 4e-4 separately. Our method is implemented with PyTorch and trained with 4 NVIDIA Tesla V100 GPUs. + +# 4.1. Expressiveness of AdaCode + +The key design in our work is to leverage the class-specific basis codebooks to construct an adaptive codebook, which supports more expressiveness even with a smaller + +![](images/2b7385bf74cd3ce9a2efb549c721dfdb99d6a270f55e502d62bde0bce15bc942.jpg) +Figure 6: Qualitative comparisons on image reconstruction task. Various scenes and semantics, i.e. text, plants, buildings, streets, and faces, are covered in these examples. Benefited from the adaptive codebook, our AdaCode is able to reconstruct images with higher quality and fidelity. (Zoom in for best view) + +codebook size. To verify our method's superiority, we evaluate the reconstruction performances using three codebook and model settings: (1) VQGAN [7] with its single general codebook. (2) VQGAN with a merged codebook concatenating all the basis codebooks, referred to as VQGAN-aux. (3) AdaCode with our adaptive codebook. The three approaches are trained with the same dataset (see Section. 4) to guarantee a fair comparison. + +Table 1: Quantitative comparison of reconstruction performance. PSNR/SSIM↑: the higher, the better. + +
MethodOverall Codebook SizePerformance
PSNRSSIM
VQGAN[3]1024 × 51221.35570.5664
VQGAN-aux1792 × 25621.92190.6030
AdaCode (Ours)1792 × 25625.76290.7705
+ +As shown in Table. 1, our AdaCode obtains overwhelming reconstruction results with a comparable or smaller codebook size. The gap between (1) and (2) certifies that training class-specific codebooks helps the codes to capture more image textures, while the great improvement between + +(2) and (3) justifies the expressiveness facilitated by our adaptive codebook design. Fig. 6 shows multiple scenarios, including plants, buildings, streets, portraits, and text which has distinct patterns but does not have a corresponding codebook in our experiments. AdaCode achieves exceedingly excellent results in all semantic cases, producing realistic and fidelitous reconstruction results. + +# 4.2. Benchmarking Image Restoration Results + +Super-Resolution We compare AdaCode with state-of-the-art models for Image Super-Resolution, including KX-Net[9], Real-ESRGAN [42], and FeMaSR[3]. Specifically, KX-Net iteratively learns the degradation kernels from the LR images; Real-ESRGAN learns super-resolution using pure synthetic data with high-order degradation model; FeMaSR utilizes a single perceptually rich codebook to restore the images. We use the original codes and weights from each method's official public repository to conduct comparisons, as shown in Table. 2 and Fig. 7. + +Image Inpainting We compare AdaCode with state-of-the-art inpainting methods GPEN [52] and MAT [19]. To + +![](images/e3e76863bc465173fce08c5b7a5e0d5e8738dbd0f0cb0dd089c35c54f00f7f37.jpg) +Figure 7: Qualitative comparisons on super-resolution task with $\times 2$ and $\times 4$ upscale factor. AdaCode restores LR with realistic and faithful details, while the competitive work either fails to deblur the LR, i.e. KX-Net [9], or generates artifacts or over-smooth areas, i.e. Real-ESRGAN [42] and FeMaSR [3]. See Appendix for more results. (Zoom in for best view) +Table 2: Quantitative comparison with state-of-the-art SISR methods. PSNR/SSIM↑: the higher, the better; LPIPS↓: the lower, the better. The best and second best performance are marked in red and blue. + +
MethodScaleSet5Set14BSDS100Urban100Manga109
PSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPS
FeMaSRx227.5130.82500.105425.4040.75650.129224.9070.72600.144922.7130.75730.110221.5840.69380.2270
KX-Netx227.8370.88840.085925.9290.82910.130125.8180.80920.173422.6750.80160.097219.5610.50490.5312
Real-ESRGANx230.0320.89300.105127.0190.83790.138226.6700.79160.152623.5770.81150.097620.8150.68170.3056
Oursx229.2130.84440.084426.2490.77020.117926.0380.75290.137423.6630.78940.100922.0230.70290.2150
FeMaSRx424.0390.74520.150022.7240.63540.204521.9570.58190.251720.5090.64260.198318.1310.57570.3449
KX-Netx421.9220.70500.208021.1820.61260.304421.7080.57680.397218.6030.55760.270418.1810.53230.6909
Real-ESRGANx425.2630.76650.171024.1000.70040.233823.7760.62610.281921.3510.66250.214018.2220.59170.4091
Oursx425.8680.77310.150524.1580.66620.203123.1290.60410.248521.4460.65680.200718.1450.56640.3425
+ +conduct a fair comparison, we retrain MAT on our training dataset as discussed in Section. 4. Moreover, we train FeMaSR [3] for this task to demonstrate the effectiveness of our adaptive codebooks over the single codebook in FeMaSR. As shown in Table. 3, AdaCode achieves state-of-the-art performance on various metrics. Qualitative comparisons in Fig. 8 also illustrate that AdaCode consistently produce high-quality inpainting results across a wide range of scenes with a single model. + +# 4.3. Ablation Study + +We investigate AdaCode's expressiveness given a various number of basis codebooks. We fix the five basis codebooks trained in Stage I and train Stage II with various combinations of basis codebooks. We adopt PSNR and SSIM to evaluate the expressiveness on the reconstruction task. Fig. 9 empirically shows that the adaptive codebook benefits from the bases in a large extent. Meanwhile, it also indicates that our basis codebooks are "non-multicollinear" + +Table 3: Quantitative comparison with state-of-the-art inpainting methods. PSNR↑: the higher, the better; LPIPS/FID↓: the lower, the better. The best and second best performance are marked in red and blue. + +
MethodDIV2KDIV8KAll
PSNRLPIPSPSNRLPIPSFID
GPEN29.1290.093331.1910.07033.0924
FeMaSR29.7900.058132.2330.04161.6741
MAT30.1240.067632.3350.04061.2385
Ours30.11510.051632.7010.03721.1657
+ +even if the semantic sub-datasets have overlapping patches. + +# 5. Conclusion and Limitation + +In this work, we propose AdaCode, a novel approach for class-agnostic image reconstruction and restoration. In par + +![](images/f13fd9c00a3dcd3b7f55e7243723ad335daa1d71154e2b5936e0381aaffdad86.jpg) +Figure 8: Qualitative comparisons on image inpainting task. The first two rows demonstrate the inpainting results of face images, while the last two rows show the recovered results of place images. See Appendix for more results. + +![](images/620eec168f790eab59940137f30f9577125c71996dc0f2f6607def8da89dd76a.jpg) +Figure 9: Ablation Study. PSNR and SSIM score of reconstructed results with varying number of basis codebooks. See supplementary for more result images. + +ticular, we train a set of class-specific basis codebooks and learn a weight map to construct an image-adaptive codebook for better image representation. Unlike previous methods that use a general codebook to represent images, our image-adaptive codebook is more flexible and suited for natural images. Extensive comparisons on image reconstruction, super-resolution, and image inpainting tasks validate our method's superiority. + +Our work is a first step towards class-agnostic generative prior for arbitrary images. It has several limitations we plan to explore in future work. First, it is yet unclear how many basis codebooks and how many code entries in each codebook we need. Stage I is trained separately from Stage II&III, which may be suboptimal. Second, we do not yet incorporate high-level explicit semantic information such as semantic segmentation into the framework, which may be also useful for general image restoration tasks. Finally, it would be interesting to extend AdaCode for high-dimensional visual appearance, such as videos and multispectral images. + +# References + +[1] Eirikur Agustsson and Radu Timofte. 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IEEE Transactions on Multimedia (MM), 16(8):2178–2190, 2014. \ No newline at end of file diff --git a/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/images.zip b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..67a097cbd3160417db4d05d72f1f95d9439b7f5f --- /dev/null +++ b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:42ecb9e6e241adc44456f623df13ab1aee3b61f7d819e18296cb52a95bb7abe5 +size 1291466 diff --git a/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/layout.json b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..61ebf3331b0be4c26ddad245f20b499cfb8498db --- /dev/null +++ b/2023/Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration/layout.json @@ -0,0 +1,7951 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 63, + 103, + 530, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 103, + 530, + 121 + ], + "spans": [ + { + "bbox": [ + 63, + 103, + 530, + 121 + ], + "type": "text", + "content": "Learning Image-Adaptive Codebooks for Class-Agnostic Image Restoration" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "spans": [ + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "text", + "content": "Kechun Liu" + }, + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "inline_equation", + "content": "^{1,3*}" + }, + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "text", + "content": " Yitong Jiang" + }, + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "text", + "content": " Inchang Choi" + }, + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "text", + "content": " Jinwei Gu" + }, + { + "bbox": [ + 140, + 142, + 443, + 157 + ], + "type": "inline_equation", + "content": "^{2}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 85, + 157, + 498, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 157, + 498, + 172 + ], + "spans": [ + { + "bbox": [ + 85, + 157, + 498, + 172 + ], + "type": "text", + "content": "1 University of Washington 2 The Chinese University of Hong Kong 3 SenseBrain" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 51, + 198, + 545, + 460 + ], + "blocks": [ + { + "bbox": [ + 51, + 198, + 545, + 460 + ], + "lines": [ + { + "bbox": [ + 51, + 198, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 51, + 198, + 545, + 460 + ], + "type": "image", + "image_path": "93be916efe1e5a676ec09fd10ee89a3729cb5a94b1e5512debeebd6736fedd93.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 475, + 547, + 536 + ], + "lines": [ + { + "bbox": [ + 45, + 475, + 547, + 536 + ], + "spans": [ + { + "bbox": [ + 45, + 475, + 547, + 536 + ], + "type": "text", + "content": "Figure 1: We propose an image-adaptive codebook learning method, named AdaCode, for class-agnostic image restoration. For a number of image reconstruction and restoration tasks (e.g., super-resolution and inpainting), the proposed AdaCode achieved significantly better performance than latest prior work, such as VQGAN[7] and VQGAN with our merged basis codebooks (referred to as VQGAN-aux) for reconstruction; KX-Net[9], Real-ESRGAN[42] and FeMaSR[3] for super-resolution; GPEN[52], MAT[19] and our trained FeMaSR[3] for image inpainting. (Zoom in for best view)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 545, + 192, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 545, + 192, + 558 + ], + "spans": [ + { + "bbox": [ + 143, + 545, + 192, + 558 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 571, + 288, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 288, + 680 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 288, + 680 + ], + "type": "text", + "content": "Recent work on discrete generative priors, in the form of codebooks, has shown exciting performance for image reconstruction and restoration, as the discrete prior space spanned by the codebooks increases the robustness against diverse image degradations. Nevertheless, these methods require separate training of codebooks for different image categories, which limits their use to specific image categories only (e.g. face, architecture, etc.), and fail to handle arbitrary natural images. In this paper, we propose" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 546, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 689 + ], + "type": "text", + "content": "AdaCode for learning image-adaptive codebooks for class-agnostic image restoration. Instead of learning a single codebook for each image category, we learn a set of basis codebooks. Given an input image, AdaCode learns a weight map with and computes a weighted combination of these basis codebooks for adaptive image restoration. Intuitively, AdaCode is a more flexible and expressive discrete generative prior than previous work. Experimental results demonstrate that AdaCode achieves state-of-the-art performance on image reconstruction and restoration tasks, including image super-resolution and inpainting. Codes are released at https://github.com/kechun1/AdaCode." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 200, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 200, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 200, + 713 + ], + "type": "text", + "content": "*kechun@cs.washington.edu \nWork done during an internship at SenseBrain." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "text", + "content": "5373" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 71, + 127, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 71, + 127, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 127, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 91, + 286, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 91, + 286, + 329 + ], + "spans": [ + { + "bbox": [ + 49, + 91, + 286, + 329 + ], + "type": "text", + "content": "In recent years, discrete generative priors (in the form of codebooks) [39, 7] have shown impressive performance for image synthesis [7, 11, 45, 61], exhibiting reduced mode collapse and more stable training. These learned codebooks essentially provide strong priors for compressing and reconstructing natural images, even in the presence of severe degradation. Nevertheless, these methods have a common limitation. The codebooks need to be learned separately for each image category (e.g., face, architecture), which restricts their applicability to arbitrary natural images [7, 45, 61]. Although FeMaSR [3] attempted to learn a single general codebook for all image categories, the expressiveness of the codebook is limited by the complexity of natural images. For example, as shown in Fig. 1, an image often includes textural and structural contents from multiple categories (e.g., face, man-made structural edges, repetitive texture, natural texture). It is challenging to rely on a single universal codebook to capture all. Prior work such as VQGAN [7] and FeMaSR [3] often introduce noticeable artifacts for image reconstruction and restoration." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 47, + 350, + 287, + 548 + ], + "blocks": [ + { + "bbox": [ + 47, + 350, + 287, + 548 + ], + "lines": [ + { + "bbox": [ + 47, + 350, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 287, + 548 + ], + "type": "image", + "image_path": "0b55270adc827965d9334d2ce43303ea54ac474dd7798218d2e856731b191dac.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 554, + 287, + 674 + ], + "lines": [ + { + "bbox": [ + 47, + 554, + 287, + 674 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 287, + 674 + ], + "type": "text", + "content": "Figure 2: Intuition of AdaCode vs a single codebook. Top: Prior work VQGAN[7] uses a single codebook as the learned representation in the discrete latent space, which may not fully capture complex visual patterns. Bottom: AdaCode learns multiple basis codebooks, each representing a different discretization of the latent space corresponding to different visual appearances. For an input image, its latent representation is a weighted linear combination of the codes from these codebooks. AdaCode thus is a more flexible representation for class-agnostic image restoration." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 689, + 286, + 712 + ], + "type": "text", + "content": "Is it possible to learn a class-agnostic discrete generative prior for image reconstruction and restoration? Inspired" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 307, + 72, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 322 + ], + "type": "text", + "content": "by a recent work [55], we propose AdaCode, which learns image-adaptive codebooks for class-agnostic image reconstruction and restoration. Instead of learning a single codebook for all categories of images, we learn a set of basis codebooks. For a given input image, AdaCode learns a weight map that determines the contribution of each basis codebook to the final representation. Intuitively, this design allows AdaCode to learn a more flexible and expressive discrete generative prior than previous work, as demonstrated in Fig. 2. In contrast to VQGAN [7] and FeMaSR [3], which utilize a single partition for the latent space and assign each image feature an exclusive discrete representation, AdaCode learns various partitions to the latent space from different perspectives – each corresponding to the learning of one of the basis codebooks. The discrete generative prior for an arbitrary image is a weighted linear combination derived from these basis codebooks, resulting in a more flexible and expressive representation. As depicted in Fig. 1, AdaCode outperforms previous work in various image restoration tasks, effectively preserving scene structure and texture." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 326, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 326, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 308, + 326, + 545, + 384 + ], + "type": "text", + "content": "We evaluated AdaCode on both image reconstruction and image restoration tasks (i.e., super-resolution and image inpainting). Across multiple benchmark datasets, AdaCode achieved state-of-the-art performance, while maintaining a comparable codebook size and computational cost." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 402, + 391, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 402, + 391, + 415 + ], + "spans": [ + { + "bbox": [ + 308, + 402, + 391, + 415 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 424, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 424, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 308, + 424, + 545, + 579 + ], + "type": "text", + "content": "Visual Representation Dictionary Learning Learning representation dictionaries in visual understanding has demonstrated its great power in image restoration tasks such as super-resolution [51, 62], denoising [59], and image inpainting [8, 36]. Using DNNs, VQVAE [39] first introduces a generative autoencoder model that learns discrete latent representations, also known as \"codebook\". The following VQGAN [7] employs perceptual and adversarial loss to train the visual codebook, resulting in better image generation quality with a relatively small codebook size. The representation dictionary-based generative model has inspired various impressive image generation work [11, 61, 53, 3, 45], as well as our AdaCode." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 582, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 582, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 582, + 545, + 712 + ], + "type": "text", + "content": "The use of dictionaries is not limited to image restoration. Referred as lookup tables (LUTs), the dictionaries are also applied to optimize color transforms [55, 23, 49, 50]. In 3D-LUT [55], multiple LUTs are learned to serve as the bases of the LUT space. And a CNN is trained to predict weights to fuse the bases into an image-adaptive LUT. Inspired by 3D LUT, we leverage the discrete codebooks from VQGAN as the bases of the image latent space to build our image-adaptive codebook, AdaCode. Such design allows our method to fully and flexibly exploit the latent codes to represent diverse and complex natural images." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 733, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 733, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 296, + 733, + 315, + 742 + ], + "type": "text", + "content": "5374" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 69, + 541, + 252 + ], + "blocks": [ + { + "bbox": [ + 49, + 69, + 541, + 252 + ], + "lines": [ + { + "bbox": [ + 49, + 69, + 541, + 252 + ], + "spans": [ + { + "bbox": [ + 49, + 69, + 541, + 252 + ], + "type": "image", + "image_path": "4feafae5fd7df9622c925e0c00d46483863cb75b6531f85a6341358841d1b3f9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 261, + 547, + 299 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 547, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 547, + 299 + ], + "type": "text", + "content": "Figure 3: The framework of the proposed AdaCode method. The training of AdaCode incorporates three stages: Class-specific Codebook Pretraining, AdaCode Representation Learning, and Restoration via AdaCode. The lock icon indicates that the codebooks " + }, + { + "bbox": [ + 46, + 261, + 547, + 299 + ], + "type": "inline_equation", + "content": "Z_{1,\\dots,K}" + }, + { + "bbox": [ + 46, + 261, + 547, + 299 + ], + "type": "text", + "content": " are fixed in Stage II&III, and the decoder " + }, + { + "bbox": [ + 46, + 261, + 547, + 299 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 261, + 547, + 299 + ], + "type": "text", + "content": " is fixed in Stage III. See Section 3 for more details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 318, + 289, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 289, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 289, + 510 + ], + "type": "text", + "content": "DNN-based Image Restoration DNN has been widely used for image restoration tasks, i.e. single image super-resolution (SISR) and image inpainting. In the field of super-resolution (SR), recent studies focus on recovering low-resolution input images with unknown degradation types, which is more relevant to real-world scenarios. They restore the images either by learning the degradation representations [33, 21, 41, 42, 57, 9], or by training unified generative networks with LR-HR pairs [16, 46, 32]. Some studies introduce additional image priors, such as latent representations [27, 2, 30] and discrete codebooks [7, 61, 3], to address unrealistic textures or over-smoothed areas commonly observed in GAN-based methods. However, a single partition of the latent space is often insufficient to model the intricate patterns in natural images, resulting in specific textures being generated regardless of the image content." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 516, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 287, + 635 + ], + "type": "text", + "content": "In the case of image inpainting, researchers often leverage deep generative models to fill missing image regions with plausible content [31, 25, 44, 56, 5]. Some approaches incorporate additional discriminators [35], partial or gated convolutions [24, 54], semantic texture or context [28, 48, 34, 13, 38, 15], or transformers [19, 6, 26, 40] to enhance the quality of inpainted results. However, these methods often require separate experiments for different image patterns, i.e. natural scenes, faces, etc., due to the significant variations among them." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Both SR and inpainting methods face the challenge of effectively modeling complex visual patterns with a single model or codebook. In our proposed approach, AdaCode, we address this challenge by leveraging adaptive codebooks, enabling realistic and robust restoration results for general images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 317, + 389, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 317, + 389, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 317, + 389, + 331 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 338, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 531 + ], + "type": "text", + "content": "Building upon VQGAN [7], we introduce an additional degree of freedom to the codebook and construct an adaptive codebook (AdaCode) to model the intricate high-resolution natural image patterns. We summarize the AdaCode model in Fig.3. Our method's overall training consists of three sequential stages. In the first stage (Sec 3.1), we divide our HQ dataset into multiple semantic subsets and train a class-specific VQGAN [7] on each subset. In the second stage, using the fixed pretrained class-specific codebooks as bases, we leverage a transformer block to generate weight maps and train the AdaCode through the self-reconstruction task (Sec 3.2). In the last stage (Sec 3.3), we employ the AdaCode with fixed codebooks and fixed image decoder to address downstream restoration tasks, e.g. Super-Resolution and Image Inpainting. The details of each stage are discussed in the following sections." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 539, + 476, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 539, + 476, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 539, + 476, + 552 + ], + "type": "text", + "content": "3.1. Codebook Pretraining (Stage I)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": "Diversify Basis Codebooks To enhance the expressiveness of AdaCode, we aim to diversify the basis codebooks. Rather than applying various initializations as 3D-LUT [55], we achieve codebook divergence by training them on different HR subsets of our dataset. To accomplish this, we utilize an off-the-shelf SegFormer model [47] to perform semantic segmentation with 150 classes from the ADE20K dataset [60]. Each HR patch is labeled according to the semantic class with the largest area. We then group the 150 classes into 5 super-classes: Architectures, Indoor objects, Natural scenes, Street views, Portraits, and obtain the 5 semantic HR subsets accordingly. It is worth noting that the separation of subsets is not rigorous and each subset may" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "text", + "content": "5375" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 282, + 169 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 282, + 169 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 282, + 169 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 282, + 169 + ], + "type": "image", + "image_path": "384e670cd4f183f44f844cb354d1e5a1b5b30b76aeda97c748a057d059600330.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 178, + 289, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 178, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 289, + 251 + ], + "type": "text", + "content": "Figure 4: Visualization of the learned codes for different categories of visual appearance. We randomly sample 10 code entries from each codebook and visualize them by projecting a tiled " + }, + { + "bbox": [ + 46, + 178, + 289, + 251 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 46, + 178, + 289, + 251 + ], + "type": "text", + "content": " feature map onto a " + }, + { + "bbox": [ + 46, + 178, + 289, + 251 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 46, + 178, + 289, + 251 + ], + "type": "text", + "content": " texture patch using the corresponding decoder. As expected, the codes from different categories exhibit distinct features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 271, + 289, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 271, + 289, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 289, + 344 + ], + "type": "text", + "content": "contain semantic contexts from other subsets, as most images contain multiple semantics. More details regarding the clustering of the 150 classes can be found in the Appendix. This approach not only diversifies the codebooks but also provides various ways to partition the latent feature space. We randomly visualize some code samples in Fig. 4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": "Learning Basis Codebooks Given a HQ subset of class " + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": ", we train a quantized autoencoder to learn the class-specific basis codebook. As shown in Fig. 3, the input HR patch " + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": " is first passed through the encoder " + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": " to generate the embedding " + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "inline_equation", + "content": "\\hat{z} = E(y) \\in \\mathbb{R}^{h \\times w \\times n_z}" + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": ". Following VQVAE [39] and VQGAN [7], each entry " + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "inline_equation", + "content": "\\hat{z}_i \\in \\mathbb{R}^{n_z}" + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": " is replaced with its nearest code in the learnable codebook " + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "inline_equation", + "content": "Z_k \\in \\mathbb{R}^{N \\times n_z}" + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": " to construct the quantized embedding " + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "inline_equation", + "content": "z_{q_k}" + }, + { + "bbox": [ + 47, + 357, + 289, + 455 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 460, + 287, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 460, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 102, + 460, + 287, + 483 + ], + "type": "interline_equation", + "content": "z _ {q _ {k}} = \\underset {c \\in \\{0, \\dots , N - 1 \\}} {\\arg \\min } | | \\hat {z} - Z _ {k, c} | | \\tag {1}", + "image_path": "2f49a2a747c22fb219ba3d696876a8c5be997f0209c0a94f87e5b3a97d37018c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{N}" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": " is the number of codes in the corresponding codebook, " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "z_{q_k}" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": " denotes the quantized representation using " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "Z_{k}" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "Z_{k,c}" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": " represent the " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": "-th entry in codebook " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "Z_{k}" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": ". After the feature quantization, the decoder " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": " reconstructs the HR patch " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "inline_equation", + "content": "z_{q_k}" + }, + { + "bbox": [ + 46, + 490, + 287, + 552 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 132, + 558, + 287, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 558, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 132, + 558, + 287, + 572 + ], + "type": "interline_equation", + "content": "\\hat {y} = G \\left(z _ {q _ {k}}\\right) \\approx y \\tag {2}", + "image_path": "656df817659f661324b4ecdf0c1dd1cbf84f399a7a94f55707b3e8a4f08c1212.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "content": "The adversarial learning scheme is employed to train the encoder " + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "content": ", codebook " + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "content": ", and decoder " + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "content": " with the discriminator " + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "content": ". The detailed architectures of " + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 579, + 288, + 628 + ], + "type": "text", + "content": " are provided in the Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "text", + "content": "Training Objective To train the quantized autoencoder, we adopt 3 image-level losses: L1 loss " + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "text", + "content": ", perceptual loss " + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{per}" + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "text", + "content": " [17], and adversarial loss " + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{adv}" + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "text", + "content": " [10], which are calculated using " + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 641, + 287, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Since the quantization in Eqn. 1 is non-differentiable, we adopt the straight-through gradient estimator in [39, 7]," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "type": "text", + "content": "which directly copies the gradients from decoder " + }, + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "type": "text", + "content": " to encoder " + }, + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "type": "text", + "content": ", enabling back-propagation and allowing end-to-end training using the code-level loss function " + }, + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{VQ}" + }, + { + "bbox": [ + 304, + 72, + 546, + 109 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 310, + 114, + 546, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 114, + 546, + 129 + ], + "spans": [ + { + "bbox": [ + 310, + 114, + 546, + 129 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {V Q} (E, G, Z _ {k}) = | | s g [ \\hat {z} ] - z _ {q} | | _ {2} ^ {2} + \\beta \\cdot | | \\hat {z} - s g [ z _ {q} ] | | _ {2} ^ {2} \\tag {3}", + "image_path": "333ec35ba6c24271414b888c346365749ed568e6030f0a57a47b6c8344a7287d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 134, + 545, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 134, + 545, + 170 + ], + "spans": [ + { + "bbox": [ + 304, + 134, + 545, + 170 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 134, + 545, + 170 + ], + "type": "inline_equation", + "content": "sg[\\cdot]" + }, + { + "bbox": [ + 304, + 134, + 545, + 170 + ], + "type": "text", + "content": " denotes the stop-gradient operation and " + }, + { + "bbox": [ + 304, + 134, + 545, + 170 + ], + "type": "inline_equation", + "content": "\\beta = 0.25" + }, + { + "bbox": [ + 304, + 134, + 545, + 170 + ], + "type": "text", + "content": " is a hyper-parameter to control the update frequency of the codebook." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 171, + 546, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 171, + 546, + 220 + ], + "spans": [ + { + "bbox": [ + 304, + 171, + 546, + 220 + ], + "type": "text", + "content": "To further reinforce the semantics in the latent codebook and improve the texture restoration [43], we incorporate a VGG19-based regularization term " + }, + { + "bbox": [ + 304, + 171, + 546, + 220 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sem}" + }, + { + "bbox": [ + 304, + 171, + 546, + 220 + ], + "type": "text", + "content": " into the codebook training process, following the approach in [3].:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 357, + 225, + 545, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 225, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 357, + 225, + 545, + 239 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s e m} = \\left| \\left| C O N V (\\hat {z}) - \\Phi \\left(y _ {k} ^ {\\prime}\\right) \\right| \\right| _ {2} ^ {2} \\tag {4}", + "image_path": "6349dcbfe9845c54bb2c343fce0990b66d8f7e0872e4d9ca4fd59bd494454355.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "text", + "content": " denotes the feature extractor of VGG19 [37], and " + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "inline_equation", + "content": "CONV" + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "text", + "content": " denotes a single convolutional layer to match the dimension of " + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\Phi(y_k')" + }, + { + "bbox": [ + 304, + 246, + 545, + 281 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 282, + 545, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 306 + ], + "type": "text", + "content": "With the above image-level and code-level losses, we can summarize the training objective in Stage I as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 313, + 545, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 313, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 312, + 313, + 545, + 327 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s t a g e 1}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {V Q} + \\lambda \\cdot \\mathcal {L} _ {\\text {s e m}} \\tag {5}", + "image_path": "e2fe43b483c172ee6b148a6de65bb3af2868f3f678828a91f0bf518ef79132eb.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 333, + 455, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 455, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 455, + 344 + ], + "type": "text", + "content": "where the loss weight " + }, + { + "bbox": [ + 304, + 333, + 455, + 344 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 333, + 455, + 344 + ], + "type": "text", + "content": " is set to 0.1." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 351, + 538, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 538, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 538, + 364 + ], + "type": "text", + "content": "3.2. AdaCode Representation Learning (Stage II)" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": "Given the pretrained class-specific basis codebooks " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "Z_{k}, k \\in \\{1, \\dots, K\\}" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": ", the latent feature space can be partitioned into non-overlapping cells in " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": " different ways. Specifically, for a given input HR patch " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": " quantized representations can be generated. Each distinct quantized representation " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "z_{q_k}" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": " obtains its code token from its corresponding semantic codebook. To combine the discrete representation " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "z_{q_{1}, \\dots, K}" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": " into the AdaCode representation " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": ", we employ a weight predictor module, which generates a " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": "-channel weight map " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "w \\in \\mathbb{R}^{h \\times w \\times K}" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": ", as illustrated in Fig. 3 and Fig. 5. The weight predictor module consists of four residual swim transformer blocks (RSTBs) [20] and a convolution layer to match the channels of weight map and " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": " is computed following Eqn. 6. Finally, the adaptive feature " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": " is reconstructed to HR patch " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": " via the decoder " + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 369, + 545, + 549 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 389, + 555, + 545, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 555, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 389, + 555, + 545, + 580 + ], + "type": "interline_equation", + "content": "z = \\sum_ {i} w _ {i} \\times z _ {q _ {i}} \\tag {6}", + "image_path": "9d7f55b9e0ad76d92acf6612b1bd4cc9483e5e501ac69adb4fa4c458b891250a.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "text", + "content": "To efficiently train AdaCode and maintain a comparable number of parameters in the codebooks to VQGAN [7] and FeMaSR [3], which both set the codebook dimension to be " + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "inline_equation", + "content": "1024 \\times 512" + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "text", + "content": ", we set each of our class-specific codebooks to be " + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "inline_equation", + "content": "512 \\times 256" + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "text", + "content": ". These codebooks are fixed during the training of stage II while the rest of the model, i.e. the encoder " + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "text", + "content": ", the weight predictor, the decoder " + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "text", + "content": ", and the discriminator " + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 586, + 546, + 694 + ], + "type": "text", + "content": ", are trained using the objective in Eqn. 7. Each term in this equation is defined in Sec. 3.1." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 322, + 701, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 701, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 322, + 701, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s t a g e 2}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {V Q} (E, G) \\tag {7}", + "image_path": "699603573ef24c5d51c2353f1e6b7bac4abf3f8e8abb9c08f080bf1ff20cc689.jpg" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "5376" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 281, + 196 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 281, + 196 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 281, + 196 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 281, + 196 + ], + "type": "image", + "image_path": "4c778202d09786f4bd59eb347c9514e5ad8d7a2d9994243c9f77899c987e6434.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 208, + 287, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 287, + 291 + ], + "type": "text", + "content": "Figure 5: An example showing the learned weight maps. The input image contains multiple semantically-meaningful content (e.g. pyramid, person, animal, sky) which cannot be well represented with a single codebook. Instead, AdaCode uses multiple basis codebooks and weight maps for discrete representations. As shown, the weight maps correlate to the semantics to some extent." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 317, + 239, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 239, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 239, + 330 + ], + "type": "text", + "content": "3.3. Restoration via AdaCode (Stage III)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "text", + "content": "With the powerful decoder " + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "text", + "content": ", various image restoration tasks can be turned into a feature refinement problem through AdaCode scheme. From the perspective of latent space partition, each representation of the degraded input " + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "text", + "content": " is pulled towards its nearest HR code entry, allowing for the information loss in " + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "text", + "content": " to be relatively compensated. In comparison to the quantized representation " + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "inline_equation", + "content": "z_{q}" + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "text", + "content": " using only one general codebook, the combination of " + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "inline_equation", + "content": "z_{q_{1},\\ldots ,K}" + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "text", + "content": " with the weight map can be considered as adding an offset to " + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "inline_equation", + "content": "z_{q}" + }, + { + "bbox": [ + 46, + 338, + 287, + 506 + ], + "type": "text", + "content": ". The offset helps to alleviate the discontinuity among the discrete codes, which is demonstrated in our ablation study. To further showcase the effectiveness of AdaCode, we train our model on two ill-posed problems, i.e. Single Image SuperResolution and Image Inpainting." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": "In super-resolution and image inpainting tasks, the mapping between the input and the HR output has more than one solutions. Despite the benefits of the AdaCode scheme, restoring damaged content or missing details remains challenging given the uncertain degradations and the diversity of natural images. To better account for the degradation and improve the gradient flow, we adopt the encoder design in [3] which utilizes a feature extraction module and a residual shortcut module during stage III." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": "Thanks to the excellent reconstruction model in stage II, given a Degraded-HR image pair, we can obtain the groundtruth representation " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "z_{gt}" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " via the fixed model. Since the decoder " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " is fixed in this stage, the restoration problem can be formulated as minimizing the distance between HR feature " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "z_{gt}" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " and degraded feature " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": ". To achieve this, we use a code-level loss that includes the InfoNCE loss in [29] and the style loss in [17]. Following the design as SimCLR[4]," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "given a degraded image feature " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": ", we use the HR feature " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "z_{gt}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " as the positive sample, while other " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "z_{gt}" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " from different source images in the same batch are treated as the negative samples. The code-level loss is defined as follows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 331, + 129, + 545, + 159 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 129, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 331, + 129, + 545, + 159 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {c o d e}} = \\mathcal {L} _ {\\text {I n f o N C E}} \\left(z _ {g t}, z\\right) + \\mathcal {L} _ {\\text {s t y l e}} \\left(z _ {g t}, z\\right) \\tag {8} \\\\ + \\beta \\cdot | | \\hat {z} - s g [ z _ {g t} ] | | _ {2} ^ {2} \\\\ \\end{array}", + "image_path": "331379c4a889c604875addfdc4f2537b7ba52f572b015f669b35198d48c4d781.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 165, + 462, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 165, + 462, + 176 + ], + "spans": [ + { + "bbox": [ + 306, + 165, + 462, + 176 + ], + "type": "text", + "content": "And the overall loss is summarized as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 340, + 186, + 545, + 199 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 186, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 340, + 186, + 545, + 199 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s t a g e 3}} = \\mathcal {L} _ {1} + \\mathcal {L} _ {\\text {p e r}} + \\lambda \\cdot \\mathcal {L} _ {\\text {a d v}} + \\mathcal {L} _ {\\text {c o d e}} \\tag {9}", + "image_path": "482c308cb108e6119f1dc6c80a69bd69f9f91c9fd8e0ecd056401cfa32072e74.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 209, + 386, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 209, + 386, + 221 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 386, + 221 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 228, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 335 + ], + "type": "text", + "content": "Datasets Our training dataset includes images from DIV2K train set [1], Flickr2K [22], DIV8K train set [12], and 10,000 face images from FFHQ [18]. We generate the training patches by cropping images into non-overlapping patches at " + }, + { + "bbox": [ + 304, + 228, + 545, + 335 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 228, + 545, + 335 + ], + "type": "text", + "content": " resolution (face images in FFHQ are randomly resized with scale factors between [0.5, 1.0] before cropping). We adopt the same degradation model as BSRGAN [57] to generate LR patches. The final training dataset consists of 198,061 patches." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 336, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 545, + 444 + ], + "type": "text", + "content": "In the test stage, we evaluate the reconstruction task on OST dataset [43], which contains 300 images with rich textures. For super-resolution, we evaluate the performance on five classical benchmarks, i.e. Set5, Set14, BSD100, Urban100, and Manga109, with " + }, + { + "bbox": [ + 304, + 336, + 545, + 444 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 304, + 336, + 545, + 444 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 336, + 545, + 444 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 304, + 336, + 545, + 444 + ], + "type": "text", + "content": " scales. For image inpainting, we apply a publicly available script [52] to randomly draw irregular polyline masks and generate masked images. The inpainting performance is evaluated on the validation sets of DIV2K [1] and DIV8K [12]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 457, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 518 + ], + "type": "text", + "content": "Evaluation Metrics For reconstruction, we adopt PSNR and SSIM as the evaluation metrics. For super-resolution, we employ an additional well-known perceptual score, LPIPS [58]. For image inpainting task, we use PSNR, LPIPS and a widely-used non-reference metric, FID [14]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": "Implementation Details According to the size of each semantic dataset, we empirically set the codebook bases sizes to be " + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\{512, 256, 512, 256, 256\\} \\times 256" + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": " for Architectures, Indoor Objects, Natural Scenes, Street Views, and Portraits. For all stages, we represent the input image as a " + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": " code sequence. We train each stage for " + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "inline_equation", + "content": "350k" + }, + { + "bbox": [ + 304, + 532, + 545, + 651 + ], + "type": "text", + "content": " iterations with an Adam optimizer and a batch size of 32. The learning rates for the generator and discriminator are fixed as 1e-4 and 4e-4 separately. Our method is implemented with PyTorch and trained with 4 NVIDIA Tesla V100 GPUs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 659, + 457, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 457, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 457, + 671 + ], + "type": "text", + "content": "4.1. Expressiveness of AdaCode" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "The key design in our work is to leverage the class-specific basis codebooks to construct an adaptive codebook, which supports more expressiveness even with a smaller" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "5377" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 75, + 521, + 375 + ], + "blocks": [ + { + "bbox": [ + 67, + 75, + 521, + 375 + ], + "lines": [ + { + "bbox": [ + 67, + 75, + 521, + 375 + ], + "spans": [ + { + "bbox": [ + 67, + 75, + 521, + 375 + ], + "type": "image", + "image_path": "2b7385bf74cd3ce9a2efb549c721dfdb99d6a270f55e502d62bde0bce15bc942.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 382, + 547, + 420 + ], + "lines": [ + { + "bbox": [ + 46, + 382, + 547, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 547, + 420 + ], + "type": "text", + "content": "Figure 6: Qualitative comparisons on image reconstruction task. Various scenes and semantics, i.e. text, plants, buildings, streets, and faces, are covered in these examples. Benefited from the adaptive codebook, our AdaCode is able to reconstruct images with higher quality and fidelity. (Zoom in for best view)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 435, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 289, + 533 + ], + "type": "text", + "content": "codebook size. To verify our method's superiority, we evaluate the reconstruction performances using three codebook and model settings: (1) VQGAN [7] with its single general codebook. (2) VQGAN with a merged codebook concatenating all the basis codebooks, referred to as VQGAN-aux. (3) AdaCode with our adaptive codebook. The three approaches are trained with the same dataset (see Section. 4) to guarantee a fair comparison." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 53, + 574, + 282, + 644 + ], + "blocks": [ + { + "bbox": [ + 47, + 540, + 287, + 565 + ], + "lines": [ + { + "bbox": [ + 47, + 540, + 287, + 565 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 287, + 565 + ], + "type": "text", + "content": "Table 1: Quantitative comparison of reconstruction performance. PSNR/SSIM↑: the higher, the better." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 574, + 282, + 644 + ], + "lines": [ + { + "bbox": [ + 53, + 574, + 282, + 644 + ], + "spans": [ + { + "bbox": [ + 53, + 574, + 282, + 644 + ], + "type": "table", + "html": "
MethodOverall Codebook SizePerformance
PSNRSSIM
VQGAN[3]1024 × 51221.35570.5664
VQGAN-aux1792 × 25621.92190.6030
AdaCode (Ours)1792 × 25625.76290.7705
", + "image_path": "55889f84cdcaab8869c097a5f9732579294d67c7b3198dcb8eb882f0a24adfc9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "As shown in Table. 1, our AdaCode obtains overwhelming reconstruction results with a comparable or smaller codebook size. The gap between (1) and (2) certifies that training class-specific codebooks helps the codes to capture more image textures, while the great improvement between" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 435, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 547, + 520 + ], + "type": "text", + "content": "(2) and (3) justifies the expressiveness facilitated by our adaptive codebook design. Fig. 6 shows multiple scenarios, including plants, buildings, streets, portraits, and text which has distinct patterns but does not have a corresponding codebook in our experiments. AdaCode achieves exceedingly excellent results in all semantic cases, producing realistic and fidelitous reconstruction results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 530, + 525, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 530, + 525, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 530, + 525, + 544 + ], + "type": "text", + "content": "4.2. Benchmarking Image Restoration Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 549, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 670 + ], + "type": "text", + "content": "Super-Resolution We compare AdaCode with state-of-the-art models for Image Super-Resolution, including KX-Net[9], Real-ESRGAN [42], and FeMaSR[3]. Specifically, KX-Net iteratively learns the degradation kernels from the LR images; Real-ESRGAN learns super-resolution using pure synthetic data with high-order degradation model; FeMaSR utilizes a single perceptually rich codebook to restore the images. We use the original codes and weights from each method's official public repository to conduct comparisons, as shown in Table. 2 and Fig. 7." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Image Inpainting We compare AdaCode with state-of-the-art inpainting methods GPEN [52] and MAT [19]. To" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "text", + "content": "5378" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 542, + 246 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 542, + 246 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 542, + 246 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 542, + 246 + ], + "type": "image", + "image_path": "e3e76863bc465173fce08c5b7a5e0d5e8738dbd0f0cb0dd089c35c54f00f7f37.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 252, + 547, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 252, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 547, + 291 + ], + "type": "text", + "content": "Figure 7: Qualitative comparisons on super-resolution task with " + }, + { + "bbox": [ + 46, + 252, + 547, + 291 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 46, + 252, + 547, + 291 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 252, + 547, + 291 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 46, + 252, + 547, + 291 + ], + "type": "text", + "content": " upscale factor. AdaCode restores LR with realistic and faithful details, while the competitive work either fails to deblur the LR, i.e. KX-Net [9], or generates artifacts or over-smooth areas, i.e. Real-ESRGAN [42] and FeMaSR [3]. See Appendix for more results. (Zoom in for best view)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 300, + 546, + 324 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 546, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 546, + 324 + ], + "type": "text", + "content": "Table 2: Quantitative comparison with state-of-the-art SISR methods. PSNR/SSIM↑: the higher, the better; LPIPS↓: the lower, the better. The best and second best performance are marked in red and blue." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 334, + 567, + 460 + ], + "blocks": [ + { + "bbox": [ + 48, + 334, + 567, + 460 + ], + "lines": [ + { + "bbox": [ + 48, + 334, + 567, + 460 + ], + "spans": [ + { + "bbox": [ + 48, + 334, + 567, + 460 + ], + "type": "table", + "html": "
MethodScaleSet5Set14BSDS100Urban100Manga109
PSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPS
FeMaSRx227.5130.82500.105425.4040.75650.129224.9070.72600.144922.7130.75730.110221.5840.69380.2270
KX-Netx227.8370.88840.085925.9290.82910.130125.8180.80920.173422.6750.80160.097219.5610.50490.5312
Real-ESRGANx230.0320.89300.105127.0190.83790.138226.6700.79160.152623.5770.81150.097620.8150.68170.3056
Oursx229.2130.84440.084426.2490.77020.117926.0380.75290.137423.6630.78940.100922.0230.70290.2150
FeMaSRx424.0390.74520.150022.7240.63540.204521.9570.58190.251720.5090.64260.198318.1310.57570.3449
KX-Netx421.9220.70500.208021.1820.61260.304421.7080.57680.397218.6030.55760.270418.1810.53230.6909
Real-ESRGANx425.2630.76650.171024.1000.70040.233823.7760.62610.281921.3510.66250.214018.2220.59170.4091
Oursx425.8680.77310.150524.1580.66620.203123.1290.60410.248521.4460.65680.200718.1450.56640.3425
", + "image_path": "99c5df1469513a68bea6e35229789308b06d0e0703cae503d0a13e103faa5ea6.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 480, + 288, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 288, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 288, + 588 + ], + "type": "text", + "content": "conduct a fair comparison, we retrain MAT on our training dataset as discussed in Section. 4. Moreover, we train FeMaSR [3] for this task to demonstrate the effectiveness of our adaptive codebooks over the single codebook in FeMaSR. As shown in Table. 3, AdaCode achieves state-of-the-art performance on various metrics. Qualitative comparisons in Fig. 8 also illustrate that AdaCode consistently produce high-quality inpainting results across a wide range of scenes with a single model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 598, + 141, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 141, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 141, + 611 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "We investigate AdaCode's expressiveness given a various number of basis codebooks. We fix the five basis codebooks trained in Stage I and train Stage II with various combinations of basis codebooks. We adopt PSNR and SSIM to evaluate the expressiveness on the reconstruction task. Fig. 9 empirically shows that the adaptive codebook benefits from the bases in a large extent. Meanwhile, it also indicates that our basis codebooks are \"non-multicollinear\"" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 322, + 536, + 531, + 620 + ], + "blocks": [ + { + "bbox": [ + 304, + 479, + 547, + 526 + ], + "lines": [ + { + "bbox": [ + 304, + 479, + 547, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 547, + 526 + ], + "type": "text", + "content": "Table 3: Quantitative comparison with state-of-the-art inpainting methods. PSNR↑: the higher, the better; LPIPS/FID↓: the lower, the better. The best and second best performance are marked in red and blue." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 536, + 531, + 620 + ], + "lines": [ + { + "bbox": [ + 322, + 536, + 531, + 620 + ], + "spans": [ + { + "bbox": [ + 322, + 536, + 531, + 620 + ], + "type": "table", + "html": "
MethodDIV2KDIV8KAll
PSNRLPIPSPSNRLPIPSFID
GPEN29.1290.093331.1910.07033.0924
FeMaSR29.7900.058132.2330.04161.6741
MAT30.1240.067632.3350.04061.2385
Ours30.11510.051632.7010.03721.1657
", + "image_path": "3dd7e7667bfbd1d4fb8afc35d99e007d5be350f8d78a082bec3ccb9c751fb930.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 642, + 544, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 544, + 654 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 544, + 654 + ], + "type": "text", + "content": "even if the semantic sub-datasets have overlapping patches." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 668, + 459, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 668, + 459, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 668, + 459, + 681 + ], + "type": "text", + "content": "5. Conclusion and Limitation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": "In this work, we propose AdaCode, a novel approach for class-agnostic image reconstruction and restoration. In par" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 315, + 742 + ], + "type": "text", + "content": "5379" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 76, + 547, + 420 + ], + "blocks": [ + { + "bbox": [ + 47, + 76, + 547, + 420 + ], + "lines": [ + { + "bbox": [ + 47, + 76, + 547, + 420 + ], + "spans": [ + { + "bbox": [ + 47, + 76, + 547, + 420 + ], + "type": "image", + "image_path": "f13fd9c00a3dcd3b7f55e7243723ad335daa1d71154e2b5936e0381aaffdad86.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 427, + 546, + 452 + ], + "lines": [ + { + "bbox": [ + 46, + 427, + 546, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 546, + 452 + ], + "type": "text", + "content": "Figure 8: Qualitative comparisons on image inpainting task. The first two rows demonstrate the inpainting results of face images, while the last two rows show the recovered results of place images. See Appendix for more results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 470, + 281, + 628 + ], + "blocks": [ + { + "bbox": [ + 53, + 470, + 281, + 628 + ], + "lines": [ + { + "bbox": [ + 53, + 470, + 281, + 628 + ], + "spans": [ + { + "bbox": [ + 53, + 470, + 281, + 628 + ], + "type": "image", + "image_path": "620eec168f790eab59940137f30f9577125c71996dc0f2f6607def8da89dd76a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 636, + 287, + 673 + ], + "lines": [ + { + "bbox": [ + 46, + 636, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 287, + 673 + ], + "type": "text", + "content": "Figure 9: Ablation Study. PSNR and SSIM score of reconstructed results with varying number of basis codebooks. See supplementary for more result images." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 473, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 569 + ], + "type": "text", + "content": "ticular, we train a set of class-specific basis codebooks and learn a weight map to construct an image-adaptive codebook for better image representation. Unlike previous methods that use a general codebook to represent images, our image-adaptive codebook is more flexible and suited for natural images. Extensive comparisons on image reconstruction, super-resolution, and image inpainting tasks validate our method's superiority." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Our work is a first step towards class-agnostic generative prior for arbitrary images. It has several limitations we plan to explore in future work. First, it is yet unclear how many basis codebooks and how many code entries in each codebook we need. Stage I is trained separately from Stage II&III, which may be suboptimal. Second, we do not yet incorporate high-level explicit semantic information such as semantic segmentation into the framework, which may be also useful for general image restoration tasks. Finally, it would be interesting to extend AdaCode for high-dimensional visual appearance, such as videos and multispectral images." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "spans": [ + { + "bbox": [ + 295, + 732, + 315, + 742 + ], + "type": "text", + "content": "5380" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Eirikur Agustsson and Radu Timofte. 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Previous scene completion methods struggle to capture long-range spatial context, resulting in unsatisfactory completion results. To alleviate the problem, we propose a novel Dual-Scale Transformer Network (DST-Net) that efficiently utilizes both long-range and short-range spatial context information to improve the quality of 3D scene completion. To reduce the heavy computation cost of extracting long-range features via transformers, DST-Net adopts a self-supervised two-stage completion strategy. In the first stage, we split the input scene into blocks and perform completion on individual blocks. In the second stage, the blocks are merged together as a whole and then further refined to improve completeness. More importantly, we propose a contrastive attention training strategy to encourage the transformers to learn distinguishable features for better scene completion. Experiments on datasets of Matterport3D, ScanNet, and ICL-NUIM demonstrate that our method can generate better completion results, and our method outperforms the state-of-the-art methods quantitatively and qualitatively.", + "bbox": [ + 75, + 358, + 473, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 719, + 209, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Indoor 3D reconstruction is an essential part of many applications like AR/VR [19, 1], building information modeling (BIM) [24, 32], automatic robot indoor navigation [14] and so on [36, 38]. Due to the limited resolution of 3D sensors and the inevitable occlusion between objects in the scene, there always exist incomplete surfaces in the reconstruction results.", + "bbox": [ + 75, + 744, + 468, + 849 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, scene 3D completion based on deep learning", + "bbox": [ + 96, + 849, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ddf8a6abeb9e84a29baaf7399055f3bd4f34a5503c5af90e94452191edb2c2a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 335, + 694, + 436 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/12e45c1dc4dc7b5dda97df662edc41df57a63527f8fbb4ac7b12daaf021c1b3a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 335, + 888, + 436 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5c176576532550bcf56db6a0534bdfa4080f334ebb99f660be783308b4083718.jpg", + "image_caption": [ + "(a) Input", + "(c) SPSG", + "Figure 1: Indoor scene completion on one case in the Matterport3D dataset. Comparison with the state-of-the-art methods SG-NN [6] and SPSG [8]." + ], + "image_footnote": [], + "bbox": [ + 506, + 459, + 694, + 569 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7041c6452032e8bea373d5660a898e4f40c1086ce2fcbcee0f2611e14f615e7e.jpg", + "image_caption": [ + "(b) SG-NN", + "(d) Ours" + ], + "image_footnote": [], + "bbox": [ + 699, + 460, + 888, + 569 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "has made great progress. Dai et al. [6] proposed a self-supervised method called SG-NN to complete the indoor scene with incomplete real-world scan data, which can get a more complete result compared to the training data. Dai et al. [8] further proposed SPSG to complete the 3D surface and texture. Most of the current methods use convolutional neural networks (CNN) for completion and achieve impressive progress. Nonetheless, receptive fields in CNN remain local at a certain resolution, limiting its ability to capture long-range information. This is very important for the scene completion task with incomplete inputs.", + "bbox": [ + 496, + 671, + 892, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, Vision Transformer (ViT) [27, 18, 10] has made great stride in the computer vision field, owing to its ability to sense long-range information. For the task of single object 3D completion, some methods [30,", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Fei Luo and Chunxia Xiao are co-responding authors", + "bbox": [ + 94, + 875, + 400, + 886 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{\\dagger}$ Xiaoxiao Long was interning at Wuhan University", + "bbox": [ + 96, + 887, + 369, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18569", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "33, 34] achieved better point cloud completion by using transformer-based architecture to extract global information with a spatial attention mechanism. However, there is few attempt to apply transformer to the task of large-scale scene completion, since the large-scale scenes contain complex layouts and various objects.", + "bbox": [ + 75, + 90, + 467, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, to use long-range information to handle large missing areas and precise completion of geometric shape in the scene, we propose a Dual-Scale Transformer Network (DST-Net) and apply it in a two-stage manner. Specifically, in the first stage, we use DST-Net to complete the blocks split from an incomplete scene, then merge the complete geometric blocks to get the entire scene output. However, the generated results still have some small holes in local areas. To tackle it, in the second stage, we utilize scene-level information to refine the output scene of stage 1. In this stage, we fuse the ground truth and the first stage output as the supervision signal to focus on learning problematic areas and ensure the consistency of learning.", + "bbox": [ + 75, + 181, + 467, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "It is difficult to obtain satisfactory performance when applying transformer for scene completion, as the long-range and sparse incomplete information is more difficult to learn. To solve this problem, our proposed DST-Net involves specific transformer modules for different-level scene information. Furthermore, we propose a contrastive attention training strategy to make the DST-Net efficiently learn similar and distinguishable shape features. Our method includes a structure loss to improve the accuracy of geometric structure, and a CIoT (Cube Intersection over Target) loss to ensure complete output voxels. One comparison case between the state-of-the-art methods and ours is illustrated in Fig. 1.", + "bbox": [ + 75, + 378, + 467, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 96, + 560, + 401, + 573 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We propose a novel Dual-Scale Transformer Network (DST-Net) for indoor scene surface completion. We conduct completion operations from the block level to the scene level to achieve better completion performance.", + "2. We propose a contrastive attention training strategy to make the transformer work robustly in scene completion. In addition, we propose a structure loss to improve the accuracy of geometric shapes and a CIoT loss to make the scene more complete." + ], + "bbox": [ + 75, + 574, + 467, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 722, + 218, + 738 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Completing the 3D surface from the 2D or 3D sparse inputs is an ill-posed task. This task greatly relies on the prior knowledge extracted from other similar scenes. We briefly introduce related traditional methods and deep learning-based methods in this field. More extensive reviews can be found in two recent works [23, 16].", + "bbox": [ + 75, + 748, + 467, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Traditional Completion", + "text_level": 1, + "bbox": [ + 76, + 847, + 294, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to lacking powerful 3D scene encoding and inferring models, most of the early traditional methods used the", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "interpolating or optimization strategy. Davis et al. [9] proposed a diffusion process with the SDF function to fill the holes in the surface. Kawai et al. [15] proposed an energy minimization surface completion method, which could complete indoor models with holes. Previtali et al. [22] designed a flexible pipeline to perform outdoor and indoor reconstruction from occluded point clouds and proposed corresponding modules for outdoor and indoor scan completion. Silberman et al. [25] proposed a probabilistic model of contour completion random fields, which could complete the boundaries of occluded surfaces. Xiao et al. [31] integrated point cloud completion and surface connectivity relation inference to obtain complete 3D models and surface connections. The traditional methods depend on certain assumption and their generalization is poor when the prerequisite is not met.", + "bbox": [ + 496, + 90, + 890, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Deep Learning based Completion", + "text_level": 1, + "bbox": [ + 500, + 354, + 792, + 371 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Supervised based completion. With the increment of 3D data resources [2, 4] and the development of deep learning, more and more methods use deep learning neural network to learn various priors to complete the scene. Some methods [13, 17, 28] focus on depth completion to fulfill surface completion. Surface completion is always combined with semantic segmentation provides both geometry and object label information. Song et al. [26] built up a synthetic indoor dataset SUNCG with dense occupancy and semantic annotation, and proposed a fully convolutional end-to-end model to solve both tasks of semantic segmentation and scene completion. Dai et al. [7] further proposed a coarse-to-fine fully convolutional model called ScanComplete based on SUNCG to solve semantic segmentation and scene completion tasks for high-resolution indoor scenes. However, it is difficult to have a complete ground truth for 3D indoor scenes due to device and data capturing imperfections.", + "bbox": [ + 496, + 382, + 890, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-supervised based completion. Self-supervised completion learns the geometric features from incomplete 3D surface ground truth and then expands such learned completion principle to boost the incomplete 3D surface ground truth itself [34, 37, 20, 35]. Dai et al. [6] proposed a self-supervised fully convolutional approach SGNN that can be trained on incomplete, real-world scan data and produced a better geometric model than the training target. SPSG [8] used a similar self-supervised idea to infer a complete scene geometry with color and used 2D data to supervise the color of the output 3D scene for generating a complete color and more accurate scene. It is a promising technical route, as it does not need a large amount of expensive GT data. But it requires the model to have a more robust capacity to observe a wider scope and a stronger completion ability.", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18570", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c6b269876912dc22e80cdc2f7a867a045d2ff3cd1dbe2de2a455180141eb7634.jpg", + "image_caption": [ + "Figure 2: Overview of our completion method. Stage 1 uses DST-Net to complete blocks of the incomplete input, and merge them to get the coarse scene output. Stage 2 proceeds to refine the coarse scene. We use different colors to represent the differences between the two-level network structures in DST-Net." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 890, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 510, + 166, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 535, + 186, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The diagram of our proposed method is illustrated in Fig. 2. Given a training dataset with a series of incomplete indoor scans, our proposed method has two stages. Stage 1 trains DST-Net to learn completion rules on small blocks split from the incomplete scene. Due to memory limitation, in the test, the input and output of stage 1 are same-sized voxel blocks split from a scene, then we merge the output blocks to get the stage 2 input. Then stage 2 aims to address the inadequate inferring result caused by the limited scope of block-level completion by processing the scene-level information, while the training target is obtained by fusing the output and target of stage 1.", + "bbox": [ + 75, + 558, + 468, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the training progress, we propose a contrastive attention training strategy that uses the information between different blocks to encourage the transformers to learn distinguishable features for better scene completion. We propose the structure loss and CIoT loss to ensure completed scenes precise and complete.", + "bbox": [ + 75, + 742, + 468, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. DST-Net Structure", + "text_level": 1, + "bbox": [ + 76, + 845, + 256, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our DST-Net is an encoder-decoder structure, as shown in the Fig. 3(a), The DST-Net basically consists of four", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "modules: geometry encoder, global structure extractor, region geometry generator, and local detail generator. The geometry encoder and local detail generator are similar to [6], consisting of 3D Sparse Convolutions [11] (SP-Convs) to encode and decode local geometry features. We propose a global structure extractor to extract and complete global-level features, as well as proposing the region geometry generator to decode region-level geometry shapes with long-range information. Considering the proportion of valid data in the scene, the modules at the two ends of our network process sparse voxels (shown in blue color), and the middle module processes dense voxels (shown in green color). Next, we will introduce the global structure extractor and region geometry generator in detail.", + "bbox": [ + 496, + 512, + 890, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Global Structure Extractor", + "text_level": 1, + "bbox": [ + 500, + 737, + 743, + 751 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To extract similar high-dimensional features from similar structures, we introduce a global structure extractor. The global structure extractor has two branches, as shown in Fig. 3(b). Inspired by PVT [29], we design a 3D multilayer transformer pyramid structure as one branch to reshape structured voxels into non-sequential voxels and encode them, which mainly focuses on long-range global information. In order not to lose details, we also reserve CNNs as the other branch to encode local information.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18571", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/20e2bc26a633b75e21cede9a6c6b7ab0cde1dd5815293576c2009499a0e9537e.jpg", + "image_caption": [ + "(a) Four Modules in Dual-Scale Transformer Network" + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 890, + 231 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c06e4db6b50f3ae95c675b362d211f9485aa87eb8d5cdb0813ef2ecaa4fb50bf.jpg", + "image_caption": [ + "Figure 3: Network structure and details. (a) The diagram of our DST-Net structure and its four main modules. The input for stage 1 are blocks and the input for stage 2 is a scene, respectively. Arrows indicate the flow of data in the network. The difference in DST-Net between stage 1 and stage 2 lies in the global structure extractor and region geometry generator. (b) Global structure extractor contains two branches of transformer and CNN. There is no transformer branch (marked with a dot line rectangle) in stage 2. (c) The component of region geometry generator in stage 1 and stage 2. (d) The network structure of two major components in region geometry generator: MR-CA (left column), and MR-VT (right column)." + ], + "image_footnote": [], + "bbox": [ + 76, + 257, + 883, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then the two branches are decoded with CNNs. We use skip-connection to connect the information of the same resolution in both branches. Finally, the global features completed by these two branches are fused by a linear layer. At stage 2, we remove the transformer branch, as the scene is relatively complete, and the need for long-range information capture is reduced.", + "bbox": [ + 75, + 527, + 470, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Region Geometry Generator", + "text_level": 1, + "bbox": [ + 76, + 648, + 331, + 664 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose a region geometry generator to hierarchically generate accurate region shapes with long-range shape similarity. The key components of this module are the multi-resolution cross-attention (MR-CA) and the multi-resolution voxel transformer (MR-VT). The organization ways of region geometry generator in stage 1 and 2 are shown in Fig. 3(c).", + "bbox": [ + 75, + 672, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-resolution cross-attention. We propose the MR-CA module to connect shape features $Y \\in \\mathbb{R}^{N \\times C}$ in the geometry encoder to high-resolution features $X \\in \\mathbb{R}^{N \\times C}$ in the region geometry generator for shape completion, as shown in the left column of Fig. 3(d). $N$ is the number of sparse voxel features, and $C$ is the number of channels. In this module, $Q$ is obtained from $X$ through $1 \\times 1$ SP-Conv, $K$ and $V$ are obtained from $Y$ through $1 \\times 1$ SP-Conv. We", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "conduct dot-product between $Q$ and $K^T$ to get the attention map $A$ .", + "bbox": [ + 496, + 527, + 890, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$A$ stores the similarity of the shape information between $Y$ and $X$ , we use $A$ to select similar shape features from $V$ :", + "bbox": [ + 498, + 561, + 890, + 590 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {a t t n} = S P - C o n v (A \\times V) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 611, + 890, + 627 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We add the result $X_{\\text{attn}}$ selected from $Y$ and the input feature $X$ to get the completed feature $X_{\\text{out}}$ :", + "bbox": [ + 498, + 640, + 890, + 671 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {o u t} = X + X _ {a t t n} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 686, + 890, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-resolution voxel transformer. Unlike MR-CA, which uses the encoder's shape information, MR-VT is proposed to perform region shape completion with the long-range complete shape feature generated in the generator. We first connect the sparse voxel features of the same resolution in the encoder and the decoder, to obtain the feature $X_{C}\\in \\mathbb{R}^{N\\times C}$ . $Q$ is projected by $X_{C}$ . $K$ and $V$ are projected by $X_{C}$ after down-sampling. The latter attention operation and more details are shown in the right column of Fig. 3(d). By using MR-VT, each voxel with incomplete shape information can capture long-range information from all other generated voxels for completion.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18572", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a0f1fd0136b32666ed6d6c7bacea56cd0a93389bf35bb767054ef813abf3dbac.jpg", + "image_caption": [ + "Figure 4: The diagram of CAT working mechanism." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 478, + 255 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Contrastive attention training", + "text_level": 1, + "bbox": [ + 76, + 304, + 349, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrast learning enhances the performance of vision tasks by contrasting samples against each other, which learns common attributes from similar samples and discriminative attributes from distinguished ones. Inspired by the idea of contrastive learning, we propose a contrastive attention training (CAT) strategy to empower the transformers for scene completion by efficiently learning common and distinguishable shape features from the training samples.", + "bbox": [ + 75, + 328, + 468, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our method randomly takes a batch containing $b$ blocks as input in training, and the input $X_{C}$ for MR-VT is a voxel set $\\{L_j,j = 0,\\dots,m_i - 1\\}$ processed from each block $i$ , where $m_{i}$ means the number of the voxels in block $i$ and each voxel $L_{j}$ contains a shape feature within a cubic space. Unlike the general self-attention approach, where the attention operation is done between $\\{L_j,j = 0,\\dots,m_i - 1\\}$ , we further randomly select the voxels sets from other blocks, and use all voxels in them to form a random voxel set $\\mathbb{L}:\\{L_j,j = 0,\\dots,\\sum_{i = 0}^{n - 1}m_i - 1\\}$ , where $n$ means the number of all the selected blocks. The physical meaning of $\\mathbb{L}$ is shown in Fig.4. In brief, we use M to denote $\\sum_{i = 0}^{n - 1}m_i$ . Similar to MR-VT, the $Q_{j}$ , $K_{j}$ and $V_{j}$ are projected from $L_{j}$ . In this way, we perform a cross-attention operation between n blocks in a training batch. For a certain voxel $L_{j}$ , we obtain the similarity set $\\{A_{j,k},k = 0,\\dots,M - 1\\}$ between $L_{j}$ and all M voxels in $\\mathbb{L}$ by computing the dot-product of $Q_{j}$ and $K_{k}$ and then normalized via softmax function:", + "bbox": [ + 75, + 449, + 472, + 734 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA _ {j, k} = \\frac {\\exp \\left(Q _ {j} \\cdot K _ {k}\\right)}{\\sum_ {k = 0} ^ {M - 1} \\exp \\left(Q _ {j} \\cdot K _ {k}\\right)}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 746, + 468, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the similarity set $\\{A_{j,k}, k = 0, \\dots, M - 1\\}$ , we can use it to select features $V_k$ derived from $L_k$ in $\\mathbb{L}$ to complete the voxel $L_j$ :", + "bbox": [ + 76, + 804, + 470, + 851 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nX _ {a t t n} = S P - C o n v \\left(\\sum_ {k = 0} ^ {M - 1} A _ {j, k} \\cdot V _ {k}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 861, + 468, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The underlying motivation is that unlike self-attention applied to individual blocks with a single layout, our contrastive attention operation requires the transformer to extract useful information from a set of random other blocks. Due to the randomness when selecting blocks in a training batch, the blocks with different layouts may share similar properties or have different attributes, which may be useful or detrimental. By explicitly adding extra information, transformers are required to identify whether the extra information is useful or not by attention scores. The learning strategy enables transformers to learn geometric features with a higher degree of discrimination, thereby improving the completion ability. We evaluate different values for $n$ with 2, 4, and 8. The experimental results indicate that the completion performance reaches its best for $n$ equal to 8.", + "bbox": [ + 496, + 90, + 893, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Loss Function and Data Generation", + "text_level": 1, + "bbox": [ + 498, + 325, + 810, + 342 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Geometry loss. We train the network with three geometry loss items: depth loss $L_{D}$ , 3D normal loss $L_{N}$ , and structure loss $L_{S}$ . Given a voxel $v$ , depth loss $L_{D}$ is used to calculate the difference between the predicted depth $D_{v}^{P}$ and the target depth $D_{v}^{T}$ in $v$ . The 3D normal loss $L_{N}$ constrains the predicted normal $N_{v}^{P}$ and the target normal $N_{v}^{T}$ in $v$ . $V$ is the set of voxels to be calculated:", + "bbox": [ + 496, + 349, + 893, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {D} = \\frac {1}{V} \\sum_ {v \\in V} \\left\\| D _ {v} ^ {P} - D _ {v} ^ {T} \\right\\| _ {1} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 462, + 890, + 500 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {N} = \\frac {1}{V} \\sum_ {v \\in V} \\left| \\left| N _ {v} ^ {P} - N _ {v} ^ {T} \\right| \\right| _ {1} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 510, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Normal loss is used to constrain the geometry structures by calculating local depth variations. However, for more complex geometry structures, like various concave and convex shapes, it is difficult to complete them well only with normal loss. Inspired by normal loss, we introduce the structure loss $L_{S}$ to further constrain the geometry structures by calculating local normal variations.", + "bbox": [ + 496, + 551, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/06195e7da7e7898902a61651de58b7c73df26fc1b2ec11c81865871365c37c80.jpg", + "image_caption": [ + "predicted normals" + ], + "image_footnote": [], + "bbox": [ + 506, + 659, + 689, + 747 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/11ad3f650cf38d6309f9b324b971cb65f75da68a958e910559ff1b49706013df.jpg", + "image_caption": [ + "GT normals", + "Figure 5: Visual comparison of two different local structures." + ], + "image_footnote": [], + "bbox": [ + 743, + 657, + 885, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 5, $N_{i,j,k}^{P}$ denotes the normal of a predicted voxel, $N_{i+1,j,k}^{P}, N_{i,j+1,k}^{P}$ , and $N_{i,j,k+1}^{P}$ denote the normals of its three adjacent voxels, where $i,j,k$ represent voxel coordinates in three directions respectively. The GT normals are represented in a similar fashion. In a brief,", + "bbox": [ + 496, + 821, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18573", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we use $N_{v}^{P}, N_{vx}^{P}, N_{vy}^{P}$ and $N_{vz}^{P}$ to denote $N_{i,j,k}^{P}, N_{i+1,j,k}^{P}, N_{i,j+1,k}^{P}$ and $N_{i,j,k+1}^{P}$ , as well as the GT normals. The normal loss of a single predicted voxel is small when calculated with GT, while the local structures of the predicted case and GT are totally different due to the accumulation of normal variations. Therefore, we use the dot-product similarity between $N_{v}^{P}$ and $N_{vx}^{P}, N_{vy}^{P}$ , and $N_{vz}^{P}$ to get $S_{vx}^{P}, S_{vy}^{P}$ , and $S_{vz}^{P}$ as structure descriptors, as shown in Equation (7), to describe the local variation of normals. The structure descriptors of GT are calculated in the same way. The loss $L_{S}$ between predicted and target structure descriptors enable the whole predicted geometry structure to represent GT more accurately.", + "bbox": [ + 76, + 88, + 472, + 292 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS _ {v x} ^ {P} = N _ {v x} ^ {P} \\cdot N _ {v} ^ {P}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 309, + 331, + 328 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS _ {v y} ^ {P} = N _ {v y} ^ {P} \\cdot N _ {v} ^ {P} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 330, + 468, + 349 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS _ {v z} ^ {P} = N _ {v z} ^ {P} \\cdot N _ {v} ^ {P}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 352, + 331, + 369 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {S} = \\frac {1}{V} \\sum_ {v \\in V} \\left\\{\\frac {1}{3} \\left(\\left| \\left| S _ {v x} ^ {P} - S _ {v x} ^ {T} \\right| \\right| _ {1} + \\right. \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 387, + 468, + 424 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n| | S _ {v y} ^ {P} - S _ {v y} ^ {T} | | _ {1} + | | S _ {v z} ^ {P} - S _ {v z} ^ {T} | | _ {1}) \\}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 426, + 385, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIoT loss. Considering incomplete real-world data, we propose CIoT (Cube Intersection over Target) loss to make output voxel distribution fit the target. Due to the voxel sparsity, the same IoT may represent a completely different distribution. To address it, we divide the entire output into $N$ small cubes of the same size. In a cube, $C_i^P$ and $C_i^T$ represent the number of predicted voxels and the number of target voxels, respectively. We only calculate the loss in the cube where $C_i^T > 0$ . CIoT loss is defined as:", + "bbox": [ + 76, + 452, + 472, + 589 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {C I o T} = 1 - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {C _ {i} ^ {P} \\cap C _ {i} ^ {T}}{C _ {i} ^ {T}} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 594, + 468, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data Generation. Both input and target in training are the representation of sparse TSDF voxel with depth information, obtained from RGB-D frames by the method of voxel fusion [3]. Following the self-supervised learning approach of SG-NN [6], the training target (GT) in stage 1 is generated using all RGB-D frames, while a certain proportion is used in getting input. The training target in stage 2 is obtained by fusing the output and target of stage 1. To focus on learning problem regions and minimize error accumulation, we select the TSDF value of target 1 voxel as the value for target 2 voxel when the coordinates of output and target of stage 1 coincide.", + "bbox": [ + 75, + 636, + 472, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments and Results", + "text_level": 1, + "bbox": [ + 76, + 829, + 312, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate our proposed method, we use the Mather-port3D [2] dataset as the training data and conduct the comparison experiments on both real-world data and synthetic", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3f7489496f46f6009a86f19347aed72d9fdfd7680678852530e381e601ee07ee.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet1.480.510.54
SG-NN0.650.690.62
SPSG0.350.740.53
Ours0.230.780.61
", + "bbox": [ + 553, + 88, + 836, + 164 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Quantitative comparison results on Matterport3D.", + "bbox": [ + 501, + 171, + 888, + 186 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "data. The training dataset includes 1788 rooms. We train our method on a single NVIDIA GeForce RTX 2080. The learning rate is 0.001, and the batch size is 8. The resolution of all voxels is $2\\mathrm{cm}$ . The training blocks are all $128 \\times 64 \\times 64$ size cutting from the scene, and parameter $n$ in contrastive attention training strategy is 8. The four terms in the loss function have equal weights. Our stage 1 model training takes about 72 hours, and the stage 2 model training takes about 24 hours. Three state-of-the-art methods of ConvOccNet [21], SG-NN [6] and SPSG (only with geometry) [8] are used to compare with ours on the metrics of Chamfer Distance (CD) in metric space, Recall, and Precision. For real-world unobserved space, we ignore it for the CD evaluation.", + "bbox": [ + 496, + 205, + 890, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Completion on Matterport3D", + "text_level": 1, + "bbox": [ + 498, + 431, + 769, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "First, we compare four methods on 394 other rooms from the Matterport3D dataset. We provide the same incomplete TSDF input, except for ConvOccNet, which requires the corresponding mesh to be pre-computed as input. Some scene completion results are shown in Fig. 6(a). In visual effect, our method completes more parts in the scenes than the other three methods, which is consistent with the recall metric in Tab. 1. The highest score on CD proves that our method's shape accuracy is the best. As the GT is incomplete and the more completion areas from our method have no corresponding GT, our precision is less than the SG-NN under this special condition.", + "bbox": [ + 496, + 458, + 890, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Completion on Synthetic Data", + "text_level": 1, + "bbox": [ + 498, + 654, + 767, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The synthetic dataset ICL-NUIM [12] has 3D surface ground truth so that it can provide a more comprehensive evaluation. As the scan frames are indoors, we only select the mesh of the surface inside the room to evaluate. Qualitative and quantitative evaluations are shown in Fig. 6(b) and Tab. 2. Owing to the full GT, the results fairly reflect our method's superiority over the other three methods.", + "bbox": [ + 496, + 679, + 890, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Completion on ScanNet", + "text_level": 1, + "bbox": [ + 498, + 799, + 725, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate the generalization of our proposed method, we also conduct the comparison experiments on a more challenging dataset ScanNet [5]. The Fig. 6(c) are the visualization results, and Tab. 3 shows the quantitative results.", + "bbox": [ + 496, + 824, + 890, + 886 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18574", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3ab6dece3038d35b9d733c13a5df176c649afbabcc872422e7e5ee64638a5294.jpg", + "image_caption": [ + "(a)Matterport3D" + ], + "image_footnote": [], + "bbox": [ + 81, + 61, + 897, + 315 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c0a3a2a9a22e9524fefe1988a67e64a173222e9a54af9d0e49cc25dd6e5f5059.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 335, + 890, + 513 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0b11f4ac0aac835720eeb254639aace7bffaca06a850fcd07ad4714b4ab299bb.jpg", + "image_caption": [ + "(b) ICL-NUIM", + "(c) ScanNet", + "Figure 6: Qualitative comparisons with state-of-the-art methods on Matterport3D, ICL-NUIM and ScanNet." + ], + "image_footnote": [], + "bbox": [ + 81, + 532, + 893, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 827, + 228, + 843 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we demonstrate how the functional components in our method affect the ultimate performance.", + "bbox": [ + 76, + 869, + 467, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Stage 1 versus Stage 2. Stage 1 in our full model has finished most of the completion. However, stage 1 may generate some inaccurate areas due to block-level scope. Stage 2 can further solve these problems by training with", + "bbox": [ + 500, + 827, + 890, + 888 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18575", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f964bcc67549d161a6cb8cf984e6c2bf4dbfa6dfa34f6f9a7e46e811e3ee65a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 89, + 230, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d785cf7089c8ed5846702db0d0c1fb079bbc77a5c5ed59b03b05c6bc83ea62bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 240, + 90, + 398, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1ab99e984c68ee57367212534779efcad372c9f74a56e7632bc4d51d46f1ea28.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 398, + 90, + 557, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8da4f8b5c12188b33687ed69b29706d845cb60ef13988dfe9e8a5608853c090a.jpg", + "image_caption": [ + "Figure 7: Qualitative comparisons with state-of-the-art methods on Matterport3D with $30\\%$ frames input." + ], + "image_footnote": [], + "bbox": [ + 558, + 90, + 720, + 204 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/26f465a9dd391f036dd1a6c4cceb1cf1e167555d784e747e26fec00867fec8c7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 723, + 90, + 883, + 204 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/664b89e1f42c2266581fab2101805424040692bd47f14b3ccb1a00f681b56340.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet0.610.170.28
SG-NN0.310.310.42
SPSG0.250.350.39
Ours0.180.390.45
", + "bbox": [ + 130, + 226, + 413, + 303 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bd549aa9079e4852820c927c84f0ccdfd8639f705f50c97d3604e99b4ae54b0e.jpg", + "table_caption": [ + "Table 2: Quantitative comparison results on ICL-NUIM." + ], + "table_footnote": [], + "table_body": "
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet0.650.790.43
SG-NN0.360.850.50
SPSG0.300.860.45
Ours0.260.880.48
", + "bbox": [ + 119, + 334, + 428, + 420 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the fused target 2 and using the whole scan as input. The qualitative and quantitative evaluation results of stage 1 and the full model are shown in the Fig. 8 and Tab. 4. The results show that stage 2 accumulates a little distance error, but completes and corrects the results of stage 1. Tab. 4 further shows the quantitative results of training the full model with GT and using only the stage 2 model that is trained with stage 1 data to process input. The results indicate that the fused target 2 works better than GT, and the two stages are necessary.", + "bbox": [ + 75, + 459, + 468, + 612 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2c21f9cbf08e5757496e0a39855b8338164e98d197ff9e4263548ee3fa5e266f.jpg", + "table_caption": [ + "Table 3: Quantitative comparison results on ScanNet." + ], + "table_footnote": [], + "table_body": "
MethodCD(×10-1)↓Recall↑Precision↑
Stage10.220.770.60
Full model0.230.780.61
Full model (train with only GT)0.460.720.60
Only Stage20.490.720.57
", + "bbox": [ + 78, + 623, + 464, + 700 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f9df177459a84612ccfeb59ff8deb8a8f5de9992fdf0f152662127f09dfd1eea.jpg", + "image_caption": [ + "Figure 8: Completion improvement in the full model made by stage 2 over stage 1." + ], + "image_footnote": [], + "bbox": [ + 76, + 762, + 475, + 869 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8b6ee3a3891753ceacdbed576500abe893aad746c439ca5270108f1231d2aea4.jpg", + "table_caption": [ + "Table 4: The improvement of the full model over stage 1, the fused target 2 over GT. And the necessity of stage 1." + ], + "table_footnote": [], + "table_body": "
MethodCD(×10-1)↓Recall↑Precision↑
SG-NN (40%)0.670.680.61
SPSG (40%)0.360.730.53
Ours (40%)0.230.770.60
SG-NN (30%)0.730.670.61
SPSG (30%)0.430.720.52
Ours (30%)0.240.770.60
SG-NN (20%)1.060.600.58
SPSG (20%)0.730.650.49
Ours (20%)0.470.720.56
", + "bbox": [ + 547, + 226, + 841, + 375 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5: Quantitative comparison results on Matterport3D with $30\\%$ frames input.", + "bbox": [ + 500, + 376, + 890, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "More incomplete inputs. To illustrate the long-range advantage of our method, we use the model trained on the input consisting of $50\\%$ proportion RGB-D frames to test on the $40\\%$ , $30\\%$ , and $20\\%$ proportion input. The qualitative and quantitative evaluation results are shown in Fig. 7 and Tab. 5. The results show that as the input information gradually decreases, our method can also output a relatively complete result.", + "bbox": [ + 496, + 429, + 892, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The impact of contrastive attention training. We validate the contribution of the contrastive attention training strategy (CAT) for training at stage 1. Its qualitative and quantitative evaluation results are shown in Fig. 9 and Tab. 6. We can find that CAT enhances the ability to restore regional shapes.", + "bbox": [ + 496, + 551, + 893, + 642 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b6c31a69c6b9413f74b73d1dccfbff05f4f79d1b19c8d354bc0b7ed9f7096238.jpg", + "image_caption": [ + "Figure 9: The visual effect of CAT on shape completion." + ], + "image_footnote": [], + "bbox": [ + 501, + 656, + 898, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effectiveness of modules. We replace the global structure extractor (GSE) and region geometry generator (RGG) with CNNs to evaluate their effectiveness. The Tab. 6 shows the quantitative evaluation, and Fig. 10 dis", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18576", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/59a1ecbdd2c0d9d2176d6778ba9ae6082b96019106f6def8b4c0dbf0c844fefc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCD(×10-1)↓Recall↑Precision↑
Stage10.220.770.60
Stage1(w/o GSE)0.320.740.57
Stage1(w/o RGG)0.260.750.58
Stage1(w/o CAT)0.240.750.59
", + "bbox": [ + 117, + 79, + 426, + 156 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/45add5d0de6d7a1e9a6360ec432e655061697e038e7fa59f5fc9399dbf7becb7.jpg", + "table_caption": [ + "Table 6: Quantitative evaluation of our proposed modules." + ], + "table_footnote": [], + "table_body": "
MethodCD(×10-1)↓Recall↑Precision↑
w/o LCloT0.250.750.60
w/o LS0.260.750.56
w/o LN0.260.740.56
w/o LD0.290.750.54
full loss0.220.770.60
", + "bbox": [ + 133, + 178, + 411, + 266 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 7: Ablation results of loss items in stage 1.", + "bbox": [ + 111, + 267, + 434, + 282 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "plays how GSE and RGG improve the completion effect in terms of global structure and region shape, respectively.", + "bbox": [ + 76, + 292, + 468, + 323 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/7eba6033b255039599bef617b222a6b0a2e570503ce14b46d3004c251db88a6b.jpg", + "image_caption": [ + "stage 1 input" + ], + "image_footnote": [], + "bbox": [ + 81, + 338, + 179, + 397 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/3bda8ee91e8db1573fdc59a44bea7df21ff4105acdf270290edb341f7963113d.jpg", + "image_caption": [ + "stage 1 w/o GSE" + ], + "image_footnote": [], + "bbox": [ + 183, + 338, + 277, + 397 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/85acc8ff401cc59dc862aad0e33167a6e366bf1305748047c59da48a5a90a86a.jpg", + "image_caption": [ + "stage 1 w/o RGG" + ], + "image_footnote": [], + "bbox": [ + 281, + 338, + 377, + 397 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0bb9fda0a80ae3fe34948567f302710bdbbb404dd482d6521fd28d6fd81a1bcb.jpg", + "image_caption": [ + "stage 1 output" + ], + "image_footnote": [], + "bbox": [ + 379, + 338, + 473, + 397 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Figure 10: Qualitative comparisons of how the completion results are affected by RGG and GSE.", + "bbox": [ + 76, + 412, + 468, + 441 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The impact of each loss item. We validate the effect of $L_{CIoT}$ , $L_S$ , $L_N$ loss on our method, and validate the case where only $L_D$ loss is applied. Tab. 7 shows the quantitative evaluation of the loss items. Fig. 11 shows the qualitative evaluation of the loss items. We can see that with $L_{CIoT}$ , the completeness of local scene completion has been improved, while $L_S$ and $L_N$ effectively constrain the accuracy of the shapes and planes, respectively. From the comparison with the results of only using $L_D$ loss, we can find that various losses acting on the connection between voxels improve the completion accuracy and completeness.", + "bbox": [ + 76, + 444, + 468, + 609 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 625, + 194, + 638 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we have proposed a dual-scale transformer method with a two-stage completion strategy to generate fairly complete scenes from real-world incomplete RGB-D scans. Our proposed contrastive attention training strategy encourages the transformers to learn distinguishable features. We introduce two new losses to constrain geometric accuracy and completeness. However, due to the limitation of memory, currently, we only use geometric information and solve the geometric completion. In the future, we would consider scene completion with other priors such as color and semantic information.", + "bbox": [ + 75, + 648, + 468, + 815 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Limitation", + "text_level": 1, + "bbox": [ + 76, + 830, + 191, + 844 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "First, our method only completes the geometric surface, without including the texture. In some conditions, the texture is also necessary. In the near future, we will try to solve", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0330afd91feebf011375a58a76247e0ab389eedb0e12cb06cefc6103da36e5bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 90, + 897, + 143 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/980a0f613aaa995efc9b86aaef7fba4dfcb4024c77ba00643c9d7b8214ac7781.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 143, + 895, + 199 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/98faf47a5783b48d51c7b001ee4f679303801684fc4c21d96ce2a1029f149070.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 200, + 895, + 253 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/37627aeec235952d02fe1abbdbb9dcc132aaa69bd2d4620c9c7f754de2038ad1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 255, + 895, + 309 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/7e8fc73101de8ca6ed1f07a3df818edf1620f47e91c098daa2eeeb85d0b07b41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 310, + 895, + 363 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/6f40528b67c94b7b0bea4b083f3f0cfc27e8088e9ca65f0d0ef9098e9cf85d76.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 364, + 895, + 419 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0227ba317c600b173a72194580587af6a2711c48c42f075b0beb2ee5dff9837a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 420, + 895, + 473 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/d2c0b603cdfe7b9665394c4f5ebde22afbb92415e5657653a56d883683f3e0f6.jpg", + "image_caption": [ + "Figure 11: Effect of loss items by switching on/off them at stage 1." + ], + "image_footnote": [], + "bbox": [ + 504, + 474, + 895, + 527 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "it. Second, surface completion mainly provides reasonable inference for the missing parts, rather than replacing the accurate reconstruction. When the geometric information of the input scene is not enough to infer the entire scene, our geometry completion result may not be accurate. Although our method does not need the GT of the complete scene, it still needs a large amount of indoor data to ensure its generalization.", + "bbox": [ + 496, + 574, + 890, + 694 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 707, + 658, + 724 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Chunxia Xiao is partially supported by NSFC (No.61972298), Bingtuan Science and Technology Program (No.2019BC008), and CAAI-Huawei MindSpore Open Fund.", + "bbox": [ + 500, + 732, + 890, + 792 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 501, + 805, + 596, + 821 + ], + "page_idx": 8 + }, + { + "type": "ref_text", + "text": "[1] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural rgb-d surface reconstruction. 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IEEE Transactions on Visualization and Computer Graphics, 2022. 1" + ], + "bbox": [ + 501, + 92, + 890, + 373 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18579", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/4473583d-9b9f-42e0-9960-ac81cde7532b_model.json b/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/4473583d-9b9f-42e0-9960-ac81cde7532b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..48af50bc02efa90b1d0341799f94fe17d2d62f87 --- /dev/null +++ b/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/4473583d-9b9f-42e0-9960-ac81cde7532b_model.json @@ -0,0 +1,2466 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.141, + 0.131, + 0.833, + 0.178 + ], + "angle": 0, + "content": "Learning Long-range Information with Dual-Scale Transformers for Indoor Scene Completion" + }, + { + "type": "text", + "bbox": [ + 0.152, + 0.215, + 0.816, + 0.235 + ], + "angle": 0, + "content": "Ziqi Wang\\(^{1}\\), Fei Luo \\(*^{1}\\), Xiaoxiao Long \\(\\dagger^{1}\\), Wenxiao Zhang\\(^{2}\\), and Chunxia Xiao \\(*^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.263, + 0.246, + 0.706, + 0.284 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Computer Science, Wuhan University \\(^{2}\\)ISTD, Singapore University of Technology and Design" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.328, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.474, + 0.692 + ], + "angle": 0, + "content": "Due to the limited resolution of 3D sensors and the inevitable mutual occlusion between objects, 3D scans of real scenes are commonly incomplete. Previous scene completion methods struggle to capture long-range spatial context, resulting in unsatisfactory completion results. To alleviate the problem, we propose a novel Dual-Scale Transformer Network (DST-Net) that efficiently utilizes both long-range and short-range spatial context information to improve the quality of 3D scene completion. To reduce the heavy computation cost of extracting long-range features via transformers, DST-Net adopts a self-supervised two-stage completion strategy. In the first stage, we split the input scene into blocks and perform completion on individual blocks. In the second stage, the blocks are merged together as a whole and then further refined to improve completeness. More importantly, we propose a contrastive attention training strategy to encourage the transformers to learn distinguishable features for better scene completion. Experiments on datasets of Matterport3D, ScanNet, and ICL-NUIM demonstrate that our method can generate better completion results, and our method outperforms the state-of-the-art methods quantitatively and qualitatively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.72, + 0.21, + 0.736 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.745, + 0.47, + 0.85 + ], + "angle": 0, + "content": "Indoor 3D reconstruction is an essential part of many applications like AR/VR [19, 1], building information modeling (BIM) [24, 32], automatic robot indoor navigation [14] and so on [36, 38]. Due to the limited resolution of 3D sensors and the inevitable occlusion between objects in the scene, there always exist incomplete surfaces in the reconstruction results." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.851, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Recently, scene 3D completion based on deep learning" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.336, + 0.695, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.448, + 0.625, + 0.46 + ], + "angle": 0, + "content": "(a) Input" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.337, + 0.889, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.763, + 0.447, + 0.825, + 0.459 + ], + "angle": 0, + "content": "(b) SG-NN" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.46, + 0.696, + 0.57 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.574, + 0.577, + 0.627, + 0.589 + ], + "angle": 0, + "content": "(c) SPSG" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.462, + 0.889, + 0.57 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.77, + 0.577, + 0.817, + 0.589 + ], + "angle": 0, + "content": "(d) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.596, + 0.895, + 0.643 + ], + "angle": 0, + "content": "Figure 1: Indoor scene completion on one case in the Matterport3D dataset. Comparison with the state-of-the-art methods SG-NN [6] and SPSG [8]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.893, + 0.838 + ], + "angle": 0, + "content": "has made great progress. Dai et al. [6] proposed a self-supervised method called SG-NN to complete the indoor scene with incomplete real-world scan data, which can get a more complete result compared to the training data. Dai et al. [8] further proposed SPSG to complete the 3D surface and texture. Most of the current methods use convolutional neural networks (CNN) for completion and achieve impressive progress. Nonetheless, receptive fields in CNN remain local at a certain resolution, limiting its ability to capture long-range information. This is very important for the scene completion task with incomplete inputs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recently, Vision Transformer (ViT) [27, 18, 10] has made great stride in the computer vision field, owing to its ability to sense long-range information. For the task of single object 3D completion, some methods [30," + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.875, + 0.401, + 0.887 + ], + "angle": 0, + "content": "*Fei Luo and Chunxia Xiao are co-responding authors" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.37, + 0.901 + ], + "angle": 0, + "content": "\\(^{\\dagger}\\)Xiaoxiao Long was interning at Wuhan University" + }, + { + "type": "list", + "bbox": [ + 0.095, + 0.875, + 0.401, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18569" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.182 + ], + "angle": 0, + "content": "33, 34] achieved better point cloud completion by using transformer-based architecture to extract global information with a spatial attention mechanism. However, there is few attempt to apply transformer to the task of large-scale scene completion, since the large-scale scenes contain complex layouts and various objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.468, + 0.378 + ], + "angle": 0, + "content": "In this work, to use long-range information to handle large missing areas and precise completion of geometric shape in the scene, we propose a Dual-Scale Transformer Network (DST-Net) and apply it in a two-stage manner. Specifically, in the first stage, we use DST-Net to complete the blocks split from an incomplete scene, then merge the complete geometric blocks to get the entire scene output. However, the generated results still have some small holes in local areas. To tackle it, in the second stage, we utilize scene-level information to refine the output scene of stage 1. In this stage, we fuse the ground truth and the first stage output as the supervision signal to focus on learning problematic areas and ensure the consistency of learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.468, + 0.56 + ], + "angle": 0, + "content": "It is difficult to obtain satisfactory performance when applying transformer for scene completion, as the long-range and sparse incomplete information is more difficult to learn. To solve this problem, our proposed DST-Net involves specific transformer modules for different-level scene information. Furthermore, we propose a contrastive attention training strategy to make the DST-Net efficiently learn similar and distinguishable shape features. Our method includes a structure loss to improve the accuracy of geometric structure, and a CIoT (Cube Intersection over Target) loss to ensure complete output voxels. One comparison case between the state-of-the-art methods and ours is illustrated in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.561, + 0.402, + 0.574 + ], + "angle": 0, + "content": "In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.575, + 0.468, + 0.635 + ], + "angle": 0, + "content": "1. We propose a novel Dual-Scale Transformer Network (DST-Net) for indoor scene surface completion. We conduct completion operations from the block level to the scene level to achieve better completion performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.468, + 0.71 + ], + "angle": 0, + "content": "2. We propose a contrastive attention training strategy to make the transformer work robustly in scene completion. In addition, we propose a structure loss to improve the accuracy of geometric shapes and a CIoT loss to make the scene more complete." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.575, + 0.468, + 0.71 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.723, + 0.219, + 0.739 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.468, + 0.839 + ], + "angle": 0, + "content": "Completing the 3D surface from the 2D or 3D sparse inputs is an ill-posed task. This task greatly relies on the prior knowledge extracted from other similar scenes. We briefly introduce related traditional methods and deep learning-based methods in this field. More extensive reviews can be found in two recent works [23, 16]." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.295, + 0.864 + ], + "angle": 0, + "content": "2.1. Traditional Completion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Due to lacking powerful 3D scene encoding and inferring models, most of the early traditional methods used the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.332 + ], + "angle": 0, + "content": "interpolating or optimization strategy. Davis et al. [9] proposed a diffusion process with the SDF function to fill the holes in the surface. Kawai et al. [15] proposed an energy minimization surface completion method, which could complete indoor models with holes. Previtali et al. [22] designed a flexible pipeline to perform outdoor and indoor reconstruction from occluded point clouds and proposed corresponding modules for outdoor and indoor scan completion. Silberman et al. [25] proposed a probabilistic model of contour completion random fields, which could complete the boundaries of occluded surfaces. Xiao et al. [31] integrated point cloud completion and surface connectivity relation inference to obtain complete 3D models and surface connections. The traditional methods depend on certain assumption and their generalization is poor when the prerequisite is not met." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.356, + 0.794, + 0.372 + ], + "angle": 0, + "content": "2.2. Deep Learning based Completion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.655 + ], + "angle": 0, + "content": "Supervised based completion. With the increment of 3D data resources [2, 4] and the development of deep learning, more and more methods use deep learning neural network to learn various priors to complete the scene. Some methods [13, 17, 28] focus on depth completion to fulfill surface completion. Surface completion is always combined with semantic segmentation provides both geometry and object label information. Song et al. [26] built up a synthetic indoor dataset SUNCG with dense occupancy and semantic annotation, and proposed a fully convolutional end-to-end model to solve both tasks of semantic segmentation and scene completion. Dai et al. [7] further proposed a coarse-to-fine fully convolutional model called ScanComplete based on SUNCG to solve semantic segmentation and scene completion tasks for high-resolution indoor scenes. However, it is difficult to have a complete ground truth for 3D indoor scenes due to device and data capturing imperfections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Self-supervised based completion. Self-supervised completion learns the geometric features from incomplete 3D surface ground truth and then expands such learned completion principle to boost the incomplete 3D surface ground truth itself [34, 37, 20, 35]. Dai et al. [6] proposed a self-supervised fully convolutional approach SGNN that can be trained on incomplete, real-world scan data and produced a better geometric model than the training target. SPSG [8] used a similar self-supervised idea to infer a complete scene geometry with color and used 2D data to supervise the color of the output 3D scene for generating a complete color and more accurate scene. It is a promising technical route, as it does not need a large amount of expensive GT data. But it requires the model to have a more robust capacity to observe a wider scope and a stronger completion ability." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18570" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.439, + 0.893, + 0.486 + ], + "angle": 0, + "content": "Figure 2: Overview of our completion method. Stage 1 uses DST-Net to complete blocks of the incomplete input, and merge them to get the coarse scene output. Stage 2 proceeds to refine the coarse scene. We use different colors to represent the differences between the two-level network structures in DST-Net." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.511, + 0.168, + 0.525 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.536, + 0.187, + 0.55 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.47, + 0.741 + ], + "angle": 0, + "content": "The diagram of our proposed method is illustrated in Fig. 2. Given a training dataset with a series of incomplete indoor scans, our proposed method has two stages. Stage 1 trains DST-Net to learn completion rules on small blocks split from the incomplete scene. Due to memory limitation, in the test, the input and output of stage 1 are same-sized voxel blocks split from a scene, then we merge the output blocks to get the stage 2 input. Then stage 2 aims to address the inadequate inferring result caused by the limited scope of block-level completion by processing the scene-level information, while the training target is obtained by fusing the output and target of stage 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.743, + 0.47, + 0.834 + ], + "angle": 0, + "content": "In the training progress, we propose a contrastive attention training strategy that uses the information between different blocks to encourage the transformers to learn distinguishable features for better scene completion. We propose the structure loss and CIoT loss to ensure completed scenes precise and complete." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.846, + 0.258, + 0.86 + ], + "angle": 0, + "content": "3.2. DST-Net Structure" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Our DST-Net is an encoder-decoder structure, as shown in the Fig. 3(a), The DST-Net basically consists of four" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.892, + 0.724 + ], + "angle": 0, + "content": "modules: geometry encoder, global structure extractor, region geometry generator, and local detail generator. The geometry encoder and local detail generator are similar to [6], consisting of 3D Sparse Convolutions [11] (SP-Convs) to encode and decode local geometry features. We propose a global structure extractor to extract and complete global-level features, as well as proposing the region geometry generator to decode region-level geometry shapes with long-range information. Considering the proportion of valid data in the scene, the modules at the two ends of our network process sparse voxels (shown in blue color), and the middle module processes dense voxels (shown in green color). Next, we will introduce the global structure extractor and region geometry generator in detail." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.738, + 0.744, + 0.752 + ], + "angle": 0, + "content": "3.2.1 Global Structure Extractor" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To extract similar high-dimensional features from similar structures, we introduce a global structure extractor. The global structure extractor has two branches, as shown in Fig. 3(b). Inspired by PVT [29], we design a 3D multilayer transformer pyramid structure as one branch to reshape structured voxels into non-sequential voxels and encode them, which mainly focuses on long-range global information. In order not to lose details, we also reserve CNNs as the other branch to encode local information." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18571" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.092, + 0.891, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.344, + 0.235, + 0.631, + 0.248 + ], + "angle": 0, + "content": "(a) Four Modules in Dual-Scale Transformer Network" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.258, + 0.885, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.412, + 0.893, + 0.504 + ], + "angle": 0, + "content": "Figure 3: Network structure and details. (a) The diagram of our DST-Net structure and its four main modules. The input for stage 1 are blocks and the input for stage 2 is a scene, respectively. Arrows indicate the flow of data in the network. The difference in DST-Net between stage 1 and stage 2 lies in the global structure extractor and region geometry generator. (b) Global structure extractor contains two branches of transformer and CNN. There is no transformer branch (marked with a dot line rectangle) in stage 2. (c) The component of region geometry generator in stage 1 and stage 2. (d) The network structure of two major components in region geometry generator: MR-CA (left column), and MR-VT (right column)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.471, + 0.635 + ], + "angle": 0, + "content": "Then the two branches are decoded with CNNs. We use skip-connection to connect the information of the same resolution in both branches. Finally, the global features completed by these two branches are fused by a linear layer. At stage 2, we remove the transformer branch, as the scene is relatively complete, and the need for long-range information capture is reduced." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.65, + 0.332, + 0.665 + ], + "angle": 0, + "content": "3.2.2 Region Geometry Generator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.78 + ], + "angle": 0, + "content": "We propose a region geometry generator to hierarchically generate accurate region shapes with long-range shape similarity. The key components of this module are the multi-resolution cross-attention (MR-CA) and the multi-resolution voxel transformer (MR-VT). The organization ways of region geometry generator in stage 1 and 2 are shown in Fig. 3(c)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Multi-resolution cross-attention. We propose the MR-CA module to connect shape features \\( Y \\in \\mathbb{R}^{N \\times C} \\) in the geometry encoder to high-resolution features \\( X \\in \\mathbb{R}^{N \\times C} \\) in the region geometry generator for shape completion, as shown in the left column of Fig. 3(d). \\( N \\) is the number of sparse voxel features, and \\( C \\) is the number of channels. In this module, \\( Q \\) is obtained from \\( X \\) through \\( 1 \\times 1 \\) SP-Conv, \\( K \\) and \\( V \\) are obtained from \\( Y \\) through \\( 1 \\times 1 \\) SP-Conv. We" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.559 + ], + "angle": 0, + "content": "conduct dot-product between \\(Q\\) and \\(K^T\\) to get the attention map \\(A\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.562, + 0.892, + 0.592 + ], + "angle": 0, + "content": "\\(A\\) stores the similarity of the shape information between \\(Y\\) and \\(X\\), we use \\(A\\) to select similar shape features from \\(V\\):" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.612, + 0.891, + 0.628 + ], + "angle": 0, + "content": "\\[\nX _ {a t t n} = S P - C o n v (A \\times V) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.641, + 0.892, + 0.672 + ], + "angle": 0, + "content": "We add the result \\( X_{\\text{attn}} \\) selected from \\( Y \\) and the input feature \\( X \\) to get the completed feature \\( X_{\\text{out}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.688, + 0.891, + 0.704 + ], + "angle": 0, + "content": "\\[\nX _ {o u t} = X + X _ {a t t n} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Multi-resolution voxel transformer. Unlike MR-CA, which uses the encoder's shape information, MR-VT is proposed to perform region shape completion with the long-range complete shape feature generated in the generator. We first connect the sparse voxel features of the same resolution in the encoder and the decoder, to obtain the feature \\(X_{C}\\in \\mathbb{R}^{N\\times C}\\). \\(Q\\) is projected by \\(X_{C}\\). \\(K\\) and \\(V\\) are projected by \\(X_{C}\\) after down-sampling. The latter attention operation and more details are shown in the right column of Fig. 3(d). By using MR-VT, each voxel with incomplete shape information can capture long-range information from all other generated voxels for completion." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18572" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.48, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.264, + 0.445, + 0.28 + ], + "angle": 0, + "content": "Figure 4: The diagram of CAT working mechanism." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.305, + 0.351, + 0.323 + ], + "angle": 0, + "content": "3.3. Contrastive attention training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.47, + 0.449 + ], + "angle": 0, + "content": "Contrast learning enhances the performance of vision tasks by contrasting samples against each other, which learns common attributes from similar samples and discriminative attributes from distinguished ones. Inspired by the idea of contrastive learning, we propose a contrastive attention training (CAT) strategy to empower the transformers for scene completion by efficiently learning common and distinguishable shape features from the training samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.473, + 0.736 + ], + "angle": 0, + "content": "Our method randomly takes a batch containing \\(b\\) blocks as input in training, and the input \\(X_{C}\\) for MR-VT is a voxel set \\(\\{L_j,j = 0,\\dots,m_i - 1\\}\\) processed from each block \\(i\\), where \\(m_{i}\\) means the number of the voxels in block \\(i\\) and each voxel \\(L_{j}\\) contains a shape feature within a cubic space. Unlike the general self-attention approach, where the attention operation is done between \\(\\{L_j,j = 0,\\dots,m_i - 1\\}\\), we further randomly select the voxels sets from other blocks, and use all voxels in them to form a random voxel set \\(\\mathbb{L}:\\{L_j,j = 0,\\dots,\\sum_{i = 0}^{n - 1}m_i - 1\\}\\), where \\(n\\) means the number of all the selected blocks. The physical meaning of \\(\\mathbb{L}\\) is shown in Fig.4. In brief, we use M to denote \\(\\sum_{i = 0}^{n - 1}m_i\\). Similar to MR-VT, the \\(Q_{j}\\), \\(K_{j}\\) and \\(V_{j}\\) are projected from \\(L_{j}\\). In this way, we perform a cross-attention operation between n blocks in a training batch. For a certain voxel \\(L_{j}\\), we obtain the similarity set \\(\\{A_{j,k},k = 0,\\dots,M - 1\\}\\) between \\(L_{j}\\) and all M voxels in \\(\\mathbb{L}\\) by computing the dot-product of \\(Q_{j}\\) and \\(K_{k}\\) and then normalized via softmax function:" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.747, + 0.47, + 0.799 + ], + "angle": 0, + "content": "\\[\nA _ {j, k} = \\frac {\\exp \\left(Q _ {j} \\cdot K _ {k}\\right)}{\\sum_ {k = 0} ^ {M - 1} \\exp \\left(Q _ {j} \\cdot K _ {k}\\right)}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.805, + 0.471, + 0.852 + ], + "angle": 0, + "content": "After obtaining the similarity set \\(\\{A_{j,k}, k = 0, \\dots, M - 1\\}\\), we can use it to select features \\(V_k\\) derived from \\(L_k\\) in \\(\\mathbb{L}\\) to complete the voxel \\(L_j\\):" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.862, + 0.47, + 0.905 + ], + "angle": 0, + "content": "\\[\nX _ {a t t n} = S P - C o n v \\left(\\sum_ {k = 0} ^ {M - 1} A _ {j, k} \\cdot V _ {k}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.32 + ], + "angle": 0, + "content": "The underlying motivation is that unlike self-attention applied to individual blocks with a single layout, our contrastive attention operation requires the transformer to extract useful information from a set of random other blocks. Due to the randomness when selecting blocks in a training batch, the blocks with different layouts may share similar properties or have different attributes, which may be useful or detrimental. By explicitly adding extra information, transformers are required to identify whether the extra information is useful or not by attention scores. The learning strategy enables transformers to learn geometric features with a higher degree of discrimination, thereby improving the completion ability. We evaluate different values for \\( n \\) with 2, 4, and 8. The experimental results indicate that the completion performance reaches its best for \\( n \\) equal to 8." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.327, + 0.812, + 0.343 + ], + "angle": 0, + "content": "3.4. Loss Function and Data Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.894, + 0.456 + ], + "angle": 0, + "content": "Geometry loss. We train the network with three geometry loss items: depth loss \\( L_{D} \\), 3D normal loss \\( L_{N} \\), and structure loss \\( L_{S} \\). Given a voxel \\( v \\), depth loss \\( L_{D} \\) is used to calculate the difference between the predicted depth \\( D_{v}^{P} \\) and the target depth \\( D_{v}^{T} \\) in \\( v \\). The 3D normal loss \\( L_{N} \\) constrains the predicted normal \\( N_{v}^{P} \\) and the target normal \\( N_{v}^{T} \\) in \\( v \\). \\( V \\) is the set of voxels to be calculated:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.463, + 0.892, + 0.5 + ], + "angle": 0, + "content": "\\[\nL _ {D} = \\frac {1}{V} \\sum_ {v \\in V} \\left\\| D _ {v} ^ {P} - D _ {v} ^ {T} \\right\\| _ {1} \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.511, + 0.892, + 0.547 + ], + "angle": 0, + "content": "\\[\nL _ {N} = \\frac {1}{V} \\sum_ {v \\in V} \\left| \\left| N _ {v} ^ {P} - N _ {v} ^ {T} \\right| \\right| _ {1} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Normal loss is used to constrain the geometry structures by calculating local depth variations. However, for more complex geometry structures, like various concave and convex shapes, it is difficult to complete them well only with normal loss. Inspired by normal loss, we introduce the structure loss \\( L_{S} \\) to further constrain the geometry structures by calculating local normal variations." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.66, + 0.691, + 0.748 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.547, + 0.751, + 0.658, + 0.764 + ], + "angle": 0, + "content": "predicted normals" + }, + { + "type": "image", + "bbox": [ + 0.745, + 0.659, + 0.887, + 0.75 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.758, + 0.751, + 0.833, + 0.763 + ], + "angle": 0, + "content": "GT normals" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.777, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Figure 5: Visual comparison of two different local structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.823, + 0.894, + 0.901 + ], + "angle": 0, + "content": "As shown in Fig. 5, \\( N_{i,j,k}^{P} \\) denotes the normal of a predicted voxel, \\( N_{i+1,j,k}^{P}, N_{i,j+1,k}^{P} \\), and \\( N_{i,j,k+1}^{P} \\) denote the normals of its three adjacent voxels, where \\( i,j,k \\) represent voxel coordinates in three directions respectively. The GT normals are represented in a similar fashion. In a brief," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18573" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.089, + 0.473, + 0.293 + ], + "angle": 0, + "content": "we use \\( N_{v}^{P}, N_{vx}^{P}, N_{vy}^{P} \\) and \\( N_{vz}^{P} \\) to denote \\( N_{i,j,k}^{P}, N_{i+1,j,k}^{P}, N_{i,j+1,k}^{P} \\) and \\( N_{i,j,k+1}^{P} \\), as well as the GT normals. The normal loss of a single predicted voxel is small when calculated with GT, while the local structures of the predicted case and GT are totally different due to the accumulation of normal variations. Therefore, we use the dot-product similarity between \\( N_{v}^{P} \\) and \\( N_{vx}^{P}, N_{vy}^{P} \\), and \\( N_{vz}^{P} \\) to get \\( S_{vx}^{P}, S_{vy}^{P} \\), and \\( S_{vz}^{P} \\) as structure descriptors, as shown in Equation (7), to describe the local variation of normals. The structure descriptors of GT are calculated in the same way. The loss \\( L_{S} \\) between predicted and target structure descriptors enable the whole predicted geometry structure to represent GT more accurately." + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.31, + 0.332, + 0.329 + ], + "angle": 0, + "content": "\\[\nS _ {v x} ^ {P} = N _ {v x} ^ {P} \\cdot N _ {v} ^ {P}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.331, + 0.469, + 0.351 + ], + "angle": 0, + "content": "\\[\nS _ {v y} ^ {P} = N _ {v y} ^ {P} \\cdot N _ {v} ^ {P} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.353, + 0.332, + 0.371 + ], + "angle": 0, + "content": "\\[\nS _ {v z} ^ {P} = N _ {v z} ^ {P} \\cdot N _ {v} ^ {P}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.388, + 0.469, + 0.425 + ], + "angle": 0, + "content": "\\[\nL _ {S} = \\frac {1}{V} \\sum_ {v \\in V} \\left\\{\\frac {1}{3} \\left(\\left| \\left| S _ {v x} ^ {P} - S _ {v x} ^ {T} \\right| \\right| _ {1} + \\right. \\right. \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.427, + 0.387, + 0.448 + ], + "angle": 0, + "content": "\\[\n| | S _ {v y} ^ {P} - S _ {v y} ^ {T} | | _ {1} + | | S _ {v z} ^ {P} - S _ {v z} ^ {T} | | _ {1}) \\}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.453, + 0.473, + 0.59 + ], + "angle": 0, + "content": "CIoT loss. Considering incomplete real-world data, we propose CIoT (Cube Intersection over Target) loss to make output voxel distribution fit the target. Due to the voxel sparsity, the same IoT may represent a completely different distribution. To address it, we divide the entire output into \\(N\\) small cubes of the same size. In a cube, \\(C_i^P\\) and \\(C_i^T\\) represent the number of predicted voxels and the number of target voxels, respectively. We only calculate the loss in the cube where \\(C_i^T > 0\\). CIoT loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.595, + 0.47, + 0.632 + ], + "angle": 0, + "content": "\\[\nL _ {C I o T} = 1 - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {C _ {i} ^ {P} \\cap C _ {i} ^ {T}}{C _ {i} ^ {T}} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.473, + 0.82 + ], + "angle": 0, + "content": "Data Generation. Both input and target in training are the representation of sparse TSDF voxel with depth information, obtained from RGB-D frames by the method of voxel fusion [3]. Following the self-supervised learning approach of SG-NN [6], the training target (GT) in stage 1 is generated using all RGB-D frames, while a certain proportion is used in getting input. The training target in stage 2 is obtained by fusing the output and target of stage 1. To focus on learning problem regions and minimize error accumulation, we select the TSDF value of target 1 voxel as the value for target 2 voxel when the coordinates of output and target of stage 1 coincide." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.313, + 0.848 + ], + "angle": 0, + "content": "4. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "To validate our proposed method, we use the Mather-port3D [2] dataset as the training data and conduct the comparison experiments on both real-world data and synthetic" + }, + { + "type": "table", + "bbox": [ + 0.554, + 0.089, + 0.838, + 0.165 + ], + "angle": 0, + "content": "
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet1.480.510.54
SG-NN0.650.690.62
SPSG0.350.740.53
Ours0.230.780.61
" + }, + { + "type": "table_caption", + "bbox": [ + 0.502, + 0.172, + 0.89, + 0.188 + ], + "angle": 0, + "content": "Table 1: Quantitative comparison results on Matterport3D." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.207, + 0.892, + 0.419 + ], + "angle": 0, + "content": "data. The training dataset includes 1788 rooms. We train our method on a single NVIDIA GeForce RTX 2080. The learning rate is 0.001, and the batch size is 8. The resolution of all voxels is \\(2\\mathrm{cm}\\). The training blocks are all \\(128 \\times 64 \\times 64\\) size cutting from the scene, and parameter \\(n\\) in contrastive attention training strategy is 8. The four terms in the loss function have equal weights. Our stage 1 model training takes about 72 hours, and the stage 2 model training takes about 24 hours. Three state-of-the-art methods of ConvOccNet [21], SG-NN [6] and SPSG (only with geometry) [8] are used to compare with ours on the metrics of Chamfer Distance (CD) in metric space, Recall, and Precision. For real-world unobserved space, we ignore it for the CD evaluation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.433, + 0.771, + 0.451 + ], + "angle": 0, + "content": "4.1. Completion on Matterport3D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.641 + ], + "angle": 0, + "content": "First, we compare four methods on 394 other rooms from the Matterport3D dataset. We provide the same incomplete TSDF input, except for ConvOccNet, which requires the corresponding mesh to be pre-computed as input. Some scene completion results are shown in Fig. 6(a). In visual effect, our method completes more parts in the scenes than the other three methods, which is consistent with the recall metric in Tab. 1. The highest score on CD proves that our method's shape accuracy is the best. As the GT is incomplete and the more completion areas from our method have no corresponding GT, our precision is less than the SG-NN under this special condition." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.655, + 0.768, + 0.672 + ], + "angle": 0, + "content": "4.2. Completion on Synthetic Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.892, + 0.788 + ], + "angle": 0, + "content": "The synthetic dataset ICL-NUIM [12] has 3D surface ground truth so that it can provide a more comprehensive evaluation. As the scan frames are indoors, we only select the mesh of the surface inside the room to evaluate. Qualitative and quantitative evaluations are shown in Fig. 6(b) and Tab. 2. Owing to the full GT, the results fairly reflect our method's superiority over the other three methods." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.8, + 0.726, + 0.817 + ], + "angle": 0, + "content": "4.3. Completion on ScanNet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.887 + ], + "angle": 0, + "content": "To validate the generalization of our proposed method, we also conduct the comparison experiments on a more challenging dataset ScanNet [5]. The Fig. 6(c) are the visualization results, and Tab. 3 shows the quantitative results." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18574" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.063, + 0.898, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.439, + 0.319, + 0.536, + 0.332 + ], + "angle": 0, + "content": "(a)Matterport3D" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.336, + 0.891, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.446, + 0.52, + 0.528, + 0.532 + ], + "angle": 0, + "content": "(b) ICL-NUIM" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.533, + 0.895, + 0.757 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.455, + 0.761, + 0.52, + 0.774 + ], + "angle": 0, + "content": "(c) ScanNet" + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.786, + 0.839, + 0.802 + ], + "angle": 0, + "content": "Figure 6: Qualitative comparisons with state-of-the-art methods on Matterport3D, ICL-NUIM and ScanNet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.828, + 0.23, + 0.844 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.468, + 0.903 + ], + "angle": 0, + "content": "In this section, we demonstrate how the functional components in our method affect the ultimate performance." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.828, + 0.892, + 0.889 + ], + "angle": 0, + "content": "Stage 1 versus Stage 2. Stage 1 in our full model has finished most of the completion. However, stage 1 may generate some inaccurate areas due to block-level scope. Stage 2 can further solve these problems by training with" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18575" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.232, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.241, + 0.091, + 0.4, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.4, + 0.092, + 0.558, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.56, + 0.092, + 0.721, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.092, + 0.885, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.207, + 0.832, + 0.223 + ], + "angle": 0, + "content": "Figure 7: Qualitative comparisons with state-of-the-art methods on Matterport3D with \\(30\\%\\) frames input." + }, + { + "type": "table", + "bbox": [ + 0.131, + 0.227, + 0.415, + 0.304 + ], + "angle": 0, + "content": "
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet0.610.170.28
SG-NN0.310.310.42
SPSG0.250.350.39
Ours0.180.390.45
" + }, + { + "type": "table_caption", + "bbox": [ + 0.087, + 0.311, + 0.46, + 0.327 + ], + "angle": 0, + "content": "Table 2: Quantitative comparison results on ICL-NUIM." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.335, + 0.429, + 0.421 + ], + "angle": 0, + "content": "
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet0.650.790.43
SG-NN0.360.850.50
SPSG0.300.860.45
Ours0.260.880.48
" + }, + { + "type": "table_caption", + "bbox": [ + 0.097, + 0.432, + 0.45, + 0.448 + ], + "angle": 0, + "content": "Table 3: Quantitative comparison results on ScanNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.613 + ], + "angle": 0, + "content": "the fused target 2 and using the whole scan as input. The qualitative and quantitative evaluation results of stage 1 and the full model are shown in the Fig. 8 and Tab. 4. The results show that stage 2 accumulates a little distance error, but completes and corrects the results of stage 1. Tab. 4 further shows the quantitative results of training the full model with GT and using only the stage 2 model that is trained with stage 1 data to process input. The results indicate that the fused target 2 works better than GT, and the two stages are necessary." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.624, + 0.465, + 0.702 + ], + "angle": 0, + "content": "
MethodCD(×10-1)↓Recall↑Precision↑
Stage10.220.770.60
Full model0.230.780.61
Full model (train with only GT)0.460.720.60
Only Stage20.490.720.57
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.737 + ], + "angle": 0, + "content": "Table 4: The improvement of the full model over stage 1, the fused target 2 over GT. And the necessity of stage 1." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.763, + 0.477, + 0.871 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.873, + 0.47, + 0.904 + ], + "angle": 0, + "content": "Figure 8: Completion improvement in the full model made by stage 2 over stage 1." + }, + { + "type": "table", + "bbox": [ + 0.548, + 0.227, + 0.842, + 0.376 + ], + "angle": 0, + "content": "
MethodCD(×10-1)↓Recall↑Precision↑
SG-NN (40%)0.670.680.61
SPSG (40%)0.360.730.53
Ours (40%)0.230.770.60
SG-NN (30%)0.730.670.61
SPSG (30%)0.430.720.52
Ours (30%)0.240.770.60
SG-NN (20%)1.060.600.58
SPSG (20%)0.730.650.49
Ours (20%)0.470.720.56
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.377, + 0.892, + 0.408 + ], + "angle": 0, + "content": "Table 5: Quantitative comparison results on Matterport3D with \\(30\\%\\) frames input." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.893, + 0.55 + ], + "angle": 0, + "content": "More incomplete inputs. To illustrate the long-range advantage of our method, we use the model trained on the input consisting of \\(50\\%\\) proportion RGB-D frames to test on the \\(40\\%\\), \\(30\\%\\), and \\(20\\%\\) proportion input. The qualitative and quantitative evaluation results are shown in Fig. 7 and Tab. 5. The results show that as the input information gradually decreases, our method can also output a relatively complete result." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.894, + 0.643 + ], + "angle": 0, + "content": "The impact of contrastive attention training. We validate the contribution of the contrastive attention training strategy (CAT) for training at stage 1. Its qualitative and quantitative evaluation results are shown in Fig. 9 and Tab. 6. We can find that CAT enhances the ability to restore regional shapes." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.657, + 0.9, + 0.804 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.509, + 0.806, + 0.882, + 0.822 + ], + "angle": 0, + "content": "Figure 9: The visual effect of CAT on shape completion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "The effectiveness of modules. We replace the global structure extractor (GSE) and region geometry generator (RGG) with CNNs to evaluate their effectiveness. The Tab. 6 shows the quantitative evaluation, and Fig. 10 dis" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18576" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.118, + 0.08, + 0.428, + 0.157 + ], + "angle": 0, + "content": "
MethodCD(×10-1)↓Recall↑Precision↑
Stage10.220.770.60
Stage1(w/o GSE)0.320.740.57
Stage1(w/o RGG)0.260.750.58
Stage1(w/o CAT)0.240.750.59
" + }, + { + "type": "table_caption", + "bbox": [ + 0.082, + 0.161, + 0.465, + 0.176 + ], + "angle": 0, + "content": "Table 6: Quantitative evaluation of our proposed modules." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.179, + 0.412, + 0.267 + ], + "angle": 0, + "content": "
MethodCD(×10-1)↓Recall↑Precision↑
w/o LCloT0.250.750.60
w/o LS0.260.750.56
w/o LN0.260.740.56
w/o LD0.290.750.54
full loss0.220.770.60
" + }, + { + "type": "table_caption", + "bbox": [ + 0.112, + 0.268, + 0.435, + 0.283 + ], + "angle": 0, + "content": "Table 7: Ablation results of loss items in stage 1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.293, + 0.47, + 0.324 + ], + "angle": 0, + "content": "plays how GSE and RGG improve the completion effect in terms of global structure and region shape, respectively." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.339, + 0.181, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.4, + 0.167, + 0.411 + ], + "angle": 0, + "content": "stage 1 input" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.339, + 0.278, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.184, + 0.4, + 0.272, + 0.411 + ], + "angle": 0, + "content": "stage 1 w/o GSE" + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.339, + 0.378, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.4, + 0.374, + 0.41 + ], + "angle": 0, + "content": "stage 1 w/o RGG" + }, + { + "type": "image", + "bbox": [ + 0.38, + 0.339, + 0.474, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.391, + 0.4, + 0.466, + 0.411 + ], + "angle": 0, + "content": "stage 1 output" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.413, + 0.47, + 0.442 + ], + "angle": 0, + "content": "Figure 10: Qualitative comparisons of how the completion results are affected by RGG and GSE." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.445, + 0.47, + 0.611 + ], + "angle": 0, + "content": "The impact of each loss item. We validate the effect of \\( L_{CIoT} \\), \\( L_S \\), \\( L_N \\) loss on our method, and validate the case where only \\( L_D \\) loss is applied. Tab. 7 shows the quantitative evaluation of the loss items. Fig. 11 shows the qualitative evaluation of the loss items. We can see that with \\( L_{CIoT} \\), the completeness of local scene completion has been improved, while \\( L_S \\) and \\( L_N \\) effectively constrain the accuracy of the shapes and planes, respectively. From the comparison with the results of only using \\( L_D \\) loss, we can find that various losses acting on the connection between voxels improve the completion accuracy and completeness." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.625, + 0.196, + 0.64 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.47, + 0.816 + ], + "angle": 0, + "content": "In this work, we have proposed a dual-scale transformer method with a two-stage completion strategy to generate fairly complete scenes from real-world incomplete RGB-D scans. Our proposed contrastive attention training strategy encourages the transformers to learn distinguishable features. We introduce two new losses to constrain geometric accuracy and completeness. However, due to the limitation of memory, currently, we only use geometric information and solve the geometric completion. In the future, we would consider scene completion with other priors such as color and semantic information." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.831, + 0.192, + 0.845 + ], + "angle": 0, + "content": "6. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "First, our method only completes the geometric surface, without including the texture. In some conditions, the texture is also necessary. In the near future, we will try to solve" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.898, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.145, + 0.897, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.201, + 0.897, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.256, + 0.897, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.311, + 0.897, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.366, + 0.897, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.421, + 0.897, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.475, + 0.897, + 0.529 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.533, + 0.892, + 0.563 + ], + "angle": 0, + "content": "Figure 11: Effect of loss items by switching on/off them at stage 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.695 + ], + "angle": 0, + "content": "it. Second, surface completion mainly provides reasonable inference for the missing parts, rather than replacing the accurate reconstruction. When the geometric information of the input scene is not enough to infer the entire scene, our geometry completion result may not be accurate. Although our method does not need the GT of the complete scene, it still needs a large amount of indoor data to ensure its generalization." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.708, + 0.659, + 0.725 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.733, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Chunxia Xiao is partially supported by NSFC (No.61972298), Bingtuan Science and Technology Program (No.2019BC008), and CAAI-Huawei MindSpore Open Fund." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.806, + 0.597, + 0.822 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.831, + 0.894, + 0.9 + ], + "angle": 0, + "content": "[1] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural rgb-d surface reconstruction. 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IEEE Transactions on Visualization and Computer Graphics, 2022. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18579" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/4473583d-9b9f-42e0-9960-ac81cde7532b_origin.pdf b/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/4473583d-9b9f-42e0-9960-ac81cde7532b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8a22378a52a4fab0c78e7083638cf86921a055b8 --- /dev/null +++ b/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/4473583d-9b9f-42e0-9960-ac81cde7532b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2771abae7decea1bd2c9c3f6a5dd47d023753ae003a8a9e61470fe26b2585738 +size 33568379 diff --git a/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/full.md b/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f1d586e4c69cc9ab546555688c7b04fae8d741c6 --- /dev/null +++ b/2023/Learning Long-Range Information with Dual-Scale Transformers for Indoor Scene Completion/full.md @@ -0,0 +1,366 @@ +# Learning Long-range Information with Dual-Scale Transformers for Indoor Scene Completion + +Ziqi Wang $^{1}$ , Fei Luo $*^{1}$ , Xiaoxiao Long $\dagger^{1}$ , Wenxiao Zhang $^{2}$ , and Chunxia Xiao $*^{1}$ + +$^{1}$ School of Computer Science, Wuhan University $^{2}$ ISTD, Singapore University of Technology and Design + +# Abstract + +Due to the limited resolution of 3D sensors and the inevitable mutual occlusion between objects, 3D scans of real scenes are commonly incomplete. Previous scene completion methods struggle to capture long-range spatial context, resulting in unsatisfactory completion results. To alleviate the problem, we propose a novel Dual-Scale Transformer Network (DST-Net) that efficiently utilizes both long-range and short-range spatial context information to improve the quality of 3D scene completion. To reduce the heavy computation cost of extracting long-range features via transformers, DST-Net adopts a self-supervised two-stage completion strategy. In the first stage, we split the input scene into blocks and perform completion on individual blocks. In the second stage, the blocks are merged together as a whole and then further refined to improve completeness. More importantly, we propose a contrastive attention training strategy to encourage the transformers to learn distinguishable features for better scene completion. Experiments on datasets of Matterport3D, ScanNet, and ICL-NUIM demonstrate that our method can generate better completion results, and our method outperforms the state-of-the-art methods quantitatively and qualitatively. + +# 1. Introduction + +Indoor 3D reconstruction is an essential part of many applications like AR/VR [19, 1], building information modeling (BIM) [24, 32], automatic robot indoor navigation [14] and so on [36, 38]. Due to the limited resolution of 3D sensors and the inevitable occlusion between objects in the scene, there always exist incomplete surfaces in the reconstruction results. + +Recently, scene 3D completion based on deep learning + +![](images/ddf8a6abeb9e84a29baaf7399055f3bd4f34a5503c5af90e94452191edb2c2a6.jpg) + +![](images/12e45c1dc4dc7b5dda97df662edc41df57a63527f8fbb4ac7b12daaf021c1b3a.jpg) + +![](images/5c176576532550bcf56db6a0534bdfa4080f334ebb99f660be783308b4083718.jpg) +(a) Input +(c) SPSG +Figure 1: Indoor scene completion on one case in the Matterport3D dataset. Comparison with the state-of-the-art methods SG-NN [6] and SPSG [8]. + +![](images/7041c6452032e8bea373d5660a898e4f40c1086ce2fcbcee0f2611e14f615e7e.jpg) +(b) SG-NN +(d) Ours + +has made great progress. Dai et al. [6] proposed a self-supervised method called SG-NN to complete the indoor scene with incomplete real-world scan data, which can get a more complete result compared to the training data. Dai et al. [8] further proposed SPSG to complete the 3D surface and texture. Most of the current methods use convolutional neural networks (CNN) for completion and achieve impressive progress. Nonetheless, receptive fields in CNN remain local at a certain resolution, limiting its ability to capture long-range information. This is very important for the scene completion task with incomplete inputs. + +Recently, Vision Transformer (ViT) [27, 18, 10] has made great stride in the computer vision field, owing to its ability to sense long-range information. For the task of single object 3D completion, some methods [30, + +33, 34] achieved better point cloud completion by using transformer-based architecture to extract global information with a spatial attention mechanism. However, there is few attempt to apply transformer to the task of large-scale scene completion, since the large-scale scenes contain complex layouts and various objects. + +In this work, to use long-range information to handle large missing areas and precise completion of geometric shape in the scene, we propose a Dual-Scale Transformer Network (DST-Net) and apply it in a two-stage manner. Specifically, in the first stage, we use DST-Net to complete the blocks split from an incomplete scene, then merge the complete geometric blocks to get the entire scene output. However, the generated results still have some small holes in local areas. To tackle it, in the second stage, we utilize scene-level information to refine the output scene of stage 1. In this stage, we fuse the ground truth and the first stage output as the supervision signal to focus on learning problematic areas and ensure the consistency of learning. + +It is difficult to obtain satisfactory performance when applying transformer for scene completion, as the long-range and sparse incomplete information is more difficult to learn. To solve this problem, our proposed DST-Net involves specific transformer modules for different-level scene information. Furthermore, we propose a contrastive attention training strategy to make the DST-Net efficiently learn similar and distinguishable shape features. Our method includes a structure loss to improve the accuracy of geometric structure, and a CIoT (Cube Intersection over Target) loss to ensure complete output voxels. One comparison case between the state-of-the-art methods and ours is illustrated in Fig. 1. + +In summary, our contributions are as follows: + +1. We propose a novel Dual-Scale Transformer Network (DST-Net) for indoor scene surface completion. We conduct completion operations from the block level to the scene level to achieve better completion performance. +2. We propose a contrastive attention training strategy to make the transformer work robustly in scene completion. In addition, we propose a structure loss to improve the accuracy of geometric shapes and a CIoT loss to make the scene more complete. + +# 2. Related Work + +Completing the 3D surface from the 2D or 3D sparse inputs is an ill-posed task. This task greatly relies on the prior knowledge extracted from other similar scenes. We briefly introduce related traditional methods and deep learning-based methods in this field. More extensive reviews can be found in two recent works [23, 16]. + +# 2.1. Traditional Completion + +Due to lacking powerful 3D scene encoding and inferring models, most of the early traditional methods used the + +interpolating or optimization strategy. Davis et al. [9] proposed a diffusion process with the SDF function to fill the holes in the surface. Kawai et al. [15] proposed an energy minimization surface completion method, which could complete indoor models with holes. Previtali et al. [22] designed a flexible pipeline to perform outdoor and indoor reconstruction from occluded point clouds and proposed corresponding modules for outdoor and indoor scan completion. Silberman et al. [25] proposed a probabilistic model of contour completion random fields, which could complete the boundaries of occluded surfaces. Xiao et al. [31] integrated point cloud completion and surface connectivity relation inference to obtain complete 3D models and surface connections. The traditional methods depend on certain assumption and their generalization is poor when the prerequisite is not met. + +# 2.2. Deep Learning based Completion + +Supervised based completion. With the increment of 3D data resources [2, 4] and the development of deep learning, more and more methods use deep learning neural network to learn various priors to complete the scene. Some methods [13, 17, 28] focus on depth completion to fulfill surface completion. Surface completion is always combined with semantic segmentation provides both geometry and object label information. Song et al. [26] built up a synthetic indoor dataset SUNCG with dense occupancy and semantic annotation, and proposed a fully convolutional end-to-end model to solve both tasks of semantic segmentation and scene completion. Dai et al. [7] further proposed a coarse-to-fine fully convolutional model called ScanComplete based on SUNCG to solve semantic segmentation and scene completion tasks for high-resolution indoor scenes. However, it is difficult to have a complete ground truth for 3D indoor scenes due to device and data capturing imperfections. + +Self-supervised based completion. Self-supervised completion learns the geometric features from incomplete 3D surface ground truth and then expands such learned completion principle to boost the incomplete 3D surface ground truth itself [34, 37, 20, 35]. Dai et al. [6] proposed a self-supervised fully convolutional approach SGNN that can be trained on incomplete, real-world scan data and produced a better geometric model than the training target. SPSG [8] used a similar self-supervised idea to infer a complete scene geometry with color and used 2D data to supervise the color of the output 3D scene for generating a complete color and more accurate scene. It is a promising technical route, as it does not need a large amount of expensive GT data. But it requires the model to have a more robust capacity to observe a wider scope and a stronger completion ability. + +![](images/c6b269876912dc22e80cdc2f7a867a045d2ff3cd1dbe2de2a455180141eb7634.jpg) +Figure 2: Overview of our completion method. Stage 1 uses DST-Net to complete blocks of the incomplete input, and merge them to get the coarse scene output. Stage 2 proceeds to refine the coarse scene. We use different colors to represent the differences between the two-level network structures in DST-Net. + +# 3. Method + +# 3.1. Overview + +The diagram of our proposed method is illustrated in Fig. 2. Given a training dataset with a series of incomplete indoor scans, our proposed method has two stages. Stage 1 trains DST-Net to learn completion rules on small blocks split from the incomplete scene. Due to memory limitation, in the test, the input and output of stage 1 are same-sized voxel blocks split from a scene, then we merge the output blocks to get the stage 2 input. Then stage 2 aims to address the inadequate inferring result caused by the limited scope of block-level completion by processing the scene-level information, while the training target is obtained by fusing the output and target of stage 1. + +In the training progress, we propose a contrastive attention training strategy that uses the information between different blocks to encourage the transformers to learn distinguishable features for better scene completion. We propose the structure loss and CIoT loss to ensure completed scenes precise and complete. + +# 3.2. DST-Net Structure + +Our DST-Net is an encoder-decoder structure, as shown in the Fig. 3(a), The DST-Net basically consists of four + +modules: geometry encoder, global structure extractor, region geometry generator, and local detail generator. The geometry encoder and local detail generator are similar to [6], consisting of 3D Sparse Convolutions [11] (SP-Convs) to encode and decode local geometry features. We propose a global structure extractor to extract and complete global-level features, as well as proposing the region geometry generator to decode region-level geometry shapes with long-range information. Considering the proportion of valid data in the scene, the modules at the two ends of our network process sparse voxels (shown in blue color), and the middle module processes dense voxels (shown in green color). Next, we will introduce the global structure extractor and region geometry generator in detail. + +# 3.2.1 Global Structure Extractor + +To extract similar high-dimensional features from similar structures, we introduce a global structure extractor. The global structure extractor has two branches, as shown in Fig. 3(b). Inspired by PVT [29], we design a 3D multilayer transformer pyramid structure as one branch to reshape structured voxels into non-sequential voxels and encode them, which mainly focuses on long-range global information. In order not to lose details, we also reserve CNNs as the other branch to encode local information. + +![](images/20e2bc26a633b75e21cede9a6c6b7ab0cde1dd5815293576c2009499a0e9537e.jpg) +(a) Four Modules in Dual-Scale Transformer Network + +![](images/c06e4db6b50f3ae95c675b362d211f9485aa87eb8d5cdb0813ef2ecaa4fb50bf.jpg) +Figure 3: Network structure and details. (a) The diagram of our DST-Net structure and its four main modules. The input for stage 1 are blocks and the input for stage 2 is a scene, respectively. Arrows indicate the flow of data in the network. The difference in DST-Net between stage 1 and stage 2 lies in the global structure extractor and region geometry generator. (b) Global structure extractor contains two branches of transformer and CNN. There is no transformer branch (marked with a dot line rectangle) in stage 2. (c) The component of region geometry generator in stage 1 and stage 2. (d) The network structure of two major components in region geometry generator: MR-CA (left column), and MR-VT (right column). + +Then the two branches are decoded with CNNs. We use skip-connection to connect the information of the same resolution in both branches. Finally, the global features completed by these two branches are fused by a linear layer. At stage 2, we remove the transformer branch, as the scene is relatively complete, and the need for long-range information capture is reduced. + +# 3.2.2 Region Geometry Generator + +We propose a region geometry generator to hierarchically generate accurate region shapes with long-range shape similarity. The key components of this module are the multi-resolution cross-attention (MR-CA) and the multi-resolution voxel transformer (MR-VT). The organization ways of region geometry generator in stage 1 and 2 are shown in Fig. 3(c). + +Multi-resolution cross-attention. We propose the MR-CA module to connect shape features $Y \in \mathbb{R}^{N \times C}$ in the geometry encoder to high-resolution features $X \in \mathbb{R}^{N \times C}$ in the region geometry generator for shape completion, as shown in the left column of Fig. 3(d). $N$ is the number of sparse voxel features, and $C$ is the number of channels. In this module, $Q$ is obtained from $X$ through $1 \times 1$ SP-Conv, $K$ and $V$ are obtained from $Y$ through $1 \times 1$ SP-Conv. We + +conduct dot-product between $Q$ and $K^T$ to get the attention map $A$ . + +$A$ stores the similarity of the shape information between $Y$ and $X$ , we use $A$ to select similar shape features from $V$ : + +$$ +X _ {a t t n} = S P - C o n v (A \times V) \tag {1} +$$ + +We add the result $X_{\text{attn}}$ selected from $Y$ and the input feature $X$ to get the completed feature $X_{\text{out}}$ : + +$$ +X _ {o u t} = X + X _ {a t t n} \tag {2} +$$ + +Multi-resolution voxel transformer. Unlike MR-CA, which uses the encoder's shape information, MR-VT is proposed to perform region shape completion with the long-range complete shape feature generated in the generator. We first connect the sparse voxel features of the same resolution in the encoder and the decoder, to obtain the feature $X_{C}\in \mathbb{R}^{N\times C}$ . $Q$ is projected by $X_{C}$ . $K$ and $V$ are projected by $X_{C}$ after down-sampling. The latter attention operation and more details are shown in the right column of Fig. 3(d). By using MR-VT, each voxel with incomplete shape information can capture long-range information from all other generated voxels for completion. + +![](images/a0f1fd0136b32666ed6d6c7bacea56cd0a93389bf35bb767054ef813abf3dbac.jpg) +Figure 4: The diagram of CAT working mechanism. + +# 3.3. Contrastive attention training + +Contrast learning enhances the performance of vision tasks by contrasting samples against each other, which learns common attributes from similar samples and discriminative attributes from distinguished ones. Inspired by the idea of contrastive learning, we propose a contrastive attention training (CAT) strategy to empower the transformers for scene completion by efficiently learning common and distinguishable shape features from the training samples. + +Our method randomly takes a batch containing $b$ blocks as input in training, and the input $X_{C}$ for MR-VT is a voxel set $\{L_j,j = 0,\dots,m_i - 1\}$ processed from each block $i$ , where $m_{i}$ means the number of the voxels in block $i$ and each voxel $L_{j}$ contains a shape feature within a cubic space. Unlike the general self-attention approach, where the attention operation is done between $\{L_j,j = 0,\dots,m_i - 1\}$ , we further randomly select the voxels sets from other blocks, and use all voxels in them to form a random voxel set $\mathbb{L}:\{L_j,j = 0,\dots,\sum_{i = 0}^{n - 1}m_i - 1\}$ , where $n$ means the number of all the selected blocks. The physical meaning of $\mathbb{L}$ is shown in Fig.4. In brief, we use M to denote $\sum_{i = 0}^{n - 1}m_i$ . Similar to MR-VT, the $Q_{j}$ , $K_{j}$ and $V_{j}$ are projected from $L_{j}$ . In this way, we perform a cross-attention operation between n blocks in a training batch. For a certain voxel $L_{j}$ , we obtain the similarity set $\{A_{j,k},k = 0,\dots,M - 1\}$ between $L_{j}$ and all M voxels in $\mathbb{L}$ by computing the dot-product of $Q_{j}$ and $K_{k}$ and then normalized via softmax function: + +$$ +A _ {j, k} = \frac {\exp \left(Q _ {j} \cdot K _ {k}\right)}{\sum_ {k = 0} ^ {M - 1} \exp \left(Q _ {j} \cdot K _ {k}\right)}, \tag {3} +$$ + +After obtaining the similarity set $\{A_{j,k}, k = 0, \dots, M - 1\}$ , we can use it to select features $V_k$ derived from $L_k$ in $\mathbb{L}$ to complete the voxel $L_j$ : + +$$ +X _ {a t t n} = S P - C o n v \left(\sum_ {k = 0} ^ {M - 1} A _ {j, k} \cdot V _ {k}\right) \tag {4} +$$ + +The underlying motivation is that unlike self-attention applied to individual blocks with a single layout, our contrastive attention operation requires the transformer to extract useful information from a set of random other blocks. Due to the randomness when selecting blocks in a training batch, the blocks with different layouts may share similar properties or have different attributes, which may be useful or detrimental. By explicitly adding extra information, transformers are required to identify whether the extra information is useful or not by attention scores. The learning strategy enables transformers to learn geometric features with a higher degree of discrimination, thereby improving the completion ability. We evaluate different values for $n$ with 2, 4, and 8. The experimental results indicate that the completion performance reaches its best for $n$ equal to 8. + +# 3.4. Loss Function and Data Generation + +Geometry loss. We train the network with three geometry loss items: depth loss $L_{D}$ , 3D normal loss $L_{N}$ , and structure loss $L_{S}$ . Given a voxel $v$ , depth loss $L_{D}$ is used to calculate the difference between the predicted depth $D_{v}^{P}$ and the target depth $D_{v}^{T}$ in $v$ . The 3D normal loss $L_{N}$ constrains the predicted normal $N_{v}^{P}$ and the target normal $N_{v}^{T}$ in $v$ . $V$ is the set of voxels to be calculated: + +$$ +L _ {D} = \frac {1}{V} \sum_ {v \in V} \left\| D _ {v} ^ {P} - D _ {v} ^ {T} \right\| _ {1} \tag {5} +$$ + +$$ +L _ {N} = \frac {1}{V} \sum_ {v \in V} \left| \left| N _ {v} ^ {P} - N _ {v} ^ {T} \right| \right| _ {1} \tag {6} +$$ + +Normal loss is used to constrain the geometry structures by calculating local depth variations. However, for more complex geometry structures, like various concave and convex shapes, it is difficult to complete them well only with normal loss. Inspired by normal loss, we introduce the structure loss $L_{S}$ to further constrain the geometry structures by calculating local normal variations. + +![](images/06195e7da7e7898902a61651de58b7c73df26fc1b2ec11c81865871365c37c80.jpg) +predicted normals + +![](images/11ad3f650cf38d6309f9b324b971cb65f75da68a958e910559ff1b49706013df.jpg) +GT normals +Figure 5: Visual comparison of two different local structures. + +As shown in Fig. 5, $N_{i,j,k}^{P}$ denotes the normal of a predicted voxel, $N_{i+1,j,k}^{P}, N_{i,j+1,k}^{P}$ , and $N_{i,j,k+1}^{P}$ denote the normals of its three adjacent voxels, where $i,j,k$ represent voxel coordinates in three directions respectively. The GT normals are represented in a similar fashion. In a brief, + +we use $N_{v}^{P}, N_{vx}^{P}, N_{vy}^{P}$ and $N_{vz}^{P}$ to denote $N_{i,j,k}^{P}, N_{i+1,j,k}^{P}, N_{i,j+1,k}^{P}$ and $N_{i,j,k+1}^{P}$ , as well as the GT normals. The normal loss of a single predicted voxel is small when calculated with GT, while the local structures of the predicted case and GT are totally different due to the accumulation of normal variations. Therefore, we use the dot-product similarity between $N_{v}^{P}$ and $N_{vx}^{P}, N_{vy}^{P}$ , and $N_{vz}^{P}$ to get $S_{vx}^{P}, S_{vy}^{P}$ , and $S_{vz}^{P}$ as structure descriptors, as shown in Equation (7), to describe the local variation of normals. The structure descriptors of GT are calculated in the same way. The loss $L_{S}$ between predicted and target structure descriptors enable the whole predicted geometry structure to represent GT more accurately. + +$$ +S _ {v x} ^ {P} = N _ {v x} ^ {P} \cdot N _ {v} ^ {P} +$$ + +$$ +S _ {v y} ^ {P} = N _ {v y} ^ {P} \cdot N _ {v} ^ {P} \tag {7} +$$ + +$$ +S _ {v z} ^ {P} = N _ {v z} ^ {P} \cdot N _ {v} ^ {P} +$$ + +$$ +L _ {S} = \frac {1}{V} \sum_ {v \in V} \left\{\frac {1}{3} \left(\left| \left| S _ {v x} ^ {P} - S _ {v x} ^ {T} \right| \right| _ {1} + \right. \right. \tag {8} +$$ + +$$ +| | S _ {v y} ^ {P} - S _ {v y} ^ {T} | | _ {1} + | | S _ {v z} ^ {P} - S _ {v z} ^ {T} | | _ {1}) \} +$$ + +CIoT loss. Considering incomplete real-world data, we propose CIoT (Cube Intersection over Target) loss to make output voxel distribution fit the target. Due to the voxel sparsity, the same IoT may represent a completely different distribution. To address it, we divide the entire output into $N$ small cubes of the same size. In a cube, $C_i^P$ and $C_i^T$ represent the number of predicted voxels and the number of target voxels, respectively. We only calculate the loss in the cube where $C_i^T > 0$ . CIoT loss is defined as: + +$$ +L _ {C I o T} = 1 - \frac {1}{N} \sum_ {i = 1} ^ {N} \frac {C _ {i} ^ {P} \cap C _ {i} ^ {T}}{C _ {i} ^ {T}} \tag {9} +$$ + +Data Generation. Both input and target in training are the representation of sparse TSDF voxel with depth information, obtained from RGB-D frames by the method of voxel fusion [3]. Following the self-supervised learning approach of SG-NN [6], the training target (GT) in stage 1 is generated using all RGB-D frames, while a certain proportion is used in getting input. The training target in stage 2 is obtained by fusing the output and target of stage 1. To focus on learning problem regions and minimize error accumulation, we select the TSDF value of target 1 voxel as the value for target 2 voxel when the coordinates of output and target of stage 1 coincide. + +# 4. Experiments and Results + +To validate our proposed method, we use the Mather-port3D [2] dataset as the training data and conduct the comparison experiments on both real-world data and synthetic + +
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet1.480.510.54
SG-NN0.650.690.62
SPSG0.350.740.53
Ours0.230.780.61
+ +Table 1: Quantitative comparison results on Matterport3D. + +data. The training dataset includes 1788 rooms. We train our method on a single NVIDIA GeForce RTX 2080. The learning rate is 0.001, and the batch size is 8. The resolution of all voxels is $2\mathrm{cm}$ . The training blocks are all $128 \times 64 \times 64$ size cutting from the scene, and parameter $n$ in contrastive attention training strategy is 8. The four terms in the loss function have equal weights. Our stage 1 model training takes about 72 hours, and the stage 2 model training takes about 24 hours. Three state-of-the-art methods of ConvOccNet [21], SG-NN [6] and SPSG (only with geometry) [8] are used to compare with ours on the metrics of Chamfer Distance (CD) in metric space, Recall, and Precision. For real-world unobserved space, we ignore it for the CD evaluation. + +# 4.1. Completion on Matterport3D + +First, we compare four methods on 394 other rooms from the Matterport3D dataset. We provide the same incomplete TSDF input, except for ConvOccNet, which requires the corresponding mesh to be pre-computed as input. Some scene completion results are shown in Fig. 6(a). In visual effect, our method completes more parts in the scenes than the other three methods, which is consistent with the recall metric in Tab. 1. The highest score on CD proves that our method's shape accuracy is the best. As the GT is incomplete and the more completion areas from our method have no corresponding GT, our precision is less than the SG-NN under this special condition. + +# 4.2. Completion on Synthetic Data + +The synthetic dataset ICL-NUIM [12] has 3D surface ground truth so that it can provide a more comprehensive evaluation. As the scan frames are indoors, we only select the mesh of the surface inside the room to evaluate. Qualitative and quantitative evaluations are shown in Fig. 6(b) and Tab. 2. Owing to the full GT, the results fairly reflect our method's superiority over the other three methods. + +# 4.3. Completion on ScanNet + +To validate the generalization of our proposed method, we also conduct the comparison experiments on a more challenging dataset ScanNet [5]. The Fig. 6(c) are the visualization results, and Tab. 3 shows the quantitative results. + +![](images/3ab6dece3038d35b9d733c13a5df176c649afbabcc872422e7e5ee64638a5294.jpg) +(a)Matterport3D + +![](images/c0a3a2a9a22e9524fefe1988a67e64a173222e9a54af9d0e49cc25dd6e5f5059.jpg) + +![](images/0b11f4ac0aac835720eeb254639aace7bffaca06a850fcd07ad4714b4ab299bb.jpg) +(b) ICL-NUIM +(c) ScanNet +Figure 6: Qualitative comparisons with state-of-the-art methods on Matterport3D, ICL-NUIM and ScanNet. + +# 4.4. Ablation Study + +In this section, we demonstrate how the functional components in our method affect the ultimate performance. + +Stage 1 versus Stage 2. Stage 1 in our full model has finished most of the completion. However, stage 1 may generate some inaccurate areas due to block-level scope. Stage 2 can further solve these problems by training with + +![](images/f964bcc67549d161a6cb8cf984e6c2bf4dbfa6dfa34f6f9a7e46e811e3ee65a1.jpg) + +![](images/d785cf7089c8ed5846702db0d0c1fb079bbc77a5c5ed59b03b05c6bc83ea62bc.jpg) + +![](images/1ab99e984c68ee57367212534779efcad372c9f74a56e7632bc4d51d46f1ea28.jpg) + +![](images/8da4f8b5c12188b33687ed69b29706d845cb60ef13988dfe9e8a5608853c090a.jpg) +Figure 7: Qualitative comparisons with state-of-the-art methods on Matterport3D with $30\%$ frames input. + +![](images/26f465a9dd391f036dd1a6c4cceb1cf1e167555d784e747e26fec00867fec8c7.jpg) + +
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet0.610.170.28
SG-NN0.310.310.42
SPSG0.250.350.39
Ours0.180.390.45
+ +Table 2: Quantitative comparison results on ICL-NUIM. + +
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet0.650.790.43
SG-NN0.360.850.50
SPSG0.300.860.45
Ours0.260.880.48
+ +the fused target 2 and using the whole scan as input. The qualitative and quantitative evaluation results of stage 1 and the full model are shown in the Fig. 8 and Tab. 4. The results show that stage 2 accumulates a little distance error, but completes and corrects the results of stage 1. Tab. 4 further shows the quantitative results of training the full model with GT and using only the stage 2 model that is trained with stage 1 data to process input. The results indicate that the fused target 2 works better than GT, and the two stages are necessary. + +Table 3: Quantitative comparison results on ScanNet. + +
MethodCD(×10-1)↓Recall↑Precision↑
Stage10.220.770.60
Full model0.230.780.61
Full model (train with only GT)0.460.720.60
Only Stage20.490.720.57
+ +![](images/f9df177459a84612ccfeb59ff8deb8a8f5de9992fdf0f152662127f09dfd1eea.jpg) +Figure 8: Completion improvement in the full model made by stage 2 over stage 1. + +Table 4: The improvement of the full model over stage 1, the fused target 2 over GT. And the necessity of stage 1. + +
MethodCD(×10-1)↓Recall↑Precision↑
SG-NN (40%)0.670.680.61
SPSG (40%)0.360.730.53
Ours (40%)0.230.770.60
SG-NN (30%)0.730.670.61
SPSG (30%)0.430.720.52
Ours (30%)0.240.770.60
SG-NN (20%)1.060.600.58
SPSG (20%)0.730.650.49
Ours (20%)0.470.720.56
+ +Table 5: Quantitative comparison results on Matterport3D with $30\%$ frames input. + +More incomplete inputs. To illustrate the long-range advantage of our method, we use the model trained on the input consisting of $50\%$ proportion RGB-D frames to test on the $40\%$ , $30\%$ , and $20\%$ proportion input. The qualitative and quantitative evaluation results are shown in Fig. 7 and Tab. 5. The results show that as the input information gradually decreases, our method can also output a relatively complete result. + +The impact of contrastive attention training. We validate the contribution of the contrastive attention training strategy (CAT) for training at stage 1. Its qualitative and quantitative evaluation results are shown in Fig. 9 and Tab. 6. We can find that CAT enhances the ability to restore regional shapes. + +![](images/b6c31a69c6b9413f74b73d1dccfbff05f4f79d1b19c8d354bc0b7ed9f7096238.jpg) +Figure 9: The visual effect of CAT on shape completion. + +The effectiveness of modules. We replace the global structure extractor (GSE) and region geometry generator (RGG) with CNNs to evaluate their effectiveness. The Tab. 6 shows the quantitative evaluation, and Fig. 10 dis + +
MethodCD(×10-1)↓Recall↑Precision↑
Stage10.220.770.60
Stage1(w/o GSE)0.320.740.57
Stage1(w/o RGG)0.260.750.58
Stage1(w/o CAT)0.240.750.59
+ +Table 6: Quantitative evaluation of our proposed modules. + +
MethodCD(×10-1)↓Recall↑Precision↑
w/o LCloT0.250.750.60
w/o LS0.260.750.56
w/o LN0.260.740.56
w/o LD0.290.750.54
full loss0.220.770.60
+ +Table 7: Ablation results of loss items in stage 1. + +plays how GSE and RGG improve the completion effect in terms of global structure and region shape, respectively. + +![](images/7eba6033b255039599bef617b222a6b0a2e570503ce14b46d3004c251db88a6b.jpg) +stage 1 input + +![](images/3bda8ee91e8db1573fdc59a44bea7df21ff4105acdf270290edb341f7963113d.jpg) +stage 1 w/o GSE + +![](images/85acc8ff401cc59dc862aad0e33167a6e366bf1305748047c59da48a5a90a86a.jpg) +stage 1 w/o RGG + +![](images/0bb9fda0a80ae3fe34948567f302710bdbbb404dd482d6521fd28d6fd81a1bcb.jpg) +stage 1 output + +Figure 10: Qualitative comparisons of how the completion results are affected by RGG and GSE. + +The impact of each loss item. We validate the effect of $L_{CIoT}$ , $L_S$ , $L_N$ loss on our method, and validate the case where only $L_D$ loss is applied. Tab. 7 shows the quantitative evaluation of the loss items. Fig. 11 shows the qualitative evaluation of the loss items. We can see that with $L_{CIoT}$ , the completeness of local scene completion has been improved, while $L_S$ and $L_N$ effectively constrain the accuracy of the shapes and planes, respectively. From the comparison with the results of only using $L_D$ loss, we can find that various losses acting on the connection between voxels improve the completion accuracy and completeness. + +# 5. Conclusion + +In this work, we have proposed a dual-scale transformer method with a two-stage completion strategy to generate fairly complete scenes from real-world incomplete RGB-D scans. Our proposed contrastive attention training strategy encourages the transformers to learn distinguishable features. We introduce two new losses to constrain geometric accuracy and completeness. However, due to the limitation of memory, currently, we only use geometric information and solve the geometric completion. In the future, we would consider scene completion with other priors such as color and semantic information. + +# 6. Limitation + +First, our method only completes the geometric surface, without including the texture. In some conditions, the texture is also necessary. In the near future, we will try to solve + +![](images/0330afd91feebf011375a58a76247e0ab389eedb0e12cb06cefc6103da36e5bd.jpg) + +![](images/980a0f613aaa995efc9b86aaef7fba4dfcb4024c77ba00643c9d7b8214ac7781.jpg) + +![](images/98faf47a5783b48d51c7b001ee4f679303801684fc4c21d96ce2a1029f149070.jpg) + +![](images/37627aeec235952d02fe1abbdbb9dcc132aaa69bd2d4620c9c7f754de2038ad1.jpg) + +![](images/7e8fc73101de8ca6ed1f07a3df818edf1620f47e91c098daa2eeeb85d0b07b41.jpg) + +![](images/6f40528b67c94b7b0bea4b083f3f0cfc27e8088e9ca65f0d0ef9098e9cf85d76.jpg) + +![](images/0227ba317c600b173a72194580587af6a2711c48c42f075b0beb2ee5dff9837a.jpg) + +![](images/d2c0b603cdfe7b9665394c4f5ebde22afbb92415e5657653a56d883683f3e0f6.jpg) +Figure 11: Effect of loss items by switching on/off them at stage 1. + +it. Second, surface completion mainly provides reasonable inference for the missing parts, rather than replacing the accurate reconstruction. When the geometric information of the input scene is not enough to infer the entire scene, our geometry completion result may not be accurate. Although our method does not need the GT of the complete scene, it still needs a large amount of indoor data to ensure its generalization. + +# Acknowledgments + +Chunxia Xiao is partially supported by NSFC (No.61972298), Bingtuan Science and Technology Program (No.2019BC008), and CAAI-Huawei MindSpore Open Fund. + +# References + +[1] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural rgb-d surface reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6290-6301, 2022. 1 + +[2] Angel Chang, Angela Dai, Thomas Funkhouser, Maciej Halber, Matthias Niessner, Manolis Savva, Shuran Song, Andy Zeng, and Yinda Zhang. 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Previous scene completion methods struggle to capture long-range spatial context, resulting in unsatisfactory completion results. To alleviate the problem, we propose a novel Dual-Scale Transformer Network (DST-Net) that efficiently utilizes both long-range and short-range spatial context information to improve the quality of 3D scene completion. To reduce the heavy computation cost of extracting long-range features via transformers, DST-Net adopts a self-supervised two-stage completion strategy. In the first stage, we split the input scene into blocks and perform completion on individual blocks. In the second stage, the blocks are merged together as a whole and then further refined to improve completeness. More importantly, we propose a contrastive attention training strategy to encourage the transformers to learn distinguishable features for better scene completion. Experiments on datasets of Matterport3D, ScanNet, and ICL-NUIM demonstrate that our method can generate better completion results, and our method outperforms the state-of-the-art methods quantitatively and qualitatively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 570, + 128, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 128, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 128, + 582 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 590, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 673 + ], + "type": "text", + "content": "Indoor 3D reconstruction is an essential part of many applications like AR/VR [19, 1], building information modeling (BIM) [24, 32], automatic robot indoor navigation [14] and so on [36, 38]. Due to the limited resolution of 3D sensors and the inevitable occlusion between objects in the scene, there always exist incomplete surfaces in the reconstruction results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 673, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 673, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 59, + 673, + 287, + 686 + ], + "type": "text", + "content": "Recently, scene 3D completion based on deep learning" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 266, + 425, + 346 + ], + "blocks": [ + { + "bbox": [ + 310, + 266, + 425, + 346 + ], + "lines": [ + { + "bbox": [ + 310, + 266, + 425, + 346 + ], + "spans": [ + { + "bbox": [ + 310, + 266, + 425, + 346 + ], + "type": "image", + "image_path": "ddf8a6abeb9e84a29baaf7399055f3bd4f34a5503c5af90e94452191edb2c2a6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 428, + 266, + 544, + 346 + ], + "blocks": [ + { + "bbox": [ + 428, + 266, + 544, + 346 + ], + "lines": [ + { + "bbox": [ + 428, + 266, + 544, + 346 + ], + "spans": [ + { + "bbox": [ + 428, + 266, + 544, + 346 + ], + "type": "image", + "image_path": "12e45c1dc4dc7b5dda97df662edc41df57a63527f8fbb4ac7b12daaf021c1b3a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 364, + 425, + 451 + ], + "blocks": [ + { + "bbox": [ + 352, + 354, + 382, + 364 + ], + "lines": [ + { + "bbox": [ + 352, + 354, + 382, + 364 + ], + "spans": [ + { + "bbox": [ + 352, + 354, + 382, + 364 + ], + "type": "text", + "content": "(a) Input" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 364, + 425, + 451 + ], + "lines": [ + { + "bbox": [ + 310, + 364, + 425, + 451 + ], + "spans": [ + { + "bbox": [ + 310, + 364, + 425, + 451 + ], + "type": "image", + "image_path": "5c176576532550bcf56db6a0534bdfa4080f334ebb99f660be783308b4083718.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 351, + 456, + 383, + 466 + ], + "lines": [ + { + "bbox": [ + 351, + 456, + 383, + 466 + ], + "spans": [ + { + "bbox": [ + 351, + 456, + 383, + 466 + ], + "type": "text", + "content": "(c) SPSG" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 472, + 547, + 509 + ], + "lines": [ + { + "bbox": [ + 305, + 472, + 547, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 547, + 509 + ], + "type": "text", + "content": "Figure 1: Indoor scene completion on one case in the Matterport3D dataset. Comparison with the state-of-the-art methods SG-NN [6] and SPSG [8]." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 428, + 365, + 544, + 451 + ], + "blocks": [ + { + "bbox": [ + 466, + 354, + 504, + 363 + ], + "lines": [ + { + "bbox": [ + 466, + 354, + 504, + 363 + ], + "spans": [ + { + "bbox": [ + 466, + 354, + 504, + 363 + ], + "type": "text", + "content": "(b) SG-NN" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 428, + 365, + 544, + 451 + ], + "lines": [ + { + "bbox": [ + 428, + 365, + 544, + 451 + ], + "spans": [ + { + "bbox": [ + 428, + 365, + 544, + 451 + ], + "type": "image", + "image_path": "7041c6452032e8bea373d5660a898e4f40c1086ce2fcbcee0f2611e14f615e7e.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 471, + 456, + 500, + 466 + ], + "lines": [ + { + "bbox": [ + 471, + 456, + 500, + 466 + ], + "spans": [ + { + "bbox": [ + 471, + 456, + 500, + 466 + ], + "type": "text", + "content": "(d) Ours" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 546, + 663 + ], + "type": "text", + "content": "has made great progress. Dai et al. [6] proposed a self-supervised method called SG-NN to complete the indoor scene with incomplete real-world scan data, which can get a more complete result compared to the training data. Dai et al. [8] further proposed SPSG to complete the 3D surface and texture. Most of the current methods use convolutional neural networks (CNN) for completion and achieve impressive progress. Nonetheless, receptive fields in CNN remain local at a certain resolution, limiting its ability to capture long-range information. This is very important for the scene completion task with incomplete inputs." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Recently, Vision Transformer (ViT) [27, 18, 10] has made great stride in the computer vision field, owing to its ability to sense long-range information. For the task of single object 3D completion, some methods [30," + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 245, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 245, + 702 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 245, + 702 + ], + "type": "text", + "content": "*Fei Luo and Chunxia Xiao are co-responding authors" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 59, + 703, + 226, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 226, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 226, + 713 + ], + "type": "inline_equation", + "content": "^{\\dagger}" + }, + { + "bbox": [ + 59, + 703, + 226, + 713 + ], + "type": "text", + "content": "Xiaoxiao Long was interning at Wuhan University" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18569" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "content": "33, 34] achieved better point cloud completion by using transformer-based architecture to extract global information with a spatial attention mechanism. However, there is few attempt to apply transformer to the task of large-scale scene completion, since the large-scale scenes contain complex layouts and various objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 286, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 286, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 286, + 299 + ], + "type": "text", + "content": "In this work, to use long-range information to handle large missing areas and precise completion of geometric shape in the scene, we propose a Dual-Scale Transformer Network (DST-Net) and apply it in a two-stage manner. Specifically, in the first stage, we use DST-Net to complete the blocks split from an incomplete scene, then merge the complete geometric blocks to get the entire scene output. However, the generated results still have some small holes in local areas. To tackle it, in the second stage, we utilize scene-level information to refine the output scene of stage 1. In this stage, we fuse the ground truth and the first stage output as the supervision signal to focus on learning problematic areas and ensure the consistency of learning." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 286, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 286, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 286, + 443 + ], + "type": "text", + "content": "It is difficult to obtain satisfactory performance when applying transformer for scene completion, as the long-range and sparse incomplete information is more difficult to learn. To solve this problem, our proposed DST-Net involves specific transformer modules for different-level scene information. Furthermore, we propose a contrastive attention training strategy to make the DST-Net efficiently learn similar and distinguishable shape features. Our method includes a structure loss to improve the accuracy of geometric structure, and a CIoT (Cube Intersection over Target) loss to ensure complete output voxels. One comparison case between the state-of-the-art methods and ours is illustrated in Fig. 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 444, + 246, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 444, + 246, + 454 + ], + "spans": [ + { + "bbox": [ + 59, + 444, + 246, + 454 + ], + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 455, + 286, + 562 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 455, + 286, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 286, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 286, + 502 + ], + "type": "text", + "content": "1. We propose a novel Dual-Scale Transformer Network (DST-Net) for indoor scene surface completion. We conduct completion operations from the block level to the scene level to achieve better completion performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 503, + 286, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 286, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 286, + 562 + ], + "type": "text", + "content": "2. We propose a contrastive attention training strategy to make the transformer work robustly in scene completion. In addition, we propose a structure loss to improve the accuracy of geometric shapes and a CIoT loss to make the scene more complete." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 572, + 134, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 134, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 134, + 585 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 593, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 286, + 664 + ], + "type": "text", + "content": "Completing the 3D surface from the 2D or 3D sparse inputs is an ill-posed task. This task greatly relies on the prior knowledge extracted from other similar scenes. We briefly introduce related traditional methods and deep learning-based methods in this field. More extensive reviews can be found in two recent works [23, 16]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 671, + 180, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 180, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 180, + 684 + ], + "type": "text", + "content": "2.1. Traditional Completion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "Due to lacking powerful 3D scene encoding and inferring models, most of the early traditional methods used the" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": "interpolating or optimization strategy. Davis et al. [9] proposed a diffusion process with the SDF function to fill the holes in the surface. Kawai et al. [15] proposed an energy minimization surface completion method, which could complete indoor models with holes. Previtali et al. [22] designed a flexible pipeline to perform outdoor and indoor reconstruction from occluded point clouds and proposed corresponding modules for outdoor and indoor scan completion. Silberman et al. [25] proposed a probabilistic model of contour completion random fields, which could complete the boundaries of occluded surfaces. Xiao et al. [31] integrated point cloud completion and surface connectivity relation inference to obtain complete 3D models and surface connections. The traditional methods depend on certain assumption and their generalization is poor when the prerequisite is not met." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 281, + 485, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 485, + 294 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 485, + 294 + ], + "type": "text", + "content": "2.2. Deep Learning based Completion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 303, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 518 + ], + "type": "text", + "content": "Supervised based completion. With the increment of 3D data resources [2, 4] and the development of deep learning, more and more methods use deep learning neural network to learn various priors to complete the scene. Some methods [13, 17, 28] focus on depth completion to fulfill surface completion. Surface completion is always combined with semantic segmentation provides both geometry and object label information. Song et al. [26] built up a synthetic indoor dataset SUNCG with dense occupancy and semantic annotation, and proposed a fully convolutional end-to-end model to solve both tasks of semantic segmentation and scene completion. Dai et al. [7] further proposed a coarse-to-fine fully convolutional model called ScanComplete based on SUNCG to solve semantic segmentation and scene completion tasks for high-resolution indoor scenes. However, it is difficult to have a complete ground truth for 3D indoor scenes due to device and data capturing imperfections." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "Self-supervised based completion. Self-supervised completion learns the geometric features from incomplete 3D surface ground truth and then expands such learned completion principle to boost the incomplete 3D surface ground truth itself [34, 37, 20, 35]. Dai et al. [6] proposed a self-supervised fully convolutional approach SGNN that can be trained on incomplete, real-world scan data and produced a better geometric model than the training target. SPSG [8] used a similar self-supervised idea to infer a complete scene geometry with color and used 2D data to supervise the color of the output 3D scene for generating a complete color and more accurate scene. It is a promising technical route, as it does not need a large amount of expensive GT data. But it requires the model to have a more robust capacity to observe a wider scope and a stronger completion ability." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18570" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 545, + 339 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 339 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 339 + ], + "type": "image", + "image_path": "c6b269876912dc22e80cdc2f7a867a045d2ff3cd1dbe2de2a455180141eb7634.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 347, + 546, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 347, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 546, + 384 + ], + "type": "text", + "content": "Figure 2: Overview of our completion method. Stage 1 uses DST-Net to complete blocks of the incomplete input, and merge them to get the coarse scene output. Stage 2 proceeds to refine the coarse scene. We use different colors to represent the differences between the two-level network structures in DST-Net." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 404, + 102, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 102, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 102, + 415 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 424, + 114, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 424, + 114, + 435 + ], + "spans": [ + { + "bbox": [ + 47, + 424, + 114, + 435 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 442, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 586 + ], + "type": "text", + "content": "The diagram of our proposed method is illustrated in Fig. 2. Given a training dataset with a series of incomplete indoor scans, our proposed method has two stages. Stage 1 trains DST-Net to learn completion rules on small blocks split from the incomplete scene. Due to memory limitation, in the test, the input and output of stage 1 are same-sized voxel blocks split from a scene, then we merge the output blocks to get the stage 2 input. Then stage 2 aims to address the inadequate inferring result caused by the limited scope of block-level completion by processing the scene-level information, while the training target is obtained by fusing the output and target of stage 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 588, + 287, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 588, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 588, + 287, + 660 + ], + "type": "text", + "content": "In the training progress, we propose a contrastive attention training strategy that uses the information between different blocks to encourage the transformers to learn distinguishable features for better scene completion. We propose the structure loss and CIoT loss to ensure completed scenes precise and complete." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 670, + 157, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 157, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 157, + 681 + ], + "type": "text", + "content": "3.2. DST-Net Structure" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Our DST-Net is an encoder-decoder structure, as shown in the Fig. 3(a), The DST-Net basically consists of four" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 406, + 545, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 545, + 573 + ], + "type": "text", + "content": "modules: geometry encoder, global structure extractor, region geometry generator, and local detail generator. The geometry encoder and local detail generator are similar to [6], consisting of 3D Sparse Convolutions [11] (SP-Convs) to encode and decode local geometry features. We propose a global structure extractor to extract and complete global-level features, as well as proposing the region geometry generator to decode region-level geometry shapes with long-range information. Considering the proportion of valid data in the scene, the modules at the two ends of our network process sparse voxels (shown in blue color), and the middle module processes dense voxels (shown in green color). Next, we will introduce the global structure extractor and region geometry generator in detail." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 584, + 455, + 595 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 584, + 455, + 595 + ], + "spans": [ + { + "bbox": [ + 306, + 584, + 455, + 595 + ], + "type": "text", + "content": "3.2.1 Global Structure Extractor" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "To extract similar high-dimensional features from similar structures, we introduce a global structure extractor. The global structure extractor has two branches, as shown in Fig. 3(b). Inspired by PVT [29], we design a 3D multilayer transformer pyramid structure as one branch to reshape structured voxels into non-sequential voxels and encode them, which mainly focuses on long-range global information. In order not to lose details, we also reserve CNNs as the other branch to encode local information." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18571" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 545, + 183 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 545, + 183 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 545, + 183 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 545, + 183 + ], + "type": "image", + "image_path": "20e2bc26a633b75e21cede9a6c6b7ab0cde1dd5815293576c2009499a0e9537e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 210, + 186, + 386, + 196 + ], + "lines": [ + { + "bbox": [ + 210, + 186, + 386, + 196 + ], + "spans": [ + { + "bbox": [ + 210, + 186, + 386, + 196 + ], + "type": "text", + "content": "(a) Four Modules in Dual-Scale Transformer Network" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 204, + 541, + 319 + ], + "blocks": [ + { + "bbox": [ + 47, + 204, + 541, + 319 + ], + "lines": [ + { + "bbox": [ + 47, + 204, + 541, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 541, + 319 + ], + "type": "image", + "image_path": "c06e4db6b50f3ae95c675b362d211f9485aa87eb8d5cdb0813ef2ecaa4fb50bf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 326, + 546, + 399 + ], + "lines": [ + { + "bbox": [ + 45, + 326, + 546, + 399 + ], + "spans": [ + { + "bbox": [ + 45, + 326, + 546, + 399 + ], + "type": "text", + "content": "Figure 3: Network structure and details. (a) The diagram of our DST-Net structure and its four main modules. The input for stage 1 are blocks and the input for stage 2 is a scene, respectively. Arrows indicate the flow of data in the network. The difference in DST-Net between stage 1 and stage 2 lies in the global structure extractor and region geometry generator. (b) Global structure extractor contains two branches of transformer and CNN. There is no transformer branch (marked with a dot line rectangle) in stage 2. (c) The component of region geometry generator in stage 1 and stage 2. (d) The network structure of two major components in region geometry generator: MR-CA (left column), and MR-VT (right column)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 418, + 288, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 288, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 288, + 502 + ], + "type": "text", + "content": "Then the two branches are decoded with CNNs. We use skip-connection to connect the information of the same resolution in both branches. Finally, the global features completed by these two branches are fused by a linear layer. At stage 2, we remove the transformer branch, as the scene is relatively complete, and the need for long-range information capture is reduced." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 514, + 203, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 203, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 203, + 526 + ], + "type": "text", + "content": "3.2.2 Region Geometry Generator" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": "We propose a region geometry generator to hierarchically generate accurate region shapes with long-range shape similarity. The key components of this module are the multi-resolution cross-attention (MR-CA) and the multi-resolution voxel transformer (MR-VT). The organization ways of region geometry generator in stage 1 and 2 are shown in Fig. 3(c)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Multi-resolution cross-attention. 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Contrastive attention training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 260, + 287, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 287, + 355 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 287, + 355 + ], + "type": "text", + "content": "Contrast learning enhances the performance of vision tasks by contrasting samples against each other, which learns common attributes from similar samples and discriminative attributes from distinguished ones. Inspired by the idea of contrastive learning, we propose a contrastive attention training (CAT) strategy to empower the transformers for scene completion by efficiently learning common and distinguishable shape features from the training samples." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": "Our method randomly takes a batch containing " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " blocks as input in training, and the input " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "X_{C}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " for MR-VT is a voxel set " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\{L_j,j = 0,\\dots,m_i - 1\\}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " processed from each block " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "m_{i}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " means the number of the voxels in block " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " and each voxel " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "L_{j}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " contains a shape feature within a cubic space. Unlike the general self-attention approach, where the attention operation is done between " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\{L_j,j = 0,\\dots,m_i - 1\\}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": ", we further randomly select the voxels sets from other blocks, and use all voxels in them to form a random voxel set " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\mathbb{L}:\\{L_j,j = 0,\\dots,\\sum_{i = 0}^{n - 1}m_i - 1\\}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " means the number of all the selected blocks. The physical meaning of " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " is shown in Fig.4. In brief, we use M to denote " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\sum_{i = 0}^{n - 1}m_i" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": ". Similar to MR-VT, the " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "Q_{j}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "K_{j}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "V_{j}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " are projected from " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "L_{j}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": ". In this way, we perform a cross-attention operation between n blocks in a training batch. For a certain voxel " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "L_{j}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": ", we obtain the similarity set " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\{A_{j,k},k = 0,\\dots,M - 1\\}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "L_{j}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " and all M voxels in " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " by computing the dot-product of " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "Q_{j}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "inline_equation", + "content": "K_{k}" + }, + { + "bbox": [ + 46, + 356, + 289, + 582 + ], + "type": "text", + "content": " and then normalized via softmax function:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 109, + 591, + 287, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 591, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 109, + 591, + 287, + 632 + ], + "type": "interline_equation", + "content": "A _ {j, k} = \\frac {\\exp \\left(Q _ {j} \\cdot K _ {k}\\right)}{\\sum_ {k = 0} ^ {M - 1} \\exp \\left(Q _ {j} \\cdot K _ {k}\\right)}, \\tag {3}", + "image_path": "e1244d4887c405dd6c56c67878df181cbc9fee383bd7b945b6813f18cd9b1bdf.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "spans": [ + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "text", + "content": "After obtaining the similarity set " + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "inline_equation", + "content": "\\{A_{j,k}, k = 0, \\dots, M - 1\\}" + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "text", + "content": ", we can use it to select features " + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "inline_equation", + "content": "V_k" + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "text", + "content": " derived from " + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "inline_equation", + "content": "L_k" + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "text", + "content": " to complete the voxel " + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "inline_equation", + "content": "L_j" + }, + { + "bbox": [ + 47, + 637, + 288, + 674 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 94, + 682, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 682, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 94, + 682, + 287, + 716 + ], + "type": "interline_equation", + "content": "X _ {a t t n} = S P - C o n v \\left(\\sum_ {k = 0} ^ {M - 1} A _ {j, k} \\cdot V _ {k}\\right) \\tag {4}", + "image_path": "cc5a3edbbdc179a88edfb55609fb2a5d682be7654fc53b3b03870e2e18ffcafe.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "content": "The underlying motivation is that unlike self-attention applied to individual blocks with a single layout, our contrastive attention operation requires the transformer to extract useful information from a set of random other blocks. Due to the randomness when selecting blocks in a training batch, the blocks with different layouts may share similar properties or have different attributes, which may be useful or detrimental. By explicitly adding extra information, transformers are required to identify whether the extra information is useful or not by attention scores. The learning strategy enables transformers to learn geometric features with a higher degree of discrimination, thereby improving the completion ability. We evaluate different values for " + }, + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "content": " with 2, 4, and 8. The experimental results indicate that the completion performance reaches its best for " + }, + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "content": " equal to 8." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 258, + 496, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 496, + 271 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 496, + 271 + ], + "type": "text", + "content": "3.4. Loss Function and Data Generation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": "Geometry loss. We train the network with three geometry loss items: depth loss " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "L_{D}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": ", 3D normal loss " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "L_{N}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": ", and structure loss " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "L_{S}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": ". Given a voxel " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": ", depth loss " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "L_{D}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " is used to calculate the difference between the predicted depth " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "D_{v}^{P}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " and the target depth " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "D_{v}^{T}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": ". The 3D normal loss " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "L_{N}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " constrains the predicted normal " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "N_{v}^{P}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " and the target normal " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "N_{v}^{T}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " is the set of voxels to be calculated:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 366, + 366, + 545, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 366, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 366, + 366, + 545, + 396 + ], + "type": "interline_equation", + "content": "L _ {D} = \\frac {1}{V} \\sum_ {v \\in V} \\left\\| D _ {v} ^ {P} - D _ {v} ^ {T} \\right\\| _ {1} \\tag {5}", + "image_path": "ba92b6e66ebc1c241542f20aed04e6e4283f8b19e66410115081411faae0a650.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 365, + 404, + 545, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 404, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 365, + 404, + 545, + 433 + ], + "type": "interline_equation", + "content": "L _ {N} = \\frac {1}{V} \\sum_ {v \\in V} \\left| \\left| N _ {v} ^ {P} - N _ {v} ^ {T} \\right| \\right| _ {1} \\tag {6}", + "image_path": "c149556f47099057ead46dbdf4dad99f19fc037e326075cf6d56c23aa1494beb.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": "Normal loss is used to constrain the geometry structures by calculating local depth variations. However, for more complex geometry structures, like various concave and convex shapes, it is difficult to complete them well only with normal loss. Inspired by normal loss, we introduce the structure loss " + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "inline_equation", + "content": "L_{S}" + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": " to further constrain the geometry structures by calculating local normal variations." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 310, + 522, + 422, + 592 + ], + "blocks": [ + { + "bbox": [ + 310, + 522, + 422, + 592 + ], + "lines": [ + { + "bbox": [ + 310, + 522, + 422, + 592 + ], + "spans": [ + { + "bbox": [ + 310, + 522, + 422, + 592 + ], + "type": "image", + "image_path": "06195e7da7e7898902a61651de58b7c73df26fc1b2ec11c81865871365c37c80.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 334, + 594, + 402, + 605 + ], + "lines": [ + { + "bbox": [ + 334, + 594, + 402, + 605 + ], + "spans": [ + { + "bbox": [ + 334, + 594, + 402, + 605 + ], + "type": "text", + "content": "predicted normals" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 455, + 521, + 542, + 594 + ], + "blocks": [ + { + "bbox": [ + 455, + 521, + 542, + 594 + ], + "lines": [ + { + "bbox": [ + 455, + 521, + 542, + 594 + ], + "spans": [ + { + "bbox": [ + 455, + 521, + 542, + 594 + ], + "type": "image", + "image_path": "11ad3f650cf38d6309f9b324b971cb65f75da68a958e910559ff1b49706013df.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 463, + 594, + 509, + 604 + ], + "lines": [ + { + "bbox": [ + 463, + 594, + 509, + 604 + ], + "spans": [ + { + "bbox": [ + 463, + 594, + 509, + 604 + ], + "type": "text", + "content": "GT normals" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 615, + 545, + 639 + ], + "lines": [ + { + "bbox": [ + 305, + 615, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 305, + 615, + 545, + 639 + ], + "type": "text", + "content": "Figure 5: Visual comparison of two different local structures." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": "As shown in Fig. 5, " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "N_{i,j,k}^{P}" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": " denotes the normal of a predicted voxel, " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "N_{i+1,j,k}^{P}, N_{i,j+1,k}^{P}" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "N_{i,j,k+1}^{P}" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": " denote the normals of its three adjacent voxels, where " + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "inline_equation", + "content": "i,j,k" + }, + { + "bbox": [ + 304, + 651, + 547, + 713 + ], + "type": "text", + "content": " represent voxel coordinates in three directions respectively. The GT normals are represented in a similar fashion. In a brief," + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18573" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": "we use " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "N_{v}^{P}, N_{vx}^{P}, N_{vy}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "N_{vz}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": " to denote " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "N_{i,j,k}^{P}, N_{i+1,j,k}^{P}, N_{i,j+1,k}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "N_{i,j,k+1}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": ", as well as the GT normals. The normal loss of a single predicted voxel is small when calculated with GT, while the local structures of the predicted case and GT are totally different due to the accumulation of normal variations. Therefore, we use the dot-product similarity between " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "N_{v}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "N_{vx}^{P}, N_{vy}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "N_{vz}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": " to get " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "S_{vx}^{P}, S_{vy}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "S_{vz}^{P}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": " as structure descriptors, as shown in Equation (7), to describe the local variation of normals. The structure descriptors of GT are calculated in the same way. The loss " + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "inline_equation", + "content": "L_{S}" + }, + { + "bbox": [ + 47, + 70, + 289, + 232 + ], + "type": "text", + "content": " between predicted and target structure descriptors enable the whole predicted geometry structure to represent GT more accurately." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 132, + 245, + 203, + 260 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 245, + 203, + 260 + ], + "spans": [ + { + "bbox": [ + 132, + 245, + 203, + 260 + ], + "type": "interline_equation", + "content": "S _ {v x} ^ {P} = N _ {v x} ^ {P} \\cdot N _ {v} ^ {P}", + "image_path": "4b94e7be87a2302d4f9a5af38d7bea5cf22e2e45519b55344dbbdbd9fa5e2f2a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 133, + 262, + 287, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 262, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 133, + 262, + 287, + 277 + ], + "type": "interline_equation", + "content": "S _ {v y} ^ {P} = N _ {v y} ^ {P} \\cdot N _ {v} ^ {P} \\tag {7}", + "image_path": "79503f3bfa50936f09dc2925efc54a44517b8a1c97854d393d4f13ed49f0cf45.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 133, + 279, + 203, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 279, + 203, + 293 + ], + "spans": [ + { + "bbox": [ + 133, + 279, + 203, + 293 + ], + "type": "interline_equation", + "content": "S _ {v z} ^ {P} = N _ {v z} ^ {P} \\cdot N _ {v} ^ {P}", + "image_path": "5ad66b98866cf628b62e8a2220e0edccdd23deec57933640de5d9771a515c5ad.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 97, + 307, + 287, + 336 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 307, + 287, + 336 + ], + "spans": [ + { + "bbox": [ + 97, + 307, + 287, + 336 + ], + "type": "interline_equation", + "content": "L _ {S} = \\frac {1}{V} \\sum_ {v \\in V} \\left\\{\\frac {1}{3} \\left(\\left| \\left| S _ {v x} ^ {P} - S _ {v x} ^ {T} \\right| \\right| _ {1} + \\right. \\right. \\tag {8}", + "image_path": "e1a8f15302066bb1b75bc99dae940525f1ba1da8394bccbd56b2864885447480.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 99, + 338, + 236, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 338, + 236, + 354 + ], + "spans": [ + { + "bbox": [ + 99, + 338, + 236, + 354 + ], + "type": "interline_equation", + "content": "| | S _ {v y} ^ {P} - S _ {v y} ^ {T} | | _ {1} + | | S _ {v z} ^ {P} - S _ {v z} ^ {T} | | _ {1}) \\}", + "image_path": "480f6693275a4affa5336b7587e8308f0d478eae63f79de69df5ca533388a55e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "text", + "content": "CIoT loss. Considering incomplete real-world data, we propose CIoT (Cube Intersection over Target) loss to make output voxel distribution fit the target. Due to the voxel sparsity, the same IoT may represent a completely different distribution. To address it, we divide the entire output into " + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "text", + "content": " small cubes of the same size. In a cube, " + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "inline_equation", + "content": "C_i^P" + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "inline_equation", + "content": "C_i^T" + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "text", + "content": " represent the number of predicted voxels and the number of target voxels, respectively. We only calculate the loss in the cube where " + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "inline_equation", + "content": "C_i^T > 0" + }, + { + "bbox": [ + 47, + 358, + 289, + 467 + ], + "type": "text", + "content": ". CIoT loss is defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 102, + 471, + 287, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 471, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 102, + 471, + 287, + 500 + ], + "type": "interline_equation", + "content": "L _ {C I o T} = 1 - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\frac {C _ {i} ^ {P} \\cap C _ {i} ^ {T}}{C _ {i} ^ {T}} \\tag {9}", + "image_path": "04392a2672d0ab8335ab7b59d80882b5d5d6ec8267e149b322080eacb841568e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 504, + 289, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 289, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 289, + 649 + ], + "type": "text", + "content": "Data Generation. Both input and target in training are the representation of sparse TSDF voxel with depth information, obtained from RGB-D frames by the method of voxel fusion [3]. Following the self-supervised learning approach of SG-NN [6], the training target (GT) in stage 1 is generated using all RGB-D frames, while a certain proportion is used in getting input. The training target in stage 2 is obtained by fusing the output and target of stage 1. To focus on learning problem regions and minimize error accumulation, we select the TSDF value of target 1 voxel as the value for target 2 voxel when the coordinates of output and target of stage 1 coincide." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 657, + 191, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 191, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 191, + 671 + ], + "type": "text", + "content": "4. Experiments and Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "To validate our proposed method, we use the Mather-port3D [2] dataset as the training data and conduct the comparison experiments on both real-world data and synthetic" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 339, + 70, + 512, + 130 + ], + "blocks": [ + { + "bbox": [ + 339, + 70, + 512, + 130 + ], + "lines": [ + { + "bbox": [ + 339, + 70, + 512, + 130 + ], + "spans": [ + { + "bbox": [ + 339, + 70, + 512, + 130 + ], + "type": "table", + "html": "
MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet1.480.510.54
SG-NN0.650.690.62
SPSG0.350.740.53
Ours0.230.780.61
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The resolution of all voxels is " + }, + { + "bbox": [ + 304, + 163, + 545, + 331 + ], + "type": "inline_equation", + "content": "2\\mathrm{cm}" + }, + { + "bbox": [ + 304, + 163, + 545, + 331 + ], + "type": "text", + "content": ". The training blocks are all " + }, + { + "bbox": [ + 304, + 163, + 545, + 331 + ], + "type": "inline_equation", + "content": "128 \\times 64 \\times 64" + }, + { + "bbox": [ + 304, + 163, + 545, + 331 + ], + "type": "text", + "content": " size cutting from the scene, and parameter " + }, + { + "bbox": [ + 304, + 163, + 545, + 331 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 163, + 545, + 331 + ], + "type": "text", + "content": " in contrastive attention training strategy is 8. The four terms in the loss function have equal weights. Our stage 1 model training takes about 72 hours, and the stage 2 model training takes about 24 hours. Three state-of-the-art methods of ConvOccNet [21], SG-NN [6] and SPSG (only with geometry) [8] are used to compare with ours on the metrics of Chamfer Distance (CD) in metric space, Recall, and Precision. For real-world unobserved space, we ignore it for the CD evaluation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 342, + 471, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 471, + 357 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 471, + 357 + ], + "type": "text", + "content": "4.1. Completion on Matterport3D" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 363, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 507 + ], + "type": "text", + "content": "First, we compare four methods on 394 other rooms from the Matterport3D dataset. We provide the same incomplete TSDF input, except for ConvOccNet, which requires the corresponding mesh to be pre-computed as input. Some scene completion results are shown in Fig. 6(a). In visual effect, our method completes more parts in the scenes than the other three methods, which is consistent with the recall metric in Tab. 1. The highest score on CD proves that our method's shape accuracy is the best. As the GT is incomplete and the more completion areas from our method have no corresponding GT, our precision is less than the SG-NN under this special condition." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 518, + 470, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 518, + 470, + 532 + ], + "spans": [ + { + "bbox": [ + 305, + 518, + 470, + 532 + ], + "type": "text", + "content": "4.2. Completion on Synthetic Data" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 538, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 545, + 624 + ], + "type": "text", + "content": "The synthetic dataset ICL-NUIM [12] has 3D surface ground truth so that it can provide a more comprehensive evaluation. As the scan frames are indoors, we only select the mesh of the surface inside the room to evaluate. Qualitative and quantitative evaluations are shown in Fig. 6(b) and Tab. 2. Owing to the full GT, the results fairly reflect our method's superiority over the other three methods." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 633, + 444, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 633, + 444, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 633, + 444, + 647 + ], + "type": "text", + "content": "4.3. 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The Fig. 6(c) are the visualization results, and Tab. 3 shows the quantitative results." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18574" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 49, + 549, + 250 + ], + "blocks": [ + { + "bbox": [ + 50, + 49, + 549, + 250 + ], + "lines": [ + { + "bbox": [ + 50, + 49, + 549, + 250 + ], + "spans": [ + { + "bbox": [ + 50, + 49, + 549, + 250 + ], + "type": "image", + "image_path": "3ab6dece3038d35b9d733c13a5df176c649afbabcc872422e7e5ee64638a5294.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 268, + 252, + 328, + 262 + ], + "lines": [ + { + "bbox": [ + 268, + 252, + 328, + 262 + ], + "spans": [ + { + "bbox": [ + 268, + 252, + 328, + 262 + ], + "type": "text", + "content": "(a)Matterport3D" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 266, + 545, + 407 + ], + "blocks": [ + { + "bbox": [ + 51, + 266, + 545, + 407 + ], + "lines": [ + { + "bbox": [ + 51, + 266, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 51, + 266, + 545, + 407 + ], + "type": "image", + "image_path": "c0a3a2a9a22e9524fefe1988a67e64a173222e9a54af9d0e49cc25dd6e5f5059.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 422, + 547, + 599 + ], + "blocks": [ + { + "bbox": [ + 272, + 411, + 323, + 421 + ], + "lines": [ + { + "bbox": [ + 272, + 411, + 323, + 421 + ], + "spans": [ + { + "bbox": [ + 272, + 411, + 323, + 421 + ], + "type": "text", + "content": "(b) ICL-NUIM" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 422, + 547, + 599 + ], + "lines": [ + { + "bbox": [ + 50, + 422, + 547, + 599 + ], + "spans": [ + { + "bbox": [ + 50, + 422, + 547, + 599 + ], + "type": "image", + "image_path": "0b11f4ac0aac835720eeb254639aace7bffaca06a850fcd07ad4714b4ab299bb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 278, + 602, + 318, + 613 + ], + "lines": [ + { + "bbox": [ + 278, + 602, + 318, + 613 + ], + "spans": [ + { + "bbox": [ + 278, + 602, + 318, + 613 + ], + "type": "text", + "content": "(c) ScanNet" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 78, + 622, + 513, + 635 + ], + "lines": [ + { + "bbox": [ + 78, + 622, + 513, + 635 + ], + "spans": [ + { + "bbox": [ + 78, + 622, + 513, + 635 + ], + "type": "text", + "content": "Figure 6: Qualitative comparisons with state-of-the-art methods on Matterport3D, ICL-NUIM and ScanNet." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 655, + 140, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 655, + 140, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 655, + 140, + 668 + ], + "type": "text", + "content": "4.4. 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MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet0.610.170.28
SG-NN0.310.310.42
SPSG0.250.350.39
Ours0.180.390.45
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MethodCD(×10-1)↓Recall↑Precision↑
ConvOccNet0.650.790.43
SG-NN0.360.850.50
SPSG0.300.860.45
Ours0.260.880.48
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MethodCD(×10-1)↓Recall↑Precision↑
Stage10.220.770.60
Full model0.230.780.61
Full model (train with only GT)0.460.720.60
Only Stage20.490.720.57
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MethodCD(×10-1)↓Recall↑Precision↑
SG-NN (40%)0.670.680.61
SPSG (40%)0.360.730.53
Ours (40%)0.230.770.60
SG-NN (30%)0.730.670.61
SPSG (30%)0.430.720.52
Ours (30%)0.240.770.60
SG-NN (20%)1.060.600.58
SPSG (20%)0.730.650.49
Ours (20%)0.470.720.56
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MethodCD(×10-1)↓Recall↑Precision↑
Stage10.220.770.60
Stage1(w/o GSE)0.320.740.57
Stage1(w/o RGG)0.260.750.58
Stage1(w/o CAT)0.240.750.59
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MethodCD(×10-1)↓Recall↑Precision↑
w/o LCloT0.250.750.60
w/o LS0.260.750.56
w/o LN0.260.740.56
w/o LD0.290.750.54
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We validate the effect of " + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "L_{CIoT}" + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "L_S" + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "L_N" + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "text", + "content": " loss on our method, and validate the case where only " + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "L_D" + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "text", + "content": " loss is applied. Tab. 7 shows the quantitative evaluation of the loss items. Fig. 11 shows the qualitative evaluation of the loss items. We can see that with " + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "L_{CIoT}" + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "text", + "content": ", the completeness of local scene completion has been improved, while " + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "L_S" + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "L_N" + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "text", + "content": " effectively constrain the accuracy of the shapes and planes, respectively. From the comparison with the results of only using " + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "L_D" + }, + { + "bbox": [ + 47, + 352, + 287, + 483 + ], + "type": "text", + "content": " loss, we can find that various losses acting on the connection between voxels improve the completion accuracy and completeness." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 495, + 119, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 119, + 506 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 119, + 506 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 514, + 287, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 646 + ], + "type": "text", + "content": "In this work, we have proposed a dual-scale transformer method with a two-stage completion strategy to generate fairly complete scenes from real-world incomplete RGB-D scans. Our proposed contrastive attention training strategy encourages the transformers to learn distinguishable features. We introduce two new losses to constrain geometric accuracy and completeness. However, due to the limitation of memory, currently, we only use geometric information and solve the geometric completion. In the future, we would consider scene completion with other priors such as color and semantic information." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 658, + 117, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 117, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 117, + 669 + ], + "type": "text", + "content": "6. Limitation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "First, our method only completes the geometric surface, without including the texture. In some conditions, the texture is also necessary. 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Second, surface completion mainly provides reasonable inference for the missing parts, rather than replacing the accurate reconstruction. When the geometric information of the input scene is not enough to infer the entire scene, our geometry completion result may not be accurate. Although our method does not need the GT of the complete scene, it still needs a large amount of indoor data to ensure its generalization." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 560, + 403, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 560, + 403, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 403, + 574 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 580, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 580, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 306, + 580, + 545, + 628 + ], + "type": "text", + "content": "Chunxia Xiao is partially supported by NSFC (No.61972298), Bingtuan Science and Technology Program (No.2019BC008), and CAAI-Huawei MindSpore Open Fund." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 307, + 638, + 365, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 638, + 365, + 651 + ], + "spans": [ + { + "bbox": [ + 307, + 638, + 365, + 651 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 310, + 658, + 547, + 712 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 658, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 310, + 658, + 547, + 712 + ], + "type": "text", + "content": "[1] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. 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However, most existing works only employ visual backbones pre-trained either with independent images for classification or with self-supervised learning methods to adapt to the indoor navigation domain, neglecting the spatial relationships that are essential to the learning of navigation. Inspired by the behavior that humans naturally build semantically and spatially meaningful cognitive maps in their brains during navigation, in this paper, we propose a novel navigational-specific visual representation learning method by contrasting the agent's egocentric views and semantic maps (Ego $^2$ -Map). We apply the visual transformer as the backbone encoder and train the model with data collected from the large-scale Habitat-Matterport3D environments. Ego $^2$ -Map learning transfers the compact and rich information from a map, such as objects, structure and transition, to the agent's egocentric representations for navigation. Experiments show that agents using our learned representations on object-goal navigation outperform recent visual pre-training methods. Moreover, our representations significantly improve vision-and-language navigation in continuous environments for both high-level and low-level action spaces, achieving new state-of-the-art results of $47\\%$ SR and $41\\%$ SPL on the test server.", + "bbox": [ + 75, + 353, + 473, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 775, + 209, + 791 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual representations for navigation should capture the rich semantics and the complex spatial relationships of the observations, which helps the agent to recognize visual entities and its transition in space for effective exploration. However, previous works usually adopt visual backbones", + "bbox": [ + 75, + 800, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "which only focus on capturing the semantics of a static image, ignoring its connection to the agent or the correspondence to other views in a continuous environment [3, 9, 40, 42, 51, 68, 98]. One common approach is to apply encoders pre-trained for object/scene classification (e.g. ResNet [39] on ImageNet [80]/Places365 [102]), object detection (e.g. RCNN [38, 78] on VisualGenome [52]/MSCOCO [57]) or semantic segmentation (e.g. RedNet [45] on SUN RGBD [87]), or more recently, to use CLIP [72], which is trained for aligning millions of images and texts to encode agent's RGB observations [31, 46, 84]. Despite the increasing generalization ability of the features and rising zero-shot performance on novel targets, there still exists a large visual domain gap between these features and the features suitable for navigation since they lack the expressiveness of spatial relationships. For example, the connection between time-dependent observations and the correspondence between egocentric views and the spatial structure of an environment, which are important to decision making during navigation.", + "bbox": [ + 500, + 321, + 893, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We suggest that there are two main difficulties in learning navigational-specific visual representations in previous research; First, there lacked a large-scale and realistic dataset of indoor environments. Popular datasets such as Matterport3D [8] and Gibson [95] provide traversable scenes rendered from real photos, but either the number of scenes is very limited, or the quality of the 3D scan is low. Synthetic datasets such as ProcTHOR [22] contain 10K generated scenes, but they are unrealistic and simple and do not capture the full complexity of real-world environments. Second, fine-tuning visual encoders while learning to navigate is very expensive because of the long traveling horizon, especially in tasks that require extensive exploration [4, 53, 63, 86]. Moreover, due to the scene scarcity, fine-tuning visual encoders is unlikely to generalize well to the novel environments. To address these problems, a large amount of research has been dedicated to augmenting the environments, either editing the agent's observations", + "bbox": [ + 496, + 628, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Intern at Adobe Research.", + "bbox": [ + 101, + 886, + 246, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3055", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[56, 90] or adding objects [62], building new spatial structures [58], applying web-images to replace the views of the same categories [35] or generating new scenes [47, 48, 55]. Unlike augmentation, which essentially requires the agent's policy network to adapt new visual data, another strategy is to first pre-train the visual encoder before learning to navigate. Those methods usually apply images captured in 3D scenes and perform self-supervised learning or tune the encoder with proxy tasks (e.g. masked region modeling, angular prediction) to mitigate the domain gap and introduce spatial awareness [15, 17, 96, 98]. Furthermore, recent works tend to apply CLIP [72] to process visual inputs, as the model can provide powerful representations for grounding semantic and spatial concepts, hence facilitating learning [1, 31, 46, 83, 84, 85]. Although these methods have demonstrated significant improvements on navigation performance, they either only use more data without addressing the learning problem, not generalizable across different tasks, or ignore the spatial correspondence between consecutive frames which the agent will capture as it moves.", + "bbox": [ + 76, + 90, + 472, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspire by the research in cognitive science that humans naturally build virtual maps from perspective observations that are helpful to track semantics, spaces and movements during navigation [29, 91, 92]; we propose a contrastive learning method between the agent's Egocentric view pairs and top-down semantic Maps (Ego $^2$ -Map) for training visual encoders appropriate for navigation. Specifically, we first sample RGBD images and create corresponding semantic maps [7] from the large-scale Habitat-Matterport3D environments (HM3D) [74, 82] which contains hundreds of photo-realistic scenes, obtaining abundant and effective visual data. Then, we encode the sampled RGBD observations and the semantic maps with two separate visual backbones, respectively, and train the entire model with our Ego $^2$ -Map contrastive learning. Once trained, the RGBD encoder will be plugged into an agent's network to facilitate visual perception. We argue that the map contains very rich and compact visual clues such as spatial structure, accessible areas and unexplored regions, object entities and their arrangement, as well as the agent's transition in the environment that are essential to navigation. Compared to existing online mapping-based approaches [10, 14, 32, 44], Ego $^2$ -Map learning efficiently produces visual features that imply a complete map of the space known a view priori, while the online map is only a partial map. Importantly, Ego $^2$ -Map explores a new possibility of modeling semantics and structures from simple RGBD inputs, which its resulting features are directly applicable to non-mapping-based navigational models and effectively generalizable to different tasks.", + "bbox": [ + 76, + 397, + 472, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We mainly evaluate the features learned from Ego $^2$ -Map on the Room-to-Room Vision-and-Language Navigation in Continuous Environments (R2R-CE) [3, 51] task, which requires an agent to navigate in photo-realistic environ", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ments following human natural language instructions such as \"Leave the bedroom and enter the kitchen. Walk forward and take a left at the couch. Stop in front of the window.\" Addressing R2R-CE highly relies on exploiting the correspondence between contextual clues and the agent's observations, hence it is crucial for the visual encoder to provide semantic and structural meaningful representations. We found that the proposed $\\mathsf{Ego}^2$ -Map features significantly boost the agent's performance, obtaining $+3.56\\%$ and $+5.10\\%$ absolute SPL improvements over the CLIP baseline [72] under the settings of high-level and low-level action spaces, respectively, and achieves the new best results on the R2R-CE test server. Moreover, our experiments show that $\\mathsf{Ego}^2$ -Map learning also outperforms other visual representation learning methods such as OVRL [96] on the Object-Goal Navigation task (ObjNav), suggesting the strong generalization potential of the proposed methods.", + "bbox": [ + 496, + 90, + 893, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 359, + 640, + 376 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Navigation A great variety of scenarios have been proposed to learn visual navigation in photo-realistic environments [8, 21, 54, 82, 86, 89, 95] with different modalities of inputs, targets and action spaces [3, 4, 11, 13, 51, 66, 70, 94]. Due to the distinct nature of the tasks, diverse methods are investigated accordingly. For instance, in Object-Nav, which only provides a high-level goal and requires exploration, mapping-based methods are frequently applied [10, 32, 60, 73, 105], whereas in vision-and-language navigation (VLN) [3], large vision-language models are employed to match instructions and agent's observations [42, 61, 71, 83, 103] to perform panoramic actions [30]. Recently, there is an emerging trend of scaling up the training data to address the common data scarcity issue, either in terms of the number of environments [22, 74] or the amount of supervision [16, 76, 93]. Unlike most of the previous works, we focus on improving the visual backbone, aiming to produce robust and generalizable visual representations specialized for navigation.", + "bbox": [ + 496, + 383, + 893, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Representations for Embodied AI Recent years have witnessed a trend of moving away from visual encoders pre-trained for object classification in Embodied AI due to their inefficiency in representing complex real-world scenes or mapping to actions. Instead, large vision-language models such as CLIP which demonstrates strong zero-shot performance across visual domains is widely applied [20, 72], enhancing the semantic representations in robotic manipulation [85], assisting 3D trajectory modification and speed control [5], benefiting the language-conditioned view-selection problem in VLN [83, 84] as well as improving other control and navigation results [31, 46, 67]. Moreover, EmbCLIP shows that the CLIP features provide much better semantic and geometric primitives such as", + "bbox": [ + 496, + 688, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3056", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b78fbc0aa404047ef0a0bc5bea16e2ab0c5b538207b8c36e2c974dce5db20f3b.jpg", + "image_caption": [ + "Figure 1: Network architecture. The Semantic MapNet [7] is applied to draw a semantic map using observations captured from a source to a target position. Then, two learnable visual encoders are applied to encode the egocentric views and the map, respectively, followed by non-linear headers $\\Pi_{i}$ and $\\Pi_{m}$ to learn the Ego $^2$ -Map contrastive objective $\\mathcal{L}_c$ . $f_{s}$ and $f_{t}$ are the paired view features of a trajectory (see §3.2). Dash arrows indicate pre-processing without gradient update." + ], + "image_footnote": [], + "bbox": [ + 84, + 90, + 883, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "object presence, object reachability, and free space that are valuable to Embodied AI [46]. In terms of self-supervised visual representation learning for indoor navigation, recent works that are the most relevant to ours include OVRL [96] which applies knowledge distillation based on DINO [6], EPC which predicts masked observations from a trajectory [75], and CRL which jointly learns a visual encoder with a policy network that maximizes the representation error [27]. In contrast to all previous works, this paper explores a novel idea of encoding the explicit structural and semantic information available in maps implicitly in the visual encoder thereby facilitating efficient and effective generalization across different visual navigation tasks and models.", + "bbox": [ + 75, + 402, + 472, + 616 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Exploiting Visual Features A great variety of proxy tasks and auxiliary objectives have been applied to exploit information from the visual data which is beneficial to navigation. For instance, Ye et al. [98, 99] promote understanding of spatiotemporal relations of observations by estimating the timestep difference between two views, Qi et al. [69] predict room-types from object features to improve scene understanding, and Se et al. [81] determine the furthest reachable waypoint on a topological graph using the node observations. To extract the geometric information, Gordon et al. [34] use the encoded visual features to predict depth and surface normals, reconstruct RGB input, and forecast the visual features by taking certain actions. Depth prediction has also been studied by Mirowski et al. [64], Desai et al. [24] and Chattopadhyay et al. [12], along with learning the inverse dynamics by predicting an action taken between two sequential observations [37, 64]. Complement", + "bbox": [ + 75, + 643, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tary to the previous methods for interpreting visual features, our Ego $^2$ -Map learning guides a visual encoder to produce representations with expressive spatial information.", + "bbox": [ + 496, + 402, + 893, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Contrastive Learning between Egocentric Views and Semantic Maps (Ego $^2$ -Map)", + "text_level": 1, + "bbox": [ + 498, + 463, + 893, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We will first describe the overall network architecture for training the visual encoders (§3.1), followed by the details of Ego²-Map objectives (§3.2), as well as two other widely applied spatial-aware auxiliary tasks which we investigated with our Ego²-Map learning (§3.3). Then, we will talk about the data collection (§3.4) and network training (§3.5) processes.", + "bbox": [ + 496, + 506, + 893, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Network Architecture", + "text_level": 1, + "bbox": [ + 500, + 623, + 705, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We build the network for $\\mathrm{Ego}^2$ -Map learning based on a ViT-B/16 model (default initialized from CLIP [72], whose effect will be studied in §4.3). Unlike previous methods for visual navigation, which mostly employ two independent encoders to process RGB and depth images, we investigate a compact representation by feeding RGB+Depth as four-channel inputs (Figure 1). To merge the two visual modalities, we use two separate convolutional layers to encode the RGB channels $I_{rgb}$ and the depth map $I_d$ , respectively, followed by a token-wise concatenation and a non-linear projection $\\Pi_v$ to merge the resulting feature maps before feeding to the transformer layers as", + "bbox": [ + 496, + 646, + 893, + 829 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv _ {r g b} = \\operatorname {C o n v} _ {r g b} \\left(I _ {r g b}\\right), \\quad v _ {d} = \\operatorname {C o n v} _ {d} \\left(I _ {d}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 840, + 890, + 858 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 501, + 869, + 529, + 883 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf = \\operatorname {V i T} \\left(\\boldsymbol {\\Pi} _ {v} \\left[ v _ {r g b}; v _ {d} \\right]\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 883, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3057", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The pooled features $f$ of the RGBD encoder are applied for learning all spatial-aware objectives $\\mathcal{L}_{\\theta}$ , $\\mathcal{L}_d$ and $\\mathcal{L}_c$ , which will be specified in the following.", + "bbox": [ + 76, + 90, + 470, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. $\\mathbf{Ego}^2$ -Map Contrastive Objective", + "text_level": 1, + "bbox": [ + 76, + 150, + 366, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The motivation of this task is to introduce the information within a map to single-view features, offering the agent high-level semantic and spatial clues to navigate towards distant targets. Specifically, we build positive samples by coupling a views-pair $(I_s$ and $I_t$ from the two endpoints of a path) with a top-down semantic map $M$ that represents the agent's transition and observations along the path, while using mismatched views-pairs and maps of different routes or environments as the negatives. Each semantic map is generated by the off-the-shelf Semantic MapNet [7], using the RGBD observations collected by an agent traveling from the source view $I_s$ to the target view $I_t$ via the shortest path $^2$ . The semantic map provides abundant information about the open space, obstacles, unexplored regions, observed objects, and the agent's action, which we consider as highly valuable and compact representations for agent navigation (see maps in Figure 2). To encode $M$ , we apply an additional ViT-B/32 [25] with the last three transformer layers unfrozen to adapt the map images. Then, the egocentric features of the two views $f_s$ and $f_t$ , and the map features $f_m$ will be passed to two MLP (multi-layer perceptrons) headers $\\Pi_i$ and $\\Pi_m$ , respectively, to compute an alignment score as:", + "bbox": [ + 75, + 175, + 472, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc ^ {I} = \\boldsymbol {\\Pi} _ {i} [ f _ {s}; f _ {t} ], \\qquad c ^ {M} = \\boldsymbol {\\Pi} _ {m} [ f _ {m} ] \\qquad (3)\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 536, + 468, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 76, + 569, + 106, + 583 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\langle c ^ {I}, c ^ {M} \\rangle = \\frac {c ^ {I} \\cdot c ^ {M}}{\\| c ^ {I} \\| \\| c ^ {M} \\|} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 584, + 468, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, the InfoNCE loss [65, 101] is applied for $\\mathrm{Ego}^2$ -Map contrastive learning. For each $j$ -th views-map pair in a minibatch of size $N$ , we have", + "bbox": [ + 76, + 628, + 468, + 674 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c, j} = \\mathcal {L} _ {c, j} ^ {I \\rightarrow M} + \\mathcal {L} _ {c, j} ^ {M \\rightarrow I} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 686, + 468, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the views to maps $(I\\to M)$ loss can be expressed as", + "bbox": [ + 76, + 720, + 464, + 736 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c, j} ^ {I \\rightarrow M} = - \\log \\frac {\\exp \\left(\\left\\langle c _ {j} ^ {I} , c _ {j} ^ {M} \\right\\rangle / \\tau\\right)}{\\sum_ {k = 1} ^ {N} \\exp \\left(\\left\\langle c _ {j} ^ {I} , c _ {k} ^ {M} \\right\\rangle / \\tau\\right)} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 750, + 468, + 790 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and the map to views loss $\\mathcal{L}_{c,j}^{M\\to I}$ likewise. Parameter $\\tau \\in \\mathbb{R}_+$ denotes a learnable temperature.", + "bbox": [ + 76, + 804, + 468, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Other Spatial-Aware Objectives", + "text_level": 1, + "bbox": [ + 500, + 90, + 781, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We investigate two additional widely applied proxy tasks with our Ego $^2$ -Map learning. Note that we do not claim any novelty for applying these tasks but focus on studying their effect on training the representations.", + "bbox": [ + 498, + 114, + 892, + 175 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Angular Offset Prediction Given two images taken from random headings at the same position, the task predicts the angular offset between them to facilitate the modeling of correspondence between views. A similar proxy task has been applied in previous works, which predicts discrete angles and uses an extra directional encoding to imply orientation [15] or regresses the agent's turning angle conditioned on language during navigation [104]. Specifically, we pass the two pooled RGBD features $f_{\\theta_0}$ and $f_{\\theta_1}$ , corresponding to images at two orientations of the same viewpoint, into a learnable non-linear header $\\Pi_{\\theta}$ to predict the offset as $\\theta^p = \\Pi_{\\theta}[f_{\\theta_0};f_{\\theta_1}]$ . The task is learned by minimizing the mean squared error $\\mathcal{L}_{\\theta} = E[(\\theta^p - \\theta^*)^2]$ , where $\\theta^*$ is the ground-truth angular difference between $[-\\pi, \\pi]$ , denoting either clockwise or counter-clockwise rotation whichever is closer to encourage agent's efficient rotation.", + "bbox": [ + 498, + 195, + 893, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Explorable Distance Prediction To benefit the searching of explorable regions and assist obstacle avoidance, the task estimates the agent's maximal distance to forward without being blocked by any obstacle [11, 36]. Using the same notations as above, the module regresses a value from an RGBD image as $d^{p} = \\Pi_{d}[f]$ , and is trained with supervision $\\mathcal{L}_d = E[(d^p - d^*)^2]$ . We cap the ground-truth distance $d^{*}$ in the range of 0.5 to 5.0 meters to match the common range of the agent's depth sensors.", + "bbox": [ + 498, + 458, + 892, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Data Collection", + "text_level": 1, + "bbox": [ + 500, + 604, + 656, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We follow the train-validation-test split of the HM3D scenes [74] and use the first 800 environments for learning. We randomly sample 252,537 viewpoint positions from the environments (see Figure 3) and render more than a million RGBD images from those positions to create 500,000 $(I_{\\theta_0}, I_{\\theta_1})$ views pairs as well as 500,000 $(I_s, I_t, M)$ triplets for learning $\\mathcal{L}_{\\theta}$ and $\\mathcal{L}_c$ , respectively, while using all the images to learn $\\mathcal{L}_d$ . The positions are sampled such that all points must be located in the open space and the minimal geodesic distance between any two points is greater than 0.40 meters. Each image collected for $\\mathrm{Ego}^2$ -Map contrastive learning is either a unique source or target view in all trajectories, and each trajectory is created by computing the shortest path between two randomly paired views within a 7 meters range. We feed the RGBD images captured from a trajectory to the Semantic MapNet [7] for drawing the corresponding semantic map. Note that the Semantic MapNet is trained on the MP3D environments [8], but we found that", + "bbox": [ + 498, + 628, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2Each resulting map is unique because the observations are determined by the unique path (actions) for connecting two views. For example, in Figure 2, only the colored regions in the map $(M)$ are the areas seen by the agent when traveling from the source to the target positions.", + "bbox": [ + 75, + 849, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3058", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1aba1a5107cfdb7683fadb67e2e841058457e25a2c3ced6ca77108e599e45a02.jpg", + "image_caption": [ + "Figure 2: Illustration of $\\mathbf{Ego}^2$ -Map contrastive learning. The method encodes the paired source and target egocentric views $(I_s, I_t)$ into feature $c^I$ , then learns to align it with the feature $c^M$ of the corresponding top-down map $M$ . Negative view pairs $(I_{s'}, I_{t'})$ and maps $(M')$ are sampled from different trajectories or different environments, which are pushed away from the reference pair. The blue dashed line on the left part of the figure indicates the agent's trajectory, which is visualized with directional color in map $M$ . The map is also powered with semantic information (denoted at the bottom right)." + ], + "image_footnote": [], + "bbox": [ + 107, + 94, + 869, + 354 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9b74359821ca4a8192244811aa642b5ec5a229167ff5d2534b3c0ce2d8b8c347.jpg", + "image_caption": [ + "(a) 3D scan" + ], + "image_footnote": [], + "bbox": [ + 81, + 450, + 267, + 549 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c136f4a2e5e6ef3609e0596ee9fde2a306a0e86278a4b937244b93897b103b3b.jpg", + "image_caption": [ + "(b) Occupancy map and sampled positions", + "Figure 3: Illustration of an HM3D environment scan and the sampled positions (blue points) in open space (gray area)." + ], + "image_footnote": [], + "bbox": [ + 279, + 450, + 450, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "it also generalizes well to the HM3D scenes. We refer to the Appendix for more sampling and dataset creation details.", + "bbox": [ + 75, + 623, + 468, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training", + "text_level": 1, + "bbox": [ + 76, + 662, + 181, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details We initialize the RGBD encoder and the map encoder of our visual representation network with CLIP, a visual transformer pre-trained for aligning image-language pairs [72]. Specifically, the additional depth convolutional layer and the projection layer in the RGBD encoder are initialized randomly. All network variants in our experiments are trained with batch size 994 for 100 epochs using the AdamW optimizer [59]. After all training iterations, only the RGBD encoder will be applied as the visual backbone for navigation agents. Image augmentations are applied to all views and maps.", + "bbox": [ + 75, + 685, + 470, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimization The overall pre-training strategy minimizes the sum over all three losses, $\\mathcal{L}_c$ , $\\mathcal{L}_{\\theta}$ and $\\mathcal{L}_d$ . All", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "losses are equally weighted and optimized simultaneously in each iteration. After all training steps, evaluate the model with batch size 128 on 10,000 novel $(I_s, I_t, M)$ triplets shows $92.02\\%$ views to maps $(I \\rightarrow M)$ and $92.03\\%$ maps to view $(M \\rightarrow I)$ alignment accuracy, indicating the correspondence between two modalities has been learned. Please see Appendix for more pre-training statistics and results.", + "bbox": [ + 496, + 452, + 890, + 560 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Downstream Experiments", + "text_level": 1, + "bbox": [ + 498, + 573, + 743, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our $\\mathrm{Ego}^2$ -Map representations mainly on the R2R-CE navigation [3, 51], as addressing the task highly relies on exploiting the semantic and structural information from observations and ground to language instructions. We also show results on ObjNav [4] to compare with other recent visual representation learning approaches.", + "bbox": [ + 496, + 599, + 890, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. R2R-CE Setup", + "text_level": 1, + "bbox": [ + 500, + 702, + 651, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our experiments consider two major setups of action spaces, either applying panorama inputs and execute high-level decisions by selecting images pointing towards navigable directions $(\\mathcal{A}_{High})^3$ , or using egocentric views and perform low-level controls $(\\mathcal{A}_{Low})$ . For $\\mathcal{A}_{High}$ , we adopt the candidate waypoint predictor proposed by Hong et al. [41], which generates navigable waypoint positions around the agent at each time step. Once a waypoint is selected, the agent will move to the position with low-level", + "bbox": [ + 496, + 726, + 890, + 864 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "$^{3}$ High-level VLN agents apply 36 egocentric images to represent its panoramic vision [3], hence, our $\\mathsf{Ego}^2$ -Map features are applicable.", + "bbox": [ + 500, + 875, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3059", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/bfa9636295a9a54da2019007ce4b67654178e231352b362c06aaf3afbd5811bf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelsPre-Training ObjectivesR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
AngularExplorableContrastiveNE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑Collision↓
Baseline4.9857.2648.6742.557.6949.2725.6123.9317.41
1✓8.3332.0216.1513.659.7730.433.753.4371.59
2✓5.8351.2542.5836.347.9447.1524.7422.9810.44
3✓4.8958.4951.7745.897.4750.3527.6225.9513.19
4✓✓5.0358.8651.2845.987.2751.9130.6129.1310.09
5✓✓5.0259.6252.0446.997.4451.3129.5327.9413.04
6✓✓5.7952.9342.9037.257.6450.1927.9526.3916.19
7✓✓✓4.9459.6751.7746.117.2552.0130.4029.0311.25
", + "bbox": [ + 81, + 90, + 893, + 243 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Ablation of $\\mathsf{Ego}^2$ -Map learning and influence of angular and explorable objectives on the R2R-CE tasks. Checkmarks indicate applying the corresponding objectives. Baseline applies a pre-trained CLIP-ViT-B/16 model to encode RGB and depth separately. Collision measures the percentage of forward steps which the agent collided with an obstacle; we only consider this metric for $\\mathcal{A}_{Low}$ since agents in $\\mathcal{A}_{High}$ apply a waypoint predictor [41] to obtain navigable positions.", + "bbox": [ + 75, + 253, + 892, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "controls. For $\\mathcal{A}_{Low}$ , an agent is only allowed to do a single low-level action at each step, including Turn Left/Right $15^{\\circ}$ , Forward 0.25 meters, and Stop. In all experiments, we apply the VLN $\\rightarrow$ BERT agent [42], a vision-language transformer pre-trained for navigation, as the policy network. To use our Ego $^2$ -Map representations, we simply replace the agent's original visual encoders (two ResNets trained on ImageNet [39] and trained in Point-Nav [94] for RGB and depth, respectively) with our RGBD encoder ( $\\S 3.1$ ). Comparing the runtime efficiency, the original encoder has around 50M parameters and the speed is about 4 GFLOPs/image, whereas our method is larger (86M parameters) but faster (20 GFLOPs/image). All visual encoders in our experiments are frozen in navigation.", + "bbox": [ + 75, + 329, + 470, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "R2R in continuous environment (R2R-CE) is established over the Matterport3D environments [8] based on the Habitat simulator [82]. The dataset contains 61 scans for training; 11 and 18 scans for validation and testing, respectively. R2R-CE evaluates the agent's performance using multiple metrics, including trajectory length (TL), navigation error (NE): the final distance between the agent and the target, normalized dynamic time warping score (nDTW): distance between the predicted and the ground-truth paths [43], oracle success rate (OSR): the ratio of reaching within 3 meters to the target, success rate (SR): the ratio of stopping within 3 meters to the target, and success weighted by the normalized inverse of the path length (SPL) [2].", + "bbox": [ + 75, + 542, + 468, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 753, + 230, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablation experiments in Table 1 reveal the influence of different pre-training objectives. We establish our Baseline by using a frozen CLIP-ViT-B/16 to encode RGB and depth separately, followed by a trainable fusion layer to merge the two features, which is a strong baseline that can achieve better results than the previous best encoders (see CLIP-ViT+Depth in Table 4).", + "bbox": [ + 75, + 777, + 468, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results of Model#1 indicate that employing angular off", + "bbox": [ + 96, + 885, + 467, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "set prediction as the only task has a devastating effect on the encoder; in fact, we found that $\\mathcal{L}_{\\theta}$ only oscillates if it is minimized alone, leading to features that are not useful in downstream tasks (see details in Appendix). Although learning $\\mathcal{L}_{\\theta}$ with $\\mathcal{L}_d$ or $\\mathcal{L}_c$ can improve the performance in both $\\mathcal{A}_{High}$ and $\\mathcal{A}_{Low}$ (Model#5, Model#6), removing the task from Model#7 will not cause a noticeable difference (Model#4). Meanwhile, learning explorable distance prediction (Model#2, Model#5) is not effective in $\\mathcal{A}_{High}$ scenario because agents with $\\mathcal{A}_{High}$ apply pre-defined waypoints on open space, which means, finding explorable directions and avoid obstacle are not necessary. However, Model#2, Model#4 and Model#6 suggest that learning $\\mathcal{L}_d$ with $\\mathcal{L}_c$ or $\\mathcal{L}_{\\theta}$ will boost the results in $\\mathcal{A}_{Low}$ and effectively reduce the collision rate during navigation.", + "bbox": [ + 496, + 329, + 893, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On the other hand, by comparing the Baseline, Model#3, Model#6, and Model#7, we can see that our proposed $\\mathsf{Ego}^2$ -Map contrastive learning has the largest impact on R2R-CE. Solely learning $\\mathcal{L}_c$ improves the SR and SPL absolutely by $3.10\\%$ and $3.34\\%$ in $\\mathcal{A}_{High}$ , as well as $2.01\\%$ and $2.02\\%$ in $\\mathcal{A}_{Low}$ , while removing $\\mathcal{L}_c$ from Model#7 dramatically lowers the results in both settings. Meanwhile, we found that $\\mathsf{Ego}^2$ -Map learning can also help avoid collision, implying the useful spatial information carried by the map. In the following experiments, all three losses are applied to pre-train the visual encoders.", + "bbox": [ + 496, + 556, + 893, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Discussion and Analysis", + "text_level": 1, + "bbox": [ + 500, + 739, + 720, + 756 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "How much does the quantity of visual data matter? In Table 2, we compare the effect of sampling a different quantity of data for pre-training our visual encoder. Results show that the agent's performance in R2R-CE drops as the amount of data decreases, and reducing the number of environments has a stronger impact on the results $(-1.08\\%)$ SPL for $50\\%$ samples vs. $-3.87\\%$ SPL for $50\\%$ envs with $\\mathcal{A}_{High}$ , suggesting the importance of having abundant scenes and structures in learning visual represent", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3060", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/50b792283d1455d9ad2c027872ab6579d62f64b78e14960b4578b839846f74df.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Pre-train DataR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
100% data4.9459.6751.7746.117.2552.0130.4029.03
50% samples4.9857.7250.4645.037.4349.9727.5726.22
30% samples5.2856.1148.6142.587.8348.6025.8324.63
10% samples5.6054.8944.4839.087.8646.8322.9521.54
50% envs5.3255.5347.8042.247.5750.3526.5425.15
30% envs5.5653.8144.4838.697.6148.6426.0524.51
10% envs5.7353.4441.9236.897.8847.6223.2222.00
MP3D5.6752.7840.7835.767.9746.7521.9720.60
", + "bbox": [ + 81, + 90, + 467, + 200 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f75b7256ad92c63ebbd6739b5f9e99e81310a8d9481a9ddeb232cd19f6d0b4a3.jpg", + "table_caption": [ + "Table 2: Effect of additional environments for pre-training. The percentages indicate the portion of HM3D environments/samples for training. MP3D only uses data collected from the 61 environments in downstream." + ], + "table_footnote": [], + "table_body": "
InitializationR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
CLIP4.9459.6751.7746.117.2552.0130.4029.03
Random4.9957.5549.3243.897.2751.3529.9128.29
IN-21K4.9558.6151.5545.737.0553.3031.0529.69
+IN-21K map5.4056.1847.0942.017.2152.6828.5527.13
", + "bbox": [ + 81, + 287, + 467, + 357 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tations. Meanwhile, we can see that applying less than $50\\%$ of samples or environments cannot yield better results than the baseline in Table 1. This is because $\\mathrm{Ego}^2$ -Map learning requires sufficient positive and negative data pairs to support its contrastive training, as observed in previous literatures [18, 72].", + "bbox": [ + 75, + 472, + 467, + 563 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "How much does initialization matter? Table 3 compares the initialization of the RGBD and the map encoders in $\\mathsf{Ego}^2$ -Map network, either from CLIP [72], from scratch or from a ViT-B/16 [25] pre-trained on ImageNet-21K (IN-21K) [23]. We find that random initialization of the RGB encoder only leads to a slight decrease in R2R-CE performance, while initializing it from pre-trained ViT can achieve comparable results to Model#7. We further investigate these results by also replacing the initialization of our map encoder from CLIP with IN-21K pre-trained ViT; although the losses of the two models saturate to the same level in pre-training, a drastic drop is observed in R2R-CE (even lower than Random). We hypothesize that some semantics from CLIP can be introduced to the RGBD encoder by the map encoder through contrastive learning. While previous works often use a convolutional network to process maps [14, 32, 33, 73], there remains a valuable open question of what model is suitable for encoding maps and how to train it to benefit navigation. We will leave the study of encoding maps for future work.", + "bbox": [ + 75, + 595, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ece422818bc59d3387a0f4c5acc0e78cdeccb319b2a956d274a250651dad31c8.jpg", + "table_caption": [ + "Table 3: Effect of using pre-trained encoders for RGBD and map. Random and IN-21K initialize the RGBD encoder randomly or from a ViT pre-trained on ImageNet-21K [23], while using the CLIP-ViT-B/32 to encode maps. +IN-21K map also uses the IN-21K pre-trained ViT to encode the semantic map." + ], + "table_footnote": [], + "table_body": "
MethodsR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
CLIP-ViT+Depth +L5.4755.5547.1541.287.9347.7622.6821.69
5.2457.7448.6743.787.0752.5930.0728.74
", + "bbox": [ + 504, + 90, + 890, + 137 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0c257c68da3e0ecb3dc46b10db7cc6af09b0764540ffc3214b0078e798fd5599.jpg", + "table_caption": [ + "Table 4: Pre-training a different visual encoder with Ego2-Map objectives. The model applies CLIP-ViT-B/16 and a ResNet-50 trained for Point-Nav [94] to encode RGB and depth, respectively." + ], + "table_footnote": [], + "table_body": "
Ego2-MapR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
No semantics5.5157.6047.0442.257.3151.5629.7428.34
No space5.2457.4248.9443.527.6649.2029.3127.75
No target5.0256.2647.2041.218.0551.0430.8329.07
", + "bbox": [ + 504, + 215, + 890, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5: Ablation of information in Ego2-Map learning.", + "bbox": [ + 509, + 287, + 879, + 304 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of $\\mathcal{L}$ on a different encoder We further evaluate our proposed $\\mathrm{Ego}^2$ -Map objective in pre-training a different visual encoder (Table 4). Here we consider the previous state-of-the-art encoder CLIP-ViT+Depth, which applies CLIP-ViT-B/16 and a ResNet-50 depth net trained on Gibson [95] for PointNav [82] to encode RGB and depth, respectively, following by a fusion module to integrate the encoded features. Pre-training the model with $\\mathcal{L}$ leads to a significant improvement, obtaining $+2.50\\%$ and $+7.05\\%$ higher SPL with $\\mathcal{A}_{High}$ and $\\mathcal{A}_{Low}$ . These results suggest that $\\mathrm{Ego}^2$ -Map learning has the potential to be generalized to other visual encoders.", + "bbox": [ + 496, + 320, + 890, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Information in $\\mathbf{Ego}^2$ -Map contrastive learning In Table 5, we ablate the information applied in the $\\mathbf{Ego}^2$ -Map contrastive learning. Specifically, we either remove the object semantics by masking their colored segmentations with the same color, or remove explorable regions by masking open space and void with the same color (see unmasked maps in Figure 2), or remove the target view from the view pairs to create ambiguity in agent's transition. The results show that learning $\\mathbf{Ego}^2$ -Map without the semantic clues or open space in the maps, or without a specified target greatly damages agent performance in $\\mathcal{A}_{High}$ , reflecting the importance of including this information. We also find that the agent with $\\mathcal{A}_{Low}$ is less sensitive to method variations in pre-training; the remaining spatial or object information on a map is still beneficial to enhance the visual representation for supporting $\\mathcal{A}_{Low}$ navigation, which could be the reason why angular offset and explorable distance predictions do not show a consistent benefit in Table 1.", + "bbox": [ + 496, + 527, + 890, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison to Previous Methods", + "text_level": 1, + "bbox": [ + 500, + 815, + 792, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Advantages of Visual Representations (R2R-CE) In Table 6, we compare our method of applying $\\mathsf{Ego}^2$ -Map RGBD encoder to the CWP-VLN $\\vec{\\circ}$ BERT agent [41] (same model as Model#7 in Table 1) with previous approaches", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3061", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "using $\\mathcal{A}_{High}$ on the R2R-CE testing split4. Results show that our proposed $\\mathrm{Ego}^2$ -Map learning brings significant improvement for all metrics, achieving a $47\\%$ SR $(+3\\%)$ and a $41\\%$ SPL $(+4\\%)$ over the previous best [50]. In addition, Table 7 establishes a fair comparison with methods using $\\mathcal{A}_{Low}$ . We can see that $\\mathrm{Ego}^2$ -Map features greatly boost the result of the base agent CWP-VLN BERT [41] (23% to 30% SR), and achieve a SPL comparable to recent mapping-based methods such as CM2 [33] and WS-MGMap [14]. Note that using $\\mathrm{Ego}^2$ -Map representations does not conflict with online mapping; while we only experiment with non-mapping-based agents, we believe the features hold great potential to facilitate modeling between views and maps in mapping-based models.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Learning Methods (ObjNav) We further compare the effect of visual representation learning methods by applying our visual encoder on ObjNav [4] as in the recent approaches [46, 96] (Table 8). All methods in the table adopt a simple pipeline as in the baseline model [94], which feeds the concatenation of visual features, GPS+Compass encodings, and the encodings of previous action to a GRU [19], then, uses a fully-connected layer to predict an action from the updated agent's state. Briefly, EmbCLIP directly uses the pre-trained CLIP-ResNet50 [72] to encode the RGB inputs, EmbCLIP-ViT+Depth applies the CLIP-ViT-B/16 to encode RGB and an extra depth net [82] pre-trained on Gibson [95] to encode the depth inputs. OVRL pre-trains the ResNet encoder with self-distillation method DINO [6], in which a student network is trained to match the output of a teacher network. Moreover, OVRL applies the Omnidata Starter Dataset $(\\mathrm{OSD})^5$ [28], which is much larger and more diverse than the data for our Ego $^2$ -Map learning (only uses the HM3D [74] subset). ObjNav measures the same metrics as R2R-CE, first, we can see that an agent using Ego $^2$ -Map features greatly improves over the baseline and the EmbCLIP. Compared to OVRL, despite the method applies OSD for pre-training and fine-tunes the network end-to-end with human demonstrations, our method obtains a better success rate $(+0.4\\%)$ and much higher SPL $(+3.2\\%)$ . Note that, although not directly comparable, as reported in the OVRL, the SPL on ImageNav [63] without fine-tuning the visual encoder will drop drastically from $26.9\\%$ to $17.0\\%$ , whereas all our experiments keep the visual encoder frozen during navigation. These results suggest that Ego $^2$ -Map representations are generalizable to different navigation tasks and provide more robust visual representations.", + "bbox": [ + 75, + 335, + 472, + 821 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1db4a235578aff21345b20633a9fc9d8e82e2d68fae7d6e5bd81ec37eaeca6fb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methods (AHigh)R2R-CE Test-Unseen
TLNE↓OSR↑SR↑SPL↑
Waypoint Models [49]8.026.65373230
CWP-CMA [41]11.856.30493833
CWP-VLN BERT [41]13.315.89514236
Sim2Sim [50]11.436.17524437
Ego2-Map+CWP-VLN BERT (ours)13.055.54564741
", + "bbox": [ + 503, + 90, + 893, + 176 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c020fede76c7aab70ee46e7ed720ab3053e16007feff13f17dce80bd6573e0f3.jpg", + "table_caption": [ + "Table 6: Comparison of agent performance on R2R-CE test server. All methods use high-level action space $(\\mathcal{A}_{High})$" + ], + "table_footnote": [], + "table_body": "
Methods (ALow)R2R-CE Val-Unseen
TLNE↓OSR↑SR↑SPL↑
CMA+PM+DA+Aug [51]8.647.37403230
SASRA [44] †7.898.32-2422
LAW [77]8.896.83443531
CWP-CMA [41]°8.227.54-2725
CWP-VLN BERT [41]°7.427.66-2322
CM2 [33] †11.547.02423428
WS-MGMap (SemMap only) [14] †10.896.80423328
Ego2-Map+CWP-VLN BERT (ours)8.037.25373029
", + "bbox": [ + 503, + 215, + 893, + 335 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b0c27b718114d49c254b651cccedc0dc31211b4c0be7acf2cae55313f9c0f311.jpg", + "table_caption": [ + "Table 7: Comparison of agents with low-level action space $(\\mathcal{A}_{Low})$ in R2R-CE Val-Unseen. $\\dagger$ : mapping-based methods. $\\circ$ : $4\\%$ of data is removed but the comparison is still valid due to the large performance gap." + ], + "table_footnote": [], + "table_body": "
MethodsPre-Training DatasetObjNav MP3D Val
NE↓SR↑SPL↑
Baseline [94]X6.908.01.8
EmbCLIP [46]*WebImageText5.2620.98.3
EmbCLIP-ViT+DepthWebImageText+Gibson4.9023.38.6
OVRL no pretrain [76] †X-24.25.9
OVRL [96] †OSD-28.67.4
Ego2-Map+Baseline (ours)HM3D5.1729.010.6
", + "bbox": [ + 503, + 417, + 893, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8: Comparison on pre-trained visual encoders for ObjNav. $\\dagger$ indicates the visual encoder is tuned end-to-end with behavior cloning on $40\\mathrm{k}$ human demonstrations collected by Habitat-Web [76], while the others freeze the visual encoder during navigation and only train the agent with DD-PPO [94] on the original data. *Results obtained by re-evaluating the officially released best model checkpoint.", + "bbox": [ + 496, + 527, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 648, + 619, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce a novel method of learning navigational visual representations with contrastive learning between egocentric views pairs and top-down semantic maps (Ego $^2$ -Map). The method transfers the compact semantic and spatial information carried by a map to the egocentric representations, which greatly facilitates the agent's visual perception. Experiments show that Ego $^2$ -Map features greatly improve the downstream navigation, such as ObjNav and VLN, and demonstrate generalization potential to different visual backbones. We believe the Ego $^2$ -Map contrastive learning proposes a new direction of visual representation learning for navigation and provides the possibility of better modeling the correspondence between views and maps, which can further benefit agent's planning and action. Note that our work also produces a potentially ef", + "bbox": [ + 496, + 674, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "$^{4}$ R2R-CE Challenge Leaderboard: https://eval.ai/web/challenges/challenge-page/719/leaderboard/1966 \n $^{5}$ OSD [28] contains approximately 14.5 million images rendered from diverse 3D environments, including Replica [88], Replica+GSO [26], Hypersim [79], Taskonomy [100], BlendedMVG [97] and HM3D [74].", + "bbox": [ + 75, + 837, + 491, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3062", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "fective map encoder whose full capability is worth investigating in future work.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Limitations The need to build semantic maps to enable the $\\mathbf{Ego}^2$ -Map contrastive learning is an inevitable cost of this method; compared to other self-supervised visual representation learning approaches, $\\mathbf{Ego}^2$ -Map requires either the semantic annotations of scenes, or traversable environments and a generalizable semantic map constructor. As a result, the data collection could be much harder. However, we also witnessed an increasing number of interactive 3D scenes being built in recent years with dense semantic annotations [22, 74, 82, 88, 95], which can facilitate scaling up our $\\mathbf{Ego}^2$ -Map learning in the future.", + "bbox": [ + 76, + 133, + 470, + 300 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 316, + 173, + 332 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Dong An, Zun Wang, Yangguang Li, Yi Wang, Yicong Hong, Yan Huang, Liang Wang, and Jing Shao. 1st place solutions for rxr-habitat vision-and-language navigation competition (cvpr 2022). arXiv preprint arXiv:2206.11610, 2022.2", + "[2] Peter Anderson, Angel Chang, Devendra Singh Chaplot, Alexey Dosovitskiy, Saurabh Gupta, Vladlen Koltun, Jana Kosecka, Jitendra Malik, Roozbeh Mottaghi, Manolis Savva, et al. 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PMLR, 2021. 3", + "[100] Amir R Zamir, Alexander Sax, William Shen, Leonidas J Guibas, Jitendra Malik, and Silvio Savarese. Taskonomy: Disentangling task transfer learning. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3712-3722, 2018. 8", + "[101] Yuhao Zhang, Hang Jiang, Yasuhide Miura, Christopher D Manning, and Curtis P Langlotz. Contrastive learning of medical visual representations from paired images and text. arXiv preprint arXiv:2010.00747, 2020. 4", + "[102] Bolei Zhou, Agata Lapedriza, Aditya Khosla, Aude Oliva, and Antonio Torralba. Places: A 10 million image database for scene recognition. IEEE transactions on pattern analysis and machine intelligence, 40(6):1452-1464, 2017. 1", + "[103] Gengze Zhou, Yicong Hong, and Qi Wu. Navgpt: Explicit reasoning in vision-and-language navigation with large language models. arXiv preprint arXiv:2305.16986, 2023. 2", + "[104] Fengda Zhu, Yi Zhu, Xiaojun Chang, and Xiaodan Liang. Vision-language navigation with self-supervised auxiliary" + ], + "bbox": [ + 78, + 92, + 468, + 900 + ], + "page_idx": 12 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "reasoning tasks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10012-10022, 2020. 4", + "[105] Minzhao Zhu, Binglei Zhao, and Tao Kong. Navigating to objects in unseen environments by distance prediction. arXiv preprint arXiv:2202.03735, 2022. 2" + ], + "bbox": [ + 501, + 92, + 890, + 176 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "3067", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/Learning Navigational Visual Representations with Semantic Map Supervision/94d1f5dd-be00-46b4-8d2e-2c6681cb4e80_model.json b/2023/Learning Navigational Visual Representations with Semantic Map Supervision/94d1f5dd-be00-46b4-8d2e-2c6681cb4e80_model.json new file mode 100644 index 0000000000000000000000000000000000000000..36ee4595ea994eea52aa9358ccecbc06c0590834 --- /dev/null +++ b/2023/Learning Navigational Visual Representations with Semantic Map Supervision/94d1f5dd-be00-46b4-8d2e-2c6681cb4e80_model.json @@ -0,0 +1,2679 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.089, + 0.131, + 0.882, + 0.154 + ], + "angle": 0, + "content": "Learning Navigational Visual Representations with Semantic Map Supervision" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.18, + 0.676, + 0.199 + ], + "angle": 0, + "content": "Yicong Hong\\(^{12,\\dagger}\\) Yang Zhou\\(^{1}\\) Ruiyi Zhang\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.199, + 0.748, + 0.216 + ], + "angle": 0, + "content": "Franck Dernoncourt1 Trung Bui1 Stephen Gould2 Hao Tan1" + }, + { + "type": "text", + "bbox": [ + 0.263, + 0.217, + 0.71, + 0.235 + ], + "angle": 0, + "content": "\\(^{1}\\)Adobe Research \\(^{2}\\)The Australian National University" + }, + { + "type": "text", + "bbox": [ + 0.382, + 0.238, + 0.59, + 0.251 + ], + "angle": 0, + "content": "mr.yiconghong@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.166, + 0.255, + 0.804, + 0.269 + ], + "angle": 0, + "content": "stephen.gould@anu.edu.au, {yazhou,ruizhang,dernonco,bui,hatan}@adobe.com" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.273, + 0.734, + 0.287 + ], + "angle": 0, + "content": "Project URL: https://github.com/YicongHong/Ego2Map-NaViT" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.474, + 0.732 + ], + "angle": 0, + "content": "Being able to perceive the semantics and the spatial structure of the environment is essential for visual navigation of a household robot. However, most existing works only employ visual backbones pre-trained either with independent images for classification or with self-supervised learning methods to adapt to the indoor navigation domain, neglecting the spatial relationships that are essential to the learning of navigation. Inspired by the behavior that humans naturally build semantically and spatially meaningful cognitive maps in their brains during navigation, in this paper, we propose a novel navigational-specific visual representation learning method by contrasting the agent's egocentric views and semantic maps (Ego\\(^2\\)-Map). We apply the visual transformer as the backbone encoder and train the model with data collected from the large-scale Habitat-Matterport3D environments. Ego\\(^2\\)-Map learning transfers the compact and rich information from a map, such as objects, structure and transition, to the agent's egocentric representations for navigation. Experiments show that agents using our learned representations on object-goal navigation outperform recent visual pre-training methods. Moreover, our representations significantly improve vision-and-language navigation in continuous environments for both high-level and low-level action spaces, achieving new state-of-the-art results of \\(47\\%\\) SR and \\(41\\%\\) SPL on the test server." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.776, + 0.21, + 0.792 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.801, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Visual representations for navigation should capture the rich semantics and the complex spatial relationships of the observations, which helps the agent to recognize visual entities and its transition in space for effective exploration. However, previous works usually adopt visual backbones" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.323, + 0.895, + 0.627 + ], + "angle": 0, + "content": "which only focus on capturing the semantics of a static image, ignoring its connection to the agent or the correspondence to other views in a continuous environment [3, 9, 40, 42, 51, 68, 98]. One common approach is to apply encoders pre-trained for object/scene classification (e.g. ResNet [39] on ImageNet [80]/Places365 [102]), object detection (e.g. RCNN [38, 78] on VisualGenome [52]/MSCOCO [57]) or semantic segmentation (e.g. RedNet [45] on SUN RGBD [87]), or more recently, to use CLIP [72], which is trained for aligning millions of images and texts to encode agent's RGB observations [31, 46, 84]. Despite the increasing generalization ability of the features and rising zero-shot performance on novel targets, there still exists a large visual domain gap between these features and the features suitable for navigation since they lack the expressiveness of spatial relationships. For example, the connection between time-dependent observations and the correspondence between egocentric views and the spatial structure of an environment, which are important to decision making during navigation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We suggest that there are two main difficulties in learning navigational-specific visual representations in previous research; First, there lacked a large-scale and realistic dataset of indoor environments. Popular datasets such as Matterport3D [8] and Gibson [95] provide traversable scenes rendered from real photos, but either the number of scenes is very limited, or the quality of the 3D scan is low. Synthetic datasets such as ProcTHOR [22] contain 10K generated scenes, but they are unrealistic and simple and do not capture the full complexity of real-world environments. Second, fine-tuning visual encoders while learning to navigate is very expensive because of the long traveling horizon, especially in tasks that require extensive exploration [4, 53, 63, 86]. Moreover, due to the scene scarcity, fine-tuning visual encoders is unlikely to generalize well to the novel environments. To address these problems, a large amount of research has been dedicated to augmenting the environments, either editing the agent's observations" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.887, + 0.248, + 0.9 + ], + "angle": 0, + "content": "†Intern at Adobe Research." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3055" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.395 + ], + "angle": 0, + "content": "[56, 90] or adding objects [62], building new spatial structures [58], applying web-images to replace the views of the same categories [35] or generating new scenes [47, 48, 55]. Unlike augmentation, which essentially requires the agent's policy network to adapt new visual data, another strategy is to first pre-train the visual encoder before learning to navigate. Those methods usually apply images captured in 3D scenes and perform self-supervised learning or tune the encoder with proxy tasks (e.g. masked region modeling, angular prediction) to mitigate the domain gap and introduce spatial awareness [15, 17, 96, 98]. Furthermore, recent works tend to apply CLIP [72] to process visual inputs, as the model can provide powerful representations for grounding semantic and spatial concepts, hence facilitating learning [1, 31, 46, 83, 84, 85]. Although these methods have demonstrated significant improvements on navigation performance, they either only use more data without addressing the learning problem, not generalizable across different tasks, or ignore the spatial correspondence between consecutive frames which the agent will capture as it moves." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.398, + 0.473, + 0.837 + ], + "angle": 0, + "content": "Inspire by the research in cognitive science that humans naturally build virtual maps from perspective observations that are helpful to track semantics, spaces and movements during navigation [29, 91, 92]; we propose a contrastive learning method between the agent's Egocentric view pairs and top-down semantic Maps (Ego\\(^2\\)-Map) for training visual encoders appropriate for navigation. Specifically, we first sample RGBD images and create corresponding semantic maps [7] from the large-scale Habitat-Matterport3D environments (HM3D) [74, 82] which contains hundreds of photo-realistic scenes, obtaining abundant and effective visual data. Then, we encode the sampled RGBD observations and the semantic maps with two separate visual backbones, respectively, and train the entire model with our Ego\\(^2\\)-Map contrastive learning. Once trained, the RGBD encoder will be plugged into an agent's network to facilitate visual perception. We argue that the map contains very rich and compact visual clues such as spatial structure, accessible areas and unexplored regions, object entities and their arrangement, as well as the agent's transition in the environment that are essential to navigation. Compared to existing online mapping-based approaches [10, 14, 32, 44], Ego\\(^2\\)-Map learning efficiently produces visual features that imply a complete map of the space known a view priori, while the online map is only a partial map. Importantly, Ego\\(^2\\)-Map explores a new possibility of modeling semantics and structures from simple RGBD inputs, which its resulting features are directly applicable to non-mapping-based navigational models and effectively generalizable to different tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We mainly evaluate the features learned from Ego\\(^2\\)-Map on the Room-to-Room Vision-and-Language Navigation in Continuous Environments (R2R-CE) [3, 51] task, which requires an agent to navigate in photo-realistic environ" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.351 + ], + "angle": 0, + "content": "ments following human natural language instructions such as \"Leave the bedroom and enter the kitchen. Walk forward and take a left at the couch. Stop in front of the window.\" Addressing R2R-CE highly relies on exploiting the correspondence between contextual clues and the agent's observations, hence it is crucial for the visual encoder to provide semantic and structural meaningful representations. We found that the proposed \\(\\mathsf{Ego}^2\\)-Map features significantly boost the agent's performance, obtaining \\(+3.56\\%\\) and \\(+5.10\\%\\) absolute SPL improvements over the CLIP baseline [72] under the settings of high-level and low-level action spaces, respectively, and achieves the new best results on the R2R-CE test server. Moreover, our experiments show that \\(\\mathsf{Ego}^2\\)-Map learning also outperforms other visual representation learning methods such as OVRL [96] on the Object-Goal Navigation task (ObjNav), suggesting the strong generalization potential of the proposed methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.36, + 0.642, + 0.377 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.895, + 0.673 + ], + "angle": 0, + "content": "Visual Navigation A great variety of scenarios have been proposed to learn visual navigation in photo-realistic environments [8, 21, 54, 82, 86, 89, 95] with different modalities of inputs, targets and action spaces [3, 4, 11, 13, 51, 66, 70, 94]. Due to the distinct nature of the tasks, diverse methods are investigated accordingly. For instance, in Object-Nav, which only provides a high-level goal and requires exploration, mapping-based methods are frequently applied [10, 32, 60, 73, 105], whereas in vision-and-language navigation (VLN) [3], large vision-language models are employed to match instructions and agent's observations [42, 61, 71, 83, 103] to perform panoramic actions [30]. Recently, there is an emerging trend of scaling up the training data to address the common data scarcity issue, either in terms of the number of environments [22, 74] or the amount of supervision [16, 76, 93]. Unlike most of the previous works, we focus on improving the visual backbone, aiming to produce robust and generalizable visual representations specialized for navigation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Visual Representations for Embodied AI Recent years have witnessed a trend of moving away from visual encoders pre-trained for object classification in Embodied AI due to their inefficiency in representing complex real-world scenes or mapping to actions. Instead, large vision-language models such as CLIP which demonstrates strong zero-shot performance across visual domains is widely applied [20, 72], enhancing the semantic representations in robotic manipulation [85], assisting 3D trajectory modification and speed control [5], benefiting the language-conditioned view-selection problem in VLN [83, 84] as well as improving other control and navigation results [31, 46, 67]. Moreover, EmbCLIP shows that the CLIP features provide much better semantic and geometric primitives such as" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "3056" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.092, + 0.885, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.326, + 0.895, + 0.39 + ], + "angle": 0, + "content": "Figure 1: Network architecture. The Semantic MapNet [7] is applied to draw a semantic map using observations captured from a source to a target position. Then, two learnable visual encoders are applied to encode the egocentric views and the map, respectively, followed by non-linear headers \\(\\Pi_{i}\\) and \\(\\Pi_{m}\\) to learn the Ego\\(^2\\)-Map contrastive objective \\(\\mathcal{L}_c\\). \\(f_{s}\\) and \\(f_{t}\\) are the paired view features of a trajectory (see §3.2). Dash arrows indicate pre-processing without gradient update." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.473, + 0.617 + ], + "angle": 0, + "content": "object presence, object reachability, and free space that are valuable to Embodied AI [46]. In terms of self-supervised visual representation learning for indoor navigation, recent works that are the most relevant to ours include OVRL [96] which applies knowledge distillation based on DINO [6], EPC which predicts masked observations from a trajectory [75], and CRL which jointly learns a visual encoder with a policy network that maximizes the representation error [27]. In contrast to all previous works, this paper explores a novel idea of encoding the explicit structural and semantic information available in maps implicitly in the visual encoder thereby facilitating efficient and effective generalization across different visual navigation tasks and models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Exploiting Visual Features A great variety of proxy tasks and auxiliary objectives have been applied to exploit information from the visual data which is beneficial to navigation. For instance, Ye et al. [98, 99] promote understanding of spatiotemporal relations of observations by estimating the timestep difference between two views, Qi et al. [69] predict room-types from object features to improve scene understanding, and Se et al. [81] determine the furthest reachable waypoint on a topological graph using the node observations. To extract the geometric information, Gordon et al. [34] use the encoded visual features to predict depth and surface normals, reconstruct RGB input, and forecast the visual features by taking certain actions. Depth prediction has also been studied by Mirowski et al. [64], Desai et al. [24] and Chattopadhyay et al. [12], along with learning the inverse dynamics by predicting an action taken between two sequential observations [37, 64]. Complement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.404, + 0.895, + 0.451 + ], + "angle": 0, + "content": "tary to the previous methods for interpreting visual features, our Ego\\(^2\\)-Map learning guides a visual encoder to produce representations with expressive spatial information." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.464, + 0.895, + 0.501 + ], + "angle": 0, + "content": "3. Contrastive Learning between Egocentric Views and Semantic Maps (Ego\\(^2\\)-Map)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.895, + 0.614 + ], + "angle": 0, + "content": "We will first describe the overall network architecture for training the visual encoders (§3.1), followed by the details of Ego²-Map objectives (§3.2), as well as two other widely applied spatial-aware auxiliary tasks which we investigated with our Ego²-Map learning (§3.3). Then, we will talk about the data collection (§3.4) and network training (§3.5) processes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.624, + 0.707, + 0.639 + ], + "angle": 0, + "content": "3.1. Network Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.647, + 0.895, + 0.83 + ], + "angle": 0, + "content": "We build the network for \\(\\mathrm{Ego}^2\\)-Map learning based on a ViT-B/16 model (default initialized from CLIP [72], whose effect will be studied in §4.3). Unlike previous methods for visual navigation, which mostly employ two independent encoders to process RGB and depth images, we investigate a compact representation by feeding RGB+Depth as four-channel inputs (Figure 1). To merge the two visual modalities, we use two separate convolutional layers to encode the RGB channels \\(I_{rgb}\\) and the depth map \\(I_d\\), respectively, followed by a token-wise concatenation and a non-linear projection \\(\\Pi_v\\) to merge the resulting feature maps before feeding to the transformer layers as" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.841, + 0.892, + 0.859 + ], + "angle": 0, + "content": "\\[\nv _ {r g b} = \\operatorname {C o n v} _ {r g b} \\left(I _ {r g b}\\right), \\quad v _ {d} = \\operatorname {C o n v} _ {d} \\left(I _ {d}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.871, + 0.531, + 0.884 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\nf = \\operatorname {V i T} \\left(\\boldsymbol {\\Pi} _ {v} \\left[ v _ {r g b}; v _ {d} \\right]\\right) \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3057" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.471, + 0.138 + ], + "angle": 0, + "content": "The pooled features \\( f \\) of the RGBD encoder are applied for learning all spatial-aware objectives \\( \\mathcal{L}_{\\theta} \\), \\( \\mathcal{L}_d \\) and \\( \\mathcal{L}_c \\), which will be specified in the following." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.151, + 0.367, + 0.168 + ], + "angle": 0, + "content": "3.2. \\(\\mathbf{Ego}^2\\) -Map Contrastive Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.176, + 0.473, + 0.525 + ], + "angle": 0, + "content": "The motivation of this task is to introduce the information within a map to single-view features, offering the agent high-level semantic and spatial clues to navigate towards distant targets. Specifically, we build positive samples by coupling a views-pair \\((I_s\\) and \\(I_t\\) from the two endpoints of a path) with a top-down semantic map \\(M\\) that represents the agent's transition and observations along the path, while using mismatched views-pairs and maps of different routes or environments as the negatives. Each semantic map is generated by the off-the-shelf Semantic MapNet [7], using the RGBD observations collected by an agent traveling from the source view \\(I_s\\) to the target view \\(I_t\\) via the shortest path\\(^2\\). The semantic map provides abundant information about the open space, obstacles, unexplored regions, observed objects, and the agent's action, which we consider as highly valuable and compact representations for agent navigation (see maps in Figure 2). To encode \\(M\\), we apply an additional ViT-B/32 [25] with the last three transformer layers unfrozen to adapt the map images. Then, the egocentric features of the two views \\(f_s\\) and \\(f_t\\), and the map features \\(f_m\\) will be passed to two MLP (multi-layer perceptrons) headers \\(\\Pi_i\\) and \\(\\Pi_m\\), respectively, to compute an alignment score as:" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.537, + 0.47, + 0.556 + ], + "angle": 0, + "content": "\\[\nc ^ {I} = \\boldsymbol {\\Pi} _ {i} [ f _ {s}; f _ {t} ], \\qquad c ^ {M} = \\boldsymbol {\\Pi} _ {m} [ f _ {m} ] \\qquad (3)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.57, + 0.107, + 0.584 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.585, + 0.47, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\langle c ^ {I}, c ^ {M} \\rangle = \\frac {c ^ {I} \\cdot c ^ {M}}{\\| c ^ {I} \\| \\| c ^ {M} \\|} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.47, + 0.675 + ], + "angle": 0, + "content": "Then, the InfoNCE loss [65, 101] is applied for \\(\\mathrm{Ego}^2\\)-Map contrastive learning. For each \\(j\\)-th views-map pair in a minibatch of size \\(N\\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.688, + 0.469, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c, j} = \\mathcal {L} _ {c, j} ^ {I \\rightarrow M} + \\mathcal {L} _ {c, j} ^ {M \\rightarrow I} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.722, + 0.465, + 0.737 + ], + "angle": 0, + "content": "where the views to maps \\((I\\to M)\\) loss can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.751, + 0.469, + 0.791 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c, j} ^ {I \\rightarrow M} = - \\log \\frac {\\exp \\left(\\left\\langle c _ {j} ^ {I} , c _ {j} ^ {M} \\right\\rangle / \\tau\\right)}{\\sum_ {k = 1} ^ {N} \\exp \\left(\\left\\langle c _ {j} ^ {I} , c _ {k} ^ {M} \\right\\rangle / \\tau\\right)} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.805, + 0.469, + 0.838 + ], + "angle": 0, + "content": "and the map to views loss \\(\\mathcal{L}_{c,j}^{M\\to I}\\) likewise. Parameter \\(\\tau \\in \\mathbb{R}_+\\) denotes a learnable temperature." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.851, + 0.47, + 0.901 + ], + "angle": 0, + "content": "2Each resulting map is unique because the observations are determined by the unique path (actions) for connecting two views. For example, in Figure 2, only the colored regions in the map \\((M)\\) are the areas seen by the agent when traveling from the source to the target positions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.782, + 0.108 + ], + "angle": 0, + "content": "3.3. Other Spatial-Aware Objectives" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.115, + 0.893, + 0.176 + ], + "angle": 0, + "content": "We investigate two additional widely applied proxy tasks with our Ego\\(^2\\)-Map learning. Note that we do not claim any novelty for applying these tasks but focus on studying their effect on training the representations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.196, + 0.895, + 0.439 + ], + "angle": 0, + "content": "Angular Offset Prediction Given two images taken from random headings at the same position, the task predicts the angular offset between them to facilitate the modeling of correspondence between views. A similar proxy task has been applied in previous works, which predicts discrete angles and uses an extra directional encoding to imply orientation [15] or regresses the agent's turning angle conditioned on language during navigation [104]. Specifically, we pass the two pooled RGBD features \\( f_{\\theta_0} \\) and \\( f_{\\theta_1} \\), corresponding to images at two orientations of the same viewpoint, into a learnable non-linear header \\( \\Pi_{\\theta} \\) to predict the offset as \\( \\theta^p = \\Pi_{\\theta}[f_{\\theta_0};f_{\\theta_1}] \\). The task is learned by minimizing the mean squared error \\( \\mathcal{L}_{\\theta} = E[(\\theta^p - \\theta^*)^2] \\), where \\( \\theta^* \\) is the ground-truth angular difference between \\( [-\\pi, \\pi] \\), denoting either clockwise or counter-clockwise rotation whichever is closer to encourage agent's efficient rotation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.459, + 0.893, + 0.596 + ], + "angle": 0, + "content": "Explorable Distance Prediction To benefit the searching of explorable regions and assist obstacle avoidance, the task estimates the agent's maximal distance to forward without being blocked by any obstacle [11, 36]. Using the same notations as above, the module regresses a value from an RGBD image as \\( d^{p} = \\Pi_{d}[f] \\), and is trained with supervision \\( \\mathcal{L}_d = E[(d^p - d^*)^2] \\). We cap the ground-truth distance \\( d^{*} \\) in the range of 0.5 to 5.0 meters to match the common range of the agent's depth sensors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.657, + 0.621 + ], + "angle": 0, + "content": "3.4. Data Collection" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.629, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We follow the train-validation-test split of the HM3D scenes [74] and use the first 800 environments for learning. We randomly sample 252,537 viewpoint positions from the environments (see Figure 3) and render more than a million RGBD images from those positions to create 500,000 \\((I_{\\theta_0}, I_{\\theta_1})\\) views pairs as well as 500,000 \\((I_s, I_t, M)\\) triplets for learning \\(\\mathcal{L}_{\\theta}\\) and \\(\\mathcal{L}_c\\), respectively, while using all the images to learn \\(\\mathcal{L}_d\\). The positions are sampled such that all points must be located in the open space and the minimal geodesic distance between any two points is greater than 0.40 meters. Each image collected for \\(\\mathrm{Ego}^2\\)-Map contrastive learning is either a unique source or target view in all trajectories, and each trajectory is created by computing the shortest path between two randomly paired views within a 7 meters range. We feed the RGBD images captured from a trajectory to the Semantic MapNet [7] for drawing the corresponding semantic map. Note that the Semantic MapNet is trained on the MP3D environments [8], but we found that" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3058" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.095, + 0.87, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.363, + 0.895, + 0.442 + ], + "angle": 0, + "content": "Figure 2: Illustration of \\(\\mathbf{Ego}^2\\)-Map contrastive learning. The method encodes the paired source and target egocentric views \\((I_s, I_t)\\) into feature \\(c^I\\), then learns to align it with the feature \\(c^M\\) of the corresponding top-down map \\(M\\). Negative view pairs \\((I_{s'}, I_{t'})\\) and maps \\((M')\\) are sampled from different trajectories or different environments, which are pushed away from the reference pair. The blue dashed line on the left part of the figure indicates the agent's trajectory, which is visualized with directional color in map \\(M\\). The map is also powered with semantic information (denoted at the bottom right)." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.452, + 0.268, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.555, + 0.205, + 0.565 + ], + "angle": 0, + "content": "(a) 3D scan" + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.451, + 0.452, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.554, + 0.465, + 0.565 + ], + "angle": 0, + "content": "(b) Occupancy map and sampled positions" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.579, + 0.47, + 0.611 + ], + "angle": 0, + "content": "Figure 3: Illustration of an HM3D environment scan and the sampled positions (blue points) in open space (gray area)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.656 + ], + "angle": 0, + "content": "it also generalizes well to the HM3D scenes. We refer to the Appendix for more sampling and dataset creation details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.663, + 0.182, + 0.679 + ], + "angle": 0, + "content": "3.5. Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.471, + 0.854 + ], + "angle": 0, + "content": "Implementation Details We initialize the RGBD encoder and the map encoder of our visual representation network with CLIP, a visual transformer pre-trained for aligning image-language pairs [72]. Specifically, the additional depth convolutional layer and the projection layer in the RGBD encoder are initialized randomly. All network variants in our experiments are trained with batch size 994 for 100 epochs using the AdamW optimizer [59]. After all training iterations, only the RGBD encoder will be applied as the visual backbone for navigation agents. Image augmentations are applied to all views and maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Optimization The overall pre-training strategy minimizes the sum over all three losses, \\(\\mathcal{L}_c\\), \\(\\mathcal{L}_{\\theta}\\) and \\(\\mathcal{L}_d\\). All" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.892, + 0.561 + ], + "angle": 0, + "content": "losses are equally weighted and optimized simultaneously in each iteration. After all training steps, evaluate the model with batch size 128 on 10,000 novel \\((I_s, I_t, M)\\) triplets shows \\(92.02\\%\\) views to maps \\((I \\rightarrow M)\\) and \\(92.03\\%\\) maps to view \\((M \\rightarrow I)\\) alignment accuracy, indicating the correspondence between two modalities has been learned. Please see Appendix for more pre-training statistics and results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.574, + 0.744, + 0.592 + ], + "angle": 0, + "content": "4. Downstream Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.892, + 0.693 + ], + "angle": 0, + "content": "We evaluate our \\(\\mathrm{Ego}^2\\)-Map representations mainly on the R2R-CE navigation [3, 51], as addressing the task highly relies on exploiting the semantic and structural information from observations and ground to language instructions. We also show results on ObjNav [4] to compare with other recent visual representation learning approaches." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.703, + 0.652, + 0.72 + ], + "angle": 0, + "content": "4.1. R2R-CE Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.865 + ], + "angle": 0, + "content": "Our experiments consider two major setups of action spaces, either applying panorama inputs and execute high-level decisions by selecting images pointing towards navigable directions \\((\\mathcal{A}_{High})^3\\), or using egocentric views and perform low-level controls \\((\\mathcal{A}_{Low})\\). For \\(\\mathcal{A}_{High}\\), we adopt the candidate waypoint predictor proposed by Hong et al. [41], which generates navigable waypoint positions around the agent at each time step. Once a waypoint is selected, the agent will move to the position with low-level" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.902 + ], + "angle": 0, + "content": "\\(^{3}\\)High-level VLN agents apply 36 egocentric images to represent its panoramic vision [3], hence, our \\(\\mathsf{Ego}^2\\)-Map features are applicable." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3059" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.091, + 0.894, + 0.244 + ], + "angle": 0, + "content": "
ModelsPre-Training ObjectivesR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
AngularExplorableContrastiveNE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑Collision↓
Baseline4.9857.2648.6742.557.6949.2725.6123.9317.41
1✓8.3332.0216.1513.659.7730.433.753.4371.59
2✓5.8351.2542.5836.347.9447.1524.7422.9810.44
3✓4.8958.4951.7745.897.4750.3527.6225.9513.19
4✓✓5.0358.8651.2845.987.2751.9130.6129.1310.09
5✓✓5.0259.6252.0446.997.4451.3129.5327.9413.04
6✓✓5.7952.9342.9037.257.6450.1927.9526.3916.19
7✓✓✓4.9459.6751.7746.117.2552.0130.4029.0311.25
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.255, + 0.893, + 0.318 + ], + "angle": 0, + "content": "Table 1: Ablation of \\(\\mathsf{Ego}^2\\)-Map learning and influence of angular and explorable objectives on the R2R-CE tasks. Checkmarks indicate applying the corresponding objectives. Baseline applies a pre-trained CLIP-ViT-B/16 model to encode RGB and depth separately. Collision measures the percentage of forward steps which the agent collided with an obstacle; we only consider this metric for \\(\\mathcal{A}_{Low}\\) since agents in \\(\\mathcal{A}_{High}\\) apply a waypoint predictor [41] to obtain navigable positions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.471, + 0.541 + ], + "angle": 0, + "content": "controls. For \\(\\mathcal{A}_{Low}\\), an agent is only allowed to do a single low-level action at each step, including Turn Left/Right \\(15^{\\circ}\\), Forward 0.25 meters, and Stop. In all experiments, we apply the VLN\\(\\rightarrow\\)BERT agent [42], a vision-language transformer pre-trained for navigation, as the policy network. To use our Ego\\(^2\\)-Map representations, we simply replace the agent's original visual encoders (two ResNets trained on ImageNet [39] and trained in Point-Nav [94] for RGB and depth, respectively) with our RGBD encoder (\\(\\S 3.1\\)). Comparing the runtime efficiency, the original encoder has around 50M parameters and the speed is about 4 GFLOPs/image, whereas our method is larger (86M parameters) but faster (20 GFLOPs/image). All visual encoders in our experiments are frozen in navigation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.741 + ], + "angle": 0, + "content": "R2R in continuous environment (R2R-CE) is established over the Matterport3D environments [8] based on the Habitat simulator [82]. The dataset contains 61 scans for training; 11 and 18 scans for validation and testing, respectively. R2R-CE evaluates the agent's performance using multiple metrics, including trajectory length (TL), navigation error (NE): the final distance between the agent and the target, normalized dynamic time warping score (nDTW): distance between the predicted and the ground-truth paths [43], oracle success rate (OSR): the ratio of reaching within 3 meters to the target, success rate (SR): the ratio of stopping within 3 meters to the target, and success weighted by the normalized inverse of the path length (SPL) [2]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.754, + 0.231, + 0.77 + ], + "angle": 0, + "content": "4.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Ablation experiments in Table 1 reveal the influence of different pre-training objectives. We establish our Baseline by using a frozen CLIP-ViT-B/16 to encode RGB and depth separately, followed by a trainable fusion layer to merge the two features, which is a strong baseline that can achieve better results than the previous best encoders (see CLIP-ViT+Depth in Table 4)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Results of Model#1 indicate that employing angular off" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.895, + 0.557 + ], + "angle": 0, + "content": "set prediction as the only task has a devastating effect on the encoder; in fact, we found that \\(\\mathcal{L}_{\\theta}\\) only oscillates if it is minimized alone, leading to features that are not useful in downstream tasks (see details in Appendix). Although learning \\(\\mathcal{L}_{\\theta}\\) with \\(\\mathcal{L}_d\\) or \\(\\mathcal{L}_c\\) can improve the performance in both \\(\\mathcal{A}_{High}\\) and \\(\\mathcal{A}_{Low}\\) (Model#5, Model#6), removing the task from Model#7 will not cause a noticeable difference (Model#4). Meanwhile, learning explorable distance prediction (Model#2, Model#5) is not effective in \\(\\mathcal{A}_{High}\\) scenario because agents with \\(\\mathcal{A}_{High}\\) apply pre-defined waypoints on open space, which means, finding explorable directions and avoid obstacle are not necessary. However, Model#2, Model#4 and Model#6 suggest that learning \\(\\mathcal{L}_d\\) with \\(\\mathcal{L}_c\\) or \\(\\mathcal{L}_{\\theta}\\) will boost the results in \\(\\mathcal{A}_{Low}\\) and effectively reduce the collision rate during navigation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.895, + 0.725 + ], + "angle": 0, + "content": "On the other hand, by comparing the Baseline, Model#3, Model#6, and Model#7, we can see that our proposed \\(\\mathsf{Ego}^2\\)-Map contrastive learning has the largest impact on R2R-CE. Solely learning \\(\\mathcal{L}_c\\) improves the SR and SPL absolutely by \\(3.10\\%\\) and \\(3.34\\%\\) in \\(\\mathcal{A}_{High}\\), as well as \\(2.01\\%\\) and \\(2.02\\%\\) in \\(\\mathcal{A}_{Low}\\), while removing \\(\\mathcal{L}_c\\) from Model#7 dramatically lowers the results in both settings. Meanwhile, we found that \\(\\mathsf{Ego}^2\\)-Map learning can also help avoid collision, implying the useful spatial information carried by the map. In the following experiments, all three losses are applied to pre-train the visual encoders." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.722, + 0.757 + ], + "angle": 0, + "content": "4.3. Discussion and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.903 + ], + "angle": 0, + "content": "How much does the quantity of visual data matter? In Table 2, we compare the effect of sampling a different quantity of data for pre-training our visual encoder. Results show that the agent's performance in R2R-CE drops as the amount of data decreases, and reducing the number of environments has a stronger impact on the results \\((-1.08\\%)\\) SPL for \\(50\\%\\) samples vs. \\(-3.87\\%\\) SPL for \\(50\\%\\) envs with \\(\\mathcal{A}_{High}\\), suggesting the importance of having abundant scenes and structures in learning visual represent" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "3060" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.091, + 0.468, + 0.201 + ], + "angle": 0, + "content": "
Pre-train DataR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
100% data4.9459.6751.7746.117.2552.0130.4029.03
50% samples4.9857.7250.4645.037.4349.9727.5726.22
30% samples5.2856.1148.6142.587.8348.6025.8324.63
10% samples5.6054.8944.4839.087.8646.8322.9521.54
50% envs5.3255.5347.8042.247.5750.3526.5425.15
30% envs5.5653.8144.4838.697.6148.6426.0524.51
10% envs5.7353.4441.9236.897.8847.6223.2222.00
MP3D5.6752.7840.7835.767.9746.7521.9720.60
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.212, + 0.47, + 0.273 + ], + "angle": 0, + "content": "Table 2: Effect of additional environments for pre-training. The percentages indicate the portion of HM3D environments/samples for training. MP3D only uses data collected from the 61 environments in downstream." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.288, + 0.468, + 0.358 + ], + "angle": 0, + "content": "
InitializationR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
CLIP4.9459.6751.7746.117.2552.0130.4029.03
Random4.9957.5549.3243.897.2751.3529.9128.29
IN-21K4.9558.6151.5545.737.0553.3031.0529.69
+IN-21K map5.4056.1847.0942.017.2152.6828.5527.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.461 + ], + "angle": 0, + "content": "Table 3: Effect of using pre-trained encoders for RGBD and map. Random and IN-21K initialize the RGBD encoder randomly or from a ViT pre-trained on ImageNet-21K [23], while using the CLIP-ViT-B/32 to encode maps. +IN-21K map also uses the IN-21K pre-trained ViT to encode the semantic map." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.468, + 0.564 + ], + "angle": 0, + "content": "tations. Meanwhile, we can see that applying less than \\(50\\%\\) of samples or environments cannot yield better results than the baseline in Table 1. This is because \\(\\mathrm{Ego}^2\\)-Map learning requires sufficient positive and negative data pairs to support its contrastive training, as observed in previous literatures [18, 72]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.47, + 0.899 + ], + "angle": 0, + "content": "How much does initialization matter? Table 3 compares the initialization of the RGBD and the map encoders in \\(\\mathsf{Ego}^2\\)-Map network, either from CLIP [72], from scratch or from a ViT-B/16 [25] pre-trained on ImageNet-21K (IN-21K) [23]. We find that random initialization of the RGB encoder only leads to a slight decrease in R2R-CE performance, while initializing it from pre-trained ViT can achieve comparable results to Model#7. We further investigate these results by also replacing the initialization of our map encoder from CLIP with IN-21K pre-trained ViT; although the losses of the two models saturate to the same level in pre-training, a drastic drop is observed in R2R-CE (even lower than Random). We hypothesize that some semantics from CLIP can be introduced to the RGBD encoder by the map encoder through contrastive learning. While previous works often use a convolutional network to process maps [14, 32, 33, 73], there remains a valuable open question of what model is suitable for encoding maps and how to train it to benefit navigation. We will leave the study of encoding maps for future work." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.091, + 0.892, + 0.138 + ], + "angle": 0, + "content": "
MethodsR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
CLIP-ViT+Depth +L5.4755.5547.1541.287.9347.7622.6821.69
5.2457.7448.6743.787.0752.5930.0728.74
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.149, + 0.892, + 0.211 + ], + "angle": 0, + "content": "Table 4: Pre-training a different visual encoder with Ego2-Map objectives. The model applies CLIP-ViT-B/16 and a ResNet-50 trained for Point-Nav [94] to encode RGB and depth, respectively." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.217, + 0.892, + 0.278 + ], + "angle": 0, + "content": "
Ego2-MapR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
No semantics5.5157.6047.0442.257.3151.5629.7428.34
No space5.2457.4248.9443.527.6649.2029.3127.75
No target5.0256.2647.2041.218.0551.0430.8329.07
" + }, + { + "type": "table_caption", + "bbox": [ + 0.51, + 0.288, + 0.88, + 0.305 + ], + "angle": 0, + "content": "Table 5: Ablation of information in Ego2-Map learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.501 + ], + "angle": 0, + "content": "Effect of \\(\\mathcal{L}\\) on a different encoder We further evaluate our proposed \\(\\mathrm{Ego}^2\\)-Map objective in pre-training a different visual encoder (Table 4). Here we consider the previous state-of-the-art encoder CLIP-ViT+Depth, which applies CLIP-ViT-B/16 and a ResNet-50 depth net trained on Gibson [95] for PointNav [82] to encode RGB and depth, respectively, following by a fusion module to integrate the encoded features. Pre-training the model with \\(\\mathcal{L}\\) leads to a significant improvement, obtaining \\(+2.50\\%\\) and \\(+7.05\\%\\) higher SPL with \\(\\mathcal{A}_{High}\\) and \\(\\mathcal{A}_{Low}\\). These results suggest that \\(\\mathrm{Ego}^2\\)-Map learning has the potential to be generalized to other visual encoders." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.801 + ], + "angle": 0, + "content": "Information in \\(\\mathbf{Ego}^2\\)-Map contrastive learning In Table 5, we ablate the information applied in the \\(\\mathbf{Ego}^2\\)-Map contrastive learning. Specifically, we either remove the object semantics by masking their colored segmentations with the same color, or remove explorable regions by masking open space and void with the same color (see unmasked maps in Figure 2), or remove the target view from the view pairs to create ambiguity in agent's transition. The results show that learning \\(\\mathbf{Ego}^2\\)-Map without the semantic clues or open space in the maps, or without a specified target greatly damages agent performance in \\(\\mathcal{A}_{High}\\), reflecting the importance of including this information. We also find that the agent with \\(\\mathcal{A}_{Low}\\) is less sensitive to method variations in pre-training; the remaining spatial or object information on a map is still beneficial to enhance the visual representation for supporting \\(\\mathcal{A}_{Low}\\) navigation, which could be the reason why angular offset and explorable distance predictions do not show a consistent benefit in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.794, + 0.832 + ], + "angle": 0, + "content": "4.4. Comparison to Previous Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Advantages of Visual Representations (R2R-CE) In Table 6, we compare our method of applying \\(\\mathsf{Ego}^2\\)-Map RGBD encoder to the CWP-VLN\\(\\vec{\\circ}\\)BERT agent [41] (same model as Model#7 in Table 1) with previous approaches" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3061" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.304 + ], + "angle": 0, + "content": "using \\(\\mathcal{A}_{High}\\) on the R2R-CE testing split4. Results show that our proposed \\(\\mathrm{Ego}^2\\)-Map learning brings significant improvement for all metrics, achieving a \\(47\\%\\) SR \\((+3\\%)\\) and a \\(41\\%\\) SPL \\((+4\\%)\\) over the previous best [50]. In addition, Table 7 establishes a fair comparison with methods using \\(\\mathcal{A}_{Low}\\). We can see that \\(\\mathrm{Ego}^2\\)-Map features greatly boost the result of the base agent CWP-VLN BERT [41] (23% to 30% SR), and achieve a SPL comparable to recent mapping-based methods such as CM2 [33] and WS-MGMap [14]. Note that using \\(\\mathrm{Ego}^2\\)-Map representations does not conflict with online mapping; while we only experiment with non-mapping-based agents, we believe the features hold great potential to facilitate modeling between views and maps in mapping-based models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.473, + 0.822 + ], + "angle": 0, + "content": "Learning Methods (ObjNav) We further compare the effect of visual representation learning methods by applying our visual encoder on ObjNav [4] as in the recent approaches [46, 96] (Table 8). All methods in the table adopt a simple pipeline as in the baseline model [94], which feeds the concatenation of visual features, GPS+Compass encodings, and the encodings of previous action to a GRU [19], then, uses a fully-connected layer to predict an action from the updated agent's state. Briefly, EmbCLIP directly uses the pre-trained CLIP-ResNet50 [72] to encode the RGB inputs, EmbCLIP-ViT+Depth applies the CLIP-ViT-B/16 to encode RGB and an extra depth net [82] pre-trained on Gibson [95] to encode the depth inputs. OVRL pre-trains the ResNet encoder with self-distillation method DINO [6], in which a student network is trained to match the output of a teacher network. Moreover, OVRL applies the Omnidata Starter Dataset \\((\\mathrm{OSD})^5\\) [28], which is much larger and more diverse than the data for our Ego\\(^2\\)-Map learning (only uses the HM3D [74] subset). ObjNav measures the same metrics as R2R-CE, first, we can see that an agent using Ego\\(^2\\)-Map features greatly improves over the baseline and the EmbCLIP. Compared to OVRL, despite the method applies OSD for pre-training and fine-tunes the network end-to-end with human demonstrations, our method obtains a better success rate \\((+0.4\\%)\\) and much higher SPL \\((+3.2\\%)\\). Note that, although not directly comparable, as reported in the OVRL, the SPL on ImageNav [63] without fine-tuning the visual encoder will drop drastically from \\(26.9\\%\\) to \\(17.0\\%\\), whereas all our experiments keep the visual encoder frozen during navigation. These results suggest that Ego\\(^2\\)-Map representations are generalizable to different navigation tasks and provide more robust visual representations." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.091, + 0.894, + 0.177 + ], + "angle": 0, + "content": "
Methods (AHigh)R2R-CE Test-Unseen
TLNE↓OSR↑SR↑SPL↑
Waypoint Models [49]8.026.65373230
CWP-CMA [41]11.856.30493833
CWP-VLN BERT [41]13.315.89514236
Sim2Sim [50]11.436.17524437
Ego2-Map+CWP-VLN BERT (ours)13.055.54564741
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.182, + 0.892, + 0.213 + ], + "angle": 0, + "content": "Table 6: Comparison of agent performance on R2R-CE test server. All methods use high-level action space \\((\\mathcal{A}_{High})\\)" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.216, + 0.894, + 0.336 + ], + "angle": 0, + "content": "
Methods (ALow)R2R-CE Val-Unseen
TLNE↓OSR↑SR↑SPL↑
CMA+PM+DA+Aug [51]8.647.37403230
SASRA [44] †7.898.32-2422
LAW [77]8.896.83443531
CWP-CMA [41]°8.227.54-2725
CWP-VLN BERT [41]°7.427.66-2322
CM2 [33] †11.547.02423428
WS-MGMap (SemMap only) [14] †10.896.80423328
Ego2-Map+CWP-VLN BERT (ours)8.037.25373029
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.346, + 0.894, + 0.408 + ], + "angle": 0, + "content": "Table 7: Comparison of agents with low-level action space \\((\\mathcal{A}_{Low})\\) in R2R-CE Val-Unseen. \\(\\dagger\\): mapping-based methods. \\(\\circ\\): \\(4\\%\\) of data is removed but the comparison is still valid due to the large performance gap." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.418, + 0.894, + 0.518 + ], + "angle": 0, + "content": "
MethodsPre-Training DatasetObjNav MP3D Val
NE↓SR↑SPL↑
Baseline [94]X6.908.01.8
EmbCLIP [46]*WebImageText5.2620.98.3
EmbCLIP-ViT+DepthWebImageText+Gibson4.9023.38.6
OVRL no pretrain [76] †X-24.25.9
OVRL [96] †OSD-28.67.4
Ego2-Map+Baseline (ours)HM3D5.1729.010.6
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.635 + ], + "angle": 0, + "content": "Table 8: Comparison on pre-trained visual encoders for ObjNav. \\(\\dagger\\) indicates the visual encoder is tuned end-to-end with behavior cloning on \\(40\\mathrm{k}\\) human demonstrations collected by Habitat-Web [76], while the others freeze the visual encoder during navigation and only train the agent with DD-PPO [94] on the original data. *Results obtained by re-evaluating the officially released best model checkpoint." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.62, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In this paper, we introduce a novel method of learning navigational visual representations with contrastive learning between egocentric views pairs and top-down semantic maps (Ego\\(^2\\)-Map). The method transfers the compact semantic and spatial information carried by a map to the egocentric representations, which greatly facilitates the agent's visual perception. Experiments show that Ego\\(^2\\)-Map features greatly improve the downstream navigation, such as ObjNav and VLN, and demonstrate generalization potential to different visual backbones. We believe the Ego\\(^2\\)-Map contrastive learning proposes a new direction of visual representation learning for navigation and provides the possibility of better modeling the correspondence between views and maps, which can further benefit agent's planning and action. Note that our work also produces a potentially ef" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.838, + 0.493, + 0.903 + ], + "angle": 0, + "content": "\\(^{4}\\)R2R-CE Challenge Leaderboard: https://eval.ai/web/challenges/challenge-page/719/leaderboard/1966 \n\\(^{5}\\)OSD [28] contains approximately 14.5 million images rendered from diverse 3D environments, including Replica [88], Replica+GSO [26], Hypersim [79], Taskonomy [100], BlendedMVG [97] and HM3D [74]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3062" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "fective map encoder whose full capability is worth investigating in future work." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.134, + 0.471, + 0.301 + ], + "angle": 0, + "content": "Limitations The need to build semantic maps to enable the \\(\\mathbf{Ego}^2\\)-Map contrastive learning is an inevitable cost of this method; compared to other self-supervised visual representation learning approaches, \\(\\mathbf{Ego}^2\\)-Map requires either the semantic annotations of scenes, or traversable environments and a generalizable semantic map constructor. As a result, the data collection could be much harder. However, we also witnessed an increasing number of interactive 3D scenes being built in recent years with dense semantic annotations [22, 74, 82, 88, 95], which can facilitate scaling up our \\(\\mathbf{Ego}^2\\)-Map learning in the future." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.318, + 0.174, + 0.333 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.344, + 0.469, + 0.411 + ], + "angle": 0, + "content": "[1] Dong An, Zun Wang, Yangguang Li, Yi Wang, Yicong Hong, Yan Huang, Liang Wang, and Jing Shao. 1st place solutions for rxr-habitat vision-and-language navigation competition (cvpr 2022). arXiv preprint arXiv:2206.11610, 2022.2" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.416, + 0.468, + 0.484 + ], + "angle": 0, + "content": "[2] Peter Anderson, Angel Chang, Devendra Singh Chaplot, Alexey Dosovitskiy, Saurabh Gupta, Vladlen Koltun, Jana Kosecka, Jitendra Malik, Roozbeh Mottaghi, Manolis Savva, et al. 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Navigating to objects in unseen environments by distance prediction. arXiv preprint arXiv:2202.03735, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3067" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Navigational Visual Representations with Semantic Map Supervision/94d1f5dd-be00-46b4-8d2e-2c6681cb4e80_origin.pdf b/2023/Learning Navigational Visual Representations with Semantic Map Supervision/94d1f5dd-be00-46b4-8d2e-2c6681cb4e80_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c02caf9473713a9cee0e0699292c1d79fc965de5 --- /dev/null +++ b/2023/Learning Navigational Visual Representations with Semantic Map Supervision/94d1f5dd-be00-46b4-8d2e-2c6681cb4e80_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:05267849b17ba8aa8a25515afa5ada8a6ab6d445eb9f400ccc4d8c37f7bf9fcf +size 2911285 diff --git a/2023/Learning Navigational Visual Representations with Semantic Map Supervision/full.md b/2023/Learning Navigational Visual Representations with Semantic Map Supervision/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ec3e2ad2e903377adbcb992b1e6cbe843936ea26 --- /dev/null +++ b/2023/Learning Navigational Visual Representations with Semantic Map Supervision/full.md @@ -0,0 +1,331 @@ +# Learning Navigational Visual Representations with Semantic Map Supervision + +Yicong Hong $^{12,\dagger}$ Yang Zhou $^{1}$ Ruiyi Zhang $^{1}$ + +Franck Dernoncourt1 Trung Bui1 Stephen Gould2 Hao Tan1 + +$^{1}$ Adobe Research $^{2}$ The Australian National University + +mr.yiconghong@gmail.com + +stephen.gould@anu.edu.au, {yazhou,ruizhang,dernonco,bui,hatan}@adobe.com + +Project URL: https://github.com/YicongHong/Ego2Map-NaViT + +# Abstract + +Being able to perceive the semantics and the spatial structure of the environment is essential for visual navigation of a household robot. However, most existing works only employ visual backbones pre-trained either with independent images for classification or with self-supervised learning methods to adapt to the indoor navigation domain, neglecting the spatial relationships that are essential to the learning of navigation. Inspired by the behavior that humans naturally build semantically and spatially meaningful cognitive maps in their brains during navigation, in this paper, we propose a novel navigational-specific visual representation learning method by contrasting the agent's egocentric views and semantic maps (Ego $^2$ -Map). We apply the visual transformer as the backbone encoder and train the model with data collected from the large-scale Habitat-Matterport3D environments. Ego $^2$ -Map learning transfers the compact and rich information from a map, such as objects, structure and transition, to the agent's egocentric representations for navigation. Experiments show that agents using our learned representations on object-goal navigation outperform recent visual pre-training methods. Moreover, our representations significantly improve vision-and-language navigation in continuous environments for both high-level and low-level action spaces, achieving new state-of-the-art results of $47\%$ SR and $41\%$ SPL on the test server. + +# 1. Introduction + +Visual representations for navigation should capture the rich semantics and the complex spatial relationships of the observations, which helps the agent to recognize visual entities and its transition in space for effective exploration. However, previous works usually adopt visual backbones + +which only focus on capturing the semantics of a static image, ignoring its connection to the agent or the correspondence to other views in a continuous environment [3, 9, 40, 42, 51, 68, 98]. One common approach is to apply encoders pre-trained for object/scene classification (e.g. ResNet [39] on ImageNet [80]/Places365 [102]), object detection (e.g. RCNN [38, 78] on VisualGenome [52]/MSCOCO [57]) or semantic segmentation (e.g. RedNet [45] on SUN RGBD [87]), or more recently, to use CLIP [72], which is trained for aligning millions of images and texts to encode agent's RGB observations [31, 46, 84]. Despite the increasing generalization ability of the features and rising zero-shot performance on novel targets, there still exists a large visual domain gap between these features and the features suitable for navigation since they lack the expressiveness of spatial relationships. For example, the connection between time-dependent observations and the correspondence between egocentric views and the spatial structure of an environment, which are important to decision making during navigation. + +We suggest that there are two main difficulties in learning navigational-specific visual representations in previous research; First, there lacked a large-scale and realistic dataset of indoor environments. Popular datasets such as Matterport3D [8] and Gibson [95] provide traversable scenes rendered from real photos, but either the number of scenes is very limited, or the quality of the 3D scan is low. Synthetic datasets such as ProcTHOR [22] contain 10K generated scenes, but they are unrealistic and simple and do not capture the full complexity of real-world environments. Second, fine-tuning visual encoders while learning to navigate is very expensive because of the long traveling horizon, especially in tasks that require extensive exploration [4, 53, 63, 86]. Moreover, due to the scene scarcity, fine-tuning visual encoders is unlikely to generalize well to the novel environments. To address these problems, a large amount of research has been dedicated to augmenting the environments, either editing the agent's observations + +[56, 90] or adding objects [62], building new spatial structures [58], applying web-images to replace the views of the same categories [35] or generating new scenes [47, 48, 55]. Unlike augmentation, which essentially requires the agent's policy network to adapt new visual data, another strategy is to first pre-train the visual encoder before learning to navigate. Those methods usually apply images captured in 3D scenes and perform self-supervised learning or tune the encoder with proxy tasks (e.g. masked region modeling, angular prediction) to mitigate the domain gap and introduce spatial awareness [15, 17, 96, 98]. Furthermore, recent works tend to apply CLIP [72] to process visual inputs, as the model can provide powerful representations for grounding semantic and spatial concepts, hence facilitating learning [1, 31, 46, 83, 84, 85]. Although these methods have demonstrated significant improvements on navigation performance, they either only use more data without addressing the learning problem, not generalizable across different tasks, or ignore the spatial correspondence between consecutive frames which the agent will capture as it moves. + +Inspire by the research in cognitive science that humans naturally build virtual maps from perspective observations that are helpful to track semantics, spaces and movements during navigation [29, 91, 92]; we propose a contrastive learning method between the agent's Egocentric view pairs and top-down semantic Maps (Ego $^2$ -Map) for training visual encoders appropriate for navigation. Specifically, we first sample RGBD images and create corresponding semantic maps [7] from the large-scale Habitat-Matterport3D environments (HM3D) [74, 82] which contains hundreds of photo-realistic scenes, obtaining abundant and effective visual data. Then, we encode the sampled RGBD observations and the semantic maps with two separate visual backbones, respectively, and train the entire model with our Ego $^2$ -Map contrastive learning. Once trained, the RGBD encoder will be plugged into an agent's network to facilitate visual perception. We argue that the map contains very rich and compact visual clues such as spatial structure, accessible areas and unexplored regions, object entities and their arrangement, as well as the agent's transition in the environment that are essential to navigation. Compared to existing online mapping-based approaches [10, 14, 32, 44], Ego $^2$ -Map learning efficiently produces visual features that imply a complete map of the space known a view priori, while the online map is only a partial map. Importantly, Ego $^2$ -Map explores a new possibility of modeling semantics and structures from simple RGBD inputs, which its resulting features are directly applicable to non-mapping-based navigational models and effectively generalizable to different tasks. + +We mainly evaluate the features learned from Ego $^2$ -Map on the Room-to-Room Vision-and-Language Navigation in Continuous Environments (R2R-CE) [3, 51] task, which requires an agent to navigate in photo-realistic environ + +ments following human natural language instructions such as "Leave the bedroom and enter the kitchen. Walk forward and take a left at the couch. Stop in front of the window." Addressing R2R-CE highly relies on exploiting the correspondence between contextual clues and the agent's observations, hence it is crucial for the visual encoder to provide semantic and structural meaningful representations. We found that the proposed $\mathsf{Ego}^2$ -Map features significantly boost the agent's performance, obtaining $+3.56\%$ and $+5.10\%$ absolute SPL improvements over the CLIP baseline [72] under the settings of high-level and low-level action spaces, respectively, and achieves the new best results on the R2R-CE test server. Moreover, our experiments show that $\mathsf{Ego}^2$ -Map learning also outperforms other visual representation learning methods such as OVRL [96] on the Object-Goal Navigation task (ObjNav), suggesting the strong generalization potential of the proposed methods. + +# 2. Related Work + +Visual Navigation A great variety of scenarios have been proposed to learn visual navigation in photo-realistic environments [8, 21, 54, 82, 86, 89, 95] with different modalities of inputs, targets and action spaces [3, 4, 11, 13, 51, 66, 70, 94]. Due to the distinct nature of the tasks, diverse methods are investigated accordingly. For instance, in Object-Nav, which only provides a high-level goal and requires exploration, mapping-based methods are frequently applied [10, 32, 60, 73, 105], whereas in vision-and-language navigation (VLN) [3], large vision-language models are employed to match instructions and agent's observations [42, 61, 71, 83, 103] to perform panoramic actions [30]. Recently, there is an emerging trend of scaling up the training data to address the common data scarcity issue, either in terms of the number of environments [22, 74] or the amount of supervision [16, 76, 93]. Unlike most of the previous works, we focus on improving the visual backbone, aiming to produce robust and generalizable visual representations specialized for navigation. + +Visual Representations for Embodied AI Recent years have witnessed a trend of moving away from visual encoders pre-trained for object classification in Embodied AI due to their inefficiency in representing complex real-world scenes or mapping to actions. Instead, large vision-language models such as CLIP which demonstrates strong zero-shot performance across visual domains is widely applied [20, 72], enhancing the semantic representations in robotic manipulation [85], assisting 3D trajectory modification and speed control [5], benefiting the language-conditioned view-selection problem in VLN [83, 84] as well as improving other control and navigation results [31, 46, 67]. Moreover, EmbCLIP shows that the CLIP features provide much better semantic and geometric primitives such as + +![](images/b78fbc0aa404047ef0a0bc5bea16e2ab0c5b538207b8c36e2c974dce5db20f3b.jpg) +Figure 1: Network architecture. The Semantic MapNet [7] is applied to draw a semantic map using observations captured from a source to a target position. Then, two learnable visual encoders are applied to encode the egocentric views and the map, respectively, followed by non-linear headers $\Pi_{i}$ and $\Pi_{m}$ to learn the Ego $^2$ -Map contrastive objective $\mathcal{L}_c$ . $f_{s}$ and $f_{t}$ are the paired view features of a trajectory (see §3.2). Dash arrows indicate pre-processing without gradient update. + +object presence, object reachability, and free space that are valuable to Embodied AI [46]. In terms of self-supervised visual representation learning for indoor navigation, recent works that are the most relevant to ours include OVRL [96] which applies knowledge distillation based on DINO [6], EPC which predicts masked observations from a trajectory [75], and CRL which jointly learns a visual encoder with a policy network that maximizes the representation error [27]. In contrast to all previous works, this paper explores a novel idea of encoding the explicit structural and semantic information available in maps implicitly in the visual encoder thereby facilitating efficient and effective generalization across different visual navigation tasks and models. + +Exploiting Visual Features A great variety of proxy tasks and auxiliary objectives have been applied to exploit information from the visual data which is beneficial to navigation. For instance, Ye et al. [98, 99] promote understanding of spatiotemporal relations of observations by estimating the timestep difference between two views, Qi et al. [69] predict room-types from object features to improve scene understanding, and Se et al. [81] determine the furthest reachable waypoint on a topological graph using the node observations. To extract the geometric information, Gordon et al. [34] use the encoded visual features to predict depth and surface normals, reconstruct RGB input, and forecast the visual features by taking certain actions. Depth prediction has also been studied by Mirowski et al. [64], Desai et al. [24] and Chattopadhyay et al. [12], along with learning the inverse dynamics by predicting an action taken between two sequential observations [37, 64]. Complement + +tary to the previous methods for interpreting visual features, our Ego $^2$ -Map learning guides a visual encoder to produce representations with expressive spatial information. + +# 3. Contrastive Learning between Egocentric Views and Semantic Maps (Ego $^2$ -Map) + +We will first describe the overall network architecture for training the visual encoders (§3.1), followed by the details of Ego²-Map objectives (§3.2), as well as two other widely applied spatial-aware auxiliary tasks which we investigated with our Ego²-Map learning (§3.3). Then, we will talk about the data collection (§3.4) and network training (§3.5) processes. + +# 3.1. Network Architecture + +We build the network for $\mathrm{Ego}^2$ -Map learning based on a ViT-B/16 model (default initialized from CLIP [72], whose effect will be studied in §4.3). Unlike previous methods for visual navigation, which mostly employ two independent encoders to process RGB and depth images, we investigate a compact representation by feeding RGB+Depth as four-channel inputs (Figure 1). To merge the two visual modalities, we use two separate convolutional layers to encode the RGB channels $I_{rgb}$ and the depth map $I_d$ , respectively, followed by a token-wise concatenation and a non-linear projection $\Pi_v$ to merge the resulting feature maps before feeding to the transformer layers as + +$$ +v _ {r g b} = \operatorname {C o n v} _ {r g b} \left(I _ {r g b}\right), \quad v _ {d} = \operatorname {C o n v} _ {d} \left(I _ {d}\right) \tag {1} +$$ + +and + +$$ +f = \operatorname {V i T} \left(\boldsymbol {\Pi} _ {v} \left[ v _ {r g b}; v _ {d} \right]\right) \tag {2} +$$ + +The pooled features $f$ of the RGBD encoder are applied for learning all spatial-aware objectives $\mathcal{L}_{\theta}$ , $\mathcal{L}_d$ and $\mathcal{L}_c$ , which will be specified in the following. + +# 3.2. $\mathbf{Ego}^2$ -Map Contrastive Objective + +The motivation of this task is to introduce the information within a map to single-view features, offering the agent high-level semantic and spatial clues to navigate towards distant targets. Specifically, we build positive samples by coupling a views-pair $(I_s$ and $I_t$ from the two endpoints of a path) with a top-down semantic map $M$ that represents the agent's transition and observations along the path, while using mismatched views-pairs and maps of different routes or environments as the negatives. Each semantic map is generated by the off-the-shelf Semantic MapNet [7], using the RGBD observations collected by an agent traveling from the source view $I_s$ to the target view $I_t$ via the shortest path $^2$ . The semantic map provides abundant information about the open space, obstacles, unexplored regions, observed objects, and the agent's action, which we consider as highly valuable and compact representations for agent navigation (see maps in Figure 2). To encode $M$ , we apply an additional ViT-B/32 [25] with the last three transformer layers unfrozen to adapt the map images. Then, the egocentric features of the two views $f_s$ and $f_t$ , and the map features $f_m$ will be passed to two MLP (multi-layer perceptrons) headers $\Pi_i$ and $\Pi_m$ , respectively, to compute an alignment score as: + +$$ +c ^ {I} = \boldsymbol {\Pi} _ {i} [ f _ {s}; f _ {t} ], \qquad c ^ {M} = \boldsymbol {\Pi} _ {m} [ f _ {m} ] \qquad (3) +$$ + +and + +$$ +\langle c ^ {I}, c ^ {M} \rangle = \frac {c ^ {I} \cdot c ^ {M}}{\| c ^ {I} \| \| c ^ {M} \|} \tag {4} +$$ + +Then, the InfoNCE loss [65, 101] is applied for $\mathrm{Ego}^2$ -Map contrastive learning. For each $j$ -th views-map pair in a minibatch of size $N$ , we have + +$$ +\mathcal {L} _ {c, j} = \mathcal {L} _ {c, j} ^ {I \rightarrow M} + \mathcal {L} _ {c, j} ^ {M \rightarrow I} \tag {5} +$$ + +where the views to maps $(I\to M)$ loss can be expressed as + +$$ +\mathcal {L} _ {c, j} ^ {I \rightarrow M} = - \log \frac {\exp \left(\left\langle c _ {j} ^ {I} , c _ {j} ^ {M} \right\rangle / \tau\right)}{\sum_ {k = 1} ^ {N} \exp \left(\left\langle c _ {j} ^ {I} , c _ {k} ^ {M} \right\rangle / \tau\right)} \tag {6} +$$ + +and the map to views loss $\mathcal{L}_{c,j}^{M\to I}$ likewise. Parameter $\tau \in \mathbb{R}_+$ denotes a learnable temperature. + +# 3.3. Other Spatial-Aware Objectives + +We investigate two additional widely applied proxy tasks with our Ego $^2$ -Map learning. Note that we do not claim any novelty for applying these tasks but focus on studying their effect on training the representations. + +Angular Offset Prediction Given two images taken from random headings at the same position, the task predicts the angular offset between them to facilitate the modeling of correspondence between views. A similar proxy task has been applied in previous works, which predicts discrete angles and uses an extra directional encoding to imply orientation [15] or regresses the agent's turning angle conditioned on language during navigation [104]. Specifically, we pass the two pooled RGBD features $f_{\theta_0}$ and $f_{\theta_1}$ , corresponding to images at two orientations of the same viewpoint, into a learnable non-linear header $\Pi_{\theta}$ to predict the offset as $\theta^p = \Pi_{\theta}[f_{\theta_0};f_{\theta_1}]$ . The task is learned by minimizing the mean squared error $\mathcal{L}_{\theta} = E[(\theta^p - \theta^*)^2]$ , where $\theta^*$ is the ground-truth angular difference between $[-\pi, \pi]$ , denoting either clockwise or counter-clockwise rotation whichever is closer to encourage agent's efficient rotation. + +Explorable Distance Prediction To benefit the searching of explorable regions and assist obstacle avoidance, the task estimates the agent's maximal distance to forward without being blocked by any obstacle [11, 36]. Using the same notations as above, the module regresses a value from an RGBD image as $d^{p} = \Pi_{d}[f]$ , and is trained with supervision $\mathcal{L}_d = E[(d^p - d^*)^2]$ . We cap the ground-truth distance $d^{*}$ in the range of 0.5 to 5.0 meters to match the common range of the agent's depth sensors. + +# 3.4. Data Collection + +We follow the train-validation-test split of the HM3D scenes [74] and use the first 800 environments for learning. We randomly sample 252,537 viewpoint positions from the environments (see Figure 3) and render more than a million RGBD images from those positions to create 500,000 $(I_{\theta_0}, I_{\theta_1})$ views pairs as well as 500,000 $(I_s, I_t, M)$ triplets for learning $\mathcal{L}_{\theta}$ and $\mathcal{L}_c$ , respectively, while using all the images to learn $\mathcal{L}_d$ . The positions are sampled such that all points must be located in the open space and the minimal geodesic distance between any two points is greater than 0.40 meters. Each image collected for $\mathrm{Ego}^2$ -Map contrastive learning is either a unique source or target view in all trajectories, and each trajectory is created by computing the shortest path between two randomly paired views within a 7 meters range. We feed the RGBD images captured from a trajectory to the Semantic MapNet [7] for drawing the corresponding semantic map. Note that the Semantic MapNet is trained on the MP3D environments [8], but we found that + +![](images/1aba1a5107cfdb7683fadb67e2e841058457e25a2c3ced6ca77108e599e45a02.jpg) +Figure 2: Illustration of $\mathbf{Ego}^2$ -Map contrastive learning. The method encodes the paired source and target egocentric views $(I_s, I_t)$ into feature $c^I$ , then learns to align it with the feature $c^M$ of the corresponding top-down map $M$ . Negative view pairs $(I_{s'}, I_{t'})$ and maps $(M')$ are sampled from different trajectories or different environments, which are pushed away from the reference pair. The blue dashed line on the left part of the figure indicates the agent's trajectory, which is visualized with directional color in map $M$ . The map is also powered with semantic information (denoted at the bottom right). + +![](images/9b74359821ca4a8192244811aa642b5ec5a229167ff5d2534b3c0ce2d8b8c347.jpg) +(a) 3D scan + +![](images/c136f4a2e5e6ef3609e0596ee9fde2a306a0e86278a4b937244b93897b103b3b.jpg) +(b) Occupancy map and sampled positions +Figure 3: Illustration of an HM3D environment scan and the sampled positions (blue points) in open space (gray area). + +it also generalizes well to the HM3D scenes. We refer to the Appendix for more sampling and dataset creation details. + +# 3.5. Training + +Implementation Details We initialize the RGBD encoder and the map encoder of our visual representation network with CLIP, a visual transformer pre-trained for aligning image-language pairs [72]. Specifically, the additional depth convolutional layer and the projection layer in the RGBD encoder are initialized randomly. All network variants in our experiments are trained with batch size 994 for 100 epochs using the AdamW optimizer [59]. After all training iterations, only the RGBD encoder will be applied as the visual backbone for navigation agents. Image augmentations are applied to all views and maps. + +Optimization The overall pre-training strategy minimizes the sum over all three losses, $\mathcal{L}_c$ , $\mathcal{L}_{\theta}$ and $\mathcal{L}_d$ . All + +losses are equally weighted and optimized simultaneously in each iteration. After all training steps, evaluate the model with batch size 128 on 10,000 novel $(I_s, I_t, M)$ triplets shows $92.02\%$ views to maps $(I \rightarrow M)$ and $92.03\%$ maps to view $(M \rightarrow I)$ alignment accuracy, indicating the correspondence between two modalities has been learned. Please see Appendix for more pre-training statistics and results. + +# 4. Downstream Experiments + +We evaluate our $\mathrm{Ego}^2$ -Map representations mainly on the R2R-CE navigation [3, 51], as addressing the task highly relies on exploiting the semantic and structural information from observations and ground to language instructions. We also show results on ObjNav [4] to compare with other recent visual representation learning approaches. + +# 4.1. R2R-CE Setup + +Our experiments consider two major setups of action spaces, either applying panorama inputs and execute high-level decisions by selecting images pointing towards navigable directions $(\mathcal{A}_{High})^3$ , or using egocentric views and perform low-level controls $(\mathcal{A}_{Low})$ . For $\mathcal{A}_{High}$ , we adopt the candidate waypoint predictor proposed by Hong et al. [41], which generates navigable waypoint positions around the agent at each time step. Once a waypoint is selected, the agent will move to the position with low-level + +
ModelsPre-Training ObjectivesR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
AngularExplorableContrastiveNE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑Collision↓
Baseline4.9857.2648.6742.557.6949.2725.6123.9317.41
1✓8.3332.0216.1513.659.7730.433.753.4371.59
2✓5.8351.2542.5836.347.9447.1524.7422.9810.44
3✓4.8958.4951.7745.897.4750.3527.6225.9513.19
4✓✓5.0358.8651.2845.987.2751.9130.6129.1310.09
5✓✓5.0259.6252.0446.997.4451.3129.5327.9413.04
6✓✓5.7952.9342.9037.257.6450.1927.9526.3916.19
7✓✓✓4.9459.6751.7746.117.2552.0130.4029.0311.25
+ +Table 1: Ablation of $\mathsf{Ego}^2$ -Map learning and influence of angular and explorable objectives on the R2R-CE tasks. Checkmarks indicate applying the corresponding objectives. Baseline applies a pre-trained CLIP-ViT-B/16 model to encode RGB and depth separately. Collision measures the percentage of forward steps which the agent collided with an obstacle; we only consider this metric for $\mathcal{A}_{Low}$ since agents in $\mathcal{A}_{High}$ apply a waypoint predictor [41] to obtain navigable positions. + +controls. For $\mathcal{A}_{Low}$ , an agent is only allowed to do a single low-level action at each step, including Turn Left/Right $15^{\circ}$ , Forward 0.25 meters, and Stop. In all experiments, we apply the VLN $\rightarrow$ BERT agent [42], a vision-language transformer pre-trained for navigation, as the policy network. To use our Ego $^2$ -Map representations, we simply replace the agent's original visual encoders (two ResNets trained on ImageNet [39] and trained in Point-Nav [94] for RGB and depth, respectively) with our RGBD encoder ( $\S 3.1$ ). Comparing the runtime efficiency, the original encoder has around 50M parameters and the speed is about 4 GFLOPs/image, whereas our method is larger (86M parameters) but faster (20 GFLOPs/image). All visual encoders in our experiments are frozen in navigation. + +R2R in continuous environment (R2R-CE) is established over the Matterport3D environments [8] based on the Habitat simulator [82]. The dataset contains 61 scans for training; 11 and 18 scans for validation and testing, respectively. R2R-CE evaluates the agent's performance using multiple metrics, including trajectory length (TL), navigation error (NE): the final distance between the agent and the target, normalized dynamic time warping score (nDTW): distance between the predicted and the ground-truth paths [43], oracle success rate (OSR): the ratio of reaching within 3 meters to the target, success rate (SR): the ratio of stopping within 3 meters to the target, and success weighted by the normalized inverse of the path length (SPL) [2]. + +# 4.2. Ablation Study + +Ablation experiments in Table 1 reveal the influence of different pre-training objectives. We establish our Baseline by using a frozen CLIP-ViT-B/16 to encode RGB and depth separately, followed by a trainable fusion layer to merge the two features, which is a strong baseline that can achieve better results than the previous best encoders (see CLIP-ViT+Depth in Table 4). + +Results of Model#1 indicate that employing angular off + +set prediction as the only task has a devastating effect on the encoder; in fact, we found that $\mathcal{L}_{\theta}$ only oscillates if it is minimized alone, leading to features that are not useful in downstream tasks (see details in Appendix). Although learning $\mathcal{L}_{\theta}$ with $\mathcal{L}_d$ or $\mathcal{L}_c$ can improve the performance in both $\mathcal{A}_{High}$ and $\mathcal{A}_{Low}$ (Model#5, Model#6), removing the task from Model#7 will not cause a noticeable difference (Model#4). Meanwhile, learning explorable distance prediction (Model#2, Model#5) is not effective in $\mathcal{A}_{High}$ scenario because agents with $\mathcal{A}_{High}$ apply pre-defined waypoints on open space, which means, finding explorable directions and avoid obstacle are not necessary. However, Model#2, Model#4 and Model#6 suggest that learning $\mathcal{L}_d$ with $\mathcal{L}_c$ or $\mathcal{L}_{\theta}$ will boost the results in $\mathcal{A}_{Low}$ and effectively reduce the collision rate during navigation. + +On the other hand, by comparing the Baseline, Model#3, Model#6, and Model#7, we can see that our proposed $\mathsf{Ego}^2$ -Map contrastive learning has the largest impact on R2R-CE. Solely learning $\mathcal{L}_c$ improves the SR and SPL absolutely by $3.10\%$ and $3.34\%$ in $\mathcal{A}_{High}$ , as well as $2.01\%$ and $2.02\%$ in $\mathcal{A}_{Low}$ , while removing $\mathcal{L}_c$ from Model#7 dramatically lowers the results in both settings. Meanwhile, we found that $\mathsf{Ego}^2$ -Map learning can also help avoid collision, implying the useful spatial information carried by the map. In the following experiments, all three losses are applied to pre-train the visual encoders. + +# 4.3. Discussion and Analysis + +How much does the quantity of visual data matter? In Table 2, we compare the effect of sampling a different quantity of data for pre-training our visual encoder. Results show that the agent's performance in R2R-CE drops as the amount of data decreases, and reducing the number of environments has a stronger impact on the results $(-1.08\%)$ SPL for $50\%$ samples vs. $-3.87\%$ SPL for $50\%$ envs with $\mathcal{A}_{High}$ , suggesting the importance of having abundant scenes and structures in learning visual represent + +
Pre-train DataR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
100% data4.9459.6751.7746.117.2552.0130.4029.03
50% samples4.9857.7250.4645.037.4349.9727.5726.22
30% samples5.2856.1148.6142.587.8348.6025.8324.63
10% samples5.6054.8944.4839.087.8646.8322.9521.54
50% envs5.3255.5347.8042.247.5750.3526.5425.15
30% envs5.5653.8144.4838.697.6148.6426.0524.51
10% envs5.7353.4441.9236.897.8847.6223.2222.00
MP3D5.6752.7840.7835.767.9746.7521.9720.60
+ +Table 2: Effect of additional environments for pre-training. The percentages indicate the portion of HM3D environments/samples for training. MP3D only uses data collected from the 61 environments in downstream. + +
InitializationR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
CLIP4.9459.6751.7746.117.2552.0130.4029.03
Random4.9957.5549.3243.897.2751.3529.9128.29
IN-21K4.9558.6151.5545.737.0553.3031.0529.69
+IN-21K map5.4056.1847.0942.017.2152.6828.5527.13
+ +tations. Meanwhile, we can see that applying less than $50\%$ of samples or environments cannot yield better results than the baseline in Table 1. This is because $\mathrm{Ego}^2$ -Map learning requires sufficient positive and negative data pairs to support its contrastive training, as observed in previous literatures [18, 72]. + +How much does initialization matter? Table 3 compares the initialization of the RGBD and the map encoders in $\mathsf{Ego}^2$ -Map network, either from CLIP [72], from scratch or from a ViT-B/16 [25] pre-trained on ImageNet-21K (IN-21K) [23]. We find that random initialization of the RGB encoder only leads to a slight decrease in R2R-CE performance, while initializing it from pre-trained ViT can achieve comparable results to Model#7. We further investigate these results by also replacing the initialization of our map encoder from CLIP with IN-21K pre-trained ViT; although the losses of the two models saturate to the same level in pre-training, a drastic drop is observed in R2R-CE (even lower than Random). We hypothesize that some semantics from CLIP can be introduced to the RGBD encoder by the map encoder through contrastive learning. While previous works often use a convolutional network to process maps [14, 32, 33, 73], there remains a valuable open question of what model is suitable for encoding maps and how to train it to benefit navigation. We will leave the study of encoding maps for future work. + +Table 3: Effect of using pre-trained encoders for RGBD and map. Random and IN-21K initialize the RGBD encoder randomly or from a ViT pre-trained on ImageNet-21K [23], while using the CLIP-ViT-B/32 to encode maps. +IN-21K map also uses the IN-21K pre-trained ViT to encode the semantic map. + +
MethodsR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
CLIP-ViT+Depth +L5.4755.5547.1541.287.9347.7622.6821.69
5.2457.7448.6743.787.0752.5930.0728.74
+ +Table 4: Pre-training a different visual encoder with Ego2-Map objectives. The model applies CLIP-ViT-B/16 and a ResNet-50 trained for Point-Nav [94] to encode RGB and depth, respectively. + +
Ego2-MapR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
No semantics5.5157.6047.0442.257.3151.5629.7428.34
No space5.2457.4248.9443.527.6649.2029.3127.75
No target5.0256.2647.2041.218.0551.0430.8329.07
+ +Table 5: Ablation of information in Ego2-Map learning. + +Effect of $\mathcal{L}$ on a different encoder We further evaluate our proposed $\mathrm{Ego}^2$ -Map objective in pre-training a different visual encoder (Table 4). Here we consider the previous state-of-the-art encoder CLIP-ViT+Depth, which applies CLIP-ViT-B/16 and a ResNet-50 depth net trained on Gibson [95] for PointNav [82] to encode RGB and depth, respectively, following by a fusion module to integrate the encoded features. Pre-training the model with $\mathcal{L}$ leads to a significant improvement, obtaining $+2.50\%$ and $+7.05\%$ higher SPL with $\mathcal{A}_{High}$ and $\mathcal{A}_{Low}$ . These results suggest that $\mathrm{Ego}^2$ -Map learning has the potential to be generalized to other visual encoders. + +Information in $\mathbf{Ego}^2$ -Map contrastive learning In Table 5, we ablate the information applied in the $\mathbf{Ego}^2$ -Map contrastive learning. Specifically, we either remove the object semantics by masking their colored segmentations with the same color, or remove explorable regions by masking open space and void with the same color (see unmasked maps in Figure 2), or remove the target view from the view pairs to create ambiguity in agent's transition. The results show that learning $\mathbf{Ego}^2$ -Map without the semantic clues or open space in the maps, or without a specified target greatly damages agent performance in $\mathcal{A}_{High}$ , reflecting the importance of including this information. We also find that the agent with $\mathcal{A}_{Low}$ is less sensitive to method variations in pre-training; the remaining spatial or object information on a map is still beneficial to enhance the visual representation for supporting $\mathcal{A}_{Low}$ navigation, which could be the reason why angular offset and explorable distance predictions do not show a consistent benefit in Table 1. + +# 4.4. Comparison to Previous Methods + +Advantages of Visual Representations (R2R-CE) In Table 6, we compare our method of applying $\mathsf{Ego}^2$ -Map RGBD encoder to the CWP-VLN $\vec{\circ}$ BERT agent [41] (same model as Model#7 in Table 1) with previous approaches + +using $\mathcal{A}_{High}$ on the R2R-CE testing split4. Results show that our proposed $\mathrm{Ego}^2$ -Map learning brings significant improvement for all metrics, achieving a $47\%$ SR $(+3\%)$ and a $41\%$ SPL $(+4\%)$ over the previous best [50]. In addition, Table 7 establishes a fair comparison with methods using $\mathcal{A}_{Low}$ . We can see that $\mathrm{Ego}^2$ -Map features greatly boost the result of the base agent CWP-VLN BERT [41] (23% to 30% SR), and achieve a SPL comparable to recent mapping-based methods such as CM2 [33] and WS-MGMap [14]. Note that using $\mathrm{Ego}^2$ -Map representations does not conflict with online mapping; while we only experiment with non-mapping-based agents, we believe the features hold great potential to facilitate modeling between views and maps in mapping-based models. + +Learning Methods (ObjNav) We further compare the effect of visual representation learning methods by applying our visual encoder on ObjNav [4] as in the recent approaches [46, 96] (Table 8). All methods in the table adopt a simple pipeline as in the baseline model [94], which feeds the concatenation of visual features, GPS+Compass encodings, and the encodings of previous action to a GRU [19], then, uses a fully-connected layer to predict an action from the updated agent's state. Briefly, EmbCLIP directly uses the pre-trained CLIP-ResNet50 [72] to encode the RGB inputs, EmbCLIP-ViT+Depth applies the CLIP-ViT-B/16 to encode RGB and an extra depth net [82] pre-trained on Gibson [95] to encode the depth inputs. OVRL pre-trains the ResNet encoder with self-distillation method DINO [6], in which a student network is trained to match the output of a teacher network. Moreover, OVRL applies the Omnidata Starter Dataset $(\mathrm{OSD})^5$ [28], which is much larger and more diverse than the data for our Ego $^2$ -Map learning (only uses the HM3D [74] subset). ObjNav measures the same metrics as R2R-CE, first, we can see that an agent using Ego $^2$ -Map features greatly improves over the baseline and the EmbCLIP. Compared to OVRL, despite the method applies OSD for pre-training and fine-tunes the network end-to-end with human demonstrations, our method obtains a better success rate $(+0.4\%)$ and much higher SPL $(+3.2\%)$ . Note that, although not directly comparable, as reported in the OVRL, the SPL on ImageNav [63] without fine-tuning the visual encoder will drop drastically from $26.9\%$ to $17.0\%$ , whereas all our experiments keep the visual encoder frozen during navigation. These results suggest that Ego $^2$ -Map representations are generalizable to different navigation tasks and provide more robust visual representations. + +
Methods (AHigh)R2R-CE Test-Unseen
TLNE↓OSR↑SR↑SPL↑
Waypoint Models [49]8.026.65373230
CWP-CMA [41]11.856.30493833
CWP-VLN BERT [41]13.315.89514236
Sim2Sim [50]11.436.17524437
Ego2-Map+CWP-VLN BERT (ours)13.055.54564741
+ +Table 6: Comparison of agent performance on R2R-CE test server. All methods use high-level action space $(\mathcal{A}_{High})$ + +
Methods (ALow)R2R-CE Val-Unseen
TLNE↓OSR↑SR↑SPL↑
CMA+PM+DA+Aug [51]8.647.37403230
SASRA [44] †7.898.32-2422
LAW [77]8.896.83443531
CWP-CMA [41]°8.227.54-2725
CWP-VLN BERT [41]°7.427.66-2322
CM2 [33] †11.547.02423428
WS-MGMap (SemMap only) [14] †10.896.80423328
Ego2-Map+CWP-VLN BERT (ours)8.037.25373029
+ +Table 7: Comparison of agents with low-level action space $(\mathcal{A}_{Low})$ in R2R-CE Val-Unseen. $\dagger$ : mapping-based methods. $\circ$ : $4\%$ of data is removed but the comparison is still valid due to the large performance gap. + +
MethodsPre-Training DatasetObjNav MP3D Val
NE↓SR↑SPL↑
Baseline [94]X6.908.01.8
EmbCLIP [46]*WebImageText5.2620.98.3
EmbCLIP-ViT+DepthWebImageText+Gibson4.9023.38.6
OVRL no pretrain [76] †X-24.25.9
OVRL [96] †OSD-28.67.4
Ego2-Map+Baseline (ours)HM3D5.1729.010.6
+ +Table 8: Comparison on pre-trained visual encoders for ObjNav. $\dagger$ indicates the visual encoder is tuned end-to-end with behavior cloning on $40\mathrm{k}$ human demonstrations collected by Habitat-Web [76], while the others freeze the visual encoder during navigation and only train the agent with DD-PPO [94] on the original data. *Results obtained by re-evaluating the officially released best model checkpoint. + +# 5. Conclusion + +In this paper, we introduce a novel method of learning navigational visual representations with contrastive learning between egocentric views pairs and top-down semantic maps (Ego $^2$ -Map). The method transfers the compact semantic and spatial information carried by a map to the egocentric representations, which greatly facilitates the agent's visual perception. Experiments show that Ego $^2$ -Map features greatly improve the downstream navigation, such as ObjNav and VLN, and demonstrate generalization potential to different visual backbones. We believe the Ego $^2$ -Map contrastive learning proposes a new direction of visual representation learning for navigation and provides the possibility of better modeling the correspondence between views and maps, which can further benefit agent's planning and action. Note that our work also produces a potentially ef + +fective map encoder whose full capability is worth investigating in future work. + +Limitations The need to build semantic maps to enable the $\mathbf{Ego}^2$ -Map contrastive learning is an inevitable cost of this method; compared to other self-supervised visual representation learning approaches, $\mathbf{Ego}^2$ -Map requires either the semantic annotations of scenes, or traversable environments and a generalizable semantic map constructor. As a result, the data collection could be much harder. 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However, most existing works only employ visual backbones pre-trained either with independent images for classification or with self-supervised learning methods to adapt to the indoor navigation domain, neglecting the spatial relationships that are essential to the learning of navigation. Inspired by the behavior that humans naturally build semantically and spatially meaningful cognitive maps in their brains during navigation, in this paper, we propose a novel navigational-specific visual representation learning method by contrasting the agent's egocentric views and semantic maps (Ego" + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "text", + "content": "-Map). We apply the visual transformer as the backbone encoder and train the model with data collected from the large-scale Habitat-Matterport3D environments. 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Moreover, our representations significantly improve vision-and-language navigation in continuous environments for both high-level and low-level action spaces, achieving new state-of-the-art results of " + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "inline_equation", + "content": "47\\%" + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "text", + "content": " SR and " + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "inline_equation", + "content": "41\\%" + }, + { + "bbox": [ + 46, + 280, + 290, + 579 + ], + "type": "text", + "content": " SPL on the test server." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 614, + 128, + 627 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 614, + 128, + 627 + ], + "spans": [ + { + "bbox": [ + 47, + 614, + 128, + 627 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 634, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 634, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 634, + 287, + 696 + ], + "type": "text", + "content": "Visual representations for navigation should capture the rich semantics and the complex spatial relationships of the observations, which helps the agent to recognize visual entities and its transition in space for effective exploration. However, previous works usually adopt visual backbones" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 255, + 547, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 255, + 547, + 496 + ], + "spans": [ + { + "bbox": [ + 306, + 255, + 547, + 496 + ], + "type": "text", + "content": "which only focus on capturing the semantics of a static image, ignoring its connection to the agent or the correspondence to other views in a continuous environment [3, 9, 40, 42, 51, 68, 98]. One common approach is to apply encoders pre-trained for object/scene classification (e.g. ResNet [39] on ImageNet [80]/Places365 [102]), object detection (e.g. RCNN [38, 78] on VisualGenome [52]/MSCOCO [57]) or semantic segmentation (e.g. RedNet [45] on SUN RGBD [87]), or more recently, to use CLIP [72], which is trained for aligning millions of images and texts to encode agent's RGB observations [31, 46, 84]. Despite the increasing generalization ability of the features and rising zero-shot performance on novel targets, there still exists a large visual domain gap between these features and the features suitable for navigation since they lack the expressiveness of spatial relationships. For example, the connection between time-dependent observations and the correspondence between egocentric views and the spatial structure of an environment, which are important to decision making during navigation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": "We suggest that there are two main difficulties in learning navigational-specific visual representations in previous research; First, there lacked a large-scale and realistic dataset of indoor environments. Popular datasets such as Matterport3D [8] and Gibson [95] provide traversable scenes rendered from real photos, but either the number of scenes is very limited, or the quality of the 3D scan is low. Synthetic datasets such as ProcTHOR [22] contain 10K generated scenes, but they are unrealistic and simple and do not capture the full complexity of real-world environments. Second, fine-tuning visual encoders while learning to navigate is very expensive because of the long traveling horizon, especially in tasks that require extensive exploration [4, 53, 63, 86]. Moreover, due to the scene scarcity, fine-tuning visual encoders is unlikely to generalize well to the novel environments. To address these problems, a large amount of research has been dedicated to augmenting the environments, either editing the agent's observations" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 702, + 151, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 702, + 151, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 702, + 151, + 712 + ], + "type": "text", + "content": "†Intern at Adobe Research." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3055" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": "[56, 90] or adding objects [62], building new spatial structures [58], applying web-images to replace the views of the same categories [35] or generating new scenes [47, 48, 55]. Unlike augmentation, which essentially requires the agent's policy network to adapt new visual data, another strategy is to first pre-train the visual encoder before learning to navigate. Those methods usually apply images captured in 3D scenes and perform self-supervised learning or tune the encoder with proxy tasks (e.g. masked region modeling, angular prediction) to mitigate the domain gap and introduce spatial awareness [15, 17, 96, 98]. Furthermore, recent works tend to apply CLIP [72] to process visual inputs, as the model can provide powerful representations for grounding semantic and spatial concepts, hence facilitating learning [1, 31, 46, 83, 84, 85]. Although these methods have demonstrated significant improvements on navigation performance, they either only use more data without addressing the learning problem, not generalizable across different tasks, or ignore the spatial correspondence between consecutive frames which the agent will capture as it moves." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "text", + "content": "Inspire by the research in cognitive science that humans naturally build virtual maps from perspective observations that are helpful to track semantics, spaces and movements during navigation [29, 91, 92]; we propose a contrastive learning method between the agent's Egocentric view pairs and top-down semantic Maps (Ego" + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "text", + "content": "-Map) for training visual encoders appropriate for navigation. Specifically, we first sample RGBD images and create corresponding semantic maps [7] from the large-scale Habitat-Matterport3D environments (HM3D) [74, 82] which contains hundreds of photo-realistic scenes, obtaining abundant and effective visual data. Then, we encode the sampled RGBD observations and the semantic maps with two separate visual backbones, respectively, and train the entire model with our Ego" + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "text", + "content": "-Map contrastive learning. Once trained, the RGBD encoder will be plugged into an agent's network to facilitate visual perception. We argue that the map contains very rich and compact visual clues such as spatial structure, accessible areas and unexplored regions, object entities and their arrangement, as well as the agent's transition in the environment that are essential to navigation. Compared to existing online mapping-based approaches [10, 14, 32, 44], Ego" + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "text", + "content": "-Map learning efficiently produces visual features that imply a complete map of the space known a view priori, while the online map is only a partial map. Importantly, Ego" + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 47, + 315, + 289, + 662 + ], + "type": "text", + "content": "-Map explores a new possibility of modeling semantics and structures from simple RGBD inputs, which its resulting features are directly applicable to non-mapping-based navigational models and effectively generalizable to different tasks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "We mainly evaluate the features learned from Ego" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "-Map on the Room-to-Room Vision-and-Language Navigation in Continuous Environments (R2R-CE) [3, 51] task, which requires an agent to navigate in photo-realistic environ" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": "ments following human natural language instructions such as \"Leave the bedroom and enter the kitchen. Walk forward and take a left at the couch. Stop in front of the window.\" Addressing R2R-CE highly relies on exploiting the correspondence between contextual clues and the agent's observations, hence it is crucial for the visual encoder to provide semantic and structural meaningful representations. We found that the proposed " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathsf{Ego}^2" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": "-Map features significantly boost the agent's performance, obtaining " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "+3.56\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "+5.10\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " absolute SPL improvements over the CLIP baseline [72] under the settings of high-level and low-level action spaces, respectively, and achieves the new best results on the R2R-CE test server. Moreover, our experiments show that " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathsf{Ego}^2" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": "-Map learning also outperforms other visual representation learning methods such as OVRL [96] on the Object-Goal Navigation task (ObjNav), suggesting the strong generalization potential of the proposed methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 285, + 392, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 392, + 298 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 392, + 298 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 304, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 533 + ], + "type": "text", + "content": "Visual Navigation A great variety of scenarios have been proposed to learn visual navigation in photo-realistic environments [8, 21, 54, 82, 86, 89, 95] with different modalities of inputs, targets and action spaces [3, 4, 11, 13, 51, 66, 70, 94]. Due to the distinct nature of the tasks, diverse methods are investigated accordingly. For instance, in Object-Nav, which only provides a high-level goal and requires exploration, mapping-based methods are frequently applied [10, 32, 60, 73, 105], whereas in vision-and-language navigation (VLN) [3], large vision-language models are employed to match instructions and agent's observations [42, 61, 71, 83, 103] to perform panoramic actions [30]. Recently, there is an emerging trend of scaling up the training data to address the common data scarcity issue, either in terms of the number of environments [22, 74] or the amount of supervision [16, 76, 93]. Unlike most of the previous works, we focus on improving the visual backbone, aiming to produce robust and generalizable visual representations specialized for navigation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": "Visual Representations for Embodied AI Recent years have witnessed a trend of moving away from visual encoders pre-trained for object classification in Embodied AI due to their inefficiency in representing complex real-world scenes or mapping to actions. Instead, large vision-language models such as CLIP which demonstrates strong zero-shot performance across visual domains is widely applied [20, 72], enhancing the semantic representations in robotic manipulation [85], assisting 3D trajectory modification and speed control [5], benefiting the language-conditioned view-selection problem in VLN [83, 84] as well as improving other control and navigation results [31, 46, 67]. Moreover, EmbCLIP shows that the CLIP features provide much better semantic and geometric primitives such as" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "3056" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 72, + 541, + 247 + ], + "blocks": [ + { + "bbox": [ + 52, + 72, + 541, + 247 + ], + "lines": [ + { + "bbox": [ + 52, + 72, + 541, + 247 + ], + "spans": [ + { + "bbox": [ + 52, + 72, + 541, + 247 + ], + "type": "image", + "image_path": "b78fbc0aa404047ef0a0bc5bea16e2ab0c5b538207b8c36e2c974dce5db20f3b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "text", + "content": "Figure 1: Network architecture. The Semantic MapNet [7] is applied to draw a semantic map using observations captured from a source to a target position. Then, two learnable visual encoders are applied to encode the egocentric views and the map, respectively, followed by non-linear headers " + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\Pi_{i}" + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\Pi_{m}" + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "text", + "content": " to learn the Ego" + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "text", + "content": "-Map contrastive objective " + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 46, + 258, + 547, + 308 + ], + "type": "text", + "content": " are the paired view features of a trajectory (see §3.2). Dash arrows indicate pre-processing without gradient update." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 319, + 289, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 289, + 488 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 289, + 488 + ], + "type": "text", + "content": "object presence, object reachability, and free space that are valuable to Embodied AI [46]. In terms of self-supervised visual representation learning for indoor navigation, recent works that are the most relevant to ours include OVRL [96] which applies knowledge distillation based on DINO [6], EPC which predicts masked observations from a trajectory [75], and CRL which jointly learns a visual encoder with a policy network that maximizes the representation error [27]. In contrast to all previous works, this paper explores a novel idea of encoding the explicit structural and semantic information available in maps implicitly in the visual encoder thereby facilitating efficient and effective generalization across different visual navigation tasks and models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 715 + ], + "type": "text", + "content": "Exploiting Visual Features A great variety of proxy tasks and auxiliary objectives have been applied to exploit information from the visual data which is beneficial to navigation. For instance, Ye et al. [98, 99] promote understanding of spatiotemporal relations of observations by estimating the timestep difference between two views, Qi et al. [69] predict room-types from object features to improve scene understanding, and Se et al. [81] determine the furthest reachable waypoint on a topological graph using the node observations. To extract the geometric information, Gordon et al. [34] use the encoded visual features to predict depth and surface normals, reconstruct RGB input, and forecast the visual features by taking certain actions. Depth prediction has also been studied by Mirowski et al. [64], Desai et al. [24] and Chattopadhyay et al. [12], along with learning the inverse dynamics by predicting an action taken between two sequential observations [37, 64]. Complement" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 319, + 547, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 547, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 547, + 357 + ], + "type": "text", + "content": "tary to the previous methods for interpreting visual features, our Ego" + }, + { + "bbox": [ + 304, + 319, + 547, + 357 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 319, + 547, + 357 + ], + "type": "text", + "content": "-Map learning guides a visual encoder to produce representations with expressive spatial information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 367, + 547, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 367, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 367, + 547, + 396 + ], + "type": "text", + "content": "3. Contrastive Learning between Egocentric Views and Semantic Maps (Ego" + }, + { + "bbox": [ + 305, + 367, + 547, + 396 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 305, + 367, + 547, + 396 + ], + "type": "text", + "content": "-Map)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 401, + 547, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 547, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 547, + 486 + ], + "type": "text", + "content": "We will first describe the overall network architecture for training the visual encoders (§3.1), followed by the details of Ego²-Map objectives (§3.2), as well as two other widely applied spatial-aware auxiliary tasks which we investigated with our Ego²-Map learning (§3.3). Then, we will talk about the data collection (§3.4) and network training (§3.5) processes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 494, + 432, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 494, + 432, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 494, + 432, + 506 + ], + "type": "text", + "content": "3.1. Network Architecture" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "text", + "content": "We build the network for " + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "text", + "content": "-Map learning based on a ViT-B/16 model (default initialized from CLIP [72], whose effect will be studied in §4.3). Unlike previous methods for visual navigation, which mostly employ two independent encoders to process RGB and depth images, we investigate a compact representation by feeding RGB+Depth as four-channel inputs (Figure 1). To merge the two visual modalities, we use two separate convolutional layers to encode the RGB channels " + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "inline_equation", + "content": "I_{rgb}" + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "text", + "content": " and the depth map " + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "inline_equation", + "content": "I_d" + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "text", + "content": ", respectively, followed by a token-wise concatenation and a non-linear projection " + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "inline_equation", + "content": "\\Pi_v" + }, + { + "bbox": [ + 304, + 512, + 547, + 657 + ], + "type": "text", + "content": " to merge the resulting feature maps before feeding to the transformer layers as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 335, + 666, + 545, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 666, + 545, + 680 + ], + "spans": [ + { + "bbox": [ + 335, + 666, + 545, + 680 + ], + "type": "interline_equation", + "content": "v _ {r g b} = \\operatorname {C o n v} _ {r g b} \\left(I _ {r g b}\\right), \\quad v _ {d} = \\operatorname {C o n v} _ {d} \\left(I _ {d}\\right) \\tag {1}", + "image_path": "a557ca30fb2e09e247b0fdc6dea59fc44d1aa1d363a44a5193c4f6b19b691373.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 689, + 324, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 689, + 324, + 700 + ], + "spans": [ + { + "bbox": [ + 307, + 689, + 324, + 700 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 376, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 376, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "f = \\operatorname {V i T} \\left(\\boldsymbol {\\Pi} _ {v} \\left[ v _ {r g b}; v _ {d} \\right]\\right) \\tag {2}", + "image_path": "019a2d1fbca519ee662ea52249af3d6f193f8d07e5508ec058c4e0491576c7ef.jpg" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3057" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "text", + "content": "The pooled features " + }, + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "text", + "content": " of the RGBD encoder are applied for learning all spatial-aware objectives " + }, + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\theta}" + }, + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 47, + 72, + 288, + 109 + ], + "type": "text", + "content": ", which will be specified in the following." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 119, + 224, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 119, + 224, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 119, + 224, + 133 + ], + "type": "text", + "content": "3.2. " + }, + { + "bbox": [ + 47, + 119, + 224, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{Ego}^2" + }, + { + "bbox": [ + 47, + 119, + 224, + 133 + ], + "type": "text", + "content": " -Map Contrastive Objective" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": "The motivation of this task is to introduce the information within a map to single-view features, offering the agent high-level semantic and spatial clues to navigate towards distant targets. Specifically, we build positive samples by coupling a views-pair " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "(I_s" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": " from the two endpoints of a path) with a top-down semantic map " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": " that represents the agent's transition and observations along the path, while using mismatched views-pairs and maps of different routes or environments as the negatives. Each semantic map is generated by the off-the-shelf Semantic MapNet [7], using the RGBD observations collected by an agent traveling from the source view " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "I_s" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": " to the target view " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": " via the shortest path" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": ". The semantic map provides abundant information about the open space, obstacles, unexplored regions, observed objects, and the agent's action, which we consider as highly valuable and compact representations for agent navigation (see maps in Figure 2). To encode " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": ", we apply an additional ViT-B/32 [25] with the last three transformer layers unfrozen to adapt the map images. Then, the egocentric features of the two views " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "f_s" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "f_t" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": ", and the map features " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "f_m" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": " will be passed to two MLP (multi-layer perceptrons) headers " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "\\Pi_i" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "inline_equation", + "content": "\\Pi_m" + }, + { + "bbox": [ + 46, + 139, + 289, + 415 + ], + "type": "text", + "content": ", respectively, to compute an alignment score as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 89, + 425, + 287, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 425, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 89, + 425, + 287, + 440 + ], + "type": "interline_equation", + "content": "c ^ {I} = \\boldsymbol {\\Pi} _ {i} [ f _ {s}; f _ {t} ], \\qquad c ^ {M} = \\boldsymbol {\\Pi} _ {m} [ f _ {m} ] \\qquad (3)", + "image_path": "960c2250b8d9e2c73a7511fb2a2eb1f2da331fc969e83588348348f792cf3af5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 451, + 65, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 65, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 65, + 462 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 119, + 463, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 463, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 119, + 463, + 287, + 491 + ], + "type": "interline_equation", + "content": "\\langle c ^ {I}, c ^ {M} \\rangle = \\frac {c ^ {I} \\cdot c ^ {M}}{\\| c ^ {I} \\| \\| c ^ {M} \\|} \\tag {4}", + "image_path": "1a2cfd7c56351de6a6fed8eed9d06bc65c6e5ec282a7f15f28e267ee6ad748eb.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": "Then, the InfoNCE loss [65, 101] is applied for " + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": "-Map contrastive learning. For each " + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": "-th views-map pair in a minibatch of size " + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 498, + 287, + 534 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 544, + 287, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 544, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 116, + 544, + 287, + 562 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c, j} = \\mathcal {L} _ {c, j} ^ {I \\rightarrow M} + \\mathcal {L} _ {c, j} ^ {M \\rightarrow I} \\tag {5}", + "image_path": "c523c3bf828318c0c3b485fd3ae51f25abca750916fdc7eebbe48f3f46cf332f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 571, + 284, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 284, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 284, + 583 + ], + "type": "text", + "content": "where the views to maps " + }, + { + "bbox": [ + 47, + 571, + 284, + 583 + ], + "type": "inline_equation", + "content": "(I\\to M)" + }, + { + "bbox": [ + 47, + 571, + 284, + 583 + ], + "type": "text", + "content": " loss can be expressed as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 87, + 594, + 287, + 626 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 594, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 87, + 594, + 287, + 626 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c, j} ^ {I \\rightarrow M} = - \\log \\frac {\\exp \\left(\\left\\langle c _ {j} ^ {I} , c _ {j} ^ {M} \\right\\rangle / \\tau\\right)}{\\sum_ {k = 1} ^ {N} \\exp \\left(\\left\\langle c _ {j} ^ {I} , c _ {k} ^ {M} \\right\\rangle / \\tau\\right)} \\tag {6}", + "image_path": "30847eb1908f8eeedf67f65a1e6cfeeefbf804f58ed064911c86a54f517c700c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 637, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 637, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 47, + 637, + 287, + 663 + ], + "type": "text", + "content": "and the map to views loss " + }, + { + "bbox": [ + 47, + 637, + 287, + 663 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{c,j}^{M\\to I}" + }, + { + "bbox": [ + 47, + 637, + 287, + 663 + ], + "type": "text", + "content": " likewise. Parameter " + }, + { + "bbox": [ + 47, + 637, + 287, + 663 + ], + "type": "inline_equation", + "content": "\\tau \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 47, + 637, + 287, + 663 + ], + "type": "text", + "content": " denotes a learnable temperature." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 478, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 478, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 478, + 85 + ], + "type": "text", + "content": "3.3. Other Spatial-Aware Objectives" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 91, + 546, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 91, + 546, + 139 + ], + "spans": [ + { + "bbox": [ + 305, + 91, + 546, + 139 + ], + "type": "text", + "content": "We investigate two additional widely applied proxy tasks with our Ego" + }, + { + "bbox": [ + 305, + 91, + 546, + 139 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 305, + 91, + 546, + 139 + ], + "type": "text", + "content": "-Map learning. Note that we do not claim any novelty for applying these tasks but focus on studying their effect on training the representations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "spans": [ + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "content": "Angular Offset Prediction Given two images taken from random headings at the same position, the task predicts the angular offset between them to facilitate the modeling of correspondence between views. A similar proxy task has been applied in previous works, which predicts discrete angles and uses an extra directional encoding to imply orientation [15] or regresses the agent's turning angle conditioned on language during navigation [104]. Specifically, we pass the two pooled RGBD features " + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "inline_equation", + "content": "f_{\\theta_0}" + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "inline_equation", + "content": "f_{\\theta_1}" + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "content": ", corresponding to images at two orientations of the same viewpoint, into a learnable non-linear header " + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "inline_equation", + "content": "\\Pi_{\\theta}" + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "content": " to predict the offset as " + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "inline_equation", + "content": "\\theta^p = \\Pi_{\\theta}[f_{\\theta_0};f_{\\theta_1}]" + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "content": ". The task is learned by minimizing the mean squared error " + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\theta} = E[(\\theta^p - \\theta^*)^2]" + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "inline_equation", + "content": "\\theta^*" + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "content": " is the ground-truth angular difference between " + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "inline_equation", + "content": "[-\\pi, \\pi]" + }, + { + "bbox": [ + 305, + 155, + 547, + 347 + ], + "type": "text", + "content": ", denoting either clockwise or counter-clockwise rotation whichever is closer to encourage agent's efficient rotation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "type": "text", + "content": "Explorable Distance Prediction To benefit the searching of explorable regions and assist obstacle avoidance, the task estimates the agent's maximal distance to forward without being blocked by any obstacle [11, 36]. Using the same notations as above, the module regresses a value from an RGBD image as " + }, + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "type": "inline_equation", + "content": "d^{p} = \\Pi_{d}[f]" + }, + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "type": "text", + "content": ", and is trained with supervision " + }, + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d = E[(d^p - d^*)^2]" + }, + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "type": "text", + "content": ". We cap the ground-truth distance " + }, + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "type": "inline_equation", + "content": "d^{*}" + }, + { + "bbox": [ + 305, + 363, + 546, + 472 + ], + "type": "text", + "content": " in the range of 0.5 to 5.0 meters to match the common range of the agent's depth sensors." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 479, + 402, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 402, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 402, + 491 + ], + "type": "text", + "content": "3.4. Data Collection" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "text", + "content": "We follow the train-validation-test split of the HM3D scenes [74] and use the first 800 environments for learning. We randomly sample 252,537 viewpoint positions from the environments (see Figure 3) and render more than a million RGBD images from those positions to create 500,000 " + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "(I_{\\theta_0}, I_{\\theta_1})" + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "text", + "content": " views pairs as well as 500,000 " + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "(I_s, I_t, M)" + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "text", + "content": " triplets for learning " + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\theta}" + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "text", + "content": ", respectively, while using all the images to learn " + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "text", + "content": ". The positions are sampled such that all points must be located in the open space and the minimal geodesic distance between any two points is greater than 0.40 meters. Each image collected for " + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 305, + 498, + 547, + 713 + ], + "type": "text", + "content": "-Map contrastive learning is either a unique source or target view in all trajectories, and each trajectory is created by computing the shortest path between two randomly paired views within a 7 meters range. We feed the RGBD images captured from a trajectory to the Semantic MapNet [7] for drawing the corresponding semantic map. Note that the Semantic MapNet is trained on the MP3D environments [8], but we found that" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "type": "text", + "content": "2Each resulting map is unique because the observations are determined by the unique path (actions) for connecting two views. For example, in Figure 2, only the colored regions in the map " + }, + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "type": "inline_equation", + "content": "(M)" + }, + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "type": "text", + "content": " are the areas seen by the agent when traveling from the source to the target positions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3058" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 75, + 532, + 281 + ], + "blocks": [ + { + "bbox": [ + 66, + 75, + 532, + 281 + ], + "lines": [ + { + "bbox": [ + 66, + 75, + 532, + 281 + ], + "spans": [ + { + "bbox": [ + 66, + 75, + 532, + 281 + ], + "type": "image", + "image_path": "1aba1a5107cfdb7683fadb67e2e841058457e25a2c3ced6ca77108e599e45a02.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": "Figure 2: Illustration of " + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{Ego}^2" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": "-Map contrastive learning. The method encodes the paired source and target egocentric views " + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "inline_equation", + "content": "(I_s, I_t)" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": " into feature " + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "inline_equation", + "content": "c^I" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": ", then learns to align it with the feature " + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "inline_equation", + "content": "c^M" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": " of the corresponding top-down map " + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": ". Negative view pairs " + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "inline_equation", + "content": "(I_{s'}, I_{t'})" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": " and maps " + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "inline_equation", + "content": "(M')" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": " are sampled from different trajectories or different environments, which are pushed away from the reference pair. The blue dashed line on the left part of the figure indicates the agent's trajectory, which is visualized with directional color in map " + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 287, + 547, + 350 + ], + "type": "text", + "content": ". The map is also powered with semantic information (denoted at the bottom right)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 357, + 164, + 435 + ], + "blocks": [ + { + "bbox": [ + 50, + 357, + 164, + 435 + ], + "lines": [ + { + "bbox": [ + 50, + 357, + 164, + 435 + ], + "spans": [ + { + "bbox": [ + 50, + 357, + 164, + 435 + ], + "type": "image", + "image_path": "9b74359821ca4a8192244811aa642b5ec5a229167ff5d2534b3c0ce2d8b8c347.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 91, + 439, + 125, + 447 + ], + "lines": [ + { + "bbox": [ + 91, + 439, + 125, + 447 + ], + "spans": [ + { + "bbox": [ + 91, + 439, + 125, + 447 + ], + "type": "text", + "content": "(a) 3D scan" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 171, + 357, + 276, + 437 + ], + "blocks": [ + { + "bbox": [ + 171, + 357, + 276, + 437 + ], + "lines": [ + { + "bbox": [ + 171, + 357, + 276, + 437 + ], + "spans": [ + { + "bbox": [ + 171, + 357, + 276, + 437 + ], + "type": "image", + "image_path": "c136f4a2e5e6ef3609e0596ee9fde2a306a0e86278a4b937244b93897b103b3b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 162, + 438, + 284, + 447 + ], + "lines": [ + { + "bbox": [ + 162, + 438, + 284, + 447 + ], + "spans": [ + { + "bbox": [ + 162, + 438, + 284, + 447 + ], + "type": "text", + "content": "(b) Occupancy map and sampled positions" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 458, + 287, + 483 + ], + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 483 + ], + "type": "text", + "content": "Figure 3: Illustration of an HM3D environment scan and the sampled positions (blue points) in open space (gray area)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 519 + ], + "type": "text", + "content": "it also generalizes well to the HM3D scenes. We refer to the Appendix for more sampling and dataset creation details." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 525, + 111, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 111, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 111, + 537 + ], + "type": "text", + "content": "3.5. Training" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 543, + 288, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 288, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 288, + 676 + ], + "type": "text", + "content": "Implementation Details We initialize the RGBD encoder and the map encoder of our visual representation network with CLIP, a visual transformer pre-trained for aligning image-language pairs [72]. Specifically, the additional depth convolutional layer and the projection layer in the RGBD encoder are initialized randomly. All network variants in our experiments are trained with batch size 994 for 100 epochs using the AdamW optimizer [59]. After all training iterations, only the RGBD encoder will be applied as the visual backbone for navigation agents. Image augmentations are applied to all views and maps." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "Optimization The overall pre-training strategy minimizes the sum over all three losses, " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\theta}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": ". All" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "text", + "content": "losses are equally weighted and optimized simultaneously in each iteration. After all training steps, evaluate the model with batch size 128 on 10,000 novel " + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "inline_equation", + "content": "(I_s, I_t, M)" + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "text", + "content": " triplets shows " + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "inline_equation", + "content": "92.02\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "text", + "content": " views to maps " + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "inline_equation", + "content": "(I \\rightarrow M)" + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "inline_equation", + "content": "92.03\\%" + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "text", + "content": " maps to view " + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "inline_equation", + "content": "(M \\rightarrow I)" + }, + { + "bbox": [ + 304, + 358, + 545, + 444 + ], + "type": "text", + "content": " alignment accuracy, indicating the correspondence between two modalities has been learned. Please see Appendix for more pre-training statistics and results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 454, + 455, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 454, + 455, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 454, + 455, + 468 + ], + "type": "text", + "content": "4. Downstream Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 475, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 548 + ], + "type": "text", + "content": "We evaluate our " + }, + { + "bbox": [ + 304, + 475, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 304, + 475, + 545, + 548 + ], + "type": "text", + "content": "-Map representations mainly on the R2R-CE navigation [3, 51], as addressing the task highly relies on exploiting the semantic and structural information from observations and ground to language instructions. We also show results on ObjNav [4] to compare with other recent visual representation learning approaches." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 556, + 399, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 556, + 399, + 570 + ], + "spans": [ + { + "bbox": [ + 306, + 556, + 399, + 570 + ], + "type": "text", + "content": "4.1. R2R-CE Setup" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "type": "text", + "content": "Our experiments consider two major setups of action spaces, either applying panorama inputs and execute high-level decisions by selecting images pointing towards navigable directions " + }, + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "type": "inline_equation", + "content": "(\\mathcal{A}_{High})^3" + }, + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "type": "text", + "content": ", or using egocentric views and perform low-level controls " + }, + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "type": "inline_equation", + "content": "(\\mathcal{A}_{Low})" + }, + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 304, + 575, + 545, + 685 + ], + "type": "text", + "content": ", we adopt the candidate waypoint predictor proposed by Hong et al. [41], which generates navigable waypoint positions around the agent at each time step. Once a waypoint is selected, the agent will move to the position with low-level" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "text", + "content": "High-level VLN agents apply 36 egocentric images to represent its panoramic vision [3], hence, our " + }, + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathsf{Ego}^2" + }, + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "text", + "content": "-Map features are applicable." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3059" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 72, + 547, + 193 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 547, + 193 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 547, + 193 + ], + "type": "table", + "html": "
ModelsPre-Training ObjectivesR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
AngularExplorableContrastiveNE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑Collision↓
Baseline4.9857.2648.6742.557.6949.2725.6123.9317.41
1✓8.3332.0216.1513.659.7730.433.753.4371.59
2✓5.8351.2542.5836.347.9447.1524.7422.9810.44
3✓4.8958.4951.7745.897.4750.3527.6225.9513.19
4✓✓5.0358.8651.2845.987.2751.9130.6129.1310.09
5✓✓5.0259.6252.0446.997.4451.3129.5327.9413.04
6✓✓5.7952.9342.9037.257.6450.1927.9526.3916.19
7✓✓✓4.9459.6751.7746.117.2552.0130.4029.0311.25
", + "image_path": "bfa9636295a9a54da2019007ce4b67654178e231352b362c06aaf3afbd5811bf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "type": "text", + "content": "Table 1: Ablation of " + }, + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "type": "inline_equation", + "content": "\\mathsf{Ego}^2" + }, + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "type": "text", + "content": "-Map learning and influence of angular and explorable objectives on the R2R-CE tasks. Checkmarks indicate applying the corresponding objectives. Baseline applies a pre-trained CLIP-ViT-B/16 model to encode RGB and depth separately. Collision measures the percentage of forward steps which the agent collided with an obstacle; we only consider this metric for " + }, + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "type": "text", + "content": " since agents in " + }, + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 46, + 201, + 546, + 251 + ], + "type": "text", + "content": " apply a waypoint predictor [41] to obtain navigable positions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "text", + "content": "controls. For " + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "text", + "content": ", an agent is only allowed to do a single low-level action at each step, including Turn Left/Right " + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "inline_equation", + "content": "15^{\\circ}" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "text", + "content": ", Forward 0.25 meters, and Stop. In all experiments, we apply the VLN" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "text", + "content": "BERT agent [42], a vision-language transformer pre-trained for navigation, as the policy network. To use our Ego" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "text", + "content": "-Map representations, we simply replace the agent's original visual encoders (two ResNets trained on ImageNet [39] and trained in Point-Nav [94] for RGB and depth, respectively) with our RGBD encoder (" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "inline_equation", + "content": "\\S 3.1" + }, + { + "bbox": [ + 46, + 261, + 288, + 428 + ], + "type": "text", + "content": "). Comparing the runtime efficiency, the original encoder has around 50M parameters and the speed is about 4 GFLOPs/image, whereas our method is larger (86M parameters) but faster (20 GFLOPs/image). All visual encoders in our experiments are frozen in navigation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 430, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 586 + ], + "type": "text", + "content": "R2R in continuous environment (R2R-CE) is established over the Matterport3D environments [8] based on the Habitat simulator [82]. The dataset contains 61 scans for training; 11 and 18 scans for validation and testing, respectively. R2R-CE evaluates the agent's performance using multiple metrics, including trajectory length (TL), navigation error (NE): the final distance between the agent and the target, normalized dynamic time warping score (nDTW): distance between the predicted and the ground-truth paths [43], oracle success rate (OSR): the ratio of reaching within 3 meters to the target, success rate (SR): the ratio of stopping within 3 meters to the target, and success weighted by the normalized inverse of the path length (SPL) [2]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 597, + 141, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 141, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 141, + 609 + ], + "type": "text", + "content": "4.2. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 700 + ], + "type": "text", + "content": "Ablation experiments in Table 1 reveal the influence of different pre-training objectives. We establish our Baseline by using a frozen CLIP-ViT-B/16 to encode RGB and depth separately, followed by a trainable fusion layer to merge the two features, which is a strong baseline that can achieve better results than the previous best encoders (see CLIP-ViT+Depth in Table 4)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 714 + ], + "type": "text", + "content": "Results of Model#1 indicate that employing angular off" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": "set prediction as the only task has a devastating effect on the encoder; in fact, we found that " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\theta}" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " only oscillates if it is minimized alone, leading to features that are not useful in downstream tasks (see details in Appendix). Although learning " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\theta}" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " can improve the performance in both " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " (Model#5, Model#6), removing the task from Model#7 will not cause a noticeable difference (Model#4). Meanwhile, learning explorable distance prediction (Model#2, Model#5) is not effective in " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " scenario because agents with " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " apply pre-defined waypoints on open space, which means, finding explorable directions and avoid obstacle are not necessary. However, Model#2, Model#4 and Model#6 suggest that learning " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\theta}" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " will boost the results in " + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 304, + 261, + 547, + 441 + ], + "type": "text", + "content": " and effectively reduce the collision rate during navigation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": "On the other hand, by comparing the Baseline, Model#3, Model#6, and Model#7, we can see that our proposed " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\mathsf{Ego}^2" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": "-Map contrastive learning has the largest impact on R2R-CE. Solely learning " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": " improves the SR and SPL absolutely by " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "3.10\\%" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "3.34\\%" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": ", as well as " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "2.01\\%" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "2.02\\%" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": ", while removing " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": " from Model#7 dramatically lowers the results in both settings. Meanwhile, we found that " + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\mathsf{Ego}^2" + }, + { + "bbox": [ + 304, + 441, + 547, + 574 + ], + "type": "text", + "content": "-Map learning can also help avoid collision, implying the useful spatial information carried by the map. In the following experiments, all three losses are applied to pre-train the visual encoders." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 586, + 441, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 441, + 599 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 441, + 599 + ], + "type": "text", + "content": "4.3. Discussion and Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "How much does the quantity of visual data matter? In Table 2, we compare the effect of sampling a different quantity of data for pre-training our visual encoder. Results show that the agent's performance in R2R-CE drops as the amount of data decreases, and reducing the number of environments has a stronger impact on the results " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "(-1.08\\%)" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " SPL for " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " samples vs. " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "-3.87\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " SPL for " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " envs with " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": ", suggesting the importance of having abundant scenes and structures in learning visual represent" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "3060" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 72, + 286, + 159 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 286, + 159 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 286, + 159 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 286, + 159 + ], + "type": "table", + "html": "
Pre-train DataR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
100% data4.9459.6751.7746.117.2552.0130.4029.03
50% samples4.9857.7250.4645.037.4349.9727.5726.22
30% samples5.2856.1148.6142.587.8348.6025.8324.63
10% samples5.6054.8944.4839.087.8646.8322.9521.54
50% envs5.3255.5347.8042.247.5750.3526.5425.15
30% envs5.5653.8144.4838.697.6148.6426.0524.51
10% envs5.7353.4441.9236.897.8847.6223.2222.00
MP3D5.6752.7840.7835.767.9746.7521.9720.60
", + "image_path": "50b792283d1455d9ad2c027872ab6579d62f64b78e14960b4578b839846f74df.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 228, + 286, + 283 + ], + "blocks": [ + { + "bbox": [ + 47, + 167, + 287, + 216 + ], + "lines": [ + { + "bbox": [ + 47, + 167, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 167, + 287, + 216 + ], + "type": "text", + "content": "Table 2: Effect of additional environments for pre-training. The percentages indicate the portion of HM3D environments/samples for training. MP3D only uses data collected from the 61 environments in downstream." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 228, + 286, + 283 + ], + "lines": [ + { + "bbox": [ + 50, + 228, + 286, + 283 + ], + "spans": [ + { + "bbox": [ + 50, + 228, + 286, + 283 + ], + "type": "table", + "html": "
InitializationR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
CLIP4.9459.6751.7746.117.2552.0130.4029.03
Random4.9957.5549.3243.897.2751.3529.9128.29
IN-21K4.9558.6151.5545.737.0553.3031.0529.69
+IN-21K map5.4056.1847.0942.017.2152.6828.5527.13
", + "image_path": "f75b7256ad92c63ebbd6739b5f9e99e81310a8d9481a9ddeb232cd19f6d0b4a3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 374, + 286, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 286, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 286, + 446 + ], + "type": "text", + "content": "tations. Meanwhile, we can see that applying less than " + }, + { + "bbox": [ + 46, + 374, + 286, + 446 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 374, + 286, + 446 + ], + "type": "text", + "content": " of samples or environments cannot yield better results than the baseline in Table 1. This is because " + }, + { + "bbox": [ + 46, + 374, + 286, + 446 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 46, + 374, + 286, + 446 + ], + "type": "text", + "content": "-Map learning requires sufficient positive and negative data pairs to support its contrastive training, as observed in previous literatures [18, 72]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 472, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 712 + ], + "type": "text", + "content": "How much does initialization matter? Table 3 compares the initialization of the RGBD and the map encoders in " + }, + { + "bbox": [ + 46, + 472, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathsf{Ego}^2" + }, + { + "bbox": [ + 46, + 472, + 287, + 712 + ], + "type": "text", + "content": "-Map network, either from CLIP [72], from scratch or from a ViT-B/16 [25] pre-trained on ImageNet-21K (IN-21K) [23]. We find that random initialization of the RGB encoder only leads to a slight decrease in R2R-CE performance, while initializing it from pre-trained ViT can achieve comparable results to Model#7. We further investigate these results by also replacing the initialization of our map encoder from CLIP with IN-21K pre-trained ViT; although the losses of the two models saturate to the same level in pre-training, a drastic drop is observed in R2R-CE (even lower than Random). We hypothesize that some semantics from CLIP can be introduced to the RGBD encoder by the map encoder through contrastive learning. While previous works often use a convolutional network to process maps [14, 32, 33, 73], there remains a valuable open question of what model is suitable for encoding maps and how to train it to benefit navigation. We will leave the study of encoding maps for future work." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 309, + 72, + 545, + 109 + ], + "blocks": [ + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 365 + ], + "type": "text", + "content": "Table 3: Effect of using pre-trained encoders for RGBD and map. Random and IN-21K initialize the RGBD encoder randomly or from a ViT pre-trained on ImageNet-21K [23], while using the CLIP-ViT-B/32 to encode maps. +IN-21K map also uses the IN-21K pre-trained ViT to encode the semantic map." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 72, + 545, + 109 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 545, + 109 + ], + "type": "table", + "html": "
MethodsR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
CLIP-ViT+Depth +L5.4755.5547.1541.287.9347.7622.6821.69
5.2457.7448.6743.787.0752.5930.0728.74
", + "image_path": "ece422818bc59d3387a0f4c5acc0e78cdeccb319b2a956d274a250651dad31c8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 171, + 545, + 220 + ], + "blocks": [ + { + "bbox": [ + 306, + 118, + 545, + 167 + ], + "lines": [ + { + "bbox": [ + 306, + 118, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 306, + 118, + 545, + 167 + ], + "type": "text", + "content": "Table 4: Pre-training a different visual encoder with Ego2-Map objectives. The model applies CLIP-ViT-B/16 and a ResNet-50 trained for Point-Nav [94] to encode RGB and depth, respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 171, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 309, + 171, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 309, + 171, + 545, + 220 + ], + "type": "table", + "html": "
Ego2-MapR2R-CE Val-Unseen (AHigh)R2R-CE Val-Unseen (ALow)
NE↓nDTW↑SR↑SPL↑NE↓nDTW↑SR↑SPL↑
No semantics5.5157.6047.0442.257.3151.5629.7428.34
No space5.2457.4248.9443.527.6649.2029.3127.75
No target5.0256.2647.2041.218.0551.0430.8329.07
", + "image_path": "0c257c68da3e0ecb3dc46b10db7cc6af09b0764540ffc3214b0078e798fd5599.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 228, + 538, + 241 + ], + "lines": [ + { + "bbox": [ + 312, + 228, + 538, + 241 + ], + "spans": [ + { + "bbox": [ + 312, + 228, + 538, + 241 + ], + "type": "text", + "content": "Table 5: Ablation of information in Ego2-Map learning." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": "Effect of " + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": " on a different encoder We further evaluate our proposed " + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": "-Map objective in pre-training a different visual encoder (Table 4). Here we consider the previous state-of-the-art encoder CLIP-ViT+Depth, which applies CLIP-ViT-B/16 and a ResNet-50 depth net trained on Gibson [95] for PointNav [82] to encode RGB and depth, respectively, following by a fusion module to integrate the encoded features. Pre-training the model with " + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": " leads to a significant improvement, obtaining " + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "inline_equation", + "content": "+2.50\\%" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "inline_equation", + "content": "+7.05\\%" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": " higher SPL with " + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": ". These results suggest that " + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 304, + 254, + 545, + 396 + ], + "type": "text", + "content": "-Map learning has the potential to be generalized to other visual encoders." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": "Information in " + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{Ego}^2" + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": "-Map contrastive learning In Table 5, we ablate the information applied in the " + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{Ego}^2" + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": "-Map contrastive learning. Specifically, we either remove the object semantics by masking their colored segmentations with the same color, or remove explorable regions by masking open space and void with the same color (see unmasked maps in Figure 2), or remove the target view from the view pairs to create ambiguity in agent's transition. The results show that learning " + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{Ego}^2" + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": "-Map without the semantic clues or open space in the maps, or without a specified target greatly damages agent performance in " + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": ", reflecting the importance of including this information. We also find that the agent with " + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": " is less sensitive to method variations in pre-training; the remaining spatial or object information on a map is still beneficial to enhance the visual representation for supporting " + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": " navigation, which could be the reason why angular offset and explorable distance predictions do not show a consistent benefit in Table 1." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 646, + 485, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 485, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 485, + 658 + ], + "type": "text", + "content": "4.4. Comparison to Previous Methods" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Advantages of Visual Representations (R2R-CE) In Table 6, we compare our method of applying " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathsf{Ego}^2" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "-Map RGBD encoder to the CWP-VLN" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\vec{\\circ}" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "BERT agent [41] (same model as Model#7 in Table 1) with previous approaches" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3061" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "using " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{High}" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " on the R2R-CE testing split4. Results show that our proposed " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "-Map learning brings significant improvement for all metrics, achieving a " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "47\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " SR " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "(+3\\%)" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " and a " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "41\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " SPL " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "(+4\\%)" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " over the previous best [50]. In addition, Table 7 establishes a fair comparison with methods using " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{Low}" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": ". We can see that " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "-Map features greatly boost the result of the base agent CWP-VLN BERT [41] (23% to 30% SR), and achieve a SPL comparable to recent mapping-based methods such as CM2 [33] and WS-MGMap [14]. Note that using " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\mathrm{Ego}^2" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "-Map representations does not conflict with online mapping; while we only experiment with non-mapping-based agents, we believe the features hold great potential to facilitate modeling between views and maps in mapping-based models." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": "Learning Methods (ObjNav) We further compare the effect of visual representation learning methods by applying our visual encoder on ObjNav [4] as in the recent approaches [46, 96] (Table 8). All methods in the table adopt a simple pipeline as in the baseline model [94], which feeds the concatenation of visual features, GPS+Compass encodings, and the encodings of previous action to a GRU [19], then, uses a fully-connected layer to predict an action from the updated agent's state. Briefly, EmbCLIP directly uses the pre-trained CLIP-ResNet50 [72] to encode the RGB inputs, EmbCLIP-ViT+Depth applies the CLIP-ViT-B/16 to encode RGB and an extra depth net [82] pre-trained on Gibson [95] to encode the depth inputs. OVRL pre-trains the ResNet encoder with self-distillation method DINO [6], in which a student network is trained to match the output of a teacher network. Moreover, OVRL applies the Omnidata Starter Dataset " + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "inline_equation", + "content": "(\\mathrm{OSD})^5" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": " [28], which is much larger and more diverse than the data for our Ego" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": "-Map learning (only uses the HM3D [74] subset). ObjNav measures the same metrics as R2R-CE, first, we can see that an agent using Ego" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": "-Map features greatly improves over the baseline and the EmbCLIP. Compared to OVRL, despite the method applies OSD for pre-training and fine-tunes the network end-to-end with human demonstrations, our method obtains a better success rate " + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "inline_equation", + "content": "(+0.4\\%)" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": " and much higher SPL " + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "inline_equation", + "content": "(+3.2\\%)" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": ". Note that, although not directly comparable, as reported in the OVRL, the SPL on ImageNav [63] without fine-tuning the visual encoder will drop drastically from " + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "inline_equation", + "content": "26.9\\%" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "inline_equation", + "content": "17.0\\%" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": ", whereas all our experiments keep the visual encoder frozen during navigation. These results suggest that Ego" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 266, + 289, + 651 + ], + "type": "text", + "content": "-Map representations are generalizable to different navigation tasks and provide more robust visual representations." + } + ] + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 308, + 72, + 547, + 140 + ], + "blocks": [ + { + "bbox": [ + 308, + 72, + 547, + 140 + ], + "lines": [ + { + "bbox": [ + 308, + 72, + 547, + 140 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 547, + 140 + ], + "type": "table", + "html": "
Methods (AHigh)R2R-CE Test-Unseen
TLNE↓OSR↑SR↑SPL↑
Waypoint Models [49]8.026.65373230
CWP-CMA [41]11.856.30493833
CWP-VLN BERT [41]13.315.89514236
Sim2Sim [50]11.436.17524437
Ego2-Map+CWP-VLN BERT (ours)13.055.54564741
", + "image_path": "1db4a235578aff21345b20633a9fc9d8e82e2d68fae7d6e5bd81ec37eaeca6fb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 308, + 171, + 547, + 266 + ], + "blocks": [ + { + "bbox": [ + 306, + 144, + 545, + 168 + ], + "lines": [ + { + "bbox": [ + 306, + 144, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 144, + 545, + 168 + ], + "type": "text", + "content": "Table 6: Comparison of agent performance on R2R-CE test server. All methods use high-level action space " + }, + { + "bbox": [ + 306, + 144, + 545, + 168 + ], + "type": "inline_equation", + "content": "(\\mathcal{A}_{High})" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 171, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 308, + 171, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 308, + 171, + 547, + 266 + ], + "type": "table", + "html": "
Methods (ALow)R2R-CE Val-Unseen
TLNE↓OSR↑SR↑SPL↑
CMA+PM+DA+Aug [51]8.647.37403230
SASRA [44] †7.898.32-2422
LAW [77]8.896.83443531
CWP-CMA [41]°8.227.54-2725
CWP-VLN BERT [41]°7.427.66-2322
CM2 [33] †11.547.02423428
WS-MGMap (SemMap only) [14] †10.896.80423328
Ego2-Map+CWP-VLN BERT (ours)8.037.25373029
", + "image_path": "c020fede76c7aab70ee46e7ed720ab3053e16007feff13f17dce80bd6573e0f3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 308, + 331, + 547, + 410 + ], + "blocks": [ + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "lines": [ + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "text", + "content": "Table 7: Comparison of agents with low-level action space " + }, + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "inline_equation", + "content": "(\\mathcal{A}_{Low})" + }, + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "text", + "content": " in R2R-CE Val-Unseen. " + }, + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "text", + "content": ": mapping-based methods. " + }, + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 305, + 274, + 547, + 323 + ], + "type": "text", + "content": " of data is removed but the comparison is still valid due to the large performance gap." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 331, + 547, + 410 + ], + "lines": [ + { + "bbox": [ + 308, + 331, + 547, + 410 + ], + "spans": [ + { + "bbox": [ + 308, + 331, + 547, + 410 + ], + "type": "table", + "html": "
MethodsPre-Training DatasetObjNav MP3D Val
NE↓SR↑SPL↑
Baseline [94]X6.908.01.8
EmbCLIP [46]*WebImageText5.2620.98.3
EmbCLIP-ViT+DepthWebImageText+Gibson4.9023.38.6
OVRL no pretrain [76] †X-24.25.9
OVRL [96] †OSD-28.67.4
Ego2-Map+Baseline (ours)HM3D5.1729.010.6
", + "image_path": "b0c27b718114d49c254b651cccedc0dc31211b4c0be7acf2cae55313f9c0f311.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "type": "text", + "content": "Table 8: Comparison on pre-trained visual encoders for ObjNav. " + }, + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "type": "text", + "content": " indicates the visual encoder is tuned end-to-end with behavior cloning on " + }, + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "type": "inline_equation", + "content": "40\\mathrm{k}" + }, + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "type": "text", + "content": " human demonstrations collected by Habitat-Web [76], while the others freeze the visual encoder during navigation and only train the agent with DD-PPO [94] on the original data. *Results obtained by re-evaluating the officially released best model checkpoint." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 514, + 379, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 379, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 379, + 526 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "text", + "content": "In this paper, we introduce a novel method of learning navigational visual representations with contrastive learning between egocentric views pairs and top-down semantic maps (Ego" + }, + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "text", + "content": "-Map). The method transfers the compact semantic and spatial information carried by a map to the egocentric representations, which greatly facilitates the agent's visual perception. Experiments show that Ego" + }, + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "text", + "content": "-Map features greatly improve the downstream navigation, such as ObjNav and VLN, and demonstrate generalization potential to different visual backbones. We believe the Ego" + }, + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 534, + 545, + 715 + ], + "type": "text", + "content": "-Map contrastive learning proposes a new direction of visual representation learning for navigation and provides the possibility of better modeling the correspondence between views and maps, which can further benefit agent's planning and action. Note that our work also produces a potentially ef" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 663, + 301, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 663, + 301, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 663, + 301, + 715 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 46, + 663, + 301, + 715 + ], + "type": "text", + "content": "R2R-CE Challenge Leaderboard: https://eval.ai/web/challenges/challenge-page/719/leaderboard/1966 \n" + }, + { + "bbox": [ + 46, + 663, + 301, + 715 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 46, + 663, + 301, + 715 + ], + "type": "text", + "content": "OSD [28] contains approximately 14.5 million images rendered from diverse 3D environments, including Replica [88], Replica+GSO [26], Hypersim [79], Taskonomy [100], BlendedMVG [97] and HM3D [74]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3062" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "fective map encoder whose full capability is worth investigating in future work." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "spans": [ + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "type": "text", + "content": "Limitations The need to build semantic maps to enable the " + }, + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "type": "inline_equation", + "content": "\\mathbf{Ego}^2" + }, + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "type": "text", + "content": "-Map contrastive learning is an inevitable cost of this method; compared to other self-supervised visual representation learning approaches, " + }, + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "type": "inline_equation", + "content": "\\mathbf{Ego}^2" + }, + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "type": "text", + "content": "-Map requires either the semantic annotations of scenes, or traversable environments and a generalizable semantic map constructor. As a result, the data collection could be much harder. However, we also witnessed an increasing number of interactive 3D scenes being built in recent years with dense semantic annotations [22, 74, 82, 88, 95], which can facilitate scaling up our " + }, + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "type": "inline_equation", + "content": "\\mathbf{Ego}^2" + }, + { + "bbox": [ + 47, + 106, + 288, + 238 + ], + "type": "text", + "content": "-Map learning in the future." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 251, + 106, + 263 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 251, + 106, + 263 + ], + "spans": [ + { + "bbox": [ + 48, + 251, + 106, + 263 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 272, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 58, + 272, + 287, + 325 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 272, + 287, + 325 + ], + "spans": [ + { + "bbox": [ + 58, + 272, + 287, + 325 + ], + "type": "text", + "content": "[1] Dong An, Zun Wang, Yangguang Li, Yi Wang, Yicong Hong, Yan Huang, Liang Wang, and Jing Shao. 1st place solutions for rxr-habitat vision-and-language navigation competition (cvpr 2022). arXiv preprint arXiv:2206.11610, 2022.2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 329, + 286, + 383 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 329, + 286, + 383 + ], + "spans": [ + { + "bbox": [ + 58, + 329, + 286, + 383 + ], + "type": "text", + "content": "[2] Peter Anderson, Angel Chang, Devendra Singh Chaplot, Alexey Dosovitskiy, Saurabh Gupta, Vladlen Koltun, Jana Kosecka, Jitendra Malik, Roozbeh Mottaghi, Manolis Savva, et al. 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Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct distinct clusters. Despite recent progress in enhancing spectral clustering with powerful pre-trained models, current approaches still suffer from inefficiencies in spectral decomposition and inflexibility in applying them to the test data. This work addresses these issues by casting spectral clustering as a parametric approach that employs neural network-based eigenfunctions to produce spectral embeddings. The outputs of the neural eigenfunctions are further restricted to discrete vectors that indicate clustering assignments directly. As a result, an end-to-end NN-based paradigm of spectral clustering emerges. In practice, the neural eigenfunctions are lightweight and take the features from pre-trained models as inputs, improving training efficiency and unleashing the potential of pre-trained models for dense prediction. We conduct extensive empirical studies to validate the effectiveness of our approach and observe significant performance gains over competitive baselines on Pascal Context, Cityscapes, and ADE20K benchmarks. The code is available at https://github.com/thudzj/NeuralEigenfunctionSegmentor.", + "bbox": [ + 75, + 318, + 472, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 709, + 207, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic segmentation is essential in understanding the inherent structure and fine-grained information of images. However, current approaches often hinge on a vast amount of manual annotations to train neural networks (NNs) effectively in an end-to-end manner [5, 40]. This is problematic, as obtaining these annotations can be both time-consuming and costly, particularly in fields such as autonomous driving and medical image processing, where annotations are usually collected from domain experts. Thus, finding a way to perform semantic segmentation without manual annotation remains a crucial unresolved problem.", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unsupervised semantic segmentation has recently attracted a great deal of attention. A number of methods attempt to tackle it by learning fine-grained image features using self-supervised objectives and then applying clustering or grouping techniques [46, 41]. They tend to recognize single objects or single semantic categories and struggle with complex images. Other approaches have tried to use vision-language cross-modal models (e.g., CLIP [35]) to achieve zero-shot semantic segmentation [48, 39], but they heavily rely on carefully-tuned text prompts and self-training. Compared to the recent approaches, the classic spectral clustering [38], which has stood the test of time, remains an appealing option. In particular, it enjoys solid foundations in spectral graph theory—it finds the minimum cut of the connectivity graph over pixels.", + "bbox": [ + 496, + 287, + 893, + 515 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, traditional spectral clustering exhibits limitations in three aspects: (i) it operates on raw image pixels, thus is sensitive to color transformations and unable to recognize semantic similarities; (ii) it is computationally inefficient due to the involved spectral decomposition; (iii) unlike NN-based methods, it is nontrivial and costly to extend to non-training samples because of its transductive manner. Thus it cannot be performed end-to-end in the test phase. Recent work reveals that pre-trained models such as ViTs [14] can mitigate the first limitation, significantly improving the applicability and effectiveness of spectral clustering [30]. Its core contribution is to build the connectivity graph over image patches based on an affinity matrix computed with the dense features from pre-trained models. Still, the limitations regarding efficiency and flexibility remain.", + "bbox": [ + 496, + 518, + 893, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The present paper aims to overcome the remaining limitations, rendering spectral clustering a simple yet effective baseline for unsupervised semantic segmentation. To tackle the inefficiency issue, we propose to cast the involved spectral decomposition problem as an NN-based optimization one using the recently developed neural eigenfunction (NeuralEF) technique [12]. Concretely, we first measure the similarities between image patches using both the features extracted from pre-trained models and raw pixels. Treating the similarity matrix (or its variants) as the output of a", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "551", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "kernel function, we then optimize NNs to approximate its principal eigenfunctions. Consequently, our method constitutes an NN-based counterpart of spectral embedding. We eliminate the need for an additional grouping step, which is required in prior work [30], by constraining the NN output to one-hot vectors that indicate clustering assignments directly. To accomplish this, we use the Gumbel-Softmax estimator [20] for gradient-based optimization during training. These strategies transform spectral clustering from a non-parametric approach to a parametric one, enabling easy and reliable out-of-sample generalization and avoiding solving complex matrix eigenvalue problems during testing.", + "bbox": [ + 80, + 90, + 467, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We perform extensive studies to evaluate the effectiveness of our approach for unsupervised semantic segmentation. We first experiment on the popularly used benchmarks Pascal Context [31] and Cityscapes [9] based on pre-trained ViTs, and report superior results compared to leading methods MaskCLIP [48] and ReCo [39]. We further consider the sliding-window-based evaluation protocol [40] and experiment on the challenging ADE20K dataset [47] to systematically study the behavior of our method. In addition, we conduct thorough ablation studies to gain insights into the specification of several core hyper-parameters.", + "bbox": [ + 80, + 273, + 467, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 80, + 452, + 215, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised segmentation. Image segmentation has numerous practical applications in various industries and scientific fields. In order to alleviate the burden of collecting annotations, prior works have comprehensively studied the problem of learning image segmenters in semi- and weakly-supervised settings [24, 18, 4, 23]. Recently, there have been increasing efforts to tackle unsupervised segmentation based on the progress in related fields like deep generative models (DGMs) and self-supervised learning (SSL). On the one hand, DGM-based segmentation approaches train specialized image generators to separate foreground from background [6, 2, 1] or extract saliency masks directly from pre-trained generators [42]. Yet, it is technically nontrivial to extend them to cope with semantic segmentation. On the other hand, SSL-based methods define objectives to perform clustering [19, 7], mutual information maximization [21, 33], contrastive learning [41] or feature correspondence distillation [16] to learn image features suitable for grouping. However, most of these methods only recognize single objects or single semantic categories and struggle with complex images. With the increasing accessibility of pre-trained image-text cross-modal models, considerable efforts have been devoted to performing zero-shot semantic segmentation with them [48, 39]. Nevertheless, the entanglement with cross-modal models places high demands on the quality of the text prompts, which correspond to the semantic categories of concern, and hinders the methods from choosing backbone models freely.", + "bbox": [ + 80, + 477, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spectral clustering. As a classic solution to image segmentation, spectral clustering [38, 32] frames the original problem as a graph partitioning one defined on the connectivity graph over image pixels. Typically, spectral clustering exploits the eigenvectors of graph Laplacians to construct minimum-energy graph partitions [13, 15]. Spectral clustering is closely related to Kernel PCA [37] as they are both learning eigenfunctions [3]. Recently, spectral clustering has been combined with pre-trained models to enjoy rich semantic information [30]. Yet, it remains unsolved that spectral decomposition is expensive for big data, and the non-parametric nature hinders out-of-sample generalization. This paper aims to address these issues.", + "bbox": [ + 503, + 90, + 888, + 285 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The deep learning variant of spectral methods. Refurbishing spectral methods with deep learning techniques is beneficial to improve the scalability and flexibility of the former. The spectral inference networks (SpIN) [34] is a seminal work in this direction. Yet, the learning objective of SpIN is ill-defined, which leads to only the subspace spanned by the principal eigenfunctions instead of the eigenfunctions themselves. SpIN hence introduces convoluted and expensive strategies to solve this problem. The recent NeuralEF technique [12] alternatively defines a new series of objective functions to break the symmetry among eigenfunctions explicitly. NeuralEF is further enhanced by weight sharing and extended to handle indefinite kernels in [11], constituting a more amenable choice for learning spectral embeddings given pre-defined kernels. We also note that there are several attempts to develop deep spectral clustering methods based on supervisions [28] or a dual autoencoder network [45], but they cannot be trivially applied to the task of unsupervised semantic segmentation due to the absence of annotations or other inefficiency issues.", + "bbox": [ + 503, + 287, + 888, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 503, + 602, + 630, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We begin with a brief review of the relevant background and then build up our approach step by step. We provide an overview of the proposed method in Figure 1.", + "bbox": [ + 503, + 627, + 888, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Background", + "text_level": 1, + "bbox": [ + 503, + 681, + 627, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic segmentation essentially targets determining the semantic consistency among image pixels. In the absence of annotations, the problem boils down to an unsupervised clustering one. Spectral clustering [38, 32] is a longstanding solution to it with solid theoretical foundations. It proceeds by partitioning a connectivity graph over image pixels. The resulting algorithm typically involves eigendecomposing the graph Laplacian matrix and stacking its eigenvectors, which are then used in a Euclidean clustering algorithm to obtain a fixed number of partitions.", + "bbox": [ + 503, + 704, + 888, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional spectral clustering operates on raw image pixels, making it sensitive to color transformations and unable to identify semantic similarities. To address this, a", + "bbox": [ + 503, + 856, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "552", + "bbox": [ + 486, + 946, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d477142d47580f07bb6363d996aa8bd6e6e774453869434fd3c66b96a9e33659.jpg", + "image_caption": [ + "Figure 1. Method overview. We establish an end-to-end NN-based pipeline for spectral clustering to perform unsupervised semantic segmentation. The box highlights modules that exist only during training. The nearest neighbor graph over pixels only has edges between pixels from the same images, while the other one is built over dense features from various images. The pre-trained model is fixed." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 893, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "natural idea is to include the inductive bias of NNs. In this spirit, the deep spectral method (DSM) [30] leverages powerful pre-trained models to translate the learning from raw pixels to patch-wise features that embed rich local semantics and are widely applicable. Specifically, let $\\pmb{x}_i \\in \\mathbb{R}^{H \\times W \\times 3}$ denote an image and $f: \\mathbb{R}^{H \\times W \\times 3} \\to \\mathbb{R}^{H / P \\times W / P \\times C}$ denote the pre-trained model with $P$ as a down-sampling factor. DSM constructs a semantic affinity matrix using both the patch-wise features $\\pmb{f}_{i,j,k} = f(\\pmb{x}_i)_{j,k} \\in \\mathbb{R}^C$ and image pixels, and performs spectral clustering on the corresponding connectivity graph. Subsequently, DSM performs bi-linear interpolation to convert patch-wise segments to pixel-wise ones. This simple workflow has surpassed various competitors regarding unsupervised semantic segmentation performance.", + "bbox": [ + 75, + 356, + 468, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Denote by $N$ the size of the dataset of concern. Semantic segmentation requires classifying pixels in different images yet with the same semantics into the same category. Thereby, it needs to ensure semantic consistency across the dataset. Therefore, DSM should, in principle, work on an affinity matrix of size $\\mathbb{R}^{NHW / P^2\\times NHW / P^2}$ , but this is computationally infeasible as the involved spectral decomposition has a cubic complexity w.r.t. $NHW / P^2$ . DSM alternatively conducts spectral clustering separately for each image and then performs cross-image synchronization, but this is inflexible compared to NN-based pipelines and arguably suboptimal. Additionally, existing spectral clustering methods, including DSM, are non-parametric, relying on costly spectral decomposition when faced with new test data.", + "bbox": [ + 75, + 582, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to address the limitations discussed above, we leverage a parametric approach to spectral decomposition based on the recent NeuralEF technique [12] and learn discrete neural eigenfunctions directly. These innovations help to scale our method to large datasets, enable the straightforward and cheap out-of-sample extension for test data, and establish an NN-based spectral clustering workflow.", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. From Eigenvectors to Eigenfunctions", + "text_level": 1, + "bbox": [ + 500, + 354, + 818, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spectral clustering involves the spectral decomposition of a matrix and hence is seemingly incompatible with the parametric NN models. To bridge this gap, we move our viewpoint from the eigenvectors to eigenfunctions.", + "bbox": [ + 496, + 378, + 890, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, abstracting the graph Laplacian matrix as the evaluation of some kernel function $\\kappa$ on the dense features, the eigenfunctions of $\\kappa$ form a function-space generalization of the aforementioned eigenvectors. Formally, the eigenfunction $\\psi$ of a kernel $\\kappa(\\pmb{x},\\pmb{x}^{\\prime})$ satisfies that", + "bbox": [ + 496, + 439, + 890, + 513 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\int \\kappa (\\boldsymbol {x}, \\boldsymbol {x} ^ {\\prime}) \\psi (\\boldsymbol {x} ^ {\\prime}) p (\\boldsymbol {x} ^ {\\prime}) d \\boldsymbol {x} ^ {\\prime} = \\mu \\psi (\\boldsymbol {x}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 525, + 890, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mu$ is the corresponding eigenvalue and $p$ a probability measure. By definition, the eigenfunction should be normalized, and different eigenfunctions are orthogonal.", + "bbox": [ + 496, + 565, + 890, + 611 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown, the eigenfunction takes input from the original space and maps it to the eigenspace specified by the kernel, where the local neighborhoods on data manifolds are preserved. Naturally, we can incorporate NNs as function approximators to the eigenfunctions. In this way, we bypass the need for expensive spectral decomposition of a matrix and can easily perform out-of-sample extension thanks to the generalization ability of NNs. Fortunately, the recently proposed NeuralEF [12] offers tools to realize this. We also note that the effectiveness of the spectral embedding yielded by neural eigenfunctions has been empirically validated in self-supervised learning [11].", + "bbox": [ + 496, + 611, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Setting up the Graph Kernel", + "text_level": 1, + "bbox": [ + 500, + 801, + 756, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To set up the kernel for spectral clustering, as suggested by DSM [30], we construct two graphs with patch-wise features from pre-trained models and down-sampled image pixels, respectively. We then define the kernel with the weighted sum of the corresponding normalized graph adja", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "553", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ency matrices. By doing so, the high-level semantics and low-level details are conjoined.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Denote by $\\mathbf{F} = \\{\\pmb {f}_i\\}_{i = 1}^N\\in \\mathbb{R}^{NHW / P^2\\times C}$ the collection of patch-wise features over the dataset. Considering that the feature space shaped by large-scale pre-training is highly structured where simple distance measures suffice to represent similarities, we leverage cosine similarity to specify a nearest neighbor graph over image patches. The corresponding affinity matrix is detailed below:", + "bbox": [ + 75, + 119, + 467, + 229 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {u, v} = \\left\\{ \\begin{array}{l l} \\mathbf {F} _ {u} \\mathbf {F} _ {v} ^ {\\top} / (\\| \\mathbf {F} _ {u} \\| \\| \\mathbf {F} _ {v} \\|), & v \\in k - \\mathrm {N N} (u, \\mathbf {F}, \\text {c o s i n e}) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 239, + 467, + 291 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $k$ -NN( $u, \\mathbf{F}, \\cos \\mathrm{i}$ ) denotes the set of the $k$ nearest neighbors of $\\mathbf{F}_u$ over $\\mathbf{F}$ under cosine similarity. The above graph deploys edges between patches that are semantically close. The corresponding graph partitioning can result in meaningful segmentation at a coarse resolution. Although other traditional graphs can also be used, the nearest neighbor graph enjoys sparsity, which reduces storage and computation costs and has been studied extensively in manifold learning and spectral clustering.", + "bbox": [ + 75, + 291, + 467, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To supplement the high-level features with low-level details, we bilinearly down-sample the original image $\\pmb{x}_i$ to $\\tilde{\\pmb{x}}_i\\in \\mathbb{R}^{H / P\\times W / P\\times 3}$ to keep resolution consistency, and fuse the spatial information $(j,k)$ and color information $\\tilde{\\pmb{x}}_{i,j,k}$ as a single vector. We stack the collection over the dataset as $\\tilde{\\mathbf{X}}\\in \\mathbb{R}^{NHW / P^2\\times 5}$ . A nearest neighbor graph over down-sampled pixels is then defined based on $L^2$ distance following DSM [30]. The affinity matrix is:", + "bbox": [ + 75, + 428, + 467, + 550 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {A}} _ {u, v} = \\left\\{ \\begin{array}{l l} 1, & v \\in \\tilde {k} - \\mathrm {N N} (u, \\tilde {\\mathbf {X}}, L ^ {2}) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 560, + 467, + 601 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{k}$ -NN $(u, \\tilde{\\mathbf{X}}, L^2)$ denotes the set of $\\tilde{k}$ nearest neighbors of $\\tilde{\\mathbf{X}}_u$ over $\\tilde{\\mathbf{X}}$ under $L^2$ distance (dissimilarity). We place a further constraint that the nearest neighbors should belong to the same image as the query to avoid establishing meaningless connections. It is expected that such a graph helps to detect sharp object boundaries.", + "bbox": [ + 75, + 611, + 467, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We symmetrize $\\mathbf{A}$ and $\\tilde{\\mathbf{A}}$ so that they can serve as graph adjacency matrices. Considering that the normalized graph cuts are more practically useful [38], we would better build a kernel with the normalized graph Laplacian matrices of $\\mathbf{A}$ and $\\tilde{\\mathbf{A}}$ , and learn the eigenfunctions associated with the smallest $K$ eigenvalues. However, the NeuralEF approach instead deploys neural approximations to the principal eigenfunctions, which correspond to the largest eigenvalues, of a kernel [12]. To this end, we move our focus from the normalized Laplacian matrix to the normalized adjacency matrix whose $K$ principal eigenfunctions exactly correspond to the eigenfunctions associated with the $K$ smallest eigenvalues of the former. Specifically, let", + "bbox": [ + 75, + 704, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{D} \\coloneqq \\operatorname{diag}(\\mathbf{A}\\mathbf{1}), \\tilde{\\mathbf{D}} \\coloneqq \\operatorname{diag}(\\tilde{\\mathbf{A}}\\mathbf{1})$ denote the degree matrices. We then define the kernel function $\\kappa$ using the weighted sum of the normalized adjacency matrices, detailed below:", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\kappa : \\kappa (\\mathbf {F}, \\mathbf {F}) = \\mathbf {D} ^ {- 1 / 2} \\mathbf {A} \\mathbf {D} ^ {- 1 / 2} + \\alpha \\tilde {\\mathbf {D}} ^ {- 1 / 2} \\tilde {\\mathbf {A}} \\tilde {\\mathbf {D}} ^ {- 1 / 2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 145, + 890, + 162 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ is a trade-off parameter. Here we define the kernel in the space of features extracted from pre-trained models while other choices are also viable: it only affects the input of neural eigenfunctions. In the current setting, the features from pre-trained models are directly fed into neural eigenfunctions, which is sensible thanks to the great potential of pre-trained models and can prevent unnecessary training costs.", + "bbox": [ + 496, + 172, + 890, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Learning Neural Eigenfunctions", + "text_level": 1, + "bbox": [ + 498, + 304, + 782, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathbf{f} \\in \\mathbb{R}^C$ denote a row vector of $\\mathbf{F}$ and $p(\\mathbf{f})$ a uniform distribution over $\\{\\mathbf{F}_i\\}_{i=1}^{NHW/P^2}$ . The NeuralEF technique [12] approximates the $K$ principal eigenfunctions of the kernel $\\kappa$ w.r.t. $p(\\mathbf{f})$ with a $K$ -output neural function $\\psi: \\mathbb{R}^C \\to \\mathbb{R}^K$ by solving the following problem:", + "bbox": [ + 498, + 325, + 890, + 406 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {\\psi} \\sum_ {j = 1} ^ {K} \\mathbf {R} _ {j, j} - \\beta \\sum_ {j = 1} ^ {K} \\sum_ {i = 1} ^ {j - 1} \\widehat {\\mathbf {R}} _ {i, j} ^ {2}, s. t. \\mathbb {E} _ {p (\\mathbf {f})} [ \\psi (\\mathbf {f}) \\circ \\psi (\\mathbf {f}) ] = \\mathbf {1}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 414, + 890, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ is a positive coefficient and $\\circ$ is Hadamard product, and", + "bbox": [ + 498, + 465, + 888, + 492 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {R} := \\mathbb {E} _ {p (\\mathbf {f})} \\mathbb {E} _ {p \\left(\\mathbf {f} ^ {\\prime}\\right)} \\left[ \\kappa \\left(\\mathbf {f}, \\mathbf {f} ^ {\\prime}\\right) \\psi (\\mathbf {f}) \\psi \\left(\\mathbf {f} ^ {\\prime}\\right) ^ {\\top} \\right] \\\\ \\widehat {\\quad} \\end{array} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 491, + 890, + 516 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathbf {R}} := \\mathbb {E} _ {p (\\mathbf {f})} \\mathbb {E} _ {p \\left(\\mathbf {f} ^ {\\prime}\\right)} \\left[ \\kappa (\\mathbf {f}, \\mathbf {f} ^ {\\prime}) \\hat {\\psi} (\\mathbf {f}) \\psi \\left(\\mathbf {f} ^ {\\prime}\\right) ^ {\\top} \\right].\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 512, + 815, + 529 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $\\hat{\\psi}$ is the non-optimizable variant of $\\psi$ .", + "bbox": [ + 500, + 534, + 787, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Adapting such results to our case and applying Monte Carlo estimation to the expectation yields", + "bbox": [ + 498, + 550, + 888, + 580 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R} \\approx \\frac {1}{B ^ {2}} \\boldsymbol {\\Psi} \\cdot \\kappa (\\mathbf {F} ^ {B}, \\mathbf {F} ^ {B}) \\cdot \\boldsymbol {\\Psi} ^ {\\top} \\text {a n d} \\widehat {\\mathbf {R}} \\approx \\frac {1}{B ^ {2}} \\widehat {\\boldsymbol {\\Psi}} \\cdot \\kappa (\\mathbf {F} ^ {B}, \\mathbf {F} ^ {B}) \\cdot \\boldsymbol {\\Psi} ^ {\\top}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 587, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{F}^B\\coloneqq [\\mathbf{f}_1,\\dots ,\\mathbf{f}_B]^\\top \\in \\mathbb{R}^{B\\times C}$ is a mini-batch of features, $\\Psi \\coloneqq [\\psi (\\mathbf{f}_1),\\ldots ,\\psi (\\mathbf{f}_B)]\\in \\mathbb{R}^{K\\times B}$ is the collection of the corresponding NN outputs, and $\\widehat{\\Psi}\\coloneqq$ stop-gradient(Ψ). The stop-gradient operation can be easily found in auto-diff libraries and plays a vital role in establishing the asymmetry between the $K$ principal eigenfunctions. We put an $L^2$ -batch normalization layer [12] at the end of model $\\psi$ to enforce the constraint in Equation (5).", + "bbox": [ + 496, + 625, + 890, + 747 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\psi$ can be implemented as a neural network composed of convolutions or transformer blocks, which takes dense image features $\\pmb{f} = f(\\pmb{x}) \\in \\mathbb{R}^{H / P \\times W / P \\times C}$ as input and outputs $\\psi(\\pmb{f}) \\in \\mathbb{R}^{H / P \\times W / P \\times K}$ . After training, it can be used to predict new test data without relying on expensive test-time spectral decomposition.", + "bbox": [ + 496, + 748, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Quantizing Neural Eigenfunctions", + "text_level": 1, + "bbox": [ + 500, + 847, + 797, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After obtaining the spectral embedding $\\psi(f(x))$ for image patches, we should, by convention, invoke a Euclidean", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "554", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "clustering algorithm such as K-means [29] to get clustering assignments. In practice, datasets can often be large, so it would be better to leverage online clustering mechanisms to avoid unaffordable storage costs. However, this approach may still be time-consuming when aiming for good convergence. Additionally, this pipeline is not as flexible as NN-based segmenters.", + "bbox": [ + 78, + 90, + 467, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To bridge the gap, we impose a constraint on the output of $\\psi$ to be $K$ -dim one-hot vectors which directly indicate clustering assignments. We resort to the Gumbel-Softmax estimator [20] for gradient-based optimization. This follows the notion that the outputs of eigenfunctions are soft clustering assignments, and we further perform quantization of them. This is also in a similar spirit to the spectral hashing approach [43] where the output of $\\psi$ is assumed to be vectors over $\\{-1,1\\}^K$ . We clarify that the Gumbel-Softmax estimator precedes the aforementioned $L^2$ batch normalization layer. In the test phase, we remove this estimator and the $L^2$ batch normalization layer, using the NN outputs directly as softmax logits for clustering. This results in a pure NN-based workflow for spectral clustering.", + "bbox": [ + 78, + 198, + 467, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. From Clusters to Image Segments", + "text_level": 1, + "bbox": [ + 78, + 416, + 372, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During inference, we up-sample the softmax logits bilinearly to match the original resolution of input images. We then apply the argmax operation to obtain discrete clustering assignments. A natural question that arises is how to match these clustering assignments to pre-defined semantics to obtain the final image segments. Two well-studied solutions are Hungarian matching [27] and majority voting. As per DSM [30], when evaluated on standard image semantic segmentation benchmarks, we first collect the clustering assignments for all validation images and then match them to ground-truth labels via these approaches to conduct a quantitative evaluation of segmentation performance.", + "bbox": [ + 78, + 439, + 467, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 78, + 632, + 207, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate the efficacy of the proposed method for unsupervised semantic segmentation, we conduct comprehensive experiments on various standard benchmarks.", + "bbox": [ + 78, + 657, + 467, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setups", + "text_level": 1, + "bbox": [ + 78, + 710, + 272, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We primarily experiment on Pascal Context and Cityscapes, which consist of 60 and 27 classes, respectively. We employ the same data pre-processing and augmentation strategies as the work [40] on the training dataset.", + "bbox": [ + 78, + 734, + 467, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pre-trained models. We use pre-trained ViTs [14] provided by the timm library [44] and consider the \"Small\", \"Base\", and \"Large\" variants. The weights have been pre-trained on ImageNet-21k [36] and fine-tuned on ImageNet [10] in a supervised manner. In particular, we consider pre-trained models at a high resolution, like $384 \\times 384$ , to obtain fine-grained segments. We fix the patch size to", + "bbox": [ + 78, + 795, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$16 \\times 16$ (i.e., $P = 16$ ) to better trade-off efficiency and accuracy. We use the output of the last attention block of ViTs as $f_{i}$ without elaborate selection. We also feed the intermediate features of the pre-trained ViTs, which can be freely accessed, to the neural eigenfunctions to enrich the input information.", + "bbox": [ + 501, + 90, + 890, + 180 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Modeling and training. We set $k = 256$ for the nearest neighbor graph defined on pre-trained models' features. To reduce the cost of searching for the nearest neighbors, we confine the search to the current mini-batch, which is shown to be empirically effective. We specify the other graph following DSM [30]. The trade-off coefficient $\\alpha$ equals 0.3 based on an ablation study reported in Section 4.4. The training objective is detailed in Equation (5) and unfolded in Equation (7). As $K$ implies the number of semantic classes uncovered automatically, we make it larger than the number of ground-truth semantic classes and, in practice, set it to 256. We set the trade-off coefficient $\\beta$ to 0.08 and linearly scale it for other values of $K$ (see the study in Section 4.4). We use 2 transformer blocks with linear self-attention [22] and a linear head to specify the neural eigenfunctions $\\psi$ for efficiency. We restrict the weight matrix of the linear head to have orthogonal columns and find it beneficial to the final performance empirically. We anneal the temperature for Gumbel-Softmax from 1 to 0.3 following a cosine schedule during training. The training relies on an Adam optimizer [25] and a learning rate of $10^{-3}$ (with cosine decay). No weight decay is employed. The training lasts for 40 epochs with batch size 16 (or 8 if an out-of-memory error occurs), which takes half a day on one RTX 3090 GPU.", + "bbox": [ + 503, + 183, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation. We test on the validation set of the datasets and report both pixel accuracy (Acc.) and mean intersection-over-union (mIoU). We follow the standard practice in unsupervised semantic segmentation where the validation images are resized and cropped to have $320 \\times 320$ pixels (see [16, 39]). In particular, the background class in the Pascal Context is excluded from evaluation. We apply a softmax operation to the outputs of $\\psi$ to obtain clustering assignments. We then use majority voting to match the resulting clusters to semantic segments. We apply CRF [26] for post-processing (although it is empirically shown that its contribution to performance gain is marginal).", + "bbox": [ + 503, + 546, + 890, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Comparison with Leading Methods", + "text_level": 1, + "bbox": [ + 503, + 739, + 805, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first compare the proposed method to leading unsupervised semantic segmentation methods. We consider two representative competitors from the literature: MaskCLIP [48] and ReCo [39], which empirical outperform a variety of baselines such as IIC [21], PiCIE [7], and STEGO [16]. In particular, MaskCLIP uses the ViT-B backbone trained by CLIP [35], whereas ReCo uses the ViT-L/14@336px, also trained by CLIP. We also try to include the self-training variants of MaskCLIP and ReCo in com", + "bbox": [ + 503, + 763, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "555", + "bbox": [ + 486, + 946, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7237db2fbe2952a076537f9cb9052709567900f702923e997bac5a26d48ec12f.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Comparisons on unsupervised semantic segmentation performance on Pascal Context [31]. The results of MaskCLIP and ReCo are from the original papers." + ], + "table_body": "
MethodAcc. (%)mIoU (%)
MaskCLIP [48]-25.5
MaskCLIP+ [48]-31.1
ReCo [39]51.627.2
K-means
ViT-S61.928.9
ViT-B58.730.9
ViT-L45.319.3
Ours
ViT-S70.438.8
ViT-B69.737.5
ViT-L63.233.2
Ours*
ViT-S74.639.6
ViT-B73.237.6
ViT-L71.935.0
", + "bbox": [ + 94, + 88, + 446, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "parison. Besides, we introduce two other baselines: (i) fit a K-means with the features of pre-trained models for training data (using the same number of clustering centers as our method) and use it to predict clustering assignments for validation data; (ii) likewise, fit a K-means with the features preceding the linear head in $\\psi$ . The two ways are referred to as \"K-means\" and \"Ours*\" in our studies. We have not compared with DSM [30] because the involved divide-and-conquer procedure for synchronizing the clustering results across different images is non-trivial to implement. In theory, DSM can lead to a similar segmentation performance to our method (yet with more resource consumption).", + "bbox": [ + 75, + 414, + 467, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We report the results in Table 1 and Table 2. As shown, our methods outperform MaskCLIP, ReCo, and K-means with significant margins, which reflects the efficacy of the learned neural eigenfunctions for unsupervised semantic segmentation. \"Ours*\" even outperforms \"Ours\", which is probably attributed to the fact that the features preceding the linear head in $\\psi$ have a much higher dimension than the final outputs and thus are more informative. While MaskCLIP+ and ReCo+ employ an extra time-consuming self-training step, they are still inferior to our methods. It is reasonable to speculate that combining our methods with self-training can further improve performance. Note also that K-means can serve as a strong baseline for unsupervised semantic segmentation. This finding appears to contradict the results reported in DSM [30] (Table 4). We deduce the reason that DSM sets the number of clusters to the number of true classes rather than a larger quantity and performs K-means directly on the validation set instead of the training set. Besides, as the size of the pre-trained model increases, both K-means and our methods yield worse unsupervised", + "bbox": [ + 75, + 598, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/883070b1260625eb334d995b0b5ae9aca4211ac25878d47da39b8d71b469d4c9.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Comparisons on unsupervised semantic segmentation performance on Cityscapes [9]. The results of MaskCLIP and ReCo are from the original papers." + ], + "table_body": "
MethodAcc. (%)mIoU (%)
MaskCLIP [48]35.910.0
ReCo [39]74.619.3
ReCo+ [39]83.724.2
K-means
ViT-S77.022.4
ViT-B74.823.2
ViT-L66.320.9
Ours
ViT-S83.428.2
ViT-B81.426.8
ViT-L80.326.3
Ours*
ViT-S84.630.0
ViT-B84.230.7
ViT-L84.230.0
", + "bbox": [ + 522, + 88, + 864, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "segmentation performance. We attribute this to larger pretrained models producing more abstract outputs that contain more overall semantics than specialized details. In contrast, smaller pre-trained models may fall short in expressiveness. Therefore, we suggest using a pre-trained model with appropriate capacity when applying the proposed method to new applications.", + "bbox": [ + 496, + 410, + 890, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative results. Figure 2 shows some qualitative results of the proposed methods on Pascal Context. We also include the K-means baseline in comparison. Most notably, unlike MaskContrast [41], our method can detect multiple semantic categories in the same image, and the generated object boundaries are sharp. Furthermore, our spectral clustering-based approach can greatly reduce the chaotic fragments produced by K-means. We defer the visualization for the learned neural eigenfunctions and the segmentation results on Cityscapes to Appendix.", + "bbox": [ + 496, + 517, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluation in More Scenarios", + "text_level": 1, + "bbox": [ + 500, + 679, + 764, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this subsection, we evaluate the proposed method in more scenarios to study its behavior systematically.", + "bbox": [ + 500, + 703, + 890, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "First, we consider the evaluation protocol popularly used in the supervised setting. Specifically, following the setup [40], we leverage a sliding window with the same resolution as training images to cope with the varying sizes of evaluation images. The background class in the Pascal Context is included for evaluation, and the results on Cityscapes cover only 19 categories. Due to implementation challenges, we have not included existing methods in comparison, but we introduce a supervised semantic segmentation baseline, DeepLabv3+ [5], which can serve as an upper bound on performance.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "556", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4917961193051f51891ba1767d570d323dd87787bda4e725182deffc64c20279.jpg", + "image_caption": [ + "Figure 2. Visualization of the unsupervised semantic segmentation results on Pascal Context [31]." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 467, + 339 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3db3a35ce5346c3ed46579e366388a73ea94b531e91cd1e1821ef7549d93b9a3.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Comparisons on semantic segmentation performance using the widely adopted evaluation protocol [40]. In particular, the background class in the Pascal Context is included for evaluation, and the results on Cityscapes cover 19 categories. The pre-trained models with ViT-S architecture are used. Supervised results for the two datasets rely on DeepLabv3+ [5] using ResNet-101 [17] and Xception-65 [8] backbones, respectively." + ], + "table_body": "
MethodAcc. (%)mIoU (%)
Pascal Context
Supervised-48.5
K-means56.331.9
Ours67.441.4
Ours*68.941.3
Cityscapes
Supervised-77.3
K-means75.534.2
Ours86.146.7
Ours*88.352.8
", + "bbox": [ + 99, + 393, + 444, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 3, in this new evaluation setting, our methods can clearly outperform K-means, and \"Ours*\" is slightly better than \"Ours\" in general. These results are consistent with those reported in Section 4.2 and help to verify the extensibility of the proposed method. We also notice that the performance gap between the proposed unsupervised segmentation method and the supervised baseline is not significant, especially on the Pascal Context dataset, which motivates further investigation on the direction of improving spectral clustering.", + "bbox": [ + 75, + 703, + 467, + 852 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "After that, we assess our method on ADE20K, one of the most challenging semantic segmentation datasets that contain 150 fine-grained semantic categories. To tackle a", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/12b0d448b028113c22ade3e5135e33ee4cb642c08ca80669ee467c0484ad30c8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAcc. (%)mIoU (%)
K-means50.719.2
Ours63.321.6
Ours*62.523.6
", + "bbox": [ + 545, + 88, + 844, + 164 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Comparisons on unsupervised semantic segmentation performance on ADE20K using the evaluation protocol of [40]. The pre-trained model with ViT-S architecture is used.", + "bbox": [ + 498, + 167, + 890, + 210 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/07380379c40c8c1c5eac91b75d6e8129bae0794128fb5c2d7aa2c418a8af7e77.jpg", + "image_caption": [ + "Figure 3. Visualization of the unsupervised semantic segmentation results of our method on ADE20K. In each pair, the left refers to the input image, and the right refers to the segmentation result. As shown, our method can yield reasonable pixel groups for images containing complex structures." + ], + "image_footnote": [], + "bbox": [ + 503, + 223, + 694, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/992761b3544dc6732bcf2913af565ca45427406f9ac15ed02f7afd5685f19911.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 223, + 888, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "large number of ground-truth semantic classes, we set $K$ to 512 with $\\beta$ as 0.04. The training lasts for 20 epochs, given that the training set is relatively large. We use the evaluation protocol of [40]. We include the K-means baseline based on our own implementation for a fair comparison.", + "bbox": [ + 496, + 445, + 890, + 521 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results are displayed in Table 4. As shown, our methods are still superior to the K-means baseline, especially regarding pixel accuracy. The best mIoU is $23.6\\%$ , much lower than the corresponding results on Pascal Context and Cityscapes. This probably stems from the large number of semantic categories in ADE20K—the used pretrained models are not trained with fine-grained objectives (e.g., losses defined on patches), so they cannot ensure the semantic richness of the extracted dense features, which makes our method tend to generate clusters that conjoin multiple fine-grained semantic categories (see the lamp and the streetlight in Figure 3). One potential solution to this problem is fine-tuning the pre-trained models with patchwise self-supervised learning loss and then invoking the proposed spectral clustering pipeline.", + "bbox": [ + 496, + 521, + 892, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 756, + 663, + 770 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we present a comprehensive study of several key hyper-parameters in our method. We evaluate using the same setting as in Section 4.2. We consider the ViT-S architecture for per-trained models given its superior performance testified in previous results.", + "bbox": [ + 496, + 779, + 890, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The output dimension $K$ . $K$ determines the number of eigenfunctions to learn and hence the dimension of the spectral embedding. It also implicitly connects to the number of", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "557", + "bbox": [ + 485, + 944, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1d878cd45acdbb007ca04fbd17ff78a2631de86a5178fdbec65f79e572ce2fd4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
K64128256512
Acc. (%)67.171.670.471.1
mIoU (%)27.833.238.837.9
", + "bbox": [ + 114, + 88, + 429, + 148 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/156a544f6b7f2100ba6cdba75aa43924e1ab814a2ed5c0db64ebc195a64de477.jpg", + "table_caption": [ + "Table 5. Performance comparison of different $K$ based on a pretrained ViT-S model on Pascal Context validation set." + ], + "table_footnote": [], + "table_body": "
α00.10.30.50.7
Pascal Context38.637.938.838.938.0
Cityscapes27.226.728.228.127.9
", + "bbox": [ + 89, + 191, + 450, + 253 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "semantic classes uncovered automatically during training. In previous experiments, we keep $K$ larger than the number of ground-truth semantic classes. Here we perform an ablation study on $K$ on Pascal Context to reflect the necessity of doing so. The results are summarized in Table 5, which indicates that a value of $K$ of at least 256 is necessary to achieve superior performance in terms of mIoU scores. A larger $K$ yields more expressive representations that capture subtleties yet at the cost of increased computational overhead. Moreover, it should be noted that the NeuralEF technique may fail to uncover the eigenfunctions with small eigenvalues [12]. Therefore, we suggest selecting a moderate value of $K$ in practice.", + "bbox": [ + 75, + 311, + 467, + 507 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The trade-off parameter $\\alpha$ . The proposed spectral clustering workflow is compatible with any kernel function that captures plausible relationships between image patches. Currently, the used kernel is a weighted sum of the normalized adjacency defined on features from pre-trained models and that defined on down-sampled pixels. To verify the robustness of our method to the trade-off parameter $\\alpha$ , we perform an ablation study on it and report the results in Table 6. We include results for both Pascal Context and Cityscapes for a thorough investigation. As shown, the mIoU on the validation data does not vary significantly w.r.t. $\\alpha$ , and limiting $\\alpha$ to [0.3, 0.5] can lead to superior results. Note that when $\\alpha = 0$ , i.e., we only use the features from pre-trained models to construct the graph kernel, the mIoU drops slightly, indicating that the features from pre-trained models can retain most information on the neighborhood relationship of raw pixels. This also presents an opportunity for enhancing performance by improving the graph defined on down-sampled image pixels.", + "bbox": [ + 75, + 507, + 467, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The trade-off parameter $\\beta$ . The trade-off parameter $\\beta$ in Equation (5) for learning neural eigenfunctions affects the empirical convergence. To investigate whether our method is sensitive to the choice of $\\beta$ , in Table 7 we ablate the influence of $\\beta$ in both \"Ours\" and \"Ours*\" approaches on the Pascal Context data. We observe that the validation mIoU remains stable across $\\beta$ ranging from 0.04 to 0.16, which", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2dbabcbb478cd1d08e0c7a84edcd86d7a8927ae562d9f9c3ac8c0c3374d878f1.jpg", + "table_caption": [ + "Table 6. Mean IoU (\\%) comparison of different trade-off coefficients $\\alpha$ based on a pre-trained ViT-S model." + ], + "table_footnote": [], + "table_body": "
β0.040.080.16
Ours38.838.839.0
Ours*39.039.639.3
", + "bbox": [ + 589, + 88, + 799, + 148 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f715f292d7d34b0b251bcc246af22e6a6711c6a4bf8dd3739f43cd93a7310a78.jpg", + "table_caption": [ + "Table 7. Mean IoU (\\%) comparison of different $\\beta$ based on a pretrained ViT-S model on Pascal Context validation set." + ], + "table_footnote": [], + "table_body": "
Acc. (%)mIoU (%)
Pascal Context55.815.2
Cityscapes81.218.5
", + "bbox": [ + 526, + 191, + 861, + 253 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Zero-shot transfer results of our method. The training is performed on ImageNet based on the pre-trained ViT-S model.", + "bbox": [ + 500, + 256, + 890, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "confirms the robustness of our method against $\\beta$ . With this, we set $\\beta$ to 0.08 in all experiments.", + "bbox": [ + 498, + 311, + 888, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Zero-shot transfer. Due to its unsupervised clustering nature, our method does not necessarily rely on target images for training. In this spirit, we perform an initial study where the training is conducted on ImageNet, but the evaluation is conducted on both Pascal Context and Cityscapes. This forms a zero-shot transfer paradigm for unsupervised semantic segmentation. The training lasts for 5 epochs under the same setting in previous studies. We report the results in Table 8. As a reference, the corresponding mIoU of MaskCLIP and ReCo on Cityscapes are 10.0 and 19.3 respectively [39], thus our method provides competitive performance. Nonetheless, the mIoUs for all the methods are much worse than those in previous studies. This is probably because images from ImageNet mostly contain clear foregrounds and single objects, which is in sharp contrast to the complex scene images in Pascal Context and Cityscapes, thus the learned neural eigenfunctions struggle to generalize. A potential remedy for this problem is training on more realistic datasets to reduce the transfer gap.", + "bbox": [ + 496, + 340, + 890, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Majority voting vs. Hungarian matching. By having the same number of clusters as the ground truth classes and utilizing Hungarian matching, we can maintain a relatively low cluster count and probably enable the assignment of clusters to semantic classes by an expert in practice. We conduct a study on Pascal Context, where the number of clusters is set to match the semantic categories. The resulting mIoU of Hungarian matching is 0.235, slightly lower than the mIoU obtained with majority voting in the same setting (0.277). One possible explanation is that the semantic categories in the benchmarks are often structured, such as a car consisting of the body and the wheels. As a result, the automatically discovered clusters may not correspond one-to-one with the semantic categories. This observation also highlights the need for a larger number of clusters to address this issue effectively.", + "bbox": [ + 496, + 628, + 890, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The pre-training method. When using ViT backbones pretrained on ImageNet classification, we observe that stronger", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "558", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/05ef3ab29fbfece50b9b13921dc1cbe07b93488857a7410c9bacdbf9f1ead187.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ViT-BViT-LViT-L/14@336px
37.238.744.0
", + "bbox": [ + 83, + 88, + 460, + 132 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 9. Mean IoU (\\%) of our method on Pascal Context when using various backbones pre-trained by CLIP.", + "bbox": [ + 76, + 133, + 468, + 165 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "pre-trained models yield worse segmentation performance. We have realized backbones pre-trained by CLIP may exhibit a different tendency because the model outputs are coerced to conform with text supervision rather than being discriminative in recognizing foreground objects. We empirically study this in Table 9. As shown, the backbone pre-trained by CLIP exhibits an increasing trend on mIoU as the model expressiveness increases.", + "bbox": [ + 75, + 188, + 470, + 309 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 321, + 194, + 338 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work establishes an end-to-end NN-based pipeline for spectral clustering for unsupervised semantic segmentation. To achieve that, we build a connectivity graph over image patches using information from both pre-trained models and raw pixels and employ neural eigenfunctions to produce spectral embeddings corresponding to suitable graph kernels. We further quantize the output of the neural eigenfunctions to obtain clustering assignments without resorting to an explicit grouping step. After training, our method can generalize to novel test data easily and reliably. The reliance on pre-trained models gives our method good training efficiency and sufficient expressiveness. Extensive results confirm its superior performance over competing baselines.", + "bbox": [ + 75, + 348, + 468, + 545 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "One limitation is that, like most clustering-based methods, our method needs to be exposed to ground-truth semantic masks to match clustering assignments to semantic segments. Introducing text prompts to guide clustering is a potential solution and deserves future investigation.", + "bbox": [ + 75, + 545, + 470, + 621 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 76, + 633, + 236, + 651 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We thank Bernhard Schölkopf for providing constructive suggestions and proofreading the paper. This work was supported by Natural Science Foundation of Shanghai (No. 23ZR1428700).", + "bbox": [ + 75, + 659, + 468, + 720 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 76, + 734, + 174, + 750 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. Labels4free: Unsupervised segmentation using stylegan. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 13970-13979, 2021.", + "[2] Relja Arandjelović and Andrew Zisserman. Object discovery with a copy-pasting gan. arXiv preprint arXiv:1905.11369, 2019.", + "[3] Yoshua Bengio, Pascal Vincent, Jean-François Paiement, O Delalleau, M Ouimet, and N LeRoux. 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In European Conference on Computer Vision (ECCV), 2022." + ], + "bbox": [ + 78, + 90, + 468, + 219 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "561", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/4dcc0481-9970-4a10-9577-a5671c84635b_model.json b/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/4dcc0481-9970-4a10-9577-a5671c84635b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..269415cc10b2f5023b1de1ebf217153d3deff72d --- /dev/null +++ b/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/4dcc0481-9970-4a10-9577-a5671c84635b_model.json @@ -0,0 +1,2169 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.112, + 0.131, + 0.859, + 0.154 + ], + "angle": 0, + "content": "Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.182, + 0.335, + 0.199 + ], + "angle": 0, + "content": "Zhijie Deng" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.201, + 0.408, + 0.234 + ], + "angle": 0, + "content": "Shanghai Jiao Tong University Shanghai, China" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.238, + 0.371, + 0.251 + ], + "angle": 0, + "content": "zhijied@sjtu.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.587, + 0.183, + 0.676, + 0.198 + ], + "angle": 0, + "content": "Yucen Luo" + }, + { + "type": "text", + "bbox": [ + 0.458, + 0.201, + 0.806, + 0.234 + ], + "angle": 0, + "content": "Max Planck Institute for Intelligent Systems Tübingen, Germany" + }, + { + "type": "text", + "bbox": [ + 0.538, + 0.238, + 0.726, + 0.251 + ], + "angle": 0, + "content": "luoyucencen@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.313, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.473, + 0.681 + ], + "angle": 0, + "content": "Unsupervised semantic segmentation is a long-standing challenge in computer vision with great significance. Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct distinct clusters. Despite recent progress in enhancing spectral clustering with powerful pre-trained models, current approaches still suffer from inefficiencies in spectral decomposition and inflexibility in applying them to the test data. This work addresses these issues by casting spectral clustering as a parametric approach that employs neural network-based eigenfunctions to produce spectral embeddings. The outputs of the neural eigenfunctions are further restricted to discrete vectors that indicate clustering assignments directly. As a result, an end-to-end NN-based paradigm of spectral clustering emerges. In practice, the neural eigenfunctions are lightweight and take the features from pre-trained models as inputs, improving training efficiency and unleashing the potential of pre-trained models for dense prediction. We conduct extensive empirical studies to validate the effectiveness of our approach and observe significant performance gains over competitive baselines on Pascal Context, Cityscapes, and ADE20K benchmarks. The code is available at https://github.com/thudzj/NeuralEigenfunctionSegmentor." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.208, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Semantic segmentation is essential in understanding the inherent structure and fine-grained information of images. However, current approaches often hinge on a vast amount of manual annotations to train neural networks (NNs) effectively in an end-to-end manner [5, 40]. This is problematic, as obtaining these annotations can be both time-consuming and costly, particularly in fields such as autonomous driving and medical image processing, where annotations are usually collected from domain experts. Thus, finding a way to perform semantic segmentation without manual annotation remains a crucial unresolved problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.895, + 0.516 + ], + "angle": 0, + "content": "Unsupervised semantic segmentation has recently attracted a great deal of attention. A number of methods attempt to tackle it by learning fine-grained image features using self-supervised objectives and then applying clustering or grouping techniques [46, 41]. They tend to recognize single objects or single semantic categories and struggle with complex images. Other approaches have tried to use vision-language cross-modal models (e.g., CLIP [35]) to achieve zero-shot semantic segmentation [48, 39], but they heavily rely on carefully-tuned text prompts and self-training. Compared to the recent approaches, the classic spectral clustering [38], which has stood the test of time, remains an appealing option. In particular, it enjoys solid foundations in spectral graph theory—it finds the minimum cut of the connectivity graph over pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.895, + 0.746 + ], + "angle": 0, + "content": "However, traditional spectral clustering exhibits limitations in three aspects: (i) it operates on raw image pixels, thus is sensitive to color transformations and unable to recognize semantic similarities; (ii) it is computationally inefficient due to the involved spectral decomposition; (iii) unlike NN-based methods, it is nontrivial and costly to extend to non-training samples because of its transductive manner. Thus it cannot be performed end-to-end in the test phase. Recent work reveals that pre-trained models such as ViTs [14] can mitigate the first limitation, significantly improving the applicability and effectiveness of spectral clustering [30]. Its core contribution is to build the connectivity graph over image patches based on an affinity matrix computed with the dense features from pre-trained models. Still, the limitations regarding efficiency and flexibility remain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "The present paper aims to overcome the remaining limitations, rendering spectral clustering a simple yet effective baseline for unsupervised semantic segmentation. To tackle the inefficiency issue, we propose to cast the involved spectral decomposition problem as an NN-based optimization one using the recently developed neural eigenfunction (NeuralEF) technique [12]. Concretely, we first measure the similarities between image patches using both the features extracted from pre-trained models and raw pixels. Treating the similarity matrix (or its variants) as the output of a" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "551" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.272 + ], + "angle": 0, + "content": "kernel function, we then optimize NNs to approximate its principal eigenfunctions. Consequently, our method constitutes an NN-based counterpart of spectral embedding. We eliminate the need for an additional grouping step, which is required in prior work [30], by constraining the NN output to one-hot vectors that indicate clustering assignments directly. To accomplish this, we use the Gumbel-Softmax estimator [20] for gradient-based optimization during training. These strategies transform spectral clustering from a non-parametric approach to a parametric one, enabling easy and reliable out-of-sample generalization and avoiding solving complex matrix eigenvalue problems during testing." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.274, + 0.468, + 0.439 + ], + "angle": 0, + "content": "We perform extensive studies to evaluate the effectiveness of our approach for unsupervised semantic segmentation. We first experiment on the popularly used benchmarks Pascal Context [31] and Cityscapes [9] based on pre-trained ViTs, and report superior results compared to leading methods MaskCLIP [48] and ReCo [39]. We further consider the sliding-window-based evaluation protocol [40] and experiment on the challenging ADE20K dataset [47] to systematically study the behavior of our method. In addition, we conduct thorough ablation studies to gain insights into the specification of several core hyper-parameters." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.453, + 0.216, + 0.469 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.478, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Unsupervised segmentation. Image segmentation has numerous practical applications in various industries and scientific fields. In order to alleviate the burden of collecting annotations, prior works have comprehensively studied the problem of learning image segmenters in semi- and weakly-supervised settings [24, 18, 4, 23]. Recently, there have been increasing efforts to tackle unsupervised segmentation based on the progress in related fields like deep generative models (DGMs) and self-supervised learning (SSL). On the one hand, DGM-based segmentation approaches train specialized image generators to separate foreground from background [6, 2, 1] or extract saliency masks directly from pre-trained generators [42]. Yet, it is technically nontrivial to extend them to cope with semantic segmentation. On the other hand, SSL-based methods define objectives to perform clustering [19, 7], mutual information maximization [21, 33], contrastive learning [41] or feature correspondence distillation [16] to learn image features suitable for grouping. However, most of these methods only recognize single objects or single semantic categories and struggle with complex images. With the increasing accessibility of pre-trained image-text cross-modal models, considerable efforts have been devoted to performing zero-shot semantic segmentation with them [48, 39]. Nevertheless, the entanglement with cross-modal models places high demands on the quality of the text prompts, which correspond to the semantic categories of concern, and hinders the methods from choosing backbone models freely." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.286 + ], + "angle": 0, + "content": "Spectral clustering. As a classic solution to image segmentation, spectral clustering [38, 32] frames the original problem as a graph partitioning one defined on the connectivity graph over image pixels. Typically, spectral clustering exploits the eigenvectors of graph Laplacians to construct minimum-energy graph partitions [13, 15]. Spectral clustering is closely related to Kernel PCA [37] as they are both learning eigenfunctions [3]. Recently, spectral clustering has been combined with pre-trained models to enjoy rich semantic information [30]. Yet, it remains unsolved that spectral decomposition is expensive for big data, and the non-parametric nature hinders out-of-sample generalization. This paper aims to address these issues." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.288, + 0.89, + 0.589 + ], + "angle": 0, + "content": "The deep learning variant of spectral methods. Refurbishing spectral methods with deep learning techniques is beneficial to improve the scalability and flexibility of the former. The spectral inference networks (SpIN) [34] is a seminal work in this direction. Yet, the learning objective of SpIN is ill-defined, which leads to only the subspace spanned by the principal eigenfunctions instead of the eigenfunctions themselves. SpIN hence introduces convoluted and expensive strategies to solve this problem. The recent NeuralEF technique [12] alternatively defines a new series of objective functions to break the symmetry among eigenfunctions explicitly. NeuralEF is further enhanced by weight sharing and extended to handle indefinite kernels in [11], constituting a more amenable choice for learning spectral embeddings given pre-defined kernels. We also note that there are several attempts to develop deep spectral clustering methods based on supervisions [28] or a dual autoencoder network [45], but they cannot be trivially applied to the task of unsupervised semantic segmentation due to the absence of annotations or other inefficiency issues." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.603, + 0.632, + 0.62 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.628, + 0.89, + 0.673 + ], + "angle": 0, + "content": "We begin with a brief review of the relevant background and then build up our approach step by step. We provide an overview of the proposed method in Figure 1." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.682, + 0.629, + 0.697 + ], + "angle": 0, + "content": "3.1. Background" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.705, + 0.89, + 0.855 + ], + "angle": 0, + "content": "Semantic segmentation essentially targets determining the semantic consistency among image pixels. In the absence of annotations, the problem boils down to an unsupervised clustering one. Spectral clustering [38, 32] is a longstanding solution to it with solid theoretical foundations. It proceeds by partitioning a connectivity graph over image pixels. The resulting algorithm typically involves eigendecomposing the graph Laplacian matrix and stacking its eigenvectors, which are then used in a Euclidean clustering algorithm to obtain a fixed number of partitions." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.857, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Traditional spectral clustering operates on raw image pixels, making it sensitive to color transformations and unable to identify semantic similarities. To address this, a" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.947, + 0.51, + 0.957 + ], + "angle": 0, + "content": "552" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.895, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.301, + 0.893, + 0.343 + ], + "angle": 0, + "content": "Figure 1. Method overview. We establish an end-to-end NN-based pipeline for spectral clustering to perform unsupervised semantic segmentation. The box highlights modules that exist only during training. The nearest neighbor graph over pixels only has edges between pixels from the same images, while the other one is built over dense features from various images. The pre-trained model is fixed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.47, + 0.581 + ], + "angle": 0, + "content": "natural idea is to include the inductive bias of NNs. In this spirit, the deep spectral method (DSM) [30] leverages powerful pre-trained models to translate the learning from raw pixels to patch-wise features that embed rich local semantics and are widely applicable. Specifically, let \\( \\pmb{x}_i \\in \\mathbb{R}^{H \\times W \\times 3} \\) denote an image and \\( f: \\mathbb{R}^{H \\times W \\times 3} \\to \\mathbb{R}^{H / P \\times W / P \\times C} \\) denote the pre-trained model with \\( P \\) as a down-sampling factor. DSM constructs a semantic affinity matrix using both the patch-wise features \\( \\pmb{f}_{i,j,k} = f(\\pmb{x}_i)_{j,k} \\in \\mathbb{R}^C \\) and image pixels, and performs spectral clustering on the corresponding connectivity graph. Subsequently, DSM performs bi-linear interpolation to convert patch-wise segments to pixel-wise ones. This simple workflow has surpassed various competitors regarding unsupervised semantic segmentation performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Denote by \\(N\\) the size of the dataset of concern. Semantic segmentation requires classifying pixels in different images yet with the same semantics into the same category. Thereby, it needs to ensure semantic consistency across the dataset. Therefore, DSM should, in principle, work on an affinity matrix of size \\(\\mathbb{R}^{NHW / P^2\\times NHW / P^2}\\), but this is computationally infeasible as the involved spectral decomposition has a cubic complexity w.r.t. \\(NHW / P^2\\). DSM alternatively conducts spectral clustering separately for each image and then performs cross-image synchronization, but this is inflexible compared to NN-based pipelines and arguably suboptimal. Additionally, existing spectral clustering methods, including DSM, are non-parametric, relying on costly spectral decomposition when faced with new test data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In order to address the limitations discussed above, we leverage a parametric approach to spectral decomposition based on the recent NeuralEF technique [12] and learn discrete neural eigenfunctions directly. These innovations help to scale our method to large datasets, enable the straightforward and cheap out-of-sample extension for test data, and establish an NN-based spectral clustering workflow." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.356, + 0.82, + 0.372 + ], + "angle": 0, + "content": "3.2. From Eigenvectors to Eigenfunctions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Spectral clustering involves the spectral decomposition of a matrix and hence is seemingly incompatible with the parametric NN models. To bridge this gap, we move our viewpoint from the eigenvectors to eigenfunctions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.515 + ], + "angle": 0, + "content": "Specifically, abstracting the graph Laplacian matrix as the evaluation of some kernel function \\(\\kappa\\) on the dense features, the eigenfunctions of \\(\\kappa\\) form a function-space generalization of the aforementioned eigenvectors. Formally, the eigenfunction \\(\\psi\\) of a kernel \\(\\kappa(\\pmb{x},\\pmb{x}^{\\prime})\\) satisfies that" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.526, + 0.892, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\int \\kappa (\\boldsymbol {x}, \\boldsymbol {x} ^ {\\prime}) \\psi (\\boldsymbol {x} ^ {\\prime}) p (\\boldsymbol {x} ^ {\\prime}) d \\boldsymbol {x} ^ {\\prime} = \\mu \\psi (\\boldsymbol {x}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.891, + 0.612 + ], + "angle": 0, + "content": "where \\(\\mu\\) is the corresponding eigenvalue and \\(p\\) a probability measure. By definition, the eigenfunction should be normalized, and different eigenfunctions are orthogonal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.793 + ], + "angle": 0, + "content": "As shown, the eigenfunction takes input from the original space and maps it to the eigenspace specified by the kernel, where the local neighborhoods on data manifolds are preserved. Naturally, we can incorporate NNs as function approximators to the eigenfunctions. In this way, we bypass the need for expensive spectral decomposition of a matrix and can easily perform out-of-sample extension thanks to the generalization ability of NNs. Fortunately, the recently proposed NeuralEF [12] offers tools to realize this. We also note that the effectiveness of the spectral embedding yielded by neural eigenfunctions has been empirically validated in self-supervised learning [11]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.757, + 0.818 + ], + "angle": 0, + "content": "3.3. Setting up the Graph Kernel" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To set up the kernel for spectral clustering, as suggested by DSM [30], we construct two graphs with patch-wise features from pre-trained models and down-sampled image pixels, respectively. We then define the kernel with the weighted sum of the corresponding normalized graph adja" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "553" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "ency matrices. By doing so, the high-level semantics and low-level details are conjoined." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.121, + 0.468, + 0.23 + ], + "angle": 0, + "content": "Denote by \\(\\mathbf{F} = \\{\\pmb {f}_i\\}_{i = 1}^N\\in \\mathbb{R}^{NHW / P^2\\times C}\\) the collection of patch-wise features over the dataset. Considering that the feature space shaped by large-scale pre-training is highly structured where simple distance measures suffice to represent similarities, we leverage cosine similarity to specify a nearest neighbor graph over image patches. The corresponding affinity matrix is detailed below:" + }, + { + "type": "equation", + "bbox": [ + 0.079, + 0.24, + 0.468, + 0.292 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {u, v} = \\left\\{ \\begin{array}{l l} \\mathbf {F} _ {u} \\mathbf {F} _ {v} ^ {\\top} / (\\| \\mathbf {F} _ {u} \\| \\| \\mathbf {F} _ {v} \\|), & v \\in k - \\mathrm {N N} (u, \\mathbf {F}, \\text {c o s i n e}) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.468, + 0.428 + ], + "angle": 0, + "content": "where \\( k \\)-NN(\\( u, \\mathbf{F}, \\cos \\mathrm{i} \\)) denotes the set of the \\( k \\) nearest neighbors of \\( \\mathbf{F}_u \\) over \\( \\mathbf{F} \\) under cosine similarity. The above graph deploys edges between patches that are semantically close. The corresponding graph partitioning can result in meaningful segmentation at a coarse resolution. Although other traditional graphs can also be used, the nearest neighbor graph enjoys sparsity, which reduces storage and computation costs and has been studied extensively in manifold learning and spectral clustering." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.468, + 0.551 + ], + "angle": 0, + "content": "To supplement the high-level features with low-level details, we bilinearly down-sample the original image \\(\\pmb{x}_i\\) to \\(\\tilde{\\pmb{x}}_i\\in \\mathbb{R}^{H / P\\times W / P\\times 3}\\) to keep resolution consistency, and fuse the spatial information \\((j,k)\\) and color information \\(\\tilde{\\pmb{x}}_{i,j,k}\\) as a single vector. We stack the collection over the dataset as \\(\\tilde{\\mathbf{X}}\\in \\mathbb{R}^{NHW / P^2\\times 5}\\). A nearest neighbor graph over down-sampled pixels is then defined based on \\(L^2\\) distance following DSM [30]. The affinity matrix is:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.561, + 0.468, + 0.602 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {A}} _ {u, v} = \\left\\{ \\begin{array}{l l} 1, & v \\in \\tilde {k} - \\mathrm {N N} (u, \\tilde {\\mathbf {X}}, L ^ {2}) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.468, + 0.704 + ], + "angle": 0, + "content": "where \\(\\tilde{k}\\)-NN\\((u, \\tilde{\\mathbf{X}}, L^2)\\) denotes the set of \\(\\tilde{k}\\) nearest neighbors of \\(\\tilde{\\mathbf{X}}_u\\) over \\(\\tilde{\\mathbf{X}}\\) under \\(L^2\\) distance (dissimilarity). We place a further constraint that the nearest neighbors should belong to the same image as the query to avoid establishing meaningless connections. It is expected that such a graph helps to detect sharp object boundaries." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We symmetrize \\(\\mathbf{A}\\) and \\(\\tilde{\\mathbf{A}}\\) so that they can serve as graph adjacency matrices. Considering that the normalized graph cuts are more practically useful [38], we would better build a kernel with the normalized graph Laplacian matrices of \\(\\mathbf{A}\\) and \\(\\tilde{\\mathbf{A}}\\), and learn the eigenfunctions associated with the smallest \\(K\\) eigenvalues. However, the NeuralEF approach instead deploys neural approximations to the principal eigenfunctions, which correspond to the largest eigenvalues, of a kernel [12]. To this end, we move our focus from the normalized Laplacian matrix to the normalized adjacency matrix whose \\(K\\) principal eigenfunctions exactly correspond to the eigenfunctions associated with the \\(K\\) smallest eigenvalues of the former. Specifically, let" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.137 + ], + "angle": 0, + "content": "\\(\\mathbf{D} \\coloneqq \\operatorname{diag}(\\mathbf{A}\\mathbf{1}), \\tilde{\\mathbf{D}} \\coloneqq \\operatorname{diag}(\\tilde{\\mathbf{A}}\\mathbf{1})\\) denote the degree matrices. We then define the kernel function \\(\\kappa\\) using the weighted sum of the normalized adjacency matrices, detailed below:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.146, + 0.892, + 0.163 + ], + "angle": 0, + "content": "\\[\n\\kappa : \\kappa (\\mathbf {F}, \\mathbf {F}) = \\mathbf {D} ^ {- 1 / 2} \\mathbf {A} \\mathbf {D} ^ {- 1 / 2} + \\alpha \\tilde {\\mathbf {D}} ^ {- 1 / 2} \\tilde {\\mathbf {A}} \\tilde {\\mathbf {D}} ^ {- 1 / 2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.174, + 0.892, + 0.295 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is a trade-off parameter. Here we define the kernel in the space of features extracted from pre-trained models while other choices are also viable: it only affects the input of neural eigenfunctions. In the current setting, the features from pre-trained models are directly fed into neural eigenfunctions, which is sensible thanks to the great potential of pre-trained models and can prevent unnecessary training costs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.305, + 0.783, + 0.32 + ], + "angle": 0, + "content": "3.4. Learning Neural Eigenfunctions" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.327, + 0.892, + 0.407 + ], + "angle": 0, + "content": "Let \\(\\mathbf{f} \\in \\mathbb{R}^C\\) denote a row vector of \\(\\mathbf{F}\\) and \\(p(\\mathbf{f})\\) a uniform distribution over \\(\\{\\mathbf{F}_i\\}_{i=1}^{NHW/P^2}\\). The NeuralEF technique [12] approximates the \\(K\\) principal eigenfunctions of the kernel \\(\\kappa\\) w.r.t. \\(p(\\mathbf{f})\\) with a \\(K\\)-output neural function \\(\\psi: \\mathbb{R}^C \\to \\mathbb{R}^K\\) by solving the following problem:" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.415, + 0.891, + 0.465 + ], + "angle": 0, + "content": "\\[\n\\max _ {\\psi} \\sum_ {j = 1} ^ {K} \\mathbf {R} _ {j, j} - \\beta \\sum_ {j = 1} ^ {K} \\sum_ {i = 1} ^ {j - 1} \\widehat {\\mathbf {R}} _ {i, j} ^ {2}, s. t. \\mathbb {E} _ {p (\\mathbf {f})} [ \\psi (\\mathbf {f}) \\circ \\psi (\\mathbf {f}) ] = \\mathbf {1}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.466, + 0.89, + 0.493 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a positive coefficient and \\(\\circ\\) is Hadamard product, and" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.492, + 0.891, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {R} := \\mathbb {E} _ {p (\\mathbf {f})} \\mathbb {E} _ {p \\left(\\mathbf {f} ^ {\\prime}\\right)} \\left[ \\kappa \\left(\\mathbf {f}, \\mathbf {f} ^ {\\prime}\\right) \\psi (\\mathbf {f}) \\psi \\left(\\mathbf {f} ^ {\\prime}\\right) ^ {\\top} \\right] \\\\ \\widehat {\\quad} \\end{array} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.513, + 0.816, + 0.53 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathbf {R}} := \\mathbb {E} _ {p (\\mathbf {f})} \\mathbb {E} _ {p \\left(\\mathbf {f} ^ {\\prime}\\right)} \\left[ \\kappa (\\mathbf {f}, \\mathbf {f} ^ {\\prime}) \\hat {\\psi} (\\mathbf {f}) \\psi \\left(\\mathbf {f} ^ {\\prime}\\right) ^ {\\top} \\right].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.535, + 0.788, + 0.55 + ], + "angle": 0, + "content": "Here \\(\\hat{\\psi}\\) is the non-optimizable variant of \\(\\psi\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.551, + 0.89, + 0.581 + ], + "angle": 0, + "content": "Adapting such results to our case and applying Monte Carlo estimation to the expectation yields" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.588, + 0.891, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R} \\approx \\frac {1}{B ^ {2}} \\boldsymbol {\\Psi} \\cdot \\kappa (\\mathbf {F} ^ {B}, \\mathbf {F} ^ {B}) \\cdot \\boldsymbol {\\Psi} ^ {\\top} \\text {a n d} \\widehat {\\mathbf {R}} \\approx \\frac {1}{B ^ {2}} \\widehat {\\boldsymbol {\\Psi}} \\cdot \\kappa (\\mathbf {F} ^ {B}, \\mathbf {F} ^ {B}) \\cdot \\boldsymbol {\\Psi} ^ {\\top}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.748 + ], + "angle": 0, + "content": "where \\(\\mathbf{F}^B\\coloneqq [\\mathbf{f}_1,\\dots ,\\mathbf{f}_B]^\\top \\in \\mathbb{R}^{B\\times C}\\) is a mini-batch of features, \\(\\Psi \\coloneqq [\\psi (\\mathbf{f}_1),\\ldots ,\\psi (\\mathbf{f}_B)]\\in \\mathbb{R}^{K\\times B}\\) is the collection of the corresponding NN outputs, and \\(\\widehat{\\Psi}\\coloneqq\\) stop-gradient(Ψ). The stop-gradient operation can be easily found in auto-diff libraries and plays a vital role in establishing the asymmetry between the \\(K\\) principal eigenfunctions. We put an \\(L^2\\) -batch normalization layer [12] at the end of model \\(\\psi\\) to enforce the constraint in Equation (5)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.839 + ], + "angle": 0, + "content": "\\(\\psi\\) can be implemented as a neural network composed of convolutions or transformer blocks, which takes dense image features \\(\\pmb{f} = f(\\pmb{x}) \\in \\mathbb{R}^{H / P \\times W / P \\times C}\\) as input and outputs \\(\\psi(\\pmb{f}) \\in \\mathbb{R}^{H / P \\times W / P \\times K}\\). After training, it can be used to predict new test data without relying on expensive test-time spectral decomposition." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.799, + 0.864 + ], + "angle": 0, + "content": "3.5. Quantizing Neural Eigenfunctions" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "After obtaining the spectral embedding \\(\\psi(f(x))\\) for image patches, we should, by convention, invoke a Euclidean" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "554" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.197 + ], + "angle": 0, + "content": "clustering algorithm such as K-means [29] to get clustering assignments. In practice, datasets can often be large, so it would be better to leverage online clustering mechanisms to avoid unaffordable storage costs. However, this approach may still be time-consuming when aiming for good convergence. Additionally, this pipeline is not as flexible as NN-based segmenters." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.199, + 0.468, + 0.408 + ], + "angle": 0, + "content": "To bridge the gap, we impose a constraint on the output of \\(\\psi\\) to be \\(K\\)-dim one-hot vectors which directly indicate clustering assignments. We resort to the Gumbel-Softmax estimator [20] for gradient-based optimization. This follows the notion that the outputs of eigenfunctions are soft clustering assignments, and we further perform quantization of them. This is also in a similar spirit to the spectral hashing approach [43] where the output of \\(\\psi\\) is assumed to be vectors over \\(\\{-1,1\\}^K\\). We clarify that the Gumbel-Softmax estimator precedes the aforementioned \\(L^2\\) batch normalization layer. In the test phase, we remove this estimator and the \\(L^2\\) batch normalization layer, using the NN outputs directly as softmax logits for clustering. This results in a pure NN-based workflow for spectral clustering." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.417, + 0.373, + 0.433 + ], + "angle": 0, + "content": "3.6. From Clusters to Image Segments" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.44, + 0.468, + 0.62 + ], + "angle": 0, + "content": "During inference, we up-sample the softmax logits bilinearly to match the original resolution of input images. We then apply the argmax operation to obtain discrete clustering assignments. A natural question that arises is how to match these clustering assignments to pre-defined semantics to obtain the final image segments. Two well-studied solutions are Hungarian matching [27] and majority voting. As per DSM [30], when evaluated on standard image semantic segmentation benchmarks, we first collect the clustering assignments for all validation images and then match them to ground-truth labels via these approaches to conduct a quantitative evaluation of segmentation performance." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.633, + 0.208, + 0.65 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.659, + 0.468, + 0.703 + ], + "angle": 0, + "content": "To evaluate the efficacy of the proposed method for unsupervised semantic segmentation, we conduct comprehensive experiments on various standard benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.712, + 0.273, + 0.728 + ], + "angle": 0, + "content": "4.1. Experimental Setups" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.735, + 0.468, + 0.795 + ], + "angle": 0, + "content": "Datasets. We primarily experiment on Pascal Context and Cityscapes, which consist of 60 and 27 classes, respectively. We employ the same data pre-processing and augmentation strategies as the work [40] on the training dataset." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.796, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Pre-trained models. We use pre-trained ViTs [14] provided by the timm library [44] and consider the \"Small\", \"Base\", and \"Large\" variants. The weights have been pre-trained on ImageNet-21k [36] and fine-tuned on ImageNet [10] in a supervised manner. In particular, we consider pre-trained models at a high resolution, like \\(384 \\times 384\\), to obtain fine-grained segments. We fix the patch size to" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.092, + 0.891, + 0.181 + ], + "angle": 0, + "content": "\\(16 \\times 16\\) (i.e., \\(P = 16\\)) to better trade-off efficiency and accuracy. We use the output of the last attention block of ViTs as \\(f_{i}\\) without elaborate selection. We also feed the intermediate features of the pre-trained ViTs, which can be freely accessed, to the neural eigenfunctions to enrich the input information." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.184, + 0.891, + 0.544 + ], + "angle": 0, + "content": "Modeling and training. We set \\( k = 256 \\) for the nearest neighbor graph defined on pre-trained models' features. To reduce the cost of searching for the nearest neighbors, we confine the search to the current mini-batch, which is shown to be empirically effective. We specify the other graph following DSM [30]. The trade-off coefficient \\( \\alpha \\) equals 0.3 based on an ablation study reported in Section 4.4. The training objective is detailed in Equation (5) and unfolded in Equation (7). As \\( K \\) implies the number of semantic classes uncovered automatically, we make it larger than the number of ground-truth semantic classes and, in practice, set it to 256. We set the trade-off coefficient \\( \\beta \\) to 0.08 and linearly scale it for other values of \\( K \\) (see the study in Section 4.4). We use 2 transformer blocks with linear self-attention [22] and a linear head to specify the neural eigenfunctions \\( \\psi \\) for efficiency. We restrict the weight matrix of the linear head to have orthogonal columns and find it beneficial to the final performance empirically. We anneal the temperature for Gumbel-Softmax from 1 to 0.3 following a cosine schedule during training. The training relies on an Adam optimizer [25] and a learning rate of \\( 10^{-3} \\) (with cosine decay). No weight decay is employed. The training lasts for 40 epochs with batch size 16 (or 8 if an out-of-memory error occurs), which takes half a day on one RTX 3090 GPU." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.547, + 0.891, + 0.728 + ], + "angle": 0, + "content": "Evaluation. We test on the validation set of the datasets and report both pixel accuracy (Acc.) and mean intersection-over-union (mIoU). We follow the standard practice in unsupervised semantic segmentation where the validation images are resized and cropped to have \\(320 \\times 320\\) pixels (see [16, 39]). In particular, the background class in the Pascal Context is excluded from evaluation. We apply a softmax operation to the outputs of \\(\\psi\\) to obtain clustering assignments. We then use majority voting to match the resulting clusters to semantic segments. We apply CRF [26] for post-processing (although it is empirically shown that its contribution to performance gain is marginal)." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.741, + 0.807, + 0.757 + ], + "angle": 0, + "content": "4.2. Comparison with Leading Methods" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.765, + 0.891, + 0.9 + ], + "angle": 0, + "content": "We first compare the proposed method to leading unsupervised semantic segmentation methods. We consider two representative competitors from the literature: MaskCLIP [48] and ReCo [39], which empirical outperform a variety of baselines such as IIC [21], PiCIE [7], and STEGO [16]. In particular, MaskCLIP uses the ViT-B backbone trained by CLIP [35], whereas ReCo uses the ViT-L/14@336px, also trained by CLIP. We also try to include the self-training variants of MaskCLIP and ReCo in com" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.947, + 0.51, + 0.957 + ], + "angle": 0, + "content": "555" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.096, + 0.089, + 0.447, + 0.346 + ], + "angle": 0, + "content": "
MethodAcc. (%)mIoU (%)
MaskCLIP [48]-25.5
MaskCLIP+ [48]-31.1
ReCo [39]51.627.2
K-means
ViT-S61.928.9
ViT-B58.730.9
ViT-L45.319.3
Ours
ViT-S70.438.8
ViT-B69.737.5
ViT-L63.233.2
Ours*
ViT-S74.639.6
ViT-B73.237.6
ViT-L71.935.0
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.35, + 0.47, + 0.392 + ], + "angle": 0, + "content": "Table 1. Comparisons on unsupervised semantic segmentation performance on Pascal Context [31]. The results of MaskCLIP and ReCo are from the original papers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.468, + 0.596 + ], + "angle": 0, + "content": "parison. Besides, we introduce two other baselines: (i) fit a K-means with the features of pre-trained models for training data (using the same number of clustering centers as our method) and use it to predict clustering assignments for validation data; (ii) likewise, fit a K-means with the features preceding the linear head in \\(\\psi\\). The two ways are referred to as \"K-means\" and \"Ours*\" in our studies. We have not compared with DSM [30] because the involved divide-and-conquer procedure for synchronizing the clustering results across different images is non-trivial to implement. In theory, DSM can lead to a similar segmentation performance to our method (yet with more resource consumption)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We report the results in Table 1 and Table 2. As shown, our methods outperform MaskCLIP, ReCo, and K-means with significant margins, which reflects the efficacy of the learned neural eigenfunctions for unsupervised semantic segmentation. \"Ours*\" even outperforms \"Ours\", which is probably attributed to the fact that the features preceding the linear head in \\( \\psi \\) have a much higher dimension than the final outputs and thus are more informative. While MaskCLIP+ and ReCo+ employ an extra time-consuming self-training step, they are still inferior to our methods. It is reasonable to speculate that combining our methods with self-training can further improve performance. Note also that K-means can serve as a strong baseline for unsupervised semantic segmentation. This finding appears to contradict the results reported in DSM [30] (Table 4). We deduce the reason that DSM sets the number of clusters to the number of true classes rather than a larger quantity and performs K-means directly on the validation set instead of the training set. Besides, as the size of the pre-trained model increases, both K-means and our methods yield worse unsupervised" + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.089, + 0.865, + 0.346 + ], + "angle": 0, + "content": "
MethodAcc. (%)mIoU (%)
MaskCLIP [48]35.910.0
ReCo [39]74.619.3
ReCo+ [39]83.724.2
K-means
ViT-S77.022.4
ViT-B74.823.2
ViT-L66.320.9
Ours
ViT-S83.428.2
ViT-B81.426.8
ViT-L80.326.3
Ours*
ViT-S84.630.0
ViT-B84.230.7
ViT-L84.230.0
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.5, + 0.35, + 0.892, + 0.392 + ], + "angle": 0, + "content": "Table 2. Comparisons on unsupervised semantic segmentation performance on Cityscapes [9]. The results of MaskCLIP and ReCo are from the original papers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.892, + 0.517 + ], + "angle": 0, + "content": "segmentation performance. We attribute this to larger pretrained models producing more abstract outputs that contain more overall semantics than specialized details. In contrast, smaller pre-trained models may fall short in expressiveness. Therefore, we suggest using a pre-trained model with appropriate capacity when applying the proposed method to new applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Qualitative results. Figure 2 shows some qualitative results of the proposed methods on Pascal Context. We also include the K-means baseline in comparison. Most notably, unlike MaskContrast [41], our method can detect multiple semantic categories in the same image, and the generated object boundaries are sharp. Furthermore, our spectral clustering-based approach can greatly reduce the chaotic fragments produced by K-means. We defer the visualization for the learned neural eigenfunctions and the segmentation results on Cityscapes to Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.765, + 0.695 + ], + "angle": 0, + "content": "4.3. Evaluation in More Scenarios" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.704, + 0.892, + 0.734 + ], + "angle": 0, + "content": "In this subsection, we evaluate the proposed method in more scenarios to study its behavior systematically." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "First, we consider the evaluation protocol popularly used in the supervised setting. Specifically, following the setup [40], we leverage a sliding window with the same resolution as training images to cope with the varying sizes of evaluation images. The background class in the Pascal Context is included for evaluation, and the results on Cityscapes cover only 19 categories. Due to implementation challenges, we have not included existing methods in comparison, but we introduce a supervised semantic segmentation baseline, DeepLabv3+ [5], which can serve as an upper bound on performance." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "556" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.468, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.354, + 0.47, + 0.384 + ], + "angle": 0, + "content": "Figure 2. Visualization of the unsupervised semantic segmentation results on Pascal Context [31]." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.394, + 0.445, + 0.582 + ], + "angle": 0, + "content": "
MethodAcc. (%)mIoU (%)
Pascal Context
Supervised-48.5
K-means56.331.9
Ours67.441.4
Ours*68.941.3
Cityscapes
Supervised-77.3
K-means75.534.2
Ours86.146.7
Ours*88.352.8
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.684 + ], + "angle": 0, + "content": "Table 3. Comparisons on semantic segmentation performance using the widely adopted evaluation protocol [40]. In particular, the background class in the Pascal Context is included for evaluation, and the results on Cityscapes cover 19 categories. The pre-trained models with ViT-S architecture are used. Supervised results for the two datasets rely on DeepLabv3+ [5] using ResNet-101 [17] and Xception-65 [8] backbones, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.468, + 0.853 + ], + "angle": 0, + "content": "As shown in Table 3, in this new evaluation setting, our methods can clearly outperform K-means, and \"Ours*\" is slightly better than \"Ours\" in general. These results are consistent with those reported in Section 4.2 and help to verify the extensibility of the proposed method. We also notice that the performance gap between the proposed unsupervised segmentation method and the supervised baseline is not significant, especially on the Pascal Context dataset, which motivates further investigation on the direction of improving spectral clustering." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "After that, we assess our method on ADE20K, one of the most challenging semantic segmentation datasets that contain 150 fine-grained semantic categories. To tackle a" + }, + { + "type": "table", + "bbox": [ + 0.546, + 0.089, + 0.845, + 0.165 + ], + "angle": 0, + "content": "
MethodAcc. (%)mIoU (%)
K-means50.719.2
Ours63.321.6
Ours*62.523.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.169, + 0.892, + 0.211 + ], + "angle": 0, + "content": "Table 4. Comparisons on unsupervised semantic segmentation performance on ADE20K using the evaluation protocol of [40]. The pre-trained model with ViT-S architecture is used." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.224, + 0.696, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.224, + 0.889, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.352, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Figure 3. Visualization of the unsupervised semantic segmentation results of our method on ADE20K. In each pair, the left refers to the input image, and the right refers to the segmentation result. As shown, our method can yield reasonable pixel groups for images containing complex structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.522 + ], + "angle": 0, + "content": "large number of ground-truth semantic classes, we set \\( K \\) to 512 with \\( \\beta \\) as 0.04. The training lasts for 20 epochs, given that the training set is relatively large. We use the evaluation protocol of [40]. We include the K-means baseline based on our own implementation for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.893, + 0.749 + ], + "angle": 0, + "content": "The results are displayed in Table 4. As shown, our methods are still superior to the K-means baseline, especially regarding pixel accuracy. The best mIoU is \\(23.6\\%\\), much lower than the corresponding results on Pascal Context and Cityscapes. This probably stems from the large number of semantic categories in ADE20K—the used pretrained models are not trained with fine-grained objectives (e.g., losses defined on patches), so they cannot ensure the semantic richness of the extracted dense features, which makes our method tend to generate clusters that conjoin multiple fine-grained semantic categories (see the lamp and the streetlight in Figure 3). One potential solution to this problem is fine-tuning the pre-trained models with patchwise self-supervised learning loss and then invoking the proposed spectral clustering pipeline." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.665, + 0.771 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.856 + ], + "angle": 0, + "content": "In this subsection, we present a comprehensive study of several key hyper-parameters in our method. We evaluate using the same setting as in Section 4.2. We consider the ViT-S architecture for per-trained models given its superior performance testified in previous results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The output dimension \\( K \\). \\( K \\) determines the number of eigenfunctions to learn and hence the dimension of the spectral embedding. It also implicitly connects to the number of" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.945, + 0.511, + 0.956 + ], + "angle": 0, + "content": "557" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.115, + 0.089, + 0.43, + 0.15 + ], + "angle": 0, + "content": "
K64128256512
Acc. (%)67.171.670.471.1
mIoU (%)27.833.238.837.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.154, + 0.468, + 0.181 + ], + "angle": 0, + "content": "Table 5. Performance comparison of different \\( K \\) based on a pretrained ViT-S model on Pascal Context validation set." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.192, + 0.452, + 0.254 + ], + "angle": 0, + "content": "
α00.10.30.50.7
Pascal Context38.637.938.838.938.0
Cityscapes27.226.728.228.127.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.257, + 0.468, + 0.285 + ], + "angle": 0, + "content": "Table 6. Mean IoU (\\%) comparison of different trade-off coefficients \\(\\alpha\\) based on a pre-trained ViT-S model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.468, + 0.508 + ], + "angle": 0, + "content": "semantic classes uncovered automatically during training. In previous experiments, we keep \\( K \\) larger than the number of ground-truth semantic classes. Here we perform an ablation study on \\( K \\) on Pascal Context to reflect the necessity of doing so. The results are summarized in Table 5, which indicates that a value of \\( K \\) of at least 256 is necessary to achieve superior performance in terms of mIoU scores. A larger \\( K \\) yields more expressive representations that capture subtleties yet at the cost of increased computational overhead. Moreover, it should be noted that the NeuralEF technique may fail to uncover the eigenfunctions with small eigenvalues [12]. Therefore, we suggest selecting a moderate value of \\( K \\) in practice." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.468, + 0.795 + ], + "angle": 0, + "content": "The trade-off parameter \\(\\alpha\\). The proposed spectral clustering workflow is compatible with any kernel function that captures plausible relationships between image patches. Currently, the used kernel is a weighted sum of the normalized adjacency defined on features from pre-trained models and that defined on down-sampled pixels. To verify the robustness of our method to the trade-off parameter \\(\\alpha\\), we perform an ablation study on it and report the results in Table 6. We include results for both Pascal Context and Cityscapes for a thorough investigation. As shown, the mIoU on the validation data does not vary significantly w.r.t. \\(\\alpha\\), and limiting \\(\\alpha\\) to [0.3, 0.5] can lead to superior results. Note that when \\(\\alpha = 0\\), i.e., we only use the features from pre-trained models to construct the graph kernel, the mIoU drops slightly, indicating that the features from pre-trained models can retain most information on the neighborhood relationship of raw pixels. This also presents an opportunity for enhancing performance by improving the graph defined on down-sampled image pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The trade-off parameter \\(\\beta\\). The trade-off parameter \\(\\beta\\) in Equation (5) for learning neural eigenfunctions affects the empirical convergence. To investigate whether our method is sensitive to the choice of \\(\\beta\\), in Table 7 we ablate the influence of \\(\\beta\\) in both \"Ours\" and \"Ours*\" approaches on the Pascal Context data. We observe that the validation mIoU remains stable across \\(\\beta\\) ranging from 0.04 to 0.16, which" + }, + { + "type": "table", + "bbox": [ + 0.591, + 0.089, + 0.8, + 0.15 + ], + "angle": 0, + "content": "
β0.040.080.16
Ours38.838.839.0
Ours*39.039.639.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.154, + 0.892, + 0.181 + ], + "angle": 0, + "content": "Table 7. Mean IoU (\\%) comparison of different \\(\\beta\\) based on a pretrained ViT-S model on Pascal Context validation set." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.192, + 0.862, + 0.254 + ], + "angle": 0, + "content": "
Acc. (%)mIoU (%)
Pascal Context55.815.2
Cityscapes81.218.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.257, + 0.892, + 0.285 + ], + "angle": 0, + "content": "Table 8. Zero-shot transfer results of our method. The training is performed on ImageNet based on the pre-trained ViT-S model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.312, + 0.89, + 0.341 + ], + "angle": 0, + "content": "confirms the robustness of our method against \\(\\beta\\). With this, we set \\(\\beta\\) to 0.08 in all experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Zero-shot transfer. Due to its unsupervised clustering nature, our method does not necessarily rely on target images for training. In this spirit, we perform an initial study where the training is conducted on ImageNet, but the evaluation is conducted on both Pascal Context and Cityscapes. This forms a zero-shot transfer paradigm for unsupervised semantic segmentation. The training lasts for 5 epochs under the same setting in previous studies. We report the results in Table 8. As a reference, the corresponding mIoU of MaskCLIP and ReCo on Cityscapes are 10.0 and 19.3 respectively [39], thus our method provides competitive performance. Nonetheless, the mIoUs for all the methods are much worse than those in previous studies. This is probably because images from ImageNet mostly contain clear foregrounds and single objects, which is in sharp contrast to the complex scene images in Pascal Context and Cityscapes, thus the learned neural eigenfunctions struggle to generalize. A potential remedy for this problem is training on more realistic datasets to reduce the transfer gap." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Majority voting vs. Hungarian matching. By having the same number of clusters as the ground truth classes and utilizing Hungarian matching, we can maintain a relatively low cluster count and probably enable the assignment of clusters to semantic classes by an expert in practice. We conduct a study on Pascal Context, where the number of clusters is set to match the semantic categories. The resulting mIoU of Hungarian matching is 0.235, slightly lower than the mIoU obtained with majority voting in the same setting (0.277). One possible explanation is that the semantic categories in the benchmarks are often structured, such as a car consisting of the body and the wheels. As a result, the automatically discovered clusters may not correspond one-to-one with the semantic categories. This observation also highlights the need for a larger number of clusters to address this issue effectively." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The pre-training method. When using ViT backbones pretrained on ImageNet classification, we observe that stronger" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "558" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.461, + 0.133 + ], + "angle": 0, + "content": "
ViT-BViT-LViT-L/14@336px
37.238.744.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.135, + 0.47, + 0.166 + ], + "angle": 0, + "content": "Table 9. Mean IoU (\\%) of our method on Pascal Context when using various backbones pre-trained by CLIP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.189, + 0.471, + 0.31 + ], + "angle": 0, + "content": "pre-trained models yield worse segmentation performance. We have realized backbones pre-trained by CLIP may exhibit a different tendency because the model outputs are coerced to conform with text supervision rather than being discriminative in recognizing foreground objects. We empirically study this in Table 9. As shown, the backbone pre-trained by CLIP exhibits an increasing trend on mIoU as the model expressiveness increases." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.323, + 0.196, + 0.339 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.546 + ], + "angle": 0, + "content": "This work establishes an end-to-end NN-based pipeline for spectral clustering for unsupervised semantic segmentation. To achieve that, we build a connectivity graph over image patches using information from both pre-trained models and raw pixels and employ neural eigenfunctions to produce spectral embeddings corresponding to suitable graph kernels. We further quantize the output of the neural eigenfunctions to obtain clustering assignments without resorting to an explicit grouping step. After training, our method can generalize to novel test data easily and reliably. The reliance on pre-trained models gives our method good training efficiency and sufficient expressiveness. Extensive results confirm its superior performance over competing baselines." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.471, + 0.622 + ], + "angle": 0, + "content": "One limitation is that, like most clustering-based methods, our method needs to be exposed to ground-truth semantic masks to match clustering assignments to semantic segments. Introducing text prompts to guide clustering is a potential solution and deserves future investigation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.635, + 0.238, + 0.652 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.721 + ], + "angle": 0, + "content": "We thank Bernhard Schölkopf for providing constructive suggestions and proofreading the paper. 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Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct distinct clusters. Despite recent progress in enhancing spectral clustering with powerful pre-trained models, current approaches still suffer from inefficiencies in spectral decomposition and inflexibility in applying them to the test data. This work addresses these issues by casting spectral clustering as a parametric approach that employs neural network-based eigenfunctions to produce spectral embeddings. The outputs of the neural eigenfunctions are further restricted to discrete vectors that indicate clustering assignments directly. As a result, an end-to-end NN-based paradigm of spectral clustering emerges. In practice, the neural eigenfunctions are lightweight and take the features from pre-trained models as inputs, improving training efficiency and unleashing the potential of pre-trained models for dense prediction. We conduct extensive empirical studies to validate the effectiveness of our approach and observe significant performance gains over competitive baselines on Pascal Context, Cityscapes, and ADE20K benchmarks. The code is available at https://github.com/thudzj/NeuralEigenfunctionSegmentor. + +# 1. Introduction + +Semantic segmentation is essential in understanding the inherent structure and fine-grained information of images. However, current approaches often hinge on a vast amount of manual annotations to train neural networks (NNs) effectively in an end-to-end manner [5, 40]. This is problematic, as obtaining these annotations can be both time-consuming and costly, particularly in fields such as autonomous driving and medical image processing, where annotations are usually collected from domain experts. Thus, finding a way to perform semantic segmentation without manual annotation remains a crucial unresolved problem. + +Unsupervised semantic segmentation has recently attracted a great deal of attention. A number of methods attempt to tackle it by learning fine-grained image features using self-supervised objectives and then applying clustering or grouping techniques [46, 41]. They tend to recognize single objects or single semantic categories and struggle with complex images. Other approaches have tried to use vision-language cross-modal models (e.g., CLIP [35]) to achieve zero-shot semantic segmentation [48, 39], but they heavily rely on carefully-tuned text prompts and self-training. Compared to the recent approaches, the classic spectral clustering [38], which has stood the test of time, remains an appealing option. In particular, it enjoys solid foundations in spectral graph theory—it finds the minimum cut of the connectivity graph over pixels. + +However, traditional spectral clustering exhibits limitations in three aspects: (i) it operates on raw image pixels, thus is sensitive to color transformations and unable to recognize semantic similarities; (ii) it is computationally inefficient due to the involved spectral decomposition; (iii) unlike NN-based methods, it is nontrivial and costly to extend to non-training samples because of its transductive manner. Thus it cannot be performed end-to-end in the test phase. Recent work reveals that pre-trained models such as ViTs [14] can mitigate the first limitation, significantly improving the applicability and effectiveness of spectral clustering [30]. Its core contribution is to build the connectivity graph over image patches based on an affinity matrix computed with the dense features from pre-trained models. Still, the limitations regarding efficiency and flexibility remain. + +The present paper aims to overcome the remaining limitations, rendering spectral clustering a simple yet effective baseline for unsupervised semantic segmentation. To tackle the inefficiency issue, we propose to cast the involved spectral decomposition problem as an NN-based optimization one using the recently developed neural eigenfunction (NeuralEF) technique [12]. Concretely, we first measure the similarities between image patches using both the features extracted from pre-trained models and raw pixels. Treating the similarity matrix (or its variants) as the output of a + +kernel function, we then optimize NNs to approximate its principal eigenfunctions. Consequently, our method constitutes an NN-based counterpart of spectral embedding. We eliminate the need for an additional grouping step, which is required in prior work [30], by constraining the NN output to one-hot vectors that indicate clustering assignments directly. To accomplish this, we use the Gumbel-Softmax estimator [20] for gradient-based optimization during training. These strategies transform spectral clustering from a non-parametric approach to a parametric one, enabling easy and reliable out-of-sample generalization and avoiding solving complex matrix eigenvalue problems during testing. + +We perform extensive studies to evaluate the effectiveness of our approach for unsupervised semantic segmentation. We first experiment on the popularly used benchmarks Pascal Context [31] and Cityscapes [9] based on pre-trained ViTs, and report superior results compared to leading methods MaskCLIP [48] and ReCo [39]. We further consider the sliding-window-based evaluation protocol [40] and experiment on the challenging ADE20K dataset [47] to systematically study the behavior of our method. In addition, we conduct thorough ablation studies to gain insights into the specification of several core hyper-parameters. + +# 2. Related Work + +Unsupervised segmentation. Image segmentation has numerous practical applications in various industries and scientific fields. In order to alleviate the burden of collecting annotations, prior works have comprehensively studied the problem of learning image segmenters in semi- and weakly-supervised settings [24, 18, 4, 23]. Recently, there have been increasing efforts to tackle unsupervised segmentation based on the progress in related fields like deep generative models (DGMs) and self-supervised learning (SSL). On the one hand, DGM-based segmentation approaches train specialized image generators to separate foreground from background [6, 2, 1] or extract saliency masks directly from pre-trained generators [42]. Yet, it is technically nontrivial to extend them to cope with semantic segmentation. On the other hand, SSL-based methods define objectives to perform clustering [19, 7], mutual information maximization [21, 33], contrastive learning [41] or feature correspondence distillation [16] to learn image features suitable for grouping. However, most of these methods only recognize single objects or single semantic categories and struggle with complex images. With the increasing accessibility of pre-trained image-text cross-modal models, considerable efforts have been devoted to performing zero-shot semantic segmentation with them [48, 39]. Nevertheless, the entanglement with cross-modal models places high demands on the quality of the text prompts, which correspond to the semantic categories of concern, and hinders the methods from choosing backbone models freely. + +Spectral clustering. As a classic solution to image segmentation, spectral clustering [38, 32] frames the original problem as a graph partitioning one defined on the connectivity graph over image pixels. Typically, spectral clustering exploits the eigenvectors of graph Laplacians to construct minimum-energy graph partitions [13, 15]. Spectral clustering is closely related to Kernel PCA [37] as they are both learning eigenfunctions [3]. Recently, spectral clustering has been combined with pre-trained models to enjoy rich semantic information [30]. Yet, it remains unsolved that spectral decomposition is expensive for big data, and the non-parametric nature hinders out-of-sample generalization. This paper aims to address these issues. + +The deep learning variant of spectral methods. Refurbishing spectral methods with deep learning techniques is beneficial to improve the scalability and flexibility of the former. The spectral inference networks (SpIN) [34] is a seminal work in this direction. Yet, the learning objective of SpIN is ill-defined, which leads to only the subspace spanned by the principal eigenfunctions instead of the eigenfunctions themselves. SpIN hence introduces convoluted and expensive strategies to solve this problem. The recent NeuralEF technique [12] alternatively defines a new series of objective functions to break the symmetry among eigenfunctions explicitly. NeuralEF is further enhanced by weight sharing and extended to handle indefinite kernels in [11], constituting a more amenable choice for learning spectral embeddings given pre-defined kernels. We also note that there are several attempts to develop deep spectral clustering methods based on supervisions [28] or a dual autoencoder network [45], but they cannot be trivially applied to the task of unsupervised semantic segmentation due to the absence of annotations or other inefficiency issues. + +# 3. Methodology + +We begin with a brief review of the relevant background and then build up our approach step by step. We provide an overview of the proposed method in Figure 1. + +# 3.1. Background + +Semantic segmentation essentially targets determining the semantic consistency among image pixels. In the absence of annotations, the problem boils down to an unsupervised clustering one. Spectral clustering [38, 32] is a longstanding solution to it with solid theoretical foundations. It proceeds by partitioning a connectivity graph over image pixels. The resulting algorithm typically involves eigendecomposing the graph Laplacian matrix and stacking its eigenvectors, which are then used in a Euclidean clustering algorithm to obtain a fixed number of partitions. + +Traditional spectral clustering operates on raw image pixels, making it sensitive to color transformations and unable to identify semantic similarities. To address this, a + +![](images/d477142d47580f07bb6363d996aa8bd6e6e774453869434fd3c66b96a9e33659.jpg) +Figure 1. Method overview. We establish an end-to-end NN-based pipeline for spectral clustering to perform unsupervised semantic segmentation. The box highlights modules that exist only during training. The nearest neighbor graph over pixels only has edges between pixels from the same images, while the other one is built over dense features from various images. The pre-trained model is fixed. + +natural idea is to include the inductive bias of NNs. In this spirit, the deep spectral method (DSM) [30] leverages powerful pre-trained models to translate the learning from raw pixels to patch-wise features that embed rich local semantics and are widely applicable. Specifically, let $\pmb{x}_i \in \mathbb{R}^{H \times W \times 3}$ denote an image and $f: \mathbb{R}^{H \times W \times 3} \to \mathbb{R}^{H / P \times W / P \times C}$ denote the pre-trained model with $P$ as a down-sampling factor. DSM constructs a semantic affinity matrix using both the patch-wise features $\pmb{f}_{i,j,k} = f(\pmb{x}_i)_{j,k} \in \mathbb{R}^C$ and image pixels, and performs spectral clustering on the corresponding connectivity graph. Subsequently, DSM performs bi-linear interpolation to convert patch-wise segments to pixel-wise ones. This simple workflow has surpassed various competitors regarding unsupervised semantic segmentation performance. + +Denote by $N$ the size of the dataset of concern. Semantic segmentation requires classifying pixels in different images yet with the same semantics into the same category. Thereby, it needs to ensure semantic consistency across the dataset. Therefore, DSM should, in principle, work on an affinity matrix of size $\mathbb{R}^{NHW / P^2\times NHW / P^2}$ , but this is computationally infeasible as the involved spectral decomposition has a cubic complexity w.r.t. $NHW / P^2$ . DSM alternatively conducts spectral clustering separately for each image and then performs cross-image synchronization, but this is inflexible compared to NN-based pipelines and arguably suboptimal. Additionally, existing spectral clustering methods, including DSM, are non-parametric, relying on costly spectral decomposition when faced with new test data. + +In order to address the limitations discussed above, we leverage a parametric approach to spectral decomposition based on the recent NeuralEF technique [12] and learn discrete neural eigenfunctions directly. These innovations help to scale our method to large datasets, enable the straightforward and cheap out-of-sample extension for test data, and establish an NN-based spectral clustering workflow. + +# 3.2. From Eigenvectors to Eigenfunctions + +Spectral clustering involves the spectral decomposition of a matrix and hence is seemingly incompatible with the parametric NN models. To bridge this gap, we move our viewpoint from the eigenvectors to eigenfunctions. + +Specifically, abstracting the graph Laplacian matrix as the evaluation of some kernel function $\kappa$ on the dense features, the eigenfunctions of $\kappa$ form a function-space generalization of the aforementioned eigenvectors. Formally, the eigenfunction $\psi$ of a kernel $\kappa(\pmb{x},\pmb{x}^{\prime})$ satisfies that + +$$ +\int \kappa (\boldsymbol {x}, \boldsymbol {x} ^ {\prime}) \psi (\boldsymbol {x} ^ {\prime}) p (\boldsymbol {x} ^ {\prime}) d \boldsymbol {x} ^ {\prime} = \mu \psi (\boldsymbol {x}), \tag {1} +$$ + +where $\mu$ is the corresponding eigenvalue and $p$ a probability measure. By definition, the eigenfunction should be normalized, and different eigenfunctions are orthogonal. + +As shown, the eigenfunction takes input from the original space and maps it to the eigenspace specified by the kernel, where the local neighborhoods on data manifolds are preserved. Naturally, we can incorporate NNs as function approximators to the eigenfunctions. In this way, we bypass the need for expensive spectral decomposition of a matrix and can easily perform out-of-sample extension thanks to the generalization ability of NNs. Fortunately, the recently proposed NeuralEF [12] offers tools to realize this. We also note that the effectiveness of the spectral embedding yielded by neural eigenfunctions has been empirically validated in self-supervised learning [11]. + +# 3.3. Setting up the Graph Kernel + +To set up the kernel for spectral clustering, as suggested by DSM [30], we construct two graphs with patch-wise features from pre-trained models and down-sampled image pixels, respectively. We then define the kernel with the weighted sum of the corresponding normalized graph adja + +ency matrices. By doing so, the high-level semantics and low-level details are conjoined. + +Denote by $\mathbf{F} = \{\pmb {f}_i\}_{i = 1}^N\in \mathbb{R}^{NHW / P^2\times C}$ the collection of patch-wise features over the dataset. Considering that the feature space shaped by large-scale pre-training is highly structured where simple distance measures suffice to represent similarities, we leverage cosine similarity to specify a nearest neighbor graph over image patches. The corresponding affinity matrix is detailed below: + +$$ +\mathbf {A} _ {u, v} = \left\{ \begin{array}{l l} \mathbf {F} _ {u} \mathbf {F} _ {v} ^ {\top} / (\| \mathbf {F} _ {u} \| \| \mathbf {F} _ {v} \|), & v \in k - \mathrm {N N} (u, \mathbf {F}, \text {c o s i n e}) \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {2} +$$ + +where $k$ -NN( $u, \mathbf{F}, \cos \mathrm{i}$ ) denotes the set of the $k$ nearest neighbors of $\mathbf{F}_u$ over $\mathbf{F}$ under cosine similarity. The above graph deploys edges between patches that are semantically close. The corresponding graph partitioning can result in meaningful segmentation at a coarse resolution. Although other traditional graphs can also be used, the nearest neighbor graph enjoys sparsity, which reduces storage and computation costs and has been studied extensively in manifold learning and spectral clustering. + +To supplement the high-level features with low-level details, we bilinearly down-sample the original image $\pmb{x}_i$ to $\tilde{\pmb{x}}_i\in \mathbb{R}^{H / P\times W / P\times 3}$ to keep resolution consistency, and fuse the spatial information $(j,k)$ and color information $\tilde{\pmb{x}}_{i,j,k}$ as a single vector. We stack the collection over the dataset as $\tilde{\mathbf{X}}\in \mathbb{R}^{NHW / P^2\times 5}$ . A nearest neighbor graph over down-sampled pixels is then defined based on $L^2$ distance following DSM [30]. The affinity matrix is: + +$$ +\tilde {\mathbf {A}} _ {u, v} = \left\{ \begin{array}{l l} 1, & v \in \tilde {k} - \mathrm {N N} (u, \tilde {\mathbf {X}}, L ^ {2}) \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +where $\tilde{k}$ -NN $(u, \tilde{\mathbf{X}}, L^2)$ denotes the set of $\tilde{k}$ nearest neighbors of $\tilde{\mathbf{X}}_u$ over $\tilde{\mathbf{X}}$ under $L^2$ distance (dissimilarity). We place a further constraint that the nearest neighbors should belong to the same image as the query to avoid establishing meaningless connections. It is expected that such a graph helps to detect sharp object boundaries. + +We symmetrize $\mathbf{A}$ and $\tilde{\mathbf{A}}$ so that they can serve as graph adjacency matrices. Considering that the normalized graph cuts are more practically useful [38], we would better build a kernel with the normalized graph Laplacian matrices of $\mathbf{A}$ and $\tilde{\mathbf{A}}$ , and learn the eigenfunctions associated with the smallest $K$ eigenvalues. However, the NeuralEF approach instead deploys neural approximations to the principal eigenfunctions, which correspond to the largest eigenvalues, of a kernel [12]. To this end, we move our focus from the normalized Laplacian matrix to the normalized adjacency matrix whose $K$ principal eigenfunctions exactly correspond to the eigenfunctions associated with the $K$ smallest eigenvalues of the former. Specifically, let + +$\mathbf{D} \coloneqq \operatorname{diag}(\mathbf{A}\mathbf{1}), \tilde{\mathbf{D}} \coloneqq \operatorname{diag}(\tilde{\mathbf{A}}\mathbf{1})$ denote the degree matrices. We then define the kernel function $\kappa$ using the weighted sum of the normalized adjacency matrices, detailed below: + +$$ +\kappa : \kappa (\mathbf {F}, \mathbf {F}) = \mathbf {D} ^ {- 1 / 2} \mathbf {A} \mathbf {D} ^ {- 1 / 2} + \alpha \tilde {\mathbf {D}} ^ {- 1 / 2} \tilde {\mathbf {A}} \tilde {\mathbf {D}} ^ {- 1 / 2}, \tag {4} +$$ + +where $\alpha$ is a trade-off parameter. Here we define the kernel in the space of features extracted from pre-trained models while other choices are also viable: it only affects the input of neural eigenfunctions. In the current setting, the features from pre-trained models are directly fed into neural eigenfunctions, which is sensible thanks to the great potential of pre-trained models and can prevent unnecessary training costs. + +# 3.4. Learning Neural Eigenfunctions + +Let $\mathbf{f} \in \mathbb{R}^C$ denote a row vector of $\mathbf{F}$ and $p(\mathbf{f})$ a uniform distribution over $\{\mathbf{F}_i\}_{i=1}^{NHW/P^2}$ . The NeuralEF technique [12] approximates the $K$ principal eigenfunctions of the kernel $\kappa$ w.r.t. $p(\mathbf{f})$ with a $K$ -output neural function $\psi: \mathbb{R}^C \to \mathbb{R}^K$ by solving the following problem: + +$$ +\max _ {\psi} \sum_ {j = 1} ^ {K} \mathbf {R} _ {j, j} - \beta \sum_ {j = 1} ^ {K} \sum_ {i = 1} ^ {j - 1} \widehat {\mathbf {R}} _ {i, j} ^ {2}, s. t. \mathbb {E} _ {p (\mathbf {f})} [ \psi (\mathbf {f}) \circ \psi (\mathbf {f}) ] = \mathbf {1}, \tag {5} +$$ + +where $\beta$ is a positive coefficient and $\circ$ is Hadamard product, and + +$$ +\begin{array}{l} \mathbf {R} := \mathbb {E} _ {p (\mathbf {f})} \mathbb {E} _ {p \left(\mathbf {f} ^ {\prime}\right)} \left[ \kappa \left(\mathbf {f}, \mathbf {f} ^ {\prime}\right) \psi (\mathbf {f}) \psi \left(\mathbf {f} ^ {\prime}\right) ^ {\top} \right] \\ \widehat {\quad} \end{array} \tag {6} +$$ + +$$ +\widehat {\mathbf {R}} := \mathbb {E} _ {p (\mathbf {f})} \mathbb {E} _ {p \left(\mathbf {f} ^ {\prime}\right)} \left[ \kappa (\mathbf {f}, \mathbf {f} ^ {\prime}) \hat {\psi} (\mathbf {f}) \psi \left(\mathbf {f} ^ {\prime}\right) ^ {\top} \right]. +$$ + +Here $\hat{\psi}$ is the non-optimizable variant of $\psi$ . + +Adapting such results to our case and applying Monte Carlo estimation to the expectation yields + +$$ +\mathbf {R} \approx \frac {1}{B ^ {2}} \boldsymbol {\Psi} \cdot \kappa (\mathbf {F} ^ {B}, \mathbf {F} ^ {B}) \cdot \boldsymbol {\Psi} ^ {\top} \text {a n d} \widehat {\mathbf {R}} \approx \frac {1}{B ^ {2}} \widehat {\boldsymbol {\Psi}} \cdot \kappa (\mathbf {F} ^ {B}, \mathbf {F} ^ {B}) \cdot \boldsymbol {\Psi} ^ {\top}, \tag {7} +$$ + +where $\mathbf{F}^B\coloneqq [\mathbf{f}_1,\dots ,\mathbf{f}_B]^\top \in \mathbb{R}^{B\times C}$ is a mini-batch of features, $\Psi \coloneqq [\psi (\mathbf{f}_1),\ldots ,\psi (\mathbf{f}_B)]\in \mathbb{R}^{K\times B}$ is the collection of the corresponding NN outputs, and $\widehat{\Psi}\coloneqq$ stop-gradient(Ψ). The stop-gradient operation can be easily found in auto-diff libraries and plays a vital role in establishing the asymmetry between the $K$ principal eigenfunctions. We put an $L^2$ -batch normalization layer [12] at the end of model $\psi$ to enforce the constraint in Equation (5). + +$\psi$ can be implemented as a neural network composed of convolutions or transformer blocks, which takes dense image features $\pmb{f} = f(\pmb{x}) \in \mathbb{R}^{H / P \times W / P \times C}$ as input and outputs $\psi(\pmb{f}) \in \mathbb{R}^{H / P \times W / P \times K}$ . After training, it can be used to predict new test data without relying on expensive test-time spectral decomposition. + +# 3.5. Quantizing Neural Eigenfunctions + +After obtaining the spectral embedding $\psi(f(x))$ for image patches, we should, by convention, invoke a Euclidean + +clustering algorithm such as K-means [29] to get clustering assignments. In practice, datasets can often be large, so it would be better to leverage online clustering mechanisms to avoid unaffordable storage costs. However, this approach may still be time-consuming when aiming for good convergence. Additionally, this pipeline is not as flexible as NN-based segmenters. + +To bridge the gap, we impose a constraint on the output of $\psi$ to be $K$ -dim one-hot vectors which directly indicate clustering assignments. We resort to the Gumbel-Softmax estimator [20] for gradient-based optimization. This follows the notion that the outputs of eigenfunctions are soft clustering assignments, and we further perform quantization of them. This is also in a similar spirit to the spectral hashing approach [43] where the output of $\psi$ is assumed to be vectors over $\{-1,1\}^K$ . We clarify that the Gumbel-Softmax estimator precedes the aforementioned $L^2$ batch normalization layer. In the test phase, we remove this estimator and the $L^2$ batch normalization layer, using the NN outputs directly as softmax logits for clustering. This results in a pure NN-based workflow for spectral clustering. + +# 3.6. From Clusters to Image Segments + +During inference, we up-sample the softmax logits bilinearly to match the original resolution of input images. We then apply the argmax operation to obtain discrete clustering assignments. A natural question that arises is how to match these clustering assignments to pre-defined semantics to obtain the final image segments. Two well-studied solutions are Hungarian matching [27] and majority voting. As per DSM [30], when evaluated on standard image semantic segmentation benchmarks, we first collect the clustering assignments for all validation images and then match them to ground-truth labels via these approaches to conduct a quantitative evaluation of segmentation performance. + +# 4. Experiments + +To evaluate the efficacy of the proposed method for unsupervised semantic segmentation, we conduct comprehensive experiments on various standard benchmarks. + +# 4.1. Experimental Setups + +Datasets. We primarily experiment on Pascal Context and Cityscapes, which consist of 60 and 27 classes, respectively. We employ the same data pre-processing and augmentation strategies as the work [40] on the training dataset. + +Pre-trained models. We use pre-trained ViTs [14] provided by the timm library [44] and consider the "Small", "Base", and "Large" variants. The weights have been pre-trained on ImageNet-21k [36] and fine-tuned on ImageNet [10] in a supervised manner. In particular, we consider pre-trained models at a high resolution, like $384 \times 384$ , to obtain fine-grained segments. We fix the patch size to + +$16 \times 16$ (i.e., $P = 16$ ) to better trade-off efficiency and accuracy. We use the output of the last attention block of ViTs as $f_{i}$ without elaborate selection. We also feed the intermediate features of the pre-trained ViTs, which can be freely accessed, to the neural eigenfunctions to enrich the input information. + +Modeling and training. We set $k = 256$ for the nearest neighbor graph defined on pre-trained models' features. To reduce the cost of searching for the nearest neighbors, we confine the search to the current mini-batch, which is shown to be empirically effective. We specify the other graph following DSM [30]. The trade-off coefficient $\alpha$ equals 0.3 based on an ablation study reported in Section 4.4. The training objective is detailed in Equation (5) and unfolded in Equation (7). As $K$ implies the number of semantic classes uncovered automatically, we make it larger than the number of ground-truth semantic classes and, in practice, set it to 256. We set the trade-off coefficient $\beta$ to 0.08 and linearly scale it for other values of $K$ (see the study in Section 4.4). We use 2 transformer blocks with linear self-attention [22] and a linear head to specify the neural eigenfunctions $\psi$ for efficiency. We restrict the weight matrix of the linear head to have orthogonal columns and find it beneficial to the final performance empirically. We anneal the temperature for Gumbel-Softmax from 1 to 0.3 following a cosine schedule during training. The training relies on an Adam optimizer [25] and a learning rate of $10^{-3}$ (with cosine decay). No weight decay is employed. The training lasts for 40 epochs with batch size 16 (or 8 if an out-of-memory error occurs), which takes half a day on one RTX 3090 GPU. + +Evaluation. We test on the validation set of the datasets and report both pixel accuracy (Acc.) and mean intersection-over-union (mIoU). We follow the standard practice in unsupervised semantic segmentation where the validation images are resized and cropped to have $320 \times 320$ pixels (see [16, 39]). In particular, the background class in the Pascal Context is excluded from evaluation. We apply a softmax operation to the outputs of $\psi$ to obtain clustering assignments. We then use majority voting to match the resulting clusters to semantic segments. We apply CRF [26] for post-processing (although it is empirically shown that its contribution to performance gain is marginal). + +# 4.2. Comparison with Leading Methods + +We first compare the proposed method to leading unsupervised semantic segmentation methods. We consider two representative competitors from the literature: MaskCLIP [48] and ReCo [39], which empirical outperform a variety of baselines such as IIC [21], PiCIE [7], and STEGO [16]. In particular, MaskCLIP uses the ViT-B backbone trained by CLIP [35], whereas ReCo uses the ViT-L/14@336px, also trained by CLIP. We also try to include the self-training variants of MaskCLIP and ReCo in com + +
MethodAcc. (%)mIoU (%)
MaskCLIP [48]-25.5
MaskCLIP+ [48]-31.1
ReCo [39]51.627.2
K-means
ViT-S61.928.9
ViT-B58.730.9
ViT-L45.319.3
Ours
ViT-S70.438.8
ViT-B69.737.5
ViT-L63.233.2
Ours*
ViT-S74.639.6
ViT-B73.237.6
ViT-L71.935.0
+ +Table 1. Comparisons on unsupervised semantic segmentation performance on Pascal Context [31]. The results of MaskCLIP and ReCo are from the original papers. + +parison. Besides, we introduce two other baselines: (i) fit a K-means with the features of pre-trained models for training data (using the same number of clustering centers as our method) and use it to predict clustering assignments for validation data; (ii) likewise, fit a K-means with the features preceding the linear head in $\psi$ . The two ways are referred to as "K-means" and "Ours*" in our studies. We have not compared with DSM [30] because the involved divide-and-conquer procedure for synchronizing the clustering results across different images is non-trivial to implement. In theory, DSM can lead to a similar segmentation performance to our method (yet with more resource consumption). + +We report the results in Table 1 and Table 2. As shown, our methods outperform MaskCLIP, ReCo, and K-means with significant margins, which reflects the efficacy of the learned neural eigenfunctions for unsupervised semantic segmentation. "Ours*" even outperforms "Ours", which is probably attributed to the fact that the features preceding the linear head in $\psi$ have a much higher dimension than the final outputs and thus are more informative. While MaskCLIP+ and ReCo+ employ an extra time-consuming self-training step, they are still inferior to our methods. It is reasonable to speculate that combining our methods with self-training can further improve performance. Note also that K-means can serve as a strong baseline for unsupervised semantic segmentation. This finding appears to contradict the results reported in DSM [30] (Table 4). We deduce the reason that DSM sets the number of clusters to the number of true classes rather than a larger quantity and performs K-means directly on the validation set instead of the training set. Besides, as the size of the pre-trained model increases, both K-means and our methods yield worse unsupervised + +
MethodAcc. (%)mIoU (%)
MaskCLIP [48]35.910.0
ReCo [39]74.619.3
ReCo+ [39]83.724.2
K-means
ViT-S77.022.4
ViT-B74.823.2
ViT-L66.320.9
Ours
ViT-S83.428.2
ViT-B81.426.8
ViT-L80.326.3
Ours*
ViT-S84.630.0
ViT-B84.230.7
ViT-L84.230.0
+ +Table 2. Comparisons on unsupervised semantic segmentation performance on Cityscapes [9]. The results of MaskCLIP and ReCo are from the original papers. + +segmentation performance. We attribute this to larger pretrained models producing more abstract outputs that contain more overall semantics than specialized details. In contrast, smaller pre-trained models may fall short in expressiveness. Therefore, we suggest using a pre-trained model with appropriate capacity when applying the proposed method to new applications. + +Qualitative results. Figure 2 shows some qualitative results of the proposed methods on Pascal Context. We also include the K-means baseline in comparison. Most notably, unlike MaskContrast [41], our method can detect multiple semantic categories in the same image, and the generated object boundaries are sharp. Furthermore, our spectral clustering-based approach can greatly reduce the chaotic fragments produced by K-means. We defer the visualization for the learned neural eigenfunctions and the segmentation results on Cityscapes to Appendix. + +# 4.3. Evaluation in More Scenarios + +In this subsection, we evaluate the proposed method in more scenarios to study its behavior systematically. + +First, we consider the evaluation protocol popularly used in the supervised setting. Specifically, following the setup [40], we leverage a sliding window with the same resolution as training images to cope with the varying sizes of evaluation images. The background class in the Pascal Context is included for evaluation, and the results on Cityscapes cover only 19 categories. Due to implementation challenges, we have not included existing methods in comparison, but we introduce a supervised semantic segmentation baseline, DeepLabv3+ [5], which can serve as an upper bound on performance. + +![](images/4917961193051f51891ba1767d570d323dd87787bda4e725182deffc64c20279.jpg) +Figure 2. Visualization of the unsupervised semantic segmentation results on Pascal Context [31]. + +
MethodAcc. (%)mIoU (%)
Pascal Context
Supervised-48.5
K-means56.331.9
Ours67.441.4
Ours*68.941.3
Cityscapes
Supervised-77.3
K-means75.534.2
Ours86.146.7
Ours*88.352.8
+ +Table 3. Comparisons on semantic segmentation performance using the widely adopted evaluation protocol [40]. In particular, the background class in the Pascal Context is included for evaluation, and the results on Cityscapes cover 19 categories. The pre-trained models with ViT-S architecture are used. Supervised results for the two datasets rely on DeepLabv3+ [5] using ResNet-101 [17] and Xception-65 [8] backbones, respectively. + +As shown in Table 3, in this new evaluation setting, our methods can clearly outperform K-means, and "Ours*" is slightly better than "Ours" in general. These results are consistent with those reported in Section 4.2 and help to verify the extensibility of the proposed method. We also notice that the performance gap between the proposed unsupervised segmentation method and the supervised baseline is not significant, especially on the Pascal Context dataset, which motivates further investigation on the direction of improving spectral clustering. + +After that, we assess our method on ADE20K, one of the most challenging semantic segmentation datasets that contain 150 fine-grained semantic categories. To tackle a + +
MethodAcc. (%)mIoU (%)
K-means50.719.2
Ours63.321.6
Ours*62.523.6
+ +Table 4. Comparisons on unsupervised semantic segmentation performance on ADE20K using the evaluation protocol of [40]. The pre-trained model with ViT-S architecture is used. + +![](images/07380379c40c8c1c5eac91b75d6e8129bae0794128fb5c2d7aa2c418a8af7e77.jpg) +Figure 3. Visualization of the unsupervised semantic segmentation results of our method on ADE20K. In each pair, the left refers to the input image, and the right refers to the segmentation result. As shown, our method can yield reasonable pixel groups for images containing complex structures. + +![](images/992761b3544dc6732bcf2913af565ca45427406f9ac15ed02f7afd5685f19911.jpg) + +large number of ground-truth semantic classes, we set $K$ to 512 with $\beta$ as 0.04. The training lasts for 20 epochs, given that the training set is relatively large. We use the evaluation protocol of [40]. We include the K-means baseline based on our own implementation for a fair comparison. + +The results are displayed in Table 4. As shown, our methods are still superior to the K-means baseline, especially regarding pixel accuracy. The best mIoU is $23.6\%$ , much lower than the corresponding results on Pascal Context and Cityscapes. This probably stems from the large number of semantic categories in ADE20K—the used pretrained models are not trained with fine-grained objectives (e.g., losses defined on patches), so they cannot ensure the semantic richness of the extracted dense features, which makes our method tend to generate clusters that conjoin multiple fine-grained semantic categories (see the lamp and the streetlight in Figure 3). One potential solution to this problem is fine-tuning the pre-trained models with patchwise self-supervised learning loss and then invoking the proposed spectral clustering pipeline. + +# 4.4. Ablation Studies + +In this subsection, we present a comprehensive study of several key hyper-parameters in our method. We evaluate using the same setting as in Section 4.2. We consider the ViT-S architecture for per-trained models given its superior performance testified in previous results. + +The output dimension $K$ . $K$ determines the number of eigenfunctions to learn and hence the dimension of the spectral embedding. It also implicitly connects to the number of + +
K64128256512
Acc. (%)67.171.670.471.1
mIoU (%)27.833.238.837.9
+ +Table 5. Performance comparison of different $K$ based on a pretrained ViT-S model on Pascal Context validation set. + +
α00.10.30.50.7
Pascal Context38.637.938.838.938.0
Cityscapes27.226.728.228.127.9
+ +semantic classes uncovered automatically during training. In previous experiments, we keep $K$ larger than the number of ground-truth semantic classes. Here we perform an ablation study on $K$ on Pascal Context to reflect the necessity of doing so. The results are summarized in Table 5, which indicates that a value of $K$ of at least 256 is necessary to achieve superior performance in terms of mIoU scores. A larger $K$ yields more expressive representations that capture subtleties yet at the cost of increased computational overhead. Moreover, it should be noted that the NeuralEF technique may fail to uncover the eigenfunctions with small eigenvalues [12]. Therefore, we suggest selecting a moderate value of $K$ in practice. + +The trade-off parameter $\alpha$ . The proposed spectral clustering workflow is compatible with any kernel function that captures plausible relationships between image patches. Currently, the used kernel is a weighted sum of the normalized adjacency defined on features from pre-trained models and that defined on down-sampled pixels. To verify the robustness of our method to the trade-off parameter $\alpha$ , we perform an ablation study on it and report the results in Table 6. We include results for both Pascal Context and Cityscapes for a thorough investigation. As shown, the mIoU on the validation data does not vary significantly w.r.t. $\alpha$ , and limiting $\alpha$ to [0.3, 0.5] can lead to superior results. Note that when $\alpha = 0$ , i.e., we only use the features from pre-trained models to construct the graph kernel, the mIoU drops slightly, indicating that the features from pre-trained models can retain most information on the neighborhood relationship of raw pixels. This also presents an opportunity for enhancing performance by improving the graph defined on down-sampled image pixels. + +The trade-off parameter $\beta$ . The trade-off parameter $\beta$ in Equation (5) for learning neural eigenfunctions affects the empirical convergence. To investigate whether our method is sensitive to the choice of $\beta$ , in Table 7 we ablate the influence of $\beta$ in both "Ours" and "Ours*" approaches on the Pascal Context data. We observe that the validation mIoU remains stable across $\beta$ ranging from 0.04 to 0.16, which + +Table 6. Mean IoU (\%) comparison of different trade-off coefficients $\alpha$ based on a pre-trained ViT-S model. + +
β0.040.080.16
Ours38.838.839.0
Ours*39.039.639.3
+ +Table 7. Mean IoU (\%) comparison of different $\beta$ based on a pretrained ViT-S model on Pascal Context validation set. + +
Acc. (%)mIoU (%)
Pascal Context55.815.2
Cityscapes81.218.5
+ +Table 8. Zero-shot transfer results of our method. The training is performed on ImageNet based on the pre-trained ViT-S model. + +confirms the robustness of our method against $\beta$ . With this, we set $\beta$ to 0.08 in all experiments. + +Zero-shot transfer. Due to its unsupervised clustering nature, our method does not necessarily rely on target images for training. In this spirit, we perform an initial study where the training is conducted on ImageNet, but the evaluation is conducted on both Pascal Context and Cityscapes. This forms a zero-shot transfer paradigm for unsupervised semantic segmentation. The training lasts for 5 epochs under the same setting in previous studies. We report the results in Table 8. As a reference, the corresponding mIoU of MaskCLIP and ReCo on Cityscapes are 10.0 and 19.3 respectively [39], thus our method provides competitive performance. Nonetheless, the mIoUs for all the methods are much worse than those in previous studies. This is probably because images from ImageNet mostly contain clear foregrounds and single objects, which is in sharp contrast to the complex scene images in Pascal Context and Cityscapes, thus the learned neural eigenfunctions struggle to generalize. A potential remedy for this problem is training on more realistic datasets to reduce the transfer gap. + +Majority voting vs. Hungarian matching. By having the same number of clusters as the ground truth classes and utilizing Hungarian matching, we can maintain a relatively low cluster count and probably enable the assignment of clusters to semantic classes by an expert in practice. We conduct a study on Pascal Context, where the number of clusters is set to match the semantic categories. The resulting mIoU of Hungarian matching is 0.235, slightly lower than the mIoU obtained with majority voting in the same setting (0.277). One possible explanation is that the semantic categories in the benchmarks are often structured, such as a car consisting of the body and the wheels. As a result, the automatically discovered clusters may not correspond one-to-one with the semantic categories. This observation also highlights the need for a larger number of clusters to address this issue effectively. + +The pre-training method. When using ViT backbones pretrained on ImageNet classification, we observe that stronger + +
ViT-BViT-LViT-L/14@336px
37.238.744.0
+ +Table 9. Mean IoU (\%) of our method on Pascal Context when using various backbones pre-trained by CLIP. + +pre-trained models yield worse segmentation performance. We have realized backbones pre-trained by CLIP may exhibit a different tendency because the model outputs are coerced to conform with text supervision rather than being discriminative in recognizing foreground objects. We empirically study this in Table 9. As shown, the backbone pre-trained by CLIP exhibits an increasing trend on mIoU as the model expressiveness increases. + +# 5. Conclusion + +This work establishes an end-to-end NN-based pipeline for spectral clustering for unsupervised semantic segmentation. To achieve that, we build a connectivity graph over image patches using information from both pre-trained models and raw pixels and employ neural eigenfunctions to produce spectral embeddings corresponding to suitable graph kernels. We further quantize the output of the neural eigenfunctions to obtain clustering assignments without resorting to an explicit grouping step. After training, our method can generalize to novel test data easily and reliably. The reliance on pre-trained models gives our method good training efficiency and sufficient expressiveness. Extensive results confirm its superior performance over competing baselines. + +One limitation is that, like most clustering-based methods, our method needs to be exposed to ground-truth semantic masks to match clustering assignments to semantic segments. Introducing text prompts to guide clustering is a potential solution and deserves future investigation. + +# Acknowledgments + +We thank Bernhard Schölkopf for providing constructive suggestions and proofreading the paper. This work was supported by Natural Science Foundation of Shanghai (No. 23ZR1428700). + +# References + +[1] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. 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In European Conference on Computer Vision (ECCV), 2022. \ No newline at end of file diff --git a/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/images.zip b/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..fb93415a5699f5e2439bb8f0079a7ed518c3eae7 --- /dev/null +++ b/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e1f561dde340a825a4aef147735b919d23139f2e8106ed3fbdbd66ec96c3d7d6 +size 369923 diff --git a/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/layout.json b/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..336741dc4c19898e7e72e2fed86d44c1733d53fa --- /dev/null +++ b/2023/Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation/layout.json @@ -0,0 +1,8810 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 68, + 103, + 525, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 103, + 525, + 121 + ], + "spans": [ + { + "bbox": [ + 68, + 103, + 525, + 121 + ], + "type": "text", + "content": "Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 144, + 144, + 205, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 144, + 205, + 157 + ], + "spans": [ + { + "bbox": [ + 144, + 144, + 205, + 157 + ], + "type": "text", + "content": "Zhijie Deng" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 100, + 159, + 249, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 159, + 249, + 185 + ], + "spans": [ + { + "bbox": [ + 100, + 159, + 249, + 185 + ], + "type": "text", + "content": "Shanghai Jiao Tong University Shanghai, China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 188, + 227, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 188, + 227, + 198 + ], + "spans": [ + { + "bbox": [ + 123, + 188, + 227, + 198 + ], + "type": "text", + "content": "zhijied@sjtu.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 359, + 144, + 413, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 144, + 413, + 156 + ], + "spans": [ + { + "bbox": [ + 359, + 144, + 413, + 156 + ], + "type": "text", + "content": "Yucen Luo" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 280, + 159, + 493, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 280, + 159, + 493, + 185 + ], + "spans": [ + { + "bbox": [ + 280, + 159, + 493, + 185 + ], + "type": "text", + "content": "Max Planck Institute for Intelligent Systems Tübingen, Germany" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 329, + 188, + 444, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 188, + 444, + 198 + ], + "spans": [ + { + "bbox": [ + 329, + 188, + 444, + 198 + ], + "type": "text", + "content": "luoyucencen@gmail.com" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 191, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 252, + 289, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 289, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 289, + 539 + ], + "type": "text", + "content": "Unsupervised semantic segmentation is a long-standing challenge in computer vision with great significance. Spectral clustering is a theoretically grounded solution to it where the spectral embeddings for pixels are computed to construct distinct clusters. Despite recent progress in enhancing spectral clustering with powerful pre-trained models, current approaches still suffer from inefficiencies in spectral decomposition and inflexibility in applying them to the test data. This work addresses these issues by casting spectral clustering as a parametric approach that employs neural network-based eigenfunctions to produce spectral embeddings. The outputs of the neural eigenfunctions are further restricted to discrete vectors that indicate clustering assignments directly. As a result, an end-to-end NN-based paradigm of spectral clustering emerges. In practice, the neural eigenfunctions are lightweight and take the features from pre-trained models as inputs, improving training efficiency and unleashing the potential of pre-trained models for dense prediction. We conduct extensive empirical studies to validate the effectiveness of our approach and observe significant performance gains over competitive baselines on Pascal Context, Cityscapes, and ADE20K benchmarks. The code is available at https://github.com/thudzj/NeuralEigenfunctionSegmentor." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 562, + 127, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 127, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 127, + 574 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "Semantic segmentation is essential in understanding the inherent structure and fine-grained information of images. However, current approaches often hinge on a vast amount of manual annotations to train neural networks (NNs) effectively in an end-to-end manner [5, 40]. This is problematic, as obtaining these annotations can be both time-consuming and costly, particularly in fields such as autonomous driving and medical image processing, where annotations are usually collected from domain experts. Thus, finding a way to perform semantic segmentation without manual annotation remains a crucial unresolved problem." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 228, + 547, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 547, + 408 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 547, + 408 + ], + "type": "text", + "content": "Unsupervised semantic segmentation has recently attracted a great deal of attention. A number of methods attempt to tackle it by learning fine-grained image features using self-supervised objectives and then applying clustering or grouping techniques [46, 41]. They tend to recognize single objects or single semantic categories and struggle with complex images. Other approaches have tried to use vision-language cross-modal models (e.g., CLIP [35]) to achieve zero-shot semantic segmentation [48, 39], but they heavily rely on carefully-tuned text prompts and self-training. Compared to the recent approaches, the classic spectral clustering [38], which has stood the test of time, remains an appealing option. In particular, it enjoys solid foundations in spectral graph theory—it finds the minimum cut of the connectivity graph over pixels." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 411, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 590 + ], + "type": "text", + "content": "However, traditional spectral clustering exhibits limitations in three aspects: (i) it operates on raw image pixels, thus is sensitive to color transformations and unable to recognize semantic similarities; (ii) it is computationally inefficient due to the involved spectral decomposition; (iii) unlike NN-based methods, it is nontrivial and costly to extend to non-training samples because of its transductive manner. Thus it cannot be performed end-to-end in the test phase. Recent work reveals that pre-trained models such as ViTs [14] can mitigate the first limitation, significantly improving the applicability and effectiveness of spectral clustering [30]. Its core contribution is to build the connectivity graph over image patches based on an affinity matrix computed with the dense features from pre-trained models. Still, the limitations regarding efficiency and flexibility remain." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "The present paper aims to overcome the remaining limitations, rendering spectral clustering a simple yet effective baseline for unsupervised semantic segmentation. To tackle the inefficiency issue, we propose to cast the involved spectral decomposition problem as an NN-based optimization one using the recently developed neural eigenfunction (NeuralEF) technique [12]. Concretely, we first measure the similarities between image patches using both the features extracted from pre-trained models and raw pixels. Treating the similarity matrix (or its variants) as the output of a" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "551" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "type": "text", + "content": "kernel function, we then optimize NNs to approximate its principal eigenfunctions. Consequently, our method constitutes an NN-based counterpart of spectral embedding. We eliminate the need for an additional grouping step, which is required in prior work [30], by constraining the NN output to one-hot vectors that indicate clustering assignments directly. To accomplish this, we use the Gumbel-Softmax estimator [20] for gradient-based optimization during training. These strategies transform spectral clustering from a non-parametric approach to a parametric one, enabling easy and reliable out-of-sample generalization and avoiding solving complex matrix eigenvalue problems during testing." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 217, + 286, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 217, + 286, + 347 + ], + "spans": [ + { + "bbox": [ + 49, + 217, + 286, + 347 + ], + "type": "text", + "content": "We perform extensive studies to evaluate the effectiveness of our approach for unsupervised semantic segmentation. We first experiment on the popularly used benchmarks Pascal Context [31] and Cityscapes [9] based on pre-trained ViTs, and report superior results compared to leading methods MaskCLIP [48] and ReCo [39]. We further consider the sliding-window-based evaluation protocol [40] and experiment on the challenging ADE20K dataset [47] to systematically study the behavior of our method. In addition, we conduct thorough ablation studies to gain insights into the specification of several core hyper-parameters." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 358, + 132, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 358, + 132, + 371 + ], + "spans": [ + { + "bbox": [ + 49, + 358, + 132, + 371 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 378, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 378, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 378, + 286, + 712 + ], + "type": "text", + "content": "Unsupervised segmentation. Image segmentation has numerous practical applications in various industries and scientific fields. In order to alleviate the burden of collecting annotations, prior works have comprehensively studied the problem of learning image segmenters in semi- and weakly-supervised settings [24, 18, 4, 23]. Recently, there have been increasing efforts to tackle unsupervised segmentation based on the progress in related fields like deep generative models (DGMs) and self-supervised learning (SSL). On the one hand, DGM-based segmentation approaches train specialized image generators to separate foreground from background [6, 2, 1] or extract saliency masks directly from pre-trained generators [42]. Yet, it is technically nontrivial to extend them to cope with semantic segmentation. On the other hand, SSL-based methods define objectives to perform clustering [19, 7], mutual information maximization [21, 33], contrastive learning [41] or feature correspondence distillation [16] to learn image features suitable for grouping. However, most of these methods only recognize single objects or single semantic categories and struggle with complex images. With the increasing accessibility of pre-trained image-text cross-modal models, considerable efforts have been devoted to performing zero-shot semantic segmentation with them [48, 39]. Nevertheless, the entanglement with cross-modal models places high demands on the quality of the text prompts, which correspond to the semantic categories of concern, and hinders the methods from choosing backbone models freely." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 72, + 544, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 226 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 226 + ], + "type": "text", + "content": "Spectral clustering. As a classic solution to image segmentation, spectral clustering [38, 32] frames the original problem as a graph partitioning one defined on the connectivity graph over image pixels. Typically, spectral clustering exploits the eigenvectors of graph Laplacians to construct minimum-energy graph partitions [13, 15]. Spectral clustering is closely related to Kernel PCA [37] as they are both learning eigenfunctions [3]. Recently, spectral clustering has been combined with pre-trained models to enjoy rich semantic information [30]. Yet, it remains unsolved that spectral decomposition is expensive for big data, and the non-parametric nature hinders out-of-sample generalization. This paper aims to address these issues." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 228, + 544, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 228, + 544, + 466 + ], + "spans": [ + { + "bbox": [ + 308, + 228, + 544, + 466 + ], + "type": "text", + "content": "The deep learning variant of spectral methods. Refurbishing spectral methods with deep learning techniques is beneficial to improve the scalability and flexibility of the former. The spectral inference networks (SpIN) [34] is a seminal work in this direction. Yet, the learning objective of SpIN is ill-defined, which leads to only the subspace spanned by the principal eigenfunctions instead of the eigenfunctions themselves. SpIN hence introduces convoluted and expensive strategies to solve this problem. The recent NeuralEF technique [12] alternatively defines a new series of objective functions to break the symmetry among eigenfunctions explicitly. NeuralEF is further enhanced by weight sharing and extended to handle indefinite kernels in [11], constituting a more amenable choice for learning spectral embeddings given pre-defined kernels. We also note that there are several attempts to develop deep spectral clustering methods based on supervisions [28] or a dual autoencoder network [45], but they cannot be trivially applied to the task of unsupervised semantic segmentation due to the absence of annotations or other inefficiency issues." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 477, + 386, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 477, + 386, + 491 + ], + "spans": [ + { + "bbox": [ + 308, + 477, + 386, + 491 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 497, + 544, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 497, + 544, + 533 + ], + "spans": [ + { + "bbox": [ + 308, + 497, + 544, + 533 + ], + "type": "text", + "content": "We begin with a brief review of the relevant background and then build up our approach step by step. We provide an overview of the proposed method in Figure 1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 540, + 384, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 540, + 384, + 552 + ], + "spans": [ + { + "bbox": [ + 308, + 540, + 384, + 552 + ], + "type": "text", + "content": "3.1. Background" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 558, + 544, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 558, + 544, + 677 + ], + "spans": [ + { + "bbox": [ + 308, + 558, + 544, + 677 + ], + "type": "text", + "content": "Semantic segmentation essentially targets determining the semantic consistency among image pixels. In the absence of annotations, the problem boils down to an unsupervised clustering one. Spectral clustering [38, 32] is a longstanding solution to it with solid theoretical foundations. It proceeds by partitioning a connectivity graph over image pixels. The resulting algorithm typically involves eigendecomposing the graph Laplacian matrix and stacking its eigenvectors, which are then used in a Euclidean clustering algorithm to obtain a fixed number of partitions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 678, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 678, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 678, + 544, + 712 + ], + "type": "text", + "content": "Traditional spectral clustering operates on raw image pixels, making it sensitive to color transformations and unable to identify semantic similarities. To address this, a" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "type": "text", + "content": "552" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 547, + 228 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 547, + 228 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 547, + 228 + ], + "type": "image", + "image_path": "d477142d47580f07bb6363d996aa8bd6e6e774453869434fd3c66b96a9e33659.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 238, + 546, + 271 + ], + "lines": [ + { + "bbox": [ + 46, + 238, + 546, + 271 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 546, + 271 + ], + "type": "text", + "content": "Figure 1. Method overview. We establish an end-to-end NN-based pipeline for spectral clustering to perform unsupervised semantic segmentation. The box highlights modules that exist only during training. The nearest neighbor graph over pixels only has edges between pixels from the same images, while the other one is built over dense features from various images. The pre-trained model is fixed." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "text", + "content": "natural idea is to include the inductive bias of NNs. In this spirit, the deep spectral method (DSM) [30] leverages powerful pre-trained models to translate the learning from raw pixels to patch-wise features that embed rich local semantics and are widely applicable. Specifically, let " + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "text", + "content": " denote an image and " + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "inline_equation", + "content": "f: \\mathbb{R}^{H \\times W \\times 3} \\to \\mathbb{R}^{H / P \\times W / P \\times C}" + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "text", + "content": " denote the pre-trained model with " + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "text", + "content": " as a down-sampling factor. DSM constructs a semantic affinity matrix using both the patch-wise features " + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\pmb{f}_{i,j,k} = f(\\pmb{x}_i)_{j,k} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 282, + 287, + 460 + ], + "type": "text", + "content": " and image pixels, and performs spectral clustering on the corresponding connectivity graph. Subsequently, DSM performs bi-linear interpolation to convert patch-wise segments to pixel-wise ones. This simple workflow has surpassed various competitors regarding unsupervised semantic segmentation performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "type": "text", + "content": "Denote by " + }, + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "type": "text", + "content": " the size of the dataset of concern. Semantic segmentation requires classifying pixels in different images yet with the same semantics into the same category. Thereby, it needs to ensure semantic consistency across the dataset. Therefore, DSM should, in principle, work on an affinity matrix of size " + }, + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{NHW / P^2\\times NHW / P^2}" + }, + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "type": "text", + "content": ", but this is computationally infeasible as the involved spectral decomposition has a cubic complexity w.r.t. " + }, + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "type": "inline_equation", + "content": "NHW / P^2" + }, + { + "bbox": [ + 46, + 461, + 287, + 628 + ], + "type": "text", + "content": ". DSM alternatively conducts spectral clustering separately for each image and then performs cross-image synchronization, but this is inflexible compared to NN-based pipelines and arguably suboptimal. Additionally, existing spectral clustering methods, including DSM, are non-parametric, relying on costly spectral decomposition when faced with new test data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "In order to address the limitations discussed above, we leverage a parametric approach to spectral decomposition based on the recent NeuralEF technique [12] and learn discrete neural eigenfunctions directly. These innovations help to scale our method to large datasets, enable the straightforward and cheap out-of-sample extension for test data, and establish an NN-based spectral clustering workflow." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 281, + 501, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 501, + 294 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 501, + 294 + ], + "type": "text", + "content": "3.2. From Eigenvectors to Eigenfunctions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 300, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 347 + ], + "type": "text", + "content": "Spectral clustering involves the spectral decomposition of a matrix and hence is seemingly incompatible with the parametric NN models. To bridge this gap, we move our viewpoint from the eigenvectors to eigenfunctions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "text", + "content": "Specifically, abstracting the graph Laplacian matrix as the evaluation of some kernel function " + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "text", + "content": " on the dense features, the eigenfunctions of " + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "text", + "content": " form a function-space generalization of the aforementioned eigenvectors. Formally, the eigenfunction " + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "text", + "content": " of a kernel " + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\kappa(\\pmb{x},\\pmb{x}^{\\prime})" + }, + { + "bbox": [ + 304, + 348, + 545, + 407 + ], + "type": "text", + "content": " satisfies that" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 349, + 416, + 545, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 416, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 349, + 416, + 545, + 441 + ], + "type": "interline_equation", + "content": "\\int \\kappa (\\boldsymbol {x}, \\boldsymbol {x} ^ {\\prime}) \\psi (\\boldsymbol {x} ^ {\\prime}) p (\\boldsymbol {x} ^ {\\prime}) d \\boldsymbol {x} ^ {\\prime} = \\mu \\psi (\\boldsymbol {x}), \\tag {1}", + "image_path": "533f995a0cca6db84a1e0a79826d0315947ca86004374f23ed9528ab6976f82a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 448, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 484 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 448, + 545, + 484 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 448, + 545, + 484 + ], + "type": "text", + "content": " is the corresponding eigenvalue and " + }, + { + "bbox": [ + 304, + 448, + 545, + 484 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 448, + 545, + 484 + ], + "type": "text", + "content": " a probability measure. By definition, the eigenfunction should be normalized, and different eigenfunctions are orthogonal." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 484, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 628 + ], + "type": "text", + "content": "As shown, the eigenfunction takes input from the original space and maps it to the eigenspace specified by the kernel, where the local neighborhoods on data manifolds are preserved. Naturally, we can incorporate NNs as function approximators to the eigenfunctions. In this way, we bypass the need for expensive spectral decomposition of a matrix and can easily perform out-of-sample extension thanks to the generalization ability of NNs. Fortunately, the recently proposed NeuralEF [12] offers tools to realize this. We also note that the effectiveness of the spectral embedding yielded by neural eigenfunctions has been empirically validated in self-supervised learning [11]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 635, + 463, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 463, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 463, + 647 + ], + "type": "text", + "content": "3.3. Setting up the Graph Kernel" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "To set up the kernel for spectral clustering, as suggested by DSM [30], we construct two graphs with patch-wise features from pre-trained models and down-sampled image pixels, respectively. We then define the kernel with the weighted sum of the corresponding normalized graph adja" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "553" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "ency matrices. By doing so, the high-level semantics and low-level details are conjoined." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 95, + 286, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 95, + 286, + 182 + ], + "spans": [ + { + "bbox": [ + 46, + 95, + 286, + 182 + ], + "type": "text", + "content": "Denote by " + }, + { + "bbox": [ + 46, + 95, + 286, + 182 + ], + "type": "inline_equation", + "content": "\\mathbf{F} = \\{\\pmb {f}_i\\}_{i = 1}^N\\in \\mathbb{R}^{NHW / P^2\\times C}" + }, + { + "bbox": [ + 46, + 95, + 286, + 182 + ], + "type": "text", + "content": " the collection of patch-wise features over the dataset. Considering that the feature space shaped by large-scale pre-training is highly structured where simple distance measures suffice to represent similarities, we leverage cosine similarity to specify a nearest neighbor graph over image patches. The corresponding affinity matrix is detailed below:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 190, + 286, + 231 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 190, + 286, + 231 + ], + "spans": [ + { + "bbox": [ + 48, + 190, + 286, + 231 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {u, v} = \\left\\{ \\begin{array}{l l} \\mathbf {F} _ {u} \\mathbf {F} _ {v} ^ {\\top} / (\\| \\mathbf {F} _ {u} \\| \\| \\mathbf {F} _ {v} \\|), & v \\in k - \\mathrm {N N} (u, \\mathbf {F}, \\text {c o s i n e}) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}", + "image_path": "fa68e3e0bd29c08aea048b2582ac0fc27d386baac1bf1b6f8f54b9ef29ab799f.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "text", + "content": "-NN(" + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "inline_equation", + "content": "u, \\mathbf{F}, \\cos \\mathrm{i}" + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "text", + "content": ") denotes the set of the " + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "text", + "content": " nearest neighbors of " + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_u" + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 231, + 286, + 338 + ], + "type": "text", + "content": " under cosine similarity. The above graph deploys edges between patches that are semantically close. The corresponding graph partitioning can result in meaningful segmentation at a coarse resolution. Although other traditional graphs can also be used, the nearest neighbor graph enjoys sparsity, which reduces storage and computation costs and has been studied extensively in manifold learning and spectral clustering." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "text", + "content": "To supplement the high-level features with low-level details, we bilinearly down-sample the original image " + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{x}}_i\\in \\mathbb{R}^{H / P\\times W / P\\times 3}" + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "text", + "content": " to keep resolution consistency, and fuse the spatial information " + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "inline_equation", + "content": "(j,k)" + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "text", + "content": " and color information " + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{x}}_{i,j,k}" + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "text", + "content": " as a single vector. We stack the collection over the dataset as " + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{X}}\\in \\mathbb{R}^{NHW / P^2\\times 5}" + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "text", + "content": ". A nearest neighbor graph over down-sampled pixels is then defined based on " + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 46, + 339, + 286, + 436 + ], + "type": "text", + "content": " distance following DSM [30]. The affinity matrix is:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 93, + 444, + 286, + 476 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 444, + 286, + 476 + ], + "spans": [ + { + "bbox": [ + 93, + 444, + 286, + 476 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {A}} _ {u, v} = \\left\\{ \\begin{array}{l l} 1, & v \\in \\tilde {k} - \\mathrm {N N} (u, \\tilde {\\mathbf {X}}, L ^ {2}) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}", + "image_path": "3954b16a79ca3b165742bb2093b418a01d7f17d715217f72ff60764528711c0c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "inline_equation", + "content": "\\tilde{k}" + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "text", + "content": "-NN" + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "inline_equation", + "content": "(u, \\tilde{\\mathbf{X}}, L^2)" + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "text", + "content": " denotes the set of " + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "inline_equation", + "content": "\\tilde{k}" + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "text", + "content": " nearest neighbors of " + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{X}}_u" + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{X}}" + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "text", + "content": " under " + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 46, + 484, + 286, + 557 + ], + "type": "text", + "content": " distance (dissimilarity). We place a further constraint that the nearest neighbors should belong to the same image as the query to avoid establishing meaningless connections. It is expected that such a graph helps to detect sharp object boundaries." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": "We symmetrize " + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{A}}" + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": " so that they can serve as graph adjacency matrices. Considering that the normalized graph cuts are more practically useful [38], we would better build a kernel with the normalized graph Laplacian matrices of " + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{A}}" + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": ", and learn the eigenfunctions associated with the smallest " + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": " eigenvalues. However, the NeuralEF approach instead deploys neural approximations to the principal eigenfunctions, which correspond to the largest eigenvalues, of a kernel [12]. To this end, we move our focus from the normalized Laplacian matrix to the normalized adjacency matrix whose " + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": " principal eigenfunctions exactly correspond to the eigenfunctions associated with the " + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": " smallest eigenvalues of the former. Specifically, let" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathbf{D} \\coloneqq \\operatorname{diag}(\\mathbf{A}\\mathbf{1}), \\tilde{\\mathbf{D}} \\coloneqq \\operatorname{diag}(\\tilde{\\mathbf{A}}\\mathbf{1})" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " denote the degree matrices. We then define the kernel function " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " using the weighted sum of the normalized adjacency matrices, detailed below:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 115, + 545, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 115, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 313, + 115, + 545, + 129 + ], + "type": "interline_equation", + "content": "\\kappa : \\kappa (\\mathbf {F}, \\mathbf {F}) = \\mathbf {D} ^ {- 1 / 2} \\mathbf {A} \\mathbf {D} ^ {- 1 / 2} + \\alpha \\tilde {\\mathbf {D}} ^ {- 1 / 2} \\tilde {\\mathbf {A}} \\tilde {\\mathbf {D}} ^ {- 1 / 2}, \\tag {4}", + "image_path": "48135c714f714a889f310f3db928c908e70908e5ca6afeffafbc4af2851ec716.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 137, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 137, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 137, + 545, + 233 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 137, + 545, + 233 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 137, + 545, + 233 + ], + "type": "text", + "content": " is a trade-off parameter. Here we define the kernel in the space of features extracted from pre-trained models while other choices are also viable: it only affects the input of neural eigenfunctions. In the current setting, the features from pre-trained models are directly fed into neural eigenfunctions, which is sensible thanks to the great potential of pre-trained models and can prevent unnecessary training costs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 241, + 479, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 241, + 479, + 253 + ], + "spans": [ + { + "bbox": [ + 305, + 241, + 479, + 253 + ], + "type": "text", + "content": "3.4. Learning Neural Eigenfunctions" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "\\mathbf{f} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": " denote a row vector of " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "p(\\mathbf{f})" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": " a uniform distribution over " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_i\\}_{i=1}^{NHW/P^2}" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": ". The NeuralEF technique [12] approximates the " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": " principal eigenfunctions of the kernel " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": " w.r.t. " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "p(\\mathbf{f})" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": " with a " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": "-output neural function " + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "inline_equation", + "content": "\\psi: \\mathbb{R}^C \\to \\mathbb{R}^K" + }, + { + "bbox": [ + 305, + 258, + 545, + 322 + ], + "type": "text", + "content": " by solving the following problem:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 310, + 328, + 545, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 328, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 310, + 328, + 545, + 368 + ], + "type": "interline_equation", + "content": "\\max _ {\\psi} \\sum_ {j = 1} ^ {K} \\mathbf {R} _ {j, j} - \\beta \\sum_ {j = 1} ^ {K} \\sum_ {i = 1} ^ {j - 1} \\widehat {\\mathbf {R}} _ {i, j} ^ {2}, s. t. \\mathbb {E} _ {p (\\mathbf {f})} [ \\psi (\\mathbf {f}) \\circ \\psi (\\mathbf {f}) ] = \\mathbf {1}, \\tag {5}", + "image_path": "9389e0bd5fe57170107712e6eeb0d38a8efdd556c69fece3981e95444f6699f1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 369, + 544, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 544, + 390 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 544, + 390 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 369, + 544, + 390 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 369, + 544, + 390 + ], + "type": "text", + "content": " is a positive coefficient and " + }, + { + "bbox": [ + 305, + 369, + 544, + 390 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 305, + 369, + 544, + 390 + ], + "type": "text", + "content": " is Hadamard product, and" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 351, + 389, + 545, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 389, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 351, + 389, + 545, + 409 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {R} := \\mathbb {E} _ {p (\\mathbf {f})} \\mathbb {E} _ {p \\left(\\mathbf {f} ^ {\\prime}\\right)} \\left[ \\kappa \\left(\\mathbf {f}, \\mathbf {f} ^ {\\prime}\\right) \\psi (\\mathbf {f}) \\psi \\left(\\mathbf {f} ^ {\\prime}\\right) ^ {\\top} \\right] \\\\ \\widehat {\\quad} \\end{array} \\tag {6}", + "image_path": "a915c261f41dcf333e922b0a8d0aaa826146a5e15c470f9318bade66de2f2a87.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 353, + 406, + 499, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 406, + 499, + 419 + ], + "spans": [ + { + "bbox": [ + 353, + 406, + 499, + 419 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathbf {R}} := \\mathbb {E} _ {p (\\mathbf {f})} \\mathbb {E} _ {p \\left(\\mathbf {f} ^ {\\prime}\\right)} \\left[ \\kappa (\\mathbf {f}, \\mathbf {f} ^ {\\prime}) \\hat {\\psi} (\\mathbf {f}) \\psi \\left(\\mathbf {f} ^ {\\prime}\\right) ^ {\\top} \\right].", + "image_path": "7b73c2b9c75bcd9a807e7697708263178509daed1e9f1fb4b142230d784714e5.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 423, + 482, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 482, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 482, + 435 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 306, + 423, + 482, + 435 + ], + "type": "inline_equation", + "content": "\\hat{\\psi}" + }, + { + "bbox": [ + 306, + 423, + 482, + 435 + ], + "type": "text", + "content": " is the non-optimizable variant of " + }, + { + "bbox": [ + 306, + 423, + 482, + 435 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 306, + 423, + 482, + 435 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 436, + 544, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 436, + 544, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 436, + 544, + 460 + ], + "type": "text", + "content": "Adapting such results to our case and applying Monte Carlo estimation to the expectation yields" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 465, + 545, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 545, + 495 + ], + "type": "interline_equation", + "content": "\\mathbf {R} \\approx \\frac {1}{B ^ {2}} \\boldsymbol {\\Psi} \\cdot \\kappa (\\mathbf {F} ^ {B}, \\mathbf {F} ^ {B}) \\cdot \\boldsymbol {\\Psi} ^ {\\top} \\text {a n d} \\widehat {\\mathbf {R}} \\approx \\frac {1}{B ^ {2}} \\widehat {\\boldsymbol {\\Psi}} \\cdot \\kappa (\\mathbf {F} ^ {B}, \\mathbf {F} ^ {B}) \\cdot \\boldsymbol {\\Psi} ^ {\\top}, \\tag {7}", + "image_path": "587d67a98373f416ea51dfa4586c3a5ca1412f63dcbba7d3741530e46a71fefe.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^B\\coloneqq [\\mathbf{f}_1,\\dots ,\\mathbf{f}_B]^\\top \\in \\mathbb{R}^{B\\times C}" + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "text", + "content": " is a mini-batch of features, " + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\Psi \\coloneqq [\\psi (\\mathbf{f}_1),\\ldots ,\\psi (\\mathbf{f}_B)]\\in \\mathbb{R}^{K\\times B}" + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "text", + "content": " is the collection of the corresponding NN outputs, and " + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\widehat{\\Psi}\\coloneqq" + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "text", + "content": " stop-gradient(Ψ). The stop-gradient operation can be easily found in auto-diff libraries and plays a vital role in establishing the asymmetry between the " + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "text", + "content": " principal eigenfunctions. We put an " + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "text", + "content": " -batch normalization layer [12] at the end of model " + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 495, + 545, + 592 + ], + "type": "text", + "content": " to enforce the constraint in Equation (5)." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 593, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 593, + 545, + 664 + ], + "type": "text", + "content": " can be implemented as a neural network composed of convolutions or transformer blocks, which takes dense image features " + }, + { + "bbox": [ + 304, + 593, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\pmb{f} = f(\\pmb{x}) \\in \\mathbb{R}^{H / P \\times W / P \\times C}" + }, + { + "bbox": [ + 304, + 593, + 545, + 664 + ], + "type": "text", + "content": " as input and outputs " + }, + { + "bbox": [ + 304, + 593, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\psi(\\pmb{f}) \\in \\mathbb{R}^{H / P \\times W / P \\times K}" + }, + { + "bbox": [ + 304, + 593, + 545, + 664 + ], + "type": "text", + "content": ". After training, it can be used to predict new test data without relying on expensive test-time spectral decomposition." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 671, + 488, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 488, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 488, + 684 + ], + "type": "text", + "content": "3.5. Quantizing Neural Eigenfunctions" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "After obtaining the spectral embedding " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\psi(f(x))" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " for image patches, we should, by convention, invoke a Euclidean" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "554" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 286, + 156 + ], + "type": "text", + "content": "clustering algorithm such as K-means [29] to get clustering assignments. In practice, datasets can often be large, so it would be better to leverage online clustering mechanisms to avoid unaffordable storage costs. However, this approach may still be time-consuming when aiming for good convergence. Additionally, this pipeline is not as flexible as NN-based segmenters." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "spans": [ + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "text", + "content": "To bridge the gap, we impose a constraint on the output of " + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "text", + "content": " to be " + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "text", + "content": "-dim one-hot vectors which directly indicate clustering assignments. We resort to the Gumbel-Softmax estimator [20] for gradient-based optimization. This follows the notion that the outputs of eigenfunctions are soft clustering assignments, and we further perform quantization of them. This is also in a similar spirit to the spectral hashing approach [43] where the output of " + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "text", + "content": " is assumed to be vectors over " + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\{-1,1\\}^K" + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "text", + "content": ". We clarify that the Gumbel-Softmax estimator precedes the aforementioned " + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "text", + "content": " batch normalization layer. In the test phase, we remove this estimator and the " + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 48, + 157, + 286, + 323 + ], + "type": "text", + "content": " batch normalization layer, using the NN outputs directly as softmax logits for clustering. This results in a pure NN-based workflow for spectral clustering." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 330, + 228, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 330, + 228, + 342 + ], + "spans": [ + { + "bbox": [ + 48, + 330, + 228, + 342 + ], + "type": "text", + "content": "3.6. From Clusters to Image Segments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 348, + 286, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 348, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 48, + 348, + 286, + 491 + ], + "type": "text", + "content": "During inference, we up-sample the softmax logits bilinearly to match the original resolution of input images. We then apply the argmax operation to obtain discrete clustering assignments. A natural question that arises is how to match these clustering assignments to pre-defined semantics to obtain the final image segments. Two well-studied solutions are Hungarian matching [27] and majority voting. As per DSM [30], when evaluated on standard image semantic segmentation benchmarks, we first collect the clustering assignments for all validation images and then match them to ground-truth labels via these approaches to conduct a quantitative evaluation of segmentation performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 501, + 127, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 501, + 127, + 514 + ], + "spans": [ + { + "bbox": [ + 48, + 501, + 127, + 514 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 521, + 286, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 521, + 286, + 556 + ], + "spans": [ + { + "bbox": [ + 48, + 521, + 286, + 556 + ], + "type": "text", + "content": "To evaluate the efficacy of the proposed method for unsupervised semantic segmentation, we conduct comprehensive experiments on various standard benchmarks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 563, + 167, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 563, + 167, + 576 + ], + "spans": [ + { + "bbox": [ + 48, + 563, + 167, + 576 + ], + "type": "text", + "content": "4.1. Experimental Setups" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 582, + 286, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 582, + 286, + 629 + ], + "spans": [ + { + "bbox": [ + 48, + 582, + 286, + 629 + ], + "type": "text", + "content": "Datasets. We primarily experiment on Pascal Context and Cityscapes, which consist of 60 and 27 classes, respectively. We employ the same data pre-processing and augmentation strategies as the work [40] on the training dataset." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "type": "text", + "content": "Pre-trained models. We use pre-trained ViTs [14] provided by the timm library [44] and consider the \"Small\", \"Base\", and \"Large\" variants. The weights have been pre-trained on ImageNet-21k [36] and fine-tuned on ImageNet [10] in a supervised manner. In particular, we consider pre-trained models at a high resolution, like " + }, + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 48, + 630, + 286, + 712 + ], + "type": "text", + "content": ", to obtain fine-grained segments. We fix the patch size to" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 72, + 545, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 143 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 307, + 72, + 545, + 143 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 307, + 72, + 545, + 143 + ], + "type": "inline_equation", + "content": "P = 16" + }, + { + "bbox": [ + 307, + 72, + 545, + 143 + ], + "type": "text", + "content": ") to better trade-off efficiency and accuracy. We use the output of the last attention block of ViTs as " + }, + { + "bbox": [ + 307, + 72, + 545, + 143 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 307, + 72, + 545, + 143 + ], + "type": "text", + "content": " without elaborate selection. We also feed the intermediate features of the pre-trained ViTs, which can be freely accessed, to the neural eigenfunctions to enrich the input information." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "content": "Modeling and training. We set " + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "inline_equation", + "content": "k = 256" + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "content": " for the nearest neighbor graph defined on pre-trained models' features. To reduce the cost of searching for the nearest neighbors, we confine the search to the current mini-batch, which is shown to be empirically effective. We specify the other graph following DSM [30]. The trade-off coefficient " + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "content": " equals 0.3 based on an ablation study reported in Section 4.4. The training objective is detailed in Equation (5) and unfolded in Equation (7). As " + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "content": " implies the number of semantic classes uncovered automatically, we make it larger than the number of ground-truth semantic classes and, in practice, set it to 256. We set the trade-off coefficient " + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "content": " to 0.08 and linearly scale it for other values of " + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "content": " (see the study in Section 4.4). We use 2 transformer blocks with linear self-attention [22] and a linear head to specify the neural eigenfunctions " + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "content": " for efficiency. We restrict the weight matrix of the linear head to have orthogonal columns and find it beneficial to the final performance empirically. We anneal the temperature for Gumbel-Softmax from 1 to 0.3 following a cosine schedule during training. The training relies on an Adam optimizer [25] and a learning rate of " + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 308, + 145, + 545, + 430 + ], + "type": "text", + "content": " (with cosine decay). No weight decay is employed. The training lasts for 40 epochs with batch size 16 (or 8 if an out-of-memory error occurs), which takes half a day on one RTX 3090 GPU." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 433, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 433, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 308, + 433, + 545, + 576 + ], + "type": "text", + "content": "Evaluation. We test on the validation set of the datasets and report both pixel accuracy (Acc.) and mean intersection-over-union (mIoU). We follow the standard practice in unsupervised semantic segmentation where the validation images are resized and cropped to have " + }, + { + "bbox": [ + 308, + 433, + 545, + 576 + ], + "type": "inline_equation", + "content": "320 \\times 320" + }, + { + "bbox": [ + 308, + 433, + 545, + 576 + ], + "type": "text", + "content": " pixels (see [16, 39]). In particular, the background class in the Pascal Context is excluded from evaluation. We apply a softmax operation to the outputs of " + }, + { + "bbox": [ + 308, + 433, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 308, + 433, + 545, + 576 + ], + "type": "text", + "content": " to obtain clustering assignments. We then use majority voting to match the resulting clusters to semantic segments. We apply CRF [26] for post-processing (although it is empirically shown that its contribution to performance gain is marginal)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 586, + 493, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 586, + 493, + 599 + ], + "spans": [ + { + "bbox": [ + 308, + 586, + 493, + 599 + ], + "type": "text", + "content": "4.2. Comparison with Leading Methods" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 605, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 605, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 605, + 545, + 712 + ], + "type": "text", + "content": "We first compare the proposed method to leading unsupervised semantic segmentation methods. We consider two representative competitors from the literature: MaskCLIP [48] and ReCo [39], which empirical outperform a variety of baselines such as IIC [21], PiCIE [7], and STEGO [16]. In particular, MaskCLIP uses the ViT-B backbone trained by CLIP [35], whereas ReCo uses the ViT-L/14@336px, also trained by CLIP. We also try to include the self-training variants of MaskCLIP and ReCo in com" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 312, + 757 + ], + "type": "text", + "content": "555" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 273, + 274 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 273, + 274 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 273, + 274 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 273, + 274 + ], + "type": "table", + "html": "
MethodAcc. (%)mIoU (%)
MaskCLIP [48]-25.5
MaskCLIP+ [48]-31.1
ReCo [39]51.627.2
K-means
ViT-S61.928.9
ViT-B58.730.9
ViT-L45.319.3
Ours
ViT-S70.438.8
ViT-B69.737.5
ViT-L63.233.2
Ours*
ViT-S74.639.6
ViT-B73.237.6
ViT-L71.935.0
", + "image_path": "7237db2fbe2952a076537f9cb9052709567900f702923e997bac5a26d48ec12f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 277, + 287, + 310 + ], + "lines": [ + { + "bbox": [ + 47, + 277, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 287, + 310 + ], + "type": "text", + "content": "Table 1. Comparisons on unsupervised semantic segmentation performance on Pascal Context [31]. The results of MaskCLIP and ReCo are from the original papers." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 328, + 286, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 286, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 286, + 472 + ], + "type": "text", + "content": "parison. Besides, we introduce two other baselines: (i) fit a K-means with the features of pre-trained models for training data (using the same number of clustering centers as our method) and use it to predict clustering assignments for validation data; (ii) likewise, fit a K-means with the features preceding the linear head in " + }, + { + "bbox": [ + 46, + 328, + 286, + 472 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 328, + 286, + 472 + ], + "type": "text", + "content": ". The two ways are referred to as \"K-means\" and \"Ours*\" in our studies. We have not compared with DSM [30] because the involved divide-and-conquer procedure for synchronizing the clustering results across different images is non-trivial to implement. In theory, DSM can lead to a similar segmentation performance to our method (yet with more resource consumption)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 474, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 286, + 713 + ], + "type": "text", + "content": "We report the results in Table 1 and Table 2. As shown, our methods outperform MaskCLIP, ReCo, and K-means with significant margins, which reflects the efficacy of the learned neural eigenfunctions for unsupervised semantic segmentation. \"Ours*\" even outperforms \"Ours\", which is probably attributed to the fact that the features preceding the linear head in " + }, + { + "bbox": [ + 46, + 474, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 474, + 286, + 713 + ], + "type": "text", + "content": " have a much higher dimension than the final outputs and thus are more informative. While MaskCLIP+ and ReCo+ employ an extra time-consuming self-training step, they are still inferior to our methods. It is reasonable to speculate that combining our methods with self-training can further improve performance. Note also that K-means can serve as a strong baseline for unsupervised semantic segmentation. This finding appears to contradict the results reported in DSM [30] (Table 4). We deduce the reason that DSM sets the number of clusters to the number of true classes rather than a larger quantity and performs K-means directly on the validation set instead of the training set. Besides, as the size of the pre-trained model increases, both K-means and our methods yield worse unsupervised" + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 320, + 70, + 529, + 274 + ], + "blocks": [ + { + "bbox": [ + 320, + 70, + 529, + 274 + ], + "lines": [ + { + "bbox": [ + 320, + 70, + 529, + 274 + ], + "spans": [ + { + "bbox": [ + 320, + 70, + 529, + 274 + ], + "type": "table", + "html": "
MethodAcc. (%)mIoU (%)
MaskCLIP [48]35.910.0
ReCo [39]74.619.3
ReCo+ [39]83.724.2
K-means
ViT-S77.022.4
ViT-B74.823.2
ViT-L66.320.9
Ours
ViT-S83.428.2
ViT-B81.426.8
ViT-L80.326.3
Ours*
ViT-S84.630.0
ViT-B84.230.7
ViT-L84.230.0
", + "image_path": "883070b1260625eb334d995b0b5ae9aca4211ac25878d47da39b8d71b469d4c9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 306, + 277, + 545, + 310 + ], + "lines": [ + { + "bbox": [ + 306, + 277, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 306, + 277, + 545, + 310 + ], + "type": "text", + "content": "Table 2. Comparisons on unsupervised semantic segmentation performance on Cityscapes [9]. The results of MaskCLIP and ReCo are from the original papers." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 325, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 545, + 409 + ], + "type": "text", + "content": "segmentation performance. We attribute this to larger pretrained models producing more abstract outputs that contain more overall semantics than specialized details. In contrast, smaller pre-trained models may fall short in expressiveness. Therefore, we suggest using a pre-trained model with appropriate capacity when applying the proposed method to new applications." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 410, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 529 + ], + "type": "text", + "content": "Qualitative results. Figure 2 shows some qualitative results of the proposed methods on Pascal Context. We also include the K-means baseline in comparison. Most notably, unlike MaskContrast [41], our method can detect multiple semantic categories in the same image, and the generated object boundaries are sharp. Furthermore, our spectral clustering-based approach can greatly reduce the chaotic fragments produced by K-means. We defer the visualization for the learned neural eigenfunctions and the segmentation results on Cityscapes to Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 538, + 468, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 468, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 468, + 550 + ], + "type": "text", + "content": "4.3. Evaluation in More Scenarios" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 557, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 557, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 306, + 557, + 545, + 581 + ], + "type": "text", + "content": "In this subsection, we evaluate the proposed method in more scenarios to study its behavior systematically." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "First, we consider the evaluation protocol popularly used in the supervised setting. Specifically, following the setup [40], we leverage a sliding window with the same resolution as training images to cope with the varying sizes of evaluation images. The background class in the Pascal Context is included for evaluation, and the results on Cityscapes cover only 19 categories. Due to implementation challenges, we have not included existing methods in comparison, but we introduce a supervised semantic segmentation baseline, DeepLabv3+ [5], which can serve as an upper bound on performance." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "556" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 286, + 269 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 286, + 269 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 286, + 269 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 286, + 269 + ], + "type": "image", + "image_path": "4917961193051f51891ba1767d570d323dd87787bda4e725182deffc64c20279.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 280, + 287, + 304 + ], + "lines": [ + { + "bbox": [ + 47, + 280, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 280, + 287, + 304 + ], + "type": "text", + "content": "Figure 2. Visualization of the unsupervised semantic segmentation results on Pascal Context [31]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 61, + 312, + 272, + 460 + ], + "blocks": [ + { + "bbox": [ + 61, + 312, + 272, + 460 + ], + "lines": [ + { + "bbox": [ + 61, + 312, + 272, + 460 + ], + "spans": [ + { + "bbox": [ + 61, + 312, + 272, + 460 + ], + "type": "table", + "html": "
MethodAcc. (%)mIoU (%)
Pascal Context
Supervised-48.5
K-means56.331.9
Ours67.441.4
Ours*68.941.3
Cityscapes
Supervised-77.3
K-means75.534.2
Ours86.146.7
Ours*88.352.8
", + "image_path": "3db3a35ce5346c3ed46579e366388a73ea94b531e91cd1e1821ef7549d93b9a3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 464, + 287, + 541 + ], + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 541 + ], + "type": "text", + "content": "Table 3. Comparisons on semantic segmentation performance using the widely adopted evaluation protocol [40]. In particular, the background class in the Pascal Context is included for evaluation, and the results on Cityscapes cover 19 categories. The pre-trained models with ViT-S architecture are used. Supervised results for the two datasets rely on DeepLabv3+ [5] using ResNet-101 [17] and Xception-65 [8] backbones, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 557, + 286, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 286, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 286, + 675 + ], + "type": "text", + "content": "As shown in Table 3, in this new evaluation setting, our methods can clearly outperform K-means, and \"Ours*\" is slightly better than \"Ours\" in general. These results are consistent with those reported in Section 4.2 and help to verify the extensibility of the proposed method. We also notice that the performance gap between the proposed unsupervised segmentation method and the supervised baseline is not significant, especially on the Pascal Context dataset, which motivates further investigation on the direction of improving spectral clustering." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "After that, we assess our method on ADE20K, one of the most challenging semantic segmentation datasets that contain 150 fine-grained semantic categories. To tackle a" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 334, + 70, + 517, + 130 + ], + "blocks": [ + { + "bbox": [ + 334, + 70, + 517, + 130 + ], + "lines": [ + { + "bbox": [ + 334, + 70, + 517, + 130 + ], + "spans": [ + { + "bbox": [ + 334, + 70, + 517, + 130 + ], + "type": "table", + "html": "
MethodAcc. (%)mIoU (%)
K-means50.719.2
Ours63.321.6
Ours*62.523.6
", + "image_path": "12b0d448b028113c22ade3e5135e33ee4cb642c08ca80669ee467c0484ad30c8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 133, + 545, + 167 + ], + "lines": [ + { + "bbox": [ + 305, + 133, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 305, + 133, + 545, + 167 + ], + "type": "text", + "content": "Table 4. Comparisons on unsupervised semantic segmentation performance on ADE20K using the evaluation protocol of [40]. The pre-trained model with ViT-S architecture is used." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 308, + 177, + 425, + 266 + ], + "blocks": [ + { + "bbox": [ + 308, + 177, + 425, + 266 + ], + "lines": [ + { + "bbox": [ + 308, + 177, + 425, + 266 + ], + "spans": [ + { + "bbox": [ + 308, + 177, + 425, + 266 + ], + "type": "image", + "image_path": "07380379c40c8c1c5eac91b75d6e8129bae0794128fb5c2d7aa2c418a8af7e77.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 278, + 545, + 334 + ], + "lines": [ + { + "bbox": [ + 305, + 278, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 545, + 334 + ], + "type": "text", + "content": "Figure 3. Visualization of the unsupervised semantic segmentation results of our method on ADE20K. In each pair, the left refers to the input image, and the right refers to the segmentation result. As shown, our method can yield reasonable pixel groups for images containing complex structures." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 427, + 177, + 544, + 266 + ], + "blocks": [ + { + "bbox": [ + 427, + 177, + 544, + 266 + ], + "lines": [ + { + "bbox": [ + 427, + 177, + 544, + 266 + ], + "spans": [ + { + "bbox": [ + 427, + 177, + 544, + 266 + ], + "type": "image", + "image_path": "992761b3544dc6732bcf2913af565ca45427406f9ac15ed02f7afd5685f19911.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "type": "text", + "content": "large number of ground-truth semantic classes, we set " + }, + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "type": "text", + "content": " to 512 with " + }, + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 353, + 545, + 413 + ], + "type": "text", + "content": " as 0.04. The training lasts for 20 epochs, given that the training set is relatively large. We use the evaluation protocol of [40]. We include the K-means baseline based on our own implementation for a fair comparison." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 413, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 546, + 593 + ], + "type": "text", + "content": "The results are displayed in Table 4. As shown, our methods are still superior to the K-means baseline, especially regarding pixel accuracy. The best mIoU is " + }, + { + "bbox": [ + 304, + 413, + 546, + 593 + ], + "type": "inline_equation", + "content": "23.6\\%" + }, + { + "bbox": [ + 304, + 413, + 546, + 593 + ], + "type": "text", + "content": ", much lower than the corresponding results on Pascal Context and Cityscapes. This probably stems from the large number of semantic categories in ADE20K—the used pretrained models are not trained with fine-grained objectives (e.g., losses defined on patches), so they cannot ensure the semantic richness of the extracted dense features, which makes our method tend to generate clusters that conjoin multiple fine-grained semantic categories (see the lamp and the streetlight in Figure 3). One potential solution to this problem is fine-tuning the pre-trained models with patchwise self-supervised learning loss and then invoking the proposed spectral clustering pipeline." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 599, + 406, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 406, + 610 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 406, + 610 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 677 + ], + "type": "text", + "content": "In this subsection, we present a comprehensive study of several key hyper-parameters in our method. We evaluate using the same setting as in Section 4.2. We consider the ViT-S architecture for per-trained models given its superior performance testified in previous results." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "The output dimension " + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": " determines the number of eigenfunctions to learn and hence the dimension of the spectral embedding. It also implicitly connects to the number of" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 748, + 312, + 757 + ], + "type": "text", + "content": "557" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 70, + 263, + 118 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 263, + 118 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 263, + 118 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 263, + 118 + ], + "type": "table", + "html": "
K64128256512
Acc. (%)67.171.670.471.1
mIoU (%)27.833.238.837.9
", + "image_path": "1d878cd45acdbb007ca04fbd17ff78a2631de86a5178fdbec65f79e572ce2fd4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 55, + 152, + 276, + 201 + ], + "blocks": [ + { + "bbox": [ + 47, + 121, + 286, + 143 + ], + "lines": [ + { + "bbox": [ + 47, + 121, + 286, + 143 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 286, + 143 + ], + "type": "text", + "content": "Table 5. Performance comparison of different " + }, + { + "bbox": [ + 47, + 121, + 286, + 143 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 121, + 286, + 143 + ], + "type": "text", + "content": " based on a pretrained ViT-S model on Pascal Context validation set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 152, + 276, + 201 + ], + "lines": [ + { + "bbox": [ + 55, + 152, + 276, + 201 + ], + "spans": [ + { + "bbox": [ + 55, + 152, + 276, + 201 + ], + "type": "table", + "html": "
α00.10.30.50.7
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", + "image_path": "156a544f6b7f2100ba6cdba75aa43924e1ab814a2ed5c0db64ebc195a64de477.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "text", + "content": "semantic classes uncovered automatically during training. In previous experiments, we keep " + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "text", + "content": " larger than the number of ground-truth semantic classes. Here we perform an ablation study on " + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "text", + "content": " on Pascal Context to reflect the necessity of doing so. The results are summarized in Table 5, which indicates that a value of " + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "text", + "content": " of at least 256 is necessary to achieve superior performance in terms of mIoU scores. A larger " + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "text", + "content": " yields more expressive representations that capture subtleties yet at the cost of increased computational overhead. Moreover, it should be noted that the NeuralEF technique may fail to uncover the eigenfunctions with small eigenvalues [12]. Therefore, we suggest selecting a moderate value of " + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 247, + 286, + 402 + ], + "type": "text", + "content": " in practice." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "text", + "content": "The trade-off parameter " + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "text", + "content": ". The proposed spectral clustering workflow is compatible with any kernel function that captures plausible relationships between image patches. Currently, the used kernel is a weighted sum of the normalized adjacency defined on features from pre-trained models and that defined on down-sampled pixels. To verify the robustness of our method to the trade-off parameter " + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "text", + "content": ", we perform an ablation study on it and report the results in Table 6. We include results for both Pascal Context and Cityscapes for a thorough investigation. As shown, the mIoU on the validation data does not vary significantly w.r.t. " + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "text", + "content": ", and limiting " + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "text", + "content": " to [0.3, 0.5] can lead to superior results. Note that when " + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 46, + 402, + 286, + 629 + ], + "type": "text", + "content": ", i.e., we only use the features from pre-trained models to construct the graph kernel, the mIoU drops slightly, indicating that the features from pre-trained models can retain most information on the neighborhood relationship of raw pixels. This also presents an opportunity for enhancing performance by improving the graph defined on down-sampled image pixels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "The trade-off parameter " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": ". The trade-off parameter " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " in Equation (5) for learning neural eigenfunctions affects the empirical convergence. To investigate whether our method is sensitive to the choice of " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": ", in Table 7 we ablate the influence of " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " in both \"Ours\" and \"Ours*\" approaches on the Pascal Context data. We observe that the validation mIoU remains stable across " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " ranging from 0.04 to 0.16, which" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 361, + 70, + 489, + 118 + ], + "blocks": [ + { + "bbox": [ + 47, + 203, + 286, + 225 + ], + "lines": [ + { + "bbox": [ + 47, + 203, + 286, + 225 + ], + "spans": [ + { + "bbox": [ + 47, + 203, + 286, + 225 + ], + "type": "text", + "content": "Table 6. Mean IoU (\\%) comparison of different trade-off coefficients " + }, + { + "bbox": [ + 47, + 203, + 286, + 225 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 203, + 286, + 225 + ], + "type": "text", + "content": " based on a pre-trained ViT-S model." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 361, + 70, + 489, + 118 + ], + "lines": [ + { + "bbox": [ + 361, + 70, + 489, + 118 + ], + "spans": [ + { + "bbox": [ + 361, + 70, + 489, + 118 + ], + "type": "table", + "html": "
β0.040.080.16
Ours38.838.839.0
Ours*39.039.639.3
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Acc. (%)mIoU (%)
Pascal Context55.815.2
Cityscapes81.218.5
", + "image_path": "f715f292d7d34b0b251bcc246af22e6a6711c6a4bf8dd3739f43cd93a7310a78.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "lines": [ + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "type": "text", + "content": "Table 8. Zero-shot transfer results of our method. The training is performed on ImageNet based on the pre-trained ViT-S model." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 247, + 544, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 247, + 544, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 544, + 270 + ], + "type": "text", + "content": "confirms the robustness of our method against " + }, + { + "bbox": [ + 305, + 247, + 544, + 270 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 247, + 544, + 270 + ], + "type": "text", + "content": ". With this, we set " + }, + { + "bbox": [ + 305, + 247, + 544, + 270 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 247, + 544, + 270 + ], + "type": "text", + "content": " to 0.08 in all experiments." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 270, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 498 + ], + "type": "text", + "content": "Zero-shot transfer. Due to its unsupervised clustering nature, our method does not necessarily rely on target images for training. In this spirit, we perform an initial study where the training is conducted on ImageNet, but the evaluation is conducted on both Pascal Context and Cityscapes. This forms a zero-shot transfer paradigm for unsupervised semantic segmentation. The training lasts for 5 epochs under the same setting in previous studies. We report the results in Table 8. As a reference, the corresponding mIoU of MaskCLIP and ReCo on Cityscapes are 10.0 and 19.3 respectively [39], thus our method provides competitive performance. Nonetheless, the mIoUs for all the methods are much worse than those in previous studies. This is probably because images from ImageNet mostly contain clear foregrounds and single objects, which is in sharp contrast to the complex scene images in Pascal Context and Cityscapes, thus the learned neural eigenfunctions struggle to generalize. A potential remedy for this problem is training on more realistic datasets to reduce the transfer gap." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 498, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 689 + ], + "type": "text", + "content": "Majority voting vs. Hungarian matching. By having the same number of clusters as the ground truth classes and utilizing Hungarian matching, we can maintain a relatively low cluster count and probably enable the assignment of clusters to semantic classes by an expert in practice. We conduct a study on Pascal Context, where the number of clusters is set to match the semantic categories. The resulting mIoU of Hungarian matching is 0.235, slightly lower than the mIoU obtained with majority voting in the same setting (0.277). One possible explanation is that the semantic categories in the benchmarks are often structured, such as a car consisting of the body and the wheels. As a result, the automatically discovered clusters may not correspond one-to-one with the semantic categories. This observation also highlights the need for a larger number of clusters to address this issue effectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "The pre-training method. When using ViT backbones pretrained on ImageNet classification, we observe that stronger" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "558" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 282, + 105 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 282, + 105 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 282, + 105 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 282, + 105 + ], + "type": "table", + "html": "
ViT-BViT-LViT-L/14@336px
37.238.744.0
", + "image_path": "05ef3ab29fbfece50b9b13921dc1cbe07b93488857a7410c9bacdbf9f1ead187.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 106, + 287, + 131 + ], + "lines": [ + { + "bbox": [ + 47, + 106, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 106, + 287, + 131 + ], + "type": "text", + "content": "Table 9. Mean IoU (\\%) of our method on Pascal Context when using various backbones pre-trained by CLIP." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 149, + 288, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 149, + 288, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 149, + 288, + 245 + ], + "type": "text", + "content": "pre-trained models yield worse segmentation performance. We have realized backbones pre-trained by CLIP may exhibit a different tendency because the model outputs are coerced to conform with text supervision rather than being discriminative in recognizing foreground objects. We empirically study this in Table 9. As shown, the backbone pre-trained by CLIP exhibits an increasing trend on mIoU as the model expressiveness increases." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 255, + 119, + 268 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 119, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 119, + 268 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 432 + ], + "type": "text", + "content": "This work establishes an end-to-end NN-based pipeline for spectral clustering for unsupervised semantic segmentation. To achieve that, we build a connectivity graph over image patches using information from both pre-trained models and raw pixels and employ neural eigenfunctions to produce spectral embeddings corresponding to suitable graph kernels. We further quantize the output of the neural eigenfunctions to obtain clustering assignments without resorting to an explicit grouping step. After training, our method can generalize to novel test data easily and reliably. The reliance on pre-trained models gives our method good training efficiency and sufficient expressiveness. Extensive results confirm its superior performance over competing baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 432, + 288, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 288, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 288, + 492 + ], + "type": "text", + "content": "One limitation is that, like most clustering-based methods, our method needs to be exposed to ground-truth semantic masks to match clustering assignments to semantic segments. Introducing text prompts to guide clustering is a potential solution and deserves future investigation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 502, + 145, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 145, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 145, + 516 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 522, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 571 + ], + "type": "text", + "content": "We thank Bernhard Schölkopf for providing constructive suggestions and proofreading the paper. 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In European Conference on Computer Vision (ECCV), 2022." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "561" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_content_list.json b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9ba83c5966b14e5cdcf8725cf2c550afb3f1c979 --- /dev/null +++ b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_content_list.json @@ -0,0 +1,1314 @@ +[ + { + "type": "text", + "text": "Learning Neural Implicit Surfaces with Object-Aware Radiance Fields", + "text_level": 1, + "bbox": [ + 127, + 130, + 841, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yiheng Zhang, Zhaofan Qiu, Yingwei Pan, Ting Yao, and Tao Mei \nUniversity of Science and Technology of China HiDream.ai Inc.", + "bbox": [ + 220, + 180, + 748, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{yihengzhang.chn, zhaofanqiu, panyw.ustc, tingyao.ustc}@gmail.com, tmei@hidream.ai", + "bbox": [ + 122, + 219, + 844, + 233 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7dee064237e669488e5fe0d960d610c69aea1c944822e206f70a9030e497e777.jpg", + "image_caption": [ + "Figure 1: The implicit surfaces learnt via (a) conventional scheme which suffers from noisy background geometry representations. In this work, we introduce (b) an object-aware volumetric scene representation by automatically recognizing rays as object-intersected or object-bypassed, aiming to highlight the key object surface in the foreground. (c) Such object surface benefits a series of applications, e.g., 3D scene composition, object moving/editing, and even skeleton assignment." + ], + "image_footnote": [], + "bbox": [ + 84, + 234, + 869, + 388 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 455, + 313, + 472 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent progress on multi-view 3D object reconstruction has featured neural implicit surfaces via learning high-fidelity radiance fields. However, most approaches hinge on the visual hull derived from cost-expensive silhouette masks to obtain object surfaces. In this paper, we propose a novel Object-aware Radiance Fields (ORF) to automatically learn an object-aware geometry reconstruction. The geometric correspondences between multi-view 2D object regions and 3D implicit/explicit object surfaces are additionally exploited to boost the learning of object surfaces. Technically, a critical transparency discriminator is designed to distinguish the object-intersected and object-bypassed rays based on the estimated 2D object regions, leading to 3D implicit object surfaces. Such implicit surfaces can be directly converted into explicit object surfaces (e.g., meshes) via marching cubes. Then, we build the geometric correspondence between 2D planes and 3D meshes by rasterization, and project the estimated object regions into 3D explicit object surfaces by aggregating the object information across multiple views. The aggregated object information in 3D explicit object surfaces is further projected back to 2D planes, aiming to update 2D object regions and enforce them to be multi-view consistent. Extensive experiments on DTU and BlendedMVS verify the capability of ORF to produce comparable surfaces against the state-of-the-art models that demand silhouette masks.", + "bbox": [ + 73, + 491, + 473, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 455, + 630, + 472 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Multi-view 3D reconstruction, i.e., the task of reconstructing 3D geometry/surface of objects from multi-view 2D images, has played a fundamental challenge to computer vision and computer graphics communities for decades. In the early stage, the mainstream solution is the classical Multi-View Stereo (MVS) [3, 5, 12, 20, 34, 35] that exploits photometric consistency across different camera views to learn explicit geometry representations (e.g., meshes or voxel grids). The ultimate reconstruction relies heavily on the quality of cross-view matching. In practice, such matching often fails to associate objects with sparse textures, resulting in severe artifact or missing parts on surfaces. To address this issue, recent studies turn their focus on investigating how to represent 3D surfaces as implicit geometry representations. Many consider learning a continuous implicit function that formulates neural implicit surfaces in occupancy field [25, 31] or signed distance field [29]. In between, surface rendering techniques [27, 47, 49] are designed to optimize these fields, leading to impressive reconstruction quality via differentiable rendering from images. Nevertheless, learning such implicit geometry representations requires additional object masks of scenes, since the color of each ray is assumed to only correspond to a single point where a surface intersects with this ray. Moreover, the gradient of differentiable rendering is only backpropagated to the local surface near intersection, resulting in a sub-optimal solution for neural implicit surfaces.", + "bbox": [ + 496, + 493, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17893", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To mitigate these limitations of local gradient propagation and the demand for the input object masks during fields optimization, a series of volume rendering based neural radiance fields techniques [9, 28, 41, 46] start to emerge. Recently, the seminal work of NeRF [26] builds up the foundation of volumetric scene in neural radiance fields for view synthesis, and performs classical volume rendering via alpha-compositing colors of the sampled points along rays. The subsequent methods further remould classical volume rendering by imposing implicit surface representations, e.g., occupancy network [28] or signed distance function [9, 41, 46]. These approaches produce more accurate surfaces by reconstructing the holistic scenery. Nevertheless, the learnt implicit surfaces are inevitably composed of rich geometry representations in both foreground and background (Figure 1 (a)), which are not distinguished during radiance fields optimization. Accordingly, existing techniques utilize additional cost-expensive silhouette masks to trim the learnt 3D meshes derived from implicit surfaces. The removal of vertices and/or surfaces outside the visual hull directly highlights the geometry of the key objects in the foreground, yielding object surfaces.", + "bbox": [ + 80, + 90, + 467, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we devise a new Object-aware Radiance Field (ORF), which goes one step further to eliminate the need of the visual hull derived from human-annotated object masks in scenes for learning object surfaces. Our launching point is to introduce an object-aware volumetric scene representation by inferring the foreground/object and background radiance fields on-the-fly. Both the geometric correspondences between multi-view 2D object regions and 3D implicit or explicit object surfaces are exploited to boost the learning of object-aware volumetric scene representation. ORF is henceforth able to encourage the reconstruction of foreground/object geometry without additional 3D supervision of visual hull. Specifically, we first estimate 2D object regions directly based on the multi-view images. Next, on the basis of the estimated 2D object regions, ORF capitalizes on a transparency discriminator to automatically recognize the transparency of each ray in the radiance field. A low transparency indicates that the ray intersects with the object, and rays with high transparency are considered to be object-bypassed. Such predicted transparency of rays is further regarded as prior information to regularize the radiance field in an object-aware manner. Especially, as shown in Figure 1 (b), all the sampled rays are divided into object-intersected rays and object-bypassed rays according to predictions given by the transparency discriminator, leading to 3D implicit object surfaces. After that, we leverage marching cubes to directly convert the 3D implicit object surfaces into 3D explicit object surfaces. The inherent geometric correspondence between 2D planes and 3D explicit object surfaces are thus constructed via rasterization. This geometric correspondence enables the projection from the es", + "bbox": [ + 80, + 433, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "timated 2D object regions into 3D explicit object surfaces, and meanwhile the object information across multiple views are aggregated. Furthermore, ORF projects the aggregated object information in 3D explicit object surfaces back to 2D planes, thereby updating the 2D object regions and enforcing them multi-view consistent. The whole process refines the estimated 2D object regions and 3D implicit/explicit object surfaces, pursuing an object reconstruction without trivial background surfaces.", + "bbox": [ + 503, + 90, + 888, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In sum, we have made the following contributions: (I) ORF designs a transparency discriminator to automatically capture useful object-aware inductive bias, which further supervises radiance fields to learn object-aware geometry reconstruction. (II) ORF additionally mines the inherent geometric correspondence between multi-view 2D object regions and 3D object surfaces to refine them along with volume rendering. (III) We evaluate ORF on two widely-used benchmarks (DTU and BlendedMVS), demonstrating the effectiveness of our proposal.", + "bbox": [ + 503, + 227, + 888, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 503, + 392, + 638, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-view 3D Reconstruction is one of the fundamental tasks in 3D vision, which attempts to reconstruct the 3D geometry from images captured from multiple views. The early works on this task has proceeded along two different dimensions: matching features across views [4, 34] and representing shapes with a voxel grid [1, 5, 10, 20, 30, 36, 38, 39]. The first dimension reconstructs the 3D scenes by matching the pixels with similar appearance, and usually requires the complex designs for fusing depth information [8, 24] or meshing [17, 18]. The second dimension represents the 3D geometry as a volume grid and is limited by the cubic increase of memory requirements. After that, inspired by the recent advance of deep learning techniques, deep neural networks are exploited as an alternative of hand-designed traditional components in 3D reconstruction. For instance, the visual feature for matching [14, 21, 23, 40, 48], depth fusion [11, 33] and depth map prediction [15, 43, 44] can be learnt by neural networks, leading to better performances thanks to the high learning capacity of deep models.", + "bbox": [ + 503, + 417, + 888, + 703 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instead of explicitly reconstructing the 3D geometry, the neural implicit surfaces are introduced to encode the characteristics of 3D scenes by neural networks. Specifically, the surfaces are represented by a neural network which outputs either an occupancy field [25, 31] or a Signed Distance Function (SDF) [29]. In this scheme, the implicit representations of surfaces are learnt via surface rendering [27, 47] which determines the radiance directly on the surface of an object and provides a differentiable rendering formulation using implicit gradients. Recently, Neural Radiance Fields (NeRF) [26] is proposed to implicitly represent scenes by volume rendering which learns alpha-compositing of the radiance field along camera rays, which benefits 3D con", + "bbox": [ + 503, + 704, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17894", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tent creation tasks [51, 6, 7, 42]. The main focus of NeRF is the quality of novel view synthesis, but the geometry is not guaranteed. To promote the quality of learnt surfaces, Unisurf [28] unifies radiance fields and occupancy-based implicit surfaces, enabling plausible reconstruction. VolSDF [46] and NeuS [41] exploit SDF as implicit surface representations and obtain better results. NeuralWarp [9] further boosts up the reconstruction by integrating photo consistency between multi-view images.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work also falls into the category of learning neural implicit surfaces with volume rendering. Despite the progress in improving rendering quality or surface extraction, the way to reconstruct object surfaces without requiring the visual hull derived from object masks in scenes has not been fully explored. The related work of DFFs [19] distills off-the-shelf 2D vision encoders into a 3D feature field to enable the decomposition of scenes conditioning on user-specified queries. Different from [19], our ORF exploits the geometric correspondence between multi-view 2D object regions and 3D object surfaces to automatically separate objects and background, and enhance the quality of the learnt object surfaces.", + "bbox": [ + 75, + 227, + 472, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Object-aware Radiance Fields", + "text_level": 1, + "bbox": [ + 76, + 435, + 354, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section first reviews the standard scheme to represent scenes via radiance fields without the consideration of object region separation (Section 3.1). Next, we describe how the designed transparency discriminator in our ORF distinguishes the object-intersected rays and object-bypassed rays in radiance fields based on the estimated object regions. And then we introduce how to learn an object-aware radiance field by optimizing rays separately with the help of the transparency discriminator (Section 3.2). Furthermore, we design a novel rasterization-based aggregation mechanism to additionally construct the geometric correspondence between 2D object regions and 3D object surfaces via rasterization. Such geometric correspondence enables the aggregation of object information from 2D planes to 3D explicit object surfaces. The aggregated object information in turn updates the 2D object regions in a multi-view consistent manner, pursuing a more high-fidelity object reconstructions (Section 3.3). Figure 2 depicts an overview of our ORF architecture.", + "bbox": [ + 75, + 460, + 472, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Representing Scene via Radiance Fields", + "text_level": 1, + "bbox": [ + 76, + 756, + 418, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural radiance field and its recent variants aim to represent 3D scenes by two implicit functions, i.e., geometry function and radiance function, which are approximated via two individual neural networks. The geometry network models the geometric structure of 3D scenes, and the radiance network encodes the color emitted by any region in space from all directions. The two networks represent the characteristics in the 3D scene and codetermine the ren-", + "bbox": [ + 75, + 780, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dered novel views. When rendering the target view $\\mathbf{R}$ taken from the direction $\\mathbf{d}$ , the rendered color $\\mathbf{R}(\\mathbf{p})$ of each pixel $\\mathbf{p}$ is computed by both geometry network $\\mathcal{G}$ and radiance network $\\mathcal{C}$ in a differentiable way. Specifically, we first sample $N_{p}$ points $\\mathbf{x}_{i}$ , $i = 1,\\dots,N_{p}$ along the corresponding ray $\\Re (\\mathbf{p})$ going through the camera center and the target pixel $\\mathbf{p}$ . Note that here we omit the notations of target pixel for simplicity. The surface normal $\\mathbf{n}_i$ , the occupancy value $\\alpha_{i}$ and the radiance value $\\mathbf{c}_i$ are measured by the geometry network $\\mathcal{G}$ and the radiance network $\\mathcal{C}$ as", + "bbox": [ + 496, + 90, + 893, + 242 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {n} _ {i}, \\alpha_ {i} = \\mathcal {G} (\\mathbf {x} _ {i}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 247, + 890, + 268 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {i} = \\mathcal {C} (\\mathbf {x} _ {i}, \\mathbf {n} _ {i}, \\mathbf {d}).\n$$\n", + "text_format": "latex", + "bbox": [ + 638, + 268, + 751, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The rendering of the scene at pixel $\\mathbf{p}$ is approximated as a weighted summation of radiance values $\\mathbf{c}_i$ at each sampled point by using the occupancy values as the weights:", + "bbox": [ + 496, + 287, + 893, + 333 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R} (\\mathbf {p}) = \\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} (1 - \\alpha_ {j}) \\mathbf {c} _ {i}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 339, + 890, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\prod_{j < i}(1 - \\alpha_j)$ is to simulate the occlusion caused by the opaque pixels in front of the target pixel. As a practical choice, we utilize transformed Signed Distance Field (SDF) encoding [41, 46] as the geometry function. Eq. (2) is actually the discrete approximation of an integral along the camera ray by sampling a limited number of points. The sampling strategies have been discussed in [26, 28, 41, 46] to improve the geometry estimation.", + "bbox": [ + 496, + 385, + 893, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At training stage, the two neural networks are jointly optimized by encouraging the reconstruction of the given views of the 3D scene. Given one reference view $\\mathbf{I}^r$ , the reconstruction loss for $\\mathbf{p} \\in \\mathbf{I}^r$ is calculated by the L1 distance between the reference view $\\mathbf{I}^r$ and the neural volume rendering results $\\mathbf{R}$ as", + "bbox": [ + 496, + 507, + 893, + 597 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {L} _ {\\text {r e c}} = \\left| \\mathbf {I} ^ {r} (\\mathbf {p}) - \\mathbf {R} (\\mathbf {p}) \\right|, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 604, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $|\\cdot|$ is the L1 loss. This loss function simply treats each camera ray corresponding to $\\mathbf{p}$ equally and constrains the difference between the input pixel and the rendered result, while ignoring the distinction of rays that either intersect or bypass the objects. As a result, the implicit 3D model often contains some trivial surfaces of the background regions (Figure 1), and thus requires the object masks derived visual hull to execute an additional trimming step at inference.", + "bbox": [ + 496, + 627, + 893, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Learning Object-aware Radiance Fields", + "text_level": 1, + "bbox": [ + 500, + 756, + 843, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To alleviate these issues, we propose to automatically distinguish the object-intersected and object-bypassed rays, making the learnt radiance fields object-aware without manually annotating the visual hull for each scene. To materialize this idea, here we first elaborate how to achieve the high-quality ray/transparency prediction via a devised transparency discriminator (Figure 2 (a)), followed by the learning scheme with different objectives (Figure 2 (b)).", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17895", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7c500a76086c48b7594715237c5bb4e7dd99e1fd88e869f558d78b38a4725f93.jpg", + "image_caption": [ + "Figure 2: An overview of the proposed Object-aware Radiance Fields (ORF) framework for learning neural implicit surfaces." + ], + "image_footnote": [], + "bbox": [ + 117, + 87, + 851, + 415 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transparency Discriminator. Formally, we consider the ray $\\Re (\\mathbf{p})$ derived from pixel $\\mathbf{p}$ of the reference view $\\mathbf{I}^r$ . One intuitive way to inspect whether the $\\Re (\\mathbf{p})$ intersects with the object is to predict the probability that the pixel $\\mathbf{p}$ belongs to the estimated object regions $\\mathbf{O}^r$ from the perspective of $\\mathbf{I}^r$ . Note that here we employ an off-the-shelf salient object segmentation model [32] to learn the prior knowledge of generic salient objects. Replacing the saliency model with other segmentation models is flexible to generalize to other reconstruction scenarios. Such saliency map generated from $\\mathbf{I}^r$ provides coarse object information that indicates the 2D object regions $\\mathbf{O}^r$ . However, the complex object appearance and challenging variation of views probably affect the quality of object information. As such, we further design a transparency discriminator that jointly exploits the 2D object regions estimated from different views for ray discrimination in radiance field.", + "bbox": [ + 75, + 444, + 472, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In particular, given a reference image $\\mathbf{I}^r$ and multiple source images $(\\mathbf{I}_i^s,i = 1,\\dots ,N_s)$ captured from different viewpoints, we can roughly estimate the object regions in each image individually via salient object segmentation. Let $\\mathbf{O}^r$ and $\\mathbf{O}_i^s$ $(i = 1,\\dots ,N_{s})$ denote the corresponding 2D object regions. We start from the ray $\\Re (\\mathbf{p})$ corresponding to pixel $\\mathbf{p}\\in \\mathbf{I}^r$ that intersects with the implicit surface for the first time at point $\\mathbf{x}^{+}$ in the radiance field. To locate the point $\\mathbf{x}^{+}$ in the world coordinates, we sample points along $\\Re (\\mathbf{p})$ from its corresponding camera center and feed the sampled points into the geometry network $\\mathcal{G}$ in order. Then, following [46], the signed distance between each sampled point and its nearest surface is derived from the output of", + "bbox": [ + 75, + 704, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{G}$ . The first point we sampled that has a positive signed distance is regarded as $\\mathbf{x}^{+}$ .", + "bbox": [ + 496, + 444, + 890, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After that, we mine the geometric correspondence between 3D implicit surfaces and 2D planes by projecting the point $\\mathbf{x}^{+}$ into the 2D plane of each source image. By denoting the projection as $\\pi_i^s (\\mathbf{x}^+)$ $(i = 1,\\dots ,N_{s})$ in source image coordinates, we formulate $\\pi_i^s (\\mathbf{x}^+)$ as:", + "bbox": [ + 496, + 474, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right) = K _ {i} ^ {s} \\left(R _ {i} ^ {s} \\mathbf {x} ^ {+} + \\mathbf {t} _ {i} ^ {s}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 556, + 890, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $K_{i}^{s}$ is the internal calibration matrix of the $i$ -th source camera, and $(R_{i}^{s},\\mathbf{t}_{i}^{s})$ are the extrinsic parameters of the camera $(R_{i}^{s}:3\\times 3$ rotation matrix, $\\mathbf{t}_i^s$ : 3-dim translation vector). In this way, each projection associates the point $\\mathbf{x}^{+}$ in world coordinates to pixels in source images.", + "bbox": [ + 496, + 582, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the estimated 2D object regions from multiple views $\\mathbf{O}^T$ and $\\mathbf{O}_i^s$ ( $i = 1, \\dots, N_s$ ), a transparency discriminator is devised to predict the transparency $\\mathcal{T}(\\Re(\\mathbf{p}))$ . Here the transparency can be interpreted as the probability that the ray $\\Re(\\mathbf{p})$ bypasses the target object. Specifically, in an effort to take all 2D object regions into account, we measure the transparency for $\\Re(\\mathbf{p})$ by averaging the probabilities of pixels belonging to objects in multiple views with regard to the same point $\\mathbf{x}^+$ :", + "bbox": [ + 496, + 657, + 890, + 792 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {T} (\\Re (\\mathbf {p})) = 1 - \\frac {\\mathbf {O} ^ {r} (\\mathbf {p}) + \\sum_ {i = 1} ^ {N _ {s}} \\mathbf {O} _ {i} ^ {s} \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}{1 + N _ {s}}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 801, + 890, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Such formulation assumes that the intersection point $\\mathbf{x}^{+}$ are observed by each source camera without any occlusion. But in practice, the intersection points may be projected outside of the source images or occluded by other surfaces which", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17896", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "are closer to the source cameras. To tackle this issue, we extend the formulation in Eq. (5) with a binary indicator $V(\\cdot)$ :", + "bbox": [ + 76, + 90, + 468, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {T} (\\Re (\\mathbf {p})) = 1 - \\frac {\\mathbf {O} ^ {r} (\\mathbf {p}) + \\sum_ {i = 1} ^ {N _ {s}} V \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right) \\mathbf {O} _ {i} ^ {s} \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}{1 + \\sum_ {i = 1} ^ {N _ {s}} V \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 128, + 468, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We set $V(\\pi_i^s (\\mathbf{x}^+))$ as 1 when $\\mathbf{x}^{+}$ is within the maximum area that can be captured by the camera of $\\mathbf{I}_i^s$ and meanwhile it is also the first intersection between ray $\\Re (\\pi_i^s (\\mathbf{x}^+))$ and implicit surfaces. In the implementation, we first check if the $\\pi_i^s (\\mathbf{x}^+)$ locates inside the source image $\\mathbf{I}_i^s$ . Then we estimate the first intersection point of ray $\\Re (\\pi_i^s (\\mathbf{x}^+))$ and check whether it is nearby $\\mathbf{x}^{+}$ . Accordingly, our transparency discriminator is able to identify an object-intersected ray with low transparency, and a ray with high transparency is considered to bypass the object.", + "bbox": [ + 75, + 174, + 468, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Objective. After classifying each ray via the transparency discriminator, we assign different objectives to different kinds of rays, pursuing an object-aware radiance field. Figure 2 (b) shows an overview of the learning scheme for our ORF. In general, given a group of multiview images of the target object, camera rays associated with pixels in images are utilized for volume rendering to optimize the radiance field, as described in Section 3.1. In the radiance field, a ray may terminate at the surface of objects (blue and golden), the ground plane (orange), or the point at infinity (green). To differentiate these kinds of rays, we feed them into a transparency discriminator and classify them as object-intersected or object-bypassed according to object regions estimated from the multi-view images.", + "bbox": [ + 75, + 325, + 468, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, for the object-intersected ray whose predicted transparency is less than 0.5, we learn in advance that the ray will go through the target object. Hence, we additionally constrain the ray to have high occupancy as a supplement to the reconstruction loss in Eq. (3):", + "bbox": [ + 75, + 537, + 468, + 612 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {L} _ {\\text {o c c}} = - \\log \\left(\\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} \\left(1 - \\alpha_ {j}\\right)\\right), \\mathcal {T} (\\Re (\\mathbf {p})) \\leq 0. 5. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 619, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In contrast, for the object-bypassed ray with $\\mathcal{T}(\\Re (\\mathbf{p})) > 0.5$ , the occupancy is enforced to be small to ensure that no trivial surface appears in the background regions:", + "bbox": [ + 76, + 666, + 468, + 712 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {L} _ {\\text {o c c}} = - \\log \\left(1 - \\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} \\left(1 - \\alpha_ {j}\\right)\\right), \\mathcal {T} (\\Re (\\mathbf {p})) > 0. 5. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 718, + 468, + 757 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, we do not require the rendering of object-bypassed ray to reconstruct the input color, which means the reconstruction loss $|\\mathbf{I}^r (\\mathbf{p}) - \\mathbf{R}(\\mathbf{p})|$ is omitted when $\\Re (\\mathbf{p})$ is object-bypassed.", + "bbox": [ + 76, + 763, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Hence, the overall objective function integrates the reconstruction loss between the reference view and the rendered results in Eq. (3), and the occupancy regularization loss in Eq. (7) and Eq. (8). To further enhance the quality of the learnt surfaces, we also consider two extra losses", + "bbox": [ + 75, + 825, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "following the recent works. The first one is the eikonal loss $\\mathrm{L}_{\\mathrm{eik}}$ [13] which encourages the geometry network to output a function similar to a signed distance field. The second one is the patch warping loss $\\mathrm{L}_{\\mathrm{warp}}$ [9] to improve the reconstruction ability by warping the existing patches from the reference views. We measure the overall objective as:", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {L} = \\lambda_ {1} \\mathrm {L} _ {\\text {r e c}} + \\lambda_ {2} \\mathrm {L} _ {\\text {o c c}} + \\lambda_ {3} \\mathrm {L} _ {\\text {e i k}} + \\lambda_ {4} \\mathrm {L} _ {\\text {w a r p}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 199, + 890, + 215 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_1 = 1$ , $\\lambda_2 = 0.1$ , $\\lambda_3 = 0.1$ , and $\\lambda_4 = 1$ are the trade-off parameters. Here we set $\\lambda_3$ and $\\lambda_4$ following [9], and $\\lambda_2$ is determined through experimental study.", + "bbox": [ + 496, + 232, + 890, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Rasterization-based Aggregation", + "text_level": 1, + "bbox": [ + 500, + 295, + 785, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The new rasterization-based aggregation mechanism additionally exploits the geometric correspondence between 3D explicit surfaces and 2D planes. This design aims to further refine the quality of the estimated 2D object regions and make them multi-view consistent.", + "bbox": [ + 496, + 321, + 890, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Technically, as shown in Figure 2 (c), the mechanism first converts the 3D implicit surfaces (i.e., geometry network $\\mathcal{G}$ ) into explicit surfaces (a explicit polygonal 3D representation like mesh) via marching cubes [22]. After that, we compute the projection from the 3D explicit surfaces (i.e., triangles) to the pixels of 2D images $\\mathcal{I}$ by rasterization. Here the rasterization refers to the typical process of taking a triangle and figuring out which pixels it covers [37]. Formally, let $\\Delta^j$ denote the $j$ -th triangle in the mesh, which corresponds to a set of pixels $\\mathcal{P}_i^j \\subseteq \\mathbf{O}_i$ in the $i$ -th view. Note that the pixel set $\\mathcal{P}_i^j$ is set as empty when $\\Delta^j$ is invisible to the camera due to invalid projections (e.g., the triangle is projected outside the image) or occlusion. Such correspondence between triangles and pixels enables the aggregation of the object information of 2D object regions into 3D explicit surface $\\Delta^j$ . In particular, we aggregate the object probabilities of all the pixels belonging to the triangle $\\Delta^j$ from multiple views, yielding the triangle-level object probability of $\\mathbf{O}_{agg}(\\Delta^j)$ :", + "bbox": [ + 496, + 398, + 892, + 689 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {O} _ {a g g} \\left(\\Delta^ {j}\\right) = \\frac {\\sum_ {i = 1} ^ {| \\mathcal {I} |} \\sum_ {\\mathbf {p} \\in \\mathcal {P} _ {i} ^ {j}} \\mathbf {O} _ {i} (\\mathbf {p})}{\\epsilon + \\sum_ {i = 1} ^ {| \\mathcal {I} |} \\sum_ {\\mathbf {p} \\in \\mathcal {P} _ {i} ^ {j}} \\mathbf {1}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 705, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\epsilon$ is a constant term added to the denominator for numerical stability. After traversing all the 3D surfaces with the triangle-level aggregation (Eq. (10)), we re-project the triangle-level object probabilities of 3D surfaces back to 2D images. More specifically, for one pixel $\\mathbf{p} \\in \\mathcal{P}_i^j \\subseteq \\mathbf{O}_i$ in each viewpoint, the object probability of $\\mathbf{O}_i(\\mathbf{p})$ is updated as the same triangle-level object probability $\\mathbf{O}_{agg}(\\Delta^j)$ . By doing so, the updated 2D multi-view object regions are enforced to be consistent across different views.", + "bbox": [ + 496, + 763, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17897", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8f0df57939f303a4d71d3dfb42e7dbeb64af8476adb1c941d6ab817663be16ec.jpg", + "table_caption": [ + "Table 1: Comparisons of our ORF with other volume rendering techniques on DTU dataset for learning neural implicit surfaces. Here all the involved techniques do not use object masks as additional supervision for training. The top part reports the reconstruction performances when using object masks to trim the estimated meshes, and the bottom part directly compares the reconstruction performances of the estimated meshes without using object masks. The best performances are marked in bold and the second-best results are underlined." + ], + "table_footnote": [], + "table_body": "
ScanID243740556365698397105106110114118122Mean
with object masks: using the visual hull derived from human-annotated object masks for mesh trimming
NeRF [26]1.901.601.850.582.281.271.471.672.051.070.882.531.061.150.961.49
Unisurf [28]1.321.361.720.441.350.790.801.491.370.890.591.470.460.590.621.02
VolSDF [46]1.141.260.810.491.250.700.721.291.180.700.661.080.420.610.550.86
NeuS [41]1.001.370.930.431.100.650.571.481.090.830.521.200.350.490.540.84
NeuralWarp [9]0.490.710.380.380.790.810.821.201.060.680.660.740.410.630.510.68
without object masks: without mask-dependent trimming at inference
VolSDF [46]1.251.701.310.912.901.080.901.621.241.090.701.390.590.710.871.22
NeuS [41]1.591.981.440.951.820.740.641.631.301.410.591.330.440.510.541.13
NeuralWarp [9]0.972.541.520.412.540.740.791.061.531.400.750.720.390.570.621.10
ORF0.560.690.430.450.740.850.750.760.860.710.610.690.380.810.520.65
", + "bbox": [ + 76, + 148, + 893, + 335 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 344, + 209, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the effectiveness of ORF on DTU [16] and BlendedMVS [45] for multi-view 3D reconstruction. We first show both qualitative and quantitative results of ORF in comparison to existing techniques on DTU. Next, we conduct experimental analysis to validate the designs in ORF. Finally, we perform the qualitative comparison over samples derived from BlendedMVS for evaluation.", + "bbox": [ + 75, + 369, + 470, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 484, + 387, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DTU is a popular multi-view 3D reconstruction benchmark, which consists of 80 scenes with large variability in materials, appearance and geometry of objects. For each scene, the dataset provides 49 or 64 images (resolution: $1,600 \\times 1,200$ ) captured from multiple camera views. The ground-truth point cloud of each scene is acquired with laser sensor. In our experiments, we follow [9, 28, 41, 46, 47] to use the selected 15 scenes in DTU for comparison. We strictly follow [9, 41] and use the official evaluation code of DTU [16] to compute the quantitative metrics. Specifically, the point clouds of objects (w/o background) in DTU are regarded as ground truth (GT). For a reconstructed mesh, we sample points on triangle surfaces in an evenly spaced manner (radius=0.2 as in [16]). Then, we report the final reconstruction score by averaging the accuracy and completeness of the sampled points (SP) (i.e., the chamfer distances of $\\mathrm{SP} \\rightarrow \\mathrm{GT}$ and $\\mathrm{GT} \\rightarrow \\mathrm{SP}$ ). It is also worthy to note that existing volume rendering techniques commonly use the additional object regions manually annotated by [27, 47] to trim the predicted mesh for only evaluating the reconstruction inside the visual hull. In contrast, our ORF learns an object-aware volumetric scene representation and directly constructs the 3D geometry of objects in the scene without the use of the visual hull derived from annotated object regions of scenes.", + "bbox": [ + 75, + 507, + 468, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "BlendedMVS is a large-scale benchmark for multi-view 3D reconstruction, including 113 scenes with multi-view", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "images. Compared to DTU, the backgrounds in BlendedMVS are more complex. We select samples from the lowres set of BlendedMVS, and each scene is equipped with 24 to 64 images (resolution: $768 \\times 576$ ). Note that the ground truth of object regions for each image is not available.", + "bbox": [ + 496, + 344, + 890, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. The whole network of ORF is built over VolSDF [46], and we adopt the same architecture as in existing volume rendering methods [28, 46, 47] for fair comparison. The whole network uses sphere initialization [2]. During training, we train our ORF with a two-stage strategy. We first optimize the network with the reconstruction loss and eikonal loss under the same setting in VolSDF (100k iterations with learning rate exponentially decayed from 5e-4 to 5e-5, batch size: 1,024 rays). Next, the network is fine-tuned with the overall objective in Eq. (9) (100k iterations with learning rate of 5e-4, batch size: 512 rays). The object probability is calculated by the transparency discriminator in each forward pass using the latest radiance field. The mesh extraction for rasterization-based aggregation is only conducted once after the first training stage of ORF.", + "bbox": [ + 496, + 422, + 892, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison on DTU Dataset", + "text_level": 1, + "bbox": [ + 500, + 679, + 759, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Results. We compare with several neural surface reconstruction techniques under two different evaluation settings for fair comparison: 1) baselines using the visual hull derived from human-annotated object masks for mesh trimming, 2) all re-implemented SDF-based baselines and our ORF without mask-dependent trimming at inference. Such two settings are denoted as with/without object masks, respectively. All the mentioned baselines are grouped into three directions: volume rendering with classical radiance fields [26], occupancy network [28], and SDF-based (Signed Distance Function) fields [46, 41, 9]. Table 1 summarizes the performance comparisons on each evaluation scenario. Note that all baselines and our ORF", + "bbox": [ + 496, + 704, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17898", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5aceae4d2f16a4f9917e97daab7415ea3ecaca47b2bfe93a20a50ab0595bc548.jpg", + "image_caption": [ + "Figure 3: Comparisons on qualitative results of our ORF with other neural radiance fields techniques on DTU dataset for 3D geometry reconstruction with or without object masks at inference. * denotes our implementation of VolSDF." + ], + "image_footnote": [], + "bbox": [ + 106, + 71, + 859, + 362 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "do not use human-annotated object masks of scenes to optimize geometry/radiance nets during training. At inference, these baselines commonly require masks to remove the background of the learnt mesh. Instead, ORF can directly produce the object mesh without masks.", + "bbox": [ + 75, + 400, + 468, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In general, our ORF exhibits better reconstruction quality against all these baselines. Remarkably, ORF achieves 0.65 in the metric of Chamfer distance without the use of the visual hull derived from object masks in scenes, which is better than the reconstruction accuracy (0.68) of NeuralWarp when exploiting demands object masks at inference. The results generally highlight the key advantage of learning object-aware geometry reconstruction for neural implicit surfaces. Specifically, under the evaluation scenario with object masks, NeRF produces unsatisfactory reconstruction results since the lack of 3D geometry constraints. Unisurf unifies volume/surface rendering and enables better results. VolSDF, NeuS, and NeuralWarp exploit SDF and obtain promising reconstructions. Nevertheless, a performance drop is observed for each SDF-based method when object masks are unavailable at inference, since the primary estimated mesh contains more trivial geometry of the background. In contrast, our ORF achieves competitive reconstruction accuracy through learning an object-aware radiance field without the use of object masks derived visual hull. This confirms the effectiveness of exploring object awareness via transparency discriminator and rasterization-based aggregation.", + "bbox": [ + 75, + 477, + 470, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results. We then visually examine the reconstruction quality of our proposal by comparing ORF with three SDF-based approaches (VolSDF, NeuS, NeuralWarp) on five selected scenes from DTU dataset. Figure 3 shows the qualitative results of the reconstructed meshes.", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Note that here we show the reconstruction results of the two different evaluation settings (with or without object masks at inference for trimming estimated meshes). In general, all the three approaches reconstruct high-fidelity object surfaces after mask-dependent mesh trimming. In between, by constraining volume rendering with photo-consistency objective across multiple views, NeuralWarp produces more accurate surfaces with high-fidelity details (e.g., the bricks with sparse textures in the first two scenes) against VolSDF and NeuS. Furthermore, when the object masks are unavailable, the output meshes of each baselines become noisy with more trivial geometry and even some artifact of the background. In contrast, under this challenging setting, our ORF performs visually on par with the NeuralWarp, while requiring no object mask dependent mesh trimming at inference. The results again validate the merit of our ORF.", + "bbox": [ + 496, + 400, + 890, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Experimental Analysis", + "text_level": 1, + "bbox": [ + 500, + 650, + 709, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study. Here we investigate how each design in our ORF influences the overall reconstruction performance. Table 2 and Figure 4 details the performances and the corresponding qualitative results across different ablated runs of ORF, respectively. We start from a basic SDF-based radiance field without ray discrimination (i.e., NeuralWarp), which achieves 1.10 of Chamfer distance. The estimated mesh of this basic model inevitably contains trivial background geometry. Next, by solely using the outputs of salient object segmentation (Saliency) to distinguish object-intersected and object-bypassed rays, we observe a clear performance boost and the background is effectively screened. However, the independently estimated object probability of each 2D object region may be inaccurate and inconsistent across different viewpoints, resulting in error", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17899", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ae503504957e73fe640e3c486245b195e8b45d24fb8573a065ef2fc0250b8c40.jpg", + "table_caption": [ + "Table 2: Ablation study on each design in ORF on DTU dataset." + ], + "table_footnote": [], + "table_body": "
Transparency Discriminator Saliency +Multiview +VerifierRasterization-based AggregationChamfer Distance
1.10
✓0.90
✓✓0.87
✓✓✓0.76
✓✓✓✓0.65
", + "bbox": [ + 81, + 95, + 465, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f369cdae7ab9788a9f664daac369815d146466599f36090b7fd00d1caa684a92.jpg", + "image_caption": [ + "Figure 4: Comparisons on qualitative results by using different ablated runs of our ORF on DTU dataset for 3D geometry reconstruction object masks dependent mesh trimming at inference." + ], + "image_footnote": [], + "bbox": [ + 94, + 223, + 210, + 315 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/99adba7364705943acf8cc1a548ad6623bd834036f419fd3c8222d400a33c70b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 222, + 224, + 272, + 315 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a38e004a07bb14e98b10ddb1f33fbd3dc5ec459b756a11437ca5378b1a284735.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 284, + 224, + 339, + 315 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/19a6e461862444af3a7c901462a917a493e554d188063e552dc19c37a7a6a37a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 348, + 224, + 401, + 315 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c90c4423ca0fb340dce470aa820a18c97912777d18bdf022620d0d254934ae69.jpg", + "image_caption": [ + "Figure 5: Comparisons on qualitative results of our ORF with other techniques on BlendedMVS for 3D geometry reconstruction without object masks at inference. * denotes our re-implemented VolSDF without the hand-crafted parametrization in NeRF++." + ], + "image_footnote": [], + "bbox": [ + 413, + 224, + 467, + 315 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "accumulation and holes in the reconstructions. To address this issue, we enhance the strategy of transparency discrimination by jointly exploiting the 2D object regions estimated from multiple views (Multiview), leading to slightly better reconstruction. We then leverage the projection verification strategy (Verifier) to screen out invalid projections (e.g., the points are projected outside of the source images or occluded by other surfaces), which further boosts up the reconstruction. Finally, by capitalizing on Rasterization-based Aggregation to refine the estimated 2D object regions, the mIoU of object regions is improved from $94\\%$ to $97\\%$ and ORF achieves the highest reconstruction quality.", + "bbox": [ + 75, + 371, + 468, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of the Trade-off Parameter $\\lambda_{2}$ . To clarify the effect of the trade-off parameter $\\lambda_{2}$ in Eq. (9), we detail the reconstruction performances (i.e., Chamfer distances) with different trade-off parameters in Table 3. In the extreme case of $\\lambda_{2} = 0$ , no occupancy regularization objective for foreground and background rays is utilized and the whole model degenerates to the conventional SDF-based approach. When enlarging $\\lambda_{2}$ as 0.05, a better reconstruction accuracy is attained, which basically demonstrates that the foreground-aware inductive bias benefits volume rendering. The performance change is relatively smooth when $\\lambda_{2}$ varies in the range from 0.05 to 0.20, and the best reconstruction accuracy is attained when $\\lambda_{2} = 0.10$ . Furthermore, the reconstruction accuracy slightly decreases when $\\lambda_{2} \\geq 0.30$ . We speculate that this may be the result of amplifying the noise of ray discrimination if we set a higher weight to occupancy regularization objective.", + "bbox": [ + 75, + 551, + 468, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of the Saliency Model's Performance. To verify how the quality of saliency influences the reconstruction, we perform salient object segmentation using another two models and obtain additional two versions of saliency maps. We evaluate the three different versions of saliency for both reconstruction and segmentation tasks on DTU (re", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/400ba7a582eac5ccbe6d9fc0ee8dddb4aa22739b9df5fb7bd8858f32b492ab38.jpg", + "table_caption": [ + "Table 3: Effect of the trade-off parameter ${\\lambda }_{2}$ in ORF on DTU." + ], + "table_footnote": [], + "table_body": "
λ20.000.050.100.200.300.400.50
Chamfer Dist.1.100.660.650.670.690.700.71
Image
VolSDF*
Neural \nWarp
ORF
", + "bbox": [ + 506, + 95, + 890, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "construction: 0.65, 0.67, 0.67; segmentation: $94\\%$ , $93\\%$ , $91\\%$ mean IoU). The results show that the saliency segmentation performance on DTU has almost saturated, and the reconstruction performances of ORF only fluctuate within the range of 0.02, which eases the difficulty on choosing saliency segmentation model in practice.", + "bbox": [ + 498, + 343, + 890, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Comparison on BlendedMVS Dataset", + "text_level": 1, + "bbox": [ + 500, + 444, + 823, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 5 further showcases the geometry reconstruction results with different techniques for six scenes in BlendedMVS. It is worthy to note that VolSDF originally utilizes an additional hand-crafted parametrization as in $\\mathrm{NeRF}++$ [50] to tackle the complex backgrounds by modeling the volume outside a radius 3 sphere with another NeRF network. For fair comparison, here we re-implement VolSDF by removing this parametrization. Similar to the observations on DTU under the setting without object masks, both VolSDF and NeuralWarp produce high-fidelity object surfaces, while more trivial background geometry is inevitably included. Instead, our ORF nicely removes the trivial geometry and performs nearly on par with these approaches.", + "bbox": [ + 498, + 468, + 890, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 678, + 625, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we circumvent the use of object masks derived visual hull, and shape a new paradigm of learning object-aware geometry reconstruction for neural implicit surfaces. To verify our claim, we novelly remould the classical neural radiance fields by involving a new transparency discriminator to distinguish object-intersected and object-bypassed rays on-the-fly. Such ray discrimination serves as object-aware inductive bias to enable a reconstruction of 3D geometry of the key object in the scene. Moreover, we exploit the geometric correspondence between multi-view 2D object regions and 3D implicit/explicit surfaces to facilitate the learning of object surfaces. Extensive experiments conducted on DTU and BlendedMVS validate our proposal.", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17900", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Motilal Agrawal and Larry S Davis. A probabilistic framework for surface reconstruction from multiple images. In CVPR, 2001.", + "[2] Matan Atzmon and Yaron Lipman. Sal: Sign agnostic learning of shapes from raw data. In CVPR, 2020.", + "[3] Connelly Barnes, Eli Shechtman, Adam Finkelstein, and Dan B Goldman. Patchmatch: A randomized correspondence algorithm for structural image editing. ACM Trans. on Graphics, 2009.", + "[4] Michael Bleyer, Christoph Rhemann, and Carsten Rother. 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Nerf++: Analyzing and improving neural radiance fields. arXiv preprint arXiv:2010.07492, 2020.", + "[51] Zicheng Zhang, Yinglu Liu, Congying Han, Yingwei Pan, Tiande Guo, and Ting Yao. Transforming radiance field with lipschitz network for photorealistic 3d scene stylization. In CVPR, 2023." + ], + "bbox": [ + 78, + 90, + 467, + 757 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17902", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_model.json b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..baa5f6c01b3a6609bd8090a5ab9d337d217ee591 --- /dev/null +++ b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_model.json @@ -0,0 +1,1859 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.129, + 0.131, + 0.842, + 0.154 + ], + "angle": 0, + "content": "Learning Neural Implicit Surfaces with Object-Aware Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.181, + 0.749, + 0.217 + ], + "angle": 0, + "content": "Yiheng Zhang, Zhaofan Qiu, Yingwei Pan, Ting Yao, and Tao Mei \nUniversity of Science and Technology of China HiDream.ai Inc." + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.22, + 0.846, + 0.234 + ], + "angle": 0, + "content": "{yihengzhang.chn, zhaofanqiu, panyw.ustc, tingyao.ustc}@gmail.com, tmei@hidream.ai" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.236, + 0.87, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.389, + 0.894, + 0.445 + ], + "angle": 0, + "content": "Figure 1: The implicit surfaces learnt via (a) conventional scheme which suffers from noisy background geometry representations. In this work, we introduce (b) an object-aware volumetric scene representation by automatically recognizing rays as object-intersected or object-bypassed, aiming to highlight the key object surface in the foreground. (c) Such object surface benefits a series of applications, e.g., 3D scene composition, object moving/editing, and even skeleton assignment." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.457, + 0.314, + 0.473 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.492, + 0.474, + 0.884 + ], + "angle": 0, + "content": "Recent progress on multi-view 3D object reconstruction has featured neural implicit surfaces via learning high-fidelity radiance fields. However, most approaches hinge on the visual hull derived from cost-expensive silhouette masks to obtain object surfaces. In this paper, we propose a novel Object-aware Radiance Fields (ORF) to automatically learn an object-aware geometry reconstruction. The geometric correspondences between multi-view 2D object regions and 3D implicit/explicit object surfaces are additionally exploited to boost the learning of object surfaces. Technically, a critical transparency discriminator is designed to distinguish the object-intersected and object-bypassed rays based on the estimated 2D object regions, leading to 3D implicit object surfaces. Such implicit surfaces can be directly converted into explicit object surfaces (e.g., meshes) via marching cubes. Then, we build the geometric correspondence between 2D planes and 3D meshes by rasterization, and project the estimated object regions into 3D explicit object surfaces by aggregating the object information across multiple views. The aggregated object information in 3D explicit object surfaces is further projected back to 2D planes, aiming to update 2D object regions and enforce them to be multi-view consistent. Extensive experiments on DTU and BlendedMVS verify the capability of ORF to produce comparable surfaces against the state-of-the-art models that demand silhouette masks." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.457, + 0.631, + 0.473 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Multi-view 3D reconstruction, i.e., the task of reconstructing 3D geometry/surface of objects from multi-view 2D images, has played a fundamental challenge to computer vision and computer graphics communities for decades. In the early stage, the mainstream solution is the classical Multi-View Stereo (MVS) [3, 5, 12, 20, 34, 35] that exploits photometric consistency across different camera views to learn explicit geometry representations (e.g., meshes or voxel grids). The ultimate reconstruction relies heavily on the quality of cross-view matching. In practice, such matching often fails to associate objects with sparse textures, resulting in severe artifact or missing parts on surfaces. To address this issue, recent studies turn their focus on investigating how to represent 3D surfaces as implicit geometry representations. Many consider learning a continuous implicit function that formulates neural implicit surfaces in occupancy field [25, 31] or signed distance field [29]. In between, surface rendering techniques [27, 47, 49] are designed to optimize these fields, leading to impressive reconstruction quality via differentiable rendering from images. Nevertheless, learning such implicit geometry representations requires additional object masks of scenes, since the color of each ray is assumed to only correspond to a single point where a surface intersects with this ray. Moreover, the gradient of differentiable rendering is only backpropagated to the local surface near intersection, resulting in a sub-optimal solution for neural implicit surfaces." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17893" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.424 + ], + "angle": 0, + "content": "To mitigate these limitations of local gradient propagation and the demand for the input object masks during fields optimization, a series of volume rendering based neural radiance fields techniques [9, 28, 41, 46] start to emerge. Recently, the seminal work of NeRF [26] builds up the foundation of volumetric scene in neural radiance fields for view synthesis, and performs classical volume rendering via alpha-compositing colors of the sampled points along rays. The subsequent methods further remould classical volume rendering by imposing implicit surface representations, e.g., occupancy network [28] or signed distance function [9, 41, 46]. These approaches produce more accurate surfaces by reconstructing the holistic scenery. Nevertheless, the learnt implicit surfaces are inevitably composed of rich geometry representations in both foreground and background (Figure 1 (a)), which are not distinguished during radiance fields optimization. Accordingly, existing techniques utilize additional cost-expensive silhouette masks to trim the learnt 3D meshes derived from implicit surfaces. The removal of vertices and/or surfaces outside the visual hull directly highlights the geometry of the key objects in the foreground, yielding object surfaces." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.434, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In this work, we devise a new Object-aware Radiance Field (ORF), which goes one step further to eliminate the need of the visual hull derived from human-annotated object masks in scenes for learning object surfaces. Our launching point is to introduce an object-aware volumetric scene representation by inferring the foreground/object and background radiance fields on-the-fly. Both the geometric correspondences between multi-view 2D object regions and 3D implicit or explicit object surfaces are exploited to boost the learning of object-aware volumetric scene representation. ORF is henceforth able to encourage the reconstruction of foreground/object geometry without additional 3D supervision of visual hull. Specifically, we first estimate 2D object regions directly based on the multi-view images. Next, on the basis of the estimated 2D object regions, ORF capitalizes on a transparency discriminator to automatically recognize the transparency of each ray in the radiance field. A low transparency indicates that the ray intersects with the object, and rays with high transparency are considered to be object-bypassed. Such predicted transparency of rays is further regarded as prior information to regularize the radiance field in an object-aware manner. Especially, as shown in Figure 1 (b), all the sampled rays are divided into object-intersected rays and object-bypassed rays according to predictions given by the transparency discriminator, leading to 3D implicit object surfaces. After that, we leverage marching cubes to directly convert the 3D implicit object surfaces into 3D explicit object surfaces. The inherent geometric correspondence between 2D planes and 3D explicit object surfaces are thus constructed via rasterization. This geometric correspondence enables the projection from the es" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.226 + ], + "angle": 0, + "content": "timated 2D object regions into 3D explicit object surfaces, and meanwhile the object information across multiple views are aggregated. Furthermore, ORF projects the aggregated object information in 3D explicit object surfaces back to 2D planes, thereby updating the 2D object regions and enforcing them multi-view consistent. The whole process refines the estimated 2D object regions and 3D implicit/explicit object surfaces, pursuing an object reconstruction without trivial background surfaces." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.228, + 0.89, + 0.378 + ], + "angle": 0, + "content": "In sum, we have made the following contributions: (I) ORF designs a transparency discriminator to automatically capture useful object-aware inductive bias, which further supervises radiance fields to learn object-aware geometry reconstruction. (II) ORF additionally mines the inherent geometric correspondence between multi-view 2D object regions and 3D object surfaces to refine them along with volume rendering. (III) We evaluate ORF on two widely-used benchmarks (DTU and BlendedMVS), demonstrating the effectiveness of our proposal." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.393, + 0.64, + 0.408 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.418, + 0.89, + 0.704 + ], + "angle": 0, + "content": "Multi-view 3D Reconstruction is one of the fundamental tasks in 3D vision, which attempts to reconstruct the 3D geometry from images captured from multiple views. The early works on this task has proceeded along two different dimensions: matching features across views [4, 34] and representing shapes with a voxel grid [1, 5, 10, 20, 30, 36, 38, 39]. The first dimension reconstructs the 3D scenes by matching the pixels with similar appearance, and usually requires the complex designs for fusing depth information [8, 24] or meshing [17, 18]. The second dimension represents the 3D geometry as a volume grid and is limited by the cubic increase of memory requirements. After that, inspired by the recent advance of deep learning techniques, deep neural networks are exploited as an alternative of hand-designed traditional components in 3D reconstruction. For instance, the visual feature for matching [14, 21, 23, 40, 48], depth fusion [11, 33] and depth map prediction [15, 43, 44] can be learnt by neural networks, leading to better performances thanks to the high learning capacity of deep models." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.705, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Instead of explicitly reconstructing the 3D geometry, the neural implicit surfaces are introduced to encode the characteristics of 3D scenes by neural networks. Specifically, the surfaces are represented by a neural network which outputs either an occupancy field [25, 31] or a Signed Distance Function (SDF) [29]. In this scheme, the implicit representations of surfaces are learnt via surface rendering [27, 47] which determines the radiance directly on the surface of an object and provides a differentiable rendering formulation using implicit gradients. Recently, Neural Radiance Fields (NeRF) [26] is proposed to implicitly represent scenes by volume rendering which learns alpha-compositing of the radiance field along camera rays, which benefits 3D con" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "17894" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.227 + ], + "angle": 0, + "content": "tent creation tasks [51, 6, 7, 42]. The main focus of NeRF is the quality of novel view synthesis, but the geometry is not guaranteed. To promote the quality of learnt surfaces, Unisurf [28] unifies radiance fields and occupancy-based implicit surfaces, enabling plausible reconstruction. VolSDF [46] and NeuS [41] exploit SDF as implicit surface representations and obtain better results. NeuralWarp [9] further boosts up the reconstruction by integrating photo consistency between multi-view images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.424 + ], + "angle": 0, + "content": "Our work also falls into the category of learning neural implicit surfaces with volume rendering. Despite the progress in improving rendering quality or surface extraction, the way to reconstruct object surfaces without requiring the visual hull derived from object masks in scenes has not been fully explored. The related work of DFFs [19] distills off-the-shelf 2D vision encoders into a 3D feature field to enable the decomposition of scenes conditioning on user-specified queries. Different from [19], our ORF exploits the geometric correspondence between multi-view 2D object regions and 3D object surfaces to automatically separate objects and background, and enhance the quality of the learnt object surfaces." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.436, + 0.355, + 0.453 + ], + "angle": 0, + "content": "3. Object-aware Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.473, + 0.749 + ], + "angle": 0, + "content": "This section first reviews the standard scheme to represent scenes via radiance fields without the consideration of object region separation (Section 3.1). Next, we describe how the designed transparency discriminator in our ORF distinguishes the object-intersected rays and object-bypassed rays in radiance fields based on the estimated object regions. And then we introduce how to learn an object-aware radiance field by optimizing rays separately with the help of the transparency discriminator (Section 3.2). Furthermore, we design a novel rasterization-based aggregation mechanism to additionally construct the geometric correspondence between 2D object regions and 3D object surfaces via rasterization. Such geometric correspondence enables the aggregation of object information from 2D planes to 3D explicit object surfaces. The aggregated object information in turn updates the 2D object regions in a multi-view consistent manner, pursuing a more high-fidelity object reconstructions (Section 3.3). Figure 2 depicts an overview of our ORF architecture." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.419, + 0.773 + ], + "angle": 0, + "content": "3.1. Representing Scene via Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Neural radiance field and its recent variants aim to represent 3D scenes by two implicit functions, i.e., geometry function and radiance function, which are approximated via two individual neural networks. The geometry network models the geometric structure of 3D scenes, and the radiance network encodes the color emitted by any region in space from all directions. The two networks represent the characteristics in the 3D scene and codetermine the ren-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.243 + ], + "angle": 0, + "content": "dered novel views. When rendering the target view \\(\\mathbf{R}\\) taken from the direction \\(\\mathbf{d}\\), the rendered color \\(\\mathbf{R}(\\mathbf{p})\\) of each pixel \\(\\mathbf{p}\\) is computed by both geometry network \\(\\mathcal{G}\\) and radiance network \\(\\mathcal{C}\\) in a differentiable way. Specifically, we first sample \\(N_{p}\\) points \\(\\mathbf{x}_{i}\\), \\(i = 1,\\dots,N_{p}\\) along the corresponding ray \\(\\Re (\\mathbf{p})\\) going through the camera center and the target pixel \\(\\mathbf{p}\\). Note that here we omit the notations of target pixel for simplicity. The surface normal \\(\\mathbf{n}_i\\), the occupancy value \\(\\alpha_{i}\\) and the radiance value \\(\\mathbf{c}_i\\) are measured by the geometry network \\(\\mathcal{G}\\) and the radiance network \\(\\mathcal{C}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.248, + 0.892, + 0.269 + ], + "angle": 0, + "content": "\\[\n\\mathbf {n} _ {i}, \\alpha_ {i} = \\mathcal {G} (\\mathbf {x} _ {i}), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.64, + 0.269, + 0.753, + 0.281 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {i} = \\mathcal {C} (\\mathbf {x} _ {i}, \\mathbf {n} _ {i}, \\mathbf {d}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.895, + 0.334 + ], + "angle": 0, + "content": "The rendering of the scene at pixel \\(\\mathbf{p}\\) is approximated as a weighted summation of radiance values \\(\\mathbf{c}_i\\) at each sampled point by using the occupancy values as the weights:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.34, + 0.892, + 0.379 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R} (\\mathbf {p}) = \\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} (1 - \\alpha_ {j}) \\mathbf {c} _ {i}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.386, + 0.895, + 0.508 + ], + "angle": 0, + "content": "where \\(\\prod_{j < i}(1 - \\alpha_j)\\) is to simulate the occlusion caused by the opaque pixels in front of the target pixel. As a practical choice, we utilize transformed Signed Distance Field (SDF) encoding [41, 46] as the geometry function. Eq. (2) is actually the discrete approximation of an integral along the camera ray by sampling a limited number of points. The sampling strategies have been discussed in [26, 28, 41, 46] to improve the geometry estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.894, + 0.598 + ], + "angle": 0, + "content": "At training stage, the two neural networks are jointly optimized by encouraging the reconstruction of the given views of the 3D scene. Given one reference view \\(\\mathbf{I}^r\\), the reconstruction loss for \\(\\mathbf{p} \\in \\mathbf{I}^r\\) is calculated by the L1 distance between the reference view \\(\\mathbf{I}^r\\) and the neural volume rendering results \\(\\mathbf{R}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.605, + 0.892, + 0.621 + ], + "angle": 0, + "content": "\\[\n\\mathrm {L} _ {\\text {r e c}} = \\left| \\mathbf {I} ^ {r} (\\mathbf {p}) - \\mathbf {R} (\\mathbf {p}) \\right|, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.75 + ], + "angle": 0, + "content": "where \\(|\\cdot|\\) is the L1 loss. This loss function simply treats each camera ray corresponding to \\(\\mathbf{p}\\) equally and constrains the difference between the input pixel and the rendered result, while ignoring the distinction of rays that either intersect or bypass the objects. As a result, the implicit 3D model often contains some trivial surfaces of the background regions (Figure 1), and thus requires the object masks derived visual hull to execute an additional trimming step at inference." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.844, + 0.773 + ], + "angle": 0, + "content": "3.2. Learning Object-aware Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.894, + 0.903 + ], + "angle": 0, + "content": "To alleviate these issues, we propose to automatically distinguish the object-intersected and object-bypassed rays, making the learnt radiance fields object-aware without manually annotating the visual hull for each scene. To materialize this idea, here we first elaborate how to achieve the high-quality ray/transparency prediction via a devised transparency discriminator (Figure 2 (a)), followed by the learning scheme with different objectives (Figure 2 (b))." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17895" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.088, + 0.852, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.421, + 0.856, + 0.436 + ], + "angle": 0, + "content": "Figure 2: An overview of the proposed Object-aware Radiance Fields (ORF) framework for learning neural implicit surfaces." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.473, + 0.702 + ], + "angle": 0, + "content": "Transparency Discriminator. Formally, we consider the ray \\(\\Re (\\mathbf{p})\\) derived from pixel \\(\\mathbf{p}\\) of the reference view \\(\\mathbf{I}^r\\). One intuitive way to inspect whether the \\(\\Re (\\mathbf{p})\\) intersects with the object is to predict the probability that the pixel \\(\\mathbf{p}\\) belongs to the estimated object regions \\(\\mathbf{O}^r\\) from the perspective of \\(\\mathbf{I}^r\\). Note that here we employ an off-the-shelf salient object segmentation model [32] to learn the prior knowledge of generic salient objects. Replacing the saliency model with other segmentation models is flexible to generalize to other reconstruction scenarios. Such saliency map generated from \\(\\mathbf{I}^r\\) provides coarse object information that indicates the 2D object regions \\(\\mathbf{O}^r\\). However, the complex object appearance and challenging variation of views probably affect the quality of object information. As such, we further design a transparency discriminator that jointly exploits the 2D object regions estimated from different views for ray discrimination in radiance field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In particular, given a reference image \\(\\mathbf{I}^r\\) and multiple source images \\((\\mathbf{I}_i^s,i = 1,\\dots ,N_s)\\) captured from different viewpoints, we can roughly estimate the object regions in each image individually via salient object segmentation. Let \\(\\mathbf{O}^r\\) and \\(\\mathbf{O}_i^s\\) \\((i = 1,\\dots ,N_{s})\\) denote the corresponding 2D object regions. We start from the ray \\(\\Re (\\mathbf{p})\\) corresponding to pixel \\(\\mathbf{p}\\in \\mathbf{I}^r\\) that intersects with the implicit surface for the first time at point \\(\\mathbf{x}^{+}\\) in the radiance field. To locate the point \\(\\mathbf{x}^{+}\\) in the world coordinates, we sample points along \\(\\Re (\\mathbf{p})\\) from its corresponding camera center and feed the sampled points into the geometry network \\(\\mathcal{G}\\) in order. Then, following [46], the signed distance between each sampled point and its nearest surface is derived from the output of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.474 + ], + "angle": 0, + "content": "\\(\\mathcal{G}\\). The first point we sampled that has a positive signed distance is regarded as \\(\\mathbf{x}^{+}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.552 + ], + "angle": 0, + "content": "After that, we mine the geometric correspondence between 3D implicit surfaces and 2D planes by projecting the point \\(\\mathbf{x}^{+}\\) into the 2D plane of each source image. By denoting the projection as \\(\\pi_i^s (\\mathbf{x}^+)\\) \\((i = 1,\\dots ,N_{s})\\) in source image coordinates, we formulate \\(\\pi_i^s (\\mathbf{x}^+)\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.558, + 0.892, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right) = K _ {i} ^ {s} \\left(R _ {i} ^ {s} \\mathbf {x} ^ {+} + \\mathbf {t} _ {i} ^ {s}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.658 + ], + "angle": 0, + "content": "where \\( K_{i}^{s} \\) is the internal calibration matrix of the \\( i \\)-th source camera, and \\( (R_{i}^{s},\\mathbf{t}_{i}^{s}) \\) are the extrinsic parameters of the camera \\( (R_{i}^{s}:3\\times 3 \\) rotation matrix, \\( \\mathbf{t}_i^s \\): 3-dim translation vector). In this way, each projection associates the point \\( \\mathbf{x}^{+} \\) in world coordinates to pixels in source images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Based on the estimated 2D object regions from multiple views \\(\\mathbf{O}^T\\) and \\(\\mathbf{O}_i^s\\) (\\(i = 1, \\dots, N_s\\)), a transparency discriminator is devised to predict the transparency \\(\\mathcal{T}(\\Re(\\mathbf{p}))\\). Here the transparency can be interpreted as the probability that the ray \\(\\Re(\\mathbf{p})\\) bypasses the target object. Specifically, in an effort to take all 2D object regions into account, we measure the transparency for \\(\\Re(\\mathbf{p})\\) by averaging the probabilities of pixels belonging to objects in multiple views with regard to the same point \\(\\mathbf{x}^+\\):" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.802, + 0.892, + 0.833 + ], + "angle": 0, + "content": "\\[\n\\mathcal {T} (\\Re (\\mathbf {p})) = 1 - \\frac {\\mathbf {O} ^ {r} (\\mathbf {p}) + \\sum_ {i = 1} ^ {N _ {s}} \\mathbf {O} _ {i} ^ {s} \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}{1 + N _ {s}}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Such formulation assumes that the intersection point \\(\\mathbf{x}^{+}\\) are observed by each source camera without any occlusion. But in practice, the intersection points may be projected outside of the source images or occluded by other surfaces which" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17896" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "are closer to the source cameras. To tackle this issue, we extend the formulation in Eq. (5) with a binary indicator \\( V(\\cdot) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.129, + 0.47, + 0.174 + ], + "angle": 0, + "content": "\\[\n\\mathcal {T} (\\Re (\\mathbf {p})) = 1 - \\frac {\\mathbf {O} ^ {r} (\\mathbf {p}) + \\sum_ {i = 1} ^ {N _ {s}} V \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right) \\mathbf {O} _ {i} ^ {s} \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}{1 + \\sum_ {i = 1} ^ {N _ {s}} V \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.175, + 0.469, + 0.326 + ], + "angle": 0, + "content": "We set \\( V(\\pi_i^s (\\mathbf{x}^+)) \\) as 1 when \\( \\mathbf{x}^{+} \\) is within the maximum area that can be captured by the camera of \\( \\mathbf{I}_i^s \\) and meanwhile it is also the first intersection between ray \\( \\Re (\\pi_i^s (\\mathbf{x}^+)) \\) and implicit surfaces. In the implementation, we first check if the \\( \\pi_i^s (\\mathbf{x}^+) \\) locates inside the source image \\( \\mathbf{I}_i^s \\). Then we estimate the first intersection point of ray \\( \\Re (\\pi_i^s (\\mathbf{x}^+)) \\) and check whether it is nearby \\( \\mathbf{x}^{+} \\). Accordingly, our transparency discriminator is able to identify an object-intersected ray with low transparency, and a ray with high transparency is considered to bypass the object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.469, + 0.537 + ], + "angle": 0, + "content": "Objective. After classifying each ray via the transparency discriminator, we assign different objectives to different kinds of rays, pursuing an object-aware radiance field. Figure 2 (b) shows an overview of the learning scheme for our ORF. In general, given a group of multiview images of the target object, camera rays associated with pixels in images are utilized for volume rendering to optimize the radiance field, as described in Section 3.1. In the radiance field, a ray may terminate at the surface of objects (blue and golden), the ground plane (orange), or the point at infinity (green). To differentiate these kinds of rays, we feed them into a transparency discriminator and classify them as object-intersected or object-bypassed according to object regions estimated from the multi-view images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Specifically, for the object-intersected ray whose predicted transparency is less than 0.5, we learn in advance that the ray will go through the target object. Hence, we additionally constrain the ray to have high occupancy as a supplement to the reconstruction loss in Eq. (3):" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.62, + 0.47, + 0.659 + ], + "angle": 0, + "content": "\\[\n\\mathrm {L} _ {\\text {o c c}} = - \\log \\left(\\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} \\left(1 - \\alpha_ {j}\\right)\\right), \\mathcal {T} (\\Re (\\mathbf {p})) \\leq 0. 5. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.667, + 0.469, + 0.713 + ], + "angle": 0, + "content": "In contrast, for the object-bypassed ray with \\(\\mathcal{T}(\\Re (\\mathbf{p})) > 0.5\\), the occupancy is enforced to be small to ensure that no trivial surface appears in the background regions:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.719, + 0.47, + 0.758 + ], + "angle": 0, + "content": "\\[\n\\mathrm {L} _ {\\text {o c c}} = - \\log \\left(1 - \\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} \\left(1 - \\alpha_ {j}\\right)\\right), \\mathcal {T} (\\Re (\\mathbf {p})) > 0. 5. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.469, + 0.825 + ], + "angle": 0, + "content": "In addition, we do not require the rendering of object-bypassed ray to reconstruct the input color, which means the reconstruction loss \\(|\\mathbf{I}^r (\\mathbf{p}) - \\mathbf{R}(\\mathbf{p})|\\) is omitted when \\(\\Re (\\mathbf{p})\\) is object-bypassed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Hence, the overall objective function integrates the reconstruction loss between the reference view and the rendered results in Eq. (3), and the occupancy regularization loss in Eq. (7) and Eq. (8). To further enhance the quality of the learnt surfaces, we also consider two extra losses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "following the recent works. The first one is the eikonal loss \\( \\mathrm{L}_{\\mathrm{eik}} \\) [13] which encourages the geometry network to output a function similar to a signed distance field. The second one is the patch warping loss \\( \\mathrm{L}_{\\mathrm{warp}} \\) [9] to improve the reconstruction ability by warping the existing patches from the reference views. We measure the overall objective as:" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.2, + 0.892, + 0.216 + ], + "angle": 0, + "content": "\\[\n\\mathrm {L} = \\lambda_ {1} \\mathrm {L} _ {\\text {r e c}} + \\lambda_ {2} \\mathrm {L} _ {\\text {o c c}} + \\lambda_ {3} \\mathrm {L} _ {\\text {e i k}} + \\lambda_ {4} \\mathrm {L} _ {\\text {w a r p}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.233, + 0.892, + 0.279 + ], + "angle": 0, + "content": "where \\(\\lambda_1 = 1\\), \\(\\lambda_2 = 0.1\\), \\(\\lambda_3 = 0.1\\), and \\(\\lambda_4 = 1\\) are the trade-off parameters. Here we set \\(\\lambda_3\\) and \\(\\lambda_4\\) following [9], and \\(\\lambda_2\\) is determined through experimental study." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.296, + 0.787, + 0.312 + ], + "angle": 0, + "content": "3.3. Rasterization-based Aggregation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.892, + 0.397 + ], + "angle": 0, + "content": "The new rasterization-based aggregation mechanism additionally exploits the geometric correspondence between 3D explicit surfaces and 2D planes. This design aims to further refine the quality of the estimated 2D object regions and make them multi-view consistent." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.893, + 0.69 + ], + "angle": 0, + "content": "Technically, as shown in Figure 2 (c), the mechanism first converts the 3D implicit surfaces (i.e., geometry network \\(\\mathcal{G}\\)) into explicit surfaces (a explicit polygonal 3D representation like mesh) via marching cubes [22]. After that, we compute the projection from the 3D explicit surfaces (i.e., triangles) to the pixels of 2D images \\(\\mathcal{I}\\) by rasterization. Here the rasterization refers to the typical process of taking a triangle and figuring out which pixels it covers [37]. Formally, let \\(\\Delta^j\\) denote the \\(j\\)-th triangle in the mesh, which corresponds to a set of pixels \\(\\mathcal{P}_i^j \\subseteq \\mathbf{O}_i\\) in the \\(i\\)-th view. Note that the pixel set \\(\\mathcal{P}_i^j\\) is set as empty when \\(\\Delta^j\\) is invisible to the camera due to invalid projections (e.g., the triangle is projected outside the image) or occlusion. Such correspondence between triangles and pixels enables the aggregation of the object information of 2D object regions into 3D explicit surface \\(\\Delta^j\\). In particular, we aggregate the object probabilities of all the pixels belonging to the triangle \\(\\Delta^j\\) from multiple views, yielding the triangle-level object probability of \\(\\mathbf{O}_{agg}(\\Delta^j)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.706, + 0.892, + 0.75 + ], + "angle": 0, + "content": "\\[\n\\mathbf {O} _ {a g g} \\left(\\Delta^ {j}\\right) = \\frac {\\sum_ {i = 1} ^ {| \\mathcal {I} |} \\sum_ {\\mathbf {p} \\in \\mathcal {P} _ {i} ^ {j}} \\mathbf {O} _ {i} (\\mathbf {p})}{\\epsilon + \\sum_ {i = 1} ^ {| \\mathcal {I} |} \\sum_ {\\mathbf {p} \\in \\mathcal {P} _ {i} ^ {j}} \\mathbf {1}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.9 + ], + "angle": 0, + "content": "where \\(\\epsilon\\) is a constant term added to the denominator for numerical stability. After traversing all the 3D surfaces with the triangle-level aggregation (Eq. (10)), we re-project the triangle-level object probabilities of 3D surfaces back to 2D images. More specifically, for one pixel \\(\\mathbf{p} \\in \\mathcal{P}_i^j \\subseteq \\mathbf{O}_i\\) in each viewpoint, the object probability of \\(\\mathbf{O}_i(\\mathbf{p})\\) is updated as the same triangle-level object probability \\(\\mathbf{O}_{agg}(\\Delta^j)\\). By doing so, the updated 2D multi-view object regions are enforced to be consistent across different views." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17897" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.09, + 0.894, + 0.146 + ], + "angle": 0, + "content": "Table 1: Comparisons of our ORF with other volume rendering techniques on DTU dataset for learning neural implicit surfaces. Here all the involved techniques do not use object masks as additional supervision for training. The top part reports the reconstruction performances when using object masks to trim the estimated meshes, and the bottom part directly compares the reconstruction performances of the estimated meshes without using object masks. The best performances are marked in bold and the second-best results are underlined." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.149, + 0.894, + 0.337 + ], + "angle": 0, + "content": "
ScanID243740556365698397105106110114118122Mean
with object masks: using the visual hull derived from human-annotated object masks for mesh trimming
NeRF [26]1.901.601.850.582.281.271.471.672.051.070.882.531.061.150.961.49
Unisurf [28]1.321.361.720.441.350.790.801.491.370.890.591.470.460.590.621.02
VolSDF [46]1.141.260.810.491.250.700.721.291.180.700.661.080.420.610.550.86
NeuS [41]1.001.370.930.431.100.650.571.481.090.830.521.200.350.490.540.84
NeuralWarp [9]0.490.710.380.380.790.810.821.201.060.680.660.740.410.630.510.68
without object masks: without mask-dependent trimming at inference
VolSDF [46]1.251.701.310.912.901.080.901.621.241.090.701.390.590.710.871.22
NeuS [41]1.591.981.440.951.820.740.641.631.301.410.591.330.440.510.541.13
NeuralWarp [9]0.972.541.520.412.540.740.791.061.531.400.750.720.390.570.621.10
ORF0.560.690.430.450.740.850.750.760.860.710.610.690.380.810.520.65
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.345, + 0.21, + 0.361 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.471, + 0.476 + ], + "angle": 0, + "content": "We evaluate the effectiveness of ORF on DTU [16] and BlendedMVS [45] for multi-view 3D reconstruction. We first show both qualitative and quantitative results of ORF in comparison to existing techniques on DTU. Next, we conduct experimental analysis to validate the designs in ORF. Finally, we perform the qualitative comparison over samples derived from BlendedMVS for evaluation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.388, + 0.502 + ], + "angle": 0, + "content": "4.1. Datasets and Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.869 + ], + "angle": 0, + "content": "DTU is a popular multi-view 3D reconstruction benchmark, which consists of 80 scenes with large variability in materials, appearance and geometry of objects. For each scene, the dataset provides 49 or 64 images (resolution: \\(1,600 \\times 1,200\\)) captured from multiple camera views. The ground-truth point cloud of each scene is acquired with laser sensor. In our experiments, we follow [9, 28, 41, 46, 47] to use the selected 15 scenes in DTU for comparison. We strictly follow [9, 41] and use the official evaluation code of DTU [16] to compute the quantitative metrics. Specifically, the point clouds of objects (w/o background) in DTU are regarded as ground truth (GT). For a reconstructed mesh, we sample points on triangle surfaces in an evenly spaced manner (radius=0.2 as in [16]). Then, we report the final reconstruction score by averaging the accuracy and completeness of the sampled points (SP) (i.e., the chamfer distances of \\(\\mathrm{SP} \\rightarrow \\mathrm{GT}\\) and \\(\\mathrm{GT} \\rightarrow \\mathrm{SP}\\)). It is also worthy to note that existing volume rendering techniques commonly use the additional object regions manually annotated by [27, 47] to trim the predicted mesh for only evaluating the reconstruction inside the visual hull. In contrast, our ORF learns an object-aware volumetric scene representation and directly constructs the 3D geometry of objects in the scene without the use of the visual hull derived from annotated object regions of scenes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "BlendedMVS is a large-scale benchmark for multi-view 3D reconstruction, including 113 scenes with multi-view" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.892, + 0.422 + ], + "angle": 0, + "content": "images. Compared to DTU, the backgrounds in BlendedMVS are more complex. We select samples from the lowres set of BlendedMVS, and each scene is equipped with 24 to 64 images (resolution: \\(768 \\times 576\\)). Note that the ground truth of object regions for each image is not available." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.893, + 0.665 + ], + "angle": 0, + "content": "Implementation Details. The whole network of ORF is built over VolSDF [46], and we adopt the same architecture as in existing volume rendering methods [28, 46, 47] for fair comparison. The whole network uses sphere initialization [2]. During training, we train our ORF with a two-stage strategy. We first optimize the network with the reconstruction loss and eikonal loss under the same setting in VolSDF (100k iterations with learning rate exponentially decayed from 5e-4 to 5e-5, batch size: 1,024 rays). Next, the network is fine-tuned with the overall objective in Eq. (9) (100k iterations with learning rate of 5e-4, batch size: 512 rays). The object probability is calculated by the transparency discriminator in each forward pass using the latest radiance field. The mesh extraction for rasterization-based aggregation is only conducted once after the first training stage of ORF." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.761, + 0.696 + ], + "angle": 0, + "content": "4.2. Comparison on DTU Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Quantitative Results. We compare with several neural surface reconstruction techniques under two different evaluation settings for fair comparison: 1) baselines using the visual hull derived from human-annotated object masks for mesh trimming, 2) all re-implemented SDF-based baselines and our ORF without mask-dependent trimming at inference. Such two settings are denoted as with/without object masks, respectively. All the mentioned baselines are grouped into three directions: volume rendering with classical radiance fields [26], occupancy network [28], and SDF-based (Signed Distance Function) fields [46, 41, 9]. Table 1 summarizes the performance comparisons on each evaluation scenario. Note that all baselines and our ORF" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17898" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.073, + 0.86, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.364, + 0.892, + 0.392 + ], + "angle": 0, + "content": "Figure 3: Comparisons on qualitative results of our ORF with other neural radiance fields techniques on DTU dataset for 3D geometry reconstruction with or without object masks at inference. * denotes our implementation of VolSDF." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.47, + 0.476 + ], + "angle": 0, + "content": "do not use human-annotated object masks of scenes to optimize geometry/radiance nets during training. At inference, these baselines commonly require masks to remove the background of the learnt mesh. Instead, ORF can directly produce the object mesh without masks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.471, + 0.825 + ], + "angle": 0, + "content": "In general, our ORF exhibits better reconstruction quality against all these baselines. Remarkably, ORF achieves 0.65 in the metric of Chamfer distance without the use of the visual hull derived from object masks in scenes, which is better than the reconstruction accuracy (0.68) of NeuralWarp when exploiting demands object masks at inference. The results generally highlight the key advantage of learning object-aware geometry reconstruction for neural implicit surfaces. Specifically, under the evaluation scenario with object masks, NeRF produces unsatisfactory reconstruction results since the lack of 3D geometry constraints. Unisurf unifies volume/surface rendering and enables better results. VolSDF, NeuS, and NeuralWarp exploit SDF and obtain promising reconstructions. Nevertheless, a performance drop is observed for each SDF-based method when object masks are unavailable at inference, since the primary estimated mesh contains more trivial geometry of the background. In contrast, our ORF achieves competitive reconstruction accuracy through learning an object-aware radiance field without the use of object masks derived visual hull. This confirms the effectiveness of exploring object awareness via transparency discriminator and rasterization-based aggregation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Qualitative Results. We then visually examine the reconstruction quality of our proposal by comparing ORF with three SDF-based approaches (VolSDF, NeuS, NeuralWarp) on five selected scenes from DTU dataset. Figure 3 shows the qualitative results of the reconstructed meshes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Note that here we show the reconstruction results of the two different evaluation settings (with or without object masks at inference for trimming estimated meshes). In general, all the three approaches reconstruct high-fidelity object surfaces after mask-dependent mesh trimming. In between, by constraining volume rendering with photo-consistency objective across multiple views, NeuralWarp produces more accurate surfaces with high-fidelity details (e.g., the bricks with sparse textures in the first two scenes) against VolSDF and NeuS. Furthermore, when the object masks are unavailable, the output meshes of each baselines become noisy with more trivial geometry and even some artifact of the background. In contrast, under this challenging setting, our ORF performs visually on par with the NeuralWarp, while requiring no object mask dependent mesh trimming at inference. The results again validate the merit of our ORF." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.71, + 0.667 + ], + "angle": 0, + "content": "4.3. Experimental Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Ablation Study. Here we investigate how each design in our ORF influences the overall reconstruction performance. Table 2 and Figure 4 details the performances and the corresponding qualitative results across different ablated runs of ORF, respectively. We start from a basic SDF-based radiance field without ray discrimination (i.e., NeuralWarp), which achieves 1.10 of Chamfer distance. The estimated mesh of this basic model inevitably contains trivial background geometry. Next, by solely using the outputs of salient object segmentation (Saliency) to distinguish object-intersected and object-bypassed rays, we observe a clear performance boost and the background is effectively screened. However, the independently estimated object probability of each 2D object region may be inaccurate and inconsistent across different viewpoints, resulting in error" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17899" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.081, + 0.466, + 0.096 + ], + "angle": 0, + "content": "Table 2: Ablation study on each design in ORF on DTU dataset." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.097, + 0.467, + 0.216 + ], + "angle": 0, + "content": "
Transparency Discriminator Saliency +Multiview +VerifierRasterization-based AggregationChamfer Distance
1.10
✓0.90
✓✓0.87
✓✓✓0.76
✓✓✓✓0.65
" + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.224, + 0.212, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.223, + 0.225, + 0.274, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.285, + 0.225, + 0.34, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.225, + 0.403, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.225, + 0.468, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.317, + 0.469, + 0.36 + ], + "angle": 0, + "content": "Figure 4: Comparisons on qualitative results by using different ablated runs of our ORF on DTU dataset for 3D geometry reconstruction object masks dependent mesh trimming at inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.469, + 0.553 + ], + "angle": 0, + "content": "accumulation and holes in the reconstructions. To address this issue, we enhance the strategy of transparency discrimination by jointly exploiting the 2D object regions estimated from multiple views (Multiview), leading to slightly better reconstruction. We then leverage the projection verification strategy (Verifier) to screen out invalid projections (e.g., the points are projected outside of the source images or occluded by other surfaces), which further boosts up the reconstruction. Finally, by capitalizing on Rasterization-based Aggregation to refine the estimated 2D object regions, the mIoU of object regions is improved from \\(94\\%\\) to \\(97\\%\\) and ORF achieves the highest reconstruction quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.81 + ], + "angle": 0, + "content": "Effect of the Trade-off Parameter \\(\\lambda_{2}\\). To clarify the effect of the trade-off parameter \\(\\lambda_{2}\\) in Eq. (9), we detail the reconstruction performances (i.e., Chamfer distances) with different trade-off parameters in Table 3. In the extreme case of \\(\\lambda_{2} = 0\\), no occupancy regularization objective for foreground and background rays is utilized and the whole model degenerates to the conventional SDF-based approach. When enlarging \\(\\lambda_{2}\\) as 0.05, a better reconstruction accuracy is attained, which basically demonstrates that the foreground-aware inductive bias benefits volume rendering. The performance change is relatively smooth when \\(\\lambda_{2}\\) varies in the range from 0.05 to 0.20, and the best reconstruction accuracy is attained when \\(\\lambda_{2} = 0.10\\). Furthermore, the reconstruction accuracy slightly decreases when \\(\\lambda_{2} \\geq 0.30\\). We speculate that this may be the result of amplifying the noise of ray discrimination if we set a higher weight to occupancy regularization objective." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Effect of the Saliency Model's Performance. To verify how the quality of saliency influences the reconstruction, we perform salient object segmentation using another two models and obtain additional two versions of saliency maps. We evaluate the three different versions of saliency for both reconstruction and segmentation tasks on DTU (re" + }, + { + "type": "table_caption", + "bbox": [ + 0.508, + 0.081, + 0.882, + 0.095 + ], + "angle": 0, + "content": "Table 3: Effect of the trade-off parameter \\( {\\lambda }_{2} \\) in ORF on DTU." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.096, + 0.891, + 0.284 + ], + "angle": 0, + "content": "
λ20.000.050.100.200.300.400.50
Chamfer Dist.1.100.660.650.670.690.700.71
Image
VolSDF*
Neural \nWarp
ORF
" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.284, + 0.892, + 0.34 + ], + "angle": 0, + "content": "Figure 5: Comparisons on qualitative results of our ORF with other techniques on BlendedMVS for 3D geometry reconstruction without object masks at inference. * denotes our re-implemented VolSDF without the hand-crafted parametrization in NeRF++." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.344, + 0.892, + 0.435 + ], + "angle": 0, + "content": "construction: 0.65, 0.67, 0.67; segmentation: \\(94\\%\\), \\(93\\%\\), \\(91\\%\\) mean IoU). The results show that the saliency segmentation performance on DTU has almost saturated, and the reconstruction performances of ORF only fluctuate within the range of 0.02, which eases the difficulty on choosing saliency segmentation model in practice." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.445, + 0.825, + 0.461 + ], + "angle": 0, + "content": "4.4. Comparison on BlendedMVS Dataset" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Figure 5 further showcases the geometry reconstruction results with different techniques for six scenes in BlendedMVS. It is worthy to note that VolSDF originally utilizes an additional hand-crafted parametrization as in \\(\\mathrm{NeRF}++\\) [50] to tackle the complex backgrounds by modeling the volume outside a radius 3 sphere with another NeRF network. For fair comparison, here we re-implement VolSDF by removing this parametrization. Similar to the observations on DTU under the setting without object masks, both VolSDF and NeuralWarp produce high-fidelity object surfaces, while more trivial background geometry is inevitably included. Instead, our ORF nicely removes the trivial geometry and performs nearly on par with these approaches." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.627, + 0.695 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this work, we circumvent the use of object masks derived visual hull, and shape a new paradigm of learning object-aware geometry reconstruction for neural implicit surfaces. To verify our claim, we novelly remould the classical neural radiance fields by involving a new transparency discriminator to distinguish object-intersected and object-bypassed rays on-the-fly. Such ray discrimination serves as object-aware inductive bias to enable a reconstruction of 3D geometry of the key object in the scene. Moreover, we exploit the geometric correspondence between multi-view 2D object regions and 3D implicit/explicit surfaces to facilitate the learning of object surfaces. Extensive experiments conducted on DTU and BlendedMVS validate our proposal." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17900" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Motilal Agrawal and Larry S Davis. A probabilistic framework for surface reconstruction from multiple images. In CVPR, 2001." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.468, + 0.185 + ], + "angle": 0, + "content": "[2] Matan Atzmon and Yaron Lipman. Sal: Sign agnostic learning of shapes from raw data. In CVPR, 2020." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.188, + 0.468, + 0.242 + ], + "angle": 0, + "content": "[3] Connelly Barnes, Eli Shechtman, Adam Finkelstein, and Dan B Goldman. 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In CVPR, 2023." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.758 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "17902" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_origin.pdf b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bdbc8ad2c55a50236eb5964484006c4cade9d8de --- /dev/null +++ b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/3c0bb7d1-9040-4c42-8743-ea0aac8c43c4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8b4d1cd937b000dbdbead92c1e681e2f642fd10d1bc68c00e5b9f8e99b4a0a54 +size 3105404 diff --git a/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/full.md b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/full.md new file mode 100644 index 0000000000000000000000000000000000000000..18338ce0d09cde23c08681bbc3d7be8965414633 --- /dev/null +++ b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/full.md @@ -0,0 +1,274 @@ +# Learning Neural Implicit Surfaces with Object-Aware Radiance Fields + +Yiheng Zhang, Zhaofan Qiu, Yingwei Pan, Ting Yao, and Tao Mei +University of Science and Technology of China HiDream.ai Inc. + +{yihengzhang.chn, zhaofanqiu, panyw.ustc, tingyao.ustc}@gmail.com, tmei@hidream.ai + +![](images/7dee064237e669488e5fe0d960d610c69aea1c944822e206f70a9030e497e777.jpg) +Figure 1: The implicit surfaces learnt via (a) conventional scheme which suffers from noisy background geometry representations. In this work, we introduce (b) an object-aware volumetric scene representation by automatically recognizing rays as object-intersected or object-bypassed, aiming to highlight the key object surface in the foreground. (c) Such object surface benefits a series of applications, e.g., 3D scene composition, object moving/editing, and even skeleton assignment. + +# Abstract + +Recent progress on multi-view 3D object reconstruction has featured neural implicit surfaces via learning high-fidelity radiance fields. However, most approaches hinge on the visual hull derived from cost-expensive silhouette masks to obtain object surfaces. In this paper, we propose a novel Object-aware Radiance Fields (ORF) to automatically learn an object-aware geometry reconstruction. The geometric correspondences between multi-view 2D object regions and 3D implicit/explicit object surfaces are additionally exploited to boost the learning of object surfaces. Technically, a critical transparency discriminator is designed to distinguish the object-intersected and object-bypassed rays based on the estimated 2D object regions, leading to 3D implicit object surfaces. Such implicit surfaces can be directly converted into explicit object surfaces (e.g., meshes) via marching cubes. Then, we build the geometric correspondence between 2D planes and 3D meshes by rasterization, and project the estimated object regions into 3D explicit object surfaces by aggregating the object information across multiple views. The aggregated object information in 3D explicit object surfaces is further projected back to 2D planes, aiming to update 2D object regions and enforce them to be multi-view consistent. Extensive experiments on DTU and BlendedMVS verify the capability of ORF to produce comparable surfaces against the state-of-the-art models that demand silhouette masks. + +# 1. Introduction + +Multi-view 3D reconstruction, i.e., the task of reconstructing 3D geometry/surface of objects from multi-view 2D images, has played a fundamental challenge to computer vision and computer graphics communities for decades. In the early stage, the mainstream solution is the classical Multi-View Stereo (MVS) [3, 5, 12, 20, 34, 35] that exploits photometric consistency across different camera views to learn explicit geometry representations (e.g., meshes or voxel grids). The ultimate reconstruction relies heavily on the quality of cross-view matching. In practice, such matching often fails to associate objects with sparse textures, resulting in severe artifact or missing parts on surfaces. To address this issue, recent studies turn their focus on investigating how to represent 3D surfaces as implicit geometry representations. Many consider learning a continuous implicit function that formulates neural implicit surfaces in occupancy field [25, 31] or signed distance field [29]. In between, surface rendering techniques [27, 47, 49] are designed to optimize these fields, leading to impressive reconstruction quality via differentiable rendering from images. Nevertheless, learning such implicit geometry representations requires additional object masks of scenes, since the color of each ray is assumed to only correspond to a single point where a surface intersects with this ray. Moreover, the gradient of differentiable rendering is only backpropagated to the local surface near intersection, resulting in a sub-optimal solution for neural implicit surfaces. + +To mitigate these limitations of local gradient propagation and the demand for the input object masks during fields optimization, a series of volume rendering based neural radiance fields techniques [9, 28, 41, 46] start to emerge. Recently, the seminal work of NeRF [26] builds up the foundation of volumetric scene in neural radiance fields for view synthesis, and performs classical volume rendering via alpha-compositing colors of the sampled points along rays. The subsequent methods further remould classical volume rendering by imposing implicit surface representations, e.g., occupancy network [28] or signed distance function [9, 41, 46]. These approaches produce more accurate surfaces by reconstructing the holistic scenery. Nevertheless, the learnt implicit surfaces are inevitably composed of rich geometry representations in both foreground and background (Figure 1 (a)), which are not distinguished during radiance fields optimization. Accordingly, existing techniques utilize additional cost-expensive silhouette masks to trim the learnt 3D meshes derived from implicit surfaces. The removal of vertices and/or surfaces outside the visual hull directly highlights the geometry of the key objects in the foreground, yielding object surfaces. + +In this work, we devise a new Object-aware Radiance Field (ORF), which goes one step further to eliminate the need of the visual hull derived from human-annotated object masks in scenes for learning object surfaces. Our launching point is to introduce an object-aware volumetric scene representation by inferring the foreground/object and background radiance fields on-the-fly. Both the geometric correspondences between multi-view 2D object regions and 3D implicit or explicit object surfaces are exploited to boost the learning of object-aware volumetric scene representation. ORF is henceforth able to encourage the reconstruction of foreground/object geometry without additional 3D supervision of visual hull. Specifically, we first estimate 2D object regions directly based on the multi-view images. Next, on the basis of the estimated 2D object regions, ORF capitalizes on a transparency discriminator to automatically recognize the transparency of each ray in the radiance field. A low transparency indicates that the ray intersects with the object, and rays with high transparency are considered to be object-bypassed. Such predicted transparency of rays is further regarded as prior information to regularize the radiance field in an object-aware manner. Especially, as shown in Figure 1 (b), all the sampled rays are divided into object-intersected rays and object-bypassed rays according to predictions given by the transparency discriminator, leading to 3D implicit object surfaces. After that, we leverage marching cubes to directly convert the 3D implicit object surfaces into 3D explicit object surfaces. The inherent geometric correspondence between 2D planes and 3D explicit object surfaces are thus constructed via rasterization. This geometric correspondence enables the projection from the es + +timated 2D object regions into 3D explicit object surfaces, and meanwhile the object information across multiple views are aggregated. Furthermore, ORF projects the aggregated object information in 3D explicit object surfaces back to 2D planes, thereby updating the 2D object regions and enforcing them multi-view consistent. The whole process refines the estimated 2D object regions and 3D implicit/explicit object surfaces, pursuing an object reconstruction without trivial background surfaces. + +In sum, we have made the following contributions: (I) ORF designs a transparency discriminator to automatically capture useful object-aware inductive bias, which further supervises radiance fields to learn object-aware geometry reconstruction. (II) ORF additionally mines the inherent geometric correspondence between multi-view 2D object regions and 3D object surfaces to refine them along with volume rendering. (III) We evaluate ORF on two widely-used benchmarks (DTU and BlendedMVS), demonstrating the effectiveness of our proposal. + +# 2. Related Work + +Multi-view 3D Reconstruction is one of the fundamental tasks in 3D vision, which attempts to reconstruct the 3D geometry from images captured from multiple views. The early works on this task has proceeded along two different dimensions: matching features across views [4, 34] and representing shapes with a voxel grid [1, 5, 10, 20, 30, 36, 38, 39]. The first dimension reconstructs the 3D scenes by matching the pixels with similar appearance, and usually requires the complex designs for fusing depth information [8, 24] or meshing [17, 18]. The second dimension represents the 3D geometry as a volume grid and is limited by the cubic increase of memory requirements. After that, inspired by the recent advance of deep learning techniques, deep neural networks are exploited as an alternative of hand-designed traditional components in 3D reconstruction. For instance, the visual feature for matching [14, 21, 23, 40, 48], depth fusion [11, 33] and depth map prediction [15, 43, 44] can be learnt by neural networks, leading to better performances thanks to the high learning capacity of deep models. + +Instead of explicitly reconstructing the 3D geometry, the neural implicit surfaces are introduced to encode the characteristics of 3D scenes by neural networks. Specifically, the surfaces are represented by a neural network which outputs either an occupancy field [25, 31] or a Signed Distance Function (SDF) [29]. In this scheme, the implicit representations of surfaces are learnt via surface rendering [27, 47] which determines the radiance directly on the surface of an object and provides a differentiable rendering formulation using implicit gradients. Recently, Neural Radiance Fields (NeRF) [26] is proposed to implicitly represent scenes by volume rendering which learns alpha-compositing of the radiance field along camera rays, which benefits 3D con + +tent creation tasks [51, 6, 7, 42]. The main focus of NeRF is the quality of novel view synthesis, but the geometry is not guaranteed. To promote the quality of learnt surfaces, Unisurf [28] unifies radiance fields and occupancy-based implicit surfaces, enabling plausible reconstruction. VolSDF [46] and NeuS [41] exploit SDF as implicit surface representations and obtain better results. NeuralWarp [9] further boosts up the reconstruction by integrating photo consistency between multi-view images. + +Our work also falls into the category of learning neural implicit surfaces with volume rendering. Despite the progress in improving rendering quality or surface extraction, the way to reconstruct object surfaces without requiring the visual hull derived from object masks in scenes has not been fully explored. The related work of DFFs [19] distills off-the-shelf 2D vision encoders into a 3D feature field to enable the decomposition of scenes conditioning on user-specified queries. Different from [19], our ORF exploits the geometric correspondence between multi-view 2D object regions and 3D object surfaces to automatically separate objects and background, and enhance the quality of the learnt object surfaces. + +# 3. Object-aware Radiance Fields + +This section first reviews the standard scheme to represent scenes via radiance fields without the consideration of object region separation (Section 3.1). Next, we describe how the designed transparency discriminator in our ORF distinguishes the object-intersected rays and object-bypassed rays in radiance fields based on the estimated object regions. And then we introduce how to learn an object-aware radiance field by optimizing rays separately with the help of the transparency discriminator (Section 3.2). Furthermore, we design a novel rasterization-based aggregation mechanism to additionally construct the geometric correspondence between 2D object regions and 3D object surfaces via rasterization. Such geometric correspondence enables the aggregation of object information from 2D planes to 3D explicit object surfaces. The aggregated object information in turn updates the 2D object regions in a multi-view consistent manner, pursuing a more high-fidelity object reconstructions (Section 3.3). Figure 2 depicts an overview of our ORF architecture. + +# 3.1. Representing Scene via Radiance Fields + +Neural radiance field and its recent variants aim to represent 3D scenes by two implicit functions, i.e., geometry function and radiance function, which are approximated via two individual neural networks. The geometry network models the geometric structure of 3D scenes, and the radiance network encodes the color emitted by any region in space from all directions. The two networks represent the characteristics in the 3D scene and codetermine the ren- + +dered novel views. When rendering the target view $\mathbf{R}$ taken from the direction $\mathbf{d}$ , the rendered color $\mathbf{R}(\mathbf{p})$ of each pixel $\mathbf{p}$ is computed by both geometry network $\mathcal{G}$ and radiance network $\mathcal{C}$ in a differentiable way. Specifically, we first sample $N_{p}$ points $\mathbf{x}_{i}$ , $i = 1,\dots,N_{p}$ along the corresponding ray $\Re (\mathbf{p})$ going through the camera center and the target pixel $\mathbf{p}$ . Note that here we omit the notations of target pixel for simplicity. The surface normal $\mathbf{n}_i$ , the occupancy value $\alpha_{i}$ and the radiance value $\mathbf{c}_i$ are measured by the geometry network $\mathcal{G}$ and the radiance network $\mathcal{C}$ as + +$$ +\mathbf {n} _ {i}, \alpha_ {i} = \mathcal {G} (\mathbf {x} _ {i}), \tag {1} +$$ + +$$ +\mathbf {c} _ {i} = \mathcal {C} (\mathbf {x} _ {i}, \mathbf {n} _ {i}, \mathbf {d}). +$$ + +The rendering of the scene at pixel $\mathbf{p}$ is approximated as a weighted summation of radiance values $\mathbf{c}_i$ at each sampled point by using the occupancy values as the weights: + +$$ +\mathbf {R} (\mathbf {p}) = \sum_ {i = 1} ^ {N _ {p}} \alpha_ {i} \prod_ {j < i} (1 - \alpha_ {j}) \mathbf {c} _ {i}, \tag {2} +$$ + +where $\prod_{j < i}(1 - \alpha_j)$ is to simulate the occlusion caused by the opaque pixels in front of the target pixel. As a practical choice, we utilize transformed Signed Distance Field (SDF) encoding [41, 46] as the geometry function. Eq. (2) is actually the discrete approximation of an integral along the camera ray by sampling a limited number of points. The sampling strategies have been discussed in [26, 28, 41, 46] to improve the geometry estimation. + +At training stage, the two neural networks are jointly optimized by encouraging the reconstruction of the given views of the 3D scene. Given one reference view $\mathbf{I}^r$ , the reconstruction loss for $\mathbf{p} \in \mathbf{I}^r$ is calculated by the L1 distance between the reference view $\mathbf{I}^r$ and the neural volume rendering results $\mathbf{R}$ as + +$$ +\mathrm {L} _ {\text {r e c}} = \left| \mathbf {I} ^ {r} (\mathbf {p}) - \mathbf {R} (\mathbf {p}) \right|, \tag {3} +$$ + +where $|\cdot|$ is the L1 loss. This loss function simply treats each camera ray corresponding to $\mathbf{p}$ equally and constrains the difference between the input pixel and the rendered result, while ignoring the distinction of rays that either intersect or bypass the objects. As a result, the implicit 3D model often contains some trivial surfaces of the background regions (Figure 1), and thus requires the object masks derived visual hull to execute an additional trimming step at inference. + +# 3.2. Learning Object-aware Radiance Fields + +To alleviate these issues, we propose to automatically distinguish the object-intersected and object-bypassed rays, making the learnt radiance fields object-aware without manually annotating the visual hull for each scene. To materialize this idea, here we first elaborate how to achieve the high-quality ray/transparency prediction via a devised transparency discriminator (Figure 2 (a)), followed by the learning scheme with different objectives (Figure 2 (b)). + +![](images/7c500a76086c48b7594715237c5bb4e7dd99e1fd88e869f558d78b38a4725f93.jpg) +Figure 2: An overview of the proposed Object-aware Radiance Fields (ORF) framework for learning neural implicit surfaces. + +Transparency Discriminator. Formally, we consider the ray $\Re (\mathbf{p})$ derived from pixel $\mathbf{p}$ of the reference view $\mathbf{I}^r$ . One intuitive way to inspect whether the $\Re (\mathbf{p})$ intersects with the object is to predict the probability that the pixel $\mathbf{p}$ belongs to the estimated object regions $\mathbf{O}^r$ from the perspective of $\mathbf{I}^r$ . Note that here we employ an off-the-shelf salient object segmentation model [32] to learn the prior knowledge of generic salient objects. Replacing the saliency model with other segmentation models is flexible to generalize to other reconstruction scenarios. Such saliency map generated from $\mathbf{I}^r$ provides coarse object information that indicates the 2D object regions $\mathbf{O}^r$ . However, the complex object appearance and challenging variation of views probably affect the quality of object information. As such, we further design a transparency discriminator that jointly exploits the 2D object regions estimated from different views for ray discrimination in radiance field. + +In particular, given a reference image $\mathbf{I}^r$ and multiple source images $(\mathbf{I}_i^s,i = 1,\dots ,N_s)$ captured from different viewpoints, we can roughly estimate the object regions in each image individually via salient object segmentation. Let $\mathbf{O}^r$ and $\mathbf{O}_i^s$ $(i = 1,\dots ,N_{s})$ denote the corresponding 2D object regions. We start from the ray $\Re (\mathbf{p})$ corresponding to pixel $\mathbf{p}\in \mathbf{I}^r$ that intersects with the implicit surface for the first time at point $\mathbf{x}^{+}$ in the radiance field. To locate the point $\mathbf{x}^{+}$ in the world coordinates, we sample points along $\Re (\mathbf{p})$ from its corresponding camera center and feed the sampled points into the geometry network $\mathcal{G}$ in order. Then, following [46], the signed distance between each sampled point and its nearest surface is derived from the output of + +$\mathcal{G}$ . The first point we sampled that has a positive signed distance is regarded as $\mathbf{x}^{+}$ . + +After that, we mine the geometric correspondence between 3D implicit surfaces and 2D planes by projecting the point $\mathbf{x}^{+}$ into the 2D plane of each source image. By denoting the projection as $\pi_i^s (\mathbf{x}^+)$ $(i = 1,\dots ,N_{s})$ in source image coordinates, we formulate $\pi_i^s (\mathbf{x}^+)$ as: + +$$ +\pi_ {i} ^ {s} \left(\mathbf {x} ^ {+}\right) = K _ {i} ^ {s} \left(R _ {i} ^ {s} \mathbf {x} ^ {+} + \mathbf {t} _ {i} ^ {s}\right), \tag {4} +$$ + +where $K_{i}^{s}$ is the internal calibration matrix of the $i$ -th source camera, and $(R_{i}^{s},\mathbf{t}_{i}^{s})$ are the extrinsic parameters of the camera $(R_{i}^{s}:3\times 3$ rotation matrix, $\mathbf{t}_i^s$ : 3-dim translation vector). In this way, each projection associates the point $\mathbf{x}^{+}$ in world coordinates to pixels in source images. + +Based on the estimated 2D object regions from multiple views $\mathbf{O}^T$ and $\mathbf{O}_i^s$ ( $i = 1, \dots, N_s$ ), a transparency discriminator is devised to predict the transparency $\mathcal{T}(\Re(\mathbf{p}))$ . Here the transparency can be interpreted as the probability that the ray $\Re(\mathbf{p})$ bypasses the target object. Specifically, in an effort to take all 2D object regions into account, we measure the transparency for $\Re(\mathbf{p})$ by averaging the probabilities of pixels belonging to objects in multiple views with regard to the same point $\mathbf{x}^+$ : + +$$ +\mathcal {T} (\Re (\mathbf {p})) = 1 - \frac {\mathbf {O} ^ {r} (\mathbf {p}) + \sum_ {i = 1} ^ {N _ {s}} \mathbf {O} _ {i} ^ {s} \left(\pi_ {i} ^ {s} \left(\mathbf {x} ^ {+}\right)\right)}{1 + N _ {s}}. \tag {5} +$$ + +Such formulation assumes that the intersection point $\mathbf{x}^{+}$ are observed by each source camera without any occlusion. But in practice, the intersection points may be projected outside of the source images or occluded by other surfaces which + +are closer to the source cameras. To tackle this issue, we extend the formulation in Eq. (5) with a binary indicator $V(\cdot)$ : + +$$ +\mathcal {T} (\Re (\mathbf {p})) = 1 - \frac {\mathbf {O} ^ {r} (\mathbf {p}) + \sum_ {i = 1} ^ {N _ {s}} V \left(\pi_ {i} ^ {s} \left(\mathbf {x} ^ {+}\right)\right) \mathbf {O} _ {i} ^ {s} \left(\pi_ {i} ^ {s} \left(\mathbf {x} ^ {+}\right)\right)}{1 + \sum_ {i = 1} ^ {N _ {s}} V \left(\pi_ {i} ^ {s} \left(\mathbf {x} ^ {+}\right)\right)}. \tag {6} +$$ + +We set $V(\pi_i^s (\mathbf{x}^+))$ as 1 when $\mathbf{x}^{+}$ is within the maximum area that can be captured by the camera of $\mathbf{I}_i^s$ and meanwhile it is also the first intersection between ray $\Re (\pi_i^s (\mathbf{x}^+))$ and implicit surfaces. In the implementation, we first check if the $\pi_i^s (\mathbf{x}^+)$ locates inside the source image $\mathbf{I}_i^s$ . Then we estimate the first intersection point of ray $\Re (\pi_i^s (\mathbf{x}^+))$ and check whether it is nearby $\mathbf{x}^{+}$ . Accordingly, our transparency discriminator is able to identify an object-intersected ray with low transparency, and a ray with high transparency is considered to bypass the object. + +Objective. After classifying each ray via the transparency discriminator, we assign different objectives to different kinds of rays, pursuing an object-aware radiance field. Figure 2 (b) shows an overview of the learning scheme for our ORF. In general, given a group of multiview images of the target object, camera rays associated with pixels in images are utilized for volume rendering to optimize the radiance field, as described in Section 3.1. In the radiance field, a ray may terminate at the surface of objects (blue and golden), the ground plane (orange), or the point at infinity (green). To differentiate these kinds of rays, we feed them into a transparency discriminator and classify them as object-intersected or object-bypassed according to object regions estimated from the multi-view images. + +Specifically, for the object-intersected ray whose predicted transparency is less than 0.5, we learn in advance that the ray will go through the target object. Hence, we additionally constrain the ray to have high occupancy as a supplement to the reconstruction loss in Eq. (3): + +$$ +\mathrm {L} _ {\text {o c c}} = - \log \left(\sum_ {i = 1} ^ {N _ {p}} \alpha_ {i} \prod_ {j < i} \left(1 - \alpha_ {j}\right)\right), \mathcal {T} (\Re (\mathbf {p})) \leq 0. 5. \tag {7} +$$ + +In contrast, for the object-bypassed ray with $\mathcal{T}(\Re (\mathbf{p})) > 0.5$ , the occupancy is enforced to be small to ensure that no trivial surface appears in the background regions: + +$$ +\mathrm {L} _ {\text {o c c}} = - \log \left(1 - \sum_ {i = 1} ^ {N _ {p}} \alpha_ {i} \prod_ {j < i} \left(1 - \alpha_ {j}\right)\right), \mathcal {T} (\Re (\mathbf {p})) > 0. 5. \tag {8} +$$ + +In addition, we do not require the rendering of object-bypassed ray to reconstruct the input color, which means the reconstruction loss $|\mathbf{I}^r (\mathbf{p}) - \mathbf{R}(\mathbf{p})|$ is omitted when $\Re (\mathbf{p})$ is object-bypassed. + +Hence, the overall objective function integrates the reconstruction loss between the reference view and the rendered results in Eq. (3), and the occupancy regularization loss in Eq. (7) and Eq. (8). To further enhance the quality of the learnt surfaces, we also consider two extra losses + +following the recent works. The first one is the eikonal loss $\mathrm{L}_{\mathrm{eik}}$ [13] which encourages the geometry network to output a function similar to a signed distance field. The second one is the patch warping loss $\mathrm{L}_{\mathrm{warp}}$ [9] to improve the reconstruction ability by warping the existing patches from the reference views. We measure the overall objective as: + +$$ +\mathrm {L} = \lambda_ {1} \mathrm {L} _ {\text {r e c}} + \lambda_ {2} \mathrm {L} _ {\text {o c c}} + \lambda_ {3} \mathrm {L} _ {\text {e i k}} + \lambda_ {4} \mathrm {L} _ {\text {w a r p}}, \tag {9} +$$ + +where $\lambda_1 = 1$ , $\lambda_2 = 0.1$ , $\lambda_3 = 0.1$ , and $\lambda_4 = 1$ are the trade-off parameters. Here we set $\lambda_3$ and $\lambda_4$ following [9], and $\lambda_2$ is determined through experimental study. + +# 3.3. Rasterization-based Aggregation + +The new rasterization-based aggregation mechanism additionally exploits the geometric correspondence between 3D explicit surfaces and 2D planes. This design aims to further refine the quality of the estimated 2D object regions and make them multi-view consistent. + +Technically, as shown in Figure 2 (c), the mechanism first converts the 3D implicit surfaces (i.e., geometry network $\mathcal{G}$ ) into explicit surfaces (a explicit polygonal 3D representation like mesh) via marching cubes [22]. After that, we compute the projection from the 3D explicit surfaces (i.e., triangles) to the pixels of 2D images $\mathcal{I}$ by rasterization. Here the rasterization refers to the typical process of taking a triangle and figuring out which pixels it covers [37]. Formally, let $\Delta^j$ denote the $j$ -th triangle in the mesh, which corresponds to a set of pixels $\mathcal{P}_i^j \subseteq \mathbf{O}_i$ in the $i$ -th view. Note that the pixel set $\mathcal{P}_i^j$ is set as empty when $\Delta^j$ is invisible to the camera due to invalid projections (e.g., the triangle is projected outside the image) or occlusion. Such correspondence between triangles and pixels enables the aggregation of the object information of 2D object regions into 3D explicit surface $\Delta^j$ . In particular, we aggregate the object probabilities of all the pixels belonging to the triangle $\Delta^j$ from multiple views, yielding the triangle-level object probability of $\mathbf{O}_{agg}(\Delta^j)$ : + +$$ +\mathbf {O} _ {a g g} \left(\Delta^ {j}\right) = \frac {\sum_ {i = 1} ^ {| \mathcal {I} |} \sum_ {\mathbf {p} \in \mathcal {P} _ {i} ^ {j}} \mathbf {O} _ {i} (\mathbf {p})}{\epsilon + \sum_ {i = 1} ^ {| \mathcal {I} |} \sum_ {\mathbf {p} \in \mathcal {P} _ {i} ^ {j}} \mathbf {1}}, \tag {10} +$$ + +where $\epsilon$ is a constant term added to the denominator for numerical stability. After traversing all the 3D surfaces with the triangle-level aggregation (Eq. (10)), we re-project the triangle-level object probabilities of 3D surfaces back to 2D images. More specifically, for one pixel $\mathbf{p} \in \mathcal{P}_i^j \subseteq \mathbf{O}_i$ in each viewpoint, the object probability of $\mathbf{O}_i(\mathbf{p})$ is updated as the same triangle-level object probability $\mathbf{O}_{agg}(\Delta^j)$ . By doing so, the updated 2D multi-view object regions are enforced to be consistent across different views. + +Table 1: Comparisons of our ORF with other volume rendering techniques on DTU dataset for learning neural implicit surfaces. Here all the involved techniques do not use object masks as additional supervision for training. The top part reports the reconstruction performances when using object masks to trim the estimated meshes, and the bottom part directly compares the reconstruction performances of the estimated meshes without using object masks. The best performances are marked in bold and the second-best results are underlined. + +
ScanID243740556365698397105106110114118122Mean
with object masks: using the visual hull derived from human-annotated object masks for mesh trimming
NeRF [26]1.901.601.850.582.281.271.471.672.051.070.882.531.061.150.961.49
Unisurf [28]1.321.361.720.441.350.790.801.491.370.890.591.470.460.590.621.02
VolSDF [46]1.141.260.810.491.250.700.721.291.180.700.661.080.420.610.550.86
NeuS [41]1.001.370.930.431.100.650.571.481.090.830.521.200.350.490.540.84
NeuralWarp [9]0.490.710.380.380.790.810.821.201.060.680.660.740.410.630.510.68
without object masks: without mask-dependent trimming at inference
VolSDF [46]1.251.701.310.912.901.080.901.621.241.090.701.390.590.710.871.22
NeuS [41]1.591.981.440.951.820.740.641.631.301.410.591.330.440.510.541.13
NeuralWarp [9]0.972.541.520.412.540.740.791.061.531.400.750.720.390.570.621.10
ORF0.560.690.430.450.740.850.750.760.860.710.610.690.380.810.520.65
+ +# 4. Experiments + +We evaluate the effectiveness of ORF on DTU [16] and BlendedMVS [45] for multi-view 3D reconstruction. We first show both qualitative and quantitative results of ORF in comparison to existing techniques on DTU. Next, we conduct experimental analysis to validate the designs in ORF. Finally, we perform the qualitative comparison over samples derived from BlendedMVS for evaluation. + +# 4.1. Datasets and Experimental Settings + +DTU is a popular multi-view 3D reconstruction benchmark, which consists of 80 scenes with large variability in materials, appearance and geometry of objects. For each scene, the dataset provides 49 or 64 images (resolution: $1,600 \times 1,200$ ) captured from multiple camera views. The ground-truth point cloud of each scene is acquired with laser sensor. In our experiments, we follow [9, 28, 41, 46, 47] to use the selected 15 scenes in DTU for comparison. We strictly follow [9, 41] and use the official evaluation code of DTU [16] to compute the quantitative metrics. Specifically, the point clouds of objects (w/o background) in DTU are regarded as ground truth (GT). For a reconstructed mesh, we sample points on triangle surfaces in an evenly spaced manner (radius=0.2 as in [16]). Then, we report the final reconstruction score by averaging the accuracy and completeness of the sampled points (SP) (i.e., the chamfer distances of $\mathrm{SP} \rightarrow \mathrm{GT}$ and $\mathrm{GT} \rightarrow \mathrm{SP}$ ). It is also worthy to note that existing volume rendering techniques commonly use the additional object regions manually annotated by [27, 47] to trim the predicted mesh for only evaluating the reconstruction inside the visual hull. In contrast, our ORF learns an object-aware volumetric scene representation and directly constructs the 3D geometry of objects in the scene without the use of the visual hull derived from annotated object regions of scenes. + +BlendedMVS is a large-scale benchmark for multi-view 3D reconstruction, including 113 scenes with multi-view + +images. Compared to DTU, the backgrounds in BlendedMVS are more complex. We select samples from the lowres set of BlendedMVS, and each scene is equipped with 24 to 64 images (resolution: $768 \times 576$ ). Note that the ground truth of object regions for each image is not available. + +Implementation Details. The whole network of ORF is built over VolSDF [46], and we adopt the same architecture as in existing volume rendering methods [28, 46, 47] for fair comparison. The whole network uses sphere initialization [2]. During training, we train our ORF with a two-stage strategy. We first optimize the network with the reconstruction loss and eikonal loss under the same setting in VolSDF (100k iterations with learning rate exponentially decayed from 5e-4 to 5e-5, batch size: 1,024 rays). Next, the network is fine-tuned with the overall objective in Eq. (9) (100k iterations with learning rate of 5e-4, batch size: 512 rays). The object probability is calculated by the transparency discriminator in each forward pass using the latest radiance field. The mesh extraction for rasterization-based aggregation is only conducted once after the first training stage of ORF. + +# 4.2. Comparison on DTU Dataset + +Quantitative Results. We compare with several neural surface reconstruction techniques under two different evaluation settings for fair comparison: 1) baselines using the visual hull derived from human-annotated object masks for mesh trimming, 2) all re-implemented SDF-based baselines and our ORF without mask-dependent trimming at inference. Such two settings are denoted as with/without object masks, respectively. All the mentioned baselines are grouped into three directions: volume rendering with classical radiance fields [26], occupancy network [28], and SDF-based (Signed Distance Function) fields [46, 41, 9]. Table 1 summarizes the performance comparisons on each evaluation scenario. Note that all baselines and our ORF + +![](images/5aceae4d2f16a4f9917e97daab7415ea3ecaca47b2bfe93a20a50ab0595bc548.jpg) +Figure 3: Comparisons on qualitative results of our ORF with other neural radiance fields techniques on DTU dataset for 3D geometry reconstruction with or without object masks at inference. * denotes our implementation of VolSDF. + +do not use human-annotated object masks of scenes to optimize geometry/radiance nets during training. At inference, these baselines commonly require masks to remove the background of the learnt mesh. Instead, ORF can directly produce the object mesh without masks. + +In general, our ORF exhibits better reconstruction quality against all these baselines. Remarkably, ORF achieves 0.65 in the metric of Chamfer distance without the use of the visual hull derived from object masks in scenes, which is better than the reconstruction accuracy (0.68) of NeuralWarp when exploiting demands object masks at inference. The results generally highlight the key advantage of learning object-aware geometry reconstruction for neural implicit surfaces. Specifically, under the evaluation scenario with object masks, NeRF produces unsatisfactory reconstruction results since the lack of 3D geometry constraints. Unisurf unifies volume/surface rendering and enables better results. VolSDF, NeuS, and NeuralWarp exploit SDF and obtain promising reconstructions. Nevertheless, a performance drop is observed for each SDF-based method when object masks are unavailable at inference, since the primary estimated mesh contains more trivial geometry of the background. In contrast, our ORF achieves competitive reconstruction accuracy through learning an object-aware radiance field without the use of object masks derived visual hull. This confirms the effectiveness of exploring object awareness via transparency discriminator and rasterization-based aggregation. + +Qualitative Results. We then visually examine the reconstruction quality of our proposal by comparing ORF with three SDF-based approaches (VolSDF, NeuS, NeuralWarp) on five selected scenes from DTU dataset. Figure 3 shows the qualitative results of the reconstructed meshes. + +Note that here we show the reconstruction results of the two different evaluation settings (with or without object masks at inference for trimming estimated meshes). In general, all the three approaches reconstruct high-fidelity object surfaces after mask-dependent mesh trimming. In between, by constraining volume rendering with photo-consistency objective across multiple views, NeuralWarp produces more accurate surfaces with high-fidelity details (e.g., the bricks with sparse textures in the first two scenes) against VolSDF and NeuS. Furthermore, when the object masks are unavailable, the output meshes of each baselines become noisy with more trivial geometry and even some artifact of the background. In contrast, under this challenging setting, our ORF performs visually on par with the NeuralWarp, while requiring no object mask dependent mesh trimming at inference. The results again validate the merit of our ORF. + +# 4.3. Experimental Analysis + +Ablation Study. Here we investigate how each design in our ORF influences the overall reconstruction performance. Table 2 and Figure 4 details the performances and the corresponding qualitative results across different ablated runs of ORF, respectively. We start from a basic SDF-based radiance field without ray discrimination (i.e., NeuralWarp), which achieves 1.10 of Chamfer distance. The estimated mesh of this basic model inevitably contains trivial background geometry. Next, by solely using the outputs of salient object segmentation (Saliency) to distinguish object-intersected and object-bypassed rays, we observe a clear performance boost and the background is effectively screened. However, the independently estimated object probability of each 2D object region may be inaccurate and inconsistent across different viewpoints, resulting in error + +Table 2: Ablation study on each design in ORF on DTU dataset. + +
Transparency Discriminator Saliency +Multiview +VerifierRasterization-based AggregationChamfer Distance
1.10
✓0.90
✓✓0.87
✓✓✓0.76
✓✓✓✓0.65
+ +![](images/f369cdae7ab9788a9f664daac369815d146466599f36090b7fd00d1caa684a92.jpg) +Figure 4: Comparisons on qualitative results by using different ablated runs of our ORF on DTU dataset for 3D geometry reconstruction object masks dependent mesh trimming at inference. + +![](images/99adba7364705943acf8cc1a548ad6623bd834036f419fd3c8222d400a33c70b.jpg) + +![](images/a38e004a07bb14e98b10ddb1f33fbd3dc5ec459b756a11437ca5378b1a284735.jpg) + +![](images/19a6e461862444af3a7c901462a917a493e554d188063e552dc19c37a7a6a37a.jpg) + +![](images/c90c4423ca0fb340dce470aa820a18c97912777d18bdf022620d0d254934ae69.jpg) +Figure 5: Comparisons on qualitative results of our ORF with other techniques on BlendedMVS for 3D geometry reconstruction without object masks at inference. * denotes our re-implemented VolSDF without the hand-crafted parametrization in NeRF++. + +accumulation and holes in the reconstructions. To address this issue, we enhance the strategy of transparency discrimination by jointly exploiting the 2D object regions estimated from multiple views (Multiview), leading to slightly better reconstruction. We then leverage the projection verification strategy (Verifier) to screen out invalid projections (e.g., the points are projected outside of the source images or occluded by other surfaces), which further boosts up the reconstruction. Finally, by capitalizing on Rasterization-based Aggregation to refine the estimated 2D object regions, the mIoU of object regions is improved from $94\%$ to $97\%$ and ORF achieves the highest reconstruction quality. + +Effect of the Trade-off Parameter $\lambda_{2}$ . To clarify the effect of the trade-off parameter $\lambda_{2}$ in Eq. (9), we detail the reconstruction performances (i.e., Chamfer distances) with different trade-off parameters in Table 3. In the extreme case of $\lambda_{2} = 0$ , no occupancy regularization objective for foreground and background rays is utilized and the whole model degenerates to the conventional SDF-based approach. When enlarging $\lambda_{2}$ as 0.05, a better reconstruction accuracy is attained, which basically demonstrates that the foreground-aware inductive bias benefits volume rendering. The performance change is relatively smooth when $\lambda_{2}$ varies in the range from 0.05 to 0.20, and the best reconstruction accuracy is attained when $\lambda_{2} = 0.10$ . Furthermore, the reconstruction accuracy slightly decreases when $\lambda_{2} \geq 0.30$ . We speculate that this may be the result of amplifying the noise of ray discrimination if we set a higher weight to occupancy regularization objective. + +Effect of the Saliency Model's Performance. To verify how the quality of saliency influences the reconstruction, we perform salient object segmentation using another two models and obtain additional two versions of saliency maps. We evaluate the three different versions of saliency for both reconstruction and segmentation tasks on DTU (re + +Table 3: Effect of the trade-off parameter ${\lambda }_{2}$ in ORF on DTU. + +
λ20.000.050.100.200.300.400.50
Chamfer Dist.1.100.660.650.670.690.700.71
Image
VolSDF*
Neural +Warp
ORF
+ +construction: 0.65, 0.67, 0.67; segmentation: $94\%$ , $93\%$ , $91\%$ mean IoU). The results show that the saliency segmentation performance on DTU has almost saturated, and the reconstruction performances of ORF only fluctuate within the range of 0.02, which eases the difficulty on choosing saliency segmentation model in practice. + +# 4.4. Comparison on BlendedMVS Dataset + +Figure 5 further showcases the geometry reconstruction results with different techniques for six scenes in BlendedMVS. It is worthy to note that VolSDF originally utilizes an additional hand-crafted parametrization as in $\mathrm{NeRF}++$ [50] to tackle the complex backgrounds by modeling the volume outside a radius 3 sphere with another NeRF network. For fair comparison, here we re-implement VolSDF by removing this parametrization. Similar to the observations on DTU under the setting without object masks, both VolSDF and NeuralWarp produce high-fidelity object surfaces, while more trivial background geometry is inevitably included. Instead, our ORF nicely removes the trivial geometry and performs nearly on par with these approaches. + +# 5. Conclusions + +In this work, we circumvent the use of object masks derived visual hull, and shape a new paradigm of learning object-aware geometry reconstruction for neural implicit surfaces. To verify our claim, we novelly remould the classical neural radiance fields by involving a new transparency discriminator to distinguish object-intersected and object-bypassed rays on-the-fly. Such ray discrimination serves as object-aware inductive bias to enable a reconstruction of 3D geometry of the key object in the scene. 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In CVPR, 2023. \ No newline at end of file diff --git a/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/images.zip b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7ba2d881d739f29f97a71d22c04d7d56b3b510bc --- /dev/null +++ b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3229e2b58c85dc91c73e3188a1d92d05be808a63c1eab44b5e74b4f0b52d3df3 +size 640995 diff --git a/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/layout.json b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6487dd7e1f85ee1bca8a5ed6f9aad3fc48e20fa9 --- /dev/null +++ b/2023/Learning Neural Implicit Surfaces with Object-Aware Radiance Fields/layout.json @@ -0,0 +1,8066 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "spans": [ + { + "bbox": [ + 78, + 103, + 515, + 121 + ], + "type": "text", + "content": "Learning Neural Implicit Surfaces with Object-Aware Radiance Fields" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 135, + 143, + 458, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 143, + 458, + 171 + ], + "spans": [ + { + "bbox": [ + 135, + 143, + 458, + 171 + ], + "type": "text", + "content": "Yiheng Zhang, Zhaofan Qiu, Yingwei Pan, Ting Yao, and Tao Mei \nUniversity of Science and Technology of China HiDream.ai Inc." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 75, + 174, + 517, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 174, + 517, + 185 + ], + "spans": [ + { + "bbox": [ + 75, + 174, + 517, + 185 + ], + "type": "text", + "content": "{yihengzhang.chn, zhaofanqiu, panyw.ustc, tingyao.ustc}@gmail.com, tmei@hidream.ai" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 52, + 186, + 532, + 308 + ], + "blocks": [ + { + "bbox": [ + 52, + 186, + 532, + 308 + ], + "lines": [ + { + "bbox": [ + 52, + 186, + 532, + 308 + ], + "spans": [ + { + "bbox": [ + 52, + 186, + 532, + 308 + ], + "type": "image", + "image_path": "7dee064237e669488e5fe0d960d610c69aea1c944822e206f70a9030e497e777.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 308, + 547, + 352 + ], + "lines": [ + { + "bbox": [ + 46, + 308, + 547, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 547, + 352 + ], + "type": "text", + "content": "Figure 1: The implicit surfaces learnt via (a) conventional scheme which suffers from noisy background geometry representations. In this work, we introduce (b) an object-aware volumetric scene representation by automatically recognizing rays as object-intersected or object-bypassed, aiming to highlight the key object surface in the foreground. (c) Such object surface benefits a series of applications, e.g., 3D scene composition, object moving/editing, and even skeleton assignment." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 361, + 192, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 361, + 192, + 374 + ], + "spans": [ + { + "bbox": [ + 143, + 361, + 192, + 374 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 389, + 290, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 389, + 290, + 700 + ], + "spans": [ + { + "bbox": [ + 45, + 389, + 290, + 700 + ], + "type": "text", + "content": "Recent progress on multi-view 3D object reconstruction has featured neural implicit surfaces via learning high-fidelity radiance fields. However, most approaches hinge on the visual hull derived from cost-expensive silhouette masks to obtain object surfaces. In this paper, we propose a novel Object-aware Radiance Fields (ORF) to automatically learn an object-aware geometry reconstruction. The geometric correspondences between multi-view 2D object regions and 3D implicit/explicit object surfaces are additionally exploited to boost the learning of object surfaces. Technically, a critical transparency discriminator is designed to distinguish the object-intersected and object-bypassed rays based on the estimated 2D object regions, leading to 3D implicit object surfaces. Such implicit surfaces can be directly converted into explicit object surfaces (e.g., meshes) via marching cubes. Then, we build the geometric correspondence between 2D planes and 3D meshes by rasterization, and project the estimated object regions into 3D explicit object surfaces by aggregating the object information across multiple views. The aggregated object information in 3D explicit object surfaces is further projected back to 2D planes, aiming to update 2D object regions and enforce them to be multi-view consistent. Extensive experiments on DTU and BlendedMVS verify the capability of ORF to produce comparable surfaces against the state-of-the-art models that demand silhouette masks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 361, + 386, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 361, + 386, + 374 + ], + "spans": [ + { + "bbox": [ + 307, + 361, + 386, + 374 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 391, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 547, + 715 + ], + "type": "text", + "content": "Multi-view 3D reconstruction, i.e., the task of reconstructing 3D geometry/surface of objects from multi-view 2D images, has played a fundamental challenge to computer vision and computer graphics communities for decades. In the early stage, the mainstream solution is the classical Multi-View Stereo (MVS) [3, 5, 12, 20, 34, 35] that exploits photometric consistency across different camera views to learn explicit geometry representations (e.g., meshes or voxel grids). The ultimate reconstruction relies heavily on the quality of cross-view matching. In practice, such matching often fails to associate objects with sparse textures, resulting in severe artifact or missing parts on surfaces. To address this issue, recent studies turn their focus on investigating how to represent 3D surfaces as implicit geometry representations. Many consider learning a continuous implicit function that formulates neural implicit surfaces in occupancy field [25, 31] or signed distance field [29]. In between, surface rendering techniques [27, 47, 49] are designed to optimize these fields, leading to impressive reconstruction quality via differentiable rendering from images. Nevertheless, learning such implicit geometry representations requires additional object masks of scenes, since the color of each ray is assumed to only correspond to a single point where a surface intersects with this ray. Moreover, the gradient of differentiable rendering is only backpropagated to the local surface near intersection, resulting in a sub-optimal solution for neural implicit surfaces." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17893" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 335 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 335 + ], + "type": "text", + "content": "To mitigate these limitations of local gradient propagation and the demand for the input object masks during fields optimization, a series of volume rendering based neural radiance fields techniques [9, 28, 41, 46] start to emerge. Recently, the seminal work of NeRF [26] builds up the foundation of volumetric scene in neural radiance fields for view synthesis, and performs classical volume rendering via alpha-compositing colors of the sampled points along rays. The subsequent methods further remould classical volume rendering by imposing implicit surface representations, e.g., occupancy network [28] or signed distance function [9, 41, 46]. These approaches produce more accurate surfaces by reconstructing the holistic scenery. Nevertheless, the learnt implicit surfaces are inevitably composed of rich geometry representations in both foreground and background (Figure 1 (a)), which are not distinguished during radiance fields optimization. Accordingly, existing techniques utilize additional cost-expensive silhouette masks to trim the learnt 3D meshes derived from implicit surfaces. The removal of vertices and/or surfaces outside the visual hull directly highlights the geometry of the key objects in the foreground, yielding object surfaces." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 343, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 343, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 343, + 286, + 712 + ], + "type": "text", + "content": "In this work, we devise a new Object-aware Radiance Field (ORF), which goes one step further to eliminate the need of the visual hull derived from human-annotated object masks in scenes for learning object surfaces. Our launching point is to introduce an object-aware volumetric scene representation by inferring the foreground/object and background radiance fields on-the-fly. Both the geometric correspondences between multi-view 2D object regions and 3D implicit or explicit object surfaces are exploited to boost the learning of object-aware volumetric scene representation. ORF is henceforth able to encourage the reconstruction of foreground/object geometry without additional 3D supervision of visual hull. Specifically, we first estimate 2D object regions directly based on the multi-view images. Next, on the basis of the estimated 2D object regions, ORF capitalizes on a transparency discriminator to automatically recognize the transparency of each ray in the radiance field. A low transparency indicates that the ray intersects with the object, and rays with high transparency are considered to be object-bypassed. Such predicted transparency of rays is further regarded as prior information to regularize the radiance field in an object-aware manner. Especially, as shown in Figure 1 (b), all the sampled rays are divided into object-intersected rays and object-bypassed rays according to predictions given by the transparency discriminator, leading to 3D implicit object surfaces. After that, we leverage marching cubes to directly convert the 3D implicit object surfaces into 3D explicit object surfaces. The inherent geometric correspondence between 2D planes and 3D explicit object surfaces are thus constructed via rasterization. This geometric correspondence enables the projection from the es" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 308, + 72, + 544, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 178 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 178 + ], + "type": "text", + "content": "timated 2D object regions into 3D explicit object surfaces, and meanwhile the object information across multiple views are aggregated. Furthermore, ORF projects the aggregated object information in 3D explicit object surfaces back to 2D planes, thereby updating the 2D object regions and enforcing them multi-view consistent. The whole process refines the estimated 2D object regions and 3D implicit/explicit object surfaces, pursuing an object reconstruction without trivial background surfaces." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 308, + 180, + 544, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 180, + 544, + 299 + ], + "spans": [ + { + "bbox": [ + 308, + 180, + 544, + 299 + ], + "type": "text", + "content": "In sum, we have made the following contributions: (I) ORF designs a transparency discriminator to automatically capture useful object-aware inductive bias, which further supervises radiance fields to learn object-aware geometry reconstruction. (II) ORF additionally mines the inherent geometric correspondence between multi-view 2D object regions and 3D object surfaces to refine them along with volume rendering. (III) We evaluate ORF on two widely-used benchmarks (DTU and BlendedMVS), demonstrating the effectiveness of our proposal." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 311, + 391, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 311, + 391, + 323 + ], + "spans": [ + { + "bbox": [ + 308, + 311, + 391, + 323 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 331, + 544, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 331, + 544, + 557 + ], + "spans": [ + { + "bbox": [ + 308, + 331, + 544, + 557 + ], + "type": "text", + "content": "Multi-view 3D Reconstruction is one of the fundamental tasks in 3D vision, which attempts to reconstruct the 3D geometry from images captured from multiple views. The early works on this task has proceeded along two different dimensions: matching features across views [4, 34] and representing shapes with a voxel grid [1, 5, 10, 20, 30, 36, 38, 39]. The first dimension reconstructs the 3D scenes by matching the pixels with similar appearance, and usually requires the complex designs for fusing depth information [8, 24] or meshing [17, 18]. The second dimension represents the 3D geometry as a volume grid and is limited by the cubic increase of memory requirements. After that, inspired by the recent advance of deep learning techniques, deep neural networks are exploited as an alternative of hand-designed traditional components in 3D reconstruction. For instance, the visual feature for matching [14, 21, 23, 40, 48], depth fusion [11, 33] and depth map prediction [15, 43, 44] can be learnt by neural networks, leading to better performances thanks to the high learning capacity of deep models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 558, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 558, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 558, + 544, + 712 + ], + "type": "text", + "content": "Instead of explicitly reconstructing the 3D geometry, the neural implicit surfaces are introduced to encode the characteristics of 3D scenes by neural networks. Specifically, the surfaces are represented by a neural network which outputs either an occupancy field [25, 31] or a Signed Distance Function (SDF) [29]. In this scheme, the implicit representations of surfaces are learnt via surface rendering [27, 47] which determines the radiance directly on the surface of an object and provides a differentiable rendering formulation using implicit gradients. Recently, Neural Radiance Fields (NeRF) [26] is proposed to implicitly represent scenes by volume rendering which learns alpha-compositing of the radiance field along camera rays, which benefits 3D con" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "17894" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "tent creation tasks [51, 6, 7, 42]. The main focus of NeRF is the quality of novel view synthesis, but the geometry is not guaranteed. To promote the quality of learnt surfaces, Unisurf [28] unifies radiance fields and occupancy-based implicit surfaces, enabling plausible reconstruction. VolSDF [46] and NeuS [41] exploit SDF as implicit surface representations and obtain better results. NeuralWarp [9] further boosts up the reconstruction by integrating photo consistency between multi-view images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 335 + ], + "type": "text", + "content": "Our work also falls into the category of learning neural implicit surfaces with volume rendering. Despite the progress in improving rendering quality or surface extraction, the way to reconstruct object surfaces without requiring the visual hull derived from object masks in scenes has not been fully explored. The related work of DFFs [19] distills off-the-shelf 2D vision encoders into a 3D feature field to enable the decomposition of scenes conditioning on user-specified queries. Different from [19], our ORF exploits the geometric correspondence between multi-view 2D object regions and 3D object surfaces to automatically separate objects and background, and enhance the quality of the learnt object surfaces." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 345, + 217, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 217, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 217, + 358 + ], + "type": "text", + "content": "3. Object-aware Radiance Fields" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 289, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 289, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 289, + 593 + ], + "type": "text", + "content": "This section first reviews the standard scheme to represent scenes via radiance fields without the consideration of object region separation (Section 3.1). Next, we describe how the designed transparency discriminator in our ORF distinguishes the object-intersected rays and object-bypassed rays in radiance fields based on the estimated object regions. And then we introduce how to learn an object-aware radiance field by optimizing rays separately with the help of the transparency discriminator (Section 3.2). Furthermore, we design a novel rasterization-based aggregation mechanism to additionally construct the geometric correspondence between 2D object regions and 3D object surfaces via rasterization. Such geometric correspondence enables the aggregation of object information from 2D planes to 3D explicit object surfaces. The aggregated object information in turn updates the 2D object regions in a multi-view consistent manner, pursuing a more high-fidelity object reconstructions (Section 3.3). Figure 2 depicts an overview of our ORF architecture." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 599, + 256, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 256, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 256, + 612 + ], + "type": "text", + "content": "3.1. Representing Scene via Radiance Fields" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "type": "text", + "content": "Neural radiance field and its recent variants aim to represent 3D scenes by two implicit functions, i.e., geometry function and radiance function, which are approximated via two individual neural networks. The geometry network models the geometric structure of 3D scenes, and the radiance network encodes the color emitted by any region in space from all directions. The two networks represent the characteristics in the 3D scene and codetermine the ren-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": "dered novel views. When rendering the target view " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " taken from the direction " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": ", the rendered color " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{R}(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " of each pixel " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " is computed by both geometry network " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " and radiance network " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " in a differentiable way. Specifically, we first sample " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " points " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "i = 1,\\dots,N_{p}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " along the corresponding ray " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\Re (\\mathbf{p})" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " going through the camera center and the target pixel " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": ". Note that here we omit the notations of target pixel for simplicity. The surface normal " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_i" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": ", the occupancy value " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " and the radiance value " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " are measured by the geometry network " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " and the radiance network " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 390, + 196, + 545, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 196, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 390, + 196, + 545, + 213 + ], + "type": "interline_equation", + "content": "\\mathbf {n} _ {i}, \\alpha_ {i} = \\mathcal {G} (\\mathbf {x} _ {i}), \\tag {1}", + "image_path": "2f4ab24b36d0cb7843c5346330317ee107a18d4e38879928e07852bb42e090f9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 391, + 213, + 460, + 222 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 213, + 460, + 222 + ], + "spans": [ + { + "bbox": [ + 391, + 213, + 460, + 222 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {i} = \\mathcal {C} (\\mathbf {x} _ {i}, \\mathbf {n} _ {i}, \\mathbf {d}).", + "image_path": "8044657ef7be58219551bc48c4224315b279e5daec0b93836ef940e0a2562712.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 228, + 547, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 547, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 547, + 264 + ], + "type": "text", + "content": "The rendering of the scene at pixel " + }, + { + "bbox": [ + 304, + 228, + 547, + 264 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 228, + 547, + 264 + ], + "type": "text", + "content": " is approximated as a weighted summation of radiance values " + }, + { + "bbox": [ + 304, + 228, + 547, + 264 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i" + }, + { + "bbox": [ + 304, + 228, + 547, + 264 + ], + "type": "text", + "content": " at each sampled point by using the occupancy values as the weights:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 366, + 269, + 545, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 269, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 366, + 269, + 545, + 300 + ], + "type": "interline_equation", + "content": "\\mathbf {R} (\\mathbf {p}) = \\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} (1 - \\alpha_ {j}) \\mathbf {c} _ {i}, \\tag {2}", + "image_path": "563cbb340877664cf8663ab7df73509f543e3a90b078afbbbad4589f107e7caa.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 305, + 547, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 305, + 547, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 305, + 547, + 402 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 305, + 547, + 402 + ], + "type": "inline_equation", + "content": "\\prod_{j < i}(1 - \\alpha_j)" + }, + { + "bbox": [ + 304, + 305, + 547, + 402 + ], + "type": "text", + "content": " is to simulate the occlusion caused by the opaque pixels in front of the target pixel. As a practical choice, we utilize transformed Signed Distance Field (SDF) encoding [41, 46] as the geometry function. Eq. (2) is actually the discrete approximation of an integral along the camera ray by sampling a limited number of points. The sampling strategies have been discussed in [26, 28, 41, 46] to improve the geometry estimation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "text", + "content": "At training stage, the two neural networks are jointly optimized by encouraging the reconstruction of the given views of the 3D scene. Given one reference view " + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^r" + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "text", + "content": ", the reconstruction loss for " + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbf{I}^r" + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "text", + "content": " is calculated by the L1 distance between the reference view " + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^r" + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "text", + "content": " and the neural volume rendering results " + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 304, + 402, + 547, + 473 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 378, + 479, + 545, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 479, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 378, + 479, + 545, + 491 + ], + "type": "interline_equation", + "content": "\\mathrm {L} _ {\\text {r e c}} = \\left| \\mathbf {I} ^ {r} (\\mathbf {p}) - \\mathbf {R} (\\mathbf {p}) \\right|, \\tag {3}", + "image_path": "fd380c0834765ca9e0e348298ee694e2a57c82002372f5f2896a59c185ec8f20.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 497, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 497, + 547, + 594 + ], + "type": "inline_equation", + "content": "|\\cdot|" + }, + { + "bbox": [ + 304, + 497, + 547, + 594 + ], + "type": "text", + "content": " is the L1 loss. This loss function simply treats each camera ray corresponding to " + }, + { + "bbox": [ + 304, + 497, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 497, + 547, + 594 + ], + "type": "text", + "content": " equally and constrains the difference between the input pixel and the rendered result, while ignoring the distinction of rays that either intersect or bypass the objects. As a result, the implicit 3D model often contains some trivial surfaces of the background regions (Figure 1), and thus requires the object masks derived visual hull to execute an additional trimming step at inference." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 599, + 516, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 516, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 516, + 612 + ], + "type": "text", + "content": "3.2. Learning Object-aware Radiance Fields" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "To alleviate these issues, we propose to automatically distinguish the object-intersected and object-bypassed rays, making the learnt radiance fields object-aware without manually annotating the visual hull for each scene. To materialize this idea, here we first elaborate how to achieve the high-quality ray/transparency prediction via a devised transparency discriminator (Figure 2 (a)), followed by the learning scheme with different objectives (Figure 2 (b))." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17895" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 69, + 521, + 329 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 521, + 329 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 521, + 329 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 521, + 329 + ], + "type": "image", + "image_path": "7c500a76086c48b7594715237c5bb4e7dd99e1fd88e869f558d78b38a4725f93.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 333, + 523, + 345 + ], + "lines": [ + { + "bbox": [ + 67, + 333, + 523, + 345 + ], + "spans": [ + { + "bbox": [ + 67, + 333, + 523, + 345 + ], + "type": "text", + "content": "Figure 2: An overview of the proposed Object-aware Radiance Fields (ORF) framework for learning neural implicit surfaces." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": "Transparency Discriminator. Formally, we consider the ray " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\Re (\\mathbf{p})" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": " derived from pixel " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": " of the reference view " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^r" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": ". One intuitive way to inspect whether the " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\Re (\\mathbf{p})" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": " intersects with the object is to predict the probability that the pixel " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": " belongs to the estimated object regions " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{O}^r" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": " from the perspective of " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^r" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": ". Note that here we employ an off-the-shelf salient object segmentation model [32] to learn the prior knowledge of generic salient objects. Replacing the saliency model with other segmentation models is flexible to generalize to other reconstruction scenarios. Such saliency map generated from " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^r" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": " provides coarse object information that indicates the 2D object regions " + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{O}^r" + }, + { + "bbox": [ + 46, + 352, + 289, + 555 + ], + "type": "text", + "content": ". However, the complex object appearance and challenging variation of views probably affect the quality of object information. As such, we further design a transparency discriminator that jointly exploits the 2D object regions estimated from different views for ray discrimination in radiance field." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "In particular, given a reference image " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I}^r" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " and multiple source images " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "(\\mathbf{I}_i^s,i = 1,\\dots ,N_s)" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " captured from different viewpoints, we can roughly estimate the object regions in each image individually via salient object segmentation. Let " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{O}^r" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_i^s" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "(i = 1,\\dots ,N_{s})" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " denote the corresponding 2D object regions. We start from the ray " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Re (\\mathbf{p})" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " corresponding to pixel " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}\\in \\mathbf{I}^r" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " that intersects with the implicit surface for the first time at point " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{+}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " in the radiance field. To locate the point " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{+}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " in the world coordinates, we sample points along " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Re (\\mathbf{p})" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " from its corresponding camera center and feed the sampled points into the geometry network " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " in order. Then, following [46], the signed distance between each sampled point and its nearest surface is derived from the output of" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 352, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 375 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 352, + 545, + 375 + ], + "type": "text", + "content": ". The first point we sampled that has a positive signed distance is regarded as " + }, + { + "bbox": [ + 304, + 352, + 545, + 375 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{+}" + }, + { + "bbox": [ + 304, + 352, + 545, + 375 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": "After that, we mine the geometric correspondence between 3D implicit surfaces and 2D planes by projecting the point " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{+}" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " into the 2D plane of each source image. By denoting the projection as " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\pi_i^s (\\mathbf{x}^+)" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "(i = 1,\\dots ,N_{s})" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " in source image coordinates, we formulate " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\pi_i^s (\\mathbf{x}^+)" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 371, + 441, + 545, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 441, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 371, + 441, + 545, + 455 + ], + "type": "interline_equation", + "content": "\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right) = K _ {i} ^ {s} \\left(R _ {i} ^ {s} \\mathbf {x} ^ {+} + \\mathbf {t} _ {i} ^ {s}\\right), \\tag {4}", + "image_path": "bbf504b2d27abdfa10959d631757678ff4e47d71100a5870a27b1d27977bb7c1.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "inline_equation", + "content": "K_{i}^{s}" + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "content": " is the internal calibration matrix of the " + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "content": "-th source camera, and " + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "inline_equation", + "content": "(R_{i}^{s},\\mathbf{t}_{i}^{s})" + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "content": " are the extrinsic parameters of the camera " + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "inline_equation", + "content": "(R_{i}^{s}:3\\times 3" + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "content": " rotation matrix, " + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_i^s" + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "content": ": 3-dim translation vector). In this way, each projection associates the point " + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{+}" + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "content": " in world coordinates to pixels in source images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": "Based on the estimated 2D object regions from multiple views " + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{O}^T" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_i^s" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, N_s" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": "), a transparency discriminator is devised to predict the transparency " + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{T}(\\Re(\\mathbf{p}))" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": ". Here the transparency can be interpreted as the probability that the ray " + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\Re(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": " bypasses the target object. Specifically, in an effort to take all 2D object regions into account, we measure the transparency for " + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\Re(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": " by averaging the probabilities of pixels belonging to objects in multiple views with regard to the same point " + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^+" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 335, + 635, + 545, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 635, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 335, + 635, + 545, + 659 + ], + "type": "interline_equation", + "content": "\\mathcal {T} (\\Re (\\mathbf {p})) = 1 - \\frac {\\mathbf {O} ^ {r} (\\mathbf {p}) + \\sum_ {i = 1} ^ {N _ {s}} \\mathbf {O} _ {i} ^ {s} \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}{1 + N _ {s}}. \\tag {5}", + "image_path": "749f0da8f2539f693124cde8a96e54fdb47a63bb28390e297a4ace4d17eb82f0.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Such formulation assumes that the intersection point " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{+}" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " are observed by each source camera without any occlusion. But in practice, the intersection points may be projected outside of the source images or occluded by other surfaces which" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17896" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": "are closer to the source cameras. To tackle this issue, we extend the formulation in Eq. (5) with a binary indicator " + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "V(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 102, + 287, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 102, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 55, + 102, + 287, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {T} (\\Re (\\mathbf {p})) = 1 - \\frac {\\mathbf {O} ^ {r} (\\mathbf {p}) + \\sum_ {i = 1} ^ {N _ {s}} V \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right) \\mathbf {O} _ {i} ^ {s} \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}{1 + \\sum_ {i = 1} ^ {N _ {s}} V \\left(\\pi_ {i} ^ {s} \\left(\\mathbf {x} ^ {+}\\right)\\right)}. \\tag {6}", + "image_path": "57de1a15f89a11d7ae94141c526d6da62e21bda34ed8383a3014aa615792963d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": "We set " + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "inline_equation", + "content": "V(\\pi_i^s (\\mathbf{x}^+))" + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": " as 1 when " + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{+}" + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": " is within the maximum area that can be captured by the camera of " + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_i^s" + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": " and meanwhile it is also the first intersection between ray " + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\Re (\\pi_i^s (\\mathbf{x}^+))" + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": " and implicit surfaces. In the implementation, we first check if the " + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\pi_i^s (\\mathbf{x}^+)" + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": " locates inside the source image " + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_i^s" + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": ". Then we estimate the first intersection point of ray " + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\Re (\\pi_i^s (\\mathbf{x}^+))" + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": " and check whether it is nearby " + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{+}" + }, + { + "bbox": [ + 46, + 138, + 287, + 258 + ], + "type": "text", + "content": ". Accordingly, our transparency discriminator is able to identify an object-intersected ray with low transparency, and a ray with high transparency is considered to bypass the object." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 258, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 425 + ], + "type": "text", + "content": "Objective. After classifying each ray via the transparency discriminator, we assign different objectives to different kinds of rays, pursuing an object-aware radiance field. Figure 2 (b) shows an overview of the learning scheme for our ORF. In general, given a group of multiview images of the target object, camera rays associated with pixels in images are utilized for volume rendering to optimize the radiance field, as described in Section 3.1. In the radiance field, a ray may terminate at the surface of objects (blue and golden), the ground plane (orange), or the point at infinity (green). To differentiate these kinds of rays, we feed them into a transparency discriminator and classify them as object-intersected or object-bypassed according to object regions estimated from the multi-view images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 426, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 485 + ], + "type": "text", + "content": "Specifically, for the object-intersected ray whose predicted transparency is less than 0.5, we learn in advance that the ray will go through the target object. Hence, we additionally constrain the ray to have high occupancy as a supplement to the reconstruction loss in Eq. (3):" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 491, + 287, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 491, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 69, + 491, + 287, + 521 + ], + "type": "interline_equation", + "content": "\\mathrm {L} _ {\\text {o c c}} = - \\log \\left(\\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} \\left(1 - \\alpha_ {j}\\right)\\right), \\mathcal {T} (\\Re (\\mathbf {p})) \\leq 0. 5. \\tag {7}", + "image_path": "e0cb85c334cd9d23ddf80fad939a969070d91b10030c66fc200a1026a76e6da8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 528, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 287, + 564 + ], + "type": "text", + "content": "In contrast, for the object-bypassed ray with " + }, + { + "bbox": [ + 47, + 528, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{T}(\\Re (\\mathbf{p})) > 0.5" + }, + { + "bbox": [ + 47, + 528, + 287, + 564 + ], + "type": "text", + "content": ", the occupancy is enforced to be small to ensure that no trivial surface appears in the background regions:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 569, + 287, + 600 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 569, + 287, + 600 + ], + "spans": [ + { + "bbox": [ + 56, + 569, + 287, + 600 + ], + "type": "interline_equation", + "content": "\\mathrm {L} _ {\\text {o c c}} = - \\log \\left(1 - \\sum_ {i = 1} ^ {N _ {p}} \\alpha_ {i} \\prod_ {j < i} \\left(1 - \\alpha_ {j}\\right)\\right), \\mathcal {T} (\\Re (\\mathbf {p})) > 0. 5. \\tag {8}", + "image_path": "4d1c15a1390bdfb4cd39b5916cf5c6e120a641588b6364c6332fcd284d655133.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "type": "text", + "content": "In addition, we do not require the rendering of object-bypassed ray to reconstruct the input color, which means the reconstruction loss " + }, + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "type": "inline_equation", + "content": "|\\mathbf{I}^r (\\mathbf{p}) - \\mathbf{R}(\\mathbf{p})|" + }, + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "type": "text", + "content": " is omitted when " + }, + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\Re (\\mathbf{p})" + }, + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "type": "text", + "content": " is object-bypassed." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "type": "text", + "content": "Hence, the overall objective function integrates the reconstruction loss between the reference view and the rendered results in Eq. (3), and the occupancy regularization loss in Eq. (7) and Eq. (8). To further enhance the quality of the learnt surfaces, we also consider two extra losses" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "following the recent works. The first one is the eikonal loss " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathrm{L}_{\\mathrm{eik}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " [13] which encourages the geometry network to output a function similar to a signed distance field. The second one is the patch warping loss " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathrm{L}_{\\mathrm{warp}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " [9] to improve the reconstruction ability by warping the existing patches from the reference views. We measure the overall objective as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 334, + 158, + 545, + 171 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 158, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 334, + 158, + 545, + 171 + ], + "type": "interline_equation", + "content": "\\mathrm {L} = \\lambda_ {1} \\mathrm {L} _ {\\text {r e c}} + \\lambda_ {2} \\mathrm {L} _ {\\text {o c c}} + \\lambda_ {3} \\mathrm {L} _ {\\text {e i k}} + \\lambda_ {4} \\mathrm {L} _ {\\text {w a r p}}, \\tag {9}", + "image_path": "6f1f9349e8bc2930adbd0490b4eb18f6474918f91ba2f605b73ee7e521f6700d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 1" + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\lambda_2 = 0.1" + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\lambda_3 = 0.1" + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\lambda_4 = 1" + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": " are the trade-off parameters. Here we set " + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\lambda_3" + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\lambda_4" + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": " following [9], and " + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "inline_equation", + "content": "\\lambda_2" + }, + { + "bbox": [ + 304, + 184, + 545, + 220 + ], + "type": "text", + "content": " is determined through experimental study." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 234, + 481, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 234, + 481, + 247 + ], + "spans": [ + { + "bbox": [ + 306, + 234, + 481, + 247 + ], + "type": "text", + "content": "3.3. Rasterization-based Aggregation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 255, + 545, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 314 + ], + "type": "text", + "content": "The new rasterization-based aggregation mechanism additionally exploits the geometric correspondence between 3D explicit surfaces and 2D planes. This design aims to further refine the quality of the estimated 2D object regions and make them multi-view consistent." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": "Technically, as shown in Figure 2 (c), the mechanism first converts the 3D implicit surfaces (i.e., geometry network " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": ") into explicit surfaces (a explicit polygonal 3D representation like mesh) via marching cubes [22]. After that, we compute the projection from the 3D explicit surfaces (i.e., triangles) to the pixels of 2D images " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": " by rasterization. Here the rasterization refers to the typical process of taking a triangle and figuring out which pixels it covers [37]. Formally, let " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\Delta^j" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": " denote the " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": "-th triangle in the mesh, which corresponds to a set of pixels " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i^j \\subseteq \\mathbf{O}_i" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": "-th view. Note that the pixel set " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i^j" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": " is set as empty when " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\Delta^j" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": " is invisible to the camera due to invalid projections (e.g., the triangle is projected outside the image) or occlusion. Such correspondence between triangles and pixels enables the aggregation of the object information of 2D object regions into 3D explicit surface " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\Delta^j" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": ". In particular, we aggregate the object probabilities of all the pixels belonging to the triangle " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\Delta^j" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": " from multiple views, yielding the triangle-level object probability of " + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_{agg}(\\Delta^j)" + }, + { + "bbox": [ + 304, + 316, + 546, + 546 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 354, + 559, + 545, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 559, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 354, + 559, + 545, + 594 + ], + "type": "interline_equation", + "content": "\\mathbf {O} _ {a g g} \\left(\\Delta^ {j}\\right) = \\frac {\\sum_ {i = 1} ^ {| \\mathcal {I} |} \\sum_ {\\mathbf {p} \\in \\mathcal {P} _ {i} ^ {j}} \\mathbf {O} _ {i} (\\mathbf {p})}{\\epsilon + \\sum_ {i = 1} ^ {| \\mathcal {I} |} \\sum_ {\\mathbf {p} \\in \\mathcal {P} _ {i} ^ {j}} \\mathbf {1}}, \\tag {10}", + "image_path": "574ba77a3cf71792092826d4a15e2460c60f22bd20b8d72d5b905005fc6aab62.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": " is a constant term added to the denominator for numerical stability. After traversing all the 3D surfaces with the triangle-level aggregation (Eq. (10)), we re-project the triangle-level object probabilities of 3D surfaces back to 2D images. More specifically, for one pixel " + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathcal{P}_i^j \\subseteq \\mathbf{O}_i" + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": " in each viewpoint, the object probability of " + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_i(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": " is updated as the same triangle-level object probability " + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{O}_{agg}(\\Delta^j)" + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": ". By doing so, the updated 2D multi-view object regions are enforced to be consistent across different views." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17897" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 118, + 547, + 266 + ], + "blocks": [ + { + "bbox": [ + 46, + 71, + 547, + 115 + ], + "lines": [ + { + "bbox": [ + 46, + 71, + 547, + 115 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 547, + 115 + ], + "type": "text", + "content": "Table 1: Comparisons of our ORF with other volume rendering techniques on DTU dataset for learning neural implicit surfaces. Here all the involved techniques do not use object masks as additional supervision for training. The top part reports the reconstruction performances when using object masks to trim the estimated meshes, and the bottom part directly compares the reconstruction performances of the estimated meshes without using object masks. The best performances are marked in bold and the second-best results are underlined." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 118, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 47, + 118, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 118, + 547, + 266 + ], + "type": "table", + "html": "
ScanID243740556365698397105106110114118122Mean
with object masks: using the visual hull derived from human-annotated object masks for mesh trimming
NeRF [26]1.901.601.850.582.281.271.471.672.051.070.882.531.061.150.961.49
Unisurf [28]1.321.361.720.441.350.790.801.491.370.890.591.470.460.590.621.02
VolSDF [46]1.141.260.810.491.250.700.721.291.180.700.661.080.420.610.550.86
NeuS [41]1.001.370.930.431.100.650.571.481.090.830.521.200.350.490.540.84
NeuralWarp [9]0.490.710.380.380.790.810.821.201.060.680.660.740.410.630.510.68
without object masks: without mask-dependent trimming at inference
VolSDF [46]1.251.701.310.912.901.080.901.621.241.090.701.390.590.710.871.22
NeuS [41]1.591.981.440.951.820.740.641.631.301.410.591.330.440.510.541.13
NeuralWarp [9]0.972.541.520.412.540.740.791.061.531.400.750.720.390.570.621.10
ORF0.560.690.430.450.740.850.750.760.860.710.610.690.380.810.520.65
", + "image_path": "8f0df57939f303a4d71d3dfb42e7dbeb64af8476adb1c941d6ab817663be16ec.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 273, + 128, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 273, + 128, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 128, + 285 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 293, + 288, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 288, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 288, + 376 + ], + "type": "text", + "content": "We evaluate the effectiveness of ORF on DTU [16] and BlendedMVS [45] for multi-view 3D reconstruction. We first show both qualitative and quantitative results of ORF in comparison to existing techniques on DTU. Next, we conduct experimental analysis to validate the designs in ORF. Finally, we perform the qualitative comparison over samples derived from BlendedMVS for evaluation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 384, + 237, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 237, + 397 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 237, + 397 + ], + "type": "text", + "content": "4.1. Datasets and Experimental Settings" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "type": "text", + "content": "DTU is a popular multi-view 3D reconstruction benchmark, which consists of 80 scenes with large variability in materials, appearance and geometry of objects. For each scene, the dataset provides 49 or 64 images (resolution: " + }, + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "type": "inline_equation", + "content": "1,600 \\times 1,200" + }, + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "type": "text", + "content": ") captured from multiple camera views. The ground-truth point cloud of each scene is acquired with laser sensor. In our experiments, we follow [9, 28, 41, 46, 47] to use the selected 15 scenes in DTU for comparison. We strictly follow [9, 41] and use the official evaluation code of DTU [16] to compute the quantitative metrics. Specifically, the point clouds of objects (w/o background) in DTU are regarded as ground truth (GT). For a reconstructed mesh, we sample points on triangle surfaces in an evenly spaced manner (radius=0.2 as in [16]). Then, we report the final reconstruction score by averaging the accuracy and completeness of the sampled points (SP) (i.e., the chamfer distances of " + }, + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{SP} \\rightarrow \\mathrm{GT}" + }, + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathrm{GT} \\rightarrow \\mathrm{SP}" + }, + { + "bbox": [ + 46, + 402, + 287, + 688 + ], + "type": "text", + "content": "). It is also worthy to note that existing volume rendering techniques commonly use the additional object regions manually annotated by [27, 47] to trim the predicted mesh for only evaluating the reconstruction inside the visual hull. In contrast, our ORF learns an object-aware volumetric scene representation and directly constructs the 3D geometry of objects in the scene without the use of the visual hull derived from annotated object regions of scenes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "BlendedMVS is a large-scale benchmark for multi-view 3D reconstruction, including 113 scenes with multi-view" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 273, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 545, + 334 + ], + "type": "text", + "content": "images. Compared to DTU, the backgrounds in BlendedMVS are more complex. We select samples from the lowres set of BlendedMVS, and each scene is equipped with 24 to 64 images (resolution: " + }, + { + "bbox": [ + 304, + 273, + 545, + 334 + ], + "type": "inline_equation", + "content": "768 \\times 576" + }, + { + "bbox": [ + 304, + 273, + 545, + 334 + ], + "type": "text", + "content": "). Note that the ground truth of object regions for each image is not available." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 335, + 546, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 546, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 546, + 526 + ], + "type": "text", + "content": "Implementation Details. The whole network of ORF is built over VolSDF [46], and we adopt the same architecture as in existing volume rendering methods [28, 46, 47] for fair comparison. The whole network uses sphere initialization [2]. During training, we train our ORF with a two-stage strategy. We first optimize the network with the reconstruction loss and eikonal loss under the same setting in VolSDF (100k iterations with learning rate exponentially decayed from 5e-4 to 5e-5, batch size: 1,024 rays). Next, the network is fine-tuned with the overall objective in Eq. (9) (100k iterations with learning rate of 5e-4, batch size: 512 rays). The object probability is calculated by the transparency discriminator in each forward pass using the latest radiance field. The mesh extraction for rasterization-based aggregation is only conducted once after the first training stage of ORF." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 538, + 465, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 465, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 465, + 551 + ], + "type": "text", + "content": "4.2. Comparison on DTU Dataset" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": "Quantitative Results. We compare with several neural surface reconstruction techniques under two different evaluation settings for fair comparison: 1) baselines using the visual hull derived from human-annotated object masks for mesh trimming, 2) all re-implemented SDF-based baselines and our ORF without mask-dependent trimming at inference. Such two settings are denoted as with/without object masks, respectively. All the mentioned baselines are grouped into three directions: volume rendering with classical radiance fields [26], occupancy network [28], and SDF-based (Signed Distance Function) fields [46, 41, 9]. Table 1 summarizes the performance comparisons on each evaluation scenario. Note that all baselines and our ORF" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17898" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 57, + 526, + 287 + ], + "blocks": [ + { + "bbox": [ + 65, + 57, + 526, + 287 + ], + "lines": [ + { + "bbox": [ + 65, + 57, + 526, + 287 + ], + "spans": [ + { + "bbox": [ + 65, + 57, + 526, + 287 + ], + "type": "image", + "image_path": "5aceae4d2f16a4f9917e97daab7415ea3ecaca47b2bfe93a20a50ab0595bc548.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 288, + 545, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 288, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 545, + 310 + ], + "type": "text", + "content": "Figure 3: Comparisons on qualitative results of our ORF with other neural radiance fields techniques on DTU dataset for 3D geometry reconstruction with or without object masks at inference. * denotes our implementation of VolSDF." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 317, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 376 + ], + "type": "text", + "content": "do not use human-annotated object masks of scenes to optimize geometry/radiance nets during training. At inference, these baselines commonly require masks to remove the background of the learnt mesh. Instead, ORF can directly produce the object mesh without masks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 378, + 288, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 288, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 288, + 653 + ], + "type": "text", + "content": "In general, our ORF exhibits better reconstruction quality against all these baselines. Remarkably, ORF achieves 0.65 in the metric of Chamfer distance without the use of the visual hull derived from object masks in scenes, which is better than the reconstruction accuracy (0.68) of NeuralWarp when exploiting demands object masks at inference. The results generally highlight the key advantage of learning object-aware geometry reconstruction for neural implicit surfaces. Specifically, under the evaluation scenario with object masks, NeRF produces unsatisfactory reconstruction results since the lack of 3D geometry constraints. Unisurf unifies volume/surface rendering and enables better results. VolSDF, NeuS, and NeuralWarp exploit SDF and obtain promising reconstructions. Nevertheless, a performance drop is observed for each SDF-based method when object masks are unavailable at inference, since the primary estimated mesh contains more trivial geometry of the background. In contrast, our ORF achieves competitive reconstruction accuracy through learning an object-aware radiance field without the use of object masks derived visual hull. This confirms the effectiveness of exploring object awareness via transparency discriminator and rasterization-based aggregation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Qualitative Results. We then visually examine the reconstruction quality of our proposal by comparing ORF with three SDF-based approaches (VolSDF, NeuS, NeuralWarp) on five selected scenes from DTU dataset. Figure 3 shows the qualitative results of the reconstructed meshes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 317, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 509 + ], + "type": "text", + "content": "Note that here we show the reconstruction results of the two different evaluation settings (with or without object masks at inference for trimming estimated meshes). In general, all the three approaches reconstruct high-fidelity object surfaces after mask-dependent mesh trimming. In between, by constraining volume rendering with photo-consistency objective across multiple views, NeuralWarp produces more accurate surfaces with high-fidelity details (e.g., the bricks with sparse textures in the first two scenes) against VolSDF and NeuS. Furthermore, when the object masks are unavailable, the output meshes of each baselines become noisy with more trivial geometry and even some artifact of the background. In contrast, under this challenging setting, our ORF performs visually on par with the NeuralWarp, while requiring no object mask dependent mesh trimming at inference. The results again validate the merit of our ORF." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 515, + 434, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 434, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 434, + 528 + ], + "type": "text", + "content": "4.3. Experimental Analysis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Ablation Study. Here we investigate how each design in our ORF influences the overall reconstruction performance. Table 2 and Figure 4 details the performances and the corresponding qualitative results across different ablated runs of ORF, respectively. We start from a basic SDF-based radiance field without ray discrimination (i.e., NeuralWarp), which achieves 1.10 of Chamfer distance. The estimated mesh of this basic model inevitably contains trivial background geometry. Next, by solely using the outputs of salient object segmentation (Saliency) to distinguish object-intersected and object-bypassed rays, we observe a clear performance boost and the background is effectively screened. However, the independently estimated object probability of each 2D object region may be inaccurate and inconsistent across different viewpoints, resulting in error" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17899" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 76, + 285, + 171 + ], + "blocks": [ + { + "bbox": [ + 48, + 64, + 285, + 76 + ], + "lines": [ + { + "bbox": [ + 48, + 64, + 285, + 76 + ], + "spans": [ + { + "bbox": [ + 48, + 64, + 285, + 76 + ], + "type": "text", + "content": "Table 2: Ablation study on each design in ORF on DTU dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 76, + 285, + 171 + ], + "lines": [ + { + "bbox": [ + 50, + 76, + 285, + 171 + ], + "spans": [ + { + "bbox": [ + 50, + 76, + 285, + 171 + ], + "type": "table", + "html": "
Transparency Discriminator Saliency +Multiview +VerifierRasterization-based AggregationChamfer Distance
1.10
✓0.90
✓✓0.87
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", + "image_path": "ae503504957e73fe640e3c486245b195e8b45d24fb8573a065ef2fc0250b8c40.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 58, + 177, + 129, + 250 + ], + "blocks": [ + { + "bbox": [ + 58, + 177, + 129, + 250 + ], + "lines": [ + { + "bbox": [ + 58, + 177, + 129, + 250 + ], + "spans": [ + { + "bbox": [ + 58, + 177, + 129, + 250 + ], + "type": "image", + "image_path": "f369cdae7ab9788a9f664daac369815d146466599f36090b7fd00d1caa684a92.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 251, + 287, + 285 + ], + "lines": [ + { + "bbox": [ + 47, + 251, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 287, + 285 + ], + "type": "text", + "content": "Figure 4: Comparisons on qualitative results by using different ablated runs of our ORF on DTU dataset for 3D geometry reconstruction object masks dependent mesh trimming at inference." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 136, + 178, + 167, + 250 + ], + "blocks": [ + { + "bbox": [ + 136, + 178, + 167, + 250 + ], + "lines": [ + { + "bbox": [ + 136, + 178, + 167, + 250 + ], + "spans": [ + { + "bbox": [ + 136, + 178, + 167, + 250 + ], + "type": "image", + "image_path": "99adba7364705943acf8cc1a548ad6623bd834036f419fd3c8222d400a33c70b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 174, + 178, + 208, + 250 + ], + "blocks": [ + { + "bbox": [ + 174, + 178, + 208, + 250 + ], + "lines": [ + { + "bbox": [ + 174, + 178, + 208, + 250 + ], + "spans": [ + { + "bbox": [ + 174, + 178, + 208, + 250 + ], + "type": "image", + "image_path": "a38e004a07bb14e98b10ddb1f33fbd3dc5ec459b756a11437ca5378b1a284735.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 213, + 178, + 246, + 250 + ], + "blocks": [ + { + "bbox": [ + 213, + 178, + 246, + 250 + ], + "lines": [ + { + "bbox": [ + 213, + 178, + 246, + 250 + ], + "spans": [ + { + "bbox": [ + 213, + 178, + 246, + 250 + ], + "type": "image", + "image_path": "19a6e461862444af3a7c901462a917a493e554d188063e552dc19c37a7a6a37a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 253, + 178, + 286, + 250 + ], + "blocks": [ + { + "bbox": [ + 253, + 178, + 286, + 250 + ], + "lines": [ + { + "bbox": [ + 253, + 178, + 286, + 250 + ], + "spans": [ + { + "bbox": [ + 253, + 178, + 286, + 250 + ], + "type": "image", + "image_path": "c90c4423ca0fb340dce470aa820a18c97912777d18bdf022620d0d254934ae69.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 269 + ], + "type": "text", + "content": "Figure 5: Comparisons on qualitative results of our ORF with other techniques on BlendedMVS for 3D geometry reconstruction without object masks at inference. * denotes our re-implemented VolSDF without the hand-crafted parametrization in NeRF++." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 294, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 437 + ], + "type": "text", + "content": "accumulation and holes in the reconstructions. To address this issue, we enhance the strategy of transparency discrimination by jointly exploiting the 2D object regions estimated from multiple views (Multiview), leading to slightly better reconstruction. We then leverage the projection verification strategy (Verifier) to screen out invalid projections (e.g., the points are projected outside of the source images or occluded by other surfaces), which further boosts up the reconstruction. Finally, by capitalizing on Rasterization-based Aggregation to refine the estimated 2D object regions, the mIoU of object regions is improved from " + }, + { + "bbox": [ + 46, + 294, + 287, + 437 + ], + "type": "inline_equation", + "content": "94\\%" + }, + { + "bbox": [ + 46, + 294, + 287, + 437 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 294, + 287, + 437 + ], + "type": "inline_equation", + "content": "97\\%" + }, + { + "bbox": [ + 46, + 294, + 287, + 437 + ], + "type": "text", + "content": " and ORF achieves the highest reconstruction quality." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "content": "Effect of the Trade-off Parameter " + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "content": ". To clarify the effect of the trade-off parameter " + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "content": " in Eq. (9), we detail the reconstruction performances (i.e., Chamfer distances) with different trade-off parameters in Table 3. In the extreme case of " + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 0" + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "content": ", no occupancy regularization objective for foreground and background rays is utilized and the whole model degenerates to the conventional SDF-based approach. When enlarging " + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "content": " as 0.05, a better reconstruction accuracy is attained, which basically demonstrates that the foreground-aware inductive bias benefits volume rendering. The performance change is relatively smooth when " + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "content": " varies in the range from 0.05 to 0.20, and the best reconstruction accuracy is attained when " + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 0.10" + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "content": ". Furthermore, the reconstruction accuracy slightly decreases when " + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\lambda_{2} \\geq 0.30" + }, + { + "bbox": [ + 46, + 437, + 287, + 641 + ], + "type": "text", + "content": ". We speculate that this may be the result of amplifying the noise of ray discrimination if we set a higher weight to occupancy regularization objective." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "Effect of the Saliency Model's Performance. To verify how the quality of saliency influences the reconstruction, we perform salient object segmentation using another two models and obtain additional two versions of saliency maps. We evaluate the three different versions of saliency for both reconstruction and segmentation tasks on DTU (re" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 310, + 76, + 545, + 224 + ], + "blocks": [ + { + "bbox": [ + 310, + 64, + 539, + 75 + ], + "lines": [ + { + "bbox": [ + 310, + 64, + 539, + 75 + ], + "spans": [ + { + "bbox": [ + 310, + 64, + 539, + 75 + ], + "type": "text", + "content": "Table 3: Effect of the trade-off parameter " + }, + { + "bbox": [ + 310, + 64, + 539, + 75 + ], + "type": "inline_equation", + "content": "{\\lambda }_{2}" + }, + { + "bbox": [ + 310, + 64, + 539, + 75 + ], + "type": "text", + "content": " in ORF on DTU." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 76, + 545, + 224 + ], + "lines": [ + { + "bbox": [ + 310, + 76, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 310, + 76, + 545, + 224 + ], + "type": "table", + "html": "
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The results show that the saliency segmentation performance on DTU has almost saturated, and the reconstruction performances of ORF only fluctuate within the range of 0.02, which eases the difficulty on choosing saliency segmentation model in practice." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 352, + 504, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 352, + 504, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 352, + 504, + 365 + ], + "type": "text", + "content": "4.4. Comparison on BlendedMVS Dataset" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 371, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 371, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 545, + 526 + ], + "type": "text", + "content": "Figure 5 further showcases the geometry reconstruction results with different techniques for six scenes in BlendedMVS. It is worthy to note that VolSDF originally utilizes an additional hand-crafted parametrization as in " + }, + { + "bbox": [ + 305, + 371, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\mathrm{NeRF}++" + }, + { + "bbox": [ + 305, + 371, + 545, + 526 + ], + "type": "text", + "content": " [50] to tackle the complex backgrounds by modeling the volume outside a radius 3 sphere with another NeRF network. For fair comparison, here we re-implement VolSDF by removing this parametrization. Similar to the observations on DTU under the setting without object masks, both VolSDF and NeuralWarp produce high-fidelity object surfaces, while more trivial background geometry is inevitably included. Instead, our ORF nicely removes the trivial geometry and performs nearly on par with these approaches." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 537, + 383, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 383, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 383, + 550 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "In this work, we circumvent the use of object masks derived visual hull, and shape a new paradigm of learning object-aware geometry reconstruction for neural implicit surfaces. To verify our claim, we novelly remould the classical neural radiance fields by involving a new transparency discriminator to distinguish object-intersected and object-bypassed rays on-the-fly. Such ray discrimination serves as object-aware inductive bias to enable a reconstruction of 3D geometry of the key object in the scene. Moreover, we exploit the geometric correspondence between multi-view 2D object regions and 3D implicit/explicit surfaces to facilitate the learning of object surfaces. Extensive experiments conducted on DTU and BlendedMVS validate our proposal." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17900" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Motilal Agrawal and Larry S Davis. 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Although many deep neural networks (DNNs) have been developed for LF image SR and achieved continuously improved performance, existing methods cannot well leverage the long-range spatial-angular correlation and thus suffer a significant performance drop when handling scenes with large disparity variations. In this paper, we propose a simple yet effective method to learn the non-local spatial-angular correlation for LF image SR. In our method, we adopt the epipolar plane image (EPI) representation to project the 4D spatial-angular correlation onto multiple 2D EPI planes, and then develop a Transformer network with repetitive self-attention operations to learn the spatial-angular correlation by modeling the dependencies between each pair of EPI pixels. Our method can fully incorporate the information from all angular views while achieving a global receptive field along the epipolar line. We conduct extensive experiments with insightful visualizations to validate the effectiveness of our method. Comparative results on five public datasets show that our method not only achieves state-of-the-art SR performance but also performs robust to disparity variations. Code is publicly available at https://github.com/ZhengyuLiang24/EPIT.", + "bbox": [ + 73, + 325, + 473, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 752, + 209, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Light field (LF) cameras record both intensity and directions of light rays, and enable various applications such as depth perception [25, 29, 32], view rendering [3, 52, 66], virtual reality [11, 74], and 3D reconstruction [6, 77]. However, due to the inherent spatial-angular trade-off [82], an LF camera can either provide dense angular samplings with low-resolution (LR) sub-aperture images (SAIs), or capture high-resolution (HR) SAIs with sparse angular sampling.", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f6c1f302903fe2f90f8d4ec0177c43abc4407b9300a7e552faa8db9fcf0cf4d6.jpg", + "image_caption": [ + "Figure 1. Visualization of $4 \\times$ SR results and the corresponding attribution maps [18] of our method and four state-of-the-art methods [26, 36, 60, 78] under different manually sheared disparity values. Here, the patch marked by the green box in the HR image is selected as the target region, and the regions that contribute to the final SR results are highlighted in red. Our method can well exploit the non-local spatial-angular correlation and achieve superior SR performance. More examples are provided in Fig. 8." + ], + "image_footnote": [], + "bbox": [ + 501, + 290, + 893, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To handle this problem, many methods have been proposed to enhance the angular resolution via novel view synthesis [28, 43, 67], or enhance the spatial resolution by performing LF image super-resolution (SR) [10, 20]. In this paper, we focus on the latter task, i.e., generating HR LF images from their LR counterparts.", + "bbox": [ + 496, + 613, + 893, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, convolutional neural networks (CNNs) have been widely applied to LF image SR and demonstrated superior performance over traditional paradigms [1, 34, 44, 49, 64]. To incorporate the complementary information (i.e., angular information) from different views, existing CNNs adopted various mechanisms such as adjacent-view combination [73], view-stack integration [26, 78, 79], bidirectional recurrent fusion [59], spatial-angular disentanglement [36, 60, 61, 72, 9], and 4D convolutions [42, 43]. However, as illustrated in both Fig. 1 and Sec. 4.3, existing methods achieve promising results on LFs with small baselines, but suffer a notable performance drop when handling scenes with large disparity variations.", + "bbox": [ + 496, + 704, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12376", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We attribute this performance drop to the contradictions between the local receptive field of CNNs and the requirement of incorporating non-local spatial-angular correlation in LF image SR. That is, LF images provide multiple observations of a scene from a number of regularly distributed viewpoints, and a scene point is projected onto different but correlated spatial locations on different angular views, which is termed as the spatial-angular correlation. Note that, the spatial-angular correlation has the non-local property since the difference between the spatial locations of two views (i.e., disparity value) depends on several factors (e.g., angular coordinates of the selected views, the depth value of the scene point, the baseline length of the LF camera, and the resolution of LF images), and can be very large in some situations. Consequently, it is appealing for LF image SR methods to incorporate complementary information from different views by exploiting the spatial-angular correlation under large disparity variations.", + "bbox": [ + 76, + 90, + 472, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a simple yet effective method to learn the non-local spatial-angular correlation for LF image SR. In our method, we re-organize 4D LFs as multiple 2D epipolar plane images (EPIs) to manifest the spatial-angular correlation to the line patterns with different slopes. Then, we develop a Transformer-based network called EPIT to learn the spatial-angular correlation by modeling the dependencies between each pair of pixels on EPIs. Specifically, we design a basic Transformer block to alternately process horizontal and vertical EPIs, and thus progressively incorporate the complementary information from all angular views. Compared to existing LF image SR methods, our method can achieve a global receptive field along the epipolar line, and thus performs robust to disparity variations.", + "bbox": [ + 75, + 364, + 472, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the contributions of this work are as follows: (1) We address the importance of exploiting non-local spatial-angular correlation in LF image SR, and propose a simple yet effective method to handle this problem. (2) We develop a Transformer-based network to learn the non-local spatial-angular correlation from horizontal and vertical EPIs, and validate the effectiveness of our method through extensive experiments and visualizations. (3) Compared to existing state-of-the-art LF image SR methods, our method achieves superior performance on public LF datasets, and is much more robust to disparity variations.", + "bbox": [ + 75, + 575, + 472, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 758, + 218, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. LF Image SR", + "text_level": 1, + "bbox": [ + 76, + 785, + 217, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LFCNN [73] is the first method to adopt CNNs to learn the correspondence among stacked SAIs. Then, it is a common practice for LF image SR networks to aggregate the complementary information from adjacent views to model the correlation in LFs. Yeung et al. [72] designed a spatial-angular separable (SAS) convolution to approximate the 4D", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "convolution to characterize the sub-pixel relationship of LF 4D structures. Wang et al. [59] proposed a bidirectional recurrent network to model the spatial correlation among views on horizontal and vertical baselines. Meng et al. [42] proposed a densely-connected network with 4D convolutions to explicitly learn the spatial-angular correlation encoded in 4D LF data. To further learn inherent corresponding relations in SAIs, Zhang et al. [78, 79] grouped LFs into four different branches according to the specific angular directions, and used four sub-networks to model the multi-directional spatial-angular correlation.", + "bbox": [ + 496, + 90, + 893, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The aforementioned networks use part of input views to super-resolve each view, and the inherent spatial-angular correlation in LF images cannot be well incorporated. To address this issue, Jin et al. [26] proposed an All-to-One framework for LF image SR, and each SAI can be individually super-resolved by combining the information from all views. Wang et al. [61, 60] organized LF images into macro-pixels, and designed a disentangling mechanism to fully incorporate the angular information. Liu et al. [38] introduced 3D convolutions based multi-view context block to exploit the correlations among all views. In addition, Wang et al. [62] adopted deformable convolutions to achieve long-range information exploitation from all SAIs. Existing methods generally learn the local correspondence across SAIs, and ignore the importance of non-local spatial-angular correlation in LF images. However, due to the limited receptive field of CNNs, existing methods generally learn the local correspondence across SAIs, and ignore the importance of non-local spatial-angular correlation in LF images.", + "bbox": [ + 496, + 258, + 893, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, Liang et al. [36] applied Transformers to LF image SR and developed an angular Transformer and a spatial Transformer to incorporate angular information and model long-range spatial dependencies, respectively. However, since 4D LFs were organized into 2D angular patches to form the input of angular Transformers, the non-local property of spatial-angular correlations reduces the robustness of LFT to large disparity variations.", + "bbox": [ + 496, + 561, + 893, + 683 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Non-Local Correlation Modeling", + "text_level": 1, + "bbox": [ + 500, + 695, + 790, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Non-local means [5] is a classical algorithm that computes the weighted mean of pixels in an image according to the self-similarity measure, and a number of studies on such non-local priors have been proposed for image restoration [12, 51, 19, 4], image and video SR [16, 76, 14, 71, 23]. Then, the attention mechanism is developed as a tool to bias the most informative components of an input signal, and achieves significant performance in various computer vision tasks [22, 8, 58, 15]. Huang et al. [24] proposed novel criss-cross attention to capture contextual information from full-image dependencies in an efficient way. Wang et al. [56, 55] proposed a parallax attention mechanism to handle", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12377", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the varying disparities problem of stereo images. Wu et al. [69] applied attention mechanisms to 3D LF reconstruction and developed a spatial-angular attention module to learn the first-order correlation on EPIs.", + "bbox": [ + 75, + 90, + 468, + 150 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, the attention mechanism is further generalized as Transformers [54] with multi-head structures and feed-forward networks. Transformers have inspired lots of works [39, 35, 7, 13] to further investigate the power of attention mechanisms in visions. Liu et al. [40] presented a pure-Transformer method to incorporate the inherent spatial-temporal locality of videos for action recognition. Naseer et al. [45] investigated the robustness and generalizability of Transformers, and demonstrated favorable merits of Transformers over CNNs for occlusion handling. Shi et al. [50] observed that Transformers can implicitly make accurate connections for misaligned pixels, and presented a new understanding of Transformers to process spatially unaligned images.", + "bbox": [ + 75, + 152, + 470, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 378, + 166, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 402, + 205, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the two-plane LF parameterization model [33], an LF image is commonly formulated as a 4D function $\\mathcal{L}(u,v,h,w)\\in \\mathbb{R}^{U\\times V\\times H\\times W}$ , where $U$ and $V$ represent angular dimensions, $H$ and $W$ represent spatial dimensions. The EPI sample of 4D LF is acquired with a fixed angular coordinate and a fixed spatial coordinate. Specifically, the horizontal EPI is obtained with constant $u$ and $h$ , and the vertical EPI is obtained with constant $v$ and $w$ .", + "bbox": [ + 75, + 426, + 468, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, the EPIs not only record spatial structures at edges or textures, but also reflect the disparity information via line patterns of different slopes. Specifically, due to large disparities, the EPIs contain abundant spatial-angular correlation of LFs in a long-range way. Therefore, we propose to explore the non-local spatial-angular correlation from horizontal and vertical EPIs for LF image SR.", + "bbox": [ + 75, + 547, + 468, + 670 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Network Design", + "text_level": 1, + "bbox": [ + 76, + 680, + 236, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 3(a), our network takes an LR LF $\\mathcal{L}_{LR} \\in \\mathbb{R}^{U \\times V \\times H \\times W}$ as its input, and produces an HR LF $\\mathcal{L}_{SR} \\in \\mathbb{R}^{U \\times V \\times \\alpha H \\times \\alpha W}$ , where $\\alpha$ presents the upscaling factor. Our network consists of three stages including initial feature extraction, deep spatial-angular correlation learning, and feature upsampling.", + "bbox": [ + 75, + 704, + 468, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Initial Feature Extraction", + "text_level": 1, + "bbox": [ + 76, + 815, + 310, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 3(b), we follow most existing works [7, 35, 75] to use three $3 \\times 3$ convolutions with LeakyReLU [41] as a SpatialConv layer to map each SAI to a high-dimensional feature. The initially extracted feature can be", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c2330a8e34a9db8434ab60bccdf9b72c9ce997ec7e4fb6c6be4e1034bb31830f.jpg", + "image_caption": [ + "Figure 2. The SAI and EPI representations of LF images. The array of $9 \\times 9$ views of a scene rosemary from HCInew [21] dataset is used as an example for illustration." + ], + "image_footnote": [], + "bbox": [ + 529, + 88, + 864, + 251 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "represented as $\\pmb{F} \\in \\mathbb{R}^{U \\times V \\times H \\times W \\times C}$ , where $C$ denotes the channel dimension.", + "bbox": [ + 498, + 309, + 890, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.2 Deep Spatial-Angular Correlation Learning", + "text_level": 1, + "bbox": [ + 500, + 362, + 859, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Non-Local Cascading Block. The basic module for spatial-angular correlation learning is the Non-Local Cascading block. As shown in Fig. 3(a), each block consists of two cascaded Basic-Transformer units to separately incorporate the complementary information along the horizontal and vertical epipolar lines. In our method, we employed five Non-Local Cascading blocks to achieve a global perception of all angular views, and followed SwinIR [35] to adopt spatial convolutions to enhance the local feature representation. The effectiveness of this inter-block spatial convolution is validated in Sec. 4.4. Note that, the weights of the two Basic-Transformer units in each block are shared to jointly learn the intrinsic properties of LFs, which is demonstrated effective in Sec. 4.4.", + "bbox": [ + 496, + 386, + 890, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 3(c), the initial features $\\pmb{F}$ can be first separately reshaped to the horizontal EPI pattern $\\pmb{F}_{hor} \\in \\mathbb{R}^{UH \\times V \\times W \\times C}$ and the vertical EPI pattern $\\pmb{F}_{ver} \\in \\mathbb{R}^{VW \\times U \\times H \\times C}$ . Next, $\\pmb{F}_{hor}$ (or $\\pmb{F}_{ver}$ ) is fed to a Basic-Transformer unit to integrate the long-range information along the horizontal (or vertical) epipolar line. Then, the enhanced feature $\\hat{\\pmb{F}}_{hor}$ (or $\\hat{\\pmb{F}}_{ver}$ ) is reshaped into the size of $UV \\times H \\times W \\times C$ , and passes through a SpatialConv layer to incorporate the spatial context information within each SAI. Without loss of generality, we take the vertical Basic-Transformer as an example to introduce the detail of our Basic-Transformer unit in the following texts.", + "bbox": [ + 498, + 598, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Basic-Transformer Unit. The objective of this unit is to capture long-range dependencies along the epipolar line via Transformers. To leverage the powerful sequence modeling capability of Transformers, we convert the vertical EPI features $\\pmb{F}_{ver}$ to the sequences of \"tokens\" for capturing spatial-angular correlation in $U$ and $H$ dimensions. As shown in Fig. 3(d), the vertical EPI features are passed through a linear projection matrix $W_{in} \\in \\mathbb{R}^{C \\times D}$ , where $D$", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12378", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cfb324391a8e3948033cb56600511a1882e7505787ae19696911c2d10fabf96a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 87, + 885, + 258 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b1c46a4306ef2c7220e272a3cd00d7bcdf7358a2e18abb2de6f3a777f2acbfe0.jpg", + "image_caption": [ + "Figure 3. An overview of our proposed EPIT. Here, a $3 \\times 3$ LF is used as an example for illustration." + ], + "image_footnote": [], + "bbox": [ + 86, + 260, + 181, + 398 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e5be6540e1a8c3fef8a44d91cb59bdd4d8eb248273cf28777e87ae20cc41836e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 187, + 260, + 545, + 398 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/db356ecabddb460d353108e05a8b99695e79273b86fa591ea5bfcdb550ef9d5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 550, + 258, + 883, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "denotes the embedding dimension of each token. The projected EPI features are a sequence of tokens with a length of $UH$ , i.e., $T_{ver} \\in \\mathbb{R}^{UH \\times D}$ . Following the PreNorm operation in [70], we also apply Layer Normalization (LN) before the attention calculation, and obtain the normalized tokens $\\bar{T}_{ver} = \\mathrm{LN}(T_{ver})$ .", + "bbox": [ + 75, + 435, + 468, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Afterwards, tokens $\\bar{T}_{ver}$ are passed through the Self-Attention layer and transformed into the deep tokens involving non-local spatial-angular information along the vertical epipolar line. Specifically, $\\bar{T}_{ver}$ need to be separately multiplied by $W_{Q} \\in \\mathbb{R}^{D \\times D}$ , $W_{K} \\in \\mathbb{R}^{D \\times D}$ and $W_{V} \\in \\mathbb{R}^{D \\times D}$ to generate corresponding query, key and value components for self-attention calculation, i.e., $Q_{ver} = \\bar{T}_{ver} W_{Q}$ , $K_{ver} = \\bar{T}_{ver} W_{K}$ and $V_{ver} = \\bar{T}_{ver} W_{V}$ .", + "bbox": [ + 75, + 526, + 468, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a query position $q = \\{1,2,\\dots ,UH\\}$ in $Q_{ver}$ and a key position $k = \\{1,2,\\dots ,UH\\}$ in $K_{ver}$ , the corresponding response $A_{ver}(q,k)\\in \\mathbb{R}$ measures the mutual similarity of the pairs by the dot-product operation, followed by a Softmax function to obtain the attention scores on the vertical EPI tokens. That is,", + "bbox": [ + 75, + 647, + 468, + 736 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} _ {\\text {v e r}} (q, k) = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {\\text {v e r}} (q) \\cdot K _ {\\text {v e r}} (k) ^ {\\mathrm {T}}}{\\sqrt {D}}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 744, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the attention scores, the output of self-attention $T_{ver}^{\\prime}$ can be calculated as the weighted sum of value. In summary, the calculation process of Self-Attention layer can be formulated as:", + "bbox": [ + 75, + 786, + 468, + 845 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {T} _ {\\text {v e r}} ^ {\\prime} = \\boldsymbol {A} _ {\\text {v e r}} V _ {\\text {v e r}} + T _ {\\text {v e r}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 857, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further incorporate the spatial-angular correlation,", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/491140b5a9b121668113d9bd8c36d28ca6fe2c391c4149348e43d3a851d6bb1b.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 514, + 434, + 586, + 487 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/840d93bdcb727dd6e47a79be57419b586313a4a5219769381ded800179d0451d.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 589, + 434, + 660, + 487 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/97d95d74cc11fdfa5c7d7aad13f58bd85380b9acbc37b9f46d1f9419311e229e.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 663, + 434, + 733, + 487 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/97fe13740bb81b5003a0ad9229bbad0cd468461168e3e6006aa93a5f46555626.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 738, + 434, + 805, + 487 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/34a93aa2968e8d822fe7df0bf38b41a2a3a10d33d06dde1028b3865753cb21b1.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 812, + 434, + 882, + 487 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6746f92dd73948d0806556b6b6b5d18dfedf4d9150b9a1f745361270bd50618c.jpg", + "image_caption": [ + "(f)" + ], + "image_footnote": [], + "bbox": [ + 513, + 498, + 586, + 550 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/39417c9fc00f538fd69b435da0b73b11210f178938dd6bcff36e07f4502000e2.jpg", + "image_caption": [ + "(g)" + ], + "image_footnote": [], + "bbox": [ + 589, + 498, + 660, + 551 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f5f5520f3696847ef422d34ccb962dabc8c3b274393527070183454737ed1a72.jpg", + "image_caption": [ + "(h)", + "Figure 4. An example of the attention maps of a Basic-Transformer unit for the spatial-angular correlation. Note that, the attention maps correspond to the correlation between the regions marked by the red and yellow strokes." + ], + "image_footnote": [], + "bbox": [ + 665, + 498, + 733, + 551 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4eb5c7164fb22cba02addc206a73e63f34c26015f7b2e165bde3f7633c46f658.jpg", + "image_caption": [ + "(i)" + ], + "image_footnote": [], + "bbox": [ + 738, + 498, + 807, + 551 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3cc2fd20bba6c037347a73431ae1e636bea25adc3d7e03352d1f045e2840968c.jpg", + "image_caption": [ + "(1)" + ], + "image_footnote": [], + "bbox": [ + 812, + 498, + 880, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "following [54], our Basic-Transformer unit also contains the multi-layer perception (MLP) and LN, and generates the enhanced $\\hat{T}_{ver}$ as:", + "bbox": [ + 498, + 636, + 890, + 681 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {T}} _ {v e r} = \\operatorname {M L P} \\left(\\operatorname {L N} \\left(\\boldsymbol {T} _ {v e r} ^ {\\prime}\\right)\\right) + \\boldsymbol {T} _ {v e r} ^ {\\prime}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 691, + 890, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At the end of the Basic-Transformer unit, the enhanced $\\hat{T}_{ver}$ is fed to another linear projection $W_{out} \\in \\mathbb{R}^{D \\times C}$ , and reshaped into the size of $UV \\times H \\times W \\times C$ for the subsequent SpatialConv layer.", + "bbox": [ + 498, + 719, + 890, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-View Similarity Analysis. Note that, the setting $[A_{ver}(q,1),\\dots,A_{ver}(q,UH)]\\in \\mathbb{R}^{1\\times UH}$ represents the similarity scores of $q$ with all $k$ in $K_{ver}$ , and thus can be re-organized as a slice of cross-view attention map according to the angular coordinate. Inspired by this, we visualized the cross-view attention maps on an example scene in Fig. 4. The regions marked by the red stripe in Fig. 4(a) are set as the query tokens, and the self-similarity (i.e.,", + "bbox": [ + 498, + 780, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12379", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/36315e07ce1969fdd49d2a1f0b7800f11d62cdc05aeffd2fe1e39121fec6176b.jpg", + "table_caption": [ + "Table 1. Quantitative comparison of different SR methods in terms of the number of parameters (#Prm.) and PSNR/SSIM. Larger PSNR and SSIM values indicate higher SR quality. We mark the best results in red and the second best results in blue." + ], + "table_footnote": [], + "table_body": "
Methods#Prm.(M)2×/4×2×4×
EPFLHCInewHCIoldINRIASTFgantryEPFLHCInewHCIoldINRIASTFgantry
Bicubic- / -29.74/.937631.89/.935637.69/.978531.33/.957731.06/.949825.14/.832427.61/.851732.42/.934426.82/.886725.93/.8452
VDSR [30]0.66 / 0.6632.50/.959834.37/.956140.61/.986734.43/.974135.54/.978927.25/.877729.31/.882334.81/.951529.19/.920428.51/.9009
EDSR [37]38.6 / 38.933.09/.962934.83/.959241.01/.987434.97/.976436.29/.981827.84/.885429.60/.886935.18/.953629.66/.925728.70/.9072
RCAN [81]15.3 / 15.433.16/.963434.98/.960341.05/.987535.01/.976936.33/.983127.88/.886329.63/.888635.20/.954829.76/.927628.90/.9131
resLF[79]7.98 / 8.6433.62/.970636.69/.973943.42/.993235.39/.980438.36/.990428.27/.903530.73/.910736.71/.968230.34/.941230.19/.9372
LFSSR [72]0.88 / 1.7733.68/.974436.81/.974943.81/.993835.28/.983237.95/.989828.27/.911830.72/.914536.70/.969630.31/.946730.15/.9426
LF-ATO [26]1.22 / 1.3634.27/.975737.24/.976744.20/.994236.15/.984239.64/.992928.52/.911530.88/.913537.00/.969930.71/.948430.61/.9430
LF-InterNet [61]5.04 / 5.4834.14/.976037.28/.976344.45/.994635.80/.984338.72/.990928.67/.916230.98/.916137.11/.971630.64/.949130.53/.9409
LF-DFnet [62]3.94 / 3.9934.44/.975537.44/.977344.23/.994136.36/.984039.61/.992628.77/.916531.23/.919637.32/.971830.83/.950331.15/.9494
MEG-Net [78]1.69 / 1.7734.30/.977337.42/.977744.08/.994236.09/.984938.77/.991528.74/.916031.10/.917737.28/.971630.66/.949030.77/.9453
LF-IINet [38]4.84 / 4.8834.68/.977337.74/.979044.84/.994836.57/.985339.86/.993629.11/.918831.36/.920837.62/.973431.08/.951531.21/.9502
DPT [57]3.73 / 3.7834.48/.975837.35/.977144.31/.994336.40/.984339.52/.992628.93/.917031.19/.918837.39/.972130.96/.950331.14/.9488
LFT [36]1.11 / 1.1634.80/.978137.84/.979144.52/.994536.59/.985540.51/.994129.25/.921031.46/.921837.63/.973531.20/.952431.86/.9548
DistgSSR [60]3.53 / 3.5834.81/.978737.96/.979644.94/.994936.59/.985940.40/.994228.99/.919531.38/.921737.56/.973230.99/.951931.65/.9535
LFSAV [9]1.22 / 1.5434.62/.977237.43/.977644.22/.994236.36/.984938.69/.991429.37/.922331.45/.921737.50/.972131.27/.953131.36/.9505
EPIT (ours)1.42 / 1.4734.83/.977538.23/.981045.08/.994936.67/.985342.17/.995729.34/.919731.51/.923137.68/.973731.37/.952632.18/.9571
", + "bbox": [ + 78, + 114, + 890, + 343 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "key are same as query) is ideally located at the diagonal, as shown in Fig. 4(f). In contrast, the yellow stripes in Figs. 4(b)-4(e) are set as the key tokens, the corresponding cross-view similarities are shown in Figs. 4(g)-4(j). It can be observed that due to the foreground occlusions, the responses of the background appear as short lines (marked by the white boxes) parallel to the diagonal in each cross-view attention map, and both of the distance to the diagonal and the length of response regions adaptively change as the key view moves along the baseline, which demonstrates the disparity-awareness of our Basic-Transformer unit.", + "bbox": [ + 75, + 354, + 472, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.3 Feature Upsampling", + "text_level": 1, + "bbox": [ + 76, + 542, + 274, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we apply the pixel shuffling operation to increase the spatial resolution of LF features, and further employ a $3 \\times 3$ convolution to obtain the super-resolved LF image $\\mathcal{L}_{SR}$ . Following most existing works [61, 60, 36, 62, 57, 38, 78, 79, 72], we use the $L_{1}$ loss function to train our network due to its robustness to outliers [2].", + "bbox": [ + 75, + 566, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 672, + 209, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first introduce the datasets and our implementation details, and then compare our method with state-of-the-art methods. Next, we investigate the performance of different SR methods with respect to disparity variations. Finally, we validate the effectiveness of our method through ablation studies.", + "bbox": [ + 75, + 699, + 468, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 801, + 397, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We followed [62, 60, 38, 57, 36] to use five public LF datasets (EPFL [48], HCInew [21], HCld [65], INRIA [46], STFgantry [53]) in the experiments. All LFs in these datasets have an angular resolution of $9 \\times 9$ . Unless specifically mentioned, we extracted the central $5 \\times 5$ SAIs for", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "training and test. In the training stage, we cropped each SAI into patches of size $64 \\times 64 / 128 \\times 128$ , and performed $0.5 \\times / 0.25 \\times$ bicubic downsampling to generate the LR patches for $2 \\times / 4 \\times$ SR, respectively. We used peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [63] as quantitative metrics for performance evaluation. To obtain the metric score for a dataset with $M$ scenes, we first calculated the metric of each scene by averaging the scores over all the SAIs separately, and then obtained the score for this dataset by averaging the scores over the $M$ scenes.", + "bbox": [ + 496, + 354, + 890, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopted the same training settings for all experiments, i.e., Xavier initialization algorithm [17] and Adam optimizer [31] with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ . The initial learning rate was set to $2\\times 10^{-4}$ and decreased by a factor of 0.5 every 15 epochs. During the training phase, we performed random horizontal flipping, vertical flipping, and 90-degree rotation to augment the training data. All models were implemented in the PyTorch framework and trained from scratch for 80 epochs with 2 Nvidia RTX 2080Ti GPUs.", + "bbox": [ + 496, + 505, + 892, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Comparisons on Benchmark Datasets", + "text_level": 1, + "bbox": [ + 498, + 650, + 823, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare our method to 14 state-of-the-art methods, including 3 single image SR methods [30, 37, 81] and 11 LF image SR methods [79, 72, 26, 61, 62, 78, 38, 57, 36, 60, 9]. Quantitative Results. A quantitative comparison among different methods is shown in Tabel 1. Our EPIT with a small model size (i.e., $1.42\\mathrm{M} / 1.47\\mathrm{M}$ for $2\\times /4\\times$ SR) achieves state-of-the-art PSNR and SSIM scores on almost all the datasets for both $2\\times$ and $4\\times$ SR. It is worth noting that LFs in the STFgantry dataset [53] have larger disparity variations, and are thus more challenging. Our EPIT significantly outperforms all the compared methods and achieves $1.66\\mathrm{dB} / 0.32\\mathrm{dB}$ PSNR improvements over the second top-performing method LFT for $2\\times /4\\times$ SR, respectively, which demonstrates the powerful capacity of our EPIT in non-local correlation modeling.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12380", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/16b959155a1ab58c76e87cb5cdb3c72226c7b76f90388f03ec6cefbb09819eee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 88, + 236, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a5e06d02973bec01fe0c9215108935b24a4a0c9bac8e002c9ed73ddaeb19dcba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 236, + 88, + 325, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f0cd8e9f9cfbb93fe6fc9c608bf38000e15cfd3e6dcb3e760077be2113fa706f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 333, + 88, + 419, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/15c025db3ad3a3ec09165c4e06c058ee6e1e09445fd8029563301d5b60509840.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 428, + 88, + 514, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a417eef488850bde9fa1104e600a83b267cfaec1387e781ae63828ea9e593ea4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 88, + 607, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/13dac46c9a8ae265fa270644671f1b7ab3ecc6a4c625d17a5db689c5ed25c851.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 609, + 88, + 700, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/06ab58db794531705698b8ffd845fc15569cd3b07e2dd8f06b656e1f81a252a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 88, + 794, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b0b7dd4de3d193f7b69d553da9d64c4fd4cf05398616128cc1c7a0b726cb94af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 800, + 88, + 887, + 224 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a3263b28349a13ef0362d75666b6bd1f1dad1b47f19ea324afad3398684c031c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 229, + 236, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4e83faabed2a7d38f6aa75a6e2673375e884f2190c239a6f89650d6ae666d065.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison of different SR methods for $2 \\times /4 \\times$ SR." + ], + "image_footnote": [], + "bbox": [ + 236, + 229, + 325, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c37d8303b5a0c745d5550d5a0a926728387d0c29147e76969f484087e2203a43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 333, + 229, + 419, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1ac5438202677123a71c187dfcbd20c4ec3c26ef474c9afdeafa8802b9b07915.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 428, + 229, + 514, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ce0ae720d7118bc378241205a37c717d15dbf7eb697798ab7c7cd374ce5ba5e7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 519, + 229, + 607, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/aa5d9c532685314237c373a5aa350eae7ddcd54ddce8cedaa7c1fd00f5270310.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 609, + 229, + 702, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6d079fa3e8a4c3c07414bfb2afaecb382c86d96b517e888473cf153a220048a9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 229, + 794, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/930fb69f12b3e989617d946a9dff0001a320840d2add0d62c57581b0976185a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 799, + 229, + 888, + 367 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a880b7111150763883d0583af329c14d4259636b59c0914e0d5a0f74beb670bb.jpg", + "image_caption": [ + "Figure 6. Quantitative and qualitative (MSE) comparisons of disparity estimation results achieved by SPO [80] using different SR results. The MSE $(\\downarrow)$ is the mean square error multiplied by 100." + ], + "image_footnote": [], + "bbox": [ + 78, + 398, + 470, + 506 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b7b6a6a5ba4b1df2955eb4176c215770aeb2469ee5a9e00fc326027a730586b6.jpg", + "table_caption": [ + "Table 2. PSNR values achieved by DistgSSR [60] and our EPIT with different angular resolution for $4 \\times$ SR." + ], + "table_footnote": [], + "table_body": "
InputEPFLHCInewHCIoldINRIASTFgantry
[60]Ours[60]Ours[60]Ours[60]Ours[60]Ours
2×228.27-0.0530.80+0.0436.77+0.1730.55-0.0330.74+0.56
3×328.67+0.0331.07+0.1937.18+0.1930.83+0.1131.12+0.74
4×428.81+0.2331.25+0.1537.32+0.2030.93+0.2631.23+0.88
5×528.99+0.3531.38+0.1337.56+0.1230.99+0.3831.65+0.56
6×629.10+0.3331.39+0.1837.52+0.2630.98+0.4731.57+0.74
7×729.38+0.2231.43+0.2037.65+0.2731.18+0.3331.63+0.77
8×829.32+0.2831.52+0.1437.76+0.2431.23+0.3131.58+0.90
9×929.41+0.3031.48+0.2137.80+0.2631.22+0.3431.66+0.84
", + "bbox": [ + 78, + 594, + 468, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Results. Figure 5 shows the qualitative results achieved by different methods for $2 \\times 4 \\times$ SR. It can be observed from the zoom-in regions that single image SR method RCAN [81] cannot recover the textures and details in the SR images. In contrast, our EPIT can incorporate sub-pixel correspondence among SAIs and generate more faithful details with fewer artifacts. Compared to most LF image SR methods, our EPIT can generate superior visual results with high angular consistency. Please refer to the supplemental material for additional visual comparisons.", + "bbox": [ + 75, + 717, + 468, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Angular Consistency. We evaluate the angular consistency by using the $4 \\times \\mathrm{SR}$ results on several challenging scenes", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/19dcd839e89b73a4111d22e628c99496b0fbcac6bb22650ca8ae5684fe6c6cdd.jpg", + "image_caption": [ + "Figure 7. Visual comparison of different SR methods on real-world LF scenes for $4 \\times \\mathrm{SR}$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 398, + 653, + 592 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/422548882194c104513f9c6fc20819c52ef67260b32af7299c07faa68d7b8f6d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 661, + 398, + 733, + 592 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b60de61e9b8be4227c1d61ceb277be90c8b750d1a0bdb47aa5476ef1ad391e23.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 738, + 398, + 812, + 592 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/473d2af88e9769003881e07d8a64c32c6e6ba9e13b8f7f18b14dd48ba5c0289e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 818, + 398, + 893, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(e.g., Backgammon and Stripes) in 4D LF benchmark [21] for disparity estimation. As shown in Fig. 6, our EPIT achieves competitive MSE scores on these challenging scenes, which demonstrates the superiority of our EPIT on angular consistency.", + "bbox": [ + 496, + 640, + 890, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance with Different Angular Resolution. Since the angular resolution of LR images can vary significantly with different LF devices, we compare our method to DistgSSR [60] on LFs with different angular resolutions. It can be observed from Table 2 that our method achieves higher PSNR values than DistgSSR on almost all the datasets with each angular resolution (except on the EPFL and INRIA datasets with $2 \\times 2$ input LFs). The consistent performance improvements demonstrate that our EPIT can well model the spatial-angular correlation with various angular resolutions. More comparisons and discussions are provided in the supplemental material.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12381", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/55bad091186292a5713bb04293b5f738ed45e12ea0ce56a387aaf599cdea7673.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 89, + 233, + 224 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0da3b149f6ce9f2b83042d25842c1197be960d94d59677a13fea944bb12e085b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 236, + 88, + 486, + 224 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/45f45cd61001aa984e0b9d92de0488ee874df06e48e1e6d6cdf24b3495261ca9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 88, + 633, + 224 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/35b1d7c4304b76b9449add29ef1bee797e6976353914719de5fba514cac6d1f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 88, + 890, + 224 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2787ba1d63f380962f5ac86edf57d9bd5ec94dbe2e114deec7e9e68b92ecfc5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 226, + 169, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1b7a3e3c0cf583c8742ee0113f707b4ae4928bc8decaceda6cef21d70e739693.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 171, + 226, + 248, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/31048687b06e352e125a26004b80e245dab052afc5c1ea10e3586701461335a5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 226, + 326, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f0479409d42fb38ff879b033d2c2dd4d5ff119f7e23553e2f8dde03154f036f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 330, + 226, + 406, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/20aa3a5548ad5073f05a8b5c7fed9c3f6cfaa9c49dc6f4ea4bad38fbcd875e17.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 410, + 226, + 486, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26719c9a640722cf36284d89ce6591db5463ca0ae5eeb64deb69fa56d3b1aac5.jpg", + "image_caption": [ + "Figure 8. Performance comparison and local attribution maps of different SR methods on two representative scenes with different shearing values for $2 \\times \\mathrm{SR}$ . Here, we plot the performance curve to quantitatively measure the effect of disparity variations on LFs, and present the visual results and corresponding attribution maps under sheared value=2, 4." + ], + "image_footnote": [], + "bbox": [ + 80, + 334, + 169, + 439 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/35d84871eba78764c0862220cd9bf06a7cc56bb5c35ae323534a9196fc268573.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 171, + 334, + 248, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/36fdcfe0909a477456dd6080de0f326d0f2401b74bbb0cd5ee6991e31b3dc9fe.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 251, + 334, + 326, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/83e2221872c024ab0bcd5e4ead593320ac6f7ff42f5849c36af12061eec0d46e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 330, + 334, + 406, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b9b53888dfec74ff3a9ec2d4041391e0e81f7778962f0170d5318c0f58e23e89.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 410, + 334, + 486, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5036e329a905709ca02dbfc75e283e2180356e575e0b5183d72df4391e3adc6c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 226, + 573, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e2a6eb41e56846296a528e89e55b5b00e8cae9040eacbd1f23819745d81735ca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 576, + 226, + 651, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/252bfc277698ff93ecc565f85a4cb050b838069f39483a154dfbc13b2f111d3e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 226, + 730, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/53f32bb0f635a1008a6d362a75c7faf951f672ed7d65aa3ae5d8f428f4a4b983.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 732, + 226, + 807, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/65f29c4731474e83d8ff14430f48e59dd858d983a0c7016c2903a29ca16a0a83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 810, + 226, + 887, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/75d27ae48b87d2bca04f9d2c3c05570e88e66fd73339a94b6d95389a83df8c73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 334, + 571, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b5f6a578fdc658e445e0dcc9427c19b316313fadfe0af169b24396f21db1e94b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 575, + 334, + 651, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ad010207f8b4a1eac109bdc3a97dffe058fe8b2501b09d4c5c860973bdf07932.jpg", + "image_caption": [ + "(f)" + ], + "image_footnote": [], + "bbox": [ + 653, + 334, + 728, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e06b00193af84669e410f14426f066afedf149751e6dc0db5a6129fd79146952.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 732, + 334, + 807, + 429 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/021d697d7dbb8c69d71e48c4b3cf582e16380fe1100db7436cb1d940cc02a2d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 810, + 334, + 887, + 429 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance on Real-World LF Scenes. We compare our method to state-of-the-art methods under real-world degradation by directly applying them to LFs in the STFlytro dataset [47]. Since no groundtruth HR images are available in this dataset, we present the LR input and their super-resolved results in Fig. 7. It can be observed that our method can recover more faithful details and generate more clear letters than other methods. Since the LF structure keeps unchanged under both bicubic and real-world degradation, our method can learn the spatial-angular correlation from bicubicly downsampled training data, and well generalize to LF images under real degradation.", + "bbox": [ + 75, + 501, + 472, + 683 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Robustness to Large Disparity Variations", + "text_level": 1, + "bbox": [ + 76, + 694, + 429, + 710 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Considering the parallax structure of LF images, we followed the shearing operation in existing works [67, 68] to linearly change the overall disparity range of LF datasets. Note that, the content of SAIs maintain unchanged after the shearing operation, and thus we can quantitatively investigate the performance of different SR methods with respect to the disparity variations.", + "bbox": [ + 75, + 718, + 468, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative & Qualitative Comparison. Figure 8 shows the quantitative and qualitative results of different SR methods with respect to sheared values, from which we can observe that: 1) Except for the single image SR method RCAN, all LF image SR methods suffer a performance drop", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "when the absolute sheared value of LF images increases. That is because, large sheared values can result in more significant misalignment among LF images, and introduce difficulties in complementary information incorporation; 2) As the absolute sheared value increases, the performance of existing LF image SR methods is even inferior to RCAN. The possible reason is that, these methods do not make full use of local spatial information, but rather rely on local angular information from adjacent views. When the sheared value exceeds their receptive fields, the large disparities can make the spatial-angular correlation non-local and thus introduce challenges in complementary information incorporation; 3) Our EPIT performs much more robust to disparity variations and achieves the highest PSNR scores under all sheared values. More quantitative comparisons on the whole datasets can be referred to the supplemental material.", + "bbox": [ + 496, + 501, + 892, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "LAM Visualization. We used Local Attribution Map (LAM) [18] to visualize the input regions that contribute to the SR results of different methods. As shown in Fig. 8, we first specify the center of green stripes in HR images as the target regions, and then re-organize the corresponding attribution maps on LR images into the EPI patterns. It can be observed that RCAN achieves a larger receptive field along the spatial dimension than other compared methods, which supports the results in Figs. 8(b) and 8(e) that RCAN achieves a relatively stable SR performance with different", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12382", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16ddaee3aa785a8a15bfedb26f9cd5ce15c6688a58c07706b414d36148199536.jpg", + "image_caption": [ + "Figure 9. PSNR distribution among different SAIs achieved by MEG-Net [78], LFT [36], and our EPIT on the INRIA dataset [46] for $2 \\times \\mathrm{SR}$ ." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 472, + 294 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sheared values. It is worth noting that our EPIT can automatically incorporate the most relevant information from different views, and can learn the non-local spatial-angular correlation regardless of disparity variations.", + "bbox": [ + 75, + 359, + 468, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Perspective Comparison. We compare the performance of MEG-Net, DistgSSR and our method with respect to different perspectives and sheared values (0 to 3). It can be observed in Fig. 9 that, both MEG-Net and DistgSSR suffer significant performance drops on all perspectives as the sheared value increases. In contrast, our EPIT can well handle the disparity variation problem, and achieve much higher PSNR values with a balanced distribution among different views regardless of the sheared values.", + "bbox": [ + 75, + 422, + 470, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 571, + 230, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this subsection, we compare the performance of our EPIT with different variants to verify the effectiveness of our design choices, and additionally, investigate their robustness to large disparity variations.", + "bbox": [ + 75, + 595, + 468, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Horizontal/Vertical Basic-Transformer Units. We demonstrated the effectiveness of the horizontal and vertical Basic-Transformer units in our EPIT by separately removing them from our network. Note that, without using horizontal or vertical Basic-Transformer unit, these variants cannot incorporate any information from the corresponding angular directions. As shown in Table 3, both variants w/o-Horizontal and w/o-Vertical suffer a decrease of $0.72\\mathrm{dB}$ in the INRIA dataset as compared to EPIT, which demonstrates the importance of exploiting spatial-angular correlations from all angular views.", + "bbox": [ + 75, + 657, + 468, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Weight Sharing in Non-Local Cascading Blocks. We introduced the variant $w/o$ -Share by removing the weight sharing between horizontal and vertical Basic-Transformer units. As shown in Table 3, the additional parameters in variant $w/o$ -Share do not introduce further performance im", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/767bcb70db54c9154d82e8676745f9ff97c10c9266b2ab833b77dff5af97f57e.jpg", + "table_caption": [ + "Table 3. The PSNR scores achieved by different variants of our EPIT on the LFs with different shearing values for $2 \\times \\mathrm{SR}$ . We adjusted the channel number of each variant to make its model size (i.e., #Prm.) not smaller than EPIT for better validation." + ], + "table_footnote": [], + "table_body": "
Variants#Prm.FLOPsEPFL (Sheared)INRIA (Sheared)
024024
w/o-Horiz1.42M80.20G33.9633.9834.0235.9536.0836.11
w/o-Verti1.42M80.20G34.0133.9433.8735.9535.9736.02
w/o-Share2.71M80.20G34.8034.6334.5136.6636.7236.45
w/o-Local1.64M96.39G34.4234.3634.2736.3636.4036.25
w/o-Trans1.60M78.82G33.9031.3231.7435.9533.2833.55
w-1-Block1.54M68.23G33.9734.2434.0835.8436.1935.93
w-2-Block1.45M73.37G34.1934.3634.2935.9836.2735.99
w-3-Block1.71M85.78G34.6434.5134.4536.5336.4736.22
EPIT1.42M74.96G34.8334.6934.5936.6736.7536.59
", + "bbox": [ + 501, + 141, + 888, + 277 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "provement. It demonstrates that the weight sharing strategy between two directional Basic-Transformer units is beneficial and efficient to regularize the network.", + "bbox": [ + 496, + 297, + 890, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SpatialConv in Non-Local Cascading Blocks. We introduced the variant w/o-Local by removing the SpatialConv layers from our EPIT, and we adjusted the channel number to make the model size of this variant not smaller than the main model. As shown in Table 3, the SpatialConv has a significant influence on the SR performance, e.g., the variant w/o-Local suffers a 0.41dB PSNR drop on the EPFL dataset. It demonstrates that local context information is crucial to the SR performance, and the simple convolutions can fully incorporate the spatial information from each SAI.", + "bbox": [ + 496, + 343, + 892, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Basic-Transformer in Non-Local Cascading Blocks. We introduced the variant $w/o$ -Trans by replacing Basic-Transformer in Non-Local Blocks with cascaded convolutions. As shown in Table 3, $w/o$ -Trans suffers a most significant performance drop as the sheared value increases, which demonstrates the effectiveness of the Basic-Transformer in incorporating global information on the EPIs.", + "bbox": [ + 496, + 496, + 890, + 601 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Basic-Transformer Number. We introduced the variants with-n-Block $(n = 1,2,3)$ by retaining $n$ Non-Local Blocks. Results in Table 3 show the effectiveness of our EPIT (having 5 Non-Local Blocks) with higher-order spatial-angular correlation modeling capability.", + "bbox": [ + 496, + 601, + 890, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 691, + 617, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a Transformer-based network for LF image SR. By modeling the dependencies between each pair of pixels on EPIs, our method can learn the spatial-angular correlation while achieving a global receptive field along the epipolar line. Extensive experimental results demonstrated that our method can not only achieve state-of-the-art SR performance on benchmark datasets, but also perform robust to large disparity variations.", + "bbox": [ + 496, + 718, + 890, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment: This work was supported in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 61921001.", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12383", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Martin Alain and Aljosa Smolic. Light field super-resolution via lfbm5d sparse coding. 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IEEE Transactions on Visualization and Computer Graphics, 27(6):3019-3033, 2019." + ], + "bbox": [ + 501, + 92, + 890, + 811 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12386", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/0facca26-8b6b-4a15-98c0-1ceb58a77d13_model.json b/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/0facca26-8b6b-4a15-98c0-1ceb58a77d13_model.json new file mode 100644 index 0000000000000000000000000000000000000000..78f404def44a1c089f4016a1e421be63c2cd30c3 --- /dev/null +++ b/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/0facca26-8b6b-4a15-98c0-1ceb58a77d13_model.json @@ -0,0 +1,3027 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.16, + 0.131, + 0.812, + 0.177 + ], + "angle": 0, + "content": "Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.203, + 0.877, + 0.24 + ], + "angle": 0, + "content": "Zhengyu Liang\\(^{1}\\), Yingqian Wang\\(^{1}\\), Longguang Wang\\(^{2}\\), Jungang Yang\\(^{1\\boxtimes}\\), Shilin Zhou\\(^{1}\\), Yulan Guo\\(^{1}\\) \n\\(^{1}\\)National University of Defense Technology, \\(^{2}\\)Aviation University of Air Force" + }, + { + "type": "text", + "bbox": [ + 0.334, + 0.242, + 0.637, + 0.258 + ], + "angle": 0, + "content": "{zyliang, yangjungang}@nudt.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.326, + 0.474, + 0.718 + ], + "angle": 0, + "content": "Exploiting spatial-angular correlation is crucial to light field (LF) image super-resolution (SR), but is highly challenging due to its non-local property caused by the disparities among LF images. Although many deep neural networks (DNNs) have been developed for LF image SR and achieved continuously improved performance, existing methods cannot well leverage the long-range spatial-angular correlation and thus suffer a significant performance drop when handling scenes with large disparity variations. In this paper, we propose a simple yet effective method to learn the non-local spatial-angular correlation for LF image SR. In our method, we adopt the epipolar plane image (EPI) representation to project the 4D spatial-angular correlation onto multiple 2D EPI planes, and then develop a Transformer network with repetitive self-attention operations to learn the spatial-angular correlation by modeling the dependencies between each pair of EPI pixels. Our method can fully incorporate the information from all angular views while achieving a global receptive field along the epipolar line. We conduct extensive experiments with insightful visualizations to validate the effectiveness of our method. Comparative results on five public datasets show that our method not only achieves state-of-the-art SR performance but also performs robust to disparity variations. Code is publicly available at https://github.com/ZhengyuLiang24/EPIT." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.753, + 0.21, + 0.768 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Light field (LF) cameras record both intensity and directions of light rays, and enable various applications such as depth perception [25, 29, 32], view rendering [3, 52, 66], virtual reality [11, 74], and 3D reconstruction [6, 77]. However, due to the inherent spatial-angular trade-off [82], an LF camera can either provide dense angular samplings with low-resolution (LR) sub-aperture images (SAIs), or capture high-resolution (HR) SAIs with sparse angular sampling." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.291, + 0.895, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.489, + 0.895, + 0.601 + ], + "angle": 0, + "content": "Figure 1. Visualization of \\(4 \\times\\) SR results and the corresponding attribution maps [18] of our method and four state-of-the-art methods [26, 36, 60, 78] under different manually sheared disparity values. Here, the patch marked by the green box in the HR image is selected as the target region, and the regions that contribute to the final SR results are highlighted in red. Our method can well exploit the non-local spatial-angular correlation and achieve superior SR performance. More examples are provided in Fig. 8." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.894, + 0.704 + ], + "angle": 0, + "content": "To handle this problem, many methods have been proposed to enhance the angular resolution via novel view synthesis [28, 43, 67], or enhance the spatial resolution by performing LF image super-resolution (SR) [10, 20]. In this paper, we focus on the latter task, i.e., generating HR LF images from their LR counterparts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Recently, convolutional neural networks (CNNs) have been widely applied to LF image SR and demonstrated superior performance over traditional paradigms [1, 34, 44, 49, 64]. To incorporate the complementary information (i.e., angular information) from different views, existing CNNs adopted various mechanisms such as adjacent-view combination [73], view-stack integration [26, 78, 79], bidirectional recurrent fusion [59], spatial-angular disentanglement [36, 60, 61, 72, 9], and 4D convolutions [42, 43]. However, as illustrated in both Fig. 1 and Sec. 4.3, existing methods achieve promising results on LFs with small baselines, but suffer a notable performance drop when handling scenes with large disparity variations." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12376" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.364 + ], + "angle": 0, + "content": "We attribute this performance drop to the contradictions between the local receptive field of CNNs and the requirement of incorporating non-local spatial-angular correlation in LF image SR. That is, LF images provide multiple observations of a scene from a number of regularly distributed viewpoints, and a scene point is projected onto different but correlated spatial locations on different angular views, which is termed as the spatial-angular correlation. Note that, the spatial-angular correlation has the non-local property since the difference between the spatial locations of two views (i.e., disparity value) depends on several factors (e.g., angular coordinates of the selected views, the depth value of the scene point, the baseline length of the LF camera, and the resolution of LF images), and can be very large in some situations. Consequently, it is appealing for LF image SR methods to incorporate complementary information from different views by exploiting the spatial-angular correlation under large disparity variations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.473, + 0.576 + ], + "angle": 0, + "content": "In this paper, we propose a simple yet effective method to learn the non-local spatial-angular correlation for LF image SR. In our method, we re-organize 4D LFs as multiple 2D epipolar plane images (EPIs) to manifest the spatial-angular correlation to the line patterns with different slopes. Then, we develop a Transformer-based network called EPIT to learn the spatial-angular correlation by modeling the dependencies between each pair of pixels on EPIs. Specifically, we design a basic Transformer block to alternately process horizontal and vertical EPIs, and thus progressively incorporate the complementary information from all angular views. Compared to existing LF image SR methods, our method can achieve a global receptive field along the epipolar line, and thus performs robust to disparity variations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.473, + 0.745 + ], + "angle": 0, + "content": "In summary, the contributions of this work are as follows: (1) We address the importance of exploiting non-local spatial-angular correlation in LF image SR, and propose a simple yet effective method to handle this problem. (2) We develop a Transformer-based network to learn the non-local spatial-angular correlation from horizontal and vertical EPIs, and validate the effectiveness of our method through extensive experiments and visualizations. (3) Compared to existing state-of-the-art LF image SR methods, our method achieves superior performance on public LF datasets, and is much more robust to disparity variations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.76, + 0.22, + 0.777 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.786, + 0.218, + 0.803 + ], + "angle": 0, + "content": "2.1. LF Image SR" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.472, + 0.903 + ], + "angle": 0, + "content": "LFCNN [73] is the first method to adopt CNNs to learn the correspondence among stacked SAIs. Then, it is a common practice for LF image SR networks to aggregate the complementary information from adjacent views to model the correlation in LFs. Yeung et al. [72] designed a spatial-angular separable (SAS) convolution to approximate the 4D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.258 + ], + "angle": 0, + "content": "convolution to characterize the sub-pixel relationship of LF 4D structures. Wang et al. [59] proposed a bidirectional recurrent network to model the spatial correlation among views on horizontal and vertical baselines. Meng et al. [42] proposed a densely-connected network with 4D convolutions to explicitly learn the spatial-angular correlation encoded in 4D LF data. To further learn inherent corresponding relations in SAIs, Zhang et al. [78, 79] grouped LFs into four different branches according to the specific angular directions, and used four sub-networks to model the multi-directional spatial-angular correlation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.895, + 0.56 + ], + "angle": 0, + "content": "The aforementioned networks use part of input views to super-resolve each view, and the inherent spatial-angular correlation in LF images cannot be well incorporated. To address this issue, Jin et al. [26] proposed an All-to-One framework for LF image SR, and each SAI can be individually super-resolved by combining the information from all views. Wang et al. [61, 60] organized LF images into macro-pixels, and designed a disentangling mechanism to fully incorporate the angular information. Liu et al. [38] introduced 3D convolutions based multi-view context block to exploit the correlations among all views. In addition, Wang et al. [62] adopted deformable convolutions to achieve long-range information exploitation from all SAIs. Existing methods generally learn the local correspondence across SAIs, and ignore the importance of non-local spatial-angular correlation in LF images. However, due to the limited receptive field of CNNs, existing methods generally learn the local correspondence across SAIs, and ignore the importance of non-local spatial-angular correlation in LF images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.895, + 0.684 + ], + "angle": 0, + "content": "Recently, Liang et al. [36] applied Transformers to LF image SR and developed an angular Transformer and a spatial Transformer to incorporate angular information and model long-range spatial dependencies, respectively. However, since 4D LFs were organized into 2D angular patches to form the input of angular Transformers, the non-local property of spatial-angular correlations reduces the robustness of LFT to large disparity variations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.791, + 0.712 + ], + "angle": 0, + "content": "2.2. Non-Local Correlation Modeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Non-local means [5] is a classical algorithm that computes the weighted mean of pixels in an image according to the self-similarity measure, and a number of studies on such non-local priors have been proposed for image restoration [12, 51, 19, 4], image and video SR [16, 76, 14, 71, 23]. Then, the attention mechanism is developed as a tool to bias the most informative components of an input signal, and achieves significant performance in various computer vision tasks [22, 8, 58, 15]. Huang et al. [24] proposed novel criss-cross attention to capture contextual information from full-image dependencies in an efficient way. Wang et al. [56, 55] proposed a parallax attention mechanism to handle" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12377" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.151 + ], + "angle": 0, + "content": "the varying disparities problem of stereo images. Wu et al. [69] applied attention mechanisms to 3D LF reconstruction and developed a spatial-angular attention module to learn the first-order correlation on EPIs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.471, + 0.364 + ], + "angle": 0, + "content": "Recently, the attention mechanism is further generalized as Transformers [54] with multi-head structures and feed-forward networks. Transformers have inspired lots of works [39, 35, 7, 13] to further investigate the power of attention mechanisms in visions. Liu et al. [40] presented a pure-Transformer method to incorporate the inherent spatial-temporal locality of videos for action recognition. Naseer et al. [45] investigated the robustness and generalizability of Transformers, and demonstrated favorable merits of Transformers over CNNs for occlusion handling. Shi et al. [50] observed that Transformers can implicitly make accurate connections for misaligned pixels, and presented a new understanding of Transformers to process spatially unaligned images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.379, + 0.168, + 0.394 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.404, + 0.206, + 0.421 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.47, + 0.547 + ], + "angle": 0, + "content": "Based on the two-plane LF parameterization model [33], an LF image is commonly formulated as a 4D function \\(\\mathcal{L}(u,v,h,w)\\in \\mathbb{R}^{U\\times V\\times H\\times W}\\), where \\(U\\) and \\(V\\) represent angular dimensions, \\(H\\) and \\(W\\) represent spatial dimensions. The EPI sample of 4D LF is acquired with a fixed angular coordinate and a fixed spatial coordinate. Specifically, the horizontal EPI is obtained with constant \\(u\\) and \\(h\\), and the vertical EPI is obtained with constant \\(v\\) and \\(w\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.671 + ], + "angle": 0, + "content": "As shown in Fig. 2, the EPIs not only record spatial structures at edges or textures, but also reflect the disparity information via line patterns of different slopes. Specifically, due to large disparities, the EPIs contain abundant spatial-angular correlation of LFs in a long-range way. Therefore, we propose to explore the non-local spatial-angular correlation from horizontal and vertical EPIs for LF image SR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.238, + 0.697 + ], + "angle": 0, + "content": "3.2. Network Design" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.469, + 0.795 + ], + "angle": 0, + "content": "As shown in Fig. 3(a), our network takes an LR LF \\(\\mathcal{L}_{LR} \\in \\mathbb{R}^{U \\times V \\times H \\times W}\\) as its input, and produces an HR LF \\(\\mathcal{L}_{SR} \\in \\mathbb{R}^{U \\times V \\times \\alpha H \\times \\alpha W}\\), where \\(\\alpha\\) presents the upscaling factor. Our network consists of three stages including initial feature extraction, deep spatial-angular correlation learning, and feature upsampling." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.312, + 0.831 + ], + "angle": 0, + "content": "3.2.1 Initial Feature Extraction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "As shown in Fig. 3(b), we follow most existing works [7, 35, 75] to use three \\(3 \\times 3\\) convolutions with LeakyReLU [41] as a SpatialConv layer to map each SAI to a high-dimensional feature. The initially extracted feature can be" + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.089, + 0.865, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.255, + 0.892, + 0.297 + ], + "angle": 0, + "content": "Figure 2. The SAI and EPI representations of LF images. The array of \\(9 \\times 9\\) views of a scene rosemary from HCInew [21] dataset is used as an example for illustration." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.31, + 0.892, + 0.341 + ], + "angle": 0, + "content": "represented as \\(\\pmb{F} \\in \\mathbb{R}^{U \\times V \\times H \\times W \\times C}\\), where \\(C\\) denotes the channel dimension." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.363, + 0.86, + 0.379 + ], + "angle": 0, + "content": "3.2.2 Deep Spatial-Angular Correlation Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.597 + ], + "angle": 0, + "content": "Non-Local Cascading Block. The basic module for spatial-angular correlation learning is the Non-Local Cascading block. As shown in Fig. 3(a), each block consists of two cascaded Basic-Transformer units to separately incorporate the complementary information along the horizontal and vertical epipolar lines. In our method, we employed five Non-Local Cascading blocks to achieve a global perception of all angular views, and followed SwinIR [35] to adopt spatial convolutions to enhance the local feature representation. The effectiveness of this inter-block spatial convolution is validated in Sec. 4.4. Note that, the weights of the two Basic-Transformer units in each block are shared to jointly learn the intrinsic properties of LFs, which is demonstrated effective in Sec. 4.4." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.599, + 0.892, + 0.78 + ], + "angle": 0, + "content": "As shown in Fig. 3(c), the initial features \\(\\pmb{F}\\) can be first separately reshaped to the horizontal EPI pattern \\(\\pmb{F}_{hor} \\in \\mathbb{R}^{UH \\times V \\times W \\times C}\\) and the vertical EPI pattern \\(\\pmb{F}_{ver} \\in \\mathbb{R}^{VW \\times U \\times H \\times C}\\). Next, \\(\\pmb{F}_{hor}\\) (or \\(\\pmb{F}_{ver}\\)) is fed to a Basic-Transformer unit to integrate the long-range information along the horizontal (or vertical) epipolar line. Then, the enhanced feature \\(\\hat{\\pmb{F}}_{hor}\\) (or \\(\\hat{\\pmb{F}}_{ver}\\)) is reshaped into the size of \\(UV \\times H \\times W \\times C\\), and passes through a SpatialConv layer to incorporate the spatial context information within each SAI. Without loss of generality, we take the vertical Basic-Transformer as an example to introduce the detail of our Basic-Transformer unit in the following texts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Basic-Transformer Unit. The objective of this unit is to capture long-range dependencies along the epipolar line via Transformers. To leverage the powerful sequence modeling capability of Transformers, we convert the vertical EPI features \\( \\pmb{F}_{ver} \\) to the sequences of \"tokens\" for capturing spatial-angular correlation in \\( U \\) and \\( H \\) dimensions. As shown in Fig. 3(d), the vertical EPI features are passed through a linear projection matrix \\( W_{in} \\in \\mathbb{R}^{C \\times D} \\), where \\( D \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12378" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.887, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.261, + 0.182, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.189, + 0.261, + 0.547, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.552, + 0.26, + 0.885, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.189, + 0.404, + 0.779, + 0.419 + ], + "angle": 0, + "content": "Figure 3. An overview of our proposed EPIT. Here, a \\(3 \\times 3\\) LF is used as an example for illustration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.527 + ], + "angle": 0, + "content": "denotes the embedding dimension of each token. The projected EPI features are a sequence of tokens with a length of \\( UH \\), i.e., \\( T_{ver} \\in \\mathbb{R}^{UH \\times D} \\). Following the PreNorm operation in [70], we also apply Layer Normalization (LN) before the attention calculation, and obtain the normalized tokens \\( \\bar{T}_{ver} = \\mathrm{LN}(T_{ver}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.469, + 0.648 + ], + "angle": 0, + "content": "Afterwards, tokens \\(\\bar{T}_{ver}\\) are passed through the Self-Attention layer and transformed into the deep tokens involving non-local spatial-angular information along the vertical epipolar line. Specifically, \\(\\bar{T}_{ver}\\) need to be separately multiplied by \\(W_{Q} \\in \\mathbb{R}^{D \\times D}\\), \\(W_{K} \\in \\mathbb{R}^{D \\times D}\\) and \\(W_{V} \\in \\mathbb{R}^{D \\times D}\\) to generate corresponding query, key and value components for self-attention calculation, i.e., \\(Q_{ver} = \\bar{T}_{ver} W_{Q}\\), \\(K_{ver} = \\bar{T}_{ver} W_{K}\\) and \\(V_{ver} = \\bar{T}_{ver} W_{V}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.47, + 0.737 + ], + "angle": 0, + "content": "Given a query position \\(q = \\{1,2,\\dots ,UH\\}\\) in \\(Q_{ver}\\) and a key position \\(k = \\{1,2,\\dots ,UH\\}\\) in \\(K_{ver}\\), the corresponding response \\(A_{ver}(q,k)\\in \\mathbb{R}\\) measures the mutual similarity of the pairs by the dot-product operation, followed by a Softmax function to obtain the attention scores on the vertical EPI tokens. That is," + }, + { + "type": "equation", + "bbox": [ + 0.119, + 0.746, + 0.469, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} _ {\\text {v e r}} (q, k) = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {\\text {v e r}} (q) \\cdot K _ {\\text {v e r}} (k) ^ {\\mathrm {T}}}{\\sqrt {D}}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.47, + 0.847 + ], + "angle": 0, + "content": "Based on the attention scores, the output of self-attention \\( T_{ver}^{\\prime} \\) can be calculated as the weighted sum of value. In summary, the calculation process of Self-Attention layer can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.858, + 0.469, + 0.875 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {T} _ {\\text {v e r}} ^ {\\prime} = \\boldsymbol {A} _ {\\text {v e r}} V _ {\\text {v e r}} + T _ {\\text {v e r}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "To further incorporate the spatial-angular correlation," + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.435, + 0.588, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.489, + 0.559, + 0.498 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.435, + 0.661, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.618, + 0.489, + 0.633, + 0.498 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.435, + 0.734, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.692, + 0.489, + 0.706, + 0.498 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.739, + 0.435, + 0.807, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.766, + 0.489, + 0.78, + 0.498 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.813, + 0.435, + 0.883, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.84, + 0.489, + 0.854, + 0.498 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.499, + 0.588, + 0.551 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.546, + 0.552, + 0.559, + 0.561 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.499, + 0.661, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.619, + 0.553, + 0.633, + 0.561 + ], + "angle": 0, + "content": "(g)" + }, + { + "type": "image", + "bbox": [ + 0.666, + 0.499, + 0.735, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.692, + 0.553, + 0.706, + 0.561 + ], + "angle": 0, + "content": "(h)" + }, + { + "type": "image", + "bbox": [ + 0.739, + 0.499, + 0.808, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.768, + 0.553, + 0.779, + 0.561 + ], + "angle": 0, + "content": "(i)" + }, + { + "type": "image", + "bbox": [ + 0.813, + 0.499, + 0.882, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.84, + 0.553, + 0.853, + 0.561 + ], + "angle": 0, + "content": "(1)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.565, + 0.892, + 0.62 + ], + "angle": 0, + "content": "Figure 4. An example of the attention maps of a Basic-Transformer unit for the spatial-angular correlation. Note that, the attention maps correspond to the correlation between the regions marked by the red and yellow strokes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.637, + 0.892, + 0.682 + ], + "angle": 0, + "content": "following [54], our Basic-Transformer unit also contains the multi-layer perception (MLP) and LN, and generates the enhanced \\(\\hat{T}_{ver}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.693, + 0.891, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {T}} _ {v e r} = \\operatorname {M L P} \\left(\\operatorname {L N} \\left(\\boldsymbol {T} _ {v e r} ^ {\\prime}\\right)\\right) + \\boldsymbol {T} _ {v e r} ^ {\\prime}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.892, + 0.78 + ], + "angle": 0, + "content": "At the end of the Basic-Transformer unit, the enhanced \\(\\hat{T}_{ver}\\) is fed to another linear projection \\(W_{out} \\in \\mathbb{R}^{D \\times C}\\), and reshaped into the size of \\(UV \\times H \\times W \\times C\\) for the subsequent SpatialConv layer." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Cross-View Similarity Analysis. Note that, the setting \\([A_{ver}(q,1),\\dots,A_{ver}(q,UH)]\\in \\mathbb{R}^{1\\times UH}\\) represents the similarity scores of \\(q\\) with all \\(k\\) in \\(K_{ver}\\), and thus can be re-organized as a slice of cross-view attention map according to the angular coordinate. Inspired by this, we visualized the cross-view attention maps on an example scene in Fig. 4. The regions marked by the red stripe in Fig. 4(a) are set as the query tokens, and the self-similarity (i.e.," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12379" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.892, + 0.114 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of different SR methods in terms of the number of parameters (#Prm.) and PSNR/SSIM. Larger PSNR and SSIM values indicate higher SR quality. We mark the best results in red and the second best results in blue." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.115, + 0.892, + 0.344 + ], + "angle": 0, + "content": "
Methods#Prm.(M)2×/4×2×4×
EPFLHCInewHCIoldINRIASTFgantryEPFLHCInewHCIoldINRIASTFgantry
Bicubic- / -29.74/.937631.89/.935637.69/.978531.33/.957731.06/.949825.14/.832427.61/.851732.42/.934426.82/.886725.93/.8452
VDSR [30]0.66 / 0.6632.50/.959834.37/.956140.61/.986734.43/.974135.54/.978927.25/.877729.31/.882334.81/.951529.19/.920428.51/.9009
EDSR [37]38.6 / 38.933.09/.962934.83/.959241.01/.987434.97/.976436.29/.981827.84/.885429.60/.886935.18/.953629.66/.925728.70/.9072
RCAN [81]15.3 / 15.433.16/.963434.98/.960341.05/.987535.01/.976936.33/.983127.88/.886329.63/.888635.20/.954829.76/.927628.90/.9131
resLF[79]7.98 / 8.6433.62/.970636.69/.973943.42/.993235.39/.980438.36/.990428.27/.903530.73/.910736.71/.968230.34/.941230.19/.9372
LFSSR [72]0.88 / 1.7733.68/.974436.81/.974943.81/.993835.28/.983237.95/.989828.27/.911830.72/.914536.70/.969630.31/.946730.15/.9426
LF-ATO [26]1.22 / 1.3634.27/.975737.24/.976744.20/.994236.15/.984239.64/.992928.52/.911530.88/.913537.00/.969930.71/.948430.61/.9430
LF-InterNet [61]5.04 / 5.4834.14/.976037.28/.976344.45/.994635.80/.984338.72/.990928.67/.916230.98/.916137.11/.971630.64/.949130.53/.9409
LF-DFnet [62]3.94 / 3.9934.44/.975537.44/.977344.23/.994136.36/.984039.61/.992628.77/.916531.23/.919637.32/.971830.83/.950331.15/.9494
MEG-Net [78]1.69 / 1.7734.30/.977337.42/.977744.08/.994236.09/.984938.77/.991528.74/.916031.10/.917737.28/.971630.66/.949030.77/.9453
LF-IINet [38]4.84 / 4.8834.68/.977337.74/.979044.84/.994836.57/.985339.86/.993629.11/.918831.36/.920837.62/.973431.08/.951531.21/.9502
DPT [57]3.73 / 3.7834.48/.975837.35/.977144.31/.994336.40/.984339.52/.992628.93/.917031.19/.918837.39/.972130.96/.950331.14/.9488
LFT [36]1.11 / 1.1634.80/.978137.84/.979144.52/.994536.59/.985540.51/.994129.25/.921031.46/.921837.63/.973531.20/.952431.86/.9548
DistgSSR [60]3.53 / 3.5834.81/.978737.96/.979644.94/.994936.59/.985940.40/.994228.99/.919531.38/.921737.56/.973230.99/.951931.65/.9535
LFSAV [9]1.22 / 1.5434.62/.977237.43/.977644.22/.994236.36/.984938.69/.991429.37/.922331.45/.921737.50/.972131.27/.953131.36/.9505
EPIT (ours)1.42 / 1.4734.83/.977538.23/.981045.08/.994936.67/.985342.17/.995729.34/.919731.51/.923137.68/.973731.37/.952632.18/.9571
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.473, + 0.522 + ], + "angle": 0, + "content": "key are same as query) is ideally located at the diagonal, as shown in Fig. 4(f). In contrast, the yellow stripes in Figs. 4(b)-4(e) are set as the key tokens, the corresponding cross-view similarities are shown in Figs. 4(g)-4(j). It can be observed that due to the foreground occlusions, the responses of the background appear as short lines (marked by the white boxes) parallel to the diagonal in each cross-view attention map, and both of the distance to the diagonal and the length of response regions adaptively change as the key view moves along the baseline, which demonstrates the disparity-awareness of our Basic-Transformer unit." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.543, + 0.275, + 0.559 + ], + "angle": 0, + "content": "3.2.3 Feature Upsampling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.659 + ], + "angle": 0, + "content": "Finally, we apply the pixel shuffling operation to increase the spatial resolution of LF features, and further employ a \\(3 \\times 3\\) convolution to obtain the super-resolved LF image \\(\\mathcal{L}_{SR}\\). Following most existing works [61, 60, 36, 62, 57, 38, 78, 79, 72], we use the \\(L_{1}\\) loss function to train our network due to its robustness to outliers [2]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.674, + 0.21, + 0.691 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.47, + 0.79 + ], + "angle": 0, + "content": "In this section, we first introduce the datasets and our implementation details, and then compare our method with state-of-the-art methods. Next, we investigate the performance of different SR methods with respect to disparity variations. Finally, we validate the effectiveness of our method through ablation studies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.398, + 0.818 + ], + "angle": 0, + "content": "4.1. Datasets and Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We followed [62, 60, 38, 57, 36] to use five public LF datasets (EPFL [48], HCInew [21], HCld [65], INRIA [46], STFgantry [53]) in the experiments. All LFs in these datasets have an angular resolution of \\(9 \\times 9\\). Unless specifically mentioned, we extracted the central \\(5 \\times 5\\) SAIs for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.505 + ], + "angle": 0, + "content": "training and test. In the training stage, we cropped each SAI into patches of size \\(64 \\times 64 / 128 \\times 128\\), and performed \\(0.5 \\times / 0.25 \\times\\) bicubic downsampling to generate the LR patches for \\(2 \\times / 4 \\times\\) SR, respectively. We used peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [63] as quantitative metrics for performance evaluation. To obtain the metric score for a dataset with \\(M\\) scenes, we first calculated the metric of each scene by averaging the scores over all the SAIs separately, and then obtained the score for this dataset by averaging the scores over the \\(M\\) scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.893, + 0.642 + ], + "angle": 0, + "content": "We adopted the same training settings for all experiments, i.e., Xavier initialization algorithm [17] and Adam optimizer [31] with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\). The initial learning rate was set to \\(2\\times 10^{-4}\\) and decreased by a factor of 0.5 every 15 epochs. During the training phase, we performed random horizontal flipping, vertical flipping, and 90-degree rotation to augment the training data. All models were implemented in the PyTorch framework and trained from scratch for 80 epochs with 2 Nvidia RTX 2080Ti GPUs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.651, + 0.825, + 0.667 + ], + "angle": 0, + "content": "4.2. Comparisons on Benchmark Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We compare our method to 14 state-of-the-art methods, including 3 single image SR methods [30, 37, 81] and 11 LF image SR methods [79, 72, 26, 61, 62, 78, 38, 57, 36, 60, 9]. Quantitative Results. A quantitative comparison among different methods is shown in Tabel 1. Our EPIT with a small model size (i.e., \\(1.42\\mathrm{M} / 1.47\\mathrm{M}\\) for \\(2\\times /4\\times\\) SR) achieves state-of-the-art PSNR and SSIM scores on almost all the datasets for both \\(2\\times\\) and \\(4\\times\\) SR. It is worth noting that LFs in the STFgantry dataset [53] have larger disparity variations, and are thus more challenging. Our EPIT significantly outperforms all the compared methods and achieves \\(1.66\\mathrm{dB} / 0.32\\mathrm{dB}\\) PSNR improvements over the second top-performing method LFT for \\(2\\times /4\\times\\) SR, respectively, which demonstrates the powerful capacity of our EPIT in non-local correlation modeling." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12380" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.237, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.238, + 0.089, + 0.326, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.334, + 0.089, + 0.421, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.429, + 0.089, + 0.516, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.089, + 0.609, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.089, + 0.701, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.089, + 0.795, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.801, + 0.089, + 0.888, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.231, + 0.237, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.238, + 0.231, + 0.326, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.334, + 0.231, + 0.421, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.429, + 0.231, + 0.516, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.231, + 0.609, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.61, + 0.231, + 0.703, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.231, + 0.795, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.8, + 0.231, + 0.89, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.372, + 0.7, + 0.385 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison of different SR methods for \\(2 \\times /4 \\times\\) SR." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.399, + 0.472, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.511, + 0.47, + 0.553 + ], + "angle": 0, + "content": "Figure 6. Quantitative and qualitative (MSE) comparisons of disparity estimation results achieved by SPO [80] using different SR results. The MSE \\((\\downarrow)\\) is the mean square error multiplied by 100." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.567, + 0.469, + 0.594 + ], + "angle": 0, + "content": "Table 2. PSNR values achieved by DistgSSR [60] and our EPIT with different angular resolution for \\(4 \\times\\) SR." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.595, + 0.469, + 0.699 + ], + "angle": 0, + "content": "
InputEPFLHCInewHCIoldINRIASTFgantry
[60]Ours[60]Ours[60]Ours[60]Ours[60]Ours
2×228.27-0.0530.80+0.0436.77+0.1730.55-0.0330.74+0.56
3×328.67+0.0331.07+0.1937.18+0.1930.83+0.1131.12+0.74
4×428.81+0.2331.25+0.1537.32+0.2030.93+0.2631.23+0.88
5×528.99+0.3531.38+0.1337.56+0.1230.99+0.3831.65+0.56
6×629.10+0.3331.39+0.1837.52+0.2630.98+0.4731.57+0.74
7×729.38+0.2231.43+0.2037.65+0.2731.18+0.3331.63+0.77
8×829.32+0.2831.52+0.1437.76+0.2431.23+0.3131.58+0.90
9×929.41+0.3031.48+0.2137.80+0.2631.22+0.3431.66+0.84
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Qualitative Results. Figure 5 shows the qualitative results achieved by different methods for \\(2 \\times 4 \\times\\) SR. It can be observed from the zoom-in regions that single image SR method RCAN [81] cannot recover the textures and details in the SR images. In contrast, our EPIT can incorporate sub-pixel correspondence among SAIs and generate more faithful details with fewer artifacts. Compared to most LF image SR methods, our EPIT can generate superior visual results with high angular consistency. Please refer to the supplemental material for additional visual comparisons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Angular Consistency. We evaluate the angular consistency by using the \\(4 \\times \\mathrm{SR}\\) results on several challenging scenes" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.399, + 0.655, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.399, + 0.734, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.74, + 0.399, + 0.813, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.82, + 0.399, + 0.894, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.597, + 0.892, + 0.624 + ], + "angle": 0, + "content": "Figure 7. Visual comparison of different SR methods on real-world LF scenes for \\(4 \\times \\mathrm{SR}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.892, + 0.716 + ], + "angle": 0, + "content": "(e.g., Backgammon and Stripes) in 4D LF benchmark [21] for disparity estimation. As shown in Fig. 6, our EPIT achieves competitive MSE scores on these challenging scenes, which demonstrates the superiority of our EPIT on angular consistency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Performance with Different Angular Resolution. Since the angular resolution of LR images can vary significantly with different LF devices, we compare our method to DistgSSR [60] on LFs with different angular resolutions. It can be observed from Table 2 that our method achieves higher PSNR values than DistgSSR on almost all the datasets with each angular resolution (except on the EPFL and INRIA datasets with \\(2 \\times 2\\) input LFs). The consistent performance improvements demonstrate that our EPIT can well model the spatial-angular correlation with various angular resolutions. More comparisons and discussions are provided in the supplemental material." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12381" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.09, + 0.235, + 0.225 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.238, + 0.089, + 0.487, + 0.225 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.089, + 0.635, + 0.225 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.089, + 0.891, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.227, + 0.17, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.172, + 0.227, + 0.249, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.227, + 0.328, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.331, + 0.227, + 0.408, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.227, + 0.487, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.335, + 0.17, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.172, + 0.335, + 0.249, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.335, + 0.328, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.331, + 0.335, + 0.408, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.335, + 0.487, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.283, + 0.432, + 0.297, + 0.44 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.227, + 0.574, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.577, + 0.227, + 0.652, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.227, + 0.731, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.733, + 0.227, + 0.808, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.812, + 0.227, + 0.888, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.335, + 0.573, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.576, + 0.335, + 0.652, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.335, + 0.73, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.733, + 0.335, + 0.808, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.812, + 0.335, + 0.888, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.686, + 0.431, + 0.698, + 0.44 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.443, + 0.894, + 0.486 + ], + "angle": 0, + "content": "Figure 8. Performance comparison and local attribution maps of different SR methods on two representative scenes with different shearing values for \\(2 \\times \\mathrm{SR}\\). Here, we plot the performance curve to quantitatively measure the effect of disparity variations on LFs, and present the visual results and corresponding attribution maps under sheared value=2, 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.473, + 0.684 + ], + "angle": 0, + "content": "Performance on Real-World LF Scenes. We compare our method to state-of-the-art methods under real-world degradation by directly applying them to LFs in the STFlytro dataset [47]. Since no groundtruth HR images are available in this dataset, we present the LR input and their super-resolved results in Fig. 7. It can be observed that our method can recover more faithful details and generate more clear letters than other methods. Since the LF structure keeps unchanged under both bicubic and real-world degradation, our method can learn the spatial-angular correlation from bicubicly downsampled training data, and well generalize to LF images under real degradation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.695, + 0.431, + 0.712 + ], + "angle": 0, + "content": "4.3. Robustness to Large Disparity Variations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Considering the parallax structure of LF images, we followed the shearing operation in existing works [67, 68] to linearly change the overall disparity range of LF datasets. Note that, the content of SAIs maintain unchanged after the shearing operation, and thus we can quantitatively investigate the performance of different SR methods with respect to the disparity variations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Quantitative & Qualitative Comparison. Figure 8 shows the quantitative and qualitative results of different SR methods with respect to sheared values, from which we can observe that: 1) Except for the single image SR method RCAN, all LF image SR methods suffer a performance drop" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.893, + 0.744 + ], + "angle": 0, + "content": "when the absolute sheared value of LF images increases. That is because, large sheared values can result in more significant misalignment among LF images, and introduce difficulties in complementary information incorporation; 2) As the absolute sheared value increases, the performance of existing LF image SR methods is even inferior to RCAN. The possible reason is that, these methods do not make full use of local spatial information, but rather rely on local angular information from adjacent views. When the sheared value exceeds their receptive fields, the large disparities can make the spatial-angular correlation non-local and thus introduce challenges in complementary information incorporation; 3) Our EPIT performs much more robust to disparity variations and achieves the highest PSNR scores under all sheared values. More quantitative comparisons on the whole datasets can be referred to the supplemental material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "LAM Visualization. We used Local Attribution Map (LAM) [18] to visualize the input regions that contribute to the SR results of different methods. As shown in Fig. 8, we first specify the center of green stripes in HR images as the target regions, and then re-organize the corresponding attribution maps on LR images into the EPI patterns. It can be observed that RCAN achieves a larger receptive field along the spatial dimension than other compared methods, which supports the results in Figs. 8(b) and 8(e) that RCAN achieves a relatively stable SR performance with different" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12382" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.473, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.3, + 0.47, + 0.342 + ], + "angle": 0, + "content": "Figure 9. PSNR distribution among different SAIs achieved by MEG-Net [78], LFT [36], and our EPIT on the INRIA dataset [46] for \\(2 \\times \\mathrm{SR}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.422 + ], + "angle": 0, + "content": "sheared values. It is worth noting that our EPIT can automatically incorporate the most relevant information from different views, and can learn the non-local spatial-angular correlation regardless of disparity variations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.471, + 0.558 + ], + "angle": 0, + "content": "Perspective Comparison. We compare the performance of MEG-Net, DistgSSR and our method with respect to different perspectives and sheared values (0 to 3). It can be observed in Fig. 9 that, both MEG-Net and DistgSSR suffer significant performance drops on all perspectives as the sheared value increases. In contrast, our EPIT can well handle the disparity variation problem, and achieve much higher PSNR values with a balanced distribution among different views regardless of the sheared values." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.572, + 0.231, + 0.589 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.657 + ], + "angle": 0, + "content": "In this subsection, we compare the performance of our EPIT with different variants to verify the effectiveness of our design choices, and additionally, investigate their robustness to large disparity variations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.824 + ], + "angle": 0, + "content": "Horizontal/Vertical Basic-Transformer Units. We demonstrated the effectiveness of the horizontal and vertical Basic-Transformer units in our EPIT by separately removing them from our network. Note that, without using horizontal or vertical Basic-Transformer unit, these variants cannot incorporate any information from the corresponding angular directions. As shown in Table 3, both variants w/o-Horizontal and w/o-Vertical suffer a decrease of \\(0.72\\mathrm{dB}\\) in the INRIA dataset as compared to EPIT, which demonstrates the importance of exploiting spatial-angular correlations from all angular views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Weight Sharing in Non-Local Cascading Blocks. We introduced the variant \\( w/o \\)-Share by removing the weight sharing between horizontal and vertical Basic-Transformer units. As shown in Table 3, the additional parameters in variant \\( w/o \\)-Share do not introduce further performance im" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.088, + 0.892, + 0.142 + ], + "angle": 0, + "content": "Table 3. The PSNR scores achieved by different variants of our EPIT on the LFs with different shearing values for \\(2 \\times \\mathrm{SR}\\). We adjusted the channel number of each variant to make its model size (i.e., #Prm.) not smaller than EPIT for better validation." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.142, + 0.89, + 0.279 + ], + "angle": 0, + "content": "
Variants#Prm.FLOPsEPFL (Sheared)INRIA (Sheared)
024024
w/o-Horiz1.42M80.20G33.9633.9834.0235.9536.0836.11
w/o-Verti1.42M80.20G34.0133.9433.8735.9535.9736.02
w/o-Share2.71M80.20G34.8034.6334.5136.6636.7236.45
w/o-Local1.64M96.39G34.4234.3634.2736.3636.4036.25
w/o-Trans1.60M78.82G33.9031.3231.7435.9533.2833.55
w-1-Block1.54M68.23G33.9734.2434.0835.8436.1935.93
w-2-Block1.45M73.37G34.1934.3634.2935.9836.2735.99
w-3-Block1.71M85.78G34.6434.5134.4536.5336.4736.22
EPIT1.42M74.96G34.8334.6934.5936.6736.7536.59
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.892, + 0.344 + ], + "angle": 0, + "content": "provement. It demonstrates that the weight sharing strategy between two directional Basic-Transformer units is beneficial and efficient to regularize the network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.893, + 0.495 + ], + "angle": 0, + "content": "SpatialConv in Non-Local Cascading Blocks. We introduced the variant w/o-Local by removing the SpatialConv layers from our EPIT, and we adjusted the channel number to make the model size of this variant not smaller than the main model. As shown in Table 3, the SpatialConv has a significant influence on the SR performance, e.g., the variant w/o-Local suffers a 0.41dB PSNR drop on the EPFL dataset. It demonstrates that local context information is crucial to the SR performance, and the simple convolutions can fully incorporate the spatial information from each SAI." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.892, + 0.602 + ], + "angle": 0, + "content": "Basic-Transformer in Non-Local Cascading Blocks. We introduced the variant \\( w/o \\)-Trans by replacing Basic-Transformer in Non-Local Blocks with cascaded convolutions. As shown in Table 3, \\( w/o \\)-Trans suffers a most significant performance drop as the sheared value increases, which demonstrates the effectiveness of the Basic-Transformer in incorporating global information on the EPIs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.892, + 0.678 + ], + "angle": 0, + "content": "Basic-Transformer Number. We introduced the variants with-n-Block \\((n = 1,2,3)\\) by retaining \\(n\\) Non-Local Blocks. Results in Table 3 show the effectiveness of our EPIT (having 5 Non-Local Blocks) with higher-order spatial-angular correlation modeling capability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.619, + 0.709 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.84 + ], + "angle": 0, + "content": "In this paper, we propose a Transformer-based network for LF image SR. By modeling the dependencies between each pair of pixels on EPIs, our method can learn the spatial-angular correlation while achieving a global receptive field along the epipolar line. Extensive experimental results demonstrated that our method can not only achieve state-of-the-art SR performance on benchmark datasets, but also perform robust to large disparity variations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgment: This work was supported in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 61921001." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12383" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Martin Alain and Aljosa Smolic. Light field super-resolution via lfbm5d sparse coding. 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IEEE Transactions on Visualization and Computer Graphics, 27(6):3019-3033, 2019." + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.813 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12386" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/0facca26-8b6b-4a15-98c0-1ceb58a77d13_origin.pdf b/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/0facca26-8b6b-4a15-98c0-1ceb58a77d13_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..828ec6e7a3588d5325436cbb1b1ff3bcbee32121 --- /dev/null +++ b/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/0facca26-8b6b-4a15-98c0-1ceb58a77d13_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6fbbe8170bc54b2aa413cc7f674c9f8d89cae1040549f40ea2944ddbf0dca9a4 +size 3420666 diff --git a/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/full.md b/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/full.md new file mode 100644 index 0000000000000000000000000000000000000000..89962d79ab0e82d9be0dd22b2969240d14c97574 --- /dev/null +++ b/2023/Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution/full.md @@ -0,0 +1,414 @@ +# Learning Non-Local Spatial-Angular Correlation for Light Field Image Super-Resolution + +Zhengyu Liang $^{1}$ , Yingqian Wang $^{1}$ , Longguang Wang $^{2}$ , Jungang Yang $^{1\boxtimes}$ , Shilin Zhou $^{1}$ , Yulan Guo $^{1}$ $^{1}$ National University of Defense Technology, $^{2}$ Aviation University of Air Force + +{zyliang, yangjungang}@nudt.edu.cn + +# Abstract + +Exploiting spatial-angular correlation is crucial to light field (LF) image super-resolution (SR), but is highly challenging due to its non-local property caused by the disparities among LF images. Although many deep neural networks (DNNs) have been developed for LF image SR and achieved continuously improved performance, existing methods cannot well leverage the long-range spatial-angular correlation and thus suffer a significant performance drop when handling scenes with large disparity variations. In this paper, we propose a simple yet effective method to learn the non-local spatial-angular correlation for LF image SR. In our method, we adopt the epipolar plane image (EPI) representation to project the 4D spatial-angular correlation onto multiple 2D EPI planes, and then develop a Transformer network with repetitive self-attention operations to learn the spatial-angular correlation by modeling the dependencies between each pair of EPI pixels. Our method can fully incorporate the information from all angular views while achieving a global receptive field along the epipolar line. We conduct extensive experiments with insightful visualizations to validate the effectiveness of our method. Comparative results on five public datasets show that our method not only achieves state-of-the-art SR performance but also performs robust to disparity variations. Code is publicly available at https://github.com/ZhengyuLiang24/EPIT. + +# 1. Introduction + +Light field (LF) cameras record both intensity and directions of light rays, and enable various applications such as depth perception [25, 29, 32], view rendering [3, 52, 66], virtual reality [11, 74], and 3D reconstruction [6, 77]. However, due to the inherent spatial-angular trade-off [82], an LF camera can either provide dense angular samplings with low-resolution (LR) sub-aperture images (SAIs), or capture high-resolution (HR) SAIs with sparse angular sampling. + +![](images/f6c1f302903fe2f90f8d4ec0177c43abc4407b9300a7e552faa8db9fcf0cf4d6.jpg) +Figure 1. Visualization of $4 \times$ SR results and the corresponding attribution maps [18] of our method and four state-of-the-art methods [26, 36, 60, 78] under different manually sheared disparity values. Here, the patch marked by the green box in the HR image is selected as the target region, and the regions that contribute to the final SR results are highlighted in red. Our method can well exploit the non-local spatial-angular correlation and achieve superior SR performance. More examples are provided in Fig. 8. + +To handle this problem, many methods have been proposed to enhance the angular resolution via novel view synthesis [28, 43, 67], or enhance the spatial resolution by performing LF image super-resolution (SR) [10, 20]. In this paper, we focus on the latter task, i.e., generating HR LF images from their LR counterparts. + +Recently, convolutional neural networks (CNNs) have been widely applied to LF image SR and demonstrated superior performance over traditional paradigms [1, 34, 44, 49, 64]. To incorporate the complementary information (i.e., angular information) from different views, existing CNNs adopted various mechanisms such as adjacent-view combination [73], view-stack integration [26, 78, 79], bidirectional recurrent fusion [59], spatial-angular disentanglement [36, 60, 61, 72, 9], and 4D convolutions [42, 43]. However, as illustrated in both Fig. 1 and Sec. 4.3, existing methods achieve promising results on LFs with small baselines, but suffer a notable performance drop when handling scenes with large disparity variations. + +We attribute this performance drop to the contradictions between the local receptive field of CNNs and the requirement of incorporating non-local spatial-angular correlation in LF image SR. That is, LF images provide multiple observations of a scene from a number of regularly distributed viewpoints, and a scene point is projected onto different but correlated spatial locations on different angular views, which is termed as the spatial-angular correlation. Note that, the spatial-angular correlation has the non-local property since the difference between the spatial locations of two views (i.e., disparity value) depends on several factors (e.g., angular coordinates of the selected views, the depth value of the scene point, the baseline length of the LF camera, and the resolution of LF images), and can be very large in some situations. Consequently, it is appealing for LF image SR methods to incorporate complementary information from different views by exploiting the spatial-angular correlation under large disparity variations. + +In this paper, we propose a simple yet effective method to learn the non-local spatial-angular correlation for LF image SR. In our method, we re-organize 4D LFs as multiple 2D epipolar plane images (EPIs) to manifest the spatial-angular correlation to the line patterns with different slopes. Then, we develop a Transformer-based network called EPIT to learn the spatial-angular correlation by modeling the dependencies between each pair of pixels on EPIs. Specifically, we design a basic Transformer block to alternately process horizontal and vertical EPIs, and thus progressively incorporate the complementary information from all angular views. Compared to existing LF image SR methods, our method can achieve a global receptive field along the epipolar line, and thus performs robust to disparity variations. + +In summary, the contributions of this work are as follows: (1) We address the importance of exploiting non-local spatial-angular correlation in LF image SR, and propose a simple yet effective method to handle this problem. (2) We develop a Transformer-based network to learn the non-local spatial-angular correlation from horizontal and vertical EPIs, and validate the effectiveness of our method through extensive experiments and visualizations. (3) Compared to existing state-of-the-art LF image SR methods, our method achieves superior performance on public LF datasets, and is much more robust to disparity variations. + +# 2. Related Work + +# 2.1. LF Image SR + +LFCNN [73] is the first method to adopt CNNs to learn the correspondence among stacked SAIs. Then, it is a common practice for LF image SR networks to aggregate the complementary information from adjacent views to model the correlation in LFs. Yeung et al. [72] designed a spatial-angular separable (SAS) convolution to approximate the 4D + +convolution to characterize the sub-pixel relationship of LF 4D structures. Wang et al. [59] proposed a bidirectional recurrent network to model the spatial correlation among views on horizontal and vertical baselines. Meng et al. [42] proposed a densely-connected network with 4D convolutions to explicitly learn the spatial-angular correlation encoded in 4D LF data. To further learn inherent corresponding relations in SAIs, Zhang et al. [78, 79] grouped LFs into four different branches according to the specific angular directions, and used four sub-networks to model the multi-directional spatial-angular correlation. + +The aforementioned networks use part of input views to super-resolve each view, and the inherent spatial-angular correlation in LF images cannot be well incorporated. To address this issue, Jin et al. [26] proposed an All-to-One framework for LF image SR, and each SAI can be individually super-resolved by combining the information from all views. Wang et al. [61, 60] organized LF images into macro-pixels, and designed a disentangling mechanism to fully incorporate the angular information. Liu et al. [38] introduced 3D convolutions based multi-view context block to exploit the correlations among all views. In addition, Wang et al. [62] adopted deformable convolutions to achieve long-range information exploitation from all SAIs. Existing methods generally learn the local correspondence across SAIs, and ignore the importance of non-local spatial-angular correlation in LF images. However, due to the limited receptive field of CNNs, existing methods generally learn the local correspondence across SAIs, and ignore the importance of non-local spatial-angular correlation in LF images. + +Recently, Liang et al. [36] applied Transformers to LF image SR and developed an angular Transformer and a spatial Transformer to incorporate angular information and model long-range spatial dependencies, respectively. However, since 4D LFs were organized into 2D angular patches to form the input of angular Transformers, the non-local property of spatial-angular correlations reduces the robustness of LFT to large disparity variations. + +# 2.2. Non-Local Correlation Modeling + +Non-local means [5] is a classical algorithm that computes the weighted mean of pixels in an image according to the self-similarity measure, and a number of studies on such non-local priors have been proposed for image restoration [12, 51, 19, 4], image and video SR [16, 76, 14, 71, 23]. Then, the attention mechanism is developed as a tool to bias the most informative components of an input signal, and achieves significant performance in various computer vision tasks [22, 8, 58, 15]. Huang et al. [24] proposed novel criss-cross attention to capture contextual information from full-image dependencies in an efficient way. Wang et al. [56, 55] proposed a parallax attention mechanism to handle + +the varying disparities problem of stereo images. Wu et al. [69] applied attention mechanisms to 3D LF reconstruction and developed a spatial-angular attention module to learn the first-order correlation on EPIs. + +Recently, the attention mechanism is further generalized as Transformers [54] with multi-head structures and feed-forward networks. Transformers have inspired lots of works [39, 35, 7, 13] to further investigate the power of attention mechanisms in visions. Liu et al. [40] presented a pure-Transformer method to incorporate the inherent spatial-temporal locality of videos for action recognition. Naseer et al. [45] investigated the robustness and generalizability of Transformers, and demonstrated favorable merits of Transformers over CNNs for occlusion handling. Shi et al. [50] observed that Transformers can implicitly make accurate connections for misaligned pixels, and presented a new understanding of Transformers to process spatially unaligned images. + +# 3. Method + +# 3.1. Preliminary + +Based on the two-plane LF parameterization model [33], an LF image is commonly formulated as a 4D function $\mathcal{L}(u,v,h,w)\in \mathbb{R}^{U\times V\times H\times W}$ , where $U$ and $V$ represent angular dimensions, $H$ and $W$ represent spatial dimensions. The EPI sample of 4D LF is acquired with a fixed angular coordinate and a fixed spatial coordinate. Specifically, the horizontal EPI is obtained with constant $u$ and $h$ , and the vertical EPI is obtained with constant $v$ and $w$ . + +As shown in Fig. 2, the EPIs not only record spatial structures at edges or textures, but also reflect the disparity information via line patterns of different slopes. Specifically, due to large disparities, the EPIs contain abundant spatial-angular correlation of LFs in a long-range way. Therefore, we propose to explore the non-local spatial-angular correlation from horizontal and vertical EPIs for LF image SR. + +# 3.2. Network Design + +As shown in Fig. 3(a), our network takes an LR LF $\mathcal{L}_{LR} \in \mathbb{R}^{U \times V \times H \times W}$ as its input, and produces an HR LF $\mathcal{L}_{SR} \in \mathbb{R}^{U \times V \times \alpha H \times \alpha W}$ , where $\alpha$ presents the upscaling factor. Our network consists of three stages including initial feature extraction, deep spatial-angular correlation learning, and feature upsampling. + +# 3.2.1 Initial Feature Extraction + +As shown in Fig. 3(b), we follow most existing works [7, 35, 75] to use three $3 \times 3$ convolutions with LeakyReLU [41] as a SpatialConv layer to map each SAI to a high-dimensional feature. The initially extracted feature can be + +![](images/c2330a8e34a9db8434ab60bccdf9b72c9ce997ec7e4fb6c6be4e1034bb31830f.jpg) +Figure 2. The SAI and EPI representations of LF images. The array of $9 \times 9$ views of a scene rosemary from HCInew [21] dataset is used as an example for illustration. + +represented as $\pmb{F} \in \mathbb{R}^{U \times V \times H \times W \times C}$ , where $C$ denotes the channel dimension. + +# 3.2.2 Deep Spatial-Angular Correlation Learning + +Non-Local Cascading Block. The basic module for spatial-angular correlation learning is the Non-Local Cascading block. As shown in Fig. 3(a), each block consists of two cascaded Basic-Transformer units to separately incorporate the complementary information along the horizontal and vertical epipolar lines. In our method, we employed five Non-Local Cascading blocks to achieve a global perception of all angular views, and followed SwinIR [35] to adopt spatial convolutions to enhance the local feature representation. The effectiveness of this inter-block spatial convolution is validated in Sec. 4.4. Note that, the weights of the two Basic-Transformer units in each block are shared to jointly learn the intrinsic properties of LFs, which is demonstrated effective in Sec. 4.4. + +As shown in Fig. 3(c), the initial features $\pmb{F}$ can be first separately reshaped to the horizontal EPI pattern $\pmb{F}_{hor} \in \mathbb{R}^{UH \times V \times W \times C}$ and the vertical EPI pattern $\pmb{F}_{ver} \in \mathbb{R}^{VW \times U \times H \times C}$ . Next, $\pmb{F}_{hor}$ (or $\pmb{F}_{ver}$ ) is fed to a Basic-Transformer unit to integrate the long-range information along the horizontal (or vertical) epipolar line. Then, the enhanced feature $\hat{\pmb{F}}_{hor}$ (or $\hat{\pmb{F}}_{ver}$ ) is reshaped into the size of $UV \times H \times W \times C$ , and passes through a SpatialConv layer to incorporate the spatial context information within each SAI. Without loss of generality, we take the vertical Basic-Transformer as an example to introduce the detail of our Basic-Transformer unit in the following texts. + +Basic-Transformer Unit. The objective of this unit is to capture long-range dependencies along the epipolar line via Transformers. To leverage the powerful sequence modeling capability of Transformers, we convert the vertical EPI features $\pmb{F}_{ver}$ to the sequences of "tokens" for capturing spatial-angular correlation in $U$ and $H$ dimensions. As shown in Fig. 3(d), the vertical EPI features are passed through a linear projection matrix $W_{in} \in \mathbb{R}^{C \times D}$ , where $D$ + +![](images/cfb324391a8e3948033cb56600511a1882e7505787ae19696911c2d10fabf96a.jpg) + +![](images/b1c46a4306ef2c7220e272a3cd00d7bcdf7358a2e18abb2de6f3a777f2acbfe0.jpg) +Figure 3. An overview of our proposed EPIT. Here, a $3 \times 3$ LF is used as an example for illustration. + +![](images/e5be6540e1a8c3fef8a44d91cb59bdd4d8eb248273cf28777e87ae20cc41836e.jpg) + +![](images/db356ecabddb460d353108e05a8b99695e79273b86fa591ea5bfcdb550ef9d5e.jpg) + +denotes the embedding dimension of each token. The projected EPI features are a sequence of tokens with a length of $UH$ , i.e., $T_{ver} \in \mathbb{R}^{UH \times D}$ . Following the PreNorm operation in [70], we also apply Layer Normalization (LN) before the attention calculation, and obtain the normalized tokens $\bar{T}_{ver} = \mathrm{LN}(T_{ver})$ . + +Afterwards, tokens $\bar{T}_{ver}$ are passed through the Self-Attention layer and transformed into the deep tokens involving non-local spatial-angular information along the vertical epipolar line. Specifically, $\bar{T}_{ver}$ need to be separately multiplied by $W_{Q} \in \mathbb{R}^{D \times D}$ , $W_{K} \in \mathbb{R}^{D \times D}$ and $W_{V} \in \mathbb{R}^{D \times D}$ to generate corresponding query, key and value components for self-attention calculation, i.e., $Q_{ver} = \bar{T}_{ver} W_{Q}$ , $K_{ver} = \bar{T}_{ver} W_{K}$ and $V_{ver} = \bar{T}_{ver} W_{V}$ . + +Given a query position $q = \{1,2,\dots ,UH\}$ in $Q_{ver}$ and a key position $k = \{1,2,\dots ,UH\}$ in $K_{ver}$ , the corresponding response $A_{ver}(q,k)\in \mathbb{R}$ measures the mutual similarity of the pairs by the dot-product operation, followed by a Softmax function to obtain the attention scores on the vertical EPI tokens. That is, + +$$ +\boldsymbol {A} _ {\text {v e r}} (q, k) = \operatorname {S o f t m a x} \left(\frac {Q _ {\text {v e r}} (q) \cdot K _ {\text {v e r}} (k) ^ {\mathrm {T}}}{\sqrt {D}}\right). \tag {1} +$$ + +Based on the attention scores, the output of self-attention $T_{ver}^{\prime}$ can be calculated as the weighted sum of value. In summary, the calculation process of Self-Attention layer can be formulated as: + +$$ +\boldsymbol {T} _ {\text {v e r}} ^ {\prime} = \boldsymbol {A} _ {\text {v e r}} V _ {\text {v e r}} + T _ {\text {v e r}}. \tag {2} +$$ + +To further incorporate the spatial-angular correlation, + +![](images/491140b5a9b121668113d9bd8c36d28ca6fe2c391c4149348e43d3a851d6bb1b.jpg) +(a) + +![](images/840d93bdcb727dd6e47a79be57419b586313a4a5219769381ded800179d0451d.jpg) +(b) + +![](images/97d95d74cc11fdfa5c7d7aad13f58bd85380b9acbc37b9f46d1f9419311e229e.jpg) +(c) + +![](images/97fe13740bb81b5003a0ad9229bbad0cd468461168e3e6006aa93a5f46555626.jpg) +(d) + +![](images/34a93aa2968e8d822fe7df0bf38b41a2a3a10d33d06dde1028b3865753cb21b1.jpg) +(e) + +![](images/6746f92dd73948d0806556b6b6b5d18dfedf4d9150b9a1f745361270bd50618c.jpg) +(f) + +![](images/39417c9fc00f538fd69b435da0b73b11210f178938dd6bcff36e07f4502000e2.jpg) +(g) + +![](images/f5f5520f3696847ef422d34ccb962dabc8c3b274393527070183454737ed1a72.jpg) +(h) +Figure 4. An example of the attention maps of a Basic-Transformer unit for the spatial-angular correlation. Note that, the attention maps correspond to the correlation between the regions marked by the red and yellow strokes. + +![](images/4eb5c7164fb22cba02addc206a73e63f34c26015f7b2e165bde3f7633c46f658.jpg) +(i) + +![](images/3cc2fd20bba6c037347a73431ae1e636bea25adc3d7e03352d1f045e2840968c.jpg) +(1) + +following [54], our Basic-Transformer unit also contains the multi-layer perception (MLP) and LN, and generates the enhanced $\hat{T}_{ver}$ as: + +$$ +\hat {\boldsymbol {T}} _ {v e r} = \operatorname {M L P} \left(\operatorname {L N} \left(\boldsymbol {T} _ {v e r} ^ {\prime}\right)\right) + \boldsymbol {T} _ {v e r} ^ {\prime}. \tag {3} +$$ + +At the end of the Basic-Transformer unit, the enhanced $\hat{T}_{ver}$ is fed to another linear projection $W_{out} \in \mathbb{R}^{D \times C}$ , and reshaped into the size of $UV \times H \times W \times C$ for the subsequent SpatialConv layer. + +Cross-View Similarity Analysis. Note that, the setting $[A_{ver}(q,1),\dots,A_{ver}(q,UH)]\in \mathbb{R}^{1\times UH}$ represents the similarity scores of $q$ with all $k$ in $K_{ver}$ , and thus can be re-organized as a slice of cross-view attention map according to the angular coordinate. Inspired by this, we visualized the cross-view attention maps on an example scene in Fig. 4. The regions marked by the red stripe in Fig. 4(a) are set as the query tokens, and the self-similarity (i.e., + +Table 1. Quantitative comparison of different SR methods in terms of the number of parameters (#Prm.) and PSNR/SSIM. Larger PSNR and SSIM values indicate higher SR quality. We mark the best results in red and the second best results in blue. + +
Methods#Prm.(M)2×/4×2×4×
EPFLHCInewHCIoldINRIASTFgantryEPFLHCInewHCIoldINRIASTFgantry
Bicubic- / -29.74/.937631.89/.935637.69/.978531.33/.957731.06/.949825.14/.832427.61/.851732.42/.934426.82/.886725.93/.8452
VDSR [30]0.66 / 0.6632.50/.959834.37/.956140.61/.986734.43/.974135.54/.978927.25/.877729.31/.882334.81/.951529.19/.920428.51/.9009
EDSR [37]38.6 / 38.933.09/.962934.83/.959241.01/.987434.97/.976436.29/.981827.84/.885429.60/.886935.18/.953629.66/.925728.70/.9072
RCAN [81]15.3 / 15.433.16/.963434.98/.960341.05/.987535.01/.976936.33/.983127.88/.886329.63/.888635.20/.954829.76/.927628.90/.9131
resLF[79]7.98 / 8.6433.62/.970636.69/.973943.42/.993235.39/.980438.36/.990428.27/.903530.73/.910736.71/.968230.34/.941230.19/.9372
LFSSR [72]0.88 / 1.7733.68/.974436.81/.974943.81/.993835.28/.983237.95/.989828.27/.911830.72/.914536.70/.969630.31/.946730.15/.9426
LF-ATO [26]1.22 / 1.3634.27/.975737.24/.976744.20/.994236.15/.984239.64/.992928.52/.911530.88/.913537.00/.969930.71/.948430.61/.9430
LF-InterNet [61]5.04 / 5.4834.14/.976037.28/.976344.45/.994635.80/.984338.72/.990928.67/.916230.98/.916137.11/.971630.64/.949130.53/.9409
LF-DFnet [62]3.94 / 3.9934.44/.975537.44/.977344.23/.994136.36/.984039.61/.992628.77/.916531.23/.919637.32/.971830.83/.950331.15/.9494
MEG-Net [78]1.69 / 1.7734.30/.977337.42/.977744.08/.994236.09/.984938.77/.991528.74/.916031.10/.917737.28/.971630.66/.949030.77/.9453
LF-IINet [38]4.84 / 4.8834.68/.977337.74/.979044.84/.994836.57/.985339.86/.993629.11/.918831.36/.920837.62/.973431.08/.951531.21/.9502
DPT [57]3.73 / 3.7834.48/.975837.35/.977144.31/.994336.40/.984339.52/.992628.93/.917031.19/.918837.39/.972130.96/.950331.14/.9488
LFT [36]1.11 / 1.1634.80/.978137.84/.979144.52/.994536.59/.985540.51/.994129.25/.921031.46/.921837.63/.973531.20/.952431.86/.9548
DistgSSR [60]3.53 / 3.5834.81/.978737.96/.979644.94/.994936.59/.985940.40/.994228.99/.919531.38/.921737.56/.973230.99/.951931.65/.9535
LFSAV [9]1.22 / 1.5434.62/.977237.43/.977644.22/.994236.36/.984938.69/.991429.37/.922331.45/.921737.50/.972131.27/.953131.36/.9505
EPIT (ours)1.42 / 1.4734.83/.977538.23/.981045.08/.994936.67/.985342.17/.995729.34/.919731.51/.923137.68/.973731.37/.952632.18/.9571
+ +key are same as query) is ideally located at the diagonal, as shown in Fig. 4(f). In contrast, the yellow stripes in Figs. 4(b)-4(e) are set as the key tokens, the corresponding cross-view similarities are shown in Figs. 4(g)-4(j). It can be observed that due to the foreground occlusions, the responses of the background appear as short lines (marked by the white boxes) parallel to the diagonal in each cross-view attention map, and both of the distance to the diagonal and the length of response regions adaptively change as the key view moves along the baseline, which demonstrates the disparity-awareness of our Basic-Transformer unit. + +# 3.2.3 Feature Upsampling + +Finally, we apply the pixel shuffling operation to increase the spatial resolution of LF features, and further employ a $3 \times 3$ convolution to obtain the super-resolved LF image $\mathcal{L}_{SR}$ . Following most existing works [61, 60, 36, 62, 57, 38, 78, 79, 72], we use the $L_{1}$ loss function to train our network due to its robustness to outliers [2]. + +# 4. Experiments + +In this section, we first introduce the datasets and our implementation details, and then compare our method with state-of-the-art methods. Next, we investigate the performance of different SR methods with respect to disparity variations. Finally, we validate the effectiveness of our method through ablation studies. + +# 4.1. Datasets and Implementation Details + +We followed [62, 60, 38, 57, 36] to use five public LF datasets (EPFL [48], HCInew [21], HCld [65], INRIA [46], STFgantry [53]) in the experiments. All LFs in these datasets have an angular resolution of $9 \times 9$ . Unless specifically mentioned, we extracted the central $5 \times 5$ SAIs for + +training and test. In the training stage, we cropped each SAI into patches of size $64 \times 64 / 128 \times 128$ , and performed $0.5 \times / 0.25 \times$ bicubic downsampling to generate the LR patches for $2 \times / 4 \times$ SR, respectively. We used peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [63] as quantitative metrics for performance evaluation. To obtain the metric score for a dataset with $M$ scenes, we first calculated the metric of each scene by averaging the scores over all the SAIs separately, and then obtained the score for this dataset by averaging the scores over the $M$ scenes. + +We adopted the same training settings for all experiments, i.e., Xavier initialization algorithm [17] and Adam optimizer [31] with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ . The initial learning rate was set to $2\times 10^{-4}$ and decreased by a factor of 0.5 every 15 epochs. During the training phase, we performed random horizontal flipping, vertical flipping, and 90-degree rotation to augment the training data. All models were implemented in the PyTorch framework and trained from scratch for 80 epochs with 2 Nvidia RTX 2080Ti GPUs. + +# 4.2. Comparisons on Benchmark Datasets + +We compare our method to 14 state-of-the-art methods, including 3 single image SR methods [30, 37, 81] and 11 LF image SR methods [79, 72, 26, 61, 62, 78, 38, 57, 36, 60, 9]. Quantitative Results. A quantitative comparison among different methods is shown in Tabel 1. Our EPIT with a small model size (i.e., $1.42\mathrm{M} / 1.47\mathrm{M}$ for $2\times /4\times$ SR) achieves state-of-the-art PSNR and SSIM scores on almost all the datasets for both $2\times$ and $4\times$ SR. It is worth noting that LFs in the STFgantry dataset [53] have larger disparity variations, and are thus more challenging. Our EPIT significantly outperforms all the compared methods and achieves $1.66\mathrm{dB} / 0.32\mathrm{dB}$ PSNR improvements over the second top-performing method LFT for $2\times /4\times$ SR, respectively, which demonstrates the powerful capacity of our EPIT in non-local correlation modeling. + +![](images/16b959155a1ab58c76e87cb5cdb3c72226c7b76f90388f03ec6cefbb09819eee.jpg) + +![](images/a5e06d02973bec01fe0c9215108935b24a4a0c9bac8e002c9ed73ddaeb19dcba.jpg) + +![](images/f0cd8e9f9cfbb93fe6fc9c608bf38000e15cfd3e6dcb3e760077be2113fa706f.jpg) + +![](images/15c025db3ad3a3ec09165c4e06c058ee6e1e09445fd8029563301d5b60509840.jpg) + +![](images/a417eef488850bde9fa1104e600a83b267cfaec1387e781ae63828ea9e593ea4.jpg) + +![](images/13dac46c9a8ae265fa270644671f1b7ab3ecc6a4c625d17a5db689c5ed25c851.jpg) + +![](images/06ab58db794531705698b8ffd845fc15569cd3b07e2dd8f06b656e1f81a252a3.jpg) + +![](images/b0b7dd4de3d193f7b69d553da9d64c4fd4cf05398616128cc1c7a0b726cb94af.jpg) + +![](images/a3263b28349a13ef0362d75666b6bd1f1dad1b47f19ea324afad3398684c031c.jpg) + +![](images/4e83faabed2a7d38f6aa75a6e2673375e884f2190c239a6f89650d6ae666d065.jpg) +Figure 5. Qualitative comparison of different SR methods for $2 \times /4 \times$ SR. + +![](images/c37d8303b5a0c745d5550d5a0a926728387d0c29147e76969f484087e2203a43.jpg) + +![](images/1ac5438202677123a71c187dfcbd20c4ec3c26ef474c9afdeafa8802b9b07915.jpg) + +![](images/ce0ae720d7118bc378241205a37c717d15dbf7eb697798ab7c7cd374ce5ba5e7.jpg) + +![](images/aa5d9c532685314237c373a5aa350eae7ddcd54ddce8cedaa7c1fd00f5270310.jpg) + +![](images/6d079fa3e8a4c3c07414bfb2afaecb382c86d96b517e888473cf153a220048a9.jpg) + +![](images/930fb69f12b3e989617d946a9dff0001a320840d2add0d62c57581b0976185a6.jpg) + +![](images/a880b7111150763883d0583af329c14d4259636b59c0914e0d5a0f74beb670bb.jpg) +Figure 6. Quantitative and qualitative (MSE) comparisons of disparity estimation results achieved by SPO [80] using different SR results. The MSE $(\downarrow)$ is the mean square error multiplied by 100. + +Table 2. PSNR values achieved by DistgSSR [60] and our EPIT with different angular resolution for $4 \times$ SR. + +
InputEPFLHCInewHCIoldINRIASTFgantry
[60]Ours[60]Ours[60]Ours[60]Ours[60]Ours
2×228.27-0.0530.80+0.0436.77+0.1730.55-0.0330.74+0.56
3×328.67+0.0331.07+0.1937.18+0.1930.83+0.1131.12+0.74
4×428.81+0.2331.25+0.1537.32+0.2030.93+0.2631.23+0.88
5×528.99+0.3531.38+0.1337.56+0.1230.99+0.3831.65+0.56
6×629.10+0.3331.39+0.1837.52+0.2630.98+0.4731.57+0.74
7×729.38+0.2231.43+0.2037.65+0.2731.18+0.3331.63+0.77
8×829.32+0.2831.52+0.1437.76+0.2431.23+0.3131.58+0.90
9×929.41+0.3031.48+0.2137.80+0.2631.22+0.3431.66+0.84
+ +Qualitative Results. Figure 5 shows the qualitative results achieved by different methods for $2 \times 4 \times$ SR. It can be observed from the zoom-in regions that single image SR method RCAN [81] cannot recover the textures and details in the SR images. In contrast, our EPIT can incorporate sub-pixel correspondence among SAIs and generate more faithful details with fewer artifacts. Compared to most LF image SR methods, our EPIT can generate superior visual results with high angular consistency. Please refer to the supplemental material for additional visual comparisons. + +Angular Consistency. We evaluate the angular consistency by using the $4 \times \mathrm{SR}$ results on several challenging scenes + +![](images/19dcd839e89b73a4111d22e628c99496b0fbcac6bb22650ca8ae5684fe6c6cdd.jpg) +Figure 7. Visual comparison of different SR methods on real-world LF scenes for $4 \times \mathrm{SR}$ . + +![](images/422548882194c104513f9c6fc20819c52ef67260b32af7299c07faa68d7b8f6d.jpg) + +![](images/b60de61e9b8be4227c1d61ceb277be90c8b750d1a0bdb47aa5476ef1ad391e23.jpg) + +![](images/473d2af88e9769003881e07d8a64c32c6e6ba9e13b8f7f18b14dd48ba5c0289e.jpg) + +(e.g., Backgammon and Stripes) in 4D LF benchmark [21] for disparity estimation. As shown in Fig. 6, our EPIT achieves competitive MSE scores on these challenging scenes, which demonstrates the superiority of our EPIT on angular consistency. + +Performance with Different Angular Resolution. Since the angular resolution of LR images can vary significantly with different LF devices, we compare our method to DistgSSR [60] on LFs with different angular resolutions. It can be observed from Table 2 that our method achieves higher PSNR values than DistgSSR on almost all the datasets with each angular resolution (except on the EPFL and INRIA datasets with $2 \times 2$ input LFs). The consistent performance improvements demonstrate that our EPIT can well model the spatial-angular correlation with various angular resolutions. More comparisons and discussions are provided in the supplemental material. + +![](images/55bad091186292a5713bb04293b5f738ed45e12ea0ce56a387aaf599cdea7673.jpg) + +![](images/0da3b149f6ce9f2b83042d25842c1197be960d94d59677a13fea944bb12e085b.jpg) + +![](images/45f45cd61001aa984e0b9d92de0488ee874df06e48e1e6d6cdf24b3495261ca9.jpg) + +![](images/35b1d7c4304b76b9449add29ef1bee797e6976353914719de5fba514cac6d1f4.jpg) + +![](images/b2787ba1d63f380962f5ac86edf57d9bd5ec94dbe2e114deec7e9e68b92ecfc5.jpg) + +![](images/1b7a3e3c0cf583c8742ee0113f707b4ae4928bc8decaceda6cef21d70e739693.jpg) + +![](images/31048687b06e352e125a26004b80e245dab052afc5c1ea10e3586701461335a5.jpg) + +![](images/f0479409d42fb38ff879b033d2c2dd4d5ff119f7e23553e2f8dde03154f036f8.jpg) + +![](images/20aa3a5548ad5073f05a8b5c7fed9c3f6cfaa9c49dc6f4ea4bad38fbcd875e17.jpg) + +![](images/26719c9a640722cf36284d89ce6591db5463ca0ae5eeb64deb69fa56d3b1aac5.jpg) +Figure 8. Performance comparison and local attribution maps of different SR methods on two representative scenes with different shearing values for $2 \times \mathrm{SR}$ . Here, we plot the performance curve to quantitatively measure the effect of disparity variations on LFs, and present the visual results and corresponding attribution maps under sheared value=2, 4. + +![](images/35d84871eba78764c0862220cd9bf06a7cc56bb5c35ae323534a9196fc268573.jpg) + +![](images/36fdcfe0909a477456dd6080de0f326d0f2401b74bbb0cd5ee6991e31b3dc9fe.jpg) +(c) + +![](images/83e2221872c024ab0bcd5e4ead593320ac6f7ff42f5849c36af12061eec0d46e.jpg) + +![](images/b9b53888dfec74ff3a9ec2d4041391e0e81f7778962f0170d5318c0f58e23e89.jpg) + +![](images/5036e329a905709ca02dbfc75e283e2180356e575e0b5183d72df4391e3adc6c.jpg) + +![](images/e2a6eb41e56846296a528e89e55b5b00e8cae9040eacbd1f23819745d81735ca.jpg) + +![](images/252bfc277698ff93ecc565f85a4cb050b838069f39483a154dfbc13b2f111d3e.jpg) + +![](images/53f32bb0f635a1008a6d362a75c7faf951f672ed7d65aa3ae5d8f428f4a4b983.jpg) + +![](images/65f29c4731474e83d8ff14430f48e59dd858d983a0c7016c2903a29ca16a0a83.jpg) + +![](images/75d27ae48b87d2bca04f9d2c3c05570e88e66fd73339a94b6d95389a83df8c73.jpg) + +![](images/b5f6a578fdc658e445e0dcc9427c19b316313fadfe0af169b24396f21db1e94b.jpg) + +![](images/ad010207f8b4a1eac109bdc3a97dffe058fe8b2501b09d4c5c860973bdf07932.jpg) +(f) + +![](images/e06b00193af84669e410f14426f066afedf149751e6dc0db5a6129fd79146952.jpg) + +![](images/021d697d7dbb8c69d71e48c4b3cf582e16380fe1100db7436cb1d940cc02a2d3.jpg) + +Performance on Real-World LF Scenes. We compare our method to state-of-the-art methods under real-world degradation by directly applying them to LFs in the STFlytro dataset [47]. Since no groundtruth HR images are available in this dataset, we present the LR input and their super-resolved results in Fig. 7. It can be observed that our method can recover more faithful details and generate more clear letters than other methods. Since the LF structure keeps unchanged under both bicubic and real-world degradation, our method can learn the spatial-angular correlation from bicubicly downsampled training data, and well generalize to LF images under real degradation. + +# 4.3. Robustness to Large Disparity Variations + +Considering the parallax structure of LF images, we followed the shearing operation in existing works [67, 68] to linearly change the overall disparity range of LF datasets. Note that, the content of SAIs maintain unchanged after the shearing operation, and thus we can quantitatively investigate the performance of different SR methods with respect to the disparity variations. + +Quantitative & Qualitative Comparison. Figure 8 shows the quantitative and qualitative results of different SR methods with respect to sheared values, from which we can observe that: 1) Except for the single image SR method RCAN, all LF image SR methods suffer a performance drop + +when the absolute sheared value of LF images increases. That is because, large sheared values can result in more significant misalignment among LF images, and introduce difficulties in complementary information incorporation; 2) As the absolute sheared value increases, the performance of existing LF image SR methods is even inferior to RCAN. The possible reason is that, these methods do not make full use of local spatial information, but rather rely on local angular information from adjacent views. When the sheared value exceeds their receptive fields, the large disparities can make the spatial-angular correlation non-local and thus introduce challenges in complementary information incorporation; 3) Our EPIT performs much more robust to disparity variations and achieves the highest PSNR scores under all sheared values. More quantitative comparisons on the whole datasets can be referred to the supplemental material. + +LAM Visualization. We used Local Attribution Map (LAM) [18] to visualize the input regions that contribute to the SR results of different methods. As shown in Fig. 8, we first specify the center of green stripes in HR images as the target regions, and then re-organize the corresponding attribution maps on LR images into the EPI patterns. It can be observed that RCAN achieves a larger receptive field along the spatial dimension than other compared methods, which supports the results in Figs. 8(b) and 8(e) that RCAN achieves a relatively stable SR performance with different + +![](images/16ddaee3aa785a8a15bfedb26f9cd5ce15c6688a58c07706b414d36148199536.jpg) +Figure 9. PSNR distribution among different SAIs achieved by MEG-Net [78], LFT [36], and our EPIT on the INRIA dataset [46] for $2 \times \mathrm{SR}$ . + +sheared values. It is worth noting that our EPIT can automatically incorporate the most relevant information from different views, and can learn the non-local spatial-angular correlation regardless of disparity variations. + +Perspective Comparison. We compare the performance of MEG-Net, DistgSSR and our method with respect to different perspectives and sheared values (0 to 3). It can be observed in Fig. 9 that, both MEG-Net and DistgSSR suffer significant performance drops on all perspectives as the sheared value increases. In contrast, our EPIT can well handle the disparity variation problem, and achieve much higher PSNR values with a balanced distribution among different views regardless of the sheared values. + +# 4.4. Ablation Study + +In this subsection, we compare the performance of our EPIT with different variants to verify the effectiveness of our design choices, and additionally, investigate their robustness to large disparity variations. + +Horizontal/Vertical Basic-Transformer Units. We demonstrated the effectiveness of the horizontal and vertical Basic-Transformer units in our EPIT by separately removing them from our network. Note that, without using horizontal or vertical Basic-Transformer unit, these variants cannot incorporate any information from the corresponding angular directions. As shown in Table 3, both variants w/o-Horizontal and w/o-Vertical suffer a decrease of $0.72\mathrm{dB}$ in the INRIA dataset as compared to EPIT, which demonstrates the importance of exploiting spatial-angular correlations from all angular views. + +Weight Sharing in Non-Local Cascading Blocks. We introduced the variant $w/o$ -Share by removing the weight sharing between horizontal and vertical Basic-Transformer units. As shown in Table 3, the additional parameters in variant $w/o$ -Share do not introduce further performance im + +Table 3. The PSNR scores achieved by different variants of our EPIT on the LFs with different shearing values for $2 \times \mathrm{SR}$ . We adjusted the channel number of each variant to make its model size (i.e., #Prm.) not smaller than EPIT for better validation. + +
Variants#Prm.FLOPsEPFL (Sheared)INRIA (Sheared)
024024
w/o-Horiz1.42M80.20G33.9633.9834.0235.9536.0836.11
w/o-Verti1.42M80.20G34.0133.9433.8735.9535.9736.02
w/o-Share2.71M80.20G34.8034.6334.5136.6636.7236.45
w/o-Local1.64M96.39G34.4234.3634.2736.3636.4036.25
w/o-Trans1.60M78.82G33.9031.3231.7435.9533.2833.55
w-1-Block1.54M68.23G33.9734.2434.0835.8436.1935.93
w-2-Block1.45M73.37G34.1934.3634.2935.9836.2735.99
w-3-Block1.71M85.78G34.6434.5134.4536.5336.4736.22
EPIT1.42M74.96G34.8334.6934.5936.6736.7536.59
+ +provement. It demonstrates that the weight sharing strategy between two directional Basic-Transformer units is beneficial and efficient to regularize the network. + +SpatialConv in Non-Local Cascading Blocks. We introduced the variant w/o-Local by removing the SpatialConv layers from our EPIT, and we adjusted the channel number to make the model size of this variant not smaller than the main model. As shown in Table 3, the SpatialConv has a significant influence on the SR performance, e.g., the variant w/o-Local suffers a 0.41dB PSNR drop on the EPFL dataset. It demonstrates that local context information is crucial to the SR performance, and the simple convolutions can fully incorporate the spatial information from each SAI. + +Basic-Transformer in Non-Local Cascading Blocks. We introduced the variant $w/o$ -Trans by replacing Basic-Transformer in Non-Local Blocks with cascaded convolutions. As shown in Table 3, $w/o$ -Trans suffers a most significant performance drop as the sheared value increases, which demonstrates the effectiveness of the Basic-Transformer in incorporating global information on the EPIs. + +Basic-Transformer Number. We introduced the variants with-n-Block $(n = 1,2,3)$ by retaining $n$ Non-Local Blocks. Results in Table 3 show the effectiveness of our EPIT (having 5 Non-Local Blocks) with higher-order spatial-angular correlation modeling capability. + +# 5. Conclusion + +In this paper, we propose a Transformer-based network for LF image SR. By modeling the dependencies between each pair of pixels on EPIs, our method can learn the spatial-angular correlation while achieving a global receptive field along the epipolar line. Extensive experimental results demonstrated that our method can not only achieve state-of-the-art SR performance on benchmark datasets, but also perform robust to large disparity variations. + +Acknowledgment: This work was supported in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 61921001. + +# References + +[1] Martin Alain and Aljosa Smolic. Light field super-resolution via lfbm5d sparse coding. In 2018 25th IEEE international conference on image processing (ICIP), pages 2501-2505, 2018. +[2] Yildiray Anagun, Sahin Isik, and Erol Seke. Srlibrary: comparing different loss functions for super-resolution over various convolutional architectures. Journal of Visual Communication and Image Representation, 61:178-187, 2019. +[3] Benjamin Attal, Jia-Bin Huang, Michael Zollhöfer, Johannes Kopf, and Changil Kim. Learning neural light fields with ray-space embedding. 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Although many deep neural networks (DNNs) have been developed for LF image SR and achieved continuously improved performance, existing methods cannot well leverage the long-range spatial-angular correlation and thus suffer a significant performance drop when handling scenes with large disparity variations. In this paper, we propose a simple yet effective method to learn the non-local spatial-angular correlation for LF image SR. In our method, we adopt the epipolar plane image (EPI) representation to project the 4D spatial-angular correlation onto multiple 2D EPI planes, and then develop a Transformer network with repetitive self-attention operations to learn the spatial-angular correlation by modeling the dependencies between each pair of EPI pixels. Our method can fully incorporate the information from all angular views while achieving a global receptive field along the epipolar line. We conduct extensive experiments with insightful visualizations to validate the effectiveness of our method. Comparative results on five public datasets show that our method not only achieves state-of-the-art SR performance but also performs robust to disparity variations. Code is publicly available at https://github.com/ZhengyuLiang24/EPIT." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "Light field (LF) cameras record both intensity and directions of light rays, and enable various applications such as depth perception [25, 29, 32], view rendering [3, 52, 66], virtual reality [11, 74], and 3D reconstruction [6, 77]. However, due to the inherent spatial-angular trade-off [82], an LF camera can either provide dense angular samplings with low-resolution (LR) sub-aperture images (SAIs), or capture high-resolution (HR) SAIs with sparse angular sampling." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 230, + 547, + 384 + ], + "blocks": [ + { + "bbox": [ + 307, + 230, + 547, + 384 + ], + "lines": [ + { + "bbox": [ + 307, + 230, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 307, + 230, + 547, + 384 + ], + "type": "image", + "image_path": "f6c1f302903fe2f90f8d4ec0177c43abc4407b9300a7e552faa8db9fcf0cf4d6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 387, + 547, + 475 + ], + "lines": [ + { + "bbox": [ + 305, + 387, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 387, + 547, + 475 + ], + "type": "text", + "content": "Figure 1. Visualization of " + }, + { + "bbox": [ + 305, + 387, + 547, + 475 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 305, + 387, + 547, + 475 + ], + "type": "text", + "content": " SR results and the corresponding attribution maps [18] of our method and four state-of-the-art methods [26, 36, 60, 78] under different manually sheared disparity values. Here, the patch marked by the green box in the HR image is selected as the target region, and the regions that contribute to the final SR results are highlighted in red. Our method can well exploit the non-local spatial-angular correlation and achieve superior SR performance. More examples are provided in Fig. 8." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 547, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 557 + ], + "type": "text", + "content": "To handle this problem, many methods have been proposed to enhance the angular resolution via novel view synthesis [28, 43, 67], or enhance the spatial resolution by performing LF image super-resolution (SR) [10, 20]. In this paper, we focus on the latter task, i.e., generating HR LF images from their LR counterparts." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": "Recently, convolutional neural networks (CNNs) have been widely applied to LF image SR and demonstrated superior performance over traditional paradigms [1, 34, 44, 49, 64]. To incorporate the complementary information (i.e., angular information) from different views, existing CNNs adopted various mechanisms such as adjacent-view combination [73], view-stack integration [26, 78, 79], bidirectional recurrent fusion [59], spatial-angular disentanglement [36, 60, 61, 72, 9], and 4D convolutions [42, 43]. However, as illustrated in both Fig. 1 and Sec. 4.3, existing methods achieve promising results on LFs with small baselines, but suffer a notable performance drop when handling scenes with large disparity variations." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12376" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "type": "text", + "content": "We attribute this performance drop to the contradictions between the local receptive field of CNNs and the requirement of incorporating non-local spatial-angular correlation in LF image SR. That is, LF images provide multiple observations of a scene from a number of regularly distributed viewpoints, and a scene point is projected onto different but correlated spatial locations on different angular views, which is termed as the spatial-angular correlation. Note that, the spatial-angular correlation has the non-local property since the difference between the spatial locations of two views (i.e., disparity value) depends on several factors (e.g., angular coordinates of the selected views, the depth value of the scene point, the baseline length of the LF camera, and the resolution of LF images), and can be very large in some situations. Consequently, it is appealing for LF image SR methods to incorporate complementary information from different views by exploiting the spatial-angular correlation under large disparity variations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 456 + ], + "type": "text", + "content": "In this paper, we propose a simple yet effective method to learn the non-local spatial-angular correlation for LF image SR. In our method, we re-organize 4D LFs as multiple 2D epipolar plane images (EPIs) to manifest the spatial-angular correlation to the line patterns with different slopes. Then, we develop a Transformer-based network called EPIT to learn the spatial-angular correlation by modeling the dependencies between each pair of pixels on EPIs. Specifically, we design a basic Transformer block to alternately process horizontal and vertical EPIs, and thus progressively incorporate the complementary information from all angular views. Compared to existing LF image SR methods, our method can achieve a global receptive field along the epipolar line, and thus performs robust to disparity variations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 456, + 289, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 289, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 289, + 590 + ], + "type": "text", + "content": "In summary, the contributions of this work are as follows: (1) We address the importance of exploiting non-local spatial-angular correlation in LF image SR, and propose a simple yet effective method to handle this problem. (2) We develop a Transformer-based network to learn the non-local spatial-angular correlation from horizontal and vertical EPIs, and validate the effectiveness of our method through extensive experiments and visualizations. (3) Compared to existing state-of-the-art LF image SR methods, our method achieves superior performance on public LF datasets, and is much more robust to disparity variations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 601, + 134, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 134, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 134, + 615 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 622, + 133, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 133, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 133, + 635 + ], + "type": "text", + "content": "2.1. LF Image SR" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "LFCNN [73] is the first method to adopt CNNs to learn the correspondence among stacked SAIs. Then, it is a common practice for LF image SR networks to aggregate the complementary information from adjacent views to model the correlation in LFs. Yeung et al. [72] designed a spatial-angular separable (SAS) convolution to approximate the 4D" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": "convolution to characterize the sub-pixel relationship of LF 4D structures. Wang et al. [59] proposed a bidirectional recurrent network to model the spatial correlation among views on horizontal and vertical baselines. Meng et al. [42] proposed a densely-connected network with 4D convolutions to explicitly learn the spatial-angular correlation encoded in 4D LF data. To further learn inherent corresponding relations in SAIs, Zhang et al. [78, 79] grouped LFs into four different branches according to the specific angular directions, and used four sub-networks to model the multi-directional spatial-angular correlation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 205, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 443 + ], + "type": "text", + "content": "The aforementioned networks use part of input views to super-resolve each view, and the inherent spatial-angular correlation in LF images cannot be well incorporated. To address this issue, Jin et al. [26] proposed an All-to-One framework for LF image SR, and each SAI can be individually super-resolved by combining the information from all views. Wang et al. [61, 60] organized LF images into macro-pixels, and designed a disentangling mechanism to fully incorporate the angular information. Liu et al. [38] introduced 3D convolutions based multi-view context block to exploit the correlations among all views. In addition, Wang et al. [62] adopted deformable convolutions to achieve long-range information exploitation from all SAIs. Existing methods generally learn the local correspondence across SAIs, and ignore the importance of non-local spatial-angular correlation in LF images. However, due to the limited receptive field of CNNs, existing methods generally learn the local correspondence across SAIs, and ignore the importance of non-local spatial-angular correlation in LF images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 445, + 547, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 541 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 541 + ], + "type": "text", + "content": "Recently, Liang et al. [36] applied Transformers to LF image SR and developed an angular Transformer and a spatial Transformer to incorporate angular information and model long-range spatial dependencies, respectively. However, since 4D LFs were organized into 2D angular patches to form the input of angular Transformers, the non-local property of spatial-angular correlations reduces the robustness of LFT to large disparity variations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 551, + 484, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 484, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 484, + 563 + ], + "type": "text", + "content": "2.2. Non-Local Correlation Modeling" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Non-local means [5] is a classical algorithm that computes the weighted mean of pixels in an image according to the self-similarity measure, and a number of studies on such non-local priors have been proposed for image restoration [12, 51, 19, 4], image and video SR [16, 76, 14, 71, 23]. Then, the attention mechanism is developed as a tool to bias the most informative components of an input signal, and achieves significant performance in various computer vision tasks [22, 8, 58, 15]. Huang et al. [24] proposed novel criss-cross attention to capture contextual information from full-image dependencies in an efficient way. Wang et al. [56, 55] proposed a parallax attention mechanism to handle" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12377" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 119 + ], + "type": "text", + "content": "the varying disparities problem of stereo images. Wu et al. [69] applied attention mechanisms to 3D LF reconstruction and developed a spatial-angular attention module to learn the first-order correlation on EPIs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 288, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 288, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 288, + 288 + ], + "type": "text", + "content": "Recently, the attention mechanism is further generalized as Transformers [54] with multi-head structures and feed-forward networks. Transformers have inspired lots of works [39, 35, 7, 13] to further investigate the power of attention mechanisms in visions. Liu et al. [40] presented a pure-Transformer method to incorporate the inherent spatial-temporal locality of videos for action recognition. Naseer et al. [45] investigated the robustness and generalizability of Transformers, and demonstrated favorable merits of Transformers over CNNs for occlusion handling. Shi et al. [50] observed that Transformers can implicitly make accurate connections for misaligned pixels, and presented a new understanding of Transformers to process spatially unaligned images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 300, + 102, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 102, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 102, + 312 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 319, + 126, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 126, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 126, + 333 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": "Based on the two-plane LF parameterization model [33], an LF image is commonly formulated as a 4D function " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(u,v,h,w)\\in \\mathbb{R}^{U\\times V\\times H\\times W}" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": " represent angular dimensions, " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": " represent spatial dimensions. The EPI sample of 4D LF is acquired with a fixed angular coordinate and a fixed spatial coordinate. Specifically, the horizontal EPI is obtained with constant " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": ", and the vertical EPI is obtained with constant " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 338, + 287, + 433 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 434, + 287, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 531 + ], + "type": "text", + "content": "As shown in Fig. 2, the EPIs not only record spatial structures at edges or textures, but also reflect the disparity information via line patterns of different slopes. Specifically, due to large disparities, the EPIs contain abundant spatial-angular correlation of LFs in a long-range way. Therefore, we propose to explore the non-local spatial-angular correlation from horizontal and vertical EPIs for LF image SR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 539, + 145, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 145, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 145, + 552 + ], + "type": "text", + "content": "3.2. Network Design" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "content": "As shown in Fig. 3(a), our network takes an LR LF " + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{LR} \\in \\mathbb{R}^{U \\times V \\times H \\times W}" + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "content": " as its input, and produces an HR LF " + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SR} \\in \\mathbb{R}^{U \\times V \\times \\alpha H \\times \\alpha W}" + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "content": " presents the upscaling factor. Our network consists of three stages including initial feature extraction, deep spatial-angular correlation learning, and feature upsampling." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 646, + 190, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 190, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 190, + 658 + ], + "type": "text", + "content": "3.2.1 Initial Feature Extraction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "As shown in Fig. 3(b), we follow most existing works [7, 35, 75] to use three " + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": " convolutions with LeakyReLU [41] as a SpatialConv layer to map each SAI to a high-dimensional feature. The initially extracted feature can be" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 324, + 70, + 529, + 199 + ], + "blocks": [ + { + "bbox": [ + 324, + 70, + 529, + 199 + ], + "lines": [ + { + "bbox": [ + 324, + 70, + 529, + 199 + ], + "spans": [ + { + "bbox": [ + 324, + 70, + 529, + 199 + ], + "type": "image", + "image_path": "c2330a8e34a9db8434ab60bccdf9b72c9ce997ec7e4fb6c6be4e1034bb31830f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 201, + 545, + 235 + ], + "lines": [ + { + "bbox": [ + 305, + 201, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 545, + 235 + ], + "type": "text", + "content": "Figure 2. The SAI and EPI representations of LF images. The array of " + }, + { + "bbox": [ + 305, + 201, + 545, + 235 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 305, + 201, + 545, + 235 + ], + "type": "text", + "content": " views of a scene rosemary from HCInew [21] dataset is used as an example for illustration." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "content": "represented as " + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "inline_equation", + "content": "\\pmb{F} \\in \\mathbb{R}^{U \\times V \\times H \\times W \\times C}" + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 245, + 545, + 270 + ], + "type": "text", + "content": " denotes the channel dimension." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 287, + 526, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 287, + 526, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 526, + 300 + ], + "type": "text", + "content": "3.2.2 Deep Spatial-Angular Correlation Learning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 306, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 472 + ], + "type": "text", + "content": "Non-Local Cascading Block. The basic module for spatial-angular correlation learning is the Non-Local Cascading block. As shown in Fig. 3(a), each block consists of two cascaded Basic-Transformer units to separately incorporate the complementary information along the horizontal and vertical epipolar lines. In our method, we employed five Non-Local Cascading blocks to achieve a global perception of all angular views, and followed SwinIR [35] to adopt spatial convolutions to enhance the local feature representation. The effectiveness of this inter-block spatial convolution is validated in Sec. 4.4. Note that, the weights of the two Basic-Transformer units in each block are shared to jointly learn the intrinsic properties of LFs, which is demonstrated effective in Sec. 4.4." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": "As shown in Fig. 3(c), the initial features " + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": " can be first separately reshaped to the horizontal EPI pattern " + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{hor} \\in \\mathbb{R}^{UH \\times V \\times W \\times C}" + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": " and the vertical EPI pattern " + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{ver} \\in \\mathbb{R}^{VW \\times U \\times H \\times C}" + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": ". Next, " + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{hor}" + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{ver}" + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": ") is fed to a Basic-Transformer unit to integrate the long-range information along the horizontal (or vertical) epipolar line. Then, the enhanced feature " + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{F}}_{hor}" + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{F}}_{ver}" + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": ") is reshaped into the size of " + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "inline_equation", + "content": "UV \\times H \\times W \\times C" + }, + { + "bbox": [ + 305, + 474, + 545, + 617 + ], + "type": "text", + "content": ", and passes through a SpatialConv layer to incorporate the spatial context information within each SAI. Without loss of generality, we take the vertical Basic-Transformer as an example to introduce the detail of our Basic-Transformer unit in the following texts." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Basic-Transformer Unit. The objective of this unit is to capture long-range dependencies along the epipolar line via Transformers. To leverage the powerful sequence modeling capability of Transformers, we convert the vertical EPI features " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{ver}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " to the sequences of \"tokens\" for capturing spatial-angular correlation in " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " dimensions. As shown in Fig. 3(d), the vertical EPI features are passed through a linear projection matrix " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "W_{in} \\in \\mathbb{R}^{C \\times D}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "D" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12378" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 542, + 205 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 542, + 205 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 542, + 205 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 542, + 205 + ], + "type": "image", + "image_path": "cfb324391a8e3948033cb56600511a1882e7505787ae19696911c2d10fabf96a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 206, + 111, + 316 + ], + "blocks": [ + { + "bbox": [ + 53, + 206, + 111, + 316 + ], + "lines": [ + { + "bbox": [ + 53, + 206, + 111, + 316 + ], + "spans": [ + { + "bbox": [ + 53, + 206, + 111, + 316 + ], + "type": "image", + "image_path": "b1c46a4306ef2c7220e272a3cd00d7bcdf7358a2e18abb2de6f3a777f2acbfe0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 115, + 319, + 476, + 331 + ], + "lines": [ + { + "bbox": [ + 115, + 319, + 476, + 331 + ], + "spans": [ + { + "bbox": [ + 115, + 319, + 476, + 331 + ], + "type": "text", + "content": "Figure 3. An overview of our proposed EPIT. Here, a " + }, + { + "bbox": [ + 115, + 319, + 476, + 331 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 115, + 319, + 476, + 331 + ], + "type": "text", + "content": " LF is used as an example for illustration." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 115, + 206, + 334, + 316 + ], + "blocks": [ + { + "bbox": [ + 115, + 206, + 334, + 316 + ], + "lines": [ + { + "bbox": [ + 115, + 206, + 334, + 316 + ], + "spans": [ + { + "bbox": [ + 115, + 206, + 334, + 316 + ], + "type": "image", + "image_path": "e5be6540e1a8c3fef8a44d91cb59bdd4d8eb248273cf28777e87ae20cc41836e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 337, + 205, + 541, + 316 + ], + "blocks": [ + { + "bbox": [ + 337, + 205, + 541, + 316 + ], + "lines": [ + { + "bbox": [ + 337, + 205, + 541, + 316 + ], + "spans": [ + { + "bbox": [ + 337, + 205, + 541, + 316 + ], + "type": "image", + "image_path": "db356ecabddb460d353108e05a8b99695e79273b86fa591ea5bfcdb550ef9d5e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "type": "text", + "content": "denotes the embedding dimension of each token. The projected EPI features are a sequence of tokens with a length of " + }, + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "type": "inline_equation", + "content": "UH" + }, + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "type": "inline_equation", + "content": "T_{ver} \\in \\mathbb{R}^{UH \\times D}" + }, + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "type": "text", + "content": ". Following the PreNorm operation in [70], we also apply Layer Normalization (LN) before the attention calculation, and obtain the normalized tokens " + }, + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "type": "inline_equation", + "content": "\\bar{T}_{ver} = \\mathrm{LN}(T_{ver})" + }, + { + "bbox": [ + 46, + 345, + 287, + 417 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": "Afterwards, tokens " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{T}_{ver}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": " are passed through the Self-Attention layer and transformed into the deep tokens involving non-local spatial-angular information along the vertical epipolar line. Specifically, " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\bar{T}_{ver}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": " need to be separately multiplied by " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "W_{Q} \\in \\mathbb{R}^{D \\times D}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "W_{K} \\in \\mathbb{R}^{D \\times D}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "W_{V} \\in \\mathbb{R}^{D \\times D}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": " to generate corresponding query, key and value components for self-attention calculation, i.e., " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "Q_{ver} = \\bar{T}_{ver} W_{Q}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "K_{ver} = \\bar{T}_{ver} W_{K}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "inline_equation", + "content": "V_{ver} = \\bar{T}_{ver} W_{V}" + }, + { + "bbox": [ + 46, + 417, + 287, + 513 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "text", + "content": "Given a query position " + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "inline_equation", + "content": "q = \\{1,2,\\dots ,UH\\}" + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "inline_equation", + "content": "Q_{ver}" + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "text", + "content": " and a key position " + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "inline_equation", + "content": "k = \\{1,2,\\dots ,UH\\}" + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "inline_equation", + "content": "K_{ver}" + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "text", + "content": ", the corresponding response " + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "inline_equation", + "content": "A_{ver}(q,k)\\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 513, + 287, + 583 + ], + "type": "text", + "content": " measures the mutual similarity of the pairs by the dot-product operation, followed by a Softmax function to obtain the attention scores on the vertical EPI tokens. That is," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 72, + 590, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 590, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 72, + 590, + 287, + 617 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} _ {\\text {v e r}} (q, k) = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {\\text {v e r}} (q) \\cdot K _ {\\text {v e r}} (k) ^ {\\mathrm {T}}}{\\sqrt {D}}\\right). \\tag {1}", + "image_path": "a9177176b2cc041c2b39dc3fecef39b04f3541fa4acde4c284f356be959048f3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 623, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 287, + 670 + ], + "type": "text", + "content": "Based on the attention scores, the output of self-attention " + }, + { + "bbox": [ + 46, + 623, + 287, + 670 + ], + "type": "inline_equation", + "content": "T_{ver}^{\\prime}" + }, + { + "bbox": [ + 46, + 623, + 287, + 670 + ], + "type": "text", + "content": " can be calculated as the weighted sum of value. In summary, the calculation process of Self-Attention layer can be formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 111, + 679, + 287, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 679, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 111, + 679, + 287, + 693 + ], + "type": "interline_equation", + "content": "\\boldsymbol {T} _ {\\text {v e r}} ^ {\\prime} = \\boldsymbol {A} _ {\\text {v e r}} V _ {\\text {v e r}} + T _ {\\text {v e r}}. \\tag {2}", + "image_path": "72f26f8bf78ae6fc64d01b00f7329ff51662647981ef60ad414cb410f80709d3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "To further incorporate the spatial-angular correlation," + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + 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An example of the attention maps of a Basic-Transformer unit for the spatial-angular correlation. Note that, the attention maps correspond to the correlation between the regions marked by the red and yellow strokes." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 452, + 395, + 494, + 437 + ], + "blocks": [ + { + "bbox": [ + 452, + 395, + 494, + 437 + ], + "lines": [ + { + "bbox": [ + 452, + 395, + 494, + 437 + ], + "spans": [ + { + "bbox": [ + 452, + 395, + 494, + 437 + ], + "type": "image", + "image_path": "4eb5c7164fb22cba02addc206a73e63f34c26015f7b2e165bde3f7633c46f658.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 470, + 437, + 476, + 444 + ], + "lines": [ + { + "bbox": [ + 470, + 437, + 476, + 444 + ], + "spans": [ + { + "bbox": [ + 470, + 437, + 476, + 444 + ], + "type": "text", + "content": "(i)" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 497, + 395, + 539, + 437 + ], + "blocks": [ + { + "bbox": [ + 497, + 395, + 539, + 437 + ], + "lines": [ + { + "bbox": [ + 497, + 395, + 539, + 437 + ], + "spans": [ + { + "bbox": [ + 497, + 395, + 539, + 437 + ], + "type": "image", + "image_path": "3cc2fd20bba6c037347a73431ae1e636bea25adc3d7e03352d1f045e2840968c.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 514, + 437, + 522, + 444 + ], + "lines": [ + { + "bbox": [ + 514, + 437, + 522, + 444 + ], + "spans": [ + { + "bbox": [ + 514, + 437, + 522, + 444 + ], + "type": "text", + "content": "(1)" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 504, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 504, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 504, + 545, + 540 + ], + "type": "text", + "content": "following [54], our Basic-Transformer unit also contains the multi-layer perception (MLP) and LN, and generates the enhanced " + }, + { + "bbox": [ + 305, + 504, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\hat{T}_{ver}" + }, + { + "bbox": [ + 305, + 504, + 545, + 540 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 356, + 548, + 545, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 548, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 356, + 548, + 545, + 562 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {T}} _ {v e r} = \\operatorname {M L P} \\left(\\operatorname {L N} \\left(\\boldsymbol {T} _ {v e r} ^ {\\prime}\\right)\\right) + \\boldsymbol {T} _ {v e r} ^ {\\prime}. \\tag {3}", + "image_path": "d0363894684b337cf97355a460ff95a216364f12578efde6e754932f7786f2f0.jpg" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "type": "text", + "content": "At the end of the Basic-Transformer unit, the enhanced " + }, + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\hat{T}_{ver}" + }, + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "type": "text", + "content": " is fed to another linear projection " + }, + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "W_{out} \\in \\mathbb{R}^{D \\times C}" + }, + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "type": "text", + "content": ", and reshaped into the size of " + }, + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "type": "inline_equation", + "content": "UV \\times H \\times W \\times C" + }, + { + "bbox": [ + 305, + 570, + 545, + 617 + ], + "type": "text", + "content": " for the subsequent SpatialConv layer." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "text", + "content": "Cross-View Similarity Analysis. Note that, the setting " + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "[A_{ver}(q,1),\\dots,A_{ver}(q,UH)]\\in \\mathbb{R}^{1\\times UH}" + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "text", + "content": " represents the similarity scores of " + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "text", + "content": " with all " + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_{ver}" + }, + { + "bbox": [ + 305, + 618, + 545, + 713 + ], + "type": "text", + "content": ", and thus can be re-organized as a slice of cross-view attention map according to the angular coordinate. Inspired by this, we visualized the cross-view attention maps on an example scene in Fig. 4. The regions marked by the red stripe in Fig. 4(a) are set as the query tokens, and the self-similarity (i.e.," + } + ] + } + ], + "index": 36 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12379" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 91, + 545, + 272 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 545, + 90 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 545, + 90 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 545, + 90 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of different SR methods in terms of the number of parameters (#Prm.) and PSNR/SSIM. Larger PSNR and SSIM values indicate higher SR quality. We mark the best results in red and the second best results in blue." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 91, + 545, + 272 + ], + "lines": [ + { + "bbox": [ + 48, + 91, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 48, + 91, + 545, + 272 + ], + "type": "table", + "html": "
Methods#Prm.(M)2×/4×2×4×
EPFLHCInewHCIoldINRIASTFgantryEPFLHCInewHCIoldINRIASTFgantry
Bicubic- / -29.74/.937631.89/.935637.69/.978531.33/.957731.06/.949825.14/.832427.61/.851732.42/.934426.82/.886725.93/.8452
VDSR [30]0.66 / 0.6632.50/.959834.37/.956140.61/.986734.43/.974135.54/.978927.25/.877729.31/.882334.81/.951529.19/.920428.51/.9009
EDSR [37]38.6 / 38.933.09/.962934.83/.959241.01/.987434.97/.976436.29/.981827.84/.885429.60/.886935.18/.953629.66/.925728.70/.9072
RCAN [81]15.3 / 15.433.16/.963434.98/.960341.05/.987535.01/.976936.33/.983127.88/.886329.63/.888635.20/.954829.76/.927628.90/.9131
resLF[79]7.98 / 8.6433.62/.970636.69/.973943.42/.993235.39/.980438.36/.990428.27/.903530.73/.910736.71/.968230.34/.941230.19/.9372
LFSSR [72]0.88 / 1.7733.68/.974436.81/.974943.81/.993835.28/.983237.95/.989828.27/.911830.72/.914536.70/.969630.31/.946730.15/.9426
LF-ATO [26]1.22 / 1.3634.27/.975737.24/.976744.20/.994236.15/.984239.64/.992928.52/.911530.88/.913537.00/.969930.71/.948430.61/.9430
LF-InterNet [61]5.04 / 5.4834.14/.976037.28/.976344.45/.994635.80/.984338.72/.990928.67/.916230.98/.916137.11/.971630.64/.949130.53/.9409
LF-DFnet [62]3.94 / 3.9934.44/.975537.44/.977344.23/.994136.36/.984039.61/.992628.77/.916531.23/.919637.32/.971830.83/.950331.15/.9494
MEG-Net [78]1.69 / 1.7734.30/.977337.42/.977744.08/.994236.09/.984938.77/.991528.74/.916031.10/.917737.28/.971630.66/.949030.77/.9453
LF-IINet [38]4.84 / 4.8834.68/.977337.74/.979044.84/.994836.57/.985339.86/.993629.11/.918831.36/.920837.62/.973431.08/.951531.21/.9502
DPT [57]3.73 / 3.7834.48/.975837.35/.977144.31/.994336.40/.984339.52/.992628.93/.917031.19/.918837.39/.972130.96/.950331.14/.9488
LFT [36]1.11 / 1.1634.80/.978137.84/.979144.52/.994536.59/.985540.51/.994129.25/.921031.46/.921837.63/.973531.20/.952431.86/.9548
DistgSSR [60]3.53 / 3.5834.81/.978737.96/.979644.94/.994936.59/.985940.40/.994228.99/.919531.38/.921737.56/.973230.99/.951931.65/.9535
LFSAV [9]1.22 / 1.5434.62/.977237.43/.977644.22/.994236.36/.984938.69/.991429.37/.922331.45/.921737.50/.972131.27/.953131.36/.9505
EPIT (ours)1.42 / 1.4734.83/.977538.23/.981045.08/.994936.67/.985342.17/.995729.34/.919731.51/.923137.68/.973731.37/.952632.18/.9571
", + "image_path": "36315e07ce1969fdd49d2a1f0b7800f11d62cdc05aeffd2fe1e39121fec6176b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 281, + 289, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 289, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 289, + 413 + ], + "type": "text", + "content": "key are same as query) is ideally located at the diagonal, as shown in Fig. 4(f). In contrast, the yellow stripes in Figs. 4(b)-4(e) are set as the key tokens, the corresponding cross-view similarities are shown in Figs. 4(g)-4(j). It can be observed that due to the foreground occlusions, the responses of the background appear as short lines (marked by the white boxes) parallel to the diagonal in each cross-view attention map, and both of the distance to the diagonal and the length of response regions adaptively change as the key view moves along the baseline, which demonstrates the disparity-awareness of our Basic-Transformer unit." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 430, + 168, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 168, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 168, + 442 + ], + "type": "text", + "content": "3.2.3 Feature Upsampling" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": "Finally, we apply the pixel shuffling operation to increase the spatial resolution of LF features, and further employ a " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": " convolution to obtain the super-resolved LF image " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{SR}" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": ". Following most existing works [61, 60, 36, 62, 57, 38, 78, 79, 72], we use the " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": " loss function to train our network due to its robustness to outliers [2]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 533, + 128, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 128, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 128, + 547 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 554, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 625 + ], + "type": "text", + "content": "In this section, we first introduce the datasets and our implementation details, and then compare our method with state-of-the-art methods. Next, we investigate the performance of different SR methods with respect to disparity variations. Finally, we validate the effectiveness of our method through ablation studies." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 635, + 243, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 243, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 243, + 647 + ], + "type": "text", + "content": "4.1. Datasets and Implementation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "We followed [62, 60, 38, 57, 36] to use five public LF datasets (EPFL [48], HCInew [21], HCld [65], INRIA [46], STFgantry [53]) in the experiments. All LFs in these datasets have an angular resolution of " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": ". Unless specifically mentioned, we extracted the central " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": " SAIs for" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "text", + "content": "training and test. In the training stage, we cropped each SAI into patches of size " + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "inline_equation", + "content": "64 \\times 64 / 128 \\times 128" + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "text", + "content": ", and performed " + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "inline_equation", + "content": "0.5 \\times / 0.25 \\times" + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "text", + "content": " bicubic downsampling to generate the LR patches for " + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "inline_equation", + "content": "2 \\times / 4 \\times" + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "text", + "content": " SR, respectively. We used peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [63] as quantitative metrics for performance evaluation. To obtain the metric score for a dataset with " + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "text", + "content": " scenes, we first calculated the metric of each scene by averaging the scores over all the SAIs separately, and then obtained the score for this dataset by averaging the scores over the " + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 281, + 545, + 399 + ], + "type": "text", + "content": " scenes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "type": "text", + "content": "We adopted the same training settings for all experiments, i.e., Xavier initialization algorithm [17] and Adam optimizer [31] with " + }, + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "type": "text", + "content": ". The initial learning rate was set to " + }, + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "type": "inline_equation", + "content": "2\\times 10^{-4}" + }, + { + "bbox": [ + 304, + 400, + 546, + 508 + ], + "type": "text", + "content": " and decreased by a factor of 0.5 every 15 epochs. During the training phase, we performed random horizontal flipping, vertical flipping, and 90-degree rotation to augment the training data. All models were implemented in the PyTorch framework and trained from scratch for 80 epochs with 2 Nvidia RTX 2080Ti GPUs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 515, + 504, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 515, + 504, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 515, + 504, + 528 + ], + "type": "text", + "content": "4.2. Comparisons on Benchmark Datasets" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "We compare our method to 14 state-of-the-art methods, including 3 single image SR methods [30, 37, 81] and 11 LF image SR methods [79, 72, 26, 61, 62, 78, 38, 57, 36, 60, 9]. Quantitative Results. A quantitative comparison among different methods is shown in Tabel 1. Our EPIT with a small model size (i.e., " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "1.42\\mathrm{M} / 1.47\\mathrm{M}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "2\\times /4\\times" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " SR) achieves state-of-the-art PSNR and SSIM scores on almost all the datasets for both " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " SR. It is worth noting that LFs in the STFgantry dataset [53] have larger disparity variations, and are thus more challenging. Our EPIT significantly outperforms all the compared methods and achieves " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "1.66\\mathrm{dB} / 0.32\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " PSNR improvements over the second top-performing method LFT for " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "2\\times /4\\times" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " SR, respectively, which demonstrates the powerful capacity of our EPIT in non-local correlation modeling." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12380" + } + ] + } + ], + 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Quantitative and qualitative (MSE) comparisons of disparity estimation results achieved by SPO [80] using different SR results. The MSE " + }, + { + "bbox": [ + 46, + 404, + 287, + 437 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 46, + 404, + 287, + 437 + ], + "type": "text", + "content": " is the mean square error multiplied by 100." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 48, + 471, + 287, + 553 + ], + "blocks": [ + { + "bbox": [ + 46, + 449, + 287, + 470 + ], + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 470 + ], + "type": "text", + "content": "Table 2. PSNR values achieved by DistgSSR [60] and our EPIT with different angular resolution for " + }, + { + "bbox": [ + 46, + 449, + 287, + 470 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 449, + 287, + 470 + ], + "type": "text", + "content": " SR." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 471, + 287, + 553 + ], + "lines": [ + { + "bbox": [ + 48, + 471, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 48, + 471, + 287, + 553 + ], + "type": "table", + "html": "
InputEPFLHCInewHCIoldINRIASTFgantry
[60]Ours[60]Ours[60]Ours[60]Ours[60]Ours
2×228.27-0.0530.80+0.0436.77+0.1730.55-0.0330.74+0.56
3×328.67+0.0331.07+0.1937.18+0.1930.83+0.1131.12+0.74
4×428.81+0.2331.25+0.1537.32+0.2030.93+0.2631.23+0.88
5×528.99+0.3531.38+0.1337.56+0.1230.99+0.3831.65+0.56
6×629.10+0.3331.39+0.1837.52+0.2630.98+0.4731.57+0.74
7×729.38+0.2231.43+0.2037.65+0.2731.18+0.3331.63+0.77
8×829.32+0.2831.52+0.1437.76+0.2431.23+0.3131.58+0.90
9×929.41+0.3031.48+0.2137.80+0.2631.22+0.3431.66+0.84
", + "image_path": "b7b6a6a5ba4b1df2955eb4176c215770aeb2469ee5a9e00fc326027a730586b6.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": "Qualitative Results. Figure 5 shows the qualitative results achieved by different methods for " + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "inline_equation", + "content": "2 \\times 4 \\times" + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": " SR. It can be observed from the zoom-in regions that single image SR method RCAN [81] cannot recover the textures and details in the SR images. In contrast, our EPIT can incorporate sub-pixel correspondence among SAIs and generate more faithful details with fewer artifacts. Compared to most LF image SR methods, our EPIT can generate superior visual results with high angular consistency. Please refer to the supplemental material for additional visual comparisons." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Angular Consistency. We evaluate the angular consistency by using the " + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "4 \\times \\mathrm{SR}" + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": " results on several challenging scenes" + } + ] + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 307, + 316, + 400, + 469 + ], + "blocks": [ + { + "bbox": [ + 307, + 316, + 400, + 469 + ], + "lines": [ + { + "bbox": [ + 307, + 316, + 400, + 469 + ], + "spans": [ + { + "bbox": [ + 307, + 316, + 400, + 469 + ], + "type": "image", + "image_path": "19dcd839e89b73a4111d22e628c99496b0fbcac6bb22650ca8ae5684fe6c6cdd.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 472, + 545, + 494 + ], + "lines": [ + { + "bbox": [ + 306, + 472, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 545, + 494 + ], + "type": "text", + "content": "Figure 7. Visual comparison of different SR methods on real-world LF scenes for " + }, + { + "bbox": [ + 306, + 472, + 545, + 494 + ], + "type": "inline_equation", + "content": "4 \\times \\mathrm{SR}" + }, + { + "bbox": [ + 306, + 472, + 545, + 494 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 405, + 316, + 449, + 469 + ], + "blocks": [ + { + "bbox": [ + 405, + 316, + 449, + 469 + ], + "lines": [ + { + "bbox": [ + 405, + 316, + 449, + 469 + ], + "spans": [ + { + "bbox": [ + 405, + 316, + 449, + 469 + ], + "type": "image", + "image_path": "422548882194c104513f9c6fc20819c52ef67260b32af7299c07faa68d7b8f6d.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 452, + 316, + 497, + 469 + ], + "blocks": [ + { + "bbox": [ + 452, + 316, + 497, + 469 + ], + "lines": [ + { + "bbox": [ + 452, + 316, + 497, + 469 + ], + "spans": [ + { + "bbox": [ + 452, + 316, + 497, + 469 + ], + "type": "image", + "image_path": "b60de61e9b8be4227c1d61ceb277be90c8b750d1a0bdb47aa5476ef1ad391e23.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 501, + 316, + 547, + 469 + ], + "blocks": [ + { + "bbox": [ + 501, + 316, + 547, + 469 + ], + "lines": [ + { + "bbox": [ + 501, + 316, + 547, + 469 + ], + "spans": [ + { + "bbox": [ + 501, + 316, + 547, + 469 + ], + "type": "image", + "image_path": "473d2af88e9769003881e07d8a64c32c6e6ba9e13b8f7f18b14dd48ba5c0289e.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 507, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 545, + 567 + ], + "type": "text", + "content": "(e.g., Backgammon and Stripes) in 4D LF benchmark [21] for disparity estimation. As shown in Fig. 6, our EPIT achieves competitive MSE scores on these challenging scenes, which demonstrates the superiority of our EPIT on angular consistency." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Performance with Different Angular Resolution. Since the angular resolution of LR images can vary significantly with different LF devices, we compare our method to DistgSSR [60] on LFs with different angular resolutions. It can be observed from Table 2 that our method achieves higher PSNR values than DistgSSR on almost all the datasets with each angular resolution (except on the EPFL and INRIA datasets with " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " input LFs). The consistent performance improvements demonstrate that our EPIT can well model the spatial-angular correlation with various angular resolutions. More comparisons and discussions are provided in the supplemental material." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12381" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 143, + 178 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 143, + 178 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 143, + 178 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 143, + 178 + ], + "type": "image", + "image_path": "55bad091186292a5713bb04293b5f738ed45e12ea0ce56a387aaf599cdea7673.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 145, + 70, 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Performance comparison and local attribution maps of different SR methods on two representative scenes with different shearing values for " + }, + { + "bbox": [ + 46, + 350, + 547, + 384 + ], + "type": "inline_equation", + "content": "2 \\times \\mathrm{SR}" + }, + { + "bbox": [ + 46, + 350, + 547, + 384 + ], + "type": "text", + "content": ". Here, we plot the performance curve to quantitatively measure the effect of disparity variations on LFs, and present the visual results and corresponding attribution maps under sheared value=2, 4." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 105, + 265, + 152, + 340 + ], + "blocks": [ + { + "bbox": [ + 105, + 265, + 152, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 265, + 152, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 265, + 152, + 340 + ], + "type": "image", + "image_path": "35d84871eba78764c0862220cd9bf06a7cc56bb5c35ae323534a9196fc268573.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 154, + 265, + 200, + 340 + ], + "blocks": [ + { + "bbox": [ + 154, + 265, + 200, + 340 + ], + "lines": [ + { + "bbox": [ + 154, + 265, + 200, + 340 + ], + "spans": [ + { + "bbox": [ + 154, + 265, + 200, + 340 + 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We compare our method to state-of-the-art methods under real-world degradation by directly applying them to LFs in the STFlytro dataset [47]. Since no groundtruth HR images are available in this dataset, we present the LR input and their super-resolved results in Fig. 7. It can be observed that our method can recover more faithful details and generate more clear letters than other methods. Since the LF structure keeps unchanged under both bicubic and real-world degradation, our method can learn the spatial-angular correlation from bicubicly downsampled training data, and well generalize to LF images under real degradation." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 47, + 550, + 263, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 263, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 263, + 563 + ], + "type": "text", + "content": "4.3. Robustness to Large Disparity Variations" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 569, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 287, + 653 + ], + "type": "text", + "content": "Considering the parallax structure of LF images, we followed the shearing operation in existing works [67, 68] to linearly change the overall disparity range of LF datasets. Note that, the content of SAIs maintain unchanged after the shearing operation, and thus we can quantitatively investigate the performance of different SR methods with respect to the disparity variations." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "Quantitative & Qualitative Comparison. Figure 8 shows the quantitative and qualitative results of different SR methods with respect to sheared values, from which we can observe that: 1) Except for the single image SR method RCAN, all LF image SR methods suffer a performance drop" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "text", + "content": "when the absolute sheared value of LF images increases. That is because, large sheared values can result in more significant misalignment among LF images, and introduce difficulties in complementary information incorporation; 2) As the absolute sheared value increases, the performance of existing LF image SR methods is even inferior to RCAN. The possible reason is that, these methods do not make full use of local spatial information, but rather rely on local angular information from adjacent views. When the sheared value exceeds their receptive fields, the large disparities can make the spatial-angular correlation non-local and thus introduce challenges in complementary information incorporation; 3) Our EPIT performs much more robust to disparity variations and achieves the highest PSNR scores under all sheared values. More quantitative comparisons on the whole datasets can be referred to the supplemental material." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "LAM Visualization. We used Local Attribution Map (LAM) [18] to visualize the input regions that contribute to the SR results of different methods. As shown in Fig. 8, we first specify the center of green stripes in HR images as the target regions, and then re-organize the corresponding attribution maps on LR images into the EPI patterns. It can be observed that RCAN achieves a larger receptive field along the spatial dimension than other compared methods, which supports the results in Figs. 8(b) and 8(e) that RCAN achieves a relatively stable SR performance with different" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12382" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 289, + 233 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 233 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 233 + ], + "type": "image", + "image_path": "16ddaee3aa785a8a15bfedb26f9cd5ce15c6688a58c07706b414d36148199536.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 237, + 287, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 237, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 287, + 270 + ], + "type": "text", + "content": "Figure 9. PSNR distribution among different SAIs achieved by MEG-Net [78], LFT [36], and our EPIT on the INRIA dataset [46] for " + }, + { + "bbox": [ + 46, + 237, + 287, + 270 + ], + "type": "inline_equation", + "content": "2 \\times \\mathrm{SR}" + }, + { + "bbox": [ + 46, + 237, + 287, + 270 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "type": "text", + "content": "sheared values. It is worth noting that our EPIT can automatically incorporate the most relevant information from different views, and can learn the non-local spatial-angular correlation regardless of disparity variations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 335, + 288, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 288, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 288, + 441 + ], + "type": "text", + "content": "Perspective Comparison. We compare the performance of MEG-Net, DistgSSR and our method with respect to different perspectives and sheared values (0 to 3). It can be observed in Fig. 9 that, both MEG-Net and DistgSSR suffer significant performance drops on all perspectives as the sheared value increases. In contrast, our EPIT can well handle the disparity variation problem, and achieve much higher PSNR values with a balanced distribution among different views regardless of the sheared values." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 453, + 141, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 141, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 141, + 466 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 520 + ], + "type": "text", + "content": "In this subsection, we compare the performance of our EPIT with different variants to verify the effectiveness of our design choices, and additionally, investigate their robustness to large disparity variations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "type": "text", + "content": "Horizontal/Vertical Basic-Transformer Units. We demonstrated the effectiveness of the horizontal and vertical Basic-Transformer units in our EPIT by separately removing them from our network. Note that, without using horizontal or vertical Basic-Transformer unit, these variants cannot incorporate any information from the corresponding angular directions. As shown in Table 3, both variants w/o-Horizontal and w/o-Vertical suffer a decrease of " + }, + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "type": "inline_equation", + "content": "0.72\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 521, + 287, + 652 + ], + "type": "text", + "content": " in the INRIA dataset as compared to EPIT, which demonstrates the importance of exploiting spatial-angular correlations from all angular views." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Weight Sharing in Non-Local Cascading Blocks. We introduced the variant " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "-Share by removing the weight sharing between horizontal and vertical Basic-Transformer units. As shown in Table 3, the additional parameters in variant " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "-Share do not introduce further performance im" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 112, + 544, + 220 + ], + "blocks": [ + { + "bbox": [ + 305, + 69, + 545, + 112 + ], + "lines": [ + { + "bbox": [ + 305, + 69, + 545, + 112 + ], + "spans": [ + { + "bbox": [ + 305, + 69, + 545, + 112 + ], + "type": "text", + "content": "Table 3. The PSNR scores achieved by different variants of our EPIT on the LFs with different shearing values for " + }, + { + "bbox": [ + 305, + 69, + 545, + 112 + ], + "type": "inline_equation", + "content": "2 \\times \\mathrm{SR}" + }, + { + "bbox": [ + 305, + 69, + 545, + 112 + ], + "type": "text", + "content": ". We adjusted the channel number of each variant to make its model size (i.e., #Prm.) not smaller than EPIT for better validation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 112, + 544, + 220 + ], + "lines": [ + { + "bbox": [ + 307, + 112, + 544, + 220 + ], + "spans": [ + { + "bbox": [ + 307, + 112, + 544, + 220 + ], + "type": "table", + "html": "
Variants#Prm.FLOPsEPFL (Sheared)INRIA (Sheared)
024024
w/o-Horiz1.42M80.20G33.9633.9834.0235.9536.0836.11
w/o-Verti1.42M80.20G34.0133.9433.8735.9535.9736.02
w/o-Share2.71M80.20G34.8034.6334.5136.6636.7236.45
w/o-Local1.64M96.39G34.4234.3634.2736.3636.4036.25
w/o-Trans1.60M78.82G33.9031.3231.7435.9533.2833.55
w-1-Block1.54M68.23G33.9734.2434.0835.8436.1935.93
w-2-Block1.45M73.37G34.1934.3634.2935.9836.2735.99
w-3-Block1.71M85.78G34.6434.5134.4536.5336.4736.22
EPIT1.42M74.96G34.8334.6934.5936.6736.7536.59
", + "image_path": "767bcb70db54c9154d82e8676745f9ff97c10c9266b2ab833b77dff5af97f57e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 236, + 545, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 272 + ], + "type": "text", + "content": "provement. It demonstrates that the weight sharing strategy between two directional Basic-Transformer units is beneficial and efficient to regularize the network." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 272, + 546, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 546, + 392 + ], + "type": "text", + "content": "SpatialConv in Non-Local Cascading Blocks. We introduced the variant w/o-Local by removing the SpatialConv layers from our EPIT, and we adjusted the channel number to make the model size of this variant not smaller than the main model. As shown in Table 3, the SpatialConv has a significant influence on the SR performance, e.g., the variant w/o-Local suffers a 0.41dB PSNR drop on the EPFL dataset. It demonstrates that local context information is crucial to the SR performance, and the simple convolutions can fully incorporate the spatial information from each SAI." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 393, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 545, + 476 + ], + "type": "text", + "content": "Basic-Transformer in Non-Local Cascading Blocks. We introduced the variant " + }, + { + "bbox": [ + 304, + 393, + 545, + 476 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 304, + 393, + 545, + 476 + ], + "type": "text", + "content": "-Trans by replacing Basic-Transformer in Non-Local Blocks with cascaded convolutions. As shown in Table 3, " + }, + { + "bbox": [ + 304, + 393, + 545, + 476 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 304, + 393, + 545, + 476 + ], + "type": "text", + "content": "-Trans suffers a most significant performance drop as the sheared value increases, which demonstrates the effectiveness of the Basic-Transformer in incorporating global information on the EPIs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 476, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 545, + 536 + ], + "type": "text", + "content": "Basic-Transformer Number. We introduced the variants with-n-Block " + }, + { + "bbox": [ + 304, + 476, + 545, + 536 + ], + "type": "inline_equation", + "content": "(n = 1,2,3)" + }, + { + "bbox": [ + 304, + 476, + 545, + 536 + ], + "type": "text", + "content": " by retaining " + }, + { + "bbox": [ + 304, + 476, + 545, + 536 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 476, + 545, + 536 + ], + "type": "text", + "content": " Non-Local Blocks. Results in Table 3 show the effectiveness of our EPIT (having 5 Non-Local Blocks) with higher-order spatial-angular correlation modeling capability." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 548, + 378, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 378, + 561 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 378, + 561 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": "In this paper, we propose a Transformer-based network for LF image SR. By modeling the dependencies between each pair of pixels on EPIs, our method can learn the spatial-angular correlation while achieving a global receptive field along the epipolar line. Extensive experimental results demonstrated that our method can not only achieve state-of-the-art SR performance on benchmark datasets, but also perform robust to large disparity variations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgment: This work was supported in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 61921001." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12383" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Martin Alain and Aljosa Smolic. 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One important issue is how to build a high-quality event-flow dataset with accurate event values and flow labels. Previous datasets are created by either capturing real scenes by event cameras or synthesizing from images with pasted foreground objects. The former case can produce real event values but with calculated flow labels, which are sparse and inaccurate. The latter case can generate dense flow labels but the interpolated events are prone to errors. In this work, we propose to render a physically correct event-flow dataset using computer graphics models. In particular, we first create indoor and outdoor 3D scenes by Blender with rich scene content variations. Second, diverse camera motions are included for the virtual capturing, producing images and accurate flow labels. Third, we render high-framerate videos between images for accurate events. The rendered dataset can adjust the density of events, based on which we further introduce an adaptive density module (ADM). Experiments show that our proposed dataset can facilitate event-flow learning, whereas previous approaches when trained on our dataset can improve their performances constantly by a relatively large margin. In addition, event-flow pipelines when equipped with our ADM can further improve performances. Our code is available at https://github.com/boomluo02/ADMFlow.", + "bbox": [ + 75, + 363, + 473, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 772, + 209, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Event cameras [29] record brightness changes at a varying framerate [4]. When a change is detected in a pixel, the camera returns an event in the form $e = (x,y,t,p)$ immediately, where $x,y$ stands for the spatial location, $t$ refers to the timestamp in microseconds, and $p$ is the polarity of the", + "bbox": [ + 75, + 799, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8fc278094f27db86618949719a63d0bbfaa65f338241cda1810563787e9d747d.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 529, + 330, + 645, + 398 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/da8c3db4e8bc2736f68549da21933706440ddc3921f0f916ed31b0ece8be3ef7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 529, + 400, + 645, + 468 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4e969935e262969e8b3d89729cd3846557f8b0755766ee8b02c8b5474c2e457f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 647, + 330, + 767, + 398 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d9d782d8a7168e8c6cab0e472e5858d7e060f98c56690f16bc9ce3f9e2d8a66c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 404, + 763, + 452 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/12626680dcaf524455ac887b6349c6e6b2e7f22828e5e917a1428a96d8ed0c83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 330, + 887, + 400 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/99432e1f5ee2bd5944c305fd6942c78c28d06ba392ee56c12fe814f10dbdfb0a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 402, + 887, + 468 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/819ad36a9267a1b141290c8abefe363d9729c5c1c6be5af3aae005c398924b6f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 469, + 647, + 537 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ae406c9036edc578ae9140e0fc79adc9217f221931a3e6a0baae9dcea764a220.jpg", + "image_caption": [ + "Images", + "Figure 1: (a) the captured dataset from real event camera [55, 54]. (b) the synthesized dataset with flying chairs foreground [50]. (c) the synthesized dataset by moving a foreground image [42]. (d) Our synthesized dataset by graphics rendering, which not only reflects the real motions under correct scene geometries, but also produces accurate dense flow labels and events." + ], + "image_footnote": [], + "bbox": [ + 529, + 539, + 686, + 609 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bf78ea4a878bcb79576f94d576f8ef2f2c2c39fe361e5fbadc168f2146ea0063.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 650, + 469, + 769, + 537 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a72ad426ebf87c17790e36f7c6e248ee6e35534c6c612bc40563ed9d9dc082c9.jpg", + "image_caption": [ + "Events" + ], + "image_footnote": [], + "bbox": [ + 686, + 539, + 771, + 609 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7f28d128398f11860d7ca434865d69f423278b381ee21278de725ca521ed0c03.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 469, + 888, + 537 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/52478f78fe365dea8dbf3e0edf5a9404b0cf7fc1cdd10565a6335fef6a78188b.jpg", + "image_caption": [ + "Flow GT" + ], + "image_footnote": [], + "bbox": [ + 769, + 540, + 888, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "change, indicating a pixel become brighter or darker. On the other hand, optical flow estimation predicts motions between two frames [44], which is fundamental and important for many applications [49, 52, 7]. In this work, we study the problem of estimating optical flow from event camera data, instead of from RGB frames. Different from traditional images, events are sparse and are often integrated in short intervals as the input for the prediction. As such, early works", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9847", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "can only estimate sparse flows at the location of events [1]. Recent deep methods can estimate dense flows but with the help of images, either as the guidance [54] or as the additional inputs [26, 38]. Here, we tackle a hard version of the problem, where dense flows are predicted based purely on the event values $e$ . One key issue is how to create high quality event-based optical flow dataset to train the network.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing methods of event flow dataset creation can be classified into two types, 1) directly capturing from real event cameras [55, 54, 16]; 2) moving foregrounds on top of a background image to create synthesized flow motions [50, 42] and apply frame interpolation [14] to create events. For the first type, the ground-truth (GT) flow labels need to be calculated based on gray images acquired along with the event data. However, the optical flow estimations cannot be perfectly accurate [48, 43, 32, 24, 51], leading to the inaccuracy of GT labels. To alleviate the problem, additional depth sensors, such as LIDAR, have been introduced [55]. The flow labels can be calculated accurately when the depth values of LIDAR scans are available. However, LIDAR scans are sparse, and so do the flow labels, which are unfriendly for dense optical flow learning. Fig. 1 (a) shows an example, LIDAR points on the ground are sparse. Moreover, some thin objects are often missing, as indicated by the red box in Fig. 1 (a).", + "bbox": [ + 75, + 199, + 470, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For the second category, the flow labels are created by moving foreground objects on top of a background image, similar to flying chairs [12] or flying things [36]. In this way, the flow labels are dense and accurate. To create events, intermediate frames are interpolated [23]. However, the frame interpolation is inaccurate due to scene depth disparities, where the occluded pixels cannot be interpolated correctly, leading to erroneous event values in these regions. To match high framerate of events, the large number of interpolated frames makes the problem even worse. Fig. 1 (b) shows an example, where the events are incorrect at the occluded chairs. Moreover, the motions are artificial, further decreasing the realism of the dataset (Fig. 1 (b) and (c)).", + "bbox": [ + 75, + 474, + 468, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we create an event-flow dataset from synthetic 3D scenes by graphics rendering (Fig. 1 (d)). While there is a domain gap between rendered and real images, this gap is empirically found insignificant in event camera based classification [41] and segmentation [14] tasks. As noted by these works, models trained on synthetic events work very well for real event data. Because events contain only positive and negative polarities, no image appearances are involved. To this end, we propose a Multi-Density Rendered (MDR) event optical flow dataset, created by Blender on indoor and outdoor scenes with accurate events and flow labels. In addition, we design an Adaptive Density Module (ADM) based on MDR, which can adjust the densities of events, one of the most important factors for event-based tasks but has been largely overlooked.", + "bbox": [ + 75, + 674, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, our MDR dataset contains 80,000 samples from 50 virtual scenes. Each data sample is created by first rendering two frames and obtaining the GT flow labels directly from the engine. Then, we render $15 \\sim 60$ frames in between based on the flow magnitude. The events are created by thresholding log intensities and recording the times-stamp for each spatial location. The density of events can be controlled by the threshold values. The ADM is designed as a plugin module, which further consists of two sub-modules, multi-density changer (MDC) and multi-density selector (MDS), where the MDC adjusts the density globally while the MDS picks the best one for every spatial location. Experiments show that previous event-flow methods, when trained on our MDR dataset, can improve their performances. Moreover, we train several recent representative flow pipelines, such as FlowFormer [21], KPA-Flow [32], GMA [24] and SKFlow [47], on our MDR dataset. When equipped with our ADM module, the performances can increase consistently.", + "bbox": [ + 496, + 90, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as:", + "bbox": [ + 519, + 380, + 769, + 393 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A rendered event-flow dataset MDR, with 80,000 samples created on 53 virtual scenes, which possess physically correct accurate events and flow label pairs, covering a wide range of densities.", + "- An adaptive density module (ADM), which is a plug-and-play module for handling varying event densities.", + "- We achieve state-of-the-art performances. Our MDR can improve the quality of previous event-flow methods. Various optical flow pipelines when adapted to the event-flow task, can benefit from our ADM module." + ], + "bbox": [ + 519, + 412, + 890, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 621, + 640, + 636 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image-based Optical Flow", + "text_level": 1, + "bbox": [ + 500, + 648, + 736, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Optical flow estimates the per-pixel motion between two frames according to photo consistency. Traditional approaches minimize energies, leveraging both feature similarities and motion smoothness [13]. Deep methods train the networks that take two frames as input and directly output dense flow motions [12, 46]. Recent deep methods design different pipelines [30, 48, 24] as well as learning modules [35, 31, 34, 33] for performance improvements. The training often requires large labeled datasets, which can be synthesized by moving a foreground on top of a background image, such as FlyingChairs [12], and AutoFlow [45], or rendered from graphics such as Sintel [5] and FlyingThings [36], or created directly from real videos [19]. In this work, we use computer graphics techniques to render accurate and physically correct event and flow values.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9848", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5c58e2c5d07b4080815f9e5f5f846f1b7cd0e0358d21961bd1d07db12ba7a4af.jpg", + "image_caption": [ + "Figure 2: Our data generation pipeline. Given 3D scenes in the graphics engine, we generate camera trajectories and render high-frame-rate videos with forward and backward optical flow labels. Then, we build the event optical flow dataset by generating events using the videos." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 880, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Event-based Optical Flow", + "text_level": 1, + "bbox": [ + 76, + 378, + 312, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Benosman et al. [1] first proposed to estimate optical flow from events, which can only estimate sparse flows at the location of event values. Recent deep methods can estimate dense optical flows. EV-FlowNet [54] learns the event and flow labels in a self-supervised manner, which minimizes the photometric distances of grey images acquired by DAVIS [4]. Different event representations were explored, e.g., EST [15] and Matrix-LSTM [6], with various network structures, such as SpikeFlowNet [27], LIF-EV-FlowNet [18], STE-FlowNet [11], Li et al. [28], and E-RAFT [17]. Some works take both events and images as input for the flow estimation [26, 38]. In general, dense flows are more desirable than sparse ones but are more difficult to train. Normally, regions with events can produce more accurate flows than empty regions where no events are triggered. Moreover, supervised training can produce better results than unsupervised ones, as long as the training dataset can provide sufficient event-flow guidance.", + "bbox": [ + 75, + 402, + 472, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3.Event Dataset", + "text_level": 1, + "bbox": [ + 76, + 681, + 220, + 695 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The applications to the event camera dataset were first explored in the context of classification [37, 2]. Early works generate events simply by applying a threshold on the image difference [25]. Frame interpolation is often adopted for high framerate [14]. The synthesized events often contain inaccurate timestamps. The DAVIS event camera can directly capture both images and events [4], based on which two driving datasets are captured, DDD17 [3] and MVSEC [55]. With respect to the event flow dataset, EV-Flownet [54] calculated sparse flow labels from LIDAR depth based on MVSEC [55]. Wan et al. [50] and Stoffregen et al. [42] created the foreground motions and interpolated the intermediate frames for events. The real captured", + "bbox": [ + 75, + 704, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dataset can only provide sparse labels while the synthesized ones contain inaccurate events. In this work, we propose to render a physically correct event dense flow dataset.", + "bbox": [ + 498, + 378, + 890, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 440, + 591, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. The event-based optical flow dataset", + "text_level": 1, + "bbox": [ + 500, + 467, + 812, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to create a realistic event dataset for optical flow learning, we propose to employ a graphics engine with 3D scenes for data generation. Given 3D scenes, we first define camera trajectories, according to which we generate optical flow labels for timestamps at 60 FPS and 15 FPS. Then we render high-frame-rate videos based on the motion magnitude of the optical flow label between two timestamps. Finally, we generate event streams by rendering high-frame-rate videos and simulating the event trigger mechanism in the event camera using the v2e toolbox [20]. The overview of our data generation pipeline is shown in Fig. 2.", + "bbox": [ + 496, + 491, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Virtual Scenes. To ensure that the generated event dataset has the correct scene structure, we utilize a variety of indoor and outdoor 3D scenes, including cities, streets, forests, ports, beaches, living rooms, bedrooms, bathrooms, kitchens, and parking lots. Totally, we obtain 53 virtual 3D scenes (31 indoor and 22 outdoor) that simulate real-world environments. Some examples are shown in Fig. 3.", + "bbox": [ + 496, + 680, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Camera Trajectory. Given a 3D scene model, we first generate the 3D camera trajectory using PyBullet [8], an open-source physics engine, to ensure that the camera does not pass through the inside of the objects and out of the effective visible region of the scene during the motion. After setting the start position, end position, and moving speed of", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9849", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3a227041f30bd02e9b2a63122da3c371d74f360edebdd662643471867aff974e.jpg", + "image_caption": [ + "Figure 3: Examples of our MDR training set. Each row shows images, events and flow labels from top to bottom." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 467, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the camera trajectory, we randomly add translation and rotation motions to create a smooth curve function $\\Gamma(t)$ that outputs the location and pose $P(t) = [x(t), y(t), z(t), r(t)]^T$ .", + "bbox": [ + 76, + 330, + 468, + 377 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "High-frame-rate Video and Optical Flow. After camera trajectory generation, we use the graphics engine to render a sequence of images $I(\\boldsymbol{u}, t_i)$ , where $\\boldsymbol{u} = (x, y)$ is the pixel coordinates and $t_i$ is the timestamp. We extract the forward and backward optical flow labels between every two timestamps $(\\boldsymbol{F}_{t_i \\to t_j}, \\boldsymbol{F}_{t_j \\to t_i})$ . Then we need to generate the event data to construct the event optical flow dataset. Here, we render high-frame-rate videos $\\{I(\\boldsymbol{u}, \\tau)\\}$ , $\\tau \\in [t_i, t_j]$ between timestamps $t_i$ and $t_j$ for events generation according to the camera trajectory $\\Gamma(t)$ .", + "bbox": [ + 76, + 398, + 468, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by ESIM [40], we adopt an adaptive sampling strategy to sample camera locations from the camera trajectory for interval $t_i$ to $t_j$ , so that the largest displacement of all pixels between two successive rendered frames $(I(\\pmb{u},\\tau_k), I(\\pmb{u},\\tau_{k + 1}))$ is under 1 pixel, we define the sampling time interval $\\Delta \\tau_{k}$ as follows:", + "bbox": [ + 76, + 550, + 468, + 642 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Delta \\tau_ {k} = \\tau_ {k + 1} - \\tau_ {k} \\\\ = \\left(\\max _ {\\boldsymbol {u}} \\max \\left\\{\\left\\| \\boldsymbol {F} _ {\\tau_ {k - 1} \\rightarrow \\tau_ {k}} \\right\\|, \\left\\| \\boldsymbol {F} _ {\\tau_ {k} \\rightarrow \\tau_ {k - 1}} \\right\\|\\right\\}\\right) ^ {- 1}, \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 655, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $|F| = \\max_{\\boldsymbol{u}} \\max \\left\\{\\left\\| \\boldsymbol{F}_{\\tau_{k-1} \\to \\tau_k} \\right\\|, \\left\\| \\boldsymbol{F}_{\\tau_k \\to \\tau_{k-1}} \\right\\|\\right\\}$ is the maximum magnitude of the motion field between images $I(\\boldsymbol{u}, \\tau_{k-1})$ and $I(\\boldsymbol{u}, \\tau_k)$ .", + "bbox": [ + 76, + 709, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Event Generation from High-frame-rate Video. Given a high-frame-rate video $\\{I(\\pmb{u},\\tau)\\}$ , $\\tau \\in [t_i,t_j]$ between timestamps $t_i$ and $t_j$ , we next generate event stream by simulating the event trigger mechanism. Similar to [40] and [14], we use linear interpolation to approximate the continuous intensity signal in time for each pixel between video frames. Events $\\{(u_e,t_e,p_e)\\}$ are generated at each pixel $\\pmb{u}_e = (x_e,y_e)$ whenever the magnitude of the change in the", + "bbox": [ + 76, + 779, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "log intensity values $(L(\\pmb{u}_e, t_e) = \\ln(I(\\pmb{u}_e, t_e))$ exceeds the threshold $C$ . This can be expressed as Eq. (2) and Eq. (3):", + "bbox": [ + 498, + 90, + 890, + 122 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, t _ {e} + \\Delta t _ {e}\\right) - L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, t _ {e}\\right) \\geq p _ {e} C, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 137, + 890, + 152 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt _ {e} = t _ {e - 1} + \\Delta \\tau_ {k} \\frac {C}{\\left| L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}} , t _ {e} + \\Delta t _ {e}\\right) - L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}} , t _ {e}\\right) \\right|}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 159, + 890, + 193 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t_{e-1}$ and $t_e$ are the timestamps of the last triggered event and the next triggered event respectively, $p_e \\in \\{-1, +1\\}$ is the polarity of the triggered event. We define it as $E(t_k, t_{k+1})$ , witch is the sequence $\\{(u_e, t_e, p_e)^N, e \\in [0, N]\\}$ with $N$ events between time $t_k$ and $t_{k+1}$ .", + "bbox": [ + 500, + 198, + 890, + 273 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-Density Rendered Events Dataset. Using the above data generation method, we can generate data with different event densities by using different threshold values $C$ . Since event stream is commonly first transformed into event representation [56, 42, 17] and then fed into deep networks. In order to measure the amount of useful information carried by the event stream, we propose to calculate the density of the event stream using the percentage of valid pixels (pixels where at least one event is triggered) in the voxel representation:", + "bbox": [ + 498, + 292, + 892, + 445 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV (\\boldsymbol {u} _ {\\boldsymbol {e}}, b) = \\sum_ {e = 0} ^ {N} p _ {e} \\max (0, 1 - | b - \\frac {t _ {e} - t _ {0}}{t _ {N} - t _ {0}} (B - 1) |), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 455, + 890, + 497 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD = \\frac {1}{H W} \\sum_ {e = 1} ^ {N} \\varepsilon \\left(\\sum_ {b = 0} ^ {B - 1} | V \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, b\\right) |\\right), \\varepsilon (x) = \\left\\{ \\begin{array}{l} 1, x > 0 \\\\ 0, x \\leq 0 \\end{array} , \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 510, + 890, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V(\\boldsymbol{u}_e) \\in \\mathbb{R}^{B \\times H \\times W}$ is the voxel representation [56] of the event stream $\\{(u_e, t_e, p_e)^N\\}$ between $t_0$ and $t_N$ , $b \\in [0, B - 1]$ indicates the temporal index, $B$ (typically set to 5) donates temporal bins and $D$ is the density of the input event representation $V$ . The notation $|\\cdot|$ denotes the absolute value operation. In practical applications, different event cameras may use different threshold values in different scenes, resulting in data with different event densities. Intuitively, event data with lower density is more difficult for optical flow estimation. In order to train models that can cover event data with various densities, in this paper, we propose to adaptively normalize the density of the input events to a certain density representation for optical flow estimation, so as to increase the generalization ability of the network.", + "bbox": [ + 498, + 564, + 892, + 790 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Event-based Optical Flow Estimation", + "text_level": 1, + "bbox": [ + 500, + 801, + 823, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Event-based optical flow estimation involves predicting dense optical flow $\\pmb{F}_{k-1\\rightarrow k}$ from consecutive event sequences $E(t_{k-1},t_k)$ and $E(t_k,t_{k+1})$ . In this paper, we find that networks perform better on event sequences with appropriate density than on those with excessively sparse or", + "bbox": [ + 498, + 825, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9850", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8ef6290d423be3198bf4fef6f56c6d2ac335e93d6a3677391682bb7a48632e1c.jpg", + "image_caption": [ + "Figure 4: The structure of the proposed network. We design a plug-and-play Adaptive Density Module (ADM) to transform input event representations $V_{1}$ and $V_{2}$ into $V_{1}^{\\mathrm{ad}}$ and $V_{2}^{\\mathrm{ad}}$ with suitable density for optical flow estimation." + ], + "image_footnote": [], + "bbox": [ + 78, + 85, + 472, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "dense events, when given events from the same scene. Motivated by this, we propose a plug-and-play Adaptive Density Module (ADM) that normalizes the input event stream to a density suited for estimating optical flow. Our network architecture is shown in Fig. 4, where the ADM transforms input event representations $V_{1}$ and $V_{2}$ to justified event representations $V_{1}^{\\mathrm{ad}}$ and $V_{2}^{\\mathrm{ad}}$ , which are then used by an existing network structure to estimate optical flow.", + "bbox": [ + 75, + 306, + 472, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adaptive Density Module. As shown in Fig. 4, our ADM module consists of two sub-modules: the multi-density changer (MDC) module and the multi-density selector (MDS) module. The MDC module globally adjusts the density of the input event representations from multi-scale features, then the MDS module picks the best pixel-wise density for optical flow estimation.", + "bbox": [ + 75, + 468, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The MDC module adopts an encoder-decoder architecture with three levels, as illustrated in Fig. 5(a). To generate multiscale transformed representations $V_{3}^{\\mathrm{MDC}}$ , $V_{2}^{\\mathrm{MDC}}$ and $V_{1}^{\\mathrm{MDC}}$ (also noted as $V_{\\mathrm{out}}^{\\mathrm{MDC}}$ ) from the concatenated input event representations $V$ , three encoding blocks are employed to extract multiple scale features, followed by three decoding blocks and two feature fusion blocks. It is worth noting that, to ensure the lightweightness of the entire module, we utilize only two $3 \\times 3$ and one $1 \\times 1$ convolutional layers in each encoding and decoding block.", + "bbox": [ + 75, + 579, + 468, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To maintain the information in the input event representation and achieve density transformation, we adopt the MDS module for adaptive selection and fusion of $V_{\\mathrm{out}}^{\\mathrm{MDC}}$ and $V$ , as depicted in Fig. 5(b). We first concatenate $V_{\\mathrm{out}}^{\\mathrm{MDC}}$ and $V$ , and then use two convolutional layers to compare them and generate selection weights via softmax. Finally, we employ the selection weights to identify and fuse $V_{\\mathrm{out}}^{\\mathrm{MDC}}$ and $V$ , producing the transformed event representation $V_1^{\\mathrm{ad}}$ and $V_2^{\\mathrm{ad}}$ , which are fed into an existing flow network for optical flow estimation. In this paper, we use KPA-Flow [32] for optical flow estimation by default.", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5e86666ebce5795b0da86a7dd9eca3a123bb67ea6997dfc8f02d65ee26b9b857.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 542, + 88, + 851, + 189 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e8f9a4fefd4636ec05e286fdac2f152470ebfd90f931898bea8830c5fe8f553f.jpg", + "image_caption": [ + "Figure 5: The detailed structure of sub-modules used in our proposed ADM model: (a) MDC, (b) MDS." + ], + "image_footnote": [], + "bbox": [ + 540, + 193, + 851, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss Function. Based on our MDR dataset, we use the event representation with a moderate density as the ground truth (noted as $V^{\\mathrm{GT}}$ ) to train our ADM module. For the MDC module, we use a multi-scale loss as follows:", + "bbox": [ + 498, + 383, + 892, + 444 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {M D C}} = \\sum_ {k = 1} ^ {3} \\sqrt {\\left(V _ {k} ^ {\\mathrm {M D C}} - V _ {k} ^ {\\mathrm {G T}}\\right) ^ {2} + \\xi^ {2}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 453, + 890, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\xi = 10^{-3}$ is a constant value, $V_{k}^{\\mathrm{MDC}}$ is the output of the $k$ -th level in MDC, and $V_{k}^{\\mathrm{GT}}$ is downsampled from $V^{\\mathrm{GT}}$ to match the spatial size.", + "bbox": [ + 498, + 505, + 890, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the MDS module, we use the distance between the density of $V^{\\mathrm{ad}}$ and $V^{\\mathrm{GT}}$ as the guidance:", + "bbox": [ + 498, + 551, + 890, + 582 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {M D S}} = \\left\\| D \\left(V ^ {\\mathrm {a d}}\\right) - D \\left(V ^ {\\mathrm {G T}}\\right) \\right\\| _ {1}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 590, + 890, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D$ means to calculate the density as in Eq. (5).", + "bbox": [ + 500, + 619, + 849, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the flow network, we use L1 loss (denoted as $L_{\\mathrm{Flow}}$ ) between flow prediction and ground truth as the guidance.", + "bbox": [ + 498, + 635, + 890, + 665 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final loss function for training the whole pipeline in Fig. 4 is determined as follows:", + "bbox": [ + 498, + 665, + 890, + 695 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {t o t a l}} = \\lambda_ {1} L _ {\\mathrm {M D C}} + \\lambda_ {2} L _ {\\mathrm {M D S}} + L _ {\\text {F l o w}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 707, + 890, + 723 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we empirically set $\\lambda_{1} = 0.1$ and $\\lambda_{2} = 10$ .", + "bbox": [ + 500, + 733, + 821, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 762, + 632, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 787, + 601, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MDR: We create the MDR dataset using the graphics engine blender. We use various 3D scenes for data generation. There are 80,000 training samples and 6,000 validation samples with accurate dense optical flow ground truth. Each sample has event sequences with different densities produced by using different thresholds $C$ . By default, for", + "bbox": [ + 498, + 809, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9851", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/72403dcda3ce95ff0798d31a88f6f7d83179b2633157a0c85a5009aaf2e11547.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method (dt=1)Train D.TypeTrain D.Setindoor flying1indoor flying2indoor flying3outdoor day1Avg
EPE%OutEPE%OutEPE%OutEPE%OutEPE%Out
ESTS[15]EM0.970.911.388.201.436.47--1.265.19
EV-FlownetS[54]I1,I2,EM1.032.201.7215.11.5311.90.490.201.197.35
Deng et al.S[10]EM0.890.661.316.441.133.53--1.113.54
Paredes et al.S[39]EM0.791.201.4010.91.187.400.925.401.076.22
Matrix-LSTMS[6]I1,I2,EM0.820.531.195.591.084.81--1.033.64
LIF-EV-FlowNetS[18]EFPV0.711.411.4412.81.169.110.530.330.965.90
Spike-FlowNetS[27]I1,I2,EM0.84-1.28-1.11-0.49-0.93-
Fusion-FlowNetD[26]I1,I2,EM0.62-0.89-0.85-1.02-0.84-
Fusion-FlowNetS[26]I1,I2,EM0.56-0.95-0.76-0.59-0.71-
E-RAFTD[17]EM1.105.721.549.791.368.240.270.001.075.94
E-RAFTS[17]EM0.871.321.136.201.034.700.240.000.823.06
Zhu et al.S[56]EM0.580.001.024.000.873.000.320.000.691.75
DCEIFlowD[50]I1,I2,EM0.560.280.640.160.570.120.910.710.670.31
DCEIFlowS[50]I1,I2,EC20.570.300.700.300.580.150.740.290.640.26
Stoffregen et al.S[42]EESIM0.561.000.661.000.591.000.680.990.620.99
STE-FlowNetS[11]I1,I2,EM0.570.100.791.600.721.300.420.000.620.75
ADM-FlowD(ours)EMDR0.480.110.560.400.470.020.520.000.510.14
ADM-FlowS(ours)EMDR0.520.140.681.180.520.040.410.000.530.34
Method (dt=4)Train D.TypeTrain D.Setindoor flying1indoor flying2indoor flying3outdoor day1Avg
EPE%OutEPE%OutEPE%OutEPE%OutEPE%Out
LIF-EV-FlowNetS[18]EFPV2.6329.64.9351.13.8841.52.0218.93.3635.3
EV-FlownetS[54]I1,I2,EM2.2524.74.0545.33.4539.71.237.302.7429.3
E-RAFTD[17]EM3.2635.44.3248.64.1448.20.841.703.1433.5
E-RAFTS[17]EM2.8130.63.9940.93.7840.50.721.122.8328.3
Zhu et al.S[56]EM2.1824.23.8546.83.1847.81.309.702.6232.1
Spike-FlowNetS[27]I1,I2,EM2.24-3.83-3.18-1.09-2.58-
Fusion-FlowNetD[26]I1,I2,EM1.81-2.90-2.46-3.06-2.55-
Fusion-FlowNetS[26]I1,I2,EM1.68-3.24-2.43-1.17-2.13-
STE-FlowNetS[11]I1,I2,EM1.7714.72.5226.12.2322.10.993.901.8716.7
DCEIFlowD[50]I1,I2,EC21.498.141.9717.41.6912.31.8719.11.7514.2
DCEIFlowS[50]I1,I2,EC21.528.792.2122.11.7413.31.378.541.7113.2
ADM-FlowD(ours)EMDR1.397.331.6311.51.519.341.9119.21.6111.8
ADM-FlowS(ours)EMDR1.427.781.8816.71.6111.41.5110.21.6011.5
", + "bbox": [ + 122, + 87, + 854, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Quantitative comparison of our method with previous methods on the MVSEC dataset [55]. Subscripts $S$ and $D$ donate the sparse and dense evaluation, respectively. We mark the best results in red and the second best results in blue.", + "bbox": [ + 75, + 553, + 893, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "training on MDR, we use the combination of all these samples with different densities to train flow networks. For the learning of our ADM module, we choose events with density between 0.45 and 0.55 as the label for $L_{\\mathrm{MDC}}$ and $L_{\\mathrm{MDS}}$ .", + "bbox": [ + 75, + 611, + 468, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MVSEC: The MVSEC dataset [55] is a real-world dataset collected in indoor and outdoor scenarios with sparse optical flow labels. As a common setting, 28, 542 data pairs of the 'outdoor day2' sequence are used as the train set, and 8, 410 data pairs of the other sequences are used as the validation set. The density ranges of MVSEC train set and validation set are [0.0003, 0.47] and [0.001, 0.31], respectively. DSEC: The DSEC dataset [16] is also collected using actual event cameras and lidar sensors on outdoor scenes. The dataset consists of 7,800 training samples and 2,100 test samples, divided into 24 sequences that include both day and night scenarios.", + "bbox": [ + 75, + 686, + 468, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Previous methods have trained on other datasets, including synthetic datasets like C2 [50] and ESIM [42], as well", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "as real-world captured datasets such as FPV [9]. To assess the performance of these methods, comparisons are made on the validation set of the MVSEC dataset. Both MVSEC and MDR datasets have two input settings for training and testing. These settings involve using the events between successive images within a time interval of $dt = 1$ and $dt = 4$ . On the other hand, for the DSEC dataset, there is a public benchmark available specifically designed to evaluate flow networks. However, this benchmark only provides one input setting for testing. We denote MVSEC, DSEC, and MDR datasets by \"M\", \"D\", and \"MDR\".", + "bbox": [ + 496, + 611, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 786, + 714, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use PyTorch to implement our method and train all networks using the same setting. The networks are trained with the AdamW optimizer, with a batch size of 6 and learning rate of $4 \\times 10^{-4}$ for 150k iterations. Since the MVSEC dataset lacks multiple density event streams required for the learning of our ADM module, we disable $L_{\\mathrm{MDC}}$ and $L_{\\mathrm{MDS}}$", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9852", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "when training on the MVSEC dataset.", + "bbox": [ + 76, + 90, + 331, + 104 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Evaluation metrics", + "text_level": 1, + "bbox": [ + 76, + 114, + 259, + 128 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The evaluation metrics used in flow prediction models are the average End-point Error (EPE) and 1PE, 2PE, and 3PE (the percentage of pixels with EPE greater than 1,2,3 pixels) for DSEC dataset, and $\\% \\text{Out}$ (the percentage of points with EPE greater than 3 pixels and $5\\%$ of the ground truth flow magnitude) for MVSEC dataset. There are two types of evaluations: dense and sparse. In emphdense evaluation, errors are calculated only at pixels with valid flow annotations. Sparse evaluation focuses on pixels with valid flow annotations that have triggered at least one event. Experiments are performed on both MVSEC and MDR, considering both dense and sparse evaluations. However, only dense dense is conducted for DSEC.", + "bbox": [ + 75, + 138, + 470, + 333 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison with State-of-the-Arts", + "text_level": 1, + "bbox": [ + 76, + 343, + 382, + 358 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on MVSEC. In Table 1, we compare our model trained on the MDR train set with previous methods on the MVSEC evaluation set, and report detailed results for each sequence. We provide information on the data types (Train D.Type) and the training sets (Train D.Set) used in the training process for each method. Specifically, $\\mathrm{I}_1,\\mathrm{I}_2,\\mathrm{E}$ indicates that both image data and event data are used in the training and inference processes of the model, while $\\mathrm{E}$ indicates that only event data is used. As shown in Table 1, our model trained on the MDR dataset achieves state-of-the-art performance for both EPE and %Out metrics in settings of $dt = 1$ and $dt = 4$ . Notably, our method demonstrates a $23.9\\%$ improvement (reducing EPE from 0.67 to 0.51) for dense optical flow estimation in $dt = 1$ settings, and an $8.0\\%$ improvement (reducing EPE from 1.75 to 1.61) in $dt = 4$ settings, surpassing previous methods. Qualitative comparison results are shown in row 1 and row 2 in Fig. 6.", + "bbox": [ + 75, + 364, + 468, + 623 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on MDR. In Table 3, we compare our method with previous methods for training on the MVSEC dataset and testing on the MDR dataset for cross-training and validation to avoid over-fitting. We use different thresholds $C$ to generate test data with different density ranges for evaluation. For the average EPE error of dense optical flow estimation, our model obtains the best result, which is a $17.1\\%$ improvement (reducing EPE from 0.82 to 0.68) in $dt = 1$ settings, and a $16.7\\%$ improvement (reducing EPE from 1.98 to 1.65) in $dt = 4$ settings. We also show some qualitative comparison results in row 3 and row 4 in Fig. 6.", + "bbox": [ + 75, + 641, + 468, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on DSEC. In Table 2, we report the results on the DSEC test set for different models that are trained on DSEC, MDR, and a combination of DSEC and MDR. As can be seen, MDR-trained models produce comparable results to in-domain learned models on the DSEC train set.", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/23866c48e0451f3963796d0c3da62ab5d00acf7b51206d2b25ca1f0f58bddf40.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsTrain D.Set1PE2PE3PEEPE
EV-FlowNet [54]D55.1328.4316.712.22
MDR42.5224.4016.321.86
D+MDR35.0615.417.841.31
E-RAFT [17]D16.196.223.590.90*
MDR18.857.444.371.00
D+MDR13.165.192.930.82
ADM-EVFLOWD42.8925.2115.801.90
MDR40.0214.8812.341.67
M+D23.4610.325.611.12
ADM-Flow(ours)D13.965.323.180.88
MDR14.535.783.590.92
D+MDR12.524.672.650.78
", + "bbox": [ + 527, + 88, + 870, + 280 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2: Results on the DSEC test set. * denotes our reproduced results of E-RAFT, since the official training code is not released. All experiments are conducted on the same training code for fair comparison.", + "bbox": [ + 498, + 292, + 890, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Moreover, training E-RAFT on the combined DSEC/MDR datasets yields improved performance, demonstrating the effectiveness of MDR. Our ADMFlow model achieves improved performance on all training datasets, highlighting the effectiveness and versatility of ADM. Some qualitative results are shown in Fig. 7.", + "bbox": [ + 498, + 369, + 890, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of the MDR dataset. To demonstrate the effectiveness of our proposed MDR dataset, we train several optical flow networks [46, 17, 53, 21, 47, 24, 32] on both MDR and MVSEC train sets using identical training settings. For training, we use a combination of data samples from the MDR dataset with a density range of $[0.09, 0.69]$ . We evaluate the trained networks on the MVSEC validation set, and the results, presented in Table 4, demonstrate that all networks trained on the MDR dataset outperform those trained on the MVSEC dataset.", + "bbox": [ + 498, + 484, + 890, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation study.", + "text_level": 1, + "bbox": [ + 500, + 650, + 653, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training with different densities. We examine the impact of input event sequence density on optical flow learning, as our MDR dataset contains event data with various densities and corresponding dense flow labels. We train SKFlow [47], GMA [24], FlowFormer [21] and KPA-Flow [32] on the same sequence from our MDR dataset but with different average densities produced by using different threshold $C$ , and then test them on the MVSEC dataset. Figure 8 shows the results in $dt = 4$ setting, indicating that these models perform better as the average density of the training set increases. However, their performance diminishes as the average density continues to increase. This phenomenon highlights the importance of selecting an appropriate density for the training set when learning event optical flow.", + "bbox": [ + 498, + 674, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9853", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eec76298cb8ce9e99f1d56987f432fe6724c9964a22ba380cecef7c05115131e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 90, + 194, + 179 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c75a4a3623d6d38d3ccd146bf30e6911b0f7716abecd25bd47ebad58071edb6b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 179, + 196, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/867ee07d161f9f6d0f39fce22012e403c50163148d8fc8ab3da1c250bb94ad00.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 268, + 194, + 356 + ], + "page_idx": 7 + }, + { + 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"images/40e1af0ef9b2d2d9d293b6dc961d943600072ce4ab8e251d2b5b112508e25bd6.jpg", + "image_caption": [ + "Flow GT" + ], + "image_footnote": [], + "bbox": [ + 777, + 358, + 888, + 444 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/00b84c01d3c253304cc90251ebb8b60c4298dd9b7dc59711f9f87aaaa26e50b1.jpg", + "image_caption": [ + "Figure 6: Qualitative comparisons compared with existing event-based methods. Row 1 and 2 are from MVSEC, whereas row 3 and 4 are from MDR. Row 1 and 3 visualize the dense predictions, whereas row 2 and 4 show the sparse." + ], + "image_footnote": [], + "bbox": [ + 81, + 529, + 174, + 584 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e7cb227cfd6749a4c76a198fad6fb240d5a2c117cdc4d1ea60c1d628faebc853.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 585, + 174, + 643 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fd4d902a07689865201ffa84cca5911d860af004debee851a37ec18aea95f8ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 647, + 174, + 704 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cc893ce19b7e4238a0504f7c688ebc1ec0f84cd9ba5740805e771dc5d03181ad.jpg", + "image_caption": [ + "Reference", + "Figure 7: Qualitative comparisons on the DSEC test set. We visualize the dense predictions and zoom in the areas where are apparent differences." + ], + "image_footnote": [], + "bbox": [ + 80, + 707, + 174, + 763 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f8237b7f8787cba75550e39d90c9aa956cfc1a74a80b29173e7a19328b3d16fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 178, + 529, + 272, + 585 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/55972bd97326c651f12e5203825048dcd719eeac555d60e9fae2f88634a08b3d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 178, + 587, + 272, + 643 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8a7a584c8ac1dfd47059eb8fb54dd0dbc5ba0b118f288da0fdcb8e6f8afa6dbe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 176, + 647, + 271, + 705 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cb889c57b08640b6dd8af3266fa0bddb331428b32189c9eaa7788fd2516297cf.jpg", + "image_caption": [ + "EV-Flownet" + ], + "image_footnote": [], + "bbox": [ + 176, + 707, + 271, + 763 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0474f06f204470057c274df77e0d0099cbcb2c8be392758768a14527075df01e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 529, + 369, + 585 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e6b86744587cfebf203d6565b285d1c37dffd7d7da52a51d6b40536e90d35c57.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 587, + 370, + 643 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d5fa74db9b7ed0ea2e7e8cc2c2b136d6f57691f865eb43a7393d2a33b5778576.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 647, + 370, + 705 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2877d5edc44e0474d1c2e9c75ee631bf90d96f102da73f1816a36f85b5f1c0f6.jpg", + "image_caption": [ + "E-RAFT" + ], + "image_footnote": [], + "bbox": [ + 274, + 707, + 370, + 763 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d34f5d349c91573b6ac51570436b9cd3d096fe3cf24b46d2e7e70873cba5bb57.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 529, + 467, + 585 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f00c81039c8f7621386d8d7a757fbee6a6becd9ae5b4058151ac53a8d77354c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 587, + 467, + 705 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/56e04cfb9c39a627c0ebdc1194d550e317a78704b8da60de836937f603111358.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 372, + 707, + 467, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation for ADM. In order to verify the impact of our proposed ADM module, we conduct ablation experiments by plugging the ADM module into several optical flow net", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/05b7d5ad1e382ff2e3f6e2cfff95331b90e419a942ee95d93c9882ea38693b31.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method (dt = 1)density rangeAvg
0.09-0.240.24-0.390.39-0.540.54-0.69
Spike-FlowS [27]1.931.201.332.011.62
STE-FlowS [11]1.171.110.821.301.10
DCEIFlowD [50]1.281.371.271.461.35
DCEIFlowS [50]1.000.840.750.820.85
E-RAFTD [17]0.930.740.690.920.82
E-RAFTS [17]0.820.650.660.820.74
ADM-FlowD(ours)0.770.690.500.740.68
ADM-FlowS(ours)0.690.640.490.740.64
Method (dt = 4)density rangeAvg
0.09-0.240.24-0.390.39-0.540.54-0.69
Spike-FlowS [27]3.951.962.092.872.72
STE-FlowS [11]2.902.271.982.172.33
DCEIFlowD [50]3.842.682.994.273.45
DCEIFlowS [50]2.251.321.192.341.78
E-RAFTD [17]2.641.421.352.511.98
E-RAFTS [17]2.181.311.242.291.76
ADM-FlowD(ours)2.121.201.242.021.65
ADM-FlowS(ours)2.031.131.091.901.54
", + "bbox": [ + 504, + 527, + 890, + 741 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3: Quantitative evaluation on our MDR dataset. The methods in the table are all trained on the MVSEC dataset for cross-training and validation to avoid over-fitting. $S$ and $D$ donate the sparse and dense evaluation, respectively. We use EPE as the evaluation metric.", + "bbox": [ + 498, + 752, + 893, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "works to selectively adjust the densities of the input events. We train these networks on both MDR and MVSEC datasets with the same setting except that the ADM module is dis", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9854", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0b665a556ada9c1b8df07f57f91c1410332dcb864ed3deafe47c9fa00c76f57e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTrain D.Setdt = 1dt = 4
EPE%OutEPE%Out
PWCNet [22]M1.255.414.0351.48
MDR1.143.482.9238.62
RAFT [48]M1.194.903.3339.78
MDR0.590.512.5730.24
GMFlowNet [53]M1.003.753.6142.31
MDR0.821.662.7031.53
FlowFromer [21]M0.873.083.3841.04
MDR0.610.402.4928.83
SKFlow [47]M1.073.973.4140.87
MDR0.590.332.4627.64
GMA [24]M0.884.052.9934.80
MDR0.580.442.1923.00
KPAFlow [32]M0.862.863.1938.32
MDR0.580.392.3326.10
", + "bbox": [ + 83, + 88, + 465, + 280 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/bd3e3ec1bc8fec642a749147c11697f06687a3b93bdf86b0eecf264e87214c5b.jpg", + "image_caption": [ + "Figure 8: The performance of some supervised optical flow networks with different densities of the training set in $dt = 4$ setting. X-axis is the average density of events in the training set, and y-axis is their average EPE on MVSEC validation set. Different colors represent the performance of different networks, and the pentagons show the performance of networks trained on the MDR training set with a widely density range of [0.09, 0.69], and the average density is 0.41." + ], + "image_footnote": [], + "bbox": [ + 81, + 352, + 460, + 486 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "abled or not, and test them on the MVSEC dataset. The experiment results are shown in Table 5, where we can notice that our ADM module can bring performance improvement for all supervised methods.", + "bbox": [ + 75, + 662, + 468, + 724 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Ablation for the design of ADM. We conduct ablation experiments to verify the effectiveness of each component in our ADM module, including MDC, MDS, and the two training loss functions $L_{\\mathrm{MDC}}$ and $L_{\\mathrm{MDS}}$ . We train models using the same settings on the MDR dataset and evaluate them on the MVSEC dataset to show the individual impact of each component in our ADM module. The results are presented in Table 6. The comparison of (a)&(b) shows that adding only the MDC plugin results in a slight performance gain. Comparison of (b)&(c) reveals that en", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/f2d24c7a52eccfb3c28b6f6f6a9baae146646b85c5ce6d6954fe2d8b6227543c.jpg", + "table_caption": [ + "Table 4: Comparison of training on MVSEC vs. MDR. Models are evaluated on MVSEC for dense optical flow estimation." + ], + "table_footnote": [], + "table_body": "
MethodM(dt = 1)MDR(dt = 1)M(dt = 4)MDR(dt = 4)
EPE%OutEPE%OutEPE%OutEPE%Out
PWCNet [22]1.255.411.143.484.0351.482.9238.62
ADM-PWCNet1.074.520.761.482.9533.311.9418.74
RAFT [48]1.194.900.590.513.3339.782.5730.24
ADM-RAFT0.823.030.560.242.7330.911.7213.83
GMFlowNet [53]1.003.750.821.663.6142.312.7031.53
ADM-GMFlowNet0.873.050.580.322.7831.261.8114.45
FlowFromer [21]0.873.080.610.403.3841.042.4928.83
ADM-FlowFromer0.782.870.530.152.5626.571.6712.78
SKFlow [47]1.073.970.590.333.4140.872.4627.64
ADM-SKFlow0.843.180.530.142.6728.171.6912.61
GMA [24]0.884.050.580.442.9934.802.1923.00
ADM-GMA0.762.650.540.222.4525.751.6311.95
KPAFlow [32]0.862.860.580.393.1938.322.3326.10
ADM-KPAFlow0.802.670.510.142.5928.421.6111.83
", + "bbox": [ + 506, + 88, + 888, + 250 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/f9734e374486e05f299880ff75c26ec3af1d2d9c8d6de6a0ec9f285336626da0.jpg", + "table_caption": [ + "Table 5: Quantitative comparison of whether using ADM. Models are trained on MVSEC and MDR, and evaluated on MVSEC for dense optical flow estimation in $dt = 1$ and $dt = 4$ settings." + ], + "table_footnote": [], + "table_body": "
MethodMDCMDSLMDCLMDSParam. (M)dt = 1dt = 4
EPE%OutEPE%Out
(a)××××6.010.580.392.3326.10
(b)✓×××7.710.570.332.2023.78
(c)✓✓××7.720.540.261.9218.26
(d)✓✓✓×7.720.520.161.6613.29
(e)✓✓✓✓7.720.510.141.6111.83
", + "bbox": [ + 504, + 337, + 888, + 412 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 6: Ablation study. Models are trained on the MDR training set, and evaluated on the MVSEC validation set for dense optical flow estimation in $dt = 1$ and $dt = 4$ settings.", + "bbox": [ + 498, + 422, + 890, + 469 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "abling the density selection function through the MDS module brings a significant improvement. Comparing (c)&(d) and (d)&(e), we notice that with the guidance of two loss functions, ADM can learn to selectively choose the best density for optical flow estimation, resulting in a relatively significant improvement.", + "bbox": [ + 498, + 496, + 890, + 587 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 602, + 617, + 618 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this work, we have created a rendered dataset for event-flow learning. Indoor and outdoor virtual scenes have been created using Blender with rich scene contents. Various camera motions are placed for the capturing of the virtual world, which can produce frames as well as accurate flow labels. The event values are generated by rendering high frame rate videos between two frames. In this way, the flow labels and event values are physically correct and accurate. The rendered dataset can adjust density of events by modifying the event trigger threshold. We have introduced a novel adaptive density module (ADM), which has shown its effectiveness by plugin into various event-flow pipelines. When trained on our dataset, previous approaches can improve their performances constantly.", + "bbox": [ + 496, + 628, + 890, + 839 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements This work was supported by Sichuan Science and Technology Program of China under grants Nos. 2023NSFSC0462, 2023NSFSC1972, 2021YFG0001, 2022YFG0011 and 2022YFG0050.", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "9855", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ryad Benosman, Sio-Hoi Ieng, Charles Clercq, Chiara Bartolozzi, and Mandyam Srinivasan. 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Learning dense and continuous optical flow from an event camera. IEEE Trans. on Image Processing, 2022. 1, 2, 3, 6, 8", + "[51] Haofei Xu, Jing Zhang, Jianfei Cai, Hamid Rezatofighi, and Dacheng Tao. Gmflow: Learning optical flow via global matching. In Proc. CVPR, 2022. 2", + "[52] Rui Xu, Xiaoxiao Li, Bolei Zhou, and Chen Change Loy. Deep flow-guided video inpainting. In Proc. CVPR, 2019. 1", + "[53] Shiyu Zhao, Long Zhao, Zhixing Zhang, Enyu Zhou, and Dimitris Metaxas. Global matching with overlapping attention for optical flow estimation. In Proc. CVPR, 2022. 7, 9", + "[54] Alex Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. Ev-flownet: Self-supervised optical flow estimation for event-based cameras. In Proceedings of Robotics: Science and Systems, 2018. 1, 2, 3, 6, 7", + "[55] Alex Zihao Zhu, Dinesh Thakur, Tolga Özaslan, Bernd Pfrommer, Vijay Kumar, and Kostas Daniilidis. The multivehicle stereo event camera dataset: An event camera dataset for 3d perception. IEEE Robotics and Automation Letters, 2018. 1, 2, 3, 6", + "[56] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. Unsupervised event-based learning of optical flow, depth, and egomotion. In Proc. CVPR, 2019. 4, 6" + ], + "bbox": [ + 501, + 92, + 890, + 502 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "9857", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Optical Flow from Event Camera with Rendered Dataset/9da70e78-d6a8-4bda-bae6-2f6d222d7409_model.json b/2023/Learning Optical Flow from Event Camera with Rendered Dataset/9da70e78-d6a8-4bda-bae6-2f6d222d7409_model.json new file mode 100644 index 0000000000000000000000000000000000000000..296a9ec8b130e8ec5f3a968f4ffedb994ac8eb36 --- /dev/null +++ b/2023/Learning Optical Flow from Event Camera with Rendered Dataset/9da70e78-d6a8-4bda-bae6-2f6d222d7409_model.json @@ -0,0 +1,2906 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.149, + 0.131, + 0.823, + 0.154 + ], + "angle": 0, + "content": "Learning Optical Flow from Event Camera with Rendered Dataset" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.192, + 0.871, + 0.213 + ], + "angle": 0, + "content": "Xinglong Luo\\(^{1,3}\\), Kunming Luo\\(^{2}\\), Ao Luo\\(^{3}\\), Zhengning Wang\\(^{1}\\), Ping Tan\\(^{2}\\), and Shuaicheng Liu\\(^{1,3*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.162, + 0.223, + 0.808, + 0.287 + ], + "angle": 0, + "content": "1University of Electronic Science and Technology of China \n2The Hong Kong University of Science and Technology 3Megvii Technology {luoboom@std.,zhengning.wang@,liushuaicheng}@uestc.edu.cn {kluoad@connect,pingtan@}.ust.hk luoao02@megvii.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.332, + 0.314, + 0.348 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.474, + 0.742 + ], + "angle": 0, + "content": "We study the problem of estimating optical flow from event cameras. One important issue is how to build a high-quality event-flow dataset with accurate event values and flow labels. Previous datasets are created by either capturing real scenes by event cameras or synthesizing from images with pasted foreground objects. The former case can produce real event values but with calculated flow labels, which are sparse and inaccurate. The latter case can generate dense flow labels but the interpolated events are prone to errors. In this work, we propose to render a physically correct event-flow dataset using computer graphics models. In particular, we first create indoor and outdoor 3D scenes by Blender with rich scene content variations. Second, diverse camera motions are included for the virtual capturing, producing images and accurate flow labels. Third, we render high-framerate videos between images for accurate events. The rendered dataset can adjust the density of events, based on which we further introduce an adaptive density module (ADM). Experiments show that our proposed dataset can facilitate event-flow learning, whereas previous approaches when trained on our dataset can improve their performances constantly by a relatively large margin. In addition, event-flow pipelines when equipped with our ADM can further improve performances. Our code is available at https://github.com/boomluo02/ADMFlow." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.773, + 0.21, + 0.789 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.8, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Event cameras [29] record brightness changes at a varying framerate [4]. When a change is detected in a pixel, the camera returns an event in the form \\( e = (x,y,t,p) \\) immediately, where \\( x,y \\) stands for the spatial location, \\( t \\) refers to the timestamp in microseconds, and \\( p \\) is the polarity of the" + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.356, + 0.525, + 0.371 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.331, + 0.647, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.401, + 0.647, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.332, + 0.768, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.405, + 0.764, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.332, + 0.888, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.403, + 0.888, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.47, + 0.648, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.54, + 0.687, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.61, + 0.612, + 0.622 + ], + "angle": 0, + "content": "Images" + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.47, + 0.77, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.54, + 0.772, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.61, + 0.732, + 0.621 + ], + "angle": 0, + "content": "Events" + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.47, + 0.89, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.771, + 0.541, + 0.89, + 0.61 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.61, + 0.857, + 0.621 + ], + "angle": 0, + "content": "Flow GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.634, + 0.894, + 0.74 + ], + "angle": 0, + "content": "Figure 1: (a) the captured dataset from real event camera [55, 54]. (b) the synthesized dataset with flying chairs foreground [50]. (c) the synthesized dataset by moving a foreground image [42]. (d) Our synthesized dataset by graphics rendering, which not only reflects the real motions under correct scene geometries, but also produces accurate dense flow labels and events." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "change, indicating a pixel become brighter or darker. On the other hand, optical flow estimation predicts motions between two frames [44], which is fundamental and important for many applications [49, 52, 7]. In this work, we study the problem of estimating optical flow from event camera data, instead of from RGB frames. Different from traditional images, events are sparse and are often integrated in short intervals as the input for the prediction. As such, early works" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9847" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "can only estimate sparse flows at the location of events [1]. Recent deep methods can estimate dense flows but with the help of images, either as the guidance [54] or as the additional inputs [26, 38]. Here, we tackle a hard version of the problem, where dense flows are predicted based purely on the event values \\( e \\). One key issue is how to create high quality event-based optical flow dataset to train the network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.471, + 0.473 + ], + "angle": 0, + "content": "Existing methods of event flow dataset creation can be classified into two types, 1) directly capturing from real event cameras [55, 54, 16]; 2) moving foregrounds on top of a background image to create synthesized flow motions [50, 42] and apply frame interpolation [14] to create events. For the first type, the ground-truth (GT) flow labels need to be calculated based on gray images acquired along with the event data. However, the optical flow estimations cannot be perfectly accurate [48, 43, 32, 24, 51], leading to the inaccuracy of GT labels. To alleviate the problem, additional depth sensors, such as LIDAR, have been introduced [55]. The flow labels can be calculated accurately when the depth values of LIDAR scans are available. However, LIDAR scans are sparse, and so do the flow labels, which are unfriendly for dense optical flow learning. Fig. 1 (a) shows an example, LIDAR points on the ground are sparse. Moreover, some thin objects are often missing, as indicated by the red box in Fig. 1 (a)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.672 + ], + "angle": 0, + "content": "For the second category, the flow labels are created by moving foreground objects on top of a background image, similar to flying chairs [12] or flying things [36]. In this way, the flow labels are dense and accurate. To create events, intermediate frames are interpolated [23]. However, the frame interpolation is inaccurate due to scene depth disparities, where the occluded pixels cannot be interpolated correctly, leading to erroneous event values in these regions. To match high framerate of events, the large number of interpolated frames makes the problem even worse. Fig. 1 (b) shows an example, where the events are incorrect at the occluded chairs. Moreover, the motions are artificial, further decreasing the realism of the dataset (Fig. 1 (b) and (c))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this work, we create an event-flow dataset from synthetic 3D scenes by graphics rendering (Fig. 1 (d)). While there is a domain gap between rendered and real images, this gap is empirically found insignificant in event camera based classification [41] and segmentation [14] tasks. As noted by these works, models trained on synthetic events work very well for real event data. Because events contain only positive and negative polarities, no image appearances are involved. To this end, we propose a Multi-Density Rendered (MDR) event optical flow dataset, created by Blender on indoor and outdoor scenes with accurate events and flow labels. In addition, we design an Adaptive Density Module (ADM) based on MDR, which can adjust the densities of events, one of the most important factors for event-based tasks but has been largely overlooked." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Specifically, our MDR dataset contains 80,000 samples from 50 virtual scenes. Each data sample is created by first rendering two frames and obtaining the GT flow labels directly from the engine. Then, we render \\(15 \\sim 60\\) frames in between based on the flow magnitude. The events are created by thresholding log intensities and recording the times-stamp for each spatial location. The density of events can be controlled by the threshold values. The ADM is designed as a plugin module, which further consists of two sub-modules, multi-density changer (MDC) and multi-density selector (MDS), where the MDC adjusts the density globally while the MDS picks the best one for every spatial location. Experiments show that previous event-flow methods, when trained on our MDR dataset, can improve their performances. Moreover, we train several recent representative flow pipelines, such as FlowFormer [21], KPA-Flow [32], GMA [24] and SKFlow [47], on our MDR dataset. When equipped with our ADM module, the performances can increase consistently." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.381, + 0.771, + 0.395 + ], + "angle": 0, + "content": "Our contributions are summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.413, + 0.892, + 0.473 + ], + "angle": 0, + "content": "- A rendered event-flow dataset MDR, with 80,000 samples created on 53 virtual scenes, which possess physically correct accurate events and flow label pairs, covering a wide range of densities." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.492, + 0.891, + 0.523 + ], + "angle": 0, + "content": "- An adaptive density module (ADM), which is a plug-and-play module for handling varying event densities." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.542, + 0.892, + 0.601 + ], + "angle": 0, + "content": "- We achieve state-of-the-art performances. Our MDR can improve the quality of previous event-flow methods. Various optical flow pipelines when adapted to the event-flow task, can benefit from our ADM module." + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.413, + 0.892, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.622, + 0.642, + 0.637 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.738, + 0.665 + ], + "angle": 0, + "content": "2.1. Image-based Optical Flow" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Optical flow estimates the per-pixel motion between two frames according to photo consistency. Traditional approaches minimize energies, leveraging both feature similarities and motion smoothness [13]. Deep methods train the networks that take two frames as input and directly output dense flow motions [12, 46]. Recent deep methods design different pipelines [30, 48, 24] as well as learning modules [35, 31, 34, 33] for performance improvements. The training often requires large labeled datasets, which can be synthesized by moving a foreground on top of a background image, such as FlyingChairs [12], and AutoFlow [45], or rendered from graphics such as Sintel [5] and FlyingThings [36], or created directly from real videos [19]. In this work, we use computer graphics techniques to render accurate and physically correct event and flow values." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9848" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.882, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.308, + 0.895, + 0.355 + ], + "angle": 0, + "content": "Figure 2: Our data generation pipeline. Given 3D scenes in the graphics engine, we generate camera trajectories and render high-frame-rate videos with forward and backward optical flow labels. Then, we build the event optical flow dataset by generating events using the videos." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.379, + 0.313, + 0.396 + ], + "angle": 0, + "content": "2.2. Event-based Optical Flow" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.473, + 0.675 + ], + "angle": 0, + "content": "Benosman et al. [1] first proposed to estimate optical flow from events, which can only estimate sparse flows at the location of event values. Recent deep methods can estimate dense optical flows. EV-FlowNet [54] learns the event and flow labels in a self-supervised manner, which minimizes the photometric distances of grey images acquired by DAVIS [4]. Different event representations were explored, e.g., EST [15] and Matrix-LSTM [6], with various network structures, such as SpikeFlowNet [27], LIF-EV-FlowNet [18], STE-FlowNet [11], Li et al. [28], and E-RAFT [17]. Some works take both events and images as input for the flow estimation [26, 38]. In general, dense flows are more desirable than sparse ones but are more difficult to train. Normally, regions with events can produce more accurate flows than empty regions where no events are triggered. Moreover, supervised training can produce better results than unsupervised ones, as long as the training dataset can provide sufficient event-flow guidance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.682, + 0.221, + 0.696 + ], + "angle": 0, + "content": "2.3.Event Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The applications to the event camera dataset were first explored in the context of classification [37, 2]. Early works generate events simply by applying a threshold on the image difference [25]. Frame interpolation is often adopted for high framerate [14]. The synthesized events often contain inaccurate timestamps. The DAVIS event camera can directly capture both images and events [4], based on which two driving datasets are captured, DDD17 [3] and MVSEC [55]. With respect to the event flow dataset, EV-Flownet [54] calculated sparse flow labels from LIDAR depth based on MVSEC [55]. Wan et al. [50] and Stoffregen et al. [42] created the foreground motions and interpolated the intermediate frames for events. The real captured" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.38, + 0.892, + 0.426 + ], + "angle": 0, + "content": "dataset can only provide sparse labels while the synthesized ones contain inaccurate events. In this work, we propose to render a physically correct event dense flow dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.441, + 0.593, + 0.457 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.813, + 0.484 + ], + "angle": 0, + "content": "3.1. The event-based optical flow dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.658 + ], + "angle": 0, + "content": "In order to create a realistic event dataset for optical flow learning, we propose to employ a graphics engine with 3D scenes for data generation. Given 3D scenes, we first define camera trajectories, according to which we generate optical flow labels for timestamps at 60 FPS and 15 FPS. Then we render high-frame-rate videos based on the motion magnitude of the optical flow label between two timestamps. Finally, we generate event streams by rendering high-frame-rate videos and simulating the event trigger mechanism in the event camera using the v2e toolbox [20]. The overview of our data generation pipeline is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.788 + ], + "angle": 0, + "content": "Virtual Scenes. To ensure that the generated event dataset has the correct scene structure, we utilize a variety of indoor and outdoor 3D scenes, including cities, streets, forests, ports, beaches, living rooms, bedrooms, bathrooms, kitchens, and parking lots. Totally, we obtain 53 virtual 3D scenes (31 indoor and 22 outdoor) that simulate real-world environments. Some examples are shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Camera Trajectory. Given a 3D scene model, we first generate the 3D camera trajectory using PyBullet [8], an open-source physics engine, to ensure that the camera does not pass through the inside of the objects and out of the effective visible region of the scene during the motion. After setting the start position, end position, and moving speed of" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9849" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.468, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.272, + 0.47, + 0.303 + ], + "angle": 0, + "content": "Figure 3: Examples of our MDR training set. Each row shows images, events and flow labels from top to bottom." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.331, + 0.47, + 0.378 + ], + "angle": 0, + "content": "the camera trajectory, we randomly add translation and rotation motions to create a smooth curve function \\(\\Gamma(t)\\) that outputs the location and pose \\(P(t) = [x(t), y(t), z(t), r(t)]^T\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.399, + 0.47, + 0.55 + ], + "angle": 0, + "content": "High-frame-rate Video and Optical Flow. After camera trajectory generation, we use the graphics engine to render a sequence of images \\( I(\\boldsymbol{u}, t_i) \\), where \\( \\boldsymbol{u} = (x, y) \\) is the pixel coordinates and \\( t_i \\) is the timestamp. We extract the forward and backward optical flow labels between every two timestamps \\( (\\boldsymbol{F}_{t_i \\to t_j}, \\boldsymbol{F}_{t_j \\to t_i}) \\). Then we need to generate the event data to construct the event optical flow dataset. Here, we render high-frame-rate videos \\( \\{I(\\boldsymbol{u}, \\tau)\\} \\), \\( \\tau \\in [t_i, t_j] \\) between timestamps \\( t_i \\) and \\( t_j \\) for events generation according to the camera trajectory \\( \\Gamma(t) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.551, + 0.47, + 0.643 + ], + "angle": 0, + "content": "Inspired by ESIM [40], we adopt an adaptive sampling strategy to sample camera locations from the camera trajectory for interval \\( t_i \\) to \\( t_j \\), so that the largest displacement of all pixels between two successive rendered frames \\( (I(\\pmb{u},\\tau_k), I(\\pmb{u},\\tau_{k + 1})) \\) is under 1 pixel, we define the sampling time interval \\( \\Delta \\tau_{k} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.656, + 0.469, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Delta \\tau_ {k} = \\tau_ {k + 1} - \\tau_ {k} \\\\ = \\left(\\max _ {\\boldsymbol {u}} \\max \\left\\{\\left\\| \\boldsymbol {F} _ {\\tau_ {k - 1} \\rightarrow \\tau_ {k}} \\right\\|, \\left\\| \\boldsymbol {F} _ {\\tau_ {k} \\rightarrow \\tau_ {k - 1}} \\right\\|\\right\\}\\right) ^ {- 1}, \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.71, + 0.47, + 0.759 + ], + "angle": 0, + "content": "where \\(|F| = \\max_{\\boldsymbol{u}} \\max \\left\\{\\left\\| \\boldsymbol{F}_{\\tau_{k-1} \\to \\tau_k} \\right\\|, \\left\\| \\boldsymbol{F}_{\\tau_k \\to \\tau_{k-1}} \\right\\|\\right\\}\\) is the maximum magnitude of the motion field between images \\(I(\\boldsymbol{u}, \\tau_{k-1})\\) and \\(I(\\boldsymbol{u}, \\tau_k)\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Event Generation from High-frame-rate Video. Given a high-frame-rate video \\(\\{I(\\pmb{u},\\tau)\\}\\), \\(\\tau \\in [t_i,t_j]\\) between timestamps \\(t_i\\) and \\(t_j\\), we next generate event stream by simulating the event trigger mechanism. Similar to [40] and [14], we use linear interpolation to approximate the continuous intensity signal in time for each pixel between video frames. Events \\(\\{(u_e,t_e,p_e)\\}\\) are generated at each pixel \\(\\pmb{u}_e = (x_e,y_e)\\) whenever the magnitude of the change in the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "log intensity values \\((L(\\pmb{u}_e, t_e) = \\ln(I(\\pmb{u}_e, t_e))\\) exceeds the threshold \\(C\\). This can be expressed as Eq. (2) and Eq. (3):" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.138, + 0.892, + 0.154 + ], + "angle": 0, + "content": "\\[\nL \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, t _ {e} + \\Delta t _ {e}\\right) - L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, t _ {e}\\right) \\geq p _ {e} C, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.16, + 0.892, + 0.194 + ], + "angle": 0, + "content": "\\[\nt _ {e} = t _ {e - 1} + \\Delta \\tau_ {k} \\frac {C}{\\left| L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}} , t _ {e} + \\Delta t _ {e}\\right) - L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}} , t _ {e}\\right) \\right|}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.199, + 0.892, + 0.275 + ], + "angle": 0, + "content": "where \\( t_{e-1} \\) and \\( t_e \\) are the timestamps of the last triggered event and the next triggered event respectively, \\( p_e \\in \\{-1, +1\\} \\) is the polarity of the triggered event. We define it as \\( E(t_k, t_{k+1}) \\), witch is the sequence \\( \\{(u_e, t_e, p_e)^N, e \\in [0, N]\\} \\) with \\( N \\) events between time \\( t_k \\) and \\( t_{k+1} \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.294, + 0.893, + 0.446 + ], + "angle": 0, + "content": "Multi-Density Rendered Events Dataset. Using the above data generation method, we can generate data with different event densities by using different threshold values \\( C \\). Since event stream is commonly first transformed into event representation [56, 42, 17] and then fed into deep networks. In order to measure the amount of useful information carried by the event stream, we propose to calculate the density of the event stream using the percentage of valid pixels (pixels where at least one event is triggered) in the voxel representation:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.457, + 0.892, + 0.498 + ], + "angle": 0, + "content": "\\[\nV (\\boldsymbol {u} _ {\\boldsymbol {e}}, b) = \\sum_ {e = 0} ^ {N} p _ {e} \\max (0, 1 - | b - \\frac {t _ {e} - t _ {0}}{t _ {N} - t _ {0}} (B - 1) |), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.511, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\nD = \\frac {1}{H W} \\sum_ {e = 1} ^ {N} \\varepsilon \\left(\\sum_ {b = 0} ^ {B - 1} | V \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, b\\right) |\\right), \\varepsilon (x) = \\left\\{ \\begin{array}{l} 1, x > 0 \\\\ 0, x \\leq 0 \\end{array} , \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.565, + 0.893, + 0.791 + ], + "angle": 0, + "content": "where \\( V(\\boldsymbol{u}_e) \\in \\mathbb{R}^{B \\times H \\times W} \\) is the voxel representation [56] of the event stream \\( \\{(u_e, t_e, p_e)^N\\} \\) between \\( t_0 \\) and \\( t_N \\), \\( b \\in [0, B - 1] \\) indicates the temporal index, \\( B \\) (typically set to 5) donates temporal bins and \\( D \\) is the density of the input event representation \\( V \\). The notation \\( |\\cdot| \\) denotes the absolute value operation. In practical applications, different event cameras may use different threshold values in different scenes, resulting in data with different event densities. Intuitively, event data with lower density is more difficult for optical flow estimation. In order to train models that can cover event data with various densities, in this paper, we propose to adaptively normalize the density of the input events to a certain density representation for optical flow estimation, so as to increase the generalization ability of the network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.824, + 0.818 + ], + "angle": 0, + "content": "3.2. Event-based Optical Flow Estimation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Event-based optical flow estimation involves predicting dense optical flow \\( \\pmb{F}_{k-1\\rightarrow k} \\) from consecutive event sequences \\( E(t_{k-1},t_k) \\) and \\( E(t_k,t_{k+1}) \\). In this paper, we find that networks perform better on event sequences with appropriate density than on those with excessively sparse or" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9850" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.087, + 0.473, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.21, + 0.47, + 0.271 + ], + "angle": 0, + "content": "Figure 4: The structure of the proposed network. We design a plug-and-play Adaptive Density Module (ADM) to transform input event representations \\( V_{1} \\) and \\( V_{2} \\) into \\( V_{1}^{\\mathrm{ad}} \\) and \\( V_{2}^{\\mathrm{ad}} \\) with suitable density for optical flow estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.473, + 0.429 + ], + "angle": 0, + "content": "dense events, when given events from the same scene. Motivated by this, we propose a plug-and-play Adaptive Density Module (ADM) that normalizes the input event stream to a density suited for estimating optical flow. Our network architecture is shown in Fig. 4, where the ADM transforms input event representations \\( V_{1} \\) and \\( V_{2} \\) to justified event representations \\( V_{1}^{\\mathrm{ad}} \\) and \\( V_{2}^{\\mathrm{ad}} \\), which are then used by an existing network structure to estimate optical flow." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.576 + ], + "angle": 0, + "content": "Adaptive Density Module. As shown in Fig. 4, our ADM module consists of two sub-modules: the multi-density changer (MDC) module and the multi-density selector (MDS) module. The MDC module globally adjusts the density of the input event representations from multi-scale features, then the MDS module picks the best pixel-wise density for optical flow estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.732 + ], + "angle": 0, + "content": "The MDC module adopts an encoder-decoder architecture with three levels, as illustrated in Fig. 5(a). To generate multiscale transformed representations \\( V_{3}^{\\mathrm{MDC}} \\), \\( V_{2}^{\\mathrm{MDC}} \\) and \\( V_{1}^{\\mathrm{MDC}} \\) (also noted as \\( V_{\\mathrm{out}}^{\\mathrm{MDC}} \\)) from the concatenated input event representations \\( V \\), three encoding blocks are employed to extract multiple scale features, followed by three decoding blocks and two feature fusion blocks. It is worth noting that, to ensure the lightweightness of the entire module, we utilize only two \\( 3 \\times 3 \\) and one \\( 1 \\times 1 \\) convolutional layers in each encoding and decoding block." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To maintain the information in the input event representation and achieve density transformation, we adopt the MDS module for adaptive selection and fusion of \\( V_{\\mathrm{out}}^{\\mathrm{MDC}} \\) and \\( V \\), as depicted in Fig. 5(b). We first concatenate \\( V_{\\mathrm{out}}^{\\mathrm{MDC}} \\) and \\( V \\), and then use two convolutional layers to compare them and generate selection weights via softmax. Finally, we employ the selection weights to identify and fuse \\( V_{\\mathrm{out}}^{\\mathrm{MDC}} \\) and \\( V \\), producing the transformed event representation \\( V_1^{\\mathrm{ad}} \\) and \\( V_2^{\\mathrm{ad}} \\), which are fed into an existing flow network for optical flow estimation. In this paper, we use KPA-Flow [32] for optical flow estimation by default." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.089, + 0.852, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.194, + 0.852, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.328, + 0.892, + 0.359 + ], + "angle": 0, + "content": "Figure 5: The detailed structure of sub-modules used in our proposed ADM model: (a) MDC, (b) MDS." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.893, + 0.445 + ], + "angle": 0, + "content": "Loss Function. Based on our MDR dataset, we use the event representation with a moderate density as the ground truth (noted as \\( V^{\\mathrm{GT}} \\)) to train our ADM module. For the MDC module, we use a multi-scale loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.454, + 0.892, + 0.495 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {M D C}} = \\sum_ {k = 1} ^ {3} \\sqrt {\\left(V _ {k} ^ {\\mathrm {M D C}} - V _ {k} ^ {\\mathrm {G T}}\\right) ^ {2} + \\xi^ {2}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.506, + 0.892, + 0.553 + ], + "angle": 0, + "content": "where \\(\\xi = 10^{-3}\\) is a constant value, \\(V_{k}^{\\mathrm{MDC}}\\) is the output of the \\(k\\)-th level in MDC, and \\(V_{k}^{\\mathrm{GT}}\\) is downsampled from \\(V^{\\mathrm{GT}}\\) to match the spatial size." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.553, + 0.892, + 0.583 + ], + "angle": 0, + "content": "For the MDS module, we use the distance between the density of \\( V^{\\mathrm{ad}} \\) and \\( V^{\\mathrm{GT}} \\) as the guidance:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.592, + 0.892, + 0.613 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {M D S}} = \\left\\| D \\left(V ^ {\\mathrm {a d}}\\right) - D \\left(V ^ {\\mathrm {G T}}\\right) \\right\\| _ {1}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.621, + 0.85, + 0.636 + ], + "angle": 0, + "content": "where \\(D\\) means to calculate the density as in Eq. (5)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.636, + 0.892, + 0.666 + ], + "angle": 0, + "content": "For the flow network, we use L1 loss (denoted as \\(L_{\\mathrm{Flow}}\\)) between flow prediction and ground truth as the guidance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.666, + 0.892, + 0.696 + ], + "angle": 0, + "content": "The final loss function for training the whole pipeline in Fig. 4 is determined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.708, + 0.892, + 0.724 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {t o t a l}} = \\lambda_ {1} L _ {\\mathrm {M D C}} + \\lambda_ {2} L _ {\\mathrm {M D S}} + L _ {\\text {F l o w}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.734, + 0.822, + 0.75 + ], + "angle": 0, + "content": "where we empirically set \\(\\lambda_{1} = 0.1\\) and \\(\\lambda_{2} = 10\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.763, + 0.633, + 0.78 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.788, + 0.602, + 0.802 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.81, + 0.892, + 0.903 + ], + "angle": 0, + "content": "MDR: We create the MDR dataset using the graphics engine blender. We use various 3D scenes for data generation. There are 80,000 training samples and 6,000 validation samples with accurate dense optical flow ground truth. Each sample has event sequences with different densities produced by using different thresholds \\( C \\). By default, for" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9851" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.088, + 0.855, + 0.543 + ], + "angle": 0, + "content": "
Method (dt=1)Train D.TypeTrain D.Setindoor flying1indoor flying2indoor flying3outdoor day1Avg
EPE%OutEPE%OutEPE%OutEPE%OutEPE%Out
ESTS[15]EM0.970.911.388.201.436.47--1.265.19
EV-FlownetS[54]I1,I2,EM1.032.201.7215.11.5311.90.490.201.197.35
Deng et al.S[10]EM0.890.661.316.441.133.53--1.113.54
Paredes et al.S[39]EM0.791.201.4010.91.187.400.925.401.076.22
Matrix-LSTMS[6]I1,I2,EM0.820.531.195.591.084.81--1.033.64
LIF-EV-FlowNetS[18]EFPV0.711.411.4412.81.169.110.530.330.965.90
Spike-FlowNetS[27]I1,I2,EM0.84-1.28-1.11-0.49-0.93-
Fusion-FlowNetD[26]I1,I2,EM0.62-0.89-0.85-1.02-0.84-
Fusion-FlowNetS[26]I1,I2,EM0.56-0.95-0.76-0.59-0.71-
E-RAFTD[17]EM1.105.721.549.791.368.240.270.001.075.94
E-RAFTS[17]EM0.871.321.136.201.034.700.240.000.823.06
Zhu et al.S[56]EM0.580.001.024.000.873.000.320.000.691.75
DCEIFlowD[50]I1,I2,EM0.560.280.640.160.570.120.910.710.670.31
DCEIFlowS[50]I1,I2,EC20.570.300.700.300.580.150.740.290.640.26
Stoffregen et al.S[42]EESIM0.561.000.661.000.591.000.680.990.620.99
STE-FlowNetS[11]I1,I2,EM0.570.100.791.600.721.300.420.000.620.75
ADM-FlowD(ours)EMDR0.480.110.560.400.470.020.520.000.510.14
ADM-FlowS(ours)EMDR0.520.140.681.180.520.040.410.000.530.34
Method (dt=4)Train D.TypeTrain D.Setindoor flying1indoor flying2indoor flying3outdoor day1Avg
EPE%OutEPE%OutEPE%OutEPE%OutEPE%Out
LIF-EV-FlowNetS[18]EFPV2.6329.64.9351.13.8841.52.0218.93.3635.3
EV-FlownetS[54]I1,I2,EM2.2524.74.0545.33.4539.71.237.302.7429.3
E-RAFTD[17]EM3.2635.44.3248.64.1448.20.841.703.1433.5
E-RAFTS[17]EM2.8130.63.9940.93.7840.50.721.122.8328.3
Zhu et al.S[56]EM2.1824.23.8546.83.1847.81.309.702.6232.1
Spike-FlowNetS[27]I1,I2,EM2.24-3.83-3.18-1.09-2.58-
Fusion-FlowNetD[26]I1,I2,EM1.81-2.90-2.46-3.06-2.55-
Fusion-FlowNetS[26]I1,I2,EM1.68-3.24-2.43-1.17-2.13-
STE-FlowNetS[11]I1,I2,EM1.7714.72.5226.12.2322.10.993.901.8716.7
DCEIFlowD[50]I1,I2,EC21.498.141.9717.41.6912.31.8719.11.7514.2
DCEIFlowS[50]I1,I2,EC21.528.792.2122.11.7413.31.378.541.7113.2
ADM-FlowD(ours)EMDR1.397.331.6311.51.519.341.9119.21.6111.8
ADM-FlowS(ours)EMDR1.427.781.8816.71.6111.41.5110.21.6011.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.554, + 0.894, + 0.586 + ], + "angle": 0, + "content": "Table 1: Quantitative comparison of our method with previous methods on the MVSEC dataset [55]. Subscripts \\( S \\) and \\( D \\) donate the sparse and dense evaluation, respectively. We mark the best results in red and the second best results in blue." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.687 + ], + "angle": 0, + "content": "training on MDR, we use the combination of all these samples with different densities to train flow networks. For the learning of our ADM module, we choose events with density between 0.45 and 0.55 as the label for \\( L_{\\mathrm{MDC}} \\) and \\( L_{\\mathrm{MDS}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.869 + ], + "angle": 0, + "content": "MVSEC: The MVSEC dataset [55] is a real-world dataset collected in indoor and outdoor scenarios with sparse optical flow labels. As a common setting, 28, 542 data pairs of the 'outdoor day2' sequence are used as the train set, and 8, 410 data pairs of the other sequences are used as the validation set. The density ranges of MVSEC train set and validation set are [0.0003, 0.47] and [0.001, 0.31], respectively. DSEC: The DSEC dataset [16] is also collected using actual event cameras and lidar sensors on outdoor scenes. The dataset consists of 7,800 training samples and 2,100 test samples, divided into 24 sequences that include both day and night scenarios." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Previous methods have trained on other datasets, including synthetic datasets like C2 [50] and ESIM [42], as well" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.779 + ], + "angle": 0, + "content": "as real-world captured datasets such as FPV [9]. To assess the performance of these methods, comparisons are made on the validation set of the MVSEC dataset. Both MVSEC and MDR datasets have two input settings for training and testing. These settings involve using the events between successive images within a time interval of \\( dt = 1 \\) and \\( dt = 4 \\). On the other hand, for the DSEC dataset, there is a public benchmark available specifically designed to evaluate flow networks. However, this benchmark only provides one input setting for testing. We denote MVSEC, DSEC, and MDR datasets by \"M\", \"D\", and \"MDR\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.715, + 0.803 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We use PyTorch to implement our method and train all networks using the same setting. The networks are trained with the AdamW optimizer, with a batch size of 6 and learning rate of \\(4 \\times 10^{-4}\\) for 150k iterations. Since the MVSEC dataset lacks multiple density event streams required for the learning of our ADM module, we disable \\(L_{\\mathrm{MDC}}\\) and \\(L_{\\mathrm{MDS}}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9852" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.332, + 0.106 + ], + "angle": 0, + "content": "when training on the MVSEC dataset." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.26, + 0.13 + ], + "angle": 0, + "content": "4.3. Evaluation metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.139, + 0.471, + 0.334 + ], + "angle": 0, + "content": "The evaluation metrics used in flow prediction models are the average End-point Error (EPE) and 1PE, 2PE, and 3PE (the percentage of pixels with EPE greater than 1,2,3 pixels) for DSEC dataset, and \\(\\% \\text{Out}\\) (the percentage of points with EPE greater than 3 pixels and \\(5\\%\\) of the ground truth flow magnitude) for MVSEC dataset. There are two types of evaluations: dense and sparse. In emphdense evaluation, errors are calculated only at pixels with valid flow annotations. Sparse evaluation focuses on pixels with valid flow annotations that have triggered at least one event. Experiments are performed on both MVSEC and MDR, considering both dense and sparse evaluations. However, only dense dense is conducted for DSEC." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.344, + 0.383, + 0.359 + ], + "angle": 0, + "content": "4.4. Comparison with State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.624 + ], + "angle": 0, + "content": "Results on MVSEC. In Table 1, we compare our model trained on the MDR train set with previous methods on the MVSEC evaluation set, and report detailed results for each sequence. We provide information on the data types (Train D.Type) and the training sets (Train D.Set) used in the training process for each method. Specifically, \\(\\mathrm{I}_1,\\mathrm{I}_2,\\mathrm{E}\\) indicates that both image data and event data are used in the training and inference processes of the model, while \\(\\mathrm{E}\\) indicates that only event data is used. As shown in Table 1, our model trained on the MDR dataset achieves state-of-the-art performance for both EPE and %Out metrics in settings of \\(dt = 1\\) and \\(dt = 4\\). Notably, our method demonstrates a \\(23.9\\%\\) improvement (reducing EPE from 0.67 to 0.51) for dense optical flow estimation in \\(dt = 1\\) settings, and an \\(8.0\\%\\) improvement (reducing EPE from 1.75 to 1.61) in \\(dt = 4\\) settings, surpassing previous methods. Qualitative comparison results are shown in row 1 and row 2 in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.808 + ], + "angle": 0, + "content": "Results on MDR. In Table 3, we compare our method with previous methods for training on the MVSEC dataset and testing on the MDR dataset for cross-training and validation to avoid over-fitting. We use different thresholds \\( C \\) to generate test data with different density ranges for evaluation. For the average EPE error of dense optical flow estimation, our model obtains the best result, which is a \\( 17.1\\% \\) improvement (reducing EPE from 0.82 to 0.68) in \\( dt = 1 \\) settings, and a \\( 16.7\\% \\) improvement (reducing EPE from 1.98 to 1.65) in \\( dt = 4 \\) settings. We also show some qualitative comparison results in row 3 and row 4 in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Results on DSEC. In Table 2, we report the results on the DSEC test set for different models that are trained on DSEC, MDR, and a combination of DSEC and MDR. As can be seen, MDR-trained models produce comparable results to in-domain learned models on the DSEC train set." + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.089, + 0.871, + 0.281 + ], + "angle": 0, + "content": "
MethodsTrain D.Set1PE2PE3PEEPE
EV-FlowNet [54]D55.1328.4316.712.22
MDR42.5224.4016.321.86
D+MDR35.0615.417.841.31
E-RAFT [17]D16.196.223.590.90*
MDR18.857.444.371.00
D+MDR13.165.192.930.82
ADM-EVFLOWD42.8925.2115.801.90
MDR40.0214.8812.341.67
M+D23.4610.325.611.12
ADM-Flow(ours)D13.965.323.180.88
MDR14.535.783.590.92
D+MDR12.524.672.650.78
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.293, + 0.892, + 0.354 + ], + "angle": 0, + "content": "Table 2: Results on the DSEC test set. * denotes our reproduced results of E-RAFT, since the official training code is not released. All experiments are conducted on the same training code for fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.37, + 0.892, + 0.462 + ], + "angle": 0, + "content": "Moreover, training E-RAFT on the combined DSEC/MDR datasets yields improved performance, demonstrating the effectiveness of MDR. Our ADMFlow model achieves improved performance on all training datasets, highlighting the effectiveness and versatility of ADM. Some qualitative results are shown in Fig. 7." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.486, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Analysis of the MDR dataset. To demonstrate the effectiveness of our proposed MDR dataset, we train several optical flow networks [46, 17, 53, 21, 47, 24, 32] on both MDR and MVSEC train sets using identical training settings. For training, we use a combination of data samples from the MDR dataset with a density range of \\([0.09, 0.69]\\). We evaluate the trained networks on the MVSEC validation set, and the results, presented in Table 4, demonstrate that all networks trained on the MDR dataset outperform those trained on the MVSEC dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.655, + 0.667 + ], + "angle": 0, + "content": "4.5. Ablation study." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training with different densities. We examine the impact of input event sequence density on optical flow learning, as our MDR dataset contains event data with various densities and corresponding dense flow labels. We train SKFlow [47], GMA [24], FlowFormer [21] and KPA-Flow [32] on the same sequence from our MDR dataset but with different average densities produced by using different threshold \\( C \\), and then test them on the MVSEC dataset. Figure 8 shows the results in \\( dt = 4 \\) setting, indicating that these models perform better as the average density of the training set increases. However, their performance diminishes as the average density continues to increase. This phenomenon highlights the importance of selecting an appropriate density for the training set when learning event optical flow." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9853" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.092, + 0.196, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.18, + 0.197, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.27, + 0.196, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.359, + 0.196, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.447, + 0.172, + 0.457 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image", + "bbox": [ + 0.2, + 0.092, + 0.312, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.201, + 0.18, + 0.312, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.201, + 0.269, + 0.312, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.201, + 0.359, + 0.312, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.215, + 0.447, + 0.298, + 0.458 + ], + "angle": 0, + "content": "Spike-Flownet" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.092, + 0.427, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.181, + 0.427, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.269, + 0.427, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.359, + 0.427, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.331, + 0.447, + 0.411, + 0.458 + ], + "angle": 0, + "content": "STE-FlowNet" + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.092, + 0.543, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.181, + 0.543, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.269, + 0.543, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.43, + 0.359, + 0.543, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.462, + 0.447, + 0.512, + 0.458 + ], + "angle": 0, + "content": "E-RAFT" + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.092, + 0.658, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.181, + 0.658, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.269, + 0.658, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.359, + 0.658, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.572, + 0.447, + 0.635, + 0.458 + ], + "angle": 0, + "content": "DCEIFlow" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.092, + 0.775, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.181, + 0.775, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.269, + 0.775, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.359, + 0.776, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.447, + 0.735, + 0.458 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.092, + 0.89, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.181, + 0.89, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.269, + 0.89, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.359, + 0.89, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.808, + 0.447, + 0.86, + 0.458 + ], + "angle": 0, + "content": "Flow GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.473, + 0.893, + 0.505 + ], + "angle": 0, + "content": "Figure 6: Qualitative comparisons compared with existing event-based methods. Row 1 and 2 are from MVSEC, whereas row 3 and 4 are from MDR. Row 1 and 3 visualize the dense predictions, whereas row 2 and 4 show the sparse." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.53, + 0.176, + 0.585 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.587, + 0.176, + 0.645 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.648, + 0.175, + 0.705 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.708, + 0.176, + 0.764 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.767, + 0.159, + 0.777 + ], + "angle": 0, + "content": "Reference" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.53, + 0.273, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.588, + 0.273, + 0.645 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.648, + 0.272, + 0.706 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.708, + 0.272, + 0.764 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.188, + 0.767, + 0.261, + 0.777 + ], + "angle": 0, + "content": "EV-Flownet" + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.53, + 0.37, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.588, + 0.371, + 0.645 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.648, + 0.371, + 0.706 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.708, + 0.371, + 0.764 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.295, + 0.767, + 0.349, + 0.777 + ], + "angle": 0, + "content": "E-RAFT" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.53, + 0.468, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.588, + 0.468, + 0.706 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.708, + 0.468, + 0.764 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.404, + 0.767, + 0.435, + 0.777 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.791, + 0.47, + 0.837 + ], + "angle": 0, + "content": "Figure 7: Qualitative comparisons on the DSEC test set. We visualize the dense predictions and zoom in the areas where are apparent differences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Ablation for ADM. In order to verify the impact of our proposed ADM module, we conduct ablation experiments by plugging the ADM module into several optical flow net" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.529, + 0.892, + 0.742 + ], + "angle": 0, + "content": "
Method (dt = 1)density rangeAvg
0.09-0.240.24-0.390.39-0.540.54-0.69
Spike-FlowS [27]1.931.201.332.011.62
STE-FlowS [11]1.171.110.821.301.10
DCEIFlowD [50]1.281.371.271.461.35
DCEIFlowS [50]1.000.840.750.820.85
E-RAFTD [17]0.930.740.690.920.82
E-RAFTS [17]0.820.650.660.820.74
ADM-FlowD(ours)0.770.690.500.740.68
ADM-FlowS(ours)0.690.640.490.740.64
Method (dt = 4)density rangeAvg
0.09-0.240.24-0.390.39-0.540.54-0.69
Spike-FlowS [27]3.951.962.092.872.72
STE-FlowS [11]2.902.271.982.172.33
DCEIFlowD [50]3.842.682.994.273.45
DCEIFlowS [50]2.251.321.192.341.78
E-RAFTD [17]2.641.421.352.511.98
E-RAFTS [17]2.181.311.242.291.76
ADM-FlowD(ours)2.121.201.242.021.65
ADM-FlowS(ours)2.031.131.091.901.54
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.753, + 0.894, + 0.829 + ], + "angle": 0, + "content": "Table 3: Quantitative evaluation on our MDR dataset. The methods in the table are all trained on the MVSEC dataset for cross-training and validation to avoid over-fitting. \\( S \\) and \\( D \\) donate the sparse and dense evaluation, respectively. We use EPE as the evaluation metric." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "works to selectively adjust the densities of the input events. We train these networks on both MDR and MVSEC datasets with the same setting except that the ADM module is dis" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9854" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.467, + 0.281 + ], + "angle": 0, + "content": "
MethodTrain D.Setdt = 1dt = 4
EPE%OutEPE%Out
PWCNet [22]M1.255.414.0351.48
MDR1.143.482.9238.62
RAFT [48]M1.194.903.3339.78
MDR0.590.512.5730.24
GMFlowNet [53]M1.003.753.6142.31
MDR0.821.662.7031.53
FlowFromer [21]M0.873.083.3841.04
MDR0.610.402.4928.83
SKFlow [47]M1.073.973.4140.87
MDR0.590.332.4627.64
GMA [24]M0.884.052.9934.80
MDR0.580.442.1923.00
KPAFlow [32]M0.862.863.1938.32
MDR0.580.392.3326.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.293, + 0.47, + 0.337 + ], + "angle": 0, + "content": "Table 4: Comparison of training on MVSEC vs. MDR. Models are evaluated on MVSEC for dense optical flow estimation." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.353, + 0.462, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.634 + ], + "angle": 0, + "content": "Figure 8: The performance of some supervised optical flow networks with different densities of the training set in \\( dt = 4 \\) setting. X-axis is the average density of events in the training set, and y-axis is their average EPE on MVSEC validation set. Different colors represent the performance of different networks, and the pentagons show the performance of networks trained on the MDR training set with a widely density range of [0.09, 0.69], and the average density is 0.41." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.47, + 0.725 + ], + "angle": 0, + "content": "abled or not, and test them on the MVSEC dataset. The experiment results are shown in Table 5, where we can notice that our ADM module can bring performance improvement for all supervised methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Ablation for the design of ADM. We conduct ablation experiments to verify the effectiveness of each component in our ADM module, including MDC, MDS, and the two training loss functions \\( L_{\\mathrm{MDC}} \\) and \\( L_{\\mathrm{MDS}} \\). We train models using the same settings on the MDR dataset and evaluate them on the MVSEC dataset to show the individual impact of each component in our ADM module. The results are presented in Table 6. The comparison of (a)&(b) shows that adding only the MDC plugin results in a slight performance gain. Comparison of (b)&(c) reveals that en" + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.089, + 0.89, + 0.251 + ], + "angle": 0, + "content": "
MethodM(dt = 1)MDR(dt = 1)M(dt = 4)MDR(dt = 4)
EPE%OutEPE%OutEPE%OutEPE%Out
PWCNet [22]1.255.411.143.484.0351.482.9238.62
ADM-PWCNet1.074.520.761.482.9533.311.9418.74
RAFT [48]1.194.900.590.513.3339.782.5730.24
ADM-RAFT0.823.030.560.242.7330.911.7213.83
GMFlowNet [53]1.003.750.821.663.6142.312.7031.53
ADM-GMFlowNet0.873.050.580.322.7831.261.8114.45
FlowFromer [21]0.873.080.610.403.3841.042.4928.83
ADM-FlowFromer0.782.870.530.152.5626.571.6712.78
SKFlow [47]1.073.970.590.333.4140.872.4627.64
ADM-SKFlow0.843.180.530.142.6728.171.6912.61
GMA [24]0.884.050.580.442.9934.802.1923.00
ADM-GMA0.762.650.540.222.4525.751.6311.95
KPAFlow [32]0.862.860.580.393.1938.322.3326.10
ADM-KPAFlow0.802.670.510.142.5928.421.6111.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.262, + 0.892, + 0.323 + ], + "angle": 0, + "content": "Table 5: Quantitative comparison of whether using ADM. Models are trained on MVSEC and MDR, and evaluated on MVSEC for dense optical flow estimation in \\( dt = 1 \\) and \\( dt = 4 \\) settings." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.338, + 0.89, + 0.413 + ], + "angle": 0, + "content": "
MethodMDCMDSLMDCLMDSParam. (M)dt = 1dt = 4
EPE%OutEPE%Out
(a)××××6.010.580.392.3326.10
(b)✓×××7.710.570.332.2023.78
(c)✓✓××7.720.540.261.9218.26
(d)✓✓✓×7.720.520.161.6613.29
(e)✓✓✓✓7.720.510.141.6111.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.424, + 0.892, + 0.47 + ], + "angle": 0, + "content": "Table 6: Ablation study. Models are trained on the MDR training set, and evaluated on the MVSEC validation set for dense optical flow estimation in \\( dt = 1 \\) and \\( dt = 4 \\) settings." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.497, + 0.892, + 0.588 + ], + "angle": 0, + "content": "abling the density selection function through the MDS module brings a significant improvement. Comparing (c)&(d) and (d)&(e), we notice that with the guidance of two loss functions, ADM can learn to selectively choose the best density for optical flow estimation, resulting in a relatively significant improvement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.603, + 0.619, + 0.619 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.84 + ], + "angle": 0, + "content": "In this work, we have created a rendered dataset for event-flow learning. Indoor and outdoor virtual scenes have been created using Blender with rich scene contents. Various camera motions are placed for the capturing of the virtual world, which can produce frames as well as accurate flow labels. The event values are generated by rendering high frame rate videos between two frames. In this way, the flow labels and event values are physically correct and accurate. The rendered dataset can adjust density of events by modifying the event trigger threshold. We have introduced a novel adaptive density module (ADM), which has shown its effectiveness by plugin into various event-flow pipelines. When trained on our dataset, previous approaches can improve their performances constantly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements This work was supported by Sichuan Science and Technology Program of China under grants Nos. 2023NSFSC0462, 2023NSFSC1972, 2021YFG0001, 2022YFG0011 and 2022YFG0050." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9855" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Ryad Benosman, Sio-Hoi Ieng, Charles Clercq, Chiara Bartolozzi, and Mandyam Srinivasan. 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One important issue is how to build a high-quality event-flow dataset with accurate event values and flow labels. Previous datasets are created by either capturing real scenes by event cameras or synthesizing from images with pasted foreground objects. The former case can produce real event values but with calculated flow labels, which are sparse and inaccurate. The latter case can generate dense flow labels but the interpolated events are prone to errors. In this work, we propose to render a physically correct event-flow dataset using computer graphics models. In particular, we first create indoor and outdoor 3D scenes by Blender with rich scene content variations. Second, diverse camera motions are included for the virtual capturing, producing images and accurate flow labels. Third, we render high-framerate videos between images for accurate events. The rendered dataset can adjust the density of events, based on which we further introduce an adaptive density module (ADM). Experiments show that our proposed dataset can facilitate event-flow learning, whereas previous approaches when trained on our dataset can improve their performances constantly by a relatively large margin. In addition, event-flow pipelines when equipped with our ADM can further improve performances. Our code is available at https://github.com/boomluo02/ADMFlow. + +# 1. Introduction + +Event cameras [29] record brightness changes at a varying framerate [4]. When a change is detected in a pixel, the camera returns an event in the form $e = (x,y,t,p)$ immediately, where $x,y$ stands for the spatial location, $t$ refers to the timestamp in microseconds, and $p$ is the polarity of the + +![](images/8fc278094f27db86618949719a63d0bbfaa65f338241cda1810563787e9d747d.jpg) +(a) + +![](images/da8c3db4e8bc2736f68549da21933706440ddc3921f0f916ed31b0ece8be3ef7.jpg) + +![](images/4e969935e262969e8b3d89729cd3846557f8b0755766ee8b02c8b5474c2e457f.jpg) + +![](images/d9d782d8a7168e8c6cab0e472e5858d7e060f98c56690f16bc9ce3f9e2d8a66c.jpg) + +![](images/12626680dcaf524455ac887b6349c6e6b2e7f22828e5e917a1428a96d8ed0c83.jpg) + +![](images/99432e1f5ee2bd5944c305fd6942c78c28d06ba392ee56c12fe814f10dbdfb0a.jpg) + +![](images/819ad36a9267a1b141290c8abefe363d9729c5c1c6be5af3aae005c398924b6f.jpg) + +![](images/ae406c9036edc578ae9140e0fc79adc9217f221931a3e6a0baae9dcea764a220.jpg) +Images +Figure 1: (a) the captured dataset from real event camera [55, 54]. (b) the synthesized dataset with flying chairs foreground [50]. (c) the synthesized dataset by moving a foreground image [42]. (d) Our synthesized dataset by graphics rendering, which not only reflects the real motions under correct scene geometries, but also produces accurate dense flow labels and events. + +![](images/bf78ea4a878bcb79576f94d576f8ef2f2c2c39fe361e5fbadc168f2146ea0063.jpg) + +![](images/a72ad426ebf87c17790e36f7c6e248ee6e35534c6c612bc40563ed9d9dc082c9.jpg) +Events + +![](images/7f28d128398f11860d7ca434865d69f423278b381ee21278de725ca521ed0c03.jpg) + +![](images/52478f78fe365dea8dbf3e0edf5a9404b0cf7fc1cdd10565a6335fef6a78188b.jpg) +Flow GT + +change, indicating a pixel become brighter or darker. On the other hand, optical flow estimation predicts motions between two frames [44], which is fundamental and important for many applications [49, 52, 7]. In this work, we study the problem of estimating optical flow from event camera data, instead of from RGB frames. Different from traditional images, events are sparse and are often integrated in short intervals as the input for the prediction. As such, early works + +can only estimate sparse flows at the location of events [1]. Recent deep methods can estimate dense flows but with the help of images, either as the guidance [54] or as the additional inputs [26, 38]. Here, we tackle a hard version of the problem, where dense flows are predicted based purely on the event values $e$ . One key issue is how to create high quality event-based optical flow dataset to train the network. + +Existing methods of event flow dataset creation can be classified into two types, 1) directly capturing from real event cameras [55, 54, 16]; 2) moving foregrounds on top of a background image to create synthesized flow motions [50, 42] and apply frame interpolation [14] to create events. For the first type, the ground-truth (GT) flow labels need to be calculated based on gray images acquired along with the event data. However, the optical flow estimations cannot be perfectly accurate [48, 43, 32, 24, 51], leading to the inaccuracy of GT labels. To alleviate the problem, additional depth sensors, such as LIDAR, have been introduced [55]. The flow labels can be calculated accurately when the depth values of LIDAR scans are available. However, LIDAR scans are sparse, and so do the flow labels, which are unfriendly for dense optical flow learning. Fig. 1 (a) shows an example, LIDAR points on the ground are sparse. Moreover, some thin objects are often missing, as indicated by the red box in Fig. 1 (a). + +For the second category, the flow labels are created by moving foreground objects on top of a background image, similar to flying chairs [12] or flying things [36]. In this way, the flow labels are dense and accurate. To create events, intermediate frames are interpolated [23]. However, the frame interpolation is inaccurate due to scene depth disparities, where the occluded pixels cannot be interpolated correctly, leading to erroneous event values in these regions. To match high framerate of events, the large number of interpolated frames makes the problem even worse. Fig. 1 (b) shows an example, where the events are incorrect at the occluded chairs. Moreover, the motions are artificial, further decreasing the realism of the dataset (Fig. 1 (b) and (c)). + +In this work, we create an event-flow dataset from synthetic 3D scenes by graphics rendering (Fig. 1 (d)). While there is a domain gap between rendered and real images, this gap is empirically found insignificant in event camera based classification [41] and segmentation [14] tasks. As noted by these works, models trained on synthetic events work very well for real event data. Because events contain only positive and negative polarities, no image appearances are involved. To this end, we propose a Multi-Density Rendered (MDR) event optical flow dataset, created by Blender on indoor and outdoor scenes with accurate events and flow labels. In addition, we design an Adaptive Density Module (ADM) based on MDR, which can adjust the densities of events, one of the most important factors for event-based tasks but has been largely overlooked. + +Specifically, our MDR dataset contains 80,000 samples from 50 virtual scenes. Each data sample is created by first rendering two frames and obtaining the GT flow labels directly from the engine. Then, we render $15 \sim 60$ frames in between based on the flow magnitude. The events are created by thresholding log intensities and recording the times-stamp for each spatial location. The density of events can be controlled by the threshold values. The ADM is designed as a plugin module, which further consists of two sub-modules, multi-density changer (MDC) and multi-density selector (MDS), where the MDC adjusts the density globally while the MDS picks the best one for every spatial location. Experiments show that previous event-flow methods, when trained on our MDR dataset, can improve their performances. Moreover, we train several recent representative flow pipelines, such as FlowFormer [21], KPA-Flow [32], GMA [24] and SKFlow [47], on our MDR dataset. When equipped with our ADM module, the performances can increase consistently. + +Our contributions are summarized as: + +- A rendered event-flow dataset MDR, with 80,000 samples created on 53 virtual scenes, which possess physically correct accurate events and flow label pairs, covering a wide range of densities. +- An adaptive density module (ADM), which is a plug-and-play module for handling varying event densities. +- We achieve state-of-the-art performances. Our MDR can improve the quality of previous event-flow methods. Various optical flow pipelines when adapted to the event-flow task, can benefit from our ADM module. + +# 2. Related Work + +# 2.1. Image-based Optical Flow + +Optical flow estimates the per-pixel motion between two frames according to photo consistency. Traditional approaches minimize energies, leveraging both feature similarities and motion smoothness [13]. Deep methods train the networks that take two frames as input and directly output dense flow motions [12, 46]. Recent deep methods design different pipelines [30, 48, 24] as well as learning modules [35, 31, 34, 33] for performance improvements. The training often requires large labeled datasets, which can be synthesized by moving a foreground on top of a background image, such as FlyingChairs [12], and AutoFlow [45], or rendered from graphics such as Sintel [5] and FlyingThings [36], or created directly from real videos [19]. In this work, we use computer graphics techniques to render accurate and physically correct event and flow values. + +![](images/5c58e2c5d07b4080815f9e5f5f846f1b7cd0e0358d21961bd1d07db12ba7a4af.jpg) +Figure 2: Our data generation pipeline. Given 3D scenes in the graphics engine, we generate camera trajectories and render high-frame-rate videos with forward and backward optical flow labels. Then, we build the event optical flow dataset by generating events using the videos. + +# 2.2. Event-based Optical Flow + +Benosman et al. [1] first proposed to estimate optical flow from events, which can only estimate sparse flows at the location of event values. Recent deep methods can estimate dense optical flows. EV-FlowNet [54] learns the event and flow labels in a self-supervised manner, which minimizes the photometric distances of grey images acquired by DAVIS [4]. Different event representations were explored, e.g., EST [15] and Matrix-LSTM [6], with various network structures, such as SpikeFlowNet [27], LIF-EV-FlowNet [18], STE-FlowNet [11], Li et al. [28], and E-RAFT [17]. Some works take both events and images as input for the flow estimation [26, 38]. In general, dense flows are more desirable than sparse ones but are more difficult to train. Normally, regions with events can produce more accurate flows than empty regions where no events are triggered. Moreover, supervised training can produce better results than unsupervised ones, as long as the training dataset can provide sufficient event-flow guidance. + +# 2.3.Event Dataset + +The applications to the event camera dataset were first explored in the context of classification [37, 2]. Early works generate events simply by applying a threshold on the image difference [25]. Frame interpolation is often adopted for high framerate [14]. The synthesized events often contain inaccurate timestamps. The DAVIS event camera can directly capture both images and events [4], based on which two driving datasets are captured, DDD17 [3] and MVSEC [55]. With respect to the event flow dataset, EV-Flownet [54] calculated sparse flow labels from LIDAR depth based on MVSEC [55]. Wan et al. [50] and Stoffregen et al. [42] created the foreground motions and interpolated the intermediate frames for events. The real captured + +dataset can only provide sparse labels while the synthesized ones contain inaccurate events. In this work, we propose to render a physically correct event dense flow dataset. + +# 3. Method + +# 3.1. The event-based optical flow dataset + +In order to create a realistic event dataset for optical flow learning, we propose to employ a graphics engine with 3D scenes for data generation. Given 3D scenes, we first define camera trajectories, according to which we generate optical flow labels for timestamps at 60 FPS and 15 FPS. Then we render high-frame-rate videos based on the motion magnitude of the optical flow label between two timestamps. Finally, we generate event streams by rendering high-frame-rate videos and simulating the event trigger mechanism in the event camera using the v2e toolbox [20]. The overview of our data generation pipeline is shown in Fig. 2. + +Virtual Scenes. To ensure that the generated event dataset has the correct scene structure, we utilize a variety of indoor and outdoor 3D scenes, including cities, streets, forests, ports, beaches, living rooms, bedrooms, bathrooms, kitchens, and parking lots. Totally, we obtain 53 virtual 3D scenes (31 indoor and 22 outdoor) that simulate real-world environments. Some examples are shown in Fig. 3. + +Camera Trajectory. Given a 3D scene model, we first generate the 3D camera trajectory using PyBullet [8], an open-source physics engine, to ensure that the camera does not pass through the inside of the objects and out of the effective visible region of the scene during the motion. After setting the start position, end position, and moving speed of + +![](images/3a227041f30bd02e9b2a63122da3c371d74f360edebdd662643471867aff974e.jpg) +Figure 3: Examples of our MDR training set. Each row shows images, events and flow labels from top to bottom. + +the camera trajectory, we randomly add translation and rotation motions to create a smooth curve function $\Gamma(t)$ that outputs the location and pose $P(t) = [x(t), y(t), z(t), r(t)]^T$ . + +High-frame-rate Video and Optical Flow. After camera trajectory generation, we use the graphics engine to render a sequence of images $I(\boldsymbol{u}, t_i)$ , where $\boldsymbol{u} = (x, y)$ is the pixel coordinates and $t_i$ is the timestamp. We extract the forward and backward optical flow labels between every two timestamps $(\boldsymbol{F}_{t_i \to t_j}, \boldsymbol{F}_{t_j \to t_i})$ . Then we need to generate the event data to construct the event optical flow dataset. Here, we render high-frame-rate videos $\{I(\boldsymbol{u}, \tau)\}$ , $\tau \in [t_i, t_j]$ between timestamps $t_i$ and $t_j$ for events generation according to the camera trajectory $\Gamma(t)$ . + +Inspired by ESIM [40], we adopt an adaptive sampling strategy to sample camera locations from the camera trajectory for interval $t_i$ to $t_j$ , so that the largest displacement of all pixels between two successive rendered frames $(I(\pmb{u},\tau_k), I(\pmb{u},\tau_{k + 1}))$ is under 1 pixel, we define the sampling time interval $\Delta \tau_{k}$ as follows: + +$$ +\begin{array}{l} \Delta \tau_ {k} = \tau_ {k + 1} - \tau_ {k} \\ = \left(\max _ {\boldsymbol {u}} \max \left\{\left\| \boldsymbol {F} _ {\tau_ {k - 1} \rightarrow \tau_ {k}} \right\|, \left\| \boldsymbol {F} _ {\tau_ {k} \rightarrow \tau_ {k - 1}} \right\|\right\}\right) ^ {- 1}, \tag {1} \\ \end{array} +$$ + +where $|F| = \max_{\boldsymbol{u}} \max \left\{\left\| \boldsymbol{F}_{\tau_{k-1} \to \tau_k} \right\|, \left\| \boldsymbol{F}_{\tau_k \to \tau_{k-1}} \right\|\right\}$ is the maximum magnitude of the motion field between images $I(\boldsymbol{u}, \tau_{k-1})$ and $I(\boldsymbol{u}, \tau_k)$ . + +Event Generation from High-frame-rate Video. Given a high-frame-rate video $\{I(\pmb{u},\tau)\}$ , $\tau \in [t_i,t_j]$ between timestamps $t_i$ and $t_j$ , we next generate event stream by simulating the event trigger mechanism. Similar to [40] and [14], we use linear interpolation to approximate the continuous intensity signal in time for each pixel between video frames. Events $\{(u_e,t_e,p_e)\}$ are generated at each pixel $\pmb{u}_e = (x_e,y_e)$ whenever the magnitude of the change in the + +log intensity values $(L(\pmb{u}_e, t_e) = \ln(I(\pmb{u}_e, t_e))$ exceeds the threshold $C$ . This can be expressed as Eq. (2) and Eq. (3): + +$$ +L \left(\boldsymbol {u} _ {\boldsymbol {e}}, t _ {e} + \Delta t _ {e}\right) - L \left(\boldsymbol {u} _ {\boldsymbol {e}}, t _ {e}\right) \geq p _ {e} C, \tag {2} +$$ + +$$ +t _ {e} = t _ {e - 1} + \Delta \tau_ {k} \frac {C}{\left| L \left(\boldsymbol {u} _ {\boldsymbol {e}} , t _ {e} + \Delta t _ {e}\right) - L \left(\boldsymbol {u} _ {\boldsymbol {e}} , t _ {e}\right) \right|}, \tag {3} +$$ + +where $t_{e-1}$ and $t_e$ are the timestamps of the last triggered event and the next triggered event respectively, $p_e \in \{-1, +1\}$ is the polarity of the triggered event. We define it as $E(t_k, t_{k+1})$ , witch is the sequence $\{(u_e, t_e, p_e)^N, e \in [0, N]\}$ with $N$ events between time $t_k$ and $t_{k+1}$ . + +Multi-Density Rendered Events Dataset. Using the above data generation method, we can generate data with different event densities by using different threshold values $C$ . Since event stream is commonly first transformed into event representation [56, 42, 17] and then fed into deep networks. In order to measure the amount of useful information carried by the event stream, we propose to calculate the density of the event stream using the percentage of valid pixels (pixels where at least one event is triggered) in the voxel representation: + +$$ +V (\boldsymbol {u} _ {\boldsymbol {e}}, b) = \sum_ {e = 0} ^ {N} p _ {e} \max (0, 1 - | b - \frac {t _ {e} - t _ {0}}{t _ {N} - t _ {0}} (B - 1) |), \tag {4} +$$ + +$$ +D = \frac {1}{H W} \sum_ {e = 1} ^ {N} \varepsilon \left(\sum_ {b = 0} ^ {B - 1} | V \left(\boldsymbol {u} _ {\boldsymbol {e}}, b\right) |\right), \varepsilon (x) = \left\{ \begin{array}{l} 1, x > 0 \\ 0, x \leq 0 \end{array} , \right. \tag {5} +$$ + +where $V(\boldsymbol{u}_e) \in \mathbb{R}^{B \times H \times W}$ is the voxel representation [56] of the event stream $\{(u_e, t_e, p_e)^N\}$ between $t_0$ and $t_N$ , $b \in [0, B - 1]$ indicates the temporal index, $B$ (typically set to 5) donates temporal bins and $D$ is the density of the input event representation $V$ . The notation $|\cdot|$ denotes the absolute value operation. In practical applications, different event cameras may use different threshold values in different scenes, resulting in data with different event densities. Intuitively, event data with lower density is more difficult for optical flow estimation. In order to train models that can cover event data with various densities, in this paper, we propose to adaptively normalize the density of the input events to a certain density representation for optical flow estimation, so as to increase the generalization ability of the network. + +# 3.2. Event-based Optical Flow Estimation + +Event-based optical flow estimation involves predicting dense optical flow $\pmb{F}_{k-1\rightarrow k}$ from consecutive event sequences $E(t_{k-1},t_k)$ and $E(t_k,t_{k+1})$ . In this paper, we find that networks perform better on event sequences with appropriate density than on those with excessively sparse or + +![](images/8ef6290d423be3198bf4fef6f56c6d2ac335e93d6a3677391682bb7a48632e1c.jpg) +Figure 4: The structure of the proposed network. We design a plug-and-play Adaptive Density Module (ADM) to transform input event representations $V_{1}$ and $V_{2}$ into $V_{1}^{\mathrm{ad}}$ and $V_{2}^{\mathrm{ad}}$ with suitable density for optical flow estimation. + +dense events, when given events from the same scene. Motivated by this, we propose a plug-and-play Adaptive Density Module (ADM) that normalizes the input event stream to a density suited for estimating optical flow. Our network architecture is shown in Fig. 4, where the ADM transforms input event representations $V_{1}$ and $V_{2}$ to justified event representations $V_{1}^{\mathrm{ad}}$ and $V_{2}^{\mathrm{ad}}$ , which are then used by an existing network structure to estimate optical flow. + +Adaptive Density Module. As shown in Fig. 4, our ADM module consists of two sub-modules: the multi-density changer (MDC) module and the multi-density selector (MDS) module. The MDC module globally adjusts the density of the input event representations from multi-scale features, then the MDS module picks the best pixel-wise density for optical flow estimation. + +The MDC module adopts an encoder-decoder architecture with three levels, as illustrated in Fig. 5(a). To generate multiscale transformed representations $V_{3}^{\mathrm{MDC}}$ , $V_{2}^{\mathrm{MDC}}$ and $V_{1}^{\mathrm{MDC}}$ (also noted as $V_{\mathrm{out}}^{\mathrm{MDC}}$ ) from the concatenated input event representations $V$ , three encoding blocks are employed to extract multiple scale features, followed by three decoding blocks and two feature fusion blocks. It is worth noting that, to ensure the lightweightness of the entire module, we utilize only two $3 \times 3$ and one $1 \times 1$ convolutional layers in each encoding and decoding block. + +To maintain the information in the input event representation and achieve density transformation, we adopt the MDS module for adaptive selection and fusion of $V_{\mathrm{out}}^{\mathrm{MDC}}$ and $V$ , as depicted in Fig. 5(b). We first concatenate $V_{\mathrm{out}}^{\mathrm{MDC}}$ and $V$ , and then use two convolutional layers to compare them and generate selection weights via softmax. Finally, we employ the selection weights to identify and fuse $V_{\mathrm{out}}^{\mathrm{MDC}}$ and $V$ , producing the transformed event representation $V_1^{\mathrm{ad}}$ and $V_2^{\mathrm{ad}}$ , which are fed into an existing flow network for optical flow estimation. In this paper, we use KPA-Flow [32] for optical flow estimation by default. + +![](images/5e86666ebce5795b0da86a7dd9eca3a123bb67ea6997dfc8f02d65ee26b9b857.jpg) + +![](images/e8f9a4fefd4636ec05e286fdac2f152470ebfd90f931898bea8830c5fe8f553f.jpg) +Figure 5: The detailed structure of sub-modules used in our proposed ADM model: (a) MDC, (b) MDS. + +Loss Function. Based on our MDR dataset, we use the event representation with a moderate density as the ground truth (noted as $V^{\mathrm{GT}}$ ) to train our ADM module. For the MDC module, we use a multi-scale loss as follows: + +$$ +L _ {\mathrm {M D C}} = \sum_ {k = 1} ^ {3} \sqrt {\left(V _ {k} ^ {\mathrm {M D C}} - V _ {k} ^ {\mathrm {G T}}\right) ^ {2} + \xi^ {2}}, \tag {6} +$$ + +where $\xi = 10^{-3}$ is a constant value, $V_{k}^{\mathrm{MDC}}$ is the output of the $k$ -th level in MDC, and $V_{k}^{\mathrm{GT}}$ is downsampled from $V^{\mathrm{GT}}$ to match the spatial size. + +For the MDS module, we use the distance between the density of $V^{\mathrm{ad}}$ and $V^{\mathrm{GT}}$ as the guidance: + +$$ +L _ {\mathrm {M D S}} = \left\| D \left(V ^ {\mathrm {a d}}\right) - D \left(V ^ {\mathrm {G T}}\right) \right\| _ {1}, \tag {7} +$$ + +where $D$ means to calculate the density as in Eq. (5). + +For the flow network, we use L1 loss (denoted as $L_{\mathrm{Flow}}$ ) between flow prediction and ground truth as the guidance. + +The final loss function for training the whole pipeline in Fig. 4 is determined as follows: + +$$ +L _ {\text {t o t a l}} = \lambda_ {1} L _ {\mathrm {M D C}} + \lambda_ {2} L _ {\mathrm {M D S}} + L _ {\text {F l o w}}, \tag {8} +$$ + +where we empirically set $\lambda_{1} = 0.1$ and $\lambda_{2} = 10$ . + +# 4. Experiments + +# 4.1. Datasets + +MDR: We create the MDR dataset using the graphics engine blender. We use various 3D scenes for data generation. There are 80,000 training samples and 6,000 validation samples with accurate dense optical flow ground truth. Each sample has event sequences with different densities produced by using different thresholds $C$ . By default, for + +
Method (dt=1)Train D.TypeTrain D.Setindoor flying1indoor flying2indoor flying3outdoor day1Avg
EPE%OutEPE%OutEPE%OutEPE%OutEPE%Out
ESTS[15]EM0.970.911.388.201.436.47--1.265.19
EV-FlownetS[54]I1,I2,EM1.032.201.7215.11.5311.90.490.201.197.35
Deng et al.S[10]EM0.890.661.316.441.133.53--1.113.54
Paredes et al.S[39]EM0.791.201.4010.91.187.400.925.401.076.22
Matrix-LSTMS[6]I1,I2,EM0.820.531.195.591.084.81--1.033.64
LIF-EV-FlowNetS[18]EFPV0.711.411.4412.81.169.110.530.330.965.90
Spike-FlowNetS[27]I1,I2,EM0.84-1.28-1.11-0.49-0.93-
Fusion-FlowNetD[26]I1,I2,EM0.62-0.89-0.85-1.02-0.84-
Fusion-FlowNetS[26]I1,I2,EM0.56-0.95-0.76-0.59-0.71-
E-RAFTD[17]EM1.105.721.549.791.368.240.270.001.075.94
E-RAFTS[17]EM0.871.321.136.201.034.700.240.000.823.06
Zhu et al.S[56]EM0.580.001.024.000.873.000.320.000.691.75
DCEIFlowD[50]I1,I2,EM0.560.280.640.160.570.120.910.710.670.31
DCEIFlowS[50]I1,I2,EC20.570.300.700.300.580.150.740.290.640.26
Stoffregen et al.S[42]EESIM0.561.000.661.000.591.000.680.990.620.99
STE-FlowNetS[11]I1,I2,EM0.570.100.791.600.721.300.420.000.620.75
ADM-FlowD(ours)EMDR0.480.110.560.400.470.020.520.000.510.14
ADM-FlowS(ours)EMDR0.520.140.681.180.520.040.410.000.530.34
Method (dt=4)Train D.TypeTrain D.Setindoor flying1indoor flying2indoor flying3outdoor day1Avg
EPE%OutEPE%OutEPE%OutEPE%OutEPE%Out
LIF-EV-FlowNetS[18]EFPV2.6329.64.9351.13.8841.52.0218.93.3635.3
EV-FlownetS[54]I1,I2,EM2.2524.74.0545.33.4539.71.237.302.7429.3
E-RAFTD[17]EM3.2635.44.3248.64.1448.20.841.703.1433.5
E-RAFTS[17]EM2.8130.63.9940.93.7840.50.721.122.8328.3
Zhu et al.S[56]EM2.1824.23.8546.83.1847.81.309.702.6232.1
Spike-FlowNetS[27]I1,I2,EM2.24-3.83-3.18-1.09-2.58-
Fusion-FlowNetD[26]I1,I2,EM1.81-2.90-2.46-3.06-2.55-
Fusion-FlowNetS[26]I1,I2,EM1.68-3.24-2.43-1.17-2.13-
STE-FlowNetS[11]I1,I2,EM1.7714.72.5226.12.2322.10.993.901.8716.7
DCEIFlowD[50]I1,I2,EC21.498.141.9717.41.6912.31.8719.11.7514.2
DCEIFlowS[50]I1,I2,EC21.528.792.2122.11.7413.31.378.541.7113.2
ADM-FlowD(ours)EMDR1.397.331.6311.51.519.341.9119.21.6111.8
ADM-FlowS(ours)EMDR1.427.781.8816.71.6111.41.5110.21.6011.5
+ +Table 1: Quantitative comparison of our method with previous methods on the MVSEC dataset [55]. Subscripts $S$ and $D$ donate the sparse and dense evaluation, respectively. We mark the best results in red and the second best results in blue. + +training on MDR, we use the combination of all these samples with different densities to train flow networks. For the learning of our ADM module, we choose events with density between 0.45 and 0.55 as the label for $L_{\mathrm{MDC}}$ and $L_{\mathrm{MDS}}$ . + +MVSEC: The MVSEC dataset [55] is a real-world dataset collected in indoor and outdoor scenarios with sparse optical flow labels. As a common setting, 28, 542 data pairs of the 'outdoor day2' sequence are used as the train set, and 8, 410 data pairs of the other sequences are used as the validation set. The density ranges of MVSEC train set and validation set are [0.0003, 0.47] and [0.001, 0.31], respectively. DSEC: The DSEC dataset [16] is also collected using actual event cameras and lidar sensors on outdoor scenes. The dataset consists of 7,800 training samples and 2,100 test samples, divided into 24 sequences that include both day and night scenarios. + +Previous methods have trained on other datasets, including synthetic datasets like C2 [50] and ESIM [42], as well + +as real-world captured datasets such as FPV [9]. To assess the performance of these methods, comparisons are made on the validation set of the MVSEC dataset. Both MVSEC and MDR datasets have two input settings for training and testing. These settings involve using the events between successive images within a time interval of $dt = 1$ and $dt = 4$ . On the other hand, for the DSEC dataset, there is a public benchmark available specifically designed to evaluate flow networks. However, this benchmark only provides one input setting for testing. We denote MVSEC, DSEC, and MDR datasets by "M", "D", and "MDR". + +# 4.2. Implementation details + +We use PyTorch to implement our method and train all networks using the same setting. The networks are trained with the AdamW optimizer, with a batch size of 6 and learning rate of $4 \times 10^{-4}$ for 150k iterations. Since the MVSEC dataset lacks multiple density event streams required for the learning of our ADM module, we disable $L_{\mathrm{MDC}}$ and $L_{\mathrm{MDS}}$ + +when training on the MVSEC dataset. + +# 4.3. Evaluation metrics + +The evaluation metrics used in flow prediction models are the average End-point Error (EPE) and 1PE, 2PE, and 3PE (the percentage of pixels with EPE greater than 1,2,3 pixels) for DSEC dataset, and $\% \text{Out}$ (the percentage of points with EPE greater than 3 pixels and $5\%$ of the ground truth flow magnitude) for MVSEC dataset. There are two types of evaluations: dense and sparse. In emphdense evaluation, errors are calculated only at pixels with valid flow annotations. Sparse evaluation focuses on pixels with valid flow annotations that have triggered at least one event. Experiments are performed on both MVSEC and MDR, considering both dense and sparse evaluations. However, only dense dense is conducted for DSEC. + +# 4.4. Comparison with State-of-the-Arts + +Results on MVSEC. In Table 1, we compare our model trained on the MDR train set with previous methods on the MVSEC evaluation set, and report detailed results for each sequence. We provide information on the data types (Train D.Type) and the training sets (Train D.Set) used in the training process for each method. Specifically, $\mathrm{I}_1,\mathrm{I}_2,\mathrm{E}$ indicates that both image data and event data are used in the training and inference processes of the model, while $\mathrm{E}$ indicates that only event data is used. As shown in Table 1, our model trained on the MDR dataset achieves state-of-the-art performance for both EPE and %Out metrics in settings of $dt = 1$ and $dt = 4$ . Notably, our method demonstrates a $23.9\%$ improvement (reducing EPE from 0.67 to 0.51) for dense optical flow estimation in $dt = 1$ settings, and an $8.0\%$ improvement (reducing EPE from 1.75 to 1.61) in $dt = 4$ settings, surpassing previous methods. Qualitative comparison results are shown in row 1 and row 2 in Fig. 6. + +Results on MDR. In Table 3, we compare our method with previous methods for training on the MVSEC dataset and testing on the MDR dataset for cross-training and validation to avoid over-fitting. We use different thresholds $C$ to generate test data with different density ranges for evaluation. For the average EPE error of dense optical flow estimation, our model obtains the best result, which is a $17.1\%$ improvement (reducing EPE from 0.82 to 0.68) in $dt = 1$ settings, and a $16.7\%$ improvement (reducing EPE from 1.98 to 1.65) in $dt = 4$ settings. We also show some qualitative comparison results in row 3 and row 4 in Fig. 6. + +Results on DSEC. In Table 2, we report the results on the DSEC test set for different models that are trained on DSEC, MDR, and a combination of DSEC and MDR. As can be seen, MDR-trained models produce comparable results to in-domain learned models on the DSEC train set. + +
MethodsTrain D.Set1PE2PE3PEEPE
EV-FlowNet [54]D55.1328.4316.712.22
MDR42.5224.4016.321.86
D+MDR35.0615.417.841.31
E-RAFT [17]D16.196.223.590.90*
MDR18.857.444.371.00
D+MDR13.165.192.930.82
ADM-EVFLOWD42.8925.2115.801.90
MDR40.0214.8812.341.67
M+D23.4610.325.611.12
ADM-Flow(ours)D13.965.323.180.88
MDR14.535.783.590.92
D+MDR12.524.672.650.78
+ +Table 2: Results on the DSEC test set. * denotes our reproduced results of E-RAFT, since the official training code is not released. All experiments are conducted on the same training code for fair comparison. + +Moreover, training E-RAFT on the combined DSEC/MDR datasets yields improved performance, demonstrating the effectiveness of MDR. Our ADMFlow model achieves improved performance on all training datasets, highlighting the effectiveness and versatility of ADM. Some qualitative results are shown in Fig. 7. + +Analysis of the MDR dataset. To demonstrate the effectiveness of our proposed MDR dataset, we train several optical flow networks [46, 17, 53, 21, 47, 24, 32] on both MDR and MVSEC train sets using identical training settings. For training, we use a combination of data samples from the MDR dataset with a density range of $[0.09, 0.69]$ . We evaluate the trained networks on the MVSEC validation set, and the results, presented in Table 4, demonstrate that all networks trained on the MDR dataset outperform those trained on the MVSEC dataset. + +# 4.5. Ablation study. + +Training with different densities. We examine the impact of input event sequence density on optical flow learning, as our MDR dataset contains event data with various densities and corresponding dense flow labels. We train SKFlow [47], GMA [24], FlowFormer [21] and KPA-Flow [32] on the same sequence from our MDR dataset but with different average densities produced by using different threshold $C$ , and then test them on the MVSEC dataset. Figure 8 shows the results in $dt = 4$ setting, indicating that these models perform better as the average density of the training set increases. However, their performance diminishes as the average density continues to increase. This phenomenon highlights the importance of selecting an appropriate density for the training set when learning event optical flow. + +![](images/eec76298cb8ce9e99f1d56987f432fe6724c9964a22ba380cecef7c05115131e.jpg) + +![](images/c75a4a3623d6d38d3ccd146bf30e6911b0f7716abecd25bd47ebad58071edb6b.jpg) + +![](images/867ee07d161f9f6d0f39fce22012e403c50163148d8fc8ab3da1c250bb94ad00.jpg) + +![](images/dd2e9e2752d50844d266f91849a348a92fa667da1ede21d6abfd499fc2da8eea.jpg) +Reference + +![](images/1be890ec454cd5e1c6e2ed7d7820fd30bc8a699177db63c9e77a578fa6e32421.jpg) + +![](images/66045b73fd9f89b447e50eb37a95cd8af2e1082befad56d7dadd957437e3c484.jpg) + +![](images/55b4fe0bac57f91c4da8050141166e28ff4b1a63423d4cceb28c440de083153c.jpg) + +![](images/f2df13a0af494fb5c367986da214fd952f943daaaf102b6685dd378ea95e7d35.jpg) +Spike-Flownet + +![](images/406d3c746ccf1ceab0c9e2732bd7437e91f9709fd09306f65595ff0cf9d8a0cc.jpg) + +![](images/61ec685efcc0521fed4d4fbe643d24982647083c0e9f5c21e8838970fb125263.jpg) + +![](images/5ddffc649726eb10dfc310f0aee134dfb776e674286dc7eefb7644c10b148d93.jpg) + +![](images/290c9ed0f2a7c50eda355cc56405b1aaf70bc5ef5241d33e4db82f1c9d719e8d.jpg) +STE-FlowNet + +![](images/3f5da2600a8738e1f002fa88cff221ab4e04e7f681486b0d7d1a4d052fc96002.jpg) + +![](images/050f2e1aa5a6042b36ef526ddada13b5d7258d539f8cea944ada92d6a5d7021d.jpg) + +![](images/6fd90e78c132b819b02f6fd65398a32a93ecc1fb36984f00fbeefb9080d7ce93.jpg) + +![](images/4b9289ebe574522dc9318ffb58d7cab6cdcf85ba09639fd563223e13b5a5681b.jpg) +E-RAFT + +![](images/5dbdded4e8e9af627f180ec8590f2ef86a4f461acff5969903b281c2cf274350.jpg) + +![](images/4b4b40fccc946ac7d7a42c765cfdefb6e4543ca7ae566ef023328896da0cefe3.jpg) + +![](images/fa6cfa245143c187cebb8a9f791f73b4b87d5bcbaf782e2006e27d8f4601b1bb.jpg) + +![](images/3e5563510cd490a38536a318db2c53e73e6b66a540733ed6ed5891bb98d96ca9.jpg) +DCEIFlow + +![](images/c627cc2445d5ae4baccc0125689996005e8afd8d7cd796dcea83739436e1751b.jpg) + +![](images/43d1675b0b83fb145e3dc6ab7f32ebc707bc62aedbe63887b1f798737459c316.jpg) + +![](images/1c03b5b240d21869674accce17e09c7496cc50ad58a42080428ffccf616c8d4b.jpg) + +![](images/f56b0443e4bbbb4d8031f5511a94f5098f36e6bec44bde8cf6ec43e721f986a2.jpg) +Ours + +![](images/3c70abe66842a1728c3e215c2b733271eb183d016b7a642f4eb4a1c11572a115.jpg) + +![](images/b7b197fc100c5841e93bc8f7c94a0157b1571b2569b83857335f07077c654740.jpg) + +![](images/c51757edfdba25972f8048668f8054200ecfeb54119bdbafcc33270501580b26.jpg) + +![](images/40e1af0ef9b2d2d9d293b6dc961d943600072ce4ab8e251d2b5b112508e25bd6.jpg) +Flow GT + +![](images/00b84c01d3c253304cc90251ebb8b60c4298dd9b7dc59711f9f87aaaa26e50b1.jpg) +Figure 6: Qualitative comparisons compared with existing event-based methods. Row 1 and 2 are from MVSEC, whereas row 3 and 4 are from MDR. Row 1 and 3 visualize the dense predictions, whereas row 2 and 4 show the sparse. + +![](images/e7cb227cfd6749a4c76a198fad6fb240d5a2c117cdc4d1ea60c1d628faebc853.jpg) + +![](images/fd4d902a07689865201ffa84cca5911d860af004debee851a37ec18aea95f8ec.jpg) + +![](images/cc893ce19b7e4238a0504f7c688ebc1ec0f84cd9ba5740805e771dc5d03181ad.jpg) +Reference +Figure 7: Qualitative comparisons on the DSEC test set. We visualize the dense predictions and zoom in the areas where are apparent differences. + +![](images/f8237b7f8787cba75550e39d90c9aa956cfc1a74a80b29173e7a19328b3d16fd.jpg) + +![](images/55972bd97326c651f12e5203825048dcd719eeac555d60e9fae2f88634a08b3d.jpg) + +![](images/8a7a584c8ac1dfd47059eb8fb54dd0dbc5ba0b118f288da0fdcb8e6f8afa6dbe.jpg) + +![](images/cb889c57b08640b6dd8af3266fa0bddb331428b32189c9eaa7788fd2516297cf.jpg) +EV-Flownet + +![](images/0474f06f204470057c274df77e0d0099cbcb2c8be392758768a14527075df01e.jpg) + +![](images/e6b86744587cfebf203d6565b285d1c37dffd7d7da52a51d6b40536e90d35c57.jpg) + +![](images/d5fa74db9b7ed0ea2e7e8cc2c2b136d6f57691f865eb43a7393d2a33b5778576.jpg) + +![](images/2877d5edc44e0474d1c2e9c75ee631bf90d96f102da73f1816a36f85b5f1c0f6.jpg) +E-RAFT + +![](images/d34f5d349c91573b6ac51570436b9cd3d096fe3cf24b46d2e7e70873cba5bb57.jpg) + +![](images/f00c81039c8f7621386d8d7a757fbee6a6becd9ae5b4058151ac53a8d77354c6.jpg) + +![](images/56e04cfb9c39a627c0ebdc1194d550e317a78704b8da60de836937f603111358.jpg) +Ours + +Ablation for ADM. In order to verify the impact of our proposed ADM module, we conduct ablation experiments by plugging the ADM module into several optical flow net + +
Method (dt = 1)density rangeAvg
0.09-0.240.24-0.390.39-0.540.54-0.69
Spike-FlowS [27]1.931.201.332.011.62
STE-FlowS [11]1.171.110.821.301.10
DCEIFlowD [50]1.281.371.271.461.35
DCEIFlowS [50]1.000.840.750.820.85
E-RAFTD [17]0.930.740.690.920.82
E-RAFTS [17]0.820.650.660.820.74
ADM-FlowD(ours)0.770.690.500.740.68
ADM-FlowS(ours)0.690.640.490.740.64
Method (dt = 4)density rangeAvg
0.09-0.240.24-0.390.39-0.540.54-0.69
Spike-FlowS [27]3.951.962.092.872.72
STE-FlowS [11]2.902.271.982.172.33
DCEIFlowD [50]3.842.682.994.273.45
DCEIFlowS [50]2.251.321.192.341.78
E-RAFTD [17]2.641.421.352.511.98
E-RAFTS [17]2.181.311.242.291.76
ADM-FlowD(ours)2.121.201.242.021.65
ADM-FlowS(ours)2.031.131.091.901.54
+ +Table 3: Quantitative evaluation on our MDR dataset. The methods in the table are all trained on the MVSEC dataset for cross-training and validation to avoid over-fitting. $S$ and $D$ donate the sparse and dense evaluation, respectively. We use EPE as the evaluation metric. + +works to selectively adjust the densities of the input events. We train these networks on both MDR and MVSEC datasets with the same setting except that the ADM module is dis + +
MethodTrain D.Setdt = 1dt = 4
EPE%OutEPE%Out
PWCNet [22]M1.255.414.0351.48
MDR1.143.482.9238.62
RAFT [48]M1.194.903.3339.78
MDR0.590.512.5730.24
GMFlowNet [53]M1.003.753.6142.31
MDR0.821.662.7031.53
FlowFromer [21]M0.873.083.3841.04
MDR0.610.402.4928.83
SKFlow [47]M1.073.973.4140.87
MDR0.590.332.4627.64
GMA [24]M0.884.052.9934.80
MDR0.580.442.1923.00
KPAFlow [32]M0.862.863.1938.32
MDR0.580.392.3326.10
+ +![](images/bd3e3ec1bc8fec642a749147c11697f06687a3b93bdf86b0eecf264e87214c5b.jpg) +Figure 8: The performance of some supervised optical flow networks with different densities of the training set in $dt = 4$ setting. X-axis is the average density of events in the training set, and y-axis is their average EPE on MVSEC validation set. Different colors represent the performance of different networks, and the pentagons show the performance of networks trained on the MDR training set with a widely density range of [0.09, 0.69], and the average density is 0.41. + +abled or not, and test them on the MVSEC dataset. The experiment results are shown in Table 5, where we can notice that our ADM module can bring performance improvement for all supervised methods. + +Ablation for the design of ADM. We conduct ablation experiments to verify the effectiveness of each component in our ADM module, including MDC, MDS, and the two training loss functions $L_{\mathrm{MDC}}$ and $L_{\mathrm{MDS}}$ . We train models using the same settings on the MDR dataset and evaluate them on the MVSEC dataset to show the individual impact of each component in our ADM module. The results are presented in Table 6. The comparison of (a)&(b) shows that adding only the MDC plugin results in a slight performance gain. Comparison of (b)&(c) reveals that en + +Table 4: Comparison of training on MVSEC vs. MDR. Models are evaluated on MVSEC for dense optical flow estimation. + +
MethodM(dt = 1)MDR(dt = 1)M(dt = 4)MDR(dt = 4)
EPE%OutEPE%OutEPE%OutEPE%Out
PWCNet [22]1.255.411.143.484.0351.482.9238.62
ADM-PWCNet1.074.520.761.482.9533.311.9418.74
RAFT [48]1.194.900.590.513.3339.782.5730.24
ADM-RAFT0.823.030.560.242.7330.911.7213.83
GMFlowNet [53]1.003.750.821.663.6142.312.7031.53
ADM-GMFlowNet0.873.050.580.322.7831.261.8114.45
FlowFromer [21]0.873.080.610.403.3841.042.4928.83
ADM-FlowFromer0.782.870.530.152.5626.571.6712.78
SKFlow [47]1.073.970.590.333.4140.872.4627.64
ADM-SKFlow0.843.180.530.142.6728.171.6912.61
GMA [24]0.884.050.580.442.9934.802.1923.00
ADM-GMA0.762.650.540.222.4525.751.6311.95
KPAFlow [32]0.862.860.580.393.1938.322.3326.10
ADM-KPAFlow0.802.670.510.142.5928.421.6111.83
+ +Table 5: Quantitative comparison of whether using ADM. Models are trained on MVSEC and MDR, and evaluated on MVSEC for dense optical flow estimation in $dt = 1$ and $dt = 4$ settings. + +
MethodMDCMDSLMDCLMDSParam. (M)dt = 1dt = 4
EPE%OutEPE%Out
(a)××××6.010.580.392.3326.10
(b)✓×××7.710.570.332.2023.78
(c)✓✓××7.720.540.261.9218.26
(d)✓✓✓×7.720.520.161.6613.29
(e)✓✓✓✓7.720.510.141.6111.83
+ +Table 6: Ablation study. Models are trained on the MDR training set, and evaluated on the MVSEC validation set for dense optical flow estimation in $dt = 1$ and $dt = 4$ settings. + +abling the density selection function through the MDS module brings a significant improvement. Comparing (c)&(d) and (d)&(e), we notice that with the guidance of two loss functions, ADM can learn to selectively choose the best density for optical flow estimation, resulting in a relatively significant improvement. + +# 5. Conclusion + +In this work, we have created a rendered dataset for event-flow learning. Indoor and outdoor virtual scenes have been created using Blender with rich scene contents. Various camera motions are placed for the capturing of the virtual world, which can produce frames as well as accurate flow labels. The event values are generated by rendering high frame rate videos between two frames. In this way, the flow labels and event values are physically correct and accurate. The rendered dataset can adjust density of events by modifying the event trigger threshold. We have introduced a novel adaptive density module (ADM), which has shown its effectiveness by plugin into various event-flow pipelines. When trained on our dataset, previous approaches can improve their performances constantly. + +Acknowledgements This work was supported by Sichuan Science and Technology Program of China under grants Nos. 2023NSFSC0462, 2023NSFSC1972, 2021YFG0001, 2022YFG0011 and 2022YFG0050. + +# References + +[1] Ryad Benosman, Sio-Hoi Ieng, Charles Clercq, Chiara Bartolozzi, and Mandyam Srinivasan. Asynchronous frameless event-based optical flow. *Neural Networks*, 2012. 2, 3 +[2] Yin Bi, Aaron Chadha, Alhabib Abbas, Eirina Bourtsovlatze, and Yiannis Andreopoulos. Graph-based object classification for neuromorphic vision sensing. In Proc. ICCV, 2019. 3 +[3] Jonathan Binas, Daniel Neil, Shih-Chii Liu, and Tobi Delbruck. 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CVPR, 2019. 4, 6 \ No newline at end of file diff --git a/2023/Learning Optical Flow from Event Camera with Rendered Dataset/images.zip b/2023/Learning Optical Flow from Event Camera with Rendered Dataset/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ffa99d9b3c99a653dc69cb7e76a1baa72ce73a09 --- /dev/null +++ b/2023/Learning Optical Flow from Event Camera with Rendered Dataset/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8d2850f3b820d5a7f0ab8ff0f2213f3ed43adb9d57712cf73822646d01694cd4 +size 1080163 diff --git a/2023/Learning Optical Flow from Event Camera with Rendered Dataset/layout.json b/2023/Learning Optical Flow from Event Camera with Rendered Dataset/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..299e12da7659bbe8576ff1a3c924df9958ecc319 --- /dev/null +++ b/2023/Learning Optical Flow from Event Camera with Rendered Dataset/layout.json @@ -0,0 +1,12136 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 91, + 103, + 503, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 103, + 503, + 121 + ], + "spans": [ + { + "bbox": [ + 91, + 103, + 503, + 121 + ], + "type": "text", + "content": "Learning Optical Flow from Event Camera with Rendered Dataset" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "spans": [ + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "text", + "content": "Xinglong Luo" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "inline_equation", + "content": "^{1,3}" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "text", + "content": ", Kunming Luo" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "text", + "content": ", Ao Luo" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "text", + "content": ", Zhengning Wang" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "text", + "content": ", Ping Tan" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "text", + "content": ", and Shuaicheng Liu" + }, + { + "bbox": [ + 64, + 152, + 533, + 168 + ], + "type": "inline_equation", + "content": "^{1,3*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 99, + 176, + 494, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 176, + 494, + 227 + ], + "spans": [ + { + "bbox": [ + 99, + 176, + 494, + 227 + ], + "type": "text", + "content": "1University of Electronic Science and Technology of China \n2The Hong Kong University of Science and Technology 3Megvii Technology {luoboom@std.,zhengning.wang@,liushuaicheng}@uestc.edu.cn {kluoad@connect,pingtan@}.ust.hk luoao02@megvii.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 262, + 192, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 262, + 192, + 275 + ], + "spans": [ + { + "bbox": [ + 143, + 262, + 192, + 275 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 288, + 290, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 290, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 290, + 587 + ], + "type": "text", + "content": "We study the problem of estimating optical flow from event cameras. One important issue is how to build a high-quality event-flow dataset with accurate event values and flow labels. Previous datasets are created by either capturing real scenes by event cameras or synthesizing from images with pasted foreground objects. The former case can produce real event values but with calculated flow labels, which are sparse and inaccurate. The latter case can generate dense flow labels but the interpolated events are prone to errors. In this work, we propose to render a physically correct event-flow dataset using computer graphics models. In particular, we first create indoor and outdoor 3D scenes by Blender with rich scene content variations. Second, diverse camera motions are included for the virtual capturing, producing images and accurate flow labels. Third, we render high-framerate videos between images for accurate events. The rendered dataset can adjust the density of events, based on which we further introduce an adaptive density module (ADM). 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(b) the synthesized dataset with flying chairs foreground [50]. (c) the synthesized dataset by moving a foreground image [42]. (d) Our synthesized dataset by graphics rendering, which not only reflects the real motions under correct scene geometries, but also produces accurate dense flow labels and events." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 398, + 372, + 471, + 426 + ], + "blocks": [ + { + "bbox": [ + 398, + 372, + 471, + 426 + ], + "lines": [ + { + "bbox": [ + 398, + 372, + 471, + 426 + ], + "spans": [ + { + "bbox": [ + 398, + 372, + 471, + 426 + ], + "type": "image", + "image_path": "bf78ea4a878bcb79576f94d576f8ef2f2c2c39fe361e5fbadc168f2146ea0063.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 420, + 427, + 472, + 483 + ], + "blocks": [ + { + "bbox": [ + 420, + 427, + 472, + 483 + ], + "lines": [ + { + "bbox": [ + 420, + 427, + 472, + 483 + ], + "spans": [ + { + "bbox": [ + 420, + 427, + 472, + 483 + ], + "type": "image", + "image_path": "a72ad426ebf87c17790e36f7c6e248ee6e35534c6c612bc40563ed9d9dc082c9.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 421, + 483, + 447, + 491 + ], + "lines": [ + { + "bbox": [ + 421, + 483, + 447, + 491 + ], + "spans": [ + { + "bbox": [ + 421, + 483, + 447, + 491 + ], + "type": "text", + "content": "Events" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 471, + 372, + 544, + 426 + ], + "blocks": [ + { + "bbox": [ + 471, + 372, + 544, + 426 + ], + "lines": [ + { + "bbox": [ + 471, + 372, + 544, + 426 + ], + "spans": [ + { + "bbox": [ + 471, + 372, + 544, + 426 + ], + "type": "image", + "image_path": "7f28d128398f11860d7ca434865d69f423278b381ee21278de725ca521ed0c03.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 471, + 428, + 544, + 483 + ], + "blocks": [ + { + "bbox": [ + 471, + 428, + 544, + 483 + ], + "lines": [ + { + "bbox": [ + 471, + 428, + 544, + 483 + ], + "spans": [ + { + "bbox": [ + 471, + 428, + 544, + 483 + ], + "type": "image", + "image_path": "52478f78fe365dea8dbf3e0edf5a9404b0cf7fc1cdd10565a6335fef6a78188b.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 490, + 483, + 524, + 491 + ], + "lines": [ + { + "bbox": [ + 490, + 483, + 524, + 491 + ], + "spans": [ + { + "bbox": [ + 490, + 483, + 524, + 491 + ], + "type": "text", + "content": "Flow GT" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "change, indicating a pixel become brighter or darker. On the other hand, optical flow estimation predicts motions between two frames [44], which is fundamental and important for many applications [49, 52, 7]. In this work, we study the problem of estimating optical flow from event camera data, instead of from RGB frames. Different from traditional images, events are sparse and are often integrated in short intervals as the input for the prediction. As such, early works" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9847" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "can only estimate sparse flows at the location of events [1]. Recent deep methods can estimate dense flows but with the help of images, either as the guidance [54] or as the additional inputs [26, 38]. Here, we tackle a hard version of the problem, where dense flows are predicted based purely on the event values " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": ". One key issue is how to create high quality event-based optical flow dataset to train the network." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 288, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 288, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 288, + 374 + ], + "type": "text", + "content": "Existing methods of event flow dataset creation can be classified into two types, 1) directly capturing from real event cameras [55, 54, 16]; 2) moving foregrounds on top of a background image to create synthesized flow motions [50, 42] and apply frame interpolation [14] to create events. For the first type, the ground-truth (GT) flow labels need to be calculated based on gray images acquired along with the event data. However, the optical flow estimations cannot be perfectly accurate [48, 43, 32, 24, 51], leading to the inaccuracy of GT labels. To alleviate the problem, additional depth sensors, such as LIDAR, have been introduced [55]. The flow labels can be calculated accurately when the depth values of LIDAR scans are available. However, LIDAR scans are sparse, and so do the flow labels, which are unfriendly for dense optical flow learning. Fig. 1 (a) shows an example, LIDAR points on the ground are sparse. Moreover, some thin objects are often missing, as indicated by the red box in Fig. 1 (a)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 376, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 532 + ], + "type": "text", + "content": "For the second category, the flow labels are created by moving foreground objects on top of a background image, similar to flying chairs [12] or flying things [36]. In this way, the flow labels are dense and accurate. To create events, intermediate frames are interpolated [23]. However, the frame interpolation is inaccurate due to scene depth disparities, where the occluded pixels cannot be interpolated correctly, leading to erroneous event values in these regions. To match high framerate of events, the large number of interpolated frames makes the problem even worse. Fig. 1 (b) shows an example, where the events are incorrect at the occluded chairs. Moreover, the motions are artificial, further decreasing the realism of the dataset (Fig. 1 (b) and (c))." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": "In this work, we create an event-flow dataset from synthetic 3D scenes by graphics rendering (Fig. 1 (d)). While there is a domain gap between rendered and real images, this gap is empirically found insignificant in event camera based classification [41] and segmentation [14] tasks. As noted by these works, models trained on synthetic events work very well for real event data. Because events contain only positive and negative polarities, no image appearances are involved. To this end, we propose a Multi-Density Rendered (MDR) event optical flow dataset, created by Blender on indoor and outdoor scenes with accurate events and flow labels. In addition, we design an Adaptive Density Module (ADM) based on MDR, which can adjust the densities of events, one of the most important factors for event-based tasks but has been largely overlooked." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": "Specifically, our MDR dataset contains 80,000 samples from 50 virtual scenes. Each data sample is created by first rendering two frames and obtaining the GT flow labels directly from the engine. Then, we render " + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "inline_equation", + "content": "15 \\sim 60" + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": " frames in between based on the flow magnitude. The events are created by thresholding log intensities and recording the times-stamp for each spatial location. The density of events can be controlled by the threshold values. The ADM is designed as a plugin module, which further consists of two sub-modules, multi-density changer (MDC) and multi-density selector (MDS), where the MDC adjusts the density globally while the MDS picks the best one for every spatial location. Experiments show that previous event-flow methods, when trained on our MDR dataset, can improve their performances. Moreover, we train several recent representative flow pipelines, such as FlowFormer [21], KPA-Flow [32], GMA [24] and SKFlow [47], on our MDR dataset. When equipped with our ADM module, the performances can increase consistently." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 318, + 301, + 471, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 301, + 471, + 312 + ], + "spans": [ + { + "bbox": [ + 318, + 301, + 471, + 312 + ], + "type": "text", + "content": "Our contributions are summarized as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 327, + 545, + 475 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 318, + 327, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 327, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 318, + 327, + 545, + 374 + ], + "type": "text", + "content": "- A rendered event-flow dataset MDR, with 80,000 samples created on 53 virtual scenes, which possess physically correct accurate events and flow label pairs, covering a wide range of densities." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 318, + 389, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 389, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 318, + 389, + 545, + 414 + ], + "type": "text", + "content": "- An adaptive density module (ADM), which is a plug-and-play module for handling varying event densities." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 318, + 429, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 429, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 318, + 429, + 545, + 475 + ], + "type": "text", + "content": "- We achieve state-of-the-art performances. Our MDR can improve the quality of previous event-flow methods. Various optical flow pipelines when adapted to the event-flow task, can benefit from our ADM module." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 492, + 392, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 492, + 392, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 492, + 392, + 504 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 514, + 451, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 451, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 451, + 526 + ], + "type": "text", + "content": "2.1. Image-based Optical Flow" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Optical flow estimates the per-pixel motion between two frames according to photo consistency. Traditional approaches minimize energies, leveraging both feature similarities and motion smoothness [13]. Deep methods train the networks that take two frames as input and directly output dense flow motions [12, 46]. Recent deep methods design different pipelines [30, 48, 24] as well as learning modules [35, 31, 34, 33] for performance improvements. The training often requires large labeled datasets, which can be synthesized by moving a foreground on top of a background image, such as FlyingChairs [12], and AutoFlow [45], or rendered from graphics such as Sintel [5] and FlyingThings [36], or created directly from real videos [19]. In this work, we use computer graphics techniques to render accurate and physically correct event and flow values." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9848" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 539, + 233 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 539, + 233 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 539, + 233 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 539, + 233 + ], + "type": "image", + "image_path": "5c58e2c5d07b4080815f9e5f5f846f1b7cd0e0358d21961bd1d07db12ba7a4af.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 547, + 281 + ], + "type": "text", + "content": "Figure 2: Our data generation pipeline. Given 3D scenes in the graphics engine, we generate camera trajectories and render high-frame-rate videos with forward and backward optical flow labels. Then, we build the event optical flow dataset by generating events using the videos." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 300, + 191, + 313 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 191, + 313 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 191, + 313 + ], + "type": "text", + "content": "2.2. Event-based Optical Flow" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 319, + 289, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 289, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 289, + 534 + ], + "type": "text", + "content": "Benosman et al. [1] first proposed to estimate optical flow from events, which can only estimate sparse flows at the location of event values. Recent deep methods can estimate dense optical flows. EV-FlowNet [54] learns the event and flow labels in a self-supervised manner, which minimizes the photometric distances of grey images acquired by DAVIS [4]. Different event representations were explored, e.g., EST [15] and Matrix-LSTM [6], with various network structures, such as SpikeFlowNet [27], LIF-EV-FlowNet [18], STE-FlowNet [11], Li et al. [28], and E-RAFT [17]. Some works take both events and images as input for the flow estimation [26, 38]. In general, dense flows are more desirable than sparse ones but are more difficult to train. Normally, regions with events can produce more accurate flows than empty regions where no events are triggered. Moreover, supervised training can produce better results than unsupervised ones, as long as the training dataset can provide sufficient event-flow guidance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 540, + 135, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 135, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 135, + 551 + ], + "type": "text", + "content": "2.3.Event Dataset" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "The applications to the event camera dataset were first explored in the context of classification [37, 2]. Early works generate events simply by applying a threshold on the image difference [25]. Frame interpolation is often adopted for high framerate [14]. The synthesized events often contain inaccurate timestamps. The DAVIS event camera can directly capture both images and events [4], based on which two driving datasets are captured, DDD17 [3] and MVSEC [55]. With respect to the event flow dataset, EV-Flownet [54] calculated sparse flow labels from LIDAR depth based on MVSEC [55]. Wan et al. [50] and Stoffregen et al. [42] created the foreground motions and interpolated the intermediate frames for events. The real captured" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 300, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 337 + ], + "type": "text", + "content": "dataset can only provide sparse labels while the synthesized ones contain inaccurate events. In this work, we propose to render a physically correct event dense flow dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 349, + 362, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 349, + 362, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 349, + 362, + 361 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 370, + 497, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 497, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 497, + 383 + ], + "type": "text", + "content": "3.1. The event-based optical flow dataset" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 521 + ], + "type": "text", + "content": "In order to create a realistic event dataset for optical flow learning, we propose to employ a graphics engine with 3D scenes for data generation. Given 3D scenes, we first define camera trajectories, according to which we generate optical flow labels for timestamps at 60 FPS and 15 FPS. Then we render high-frame-rate videos based on the motion magnitude of the optical flow label between two timestamps. Finally, we generate event streams by rendering high-frame-rate videos and simulating the event trigger mechanism in the event camera using the v2e toolbox [20]. The overview of our data generation pipeline is shown in Fig. 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "text", + "content": "Virtual Scenes. To ensure that the generated event dataset has the correct scene structure, we utilize a variety of indoor and outdoor 3D scenes, including cities, streets, forests, ports, beaches, living rooms, bedrooms, bathrooms, kitchens, and parking lots. Totally, we obtain 53 virtual 3D scenes (31 indoor and 22 outdoor) that simulate real-world environments. Some examples are shown in Fig. 3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Camera Trajectory. Given a 3D scene model, we first generate the 3D camera trajectory using PyBullet [8], an open-source physics engine, to ensure that the camera does not pass through the inside of the objects and out of the effective visible region of the scene during the motion. After setting the start position, end position, and moving speed of" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9849" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 286, + 205 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 286, + 205 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 286, + 205 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 286, + 205 + ], + "type": "image", + "image_path": "3a227041f30bd02e9b2a63122da3c371d74f360edebdd662643471867aff974e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 215, + 287, + 239 + ], + "lines": [ + { + "bbox": [ + 47, + 215, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 215, + 287, + 239 + ], + "type": "text", + "content": "Figure 3: Examples of our MDR training set. Each row shows images, events and flow labels from top to bottom." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "text", + "content": "the camera trajectory, we randomly add translation and rotation motions to create a smooth curve function " + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "inline_equation", + "content": "\\Gamma(t)" + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "text", + "content": " that outputs the location and pose " + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "inline_equation", + "content": "P(t) = [x(t), y(t), z(t), r(t)]^T" + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": "High-frame-rate Video and Optical Flow. After camera trajectory generation, we use the graphics engine to render a sequence of images " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "I(\\boldsymbol{u}, t_i)" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\boldsymbol{u} = (x, y)" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": " is the pixel coordinates and " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": " is the timestamp. We extract the forward and backward optical flow labels between every two timestamps " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "(\\boldsymbol{F}_{t_i \\to t_j}, \\boldsymbol{F}_{t_j \\to t_i})" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": ". Then we need to generate the event data to construct the event optical flow dataset. Here, we render high-frame-rate videos " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\{I(\\boldsymbol{u}, \\tau)\\}" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\tau \\in [t_i, t_j]" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": " between timestamps " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "t_j" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": " for events generation according to the camera trajectory " + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\Gamma(t)" + }, + { + "bbox": [ + 47, + 316, + 287, + 435 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "text", + "content": "Inspired by ESIM [40], we adopt an adaptive sampling strategy to sample camera locations from the camera trajectory for interval " + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "inline_equation", + "content": "t_j" + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "text", + "content": ", so that the largest displacement of all pixels between two successive rendered frames " + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "inline_equation", + "content": "(I(\\pmb{u},\\tau_k), I(\\pmb{u},\\tau_{k + 1}))" + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "text", + "content": " is under 1 pixel, we define the sampling time interval " + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\Delta \\tau_{k}" + }, + { + "bbox": [ + 47, + 436, + 287, + 509 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 519, + 287, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 519, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 55, + 519, + 287, + 552 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Delta \\tau_ {k} = \\tau_ {k + 1} - \\tau_ {k} \\\\ = \\left(\\max _ {\\boldsymbol {u}} \\max \\left\\{\\left\\| \\boldsymbol {F} _ {\\tau_ {k - 1} \\rightarrow \\tau_ {k}} \\right\\|, \\left\\| \\boldsymbol {F} _ {\\tau_ {k} \\rightarrow \\tau_ {k - 1}} \\right\\|\\right\\}\\right) ^ {- 1}, \\tag {1} \\\\ \\end{array}", + "image_path": "a2a7b450710fdfacbc56469dcb82b04d0221f90b3a11524da5b9eacd10571ab4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "type": "inline_equation", + "content": "|F| = \\max_{\\boldsymbol{u}} \\max \\left\\{\\left\\| \\boldsymbol{F}_{\\tau_{k-1} \\to \\tau_k} \\right\\|, \\left\\| \\boldsymbol{F}_{\\tau_k \\to \\tau_{k-1}} \\right\\|\\right\\}" + }, + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "type": "text", + "content": " is the maximum magnitude of the motion field between images " + }, + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "type": "inline_equation", + "content": "I(\\boldsymbol{u}, \\tau_{k-1})" + }, + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "type": "inline_equation", + "content": "I(\\boldsymbol{u}, \\tau_k)" + }, + { + "bbox": [ + 47, + 562, + 287, + 601 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": "Event Generation from High-frame-rate Video. Given a high-frame-rate video " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{I(\\pmb{u},\\tau)\\}" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\tau \\in [t_i,t_j]" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": " between timestamps " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "t_j" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": ", we next generate event stream by simulating the event trigger mechanism. Similar to [40] and [14], we use linear interpolation to approximate the continuous intensity signal in time for each pixel between video frames. Events " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{(u_e,t_e,p_e)\\}" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": " are generated at each pixel " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{u}_e = (x_e,y_e)" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": " whenever the magnitude of the change in the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": "log intensity values " + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "(L(\\pmb{u}_e, t_e) = \\ln(I(\\pmb{u}_e, t_e))" + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": " exceeds the threshold " + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": ". This can be expressed as Eq. (2) and Eq. (3):" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 349, + 109, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 109, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 349, + 109, + 545, + 121 + ], + "type": "interline_equation", + "content": "L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, t _ {e} + \\Delta t _ {e}\\right) - L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, t _ {e}\\right) \\geq p _ {e} C, \\tag {2}", + "image_path": "5273c17baceb405b2e1ee3dd2e5ce087f00809b6d52699a29f9a3256b1bbf57f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 319, + 126, + 545, + 153 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 126, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 319, + 126, + 545, + 153 + ], + "type": "interline_equation", + "content": "t _ {e} = t _ {e - 1} + \\Delta \\tau_ {k} \\frac {C}{\\left| L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}} , t _ {e} + \\Delta t _ {e}\\right) - L \\left(\\boldsymbol {u} _ {\\boldsymbol {e}} , t _ {e}\\right) \\right|}, \\tag {3}", + "image_path": "9e6f54def2d4b2be5f513ebedb99f90dda2a50ce9e582f7f8eabe64b5b766b20.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "inline_equation", + "content": "t_{e-1}" + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "inline_equation", + "content": "t_e" + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": " are the timestamps of the last triggered event and the next triggered event respectively, " + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "inline_equation", + "content": "p_e \\in \\{-1, +1\\}" + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": " is the polarity of the triggered event. We define it as " + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "inline_equation", + "content": "E(t_k, t_{k+1})" + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": ", witch is the sequence " + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\{(u_e, t_e, p_e)^N, e \\in [0, N]\\}" + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": " events between time " + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "inline_equation", + "content": "t_{k+1}" + }, + { + "bbox": [ + 306, + 157, + 545, + 217 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 232, + 546, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 232, + 546, + 353 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 546, + 353 + ], + "type": "text", + "content": "Multi-Density Rendered Events Dataset. Using the above data generation method, we can generate data with different event densities by using different threshold values " + }, + { + "bbox": [ + 305, + 232, + 546, + 353 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 232, + 546, + 353 + ], + "type": "text", + "content": ". Since event stream is commonly first transformed into event representation [56, 42, 17] and then fed into deep networks. In order to measure the amount of useful information carried by the event stream, we propose to calculate the density of the event stream using the percentage of valid pixels (pixels where at least one event is triggered) in the voxel representation:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 310, + 361, + 545, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 361, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 310, + 361, + 545, + 394 + ], + "type": "interline_equation", + "content": "V (\\boldsymbol {u} _ {\\boldsymbol {e}}, b) = \\sum_ {e = 0} ^ {N} p _ {e} \\max (0, 1 - | b - \\frac {t _ {e} - t _ {0}}{t _ {N} - t _ {0}} (B - 1) |), \\tag {4}", + "image_path": "cfafb3c7ee95e5b95316ac622b34c2cec9c0c6015db793178933fc23fb6c5745.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 404, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 404, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 315, + 404, + 545, + 447 + ], + "type": "interline_equation", + "content": "D = \\frac {1}{H W} \\sum_ {e = 1} ^ {N} \\varepsilon \\left(\\sum_ {b = 0} ^ {B - 1} | V \\left(\\boldsymbol {u} _ {\\boldsymbol {e}}, b\\right) |\\right), \\varepsilon (x) = \\left\\{ \\begin{array}{l} 1, x > 0 \\\\ 0, x \\leq 0 \\end{array} , \\right. \\tag {5}", + "image_path": "36e8e9c7606a78fbd0d3e2df653beb0e0d6e7767819ed08eb1b69db57dcebbfa.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "V(\\boldsymbol{u}_e) \\in \\mathbb{R}^{B \\times H \\times W}" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": " is the voxel representation [56] of the event stream " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "\\{(u_e, t_e, p_e)^N\\}" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "t_0" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "t_N" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "b \\in [0, B - 1]" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": " indicates the temporal index, " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": " (typically set to 5) donates temporal bins and " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": " is the density of the input event representation " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": ". The notation " + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "inline_equation", + "content": "|\\cdot|" + }, + { + "bbox": [ + 305, + 447, + 546, + 626 + ], + "type": "text", + "content": " denotes the absolute value operation. In practical applications, different event cameras may use different threshold values in different scenes, resulting in data with different event densities. Intuitively, event data with lower density is more difficult for optical flow estimation. In order to train models that can cover event data with various densities, in this paper, we propose to adaptively normalize the density of the input events to a certain density representation for optical flow estimation, so as to increase the generalization ability of the network." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 635, + 504, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 504, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 504, + 647 + ], + "type": "text", + "content": "3.2. Event-based Optical Flow Estimation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": "Event-based optical flow estimation involves predicting dense optical flow " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{k-1\\rightarrow k}" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": " from consecutive event sequences " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "E(t_{k-1},t_k)" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "inline_equation", + "content": "E(t_k,t_{k+1})" + }, + { + "bbox": [ + 305, + 654, + 545, + 714 + ], + "type": "text", + "content": ". In this paper, we find that networks perform better on event sequences with appropriate density than on those with excessively sparse or" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9850" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 289, + 159 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 289, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 289, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 289, + 159 + ], + "type": "image", + "image_path": "8ef6290d423be3198bf4fef6f56c6d2ac335e93d6a3677391682bb7a48632e1c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "lines": [ + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "text", + "content": "Figure 4: The structure of the proposed network. We design a plug-and-play Adaptive Density Module (ADM) to transform input event representations " + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "inline_equation", + "content": "V_{1}" + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "inline_equation", + "content": "V_{2}" + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "inline_equation", + "content": "V_{1}^{\\mathrm{ad}}" + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "inline_equation", + "content": "V_{2}^{\\mathrm{ad}}" + }, + { + "bbox": [ + 46, + 166, + 287, + 214 + ], + "type": "text", + "content": " with suitable density for optical flow estimation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "text", + "content": "dense events, when given events from the same scene. Motivated by this, we propose a plug-and-play Adaptive Density Module (ADM) that normalizes the input event stream to a density suited for estimating optical flow. Our network architecture is shown in Fig. 4, where the ADM transforms input event representations " + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "inline_equation", + "content": "V_{1}" + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "inline_equation", + "content": "V_{2}" + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "text", + "content": " to justified event representations " + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "inline_equation", + "content": "V_{1}^{\\mathrm{ad}}" + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "inline_equation", + "content": "V_{2}^{\\mathrm{ad}}" + }, + { + "bbox": [ + 46, + 243, + 289, + 339 + ], + "type": "text", + "content": ", which are then used by an existing network structure to estimate optical flow." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 371, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 456 + ], + "type": "text", + "content": "Adaptive Density Module. As shown in Fig. 4, our ADM module consists of two sub-modules: the multi-density changer (MDC) module and the multi-density selector (MDS) module. The MDC module globally adjusts the density of the input event representations from multi-scale features, then the MDS module picks the best pixel-wise density for optical flow estimation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "content": "The MDC module adopts an encoder-decoder architecture with three levels, as illustrated in Fig. 5(a). To generate multiscale transformed representations " + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "inline_equation", + "content": "V_{3}^{\\mathrm{MDC}}" + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "inline_equation", + "content": "V_{2}^{\\mathrm{MDC}}" + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "inline_equation", + "content": "V_{1}^{\\mathrm{MDC}}" + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "content": " (also noted as " + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{out}}^{\\mathrm{MDC}}" + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "content": ") from the concatenated input event representations " + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "content": ", three encoding blocks are employed to extract multiple scale features, followed by three decoding blocks and two feature fusion blocks. It is worth noting that, to ensure the lightweightness of the entire module, we utilize only two " + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "content": " and one " + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 459, + 287, + 579 + ], + "type": "text", + "content": " convolutional layers in each encoding and decoding block." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "To maintain the information in the input event representation and achieve density transformation, we adopt the MDS module for adaptive selection and fusion of " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{out}}^{\\mathrm{MDC}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": ", as depicted in Fig. 5(b). We first concatenate " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{out}}^{\\mathrm{MDC}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": ", and then use two convolutional layers to compare them and generate selection weights via softmax. Finally, we employ the selection weights to identify and fuse " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{out}}^{\\mathrm{MDC}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": ", producing the transformed event representation " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "V_1^{\\mathrm{ad}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "V_2^{\\mathrm{ad}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": ", which are fed into an existing flow network for optical flow estimation. In this paper, we use KPA-Flow [32] for optical flow estimation by default." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 332, + 70, + 521, + 150 + ], + "blocks": [ + { + "bbox": [ + 332, + 70, + 521, + 150 + ], + "lines": [ + { + "bbox": [ + 332, + 70, + 521, + 150 + ], + "spans": [ + { + "bbox": [ + 332, + 70, + 521, + 150 + ], + "type": "image", + "image_path": "5e86666ebce5795b0da86a7dd9eca3a123bb67ea6997dfc8f02d65ee26b9b857.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 331, + 153, + 521, + 251 + ], + "blocks": [ + { + "bbox": [ + 331, + 153, + 521, + 251 + ], + "lines": [ + { + "bbox": [ + 331, + 153, + 521, + 251 + ], + "spans": [ + { + "bbox": [ + 331, + 153, + 521, + 251 + ], + "type": "image", + "image_path": "e8f9a4fefd4636ec05e286fdac2f152470ebfd90f931898bea8830c5fe8f553f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 259, + 545, + 284 + ], + "lines": [ + { + "bbox": [ + 305, + 259, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 305, + 259, + 545, + 284 + ], + "type": "text", + "content": "Figure 5: The detailed structure of sub-modules used in our proposed ADM model: (a) MDC, (b) MDS." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 304, + 546, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 546, + 352 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 546, + 352 + ], + "type": "text", + "content": "Loss Function. Based on our MDR dataset, we use the event representation with a moderate density as the ground truth (noted as " + }, + { + "bbox": [ + 305, + 304, + 546, + 352 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{GT}}" + }, + { + "bbox": [ + 305, + 304, + 546, + 352 + ], + "type": "text", + "content": ") to train our ADM module. For the MDC module, we use a multi-scale loss as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 343, + 359, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 359, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 343, + 359, + 545, + 392 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {M D C}} = \\sum_ {k = 1} ^ {3} \\sqrt {\\left(V _ {k} ^ {\\mathrm {M D C}} - V _ {k} ^ {\\mathrm {G T}}\\right) ^ {2} + \\xi^ {2}}, \\tag {6}", + "image_path": "7681f44bb6e1789cdbac942eec3871704cb667de6e63251e377f0b413b1a9b9f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\xi = 10^{-3}" + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "text", + "content": " is a constant value, " + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "inline_equation", + "content": "V_{k}^{\\mathrm{MDC}}" + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "text", + "content": " is the output of the " + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "text", + "content": "-th level in MDC, and " + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "inline_equation", + "content": "V_{k}^{\\mathrm{GT}}" + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "text", + "content": " is downsampled from " + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{GT}}" + }, + { + "bbox": [ + 305, + 400, + 545, + 437 + ], + "type": "text", + "content": " to match the spatial size." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 437, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 461 + ], + "type": "text", + "content": "For the MDS module, we use the distance between the density of " + }, + { + "bbox": [ + 305, + 437, + 545, + 461 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{ad}}" + }, + { + "bbox": [ + 305, + 437, + 545, + 461 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 437, + 545, + 461 + ], + "type": "inline_equation", + "content": "V^{\\mathrm{GT}}" + }, + { + "bbox": [ + 305, + 437, + 545, + 461 + ], + "type": "text", + "content": " as the guidance:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 354, + 468, + 545, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 468, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 354, + 468, + 545, + 485 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {M D S}} = \\left\\| D \\left(V ^ {\\mathrm {a d}}\\right) - D \\left(V ^ {\\mathrm {G T}}\\right) \\right\\| _ {1}, \\tag {7}", + "image_path": "1b4d744381e89d745dbe06cc38e416291bc2a510aeb61d8fc85c038200351cc4.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 491, + 520, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 520, + 503 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 520, + 503 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 491, + 520, + 503 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 306, + 491, + 520, + 503 + ], + "type": "text", + "content": " means to calculate the density as in Eq. (5)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 503, + 545, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 503, + 545, + 527 + ], + "spans": [ + { + "bbox": [ + 305, + 503, + 545, + 527 + ], + "type": "text", + "content": "For the flow network, we use L1 loss (denoted as " + }, + { + "bbox": [ + 305, + 503, + 545, + 527 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{Flow}}" + }, + { + "bbox": [ + 305, + 503, + 545, + 527 + ], + "type": "text", + "content": ") between flow prediction and ground truth as the guidance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 527, + 545, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 527, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 545, + 551 + ], + "type": "text", + "content": "The final loss function for training the whole pipeline in Fig. 4 is determined as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 343, + 560, + 545, + 573 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 560, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 343, + 560, + 545, + 573 + ], + "type": "interline_equation", + "content": "L _ {\\text {t o t a l}} = \\lambda_ {1} L _ {\\mathrm {M D C}} + \\lambda_ {2} L _ {\\mathrm {M D S}} + L _ {\\text {F l o w}}, \\tag {8}", + "image_path": "24ec68adb4efde64cada1ad6a3ecb016a1e4954a7008f605460bd5699b57bff3.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 581, + 503, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 581, + 503, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 581, + 503, + 594 + ], + "type": "text", + "content": "where we empirically set " + }, + { + "bbox": [ + 306, + 581, + 503, + 594 + ], + "type": "inline_equation", + "content": "\\lambda_{1} = 0.1" + }, + { + "bbox": [ + 306, + 581, + 503, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 581, + 503, + 594 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 10" + }, + { + "bbox": [ + 306, + 581, + 503, + 594 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 604, + 387, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 387, + 617 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 387, + 617 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 624, + 368, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 624, + 368, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 624, + 368, + 635 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 641, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 641, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 641, + 545, + 715 + ], + "type": "text", + "content": "MDR: We create the MDR dataset using the graphics engine blender. We use various 3D scenes for data generation. There are 80,000 training samples and 6,000 validation samples with accurate dense optical flow ground truth. Each sample has event sequences with different densities produced by using different thresholds " + }, + { + "bbox": [ + 305, + 641, + 545, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 641, + 545, + 715 + ], + "type": "text", + "content": ". By default, for" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "9851" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 69, + 523, + 430 + ], + "blocks": [ + { + "bbox": [ + 75, + 69, + 523, + 430 + ], + "lines": [ + { + "bbox": [ + 75, + 69, + 523, + 430 + ], + "spans": [ + { + "bbox": [ + 75, + 69, + 523, + 430 + ], + "type": "table", + "html": "
Method (dt=1)Train D.TypeTrain D.Setindoor flying1indoor flying2indoor flying3outdoor day1Avg
EPE%OutEPE%OutEPE%OutEPE%OutEPE%Out
ESTS[15]EM0.970.911.388.201.436.47--1.265.19
EV-FlownetS[54]I1,I2,EM1.032.201.7215.11.5311.90.490.201.197.35
Deng et al.S[10]EM0.890.661.316.441.133.53--1.113.54
Paredes et al.S[39]EM0.791.201.4010.91.187.400.925.401.076.22
Matrix-LSTMS[6]I1,I2,EM0.820.531.195.591.084.81--1.033.64
LIF-EV-FlowNetS[18]EFPV0.711.411.4412.81.169.110.530.330.965.90
Spike-FlowNetS[27]I1,I2,EM0.84-1.28-1.11-0.49-0.93-
Fusion-FlowNetD[26]I1,I2,EM0.62-0.89-0.85-1.02-0.84-
Fusion-FlowNetS[26]I1,I2,EM0.56-0.95-0.76-0.59-0.71-
E-RAFTD[17]EM1.105.721.549.791.368.240.270.001.075.94
E-RAFTS[17]EM0.871.321.136.201.034.700.240.000.823.06
Zhu et al.S[56]EM0.580.001.024.000.873.000.320.000.691.75
DCEIFlowD[50]I1,I2,EM0.560.280.640.160.570.120.910.710.670.31
DCEIFlowS[50]I1,I2,EC20.570.300.700.300.580.150.740.290.640.26
Stoffregen et al.S[42]EESIM0.561.000.661.000.591.000.680.990.620.99
STE-FlowNetS[11]I1,I2,EM0.570.100.791.600.721.300.420.000.620.75
ADM-FlowD(ours)EMDR0.480.110.560.400.470.020.520.000.510.14
ADM-FlowS(ours)EMDR0.520.140.681.180.520.040.410.000.530.34
Method (dt=4)Train D.TypeTrain D.Setindoor flying1indoor flying2indoor flying3outdoor day1Avg
EPE%OutEPE%OutEPE%OutEPE%OutEPE%Out
LIF-EV-FlowNetS[18]EFPV2.6329.64.9351.13.8841.52.0218.93.3635.3
EV-FlownetS[54]I1,I2,EM2.2524.74.0545.33.4539.71.237.302.7429.3
E-RAFTD[17]EM3.2635.44.3248.64.1448.20.841.703.1433.5
E-RAFTS[17]EM2.8130.63.9940.93.7840.50.721.122.8328.3
Zhu et al.S[56]EM2.1824.23.8546.83.1847.81.309.702.6232.1
Spike-FlowNetS[27]I1,I2,EM2.24-3.83-3.18-1.09-2.58-
Fusion-FlowNetD[26]I1,I2,EM1.81-2.90-2.46-3.06-2.55-
Fusion-FlowNetS[26]I1,I2,EM1.68-3.24-2.43-1.17-2.13-
STE-FlowNetS[11]I1,I2,EM1.7714.72.5226.12.2322.10.993.901.8716.7
DCEIFlowD[50]I1,I2,EC21.498.141.9717.41.6912.31.8719.11.7514.2
DCEIFlowS[50]I1,I2,EC21.528.792.2122.11.7413.31.378.541.7113.2
ADM-FlowD(ours)EMDR1.397.331.6311.51.519.341.9119.21.6111.8
ADM-FlowS(ours)EMDR1.427.781.8816.71.6111.41.5110.21.6011.5
", + "image_path": "72403dcda3ce95ff0798d31a88f6f7d83179b2633157a0c85a5009aaf2e11547.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 438, + 547, + 464 + ], + "lines": [ + { + "bbox": [ + 46, + 438, + 547, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 547, + 464 + ], + "type": "text", + "content": "Table 1: Quantitative comparison of our method with previous methods on the MVSEC dataset [55]. Subscripts " + }, + { + "bbox": [ + 46, + 438, + 547, + 464 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 438, + 547, + 464 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 438, + 547, + 464 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 438, + 547, + 464 + ], + "type": "text", + "content": " donate the sparse and dense evaluation, respectively. We mark the best results in red and the second best results in blue." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "type": "text", + "content": "training on MDR, we use the combination of all these samples with different densities to train flow networks. For the learning of our ADM module, we choose events with density between 0.45 and 0.55 as the label for " + }, + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{MDC}}" + }, + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{MDS}}" + }, + { + "bbox": [ + 46, + 484, + 287, + 544 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 544, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 688 + ], + "type": "text", + "content": "MVSEC: The MVSEC dataset [55] is a real-world dataset collected in indoor and outdoor scenarios with sparse optical flow labels. As a common setting, 28, 542 data pairs of the 'outdoor day2' sequence are used as the train set, and 8, 410 data pairs of the other sequences are used as the validation set. The density ranges of MVSEC train set and validation set are [0.0003, 0.47] and [0.001, 0.31], respectively. DSEC: The DSEC dataset [16] is also collected using actual event cameras and lidar sensors on outdoor scenes. The dataset consists of 7,800 training samples and 2,100 test samples, divided into 24 sequences that include both day and night scenarios." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Previous methods have trained on other datasets, including synthetic datasets like C2 [50] and ESIM [42], as well" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 484, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 616 + ], + "type": "text", + "content": "as real-world captured datasets such as FPV [9]. To assess the performance of these methods, comparisons are made on the validation set of the MVSEC dataset. Both MVSEC and MDR datasets have two input settings for training and testing. These settings involve using the events between successive images within a time interval of " + }, + { + "bbox": [ + 304, + 484, + 545, + 616 + ], + "type": "inline_equation", + "content": "dt = 1" + }, + { + "bbox": [ + 304, + 484, + 545, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 484, + 545, + 616 + ], + "type": "inline_equation", + "content": "dt = 4" + }, + { + "bbox": [ + 304, + 484, + 545, + 616 + ], + "type": "text", + "content": ". On the other hand, for the DSEC dataset, there is a public benchmark available specifically designed to evaluate flow networks. However, this benchmark only provides one input setting for testing. We denote MVSEC, DSEC, and MDR datasets by \"M\", \"D\", and \"MDR\"." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 623, + 437, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 437, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 437, + 635 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "We use PyTorch to implement our method and train all networks using the same setting. The networks are trained with the AdamW optimizer, with a batch size of 6 and learning rate of " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "4 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " for 150k iterations. Since the MVSEC dataset lacks multiple density event streams required for the learning of our ADM module, we disable " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{MDC}}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{MDS}}" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9852" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 203, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 203, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 203, + 83 + ], + "type": "text", + "content": "when training on the MVSEC dataset." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 159, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 159, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 159, + 102 + ], + "type": "text", + "content": "4.3. Evaluation metrics" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 288, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 288, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 288, + 264 + ], + "type": "text", + "content": "The evaluation metrics used in flow prediction models are the average End-point Error (EPE) and 1PE, 2PE, and 3PE (the percentage of pixels with EPE greater than 1,2,3 pixels) for DSEC dataset, and " + }, + { + "bbox": [ + 46, + 110, + 288, + 264 + ], + "type": "inline_equation", + "content": "\\% \\text{Out}" + }, + { + "bbox": [ + 46, + 110, + 288, + 264 + ], + "type": "text", + "content": " (the percentage of points with EPE greater than 3 pixels and " + }, + { + "bbox": [ + 46, + 110, + 288, + 264 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 110, + 288, + 264 + ], + "type": "text", + "content": " of the ground truth flow magnitude) for MVSEC dataset. There are two types of evaluations: dense and sparse. In emphdense evaluation, errors are calculated only at pixels with valid flow annotations. Sparse evaluation focuses on pixels with valid flow annotations that have triggered at least one event. Experiments are performed on both MVSEC and MDR, considering both dense and sparse evaluations. However, only dense dense is conducted for DSEC." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 272, + 234, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 272, + 234, + 284 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 234, + 284 + ], + "type": "text", + "content": "4.4. Comparison with State-of-the-Arts" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": "Results on MVSEC. In Table 1, we compare our model trained on the MDR train set with previous methods on the MVSEC evaluation set, and report detailed results for each sequence. We provide information on the data types (Train D.Type) and the training sets (Train D.Set) used in the training process for each method. Specifically, " + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_1,\\mathrm{I}_2,\\mathrm{E}" + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": " indicates that both image data and event data are used in the training and inference processes of the model, while " + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\mathrm{E}" + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": " indicates that only event data is used. As shown in Table 1, our model trained on the MDR dataset achieves state-of-the-art performance for both EPE and %Out metrics in settings of " + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "inline_equation", + "content": "dt = 1" + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "inline_equation", + "content": "dt = 4" + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": ". Notably, our method demonstrates a " + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "inline_equation", + "content": "23.9\\%" + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": " improvement (reducing EPE from 0.67 to 0.51) for dense optical flow estimation in " + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "inline_equation", + "content": "dt = 1" + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": " settings, and an " + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "inline_equation", + "content": "8.0\\%" + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": " improvement (reducing EPE from 1.75 to 1.61) in " + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "inline_equation", + "content": "dt = 4" + }, + { + "bbox": [ + 46, + 289, + 287, + 494 + ], + "type": "text", + "content": " settings, surpassing previous methods. Qualitative comparison results are shown in row 1 and row 2 in Fig. 6." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "text", + "content": "Results on MDR. In Table 3, we compare our method with previous methods for training on the MVSEC dataset and testing on the MDR dataset for cross-training and validation to avoid over-fitting. We use different thresholds " + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "text", + "content": " to generate test data with different density ranges for evaluation. For the average EPE error of dense optical flow estimation, our model obtains the best result, which is a " + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "inline_equation", + "content": "17.1\\%" + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "text", + "content": " improvement (reducing EPE from 0.82 to 0.68) in " + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "inline_equation", + "content": "dt = 1" + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "text", + "content": " settings, and a " + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "inline_equation", + "content": "16.7\\%" + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "text", + "content": " improvement (reducing EPE from 1.98 to 1.65) in " + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "inline_equation", + "content": "dt = 4" + }, + { + "bbox": [ + 46, + 508, + 287, + 639 + ], + "type": "text", + "content": " settings. We also show some qualitative comparison results in row 3 and row 4 in Fig. 6." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Results on DSEC. In Table 2, we report the results on the DSEC test set for different models that are trained on DSEC, MDR, and a combination of DSEC and MDR. As can be seen, MDR-trained models produce comparable results to in-domain learned models on the DSEC train set." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 323, + 70, + 533, + 222 + ], + "blocks": [ + { + "bbox": [ + 323, + 70, + 533, + 222 + ], + "lines": [ + { + "bbox": [ + 323, + 70, + 533, + 222 + ], + "spans": [ + { + "bbox": [ + 323, + 70, + 533, + 222 + ], + "type": "table", + "html": "
MethodsTrain D.Set1PE2PE3PEEPE
EV-FlowNet [54]D55.1328.4316.712.22
MDR42.5224.4016.321.86
D+MDR35.0615.417.841.31
E-RAFT [17]D16.196.223.590.90*
MDR18.857.444.371.00
D+MDR13.165.192.930.82
ADM-EVFLOWD42.8925.2115.801.90
MDR40.0214.8812.341.67
M+D23.4610.325.611.12
ADM-Flow(ours)D13.965.323.180.88
MDR14.535.783.590.92
D+MDR12.524.672.650.78
", + "image_path": "23866c48e0451f3963796d0c3da62ab5d00acf7b51206d2b25ca1f0f58bddf40.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 232, + 545, + 280 + ], + "lines": [ + { + "bbox": [ + 305, + 232, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 545, + 280 + ], + "type": "text", + "content": "Table 2: Results on the DSEC test set. * denotes our reproduced results of E-RAFT, since the official training code is not released. All experiments are conducted on the same training code for fair comparison." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 293, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 365 + ], + "type": "text", + "content": "Moreover, training E-RAFT on the combined DSEC/MDR datasets yields improved performance, demonstrating the effectiveness of MDR. Our ADMFlow model achieves improved performance on all training datasets, highlighting the effectiveness and versatility of ADM. Some qualitative results are shown in Fig. 7." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 384, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 503 + ], + "type": "text", + "content": "Analysis of the MDR dataset. To demonstrate the effectiveness of our proposed MDR dataset, we train several optical flow networks [46, 17, 53, 21, 47, 24, 32] on both MDR and MVSEC train sets using identical training settings. For training, we use a combination of data samples from the MDR dataset with a density range of " + }, + { + "bbox": [ + 305, + 384, + 545, + 503 + ], + "type": "inline_equation", + "content": "[0.09, 0.69]" + }, + { + "bbox": [ + 305, + 384, + 545, + 503 + ], + "type": "text", + "content": ". We evaluate the trained networks on the MVSEC validation set, and the results, presented in Table 4, demonstrate that all networks trained on the MDR dataset outperform those trained on the MVSEC dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 515, + 400, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 400, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 400, + 528 + ], + "type": "text", + "content": "4.5. Ablation study." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "text", + "content": "Training with different densities. We examine the impact of input event sequence density on optical flow learning, as our MDR dataset contains event data with various densities and corresponding dense flow labels. We train SKFlow [47], GMA [24], FlowFormer [21] and KPA-Flow [32] on the same sequence from our MDR dataset but with different average densities produced by using different threshold " + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "text", + "content": ", and then test them on the MVSEC dataset. Figure 8 shows the results in " + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "dt = 4" + }, + { + "bbox": [ + 305, + 534, + 545, + 713 + ], + "type": "text", + "content": " setting, indicating that these models perform better as the average density of the training set increases. However, their performance diminishes as the average density continues to increase. This phenomenon highlights the importance of selecting an appropriate density for the training set when learning event optical flow." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9853" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 119, + 142 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 119, + 142 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 119, + 142 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 119, + 142 + ], + "type": "image", + "image_path": "eec76298cb8ce9e99f1d56987f432fe6724c9964a22ba380cecef7c05115131e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 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"Ours" + } + ] + } + ], + "index": 54, + "angle": 0, + "type": "image_caption" + } + ], + "index": 53 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "Ablation for ADM. In order to verify the impact of our proposed ADM module, we conduct ablation experiments by plugging the ADM module into several optical flow net" + } + ] + } + ], + "index": 56 + }, + { + "type": "table", + "bbox": [ + 309, + 418, + 545, + 587 + ], + "blocks": [ + { + "bbox": [ + 309, + 418, + 545, + 587 + ], + "lines": [ + { + "bbox": [ + 309, + 418, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 309, + 418, + 545, + 587 + ], + "type": "table", + "html": "
Method (dt = 1)density rangeAvg
0.09-0.240.24-0.390.39-0.540.54-0.69
Spike-FlowS [27]1.931.201.332.011.62
STE-FlowS [11]1.171.110.821.301.10
DCEIFlowD [50]1.281.371.271.461.35
DCEIFlowS [50]1.000.840.750.820.85
E-RAFTD [17]0.930.740.690.920.82
E-RAFTS [17]0.820.650.660.820.74
ADM-FlowD(ours)0.770.690.500.740.68
ADM-FlowS(ours)0.690.640.490.740.64
Method (dt = 4)density rangeAvg
0.09-0.240.24-0.390.39-0.540.54-0.69
Spike-FlowS [27]3.951.962.092.872.72
STE-FlowS [11]2.902.271.982.172.33
DCEIFlowD [50]3.842.682.994.273.45
DCEIFlowS [50]2.251.321.192.341.78
E-RAFTD [17]2.641.421.352.511.98
E-RAFTS [17]2.181.311.242.291.76
ADM-FlowD(ours)2.121.201.242.021.65
ADM-FlowS(ours)2.031.131.091.901.54
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MethodTrain D.Setdt = 1dt = 4
EPE%OutEPE%Out
PWCNet [22]M1.255.414.0351.48
MDR1.143.482.9238.62
RAFT [48]M1.194.903.3339.78
MDR0.590.512.5730.24
GMFlowNet [53]M1.003.753.6142.31
MDR0.821.662.7031.53
FlowFromer [21]M0.873.083.3841.04
MDR0.610.402.4928.83
SKFlow [47]M1.073.973.4140.87
MDR0.590.332.4627.64
GMA [24]M0.884.052.9934.80
MDR0.580.442.1923.00
KPAFlow [32]M0.862.863.1938.32
MDR0.580.392.3326.10
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MethodM(dt = 1)MDR(dt = 1)M(dt = 4)MDR(dt = 4)
EPE%OutEPE%OutEPE%OutEPE%Out
PWCNet [22]1.255.411.143.484.0351.482.9238.62
ADM-PWCNet1.074.520.761.482.9533.311.9418.74
RAFT [48]1.194.900.590.513.3339.782.5730.24
ADM-RAFT0.823.030.560.242.7330.911.7213.83
GMFlowNet [53]1.003.750.821.663.6142.312.7031.53
ADM-GMFlowNet0.873.050.580.322.7831.261.8114.45
FlowFromer [21]0.873.080.610.403.3841.042.4928.83
ADM-FlowFromer0.782.870.530.152.5626.571.6712.78
SKFlow [47]1.073.970.590.333.4140.872.4627.64
ADM-SKFlow0.843.180.530.142.6728.171.6912.61
GMA [24]0.884.050.580.442.9934.802.1923.00
ADM-GMA0.762.650.540.222.4525.751.6311.95
KPAFlow [32]0.862.860.580.393.1938.322.3326.10
ADM-KPAFlow0.802.670.510.142.5928.421.6111.83
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MethodMDCMDSLMDCLMDSParam. (M)dt = 1dt = 4
EPE%OutEPE%Out
(a)××××6.010.580.392.3326.10
(b)✓×××7.710.570.332.2023.78
(c)✓✓××7.720.540.261.9218.26
(d)✓✓✓×7.720.520.161.6613.29
(e)✓✓✓✓7.720.510.141.6111.83
", + "image_path": "f9734e374486e05f299880ff75c26ec3af1d2d9c8d6de6a0ec9f285336626da0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 335, + 545, + 372 + ], + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 372 + ], + "type": "text", + "content": "Table 6: Ablation study. Models are trained on the MDR training set, and evaluated on the MVSEC validation set for dense optical flow estimation in " + }, + { + "bbox": [ + 305, + 335, + 545, + 372 + ], + "type": "inline_equation", + "content": "dt = 1" + }, + { + "bbox": [ + 305, + 335, + 545, + 372 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 335, + 545, + 372 + ], + "type": "inline_equation", + "content": "dt = 4" + }, + { + "bbox": [ + 305, + 335, + 545, + 372 + ], + "type": "text", + "content": " settings." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 393, + 545, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 393, + 545, + 465 + ], + "spans": [ + { + "bbox": [ + 305, + 393, + 545, + 465 + ], + "type": "text", + "content": "abling the density selection function through the MDS module brings a significant improvement. Comparing (c)&(d) and (d)&(e), we notice that with the guidance of two loss functions, ADM can learn to selectively choose the best density for optical flow estimation, resulting in a relatively significant improvement." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": "In this work, we have created a rendered dataset for event-flow learning. Indoor and outdoor virtual scenes have been created using Blender with rich scene contents. Various camera motions are placed for the capturing of the virtual world, which can produce frames as well as accurate flow labels. The event values are generated by rendering high frame rate videos between two frames. In this way, the flow labels and event values are physically correct and accurate. The rendered dataset can adjust density of events by modifying the event trigger threshold. We have introduced a novel adaptive density module (ADM), which has shown its effectiveness by plugin into various event-flow pipelines. When trained on our dataset, previous approaches can improve their performances constantly." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements This work was supported by Sichuan Science and Technology Program of China under grants Nos. 2023NSFSC0462, 2023NSFSC1972, 2021YFG0001, 2022YFG0011 and 2022YFG0050." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9855" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Ryad Benosman, Sio-Hoi Ieng, Charles Clercq, Chiara Bartolozzi, and Mandyam Srinivasan. 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Existing fully-supervised methods rely on paired datasets of incomplete and complete point clouds, which are labor-intensive to obtain. Unpaired methods have been proposed, but still require a set of complete point clouds as a reference. As a remedy, in this paper, we propose a novel point cloud completion framework without using any complete point cloud at all. Our main idea is to generate multiple incomplete point clouds of various poses and integrate them into a complete point cloud. We train our framework based on cycle consistency, to generate an incomplete point cloud such that 1) shares the same object as the input incomplete point cloud and 2) corresponds to an arbitrarily given pose. In addition, we devise a novel projection method conditioned by pose to gather visible features, from a volumetric feature extracted by an encoder. Extensive experiments demonstrate that the proposed method achieves comparable or better results than existing unpaired methods. Further, we show that our method also can be applied to real incomplete point clouds.", + "bbox": [ + 78, + 304, + 484, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 627, + 215, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A point cloud is a commonly used representation of 3D scenes and objects in the fields of computer vision and robotics [14, 20, 21, 22, 28, 9, 24, 2, 3, 7, 15]. However, obtaining complete point clouds is often difficult due to the lack of observation or the limitations of sensors. As a remedy, the point cloud completion task has been spotlighted to restore complete point clouds from incomplete ones.", + "bbox": [ + 78, + 647, + 482, + 745 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The existing fully-supervised point cloud completion methods [16, 17, 19, 38, 39, 40, 42, 43, 44] have shown promising results; however, they typically rely on datasets that include incomplete point clouds paired with complete point clouds serving as ground truth (GT). Since obtaining GT complete point clouds is labor-intensive, several works [6, 36, 45, 4] have employed two sets of point clouds:", + "bbox": [ + 78, + 747, + 482, + 847 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c72d5cdf184a7937483bebd3d031e70dcfb0bbf702842a3efc1cd2470082ce33.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 519, + 274, + 757, + 355 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/15c7593d40784ffff5672f5fe97e813588fcf49b01577d3c914758534d14d2eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 771, + 274, + 905, + 353 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/31d91d768bba3b8549ffa8fd9bb819a4a3fa49368ab5040e7d476672127352b7.jpg", + "image_caption": [ + "(c) Generate incomplete PCs of various poses $\\rightarrow$ Integrate them as complete PC", + "Figure 1. Illustration of our main idea. We re-interpret the point cloud completion task as generating multiple incomplete point clouds that correspond to various poses and integrating them." + ], + "image_footnote": [], + "bbox": [ + 539, + 371, + 902, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "one with incomplete point clouds and the other with complete point clouds, which are not directly paired with each other. This unpaired setting could learn the mapping between the incomplete and complete point clouds, while reducing the reliance on paired GT complete point clouds. Nevertheless, the requirement of a set of complete point clouds still remains a major limitation to the practical application of point cloud completion.", + "bbox": [ + 510, + 504, + 917, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose a novel point cloud completion framework that does not use any complete point clouds. Our main novelty lies in how to learn a mapping from an incomplete point cloud to a complete point cloud when the latter is not available at all. For this, we present a simple yet effective idea shown in Fig. 1. An incomplete point cloud usually results from self-occlusion occurs when observing an object from a certain viewpoint, as in (a). Therefore, if we obtain multiple incomplete point clouds of the object from various viewpoints, a union of them would be equivalent to the complete point cloud of that object. Based on this idea, we formulate the point cloud completion as generating multiple incomplete point clouds using a single input incomplete point cloud and sampled poses. Here, the generated incomplete point clouds should 1) share the same object as the input incomplete point cloud and 2) correspond", + "bbox": [ + 510, + 619, + 917, + 847 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 95, + 9, + 171, + 46 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 231, + 7, + 815, + 48 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14203", + "bbox": [ + 465, + 877, + 504, + 888 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to the arbitrarily given input poses. If the poses are various enough to cover the entire object, we could obtain the complete point cloud by integrating the incomplete point clouds.", + "bbox": [ + 80, + 85, + 480, + 127 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve the above, our framework starts with an encoder that extracts a volumetric shape feature from the input incomplete point cloud. This feature is designed to contain complete information about the shape of the target object. To generate an incomplete point cloud from the volumetric feature, we propose a novel projection method conditioned by the pose, similar to obtaining an incomplete point cloud as a capture of the target object from a certain viewpoint. The method determines the region visible at the given pose and obtains a projected feature by gathering the volumetric feature of that region. A decoder is then trained to generate an incomplete point cloud from the projected feature.", + "bbox": [ + 80, + 128, + 480, + 298 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We do not have access to either the complete point cloud or the incomplete point cloud of another pose. Therefore, for training, we propose a novel dataset that provides both incomplete point clouds and corresponding poses, based on the ShapeNet dataset [5]. Note that our dataset includes only one incomplete point cloud per each object, unlike the setting of [13]. Using our dataset, we make our framework reconstruct the input incomplete point cloud itself by gathering the projected feature using the pose corresponding to the input. On the other hand, when using randomly sampled poses, we impose cycle consistency by feeding the generated incomplete point cloud to the encoder/decoder again.", + "bbox": [ + 80, + 299, + 480, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "During the inference phase, we extract the volumetric shape feature from the input and obtain the projected features using various poses that cover the entire object. By decoding the features and integrating the generated incomplete point clouds, we can obtain a complete point cloud as the final output. To verify the proposed method, we conduct extensive experiments and comparisons with the existing unpaired point cloud completion methods, on the proposed dataset. The results support that, the proposed method is comparable to the existing studies and sometimes achieves even more substantial completion results, without using any complete point cloud. Further, we conduct an experiment on the KITTI dataset [10] to show that the proposed method can be also applied to the real incomplete point clouds. Our main contributions are as follows:", + "bbox": [ + 80, + 469, + 480, + 680 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We formulate a point cloud completion task as generating and integrating multiple incomplete point clouds corresponding to various poses.", + "- We propose a novel framework that generates an incomplete point cloud using the input incomplete point cloud and the given arbitrary pose.", + "- We introduce a new dataset consisting of incomplete point clouds and poses.", + "- We experimentally verify that the proposed method is comparable or even superior to existing studies, without using complete point cloud at all." + ], + "bbox": [ + 80, + 686, + 480, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 517, + 84, + 665, + 98 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Point Cloud Completion", + "text_level": 1, + "bbox": [ + 517, + 103, + 741, + 118 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Point cloud completion aims to restore a complete point cloud from an input incomplete point cloud. Although fully-supervised completion methods [8, 17, 19, 23, 32, 34, 37, 40, 43, 46, 35, 31] achieve substantial completion result, they rely on the dataset including paired incomplete point cloud and GT complete point cloud, which is difficult to acquire, especially for real scenes. To overcome the limitation, unpaired approaches [6, 36, 45, 11] have been proposed to learn the mapping between the sets of complete and incomplete point clouds. Pcl2pcl [6] is the first unpaired point cloud completion method, which allows translation between partial and complete latent spaces by adversarial training. Subsequently, Cycle4completion [36] has achieved more advanced results by considering bidirectional geometric correspondence by cycle transformation and missing region coding. ShapeInversion [45] obtained optimal shape code for reconstructing 3D shapes based on the concept of GAN inversion. OptDE [11] proposed cross-domain completion by disentangling shape, domain, and occlusion factors, using domain-invariant geometric information and viewpoint prediction. Although the unpaired methods have shown promising results, their practical application is still limited by the requirement for a number of complete point clouds. [13] has proposed to utilize multiple incomplete point clouds of the same object, obtained from observations at different poses; however, such multiple observations are often not available. Unlike the existing methods, our method does not access the complete point cloud at all, and also uses only one incomplete point cloud per each object, throughout the entire training process.", + "bbox": [ + 515, + 127, + 915, + 552 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Pose-Aware 3D Processing", + "text_level": 1, + "bbox": [ + 517, + 567, + 757, + 581 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One of the most representative 3D tasks dealing with the pose is point cloud canonicalization [29, 30, 26]. Condor [29] takes an un-canonicalized collection of full or partial point clouds obtained through the internet or depth sensor as input. Meanwhile, [33] proposed self-supervised learning via disentangling content and pose information for the point cloud feature representation. As such, numerous studies have been conducted to exploit these two factors, since 3D data usually contains pose attributes as well as the shape of the object. Nevertheless, in the field of point cloud completion, using pose has not been deeply studied despite its usefulness. Since an incomplete point cloud is usually obtained by scanning the object from a single viewpoint through a scanner, information about the viewpoint (i.e., pose) can be beneficial for recovering the self-occluded regions. In this light, we utilize the pose information to complete the point cloud by generating multiple incomplete point clouds.", + "bbox": [ + 515, + 591, + 915, + 846 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14204", + "bbox": [ + 467, + 878, + 504, + 888 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b2b7c76a4e8d81c35b6f97735065e4aee56bd8ed11c8c3ebfaa93b4f8db64f0a.jpg", + "image_caption": [ + "Figure 2. Illustration of a framework for generating a pose-aware point cloud. First, the encoder extracts the volumetric shape feature $V$ from the input point cloud $P_{i}$ . Then, projected features $F_{i}$ and $F_{r}$ are generated by determining the visible region with input pose $o_{i}$ and random pose $o_{r}$ . Incomplete point cloud $\\hat{P}_{i,rec}$ is decoded to constrain with $\\mathcal{L}_{rec}$ . Incomplete point cloud $\\hat{P}_{r}$ is decoded and entered into the model again with input pose $o_{i}$ . After that, volumetric feature $\\hat{V}$ , projected feature $\\hat{F}_{i}$ , and $\\hat{P}_{i,cycle}$ are generated sequentially. We use $\\mathcal{L}_{shape}$ and $\\mathcal{L}_{cycle}$ to constrain our network." + ], + "image_footnote": [], + "bbox": [ + 122, + 81, + 875, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Volumetric Feature Representation", + "text_level": 1, + "bbox": [ + 78, + 433, + 394, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Volumetric features are commonly used in tasks such as multi-view stereo [25, 27], 3D semantic segmentation [12, 47], and point cloud completion [8, 41, 40] due to their capability to preserve the spatial information of the input. However, standard voxelization can result in geometric information loss and quantization effects. To address this issue, GRNet [40] proposed a differentiable completion network that aggregates features between 3D grid vertices using interpolation. Similarly, our approach also utilizes the volumetric representation and pose to perform completion.", + "bbox": [ + 77, + 456, + 482, + 600 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Methods", + "text_level": 1, + "bbox": [ + 78, + 614, + 265, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 78, + 638, + 193, + 653 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we refer to an incomplete point cloud as $P_{i} \\in \\mathbb{R}^{N \\times 3}$ , where $N$ is the number of points in the point cloud, and the subscript $i$ represents the pose at which $P_{i}$ is captured. For convenience, we define the pose as a two-dimensional vector $o = (\\phi, \\theta)$ , as the incomplete point cloud is usually not significantly affected by the distance between the scanner and the target object.", + "bbox": [ + 78, + 661, + 482, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of our work is to achieve point cloud completion without relying on using complete point clouds. To accomplish this, we generate multiple incomplete point clouds from a single input point cloud, where each generated incomplete point cloud shares the same object as the input but corresponds to a different pose.", + "bbox": [ + 78, + 761, + 482, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, we begin by using an encoder $E$ to obtain the volumetric shape feature $V$ from the input incomplete point cloud $P_{i}$ . We assume that the encoder can extract complete shape information of the object from the input incomplete point cloud. In other words, the volumetric shape feature serves as a complete target object at the feature level. To mimic the process of obtaining an incomplete point cloud as a capture of the target object at a certain pose, we gather the features corresponding to the arbitrarily given pose $o_{r}$ (or $o_{i}$ for the upper branch) from the volumetric shape feature. Then, with a decoder $D$ , we decode the gathered feature $F$ to generate the incomplete point cloud.", + "bbox": [ + 510, + 434, + 917, + 605 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To ensure that the incomplete point cloud generated by our framework correctly corresponds to the given pose, we impose reconstruction loss and cycle consistency loss, which will be explained in Section 3.2. Further, we introduce a novel method to determine the visible region and gather the features on it into the projected feature. We describe the details of the projection method in Section 3.3. Finally, in Section 3.4, we demonstrate how we obtain the complete point cloud using our framework, in the inference phase. It is worth noting that throughout the entire process, we do not use any complete point cloud.", + "bbox": [ + 510, + 605, + 917, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Pose-Aware Point Cloud Generation", + "text_level": 1, + "bbox": [ + 512, + 768, + 836, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since we have neither a complete point cloud nor an incomplete point cloud captured from another view, the input incomplete point cloud is the only available data in the point cloud domain that can be used as supervision. Therefore,", + "bbox": [ + 510, + 790, + 917, + 847 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14205", + "bbox": [ + 465, + 877, + 504, + 888 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ecf98247a6cd5c7ac46bdfad08412593da935c04d2efc4fe493de8c08b0ff524.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 85, + 108, + 250, + 233 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9d63049140899cc64a672443c5699cf105e3c55549d10ac49ac61348ca60c3c5.jpg", + "image_caption": [ + "Case I", + "↓" + ], + "image_footnote": [], + "bbox": [ + 267, + 110, + 394, + 203 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/285c84f022c51673e3c5e455c406876c733a838666fd8fd26e601ef71d5e6328.jpg", + "image_caption": [ + "Case II", + "↓" + ], + "image_footnote": [], + "bbox": [ + 430, + 111, + 552, + 203 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c59cd38030898a7c2fc93c2260720ef098a2f6ec59de2c6a86ac34034e4e8a0a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 430, + 233, + 559, + 320 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ff4eb31ff4227f5f7b1bc991fbd9d938dd6c157d5bfd1b4a8c7472a44badcbd1.jpg", + "image_caption": [ + "Case III", + "↓" + ], + "image_footnote": [], + "bbox": [ + 589, + 112, + 710, + 201 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/42a1d7cad7f63daf9c21ac24c0c26ae943a3ff28720640c9216087738c587f75.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 588, + 233, + 715, + 320 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2a73dba570edd6a4afe2416c0869c60a39c8113f0ab5b2c2acdf5d917e1192c2.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 754, + 93, + 897, + 163 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b96df3b203bd8a6b8f8ac0d8426288d40a2c92006b9bb65262d0c06066636333.jpg", + "image_caption": [ + "Figure 3. Illustration of our projection method. (a) We first determine the base region (covered by yellow) according to the given pose. Note that any pose can be categorized as one of cases I, II, and III, after a proper rotation. Then, the features on the base region are gathered into a 2D feature grid. (b) The visible region (covered by blue) defined on the grid is obtained by interpolating the neighboring base features." + ], + "image_footnote": [], + "bbox": [ + 739, + 163, + 895, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we devise two branches that can be effectively trained using the input incomplete point cloud. The first branch uses the input pose $o_i$ to generate the projected feature $F_{i}$ and decode $\\hat{P}_{i,rec}$ , which should be identical to the input point cloud $P_{i}$ . To ensure this, we minimize the following reconstruction loss $\\mathcal{L}_{rec}$ :", + "bbox": [ + 78, + 385, + 482, + 471 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} = \\mathcal {L} _ {C D} \\left(P _ {i}, \\hat {P} _ {i, r e c}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 477, + 480, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\mathcal{L}_{CD}$ denotes the Chamfer Distance (CD), commonly used in the point cloud field. Note that, for two given point clouds $P_{1}$ and $P_{2}$ , the CD is formulated as", + "bbox": [ + 78, + 500, + 480, + 541 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C D} \\left(P _ {1}, P _ {2}\\right) = \\sum_ {p _ {i} \\in P _ {1}} \\min _ {p _ {j} \\in P _ {2}} \\left\\| p _ {i} - p _ {j} \\right\\| + \\sum_ {p _ {j} \\in P _ {2}} \\min _ {p _ {i} \\in P _ {1}} \\left\\| p _ {j} - p _ {i} \\right\\|. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 546, + 494, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Further, we randomly sample an arbitrary pose $o_r$ , which is different from the input pose $o_i$ , and generate projected feature $F_r$ . If we decode $F_r$ , the resulting incomplete point cloud $\\hat{P}_r$ should share the same shape with $P_i$ but correspond to the sampled pose $o_r$ . However, as mentioned, we cannot access the GT $P_r$ . Therefore, we impose cycle consistency on our framework. In specific, we put $\\hat{P}_r$ into the encoder again and get $\\hat{V}$ , which is the shape feature of the $\\hat{P}_r$ . Since the original input $P_i$ and $\\hat{P}_r$ should have the same shape, we minimize a shape loss $\\mathcal{L}_{shape}$ defined as follows:", + "bbox": [ + 78, + 591, + 482, + 733 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s h a p e} = \\left| \\left| V - \\hat {V} \\right| \\right| _ {1}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 203, + 745, + 480, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Besides, using the $\\hat{V}$ and the input pose $o_i$ , we gather the projected feature $\\hat{F}_i$ and decode it into $\\hat{P}_{i,cycle}$ , which should be identical to the input point cloud. Therefore, we define cycle loss $\\mathcal{L}_{cycle}$ as follow:", + "bbox": [ + 78, + 767, + 480, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c y c l e}} = \\mathcal {L} _ {C D} \\left(P _ {i}, \\hat {P} _ {i, \\text {c y c l e}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 831, + 480, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "These loss terms, $\\mathcal{L}_{shape}$ and $\\mathcal{L}_{cycle}$ , enable the encoder to extract the shape feature containing complete shape information and also help the decoder to generate incomplete point cloud that reflects the pose.", + "bbox": [ + 512, + 385, + 915, + 442 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To sum up, we train our framework by using a combination of $\\mathcal{L}_{rec}$ , $\\mathcal{L}_{cycle}$ , and $\\mathcal{L}_{shape}$ . The total loss function is defined as follow:", + "bbox": [ + 512, + 442, + 917, + 484 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e c}} + \\mathcal {L} _ {\\text {c y c l e}} + \\lambda \\mathcal {L} _ {\\text {s h a p e}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 500, + 915, + 514 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is the weight for $\\mathcal{L}_{shape}$ .", + "bbox": [ + 512, + 527, + 742, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. The Proposed Projection Method", + "text_level": 1, + "bbox": [ + 512, + 552, + 811, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to effectively incorporate pose information into our learning framework, we devise the encoder to extract the shape information as a form of volumetric feature, denoted as $V = \\{v_{i}\\}_{i = 1}^{N^{3}}$ . Here, $v_{i} \\in \\mathbb{R}^{d}$ , where $N$ is the resolution of the volumetric feature and $d$ is the feature dimension. Similar to the target object being captured as an incomplete point cloud from a certain viewpoint, we devise a gathering process that selects the features that are visible from an arbitrarily given pose.", + "bbox": [ + 510, + 574, + 917, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the volumetric feature is a spatially discrete 3D grid, and thereby a naive visibility test returns the same results for the wide range of poses. To mitigate this, we establish a projection rule that can be applied for arbitrary poses, as shown in Fig. 3 (a). In specific, we subdivide the entire set of poses into the pose subsets, per 30 degrees. Then, we predefine the base region (covered by yellow) for each pose subset. Note that, without loss of generality, any arbitrary pose segment can be categorized into one of the three cases (I, II, and III), after a proper rotation.", + "bbox": [ + 510, + 705, + 917, + 847 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14206", + "bbox": [ + 465, + 877, + 505, + 888 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d79aacb37af49ce9b9a37e7a664d3b72e2a6c88f3013b57d1eb376f7ba086054.jpg", + "image_caption": [ + "Figure 4. Illustration of obtaining the complete point cloud with the proposed framework in the inference phase. We gather the projected features $F_{1:8}$ from the shape feature $V$ , according to the various poses $o_{1:8}$ . Then, each projected feature is decoded into the incomplete point cloud $\\hat{P}_{1:8}$ . A union of the generated incomplete point clouds serves as the resulting complete point cloud $\\hat{C}$ ." + ], + "image_footnote": [], + "bbox": [ + 82, + 81, + 478, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once the base region is determined, we unfold the volumetric features located in that region into the 2D grid. During the unfolding, we compute the feature of the empty nodes by interpolating the neighboring volumetric features. In detail, we simply average the neighboring features and use the result as the feature of the node. Then, we define the visible region (covered by blue) on the 2D base grid, as shown in Fig. 3 (b). Here, as $\\theta$ and $\\phi$ increase, the visible region would move up and right, respectively. Finally, to obtain the feature map that represents the visible region, we perform bilinear interpolation using the neighboring base features. The weights for interpolation are determined according to the values of $\\theta$ and $\\phi$ . Further details of the projection method are provided in Supp. Material.", + "bbox": [ + 77, + 372, + 482, + 572 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Obtaining Complete Point Cloud", + "text_level": 1, + "bbox": [ + 78, + 581, + 376, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As aforementioned, in the inference phase, we generate multiple incomplete point clouds of various poses and integrate them into a complete one. In detail, we first extract the volumetric shape feature $V$ from the input incomplete point cloud, as shown in Fig. 4. From the shape feature, we obtain the projected features $F_{1:8}$ by using a set of poses $o_{1:8}$ . Here, we use a predefined set of eight poses, $\\left\\{\\left(\\frac{\\pi}{4}, \\frac{\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{3\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{5\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{7\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{3\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{5\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{7\\pi}{4}\\right)\\right\\}$ , which can cover the entire object. Then, we decode the projected features into the incomplete point cloud $\\hat{P}_{1:8}$ . Finally, a union of the generated incomplete point clouds serves as the resulting complete point cloud $\\hat{C}$ . Note that we use the incomplete point cloud as the only input for the inference, and the pose of the input is not required.", + "bbox": [ + 77, + 605, + 482, + 802 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We observe that the resulting integrated point cloud $\\hat{C}$ has substantial quality. However, our generate-and-integrate approach involves repeated decoding to generate", + "bbox": [ + 78, + 804, + 482, + 847 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/06eeb301d91749fa49f1afa7be1cb3eb11458fe0ed902b93728c13aeacc7e3ab.jpg", + "image_caption": [ + "Figure 5. Illustration of the proposed re-training strategy. We use the frozen framework to obtain pseudo-GT $\\hat{C}$ . Then, a new point cloud completion network $G$ is trained to learn a mapping between the input $P_{i}$ and the pseudo-GT." + ], + "image_footnote": [], + "bbox": [ + 517, + 84, + 905, + 187 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "multiple incomplete point clouds, which can be computationally inefficient. In Section 4.3, we conduct an experiment to verify the completion performance while changing the number of used poses. It shows that there is a trade-off between the performance and the number of poses. To alleviate this issue, we propose a strategy named Re-Training (RT). As visualized in Fig. 5, this strategy uses the integrated complete point cloud as supervision for training another completion network.", + "bbox": [ + 510, + 248, + 917, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, our framework is trained as in Section 3 and frozen. Then, we obtain an integrated complete point cloud for each incomplete point cloud in the training dataset. Since the obtained complete point cloud is a reasonable completion result, it can serve as a pseudo-GT for the corresponding incomplete point cloud (which was originally used as input). In other words, starting from the initial dataset including incomplete point clouds without any complete point cloud at all, we now have a paired dataset including the incomplete point cloud and the pseudo-GT pairs. Using the incomplete point cloud and pseudo-GT pairs, we train another point cloud completion network $G$ , like the conventional fully-supervised point cloud completion methods. For this, we use the Chamfer Distance loss between the input $P_{i}$ and pseudo-GT $\\hat{C}$ , which is denoted as $\\mathcal{L}_{RT}$ . Note that, we still do not access the real GT complete point clouds at all, throughout the whole process of the re-training.", + "bbox": [ + 510, + 377, + 917, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared to directly using the output of our framework as a final output, the re-training can be advantageous in several aspects. First, as we mentioned, re-training is much more efficient and practical in the inference phase, since it requires only one inference per input and can perform multiclass point cloud completion. Further, in terms of the completion performance, the re-training enables learning more complex and beneficial concepts. For example, during retraining, we can expect the network to learn the geometric relation between the incomplete and (pseudo-)complete point clouds. It is especially helpful when the input is severely self-occluded (e.g., when only the upper side of the table can be observed), which cannot be dealt with directly using the pseudo-complete point cloud. In addition, we observe that the re-training can reject some outlier points in the pseudo-GT.", + "bbox": [ + 510, + 619, + 917, + 847 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14207", + "bbox": [ + 465, + 877, + 505, + 889 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e699a2fd460adfc17cc3a35836c88179a069af6a9e654d930f124b02698b1482.jpg", + "table_caption": [ + "Table 1. Completion results on our dataset. The numbers shown are [CD ↓/F1 ↑], where CD is Chamfer Distance scaled with $\\times 10^4$ . Best results are indicated as **bold**." + ], + "table_footnote": [], + "table_body": "
MethodsUsing Complete PC.AirplaneCabinetCarChairSofaTableVesselAverage
Cycle. [36]Yes14.71/81.5316.64/74.9435.02/49.3322.23/70.5320.38/47.0721.45/77.1816.09/76.4920.93/68.15
ShapeInv. [45]Yes4.16/96.0514.20/79.9110.69/87.0916.67/81.3916.01/80.8223.86/82.9310.55/ 87.7213.74/85.13
OursNo4.84/95.1315.11/77.529.63/88.0118.25/75.3417.50/74.6219.02/80.9312.45/84.4313.73/82.46
Ours (+RT)No4.87/94.8515.14/81.209.06/88.8416.22/77.9215.41/77.6718.04/80.7310.95/86.3612.81/83.94
", + "bbox": [ + 80, + 111, + 915, + 191 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dbf5504909040f896005d74d15706aa0ba3dfe114febfe56fd691d2546080fc3.jpg", + "image_caption": [ + "Figure 6. Qualitative results of the point cloud completion methods on our dataset. From left to right: incomplete input, completion results of Cycle4completion [36], ShapeInversion [45], ours, ours (+RT), and GT." + ], + "image_footnote": [], + "bbox": [ + 115, + 201, + 880, + 492 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 78, + 542, + 290, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset Generation", + "text_level": 1, + "bbox": [ + 78, + 566, + 270, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The datasets [8, 34] widely used for the existing point cloud completion studies consist of input point clouds and complete point clouds, which are suitable for the fully-supervised or unpaired settings. On the other hand, to train and evaluate our study, a dataset consisting of complete/incomplete point clouds and corresponding poses is required. Therefore, we build and publish a new dataset for this setting. We use the complete point clouds in the ShapeNet Benchmark [5]. First, we randomly sample the pose as a viewpoint located on the sphere. Then, with the sampled pose, we use [18] to remove unobserved points from the complete point cloud. The resulting point cloud can serve as an incomplete point cloud, where the sampled pose is the corresponding pose. Note that, in our dataset, there is only one incomplete point cloud per the complete point cloud. It means that any complete point cloud cannot be observed from more than one view. More details about the proposed dataset can be found in the Supp. Material.", + "bbox": [ + 78, + 591, + 482, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparisons with Other Methods", + "text_level": 1, + "bbox": [ + 512, + 542, + 821, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to evaluate the effectiveness of the proposed method, we conduct a comparison with existing methods (Cycle. [36] and ShapeInv. [45]), which access a set of complete point clouds during training. To ensure a fair comparison, we trained and evaluated all methods on the proposed dataset, using official codes provided by the authors. We evaluate and compare our method with and without using Re-Training (RT) strategy.", + "bbox": [ + 512, + 571, + 915, + 685 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Results We use Chamfer Distance and F1-score to evaluate the performance of point cloud completion. As shown in Table 1, we evaluate seven categories. Overall, the re-training process improves the performance in most categories, indicating its effectiveness in enhancing the results. Compared to ShapeInv., our proposed method has a lower average Chamfer Distance and a slightly lower F1-score of 1.19. Interestingly, our results outperform Cycle for all metrics. In other words, our results outperform or achieve comparable performance to existing studies despite not using a complete point cloud.", + "bbox": [ + 510, + 690, + 915, + 847 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14208", + "bbox": [ + 465, + 877, + 505, + 888 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/631e45df9d7a520e310178a063000186152bc4834a7639e87e0ca3c53b50c946.jpg", + "image_caption": [ + "Figure 7. Visualization of pose-aware incomplete point clouds. The cuboids in the top part indicate the volumetric shape features viewed from an arbitrary pose, highlighted in red. The right side of the figure shows the input and ground truth complete point clouds. Two scenarios are considered for generating incomplete point clouds: one that uses only the $\\mathcal{L}_{rec}$ loss term, and the other with the full loss term. We also generate ground truth incomplete point clouds to evaluate how well the incomplete point clouds are generated." + ], + "image_footnote": [], + "bbox": [ + 95, + 95, + 902, + 302 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results We qualitatively compare the point cloud completion results on our dataset. Figure 6 shows complete point cloud results from existing methods, Cycle., ShapeInv., ours, and ours with re-training technique. Compared to the results of the existing methods, the results support that our method successfully completes the parts that were originally invisible at the input point cloud. Also, we find that the conventional methods fail to restore certain details that are present in the input point cloud. For instance, as shown in the dashed boxes, some fine details such as the exhaust port of the airplane or the armrest parts of the chair are not completely generated, even though they are present in the input point cloud. However, our method can reconstruct them sharply, resulting in a more accurate and realistic airplane model. To sum up, both the quantitative and qualitative results support that the proposed method can achieve substantial completion results, considering that GT complete point cloud is not used at all.", + "bbox": [ + 78, + 383, + 484, + 640 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 78, + 650, + 247, + 663 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Each Loss Term We conduct the ablation studies to verify the effectiveness of each term in Eq. 5. As shown in Table 2, we use Chamfer Distance and F1-score as a metric in several categories. The case with only reconstruction loss is used as the baseline. As shown in first row and second row, Chamfer Distance decreases 1.01 CD and F1-score increases 1.30 in average after adding shape loss. We can see that there are performance improvements in every category. As shown in first row and third row, Chamfer Distance decreases 1.55 CD and F1-score increases 1.75 after adding cycle loss. Also, there are performance improvements in every categories. As shown in last row, it", + "bbox": [ + 78, + 676, + 482, + 847 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0db9b7ef1c06aa30ca1a53291ab672a06cae901f9c5ea309f51e52e23e4cf7f2.jpg", + "table_caption": [ + "Table 2. Ablation studies on the proposed dataset. The numbers shown are $[\\mathrm{CD} \\downarrow / \\mathrm{F1} \\uparrow]$ , where CD is Chamfer Distance scaled with $\\times 10^4$ . Best results are indicated as bold." + ], + "table_footnote": [], + "table_body": "
LrecLshapeLcycleAirplaneCabinetSofaAverage
✓5.63/94.1117.66/73.4119.97/72.4714.42/79.99
✓✓5.58/94.2915.86/76.3918.80/73.1913.41/81.29
✓✓5.08/94.9515.47/76.3818.08/73.8912.87/81.74
✓✓✓4.84/95.1314.90/88.0117.50/74.6212.42/82.69
", + "bbox": [ + 517, + 421, + 914, + 480 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "shows best performance in both Chamfer Distance and F1-score with all constraints. From these results, proposed constraints are all effective in point cloud completion.", + "bbox": [ + 512, + 490, + 917, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Number of Poses We examine the effect of the number of input poses on the quality of the complete point cloud generated from our method without re-training. Intuitively, if we use more poses, the generated point clouds that are aware of the input poses and incomplete could cover a wider range of partial views, and thereby complete point cloud would be better. We conduct an experiment with 2, 4, 8, 10, and 14 poses for some categories, where the configurations of 2, 4, and 8 poses are shown in Fig. 8. For a configuration of 10 poses, upward and downward poses are added to the 8 poses. Likewise, additional 4 sideward poses are incorporated into the case of 10 poses for the configuration of 14 poses. Fig. 9 shows how the completion performance changes depending on the number of poses used. As we expected, Chamfer Distance decreases meaningfully as more poses are used until 8 poses. However, the performance becomes saturated as we increase the number of poses to 10 and 14. Therefore, we use 8 poses for our default setting.", + "bbox": [ + 510, + 533, + 917, + 790 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Additional Experiments", + "text_level": 1, + "bbox": [ + 512, + 796, + 741, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results of Pose-Aware Incomplete Point Cloud Since our main idea is generating and integrating the multiple incom", + "bbox": [ + 512, + 818, + 917, + 847 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14209", + "bbox": [ + 465, + 877, + 505, + 888 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6107daf66e11f2b5798f456c644e09c57c2d69184d9917a21d3e97848f651fc3.jpg", + "image_caption": [ + "Figure 8. Illustration of pose configurations, which are used to verify the effectiveness of the number of poses. The black dots represent the location of the poses." + ], + "image_footnote": [], + "bbox": [ + 104, + 86, + 211, + 159 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/97eadff4b42fdd692b1f8d5b357b5fe2ecf815d4c4b121b62e310398656e2282.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 218, + 86, + 331, + 159 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c78dcf3c2a6a1c4c3b84e5b6e38f97e5af88470e2110643248a9268451a9ffc5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 334, + 84, + 452, + 161 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51b1d693c682817ef0c56d41804ff78ee29be1e194561bccdc3b5021942332dc.jpg", + "image_caption": [ + "Figure 9. Impact of the number of poses on performance. CD is Chamfer Distance scaled with $\\times 10^4$ ." + ], + "image_footnote": [], + "bbox": [ + 85, + 217, + 458, + 290 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "plete point clouds corresponding to the given poses, we qualitatively verify whether our network can generate high-quality incomplete point clouds that correspond to the desired poses. Figure 7 shows incomplete point clouds generated from our method. The top row of the figure indicates the various poses we used, and the right side shows the input incomplete input point cloud and the GT complete point cloud. According to them, we generate incomplete point clouds using the models, which are (1) trained with reconstruction loss only and (2) trained with all loss terms. We also provide the GT incomplete point clouds obtained by applying hidden point removal [18] on the GT complete point cloud. When using only $\\mathcal{L}_{rec}$ , we can observe that the generated incomplete point clouds do not reflect the given poses correctly, and also fail to preserve fine details overall. On the other hand, we can see that incomplete point clouds obtained by the proposed method are well-corresponded to their respective poses appearing as if they had been captured from those viewpoints. Notably, the fine details (e.g., exhaust ports on the wings) are well-completed for all incomplete point clouds, indicating that the network could effectively capture detailed shapes from the input point cloud across various poses. The results support that our framework correctly learns to generate incomplete point clouds according to the given poses, and achieve substantial completion results in the ultimate.", + "bbox": [ + 78, + 331, + 482, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Using Noisy Poses In the real scenario, there can be a noise in the poses corresponding to the obtained incomplete point cloud. Therefore, we conduct an experiment to verify the sensitivity of the proposed method against the noise in the poses that we used for training. We observe that our method is robust to the noise in poses to some extent. We conduct an experiment by introducing Gaussian noise to the given poses. Specifically, we add a noise sampled from normal distribution to the given pose $o_i = (\\phi, \\theta)$ . The resulting noisy pose, denoted as $\\phi_{noise}$ and $\\theta_{noise}$ , is defined as follows:", + "bbox": [ + 78, + 704, + 482, + 847 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/625b1f31668a4bf51b3d17a1c9db87eea030f66499200eee7aaa3f4b367423a9.jpg", + "table_caption": [ + "Table 3. Effect of noise in pose. The numbers shown are [CD ↓ / F1 ↑], where CD is Chamfer Distance scaled with $\\times 10^4$ . Best results are indicated as bold." + ], + "table_footnote": [], + "table_body": "
σAirplaneCabinetSofaAverage
0.14.94/95.2216.79/75.0519.79/72.0813.84/80.79
0.034.89/95.2315.44/77.4218.07/73.3812.80/82.01
04.84/95.1314.90/78.3117.50/74.6212.42/82.69
AirplaneInput0.10.030
Cabinet
Sofa
", + "bbox": [ + 527, + 122, + 904, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 10. Qualitative results with noisy poses. 0.1, 0.03, and 0 are value of $\\sigma$ in Eq. 6, 7.", + "bbox": [ + 512, + 363, + 917, + 390 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "lows:", + "bbox": [ + 514, + 399, + 554, + 412 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {\\text {n o i s e}} = \\phi + \\sigma N (0, 1) \\times 1 8 0 ^ {\\circ} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 422, + 915, + 437 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {\\text {n o i s e}} = \\theta + \\sigma N (0, 1) \\times 1 8 0 ^ {\\circ}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 440, + 915, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here, $N(0,1)$ is a normal distribution with mean 0 and variance 1. We train and evaluate the model by varying the value of $\\sigma$ . We set the $\\sigma$ as 0.03 and 0.1. For these values, the errors in the pose are mostly within $11^{\\circ}$ and $36^{\\circ}$ , respectively. Table 3 demonstrates the impact of the noise on pose information. A value of $\\sigma = 0$ means that there is no noise in the pose, which is the default setting provided in the main paper. As noise increases, the average performance decreases compared to the case without any noise. The average Chamfer distance increases by 1.42 CD, and F1-score decreases by 1.90 compared to the case without noise. It should be noted that the effect of noise on performance is not significant. Figure 10 shows the qualitative results when adding noise to the pose. Although the pose is perturbed, the generated complete point clouds remain similar to the case without any noise. From these results, we can conclude that errors in pose have a limited effect on performance.", + "bbox": [ + 512, + 463, + 917, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Completing the Real Incomplete Point Clouds To assess the scalability of our method, we conduct an experiment using the real dataset. We train and test our framework on the point cloud data in KITTI [10] and nuScenes [1], using the provided bounding boxes to calculate the relative pose. Since the real dataset does not include incomplete point clouds observed from upward or downward directions, we enforce a constraint to ensure that the sampled poses fall within a range of the poses of the incomplete point", + "bbox": [ + 512, + 719, + 917, + 847 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14210", + "bbox": [ + 465, + 877, + 505, + 888 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7f03079c5b049ee204bd8269e40549ad5832ebc71521d9f76c1ae1f0ae57ea63.jpg", + "table_caption": [ + "Table 4. Quantitative comparison on KITTI dataset [10]. Minimum Matching Distance (MMD, ↓) and Unidirectional Chamfer Distance (UCD, ↓) are scaled with $\\times 10^3$ and $\\times 10^4$ , respectively." + ], + "table_footnote": [], + "table_body": "
Cycle. [36]ShapeInv. [45]Ours
MMD32.21.62.4
UCD12.763.611.47
", + "bbox": [ + 114, + 124, + 448, + 171 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/33ae8f4d446148cdbb8c7a89d90fd60e784b575c3f90babda76e382032dcaf84.jpg", + "image_caption": [ + "Figure 11. Completion results of Real dataset. (A: Real incomplete point cloud, B: Our result)" + ], + "image_footnote": [], + "bbox": [ + 85, + 186, + 475, + 236 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "clouds. Table 4 compares the quantitative performance of Cycle.[36] and ShapeInv.[45] using Minimum Matching Distance (MMD) and Unidirectional Chamfer Distance (UCD). To calculate MMD, we use complete point clouds in ShapeNet [5]. MMD evaluates the quality of the result in terms of how realistically the point cloud is generated, and ShapeInv. shows the best performance in this regard. However, our approach also shows comparable performance. Additionally, our approach outperforms the others on the UCD metric, which evaluates how well the generated point cloud reflects the input shape. We show the qualitative results in Fig. 11. In each section, the left side displays input incomplete point clouds, while the right side showcases predicted complete point clouds. Our network successfully generates the complete shape of cars and vans, even when the input point clouds are severely sparse. We can also observe that the obtained complete point clouds well-reflect the detailed shapes. These results demonstrate the potential practicality of our method for real-world applications.", + "bbox": [ + 82, + 274, + 484, + 545 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 78, + 555, + 201, + 570 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose a novel method for point cloud completion that does not require any complete point clouds. The proposed method generates multiple incomplete point clouds corresponding to various poses and integrates them to obtain the complete point cloud. Our method employs an encoder-decoder framework where the encoder extracts a volumetric shape feature from the input incomplete point cloud, and the decoder generates pose-aware incomplete point clouds. To train the model, we introduce a novel dataset with incomplete point clouds and corresponding poses. The proposed method achieves comparable results with the existing state-of-the-art methods and outperforms some categories. Additionally, we demonstrate that the method can be applied to real incomplete point clouds. In future work, we plan to use a neural implicit representation for the shape feature instead of the volumetric feature, which can achieve better 3D representation capability. In addition, we will further enhance the projection method using a visibility check with learnable opacity.", + "bbox": [ + 78, + 577, + 482, + 847 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636) and Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by Korea government(MSIT) (No.2020-0-00440, Development of Artificial Intelligence Technology that Continuously Improves Itself as the Situation Changes in the Real World).", + "bbox": [ + 512, + 85, + 917, + 213 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 514, + 226, + 613, + 239 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giacarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. 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Cylinder3d: An effective 3d framework for driving-scene lidar semantic segmentation. arXiv preprint arXiv:2008.01550, 2020. 3" + ], + "bbox": [ + 515, + 86, + 915, + 271 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14213", + "bbox": [ + 465, + 878, + 504, + 888 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/c5a386b7-062e-40bf-ab26-f63c862742fe_model.json b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/c5a386b7-062e-40bf-ab26-f63c862742fe_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4e118c6828536cfc1c206c22317235eb428541de --- /dev/null +++ b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/c5a386b7-062e-40bf-ab26-f63c862742fe_model.json @@ -0,0 +1,2180 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.096, + 0.01, + 0.172, + 0.047 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.232, + 0.008, + 0.816, + 0.049 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.154, + 0.122, + 0.844, + 0.166 + ], + "angle": 0, + "content": "Learning Point Cloud Completion without Complete Point Clouds: A Pose-Aware Approach" + }, + { + "type": "text", + "bbox": [ + 0.246, + 0.192, + 0.751, + 0.226 + ], + "angle": 0, + "content": "Jihun Kim, Hyeokjun Kwon, Yunseo Yang, and Kuk-Jin Yoon \nKorea Advanced Institute of Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.295, + 0.228, + 0.704, + 0.242 + ], + "angle": 0, + "content": "{jihun1998,0327june,acorn,kjyoon}@kaist.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.242, + 0.275, + 0.321, + 0.289 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.305, + 0.485, + 0.604 + ], + "angle": 0, + "content": "Point cloud completion is to restore complete 3D scenes and objects from incomplete observations or limited sensor data. Existing fully-supervised methods rely on paired datasets of incomplete and complete point clouds, which are labor-intensive to obtain. Unpaired methods have been proposed, but still require a set of complete point clouds as a reference. As a remedy, in this paper, we propose a novel point cloud completion framework without using any complete point cloud at all. Our main idea is to generate multiple incomplete point clouds of various poses and integrate them into a complete point cloud. We train our framework based on cycle consistency, to generate an incomplete point cloud such that 1) shares the same object as the input incomplete point cloud and 2) corresponds to an arbitrarily given pose. In addition, we devise a novel projection method conditioned by pose to gather visible features, from a volumetric feature extracted by an encoder. Extensive experiments demonstrate that the proposed method achieves comparable or better results than existing unpaired methods. Further, we show that our method also can be applied to real incomplete point clouds." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.628, + 0.216, + 0.643 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.648, + 0.483, + 0.747 + ], + "angle": 0, + "content": "A point cloud is a commonly used representation of 3D scenes and objects in the fields of computer vision and robotics [14, 20, 21, 22, 28, 9, 24, 2, 3, 7, 15]. However, obtaining complete point clouds is often difficult due to the lack of observation or the limitations of sensors. As a remedy, the point cloud completion task has been spotlighted to restore complete point clouds from incomplete ones." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.748, + 0.483, + 0.848 + ], + "angle": 0, + "content": "The existing fully-supervised point cloud completion methods [16, 17, 19, 38, 39, 40, 42, 43, 44] have shown promising results; however, they typically rely on datasets that include incomplete point clouds paired with complete point clouds serving as ground truth (GT). Since obtaining GT complete point clouds is labor-intensive, several works [6, 36, 45, 4] have employed two sets of point clouds:" + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.275, + 0.758, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.772, + 0.275, + 0.907, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.359, + 0.886, + 0.371 + ], + "angle": 0, + "content": "(c) Generate incomplete PCs of various poses \\(\\rightarrow\\) Integrate them as complete PC" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.372, + 0.904, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.452, + 0.918, + 0.491 + ], + "angle": 0, + "content": "Figure 1. Illustration of our main idea. We re-interpret the point cloud completion task as generating multiple incomplete point clouds that correspond to various poses and integrating them." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.505, + 0.918, + 0.62 + ], + "angle": 0, + "content": "one with incomplete point clouds and the other with complete point clouds, which are not directly paired with each other. This unpaired setting could learn the mapping between the incomplete and complete point clouds, while reducing the reliance on paired GT complete point clouds. Nevertheless, the requirement of a set of complete point clouds still remains a major limitation to the practical application of point cloud completion." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.621, + 0.919, + 0.849 + ], + "angle": 0, + "content": "In this paper, we propose a novel point cloud completion framework that does not use any complete point clouds. Our main novelty lies in how to learn a mapping from an incomplete point cloud to a complete point cloud when the latter is not available at all. For this, we present a simple yet effective idea shown in Fig. 1. An incomplete point cloud usually results from self-occlusion occurs when observing an object from a certain viewpoint, as in (a). Therefore, if we obtain multiple incomplete point clouds of the object from various viewpoints, a union of them would be equivalent to the complete point cloud of that object. Based on this idea, we formulate the point cloud completion as generating multiple incomplete point clouds using a single input incomplete point cloud and sampled poses. Here, the generated incomplete point clouds should 1) share the same object as the input incomplete point cloud and 2) correspond" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.878, + 0.505, + 0.889 + ], + "angle": 0, + "content": "14203" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.086, + 0.481, + 0.128 + ], + "angle": 0, + "content": "to the arbitrarily given input poses. If the poses are various enough to cover the entire object, we could obtain the complete point cloud by integrating the incomplete point clouds." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.129, + 0.481, + 0.299 + ], + "angle": 0, + "content": "To achieve the above, our framework starts with an encoder that extracts a volumetric shape feature from the input incomplete point cloud. This feature is designed to contain complete information about the shape of the target object. To generate an incomplete point cloud from the volumetric feature, we propose a novel projection method conditioned by the pose, similar to obtaining an incomplete point cloud as a capture of the target object from a certain viewpoint. The method determines the region visible at the given pose and obtains a projected feature by gathering the volumetric feature of that region. A decoder is then trained to generate an incomplete point cloud from the projected feature." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.3, + 0.481, + 0.469 + ], + "angle": 0, + "content": "We do not have access to either the complete point cloud or the incomplete point cloud of another pose. Therefore, for training, we propose a novel dataset that provides both incomplete point clouds and corresponding poses, based on the ShapeNet dataset [5]. Note that our dataset includes only one incomplete point cloud per each object, unlike the setting of [13]. Using our dataset, we make our framework reconstruct the input incomplete point cloud itself by gathering the projected feature using the pose corresponding to the input. On the other hand, when using randomly sampled poses, we impose cycle consistency by feeding the generated incomplete point cloud to the encoder/decoder again." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.47, + 0.481, + 0.681 + ], + "angle": 0, + "content": "During the inference phase, we extract the volumetric shape feature from the input and obtain the projected features using various poses that cover the entire object. By decoding the features and integrating the generated incomplete point clouds, we can obtain a complete point cloud as the final output. To verify the proposed method, we conduct extensive experiments and comparisons with the existing unpaired point cloud completion methods, on the proposed dataset. The results support that, the proposed method is comparable to the existing studies and sometimes achieves even more substantial completion results, without using any complete point cloud. Further, we conduct an experiment on the KITTI dataset [10] to show that the proposed method can be also applied to the real incomplete point clouds. Our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.687, + 0.481, + 0.729 + ], + "angle": 0, + "content": "- We formulate a point cloud completion task as generating and integrating multiple incomplete point clouds corresponding to various poses." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.731, + 0.481, + 0.772 + ], + "angle": 0, + "content": "- We propose a novel framework that generates an incomplete point cloud using the input incomplete point cloud and the given arbitrary pose." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.775, + 0.481, + 0.801 + ], + "angle": 0, + "content": "- We introduce a new dataset consisting of incomplete point clouds and poses." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.804, + 0.481, + 0.845 + ], + "angle": 0, + "content": "- We experimentally verify that the proposed method is comparable or even superior to existing studies, without using complete point cloud at all." + }, + { + "type": "list", + "bbox": [ + 0.081, + 0.687, + 0.481, + 0.845 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.085, + 0.667, + 0.099 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.104, + 0.742, + 0.119 + ], + "angle": 0, + "content": "2.1. Point Cloud Completion" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.128, + 0.916, + 0.553 + ], + "angle": 0, + "content": "Point cloud completion aims to restore a complete point cloud from an input incomplete point cloud. Although fully-supervised completion methods [8, 17, 19, 23, 32, 34, 37, 40, 43, 46, 35, 31] achieve substantial completion result, they rely on the dataset including paired incomplete point cloud and GT complete point cloud, which is difficult to acquire, especially for real scenes. To overcome the limitation, unpaired approaches [6, 36, 45, 11] have been proposed to learn the mapping between the sets of complete and incomplete point clouds. Pcl2pcl [6] is the first unpaired point cloud completion method, which allows translation between partial and complete latent spaces by adversarial training. Subsequently, Cycle4completion [36] has achieved more advanced results by considering bidirectional geometric correspondence by cycle transformation and missing region coding. ShapeInversion [45] obtained optimal shape code for reconstructing 3D shapes based on the concept of GAN inversion. OptDE [11] proposed cross-domain completion by disentangling shape, domain, and occlusion factors, using domain-invariant geometric information and viewpoint prediction. Although the unpaired methods have shown promising results, their practical application is still limited by the requirement for a number of complete point clouds. [13] has proposed to utilize multiple incomplete point clouds of the same object, obtained from observations at different poses; however, such multiple observations are often not available. Unlike the existing methods, our method does not access the complete point cloud at all, and also uses only one incomplete point cloud per each object, throughout the entire training process." + }, + { + "type": "title", + "bbox": [ + 0.518, + 0.568, + 0.758, + 0.583 + ], + "angle": 0, + "content": "2.2. Pose-Aware 3D Processing" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.592, + 0.916, + 0.847 + ], + "angle": 0, + "content": "One of the most representative 3D tasks dealing with the pose is point cloud canonicalization [29, 30, 26]. Condor [29] takes an un-canonicalized collection of full or partial point clouds obtained through the internet or depth sensor as input. Meanwhile, [33] proposed self-supervised learning via disentangling content and pose information for the point cloud feature representation. As such, numerous studies have been conducted to exploit these two factors, since 3D data usually contains pose attributes as well as the shape of the object. Nevertheless, in the field of point cloud completion, using pose has not been deeply studied despite its usefulness. Since an incomplete point cloud is usually obtained by scanning the object from a single viewpoint through a scanner, information about the viewpoint (i.e., pose) can be beneficial for recovering the self-occluded regions. In this light, we utilize the pose information to complete the point cloud by generating multiple incomplete point clouds." + }, + { + "type": "page_number", + "bbox": [ + 0.468, + 0.879, + 0.505, + 0.889 + ], + "angle": 0, + "content": "14204" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.082, + 0.876, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.351, + 0.918, + 0.417 + ], + "angle": 0, + "content": "Figure 2. Illustration of a framework for generating a pose-aware point cloud. First, the encoder extracts the volumetric shape feature \\( V \\) from the input point cloud \\( P_{i} \\). Then, projected features \\( F_{i} \\) and \\( F_{r} \\) are generated by determining the visible region with input pose \\( o_{i} \\) and random pose \\( o_{r} \\). Incomplete point cloud \\( \\hat{P}_{i,rec} \\) is decoded to constrain with \\( \\mathcal{L}_{rec} \\). Incomplete point cloud \\( \\hat{P}_{r} \\) is decoded and entered into the model again with input pose \\( o_{i} \\). After that, volumetric feature \\( \\hat{V} \\), projected feature \\( \\hat{F}_{i} \\), and \\( \\hat{P}_{i,cycle} \\) are generated sequentially. We use \\( \\mathcal{L}_{shape} \\) and \\( \\mathcal{L}_{cycle} \\) to constrain our network." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.434, + 0.395, + 0.451 + ], + "angle": 0, + "content": "2.3. Volumetric Feature Representation" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.457, + 0.484, + 0.601 + ], + "angle": 0, + "content": "Volumetric features are commonly used in tasks such as multi-view stereo [25, 27], 3D semantic segmentation [12, 47], and point cloud completion [8, 41, 40] due to their capability to preserve the spatial information of the input. However, standard voxelization can result in geometric information loss and quantization effects. To address this issue, GRNet [40] proposed a differentiable completion network that aggregates features between 3D grid vertices using interpolation. Similarly, our approach also utilizes the volumetric representation and pose to perform completion." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.615, + 0.266, + 0.631 + ], + "angle": 0, + "content": "3. Proposed Methods" + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.639, + 0.194, + 0.654 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.662, + 0.483, + 0.761 + ], + "angle": 0, + "content": "In this paper, we refer to an incomplete point cloud as \\( P_{i} \\in \\mathbb{R}^{N \\times 3} \\), where \\( N \\) is the number of points in the point cloud, and the subscript \\( i \\) represents the pose at which \\( P_{i} \\) is captured. For convenience, we define the pose as a two-dimensional vector \\( o = (\\phi, \\theta) \\), as the incomplete point cloud is usually not significantly affected by the distance between the scanner and the target object." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.762, + 0.483, + 0.848 + ], + "angle": 0, + "content": "The goal of our work is to achieve point cloud completion without relying on using complete point clouds. To accomplish this, we generate multiple incomplete point clouds from a single input point cloud, where each generated incomplete point cloud shares the same object as the input but corresponds to a different pose." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.435, + 0.918, + 0.606 + ], + "angle": 0, + "content": "As shown in Fig. 2, we begin by using an encoder \\( E \\) to obtain the volumetric shape feature \\( V \\) from the input incomplete point cloud \\( P_{i} \\). We assume that the encoder can extract complete shape information of the object from the input incomplete point cloud. In other words, the volumetric shape feature serves as a complete target object at the feature level. To mimic the process of obtaining an incomplete point cloud as a capture of the target object at a certain pose, we gather the features corresponding to the arbitrarily given pose \\( o_{r} \\) (or \\( o_{i} \\) for the upper branch) from the volumetric shape feature. Then, with a decoder \\( D \\), we decode the gathered feature \\( F \\) to generate the incomplete point cloud." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.606, + 0.918, + 0.763 + ], + "angle": 0, + "content": "To ensure that the incomplete point cloud generated by our framework correctly corresponds to the given pose, we impose reconstruction loss and cycle consistency loss, which will be explained in Section 3.2. Further, we introduce a novel method to determine the visible region and gather the features on it into the projected feature. We describe the details of the projection method in Section 3.3. Finally, in Section 3.4, we demonstrate how we obtain the complete point cloud using our framework, in the inference phase. It is worth noting that throughout the entire process, we do not use any complete point cloud." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.769, + 0.837, + 0.783 + ], + "angle": 0, + "content": "3.2. Pose-Aware Point Cloud Generation" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.791, + 0.918, + 0.848 + ], + "angle": 0, + "content": "Since we have neither a complete point cloud nor an incomplete point cloud captured from another view, the input incomplete point cloud is the only available data in the point cloud domain that can be used as supervision. Therefore," + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.878, + 0.505, + 0.889 + ], + "angle": 0, + "content": "14205" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.094, + 0.09, + 0.12, + 0.105 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.109, + 0.252, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.094, + 0.354, + 0.106 + ], + "angle": 0, + "content": "Case I" + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.111, + 0.395, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.21, + 0.344, + 0.228 + ], + "angle": 0, + "content": "↓" + }, + { + "type": "image_caption", + "bbox": [ + 0.468, + 0.094, + 0.52, + 0.106 + ], + "angle": 0, + "content": "Case II" + }, + { + "type": "image", + "bbox": [ + 0.431, + 0.112, + 0.554, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.481, + 0.21, + 0.506, + 0.228 + ], + "angle": 0, + "content": "↓" + }, + { + "type": "image", + "bbox": [ + 0.431, + 0.235, + 0.56, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.623, + 0.094, + 0.68, + 0.106 + ], + "angle": 0, + "content": "Case III" + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.113, + 0.712, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.209, + 0.663, + 0.228 + ], + "angle": 0, + "content": "↓" + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.235, + 0.716, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.743, + 0.091, + 0.768, + 0.105 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.094, + 0.898, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.741, + 0.164, + 0.896, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.328, + 0.918, + 0.368 + ], + "angle": 0, + "content": "Figure 3. Illustration of our projection method. (a) We first determine the base region (covered by yellow) according to the given pose. Note that any pose can be categorized as one of cases I, II, and III, after a proper rotation. Then, the features on the base region are gathered into a 2D feature grid. (b) The visible region (covered by blue) defined on the grid is obtained by interpolating the neighboring base features." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.386, + 0.484, + 0.472 + ], + "angle": 0, + "content": "we devise two branches that can be effectively trained using the input incomplete point cloud. The first branch uses the input pose \\(o_i\\) to generate the projected feature \\(F_{i}\\) and decode \\(\\hat{P}_{i,rec}\\), which should be identical to the input point cloud \\(P_{i}\\). To ensure this, we minimize the following reconstruction loss \\(\\mathcal{L}_{rec}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.478, + 0.482, + 0.494 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} = \\mathcal {L} _ {C D} \\left(P _ {i}, \\hat {P} _ {i, r e c}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.5, + 0.482, + 0.542 + ], + "angle": 0, + "content": "Here, \\(\\mathcal{L}_{CD}\\) denotes the Chamfer Distance (CD), commonly used in the point cloud field. Note that, for two given point clouds \\(P_{1}\\) and \\(P_{2}\\), the CD is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.547, + 0.495, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C D} \\left(P _ {1}, P _ {2}\\right) = \\sum_ {p _ {i} \\in P _ {1}} \\min _ {p _ {j} \\in P _ {2}} \\left\\| p _ {i} - p _ {j} \\right\\| + \\sum_ {p _ {j} \\in P _ {2}} \\min _ {p _ {i} \\in P _ {1}} \\left\\| p _ {j} - p _ {i} \\right\\|. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.592, + 0.484, + 0.734 + ], + "angle": 0, + "content": "Further, we randomly sample an arbitrary pose \\(o_r\\), which is different from the input pose \\(o_i\\), and generate projected feature \\(F_r\\). If we decode \\(F_r\\), the resulting incomplete point cloud \\(\\hat{P}_r\\) should share the same shape with \\(P_i\\) but correspond to the sampled pose \\(o_r\\). However, as mentioned, we cannot access the GT \\(P_r\\). Therefore, we impose cycle consistency on our framework. In specific, we put \\(\\hat{P}_r\\) into the encoder again and get \\(\\hat{V}\\), which is the shape feature of the \\(\\hat{P}_r\\). Since the original input \\(P_i\\) and \\(\\hat{P}_r\\) should have the same shape, we minimize a shape loss \\(\\mathcal{L}_{shape}\\) defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.746, + 0.482, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s h a p e} = \\left| \\left| V - \\hat {V} \\right| \\right| _ {1}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.768, + 0.482, + 0.826 + ], + "angle": 0, + "content": "Besides, using the \\(\\hat{V}\\) and the input pose \\(o_i\\), we gather the projected feature \\(\\hat{F}_i\\) and decode it into \\(\\hat{P}_{i,cycle}\\), which should be identical to the input point cloud. Therefore, we define cycle loss \\(\\mathcal{L}_{cycle}\\) as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.832, + 0.482, + 0.849 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c y c l e}} = \\mathcal {L} _ {C D} \\left(P _ {i}, \\hat {P} _ {i, \\text {c y c l e}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.386, + 0.916, + 0.443 + ], + "angle": 0, + "content": "These loss terms, \\(\\mathcal{L}_{shape}\\) and \\(\\mathcal{L}_{cycle}\\), enable the encoder to extract the shape feature containing complete shape information and also help the decoder to generate incomplete point cloud that reflects the pose." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.444, + 0.918, + 0.485 + ], + "angle": 0, + "content": "To sum up, we train our framework by using a combination of \\(\\mathcal{L}_{rec}\\), \\(\\mathcal{L}_{cycle}\\), and \\(\\mathcal{L}_{shape}\\). The total loss function is defined as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.5, + 0.917, + 0.515 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e c}} + \\mathcal {L} _ {\\text {c y c l e}} + \\lambda \\mathcal {L} _ {\\text {s h a p e}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.528, + 0.744, + 0.543 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the weight for \\(\\mathcal{L}_{shape}\\)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.553, + 0.813, + 0.569 + ], + "angle": 0, + "content": "3.3. The Proposed Projection Method" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.576, + 0.918, + 0.705 + ], + "angle": 0, + "content": "In order to effectively incorporate pose information into our learning framework, we devise the encoder to extract the shape information as a form of volumetric feature, denoted as \\( V = \\{v_{i}\\}_{i = 1}^{N^{3}} \\). Here, \\( v_{i} \\in \\mathbb{R}^{d} \\), where \\( N \\) is the resolution of the volumetric feature and \\( d \\) is the feature dimension. Similar to the target object being captured as an incomplete point cloud from a certain viewpoint, we devise a gathering process that selects the features that are visible from an arbitrarily given pose." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.706, + 0.918, + 0.848 + ], + "angle": 0, + "content": "However, the volumetric feature is a spatially discrete 3D grid, and thereby a naive visibility test returns the same results for the wide range of poses. To mitigate this, we establish a projection rule that can be applied for arbitrary poses, as shown in Fig. 3 (a). In specific, we subdivide the entire set of poses into the pose subsets, per 30 degrees. Then, we predefine the base region (covered by yellow) for each pose subset. Note that, without loss of generality, any arbitrary pose segment can be categorized into one of the three cases (I, II, and III), after a proper rotation." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.878, + 0.506, + 0.889 + ], + "angle": 0, + "content": "14206" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.082, + 0.48, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.282, + 0.482, + 0.361 + ], + "angle": 0, + "content": "Figure 4. Illustration of obtaining the complete point cloud with the proposed framework in the inference phase. We gather the projected features \\( F_{1:8} \\) from the shape feature \\( V \\), according to the various poses \\( o_{1:8} \\). Then, each projected feature is decoded into the incomplete point cloud \\( \\hat{P}_{1:8} \\). A union of the generated incomplete point clouds serves as the resulting complete point cloud \\( \\hat{C} \\)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.373, + 0.483, + 0.573 + ], + "angle": 0, + "content": "Once the base region is determined, we unfold the volumetric features located in that region into the 2D grid. During the unfolding, we compute the feature of the empty nodes by interpolating the neighboring volumetric features. In detail, we simply average the neighboring features and use the result as the feature of the node. Then, we define the visible region (covered by blue) on the 2D base grid, as shown in Fig. 3 (b). Here, as \\(\\theta\\) and \\(\\phi\\) increase, the visible region would move up and right, respectively. Finally, to obtain the feature map that represents the visible region, we perform bilinear interpolation using the neighboring base features. The weights for interpolation are determined according to the values of \\(\\theta\\) and \\(\\phi\\). Further details of the projection method are provided in Supp. Material." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.583, + 0.377, + 0.598 + ], + "angle": 0, + "content": "3.4. Obtaining Complete Point Cloud" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.606, + 0.483, + 0.804 + ], + "angle": 0, + "content": "As aforementioned, in the inference phase, we generate multiple incomplete point clouds of various poses and integrate them into a complete one. In detail, we first extract the volumetric shape feature \\(V\\) from the input incomplete point cloud, as shown in Fig. 4. From the shape feature, we obtain the projected features \\(F_{1:8}\\) by using a set of poses \\(o_{1:8}\\). Here, we use a predefined set of eight poses, \\(\\left\\{\\left(\\frac{\\pi}{4}, \\frac{\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{3\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{5\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{7\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{3\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{5\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{7\\pi}{4}\\right)\\right\\}\\), which can cover the entire object. Then, we decode the projected features into the incomplete point cloud \\(\\hat{P}_{1:8}\\). Finally, a union of the generated incomplete point clouds serves as the resulting complete point cloud \\(\\hat{C}\\). Note that we use the incomplete point cloud as the only input for the inference, and the pose of the input is not required." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.805, + 0.484, + 0.849 + ], + "angle": 0, + "content": "We observe that the resulting integrated point cloud \\(\\hat{C}\\) has substantial quality. However, our generate-and-integrate approach involves repeated decoding to generate" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.085, + 0.907, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.189, + 0.918, + 0.243 + ], + "angle": 0, + "content": "Figure 5. Illustration of the proposed re-training strategy. We use the frozen framework to obtain pseudo-GT \\(\\hat{C}\\). Then, a new point cloud completion network \\(G\\) is trained to learn a mapping between the input \\(P_{i}\\) and the pseudo-GT." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.249, + 0.918, + 0.377 + ], + "angle": 0, + "content": "multiple incomplete point clouds, which can be computationally inefficient. In Section 4.3, we conduct an experiment to verify the completion performance while changing the number of used poses. It shows that there is a trade-off between the performance and the number of poses. To alleviate this issue, we propose a strategy named Re-Training (RT). As visualized in Fig. 5, this strategy uses the integrated complete point cloud as supervision for training another completion network." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.378, + 0.918, + 0.62 + ], + "angle": 0, + "content": "First, our framework is trained as in Section 3 and frozen. Then, we obtain an integrated complete point cloud for each incomplete point cloud in the training dataset. Since the obtained complete point cloud is a reasonable completion result, it can serve as a pseudo-GT for the corresponding incomplete point cloud (which was originally used as input). In other words, starting from the initial dataset including incomplete point clouds without any complete point cloud at all, we now have a paired dataset including the incomplete point cloud and the pseudo-GT pairs. Using the incomplete point cloud and pseudo-GT pairs, we train another point cloud completion network \\( G \\), like the conventional fully-supervised point cloud completion methods. For this, we use the Chamfer Distance loss between the input \\( P_{i} \\) and pseudo-GT \\( \\hat{C} \\), which is denoted as \\( \\mathcal{L}_{RT} \\). Note that, we still do not access the real GT complete point clouds at all, throughout the whole process of the re-training." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.62, + 0.919, + 0.848 + ], + "angle": 0, + "content": "Compared to directly using the output of our framework as a final output, the re-training can be advantageous in several aspects. First, as we mentioned, re-training is much more efficient and practical in the inference phase, since it requires only one inference per input and can perform multiclass point cloud completion. Further, in terms of the completion performance, the re-training enables learning more complex and beneficial concepts. For example, during retraining, we can expect the network to learn the geometric relation between the incomplete and (pseudo-)complete point clouds. It is especially helpful when the input is severely self-occluded (e.g., when only the upper side of the table can be observed), which cannot be dealt with directly using the pseudo-complete point cloud. In addition, we observe that the re-training can reject some outlier points in the pseudo-GT." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.878, + 0.506, + 0.89 + ], + "angle": 0, + "content": "14207" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.084, + 0.916, + 0.109 + ], + "angle": 0, + "content": "Table 1. Completion results on our dataset. The numbers shown are [CD ↓/F1 ↑], where CD is Chamfer Distance scaled with \\(\\times 10^4\\). Best results are indicated as **bold**." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.112, + 0.916, + 0.192 + ], + "angle": 0, + "content": "
MethodsUsing Complete PC.AirplaneCabinetCarChairSofaTableVesselAverage
Cycle. [36]Yes14.71/81.5316.64/74.9435.02/49.3322.23/70.5320.38/47.0721.45/77.1816.09/76.4920.93/68.15
ShapeInv. [45]Yes4.16/96.0514.20/79.9110.69/87.0916.67/81.3916.01/80.8223.86/82.9310.55/ 87.7213.74/85.13
OursNo4.84/95.1315.11/77.529.63/88.0118.25/75.3417.50/74.6219.02/80.9312.45/84.4313.73/82.46
Ours (+RT)No4.87/94.8515.14/81.209.06/88.8416.22/77.9215.41/77.6718.04/80.7310.95/86.3612.81/83.94
" + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.203, + 0.882, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.5, + 0.916, + 0.527 + ], + "angle": 0, + "content": "Figure 6. Qualitative results of the point cloud completion methods on our dataset. From left to right: incomplete input, completion results of Cycle4completion [36], ShapeInversion [45], ours, ours (+RT), and GT." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.543, + 0.291, + 0.559 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.567, + 0.271, + 0.581 + ], + "angle": 0, + "content": "4.1. Dataset Generation" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.592, + 0.484, + 0.848 + ], + "angle": 0, + "content": "The datasets [8, 34] widely used for the existing point cloud completion studies consist of input point clouds and complete point clouds, which are suitable for the fully-supervised or unpaired settings. On the other hand, to train and evaluate our study, a dataset consisting of complete/incomplete point clouds and corresponding poses is required. Therefore, we build and publish a new dataset for this setting. We use the complete point clouds in the ShapeNet Benchmark [5]. First, we randomly sample the pose as a viewpoint located on the sphere. Then, with the sampled pose, we use [18] to remove unobserved points from the complete point cloud. The resulting point cloud can serve as an incomplete point cloud, where the sampled pose is the corresponding pose. Note that, in our dataset, there is only one incomplete point cloud per the complete point cloud. It means that any complete point cloud cannot be observed from more than one view. More details about the proposed dataset can be found in the Supp. Material." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.543, + 0.822, + 0.56 + ], + "angle": 0, + "content": "4.2. Comparisons with Other Methods" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.572, + 0.917, + 0.686 + ], + "angle": 0, + "content": "In order to evaluate the effectiveness of the proposed method, we conduct a comparison with existing methods (Cycle. [36] and ShapeInv. [45]), which access a set of complete point clouds during training. To ensure a fair comparison, we trained and evaluated all methods on the proposed dataset, using official codes provided by the authors. We evaluate and compare our method with and without using Re-Training (RT) strategy." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.691, + 0.917, + 0.848 + ], + "angle": 0, + "content": "Quantitative Results We use Chamfer Distance and F1-score to evaluate the performance of point cloud completion. As shown in Table 1, we evaluate seven categories. Overall, the re-training process improves the performance in most categories, indicating its effectiveness in enhancing the results. Compared to ShapeInv., our proposed method has a lower average Chamfer Distance and a slightly lower F1-score of 1.19. Interestingly, our results outperform Cycle for all metrics. In other words, our results outperform or achieve comparable performance to existing studies despite not using a complete point cloud." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.878, + 0.506, + 0.889 + ], + "angle": 0, + "content": "14208" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.096, + 0.904, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.314, + 0.92, + 0.368 + ], + "angle": 0, + "content": "Figure 7. Visualization of pose-aware incomplete point clouds. The cuboids in the top part indicate the volumetric shape features viewed from an arbitrary pose, highlighted in red. The right side of the figure shows the input and ground truth complete point clouds. Two scenarios are considered for generating incomplete point clouds: one that uses only the \\(\\mathcal{L}_{rec}\\) loss term, and the other with the full loss term. We also generate ground truth incomplete point clouds to evaluate how well the incomplete point clouds are generated." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.384, + 0.485, + 0.641 + ], + "angle": 0, + "content": "Qualitative Results We qualitatively compare the point cloud completion results on our dataset. Figure 6 shows complete point cloud results from existing methods, Cycle., ShapeInv., ours, and ours with re-training technique. Compared to the results of the existing methods, the results support that our method successfully completes the parts that were originally invisible at the input point cloud. Also, we find that the conventional methods fail to restore certain details that are present in the input point cloud. For instance, as shown in the dashed boxes, some fine details such as the exhaust port of the airplane or the armrest parts of the chair are not completely generated, even though they are present in the input point cloud. However, our method can reconstruct them sharply, resulting in a more accurate and realistic airplane model. To sum up, both the quantitative and qualitative results support that the proposed method can achieve substantial completion results, considering that GT complete point cloud is not used at all." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.651, + 0.248, + 0.665 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.677, + 0.484, + 0.849 + ], + "angle": 0, + "content": "Effectiveness of Each Loss Term We conduct the ablation studies to verify the effectiveness of each term in Eq. 5. As shown in Table 2, we use Chamfer Distance and F1-score as a metric in several categories. The case with only reconstruction loss is used as the baseline. As shown in first row and second row, Chamfer Distance decreases 1.01 CD and F1-score increases 1.30 in average after adding shape loss. We can see that there are performance improvements in every category. As shown in first row and third row, Chamfer Distance decreases 1.55 CD and F1-score increases 1.75 after adding cycle loss. Also, there are performance improvements in every categories. As shown in last row, it" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.381, + 0.918, + 0.419 + ], + "angle": 0, + "content": "Table 2. Ablation studies on the proposed dataset. The numbers shown are \\([\\mathrm{CD} \\downarrow / \\mathrm{F1} \\uparrow]\\), where CD is Chamfer Distance scaled with \\(\\times 10^4\\). Best results are indicated as bold." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.422, + 0.915, + 0.481 + ], + "angle": 0, + "content": "
LrecLshapeLcycleAirplaneCabinetSofaAverage
✓5.63/94.1117.66/73.4119.97/72.4714.42/79.99
✓✓5.58/94.2915.86/76.3918.80/73.1913.41/81.29
✓✓5.08/94.9515.47/76.3818.08/73.8912.87/81.74
✓✓✓4.84/95.1314.90/88.0117.50/74.6212.42/82.69
" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.491, + 0.918, + 0.533 + ], + "angle": 0, + "content": "shows best performance in both Chamfer Distance and F1-score with all constraints. From these results, proposed constraints are all effective in point cloud completion." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.534, + 0.919, + 0.791 + ], + "angle": 0, + "content": "Effectiveness of Number of Poses We examine the effect of the number of input poses on the quality of the complete point cloud generated from our method without re-training. Intuitively, if we use more poses, the generated point clouds that are aware of the input poses and incomplete could cover a wider range of partial views, and thereby complete point cloud would be better. We conduct an experiment with 2, 4, 8, 10, and 14 poses for some categories, where the configurations of 2, 4, and 8 poses are shown in Fig. 8. For a configuration of 10 poses, upward and downward poses are added to the 8 poses. Likewise, additional 4 sideward poses are incorporated into the case of 10 poses for the configuration of 14 poses. Fig. 9 shows how the completion performance changes depending on the number of poses used. As we expected, Chamfer Distance decreases meaningfully as more poses are used until 8 poses. However, the performance becomes saturated as we increase the number of poses to 10 and 14. Therefore, we use 8 poses for our default setting." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.798, + 0.742, + 0.812 + ], + "angle": 0, + "content": "4.4. Additional Experiments" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.819, + 0.918, + 0.849 + ], + "angle": 0, + "content": "Results of Pose-Aware Incomplete Point Cloud Since our main idea is generating and integrating the multiple incom" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.878, + 0.506, + 0.889 + ], + "angle": 0, + "content": "14209" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.105, + 0.087, + 0.212, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.219, + 0.087, + 0.332, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.336, + 0.085, + 0.453, + 0.162 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.165, + 0.483, + 0.207 + ], + "angle": 0, + "content": "Figure 8. Illustration of pose configurations, which are used to verify the effectiveness of the number of poses. The black dots represent the location of the poses." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.218, + 0.46, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.292, + 0.483, + 0.318 + ], + "angle": 0, + "content": "Figure 9. Impact of the number of poses on performance. CD is Chamfer Distance scaled with \\(\\times 10^4\\)." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.332, + 0.484, + 0.701 + ], + "angle": 0, + "content": "plete point clouds corresponding to the given poses, we qualitatively verify whether our network can generate high-quality incomplete point clouds that correspond to the desired poses. Figure 7 shows incomplete point clouds generated from our method. The top row of the figure indicates the various poses we used, and the right side shows the input incomplete input point cloud and the GT complete point cloud. According to them, we generate incomplete point clouds using the models, which are (1) trained with reconstruction loss only and (2) trained with all loss terms. We also provide the GT incomplete point clouds obtained by applying hidden point removal [18] on the GT complete point cloud. When using only \\(\\mathcal{L}_{rec}\\), we can observe that the generated incomplete point clouds do not reflect the given poses correctly, and also fail to preserve fine details overall. On the other hand, we can see that incomplete point clouds obtained by the proposed method are well-corresponded to their respective poses appearing as if they had been captured from those viewpoints. Notably, the fine details (e.g., exhaust ports on the wings) are well-completed for all incomplete point clouds, indicating that the network could effectively capture detailed shapes from the input point cloud across various poses. The results support that our framework correctly learns to generate incomplete point clouds according to the given poses, and achieve substantial completion results in the ultimate." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.705, + 0.484, + 0.849 + ], + "angle": 0, + "content": "Using Noisy Poses In the real scenario, there can be a noise in the poses corresponding to the obtained incomplete point cloud. Therefore, we conduct an experiment to verify the sensitivity of the proposed method against the noise in the poses that we used for training. We observe that our method is robust to the noise in poses to some extent. We conduct an experiment by introducing Gaussian noise to the given poses. Specifically, we add a noise sampled from normal distribution to the given pose \\( o_i = (\\phi, \\theta) \\). The resulting noisy pose, denoted as \\( \\phi_{noise} \\) and \\( \\theta_{noise} \\), is defined as follows:" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.083, + 0.918, + 0.121 + ], + "angle": 0, + "content": "Table 3. Effect of noise in pose. The numbers shown are [CD ↓ / F1 ↑], where CD is Chamfer Distance scaled with \\(\\times 10^4\\). Best results are indicated as bold." + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.123, + 0.905, + 0.359 + ], + "angle": 0, + "content": "
σAirplaneCabinetSofaAverage
0.14.94/95.2216.79/75.0519.79/72.0813.84/80.79
0.034.89/95.2315.44/77.4218.07/73.3812.80/82.01
04.84/95.1314.90/78.3117.50/74.6212.42/82.69
AirplaneInput0.10.030
Cabinet
Sofa
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.364, + 0.918, + 0.391 + ], + "angle": 0, + "content": "Figure 10. Qualitative results with noisy poses. 0.1, 0.03, and 0 are value of \\(\\sigma\\) in Eq. 6, 7." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.4, + 0.556, + 0.413 + ], + "angle": 0, + "content": "lows:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.423, + 0.917, + 0.438 + ], + "angle": 0, + "content": "\\[\n\\phi_ {\\text {n o i s e}} = \\phi + \\sigma N (0, 1) \\times 1 8 0 ^ {\\circ} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.441, + 0.917, + 0.456 + ], + "angle": 0, + "content": "\\[\n\\theta_ {\\text {n o i s e}} = \\theta + \\sigma N (0, 1) \\times 1 8 0 ^ {\\circ}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.464, + 0.918, + 0.719 + ], + "angle": 0, + "content": "Here, \\( N(0,1) \\) is a normal distribution with mean 0 and variance 1. We train and evaluate the model by varying the value of \\( \\sigma \\). We set the \\( \\sigma \\) as 0.03 and 0.1. For these values, the errors in the pose are mostly within \\( 11^{\\circ} \\) and \\( 36^{\\circ} \\), respectively. Table 3 demonstrates the impact of the noise on pose information. A value of \\( \\sigma = 0 \\) means that there is no noise in the pose, which is the default setting provided in the main paper. As noise increases, the average performance decreases compared to the case without any noise. The average Chamfer distance increases by 1.42 CD, and F1-score decreases by 1.90 compared to the case without noise. It should be noted that the effect of noise on performance is not significant. Figure 10 shows the qualitative results when adding noise to the pose. Although the pose is perturbed, the generated complete point clouds remain similar to the case without any noise. From these results, we can conclude that errors in pose have a limited effect on performance." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.72, + 0.919, + 0.849 + ], + "angle": 0, + "content": "Completing the Real Incomplete Point Clouds To assess the scalability of our method, we conduct an experiment using the real dataset. We train and test our framework on the point cloud data in KITTI [10] and nuScenes [1], using the provided bounding boxes to calculate the relative pose. Since the real dataset does not include incomplete point clouds observed from upward or downward directions, we enforce a constraint to ensure that the sampled poses fall within a range of the poses of the incomplete point" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.878, + 0.506, + 0.889 + ], + "angle": 0, + "content": "14210" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.082, + 0.483, + 0.122 + ], + "angle": 0, + "content": "Table 4. Quantitative comparison on KITTI dataset [10]. Minimum Matching Distance (MMD, ↓) and Unidirectional Chamfer Distance (UCD, ↓) are scaled with \\(\\times 10^3\\) and \\(\\times 10^4\\), respectively." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.125, + 0.449, + 0.172 + ], + "angle": 0, + "content": "
Cycle. [36]ShapeInv. [45]Ours
MMD32.21.62.4
UCD12.763.611.47
" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.187, + 0.477, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.241, + 0.482, + 0.268 + ], + "angle": 0, + "content": "Figure 11. Completion results of Real dataset. (A: Real incomplete point cloud, B: Our result)" + }, + { + "type": "text", + "bbox": [ + 0.083, + 0.275, + 0.485, + 0.546 + ], + "angle": 0, + "content": "clouds. Table 4 compares the quantitative performance of Cycle.[36] and ShapeInv.[45] using Minimum Matching Distance (MMD) and Unidirectional Chamfer Distance (UCD). To calculate MMD, we use complete point clouds in ShapeNet [5]. MMD evaluates the quality of the result in terms of how realistically the point cloud is generated, and ShapeInv. shows the best performance in this regard. However, our approach also shows comparable performance. Additionally, our approach outperforms the others on the UCD metric, which evaluates how well the generated point cloud reflects the input shape. We show the qualitative results in Fig. 11. In each section, the left side displays input incomplete point clouds, while the right side showcases predicted complete point clouds. Our network successfully generates the complete shape of cars and vans, even when the input point clouds are severely sparse. We can also observe that the obtained complete point clouds well-reflect the detailed shapes. These results demonstrate the potential practicality of our method for real-world applications." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.557, + 0.202, + 0.571 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.578, + 0.483, + 0.848 + ], + "angle": 0, + "content": "In this paper, we propose a novel method for point cloud completion that does not require any complete point clouds. The proposed method generates multiple incomplete point clouds corresponding to various poses and integrates them to obtain the complete point cloud. Our method employs an encoder-decoder framework where the encoder extracts a volumetric shape feature from the input incomplete point cloud, and the decoder generates pose-aware incomplete point clouds. To train the model, we introduce a novel dataset with incomplete point clouds and corresponding poses. The proposed method achieves comparable results with the existing state-of-the-art methods and outperforms some categories. Additionally, we demonstrate that the method can be applied to real incomplete point clouds. In future work, we plan to use a neural implicit representation for the shape feature instead of the volumetric feature, which can achieve better 3D representation capability. In addition, we will further enhance the projection method using a visibility check with learnable opacity." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.086, + 0.918, + 0.214 + ], + "angle": 0, + "content": "Acknowledgments This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636) and Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by Korea government(MSIT) (No.2020-0-00440, Development of Artificial Intelligence Technology that Continuously Improves Itself as the Situation Changes in the Real World)." + }, + { + "type": "title", + "bbox": [ + 0.515, + 0.227, + 0.614, + 0.241 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.522, + 0.25, + 0.918, + 0.329 + ], + "angle": 0, + "content": "[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giacarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. 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Cylinder3d: An effective 3d framework for driving-scene lidar semantic segmentation. arXiv preprint arXiv:2008.01550, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.087, + 0.916, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.467, + 0.879, + 0.505, + 0.889 + ], + "angle": 0, + "content": "14213" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/c5a386b7-062e-40bf-ab26-f63c862742fe_origin.pdf b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/c5a386b7-062e-40bf-ab26-f63c862742fe_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f092c9dd0baf59ae3de4dd6d18d1bc44463262f3 --- /dev/null +++ b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/c5a386b7-062e-40bf-ab26-f63c862742fe_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:87343de937b755ae570707e2bf75cb6b7fc37e3721aefe684605a4d8641aebed +size 4462981 diff --git a/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/full.md b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3cdff25fe566f642eae9122a41c4f909e538e353 --- /dev/null +++ b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/full.md @@ -0,0 +1,303 @@ +# Learning Point Cloud Completion without Complete Point Clouds: A Pose-Aware Approach + +Jihun Kim, Hyeokjun Kwon, Yunseo Yang, and Kuk-Jin Yoon +Korea Advanced Institute of Science and Technology + +{jihun1998,0327june,acorn,kjyoon}@kaist.ac.kr + +# Abstract + +Point cloud completion is to restore complete 3D scenes and objects from incomplete observations or limited sensor data. Existing fully-supervised methods rely on paired datasets of incomplete and complete point clouds, which are labor-intensive to obtain. Unpaired methods have been proposed, but still require a set of complete point clouds as a reference. As a remedy, in this paper, we propose a novel point cloud completion framework without using any complete point cloud at all. Our main idea is to generate multiple incomplete point clouds of various poses and integrate them into a complete point cloud. We train our framework based on cycle consistency, to generate an incomplete point cloud such that 1) shares the same object as the input incomplete point cloud and 2) corresponds to an arbitrarily given pose. In addition, we devise a novel projection method conditioned by pose to gather visible features, from a volumetric feature extracted by an encoder. Extensive experiments demonstrate that the proposed method achieves comparable or better results than existing unpaired methods. Further, we show that our method also can be applied to real incomplete point clouds. + +# 1. Introduction + +A point cloud is a commonly used representation of 3D scenes and objects in the fields of computer vision and robotics [14, 20, 21, 22, 28, 9, 24, 2, 3, 7, 15]. However, obtaining complete point clouds is often difficult due to the lack of observation or the limitations of sensors. As a remedy, the point cloud completion task has been spotlighted to restore complete point clouds from incomplete ones. + +The existing fully-supervised point cloud completion methods [16, 17, 19, 38, 39, 40, 42, 43, 44] have shown promising results; however, they typically rely on datasets that include incomplete point clouds paired with complete point clouds serving as ground truth (GT). Since obtaining GT complete point clouds is labor-intensive, several works [6, 36, 45, 4] have employed two sets of point clouds: + +![](images/c72d5cdf184a7937483bebd3d031e70dcfb0bbf702842a3efc1cd2470082ce33.jpg) + +![](images/15c7593d40784ffff5672f5fe97e813588fcf49b01577d3c914758534d14d2eb.jpg) + +![](images/31d91d768bba3b8549ffa8fd9bb819a4a3fa49368ab5040e7d476672127352b7.jpg) +(c) Generate incomplete PCs of various poses $\rightarrow$ Integrate them as complete PC +Figure 1. Illustration of our main idea. We re-interpret the point cloud completion task as generating multiple incomplete point clouds that correspond to various poses and integrating them. + +one with incomplete point clouds and the other with complete point clouds, which are not directly paired with each other. This unpaired setting could learn the mapping between the incomplete and complete point clouds, while reducing the reliance on paired GT complete point clouds. Nevertheless, the requirement of a set of complete point clouds still remains a major limitation to the practical application of point cloud completion. + +In this paper, we propose a novel point cloud completion framework that does not use any complete point clouds. Our main novelty lies in how to learn a mapping from an incomplete point cloud to a complete point cloud when the latter is not available at all. For this, we present a simple yet effective idea shown in Fig. 1. An incomplete point cloud usually results from self-occlusion occurs when observing an object from a certain viewpoint, as in (a). Therefore, if we obtain multiple incomplete point clouds of the object from various viewpoints, a union of them would be equivalent to the complete point cloud of that object. Based on this idea, we formulate the point cloud completion as generating multiple incomplete point clouds using a single input incomplete point cloud and sampled poses. Here, the generated incomplete point clouds should 1) share the same object as the input incomplete point cloud and 2) correspond + +to the arbitrarily given input poses. If the poses are various enough to cover the entire object, we could obtain the complete point cloud by integrating the incomplete point clouds. + +To achieve the above, our framework starts with an encoder that extracts a volumetric shape feature from the input incomplete point cloud. This feature is designed to contain complete information about the shape of the target object. To generate an incomplete point cloud from the volumetric feature, we propose a novel projection method conditioned by the pose, similar to obtaining an incomplete point cloud as a capture of the target object from a certain viewpoint. The method determines the region visible at the given pose and obtains a projected feature by gathering the volumetric feature of that region. A decoder is then trained to generate an incomplete point cloud from the projected feature. + +We do not have access to either the complete point cloud or the incomplete point cloud of another pose. Therefore, for training, we propose a novel dataset that provides both incomplete point clouds and corresponding poses, based on the ShapeNet dataset [5]. Note that our dataset includes only one incomplete point cloud per each object, unlike the setting of [13]. Using our dataset, we make our framework reconstruct the input incomplete point cloud itself by gathering the projected feature using the pose corresponding to the input. On the other hand, when using randomly sampled poses, we impose cycle consistency by feeding the generated incomplete point cloud to the encoder/decoder again. + +During the inference phase, we extract the volumetric shape feature from the input and obtain the projected features using various poses that cover the entire object. By decoding the features and integrating the generated incomplete point clouds, we can obtain a complete point cloud as the final output. To verify the proposed method, we conduct extensive experiments and comparisons with the existing unpaired point cloud completion methods, on the proposed dataset. The results support that, the proposed method is comparable to the existing studies and sometimes achieves even more substantial completion results, without using any complete point cloud. Further, we conduct an experiment on the KITTI dataset [10] to show that the proposed method can be also applied to the real incomplete point clouds. Our main contributions are as follows: + +- We formulate a point cloud completion task as generating and integrating multiple incomplete point clouds corresponding to various poses. +- We propose a novel framework that generates an incomplete point cloud using the input incomplete point cloud and the given arbitrary pose. +- We introduce a new dataset consisting of incomplete point clouds and poses. +- We experimentally verify that the proposed method is comparable or even superior to existing studies, without using complete point cloud at all. + +# 2. Related Works + +# 2.1. Point Cloud Completion + +Point cloud completion aims to restore a complete point cloud from an input incomplete point cloud. Although fully-supervised completion methods [8, 17, 19, 23, 32, 34, 37, 40, 43, 46, 35, 31] achieve substantial completion result, they rely on the dataset including paired incomplete point cloud and GT complete point cloud, which is difficult to acquire, especially for real scenes. To overcome the limitation, unpaired approaches [6, 36, 45, 11] have been proposed to learn the mapping between the sets of complete and incomplete point clouds. Pcl2pcl [6] is the first unpaired point cloud completion method, which allows translation between partial and complete latent spaces by adversarial training. Subsequently, Cycle4completion [36] has achieved more advanced results by considering bidirectional geometric correspondence by cycle transformation and missing region coding. ShapeInversion [45] obtained optimal shape code for reconstructing 3D shapes based on the concept of GAN inversion. OptDE [11] proposed cross-domain completion by disentangling shape, domain, and occlusion factors, using domain-invariant geometric information and viewpoint prediction. Although the unpaired methods have shown promising results, their practical application is still limited by the requirement for a number of complete point clouds. [13] has proposed to utilize multiple incomplete point clouds of the same object, obtained from observations at different poses; however, such multiple observations are often not available. Unlike the existing methods, our method does not access the complete point cloud at all, and also uses only one incomplete point cloud per each object, throughout the entire training process. + +# 2.2. Pose-Aware 3D Processing + +One of the most representative 3D tasks dealing with the pose is point cloud canonicalization [29, 30, 26]. Condor [29] takes an un-canonicalized collection of full or partial point clouds obtained through the internet or depth sensor as input. Meanwhile, [33] proposed self-supervised learning via disentangling content and pose information for the point cloud feature representation. As such, numerous studies have been conducted to exploit these two factors, since 3D data usually contains pose attributes as well as the shape of the object. Nevertheless, in the field of point cloud completion, using pose has not been deeply studied despite its usefulness. Since an incomplete point cloud is usually obtained by scanning the object from a single viewpoint through a scanner, information about the viewpoint (i.e., pose) can be beneficial for recovering the self-occluded regions. In this light, we utilize the pose information to complete the point cloud by generating multiple incomplete point clouds. + +![](images/b2b7c76a4e8d81c35b6f97735065e4aee56bd8ed11c8c3ebfaa93b4f8db64f0a.jpg) +Figure 2. Illustration of a framework for generating a pose-aware point cloud. First, the encoder extracts the volumetric shape feature $V$ from the input point cloud $P_{i}$ . Then, projected features $F_{i}$ and $F_{r}$ are generated by determining the visible region with input pose $o_{i}$ and random pose $o_{r}$ . Incomplete point cloud $\hat{P}_{i,rec}$ is decoded to constrain with $\mathcal{L}_{rec}$ . Incomplete point cloud $\hat{P}_{r}$ is decoded and entered into the model again with input pose $o_{i}$ . After that, volumetric feature $\hat{V}$ , projected feature $\hat{F}_{i}$ , and $\hat{P}_{i,cycle}$ are generated sequentially. We use $\mathcal{L}_{shape}$ and $\mathcal{L}_{cycle}$ to constrain our network. + +# 2.3. Volumetric Feature Representation + +Volumetric features are commonly used in tasks such as multi-view stereo [25, 27], 3D semantic segmentation [12, 47], and point cloud completion [8, 41, 40] due to their capability to preserve the spatial information of the input. However, standard voxelization can result in geometric information loss and quantization effects. To address this issue, GRNet [40] proposed a differentiable completion network that aggregates features between 3D grid vertices using interpolation. Similarly, our approach also utilizes the volumetric representation and pose to perform completion. + +# 3. Proposed Methods + +# 3.1. Overview + +In this paper, we refer to an incomplete point cloud as $P_{i} \in \mathbb{R}^{N \times 3}$ , where $N$ is the number of points in the point cloud, and the subscript $i$ represents the pose at which $P_{i}$ is captured. For convenience, we define the pose as a two-dimensional vector $o = (\phi, \theta)$ , as the incomplete point cloud is usually not significantly affected by the distance between the scanner and the target object. + +The goal of our work is to achieve point cloud completion without relying on using complete point clouds. To accomplish this, we generate multiple incomplete point clouds from a single input point cloud, where each generated incomplete point cloud shares the same object as the input but corresponds to a different pose. + +As shown in Fig. 2, we begin by using an encoder $E$ to obtain the volumetric shape feature $V$ from the input incomplete point cloud $P_{i}$ . We assume that the encoder can extract complete shape information of the object from the input incomplete point cloud. In other words, the volumetric shape feature serves as a complete target object at the feature level. To mimic the process of obtaining an incomplete point cloud as a capture of the target object at a certain pose, we gather the features corresponding to the arbitrarily given pose $o_{r}$ (or $o_{i}$ for the upper branch) from the volumetric shape feature. Then, with a decoder $D$ , we decode the gathered feature $F$ to generate the incomplete point cloud. + +To ensure that the incomplete point cloud generated by our framework correctly corresponds to the given pose, we impose reconstruction loss and cycle consistency loss, which will be explained in Section 3.2. Further, we introduce a novel method to determine the visible region and gather the features on it into the projected feature. We describe the details of the projection method in Section 3.3. Finally, in Section 3.4, we demonstrate how we obtain the complete point cloud using our framework, in the inference phase. It is worth noting that throughout the entire process, we do not use any complete point cloud. + +# 3.2. Pose-Aware Point Cloud Generation + +Since we have neither a complete point cloud nor an incomplete point cloud captured from another view, the input incomplete point cloud is the only available data in the point cloud domain that can be used as supervision. Therefore, + +![](images/ecf98247a6cd5c7ac46bdfad08412593da935c04d2efc4fe493de8c08b0ff524.jpg) +(a) + +![](images/9d63049140899cc64a672443c5699cf105e3c55549d10ac49ac61348ca60c3c5.jpg) +Case I +↓ + +![](images/285c84f022c51673e3c5e455c406876c733a838666fd8fd26e601ef71d5e6328.jpg) +Case II +↓ + +![](images/c59cd38030898a7c2fc93c2260720ef098a2f6ec59de2c6a86ac34034e4e8a0a.jpg) + +![](images/ff4eb31ff4227f5f7b1bc991fbd9d938dd6c157d5bfd1b4a8c7472a44badcbd1.jpg) +Case III +↓ + +![](images/42a1d7cad7f63daf9c21ac24c0c26ae943a3ff28720640c9216087738c587f75.jpg) + +![](images/2a73dba570edd6a4afe2416c0869c60a39c8113f0ab5b2c2acdf5d917e1192c2.jpg) +(b) + +![](images/b96df3b203bd8a6b8f8ac0d8426288d40a2c92006b9bb65262d0c06066636333.jpg) +Figure 3. Illustration of our projection method. (a) We first determine the base region (covered by yellow) according to the given pose. Note that any pose can be categorized as one of cases I, II, and III, after a proper rotation. Then, the features on the base region are gathered into a 2D feature grid. (b) The visible region (covered by blue) defined on the grid is obtained by interpolating the neighboring base features. + +we devise two branches that can be effectively trained using the input incomplete point cloud. The first branch uses the input pose $o_i$ to generate the projected feature $F_{i}$ and decode $\hat{P}_{i,rec}$ , which should be identical to the input point cloud $P_{i}$ . To ensure this, we minimize the following reconstruction loss $\mathcal{L}_{rec}$ : + +$$ +\mathcal {L} _ {r e c} = \mathcal {L} _ {C D} \left(P _ {i}, \hat {P} _ {i, r e c}\right). \tag {1} +$$ + +Here, $\mathcal{L}_{CD}$ denotes the Chamfer Distance (CD), commonly used in the point cloud field. Note that, for two given point clouds $P_{1}$ and $P_{2}$ , the CD is formulated as + +$$ +\mathcal {L} _ {C D} \left(P _ {1}, P _ {2}\right) = \sum_ {p _ {i} \in P _ {1}} \min _ {p _ {j} \in P _ {2}} \left\| p _ {i} - p _ {j} \right\| + \sum_ {p _ {j} \in P _ {2}} \min _ {p _ {i} \in P _ {1}} \left\| p _ {j} - p _ {i} \right\|. \tag {2} +$$ + +Further, we randomly sample an arbitrary pose $o_r$ , which is different from the input pose $o_i$ , and generate projected feature $F_r$ . If we decode $F_r$ , the resulting incomplete point cloud $\hat{P}_r$ should share the same shape with $P_i$ but correspond to the sampled pose $o_r$ . However, as mentioned, we cannot access the GT $P_r$ . Therefore, we impose cycle consistency on our framework. In specific, we put $\hat{P}_r$ into the encoder again and get $\hat{V}$ , which is the shape feature of the $\hat{P}_r$ . Since the original input $P_i$ and $\hat{P}_r$ should have the same shape, we minimize a shape loss $\mathcal{L}_{shape}$ defined as follows: + +$$ +\mathcal {L} _ {s h a p e} = \left| \left| V - \hat {V} \right| \right| _ {1}. \tag {3} +$$ + +Besides, using the $\hat{V}$ and the input pose $o_i$ , we gather the projected feature $\hat{F}_i$ and decode it into $\hat{P}_{i,cycle}$ , which should be identical to the input point cloud. Therefore, we define cycle loss $\mathcal{L}_{cycle}$ as follow: + +$$ +\mathcal {L} _ {\text {c y c l e}} = \mathcal {L} _ {C D} \left(P _ {i}, \hat {P} _ {i, \text {c y c l e}}\right). \tag {4} +$$ + +These loss terms, $\mathcal{L}_{shape}$ and $\mathcal{L}_{cycle}$ , enable the encoder to extract the shape feature containing complete shape information and also help the decoder to generate incomplete point cloud that reflects the pose. + +To sum up, we train our framework by using a combination of $\mathcal{L}_{rec}$ , $\mathcal{L}_{cycle}$ , and $\mathcal{L}_{shape}$ . The total loss function is defined as follow: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {r e c}} + \mathcal {L} _ {\text {c y c l e}} + \lambda \mathcal {L} _ {\text {s h a p e}} \tag {5} +$$ + +where $\lambda$ is the weight for $\mathcal{L}_{shape}$ . + +# 3.3. The Proposed Projection Method + +In order to effectively incorporate pose information into our learning framework, we devise the encoder to extract the shape information as a form of volumetric feature, denoted as $V = \{v_{i}\}_{i = 1}^{N^{3}}$ . Here, $v_{i} \in \mathbb{R}^{d}$ , where $N$ is the resolution of the volumetric feature and $d$ is the feature dimension. Similar to the target object being captured as an incomplete point cloud from a certain viewpoint, we devise a gathering process that selects the features that are visible from an arbitrarily given pose. + +However, the volumetric feature is a spatially discrete 3D grid, and thereby a naive visibility test returns the same results for the wide range of poses. To mitigate this, we establish a projection rule that can be applied for arbitrary poses, as shown in Fig. 3 (a). In specific, we subdivide the entire set of poses into the pose subsets, per 30 degrees. Then, we predefine the base region (covered by yellow) for each pose subset. Note that, without loss of generality, any arbitrary pose segment can be categorized into one of the three cases (I, II, and III), after a proper rotation. + +![](images/d79aacb37af49ce9b9a37e7a664d3b72e2a6c88f3013b57d1eb376f7ba086054.jpg) +Figure 4. Illustration of obtaining the complete point cloud with the proposed framework in the inference phase. We gather the projected features $F_{1:8}$ from the shape feature $V$ , according to the various poses $o_{1:8}$ . Then, each projected feature is decoded into the incomplete point cloud $\hat{P}_{1:8}$ . A union of the generated incomplete point clouds serves as the resulting complete point cloud $\hat{C}$ . + +Once the base region is determined, we unfold the volumetric features located in that region into the 2D grid. During the unfolding, we compute the feature of the empty nodes by interpolating the neighboring volumetric features. In detail, we simply average the neighboring features and use the result as the feature of the node. Then, we define the visible region (covered by blue) on the 2D base grid, as shown in Fig. 3 (b). Here, as $\theta$ and $\phi$ increase, the visible region would move up and right, respectively. Finally, to obtain the feature map that represents the visible region, we perform bilinear interpolation using the neighboring base features. The weights for interpolation are determined according to the values of $\theta$ and $\phi$ . Further details of the projection method are provided in Supp. Material. + +# 3.4. Obtaining Complete Point Cloud + +As aforementioned, in the inference phase, we generate multiple incomplete point clouds of various poses and integrate them into a complete one. In detail, we first extract the volumetric shape feature $V$ from the input incomplete point cloud, as shown in Fig. 4. From the shape feature, we obtain the projected features $F_{1:8}$ by using a set of poses $o_{1:8}$ . Here, we use a predefined set of eight poses, $\left\{\left(\frac{\pi}{4}, \frac{\pi}{4}\right), \left(\frac{\pi}{4}, \frac{3\pi}{4}\right), \left(\frac{\pi}{4}, \frac{5\pi}{4}\right), \left(\frac{\pi}{4}, \frac{7\pi}{4}\right), \left(\frac{3\pi}{4}, \frac{\pi}{4}\right), \left(\frac{3\pi}{4}, \frac{3\pi}{4}\right), \left(\frac{3\pi}{4}, \frac{5\pi}{4}\right), \left(\frac{3\pi}{4}, \frac{7\pi}{4}\right)\right\}$ , which can cover the entire object. Then, we decode the projected features into the incomplete point cloud $\hat{P}_{1:8}$ . Finally, a union of the generated incomplete point clouds serves as the resulting complete point cloud $\hat{C}$ . Note that we use the incomplete point cloud as the only input for the inference, and the pose of the input is not required. + +We observe that the resulting integrated point cloud $\hat{C}$ has substantial quality. However, our generate-and-integrate approach involves repeated decoding to generate + +![](images/06eeb301d91749fa49f1afa7be1cb3eb11458fe0ed902b93728c13aeacc7e3ab.jpg) +Figure 5. Illustration of the proposed re-training strategy. We use the frozen framework to obtain pseudo-GT $\hat{C}$ . Then, a new point cloud completion network $G$ is trained to learn a mapping between the input $P_{i}$ and the pseudo-GT. + +multiple incomplete point clouds, which can be computationally inefficient. In Section 4.3, we conduct an experiment to verify the completion performance while changing the number of used poses. It shows that there is a trade-off between the performance and the number of poses. To alleviate this issue, we propose a strategy named Re-Training (RT). As visualized in Fig. 5, this strategy uses the integrated complete point cloud as supervision for training another completion network. + +First, our framework is trained as in Section 3 and frozen. Then, we obtain an integrated complete point cloud for each incomplete point cloud in the training dataset. Since the obtained complete point cloud is a reasonable completion result, it can serve as a pseudo-GT for the corresponding incomplete point cloud (which was originally used as input). In other words, starting from the initial dataset including incomplete point clouds without any complete point cloud at all, we now have a paired dataset including the incomplete point cloud and the pseudo-GT pairs. Using the incomplete point cloud and pseudo-GT pairs, we train another point cloud completion network $G$ , like the conventional fully-supervised point cloud completion methods. For this, we use the Chamfer Distance loss between the input $P_{i}$ and pseudo-GT $\hat{C}$ , which is denoted as $\mathcal{L}_{RT}$ . Note that, we still do not access the real GT complete point clouds at all, throughout the whole process of the re-training. + +Compared to directly using the output of our framework as a final output, the re-training can be advantageous in several aspects. First, as we mentioned, re-training is much more efficient and practical in the inference phase, since it requires only one inference per input and can perform multiclass point cloud completion. Further, in terms of the completion performance, the re-training enables learning more complex and beneficial concepts. For example, during retraining, we can expect the network to learn the geometric relation between the incomplete and (pseudo-)complete point clouds. It is especially helpful when the input is severely self-occluded (e.g., when only the upper side of the table can be observed), which cannot be dealt with directly using the pseudo-complete point cloud. In addition, we observe that the re-training can reject some outlier points in the pseudo-GT. + +Table 1. Completion results on our dataset. The numbers shown are [CD ↓/F1 ↑], where CD is Chamfer Distance scaled with $\times 10^4$ . Best results are indicated as **bold**. + +
MethodsUsing Complete PC.AirplaneCabinetCarChairSofaTableVesselAverage
Cycle. [36]Yes14.71/81.5316.64/74.9435.02/49.3322.23/70.5320.38/47.0721.45/77.1816.09/76.4920.93/68.15
ShapeInv. [45]Yes4.16/96.0514.20/79.9110.69/87.0916.67/81.3916.01/80.8223.86/82.9310.55/ 87.7213.74/85.13
OursNo4.84/95.1315.11/77.529.63/88.0118.25/75.3417.50/74.6219.02/80.9312.45/84.4313.73/82.46
Ours (+RT)No4.87/94.8515.14/81.209.06/88.8416.22/77.9215.41/77.6718.04/80.7310.95/86.3612.81/83.94
+ +![](images/dbf5504909040f896005d74d15706aa0ba3dfe114febfe56fd691d2546080fc3.jpg) +Figure 6. Qualitative results of the point cloud completion methods on our dataset. From left to right: incomplete input, completion results of Cycle4completion [36], ShapeInversion [45], ours, ours (+RT), and GT. + +# 4. Experimental Results + +# 4.1. Dataset Generation + +The datasets [8, 34] widely used for the existing point cloud completion studies consist of input point clouds and complete point clouds, which are suitable for the fully-supervised or unpaired settings. On the other hand, to train and evaluate our study, a dataset consisting of complete/incomplete point clouds and corresponding poses is required. Therefore, we build and publish a new dataset for this setting. We use the complete point clouds in the ShapeNet Benchmark [5]. First, we randomly sample the pose as a viewpoint located on the sphere. Then, with the sampled pose, we use [18] to remove unobserved points from the complete point cloud. The resulting point cloud can serve as an incomplete point cloud, where the sampled pose is the corresponding pose. Note that, in our dataset, there is only one incomplete point cloud per the complete point cloud. It means that any complete point cloud cannot be observed from more than one view. More details about the proposed dataset can be found in the Supp. Material. + +# 4.2. Comparisons with Other Methods + +In order to evaluate the effectiveness of the proposed method, we conduct a comparison with existing methods (Cycle. [36] and ShapeInv. [45]), which access a set of complete point clouds during training. To ensure a fair comparison, we trained and evaluated all methods on the proposed dataset, using official codes provided by the authors. We evaluate and compare our method with and without using Re-Training (RT) strategy. + +Quantitative Results We use Chamfer Distance and F1-score to evaluate the performance of point cloud completion. As shown in Table 1, we evaluate seven categories. Overall, the re-training process improves the performance in most categories, indicating its effectiveness in enhancing the results. Compared to ShapeInv., our proposed method has a lower average Chamfer Distance and a slightly lower F1-score of 1.19. Interestingly, our results outperform Cycle for all metrics. In other words, our results outperform or achieve comparable performance to existing studies despite not using a complete point cloud. + +![](images/631e45df9d7a520e310178a063000186152bc4834a7639e87e0ca3c53b50c946.jpg) +Figure 7. Visualization of pose-aware incomplete point clouds. The cuboids in the top part indicate the volumetric shape features viewed from an arbitrary pose, highlighted in red. The right side of the figure shows the input and ground truth complete point clouds. Two scenarios are considered for generating incomplete point clouds: one that uses only the $\mathcal{L}_{rec}$ loss term, and the other with the full loss term. We also generate ground truth incomplete point clouds to evaluate how well the incomplete point clouds are generated. + +Qualitative Results We qualitatively compare the point cloud completion results on our dataset. Figure 6 shows complete point cloud results from existing methods, Cycle., ShapeInv., ours, and ours with re-training technique. Compared to the results of the existing methods, the results support that our method successfully completes the parts that were originally invisible at the input point cloud. Also, we find that the conventional methods fail to restore certain details that are present in the input point cloud. For instance, as shown in the dashed boxes, some fine details such as the exhaust port of the airplane or the armrest parts of the chair are not completely generated, even though they are present in the input point cloud. However, our method can reconstruct them sharply, resulting in a more accurate and realistic airplane model. To sum up, both the quantitative and qualitative results support that the proposed method can achieve substantial completion results, considering that GT complete point cloud is not used at all. + +# 4.3. Ablation Studies + +Effectiveness of Each Loss Term We conduct the ablation studies to verify the effectiveness of each term in Eq. 5. As shown in Table 2, we use Chamfer Distance and F1-score as a metric in several categories. The case with only reconstruction loss is used as the baseline. As shown in first row and second row, Chamfer Distance decreases 1.01 CD and F1-score increases 1.30 in average after adding shape loss. We can see that there are performance improvements in every category. As shown in first row and third row, Chamfer Distance decreases 1.55 CD and F1-score increases 1.75 after adding cycle loss. Also, there are performance improvements in every categories. As shown in last row, it + +Table 2. Ablation studies on the proposed dataset. The numbers shown are $[\mathrm{CD} \downarrow / \mathrm{F1} \uparrow]$ , where CD is Chamfer Distance scaled with $\times 10^4$ . Best results are indicated as bold. + +
LrecLshapeLcycleAirplaneCabinetSofaAverage
✓5.63/94.1117.66/73.4119.97/72.4714.42/79.99
✓✓5.58/94.2915.86/76.3918.80/73.1913.41/81.29
✓✓5.08/94.9515.47/76.3818.08/73.8912.87/81.74
✓✓✓4.84/95.1314.90/88.0117.50/74.6212.42/82.69
+ +shows best performance in both Chamfer Distance and F1-score with all constraints. From these results, proposed constraints are all effective in point cloud completion. + +Effectiveness of Number of Poses We examine the effect of the number of input poses on the quality of the complete point cloud generated from our method without re-training. Intuitively, if we use more poses, the generated point clouds that are aware of the input poses and incomplete could cover a wider range of partial views, and thereby complete point cloud would be better. We conduct an experiment with 2, 4, 8, 10, and 14 poses for some categories, where the configurations of 2, 4, and 8 poses are shown in Fig. 8. For a configuration of 10 poses, upward and downward poses are added to the 8 poses. Likewise, additional 4 sideward poses are incorporated into the case of 10 poses for the configuration of 14 poses. Fig. 9 shows how the completion performance changes depending on the number of poses used. As we expected, Chamfer Distance decreases meaningfully as more poses are used until 8 poses. However, the performance becomes saturated as we increase the number of poses to 10 and 14. Therefore, we use 8 poses for our default setting. + +# 4.4. Additional Experiments + +Results of Pose-Aware Incomplete Point Cloud Since our main idea is generating and integrating the multiple incom + +![](images/6107daf66e11f2b5798f456c644e09c57c2d69184d9917a21d3e97848f651fc3.jpg) +Figure 8. Illustration of pose configurations, which are used to verify the effectiveness of the number of poses. The black dots represent the location of the poses. + +![](images/97eadff4b42fdd692b1f8d5b357b5fe2ecf815d4c4b121b62e310398656e2282.jpg) + +![](images/c78dcf3c2a6a1c4c3b84e5b6e38f97e5af88470e2110643248a9268451a9ffc5.jpg) + +![](images/51b1d693c682817ef0c56d41804ff78ee29be1e194561bccdc3b5021942332dc.jpg) +Figure 9. Impact of the number of poses on performance. CD is Chamfer Distance scaled with $\times 10^4$ . + +plete point clouds corresponding to the given poses, we qualitatively verify whether our network can generate high-quality incomplete point clouds that correspond to the desired poses. Figure 7 shows incomplete point clouds generated from our method. The top row of the figure indicates the various poses we used, and the right side shows the input incomplete input point cloud and the GT complete point cloud. According to them, we generate incomplete point clouds using the models, which are (1) trained with reconstruction loss only and (2) trained with all loss terms. We also provide the GT incomplete point clouds obtained by applying hidden point removal [18] on the GT complete point cloud. When using only $\mathcal{L}_{rec}$ , we can observe that the generated incomplete point clouds do not reflect the given poses correctly, and also fail to preserve fine details overall. On the other hand, we can see that incomplete point clouds obtained by the proposed method are well-corresponded to their respective poses appearing as if they had been captured from those viewpoints. Notably, the fine details (e.g., exhaust ports on the wings) are well-completed for all incomplete point clouds, indicating that the network could effectively capture detailed shapes from the input point cloud across various poses. The results support that our framework correctly learns to generate incomplete point clouds according to the given poses, and achieve substantial completion results in the ultimate. + +Using Noisy Poses In the real scenario, there can be a noise in the poses corresponding to the obtained incomplete point cloud. Therefore, we conduct an experiment to verify the sensitivity of the proposed method against the noise in the poses that we used for training. We observe that our method is robust to the noise in poses to some extent. We conduct an experiment by introducing Gaussian noise to the given poses. Specifically, we add a noise sampled from normal distribution to the given pose $o_i = (\phi, \theta)$ . The resulting noisy pose, denoted as $\phi_{noise}$ and $\theta_{noise}$ , is defined as follows: + +Table 3. Effect of noise in pose. The numbers shown are [CD ↓ / F1 ↑], where CD is Chamfer Distance scaled with $\times 10^4$ . Best results are indicated as bold. + +
σAirplaneCabinetSofaAverage
0.14.94/95.2216.79/75.0519.79/72.0813.84/80.79
0.034.89/95.2315.44/77.4218.07/73.3812.80/82.01
04.84/95.1314.90/78.3117.50/74.6212.42/82.69
AirplaneInput0.10.030
Cabinet
Sofa
+ +Figure 10. Qualitative results with noisy poses. 0.1, 0.03, and 0 are value of $\sigma$ in Eq. 6, 7. + +lows: + +$$ +\phi_ {\text {n o i s e}} = \phi + \sigma N (0, 1) \times 1 8 0 ^ {\circ} \tag {6} +$$ + +$$ +\theta_ {\text {n o i s e}} = \theta + \sigma N (0, 1) \times 1 8 0 ^ {\circ}. \tag {7} +$$ + +Here, $N(0,1)$ is a normal distribution with mean 0 and variance 1. We train and evaluate the model by varying the value of $\sigma$ . We set the $\sigma$ as 0.03 and 0.1. For these values, the errors in the pose are mostly within $11^{\circ}$ and $36^{\circ}$ , respectively. Table 3 demonstrates the impact of the noise on pose information. A value of $\sigma = 0$ means that there is no noise in the pose, which is the default setting provided in the main paper. As noise increases, the average performance decreases compared to the case without any noise. The average Chamfer distance increases by 1.42 CD, and F1-score decreases by 1.90 compared to the case without noise. It should be noted that the effect of noise on performance is not significant. Figure 10 shows the qualitative results when adding noise to the pose. Although the pose is perturbed, the generated complete point clouds remain similar to the case without any noise. From these results, we can conclude that errors in pose have a limited effect on performance. + +Completing the Real Incomplete Point Clouds To assess the scalability of our method, we conduct an experiment using the real dataset. We train and test our framework on the point cloud data in KITTI [10] and nuScenes [1], using the provided bounding boxes to calculate the relative pose. Since the real dataset does not include incomplete point clouds observed from upward or downward directions, we enforce a constraint to ensure that the sampled poses fall within a range of the poses of the incomplete point + +Table 4. Quantitative comparison on KITTI dataset [10]. Minimum Matching Distance (MMD, ↓) and Unidirectional Chamfer Distance (UCD, ↓) are scaled with $\times 10^3$ and $\times 10^4$ , respectively. + +
Cycle. [36]ShapeInv. [45]Ours
MMD32.21.62.4
UCD12.763.611.47
+ +![](images/33ae8f4d446148cdbb8c7a89d90fd60e784b575c3f90babda76e382032dcaf84.jpg) +Figure 11. Completion results of Real dataset. (A: Real incomplete point cloud, B: Our result) + +clouds. Table 4 compares the quantitative performance of Cycle.[36] and ShapeInv.[45] using Minimum Matching Distance (MMD) and Unidirectional Chamfer Distance (UCD). To calculate MMD, we use complete point clouds in ShapeNet [5]. MMD evaluates the quality of the result in terms of how realistically the point cloud is generated, and ShapeInv. shows the best performance in this regard. However, our approach also shows comparable performance. Additionally, our approach outperforms the others on the UCD metric, which evaluates how well the generated point cloud reflects the input shape. We show the qualitative results in Fig. 11. In each section, the left side displays input incomplete point clouds, while the right side showcases predicted complete point clouds. Our network successfully generates the complete shape of cars and vans, even when the input point clouds are severely sparse. We can also observe that the obtained complete point clouds well-reflect the detailed shapes. These results demonstrate the potential practicality of our method for real-world applications. + +# 5. Conclusion + +In this paper, we propose a novel method for point cloud completion that does not require any complete point clouds. The proposed method generates multiple incomplete point clouds corresponding to various poses and integrates them to obtain the complete point cloud. Our method employs an encoder-decoder framework where the encoder extracts a volumetric shape feature from the input incomplete point cloud, and the decoder generates pose-aware incomplete point clouds. To train the model, we introduce a novel dataset with incomplete point clouds and corresponding poses. The proposed method achieves comparable results with the existing state-of-the-art methods and outperforms some categories. Additionally, we demonstrate that the method can be applied to real incomplete point clouds. In future work, we plan to use a neural implicit representation for the shape feature instead of the volumetric feature, which can achieve better 3D representation capability. In addition, we will further enhance the projection method using a visibility check with learnable opacity. + +Acknowledgments This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636) and Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by Korea government(MSIT) (No.2020-0-00440, Development of Artificial Intelligence Technology that Continuously Improves Itself as the Situation Changes in the Real World). + +# References + +[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giacarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11621-11631, 2020. 8 +[2] Yingjie Cai, Xuesong Chen, Chao Zhang, Kwan-Yee Lin, Xiaogang Wang, and Hongsheng Li. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7443-7452, 2021. 1 +[39] Peng Xiang, Xin Wen, Yu-Shen Liu, Yan-Pei Cao, Pengfei Wan, Wen Zheng, and Zhizhong Han. Snowflakenet: Point cloud completion by snowflake point deconvolution with skip-transformer. In Proceedings of the IEEE/CVF international conference on computer vision, pages 5499-5509, 2021. 1 +[40] Haozhe Xie, Hongxun Yao, Shangchen Zhou, Jiageng Mao, Shengping Zhang, and Wenxiu Sun. Grnet: Gridding residual network for dense point cloud completion. In European Conference on Computer Vision, pages 365-381. Springer, 2020. 1, 2, 3 +[41] Bo Yang, Stefano Rosa, Andrew Markham, Niki Trigoni, and Hongkai Wen. Dense 3d object reconstruction from a single depth view. IEEE transactions on pattern analysis and machine intelligence, 41(12):2820-2834, 2018. 3 +[42] Kangxue Yin, Hui Huang, Daniel Cohen-Or, and Hao Zhang. P2p-net: Bidirectional point displacement net for shape transform. ACM Transactions on Graphics (TOG), 37(4):1-13, 2018. 1 +[43] Xumin Yu, Yongming Rao, Ziyi Wang, Zuyan Liu, Jiwen Lu, and Jie Zhou. Pointr: Diverse point cloud completion with geometry-aware transformers. In Proceedings of the IEEE/CVF international conference on computer vision, pages 12498-12507, 2021. 1, 2 +[44] Wentao Yuan, Tejas Khot, David Held, Christoph Mertz, and Martial Hebert. Pcn: Point completion network. In 2018 International Conference on 3D Vision (3DV), pages 728-737. IEEE, 2018. 1 + +[45] Junzhe Zhang, Xinyi Chen, Zhongang Cai, Liang Pan, Haiyu Zhao, Shuai Yi, Chai Kiat Yeo, Bo Dai, and Chen Change Loy. Unsupervised 3d shape completion through gan inversion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1768-1777, 2021. 1, 2, 6, 9 +[46] Wenxiao Zhang, Qingan Yan, and Chunxia Xiao. Detail preserved point cloud completion via separated feature aggregation. In European Conference on Computer Vision, pages 512-528. 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Cylinder3d: An effective 3d framework for driving-scene lidar semantic segmentation. arXiv preprint arXiv:2008.01550, 2020. 3 \ No newline at end of file diff --git a/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/images.zip b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..bf5a775b53bd5a5880f0e35fbb6c52f27b75b2e0 --- /dev/null +++ b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d81d5decaa00413aa1362df3b7ea1461fbcef110ee038932db71cd0dce7c9cc0 +size 728963 diff --git a/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/layout.json b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e57bd323735dcc7004e720753e273c2b4dd31a43 --- /dev/null +++ b/2023/Learning Point Cloud Completion without Complete Point Clouds_ A Pose-Aware Approach/layout.json @@ -0,0 +1,8952 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 91, + 102, + 502, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 102, + 502, + 139 + ], + "spans": [ + { + "bbox": [ + 91, + 102, + 502, + 139 + ], + "type": "text", + "content": "Learning Point Cloud Completion without Complete Point Clouds: A Pose-Aware Approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 146, + 161, + 446, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 161, + 446, + 190 + ], + "spans": [ + { + "bbox": [ + 146, + 161, + 446, + 190 + ], + "type": "text", + "content": "Jihun Kim, Hyeokjun Kwon, Yunseo Yang, and Kuk-Jin Yoon \nKorea Advanced Institute of Science and Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 175, + 191, + 418, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 191, + 418, + 203 + ], + "spans": [ + { + "bbox": [ + 175, + 191, + 418, + 203 + ], + "type": "text", + "content": "{jihun1998,0327june,acorn,kjyoon}@kaist.ac.kr" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 190, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 190, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 190, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 256, + 288, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 288, + 508 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 288, + 508 + ], + "type": "text", + "content": "Point cloud completion is to restore complete 3D scenes and objects from incomplete observations or limited sensor data. Existing fully-supervised methods rely on paired datasets of incomplete and complete point clouds, which are labor-intensive to obtain. Unpaired methods have been proposed, but still require a set of complete point clouds as a reference. As a remedy, in this paper, we propose a novel point cloud completion framework without using any complete point cloud at all. Our main idea is to generate multiple incomplete point clouds of various poses and integrate them into a complete point cloud. We train our framework based on cycle consistency, to generate an incomplete point cloud such that 1) shares the same object as the input incomplete point cloud and 2) corresponds to an arbitrarily given pose. In addition, we devise a novel projection method conditioned by pose to gather visible features, from a volumetric feature extracted by an encoder. Extensive experiments demonstrate that the proposed method achieves comparable or better results than existing unpaired methods. Further, we show that our method also can be applied to real incomplete point clouds." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 528, + 128, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 128, + 541 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 128, + 541 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 545, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 545, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 545, + 287, + 628 + ], + "type": "text", + "content": "A point cloud is a commonly used representation of 3D scenes and objects in the fields of computer vision and robotics [14, 20, 21, 22, 28, 9, 24, 2, 3, 7, 15]. However, obtaining complete point clouds is often difficult due to the lack of observation or the limitations of sensors. As a remedy, the point cloud completion task has been spotlighted to restore complete point clouds from incomplete ones." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 629, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 287, + 714 + ], + "type": "text", + "content": "The existing fully-supervised point cloud completion methods [16, 17, 19, 38, 39, 40, 42, 43, 44] have shown promising results; however, they typically rely on datasets that include incomplete point clouds paired with complete point clouds serving as ground truth (GT). Since obtaining GT complete point clouds is labor-intensive, several works [6, 36, 45, 4] have employed two sets of point clouds:" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 231, + 451, + 299 + ], + "blocks": [ + { + "bbox": [ + 309, + 231, + 451, + 299 + ], + "lines": [ + { + "bbox": [ + 309, + 231, + 451, + 299 + ], + "spans": [ + { + "bbox": [ + 309, + 231, + 451, + 299 + ], + "type": "image", + "image_path": "c72d5cdf184a7937483bebd3d031e70dcfb0bbf702842a3efc1cd2470082ce33.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 459, + 231, + 539, + 298 + ], + "blocks": [ + { + "bbox": [ + 459, + 231, + 539, + 298 + ], + "lines": [ + { + "bbox": [ + 459, + 231, + 539, + 298 + ], + "spans": [ + { + "bbox": [ + 459, + 231, + 539, + 298 + ], + "type": "image", + "image_path": "15c7593d40784ffff5672f5fe97e813588fcf49b01577d3c914758534d14d2eb.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 321, + 313, + 537, + 378 + ], + "blocks": [ + { + "bbox": [ + 310, + 302, + 527, + 312 + ], + "lines": [ + { + "bbox": [ + 310, + 302, + 527, + 312 + ], + "spans": [ + { + "bbox": [ + 310, + 302, + 527, + 312 + ], + "type": "text", + "content": "(c) Generate incomplete PCs of various poses " + }, + { + "bbox": [ + 310, + 302, + 527, + 312 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 310, + 302, + 527, + 312 + ], + "type": "text", + "content": " Integrate them as complete PC" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 321, + 313, + 537, + 378 + ], + "lines": [ + { + "bbox": [ + 321, + 313, + 537, + 378 + ], + "spans": [ + { + "bbox": [ + 321, + 313, + 537, + 378 + ], + "type": "image", + "image_path": "31d91d768bba3b8549ffa8fd9bb819a4a3fa49368ab5040e7d476672127352b7.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 380, + 546, + 413 + ], + "lines": [ + { + "bbox": [ + 305, + 380, + 546, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 546, + 413 + ], + "type": "text", + "content": "Figure 1. Illustration of our main idea. We re-interpret the point cloud completion task as generating multiple incomplete point clouds that correspond to various poses and integrating them." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 425, + 546, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 546, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 546, + 522 + ], + "type": "text", + "content": "one with incomplete point clouds and the other with complete point clouds, which are not directly paired with each other. This unpaired setting could learn the mapping between the incomplete and complete point clouds, while reducing the reliance on paired GT complete point clouds. Nevertheless, the requirement of a set of complete point clouds still remains a major limitation to the practical application of point cloud completion." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "type": "text", + "content": "In this paper, we propose a novel point cloud completion framework that does not use any complete point clouds. Our main novelty lies in how to learn a mapping from an incomplete point cloud to a complete point cloud when the latter is not available at all. For this, we present a simple yet effective idea shown in Fig. 1. An incomplete point cloud usually results from self-occlusion occurs when observing an object from a certain viewpoint, as in (a). Therefore, if we obtain multiple incomplete point clouds of the object from various viewpoints, a union of them would be equivalent to the complete point cloud of that object. Based on this idea, we formulate the point cloud completion as generating multiple incomplete point clouds using a single input incomplete point cloud and sampled poses. Here, the generated incomplete point clouds should 1) share the same object as the input incomplete point cloud and 2) correspond" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 8, + 102, + 39 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 8, + 102, + 39 + ], + "spans": [ + { + "bbox": [ + 57, + 8, + 102, + 39 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 138, + 6, + 485, + 41 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 6, + 485, + 41 + ], + "spans": [ + { + "bbox": [ + 138, + 6, + 485, + 41 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 277, + 739, + 300, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 739, + 300, + 748 + ], + "spans": [ + { + "bbox": [ + 277, + 739, + 300, + 748 + ], + "type": "text", + "content": "14203" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 286, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 286, + 107 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 286, + 107 + ], + "type": "text", + "content": "to the arbitrarily given input poses. If the poses are various enough to cover the entire object, we could obtain the complete point cloud by integrating the incomplete point clouds." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 108, + 286, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 108, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 48, + 108, + 286, + 251 + ], + "type": "text", + "content": "To achieve the above, our framework starts with an encoder that extracts a volumetric shape feature from the input incomplete point cloud. This feature is designed to contain complete information about the shape of the target object. To generate an incomplete point cloud from the volumetric feature, we propose a novel projection method conditioned by the pose, similar to obtaining an incomplete point cloud as a capture of the target object from a certain viewpoint. The method determines the region visible at the given pose and obtains a projected feature by gathering the volumetric feature of that region. A decoder is then trained to generate an incomplete point cloud from the projected feature." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 252, + 286, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 252, + 286, + 394 + ], + "spans": [ + { + "bbox": [ + 48, + 252, + 286, + 394 + ], + "type": "text", + "content": "We do not have access to either the complete point cloud or the incomplete point cloud of another pose. Therefore, for training, we propose a novel dataset that provides both incomplete point clouds and corresponding poses, based on the ShapeNet dataset [5]. Note that our dataset includes only one incomplete point cloud per each object, unlike the setting of [13]. Using our dataset, we make our framework reconstruct the input incomplete point cloud itself by gathering the projected feature using the pose corresponding to the input. On the other hand, when using randomly sampled poses, we impose cycle consistency by feeding the generated incomplete point cloud to the encoder/decoder again." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 395, + 286, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 395, + 286, + 573 + ], + "spans": [ + { + "bbox": [ + 48, + 395, + 286, + 573 + ], + "type": "text", + "content": "During the inference phase, we extract the volumetric shape feature from the input and obtain the projected features using various poses that cover the entire object. By decoding the features and integrating the generated incomplete point clouds, we can obtain a complete point cloud as the final output. To verify the proposed method, we conduct extensive experiments and comparisons with the existing unpaired point cloud completion methods, on the proposed dataset. The results support that, the proposed method is comparable to the existing studies and sometimes achieves even more substantial completion results, without using any complete point cloud. Further, we conduct an experiment on the KITTI dataset [10] to show that the proposed method can be also applied to the real incomplete point clouds. Our main contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 578, + 286, + 711 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 48, + 578, + 286, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 578, + 286, + 613 + ], + "spans": [ + { + "bbox": [ + 48, + 578, + 286, + 613 + ], + "type": "text", + "content": "- We formulate a point cloud completion task as generating and integrating multiple incomplete point clouds corresponding to various poses." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 615, + 286, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 615, + 286, + 650 + ], + "spans": [ + { + "bbox": [ + 48, + 615, + 286, + 650 + ], + "type": "text", + "content": "- We propose a novel framework that generates an incomplete point cloud using the input incomplete point cloud and the given arbitrary pose." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 652, + 286, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 652, + 286, + 674 + ], + "spans": [ + { + "bbox": [ + 48, + 652, + 286, + 674 + ], + "type": "text", + "content": "- We introduce a new dataset consisting of incomplete point clouds and poses." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 676, + 286, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 676, + 286, + 711 + ], + "spans": [ + { + "bbox": [ + 48, + 676, + 286, + 711 + ], + "type": "text", + "content": "- We experimentally verify that the proposed method is comparable or even superior to existing studies, without using complete point cloud at all." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 308, + 71, + 396, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 71, + 396, + 83 + ], + "spans": [ + { + "bbox": [ + 308, + 71, + 396, + 83 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 87, + 441, + 100 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 87, + 441, + 100 + ], + "spans": [ + { + "bbox": [ + 308, + 87, + 441, + 100 + ], + "type": "text", + "content": "2.1. Point Cloud Completion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 107, + 545, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 107, + 545, + 465 + ], + "spans": [ + { + "bbox": [ + 307, + 107, + 545, + 465 + ], + "type": "text", + "content": "Point cloud completion aims to restore a complete point cloud from an input incomplete point cloud. Although fully-supervised completion methods [8, 17, 19, 23, 32, 34, 37, 40, 43, 46, 35, 31] achieve substantial completion result, they rely on the dataset including paired incomplete point cloud and GT complete point cloud, which is difficult to acquire, especially for real scenes. To overcome the limitation, unpaired approaches [6, 36, 45, 11] have been proposed to learn the mapping between the sets of complete and incomplete point clouds. Pcl2pcl [6] is the first unpaired point cloud completion method, which allows translation between partial and complete latent spaces by adversarial training. Subsequently, Cycle4completion [36] has achieved more advanced results by considering bidirectional geometric correspondence by cycle transformation and missing region coding. ShapeInversion [45] obtained optimal shape code for reconstructing 3D shapes based on the concept of GAN inversion. OptDE [11] proposed cross-domain completion by disentangling shape, domain, and occlusion factors, using domain-invariant geometric information and viewpoint prediction. Although the unpaired methods have shown promising results, their practical application is still limited by the requirement for a number of complete point clouds. [13] has proposed to utilize multiple incomplete point clouds of the same object, obtained from observations at different poses; however, such multiple observations are often not available. Unlike the existing methods, our method does not access the complete point cloud at all, and also uses only one incomplete point cloud per each object, throughout the entire training process." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 478, + 451, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 478, + 451, + 490 + ], + "spans": [ + { + "bbox": [ + 308, + 478, + 451, + 490 + ], + "type": "text", + "content": "2.2. Pose-Aware 3D Processing" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 307, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 307, + 498, + 545, + 713 + ], + "type": "text", + "content": "One of the most representative 3D tasks dealing with the pose is point cloud canonicalization [29, 30, 26]. Condor [29] takes an un-canonicalized collection of full or partial point clouds obtained through the internet or depth sensor as input. Meanwhile, [33] proposed self-supervised learning via disentangling content and pose information for the point cloud feature representation. As such, numerous studies have been conducted to exploit these two factors, since 3D data usually contains pose attributes as well as the shape of the object. Nevertheless, in the field of point cloud completion, using pose has not been deeply studied despite its usefulness. Since an incomplete point cloud is usually obtained by scanning the object from a single viewpoint through a scanner, information about the viewpoint (i.e., pose) can be beneficial for recovering the self-occluded regions. In this light, we utilize the pose information to complete the point cloud by generating multiple incomplete point clouds." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 278, + 740, + 300, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 278, + 740, + 300, + 748 + ], + "spans": [ + { + "bbox": [ + 278, + 740, + 300, + 748 + ], + "type": "text", + "content": "14204" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 69, + 521, + 293 + ], + "blocks": [ + { + "bbox": [ + 73, + 69, + 521, + 293 + ], + "lines": [ + { + "bbox": [ + 73, + 69, + 521, + 293 + ], + "spans": [ + { + "bbox": [ + 73, + 69, + 521, + 293 + ], + "type": "image", + "image_path": "b2b7c76a4e8d81c35b6f97735065e4aee56bd8ed11c8c3ebfaa93b4f8db64f0a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "lines": [ + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": "Figure 2. Illustration of a framework for generating a pose-aware point cloud. First, the encoder extracts the volumetric shape feature " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " from the input point cloud " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": ". Then, projected features " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "F_{r}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " are generated by determining the visible region with input pose " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "o_{i}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " and random pose " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "o_{r}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": ". Incomplete point cloud " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "\\hat{P}_{i,rec}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " is decoded to constrain with " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": ". Incomplete point cloud " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "\\hat{P}_{r}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " is decoded and entered into the model again with input pose " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "o_{i}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": ". After that, volumetric feature " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "\\hat{V}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": ", projected feature " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "\\hat{F}_{i}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "\\hat{P}_{i,cycle}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " are generated sequentially. We use " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{shape}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cycle}" + }, + { + "bbox": [ + 46, + 295, + 546, + 351 + ], + "type": "text", + "content": " to constrain our network." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 365, + 235, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 235, + 379 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 235, + 379 + ], + "type": "text", + "content": "2.3. Volumetric Feature Representation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 506 + ], + "type": "text", + "content": "Volumetric features are commonly used in tasks such as multi-view stereo [25, 27], 3D semantic segmentation [12, 47], and point cloud completion [8, 41, 40] due to their capability to preserve the spatial information of the input. However, standard voxelization can result in geometric information loss and quantization effects. To address this issue, GRNet [40] proposed a differentiable completion network that aggregates features between 3D grid vertices using interpolation. Similarly, our approach also utilizes the volumetric representation and pose to perform completion." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 517, + 158, + 531 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 517, + 158, + 531 + ], + "spans": [ + { + "bbox": [ + 47, + 517, + 158, + 531 + ], + "type": "text", + "content": "3. Proposed Methods" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 538, + 115, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 115, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 115, + 550 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "text", + "content": "In this paper, we refer to an incomplete point cloud as " + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "inline_equation", + "content": "P_{i} \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "text", + "content": " is the number of points in the point cloud, and the subscript " + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "text", + "content": " represents the pose at which " + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "text", + "content": " is captured. For convenience, we define the pose as a two-dimensional vector " + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "inline_equation", + "content": "o = (\\phi, \\theta)" + }, + { + "bbox": [ + 47, + 557, + 287, + 640 + ], + "type": "text", + "content": ", as the incomplete point cloud is usually not significantly affected by the distance between the scanner and the target object." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 287, + 714 + ], + "type": "text", + "content": "The goal of our work is to achieve point cloud completion without relying on using complete point clouds. To accomplish this, we generate multiple incomplete point clouds from a single input point cloud, where each generated incomplete point cloud shares the same object as the input but corresponds to a different pose." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "content": "As shown in Fig. 2, we begin by using an encoder " + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "content": " to obtain the volumetric shape feature " + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "content": " from the input incomplete point cloud " + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "content": ". We assume that the encoder can extract complete shape information of the object from the input incomplete point cloud. In other words, the volumetric shape feature serves as a complete target object at the feature level. To mimic the process of obtaining an incomplete point cloud as a capture of the target object at a certain pose, we gather the features corresponding to the arbitrarily given pose " + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "inline_equation", + "content": "o_{r}" + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "inline_equation", + "content": "o_{i}" + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "content": " for the upper branch) from the volumetric shape feature. Then, with a decoder " + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "content": ", we decode the gathered feature " + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 366, + 546, + 510 + ], + "type": "text", + "content": " to generate the incomplete point cloud." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 510, + 546, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 642 + ], + "type": "text", + "content": "To ensure that the incomplete point cloud generated by our framework correctly corresponds to the given pose, we impose reconstruction loss and cycle consistency loss, which will be explained in Section 3.2. Further, we introduce a novel method to determine the visible region and gather the features on it into the projected feature. We describe the details of the projection method in Section 3.3. Finally, in Section 3.4, we demonstrate how we obtain the complete point cloud using our framework, in the inference phase. It is worth noting that throughout the entire process, we do not use any complete point cloud." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 647, + 498, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 647, + 498, + 659 + ], + "spans": [ + { + "bbox": [ + 305, + 647, + 498, + 659 + ], + "type": "text", + "content": "3.2. Pose-Aware Point Cloud Generation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 666, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 546, + 714 + ], + "type": "text", + "content": "Since we have neither a complete point cloud nor an incomplete point cloud captured from another view, the input incomplete point cloud is the only available data in the point cloud domain that can be used as supervision. 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Illustration of our projection method. (a) We first determine the base region (covered by yellow) according to the given pose. Note that any pose can be categorized as one of cases I, II, and III, after a proper rotation. Then, the features on the base region are gathered into a 2D feature grid. (b) The visible region (covered by blue) defined on the grid is obtained by interpolating the neighboring base features." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "text", + "content": "we devise two branches that can be effectively trained using the input incomplete point cloud. The first branch uses the input pose " + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "text", + "content": " to generate the projected feature " + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "text", + "content": " and decode " + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "inline_equation", + "content": "\\hat{P}_{i,rec}" + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "text", + "content": ", which should be identical to the input point cloud " + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "text", + "content": ". To ensure this, we minimize the following reconstruction loss " + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 47, + 325, + 287, + 397 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 114, + 402, + 286, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 402, + 286, + 415 + ], + "spans": [ + { + "bbox": [ + 114, + 402, + 286, + 415 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} = \\mathcal {L} _ {C D} \\left(P _ {i}, \\hat {P} _ {i, r e c}\\right). \\tag {1}", + "image_path": "6538cde530486c0056850523256df413e7877945f7d1fef91d8af74aaf0fb257.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CD}" + }, + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "type": "text", + "content": " denotes the Chamfer Distance (CD), commonly used in the point cloud field. Note that, for two given point clouds " + }, + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "type": "inline_equation", + "content": "P_{1}" + }, + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "type": "inline_equation", + "content": "P_{2}" + }, + { + "bbox": [ + 47, + 421, + 286, + 456 + ], + "type": "text", + "content": ", the CD is formulated as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 460, + 294, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 294, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 294, + 496 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C D} \\left(P _ {1}, P _ {2}\\right) = \\sum_ {p _ {i} \\in P _ {1}} \\min _ {p _ {j} \\in P _ {2}} \\left\\| p _ {i} - p _ {j} \\right\\| + \\sum_ {p _ {j} \\in P _ {2}} \\min _ {p _ {i} \\in P _ {1}} \\left\\| p _ {j} - p _ {i} \\right\\|. \\tag {2}", + "image_path": "539565c071b30171f89ecb320176faffaa3a865a9f833567b893c78201f2a737.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": "Further, we randomly sample an arbitrary pose " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "o_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": ", which is different from the input pose " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": ", and generate projected feature " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "F_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": ". If we decode " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "F_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": ", the resulting incomplete point cloud " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\hat{P}_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": " should share the same shape with " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": " but correspond to the sampled pose " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "o_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": ". However, as mentioned, we cannot access the GT " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": ". Therefore, we impose cycle consistency on our framework. In specific, we put " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\hat{P}_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": " into the encoder again and get " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\hat{V}" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": ", which is the shape feature of the " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\hat{P}_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": ". Since the original input " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "P_i" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\hat{P}_r" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": " should have the same shape, we minimize a shape loss " + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{shape}" + }, + { + "bbox": [ + 47, + 498, + 287, + 618 + ], + "type": "text", + "content": " defined as follows:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 121, + 628, + 286, + 642 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 628, + 286, + 642 + ], + "spans": [ + { + "bbox": [ + 121, + 628, + 286, + 642 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s h a p e} = \\left| \\left| V - \\hat {V} \\right| \\right| _ {1}. \\tag {3}", + "image_path": "0e0b82464d53f2c77bd942560cb150c0fba3e6bbe9359d8ba2e460473e8e1281.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "text", + "content": "Besides, using the " + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "inline_equation", + "content": "\\hat{V}" + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "text", + "content": " and the input pose " + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "text", + "content": ", we gather the projected feature " + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "inline_equation", + "content": "\\hat{F}_i" + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "text", + "content": " and decode it into " + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "inline_equation", + "content": "\\hat{P}_{i,cycle}" + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "text", + "content": ", which should be identical to the input point cloud. Therefore, we define cycle loss " + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cycle}" + }, + { + "bbox": [ + 47, + 646, + 286, + 695 + ], + "type": "text", + "content": " as follow:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 108, + 700, + 286, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 700, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 108, + 700, + 286, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c y c l e}} = \\mathcal {L} _ {C D} \\left(P _ {i}, \\hat {P} _ {i, \\text {c y c l e}}\\right). \\tag {4}", + "image_path": "e1af11e738217f909b45bba0f3952e0322aad491c46b25b359b758c14ceb7f3f.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 325, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 325, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 545, + 373 + ], + "type": "text", + "content": "These loss terms, " + }, + { + "bbox": [ + 305, + 325, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{shape}" + }, + { + "bbox": [ + 305, + 325, + 545, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 325, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cycle}" + }, + { + "bbox": [ + 305, + 325, + 545, + 373 + ], + "type": "text", + "content": ", enable the encoder to extract the shape feature containing complete shape information and also help the decoder to generate incomplete point cloud that reflects the pose." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "spans": [ + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "type": "text", + "content": "To sum up, we train our framework by using a combination of " + }, + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cycle}" + }, + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{shape}" + }, + { + "bbox": [ + 305, + 373, + 546, + 408 + ], + "type": "text", + "content": ". The total loss function is defined as follow:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 354, + 421, + 545, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 421, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 354, + 421, + 545, + 433 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e c}} + \\mathcal {L} _ {\\text {c y c l e}} + \\lambda \\mathcal {L} _ {\\text {s h a p e}} \\tag {5}", + "image_path": "a1345345af734c9b7bb3a874b68c2f8d88e18b4cef633f5998ea80292ff8fcbb.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 444, + 442, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 444, + 442, + 457 + ], + "spans": [ + { + "bbox": [ + 305, + 444, + 442, + 457 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 444, + 442, + 457 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 444, + 442, + 457 + ], + "type": "text", + "content": " is the weight for " + }, + { + "bbox": [ + 305, + 444, + 442, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{shape}" + }, + { + "bbox": [ + 305, + 444, + 442, + 457 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 465, + 483, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 465, + 483, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 465, + 483, + 479 + ], + "type": "text", + "content": "3.3. The Proposed Projection Method" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "text", + "content": "In order to effectively incorporate pose information into our learning framework, we devise the encoder to extract the shape information as a form of volumetric feature, denoted as " + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "inline_equation", + "content": "V = \\{v_{i}\\}_{i = 1}^{N^{3}}" + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "inline_equation", + "content": "v_{i} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "text", + "content": " is the resolution of the volumetric feature and " + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "text", + "content": " is the feature dimension. Similar to the target object being captured as an incomplete point cloud from a certain viewpoint, we devise a gathering process that selects the features that are visible from an arbitrarily given pose." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": "However, the volumetric feature is a spatially discrete 3D grid, and thereby a naive visibility test returns the same results for the wide range of poses. To mitigate this, we establish a projection rule that can be applied for arbitrary poses, as shown in Fig. 3 (a). In specific, we subdivide the entire set of poses into the pose subsets, per 30 degrees. Then, we predefine the base region (covered by yellow) for each pose subset. Note that, without loss of generality, any arbitrary pose segment can be categorized into one of the three cases (I, II, and III), after a proper rotation." + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "spans": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "type": "text", + "content": "14206" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 69, + 285, + 236 + ], + "blocks": [ + { + "bbox": [ + 49, + 69, + 285, + 236 + ], + "lines": [ + { + "bbox": [ + 49, + 69, + 285, + 236 + ], + "spans": [ + { + "bbox": [ + 49, + 69, + 285, + 236 + ], + "type": "image", + "image_path": "d79aacb37af49ce9b9a37e7a664d3b72e2a6c88f3013b57d1eb376f7ba086054.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "lines": [ + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "text", + "content": "Figure 4. Illustration of obtaining the complete point cloud with the proposed framework in the inference phase. We gather the projected features " + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "inline_equation", + "content": "F_{1:8}" + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "text", + "content": " from the shape feature " + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "text", + "content": ", according to the various poses " + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "inline_equation", + "content": "o_{1:8}" + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "text", + "content": ". Then, each projected feature is decoded into the incomplete point cloud " + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "inline_equation", + "content": "\\hat{P}_{1:8}" + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "text", + "content": ". A union of the generated incomplete point clouds serves as the resulting complete point cloud " + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 46, + 237, + 286, + 303 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "text", + "content": "Once the base region is determined, we unfold the volumetric features located in that region into the 2D grid. During the unfolding, we compute the feature of the empty nodes by interpolating the neighboring volumetric features. In detail, we simply average the neighboring features and use the result as the feature of the node. Then, we define the visible region (covered by blue) on the 2D base grid, as shown in Fig. 3 (b). Here, as " + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "text", + "content": " increase, the visible region would move up and right, respectively. Finally, to obtain the feature map that represents the visible region, we perform bilinear interpolation using the neighboring base features. The weights for interpolation are determined according to the values of " + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 314, + 287, + 482 + ], + "type": "text", + "content": ". Further details of the projection method are provided in Supp. Material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 490, + 224, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 224, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 224, + 503 + ], + "type": "text", + "content": "3.4. Obtaining Complete Point Cloud" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "text", + "content": "As aforementioned, in the inference phase, we generate multiple incomplete point clouds of various poses and integrate them into a complete one. In detail, we first extract the volumetric shape feature " + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "text", + "content": " from the input incomplete point cloud, as shown in Fig. 4. From the shape feature, we obtain the projected features " + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "inline_equation", + "content": "F_{1:8}" + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "text", + "content": " by using a set of poses " + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "inline_equation", + "content": "o_{1:8}" + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "text", + "content": ". Here, we use a predefined set of eight poses, " + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\left\\{\\left(\\frac{\\pi}{4}, \\frac{\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{3\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{5\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, \\frac{7\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{3\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{5\\pi}{4}\\right), \\left(\\frac{3\\pi}{4}, \\frac{7\\pi}{4}\\right)\\right\\}" + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "text", + "content": ", which can cover the entire object. Then, we decode the projected features into the incomplete point cloud " + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\hat{P}_{1:8}" + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "text", + "content": ". Finally, a union of the generated incomplete point clouds serves as the resulting complete point cloud " + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 46, + 510, + 287, + 676 + ], + "type": "text", + "content": ". Note that we use the incomplete point cloud as the only input for the inference, and the pose of the input is not required." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "We observe that the resulting integrated point cloud " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " has substantial quality. However, our generate-and-integrate approach involves repeated decoding to generate" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 308, + 71, + 539, + 158 + ], + "blocks": [ + { + "bbox": [ + 308, + 71, + 539, + 158 + ], + "lines": [ + { + "bbox": [ + 308, + 71, + 539, + 158 + ], + "spans": [ + { + "bbox": [ + 308, + 71, + 539, + 158 + ], + "type": "image", + "image_path": "06eeb301d91749fa49f1afa7be1cb3eb11458fe0ed902b93728c13aeacc7e3ab.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "lines": [ + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "spans": [ + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "type": "text", + "content": "Figure 5. Illustration of the proposed re-training strategy. We use the frozen framework to obtain pseudo-GT " + }, + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "type": "text", + "content": ". Then, a new point cloud completion network " + }, + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "type": "text", + "content": " is trained to learn a mapping between the input " + }, + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 305, + 159, + 546, + 204 + ], + "type": "text", + "content": " and the pseudo-GT." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 209, + 546, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 546, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 546, + 317 + ], + "type": "text", + "content": "multiple incomplete point clouds, which can be computationally inefficient. In Section 4.3, we conduct an experiment to verify the completion performance while changing the number of used poses. It shows that there is a trade-off between the performance and the number of poses. To alleviate this issue, we propose a strategy named Re-Training (RT). As visualized in Fig. 5, this strategy uses the integrated complete point cloud as supervision for training another completion network." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "text", + "content": "First, our framework is trained as in Section 3 and frozen. Then, we obtain an integrated complete point cloud for each incomplete point cloud in the training dataset. Since the obtained complete point cloud is a reasonable completion result, it can serve as a pseudo-GT for the corresponding incomplete point cloud (which was originally used as input). In other words, starting from the initial dataset including incomplete point clouds without any complete point cloud at all, we now have a paired dataset including the incomplete point cloud and the pseudo-GT pairs. Using the incomplete point cloud and pseudo-GT pairs, we train another point cloud completion network " + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "text", + "content": ", like the conventional fully-supervised point cloud completion methods. For this, we use the Chamfer Distance loss between the input " + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "text", + "content": " and pseudo-GT " + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "text", + "content": ", which is denoted as " + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{RT}" + }, + { + "bbox": [ + 304, + 318, + 546, + 522 + ], + "type": "text", + "content": ". Note that, we still do not access the real GT complete point clouds at all, throughout the whole process of the re-training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 714 + ], + "type": "text", + "content": "Compared to directly using the output of our framework as a final output, the re-training can be advantageous in several aspects. First, as we mentioned, re-training is much more efficient and practical in the inference phase, since it requires only one inference per input and can perform multiclass point cloud completion. Further, in terms of the completion performance, the re-training enables learning more complex and beneficial concepts. For example, during retraining, we can expect the network to learn the geometric relation between the incomplete and (pseudo-)complete point clouds. It is especially helpful when the input is severely self-occluded (e.g., when only the upper side of the table can be observed), which cannot be dealt with directly using the pseudo-complete point cloud. In addition, we observe that the re-training can reject some outlier points in the pseudo-GT." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 739, + 301, + 749 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 739, + 301, + 749 + ], + "spans": [ + { + "bbox": [ + 277, + 739, + 301, + 749 + ], + "type": "text", + "content": "14207" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 94, + 545, + 161 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 91 + ], + "type": "text", + "content": "Table 1. Completion results on our dataset. The numbers shown are [CD ↓/F1 ↑], where CD is Chamfer Distance scaled with " + }, + { + "bbox": [ + 47, + 70, + 545, + 91 + ], + "type": "inline_equation", + "content": "\\times 10^4" + }, + { + "bbox": [ + 47, + 70, + 545, + 91 + ], + "type": "text", + "content": ". Best results are indicated as **bold**." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 94, + 545, + 161 + ], + "lines": [ + { + "bbox": [ + 48, + 94, + 545, + 161 + ], + "spans": [ + { + "bbox": [ + 48, + 94, + 545, + 161 + ], + "type": "table", + "html": "
MethodsUsing Complete PC.AirplaneCabinetCarChairSofaTableVesselAverage
Cycle. [36]Yes14.71/81.5316.64/74.9435.02/49.3322.23/70.5320.38/47.0721.45/77.1816.09/76.4920.93/68.15
ShapeInv. [45]Yes4.16/96.0514.20/79.9110.69/87.0916.67/81.3916.01/80.8223.86/82.9310.55/ 87.7213.74/85.13
OursNo4.84/95.1315.11/77.529.63/88.0118.25/75.3417.50/74.6219.02/80.9312.45/84.4313.73/82.46
Ours (+RT)No4.87/94.8515.14/81.209.06/88.8416.22/77.9215.41/77.6718.04/80.7310.95/86.3612.81/83.94
", + "image_path": "e699a2fd460adfc17cc3a35836c88179a069af6a9e654d930f124b02698b1482.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 69, + 170, + 524, + 415 + ], + "blocks": [ + { + "bbox": [ + 69, + 170, + 524, + 415 + ], + "lines": [ + { + "bbox": [ + 69, + 170, + 524, + 415 + ], + "spans": [ + { + "bbox": [ + 69, + 170, + 524, + 415 + ], + "type": "image", + "image_path": "dbf5504909040f896005d74d15706aa0ba3dfe114febfe56fd691d2546080fc3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 421, + 545, + 443 + ], + "lines": [ + { + "bbox": [ + 47, + 421, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 421, + 545, + 443 + ], + "type": "text", + "content": "Figure 6. Qualitative results of the point cloud completion methods on our dataset. From left to right: incomplete input, completion results of Cycle4completion [36], ShapeInversion [45], ours, ours (+RT), and GT." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 457, + 173, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 173, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 173, + 470 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 477, + 161, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 161, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 161, + 489 + ], + "type": "text", + "content": "4.1. Dataset Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 498, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 714 + ], + "type": "text", + "content": "The datasets [8, 34] widely used for the existing point cloud completion studies consist of input point clouds and complete point clouds, which are suitable for the fully-supervised or unpaired settings. On the other hand, to train and evaluate our study, a dataset consisting of complete/incomplete point clouds and corresponding poses is required. Therefore, we build and publish a new dataset for this setting. We use the complete point clouds in the ShapeNet Benchmark [5]. First, we randomly sample the pose as a viewpoint located on the sphere. Then, with the sampled pose, we use [18] to remove unobserved points from the complete point cloud. The resulting point cloud can serve as an incomplete point cloud, where the sampled pose is the corresponding pose. Note that, in our dataset, there is only one incomplete point cloud per the complete point cloud. It means that any complete point cloud cannot be observed from more than one view. More details about the proposed dataset can be found in the Supp. Material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 457, + 489, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 457, + 489, + 471 + ], + "spans": [ + { + "bbox": [ + 305, + 457, + 489, + 471 + ], + "type": "text", + "content": "4.2. Comparisons with Other Methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 481, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 481, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 305, + 481, + 545, + 577 + ], + "type": "text", + "content": "In order to evaluate the effectiveness of the proposed method, we conduct a comparison with existing methods (Cycle. [36] and ShapeInv. [45]), which access a set of complete point clouds during training. To ensure a fair comparison, we trained and evaluated all methods on the proposed dataset, using official codes provided by the authors. We evaluate and compare our method with and without using Re-Training (RT) strategy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 581, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 714 + ], + "type": "text", + "content": "Quantitative Results We use Chamfer Distance and F1-score to evaluate the performance of point cloud completion. As shown in Table 1, we evaluate seven categories. Overall, the re-training process improves the performance in most categories, indicating its effectiveness in enhancing the results. Compared to ShapeInv., our proposed method has a lower average Chamfer Distance and a slightly lower F1-score of 1.19. Interestingly, our results outperform Cycle for all metrics. In other words, our results outperform or achieve comparable performance to existing studies despite not using a complete point cloud." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "spans": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "type": "text", + "content": "14208" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 80, + 537, + 255 + ], + "blocks": [ + { + "bbox": [ + 57, + 80, + 537, + 255 + ], + "lines": [ + { + "bbox": [ + 57, + 80, + 537, + 255 + ], + "spans": [ + { + "bbox": [ + 57, + 80, + 537, + 255 + ], + "type": "image", + "image_path": "631e45df9d7a520e310178a063000186152bc4834a7639e87e0ca3c53b50c946.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 264, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 47, + 264, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 547, + 309 + ], + "type": "text", + "content": "Figure 7. Visualization of pose-aware incomplete point clouds. The cuboids in the top part indicate the volumetric shape features viewed from an arbitrary pose, highlighted in red. The right side of the figure shows the input and ground truth complete point clouds. Two scenarios are considered for generating incomplete point clouds: one that uses only the " + }, + { + "bbox": [ + 47, + 264, + 547, + 309 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 47, + 264, + 547, + 309 + ], + "type": "text", + "content": " loss term, and the other with the full loss term. We also generate ground truth incomplete point clouds to evaluate how well the incomplete point clouds are generated." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 323, + 288, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 288, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 288, + 539 + ], + "type": "text", + "content": "Qualitative Results We qualitatively compare the point cloud completion results on our dataset. Figure 6 shows complete point cloud results from existing methods, Cycle., ShapeInv., ours, and ours with re-training technique. Compared to the results of the existing methods, the results support that our method successfully completes the parts that were originally invisible at the input point cloud. Also, we find that the conventional methods fail to restore certain details that are present in the input point cloud. For instance, as shown in the dashed boxes, some fine details such as the exhaust port of the airplane or the armrest parts of the chair are not completely generated, even though they are present in the input point cloud. However, our method can reconstruct them sharply, resulting in a more accurate and realistic airplane model. To sum up, both the quantitative and qualitative results support that the proposed method can achieve substantial completion results, considering that GT complete point cloud is not used at all." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 548, + 147, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 147, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 147, + 559 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 570, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 714 + ], + "type": "text", + "content": "Effectiveness of Each Loss Term We conduct the ablation studies to verify the effectiveness of each term in Eq. 5. As shown in Table 2, we use Chamfer Distance and F1-score as a metric in several categories. The case with only reconstruction loss is used as the baseline. As shown in first row and second row, Chamfer Distance decreases 1.01 CD and F1-score increases 1.30 in average after adding shape loss. We can see that there are performance improvements in every category. As shown in first row and third row, Chamfer Distance decreases 1.55 CD and F1-score increases 1.75 after adding cycle loss. Also, there are performance improvements in every categories. As shown in last row, it" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 308, + 355, + 544, + 405 + ], + "blocks": [ + { + "bbox": [ + 305, + 320, + 546, + 352 + ], + "lines": [ + { + "bbox": [ + 305, + 320, + 546, + 352 + ], + "spans": [ + { + "bbox": [ + 305, + 320, + 546, + 352 + ], + "type": "text", + "content": "Table 2. Ablation studies on the proposed dataset. The numbers shown are " + }, + { + "bbox": [ + 305, + 320, + 546, + 352 + ], + "type": "inline_equation", + "content": "[\\mathrm{CD} \\downarrow / \\mathrm{F1} \\uparrow]" + }, + { + "bbox": [ + 305, + 320, + 546, + 352 + ], + "type": "text", + "content": ", where CD is Chamfer Distance scaled with " + }, + { + "bbox": [ + 305, + 320, + 546, + 352 + ], + "type": "inline_equation", + "content": "\\times 10^4" + }, + { + "bbox": [ + 305, + 320, + 546, + 352 + ], + "type": "text", + "content": ". Best results are indicated as bold." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 355, + 544, + 405 + ], + "lines": [ + { + "bbox": [ + 308, + 355, + 544, + 405 + ], + "spans": [ + { + "bbox": [ + 308, + 355, + 544, + 405 + ], + "type": "table", + "html": "
LrecLshapeLcycleAirplaneCabinetSofaAverage
✓5.63/94.1117.66/73.4119.97/72.4714.42/79.99
✓✓5.58/94.2915.86/76.3918.80/73.1913.41/81.29
✓✓5.08/94.9515.47/76.3818.08/73.8912.87/81.74
✓✓✓4.84/95.1314.90/88.0117.50/74.6212.42/82.69
", + "image_path": "0db9b7ef1c06aa30ca1a53291ab672a06cae901f9c5ea309f51e52e23e4cf7f2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 413, + 546, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 413, + 546, + 448 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 546, + 448 + ], + "type": "text", + "content": "shows best performance in both Chamfer Distance and F1-score with all constraints. From these results, proposed constraints are all effective in point cloud completion." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 449, + 546, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 546, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 546, + 666 + ], + "type": "text", + "content": "Effectiveness of Number of Poses We examine the effect of the number of input poses on the quality of the complete point cloud generated from our method without re-training. Intuitively, if we use more poses, the generated point clouds that are aware of the input poses and incomplete could cover a wider range of partial views, and thereby complete point cloud would be better. We conduct an experiment with 2, 4, 8, 10, and 14 poses for some categories, where the configurations of 2, 4, and 8 poses are shown in Fig. 8. For a configuration of 10 poses, upward and downward poses are added to the 8 poses. Likewise, additional 4 sideward poses are incorporated into the case of 10 poses for the configuration of 14 poses. Fig. 9 shows how the completion performance changes depending on the number of poses used. As we expected, Chamfer Distance decreases meaningfully as more poses are used until 8 poses. However, the performance becomes saturated as we increase the number of poses to 10 and 14. Therefore, we use 8 poses for our default setting." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 671, + 441, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 671, + 441, + 683 + ], + "spans": [ + { + "bbox": [ + 305, + 671, + 441, + 683 + ], + "type": "text", + "content": "4.4. Additional Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": "Results of Pose-Aware Incomplete Point Cloud Since our main idea is generating and integrating the multiple incom" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "spans": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "type": "text", + "content": "14209" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 73, + 126, + 134 + ], + "blocks": [ + { + "bbox": [ + 62, + 73, + 126, + 134 + ], + "lines": [ + { + "bbox": [ + 62, + 73, + 126, + 134 + ], + "spans": [ + { + "bbox": [ + 62, + 73, + 126, + 134 + ], + "type": "image", + "image_path": "6107daf66e11f2b5798f456c644e09c57c2d69184d9917a21d3e97848f651fc3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 138, + 287, + 174 + ], + "lines": [ + { + "bbox": [ + 47, + 138, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 47, + 138, + 287, + 174 + ], + "type": "text", + "content": "Figure 8. Illustration of pose configurations, which are used to verify the effectiveness of the number of poses. The black dots represent the location of the poses." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 130, + 73, + 197, + 134 + ], + "blocks": [ + { + "bbox": [ + 130, + 73, + 197, + 134 + ], + "lines": [ + { + "bbox": [ + 130, + 73, + 197, + 134 + ], + "spans": [ + { + "bbox": [ + 130, + 73, + 197, + 134 + ], + "type": "image", + "image_path": "97eadff4b42fdd692b1f8d5b357b5fe2ecf815d4c4b121b62e310398656e2282.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 199, + 71, + 269, + 136 + ], + "blocks": [ + { + "bbox": [ + 199, + 71, + 269, + 136 + ], + "lines": [ + { + "bbox": [ + 199, + 71, + 269, + 136 + ], + "spans": [ + { + "bbox": [ + 199, + 71, + 269, + 136 + ], + "type": "image", + "image_path": "c78dcf3c2a6a1c4c3b84e5b6e38f97e5af88470e2110643248a9268451a9ffc5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 51, + 183, + 273, + 245 + ], + "blocks": [ + { + "bbox": [ + 51, + 183, + 273, + 245 + ], + "lines": [ + { + "bbox": [ + 51, + 183, + 273, + 245 + ], + "spans": [ + { + "bbox": [ + 51, + 183, + 273, + 245 + ], + "type": "image", + "image_path": "51b1d693c682817ef0c56d41804ff78ee29be1e194561bccdc3b5021942332dc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 245, + 287, + 267 + ], + "lines": [ + { + "bbox": [ + 47, + 245, + 287, + 267 + ], + "spans": [ + { + "bbox": [ + 47, + 245, + 287, + 267 + ], + "type": "text", + "content": "Figure 9. Impact of the number of poses on performance. CD is Chamfer Distance scaled with " + }, + { + "bbox": [ + 47, + 245, + 287, + 267 + ], + "type": "inline_equation", + "content": "\\times 10^4" + }, + { + "bbox": [ + 47, + 245, + 287, + 267 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 279, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 287, + 590 + ], + "type": "text", + "content": "plete point clouds corresponding to the given poses, we qualitatively verify whether our network can generate high-quality incomplete point clouds that correspond to the desired poses. Figure 7 shows incomplete point clouds generated from our method. The top row of the figure indicates the various poses we used, and the right side shows the input incomplete input point cloud and the GT complete point cloud. According to them, we generate incomplete point clouds using the models, which are (1) trained with reconstruction loss only and (2) trained with all loss terms. We also provide the GT incomplete point clouds obtained by applying hidden point removal [18] on the GT complete point cloud. When using only " + }, + { + "bbox": [ + 47, + 279, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 47, + 279, + 287, + 590 + ], + "type": "text", + "content": ", we can observe that the generated incomplete point clouds do not reflect the given poses correctly, and also fail to preserve fine details overall. On the other hand, we can see that incomplete point clouds obtained by the proposed method are well-corresponded to their respective poses appearing as if they had been captured from those viewpoints. Notably, the fine details (e.g., exhaust ports on the wings) are well-completed for all incomplete point clouds, indicating that the network could effectively capture detailed shapes from the input point cloud across various poses. The results support that our framework correctly learns to generate incomplete point clouds according to the given poses, and achieve substantial completion results in the ultimate." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "type": "text", + "content": "Using Noisy Poses In the real scenario, there can be a noise in the poses corresponding to the obtained incomplete point cloud. Therefore, we conduct an experiment to verify the sensitivity of the proposed method against the noise in the poses that we used for training. We observe that our method is robust to the noise in poses to some extent. We conduct an experiment by introducing Gaussian noise to the given poses. Specifically, we add a noise sampled from normal distribution to the given pose " + }, + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "type": "inline_equation", + "content": "o_i = (\\phi, \\theta)" + }, + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "type": "text", + "content": ". The resulting noisy pose, denoted as " + }, + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\phi_{noise}" + }, + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{noise}" + }, + { + "bbox": [ + 47, + 593, + 287, + 714 + ], + "type": "text", + "content": ", is defined as follows:" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 314, + 103, + 538, + 302 + ], + "blocks": [ + { + "bbox": [ + 305, + 69, + 546, + 101 + ], + "lines": [ + { + "bbox": [ + 305, + 69, + 546, + 101 + ], + "spans": [ + { + "bbox": [ + 305, + 69, + 546, + 101 + ], + "type": "text", + "content": "Table 3. Effect of noise in pose. The numbers shown are [CD ↓ / F1 ↑], where CD is Chamfer Distance scaled with " + }, + { + "bbox": [ + 305, + 69, + 546, + 101 + ], + "type": "inline_equation", + "content": "\\times 10^4" + }, + { + "bbox": [ + 305, + 69, + 546, + 101 + ], + "type": "text", + "content": ". Best results are indicated as bold." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 314, + 103, + 538, + 302 + ], + "lines": [ + { + "bbox": [ + 314, + 103, + 538, + 302 + ], + "spans": [ + { + "bbox": [ + 314, + 103, + 538, + 302 + ], + "type": "table", + "html": "
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Qualitative results with noisy poses. 0.1, 0.03, and 0 are value of " + }, + { + "bbox": [ + 305, + 306, + 546, + 329 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 306, + 546, + 329 + ], + "type": "text", + "content": " in Eq. 6, 7." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 336, + 330, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 336, + 330, + 347 + ], + "spans": [ + { + "bbox": [ + 306, + 336, + 330, + 347 + ], + "type": "text", + "content": "lows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 361, + 356, + 545, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 356, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 361, + 356, + 545, + 368 + ], + "type": "interline_equation", + "content": "\\phi_ {\\text {n o i s e}} = \\phi + \\sigma N (0, 1) \\times 1 8 0 ^ {\\circ} \\tag {6}", + "image_path": "4089a312a4723f08b40e7f156f77947d8ec7860aefbc83663d6f464fe0bddcca.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 361, + 371, + 545, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 371, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 361, + 371, + 545, + 383 + ], + "type": "interline_equation", + "content": "\\theta_ {\\text {n o i s e}} = \\theta + \\sigma N (0, 1) \\times 1 8 0 ^ {\\circ}. \\tag {7}", + "image_path": "7d27c49e0c2b14f24238c5918c339fc47ab6674f4c330003bd60b8a9dded5b35.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "inline_equation", + "content": "N(0,1)" + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "text", + "content": " is a normal distribution with mean 0 and variance 1. We train and evaluate the model by varying the value of " + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "text", + "content": ". We set the " + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "text", + "content": " as 0.03 and 0.1. For these values, the errors in the pose are mostly within " + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "inline_equation", + "content": "11^{\\circ}" + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "inline_equation", + "content": "36^{\\circ}" + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "text", + "content": ", respectively. Table 3 demonstrates the impact of the noise on pose information. A value of " + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "inline_equation", + "content": "\\sigma = 0" + }, + { + "bbox": [ + 305, + 390, + 546, + 605 + ], + "type": "text", + "content": " means that there is no noise in the pose, which is the default setting provided in the main paper. As noise increases, the average performance decreases compared to the case without any noise. The average Chamfer distance increases by 1.42 CD, and F1-score decreases by 1.90 compared to the case without noise. It should be noted that the effect of noise on performance is not significant. Figure 10 shows the qualitative results when adding noise to the pose. Although the pose is perturbed, the generated complete point clouds remain similar to the case without any noise. From these results, we can conclude that errors in pose have a limited effect on performance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 606, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 606, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 606, + 546, + 714 + ], + "type": "text", + "content": "Completing the Real Incomplete Point Clouds To assess the scalability of our method, we conduct an experiment using the real dataset. We train and test our framework on the point cloud data in KITTI [10] and nuScenes [1], using the provided bounding boxes to calculate the relative pose. Since the real dataset does not include incomplete point clouds observed from upward or downward directions, we enforce a constraint to ensure that the sampled poses fall within a range of the poses of the incomplete point" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "spans": [ + { + "bbox": [ + 277, + 739, + 301, + 748 + ], + "type": "text", + "content": "14210" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 68, + 105, + 267, + 144 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "text", + "content": "Table 4. Quantitative comparison on KITTI dataset [10]. Minimum Matching Distance (MMD, ↓) and Unidirectional Chamfer Distance (UCD, ↓) are scaled with " + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "inline_equation", + "content": "\\times 10^3" + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "inline_equation", + "content": "\\times 10^4" + }, + { + "bbox": [ + 47, + 69, + 287, + 102 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 68, + 105, + 267, + 144 + ], + "lines": [ + { + "bbox": [ + 68, + 105, + 267, + 144 + ], + "spans": [ + { + "bbox": [ + 68, + 105, + 267, + 144 + ], + "type": "table", + "html": "
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(A: Real incomplete point cloud, B: Our result)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 231, + 288, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 231, + 288, + 459 + ], + "spans": [ + { + "bbox": [ + 49, + 231, + 288, + 459 + ], + "type": "text", + "content": "clouds. Table 4 compares the quantitative performance of Cycle.[36] and ShapeInv.[45] using Minimum Matching Distance (MMD) and Unidirectional Chamfer Distance (UCD). To calculate MMD, we use complete point clouds in ShapeNet [5]. MMD evaluates the quality of the result in terms of how realistically the point cloud is generated, and ShapeInv. shows the best performance in this regard. However, our approach also shows comparable performance. Additionally, our approach outperforms the others on the UCD metric, which evaluates how well the generated point cloud reflects the input shape. We show the qualitative results in Fig. 11. In each section, the left side displays input incomplete point clouds, while the right side showcases predicted complete point clouds. Our network successfully generates the complete shape of cars and vans, even when the input point clouds are severely sparse. We can also observe that the obtained complete point clouds well-reflect the detailed shapes. These results demonstrate the potential practicality of our method for real-world applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 468, + 120, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 120, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 120, + 480 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 486, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 287, + 714 + ], + "type": "text", + "content": "In this paper, we propose a novel method for point cloud completion that does not require any complete point clouds. The proposed method generates multiple incomplete point clouds corresponding to various poses and integrates them to obtain the complete point cloud. Our method employs an encoder-decoder framework where the encoder extracts a volumetric shape feature from the input incomplete point cloud, and the decoder generates pose-aware incomplete point clouds. To train the model, we introduce a novel dataset with incomplete point clouds and corresponding poses. The proposed method achieves comparable results with the existing state-of-the-art methods and outperforms some categories. Additionally, we demonstrate that the method can be applied to real incomplete point clouds. In future work, we plan to use a neural implicit representation for the shape feature instead of the volumetric feature, which can achieve better 3D representation capability. In addition, we will further enhance the projection method using a visibility check with learnable opacity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 546, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 546, + 180 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 546, + 180 + ], + "type": "text", + "content": "Acknowledgments This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636) and Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by Korea government(MSIT) (No.2020-0-00440, Development of Artificial Intelligence Technology that Continuously Improves Itself as the Situation Changes in the Real World)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 191, + 365, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 191, + 365, + 202 + ], + "spans": [ + { + "bbox": [ + 306, + 191, + 365, + 202 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 310, + 210, + 546, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 310, + 210, + 546, + 277 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 210, + 546, + 277 + ], + "spans": [ + { + "bbox": [ + 310, + 210, + 546, + 277 + ], + "type": "text", + "content": "[1] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giacarlo Baldan, and Oscar Beijbom. nuscenes: A multimodal dataset for autonomous driving. 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Cylinder3d: An effective 3d framework for driving-scene lidar semantic segmentation. arXiv preprint arXiv:2008.01550, 2020. 3" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 740, + 300, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 740, + 300, + 748 + ], + "spans": [ + { + "bbox": [ + 277, + 740, + 300, + 748 + ], + "type": "text", + "content": "14213" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_content_list.json b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a80409478ad0ee7a2151442e7e6be8d11f45a29e --- /dev/null +++ b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_content_list.json @@ -0,0 +1,2008 @@ +[ + { + "type": "text", + "text": "Learning Pseudo-Relations for Cross-domain Semantic Segmentation", + "text_level": 1, + "bbox": [ + 135, + 130, + 833, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dong Zhao, Shuang Wang $^{\\text{心}}$ , Qi Zang, Dou Quan, Xiutiao Ye, Rui Yang, Licheng Jiao \nSchool of Artificial Intelligence, Xidian University, Shaanxi, China", + "bbox": [ + 142, + 180, + 825, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zhaodong01@stu.xidian.edu.cn; shwang@mail.xidian.edu.cn", + "bbox": [ + 238, + 219, + 728, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Domain adaptive semantic segmentation aims to adapt a model trained on labeled source domain to unlabeled target domain. Self-training shows competitive potential in this field. Existing methods along this stream mainly focus on selecting reliable predictions on target data as pseudolabels for category learning, while ignoring the useful relations between pixels for relation learning. In this paper, we propose a pseudo-relation learning framework, Relation Teacher (RTea), which can exploitable pixel relations to efficiently use unreliable pixels and learn generalized representations. In this framework, we build reasonable pseudorelations on local grids and fuse them with low-level relations in the image space, which are motivated by the reliable local relations prior and available low-level relations prior. Then, we design a pseudo-relation learning strategy and optimize the class probability to meet the relation consistency by finding the optimal sub-graph division. In this way, the model's certainty and consistency of prediction are enhanced on the target domain, and the cross-domain inadaptation is further eliminated. Extensive experiments on three datasets demonstrate the effectiveness of the proposed method. The code will be available at https://github.com/DZhaoXd/RTea.", + "bbox": [ + 75, + 300, + 473, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 675, + 209, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic segmentation is a challenging problem of assigning each pixel a class label in an image. Driven by deep neural networks, significant progress has been made in this field. Despite these efforts, a segmentation model trained with a specific domain does not generalize well to other domains. It is known to be caused by the domain gap between the training (source) and testing (target) domains [13]. To", + "bbox": [ + 75, + 700, + 468, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This work is supported by the National Key R&D Program of China under Grant No. 2021ZD0110400, the National Natural Science Foundation of China (No.62271377, No.62201407), the Key Research and Development Program of Shannxi (No.2021ZDLGY01-06, No.2022ZDLGY01-12), the China Postdoctoral Science Foundation (No. 2022M722496), the Foreign Scholars in University Research and Teaching Program's 111 Project (B07048).", + "bbox": [ + 75, + 814, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c011a64d67fb04e16668099ab9df89cc06c66b9d00eb1c9a0482a0bf32eadffa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 271, + 880, + 356 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0101dc3cc61716f2da9d90e24b55e2f47b861adb4cb11754df61b2f14222d8ff.jpg", + "image_caption": [ + "Figure 1: Overview of our motivation. In A, previous self-training methods select reliable pseudo-labels for category learning. In B, our method reasonably utilizes reliable pseudo-labels and unreliable ones for relation learning." + ], + "image_footnote": [], + "bbox": [ + 511, + 359, + 879, + 496 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "solve this problem, unsupervised domain adaptation (UDA) is proposed to improve the segmentation model's adaptability to the target domain.", + "bbox": [ + 498, + 593, + 890, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Domain alignment is one of the mainstream UDA semantic segmentation methods, aiming to align the distribution of source and target domains in input [30, 60, 25, 4], feature [53, 32, 19, 22, 35, 65, 50, 56], or output spaces [48, 33, 49]. Works along this line achieve positive adaptation benefits but the lack of specific target domain knowledge leads to slight improvement [39, 68, 66].", + "bbox": [ + 496, + 641, + 892, + 747 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, self-training methods [27, 10, 1, 69, 64, 67] are proposed to mine target-specific knowledge. These methods use the pseudo-labels generated by the pre-adapted model to further train the model on the target domain. Consequently, the quality of pseudo-labels for training directly determines the performance of self-training. Following this key point, reliability measure-based and uncertainty estimation-based self-training methods are proposed [71, 27, 69, 10, 1, 64, 52]. These methods reduce the noise interference of pseudo-labels for category learning, bring", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19191", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing considerable performance improvement.", + "bbox": [ + 76, + 90, + 372, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we explore the potential of self-training from another perspective, as shown in Fig. 1. In Fig. 1 A, previous self-training methods perform category learning on reliable pseudo-labels and discard unreliable ones. However, we find that not only category learning but relation learning can be performed in pseudo-labels to further improve the adaptability of the model. In Fig. 1 B, we argue that relation learning in pseudo-labels can be performed in two ways: (1) The relations between reliable pseudo-labels can be additionally used for representation learning to build a more generalized representation space. (2) By establishing the relations between reliable and unreliable pseudolabels, discarded pixels can also be effectively used for self-training to increase the certainty of the model. In this way, the available knowledge contained in pseudo-labels can be fully exploited, both reliable and unreliable pixels.", + "bbox": [ + 75, + 109, + 473, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve the above goals, building reasonable relations between pixels is the core. Dense pixel relations can be represented by a relation matrix (or affinity matrix) [8, 20, 29], modeling the similarity between pixels on an image. Due to massive noise contained in the pseudo-labels, the relation matrix constructed by them also contain noisy relations. We explore two observational priors to guide the building of relations, as shown in Fig. 2. We use the predictions of the unadapted model for the target images to observe noise distribution of relations. Comparing Fig. 2 (e) and (f), we observe that high-level relations built by pseudo-labels are noisy in long-distance association but are reliable within local areas, which are termed as reliable local relations prior. We analyze this because the insufficiently adapted model cannot transfer global semantics and can only give reasonable relations in local regions. Besides, in Fig. 2(d), we further explore the low-level relations built on each local grid in image space using Gaussian kernel. We find that the low-level relations in local grids can capture the boundaries of objects and contain exploitable relations, which are termed as available low-level relations prior. We argue that such relations, although lacking in semantics, provides class boundary clues can be reasonably exploited.", + "bbox": [ + 75, + 354, + 472, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With these aspects in mind, we propose a pseudo-relation learning-based self-training framework, Relation Teacher (RTea), forcing the student model to learn the pseudo-relations between pixels from the teacher model and achieve co-evolution for both models. In this framework, with the guidance of the above two priors, we first use pseudo-labels to build high-level relations in each divided grid, which avoids being misled by long-distance relationships. Then, we fuse low-level relations in image space into high-level relations to attenuate noisy relations and assist semantic relations in identifying category boundaries. Next, we explore the way of learning pseudo-relations and devise a novel pseudo-relations loss, which optimizes the class", + "bbox": [ + 75, + 704, + 473, + 902 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7f743b37a18ae73cfb5ac3832af2dd81ec61e0f3bebb185c7e501d56b8902bd8.jpg", + "image_caption": [ + "(a).Image" + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 625, + 142 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d18924e7756a28d990d38535d79507175d310c5c50d1fecb5e94e449551faf4f.jpg", + "image_caption": [ + "(b).Prediction" + ], + "image_footnote": [], + "bbox": [ + 635, + 89, + 764, + 142 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/58d5a3c74230877663367ae214ca143ff1a3a12f790db154b05b189e5bc87d5d.jpg", + "image_caption": [ + "↓" + ], + "image_footnote": [], + "bbox": [ + 521, + 155, + 604, + 214 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3e6bacf1391cb7f46bec1601a34ace35f79da9d7644fdc862d10e823fd99be1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 643, + 155, + 753, + 212 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1deaca3fe9718329bcf70689d59fd57c12edb57d1a2a648368666414537a5e77.jpg", + "image_caption": [ + "(e). Relations from Pred." + ], + "image_footnote": [], + "bbox": [ + 635, + 214, + 759, + 304 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/20c7b52989277a1265c847221405c7848ab1d5ff644123a289f60547dca6d399.jpg", + "image_caption": [ + "(c).Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 776, + 94, + 895, + 142 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/295c2ced34e5effa9e010372649c4e44e5a1081023d29d5690b6a212463d9c04.jpg", + "image_caption": [ + "similarity" + ], + "image_footnote": [], + "bbox": [ + 774, + 155, + 888, + 203 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/18f0f17ee805bb30e8314cab4f89f3ba3c4261204397d6763bfc096b09692b8b.jpg", + "image_caption": [ + "(f).Relations from GT." + ], + "image_footnote": [], + "bbox": [ + 772, + 213, + 893, + 304 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/415b79f83346cd4aaecc7672860d21607deb4a7e6b99fefeb86ea1e044bbc983.jpg", + "image_caption": [ + "Density Bar:", + "Figure 2: Overview of two observational priors. (b) is the source-only model's prediction, (d) is the local relation map in image space built by Gaussian kernel in each grid, (e) is the pseudo-relation matrix. (f) is the relation matrix built by ground truth." + ], + "image_footnote": [], + "bbox": [ + 622, + 321, + 844, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "probability to meet the relation consistency by finding the optimal sub-graph division from the global pseudo-relation of each class. It has two advantages over the naive relation-learning loss: one is global relational modeling, which can be easily implemented by matrix multiplication; the other is threshold-free learning by dynamically weighting class probabilities and pseudo-relations.", + "bbox": [ + 496, + 435, + 890, + 541 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With RTea, the model's certainty and consistency of prediction can be enhanced on the target domain, and the cross-domain inadaptation is further eliminated. Sufficient experiments show our method can further mine the available knowledge in pseudo-labels, and it can be easily incorporated into existing self-training method to further boost their performance.", + "bbox": [ + 496, + 542, + 892, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 662, + 637, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised Domain Adaptation (UDA). UDA methods can be divided into domain alignment and self-training. Alignment-based methods narrow the domain gap by aligning distributions at different levels, e.g., input [12, 30, 25, 60], feature [32, 33, 7, 50, 56, 22] and output [48, 49, 59]. Although they achieve positive adaptation benefits, the lack of specific target domain knowledge leads to slight improvement. To this end, self-training methods are proposed to train the network with pseudo-labels for the target domain, which can be divided into two categories, offline and online pseudo-label-based methods. Offline self-training (OFFST) methods save the target domain pseudo-labels generated by the pre-trained model and use them to train the model iteratively [27, 10, 37]. To avoid noise interfer", + "bbox": [ + 496, + 688, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19192", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ence, these methods select high-quality pseudo-labels via threshold setting [70, 71], consistent prediction [68], and pseudo-label prototypes [64]. These methods require additional storage of pseudo-labels and an iterative training, which is not conducive to practical use. Online self-training (ONST) uses the model's output during training as supervision without saving intermediate results [58, 4, 51, 1]. ONST avoids the inconvenience of multiple training rounds and manual intervention between consecutive rounds in OFFST. Our work is designed in online self-training fashion. Besides, our method further mines the available knowledge in pseudo-labels from the novel perspective of pixel relations, which can further promote pseudo-label learning and boosting self-training performance.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Relation Learning (RL) in Semantic Segmentation. In supervised semantic segmentation, capturing relations between pixels is continuously studied at feature [8, 20, 29] and output layers[24, 17]. At the feature layer, several work [8, 20, 62, 29] use the label-guided pixel relation to build a compact feature space, in which features of the same class are close and of different classes are far. At the output layer, AAF [24] and CDGC [17] exploit pixel relations in the ground truth to correct the output probabilities, forcing the model to adjust both the classifier and the feature extractor to output reasonable relations and semantic structure. These supervised RL methods achieve huge performance improvements, emphasizing the importance of maintaining the relation between pixels. However, in the UDA task, the lack of annotations makes it impossible to build relations as these works. Our method proposes a novel pseudo-relation building and learning strategy so that the above advantages can be also achieved to the UDA segmentation task.", + "bbox": [ + 75, + 303, + 472, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pseudo Label Correction. As a classic technique of semi-supervised learning, pseudo-labeling has shown favorable competitive advantages in many visual tasks with limited labels. Due to the limitation of confidence bias and error accumulation [41], pseudo-labeling are easy to overfit the noise and lead to model divergence[61]. Some pioneering works alleviate the problems from pseudo-label selection[63], negative label learning[41], contrastive learning [55], model calibration [23, 54]. However, the task-specific and domain-dependent design limits the application of these methods in complex cross-domain tasks. In contrast, our work proposes a novel perspective to rectify pseudo-labels and a tailored solution for cross-domain segmentation tasks.", + "bbox": [ + 75, + 575, + 472, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 805, + 212, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background and Overview", + "text_level": 1, + "bbox": [ + 76, + 830, + 318, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This paper focuses on the unsupervised domain adaptation (UDA) semantic segmentation, where source domain data $\\mathcal{X}_s = \\{x_s\\}$ with pixel-level labels $\\mathcal{Y}_s = \\{y_s\\}$", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and unlabeled target domain data $\\mathcal{X}_t = \\{x_t\\}$ are given. Our goal is to train a segmentation model $G$ that can work well on target domain. $G$ consists of a feature extractor $F$ and a classifier $C$ . Given sampled image $x\\in \\mathcal{X}_s\\cup \\mathcal{X}_t$ , $F$ mapping $x$ to the feature space $f = F(x)$ , and $C$ categorizes each feature in $f$ to obtain a class probability map $p = C(F(x))\\in \\mathbb{R}^{h\\times w\\times K}$ . For the source domain, the cross entropy loss $L_{s}$ is calculated to optimize the model,", + "bbox": [ + 496, + 90, + 893, + 213 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s} = - \\frac {1}{\\left| \\mathcal {X} _ {s} \\right|} \\sum_ {x _ {s} \\in \\mathcal {X} _ {s}} \\log C (F (x _ {s})) (y _ {s}). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 222, + 892, + 260 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the target domain, to narrow the domain gap, self-training methods adopt pseudo-labels $\\hat{y}_t$ generated by the pre-adapted model to retrain the unadapted model,", + "bbox": [ + 496, + 268, + 893, + 316 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s t} = - \\frac {1}{| \\mathcal {X} _ {t} |} \\sum_ {x _ {t} \\in \\mathcal {X} _ {t}} \\log C (F (x _ {t})) (\\hat {y} _ {t}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 325, + 892, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this way, the model's adaptability can be enhanced by relearning the knowledge of the pseudo-labels in the target domain. However, using Eq. 2 tends to interfere with training because the pseudo-labels contain massive noise. Thus, some works select high-confidence pseudo-labels by setting threshold $\\zeta^k$ for each class,", + "bbox": [ + 496, + 373, + 893, + 464 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {t} = \\left\\{ \\begin{array}{c l} \\arg \\max _ {k} p _ {t} ^ {k}, & \\text {i f} \\max \\left(p _ {t} ^ {k}\\right) > \\zeta^ {k} \\\\ \\text {i g n o r e}, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 474, + 892, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $p_t^k$ is the $k$ -th class probability score. In Eq. 3, the $\\zeta^k$ determines the quality of the selected pixels, which needs to be dynamically adjusted according to the adaptation degree. Thus, in the subsequent works, scholars [58, 4, 51, 1] mainly focus on setting reasonable thresholds or uncertainty estimation strategies to select reliable pixels.", + "bbox": [ + 496, + 518, + 893, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we explore the potential of self-training from another perspective. Different from mining category knowledge in pseudo-labels, we propose to mine relation knowledge in pseudo-relations between pixels. The overview of our method is shown in Fig 3. For the source domain, images are input to the student model, which is optimized by the $L_{s}$ . For the target domain, the original image and its data-transformed version are input into the student model and teacher model, respectively. After that, the output of the teacher model is used to build pseudo-relations $S_{pr}$ to further supervise the student model of category learning by $L_{st}$ and relation learning by $L_{pr}$ . We detail the pseudo-relation $S_{pr}$ building in Sec.3.2, and detail the pseudo-relation learning by optimizing $L_{pr}$ in Sec.3.3.", + "bbox": [ + 496, + 611, + 895, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Pseudo-relation Building", + "text_level": 1, + "bbox": [ + 500, + 832, + 728, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the supervised segmentation task, relations can be driven by ground truth, which is not achievable for the UDA segmentation. Thus, how to build the relations between", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19193", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/473a1abc6e400ec0d63067a55eacaca6a37b13009b17961de2247b38a1bc59ab.jpg", + "image_caption": [ + "Figure 3: The overall pipeline of the proposed Relation Teacher that includes a student model and a teacher model. $S_{low}$ , $S_{high}$ and $S_{pr}$ represent low-level relation matrix, high-level relation matrix and pseudo-relation matrix. $L_{st}$ is the traditional loss function for pseudo-label learning. $L_{pr}$ is the proposed loss function for pseudo-relation learning." + ], + "image_footnote": [], + "bbox": [ + 101, + 97, + 857, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "pixels in the target domain is the key. A naive solution is to build by measuring the class similarity between pseudolabels from a pre-adapted model. Given any two pixels $p_{(t,i)}$ and $p_{(t,j)}$ ( $i,j = 0,1,2,\\dots,w\\times h$ ) on the class probability map $p_t\\in \\mathbb{R}^{h\\times w\\times K}$ of the target domain, the high-level relation between them can be defined as,", + "bbox": [ + 75, + 433, + 470, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {(i, j)} = \\operatorname {S I M} \\left(p _ {(t, i)}, p _ {(t, j)}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 537, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{SIM}(\\cdot ,\\cdot)$ is the cosine similarity measure. Extending this relation to all pixels in an image, we can derive a highlevel relation matrix $S = \\{s(i,j)\\} \\in \\mathbb{R}^{hw\\times hw}$ . However, such a relation modeling mechanism will introduce massive noise due to the unadapted model. As mentioned in reliable local relations prior, these noises are mainly in the long-distance relations but relations in local grids are relatively accurate.", + "bbox": [ + 75, + 566, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, we devise a local relation modeling mechanism. We divide the target image into $N\\times N$ grids $\\{G_l\\}_{l = 1}^{hw / N^2}$ and model the relations inside the grid. Then the high-level relation matrix for each grid can be obtained,", + "bbox": [ + 76, + 686, + 470, + 752 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {h i g h} = \\left\\{s _ {(m, n)} \\right\\} _ {(m, n) \\in G _ {l}} \\in \\mathbb {R} ^ {N ^ {2} \\times N ^ {2}}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 763, + 468, + 782 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Nonetheless, local pseudo-relations may still contain noise due to domain shifts.", + "bbox": [ + 75, + 794, + 468, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further mitigate unreliable relations in local grids, we introduce low-level relation constraints in each grid. The motivation stems from available low-level relations prior that local low-level relations (RGB space) can be well used to capture the edges and internal structures of", + "bbox": [ + 75, + 824, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "objects. Drawing on the traditional potential energy function constructing the potential energy field [43, 44, 38], we use the Gaussian function to calculate the energy on the RGBXY[43] space as low-level relation constraints,", + "bbox": [ + 496, + 433, + 892, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {l o w} = \\left\\{\\Psi_ {(m, n)} \\right\\} _ {(m, n) \\in G _ {l}} \\in \\mathbb {R} ^ {N ^ {2} \\times N ^ {2}},\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 513, + 826, + 535 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Psi (m, n) = \\exp \\left(- \\left| \\frac {I _ {m} - I _ {n}}{\\sigma} \\right| ^ {2}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 537, + 890, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I_{(\\cdot)}$ is the feature vector on RGBXY space, $\\sigma$ is the bandwidth parameter of the Gaussian function. Due to the nature of the Gaussian function[16], the value range of the $S_{low}$ are [0, 1], which is the same as that of $S_{high}$ . A higher value indicates a stronger association between pixels. Although it lacks high-level semantics, it can better regularize relations (See Tab. 4 for verification). We linearly combine the low- and high-level relations as final pseudo-relations,", + "bbox": [ + 496, + 592, + 892, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {p r} = \\alpha S _ {l o w} + (1 - \\alpha) S _ {h i g h}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 734, + 890, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the $\\alpha$ is a hyper-parameter and is simply set to 0.5.", + "bbox": [ + 500, + 773, + 879, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Pseudo-relation Learning", + "text_level": 1, + "bbox": [ + 500, + 811, + 732, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following the paradigm of pseudo-label learning, we can exploit the reliable relations in the pseudo-relation matrix to perform pseudo-relation learning. Specifically, for any pixel pair $p_{(t,i)}$ and $p_{(t,j)}$ in $l$ -th grid, we can perform a pairwise", + "bbox": [ + 496, + 839, + 892, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19194", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "relation loss [24, 17] in a pseudo manner as follows,", + "bbox": [ + 76, + 90, + 424, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {L} _ {p r} = \\sum_ {l} \\sum_ {i, j} \\operatorname {K L} \\left(p _ {(t, i)} \\mid \\mid p _ {(t, j)}\\right) \\cdot \\mathbb {1} \\left(S _ {p r; l} (i, j) > M _ {u p}\\right) + \\\\ (1 - \\mathrm {K L} (p _ {(t, i)} | | p _ {(t, j)})) \\cdot \\mathbb {1} \\left(S _ {p r; l} (i, j) < M _ {l o w}\\right). \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 118, + 468, + 184 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathrm{KL}(\\cdot ||\\cdot)$ is the Kullback-Leibler divergence between two distributions. $\\mathbb{1}(\\cdot)$ is the indicator function for thresholding. $M_{up}$ and $M_{low}$ are upper and lower thresholds for filtering unreliable relations. Optimizing this loss pulls the class distribution of the pixel pairs with a pseudo-relation higher than $M_{up}$ closer and pushes those with a pseudorelation lower than $M_{low}$ further away. In this way, pseudorelation learning can assist pseudo-label learning (in Eq.2) in the following aspects. Let the pixels used by Eq.2 be denoted as reliable pixels, and the rest are unreliable ones. 1). Relations between reliable pixels. Those reliable inter- and intra-class relations are informative and can be incorporated into learning as structural inference. 2). Relations between reliable and unreliable pixels. Pushing or Pulling the class probabilities of the unreliable pixels towards reliable ones will greatly enhance the confidence of the model. 3). Relations between unreliable pixels. Although we cannot give these pixel pairs explicit class targets, implicit class cues may help the model to enhance confidence. See further instructions in Appendix A.", + "bbox": [ + 75, + 185, + 468, + 487 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, in $\\hat{L}_{pr}$ , the pair of class distribution input to $\\mathrm{KL}(\\cdot ||\\cdot)$ should assign the more sharp one as the target. This makes it require pair-by-pair index calculation, which greatly increases the training time. Besides, $M_{up}$ and $M_{low}$ requires hyper-parameter search under different adaptation tasks, hindering the flexibility of application. Here, we learn from the idea of graph cut [57] and devise a new pseudorelation loss, which can be performed by matrix multiplication without explicit thresholding.", + "bbox": [ + 75, + 487, + 468, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, in $l$ -th grid, we construct an undirected weighted graph $\\mathcal{G}$ , treating all pixels in this grid as nodes of the graph and the similarity between these pixels as the weights of edges. Thus, the corresponding $S_{pr;l}$ can be seen as a pseudo-adjacency matrix of the $\\mathcal{G}$ . With the $\\mathcal{G}$ , the $K$ classification problem is regarded as a graph cutting problem of cutting a graph into $K$ subgraphs. Then, the $k$ -th class probability $p_{t;l}^{k}$ of this grid is regarded as the probability of the corresponding nodes cut into $k$ -th subgraph ( $k \\in [0, K - 1]$ ). According to the properties of the graph, we can calculate the soft cost of cutting the $k$ -th subgraph as follows,", + "bbox": [ + 75, + 623, + 468, + 804 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nc u t ^ {k} = \\hat {p} _ {t; l} ^ {k} S _ {p r; l} \\mathbf {1} - \\hat {p} _ {t; l} ^ {k} S _ {p r; l} \\left(\\hat {p} _ {t; l} ^ {k}\\right) ^ {T}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 816, + 468, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\hat{p}_{t;l}^{k}\\in \\mathbb{R}^{1\\times N^{2}}$ is the vector flatten by $p_{t;l}^{k}\\in \\mathbb{R}^{1\\times N\\times N}$ $\\mathbf{1}\\in \\mathbb{R}^{N^2\\times 1}$ is an all-ones vector. We show an example to illustrate Eq.9 in Fig.4. The smaller the cut value, the smaller", + "bbox": [ + 76, + 848, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/be8373f0132529ceab12448f66dc6f2fd88cb209f7ed25b8f2b389c492cab8c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 553, + 93, + 679, + 172 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} P ^ {0} S 1: \\text {- - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - } \\\\ P ^ {0} S P ^ {0}: \\text {- - } \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 174, + 699, + 205 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{c} \\hline P: \\text {c l a s s p r o b a b i l i t y} \\\\ p _ {1} \\quad 1 \\quad 0 \\\\ p _ {2} \\quad 1 \\quad 0 \\\\ p _ {3} \\quad 1 \\quad 0 \\\\ p _ {4} \\quad 0 \\quad 1 \\\\ p _ {5} \\quad 0 \\quad 1 \\\\ S: \\text {a d j a c e n c y m a t r i x} \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 709, + 93, + 846, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 4: We show an example of binary classification to illustrate Eq.9. Given five samples and their class probability $P$ , take the cut of class 0 as an example. $P^0 S1$ is the sum of all edges connected to the nodes of class 0, i.e., the green and dashed lines. $P^0 SP^0$ is the sum of all edges connecting two nodes of class 0, i.e., the green lines, and $P^0 S1 - P^0 SP^0$ is the cost consumed of the 0 class. To minimize the cost, nodes with high affinity should be classified into the same class, and vice versa.", + "bbox": [ + 496, + 220, + 890, + 356 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the correlation between the subgraphs and the larger the correlation within the subgraphs. Thus, $cut^k$ can be regarded as a proxy, when the $cut^k$ value is small, the class probability $p_{t;l}^k$ better conforms to the pseudo-relations $S_{pr;l}$ , and vice versa. Moreover, the Eq.9 is derivable with respect to $p_{t;l}^k$ , and its gradient w.r.t. $p^k$ is,", + "bbox": [ + 496, + 371, + 890, + 463 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial c u t ^ {k}}{\\partial p ^ {k}} = S _ {p r} \\left(\\mathbf {1} - 2 p ^ {k}\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 474, + 890, + 510 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proxy's gradient is proportional to the $S_{pr}$ and $1 - 2p^{k}$ , which implicitly weight high-confidence relations and reliable pixels (class probability far from 0.5). This explains that unreliable edges (relations) on the graph play a minor role in pulling or pushing away the class distribution, enabling adaptive weighting without threshold. Consequently, we modify Eq.9 as a threshold-free pseudo-relation loss function to optimize $p_t$ as follows,", + "bbox": [ + 496, + 521, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {p r} = \\sum_ {l} ^ {h w / N ^ {2}} \\sum_ {k} ^ {K} \\hat {p} _ {t; l} ^ {k} S _ {p r} \\left(\\mathbf {1} - \\hat {p} _ {t; l} ^ {k}\\right) ^ {T}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 654, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$L_{pr}$ can be calculated using matrix multiplication in a simple and quick way.", + "bbox": [ + 498, + 708, + 890, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Relation Teacher", + "text_level": 1, + "bbox": [ + 500, + 748, + 666, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We embed the learning of pseudo-relation into the optimization of mean-teacher [45] framework to realize online self-training as shown in Fig 3. The final optimization objective is,", + "bbox": [ + 496, + 771, + 890, + 830 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {f} = L _ {s} + \\lambda_ {s t} L _ {s t} + \\lambda_ {p r} L _ {p r}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 832, + 890, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{pr}$ , $\\lambda_{st}$ are the trade-off coefficients. $\\lambda_{st}$ is set as 0.001 following SAC [1]. $\\lambda_{pr}$ is empirically set to 0.01 to balance the loss value.", + "bbox": [ + 496, + 854, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19195", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a6e65c2147de9298f52b0de270d45be97688f64c1448a8fc9e6200750b66648b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodroadsidewalkBuildingWallfencepolelightsignvege.terrainskypersonridercartruckbustrainmbikebikemIoU
FADA (ECCV 2020) [50]91.050.686.043.429.836.843.425.086.838.387.464.038.085.231.646.16.525.437.150.1
FDA (CVPR 2020) [60]92.553.382.326.527.636.440.538.882.239.878.062.634.484.934.153.116.827.746.450.4
IAST (ECCV 2020) [37]93.857.885.139.526.726.243.134.784.932.988.062.629.087.339.249.623.234.739.651.5
MetaCorr (CVPR 2021) [10]92.858.186.239.733.136.342.038.685.537.887.662.831.784.835.750.32.036.848.052.1
RPT (CVPR 2021) [66]89.243.386.139.529.940.249.633.187.438.586.064.425.188.536.645.823.936.556.852.6
SAC (CVPR 2021) [1]90.453.986.642.427.345.148.542.787.440.186.167.529.788.549.154.69.826.645.353.8
CFDAN (CVPR 2021) [36]92.558.386.527.428.838.146.742.585.438.491.866.437.087.840.752.444.641.759.056.1
SDFA (ICCV 2021) [26]94.859.486.240.529.525.543.834.785.934.989.563.430.888.342.650.725.335.740.952.8
ProDA (CVPR 2021) [64]87.85679.746.344.845.653.553.588.645.282.170.739.288.845.559.41.048.956.457.5
SimT (CVPR2022) [9]94.26088.530.339.741.247.860.888.647.389.371.545.090.754.260.20.051.858.458.9
CPST (CVPR 2022) [28]92.359.984.945.729.752.861.559.587.941.585.073.035.590.448.773.926.353.853.960.8
Undoing (CVPR 2022) [31]92.952.787.239.441.343.95552.989.348.291.271.43690.267.959.8048.559.359.3
DAP (CVPR 2022) [21]94.563.189.129.847.550.456.758.789.550.28773.638.691.350.252.9050.263.559.8
CaCo (CVPR 2022) [18]93.864.185.743.742.246.150.154.088.74786.568.12.988.043.460.131.546.160.958.0
ADPL (TPAMI 2023) [3]93.460.687.545.332.637.343.355.587.244.88864.534.288.352.661.849.841.859.459.4
RTea (Ours)95.467.187.946.144.046.053.859.589.749.889.871.540.590.855.057.922.147.762.561.9
Daformer (CVPR 2022) [14]95.770.289.453.548.149.655.859.489.947.992.572.244.792.374.578.265.155.961.868.3
Daformer + RTea (Ours)96.171.789.157.850.455.959.366.790.448.294.574.846.593.878.781.665.857.162.870.6
HRDA (ECCV 2022) [15]96.474.491.061.651.557.163.969.391.348.494.279.052.993.984.185.775.963.967.573.8
HRDA + RTea (Ours)97.175.292.663.551.858.266.571.291.149.096.881.554.294.284.886.675.762.266.774.7
", + "bbox": [ + 81, + 89, + 890, + 340 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d9e2e6201fc238724ffced8d113aad744164e5ee18cae5b2e508894fd3185ebf.jpg", + "table_caption": [ + "Table 1: Experimental results for GTA5 $\\rightarrow$ Cityscapes adaptation task. The best results in every column are highlighted." + ], + "table_footnote": [], + "table_body": "
MethodroadsidewalkBuildingWall*fence*pole*lightsignvege.skypersonridercarbusmbikebikemIoUmIoU*
FADA (ECCV 2020)[50]84.540.183.14.8034.320.127.284.88453.522.685.443.726.827.845.252.5
FDA (CVPR 2020) [60]79.335.073.2---19.924.061.782.661.431.183.940.838.451.1-52.5
IAST (ECCV 2020) [37]81.941.583.317.74.632.330.928.883.485.065.530.886.538.233.152.749.857.0
MetaCorr (CVPR 2021) [10]92.652.781.38.92.428.113.07.383.585.060.119.784.837.221.543.945.152.5
RPT (CVPR 2021) [66]88.946.584.515.10.538.539.530.185.985.859.826.188.146.827.756.151.258.9
SAC (CVPR 2021) [1]89.347.285.526.51.343.045.532.087.189.363.625.486.935.630.453.052.659.3
CFDAN (CVPR 2021) [36]75.730.081.911.52.535.318.032.786.290.165.133.283.336.535.354.348.255.5
SFDA (ICCV 2021) [26]90.550.081.613.32.834.725.733.183.889.266.034.985.353.446.146.652.060.1
ProDA (CVPR 2021) [64]87.845.784.637.10.644.054.637.088.184.474.224.388.251.140.545.655.562.0
CPST (CVPR 2022) [28]87.243.985.533.60.347.757.437.287.888.579.032.090.649.450.859.857.965.3
Undoing (CVPR 2022) [31]82.537.281.123.8045.757.247.687.785.874.128.688.466.047.055.356.764.5
CaCo (CVPR 2022) [18]87.448.979.68.80.230.117.428.379.981.256.324.278.639.228.148.346.053.6
ADPL (TPAMI 2023) [3]86.138.685.929.71.336.641.347.28590.467.544.387.457.143.951.455.963.6
RTea (ours)93.259.686.331.34.843.141.844.088.690.570.442.689.556.740.259.958.966.4
Daformer (CVPR 2022) [14]84.540.788.441.56.550.05554.68689.873.248.287.253.253.961.767.460.9
Daformer + RTea (Ours)85.943.290.145.16.352.460.557.187.892.275.351.887.455.954.162.669.563.0
HRDA (ECCV 2022) [15]85.247.788.849.54.857.265.760.985.392.979.452.88964.763.964.972.465.8
HRDA + RTea (Ours)87.849.090.350.35.558.666.061.486.893.179.553.189.565.163.764.673.066.5
", + "bbox": [ + 81, + 371, + 890, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2: Experimental results for SYNTHIA $\\rightarrow$ Cityscapes adaptation task. The best results in every column are highlighted. The mIoU and mIoU* are averaged over 16 and 13 categories, respectively.", + "bbox": [ + 78, + 623, + 890, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 78, + 675, + 200, + 693 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Experimental Setup", + "text_level": 1, + "bbox": [ + 78, + 703, + 369, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We use one real dataset (Cityscapes [5]) and two synthetic datasets (GTA5 [40] and SYNTHIA [42]). The Cityscapes dataset contains 2,975 training images and 500 validation images of resolution $2048 \\times 1024$ . The GTA5 dataset contains 24,966 images with resolution $1914 \\times 1052$ and has 19 common categories with Cityscapes. The SYNTHIA dataset contains 9,400 images with resolution $1280 \\times 760$ and has 16 common categories with Cityscapes.", + "bbox": [ + 78, + 729, + 467, + 851 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We adopt Deeplab-v2 [2] as the base network, ResNet-101 [11] as the feature extractor and the aspp [2] module as the classifier. The network is pre", + "bbox": [ + 78, + 854, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "trained on ImageNet. The optimizer is SGD with the momentum of 0.9 and weight decay of $10^{-4}$ . The initial learning rate is set to $2.5 \\times 10^{-4}$ , and then is reduced following a poly policy with a power of 0.9. The batch size is set as 4. The final $\\lambda_{f}$ and $\\lambda_{o}$ values are set to 0.025 and 0.005, respectively. We apply the $L^{pr}$ to the model's output class probability, which is 8 times smaller than the original resolution. And the grid size $N$ is set to 8. The weighting factor $\\alpha$ is set to 0.5. The $\\sigma$ for XY and RGB space in Gaussian function is set to 6 and 0.1, following [43]. Data augmentation strategies performed on the data input to the student model include random flipping, Gaussian noise, color transformation, cutout[6], and contrast enhancement, a similar and common operation in online self", + "bbox": [ + 501, + 676, + 890, + 888 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19196", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "training methods [58, 4, 51, 1]. Besides, we also preform the class-mixing resampling strategy [47] on the source domain to focus on the minority class. When performing $L_{st}$ for pseudo-label learning, we adopt the thresholding selection method in SAC [1] to pick high-quality samples. After training with Rtea, we retrained the model using the distillation strategy [64] for better adaptation, which is commonly used in recently published UDA work [31, 21, 28, 3]. The detailed scores for each stage are in the Tab. 3. Our network is trained with four RTX3090 GPUs on PyTorch.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparisons with State-of-the-Arts", + "text_level": 1, + "bbox": [ + 76, + 255, + 390, + 272 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\mathrm{GTA5} \\rightarrow \\mathrm{Cityscapes}$ . We report the comparison results with existing methods on $\\mathrm{GTA5} \\rightarrow \\mathrm{Cityscapes}$ task in Tab. 1. We compared two structures based on resnet-101 and transformer structures. Overall, our RTea achieves new state-of-the-art performance than related works, and the category performance scores are also highly competitive, demonstrating the effectiveness of RTea. Compared with the domain alignment method, the performance of RTea show an advantage over the state-of-the-art method FDA [60] by $11.5\\%$ . Compared with the offline self-training method, the mIoU score of RTea is $10.4\\%$ and $9.8\\%$ higher than IAST [37] and RPT[66]. Compared with the online self-training method, RTea exceeds SAC [1] and ProDA [64] by $8.1\\%$ and $4.4\\%$ . Compared with the newly released method Undoing[31], DAP[21] and ADPL[3], our RTea still outperforms these methods by more than $2.0\\%$ mIoU scores, showing the potential of our method even more. Compared with the method of transformer structure, our method improves the mIoU score by $0.7\\%$ and $0.9\\%$ on Daformer [14] and HRDA [15] respectively, which shows that RTea has good scalability and transferability. Qualitative results on both tasks can be found in Appendix B.", + "bbox": [ + 75, + 279, + 472, + 613 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SYNTHIA $\\rightarrow$ Cityscapes. The results of using SYNTHIA as the source domain are reported in Tab. 2, including mIoU/mIoU* covering 16/13 classes. On the whole, our method still achieves significant improvements, showing gains over advanced methods. In particular, SYNTHIA and Cityscapes suffer from significant visual domain differences in 'road', and 'sidewalk', which leads to the poor performance of the most UDA methods in these categories. Our method uses the pseudo-relations of these categories and achieves higher performance improvements, and we argue this is due to the local pseudo-relation learning to better capture the structure of these categories. Compared with the domain alignment and offline self-training methods, RTea maintains similar performance gains to the GTA5 transfer task. Compared with online self-training method, we achieve better performance than CPST [28] over 16 and 13 classes, exceeding its by $1.0\\%$ and $1.1\\%$ mIoU score. Compared with the adaptation method using transformer structure, our method improves the mIoU score by $2.1\\%$ and", + "bbox": [ + 75, + 613, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/09359220b81cbba30eabb4fc0315f5718fa7eff8fc7b8ca5650b1794b0e48260.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3: Ablation experiments of each module in GTA5 and SYNTHIA $\\rightarrow$ Cityscapes adaptation task. The basic self-training $(L_{s} + L_{st})$ is following SAC[1]. The copy-paste means that we adopt the resampling strategy in [47] for minority learning. Here, we report a result of $\\hat{L}_{pr}$ with the fine-tuned thresholds by grid search. $L_{pr}^{s}$ denotes that relation learning is performed on the source domain. Dist denote the distillation strategy in [50, 64]. All numbers are mIoU(%) score." + ], + "table_body": "
\\(L_s\\)\\(L_{st}\\)copy-paste\\(\\hat{L}_{pr}\\)\\(L_{pr}\\)\\(L_{pr}^s\\)DistGTA5SYNTHIA
✓✓53.551.2
✓✓✓55.853.9
✓✓✓✓58.956.3
✓✓✓✓59.656.8
✓✓✓✓✓59.656.9
✓✓✓✓✓✓61.958.9
", + "bbox": [ + 504, + 88, + 893, + 183 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$0.7\\%$ on Daformer [14] and HRDA [15], which further verifies the effectiveness of the method.", + "bbox": [ + 496, + 345, + 890, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 498, + 390, + 665, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation for Each Module. Tab.3 reports the ablation results for different modules. We adopt SAC [1] with the copy-paste [47] argumentation as the baseline, achieving the $55.8\\%$ and $53.9\\%$ mIoU score on two adaptation tasks. Overall, Rtea achieves $3.8\\%$ and $3.0\\%$ performance improvements on the two tasks on this competitive baseline, respectively, showing the effectiveness of the pseudorelation learning. Specifically, the naive $\\hat{L}_{pr}$ loss, although, can improve performance, the screening of the threshold makes it difficult to be directly applied to practice, because the threshold may be very sensitive in different adaptation scenarios. The proposed $L_{pr}$ loss does not require explicit threshold while improving the performance, showing its flexibility and effectiveness. In addition, we also tried to perform pseudo-relation learning on the source domain $L_{pr}^{s}$ , and we did not find a significant performance improvement, which may be because it cannot directly benefit the target domain. After training with RTea, the self-distillation method can still be used to further improve the adaptability of the model in the target domain.", + "bbox": [ + 496, + 415, + 893, + 718 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation for Pseudo-Relation Building. Tab.4 shows the ablation results for building pseudo-relation. When the relations are built on RGBXY space ( $S_{low}$ ), the performance achieves a good improvement, $2.0\\%$ and $2.1\\%$ on two tasks, respectively, which suggests that low-level relations on local grids can propagate effective category knowledge. When the relations are built on pseudo labels ( $S_{high}$ ), the performance is only improved by $1.0\\%$ and $0.7\\%$ on two tasks, respectively. This is because it is not easy to find valuable relation pairs in this way, and their effects may overlap with label learning. Specifically, unreliable pixels discarded by pseudo-label learning are still difficult to use, and high", + "bbox": [ + 496, + 719, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19197", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/eb134efebcfd42447a14b6dbc6b6f64912203620c7430038b9a234befc387d6c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SlowShighSprGTA5SYNTHIA
✓55.853.9
57.855.8
✓56.854.6
✓59.656.8
", + "bbox": [ + 133, + 88, + 416, + 172 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/170949ac746fa524fd08d26950acbac38b9e9f2729edcc4cdfb0f5e3c35bf58c.jpg", + "table_caption": [ + "Table 4: Ablation experiments on the pseudo-relation building. $S_{low}$ , $S_{high}$ and $S_{pr}$ are low-level, high-level and final pseudo relation matrix." + ], + "table_footnote": [], + "table_body": "
R-RR-UU-UGTA5SYNTHIA
55.853.9
✓✓58.255.2
✓✓57.254.9
✓✓59.356.6
✓✓✓59.656.8
", + "bbox": [ + 133, + 233, + 416, + 319 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "confidence relationships still contain massive noise, When $S_{low}$ and $S_{high}$ are combined, the best effect is achieved. We argue that the advantage is that, the noisy relations in the high level are corrected and the lack of semantics of the low-level relations is also made up, and more unreliable pixels are better exploited.", + "bbox": [ + 75, + 409, + 468, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation for Pseudo-Relation Learning. To verify the effect of different pixel pairs on pseudo-relation learning, we devise the ablation study in Tab. 5. We follow 1), 2) and 3) explained in the Eq. 8, and divide them into R-R (two reliable pixels), R-U (one reliable and one unreliable pixel) and U-U (two unreliable pixels). During training, we clear all gradients for one of the pairs to verify its effect on adaptation. We find that R-U pairs play the most important role in adaptation, R-R pairs come second, and U-U pairs come last. We analyze learning R-U pairs can make full use of valuable pixels from unexploited target domains, which is the most direct to enhance the target domain adaptability.", + "bbox": [ + 75, + 500, + 470, + 683 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Discussion", + "text_level": 1, + "bbox": [ + 76, + 694, + 194, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sensitivity for reliable sample selection. In this section, we perform two experiments to explore how sensitive RTea is to reliable sample selection. First, we report the results when the parameters of the heuristic threshold (Eq. 3) are varied. The thresholding strategy consists of two hyperparameters, namely the upper threshold $\\theta$ and the decay rate $\\beta$ . Table 6 shows that our method maintains a stable performance improvement when thresholding parameters vary within a certain range. Second, we report Rtea's performance on different reliable sample selection methods in Table 7. It verifies the effectiveness of RTea, which improves the performance of different self-training methods.", + "bbox": [ + 75, + 719, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5193f69ccf2745ccdd13b0e21d08f5ec29139797b96916108d72d1d83e70b043.jpg", + "table_caption": [ + "Table 5: Ablation experiments on the pseudo-relation learning. $R - R$ denotes pairs with two reliable pixels. $R - U$ denotes pairs with one reliable and one unreliable pixel. $U - U$ denotes pairs with two unreliable pixels." + ], + "table_footnote": [], + "table_body": "
β=0.0001β=0.001β=0.01
θ=0.7559.059.258.8
θ=0.8059.259.659.1
", + "bbox": [ + 534, + 89, + 857, + 147 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/005d97ee13dc40e799e9350d81c9d9ad0918026a43cda6797475bd8a2071c1fc.jpg", + "table_caption": [ + "Table 6: The mIoU scores (\\%) on GTA5 → Cityscapes task with varying thresholding parameters in Eq. 3." + ], + "table_footnote": [], + "table_body": "
PDCDADHT
without Rtea55.054.453.255.8
with Rtea58.856.854.859.6
", + "bbox": [ + 542, + 193, + 849, + 250 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "How local grids affect each relation pair. We perform experiments on $\\mathrm{GTA5} \\rightarrow$ Cityscapes to verify which relation pairs are most affected by local grids. Pixels are still classified as reliable (R) and unreliable (U) according to whether they are used for category learning in traditional self-training, see Tabel 8. In the first line, we find that (1) the global grid is good for $R - R$ because it extends the spatial scope of relational learning, while it does harm to $R - U$ and $U - U$ due to the long-range relation noise. As a result, performing pseudo-relation learning on global region lead model degradation. In the second line, we argue that (2) performing pseudo-relation on the local grids slightly reduces the gain of $R - R$ , but greatly reduces the interference of noise on $R - U$ and $U - U$ . Finally, the model can obtain better performance improvement.", + "bbox": [ + 496, + 353, + 890, + 582 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fb7169564afea66dd16b50eab4223a0a0c11b153b4e0d0e605cdf7a8a73dec8c.jpg", + "table_caption": [ + "Table 7: The mIoU scores (\\%) on GTA5 → Cityscapes task with different reliable sample selection strategies. PD denotes feature-prototype distance [64], CD denotes classifier discrepancy [69], AD denotes adversarial difficulty [34] and HT is our used heuristic threshold [1]." + ], + "table_footnote": [], + "table_body": "
BaselineR-RR-UU-U
Global55.857.2 (+1.4)51.4 (-4.4)52.5 (-3.3)
Local grid55.856.6 (+0.8)57.9 (+2.1)55.9(+0.1)
", + "bbox": [ + 503, + 592, + 887, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8: The mIoU (%) of local grids effect on GTA5 → Cityscapes adaptation task.", + "bbox": [ + 498, + 642, + 888, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Computational overhead. Performing relation learning on dense prediction tasks such as semantic segmentation is time-consuming. Therefore, it is necessary to discuss the computational overhead introduced in Rtea. Overall, we think the pseudo-relation computational overhead is acceptable. First, for complexity, our computational cost is $\\mathcal{O}(N^2 WH)$ ( $H, W$ : width and height of feature map, $N$ : grid size, $N \\ll W, H$ ), which is greatly reduced compared to the global similarity $\\mathcal{O}(W^2 H^2)$ . Second, the pseudorelation can be computed in parallel using matrix operations in PyTorch. On a Nvidia RTX-3090, it only takes almost 40 ms for each batch and only increases about $3\\%$ computational overhead in each iteration. Third, the cost is only for training and not for inference.", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19198", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Align low- and high-level relation matrix with the same Gaussian function. In the method section, we use the cosine distance (Eq. 5) and Gaussian distance (Eq. 6) to model the similarity of high- and low-level, respectively. It is interesting to explore unifying the modeling of high- and low-level pseudo-relations into the same metric function, e.g. Gaussian distance. With the same metric function, for any local grid $G_{l}$ , the local relation can be built as, $s(m,n) = \\sum_{m,n\\in G_l}\\Psi_{\\sigma_{rgbxy}}(m,n)\\cdot \\Psi_{\\sigma_{prob}}(m,n)$ , where $\\sigma_{rgbxy}$ and $\\sigma_{prob}$ are the bandwidth of the low- and highlevel Gaussian function. This formula is similar to the kernels of bilateral filtering[46], inspiring us to understand the pseudo-relation learning from the filtering perspective, i.e. smoothing and correcting the noise on output probability. Table 9 presents the comparison results, showing unifying the same metric function can maintain performance with less computational overhead.", + "bbox": [ + 76, + 90, + 472, + 349 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/bbf98614b8fe9e02f789a8f41259312e970ed8025d315b0e257922461cf5f05c.jpg", + "table_caption": [], + "table_footnote": [ + "Table 9: The mIoU (\\%) and computational cost (time/batch) using different similarity metric functions on GTA5 → Cityscapes adaptation task." + ], + "table_body": "
MetricGTA5SYN.TimeMetricGTA5SYN.Time
Current59.656.940msSame Gaussian59.657.129ms
", + "bbox": [ + 78, + 358, + 465, + 388 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Hyper-parameters Impacts. We analyze the sensitivity of the hyper-parameters $\\alpha$ (trade-off coefficient), grid size $N$ , the results are presented in the Appendix C.", + "bbox": [ + 76, + 446, + 470, + 494 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.5. Visualization", + "text_level": 1, + "bbox": [ + 76, + 500, + 215, + 513 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Visualization of pixel relations. Fig. 5 visualizes the learned relations on $\\mathrm{GTA5} \\rightarrow$ Cityscapes task. Comparing Fig. 5 a, b and e, it shows that the feature associations of the baseline are chaotic while our method builds more accurate feature relations. Comparing Fig. 5 c, d and e, it indicts that our method captures category relations more accurately than baseline, resulting in more structured outputs.", + "bbox": [ + 76, + 522, + 468, + 628 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Comparison of Pixel Utilization and Model Confidence. Fig. 6 compares the correct pixel utilization (PU) and average confidence (AC) of the model before and after adding RTea. With RTea, the PU is significantly improved and the AC also shows better results. It illustrates RTea can exploit more uncertain pixels around high-confidence pixels and propagate relation information to them, thereby fully improving the certainty of the model.", + "bbox": [ + 76, + 628, + 468, + 748 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Visualization of Pseudo-Labels. Fig. 7 visualizes the pseudo-labels of the baseline and our RTea to demonstrate the benefits of pseudo-relation learning. It shows that the RTea makes better use of pseudo-labels than the baseline model. For the areas are hard to distinguish (framed by the red box), RTea can enlarge the reliable pseudo-label area by capturing relations between pixels. Moreover, RTea provides clear class boundaries for the classes such as roads, sidewalks and buildings, which is more helpful for pseudolabel learning.", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/5811ba1309e25558465de4962c75567ef1d6d781b81175932656aeac564bc93e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 89, + 651, + 145 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/93b8535da3c7ecf7d5f66ff92ccba366e225fab53bc68672da7b2db7551521d1.jpg", + "image_caption": [ + "Figure 5: Visualization of the learned relations of RTea model on the GTA5 $\\rightarrow$ Cityscapes task." + ], + "image_footnote": [ + "a. Feature relations of baseline b. Feature relations of RTEca" + ], + "bbox": [ + 511, + 145, + 651, + 199 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/3b45fd8d5e52f3fe52b75908055f8fcc3ef0a3285cbaa97e00b1e9f26c9ce9bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 653, + 90, + 725, + 143 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/637f7bd81d8c696b3643b9fda29bdd1902b90058885522ea3b14ea802d20a57f.jpg", + "image_caption": [], + "image_footnote": [ + "c. Prediction relations of baseline" + ], + "bbox": [ + 653, + 145, + 725, + 199 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/09ec71f09fc6ec23459b00ac2125bb6d1cd1180aa727eb158e35a6d311648258.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 725, + 90, + 799, + 145 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/d3519cce78b15802a00fbe117bfa2ae47776833e75aa615a4df7d27f6b7b37f4.jpg", + "image_caption": [], + "image_footnote": [ + "d. Prediction relations of RTea." + ], + "bbox": [ + 725, + 145, + 799, + 199 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/43282e3b971dd54296185c03edcc8e4660a4b07d5bb05fcd7346c5fb2f05226a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 799, + 90, + 890, + 145 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/41d31133db4cf8311826f3cd7e4086ea77f38cbfdad7415676e85de6b7ea521e.jpg", + "image_caption": [], + "image_footnote": [ + "c. Relations of ground truth" + ], + "bbox": [ + 799, + 145, + 890, + 199 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/6a9fddb6865fac27d7c76ba275346c8d6b159165e6c213fe4ec164146431b623.jpg", + "image_caption": [ + "Figure 6: Comparison of the average correct pixel utilization and confidence of the target domain." + ], + "image_footnote": [], + "bbox": [ + 501, + 267, + 697, + 377 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/3d7d148a51cbe8305f2e5a344dd9bdbcc72051626259ca8158c2f76a368ca598.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 268, + 890, + 377 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/b539d5eb420839cfccd88c0dde3278b7ca547a2768371d6dc26fe7fc98676120.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 420, + 697, + 500 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/88e8c1907e5d1ce50caed4c169363a75a06583009c03d568c288177b8809c5c9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 500, + 697, + 577 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/41e402e599a716e68b26e55dc1443d20b1ae93e81877f75dd6a26368040ddfa8.jpg", + "image_caption": [ + "a. Baseline" + ], + "image_footnote": [], + "bbox": [ + 506, + 577, + 697, + 654 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/a52f998cc8ef724e373db891c0d34ba54609e1cf2d2cba03e61359a8d12da073.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 420, + 890, + 500 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/64be5e7ef81f1b5783565b42e056d8cca4268298191f6dcd6bbcf3334dedbd63.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 500, + 890, + 577 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/07025181b5cdf0daabeb087cc69f5d7a28d908c9e0946bf095c0bc3fc47b50e5.jpg", + "image_caption": [ + "b. Ours", + "Figure 7: Comparison of pseudo-labels of baseline and RTea. The white masked area is unreliable pseudo-labels." + ], + "image_footnote": [], + "bbox": [ + 697, + 577, + 890, + 654 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 718, + 617, + 734 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we propose pseudo-relation learning framework for UDA semantic segmentation. In RTea, we provide two prior guidelines for pseudo-relation building, which may help more works exploiting pseudo-relations. Moreover, we explore how to use pseudo-relations from the constraints and do detailed analysis and experiments on the proposed solution. Sufficient experiments on two datasets demonstrate the effectiveness of the proposed method. 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In Proceedings of the IEEE/CVF Conference on International Conference on Computer Vision, pages 5982-5991, October 2019. 1, 3" + ], + "bbox": [ + 78, + 90, + 468, + 316 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "19203", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_model.json b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_model.json new file mode 100644 index 0000000000000000000000000000000000000000..65d95fcb9a5dcf70039232ae07dd47756cc756f6 --- /dev/null +++ b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_model.json @@ -0,0 +1,2888 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.136, + 0.131, + 0.834, + 0.154 + ], + "angle": 0, + "content": "Learning Pseudo-Relations for Cross-domain Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.143, + 0.181, + 0.826, + 0.217 + ], + "angle": 0, + "content": "Dong Zhao, Shuang Wang\\(^{\\text{心}}\\), Qi Zang, Dou Quan, Xiutiao Ye, Rui Yang, Licheng Jiao \nSchool of Artificial Intelligence, Xidian University, Shaanxi, China" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.22, + 0.729, + 0.234 + ], + "angle": 0, + "content": "zhaodong01@stu.xidian.edu.cn; shwang@mail.xidian.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.65 + ], + "angle": 0, + "content": "Domain adaptive semantic segmentation aims to adapt a model trained on labeled source domain to unlabeled target domain. Self-training shows competitive potential in this field. Existing methods along this stream mainly focus on selecting reliable predictions on target data as pseudolabels for category learning, while ignoring the useful relations between pixels for relation learning. In this paper, we propose a pseudo-relation learning framework, Relation Teacher (RTea), which can exploitable pixel relations to efficiently use unreliable pixels and learn generalized representations. In this framework, we build reasonable pseudorelations on local grids and fuse them with low-level relations in the image space, which are motivated by the reliable local relations prior and available low-level relations prior. Then, we design a pseudo-relation learning strategy and optimize the class probability to meet the relation consistency by finding the optimal sub-graph division. In this way, the model's certainty and consistency of prediction are enhanced on the target domain, and the cross-domain inadaptation is further eliminated. Extensive experiments on three datasets demonstrate the effectiveness of the proposed method. The code will be available at https://github.com/DZhaoXd/RTea." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.676, + 0.21, + 0.691 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Semantic segmentation is a challenging problem of assigning each pixel a class label in an image. Driven by deep neural networks, significant progress has been made in this field. Despite these efforts, a segmentation model trained with a specific domain does not generalize well to other domains. It is known to be caused by the domain gap between the training (source) and testing (target) domains [13]. To" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.815, + 0.471, + 0.902 + ], + "angle": 0, + "content": "This work is supported by the National Key R&D Program of China under Grant No. 2021ZD0110400, the National Natural Science Foundation of China (No.62271377, No.62201407), the Key Research and Development Program of Shannxi (No.2021ZDLGY01-06, No.2022ZDLGY01-12), the China Postdoctoral Science Foundation (No. 2022M722496), the Foreign Scholars in University Research and Teaching Program's 111 Project (B07048)." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.272, + 0.882, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.36, + 0.88, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.511, + 0.893, + 0.572 + ], + "angle": 0, + "content": "Figure 1: Overview of our motivation. In A, previous self-training methods select reliable pseudo-labels for category learning. In B, our method reasonably utilizes reliable pseudo-labels and unreliable ones for relation learning." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.594, + 0.892, + 0.64 + ], + "angle": 0, + "content": "solve this problem, unsupervised domain adaptation (UDA) is proposed to improve the segmentation model's adaptability to the target domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.893, + 0.748 + ], + "angle": 0, + "content": "Domain alignment is one of the mainstream UDA semantic segmentation methods, aiming to align the distribution of source and target domains in input [30, 60, 25, 4], feature [53, 32, 19, 22, 35, 65, 50, 56], or output spaces [48, 33, 49]. Works along this line achieve positive adaptation benefits but the lack of specific target domain knowledge leads to slight improvement [39, 68, 66]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To this end, self-training methods [27, 10, 1, 69, 64, 67] are proposed to mine target-specific knowledge. These methods use the pseudo-labels generated by the pre-adapted model to further train the model on the target domain. Consequently, the quality of pseudo-labels for training directly determines the performance of self-training. Following this key point, reliability measure-based and uncertainty estimation-based self-training methods are proposed [71, 27, 69, 10, 1, 64, 52]. These methods reduce the noise interference of pseudo-labels for category learning, bring" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19191" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.373, + 0.107 + ], + "angle": 0, + "content": "ing considerable performance improvement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.11, + 0.474, + 0.352 + ], + "angle": 0, + "content": "In this paper, we explore the potential of self-training from another perspective, as shown in Fig. 1. In Fig. 1 A, previous self-training methods perform category learning on reliable pseudo-labels and discard unreliable ones. However, we find that not only category learning but relation learning can be performed in pseudo-labels to further improve the adaptability of the model. In Fig. 1 B, we argue that relation learning in pseudo-labels can be performed in two ways: (1) The relations between reliable pseudo-labels can be additionally used for representation learning to build a more generalized representation space. (2) By establishing the relations between reliable and unreliable pseudolabels, discarded pixels can also be effectively used for self-training to increase the certainty of the model. In this way, the available knowledge contained in pseudo-labels can be fully exploited, both reliable and unreliable pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.473, + 0.702 + ], + "angle": 0, + "content": "To achieve the above goals, building reasonable relations between pixels is the core. Dense pixel relations can be represented by a relation matrix (or affinity matrix) [8, 20, 29], modeling the similarity between pixels on an image. Due to massive noise contained in the pseudo-labels, the relation matrix constructed by them also contain noisy relations. We explore two observational priors to guide the building of relations, as shown in Fig. 2. We use the predictions of the unadapted model for the target images to observe noise distribution of relations. Comparing Fig. 2 (e) and (f), we observe that high-level relations built by pseudo-labels are noisy in long-distance association but are reliable within local areas, which are termed as reliable local relations prior. We analyze this because the insufficiently adapted model cannot transfer global semantics and can only give reasonable relations in local regions. Besides, in Fig. 2(d), we further explore the low-level relations built on each local grid in image space using Gaussian kernel. We find that the low-level relations in local grids can capture the boundaries of objects and contain exploitable relations, which are termed as available low-level relations prior. We argue that such relations, although lacking in semantics, provides class boundary clues can be reasonably exploited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.474, + 0.903 + ], + "angle": 0, + "content": "With these aspects in mind, we propose a pseudo-relation learning-based self-training framework, Relation Teacher (RTea), forcing the student model to learn the pseudo-relations between pixels from the teacher model and achieve co-evolution for both models. In this framework, with the guidance of the above two priors, we first use pseudo-labels to build high-level relations in each divided grid, which avoids being misled by long-distance relationships. Then, we fuse low-level relations in image space into high-level relations to attenuate noisy relations and assist semantic relations in identifying category boundaries. Next, we explore the way of learning pseudo-relations and devise a novel pseudo-relations loss, which optimizes the class" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.627, + 0.143 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.143, + 0.593, + 0.155 + ], + "angle": 0, + "content": "(a).Image" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.09, + 0.765, + 0.143 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.656, + 0.144, + 0.735, + 0.155 + ], + "angle": 0, + "content": "(b).Prediction" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.156, + 0.605, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.216, + 0.568, + 0.23 + ], + "angle": 0, + "content": "↓" + }, + { + "type": "image", + "bbox": [ + 0.644, + 0.156, + 0.754, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.215, + 0.761, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.632, + 0.306, + 0.756, + 0.317 + ], + "angle": 0, + "content": "(e). Relations from Pred." + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.095, + 0.897, + 0.143 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.144, + 0.882, + 0.155 + ], + "angle": 0, + "content": "(c).Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.156, + 0.89, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.817, + 0.204, + 0.856, + 0.212 + ], + "angle": 0, + "content": "similarity" + }, + { + "type": "image", + "bbox": [ + 0.773, + 0.214, + 0.894, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.306, + 0.895, + 0.317 + ], + "angle": 0, + "content": "(f).Relations from GT." + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.323, + 0.61, + 0.335 + ], + "angle": 0, + "content": "Density Bar:" + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.323, + 0.845, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.342, + 0.895, + 0.418 + ], + "angle": 0, + "content": "Figure 2: Overview of two observational priors. (b) is the source-only model's prediction, (d) is the local relation map in image space built by Gaussian kernel in each grid, (e) is the pseudo-relation matrix. (f) is the relation matrix built by ground truth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.892, + 0.542 + ], + "angle": 0, + "content": "probability to meet the relation consistency by finding the optimal sub-graph division from the global pseudo-relation of each class. It has two advantages over the naive relation-learning loss: one is global relational modeling, which can be easily implemented by matrix multiplication; the other is threshold-free learning by dynamically weighting class probabilities and pseudo-relations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.893, + 0.649 + ], + "angle": 0, + "content": "With RTea, the model's certainty and consistency of prediction can be enhanced on the target domain, and the cross-domain inadaptation is further eliminated. Sufficient experiments show our method can further mine the available knowledge in pseudo-labels, and it can be easily incorporated into existing self-training method to further boost their performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.664, + 0.638, + 0.68 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Unsupervised Domain Adaptation (UDA). UDA methods can be divided into domain alignment and self-training. Alignment-based methods narrow the domain gap by aligning distributions at different levels, e.g., input [12, 30, 25, 60], feature [32, 33, 7, 50, 56, 22] and output [48, 49, 59]. Although they achieve positive adaptation benefits, the lack of specific target domain knowledge leads to slight improvement. To this end, self-training methods are proposed to train the network with pseudo-labels for the target domain, which can be divided into two categories, offline and online pseudo-label-based methods. Offline self-training (OFFST) methods save the target domain pseudo-labels generated by the pre-trained model and use them to train the model iteratively [27, 10, 37]. To avoid noise interfer" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19192" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "ence, these methods select high-quality pseudo-labels via threshold setting [70, 71], consistent prediction [68], and pseudo-label prototypes [64]. These methods require additional storage of pseudo-labels and an iterative training, which is not conducive to practical use. Online self-training (ONST) uses the model's output during training as supervision without saving intermediate results [58, 4, 51, 1]. ONST avoids the inconvenience of multiple training rounds and manual intervention between consecutive rounds in OFFST. Our work is designed in online self-training fashion. Besides, our method further mines the available knowledge in pseudo-labels from the novel perspective of pixel relations, which can further promote pseudo-label learning and boosting self-training performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.473, + 0.576 + ], + "angle": 0, + "content": "Relation Learning (RL) in Semantic Segmentation. In supervised semantic segmentation, capturing relations between pixels is continuously studied at feature [8, 20, 29] and output layers[24, 17]. At the feature layer, several work [8, 20, 62, 29] use the label-guided pixel relation to build a compact feature space, in which features of the same class are close and of different classes are far. At the output layer, AAF [24] and CDGC [17] exploit pixel relations in the ground truth to correct the output probabilities, forcing the model to adjust both the classifier and the feature extractor to output reasonable relations and semantic structure. These supervised RL methods achieve huge performance improvements, emphasizing the importance of maintaining the relation between pixels. However, in the UDA task, the lack of annotations makes it impossible to build relations as these works. Our method proposes a novel pseudo-relation building and learning strategy so that the above advantages can be also achieved to the UDA segmentation task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.473, + 0.789 + ], + "angle": 0, + "content": "Pseudo Label Correction. As a classic technique of semi-supervised learning, pseudo-labeling has shown favorable competitive advantages in many visual tasks with limited labels. Due to the limitation of confidence bias and error accumulation [41], pseudo-labeling are easy to overfit the noise and lead to model divergence[61]. Some pioneering works alleviate the problems from pseudo-label selection[63], negative label learning[41], contrastive learning [55], model calibration [23, 54]. However, the task-specific and domain-dependent design limits the application of these methods in complex cross-domain tasks. In contrast, our work proposes a novel perspective to rectify pseudo-labels and a tailored solution for cross-domain segmentation tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.806, + 0.214, + 0.822 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.32, + 0.847 + ], + "angle": 0, + "content": "3.1. Background and Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "This paper focuses on the unsupervised domain adaptation (UDA) semantic segmentation, where source domain data \\(\\mathcal{X}_s = \\{x_s\\}\\) with pixel-level labels \\(\\mathcal{Y}_s = \\{y_s\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.214 + ], + "angle": 0, + "content": "and unlabeled target domain data \\(\\mathcal{X}_t = \\{x_t\\}\\) are given. Our goal is to train a segmentation model \\(G\\) that can work well on target domain. \\(G\\) consists of a feature extractor \\(F\\) and a classifier \\(C\\). Given sampled image \\(x\\in \\mathcal{X}_s\\cup \\mathcal{X}_t\\), \\(F\\) mapping \\(x\\) to the feature space \\(f = F(x)\\), and \\(C\\) categorizes each feature in \\(f\\) to obtain a class probability map \\(p = C(F(x))\\in \\mathbb{R}^{h\\times w\\times K}\\). For the source domain, the cross entropy loss \\(L_{s}\\) is calculated to optimize the model," + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.223, + 0.893, + 0.261 + ], + "angle": 0, + "content": "\\[\nL _ {s} = - \\frac {1}{\\left| \\mathcal {X} _ {s} \\right|} \\sum_ {x _ {s} \\in \\mathcal {X} _ {s}} \\log C (F (x _ {s})) (y _ {s}). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.895, + 0.317 + ], + "angle": 0, + "content": "For the target domain, to narrow the domain gap, self-training methods adopt pseudo-labels \\(\\hat{y}_t\\) generated by the pre-adapted model to retrain the unadapted model," + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.327, + 0.893, + 0.363 + ], + "angle": 0, + "content": "\\[\nL _ {s t} = - \\frac {1}{| \\mathcal {X} _ {t} |} \\sum_ {x _ {t} \\in \\mathcal {X} _ {t}} \\log C (F (x _ {t})) (\\hat {y} _ {t}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.374, + 0.895, + 0.465 + ], + "angle": 0, + "content": "In this way, the model's adaptability can be enhanced by relearning the knowledge of the pseudo-labels in the target domain. However, using Eq. 2 tends to interfere with training because the pseudo-labels contain massive noise. Thus, some works select high-confidence pseudo-labels by setting threshold \\(\\zeta^k\\) for each class," + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.475, + 0.893, + 0.508 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {t} = \\left\\{ \\begin{array}{c l} \\arg \\max _ {k} p _ {t} ^ {k}, & \\text {i f} \\max \\left(p _ {t} ^ {k}\\right) > \\zeta^ {k} \\\\ \\text {i g n o r e}, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.895, + 0.611 + ], + "angle": 0, + "content": "where \\( p_t^k \\) is the \\( k \\)-th class probability score. In Eq. 3, the \\( \\zeta^k \\) determines the quality of the selected pixels, which needs to be dynamically adjusted according to the adaptation degree. Thus, in the subsequent works, scholars [58, 4, 51, 1] mainly focus on setting reasonable thresholds or uncertainty estimation strategies to select reliable pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.896, + 0.825 + ], + "angle": 0, + "content": "In this paper, we explore the potential of self-training from another perspective. Different from mining category knowledge in pseudo-labels, we propose to mine relation knowledge in pseudo-relations between pixels. The overview of our method is shown in Fig 3. For the source domain, images are input to the student model, which is optimized by the \\( L_{s} \\). For the target domain, the original image and its data-transformed version are input into the student model and teacher model, respectively. After that, the output of the teacher model is used to build pseudo-relations \\( S_{pr} \\) to further supervise the student model of category learning by \\( L_{st} \\) and relation learning by \\( L_{pr} \\). We detail the pseudo-relation \\( S_{pr} \\) building in Sec.3.2, and detail the pseudo-relation learning by optimizing \\( L_{pr} \\) in Sec.3.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.729, + 0.849 + ], + "angle": 0, + "content": "3.2. Pseudo-relation Building" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In the supervised segmentation task, relations can be driven by ground truth, which is not achievable for the UDA segmentation. Thus, how to build the relations between" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19193" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.098, + 0.859, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.893, + 0.416 + ], + "angle": 0, + "content": "Figure 3: The overall pipeline of the proposed Relation Teacher that includes a student model and a teacher model. \\( S_{low} \\), \\( S_{high} \\) and \\( S_{pr} \\) represent low-level relation matrix, high-level relation matrix and pseudo-relation matrix. \\( L_{st} \\) is the traditional loss function for pseudo-label learning. \\( L_{pr} \\) is the proposed loss function for pseudo-relation learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.471, + 0.526 + ], + "angle": 0, + "content": "pixels in the target domain is the key. A naive solution is to build by measuring the class similarity between pseudolabels from a pre-adapted model. Given any two pixels \\( p_{(t,i)} \\) and \\( p_{(t,j)} \\) (\\( i,j = 0,1,2,\\dots,w\\times h \\)) on the class probability map \\( p_t\\in \\mathbb{R}^{h\\times w\\times K} \\) of the target domain, the high-level relation between them can be defined as," + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.539, + 0.47, + 0.557 + ], + "angle": 0, + "content": "\\[\ns _ {(i, j)} = \\operatorname {S I M} \\left(p _ {(t, i)}, p _ {(t, j)}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.687 + ], + "angle": 0, + "content": "where \\(\\mathrm{SIM}(\\cdot ,\\cdot)\\) is the cosine similarity measure. Extending this relation to all pixels in an image, we can derive a highlevel relation matrix \\(S = \\{s(i,j)\\} \\in \\mathbb{R}^{hw\\times hw}\\). However, such a relation modeling mechanism will introduce massive noise due to the unadapted model. As mentioned in reliable local relations prior, these noises are mainly in the long-distance relations but relations in local grids are relatively accurate." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.688, + 0.471, + 0.753 + ], + "angle": 0, + "content": "To this end, we devise a local relation modeling mechanism. We divide the target image into \\(N\\times N\\) grids \\(\\{G_l\\}_{l = 1}^{hw / N^2}\\) and model the relations inside the grid. Then the high-level relation matrix for each grid can be obtained," + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.764, + 0.47, + 0.784 + ], + "angle": 0, + "content": "\\[\nS _ {h i g h} = \\left\\{s _ {(m, n)} \\right\\} _ {(m, n) \\in G _ {l}} \\in \\mathbb {R} ^ {N ^ {2} \\times N ^ {2}}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.824 + ], + "angle": 0, + "content": "Nonetheless, local pseudo-relations may still contain noise due to domain shifts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.902 + ], + "angle": 0, + "content": "To further mitigate unreliable relations in local grids, we introduce low-level relation constraints in each grid. The motivation stems from available low-level relations prior that local low-level relations (RGB space) can be well used to capture the edges and internal structures of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.893, + 0.495 + ], + "angle": 0, + "content": "objects. Drawing on the traditional potential energy function constructing the potential energy field [43, 44, 38], we use the Gaussian function to calculate the energy on the RGBXY[43] space as low-level relation constraints," + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.515, + 0.828, + 0.536 + ], + "angle": 0, + "content": "\\[\nS _ {l o w} = \\left\\{\\Psi_ {(m, n)} \\right\\} _ {(m, n) \\in G _ {l}} \\in \\mathbb {R} ^ {N ^ {2} \\times N ^ {2}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.538, + 0.892, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\Psi (m, n) = \\exp \\left(- \\left| \\frac {I _ {m} - I _ {n}}{\\sigma} \\right| ^ {2}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.893, + 0.716 + ], + "angle": 0, + "content": "where \\(I_{(\\cdot)}\\) is the feature vector on RGBXY space, \\(\\sigma\\) is the bandwidth parameter of the Gaussian function. Due to the nature of the Gaussian function[16], the value range of the \\(S_{low}\\) are [0, 1], which is the same as that of \\(S_{high}\\). A higher value indicates a stronger association between pixels. Although it lacks high-level semantics, it can better regularize relations (See Tab. 4 for verification). We linearly combine the low- and high-level relations as final pseudo-relations," + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.736, + 0.892, + 0.753 + ], + "angle": 0, + "content": "\\[\nS _ {p r} = \\alpha S _ {l o w} + (1 - \\alpha) S _ {h i g h}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.774, + 0.88, + 0.79 + ], + "angle": 0, + "content": "where the \\(\\alpha\\) is a hyper-parameter and is simply set to 0.5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.813, + 0.733, + 0.83 + ], + "angle": 0, + "content": "3.3. Pseudo-relation Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.904 + ], + "angle": 0, + "content": "Following the paradigm of pseudo-label learning, we can exploit the reliable relations in the pseudo-relation matrix to perform pseudo-relation learning. Specifically, for any pixel pair \\( p_{(t,i)} \\) and \\( p_{(t,j)} \\) in \\( l \\)-th grid, we can perform a pairwise" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19194" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.426, + 0.108 + ], + "angle": 0, + "content": "relation loss [24, 17] in a pseudo manner as follows," + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.119, + 0.469, + 0.185 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {L} _ {p r} = \\sum_ {l} \\sum_ {i, j} \\operatorname {K L} \\left(p _ {(t, i)} \\mid \\mid p _ {(t, j)}\\right) \\cdot \\mathbb {1} \\left(S _ {p r; l} (i, j) > M _ {u p}\\right) + \\\\ (1 - \\mathrm {K L} (p _ {(t, i)} | | p _ {(t, j)})) \\cdot \\mathbb {1} \\left(S _ {p r; l} (i, j) < M _ {l o w}\\right). \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.186, + 0.47, + 0.488 + ], + "angle": 0, + "content": "\\(\\mathrm{KL}(\\cdot ||\\cdot)\\) is the Kullback-Leibler divergence between two distributions. \\(\\mathbb{1}(\\cdot)\\) is the indicator function for thresholding. \\(M_{up}\\) and \\(M_{low}\\) are upper and lower thresholds for filtering unreliable relations. Optimizing this loss pulls the class distribution of the pixel pairs with a pseudo-relation higher than \\(M_{up}\\) closer and pushes those with a pseudorelation lower than \\(M_{low}\\) further away. In this way, pseudorelation learning can assist pseudo-label learning (in Eq.2) in the following aspects. Let the pixels used by Eq.2 be denoted as reliable pixels, and the rest are unreliable ones. 1). Relations between reliable pixels. Those reliable inter- and intra-class relations are informative and can be incorporated into learning as structural inference. 2). Relations between reliable and unreliable pixels. Pushing or Pulling the class probabilities of the unreliable pixels towards reliable ones will greatly enhance the confidence of the model. 3). Relations between unreliable pixels. Although we cannot give these pixel pairs explicit class targets, implicit class cues may help the model to enhance confidence. See further instructions in Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.469, + 0.623 + ], + "angle": 0, + "content": "In practice, in \\(\\hat{L}_{pr}\\), the pair of class distribution input to \\(\\mathrm{KL}(\\cdot ||\\cdot)\\) should assign the more sharp one as the target. This makes it require pair-by-pair index calculation, which greatly increases the training time. Besides, \\(M_{up}\\) and \\(M_{low}\\) requires hyper-parameter search under different adaptation tasks, hindering the flexibility of application. Here, we learn from the idea of graph cut [57] and devise a new pseudorelation loss, which can be performed by matrix multiplication without explicit thresholding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.469, + 0.805 + ], + "angle": 0, + "content": "Specifically, in \\(l\\)-th grid, we construct an undirected weighted graph \\(\\mathcal{G}\\), treating all pixels in this grid as nodes of the graph and the similarity between these pixels as the weights of edges. Thus, the corresponding \\(S_{pr;l}\\) can be seen as a pseudo-adjacency matrix of the \\(\\mathcal{G}\\). With the \\(\\mathcal{G}\\), the \\(K\\) classification problem is regarded as a graph cutting problem of cutting a graph into \\(K\\) subgraphs. Then, the \\(k\\)-th class probability \\(p_{t;l}^{k}\\) of this grid is regarded as the probability of the corresponding nodes cut into \\(k\\)-th subgraph (\\(k \\in [0, K - 1]\\)). According to the properties of the graph, we can calculate the soft cost of cutting the \\(k\\)-th subgraph as follows," + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.817, + 0.469, + 0.837 + ], + "angle": 0, + "content": "\\[\nc u t ^ {k} = \\hat {p} _ {t; l} ^ {k} S _ {p r; l} \\mathbf {1} - \\hat {p} _ {t; l} ^ {k} S _ {p r; l} \\left(\\hat {p} _ {t; l} ^ {k}\\right) ^ {T}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.849, + 0.469, + 0.901 + ], + "angle": 0, + "content": "\\(\\hat{p}_{t;l}^{k}\\in \\mathbb{R}^{1\\times N^{2}}\\) is the vector flatten by \\(p_{t;l}^{k}\\in \\mathbb{R}^{1\\times N\\times N}\\) \\(\\mathbf{1}\\in \\mathbb{R}^{N^2\\times 1}\\) is an all-ones vector. We show an example to illustrate Eq.9 in Fig.4. The smaller the cut value, the smaller" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.094, + 0.681, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.175, + 0.7, + 0.207 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} P ^ {0} S 1: \\text {- - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - } \\\\ P ^ {0} S P ^ {0}: \\text {- - } \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.71, + 0.094, + 0.847, + 0.207 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{c} \\hline P: \\text {c l a s s p r o b a b i l i t y} \\\\ p _ {1} \\quad 1 \\quad 0 \\\\ p _ {2} \\quad 1 \\quad 0 \\\\ p _ {3} \\quad 1 \\quad 0 \\\\ p _ {4} \\quad 0 \\quad 1 \\\\ p _ {5} \\quad 0 \\quad 1 \\\\ S: \\text {a d j a c e n c y m a t r i x} \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.222, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Figure 4: We show an example of binary classification to illustrate Eq.9. Given five samples and their class probability \\( P \\), take the cut of class 0 as an example. \\( P^0 S1 \\) is the sum of all edges connected to the nodes of class 0, i.e., the green and dashed lines. \\( P^0 SP^0 \\) is the sum of all edges connecting two nodes of class 0, i.e., the green lines, and \\( P^0 S1 - P^0 SP^0 \\) is the cost consumed of the 0 class. To minimize the cost, nodes with high affinity should be classified into the same class, and vice versa." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.464 + ], + "angle": 0, + "content": "the correlation between the subgraphs and the larger the correlation within the subgraphs. Thus, \\(cut^k\\) can be regarded as a proxy, when the \\(cut^k\\) value is small, the class probability \\(p_{t;l}^k\\) better conforms to the pseudo-relations \\(S_{pr;l}\\), and vice versa. Moreover, the Eq.9 is derivable with respect to \\(p_{t;l}^k\\), and its gradient w.r.t. \\(p^k\\) is," + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.476, + 0.891, + 0.511 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial c u t ^ {k}}{\\partial p ^ {k}} = S _ {p r} \\left(\\mathbf {1} - 2 p ^ {k}\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.643 + ], + "angle": 0, + "content": "The proxy's gradient is proportional to the \\( S_{pr} \\) and \\( 1 - 2p^{k} \\), which implicitly weight high-confidence relations and reliable pixels (class probability far from 0.5). This explains that unreliable edges (relations) on the graph play a minor role in pulling or pushing away the class distribution, enabling adaptive weighting without threshold. Consequently, we modify Eq.9 as a threshold-free pseudo-relation loss function to optimize \\( p_t \\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.655, + 0.891, + 0.699 + ], + "angle": 0, + "content": "\\[\nL _ {p r} = \\sum_ {l} ^ {h w / N ^ {2}} \\sum_ {k} ^ {K} \\hat {p} _ {t; l} ^ {k} S _ {p r} \\left(\\mathbf {1} - \\hat {p} _ {t; l} ^ {k}\\right) ^ {T}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.709, + 0.891, + 0.74 + ], + "angle": 0, + "content": "\\(L_{pr}\\) can be calculated using matrix multiplication in a simple and quick way." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.749, + 0.667, + 0.763 + ], + "angle": 0, + "content": "3.4. Relation Teacher" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.772, + 0.891, + 0.832 + ], + "angle": 0, + "content": "We embed the learning of pseudo-relation into the optimization of mean-teacher [45] framework to realize online self-training as shown in Fig 3. The final optimization objective is," + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.833, + 0.891, + 0.85 + ], + "angle": 0, + "content": "\\[\nL _ {f} = L _ {s} + \\lambda_ {s t} L _ {s t} + \\lambda_ {p r} L _ {p r}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "where \\(\\lambda_{pr}\\), \\(\\lambda_{st}\\) are the trade-off coefficients. \\(\\lambda_{st}\\) is set as 0.001 following SAC [1]. \\(\\lambda_{pr}\\) is empirically set to 0.01 to balance the loss value." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19195" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.892, + 0.342 + ], + "angle": 0, + "content": "
MethodroadsidewalkBuildingWallfencepolelightsignvege.terrainskypersonridercartruckbustrainmbikebikemIoU
FADA (ECCV 2020) [50]91.050.686.043.429.836.843.425.086.838.387.464.038.085.231.646.16.525.437.150.1
FDA (CVPR 2020) [60]92.553.382.326.527.636.440.538.882.239.878.062.634.484.934.153.116.827.746.450.4
IAST (ECCV 2020) [37]93.857.885.139.526.726.243.134.784.932.988.062.629.087.339.249.623.234.739.651.5
MetaCorr (CVPR 2021) [10]92.858.186.239.733.136.342.038.685.537.887.662.831.784.835.750.32.036.848.052.1
RPT (CVPR 2021) [66]89.243.386.139.529.940.249.633.187.438.586.064.425.188.536.645.823.936.556.852.6
SAC (CVPR 2021) [1]90.453.986.642.427.345.148.542.787.440.186.167.529.788.549.154.69.826.645.353.8
CFDAN (CVPR 2021) [36]92.558.386.527.428.838.146.742.585.438.491.866.437.087.840.752.444.641.759.056.1
SDFA (ICCV 2021) [26]94.859.486.240.529.525.543.834.785.934.989.563.430.888.342.650.725.335.740.952.8
ProDA (CVPR 2021) [64]87.85679.746.344.845.653.553.588.645.282.170.739.288.845.559.41.048.956.457.5
SimT (CVPR2022) [9]94.26088.530.339.741.247.860.888.647.389.371.545.090.754.260.20.051.858.458.9
CPST (CVPR 2022) [28]92.359.984.945.729.752.861.559.587.941.585.073.035.590.448.773.926.353.853.960.8
Undoing (CVPR 2022) [31]92.952.787.239.441.343.95552.989.348.291.271.43690.267.959.8048.559.359.3
DAP (CVPR 2022) [21]94.563.189.129.847.550.456.758.789.550.28773.638.691.350.252.9050.263.559.8
CaCo (CVPR 2022) [18]93.864.185.743.742.246.150.154.088.74786.568.12.988.043.460.131.546.160.958.0
ADPL (TPAMI 2023) [3]93.460.687.545.332.637.343.355.587.244.88864.534.288.352.661.849.841.859.459.4
RTea (Ours)95.467.187.946.144.046.053.859.589.749.889.871.540.590.855.057.922.147.762.561.9
Daformer (CVPR 2022) [14]95.770.289.453.548.149.655.859.489.947.992.572.244.792.374.578.265.155.961.868.3
Daformer + RTea (Ours)96.171.789.157.850.455.959.366.790.448.294.574.846.593.878.781.665.857.162.870.6
HRDA (ECCV 2022) [15]96.474.491.061.651.557.163.969.391.348.494.279.052.993.984.185.775.963.967.573.8
HRDA + RTea (Ours)97.175.292.663.551.858.266.571.291.149.096.881.554.294.284.886.675.762.266.774.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.345, + 0.881, + 0.361 + ], + "angle": 0, + "content": "Table 1: Experimental results for GTA5 \\( \\rightarrow \\) Cityscapes adaptation task. The best results in every column are highlighted." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.372, + 0.892, + 0.621 + ], + "angle": 0, + "content": "
MethodroadsidewalkBuildingWall*fence*pole*lightsignvege.skypersonridercarbusmbikebikemIoUmIoU*
FADA (ECCV 2020)[50]84.540.183.14.8034.320.127.284.88453.522.685.443.726.827.845.252.5
FDA (CVPR 2020) [60]79.335.073.2---19.924.061.782.661.431.183.940.838.451.1-52.5
IAST (ECCV 2020) [37]81.941.583.317.74.632.330.928.883.485.065.530.886.538.233.152.749.857.0
MetaCorr (CVPR 2021) [10]92.652.781.38.92.428.113.07.383.585.060.119.784.837.221.543.945.152.5
RPT (CVPR 2021) [66]88.946.584.515.10.538.539.530.185.985.859.826.188.146.827.756.151.258.9
SAC (CVPR 2021) [1]89.347.285.526.51.343.045.532.087.189.363.625.486.935.630.453.052.659.3
CFDAN (CVPR 2021) [36]75.730.081.911.52.535.318.032.786.290.165.133.283.336.535.354.348.255.5
SFDA (ICCV 2021) [26]90.550.081.613.32.834.725.733.183.889.266.034.985.353.446.146.652.060.1
ProDA (CVPR 2021) [64]87.845.784.637.10.644.054.637.088.184.474.224.388.251.140.545.655.562.0
CPST (CVPR 2022) [28]87.243.985.533.60.347.757.437.287.888.579.032.090.649.450.859.857.965.3
Undoing (CVPR 2022) [31]82.537.281.123.8045.757.247.687.785.874.128.688.466.047.055.356.764.5
CaCo (CVPR 2022) [18]87.448.979.68.80.230.117.428.379.981.256.324.278.639.228.148.346.053.6
ADPL (TPAMI 2023) [3]86.138.685.929.71.336.641.347.28590.467.544.387.457.143.951.455.963.6
RTea (ours)93.259.686.331.34.843.141.844.088.690.570.442.689.556.740.259.958.966.4
Daformer (CVPR 2022) [14]84.540.788.441.56.550.05554.68689.873.248.287.253.253.961.767.460.9
Daformer + RTea (Ours)85.943.290.145.16.352.460.557.187.892.275.351.887.455.954.162.669.563.0
HRDA (ECCV 2022) [15]85.247.788.849.54.857.265.760.985.392.979.452.88964.763.964.972.465.8
HRDA + RTea (Ours)87.849.090.350.35.558.666.061.486.893.179.553.189.565.163.764.673.066.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.079, + 0.624, + 0.892, + 0.655 + ], + "angle": 0, + "content": "Table 2: Experimental results for SYNTHIA \\(\\rightarrow\\) Cityscapes adaptation task. The best results in every column are highlighted. The mIoU and mIoU* are averaged over 16 and 13 categories, respectively." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.676, + 0.201, + 0.694 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.704, + 0.37, + 0.721 + ], + "angle": 0, + "content": "4.1. Datasets and Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.731, + 0.468, + 0.852 + ], + "angle": 0, + "content": "Datasets. We use one real dataset (Cityscapes [5]) and two synthetic datasets (GTA5 [40] and SYNTHIA [42]). The Cityscapes dataset contains 2,975 training images and 500 validation images of resolution \\(2048 \\times 1024\\). The GTA5 dataset contains 24,966 images with resolution \\(1914 \\times 1052\\) and has 19 common categories with Cityscapes. The SYNTHIA dataset contains 9,400 images with resolution \\(1280 \\times 760\\) and has 16 common categories with Cityscapes." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. We adopt Deeplab-v2 [2] as the base network, ResNet-101 [11] as the feature extractor and the aspp [2] module as the classifier. The network is pre" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.678, + 0.892, + 0.889 + ], + "angle": 0, + "content": "trained on ImageNet. The optimizer is SGD with the momentum of 0.9 and weight decay of \\(10^{-4}\\). The initial learning rate is set to \\(2.5 \\times 10^{-4}\\), and then is reduced following a poly policy with a power of 0.9. The batch size is set as 4. The final \\(\\lambda_{f}\\) and \\(\\lambda_{o}\\) values are set to 0.025 and 0.005, respectively. We apply the \\(L^{pr}\\) to the model's output class probability, which is 8 times smaller than the original resolution. And the grid size \\(N\\) is set to 8. The weighting factor \\(\\alpha\\) is set to 0.5. The \\(\\sigma\\) for XY and RGB space in Gaussian function is set to 6 and 0.1, following [43]. Data augmentation strategies performed on the data input to the student model include random flipping, Gaussian noise, color transformation, cutout[6], and contrast enhancement, a similar and common operation in online self" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19196" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "training methods [58, 4, 51, 1]. Besides, we also preform the class-mixing resampling strategy [47] on the source domain to focus on the minority class. When performing \\( L_{st} \\) for pseudo-label learning, we adopt the thresholding selection method in SAC [1] to pick high-quality samples. After training with Rtea, we retrained the model using the distillation strategy [64] for better adaptation, which is commonly used in recently published UDA work [31, 21, 28, 3]. The detailed scores for each stage are in the Tab. 3. Our network is trained with four RTX3090 GPUs on PyTorch." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.256, + 0.391, + 0.273 + ], + "angle": 0, + "content": "4.2. Comparisons with State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.473, + 0.614 + ], + "angle": 0, + "content": "\\(\\mathrm{GTA5} \\rightarrow \\mathrm{Cityscapes}\\). We report the comparison results with existing methods on \\(\\mathrm{GTA5} \\rightarrow \\mathrm{Cityscapes}\\) task in Tab. 1. We compared two structures based on resnet-101 and transformer structures. Overall, our RTea achieves new state-of-the-art performance than related works, and the category performance scores are also highly competitive, demonstrating the effectiveness of RTea. Compared with the domain alignment method, the performance of RTea show an advantage over the state-of-the-art method FDA [60] by \\(11.5\\%\\). Compared with the offline self-training method, the mIoU score of RTea is \\(10.4\\%\\) and \\(9.8\\%\\) higher than IAST [37] and RPT[66]. Compared with the online self-training method, RTea exceeds SAC [1] and ProDA [64] by \\(8.1\\%\\) and \\(4.4\\%\\). Compared with the newly released method Undoing[31], DAP[21] and ADPL[3], our RTea still outperforms these methods by more than \\(2.0\\%\\) mIoU scores, showing the potential of our method even more. Compared with the method of transformer structure, our method improves the mIoU score by \\(0.7\\%\\) and \\(0.9\\%\\) on Daformer [14] and HRDA [15] respectively, which shows that RTea has good scalability and transferability. Qualitative results on both tasks can be found in Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.902 + ], + "angle": 0, + "content": "SYNTHIA \\(\\rightarrow\\) Cityscapes. The results of using SYNTHIA as the source domain are reported in Tab. 2, including mIoU/mIoU* covering 16/13 classes. On the whole, our method still achieves significant improvements, showing gains over advanced methods. In particular, SYNTHIA and Cityscapes suffer from significant visual domain differences in 'road', and 'sidewalk', which leads to the poor performance of the most UDA methods in these categories. Our method uses the pseudo-relations of these categories and achieves higher performance improvements, and we argue this is due to the local pseudo-relation learning to better capture the structure of these categories. Compared with the domain alignment and offline self-training methods, RTea maintains similar performance gains to the GTA5 transfer task. Compared with online self-training method, we achieve better performance than CPST [28] over 16 and 13 classes, exceeding its by \\(1.0\\%\\) and \\(1.1\\%\\) mIoU score. Compared with the adaptation method using transformer structure, our method improves the mIoU score by \\(2.1\\%\\) and" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.895, + 0.184 + ], + "angle": 0, + "content": "
\\(L_s\\)\\(L_{st}\\)copy-paste\\(\\hat{L}_{pr}\\)\\(L_{pr}\\)\\(L_{pr}^s\\)DistGTA5SYNTHIA
✓✓53.551.2
✓✓✓55.853.9
✓✓✓✓58.956.3
✓✓✓✓59.656.8
✓✓✓✓✓59.656.9
✓✓✓✓✓✓61.958.9
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.498, + 0.185, + 0.895, + 0.321 + ], + "angle": 0, + "content": "Table 3: Ablation experiments of each module in GTA5 and SYNTHIA \\(\\rightarrow\\) Cityscapes adaptation task. The basic self-training \\((L_{s} + L_{st})\\) is following SAC[1]. The copy-paste means that we adopt the resampling strategy in [47] for minority learning. Here, we report a result of \\(\\hat{L}_{pr}\\) with the fine-tuned thresholds by grid search. \\(L_{pr}^{s}\\) denotes that relation learning is performed on the source domain. Dist denote the distillation strategy in [50, 64]. All numbers are mIoU(%) score." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.347, + 0.892, + 0.378 + ], + "angle": 0, + "content": "\\(0.7\\%\\) on Daformer [14] and HRDA [15], which further verifies the effectiveness of the method." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.391, + 0.666, + 0.407 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.895, + 0.719 + ], + "angle": 0, + "content": "Ablation for Each Module. Tab.3 reports the ablation results for different modules. We adopt SAC [1] with the copy-paste [47] argumentation as the baseline, achieving the \\(55.8\\%\\) and \\(53.9\\%\\) mIoU score on two adaptation tasks. Overall, Rtea achieves \\(3.8\\%\\) and \\(3.0\\%\\) performance improvements on the two tasks on this competitive baseline, respectively, showing the effectiveness of the pseudorelation learning. Specifically, the naive \\(\\hat{L}_{pr}\\) loss, although, can improve performance, the screening of the threshold makes it difficult to be directly applied to practice, because the threshold may be very sensitive in different adaptation scenarios. The proposed \\(L_{pr}\\) loss does not require explicit threshold while improving the performance, showing its flexibility and effectiveness. In addition, we also tried to perform pseudo-relation learning on the source domain \\(L_{pr}^{s}\\), and we did not find a significant performance improvement, which may be because it cannot directly benefit the target domain. After training with RTea, the self-distillation method can still be used to further improve the adaptability of the model in the target domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Ablation for Pseudo-Relation Building. Tab.4 shows the ablation results for building pseudo-relation. When the relations are built on RGBXY space (\\(S_{low}\\)), the performance achieves a good improvement, \\(2.0\\%\\) and \\(2.1\\%\\) on two tasks, respectively, which suggests that low-level relations on local grids can propagate effective category knowledge. When the relations are built on pseudo labels (\\(S_{high}\\)), the performance is only improved by \\(1.0\\%\\) and \\(0.7\\%\\) on two tasks, respectively. This is because it is not easy to find valuable relation pairs in this way, and their effects may overlap with label learning. Specifically, unreliable pixels discarded by pseudo-label learning are still difficult to use, and high" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19197" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.134, + 0.089, + 0.418, + 0.173 + ], + "angle": 0, + "content": "
SlowShighSprGTA5SYNTHIA
✓55.853.9
57.855.8
✓56.854.6
✓59.656.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.176, + 0.47, + 0.222 + ], + "angle": 0, + "content": "Table 4: Ablation experiments on the pseudo-relation building. \\( S_{low} \\), \\( S_{high} \\) and \\( S_{pr} \\) are low-level, high-level and final pseudo relation matrix." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.234, + 0.418, + 0.32 + ], + "angle": 0, + "content": "
R-RR-UU-UGTA5SYNTHIA
55.853.9
✓✓58.255.2
✓✓57.254.9
✓✓59.356.6
✓✓✓59.656.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.323, + 0.47, + 0.385 + ], + "angle": 0, + "content": "Table 5: Ablation experiments on the pseudo-relation learning. \\( R - R \\) denotes pairs with two reliable pixels. \\( R - U \\) denotes pairs with one reliable and one unreliable pixel. \\( U - U \\) denotes pairs with two unreliable pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.47, + 0.501 + ], + "angle": 0, + "content": "confidence relationships still contain massive noise, When \\(S_{low}\\) and \\(S_{high}\\) are combined, the best effect is achieved. We argue that the advantage is that, the noisy relations in the high level are corrected and the lack of semantics of the low-level relations is also made up, and more unreliable pixels are better exploited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.471, + 0.684 + ], + "angle": 0, + "content": "Ablation for Pseudo-Relation Learning. To verify the effect of different pixel pairs on pseudo-relation learning, we devise the ablation study in Tab. 5. We follow 1), 2) and 3) explained in the Eq. 8, and divide them into R-R (two reliable pixels), R-U (one reliable and one unreliable pixel) and U-U (two unreliable pixels). During training, we clear all gradients for one of the pairs to verify its effect on adaptation. We find that R-U pairs play the most important role in adaptation, R-R pairs come second, and U-U pairs come last. We analyze learning R-U pairs can make full use of valuable pixels from unexploited target domains, which is the most direct to enhance the target domain adaptability." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.695, + 0.195, + 0.71 + ], + "angle": 0, + "content": "4.4. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Sensitivity for reliable sample selection. In this section, we perform two experiments to explore how sensitive RTea is to reliable sample selection. First, we report the results when the parameters of the heuristic threshold (Eq. 3) are varied. The thresholding strategy consists of two hyperparameters, namely the upper threshold \\(\\theta\\) and the decay rate \\(\\beta\\). Table 6 shows that our method maintains a stable performance improvement when thresholding parameters vary within a certain range. Second, we report Rtea's performance on different reliable sample selection methods in Table 7. It verifies the effectiveness of RTea, which improves the performance of different self-training methods." + }, + { + "type": "table", + "bbox": [ + 0.535, + 0.09, + 0.858, + 0.148 + ], + "angle": 0, + "content": "
β=0.0001β=0.001β=0.01
θ=0.7559.059.258.8
θ=0.8059.259.659.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.15, + 0.892, + 0.181 + ], + "angle": 0, + "content": "Table 6: The mIoU scores (\\%) on GTA5 → Cityscapes task with varying thresholding parameters in Eq. 3." + }, + { + "type": "table", + "bbox": [ + 0.543, + 0.194, + 0.851, + 0.251 + ], + "angle": 0, + "content": "
PDCDADHT
without Rtea55.054.453.255.8
with Rtea58.856.854.859.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.253, + 0.892, + 0.33 + ], + "angle": 0, + "content": "Table 7: The mIoU scores (\\%) on GTA5 → Cityscapes task with different reliable sample selection strategies. PD denotes feature-prototype distance [64], CD denotes classifier discrepancy [69], AD denotes adversarial difficulty [34] and HT is our used heuristic threshold [1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.354, + 0.892, + 0.583 + ], + "angle": 0, + "content": "How local grids affect each relation pair. We perform experiments on \\(\\mathrm{GTA5} \\rightarrow\\) Cityscapes to verify which relation pairs are most affected by local grids. Pixels are still classified as reliable (R) and unreliable (U) according to whether they are used for category learning in traditional self-training, see Tabel 8. In the first line, we find that (1) the global grid is good for \\(R - R\\) because it extends the spatial scope of relational learning, while it does harm to \\(R - U\\) and \\(U - U\\) due to the long-range relation noise. As a result, performing pseudo-relation learning on global region lead model degradation. In the second line, we argue that (2) performing pseudo-relation on the local grids slightly reduces the gain of \\(R - R\\), but greatly reduces the interference of noise on \\(R - U\\) and \\(U - U\\). Finally, the model can obtain better performance improvement." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.593, + 0.888, + 0.642 + ], + "angle": 0, + "content": "
BaselineR-RR-UU-U
Global55.857.2 (+1.4)51.4 (-4.4)52.5 (-3.3)
Local grid55.856.6 (+0.8)57.9 (+2.1)55.9(+0.1)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.643, + 0.89, + 0.674 + ], + "angle": 0, + "content": "Table 8: The mIoU (%) of local grids effect on GTA5 → Cityscapes adaptation task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Computational overhead. Performing relation learning on dense prediction tasks such as semantic segmentation is time-consuming. Therefore, it is necessary to discuss the computational overhead introduced in Rtea. Overall, we think the pseudo-relation computational overhead is acceptable. First, for complexity, our computational cost is \\(\\mathcal{O}(N^2 WH)\\) (\\(H, W\\): width and height of feature map, \\(N\\): grid size, \\(N \\ll W, H\\)), which is greatly reduced compared to the global similarity \\(\\mathcal{O}(W^2 H^2)\\). Second, the pseudorelation can be computed in parallel using matrix operations in PyTorch. On a Nvidia RTX-3090, it only takes almost 40 ms for each batch and only increases about \\(3\\%\\) computational overhead in each iteration. Third, the cost is only for training and not for inference." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19198" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.35 + ], + "angle": 0, + "content": "Align low- and high-level relation matrix with the same Gaussian function. In the method section, we use the cosine distance (Eq. 5) and Gaussian distance (Eq. 6) to model the similarity of high- and low-level, respectively. It is interesting to explore unifying the modeling of high- and low-level pseudo-relations into the same metric function, e.g. Gaussian distance. With the same metric function, for any local grid \\( G_{l} \\), the local relation can be built as, \\( s(m,n) = \\sum_{m,n\\in G_l}\\Psi_{\\sigma_{rgbxy}}(m,n)\\cdot \\Psi_{\\sigma_{prob}}(m,n) \\), where \\( \\sigma_{rgbxy} \\) and \\( \\sigma_{prob} \\) are the bandwidth of the low- and highlevel Gaussian function. This formula is similar to the kernels of bilateral filtering[46], inspiring us to understand the pseudo-relation learning from the filtering perspective, i.e. smoothing and correcting the noise on output probability. Table 9 presents the comparison results, showing unifying the same metric function can maintain performance with less computational overhead." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.359, + 0.466, + 0.389 + ], + "angle": 0, + "content": "
MetricGTA5SYN.TimeMetricGTA5SYN.Time
Current59.656.940msSame Gaussian59.657.129ms
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.39, + 0.469, + 0.436 + ], + "angle": 0, + "content": "Table 9: The mIoU (\\%) and computational cost (time/batch) using different similarity metric functions on GTA5 → Cityscapes adaptation task." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.447, + 0.472, + 0.495 + ], + "angle": 0, + "content": "Hyper-parameters Impacts. We analyze the sensitivity of the hyper-parameters \\(\\alpha\\) (trade-off coefficient), grid size \\(N\\), the results are presented in the Appendix C." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.5, + 0.216, + 0.515 + ], + "angle": 0, + "content": "4.5. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.523, + 0.47, + 0.629 + ], + "angle": 0, + "content": "Visualization of pixel relations. Fig. 5 visualizes the learned relations on \\(\\mathrm{GTA5} \\rightarrow\\) Cityscapes task. Comparing Fig. 5 a, b and e, it shows that the feature associations of the baseline are chaotic while our method builds more accurate feature relations. Comparing Fig. 5 c, d and e, it indicts that our method captures category relations more accurately than baseline, resulting in more structured outputs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.469, + 0.749 + ], + "angle": 0, + "content": "Comparison of Pixel Utilization and Model Confidence. Fig. 6 compares the correct pixel utilization (PU) and average confidence (AC) of the model before and after adding RTea. With RTea, the PU is significantly improved and the AC also shows better results. It illustrates RTea can exploit more uncertain pixels around high-confidence pixels and propagate relation information to them, thereby fully improving the certainty of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Visualization of Pseudo-Labels. Fig. 7 visualizes the pseudo-labels of the baseline and our RTea to demonstrate the benefits of pseudo-relation learning. It shows that the RTea makes better use of pseudo-labels than the baseline model. For the areas are hard to distinguish (framed by the red box), RTea can enlarge the reliable pseudo-label area by capturing relations between pixels. Moreover, RTea provides clear class boundaries for the classes such as roads, sidewalks and buildings, which is more helpful for pseudolabel learning." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.09, + 0.653, + 0.146 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.146, + 0.653, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.517, + 0.202, + 0.655, + 0.215 + ], + "angle": 0, + "content": "a. Feature relations of baseline b. Feature relations of RTEca" + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.091, + 0.726, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.655, + 0.146, + 0.726, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.66, + 0.202, + 0.721, + 0.215 + ], + "angle": 0, + "content": "c. Prediction relations of baseline" + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.091, + 0.8, + 0.146 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.146, + 0.8, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.731, + 0.202, + 0.793, + 0.215 + ], + "angle": 0, + "content": "d. Prediction relations of RTea." + }, + { + "type": "image", + "bbox": [ + 0.8, + 0.091, + 0.892, + 0.146 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.8, + 0.146, + 0.892, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.8, + 0.202, + 0.873, + 0.214 + ], + "angle": 0, + "content": "c. Relations of ground truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.215, + 0.892, + 0.246 + ], + "angle": 0, + "content": "Figure 5: Visualization of the learned relations of RTea model on the GTA5 \\(\\rightarrow\\) Cityscapes task." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.268, + 0.698, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.27, + 0.892, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.379, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Figure 6: Comparison of the average correct pixel utilization and confidence of the target domain." + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.421, + 0.699, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.5, + 0.698, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.578, + 0.698, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.658, + 0.653, + 0.67 + ], + "angle": 0, + "content": "a. Baseline" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.421, + 0.892, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.5, + 0.892, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.578, + 0.892, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.658, + 0.822, + 0.67 + ], + "angle": 0, + "content": "b. Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.67, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Figure 7: Comparison of pseudo-labels of baseline and RTea. The white masked area is unreliable pseudo-labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.719, + 0.619, + 0.735 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose pseudo-relation learning framework for UDA semantic segmentation. In RTea, we provide two prior guidelines for pseudo-relation building, which may help more works exploiting pseudo-relations. Moreover, we explore how to use pseudo-relations from the constraints and do detailed analysis and experiments on the proposed solution. Sufficient experiments on two datasets demonstrate the effectiveness of the proposed method. In general, RTea provides a new idea for self-training methods and may inspire more works in this field." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "19199" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.186 + ], + "angle": 0, + "content": "[1] Nikita Araslanov and Stefan Roth. Self-supervised augmentation consistency for adapting semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15384-15394, June 2021. 1, 3, 5, 6, 7, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.188, + 0.472, + 0.257 + ], + "angle": 0, + "content": "[2] L. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille. 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In Proceedings of the IEEE/CVF Conference on International Conference on Computer Vision, pages 5982-5991, October 2019. 1, 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "19203" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_origin.pdf b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3091e7f8c4fc269667ae6f2d290f0c6a7c2e8173 --- /dev/null +++ b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/10b88ddb-f472-4de5-8cfb-db9e250c0176_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0900ace4a741f68162c60273ec8452426498ca5908d41c6e38ec0b466255371b +size 5646871 diff --git a/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/full.md b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ab36eb4bbdee97d410430afb2f0b7a3ffaaefb37 --- /dev/null +++ b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/full.md @@ -0,0 +1,419 @@ +# Learning Pseudo-Relations for Cross-domain Semantic Segmentation + +Dong Zhao, Shuang Wang $^{\text{心}}$ , Qi Zang, Dou Quan, Xiutiao Ye, Rui Yang, Licheng Jiao +School of Artificial Intelligence, Xidian University, Shaanxi, China + +zhaodong01@stu.xidian.edu.cn; shwang@mail.xidian.edu.cn + +# Abstract + +Domain adaptive semantic segmentation aims to adapt a model trained on labeled source domain to unlabeled target domain. Self-training shows competitive potential in this field. Existing methods along this stream mainly focus on selecting reliable predictions on target data as pseudolabels for category learning, while ignoring the useful relations between pixels for relation learning. In this paper, we propose a pseudo-relation learning framework, Relation Teacher (RTea), which can exploitable pixel relations to efficiently use unreliable pixels and learn generalized representations. In this framework, we build reasonable pseudorelations on local grids and fuse them with low-level relations in the image space, which are motivated by the reliable local relations prior and available low-level relations prior. Then, we design a pseudo-relation learning strategy and optimize the class probability to meet the relation consistency by finding the optimal sub-graph division. In this way, the model's certainty and consistency of prediction are enhanced on the target domain, and the cross-domain inadaptation is further eliminated. Extensive experiments on three datasets demonstrate the effectiveness of the proposed method. The code will be available at https://github.com/DZhaoXd/RTea. + +# 1. Introduction + +Semantic segmentation is a challenging problem of assigning each pixel a class label in an image. Driven by deep neural networks, significant progress has been made in this field. Despite these efforts, a segmentation model trained with a specific domain does not generalize well to other domains. It is known to be caused by the domain gap between the training (source) and testing (target) domains [13]. To + +This work is supported by the National Key R&D Program of China under Grant No. 2021ZD0110400, the National Natural Science Foundation of China (No.62271377, No.62201407), the Key Research and Development Program of Shannxi (No.2021ZDLGY01-06, No.2022ZDLGY01-12), the China Postdoctoral Science Foundation (No. 2022M722496), the Foreign Scholars in University Research and Teaching Program's 111 Project (B07048). + +![](images/c011a64d67fb04e16668099ab9df89cc06c66b9d00eb1c9a0482a0bf32eadffa.jpg) + +![](images/0101dc3cc61716f2da9d90e24b55e2f47b861adb4cb11754df61b2f14222d8ff.jpg) +Figure 1: Overview of our motivation. In A, previous self-training methods select reliable pseudo-labels for category learning. In B, our method reasonably utilizes reliable pseudo-labels and unreliable ones for relation learning. + +solve this problem, unsupervised domain adaptation (UDA) is proposed to improve the segmentation model's adaptability to the target domain. + +Domain alignment is one of the mainstream UDA semantic segmentation methods, aiming to align the distribution of source and target domains in input [30, 60, 25, 4], feature [53, 32, 19, 22, 35, 65, 50, 56], or output spaces [48, 33, 49]. Works along this line achieve positive adaptation benefits but the lack of specific target domain knowledge leads to slight improvement [39, 68, 66]. + +To this end, self-training methods [27, 10, 1, 69, 64, 67] are proposed to mine target-specific knowledge. These methods use the pseudo-labels generated by the pre-adapted model to further train the model on the target domain. Consequently, the quality of pseudo-labels for training directly determines the performance of self-training. Following this key point, reliability measure-based and uncertainty estimation-based self-training methods are proposed [71, 27, 69, 10, 1, 64, 52]. These methods reduce the noise interference of pseudo-labels for category learning, bring + +ing considerable performance improvement. + +In this paper, we explore the potential of self-training from another perspective, as shown in Fig. 1. In Fig. 1 A, previous self-training methods perform category learning on reliable pseudo-labels and discard unreliable ones. However, we find that not only category learning but relation learning can be performed in pseudo-labels to further improve the adaptability of the model. In Fig. 1 B, we argue that relation learning in pseudo-labels can be performed in two ways: (1) The relations between reliable pseudo-labels can be additionally used for representation learning to build a more generalized representation space. (2) By establishing the relations between reliable and unreliable pseudolabels, discarded pixels can also be effectively used for self-training to increase the certainty of the model. In this way, the available knowledge contained in pseudo-labels can be fully exploited, both reliable and unreliable pixels. + +To achieve the above goals, building reasonable relations between pixels is the core. Dense pixel relations can be represented by a relation matrix (or affinity matrix) [8, 20, 29], modeling the similarity between pixels on an image. Due to massive noise contained in the pseudo-labels, the relation matrix constructed by them also contain noisy relations. We explore two observational priors to guide the building of relations, as shown in Fig. 2. We use the predictions of the unadapted model for the target images to observe noise distribution of relations. Comparing Fig. 2 (e) and (f), we observe that high-level relations built by pseudo-labels are noisy in long-distance association but are reliable within local areas, which are termed as reliable local relations prior. We analyze this because the insufficiently adapted model cannot transfer global semantics and can only give reasonable relations in local regions. Besides, in Fig. 2(d), we further explore the low-level relations built on each local grid in image space using Gaussian kernel. We find that the low-level relations in local grids can capture the boundaries of objects and contain exploitable relations, which are termed as available low-level relations prior. We argue that such relations, although lacking in semantics, provides class boundary clues can be reasonably exploited. + +With these aspects in mind, we propose a pseudo-relation learning-based self-training framework, Relation Teacher (RTea), forcing the student model to learn the pseudo-relations between pixels from the teacher model and achieve co-evolution for both models. In this framework, with the guidance of the above two priors, we first use pseudo-labels to build high-level relations in each divided grid, which avoids being misled by long-distance relationships. Then, we fuse low-level relations in image space into high-level relations to attenuate noisy relations and assist semantic relations in identifying category boundaries. Next, we explore the way of learning pseudo-relations and devise a novel pseudo-relations loss, which optimizes the class + +![](images/7f743b37a18ae73cfb5ac3832af2dd81ec61e0f3bebb185c7e501d56b8902bd8.jpg) +(a).Image + +![](images/d18924e7756a28d990d38535d79507175d310c5c50d1fecb5e94e449551faf4f.jpg) +(b).Prediction + +![](images/58d5a3c74230877663367ae214ca143ff1a3a12f790db154b05b189e5bc87d5d.jpg) +↓ + +![](images/3e6bacf1391cb7f46bec1601a34ace35f79da9d7644fdc862d10e823fd99be1b.jpg) + +![](images/1deaca3fe9718329bcf70689d59fd57c12edb57d1a2a648368666414537a5e77.jpg) +(e). Relations from Pred. + +![](images/20c7b52989277a1265c847221405c7848ab1d5ff644123a289f60547dca6d399.jpg) +(c).Ground Truth + +![](images/295c2ced34e5effa9e010372649c4e44e5a1081023d29d5690b6a212463d9c04.jpg) +similarity + +![](images/18f0f17ee805bb30e8314cab4f89f3ba3c4261204397d6763bfc096b09692b8b.jpg) +(f).Relations from GT. + +![](images/415b79f83346cd4aaecc7672860d21607deb4a7e6b99fefeb86ea1e044bbc983.jpg) +Density Bar: +Figure 2: Overview of two observational priors. (b) is the source-only model's prediction, (d) is the local relation map in image space built by Gaussian kernel in each grid, (e) is the pseudo-relation matrix. (f) is the relation matrix built by ground truth. + +probability to meet the relation consistency by finding the optimal sub-graph division from the global pseudo-relation of each class. It has two advantages over the naive relation-learning loss: one is global relational modeling, which can be easily implemented by matrix multiplication; the other is threshold-free learning by dynamically weighting class probabilities and pseudo-relations. + +With RTea, the model's certainty and consistency of prediction can be enhanced on the target domain, and the cross-domain inadaptation is further eliminated. Sufficient experiments show our method can further mine the available knowledge in pseudo-labels, and it can be easily incorporated into existing self-training method to further boost their performance. + +# 2. Related work + +Unsupervised Domain Adaptation (UDA). UDA methods can be divided into domain alignment and self-training. Alignment-based methods narrow the domain gap by aligning distributions at different levels, e.g., input [12, 30, 25, 60], feature [32, 33, 7, 50, 56, 22] and output [48, 49, 59]. Although they achieve positive adaptation benefits, the lack of specific target domain knowledge leads to slight improvement. To this end, self-training methods are proposed to train the network with pseudo-labels for the target domain, which can be divided into two categories, offline and online pseudo-label-based methods. Offline self-training (OFFST) methods save the target domain pseudo-labels generated by the pre-trained model and use them to train the model iteratively [27, 10, 37]. To avoid noise interfer + +ence, these methods select high-quality pseudo-labels via threshold setting [70, 71], consistent prediction [68], and pseudo-label prototypes [64]. These methods require additional storage of pseudo-labels and an iterative training, which is not conducive to practical use. Online self-training (ONST) uses the model's output during training as supervision without saving intermediate results [58, 4, 51, 1]. ONST avoids the inconvenience of multiple training rounds and manual intervention between consecutive rounds in OFFST. Our work is designed in online self-training fashion. Besides, our method further mines the available knowledge in pseudo-labels from the novel perspective of pixel relations, which can further promote pseudo-label learning and boosting self-training performance. + +Relation Learning (RL) in Semantic Segmentation. In supervised semantic segmentation, capturing relations between pixels is continuously studied at feature [8, 20, 29] and output layers[24, 17]. At the feature layer, several work [8, 20, 62, 29] use the label-guided pixel relation to build a compact feature space, in which features of the same class are close and of different classes are far. At the output layer, AAF [24] and CDGC [17] exploit pixel relations in the ground truth to correct the output probabilities, forcing the model to adjust both the classifier and the feature extractor to output reasonable relations and semantic structure. These supervised RL methods achieve huge performance improvements, emphasizing the importance of maintaining the relation between pixels. However, in the UDA task, the lack of annotations makes it impossible to build relations as these works. Our method proposes a novel pseudo-relation building and learning strategy so that the above advantages can be also achieved to the UDA segmentation task. + +Pseudo Label Correction. As a classic technique of semi-supervised learning, pseudo-labeling has shown favorable competitive advantages in many visual tasks with limited labels. Due to the limitation of confidence bias and error accumulation [41], pseudo-labeling are easy to overfit the noise and lead to model divergence[61]. Some pioneering works alleviate the problems from pseudo-label selection[63], negative label learning[41], contrastive learning [55], model calibration [23, 54]. However, the task-specific and domain-dependent design limits the application of these methods in complex cross-domain tasks. In contrast, our work proposes a novel perspective to rectify pseudo-labels and a tailored solution for cross-domain segmentation tasks. + +# 3. Methodology + +# 3.1. Background and Overview + +This paper focuses on the unsupervised domain adaptation (UDA) semantic segmentation, where source domain data $\mathcal{X}_s = \{x_s\}$ with pixel-level labels $\mathcal{Y}_s = \{y_s\}$ + +and unlabeled target domain data $\mathcal{X}_t = \{x_t\}$ are given. Our goal is to train a segmentation model $G$ that can work well on target domain. $G$ consists of a feature extractor $F$ and a classifier $C$ . Given sampled image $x\in \mathcal{X}_s\cup \mathcal{X}_t$ , $F$ mapping $x$ to the feature space $f = F(x)$ , and $C$ categorizes each feature in $f$ to obtain a class probability map $p = C(F(x))\in \mathbb{R}^{h\times w\times K}$ . For the source domain, the cross entropy loss $L_{s}$ is calculated to optimize the model, + +$$ +L _ {s} = - \frac {1}{\left| \mathcal {X} _ {s} \right|} \sum_ {x _ {s} \in \mathcal {X} _ {s}} \log C (F (x _ {s})) (y _ {s}). \tag {1} +$$ + +For the target domain, to narrow the domain gap, self-training methods adopt pseudo-labels $\hat{y}_t$ generated by the pre-adapted model to retrain the unadapted model, + +$$ +L _ {s t} = - \frac {1}{| \mathcal {X} _ {t} |} \sum_ {x _ {t} \in \mathcal {X} _ {t}} \log C (F (x _ {t})) (\hat {y} _ {t}). \tag {2} +$$ + +In this way, the model's adaptability can be enhanced by relearning the knowledge of the pseudo-labels in the target domain. However, using Eq. 2 tends to interfere with training because the pseudo-labels contain massive noise. Thus, some works select high-confidence pseudo-labels by setting threshold $\zeta^k$ for each class, + +$$ +\hat {y} _ {t} = \left\{ \begin{array}{c l} \arg \max _ {k} p _ {t} ^ {k}, & \text {i f} \max \left(p _ {t} ^ {k}\right) > \zeta^ {k} \\ \text {i g n o r e}, & \text {o t h e r w i s e}, \end{array} \right. \tag {3} +$$ + +where $p_t^k$ is the $k$ -th class probability score. In Eq. 3, the $\zeta^k$ determines the quality of the selected pixels, which needs to be dynamically adjusted according to the adaptation degree. Thus, in the subsequent works, scholars [58, 4, 51, 1] mainly focus on setting reasonable thresholds or uncertainty estimation strategies to select reliable pixels. + +In this paper, we explore the potential of self-training from another perspective. Different from mining category knowledge in pseudo-labels, we propose to mine relation knowledge in pseudo-relations between pixels. The overview of our method is shown in Fig 3. For the source domain, images are input to the student model, which is optimized by the $L_{s}$ . For the target domain, the original image and its data-transformed version are input into the student model and teacher model, respectively. After that, the output of the teacher model is used to build pseudo-relations $S_{pr}$ to further supervise the student model of category learning by $L_{st}$ and relation learning by $L_{pr}$ . We detail the pseudo-relation $S_{pr}$ building in Sec.3.2, and detail the pseudo-relation learning by optimizing $L_{pr}$ in Sec.3.3. + +# 3.2. Pseudo-relation Building + +In the supervised segmentation task, relations can be driven by ground truth, which is not achievable for the UDA segmentation. Thus, how to build the relations between + +![](images/473a1abc6e400ec0d63067a55eacaca6a37b13009b17961de2247b38a1bc59ab.jpg) +Figure 3: The overall pipeline of the proposed Relation Teacher that includes a student model and a teacher model. $S_{low}$ , $S_{high}$ and $S_{pr}$ represent low-level relation matrix, high-level relation matrix and pseudo-relation matrix. $L_{st}$ is the traditional loss function for pseudo-label learning. $L_{pr}$ is the proposed loss function for pseudo-relation learning. + +pixels in the target domain is the key. A naive solution is to build by measuring the class similarity between pseudolabels from a pre-adapted model. Given any two pixels $p_{(t,i)}$ and $p_{(t,j)}$ ( $i,j = 0,1,2,\dots,w\times h$ ) on the class probability map $p_t\in \mathbb{R}^{h\times w\times K}$ of the target domain, the high-level relation between them can be defined as, + +$$ +s _ {(i, j)} = \operatorname {S I M} \left(p _ {(t, i)}, p _ {(t, j)}\right), \tag {4} +$$ + +where $\mathrm{SIM}(\cdot ,\cdot)$ is the cosine similarity measure. Extending this relation to all pixels in an image, we can derive a highlevel relation matrix $S = \{s(i,j)\} \in \mathbb{R}^{hw\times hw}$ . However, such a relation modeling mechanism will introduce massive noise due to the unadapted model. As mentioned in reliable local relations prior, these noises are mainly in the long-distance relations but relations in local grids are relatively accurate. + +To this end, we devise a local relation modeling mechanism. We divide the target image into $N\times N$ grids $\{G_l\}_{l = 1}^{hw / N^2}$ and model the relations inside the grid. Then the high-level relation matrix for each grid can be obtained, + +$$ +S _ {h i g h} = \left\{s _ {(m, n)} \right\} _ {(m, n) \in G _ {l}} \in \mathbb {R} ^ {N ^ {2} \times N ^ {2}}. \tag {5} +$$ + +Nonetheless, local pseudo-relations may still contain noise due to domain shifts. + +To further mitigate unreliable relations in local grids, we introduce low-level relation constraints in each grid. The motivation stems from available low-level relations prior that local low-level relations (RGB space) can be well used to capture the edges and internal structures of + +objects. Drawing on the traditional potential energy function constructing the potential energy field [43, 44, 38], we use the Gaussian function to calculate the energy on the RGBXY[43] space as low-level relation constraints, + +$$ +S _ {l o w} = \left\{\Psi_ {(m, n)} \right\} _ {(m, n) \in G _ {l}} \in \mathbb {R} ^ {N ^ {2} \times N ^ {2}}, +$$ + +$$ +\Psi (m, n) = \exp \left(- \left| \frac {I _ {m} - I _ {n}}{\sigma} \right| ^ {2}\right), \tag {6} +$$ + +where $I_{(\cdot)}$ is the feature vector on RGBXY space, $\sigma$ is the bandwidth parameter of the Gaussian function. Due to the nature of the Gaussian function[16], the value range of the $S_{low}$ are [0, 1], which is the same as that of $S_{high}$ . A higher value indicates a stronger association between pixels. Although it lacks high-level semantics, it can better regularize relations (See Tab. 4 for verification). We linearly combine the low- and high-level relations as final pseudo-relations, + +$$ +S _ {p r} = \alpha S _ {l o w} + (1 - \alpha) S _ {h i g h}, \tag {7} +$$ + +where the $\alpha$ is a hyper-parameter and is simply set to 0.5. + +# 3.3. Pseudo-relation Learning + +Following the paradigm of pseudo-label learning, we can exploit the reliable relations in the pseudo-relation matrix to perform pseudo-relation learning. Specifically, for any pixel pair $p_{(t,i)}$ and $p_{(t,j)}$ in $l$ -th grid, we can perform a pairwise + +relation loss [24, 17] in a pseudo manner as follows, + +$$ +\begin{array}{l} \hat {L} _ {p r} = \sum_ {l} \sum_ {i, j} \operatorname {K L} \left(p _ {(t, i)} \mid \mid p _ {(t, j)}\right) \cdot \mathbb {1} \left(S _ {p r; l} (i, j) > M _ {u p}\right) + \\ (1 - \mathrm {K L} (p _ {(t, i)} | | p _ {(t, j)})) \cdot \mathbb {1} \left(S _ {p r; l} (i, j) < M _ {l o w}\right). \tag {8} \\ \end{array} +$$ + +$\mathrm{KL}(\cdot ||\cdot)$ is the Kullback-Leibler divergence between two distributions. $\mathbb{1}(\cdot)$ is the indicator function for thresholding. $M_{up}$ and $M_{low}$ are upper and lower thresholds for filtering unreliable relations. Optimizing this loss pulls the class distribution of the pixel pairs with a pseudo-relation higher than $M_{up}$ closer and pushes those with a pseudorelation lower than $M_{low}$ further away. In this way, pseudorelation learning can assist pseudo-label learning (in Eq.2) in the following aspects. Let the pixels used by Eq.2 be denoted as reliable pixels, and the rest are unreliable ones. 1). Relations between reliable pixels. Those reliable inter- and intra-class relations are informative and can be incorporated into learning as structural inference. 2). Relations between reliable and unreliable pixels. Pushing or Pulling the class probabilities of the unreliable pixels towards reliable ones will greatly enhance the confidence of the model. 3). Relations between unreliable pixels. Although we cannot give these pixel pairs explicit class targets, implicit class cues may help the model to enhance confidence. See further instructions in Appendix A. + +In practice, in $\hat{L}_{pr}$ , the pair of class distribution input to $\mathrm{KL}(\cdot ||\cdot)$ should assign the more sharp one as the target. This makes it require pair-by-pair index calculation, which greatly increases the training time. Besides, $M_{up}$ and $M_{low}$ requires hyper-parameter search under different adaptation tasks, hindering the flexibility of application. Here, we learn from the idea of graph cut [57] and devise a new pseudorelation loss, which can be performed by matrix multiplication without explicit thresholding. + +Specifically, in $l$ -th grid, we construct an undirected weighted graph $\mathcal{G}$ , treating all pixels in this grid as nodes of the graph and the similarity between these pixels as the weights of edges. Thus, the corresponding $S_{pr;l}$ can be seen as a pseudo-adjacency matrix of the $\mathcal{G}$ . With the $\mathcal{G}$ , the $K$ classification problem is regarded as a graph cutting problem of cutting a graph into $K$ subgraphs. Then, the $k$ -th class probability $p_{t;l}^{k}$ of this grid is regarded as the probability of the corresponding nodes cut into $k$ -th subgraph ( $k \in [0, K - 1]$ ). According to the properties of the graph, we can calculate the soft cost of cutting the $k$ -th subgraph as follows, + +$$ +c u t ^ {k} = \hat {p} _ {t; l} ^ {k} S _ {p r; l} \mathbf {1} - \hat {p} _ {t; l} ^ {k} S _ {p r; l} \left(\hat {p} _ {t; l} ^ {k}\right) ^ {T}. \tag {9} +$$ + +$\hat{p}_{t;l}^{k}\in \mathbb{R}^{1\times N^{2}}$ is the vector flatten by $p_{t;l}^{k}\in \mathbb{R}^{1\times N\times N}$ $\mathbf{1}\in \mathbb{R}^{N^2\times 1}$ is an all-ones vector. We show an example to illustrate Eq.9 in Fig.4. The smaller the cut value, the smaller + +![](images/be8373f0132529ceab12448f66dc6f2fd88cb209f7ed25b8f2b389c492cab8c2.jpg) + +$$ +\begin{array}{l} P ^ {0} S 1: \text {- - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - } \\ P ^ {0} S P ^ {0}: \text {- - } \end{array} +$$ + +$$ +\begin{array}{c} \hline P: \text {c l a s s p r o b a b i l i t y} \\ p _ {1} \quad 1 \quad 0 \\ p _ {2} \quad 1 \quad 0 \\ p _ {3} \quad 1 \quad 0 \\ p _ {4} \quad 0 \quad 1 \\ p _ {5} \quad 0 \quad 1 \\ S: \text {a d j a c e n c y m a t r i x} \end{array} +$$ + +Figure 4: We show an example of binary classification to illustrate Eq.9. Given five samples and their class probability $P$ , take the cut of class 0 as an example. $P^0 S1$ is the sum of all edges connected to the nodes of class 0, i.e., the green and dashed lines. $P^0 SP^0$ is the sum of all edges connecting two nodes of class 0, i.e., the green lines, and $P^0 S1 - P^0 SP^0$ is the cost consumed of the 0 class. To minimize the cost, nodes with high affinity should be classified into the same class, and vice versa. + +the correlation between the subgraphs and the larger the correlation within the subgraphs. Thus, $cut^k$ can be regarded as a proxy, when the $cut^k$ value is small, the class probability $p_{t;l}^k$ better conforms to the pseudo-relations $S_{pr;l}$ , and vice versa. Moreover, the Eq.9 is derivable with respect to $p_{t;l}^k$ , and its gradient w.r.t. $p^k$ is, + +$$ +\frac {\partial c u t ^ {k}}{\partial p ^ {k}} = S _ {p r} \left(\mathbf {1} - 2 p ^ {k}\right). \tag {10} +$$ + +The proxy's gradient is proportional to the $S_{pr}$ and $1 - 2p^{k}$ , which implicitly weight high-confidence relations and reliable pixels (class probability far from 0.5). This explains that unreliable edges (relations) on the graph play a minor role in pulling or pushing away the class distribution, enabling adaptive weighting without threshold. Consequently, we modify Eq.9 as a threshold-free pseudo-relation loss function to optimize $p_t$ as follows, + +$$ +L _ {p r} = \sum_ {l} ^ {h w / N ^ {2}} \sum_ {k} ^ {K} \hat {p} _ {t; l} ^ {k} S _ {p r} \left(\mathbf {1} - \hat {p} _ {t; l} ^ {k}\right) ^ {T}. \tag {11} +$$ + +$L_{pr}$ can be calculated using matrix multiplication in a simple and quick way. + +# 3.4. Relation Teacher + +We embed the learning of pseudo-relation into the optimization of mean-teacher [45] framework to realize online self-training as shown in Fig 3. The final optimization objective is, + +$$ +L _ {f} = L _ {s} + \lambda_ {s t} L _ {s t} + \lambda_ {p r} L _ {p r}. \tag {12} +$$ + +where $\lambda_{pr}$ , $\lambda_{st}$ are the trade-off coefficients. $\lambda_{st}$ is set as 0.001 following SAC [1]. $\lambda_{pr}$ is empirically set to 0.01 to balance the loss value. + +
MethodroadsidewalkBuildingWallfencepolelightsignvege.terrainskypersonridercartruckbustrainmbikebikemIoU
FADA (ECCV 2020) [50]91.050.686.043.429.836.843.425.086.838.387.464.038.085.231.646.16.525.437.150.1
FDA (CVPR 2020) [60]92.553.382.326.527.636.440.538.882.239.878.062.634.484.934.153.116.827.746.450.4
IAST (ECCV 2020) [37]93.857.885.139.526.726.243.134.784.932.988.062.629.087.339.249.623.234.739.651.5
MetaCorr (CVPR 2021) [10]92.858.186.239.733.136.342.038.685.537.887.662.831.784.835.750.32.036.848.052.1
RPT (CVPR 2021) [66]89.243.386.139.529.940.249.633.187.438.586.064.425.188.536.645.823.936.556.852.6
SAC (CVPR 2021) [1]90.453.986.642.427.345.148.542.787.440.186.167.529.788.549.154.69.826.645.353.8
CFDAN (CVPR 2021) [36]92.558.386.527.428.838.146.742.585.438.491.866.437.087.840.752.444.641.759.056.1
SDFA (ICCV 2021) [26]94.859.486.240.529.525.543.834.785.934.989.563.430.888.342.650.725.335.740.952.8
ProDA (CVPR 2021) [64]87.85679.746.344.845.653.553.588.645.282.170.739.288.845.559.41.048.956.457.5
SimT (CVPR2022) [9]94.26088.530.339.741.247.860.888.647.389.371.545.090.754.260.20.051.858.458.9
CPST (CVPR 2022) [28]92.359.984.945.729.752.861.559.587.941.585.073.035.590.448.773.926.353.853.960.8
Undoing (CVPR 2022) [31]92.952.787.239.441.343.95552.989.348.291.271.43690.267.959.8048.559.359.3
DAP (CVPR 2022) [21]94.563.189.129.847.550.456.758.789.550.28773.638.691.350.252.9050.263.559.8
CaCo (CVPR 2022) [18]93.864.185.743.742.246.150.154.088.74786.568.12.988.043.460.131.546.160.958.0
ADPL (TPAMI 2023) [3]93.460.687.545.332.637.343.355.587.244.88864.534.288.352.661.849.841.859.459.4
RTea (Ours)95.467.187.946.144.046.053.859.589.749.889.871.540.590.855.057.922.147.762.561.9
Daformer (CVPR 2022) [14]95.770.289.453.548.149.655.859.489.947.992.572.244.792.374.578.265.155.961.868.3
Daformer + RTea (Ours)96.171.789.157.850.455.959.366.790.448.294.574.846.593.878.781.665.857.162.870.6
HRDA (ECCV 2022) [15]96.474.491.061.651.557.163.969.391.348.494.279.052.993.984.185.775.963.967.573.8
HRDA + RTea (Ours)97.175.292.663.551.858.266.571.291.149.096.881.554.294.284.886.675.762.266.774.7
+ +Table 1: Experimental results for GTA5 $\rightarrow$ Cityscapes adaptation task. The best results in every column are highlighted. + +
MethodroadsidewalkBuildingWall*fence*pole*lightsignvege.skypersonridercarbusmbikebikemIoUmIoU*
FADA (ECCV 2020)[50]84.540.183.14.8034.320.127.284.88453.522.685.443.726.827.845.252.5
FDA (CVPR 2020) [60]79.335.073.2---19.924.061.782.661.431.183.940.838.451.1-52.5
IAST (ECCV 2020) [37]81.941.583.317.74.632.330.928.883.485.065.530.886.538.233.152.749.857.0
MetaCorr (CVPR 2021) [10]92.652.781.38.92.428.113.07.383.585.060.119.784.837.221.543.945.152.5
RPT (CVPR 2021) [66]88.946.584.515.10.538.539.530.185.985.859.826.188.146.827.756.151.258.9
SAC (CVPR 2021) [1]89.347.285.526.51.343.045.532.087.189.363.625.486.935.630.453.052.659.3
CFDAN (CVPR 2021) [36]75.730.081.911.52.535.318.032.786.290.165.133.283.336.535.354.348.255.5
SFDA (ICCV 2021) [26]90.550.081.613.32.834.725.733.183.889.266.034.985.353.446.146.652.060.1
ProDA (CVPR 2021) [64]87.845.784.637.10.644.054.637.088.184.474.224.388.251.140.545.655.562.0
CPST (CVPR 2022) [28]87.243.985.533.60.347.757.437.287.888.579.032.090.649.450.859.857.965.3
Undoing (CVPR 2022) [31]82.537.281.123.8045.757.247.687.785.874.128.688.466.047.055.356.764.5
CaCo (CVPR 2022) [18]87.448.979.68.80.230.117.428.379.981.256.324.278.639.228.148.346.053.6
ADPL (TPAMI 2023) [3]86.138.685.929.71.336.641.347.28590.467.544.387.457.143.951.455.963.6
RTea (ours)93.259.686.331.34.843.141.844.088.690.570.442.689.556.740.259.958.966.4
Daformer (CVPR 2022) [14]84.540.788.441.56.550.05554.68689.873.248.287.253.253.961.767.460.9
Daformer + RTea (Ours)85.943.290.145.16.352.460.557.187.892.275.351.887.455.954.162.669.563.0
HRDA (ECCV 2022) [15]85.247.788.849.54.857.265.760.985.392.979.452.88964.763.964.972.465.8
HRDA + RTea (Ours)87.849.090.350.35.558.666.061.486.893.179.553.189.565.163.764.673.066.5
+ +Table 2: Experimental results for SYNTHIA $\rightarrow$ Cityscapes adaptation task. The best results in every column are highlighted. The mIoU and mIoU* are averaged over 16 and 13 categories, respectively. + +# 4. Experiment + +# 4.1. Datasets and Experimental Setup + +Datasets. We use one real dataset (Cityscapes [5]) and two synthetic datasets (GTA5 [40] and SYNTHIA [42]). The Cityscapes dataset contains 2,975 training images and 500 validation images of resolution $2048 \times 1024$ . The GTA5 dataset contains 24,966 images with resolution $1914 \times 1052$ and has 19 common categories with Cityscapes. The SYNTHIA dataset contains 9,400 images with resolution $1280 \times 760$ and has 16 common categories with Cityscapes. + +Implementation Details. We adopt Deeplab-v2 [2] as the base network, ResNet-101 [11] as the feature extractor and the aspp [2] module as the classifier. The network is pre + +trained on ImageNet. The optimizer is SGD with the momentum of 0.9 and weight decay of $10^{-4}$ . The initial learning rate is set to $2.5 \times 10^{-4}$ , and then is reduced following a poly policy with a power of 0.9. The batch size is set as 4. The final $\lambda_{f}$ and $\lambda_{o}$ values are set to 0.025 and 0.005, respectively. We apply the $L^{pr}$ to the model's output class probability, which is 8 times smaller than the original resolution. And the grid size $N$ is set to 8. The weighting factor $\alpha$ is set to 0.5. The $\sigma$ for XY and RGB space in Gaussian function is set to 6 and 0.1, following [43]. Data augmentation strategies performed on the data input to the student model include random flipping, Gaussian noise, color transformation, cutout[6], and contrast enhancement, a similar and common operation in online self + +training methods [58, 4, 51, 1]. Besides, we also preform the class-mixing resampling strategy [47] on the source domain to focus on the minority class. When performing $L_{st}$ for pseudo-label learning, we adopt the thresholding selection method in SAC [1] to pick high-quality samples. After training with Rtea, we retrained the model using the distillation strategy [64] for better adaptation, which is commonly used in recently published UDA work [31, 21, 28, 3]. The detailed scores for each stage are in the Tab. 3. Our network is trained with four RTX3090 GPUs on PyTorch. + +# 4.2. Comparisons with State-of-the-Arts + +$\mathrm{GTA5} \rightarrow \mathrm{Cityscapes}$ . We report the comparison results with existing methods on $\mathrm{GTA5} \rightarrow \mathrm{Cityscapes}$ task in Tab. 1. We compared two structures based on resnet-101 and transformer structures. Overall, our RTea achieves new state-of-the-art performance than related works, and the category performance scores are also highly competitive, demonstrating the effectiveness of RTea. Compared with the domain alignment method, the performance of RTea show an advantage over the state-of-the-art method FDA [60] by $11.5\%$ . Compared with the offline self-training method, the mIoU score of RTea is $10.4\%$ and $9.8\%$ higher than IAST [37] and RPT[66]. Compared with the online self-training method, RTea exceeds SAC [1] and ProDA [64] by $8.1\%$ and $4.4\%$ . Compared with the newly released method Undoing[31], DAP[21] and ADPL[3], our RTea still outperforms these methods by more than $2.0\%$ mIoU scores, showing the potential of our method even more. Compared with the method of transformer structure, our method improves the mIoU score by $0.7\%$ and $0.9\%$ on Daformer [14] and HRDA [15] respectively, which shows that RTea has good scalability and transferability. Qualitative results on both tasks can be found in Appendix B. + +SYNTHIA $\rightarrow$ Cityscapes. The results of using SYNTHIA as the source domain are reported in Tab. 2, including mIoU/mIoU* covering 16/13 classes. On the whole, our method still achieves significant improvements, showing gains over advanced methods. In particular, SYNTHIA and Cityscapes suffer from significant visual domain differences in 'road', and 'sidewalk', which leads to the poor performance of the most UDA methods in these categories. Our method uses the pseudo-relations of these categories and achieves higher performance improvements, and we argue this is due to the local pseudo-relation learning to better capture the structure of these categories. Compared with the domain alignment and offline self-training methods, RTea maintains similar performance gains to the GTA5 transfer task. Compared with online self-training method, we achieve better performance than CPST [28] over 16 and 13 classes, exceeding its by $1.0\%$ and $1.1\%$ mIoU score. Compared with the adaptation method using transformer structure, our method improves the mIoU score by $2.1\%$ and + +
\(L_s\)\(L_{st}\)copy-paste\(\hat{L}_{pr}\)\(L_{pr}\)\(L_{pr}^s\)DistGTA5SYNTHIA
✓✓53.551.2
✓✓✓55.853.9
✓✓✓✓58.956.3
✓✓✓✓59.656.8
✓✓✓✓✓59.656.9
✓✓✓✓✓✓61.958.9
+ +Table 3: Ablation experiments of each module in GTA5 and SYNTHIA $\rightarrow$ Cityscapes adaptation task. The basic self-training $(L_{s} + L_{st})$ is following SAC[1]. The copy-paste means that we adopt the resampling strategy in [47] for minority learning. Here, we report a result of $\hat{L}_{pr}$ with the fine-tuned thresholds by grid search. $L_{pr}^{s}$ denotes that relation learning is performed on the source domain. Dist denote the distillation strategy in [50, 64]. All numbers are mIoU(%) score. + +$0.7\%$ on Daformer [14] and HRDA [15], which further verifies the effectiveness of the method. + +# 4.3. Ablation Studies + +Ablation for Each Module. Tab.3 reports the ablation results for different modules. We adopt SAC [1] with the copy-paste [47] argumentation as the baseline, achieving the $55.8\%$ and $53.9\%$ mIoU score on two adaptation tasks. Overall, Rtea achieves $3.8\%$ and $3.0\%$ performance improvements on the two tasks on this competitive baseline, respectively, showing the effectiveness of the pseudorelation learning. Specifically, the naive $\hat{L}_{pr}$ loss, although, can improve performance, the screening of the threshold makes it difficult to be directly applied to practice, because the threshold may be very sensitive in different adaptation scenarios. The proposed $L_{pr}$ loss does not require explicit threshold while improving the performance, showing its flexibility and effectiveness. In addition, we also tried to perform pseudo-relation learning on the source domain $L_{pr}^{s}$ , and we did not find a significant performance improvement, which may be because it cannot directly benefit the target domain. After training with RTea, the self-distillation method can still be used to further improve the adaptability of the model in the target domain. + +Ablation for Pseudo-Relation Building. Tab.4 shows the ablation results for building pseudo-relation. When the relations are built on RGBXY space ( $S_{low}$ ), the performance achieves a good improvement, $2.0\%$ and $2.1\%$ on two tasks, respectively, which suggests that low-level relations on local grids can propagate effective category knowledge. When the relations are built on pseudo labels ( $S_{high}$ ), the performance is only improved by $1.0\%$ and $0.7\%$ on two tasks, respectively. This is because it is not easy to find valuable relation pairs in this way, and their effects may overlap with label learning. Specifically, unreliable pixels discarded by pseudo-label learning are still difficult to use, and high + +
SlowShighSprGTA5SYNTHIA
✓55.853.9
57.855.8
✓56.854.6
✓59.656.8
+ +Table 4: Ablation experiments on the pseudo-relation building. $S_{low}$ , $S_{high}$ and $S_{pr}$ are low-level, high-level and final pseudo relation matrix. + +
R-RR-UU-UGTA5SYNTHIA
55.853.9
✓✓58.255.2
✓✓57.254.9
✓✓59.356.6
✓✓✓59.656.8
+ +confidence relationships still contain massive noise, When $S_{low}$ and $S_{high}$ are combined, the best effect is achieved. We argue that the advantage is that, the noisy relations in the high level are corrected and the lack of semantics of the low-level relations is also made up, and more unreliable pixels are better exploited. + +Ablation for Pseudo-Relation Learning. To verify the effect of different pixel pairs on pseudo-relation learning, we devise the ablation study in Tab. 5. We follow 1), 2) and 3) explained in the Eq. 8, and divide them into R-R (two reliable pixels), R-U (one reliable and one unreliable pixel) and U-U (two unreliable pixels). During training, we clear all gradients for one of the pairs to verify its effect on adaptation. We find that R-U pairs play the most important role in adaptation, R-R pairs come second, and U-U pairs come last. We analyze learning R-U pairs can make full use of valuable pixels from unexploited target domains, which is the most direct to enhance the target domain adaptability. + +# 4.4. Discussion + +Sensitivity for reliable sample selection. In this section, we perform two experiments to explore how sensitive RTea is to reliable sample selection. First, we report the results when the parameters of the heuristic threshold (Eq. 3) are varied. The thresholding strategy consists of two hyperparameters, namely the upper threshold $\theta$ and the decay rate $\beta$ . Table 6 shows that our method maintains a stable performance improvement when thresholding parameters vary within a certain range. Second, we report Rtea's performance on different reliable sample selection methods in Table 7. It verifies the effectiveness of RTea, which improves the performance of different self-training methods. + +Table 5: Ablation experiments on the pseudo-relation learning. $R - R$ denotes pairs with two reliable pixels. $R - U$ denotes pairs with one reliable and one unreliable pixel. $U - U$ denotes pairs with two unreliable pixels. + +
β=0.0001β=0.001β=0.01
θ=0.7559.059.258.8
θ=0.8059.259.659.1
+ +Table 6: The mIoU scores (\%) on GTA5 → Cityscapes task with varying thresholding parameters in Eq. 3. + +
PDCDADHT
without Rtea55.054.453.255.8
with Rtea58.856.854.859.6
+ +How local grids affect each relation pair. We perform experiments on $\mathrm{GTA5} \rightarrow$ Cityscapes to verify which relation pairs are most affected by local grids. Pixels are still classified as reliable (R) and unreliable (U) according to whether they are used for category learning in traditional self-training, see Tabel 8. In the first line, we find that (1) the global grid is good for $R - R$ because it extends the spatial scope of relational learning, while it does harm to $R - U$ and $U - U$ due to the long-range relation noise. As a result, performing pseudo-relation learning on global region lead model degradation. In the second line, we argue that (2) performing pseudo-relation on the local grids slightly reduces the gain of $R - R$ , but greatly reduces the interference of noise on $R - U$ and $U - U$ . Finally, the model can obtain better performance improvement. + +Table 7: The mIoU scores (\%) on GTA5 → Cityscapes task with different reliable sample selection strategies. PD denotes feature-prototype distance [64], CD denotes classifier discrepancy [69], AD denotes adversarial difficulty [34] and HT is our used heuristic threshold [1]. + +
BaselineR-RR-UU-U
Global55.857.2 (+1.4)51.4 (-4.4)52.5 (-3.3)
Local grid55.856.6 (+0.8)57.9 (+2.1)55.9(+0.1)
+ +Table 8: The mIoU (%) of local grids effect on GTA5 → Cityscapes adaptation task. + +Computational overhead. Performing relation learning on dense prediction tasks such as semantic segmentation is time-consuming. Therefore, it is necessary to discuss the computational overhead introduced in Rtea. Overall, we think the pseudo-relation computational overhead is acceptable. First, for complexity, our computational cost is $\mathcal{O}(N^2 WH)$ ( $H, W$ : width and height of feature map, $N$ : grid size, $N \ll W, H$ ), which is greatly reduced compared to the global similarity $\mathcal{O}(W^2 H^2)$ . Second, the pseudorelation can be computed in parallel using matrix operations in PyTorch. On a Nvidia RTX-3090, it only takes almost 40 ms for each batch and only increases about $3\%$ computational overhead in each iteration. Third, the cost is only for training and not for inference. + +Align low- and high-level relation matrix with the same Gaussian function. In the method section, we use the cosine distance (Eq. 5) and Gaussian distance (Eq. 6) to model the similarity of high- and low-level, respectively. It is interesting to explore unifying the modeling of high- and low-level pseudo-relations into the same metric function, e.g. Gaussian distance. With the same metric function, for any local grid $G_{l}$ , the local relation can be built as, $s(m,n) = \sum_{m,n\in G_l}\Psi_{\sigma_{rgbxy}}(m,n)\cdot \Psi_{\sigma_{prob}}(m,n)$ , where $\sigma_{rgbxy}$ and $\sigma_{prob}$ are the bandwidth of the low- and highlevel Gaussian function. This formula is similar to the kernels of bilateral filtering[46], inspiring us to understand the pseudo-relation learning from the filtering perspective, i.e. smoothing and correcting the noise on output probability. Table 9 presents the comparison results, showing unifying the same metric function can maintain performance with less computational overhead. + +
MetricGTA5SYN.TimeMetricGTA5SYN.Time
Current59.656.940msSame Gaussian59.657.129ms
+ +Table 9: The mIoU (\%) and computational cost (time/batch) using different similarity metric functions on GTA5 → Cityscapes adaptation task. + +Hyper-parameters Impacts. We analyze the sensitivity of the hyper-parameters $\alpha$ (trade-off coefficient), grid size $N$ , the results are presented in the Appendix C. + +# 4.5. Visualization + +Visualization of pixel relations. Fig. 5 visualizes the learned relations on $\mathrm{GTA5} \rightarrow$ Cityscapes task. Comparing Fig. 5 a, b and e, it shows that the feature associations of the baseline are chaotic while our method builds more accurate feature relations. Comparing Fig. 5 c, d and e, it indicts that our method captures category relations more accurately than baseline, resulting in more structured outputs. + +Comparison of Pixel Utilization and Model Confidence. Fig. 6 compares the correct pixel utilization (PU) and average confidence (AC) of the model before and after adding RTea. With RTea, the PU is significantly improved and the AC also shows better results. It illustrates RTea can exploit more uncertain pixels around high-confidence pixels and propagate relation information to them, thereby fully improving the certainty of the model. + +Visualization of Pseudo-Labels. Fig. 7 visualizes the pseudo-labels of the baseline and our RTea to demonstrate the benefits of pseudo-relation learning. It shows that the RTea makes better use of pseudo-labels than the baseline model. For the areas are hard to distinguish (framed by the red box), RTea can enlarge the reliable pseudo-label area by capturing relations between pixels. Moreover, RTea provides clear class boundaries for the classes such as roads, sidewalks and buildings, which is more helpful for pseudolabel learning. + +![](images/5811ba1309e25558465de4962c75567ef1d6d781b81175932656aeac564bc93e.jpg) + +Figure 5: Visualization of the learned relations of RTea model on the GTA5 $\rightarrow$ Cityscapes task. +![](images/93b8535da3c7ecf7d5f66ff92ccba366e225fab53bc68672da7b2db7551521d1.jpg) +a. Feature relations of baseline b. Feature relations of RTEca + +![](images/3b45fd8d5e52f3fe52b75908055f8fcc3ef0a3285cbaa97e00b1e9f26c9ce9bc.jpg) + +![](images/637f7bd81d8c696b3643b9fda29bdd1902b90058885522ea3b14ea802d20a57f.jpg) +c. Prediction relations of baseline + +![](images/09ec71f09fc6ec23459b00ac2125bb6d1cd1180aa727eb158e35a6d311648258.jpg) + +![](images/d3519cce78b15802a00fbe117bfa2ae47776833e75aa615a4df7d27f6b7b37f4.jpg) +d. Prediction relations of RTea. + +![](images/43282e3b971dd54296185c03edcc8e4660a4b07d5bb05fcd7346c5fb2f05226a.jpg) + +![](images/41d31133db4cf8311826f3cd7e4086ea77f38cbfdad7415676e85de6b7ea521e.jpg) +c. Relations of ground truth + +![](images/6a9fddb6865fac27d7c76ba275346c8d6b159165e6c213fe4ec164146431b623.jpg) +Figure 6: Comparison of the average correct pixel utilization and confidence of the target domain. + +![](images/3d7d148a51cbe8305f2e5a344dd9bdbcc72051626259ca8158c2f76a368ca598.jpg) + +![](images/b539d5eb420839cfccd88c0dde3278b7ca547a2768371d6dc26fe7fc98676120.jpg) + +![](images/88e8c1907e5d1ce50caed4c169363a75a06583009c03d568c288177b8809c5c9.jpg) + +![](images/41e402e599a716e68b26e55dc1443d20b1ae93e81877f75dd6a26368040ddfa8.jpg) +a. Baseline + +![](images/a52f998cc8ef724e373db891c0d34ba54609e1cf2d2cba03e61359a8d12da073.jpg) + +![](images/64be5e7ef81f1b5783565b42e056d8cca4268298191f6dcd6bbcf3334dedbd63.jpg) + +![](images/07025181b5cdf0daabeb087cc69f5d7a28d908c9e0946bf095c0bc3fc47b50e5.jpg) +b. Ours +Figure 7: Comparison of pseudo-labels of baseline and RTea. The white masked area is unreliable pseudo-labels. + +# 5. Conclusion + +In this paper, we propose pseudo-relation learning framework for UDA semantic segmentation. In RTea, we provide two prior guidelines for pseudo-relation building, which may help more works exploiting pseudo-relations. Moreover, we explore how to use pseudo-relations from the constraints and do detailed analysis and experiments on the proposed solution. Sufficient experiments on two datasets demonstrate the effectiveness of the proposed method. In general, RTea provides a new idea for self-training methods and may inspire more works in this field. + +# References + +[1] Nikita Araslanov and Stefan Roth. Self-supervised augmentation consistency for adapting semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15384-15394, June 2021. 1, 3, 5, 6, 7, 8 +[2] L. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille. Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(4):834-848, 2018. 6 +[3] Yiting Cheng, Fangyun Wei, Jianmin Bao, Dong Chen, and Wenqiang Zhang. Adpl: Adaptive dual path learning for domain adaptation of semantic segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023. 6, 7 +[4] Jaehoon Choi, Taekyung Kim, and Changick Kim. 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In Proceedings of the IEEE/CVF Conference on International Conference on Computer Vision, pages 5982-5991, October 2019. 1, 3 \ No newline at end of file diff --git a/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/images.zip b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..06a21712be21758ff14963f9ae03c9c6fa1fe85b --- /dev/null +++ b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b170de9b419cdbbec7935475de8c242a280e235e00211ee2bdf65bca86b98344 +size 866278 diff --git a/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/layout.json b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a97a3afcd4da01b4ce49e5426bafbd2d9e4f3620 --- /dev/null +++ b/2023/Learning Pseudo-Relations for Cross-domain Semantic Segmentation/layout.json @@ -0,0 +1,12366 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "spans": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "type": "text", + "content": "Learning Pseudo-Relations for Cross-domain Semantic Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 87, + 143, + 505, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 143, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 87, + 143, + 505, + 171 + ], + "type": "text", + "content": "Dong Zhao, Shuang Wang" + }, + { + "bbox": [ + 87, + 143, + 505, + 171 + ], + "type": "inline_equation", + "content": "^{\\text{心}}" + }, + { + "bbox": [ + 87, + 143, + 505, + 171 + ], + "type": "text", + "content": ", Qi Zang, Dou Quan, Xiutiao Ye, Rui Yang, Licheng Jiao \nSchool of Artificial Intelligence, Xidian University, Shaanxi, China" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 146, + 174, + 446, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 174, + 446, + 185 + ], + "spans": [ + { + "bbox": [ + 146, + 174, + 446, + 185 + ], + "type": "text", + "content": "zhaodong01@stu.xidian.edu.cn; shwang@mail.xidian.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "type": "text", + "content": "Domain adaptive semantic segmentation aims to adapt a model trained on labeled source domain to unlabeled target domain. Self-training shows competitive potential in this field. Existing methods along this stream mainly focus on selecting reliable predictions on target data as pseudolabels for category learning, while ignoring the useful relations between pixels for relation learning. In this paper, we propose a pseudo-relation learning framework, Relation Teacher (RTea), which can exploitable pixel relations to efficiently use unreliable pixels and learn generalized representations. In this framework, we build reasonable pseudorelations on local grids and fuse them with low-level relations in the image space, which are motivated by the reliable local relations prior and available low-level relations prior. Then, we design a pseudo-relation learning strategy and optimize the class probability to meet the relation consistency by finding the optimal sub-graph division. In this way, the model's certainty and consistency of prediction are enhanced on the target domain, and the cross-domain inadaptation is further eliminated. Extensive experiments on three datasets demonstrate the effectiveness of the proposed method. The code will be available at https://github.com/DZhaoXd/RTea." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 555, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 640 + ], + "type": "text", + "content": "Semantic segmentation is a challenging problem of assigning each pixel a class label in an image. Driven by deep neural networks, significant progress has been made in this field. Despite these efforts, a segmentation model trained with a specific domain does not generalize well to other domains. It is known to be caused by the domain gap between the training (source) and testing (target) domains [13]. To" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 645, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 645, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 645, + 288, + 714 + ], + "type": "text", + "content": "This work is supported by the National Key R&D Program of China under Grant No. 2021ZD0110400, the National Natural Science Foundation of China (No.62271377, No.62201407), the Key Research and Development Program of Shannxi (No.2021ZDLGY01-06, No.2022ZDLGY01-12), the China Postdoctoral Science Foundation (No. 2022M722496), the Foreign Scholars in University Research and Teaching Program's 111 Project (B07048)." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 312, + 215, + 539, + 282 + ], + "blocks": [ + { + "bbox": [ + 312, + 215, + 539, + 282 + ], + "lines": [ + { + "bbox": [ + 312, + 215, + 539, + 282 + ], + "spans": [ + { + "bbox": [ + 312, + 215, + 539, + 282 + ], + "type": "image", + "image_path": "c011a64d67fb04e16668099ab9df89cc06c66b9d00eb1c9a0482a0bf32eadffa.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 313, + 285, + 538, + 393 + ], + "blocks": [ + { + "bbox": [ + 313, + 285, + 538, + 393 + ], + "lines": [ + { + "bbox": [ + 313, + 285, + 538, + 393 + ], + "spans": [ + { + "bbox": [ + 313, + 285, + 538, + 393 + ], + "type": "image", + "image_path": "0101dc3cc61716f2da9d90e24b55e2f47b861adb4cb11754df61b2f14222d8ff.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 404, + 546, + 453 + ], + "lines": [ + { + "bbox": [ + 305, + 404, + 546, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 404, + 546, + 453 + ], + "type": "text", + "content": "Figure 1: Overview of our motivation. In A, previous self-training methods select reliable pseudo-labels for category learning. In B, our method reasonably utilizes reliable pseudo-labels and unreliable ones for relation learning." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 470, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 470, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 305, + 470, + 545, + 506 + ], + "type": "text", + "content": "solve this problem, unsupervised domain adaptation (UDA) is proposed to improve the segmentation model's adaptability to the target domain." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 508, + 546, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 546, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 546, + 592 + ], + "type": "text", + "content": "Domain alignment is one of the mainstream UDA semantic segmentation methods, aiming to align the distribution of source and target domains in input [30, 60, 25, 4], feature [53, 32, 19, 22, 35, 65, 50, 56], or output spaces [48, 33, 49]. Works along this line achieve positive adaptation benefits but the lack of specific target domain knowledge leads to slight improvement [39, 68, 66]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "To this end, self-training methods [27, 10, 1, 69, 64, 67] are proposed to mine target-specific knowledge. These methods use the pseudo-labels generated by the pre-adapted model to further train the model on the target domain. Consequently, the quality of pseudo-labels for training directly determines the performance of self-training. Following this key point, reliability measure-based and uncertainty estimation-based self-training methods are proposed [71, 27, 69, 10, 1, 64, 52]. These methods reduce the noise interference of pseudo-labels for category learning, bring" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19191" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 228, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 228, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 228, + 84 + ], + "type": "text", + "content": "ing considerable performance improvement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 87, + 290, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 87, + 290, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 87, + 290, + 278 + ], + "type": "text", + "content": "In this paper, we explore the potential of self-training from another perspective, as shown in Fig. 1. In Fig. 1 A, previous self-training methods perform category learning on reliable pseudo-labels and discard unreliable ones. However, we find that not only category learning but relation learning can be performed in pseudo-labels to further improve the adaptability of the model. In Fig. 1 B, we argue that relation learning in pseudo-labels can be performed in two ways: (1) The relations between reliable pseudo-labels can be additionally used for representation learning to build a more generalized representation space. (2) By establishing the relations between reliable and unreliable pseudolabels, discarded pixels can also be effectively used for self-training to increase the certainty of the model. In this way, the available knowledge contained in pseudo-labels can be fully exploited, both reliable and unreliable pixels." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 281, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 289, + 555 + ], + "type": "text", + "content": "To achieve the above goals, building reasonable relations between pixels is the core. Dense pixel relations can be represented by a relation matrix (or affinity matrix) [8, 20, 29], modeling the similarity between pixels on an image. Due to massive noise contained in the pseudo-labels, the relation matrix constructed by them also contain noisy relations. We explore two observational priors to guide the building of relations, as shown in Fig. 2. We use the predictions of the unadapted model for the target images to observe noise distribution of relations. Comparing Fig. 2 (e) and (f), we observe that high-level relations built by pseudo-labels are noisy in long-distance association but are reliable within local areas, which are termed as reliable local relations prior. We analyze this because the insufficiently adapted model cannot transfer global semantics and can only give reasonable relations in local regions. Besides, in Fig. 2(d), we further explore the low-level relations built on each local grid in image space using Gaussian kernel. We find that the low-level relations in local grids can capture the boundaries of objects and contain exploitable relations, which are termed as available low-level relations prior. We argue that such relations, although lacking in semantics, provides class boundary clues can be reasonably exploited." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 558, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 290, + 715 + ], + "type": "text", + "content": "With these aspects in mind, we propose a pseudo-relation learning-based self-training framework, Relation Teacher (RTea), forcing the student model to learn the pseudo-relations between pixels from the teacher model and achieve co-evolution for both models. In this framework, with the guidance of the above two priors, we first use pseudo-labels to build high-level relations in each divided grid, which avoids being misled by long-distance relationships. Then, we fuse low-level relations in image space into high-level relations to attenuate noisy relations and assist semantic relations in identifying category boundaries. Next, we explore the way of learning pseudo-relations and devise a novel pseudo-relations loss, which optimizes the class" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 383, + 113 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 383, + 113 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 383, + 113 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 383, + 113 + ], + "type": "image", + "image_path": "7f743b37a18ae73cfb5ac3832af2dd81ec61e0f3bebb185c7e501d56b8902bd8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 327, + 113, + 362, + 122 + ], + "lines": [ + { + "bbox": [ + 327, + 113, + 362, + 122 + ], + "spans": [ + { + "bbox": [ + 327, + 113, + 362, + 122 + ], + "type": "text", + "content": "(a).Image" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 389, + 71, + 468, + 113 + ], + "blocks": [ + { + "bbox": [ + 389, + 71, + 468, + 113 + ], + "lines": [ + { + "bbox": [ + 389, + 71, + 468, + 113 + ], + "spans": [ + { + "bbox": [ + 389, + 71, + 468, + 113 + ], + "type": "image", + "image_path": "d18924e7756a28d990d38535d79507175d310c5c50d1fecb5e94e449551faf4f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 401, + 114, + 449, + 122 + ], + "lines": [ + { + "bbox": [ + 401, + 114, + 449, + 122 + ], + "spans": [ + { + "bbox": [ + 401, + 114, + 449, + 122 + ], + "type": "text", + "content": "(b).Prediction" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 319, + 123, + 370, + 170 + ], + "blocks": [ + { + "bbox": [ + 319, + 123, + 370, + 170 + ], + "lines": [ + { + "bbox": [ + 319, + 123, + 370, + 170 + ], + "spans": [ + { + "bbox": [ + 319, + 123, + 370, + 170 + ], + "type": "image", + "image_path": "58d5a3c74230877663367ae214ca143ff1a3a12f790db154b05b189e5bc87d5d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 171, + 347, + 182 + ], + "lines": [ + { + "bbox": [ + 326, + 171, + 347, + 182 + ], + "spans": [ + { + "bbox": [ + 326, + 171, + 347, + 182 + ], + "type": "text", + "content": "↓" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 394, + 123, + 461, + 168 + ], + "blocks": [ + { + "bbox": [ + 394, + 123, + 461, + 168 + ], + "lines": [ + { + "bbox": [ + 394, + 123, + 461, + 168 + ], + "spans": [ + { + "bbox": [ + 394, + 123, + 461, + 168 + ], + "type": "image", + "image_path": "3e6bacf1391cb7f46bec1601a34ace35f79da9d7644fdc862d10e823fd99be1b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 389, + 170, + 465, + 241 + ], + "blocks": [ + { + "bbox": [ + 389, + 170, + 465, + 241 + ], + "lines": [ + { + "bbox": [ + 389, + 170, + 465, + 241 + ], + "spans": [ + { + "bbox": [ + 389, + 170, + 465, + 241 + ], + "type": "image", + "image_path": "1deaca3fe9718329bcf70689d59fd57c12edb57d1a2a648368666414537a5e77.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 386, + 242, + 462, + 251 + ], + "lines": [ + { + "bbox": [ + 386, + 242, + 462, + 251 + ], + "spans": [ + { + "bbox": [ + 386, + 242, + 462, + 251 + ], + "type": "text", + "content": "(e). 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(b) is the source-only model's prediction, (d) is the local relation map in image space built by Gaussian kernel in each grid, (e) is the pseudo-relation matrix. (f) is the relation matrix built by ground truth." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 345, + 545, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 545, + 429 + ], + "type": "text", + "content": "probability to meet the relation consistency by finding the optimal sub-graph division from the global pseudo-relation of each class. It has two advantages over the naive relation-learning loss: one is global relational modeling, which can be easily implemented by matrix multiplication; the other is threshold-free learning by dynamically weighting class probabilities and pseudo-relations." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 430, + 546, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 546, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 546, + 514 + ], + "type": "text", + "content": "With RTea, the model's certainty and consistency of prediction can be enhanced on the target domain, and the cross-domain inadaptation is further eliminated. Sufficient experiments show our method can further mine the available knowledge in pseudo-labels, and it can be easily incorporated into existing self-training method to further boost their performance." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 525, + 390, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 390, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 390, + 538 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": "Unsupervised Domain Adaptation (UDA). UDA methods can be divided into domain alignment and self-training. Alignment-based methods narrow the domain gap by aligning distributions at different levels, e.g., input [12, 30, 25, 60], feature [32, 33, 7, 50, 56, 22] and output [48, 49, 59]. Although they achieve positive adaptation benefits, the lack of specific target domain knowledge leads to slight improvement. To this end, self-training methods are proposed to train the network with pseudo-labels for the target domain, which can be divided into two categories, offline and online pseudo-label-based methods. Offline self-training (OFFST) methods save the target domain pseudo-labels generated by the pre-trained model and use them to train the model iteratively [27, 10, 37]. To avoid noise interfer" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19192" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "ence, these methods select high-quality pseudo-labels via threshold setting [70, 71], consistent prediction [68], and pseudo-label prototypes [64]. These methods require additional storage of pseudo-labels and an iterative training, which is not conducive to practical use. Online self-training (ONST) uses the model's output during training as supervision without saving intermediate results [58, 4, 51, 1]. ONST avoids the inconvenience of multiple training rounds and manual intervention between consecutive rounds in OFFST. Our work is designed in online self-training fashion. Besides, our method further mines the available knowledge in pseudo-labels from the novel perspective of pixel relations, which can further promote pseudo-label learning and boosting self-training performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 240, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 289, + 456 + ], + "type": "text", + "content": "Relation Learning (RL) in Semantic Segmentation. In supervised semantic segmentation, capturing relations between pixels is continuously studied at feature [8, 20, 29] and output layers[24, 17]. At the feature layer, several work [8, 20, 62, 29] use the label-guided pixel relation to build a compact feature space, in which features of the same class are close and of different classes are far. At the output layer, AAF [24] and CDGC [17] exploit pixel relations in the ground truth to correct the output probabilities, forcing the model to adjust both the classifier and the feature extractor to output reasonable relations and semantic structure. These supervised RL methods achieve huge performance improvements, emphasizing the importance of maintaining the relation between pixels. However, in the UDA task, the lack of annotations makes it impossible to build relations as these works. Our method proposes a novel pseudo-relation building and learning strategy so that the above advantages can be also achieved to the UDA segmentation task." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 456, + 289, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 289, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 289, + 624 + ], + "type": "text", + "content": "Pseudo Label Correction. As a classic technique of semi-supervised learning, pseudo-labeling has shown favorable competitive advantages in many visual tasks with limited labels. Due to the limitation of confidence bias and error accumulation [41], pseudo-labeling are easy to overfit the noise and lead to model divergence[61]. Some pioneering works alleviate the problems from pseudo-label selection[63], negative label learning[41], contrastive learning [55], model calibration [23, 54]. However, the task-specific and domain-dependent design limits the application of these methods in complex cross-domain tasks. In contrast, our work proposes a novel perspective to rectify pseudo-labels and a tailored solution for cross-domain segmentation tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 638, + 130, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 638, + 130, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 638, + 130, + 651 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 658, + 195, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 195, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 195, + 670 + ], + "type": "text", + "content": "3.1. Background and Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "This paper focuses on the unsupervised domain adaptation (UDA) semantic segmentation, where source domain data " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_s = \\{x_s\\}" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " with pixel-level labels " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_s = \\{y_s\\}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": "and unlabeled target domain data " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_t = \\{x_t\\}" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " are given. Our goal is to train a segmentation model " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " that can work well on target domain. " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " consists of a feature extractor " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " and a classifier " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": ". Given sampled image " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "x\\in \\mathcal{X}_s\\cup \\mathcal{X}_t" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " mapping " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " to the feature space " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "f = F(x)" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " categorizes each feature in " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " to obtain a class probability map " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "p = C(F(x))\\in \\mathbb{R}^{h\\times w\\times K}" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": ". For the source domain, the cross entropy loss " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "L_{s}" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " is calculated to optimize the model," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 347, + 176, + 546, + 206 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 176, + 546, + 206 + ], + "spans": [ + { + "bbox": [ + 347, + 176, + 546, + 206 + ], + "type": "interline_equation", + "content": "L _ {s} = - \\frac {1}{\\left| \\mathcal {X} _ {s} \\right|} \\sum_ {x _ {s} \\in \\mathcal {X} _ {s}} \\log C (F (x _ {s})) (y _ {s}). \\tag {1}", + "image_path": "4d6b82b551a5626d31ceb014641d6aca4f01c011fe2bc5300879bfe4e88bb851.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 213, + 547, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 547, + 251 + ], + "type": "text", + "content": "For the target domain, to narrow the domain gap, self-training methods adopt pseudo-labels " + }, + { + "bbox": [ + 304, + 213, + 547, + 251 + ], + "type": "inline_equation", + "content": "\\hat{y}_t" + }, + { + "bbox": [ + 304, + 213, + 547, + 251 + ], + "type": "text", + "content": " generated by the pre-adapted model to retrain the unadapted model," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 347, + 258, + 546, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 258, + 546, + 287 + ], + "spans": [ + { + "bbox": [ + 347, + 258, + 546, + 287 + ], + "type": "interline_equation", + "content": "L _ {s t} = - \\frac {1}{| \\mathcal {X} _ {t} |} \\sum_ {x _ {t} \\in \\mathcal {X} _ {t}} \\log C (F (x _ {t})) (\\hat {y} _ {t}). \\tag {2}", + "image_path": "8cf1d58da1d2b9542a6a122755f63c8a529c9e59ade7bbdb6a1e22e9cdb20675.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 296, + 547, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 296, + 547, + 368 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 547, + 368 + ], + "type": "text", + "content": "In this way, the model's adaptability can be enhanced by relearning the knowledge of the pseudo-labels in the target domain. However, using Eq. 2 tends to interfere with training because the pseudo-labels contain massive noise. Thus, some works select high-confidence pseudo-labels by setting threshold " + }, + { + "bbox": [ + 304, + 296, + 547, + 368 + ], + "type": "inline_equation", + "content": "\\zeta^k" + }, + { + "bbox": [ + 304, + 296, + 547, + 368 + ], + "type": "text", + "content": " for each class," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 376, + 546, + 402 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 376, + 546, + 402 + ], + "spans": [ + { + "bbox": [ + 321, + 376, + 546, + 402 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {t} = \\left\\{ \\begin{array}{c l} \\arg \\max _ {k} p _ {t} ^ {k}, & \\text {i f} \\max \\left(p _ {t} ^ {k}\\right) > \\zeta^ {k} \\\\ \\text {i g n o r e}, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {3}", + "image_path": "ea103c615b7b1e637ad00c6137f5f8cda0e7660371ab41f6c567e196bd545d32.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "type": "inline_equation", + "content": "p_t^k" + }, + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "type": "text", + "content": "-th class probability score. In Eq. 3, the " + }, + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "type": "inline_equation", + "content": "\\zeta^k" + }, + { + "bbox": [ + 304, + 411, + 547, + 483 + ], + "type": "text", + "content": " determines the quality of the selected pixels, which needs to be dynamically adjusted according to the adaptation degree. Thus, in the subsequent works, scholars [58, 4, 51, 1] mainly focus on setting reasonable thresholds or uncertainty estimation strategies to select reliable pixels." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "text", + "content": "In this paper, we explore the potential of self-training from another perspective. Different from mining category knowledge in pseudo-labels, we propose to mine relation knowledge in pseudo-relations between pixels. The overview of our method is shown in Fig 3. For the source domain, images are input to the student model, which is optimized by the " + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "inline_equation", + "content": "L_{s}" + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "text", + "content": ". For the target domain, the original image and its data-transformed version are input into the student model and teacher model, respectively. After that, the output of the teacher model is used to build pseudo-relations " + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "inline_equation", + "content": "S_{pr}" + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "text", + "content": " to further supervise the student model of category learning by " + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "inline_equation", + "content": "L_{st}" + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "text", + "content": " and relation learning by " + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "inline_equation", + "content": "L_{pr}" + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "text", + "content": ". We detail the pseudo-relation " + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "inline_equation", + "content": "S_{pr}" + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "text", + "content": " building in Sec.3.2, and detail the pseudo-relation learning by optimizing " + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "inline_equation", + "content": "L_{pr}" + }, + { + "bbox": [ + 304, + 484, + 548, + 653 + ], + "type": "text", + "content": " in Sec.3.3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 659, + 446, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 446, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 446, + 672 + ], + "type": "text", + "content": "3.2. Pseudo-relation Building" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "In the supervised segmentation task, relations can be driven by ground truth, which is not achievable for the UDA segmentation. Thus, how to build the relations between" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19193" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 77, + 525, + 289 + ], + "blocks": [ + { + "bbox": [ + 62, + 77, + 525, + 289 + ], + "lines": [ + { + "bbox": [ + 62, + 77, + 525, + 289 + ], + "spans": [ + { + "bbox": [ + 62, + 77, + 525, + 289 + ], + "type": "image", + "image_path": "473a1abc6e400ec0d63067a55eacaca6a37b13009b17961de2247b38a1bc59ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "lines": [ + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "text", + "content": "Figure 3: The overall pipeline of the proposed Relation Teacher that includes a student model and a teacher model. " + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "inline_equation", + "content": "S_{low}" + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "inline_equation", + "content": "S_{high}" + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "inline_equation", + "content": "S_{pr}" + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "text", + "content": " represent low-level relation matrix, high-level relation matrix and pseudo-relation matrix. " + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "inline_equation", + "content": "L_{st}" + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "text", + "content": " is the traditional loss function for pseudo-label learning. " + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "inline_equation", + "content": "L_{pr}" + }, + { + "bbox": [ + 46, + 292, + 546, + 329 + ], + "type": "text", + "content": " is the proposed loss function for pseudo-relation learning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "text", + "content": "pixels in the target domain is the key. A naive solution is to build by measuring the class similarity between pseudolabels from a pre-adapted model. Given any two pixels " + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "inline_equation", + "content": "p_{(t,i)}" + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "inline_equation", + "content": "p_{(t,j)}" + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "inline_equation", + "content": "i,j = 0,1,2,\\dots,w\\times h" + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "text", + "content": ") on the class probability map " + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "inline_equation", + "content": "p_t\\in \\mathbb{R}^{h\\times w\\times K}" + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "text", + "content": " of the target domain, the high-level relation between them can be defined as," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 111, + 426, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 426, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 111, + 426, + 287, + 441 + ], + "type": "interline_equation", + "content": "s _ {(i, j)} = \\operatorname {S I M} \\left(p _ {(t, i)}, p _ {(t, j)}\\right), \\tag {4}", + "image_path": "7ca759309850d9e2f01002685b3802079255651a25a1329982db4305a41c0259.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathrm{SIM}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "text", + "content": " is the cosine similarity measure. Extending this relation to all pixels in an image, we can derive a highlevel relation matrix " + }, + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "inline_equation", + "content": "S = \\{s(i,j)\\} \\in \\mathbb{R}^{hw\\times hw}" + }, + { + "bbox": [ + 46, + 449, + 287, + 544 + ], + "type": "text", + "content": ". However, such a relation modeling mechanism will introduce massive noise due to the unadapted model. As mentioned in reliable local relations prior, these noises are mainly in the long-distance relations but relations in local grids are relatively accurate." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 544, + 288, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 288, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 288, + 596 + ], + "type": "text", + "content": "To this end, we devise a local relation modeling mechanism. We divide the target image into " + }, + { + "bbox": [ + 47, + 544, + 288, + 596 + ], + "type": "inline_equation", + "content": "N\\times N" + }, + { + "bbox": [ + 47, + 544, + 288, + 596 + ], + "type": "text", + "content": " grids " + }, + { + "bbox": [ + 47, + 544, + 288, + 596 + ], + "type": "inline_equation", + "content": "\\{G_l\\}_{l = 1}^{hw / N^2}" + }, + { + "bbox": [ + 47, + 544, + 288, + 596 + ], + "type": "text", + "content": " and model the relations inside the grid. Then the high-level relation matrix for each grid can be obtained," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 86, + 605, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 605, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 86, + 605, + 287, + 620 + ], + "type": "interline_equation", + "content": "S _ {h i g h} = \\left\\{s _ {(m, n)} \\right\\} _ {(m, n) \\in G _ {l}} \\in \\mathbb {R} ^ {N ^ {2} \\times N ^ {2}}. \\tag {5}", + "image_path": "c2de278425b12d52a4b0723df310cce11c8ec5fa7fabd5ad4d96c18f94030e00.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 652 + ], + "type": "text", + "content": "Nonetheless, local pseudo-relations may still contain noise due to domain shifts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": "To further mitigate unreliable relations in local grids, we introduce low-level relation constraints in each grid. The motivation stems from available low-level relations prior that local low-level relations (RGB space) can be well used to capture the edges and internal structures of" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 343, + 546, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 546, + 392 + ], + "type": "text", + "content": "objects. Drawing on the traditional potential energy function constructing the potential energy field [43, 44, 38], we use the Gaussian function to calculate the energy on the RGBXY[43] space as low-level relation constraints," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 345, + 407, + 506, + 424 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 407, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 345, + 407, + 506, + 424 + ], + "type": "interline_equation", + "content": "S _ {l o w} = \\left\\{\\Psi_ {(m, n)} \\right\\} _ {(m, n) \\in G _ {l}} \\in \\mathbb {R} ^ {N ^ {2} \\times N ^ {2}},", + "image_path": "77907bda5c4fab71ff6f5f6fc1d27b1506463599f3925c1119d42483827c8b28.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 347, + 426, + 545, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 426, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 347, + 426, + 545, + 455 + ], + "type": "interline_equation", + "content": "\\Psi (m, n) = \\exp \\left(- \\left| \\frac {I _ {m} - I _ {n}}{\\sigma} \\right| ^ {2}\\right), \\tag {6}", + "image_path": "28fa413c0344f0d2ac1d6a0a508d35834ae45a2d0106c0a7ec4c2a2e8ed1d3a6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "inline_equation", + "content": "I_{(\\cdot)}" + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "text", + "content": " is the feature vector on RGBXY space, " + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "text", + "content": " is the bandwidth parameter of the Gaussian function. Due to the nature of the Gaussian function[16], the value range of the " + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "inline_equation", + "content": "S_{low}" + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "text", + "content": " are [0, 1], which is the same as that of " + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "inline_equation", + "content": "S_{high}" + }, + { + "bbox": [ + 304, + 469, + 546, + 567 + ], + "type": "text", + "content": ". A higher value indicates a stronger association between pixels. Although it lacks high-level semantics, it can better regularize relations (See Tab. 4 for verification). We linearly combine the low- and high-level relations as final pseudo-relations," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 362, + 582, + 545, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 582, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 362, + 582, + 545, + 596 + ], + "type": "interline_equation", + "content": "S _ {p r} = \\alpha S _ {l o w} + (1 - \\alpha) S _ {h i g h}, \\tag {7}", + "image_path": "cb43fe6678924fc65e869ca358fa0037f1fb6aa9aa819b887149bb1c0ef9b72a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 613, + 538, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 613, + 538, + 625 + ], + "spans": [ + { + "bbox": [ + 306, + 613, + 538, + 625 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 306, + 613, + 538, + 625 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 613, + 538, + 625 + ], + "type": "text", + "content": " is a hyper-parameter and is simply set to 0.5." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 643, + 448, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 448, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 448, + 657 + ], + "type": "text", + "content": "3.3. Pseudo-relation Learning" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "text", + "content": "Following the paradigm of pseudo-label learning, we can exploit the reliable relations in the pseudo-relation matrix to perform pseudo-relation learning. Specifically, for any pixel pair " + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "inline_equation", + "content": "p_{(t,i)}" + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "inline_equation", + "content": "p_{(t,j)}" + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "text", + "content": "-th grid, we can perform a pairwise" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19194" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 260, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 260, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 260, + 85 + ], + "type": "text", + "content": "relation loss [24, 17] in a pseudo manner as follows," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 94, + 287, + 146 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 94, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 48, + 94, + 287, + 146 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {L} _ {p r} = \\sum_ {l} \\sum_ {i, j} \\operatorname {K L} \\left(p _ {(t, i)} \\mid \\mid p _ {(t, j)}\\right) \\cdot \\mathbb {1} \\left(S _ {p r; l} (i, j) > M _ {u p}\\right) + \\\\ (1 - \\mathrm {K L} (p _ {(t, i)} | | p _ {(t, j)})) \\cdot \\mathbb {1} \\left(S _ {p r; l} (i, j) < M _ {l o w}\\right). \\tag {8} \\\\ \\end{array}", + "image_path": "b8597211070f3c9bec65109c8f5f6ff9e7ac1bc8edb789321acf6b78087e8b53.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "inline_equation", + "content": "\\mathrm{KL}(\\cdot ||\\cdot)" + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "text", + "content": " is the Kullback-Leibler divergence between two distributions. " + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "inline_equation", + "content": "\\mathbb{1}(\\cdot)" + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "text", + "content": " is the indicator function for thresholding. " + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "inline_equation", + "content": "M_{up}" + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "inline_equation", + "content": "M_{low}" + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "text", + "content": " are upper and lower thresholds for filtering unreliable relations. Optimizing this loss pulls the class distribution of the pixel pairs with a pseudo-relation higher than " + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "inline_equation", + "content": "M_{up}" + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "text", + "content": " closer and pushes those with a pseudorelation lower than " + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "inline_equation", + "content": "M_{low}" + }, + { + "bbox": [ + 46, + 147, + 287, + 386 + ], + "type": "text", + "content": " further away. In this way, pseudorelation learning can assist pseudo-label learning (in Eq.2) in the following aspects. Let the pixels used by Eq.2 be denoted as reliable pixels, and the rest are unreliable ones. 1). Relations between reliable pixels. Those reliable inter- and intra-class relations are informative and can be incorporated into learning as structural inference. 2). Relations between reliable and unreliable pixels. Pushing or Pulling the class probabilities of the unreliable pixels towards reliable ones will greatly enhance the confidence of the model. 3). Relations between unreliable pixels. Although we cannot give these pixel pairs explicit class targets, implicit class cues may help the model to enhance confidence. See further instructions in Appendix A." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "text", + "content": "In practice, in " + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\hat{L}_{pr}" + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "text", + "content": ", the pair of class distribution input to " + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\mathrm{KL}(\\cdot ||\\cdot)" + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "text", + "content": " should assign the more sharp one as the target. This makes it require pair-by-pair index calculation, which greatly increases the training time. Besides, " + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "inline_equation", + "content": "M_{up}" + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "inline_equation", + "content": "M_{low}" + }, + { + "bbox": [ + 46, + 386, + 287, + 493 + ], + "type": "text", + "content": " requires hyper-parameter search under different adaptation tasks, hindering the flexibility of application. Here, we learn from the idea of graph cut [57] and devise a new pseudorelation loss, which can be performed by matrix multiplication without explicit thresholding." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": "Specifically, in " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": "-th grid, we construct an undirected weighted graph " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": ", treating all pixels in this grid as nodes of the graph and the similarity between these pixels as the weights of edges. Thus, the corresponding " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "S_{pr;l}" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": " can be seen as a pseudo-adjacency matrix of the " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": ". With the " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": " classification problem is regarded as a graph cutting problem of cutting a graph into " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": " subgraphs. Then, the " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": "-th class probability " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "p_{t;l}^{k}" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": " of this grid is regarded as the probability of the corresponding nodes cut into " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": "-th subgraph (" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "k \\in [0, K - 1]" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": "). According to the properties of the graph, we can calculate the soft cost of cutting the " + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 494, + 287, + 637 + ], + "type": "text", + "content": "-th subgraph as follows," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 92, + 647, + 287, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 647, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 92, + 647, + 287, + 662 + ], + "type": "interline_equation", + "content": "c u t ^ {k} = \\hat {p} _ {t; l} ^ {k} S _ {p r; l} \\mathbf {1} - \\hat {p} _ {t; l} ^ {k} S _ {p r; l} \\left(\\hat {p} _ {t; l} ^ {k}\\right) ^ {T}. \\tag {9}", + "image_path": "83ffe4e3d6257481bbc08a0bb8b62f49a60df0d3a236b59259b52d2d77d75ad7.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 672, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{p}_{t;l}^{k}\\in \\mathbb{R}^{1\\times N^{2}}" + }, + { + "bbox": [ + 47, + 672, + 287, + 713 + ], + "type": "text", + "content": " is the vector flatten by " + }, + { + "bbox": [ + 47, + 672, + 287, + 713 + ], + "type": "inline_equation", + "content": "p_{t;l}^{k}\\in \\mathbb{R}^{1\\times N\\times N}" + }, + { + "bbox": [ + 47, + 672, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{1}\\in \\mathbb{R}^{N^2\\times 1}" + }, + { + "bbox": [ + 47, + 672, + 287, + 713 + ], + "type": "text", + "content": " is an all-ones vector. We show an example to illustrate Eq.9 in Fig.4. The smaller the cut value, the smaller" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 339, + 74, + 416, + 137 + ], + "blocks": [ + { + "bbox": [ + 339, + 74, + 416, + 137 + ], + "lines": [ + { + "bbox": [ + 339, + 74, + 416, + 137 + ], + "spans": [ + { + "bbox": [ + 339, + 74, + 416, + 137 + ], + "type": "image", + "image_path": "be8373f0132529ceab12448f66dc6f2fd88cb209f7ed25b8f2b389c492cab8c2.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 340, + 138, + 428, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 138, + 428, + 163 + ], + "spans": [ + { + "bbox": [ + 340, + 138, + 428, + 163 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} P ^ {0} S 1: \\text {- - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - } \\\\ P ^ {0} S P ^ {0}: \\text {- - } \\end{array}", + "image_path": "5fccfd9b646dc4a50f1747c0a00ce772d6f1a3c029d07b552a4a055c2de6ca78.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 434, + 74, + 518, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 434, + 74, + 518, + 163 + ], + "spans": [ + { + "bbox": [ + 434, + 74, + 518, + 163 + ], + "type": "interline_equation", + "content": "\\begin{array}{c} \\hline P: \\text {c l a s s p r o b a b i l i t y} \\\\ p _ {1} \\quad 1 \\quad 0 \\\\ p _ {2} \\quad 1 \\quad 0 \\\\ p _ {3} \\quad 1 \\quad 0 \\\\ p _ {4} \\quad 0 \\quad 1 \\\\ p _ {5} \\quad 0 \\quad 1 \\\\ S: \\text {a d j a c e n c y m a t r i x} \\end{array}", + "image_path": "d4b23a1afef089a676db345e69b9c7091ce1188d2dceca49bb742706c9f74c27.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "text", + "content": "Figure 4: We show an example of binary classification to illustrate Eq.9. Given five samples and their class probability " + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "text", + "content": ", take the cut of class 0 as an example. " + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "inline_equation", + "content": "P^0 S1" + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "text", + "content": " is the sum of all edges connected to the nodes of class 0, i.e., the green and dashed lines. " + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "inline_equation", + "content": "P^0 SP^0" + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "text", + "content": " is the sum of all edges connecting two nodes of class 0, i.e., the green lines, and " + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "inline_equation", + "content": "P^0 S1 - P^0 SP^0" + }, + { + "bbox": [ + 304, + 175, + 545, + 282 + ], + "type": "text", + "content": " is the cost consumed of the 0 class. To minimize the cost, nodes with high affinity should be classified into the same class, and vice versa." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "text", + "content": "the correlation between the subgraphs and the larger the correlation within the subgraphs. Thus, " + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "inline_equation", + "content": "cut^k" + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "text", + "content": " can be regarded as a proxy, when the " + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "inline_equation", + "content": "cut^k" + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "text", + "content": " value is small, the class probability " + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "inline_equation", + "content": "p_{t;l}^k" + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "text", + "content": " better conforms to the pseudo-relations " + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "inline_equation", + "content": "S_{pr;l}" + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "text", + "content": ", and vice versa. Moreover, the Eq.9 is derivable with respect to " + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "inline_equation", + "content": "p_{t;l}^k" + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "text", + "content": ", and its gradient w.r.t. " + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "inline_equation", + "content": "p^k" + }, + { + "bbox": [ + 304, + 294, + 545, + 367 + ], + "type": "text", + "content": " is," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 375, + 376, + 545, + 404 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 376, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 375, + 376, + 545, + 404 + ], + "type": "interline_equation", + "content": "\\frac {\\partial c u t ^ {k}}{\\partial p ^ {k}} = S _ {p r} \\left(\\mathbf {1} - 2 p ^ {k}\\right). \\tag {10}", + "image_path": "1cb4adf78c82cb8890908636ee5acd38fa363ef374b9b8875db31ca5563f7ac1.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": "The proxy's gradient is proportional to the " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "S_{pr}" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "1 - 2p^{k}" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": ", which implicitly weight high-confidence relations and reliable pixels (class probability far from 0.5). This explains that unreliable edges (relations) on the graph play a minor role in pulling or pushing away the class distribution, enabling adaptive weighting without threshold. Consequently, we modify Eq.9 as a threshold-free pseudo-relation loss function to optimize " + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 304, + 413, + 545, + 509 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 350, + 518, + 545, + 553 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 518, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 350, + 518, + 545, + 553 + ], + "type": "interline_equation", + "content": "L _ {p r} = \\sum_ {l} ^ {h w / N ^ {2}} \\sum_ {k} ^ {K} \\hat {p} _ {t; l} ^ {k} S _ {p r} \\left(\\mathbf {1} - \\hat {p} _ {t; l} ^ {k}\\right) ^ {T}. \\tag {11}", + "image_path": "d1bc80cb9cd30235bc9a4e96ab6ea1b734759afd1b6573c9bacff6249f9778f7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 561, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 561, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 305, + 561, + 545, + 586 + ], + "type": "inline_equation", + "content": "L_{pr}" + }, + { + "bbox": [ + 305, + 561, + 545, + 586 + ], + "type": "text", + "content": " can be calculated using matrix multiplication in a simple and quick way." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 593, + 408, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 593, + 408, + 604 + ], + "spans": [ + { + "bbox": [ + 306, + 593, + 408, + 604 + ], + "type": "text", + "content": "3.4. Relation Teacher" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 611, + 545, + 658 + ], + "type": "text", + "content": "We embed the learning of pseudo-relation into the optimization of mean-teacher [45] framework to realize online self-training as shown in Fig 3. The final optimization objective is," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 364, + 659, + 545, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 659, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 364, + 659, + 545, + 673 + ], + "type": "interline_equation", + "content": "L _ {f} = L _ {s} + \\lambda_ {s t} L _ {s t} + \\lambda_ {p r} L _ {p r}. \\tag {12}", + "image_path": "75253424bb30be5df6a14eafd5a86fdfa565e0f980cece0384d1e314e9cbdbed.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{pr}" + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{st}" + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": " are the trade-off coefficients. " + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{st}" + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": " is set as 0.001 following SAC [1]. " + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{pr}" + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": " is empirically set to 0.01 to balance the loss value." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19195" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 71, + 545, + 270 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 270 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 270 + ], + "type": "table", + "html": "
MethodroadsidewalkBuildingWallfencepolelightsignvege.terrainskypersonridercartruckbustrainmbikebikemIoU
FADA (ECCV 2020) [50]91.050.686.043.429.836.843.425.086.838.387.464.038.085.231.646.16.525.437.150.1
FDA (CVPR 2020) [60]92.553.382.326.527.636.440.538.882.239.878.062.634.484.934.153.116.827.746.450.4
IAST (ECCV 2020) [37]93.857.885.139.526.726.243.134.784.932.988.062.629.087.339.249.623.234.739.651.5
MetaCorr (CVPR 2021) [10]92.858.186.239.733.136.342.038.685.537.887.662.831.784.835.750.32.036.848.052.1
RPT (CVPR 2021) [66]89.243.386.139.529.940.249.633.187.438.586.064.425.188.536.645.823.936.556.852.6
SAC (CVPR 2021) [1]90.453.986.642.427.345.148.542.787.440.186.167.529.788.549.154.69.826.645.353.8
CFDAN (CVPR 2021) [36]92.558.386.527.428.838.146.742.585.438.491.866.437.087.840.752.444.641.759.056.1
SDFA (ICCV 2021) [26]94.859.486.240.529.525.543.834.785.934.989.563.430.888.342.650.725.335.740.952.8
ProDA (CVPR 2021) [64]87.85679.746.344.845.653.553.588.645.282.170.739.288.845.559.41.048.956.457.5
SimT (CVPR2022) [9]94.26088.530.339.741.247.860.888.647.389.371.545.090.754.260.20.051.858.458.9
CPST (CVPR 2022) [28]92.359.984.945.729.752.861.559.587.941.585.073.035.590.448.773.926.353.853.960.8
Undoing (CVPR 2022) [31]92.952.787.239.441.343.95552.989.348.291.271.43690.267.959.8048.559.359.3
DAP (CVPR 2022) [21]94.563.189.129.847.550.456.758.789.550.28773.638.691.350.252.9050.263.559.8
CaCo (CVPR 2022) [18]93.864.185.743.742.246.150.154.088.74786.568.12.988.043.460.131.546.160.958.0
ADPL (TPAMI 2023) [3]93.460.687.545.332.637.343.355.587.244.88864.534.288.352.661.849.841.859.459.4
RTea (Ours)95.467.187.946.144.046.053.859.589.749.889.871.540.590.855.057.922.147.762.561.9
Daformer (CVPR 2022) [14]95.770.289.453.548.149.655.859.489.947.992.572.244.792.374.578.265.155.961.868.3
Daformer + RTea (Ours)96.171.789.157.850.455.959.366.790.448.294.574.846.593.878.781.665.857.162.870.6
HRDA (ECCV 2022) [15]96.474.491.061.651.557.163.969.391.348.494.279.052.993.984.185.775.963.967.573.8
HRDA + RTea (Ours)97.175.292.663.551.858.266.571.291.149.096.881.554.294.284.886.675.762.266.774.7
", + "image_path": "a6e65c2147de9298f52b0de270d45be97688f64c1448a8fc9e6200750b66648b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 294, + 545, + 491 + ], + "blocks": [ + { + "bbox": [ + 55, + 273, + 539, + 285 + ], + "lines": [ + { + "bbox": [ + 55, + 273, + 539, + 285 + ], + "spans": [ + { + "bbox": [ + 55, + 273, + 539, + 285 + ], + "type": "text", + "content": "Table 1: Experimental results for GTA5 " + }, + { + "bbox": [ + 55, + 273, + 539, + 285 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 55, + 273, + 539, + 285 + ], + "type": "text", + "content": " Cityscapes adaptation task. The best results in every column are highlighted." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 294, + 545, + 491 + ], + "lines": [ + { + "bbox": [ + 50, + 294, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 50, + 294, + 545, + 491 + ], + "type": "table", + "html": "
MethodroadsidewalkBuildingWall*fence*pole*lightsignvege.skypersonridercarbusmbikebikemIoUmIoU*
FADA (ECCV 2020)[50]84.540.183.14.8034.320.127.284.88453.522.685.443.726.827.845.252.5
FDA (CVPR 2020) [60]79.335.073.2---19.924.061.782.661.431.183.940.838.451.1-52.5
IAST (ECCV 2020) [37]81.941.583.317.74.632.330.928.883.485.065.530.886.538.233.152.749.857.0
MetaCorr (CVPR 2021) [10]92.652.781.38.92.428.113.07.383.585.060.119.784.837.221.543.945.152.5
RPT (CVPR 2021) [66]88.946.584.515.10.538.539.530.185.985.859.826.188.146.827.756.151.258.9
SAC (CVPR 2021) [1]89.347.285.526.51.343.045.532.087.189.363.625.486.935.630.453.052.659.3
CFDAN (CVPR 2021) [36]75.730.081.911.52.535.318.032.786.290.165.133.283.336.535.354.348.255.5
SFDA (ICCV 2021) [26]90.550.081.613.32.834.725.733.183.889.266.034.985.353.446.146.652.060.1
ProDA (CVPR 2021) [64]87.845.784.637.10.644.054.637.088.184.474.224.388.251.140.545.655.562.0
CPST (CVPR 2022) [28]87.243.985.533.60.347.757.437.287.888.579.032.090.649.450.859.857.965.3
Undoing (CVPR 2022) [31]82.537.281.123.8045.757.247.687.785.874.128.688.466.047.055.356.764.5
CaCo (CVPR 2022) [18]87.448.979.68.80.230.117.428.379.981.256.324.278.639.228.148.346.053.6
ADPL (TPAMI 2023) [3]86.138.685.929.71.336.641.347.28590.467.544.387.457.143.951.455.963.6
RTea (ours)93.259.686.331.34.843.141.844.088.690.570.442.689.556.740.259.958.966.4
Daformer (CVPR 2022) [14]84.540.788.441.56.550.05554.68689.873.248.287.253.253.961.767.460.9
Daformer + RTea (Ours)85.943.290.145.16.352.460.557.187.892.275.351.887.455.954.162.669.563.0
HRDA (ECCV 2022) [15]85.247.788.849.54.857.265.760.985.392.979.452.88964.763.964.972.465.8
HRDA + RTea (Ours)87.849.090.350.35.558.666.061.486.893.179.553.189.565.163.764.673.066.5
", + "image_path": "d9e2e6201fc238724ffced8d113aad744164e5ee18cae5b2e508894fd3185ebf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 494, + 545, + 518 + ], + "lines": [ + { + "bbox": [ + 48, + 494, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 48, + 494, + 545, + 518 + ], + "type": "text", + "content": "Table 2: Experimental results for SYNTHIA " + }, + { + "bbox": [ + 48, + 494, + 545, + 518 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 48, + 494, + 545, + 518 + ], + "type": "text", + "content": " Cityscapes adaptation task. The best results in every column are highlighted. The mIoU and mIoU* are averaged over 16 and 13 categories, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 48, + 535, + 123, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 535, + 123, + 549 + ], + "spans": [ + { + "bbox": [ + 48, + 535, + 123, + 549 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 557, + 226, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 557, + 226, + 571 + ], + "spans": [ + { + "bbox": [ + 48, + 557, + 226, + 571 + ], + "type": "text", + "content": "4.1. Datasets and Experimental Setup" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "spans": [ + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "type": "text", + "content": "Datasets. We use one real dataset (Cityscapes [5]) and two synthetic datasets (GTA5 [40] and SYNTHIA [42]). The Cityscapes dataset contains 2,975 training images and 500 validation images of resolution " + }, + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "type": "inline_equation", + "content": "2048 \\times 1024" + }, + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "type": "text", + "content": ". The GTA5 dataset contains 24,966 images with resolution " + }, + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "type": "inline_equation", + "content": "1914 \\times 1052" + }, + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "type": "text", + "content": " and has 19 common categories with Cityscapes. The SYNTHIA dataset contains 9,400 images with resolution " + }, + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "type": "inline_equation", + "content": "1280 \\times 760" + }, + { + "bbox": [ + 48, + 578, + 286, + 674 + ], + "type": "text", + "content": " and has 16 common categories with Cityscapes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 48, + 677, + 286, + 713 + ], + "type": "text", + "content": "Implementation Details. We adopt Deeplab-v2 [2] as the base network, ResNet-101 [11] as the feature extractor and the aspp [2] module as the classifier. The network is pre" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": "trained on ImageNet. The optimizer is SGD with the momentum of 0.9 and weight decay of " + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": ". The initial learning rate is set to " + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "inline_equation", + "content": "2.5 \\times 10^{-4}" + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": ", and then is reduced following a poly policy with a power of 0.9. The batch size is set as 4. The final " + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "inline_equation", + "content": "\\lambda_{f}" + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "inline_equation", + "content": "\\lambda_{o}" + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": " values are set to 0.025 and 0.005, respectively. We apply the " + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "inline_equation", + "content": "L^{pr}" + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": " to the model's output class probability, which is 8 times smaller than the original resolution. And the grid size " + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": " is set to 8. The weighting factor " + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": " is set to 0.5. The " + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 307, + 536, + 545, + 704 + ], + "type": "text", + "content": " for XY and RGB space in Gaussian function is set to 6 and 0.1, following [43]. Data augmentation strategies performed on the data input to the student model include random flipping, Gaussian noise, color transformation, cutout[6], and contrast enhancement, a similar and common operation in online self" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "19196" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "training methods [58, 4, 51, 1]. Besides, we also preform the class-mixing resampling strategy [47] on the source domain to focus on the minority class. When performing " + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "L_{st}" + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": " for pseudo-label learning, we adopt the thresholding selection method in SAC [1] to pick high-quality samples. After training with Rtea, we retrained the model using the distillation strategy [64] for better adaptation, which is commonly used in recently published UDA work [31, 21, 28, 3]. The detailed scores for each stage are in the Tab. 3. Our network is trained with four RTX3090 GPUs on PyTorch." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 202, + 239, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 202, + 239, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 202, + 239, + 216 + ], + "type": "text", + "content": "4.2. Comparisons with State-of-the-Arts" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\mathrm{GTA5} \\rightarrow \\mathrm{Cityscapes}" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": ". We report the comparison results with existing methods on " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\mathrm{GTA5} \\rightarrow \\mathrm{Cityscapes}" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": " task in Tab. 1. We compared two structures based on resnet-101 and transformer structures. Overall, our RTea achieves new state-of-the-art performance than related works, and the category performance scores are also highly competitive, demonstrating the effectiveness of RTea. Compared with the domain alignment method, the performance of RTea show an advantage over the state-of-the-art method FDA [60] by " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "11.5\\%" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": ". Compared with the offline self-training method, the mIoU score of RTea is " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "10.4\\%" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "9.8\\%" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": " higher than IAST [37] and RPT[66]. Compared with the online self-training method, RTea exceeds SAC [1] and ProDA [64] by " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "8.1\\%" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "4.4\\%" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": ". Compared with the newly released method Undoing[31], DAP[21] and ADPL[3], our RTea still outperforms these methods by more than " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "2.0\\%" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": " mIoU scores, showing the potential of our method even more. Compared with the method of transformer structure, our method improves the mIoU score by " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 46, + 221, + 289, + 486 + ], + "type": "text", + "content": " on Daformer [14] and HRDA [15] respectively, which shows that RTea has good scalability and transferability. Qualitative results on both tasks can be found in Appendix B." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "text", + "content": "SYNTHIA " + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "text", + "content": " Cityscapes. The results of using SYNTHIA as the source domain are reported in Tab. 2, including mIoU/mIoU* covering 16/13 classes. On the whole, our method still achieves significant improvements, showing gains over advanced methods. In particular, SYNTHIA and Cityscapes suffer from significant visual domain differences in 'road', and 'sidewalk', which leads to the poor performance of the most UDA methods in these categories. Our method uses the pseudo-relations of these categories and achieves higher performance improvements, and we argue this is due to the local pseudo-relation learning to better capture the structure of these categories. Compared with the domain alignment and offline self-training methods, RTea maintains similar performance gains to the GTA5 transfer task. Compared with online self-training method, we achieve better performance than CPST [28] over 16 and 13 classes, exceeding its by " + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "text", + "content": " mIoU score. Compared with the adaptation method using transformer structure, our method improves the mIoU score by " + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 46, + 486, + 289, + 714 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 547, + 145 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 547, + 145 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 547, + 145 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 547, + 145 + ], + "type": "table", + "html": "
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Here, we report a result of " + }, + { + "bbox": [ + 304, + 146, + 547, + 254 + ], + "type": "inline_equation", + "content": "\\hat{L}_{pr}" + }, + { + "bbox": [ + 304, + 146, + 547, + 254 + ], + "type": "text", + "content": " with the fine-tuned thresholds by grid search. " + }, + { + "bbox": [ + 304, + 146, + 547, + 254 + ], + "type": "inline_equation", + "content": "L_{pr}^{s}" + }, + { + "bbox": [ + 304, + 146, + 547, + 254 + ], + "type": "text", + "content": " denotes that relation learning is performed on the source domain. Dist denote the distillation strategy in [50, 64]. All numbers are mIoU(%) score." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 274, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 299 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 304, + 274, + 545, + 299 + ], + "type": "text", + "content": " on Daformer [14] and HRDA [15], which further verifies the effectiveness of the method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 309, + 407, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 309, + 407, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 407, + 322 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "content": "Ablation for Each Module. Tab.3 reports the ablation results for different modules. We adopt SAC [1] with the copy-paste [47] argumentation as the baseline, achieving the " + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "inline_equation", + "content": "55.8\\%" + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "inline_equation", + "content": "53.9\\%" + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "content": " mIoU score on two adaptation tasks. Overall, Rtea achieves " + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "inline_equation", + "content": "3.8\\%" + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "inline_equation", + "content": "3.0\\%" + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "content": " performance improvements on the two tasks on this competitive baseline, respectively, showing the effectiveness of the pseudorelation learning. Specifically, the naive " + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "inline_equation", + "content": "\\hat{L}_{pr}" + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "content": " loss, although, can improve performance, the screening of the threshold makes it difficult to be directly applied to practice, because the threshold may be very sensitive in different adaptation scenarios. The proposed " + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "inline_equation", + "content": "L_{pr}" + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "content": " loss does not require explicit threshold while improving the performance, showing its flexibility and effectiveness. In addition, we also tried to perform pseudo-relation learning on the source domain " + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "inline_equation", + "content": "L_{pr}^{s}" + }, + { + "bbox": [ + 304, + 329, + 547, + 569 + ], + "type": "text", + "content": ", and we did not find a significant performance improvement, which may be because it cannot directly benefit the target domain. After training with RTea, the self-distillation method can still be used to further improve the adaptability of the model in the target domain." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "Ablation for Pseudo-Relation Building. Tab.4 shows the ablation results for building pseudo-relation. When the relations are built on RGBXY space (" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "S_{low}" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "), the performance achieves a good improvement, " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "2.0\\%" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " on two tasks, respectively, which suggests that low-level relations on local grids can propagate effective category knowledge. When the relations are built on pseudo labels (" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "S_{high}" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "), the performance is only improved by " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " on two tasks, respectively. This is because it is not easy to find valuable relation pairs in this way, and their effects may overlap with label learning. Specifically, unreliable pixels discarded by pseudo-label learning are still difficult to use, and high" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19197" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 82, + 70, + 255, + 137 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 255, + 137 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 255, + 137 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 255, + 137 + ], + "type": "table", + "html": "
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R-RR-UU-UGTA5SYNTHIA
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", + "image_path": "170949ac746fa524fd08d26950acbac38b9e9f2729edcc4cdfb0f5e3c35bf58c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 324, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 287, + 396 + ], + "type": "text", + "content": "confidence relationships still contain massive noise, When " + }, + { + "bbox": [ + 46, + 324, + 287, + 396 + ], + "type": "inline_equation", + "content": "S_{low}" + }, + { + "bbox": [ + 46, + 324, + 287, + 396 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 324, + 287, + 396 + ], + "type": "inline_equation", + "content": "S_{high}" + }, + { + "bbox": [ + 46, + 324, + 287, + 396 + ], + "type": "text", + "content": " are combined, the best effect is achieved. We argue that the advantage is that, the noisy relations in the high level are corrected and the lack of semantics of the low-level relations is also made up, and more unreliable pixels are better exploited." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 396, + 288, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 541 + ], + "type": "text", + "content": "Ablation for Pseudo-Relation Learning. To verify the effect of different pixel pairs on pseudo-relation learning, we devise the ablation study in Tab. 5. We follow 1), 2) and 3) explained in the Eq. 8, and divide them into R-R (two reliable pixels), R-U (one reliable and one unreliable pixel) and U-U (two unreliable pixels). During training, we clear all gradients for one of the pairs to verify its effect on adaptation. We find that R-U pairs play the most important role in adaptation, R-R pairs come second, and U-U pairs come last. We analyze learning R-U pairs can make full use of valuable pixels from unexploited target domains, which is the most direct to enhance the target domain adaptability." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 550, + 119, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 119, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 119, + 562 + ], + "type": "text", + "content": "4.4. Discussion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": "Sensitivity for reliable sample selection. In this section, we perform two experiments to explore how sensitive RTea is to reliable sample selection. First, we report the results when the parameters of the heuristic threshold (Eq. 3) are varied. The thresholding strategy consists of two hyperparameters, namely the upper threshold " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": " and the decay rate " + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 570, + 287, + 715 + ], + "type": "text", + "content": ". Table 6 shows that our method maintains a stable performance improvement when thresholding parameters vary within a certain range. Second, we report Rtea's performance on different reliable sample selection methods in Table 7. It verifies the effectiveness of RTea, which improves the performance of different self-training methods." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 327, + 71, + 525, + 117 + ], + "blocks": [ + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "type": "text", + "content": "Table 5: Ablation experiments on the pseudo-relation learning. " + }, + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "type": "inline_equation", + "content": "R - R" + }, + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "type": "text", + "content": " denotes pairs with two reliable pixels. " + }, + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "type": "inline_equation", + "content": "R - U" + }, + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "type": "text", + "content": " denotes pairs with one reliable and one unreliable pixel. " + }, + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "type": "inline_equation", + "content": "U - U" + }, + { + "bbox": [ + 46, + 255, + 287, + 304 + ], + "type": "text", + "content": " denotes pairs with two unreliable pixels." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 327, + 71, + 525, + 117 + ], + "lines": [ + { + "bbox": [ + 327, + 71, + 525, + 117 + ], + "spans": [ + { + "bbox": [ + 327, + 71, + 525, + 117 + ], + "type": "table", + "html": "
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θ=0.7559.059.258.8
θ=0.8059.259.659.1
", + "image_path": "5193f69ccf2745ccdd13b0e21d08f5ec29139797b96916108d72d1d83e70b043.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 332, + 153, + 520, + 198 + ], + "blocks": [ + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "lines": [ + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "text", + "content": "Table 6: The mIoU scores (\\%) on GTA5 → Cityscapes task with varying thresholding parameters in Eq. 3." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 332, + 153, + 520, + 198 + ], + "lines": [ + { + "bbox": [ + 332, + 153, + 520, + 198 + ], + "spans": [ + { + "bbox": [ + 332, + 153, + 520, + 198 + ], + "type": "table", + "html": "
PDCDADHT
without Rtea55.054.453.255.8
with Rtea58.856.854.859.6
", + "image_path": "005d97ee13dc40e799e9350d81c9d9ad0918026a43cda6797475bd8a2071c1fc.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "content": "How local grids affect each relation pair. We perform experiments on " + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\mathrm{GTA5} \\rightarrow" + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "content": " Cityscapes to verify which relation pairs are most affected by local grids. Pixels are still classified as reliable (R) and unreliable (U) according to whether they are used for category learning in traditional self-training, see Tabel 8. In the first line, we find that (1) the global grid is good for " + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "inline_equation", + "content": "R - R" + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "content": " because it extends the spatial scope of relational learning, while it does harm to " + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "inline_equation", + "content": "R - U" + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "inline_equation", + "content": "U - U" + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "content": " due to the long-range relation noise. As a result, performing pseudo-relation learning on global region lead model degradation. In the second line, we argue that (2) performing pseudo-relation on the local grids slightly reduces the gain of " + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "inline_equation", + "content": "R - R" + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "content": ", but greatly reduces the interference of noise on " + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "inline_equation", + "content": "R - U" + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "inline_equation", + "content": "U - U" + }, + { + "bbox": [ + 304, + 280, + 545, + 461 + ], + "type": "text", + "content": ". Finally, the model can obtain better performance improvement." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 308, + 469, + 543, + 508 + ], + "blocks": [ + { + "bbox": [ + 305, + 200, + 545, + 261 + ], + "lines": [ + { + "bbox": [ + 305, + 200, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 200, + 545, + 261 + ], + "type": "text", + "content": "Table 7: The mIoU scores (\\%) on GTA5 → Cityscapes task with different reliable sample selection strategies. PD denotes feature-prototype distance [64], CD denotes classifier discrepancy [69], AD denotes adversarial difficulty [34] and HT is our used heuristic threshold [1]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 469, + 543, + 508 + ], + "lines": [ + { + "bbox": [ + 308, + 469, + 543, + 508 + ], + "spans": [ + { + "bbox": [ + 308, + 469, + 543, + 508 + ], + "type": "table", + "html": "
BaselineR-RR-UU-U
Global55.857.2 (+1.4)51.4 (-4.4)52.5 (-3.3)
Local grid55.856.6 (+0.8)57.9 (+2.1)55.9(+0.1)
", + "image_path": "fb7169564afea66dd16b50eab4223a0a0c11b153b4e0d0e605cdf7a8a73dec8c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 509, + 544, + 533 + ], + "lines": [ + { + "bbox": [ + 305, + 509, + 544, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 509, + 544, + 533 + ], + "type": "text", + "content": "Table 8: The mIoU (%) of local grids effect on GTA5 → Cityscapes adaptation task." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Computational overhead. Performing relation learning on dense prediction tasks such as semantic segmentation is time-consuming. Therefore, it is necessary to discuss the computational overhead introduced in Rtea. Overall, we think the pseudo-relation computational overhead is acceptable. First, for complexity, our computational cost is " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(N^2 WH)" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ": width and height of feature map, " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ": grid size, " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "N \\ll W, H" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "), which is greatly reduced compared to the global similarity " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(W^2 H^2)" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". Second, the pseudorelation can be computed in parallel using matrix operations in PyTorch. On a Nvidia RTX-3090, it only takes almost 40 ms for each batch and only increases about " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " computational overhead in each iteration. Third, the cost is only for training and not for inference." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19198" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": "Align low- and high-level relation matrix with the same Gaussian function. In the method section, we use the cosine distance (Eq. 5) and Gaussian distance (Eq. 6) to model the similarity of high- and low-level, respectively. It is interesting to explore unifying the modeling of high- and low-level pseudo-relations into the same metric function, e.g. Gaussian distance. With the same metric function, for any local grid " + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "G_{l}" + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": ", the local relation can be built as, " + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "s(m,n) = \\sum_{m,n\\in G_l}\\Psi_{\\sigma_{rgbxy}}(m,n)\\cdot \\Psi_{\\sigma_{prob}}(m,n)" + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\sigma_{rgbxy}" + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\sigma_{prob}" + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": " are the bandwidth of the low- and highlevel Gaussian function. This formula is similar to the kernels of bilateral filtering[46], inspiring us to understand the pseudo-relation learning from the filtering perspective, i.e. smoothing and correcting the noise on output probability. Table 9 presents the comparison results, showing unifying the same metric function can maintain performance with less computational overhead." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 284, + 285, + 308 + ], + "blocks": [ + { + "bbox": [ + 48, + 284, + 285, + 308 + ], + "lines": [ + { + "bbox": [ + 48, + 284, + 285, + 308 + ], + "spans": [ + { + "bbox": [ + 48, + 284, + 285, + 308 + ], + "type": "table", + "html": "
MetricGTA5SYN.TimeMetricGTA5SYN.Time
Current59.656.940msSame Gaussian59.657.129ms
", + "image_path": "bbf98614b8fe9e02f789a8f41259312e970ed8025d315b0e257922461cf5f05c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 308, + 287, + 345 + ], + "lines": [ + { + "bbox": [ + 47, + 308, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 287, + 345 + ], + "type": "text", + "content": "Table 9: The mIoU (\\%) and computational cost (time/batch) using different similarity metric functions on GTA5 → Cityscapes adaptation task." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 354, + 288, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 288, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 288, + 392 + ], + "type": "text", + "content": "Hyper-parameters Impacts. We analyze the sensitivity of the hyper-parameters " + }, + { + "bbox": [ + 47, + 354, + 288, + 392 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 354, + 288, + 392 + ], + "type": "text", + "content": " (trade-off coefficient), grid size " + }, + { + "bbox": [ + 47, + 354, + 288, + 392 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 354, + 288, + 392 + ], + "type": "text", + "content": ", the results are presented in the Appendix C." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 396, + 132, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 132, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 132, + 407 + ], + "type": "text", + "content": "4.5. Visualization" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 414, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 414, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 414, + 287, + 498 + ], + "type": "text", + "content": "Visualization of pixel relations. Fig. 5 visualizes the learned relations on " + }, + { + "bbox": [ + 47, + 414, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathrm{GTA5} \\rightarrow" + }, + { + "bbox": [ + 47, + 414, + 287, + 498 + ], + "type": "text", + "content": " Cityscapes task. Comparing Fig. 5 a, b and e, it shows that the feature associations of the baseline are chaotic while our method builds more accurate feature relations. Comparing Fig. 5 c, d and e, it indicts that our method captures category relations more accurately than baseline, resulting in more structured outputs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 498, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 593 + ], + "type": "text", + "content": "Comparison of Pixel Utilization and Model Confidence. Fig. 6 compares the correct pixel utilization (PU) and average confidence (AC) of the model before and after adding RTea. With RTea, the PU is significantly improved and the AC also shows better results. It illustrates RTea can exploit more uncertain pixels around high-confidence pixels and propagate relation information to them, thereby fully improving the certainty of the model." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "Visualization of Pseudo-Labels. Fig. 7 visualizes the pseudo-labels of the baseline and our RTea to demonstrate the benefits of pseudo-relation learning. It shows that the RTea makes better use of pseudo-labels than the baseline model. For the areas are hard to distinguish (framed by the red box), RTea can enlarge the reliable pseudo-label area by capturing relations between pixels. Moreover, RTea provides clear class boundaries for the classes such as roads, sidewalks and buildings, which is more helpful for pseudolabel learning." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 71, + 399, + 115 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 399, + 115 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 399, + 115 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 399, + 115 + ], + "type": "image", + "image_path": "5811ba1309e25558465de4962c75567ef1d6d781b81175932656aeac564bc93e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 313, + 115, + 399, + 158 + ], + "blocks": [ + { + "bbox": [ + 313, + 115, + 399, + 158 + ], + "lines": [ + { + "bbox": [ + 313, + 115, + 399, + 158 + ], + "spans": [ + { + "bbox": [ + 313, + 115, + 399, + 158 + ], + "type": "image", + "image_path": "93b8535da3c7ecf7d5f66ff92ccba366e225fab53bc68672da7b2db7551521d1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 316, + 159, + 400, + 170 + ], + "lines": [ + { + "bbox": [ + 316, + 159, + 400, + 170 + ], + "spans": [ + { + "bbox": [ + 316, + 159, + 400, + 170 + ], + "type": "text", + "content": "a. Feature relations of baseline b. Feature relations of RTEca" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 306, + 170, + 545, + 194 + ], + "lines": [ + { + "bbox": [ + 306, + 170, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 170, + 545, + 194 + ], + "type": "text", + "content": "Figure 5: Visualization of the learned relations of RTea model on the GTA5 " + }, + { + "bbox": [ + 306, + 170, + 545, + 194 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 306, + 170, + 545, + 194 + ], + "type": "text", + "content": " Cityscapes task." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 400, + 72, + 444, + 114 + ], + "blocks": [ + { + "bbox": [ + 400, + 72, + 444, + 114 + ], + "lines": [ + { + "bbox": [ + 400, + 72, + 444, + 114 + ], + "spans": [ + { + "bbox": [ + 400, + 72, + 444, + 114 + ], + "type": "image", + "image_path": "3b45fd8d5e52f3fe52b75908055f8fcc3ef0a3285cbaa97e00b1e9f26c9ce9bc.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 400, + 115, + 444, + 158 + ], + "blocks": [ + { + "bbox": [ + 400, + 115, + 444, + 158 + ], + "lines": [ + { + "bbox": [ + 400, + 115, + 444, + 158 + ], + "spans": [ + { + "bbox": [ + 400, + 115, + 444, + 158 + ], + "type": "image", + "image_path": "637f7bd81d8c696b3643b9fda29bdd1902b90058885522ea3b14ea802d20a57f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 403, + 159, + 441, + 170 + ], + "lines": [ + { + "bbox": [ + 403, + 159, + 441, + 170 + ], + "spans": [ + { + "bbox": [ + 403, + 159, + 441, + 170 + ], + "type": "text", + "content": "c. 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Ours" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 530, + 545, + 555 + ], + "lines": [ + { + "bbox": [ + 306, + 530, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 306, + 530, + 545, + 555 + ], + "type": "text", + "content": "Figure 7: Comparison of pseudo-labels of baseline and RTea. The white masked area is unreliable pseudo-labels." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 569, + 378, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 569, + 378, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 569, + 378, + 582 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "In this paper, we propose pseudo-relation learning framework for UDA semantic segmentation. In RTea, we provide two prior guidelines for pseudo-relation building, which may help more works exploiting pseudo-relations. Moreover, we explore how to use pseudo-relations from the constraints and do detailed analysis and experiments on the proposed solution. Sufficient experiments on two datasets demonstrate the effectiveness of the proposed method. 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In Proceedings of the IEEE/CVF Conference on International Conference on Computer Vision, pages 5982-5991, October 2019. 1, 3" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "19203" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Rain Location Prior for Nighttime Deraining/f13e3907-fb21-485a-916a-d1036549cfe5_content_list.json b/2023/Learning Rain Location Prior for Nighttime Deraining/f13e3907-fb21-485a-916a-d1036549cfe5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..cb3c20f2569cea6fe0b5164b99152512c156e029 --- /dev/null +++ b/2023/Learning Rain Location Prior for Nighttime Deraining/f13e3907-fb21-485a-916a-d1036549cfe5_content_list.json @@ -0,0 +1,2004 @@ +[ + { + "type": "text", + "text": "Learning Rain Location Prior for Nighttime Deraining", + "text_level": 1, + "bbox": [ + 207, + 130, + 759, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fan Zhang1 Shaodi You2 Yu Li3 Ying Fu1* \n1Beijing Institute of Technology 2University of Amsterdam \n3International Digital Economy Academy", + "bbox": [ + 240, + 179, + 730, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Rain can significantly degrade image quality and visibility, making deraining a critical area of research in computer vision. Despite recent progress in learning-based deraining methods, there is a lack of focus on nighttime deraining due to the unique challenges posed by non-uniform local illuminations from artificial light sources. Rain streaks in these scenes have diverse appearances that are tightly related to their relative positions to light sources, making it difficult for existing deraining methods to effectively handle them. In this paper, we highlight the importance of rain streak location information in nighttime deraining. Specifically, we propose a Rain Location Prior (RLP) that is learned implicitly from rainy images using a recurrent residual model. This learned prior contains location information of rain streaks and, when injected into deraining models, can significantly improve their performance. To further improve the effectiveness of the learned prior, we also propose a Rain Prior Injection Module (RPIM) to modulate the prior before injection, increasing the importance of features within rain streak areas. Experimental results demonstrate that our approach outperforms existing state-of-the-art methods by about 1dB and effectively improves the performance of deraining models. We also evaluate our method on real night rainy images to show the capability to handle real scenes with fully synthetic data for training. Our method represents a significant step forward in the area of nighttime deraining and highlights the importance of location information in this challenging problem. The code is publicly available at https://github.com/zkawfanx/RLP.", + "bbox": [ + 75, + 301, + 473, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 786, + 209, + 801 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While rain degrades image quality and visibility, it can be particularly problematic at night, because the low light condition and complex illuminations make it more difficult to distinguish rain streaks from other image features. This", + "bbox": [ + 75, + 811, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/94d70391ef37384812547ed097a35e1d2e7d611d93f51cc8219befba276ba559.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 267, + 692, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3a02dc2d32aca75275f320dc4fa73691a25833519370d15ecff607cb40b5ffc2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 267, + 888, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f55e122108e7f3b0a369d0f6294ce37f6eae688e23ca9d87b8a48aecc98a86db.jpg", + "image_caption": [ + "(a) Rainy", + "(c) RLP", + "Figure 1: (a) In night scenes, appearances of rain are highly dependent on locations relative to light sources. (b) Derain result of state-of-the-art method Uformer [34]. (c) Visualization of the proposed Rain Location Prior (RLP), which indicates the location of rain streaks and suppresses areas of light sources. (d) Derain result of our method." + ], + "image_footnote": [], + "bbox": [ + 504, + 340, + 696, + 398 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4b8330a81762e5ae9ff7ca42d5482caa2b07446194e91d988d29c6015391226a.jpg", + "image_caption": [ + "(b) Uformer", + "(d) Ours" + ], + "image_footnote": [], + "bbox": [ + 697, + 340, + 888, + 398 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "not only hinders the performance of high-level vision algorithms, e.g., object detection [13, 29] and tracking [2, 35], but also poses a safety risk for autonomous vehicles [6, 28] and other applications that rely on accurate visual information. Therefore, there is an increasing need for developing nighttime deraining methods.", + "bbox": [ + 496, + 522, + 892, + 613 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unfortunately, despite recent advances in deep learning [34, 39, 40], which have significantly improved the performance, current endeavors predominantly focus on daytime scenarios, leaving the realm of nighttime deraining still largely unexplored. The most frequently utilized datasets [16, 32] scarcely encompass night scenes, neither does the synthesizing procedure consider interactions between rain and light sources. This hinders the direct application of existing methods to nighttime deraining. Recently, some datasets [20, 42] have started to cover previously ignored night scenes, which may enable careful study on nighttime deraining. Since there is no prior method specifically targeting nighttime deraining, we attempt to handle real night rainy scenes with the help of the recently developed dataset.", + "bbox": [ + 496, + 613, + 893, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Night scenes differ from day scenes in that there is no uniform global illumination; instead, darkness and nonuniform local illuminations dominate [12, 22, 25, 41, 45]. It results in the totally different appearance of night rain, which varies drastically at different spatial locations (i.e.", + "bbox": [ + 496, + 824, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: fuying@bit.edu.cn", + "bbox": [ + 94, + 886, + 323, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13148", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "only rain streaks near light sources are more discernible, as shown in Figure 2). Intuitively, it could facilitate the removal of rain streaks if precise locations were obtained in advance, which is often impractical in real scenes. Likewise, it is a common practice [14, 26] to train deep models to predict the locations of raindrop (i.e. raindrop mask) in the raindrop removal community. Therefore, identifying the rain location becomes more crucial than in day scenes.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel deraining method targeting night scenes. Firstly, we highlight the importance of location information of rain streaks for nighttime deraining, as the appearance of rain streaks is highly varying at different spatial locations at night. Thus, we propose a Rain Location Prior (RLP) which can be implicitly learned by recurrent residual models. It can reveal the location information of rain streaks in night scenes and be incorporated into deraining methods to improve their performance, including CNN-based and Transformer-based ones. Secondly, we propose a Rain Prior Injection Module (RPIM) to increase the importance of features within rain streak areas indicated by RLP. Deraining models can focus more on recovering lost information within rain streak areas and get a further increase in performance. Finally, we perform comprehensive experiments to demonstrate the effectiveness of our method. Our method outperforms existing state-of-the-art methods quantitatively and qualitatively on synthetic data. Furthermore, we demonstrate the capability of our method in handling real scenes. We also conduct ablation studies to evaluate the effectiveness of each component in our method. To summarize, the contributions of our paper are as follows:", + "bbox": [ + 75, + 212, + 472, + 544 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a nighttime deraining method, which highlights the importance of location information of rain streaks for night scenes.", + "- We propose Rain Location Prior (RLP) and Rain Prior Injection Module (RPIM), which are the keys to revealing location information and boosting the performance of nighttime deraining.", + "- We demonstrate the state-of-the-art performance of our method on both synthetic and real night rainy scenes from rigorous experiments and ablation studies." + ], + "bbox": [ + 96, + 555, + 470, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 736, + 218, + 752 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we briefly review some existing deraining methods and image restoration backbones as well as existing deraining datasets.", + "bbox": [ + 76, + 762, + 468, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deraining methods. Recurrent and residual learning are common practices for deraining models. Yang et al. [36] proposed a multi-task network to jointly perform rain detection, estimation and removal in a recurrent manner. Fu et al. [8] proposed to predict the residue of rain streaks with", + "bbox": [ + 76, + 825, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a9b1dc81ed6d4e32ccd53cd22217e5bc5493e8fa4bfafc3fb20575801c612dd4.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 638, + 148 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/01c4da1396a09fee5ee650bb95d1207109c9dc39bd7c1b965077f78fd63cb9d3.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 638, + 90, + 758, + 147 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/100a1c1ddf573965d73822c0e10a20dfb4d1c43b08ec1cf7353ff1966dea92ce.jpg", + "image_caption": [ + "(c)", + "Figure 2: Comparisons between synthetic and real rainy images. Synthetic images from (a) Rain100H [36], (b) GTAV-NightRain [42] and (c) real image from the Internet." + ], + "image_footnote": [], + "bbox": [ + 759, + 89, + 890, + 148 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "high-frequency details as input. Li et al. [21] proposed Recurrent Squeeze-and-Excitation Context Aggregation Net (RESCAN) which is a recurrent network feeding output of the previous stage to the next one. Ren et al. [27] proposed PReNet with recurrent and residual design to balance performance and model complexity. Jiang et al. [16] proposed Multi-Scale Progressive Fusion Network (MSPFN) utilizing the multi-scale and recurrent strategy. Deng et al. [7] proposed to remove rain streaks and recover lost details with two parallel sub-networks. Yi et al. [37] proposed to protect structure information and guide network training with residue channel prior. Wang et al. [32] proposed SPatial Attentive Network (SPANet) which also utilizes residual blocks. Wang et al. [31] proposed Rain Convolutional Dictionary Network (RCDNet) to integrate the physical structure of residual rain streaks. Liang et al. [24] proposed a Deraining Recursive Transformer (DRT) with less parameters. In this work, we compare with some recent deraining models on night scenes.", + "bbox": [ + 496, + 229, + 893, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image restoration backbones. Recently, powerful image restoration backbones [4, 5, 9] outperform previous methods on multiple tasks. Zamir et al. [40] proposed MPRNet making full use of encoder-decoder architecture and multistage strategies. They also proposed Restormer [39] to efficiently handle high-resolution images with the Transformer model. Wang et al. [34] also proposed a Transformer-based model following U-Net architecture and achieved promising performance on several tasks. While Tu et al. [30] proposed a multi-axis MLP-based architecture in a UNet-shaped hierarchical structure. Despite their robustness and capability, they fail to remove rain streaks in night scenes.", + "bbox": [ + 496, + 535, + 893, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deraining datasets. Most deraining datasets are synthesized by superposing the rain layer onto clean images. Li et al. [23] synthesized 12 rainy images following Garg and Shree [10, 11]. Yang et al. [36] proposed the Rain100L and Rain100H datasets. Fu et al. [8] synthesized 14000 rainy images using Photoshop. Zhang et al. [44] proposed the Rain800 dataset following their practice. Zhang and Patel [43] proposed the Rain1200 dataset with different density labels. Li et al. [18] proposed the NYU-Rain dataset and Hu et al. [15] proposed the RainCityscapes dataset based on depth information. Li et al. [19] proposed the MPID", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13149", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/320a3cadd63ec3a4fb4a41afe6515fa80769417a6cad8b12377563afd160e4b8.jpg", + "image_caption": [ + "Figure 3: Illustration on the framework of our method for nighttime deraining, which consists of three parts. The Rain Location Prior (RLP) is the prior that we propose to learn from rainy images with recurrent residual model implicitly and indicates the location information of rain streaks. To further emphasize features within rain streaks areas, we propose the second part, namely Rain Prior Injection Module (RPIM), to modulate the RLP with attention mechanism. The final part is the deraining module, which consumes the original rainy input and the learned RLP to get boosted deraining performance." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 885, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dataset with different rain types as well as annotations for the detection task. Wang et al. [32] proposed the first real paired dataset, called SPA-data, using the semi-automatic method to generate clean images from rainy videos. Ba et al. [1] proposed GT-Rain dataset which contains real paired data. Recently, datasets turned their focus on night rainy scenes. Li et al. [20] proposed a real dataset with the ratio of night scenes to be around $50\\%$ . Zhang et al. [42] proposed a synthetic night rain dataset, namely GTAV-NightRain, using the game engine for rendering. The emergence of these datasets enables careful study on nighttime deraining.", + "bbox": [ + 75, + 414, + 472, + 582 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 597, + 171, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first introduce the motivation. Then we describe the Rain Location Prior (RLP) and the Rain Prior Injection Module (RPIM) in detail. The framework of our method is illustrated in Figure 3.", + "bbox": [ + 75, + 623, + 470, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Formulation and Motivation", + "text_level": 1, + "bbox": [ + 76, + 696, + 333, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The appearance and photometry of rain have been extensively studied for decades [10, 11]. However, most existing synthetic datasets [8, 23, 36, 43] adopt a simplified formulation of rain streaks, where the rainy image $I$ is modeled as the sum of a rain streak layer $R$ and a clean image $B$ :", + "bbox": [ + 75, + 720, + 468, + 797 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI = R + B. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 810, + 468, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A common strategy for rain removal is to model rain streaks with specific properties like direction, scale and space distribution and separate the rain layer from the background. This is usually achieved [8, 16, 21, 31, 36] by estimating the", + "bbox": [ + 75, + 840, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "rain layer as an intermediate output before the final module and subtract it to restore the clean image.", + "bbox": [ + 496, + 414, + 890, + 444 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, the importance of location information embedded in the rain layer has been underestimated. As discussed in Section 1, since rain location is beneficial for rain removal and night rain appearance varies with spatial locations, obtaining the rain layer in advance is more necessary than in day scenes. Moreover, discriminating the rain layer from the night scene is more difficult due to the coupling of rain appearance and light sources, thus aforementioned practice (i.e., estimating the rain layer and subtracting it to get the final output using the same model) is inefficient.", + "bbox": [ + 496, + 445, + 892, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, therefore, we propose a novel framework for nighttime deraining, encompassing a model specializing the rain layer estimation, and a module that takes full advantage of the information of rain location. Specifically, we decouple the rain layer estimation and clean background reconstruction by introducing the Rain Location Prior (RLP) and Rain Prior Injection Module (RPIM). We learn to mine the information of rain location from nighttime rainy image and restore the clean scene respectively in an end-to-end manner. We further emphasize the features within rain regions by modulating them before rain revoal and background reconstruction. In this way, useful information of rain location can be better extracted and exploited, boosting the performance of nighttime deraining.", + "bbox": [ + 496, + 595, + 893, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Rain Location Prior (RLP)", + "text_level": 1, + "bbox": [ + 500, + 816, + 743, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As mentioned above, the rain layer is commonly assumed to be superposed onto the background, which facilitates the design ideas of progressive and residual learning for many deraining models [8, 16, 27, 32, 37]. These mod", + "bbox": [ + 496, + 840, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13150", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "els typically regard the rain layer as a residual component to the clean image, and some of them learn to progressively model these high-frequency patterns with recurrent structures. These designs, in turn, can reveal location information of rain streaks in night scenes, where the appearance of rain highly depends on its spatial location. For deraining, it would be beneficial if accurate rain locations were provided in advance, which is impractical in real scenes. Therefore, we propose to use recurrent residual architecture to mine the prior knowledge of rain location before removing rain streaks. It can provide the location information to deraining models, thereby further boosting their performance, which highlights its importance for nighttime deraining.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our proposed formulation, we introduce a module to learn and capture the prior knowledge of rain location, namely Rain Location Prior (RLP), before removing rain streaks. This module is composed of several residual blocks, which are effective in modeling rain streaks as a residual component. Meanwhile, it learns to progressively capture the rain through a recurrent design that utilizes the high-frequency characteristics of rain. When fed with the rainy input and an initial prior map, the module learns to extract deep features and recurrently update the prior map. The process of RLP can be formulated as follows:", + "bbox": [ + 75, + 287, + 472, + 455 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {R} _ {k} = \\mathcal {F} _ {R L P} (I \\odot \\bar {R} _ {k - 1}; \\theta), \\quad k = 1, \\dots , N, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 468, + 468, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I$ denotes the input and $\\bar{R}_k$ is the RLP output at the $k$ -th stage. $\\bar{R}_0$ is the initial map and all values are set to 0.5. $\\mathcal{F}_{RLP}(\\circ ;\\theta)$ refers to the RLP module and $\\theta$ is its parameters. $\\odot$ denotes the channel-wise concatenation. $N$ denotes the total number of recurrent stages, which is empirically set to 6 and 4 for CNN-based and Transformer-based models, respectively. Concretely, PReNet [27] is a lightweight deraining network with the residual and recurrent design for a balance between complexity and performance. Its simplicity in design tightly fits the role of the RLP module and is adopted in our experiment.", + "bbox": [ + 75, + 500, + 468, + 665 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that we do not impose additional constraints on the RLP output, because we found that supervision signals from rain streak masks obtained by thresholding following the practice in raindrop removal [14, 26, 38] do not improve the performance. For simplicity, we do not apply regularization terms to the RLP output during training and encourage the module to learn it implicitly from training data. Corresponding experimental results are provided in the supplementary material.", + "bbox": [ + 75, + 667, + 468, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Rain Prior Injection Module (RPIM)", + "text_level": 1, + "bbox": [ + 76, + 815, + 397, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In night scenes, the appearance of rain heavily depends on its spatial position relative to light sources. Therefore, deraining models should treat different areas with varying levels of importance. With the RLP indicating location in", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "formation of rain streaks, we further emphasize the importance of these areas with the attention mechanism [40].", + "bbox": [ + 496, + 90, + 888, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we propose the Rain Prior Injection Module (RPIM). It takes the deep features extracted by the RLP module and further updates the prior map in a residual manner. The updated prior map is then used to generate the attention weights that increase the importance of rain streak areas and suppress other irrelevant areas. Finally, the features within rain streak areas are emphasized by the weights by element-wise multiplication of deep features and the attention weights. The RPIM can be described as follows:", + "bbox": [ + 496, + 121, + 890, + 257 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {R}, z = \\mathcal {M} _ {R P I M} (\\bar {R} _ {N}, f; \\sigma), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 271, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{R}_N$ and $f$ are the final prior map and deep features extracted by residual blocks in the RLP module. $\\mathcal{M}_{RPIM}(\\circ ;\\sigma)$ denotes our Rain Prior Injection Module. $\\bar{R}$ and $z$ are the modulated output and feature tensor ready for injection into the deraining network, respectively.", + "bbox": [ + 496, + 292, + 892, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Deraining Module (DM)", + "text_level": 1, + "bbox": [ + 498, + 376, + 723, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For pixel-wise image restoration tasks, U-shaped architectures with skip connections are commonly adopted as they have shown good capability in capturing contextual information without losing much spatial information [30, 34, 40]. CNN-based and Transformer-based models with such architecture are two main streams and many methods make further improvements based on them.", + "bbox": [ + 496, + 400, + 890, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Encoder-Decoder models, the input is typically projected into a feature space through a convolution layer, which is suitable for prior injection. After obtaining RLP and modulating the prior, we inject it into deraining models to further enhance deraining performance. We feed the rainy input and the RLP into the deraining module, which is a U-shaped model (either CNN-based or Transformer-based) for rain streak removal and background restoration. The process of this stage can be formulated as follows:", + "bbox": [ + 496, + 506, + 890, + 642 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {I} = \\mathcal {F} _ {D M} (I \\odot \\bar {R}, z; \\Theta), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 648, + 890, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{I}$ is the restored image by deraining module, $\\bar{R}$ is the updated RLP and $\\odot$ denotes the channel-wise concatenation. $\\mathcal{F}_{DM}(\\circ ;\\Theta)$ represents the deraining model, which focuses on the contextual information of neighboring pixels, and $\\Theta$ is its parameters to be optimized. $z$ refers to the modulated prior by RPIM and is injected into the deraining module by channel-wise concatenation with the projected feature after the first convolution layer.", + "bbox": [ + 496, + 675, + 890, + 796 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the training of the whole model, we apply the Charbonnier loss [3] on the final output:", + "bbox": [ + 496, + 797, + 890, + 827 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sqrt {\\left\\| \\bar {I} - Y \\right\\| ^ {2} + \\varepsilon^ {2}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 835, + 890, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\bar{I}$ is the final output of the deraining model, $Y$ denotes the clean ground truth and $\\varepsilon = 10^{-3}$ is a constant.", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13151", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first introduce the experimental setups. Then we provide quantitative and qualitative results on synthetic data and evaluations on real night rainy images, to show the superior performance of our method compared to existing deraining methods, under the nighttime deraining setting. Moreover, we conduct ablation studies to validate the effectiveness of the proposed modules. Finally, we conduct experiments to show the generalization of our method on daytime datasets. Due to limited space, we provide more visual results in the supplementary material.", + "bbox": [ + 75, + 114, + 470, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setups", + "text_level": 1, + "bbox": [ + 76, + 273, + 272, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Rain streaks in GTAV-NightRain dataset [42] are sparse with low difficulty, which is unfavorable for observing the difference since all methods behaves well. Thus we follow the instructions to render more difficult data (27dB v.s. 32dB in [42]) for experiments, by increasing the scale and density of rain streaks. We turn on and off the rain effect while keeping other settings unchanged for the same scene to render the rainy and clean image pairs. Please refer to [42] for more details on data collection. We collect 10 rainy images and 1 clean image for each scene and cover non-overlapping scenes for training and test sets. Finally, we get a total of 5,000 pairs of training data and 500 pairs of test data. Our collected data will be released with the code. Additionally, we conduct experiments on Rain13k [16, 40] and GT-Rain [1] datasets, to further show the generalization of our method to daytime data. We train our model with different modules on Rain13k and evaluate on its test sets, which are Test100 [44], Rain100H [36], Rain100L [36], Test2800 [8], Test1200 [43]. We also train our method on GT-Rain and compare it with other methods on its test set.", + "bbox": [ + 75, + 296, + 470, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Our method is implemented in PyTorch and trained with Adam optimizer [17] with default parameters. The initial learning rate is set to $2 \\times 10^{-4}$ and finally decreases to $1 \\times 10^{-6}$ following a cosine scheduler. The model is trained for 250 epochs with a batch size of 8 on $256 \\times 256$ patches. Training is performed on a single NVIDIA RTX 3090 GPU. We adopt U-Net and Uformer (the Uformer-T variant) for CNN-based and Transformer-based architectures. All experiments are performed on a single NVIDIA RTX 3090 GPU.", + "bbox": [ + 75, + 598, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared Methods. To show the effectiveness of our method, we make comparisons with PReNet [27], SPANet [32], DRDNet [7], RCDNet [31], SPDNet [37], MPRNet [40], GT-Rain [1], DRT [24], U-Net [26] and Uformer [34] (the Uformer-T variant) on both synthetic and real data. All methods are trained on synthetic data from scratch with publicly available codes provided by authors following their default settings. Among them, representative methods are selected for visual comparison.", + "bbox": [ + 75, + 750, + 470, + 885 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics. For quantitative evaluation, we adopt commonly", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/041006c3c73564bee83feb41c2a4806bc779aa5cc51eebb68d006a74f179288d.jpg", + "table_caption": [ + "Table 1: Quantitative results of compared methods on synthetic data. All the models are trained on our collected data following the default setting by authors. Higher metric is better for PSNR and SSIM. #GMACs is calculated on $256 \\times 256$ patch." + ], + "table_footnote": [], + "table_body": "
MethodPSNRSSIM#Params#GMACs
Input27.100.8237//
PReLU [27]34.770.96220.17M66.4G
SPANet [32]31.100.92450.28M36.3G
DRDNet [7]32.200.92145.23M689.8G
RCDNet [31]34.170.94933.16M195.1G
SPDNet [37]33.900.93843.32M96.6G
MPRNet [40]36.630.96613.63M548.7G
GT-Rain [1]34.100.95722.29M29.6G
DRT [24]33.810.93811.18M165.4G
U-Net [26]36.630.96936.06M45.3G
Uformer [34]37.450.97205.20M10.7G
Ours (U-Net)37.280.97166.33M117.8G
Ours (Uformer)38.440.97495.52M63.4G
", + "bbox": [ + 511, + 169, + 879, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "used PSNR and SSIM [33] for comparison using the Y channel (in YCbCr color space) following [16].", + "bbox": [ + 496, + 381, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Quantitative Results on Synthetic Data", + "text_level": 1, + "bbox": [ + 498, + 421, + 834, + 438 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Table 1, the performance of both SPANet [32] and DRDNet [7] is inferior to that of other competitors, even though there exists large difference between their model size and computational cost. While PReNet [27], RCDNet [31], SPDNet [37], GT-Rain [1] and DRT [24] perform better than the former two methods and their performance is comparable to others. Among all compared methods, MPRNet [40] and Uformer [34], as representative CNN-based and Transformer-based image restoration models, show superior performance to other competitors, which well validates their model capacity.", + "bbox": [ + 496, + 444, + 890, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, with the help of our proposed RLP and RPIM, the performance of both CNN-based and Transformer-based models can be boosted by a large margin. For CNN-based model U-Net [26], our method can get an increase of 0.65dB on PSNR and surpasses MPRNet [40] by 0.65dB. For the Transformer-based model Uformer [34], a large gain of 0.99dB on PSNR can be obtained and our proposed method outperforms all compared methods. These results can well validate the effectiveness of our proposed method.", + "bbox": [ + 496, + 611, + 890, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Qualitative Results on Synthetic Data", + "text_level": 1, + "bbox": [ + 498, + 756, + 823, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Figure 4, SPANet [32] and DRDNet [7] can only remove a few rain streaks in night scenes and large amounts of rain streaks remain, which corresponds to inferior performance in quantitative results. While PReNet [27], RCDNet [31] and SPDNet [37] can remove more rain streaks than the former two competitors but there are still some rain streaks left there. MPRNet [40], U-Net [26] and Uformer [34] perform much better than these methods but", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13152", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5a1019b2d7742c22a4e89236138743cf478b2d4c4abf5d27905878e6c76e1fb9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 88, + 217, + 172 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/915a727c6607416a2e9bbb003d07d0d417d8babe0bc3b58498c5bf9825a07482.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 218, + 88, + 349, + 172 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ec905900dcc1d21b2cdfe823fa59d1b3a162add2d207cfdc1236ff7c91b117bf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 88, + 482, + 172 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b5069c271ada002f3b24244056ac72631f1fb65ec6ef692aae679e525b525048.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 614, + 172 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dedd5c6f71dd6b3d99b83be9dc575ecb1ad5549895a1e4a01a0b531faad1d849.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 88, + 746, + 172 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b07e0fba3dc59fddc05f30eb12f21c6c0f1b1a7034b285bc3621b906fe551429.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 750, + 88, + 880, + 172 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e9bd5359034f1014a9e7be0144ba7fb38592b3a6bee202fed5a1cc2849f2a019.jpg", + "image_caption": [ + "Rainy", + "MPRNet [40]" + ], + "image_footnote": [], + "bbox": [ + 84, + 189, + 215, + 275 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/41f26308cc85ad93f5736e3347ca341f37aeb58905a38a49a8b2cef3171a8076.jpg", + "image_caption": [ + "PRENet [27]", + "U-Net [26]" + ], + "image_footnote": [], + "bbox": [ + 217, + 189, + 349, + 275 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8015a90024f38b71cb2f3edc48d5845514113b5147ffbaa8417ffc4b602eabbe.jpg", + "image_caption": [ + "SPANet [32]", + "Uformer [34]" + ], + "image_footnote": [], + "bbox": [ + 351, + 189, + 482, + 275 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/40c3a9c6b01ab9d7979b855cae7fb0cbf42ba6faeef2bb50bacb46e595d4315f.jpg", + "image_caption": [ + "DRDNet [7]", + "Ours (U-Net)" + ], + "image_footnote": [], + "bbox": [ + 483, + 189, + 614, + 275 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5e884d3e2f348e364a25bb91a833b6a69c1917d94014ce034ab82d3e4f8c23d9.jpg", + "image_caption": [ + "RCDNet [31]", + "Ours (Uformer)" + ], + "image_footnote": [], + "bbox": [ + 616, + 189, + 746, + 275 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b161e3d276be8a9041acab8c58d5014d247116caa924b67478bab87aba6192e0.jpg", + "image_caption": [ + "SPDNet [37]", + "GT" + ], + "image_footnote": [], + "bbox": [ + 750, + 189, + 880, + 275 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0be8b25da8041040f7372f0f78b2680bc8a79b3b49baebe401516d2642b20c2b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 294, + 217, + 380 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7c7fcb43b3cd9b12d52498dfad506fff7157ecca0f4bbe0febbb417d80ebc5e5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 218, + 294, + 349, + 380 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f974ac798b454dee352944b0707412ec95664ee5e05a8bda3bb36f23c764ad52.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 349, + 294, + 482, + 380 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d024678764822b1c895a820bb59cb161b5b7243cc3f3db85c3398f9c0682be7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 294, + 614, + 380 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dd2cbcfb8bd220aa8af7c29ca73d5d5bb92598e5b9a25ebf39c975fd2d251bcd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 294, + 746, + 380 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0848a6d6ceb004ef1395c579bd0a3c07433e6c0359642e84f1f8393431a48eaf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 750, + 294, + 880, + 380 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3e0efc5bbd1932f1a963b012f9cd392dd7676032830c404241d689f2de7bd787.jpg", + "image_caption": [ + "Real", + "MPRNet [40]", + "Figure 4: Qualitative results on synthetic data (gamma correction is applied for better visualization). SPANet and DRDNet can only remove a few rain streaks while PReNet, RCDNet and SPDNet behave better than the former two methods. MPRNet, U-Net and Uformer outperform other competitors but our proposed prior can boost the performance of U-Net and Uformer even further, in terms of removing more rain streaks (Uformer for the first scene) and preserving background details (Uformer for the second scene). These results demonstrate the effectiveness of our proposed method." + ], + "image_footnote": [], + "bbox": [ + 84, + 396, + 215, + 481 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6546322f291c95968c703eff0990c1af4fa1c54fa28ad6605bb244ed33d2df10.jpg", + "image_caption": [ + "PRENet [27]", + "U-Net [26]" + ], + "image_footnote": [], + "bbox": [ + 217, + 396, + 349, + 481 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/63f0cf6e3a84f08fd235e94849decc58947474703b50d07549edb2e5f895e402.jpg", + "image_caption": [ + "SPANet [32]", + "Uformer [34]" + ], + "image_footnote": [], + "bbox": [ + 349, + 396, + 482, + 481 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/93fa1329d7ea5b9d2f33378fbc67e572754f3a856b1d11e1863a90dbcb79bd86.jpg", + "image_caption": [ + "DRDNet [7]", + "Ours (U-Net)" + ], + "image_footnote": [], + "bbox": [ + 483, + 396, + 614, + 481 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/44c7271a611387e842ef8e9c19ea098cc6ca5018dd667c7c42ad2185cef25603.jpg", + "image_caption": [ + "RCDNet [31]", + "Ours (Uformer)" + ], + "image_footnote": [], + "bbox": [ + 616, + 396, + 746, + 481 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ecf258402e645e17c4feb5dde9b95ece72afe5d263e693950e845b71604b1dce.jpg", + "image_caption": [ + "SPDNet [37]", + "GT" + ], + "image_footnote": [], + "bbox": [ + 750, + 396, + 880, + 481 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "also face challenges for different scenes. Among all compared methods, Ours (Uformer) can get the best results.", + "bbox": [ + 75, + 595, + 468, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the first image, the illumination is dominated by the red neon cylinder and rain streaks look red. MPRNet [40] surprisingly fails the case and its result is similar to that of SPANet [32] and DRDNet [7]. For U-Net [26], Uformer [34] and Ours (U-Net), there are only a few rain streaks left on the image. However, Ours (Uformer) can fully remove the rain streaks, which demonstrates the effectiveness of our method. In the second image, bright windows consist of similar textures to rain streaks and the scene is relatively complex. We can find that almost all compared methods including Ours (U-Net) fail to preserve the texture of streetlight and it even totally disappears in some results. DRDNet [7] and SPDNet [37] keep the streetlight unchanged but there are some rain streaks left. Only Ours (Uformer) remove most rain streaks and preserve the texture of streetlight at the same time. We can infer that deraining models tend to recognize long thin textures with high pixel intensity as rain streaks in night scenes because rain streaks near", + "bbox": [ + 75, + 628, + 472, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "light sources have higher pixel values. In such cases, location priors of rain streaks become more crucial for deraining models to accurately handle rain streaks in night scenes, which further confirms the effectiveness of our method.", + "bbox": [ + 496, + 595, + 890, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Qualitative Results on Real Night Rainy Images", + "text_level": 1, + "bbox": [ + 498, + 665, + 890, + 683 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, we present the qualitative results on real data in Figure 5. Due to the domain gap between synthetic and real data, models trained with GTAV-NightRain still behave poorly in real night scenes [42]. To further handle real night rainy images, we additionally add JPEG compression as a data augmentation in our training. Compared methods can partially remove rain streaks in real night rainy images but behave inconsistently for different rainy images. We can see that DRDNet [7], RCDNet [31] and SPDNet [37] perform better than PReNet [27], SPANet [32] and MPRNet [40] for the first image while U-Net [26] and Uformer [34] get better results. But they all fail to remove rain streaks in the second image. However, our method succeeds in handling both images. It can remove most rain streaks while keep", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13153", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3596a03b805c053aa28d8551e9be738a2ca190d995caec1b4c208f7c9487b40b.jpg", + "image_caption": [ + "Real" + ], + "image_footnote": [], + "bbox": [ + 89, + 87, + 246, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/64811a296d4ca816b59de79693944a034988db428ccbe727fc583d8b88ff1c40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 246, + 88, + 403, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/63c694766f785736171c44f4a92a552a02a7fcb55c3342ab3e20fde169b98eee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 405, + 88, + 560, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/53f98c6c713c4057233fcc65f454d564c8459dc32e84e4a51d53917b3be7d070.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 560, + 88, + 717, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8152160a6b3a2ce47d89c6cc386e5e3b76a6a6f622913f66c9baa6271b07d877.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 718, + 88, + 875, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b62617b7b6e25830428a365cdea4135da65aba9cc62f97a60038225f706da600.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 196, + 246, + 291 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/89d28da5668b8474453e5120715ca3f00267f42ee9fc9c470fda9d59b1edd9ea.jpg", + "image_caption": [ + "PRENet [27]", + "MPRNet [40]" + ], + "image_footnote": [], + "bbox": [ + 246, + 196, + 403, + 291 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0adbc5d05489c78d15c83151c36ac4b12bbe7753ca073b23efb4dbf0d71a9e00.jpg", + "image_caption": [ + "SPANet [32]", + "U-Net [26]" + ], + "image_footnote": [], + "bbox": [ + 405, + 196, + 560, + 291 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1bbc9c588dac4317b50f39c5cbbb25fb67373eaf50e323bf323e969b4a586fed.jpg", + "image_caption": [ + "DRDNet [7]", + "Uformer [34]" + ], + "image_footnote": [], + "bbox": [ + 560, + 196, + 717, + 291 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed6c8d50847789697789eaea16c85ba636b8e65be33dc75f4fea24a545817928.jpg", + "image_caption": [ + "RCDNet [31]", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 718, + 196, + 875, + 291 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0064ee91e0610fcfab60665733c9b36cc55d96031690c795b49c1af4404ba218.jpg", + "image_caption": [ + "SPDNet [37]" + ], + "image_footnote": [], + "bbox": [ + 89, + 306, + 246, + 397 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fc5e8096cb85f3d47aef6b019a987e84b6df173cab460e6d64fcff3bd6ade8b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 246, + 309, + 403, + 397 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e088dfc554a4dcfbc46658d3b3e6b0615f944a25be59f9a9ed7d5da2f3c03f67.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 405, + 309, + 560, + 397 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5ae5fbae4dec4fdd6603c02b4020ff65a3958ac50831c0b2416fe5a09966ee6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 560, + 309, + 717, + 397 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2f4944129fac54f52ee9c530c86d9437c45a728c177f2516a8b913dd68869e3f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 718, + 309, + 875, + 397 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/24cbd4bf9e34954e2e56506e8c9800dbf6d7f1be41b2f9b707677f8fcf397c2f.jpg", + "image_caption": [ + "Real", + "SPDNet [37]", + "Figure 5: Qualitative results on real night rainy images. Our method gets the best visual results. Please zoom in for details." + ], + "image_footnote": [], + "bbox": [ + 89, + 412, + 246, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ca9223672051ef0150b2f9eca311e2deaddc44dc18abe106f05114e5fd310918.jpg", + "image_caption": [ + "PRENet [27]", + "MPRNet [40]" + ], + "image_footnote": [], + "bbox": [ + 246, + 412, + 403, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e7a56cb0e121fd9bee6af5de5b94193ba93854655457e5ff58eff8371f148393.jpg", + "image_caption": [ + "SPANet [32]", + "U-Net [26]" + ], + "image_footnote": [], + "bbox": [ + 405, + 412, + 560, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/052fba699fa7fc991cee60bb69fd0f8450bf85a6ba4d6313a94f75dcc717e2c9.jpg", + "image_caption": [ + "DRDNet [7]", + "Uformer [34]" + ], + "image_footnote": [], + "bbox": [ + 560, + 412, + 717, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/433a07b99dc80f1ae807e13fd05f02f7ff413932105b0f30d877a587b9e08429.jpg", + "image_caption": [ + "RCDNet [31]", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 718, + 412, + 875, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing backgrounds tidy, showing the effectiveness of our proposed method for removing rain streaks in real night scenes.", + "bbox": [ + 75, + 551, + 468, + 582 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Qualitative Results of RLP", + "text_level": 1, + "bbox": [ + 76, + 589, + 318, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To further illustrate the effectiveness of our Rain Location Prior, we provide visualizations on both synthetic and real night rainy images in Figure 6. Our RLP module can learn to recognize rain streaks and emphasize these areas with higher weights. Notably, RLP can learn by itself to suppress areas of light sources, i.e., these areas are much darker than neighboring areas of rain streaks. We can also notice that rain streaks in the sky can also be recognized even though they are not obvious in the rainy image.", + "bbox": [ + 75, + 612, + 468, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in the right half of Figure 6, our RLP module can also generalize well to real night rainy images with only synthetic data for training. Same to the synthetic case, light sources are suppressed in RLP and those areas are darker than areas of rain streaks. These results all show the effectiveness of RLP, which is beneficial for nighttime deraining.", + "bbox": [ + 75, + 750, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 847, + 240, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we study the effect of each component of our method, including Rain Location Prior (RLP) and", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/757988b96c3a3b6bcb7a50f2c2dae61e3f4ec5b5ce8dfd2cbdef4b2bc7f4aa32.jpg", + "table_caption": [ + "Table 2: Ablation study on individual components of our proposed method & different model structures and sizes." + ], + "table_footnote": [], + "table_body": "
DMRLPRPIMPSNRΔSSIMΔ
PReLUNetXX34.77-0.9622-
✓X35.00+0.230.9649+0.0027
✓✓34.31-0.460.9621-0.0001
MPRNetXX35.21-0.9627-
✓X35.42+0.210.9641+0.0014
✓✓35.67+0.460.9633+0.0006
U-NetXX36.63-0.9693-
✓X37.08+0.450.9715+0.0022
✓✓37.28+0.650.9716+0.0023
Uformer-TXX37.45-0.9720-
✓X37.95+0.500.9733+0.0013
✓✓38.44+0.990.9749+0.0029
Uformer-BXX39.41-0.9763-
✓X39.65+0.240.9770+0.0007
✓✓39.77+0.360.9773+0.0010
", + "bbox": [ + 501, + 580, + 897, + 815 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Rain Prior Injection Module (RPIM). We choose U-Net [26] and Uformer [34] out of CNN-based and Transformer-based models as the deraining module in our method, with U-shaped Encoder-Decoder architecture. Besides, we examine the effects of RLP on PReNet [27] and MPRNet", + "bbox": [ + 498, + 824, + 892, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13154", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fac82bba6842e9bca9587ef9e4905aa0aca4eb459e99c68200ac65d594fb5025.jpg", + "image_caption": [ + "Figure 6: Visualizations of Rain Location Prior (RLP) on synthetic and real night rainy images. Please zoom in for details. Table 3: Generalization to daytime datasets. Models are trained on Rain13k dataset [16] and evaluated on five test sets." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 890, + 186 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e4f0412c7a9ce76f26b2da1a33c043c1a52eaf7c11416df915514db25a3c1156.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DMRLPRPIMTest100 [44]Rain100H [36]Rain100L [36]Test2800 [8]Test1200 [43]Avg.
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Input22.550.686313.550.378426.900.838324.350.782923.630.732422.200.6837
U-NetXX24.910.858424.210.826730.520.925631.310.919931.010.902628.390.8866
U-Net✓X25.040.855026.820.846730.560.918531.320.917630.710.891728.890.8859
U-Net✓✓25.320.866526.060.838031.200.932431.320.920331.590.908929.100.8932
UformerXX28.010.878028.210.851632.160.934432.430.928731.660.907830.500.9001
Uformer✓X28.080.877528.370.854532.590.938532.490.928731.860.909330.680.9017
Uformer✓✓28.500.882128.340.857632.670.939032.550.929531.670.904230.740.9025
", + "bbox": [ + 81, + 232, + 883, + 375 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "[40] with other architecture designs. Finally, we apply our method to the Uformer-B variant to investigate RLP's effect on model with more parameters. Experiments are carried out on the same test set and results are listed in Table 2.", + "bbox": [ + 75, + 386, + 468, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "RLP. With the prior map learned by the RLP module, directly feeding it into the deraining module brings an increase of 0.23dB, 0.21dB, 0.45dB, 0.50dB and 0.24dB in PSNR for five different deraining modules. It shows the effectiveness of the proposed RLP which can reveal location information of rain streaks and improve the deraining performance. The benefit of accurate location is straightforward and it is also effective for PReNet and MPRNet with other model structures.", + "bbox": [ + 75, + 450, + 468, + 587 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "RPIM. In night scenes where location information plays a vital role in deraining, emphasizing the importance of RLP in rain streak areas is beneficial. As shown in Table 2, the performance of deraining modules can be further boosted with the help of RPIM. MPRNet [40], U-Net [26] and Uformer-T/-B [34] can get an additional increase of $0.25\\mathrm{dB}$ , $0.20\\mathrm{dB}$ and $0.49\\mathrm{dB}/0.12\\mathrm{dB}$ in PSNR. While PReNet [27] gets worse results and the repeated feature injections in its recurrent structure may leads to the performance drop.", + "bbox": [ + 75, + 592, + 468, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model Structure and Capability. With different models compared, we can find that (i) recurrent structure may suffer from repeated feature injection (e.g., PReNet); (ii) models with vanilla Encoder-Decoder structure may benefit more from RLP (e.g., U-Net v.s. MPRNet); (iii) moderate models with better capability may benefit more from RLP (Uformer v.s. U-Net); (iv) moderate models may prefer additional knowledge from RLP than big models (e.g., Uformer-B v.s. Uformer-T). The comparisons demonstrate the effectiveness of our proposed RLP and RPIM and further provide insights on further improvement.", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Generalization to Daytime Datasets", + "text_level": 1, + "bbox": [ + 498, + 385, + 808, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Despite our goal of nighttime deraining, we also conduct experiments on Rain13k [16] and GT-Rain [1] to demonstrate the generalization of our method on day scenes. As listed in Table 3, our method is also beneficial for CNN-based and Transformer-based models on daytime deraining. Additionally, we can find that the improvement is smaller than that on the nighttime dataset, which suggests the greater importance of location information for nighttime deraining. We also test our method on the GT-Rain dataset [1] and results are provided in the supplementary material.", + "bbox": [ + 496, + 411, + 890, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 585, + 617, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Nighttime rain removal is a challenging task due to complex illumination conditions. In night scenes, the location information of rain streaks becomes more critical for rain removal. In this paper, we propose the Rain Location Prior (RLP), which can be learned implicitly from rainy images using a recurrent residual model to reveal the location information of rain streaks. To further improve the deraining performance, we propose the Rain Prior Injection Module (RPIM) to modulate the learned RLP with the attention mechanism and emphasize the features within rain streak areas. Together, they help deraining modules focus more on recovering clean background rather than recognizing complex rain streaks. Despite the original goal of nighttime deraining, our method also works in day scenes. Experimental results show the effectiveness and generalization of our method on both synthetic data and real nighttime rainy images, which may be helpful for future research on nighttime deraining. We plan to explore more architectures for learning and extending RLP in the future.", + "bbox": [ + 496, + 613, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13155", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work was supported by the National Natural Science Foundation of China (62171038, 62088101, 61931008, and 62006101), the R&D Program of Beijing Municipal Education Commission (KZ202211417048), and the Fundamental Research Funds for the Central Universities.", + "bbox": [ + 76, + 90, + 472, + 181 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 196, + 174, + 212 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yunhao Ba, Howard Zhang, Ethan Yang, Akira Suzuki, Arnold Pfahnl, Chethan Chinder Chandrappa, Celso M de Melo, Suya You, Stefano Soatto, Alex Wong, et al. 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In ICIP, 2014. 1" + ], + "bbox": [ + 78, + 90, + 468, + 758 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13157", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Rain Location Prior for Nighttime Deraining/f13e3907-fb21-485a-916a-d1036549cfe5_model.json b/2023/Learning Rain Location Prior for Nighttime Deraining/f13e3907-fb21-485a-916a-d1036549cfe5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5b8690867beb8651d7786525cfc1ad66910bddf9 --- /dev/null +++ b/2023/Learning Rain Location Prior for Nighttime Deraining/f13e3907-fb21-485a-916a-d1036549cfe5_model.json @@ -0,0 +1,2915 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.209, + 0.131, + 0.761, + 0.154 + ], + "angle": 0, + "content": "Learning Rain Location Prior for Nighttime Deraining" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.18, + 0.731, + 0.235 + ], + "angle": 0, + "content": "Fan Zhang1 Shaodi You2 Yu Li3 Ying Fu1* \n1Beijing Institute of Technology 2University of Amsterdam \n3International Digital Economy Academy" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.755 + ], + "angle": 0, + "content": "Rain can significantly degrade image quality and visibility, making deraining a critical area of research in computer vision. Despite recent progress in learning-based deraining methods, there is a lack of focus on nighttime deraining due to the unique challenges posed by non-uniform local illuminations from artificial light sources. Rain streaks in these scenes have diverse appearances that are tightly related to their relative positions to light sources, making it difficult for existing deraining methods to effectively handle them. In this paper, we highlight the importance of rain streak location information in nighttime deraining. Specifically, we propose a Rain Location Prior (RLP) that is learned implicitly from rainy images using a recurrent residual model. This learned prior contains location information of rain streaks and, when injected into deraining models, can significantly improve their performance. To further improve the effectiveness of the learned prior, we also propose a Rain Prior Injection Module (RPIM) to modulate the prior before injection, increasing the importance of features within rain streak areas. Experimental results demonstrate that our approach outperforms existing state-of-the-art methods by about 1dB and effectively improves the performance of deraining models. We also evaluate our method on real night rainy images to show the capability to handle real scenes with fully synthetic data for training. Our method represents a significant step forward in the area of nighttime deraining and highlights the importance of location information in this challenging problem. The code is publicly available at https://github.com/zkawfanx/RLP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.787, + 0.21, + 0.803 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.813, + 0.47, + 0.875 + ], + "angle": 0, + "content": "While rain degrades image quality and visibility, it can be particularly problematic at night, because the low light condition and complex illuminations make it more difficult to distinguish rain streaks from other image features. This" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.268, + 0.694, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.572, + 0.329, + 0.629, + 0.342 + ], + "angle": 0, + "content": "(a) Rainy" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.268, + 0.889, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.756, + 0.329, + 0.83, + 0.342 + ], + "angle": 0, + "content": "(b) Uformer" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.342, + 0.697, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.402, + 0.626, + 0.415 + ], + "angle": 0, + "content": "(c) RLP" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.342, + 0.889, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.767, + 0.402, + 0.82, + 0.415 + ], + "angle": 0, + "content": "(d) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.423, + 0.893, + 0.514 + ], + "angle": 0, + "content": "Figure 1: (a) In night scenes, appearances of rain are highly dependent on locations relative to light sources. (b) Derain result of state-of-the-art method Uformer [34]. (c) Visualization of the proposed Rain Location Prior (RLP), which indicates the location of rain streaks and suppresses areas of light sources. (d) Derain result of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.893, + 0.614 + ], + "angle": 0, + "content": "not only hinders the performance of high-level vision algorithms, e.g., object detection [13, 29] and tracking [2, 35], but also poses a safety risk for autonomous vehicles [6, 28] and other applications that rely on accurate visual information. Therefore, there is an increasing need for developing nighttime deraining methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.825 + ], + "angle": 0, + "content": "Unfortunately, despite recent advances in deep learning [34, 39, 40], which have significantly improved the performance, current endeavors predominantly focus on daytime scenarios, leaving the realm of nighttime deraining still largely unexplored. The most frequently utilized datasets [16, 32] scarcely encompass night scenes, neither does the synthesizing procedure consider interactions between rain and light sources. This hinders the direct application of existing methods to nighttime deraining. Recently, some datasets [20, 42] have started to cover previously ignored night scenes, which may enable careful study on nighttime deraining. Since there is no prior method specifically targeting nighttime deraining, we attempt to handle real night rainy scenes with the help of the recently developed dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Night scenes differ from day scenes in that there is no uniform global illumination; instead, darkness and nonuniform local illuminations dominate [12, 22, 25, 41, 45]. It results in the totally different appearance of night rain, which varies drastically at different spatial locations (i.e." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.325, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author: fuying@bit.edu.cn" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13148" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "only rain streaks near light sources are more discernible, as shown in Figure 2). Intuitively, it could facilitate the removal of rain streaks if precise locations were obtained in advance, which is often impractical in real scenes. Likewise, it is a common practice [14, 26] to train deep models to predict the locations of raindrop (i.e. raindrop mask) in the raindrop removal community. Therefore, identifying the rain location becomes more crucial than in day scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.545 + ], + "angle": 0, + "content": "In this paper, we propose a novel deraining method targeting night scenes. Firstly, we highlight the importance of location information of rain streaks for nighttime deraining, as the appearance of rain streaks is highly varying at different spatial locations at night. Thus, we propose a Rain Location Prior (RLP) which can be implicitly learned by recurrent residual models. It can reveal the location information of rain streaks in night scenes and be incorporated into deraining methods to improve their performance, including CNN-based and Transformer-based ones. Secondly, we propose a Rain Prior Injection Module (RPIM) to increase the importance of features within rain streak areas indicated by RLP. Deraining models can focus more on recovering lost information within rain streak areas and get a further increase in performance. Finally, we perform comprehensive experiments to demonstrate the effectiveness of our method. Our method outperforms existing state-of-the-art methods quantitatively and qualitatively on synthetic data. Furthermore, we demonstrate the capability of our method in handling real scenes. We also conduct ablation studies to evaluate the effectiveness of each component in our method. To summarize, the contributions of our paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.556, + 0.47, + 0.601 + ], + "angle": 0, + "content": "- We propose a nighttime deraining method, which highlights the importance of location information of rain streaks for night scenes." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.61, + 0.47, + 0.672 + ], + "angle": 0, + "content": "- We propose Rain Location Prior (RLP) and Rain Prior Injection Module (RPIM), which are the keys to revealing location information and boosting the performance of nighttime deraining." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.68, + 0.472, + 0.725 + ], + "angle": 0, + "content": "- We demonstrate the state-of-the-art performance of our method on both synthetic and real night rainy scenes from rigorous experiments and ablation studies." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.556, + 0.472, + 0.725 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.737, + 0.22, + 0.753 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.763, + 0.47, + 0.809 + ], + "angle": 0, + "content": "In this section, we briefly review some existing deraining methods and image restoration backbones as well as existing deraining datasets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Deraining methods. Recurrent and residual learning are common practices for deraining models. Yang et al. [36] proposed a multi-task network to jointly perform rain detection, estimation and removal in a recurrent manner. Fu et al. [8] proposed to predict the residue of rain streaks with" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.09, + 0.639, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.566, + 0.153, + 0.586, + 0.165 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.091, + 0.759, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.686, + 0.152, + 0.704, + 0.164 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.09, + 0.892, + 0.149 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.82, + 0.152, + 0.838, + 0.165 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.169, + 0.892, + 0.214 + ], + "angle": 0, + "content": "Figure 2: Comparisons between synthetic and real rainy images. Synthetic images from (a) Rain100H [36], (b) GTAV-NightRain [42] and (c) real image from the Internet." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.895, + 0.518 + ], + "angle": 0, + "content": "high-frequency details as input. Li et al. [21] proposed Recurrent Squeeze-and-Excitation Context Aggregation Net (RESCAN) which is a recurrent network feeding output of the previous stage to the next one. Ren et al. [27] proposed PReNet with recurrent and residual design to balance performance and model complexity. Jiang et al. [16] proposed Multi-Scale Progressive Fusion Network (MSPFN) utilizing the multi-scale and recurrent strategy. Deng et al. [7] proposed to remove rain streaks and recover lost details with two parallel sub-networks. Yi et al. [37] proposed to protect structure information and guide network training with residue channel prior. Wang et al. [32] proposed SPatial Attentive Network (SPANet) which also utilizes residual blocks. Wang et al. [31] proposed Rain Convolutional Dictionary Network (RCDNet) to integrate the physical structure of residual rain streaks. Liang et al. [24] proposed a Deraining Recursive Transformer (DRT) with less parameters. In this work, we compare with some recent deraining models on night scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.894, + 0.718 + ], + "angle": 0, + "content": "Image restoration backbones. Recently, powerful image restoration backbones [4, 5, 9] outperform previous methods on multiple tasks. Zamir et al. [40] proposed MPRNet making full use of encoder-decoder architecture and multistage strategies. They also proposed Restormer [39] to efficiently handle high-resolution images with the Transformer model. Wang et al. [34] also proposed a Transformer-based model following U-Net architecture and achieved promising performance on several tasks. While Tu et al. [30] proposed a multi-axis MLP-based architecture in a UNet-shaped hierarchical structure. Despite their robustness and capability, they fail to remove rain streaks in night scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Deraining datasets. Most deraining datasets are synthesized by superposing the rain layer onto clean images. Li et al. [23] synthesized 12 rainy images following Garg and Shree [10, 11]. Yang et al. [36] proposed the Rain100L and Rain100H datasets. Fu et al. [8] synthesized 14000 rainy images using Photoshop. Zhang et al. [44] proposed the Rain800 dataset following their practice. Zhang and Patel [43] proposed the Rain1200 dataset with different density labels. Li et al. [18] proposed the NYU-Rain dataset and Hu et al. [15] proposed the RainCityscapes dataset based on depth information. Li et al. [19] proposed the MPID" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13149" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.887, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.33, + 0.895, + 0.409 + ], + "angle": 0, + "content": "Figure 3: Illustration on the framework of our method for nighttime deraining, which consists of three parts. The Rain Location Prior (RLP) is the prior that we propose to learn from rainy images with recurrent residual model implicitly and indicates the location information of rain streaks. To further emphasize features within rain streaks areas, we propose the second part, namely Rain Prior Injection Module (RPIM), to modulate the RLP with attention mechanism. The final part is the deraining module, which consumes the original rainy input and the learned RLP to get boosted deraining performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.473, + 0.583 + ], + "angle": 0, + "content": "dataset with different rain types as well as annotations for the detection task. Wang et al. [32] proposed the first real paired dataset, called SPA-data, using the semi-automatic method to generate clean images from rainy videos. Ba et al. [1] proposed GT-Rain dataset which contains real paired data. Recently, datasets turned their focus on night rainy scenes. Li et al. [20] proposed a real dataset with the ratio of night scenes to be around \\(50\\%\\). Zhang et al. [42] proposed a synthetic night rain dataset, namely GTAV-NightRain, using the game engine for rendering. The emergence of these datasets enables careful study on nighttime deraining." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.598, + 0.172, + 0.613 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.471, + 0.686 + ], + "angle": 0, + "content": "In this section, we first introduce the motivation. Then we describe the Rain Location Prior (RLP) and the Rain Prior Injection Module (RPIM) in detail. The framework of our method is illustrated in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.697, + 0.334, + 0.712 + ], + "angle": 0, + "content": "3.1. Formulation and Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.721, + 0.47, + 0.798 + ], + "angle": 0, + "content": "The appearance and photometry of rain have been extensively studied for decades [10, 11]. However, most existing synthetic datasets [8, 23, 36, 43] adopt a simplified formulation of rain streaks, where the rainy image \\(I\\) is modeled as the sum of a rain streak layer \\(R\\) and a clean image \\(B\\):" + }, + { + "type": "equation", + "bbox": [ + 0.23, + 0.811, + 0.47, + 0.827 + ], + "angle": 0, + "content": "\\[\nI = R + B. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.471, + 0.903 + ], + "angle": 0, + "content": "A common strategy for rain removal is to model rain streaks with specific properties like direction, scale and space distribution and separate the rain layer from the background. This is usually achieved [8, 16, 21, 31, 36] by estimating the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.445 + ], + "angle": 0, + "content": "rain layer as an intermediate output before the final module and subtract it to restore the clean image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.893, + 0.596 + ], + "angle": 0, + "content": "However, the importance of location information embedded in the rain layer has been underestimated. As discussed in Section 1, since rain location is beneficial for rain removal and night rain appearance varies with spatial locations, obtaining the rain layer in advance is more necessary than in day scenes. Moreover, discriminating the rain layer from the night scene is more difficult due to the coupling of rain appearance and light sources, thus aforementioned practice (i.e., estimating the rain layer and subtracting it to get the final output using the same model) is inefficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.895, + 0.809 + ], + "angle": 0, + "content": "In this work, therefore, we propose a novel framework for nighttime deraining, encompassing a model specializing the rain layer estimation, and a module that takes full advantage of the information of rain location. Specifically, we decouple the rain layer estimation and clean background reconstruction by introducing the Rain Location Prior (RLP) and Rain Prior Injection Module (RPIM). We learn to mine the information of rain location from nighttime rainy image and restore the clean scene respectively in an end-to-end manner. We further emphasize the features within rain regions by modulating them before rain revoal and background reconstruction. In this way, useful information of rain location can be better extracted and exploited, boosting the performance of nighttime deraining." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.745, + 0.833 + ], + "angle": 0, + "content": "3.2. Rain Location Prior (RLP)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.894, + 0.903 + ], + "angle": 0, + "content": "As mentioned above, the rain layer is commonly assumed to be superposed onto the background, which facilitates the design ideas of progressive and residual learning for many deraining models [8, 16, 27, 32, 37]. These mod" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13150" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "els typically regard the rain layer as a residual component to the clean image, and some of them learn to progressively model these high-frequency patterns with recurrent structures. These designs, in turn, can reveal location information of rain streaks in night scenes, where the appearance of rain highly depends on its spatial location. For deraining, it would be beneficial if accurate rain locations were provided in advance, which is impractical in real scenes. Therefore, we propose to use recurrent residual architecture to mine the prior knowledge of rain location before removing rain streaks. It can provide the location information to deraining models, thereby further boosting their performance, which highlights its importance for nighttime deraining." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.456 + ], + "angle": 0, + "content": "In our proposed formulation, we introduce a module to learn and capture the prior knowledge of rain location, namely Rain Location Prior (RLP), before removing rain streaks. This module is composed of several residual blocks, which are effective in modeling rain streaks as a residual component. Meanwhile, it learns to progressively capture the rain through a recurrent design that utilizes the high-frequency characteristics of rain. When fed with the rainy input and an initial prior map, the module learns to extract deep features and recurrently update the prior map. The process of RLP can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.469, + 0.47, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\bar {R} _ {k} = \\mathcal {F} _ {R L P} (I \\odot \\bar {R} _ {k - 1}; \\theta), \\quad k = 1, \\dots , N, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.666 + ], + "angle": 0, + "content": "where \\(I\\) denotes the input and \\(\\bar{R}_k\\) is the RLP output at the \\(k\\)-th stage. \\(\\bar{R}_0\\) is the initial map and all values are set to 0.5. \\(\\mathcal{F}_{RLP}(\\circ ;\\theta)\\) refers to the RLP module and \\(\\theta\\) is its parameters. \\(\\odot\\) denotes the channel-wise concatenation. \\(N\\) denotes the total number of recurrent stages, which is empirically set to 6 and 4 for CNN-based and Transformer-based models, respectively. Concretely, PReNet [27] is a lightweight deraining network with the residual and recurrent design for a balance between complexity and performance. Its simplicity in design tightly fits the role of the RLP module and is adopted in our experiment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.804 + ], + "angle": 0, + "content": "Note that we do not impose additional constraints on the RLP output, because we found that supervision signals from rain streak masks obtained by thresholding following the practice in raindrop removal [14, 26, 38] do not improve the performance. For simplicity, we do not apply regularization terms to the RLP output during training and encourage the module to learn it implicitly from training data. Corresponding experimental results are provided in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.398, + 0.833 + ], + "angle": 0, + "content": "3.3. Rain Prior Injection Module (RPIM)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In night scenes, the appearance of rain heavily depends on its spatial position relative to light sources. Therefore, deraining models should treat different areas with varying levels of importance. With the RLP indicating location in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.89, + 0.121 + ], + "angle": 0, + "content": "formation of rain streaks, we further emphasize the importance of these areas with the attention mechanism [40]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.892, + 0.258 + ], + "angle": 0, + "content": "Specifically, we propose the Rain Prior Injection Module (RPIM). It takes the deep features extracted by the RLP module and further updates the prior map in a residual manner. The updated prior map is then used to generate the attention weights that increase the importance of rain streak areas and suppress other irrelevant areas. Finally, the features within rain streak areas are emphasized by the weights by element-wise multiplication of deep features and the attention weights. The RPIM can be described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.272, + 0.892, + 0.289 + ], + "angle": 0, + "content": "\\[\n\\bar {R}, z = \\mathcal {M} _ {R P I M} (\\bar {R} _ {N}, f; \\sigma), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.893, + 0.37 + ], + "angle": 0, + "content": "where \\(\\bar{R}_N\\) and \\(f\\) are the final prior map and deep features extracted by residual blocks in the RLP module. \\(\\mathcal{M}_{RPIM}(\\circ ;\\sigma)\\) denotes our Rain Prior Injection Module. \\(\\bar{R}\\) and \\(z\\) are the modulated output and feature tensor ready for injection into the deraining network, respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.377, + 0.724, + 0.394 + ], + "angle": 0, + "content": "3.4. Deraining Module (DM)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.506 + ], + "angle": 0, + "content": "For pixel-wise image restoration tasks, U-shaped architectures with skip connections are commonly adopted as they have shown good capability in capturing contextual information without losing much spatial information [30, 34, 40]. CNN-based and Transformer-based models with such architecture are two main streams and many methods make further improvements based on them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.643 + ], + "angle": 0, + "content": "In Encoder-Decoder models, the input is typically projected into a feature space through a convolution layer, which is suitable for prior injection. After obtaining RLP and modulating the prior, we inject it into deraining models to further enhance deraining performance. We feed the rainy input and the RLP into the deraining module, which is a U-shaped model (either CNN-based or Transformer-based) for rain streak removal and background restoration. The process of this stage can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.65, + 0.892, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\bar {I} = \\mathcal {F} _ {D M} (I \\odot \\bar {R}, z; \\Theta), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.676, + 0.892, + 0.797 + ], + "angle": 0, + "content": "where \\(\\bar{I}\\) is the restored image by deraining module, \\(\\bar{R}\\) is the updated RLP and \\(\\odot\\) denotes the channel-wise concatenation. \\(\\mathcal{F}_{DM}(\\circ ;\\Theta)\\) represents the deraining model, which focuses on the contextual information of neighboring pixels, and \\(\\Theta\\) is its parameters to be optimized. \\(z\\) refers to the modulated prior by RPIM and is injected into the deraining module by channel-wise concatenation with the projected feature after the first convolution layer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.828 + ], + "angle": 0, + "content": "For the training of the whole model, we apply the Charbonnier loss [3] on the final output:" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.837, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sqrt {\\left\\| \\bar {I} - Y \\right\\| ^ {2} + \\varepsilon^ {2}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.87, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\bar{I}\\) is the final output of the deraining model, \\(Y\\) denotes the clean ground truth and \\(\\varepsilon = 10^{-3}\\) is a constant." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13151" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.21, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.471, + 0.268 + ], + "angle": 0, + "content": "In this section, we first introduce the experimental setups. Then we provide quantitative and qualitative results on synthetic data and evaluations on real night rainy images, to show the superior performance of our method compared to existing deraining methods, under the nighttime deraining setting. Moreover, we conduct ablation studies to validate the effectiveness of the proposed modules. Finally, we conduct experiments to show the generalization of our method on daytime datasets. Due to limited space, we provide more visual results in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.274, + 0.274, + 0.29 + ], + "angle": 0, + "content": "4.1. Experimental Setups" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.471, + 0.599 + ], + "angle": 0, + "content": "Datasets. Rain streaks in GTAV-NightRain dataset [42] are sparse with low difficulty, which is unfavorable for observing the difference since all methods behaves well. Thus we follow the instructions to render more difficult data (27dB v.s. 32dB in [42]) for experiments, by increasing the scale and density of rain streaks. We turn on and off the rain effect while keeping other settings unchanged for the same scene to render the rainy and clean image pairs. Please refer to [42] for more details on data collection. We collect 10 rainy images and 1 clean image for each scene and cover non-overlapping scenes for training and test sets. Finally, we get a total of 5,000 pairs of training data and 500 pairs of test data. Our collected data will be released with the code. Additionally, we conduct experiments on Rain13k [16, 40] and GT-Rain [1] datasets, to further show the generalization of our method to daytime data. We train our model with different modules on Rain13k and evaluate on its test sets, which are Test100 [44], Rain100H [36], Rain100L [36], Test2800 [8], Test1200 [43]. We also train our method on GT-Rain and compare it with other methods on its test set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Implementation Details. Our method is implemented in PyTorch and trained with Adam optimizer [17] with default parameters. The initial learning rate is set to \\(2 \\times 10^{-4}\\) and finally decreases to \\(1 \\times 10^{-6}\\) following a cosine scheduler. The model is trained for 250 epochs with a batch size of 8 on \\(256 \\times 256\\) patches. Training is performed on a single NVIDIA RTX 3090 GPU. We adopt U-Net and Uformer (the Uformer-T variant) for CNN-based and Transformer-based architectures. All experiments are performed on a single NVIDIA RTX 3090 GPU." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.886 + ], + "angle": 0, + "content": "Compared Methods. To show the effectiveness of our method, we make comparisons with PReNet [27], SPANet [32], DRDNet [7], RCDNet [31], SPDNet [37], MPRNet [40], GT-Rain [1], DRT [24], U-Net [26] and Uformer [34] (the Uformer-T variant) on both synthetic and real data. All methods are trained on synthetic data from scratch with publicly available codes provided by authors following their default settings. Among them, representative methods are selected for visual comparison." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Metrics. For quantitative evaluation, we adopt commonly" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.892, + 0.166 + ], + "angle": 0, + "content": "Table 1: Quantitative results of compared methods on synthetic data. All the models are trained on our collected data following the default setting by authors. Higher metric is better for PSNR and SSIM. #GMACs is calculated on \\(256 \\times 256\\) patch." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.17, + 0.88, + 0.375 + ], + "angle": 0, + "content": "
MethodPSNRSSIM#Params#GMACs
Input27.100.8237//
PReLU [27]34.770.96220.17M66.4G
SPANet [32]31.100.92450.28M36.3G
DRDNet [7]32.200.92145.23M689.8G
RCDNet [31]34.170.94933.16M195.1G
SPDNet [37]33.900.93843.32M96.6G
MPRNet [40]36.630.96613.63M548.7G
GT-Rain [1]34.100.95722.29M29.6G
DRT [24]33.810.93811.18M165.4G
U-Net [26]36.630.96936.06M45.3G
Uformer [34]37.450.97205.20M10.7G
Ours (U-Net)37.280.97166.33M117.8G
Ours (Uformer)38.440.97495.52M63.4G
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.892, + 0.413 + ], + "angle": 0, + "content": "used PSNR and SSIM [33] for comparison using the Y channel (in YCbCr color space) following [16]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.422, + 0.836, + 0.439 + ], + "angle": 0, + "content": "4.2. Quantitative Results on Synthetic Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.612 + ], + "angle": 0, + "content": "As shown in Table 1, the performance of both SPANet [32] and DRDNet [7] is inferior to that of other competitors, even though there exists large difference between their model size and computational cost. While PReNet [27], RCDNet [31], SPDNet [37], GT-Rain [1] and DRT [24] perform better than the former two methods and their performance is comparable to others. Among all compared methods, MPRNet [40] and Uformer [34], as representative CNN-based and Transformer-based image restoration models, show superior performance to other competitors, which well validates their model capacity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.748 + ], + "angle": 0, + "content": "However, with the help of our proposed RLP and RPIM, the performance of both CNN-based and Transformer-based models can be boosted by a large margin. For CNN-based model U-Net [26], our method can get an increase of 0.65dB on PSNR and surpasses MPRNet [40] by 0.65dB. For the Transformer-based model Uformer [34], a large gain of 0.99dB on PSNR can be obtained and our proposed method outperforms all compared methods. These results can well validate the effectiveness of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.757, + 0.825, + 0.773 + ], + "angle": 0, + "content": "4.3. Qualitative Results on Synthetic Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As shown in Figure 4, SPANet [32] and DRDNet [7] can only remove a few rain streaks in night scenes and large amounts of rain streaks remain, which corresponds to inferior performance in quantitative results. While PReNet [27], RCDNet [31] and SPDNet [37] can remove more rain streaks than the former two competitors but there are still some rain streaks left there. MPRNet [40], U-Net [26] and Uformer [34] perform much better than these methods but" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13152" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.089, + 0.218, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.178, + 0.171, + 0.19 + ], + "angle": 0, + "content": "Rainy" + }, + { + "type": "image", + "bbox": [ + 0.219, + 0.089, + 0.351, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.246, + 0.177, + 0.322, + 0.19 + ], + "angle": 0, + "content": "PRENet [27]" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.089, + 0.483, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.378, + 0.177, + 0.456, + 0.19 + ], + "angle": 0, + "content": "SPANet [32]" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.089, + 0.616, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.177, + 0.587, + 0.19 + ], + "angle": 0, + "content": "DRDNet [7]" + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.089, + 0.748, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.177, + 0.723, + 0.19 + ], + "angle": 0, + "content": "RCDNet [31]" + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.089, + 0.882, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.177, + 0.854, + 0.19 + ], + "angle": 0, + "content": "SPDNet [37]" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.19, + 0.217, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.279, + 0.193, + 0.291 + ], + "angle": 0, + "content": "MPRNet [40]" + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.19, + 0.351, + 0.276 + ], + "angle": 0, + "content": null + 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}, + { + "type": "image", + "bbox": [ + 0.351, + 0.397, + 0.483, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.377, + 0.485, + 0.458, + 0.498 + ], + "angle": 0, + "content": "Uformer [34]" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.397, + 0.616, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.509, + 0.485, + 0.59, + 0.498 + ], + "angle": 0, + "content": "Ours (U-Net)" + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.397, + 0.748, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.485, + 0.73, + 0.498 + ], + "angle": 0, + "content": "Ours (Uformer)" + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.397, + 0.882, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.804, + 0.485, + 0.826, + 0.497 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.504, + 0.894, + 0.581 + ], + "angle": 0, + "content": "Figure 4: Qualitative results on synthetic data (gamma correction is applied for better visualization). SPANet and DRDNet can only remove a few rain streaks while PReNet, RCDNet and SPDNet behave better than the former two methods. MPRNet, U-Net and Uformer outperform other competitors but our proposed prior can boost the performance of U-Net and Uformer even further, in terms of removing more rain streaks (Uformer for the first scene) and preserving background details (Uformer for the second scene). These results demonstrate the effectiveness of our proposed method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.469, + 0.626 + ], + "angle": 0, + "content": "also face challenges for different scenes. Among all compared methods, Ours (Uformer) can get the best results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.901 + ], + "angle": 0, + "content": "In the first image, the illumination is dominated by the red neon cylinder and rain streaks look red. MPRNet [40] surprisingly fails the case and its result is similar to that of SPANet [32] and DRDNet [7]. For U-Net [26], Uformer [34] and Ours (U-Net), there are only a few rain streaks left on the image. However, Ours (Uformer) can fully remove the rain streaks, which demonstrates the effectiveness of our method. In the second image, bright windows consist of similar textures to rain streaks and the scene is relatively complex. We can find that almost all compared methods including Ours (U-Net) fail to preserve the texture of streetlight and it even totally disappears in some results. DRDNet [7] and SPDNet [37] keep the streetlight unchanged but there are some rain streaks left. Only Ours (Uformer) remove most rain streaks and preserve the texture of streetlight at the same time. We can infer that deraining models tend to recognize long thin textures with high pixel intensity as rain streaks in night scenes because rain streaks near" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.892, + 0.657 + ], + "angle": 0, + "content": "light sources have higher pixel values. In such cases, location priors of rain streaks become more crucial for deraining models to accurately handle rain streaks in night scenes, which further confirms the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.666, + 0.892, + 0.684 + ], + "angle": 0, + "content": "4.4. Qualitative Results on Real Night Rainy Images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Here, we present the qualitative results on real data in Figure 5. Due to the domain gap between synthetic and real data, models trained with GTAV-NightRain still behave poorly in real night scenes [42]. To further handle real night rainy images, we additionally add JPEG compression as a data augmentation in our training. Compared methods can partially remove rain streaks in real night rainy images but behave inconsistently for different rainy images. We can see that DRDNet [7], RCDNet [31] and SPDNet [37] perform better than PReNet [27], SPANet [32] and MPRNet [40] for the first image while U-Net [26] and Uformer [34] get better results. But they all fail to remove rain streaks in the second image. However, our method succeeds in handling both images. It can remove most rain streaks while keep" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13153" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.088, + 0.248, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.185, + 0.184, + 0.196 + ], + "angle": 0, + "content": "Real" + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.089, + 0.405, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.288, + 0.185, + 0.365, + 0.197 + ], + "angle": 0, + "content": "PRENet [27]" + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.089, + 0.562, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.445, + 0.185, + 0.522, + 0.197 + ], + "angle": 0, + "content": "SPANet [32]" + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.089, + 0.718, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.604, + 0.185, + 0.678, + 0.198 + ], + "angle": 0, + "content": "DRDNet [7]" + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.089, + 0.876, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.185, + 0.838, + 0.198 + ], + "angle": 0, + "content": "RCDNet [31]" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.198, + 0.248, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.294, + 0.21, + 0.307 + ], + "angle": 0, + "content": "SPDNet [37]" + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.198, + 0.405, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.294, + 0.367, + 0.307 + ], + "angle": 0, + "content": "MPRNet [40]" + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.198, + 0.562, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + 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"angle": 0, + "content": "PRENet [27]" + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.31, + 0.562, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.445, + 0.401, + 0.522, + 0.413 + ], + "angle": 0, + "content": "SPANet [32]" + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.31, + 0.718, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.604, + 0.401, + 0.678, + 0.413 + ], + "angle": 0, + "content": "DRDNet [7]" + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.31, + 0.876, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.401, + 0.838, + 0.413 + ], + "angle": 0, + "content": "RCDNet [31]" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.413, + 0.248, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.503, + 0.21, + 0.516 + ], + "angle": 0, + "content": "SPDNet [37]" + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.413, + 0.405, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.503, + 0.367, + 0.516 + ], + "angle": 0, + "content": "MPRNet [40]" + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.413, + 0.562, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.45, + 0.503, + 0.517, + 0.516 + ], + "angle": 0, + "content": "U-Net [26]" + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.413, + 0.718, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.6, + 0.503, + 0.681, + 0.516 + ], + "angle": 0, + "content": "Uformer [34]" + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.413, + 0.876, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.503, + 0.813, + 0.515 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.521, + 0.885, + 0.537 + ], + "angle": 0, + "content": "Figure 5: Qualitative results on real night rainy images. Our method gets the best visual results. Please zoom in for details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.583 + ], + "angle": 0, + "content": "ing backgrounds tidy, showing the effectiveness of our proposed method for removing rain streaks in real night scenes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.59, + 0.32, + 0.606 + ], + "angle": 0, + "content": "4.5. Qualitative Results of RLP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.469, + 0.749 + ], + "angle": 0, + "content": "To further illustrate the effectiveness of our Rain Location Prior, we provide visualizations on both synthetic and real night rainy images in Figure 6. Our RLP module can learn to recognize rain streaks and emphasize these areas with higher weights. Notably, RLP can learn by itself to suppress areas of light sources, i.e., these areas are much darker than neighboring areas of rain streaks. We can also notice that rain streaks in the sky can also be recognized even though they are not obvious in the rainy image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.84 + ], + "angle": 0, + "content": "As shown in the right half of Figure 6, our RLP module can also generalize well to real night rainy images with only synthetic data for training. Same to the synthetic case, light sources are suppressed in RLP and those areas are darker than areas of rain streaks. These results all show the effectiveness of RLP, which is beneficial for nighttime deraining." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.241, + 0.862 + ], + "angle": 0, + "content": "4.6. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In this section, we study the effect of each component of our method, including Rain Location Prior (RLP) and" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.551, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Table 2: Ablation study on individual components of our proposed method & different model structures and sizes." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.582, + 0.898, + 0.816 + ], + "angle": 0, + "content": "
DMRLPRPIMPSNRΔSSIMΔ
PReLUNetXX34.77-0.9622-
✓X35.00+0.230.9649+0.0027
✓✓34.31-0.460.9621-0.0001
MPRNetXX35.21-0.9627-
✓X35.42+0.210.9641+0.0014
✓✓35.67+0.460.9633+0.0006
U-NetXX36.63-0.9693-
✓X37.08+0.450.9715+0.0022
✓✓37.28+0.650.9716+0.0023
Uformer-TXX37.45-0.9720-
✓X37.95+0.500.9733+0.0013
✓✓38.44+0.990.9749+0.0029
Uformer-BXX39.41-0.9763-
✓X39.65+0.240.9770+0.0007
✓✓39.77+0.360.9773+0.0010
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.893, + 0.9 + ], + "angle": 0, + "content": "Rain Prior Injection Module (RPIM). We choose U-Net [26] and Uformer [34] out of CNN-based and Transformer-based models as the deraining module in our method, with U-shaped Encoder-Decoder architecture. Besides, we examine the effects of RLP on PReNet [27] and MPRNet" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13154" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.891, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.193, + 0.885, + 0.228 + ], + "angle": 0, + "content": "Figure 6: Visualizations of Rain Location Prior (RLP) on synthetic and real night rainy images. Please zoom in for details. Table 3: Generalization to daytime datasets. Models are trained on Rain13k dataset [16] and evaluated on five test sets." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.233, + 0.885, + 0.376 + ], + "angle": 0, + "content": "
DMRLPRPIMTest100 [44]Rain100H [36]Rain100L [36]Test2800 [8]Test1200 [43]Avg.
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Input22.550.686313.550.378426.900.838324.350.782923.630.732422.200.6837
U-NetXX24.910.858424.210.826730.520.925631.310.919931.010.902628.390.8866
U-Net✓X25.040.855026.820.846730.560.918531.320.917630.710.891728.890.8859
U-Net✓✓25.320.866526.060.838031.200.932431.320.920331.590.908929.100.8932
UformerXX28.010.878028.210.851632.160.934432.430.928731.660.907830.500.9001
Uformer✓X28.080.877528.370.854532.590.938532.490.928731.860.909330.680.9017
Uformer✓✓28.500.882128.340.857632.670.939032.550.929531.670.904230.740.9025
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.448 + ], + "angle": 0, + "content": "[40] with other architecture designs. Finally, we apply our method to the Uformer-B variant to investigate RLP's effect on model with more parameters. Experiments are carried out on the same test set and results are listed in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.588 + ], + "angle": 0, + "content": "RLP. With the prior map learned by the RLP module, directly feeding it into the deraining module brings an increase of 0.23dB, 0.21dB, 0.45dB, 0.50dB and 0.24dB in PSNR for five different deraining modules. It shows the effectiveness of the proposed RLP which can reveal location information of rain streaks and improve the deraining performance. The benefit of accurate location is straightforward and it is also effective for PReNet and MPRNet with other model structures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.731 + ], + "angle": 0, + "content": "RPIM. In night scenes where location information plays a vital role in deraining, emphasizing the importance of RLP in rain streak areas is beneficial. As shown in Table 2, the performance of deraining modules can be further boosted with the help of RPIM. MPRNet [40], U-Net [26] and Uformer-T/-B [34] can get an additional increase of \\(0.25\\mathrm{dB}\\), \\(0.20\\mathrm{dB}\\) and \\(0.49\\mathrm{dB}/0.12\\mathrm{dB}\\) in PSNR. While PReNet [27] gets worse results and the repeated feature injections in its recurrent structure may leads to the performance drop." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Model Structure and Capability. With different models compared, we can find that (i) recurrent structure may suffer from repeated feature injection (e.g., PReNet); (ii) models with vanilla Encoder-Decoder structure may benefit more from RLP (e.g., U-Net v.s. MPRNet); (iii) moderate models with better capability may benefit more from RLP (Uformer v.s. U-Net); (iv) moderate models may prefer additional knowledge from RLP than big models (e.g., Uformer-B v.s. Uformer-T). The comparisons demonstrate the effectiveness of our proposed RLP and RPIM and further provide insights on further improvement." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.386, + 0.809, + 0.403 + ], + "angle": 0, + "content": "4.7. Generalization to Daytime Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Despite our goal of nighttime deraining, we also conduct experiments on Rain13k [16] and GT-Rain [1] to demonstrate the generalization of our method on day scenes. As listed in Table 3, our method is also beneficial for CNN-based and Transformer-based models on daytime deraining. Additionally, we can find that the improvement is smaller than that on the nighttime dataset, which suggests the greater importance of location information for nighttime deraining. We also test our method on the GT-Rain dataset [1] and results are provided in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.586, + 0.619, + 0.603 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Nighttime rain removal is a challenging task due to complex illumination conditions. In night scenes, the location information of rain streaks becomes more critical for rain removal. In this paper, we propose the Rain Location Prior (RLP), which can be learned implicitly from rainy images using a recurrent residual model to reveal the location information of rain streaks. To further improve the deraining performance, we propose the Rain Prior Injection Module (RPIM) to modulate the learned RLP with the attention mechanism and emphasize the features within rain streak areas. Together, they help deraining modules focus more on recovering clean background rather than recognizing complex rain streaks. Despite the original goal of nighttime deraining, our method also works in day scenes. Experimental results show the effectiveness and generalization of our method on both synthetic data and real nighttime rainy images, which may be helpful for future research on nighttime deraining. We plan to explore more architectures for learning and extending RLP in the future." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13155" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.182 + ], + "angle": 0, + "content": "Acknowledgments This work was supported by the National Natural Science Foundation of China (62171038, 62088101, 61931008, and 62006101), the R&D Program of Beijing Municipal Education Commission (KZ202211417048), and the Fundamental Research Funds for the Central Universities." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.197, + 0.175, + 0.213 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.223, + 0.47, + 0.293 + ], + "angle": 0, + "content": "[1] Yunhao Ba, Howard Zhang, Ethan Yang, Akira Suzuki, Arnold Pfahnl, Chethan Chinder Chandrappa, Celso M de Melo, Suya You, Stefano Soatto, Alex Wong, et al. 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Despite recent progress in learning-based deraining methods, there is a lack of focus on nighttime deraining due to the unique challenges posed by non-uniform local illuminations from artificial light sources. Rain streaks in these scenes have diverse appearances that are tightly related to their relative positions to light sources, making it difficult for existing deraining methods to effectively handle them. In this paper, we highlight the importance of rain streak location information in nighttime deraining. Specifically, we propose a Rain Location Prior (RLP) that is learned implicitly from rainy images using a recurrent residual model. This learned prior contains location information of rain streaks and, when injected into deraining models, can significantly improve their performance. To further improve the effectiveness of the learned prior, we also propose a Rain Prior Injection Module (RPIM) to modulate the prior before injection, increasing the importance of features within rain streak areas. Experimental results demonstrate that our approach outperforms existing state-of-the-art methods by about 1dB and effectively improves the performance of deraining models. We also evaluate our method on real night rainy images to show the capability to handle real scenes with fully synthetic data for training. Our method represents a significant step forward in the area of nighttime deraining and highlights the importance of location information in this challenging problem. The code is publicly available at https://github.com/zkawfanx/RLP. + +# 1. Introduction + +While rain degrades image quality and visibility, it can be particularly problematic at night, because the low light condition and complex illuminations make it more difficult to distinguish rain streaks from other image features. This + +![](images/94d70391ef37384812547ed097a35e1d2e7d611d93f51cc8219befba276ba559.jpg) + +![](images/3a02dc2d32aca75275f320dc4fa73691a25833519370d15ecff607cb40b5ffc2.jpg) + +![](images/f55e122108e7f3b0a369d0f6294ce37f6eae688e23ca9d87b8a48aecc98a86db.jpg) +(a) Rainy +(c) RLP +Figure 1: (a) In night scenes, appearances of rain are highly dependent on locations relative to light sources. (b) Derain result of state-of-the-art method Uformer [34]. (c) Visualization of the proposed Rain Location Prior (RLP), which indicates the location of rain streaks and suppresses areas of light sources. (d) Derain result of our method. + +![](images/4b8330a81762e5ae9ff7ca42d5482caa2b07446194e91d988d29c6015391226a.jpg) +(b) Uformer +(d) Ours + +not only hinders the performance of high-level vision algorithms, e.g., object detection [13, 29] and tracking [2, 35], but also poses a safety risk for autonomous vehicles [6, 28] and other applications that rely on accurate visual information. Therefore, there is an increasing need for developing nighttime deraining methods. + +Unfortunately, despite recent advances in deep learning [34, 39, 40], which have significantly improved the performance, current endeavors predominantly focus on daytime scenarios, leaving the realm of nighttime deraining still largely unexplored. The most frequently utilized datasets [16, 32] scarcely encompass night scenes, neither does the synthesizing procedure consider interactions between rain and light sources. This hinders the direct application of existing methods to nighttime deraining. Recently, some datasets [20, 42] have started to cover previously ignored night scenes, which may enable careful study on nighttime deraining. Since there is no prior method specifically targeting nighttime deraining, we attempt to handle real night rainy scenes with the help of the recently developed dataset. + +Night scenes differ from day scenes in that there is no uniform global illumination; instead, darkness and nonuniform local illuminations dominate [12, 22, 25, 41, 45]. It results in the totally different appearance of night rain, which varies drastically at different spatial locations (i.e. + +only rain streaks near light sources are more discernible, as shown in Figure 2). Intuitively, it could facilitate the removal of rain streaks if precise locations were obtained in advance, which is often impractical in real scenes. Likewise, it is a common practice [14, 26] to train deep models to predict the locations of raindrop (i.e. raindrop mask) in the raindrop removal community. Therefore, identifying the rain location becomes more crucial than in day scenes. + +In this paper, we propose a novel deraining method targeting night scenes. Firstly, we highlight the importance of location information of rain streaks for nighttime deraining, as the appearance of rain streaks is highly varying at different spatial locations at night. Thus, we propose a Rain Location Prior (RLP) which can be implicitly learned by recurrent residual models. It can reveal the location information of rain streaks in night scenes and be incorporated into deraining methods to improve their performance, including CNN-based and Transformer-based ones. Secondly, we propose a Rain Prior Injection Module (RPIM) to increase the importance of features within rain streak areas indicated by RLP. Deraining models can focus more on recovering lost information within rain streak areas and get a further increase in performance. Finally, we perform comprehensive experiments to demonstrate the effectiveness of our method. Our method outperforms existing state-of-the-art methods quantitatively and qualitatively on synthetic data. Furthermore, we demonstrate the capability of our method in handling real scenes. We also conduct ablation studies to evaluate the effectiveness of each component in our method. To summarize, the contributions of our paper are as follows: + +- We propose a nighttime deraining method, which highlights the importance of location information of rain streaks for night scenes. +- We propose Rain Location Prior (RLP) and Rain Prior Injection Module (RPIM), which are the keys to revealing location information and boosting the performance of nighttime deraining. +- We demonstrate the state-of-the-art performance of our method on both synthetic and real night rainy scenes from rigorous experiments and ablation studies. + +# 2. Related Work + +In this section, we briefly review some existing deraining methods and image restoration backbones as well as existing deraining datasets. + +Deraining methods. Recurrent and residual learning are common practices for deraining models. Yang et al. [36] proposed a multi-task network to jointly perform rain detection, estimation and removal in a recurrent manner. Fu et al. [8] proposed to predict the residue of rain streaks with + +![](images/a9b1dc81ed6d4e32ccd53cd22217e5bc5493e8fa4bfafc3fb20575801c612dd4.jpg) +(a) + +![](images/01c4da1396a09fee5ee650bb95d1207109c9dc39bd7c1b965077f78fd63cb9d3.jpg) +(b) + +![](images/100a1c1ddf573965d73822c0e10a20dfb4d1c43b08ec1cf7353ff1966dea92ce.jpg) +(c) +Figure 2: Comparisons between synthetic and real rainy images. Synthetic images from (a) Rain100H [36], (b) GTAV-NightRain [42] and (c) real image from the Internet. + +high-frequency details as input. Li et al. [21] proposed Recurrent Squeeze-and-Excitation Context Aggregation Net (RESCAN) which is a recurrent network feeding output of the previous stage to the next one. Ren et al. [27] proposed PReNet with recurrent and residual design to balance performance and model complexity. Jiang et al. [16] proposed Multi-Scale Progressive Fusion Network (MSPFN) utilizing the multi-scale and recurrent strategy. Deng et al. [7] proposed to remove rain streaks and recover lost details with two parallel sub-networks. Yi et al. [37] proposed to protect structure information and guide network training with residue channel prior. Wang et al. [32] proposed SPatial Attentive Network (SPANet) which also utilizes residual blocks. Wang et al. [31] proposed Rain Convolutional Dictionary Network (RCDNet) to integrate the physical structure of residual rain streaks. Liang et al. [24] proposed a Deraining Recursive Transformer (DRT) with less parameters. In this work, we compare with some recent deraining models on night scenes. + +Image restoration backbones. Recently, powerful image restoration backbones [4, 5, 9] outperform previous methods on multiple tasks. Zamir et al. [40] proposed MPRNet making full use of encoder-decoder architecture and multistage strategies. They also proposed Restormer [39] to efficiently handle high-resolution images with the Transformer model. Wang et al. [34] also proposed a Transformer-based model following U-Net architecture and achieved promising performance on several tasks. While Tu et al. [30] proposed a multi-axis MLP-based architecture in a UNet-shaped hierarchical structure. Despite their robustness and capability, they fail to remove rain streaks in night scenes. + +Deraining datasets. Most deraining datasets are synthesized by superposing the rain layer onto clean images. Li et al. [23] synthesized 12 rainy images following Garg and Shree [10, 11]. Yang et al. [36] proposed the Rain100L and Rain100H datasets. Fu et al. [8] synthesized 14000 rainy images using Photoshop. Zhang et al. [44] proposed the Rain800 dataset following their practice. Zhang and Patel [43] proposed the Rain1200 dataset with different density labels. Li et al. [18] proposed the NYU-Rain dataset and Hu et al. [15] proposed the RainCityscapes dataset based on depth information. Li et al. [19] proposed the MPID + +![](images/320a3cadd63ec3a4fb4a41afe6515fa80769417a6cad8b12377563afd160e4b8.jpg) +Figure 3: Illustration on the framework of our method for nighttime deraining, which consists of three parts. The Rain Location Prior (RLP) is the prior that we propose to learn from rainy images with recurrent residual model implicitly and indicates the location information of rain streaks. To further emphasize features within rain streaks areas, we propose the second part, namely Rain Prior Injection Module (RPIM), to modulate the RLP with attention mechanism. The final part is the deraining module, which consumes the original rainy input and the learned RLP to get boosted deraining performance. + +dataset with different rain types as well as annotations for the detection task. Wang et al. [32] proposed the first real paired dataset, called SPA-data, using the semi-automatic method to generate clean images from rainy videos. Ba et al. [1] proposed GT-Rain dataset which contains real paired data. Recently, datasets turned their focus on night rainy scenes. Li et al. [20] proposed a real dataset with the ratio of night scenes to be around $50\%$ . Zhang et al. [42] proposed a synthetic night rain dataset, namely GTAV-NightRain, using the game engine for rendering. The emergence of these datasets enables careful study on nighttime deraining. + +# 3. Method + +In this section, we first introduce the motivation. Then we describe the Rain Location Prior (RLP) and the Rain Prior Injection Module (RPIM) in detail. The framework of our method is illustrated in Figure 3. + +# 3.1. Formulation and Motivation + +The appearance and photometry of rain have been extensively studied for decades [10, 11]. However, most existing synthetic datasets [8, 23, 36, 43] adopt a simplified formulation of rain streaks, where the rainy image $I$ is modeled as the sum of a rain streak layer $R$ and a clean image $B$ : + +$$ +I = R + B. \tag {1} +$$ + +A common strategy for rain removal is to model rain streaks with specific properties like direction, scale and space distribution and separate the rain layer from the background. This is usually achieved [8, 16, 21, 31, 36] by estimating the + +rain layer as an intermediate output before the final module and subtract it to restore the clean image. + +However, the importance of location information embedded in the rain layer has been underestimated. As discussed in Section 1, since rain location is beneficial for rain removal and night rain appearance varies with spatial locations, obtaining the rain layer in advance is more necessary than in day scenes. Moreover, discriminating the rain layer from the night scene is more difficult due to the coupling of rain appearance and light sources, thus aforementioned practice (i.e., estimating the rain layer and subtracting it to get the final output using the same model) is inefficient. + +In this work, therefore, we propose a novel framework for nighttime deraining, encompassing a model specializing the rain layer estimation, and a module that takes full advantage of the information of rain location. Specifically, we decouple the rain layer estimation and clean background reconstruction by introducing the Rain Location Prior (RLP) and Rain Prior Injection Module (RPIM). We learn to mine the information of rain location from nighttime rainy image and restore the clean scene respectively in an end-to-end manner. We further emphasize the features within rain regions by modulating them before rain revoal and background reconstruction. In this way, useful information of rain location can be better extracted and exploited, boosting the performance of nighttime deraining. + +# 3.2. Rain Location Prior (RLP) + +As mentioned above, the rain layer is commonly assumed to be superposed onto the background, which facilitates the design ideas of progressive and residual learning for many deraining models [8, 16, 27, 32, 37]. These mod + +els typically regard the rain layer as a residual component to the clean image, and some of them learn to progressively model these high-frequency patterns with recurrent structures. These designs, in turn, can reveal location information of rain streaks in night scenes, where the appearance of rain highly depends on its spatial location. For deraining, it would be beneficial if accurate rain locations were provided in advance, which is impractical in real scenes. Therefore, we propose to use recurrent residual architecture to mine the prior knowledge of rain location before removing rain streaks. It can provide the location information to deraining models, thereby further boosting their performance, which highlights its importance for nighttime deraining. + +In our proposed formulation, we introduce a module to learn and capture the prior knowledge of rain location, namely Rain Location Prior (RLP), before removing rain streaks. This module is composed of several residual blocks, which are effective in modeling rain streaks as a residual component. Meanwhile, it learns to progressively capture the rain through a recurrent design that utilizes the high-frequency characteristics of rain. When fed with the rainy input and an initial prior map, the module learns to extract deep features and recurrently update the prior map. The process of RLP can be formulated as follows: + +$$ +\bar {R} _ {k} = \mathcal {F} _ {R L P} (I \odot \bar {R} _ {k - 1}; \theta), \quad k = 1, \dots , N, \tag {2} +$$ + +where $I$ denotes the input and $\bar{R}_k$ is the RLP output at the $k$ -th stage. $\bar{R}_0$ is the initial map and all values are set to 0.5. $\mathcal{F}_{RLP}(\circ ;\theta)$ refers to the RLP module and $\theta$ is its parameters. $\odot$ denotes the channel-wise concatenation. $N$ denotes the total number of recurrent stages, which is empirically set to 6 and 4 for CNN-based and Transformer-based models, respectively. Concretely, PReNet [27] is a lightweight deraining network with the residual and recurrent design for a balance between complexity and performance. Its simplicity in design tightly fits the role of the RLP module and is adopted in our experiment. + +Note that we do not impose additional constraints on the RLP output, because we found that supervision signals from rain streak masks obtained by thresholding following the practice in raindrop removal [14, 26, 38] do not improve the performance. For simplicity, we do not apply regularization terms to the RLP output during training and encourage the module to learn it implicitly from training data. Corresponding experimental results are provided in the supplementary material. + +# 3.3. Rain Prior Injection Module (RPIM) + +In night scenes, the appearance of rain heavily depends on its spatial position relative to light sources. Therefore, deraining models should treat different areas with varying levels of importance. With the RLP indicating location in + +formation of rain streaks, we further emphasize the importance of these areas with the attention mechanism [40]. + +Specifically, we propose the Rain Prior Injection Module (RPIM). It takes the deep features extracted by the RLP module and further updates the prior map in a residual manner. The updated prior map is then used to generate the attention weights that increase the importance of rain streak areas and suppress other irrelevant areas. Finally, the features within rain streak areas are emphasized by the weights by element-wise multiplication of deep features and the attention weights. The RPIM can be described as follows: + +$$ +\bar {R}, z = \mathcal {M} _ {R P I M} (\bar {R} _ {N}, f; \sigma), \tag {3} +$$ + +where $\bar{R}_N$ and $f$ are the final prior map and deep features extracted by residual blocks in the RLP module. $\mathcal{M}_{RPIM}(\circ ;\sigma)$ denotes our Rain Prior Injection Module. $\bar{R}$ and $z$ are the modulated output and feature tensor ready for injection into the deraining network, respectively. + +# 3.4. Deraining Module (DM) + +For pixel-wise image restoration tasks, U-shaped architectures with skip connections are commonly adopted as they have shown good capability in capturing contextual information without losing much spatial information [30, 34, 40]. CNN-based and Transformer-based models with such architecture are two main streams and many methods make further improvements based on them. + +In Encoder-Decoder models, the input is typically projected into a feature space through a convolution layer, which is suitable for prior injection. After obtaining RLP and modulating the prior, we inject it into deraining models to further enhance deraining performance. We feed the rainy input and the RLP into the deraining module, which is a U-shaped model (either CNN-based or Transformer-based) for rain streak removal and background restoration. The process of this stage can be formulated as follows: + +$$ +\bar {I} = \mathcal {F} _ {D M} (I \odot \bar {R}, z; \Theta), \tag {4} +$$ + +where $\bar{I}$ is the restored image by deraining module, $\bar{R}$ is the updated RLP and $\odot$ denotes the channel-wise concatenation. $\mathcal{F}_{DM}(\circ ;\Theta)$ represents the deraining model, which focuses on the contextual information of neighboring pixels, and $\Theta$ is its parameters to be optimized. $z$ refers to the modulated prior by RPIM and is injected into the deraining module by channel-wise concatenation with the projected feature after the first convolution layer. + +For the training of the whole model, we apply the Charbonnier loss [3] on the final output: + +$$ +\mathcal {L} = \sqrt {\left\| \bar {I} - Y \right\| ^ {2} + \varepsilon^ {2}}, \tag {5} +$$ + +where $\bar{I}$ is the final output of the deraining model, $Y$ denotes the clean ground truth and $\varepsilon = 10^{-3}$ is a constant. + +# 4. Experiments + +In this section, we first introduce the experimental setups. Then we provide quantitative and qualitative results on synthetic data and evaluations on real night rainy images, to show the superior performance of our method compared to existing deraining methods, under the nighttime deraining setting. Moreover, we conduct ablation studies to validate the effectiveness of the proposed modules. Finally, we conduct experiments to show the generalization of our method on daytime datasets. Due to limited space, we provide more visual results in the supplementary material. + +# 4.1. Experimental Setups + +Datasets. Rain streaks in GTAV-NightRain dataset [42] are sparse with low difficulty, which is unfavorable for observing the difference since all methods behaves well. Thus we follow the instructions to render more difficult data (27dB v.s. 32dB in [42]) for experiments, by increasing the scale and density of rain streaks. We turn on and off the rain effect while keeping other settings unchanged for the same scene to render the rainy and clean image pairs. Please refer to [42] for more details on data collection. We collect 10 rainy images and 1 clean image for each scene and cover non-overlapping scenes for training and test sets. Finally, we get a total of 5,000 pairs of training data and 500 pairs of test data. Our collected data will be released with the code. Additionally, we conduct experiments on Rain13k [16, 40] and GT-Rain [1] datasets, to further show the generalization of our method to daytime data. We train our model with different modules on Rain13k and evaluate on its test sets, which are Test100 [44], Rain100H [36], Rain100L [36], Test2800 [8], Test1200 [43]. We also train our method on GT-Rain and compare it with other methods on its test set. + +Implementation Details. Our method is implemented in PyTorch and trained with Adam optimizer [17] with default parameters. The initial learning rate is set to $2 \times 10^{-4}$ and finally decreases to $1 \times 10^{-6}$ following a cosine scheduler. The model is trained for 250 epochs with a batch size of 8 on $256 \times 256$ patches. Training is performed on a single NVIDIA RTX 3090 GPU. We adopt U-Net and Uformer (the Uformer-T variant) for CNN-based and Transformer-based architectures. All experiments are performed on a single NVIDIA RTX 3090 GPU. + +Compared Methods. To show the effectiveness of our method, we make comparisons with PReNet [27], SPANet [32], DRDNet [7], RCDNet [31], SPDNet [37], MPRNet [40], GT-Rain [1], DRT [24], U-Net [26] and Uformer [34] (the Uformer-T variant) on both synthetic and real data. All methods are trained on synthetic data from scratch with publicly available codes provided by authors following their default settings. Among them, representative methods are selected for visual comparison. + +Metrics. For quantitative evaluation, we adopt commonly + +Table 1: Quantitative results of compared methods on synthetic data. All the models are trained on our collected data following the default setting by authors. Higher metric is better for PSNR and SSIM. #GMACs is calculated on $256 \times 256$ patch. + +
MethodPSNRSSIM#Params#GMACs
Input27.100.8237//
PReLU [27]34.770.96220.17M66.4G
SPANet [32]31.100.92450.28M36.3G
DRDNet [7]32.200.92145.23M689.8G
RCDNet [31]34.170.94933.16M195.1G
SPDNet [37]33.900.93843.32M96.6G
MPRNet [40]36.630.96613.63M548.7G
GT-Rain [1]34.100.95722.29M29.6G
DRT [24]33.810.93811.18M165.4G
U-Net [26]36.630.96936.06M45.3G
Uformer [34]37.450.97205.20M10.7G
Ours (U-Net)37.280.97166.33M117.8G
Ours (Uformer)38.440.97495.52M63.4G
+ +used PSNR and SSIM [33] for comparison using the Y channel (in YCbCr color space) following [16]. + +# 4.2. Quantitative Results on Synthetic Data + +As shown in Table 1, the performance of both SPANet [32] and DRDNet [7] is inferior to that of other competitors, even though there exists large difference between their model size and computational cost. While PReNet [27], RCDNet [31], SPDNet [37], GT-Rain [1] and DRT [24] perform better than the former two methods and their performance is comparable to others. Among all compared methods, MPRNet [40] and Uformer [34], as representative CNN-based and Transformer-based image restoration models, show superior performance to other competitors, which well validates their model capacity. + +However, with the help of our proposed RLP and RPIM, the performance of both CNN-based and Transformer-based models can be boosted by a large margin. For CNN-based model U-Net [26], our method can get an increase of 0.65dB on PSNR and surpasses MPRNet [40] by 0.65dB. For the Transformer-based model Uformer [34], a large gain of 0.99dB on PSNR can be obtained and our proposed method outperforms all compared methods. These results can well validate the effectiveness of our proposed method. + +# 4.3. Qualitative Results on Synthetic Data + +As shown in Figure 4, SPANet [32] and DRDNet [7] can only remove a few rain streaks in night scenes and large amounts of rain streaks remain, which corresponds to inferior performance in quantitative results. While PReNet [27], RCDNet [31] and SPDNet [37] can remove more rain streaks than the former two competitors but there are still some rain streaks left there. MPRNet [40], U-Net [26] and Uformer [34] perform much better than these methods but + +![](images/5a1019b2d7742c22a4e89236138743cf478b2d4c4abf5d27905878e6c76e1fb9.jpg) + +![](images/915a727c6607416a2e9bbb003d07d0d417d8babe0bc3b58498c5bf9825a07482.jpg) + +![](images/ec905900dcc1d21b2cdfe823fa59d1b3a162add2d207cfdc1236ff7c91b117bf.jpg) + +![](images/b5069c271ada002f3b24244056ac72631f1fb65ec6ef692aae679e525b525048.jpg) + +![](images/dedd5c6f71dd6b3d99b83be9dc575ecb1ad5549895a1e4a01a0b531faad1d849.jpg) + +![](images/b07e0fba3dc59fddc05f30eb12f21c6c0f1b1a7034b285bc3621b906fe551429.jpg) + +![](images/e9bd5359034f1014a9e7be0144ba7fb38592b3a6bee202fed5a1cc2849f2a019.jpg) +Rainy +MPRNet [40] + +![](images/41f26308cc85ad93f5736e3347ca341f37aeb58905a38a49a8b2cef3171a8076.jpg) +PRENet [27] +U-Net [26] + +![](images/8015a90024f38b71cb2f3edc48d5845514113b5147ffbaa8417ffc4b602eabbe.jpg) +SPANet [32] +Uformer [34] + +![](images/40c3a9c6b01ab9d7979b855cae7fb0cbf42ba6faeef2bb50bacb46e595d4315f.jpg) +DRDNet [7] +Ours (U-Net) + +![](images/5e884d3e2f348e364a25bb91a833b6a69c1917d94014ce034ab82d3e4f8c23d9.jpg) +RCDNet [31] +Ours (Uformer) + +![](images/b161e3d276be8a9041acab8c58d5014d247116caa924b67478bab87aba6192e0.jpg) +SPDNet [37] +GT + +![](images/0be8b25da8041040f7372f0f78b2680bc8a79b3b49baebe401516d2642b20c2b.jpg) + +![](images/7c7fcb43b3cd9b12d52498dfad506fff7157ecca0f4bbe0febbb417d80ebc5e5.jpg) + +![](images/f974ac798b454dee352944b0707412ec95664ee5e05a8bda3bb36f23c764ad52.jpg) + +![](images/d024678764822b1c895a820bb59cb161b5b7243cc3f3db85c3398f9c0682be7c.jpg) + +![](images/dd2cbcfb8bd220aa8af7c29ca73d5d5bb92598e5b9a25ebf39c975fd2d251bcd.jpg) + +![](images/0848a6d6ceb004ef1395c579bd0a3c07433e6c0359642e84f1f8393431a48eaf.jpg) + +![](images/3e0efc5bbd1932f1a963b012f9cd392dd7676032830c404241d689f2de7bd787.jpg) +Real +MPRNet [40] +Figure 4: Qualitative results on synthetic data (gamma correction is applied for better visualization). SPANet and DRDNet can only remove a few rain streaks while PReNet, RCDNet and SPDNet behave better than the former two methods. MPRNet, U-Net and Uformer outperform other competitors but our proposed prior can boost the performance of U-Net and Uformer even further, in terms of removing more rain streaks (Uformer for the first scene) and preserving background details (Uformer for the second scene). These results demonstrate the effectiveness of our proposed method. + +![](images/6546322f291c95968c703eff0990c1af4fa1c54fa28ad6605bb244ed33d2df10.jpg) +PRENet [27] +U-Net [26] + +![](images/63f0cf6e3a84f08fd235e94849decc58947474703b50d07549edb2e5f895e402.jpg) +SPANet [32] +Uformer [34] + +![](images/93fa1329d7ea5b9d2f33378fbc67e572754f3a856b1d11e1863a90dbcb79bd86.jpg) +DRDNet [7] +Ours (U-Net) + +![](images/44c7271a611387e842ef8e9c19ea098cc6ca5018dd667c7c42ad2185cef25603.jpg) +RCDNet [31] +Ours (Uformer) + +![](images/ecf258402e645e17c4feb5dde9b95ece72afe5d263e693950e845b71604b1dce.jpg) +SPDNet [37] +GT + +also face challenges for different scenes. Among all compared methods, Ours (Uformer) can get the best results. + +In the first image, the illumination is dominated by the red neon cylinder and rain streaks look red. MPRNet [40] surprisingly fails the case and its result is similar to that of SPANet [32] and DRDNet [7]. For U-Net [26], Uformer [34] and Ours (U-Net), there are only a few rain streaks left on the image. However, Ours (Uformer) can fully remove the rain streaks, which demonstrates the effectiveness of our method. In the second image, bright windows consist of similar textures to rain streaks and the scene is relatively complex. We can find that almost all compared methods including Ours (U-Net) fail to preserve the texture of streetlight and it even totally disappears in some results. DRDNet [7] and SPDNet [37] keep the streetlight unchanged but there are some rain streaks left. Only Ours (Uformer) remove most rain streaks and preserve the texture of streetlight at the same time. We can infer that deraining models tend to recognize long thin textures with high pixel intensity as rain streaks in night scenes because rain streaks near + +light sources have higher pixel values. In such cases, location priors of rain streaks become more crucial for deraining models to accurately handle rain streaks in night scenes, which further confirms the effectiveness of our method. + +# 4.4. Qualitative Results on Real Night Rainy Images + +Here, we present the qualitative results on real data in Figure 5. Due to the domain gap between synthetic and real data, models trained with GTAV-NightRain still behave poorly in real night scenes [42]. To further handle real night rainy images, we additionally add JPEG compression as a data augmentation in our training. Compared methods can partially remove rain streaks in real night rainy images but behave inconsistently for different rainy images. We can see that DRDNet [7], RCDNet [31] and SPDNet [37] perform better than PReNet [27], SPANet [32] and MPRNet [40] for the first image while U-Net [26] and Uformer [34] get better results. But they all fail to remove rain streaks in the second image. However, our method succeeds in handling both images. It can remove most rain streaks while keep + +![](images/3596a03b805c053aa28d8551e9be738a2ca190d995caec1b4c208f7c9487b40b.jpg) +Real + +![](images/64811a296d4ca816b59de79693944a034988db428ccbe727fc583d8b88ff1c40.jpg) + +![](images/63c694766f785736171c44f4a92a552a02a7fcb55c3342ab3e20fde169b98eee.jpg) + +![](images/53f98c6c713c4057233fcc65f454d564c8459dc32e84e4a51d53917b3be7d070.jpg) + +![](images/8152160a6b3a2ce47d89c6cc386e5e3b76a6a6f622913f66c9baa6271b07d877.jpg) + +![](images/b62617b7b6e25830428a365cdea4135da65aba9cc62f97a60038225f706da600.jpg) + +![](images/89d28da5668b8474453e5120715ca3f00267f42ee9fc9c470fda9d59b1edd9ea.jpg) +PRENet [27] +MPRNet [40] + +![](images/0adbc5d05489c78d15c83151c36ac4b12bbe7753ca073b23efb4dbf0d71a9e00.jpg) +SPANet [32] +U-Net [26] + +![](images/1bbc9c588dac4317b50f39c5cbbb25fb67373eaf50e323bf323e969b4a586fed.jpg) +DRDNet [7] +Uformer [34] + +![](images/ed6c8d50847789697789eaea16c85ba636b8e65be33dc75f4fea24a545817928.jpg) +RCDNet [31] +Ours + +![](images/0064ee91e0610fcfab60665733c9b36cc55d96031690c795b49c1af4404ba218.jpg) +SPDNet [37] + +![](images/fc5e8096cb85f3d47aef6b019a987e84b6df173cab460e6d64fcff3bd6ade8b4.jpg) + +![](images/e088dfc554a4dcfbc46658d3b3e6b0615f944a25be59f9a9ed7d5da2f3c03f67.jpg) + +![](images/a5ae5fbae4dec4fdd6603c02b4020ff65a3958ac50831c0b2416fe5a09966ee6.jpg) + +![](images/2f4944129fac54f52ee9c530c86d9437c45a728c177f2516a8b913dd68869e3f.jpg) + +![](images/24cbd4bf9e34954e2e56506e8c9800dbf6d7f1be41b2f9b707677f8fcf397c2f.jpg) +Real +SPDNet [37] +Figure 5: Qualitative results on real night rainy images. Our method gets the best visual results. Please zoom in for details. + +![](images/ca9223672051ef0150b2f9eca311e2deaddc44dc18abe106f05114e5fd310918.jpg) +PRENet [27] +MPRNet [40] + +![](images/e7a56cb0e121fd9bee6af5de5b94193ba93854655457e5ff58eff8371f148393.jpg) +SPANet [32] +U-Net [26] + +![](images/052fba699fa7fc991cee60bb69fd0f8450bf85a6ba4d6313a94f75dcc717e2c9.jpg) +DRDNet [7] +Uformer [34] + +![](images/433a07b99dc80f1ae807e13fd05f02f7ff413932105b0f30d877a587b9e08429.jpg) +RCDNet [31] +Ours + +ing backgrounds tidy, showing the effectiveness of our proposed method for removing rain streaks in real night scenes. + +# 4.5. Qualitative Results of RLP + +To further illustrate the effectiveness of our Rain Location Prior, we provide visualizations on both synthetic and real night rainy images in Figure 6. Our RLP module can learn to recognize rain streaks and emphasize these areas with higher weights. Notably, RLP can learn by itself to suppress areas of light sources, i.e., these areas are much darker than neighboring areas of rain streaks. We can also notice that rain streaks in the sky can also be recognized even though they are not obvious in the rainy image. + +As shown in the right half of Figure 6, our RLP module can also generalize well to real night rainy images with only synthetic data for training. Same to the synthetic case, light sources are suppressed in RLP and those areas are darker than areas of rain streaks. These results all show the effectiveness of RLP, which is beneficial for nighttime deraining. + +# 4.6. Ablation Studies + +In this section, we study the effect of each component of our method, including Rain Location Prior (RLP) and + +Table 2: Ablation study on individual components of our proposed method & different model structures and sizes. + +
DMRLPRPIMPSNRΔSSIMΔ
PReLUNetXX34.77-0.9622-
✓X35.00+0.230.9649+0.0027
✓✓34.31-0.460.9621-0.0001
MPRNetXX35.21-0.9627-
✓X35.42+0.210.9641+0.0014
✓✓35.67+0.460.9633+0.0006
U-NetXX36.63-0.9693-
✓X37.08+0.450.9715+0.0022
✓✓37.28+0.650.9716+0.0023
Uformer-TXX37.45-0.9720-
✓X37.95+0.500.9733+0.0013
✓✓38.44+0.990.9749+0.0029
Uformer-BXX39.41-0.9763-
✓X39.65+0.240.9770+0.0007
✓✓39.77+0.360.9773+0.0010
+ +Rain Prior Injection Module (RPIM). We choose U-Net [26] and Uformer [34] out of CNN-based and Transformer-based models as the deraining module in our method, with U-shaped Encoder-Decoder architecture. Besides, we examine the effects of RLP on PReNet [27] and MPRNet + +![](images/fac82bba6842e9bca9587ef9e4905aa0aca4eb459e99c68200ac65d594fb5025.jpg) +Figure 6: Visualizations of Rain Location Prior (RLP) on synthetic and real night rainy images. Please zoom in for details. Table 3: Generalization to daytime datasets. Models are trained on Rain13k dataset [16] and evaluated on five test sets. + +
DMRLPRPIMTest100 [44]Rain100H [36]Rain100L [36]Test2800 [8]Test1200 [43]Avg.
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Input22.550.686313.550.378426.900.838324.350.782923.630.732422.200.6837
U-NetXX24.910.858424.210.826730.520.925631.310.919931.010.902628.390.8866
U-Net✓X25.040.855026.820.846730.560.918531.320.917630.710.891728.890.8859
U-Net✓✓25.320.866526.060.838031.200.932431.320.920331.590.908929.100.8932
UformerXX28.010.878028.210.851632.160.934432.430.928731.660.907830.500.9001
Uformer✓X28.080.877528.370.854532.590.938532.490.928731.860.909330.680.9017
Uformer✓✓28.500.882128.340.857632.670.939032.550.929531.670.904230.740.9025
+ +[40] with other architecture designs. Finally, we apply our method to the Uformer-B variant to investigate RLP's effect on model with more parameters. Experiments are carried out on the same test set and results are listed in Table 2. + +RLP. With the prior map learned by the RLP module, directly feeding it into the deraining module brings an increase of 0.23dB, 0.21dB, 0.45dB, 0.50dB and 0.24dB in PSNR for five different deraining modules. It shows the effectiveness of the proposed RLP which can reveal location information of rain streaks and improve the deraining performance. The benefit of accurate location is straightforward and it is also effective for PReNet and MPRNet with other model structures. + +RPIM. In night scenes where location information plays a vital role in deraining, emphasizing the importance of RLP in rain streak areas is beneficial. As shown in Table 2, the performance of deraining modules can be further boosted with the help of RPIM. MPRNet [40], U-Net [26] and Uformer-T/-B [34] can get an additional increase of $0.25\mathrm{dB}$ , $0.20\mathrm{dB}$ and $0.49\mathrm{dB}/0.12\mathrm{dB}$ in PSNR. While PReNet [27] gets worse results and the repeated feature injections in its recurrent structure may leads to the performance drop. + +Model Structure and Capability. With different models compared, we can find that (i) recurrent structure may suffer from repeated feature injection (e.g., PReNet); (ii) models with vanilla Encoder-Decoder structure may benefit more from RLP (e.g., U-Net v.s. MPRNet); (iii) moderate models with better capability may benefit more from RLP (Uformer v.s. U-Net); (iv) moderate models may prefer additional knowledge from RLP than big models (e.g., Uformer-B v.s. Uformer-T). The comparisons demonstrate the effectiveness of our proposed RLP and RPIM and further provide insights on further improvement. + +# 4.7. Generalization to Daytime Datasets + +Despite our goal of nighttime deraining, we also conduct experiments on Rain13k [16] and GT-Rain [1] to demonstrate the generalization of our method on day scenes. As listed in Table 3, our method is also beneficial for CNN-based and Transformer-based models on daytime deraining. Additionally, we can find that the improvement is smaller than that on the nighttime dataset, which suggests the greater importance of location information for nighttime deraining. We also test our method on the GT-Rain dataset [1] and results are provided in the supplementary material. + +# 5. Conclusion + +Nighttime rain removal is a challenging task due to complex illumination conditions. In night scenes, the location information of rain streaks becomes more critical for rain removal. In this paper, we propose the Rain Location Prior (RLP), which can be learned implicitly from rainy images using a recurrent residual model to reveal the location information of rain streaks. To further improve the deraining performance, we propose the Rain Prior Injection Module (RPIM) to modulate the learned RLP with the attention mechanism and emphasize the features within rain streak areas. Together, they help deraining modules focus more on recovering clean background rather than recognizing complex rain streaks. Despite the original goal of nighttime deraining, our method also works in day scenes. Experimental results show the effectiveness and generalization of our method on both synthetic data and real nighttime rainy images, which may be helpful for future research on nighttime deraining. We plan to explore more architectures for learning and extending RLP in the future. + +Acknowledgments This work was supported by the National Natural Science Foundation of China (62171038, 62088101, 61931008, and 62006101), the R&D Program of Beijing Municipal Education Commission (KZ202211417048), and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Yunhao Ba, Howard Zhang, Ethan Yang, Akira Suzuki, Arnold Pfahnl, Chethan Chinder Chandrappa, Celso M de Melo, Suya You, Stefano Soatto, Alex Wong, et al. Not just streaks: Towards ground truth for single image deraining. In ECCV, 2022. 3, 5, 8 +[2] Luca Bertinetto, Jack Valmadre, Joao F Henriques, Andrea Vedaldi, and Philip HS Torr. Fully-convolutional siamese networks for object tracking. In ECCVW, 2016. 1 +[3] Pierre Charbonnier, Laure Blanc-Feraud, Gilles Aubert, and Michel Barlaud. Two deterministic half-quadratic regularization algorithms for computed imaging. 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Despite recent progress in learning-based deraining methods, there is a lack of focus on nighttime deraining due to the unique challenges posed by non-uniform local illuminations from artificial light sources. Rain streaks in these scenes have diverse appearances that are tightly related to their relative positions to light sources, making it difficult for existing deraining methods to effectively handle them. In this paper, we highlight the importance of rain streak location information in nighttime deraining. Specifically, we propose a Rain Location Prior (RLP) that is learned implicitly from rainy images using a recurrent residual model. This learned prior contains location information of rain streaks and, when injected into deraining models, can significantly improve their performance. To further improve the effectiveness of the learned prior, we also propose a Rain Prior Injection Module (RPIM) to modulate the prior before injection, increasing the importance of features within rain streak areas. Experimental results demonstrate that our approach outperforms existing state-of-the-art methods by about 1dB and effectively improves the performance of deraining models. We also evaluate our method on real night rainy images to show the capability to handle real scenes with fully synthetic data for training. Our method represents a significant step forward in the area of nighttime deraining and highlights the importance of location information in this challenging problem. 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(b) Derain result of state-of-the-art method Uformer [34]. (c) Visualization of the proposed Rain Location Prior (RLP), which indicates the location of rain streaks and suppresses areas of light sources. (d) Derain result of our method." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 427, + 270, + 544, + 316 + ], + "blocks": [ + { + "bbox": [ + 462, + 260, + 507, + 270 + ], + "lines": [ + { + "bbox": [ + 462, + 260, + 507, + 270 + ], + "spans": [ + { + "bbox": [ + 462, + 260, + 507, + 270 + ], + "type": "text", + "content": "(b) Uformer" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 270, + 544, + 316 + ], + "lines": [ + { + "bbox": [ + 427, + 270, + 544, + 316 + ], + "spans": [ + { + "bbox": [ + 427, + 270, + 544, + 316 + ], + "type": "image", + "image_path": "4b8330a81762e5ae9ff7ca42d5482caa2b07446194e91d988d29c6015391226a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 469, + 318, + 501, + 328 + ], + "lines": [ + { + "bbox": [ + 469, + 318, + 501, + 328 + ], + "spans": [ + { + "bbox": [ + 469, + 318, + 501, + 328 + ], + "type": "text", + "content": "(d) Ours" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 414, + 546, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 546, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 546, + 486 + ], + "type": "text", + "content": "not only hinders the performance of high-level vision algorithms, e.g., object detection [13, 29] and tracking [2, 35], but also poses a safety risk for autonomous vehicles [6, 28] and other applications that rely on accurate visual information. Therefore, there is an increasing need for developing nighttime deraining methods." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 486, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 653 + ], + "type": "text", + "content": "Unfortunately, despite recent advances in deep learning [34, 39, 40], which have significantly improved the performance, current endeavors predominantly focus on daytime scenarios, leaving the realm of nighttime deraining still largely unexplored. The most frequently utilized datasets [16, 32] scarcely encompass night scenes, neither does the synthesizing procedure consider interactions between rain and light sources. This hinders the direct application of existing methods to nighttime deraining. Recently, some datasets [20, 42] have started to cover previously ignored night scenes, which may enable careful study on nighttime deraining. Since there is no prior method specifically targeting nighttime deraining, we attempt to handle real night rainy scenes with the help of the recently developed dataset." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 653, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 714 + ], + "type": "text", + "content": "Night scenes differ from day scenes in that there is no uniform global illumination; instead, darkness and nonuniform local illuminations dominate [12, 22, 25, 41, 45]. It results in the totally different appearance of night rain, which varies drastically at different spatial locations (i.e." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 198, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 198, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 198, + 712 + ], + "type": "text", + "content": "*Corresponding author: fuying@bit.edu.cn" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13148" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "only rain streaks near light sources are more discernible, as shown in Figure 2). Intuitively, it could facilitate the removal of rain streaks if precise locations were obtained in advance, which is often impractical in real scenes. Likewise, it is a common practice [14, 26] to train deep models to predict the locations of raindrop (i.e. raindrop mask) in the raindrop removal community. Therefore, identifying the rain location becomes more crucial than in day scenes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 431 + ], + "type": "text", + "content": "In this paper, we propose a novel deraining method targeting night scenes. Firstly, we highlight the importance of location information of rain streaks for nighttime deraining, as the appearance of rain streaks is highly varying at different spatial locations at night. Thus, we propose a Rain Location Prior (RLP) which can be implicitly learned by recurrent residual models. It can reveal the location information of rain streaks in night scenes and be incorporated into deraining methods to improve their performance, including CNN-based and Transformer-based ones. Secondly, we propose a Rain Prior Injection Module (RPIM) to increase the importance of features within rain streak areas indicated by RLP. Deraining models can focus more on recovering lost information within rain streak areas and get a further increase in performance. Finally, we perform comprehensive experiments to demonstrate the effectiveness of our method. Our method outperforms existing state-of-the-art methods quantitatively and qualitatively on synthetic data. Furthermore, we demonstrate the capability of our method in handling real scenes. We also conduct ablation studies to evaluate the effectiveness of each component in our method. To summarize, the contributions of our paper are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 440, + 288, + 574 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 59, + 440, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 440, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 59, + 440, + 287, + 475 + ], + "type": "text", + "content": "- We propose a nighttime deraining method, which highlights the importance of location information of rain streaks for night scenes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 483, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 483, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 59, + 483, + 287, + 532 + ], + "type": "text", + "content": "- We propose Rain Location Prior (RLP) and Rain Prior Injection Module (RPIM), which are the keys to revealing location information and boosting the performance of nighttime deraining." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 538, + 288, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 538, + 288, + 574 + ], + "spans": [ + { + "bbox": [ + 59, + 538, + 288, + 574 + ], + "type": "text", + "content": "- We demonstrate the state-of-the-art performance of our method on both synthetic and real night rainy scenes from rigorous experiments and ablation studies." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 583, + 134, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 583, + 134, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 583, + 134, + 596 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 604, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 287, + 640 + ], + "type": "text", + "content": "In this section, we briefly review some existing deraining methods and image restoration backbones as well as existing deraining datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": "Deraining methods. Recurrent and residual learning are common practices for deraining models. Yang et al. [36] proposed a multi-task network to jointly perform rain detection, estimation and removal in a recurrent manner. Fu et al. [8] proposed to predict the residue of rain streaks with" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 391, + 118 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 391, + 118 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 391, + 118 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 391, + 118 + ], + "type": "image", + "image_path": "a9b1dc81ed6d4e32ccd53cd22217e5bc5493e8fa4bfafc3fb20575801c612dd4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 346, + 121, + 358, + 130 + ], + "lines": [ + { + "bbox": [ + 346, + 121, + 358, + 130 + ], + "spans": [ + { + "bbox": [ + 346, + 121, + 358, + 130 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 391, + 72, + 464, + 117 + ], + "blocks": [ + { + "bbox": [ + 391, + 72, + 464, + 117 + ], + "lines": [ + { + "bbox": [ + 391, + 72, + 464, + 117 + ], + "spans": [ + { + "bbox": [ + 391, + 72, + 464, + 117 + ], + "type": "image", + "image_path": "01c4da1396a09fee5ee650bb95d1207109c9dc39bd7c1b965077f78fd63cb9d3.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 419, + 120, + 430, + 129 + ], + "lines": [ + { + "bbox": [ + 419, + 120, + 430, + 129 + ], + "spans": [ + { + "bbox": [ + 419, + 120, + 430, + 129 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 465, + 71, + 545, + 118 + ], + "blocks": [ + { + "bbox": [ + 465, + 71, + 545, + 118 + ], + "lines": [ + { + "bbox": [ + 465, + 71, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 465, + 71, + 545, + 118 + ], + "type": "image", + "image_path": "100a1c1ddf573965d73822c0e10a20dfb4d1c43b08ec1cf7353ff1966dea92ce.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 120, + 512, + 130 + ], + "lines": [ + { + "bbox": [ + 501, + 120, + 512, + 130 + ], + "spans": [ + { + "bbox": [ + 501, + 120, + 512, + 130 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 133, + 545, + 169 + ], + "lines": [ + { + "bbox": [ + 306, + 133, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 545, + 169 + ], + "type": "text", + "content": "Figure 2: Comparisons between synthetic and real rainy images. Synthetic images from (a) Rain100H [36], (b) GTAV-NightRain [42] and (c) real image from the Internet." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 182, + 547, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 410 + ], + "type": "text", + "content": "high-frequency details as input. Li et al. [21] proposed Recurrent Squeeze-and-Excitation Context Aggregation Net (RESCAN) which is a recurrent network feeding output of the previous stage to the next one. Ren et al. [27] proposed PReNet with recurrent and residual design to balance performance and model complexity. Jiang et al. [16] proposed Multi-Scale Progressive Fusion Network (MSPFN) utilizing the multi-scale and recurrent strategy. Deng et al. [7] proposed to remove rain streaks and recover lost details with two parallel sub-networks. Yi et al. [37] proposed to protect structure information and guide network training with residue channel prior. Wang et al. [32] proposed SPatial Attentive Network (SPANet) which also utilizes residual blocks. Wang et al. [31] proposed Rain Convolutional Dictionary Network (RCDNet) to integrate the physical structure of residual rain streaks. Liang et al. [24] proposed a Deraining Recursive Transformer (DRT) with less parameters. In this work, we compare with some recent deraining models on night scenes." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 424, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 547, + 568 + ], + "type": "text", + "content": "Image restoration backbones. Recently, powerful image restoration backbones [4, 5, 9] outperform previous methods on multiple tasks. Zamir et al. [40] proposed MPRNet making full use of encoder-decoder architecture and multistage strategies. They also proposed Restormer [39] to efficiently handle high-resolution images with the Transformer model. Wang et al. [34] also proposed a Transformer-based model following U-Net architecture and achieved promising performance on several tasks. While Tu et al. [30] proposed a multi-axis MLP-based architecture in a UNet-shaped hierarchical structure. Despite their robustness and capability, they fail to remove rain streaks in night scenes." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Deraining datasets. Most deraining datasets are synthesized by superposing the rain layer onto clean images. Li et al. [23] synthesized 12 rainy images following Garg and Shree [10, 11]. Yang et al. [36] proposed the Rain100L and Rain100H datasets. Fu et al. [8] synthesized 14000 rainy images using Photoshop. Zhang et al. [44] proposed the Rain800 dataset following their practice. Zhang and Patel [43] proposed the Rain1200 dataset with different density labels. Li et al. [18] proposed the NYU-Rain dataset and Hu et al. [15] proposed the RainCityscapes dataset based on depth information. Li et al. [19] proposed the MPID" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13149" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 542, + 255 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 542, + 255 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 542, + 255 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 542, + 255 + ], + "type": "image", + "image_path": "320a3cadd63ec3a4fb4a41afe6515fa80769417a6cad8b12377563afd160e4b8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 261, + 547, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 547, + 323 + ], + "type": "text", + "content": "Figure 3: Illustration on the framework of our method for nighttime deraining, which consists of three parts. The Rain Location Prior (RLP) is the prior that we propose to learn from rainy images with recurrent residual model implicitly and indicates the location information of rain streaks. To further emphasize features within rain streaks areas, we propose the second part, namely Rain Prior Injection Module (RPIM), to modulate the RLP with attention mechanism. The final part is the deraining module, which consumes the original rainy input and the learned RLP to get boosted deraining performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 328, + 289, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 289, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 289, + 461 + ], + "type": "text", + "content": "dataset with different rain types as well as annotations for the detection task. Wang et al. [32] proposed the first real paired dataset, called SPA-data, using the semi-automatic method to generate clean images from rainy videos. Ba et al. [1] proposed GT-Rain dataset which contains real paired data. Recently, datasets turned their focus on night rainy scenes. Li et al. [20] proposed a real dataset with the ratio of night scenes to be around " + }, + { + "bbox": [ + 46, + 328, + 289, + 461 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 328, + 289, + 461 + ], + "type": "text", + "content": ". Zhang et al. [42] proposed a synthetic night rain dataset, namely GTAV-NightRain, using the game engine for rendering. The emergence of these datasets enables careful study on nighttime deraining." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 473, + 105, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 473, + 105, + 485 + ], + "spans": [ + { + "bbox": [ + 47, + 473, + 105, + 485 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 494, + 288, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 288, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 288, + 543 + ], + "type": "text", + "content": "In this section, we first introduce the motivation. Then we describe the Rain Location Prior (RLP) and the Rain Prior Injection Module (RPIM) in detail. The framework of our method is illustrated in Figure 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 552, + 204, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 204, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 204, + 563 + ], + "type": "text", + "content": "3.1. Formulation and Motivation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "type": "text", + "content": "The appearance and photometry of rain have been extensively studied for decades [10, 11]. However, most existing synthetic datasets [8, 23, 36, 43] adopt a simplified formulation of rain streaks, where the rainy image " + }, + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "type": "text", + "content": " is modeled as the sum of a rain streak layer " + }, + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "type": "text", + "content": " and a clean image " + }, + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 571, + 287, + 632 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 140, + 642, + 287, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 642, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 140, + 642, + 287, + 654 + ], + "type": "interline_equation", + "content": "I = R + B. \\tag {1}", + "image_path": "04c8d8de52381cb93d10837888b7772caa176343062f1a3dcecc6ae1655bcdd8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 666, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 715 + ], + "type": "text", + "content": "A common strategy for rain removal is to model rain streaks with specific properties like direction, scale and space distribution and separate the rain layer from the background. This is usually achieved [8, 16, 21, 31, 36] by estimating the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 328, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 352 + ], + "type": "text", + "content": "rain layer as an intermediate output before the final module and subtract it to restore the clean image." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 353, + 546, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 546, + 472 + ], + "type": "text", + "content": "However, the importance of location information embedded in the rain layer has been underestimated. As discussed in Section 1, since rain location is beneficial for rain removal and night rain appearance varies with spatial locations, obtaining the rain layer in advance is more necessary than in day scenes. Moreover, discriminating the rain layer from the night scene is more difficult due to the coupling of rain appearance and light sources, thus aforementioned practice (i.e., estimating the rain layer and subtracting it to get the final output using the same model) is inefficient." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 472, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 640 + ], + "type": "text", + "content": "In this work, therefore, we propose a novel framework for nighttime deraining, encompassing a model specializing the rain layer estimation, and a module that takes full advantage of the information of rain location. Specifically, we decouple the rain layer estimation and clean background reconstruction by introducing the Rain Location Prior (RLP) and Rain Prior Injection Module (RPIM). We learn to mine the information of rain location from nighttime rainy image and restore the clean scene respectively in an end-to-end manner. We further emphasize the features within rain regions by modulating them before rain revoal and background reconstruction. In this way, useful information of rain location can be better extracted and exploited, boosting the performance of nighttime deraining." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 647, + 455, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 455, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 455, + 659 + ], + "type": "text", + "content": "3.2. Rain Location Prior (RLP)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "content": "As mentioned above, the rain layer is commonly assumed to be superposed onto the background, which facilitates the design ideas of progressive and residual learning for many deraining models [8, 16, 27, 32, 37]. These mod" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13150" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "els typically regard the rain layer as a residual component to the clean image, and some of them learn to progressively model these high-frequency patterns with recurrent structures. These designs, in turn, can reveal location information of rain streaks in night scenes, where the appearance of rain highly depends on its spatial location. For deraining, it would be beneficial if accurate rain locations were provided in advance, which is impractical in real scenes. Therefore, we propose to use recurrent residual architecture to mine the prior knowledge of rain location before removing rain streaks. It can provide the location information to deraining models, thereby further boosting their performance, which highlights its importance for nighttime deraining." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 361 + ], + "type": "text", + "content": "In our proposed formulation, we introduce a module to learn and capture the prior knowledge of rain location, namely Rain Location Prior (RLP), before removing rain streaks. This module is composed of several residual blocks, which are effective in modeling rain streaks as a residual component. Meanwhile, it learns to progressively capture the rain through a recurrent design that utilizes the high-frequency characteristics of rain. When fed with the rainy input and an initial prior map, the module learns to extract deep features and recurrently update the prior map. The process of RLP can be formulated as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 78, + 371, + 287, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 371, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 78, + 371, + 287, + 385 + ], + "type": "interline_equation", + "content": "\\bar {R} _ {k} = \\mathcal {F} _ {R L P} (I \\odot \\bar {R} _ {k - 1}; \\theta), \\quad k = 1, \\dots , N, \\tag {2}", + "image_path": "f68f0dc51e4485f1b7332189adb130a62842273dc56f0f973667dc09b6e15a73.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": " denotes the input and " + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\bar{R}_k" + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": " is the RLP output at the " + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": "-th stage. " + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\bar{R}_0" + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": " is the initial map and all values are set to 0.5. " + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{RLP}(\\circ ;\\theta)" + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": " refers to the RLP module and " + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": " is its parameters. " + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": " denotes the channel-wise concatenation. " + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 396, + 287, + 527 + ], + "type": "text", + "content": " denotes the total number of recurrent stages, which is empirically set to 6 and 4 for CNN-based and Transformer-based models, respectively. Concretely, PReNet [27] is a lightweight deraining network with the residual and recurrent design for a balance between complexity and performance. Its simplicity in design tightly fits the role of the RLP module and is adopted in our experiment." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 529, + 287, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 636 + ], + "type": "text", + "content": "Note that we do not impose additional constraints on the RLP output, because we found that supervision signals from rain streak masks obtained by thresholding following the practice in raindrop removal [14, 26, 38] do not improve the performance. For simplicity, we do not apply regularization terms to the RLP output during training and encourage the module to learn it implicitly from training data. Corresponding experimental results are provided in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 646, + 243, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 243, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 243, + 659 + ], + "type": "text", + "content": "3.3. Rain Prior Injection Module (RPIM)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "In night scenes, the appearance of rain heavily depends on its spatial position relative to light sources. Therefore, deraining models should treat different areas with varying levels of importance. With the RLP indicating location in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 544, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 544, + 95 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 544, + 95 + ], + "type": "text", + "content": "formation of rain streaks, we further emphasize the importance of these areas with the attention mechanism [40]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "type": "text", + "content": "Specifically, we propose the Rain Prior Injection Module (RPIM). It takes the deep features extracted by the RLP module and further updates the prior map in a residual manner. The updated prior map is then used to generate the attention weights that increase the importance of rain streak areas and suppress other irrelevant areas. Finally, the features within rain streak areas are emphasized by the weights by element-wise multiplication of deep features and the attention weights. The RPIM can be described as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 367, + 215, + 545, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 215, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 367, + 215, + 545, + 228 + ], + "type": "interline_equation", + "content": "\\bar {R}, z = \\mathcal {M} _ {R P I M} (\\bar {R} _ {N}, f; \\sigma), \\tag {3}", + "image_path": "6cf324ce3b4ad0d5a62267f7747643e963a6fb6aaf58ee314da033daae33d042.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "inline_equation", + "content": "\\bar{R}_N" + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "text", + "content": " are the final prior map and deep features extracted by residual blocks in the RLP module. " + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{RPIM}(\\circ ;\\sigma)" + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "text", + "content": " denotes our Rain Prior Injection Module. " + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "inline_equation", + "content": "\\bar{R}" + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 232, + 546, + 293 + ], + "type": "text", + "content": " are the modulated output and feature tensor ready for injection into the deraining network, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 298, + 443, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 298, + 443, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 298, + 443, + 312 + ], + "type": "text", + "content": "3.4. Deraining Module (DM)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 317, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 400 + ], + "type": "text", + "content": "For pixel-wise image restoration tasks, U-shaped architectures with skip connections are commonly adopted as they have shown good capability in capturing contextual information without losing much spatial information [30, 34, 40]. CNN-based and Transformer-based models with such architecture are two main streams and many methods make further improvements based on them." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 401, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 509 + ], + "type": "text", + "content": "In Encoder-Decoder models, the input is typically projected into a feature space through a convolution layer, which is suitable for prior injection. After obtaining RLP and modulating the prior, we inject it into deraining models to further enhance deraining performance. We feed the rainy input and the RLP into the deraining module, which is a U-shaped model (either CNN-based or Transformer-based) for rain streak removal and background restoration. The process of this stage can be formulated as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 374, + 514, + 545, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 514, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 374, + 514, + 545, + 529 + ], + "type": "interline_equation", + "content": "\\bar {I} = \\mathcal {F} _ {D M} (I \\odot \\bar {R}, z; \\Theta), \\tag {4}", + "image_path": "d20fac7fe5d88ef52f5e6a27e6fd06348d690bfd33adfafed0ed9bc8f8b902d6.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\bar{I}" + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "text", + "content": " is the restored image by deraining module, " + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\bar{R}" + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "text", + "content": " is the updated RLP and " + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "text", + "content": " denotes the channel-wise concatenation. " + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{DM}(\\circ ;\\Theta)" + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "text", + "content": " represents the deraining model, which focuses on the contextual information of neighboring pixels, and " + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "text", + "content": " is its parameters to be optimized. " + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 535, + 545, + 631 + ], + "type": "text", + "content": " refers to the modulated prior by RPIM and is injected into the deraining module by channel-wise concatenation with the projected feature after the first convolution layer." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 632, + 545, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 655 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 655 + ], + "type": "text", + "content": "For the training of the whole model, we apply the Charbonnier loss [3] on the final output:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 376, + 662, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 662, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 376, + 662, + 545, + 682 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sqrt {\\left\\| \\bar {I} - Y \\right\\| ^ {2} + \\varepsilon^ {2}}, \\tag {5}", + "image_path": "0edc792d25b8cbff0bfcba7449480834c90fc8fab8477cf132e2f76625f88841.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\bar{I}" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " is the final output of the deraining model, " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " denotes the clean ground truth and " + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = 10^{-3}" + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": " is a constant." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13151" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 288, + 212 + ], + "type": "text", + "content": "In this section, we first introduce the experimental setups. Then we provide quantitative and qualitative results on synthetic data and evaluations on real night rainy images, to show the superior performance of our method compared to existing deraining methods, under the nighttime deraining setting. Moreover, we conduct ablation studies to validate the effectiveness of the proposed modules. Finally, we conduct experiments to show the generalization of our method on daytime datasets. Due to limited space, we provide more visual results in the supplementary material." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 217, + 167, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 167, + 229 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 167, + 229 + ], + "type": "text", + "content": "4.1. Experimental Setups" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 235, + 288, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 474 + ], + "type": "text", + "content": "Datasets. Rain streaks in GTAV-NightRain dataset [42] are sparse with low difficulty, which is unfavorable for observing the difference since all methods behaves well. Thus we follow the instructions to render more difficult data (27dB v.s. 32dB in [42]) for experiments, by increasing the scale and density of rain streaks. We turn on and off the rain effect while keeping other settings unchanged for the same scene to render the rainy and clean image pairs. Please refer to [42] for more details on data collection. We collect 10 rainy images and 1 clean image for each scene and cover non-overlapping scenes for training and test sets. Finally, we get a total of 5,000 pairs of training data and 500 pairs of test data. Our collected data will be released with the code. Additionally, we conduct experiments on Rain13k [16, 40] and GT-Rain [1] datasets, to further show the generalization of our method to daytime data. We train our model with different modules on Rain13k and evaluate on its test sets, which are Test100 [44], Rain100H [36], Rain100L [36], Test2800 [8], Test1200 [43]. We also train our method on GT-Rain and compare it with other methods on its test set." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": "Implementation Details. Our method is implemented in PyTorch and trained with Adam optimizer [17] with default parameters. The initial learning rate is set to " + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": " and finally decreases to " + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-6}" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": " following a cosine scheduler. The model is trained for 250 epochs with a batch size of 8 on " + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": " patches. Training is performed on a single NVIDIA RTX 3090 GPU. We adopt U-Net and Uformer (the Uformer-T variant) for CNN-based and Transformer-based architectures. All experiments are performed on a single NVIDIA RTX 3090 GPU." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 288, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 701 + ], + "type": "text", + "content": "Compared Methods. To show the effectiveness of our method, we make comparisons with PReNet [27], SPANet [32], DRDNet [7], RCDNet [31], SPDNet [37], MPRNet [40], GT-Rain [1], DRT [24], U-Net [26] and Uformer [34] (the Uformer-T variant) on both synthetic and real data. All methods are trained on synthetic data from scratch with publicly available codes provided by authors following their default settings. Among them, representative methods are selected for visual comparison." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "Metrics. For quantitative evaluation, we adopt commonly" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 313, + 134, + 538, + 297 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 545, + 131 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 545, + 131 + ], + "type": "text", + "content": "Table 1: Quantitative results of compared methods on synthetic data. All the models are trained on our collected data following the default setting by authors. Higher metric is better for PSNR and SSIM. #GMACs is calculated on " + }, + { + "bbox": [ + 304, + 70, + 545, + 131 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 70, + 545, + 131 + ], + "type": "text", + "content": " patch." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 134, + 538, + 297 + ], + "lines": [ + { + "bbox": [ + 313, + 134, + 538, + 297 + ], + "spans": [ + { + "bbox": [ + 313, + 134, + 538, + 297 + ], + "type": "table", + "html": "
MethodPSNRSSIM#Params#GMACs
Input27.100.8237//
PReLU [27]34.770.96220.17M66.4G
SPANet [32]31.100.92450.28M36.3G
DRDNet [7]32.200.92145.23M689.8G
RCDNet [31]34.170.94933.16M195.1G
SPDNet [37]33.900.93843.32M96.6G
MPRNet [40]36.630.96613.63M548.7G
GT-Rain [1]34.100.95722.29M29.6G
DRT [24]33.810.93811.18M165.4G
U-Net [26]36.630.96936.06M45.3G
Uformer [34]37.450.97205.20M10.7G
Ours (U-Net)37.280.97166.33M117.8G
Ours (Uformer)38.440.97495.52M63.4G
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Quantitative Results on Synthetic Data" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 352, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 484 + ], + "type": "text", + "content": "As shown in Table 1, the performance of both SPANet [32] and DRDNet [7] is inferior to that of other competitors, even though there exists large difference between their model size and computational cost. While PReNet [27], RCDNet [31], SPDNet [37], GT-Rain [1] and DRT [24] perform better than the former two methods and their performance is comparable to others. Among all compared methods, MPRNet [40] and Uformer [34], as representative CNN-based and Transformer-based image restoration models, show superior performance to other competitors, which well validates their model capacity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 484, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 592 + ], + "type": "text", + "content": "However, with the help of our proposed RLP and RPIM, the performance of both CNN-based and Transformer-based models can be boosted by a large margin. For CNN-based model U-Net [26], our method can get an increase of 0.65dB on PSNR and surpasses MPRNet [40] by 0.65dB. For the Transformer-based model Uformer [34], a large gain of 0.99dB on PSNR can be obtained and our proposed method outperforms all compared methods. These results can well validate the effectiveness of our proposed method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 599, + 504, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 599, + 504, + 612 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 504, + 612 + ], + "type": "text", + "content": "4.3. Qualitative Results on Synthetic Data" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "As shown in Figure 4, SPANet [32] and DRDNet [7] can only remove a few rain streaks in night scenes and large amounts of rain streaks remain, which corresponds to inferior performance in quantitative results. 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SPANet and DRDNet can only remove a few rain streaks while PReNet, RCDNet and SPDNet behave better than the former two methods. MPRNet, U-Net and Uformer outperform other competitors but our proposed prior can boost the performance of U-Net and Uformer even further, in terms of removing more rain streaks (Uformer for the first scene) and preserving background details (Uformer for the second scene). 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Among all compared methods, Ours (Uformer) can get the best results." + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 46, + 498, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 713 + ], + "type": "text", + "content": "In the first image, the illumination is dominated by the red neon cylinder and rain streaks look red. MPRNet [40] surprisingly fails the case and its result is similar to that of SPANet [32] and DRDNet [7]. For U-Net [26], Uformer [34] and Ours (U-Net), there are only a few rain streaks left on the image. However, Ours (Uformer) can fully remove the rain streaks, which demonstrates the effectiveness of our method. In the second image, bright windows consist of similar textures to rain streaks and the scene is relatively complex. We can find that almost all compared methods including Ours (U-Net) fail to preserve the texture of streetlight and it even totally disappears in some results. DRDNet [7] and SPDNet [37] keep the streetlight unchanged but there are some rain streaks left. Only Ours (Uformer) remove most rain streaks and preserve the texture of streetlight at the same time. We can infer that deraining models tend to recognize long thin textures with high pixel intensity as rain streaks in night scenes because rain streaks near" + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 472, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 520 + ], + "type": "text", + "content": "light sources have higher pixel values. In such cases, location priors of rain streaks become more crucial for deraining models to accurately handle rain streaks in night scenes, which further confirms the effectiveness of our method." + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 305, + 527, + 545, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 527, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 545, + 541 + ], + "type": "text", + "content": "4.4. Qualitative Results on Real Night Rainy Images" + } + ] + } + ], + "index": 52 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Here, we present the qualitative results on real data in Figure 5. Due to the domain gap between synthetic and real data, models trained with GTAV-NightRain still behave poorly in real night scenes [42]. To further handle real night rainy images, we additionally add JPEG compression as a data augmentation in our training. Compared methods can partially remove rain streaks in real night rainy images but behave inconsistently for different rainy images. We can see that DRDNet [7], RCDNet [31] and SPDNet [37] perform better than PReNet [27], SPANet [32] and MPRNet [40] for the first image while U-Net [26] and Uformer [34] get better results. But they all fail to remove rain streaks in the second image. However, our method succeeds in handling both images. 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Our method gets the best visual results. Please zoom in for details." + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 151, + 327, + 247, + 396 + ], + "blocks": [ + { + "bbox": [ + 176, + 317, + 223, + 327 + ], + "lines": [ + { + "bbox": [ + 176, + 317, + 223, + 327 + ], + "spans": [ + { + "bbox": [ + 176, + 317, + 223, + 327 + ], + "type": "text", + "content": "PRENet [27]" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 151, + 327, + 247, + 396 + ], + "lines": [ + { + "bbox": [ + 151, + 327, + 247, + 396 + ], + "spans": [ + { + "bbox": [ + 151, + 327, + 247, + 396 + ], + "type": "image", + "image_path": "ca9223672051ef0150b2f9eca311e2deaddc44dc18abe106f05114e5fd310918.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 174, + 398, + 224, + 408 + ], + "lines": [ + { + "bbox": [ + 174, + 398, + 224, + 408 + ], + "spans": [ + { + "bbox": [ + 174, + 398, + 224, + 408 + ], + "type": "text", + "content": "MPRNet [40]" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 248, + 327, + 343, + 396 + ], + "blocks": [ + { + "bbox": [ + 272, + 317, + 319, + 327 + ], + "lines": [ + { + "bbox": [ + 272, + 317, + 319, + 327 + ], + "spans": [ + { + "bbox": [ + 272, + 317, + 319, + 327 + ], + "type": "text", + "content": "SPANet [32]" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 248, + 327, + 343, + 396 + ], + "lines": [ + { + "bbox": [ + 248, + 327, + 343, + 396 + ], + "spans": [ + { + "bbox": [ + 248, + 327, + 343, + 396 + ], + "type": "image", + "image_path": "e7a56cb0e121fd9bee6af5de5b94193ba93854655457e5ff58eff8371f148393.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 275, + 398, + 316, + 408 + ], + "lines": [ + { + "bbox": [ + 275, + 398, + 316, + 408 + ], + "spans": [ + { + "bbox": [ + 275, + 398, + 316, + 408 + ], + "type": "text", + "content": "U-Net [26]" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 34 + }, + { + "type": "image", + "bbox": [ + 343, + 327, + 439, + 396 + ], + "blocks": [ + { + "bbox": [ + 369, + 317, + 414, + 327 + ], + "lines": [ + { + "bbox": [ + 369, + 317, + 414, + 327 + ], + "spans": [ + { + "bbox": [ + 369, + 317, + 414, + 327 + ], + "type": "text", + "content": "DRDNet [7]" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 343, + 327, + 439, + 396 + ], + "lines": [ + { + "bbox": [ + 343, + 327, + 439, + 396 + ], + "spans": [ + { + "bbox": [ + 343, + 327, + 439, + 396 + ], + "type": "image", + "image_path": "052fba699fa7fc991cee60bb69fd0f8450bf85a6ba4d6313a94f75dcc717e2c9.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 367, + 398, + 416, + 408 + ], + "lines": [ + { + "bbox": [ + 367, + 398, + 416, + 408 + ], + "spans": [ + { + "bbox": [ + 367, + 398, + 416, + 408 + ], + "type": "text", + "content": "Uformer [34]" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 36 + }, + { + "type": "image", + "bbox": [ + 440, + 327, + 536, + 396 + ], + "blocks": [ + { + "bbox": [ + 463, + 317, + 512, + 327 + ], + "lines": [ + { + "bbox": [ + 463, + 317, + 512, + 327 + ], + "spans": [ + { + "bbox": [ + 463, + 317, + 512, + 327 + ], + "type": "text", + "content": "RCDNet [31]" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 440, + 327, + 536, + 396 + ], + "lines": [ + { + "bbox": [ + 440, + 327, + 536, + 396 + ], + "spans": [ + { + "bbox": [ + 440, + 327, + 536, + 396 + ], + "type": "image", + "image_path": "433a07b99dc80f1ae807e13fd05f02f7ff413932105b0f30d877a587b9e08429.jpg" + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 478, + 398, + 497, + 407 + ], + "lines": [ + { + "bbox": [ + 478, + 398, + 497, + 407 + ], + "spans": [ + { + "bbox": [ + 478, + 398, + 497, + 407 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_caption" + } + ], + "index": 38 + }, + { + "bbox": [ + 46, + 437, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 461 + ], + "type": "text", + "content": "ing backgrounds tidy, showing the effectiveness of our proposed method for removing rain streaks in real night scenes." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 47, + 467, + 195, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 195, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 195, + 479 + ], + "type": "text", + "content": "4.5. Qualitative Results of RLP" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 46, + 485, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 593 + ], + "type": "text", + "content": "To further illustrate the effectiveness of our Rain Location Prior, we provide visualizations on both synthetic and real night rainy images in Figure 6. Our RLP module can learn to recognize rain streaks and emphasize these areas with higher weights. Notably, RLP can learn by itself to suppress areas of light sources, i.e., these areas are much darker than neighboring areas of rain streaks. We can also notice that rain streaks in the sky can also be recognized even though they are not obvious in the rainy image." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 665 + ], + "type": "text", + "content": "As shown in the right half of Figure 6, our RLP module can also generalize well to real night rainy images with only synthetic data for training. Same to the synthetic case, light sources are suppressed in RLP and those areas are darker than areas of rain streaks. These results all show the effectiveness of RLP, which is beneficial for nighttime deraining." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 47, + 671, + 147, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 147, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 147, + 682 + ], + "type": "text", + "content": "4.6. Ablation Studies" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "In this section, we study the effect of each component of our method, including Rain Location Prior (RLP) and" + } + ] + } + ], + "index": 46 + }, + { + "type": "table", + "bbox": [ + 307, + 460, + 549, + 646 + ], + "blocks": [ + { + "bbox": [ + 305, + 436, + 545, + 460 + ], + "lines": [ + { + "bbox": [ + 305, + 436, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 436, + 545, + 460 + ], + "type": "text", + "content": "Table 2: Ablation study on individual components of our proposed method & different model structures and sizes." + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 460, + 549, + 646 + ], + "lines": [ + { + "bbox": [ + 307, + 460, + 549, + 646 + ], + "spans": [ + { + "bbox": [ + 307, + 460, + 549, + 646 + ], + "type": "table", + "html": "
DMRLPRPIMPSNRΔSSIMΔ
PReLUNetXX34.77-0.9622-
✓X35.00+0.230.9649+0.0027
✓✓34.31-0.460.9621-0.0001
MPRNetXX35.21-0.9627-
✓X35.42+0.210.9641+0.0014
✓✓35.67+0.460.9633+0.0006
U-NetXX36.63-0.9693-
✓X37.08+0.450.9715+0.0022
✓✓37.28+0.650.9716+0.0023
Uformer-TXX37.45-0.9720-
✓X37.95+0.500.9733+0.0013
✓✓38.44+0.990.9749+0.0029
Uformer-BXX39.41-0.9763-
✓X39.65+0.240.9770+0.0007
✓✓39.77+0.360.9773+0.0010
", + "image_path": "757988b96c3a3b6bcb7a50f2c2dae61e3f4ec5b5ce8dfd2cbdef4b2bc7f4aa32.jpg" + } + ] + } + ], + "index": 48, + "angle": 0, + "type": "table_body" + } + ], + "index": 48 + }, + { + "bbox": [ + 305, + 653, + 546, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 546, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 546, + 712 + ], + "type": "text", + "content": "Rain Prior Injection Module (RPIM). We choose U-Net [26] and Uformer [34] out of CNN-based and Transformer-based models as the deraining module in our method, with U-shaped Encoder-Decoder architecture. Besides, we examine the effects of RLP on PReNet [27] and MPRNet" + } + ] + } + ], + "index": 49 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13154" + } + ] + } + ], + "index": 50 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 545, + 148 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 545, + 148 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 545, + 148 + ], + "type": "image", + "image_path": "fac82bba6842e9bca9587ef9e4905aa0aca4eb459e99c68200ac65d594fb5025.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 152, + 541, + 180 + ], + "lines": [ + { + "bbox": [ + 50, + 152, + 541, + 180 + ], + "spans": [ + { + "bbox": [ + 50, + 152, + 541, + 180 + ], + "type": "text", + "content": "Figure 6: Visualizations of Rain Location Prior (RLP) on synthetic and real night rainy images. Please zoom in for details. Table 3: Generalization to daytime datasets. Models are trained on Rain13k dataset [16] and evaluated on five test sets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 184, + 541, + 297 + ], + "blocks": [ + { + "bbox": [ + 50, + 184, + 541, + 297 + ], + "lines": [ + { + "bbox": [ + 50, + 184, + 541, + 297 + ], + "spans": [ + { + "bbox": [ + 50, + 184, + 541, + 297 + ], + "type": "table", + "html": "
DMRLPRPIMTest100 [44]Rain100H [36]Rain100L [36]Test2800 [8]Test1200 [43]Avg.
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Input22.550.686313.550.378426.900.838324.350.782923.630.732422.200.6837
U-NetXX24.910.858424.210.826730.520.925631.310.919931.010.902628.390.8866
U-Net✓X25.040.855026.820.846730.560.918531.320.917630.710.891728.890.8859
U-Net✓✓25.320.866526.060.838031.200.932431.320.920331.590.908929.100.8932
UformerXX28.010.878028.210.851632.160.934432.430.928731.660.907830.500.9001
Uformer✓X28.080.877528.370.854532.590.938532.490.928731.860.909330.680.9017
Uformer✓✓28.500.882128.340.857632.670.939032.550.929531.670.904230.740.9025
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With the prior map learned by the RLP module, directly feeding it into the deraining module brings an increase of 0.23dB, 0.21dB, 0.45dB, 0.50dB and 0.24dB in PSNR for five different deraining modules. It shows the effectiveness of the proposed RLP which can reveal location information of rain streaks and improve the deraining performance. The benefit of accurate location is straightforward and it is also effective for PReNet and MPRNet with other model structures." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "type": "text", + "content": "RPIM. In night scenes where location information plays a vital role in deraining, emphasizing the importance of RLP in rain streak areas is beneficial. As shown in Table 2, the performance of deraining modules can be further boosted with the help of RPIM. MPRNet [40], U-Net [26] and Uformer-T/-B [34] can get an additional increase of " + }, + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "type": "inline_equation", + "content": "0.25\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "type": "inline_equation", + "content": "0.20\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "type": "inline_equation", + "content": "0.49\\mathrm{dB}/0.12\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 469, + 287, + 578 + ], + "type": "text", + "content": " in PSNR. While PReNet [27] gets worse results and the repeated feature injections in its recurrent structure may leads to the performance drop." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "Model Structure and Capability. With different models compared, we can find that (i) recurrent structure may suffer from repeated feature injection (e.g., PReNet); (ii) models with vanilla Encoder-Decoder structure may benefit more from RLP (e.g., U-Net v.s. MPRNet); (iii) moderate models with better capability may benefit more from RLP (Uformer v.s. U-Net); (iv) moderate models may prefer additional knowledge from RLP than big models (e.g., Uformer-B v.s. Uformer-T). The comparisons demonstrate the effectiveness of our proposed RLP and RPIM and further provide insights on further improvement." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 305, + 495, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 305, + 495, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 305, + 495, + 319 + ], + "type": "text", + "content": "4.7. Generalization to Daytime Datasets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 326, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 447 + ], + "type": "text", + "content": "Despite our goal of nighttime deraining, we also conduct experiments on Rain13k [16] and GT-Rain [1] to demonstrate the generalization of our method on day scenes. As listed in Table 3, our method is also beneficial for CNN-based and Transformer-based models on daytime deraining. Additionally, we can find that the improvement is smaller than that on the nighttime dataset, which suggests the greater importance of location information for nighttime deraining. We also test our method on the GT-Rain dataset [1] and results are provided in the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 464, + 378, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 378, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 378, + 477 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "type": "text", + "content": "Nighttime rain removal is a challenging task due to complex illumination conditions. In night scenes, the location information of rain streaks becomes more critical for rain removal. In this paper, we propose the Rain Location Prior (RLP), which can be learned implicitly from rainy images using a recurrent residual model to reveal the location information of rain streaks. To further improve the deraining performance, we propose the Rain Prior Injection Module (RPIM) to modulate the learned RLP with the attention mechanism and emphasize the features within rain streak areas. Together, they help deraining modules focus more on recovering clean background rather than recognizing complex rain streaks. Despite the original goal of nighttime deraining, our method also works in day scenes. Experimental results show the effectiveness and generalization of our method on both synthetic data and real nighttime rainy images, which may be helpful for future research on nighttime deraining. We plan to explore more architectures for learning and extending RLP in the future." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13155" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": "Acknowledgments This work was supported by the National Natural Science Foundation of China (62171038, 62088101, 61931008, and 62006101), the R&D Program of Beijing Municipal Education Commission (KZ202211417048), and the Fundamental Research Funds for the Central Universities." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 156, + 107, + 168 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 156, + 107, + 168 + ], + "spans": [ + { + "bbox": [ + 48, + 156, + 107, + 168 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 176, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 176, + 287, + 232 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 176, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 53, + 176, + 287, + 232 + ], + "type": "text", + "content": "[1] Yunhao Ba, Howard Zhang, Ethan Yang, Akira Suzuki, Arnold Pfahnl, Chethan Chinder Chandrappa, Celso M de Melo, Suya You, Stefano Soatto, Alex Wong, et al. 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In ICIP, 2014. 1" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13157" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Robust Representations with Information Bottleneck and Memory Network for RGB-D-based Gesture Recognition/ffcfd550-d4a2-4cb4-a120-2a5976bb8508_content_list.json b/2023/Learning Robust Representations with Information Bottleneck and Memory Network for RGB-D-based Gesture Recognition/ffcfd550-d4a2-4cb4-a120-2a5976bb8508_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ff91cd0aefed1a1a552498e2e1fa60dfcfafa32a --- /dev/null +++ b/2023/Learning Robust Representations with Information Bottleneck and Memory Network for RGB-D-based Gesture Recognition/ffcfd550-d4a2-4cb4-a120-2a5976bb8508_content_list.json @@ -0,0 +1,1822 @@ +[ + { + "type": "text", + "text": "Learning Robust Representations with Information Bottleneck and Memory Network for RGB-D-based Gesture Recognition", + "text_level": 1, + "bbox": [ + 169, + 130, + 802, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yunan Li $^{1,2,3}$ Huizhou Chen $^{1,2}$ Guanwen Feng $^{1,2}$ Qiguang Miao $^{1,2,3*}$", + "bbox": [ + 184, + 200, + 789, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Computer Science and Technology, Xidian University, China", + "bbox": [ + 243, + 222, + 725, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Xi'an Key Laboratory of Big Data and Intelligent Vision, China", + "bbox": [ + 267, + 239, + 700, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3 Key Laboratory of Smart Human-Computer Interaction and Wearable Technology of Shaanxi Province, China", + "bbox": [ + 116, + 257, + 849, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{yunanli, qgmiao}@xidian.edu.cn, {huizhouchen, gwfeng-1}@stu.xidian.edu.cn", + "bbox": [ + 161, + 277, + 807, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 325, + 313, + 343 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although previous RGB-D-based gesture recognition methods have shown promising performance, researchers often overlook the interference of task-irrelevant cues like illumination and background. These unnecessary factors are learned together with the predictive ones by the network and hinder accurate recognition. In this paper, we propose a convenient and analytical framework to learn a robust feature representation that is impervious to gesture-irrelevant factors. Based on the Information Bottleneck theory, two rules of Sufficiency and Compactness are derived to develop a new information-theoretic loss function, which cultivates a more sufficient and compact representation from the feature encoding and mitigates the impact of gesture-irrelevant information. To highlight the predictive information, we further integrate a memory network. Using our proposed content-based and contextual memory addressing scheme, we weaken the nuisances while preserving the task-relevant information, providing guidance for refining the feature representation. Experiments conducted on three public datasets demonstrate that our approach leads to a better feature representation and achieves better performance than state-of-the-art methods. The code of our method is available at: https://github.com/Carpumpkin/InBoMem.", + "bbox": [ + 75, + 359, + 473, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gesture recognition based on RGB-D video has raised much attention of researchers since it has many applications, such as visual surveillance, intelligent transportation, and particularly, human-computer interaction (HCI) [48]. The development of CNN family [35, 5, 26], RNN family [27, 11], and Transformer-based methods [15, 57, 54]", + "bbox": [ + 75, + 781, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7626cc362a25155f74395f367633f72e226bec79a2828f897ecc90cd3e8e8d1f.jpg", + "image_caption": [ + "Figure 1. Diagram of our principle. The feature of a gesture sample can be decomposed into the essential gesture feature and gesture-irrelevant ones, such as the background, illumination, and the performer's appearance. The former provides predictive information whereas the latter is superfluous. Based on the information bottleneck theory, we can eliminate these disturbing nuisances by minimizing the superfluous information. Meanwhile, as the predictive feature in different samples is all the same, we leverage the memory network to store and \"overlay\" them, and then highlight the gesture-relevant predictive feature as the guidance for learning a robust feature representation." + ], + "image_footnote": [], + "bbox": [ + 501, + 324, + 893, + 496 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "promote the improvement of recognition performance significantly.", + "bbox": [ + 496, + 685, + 890, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although great progress has been made in this field, the attention has always been drawn to boost performance via better network structure [50, 48, 55, 56] or by introducing extra modalities of data [6, 18, 23, 19]. The interference of gesture-irrelevant factors is hardly noticed. In most real-world gesture recognition scenarios, the dynamic variations are in two aspects. One is based on the motion of the gesture itself like trajectories of hands/arms, and is crucial to the recognition task. The other is related to environmental influences like illumination, backgrounds, and the performers' appearances as depicted in Fig.1. The gesture performing-related factors, such as the velocity, performer's", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20968", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "concentration, and understanding of the gesture can also affect the quality of gesture presentation. When training a network for gesture recognition, these gesture-irrelevant factors may be learned as a kind of feature, and thus result in some inner-class differences hindering the recognition performance. Therefore, it is necessary to disentangle the recognition-relevant and redundant information to refine the feature representation.", + "bbox": [ + 75, + 90, + 470, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to disentangle the recognition task-relevant information and the disturbing gesture-irrelevant factors, we refer to the theory of Information Bottleneck (IB) [34], which engages mutual information (MI) and provides an information-theoretic objective for solving this problem. The essential idea of IB is mapping the observation of an input to a sophisticated representation, which retains the desired characteristics with respect to the prediction of label and simultaneously minimizes the redundant information. Many methods leverage IB to learn robust representations for downstream tasks like unsupervised multi-view learning [8], Person Re-identification [33] and human pose estimation [20]. In this process, the sophisticated representation is critical since it ensures a compact feature encoding that avoids the interference of task-irrelevant factors. However, it is difficult to obtain such a representation directly with the original IB theory. Approximating MI in high dimensions is hard [25], and thus the task-irrelevant distractors may not be removed. Even though some recent techniques ease the constraint by transforming this issue to a network optimization problem without explicitly estimating MI [33], the joint optimization of feature encoding and such a representation encoding blindly may fail to reach a satisfied representation since no explicit standard of \"good representation\" is given. Therefore, to refine the feature representation, we should explicitly highlight what the predictive information is, and take it as guidance for the refinement of the feature representation.", + "bbox": [ + 75, + 217, + 470, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Combining these concerns, we propose an analytic framework to learn a robust representation for RGB-D-based gesture recognition. To address gesture-irrelevant factors, we employ the Information Bottleneck (IB) principle to unify them as \"superfluous information\", in contrast to predictive information like motion trajectories. Then we derive a new objective that compresses the superfluous information in the encoding space and emphasizes the predictive one. To achieve a sufficient yet compact feature representation required by IB, a memory network is incorporated for explicit guidance. We create a large external memory bank, where the shared predictive information is highlighted by overlaying the features in different memory slots. This process is achieved through memory manipulations of writing and reading. Then with the derived objective, the distribution of encoding features is pulled towards that of the robust representation, resulting in improved ges", + "bbox": [ + 75, + 643, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ture recognition performance.", + "bbox": [ + 498, + 92, + 699, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of our method can be summarized as three-fold:", + "bbox": [ + 498, + 107, + 890, + 137 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. A framework to develop a robust feature representation for gesture recognition, along with the theoretical analysis based on IB. We extend the existing theoretical analysis and optimize the feature encoding to mitigate the interference of gesture-irrelevant factors. To the best of our knowledge, we are the first to provide insights from an information-theoretic view in this field.", + "2. A scheme to explicitly distill the predictive information. Utilizing the memory network, we learn the predictive information from various samples to derive a sufficient and compact feature representation.", + "3. Experiments prove the effectiveness of our design and demonstrate that the proposed method achieves the state-of-the-art performance on three public RGB-D gesture datasets of IsoGD [40, 38], EgoGesture [4, 52] and THU-READ [31, 32]." + ], + "bbox": [ + 511, + 150, + 890, + 419 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 436, + 637, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Evolution of gesture recognition. Conventional methods [39, 37] always employ spatiotemporal handcrafted features for gesture recognition. Recently, promotions of deep learning also bring new developments in dynamic gesture recognition. 3D CNNs [35] emerge for extracting spatiotemporal features, and many gesture recognition methods [17, 41, 53, 18, 6, 23, 19] are developed based on them. Meanwhile, RNN family [27, 11] that enables modeling sequence information also draws extensive attention in gesture recognition [53, 50, 58]. With the success of Transformer in computer vision tasks, there are also some researchers trying to improve the recognition performance by introducing Transformer-based structures [15, 57, 54]. Besides proposing new architectures, optimizing the network connection and structure is another option. Zhou et al. [55] and Yu et al. [48] notice the influence of network connection on low-level and high-level features, and employ network architecture search (NAS) for better architecture. Unlike previous methods that focus on improving the structure or connection of the network, we pay more attention to eliminating the disturbing gesture-irrelevant factors, which potentially lead to inner-class differences influencing recognition performance. With the theoretical analysis based on IB, we propose a new objective to achieve such an elimination.", + "bbox": [ + 496, + 460, + 890, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Information bottleneck for representation learning. Information bottleneck [34] is an information-theoretic principle that has made great progress in representation learning and theoretical understanding of Deep Neural Networks (DNNs) [28]. However, the difficulty of calculating", + "bbox": [ + 496, + 825, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20969", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a89e34bfb3433df569393dc097e1be2b34d9a925c69ba528e7da54e884201715.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 117, + 90, + 596, + 232 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/949b474d1ca209294d963d3b1660e11578a386c312772685554f0a614d5d19d7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 93, + 846, + 186 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9077c55c3db85a6b64c0dca185dd0d68c71b936886c9fc18805aac56d7228468.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed framework. The encoding feature of a gesture video sample is first obtained as the observation $v$ . Then the predictive information is highlighted in the memory network via writing and reading, and the guidance of representation $z$ is derived. With $\\mathcal{L}_{IB}$ further refining the representation of $z$ and pulling the distribution of $v$ to $z$ , a more robust representation for gesture recognition is developed. (a) The pipeline of the framework. (b) Memory writing manipulation. (c) Memory reading manipulation. (Best viewed in color.)" + ], + "image_footnote": [], + "bbox": [ + 606, + 185, + 846, + 255 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mutual information in high dimensions hinders its applications. To solve this problem, Alexenders et al. [2] demonstrate a variational approximation to parameterize the IB model. Peng et al. [24] propose a variational discriminator bottleneck for stable adversarial learning. Federici et al. [8] extend the IB theory to multi-view unsupervised learning. Tian et al. [33] present an analytical solution to fitting the mutual information via transferring the objective of IB to a variational self-distillation loss, and they also extend it to multi-view tasks. In contrast to these methods, our approach focuses on leveraging IB theory to disentangle the gesture-irrelevant factors and the predictive factors when encoding the features of a gesture sample. To fit the condition of feature disentanglement, beyond the Sufficiency constraint used in [33], we extend the IB theory by adding a Compactness constraint and give a more theoretically sound explanation of why they are both critical for eliminating task-irrelevant factors.", + "bbox": [ + 75, + 354, + 472, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Memory networks. Memory network [45, 10] is employed in both low-level and high-level vision tasks owing to its good ability in modeling long-term information. Li et al. [16] employ the memory networks to restore and calculate the weights for different stages in image dehazing. Zhu et al. [59] use dynamic memory to achieve text-to-image synthesis. For high-level tasks, Yang and Chen [47] employ a dynamic memory network for visual tracking. Cai et al. [3] design a memory matching network for one-shot learning, which writes/reads for training and inference phases, respectively. Zhang et al. [49] design a cross-modal memory structure to store multimodal information for a few-shot recognition task. Eom et al. [7] design a spatial and temporal memory network (STMN) for video-based pedestrian re-identification tasks. Compared with the above literature, the role that the memory network plays in this study is quite different. We do not simply use it for a large external space, but design different addressing strategies for writing and read", + "bbox": [ + 75, + 628, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing according to their different goals.", + "bbox": [ + 500, + 354, + 746, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 383, + 671, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Refining Feature Representation with Information Bottleneck", + "text_level": 1, + "bbox": [ + 500, + 409, + 890, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gesture-irrelevant factors are non-negligible since they cause significant divergence in even one class of gesture videos. However, these factors are always intertwined with predictive information like the hands/arms movement when encoding. Even some approaches [43, 55] attempt to leverage the attention mechanism to focus on motion trajectories of gestures, the nuisances are inevitably learned and impact the recognition performance. The principle of information bottleneck [34] is to build a robust feature representation by discarding all information that is not useful for a given task while retaining the predictive one. Based on it, we disentangle the gesture-relevant and -irrelevant factors, and thereby refine the feature representation.", + "bbox": [ + 496, + 448, + 890, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 664, + 648, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Suppose we have a set of input gesture videos, which are marked as $\\mathcal{X} = \\{x_1,x_2,\\ldots ,x_n\\}$ . These inputs fall into $\\mathcal{V} = \\{y_{1},y_{2},\\dots,y_{m}\\}$ classes. Obviously, the task of gesture recognition is mapping arbitrary gesture sample $x\\in \\mathcal{X}$ into the corresponding class $y$ . Let $v\\in \\mathcal{V}$ be an observation of $x$ , where $\\mathcal{V}$ is the set of features. In deep learning, $v$ is usually the feature of $x$ extracted by an encoder parameterized by $\\theta$ , namely $v = E_{\\theta}(x)$ . In general, supervised learning promotes $v$ to involve more predictive information with respect to $y$ , but it inevitably contains some task-irrelevant factors. As shown in Fig.3, imagining there is a good representation $z\\in \\mathcal{Z}$ , which keeps sufficient predictive information but no task-irrelevant information. Then pulling $v$ to $z$ can result in a more robust feature representation. Theoretically, tak", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20970", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/805f20162e52eefb49b64031603bd73da1cc8475f271ae5ebba2c28c1bc7ce0c.jpg", + "image_caption": [ + "Figure 3. The relations of the information entropy and mutual information among observation $v$ , representation $z$ and label $y$ . The predictive information is the mutual information between $v$ or $z$ and $y$ . The superfluous information is the conditional mutual information of $v$ and $z$ given $y$ , namely $I(v;z) - I(z;y)$ ." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 428, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ing $v, z$ , and $y$ as three random variables, the optimization goal is to maximize the mutual information between $z$ and $y$ while minimizing that of $z$ and $v$ , and that is the essential principle of IB.", + "bbox": [ + 75, + 377, + 468, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.2 Information Bottleneck Objective", + "text_level": 1, + "bbox": [ + 76, + 455, + 366, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to the definition of IB, a good representation $z$ should satisfy two rules: 1) keeping sufficient discriminative information to identity $y$ , and 2) avoiding encoding task-irrelevant information, specifically, the gesture-irrelevant appearance variations in this task. The first one is defined as Sufficiency of $z$ for $y$ [1, 8, 33]. Ideally, the Sufficiency rule is satisfied if and only if $I(z; y) = I(v; y)$ . However, in general, $I(z; y)$ is less than $I(v; y)$ due to the information loss during encoding. Therefore, we need to minimize such a loss and derive an objective function as:", + "bbox": [ + 75, + 479, + 468, + 630 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min [ I (v; y) - I (z; y) ]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 637, + 468, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The second one can be defined as Compactness. According to [8], the mutual information $I(v;z)$ between $v$ and $z$ can be subdivided as:", + "bbox": [ + 75, + 661, + 468, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI (v; z) = \\underbrace {I (z ; y)} _ {\\text {p r e d i c t i v e i n f o r m a t i o n}} + \\underbrace {I (v ; z | y)} _ {\\text {s u p e r f l u o u s i n f o r m a t i o n}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 713, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the first term on the right side is the mutual information between $z$ and $y$ , indicating the information contained in $z$ for label prediction. The second one is the conditional mutual information of $v$ and $z$ given the value of $y$ . In other words, it is the task-irrelevant information in $z$ . A compact feature representation requires $I(v;z|y)$ approaching 0. Therefore, we need to minimize $I(v;z|y)$ , and we have the second objective function as:", + "bbox": [ + 75, + 756, + 468, + 878 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min [ I (v; z) - I (z; y) ]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Combine Eq.(1) and Eq.(3), the entire objective can be written as:", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min \\left[ I (v; y) - I (z; y) + I (v; z) - I (z; y) \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 133, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with which both the rules of Sufficiency and Compactness can be satisfied. However, solving it by directly approximating MI is hard. According to the definition of mutual information, we can use conditional entropy and joint entropy to express Eq.(4) as:", + "bbox": [ + 498, + 162, + 890, + 239 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min [ H (y | z) - H (y | v) + H (z, y) ], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 251, + 890, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $H(y|z)$ is the conditional entropy of $y$ with $z$ given, and $H(z,y)$ is the joint entropy of $z$ and $y$ . Inspired by [33], we can approximate Eq.(5) via a loss function as:", + "bbox": [ + 498, + 280, + 890, + 325 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I B} = \\mathcal {L} _ {K L D} \\left(\\mathbb {P} _ {v} | | \\mathbb {P} _ {z}\\right) + \\mathcal {L} _ {c e} (z, y), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 339, + 890, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{KLD}(\\cdot ||\\cdot)$ and $\\mathcal{L}_{ce}(\\cdot ,\\cdot)$ are KL-divergence and cross-entropy loss, respectively. $\\mathbb{P}_v = p(y|v)$ and $\\mathbb{P}_z = p(y|z)$ are the probability of $v$ and $z$ in predicting $y$ , respectively. The detailed derivation can be found in the supplementary material.", + "bbox": [ + 498, + 367, + 890, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Distilling Predictive Information with Memory Network", + "text_level": 1, + "bbox": [ + 500, + 453, + 890, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that according to Sufficient and Compactness rules, $z$ is from $v$ and is supposed to contain all the predictive information with respect to $y$ . Tian et al. [33] design a new encoder $E_{\\phi}$ to derive $z$ . However, optimizing $E_{\\theta}(v|x)$ and $E_{\\phi}(z|v)$ simultaneously can only ensure the consistency of $v$ and $z$ . There is no guarantee that one more encoder can lead to a more compact representation. As shown in Fig.1, overlaying the samples can emphasize the shared predictive information, i.e., motions of hands and arms related to the gesture, and weaken the sample-specific gesture-irrelevant factors. To this end, we achieve such an \"overlay\" process in a differentiable way via memory network.", + "bbox": [ + 498, + 492, + 890, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our implementation, we construct a $n \\times m$ memory bank for each gesture class, where $n$ is the number of memory slots, and $m$ is the length of feature vector in each slot. The explicit optimization on $z$ is performed by two manipulations of memory, writing and reading.", + "bbox": [ + 498, + 675, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Memory Writing", + "text_level": 1, + "bbox": [ + 500, + 770, + 671, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Memory writing is a manipulation that writes the encoding feature of observation $v$ into the memory bank. In practice, it is achieved in a two-stage process. In the first stage, if there is an available memory slot, $v$ can be directly written to it. In the second stage, when all memory slots are full, the process becomes more complicated and consists of two steps as follows.", + "bbox": [ + 498, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20971", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Forget. In the early stage, $E_{\\theta}(v|x)$ is not well trained, and thus $v$ inevitably contains some interference factors. These features may contaminate the memories. Therefore, we impose a forget vector $\\mathbf{e}$ , a $n \\times 1$ vector that has $n$ components corresponding to $n$ memory slots. It attenuates along with the training epoch since the predictive information dominates after times of training. The forget step can be expressed as:", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {M}} ^ {t} (i) = \\mathbf {M} ^ {t - 1} (i) \\left(1 - e ^ {t} (i)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 220, + 468, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{M}$ is the memory bank, and $i\\in \\{1,2,\\dots ,n\\}$ indicates the position of memory slot. $t - 1$ and $t$ imply two adjacent iterations of the optimization process. Updating memory from iteration $t - 1$ to $t$ is implemented by the Hadamard product.", + "bbox": [ + 75, + 247, + 468, + 323 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gated writing. When writing the encoding feature of $v^t$ into the memory, we utilize a gated writing strategy. We calculate the correlation between the $v^t$ and features in each slot and update the memory as:", + "bbox": [ + 76, + 323, + 470, + 385 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} ^ {t} (i) = \\tilde {\\mathbf {M}} ^ {t} (i) + w _ {o} ^ {t} (i) v ^ {t}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 393, + 468, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{o}^{t}(i)$ is a gating weight at $i$ -th slots of $\\mathbf{w}_{o}^{t}$ . It measures the correlation between $v^{t1}$ and $\\tilde{\\mathbf{M}}^t (i)$ . We have a constraint on $\\mathbf{w}_o$ as:", + "bbox": [ + 75, + 419, + 468, + 465 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\sum_ {i} w _ {o} (i) = 1, \\\\ 0 \\leq w _ {o} (i) \\leq 1. \\end{array} \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 473, + 468, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the gating strategy, we can write $v^t$ to different memory slots adaptively.", + "bbox": [ + 76, + 523, + 468, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2 Memory Reading", + "text_level": 1, + "bbox": [ + 76, + 571, + 253, + 588 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Memory reading is the key step for deriving $z$ . It is defined as a weighted sum of features in the memory slots:", + "bbox": [ + 75, + 595, + 468, + 626 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nz ^ {t} = \\sum_ {i} w _ {r} ^ {t} (i) \\mathbf {M} ^ {t} (i), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 635, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z^t$ is the representation yielded from the memory at iteration $t$ with predictive information highlighted. Like writing, the reading weight also obeys the constraints in Eq.(9).", + "bbox": [ + 75, + 676, + 468, + 737 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.3 Memory Addressing", + "text_level": 1, + "bbox": [ + 76, + 755, + 274, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Although we have shown the way to access memories according to Eq.(7)-(10), the weighting mechanism remains unveiled. As shown in Fig.4, we design a two-level addressing scheme to ensure the addressing process can meet the essential requirement of memory writing and reading.", + "bbox": [ + 75, + 779, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cfa5a0a453cc86a46c8ae49d47985b896f499bcd3d78efef0108eb452d88163e.jpg", + "image_caption": [ + "Figure 4. Diagram of two memory addressing strategies. (The length of the feature vector is omitted for simplicity. Best viewed in color.)" + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 883, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Content-based addressing. The content-based addressing focuses on the correlation between $v$ and features in each slot. It can be expressed as:", + "bbox": [ + 498, + 303, + 892, + 348 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {c} (i) = \\frac {\\exp (\\phi [ v , \\mathbf {M} (i) ])}{\\sum_ {j} \\exp (\\phi [ v , \\mathbf {M} (j) ])}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 353, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi[\\cdot, \\cdot]$ is the correlation measurement function. Unlike [10], our measurement for writing and reading is different. When writing into the memory, the process is analogous to clustering. Similar $v$ should be put into one slot to keep the variety of the memory bank. Memory reading is the contrary. If we weigh the slots containing similar features to $v$ higher, the superfluous information cannot be removed. Therefore, instead of simply calculating the similarity, we add a gating parameter $\\sigma$ for the correlation measurement $\\phi$ . Taking the cosine similarity as the naive similarity measurement, we define $\\phi[\\cdot, \\cdot]$ as:", + "bbox": [ + 498, + 393, + 892, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi [ \\cdot , \\cdot ] = 1 ^ {\\sigma} + (- 1) ^ {\\sigma} D _ {c o s s i m} (\\cdot , \\cdot), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 566, + 890, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $D_{\\text{cossim}}$ is the cosine similarity and the gating flag $\\sigma$ is set to 1 for reading and 0 for writing.", + "bbox": [ + 498, + 592, + 888, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contextual addressing. Content-based addressing considers from the view of relations between $v$ itself and the feature in each memory slot. Analyzing the relations between memory slots also benefits the learning of predictive information. Therefore, we develop the contextual addressing scheme by imposing the influence of neighbor slots' weights as:", + "bbox": [ + 498, + 622, + 890, + 728 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {t} (i) = \\sum_ {i} w _ {c} (i) b _ {\\Omega} \\left(d _ {i}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 733, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $b_{\\Omega}(d_i) = \\exp (d_i^2 / 2\\sigma^2)$ is a bell-shaped balance function, which gives slots in neighbor $\\Omega$ decreasing weights along with their distances $d_i$ to slot $i$ .", + "bbox": [ + 498, + 771, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Like [46], we also introduce a temperature parameter that controls the concentration level of the distribution. Then we obtain the final weight as:", + "bbox": [ + 498, + 816, + 890, + 863 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw (i) = \\frac {\\exp \\left(w _ {t} (i) ^ {\\tau}\\right)}{\\sum_ {j} \\exp \\left(w _ {t} (j) ^ {\\tau}\\right)}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 868, + 890, + 904 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "$^1 v$ and $z$ are $n\\times 1$ feature vectors in the memory manipulations. Their notations hereby are not changed for the consistency with the expressions in information bottleneck theory in Sec.3.1.", + "bbox": [ + 75, + 862, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "footer", + "text": "20972", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is the temperature factor that can amplify the focusing degree on each memory slot by enlargement.", + "bbox": [ + 76, + 90, + 468, + 122 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Training Scheme", + "text_level": 1, + "bbox": [ + 76, + 130, + 243, + 147 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The training process consists of two parts. One is related to the original gesture recognition task, and it can be accomplished by using the cross-entropy loss function. The other is focused on refining the feature representation, which is achieved by Eq.(6), namely our proposed loss function based on IB. Then the overall loss is:", + "bbox": [ + 76, + 154, + 467, + 243 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c e} + \\beta (W \\cdot \\mathcal {L} _ {I B}), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 258, + 467, + 276 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{ce}$ refers to cross-entropy loss, which is the only task-relevant loss for the original gesture recognition, and $\\beta$ is a balance parameter. Since the memory relies on a series of $v$ , it needs some time to optimize the encoder $E_{\\theta}$ first. Therefore, we add a warm-up coefficient $W$ , which can be expressed as:", + "bbox": [ + 76, + 282, + 467, + 372 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nW = \\max (0, (1 - \\exp (- E + \\varepsilon))), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 385, + 467, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $E$ represents the current epoch and $\\varepsilon$ is a warm-up hyper-parameter that determines when $L_{IB}$ starts to effect.", + "bbox": [ + 76, + 412, + 467, + 444 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 457, + 200, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setups", + "text_level": 1, + "bbox": [ + 76, + 482, + 272, + 498 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proposed method is implemented with PyTorch on a NVIDIA RTX 3090 GPU. We choose Res3D-18 [36] as our backbone. The input data is spatially resized to $256 \\times 256$ first, and then randomly/center cropped into $224 \\times 224$ in the training/inference phase, respectively. In the temporal domain, it is randomly/uniformly sampled to 32-frame videos in the training/inference phase, respectively. We use the SGD optimizer with a weight decay of 0.0004 and momentum of 0.9. We fix the mini-batch size as 7. The initial learning rate is set to 0.003 and then it decreases with a scheme of noisy linear cosine decay. The training process stops after 15 epochs for IsoGD and EgoGesture datasets and 80 epochs for THU-READ dataset since the last one has fewer samples. The temperature parameter $\\tau$ for memory bank is set to 10, and the number of memory slots is 5. The warm-up parameter $\\varepsilon$ is 3 for IsoGD and EgoGesture datasets is 10 for THU-READ, respectively. The balance parameter $\\beta$ is set to 10 due to the ratio of two losses.", + "bbox": [ + 75, + 505, + 467, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 786, + 441, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proposed method is compared with state-of-the-art methods on three datasets of IsoGD [40, 38], EgoGesture [4, 52], and THU-READ [31, 32]. Unlike recent SOTA methods [48, 55, 57] that are first pre-trained on the 20BN-Jester gesture dataset [21], our network does not need any other extra pre-train models but employs the backbone", + "bbox": [ + 76, + 810, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Res3D-18 model with its default settings in PyTorch. As the proposed method does not focus on multimodal fusion, we just employ a simple average fusion scheme to obtain the RGB+D result.", + "bbox": [ + 498, + 90, + 890, + 150 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Performance on IsoGD", + "text_level": 1, + "bbox": [ + 500, + 170, + 714, + 184 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Chalearn IsoGD dataset is a large-scale RGB-D dataset with 249 classes of gestures. It can be divided into three subsets: training set (35,878 videos), validation set (5,784 videos), and testing set (6,271 videos). This dataset is also used from two rounds of Chalearn LAP large-scale isolated gesture recognition challenge. Samples in Fig.1 are from this dataset. The various appearances in this dataset make it hard to achieve accurate recognition. Thus it can be a good benchmark to verify whether our framework is effective to eliminate the influence of gesture-irrelevant factors or not.", + "bbox": [ + 496, + 193, + 890, + 344 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The comparison on the Chalearn IsoGD dataset is shown in Table 1. Following the previous methods [50, 58, 55, 48, 57], we also report the performance on the validation subset for a fair comparison. Without loss of generality, the performance on the testing subset is also reported in the supplementary material. As can be seen, employing CNNs can bring a large improvement when compared with the hand-icraft feature-based method [37]. Then improving the network structure or altering the connection via NAS can also promote performance to a varying extent. Compared with these methods, our framework focuses on finding a better feature representation to eliminate gesture-irrelevant factors and achieves significant boosting. The proposed method outperforms the previous SOTA, Zhou et al.'s [55] near $8\\%$ and $4\\%$ on RGB and depth data, respectively. Besides the good performance on single modality, the RGB-D result is also better than Zhou et al.'s [57] at about $7\\%$ , even though they design a new fusion module whereas ours is a simple average fusion. It proves a good feature representation is critical for improving recognition performance.", + "bbox": [ + 496, + 345, + 890, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2 Performance on EgoGesture", + "text_level": 1, + "bbox": [ + 500, + 665, + 751, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "EgoGesture dataset contains 24,161 egocentric hand gesture clips of 83 classes from 50 distinct subjects. Videos in this dataset focus on the interaction with wearable devices from a first-person view across multiple indoor and outdoor scenes. Compared with Chalearn IsoGD dataset, the number of classes of this dataset is fewer, but this first-person dataset suffers more problems like blurring and various viewpoints since the camera is on the performers' heads.", + "bbox": [ + 496, + 688, + 890, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As demonstrated in Table 2, the proposed method can also achieve a remarkable performance on the EgoGesture dataset. As the top accuracy on this dataset is very high (mostly beyond $90\\%$ ), it is not easy to make a significant improvement. However, ours still outperforms the second best one, Kopuklu et al.'s [14] over $1\\%$ on RGB data despite", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20973", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1828993b9c7dc5fe14142106c8724a1ecbe50fea2a47c6b64b56d9337ad8f747.jpg", + "table_caption": [], + "table_footnote": [ + "* Including saliency data as reported in [18].", + "** Including flow data as reported in [22]." + ], + "table_body": "
ModalityMethodMain modelAccuracy(%)
RGBWang [44]bi-direction VDI36.60
Li [18]3D CNN37.28
Hu [12]DNN44.88
Miao [22]ResC3D45.07
Duan [6]2-stream CNN+C3D46.08
Zhang [51]convLSTM+C3D51.31
Zhang [50]ResC3D+convLSTM +MobileNet55.98
Zhu [58]ResC3D+ GatedConvLSTM +MobileNet+Pyramid57.42
Yu [48]SlowFast+NAS²58.88
Zhou [57]I3D+Transformer60.87
Zhou [55]I3D+DI+NAS62.66
OursRes3D-1870.88
depthWang [44]bi-direction DDI40.08
Li [18]3D CNN40.49
Hu [12]DNN48.96
Miao [22]ResC3D48.44
Duan [6]2-stream CNN+C3D54.95
Zhang [51]convLSTM+C3D49.81
Zhang [50]ResC3D+convLSTM +MobileNet53.28
Zhu [58]ResC3D+ GatedConvLSTM +MobileNet+Pyramid54.18
Yu [48]SlowFast+NAS²55.68
Zhou [57]I3D+Transformer60.17
Zhou [55]I3D+DI+NAS60.66
OursRes3D-1864.38
RGB+DWan [37]MFSK+BoVW18.65
Wang [44]bi-direction VDI+DDI44.80
Li [18]3D CNN52.04*
Hu [12]DNN54.14
Zhang [51]convLSTM+C3D55.29
Zhu [58]ResC3D+ GatedConvLSTM+ +MobileNet+Pyramid61.05
Miao [22]ResC3D64.40**
Yu [48]SlowFast+NAS²65.54
Zhou [55]I3D+DI+NAS66.62
Zhou [57]I3D+Transformer66.79
OursRes3D-1874.08
", + "bbox": [ + 89, + 87, + 460, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "just using a much simpler backbone of Res3D-18. The performance on depth data is also competitive but $0.66\\%$ lower than the best one of Kopuklü et al.'s. It implies our feature representation refinement is more effective on RGB data. The reason behind it may be that compared with RGB data, the differences between depth samples are smaller (only the grayscale value changes), which makes it hard to distinguish the predictive cue from the excess information with", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/235c5ec3de5413b509ca0e1d99883719f81ba9553bec13a37025304a043a0dce.jpg", + "table_caption": [ + "Table 1. Comparison with SOTAs on Chalearn IsoGD Dataset." + ], + "table_footnote": [], + "table_body": "
ModalityMethodMain ModelAccuary(%)
RGBGraves [10]VGG16+LSTM74.70
Cao [4]C3D+LSTM +RLSTM89.30
Carreira [5]I3D90.33
Tang [30]SeST93.20
Yu [48]SlowFast+NAS293.31
Köpüklü [14]ResNeXt-10193.75
OursRes3D-1894.93
depthGraves [10]VGG16+LSTM77.70
Carreira [5]I3D89.47
Cao [4]C3D+LSTM +RLSTM90.60
Tang [30]SeST93.35
Köpüklü [14]ResNeXt-10194.03
Yu [48]SlowFast+NAS294.13
OursRes3D-1893.47
RGB+DGraves [10]VGG16+LSTM81.40
Cao [4]C3D+LSTM +RLSTM92.20
Carreira[5]I3D92.78
Joze[13]MMTM93.87
Yu[48]SlowFast+NAS295.52
OursRes3D-1895.72
", + "bbox": [ + 504, + 87, + 890, + 431 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/27bf555a1f436413533fa3aaac22e2841670692bf3aa8ae6821052f6463b7667.jpg", + "table_caption": [ + "Table 2. Comparison with SOTAs on EgoGesture Dataset." + ], + "table_footnote": [], + "table_body": "
ModalityMethodMain ModelAccuary(%)
RGBSimonyan [29]VGG41.90
Feichtenhofer [9]SlowFast69.58
Yu [48]SlowFast+NAS²71.25
Wang [42]ConvNet73.85
Li [15]Transformer80.42
Zhou [57]I3D+Transformer81.25
OursRes3D-1888.33
depthSimonyan [29]VGG34.06
Wang [42]ConvNet65.00
Feichtenhofer [9]SlowFast68.75
Yu [48]SlowFast+NAS²69.58
Li [15]Transformer76.04
Zhou [57]I3D+Transformer77.92
OursRes3D-1882.91
RGB+DFeichtenhofer [9]SlowFast76.25
Yu [48]SlowFast+NAS²78.38
Li [15]Transformer84.90
Zhou [57]I3D+Transformer87.04
OursRes3D-1890.51
", + "bbox": [ + 504, + 464, + 893, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Comparison with SOTAs on THU-READ Dataset.", + "bbox": [ + 519, + 738, + 870, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the memory network.", + "bbox": [ + 500, + 779, + 643, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.3 Performance on THU-READ", + "text_level": 1, + "bbox": [ + 500, + 815, + 756, + 829 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "THU-READ dataset has 1920 videos of 40 classes, which are performed by 8 subjects. Although involving fewer videos and fewer classes, it is yet challenging due to the subtle intra-class differences and the background noise.", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20974", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/476e1979e7ce7f94a9a4468d4390e8247a1caa8379b7f8fa0f9a0ac9985c5b47.jpg", + "table_caption": [], + "table_footnote": [ + "$^{*}$ Suff. $=$ Sufficiency, Comp. $=$ Compactness Table 4. Impacts of components of the proposed framework." + ], + "table_body": "
Suff.Comp.memory networkAcc(%)
RGBdepth
×××78.3369.58
✓××82.2973.43
✓✓×85.4176.76
✓✓✓88.3382.91
", + "bbox": [ + 106, + 88, + 439, + 175 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3 reports the comparison on the THU-READ dataset. The results are reported by averaging all 4 splits under CS protocol as per [32]. The proposed method also achieves the best performance on this dataset. Compared with the second best one of Zhou et al. [57], which employs a combination of I3D and Transformer network, our results are still $7\\%$ and $5\\%$ better than theirs on RGB and depth data, respectively. For the RGB-D fusion result, the performance of the proposed method reaches $90.51\\%$ , and outperforms Zhou et al.'s at about $3\\%$ , even though we just utilize a simple average fusion.", + "bbox": [ + 76, + 229, + 472, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 407, + 230, + 424 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The studies on the effectiveness of our designs, including representation refinement with IB and predictive information distillation with memory network, are first presented in this section. In order to evaluate our scheme using a memory network, we have also compared several different addressing strategies, including using cosine similarity only for addressing and using content-based addressing only. THU-READ dataset is employed for this ablation study. Without specific saying, the experimental settings are the same as mentioned in Section 4.1.", + "bbox": [ + 75, + 431, + 468, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impacts of components of the proposed framework. In Table 4, we show how the proposed framework helps to eliminate gesture-irrelevant factors and leads to a more compact and robust feature representation. We compare several strategies, including 1) the baseline of using Res3D-18 only, 2) optimizing with the Sufficiency rule only, 3) using both Sufficiency and Compactness rules, namely using the IB loss in Eq.(6), and 4) using IB loss and memory network. The performance is marked in rows with a checkmark or a cross, denoting whether the corresponding module is used or not. Compared with the baseline, optimizing under the IB theory, even only considering the Sufficiency rule can lead to a significant performance improvement. This demonstrates the importance of a good representation for recognition tasks. When extending the loss to involve the Compactness rule, even better performance can be achieved. Replacing the convolution-based IB module with the memory network encourages the deposition of predictive information and leads to another performance gain. This suggests the effectiveness of memory network for highlighting the predictive information explicitly.", + "bbox": [ + 75, + 584, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9c6e1b4e3ac4a0ff9ce8b66c8beaf0d871688a138b2f27d00342fc218302d2ba.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
addressing strategyAccuracy(%)
RGBdepth
cosine similarity only80.5171.76
content-based only84.5775.62
proposed method88.3382.91
", + "bbox": [ + 558, + 88, + 834, + 167 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Performance with different memory addressing strategies.", + "bbox": [ + 500, + 172, + 890, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of different addressing strategies. The effect of different addressing strategies is shown in Table 5. When only the cosine similarity is used for addressing, the performance is poor. This implies that similar $z$ and $v$ weaken the effectiveness of IB loss. After adding the gating flag $\\sigma$ , and even just using content-based addressing, the performance is improved significantly. When all the addressing strategies are combined, the performance is further boosted. This indicates that a combination of content-based and contextual addressing can leverage both inter- and intra-memory feature relations and achieve better performance.", + "bbox": [ + 496, + 212, + 890, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization. To better illustrate how the robust presentation derived from our proposed framework shrinks the inner-class difference, which is mainly caused by gesture-irrelevant variations, we present a visualization of a 2D projection of feature encoding by t-SNE. The visualization is conducted on RGB data of the THU-READ dataset (CS3).", + "bbox": [ + 496, + 378, + 890, + 469 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/74b9626122022bcf2be67dbb2e106d529b068a128714ac421169324c2320276e.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 504, + 487, + 632, + 582 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d8dc7cb867b9900a4171621cb66d02aa71cfc32eb47cea0644e9e90788e7aab8.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 635, + 488, + 759, + 580 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/376db8a530079928b572209e8c7a3acbb7662e2817b63b26b9355ef181ef38c6.jpg", + "image_caption": [ + "(c)", + "Figure 5. Visualizing the projection of feature distribution by t-SNE associated with the class label. (a) Feature extracted by baseline model. (b) Feature extracted by the network with proposed IB loss only. (c) Feature extracted by the proposed model. (Best viewed in color and zooming in.)" + ], + "image_footnote": [], + "bbox": [ + 763, + 488, + 885, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The visualization result is consistent with the performance comparison in Table 4. As can be seen, the mixed classes of the baseline model in Fig.5(a) are no longer intermingled in Fig.5(b). It means our framework with IB loss can effectively improve the discriminative power of the features. When adding the memory network, almost all the clusters can concentrate on their centroids. It indicates that with the memory network, the predictive information can be clearer, and the inner-class differences become narrowed. It allows the mixed classes to be more easily distinguished from each other in the encoding space.", + "bbox": [ + 496, + 688, + 890, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition to utilizing t-SNE visualizations, we give some more examples to effectively illustrate how the proposed network mitigates the impact of gesture-irrelevant", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20975", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eafc46a40ab01c08fb204925b29ccfc3d65dac70f8445d125dd5755777ecdac8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 90, + 447, + 219 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/4e87df8e023872fe0f63ec3de54e5c1088817c4c374fae8ca3bbf512857c09f7.jpg", + "image_caption": [ + "Figure 6. An analysis of how the proposed network improves the performance. (a) The confusion matrix of baseline. (b) The confusion matrix of the proposed network. (c) Intuitive presentation of the irrelevant factors affecting gesture recognition." + ], + "image_footnote": [], + "bbox": [ + 78, + 222, + 468, + 289 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "factors and ultimately enhances performance. In Fig.6(a) and (b), we first visualize the confusion matrice of the baseline and the proposed network. As can be seen, ours can apparently avoid most of the wrong classifications. Then let us consider some concrete instances of gestures that are misclassified by the baseline model. As illustrated in the confusion matrix of the baseline model, Class 5, namely cut paper is wrongly categorized as Class 15 of open laptop. This confusion is primarily attributed to the resemblance in environmental conditions. As shown in Fig.6(c), both scenarios share a similar desk setup, and the overexposed laptop seems also like a white paper to some extent. Another example is Class 2 of clean table being wrongly deemed as Class 35 of wave hand. The similarities in hand movement and positioning lead to the misguided classification of these gestures. These examples prove that overfitting to these environmental cues rather than learning a robust feature representation of gesture-relevant factors results in the wrong predictions. By contrast, our method is designed to learn the essential feature of one type of gesture. Therefore, it avoids being influenced by extraneous contextual information, leading to remarkable improvement in performance.", + "bbox": [ + 75, + 377, + 472, + 710 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 723, + 194, + 739 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we present a framework that aims to improve the robustness of feature representation for RGB-D gesture recognition based on the information bottleneck theory. We analyze the factors that are relevant and irrelevant to gestures using mutual information and design a loss function that disentangles the task-relevant predictive cues from disturbing superfluous information. Additionally, we use a memory network to overlay the encoding feature of each sample by memory writing and reading. This process attenuates nuisances and highlights task-relevant informa", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "tion shared by all samples. Experiments on three public datasets demonstrate that our approach produces a superior feature representation and achieves better performance than state-of-the-art methods.", + "bbox": [ + 496, + 90, + 892, + 151 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 167, + 660, + 185 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "The work was jointly supported by the National Natural Science Foundation of China under grants No.62002271, 62272364, and 62202360, the National Key R&D Program of China under No.2022ZD0117103, Teaching Reform Project of Shaanxi Higher Continuing Education under No.21XJZ004, Guangxi Key Laboratory of Trusted Software under No.KX202041 and the Fundamental Research Funds for the Central Universities under No.ZYTS23213.", + "bbox": [ + 496, + 194, + 893, + 315 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 501, + 330, + 596, + 347 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alessandro Achille and Stefano Soatto. 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In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pages 5802-5810, 2019." + ], + "bbox": [ + 501, + 92, + 893, + 809 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20978", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Robust Representations with Information Bottleneck and Memory Network for RGB-D-based Gesture Recognition/ffcfd550-d4a2-4cb4-a120-2a5976bb8508_model.json b/2023/Learning Robust Representations with Information Bottleneck and Memory Network for RGB-D-based Gesture Recognition/ffcfd550-d4a2-4cb4-a120-2a5976bb8508_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7f403e6890ca47d8a112ed2a46fce6f806c586 --- /dev/null +++ b/2023/Learning Robust Representations with Information Bottleneck and Memory Network for RGB-D-based Gesture Recognition/ffcfd550-d4a2-4cb4-a120-2a5976bb8508_model.json @@ -0,0 +1,2554 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.17, + 0.131, + 0.803, + 0.177 + ], + "angle": 0, + "content": "Learning Robust Representations with Information Bottleneck and Memory Network for RGB-D-based Gesture Recognition" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.202, + 0.79, + 0.223 + ], + "angle": 0, + "content": "Yunan Li\\(^{1,2,3}\\) Huizhou Chen\\(^{1,2}\\) Guanwen Feng\\(^{1,2}\\) Qiguang Miao\\(^{1,2,3*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.223, + 0.726, + 0.239 + ], + "angle": 0, + "content": "\\(^{1}\\) School of Computer Science and Technology, Xidian University, China" + }, + { + "type": "text", + "bbox": [ + 0.269, + 0.24, + 0.702, + 0.256 + ], + "angle": 0, + "content": "\\(^{2}\\) Xi'an Key Laboratory of Big Data and Intelligent Vision, China" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.258, + 0.851, + 0.275 + ], + "angle": 0, + "content": "3 Key Laboratory of Smart Human-Computer Interaction and Wearable Technology of Shaanxi Province, China" + }, + { + "type": "text", + "bbox": [ + 0.162, + 0.278, + 0.808, + 0.293 + ], + "angle": 0, + "content": "{yunanli, qgmiao}@xidian.edu.cn, {huizhouchen, gwfeng-1}@stu.xidian.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.474, + 0.722 + ], + "angle": 0, + "content": "Although previous RGB-D-based gesture recognition methods have shown promising performance, researchers often overlook the interference of task-irrelevant cues like illumination and background. These unnecessary factors are learned together with the predictive ones by the network and hinder accurate recognition. In this paper, we propose a convenient and analytical framework to learn a robust feature representation that is impervious to gesture-irrelevant factors. Based on the Information Bottleneck theory, two rules of Sufficiency and Compactness are derived to develop a new information-theoretic loss function, which cultivates a more sufficient and compact representation from the feature encoding and mitigates the impact of gesture-irrelevant information. To highlight the predictive information, we further integrate a memory network. Using our proposed content-based and contextual memory addressing scheme, we weaken the nuisances while preserving the task-relevant information, providing guidance for refining the feature representation. Experiments conducted on three public datasets demonstrate that our approach leads to a better feature representation and achieves better performance than state-of-the-art methods. The code of our method is available at: https://github.com/Carpumpkin/InBoMem." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Gesture recognition based on RGB-D video has raised much attention of researchers since it has many applications, such as visual surveillance, intelligent transportation, and particularly, human-computer interaction (HCI) [48]. The development of CNN family [35, 5, 26], RNN family [27, 11], and Transformer-based methods [15, 57, 54]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.325, + 0.895, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.5, + 0.895, + 0.653 + ], + "angle": 0, + "content": "Figure 1. Diagram of our principle. The feature of a gesture sample can be decomposed into the essential gesture feature and gesture-irrelevant ones, such as the background, illumination, and the performer's appearance. The former provides predictive information whereas the latter is superfluous. Based on the information bottleneck theory, we can eliminate these disturbing nuisances by minimizing the superfluous information. Meanwhile, as the predictive feature in different samples is all the same, we leverage the memory network to store and \"overlay\" them, and then highlight the gesture-relevant predictive feature as the guidance for learning a robust feature representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.892, + 0.716 + ], + "angle": 0, + "content": "promote the improvement of recognition performance significantly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Although great progress has been made in this field, the attention has always been drawn to boost performance via better network structure [50, 48, 55, 56] or by introducing extra modalities of data [6, 18, 23, 19]. The interference of gesture-irrelevant factors is hardly noticed. In most real-world gesture recognition scenarios, the dynamic variations are in two aspects. One is based on the motion of the gesture itself like trajectories of hands/arms, and is crucial to the recognition task. The other is related to environmental influences like illumination, backgrounds, and the performers' appearances as depicted in Fig.1. The gesture performing-related factors, such as the velocity, performer's" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20968" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.212 + ], + "angle": 0, + "content": "concentration, and understanding of the gesture can also affect the quality of gesture presentation. When training a network for gesture recognition, these gesture-irrelevant factors may be learned as a kind of feature, and thus result in some inner-class differences hindering the recognition performance. Therefore, it is necessary to disentangle the recognition-relevant and redundant information to refine the feature representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.218, + 0.471, + 0.64 + ], + "angle": 0, + "content": "In order to disentangle the recognition task-relevant information and the disturbing gesture-irrelevant factors, we refer to the theory of Information Bottleneck (IB) [34], which engages mutual information (MI) and provides an information-theoretic objective for solving this problem. The essential idea of IB is mapping the observation of an input to a sophisticated representation, which retains the desired characteristics with respect to the prediction of label and simultaneously minimizes the redundant information. Many methods leverage IB to learn robust representations for downstream tasks like unsupervised multi-view learning [8], Person Re-identification [33] and human pose estimation [20]. In this process, the sophisticated representation is critical since it ensures a compact feature encoding that avoids the interference of task-irrelevant factors. However, it is difficult to obtain such a representation directly with the original IB theory. Approximating MI in high dimensions is hard [25], and thus the task-irrelevant distractors may not be removed. Even though some recent techniques ease the constraint by transforming this issue to a network optimization problem without explicitly estimating MI [33], the joint optimization of feature encoding and such a representation encoding blindly may fail to reach a satisfied representation since no explicit standard of \"good representation\" is given. Therefore, to refine the feature representation, we should explicitly highlight what the predictive information is, and take it as guidance for the refinement of the feature representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Combining these concerns, we propose an analytic framework to learn a robust representation for RGB-D-based gesture recognition. To address gesture-irrelevant factors, we employ the Information Bottleneck (IB) principle to unify them as \"superfluous information\", in contrast to predictive information like motion trajectories. Then we derive a new objective that compresses the superfluous information in the encoding space and emphasizes the predictive one. To achieve a sufficient yet compact feature representation required by IB, a memory network is incorporated for explicit guidance. We create a large external memory bank, where the shared predictive information is highlighted by overlaying the features in different memory slots. This process is achieved through memory manipulations of writing and reading. Then with the derived objective, the distribution of encoding features is pulled towards that of the robust representation, resulting in improved ges" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.093, + 0.7, + 0.107 + ], + "angle": 0, + "content": "ture recognition performance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.108, + 0.892, + 0.138 + ], + "angle": 0, + "content": "The contributions of our method can be summarized as three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.151, + 0.892, + 0.258 + ], + "angle": 0, + "content": "1. A framework to develop a robust feature representation for gesture recognition, along with the theoretical analysis based on IB. We extend the existing theoretical analysis and optimize the feature encoding to mitigate the interference of gesture-irrelevant factors. To the best of our knowledge, we are the first to provide insights from an information-theoretic view in this field." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.27, + 0.892, + 0.332 + ], + "angle": 0, + "content": "2. A scheme to explicitly distill the predictive information. Utilizing the memory network, we learn the predictive information from various samples to derive a sufficient and compact feature representation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.344, + 0.892, + 0.42 + ], + "angle": 0, + "content": "3. Experiments prove the effectiveness of our design and demonstrate that the proposed method achieves the state-of-the-art performance on three public RGB-D gesture datasets of IsoGD [40, 38], EgoGesture [4, 52] and THU-READ [31, 32]." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.151, + 0.892, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.638, + 0.452 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Evolution of gesture recognition. Conventional methods [39, 37] always employ spatiotemporal handcrafted features for gesture recognition. Recently, promotions of deep learning also bring new developments in dynamic gesture recognition. 3D CNNs [35] emerge for extracting spatiotemporal features, and many gesture recognition methods [17, 41, 53, 18, 6, 23, 19] are developed based on them. Meanwhile, RNN family [27, 11] that enables modeling sequence information also draws extensive attention in gesture recognition [53, 50, 58]. With the success of Transformer in computer vision tasks, there are also some researchers trying to improve the recognition performance by introducing Transformer-based structures [15, 57, 54]. Besides proposing new architectures, optimizing the network connection and structure is another option. Zhou et al. [55] and Yu et al. [48] notice the influence of network connection on low-level and high-level features, and employ network architecture search (NAS) for better architecture. Unlike previous methods that focus on improving the structure or connection of the network, we pay more attention to eliminating the disturbing gesture-irrelevant factors, which potentially lead to inner-class differences influencing recognition performance. With the theoretical analysis based on IB, we propose a new objective to achieve such an elimination." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Information bottleneck for representation learning. Information bottleneck [34] is an information-theoretic principle that has made great progress in representation learning and theoretical understanding of Deep Neural Networks (DNNs) [28]. However, the difficulty of calculating" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20969" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.092, + 0.597, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.236, + 0.378, + 0.248 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.604, + 0.094, + 0.847, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.186, + 0.848, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.261, + 0.892, + 0.331 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed framework. The encoding feature of a gesture video sample is first obtained as the observation \\( v \\). Then the predictive information is highlighted in the memory network via writing and reading, and the guidance of representation \\( z \\) is derived. With \\( \\mathcal{L}_{IB} \\) further refining the representation of \\( z \\) and pulling the distribution of \\( v \\) to \\( z \\), a more robust representation for gesture recognition is developed. (a) The pipeline of the framework. (b) Memory writing manipulation. (c) Memory reading manipulation. (Best viewed in color.)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.473, + 0.627 + ], + "angle": 0, + "content": "mutual information in high dimensions hinders its applications. To solve this problem, Alexenders et al. [2] demonstrate a variational approximation to parameterize the IB model. Peng et al. [24] propose a variational discriminator bottleneck for stable adversarial learning. Federici et al. [8] extend the IB theory to multi-view unsupervised learning. Tian et al. [33] present an analytical solution to fitting the mutual information via transferring the objective of IB to a variational self-distillation loss, and they also extend it to multi-view tasks. In contrast to these methods, our approach focuses on leveraging IB theory to disentangle the gesture-irrelevant factors and the predictive factors when encoding the features of a gesture sample. To fit the condition of feature disentanglement, beyond the Sufficiency constraint used in [33], we extend the IB theory by adding a Compactness constraint and give a more theoretically sound explanation of why they are both critical for eliminating task-irrelevant factors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Memory networks. Memory network [45, 10] is employed in both low-level and high-level vision tasks owing to its good ability in modeling long-term information. Li et al. [16] employ the memory networks to restore and calculate the weights for different stages in image dehazing. Zhu et al. [59] use dynamic memory to achieve text-to-image synthesis. For high-level tasks, Yang and Chen [47] employ a dynamic memory network for visual tracking. Cai et al. [3] design a memory matching network for one-shot learning, which writes/reads for training and inference phases, respectively. Zhang et al. [49] design a cross-modal memory structure to store multimodal information for a few-shot recognition task. Eom et al. [7] design a spatial and temporal memory network (STMN) for video-based pedestrian re-identification tasks. Compared with the above literature, the role that the memory network plays in this study is quite different. We do not simply use it for a large external space, but design different addressing strategies for writing and read" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.355, + 0.747, + 0.371 + ], + "angle": 0, + "content": "ing according to their different goals." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.385, + 0.673, + 0.403 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.892, + 0.44 + ], + "angle": 0, + "content": "3.1. Refining Feature Representation with Information Bottleneck" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.646 + ], + "angle": 0, + "content": "Gesture-irrelevant factors are non-negligible since they cause significant divergence in even one class of gesture videos. However, these factors are always intertwined with predictive information like the hands/arms movement when encoding. Even some approaches [43, 55] attempt to leverage the attention mechanism to focus on motion trajectories of gestures, the nuisances are inevitably learned and impact the recognition performance. The principle of information bottleneck [34] is to build a robust feature representation by discarding all information that is not useful for a given task while retaining the predictive one. Based on it, we disentangle the gesture-relevant and -irrelevant factors, and thereby refine the feature representation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.665, + 0.649, + 0.68 + ], + "angle": 0, + "content": "3.1.1 Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Suppose we have a set of input gesture videos, which are marked as \\(\\mathcal{X} = \\{x_1,x_2,\\ldots ,x_n\\}\\). These inputs fall into \\(\\mathcal{V} = \\{y_{1},y_{2},\\dots,y_{m}\\}\\) classes. Obviously, the task of gesture recognition is mapping arbitrary gesture sample \\(x\\in \\mathcal{X}\\) into the corresponding class \\(y\\). Let \\(v\\in \\mathcal{V}\\) be an observation of \\(x\\), where \\(\\mathcal{V}\\) is the set of features. In deep learning, \\(v\\) is usually the feature of \\(x\\) extracted by an encoder parameterized by \\(\\theta\\), namely \\(v = E_{\\theta}(x)\\). In general, supervised learning promotes \\(v\\) to involve more predictive information with respect to \\(y\\), but it inevitably contains some task-irrelevant factors. As shown in Fig.3, imagining there is a good representation \\(z\\in \\mathcal{Z}\\), which keeps sufficient predictive information but no task-irrelevant information. Then pulling \\(v\\) to \\(z\\) can result in a more robust feature representation. Theoretically, tak" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20970" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.089, + 0.429, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.286, + 0.471, + 0.358 + ], + "angle": 0, + "content": "Figure 3. The relations of the information entropy and mutual information among observation \\( v \\), representation \\( z \\) and label \\( y \\). The predictive information is the mutual information between \\( v \\) or \\( z \\) and \\( y \\). The superfluous information is the conditional mutual information of \\( v \\) and \\( z \\) given \\( y \\), namely \\( I(v;z) - I(z;y) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.47, + 0.44 + ], + "angle": 0, + "content": "ing \\( v, z \\), and \\( y \\) as three random variables, the optimization goal is to maximize the mutual information between \\( z \\) and \\( y \\) while minimizing that of \\( z \\) and \\( v \\), and that is the essential principle of IB." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.456, + 0.367, + 0.472 + ], + "angle": 0, + "content": "3.1.2 Information Bottleneck Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.47, + 0.631 + ], + "angle": 0, + "content": "According to the definition of IB, a good representation \\( z \\) should satisfy two rules: 1) keeping sufficient discriminative information to identity \\( y \\), and 2) avoiding encoding task-irrelevant information, specifically, the gesture-irrelevant appearance variations in this task. The first one is defined as Sufficiency of \\( z \\) for \\( y \\) [1, 8, 33]. Ideally, the Sufficiency rule is satisfied if and only if \\( I(z; y) = I(v; y) \\). However, in general, \\( I(z; y) \\) is less than \\( I(v; y) \\) due to the information loss during encoding. Therefore, we need to minimize such a loss and derive an objective function as:" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.638, + 0.47, + 0.656 + ], + "angle": 0, + "content": "\\[\n\\min [ I (v; y) - I (z; y) ]. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.662, + 0.47, + 0.707 + ], + "angle": 0, + "content": "The second one can be defined as Compactness. According to [8], the mutual information \\( I(v;z) \\) between \\( v \\) and \\( z \\) can be subdivided as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.714, + 0.469, + 0.751 + ], + "angle": 0, + "content": "\\[\nI (v; z) = \\underbrace {I (z ; y)} _ {\\text {p r e d i c t i v e i n f o r m a t i o n}} + \\underbrace {I (v ; z | y)} _ {\\text {s u p e r f l u o u s i n f o r m a t i o n}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.757, + 0.47, + 0.879 + ], + "angle": 0, + "content": "where the first term on the right side is the mutual information between \\( z \\) and \\( y \\), indicating the information contained in \\( z \\) for label prediction. The second one is the conditional mutual information of \\( v \\) and \\( z \\) given the value of \\( y \\). In other words, it is the task-irrelevant information in \\( z \\). A compact feature representation requires \\( I(v;z|y) \\) approaching 0. Therefore, we need to minimize \\( I(v;z|y) \\), and we have the second objective function as:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.885, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\min [ I (v; z) - I (z; y) ]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "Combine Eq.(1) and Eq.(3), the entire objective can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.135, + 0.892, + 0.152 + ], + "angle": 0, + "content": "\\[\n\\min \\left[ I (v; y) - I (z; y) + I (v; z) - I (z; y) \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.164, + 0.892, + 0.24 + ], + "angle": 0, + "content": "with which both the rules of Sufficiency and Compactness can be satisfied. However, solving it by directly approximating MI is hard. According to the definition of mutual information, we can use conditional entropy and joint entropy to express Eq.(4) as:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.252, + 0.892, + 0.27 + ], + "angle": 0, + "content": "\\[\n\\min [ H (y | z) - H (y | v) + H (z, y) ], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.281, + 0.892, + 0.327 + ], + "angle": 0, + "content": "where \\( H(y|z) \\) is the conditional entropy of \\( y \\) with \\( z \\) given, and \\( H(z,y) \\) is the joint entropy of \\( z \\) and \\( y \\). Inspired by [33], we can approximate Eq.(5) via a loss function as:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.34, + 0.892, + 0.357 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I B} = \\mathcal {L} _ {K L D} \\left(\\mathbb {P} _ {v} | | \\mathbb {P} _ {z}\\right) + \\mathcal {L} _ {c e} (z, y), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.368, + 0.892, + 0.445 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{KLD}(\\cdot ||\\cdot)\\) and \\(\\mathcal{L}_{ce}(\\cdot ,\\cdot)\\) are KL-divergence and cross-entropy loss, respectively. \\(\\mathbb{P}_v = p(y|v)\\) and \\(\\mathbb{P}_z = p(y|z)\\) are the probability of \\(v\\) and \\(z\\) in predicting \\(y\\), respectively. The detailed derivation can be found in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.454, + 0.892, + 0.485 + ], + "angle": 0, + "content": "3.2. Distilling Predictive Information with Memory Network" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.493, + 0.892, + 0.675 + ], + "angle": 0, + "content": "Note that according to Sufficient and Compactness rules, \\( z \\) is from \\( v \\) and is supposed to contain all the predictive information with respect to \\( y \\). Tian et al. [33] design a new encoder \\( E_{\\phi} \\) to derive \\( z \\). However, optimizing \\( E_{\\theta}(v|x) \\) and \\( E_{\\phi}(z|v) \\) simultaneously can only ensure the consistency of \\( v \\) and \\( z \\). There is no guarantee that one more encoder can lead to a more compact representation. As shown in Fig.1, overlaying the samples can emphasize the shared predictive information, i.e., motions of hands and arms related to the gesture, and weaken the sample-specific gesture-irrelevant factors. To this end, we achieve such an \"overlay\" process in a differentiable way via memory network." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.676, + 0.892, + 0.751 + ], + "angle": 0, + "content": "In our implementation, we construct a \\(n \\times m\\) memory bank for each gesture class, where \\(n\\) is the number of memory slots, and \\(m\\) is the length of feature vector in each slot. The explicit optimization on \\(z\\) is performed by two manipulations of memory, writing and reading." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.673, + 0.787 + ], + "angle": 0, + "content": "3.2.1 Memory Writing" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Memory writing is a manipulation that writes the encoding feature of observation \\( v \\) into the memory bank. In practice, it is achieved in a two-stage process. In the first stage, if there is an available memory slot, \\( v \\) can be directly written to it. In the second stage, when all memory slots are full, the process becomes more complicated and consists of two steps as follows." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20971" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "Forget. In the early stage, \\( E_{\\theta}(v|x) \\) is not well trained, and thus \\( v \\) inevitably contains some interference factors. These features may contaminate the memories. Therefore, we impose a forget vector \\( \\mathbf{e} \\), a \\( n \\times 1 \\) vector that has \\( n \\) components corresponding to \\( n \\) memory slots. It attenuates along with the training epoch since the predictive information dominates after times of training. The forget step can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.221, + 0.47, + 0.24 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {M}} ^ {t} (i) = \\mathbf {M} ^ {t - 1} (i) \\left(1 - e ^ {t} (i)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.47, + 0.324 + ], + "angle": 0, + "content": "where \\(\\mathbf{M}\\) is the memory bank, and \\(i\\in \\{1,2,\\dots ,n\\}\\) indicates the position of memory slot. \\(t - 1\\) and \\(t\\) imply two adjacent iterations of the optimization process. Updating memory from iteration \\(t - 1\\) to \\(t\\) is implemented by the Hadamard product." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.324, + 0.471, + 0.386 + ], + "angle": 0, + "content": "Gated writing. When writing the encoding feature of \\( v^t \\) into the memory, we utilize a gated writing strategy. We calculate the correlation between the \\( v^t \\) and features in each slot and update the memory as:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.394, + 0.47, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} ^ {t} (i) = \\tilde {\\mathbf {M}} ^ {t} (i) + w _ {o} ^ {t} (i) v ^ {t}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.47, + 0.466 + ], + "angle": 0, + "content": "where \\( w_{o}^{t}(i) \\) is a gating weight at \\( i \\)-th slots of \\( \\mathbf{w}_{o}^{t} \\). It measures the correlation between \\( v^{t1} \\) and \\( \\tilde{\\mathbf{M}}^t (i) \\). We have a constraint on \\( \\mathbf{w}_o \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.474, + 0.469, + 0.515 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\sum_ {i} w _ {o} (i) = 1, \\\\ 0 \\leq w _ {o} (i) \\leq 1. \\end{array} \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.525, + 0.47, + 0.556 + ], + "angle": 0, + "content": "With the gating strategy, we can write \\( v^t \\) to different memory slots adaptively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.573, + 0.254, + 0.589 + ], + "angle": 0, + "content": "3.2.2 Memory Reading" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.627 + ], + "angle": 0, + "content": "Memory reading is the key step for deriving \\( z \\). It is defined as a weighted sum of features in the memory slots:" + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.636, + 0.47, + 0.668 + ], + "angle": 0, + "content": "\\[\nz ^ {t} = \\sum_ {i} w _ {r} ^ {t} (i) \\mathbf {M} ^ {t} (i), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.47, + 0.738 + ], + "angle": 0, + "content": "where \\( z^t \\) is the representation yielded from the memory at iteration \\( t \\) with predictive information highlighted. Like writing, the reading weight also obeys the constraints in Eq.(9)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.275, + 0.772 + ], + "angle": 0, + "content": "3.2.3 Memory Addressing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.856 + ], + "angle": 0, + "content": "Although we have shown the way to access memories according to Eq.(7)-(10), the weighting mechanism remains unveiled. As shown in Fig.4, we design a two-level addressing scheme to ensure the addressing process can meet the essential requirement of memory writing and reading." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": "\\(^1 v\\) and \\(z\\) are \\(n\\times 1\\) feature vectors in the memory manipulations. Their notations hereby are not changed for the consistency with the expressions in information bottleneck theory in Sec.3.1." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.885, + 0.237 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.241, + 0.894, + 0.283 + ], + "angle": 0, + "content": "Figure 4. Diagram of two memory addressing strategies. (The length of the feature vector is omitted for simplicity. Best viewed in color.)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.304, + 0.893, + 0.349 + ], + "angle": 0, + "content": "Content-based addressing. The content-based addressing focuses on the correlation between \\( v \\) and features in each slot. It can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.354, + 0.892, + 0.39 + ], + "angle": 0, + "content": "\\[\nw _ {c} (i) = \\frac {\\exp (\\phi [ v , \\mathbf {M} (i) ])}{\\sum_ {j} \\exp (\\phi [ v , \\mathbf {M} (j) ])}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.395, + 0.893, + 0.563 + ], + "angle": 0, + "content": "where \\(\\phi[\\cdot, \\cdot]\\) is the correlation measurement function. Unlike [10], our measurement for writing and reading is different. When writing into the memory, the process is analogous to clustering. Similar \\(v\\) should be put into one slot to keep the variety of the memory bank. Memory reading is the contrary. If we weigh the slots containing similar features to \\(v\\) higher, the superfluous information cannot be removed. Therefore, instead of simply calculating the similarity, we add a gating parameter \\(\\sigma\\) for the correlation measurement \\(\\phi\\). Taking the cosine similarity as the naive similarity measurement, we define \\(\\phi[\\cdot, \\cdot]\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.568, + 0.891, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\phi [ \\cdot , \\cdot ] = 1 ^ {\\sigma} + (- 1) ^ {\\sigma} D _ {c o s s i m} (\\cdot , \\cdot), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.593, + 0.89, + 0.622 + ], + "angle": 0, + "content": "where \\( D_{\\text{cossim}} \\) is the cosine similarity and the gating flag \\( \\sigma \\) is set to 1 for reading and 0 for writing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.623, + 0.892, + 0.729 + ], + "angle": 0, + "content": "Contextual addressing. Content-based addressing considers from the view of relations between \\( v \\) itself and the feature in each memory slot. Analyzing the relations between memory slots also benefits the learning of predictive information. Therefore, we develop the contextual addressing scheme by imposing the influence of neighbor slots' weights as:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.734, + 0.892, + 0.765 + ], + "angle": 0, + "content": "\\[\nw _ {t} (i) = \\sum_ {i} w _ {c} (i) b _ {\\Omega} \\left(d _ {i}\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.772, + 0.892, + 0.817 + ], + "angle": 0, + "content": "where \\( b_{\\Omega}(d_i) = \\exp (d_i^2 / 2\\sigma^2) \\) is a bell-shaped balance function, which gives slots in neighbor \\( \\Omega \\) decreasing weights along with their distances \\( d_i \\) to slot \\( i \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.818, + 0.892, + 0.864 + ], + "angle": 0, + "content": "Like [46], we also introduce a temperature parameter that controls the concentration level of the distribution. Then we obtain the final weight as:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.869, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\nw (i) = \\frac {\\exp \\left(w _ {t} (i) ^ {\\tau}\\right)}{\\sum_ {j} \\exp \\left(w _ {t} (j) ^ {\\tau}\\right)}, \\tag {14}\n\\]" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20972" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "where \\(\\tau\\) is the temperature factor that can amplify the focusing degree on each memory slot by enlargement." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.131, + 0.245, + 0.148 + ], + "angle": 0, + "content": "3.3. Training Scheme" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.155, + 0.468, + 0.244 + ], + "angle": 0, + "content": "The training process consists of two parts. One is related to the original gesture recognition task, and it can be accomplished by using the cross-entropy loss function. The other is focused on refining the feature representation, which is achieved by Eq.(6), namely our proposed loss function based on IB. Then the overall loss is:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.26, + 0.468, + 0.277 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {c e} + \\beta (W \\cdot \\mathcal {L} _ {I B}), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.283, + 0.468, + 0.373 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{ce}\\) refers to cross-entropy loss, which is the only task-relevant loss for the original gesture recognition, and \\(\\beta\\) is a balance parameter. Since the memory relies on a series of \\(v\\), it needs some time to optimize the encoder \\(E_{\\theta}\\) first. Therefore, we add a warm-up coefficient \\(W\\), which can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.386, + 0.468, + 0.403 + ], + "angle": 0, + "content": "\\[\nW = \\max (0, (1 - \\exp (- E + \\varepsilon))), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.414, + 0.468, + 0.445 + ], + "angle": 0, + "content": "where \\(E\\) represents the current epoch and \\(\\varepsilon\\) is a warm-up hyper-parameter that determines when \\(L_{IB}\\) starts to effect." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.458, + 0.202, + 0.475 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.483, + 0.274, + 0.499 + ], + "angle": 0, + "content": "4.1. Experimental Setups" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.468, + 0.779 + ], + "angle": 0, + "content": "The proposed method is implemented with PyTorch on a NVIDIA RTX 3090 GPU. We choose Res3D-18 [36] as our backbone. The input data is spatially resized to \\(256 \\times 256\\) first, and then randomly/center cropped into \\(224 \\times 224\\) in the training/inference phase, respectively. In the temporal domain, it is randomly/uniformly sampled to 32-frame videos in the training/inference phase, respectively. We use the SGD optimizer with a weight decay of 0.0004 and momentum of 0.9. We fix the mini-batch size as 7. The initial learning rate is set to 0.003 and then it decreases with a scheme of noisy linear cosine decay. The training process stops after 15 epochs for IsoGD and EgoGesture datasets and 80 epochs for THU-READ dataset since the last one has fewer samples. The temperature parameter \\(\\tau\\) for memory bank is set to 10, and the number of memory slots is 5. The warm-up parameter \\(\\varepsilon\\) is 3 for IsoGD and EgoGesture datasets is 10 for THU-READ, respectively. The balance parameter \\(\\beta\\) is set to 10 due to the ratio of two losses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.442, + 0.803 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The proposed method is compared with state-of-the-art methods on three datasets of IsoGD [40, 38], EgoGesture [4, 52], and THU-READ [31, 32]. Unlike recent SOTA methods [48, 55, 57] that are first pre-trained on the 20BN-Jester gesture dataset [21], our network does not need any other extra pre-train models but employs the backbone" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "Res3D-18 model with its default settings in PyTorch. As the proposed method does not focus on multimodal fusion, we just employ a simple average fusion scheme to obtain the RGB+D result." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.171, + 0.715, + 0.185 + ], + "angle": 0, + "content": "4.2.1 Performance on IsoGD" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.194, + 0.892, + 0.345 + ], + "angle": 0, + "content": "Chalearn IsoGD dataset is a large-scale RGB-D dataset with 249 classes of gestures. It can be divided into three subsets: training set (35,878 videos), validation set (5,784 videos), and testing set (6,271 videos). This dataset is also used from two rounds of Chalearn LAP large-scale isolated gesture recognition challenge. Samples in Fig.1 are from this dataset. The various appearances in this dataset make it hard to achieve accurate recognition. Thus it can be a good benchmark to verify whether our framework is effective to eliminate the influence of gesture-irrelevant factors or not." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.346, + 0.892, + 0.648 + ], + "angle": 0, + "content": "The comparison on the Chalearn IsoGD dataset is shown in Table 1. Following the previous methods [50, 58, 55, 48, 57], we also report the performance on the validation subset for a fair comparison. Without loss of generality, the performance on the testing subset is also reported in the supplementary material. As can be seen, employing CNNs can bring a large improvement when compared with the hand-icraft feature-based method [37]. Then improving the network structure or altering the connection via NAS can also promote performance to a varying extent. Compared with these methods, our framework focuses on finding a better feature representation to eliminate gesture-irrelevant factors and achieves significant boosting. The proposed method outperforms the previous SOTA, Zhou et al.'s [55] near \\(8\\%\\) and \\(4\\%\\) on RGB and depth data, respectively. Besides the good performance on single modality, the RGB-D result is also better than Zhou et al.'s [57] at about \\(7\\%\\), even though they design a new fusion module whereas ours is a simple average fusion. It proves a good feature representation is critical for improving recognition performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.753, + 0.681 + ], + "angle": 0, + "content": "4.2.2 Performance on EgoGesture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.81 + ], + "angle": 0, + "content": "EgoGesture dataset contains 24,161 egocentric hand gesture clips of 83 classes from 50 distinct subjects. Videos in this dataset focus on the interaction with wearable devices from a first-person view across multiple indoor and outdoor scenes. Compared with Chalearn IsoGD dataset, the number of classes of this dataset is fewer, but this first-person dataset suffers more problems like blurring and various viewpoints since the camera is on the performers' heads." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As demonstrated in Table 2, the proposed method can also achieve a remarkable performance on the EgoGesture dataset. As the top accuracy on this dataset is very high (mostly beyond \\(90\\%\\)), it is not easy to make a significant improvement. However, ours still outperforms the second best one, Kopuklu et al.'s [14] over \\(1\\%\\) on RGB data despite" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20973" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.091, + 0.088, + 0.462, + 0.704 + ], + "angle": 0, + "content": "
ModalityMethodMain modelAccuracy(%)
RGBWang [44]bi-direction VDI36.60
Li [18]3D CNN37.28
Hu [12]DNN44.88
Miao [22]ResC3D45.07
Duan [6]2-stream CNN+C3D46.08
Zhang [51]convLSTM+C3D51.31
Zhang [50]ResC3D+convLSTM +MobileNet55.98
Zhu [58]ResC3D+ GatedConvLSTM +MobileNet+Pyramid57.42
Yu [48]SlowFast+NAS²58.88
Zhou [57]I3D+Transformer60.87
Zhou [55]I3D+DI+NAS62.66
OursRes3D-1870.88
depthWang [44]bi-direction DDI40.08
Li [18]3D CNN40.49
Hu [12]DNN48.96
Miao [22]ResC3D48.44
Duan [6]2-stream CNN+C3D54.95
Zhang [51]convLSTM+C3D49.81
Zhang [50]ResC3D+convLSTM +MobileNet53.28
Zhu [58]ResC3D+ GatedConvLSTM +MobileNet+Pyramid54.18
Yu [48]SlowFast+NAS²55.68
Zhou [57]I3D+Transformer60.17
Zhou [55]I3D+DI+NAS60.66
OursRes3D-1864.38
RGB+DWan [37]MFSK+BoVW18.65
Wang [44]bi-direction VDI+DDI44.80
Li [18]3D CNN52.04*
Hu [12]DNN54.14
Zhang [51]convLSTM+C3D55.29
Zhu [58]ResC3D+ GatedConvLSTM+ +MobileNet+Pyramid61.05
Miao [22]ResC3D64.40**
Yu [48]SlowFast+NAS²65.54
Zhou [55]I3D+DI+NAS66.62
Zhou [57]I3D+Transformer66.79
OursRes3D-1874.08
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.093, + 0.704, + 0.329, + 0.717 + ], + "angle": 0, + "content": "* Including saliency data as reported in [18]." + }, + { + "type": "table_footnote", + "bbox": [ + 0.093, + 0.717, + 0.312, + 0.73 + ], + "angle": 0, + "content": "** Including flow data as reported in [22]." + }, + { + "type": "list", + "bbox": [ + 0.093, + 0.704, + 0.329, + 0.73 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.737, + 0.449, + 0.751 + ], + "angle": 0, + "content": "Table 1. Comparison with SOTAs on Chalearn IsoGD Dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.901 + ], + "angle": 0, + "content": "just using a much simpler backbone of Res3D-18. The performance on depth data is also competitive but \\(0.66\\%\\) lower than the best one of Kopuklü et al.'s. It implies our feature representation refinement is more effective on RGB data. The reason behind it may be that compared with RGB data, the differences between depth samples are smaller (only the grayscale value changes), which makes it hard to distinguish the predictive cue from the excess information with" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.088, + 0.892, + 0.432 + ], + "angle": 0, + "content": "
ModalityMethodMain ModelAccuary(%)
RGBGraves [10]VGG16+LSTM74.70
Cao [4]C3D+LSTM +RLSTM89.30
Carreira [5]I3D90.33
Tang [30]SeST93.20
Yu [48]SlowFast+NAS293.31
Köpüklü [14]ResNeXt-10193.75
OursRes3D-1894.93
depthGraves [10]VGG16+LSTM77.70
Carreira [5]I3D89.47
Cao [4]C3D+LSTM +RLSTM90.60
Tang [30]SeST93.35
Köpüklü [14]ResNeXt-10194.03
Yu [48]SlowFast+NAS294.13
OursRes3D-1893.47
RGB+DGraves [10]VGG16+LSTM81.40
Cao [4]C3D+LSTM +RLSTM92.20
Carreira[5]I3D92.78
Joze[13]MMTM93.87
Yu[48]SlowFast+NAS295.52
OursRes3D-1895.72
" + }, + { + "type": "table_caption", + "bbox": [ + 0.523, + 0.439, + 0.869, + 0.454 + ], + "angle": 0, + "content": "Table 2. Comparison with SOTAs on EgoGesture Dataset." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.465, + 0.895, + 0.732 + ], + "angle": 0, + "content": "
ModalityMethodMain ModelAccuary(%)
RGBSimonyan [29]VGG41.90
Feichtenhofer [9]SlowFast69.58
Yu [48]SlowFast+NAS²71.25
Wang [42]ConvNet73.85
Li [15]Transformer80.42
Zhou [57]I3D+Transformer81.25
OursRes3D-1888.33
depthSimonyan [29]VGG34.06
Wang [42]ConvNet65.00
Feichtenhofer [9]SlowFast68.75
Yu [48]SlowFast+NAS²69.58
Li [15]Transformer76.04
Zhou [57]I3D+Transformer77.92
OursRes3D-1882.91
RGB+DFeichtenhofer [9]SlowFast76.25
Yu [48]SlowFast+NAS²78.38
Li [15]Transformer84.90
Zhou [57]I3D+Transformer87.04
OursRes3D-1890.51
" + }, + { + "type": "table_caption", + "bbox": [ + 0.52, + 0.739, + 0.871, + 0.754 + ], + "angle": 0, + "content": "Table 3. Comparison with SOTAs on THU-READ Dataset." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.78, + 0.644, + 0.795 + ], + "angle": 0, + "content": "the memory network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.757, + 0.83 + ], + "angle": 0, + "content": "4.2.3 Performance on THU-READ" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "THU-READ dataset has 1920 videos of 40 classes, which are performed by 8 subjects. Although involving fewer videos and fewer classes, it is yet challenging due to the subtle intra-class differences and the background noise." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20974" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.089, + 0.441, + 0.176 + ], + "angle": 0, + "content": "
Suff.Comp.memory networkAcc(%)
RGBdepth
×××78.3369.58
✓××82.2973.43
✓✓×85.4176.76
✓✓✓88.3382.91
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.078, + 0.179, + 0.435, + 0.206 + ], + "angle": 0, + "content": "\\(^{*}\\) Suff. \\(=\\) Sufficiency, Comp. \\(=\\) Compactness Table 4. Impacts of components of the proposed framework." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.231, + 0.473, + 0.399 + ], + "angle": 0, + "content": "Table 3 reports the comparison on the THU-READ dataset. The results are reported by averaging all 4 splits under CS protocol as per [32]. The proposed method also achieves the best performance on this dataset. Compared with the second best one of Zhou et al. [57], which employs a combination of I3D and Transformer network, our results are still \\(7\\%\\) and \\(5\\%\\) better than theirs on RGB and depth data, respectively. For the RGB-D fusion result, the performance of the proposed method reaches \\(90.51\\%\\), and outperforms Zhou et al.'s at about \\(3\\%\\), even though we just utilize a simple average fusion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.409, + 0.231, + 0.425 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.47, + 0.583 + ], + "angle": 0, + "content": "The studies on the effectiveness of our designs, including representation refinement with IB and predictive information distillation with memory network, are first presented in this section. In order to evaluate our scheme using a memory network, we have also compared several different addressing strategies, including using cosine similarity only for addressing and using content-based addressing only. THU-READ dataset is employed for this ablation study. Without specific saying, the experimental settings are the same as mentioned in Section 4.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Impacts of components of the proposed framework. In Table 4, we show how the proposed framework helps to eliminate gesture-irrelevant factors and leads to a more compact and robust feature representation. We compare several strategies, including 1) the baseline of using Res3D-18 only, 2) optimizing with the Sufficiency rule only, 3) using both Sufficiency and Compactness rules, namely using the IB loss in Eq.(6), and 4) using IB loss and memory network. The performance is marked in rows with a checkmark or a cross, denoting whether the corresponding module is used or not. Compared with the baseline, optimizing under the IB theory, even only considering the Sufficiency rule can lead to a significant performance improvement. This demonstrates the importance of a good representation for recognition tasks. When extending the loss to involve the Compactness rule, even better performance can be achieved. Replacing the convolution-based IB module with the memory network encourages the deposition of predictive information and leads to another performance gain. This suggests the effectiveness of memory network for highlighting the predictive information explicitly." + }, + { + "type": "table", + "bbox": [ + 0.559, + 0.089, + 0.835, + 0.169 + ], + "angle": 0, + "content": "
addressing strategyAccuracy(%)
RGBdepth
cosine similarity only80.5171.76
content-based only84.5775.62
proposed method88.3382.91
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.173, + 0.892, + 0.188 + ], + "angle": 0, + "content": "Table 5. Performance with different memory addressing strategies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Effect of different addressing strategies. The effect of different addressing strategies is shown in Table 5. When only the cosine similarity is used for addressing, the performance is poor. This implies that similar \\( z \\) and \\( v \\) weaken the effectiveness of IB loss. After adding the gating flag \\( \\sigma \\), and even just using content-based addressing, the performance is improved significantly. When all the addressing strategies are combined, the performance is further boosted. This indicates that a combination of content-based and contextual addressing can leverage both inter- and intra-memory feature relations and achieve better performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.47 + ], + "angle": 0, + "content": "Visualization. To better illustrate how the robust presentation derived from our proposed framework shrinks the inner-class difference, which is mainly caused by gesture-irrelevant variations, we present a visualization of a 2D projection of feature encoding by t-SNE. The visualization is conducted on RGB data of the THU-READ dataset (CS3)." + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.488, + 0.633, + 0.583 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.558, + 0.589, + 0.576, + 0.6 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.489, + 0.761, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.686, + 0.589, + 0.702, + 0.6 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.489, + 0.887, + 0.583 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.814, + 0.589, + 0.83, + 0.6 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.604, + 0.892, + 0.675 + ], + "angle": 0, + "content": "Figure 5. Visualizing the projection of feature distribution by t-SNE associated with the class label. (a) Feature extracted by baseline model. (b) Feature extracted by the network with proposed IB loss only. (c) Feature extracted by the proposed model. (Best viewed in color and zooming in.)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.856 + ], + "angle": 0, + "content": "The visualization result is consistent with the performance comparison in Table 4. As can be seen, the mixed classes of the baseline model in Fig.5(a) are no longer intermingled in Fig.5(b). It means our framework with IB loss can effectively improve the discriminative power of the features. When adding the memory network, almost all the clusters can concentrate on their centroids. It indicates that with the memory network, the predictive information can be clearer, and the inner-class differences become narrowed. It allows the mixed classes to be more easily distinguished from each other in the encoding space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In addition to utilizing t-SNE visualizations, we give some more examples to effectively illustrate how the proposed network mitigates the impact of gesture-irrelevant" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20975" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.091, + 0.449, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.223, + 0.47, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.471, + 0.354 + ], + "angle": 0, + "content": "Figure 6. An analysis of how the proposed network improves the performance. (a) The confusion matrix of baseline. (b) The confusion matrix of the proposed network. (c) Intuitive presentation of the irrelevant factors affecting gesture recognition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.473, + 0.711 + ], + "angle": 0, + "content": "factors and ultimately enhances performance. In Fig.6(a) and (b), we first visualize the confusion matrice of the baseline and the proposed network. As can be seen, ours can apparently avoid most of the wrong classifications. Then let us consider some concrete instances of gestures that are misclassified by the baseline model. As illustrated in the confusion matrix of the baseline model, Class 5, namely cut paper is wrongly categorized as Class 15 of open laptop. This confusion is primarily attributed to the resemblance in environmental conditions. As shown in Fig.6(c), both scenarios share a similar desk setup, and the overexposed laptop seems also like a white paper to some extent. Another example is Class 2 of clean table being wrongly deemed as Class 35 of wave hand. The similarities in hand movement and positioning lead to the misguided classification of these gestures. These examples prove that overfitting to these environmental cues rather than learning a robust feature representation of gesture-relevant factors results in the wrong predictions. By contrast, our method is designed to learn the essential feature of one type of gesture. Therefore, it avoids being influenced by extraneous contextual information, leading to remarkable improvement in performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.196, + 0.74 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present a framework that aims to improve the robustness of feature representation for RGB-D gesture recognition based on the information bottleneck theory. We analyze the factors that are relevant and irrelevant to gestures using mutual information and design a loss function that disentangles the task-relevant predictive cues from disturbing superfluous information. Additionally, we use a memory network to overlay the encoding feature of each sample by memory writing and reading. This process attenuates nuisances and highlights task-relevant informa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.152 + ], + "angle": 0, + "content": "tion shared by all samples. Experiments on three public datasets demonstrate that our approach produces a superior feature representation and achieves better performance than state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.169, + 0.661, + 0.186 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.195, + 0.895, + 0.316 + ], + "angle": 0, + "content": "The work was jointly supported by the National Natural Science Foundation of China under grants No.62002271, 62272364, and 62202360, the National Key R&D Program of China under No.2022ZD0117103, Teaching Reform Project of Shaanxi Higher Continuing Education under No.21XJZ004, Guangxi Key Laboratory of Trusted Software under No.KX202041 and the Fundamental Research Funds for the Central Universities under No.ZYTS23213." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.332, + 0.597, + 0.348 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.358, + 0.895, + 0.399 + ], + "angle": 0, + "content": "[1] Alessandro Achille and Stefano Soatto. 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These unnecessary factors are learned together with the predictive ones by the network and hinder accurate recognition. In this paper, we propose a convenient and analytical framework to learn a robust feature representation that is impervious to gesture-irrelevant factors. Based on the Information Bottleneck theory, two rules of Sufficiency and Compactness are derived to develop a new information-theoretic loss function, which cultivates a more sufficient and compact representation from the feature encoding and mitigates the impact of gesture-irrelevant information. To highlight the predictive information, we further integrate a memory network. Using our proposed content-based and contextual memory addressing scheme, we weaken the nuisances while preserving the task-relevant information, providing guidance for refining the feature representation. Experiments conducted on three public datasets demonstrate that our approach leads to a better feature representation and achieves better performance than state-of-the-art methods. The code of our method is available at: https://github.com/Carpumpkin/InBoMem. + +# 1. Introduction + +Gesture recognition based on RGB-D video has raised much attention of researchers since it has many applications, such as visual surveillance, intelligent transportation, and particularly, human-computer interaction (HCI) [48]. The development of CNN family [35, 5, 26], RNN family [27, 11], and Transformer-based methods [15, 57, 54] + +![](images/7626cc362a25155f74395f367633f72e226bec79a2828f897ecc90cd3e8e8d1f.jpg) +Figure 1. Diagram of our principle. The feature of a gesture sample can be decomposed into the essential gesture feature and gesture-irrelevant ones, such as the background, illumination, and the performer's appearance. The former provides predictive information whereas the latter is superfluous. Based on the information bottleneck theory, we can eliminate these disturbing nuisances by minimizing the superfluous information. Meanwhile, as the predictive feature in different samples is all the same, we leverage the memory network to store and "overlay" them, and then highlight the gesture-relevant predictive feature as the guidance for learning a robust feature representation. + +promote the improvement of recognition performance significantly. + +Although great progress has been made in this field, the attention has always been drawn to boost performance via better network structure [50, 48, 55, 56] or by introducing extra modalities of data [6, 18, 23, 19]. The interference of gesture-irrelevant factors is hardly noticed. In most real-world gesture recognition scenarios, the dynamic variations are in two aspects. One is based on the motion of the gesture itself like trajectories of hands/arms, and is crucial to the recognition task. The other is related to environmental influences like illumination, backgrounds, and the performers' appearances as depicted in Fig.1. The gesture performing-related factors, such as the velocity, performer's + +concentration, and understanding of the gesture can also affect the quality of gesture presentation. When training a network for gesture recognition, these gesture-irrelevant factors may be learned as a kind of feature, and thus result in some inner-class differences hindering the recognition performance. Therefore, it is necessary to disentangle the recognition-relevant and redundant information to refine the feature representation. + +In order to disentangle the recognition task-relevant information and the disturbing gesture-irrelevant factors, we refer to the theory of Information Bottleneck (IB) [34], which engages mutual information (MI) and provides an information-theoretic objective for solving this problem. The essential idea of IB is mapping the observation of an input to a sophisticated representation, which retains the desired characteristics with respect to the prediction of label and simultaneously minimizes the redundant information. Many methods leverage IB to learn robust representations for downstream tasks like unsupervised multi-view learning [8], Person Re-identification [33] and human pose estimation [20]. In this process, the sophisticated representation is critical since it ensures a compact feature encoding that avoids the interference of task-irrelevant factors. However, it is difficult to obtain such a representation directly with the original IB theory. Approximating MI in high dimensions is hard [25], and thus the task-irrelevant distractors may not be removed. Even though some recent techniques ease the constraint by transforming this issue to a network optimization problem without explicitly estimating MI [33], the joint optimization of feature encoding and such a representation encoding blindly may fail to reach a satisfied representation since no explicit standard of "good representation" is given. Therefore, to refine the feature representation, we should explicitly highlight what the predictive information is, and take it as guidance for the refinement of the feature representation. + +Combining these concerns, we propose an analytic framework to learn a robust representation for RGB-D-based gesture recognition. To address gesture-irrelevant factors, we employ the Information Bottleneck (IB) principle to unify them as "superfluous information", in contrast to predictive information like motion trajectories. Then we derive a new objective that compresses the superfluous information in the encoding space and emphasizes the predictive one. To achieve a sufficient yet compact feature representation required by IB, a memory network is incorporated for explicit guidance. We create a large external memory bank, where the shared predictive information is highlighted by overlaying the features in different memory slots. This process is achieved through memory manipulations of writing and reading. Then with the derived objective, the distribution of encoding features is pulled towards that of the robust representation, resulting in improved ges + +ture recognition performance. + +The contributions of our method can be summarized as three-fold: + +1. A framework to develop a robust feature representation for gesture recognition, along with the theoretical analysis based on IB. We extend the existing theoretical analysis and optimize the feature encoding to mitigate the interference of gesture-irrelevant factors. To the best of our knowledge, we are the first to provide insights from an information-theoretic view in this field. +2. A scheme to explicitly distill the predictive information. Utilizing the memory network, we learn the predictive information from various samples to derive a sufficient and compact feature representation. +3. Experiments prove the effectiveness of our design and demonstrate that the proposed method achieves the state-of-the-art performance on three public RGB-D gesture datasets of IsoGD [40, 38], EgoGesture [4, 52] and THU-READ [31, 32]. + +# 2. Related work + +Evolution of gesture recognition. Conventional methods [39, 37] always employ spatiotemporal handcrafted features for gesture recognition. Recently, promotions of deep learning also bring new developments in dynamic gesture recognition. 3D CNNs [35] emerge for extracting spatiotemporal features, and many gesture recognition methods [17, 41, 53, 18, 6, 23, 19] are developed based on them. Meanwhile, RNN family [27, 11] that enables modeling sequence information also draws extensive attention in gesture recognition [53, 50, 58]. With the success of Transformer in computer vision tasks, there are also some researchers trying to improve the recognition performance by introducing Transformer-based structures [15, 57, 54]. Besides proposing new architectures, optimizing the network connection and structure is another option. Zhou et al. [55] and Yu et al. [48] notice the influence of network connection on low-level and high-level features, and employ network architecture search (NAS) for better architecture. Unlike previous methods that focus on improving the structure or connection of the network, we pay more attention to eliminating the disturbing gesture-irrelevant factors, which potentially lead to inner-class differences influencing recognition performance. With the theoretical analysis based on IB, we propose a new objective to achieve such an elimination. + +Information bottleneck for representation learning. Information bottleneck [34] is an information-theoretic principle that has made great progress in representation learning and theoretical understanding of Deep Neural Networks (DNNs) [28]. However, the difficulty of calculating + +![](images/a89e34bfb3433df569393dc097e1be2b34d9a925c69ba528e7da54e884201715.jpg) +(a) + +![](images/949b474d1ca209294d963d3b1660e11578a386c312772685554f0a614d5d19d7.jpg) + +![](images/9077c55c3db85a6b64c0dca185dd0d68c71b936886c9fc18805aac56d7228468.jpg) +Figure 2. Overview of the proposed framework. The encoding feature of a gesture video sample is first obtained as the observation $v$ . Then the predictive information is highlighted in the memory network via writing and reading, and the guidance of representation $z$ is derived. With $\mathcal{L}_{IB}$ further refining the representation of $z$ and pulling the distribution of $v$ to $z$ , a more robust representation for gesture recognition is developed. (a) The pipeline of the framework. (b) Memory writing manipulation. (c) Memory reading manipulation. (Best viewed in color.) + +mutual information in high dimensions hinders its applications. To solve this problem, Alexenders et al. [2] demonstrate a variational approximation to parameterize the IB model. Peng et al. [24] propose a variational discriminator bottleneck for stable adversarial learning. Federici et al. [8] extend the IB theory to multi-view unsupervised learning. Tian et al. [33] present an analytical solution to fitting the mutual information via transferring the objective of IB to a variational self-distillation loss, and they also extend it to multi-view tasks. In contrast to these methods, our approach focuses on leveraging IB theory to disentangle the gesture-irrelevant factors and the predictive factors when encoding the features of a gesture sample. To fit the condition of feature disentanglement, beyond the Sufficiency constraint used in [33], we extend the IB theory by adding a Compactness constraint and give a more theoretically sound explanation of why they are both critical for eliminating task-irrelevant factors. + +Memory networks. Memory network [45, 10] is employed in both low-level and high-level vision tasks owing to its good ability in modeling long-term information. Li et al. [16] employ the memory networks to restore and calculate the weights for different stages in image dehazing. Zhu et al. [59] use dynamic memory to achieve text-to-image synthesis. For high-level tasks, Yang and Chen [47] employ a dynamic memory network for visual tracking. Cai et al. [3] design a memory matching network for one-shot learning, which writes/reads for training and inference phases, respectively. Zhang et al. [49] design a cross-modal memory structure to store multimodal information for a few-shot recognition task. Eom et al. [7] design a spatial and temporal memory network (STMN) for video-based pedestrian re-identification tasks. Compared with the above literature, the role that the memory network plays in this study is quite different. We do not simply use it for a large external space, but design different addressing strategies for writing and read + +ing according to their different goals. + +# 3. Proposed Method + +# 3.1. Refining Feature Representation with Information Bottleneck + +Gesture-irrelevant factors are non-negligible since they cause significant divergence in even one class of gesture videos. However, these factors are always intertwined with predictive information like the hands/arms movement when encoding. Even some approaches [43, 55] attempt to leverage the attention mechanism to focus on motion trajectories of gestures, the nuisances are inevitably learned and impact the recognition performance. The principle of information bottleneck [34] is to build a robust feature representation by discarding all information that is not useful for a given task while retaining the predictive one. Based on it, we disentangle the gesture-relevant and -irrelevant factors, and thereby refine the feature representation. + +# 3.1.1 Preliminaries + +Suppose we have a set of input gesture videos, which are marked as $\mathcal{X} = \{x_1,x_2,\ldots ,x_n\}$ . These inputs fall into $\mathcal{V} = \{y_{1},y_{2},\dots,y_{m}\}$ classes. Obviously, the task of gesture recognition is mapping arbitrary gesture sample $x\in \mathcal{X}$ into the corresponding class $y$ . Let $v\in \mathcal{V}$ be an observation of $x$ , where $\mathcal{V}$ is the set of features. In deep learning, $v$ is usually the feature of $x$ extracted by an encoder parameterized by $\theta$ , namely $v = E_{\theta}(x)$ . In general, supervised learning promotes $v$ to involve more predictive information with respect to $y$ , but it inevitably contains some task-irrelevant factors. As shown in Fig.3, imagining there is a good representation $z\in \mathcal{Z}$ , which keeps sufficient predictive information but no task-irrelevant information. Then pulling $v$ to $z$ can result in a more robust feature representation. Theoretically, tak + +![](images/805f20162e52eefb49b64031603bd73da1cc8475f271ae5ebba2c28c1bc7ce0c.jpg) +Figure 3. The relations of the information entropy and mutual information among observation $v$ , representation $z$ and label $y$ . The predictive information is the mutual information between $v$ or $z$ and $y$ . The superfluous information is the conditional mutual information of $v$ and $z$ given $y$ , namely $I(v;z) - I(z;y)$ . + +ing $v, z$ , and $y$ as three random variables, the optimization goal is to maximize the mutual information between $z$ and $y$ while minimizing that of $z$ and $v$ , and that is the essential principle of IB. + +# 3.1.2 Information Bottleneck Objective + +According to the definition of IB, a good representation $z$ should satisfy two rules: 1) keeping sufficient discriminative information to identity $y$ , and 2) avoiding encoding task-irrelevant information, specifically, the gesture-irrelevant appearance variations in this task. The first one is defined as Sufficiency of $z$ for $y$ [1, 8, 33]. Ideally, the Sufficiency rule is satisfied if and only if $I(z; y) = I(v; y)$ . However, in general, $I(z; y)$ is less than $I(v; y)$ due to the information loss during encoding. Therefore, we need to minimize such a loss and derive an objective function as: + +$$ +\min [ I (v; y) - I (z; y) ]. \tag {1} +$$ + +The second one can be defined as Compactness. According to [8], the mutual information $I(v;z)$ between $v$ and $z$ can be subdivided as: + +$$ +I (v; z) = \underbrace {I (z ; y)} _ {\text {p r e d i c t i v e i n f o r m a t i o n}} + \underbrace {I (v ; z | y)} _ {\text {s u p e r f l u o u s i n f o r m a t i o n}}, \tag {2} +$$ + +where the first term on the right side is the mutual information between $z$ and $y$ , indicating the information contained in $z$ for label prediction. The second one is the conditional mutual information of $v$ and $z$ given the value of $y$ . In other words, it is the task-irrelevant information in $z$ . A compact feature representation requires $I(v;z|y)$ approaching 0. Therefore, we need to minimize $I(v;z|y)$ , and we have the second objective function as: + +$$ +\min [ I (v; z) - I (z; y) ]. \tag {3} +$$ + +Combine Eq.(1) and Eq.(3), the entire objective can be written as: + +$$ +\min \left[ I (v; y) - I (z; y) + I (v; z) - I (z; y) \right], \tag {4} +$$ + +with which both the rules of Sufficiency and Compactness can be satisfied. However, solving it by directly approximating MI is hard. According to the definition of mutual information, we can use conditional entropy and joint entropy to express Eq.(4) as: + +$$ +\min [ H (y | z) - H (y | v) + H (z, y) ], \tag {5} +$$ + +where $H(y|z)$ is the conditional entropy of $y$ with $z$ given, and $H(z,y)$ is the joint entropy of $z$ and $y$ . Inspired by [33], we can approximate Eq.(5) via a loss function as: + +$$ +\mathcal {L} _ {I B} = \mathcal {L} _ {K L D} \left(\mathbb {P} _ {v} | | \mathbb {P} _ {z}\right) + \mathcal {L} _ {c e} (z, y), \tag {6} +$$ + +where $\mathcal{L}_{KLD}(\cdot ||\cdot)$ and $\mathcal{L}_{ce}(\cdot ,\cdot)$ are KL-divergence and cross-entropy loss, respectively. $\mathbb{P}_v = p(y|v)$ and $\mathbb{P}_z = p(y|z)$ are the probability of $v$ and $z$ in predicting $y$ , respectively. The detailed derivation can be found in the supplementary material. + +# 3.2. Distilling Predictive Information with Memory Network + +Note that according to Sufficient and Compactness rules, $z$ is from $v$ and is supposed to contain all the predictive information with respect to $y$ . Tian et al. [33] design a new encoder $E_{\phi}$ to derive $z$ . However, optimizing $E_{\theta}(v|x)$ and $E_{\phi}(z|v)$ simultaneously can only ensure the consistency of $v$ and $z$ . There is no guarantee that one more encoder can lead to a more compact representation. As shown in Fig.1, overlaying the samples can emphasize the shared predictive information, i.e., motions of hands and arms related to the gesture, and weaken the sample-specific gesture-irrelevant factors. To this end, we achieve such an "overlay" process in a differentiable way via memory network. + +In our implementation, we construct a $n \times m$ memory bank for each gesture class, where $n$ is the number of memory slots, and $m$ is the length of feature vector in each slot. The explicit optimization on $z$ is performed by two manipulations of memory, writing and reading. + +# 3.2.1 Memory Writing + +Memory writing is a manipulation that writes the encoding feature of observation $v$ into the memory bank. In practice, it is achieved in a two-stage process. In the first stage, if there is an available memory slot, $v$ can be directly written to it. In the second stage, when all memory slots are full, the process becomes more complicated and consists of two steps as follows. + +Forget. In the early stage, $E_{\theta}(v|x)$ is not well trained, and thus $v$ inevitably contains some interference factors. These features may contaminate the memories. Therefore, we impose a forget vector $\mathbf{e}$ , a $n \times 1$ vector that has $n$ components corresponding to $n$ memory slots. It attenuates along with the training epoch since the predictive information dominates after times of training. The forget step can be expressed as: + +$$ +\tilde {\mathbf {M}} ^ {t} (i) = \mathbf {M} ^ {t - 1} (i) \left(1 - e ^ {t} (i)\right), \tag {7} +$$ + +where $\mathbf{M}$ is the memory bank, and $i\in \{1,2,\dots ,n\}$ indicates the position of memory slot. $t - 1$ and $t$ imply two adjacent iterations of the optimization process. Updating memory from iteration $t - 1$ to $t$ is implemented by the Hadamard product. + +Gated writing. When writing the encoding feature of $v^t$ into the memory, we utilize a gated writing strategy. We calculate the correlation between the $v^t$ and features in each slot and update the memory as: + +$$ +\mathbf {M} ^ {t} (i) = \tilde {\mathbf {M}} ^ {t} (i) + w _ {o} ^ {t} (i) v ^ {t}, \tag {8} +$$ + +where $w_{o}^{t}(i)$ is a gating weight at $i$ -th slots of $\mathbf{w}_{o}^{t}$ . It measures the correlation between $v^{t1}$ and $\tilde{\mathbf{M}}^t (i)$ . We have a constraint on $\mathbf{w}_o$ as: + +$$ +\left\{ \begin{array}{l} \sum_ {i} w _ {o} (i) = 1, \\ 0 \leq w _ {o} (i) \leq 1. \end{array} \right. \tag {9} +$$ + +With the gating strategy, we can write $v^t$ to different memory slots adaptively. + +# 3.2.2 Memory Reading + +Memory reading is the key step for deriving $z$ . It is defined as a weighted sum of features in the memory slots: + +$$ +z ^ {t} = \sum_ {i} w _ {r} ^ {t} (i) \mathbf {M} ^ {t} (i), \tag {10} +$$ + +where $z^t$ is the representation yielded from the memory at iteration $t$ with predictive information highlighted. Like writing, the reading weight also obeys the constraints in Eq.(9). + +# 3.2.3 Memory Addressing + +Although we have shown the way to access memories according to Eq.(7)-(10), the weighting mechanism remains unveiled. As shown in Fig.4, we design a two-level addressing scheme to ensure the addressing process can meet the essential requirement of memory writing and reading. + +![](images/cfa5a0a453cc86a46c8ae49d47985b896f499bcd3d78efef0108eb452d88163e.jpg) +Figure 4. Diagram of two memory addressing strategies. (The length of the feature vector is omitted for simplicity. Best viewed in color.) + +Content-based addressing. The content-based addressing focuses on the correlation between $v$ and features in each slot. It can be expressed as: + +$$ +w _ {c} (i) = \frac {\exp (\phi [ v , \mathbf {M} (i) ])}{\sum_ {j} \exp (\phi [ v , \mathbf {M} (j) ])}, \tag {11} +$$ + +where $\phi[\cdot, \cdot]$ is the correlation measurement function. Unlike [10], our measurement for writing and reading is different. When writing into the memory, the process is analogous to clustering. Similar $v$ should be put into one slot to keep the variety of the memory bank. Memory reading is the contrary. If we weigh the slots containing similar features to $v$ higher, the superfluous information cannot be removed. Therefore, instead of simply calculating the similarity, we add a gating parameter $\sigma$ for the correlation measurement $\phi$ . Taking the cosine similarity as the naive similarity measurement, we define $\phi[\cdot, \cdot]$ as: + +$$ +\phi [ \cdot , \cdot ] = 1 ^ {\sigma} + (- 1) ^ {\sigma} D _ {c o s s i m} (\cdot , \cdot), \tag {12} +$$ + +where $D_{\text{cossim}}$ is the cosine similarity and the gating flag $\sigma$ is set to 1 for reading and 0 for writing. + +Contextual addressing. Content-based addressing considers from the view of relations between $v$ itself and the feature in each memory slot. Analyzing the relations between memory slots also benefits the learning of predictive information. Therefore, we develop the contextual addressing scheme by imposing the influence of neighbor slots' weights as: + +$$ +w _ {t} (i) = \sum_ {i} w _ {c} (i) b _ {\Omega} \left(d _ {i}\right), \tag {13} +$$ + +where $b_{\Omega}(d_i) = \exp (d_i^2 / 2\sigma^2)$ is a bell-shaped balance function, which gives slots in neighbor $\Omega$ decreasing weights along with their distances $d_i$ to slot $i$ . + +Like [46], we also introduce a temperature parameter that controls the concentration level of the distribution. Then we obtain the final weight as: + +$$ +w (i) = \frac {\exp \left(w _ {t} (i) ^ {\tau}\right)}{\sum_ {j} \exp \left(w _ {t} (j) ^ {\tau}\right)}, \tag {14} +$$ + +where $\tau$ is the temperature factor that can amplify the focusing degree on each memory slot by enlargement. + +# 3.3. Training Scheme + +The training process consists of two parts. One is related to the original gesture recognition task, and it can be accomplished by using the cross-entropy loss function. The other is focused on refining the feature representation, which is achieved by Eq.(6), namely our proposed loss function based on IB. Then the overall loss is: + +$$ +\mathcal {L} = \mathcal {L} _ {c e} + \beta (W \cdot \mathcal {L} _ {I B}), \tag {15} +$$ + +where $\mathcal{L}_{ce}$ refers to cross-entropy loss, which is the only task-relevant loss for the original gesture recognition, and $\beta$ is a balance parameter. Since the memory relies on a series of $v$ , it needs some time to optimize the encoder $E_{\theta}$ first. Therefore, we add a warm-up coefficient $W$ , which can be expressed as: + +$$ +W = \max (0, (1 - \exp (- E + \varepsilon))), \tag {16} +$$ + +where $E$ represents the current epoch and $\varepsilon$ is a warm-up hyper-parameter that determines when $L_{IB}$ starts to effect. + +# 4. Experiment + +# 4.1. Experimental Setups + +The proposed method is implemented with PyTorch on a NVIDIA RTX 3090 GPU. We choose Res3D-18 [36] as our backbone. The input data is spatially resized to $256 \times 256$ first, and then randomly/center cropped into $224 \times 224$ in the training/inference phase, respectively. In the temporal domain, it is randomly/uniformly sampled to 32-frame videos in the training/inference phase, respectively. We use the SGD optimizer with a weight decay of 0.0004 and momentum of 0.9. We fix the mini-batch size as 7. The initial learning rate is set to 0.003 and then it decreases with a scheme of noisy linear cosine decay. The training process stops after 15 epochs for IsoGD and EgoGesture datasets and 80 epochs for THU-READ dataset since the last one has fewer samples. The temperature parameter $\tau$ for memory bank is set to 10, and the number of memory slots is 5. The warm-up parameter $\varepsilon$ is 3 for IsoGD and EgoGesture datasets is 10 for THU-READ, respectively. The balance parameter $\beta$ is set to 10 due to the ratio of two losses. + +# 4.2. Comparison with State-of-the-art Methods + +The proposed method is compared with state-of-the-art methods on three datasets of IsoGD [40, 38], EgoGesture [4, 52], and THU-READ [31, 32]. Unlike recent SOTA methods [48, 55, 57] that are first pre-trained on the 20BN-Jester gesture dataset [21], our network does not need any other extra pre-train models but employs the backbone + +Res3D-18 model with its default settings in PyTorch. As the proposed method does not focus on multimodal fusion, we just employ a simple average fusion scheme to obtain the RGB+D result. + +# 4.2.1 Performance on IsoGD + +Chalearn IsoGD dataset is a large-scale RGB-D dataset with 249 classes of gestures. It can be divided into three subsets: training set (35,878 videos), validation set (5,784 videos), and testing set (6,271 videos). This dataset is also used from two rounds of Chalearn LAP large-scale isolated gesture recognition challenge. Samples in Fig.1 are from this dataset. The various appearances in this dataset make it hard to achieve accurate recognition. Thus it can be a good benchmark to verify whether our framework is effective to eliminate the influence of gesture-irrelevant factors or not. + +The comparison on the Chalearn IsoGD dataset is shown in Table 1. Following the previous methods [50, 58, 55, 48, 57], we also report the performance on the validation subset for a fair comparison. Without loss of generality, the performance on the testing subset is also reported in the supplementary material. As can be seen, employing CNNs can bring a large improvement when compared with the hand-icraft feature-based method [37]. Then improving the network structure or altering the connection via NAS can also promote performance to a varying extent. Compared with these methods, our framework focuses on finding a better feature representation to eliminate gesture-irrelevant factors and achieves significant boosting. The proposed method outperforms the previous SOTA, Zhou et al.'s [55] near $8\%$ and $4\%$ on RGB and depth data, respectively. Besides the good performance on single modality, the RGB-D result is also better than Zhou et al.'s [57] at about $7\%$ , even though they design a new fusion module whereas ours is a simple average fusion. It proves a good feature representation is critical for improving recognition performance. + +# 4.2.2 Performance on EgoGesture + +EgoGesture dataset contains 24,161 egocentric hand gesture clips of 83 classes from 50 distinct subjects. Videos in this dataset focus on the interaction with wearable devices from a first-person view across multiple indoor and outdoor scenes. Compared with Chalearn IsoGD dataset, the number of classes of this dataset is fewer, but this first-person dataset suffers more problems like blurring and various viewpoints since the camera is on the performers' heads. + +As demonstrated in Table 2, the proposed method can also achieve a remarkable performance on the EgoGesture dataset. As the top accuracy on this dataset is very high (mostly beyond $90\%$ ), it is not easy to make a significant improvement. However, ours still outperforms the second best one, Kopuklu et al.'s [14] over $1\%$ on RGB data despite + +
ModalityMethodMain modelAccuracy(%)
RGBWang [44]bi-direction VDI36.60
Li [18]3D CNN37.28
Hu [12]DNN44.88
Miao [22]ResC3D45.07
Duan [6]2-stream CNN+C3D46.08
Zhang [51]convLSTM+C3D51.31
Zhang [50]ResC3D+convLSTM +MobileNet55.98
Zhu [58]ResC3D+ GatedConvLSTM +MobileNet+Pyramid57.42
Yu [48]SlowFast+NAS²58.88
Zhou [57]I3D+Transformer60.87
Zhou [55]I3D+DI+NAS62.66
OursRes3D-1870.88
depthWang [44]bi-direction DDI40.08
Li [18]3D CNN40.49
Hu [12]DNN48.96
Miao [22]ResC3D48.44
Duan [6]2-stream CNN+C3D54.95
Zhang [51]convLSTM+C3D49.81
Zhang [50]ResC3D+convLSTM +MobileNet53.28
Zhu [58]ResC3D+ GatedConvLSTM +MobileNet+Pyramid54.18
Yu [48]SlowFast+NAS²55.68
Zhou [57]I3D+Transformer60.17
Zhou [55]I3D+DI+NAS60.66
OursRes3D-1864.38
RGB+DWan [37]MFSK+BoVW18.65
Wang [44]bi-direction VDI+DDI44.80
Li [18]3D CNN52.04*
Hu [12]DNN54.14
Zhang [51]convLSTM+C3D55.29
Zhu [58]ResC3D+ GatedConvLSTM+ +MobileNet+Pyramid61.05
Miao [22]ResC3D64.40**
Yu [48]SlowFast+NAS²65.54
Zhou [55]I3D+DI+NAS66.62
Zhou [57]I3D+Transformer66.79
OursRes3D-1874.08
+ +* Including saliency data as reported in [18]. +** Including flow data as reported in [22]. + +just using a much simpler backbone of Res3D-18. The performance on depth data is also competitive but $0.66\%$ lower than the best one of Kopuklü et al.'s. It implies our feature representation refinement is more effective on RGB data. The reason behind it may be that compared with RGB data, the differences between depth samples are smaller (only the grayscale value changes), which makes it hard to distinguish the predictive cue from the excess information with + +Table 1. Comparison with SOTAs on Chalearn IsoGD Dataset. + +
ModalityMethodMain ModelAccuary(%)
RGBGraves [10]VGG16+LSTM74.70
Cao [4]C3D+LSTM +RLSTM89.30
Carreira [5]I3D90.33
Tang [30]SeST93.20
Yu [48]SlowFast+NAS293.31
Köpüklü [14]ResNeXt-10193.75
OursRes3D-1894.93
depthGraves [10]VGG16+LSTM77.70
Carreira [5]I3D89.47
Cao [4]C3D+LSTM +RLSTM90.60
Tang [30]SeST93.35
Köpüklü [14]ResNeXt-10194.03
Yu [48]SlowFast+NAS294.13
OursRes3D-1893.47
RGB+DGraves [10]VGG16+LSTM81.40
Cao [4]C3D+LSTM +RLSTM92.20
Carreira[5]I3D92.78
Joze[13]MMTM93.87
Yu[48]SlowFast+NAS295.52
OursRes3D-1895.72
+ +Table 2. Comparison with SOTAs on EgoGesture Dataset. + +
ModalityMethodMain ModelAccuary(%)
RGBSimonyan [29]VGG41.90
Feichtenhofer [9]SlowFast69.58
Yu [48]SlowFast+NAS²71.25
Wang [42]ConvNet73.85
Li [15]Transformer80.42
Zhou [57]I3D+Transformer81.25
OursRes3D-1888.33
depthSimonyan [29]VGG34.06
Wang [42]ConvNet65.00
Feichtenhofer [9]SlowFast68.75
Yu [48]SlowFast+NAS²69.58
Li [15]Transformer76.04
Zhou [57]I3D+Transformer77.92
OursRes3D-1882.91
RGB+DFeichtenhofer [9]SlowFast76.25
Yu [48]SlowFast+NAS²78.38
Li [15]Transformer84.90
Zhou [57]I3D+Transformer87.04
OursRes3D-1890.51
+ +Table 3. Comparison with SOTAs on THU-READ Dataset. + +the memory network. + +# 4.2.3 Performance on THU-READ + +THU-READ dataset has 1920 videos of 40 classes, which are performed by 8 subjects. Although involving fewer videos and fewer classes, it is yet challenging due to the subtle intra-class differences and the background noise. + +
Suff.Comp.memory networkAcc(%)
RGBdepth
×××78.3369.58
✓××82.2973.43
✓✓×85.4176.76
✓✓✓88.3382.91
+ +$^{*}$ Suff. $=$ Sufficiency, Comp. $=$ Compactness Table 4. Impacts of components of the proposed framework. + +Table 3 reports the comparison on the THU-READ dataset. The results are reported by averaging all 4 splits under CS protocol as per [32]. The proposed method also achieves the best performance on this dataset. Compared with the second best one of Zhou et al. [57], which employs a combination of I3D and Transformer network, our results are still $7\%$ and $5\%$ better than theirs on RGB and depth data, respectively. For the RGB-D fusion result, the performance of the proposed method reaches $90.51\%$ , and outperforms Zhou et al.'s at about $3\%$ , even though we just utilize a simple average fusion. + +# 4.3. Ablation Study + +The studies on the effectiveness of our designs, including representation refinement with IB and predictive information distillation with memory network, are first presented in this section. In order to evaluate our scheme using a memory network, we have also compared several different addressing strategies, including using cosine similarity only for addressing and using content-based addressing only. THU-READ dataset is employed for this ablation study. Without specific saying, the experimental settings are the same as mentioned in Section 4.1. + +Impacts of components of the proposed framework. In Table 4, we show how the proposed framework helps to eliminate gesture-irrelevant factors and leads to a more compact and robust feature representation. We compare several strategies, including 1) the baseline of using Res3D-18 only, 2) optimizing with the Sufficiency rule only, 3) using both Sufficiency and Compactness rules, namely using the IB loss in Eq.(6), and 4) using IB loss and memory network. The performance is marked in rows with a checkmark or a cross, denoting whether the corresponding module is used or not. Compared with the baseline, optimizing under the IB theory, even only considering the Sufficiency rule can lead to a significant performance improvement. This demonstrates the importance of a good representation for recognition tasks. When extending the loss to involve the Compactness rule, even better performance can be achieved. Replacing the convolution-based IB module with the memory network encourages the deposition of predictive information and leads to another performance gain. This suggests the effectiveness of memory network for highlighting the predictive information explicitly. + +
addressing strategyAccuracy(%)
RGBdepth
cosine similarity only80.5171.76
content-based only84.5775.62
proposed method88.3382.91
+ +Table 5. Performance with different memory addressing strategies. + +Effect of different addressing strategies. The effect of different addressing strategies is shown in Table 5. When only the cosine similarity is used for addressing, the performance is poor. This implies that similar $z$ and $v$ weaken the effectiveness of IB loss. After adding the gating flag $\sigma$ , and even just using content-based addressing, the performance is improved significantly. When all the addressing strategies are combined, the performance is further boosted. This indicates that a combination of content-based and contextual addressing can leverage both inter- and intra-memory feature relations and achieve better performance. + +Visualization. To better illustrate how the robust presentation derived from our proposed framework shrinks the inner-class difference, which is mainly caused by gesture-irrelevant variations, we present a visualization of a 2D projection of feature encoding by t-SNE. The visualization is conducted on RGB data of the THU-READ dataset (CS3). + +![](images/74b9626122022bcf2be67dbb2e106d529b068a128714ac421169324c2320276e.jpg) +(a) + +![](images/d8dc7cb867b9900a4171621cb66d02aa71cfc32eb47cea0644e9e90788e7aab8.jpg) +(b) + +![](images/376db8a530079928b572209e8c7a3acbb7662e2817b63b26b9355ef181ef38c6.jpg) +(c) +Figure 5. Visualizing the projection of feature distribution by t-SNE associated with the class label. (a) Feature extracted by baseline model. (b) Feature extracted by the network with proposed IB loss only. (c) Feature extracted by the proposed model. (Best viewed in color and zooming in.) + +The visualization result is consistent with the performance comparison in Table 4. As can be seen, the mixed classes of the baseline model in Fig.5(a) are no longer intermingled in Fig.5(b). It means our framework with IB loss can effectively improve the discriminative power of the features. When adding the memory network, almost all the clusters can concentrate on their centroids. It indicates that with the memory network, the predictive information can be clearer, and the inner-class differences become narrowed. It allows the mixed classes to be more easily distinguished from each other in the encoding space. + +In addition to utilizing t-SNE visualizations, we give some more examples to effectively illustrate how the proposed network mitigates the impact of gesture-irrelevant + +![](images/eafc46a40ab01c08fb204925b29ccfc3d65dac70f8445d125dd5755777ecdac8.jpg) + +![](images/4e87df8e023872fe0f63ec3de54e5c1088817c4c374fae8ca3bbf512857c09f7.jpg) +Figure 6. An analysis of how the proposed network improves the performance. (a) The confusion matrix of baseline. (b) The confusion matrix of the proposed network. (c) Intuitive presentation of the irrelevant factors affecting gesture recognition. + +factors and ultimately enhances performance. In Fig.6(a) and (b), we first visualize the confusion matrice of the baseline and the proposed network. As can be seen, ours can apparently avoid most of the wrong classifications. Then let us consider some concrete instances of gestures that are misclassified by the baseline model. As illustrated in the confusion matrix of the baseline model, Class 5, namely cut paper is wrongly categorized as Class 15 of open laptop. This confusion is primarily attributed to the resemblance in environmental conditions. As shown in Fig.6(c), both scenarios share a similar desk setup, and the overexposed laptop seems also like a white paper to some extent. Another example is Class 2 of clean table being wrongly deemed as Class 35 of wave hand. The similarities in hand movement and positioning lead to the misguided classification of these gestures. These examples prove that overfitting to these environmental cues rather than learning a robust feature representation of gesture-relevant factors results in the wrong predictions. By contrast, our method is designed to learn the essential feature of one type of gesture. Therefore, it avoids being influenced by extraneous contextual information, leading to remarkable improvement in performance. + +# 5. Conclusion + +In this paper, we present a framework that aims to improve the robustness of feature representation for RGB-D gesture recognition based on the information bottleneck theory. We analyze the factors that are relevant and irrelevant to gestures using mutual information and design a loss function that disentangles the task-relevant predictive cues from disturbing superfluous information. Additionally, we use a memory network to overlay the encoding feature of each sample by memory writing and reading. 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Dmagan: Dynamic memory generative adversarial networks for text-to-image synthesis. 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Shaanxi Province, China" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 99, + 220, + 494, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 220, + 494, + 232 + ], + "spans": [ + { + "bbox": [ + 99, + 220, + 494, + 232 + ], + "type": "text", + "content": "{yunanli, qgmiao}@xidian.edu.cn, {huizhouchen, gwfeng-1}@stu.xidian.edu.cn" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "spans": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 285, + 290, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 290, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 290, + 571 + ], + "type": "text", + "content": "Although previous RGB-D-based gesture recognition methods have shown promising performance, researchers often overlook the interference of task-irrelevant cues like illumination and background. These unnecessary factors are learned together with the predictive ones by the network and hinder accurate recognition. In this paper, we propose a convenient and analytical framework to learn a robust feature representation that is impervious to gesture-irrelevant factors. Based on the Information Bottleneck theory, two rules of Sufficiency and Compactness are derived to develop a new information-theoretic loss function, which cultivates a more sufficient and compact representation from the feature encoding and mitigates the impact of gesture-irrelevant information. To highlight the predictive information, we further integrate a memory network. Using our proposed content-based and contextual memory addressing scheme, we weaken the nuisances while preserving the task-relevant information, providing guidance for refining the feature representation. Experiments conducted on three public datasets demonstrate that our approach leads to a better feature representation and achieves better performance than state-of-the-art methods. The code of our method is available at: https://github.com/Carpumpkin/InBoMem." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 619, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 287, + 693 + ], + "type": "text", + "content": "Gesture recognition based on RGB-D video has raised much attention of researchers since it has many applications, such as visual surveillance, intelligent transportation, and particularly, human-computer interaction (HCI) [48]. The development of CNN family [35, 5, 26], RNN family [27, 11], and Transformer-based methods [15, 57, 54]" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 257, + 547, + 393 + ], + "blocks": [ + { + "bbox": [ + 307, + 257, + 547, + 393 + ], + "lines": [ + { + "bbox": [ + 307, + 257, + 547, + 393 + ], + "spans": [ + { + "bbox": [ + 307, + 257, + 547, + 393 + ], + "type": "image", + "image_path": "7626cc362a25155f74395f367633f72e226bec79a2828f897ecc90cd3e8e8d1f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 396, + 547, + 517 + ], + "lines": [ + { + "bbox": [ + 304, + 396, + 547, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 547, + 517 + ], + "type": "text", + "content": "Figure 1. Diagram of our principle. The feature of a gesture sample can be decomposed into the essential gesture feature and gesture-irrelevant ones, such as the background, illumination, and the performer's appearance. The former provides predictive information whereas the latter is superfluous. Based on the information bottleneck theory, we can eliminate these disturbing nuisances by minimizing the superfluous information. Meanwhile, as the predictive feature in different samples is all the same, we leverage the memory network to store and \"overlay\" them, and then highlight the gesture-relevant predictive feature as the guidance for learning a robust feature representation." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 543, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 545, + 567 + ], + "type": "text", + "content": "promote the improvement of recognition performance significantly." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Although great progress has been made in this field, the attention has always been drawn to boost performance via better network structure [50, 48, 55, 56] or by introducing extra modalities of data [6, 18, 23, 19]. The interference of gesture-irrelevant factors is hardly noticed. In most real-world gesture recognition scenarios, the dynamic variations are in two aspects. One is based on the motion of the gesture itself like trajectories of hands/arms, and is crucial to the recognition task. The other is related to environmental influences like illumination, backgrounds, and the performers' appearances as depicted in Fig.1. The gesture performing-related factors, such as the velocity, performer's" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20968" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "content": "concentration, and understanding of the gesture can also affect the quality of gesture presentation. When training a network for gesture recognition, these gesture-irrelevant factors may be learned as a kind of feature, and thus result in some inner-class differences hindering the recognition performance. Therefore, it is necessary to disentangle the recognition-relevant and redundant information to refine the feature representation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 172, + 288, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 172, + 288, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 288, + 506 + ], + "type": "text", + "content": "In order to disentangle the recognition task-relevant information and the disturbing gesture-irrelevant factors, we refer to the theory of Information Bottleneck (IB) [34], which engages mutual information (MI) and provides an information-theoretic objective for solving this problem. The essential idea of IB is mapping the observation of an input to a sophisticated representation, which retains the desired characteristics with respect to the prediction of label and simultaneously minimizes the redundant information. Many methods leverage IB to learn robust representations for downstream tasks like unsupervised multi-view learning [8], Person Re-identification [33] and human pose estimation [20]. In this process, the sophisticated representation is critical since it ensures a compact feature encoding that avoids the interference of task-irrelevant factors. However, it is difficult to obtain such a representation directly with the original IB theory. Approximating MI in high dimensions is hard [25], and thus the task-irrelevant distractors may not be removed. Even though some recent techniques ease the constraint by transforming this issue to a network optimization problem without explicitly estimating MI [33], the joint optimization of feature encoding and such a representation encoding blindly may fail to reach a satisfied representation since no explicit standard of \"good representation\" is given. Therefore, to refine the feature representation, we should explicitly highlight what the predictive information is, and take it as guidance for the refinement of the feature representation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 510, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 715 + ], + "type": "text", + "content": "Combining these concerns, we propose an analytic framework to learn a robust representation for RGB-D-based gesture recognition. To address gesture-irrelevant factors, we employ the Information Bottleneck (IB) principle to unify them as \"superfluous information\", in contrast to predictive information like motion trajectories. Then we derive a new objective that compresses the superfluous information in the encoding space and emphasizes the predictive one. To achieve a sufficient yet compact feature representation required by IB, a memory network is incorporated for explicit guidance. We create a large external memory bank, where the shared predictive information is highlighted by overlaying the features in different memory slots. This process is achieved through memory manipulations of writing and reading. Then with the derived objective, the distribution of encoding features is pulled towards that of the robust representation, resulting in improved ges" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 73, + 428, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 73, + 428, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 73, + 428, + 84 + ], + "type": "text", + "content": "ture recognition performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "text", + "content": "The contributions of our method can be summarized as three-fold:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 313, + 119, + 545, + 332 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 313, + 119, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 119, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 119, + 545, + 204 + ], + "type": "text", + "content": "1. A framework to develop a robust feature representation for gesture recognition, along with the theoretical analysis based on IB. We extend the existing theoretical analysis and optimize the feature encoding to mitigate the interference of gesture-irrelevant factors. To the best of our knowledge, we are the first to provide insights from an information-theoretic view in this field." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 213, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 213, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 545, + 262 + ], + "type": "text", + "content": "2. A scheme to explicitly distill the predictive information. Utilizing the memory network, we learn the predictive information from various samples to derive a sufficient and compact feature representation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 272, + 545, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 272, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 313, + 272, + 545, + 332 + ], + "type": "text", + "content": "3. Experiments prove the effectiveness of our design and demonstrate that the proposed method achieves the state-of-the-art performance on three public RGB-D gesture datasets of IsoGD [40, 38], EgoGesture [4, 52] and THU-READ [31, 32]." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 346, + 390, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 390, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 390, + 357 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 365, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 653 + ], + "type": "text", + "content": "Evolution of gesture recognition. Conventional methods [39, 37] always employ spatiotemporal handcrafted features for gesture recognition. Recently, promotions of deep learning also bring new developments in dynamic gesture recognition. 3D CNNs [35] emerge for extracting spatiotemporal features, and many gesture recognition methods [17, 41, 53, 18, 6, 23, 19] are developed based on them. Meanwhile, RNN family [27, 11] that enables modeling sequence information also draws extensive attention in gesture recognition [53, 50, 58]. With the success of Transformer in computer vision tasks, there are also some researchers trying to improve the recognition performance by introducing Transformer-based structures [15, 57, 54]. Besides proposing new architectures, optimizing the network connection and structure is another option. Zhou et al. [55] and Yu et al. [48] notice the influence of network connection on low-level and high-level features, and employ network architecture search (NAS) for better architecture. Unlike previous methods that focus on improving the structure or connection of the network, we pay more attention to eliminating the disturbing gesture-irrelevant factors, which potentially lead to inner-class differences influencing recognition performance. With the theoretical analysis based on IB, we propose a new objective to achieve such an elimination." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "content": "Information bottleneck for representation learning. Information bottleneck [34] is an information-theoretic principle that has made great progress in representation learning and theoretical understanding of Deep Neural Networks (DNNs) [28]. However, the difficulty of calculating" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20969" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 72, + 365, + 184 + ], + "blocks": [ + { + "bbox": [ + 72, + 72, + 365, + 184 + ], + "lines": [ + { + "bbox": [ + 72, + 72, + 365, + 184 + ], + "spans": [ + { + "bbox": [ + 72, + 72, + 365, + 184 + ], + "type": "image", + "image_path": "a89e34bfb3433df569393dc097e1be2b34d9a925c69ba528e7da54e884201715.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 186, + 231, + 196 + ], + "lines": [ + { + "bbox": [ + 220, + 186, + 231, + 196 + ], + "spans": [ + { + "bbox": [ + 220, + 186, + 231, + 196 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 369, + 74, + 518, + 148 + ], + "blocks": [ + { + "bbox": [ + 369, + 74, + 518, + 148 + ], + "lines": [ + { + "bbox": [ + 369, + 74, + 518, + 148 + ], + "spans": [ + { + "bbox": [ + 369, + 74, + 518, + 148 + ], + "type": "image", + "image_path": "949b474d1ca209294d963d3b1660e11578a386c312772685554f0a614d5d19d7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 371, + 147, + 518, + 202 + ], + "blocks": [ + { + "bbox": [ + 371, + 147, + 518, + 202 + ], + "lines": [ + { + "bbox": [ + 371, + 147, + 518, + 202 + ], + "spans": [ + { + "bbox": [ + 371, + 147, + 518, + 202 + ], + "type": "image", + "image_path": "9077c55c3db85a6b64c0dca185dd0d68c71b936886c9fc18805aac56d7228468.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed framework. The encoding feature of a gesture video sample is first obtained as the observation " + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "text", + "content": ". Then the predictive information is highlighted in the memory network via writing and reading, and the guidance of representation " + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "text", + "content": " is derived. With " + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{IB}" + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "text", + "content": " further refining the representation of " + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "text", + "content": " and pulling the distribution of " + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 45, + 206, + 545, + 262 + ], + "type": "text", + "content": ", a more robust representation for gesture recognition is developed. (a) The pipeline of the framework. (b) Memory writing manipulation. (c) Memory reading manipulation. (Best viewed in color.)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 281, + 289, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 289, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 289, + 496 + ], + "type": "text", + "content": "mutual information in high dimensions hinders its applications. To solve this problem, Alexenders et al. [2] demonstrate a variational approximation to parameterize the IB model. Peng et al. [24] propose a variational discriminator bottleneck for stable adversarial learning. Federici et al. [8] extend the IB theory to multi-view unsupervised learning. Tian et al. [33] present an analytical solution to fitting the mutual information via transferring the objective of IB to a variational self-distillation loss, and they also extend it to multi-view tasks. In contrast to these methods, our approach focuses on leveraging IB theory to disentangle the gesture-irrelevant factors and the predictive factors when encoding the features of a gesture sample. To fit the condition of feature disentanglement, beyond the Sufficiency constraint used in [33], we extend the IB theory by adding a Compactness constraint and give a more theoretically sound explanation of why they are both critical for eliminating task-irrelevant factors." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": "Memory networks. Memory network [45, 10] is employed in both low-level and high-level vision tasks owing to its good ability in modeling long-term information. Li et al. [16] employ the memory networks to restore and calculate the weights for different stages in image dehazing. Zhu et al. [59] use dynamic memory to achieve text-to-image synthesis. For high-level tasks, Yang and Chen [47] employ a dynamic memory network for visual tracking. Cai et al. [3] design a memory matching network for one-shot learning, which writes/reads for training and inference phases, respectively. Zhang et al. [49] design a cross-modal memory structure to store multimodal information for a few-shot recognition task. Eom et al. [7] design a spatial and temporal memory network (STMN) for video-based pedestrian re-identification tasks. Compared with the above literature, the role that the memory network plays in this study is quite different. We do not simply use it for a large external space, but design different addressing strategies for writing and read" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 281, + 457, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 457, + 293 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 457, + 293 + ], + "type": "text", + "content": "ing according to their different goals." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 304, + 411, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 411, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 411, + 319 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "type": "text", + "content": "3.1. Refining Feature Representation with Information Bottleneck" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 355, + 545, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 511 + ], + "type": "text", + "content": "Gesture-irrelevant factors are non-negligible since they cause significant divergence in even one class of gesture videos. However, these factors are always intertwined with predictive information like the hands/arms movement when encoding. Even some approaches [43, 55] attempt to leverage the attention mechanism to focus on motion trajectories of gestures, the nuisances are inevitably learned and impact the recognition performance. The principle of information bottleneck [34] is to build a robust feature representation by discarding all information that is not useful for a given task while retaining the predictive one. Based on it, we disentangle the gesture-relevant and -irrelevant factors, and thereby refine the feature representation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 526, + 397, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 526, + 397, + 538 + ], + "spans": [ + { + "bbox": [ + 306, + 526, + 397, + 538 + ], + "type": "text", + "content": "3.1.1 Preliminaries" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Suppose we have a set of input gesture videos, which are marked as " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = \\{x_1,x_2,\\ldots ,x_n\\}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". These inputs fall into " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{y_{1},y_{2},\\dots,y_{m}\\}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " classes. Obviously, the task of gesture recognition is mapping arbitrary gesture sample " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "x\\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " into the corresponding class " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v\\in \\mathcal{V}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " be an observation of " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " is the set of features. In deep learning, " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " is usually the feature of " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " extracted by an encoder parameterized by " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", namely " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v = E_{\\theta}(x)" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". 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Then pulling " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " can result in a more robust feature representation. 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The relations of the information entropy and mutual information among observation " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": ", representation " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": " and label " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": ". The predictive information is the mutual information between " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": ". The superfluous information is the conditional mutual information of " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": ", namely " + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "inline_equation", + "content": "I(v;z) - I(z;y)" + }, + { + "bbox": [ + 46, + 226, + 288, + 283 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "text", + "content": "ing " + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "inline_equation", + "content": "v, z" + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "text", + "content": " as three random variables, the optimization goal is to maximize the mutual information between " + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "text", + "content": " while minimizing that of " + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 299, + 287, + 348 + ], + "type": "text", + "content": ", and that is the essential principle of IB." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 361, + 224, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 224, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 224, + 373 + ], + "type": "text", + "content": "3.1.2 Information Bottleneck Objective" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": "According to the definition of IB, a good representation " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": " should satisfy two rules: 1) keeping sufficient discriminative information to identity " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": ", and 2) avoiding encoding task-irrelevant information, specifically, the gesture-irrelevant appearance variations in this task. The first one is defined as Sufficiency of " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": " [1, 8, 33]. Ideally, the Sufficiency rule is satisfied if and only if " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "I(z; y) = I(v; y)" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": ". However, in general, " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "I(z; y)" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": " is less than " + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "inline_equation", + "content": "I(v; y)" + }, + { + "bbox": [ + 46, + 380, + 287, + 499 + ], + "type": "text", + "content": " due to the information loss during encoding. Therefore, we need to minimize such a loss and derive an objective function as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 118, + 505, + 287, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 505, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 118, + 505, + 287, + 519 + ], + "type": "interline_equation", + "content": "\\min [ I (v; y) - I (z; y) ]. \\tag {1}", + "image_path": "dc8750ce4eb818fdc03192bdfbf3c7f76d65b21a7ce71eebdb0d37fb78fd51ff.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "type": "text", + "content": "The second one can be defined as Compactness. According to [8], the mutual information " + }, + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "type": "inline_equation", + "content": "I(v;z)" + }, + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "type": "text", + "content": " between " + }, + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 524, + 287, + 559 + ], + "type": "text", + "content": " can be subdivided as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 73, + 565, + 287, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 565, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 73, + 565, + 287, + 594 + ], + "type": "interline_equation", + "content": "I (v; z) = \\underbrace {I (z ; y)} _ {\\text {p r e d i c t i v e i n f o r m a t i o n}} + \\underbrace {I (v ; z | y)} _ {\\text {s u p e r f l u o u s i n f o r m a t i o n}}, \\tag {2}", + "image_path": "7cb6a7be77f5716d3a24146eac27587c77d13ce539f8f545ef9a569ed8fa8136.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": "where the first term on the right side is the mutual information between " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": ", indicating the information contained in " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": " for label prediction. The second one is the conditional mutual information of " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": " given the value of " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": ". In other words, it is the task-irrelevant information in " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": ". A compact feature representation requires " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "I(v;z|y)" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": " approaching 0. Therefore, we need to minimize " + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "inline_equation", + "content": "I(v;z|y)" + }, + { + "bbox": [ + 46, + 599, + 287, + 696 + ], + "type": "text", + "content": ", and we have the second objective function as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 119, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 119, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\min [ I (v; z) - I (z; y) ]. \\tag {3}", + "image_path": "67ce2558e29c1e6a47b6e1920eeaef34084084d947b2285cd3e9d8f8ed4f8def.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "Combine Eq.(1) and Eq.(3), the entire objective can be written as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 337, + 106, + 545, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 106, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 337, + 106, + 545, + 120 + ], + "type": "interline_equation", + "content": "\\min \\left[ I (v; y) - I (z; y) + I (v; z) - I (z; y) \\right], \\tag {4}", + "image_path": "678e36e615ddf7bd4f840d6dc9dc1caf97a9ca3d9d2e99a3abb927d46d611941.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 129, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 129, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 129, + 545, + 190 + ], + "type": "text", + "content": "with which both the rules of Sufficiency and Compactness can be satisfied. However, solving it by directly approximating MI is hard. According to the definition of mutual information, we can use conditional entropy and joint entropy to express Eq.(4) as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 352, + 199, + 545, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 199, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 352, + 199, + 545, + 213 + ], + "type": "interline_equation", + "content": "\\min [ H (y | z) - H (y | v) + H (z, y) ], \\tag {5}", + "image_path": "d099a37cf55d1e27cdbd2f0df647b97d4206a9b62f1de9705e0195f5d30874cf.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "inline_equation", + "content": "H(y|z)" + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "content": " is the conditional entropy of " + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "content": " given, and " + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "inline_equation", + "content": "H(z,y)" + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "content": " is the joint entropy of " + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "content": ". Inspired by [33], we can approximate Eq.(5) via a loss function as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 351, + 269, + 545, + 282 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 269, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 351, + 269, + 545, + 282 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I B} = \\mathcal {L} _ {K L D} \\left(\\mathbb {P} _ {v} | | \\mathbb {P} _ {z}\\right) + \\mathcal {L} _ {c e} (z, y), \\tag {6}", + "image_path": "52aa7766afa404b630e9436346dd285f99928c5ac09bbb28e55e2c71c0f106c9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{KLD}(\\cdot ||\\cdot)" + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "content": " are KL-divergence and cross-entropy loss, respectively. " + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_v = p(y|v)" + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_z = p(y|z)" + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "content": " are the probability of " + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "content": " in predicting " + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 291, + 545, + 352 + ], + "type": "text", + "content": ", respectively. The detailed derivation can be found in the supplementary material." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 359, + 545, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 359, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 306, + 359, + 545, + 384 + ], + "type": "text", + "content": "3.2. Distilling Predictive Information with Memory Network" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": "Note that according to Sufficient and Compactness rules, " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": " is from " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": " and is supposed to contain all the predictive information with respect to " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": ". Tian et al. [33] design a new encoder " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "E_{\\phi}" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": " to derive " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": ". However, optimizing " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "E_{\\theta}(v|x)" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "E_{\\phi}(z|v)" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": " simultaneously can only ensure the consistency of " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 390, + 545, + 534 + ], + "type": "text", + "content": ". There is no guarantee that one more encoder can lead to a more compact representation. As shown in Fig.1, overlaying the samples can emphasize the shared predictive information, i.e., motions of hands and arms related to the gesture, and weaken the sample-specific gesture-irrelevant factors. To this end, we achieve such an \"overlay\" process in a differentiable way via memory network." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "text", + "content": "In our implementation, we construct a " + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "inline_equation", + "content": "n \\times m" + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "text", + "content": " memory bank for each gesture class, where " + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "text", + "content": " is the number of memory slots, and " + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "text", + "content": " is the length of feature vector in each slot. The explicit optimization on " + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 535, + 545, + 594 + ], + "type": "text", + "content": " is performed by two manipulations of memory, writing and reading." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 610, + 411, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 411, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 411, + 623 + ], + "type": "text", + "content": "3.2.1 Memory Writing" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": "Memory writing is a manipulation that writes the encoding feature of observation " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " into the memory bank. In practice, it is achieved in a two-stage process. In the first stage, if there is an available memory slot, " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " can be directly written to it. In the second stage, when all memory slots are full, the process becomes more complicated and consists of two steps as follows." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20971" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "Forget. In the early stage, " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "E_{\\theta}(v|x)" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " is not well trained, and thus " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " inevitably contains some interference factors. These features may contaminate the memories. Therefore, we impose a forget vector " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{e}" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": ", a " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "n \\times 1" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " vector that has " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " components corresponding to " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " memory slots. It attenuates along with the training epoch since the predictive information dominates after times of training. The forget step can be expressed as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 175, + 287, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 175, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 104, + 175, + 287, + 190 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {M}} ^ {t} (i) = \\mathbf {M} ^ {t - 1} (i) \\left(1 - e ^ {t} (i)\\right), \\tag {7}", + "image_path": "9872898527b1b118f328ba4d5a40855833929abbb8258c6a78a28fca94def925.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "text", + "content": " is the memory bank, and " + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "inline_equation", + "content": "i\\in \\{1,2,\\dots ,n\\}" + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "text", + "content": " indicates the position of memory slot. " + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "text", + "content": " imply two adjacent iterations of the optimization process. Updating memory from iteration " + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 196, + 287, + 256 + ], + "type": "text", + "content": " is implemented by the Hadamard product." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 256, + 288, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 288, + 305 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 288, + 305 + ], + "type": "text", + "content": "Gated writing. When writing the encoding feature of " + }, + { + "bbox": [ + 47, + 256, + 288, + 305 + ], + "type": "inline_equation", + "content": "v^t" + }, + { + "bbox": [ + 47, + 256, + 288, + 305 + ], + "type": "text", + "content": " into the memory, we utilize a gated writing strategy. We calculate the correlation between the " + }, + { + "bbox": [ + 47, + 256, + 288, + 305 + ], + "type": "inline_equation", + "content": "v^t" + }, + { + "bbox": [ + 47, + 256, + 288, + 305 + ], + "type": "text", + "content": " and features in each slot and update the memory as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 312, + 287, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 312, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 110, + 312, + 287, + 326 + ], + "type": "interline_equation", + "content": "\\mathbf {M} ^ {t} (i) = \\tilde {\\mathbf {M}} ^ {t} (i) + w _ {o} ^ {t} (i) v ^ {t}, \\tag {8}", + "image_path": "13888885a4682d4494090fdfd59f09b90566629c7e7b389a664277dfa2011367.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "w_{o}^{t}(i)" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": " is a gating weight at " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": "-th slots of " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{o}^{t}" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": ". It measures the correlation between " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "v^{t1}" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{M}}^t (i)" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": ". We have a constraint on " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_o" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 125, + 375, + 287, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 375, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 125, + 375, + 287, + 407 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\sum_ {i} w _ {o} (i) = 1, \\\\ 0 \\leq w _ {o} (i) \\leq 1. \\end{array} \\right. \\tag {9}", + "image_path": "6b2f5016c23edf5d7cdb839b5efde493f6c499b0ff1e547fc45398e3147767ce.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 415, + 287, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 287, + 440 + ], + "type": "text", + "content": "With the gating strategy, we can write " + }, + { + "bbox": [ + 47, + 415, + 287, + 440 + ], + "type": "inline_equation", + "content": "v^t" + }, + { + "bbox": [ + 47, + 415, + 287, + 440 + ], + "type": "text", + "content": " to different memory slots adaptively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 453, + 155, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 155, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 155, + 466 + ], + "type": "text", + "content": "3.2.2 Memory Reading" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 472, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 496 + ], + "type": "text", + "content": "Memory reading is the key step for deriving " + }, + { + "bbox": [ + 46, + 472, + 287, + 496 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 472, + 287, + 496 + ], + "type": "text", + "content": ". It is defined as a weighted sum of features in the memory slots:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 121, + 503, + 287, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 503, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 121, + 503, + 287, + 529 + ], + "type": "interline_equation", + "content": "z ^ {t} = \\sum_ {i} w _ {r} ^ {t} (i) \\mathbf {M} ^ {t} (i), \\tag {10}", + "image_path": "0b43da6e297c1abafa93df648885c1058d987d4db57a3b869bea0a218d8a4e6a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 536, + 287, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 584 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 584 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 536, + 287, + 584 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 46, + 536, + 287, + 584 + ], + "type": "text", + "content": " is the representation yielded from the memory at iteration " + }, + { + "bbox": [ + 46, + 536, + 287, + 584 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 536, + 287, + 584 + ], + "type": "text", + "content": " with predictive information highlighted. Like writing, the reading weight also obeys the constraints in Eq.(9)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 598, + 168, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 168, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 168, + 611 + ], + "type": "text", + "content": "3.2.3 Memory Addressing" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": "Although we have shown the way to access memories according to Eq.(7)-(10), the weighting mechanism remains unveiled. As shown in Fig.4, we design a two-level addressing scheme to ensure the addressing process can meet the essential requirement of memory writing and reading." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 541, + 187 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 541, + 187 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 541, + 187 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 541, + 187 + ], + "type": "image", + "image_path": "cfa5a0a453cc86a46c8ae49d47985b896f499bcd3d78efef0108eb452d88163e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 190, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 305, + 190, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 547, + 224 + ], + "type": "text", + "content": "Figure 4. Diagram of two memory addressing strategies. (The length of the feature vector is omitted for simplicity. Best viewed in color.)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 240, + 546, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 240, + 546, + 276 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 546, + 276 + ], + "type": "text", + "content": "Content-based addressing. The content-based addressing focuses on the correlation between " + }, + { + "bbox": [ + 305, + 240, + 546, + 276 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 240, + 546, + 276 + ], + "type": "text", + "content": " and features in each slot. It can be expressed as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 359, + 280, + 545, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 280, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 359, + 280, + 545, + 308 + ], + "type": "interline_equation", + "content": "w _ {c} (i) = \\frac {\\exp (\\phi [ v , \\mathbf {M} (i) ])}{\\sum_ {j} \\exp (\\phi [ v , \\mathbf {M} (j) ])}, \\tag {11}", + "image_path": "f5e7bbd49bf4b318e02542e77db231b9c5b536460c0f65acd42801ccf5c9b487.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "inline_equation", + "content": "\\phi[\\cdot, \\cdot]" + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "text", + "content": " is the correlation measurement function. Unlike [10], our measurement for writing and reading is different. When writing into the memory, the process is analogous to clustering. Similar " + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "text", + "content": " should be put into one slot to keep the variety of the memory bank. Memory reading is the contrary. If we weigh the slots containing similar features to " + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "text", + "content": " higher, the superfluous information cannot be removed. Therefore, instead of simply calculating the similarity, we add a gating parameter " + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "text", + "content": " for the correlation measurement " + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "text", + "content": ". Taking the cosine similarity as the naive similarity measurement, we define " + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "inline_equation", + "content": "\\phi[\\cdot, \\cdot]" + }, + { + "bbox": [ + 305, + 312, + 546, + 445 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 355, + 449, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 449, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 355, + 449, + 545, + 464 + ], + "type": "interline_equation", + "content": "\\phi [ \\cdot , \\cdot ] = 1 ^ {\\sigma} + (- 1) ^ {\\sigma} D _ {c o s s i m} (\\cdot , \\cdot), \\tag {12}", + "image_path": "1649ffa84431132596fb0b0ace6d28e90d9426cce8fe9d87ad018fcfc9da6c19.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "spans": [ + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "type": "inline_equation", + "content": "D_{\\text{cossim}}" + }, + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "type": "text", + "content": " is the cosine similarity and the gating flag " + }, + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "type": "text", + "content": " is set to 1 for reading and 0 for writing." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 493, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 493, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 305, + 493, + 545, + 577 + ], + "type": "text", + "content": "Contextual addressing. Content-based addressing considers from the view of relations between " + }, + { + "bbox": [ + 305, + 493, + 545, + 577 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 493, + 545, + 577 + ], + "type": "text", + "content": " itself and the feature in each memory slot. Analyzing the relations between memory slots also benefits the learning of predictive information. Therefore, we develop the contextual addressing scheme by imposing the influence of neighbor slots' weights as:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 372, + 581, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 581, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 372, + 581, + 545, + 605 + ], + "type": "interline_equation", + "content": "w _ {t} (i) = \\sum_ {i} w _ {c} (i) b _ {\\Omega} \\left(d _ {i}\\right), \\tag {13}", + "image_path": "690cbfff68bc1c153f1ea0067276b935f7498d8022c8e47fccd9acf139d55490.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "inline_equation", + "content": "b_{\\Omega}(d_i) = \\exp (d_i^2 / 2\\sigma^2)" + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "text", + "content": " is a bell-shaped balance function, which gives slots in neighbor " + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "text", + "content": " decreasing weights along with their distances " + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "text", + "content": " to slot " + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 611, + 545, + 647 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 647, + 545, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 647, + 545, + 684 + ], + "spans": [ + { + "bbox": [ + 305, + 647, + 545, + 684 + ], + "type": "text", + "content": "Like [46], we also introduce a temperature parameter that controls the concentration level of the distribution. Then we obtain the final weight as:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 372, + 688, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 688, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 372, + 688, + 545, + 716 + ], + "type": "interline_equation", + "content": "w (i) = \\frac {\\exp \\left(w _ {t} (i) ^ {\\tau}\\right)}{\\sum_ {j} \\exp \\left(w _ {t} (j) ^ {\\tau}\\right)}, \\tag {14}", + "image_path": "092055ef21ace9477f268ee21d4d71ca7d005802be119e6439ee831cc5c1ec2d.jpg" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "inline_equation", + "content": "^1 v" + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "inline_equation", + "content": "n\\times 1" + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": " feature vectors in the memory manipulations. Their notations hereby are not changed for the consistency with the expressions in information bottleneck theory in Sec.3.1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20972" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": " is the temperature factor that can amplify the focusing degree on each memory slot by enlargement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 103, + 149, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 103, + 149, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 103, + 149, + 117 + ], + "type": "text", + "content": "3.3. Training Scheme" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 122, + 286, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 122, + 286, + 193 + ], + "spans": [ + { + "bbox": [ + 47, + 122, + 286, + 193 + ], + "type": "text", + "content": "The training process consists of two parts. One is related to the original gesture recognition task, and it can be accomplished by using the cross-entropy loss function. The other is focused on refining the feature representation, which is achieved by Eq.(6), namely our proposed loss function based on IB. Then the overall loss is:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 205, + 286, + 219 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 205, + 286, + 219 + ], + "spans": [ + { + "bbox": [ + 116, + 205, + 286, + 219 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {c e} + \\beta (W \\cdot \\mathcal {L} _ {I B}), \\tag {15}", + "image_path": "454e170d19e7566f0b666ab543acdabe1a9e99db4192824e842c4f48515ca559.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ce}" + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "text", + "content": " refers to cross-entropy loss, which is the only task-relevant loss for the original gesture recognition, and " + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "text", + "content": " is a balance parameter. Since the memory relies on a series of " + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "text", + "content": ", it needs some time to optimize the encoder " + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "inline_equation", + "content": "E_{\\theta}" + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "text", + "content": " first. Therefore, we add a warm-up coefficient " + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 224, + 286, + 295 + ], + "type": "text", + "content": ", which can be expressed as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 94, + 305, + 286, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 305, + 286, + 319 + ], + "spans": [ + { + "bbox": [ + 94, + 305, + 286, + 319 + ], + "type": "interline_equation", + "content": "W = \\max (0, (1 - \\exp (- E + \\varepsilon))), \\tag {16}", + "image_path": "da9169611beb4d6f7a7755d916c256f74f7763a91f8ffd3a350929b10948d076.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "type": "text", + "content": " represents the current epoch and " + }, + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "type": "text", + "content": " is a warm-up hyper-parameter that determines when " + }, + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "type": "inline_equation", + "content": "L_{IB}" + }, + { + "bbox": [ + 47, + 327, + 286, + 352 + ], + "type": "text", + "content": " starts to effect." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 362, + 123, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 362, + 123, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 362, + 123, + 376 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 382, + 167, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 167, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 167, + 395 + ], + "type": "text", + "content": "4.1. Experimental Setups" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "text", + "content": "The proposed method is implemented with PyTorch on a NVIDIA RTX 3090 GPU. We choose Res3D-18 [36] as our backbone. The input data is spatially resized to " + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "text", + "content": " first, and then randomly/center cropped into " + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "text", + "content": " in the training/inference phase, respectively. In the temporal domain, it is randomly/uniformly sampled to 32-frame videos in the training/inference phase, respectively. We use the SGD optimizer with a weight decay of 0.0004 and momentum of 0.9. We fix the mini-batch size as 7. The initial learning rate is set to 0.003 and then it decreases with a scheme of noisy linear cosine decay. The training process stops after 15 epochs for IsoGD and EgoGesture datasets and 80 epochs for THU-READ dataset since the last one has fewer samples. The temperature parameter " + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "text", + "content": " for memory bank is set to 10, and the number of memory slots is 5. The warm-up parameter " + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "text", + "content": " is 3 for IsoGD and EgoGesture datasets is 10 for THU-READ, respectively. The balance parameter " + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 400, + 286, + 616 + ], + "type": "text", + "content": " is set to 10 due to the ratio of two losses." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 623, + 270, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 270, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 270, + 635 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "content": "The proposed method is compared with state-of-the-art methods on three datasets of IsoGD [40, 38], EgoGesture [4, 52], and THU-READ [31, 32]. Unlike recent SOTA methods [48, 55, 57] that are first pre-trained on the 20BN-Jester gesture dataset [21], our network does not need any other extra pre-train models but employs the backbone" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 119 + ], + "type": "text", + "content": "Res3D-18 model with its default settings in PyTorch. As the proposed method does not focus on multimodal fusion, we just employ a simple average fusion scheme to obtain the RGB+D result." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 135, + 437, + 146 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 135, + 437, + 146 + ], + "spans": [ + { + "bbox": [ + 306, + 135, + 437, + 146 + ], + "type": "text", + "content": "4.2.1 Performance on IsoGD" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 153, + 545, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 153, + 545, + 273 + ], + "spans": [ + { + "bbox": [ + 304, + 153, + 545, + 273 + ], + "type": "text", + "content": "Chalearn IsoGD dataset is a large-scale RGB-D dataset with 249 classes of gestures. It can be divided into three subsets: training set (35,878 videos), validation set (5,784 videos), and testing set (6,271 videos). This dataset is also used from two rounds of Chalearn LAP large-scale isolated gesture recognition challenge. Samples in Fig.1 are from this dataset. The various appearances in this dataset make it hard to achieve accurate recognition. Thus it can be a good benchmark to verify whether our framework is effective to eliminate the influence of gesture-irrelevant factors or not." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "type": "text", + "content": "The comparison on the Chalearn IsoGD dataset is shown in Table 1. Following the previous methods [50, 58, 55, 48, 57], we also report the performance on the validation subset for a fair comparison. Without loss of generality, the performance on the testing subset is also reported in the supplementary material. As can be seen, employing CNNs can bring a large improvement when compared with the hand-icraft feature-based method [37]. Then improving the network structure or altering the connection via NAS can also promote performance to a varying extent. Compared with these methods, our framework focuses on finding a better feature representation to eliminate gesture-irrelevant factors and achieves significant boosting. The proposed method outperforms the previous SOTA, Zhou et al.'s [55] near " + }, + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "type": "text", + "content": " on RGB and depth data, respectively. Besides the good performance on single modality, the RGB-D result is also better than Zhou et al.'s [57] at about " + }, + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 304, + 274, + 545, + 513 + ], + "type": "text", + "content": ", even though they design a new fusion module whereas ours is a simple average fusion. It proves a good feature representation is critical for improving recognition performance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 527, + 460, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 460, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 460, + 539 + ], + "type": "text", + "content": "4.2.2 Performance on EgoGesture" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "content": "EgoGesture dataset contains 24,161 egocentric hand gesture clips of 83 classes from 50 distinct subjects. Videos in this dataset focus on the interaction with wearable devices from a first-person view across multiple indoor and outdoor scenes. Compared with Chalearn IsoGD dataset, the number of classes of this dataset is fewer, but this first-person dataset suffers more problems like blurring and various viewpoints since the camera is on the performers' heads." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "As demonstrated in Table 2, the proposed method can also achieve a remarkable performance on the EgoGesture dataset. As the top accuracy on this dataset is very high (mostly beyond " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "), it is not easy to make a significant improvement. However, ours still outperforms the second best one, Kopuklu et al.'s [14] over " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " on RGB data despite" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20973" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 69, + 282, + 557 + ], + "blocks": [ + { + "bbox": [ + 55, + 69, + 282, + 557 + ], + "lines": [ + { + "bbox": [ + 55, + 69, + 282, + 557 + ], + "spans": [ + { + "bbox": [ + 55, + 69, + 282, + 557 + ], + "type": "table", + "html": "
ModalityMethodMain modelAccuracy(%)
RGBWang [44]bi-direction VDI36.60
Li [18]3D CNN37.28
Hu [12]DNN44.88
Miao [22]ResC3D45.07
Duan [6]2-stream CNN+C3D46.08
Zhang [51]convLSTM+C3D51.31
Zhang [50]ResC3D+convLSTM +MobileNet55.98
Zhu [58]ResC3D+ GatedConvLSTM +MobileNet+Pyramid57.42
Yu [48]SlowFast+NAS²58.88
Zhou [57]I3D+Transformer60.87
Zhou [55]I3D+DI+NAS62.66
OursRes3D-1870.88
depthWang [44]bi-direction DDI40.08
Li [18]3D CNN40.49
Hu [12]DNN48.96
Miao [22]ResC3D48.44
Duan [6]2-stream CNN+C3D54.95
Zhang [51]convLSTM+C3D49.81
Zhang [50]ResC3D+convLSTM +MobileNet53.28
Zhu [58]ResC3D+ GatedConvLSTM +MobileNet+Pyramid54.18
Yu [48]SlowFast+NAS²55.68
Zhou [57]I3D+Transformer60.17
Zhou [55]I3D+DI+NAS60.66
OursRes3D-1864.38
RGB+DWan [37]MFSK+BoVW18.65
Wang [44]bi-direction VDI+DDI44.80
Li [18]3D CNN52.04*
Hu [12]DNN54.14
Zhang [51]convLSTM+C3D55.29
Zhu [58]ResC3D+ GatedConvLSTM+ +MobileNet+Pyramid61.05
Miao [22]ResC3D64.40**
Yu [48]SlowFast+NAS²65.54
Zhou [55]I3D+DI+NAS66.62
Zhou [57]I3D+Transformer66.79
OursRes3D-1874.08
", + "image_path": "1828993b9c7dc5fe14142106c8724a1ecbe50fea2a47c6b64b56d9337ad8f747.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 56, + 557, + 201, + 567 + ], + "lines": [ + { + "bbox": [ + 56, + 557, + 201, + 567 + ], + "spans": [ + { + "bbox": [ + 56, + 557, + 201, + 567 + ], + "type": "text", + "content": "* Including saliency data as reported in [18]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 56, + 567, + 190, + 578 + ], + "lines": [ + { + "bbox": [ + 56, + 567, + 190, + 578 + ], + "spans": [ + { + "bbox": [ + 56, + 567, + 190, + 578 + ], + "type": "text", + "content": "** Including flow data as reported in [22]." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "just using a much simpler backbone of Res3D-18. The performance on depth data is also competitive but " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "0.66\\%" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " lower than the best one of Kopuklü et al.'s. It implies our feature representation refinement is more effective on RGB data. The reason behind it may be that compared with RGB data, the differences between depth samples are smaller (only the grayscale value changes), which makes it hard to distinguish the predictive cue from the excess information with" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 309, + 69, + 545, + 342 + ], + "blocks": [ + { + "bbox": [ + 47, + 583, + 274, + 594 + ], + "lines": [ + { + "bbox": [ + 47, + 583, + 274, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 583, + 274, + 594 + ], + "type": "text", + "content": "Table 1. Comparison with SOTAs on Chalearn IsoGD Dataset." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 69, + 545, + 342 + ], + "lines": [ + { + "bbox": [ + 309, + 69, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 309, + 69, + 545, + 342 + ], + "type": "table", + "html": "
ModalityMethodMain ModelAccuary(%)
RGBGraves [10]VGG16+LSTM74.70
Cao [4]C3D+LSTM +RLSTM89.30
Carreira [5]I3D90.33
Tang [30]SeST93.20
Yu [48]SlowFast+NAS293.31
Köpüklü [14]ResNeXt-10193.75
OursRes3D-1894.93
depthGraves [10]VGG16+LSTM77.70
Carreira [5]I3D89.47
Cao [4]C3D+LSTM +RLSTM90.60
Tang [30]SeST93.35
Köpüklü [14]ResNeXt-10194.03
Yu [48]SlowFast+NAS294.13
OursRes3D-1893.47
RGB+DGraves [10]VGG16+LSTM81.40
Cao [4]C3D+LSTM +RLSTM92.20
Carreira[5]I3D92.78
Joze[13]MMTM93.87
Yu[48]SlowFast+NAS295.52
OursRes3D-1895.72
", + "image_path": "235c5ec3de5413b509ca0e1d99883719f81ba9553bec13a37025304a043a0dce.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 368, + 547, + 579 + ], + "blocks": [ + { + "bbox": [ + 320, + 347, + 531, + 359 + ], + "lines": [ + { + "bbox": [ + 320, + 347, + 531, + 359 + ], + "spans": [ + { + "bbox": [ + 320, + 347, + 531, + 359 + ], + "type": "text", + "content": "Table 2. Comparison with SOTAs on EgoGesture Dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 368, + 547, + 579 + ], + "lines": [ + { + "bbox": [ + 309, + 368, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 309, + 368, + 547, + 579 + ], + "type": "table", + "html": "
ModalityMethodMain ModelAccuary(%)
RGBSimonyan [29]VGG41.90
Feichtenhofer [9]SlowFast69.58
Yu [48]SlowFast+NAS²71.25
Wang [42]ConvNet73.85
Li [15]Transformer80.42
Zhou [57]I3D+Transformer81.25
OursRes3D-1888.33
depthSimonyan [29]VGG34.06
Wang [42]ConvNet65.00
Feichtenhofer [9]SlowFast68.75
Yu [48]SlowFast+NAS²69.58
Li [15]Transformer76.04
Zhou [57]I3D+Transformer77.92
OursRes3D-1882.91
RGB+DFeichtenhofer [9]SlowFast76.25
Yu [48]SlowFast+NAS²78.38
Li [15]Transformer84.90
Zhou [57]I3D+Transformer87.04
OursRes3D-1890.51
", + "image_path": "27bf555a1f436413533fa3aaac22e2841670692bf3aa8ae6821052f6463b7667.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 585, + 533, + 597 + ], + "lines": [ + { + "bbox": [ + 318, + 585, + 533, + 597 + ], + "spans": [ + { + "bbox": [ + 318, + 585, + 533, + 597 + ], + "type": "text", + "content": "Table 3. Comparison with SOTAs on THU-READ Dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 617, + 394, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 617, + 394, + 629 + ], + "spans": [ + { + "bbox": [ + 306, + 617, + 394, + 629 + ], + "type": "text", + "content": "the memory network." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 646, + 463, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 463, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 463, + 657 + ], + "type": "text", + "content": "4.2.3 Performance on THU-READ" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "THU-READ dataset has 1920 videos of 40 classes, which are performed by 8 subjects. Although involving fewer videos and fewer classes, it is yet challenging due to the subtle intra-class differences and the background noise." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20974" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 70, + 269, + 139 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 269, + 139 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 269, + 139 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 269, + 139 + ], + "type": "table", + "html": "
Suff.Comp.memory networkAcc(%)
RGBdepth
×××78.3369.58
✓××82.2973.43
✓✓×85.4176.76
✓✓✓88.3382.91
", + "image_path": "476e1979e7ce7f94a9a4468d4390e8247a1caa8379b7f8fa0f9a0ac9985c5b47.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 141, + 266, + 163 + ], + "lines": [ + { + "bbox": [ + 47, + 141, + 266, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 141, + 266, + 163 + ], + "type": "inline_equation", + "content": "^{*}" + }, + { + "bbox": [ + 47, + 141, + 266, + 163 + ], + "type": "text", + "content": " Suff. " + }, + { + "bbox": [ + 47, + 141, + 266, + 163 + ], + "type": "inline_equation", + "content": "=" + }, + { + "bbox": [ + 47, + 141, + 266, + 163 + ], + "type": "text", + "content": " Sufficiency, Comp. " + }, + { + "bbox": [ + 47, + 141, + 266, + 163 + ], + "type": "inline_equation", + "content": "=" + }, + { + "bbox": [ + 47, + 141, + 266, + 163 + ], + "type": "text", + "content": " Compactness Table 4. Impacts of components of the proposed framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "text", + "content": "Table 3 reports the comparison on the THU-READ dataset. The results are reported by averaging all 4 splits under CS protocol as per [32]. The proposed method also achieves the best performance on this dataset. Compared with the second best one of Zhou et al. [57], which employs a combination of I3D and Transformer network, our results are still " + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "text", + "content": " better than theirs on RGB and depth data, respectively. For the RGB-D fusion result, the performance of the proposed method reaches " + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "inline_equation", + "content": "90.51\\%" + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "text", + "content": ", and outperforms Zhou et al.'s at about " + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 47, + 182, + 289, + 316 + ], + "type": "text", + "content": ", even though we just utilize a simple average fusion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 141, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 141, + 336 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 141, + 336 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 342, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 461 + ], + "type": "text", + "content": "The studies on the effectiveness of our designs, including representation refinement with IB and predictive information distillation with memory network, are first presented in this section. In order to evaluate our scheme using a memory network, we have also compared several different addressing strategies, including using cosine similarity only for addressing and using content-based addressing only. THU-READ dataset is employed for this ablation study. Without specific saying, the experimental settings are the same as mentioned in Section 4.1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 463, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 288, + 715 + ], + "type": "text", + "content": "Impacts of components of the proposed framework. In Table 4, we show how the proposed framework helps to eliminate gesture-irrelevant factors and leads to a more compact and robust feature representation. We compare several strategies, including 1) the baseline of using Res3D-18 only, 2) optimizing with the Sufficiency rule only, 3) using both Sufficiency and Compactness rules, namely using the IB loss in Eq.(6), and 4) using IB loss and memory network. The performance is marked in rows with a checkmark or a cross, denoting whether the corresponding module is used or not. Compared with the baseline, optimizing under the IB theory, even only considering the Sufficiency rule can lead to a significant performance improvement. This demonstrates the importance of a good representation for recognition tasks. When extending the loss to involve the Compactness rule, even better performance can be achieved. Replacing the convolution-based IB module with the memory network encourages the deposition of predictive information and leads to another performance gain. This suggests the effectiveness of memory network for highlighting the predictive information explicitly." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 342, + 70, + 511, + 133 + ], + "blocks": [ + { + "bbox": [ + 342, + 70, + 511, + 133 + ], + "lines": [ + { + "bbox": [ + 342, + 70, + 511, + 133 + ], + "spans": [ + { + "bbox": [ + 342, + 70, + 511, + 133 + ], + "type": "table", + "html": "
addressing strategyAccuracy(%)
RGBdepth
cosine similarity only80.5171.76
content-based only84.5775.62
proposed method88.3382.91
", + "image_path": "9c6e1b4e3ac4a0ff9ce8b66c8beaf0d871688a138b2f27d00342fc218302d2ba.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 137, + 545, + 148 + ], + "lines": [ + { + "bbox": [ + 306, + 137, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 306, + 137, + 545, + 148 + ], + "type": "text", + "content": "Table 5. Performance with different memory addressing strategies." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "type": "text", + "content": "Effect of different addressing strategies. The effect of different addressing strategies is shown in Table 5. When only the cosine similarity is used for addressing, the performance is poor. This implies that similar " + }, + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "type": "text", + "content": " weaken the effectiveness of IB loss. After adding the gating flag " + }, + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 168, + 545, + 300 + ], + "type": "text", + "content": ", and even just using content-based addressing, the performance is improved significantly. When all the addressing strategies are combined, the performance is further boosted. This indicates that a combination of content-based and contextual addressing can leverage both inter- and intra-memory feature relations and achieve better performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 300, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 372 + ], + "type": "text", + "content": "Visualization. To better illustrate how the robust presentation derived from our proposed framework shrinks the inner-class difference, which is mainly caused by gesture-irrelevant variations, we present a visualization of a 2D projection of feature encoding by t-SNE. The visualization is conducted on RGB data of the THU-READ dataset (CS3)." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 386, + 387, + 461 + ], + "blocks": [ + { + "bbox": [ + 309, + 386, + 387, + 461 + ], + "lines": [ + { + "bbox": [ + 309, + 386, + 387, + 461 + ], + "spans": [ + { + "bbox": [ + 309, + 386, + 387, + 461 + ], + "type": "image", + "image_path": "74b9626122022bcf2be67dbb2e106d529b068a128714ac421169324c2320276e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 341, + 466, + 352, + 475 + ], + "lines": [ + { + "bbox": [ + 341, + 466, + 352, + 475 + ], + "spans": [ + { + "bbox": [ + 341, + 466, + 352, + 475 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 389, + 387, + 465, + 460 + ], + "blocks": [ + { + "bbox": [ + 389, + 387, + 465, + 460 + ], + "lines": [ + { + "bbox": [ + 389, + 387, + 465, + 460 + ], + "spans": [ + { + "bbox": [ + 389, + 387, + 465, + 460 + ], + "type": "image", + "image_path": "d8dc7cb867b9900a4171621cb66d02aa71cfc32eb47cea0644e9e90788e7aab8.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 419, + 466, + 429, + 475 + ], + "lines": [ + { + "bbox": [ + 419, + 466, + 429, + 475 + ], + "spans": [ + { + "bbox": [ + 419, + 466, + 429, + 475 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 467, + 387, + 542, + 461 + ], + "blocks": [ + { + "bbox": [ + 467, + 387, + 542, + 461 + ], + "lines": [ + { + "bbox": [ + 467, + 387, + 542, + 461 + ], + "spans": [ + { + "bbox": [ + 467, + 387, + 542, + 461 + ], + "type": "image", + "image_path": "376db8a530079928b572209e8c7a3acbb7662e2817b63b26b9355ef181ef38c6.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 498, + 466, + 507, + 475 + ], + "lines": [ + { + "bbox": [ + 498, + 466, + 507, + 475 + ], + "spans": [ + { + "bbox": [ + 498, + 466, + 507, + 475 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 478, + 545, + 534 + ], + "lines": [ + { + "bbox": [ + 304, + 478, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 478, + 545, + 534 + ], + "type": "text", + "content": "Figure 5. Visualizing the projection of feature distribution by t-SNE associated with the class label. (a) Feature extracted by baseline model. (b) Feature extracted by the network with proposed IB loss only. (c) Feature extracted by the proposed model. (Best viewed in color and zooming in.)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 545, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 677 + ], + "type": "text", + "content": "The visualization result is consistent with the performance comparison in Table 4. As can be seen, the mixed classes of the baseline model in Fig.5(a) are no longer intermingled in Fig.5(b). It means our framework with IB loss can effectively improve the discriminative power of the features. When adding the memory network, almost all the clusters can concentrate on their centroids. It indicates that with the memory network, the predictive information can be clearer, and the inner-class differences become narrowed. It allows the mixed classes to be more easily distinguished from each other in the encoding space." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "In addition to utilizing t-SNE visualizations, we give some more examples to effectively illustrate how the proposed network mitigates the impact of gesture-irrelevant" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20975" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 274, + 174 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 274, + 174 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 274, + 174 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 274, + 174 + ], + "type": "image", + "image_path": "eafc46a40ab01c08fb204925b29ccfc3d65dac70f8445d125dd5755777ecdac8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 176, + 287, + 229 + ], + "blocks": [ + { + "bbox": [ + 48, + 176, + 287, + 229 + ], + "lines": [ + { + "bbox": [ + 48, + 176, + 287, + 229 + ], + "spans": [ + { + "bbox": [ + 48, + 176, + 287, + 229 + ], + "type": "image", + "image_path": "4e87df8e023872fe0f63ec3de54e5c1088817c4c374fae8ca3bbf512857c09f7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 288, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 280 + ], + "type": "text", + "content": "Figure 6. An analysis of how the proposed network improves the performance. (a) The confusion matrix of baseline. (b) The confusion matrix of the proposed network. (c) Intuitive presentation of the irrelevant factors affecting gesture recognition." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 299, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 289, + 563 + ], + "type": "text", + "content": "factors and ultimately enhances performance. In Fig.6(a) and (b), we first visualize the confusion matrice of the baseline and the proposed network. As can be seen, ours can apparently avoid most of the wrong classifications. Then let us consider some concrete instances of gestures that are misclassified by the baseline model. As illustrated in the confusion matrix of the baseline model, Class 5, namely cut paper is wrongly categorized as Class 15 of open laptop. This confusion is primarily attributed to the resemblance in environmental conditions. As shown in Fig.6(c), both scenarios share a similar desk setup, and the overexposed laptop seems also like a white paper to some extent. Another example is Class 2 of clean table being wrongly deemed as Class 35 of wave hand. The similarities in hand movement and positioning lead to the misguided classification of these gestures. These examples prove that overfitting to these environmental cues rather than learning a robust feature representation of gesture-relevant factors results in the wrong predictions. By contrast, our method is designed to learn the essential feature of one type of gesture. Therefore, it avoids being influenced by extraneous contextual information, leading to remarkable improvement in performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 573, + 119, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 119, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 119, + 586 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we present a framework that aims to improve the robustness of feature representation for RGB-D gesture recognition based on the information bottleneck theory. We analyze the factors that are relevant and irrelevant to gestures using mutual information and design a loss function that disentangles the task-relevant predictive cues from disturbing superfluous information. Additionally, we use a memory network to overlay the encoding feature of each sample by memory writing and reading. This process attenuates nuisances and highlights task-relevant informa" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 120 + ], + "type": "text", + "content": "tion shared by all samples. Experiments on three public datasets demonstrate that our approach produces a superior feature representation and achieves better performance than state-of-the-art methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 133, + 404, + 147 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 404, + 147 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 404, + 147 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 154, + 547, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 154, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 154, + 547, + 250 + ], + "type": "text", + "content": "The work was jointly supported by the National Natural Science Foundation of China under grants No.62002271, 62272364, and 62202360, the National Key R&D Program of China under No.2022ZD0117103, Teaching Reform Project of Shaanxi Higher Continuing Education under No.21XJZ004, Guangxi Key Laboratory of Trusted Software under No.KX202041 and the Fundamental Research Funds for the Central Universities under No.ZYTS23213." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 262, + 365, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 262, + 365, + 275 + ], + "spans": [ + { + "bbox": [ + 307, + 262, + 365, + 275 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 310, + 283, + 547, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 310, + 283, + 547, + 316 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 283, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 310, + 283, + 547, + 316 + ], + "type": "text", + "content": "[1] Alessandro Achille and Stefano Soatto. 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GCD is similar to semi-supervised learning (SSL) but is more realistic and challenging, as SSL assumes all the unlabelled images are from the same classes as the labelled ones. We also do not assume the class number in the unlabelled data is known a-priori, making the GCD problem even harder. To tackle the problem of GCD without knowing the class number, we propose an EM-like framework that alternates between representation learning and class number estimation. We propose a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to dynamically determine the prototypes by examining the cluster compactness and separability. With these prototypes, we leverage prototypical contrastive learning for representation learning on the partially labelled data subject to the constraints imposed by the labelled data. Our framework alternates between these two steps until convergence. The cluster assignment for an unlabelled instance can then be retrieved by identifying its nearest prototype. We comprehensively evaluate our framework on both generic image classification datasets and challenging fine-grained object recognition datasets, achieving state-of-the-art performance. Our code is available at https://github.com/DTennant/GPC.", + "bbox": [ + 75, + 323, + 473, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 790, + 209, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of deep learning is driven by the availability of large-scale data with human annotations. Given enough annotated data, deep learning models are able to surpass human-level performance on many important computer vi", + "bbox": [ + 76, + 816, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3c0ec6fee07670b105b3a428fed05ac6b313a1c5582eb17621b957579712d86f.jpg", + "image_caption": [ + "Figure 1: Overview of our proposed EM-like framework. The input images are fed into a ViT-B model to obtain a 768-dimensional feature vector, then the feature vector will be projected to a lower dimensional space using the projection calculated from PCA. We perform class number estimation and representation learning in this projected space. In the E-step, we use a semi-supervised GMM that can split separable clusters and merge cluttered clusters to estimate the class number and prototypes, which will be used in the M-step of representation learning with prototypical contrastive learning." + ], + "image_footnote": [], + "bbox": [ + 503, + 289, + 890, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sion tasks such as image classification [21]. But the cost of collecting a large annotated dataset is not always affordable, and it is also not possible to annotate all new classes emerging from the real world. Thus, designing models that can learn to deal with large-scale unlabelled data in the open world is of great value and importance. Semi-supervised learning (SSL) [38] is proposed as a solution to learn a model on both labelled data and unlabelled data, with many works achieving promising performance [1, 46, 44]. However, SSL assumes that labelled instances are provided for all object classes in the unlabelled data. The novel category discovery (NCD) task is introduced [17, 16] to automatically discover novel classes by transferring the knowledge learned from the labelled instances of known classes, assuming the unlabelled data only contain instances from new classes. Generalized category discovery (GCD) [48] further relaxes the assumption in NCD, and tackles a more", + "bbox": [ + 496, + 643, + 895, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16623", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "generalized setting where the unlabelled data contains instances from both known and novel categories. Existing methods for NCD [17, 16, 58, 60, 61, 12, 26] and GCD [48, 11, 51, 45, 56, 59, 34] learn the representation and cluster assignment assuming the class number is known a priori [58, 26, 60, 12, 61] or precomputed [17, 48]. In practice, the number of categories in the unlabelled data is often unknown, while precomputing the class number without taking the representation learning into consideration is likely to lead to a sub-optimal solution.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we argue that representation learning and the estimation of class numbers should be considered together and could reinforce each other, i.e., a strong representation could help a more accurate estimation of the class numbers, and an accurate class number could help learn a better feature representation. To this end, we propose a unified EM-like framework that alternates between feature representation learning and class number estimation where the E-step is aimed at automatically estimating a proper class number and a set of class prototypes in the unlabelled data and the M-step is aimed at learning better representation with the class number and class prototypes estimated. In particular, we propose using a prototype contrastive representation learning [33] method for GCD, which requires a set of prototypes to serve as anchors for representation learning. Prototypical contrastive learning [33] is developed for unsupervised representation learning to generalize to different tasks, where the prototypes are obtained by over-clustering the dataset with one or multiple given prototype numbers, using non-parametric clustering algorithms like $k$ -means. Instead, to handle the problem of GCD, we propose to estimate the prototype number and prototypes automatically and simultaneously. To do so, we introduce a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to determine the most suitable clusters based on current representation. These clusters can then be used to form prototypes to facilitate contrastive representation learning. Our framework alternates between the E- and M-step until converging to achieve robust representation and reliable category estimation. After learning, the cluster assignment for an unlabelled instance, either from known or novel classes, can be retrieved by finding the nearest prototypes. Thus we name our framework as GPC: Gaussian mixture model for generalized category discovery with Protypical Contrastive learning.", + "bbox": [ + 75, + 244, + 472, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions in this paper are as follows: (1) We demonstrate that in generalized category discovery, the class number estimation and representation learning can reinforce each other in the learning process. Strong representations can give a better estimation of the class number, and vice versa. (2) We propose an EM-like framework that alternates between prototype estimation with a variant of GMM (E-step) and representation learning based on prototypical", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "contrastive learning (M-step). (3) We introduce a semi-supervised variant of GMM with a stochastic splitting and merging mechanism to allow dynamic change of the prototypes by examining the cluster compactness and separability based on the Metropolis-Hastings ratio [19]. (4) We comprehensively evaluated our framework on both the generic image classification benchmark, including CIFAR10, CIFAR100, ImageNet-100, and the challenging fine-grained Semantic Shifts Benchmark suite, which includes CUB-200, Stanford-Cars, and FGVC-aircrafts, achieving the state-of-the-art results.", + "bbox": [ + 496, + 90, + 895, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 498, + 271, + 638, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Novel category discovery (NCD) is first formalized in DTC [17], where the task is to discover new categories leveraging the knowledge of a set of labelled categories. Many methods have been proposed to tackle this challenge. To name a few, RankStat [15, 16] and DualRank [58] transfer knowledge from labelled to unlabelled classes using feature ranking statistics. OpenMix [61] shows that mixing labelled and unlabelled data can prevent overfitting. NCL [60] and WTA [26] use contrastive learning for NCD. UNO [12] introduces a unified cross-entropy loss for joint training on labelled and unlabelled data. [29] introduces a spacing loss for representation learning in NCD. NCDwF [28] studies the NCD problem under an incremental learning setting. Earlier methods like [22, 23] for generalized transfer learning can also be applied to NCD. Generalized category discovery (GCD) [48] extends NCD to a more open-world setting where unlabelled instances can come from both labelled and unlabelled categories. ORCA [2] also tackles GCD from a semi-supervised learning perspective. Several improved methods have been proposed for generalized category discovery (GCD), such as [11, 51, 39, 56, 45], which have shown promising results. Incremental GCD is considered in [57, 59]. Concurrently, CiPR [18] presents a hierarchical GCD approach employing selective neighbor clustering, leading to improved efficiency and performance without necessitating knowledge of the class number. [14] studies semantic category discovery by leveraging vision-language representations, thereby enabling GCD with class name prediction. However, most existing GCD methods assume that the novel class number is known a priori, which is often not the case in the real world. To address this limitation, [17, 48] precompute the number of novel classes with a semi-supervised $k$ -means algorithm from pretrained representations. In this paper, we demonstrate that class number estimation and representation learning can be jointly considered to mutually benefit each other.", + "bbox": [ + 496, + 296, + 895, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contrastive learning [4, 5, 20, 7, 62] (CL) has been shown very effective for representation learning in a self-supervised manner, using the instance discrimination pretext [52] as the learning objective. The instance discrimination task learns", + "bbox": [ + 498, + 839, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16624", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a representation by pulling positive samples from the augmentations of the same images closer and pushing negative samples from different images apart in the embedding space. Instead of contrasting over all instances in a mini-bath, prototypical contrastive learning (PCL) [33] proposes to contrast the features with a set of prototypes which can provide a higher level abstraction of dataset than instances and has been shown to be more data efficient without the need of large batch size. Though PCL is developed for unsupervised representation learning, if the prototypes are viewed as cluster centers, it can be leveraged in the partially supervised setting of GCD for representation learning to better fit the GCD task of partitioning data into different clusters. Thus, in this paper, we adopt PCL to fit the GCD setting for representation learning in which the downstream clustering task is directly considered.", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semi-supervised learning (SSL) has been a long standing research topic which many effective method proposed [40, 44, 1, 32, 46]. In SSL, the labelled and the unlabelled data are assumed to come from the same set of classes, and the task is to learn a classification model that can take advantage of both labelled and unlabelled data. Consistency-based methods are among the most effective methods for SSL, such as Mean-teacher [46], MixMatch [1], and FixMatch [44]. Self-supervised representation learning also shows to be helpful for SSL because it can provide a strong representation [55, 40]. Recent works extend semi-supervised learning by relaxing the assumption of exactly the same classes in the labeled and unlabelled data [43, 25, 54], but their focus is improving the performance of the labeled categories without discovering novel categories in the unlabeled set.", + "bbox": [ + 75, + 332, + 472, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unsupervised clustering has been studied for decades, and there are many existing classical approaches [35, 10, 6] as well as deep learning based approaches [53, 41, 13]. Recently, DeepDPM [42] is proposed to automatically determine the number of clusters for a given dataset by adopting a similar split/merge framework that changes the inferred number of clusters. However, due to the unsupervised nature of these methods, there is no prior or supervision over how a cluster should be formed, thus multiple equally valid clustering results following different clustering criteria can be produced. Thus, directly applying unsupervised clustering methods to the task of generalized category discovery is not feasible, as we would want the model to use one unique clustering criteria implicitly given by the labelled data.", + "bbox": [ + 75, + 560, + 472, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 784, + 169, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a collection of partially labelled data, $\\mathcal{D} = \\mathcal{D}^l\\cup \\mathcal{D}^u$ where $\\mathcal{D}^l = \\{(x_i,y_i^l)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_l$ is labelled, $\\mathcal{D}^u = \\{x_i,y_i^u\\} \\in \\mathcal{X}\\times \\mathcal{Y}_u$ is unlabelled, and $\\mathcal{V}_l\\subset \\mathcal{V}_u$ Generalized category discovery (GCD) aims at automatically assign labels for the unlabelled instances in $\\mathcal{D}^u$ , by transferring knowledge acquired from $\\mathcal{D}^l$ . Let the category number in", + "bbox": [ + 75, + 809, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathcal{D}^l$ be $K^l = |\\mathcal{Y}_l|$ and that in $\\mathcal{D}^u$ be $K^u = |\\mathcal{Y}_u|$ . The number of new categories $\\mathcal{D}^u$ is then $K^n = |\\mathcal{Y}_u \\setminus \\mathcal{Y}_l| = K^u - K^l$ . Though $K^l$ can be accessed from the labelled data, we do not assume $K^n$ or $K^u$ to be known. This is a realistic setting to reflect the real open world, where we often have access to some labelled data, but in the unlabelled data, we also have instances from unseen new categories.", + "bbox": [ + 496, + 90, + 893, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The key challenges for GCD are representation learning, category number estimation, and label assignment. Existing methods for NCD and GCD [17, 48] deal with these three challenges independently. However, we believe they are inherently linked with each other. Label assignment depends on representation and category number estimation. A good class number estimation can facilitate representation learning, thus better label assignment, and vice versa. Thus, in this paper, we aim to jointly handle these challenges in the learning process for a more reliable GCD.", + "bbox": [ + 496, + 196, + 893, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To this end, we propose a unified EM-like framework that alternates between representation learning and class number estimation, while the label assignment turns out to be a by-product during class number estimation. In the E-step, we introduce a semi-supervised variant of the Gaussian Mixture Model (GMM) to estimate the class numbers by dynamically splitting separable clusters and merging cluttered clusters based on current representation, forming a set of class prototypes for both seen and unseen classes, and in the M-step, we train the model to produce discriminative representation by prototypical contrastive learning using the cluster centers from the GMM prototypes derived from the E-step during class number estimation. After training, the class assignment for each instance can be retrieved by simply identifying the nearest prototype.", + "bbox": [ + 496, + 347, + 895, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Representation learning", + "text_level": 1, + "bbox": [ + 500, + 583, + 723, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of representation learning is to learn a discriminative representation that can well separate different categories, not only the old ones, but also the new ones. Contrastive learning (CL) has been shown to be an effective choice for NCD [26] and GCD [48]. Self-supervised contrastive learning is defined as", + "bbox": [ + 496, + 606, + 893, + 698 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C L} = - \\log \\frac {\\exp \\left(z _ {i} \\cdot z _ {i} ^ {\\prime} / \\tau\\right)}{\\sum_ {j = 1} ^ {n} \\exp \\left(z _ {i} \\cdot z _ {j} ^ {\\prime} / \\tau\\right)} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 705, + 893, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $z_{i}$ and $z_{i}^{\\prime}$ are the representations of two views obtained from the same image using random augmentations and $\\tau$ is the temperature. Two views of the same instance are pulled closer, and different instances are pushed away during training. Self-supervised contrastive learning and its supervised variant, in which different instances from the same category are also pulled closer, are used in [48] for representation learning. However, as a stronger training signal is used for the labelled data, the representation is likely biased to the labelled data to some extent. Moreover, such a method does", + "bbox": [ + 496, + 750, + 895, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16625", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "not take the downstream clustering task into account during learning, thus a clustering algorithm is required to run independently after the representation learning.", + "bbox": [ + 75, + 90, + 470, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, we adopt prototypical contrastive learning (PCL) [33] to the GCD setting to learn the representation $z_{i} = f(x_{i}) \\in \\mathbb{R}^{d}$ . PCL uses a set of prototypes $\\mathcal{C} = \\{\\mu_1, \\dots, \\mu_K\\}$ to represent the dataset for contrastive learning instead of the random augmentation generated views $z_{i}'$ . PCL loss can be written as", + "bbox": [ + 75, + 136, + 470, + 228 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {P C L} = - \\log \\frac {\\exp \\left(z _ {i} \\cdot \\mu_ {s} / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(z _ {i} \\cdot \\mu_ {j} / \\tau\\right)} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 238, + 470, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu_{s}$ is the corresponding prototype for $z_{i}$ . It was originally designed as an alternative for self-supervised contrastive learning by over-clustering the training data to obtain the prototypes during training. We employ PCL here to learn reliable representation while taking the downstream clustering into account for GCD, where we have a set of partially labelled data. In our case, the prototypes can be interpreted as the class centers for each of the categories. To obtain the prototypes for the seen categories, we directly calculate the class mean by averaging all the feature vectors of the labelled instances. For the unseen categories, we obtain the prototypes with a semi-supervised variant of the Gaussian Mixture Model (GMM), as will be introduced in Sec. 3.2. This way, the cluster assignment for an unlabelled image can be readily achieved by finding the nearest prototype.", + "bbox": [ + 75, + 286, + 472, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Additionally, we observe that only a few principal dimensions can already recover most of the variances in the representation space of $z_{i}$ , which is known as dimensional collapse (DC) in [27, 24], and it is shown that DC can be caused by strong augmentations or implicit regularizations in the model, and preventing DC during training can lead to a better feature representation. To alleviate DC for representation learning in our case, we propose to first project the feature to a subspace obtained by principal component analysis (PCA) before the contrastive learning. Specifically, we apply PCA on a matrix $Z$ formed by a mini-batch of features $z_{i}$ , with a batch size of $n$ , the feature dimension $d$ , and the number of effective principal directions $q$ . We have $Z \\approx U\\mathrm{diag}(S)V^{\\top}$ , where $U \\in \\mathbb{R}^{n \\times q}$ , $S \\in \\mathbb{R}^q$ and $V \\in \\mathbb{R}^{d \\times q}$ . We can then project features $z_{i}$ to principal directions to obtain a more compact feature $v_{i} = V \\cdot z_{i}$ , and replace feature $z_{i}$ with $v_{i}$ in Eq. (2) for PCL. The prototypes are also computed in the projected space.", + "bbox": [ + 75, + 512, + 470, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We jointly use self-supervised contrastive learning and PCL to train our model. The overall learning objective can be written as", + "bbox": [ + 75, + 784, + 470, + 829 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {C L} + \\lambda (t) \\mathcal {L} _ {P C L} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 842, + 470, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda(t)$ is a linear warmup function defined as $\\lambda(t) = \\min(1, \\frac{t}{T})$ where $t$ is the current epoch and $T$ warmup length", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/451c293d30123ad4dcd7869fbe76c22e28e585d84e9b7b0f951b2601d5c728bc.jpg", + "image_caption": [ + "Figure 2: Examples for splitting a separable cluster and merging two cluttered clusters. Left: the cluster is split because the two sub-component in this cluster are easily separable. Right: two clusters are merged as they are cluttered and likely from the same class." + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 883, + 147 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$(T = 20$ in our experiments). The reason we use both CL and PCL is that, in the beginning, the representation is not well suited for clustering, and thus the obtained prototypes are not informative to facilitate the representation learning. Hence, we gradually increase the weight of PCL during training from 0 to 1 in the first $T$ epochs.", + "bbox": [ + 498, + 257, + 893, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Class number and prototypes estimation with semi-supervised Gaussian mixture model", + "text_level": 1, + "bbox": [ + 500, + 359, + 890, + 390 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we present a semi-supervised variant of the Gaussian mixture model (GMM) with each Gaussian component consisting of two sub-components to estimate the prototypes for representation learning in Sec. 3.1 and the unknown class number. GMM estimates the prototypes and assigns a label for each data point by finding its nearest prototype. The cluster label assignment and the prototypes are then used for prototypical contrastive learning. The GMM is defined as", + "bbox": [ + 498, + 398, + 892, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (z) = \\sum_ {i = 1} ^ {K} \\pi_ {i} \\mathcal {N} \\left(z \\mid \\mu_ {i}, \\Sigma_ {i}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 542, + 892, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{N}(z|\\mu_i,\\Sigma_i)$ is the Gaussian probability density function with mean $\\mu_{i}\\in \\mathbb{R}^{d}$ and covariance $\\Sigma_{i}\\in \\mathbb{R}^{d\\times d}$ , and $\\pi_{i}$ is the weight for $i$ -th Gaussian component and we have $\\sum_{i = 1}^{N}\\pi_{i} = 1$ . Ideally, we would expect the component number $K$ in the GMM to be equal to the class number $K^u$ in $\\mathcal{D}$ . To estimate the unknown class number $K^u$ , we leverage an automatic splitting-and-merging strategy into the modeling process to obtain an optimal $K$ , which is expected to be as close to $K^u$ as possible. We alternate between representation learning and $K^u$ estimation until convergence to get discriminative representation learning and a reliable class number estimation. For initialization, $K$ can be set to any number greater than $K^l$ . In our experiments, we simply set the initial number of components to a default $K_{init} = K^l +\\frac{K^l}{2}$ . We run a semi-supervised $k$ -means algorithm [48] with $k = K$ to obtain the $\\mu$ and $\\Sigma$ for each component in the mixture model. Note that the semi-supervised $k$ -means algorithm is constrained to the labelled data in a way that labelled instances from the same class are assigned to the same cluster, and labelled instances from different classes will not be", + "bbox": [ + 498, + 595, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16626", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: The overall algorithm of our method." + ], + "code_body": "Input: $\\mathcal{D},\\mathcal{D}^l$ , and $\\mathcal{D}^u$ The datasets. $K_{init}$ Initial guess of $K$ \n1 $K\\gets K_{init}$ \n2 for $e = 1$ to $E$ do \n3 $z\\gets f(x),x\\in \\mathcal{D}\\quad /$ extract features \n4 $\\mu ,\\Sigma \\gets \\arg \\max \\sum_{i = 1}^{K}\\pi_{i}\\mathcal{N}(z|\\mu_{i},\\Sigma_{i})$ // estimate prototypes using GMM \n5 for $i = 1$ to len(D) do \n6 $\\mathcal{B}^l\\gets \\{x_i^l\\sim \\mathcal{D}^l\\}_{i = 1}^{N^l}\\quad /$ sample a batch of $N^l$ labelled images \n7 $\\mathcal{B}^u\\gets \\{x_i^u\\sim \\mathcal{D}^u\\}_{i = 1}^{N^u}\\quad /$ sample a batch of $N^u$ unlabelled images \n8 $f\\gets \\arg \\min \\mathcal{L}(f,\\mu ,\\mathcal{B}^l,\\mathcal{B}^u)$ // prototypical contrastive learning \n9 end \n10 $H_{s},H_{m}\\gets \\mathrm{calc\\_prob}(\\mu ,\\Sigma)$ // probability for split and merge \n11 $\\mu ,\\Sigma \\gets \\mathrm{perform\\_op}(H_s,H_m)\\quad /$ perform operations \n12 $K\\gets \\mathrm{len}(\\mu)$ // update $K$ \n13 end Output: feature extractor $f(\\cdot)$ , cluster centers $\\mu_{i}$", + "bbox": [ + 78, + 111, + 472, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "assigned to the same cluster. To facilitate the splitting and merging process, for each Gaussian component defined by $\\mu_{i}$ and $\\Sigma_{i}$ , we further depict it with a GMM with two subcomponents $\\mu_{i,1},\\mu_{i,2}$ and $\\Sigma_{i,1},\\Sigma_{i,2}$ with $\\pi_{i,1} + \\pi_{i,2} = 1$ . We run a $k$ -means with $k = 2$ on the $i$ -th component to obtain $\\mu_{i,1},\\mu_{i,2}$ and $\\Sigma_{i,1},\\Sigma_{i,2}$ .", + "bbox": [ + 75, + 566, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For a cluster whose two sub-components are roughly independent and equally sized (e.g., left part of Fig. 2), i.e., they are easily separable, we would like the model to split it into two such that the model can better fit the data distribution and the class assignment will be more accurate because it is less likely that such distinct clusters will belong to the same class. For two clusters that are cluttered with each other (e.g., right part of Fig. 2), i.e., difficult to distinguish, we would like to merge them into one, so that they will be considered as from the same class. Following this intuition, we use the Metropolis-Hastings framework [19] to compute a probability $p_{s} = \\min(1, H_{s})$ to stochastically split a cluster into two. The Hastings ratio is defined as", + "bbox": [ + 75, + 657, + 470, + 852 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH _ {s} = \\frac {\\Gamma \\left(N _ {i , 1}\\right) h \\left(\\mathcal {Z} _ {i , 1} ; \\theta\\right) \\Gamma \\left(N _ {i , 2}\\right) h \\left(\\mathcal {Z} _ {i , 2} ; \\theta\\right)}{\\Gamma \\left(N _ {i}\\right) h \\left(\\mathcal {Z} _ {i} ; \\theta\\right)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 864, + 468, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Gamma$ is the factorial function, i.e., $\\Gamma (n) = n! = n\\times (n - 1)\\times \\dots \\times 1$ , $\\mathcal{Z}_i$ is the set of data points in cluster $i$ , $\\mathcal{Z}_{i,j}$ is the set of data points in the $j$ -th sub-cluster of cluster $i$ , $N_{i} = |\\mathcal{Z}_{i}|, N_{i,j} = |\\mathcal{Z}_{i,j}|$ , $h(Z;\\theta)$ is the marginal likelihood of the observed data $\\mathcal{Z}$ by integrating out the $\\mu$ and $\\Sigma$ parameters in the Gaussian, and $\\theta$ is the prior distribution of $\\mu$ and $\\Sigma$ . More details can be found in the supplementary. The intuition behind this $H_{s}$ is that, if the number of data points in two sub-components is roughly balanced, which is measured by the $\\Gamma (\\cdot)$ terms, and the data points in the two sub-components are independent of each other, which is measure by the $h(\\cdot ;\\theta)$ terms, there should be a greater chance of splitting the cluster. After performing a split operation, the $\\mu_{i}$ and $\\Sigma_{i}$ of previous components $i$ will be replaced with $\\mu_{i,1},\\mu_{i,2}$ and $\\Sigma_{i,1},\\Sigma_{i,2}$ of two sub-components. We will then run two $k$ -means within the two newly formed components to obtain their corresponding sub-components. On the contrary, if two clusters are cluttered with each other, they should be merged. Similar to splitting, we determine the merging probability by $p_m = \\min (1,H_m)$ , where $H_{m}$ is calculated similarly for two clusters $i$ and $j$ :", + "bbox": [ + 496, + 90, + 893, + 409 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH _ {m} = \\frac {\\Gamma \\left(N _ {i} + N _ {j}\\right) h \\left(\\mathcal {Z} _ {i} \\cup \\mathcal {Z} _ {j} ; \\theta\\right)}{\\Gamma \\left(N _ {i}\\right) h \\left(\\mathcal {Z} _ {i} ; \\theta\\right) \\Gamma \\left(N _ {j}\\right) h \\left(\\mathcal {Z} _ {j} ; \\theta\\right)}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 420, + 890, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that both $H_{s}$ and $H_{m}$ are within the range of $(0, +\\infty)$ , so we use $p_{s} = \\min(1, H_{s})$ and $p_{m} = \\min(1, H_{m})$ to convert it into a valid probability.", + "bbox": [ + 496, + 467, + 893, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To take the labelled instances into consideration during the splitting-and-merging process, if a cluster consists of labelled instances, we set its $p_s = 0$ ; if for any two clusters containing instances from two labelled classes, we set their $p_m = 0$ .", + "bbox": [ + 496, + 513, + 893, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the splitting-and-merging process, we first apply splitting according to the $p_s$ and then apply merging according to $p_m$ . The newly formed clusters by splitting will not be reused during the merging step. After finishing the splitting and merging, we can obtain the prototypes, and thus can estimate $K$ , for our PCL-based representation learning. We alternate between representation learning and class number estimation for each training epoch until converge. The final $K$ will be considered the estimated class number in $\\mathcal{D}$ . The cluster assignment for each unlabelled instance can be easily retrieved by identifying its nearest prototype, without the need of running a non-parametric clustering algorithm as [48]. The overall training process is summarized in Algorithm 1.", + "bbox": [ + 496, + 590, + 893, + 800 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 819, + 632, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental setup", + "text_level": 1, + "bbox": [ + 500, + 845, + 687, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Benchmark and evaluation metric. We validate the effectiveness of our method on the generic image classification", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16627", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ee77cfa270a6dcb011cb7d5cc7f0ba61184dc67e6b13db29a5d6b03208ee651f.jpg", + "table_caption": [ + "Table 1: Results on generic image classification datasets." + ], + "table_footnote": [], + "table_body": "
No.MethodsKnown KPCACIFAR10CIFAR100ImageNet-100
AllOldNewAllOldNewAllOldNew
(1)k-means [35]✓X83.685.782.552.052.250.872.775.571.3
(2)RankStats+ [16]✓X46.819.260.558.277.619.337.161.624.8
(3)UNO+ [12]✓X68.698.353.869.580.647.270.395.057.9
(4)ORCA [2]✓X81.886.279.669.077.452.073.592.663.9
(5)Vaze et al. [48]✓X91.597.988.273.076.266.574.189.866.3
(6)Ours (GPC)✓X92.098.388.777.484.862.476.594.068.5
(7)Ours (GPC)✓✓92.298.289.177.985.063.076.994.371.0
(8)Vaze et al. [48]XX88.696.284.973.283.557.972.791.863.8
(9)Vaze et al. [48]X✓89.797.386.374.883.858.773.892.164.6
(10)Ours (GPC)XX88.297.085.874.984.359.674.792.965.1
(11)Ours (GPC)X✓90.697.687.075.484.660.175.393.466.7
", + "bbox": [ + 80, + 109, + 888, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "benchmark (including CIFAR-10/100 [31] and ImageNet-100 [47]) and also the recently proposed Semantic Shift Benchmark [49] (SSB) (including CUB-200 [50], Stanford Cars [30], and FGVC-Aircraft [36]). For each of the datasets, we follow [48] and sample a subset of all classes for which we have annotated labels during training. For experiments on SSB datasets, we directly use the class split from [49]. $50\\%$ of the images from these labelled classes will be used as the labelled instances in $\\mathcal{D}^l$ , and the remaining images are regarded as the unlabelled data $\\mathcal{D}^u$ containing instances from labelled and unlabelled classes. See Tab. 2 for statistics of the datasets we evaluated. We evaluate model performance with clustering accuracy (ACC) following standard practice in the literature. At test-time, given ground truth labels $y^{*}$ and model predicted cluster assignments $\\hat{y}$ , the ACC is calculated as $ACC = \\frac{1}{M}\\sum_{i = 1}^{M}\\mathbb{1}(y_i^* = g(\\hat{y}_i))$ where $g$ is the optimal permutation for matching predicted cluster assignment $\\hat{y}$ to actual class label $y_i^*$ and $M = |\\mathcal{D}^u|$ .", + "bbox": [ + 75, + 378, + 473, + 652 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8035b72f8ad2d021a0a217e5cf9b16eb5e90578731003cb20d91d7746f968595.jpg", + "table_caption": [ + "Table 2: Data splits in the experiments." + ], + "table_footnote": [], + "table_body": "
labelledunlabelled
CIFAR-1055
CIFAR-1008020
ImageNet-1005050
CUB-200100100
Stanford-Cars9898
FGVC-aircraft5050
", + "bbox": [ + 133, + 684, + 410, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We train and test all the methods with a ViT-B/16 backbone [9] with pretrained weights from DINO [3]. We use the output of [CLS] token with a dimension of 768 as the feature representation for an input image. We only finetune the last block of the ViT-B backbone to", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "prevent the model from overfitting to the labelled classes during training. We set the batch size for training the model to 128 with 64 labelled images and 64 unlabelled images and use a cosine annealing schedule for the learning rate starting from 0.1. The number of principal directions in the PCA is set to 128, which we found performs the best across all the datasets evaluated. We train all the methods for 200 epochs on each dataset for a fair comparison with previous works, and the best-performing model is selected using the accuracy on the validation set of the labelled classes. All experiments are done with an NVIDIA V100 GPU with 32GB memory.", + "bbox": [ + 496, + 378, + 893, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with the state-of-the-art", + "text_level": 1, + "bbox": [ + 498, + 559, + 818, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Tab. 1, we report the comparison with the state-of-the-art method of [48], strong baselines derived from NCD methods, and the $k$ -means on the generic classification datasets. Notably, our method consistently achieves the best overall performance on all datasets, under the challenging setting where the class number is unknown. When the class number is known, our method also achieves the best performance on all datasets, except ImageNet-100, on which the best performance is achieved by ORCA [2]. In rows 1-7, we compare with other methods with the known class number in the unlabelled data, while in rows 8-11 we compare with [48] for the case of the unknown class number. We can see that our proposed framework outperforms other methods in most cases and especially when the number of classes is unknown. Comparing rows 10 and 11 to row 5, we can see that our proposed method without knowing the number of classes can even match the performance of previous strong baseline with the number of classes known to the model. Furthermore, from row 6 vs row 7 and row 10 vs row 11, we can see that the additional PCA layer can effectively improve the performance, also the performance", + "bbox": [ + 496, + 583, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16628", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3111102f653d8bbdd1b9ce8d51ef90d025f7bc20e9fa5ff5a899a733d7e2ad82.jpg", + "table_caption": [ + "Table 3: Results on Semantic Shift Benchmark datasets." + ], + "table_footnote": [], + "table_body": "
No.MethodsKnown KPCACUBStanford CarsFGVC-aircraft
AllOldNewAllOldNewAllOldNew
(1)k-means [35]✓X34.338.932.112.810.613.816.014.416.8
(2)RankStats+ [16]✓X33.351.624.228.361.812.126.936.422.2
(3)UNO+ [12]✓X35.149.028.135.570.518.640.356.432.2
(4)ORCA [2]✓X35.345.630.223.550.110.722.031.817.1
(5)Vaze et al. [48]✓X51.356.648.739.057.629.945.041.146.9
(6)Ours (GPC)✓X54.254.950.341.258.831.646.142.447.2
(7)Ours (GPC)✓✓55.458.253.142.859.232.846.342.547.9
(8)Vaze et al. [48]XX47.155.144.835.056.024.840.140.842.8
(9)Vaze et al. [48]X✓49.256.246.336.356.625.943.240.944.6
(10)Ours (GPC)XX50.252.845.636.756.326.339.739.642.7
(11)Ours (GPC)X✓52.055.547.538.258.927.443.340.744.8
", + "bbox": [ + 80, + 109, + 888, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "improvement from PCA is larger on the 'New' classes than on the 'Old' classes, which validates that the PCA can keep the representation space from collapsing and improve the performance on classes without using any labels. Due to the fact that labelled instances provide a stronger training signal, we can see from rows 6 - 11 that performance on 'Old' classes is generally steady. Comparing row 7 to row 5 and row 11 to row 8, we can see our full method outperforms the previous state-of-the-art method Vaze et al. [48] by large margins on both known and unknown class number cases. Tab. 3 shows performance comparison on the more challenging fine-grained Semantic Shift Benchmark [49]. A similar trend of Tab. 1 holds true for the results on SSB. Our approach achieves competitive performance in all cases and again reaches a better performance when the number of classes is unknown. In Tab. 4, we present the results on the Herbarium-19 dataset which is a long-tailed dataset, adding additional challenges for the GCD task. Again, our method performs the best on 'All' and 'New' classes. These results demonstrate the effectiveness of our method.", + "bbox": [ + 75, + 378, + 473, + 681 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/11390253e331f4f035464bb6d637b487b828fb3d71a3849d4a041690a8da8949.jpg", + "table_caption": [ + "Table 4: Results on the Herbarium-19 Dataset." + ], + "table_footnote": [], + "table_body": "
MethodsAllOldNew
k-means [35]13.012.213.4
RS+ [16]27.955.812.8
UNO+ [12]28.353.714.7
ORCA [2]20.930.915.5
GCD [48]35.451.027.0
Ours (GPC)36.551.727.9
", + "bbox": [ + 145, + 741, + 401, + 869 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d7ce1b599271ba5b8e442405c1d2efd04e817acf4b8b38de6e4ec886e3d52270.jpg", + "image_caption": [ + "(a) Explained variance of the original feature w.r.t. the number of principal directions." + ], + "image_footnote": [], + "bbox": [ + 542, + 383, + 851, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/64e7895dd7657664189b3aedc58320f39e22a955b79d2e8b1cab66e824210a04.jpg", + "image_caption": [ + "(b) The clustering ACC on validation set w.r.t. the number of principal directions", + "Figure 3: The effects of the number of principal directions in PCA on the feature representations." + ], + "image_footnote": [], + "bbox": [ + 540, + 544, + 851, + 656 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Novel class number estimation", + "text_level": 1, + "bbox": [ + 500, + 767, + 769, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "One of the important yet overlooked components in the NCD and GCD literature is the estimation of unknown class numbers. Our proposed framework leverages a modified GMM to estimate the class number, in which we need to define an initial guess of the class number. We validate the effects of different choices of the initial guess $K_{init}$ w.r.t. the estimated class number in Tab. 5. Note that the number", + "bbox": [ + 500, + 795, + 893, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16629", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/78f5def2f7c2b2194459c9a018a2253190566b6a0aa696365be8f7e330d63581.jpg", + "table_caption": [ + "Table 5: Results of varying the initial guessed $K_{init}^{n}$ . 'GT $K^{n}$ ' is the ground truth number of novel classes. $K^{n}$ is the estimated number of novel classes. Our proposed framework is generally robust in estimating the number of novel classes, and we found that using the initial guess of $K_{init} = K^{l} + \\frac{K^{l}}{2}$ can be a simple and reliable choice." + ], + "table_footnote": [], + "table_body": "
DatasetKlGT KnVaze et al. [48]Kninit = 3510203050100
CIFAR-10554Kn = 55566814
CIFAR-100802020Kn = 16202021222736
ImageNet-100505059Kn = 58485755545060
CUB100100131Kn = 7987868892112101
SCars9898132Kn = 8490868789115104
", + "bbox": [ + 158, + 143, + 807, + 258 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in Tab. 5 is $K_{init}^{n} = K_{init} - K^{l}$ . We can see that our proposed framework is generally robust to a wide range of initial guesses. We found that $K_{init} = K^{l} + \\frac{K^{l}}{2}$ is a simple and reliable choice. Hence we use this for all datasets.", + "bbox": [ + 75, + 277, + 470, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Training complexity", + "text_level": 1, + "bbox": [ + 75, + 349, + 269, + 366 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Given that our framework necessitates the fitting of GMMs, an extended training duration is required. We compare the performance of our method to the extended method of Vaze et al. [48], which is pushed to $1.5 \\times$ its original number of training epochs. The results in Tab. 6 demonstrate that our method outperforms [48] across both CUB and ImageNet-100 datasets while maintaining a similar training duration. Furthermore, in contrast to the baseline method, our approach eliminates the need for additional post-training procedures such as running SS- $k$ -means on the entire dataset for label assignment.", + "bbox": [ + 73, + 373, + 470, + 540 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d1950af9d80938e266fbb5e50638092a07ad001ecd081ae5410253934018166b.jpg", + "table_caption": [ + "Table 6: Comparison between GPC and Vaze et al. [48] $(1.5\\times)$ on CUB and ImageNet-100 Datasets." + ], + "table_footnote": [], + "table_body": "
MethodCUBImageNet-100
AllOldNewAllOldNew
Vaze et al. [48]51.356.648.774.189.866.3
Vaze et al.(1.5×)52.056.849.074.790.366.7
Ours (GPC)55.458.253.176.994.371.0
", + "bbox": [ + 93, + 589, + 454, + 689 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation study", + "text_level": 1, + "bbox": [ + 75, + 710, + 227, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of dimensions in PCA The PCA in our framework requires setting a number for the number of principal directions to extract from data. In Fig. 3, we show the results of using a different number of principal directions in PCA on CUB-200 and ImageNet-100 datasets. We can see from Fig. 3a that for both datasets, 128 principal directions can already explain most of the variances in the data, thus we choose the PCA dimension to be 128 for all our experiments. We further experiment with other different choices of the PCA dimension and shows the result in Fig. 3b, which again confirms that 128 principal directions are already expensive", + "bbox": [ + 73, + 734, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "enough, and obtain the best performance over other choices, that are either too few or too many, effectively avoiding DC.", + "bbox": [ + 498, + 277, + 893, + 310 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different methods for prototype estimation Our semi-supervised GMM plays an important role in prototype estimation for representation learning based on prototypical contrastive learning. Here, we replace our semi-supervised GMM with other alternatives that do not produce prototypes automatically. Particularly, we compare our method with DBSCAN [10], Agglomerative clustering [37], and semi-supervised $k$ -means [17, 48]. The prototypes are then obtained by averaging the data points that are assigned to the same cluster. For a fair comparison, the same regulations to prevent the wrong clustering results for labelled instances are applied to all methods, i.e., during the clustering process, two labelled instances with the same label will fall into the same cluster, and two instances with different labels will be assigned to different clusters. The results are reported in Tab. 7a. Our method achieves the best performance on all three datasets, indicating that better prototypes are obtained by our approach to facilitate representation learning. Note that DBSCAN requires two important user-defined parameters, radius, and minimum core points, the ideal values of which lack a principled way to obtain in practice, while our method is parameter-free and can seamlessly be combined with the representation learning to jointly enhance each other, obtaining better performance.", + "bbox": [ + 496, + 333, + 893, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Combining our GMM with other GCD methods We further combine our semi-supervised GMM with automatic splitting and merging with other methods, allowing joint representation learning and category discovery without a predefined category number. As the state-of-the-art GCD method [48] does not contain any parametric classifier during representation, so it can be directly combined with our GMM. For the RankStat and the DualRank methods that have a parametric classifier for category discovery, we treat the weights of the classifier as the cluster centers and run our GMM to automatically determine the category number during representation learning. The results are presented", + "bbox": [ + 496, + 719, + 895, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16630", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3f826839a968bc0befd3c137be303d547ee35edaec93b1f14e83b1af6523cbd7.jpg", + "table_caption": [ + "Table 7: Combining components of GPC with other methods. \"IM-100\" denotes ImageNet-100.", + "(a) Different prototype estimation methods." + ], + "table_footnote": [], + "table_body": "
Clustering Algo.CUBIM-100SCars
Ester et al. [10]45.666.134.8
Murtagh et al. [37]52.174.639.8
Vaze et al. [48]49.273.237.4
Ours (GPC)54.176.641.9
", + "bbox": [ + 116, + 147, + 444, + 247 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/a633b766137344604e90d165c8b5fd1b5c51c530f195f011181577a01ae5e71c.jpg", + "table_caption": [ + "(b) Combining our GMM with other methods." + ], + "table_footnote": [], + "table_body": "
RepresentationCUBIM-100SCars
Han et al. [16]34.638.429.3
Zhao et al. [58]37.839.733.2
Vaze et al. [48]50.673.437.8
Ours (GPC)54.176.641.9
", + "bbox": [ + 129, + 277, + 436, + 377 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "in Tab. 7b. Comparing with row 9 in Tab. 1 and Tab. 3, we can see using our GMM can also improve [48] on CUB and Stanford Cars, while our proposed framework consistently achieves better performance on all datasets, again validating that our design choices.", + "bbox": [ + 75, + 395, + 470, + 472 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Class number estimation with different representations Here, we validate our class number estimation method on top of the representations learned by other GCD approaches and report the results in Tab. 8. It can be seen, applying our method on other GCD representations can achieve reasonably well results. Notably, by applying our class number estimation method on top of the representation by the existing state-of-the-art method, we can obtain better class number estimation results, though the overall best results are obtained with the representation learned in our framework.", + "bbox": [ + 75, + 491, + 468, + 643 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/4365a32503bf784722b0e34bcba49f7fb4daa9cb50dafc9129ca3a5fb9d13a7c.jpg", + "table_caption": [ + "Table 8: Class number estimation with different learned representations. \"C-100\" stands for the CIFAR-100 dataset." + ], + "table_footnote": [], + "table_body": "
RepresentationC-100CUBSCarsIM-100
Ground Truth Kn201009850
Vaze et al.[48]2013113259
Ours w/ [16] feat.191119455
Ours w/ [58] feat.221168949
Ours w/ [48] feat.2112110957
Ours (GPC)2011210353
", + "bbox": [ + 81, + 693, + 465, + 835 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Partial overlap between $\\mathcal{V}_l$ and $\\mathcal{V}_u$ We evaluate the performance of our method when we relax $\\mathcal{V}_l\\subset \\mathcal{V}_u$ to", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "$\\mathcal{Y}_l \\cap \\mathcal{Y}_u \\neq \\emptyset$ , i.e., the two sets may only partially overlap. We vary the number of overlapped classes and report the results in Tab. 9. Our approach consistently outperforms the method proposed by Vaze et al. [48] in all configurations. These compelling results not only showcase the robustness of our method but also highlight its effectiveness in scenarios involving partial overlap between known and unknown classes.", + "bbox": [ + 496, + 90, + 893, + 210 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/321b71af7326a3cfe2fe6f3b64a17d66acd2d06708624aab277218859e2467ec.jpg", + "table_caption": [ + "Table 9: Results on CUB of only partial overlap between $\\mathcal{V}_l$ and $\\mathcal{V}_u$ ." + ], + "table_footnote": [], + "table_body": "
|Yl∩Yu|255075
AllOldNewAllOldNewAllOldNew
Vaze et al. [48]49.550.148.251.250.752.252.750.954.5
Ours (GPC)51.252.649.552.351.654.853.651.455.9
", + "bbox": [ + 500, + 261, + 893, + 333 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Varying ratio of Old/New categories We measure the estimated new class numbers when varying the ratio of Old/New categories while having $K_{init} = K^{l} + \\frac{K^{l}}{2}$ on CUB in Tab. 10. As can be seen, for all cases, our method outperforms [48]. Meanwhile, we can also see that when the initial guess is too far from the ground truth, the estimation will be less accurate.", + "bbox": [ + 496, + 372, + 893, + 479 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/ffcafe583f47df80e7d1fa6c392a7ef1e944577e98e4d3dbc947f67ebcaea0fb.jpg", + "table_caption": [ + "Table 10: Estimated class numbers on CUB with a varying ratio of Old/New classes." + ], + "table_footnote": [], + "table_body": "
Old/New20/18040/16060/14080/120
GCD [48]87102114104
Ours (GPC)93126135116
", + "bbox": [ + 514, + 529, + 877, + 592 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 625, + 617, + 641 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we present an EM-like framework for the challenging GCD problem without knowing the number of new classes, with the E-step automatically determining the class number and prototypes and the M-step being robust representation learning. We introduce a semi-supervised variant of GMM with a stochastic splitting and merging mechanism to obtain the prototypes and leverage these evolving prototypes for representation learning by prototypical contrastive learning. We demonstrated that class number estimation and representation learning can facilitate each other for more robust category discovery. Our framework obtains state-of-the-art performance on multiple public benchmarks.", + "bbox": [ + 496, + 651, + 893, + 834 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements This work is supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research.", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "16631", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin Raffel. Mixmatch: A holistic approach to semi-supervised learning. In NeurIPS, 2019. 1, 3", + "[2] Kaidi Cao, Maria Brbić, and Jure Leskovec. Open-world semi-supervised learning. 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In ICCV, 2021. 2" + ], + "bbox": [ + 501, + 92, + 893, + 545 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16633", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/c328493e-9994-4352-8a93-3b569e354069_model.json b/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/c328493e-9994-4352-8a93-3b569e354069_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e0842b6d958b7de27a987c093bcb57427172afd6 --- /dev/null +++ b/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/c328493e-9994-4352-8a93-3b569e354069_model.json @@ -0,0 +1,2103 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.22, + 0.131, + 0.753, + 0.177 + ], + "angle": 0, + "content": "Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.226, + 0.203, + 0.744, + 0.257 + ], + "angle": 0, + "content": "Bingchen Zhao† Xin Wen‡ Kai Han‡* \n†University of Edinburgh ‡The University of Hong Kong \nbingchen.zhao@ed.ac.uk wenxin@eee.hku.hk kaihanx@hku.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.761 + ], + "angle": 0, + "content": "In this paper, we address the problem of generalized category discovery (GCD), i.e., given a set of images where part of them are labelled and the rest are not, the task is to automatically cluster the images in the unlabelled data, leveraging the information from the labelled data, while the unlabelled data contain images from the labelled classes and also new ones. GCD is similar to semi-supervised learning (SSL) but is more realistic and challenging, as SSL assumes all the unlabelled images are from the same classes as the labelled ones. We also do not assume the class number in the unlabelled data is known a-priori, making the GCD problem even harder. To tackle the problem of GCD without knowing the class number, we propose an EM-like framework that alternates between representation learning and class number estimation. We propose a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to dynamically determine the prototypes by examining the cluster compactness and separability. With these prototypes, we leverage prototypical contrastive learning for representation learning on the partially labelled data subject to the constraints imposed by the labelled data. Our framework alternates between these two steps until convergence. The cluster assignment for an unlabelled instance can then be retrieved by identifying its nearest prototype. We comprehensively evaluate our framework on both generic image classification datasets and challenging fine-grained object recognition datasets, achieving state-of-the-art performance. Our code is available at https://github.com/DTennant/GPC." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.791, + 0.21, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.817, + 0.471, + 0.879 + ], + "angle": 0, + "content": "The success of deep learning is driven by the availability of large-scale data with human annotations. Given enough annotated data, deep learning models are able to surpass human-level performance on many important computer vi" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.29, + 0.891, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.444, + 0.896, + 0.611 + ], + "angle": 0, + "content": "Figure 1: Overview of our proposed EM-like framework. The input images are fed into a ViT-B model to obtain a 768-dimensional feature vector, then the feature vector will be projected to a lower dimensional space using the projection calculated from PCA. We perform class number estimation and representation learning in this projected space. In the E-step, we use a semi-supervised GMM that can split separable clusters and merge cluttered clusters to estimate the class number and prototypes, which will be used in the M-step of representation learning with prototypical contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.897, + 0.901 + ], + "angle": 0, + "content": "sion tasks such as image classification [21]. But the cost of collecting a large annotated dataset is not always affordable, and it is also not possible to annotate all new classes emerging from the real world. Thus, designing models that can learn to deal with large-scale unlabelled data in the open world is of great value and importance. Semi-supervised learning (SSL) [38] is proposed as a solution to learn a model on both labelled data and unlabelled data, with many works achieving promising performance [1, 46, 44]. However, SSL assumes that labelled instances are provided for all object classes in the unlabelled data. The novel category discovery (NCD) task is introduced [17, 16] to automatically discover novel classes by transferring the knowledge learned from the labelled instances of known classes, assuming the unlabelled data only contain instances from new classes. Generalized category discovery (GCD) [48] further relaxes the assumption in NCD, and tackles a more" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16623" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "generalized setting where the unlabelled data contains instances from both known and novel categories. Existing methods for NCD [17, 16, 58, 60, 61, 12, 26] and GCD [48, 11, 51, 45, 56, 59, 34] learn the representation and cluster assignment assuming the class number is known a priori [58, 26, 60, 12, 61] or precomputed [17, 48]. In practice, the number of categories in the unlabelled data is often unknown, while precomputing the class number without taking the representation learning into consideration is likely to lead to a sub-optimal solution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.473, + 0.779 + ], + "angle": 0, + "content": "In this paper, we argue that representation learning and the estimation of class numbers should be considered together and could reinforce each other, i.e., a strong representation could help a more accurate estimation of the class numbers, and an accurate class number could help learn a better feature representation. To this end, we propose a unified EM-like framework that alternates between feature representation learning and class number estimation where the E-step is aimed at automatically estimating a proper class number and a set of class prototypes in the unlabelled data and the M-step is aimed at learning better representation with the class number and class prototypes estimated. In particular, we propose using a prototype contrastive representation learning [33] method for GCD, which requires a set of prototypes to serve as anchors for representation learning. Prototypical contrastive learning [33] is developed for unsupervised representation learning to generalize to different tasks, where the prototypes are obtained by over-clustering the dataset with one or multiple given prototype numbers, using non-parametric clustering algorithms like \\( k \\)-means. Instead, to handle the problem of GCD, we propose to estimate the prototype number and prototypes automatically and simultaneously. To do so, we introduce a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to determine the most suitable clusters based on current representation. These clusters can then be used to form prototypes to facilitate contrastive representation learning. Our framework alternates between the E- and M-step until converging to achieve robust representation and reliable category estimation. After learning, the cluster assignment for an unlabelled instance, either from known or novel classes, can be retrieved by finding the nearest prototypes. Thus we name our framework as GPC: Gaussian mixture model for generalized category discovery with Protypical Contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.904 + ], + "angle": 0, + "content": "Our contributions in this paper are as follows: (1) We demonstrate that in generalized category discovery, the class number estimation and representation learning can reinforce each other in the learning process. Strong representations can give a better estimation of the class number, and vice versa. (2) We propose an EM-like framework that alternates between prototype estimation with a variant of GMM (E-step) and representation learning based on prototypical" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.896, + 0.258 + ], + "angle": 0, + "content": "contrastive learning (M-step). (3) We introduce a semi-supervised variant of GMM with a stochastic splitting and merging mechanism to allow dynamic change of the prototypes by examining the cluster compactness and separability based on the Metropolis-Hastings ratio [19]. (4) We comprehensively evaluated our framework on both the generic image classification benchmark, including CIFAR10, CIFAR100, ImageNet-100, and the challenging fine-grained Semantic Shifts Benchmark suite, which includes CUB-200, Stanford-Cars, and FGVC-aircrafts, achieving the state-of-the-art results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.272, + 0.64, + 0.287 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.896, + 0.84 + ], + "angle": 0, + "content": "Novel category discovery (NCD) is first formalized in DTC [17], where the task is to discover new categories leveraging the knowledge of a set of labelled categories. Many methods have been proposed to tackle this challenge. To name a few, RankStat [15, 16] and DualRank [58] transfer knowledge from labelled to unlabelled classes using feature ranking statistics. OpenMix [61] shows that mixing labelled and unlabelled data can prevent overfitting. NCL [60] and WTA [26] use contrastive learning for NCD. UNO [12] introduces a unified cross-entropy loss for joint training on labelled and unlabelled data. [29] introduces a spacing loss for representation learning in NCD. NCDwF [28] studies the NCD problem under an incremental learning setting. Earlier methods like [22, 23] for generalized transfer learning can also be applied to NCD. Generalized category discovery (GCD) [48] extends NCD to a more open-world setting where unlabelled instances can come from both labelled and unlabelled categories. ORCA [2] also tackles GCD from a semi-supervised learning perspective. Several improved methods have been proposed for generalized category discovery (GCD), such as [11, 51, 39, 56, 45], which have shown promising results. Incremental GCD is considered in [57, 59]. Concurrently, CiPR [18] presents a hierarchical GCD approach employing selective neighbor clustering, leading to improved efficiency and performance without necessitating knowledge of the class number. [14] studies semantic category discovery by leveraging vision-language representations, thereby enabling GCD with class name prediction. However, most existing GCD methods assume that the novel class number is known a priori, which is often not the case in the real world. To address this limitation, [17, 48] precompute the number of novel classes with a semi-supervised \\(k\\)-means algorithm from pretrained representations. In this paper, we demonstrate that class number estimation and representation learning can be jointly considered to mutually benefit each other." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Contrastive learning [4, 5, 20, 7, 62] (CL) has been shown very effective for representation learning in a self-supervised manner, using the instance discrimination pretext [52] as the learning objective. The instance discrimination task learns" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "16624" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "a representation by pulling positive samples from the augmentations of the same images closer and pushing negative samples from different images apart in the embedding space. Instead of contrasting over all instances in a mini-bath, prototypical contrastive learning (PCL) [33] proposes to contrast the features with a set of prototypes which can provide a higher level abstraction of dataset than instances and has been shown to be more data efficient without the need of large batch size. Though PCL is developed for unsupervised representation learning, if the prototypes are viewed as cluster centers, it can be leveraged in the partially supervised setting of GCD for representation learning to better fit the GCD task of partitioning data into different clusters. Thus, in this paper, we adopt PCL to fit the GCD setting for representation learning in which the downstream clustering task is directly considered." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.473, + 0.56 + ], + "angle": 0, + "content": "Semi-supervised learning (SSL) has been a long standing research topic which many effective method proposed [40, 44, 1, 32, 46]. In SSL, the labelled and the unlabelled data are assumed to come from the same set of classes, and the task is to learn a classification model that can take advantage of both labelled and unlabelled data. Consistency-based methods are among the most effective methods for SSL, such as Mean-teacher [46], MixMatch [1], and FixMatch [44]. Self-supervised representation learning also shows to be helpful for SSL because it can provide a strong representation [55, 40]. Recent works extend semi-supervised learning by relaxing the assumption of exactly the same classes in the labeled and unlabelled data [43, 25, 54], but their focus is improving the performance of the labeled categories without discovering novel categories in the unlabeled set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.473, + 0.773 + ], + "angle": 0, + "content": "Unsupervised clustering has been studied for decades, and there are many existing classical approaches [35, 10, 6] as well as deep learning based approaches [53, 41, 13]. Recently, DeepDPM [42] is proposed to automatically determine the number of clusters for a given dataset by adopting a similar split/merge framework that changes the inferred number of clusters. However, due to the unsupervised nature of these methods, there is no prior or supervision over how a cluster should be formed, thus multiple equally valid clustering results following different clustering criteria can be produced. Thus, directly applying unsupervised clustering methods to the task of generalized category discovery is not feasible, as we would want the model to use one unique clustering criteria implicitly given by the labelled data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.17, + 0.801 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Given a collection of partially labelled data, \\(\\mathcal{D} = \\mathcal{D}^l\\cup \\mathcal{D}^u\\) where \\(\\mathcal{D}^l = \\{(x_i,y_i^l)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_l\\) is labelled, \\(\\mathcal{D}^u = \\{x_i,y_i^u\\} \\in \\mathcal{X}\\times \\mathcal{Y}_u\\) is unlabelled, and \\(\\mathcal{V}_l\\subset \\mathcal{V}_u\\) Generalized category discovery (GCD) aims at automatically assign labels for the unlabelled instances in \\(\\mathcal{D}^u\\) , by transferring knowledge acquired from \\(\\mathcal{D}^l\\) . Let the category number in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.895, + 0.198 + ], + "angle": 0, + "content": "\\(\\mathcal{D}^l\\) be \\(K^l = |\\mathcal{Y}_l|\\) and that in \\(\\mathcal{D}^u\\) be \\(K^u = |\\mathcal{Y}_u|\\). The number of new categories \\(\\mathcal{D}^u\\) is then \\(K^n = |\\mathcal{Y}_u \\setminus \\mathcal{Y}_l| = K^u - K^l\\). Though \\(K^l\\) can be accessed from the labelled data, we do not assume \\(K^n\\) or \\(K^u\\) to be known. This is a realistic setting to reflect the real open world, where we often have access to some labelled data, but in the unlabelled data, we also have instances from unseen new categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.895, + 0.348 + ], + "angle": 0, + "content": "The key challenges for GCD are representation learning, category number estimation, and label assignment. Existing methods for NCD and GCD [17, 48] deal with these three challenges independently. However, we believe they are inherently linked with each other. Label assignment depends on representation and category number estimation. A good class number estimation can facilitate representation learning, thus better label assignment, and vice versa. Thus, in this paper, we aim to jointly handle these challenges in the learning process for a more reliable GCD." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.897, + 0.576 + ], + "angle": 0, + "content": "To this end, we propose a unified EM-like framework that alternates between representation learning and class number estimation, while the label assignment turns out to be a by-product during class number estimation. In the E-step, we introduce a semi-supervised variant of the Gaussian Mixture Model (GMM) to estimate the class numbers by dynamically splitting separable clusters and merging cluttered clusters based on current representation, forming a set of class prototypes for both seen and unseen classes, and in the M-step, we train the model to produce discriminative representation by prototypical contrastive learning using the cluster centers from the GMM prototypes derived from the E-step during class number estimation. After training, the class assignment for each instance can be retrieved by simply identifying the nearest prototype." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.584, + 0.724, + 0.601 + ], + "angle": 0, + "content": "3.1. Representation learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.895, + 0.699 + ], + "angle": 0, + "content": "The goal of representation learning is to learn a discriminative representation that can well separate different categories, not only the old ones, but also the new ones. Contrastive learning (CL) has been shown to be an effective choice for NCD [26] and GCD [48]. Self-supervised contrastive learning is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.706, + 0.895, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C L} = - \\log \\frac {\\exp \\left(z _ {i} \\cdot z _ {i} ^ {\\prime} / \\tau\\right)}{\\sum_ {j = 1} ^ {n} \\exp \\left(z _ {i} \\cdot z _ {j} ^ {\\prime} / \\tau\\right)} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.901 + ], + "angle": 0, + "content": "where \\( z_{i} \\) and \\( z_{i}^{\\prime} \\) are the representations of two views obtained from the same image using random augmentations and \\( \\tau \\) is the temperature. Two views of the same instance are pulled closer, and different instances are pushed away during training. Self-supervised contrastive learning and its supervised variant, in which different instances from the same category are also pulled closer, are used in [48] for representation learning. However, as a stronger training signal is used for the labelled data, the representation is likely biased to the labelled data to some extent. Moreover, such a method does" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16625" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.137 + ], + "angle": 0, + "content": "not take the downstream clustering task into account during learning, thus a clustering algorithm is required to run independently after the representation learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.472, + 0.229 + ], + "angle": 0, + "content": "In this paper, we adopt prototypical contrastive learning (PCL) [33] to the GCD setting to learn the representation \\( z_{i} = f(x_{i}) \\in \\mathbb{R}^{d} \\). PCL uses a set of prototypes \\( \\mathcal{C} = \\{\\mu_1, \\dots, \\mu_K\\} \\) to represent the dataset for contrastive learning instead of the random augmentation generated views \\( z_{i}' \\). PCL loss can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.239, + 0.471, + 0.277 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {P C L} = - \\log \\frac {\\exp \\left(z _ {i} \\cdot \\mu_ {s} / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(z _ {i} \\cdot \\mu_ {j} / \\tau\\right)} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.473, + 0.514 + ], + "angle": 0, + "content": "where \\(\\mu_{s}\\) is the corresponding prototype for \\(z_{i}\\). It was originally designed as an alternative for self-supervised contrastive learning by over-clustering the training data to obtain the prototypes during training. We employ PCL here to learn reliable representation while taking the downstream clustering into account for GCD, where we have a set of partially labelled data. In our case, the prototypes can be interpreted as the class centers for each of the categories. To obtain the prototypes for the seen categories, we directly calculate the class mean by averaging all the feature vectors of the labelled instances. For the unseen categories, we obtain the prototypes with a semi-supervised variant of the Gaussian Mixture Model (GMM), as will be introduced in Sec. 3.2. This way, the cluster assignment for an unlabelled image can be readily achieved by finding the nearest prototype." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.472, + 0.786 + ], + "angle": 0, + "content": "Additionally, we observe that only a few principal dimensions can already recover most of the variances in the representation space of \\( z_{i} \\), which is known as dimensional collapse (DC) in [27, 24], and it is shown that DC can be caused by strong augmentations or implicit regularizations in the model, and preventing DC during training can lead to a better feature representation. To alleviate DC for representation learning in our case, we propose to first project the feature to a subspace obtained by principal component analysis (PCA) before the contrastive learning. Specifically, we apply PCA on a matrix \\( Z \\) formed by a mini-batch of features \\( z_{i} \\), with a batch size of \\( n \\), the feature dimension \\( d \\), and the number of effective principal directions \\( q \\). We have \\( Z \\approx U\\mathrm{diag}(S)V^{\\top} \\), where \\( U \\in \\mathbb{R}^{n \\times q} \\), \\( S \\in \\mathbb{R}^q \\) and \\( V \\in \\mathbb{R}^{d \\times q} \\). We can then project features \\( z_{i} \\) to principal directions to obtain a more compact feature \\( v_{i} = V \\cdot z_{i} \\), and replace feature \\( z_{i} \\) with \\( v_{i} \\) in Eq. (2) for PCL. The prototypes are also computed in the projected space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.785, + 0.471, + 0.83 + ], + "angle": 0, + "content": "We jointly use self-supervised contrastive learning and PCL to train our model. The overall learning objective can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.843, + 0.471, + 0.86 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {C L} + \\lambda (t) \\mathcal {L} _ {P C L} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.87, + 0.471, + 0.904 + ], + "angle": 0, + "content": "where \\(\\lambda(t)\\) is a linear warmup function defined as \\(\\lambda(t) = \\min(1, \\frac{t}{T})\\) where \\(t\\) is the current epoch and \\(T\\) warmup length" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.092, + 0.885, + 0.148 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.155, + 0.894, + 0.232 + ], + "angle": 0, + "content": "Figure 2: Examples for splitting a separable cluster and merging two cluttered clusters. Left: the cluster is split because the two sub-component in this cluster are easily separable. Right: two clusters are merged as they are cluttered and likely from the same class." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.258, + 0.894, + 0.351 + ], + "angle": 0, + "content": "\\((T = 20\\) in our experiments). The reason we use both CL and PCL is that, in the beginning, the representation is not well suited for clustering, and thus the obtained prototypes are not informative to facilitate the representation learning. Hence, we gradually increase the weight of PCL during training from 0 to 1 in the first \\(T\\) epochs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.36, + 0.892, + 0.391 + ], + "angle": 0, + "content": "3.2. Class number and prototypes estimation with semi-supervised Gaussian mixture model" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.399, + 0.893, + 0.533 + ], + "angle": 0, + "content": "In this section, we present a semi-supervised variant of the Gaussian mixture model (GMM) with each Gaussian component consisting of two sub-components to estimate the prototypes for representation learning in Sec. 3.1 and the unknown class number. GMM estimates the prototypes and assigns a label for each data point by finding its nearest prototype. The cluster label assignment and the prototypes are then used for prototypical contrastive learning. The GMM is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.544, + 0.893, + 0.584 + ], + "angle": 0, + "content": "\\[\np (z) = \\sum_ {i = 1} ^ {K} \\pi_ {i} \\mathcal {N} \\left(z \\mid \\mu_ {i}, \\Sigma_ {i}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.597, + 0.895, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}(z|\\mu_i,\\Sigma_i)\\) is the Gaussian probability density function with mean \\(\\mu_{i}\\in \\mathbb{R}^{d}\\) and covariance \\(\\Sigma_{i}\\in \\mathbb{R}^{d\\times d}\\), and \\(\\pi_{i}\\) is the weight for \\(i\\)-th Gaussian component and we have \\(\\sum_{i = 1}^{N}\\pi_{i} = 1\\). Ideally, we would expect the component number \\(K\\) in the GMM to be equal to the class number \\(K^u\\) in \\(\\mathcal{D}\\). To estimate the unknown class number \\(K^u\\), we leverage an automatic splitting-and-merging strategy into the modeling process to obtain an optimal \\(K\\), which is expected to be as close to \\(K^u\\) as possible. We alternate between representation learning and \\(K^u\\) estimation until convergence to get discriminative representation learning and a reliable class number estimation. For initialization, \\(K\\) can be set to any number greater than \\(K^l\\). In our experiments, we simply set the initial number of components to a default \\(K_{init} = K^l +\\frac{K^l}{2}\\). We run a semi-supervised \\(k\\)-means algorithm [48] with \\(k = K\\) to obtain the \\(\\mu\\) and \\(\\Sigma\\) for each component in the mixture model. Note that the semi-supervised \\(k\\)-means algorithm is constrained to the labelled data in a way that labelled instances from the same class are assigned to the same cluster, and labelled instances from different classes will not be" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16626" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.088, + 0.095, + 0.427, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: The overall algorithm of our method." + }, + { + "type": "algorithm", + "bbox": [ + 0.08, + 0.112, + 0.473, + 0.536 + ], + "angle": 0, + "content": "Input: \\(\\mathcal{D},\\mathcal{D}^l\\) , and \\(\\mathcal{D}^u\\) The datasets. \\(K_{init}\\) Initial guess of \\(K\\) \n1 \\(K\\gets K_{init}\\) \n2 for \\(e = 1\\) to \\(E\\) do \n3 \\(z\\gets f(x),x\\in \\mathcal{D}\\quad /\\) extract features \n4 \\(\\mu ,\\Sigma \\gets \\arg \\max \\sum_{i = 1}^{K}\\pi_{i}\\mathcal{N}(z|\\mu_{i},\\Sigma_{i})\\) // estimate prototypes using GMM \n5 for \\(i = 1\\) to len(D) do \n6 \\(\\mathcal{B}^l\\gets \\{x_i^l\\sim \\mathcal{D}^l\\}_{i = 1}^{N^l}\\quad /\\) sample a batch of \\(N^l\\) labelled images \n7 \\(\\mathcal{B}^u\\gets \\{x_i^u\\sim \\mathcal{D}^u\\}_{i = 1}^{N^u}\\quad /\\) sample a batch of \\(N^u\\) unlabelled images \n8 \\(f\\gets \\arg \\min \\mathcal{L}(f,\\mu ,\\mathcal{B}^l,\\mathcal{B}^u)\\) // prototypical contrastive learning \n9 end \n10 \\(H_{s},H_{m}\\gets \\mathrm{calc\\_prob}(\\mu ,\\Sigma)\\) // probability for split and merge \n11 \\(\\mu ,\\Sigma \\gets \\mathrm{perform\\_op}(H_s,H_m)\\quad /\\) perform operations \n12 \\(K\\gets \\mathrm{len}(\\mu)\\) // update \\(K\\) \n13 end Output: feature extractor \\(f(\\cdot)\\) , cluster centers \\(\\mu_{i}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.658 + ], + "angle": 0, + "content": "assigned to the same cluster. To facilitate the splitting and merging process, for each Gaussian component defined by \\(\\mu_{i}\\) and \\(\\Sigma_{i}\\), we further depict it with a GMM with two subcomponents \\(\\mu_{i,1},\\mu_{i,2}\\) and \\(\\Sigma_{i,1},\\Sigma_{i,2}\\) with \\(\\pi_{i,1} + \\pi_{i,2} = 1\\). We run a \\(k\\)-means with \\(k = 2\\) on the \\(i\\)-th component to obtain \\(\\mu_{i,1},\\mu_{i,2}\\) and \\(\\Sigma_{i,1},\\Sigma_{i,2}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.472, + 0.853 + ], + "angle": 0, + "content": "For a cluster whose two sub-components are roughly independent and equally sized (e.g., left part of Fig. 2), i.e., they are easily separable, we would like the model to split it into two such that the model can better fit the data distribution and the class assignment will be more accurate because it is less likely that such distinct clusters will belong to the same class. For two clusters that are cluttered with each other (e.g., right part of Fig. 2), i.e., difficult to distinguish, we would like to merge them into one, so that they will be considered as from the same class. Following this intuition, we use the Metropolis-Hastings framework [19] to compute a probability \\( p_{s} = \\min(1, H_{s}) \\) to stochastically split a cluster into two. The Hastings ratio is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.865, + 0.47, + 0.898 + ], + "angle": 0, + "content": "\\[\nH _ {s} = \\frac {\\Gamma \\left(N _ {i , 1}\\right) h \\left(\\mathcal {Z} _ {i , 1} ; \\theta\\right) \\Gamma \\left(N _ {i , 2}\\right) h \\left(\\mathcal {Z} _ {i , 2} ; \\theta\\right)}{\\Gamma \\left(N _ {i}\\right) h \\left(\\mathcal {Z} _ {i} ; \\theta\\right)}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.895, + 0.41 + ], + "angle": 0, + "content": "where \\(\\Gamma\\) is the factorial function, i.e., \\(\\Gamma (n) = n! = n\\times (n - 1)\\times \\dots \\times 1\\), \\(\\mathcal{Z}_i\\) is the set of data points in cluster \\(i\\), \\(\\mathcal{Z}_{i,j}\\) is the set of data points in the \\(j\\)-th sub-cluster of cluster \\(i\\), \\(N_{i} = |\\mathcal{Z}_{i}|, N_{i,j} = |\\mathcal{Z}_{i,j}|\\), \\(h(Z;\\theta)\\) is the marginal likelihood of the observed data \\(\\mathcal{Z}\\) by integrating out the \\(\\mu\\) and \\(\\Sigma\\) parameters in the Gaussian, and \\(\\theta\\) is the prior distribution of \\(\\mu\\) and \\(\\Sigma\\). More details can be found in the supplementary. The intuition behind this \\(H_{s}\\) is that, if the number of data points in two sub-components is roughly balanced, which is measured by the \\(\\Gamma (\\cdot)\\) terms, and the data points in the two sub-components are independent of each other, which is measure by the \\(h(\\cdot ;\\theta)\\) terms, there should be a greater chance of splitting the cluster. After performing a split operation, the \\(\\mu_{i}\\) and \\(\\Sigma_{i}\\) of previous components \\(i\\) will be replaced with \\(\\mu_{i,1},\\mu_{i,2}\\) and \\(\\Sigma_{i,1},\\Sigma_{i,2}\\) of two sub-components. We will then run two \\(k\\)-means within the two newly formed components to obtain their corresponding sub-components. On the contrary, if two clusters are cluttered with each other, they should be merged. Similar to splitting, we determine the merging probability by \\(p_m = \\min (1,H_m)\\), where \\(H_{m}\\) is calculated similarly for two clusters \\(i\\) and \\(j\\):" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.421, + 0.892, + 0.456 + ], + "angle": 0, + "content": "\\[\nH _ {m} = \\frac {\\Gamma \\left(N _ {i} + N _ {j}\\right) h \\left(\\mathcal {Z} _ {i} \\cup \\mathcal {Z} _ {j} ; \\theta\\right)}{\\Gamma \\left(N _ {i}\\right) h \\left(\\mathcal {Z} _ {i} ; \\theta\\right) \\Gamma \\left(N _ {j}\\right) h \\left(\\mathcal {Z} _ {j} ; \\theta\\right)}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.894, + 0.514 + ], + "angle": 0, + "content": "Note that both \\( H_{s} \\) and \\( H_{m} \\) are within the range of \\( (0, +\\infty) \\), so we use \\( p_{s} = \\min(1, H_{s}) \\) and \\( p_{m} = \\min(1, H_{m}) \\) to convert it into a valid probability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.894, + 0.59 + ], + "angle": 0, + "content": "To take the labelled instances into consideration during the splitting-and-merging process, if a cluster consists of labelled instances, we set its \\( p_s = 0 \\); if for any two clusters containing instances from two labelled classes, we set their \\( p_m = 0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.592, + 0.895, + 0.801 + ], + "angle": 0, + "content": "During the splitting-and-merging process, we first apply splitting according to the \\( p_s \\) and then apply merging according to \\( p_m \\). The newly formed clusters by splitting will not be reused during the merging step. After finishing the splitting and merging, we can obtain the prototypes, and thus can estimate \\( K \\), for our PCL-based representation learning. We alternate between representation learning and class number estimation for each training epoch until converge. The final \\( K \\) will be considered the estimated class number in \\( \\mathcal{D} \\). The cluster assignment for each unlabelled instance can be easily retrieved by identifying its nearest prototype, without the need of running a non-parametric clustering algorithm as [48]. The overall training process is summarized in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.82, + 0.633, + 0.837 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.688, + 0.863 + ], + "angle": 0, + "content": "4.1. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Benchmark and evaluation metric. We validate the effectiveness of our method on the generic image classification" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16627" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.289, + 0.089, + 0.68, + 0.105 + ], + "angle": 0, + "content": "Table 1: Results on generic image classification datasets." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.111, + 0.89, + 0.355 + ], + "angle": 0, + "content": "
No.MethodsKnown KPCACIFAR10CIFAR100ImageNet-100
AllOldNewAllOldNewAllOldNew
(1)k-means [35]✓X83.685.782.552.052.250.872.775.571.3
(2)RankStats+ [16]✓X46.819.260.558.277.619.337.161.624.8
(3)UNO+ [12]✓X68.698.353.869.580.647.270.395.057.9
(4)ORCA [2]✓X81.886.279.669.077.452.073.592.663.9
(5)Vaze et al. [48]✓X91.597.988.273.076.266.574.189.866.3
(6)Ours (GPC)✓X92.098.388.777.484.862.476.594.068.5
(7)Ours (GPC)✓✓92.298.289.177.985.063.076.994.371.0
(8)Vaze et al. [48]XX88.696.284.973.283.557.972.791.863.8
(9)Vaze et al. [48]X✓89.797.386.374.883.858.773.892.164.6
(10)Ours (GPC)XX88.297.085.874.984.359.674.792.965.1
(11)Ours (GPC)X✓90.697.687.075.484.660.175.393.466.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.474, + 0.653 + ], + "angle": 0, + "content": "benchmark (including CIFAR-10/100 [31] and ImageNet-100 [47]) and also the recently proposed Semantic Shift Benchmark [49] (SSB) (including CUB-200 [50], Stanford Cars [30], and FGVC-Aircraft [36]). For each of the datasets, we follow [48] and sample a subset of all classes for which we have annotated labels during training. For experiments on SSB datasets, we directly use the class split from [49]. \\(50\\%\\) of the images from these labelled classes will be used as the labelled instances in \\(\\mathcal{D}^l\\), and the remaining images are regarded as the unlabelled data \\(\\mathcal{D}^u\\) containing instances from labelled and unlabelled classes. See Tab. 2 for statistics of the datasets we evaluated. We evaluate model performance with clustering accuracy (ACC) following standard practice in the literature. At test-time, given ground truth labels \\(y^{*}\\) and model predicted cluster assignments \\(\\hat{y}\\), the ACC is calculated as \\(ACC = \\frac{1}{M}\\sum_{i = 1}^{M}\\mathbb{1}(y_i^* = g(\\hat{y}_i))\\) where \\(g\\) is the optimal permutation for matching predicted cluster assignment \\(\\hat{y}\\) to actual class label \\(y_i^*\\) and \\(M = |\\mathcal{D}^u|\\)." + }, + { + "type": "table_caption", + "bbox": [ + 0.136, + 0.663, + 0.411, + 0.679 + ], + "angle": 0, + "content": "Table 2: Data splits in the experiments." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.685, + 0.411, + 0.814 + ], + "angle": 0, + "content": "
labelledunlabelled
CIFAR-1055
CIFAR-1008020
ImageNet-1005050
CUB-200100100
Stanford-Cars9898
FGVC-aircraft5050
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Implementation details. We train and test all the methods with a ViT-B/16 backbone [9] with pretrained weights from DINO [3]. We use the output of [CLS] token with a dimension of 768 as the feature representation for an input image. We only finetune the last block of the ViT-B backbone to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.895, + 0.547 + ], + "angle": 0, + "content": "prevent the model from overfitting to the labelled classes during training. We set the batch size for training the model to 128 with 64 labelled images and 64 unlabelled images and use a cosine annealing schedule for the learning rate starting from 0.1. The number of principal directions in the PCA is set to 128, which we found performs the best across all the datasets evaluated. We train all the methods for 200 epochs on each dataset for a fair comparison with previous works, and the best-performing model is selected using the accuracy on the validation set of the labelled classes. All experiments are done with an NVIDIA V100 GPU with 32GB memory." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.56, + 0.82, + 0.575 + ], + "angle": 0, + "content": "4.2. Comparison with the state-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In Tab. 1, we report the comparison with the state-of-the-art method of [48], strong baselines derived from NCD methods, and the \\(k\\)-means on the generic classification datasets. Notably, our method consistently achieves the best overall performance on all datasets, under the challenging setting where the class number is unknown. When the class number is known, our method also achieves the best performance on all datasets, except ImageNet-100, on which the best performance is achieved by ORCA [2]. In rows 1-7, we compare with other methods with the known class number in the unlabelled data, while in rows 8-11 we compare with [48] for the case of the unknown class number. We can see that our proposed framework outperforms other methods in most cases and especially when the number of classes is unknown. Comparing rows 10 and 11 to row 5, we can see that our proposed method without knowing the number of classes can even match the performance of previous strong baseline with the number of classes known to the model. Furthermore, from row 6 vs row 7 and row 10 vs row 11, we can see that the additional PCA layer can effectively improve the performance, also the performance" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16628" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.29, + 0.09, + 0.68, + 0.104 + ], + "angle": 0, + "content": "Table 3: Results on Semantic Shift Benchmark datasets." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.111, + 0.89, + 0.356 + ], + "angle": 0, + "content": "
No.MethodsKnown KPCACUBStanford CarsFGVC-aircraft
AllOldNewAllOldNewAllOldNew
(1)k-means [35]✓X34.338.932.112.810.613.816.014.416.8
(2)RankStats+ [16]✓X33.351.624.228.361.812.126.936.422.2
(3)UNO+ [12]✓X35.149.028.135.570.518.640.356.432.2
(4)ORCA [2]✓X35.345.630.223.550.110.722.031.817.1
(5)Vaze et al. [48]✓X51.356.648.739.057.629.945.041.146.9
(6)Ours (GPC)✓X54.254.950.341.258.831.646.142.447.2
(7)Ours (GPC)✓✓55.458.253.142.859.232.846.342.547.9
(8)Vaze et al. [48]XX47.155.144.835.056.024.840.140.842.8
(9)Vaze et al. [48]X✓49.256.246.336.356.625.943.240.944.6
(10)Ours (GPC)XX50.252.845.636.756.326.339.739.642.7
(11)Ours (GPC)X✓52.055.547.538.258.927.443.340.744.8
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.474, + 0.683 + ], + "angle": 0, + "content": "improvement from PCA is larger on the 'New' classes than on the 'Old' classes, which validates that the PCA can keep the representation space from collapsing and improve the performance on classes without using any labels. Due to the fact that labelled instances provide a stronger training signal, we can see from rows 6 - 11 that performance on 'Old' classes is generally steady. Comparing row 7 to row 5 and row 11 to row 8, we can see our full method outperforms the previous state-of-the-art method Vaze et al. [48] by large margins on both known and unknown class number cases. Tab. 3 shows performance comparison on the more challenging fine-grained Semantic Shift Benchmark [49]. A similar trend of Tab. 1 holds true for the results on SSB. Our approach achieves competitive performance in all cases and again reaches a better performance when the number of classes is unknown. In Tab. 4, we present the results on the Herbarium-19 dataset which is a long-tailed dataset, adding additional challenges for the GCD task. Again, our method performs the best on 'All' and 'New' classes. These results demonstrate the effectiveness of our method." + }, + { + "type": "table_caption", + "bbox": [ + 0.111, + 0.719, + 0.436, + 0.734 + ], + "angle": 0, + "content": "Table 4: Results on the Herbarium-19 Dataset." + }, + { + "type": "table", + "bbox": [ + 0.146, + 0.742, + 0.403, + 0.87 + ], + "angle": 0, + "content": "
MethodsAllOldNew
k-means [35]13.012.213.4
RS+ [16]27.955.812.8
UNO+ [12]28.353.714.7
ORCA [2]20.930.915.5
GCD [48]35.451.027.0
Ours (GPC)36.551.727.9
" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.384, + 0.852, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.51, + 0.86, + 0.538 + ], + "angle": 0, + "content": "(a) Explained variance of the original feature w.r.t. the number of principal directions." + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.545, + 0.852, + 0.657 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.672, + 0.861, + 0.7 + ], + "angle": 0, + "content": "(b) The clustering ACC on validation set w.r.t. the number of principal directions" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.708, + 0.892, + 0.739 + ], + "angle": 0, + "content": "Figure 3: The effects of the number of principal directions in PCA on the feature representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.768, + 0.771, + 0.783 + ], + "angle": 0, + "content": "4.3. Novel class number estimation" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.796, + 0.894, + 0.9 + ], + "angle": 0, + "content": "One of the important yet overlooked components in the NCD and GCD literature is the estimation of unknown class numbers. Our proposed framework leverages a modified GMM to estimate the class number, in which we need to define an initial guess of the class number. We validate the effects of different choices of the initial guess \\( K_{init} \\) w.r.t. the estimated class number in Tab. 5. Note that the number" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16629" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.075, + 0.089, + 0.895, + 0.14 + ], + "angle": 0, + "content": "Table 5: Results of varying the initial guessed \\( K_{init}^{n} \\). 'GT \\( K^{n} \\)' is the ground truth number of novel classes. \\( K^{n} \\) is the estimated number of novel classes. Our proposed framework is generally robust in estimating the number of novel classes, and we found that using the initial guess of \\( K_{init} = K^{l} + \\frac{K^{l}}{2} \\) can be a simple and reliable choice." + }, + { + "type": "table", + "bbox": [ + 0.16, + 0.144, + 0.808, + 0.26 + ], + "angle": 0, + "content": "
DatasetKlGT KnVaze et al. [48]Kninit = 3510203050100
CIFAR-10554Kn = 55566814
CIFAR-100802020Kn = 16202021222736
ImageNet-100505059Kn = 58485755545060
CUB100100131Kn = 7987868892112101
SCars9898132Kn = 8490868789115104
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.279, + 0.471, + 0.342 + ], + "angle": 0, + "content": "in Tab. 5 is \\( K_{init}^{n} = K_{init} - K^{l} \\). We can see that our proposed framework is generally robust to a wide range of initial guesses. We found that \\( K_{init} = K^{l} + \\frac{K^{l}}{2} \\) is a simple and reliable choice. Hence we use this for all datasets." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.351, + 0.27, + 0.367 + ], + "angle": 0, + "content": "4.4. Training complexity" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.374, + 0.471, + 0.541 + ], + "angle": 0, + "content": "Given that our framework necessitates the fitting of GMMs, an extended training duration is required. We compare the performance of our method to the extended method of Vaze et al. [48], which is pushed to \\(1.5 \\times\\) its original number of training epochs. The results in Tab. 6 demonstrate that our method outperforms [48] across both CUB and ImageNet-100 datasets while maintaining a similar training duration. Furthermore, in contrast to the baseline method, our approach eliminates the need for additional post-training procedures such as running SS-\\(k\\)-means on the entire dataset for label assignment." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.552, + 0.47, + 0.584 + ], + "angle": 0, + "content": "Table 6: Comparison between GPC and Vaze et al. [48] \\((1.5\\times)\\) on CUB and ImageNet-100 Datasets." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.59, + 0.455, + 0.69 + ], + "angle": 0, + "content": "
MethodCUBImageNet-100
AllOldNewAllOldNew
Vaze et al. [48]51.356.648.774.189.866.3
Vaze et al.(1.5×)52.056.849.074.790.366.7
Ours (GPC)55.458.253.176.994.371.0
" + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.711, + 0.228, + 0.727 + ], + "angle": 0, + "content": "4.5. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.735, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Number of dimensions in PCA The PCA in our framework requires setting a number for the number of principal directions to extract from data. In Fig. 3, we show the results of using a different number of principal directions in PCA on CUB-200 and ImageNet-100 datasets. We can see from Fig. 3a that for both datasets, 128 principal directions can already explain most of the variances in the data, thus we choose the PCA dimension to be 128 for all our experiments. We further experiment with other different choices of the PCA dimension and shows the result in Fig. 3b, which again confirms that 128 principal directions are already expensive" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.279, + 0.895, + 0.311 + ], + "angle": 0, + "content": "enough, and obtain the best performance over other choices, that are either too few or too many, effectively avoiding DC." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.895, + 0.697 + ], + "angle": 0, + "content": "Different methods for prototype estimation Our semi-supervised GMM plays an important role in prototype estimation for representation learning based on prototypical contrastive learning. Here, we replace our semi-supervised GMM with other alternatives that do not produce prototypes automatically. Particularly, we compare our method with DBSCAN [10], Agglomerative clustering [37], and semi-supervised \\( k \\)-means [17, 48]. The prototypes are then obtained by averaging the data points that are assigned to the same cluster. For a fair comparison, the same regulations to prevent the wrong clustering results for labelled instances are applied to all methods, i.e., during the clustering process, two labelled instances with the same label will fall into the same cluster, and two instances with different labels will be assigned to different clusters. The results are reported in Tab. 7a. Our method achieves the best performance on all three datasets, indicating that better prototypes are obtained by our approach to facilitate representation learning. Note that DBSCAN requires two important user-defined parameters, radius, and minimum core points, the ideal values of which lack a principled way to obtain in practice, while our method is parameter-free and can seamlessly be combined with the representation learning to jointly enhance each other, obtaining better performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Combining our GMM with other GCD methods We further combine our semi-supervised GMM with automatic splitting and merging with other methods, allowing joint representation learning and category discovery without a predefined category number. As the state-of-the-art GCD method [48] does not contain any parametric classifier during representation, so it can be directly combined with our GMM. For the RankStat and the DualRank methods that have a parametric classifier for category discovery, we treat the weights of the classifier as the cluster centers and run our GMM to automatically determine the category number during representation learning. The results are presented" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16630" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.12 + ], + "angle": 0, + "content": "Table 7: Combining components of GPC with other methods. \"IM-100\" denotes ImageNet-100." + }, + { + "type": "table_caption", + "bbox": [ + 0.152, + 0.128, + 0.411, + 0.142 + ], + "angle": 0, + "content": "(a) Different prototype estimation methods." + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.148, + 0.446, + 0.248 + ], + "angle": 0, + "content": "
Clustering Algo.CUBIM-100SCars
Ester et al. [10]45.666.134.8
Murtagh et al. [37]52.174.639.8
Vaze et al. [48]49.273.237.4
Ours (GPC)54.176.641.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.145, + 0.259, + 0.419, + 0.273 + ], + "angle": 0, + "content": "(b) Combining our GMM with other methods." + }, + { + "type": "table", + "bbox": [ + 0.13, + 0.279, + 0.437, + 0.378 + ], + "angle": 0, + "content": "
RepresentationCUBIM-100SCars
Han et al. [16]34.638.429.3
Zhao et al. [58]37.839.733.2
Vaze et al. [48]50.673.437.8
Ours (GPC)54.176.641.9
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.471, + 0.473 + ], + "angle": 0, + "content": "in Tab. 7b. Comparing with row 9 in Tab. 1 and Tab. 3, we can see using our GMM can also improve [48] on CUB and Stanford Cars, while our proposed framework consistently achieves better performance on all datasets, again validating that our design choices." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.47, + 0.645 + ], + "angle": 0, + "content": "Class number estimation with different representations Here, we validate our class number estimation method on top of the representations learned by other GCD approaches and report the results in Tab. 8. It can be seen, applying our method on other GCD representations can achieve reasonably well results. Notably, by applying our class number estimation method on top of the representation by the existing state-of-the-art method, we can obtain better class number estimation results, though the overall best results are obtained with the representation learned in our framework." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.657, + 0.469, + 0.687 + ], + "angle": 0, + "content": "Table 8: Class number estimation with different learned representations. \"C-100\" stands for the CIFAR-100 dataset." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.694, + 0.466, + 0.837 + ], + "angle": 0, + "content": "
RepresentationC-100CUBSCarsIM-100
Ground Truth Kn201009850
Vaze et al.[48]2013113259
Ours w/ [16] feat.191119455
Ours w/ [58] feat.221168949
Ours w/ [48] feat.2112110957
Ours (GPC)2011210353
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Partial overlap between \\(\\mathcal{V}_l\\) and \\(\\mathcal{V}_u\\) We evaluate the performance of our method when we relax \\(\\mathcal{V}_l\\subset \\mathcal{V}_u\\) to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.895, + 0.212 + ], + "angle": 0, + "content": "\\(\\mathcal{Y}_l \\cap \\mathcal{Y}_u \\neq \\emptyset\\), i.e., the two sets may only partially overlap. We vary the number of overlapped classes and report the results in Tab. 9. Our approach consistently outperforms the method proposed by Vaze et al. [48] in all configurations. These compelling results not only showcase the robustness of our method but also highlight its effectiveness in scenarios involving partial overlap between known and unknown classes." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.224, + 0.892, + 0.255 + ], + "angle": 0, + "content": "Table 9: Results on CUB of only partial overlap between \\(\\mathcal{V}_l\\) and \\(\\mathcal{V}_u\\)." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.262, + 0.894, + 0.334 + ], + "angle": 0, + "content": "
|Yl∩Yu|255075
AllOldNewAllOldNewAllOldNew
Vaze et al. [48]49.550.148.251.250.752.252.750.954.5
Ours (GPC)51.252.649.552.351.654.853.651.455.9
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.895, + 0.48 + ], + "angle": 0, + "content": "Varying ratio of Old/New categories We measure the estimated new class numbers when varying the ratio of Old/New categories while having \\( K_{init} = K^{l} + \\frac{K^{l}}{2} \\) on CUB in Tab. 10. As can be seen, for all cases, our method outperforms [48]. Meanwhile, we can also see that when the initial guess is too far from the ground truth, the estimation will be less accurate." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.493, + 0.894, + 0.523 + ], + "angle": 0, + "content": "Table 10: Estimated class numbers on CUB with a varying ratio of Old/New classes." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.53, + 0.878, + 0.593 + ], + "angle": 0, + "content": "
Old/New20/18040/16060/14080/120
GCD [48]87102114104
Ours (GPC)93126135116
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.626, + 0.619, + 0.642 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.895, + 0.835 + ], + "angle": 0, + "content": "In this paper, we present an EM-like framework for the challenging GCD problem without knowing the number of new classes, with the E-step automatically determining the class number and prototypes and the M-step being robust representation learning. We introduce a semi-supervised variant of GMM with a stochastic splitting and merging mechanism to obtain the prototypes and leverage these evolving prototypes for representation learning by prototypical contrastive learning. We demonstrated that class number estimation and representation learning can facilitate each other for more robust category discovery. Our framework obtains state-of-the-art performance on multiple public benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements This work is supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16631" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin Raffel. Mixmatch: A holistic approach to semi-supervised learning. 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GCD is similar to semi-supervised learning (SSL) but is more realistic and challenging, as SSL assumes all the unlabelled images are from the same classes as the labelled ones. We also do not assume the class number in the unlabelled data is known a-priori, making the GCD problem even harder. To tackle the problem of GCD without knowing the class number, we propose an EM-like framework that alternates between representation learning and class number estimation. We propose a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to dynamically determine the prototypes by examining the cluster compactness and separability. With these prototypes, we leverage prototypical contrastive learning for representation learning on the partially labelled data subject to the constraints imposed by the labelled data. Our framework alternates between these two steps until convergence. The cluster assignment for an unlabelled instance can then be retrieved by identifying its nearest prototype. We comprehensively evaluate our framework on both generic image classification datasets and challenging fine-grained object recognition datasets, achieving state-of-the-art performance. Our code is available at https://github.com/DTennant/GPC. + +# 1. Introduction + +The success of deep learning is driven by the availability of large-scale data with human annotations. Given enough annotated data, deep learning models are able to surpass human-level performance on many important computer vi + +![](images/3c0ec6fee07670b105b3a428fed05ac6b313a1c5582eb17621b957579712d86f.jpg) +Figure 1: Overview of our proposed EM-like framework. The input images are fed into a ViT-B model to obtain a 768-dimensional feature vector, then the feature vector will be projected to a lower dimensional space using the projection calculated from PCA. We perform class number estimation and representation learning in this projected space. In the E-step, we use a semi-supervised GMM that can split separable clusters and merge cluttered clusters to estimate the class number and prototypes, which will be used in the M-step of representation learning with prototypical contrastive learning. + +sion tasks such as image classification [21]. But the cost of collecting a large annotated dataset is not always affordable, and it is also not possible to annotate all new classes emerging from the real world. Thus, designing models that can learn to deal with large-scale unlabelled data in the open world is of great value and importance. Semi-supervised learning (SSL) [38] is proposed as a solution to learn a model on both labelled data and unlabelled data, with many works achieving promising performance [1, 46, 44]. However, SSL assumes that labelled instances are provided for all object classes in the unlabelled data. The novel category discovery (NCD) task is introduced [17, 16] to automatically discover novel classes by transferring the knowledge learned from the labelled instances of known classes, assuming the unlabelled data only contain instances from new classes. Generalized category discovery (GCD) [48] further relaxes the assumption in NCD, and tackles a more + +generalized setting where the unlabelled data contains instances from both known and novel categories. Existing methods for NCD [17, 16, 58, 60, 61, 12, 26] and GCD [48, 11, 51, 45, 56, 59, 34] learn the representation and cluster assignment assuming the class number is known a priori [58, 26, 60, 12, 61] or precomputed [17, 48]. In practice, the number of categories in the unlabelled data is often unknown, while precomputing the class number without taking the representation learning into consideration is likely to lead to a sub-optimal solution. + +In this paper, we argue that representation learning and the estimation of class numbers should be considered together and could reinforce each other, i.e., a strong representation could help a more accurate estimation of the class numbers, and an accurate class number could help learn a better feature representation. To this end, we propose a unified EM-like framework that alternates between feature representation learning and class number estimation where the E-step is aimed at automatically estimating a proper class number and a set of class prototypes in the unlabelled data and the M-step is aimed at learning better representation with the class number and class prototypes estimated. In particular, we propose using a prototype contrastive representation learning [33] method for GCD, which requires a set of prototypes to serve as anchors for representation learning. Prototypical contrastive learning [33] is developed for unsupervised representation learning to generalize to different tasks, where the prototypes are obtained by over-clustering the dataset with one or multiple given prototype numbers, using non-parametric clustering algorithms like $k$ -means. Instead, to handle the problem of GCD, we propose to estimate the prototype number and prototypes automatically and simultaneously. To do so, we introduce a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to determine the most suitable clusters based on current representation. These clusters can then be used to form prototypes to facilitate contrastive representation learning. Our framework alternates between the E- and M-step until converging to achieve robust representation and reliable category estimation. After learning, the cluster assignment for an unlabelled instance, either from known or novel classes, can be retrieved by finding the nearest prototypes. Thus we name our framework as GPC: Gaussian mixture model for generalized category discovery with Protypical Contrastive learning. + +Our contributions in this paper are as follows: (1) We demonstrate that in generalized category discovery, the class number estimation and representation learning can reinforce each other in the learning process. Strong representations can give a better estimation of the class number, and vice versa. (2) We propose an EM-like framework that alternates between prototype estimation with a variant of GMM (E-step) and representation learning based on prototypical + +contrastive learning (M-step). (3) We introduce a semi-supervised variant of GMM with a stochastic splitting and merging mechanism to allow dynamic change of the prototypes by examining the cluster compactness and separability based on the Metropolis-Hastings ratio [19]. (4) We comprehensively evaluated our framework on both the generic image classification benchmark, including CIFAR10, CIFAR100, ImageNet-100, and the challenging fine-grained Semantic Shifts Benchmark suite, which includes CUB-200, Stanford-Cars, and FGVC-aircrafts, achieving the state-of-the-art results. + +# 2. Related work + +Novel category discovery (NCD) is first formalized in DTC [17], where the task is to discover new categories leveraging the knowledge of a set of labelled categories. Many methods have been proposed to tackle this challenge. To name a few, RankStat [15, 16] and DualRank [58] transfer knowledge from labelled to unlabelled classes using feature ranking statistics. OpenMix [61] shows that mixing labelled and unlabelled data can prevent overfitting. NCL [60] and WTA [26] use contrastive learning for NCD. UNO [12] introduces a unified cross-entropy loss for joint training on labelled and unlabelled data. [29] introduces a spacing loss for representation learning in NCD. NCDwF [28] studies the NCD problem under an incremental learning setting. Earlier methods like [22, 23] for generalized transfer learning can also be applied to NCD. Generalized category discovery (GCD) [48] extends NCD to a more open-world setting where unlabelled instances can come from both labelled and unlabelled categories. ORCA [2] also tackles GCD from a semi-supervised learning perspective. Several improved methods have been proposed for generalized category discovery (GCD), such as [11, 51, 39, 56, 45], which have shown promising results. Incremental GCD is considered in [57, 59]. Concurrently, CiPR [18] presents a hierarchical GCD approach employing selective neighbor clustering, leading to improved efficiency and performance without necessitating knowledge of the class number. [14] studies semantic category discovery by leveraging vision-language representations, thereby enabling GCD with class name prediction. However, most existing GCD methods assume that the novel class number is known a priori, which is often not the case in the real world. To address this limitation, [17, 48] precompute the number of novel classes with a semi-supervised $k$ -means algorithm from pretrained representations. In this paper, we demonstrate that class number estimation and representation learning can be jointly considered to mutually benefit each other. + +Contrastive learning [4, 5, 20, 7, 62] (CL) has been shown very effective for representation learning in a self-supervised manner, using the instance discrimination pretext [52] as the learning objective. The instance discrimination task learns + +a representation by pulling positive samples from the augmentations of the same images closer and pushing negative samples from different images apart in the embedding space. Instead of contrasting over all instances in a mini-bath, prototypical contrastive learning (PCL) [33] proposes to contrast the features with a set of prototypes which can provide a higher level abstraction of dataset than instances and has been shown to be more data efficient without the need of large batch size. Though PCL is developed for unsupervised representation learning, if the prototypes are viewed as cluster centers, it can be leveraged in the partially supervised setting of GCD for representation learning to better fit the GCD task of partitioning data into different clusters. Thus, in this paper, we adopt PCL to fit the GCD setting for representation learning in which the downstream clustering task is directly considered. + +Semi-supervised learning (SSL) has been a long standing research topic which many effective method proposed [40, 44, 1, 32, 46]. In SSL, the labelled and the unlabelled data are assumed to come from the same set of classes, and the task is to learn a classification model that can take advantage of both labelled and unlabelled data. Consistency-based methods are among the most effective methods for SSL, such as Mean-teacher [46], MixMatch [1], and FixMatch [44]. Self-supervised representation learning also shows to be helpful for SSL because it can provide a strong representation [55, 40]. Recent works extend semi-supervised learning by relaxing the assumption of exactly the same classes in the labeled and unlabelled data [43, 25, 54], but their focus is improving the performance of the labeled categories without discovering novel categories in the unlabeled set. + +Unsupervised clustering has been studied for decades, and there are many existing classical approaches [35, 10, 6] as well as deep learning based approaches [53, 41, 13]. Recently, DeepDPM [42] is proposed to automatically determine the number of clusters for a given dataset by adopting a similar split/merge framework that changes the inferred number of clusters. However, due to the unsupervised nature of these methods, there is no prior or supervision over how a cluster should be formed, thus multiple equally valid clustering results following different clustering criteria can be produced. Thus, directly applying unsupervised clustering methods to the task of generalized category discovery is not feasible, as we would want the model to use one unique clustering criteria implicitly given by the labelled data. + +# 3. Method + +Given a collection of partially labelled data, $\mathcal{D} = \mathcal{D}^l\cup \mathcal{D}^u$ where $\mathcal{D}^l = \{(x_i,y_i^l)\} \in \mathcal{X}\times \mathcal{Y}_l$ is labelled, $\mathcal{D}^u = \{x_i,y_i^u\} \in \mathcal{X}\times \mathcal{Y}_u$ is unlabelled, and $\mathcal{V}_l\subset \mathcal{V}_u$ Generalized category discovery (GCD) aims at automatically assign labels for the unlabelled instances in $\mathcal{D}^u$ , by transferring knowledge acquired from $\mathcal{D}^l$ . Let the category number in + +$\mathcal{D}^l$ be $K^l = |\mathcal{Y}_l|$ and that in $\mathcal{D}^u$ be $K^u = |\mathcal{Y}_u|$ . The number of new categories $\mathcal{D}^u$ is then $K^n = |\mathcal{Y}_u \setminus \mathcal{Y}_l| = K^u - K^l$ . Though $K^l$ can be accessed from the labelled data, we do not assume $K^n$ or $K^u$ to be known. This is a realistic setting to reflect the real open world, where we often have access to some labelled data, but in the unlabelled data, we also have instances from unseen new categories. + +The key challenges for GCD are representation learning, category number estimation, and label assignment. Existing methods for NCD and GCD [17, 48] deal with these three challenges independently. However, we believe they are inherently linked with each other. Label assignment depends on representation and category number estimation. A good class number estimation can facilitate representation learning, thus better label assignment, and vice versa. Thus, in this paper, we aim to jointly handle these challenges in the learning process for a more reliable GCD. + +To this end, we propose a unified EM-like framework that alternates between representation learning and class number estimation, while the label assignment turns out to be a by-product during class number estimation. In the E-step, we introduce a semi-supervised variant of the Gaussian Mixture Model (GMM) to estimate the class numbers by dynamically splitting separable clusters and merging cluttered clusters based on current representation, forming a set of class prototypes for both seen and unseen classes, and in the M-step, we train the model to produce discriminative representation by prototypical contrastive learning using the cluster centers from the GMM prototypes derived from the E-step during class number estimation. After training, the class assignment for each instance can be retrieved by simply identifying the nearest prototype. + +# 3.1. Representation learning + +The goal of representation learning is to learn a discriminative representation that can well separate different categories, not only the old ones, but also the new ones. Contrastive learning (CL) has been shown to be an effective choice for NCD [26] and GCD [48]. Self-supervised contrastive learning is defined as + +$$ +\mathcal {L} _ {C L} = - \log \frac {\exp \left(z _ {i} \cdot z _ {i} ^ {\prime} / \tau\right)}{\sum_ {j = 1} ^ {n} \exp \left(z _ {i} \cdot z _ {j} ^ {\prime} / \tau\right)} \tag {1} +$$ + +where $z_{i}$ and $z_{i}^{\prime}$ are the representations of two views obtained from the same image using random augmentations and $\tau$ is the temperature. Two views of the same instance are pulled closer, and different instances are pushed away during training. Self-supervised contrastive learning and its supervised variant, in which different instances from the same category are also pulled closer, are used in [48] for representation learning. However, as a stronger training signal is used for the labelled data, the representation is likely biased to the labelled data to some extent. Moreover, such a method does + +not take the downstream clustering task into account during learning, thus a clustering algorithm is required to run independently after the representation learning. + +In this paper, we adopt prototypical contrastive learning (PCL) [33] to the GCD setting to learn the representation $z_{i} = f(x_{i}) \in \mathbb{R}^{d}$ . PCL uses a set of prototypes $\mathcal{C} = \{\mu_1, \dots, \mu_K\}$ to represent the dataset for contrastive learning instead of the random augmentation generated views $z_{i}'$ . PCL loss can be written as + +$$ +\mathcal {L} _ {P C L} = - \log \frac {\exp \left(z _ {i} \cdot \mu_ {s} / \tau\right)}{\sum_ {j = 1} ^ {K} \exp \left(z _ {i} \cdot \mu_ {j} / \tau\right)} \tag {2} +$$ + +where $\mu_{s}$ is the corresponding prototype for $z_{i}$ . It was originally designed as an alternative for self-supervised contrastive learning by over-clustering the training data to obtain the prototypes during training. We employ PCL here to learn reliable representation while taking the downstream clustering into account for GCD, where we have a set of partially labelled data. In our case, the prototypes can be interpreted as the class centers for each of the categories. To obtain the prototypes for the seen categories, we directly calculate the class mean by averaging all the feature vectors of the labelled instances. For the unseen categories, we obtain the prototypes with a semi-supervised variant of the Gaussian Mixture Model (GMM), as will be introduced in Sec. 3.2. This way, the cluster assignment for an unlabelled image can be readily achieved by finding the nearest prototype. + +Additionally, we observe that only a few principal dimensions can already recover most of the variances in the representation space of $z_{i}$ , which is known as dimensional collapse (DC) in [27, 24], and it is shown that DC can be caused by strong augmentations or implicit regularizations in the model, and preventing DC during training can lead to a better feature representation. To alleviate DC for representation learning in our case, we propose to first project the feature to a subspace obtained by principal component analysis (PCA) before the contrastive learning. Specifically, we apply PCA on a matrix $Z$ formed by a mini-batch of features $z_{i}$ , with a batch size of $n$ , the feature dimension $d$ , and the number of effective principal directions $q$ . We have $Z \approx U\mathrm{diag}(S)V^{\top}$ , where $U \in \mathbb{R}^{n \times q}$ , $S \in \mathbb{R}^q$ and $V \in \mathbb{R}^{d \times q}$ . We can then project features $z_{i}$ to principal directions to obtain a more compact feature $v_{i} = V \cdot z_{i}$ , and replace feature $z_{i}$ with $v_{i}$ in Eq. (2) for PCL. The prototypes are also computed in the projected space. + +We jointly use self-supervised contrastive learning and PCL to train our model. The overall learning objective can be written as + +$$ +\mathcal {L} = \mathcal {L} _ {C L} + \lambda (t) \mathcal {L} _ {P C L} \tag {3} +$$ + +where $\lambda(t)$ is a linear warmup function defined as $\lambda(t) = \min(1, \frac{t}{T})$ where $t$ is the current epoch and $T$ warmup length + +![](images/451c293d30123ad4dcd7869fbe76c22e28e585d84e9b7b0f951b2601d5c728bc.jpg) +Figure 2: Examples for splitting a separable cluster and merging two cluttered clusters. Left: the cluster is split because the two sub-component in this cluster are easily separable. Right: two clusters are merged as they are cluttered and likely from the same class. + +$(T = 20$ in our experiments). The reason we use both CL and PCL is that, in the beginning, the representation is not well suited for clustering, and thus the obtained prototypes are not informative to facilitate the representation learning. Hence, we gradually increase the weight of PCL during training from 0 to 1 in the first $T$ epochs. + +# 3.2. Class number and prototypes estimation with semi-supervised Gaussian mixture model + +In this section, we present a semi-supervised variant of the Gaussian mixture model (GMM) with each Gaussian component consisting of two sub-components to estimate the prototypes for representation learning in Sec. 3.1 and the unknown class number. GMM estimates the prototypes and assigns a label for each data point by finding its nearest prototype. The cluster label assignment and the prototypes are then used for prototypical contrastive learning. The GMM is defined as + +$$ +p (z) = \sum_ {i = 1} ^ {K} \pi_ {i} \mathcal {N} \left(z \mid \mu_ {i}, \Sigma_ {i}\right), \tag {4} +$$ + +where $\mathcal{N}(z|\mu_i,\Sigma_i)$ is the Gaussian probability density function with mean $\mu_{i}\in \mathbb{R}^{d}$ and covariance $\Sigma_{i}\in \mathbb{R}^{d\times d}$ , and $\pi_{i}$ is the weight for $i$ -th Gaussian component and we have $\sum_{i = 1}^{N}\pi_{i} = 1$ . Ideally, we would expect the component number $K$ in the GMM to be equal to the class number $K^u$ in $\mathcal{D}$ . To estimate the unknown class number $K^u$ , we leverage an automatic splitting-and-merging strategy into the modeling process to obtain an optimal $K$ , which is expected to be as close to $K^u$ as possible. We alternate between representation learning and $K^u$ estimation until convergence to get discriminative representation learning and a reliable class number estimation. For initialization, $K$ can be set to any number greater than $K^l$ . In our experiments, we simply set the initial number of components to a default $K_{init} = K^l +\frac{K^l}{2}$ . We run a semi-supervised $k$ -means algorithm [48] with $k = K$ to obtain the $\mu$ and $\Sigma$ for each component in the mixture model. Note that the semi-supervised $k$ -means algorithm is constrained to the labelled data in a way that labelled instances from the same class are assigned to the same cluster, and labelled instances from different classes will not be + +Algorithm 1: The overall algorithm of our method. +Input: $\mathcal{D},\mathcal{D}^l$ , and $\mathcal{D}^u$ The datasets. $K_{init}$ Initial guess of $K$ +1 $K\gets K_{init}$ +2 for $e = 1$ to $E$ do +3 $z\gets f(x),x\in \mathcal{D}\quad /$ extract features +4 $\mu ,\Sigma \gets \arg \max \sum_{i = 1}^{K}\pi_{i}\mathcal{N}(z|\mu_{i},\Sigma_{i})$ // estimate prototypes using GMM +5 for $i = 1$ to len(D) do +6 $\mathcal{B}^l\gets \{x_i^l\sim \mathcal{D}^l\}_{i = 1}^{N^l}\quad /$ sample a batch of $N^l$ labelled images +7 $\mathcal{B}^u\gets \{x_i^u\sim \mathcal{D}^u\}_{i = 1}^{N^u}\quad /$ sample a batch of $N^u$ unlabelled images +8 $f\gets \arg \min \mathcal{L}(f,\mu ,\mathcal{B}^l,\mathcal{B}^u)$ // prototypical contrastive learning +9 end +10 $H_{s},H_{m}\gets \mathrm{calc\_prob}(\mu ,\Sigma)$ // probability for split and merge +11 $\mu ,\Sigma \gets \mathrm{perform\_op}(H_s,H_m)\quad /$ perform operations +12 $K\gets \mathrm{len}(\mu)$ // update $K$ +13 end Output: feature extractor $f(\cdot)$ , cluster centers $\mu_{i}$ + +assigned to the same cluster. To facilitate the splitting and merging process, for each Gaussian component defined by $\mu_{i}$ and $\Sigma_{i}$ , we further depict it with a GMM with two subcomponents $\mu_{i,1},\mu_{i,2}$ and $\Sigma_{i,1},\Sigma_{i,2}$ with $\pi_{i,1} + \pi_{i,2} = 1$ . We run a $k$ -means with $k = 2$ on the $i$ -th component to obtain $\mu_{i,1},\mu_{i,2}$ and $\Sigma_{i,1},\Sigma_{i,2}$ . + +For a cluster whose two sub-components are roughly independent and equally sized (e.g., left part of Fig. 2), i.e., they are easily separable, we would like the model to split it into two such that the model can better fit the data distribution and the class assignment will be more accurate because it is less likely that such distinct clusters will belong to the same class. For two clusters that are cluttered with each other (e.g., right part of Fig. 2), i.e., difficult to distinguish, we would like to merge them into one, so that they will be considered as from the same class. Following this intuition, we use the Metropolis-Hastings framework [19] to compute a probability $p_{s} = \min(1, H_{s})$ to stochastically split a cluster into two. The Hastings ratio is defined as + +$$ +H _ {s} = \frac {\Gamma \left(N _ {i , 1}\right) h \left(\mathcal {Z} _ {i , 1} ; \theta\right) \Gamma \left(N _ {i , 2}\right) h \left(\mathcal {Z} _ {i , 2} ; \theta\right)}{\Gamma \left(N _ {i}\right) h \left(\mathcal {Z} _ {i} ; \theta\right)}, \tag {5} +$$ + +where $\Gamma$ is the factorial function, i.e., $\Gamma (n) = n! = n\times (n - 1)\times \dots \times 1$ , $\mathcal{Z}_i$ is the set of data points in cluster $i$ , $\mathcal{Z}_{i,j}$ is the set of data points in the $j$ -th sub-cluster of cluster $i$ , $N_{i} = |\mathcal{Z}_{i}|, N_{i,j} = |\mathcal{Z}_{i,j}|$ , $h(Z;\theta)$ is the marginal likelihood of the observed data $\mathcal{Z}$ by integrating out the $\mu$ and $\Sigma$ parameters in the Gaussian, and $\theta$ is the prior distribution of $\mu$ and $\Sigma$ . More details can be found in the supplementary. The intuition behind this $H_{s}$ is that, if the number of data points in two sub-components is roughly balanced, which is measured by the $\Gamma (\cdot)$ terms, and the data points in the two sub-components are independent of each other, which is measure by the $h(\cdot ;\theta)$ terms, there should be a greater chance of splitting the cluster. After performing a split operation, the $\mu_{i}$ and $\Sigma_{i}$ of previous components $i$ will be replaced with $\mu_{i,1},\mu_{i,2}$ and $\Sigma_{i,1},\Sigma_{i,2}$ of two sub-components. We will then run two $k$ -means within the two newly formed components to obtain their corresponding sub-components. On the contrary, if two clusters are cluttered with each other, they should be merged. Similar to splitting, we determine the merging probability by $p_m = \min (1,H_m)$ , where $H_{m}$ is calculated similarly for two clusters $i$ and $j$ : + +$$ +H _ {m} = \frac {\Gamma \left(N _ {i} + N _ {j}\right) h \left(\mathcal {Z} _ {i} \cup \mathcal {Z} _ {j} ; \theta\right)}{\Gamma \left(N _ {i}\right) h \left(\mathcal {Z} _ {i} ; \theta\right) \Gamma \left(N _ {j}\right) h \left(\mathcal {Z} _ {j} ; \theta\right)}. \tag {6} +$$ + +Note that both $H_{s}$ and $H_{m}$ are within the range of $(0, +\infty)$ , so we use $p_{s} = \min(1, H_{s})$ and $p_{m} = \min(1, H_{m})$ to convert it into a valid probability. + +To take the labelled instances into consideration during the splitting-and-merging process, if a cluster consists of labelled instances, we set its $p_s = 0$ ; if for any two clusters containing instances from two labelled classes, we set their $p_m = 0$ . + +During the splitting-and-merging process, we first apply splitting according to the $p_s$ and then apply merging according to $p_m$ . The newly formed clusters by splitting will not be reused during the merging step. After finishing the splitting and merging, we can obtain the prototypes, and thus can estimate $K$ , for our PCL-based representation learning. We alternate between representation learning and class number estimation for each training epoch until converge. The final $K$ will be considered the estimated class number in $\mathcal{D}$ . The cluster assignment for each unlabelled instance can be easily retrieved by identifying its nearest prototype, without the need of running a non-parametric clustering algorithm as [48]. The overall training process is summarized in Algorithm 1. + +# 4. Experiments + +# 4.1. Experimental setup + +Benchmark and evaluation metric. We validate the effectiveness of our method on the generic image classification + +Table 1: Results on generic image classification datasets. + +
No.MethodsKnown KPCACIFAR10CIFAR100ImageNet-100
AllOldNewAllOldNewAllOldNew
(1)k-means [35]✓X83.685.782.552.052.250.872.775.571.3
(2)RankStats+ [16]✓X46.819.260.558.277.619.337.161.624.8
(3)UNO+ [12]✓X68.698.353.869.580.647.270.395.057.9
(4)ORCA [2]✓X81.886.279.669.077.452.073.592.663.9
(5)Vaze et al. [48]✓X91.597.988.273.076.266.574.189.866.3
(6)Ours (GPC)✓X92.098.388.777.484.862.476.594.068.5
(7)Ours (GPC)✓✓92.298.289.177.985.063.076.994.371.0
(8)Vaze et al. [48]XX88.696.284.973.283.557.972.791.863.8
(9)Vaze et al. [48]X✓89.797.386.374.883.858.773.892.164.6
(10)Ours (GPC)XX88.297.085.874.984.359.674.792.965.1
(11)Ours (GPC)X✓90.697.687.075.484.660.175.393.466.7
+ +benchmark (including CIFAR-10/100 [31] and ImageNet-100 [47]) and also the recently proposed Semantic Shift Benchmark [49] (SSB) (including CUB-200 [50], Stanford Cars [30], and FGVC-Aircraft [36]). For each of the datasets, we follow [48] and sample a subset of all classes for which we have annotated labels during training. For experiments on SSB datasets, we directly use the class split from [49]. $50\%$ of the images from these labelled classes will be used as the labelled instances in $\mathcal{D}^l$ , and the remaining images are regarded as the unlabelled data $\mathcal{D}^u$ containing instances from labelled and unlabelled classes. See Tab. 2 for statistics of the datasets we evaluated. We evaluate model performance with clustering accuracy (ACC) following standard practice in the literature. At test-time, given ground truth labels $y^{*}$ and model predicted cluster assignments $\hat{y}$ , the ACC is calculated as $ACC = \frac{1}{M}\sum_{i = 1}^{M}\mathbb{1}(y_i^* = g(\hat{y}_i))$ where $g$ is the optimal permutation for matching predicted cluster assignment $\hat{y}$ to actual class label $y_i^*$ and $M = |\mathcal{D}^u|$ . + +Table 2: Data splits in the experiments. + +
labelledunlabelled
CIFAR-1055
CIFAR-1008020
ImageNet-1005050
CUB-200100100
Stanford-Cars9898
FGVC-aircraft5050
+ +Implementation details. We train and test all the methods with a ViT-B/16 backbone [9] with pretrained weights from DINO [3]. We use the output of [CLS] token with a dimension of 768 as the feature representation for an input image. We only finetune the last block of the ViT-B backbone to + +prevent the model from overfitting to the labelled classes during training. We set the batch size for training the model to 128 with 64 labelled images and 64 unlabelled images and use a cosine annealing schedule for the learning rate starting from 0.1. The number of principal directions in the PCA is set to 128, which we found performs the best across all the datasets evaluated. We train all the methods for 200 epochs on each dataset for a fair comparison with previous works, and the best-performing model is selected using the accuracy on the validation set of the labelled classes. All experiments are done with an NVIDIA V100 GPU with 32GB memory. + +# 4.2. Comparison with the state-of-the-art + +In Tab. 1, we report the comparison with the state-of-the-art method of [48], strong baselines derived from NCD methods, and the $k$ -means on the generic classification datasets. Notably, our method consistently achieves the best overall performance on all datasets, under the challenging setting where the class number is unknown. When the class number is known, our method also achieves the best performance on all datasets, except ImageNet-100, on which the best performance is achieved by ORCA [2]. In rows 1-7, we compare with other methods with the known class number in the unlabelled data, while in rows 8-11 we compare with [48] for the case of the unknown class number. We can see that our proposed framework outperforms other methods in most cases and especially when the number of classes is unknown. Comparing rows 10 and 11 to row 5, we can see that our proposed method without knowing the number of classes can even match the performance of previous strong baseline with the number of classes known to the model. Furthermore, from row 6 vs row 7 and row 10 vs row 11, we can see that the additional PCA layer can effectively improve the performance, also the performance + +Table 3: Results on Semantic Shift Benchmark datasets. + +
No.MethodsKnown KPCACUBStanford CarsFGVC-aircraft
AllOldNewAllOldNewAllOldNew
(1)k-means [35]✓X34.338.932.112.810.613.816.014.416.8
(2)RankStats+ [16]✓X33.351.624.228.361.812.126.936.422.2
(3)UNO+ [12]✓X35.149.028.135.570.518.640.356.432.2
(4)ORCA [2]✓X35.345.630.223.550.110.722.031.817.1
(5)Vaze et al. [48]✓X51.356.648.739.057.629.945.041.146.9
(6)Ours (GPC)✓X54.254.950.341.258.831.646.142.447.2
(7)Ours (GPC)✓✓55.458.253.142.859.232.846.342.547.9
(8)Vaze et al. [48]XX47.155.144.835.056.024.840.140.842.8
(9)Vaze et al. [48]X✓49.256.246.336.356.625.943.240.944.6
(10)Ours (GPC)XX50.252.845.636.756.326.339.739.642.7
(11)Ours (GPC)X✓52.055.547.538.258.927.443.340.744.8
+ +improvement from PCA is larger on the 'New' classes than on the 'Old' classes, which validates that the PCA can keep the representation space from collapsing and improve the performance on classes without using any labels. Due to the fact that labelled instances provide a stronger training signal, we can see from rows 6 - 11 that performance on 'Old' classes is generally steady. Comparing row 7 to row 5 and row 11 to row 8, we can see our full method outperforms the previous state-of-the-art method Vaze et al. [48] by large margins on both known and unknown class number cases. Tab. 3 shows performance comparison on the more challenging fine-grained Semantic Shift Benchmark [49]. A similar trend of Tab. 1 holds true for the results on SSB. Our approach achieves competitive performance in all cases and again reaches a better performance when the number of classes is unknown. In Tab. 4, we present the results on the Herbarium-19 dataset which is a long-tailed dataset, adding additional challenges for the GCD task. Again, our method performs the best on 'All' and 'New' classes. These results demonstrate the effectiveness of our method. + +Table 4: Results on the Herbarium-19 Dataset. + +
MethodsAllOldNew
k-means [35]13.012.213.4
RS+ [16]27.955.812.8
UNO+ [12]28.353.714.7
ORCA [2]20.930.915.5
GCD [48]35.451.027.0
Ours (GPC)36.551.727.9
+ +![](images/d7ce1b599271ba5b8e442405c1d2efd04e817acf4b8b38de6e4ec886e3d52270.jpg) +(a) Explained variance of the original feature w.r.t. the number of principal directions. + +![](images/64e7895dd7657664189b3aedc58320f39e22a955b79d2e8b1cab66e824210a04.jpg) +(b) The clustering ACC on validation set w.r.t. the number of principal directions +Figure 3: The effects of the number of principal directions in PCA on the feature representations. + +# 4.3. Novel class number estimation + +One of the important yet overlooked components in the NCD and GCD literature is the estimation of unknown class numbers. Our proposed framework leverages a modified GMM to estimate the class number, in which we need to define an initial guess of the class number. We validate the effects of different choices of the initial guess $K_{init}$ w.r.t. the estimated class number in Tab. 5. Note that the number + +Table 5: Results of varying the initial guessed $K_{init}^{n}$ . 'GT $K^{n}$ ' is the ground truth number of novel classes. $K^{n}$ is the estimated number of novel classes. Our proposed framework is generally robust in estimating the number of novel classes, and we found that using the initial guess of $K_{init} = K^{l} + \frac{K^{l}}{2}$ can be a simple and reliable choice. + +
DatasetKlGT KnVaze et al. [48]Kninit = 3510203050100
CIFAR-10554Kn = 55566814
CIFAR-100802020Kn = 16202021222736
ImageNet-100505059Kn = 58485755545060
CUB100100131Kn = 7987868892112101
SCars9898132Kn = 8490868789115104
+ +in Tab. 5 is $K_{init}^{n} = K_{init} - K^{l}$ . We can see that our proposed framework is generally robust to a wide range of initial guesses. We found that $K_{init} = K^{l} + \frac{K^{l}}{2}$ is a simple and reliable choice. Hence we use this for all datasets. + +# 4.4. Training complexity + +Given that our framework necessitates the fitting of GMMs, an extended training duration is required. We compare the performance of our method to the extended method of Vaze et al. [48], which is pushed to $1.5 \times$ its original number of training epochs. The results in Tab. 6 demonstrate that our method outperforms [48] across both CUB and ImageNet-100 datasets while maintaining a similar training duration. Furthermore, in contrast to the baseline method, our approach eliminates the need for additional post-training procedures such as running SS- $k$ -means on the entire dataset for label assignment. + +Table 6: Comparison between GPC and Vaze et al. [48] $(1.5\times)$ on CUB and ImageNet-100 Datasets. + +
MethodCUBImageNet-100
AllOldNewAllOldNew
Vaze et al. [48]51.356.648.774.189.866.3
Vaze et al.(1.5×)52.056.849.074.790.366.7
Ours (GPC)55.458.253.176.994.371.0
+ +# 4.5. Ablation study + +Number of dimensions in PCA The PCA in our framework requires setting a number for the number of principal directions to extract from data. In Fig. 3, we show the results of using a different number of principal directions in PCA on CUB-200 and ImageNet-100 datasets. We can see from Fig. 3a that for both datasets, 128 principal directions can already explain most of the variances in the data, thus we choose the PCA dimension to be 128 for all our experiments. We further experiment with other different choices of the PCA dimension and shows the result in Fig. 3b, which again confirms that 128 principal directions are already expensive + +enough, and obtain the best performance over other choices, that are either too few or too many, effectively avoiding DC. + +Different methods for prototype estimation Our semi-supervised GMM plays an important role in prototype estimation for representation learning based on prototypical contrastive learning. Here, we replace our semi-supervised GMM with other alternatives that do not produce prototypes automatically. Particularly, we compare our method with DBSCAN [10], Agglomerative clustering [37], and semi-supervised $k$ -means [17, 48]. The prototypes are then obtained by averaging the data points that are assigned to the same cluster. For a fair comparison, the same regulations to prevent the wrong clustering results for labelled instances are applied to all methods, i.e., during the clustering process, two labelled instances with the same label will fall into the same cluster, and two instances with different labels will be assigned to different clusters. The results are reported in Tab. 7a. Our method achieves the best performance on all three datasets, indicating that better prototypes are obtained by our approach to facilitate representation learning. Note that DBSCAN requires two important user-defined parameters, radius, and minimum core points, the ideal values of which lack a principled way to obtain in practice, while our method is parameter-free and can seamlessly be combined with the representation learning to jointly enhance each other, obtaining better performance. + +Combining our GMM with other GCD methods We further combine our semi-supervised GMM with automatic splitting and merging with other methods, allowing joint representation learning and category discovery without a predefined category number. As the state-of-the-art GCD method [48] does not contain any parametric classifier during representation, so it can be directly combined with our GMM. For the RankStat and the DualRank methods that have a parametric classifier for category discovery, we treat the weights of the classifier as the cluster centers and run our GMM to automatically determine the category number during representation learning. The results are presented + +Table 7: Combining components of GPC with other methods. "IM-100" denotes ImageNet-100. +(a) Different prototype estimation methods. + +
Clustering Algo.CUBIM-100SCars
Ester et al. [10]45.666.134.8
Murtagh et al. [37]52.174.639.8
Vaze et al. [48]49.273.237.4
Ours (GPC)54.176.641.9
+ +(b) Combining our GMM with other methods. + +
RepresentationCUBIM-100SCars
Han et al. [16]34.638.429.3
Zhao et al. [58]37.839.733.2
Vaze et al. [48]50.673.437.8
Ours (GPC)54.176.641.9
+ +in Tab. 7b. Comparing with row 9 in Tab. 1 and Tab. 3, we can see using our GMM can also improve [48] on CUB and Stanford Cars, while our proposed framework consistently achieves better performance on all datasets, again validating that our design choices. + +Class number estimation with different representations Here, we validate our class number estimation method on top of the representations learned by other GCD approaches and report the results in Tab. 8. It can be seen, applying our method on other GCD representations can achieve reasonably well results. Notably, by applying our class number estimation method on top of the representation by the existing state-of-the-art method, we can obtain better class number estimation results, though the overall best results are obtained with the representation learned in our framework. + +Table 8: Class number estimation with different learned representations. "C-100" stands for the CIFAR-100 dataset. + +
RepresentationC-100CUBSCarsIM-100
Ground Truth Kn201009850
Vaze et al.[48]2013113259
Ours w/ [16] feat.191119455
Ours w/ [58] feat.221168949
Ours w/ [48] feat.2112110957
Ours (GPC)2011210353
+ +Partial overlap between $\mathcal{V}_l$ and $\mathcal{V}_u$ We evaluate the performance of our method when we relax $\mathcal{V}_l\subset \mathcal{V}_u$ to + +$\mathcal{Y}_l \cap \mathcal{Y}_u \neq \emptyset$ , i.e., the two sets may only partially overlap. We vary the number of overlapped classes and report the results in Tab. 9. Our approach consistently outperforms the method proposed by Vaze et al. [48] in all configurations. These compelling results not only showcase the robustness of our method but also highlight its effectiveness in scenarios involving partial overlap between known and unknown classes. + +Table 9: Results on CUB of only partial overlap between $\mathcal{V}_l$ and $\mathcal{V}_u$ . + +
|Yl∩Yu|255075
AllOldNewAllOldNewAllOldNew
Vaze et al. [48]49.550.148.251.250.752.252.750.954.5
Ours (GPC)51.252.649.552.351.654.853.651.455.9
+ +Varying ratio of Old/New categories We measure the estimated new class numbers when varying the ratio of Old/New categories while having $K_{init} = K^{l} + \frac{K^{l}}{2}$ on CUB in Tab. 10. As can be seen, for all cases, our method outperforms [48]. Meanwhile, we can also see that when the initial guess is too far from the ground truth, the estimation will be less accurate. + +Table 10: Estimated class numbers on CUB with a varying ratio of Old/New classes. + +
Old/New20/18040/16060/14080/120
GCD [48]87102114104
Ours (GPC)93126135116
+ +# 5. Conclusion + +In this paper, we present an EM-like framework for the challenging GCD problem without knowing the number of new classes, with the E-step automatically determining the class number and prototypes and the M-step being robust representation learning. We introduce a semi-supervised variant of GMM with a stochastic splitting and merging mechanism to obtain the prototypes and leverage these evolving prototypes for representation learning by prototypical contrastive learning. We demonstrated that class number estimation and representation learning can facilitate each other for more robust category discovery. Our framework obtains state-of-the-art performance on multiple public benchmarks. + +Acknowledgements This work is supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research. + +# References + +[1] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin Raffel. 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In ICCV, 2021. 2 \ No newline at end of file diff --git a/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/images.zip b/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..4e84f1d8c9c869671a0c312a9fa27d5640f6c694 --- /dev/null +++ b/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:be404d4114aee075530648b23abc137bae97f66d9794d5af9c9b34a14b799cae +size 494843 diff --git a/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/layout.json b/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..3c6fee2746fb834ebfc6bcda391da4465b234517 --- /dev/null +++ b/2023/Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery/layout.json @@ -0,0 +1,9798 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 134, + 103, + 460, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 103, + 460, + 140 + ], + "spans": [ + { + "bbox": [ + 134, + 103, + 460, + 140 + ], + "type": "text", + "content": "Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 138, + 160, + 455, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 160, + 455, + 203 + ], + "spans": [ + { + "bbox": [ + 138, + 160, + 455, + 203 + ], + "type": "text", + "content": "Bingchen Zhao† Xin Wen‡ Kai Han‡* \n†University of Edinburgh ‡The University of Hong Kong \nbingchen.zhao@ed.ac.uk wenxin@eee.hku.hk kaihanx@hku.hk" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 256, + 290, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 602 + ], + "type": "text", + "content": "In this paper, we address the problem of generalized category discovery (GCD), i.e., given a set of images where part of them are labelled and the rest are not, the task is to automatically cluster the images in the unlabelled data, leveraging the information from the labelled data, while the unlabelled data contain images from the labelled classes and also new ones. GCD is similar to semi-supervised learning (SSL) but is more realistic and challenging, as SSL assumes all the unlabelled images are from the same classes as the labelled ones. We also do not assume the class number in the unlabelled data is known a-priori, making the GCD problem even harder. To tackle the problem of GCD without knowing the class number, we propose an EM-like framework that alternates between representation learning and class number estimation. We propose a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to dynamically determine the prototypes by examining the cluster compactness and separability. With these prototypes, we leverage prototypical contrastive learning for representation learning on the partially labelled data subject to the constraints imposed by the labelled data. Our framework alternates between these two steps until convergence. The cluster assignment for an unlabelled instance can then be retrieved by identifying its nearest prototype. We comprehensively evaluate our framework on both generic image classification datasets and challenging fine-grained object recognition datasets, achieving state-of-the-art performance. Our code is available at https://github.com/DTennant/GPC." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 128, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 288, + 696 + ], + "type": "text", + "content": "The success of deep learning is driven by the availability of large-scale data with human annotations. Given enough annotated data, deep learning models are able to surpass human-level performance on many important computer vi" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 229, + 545, + 342 + ], + "blocks": [ + { + "bbox": [ + 308, + 229, + 545, + 342 + ], + "lines": [ + { + "bbox": [ + 308, + 229, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 308, + 229, + 545, + 342 + ], + "type": "image", + "image_path": "3c0ec6fee07670b105b3a428fed05ac6b313a1c5582eb17621b957579712d86f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 351, + 548, + 483 + ], + "lines": [ + { + "bbox": [ + 304, + 351, + 548, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 548, + 483 + ], + "type": "text", + "content": "Figure 1: Overview of our proposed EM-like framework. The input images are fed into a ViT-B model to obtain a 768-dimensional feature vector, then the feature vector will be projected to a lower dimensional space using the projection calculated from PCA. We perform class number estimation and representation learning in this projected space. In the E-step, we use a semi-supervised GMM that can split separable clusters and merge cluttered clusters to estimate the class number and prototypes, which will be used in the M-step of representation learning with prototypical contrastive learning." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 510, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 548, + 713 + ], + "type": "text", + "content": "sion tasks such as image classification [21]. But the cost of collecting a large annotated dataset is not always affordable, and it is also not possible to annotate all new classes emerging from the real world. Thus, designing models that can learn to deal with large-scale unlabelled data in the open world is of great value and importance. Semi-supervised learning (SSL) [38] is proposed as a solution to learn a model on both labelled data and unlabelled data, with many works achieving promising performance [1, 46, 44]. However, SSL assumes that labelled instances are provided for all object classes in the unlabelled data. The novel category discovery (NCD) task is introduced [17, 16] to automatically discover novel classes by transferring the knowledge learned from the labelled instances of known classes, assuming the unlabelled data only contain instances from new classes. Generalized category discovery (GCD) [48] further relaxes the assumption in NCD, and tackles a more" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16623" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "generalized setting where the unlabelled data contains instances from both known and novel categories. Existing methods for NCD [17, 16, 58, 60, 61, 12, 26] and GCD [48, 11, 51, 45, 56, 59, 34] learn the representation and cluster assignment assuming the class number is known a priori [58, 26, 60, 12, 61] or precomputed [17, 48]. In practice, the number of categories in the unlabelled data is often unknown, while precomputing the class number without taking the representation learning into consideration is likely to lead to a sub-optimal solution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 616 + ], + "type": "text", + "content": "In this paper, we argue that representation learning and the estimation of class numbers should be considered together and could reinforce each other, i.e., a strong representation could help a more accurate estimation of the class numbers, and an accurate class number could help learn a better feature representation. To this end, we propose a unified EM-like framework that alternates between feature representation learning and class number estimation where the E-step is aimed at automatically estimating a proper class number and a set of class prototypes in the unlabelled data and the M-step is aimed at learning better representation with the class number and class prototypes estimated. In particular, we propose using a prototype contrastive representation learning [33] method for GCD, which requires a set of prototypes to serve as anchors for representation learning. Prototypical contrastive learning [33] is developed for unsupervised representation learning to generalize to different tasks, where the prototypes are obtained by over-clustering the dataset with one or multiple given prototype numbers, using non-parametric clustering algorithms like " + }, + { + "bbox": [ + 46, + 194, + 289, + 616 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 194, + 289, + 616 + ], + "type": "text", + "content": "-means. Instead, to handle the problem of GCD, we propose to estimate the prototype number and prototypes automatically and simultaneously. To do so, we introduce a semi-supervised variant of the Gaussian Mixture Model (GMM) with a stochastic splitting and merging mechanism to determine the most suitable clusters based on current representation. These clusters can then be used to form prototypes to facilitate contrastive representation learning. Our framework alternates between the E- and M-step until converging to achieve robust representation and reliable category estimation. After learning, the cluster assignment for an unlabelled instance, either from known or novel classes, can be retrieved by finding the nearest prototypes. Thus we name our framework as GPC: Gaussian mixture model for generalized category discovery with Protypical Contrastive learning." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "Our contributions in this paper are as follows: (1) We demonstrate that in generalized category discovery, the class number estimation and representation learning can reinforce each other in the learning process. Strong representations can give a better estimation of the class number, and vice versa. (2) We propose an EM-like framework that alternates between prototype estimation with a variant of GMM (E-step) and representation learning based on prototypical" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 548, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 548, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 548, + 204 + ], + "type": "text", + "content": "contrastive learning (M-step). (3) We introduce a semi-supervised variant of GMM with a stochastic splitting and merging mechanism to allow dynamic change of the prototypes by examining the cluster compactness and separability based on the Metropolis-Hastings ratio [19]. (4) We comprehensively evaluated our framework on both the generic image classification benchmark, including CIFAR10, CIFAR100, ImageNet-100, and the challenging fine-grained Semantic Shifts Benchmark suite, which includes CUB-200, Stanford-Cars, and FGVC-aircrafts, achieving the state-of-the-art results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 215, + 391, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 215, + 391, + 227 + ], + "spans": [ + { + "bbox": [ + 305, + 215, + 391, + 227 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 235, + 548, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 548, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 548, + 665 + ], + "type": "text", + "content": "Novel category discovery (NCD) is first formalized in DTC [17], where the task is to discover new categories leveraging the knowledge of a set of labelled categories. Many methods have been proposed to tackle this challenge. To name a few, RankStat [15, 16] and DualRank [58] transfer knowledge from labelled to unlabelled classes using feature ranking statistics. OpenMix [61] shows that mixing labelled and unlabelled data can prevent overfitting. NCL [60] and WTA [26] use contrastive learning for NCD. UNO [12] introduces a unified cross-entropy loss for joint training on labelled and unlabelled data. [29] introduces a spacing loss for representation learning in NCD. NCDwF [28] studies the NCD problem under an incremental learning setting. Earlier methods like [22, 23] for generalized transfer learning can also be applied to NCD. Generalized category discovery (GCD) [48] extends NCD to a more open-world setting where unlabelled instances can come from both labelled and unlabelled categories. ORCA [2] also tackles GCD from a semi-supervised learning perspective. Several improved methods have been proposed for generalized category discovery (GCD), such as [11, 51, 39, 56, 45], which have shown promising results. Incremental GCD is considered in [57, 59]. Concurrently, CiPR [18] presents a hierarchical GCD approach employing selective neighbor clustering, leading to improved efficiency and performance without necessitating knowledge of the class number. [14] studies semantic category discovery by leveraging vision-language representations, thereby enabling GCD with class name prediction. However, most existing GCD methods assume that the novel class number is known a priori, which is often not the case in the real world. To address this limitation, [17, 48] precompute the number of novel classes with a semi-supervised " + }, + { + "bbox": [ + 304, + 235, + 548, + 665 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 235, + 548, + 665 + ], + "type": "text", + "content": "-means algorithm from pretrained representations. In this paper, we demonstrate that class number estimation and representation learning can be jointly considered to mutually benefit each other." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": "Contrastive learning [4, 5, 20, 7, 62] (CL) has been shown very effective for representation learning in a self-supervised manner, using the instance discrimination pretext [52] as the learning objective. The instance discrimination task learns" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "16624" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "a representation by pulling positive samples from the augmentations of the same images closer and pushing negative samples from different images apart in the embedding space. Instead of contrasting over all instances in a mini-bath, prototypical contrastive learning (PCL) [33] proposes to contrast the features with a set of prototypes which can provide a higher level abstraction of dataset than instances and has been shown to be more data efficient without the need of large batch size. Though PCL is developed for unsupervised representation learning, if the prototypes are viewed as cluster centers, it can be leveraged in the partially supervised setting of GCD for representation learning to better fit the GCD task of partitioning data into different clusters. Thus, in this paper, we adopt PCL to fit the GCD setting for representation learning in which the downstream clustering task is directly considered." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 263, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 289, + 443 + ], + "type": "text", + "content": "Semi-supervised learning (SSL) has been a long standing research topic which many effective method proposed [40, 44, 1, 32, 46]. In SSL, the labelled and the unlabelled data are assumed to come from the same set of classes, and the task is to learn a classification model that can take advantage of both labelled and unlabelled data. Consistency-based methods are among the most effective methods for SSL, such as Mean-teacher [46], MixMatch [1], and FixMatch [44]. Self-supervised representation learning also shows to be helpful for SSL because it can provide a strong representation [55, 40]. Recent works extend semi-supervised learning by relaxing the assumption of exactly the same classes in the labeled and unlabelled data [43, 25, 54], but their focus is improving the performance of the labeled categories without discovering novel categories in the unlabeled set." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 444, + 289, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 289, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 289, + 612 + ], + "type": "text", + "content": "Unsupervised clustering has been studied for decades, and there are many existing classical approaches [35, 10, 6] as well as deep learning based approaches [53, 41, 13]. Recently, DeepDPM [42] is proposed to automatically determine the number of clusters for a given dataset by adopting a similar split/merge framework that changes the inferred number of clusters. However, due to the unsupervised nature of these methods, there is no prior or supervision over how a cluster should be formed, thus multiple equally valid clustering results following different clustering criteria can be produced. Thus, directly applying unsupervised clustering methods to the task of generalized category discovery is not feasible, as we would want the model to use one unique clustering criteria implicitly given by the labelled data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 621, + 104, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 104, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 104, + 634 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": "Given a collection of partially labelled data, " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\mathcal{D}^l\\cup \\mathcal{D}^u" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^l = \\{(x_i,y_i^l)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_l" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " is labelled, " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u = \\{x_i,y_i^u\\} \\in \\mathcal{X}\\times \\mathcal{Y}_u" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " is unlabelled, and " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_l\\subset \\mathcal{V}_u" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " Generalized category discovery (GCD) aims at automatically assign labels for the unlabelled instances in " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " , by transferring knowledge acquired from " + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^l" + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": " . Let the category number in" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^l" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": " be " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "K^l = |\\mathcal{Y}_l|" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": " and that in " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": " be " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "K^u = |\\mathcal{Y}_u|" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": ". The number of new categories " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": " is then " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "K^n = |\\mathcal{Y}_u \\setminus \\mathcal{Y}_l| = K^u - K^l" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": ". Though " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "K^l" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": " can be accessed from the labelled data, we do not assume " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "K^n" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "inline_equation", + "content": "K^u" + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": " to be known. This is a realistic setting to reflect the real open world, where we often have access to some labelled data, but in the unlabelled data, we also have instances from unseen new categories." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 156, + 547, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 547, + 275 + ], + "type": "text", + "content": "The key challenges for GCD are representation learning, category number estimation, and label assignment. Existing methods for NCD and GCD [17, 48] deal with these three challenges independently. However, we believe they are inherently linked with each other. Label assignment depends on representation and category number estimation. A good class number estimation can facilitate representation learning, thus better label assignment, and vice versa. Thus, in this paper, we aim to jointly handle these challenges in the learning process for a more reliable GCD." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 275, + 548, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 548, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 548, + 456 + ], + "type": "text", + "content": "To this end, we propose a unified EM-like framework that alternates between representation learning and class number estimation, while the label assignment turns out to be a by-product during class number estimation. In the E-step, we introduce a semi-supervised variant of the Gaussian Mixture Model (GMM) to estimate the class numbers by dynamically splitting separable clusters and merging cluttered clusters based on current representation, forming a set of class prototypes for both seen and unseen classes, and in the M-step, we train the model to produce discriminative representation by prototypical contrastive learning using the cluster centers from the GMM prototypes derived from the E-step during class number estimation. After training, the class assignment for each instance can be retrieved by simply identifying the nearest prototype." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 462, + 443, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 462, + 443, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 462, + 443, + 475 + ], + "type": "text", + "content": "3.1. Representation learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 480, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 547, + 553 + ], + "type": "text", + "content": "The goal of representation learning is to learn a discriminative representation that can well separate different categories, not only the old ones, but also the new ones. Contrastive learning (CL) has been shown to be an effective choice for NCD [26] and GCD [48]. Self-supervised contrastive learning is defined as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 352, + 559, + 547, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 559, + 547, + 587 + ], + "spans": [ + { + "bbox": [ + 352, + 559, + 547, + 587 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C L} = - \\log \\frac {\\exp \\left(z _ {i} \\cdot z _ {i} ^ {\\prime} / \\tau\\right)}{\\sum_ {j = 1} ^ {n} \\exp \\left(z _ {i} \\cdot z _ {j} ^ {\\prime} / \\tau\\right)} \\tag {1}", + "image_path": "6bfb88d1e02a9e434394733513c1ca8d966835864f6fb89f46483888dcbef0de.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "inline_equation", + "content": "z_{i}^{\\prime}" + }, + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "text", + "content": " are the representations of two views obtained from the same image using random augmentations and " + }, + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "text", + "content": " is the temperature. Two views of the same instance are pulled closer, and different instances are pushed away during training. Self-supervised contrastive learning and its supervised variant, in which different instances from the same category are also pulled closer, are used in [48] for representation learning. However, as a stronger training signal is used for the labelled data, the representation is likely biased to the labelled data to some extent. Moreover, such a method does" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16625" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 108 + ], + "type": "text", + "content": "not take the downstream clustering task into account during learning, thus a clustering algorithm is required to run independently after the representation learning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "type": "text", + "content": "In this paper, we adopt prototypical contrastive learning (PCL) [33] to the GCD setting to learn the representation " + }, + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "type": "inline_equation", + "content": "z_{i} = f(x_{i}) \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "type": "text", + "content": ". PCL uses a set of prototypes " + }, + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = \\{\\mu_1, \\dots, \\mu_K\\}" + }, + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "type": "text", + "content": " to represent the dataset for contrastive learning instead of the random augmentation generated views " + }, + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "type": "inline_equation", + "content": "z_{i}'" + }, + { + "bbox": [ + 46, + 108, + 288, + 181 + ], + "type": "text", + "content": ". PCL loss can be written as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 89, + 189, + 288, + 219 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 189, + 288, + 219 + ], + "spans": [ + { + "bbox": [ + 89, + 189, + 288, + 219 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {P C L} = - \\log \\frac {\\exp \\left(z _ {i} \\cdot \\mu_ {s} / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(z _ {i} \\cdot \\mu_ {j} / \\tau\\right)} \\tag {2}", + "image_path": "04b04d9a76b38fea766b952a88b2649840fc2c4bf6f2ebcc0704a55bf2b53f25.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 227, + 289, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 227, + 289, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 289, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 227, + 289, + 407 + ], + "type": "inline_equation", + "content": "\\mu_{s}" + }, + { + "bbox": [ + 46, + 227, + 289, + 407 + ], + "type": "text", + "content": " is the corresponding prototype for " + }, + { + "bbox": [ + 46, + 227, + 289, + 407 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 227, + 289, + 407 + ], + "type": "text", + "content": ". It was originally designed as an alternative for self-supervised contrastive learning by over-clustering the training data to obtain the prototypes during training. We employ PCL here to learn reliable representation while taking the downstream clustering into account for GCD, where we have a set of partially labelled data. In our case, the prototypes can be interpreted as the class centers for each of the categories. To obtain the prototypes for the seen categories, we directly calculate the class mean by averaging all the feature vectors of the labelled instances. For the unseen categories, we obtain the prototypes with a semi-supervised variant of the Gaussian Mixture Model (GMM), as will be introduced in Sec. 3.2. This way, the cluster assignment for an unlabelled image can be readily achieved by finding the nearest prototype." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": "Additionally, we observe that only a few principal dimensions can already recover most of the variances in the representation space of " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ", which is known as dimensional collapse (DC) in [27, 24], and it is shown that DC can be caused by strong augmentations or implicit regularizations in the model, and preventing DC during training can lead to a better feature representation. To alleviate DC for representation learning in our case, we propose to first project the feature to a subspace obtained by principal component analysis (PCA) before the contrastive learning. Specifically, we apply PCA on a matrix " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": " formed by a mini-batch of features " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ", with a batch size of " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ", the feature dimension " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ", and the number of effective principal directions " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ". We have " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "Z \\approx U\\mathrm{diag}(S)V^{\\top}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "U \\in \\mathbb{R}^{n \\times q}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^q" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{d \\times q}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ". We can then project features " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": " to principal directions to obtain a more compact feature " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "v_{i} = V \\cdot z_{i}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": ", and replace feature " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 46, + 406, + 288, + 622 + ], + "type": "text", + "content": " in Eq. (2) for PCL. The prototypes are also computed in the projected space." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 621, + 288, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 621, + 288, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 621, + 288, + 657 + ], + "type": "text", + "content": "We jointly use self-supervised contrastive learning and PCL to train our model. The overall learning objective can be written as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 118, + 667, + 288, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 667, + 288, + 681 + ], + "spans": [ + { + "bbox": [ + 118, + 667, + 288, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {C L} + \\lambda (t) \\mathcal {L} _ {P C L} \\tag {3}", + "image_path": "f03d08373aa925a41e2ef723256d1b228ac14fc041a056e2da892a97c3eb7a4c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\lambda(t)" + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": " is a linear warmup function defined as " + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\lambda(t) = \\min(1, \\frac{t}{T})" + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": " is the current epoch and " + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": " warmup length" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 541, + 117 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 541, + 117 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 541, + 117 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 541, + 117 + ], + "type": "image", + "image_path": "451c293d30123ad4dcd7869fbe76c22e28e585d84e9b7b0f951b2601d5c728bc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 122, + 547, + 183 + ], + "lines": [ + { + "bbox": [ + 305, + 122, + 547, + 183 + ], + "spans": [ + { + "bbox": [ + 305, + 122, + 547, + 183 + ], + "type": "text", + "content": "Figure 2: Examples for splitting a separable cluster and merging two cluttered clusters. Left: the cluster is split because the two sub-component in this cluster are easily separable. Right: two clusters are merged as they are cluttered and likely from the same class." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 204, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 204, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 204, + 547, + 277 + ], + "type": "inline_equation", + "content": "(T = 20" + }, + { + "bbox": [ + 305, + 204, + 547, + 277 + ], + "type": "text", + "content": " in our experiments). The reason we use both CL and PCL is that, in the beginning, the representation is not well suited for clustering, and thus the obtained prototypes are not informative to facilitate the representation learning. Hence, we gradually increase the weight of PCL during training from 0 to 1 in the first " + }, + { + "bbox": [ + 305, + 204, + 547, + 277 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 204, + 547, + 277 + ], + "type": "text", + "content": " epochs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 285, + 545, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 545, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 545, + 309 + ], + "type": "text", + "content": "3.2. Class number and prototypes estimation with semi-supervised Gaussian mixture model" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 316, + 546, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 546, + 422 + ], + "type": "text", + "content": "In this section, we present a semi-supervised variant of the Gaussian mixture model (GMM) with each Gaussian component consisting of two sub-components to estimate the prototypes for representation learning in Sec. 3.1 and the unknown class number. GMM estimates the prototypes and assigns a label for each data point by finding its nearest prototype. The cluster label assignment and the prototypes are then used for prototypical contrastive learning. The GMM is defined as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 369, + 430, + 546, + 462 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 430, + 546, + 462 + ], + "spans": [ + { + "bbox": [ + 369, + 430, + 546, + 462 + ], + "type": "interline_equation", + "content": "p (z) = \\sum_ {i = 1} ^ {K} \\pi_ {i} \\mathcal {N} \\left(z \\mid \\mu_ {i}, \\Sigma_ {i}\\right), \\tag {4}", + "image_path": "9c6ed6e4717e9b39832ff54fb87fdf6f72ef2b97c38a4deade9bdd65dcb65995.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(z|\\mu_i,\\Sigma_i)" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " is the Gaussian probability density function with mean " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mu_{i}\\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " and covariance " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\Sigma_{i}\\in \\mathbb{R}^{d\\times d}" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\pi_{i}" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " is the weight for " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": "-th Gaussian component and we have " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sum_{i = 1}^{N}\\pi_{i} = 1" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": ". Ideally, we would expect the component number " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " in the GMM to be equal to the class number " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K^u" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": ". To estimate the unknown class number " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K^u" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": ", we leverage an automatic splitting-and-merging strategy into the modeling process to obtain an optimal " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": ", which is expected to be as close to " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K^u" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " as possible. We alternate between representation learning and " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K^u" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " estimation until convergence to get discriminative representation learning and a reliable class number estimation. For initialization, " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " can be set to any number greater than " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K^l" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": ". In our experiments, we simply set the initial number of components to a default " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "K_{init} = K^l +\\frac{K^l}{2}" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": ". We run a semi-supervised " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": "-means algorithm [48] with " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "k = K" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " to obtain the " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": " for each component in the mixture model. Note that the semi-supervised " + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 472, + 547, + 713 + ], + "type": "text", + "content": "-means algorithm is constrained to the labelled data in a way that labelled instances from the same class are assigned to the same cluster, and labelled instances from different classes will not be" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16626" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 48, + 88, + 289, + 424 + ], + "blocks": [ + { + "bbox": [ + 53, + 75, + 261, + 87 + ], + "lines": [ + { + "bbox": [ + 53, + 75, + 261, + 87 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 261, + 87 + ], + "type": "text", + "content": "Algorithm 1: The overall algorithm of our method." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "lines": [ + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "spans": [ + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": "Input: " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{D},\\mathcal{D}^l" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " The datasets. " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "K_{init}" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " Initial guess of " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " \n1 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "K\\gets K_{init}" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " \n2 for " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "e = 1" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " do \n3 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "z\\gets f(x),x\\in \\mathcal{D}\\quad /" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " extract features \n4 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "\\mu ,\\Sigma \\gets \\arg \\max \\sum_{i = 1}^{K}\\pi_{i}\\mathcal{N}(z|\\mu_{i},\\Sigma_{i})" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " // estimate prototypes using GMM \n5 for " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " to len(D) do \n6 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^l\\gets \\{x_i^l\\sim \\mathcal{D}^l\\}_{i = 1}^{N^l}\\quad /" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " sample a batch of " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "N^l" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " labelled images \n7 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^u\\gets \\{x_i^u\\sim \\mathcal{D}^u\\}_{i = 1}^{N^u}\\quad /" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " sample a batch of " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "N^u" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " unlabelled images \n8 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "f\\gets \\arg \\min \\mathcal{L}(f,\\mu ,\\mathcal{B}^l,\\mathcal{B}^u)" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " // prototypical contrastive learning \n9 end \n10 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "H_{s},H_{m}\\gets \\mathrm{calc\\_prob}(\\mu ,\\Sigma)" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " // probability for split and merge \n11 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "\\mu ,\\Sigma \\gets \\mathrm{perform\\_op}(H_s,H_m)\\quad /" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " perform operations \n12 " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "K\\gets \\mathrm{len}(\\mu)" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " // update " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " \n13 end Output: feature extractor " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "text", + "content": " , cluster centers " + }, + { + "bbox": [ + 48, + 88, + 289, + 424 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": "assigned to the same cluster. To facilitate the splitting and merging process, for each Gaussian component defined by " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\Sigma_{i}" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": ", we further depict it with a GMM with two subcomponents " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mu_{i,1},\\mu_{i,2}" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\Sigma_{i,1},\\Sigma_{i,2}" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\pi_{i,1} + \\pi_{i,2} = 1" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": ". We run a " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": "-means with " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "k = 2" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": " on the " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": "-th component to obtain " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mu_{i,1},\\mu_{i,2}" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\Sigma_{i,1},\\Sigma_{i,2}" + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 521, + 288, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 675 + ], + "type": "text", + "content": "For a cluster whose two sub-components are roughly independent and equally sized (e.g., left part of Fig. 2), i.e., they are easily separable, we would like the model to split it into two such that the model can better fit the data distribution and the class assignment will be more accurate because it is less likely that such distinct clusters will belong to the same class. For two clusters that are cluttered with each other (e.g., right part of Fig. 2), i.e., difficult to distinguish, we would like to merge them into one, so that they will be considered as from the same class. Following this intuition, we use the Metropolis-Hastings framework [19] to compute a probability " + }, + { + "bbox": [ + 46, + 521, + 288, + 675 + ], + "type": "inline_equation", + "content": "p_{s} = \\min(1, H_{s})" + }, + { + "bbox": [ + 46, + 521, + 288, + 675 + ], + "type": "text", + "content": " to stochastically split a cluster into two. The Hastings ratio is defined as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 78, + 685, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 685, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 78, + 685, + 287, + 711 + ], + "type": "interline_equation", + "content": "H _ {s} = \\frac {\\Gamma \\left(N _ {i , 1}\\right) h \\left(\\mathcal {Z} _ {i , 1} ; \\theta\\right) \\Gamma \\left(N _ {i , 2}\\right) h \\left(\\mathcal {Z} _ {i , 2} ; \\theta\\right)}{\\Gamma \\left(N _ {i}\\right) h \\left(\\mathcal {Z} _ {i} ; \\theta\\right)}, \\tag {5}", + "image_path": "f56c15c579a4be0ef0f9fa0d96ce4149ca1bad1a3d58918306a16a07e253b1bd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " is the factorial function, i.e., " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\Gamma (n) = n! = n\\times (n - 1)\\times \\dots \\times 1" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " is the set of data points in cluster " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_{i,j}" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " is the set of data points in the " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": "-th sub-cluster of cluster " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "N_{i} = |\\mathcal{Z}_{i}|, N_{i,j} = |\\mathcal{Z}_{i,j}|" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "h(Z;\\theta)" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " is the marginal likelihood of the observed data " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " by integrating out the " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " parameters in the Gaussian, and " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " is the prior distribution of " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": ". More details can be found in the supplementary. The intuition behind this " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "H_{s}" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " is that, if the number of data points in two sub-components is roughly balanced, which is measured by the " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\Gamma (\\cdot)" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " terms, and the data points in the two sub-components are independent of each other, which is measure by the " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "h(\\cdot ;\\theta)" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " terms, there should be a greater chance of splitting the cluster. After performing a split operation, the " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\Sigma_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " of previous components " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " will be replaced with " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\mu_{i,1},\\mu_{i,2}" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "\\Sigma_{i,1},\\Sigma_{i,2}" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " of two sub-components. We will then run two " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": "-means within the two newly formed components to obtain their corresponding sub-components. On the contrary, if two clusters are cluttered with each other, they should be merged. Similar to splitting, we determine the merging probability by " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "p_m = \\min (1,H_m)" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "H_{m}" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " is calculated similarly for two clusters " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 72, + 547, + 324 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 347, + 333, + 545, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 333, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 347, + 333, + 545, + 361 + ], + "type": "interline_equation", + "content": "H _ {m} = \\frac {\\Gamma \\left(N _ {i} + N _ {j}\\right) h \\left(\\mathcal {Z} _ {i} \\cup \\mathcal {Z} _ {j} ; \\theta\\right)}{\\Gamma \\left(N _ {i}\\right) h \\left(\\mathcal {Z} _ {i} ; \\theta\\right) \\Gamma \\left(N _ {j}\\right) h \\left(\\mathcal {Z} _ {j} ; \\theta\\right)}. \\tag {6}", + "image_path": "d1c1350030ebbd4ed7e2d97549b531ec6153fd8aa511b810c77d4ed85c118cc4.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "text", + "content": "Note that both " + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "inline_equation", + "content": "H_{s}" + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "inline_equation", + "content": "H_{m}" + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "text", + "content": " are within the range of " + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "inline_equation", + "content": "(0, +\\infty)" + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "text", + "content": ", so we use " + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "inline_equation", + "content": "p_{s} = \\min(1, H_{s})" + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "inline_equation", + "content": "p_{m} = \\min(1, H_{m})" + }, + { + "bbox": [ + 304, + 370, + 547, + 407 + ], + "type": "text", + "content": " to convert it into a valid probability." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 407, + 547, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 547, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 547, + 467 + ], + "type": "text", + "content": "To take the labelled instances into consideration during the splitting-and-merging process, if a cluster consists of labelled instances, we set its " + }, + { + "bbox": [ + 304, + 407, + 547, + 467 + ], + "type": "inline_equation", + "content": "p_s = 0" + }, + { + "bbox": [ + 304, + 407, + 547, + 467 + ], + "type": "text", + "content": "; if for any two clusters containing instances from two labelled classes, we set their " + }, + { + "bbox": [ + 304, + 407, + 547, + 467 + ], + "type": "inline_equation", + "content": "p_m = 0" + }, + { + "bbox": [ + 304, + 407, + 547, + 467 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "text", + "content": "During the splitting-and-merging process, we first apply splitting according to the " + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "inline_equation", + "content": "p_s" + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "text", + "content": " and then apply merging according to " + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "inline_equation", + "content": "p_m" + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "text", + "content": ". The newly formed clusters by splitting will not be reused during the merging step. After finishing the splitting and merging, we can obtain the prototypes, and thus can estimate " + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "text", + "content": ", for our PCL-based representation learning. We alternate between representation learning and class number estimation for each training epoch until converge. The final " + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "text", + "content": " will be considered the estimated class number in " + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 468, + 547, + 634 + ], + "type": "text", + "content": ". The cluster assignment for each unlabelled instance can be easily retrieved by identifying its nearest prototype, without the need of running a non-parametric clustering algorithm as [48]. The overall training process is summarized in Algorithm 1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 649, + 387, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 649, + 387, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 649, + 387, + 662 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 670, + 421, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 421, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 421, + 683 + ], + "type": "text", + "content": "4.1. Experimental setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "Benchmark and evaluation metric. We validate the effectiveness of our method on the generic image classification" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16627" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 87, + 544, + 281 + ], + "blocks": [ + { + "bbox": [ + 176, + 70, + 416, + 83 + ], + "lines": [ + { + "bbox": [ + 176, + 70, + 416, + 83 + ], + "spans": [ + { + "bbox": [ + 176, + 70, + 416, + 83 + ], + "type": "text", + "content": "Table 1: Results on generic image classification datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 87, + 544, + 281 + ], + "lines": [ + { + "bbox": [ + 49, + 87, + 544, + 281 + ], + "spans": [ + { + "bbox": [ + 49, + 87, + 544, + 281 + ], + "type": "table", + "html": "
No.MethodsKnown KPCACIFAR10CIFAR100ImageNet-100
AllOldNewAllOldNewAllOldNew
(1)k-means [35]✓X83.685.782.552.052.250.872.775.571.3
(2)RankStats+ [16]✓X46.819.260.558.277.619.337.161.624.8
(3)UNO+ [12]✓X68.698.353.869.580.647.270.395.057.9
(4)ORCA [2]✓X81.886.279.669.077.452.073.592.663.9
(5)Vaze et al. [48]✓X91.597.988.273.076.266.574.189.866.3
(6)Ours (GPC)✓X92.098.388.777.484.862.476.594.068.5
(7)Ours (GPC)✓✓92.298.289.177.985.063.076.994.371.0
(8)Vaze et al. [48]XX88.696.284.973.283.557.972.791.863.8
(9)Vaze et al. [48]X✓89.797.386.374.883.858.773.892.164.6
(10)Ours (GPC)XX88.297.085.874.984.359.674.792.965.1
(11)Ours (GPC)X✓90.697.687.075.484.660.175.393.466.7
", + "image_path": "ee77cfa270a6dcb011cb7d5cc7f0ba61184dc67e6b13db29a5d6b03208ee651f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": "benchmark (including CIFAR-10/100 [31] and ImageNet-100 [47]) and also the recently proposed Semantic Shift Benchmark [49] (SSB) (including CUB-200 [50], Stanford Cars [30], and FGVC-Aircraft [36]). For each of the datasets, we follow [48] and sample a subset of all classes for which we have annotated labels during training. For experiments on SSB datasets, we directly use the class split from [49]. " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": " of the images from these labelled classes will be used as the labelled instances in " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^l" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": ", and the remaining images are regarded as the unlabelled data " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": " containing instances from labelled and unlabelled classes. See Tab. 2 for statistics of the datasets we evaluated. We evaluate model performance with clustering accuracy (ACC) following standard practice in the literature. At test-time, given ground truth labels " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "y^{*}" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": " and model predicted cluster assignments " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": ", the ACC is calculated as " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "ACC = \\frac{1}{M}\\sum_{i = 1}^{M}\\mathbb{1}(y_i^* = g(\\hat{y}_i))" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": " is the optimal permutation for matching predicted cluster assignment " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": " to actual class label " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "y_i^*" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "inline_equation", + "content": "M = |\\mathcal{D}^u|" + }, + { + "bbox": [ + 46, + 300, + 290, + 517 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 82, + 542, + 251, + 644 + ], + "blocks": [ + { + "bbox": [ + 83, + 525, + 251, + 537 + ], + "lines": [ + { + "bbox": [ + 83, + 525, + 251, + 537 + ], + "spans": [ + { + "bbox": [ + 83, + 525, + 251, + 537 + ], + "type": "text", + "content": "Table 2: Data splits in the experiments." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 82, + 542, + 251, + 644 + ], + "lines": [ + { + "bbox": [ + 82, + 542, + 251, + 644 + ], + "spans": [ + { + "bbox": [ + 82, + 542, + 251, + 644 + ], + "type": "table", + "html": "
labelledunlabelled
CIFAR-1055
CIFAR-1008020
ImageNet-1005050
CUB-200100100
Stanford-Cars9898
FGVC-aircraft5050
", + "image_path": "8035b72f8ad2d021a0a217e5cf9b16eb5e90578731003cb20d91d7746f968595.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Implementation details. We train and test all the methods with a ViT-B/16 backbone [9] with pretrained weights from DINO [3]. We use the output of [CLS] token with a dimension of 768 as the feature representation for an input image. We only finetune the last block of the ViT-B backbone to" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 300, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 547, + 433 + ], + "type": "text", + "content": "prevent the model from overfitting to the labelled classes during training. We set the batch size for training the model to 128 with 64 labelled images and 64 unlabelled images and use a cosine annealing schedule for the learning rate starting from 0.1. The number of principal directions in the PCA is set to 128, which we found performs the best across all the datasets evaluated. We train all the methods for 200 epochs on each dataset for a fair comparison with previous works, and the best-performing model is selected using the accuracy on the validation set of the labelled classes. All experiments are done with an NVIDIA V100 GPU with 32GB memory." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 443, + 501, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 443, + 501, + 455 + ], + "spans": [ + { + "bbox": [ + 305, + 443, + 501, + 455 + ], + "type": "text", + "content": "4.2. Comparison with the state-of-the-art" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "In Tab. 1, we report the comparison with the state-of-the-art method of [48], strong baselines derived from NCD methods, and the " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "-means on the generic classification datasets. Notably, our method consistently achieves the best overall performance on all datasets, under the challenging setting where the class number is unknown. When the class number is known, our method also achieves the best performance on all datasets, except ImageNet-100, on which the best performance is achieved by ORCA [2]. In rows 1-7, we compare with other methods with the known class number in the unlabelled data, while in rows 8-11 we compare with [48] for the case of the unknown class number. We can see that our proposed framework outperforms other methods in most cases and especially when the number of classes is unknown. Comparing rows 10 and 11 to row 5, we can see that our proposed method without knowing the number of classes can even match the performance of previous strong baseline with the number of classes known to the model. Furthermore, from row 6 vs row 7 and row 10 vs row 11, we can see that the additional PCA layer can effectively improve the performance, also the performance" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16628" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 87, + 544, + 281 + ], + "blocks": [ + { + "bbox": [ + 177, + 71, + 416, + 82 + ], + "lines": [ + { + "bbox": [ + 177, + 71, + 416, + 82 + ], + "spans": [ + { + "bbox": [ + 177, + 71, + 416, + 82 + ], + "type": "text", + "content": "Table 3: Results on Semantic Shift Benchmark datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 87, + 544, + 281 + ], + "lines": [ + { + "bbox": [ + 49, + 87, + 544, + 281 + ], + "spans": [ + { + "bbox": [ + 49, + 87, + 544, + 281 + ], + "type": "table", + "html": "
No.MethodsKnown KPCACUBStanford CarsFGVC-aircraft
AllOldNewAllOldNewAllOldNew
(1)k-means [35]✓X34.338.932.112.810.613.816.014.416.8
(2)RankStats+ [16]✓X33.351.624.228.361.812.126.936.422.2
(3)UNO+ [12]✓X35.149.028.135.570.518.640.356.432.2
(4)ORCA [2]✓X35.345.630.223.550.110.722.031.817.1
(5)Vaze et al. [48]✓X51.356.648.739.057.629.945.041.146.9
(6)Ours (GPC)✓X54.254.950.341.258.831.646.142.447.2
(7)Ours (GPC)✓✓55.458.253.142.859.232.846.342.547.9
(8)Vaze et al. [48]XX47.155.144.835.056.024.840.140.842.8
(9)Vaze et al. [48]X✓49.256.246.336.356.625.943.240.944.6
(10)Ours (GPC)XX50.252.845.636.756.326.339.739.642.7
(11)Ours (GPC)X✓52.055.547.538.258.927.443.340.744.8
", + "image_path": "3111102f653d8bbdd1b9ce8d51ef90d025f7bc20e9fa5ff5a899a733d7e2ad82.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 290, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 290, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 290, + 540 + ], + "type": "text", + "content": "improvement from PCA is larger on the 'New' classes than on the 'Old' classes, which validates that the PCA can keep the representation space from collapsing and improve the performance on classes without using any labels. Due to the fact that labelled instances provide a stronger training signal, we can see from rows 6 - 11 that performance on 'Old' classes is generally steady. Comparing row 7 to row 5 and row 11 to row 8, we can see our full method outperforms the previous state-of-the-art method Vaze et al. [48] by large margins on both known and unknown class number cases. Tab. 3 shows performance comparison on the more challenging fine-grained Semantic Shift Benchmark [49]. A similar trend of Tab. 1 holds true for the results on SSB. Our approach achieves competitive performance in all cases and again reaches a better performance when the number of classes is unknown. In Tab. 4, we present the results on the Herbarium-19 dataset which is a long-tailed dataset, adding additional challenges for the GCD task. Again, our method performs the best on 'All' and 'New' classes. These results demonstrate the effectiveness of our method." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 89, + 587, + 246, + 689 + ], + "blocks": [ + { + "bbox": [ + 67, + 569, + 266, + 581 + ], + "lines": [ + { + "bbox": [ + 67, + 569, + 266, + 581 + ], + "spans": [ + { + "bbox": [ + 67, + 569, + 266, + 581 + ], + "type": "text", + "content": "Table 4: Results on the Herbarium-19 Dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 89, + 587, + 246, + 689 + ], + "lines": [ + { + "bbox": [ + 89, + 587, + 246, + 689 + ], + "spans": [ + { + "bbox": [ + 89, + 587, + 246, + 689 + ], + "type": "table", + "html": "
MethodsAllOldNew
k-means [35]13.012.213.4
RS+ [16]27.955.812.8
UNO+ [12]28.353.714.7
ORCA [2]20.930.915.5
GCD [48]35.451.027.0
Ours (GPC)36.551.727.9
", + "image_path": "11390253e331f4f035464bb6d637b487b828fb3d71a3849d4a041690a8da8949.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 332, + 304, + 521, + 392 + ], + "blocks": [ + { + "bbox": [ + 332, + 304, + 521, + 392 + ], + "lines": [ + { + "bbox": [ + 332, + 304, + 521, + 392 + ], + "spans": [ + { + "bbox": [ + 332, + 304, + 521, + 392 + ], + "type": "image", + "image_path": "d7ce1b599271ba5b8e442405c1d2efd04e817acf4b8b38de6e4ec886e3d52270.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 403, + 526, + 426 + ], + "lines": [ + { + "bbox": [ + 324, + 403, + 526, + 426 + ], + "spans": [ + { + "bbox": [ + 324, + 403, + 526, + 426 + ], + "type": "text", + "content": "(a) Explained variance of the original feature w.r.t. the number of principal directions." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 331, + 431, + 521, + 520 + ], + "blocks": [ + { + "bbox": [ + 331, + 431, + 521, + 520 + ], + "lines": [ + { + "bbox": [ + 331, + 431, + 521, + 520 + ], + "spans": [ + { + "bbox": [ + 331, + 431, + 521, + 520 + ], + "type": "image", + "image_path": "64e7895dd7657664189b3aedc58320f39e22a955b79d2e8b1cab66e824210a04.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 532, + 526, + 554 + ], + "lines": [ + { + "bbox": [ + 324, + 532, + 526, + 554 + ], + "spans": [ + { + "bbox": [ + 324, + 532, + 526, + 554 + ], + "type": "text", + "content": "(b) The clustering ACC on validation set w.r.t. the number of principal directions" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 560, + 545, + 585 + ], + "lines": [ + { + "bbox": [ + 306, + 560, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 545, + 585 + ], + "type": "text", + "content": "Figure 3: The effects of the number of principal directions in PCA on the feature representations." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 608, + 471, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 471, + 620 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 471, + 620 + ], + "type": "text", + "content": "4.3. Novel class number estimation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 630, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 547, + 712 + ], + "type": "text", + "content": "One of the important yet overlooked components in the NCD and GCD literature is the estimation of unknown class numbers. Our proposed framework leverages a modified GMM to estimate the class number, in which we need to define an initial guess of the class number. We validate the effects of different choices of the initial guess " + }, + { + "bbox": [ + 306, + 630, + 547, + 712 + ], + "type": "inline_equation", + "content": "K_{init}" + }, + { + "bbox": [ + 306, + 630, + 547, + 712 + ], + "type": "text", + "content": " w.r.t. the estimated class number in Tab. 5. Note that the number" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16629" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 97, + 114, + 494, + 205 + ], + "blocks": [ + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "lines": [ + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "spans": [ + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "text", + "content": "Table 5: Results of varying the initial guessed " + }, + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "inline_equation", + "content": "K_{init}^{n}" + }, + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "text", + "content": ". 'GT " + }, + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "inline_equation", + "content": "K^{n}" + }, + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "text", + "content": "' is the ground truth number of novel classes. " + }, + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "inline_equation", + "content": "K^{n}" + }, + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "text", + "content": " is the estimated number of novel classes. Our proposed framework is generally robust in estimating the number of novel classes, and we found that using the initial guess of " + }, + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "inline_equation", + "content": "K_{init} = K^{l} + \\frac{K^{l}}{2}" + }, + { + "bbox": [ + 45, + 70, + 547, + 110 + ], + "type": "text", + "content": " can be a simple and reliable choice." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 97, + 114, + 494, + 205 + ], + "lines": [ + { + "bbox": [ + 97, + 114, + 494, + 205 + ], + "spans": [ + { + "bbox": [ + 97, + 114, + 494, + 205 + ], + "type": "table", + "html": "
DatasetKlGT KnVaze et al. [48]Kninit = 3510203050100
CIFAR-10554Kn = 55566814
CIFAR-100802020Kn = 16202021222736
ImageNet-100505059Kn = 58485755545060
CUB100100131Kn = 7987868892112101
SCars9898132Kn = 8490868789115104
", + "image_path": "78f5def2f7c2b2194459c9a018a2253190566b6a0aa696365be8f7e330d63581.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 220, + 288, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 288, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 288, + 270 + ], + "type": "text", + "content": "in Tab. 5 is " + }, + { + "bbox": [ + 46, + 220, + 288, + 270 + ], + "type": "inline_equation", + "content": "K_{init}^{n} = K_{init} - K^{l}" + }, + { + "bbox": [ + 46, + 220, + 288, + 270 + ], + "type": "text", + "content": ". We can see that our proposed framework is generally robust to a wide range of initial guesses. We found that " + }, + { + "bbox": [ + 46, + 220, + 288, + 270 + ], + "type": "inline_equation", + "content": "K_{init} = K^{l} + \\frac{K^{l}}{2}" + }, + { + "bbox": [ + 46, + 220, + 288, + 270 + ], + "type": "text", + "content": " is a simple and reliable choice. Hence we use this for all datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 165, + 290 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 165, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 165, + 290 + ], + "type": "text", + "content": "4.4. Training complexity" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 296, + 288, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 296, + 288, + 428 + ], + "spans": [ + { + "bbox": [ + 45, + 296, + 288, + 428 + ], + "type": "text", + "content": "Given that our framework necessitates the fitting of GMMs, an extended training duration is required. We compare the performance of our method to the extended method of Vaze et al. [48], which is pushed to " + }, + { + "bbox": [ + 45, + 296, + 288, + 428 + ], + "type": "inline_equation", + "content": "1.5 \\times" + }, + { + "bbox": [ + 45, + 296, + 288, + 428 + ], + "type": "text", + "content": " its original number of training epochs. The results in Tab. 6 demonstrate that our method outperforms [48] across both CUB and ImageNet-100 datasets while maintaining a similar training duration. Furthermore, in contrast to the baseline method, our approach eliminates the need for additional post-training procedures such as running SS-" + }, + { + "bbox": [ + 45, + 296, + 288, + 428 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 296, + 288, + 428 + ], + "type": "text", + "content": "-means on the entire dataset for label assignment." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 57, + 467, + 278, + 546 + ], + "blocks": [ + { + "bbox": [ + 46, + 437, + 287, + 462 + ], + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 462 + ], + "type": "text", + "content": "Table 6: Comparison between GPC and Vaze et al. [48] " + }, + { + "bbox": [ + 46, + 437, + 287, + 462 + ], + "type": "inline_equation", + "content": "(1.5\\times)" + }, + { + "bbox": [ + 46, + 437, + 287, + 462 + ], + "type": "text", + "content": " on CUB and ImageNet-100 Datasets." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 467, + 278, + 546 + ], + "lines": [ + { + "bbox": [ + 57, + 467, + 278, + 546 + ], + "spans": [ + { + "bbox": [ + 57, + 467, + 278, + 546 + ], + "type": "table", + "html": "
MethodCUBImageNet-100
AllOldNewAllOldNew
Vaze et al. [48]51.356.648.774.189.866.3
Vaze et al.(1.5×)52.056.849.074.790.366.7
Ours (GPC)55.458.253.176.994.371.0
", + "image_path": "d1950af9d80938e266fbb5e50638092a07ad001ecd081ae5410253934018166b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 563, + 139, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 139, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 139, + 575 + ], + "type": "text", + "content": "4.5. Ablation study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 582, + 288, + 715 + ], + "type": "text", + "content": "Number of dimensions in PCA The PCA in our framework requires setting a number for the number of principal directions to extract from data. In Fig. 3, we show the results of using a different number of principal directions in PCA on CUB-200 and ImageNet-100 datasets. We can see from Fig. 3a that for both datasets, 128 principal directions can already explain most of the variances in the data, thus we choose the PCA dimension to be 128 for all our experiments. We further experiment with other different choices of the PCA dimension and shows the result in Fig. 3b, which again confirms that 128 principal directions are already expensive" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 220, + 547, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 220, + 547, + 246 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 547, + 246 + ], + "type": "text", + "content": "enough, and obtain the best performance over other choices, that are either too few or too many, effectively avoiding DC." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 264, + 547, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 547, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 547, + 552 + ], + "type": "text", + "content": "Different methods for prototype estimation Our semi-supervised GMM plays an important role in prototype estimation for representation learning based on prototypical contrastive learning. Here, we replace our semi-supervised GMM with other alternatives that do not produce prototypes automatically. Particularly, we compare our method with DBSCAN [10], Agglomerative clustering [37], and semi-supervised " + }, + { + "bbox": [ + 304, + 264, + 547, + 552 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 264, + 547, + 552 + ], + "type": "text", + "content": "-means [17, 48]. The prototypes are then obtained by averaging the data points that are assigned to the same cluster. For a fair comparison, the same regulations to prevent the wrong clustering results for labelled instances are applied to all methods, i.e., during the clustering process, two labelled instances with the same label will fall into the same cluster, and two instances with different labels will be assigned to different clusters. The results are reported in Tab. 7a. Our method achieves the best performance on all three datasets, indicating that better prototypes are obtained by our approach to facilitate representation learning. Note that DBSCAN requires two important user-defined parameters, radius, and minimum core points, the ideal values of which lack a principled way to obtain in practice, while our method is parameter-free and can seamlessly be combined with the representation learning to jointly enhance each other, obtaining better performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 714 + ], + "type": "text", + "content": "Combining our GMM with other GCD methods We further combine our semi-supervised GMM with automatic splitting and merging with other methods, allowing joint representation learning and category discovery without a predefined category number. As the state-of-the-art GCD method [48] does not contain any parametric classifier during representation, so it can be directly combined with our GMM. For the RankStat and the DualRank methods that have a parametric classifier for category discovery, we treat the weights of the classifier as the cluster centers and run our GMM to automatically determine the category number during representation learning. The results are presented" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16630" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 117, + 272, + 196 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 95 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 95 + ], + "type": "text", + "content": "Table 7: Combining components of GPC with other methods. \"IM-100\" denotes ImageNet-100." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 93, + 101, + 251, + 112 + ], + "lines": [ + { + "bbox": [ + 93, + 101, + 251, + 112 + ], + "spans": [ + { + "bbox": [ + 93, + 101, + 251, + 112 + ], + "type": "text", + "content": "(a) Different prototype estimation methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 117, + 272, + 196 + ], + "lines": [ + { + "bbox": [ + 71, + 117, + 272, + 196 + ], + "spans": [ + { + "bbox": [ + 71, + 117, + 272, + 196 + ], + "type": "table", + "html": "
Clustering Algo.CUBIM-100SCars
Ester et al. [10]45.666.134.8
Murtagh et al. [37]52.174.639.8
Vaze et al. [48]49.273.237.4
Ours (GPC)54.176.641.9
", + "image_path": "3f826839a968bc0befd3c137be303d547ee35edaec93b1f14e83b1af6523cbd7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 79, + 220, + 267, + 299 + ], + "blocks": [ + { + "bbox": [ + 88, + 205, + 256, + 216 + ], + "lines": [ + { + "bbox": [ + 88, + 205, + 256, + 216 + ], + "spans": [ + { + "bbox": [ + 88, + 205, + 256, + 216 + ], + "type": "text", + "content": "(b) Combining our GMM with other methods." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 79, + 220, + 267, + 299 + ], + "lines": [ + { + "bbox": [ + 79, + 220, + 267, + 299 + ], + "spans": [ + { + "bbox": [ + 79, + 220, + 267, + 299 + ], + "type": "table", + "html": "
RepresentationCUBIM-100SCars
Han et al. [16]34.638.429.3
Zhao et al. [58]37.839.733.2
Vaze et al. [48]50.673.437.8
Ours (GPC)54.176.641.9
", + "image_path": "a633b766137344604e90d165c8b5fd1b5c51c530f195f011181577a01ae5e71c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 313, + 288, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 288, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 288, + 374 + ], + "type": "text", + "content": "in Tab. 7b. Comparing with row 9 in Tab. 1 and Tab. 3, we can see using our GMM can also improve [48] on CUB and Stanford Cars, while our proposed framework consistently achieves better performance on all datasets, again validating that our design choices." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 389, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 510 + ], + "type": "text", + "content": "Class number estimation with different representations Here, we validate our class number estimation method on top of the representations learned by other GCD approaches and report the results in Tab. 8. It can be seen, applying our method on other GCD representations can achieve reasonably well results. Notably, by applying our class number estimation method on top of the representation by the existing state-of-the-art method, we can obtain better class number estimation results, though the overall best results are obtained with the representation learned in our framework." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 549, + 285, + 662 + ], + "blocks": [ + { + "bbox": [ + 47, + 520, + 287, + 544 + ], + "lines": [ + { + "bbox": [ + 47, + 520, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 520, + 287, + 544 + ], + "type": "text", + "content": "Table 8: Class number estimation with different learned representations. \"C-100\" stands for the CIFAR-100 dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 549, + 285, + 662 + ], + "lines": [ + { + "bbox": [ + 50, + 549, + 285, + 662 + ], + "spans": [ + { + "bbox": [ + 50, + 549, + 285, + 662 + ], + "type": "table", + "html": "
RepresentationC-100CUBSCarsIM-100
Ground Truth Kn201009850
Vaze et al.[48]2013113259
Ours w/ [16] feat.191119455
Ours w/ [58] feat.221168949
Ours w/ [48] feat.2112110957
Ours (GPC)2011210353
", + "image_path": "4365a32503bf784722b0e34bcba49f7fb4daa9cb50dafc9129ca3a5fb9d13a7c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Partial overlap between " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_l" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_u" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " We evaluate the performance of our method when we relax " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_l\\subset \\mathcal{V}_u" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " to" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_l \\cap \\mathcal{Y}_u \\neq \\emptyset" + }, + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "content": ", i.e., the two sets may only partially overlap. We vary the number of overlapped classes and report the results in Tab. 9. Our approach consistently outperforms the method proposed by Vaze et al. [48] in all configurations. These compelling results not only showcase the robustness of our method but also highlight its effectiveness in scenarios involving partial overlap between known and unknown classes." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 306, + 207, + 547, + 264 + ], + "blocks": [ + { + "bbox": [ + 305, + 177, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 305, + 177, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 305, + 177, + 545, + 201 + ], + "type": "text", + "content": "Table 9: Results on CUB of only partial overlap between " + }, + { + "bbox": [ + 305, + 177, + 545, + 201 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_l" + }, + { + "bbox": [ + 305, + 177, + 545, + 201 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 177, + 545, + 201 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_u" + }, + { + "bbox": [ + 305, + 177, + 545, + 201 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 207, + 547, + 264 + ], + "lines": [ + { + "bbox": [ + 306, + 207, + 547, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 207, + 547, + 264 + ], + "type": "table", + "html": "
|Yl∩Yu|255075
AllOldNewAllOldNewAllOldNew
Vaze et al. [48]49.550.148.251.250.752.252.750.954.5
Ours (GPC)51.252.649.552.351.654.853.651.455.9
", + "image_path": "321b71af7326a3cfe2fe6f3b64a17d66acd2d06708624aab277218859e2467ec.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 295, + 547, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 547, + 380 + ], + "type": "text", + "content": "Varying ratio of Old/New categories We measure the estimated new class numbers when varying the ratio of Old/New categories while having " + }, + { + "bbox": [ + 304, + 295, + 547, + 380 + ], + "type": "inline_equation", + "content": "K_{init} = K^{l} + \\frac{K^{l}}{2}" + }, + { + "bbox": [ + 304, + 295, + 547, + 380 + ], + "type": "text", + "content": " on CUB in Tab. 10. As can be seen, for all cases, our method outperforms [48]. Meanwhile, we can also see that when the initial guess is too far from the ground truth, the estimation will be less accurate." + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 315, + 419, + 537, + 469 + ], + "blocks": [ + { + "bbox": [ + 305, + 390, + 547, + 414 + ], + "lines": [ + { + "bbox": [ + 305, + 390, + 547, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 390, + 547, + 414 + ], + "type": "text", + "content": "Table 10: Estimated class numbers on CUB with a varying ratio of Old/New classes." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 419, + 537, + 469 + ], + "lines": [ + { + "bbox": [ + 315, + 419, + 537, + 469 + ], + "spans": [ + { + "bbox": [ + 315, + 419, + 537, + 469 + ], + "type": "table", + "html": "
Old/New20/18040/16060/14080/120
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", + "image_path": "ffcafe583f47df80e7d1fa6c392a7ef1e944577e98e4d3dbc947f67ebcaea0fb.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 495, + 378, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 378, + 508 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 378, + 508 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 516, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 547, + 661 + ], + "type": "text", + "content": "In this paper, we present an EM-like framework for the challenging GCD problem without knowing the number of new classes, with the E-step automatically determining the class number and prototypes and the M-step being robust representation learning. We introduce a semi-supervised variant of GMM with a stochastic splitting and merging mechanism to obtain the prototypes and leverage these evolving prototypes for representation learning by prototypical contrastive learning. We demonstrated that class number estimation and representation learning can facilitate each other for more robust category discovery. Our framework obtains state-of-the-art performance on multiple public benchmarks." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements This work is supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16631" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin Raffel. 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Prior arts heavily rely on 3D point clouds or voxel data for shape primitives extraction, which are less practical in real-world scenarios. This paper proposes to learn shape primitives from multi-view images by introducing implicit surface rendering. It is challenging since implicit shapes have a high degree of freedom, which violates the simplicity property of shape primitives. In this work, a novel regularization term named Implicit Convexity Regularization (ICR) imposed on implicit primitive learning is proposed to tackle this problem. We start with the convexity definition of general 3D shapes, and then derive the equivalent expression for implicit shapes represented by signed distance functions (SDFs). Further, instead of directly constraining the output SDF values which cause unstable optimization, we alternatively impose constraint on second order directional derivatives on line segments inside the shapes, which proves to be a tighter condition for 3D convexity. Implicit primitives constrained by the proposed ICR are combined into a whole object via softmax-weighted-sum operation over all primitive SDFs. Experiments on synthetic and real-world datasets show that our method is able to decompose objects into simple and reasonable shape primitives without the need of segmentation labels or 3D data. Code and data is publicly available in https://github.com/seanywang0408/ICR.", + "bbox": [ + 75, + 318, + 473, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 757, + 209, + 772 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shape primitives extraction aims at decomposing a complex object into simple geometry. It has been a fundamental task in 3D shape representation [7] which imitates human visual perception, abstraction and understanding of real-world objects, and also facilitates industrial manufacturing which fabricates complex objects via component as", + "bbox": [ + 75, + 784, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/392d05075a3b97097c79be6ccf1a9dc347be099b8be57202ede4a698afb7f68f.jpg", + "image_caption": [ + "Figure 1. We propose a shape primitive decomposition method from multi-view images with a novel Implicit Convexity Regularization scheme (ICR), which theoretically guarantees the convexity of implicit primitives. Our method generates shape primitives that satisfy simplicity, semantics preserving and fidelity." + ], + "image_footnote": [], + "bbox": [ + 506, + 282, + 888, + 386 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "seembling. There are several fundamental properties for shape primitives: i) simplicity, which means that each primitive should be composed of simple geometry; ii) semantics, which means that the decomposition should reveal the semantic parts of an object; iii) fidelity, which means that the primitives should fit the original object as close as possible. Prior methods using parameterized shapes as primitive basis, such as cuboids [11] and superquadrics [13], could guarantee the simplicity property. However, parameterized primitives are less expressive due to their limited pre-defined geometry, which generally cause low fidelity. Though leveraging the flexibility of implicit functions to represent primitives could achieve higher fidelity, it also comes with a drawback that the semantic information generally diminishes during decomposition [5, 9]. Most importantly, all prior works require 3D data either for single-object fitting or multi-object learning. These data are not accessible in many cases, which makes them unpractical in real-world applications. In this work, we address this problem by learning implicit primitives from multi-view images.", + "bbox": [ + 496, + 489, + 892, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning implicit primitives from multi-view images is an even more challenging task. It is non-trivial to introduce prior implicit primitives [9, 19] into a neural rendering pipeline due to their specific modeling. Besides, implicit shapes without explicit regularization has a high degree of freedom, which could hardly meet the requirements of primitives. To this end, we propose a convex regulariza", + "bbox": [ + 496, + 795, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author.", + "bbox": [ + 94, + 886, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3642", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion term imposed on a common signed distance function (SDF), which could be readily integrated into any implicit surface reconstruction pipeline, as shown in Figure 1. Convexity is a plausible property for primitives. First, it is a subconcept of simplicity, that is, a convex shape is generally regarded as simple (Figure 2). Second, most semantic parts are convex (see Figure 5 for example). Therefore convexity regularization benefits semantics preservation in primitive decomposition. Lastly, convexity is welcomed in some industrial manufacturing process, such as 3D printing and furniture making, in which convex parts are first fabricated respectively and then adhered into one object.", + "bbox": [ + 80, + 90, + 467, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To derive our implicit convexity regularization, we first start with the general definition of 3D convexity, which is formulated on arbitrary two points inside a shape. Then we tailor this definition to an implicit shape represented by a signed distance function (SDF) without loss of generality. This conversion also allows more lightweight computation. Further, to avoid the training instability and oscillation caused by direct constraint on the output SDF value, we tighten the convexity condition by alternatively constraining the second order directional derivatives along a line segment. We theoretically prove that this constraint is a sufficient condition for convexity. Besides, using the Finite Difference Method could easily implement this constraint.", + "bbox": [ + 80, + 273, + 467, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the proposed implicit convexity regularization, each primitive is guaranteed to be convex. We combine all primitives into a whole object by conducting softmax-weighted-sum operation over all primitive SDFs and deriving the object SDF. The object SDF is incorporated into a common implicit surface rendering pipeline [17], allowing primitive decomposition from multi-view images. We experiment on both synthetic and real-world datasets, demonstrating the simplicity, semantics and fidelity of our generated primitives, especially on CO3D [21] dataset where prior primitive methods are infeasible without 3D data.", + "bbox": [ + 80, + 470, + 467, + 635 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 80, + 652, + 215, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Parameterized Primitives", + "text_level": 1, + "bbox": [ + 80, + 678, + 305, + 693 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Cuboids with scaling, rotation and translation are first used as an abstraction of object parts. 3DPRNN [33] uses a recurrent network to generate cuboid primitives step-by-step. Tulsian et al. [24] obtain a consistent parsing across objects based on cuboids assembling. Niu et al. [16] infer hierarchical cuboid structure from single images. Lin et al. [12] propose a reinforcement learning algorithm to learn primitive decomposing policies. Kluger et al. [11] expand cuboids fitting from simple objects to more complex indoor scenes. Although cuboids decomposition could produce compact and semantic primitives, it also cause low fidelity due to its singular geometry.", + "bbox": [ + 80, + 703, + 467, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another line of shape primitives is super-quadrics [20],", + "bbox": [ + 99, + 885, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "which are more expressive than quadrics using 6 control parameters. Paschalidou et al. [18] decompose objects in to a hierarchical binary tree of super-quadrics, providing shape abstraction in different levels. EMS [13] aims at extraction super-quadric primitives from a noisy point cloud from a probabilistic view, which makes it more robust to outliers. Besides super-quadrics, ParseNet [23] proposes to use B-spline, cylinder and cones as primitives to reconstruct continuous surface from point clouds. Genova et al. [6] learn category-specific templates based on scaled axis-aligned anisotropic 3D Gaussian prior. ExtrudeNet [22] encodes point clouds into several primitives extruded from 2D Bezier curves that could be integrated into modern CAD software. Although these parameterized primitives provide higher fidelity than cuboids, it still does not meet the complexity of real-world objects.", + "bbox": [ + 503, + 90, + 888, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Constructive Solid Geometry (CSG) Tree [8, 32, 31] uses iterative boolean operators including union and intersection to construct convex or concave geometry, which is well-suited in computer-aided design (CAD). Although it still uses singular primitives like spheres and rectangles, CSG Tree is able to reconstruct accurate geometry as the iterative boolean operation gets deeper. However, it comes with a drawback that objects are eventually divided into patches in pieces with little semantic information preserved.", + "bbox": [ + 503, + 333, + 888, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Implicit Primitives", + "text_level": 1, + "bbox": [ + 503, + 482, + 678, + 497 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "BSPNet [3] and CvxNet [5] both use hyperplanes to construct a convex polytype and then assemble these convexes into a non-convex shape. Although these two methods are able to derive convex primitives like ours, the computation and storage cost grow quadratically as the number of hyperplanes increases, which makes it unsuitable for neural rendering in a multi-view scenario. Latent Partition Implicit [2] proposes shape partition in latent space for accurate modeling. Neural Star Domain (NSD) [9] models each primitive as a continuous function defined on a sphere, ensuring the simplicity property of primitives. However it still shares the deficiency of BSPNet and CvxNet that the semantic parts are broken into multiple primitives, as shown in Figure ?? Similar to NSD, Neural Parts [19] define homeomorphic mappings between spheres and primitives, which is able to generate various primitives with single connectivity. Nonetheless it is non-trivial to apply such a homeomorphic mapping in a neural rendering pipeline. Another relevant work to ours is BAENet [4], which uses a branched decoder to learn recurring parts in a shape collection. Although it is capable of producing accurate semantic segmentation results given a ground-truth shape, its reconstruction fidelity is notably inferior to ours.", + "bbox": [ + 503, + 506, + 888, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, all the above methods strongly rely on 3D data input for primitive decomposition, most of which even require a large set of shape collection within the same cat", + "bbox": [ + 503, + 854, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3643", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/979442117d86760f63ddb95cd3b2a1638644092ff972fd7eb6cd309d2be11101.jpg", + "image_caption": [ + "Figure 2. Convexity is a subconcept of simplicity, since a convex shape is generally regarded as simple, while a non-convex shape tends to be more complex." + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 468, + 195 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "egory for training, such as ShapeNet [1] or ModelNet [26], which makes them less practical in real-world scenarios. Our method derives implicit convex primitives from multiview images with well-defined semantics.", + "bbox": [ + 75, + 271, + 470, + 333 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Implicit Surface Rendering", + "text_level": 1, + "bbox": [ + 76, + 343, + 326, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, implicit neural representations have advanced surface reconstruction from multi-view images. DVR [15] proposes a differentiable rendering formulation for implicit surface and texture representations. IDR [29] approximates the light reflected from a 3D shape represented as the zero level set of a neural network. UNISURF [17] presents a unified framework for implicit surfaces and radiance fields, with the goal of reconstructing nontransparent objects. NeuS [25] develops a volume rendering method to train a neural SDF representation. Yariv et al. [28] define the volume density function as Laplace's cumulative distribution function applied to a SDF for surface rendering.", + "bbox": [ + 75, + 368, + 472, + 550 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 565, + 212, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first demonstrate the derivation of the proposed implicit convexity regularization (ICR) scheme, and then explain the application of primitive fitting with ICR in a neural rendering pipeline.", + "bbox": [ + 75, + 590, + 468, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Implicit Convexity Regularization", + "text_level": 1, + "bbox": [ + 76, + 662, + 375, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is challenging to preserve simplicity in implicit primitives learning from multi-view images. In prior arts, there was little discussion on the simplicity of implicit shapes represented by signed distance functions. In this work, we investigate this problem in the view of convexity. A convex shape is the boundary of a convex set. We show some examples of convex and non-convex shapes in Figure 2. Intuitively, convexity is a subconcept of simplicity, since a convex shape is generally regarded as simple, while a nonconvex shape tends to be more complex. Mathematically, convexity could be defined as follows:", + "bbox": [ + 75, + 686, + 470, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 1 A shape $C$ is convex $\\iff$ For arbitrary two points located inside the shape $C$ , the convex combination of", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3577a572eb383ce7ab2d909639dda6f2c43002a76a1ecb928ed4f67c9596e4ac.jpg", + "image_caption": [ + "Figure 3. We start with the general definition of convexity in Theorem 1. Then we convert the definition to an implicit shape represented by a signed distance function (SDF), which directly constrains the output SDF value. Lastly, to address the training instability issue in Theorem 2, we alternatively impose constraint on the second order directional derivatives, which proves to be a tighter condition of Theorem 2. The computation of second order directional derivatives could be easily implemented with Finite Difference Method." + ], + "image_footnote": [], + "bbox": [ + 511, + 85, + 888, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the two points are also located inside the shape, i.e., for any $x_{1}, x_{2} \\in C$ and $0 \\leq \\theta \\leq 1$ , we have $\\theta x_{1} + (1 - \\theta)x_{2} \\in C$ .", + "bbox": [ + 498, + 580, + 892, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is computation-inefficient to directly apply the vanilla convexity formulation to an implicit function, since it requires queries of arbitrary two points inside the shape. To adapt the convexity definition to a shape represented by an SDF with higher efficiency, we convert the above definition to a surface-based formulation:", + "bbox": [ + 496, + 621, + 893, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 2 A shape $C$ represented by an signed distance function $f$ is convex $\\iff$ For arbitrary two points that are located on the surface of the shape, the convex combination of these two points is located inside the shape, i.e., for any $x_1, x_2 \\in \\{x | f(x) = 0\\}$ and $0 < \\theta < 1$ , we have $f(\\theta x_1 + (1 - \\theta) x_2) < 0$ .", + "bbox": [ + 496, + 722, + 893, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is self-evident that Theorem 2 is equivalent to Theorem 1 for a SDF-based shape. It also ease the sampling process since only line segment between surface points are evaluated. In practice, we first randomly sample a set of rays of arbitrary starting points and directions, and retrieve", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3644", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the first and last intersection point $x_{1}, x_{2}$ against the shape by a root-finding algorithm. Those rays which do not intersect with the shape are ignored. Next we sample a set of points which is the convex combination of $x_{1}, x_{2}$ , i.e., points located on the line segment between $x_{1}, x_{2}$ . Lastly we penalize the positive SDF values of these points, meaning that they are outside the shape.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, we empirically find that directly imposing constraint on the output SDF values could cause serious training instability and oscillation, or even collapse. The reason is that there is a shortcut for the SDF function to satisfy this constraint, that is to scale up the SDF value of the whole function, which only needs to scale up the value of the final layer of the MLP. As an alternative, we propose to impose constraint on the second order directional derivative along the ray direction in the implicit field.", + "bbox": [ + 75, + 196, + 470, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 3 A shape $C$ represented by an signed distance function $f$ is convex $\\Longleftarrow$ For arbitrary two points $x_{1}, x_{2}$ located on the surface of the shape, we have positive second order directional derivative along the direction $x_{2} - x_{1}$ on the convex combination of $x_{1}, x_{2}$ , i.e., for any $x_{1}, x_{2} \\in \\{x | f(x) = 0\\}$ , $d = x_{2} - x_{1}$ and $0 < \\theta < 1$ , we have $\\frac{\\partial^2 f}{\\partial^2 d} (\\theta x_1 + (1 - \\theta)x_2) \\geq 0$ .", + "bbox": [ + 75, + 342, + 470, + 453 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proof. If the condition in Theorem 3 is satisfied, it means that the 1D function $f_{SDF}(x_0)$ w.r.t $x_0 = \\theta x_1 + (1 - \\theta)x_2$ , $0 < \\theta < 1$ is a convex function. By the definition of convex functions, we have $f(x_0) < \\theta f(x_1) + (1 - \\theta)f(x_2) = \\theta \\times 0 + (1 - \\theta) \\times 0 = 0$ . Through Theorem 2, we know shape $C$ is convex. Constraint on second order directional derivatives is a tighter condition for convexity than constraint on SDF values. Intuitively, when the second order directional derivatives are positive everywhere between $x_1, x_2$ , we have a monotonically increasing first order directional derivative along the line segment, meaning that no inflection point exists in the interval.", + "bbox": [ + 75, + 460, + 468, + 641 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on Theorem 3, we encourage convexity by penalizing negative second order directional derivatives between $x_{1}, x_{2}$ . However, differentiating second order gradient of a neural network involves extremely intense computation. To this end, we replace accurate gradient derivation with Finite Difference, in which we view the continuous SDF as a discrete function via uniform sampling between the two intersection points $x_{1}, x_{2}$ . The detailed algorithm is presented in Algorithm 1. We also visualize the convexity defined by the three theorems using a 2D case in Figure 3.", + "bbox": [ + 75, + 642, + 470, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Learning Primitives from Multi-View Images", + "text_level": 1, + "bbox": [ + 76, + 801, + 460, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Primitive Representations. We represent implicit shape primitives with a set of general signed distance functions (SDFs). Given a 3D point $\\mathbf{p}$ as input, we use a multilayer perceptron (MLP) $f$ to predict the signed distance $SDF_{primi}(\\mathbf{p})$ from the point $\\mathbf{p}$ to the object surface. The", + "bbox": [ + 76, + 824, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Implicit Convexity Regularization (ICR)", + "text_level": 1, + "bbox": [ + 500, + 90, + 857, + 106 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Input: signed distance function $f$", + "2: Output: convexity penalty $\\mathcal{L}_{ICR}$", + "3: Generate a ray with random starting points and directions;", + "4: Retrieve the first and last intersection points $x_{1}, x_{2}$ by root-finding algorithm;", + "5: Uniformly sample $\\mathbf{K}$ points between $x_{1}, x_{2}$ : $\\{p_{j} = \\theta_{j}x_{1} + (1 - \\theta_{j})x_{2} | \\theta_{j} = \\frac{j}{K + 1}, j = 1, 2, \\dots, K\\}$ ;", + "6: Query the SDF values of the sampled points: $\\{f(p_j)|j = 1,2,\\dots,K\\}$", + "7: Compute 1st order direction derivative with finite difference: $\\{\\nabla f = f(p_j) - f(p_{j - 1})|j = 2,\\dots,K\\}$ ;", + "8: Compute 2rd order direction derivative with finite difference: $\\{\\nabla^2 f = \\nabla f(p_j) - \\nabla f(p_{j-1})|j = 3,\\dots,K\\}$ ;", + "9: Compute the penalty term $L = \\sum max(-\\nabla^2 f, 0)$ ;", + "10: return $\\mathcal{L}_{ICR}$" + ], + "bbox": [ + 506, + 108, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "signed distance is positive when the point is located outside of the surface, while the signed distance is negative when the point is located inside of the surface. To unify the primitives into a complete object, one could take the minimal value over all primitive SDFs as the final object SDF. However, doing so would block the gradient flow from the object SDF to the subminimal primitive SDFs, which leads to suboptimal convergence. To this end, we conduct a soft minimization, composed of a softmax and a weighted sum operation. Formally, suppose each primitive SDF is implemented as a MLP network $f_{i}$ , the object signed distance of point $\\mathbf{p}$ could be computed as:", + "bbox": [ + 496, + 380, + 893, + 561 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} S D F _ {p r i m i} ^ {i} (\\mathbf {p}) = f _ {i} (\\mathbf {p}), \\\\ \\omega_ {i} = \\operatorname {s o f t m a x} _ {N} (- \\beta \\cdot S D F _ {p r i m i} ^ {i} (\\mathbf {p})), \\tag {1} \\\\ S D F _ {o b j} (\\mathbf {p}) = \\sum_ {i = 1} ^ {N} \\omega_ {i} \\cdot S D F _ {p r i m i} ^ {i} (\\mathbf {p}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 573, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ is the scaling temperature (set to 10 in our experiments) in softmax operation, $\\omega_{i}$ denotes the weight of $i$ th primitive and $N$ is the number of the primitives.", + "bbox": [ + 496, + 667, + 890, + 714 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Surface Rendering. Considering the difficulty of acquiring 3D data in application, we aim at learning the implicit primitives from multi-view images. Although prior works such as BSPNet [3] and CvxNet [5] proposes 3D convexity representation based on hyper-planes, these representations are infeasible in current neural rendering pipelines, hindering the acquisition of convexity primitives from multi-view data. One key contribution of our method is that we extend convexity primitives to a implicit surface distance function, which is the common 3D representation of neural rendering pipelines.", + "bbox": [ + 496, + 734, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3645", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d399db9980f65e01b265ee93d15926394e60d832d5d43a9b67263b4931867ba7.jpg", + "image_caption": [ + "Figure 4. Our network consists of N primitive MLPs and one color MLP. Each primitive MLP outputs an SDF value and a geometry latent code of the primitive from the input $\\mathbf{p}$ . The primitive SDF values and latent codes go through a softmax-weighted-sum layer to obtain the object SDF and latent code, which are then respectively processed by a sigmoid layer and a color MLP. The obtained volume density $\\sigma$ and RGB are applied in a standard implicit surface volume rendering method. The loss is computed by the weighted sum of reconstruction error and Implicit Convexity Regularization on each primitive." + ], + "image_footnote": [], + "bbox": [ + 98, + 97, + 875, + 275 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we integrate the implicit primitives into a neural rendering pipeline based on UNISURF [17]. To this end, we first extend the pirmitive MLPs in Sec 3.2 to additionally output a geometry latent code except for SDF value in the final layer, such that", + "bbox": [ + 75, + 381, + 470, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ S D F _ {p r i m i} ^ {i} (\\mathbf {p}), L _ {p r i m i} ^ {i} (\\mathbf {p}) \\right] = f _ {i} (\\mathbf {p}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 465, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{primi}^{i}(\\mathbf{p})$ is the latent code of $\\mathbf{p}$ . Similar to $SDF_{obj}(\\mathbf{p})$ , the object latent code $L_{obj}(\\mathbf{p})$ is obtained by the softmax-weighted-sum over all primitive latent codes. We further implement a color MLP which receives the object latent code as input and predicts the RGB value $\\mathbf{c}$ of $\\mathbf{p}$ . Then we apply the volume rendering as follows.", + "bbox": [ + 75, + 491, + 468, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For a ray $\\mathbf{r}$ starting from the camera position to the pixel location, we first retrieve the surface point $\\mathbf{x}_s$ defined by $SDF_{obj}(\\mathbf{x}_s) = 0$ using a root-finding algorithm. Then, we sample $N$ points $\\mathbf{x}_j$ along ray $\\mathbf{r}$ within a interval around $\\mathbf{x}_s$ . We infer the object SDF value for each sample and convert it to volume density $\\sigma_j$ as follows:", + "bbox": [ + 75, + 583, + 468, + 674 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {j} = \\operatorname {S i g m o i d} (- \\mu \\cdot S D F _ {o b j} (\\mathbf {x} _ {j})), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 681, + 468, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mu$ is a hyper-parameter that controls the sharpness of density distribution (set to 25 in all our experiments). The ray color is then obtained by the following volume rendering equation:", + "bbox": [ + 75, + 707, + 468, + 768 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (\\mathbf {r}) = \\sum_ {j = 1} ^ {N} \\sigma_ {j} \\prod_ {k < j} (1 - \\sigma_ {k}) \\mathbf {c} _ {j}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 775, + 468, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The reconstruction loss is computed over all sampled rays $\\mathbf{r} \\in \\mathcal{R}$ , with $C(\\mathbf{r})$ as the ground-truth pixel color:", + "bbox": [ + 76, + 825, + 468, + 858 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\hat {C} (\\mathbf {r}) - C (\\mathbf {r}) \\right\\| ^ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 867, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For more details on the neural rendering process, please refer to UNISURF [17]. Overall, we train our model with the following loss function:", + "bbox": [ + 498, + 381, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {r e c} + \\lambda \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {I C R} ^ {i}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 436, + 890, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{ICR}^i$ is the proposed implicit convexity regularization derived in Algorithm 1, which is imposed on each primitive, and $\\lambda$ is the weighting hyper-parameter. Since $\\mathcal{L}_{ICR}$ is generally a small value, we set $\\lambda$ to 100 in our experiments. Illustration of the pipeline is presented in Figure 4.", + "bbox": [ + 498, + 489, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Implementation", + "text_level": 1, + "bbox": [ + 500, + 574, + 660, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In all our experiments, each primitive SDF is implemented as a 4-layer MLP, with a skip connection from the input to the third layer. The color MLP also contains 4 layers. All layers have 64 hidden units. The input coordinates are first encoded by a sinusoidal embedding layer with $L = 6$ , as done in UNISURF [17]. We use the Adam optimizer [10] with an initial learning rate of $10^{-5}$ . The learning rate is multiplied by 0.5 in 4,000th and 5,000th iteration. For each iteration, we sample 1,024 rays for volume rendering. The model is trained for 10,000 iterations.", + "bbox": [ + 496, + 597, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 762, + 633, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Synthetic Dataset", + "text_level": 1, + "bbox": [ + 500, + 786, + 669, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. ShapeNet [1] is a shape collection composed of multiple categories. We conduct experiments on six categories including airplane, car, chair, lamp, table and pistol. We evaluate our method and prior works on randomly-selected 20 shapes for each category. For our method and UNISURF, we use the multi-view images rendered by", + "bbox": [ + 496, + 809, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3646", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7fd5aeb5a780da6a9ea56cf8e55d2902abb7ac4a76b2d50b926881af15eb5189.jpg", + "image_caption": [ + "Figure 5. We visualize the ShapeNet results of our method and prior works, including BAENet, EMS and UNISURF. Our method achieves notably better decomposition and fidelity than BAENet and EMS." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 465, + 588 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/21d940d97650e97753c8db551aa80105073cfba546a4e2825902a00da467e99e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 470, + 95, + 888, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DISN [27], which includes 36 views for each object with known camera intrinsic and extrinsic parameters. The images are rendered in $224 \\times 224$ resolution.", + "bbox": [ + 75, + 647, + 468, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons. We compare our method with the following works. i) BAENet [4]: BAENet is a learning-based primitive decomposition method that is trained on a shape collection within a category. It receives 3D voxel as input and predict an implicit field for each primitive. We follow its default settings which train the models on the complete collection for each categories without segmentation supervision, e.g. 2,690 objects for airplane. ii) EMS [13]: EMS is the state-of-the-art parameterized primitive decomposition method which derives superquadric primitives from a point cloud via a robust optimization algorithm. We follow its default setting in multi-superquadric optimization, and feed the ground-truth point cloud as input data. iii)", + "bbox": [ + 75, + 703, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "UNISURF [17]: UNISURF is a state-of-the-art implicit surface reconstruction method which derive the implicit field of an object from multi-view images. We include UNISURF for comparisons with a standard implicit surface reconstruction method in terms of fidelity. The above methods are summarized in Table 1. We use two metrics for evaluation, including Chamfer Distance (CD) and Intersection over Union (IoU). The quantitative results are reported in Table 2. We also visualize the meshes in Figure 5, with different colors for different primitives.", + "bbox": [ + 496, + 647, + 893, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. Figure 5 and Table 2 show that our method achieves notably better decomposition and fidelity than BAENet and EMS. In Figure 5, our method consistently decomposes objects into semantic elements in convex geometry for different categories. BAENet fails in chair, lamp and pistol cases, where the chair back and cushion, lamp", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3647", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0176cadd243fb8f268f6e3b6d07f89291d2e0ab84f7feb4861a0aafc0f1aab77.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodData SourceRecon Semantic
UNISURFFitted on 2D data✓X
EMSFitted on 3D data✓✓
BAENetTrained on large-scale 3D data✓✓
CvxNetTrained on large-scale 3D data✓X
ICR (Ours)Fitted on 2D data✓✓
", + "bbox": [ + 76, + 88, + 470, + 195 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6279fa2b0201ff6f72e91ad04b022ff1549fba236aedd09ac1c1dca7b9d78717.jpg", + "table_caption": [ + "Table 1. Summary of compared methods. Recon and Semantic denote capability of reconstruction and semantic decomposition." + ], + "table_footnote": [], + "table_body": "
CD↓\\IoU↑UNISURFOursBAENetEMS
Airplane0.32\\86.30.50\\79.20.91\\57.83.12\\26.8
Pistol0.53\\74.80.85\\62.51.67\\38.42.32\\32.6
Table1.57\\42.11.40\\43.22.86\\22.46.85\\18.5
Chair1.00\\49.21.29\\47.41.45\\41.75.74\\16.9
Lamp0.27\\89.60.99\\53.81.56\\38.62.76\\25.0
Car1.46\\48.51.86\\37.22.06\\31.52.36\\27.5
Mean0.86\\65.11.15\\53.91.75\\38.43.86\\24.6
", + "bbox": [ + 76, + 239, + 468, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. We measure the Chamfer Distance $(10^{-3},\\downarrow)$ and Intersection over Union $(\\uparrow)$ between the reconstructed surface and the ground-truth shapes. Our method achieves better reconstruction accuracy compared to prior primitive decomposition methods, even comparable to UNISURF, which is a state-of-the-art surface reconstruction method.", + "bbox": [ + 75, + 383, + 467, + 465 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "bulb and base, pistol barrel and handle are mixing together. Besides, Table 2 shows that BAENet achieves lower reconstruction accuracy than ours, even though it is trained on 3D data and receives 3D voxel as input. In table category, it fails to reconstruct the table leg. EMS fails in most cases with low fidelity and unreasonable decomposition. The reason for that is that EMS is based on a iterative optimization, where one primitive is fitted to the point cloud until convergence and then another primitive is fitted to the rest outliers and so on. It generally falls into a local minimum for objects that do not consist of a main stem and branches. Compared to UNISURF, we achieve comparable reconstruction accuracy in most cases. For table category, we even surpass UNISURF on modeling thin geometry such as the table legs, owing to convexity prior of our method.", + "bbox": [ + 75, + 494, + 467, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Real-World Dataset", + "text_level": 1, + "bbox": [ + 76, + 738, + 264, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "One question might be raised that if we have access to multi-view images, why not just recover its 3D representation using multi-view reconstruction methods. However, even though we could reconstruct 3D representation for one sample, it is still inefficient or even impractical to conduct reconstruction for a large-scale dataset. What's more, the common case in real-world scenarios is that we are not able to acquire a large-scale real-world datasets for ONE target object. It is demonstrated by our experiments on CO3D.", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset. CO3D [21] is a multi-view dataset collected on real-world objects with known camera intrinsic and extrinsic parameters. Each object includes a varied number of views ranging from tens to hundreds. The resolution of each image also varies from $1000 \\times 500$ to $1600 \\times 1000$ . We crop the images with a square bounding box centered at the object and then resize them to $224 \\times 224$ for training.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons. Note that prior works which are trained on a 3D shape collection are basically infeasible in this dataset, since CO3D lacks regular 3D data form (except for some objects that have a noisy point cloud generated by MVS algorithm). Therefore we compare our method with UNISURF (based on multi-view images) and EMS (based on point clouds) in terms of visual effects.", + "bbox": [ + 496, + 203, + 890, + 309 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. As shown in Figure 6, our method is able to decompose objects into convex primitives with rich semantics. The reconstruction accuracy is comparable to UNISURF in terms of visual effect. EMS generates several invalid primitives which do not match the object geometry.", + "bbox": [ + 496, + 316, + 890, + 391 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 401, + 651, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Convexity Regularization. We evaluate the effectiveness of the proposed implicit convexity regularization by removing this regularization in the neural rendering pipeline, while other settings remain the same. We show the comparisons in Figure 7. Comparing results with and without ICR, we see that ICR successfully guarantees the convexity of each primitive, which benefits consistent semantic decomposition. Although optimization without ICR could sometimes obtain higher fidelity, such as the reconstruction of wings and tails of the planes, it generally causes illogical decomposition, i.e., part of the wing is assigned to the stem primitive, and part of the chair cushion is assigned to the back primitive. Besides, we also find that with the convexity prior, the reconstructions of the thin objects are more plausible, such as the chair legs. The reason is that convex regularization encourages simple geometry. By contrast, in the case of removing ICR, the reconstruction is done by ray sampling, which could be insufficient to recover a smooth object surface. More example primitives obtained with and without ICR could be found in left and right column respectively in Figure 2.", + "bbox": [ + 496, + 425, + 890, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Convexity Controlling. We demonstrate that controlling the weight of implicit convexity regularization could achieve trade-off between primitive simplicity and fidelity. Specifically, we convert Equation 6 into $\\mathcal{L} = \\mathcal{L}_{rec} + \\sum_{i=1}^{N} \\lambda_i \\mathcal{L}_{ICR}^i$ , in which $\\lambda_i$ are tunable for individual primitive. We then apply a smaller weight $\\lambda_i$ on $L_{ICR}^i$ for those primitives which we prefer higher fidelity than simplicity, while other primitives remain still. We show some examples in Figure 8. In the bottom row, we set the $\\lambda$ of the primitives circled in red (tail of the plane and trigger of the", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3648", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0414152f0dd8b0c9732026ac5881c27c301e1d928ad399895a426a2c23554793.jpg", + "image_caption": [ + "Figure 6. Visualization of CO3D experiments. Our method is able to decompose objects into plausible shape primitives from multiview input. EMS obtains shape primitives from point clouds." + ], + "image_footnote": [], + "bbox": [ + 86, + 85, + 467, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3863a28aca959711fdca4e02f30785adadfb4a903fcdebd23fb517ee1d42118c.jpg", + "image_caption": [ + "Figure 7. The proposed Implicit Convexity Regularization (ICR) theoretically guarantees the convexity and simplicity of each primitive. Removing ICR causes unreasonable decomposition." + ], + "image_footnote": [], + "bbox": [ + 78, + 308, + 467, + 460 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7e5270e9daa822f86a216918808cc5190887a0e8f6bfadf237e38090ef94814e.jpg", + "image_caption": [ + "Figure 8. Tuning $\\lambda$ , the weight of ICR, for individual primitive could achieve trade-off between fidelity and simplicity. In the bottom row, we set the $\\lambda$ of the primitives circled in red (tail of the plane and trigger of the pistol) to 1 and others to 100. In this way we obtain a flexible primitive with higher accuracy, while other parts still preserve their semantics and simplicity. We compute the chamfer distance (CD) to evaluate the fidelity." + ], + "image_footnote": [], + "bbox": [ + 81, + 522, + 464, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "pistol) to 1 and others to 100. In this way we obtain a flexible primitive with higher accuracy, while other parts still preserve their semantics and simplicity. The adjusted primitives achieve lower chamfer distance than the vanilla ones.", + "bbox": [ + 75, + 852, + 468, + 912 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/111b5ea32dc1e13818d5b0e1f2e2cc2e9cef3fdc30ffe1154420ab593845b3c2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SVR\\SegAirplaneTableChairLamp
OccNet57.1\\—50.6\\—50.1\\—37.1\\—
CvxNet59.8\\—47.3\\—49.1\\—31.1\\—
BAENet52.4\\80.441.6\\87.045.2\\84.832.8\\63.9
Ours64.1\\69.546.7\\89.249.3\\88.337.7\\68.2
", + "bbox": [ + 500, + 88, + 893, + 180 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. We extend our proposed ICR term to a large-scale 3D training setting. We compare our method with prior works on single-view 3D reconstruction (IoU ↑) and semantic segmentation (IoU ↑) tasks. Since OccNet and CvxNet are incapable of decomposing objects into semantic parts, their segmentation performance are absent.", + "bbox": [ + 498, + 186, + 893, + 268 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Training on 3D datasets. Although our method is designed for multi-view data, we would also like to test its performance in a large-scale 3D training setting that is similar with prior primitive-learning methods. To this end, we further conduct a set of experiments on ShapeNet, in which we integrate our ICR term into an encoder-decoder network and train it on a dataset within one category. The network receives 3D voxels as input and predict SDF value of query points. The encoder is implemented as a 3D CNN, similar to prior works [3, 4], while the decoder is implemented by our primitive representation in Equ. 1. Following prior works [3], after the training is finished, we replace the 3D encoder with a 2D CNN and train it on a single-view reconstruction task while the decoder is fixed. We measure single-view reconstruction accuracy as well as semantic decomposition performance using the segmentation labels from ShapeNetPart [30]. Intersection over Union (IoU) is used as the metric for both tasks. We experiment on four categories of ShapeNet: airplane, chair, lamp and table. We follow the train-test-split in BAENet. The detailed network architecture and experiment setting is presented in the appendix. We compare our method with OccNet [14], BAENet [4] and CvxNet [5]. The results are listed in Table 3. Compared to BAENet and CvxNet, our method achieves similar or even better reconstruction accuracy in single-view reconstruction task. We found that the artifact of disappearance (see Fig. ?? table) and dilation (see Fig. ?? chair and lamp) exists in the results of BAENet and CvxNet, which is the main reason that their reconstruction accuracy is lower. Besides, our method is able to achieve better semantics decomposition. Note that all methods are validated without fine-tuning on test samples.", + "bbox": [ + 496, + 296, + 893, + 780 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 797, + 619, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose a regularization term named Implicit Convexity Regularization (ICR) for primitive decomposition. We theoretically prove that imposing constraint on the second order directional derivatives on line segments inside a shape could encourage convexity for im", + "bbox": [ + 498, + 825, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3649", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "plicit shapes represented by signed distance functions. Experiments on synthetic and real-world datasets demonstrate the superiority of our method over prior arts with respect to primitive simplicity, fidelity and semantics.", + "bbox": [ + 76, + 90, + 472, + 151 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 76, + 166, + 264, + 183 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by National Science Foundation of China (U20B2072, 61976137). This work was also partially supported by Grant YG2021ZD18 from Shanghai Jiao Tong University Medical Engineering Cross Research.", + "bbox": [ + 76, + 191, + 468, + 252 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 266, + 173, + 282 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford University — Princeton University — Toyota Technological Institute at Chicago, 2015.", + "[2] Chao Chen, Yu-Shen Liu, and Zhizhong Han. Latent partition implicit with surface codes for 3d representation. In European Conference on Computer Vision, pages 322-343. 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In Proceedings of the IEEE International Conference on Computer Vision, pages 900-909, 2017." + ], + "bbox": [ + 78, + 90, + 468, + 823 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "3651", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Shape Primitives via Implicit Convexity Regularization/4387a009-eca0-4928-920d-1473c95da518_model.json b/2023/Learning Shape Primitives via Implicit Convexity Regularization/4387a009-eca0-4928-920d-1473c95da518_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5f7a38e9119b30c14006f7c83d8906af7d9dce75 --- /dev/null +++ b/2023/Learning Shape Primitives via Implicit Convexity Regularization/4387a009-eca0-4928-920d-1473c95da518_model.json @@ -0,0 +1,1848 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.158, + 0.131, + 0.815, + 0.154 + ], + "angle": 0, + "content": "Learning Shape Primitives via Implicit Convexity Regularization" + }, + { + "type": "text", + "bbox": [ + 0.131, + 0.18, + 0.846, + 0.235 + ], + "angle": 0, + "content": "Xiaoyang Huang1 Yi Zhang1 Kai Chen1 Teng Li2 Wenjun Zhang1 Bingbing Ni1,3* \n1Shanghai Jiao Tong University, Shanghai 200240, China \n2Anhui University \n3USC-SJTU Institute of Cultural and Creative Industry" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.237, + 0.658, + 0.253 + ], + "angle": 0, + "content": "{huangxiaoyang, nibingbing}@sjtu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.286, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.728 + ], + "angle": 0, + "content": "Shape primitives decomposition has been an important and long-standing task in 3D shape analysis. Prior arts heavily rely on 3D point clouds or voxel data for shape primitives extraction, which are less practical in real-world scenarios. This paper proposes to learn shape primitives from multi-view images by introducing implicit surface rendering. It is challenging since implicit shapes have a high degree of freedom, which violates the simplicity property of shape primitives. In this work, a novel regularization term named Implicit Convexity Regularization (ICR) imposed on implicit primitive learning is proposed to tackle this problem. We start with the convexity definition of general 3D shapes, and then derive the equivalent expression for implicit shapes represented by signed distance functions (SDFs). Further, instead of directly constraining the output SDF values which cause unstable optimization, we alternatively impose constraint on second order directional derivatives on line segments inside the shapes, which proves to be a tighter condition for 3D convexity. Implicit primitives constrained by the proposed ICR are combined into a whole object via softmax-weighted-sum operation over all primitive SDFs. Experiments on synthetic and real-world datasets show that our method is able to decompose objects into simple and reasonable shape primitives without the need of segmentation labels or 3D data. Code and data is publicly available in https://github.com/seanywang0408/ICR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.758, + 0.21, + 0.773 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.785, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Shape primitives extraction aims at decomposing a complex object into simple geometry. It has been a fundamental task in 3D shape representation [7] which imitates human visual perception, abstraction and understanding of real-world objects, and also facilitates industrial manufacturing which fabricates complex objects via component as" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.284, + 0.889, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.394, + 0.893, + 0.465 + ], + "angle": 0, + "content": "Figure 1. We propose a shape primitive decomposition method from multi-view images with a novel Implicit Convexity Regularization scheme (ICR), which theoretically guarantees the convexity of implicit primitives. Our method generates shape primitives that satisfy simplicity, semantics preserving and fidelity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.491, + 0.893, + 0.794 + ], + "angle": 0, + "content": "seembling. There are several fundamental properties for shape primitives: i) simplicity, which means that each primitive should be composed of simple geometry; ii) semantics, which means that the decomposition should reveal the semantic parts of an object; iii) fidelity, which means that the primitives should fit the original object as close as possible. Prior methods using parameterized shapes as primitive basis, such as cuboids [11] and superquadrics [13], could guarantee the simplicity property. However, parameterized primitives are less expressive due to their limited pre-defined geometry, which generally cause low fidelity. Though leveraging the flexibility of implicit functions to represent primitives could achieve higher fidelity, it also comes with a drawback that the semantic information generally diminishes during decomposition [5, 9]. Most importantly, all prior works require 3D data either for single-object fitting or multi-object learning. These data are not accessible in many cases, which makes them unpractical in real-world applications. In this work, we address this problem by learning implicit primitives from multi-view images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Learning implicit primitives from multi-view images is an even more challenging task. It is non-trivial to introduce prior implicit primitives [9, 19] into a neural rendering pipeline due to their specific modeling. Besides, implicit shapes without explicit regularization has a high degree of freedom, which could hardly meet the requirements of primitives. To this end, we propose a convex regulariza" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.227, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3642" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.272 + ], + "angle": 0, + "content": "tion term imposed on a common signed distance function (SDF), which could be readily integrated into any implicit surface reconstruction pipeline, as shown in Figure 1. Convexity is a plausible property for primitives. First, it is a subconcept of simplicity, that is, a convex shape is generally regarded as simple (Figure 2). Second, most semantic parts are convex (see Figure 5 for example). Therefore convexity regularization benefits semantics preservation in primitive decomposition. Lastly, convexity is welcomed in some industrial manufacturing process, such as 3D printing and furniture making, in which convex parts are first fabricated respectively and then adhered into one object." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.274, + 0.468, + 0.469 + ], + "angle": 0, + "content": "To derive our implicit convexity regularization, we first start with the general definition of 3D convexity, which is formulated on arbitrary two points inside a shape. Then we tailor this definition to an implicit shape represented by a signed distance function (SDF) without loss of generality. This conversion also allows more lightweight computation. Further, to avoid the training instability and oscillation caused by direct constraint on the output SDF value, we tighten the convexity condition by alternatively constraining the second order directional derivatives along a line segment. We theoretically prove that this constraint is a sufficient condition for convexity. Besides, using the Finite Difference Method could easily implement this constraint." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.471, + 0.468, + 0.636 + ], + "angle": 0, + "content": "With the proposed implicit convexity regularization, each primitive is guaranteed to be convex. We combine all primitives into a whole object by conducting softmax-weighted-sum operation over all primitive SDFs and deriving the object SDF. The object SDF is incorporated into a common implicit surface rendering pipeline [17], allowing primitive decomposition from multi-view images. We experiment on both synthetic and real-world datasets, demonstrating the simplicity, semantics and fidelity of our generated primitives, especially on CO3D [21] dataset where prior primitive methods are infeasible without 3D data." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.654, + 0.216, + 0.669 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.679, + 0.307, + 0.694 + ], + "angle": 0, + "content": "2.1. Parameterized Primitives" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.704, + 0.468, + 0.884 + ], + "angle": 0, + "content": "Cuboids with scaling, rotation and translation are first used as an abstraction of object parts. 3DPRNN [33] uses a recurrent network to generate cuboid primitives step-by-step. Tulsian et al. [24] obtain a consistent parsing across objects based on cuboids assembling. Niu et al. [16] infer hierarchical cuboid structure from single images. Lin et al. [12] propose a reinforcement learning algorithm to learn primitive decomposing policies. Kluger et al. [11] expand cuboids fitting from simple objects to more complex indoor scenes. Although cuboids decomposition could produce compact and semantic primitives, it also cause low fidelity due to its singular geometry." + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Another line of shape primitives is super-quadrics [20]," + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.332 + ], + "angle": 0, + "content": "which are more expressive than quadrics using 6 control parameters. Paschalidou et al. [18] decompose objects in to a hierarchical binary tree of super-quadrics, providing shape abstraction in different levels. EMS [13] aims at extraction super-quadric primitives from a noisy point cloud from a probabilistic view, which makes it more robust to outliers. Besides super-quadrics, ParseNet [23] proposes to use B-spline, cylinder and cones as primitives to reconstruct continuous surface from point clouds. Genova et al. [6] learn category-specific templates based on scaled axis-aligned anisotropic 3D Gaussian prior. ExtrudeNet [22] encodes point clouds into several primitives extruded from 2D Bezier curves that could be integrated into modern CAD software. Although these parameterized primitives provide higher fidelity than cuboids, it still does not meet the complexity of real-world objects." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.334, + 0.89, + 0.469 + ], + "angle": 0, + "content": "Constructive Solid Geometry (CSG) Tree [8, 32, 31] uses iterative boolean operators including union and intersection to construct convex or concave geometry, which is well-suited in computer-aided design (CAD). Although it still uses singular primitives like spheres and rectangles, CSG Tree is able to reconstruct accurate geometry as the iterative boolean operation gets deeper. However, it comes with a drawback that objects are eventually divided into patches in pieces with little semantic information preserved." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.483, + 0.679, + 0.498 + ], + "angle": 0, + "content": "2.2. Implicit Primitives" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.507, + 0.89, + 0.853 + ], + "angle": 0, + "content": "BSPNet [3] and CvxNet [5] both use hyperplanes to construct a convex polytype and then assemble these convexes into a non-convex shape. Although these two methods are able to derive convex primitives like ours, the computation and storage cost grow quadratically as the number of hyperplanes increases, which makes it unsuitable for neural rendering in a multi-view scenario. Latent Partition Implicit [2] proposes shape partition in latent space for accurate modeling. Neural Star Domain (NSD) [9] models each primitive as a continuous function defined on a sphere, ensuring the simplicity property of primitives. However it still shares the deficiency of BSPNet and CvxNet that the semantic parts are broken into multiple primitives, as shown in Figure ?? Similar to NSD, Neural Parts [19] define homeomorphic mappings between spheres and primitives, which is able to generate various primitives with single connectivity. Nonetheless it is non-trivial to apply such a homeomorphic mapping in a neural rendering pipeline. Another relevant work to ours is BAENet [4], which uses a branched decoder to learn recurring parts in a shape collection. Although it is capable of producing accurate semantic segmentation results given a ground-truth shape, its reconstruction fidelity is notably inferior to ours." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.856, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Moreover, all the above methods strongly rely on 3D data input for primitive decomposition, most of which even require a large set of shape collection within the same cat" + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.514, + 0.956 + ], + "angle": 0, + "content": "3643" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.469, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.203, + 0.471, + 0.248 + ], + "angle": 0, + "content": "Figure 2. Convexity is a subconcept of simplicity, since a convex shape is generally regarded as simple, while a non-convex shape tends to be more complex." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.471, + 0.334 + ], + "angle": 0, + "content": "egory for training, such as ShapeNet [1] or ModelNet [26], which makes them less practical in real-world scenarios. Our method derives implicit convex primitives from multiview images with well-defined semantics." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.344, + 0.327, + 0.361 + ], + "angle": 0, + "content": "2.3. Implicit Surface Rendering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.473, + 0.551 + ], + "angle": 0, + "content": "Recently, implicit neural representations have advanced surface reconstruction from multi-view images. DVR [15] proposes a differentiable rendering formulation for implicit surface and texture representations. IDR [29] approximates the light reflected from a 3D shape represented as the zero level set of a neural network. UNISURF [17] presents a unified framework for implicit surfaces and radiance fields, with the goal of reconstructing nontransparent objects. NeuS [25] develops a volume rendering method to train a neural SDF representation. Yariv et al. [28] define the volume density function as Laplace's cumulative distribution function applied to a SDF for surface rendering." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.566, + 0.214, + 0.584 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.655 + ], + "angle": 0, + "content": "We first demonstrate the derivation of the proposed implicit convexity regularization (ICR) scheme, and then explain the application of primitive fitting with ICR in a neural rendering pipeline." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.377, + 0.681 + ], + "angle": 0, + "content": "3.1. Implicit Convexity Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.471, + 0.854 + ], + "angle": 0, + "content": "It is challenging to preserve simplicity in implicit primitives learning from multi-view images. In prior arts, there was little discussion on the simplicity of implicit shapes represented by signed distance functions. In this work, we investigate this problem in the view of convexity. A convex shape is the boundary of a convex set. We show some examples of convex and non-convex shapes in Figure 2. Intuitively, convexity is a subconcept of simplicity, since a convex shape is generally regarded as simple, while a nonconvex shape tends to be more complex. Mathematically, convexity could be defined as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Theorem 1 A shape \\( C \\) is convex \\(\\iff\\) For arbitrary two points located inside the shape \\( C \\), the convex combination of" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.087, + 0.889, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.432, + 0.895, + 0.557 + ], + "angle": 0, + "content": "Figure 3. We start with the general definition of convexity in Theorem 1. Then we convert the definition to an implicit shape represented by a signed distance function (SDF), which directly constrains the output SDF value. Lastly, to address the training instability issue in Theorem 2, we alternatively impose constraint on the second order directional derivatives, which proves to be a tighter condition of Theorem 2. The computation of second order directional derivatives could be easily implemented with Finite Difference Method." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.893, + 0.613 + ], + "angle": 0, + "content": "the two points are also located inside the shape, i.e., for any \\( x_{1}, x_{2} \\in C \\) and \\( 0 \\leq \\theta \\leq 1 \\), we have \\( \\theta x_{1} + (1 - \\theta)x_{2} \\in C \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.894, + 0.713 + ], + "angle": 0, + "content": "It is computation-inefficient to directly apply the vanilla convexity formulation to an implicit function, since it requires queries of arbitrary two points inside the shape. To adapt the convexity definition to a shape represented by an SDF with higher efficiency, we convert the above definition to a surface-based formulation:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.894, + 0.817 + ], + "angle": 0, + "content": "Theorem 2 A shape \\( C \\) represented by an signed distance function \\( f \\) is convex \\( \\iff \\) For arbitrary two points that are located on the surface of the shape, the convex combination of these two points is located inside the shape, i.e., for any \\( x_1, x_2 \\in \\{x | f(x) = 0\\} \\) and \\( 0 < \\theta < 1 \\), we have \\( f(\\theta x_1 + (1 - \\theta) x_2) < 0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "It is self-evident that Theorem 2 is equivalent to Theorem 1 for a SDF-based shape. It also ease the sampling process since only line segment between surface points are evaluated. In practice, we first randomly sample a set of rays of arbitrary starting points and directions, and retrieve" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3644" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "the first and last intersection point \\( x_{1}, x_{2} \\) against the shape by a root-finding algorithm. Those rays which do not intersect with the shape are ignored. Next we sample a set of points which is the convex combination of \\( x_{1}, x_{2} \\), i.e., points located on the line segment between \\( x_{1}, x_{2} \\). Lastly we penalize the positive SDF values of these points, meaning that they are outside the shape." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.198, + 0.471, + 0.334 + ], + "angle": 0, + "content": "However, we empirically find that directly imposing constraint on the output SDF values could cause serious training instability and oscillation, or even collapse. The reason is that there is a shortcut for the SDF function to satisfy this constraint, that is to scale up the SDF value of the whole function, which only needs to scale up the value of the final layer of the MLP. As an alternative, we propose to impose constraint on the second order directional derivative along the ray direction in the implicit field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.471, + 0.454 + ], + "angle": 0, + "content": "Theorem 3 A shape \\( C \\) represented by an signed distance function \\( f \\) is convex \\( \\Longleftarrow \\) For arbitrary two points \\( x_{1}, x_{2} \\) located on the surface of the shape, we have positive second order directional derivative along the direction \\( x_{2} - x_{1} \\) on the convex combination of \\( x_{1}, x_{2} \\), i.e., for any \\( x_{1}, x_{2} \\in \\{x | f(x) = 0\\} \\), \\( d = x_{2} - x_{1} \\) and \\( 0 < \\theta < 1 \\), we have \\( \\frac{\\partial^2 f}{\\partial^2 d} (\\theta x_1 + (1 - \\theta)x_2) \\geq 0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.642 + ], + "angle": 0, + "content": "Proof. If the condition in Theorem 3 is satisfied, it means that the 1D function \\( f_{SDF}(x_0) \\) w.r.t \\( x_0 = \\theta x_1 + (1 - \\theta)x_2 \\), \\( 0 < \\theta < 1 \\) is a convex function. By the definition of convex functions, we have \\( f(x_0) < \\theta f(x_1) + (1 - \\theta)f(x_2) = \\theta \\times 0 + (1 - \\theta) \\times 0 = 0 \\). Through Theorem 2, we know shape \\( C \\) is convex. Constraint on second order directional derivatives is a tighter condition for convexity than constraint on SDF values. Intuitively, when the second order directional derivatives are positive everywhere between \\( x_1, x_2 \\), we have a monotonically increasing first order directional derivative along the line segment, meaning that no inflection point exists in the interval." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.471, + 0.794 + ], + "angle": 0, + "content": "Based on Theorem 3, we encourage convexity by penalizing negative second order directional derivatives between \\( x_{1}, x_{2} \\). However, differentiating second order gradient of a neural network involves extremely intense computation. To this end, we replace accurate gradient derivation with Finite Difference, in which we view the continuous SDF as a discrete function via uniform sampling between the two intersection points \\( x_{1}, x_{2} \\). The detailed algorithm is presented in Algorithm 1. We also visualize the convexity defined by the three theorems using a 2D case in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.462, + 0.818 + ], + "angle": 0, + "content": "3.2. Learning Primitives from Multi-View Images" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Primitive Representations. We represent implicit shape primitives with a set of general signed distance functions (SDFs). Given a 3D point \\(\\mathbf{p}\\) as input, we use a multilayer perceptron (MLP) \\(f\\) to predict the signed distance \\(SDF_{primi}(\\mathbf{p})\\) from the point \\(\\mathbf{p}\\) to the object surface. The" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.859, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Implicit Convexity Regularization (ICR)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.109, + 0.757, + 0.124 + ], + "angle": 0, + "content": "1: Input: signed distance function \\( f \\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.124, + 0.753, + 0.139 + ], + "angle": 0, + "content": "2: Output: convexity penalty \\(\\mathcal{L}_{ICR}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.14, + 0.892, + 0.168 + ], + "angle": 0, + "content": "3: Generate a ray with random starting points and directions;" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.169, + 0.892, + 0.199 + ], + "angle": 0, + "content": "4: Retrieve the first and last intersection points \\( x_{1}, x_{2} \\) by root-finding algorithm;" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.2, + 0.892, + 0.231 + ], + "angle": 0, + "content": "5: Uniformly sample \\(\\mathbf{K}\\) points between \\(x_{1}, x_{2}\\): \\(\\{p_{j} = \\theta_{j}x_{1} + (1 - \\theta_{j})x_{2} | \\theta_{j} = \\frac{j}{K + 1}, j = 1, 2, \\dots, K\\}\\);" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.231, + 0.892, + 0.26 + ], + "angle": 0, + "content": "6: Query the SDF values of the sampled points: \\(\\{f(p_j)|j = 1,2,\\dots,K\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.26, + 0.892, + 0.291 + ], + "angle": 0, + "content": "7: Compute 1st order direction derivative with finite difference: \\(\\{\\nabla f = f(p_j) - f(p_{j - 1})|j = 2,\\dots,K\\}\\);" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.291, + 0.892, + 0.321 + ], + "angle": 0, + "content": "8: Compute 2rd order direction derivative with finite difference: \\(\\{\\nabla^2 f = \\nabla f(p_j) - \\nabla f(p_{j-1})|j = 3,\\dots,K\\}\\);" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.321, + 0.867, + 0.336 + ], + "angle": 0, + "content": "9: Compute the penalty term \\( L = \\sum max(-\\nabla^2 f, 0) \\);" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.336, + 0.624, + 0.35 + ], + "angle": 0, + "content": "10: return \\(\\mathcal{L}_{ICR}\\)" + }, + { + "type": "list", + "bbox": [ + 0.508, + 0.109, + 0.892, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.895, + 0.563 + ], + "angle": 0, + "content": "signed distance is positive when the point is located outside of the surface, while the signed distance is negative when the point is located inside of the surface. To unify the primitives into a complete object, one could take the minimal value over all primitive SDFs as the final object SDF. However, doing so would block the gradient flow from the object SDF to the subminimal primitive SDFs, which leads to suboptimal convergence. To this end, we conduct a soft minimization, composed of a softmax and a weighted sum operation. Formally, suppose each primitive SDF is implemented as a MLP network \\( f_{i} \\), the object signed distance of point \\( \\mathbf{p} \\) could be computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.574, + 0.892, + 0.657 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} S D F _ {p r i m i} ^ {i} (\\mathbf {p}) = f _ {i} (\\mathbf {p}), \\\\ \\omega_ {i} = \\operatorname {s o f t m a x} _ {N} (- \\beta \\cdot S D F _ {p r i m i} ^ {i} (\\mathbf {p})), \\tag {1} \\\\ S D F _ {o b j} (\\mathbf {p}) = \\sum_ {i = 1} ^ {N} \\omega_ {i} \\cdot S D F _ {p r i m i} ^ {i} (\\mathbf {p}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.892, + 0.715 + ], + "angle": 0, + "content": "where \\(\\beta\\) is the scaling temperature (set to 10 in our experiments) in softmax operation, \\(\\omega_{i}\\) denotes the weight of \\(i\\)th primitive and \\(N\\) is the number of the primitives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Surface Rendering. Considering the difficulty of acquiring 3D data in application, we aim at learning the implicit primitives from multi-view images. Although prior works such as BSPNet [3] and CvxNet [5] proposes 3D convexity representation based on hyper-planes, these representations are infeasible in current neural rendering pipelines, hindering the acquisition of convexity primitives from multi-view data. One key contribution of our method is that we extend convexity primitives to a implicit surface distance function, which is the common 3D representation of neural rendering pipelines." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3645" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.098, + 0.877, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.287, + 0.894, + 0.358 + ], + "angle": 0, + "content": "Figure 4. Our network consists of N primitive MLPs and one color MLP. Each primitive MLP outputs an SDF value and a geometry latent code of the primitive from the input \\(\\mathbf{p}\\). The primitive SDF values and latent codes go through a softmax-weighted-sum layer to obtain the object SDF and latent code, which are then respectively processed by a sigmoid layer and a color MLP. The obtained volume density \\(\\sigma\\) and RGB are applied in a standard implicit surface volume rendering method. The loss is computed by the weighted sum of reconstruction error and Implicit Convexity Regularization on each primitive." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.471, + 0.457 + ], + "angle": 0, + "content": "Specifically, we integrate the implicit primitives into a neural rendering pipeline based on UNISURF [17]. To this end, we first extend the pirmitive MLPs in Sec 3.2 to additionally output a geometry latent code except for SDF value in the final layer, such that" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.466, + 0.47, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\left[ S D F _ {p r i m i} ^ {i} (\\mathbf {p}), L _ {p r i m i} ^ {i} (\\mathbf {p}) \\right] = f _ {i} (\\mathbf {p}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.583 + ], + "angle": 0, + "content": "where \\( L_{primi}^{i}(\\mathbf{p}) \\) is the latent code of \\( \\mathbf{p} \\). Similar to \\( SDF_{obj}(\\mathbf{p}) \\), the object latent code \\( L_{obj}(\\mathbf{p}) \\) is obtained by the softmax-weighted-sum over all primitive latent codes. We further implement a color MLP which receives the object latent code as input and predicts the RGB value \\( \\mathbf{c} \\) of \\( \\mathbf{p} \\). Then we apply the volume rendering as follows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.675 + ], + "angle": 0, + "content": "For a ray \\(\\mathbf{r}\\) starting from the camera position to the pixel location, we first retrieve the surface point \\(\\mathbf{x}_s\\) defined by \\(SDF_{obj}(\\mathbf{x}_s) = 0\\) using a root-finding algorithm. Then, we sample \\(N\\) points \\(\\mathbf{x}_j\\) along ray \\(\\mathbf{r}\\) within a interval around \\(\\mathbf{x}_s\\). We infer the object SDF value for each sample and convert it to volume density \\(\\sigma_j\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.683, + 0.47, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {j} = \\operatorname {S i g m o i d} (- \\mu \\cdot S D F _ {o b j} (\\mathbf {x} _ {j})), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.708, + 0.47, + 0.769 + ], + "angle": 0, + "content": "where \\(\\mu\\) is a hyper-parameter that controls the sharpness of density distribution (set to 25 in all our experiments). The ray color is then obtained by the following volume rendering equation:" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.776, + 0.47, + 0.82 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (\\mathbf {r}) = \\sum_ {j = 1} ^ {N} \\sigma_ {j} \\prod_ {k < j} (1 - \\sigma_ {k}) \\mathbf {c} _ {j}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.827, + 0.47, + 0.859 + ], + "angle": 0, + "content": "The reconstruction loss is computed over all sampled rays \\(\\mathbf{r} \\in \\mathcal{R}\\), with \\(C(\\mathbf{r})\\) as the ground-truth pixel color:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.868, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\hat {C} (\\mathbf {r}) - C (\\mathbf {r}) \\right\\| ^ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.382, + 0.892, + 0.428 + ], + "angle": 0, + "content": "For more details on the neural rendering process, please refer to UNISURF [17]. Overall, we train our model with the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.438, + 0.892, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {r e c} + \\lambda \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {I C R} ^ {i}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.567 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{ICR}^i\\) is the proposed implicit convexity regularization derived in Algorithm 1, which is imposed on each primitive, and \\(\\lambda\\) is the weighting hyper-parameter. Since \\(\\mathcal{L}_{ICR}\\) is generally a small value, we set \\(\\lambda\\) to 100 in our experiments. Illustration of the pipeline is presented in Figure 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.661, + 0.591 + ], + "angle": 0, + "content": "3.3. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.75 + ], + "angle": 0, + "content": "In all our experiments, each primitive SDF is implemented as a 4-layer MLP, with a skip connection from the input to the third layer. The color MLP also contains 4 layers. All layers have 64 hidden units. The input coordinates are first encoded by a sinusoidal embedding layer with \\( L = 6 \\), as done in UNISURF [17]. We use the Adam optimizer [10] with an initial learning rate of \\( 10^{-5} \\). The learning rate is multiplied by 0.5 in 4,000th and 5,000th iteration. For each iteration, we sample 1,024 rays for volume rendering. The model is trained for 10,000 iterations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.763, + 0.634, + 0.78 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.671, + 0.803 + ], + "angle": 0, + "content": "4.1. Synthetic Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Dataset. ShapeNet [1] is a shape collection composed of multiple categories. We conduct experiments on six categories including airplane, car, chair, lamp, table and pistol. We evaluate our method and prior works on randomly-selected 20 shapes for each category. For our method and UNISURF, we use the multi-view images rendered by" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3646" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.466, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.472, + 0.097, + 0.889, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.596, + 0.893, + 0.625 + ], + "angle": 0, + "content": "Figure 5. We visualize the ShapeNet results of our method and prior works, including BAENet, EMS and UNISURF. Our method achieves notably better decomposition and fidelity than BAENet and EMS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.47, + 0.695 + ], + "angle": 0, + "content": "DISN [27], which includes 36 views for each object with known camera intrinsic and extrinsic parameters. The images are rendered in \\(224 \\times 224\\) resolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Comparisons. We compare our method with the following works. i) BAENet [4]: BAENet is a learning-based primitive decomposition method that is trained on a shape collection within a category. It receives 3D voxel as input and predict an implicit field for each primitive. We follow its default settings which train the models on the complete collection for each categories without segmentation supervision, e.g. 2,690 objects for airplane. ii) EMS [13]: EMS is the state-of-the-art parameterized primitive decomposition method which derives superquadric primitives from a point cloud via a robust optimization algorithm. We follow its default setting in multi-superquadric optimization, and feed the ground-truth point cloud as input data. iii)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.895, + 0.801 + ], + "angle": 0, + "content": "UNISURF [17]: UNISURF is a state-of-the-art implicit surface reconstruction method which derive the implicit field of an object from multi-view images. We include UNISURF for comparisons with a standard implicit surface reconstruction method in terms of fidelity. The above methods are summarized in Table 1. We use two metrics for evaluation, including Chamfer Distance (CD) and Intersection over Union (IoU). The quantitative results are reported in Table 2. We also visualize the meshes in Figure 5, with different colors for different primitives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Results. Figure 5 and Table 2 show that our method achieves notably better decomposition and fidelity than BAENet and EMS. In Figure 5, our method consistently decomposes objects into semantic elements in convex geometry for different categories. BAENet fails in chair, lamp and pistol cases, where the chair back and cushion, lamp" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3647" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.472, + 0.196 + ], + "angle": 0, + "content": "
MethodData SourceRecon Semantic
UNISURFFitted on 2D data✓X
EMSFitted on 3D data✓✓
BAENetTrained on large-scale 3D data✓✓
CvxNetTrained on large-scale 3D data✓X
ICR (Ours)Fitted on 2D data✓✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.202, + 0.468, + 0.23 + ], + "angle": 0, + "content": "Table 1. Summary of compared methods. Recon and Semantic denote capability of reconstruction and semantic decomposition." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.241, + 0.47, + 0.378 + ], + "angle": 0, + "content": "
CD↓\\IoU↑UNISURFOursBAENetEMS
Airplane0.32\\86.30.50\\79.20.91\\57.83.12\\26.8
Pistol0.53\\74.80.85\\62.51.67\\38.42.32\\32.6
Table1.57\\42.11.40\\43.22.86\\22.46.85\\18.5
Chair1.00\\49.21.29\\47.41.45\\41.75.74\\16.9
Lamp0.27\\89.60.99\\53.81.56\\38.62.76\\25.0
Car1.46\\48.51.86\\37.22.06\\31.52.36\\27.5
Mean0.86\\65.11.15\\53.91.75\\38.43.86\\24.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.384, + 0.468, + 0.466 + ], + "angle": 0, + "content": "Table 2. We measure the Chamfer Distance \\((10^{-3},\\downarrow)\\) and Intersection over Union \\((\\uparrow)\\) between the reconstructed surface and the ground-truth shapes. Our method achieves better reconstruction accuracy compared to prior primitive decomposition methods, even comparable to UNISURF, which is a state-of-the-art surface reconstruction method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.468, + 0.722 + ], + "angle": 0, + "content": "bulb and base, pistol barrel and handle are mixing together. Besides, Table 2 shows that BAENet achieves lower reconstruction accuracy than ours, even though it is trained on 3D data and receives 3D voxel as input. In table category, it fails to reconstruct the table leg. EMS fails in most cases with low fidelity and unreasonable decomposition. The reason for that is that EMS is based on a iterative optimization, where one primitive is fitted to the point cloud until convergence and then another primitive is fitted to the rest outliers and so on. It generally falls into a local minimum for objects that do not consist of a main stem and branches. Compared to UNISURF, we achieve comparable reconstruction accuracy in most cases. For table category, we even surpass UNISURF on modeling thin geometry such as the table legs, owing to convexity prior of our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.739, + 0.265, + 0.754 + ], + "angle": 0, + "content": "4.2. Real-World Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "One question might be raised that if we have access to multi-view images, why not just recover its 3D representation using multi-view reconstruction methods. However, even though we could reconstruct 3D representation for one sample, it is still inefficient or even impractical to conduct reconstruction for a large-scale dataset. What's more, the common case in real-world scenarios is that we are not able to acquire a large-scale real-world datasets for ONE target object. It is demonstrated by our experiments on CO3D." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Dataset. CO3D [21] is a multi-view dataset collected on real-world objects with known camera intrinsic and extrinsic parameters. Each object includes a varied number of views ranging from tens to hundreds. The resolution of each image also varies from \\(1000 \\times 500\\) to \\(1600 \\times 1000\\). We crop the images with a square bounding box centered at the object and then resize them to \\(224 \\times 224\\) for training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.204, + 0.892, + 0.31 + ], + "angle": 0, + "content": "Comparisons. Note that prior works which are trained on a 3D shape collection are basically infeasible in this dataset, since CO3D lacks regular 3D data form (except for some objects that have a noisy point cloud generated by MVS algorithm). Therefore we compare our method with UNISURF (based on multi-view images) and EMS (based on point clouds) in terms of visual effects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.317, + 0.892, + 0.392 + ], + "angle": 0, + "content": "Results. As shown in Figure 6, our method is able to decompose objects into convex primitives with rich semantics. The reconstruction accuracy is comparable to UNISURF in terms of visual effect. EMS generates several invalid primitives which do not match the object geometry." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.402, + 0.653, + 0.419 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.892, + 0.743 + ], + "angle": 0, + "content": "Effectiveness of Convexity Regularization. We evaluate the effectiveness of the proposed implicit convexity regularization by removing this regularization in the neural rendering pipeline, while other settings remain the same. We show the comparisons in Figure 7. Comparing results with and without ICR, we see that ICR successfully guarantees the convexity of each primitive, which benefits consistent semantic decomposition. Although optimization without ICR could sometimes obtain higher fidelity, such as the reconstruction of wings and tails of the planes, it generally causes illogical decomposition, i.e., part of the wing is assigned to the stem primitive, and part of the chair cushion is assigned to the back primitive. Besides, we also find that with the convexity prior, the reconstructions of the thin objects are more plausible, such as the chair legs. The reason is that convex regularization encourages simple geometry. By contrast, in the case of removing ICR, the reconstruction is done by ray sampling, which could be insufficient to recover a smooth object surface. More example primitives obtained with and without ICR could be found in left and right column respectively in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Convexity Controlling. We demonstrate that controlling the weight of implicit convexity regularization could achieve trade-off between primitive simplicity and fidelity. Specifically, we convert Equation 6 into \\(\\mathcal{L} = \\mathcal{L}_{rec} + \\sum_{i=1}^{N} \\lambda_i \\mathcal{L}_{ICR}^i\\), in which \\(\\lambda_i\\) are tunable for individual primitive. We then apply a smaller weight \\(\\lambda_i\\) on \\(L_{ICR}^i\\) for those primitives which we prefer higher fidelity than simplicity, while other primitives remain still. We show some examples in Figure 8. In the bottom row, we set the \\(\\lambda\\) of the primitives circled in red (tail of the plane and trigger of the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3648" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.087, + 0.468, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.25, + 0.472, + 0.294 + ], + "angle": 0, + "content": "Figure 6. Visualization of CO3D experiments. Our method is able to decompose objects into plausible shape primitives from multiview input. EMS obtains shape primitives from point clouds." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.309, + 0.468, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.464, + 0.47, + 0.507 + ], + "angle": 0, + "content": "Figure 7. The proposed Implicit Convexity Regularization (ICR) theoretically guarantees the convexity and simplicity of each primitive. Removing ICR causes unreasonable decomposition." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.523, + 0.465, + 0.727 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.732, + 0.473, + 0.83 + ], + "angle": 0, + "content": "Figure 8. Tuning \\(\\lambda\\), the weight of ICR, for individual primitive could achieve trade-off between fidelity and simplicity. In the bottom row, we set the \\(\\lambda\\) of the primitives circled in red (tail of the plane and trigger of the pistol) to 1 and others to 100. In this way we obtain a flexible primitive with higher accuracy, while other parts still preserve their semantics and simplicity. We compute the chamfer distance (CD) to evaluate the fidelity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.853, + 0.47, + 0.914 + ], + "angle": 0, + "content": "pistol) to 1 and others to 100. In this way we obtain a flexible primitive with higher accuracy, while other parts still preserve their semantics and simplicity. The adjusted primitives achieve lower chamfer distance than the vanilla ones." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.895, + 0.181 + ], + "angle": 0, + "content": "
SVR\\SegAirplaneTableChairLamp
OccNet57.1\\—50.6\\—50.1\\—37.1\\—
CvxNet59.8\\—47.3\\—49.1\\—31.1\\—
BAENet52.4\\80.441.6\\87.045.2\\84.832.8\\63.9
Ours64.1\\69.546.7\\89.249.3\\88.337.7\\68.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.187, + 0.895, + 0.27 + ], + "angle": 0, + "content": "Table 3. We extend our proposed ICR term to a large-scale 3D training setting. We compare our method with prior works on single-view 3D reconstruction (IoU ↑) and semantic segmentation (IoU ↑) tasks. Since OccNet and CvxNet are incapable of decomposing objects into semantic parts, their segmentation performance are absent." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.895, + 0.781 + ], + "angle": 0, + "content": "Training on 3D datasets. Although our method is designed for multi-view data, we would also like to test its performance in a large-scale 3D training setting that is similar with prior primitive-learning methods. To this end, we further conduct a set of experiments on ShapeNet, in which we integrate our ICR term into an encoder-decoder network and train it on a dataset within one category. The network receives 3D voxels as input and predict SDF value of query points. The encoder is implemented as a 3D CNN, similar to prior works [3, 4], while the decoder is implemented by our primitive representation in Equ. 1. Following prior works [3], after the training is finished, we replace the 3D encoder with a 2D CNN and train it on a single-view reconstruction task while the decoder is fixed. We measure single-view reconstruction accuracy as well as semantic decomposition performance using the segmentation labels from ShapeNetPart [30]. Intersection over Union (IoU) is used as the metric for both tasks. We experiment on four categories of ShapeNet: airplane, chair, lamp and table. We follow the train-test-split in BAENet. The detailed network architecture and experiment setting is presented in the appendix. We compare our method with OccNet [14], BAENet [4] and CvxNet [5]. The results are listed in Table 3. Compared to BAENet and CvxNet, our method achieves similar or even better reconstruction accuracy in single-view reconstruction task. We found that the artifact of disappearance (see Fig. ?? table) and dilation (see Fig. ?? chair and lamp) exists in the results of BAENet and CvxNet, which is the main reason that their reconstruction accuracy is lower. Besides, our method is able to achieve better semantics decomposition. Note that all methods are validated without fine-tuning on test samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.62, + 0.815 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "In this work, we propose a regularization term named Implicit Convexity Regularization (ICR) for primitive decomposition. We theoretically prove that imposing constraint on the second order directional derivatives on line segments inside a shape could encourage convexity for im" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3649" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.152 + ], + "angle": 0, + "content": "plicit shapes represented by signed distance functions. Experiments on synthetic and real-world datasets demonstrate the superiority of our method over prior arts with respect to primitive simplicity, fidelity and semantics." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.167, + 0.265, + 0.184 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.192, + 0.47, + 0.253 + ], + "angle": 0, + "content": "This work was supported by National Science Foundation of China (U20B2072, 61976137). This work was also partially supported by Grant YG2021ZD18 from Shanghai Jiao Tong University Medical Engineering Cross Research." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.267, + 0.174, + 0.283 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.292, + 0.47, + 0.389 + ], + "angle": 0, + "content": "[1] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford University — Princeton University — Toyota Technological Institute at Chicago, 2015." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.391, + 0.469, + 0.446 + ], + "angle": 0, + "content": "[2] Chao Chen, Yu-Shen Liu, and Zhizhong Han. Latent partition implicit with surface codes for 3d representation. 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In Proceedings of the IEEE International Conference on Computer Vision, pages 900-909, 2017." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.824 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3651" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Shape Primitives via Implicit Convexity Regularization/4387a009-eca0-4928-920d-1473c95da518_origin.pdf b/2023/Learning Shape Primitives via Implicit Convexity Regularization/4387a009-eca0-4928-920d-1473c95da518_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..385ee07f5b4e2e831899c0e4cc1b7a8ea5f0a3bc --- /dev/null +++ b/2023/Learning Shape Primitives via Implicit Convexity Regularization/4387a009-eca0-4928-920d-1473c95da518_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3975c6257338d597368ee5c9a441bd2d5a385f945fe143ef38d2e7ab2cb66a98 +size 4830211 diff --git a/2023/Learning Shape Primitives via Implicit Convexity Regularization/full.md b/2023/Learning Shape Primitives via Implicit Convexity Regularization/full.md new file mode 100644 index 0000000000000000000000000000000000000000..982c396cf127c600df3ccce885821ef96375ad02 --- /dev/null +++ b/2023/Learning Shape Primitives via Implicit Convexity Regularization/full.md @@ -0,0 +1,265 @@ +# Learning Shape Primitives via Implicit Convexity Regularization + +Xiaoyang Huang1 Yi Zhang1 Kai Chen1 Teng Li2 Wenjun Zhang1 Bingbing Ni1,3* +1Shanghai Jiao Tong University, Shanghai 200240, China +2Anhui University +3USC-SJTU Institute of Cultural and Creative Industry + +{huangxiaoyang, nibingbing}@sjtu.edu.cn + +# Abstract + +Shape primitives decomposition has been an important and long-standing task in 3D shape analysis. Prior arts heavily rely on 3D point clouds or voxel data for shape primitives extraction, which are less practical in real-world scenarios. This paper proposes to learn shape primitives from multi-view images by introducing implicit surface rendering. It is challenging since implicit shapes have a high degree of freedom, which violates the simplicity property of shape primitives. In this work, a novel regularization term named Implicit Convexity Regularization (ICR) imposed on implicit primitive learning is proposed to tackle this problem. We start with the convexity definition of general 3D shapes, and then derive the equivalent expression for implicit shapes represented by signed distance functions (SDFs). Further, instead of directly constraining the output SDF values which cause unstable optimization, we alternatively impose constraint on second order directional derivatives on line segments inside the shapes, which proves to be a tighter condition for 3D convexity. Implicit primitives constrained by the proposed ICR are combined into a whole object via softmax-weighted-sum operation over all primitive SDFs. Experiments on synthetic and real-world datasets show that our method is able to decompose objects into simple and reasonable shape primitives without the need of segmentation labels or 3D data. Code and data is publicly available in https://github.com/seanywang0408/ICR. + +# 1. Introduction + +Shape primitives extraction aims at decomposing a complex object into simple geometry. It has been a fundamental task in 3D shape representation [7] which imitates human visual perception, abstraction and understanding of real-world objects, and also facilitates industrial manufacturing which fabricates complex objects via component as + +![](images/392d05075a3b97097c79be6ccf1a9dc347be099b8be57202ede4a698afb7f68f.jpg) +Figure 1. We propose a shape primitive decomposition method from multi-view images with a novel Implicit Convexity Regularization scheme (ICR), which theoretically guarantees the convexity of implicit primitives. Our method generates shape primitives that satisfy simplicity, semantics preserving and fidelity. + +seembling. There are several fundamental properties for shape primitives: i) simplicity, which means that each primitive should be composed of simple geometry; ii) semantics, which means that the decomposition should reveal the semantic parts of an object; iii) fidelity, which means that the primitives should fit the original object as close as possible. Prior methods using parameterized shapes as primitive basis, such as cuboids [11] and superquadrics [13], could guarantee the simplicity property. However, parameterized primitives are less expressive due to their limited pre-defined geometry, which generally cause low fidelity. Though leveraging the flexibility of implicit functions to represent primitives could achieve higher fidelity, it also comes with a drawback that the semantic information generally diminishes during decomposition [5, 9]. Most importantly, all prior works require 3D data either for single-object fitting or multi-object learning. These data are not accessible in many cases, which makes them unpractical in real-world applications. In this work, we address this problem by learning implicit primitives from multi-view images. + +Learning implicit primitives from multi-view images is an even more challenging task. It is non-trivial to introduce prior implicit primitives [9, 19] into a neural rendering pipeline due to their specific modeling. Besides, implicit shapes without explicit regularization has a high degree of freedom, which could hardly meet the requirements of primitives. To this end, we propose a convex regulariza + +tion term imposed on a common signed distance function (SDF), which could be readily integrated into any implicit surface reconstruction pipeline, as shown in Figure 1. Convexity is a plausible property for primitives. First, it is a subconcept of simplicity, that is, a convex shape is generally regarded as simple (Figure 2). Second, most semantic parts are convex (see Figure 5 for example). Therefore convexity regularization benefits semantics preservation in primitive decomposition. Lastly, convexity is welcomed in some industrial manufacturing process, such as 3D printing and furniture making, in which convex parts are first fabricated respectively and then adhered into one object. + +To derive our implicit convexity regularization, we first start with the general definition of 3D convexity, which is formulated on arbitrary two points inside a shape. Then we tailor this definition to an implicit shape represented by a signed distance function (SDF) without loss of generality. This conversion also allows more lightweight computation. Further, to avoid the training instability and oscillation caused by direct constraint on the output SDF value, we tighten the convexity condition by alternatively constraining the second order directional derivatives along a line segment. We theoretically prove that this constraint is a sufficient condition for convexity. Besides, using the Finite Difference Method could easily implement this constraint. + +With the proposed implicit convexity regularization, each primitive is guaranteed to be convex. We combine all primitives into a whole object by conducting softmax-weighted-sum operation over all primitive SDFs and deriving the object SDF. The object SDF is incorporated into a common implicit surface rendering pipeline [17], allowing primitive decomposition from multi-view images. We experiment on both synthetic and real-world datasets, demonstrating the simplicity, semantics and fidelity of our generated primitives, especially on CO3D [21] dataset where prior primitive methods are infeasible without 3D data. + +# 2. Related Work + +# 2.1. Parameterized Primitives + +Cuboids with scaling, rotation and translation are first used as an abstraction of object parts. 3DPRNN [33] uses a recurrent network to generate cuboid primitives step-by-step. Tulsian et al. [24] obtain a consistent parsing across objects based on cuboids assembling. Niu et al. [16] infer hierarchical cuboid structure from single images. Lin et al. [12] propose a reinforcement learning algorithm to learn primitive decomposing policies. Kluger et al. [11] expand cuboids fitting from simple objects to more complex indoor scenes. Although cuboids decomposition could produce compact and semantic primitives, it also cause low fidelity due to its singular geometry. + +Another line of shape primitives is super-quadrics [20], + +which are more expressive than quadrics using 6 control parameters. Paschalidou et al. [18] decompose objects in to a hierarchical binary tree of super-quadrics, providing shape abstraction in different levels. EMS [13] aims at extraction super-quadric primitives from a noisy point cloud from a probabilistic view, which makes it more robust to outliers. Besides super-quadrics, ParseNet [23] proposes to use B-spline, cylinder and cones as primitives to reconstruct continuous surface from point clouds. Genova et al. [6] learn category-specific templates based on scaled axis-aligned anisotropic 3D Gaussian prior. ExtrudeNet [22] encodes point clouds into several primitives extruded from 2D Bezier curves that could be integrated into modern CAD software. Although these parameterized primitives provide higher fidelity than cuboids, it still does not meet the complexity of real-world objects. + +Constructive Solid Geometry (CSG) Tree [8, 32, 31] uses iterative boolean operators including union and intersection to construct convex or concave geometry, which is well-suited in computer-aided design (CAD). Although it still uses singular primitives like spheres and rectangles, CSG Tree is able to reconstruct accurate geometry as the iterative boolean operation gets deeper. However, it comes with a drawback that objects are eventually divided into patches in pieces with little semantic information preserved. + +# 2.2. Implicit Primitives + +BSPNet [3] and CvxNet [5] both use hyperplanes to construct a convex polytype and then assemble these convexes into a non-convex shape. Although these two methods are able to derive convex primitives like ours, the computation and storage cost grow quadratically as the number of hyperplanes increases, which makes it unsuitable for neural rendering in a multi-view scenario. Latent Partition Implicit [2] proposes shape partition in latent space for accurate modeling. Neural Star Domain (NSD) [9] models each primitive as a continuous function defined on a sphere, ensuring the simplicity property of primitives. However it still shares the deficiency of BSPNet and CvxNet that the semantic parts are broken into multiple primitives, as shown in Figure ?? Similar to NSD, Neural Parts [19] define homeomorphic mappings between spheres and primitives, which is able to generate various primitives with single connectivity. Nonetheless it is non-trivial to apply such a homeomorphic mapping in a neural rendering pipeline. Another relevant work to ours is BAENet [4], which uses a branched decoder to learn recurring parts in a shape collection. Although it is capable of producing accurate semantic segmentation results given a ground-truth shape, its reconstruction fidelity is notably inferior to ours. + +Moreover, all the above methods strongly rely on 3D data input for primitive decomposition, most of which even require a large set of shape collection within the same cat + +![](images/979442117d86760f63ddb95cd3b2a1638644092ff972fd7eb6cd309d2be11101.jpg) +Figure 2. Convexity is a subconcept of simplicity, since a convex shape is generally regarded as simple, while a non-convex shape tends to be more complex. + +egory for training, such as ShapeNet [1] or ModelNet [26], which makes them less practical in real-world scenarios. Our method derives implicit convex primitives from multiview images with well-defined semantics. + +# 2.3. Implicit Surface Rendering + +Recently, implicit neural representations have advanced surface reconstruction from multi-view images. DVR [15] proposes a differentiable rendering formulation for implicit surface and texture representations. IDR [29] approximates the light reflected from a 3D shape represented as the zero level set of a neural network. UNISURF [17] presents a unified framework for implicit surfaces and radiance fields, with the goal of reconstructing nontransparent objects. NeuS [25] develops a volume rendering method to train a neural SDF representation. Yariv et al. [28] define the volume density function as Laplace's cumulative distribution function applied to a SDF for surface rendering. + +# 3. Methodology + +We first demonstrate the derivation of the proposed implicit convexity regularization (ICR) scheme, and then explain the application of primitive fitting with ICR in a neural rendering pipeline. + +# 3.1. Implicit Convexity Regularization + +It is challenging to preserve simplicity in implicit primitives learning from multi-view images. In prior arts, there was little discussion on the simplicity of implicit shapes represented by signed distance functions. In this work, we investigate this problem in the view of convexity. A convex shape is the boundary of a convex set. We show some examples of convex and non-convex shapes in Figure 2. Intuitively, convexity is a subconcept of simplicity, since a convex shape is generally regarded as simple, while a nonconvex shape tends to be more complex. Mathematically, convexity could be defined as follows: + +Theorem 1 A shape $C$ is convex $\iff$ For arbitrary two points located inside the shape $C$ , the convex combination of + +![](images/3577a572eb383ce7ab2d909639dda6f2c43002a76a1ecb928ed4f67c9596e4ac.jpg) +Figure 3. We start with the general definition of convexity in Theorem 1. Then we convert the definition to an implicit shape represented by a signed distance function (SDF), which directly constrains the output SDF value. Lastly, to address the training instability issue in Theorem 2, we alternatively impose constraint on the second order directional derivatives, which proves to be a tighter condition of Theorem 2. The computation of second order directional derivatives could be easily implemented with Finite Difference Method. + +the two points are also located inside the shape, i.e., for any $x_{1}, x_{2} \in C$ and $0 \leq \theta \leq 1$ , we have $\theta x_{1} + (1 - \theta)x_{2} \in C$ . + +It is computation-inefficient to directly apply the vanilla convexity formulation to an implicit function, since it requires queries of arbitrary two points inside the shape. To adapt the convexity definition to a shape represented by an SDF with higher efficiency, we convert the above definition to a surface-based formulation: + +Theorem 2 A shape $C$ represented by an signed distance function $f$ is convex $\iff$ For arbitrary two points that are located on the surface of the shape, the convex combination of these two points is located inside the shape, i.e., for any $x_1, x_2 \in \{x | f(x) = 0\}$ and $0 < \theta < 1$ , we have $f(\theta x_1 + (1 - \theta) x_2) < 0$ . + +It is self-evident that Theorem 2 is equivalent to Theorem 1 for a SDF-based shape. It also ease the sampling process since only line segment between surface points are evaluated. In practice, we first randomly sample a set of rays of arbitrary starting points and directions, and retrieve + +the first and last intersection point $x_{1}, x_{2}$ against the shape by a root-finding algorithm. Those rays which do not intersect with the shape are ignored. Next we sample a set of points which is the convex combination of $x_{1}, x_{2}$ , i.e., points located on the line segment between $x_{1}, x_{2}$ . Lastly we penalize the positive SDF values of these points, meaning that they are outside the shape. + +However, we empirically find that directly imposing constraint on the output SDF values could cause serious training instability and oscillation, or even collapse. The reason is that there is a shortcut for the SDF function to satisfy this constraint, that is to scale up the SDF value of the whole function, which only needs to scale up the value of the final layer of the MLP. As an alternative, we propose to impose constraint on the second order directional derivative along the ray direction in the implicit field. + +Theorem 3 A shape $C$ represented by an signed distance function $f$ is convex $\Longleftarrow$ For arbitrary two points $x_{1}, x_{2}$ located on the surface of the shape, we have positive second order directional derivative along the direction $x_{2} - x_{1}$ on the convex combination of $x_{1}, x_{2}$ , i.e., for any $x_{1}, x_{2} \in \{x | f(x) = 0\}$ , $d = x_{2} - x_{1}$ and $0 < \theta < 1$ , we have $\frac{\partial^2 f}{\partial^2 d} (\theta x_1 + (1 - \theta)x_2) \geq 0$ . + +Proof. If the condition in Theorem 3 is satisfied, it means that the 1D function $f_{SDF}(x_0)$ w.r.t $x_0 = \theta x_1 + (1 - \theta)x_2$ , $0 < \theta < 1$ is a convex function. By the definition of convex functions, we have $f(x_0) < \theta f(x_1) + (1 - \theta)f(x_2) = \theta \times 0 + (1 - \theta) \times 0 = 0$ . Through Theorem 2, we know shape $C$ is convex. Constraint on second order directional derivatives is a tighter condition for convexity than constraint on SDF values. Intuitively, when the second order directional derivatives are positive everywhere between $x_1, x_2$ , we have a monotonically increasing first order directional derivative along the line segment, meaning that no inflection point exists in the interval. + +Based on Theorem 3, we encourage convexity by penalizing negative second order directional derivatives between $x_{1}, x_{2}$ . However, differentiating second order gradient of a neural network involves extremely intense computation. To this end, we replace accurate gradient derivation with Finite Difference, in which we view the continuous SDF as a discrete function via uniform sampling between the two intersection points $x_{1}, x_{2}$ . The detailed algorithm is presented in Algorithm 1. We also visualize the convexity defined by the three theorems using a 2D case in Figure 3. + +# 3.2. Learning Primitives from Multi-View Images + +Primitive Representations. We represent implicit shape primitives with a set of general signed distance functions (SDFs). Given a 3D point $\mathbf{p}$ as input, we use a multilayer perceptron (MLP) $f$ to predict the signed distance $SDF_{primi}(\mathbf{p})$ from the point $\mathbf{p}$ to the object surface. The + +# Algorithm 1 Implicit Convexity Regularization (ICR) + +1: Input: signed distance function $f$ +2: Output: convexity penalty $\mathcal{L}_{ICR}$ +3: Generate a ray with random starting points and directions; +4: Retrieve the first and last intersection points $x_{1}, x_{2}$ by root-finding algorithm; +5: Uniformly sample $\mathbf{K}$ points between $x_{1}, x_{2}$ : $\{p_{j} = \theta_{j}x_{1} + (1 - \theta_{j})x_{2} | \theta_{j} = \frac{j}{K + 1}, j = 1, 2, \dots, K\}$ ; +6: Query the SDF values of the sampled points: $\{f(p_j)|j = 1,2,\dots,K\}$ +7: Compute 1st order direction derivative with finite difference: $\{\nabla f = f(p_j) - f(p_{j - 1})|j = 2,\dots,K\}$ ; +8: Compute 2rd order direction derivative with finite difference: $\{\nabla^2 f = \nabla f(p_j) - \nabla f(p_{j-1})|j = 3,\dots,K\}$ ; +9: Compute the penalty term $L = \sum max(-\nabla^2 f, 0)$ ; +10: return $\mathcal{L}_{ICR}$ + +signed distance is positive when the point is located outside of the surface, while the signed distance is negative when the point is located inside of the surface. To unify the primitives into a complete object, one could take the minimal value over all primitive SDFs as the final object SDF. However, doing so would block the gradient flow from the object SDF to the subminimal primitive SDFs, which leads to suboptimal convergence. To this end, we conduct a soft minimization, composed of a softmax and a weighted sum operation. Formally, suppose each primitive SDF is implemented as a MLP network $f_{i}$ , the object signed distance of point $\mathbf{p}$ could be computed as: + +$$ +\begin{array}{l} S D F _ {p r i m i} ^ {i} (\mathbf {p}) = f _ {i} (\mathbf {p}), \\ \omega_ {i} = \operatorname {s o f t m a x} _ {N} (- \beta \cdot S D F _ {p r i m i} ^ {i} (\mathbf {p})), \tag {1} \\ S D F _ {o b j} (\mathbf {p}) = \sum_ {i = 1} ^ {N} \omega_ {i} \cdot S D F _ {p r i m i} ^ {i} (\mathbf {p}), \\ \end{array} +$$ + +where $\beta$ is the scaling temperature (set to 10 in our experiments) in softmax operation, $\omega_{i}$ denotes the weight of $i$ th primitive and $N$ is the number of the primitives. + +Surface Rendering. Considering the difficulty of acquiring 3D data in application, we aim at learning the implicit primitives from multi-view images. Although prior works such as BSPNet [3] and CvxNet [5] proposes 3D convexity representation based on hyper-planes, these representations are infeasible in current neural rendering pipelines, hindering the acquisition of convexity primitives from multi-view data. One key contribution of our method is that we extend convexity primitives to a implicit surface distance function, which is the common 3D representation of neural rendering pipelines. + +![](images/d399db9980f65e01b265ee93d15926394e60d832d5d43a9b67263b4931867ba7.jpg) +Figure 4. Our network consists of N primitive MLPs and one color MLP. Each primitive MLP outputs an SDF value and a geometry latent code of the primitive from the input $\mathbf{p}$ . The primitive SDF values and latent codes go through a softmax-weighted-sum layer to obtain the object SDF and latent code, which are then respectively processed by a sigmoid layer and a color MLP. The obtained volume density $\sigma$ and RGB are applied in a standard implicit surface volume rendering method. The loss is computed by the weighted sum of reconstruction error and Implicit Convexity Regularization on each primitive. + +Specifically, we integrate the implicit primitives into a neural rendering pipeline based on UNISURF [17]. To this end, we first extend the pirmitive MLPs in Sec 3.2 to additionally output a geometry latent code except for SDF value in the final layer, such that + +$$ +\left[ S D F _ {p r i m i} ^ {i} (\mathbf {p}), L _ {p r i m i} ^ {i} (\mathbf {p}) \right] = f _ {i} (\mathbf {p}), \tag {2} +$$ + +where $L_{primi}^{i}(\mathbf{p})$ is the latent code of $\mathbf{p}$ . Similar to $SDF_{obj}(\mathbf{p})$ , the object latent code $L_{obj}(\mathbf{p})$ is obtained by the softmax-weighted-sum over all primitive latent codes. We further implement a color MLP which receives the object latent code as input and predicts the RGB value $\mathbf{c}$ of $\mathbf{p}$ . Then we apply the volume rendering as follows. + +For a ray $\mathbf{r}$ starting from the camera position to the pixel location, we first retrieve the surface point $\mathbf{x}_s$ defined by $SDF_{obj}(\mathbf{x}_s) = 0$ using a root-finding algorithm. Then, we sample $N$ points $\mathbf{x}_j$ along ray $\mathbf{r}$ within a interval around $\mathbf{x}_s$ . We infer the object SDF value for each sample and convert it to volume density $\sigma_j$ as follows: + +$$ +\sigma_ {j} = \operatorname {S i g m o i d} (- \mu \cdot S D F _ {o b j} (\mathbf {x} _ {j})), \tag {3} +$$ + +where $\mu$ is a hyper-parameter that controls the sharpness of density distribution (set to 25 in all our experiments). The ray color is then obtained by the following volume rendering equation: + +$$ +\hat {C} (\mathbf {r}) = \sum_ {j = 1} ^ {N} \sigma_ {j} \prod_ {k < j} (1 - \sigma_ {k}) \mathbf {c} _ {j}. \tag {4} +$$ + +The reconstruction loss is computed over all sampled rays $\mathbf{r} \in \mathcal{R}$ , with $C(\mathbf{r})$ as the ground-truth pixel color: + +$$ +\mathcal {L} _ {r e c} = \sum_ {\mathbf {r} \in \mathcal {R}} \left\| \hat {C} (\mathbf {r}) - C (\mathbf {r}) \right\| ^ {2}. \tag {5} +$$ + +For more details on the neural rendering process, please refer to UNISURF [17]. Overall, we train our model with the following loss function: + +$$ +\mathcal {L} = \mathcal {L} _ {r e c} + \lambda \sum_ {i = 1} ^ {N} \mathcal {L} _ {I C R} ^ {i}, \tag {6} +$$ + +where $\mathcal{L}_{ICR}^i$ is the proposed implicit convexity regularization derived in Algorithm 1, which is imposed on each primitive, and $\lambda$ is the weighting hyper-parameter. Since $\mathcal{L}_{ICR}$ is generally a small value, we set $\lambda$ to 100 in our experiments. Illustration of the pipeline is presented in Figure 4. + +# 3.3. Implementation + +In all our experiments, each primitive SDF is implemented as a 4-layer MLP, with a skip connection from the input to the third layer. The color MLP also contains 4 layers. All layers have 64 hidden units. The input coordinates are first encoded by a sinusoidal embedding layer with $L = 6$ , as done in UNISURF [17]. We use the Adam optimizer [10] with an initial learning rate of $10^{-5}$ . The learning rate is multiplied by 0.5 in 4,000th and 5,000th iteration. For each iteration, we sample 1,024 rays for volume rendering. The model is trained for 10,000 iterations. + +# 4. Experiments + +# 4.1. Synthetic Dataset + +Dataset. ShapeNet [1] is a shape collection composed of multiple categories. We conduct experiments on six categories including airplane, car, chair, lamp, table and pistol. We evaluate our method and prior works on randomly-selected 20 shapes for each category. For our method and UNISURF, we use the multi-view images rendered by + +![](images/7fd5aeb5a780da6a9ea56cf8e55d2902abb7ac4a76b2d50b926881af15eb5189.jpg) +Figure 5. We visualize the ShapeNet results of our method and prior works, including BAENet, EMS and UNISURF. Our method achieves notably better decomposition and fidelity than BAENet and EMS. + +![](images/21d940d97650e97753c8db551aa80105073cfba546a4e2825902a00da467e99e.jpg) + +DISN [27], which includes 36 views for each object with known camera intrinsic and extrinsic parameters. The images are rendered in $224 \times 224$ resolution. + +Comparisons. We compare our method with the following works. i) BAENet [4]: BAENet is a learning-based primitive decomposition method that is trained on a shape collection within a category. It receives 3D voxel as input and predict an implicit field for each primitive. We follow its default settings which train the models on the complete collection for each categories without segmentation supervision, e.g. 2,690 objects for airplane. ii) EMS [13]: EMS is the state-of-the-art parameterized primitive decomposition method which derives superquadric primitives from a point cloud via a robust optimization algorithm. We follow its default setting in multi-superquadric optimization, and feed the ground-truth point cloud as input data. iii) + +UNISURF [17]: UNISURF is a state-of-the-art implicit surface reconstruction method which derive the implicit field of an object from multi-view images. We include UNISURF for comparisons with a standard implicit surface reconstruction method in terms of fidelity. The above methods are summarized in Table 1. We use two metrics for evaluation, including Chamfer Distance (CD) and Intersection over Union (IoU). The quantitative results are reported in Table 2. We also visualize the meshes in Figure 5, with different colors for different primitives. + +Results. Figure 5 and Table 2 show that our method achieves notably better decomposition and fidelity than BAENet and EMS. In Figure 5, our method consistently decomposes objects into semantic elements in convex geometry for different categories. BAENet fails in chair, lamp and pistol cases, where the chair back and cushion, lamp + +
MethodData SourceRecon Semantic
UNISURFFitted on 2D data✓X
EMSFitted on 3D data✓✓
BAENetTrained on large-scale 3D data✓✓
CvxNetTrained on large-scale 3D data✓X
ICR (Ours)Fitted on 2D data✓✓
+ +Table 1. Summary of compared methods. Recon and Semantic denote capability of reconstruction and semantic decomposition. + +
CD↓\IoU↑UNISURFOursBAENetEMS
Airplane0.32\86.30.50\79.20.91\57.83.12\26.8
Pistol0.53\74.80.85\62.51.67\38.42.32\32.6
Table1.57\42.11.40\43.22.86\22.46.85\18.5
Chair1.00\49.21.29\47.41.45\41.75.74\16.9
Lamp0.27\89.60.99\53.81.56\38.62.76\25.0
Car1.46\48.51.86\37.22.06\31.52.36\27.5
Mean0.86\65.11.15\53.91.75\38.43.86\24.6
+ +Table 2. We measure the Chamfer Distance $(10^{-3},\downarrow)$ and Intersection over Union $(\uparrow)$ between the reconstructed surface and the ground-truth shapes. Our method achieves better reconstruction accuracy compared to prior primitive decomposition methods, even comparable to UNISURF, which is a state-of-the-art surface reconstruction method. + +bulb and base, pistol barrel and handle are mixing together. Besides, Table 2 shows that BAENet achieves lower reconstruction accuracy than ours, even though it is trained on 3D data and receives 3D voxel as input. In table category, it fails to reconstruct the table leg. EMS fails in most cases with low fidelity and unreasonable decomposition. The reason for that is that EMS is based on a iterative optimization, where one primitive is fitted to the point cloud until convergence and then another primitive is fitted to the rest outliers and so on. It generally falls into a local minimum for objects that do not consist of a main stem and branches. Compared to UNISURF, we achieve comparable reconstruction accuracy in most cases. For table category, we even surpass UNISURF on modeling thin geometry such as the table legs, owing to convexity prior of our method. + +# 4.2. Real-World Dataset + +One question might be raised that if we have access to multi-view images, why not just recover its 3D representation using multi-view reconstruction methods. However, even though we could reconstruct 3D representation for one sample, it is still inefficient or even impractical to conduct reconstruction for a large-scale dataset. What's more, the common case in real-world scenarios is that we are not able to acquire a large-scale real-world datasets for ONE target object. It is demonstrated by our experiments on CO3D. + +Dataset. CO3D [21] is a multi-view dataset collected on real-world objects with known camera intrinsic and extrinsic parameters. Each object includes a varied number of views ranging from tens to hundreds. The resolution of each image also varies from $1000 \times 500$ to $1600 \times 1000$ . We crop the images with a square bounding box centered at the object and then resize them to $224 \times 224$ for training. + +Comparisons. Note that prior works which are trained on a 3D shape collection are basically infeasible in this dataset, since CO3D lacks regular 3D data form (except for some objects that have a noisy point cloud generated by MVS algorithm). Therefore we compare our method with UNISURF (based on multi-view images) and EMS (based on point clouds) in terms of visual effects. + +Results. As shown in Figure 6, our method is able to decompose objects into convex primitives with rich semantics. The reconstruction accuracy is comparable to UNISURF in terms of visual effect. EMS generates several invalid primitives which do not match the object geometry. + +# 4.3. Ablation Study + +Effectiveness of Convexity Regularization. We evaluate the effectiveness of the proposed implicit convexity regularization by removing this regularization in the neural rendering pipeline, while other settings remain the same. We show the comparisons in Figure 7. Comparing results with and without ICR, we see that ICR successfully guarantees the convexity of each primitive, which benefits consistent semantic decomposition. Although optimization without ICR could sometimes obtain higher fidelity, such as the reconstruction of wings and tails of the planes, it generally causes illogical decomposition, i.e., part of the wing is assigned to the stem primitive, and part of the chair cushion is assigned to the back primitive. Besides, we also find that with the convexity prior, the reconstructions of the thin objects are more plausible, such as the chair legs. The reason is that convex regularization encourages simple geometry. By contrast, in the case of removing ICR, the reconstruction is done by ray sampling, which could be insufficient to recover a smooth object surface. More example primitives obtained with and without ICR could be found in left and right column respectively in Figure 2. + +Convexity Controlling. We demonstrate that controlling the weight of implicit convexity regularization could achieve trade-off between primitive simplicity and fidelity. Specifically, we convert Equation 6 into $\mathcal{L} = \mathcal{L}_{rec} + \sum_{i=1}^{N} \lambda_i \mathcal{L}_{ICR}^i$ , in which $\lambda_i$ are tunable for individual primitive. We then apply a smaller weight $\lambda_i$ on $L_{ICR}^i$ for those primitives which we prefer higher fidelity than simplicity, while other primitives remain still. We show some examples in Figure 8. In the bottom row, we set the $\lambda$ of the primitives circled in red (tail of the plane and trigger of the + +![](images/0414152f0dd8b0c9732026ac5881c27c301e1d928ad399895a426a2c23554793.jpg) +Figure 6. Visualization of CO3D experiments. Our method is able to decompose objects into plausible shape primitives from multiview input. EMS obtains shape primitives from point clouds. + +![](images/3863a28aca959711fdca4e02f30785adadfb4a903fcdebd23fb517ee1d42118c.jpg) +Figure 7. The proposed Implicit Convexity Regularization (ICR) theoretically guarantees the convexity and simplicity of each primitive. Removing ICR causes unreasonable decomposition. + +![](images/7e5270e9daa822f86a216918808cc5190887a0e8f6bfadf237e38090ef94814e.jpg) +Figure 8. Tuning $\lambda$ , the weight of ICR, for individual primitive could achieve trade-off between fidelity and simplicity. In the bottom row, we set the $\lambda$ of the primitives circled in red (tail of the plane and trigger of the pistol) to 1 and others to 100. In this way we obtain a flexible primitive with higher accuracy, while other parts still preserve their semantics and simplicity. We compute the chamfer distance (CD) to evaluate the fidelity. + +pistol) to 1 and others to 100. In this way we obtain a flexible primitive with higher accuracy, while other parts still preserve their semantics and simplicity. The adjusted primitives achieve lower chamfer distance than the vanilla ones. + +
SVR\SegAirplaneTableChairLamp
OccNet57.1\—50.6\—50.1\—37.1\—
CvxNet59.8\—47.3\—49.1\—31.1\—
BAENet52.4\80.441.6\87.045.2\84.832.8\63.9
Ours64.1\69.546.7\89.249.3\88.337.7\68.2
+ +Table 3. We extend our proposed ICR term to a large-scale 3D training setting. We compare our method with prior works on single-view 3D reconstruction (IoU ↑) and semantic segmentation (IoU ↑) tasks. Since OccNet and CvxNet are incapable of decomposing objects into semantic parts, their segmentation performance are absent. + +Training on 3D datasets. Although our method is designed for multi-view data, we would also like to test its performance in a large-scale 3D training setting that is similar with prior primitive-learning methods. To this end, we further conduct a set of experiments on ShapeNet, in which we integrate our ICR term into an encoder-decoder network and train it on a dataset within one category. The network receives 3D voxels as input and predict SDF value of query points. The encoder is implemented as a 3D CNN, similar to prior works [3, 4], while the decoder is implemented by our primitive representation in Equ. 1. Following prior works [3], after the training is finished, we replace the 3D encoder with a 2D CNN and train it on a single-view reconstruction task while the decoder is fixed. We measure single-view reconstruction accuracy as well as semantic decomposition performance using the segmentation labels from ShapeNetPart [30]. Intersection over Union (IoU) is used as the metric for both tasks. We experiment on four categories of ShapeNet: airplane, chair, lamp and table. We follow the train-test-split in BAENet. The detailed network architecture and experiment setting is presented in the appendix. We compare our method with OccNet [14], BAENet [4] and CvxNet [5]. The results are listed in Table 3. Compared to BAENet and CvxNet, our method achieves similar or even better reconstruction accuracy in single-view reconstruction task. We found that the artifact of disappearance (see Fig. ?? table) and dilation (see Fig. ?? chair and lamp) exists in the results of BAENet and CvxNet, which is the main reason that their reconstruction accuracy is lower. Besides, our method is able to achieve better semantics decomposition. Note that all methods are validated without fine-tuning on test samples. + +# 5. Conclusion + +In this work, we propose a regularization term named Implicit Convexity Regularization (ICR) for primitive decomposition. We theoretically prove that imposing constraint on the second order directional derivatives on line segments inside a shape could encourage convexity for im + +plicit shapes represented by signed distance functions. Experiments on synthetic and real-world datasets demonstrate the superiority of our method over prior arts with respect to primitive simplicity, fidelity and semantics. + +# 6. Acknowledgements + +This work was supported by National Science Foundation of China (U20B2072, 61976137). This work was also partially supported by Grant YG2021ZD18 from Shanghai Jiao Tong University Medical Engineering Cross Research. + +# References + +[1] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet: An Information-Rich 3D Model Repository. Technical Report arXiv:1512.03012 [cs.GR], Stanford University — Princeton University — Toyota Technological Institute at Chicago, 2015. +[2] Chao Chen, Yu-Shen Liu, and Zhizhong Han. Latent partition implicit with surface codes for 3d representation. In European Conference on Computer Vision, pages 322-343. Springer, 2022. +[3] Zhiqin Chen, Andrea Tagliasacchi, and Hao Zhang. Bsp-net: Generating compact meshes via binary space partitioning. 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Prior arts heavily rely on 3D point clouds or voxel data for shape primitives extraction, which are less practical in real-world scenarios. This paper proposes to learn shape primitives from multi-view images by introducing implicit surface rendering. It is challenging since implicit shapes have a high degree of freedom, which violates the simplicity property of shape primitives. In this work, a novel regularization term named Implicit Convexity Regularization (ICR) imposed on implicit primitive learning is proposed to tackle this problem. We start with the convexity definition of general 3D shapes, and then derive the equivalent expression for implicit shapes represented by signed distance functions (SDFs). Further, instead of directly constraining the output SDF values which cause unstable optimization, we alternatively impose constraint on second order directional derivatives on line segments inside the shapes, which proves to be a tighter condition for 3D convexity. Implicit primitives constrained by the proposed ICR are combined into a whole object via softmax-weighted-sum operation over all primitive SDFs. Experiments on synthetic and real-world datasets show that our method is able to decompose objects into simple and reasonable shape primitives without the need of segmentation labels or 3D data. Code and data is publicly available in https://github.com/seanywang0408/ICR." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 600, + 128, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 600, + 128, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 600, + 128, + 612 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 621, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 621, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 621, + 287, + 693 + ], + "type": "text", + "content": "Shape primitives extraction aims at decomposing a complex object into simple geometry. It has been a fundamental task in 3D shape representation [7] which imitates human visual perception, abstraction and understanding of real-world objects, and also facilitates industrial manufacturing which fabricates complex objects via component as" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 224, + 544, + 306 + ], + "blocks": [ + { + "bbox": [ + 310, + 224, + 544, + 306 + ], + "lines": [ + { + "bbox": [ + 310, + 224, + 544, + 306 + ], + "spans": [ + { + "bbox": [ + 310, + 224, + 544, + 306 + ], + "type": "image", + "image_path": "392d05075a3b97097c79be6ccf1a9dc347be099b8be57202ede4a698afb7f68f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 312, + 546, + 368 + ], + "lines": [ + { + "bbox": [ + 305, + 312, + 546, + 368 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 546, + 368 + ], + "type": "text", + "content": "Figure 1. We propose a shape primitive decomposition method from multi-view images with a novel Implicit Convexity Regularization scheme (ICR), which theoretically guarantees the convexity of implicit primitives. Our method generates shape primitives that satisfy simplicity, semantics preserving and fidelity." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 388, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 628 + ], + "type": "text", + "content": "seembling. There are several fundamental properties for shape primitives: i) simplicity, which means that each primitive should be composed of simple geometry; ii) semantics, which means that the decomposition should reveal the semantic parts of an object; iii) fidelity, which means that the primitives should fit the original object as close as possible. Prior methods using parameterized shapes as primitive basis, such as cuboids [11] and superquadrics [13], could guarantee the simplicity property. However, parameterized primitives are less expressive due to their limited pre-defined geometry, which generally cause low fidelity. Though leveraging the flexibility of implicit functions to represent primitives could achieve higher fidelity, it also comes with a drawback that the semantic information generally diminishes during decomposition [5, 9]. Most importantly, all prior works require 3D data either for single-object fitting or multi-object learning. These data are not accessible in many cases, which makes them unpractical in real-world applications. In this work, we address this problem by learning implicit primitives from multi-view images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": "Learning implicit primitives from multi-view images is an even more challenging task. It is non-trivial to introduce prior implicit primitives [9, 19] into a neural rendering pipeline due to their specific modeling. Besides, implicit shapes without explicit regularization has a high degree of freedom, which could hardly meet the requirements of primitives. To this end, we propose a convex regulariza" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "text", + "content": "*Corresponding Author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3642" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 215 + ], + "type": "text", + "content": "tion term imposed on a common signed distance function (SDF), which could be readily integrated into any implicit surface reconstruction pipeline, as shown in Figure 1. Convexity is a plausible property for primitives. First, it is a subconcept of simplicity, that is, a convex shape is generally regarded as simple (Figure 2). Second, most semantic parts are convex (see Figure 5 for example). Therefore convexity regularization benefits semantics preservation in primitive decomposition. Lastly, convexity is welcomed in some industrial manufacturing process, such as 3D printing and furniture making, in which convex parts are first fabricated respectively and then adhered into one object." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 217, + 286, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 217, + 286, + 371 + ], + "spans": [ + { + "bbox": [ + 49, + 217, + 286, + 371 + ], + "type": "text", + "content": "To derive our implicit convexity regularization, we first start with the general definition of 3D convexity, which is formulated on arbitrary two points inside a shape. Then we tailor this definition to an implicit shape represented by a signed distance function (SDF) without loss of generality. This conversion also allows more lightweight computation. Further, to avoid the training instability and oscillation caused by direct constraint on the output SDF value, we tighten the convexity condition by alternatively constraining the second order directional derivatives along a line segment. We theoretically prove that this constraint is a sufficient condition for convexity. Besides, using the Finite Difference Method could easily implement this constraint." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 373, + 286, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 373, + 286, + 503 + ], + "spans": [ + { + "bbox": [ + 49, + 373, + 286, + 503 + ], + "type": "text", + "content": "With the proposed implicit convexity regularization, each primitive is guaranteed to be convex. We combine all primitives into a whole object by conducting softmax-weighted-sum operation over all primitive SDFs and deriving the object SDF. The object SDF is incorporated into a common implicit surface rendering pipeline [17], allowing primitive decomposition from multi-view images. We experiment on both synthetic and real-world datasets, demonstrating the simplicity, semantics and fidelity of our generated primitives, especially on CO3D [21] dataset where prior primitive methods are infeasible without 3D data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 517, + 132, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 517, + 132, + 529 + ], + "spans": [ + { + "bbox": [ + 49, + 517, + 132, + 529 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 537, + 187, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 537, + 187, + 549 + ], + "spans": [ + { + "bbox": [ + 49, + 537, + 187, + 549 + ], + "type": "text", + "content": "2.1. Parameterized Primitives" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 557, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 557, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 49, + 557, + 286, + 700 + ], + "type": "text", + "content": "Cuboids with scaling, rotation and translation are first used as an abstraction of object parts. 3DPRNN [33] uses a recurrent network to generate cuboid primitives step-by-step. Tulsian et al. [24] obtain a consistent parsing across objects based on cuboids assembling. Niu et al. [16] infer hierarchical cuboid structure from single images. Lin et al. [12] propose a reinforcement learning algorithm to learn primitive decomposing policies. Kluger et al. [11] expand cuboids fitting from simple objects to more complex indoor scenes. Although cuboids decomposition could produce compact and semantic primitives, it also cause low fidelity due to its singular geometry." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 701, + 286, + 713 + ], + "type": "text", + "content": "Another line of shape primitives is super-quadrics [20]," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 72, + 544, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 262 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 262 + ], + "type": "text", + "content": "which are more expressive than quadrics using 6 control parameters. Paschalidou et al. [18] decompose objects in to a hierarchical binary tree of super-quadrics, providing shape abstraction in different levels. EMS [13] aims at extraction super-quadric primitives from a noisy point cloud from a probabilistic view, which makes it more robust to outliers. Besides super-quadrics, ParseNet [23] proposes to use B-spline, cylinder and cones as primitives to reconstruct continuous surface from point clouds. Genova et al. [6] learn category-specific templates based on scaled axis-aligned anisotropic 3D Gaussian prior. ExtrudeNet [22] encodes point clouds into several primitives extruded from 2D Bezier curves that could be integrated into modern CAD software. Although these parameterized primitives provide higher fidelity than cuboids, it still does not meet the complexity of real-world objects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 264, + 544, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 264, + 544, + 371 + ], + "spans": [ + { + "bbox": [ + 308, + 264, + 544, + 371 + ], + "type": "text", + "content": "Constructive Solid Geometry (CSG) Tree [8, 32, 31] uses iterative boolean operators including union and intersection to construct convex or concave geometry, which is well-suited in computer-aided design (CAD). Although it still uses singular primitives like spheres and rectangles, CSG Tree is able to reconstruct accurate geometry as the iterative boolean operation gets deeper. However, it comes with a drawback that objects are eventually divided into patches in pieces with little semantic information preserved." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 382, + 415, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 382, + 415, + 394 + ], + "spans": [ + { + "bbox": [ + 308, + 382, + 415, + 394 + ], + "type": "text", + "content": "2.2. Implicit Primitives" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 401, + 544, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 401, + 544, + 675 + ], + "spans": [ + { + "bbox": [ + 308, + 401, + 544, + 675 + ], + "type": "text", + "content": "BSPNet [3] and CvxNet [5] both use hyperplanes to construct a convex polytype and then assemble these convexes into a non-convex shape. Although these two methods are able to derive convex primitives like ours, the computation and storage cost grow quadratically as the number of hyperplanes increases, which makes it unsuitable for neural rendering in a multi-view scenario. Latent Partition Implicit [2] proposes shape partition in latent space for accurate modeling. Neural Star Domain (NSD) [9] models each primitive as a continuous function defined on a sphere, ensuring the simplicity property of primitives. However it still shares the deficiency of BSPNet and CvxNet that the semantic parts are broken into multiple primitives, as shown in Figure ?? Similar to NSD, Neural Parts [19] define homeomorphic mappings between spheres and primitives, which is able to generate various primitives with single connectivity. Nonetheless it is non-trivial to apply such a homeomorphic mapping in a neural rendering pipeline. Another relevant work to ours is BAENet [4], which uses a branched decoder to learn recurring parts in a shape collection. Although it is capable of producing accurate semantic segmentation results given a ground-truth shape, its reconstruction fidelity is notably inferior to ours." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 677, + 544, + 712 + ], + "type": "text", + "content": "Moreover, all the above methods strongly rely on 3D data input for primitive decomposition, most of which even require a large set of shape collection within the same cat" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "3643" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 287, + 155 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 287, + 155 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 287, + 155 + ], + "type": "image", + "image_path": "979442117d86760f63ddb95cd3b2a1638644092ff972fd7eb6cd309d2be11101.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 160, + 288, + 196 + ], + "lines": [ + { + "bbox": [ + 46, + 160, + 288, + 196 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 288, + 196 + ], + "type": "text", + "content": "Figure 2. Convexity is a subconcept of simplicity, since a convex shape is generally regarded as simple, while a non-convex shape tends to be more complex." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 215, + 288, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 288, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 288, + 264 + ], + "type": "text", + "content": "egory for training, such as ShapeNet [1] or ModelNet [26], which makes them less practical in real-world scenarios. Our method derives implicit convex primitives from multiview images with well-defined semantics." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 272, + 200, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 272, + 200, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 200, + 285 + ], + "type": "text", + "content": "2.3. Implicit Surface Rendering" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 292, + 289, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 289, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 289, + 436 + ], + "type": "text", + "content": "Recently, implicit neural representations have advanced surface reconstruction from multi-view images. DVR [15] proposes a differentiable rendering formulation for implicit surface and texture representations. IDR [29] approximates the light reflected from a 3D shape represented as the zero level set of a neural network. UNISURF [17] presents a unified framework for implicit surfaces and radiance fields, with the goal of reconstructing nontransparent objects. NeuS [25] develops a volume rendering method to train a neural SDF representation. Yariv et al. [28] define the volume density function as Laplace's cumulative distribution function applied to a SDF for surface rendering." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 448, + 130, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 448, + 130, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 448, + 130, + 462 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 468, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 518 + ], + "type": "text", + "content": "We first demonstrate the derivation of the proposed implicit convexity regularization (ICR) scheme, and then explain the application of primitive fitting with ICR in a neural rendering pipeline." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 525, + 230, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 230, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 230, + 539 + ], + "type": "text", + "content": "3.1. Implicit Convexity Regularization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 544, + 288, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 288, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 288, + 676 + ], + "type": "text", + "content": "It is challenging to preserve simplicity in implicit primitives learning from multi-view images. In prior arts, there was little discussion on the simplicity of implicit shapes represented by signed distance functions. In this work, we investigate this problem in the view of convexity. A convex shape is the boundary of a convex set. We show some examples of convex and non-convex shapes in Figure 2. Intuitively, convexity is a subconcept of simplicity, since a convex shape is generally regarded as simple, while a nonconvex shape tends to be more complex. Mathematically, convexity could be defined as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "Theorem 1 A shape " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " is convex " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\iff" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " For arbitrary two points located inside the shape " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": ", the convex combination of" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 313, + 68, + 544, + 340 + ], + "blocks": [ + { + "bbox": [ + 313, + 68, + 544, + 340 + ], + "lines": [ + { + "bbox": [ + 313, + 68, + 544, + 340 + ], + "spans": [ + { + "bbox": [ + 313, + 68, + 544, + 340 + ], + "type": "image", + "image_path": "3577a572eb383ce7ab2d909639dda6f2c43002a76a1ecb928ed4f67c9596e4ac.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 342, + 547, + 441 + ], + "lines": [ + { + "bbox": [ + 304, + 342, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 547, + 441 + ], + "type": "text", + "content": "Figure 3. We start with the general definition of convexity in Theorem 1. Then we convert the definition to an implicit shape represented by a signed distance function (SDF), which directly constrains the output SDF value. Lastly, to address the training instability issue in Theorem 2, we alternatively impose constraint on the second order directional derivatives, which proves to be a tighter condition of Theorem 2. The computation of second order directional derivatives could be easily implemented with Finite Difference Method." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "type": "text", + "content": "the two points are also located inside the shape, i.e., for any " + }, + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2} \\in C" + }, + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "type": "inline_equation", + "content": "0 \\leq \\theta \\leq 1" + }, + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "type": "inline_equation", + "content": "\\theta x_{1} + (1 - \\theta)x_{2} \\in C" + }, + { + "bbox": [ + 305, + 460, + 546, + 485 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 492, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 547, + 564 + ], + "type": "text", + "content": "It is computation-inefficient to directly apply the vanilla convexity formulation to an implicit function, since it requires queries of arbitrary two points inside the shape. To adapt the convexity definition to a shape represented by an SDF with higher efficiency, we convert the above definition to a surface-based formulation:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "text", + "content": "Theorem 2 A shape " + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "text", + "content": " represented by an signed distance function " + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "text", + "content": " is convex " + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\iff" + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "text", + "content": " For arbitrary two points that are located on the surface of the shape, the convex combination of these two points is located inside the shape, i.e., for any " + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "inline_equation", + "content": "x_1, x_2 \\in \\{x | f(x) = 0\\}" + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "inline_equation", + "content": "0 < \\theta < 1" + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "inline_equation", + "content": "f(\\theta x_1 + (1 - \\theta) x_2) < 0" + }, + { + "bbox": [ + 304, + 572, + 547, + 647 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "It is self-evident that Theorem 2 is equivalent to Theorem 1 for a SDF-based shape. It also ease the sampling process since only line segment between surface points are evaluated. In practice, we first randomly sample a set of rays of arbitrary starting points and directions, and retrieve" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3644" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "the first and last intersection point " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": " against the shape by a root-finding algorithm. Those rays which do not intersect with the shape are ignored. Next we sample a set of points which is the convex combination of " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": ", i.e., points located on the line segment between " + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": ". Lastly we penalize the positive SDF values of these points, meaning that they are outside the shape." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 288, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 288, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 288, + 264 + ], + "type": "text", + "content": "However, we empirically find that directly imposing constraint on the output SDF values could cause serious training instability and oscillation, or even collapse. The reason is that there is a shortcut for the SDF function to satisfy this constraint, that is to scale up the SDF value of the whole function, which only needs to scale up the value of the final layer of the MLP. As an alternative, we propose to impose constraint on the second order directional derivative along the ray direction in the implicit field." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": "Theorem 3 A shape " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": " represented by an signed distance function " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": " is convex " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "\\Longleftarrow" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": " For arbitrary two points " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": " located on the surface of the shape, we have positive second order directional derivative along the direction " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "x_{2} - x_{1}" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": " on the convex combination of " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": ", i.e., for any " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2} \\in \\{x | f(x) = 0\\}" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "d = x_{2} - x_{1}" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "0 < \\theta < 1" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "inline_equation", + "content": "\\frac{\\partial^2 f}{\\partial^2 d} (\\theta x_1 + (1 - \\theta)x_2) \\geq 0" + }, + { + "bbox": [ + 46, + 271, + 288, + 359 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "content": "Proof. If the condition in Theorem 3 is satisfied, it means that the 1D function " + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "inline_equation", + "content": "f_{SDF}(x_0)" + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "content": " w.r.t " + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "inline_equation", + "content": "x_0 = \\theta x_1 + (1 - \\theta)x_2" + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "inline_equation", + "content": "0 < \\theta < 1" + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "content": " is a convex function. By the definition of convex functions, we have " + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "inline_equation", + "content": "f(x_0) < \\theta f(x_1) + (1 - \\theta)f(x_2) = \\theta \\times 0 + (1 - \\theta) \\times 0 = 0" + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "content": ". Through Theorem 2, we know shape " + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "content": " is convex. Constraint on second order directional derivatives is a tighter condition for convexity than constraint on SDF values. Intuitively, when the second order directional derivatives are positive everywhere between " + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "inline_equation", + "content": "x_1, x_2" + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "content": ", we have a monotonically increasing first order directional derivative along the line segment, meaning that no inflection point exists in the interval." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "type": "text", + "content": "Based on Theorem 3, we encourage convexity by penalizing negative second order directional derivatives between " + }, + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "type": "text", + "content": ". However, differentiating second order gradient of a neural network involves extremely intense computation. To this end, we replace accurate gradient derivation with Finite Difference, in which we view the continuous SDF as a discrete function via uniform sampling between the two intersection points " + }, + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 46, + 509, + 288, + 628 + ], + "type": "text", + "content": ". The detailed algorithm is presented in Algorithm 1. We also visualize the convexity defined by the three theorems using a 2D case in Figure 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 635, + 282, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 282, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 282, + 647 + ], + "type": "text", + "content": "3.2. Learning Primitives from Multi-View Images" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": "Primitive Representations. We represent implicit shape primitives with a set of general signed distance functions (SDFs). Given a 3D point " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": " as input, we use a multilayer perceptron (MLP) " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": " to predict the signed distance " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "SDF_{primi}(\\mathbf{p})" + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": " from the point " + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 47, + 653, + 287, + 715 + ], + "type": "text", + "content": " to the object surface. The" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 525, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 525, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 525, + 84 + ], + "type": "text", + "content": "Algorithm 1 Implicit Convexity Regularization (ICR)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 310, + 86, + 545, + 277 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 312, + 86, + 463, + 98 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 86, + 463, + 98 + ], + "spans": [ + { + "bbox": [ + 312, + 86, + 463, + 98 + ], + "type": "text", + "content": "1: Input: signed distance function " + }, + { + "bbox": [ + 312, + 86, + 463, + 98 + ], + "type": "inline_equation", + "content": "f" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 98, + 460, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 98, + 460, + 110 + ], + "spans": [ + { + "bbox": [ + 312, + 98, + 460, + 110 + ], + "type": "text", + "content": "2: Output: convexity penalty " + }, + { + "bbox": [ + 312, + 98, + 460, + 110 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ICR}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 110, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 110, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 312, + 110, + 545, + 133 + ], + "type": "text", + "content": "3: Generate a ray with random starting points and directions;" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 133, + 545, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 133, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 312, + 133, + 545, + 157 + ], + "type": "text", + "content": "4: Retrieve the first and last intersection points " + }, + { + "bbox": [ + 312, + 133, + 545, + 157 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 312, + 133, + 545, + 157 + ], + "type": "text", + "content": " by root-finding algorithm;" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "type": "text", + "content": "5: Uniformly sample " + }, + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "type": "text", + "content": " points between " + }, + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "type": "inline_equation", + "content": "x_{1}, x_{2}" + }, + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\{p_{j} = \\theta_{j}x_{1} + (1 - \\theta_{j})x_{2} | \\theta_{j} = \\frac{j}{K + 1}, j = 1, 2, \\dots, K\\}" + }, + { + "bbox": [ + 312, + 158, + 545, + 182 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 182, + 545, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 182, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 312, + 182, + 545, + 205 + ], + "type": "text", + "content": "6: Query the SDF values of the sampled points: " + }, + { + "bbox": [ + 312, + 182, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\{f(p_j)|j = 1,2,\\dots,K\\}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 205, + 545, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 205, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 312, + 205, + 545, + 230 + ], + "type": "text", + "content": "7: Compute 1st order direction derivative with finite difference: " + }, + { + "bbox": [ + 312, + 205, + 545, + 230 + ], + "type": "inline_equation", + "content": "\\{\\nabla f = f(p_j) - f(p_{j - 1})|j = 2,\\dots,K\\}" + }, + { + "bbox": [ + 312, + 205, + 545, + 230 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 312, + 230, + 545, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 230, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 312, + 230, + 545, + 254 + ], + "type": "text", + "content": "8: Compute 2rd order direction derivative with finite difference: " + }, + { + "bbox": [ + 312, + 230, + 545, + 254 + ], + "type": "inline_equation", + "content": "\\{\\nabla^2 f = \\nabla f(p_j) - \\nabla f(p_{j-1})|j = 3,\\dots,K\\}" + }, + { + "bbox": [ + 312, + 230, + 545, + 254 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 311, + 254, + 530, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 254, + 530, + 266 + ], + "spans": [ + { + "bbox": [ + 311, + 254, + 530, + 266 + ], + "type": "text", + "content": "9: Compute the penalty term " + }, + { + "bbox": [ + 311, + 254, + 530, + 266 + ], + "type": "inline_equation", + "content": "L = \\sum max(-\\nabla^2 f, 0)" + }, + { + "bbox": [ + 311, + 254, + 530, + 266 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 310, + 266, + 381, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 266, + 381, + 277 + ], + "spans": [ + { + "bbox": [ + 310, + 266, + 381, + 277 + ], + "type": "text", + "content": "10: return " + }, + { + "bbox": [ + 310, + 266, + 381, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ICR}" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 301, + 547, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 547, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 547, + 445 + ], + "type": "text", + "content": "signed distance is positive when the point is located outside of the surface, while the signed distance is negative when the point is located inside of the surface. To unify the primitives into a complete object, one could take the minimal value over all primitive SDFs as the final object SDF. However, doing so would block the gradient flow from the object SDF to the subminimal primitive SDFs, which leads to suboptimal convergence. To this end, we conduct a soft minimization, composed of a softmax and a weighted sum operation. Formally, suppose each primitive SDF is implemented as a MLP network " + }, + { + "bbox": [ + 304, + 301, + 547, + 445 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 301, + 547, + 445 + ], + "type": "text", + "content": ", the object signed distance of point " + }, + { + "bbox": [ + 304, + 301, + 547, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 301, + 547, + 445 + ], + "type": "text", + "content": " could be computed as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 347, + 454, + 545, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 454, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 347, + 454, + 545, + 520 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} S D F _ {p r i m i} ^ {i} (\\mathbf {p}) = f _ {i} (\\mathbf {p}), \\\\ \\omega_ {i} = \\operatorname {s o f t m a x} _ {N} (- \\beta \\cdot S D F _ {p r i m i} ^ {i} (\\mathbf {p})), \\tag {1} \\\\ S D F _ {o b j} (\\mathbf {p}) = \\sum_ {i = 1} ^ {N} \\omega_ {i} \\cdot S D F _ {p r i m i} ^ {i} (\\mathbf {p}), \\\\ \\end{array}", + "image_path": "b98cacfc5e4e945955369f4d7c7ab6ce94248427e32269be10d0630fc0184573.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "text", + "content": " is the scaling temperature (set to 10 in our experiments) in softmax operation, " + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "inline_equation", + "content": "\\omega_{i}" + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "text", + "content": " denotes the weight of " + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "text", + "content": "th primitive and " + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 529, + 545, + 566 + ], + "type": "text", + "content": " is the number of the primitives." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 714 + ], + "type": "text", + "content": "Surface Rendering. Considering the difficulty of acquiring 3D data in application, we aim at learning the implicit primitives from multi-view images. Although prior works such as BSPNet [3] and CvxNet [5] proposes 3D convexity representation based on hyper-planes, these representations are infeasible in current neural rendering pipelines, hindering the acquisition of convexity primitives from multi-view data. One key contribution of our method is that we extend convexity primitives to a implicit surface distance function, which is the common 3D representation of neural rendering pipelines." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3645" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 77, + 536, + 218 + ], + "blocks": [ + { + "bbox": [ + 60, + 77, + 536, + 218 + ], + "lines": [ + { + "bbox": [ + 60, + 77, + 536, + 218 + ], + "spans": [ + { + "bbox": [ + 60, + 77, + 536, + 218 + ], + "type": "image", + "image_path": "d399db9980f65e01b265ee93d15926394e60d832d5d43a9b67263b4931867ba7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 227, + 547, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 227, + 547, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 547, + 283 + ], + "type": "text", + "content": "Figure 4. Our network consists of N primitive MLPs and one color MLP. Each primitive MLP outputs an SDF value and a geometry latent code of the primitive from the input " + }, + { + "bbox": [ + 46, + 227, + 547, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 227, + 547, + 283 + ], + "type": "text", + "content": ". The primitive SDF values and latent codes go through a softmax-weighted-sum layer to obtain the object SDF and latent code, which are then respectively processed by a sigmoid layer and a color MLP. The obtained volume density " + }, + { + "bbox": [ + 46, + 227, + 547, + 283 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 227, + 547, + 283 + ], + "type": "text", + "content": " and RGB are applied in a standard implicit surface volume rendering method. The loss is computed by the weighted sum of reconstruction error and Implicit Convexity Regularization on each primitive." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 302, + 288, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 288, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 288, + 361 + ], + "type": "text", + "content": "Specifically, we integrate the implicit primitives into a neural rendering pipeline based on UNISURF [17]. To this end, we first extend the pirmitive MLPs in Sec 3.2 to additionally output a geometry latent code except for SDF value in the final layer, such that" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 369, + 287, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 369, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 91, + 369, + 287, + 384 + ], + "type": "interline_equation", + "content": "\\left[ S D F _ {p r i m i} ^ {i} (\\mathbf {p}), L _ {p r i m i} ^ {i} (\\mathbf {p}) \\right] = f _ {i} (\\mathbf {p}), \\tag {2}", + "image_path": "03229b4553af1d6cf2fc306e3d89d69cf406cc27ad40a79bb4c1573045d82dd8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{primi}^{i}(\\mathbf{p})" + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "text", + "content": " is the latent code of " + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "text", + "content": ". Similar to " + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "inline_equation", + "content": "SDF_{obj}(\\mathbf{p})" + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "text", + "content": ", the object latent code " + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "inline_equation", + "content": "L_{obj}(\\mathbf{p})" + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "text", + "content": " is obtained by the softmax-weighted-sum over all primitive latent codes. We further implement a color MLP which receives the object latent code as input and predicts the RGB value " + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 389, + 287, + 461 + ], + "type": "text", + "content": ". Then we apply the volume rendering as follows." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": "For a ray " + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": " starting from the camera position to the pixel location, we first retrieve the surface point " + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": " defined by " + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "inline_equation", + "content": "SDF_{obj}(\\mathbf{x}_s) = 0" + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": " using a root-finding algorithm. Then, we sample " + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": " points " + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": " along ray " + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": " within a interval around " + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_s" + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": ". We infer the object SDF value for each sample and convert it to volume density " + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\sigma_j" + }, + { + "bbox": [ + 46, + 462, + 287, + 534 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 95, + 540, + 287, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 540, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 95, + 540, + 287, + 554 + ], + "type": "interline_equation", + "content": "\\sigma_ {j} = \\operatorname {S i g m o i d} (- \\mu \\cdot S D F _ {o b j} (\\mathbf {x} _ {j})), \\tag {3}", + "image_path": "eb214445e2be658d5b5037977a916eb3605979cefa63dd34429baa817b077ff2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 560, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 560, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 560, + 287, + 609 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 560, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 560, + 287, + 609 + ], + "type": "text", + "content": " is a hyper-parameter that controls the sharpness of density distribution (set to 25 in all our experiments). The ray color is then obtained by the following volume rendering equation:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 102, + 614, + 287, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 614, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 102, + 614, + 287, + 649 + ], + "type": "interline_equation", + "content": "\\hat {C} (\\mathbf {r}) = \\sum_ {j = 1} ^ {N} \\sigma_ {j} \\prod_ {k < j} (1 - \\sigma_ {k}) \\mathbf {c} _ {j}. \\tag {4}", + "image_path": "8296e0b54f3c94320737cc07b4fe0596217f411fb6fb3a12b3945feae926b8c3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 654, + 287, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 680 + ], + "type": "text", + "content": "The reconstruction loss is computed over all sampled rays " + }, + { + "bbox": [ + 47, + 654, + 287, + 680 + ], + "type": "inline_equation", + "content": "\\mathbf{r} \\in \\mathcal{R}" + }, + { + "bbox": [ + 47, + 654, + 287, + 680 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 47, + 654, + 287, + 680 + ], + "type": "inline_equation", + "content": "C(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 654, + 287, + 680 + ], + "type": "text", + "content": " as the ground-truth pixel color:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 687, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 687, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 104, + 687, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left\\| \\hat {C} (\\mathbf {r}) - C (\\mathbf {r}) \\right\\| ^ {2}. \\tag {5}", + "image_path": "f7f77146e009940cdcfaeb3050ca40cc79bd3ddc9b583d2cadb4d65596f2a6b5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 302, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 302, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 545, + 338 + ], + "type": "text", + "content": "For more details on the neural rendering process, please refer to UNISURF [17]. Overall, we train our model with the following loss function:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 373, + 346, + 545, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 346, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 373, + 346, + 545, + 379 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {r e c} + \\lambda \\sum_ {i = 1} ^ {N} \\mathcal {L} _ {I C R} ^ {i}, \\tag {6}", + "image_path": "efecd5e39cd838a84a62e82f8c40c9a1ef8cb8ab7b01f2cb3e5344b103d1cf2e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ICR}^i" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": " is the proposed implicit convexity regularization derived in Algorithm 1, which is imposed on each primitive, and " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": " is the weighting hyper-parameter. Since " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ICR}" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": " is generally a small value, we set " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": " to 100 in our experiments. Illustration of the pipeline is presented in Figure 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 455, + 404, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 404, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 404, + 468 + ], + "type": "text", + "content": "3.3. Implementation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 473, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 594 + ], + "type": "text", + "content": "In all our experiments, each primitive SDF is implemented as a 4-layer MLP, with a skip connection from the input to the third layer. The color MLP also contains 4 layers. All layers have 64 hidden units. The input coordinates are first encoded by a sinusoidal embedding layer with " + }, + { + "bbox": [ + 304, + 473, + 545, + 594 + ], + "type": "inline_equation", + "content": "L = 6" + }, + { + "bbox": [ + 304, + 473, + 545, + 594 + ], + "type": "text", + "content": ", as done in UNISURF [17]. We use the Adam optimizer [10] with an initial learning rate of " + }, + { + "bbox": [ + 304, + 473, + 545, + 594 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 304, + 473, + 545, + 594 + ], + "type": "text", + "content": ". The learning rate is multiplied by 0.5 in 4,000th and 5,000th iteration. For each iteration, we sample 1,024 rays for volume rendering. The model is trained for 10,000 iterations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 604, + 388, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 388, + 617 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 388, + 617 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 623, + 410, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 410, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 410, + 635 + ], + "type": "text", + "content": "4.1. Synthetic Dataset" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "content": "Dataset. ShapeNet [1] is a shape collection composed of multiple categories. We conduct experiments on six categories including airplane, car, chair, lamp, table and pistol. We evaluate our method and prior works on randomly-selected 20 shapes for each category. For our method and UNISURF, we use the multi-view images rendered by" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3646" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 285, + 466 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 285, + 466 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 285, + 466 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 285, + 466 + ], + "type": "image", + "image_path": "7fd5aeb5a780da6a9ea56cf8e55d2902abb7ac4a76b2d50b926881af15eb5189.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 472, + 546, + 495 + ], + "lines": [ + { + "bbox": [ + 46, + 472, + 546, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 546, + 495 + ], + "type": "text", + "content": "Figure 5. We visualize the ShapeNet results of our method and prior works, including BAENet, EMS and UNISURF. Our method achieves notably better decomposition and fidelity than BAENet and EMS." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 288, + 76, + 544, + 466 + ], + "blocks": [ + { + "bbox": [ + 288, + 76, + 544, + 466 + ], + "lines": [ + { + "bbox": [ + 288, + 76, + 544, + 466 + ], + "spans": [ + { + "bbox": [ + 288, + 76, + 544, + 466 + ], + "type": "image", + "image_path": "21d940d97650e97753c8db551aa80105073cfba546a4e2825902a00da467e99e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 513, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 550 + ], + "type": "text", + "content": "DISN [27], which includes 36 views for each object with known camera intrinsic and extrinsic parameters. The images are rendered in " + }, + { + "bbox": [ + 46, + 513, + 287, + 550 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 513, + 287, + 550 + ], + "type": "text", + "content": " resolution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "Comparisons. We compare our method with the following works. i) BAENet [4]: BAENet is a learning-based primitive decomposition method that is trained on a shape collection within a category. It receives 3D voxel as input and predict an implicit field for each primitive. We follow its default settings which train the models on the complete collection for each categories without segmentation supervision, e.g. 2,690 objects for airplane. ii) EMS [13]: EMS is the state-of-the-art parameterized primitive decomposition method which derives superquadric primitives from a point cloud via a robust optimization algorithm. We follow its default setting in multi-superquadric optimization, and feed the ground-truth point cloud as input data. iii)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 513, + 547, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 547, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 547, + 634 + ], + "type": "text", + "content": "UNISURF [17]: UNISURF is a state-of-the-art implicit surface reconstruction method which derive the implicit field of an object from multi-view images. We include UNISURF for comparisons with a standard implicit surface reconstruction method in terms of fidelity. The above methods are summarized in Table 1. We use two metrics for evaluation, including Chamfer Distance (CD) and Intersection over Union (IoU). The quantitative results are reported in Table 2. We also visualize the meshes in Figure 5, with different colors for different primitives." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Results. Figure 5 and Table 2 show that our method achieves notably better decomposition and fidelity than BAENet and EMS. In Figure 5, our method consistently decomposes objects into semantic elements in convex geometry for different categories. BAENet fails in chair, lamp and pistol cases, where the chair back and cushion, lamp" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3647" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 288, + 155 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 155 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 155 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 155 + ], + "type": "table", + "html": "
MethodData SourceRecon Semantic
UNISURFFitted on 2D data✓X
EMSFitted on 3D data✓✓
BAENetTrained on large-scale 3D data✓✓
CvxNetTrained on large-scale 3D data✓X
ICR (Ours)Fitted on 2D data✓✓
", + "image_path": "0176cadd243fb8f268f6e3b6d07f89291d2e0ab84f7feb4861a0aafc0f1aab77.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 47, + 190, + 287, + 299 + ], + "blocks": [ + { + "bbox": [ + 47, + 159, + 286, + 182 + ], + "lines": [ + { + "bbox": [ + 47, + 159, + 286, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 159, + 286, + 182 + ], + "type": "text", + "content": "Table 1. Summary of compared methods. Recon and Semantic denote capability of reconstruction and semantic decomposition." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 190, + 287, + 299 + ], + "lines": [ + { + "bbox": [ + 47, + 190, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 190, + 287, + 299 + ], + "type": "table", + "html": "
CD↓\\IoU↑UNISURFOursBAENetEMS
Airplane0.32\\86.30.50\\79.20.91\\57.83.12\\26.8
Pistol0.53\\74.80.85\\62.51.67\\38.42.32\\32.6
Table1.57\\42.11.40\\43.22.86\\22.46.85\\18.5
Chair1.00\\49.21.29\\47.41.45\\41.75.74\\16.9
Lamp0.27\\89.60.99\\53.81.56\\38.62.76\\25.0
Car1.46\\48.51.86\\37.22.06\\31.52.36\\27.5
Mean0.86\\65.11.15\\53.91.75\\38.43.86\\24.6
", + "image_path": "6279fa2b0201ff6f72e91ad04b022ff1549fba236aedd09ac1c1dca7b9d78717.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 304, + 286, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 286, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 286, + 369 + ], + "type": "text", + "content": "Table 2. We measure the Chamfer Distance " + }, + { + "bbox": [ + 46, + 304, + 286, + 369 + ], + "type": "inline_equation", + "content": "(10^{-3},\\downarrow)" + }, + { + "bbox": [ + 46, + 304, + 286, + 369 + ], + "type": "text", + "content": " and Intersection over Union " + }, + { + "bbox": [ + 46, + 304, + 286, + 369 + ], + "type": "inline_equation", + "content": "(\\uparrow)" + }, + { + "bbox": [ + 46, + 304, + 286, + 369 + ], + "type": "text", + "content": " between the reconstructed surface and the ground-truth shapes. Our method achieves better reconstruction accuracy compared to prior primitive decomposition methods, even comparable to UNISURF, which is a state-of-the-art surface reconstruction method." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 392, + 286, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 286, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 286, + 571 + ], + "type": "text", + "content": "bulb and base, pistol barrel and handle are mixing together. Besides, Table 2 shows that BAENet achieves lower reconstruction accuracy than ours, even though it is trained on 3D data and receives 3D voxel as input. In table category, it fails to reconstruct the table leg. EMS fails in most cases with low fidelity and unreasonable decomposition. The reason for that is that EMS is based on a iterative optimization, where one primitive is fitted to the point cloud until convergence and then another primitive is fitted to the rest outliers and so on. It generally falls into a local minimum for objects that do not consist of a main stem and branches. Compared to UNISURF, we achieve comparable reconstruction accuracy in most cases. For table category, we even surpass UNISURF on modeling thin geometry such as the table legs, owing to convexity prior of our method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 585, + 162, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 585, + 162, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 585, + 162, + 597 + ], + "type": "text", + "content": "4.2. Real-World Dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "One question might be raised that if we have access to multi-view images, why not just recover its 3D representation using multi-view reconstruction methods. However, even though we could reconstruct 3D representation for one sample, it is still inefficient or even impractical to conduct reconstruction for a large-scale dataset. What's more, the common case in real-world scenarios is that we are not able to acquire a large-scale real-world datasets for ONE target object. It is demonstrated by our experiments on CO3D." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "Dataset. CO3D [21] is a multi-view dataset collected on real-world objects with known camera intrinsic and extrinsic parameters. Each object includes a varied number of views ranging from tens to hundreds. The resolution of each image also varies from " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "1000 \\times 500" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "1600 \\times 1000" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ". We crop the images with a square bounding box centered at the object and then resize them to " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " for training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 161, + 545, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 161, + 545, + 245 + ], + "spans": [ + { + "bbox": [ + 304, + 161, + 545, + 245 + ], + "type": "text", + "content": "Comparisons. Note that prior works which are trained on a 3D shape collection are basically infeasible in this dataset, since CO3D lacks regular 3D data form (except for some objects that have a noisy point cloud generated by MVS algorithm). Therefore we compare our method with UNISURF (based on multi-view images) and EMS (based on point clouds) in terms of visual effects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 251, + 545, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 310 + ], + "type": "text", + "content": "Results. As shown in Figure 6, our method is able to decompose objects into convex primitives with rich semantics. The reconstruction accuracy is comparable to UNISURF in terms of visual effect. EMS generates several invalid primitives which do not match the object geometry." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 318, + 399, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 318, + 399, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 318, + 399, + 331 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 337, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 545, + 588 + ], + "type": "text", + "content": "Effectiveness of Convexity Regularization. We evaluate the effectiveness of the proposed implicit convexity regularization by removing this regularization in the neural rendering pipeline, while other settings remain the same. We show the comparisons in Figure 7. Comparing results with and without ICR, we see that ICR successfully guarantees the convexity of each primitive, which benefits consistent semantic decomposition. Although optimization without ICR could sometimes obtain higher fidelity, such as the reconstruction of wings and tails of the planes, it generally causes illogical decomposition, i.e., part of the wing is assigned to the stem primitive, and part of the chair cushion is assigned to the back primitive. Besides, we also find that with the convexity prior, the reconstructions of the thin objects are more plausible, such as the chair legs. The reason is that convex regularization encourages simple geometry. By contrast, in the case of removing ICR, the reconstruction is done by ray sampling, which could be insufficient to recover a smooth object surface. More example primitives obtained with and without ICR could be found in left and right column respectively in Figure 2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Convexity Controlling. We demonstrate that controlling the weight of implicit convexity regularization could achieve trade-off between primitive simplicity and fidelity. Specifically, we convert Equation 6 into " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_{rec} + \\sum_{i=1}^{N} \\lambda_i \\mathcal{L}_{ICR}^i" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", in which " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_i" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " are tunable for individual primitive. We then apply a smaller weight " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_i" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{ICR}^i" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " for those primitives which we prefer higher fidelity than simplicity, while other primitives remain still. We show some examples in Figure 8. In the bottom row, we set the " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " of the primitives circled in red (tail of the plane and trigger of the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3648" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 68, + 286, + 194 + ], + "blocks": [ + { + "bbox": [ + 53, + 68, + 286, + 194 + ], + "lines": [ + { + "bbox": [ + 53, + 68, + 286, + 194 + ], + "spans": [ + { + "bbox": [ + 53, + 68, + 286, + 194 + ], + "type": "image", + "image_path": "0414152f0dd8b0c9732026ac5881c27c301e1d928ad399895a426a2c23554793.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 288, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 288, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 288, + 232 + ], + "type": "text", + "content": "Figure 6. Visualization of CO3D experiments. Our method is able to decompose objects into plausible shape primitives from multiview input. EMS obtains shape primitives from point clouds." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 244, + 286, + 365 + ], + "blocks": [ + { + "bbox": [ + 48, + 244, + 286, + 365 + ], + "lines": [ + { + "bbox": [ + 48, + 244, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 48, + 244, + 286, + 365 + ], + "type": "image", + "image_path": "3863a28aca959711fdca4e02f30785adadfb4a903fcdebd23fb517ee1d42118c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 367, + 287, + 401 + ], + "lines": [ + { + "bbox": [ + 46, + 367, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 287, + 401 + ], + "type": "text", + "content": "Figure 7. The proposed Implicit Convexity Regularization (ICR) theoretically guarantees the convexity and simplicity of each primitive. Removing ICR causes unreasonable decomposition." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 414, + 284, + 575 + ], + "blocks": [ + { + "bbox": [ + 50, + 414, + 284, + 575 + ], + "lines": [ + { + "bbox": [ + 50, + 414, + 284, + 575 + ], + "spans": [ + { + "bbox": [ + 50, + 414, + 284, + 575 + ], + "type": "image", + "image_path": "7e5270e9daa822f86a216918808cc5190887a0e8f6bfadf237e38090ef94814e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 579, + 289, + 657 + ], + "lines": [ + { + "bbox": [ + 46, + 579, + 289, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 289, + 657 + ], + "type": "text", + "content": "Figure 8. Tuning " + }, + { + "bbox": [ + 46, + 579, + 289, + 657 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 579, + 289, + 657 + ], + "type": "text", + "content": ", the weight of ICR, for individual primitive could achieve trade-off between fidelity and simplicity. In the bottom row, we set the " + }, + { + "bbox": [ + 46, + 579, + 289, + 657 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 579, + 289, + 657 + ], + "type": "text", + "content": " of the primitives circled in red (tail of the plane and trigger of the pistol) to 1 and others to 100. In this way we obtain a flexible primitive with higher accuracy, while other parts still preserve their semantics and simplicity. We compute the chamfer distance (CD) to evaluate the fidelity." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 675, + 287, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 675, + 287, + 723 + ], + "spans": [ + { + "bbox": [ + 46, + 675, + 287, + 723 + ], + "type": "text", + "content": "pistol) to 1 and others to 100. In this way we obtain a flexible primitive with higher accuracy, while other parts still preserve their semantics and simplicity. The adjusted primitives achieve lower chamfer distance than the vanilla ones." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 547, + 143 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 547, + 143 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 547, + 143 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 547, + 143 + ], + "type": "table", + "html": "
SVR\\SegAirplaneTableChairLamp
OccNet57.1\\—50.6\\—50.1\\—37.1\\—
CvxNet59.8\\—47.3\\—49.1\\—31.1\\—
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", + "image_path": "111b5ea32dc1e13818d5b0e1f2e2cc2e9cef3fdc30ffe1154420ab593845b3c2.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 148, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 305, + 148, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 547, + 213 + ], + "type": "text", + "content": "Table 3. We extend our proposed ICR term to a large-scale 3D training setting. We compare our method with prior works on single-view 3D reconstruction (IoU ↑) and semantic segmentation (IoU ↑) tasks. Since OccNet and CvxNet are incapable of decomposing objects into semantic parts, their segmentation performance are absent." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 235, + 547, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 547, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 547, + 618 + ], + "type": "text", + "content": "Training on 3D datasets. Although our method is designed for multi-view data, we would also like to test its performance in a large-scale 3D training setting that is similar with prior primitive-learning methods. To this end, we further conduct a set of experiments on ShapeNet, in which we integrate our ICR term into an encoder-decoder network and train it on a dataset within one category. The network receives 3D voxels as input and predict SDF value of query points. The encoder is implemented as a 3D CNN, similar to prior works [3, 4], while the decoder is implemented by our primitive representation in Equ. 1. Following prior works [3], after the training is finished, we replace the 3D encoder with a 2D CNN and train it on a single-view reconstruction task while the decoder is fixed. We measure single-view reconstruction accuracy as well as semantic decomposition performance using the segmentation labels from ShapeNetPart [30]. Intersection over Union (IoU) is used as the metric for both tasks. We experiment on four categories of ShapeNet: airplane, chair, lamp and table. We follow the train-test-split in BAENet. The detailed network architecture and experiment setting is presented in the appendix. We compare our method with OccNet [14], BAENet [4] and CvxNet [5]. The results are listed in Table 3. Compared to BAENet and CvxNet, our method achieves similar or even better reconstruction accuracy in single-view reconstruction task. We found that the artifact of disappearance (see Fig. ?? table) and dilation (see Fig. ?? chair and lamp) exists in the results of BAENet and CvxNet, which is the main reason that their reconstruction accuracy is lower. Besides, our method is able to achieve better semantics decomposition. Note that all methods are validated without fine-tuning on test samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 632, + 379, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 379, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 379, + 645 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 547, + 715 + ], + "type": "text", + "content": "In this work, we propose a regularization term named Implicit Convexity Regularization (ICR) for primitive decomposition. We theoretically prove that imposing constraint on the second order directional derivatives on line segments inside a shape could encourage convexity for im" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3649" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 120 + ], + "type": "text", + "content": "plicit shapes represented by signed distance functions. Experiments on synthetic and real-world datasets demonstrate the superiority of our method over prior arts with respect to primitive simplicity, fidelity and semantics." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 132, + 162, + 145 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 132, + 162, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 132, + 162, + 145 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 152, + 287, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 287, + 200 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 287, + 200 + ], + "type": "text", + "content": "This work was supported by National Science Foundation of China (U20B2072, 61976137). 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In Proceedings of the IEEE International Conference on Computer Vision, pages 900-909, 2017." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3651" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_content_list.json b/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2836f12c442efc27860236270d4a1179082e30b4 --- /dev/null +++ b/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_content_list.json @@ -0,0 +1,1584 @@ +[ + { + "type": "text", + "text": "Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval", + "text_level": 1, + "bbox": [ + 133, + 130, + 836, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhongyan Zhang $^{1}$ , Lei Wang $^{1}$ , Luping Zhou $^{2}$ , Piotr Koniusz $^{3,4}$", + "bbox": [ + 238, + 202, + 732, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "University of Wollongong1, University of Sydney2, Data61♥CSIRO3, Australian National University4", + "bbox": [ + 86, + 220, + 883, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zhongyan@uow.edu.au, leiw@uow.edu.au, luping.zhou@sydney.edu.au, peter.koniusz@data61.csiro.au", + "bbox": [ + 122, + 241, + 849, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 312, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In instance image retrieval, considering local spatial information within an image has proven effective to boost retrieval performance, as demonstrated by local visual descriptor based geometric verification. Nevertheless, it will be highly valuable to make ordinary global image representations spatial-context-aware because global representation based image retrieval is appealing thanks to its algorithmic simplicity, low memory cost, and being friendly to sophisticated data structures. To this end, we propose a novel feature learning framework for instance image retrieval, which embeds local spatial context information into the learned global feature representations. Specifically, in parallel to the visual feature branch in a CNN backbone, we design a spatial context branch that consists of two modules called online token learning and distance encoding. For each local descriptor learned in CNN, the former module is used to indicate the types of its surrounding descriptors, while their spatial distribution information is captured by the latter module. After that, the visual feature branch and the spatial context branch are fused to produce a single global feature representation per image. As experimentally demonstrated, with the spatial-context-aware characteristic, we can well improve the performance of global representation based image retrieval while maintaining all of its appealing properties. Our code is available at https://github.com/Zy-Zhang/SpCa.", + "bbox": [ + 76, + 325, + 472, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 752, + 209, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Given a query image, the purpose of instance-level image retrieval is to search and retrieve the images containing the identical object described by the query from a largescale image dataset. In this task, visual feature representations of images play a crucial role in measuring the similarities between a query and candidate images. A variety of handcrafted feature-based methods [14, 38, 2] have been proposed to significantly improve the performance in", + "bbox": [ + 75, + 780, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the past two decades. Recently, due to the development of deep learning technologies, deep feature representations have been overtaking the position of conventional handcrafted ones and bringing great progress in the task of instance image retrieval [1, 3, 17, 28, 15].", + "bbox": [ + 496, + 292, + 890, + 368 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generally, deep feature representations used in instance image retrieval can be categorized into two types. One type is global feature representation, which describes the visual content of an image as a whole. As a multi-dimensional vector, it can be efficiently used to measure the similarity of two images, say, via Euclidean distance or cosine similarity. For a retrieval task, the total number of global feature representations is just the size of image database, and they can be pre-extracted and economically stored for use. In addition, one global feature representation per image works well with the classic data structures designed for searching. The other type is local descriptors, which describe the local information within an image and collectively reflect the spatial information of the visual cues in an image. In image retrieval, they are important for conducting geometric verification to confirm if two images truly match or not. However, the total number of local descriptors per image could be large (e.g., 1,000) and the verification involves non-trivial computation, making this process expensive in computational cost and memory footprint.", + "bbox": [ + 496, + 369, + 892, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This situation leads to a wide use of \"two-stage\" paradigm in instance image retrieval [23, 3, 17]. An initial retrieval result is firstly obtained via the global feature representation. After that, a re-ranking step utilizes the local descriptors to refine a small number of top-retrieved images. Nevertheless, this two-stage paradigm not only results in two separate procedures [26, 10] but also considerably increases retrieval time and memory expense for practical retrieval tasks [18], due to the presence of the local descriptor-based spatial verification step. Therefore, it will be highly valuable to make ordinary global image representations spatial-context-aware by considering their appealing properties of algorithmic simplicity, low memory cost, and being friendly to data structures.", + "bbox": [ + 496, + 672, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To achieve this, we propose a novel feature learning", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 805, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11250", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "framework to effectively embed spatial context information into global feature representation of images. Doing so will help to boost the retrieval performance of global feature representation, improving its efficacy when the local descriptor based re-ranking becomes costly or infeasible.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, two types of information are extracted in our framework. One is conventional visual information obtained by a visual feature branch in a CNN backbone. The other one is spatial context information that describes for each local descriptor learned in CNN, what kind of surrounding local descriptors are and how they spatially distribute on a feature map. To obtain this information, we develop a spatial context branch that operates in parallel to the visual feature branch in CNN. This branch consists of two modules called online token learning and distance encoding. The module of online token learning addresses the \"what kind\" issue. A set of semantic tokens that could be regarded as anchors in the space of local descriptors is learned in an online manner. Comparing the tokens to the visual words in a visual dictionary, each local descriptor can be uniquely labelled via soft coding as a token-based identification. The module of distance encoding cares about the \"spatial distribution\" issue. A probability transition based encoding is devised to reflect the relative spatial distance between each pair of local descriptors, so as to capture their spatial distribution information in a feature map. After that, the token-based identification and the spatial distribution information are integrated to produce a spatial context clue for each local descriptor. With both visual and spatial information, a feature fusion operation is conducted to fuse them together to generate spatial-context-aware local descriptors. Finally, a global pooling followed by a whitening layer is added to embed the context-aware local descriptors into a global feature representation for each image.", + "bbox": [ + 75, + 167, + 472, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarised as follows:", + "bbox": [ + 96, + 606, + 398, + 619 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "i. We propose an end-to-end feature learning framework to characterise and embed spatial context information into the process of information processing and extraction in CNN. It makes global feature representations become more capable for instance image retrieval.", + "ii. To implement the framework, we design a spatial context branch. With its online token learning module, the types of local descriptors are identified and easily compared. With the distance encoding module, the information about the spatial distribution of different types of local descriptors around a given descriptor is obtained.", + "iii. To verify the efficacy of the proposed framework, we conduct extensive experiments on instance image retrieval benchmark datasets, ROxford and RParis, with one million distractors. As demonstrated, our global feature representations effectively improve the perfor" + ], + "bbox": [ + 73, + 633, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mance of instance image retrieval, making global representation a more competitive option for practical tasks.", + "bbox": [ + 522, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 136, + 640, + 152 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we briefly review deep instance image retrieval, including local and global feature learning methods.", + "bbox": [ + 500, + 162, + 890, + 193 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Global features", + "text_level": 1, + "bbox": [ + 500, + 203, + 653, + 218 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Global feature has been widely used to represent the content of images for a wide range of computer vision tasks [21, 13, 8, 36, 37, 12, 11]. Due to its compactness and efficiency, a variety of global methods [24, 32, 35, 15] have been proposed to learn discriminative feature representations via deep models in the instance image retrieval community. Some of the studies focus on applying more effective loss functions, including triplet losses [29], list-wise losses [22], and classification losses [5] to train the model. Others explore how to pool the entire feature maps into a compact feature vector while maintaining their discrepancies. For instance, weighted-sum-pooling (CroW) [9], regional-max-pooling (R-MAC) [29], and GeM pooling [20]. Recently, several methods try to modify the training model architecture to capture more useful information during the training process. SOLAR [15] combines normal training with second-order information by adding self-attention modules in the conventional CNN backbones. Token [32] jointly learns a set of tokens and the corresponding visual representations to mimic the conventional dictionary learning plus feature encoding scheme to represent images. Some other studies [32, 35] propose multiple branches for CNN models to mine more complementary information and fuse them into the final feature vectors. We follow the global feature type to learn compact features to conduct retrieval.", + "bbox": [ + 498, + 227, + 890, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Local features", + "text_level": 1, + "bbox": [ + 500, + 614, + 645, + 630 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep local descriptors [28, 30, 33, 17] have been extensively researched and made significant progress in instance image retrieval [4]. The key to their success lies in the spatial information these local descriptors hold, and it is usually utilized by kernel alignment aggregation (e.g., ASMK [27]) or geometric verification (e.g., RANSAC [6]) for image similarity measure. In recent studies, several methods [26, 10] individually train a matching model to directly compare the similarity of two images (or their preextracted local descriptors) in a data-driven manner. However, they need more inference time and memory footprint. Therefore, they are usually applied to only top k retrieved images obtained by a global retrieval method as a reranking.", + "bbox": [ + 498, + 638, + 890, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Learning local and global features jointly", + "text_level": 1, + "bbox": [ + 500, + 845, + 852, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Driven by the complementary properties of global and local features, jointly learning the two types of features", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11251", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f2251ae6b4e61f4031aaa5f42f3b6e8b4274391297ae37ea7ff703bf923e5c60.jpg", + "image_caption": [ + "Figure 1. Overview of our framework. After an initial feature extraction by a CNN backbone, two branches of \"Visual Feature Branch\" and \"Spatial Context Branch\" are used to extract visual and spatial context information. After that, a cross-attention module is used to fuse the visual feature and the corresponding spatial context feature to generate spatial-context-aware visual representations for images. In particular, \"GMM\" denotes the Gaussian Mixture Model process, and \"GP+W\" refers to global pooling followed by whitening." + ], + "image_footnote": [], + "bbox": [ + 120, + 87, + 851, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "becomes a straightforward idea. Recently, several studies demonstrate the advantages of learning features in this manner. DELG [3] creatively unifies the two separate learning processes into one training framework. However, even though the training procedure is unified, the learning processes of the two feature types are still somehow irrelevant. To further explore this approach, DOLG [35] and DALG [25] firstly separate the feature extractor into two branches to learn the local and global features and then fuse them via a manual or learnable way to obtain compact feature representations for images. Both of them try to extract individual visual information from the two types of features to make them complementary to each other. However, the powerful spatial context information held by local features is neither exploited nor embedded into the final feature representations. In this work, we argue that spatial context information is more beneficial than visual information from local descriptors to the final global feature representations for instance image retrieval. To this end, we propose a novel feature learning framework to effectively embed the spatial context information into final global features.", + "bbox": [ + 75, + 335, + 472, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 676, + 287, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of our framework is in Figure 1. Given an image $I$ , a conventional CNN backbone is used to generate a feature map $\\mathbf{V} \\in \\mathbb{R}^{D \\times H \\times W}$ , in which each spatial position corresponds to a $D$ -dimensional local visual descriptor. Besides, a spatial context branch is split from the feature map to extract the spatial context information of all the descriptors, which is represented in the form of $\\mathbf{S} \\in \\mathbb{R}^{C \\times H \\times W}$ with $C$ being the dimensions. After that, for each local descriptor, its two kinds of information are fused together, say, with a cross-attention module or a simple concatenation operation. After the fusion, a global pooling and a fully-connected layer are used to generate the final global spatial-context-aware feature $\\mathbf{f}_{spca}$ to represent the image. In the following,", + "bbox": [ + 75, + 704, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "we focus on describing the spatial context branch since the visual branch follows its original design in CNN backbones.", + "bbox": [ + 498, + 335, + 890, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Spatial Context Branch", + "text_level": 1, + "bbox": [ + 498, + 376, + 718, + 392 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the spatial context branch, there are two main issues to be addressed for each spatial position on the feature map: 1) what kinds of local descriptors are there in its surrounding region (i.e., identification task); 2) how they spatially distribute on the feature map (i.e., spatial distribution task). We now introduce how we address the two issues orderly.", + "bbox": [ + 498, + 398, + 890, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Token-based Identification. For existing local feature-based retrieval methods [28, 30, 33], learning tokens to capture discriminative visual patterns in a dataset has proven reliable to identify local descriptors. With the tokens, the encoded features could become more robust against illumination change, the information loss due to occlusion, and the adverse impact of the background in an image. In our framework, we generally follow this \"tokens plus encoding\" pipeline to identify local descriptors. However, in the literature, the tokens are usually learned by clustering (e.g., by k-means) a sampled subset of local descriptors obtained from an image dataset in an offline manner. This way separates the process of token learning from encoding, potentially causing a discrepancy between the training and the inference stages. In addition, using a sampled subset of local descriptors could lead to learning biased tokens since the information available in an image dataset is not fully utilized. To improve this situation, we perform token learning via an online mini-batch based Gaussian Mixture Model (GMM) process. This helps to adequately utilize all the local descriptors to learn tokens and makes our framework fully end-to-end trainable.", + "bbox": [ + 496, + 507, + 892, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, we model the distribution of local descriptors by a $K$ -component Gaussian mixture model $p(\\mathbf{v}|\\Theta) = \\sum_{k}\\alpha_{k}N(\\mathbf{v};\\boldsymbol{\\mu}_{k},\\Sigma_{k})$ , where $\\mathbf{v}$ denotes the a local descriptor, while $\\alpha_{k},\\boldsymbol{\\mu}_{k}$ , and $\\Sigma_{k} = \\sigma_{k}^{2}I_{D}$ denote the prior probability, the", + "bbox": [ + 498, + 839, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11252", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mean, and the (spherical) covariance matrix for component $k$ , respectively. In this case, token learning boils down to the parameter estimation for this Gaussian mixture model. At the beginning, $\\mu$ and $\\sigma^2$ are randomly generated and $\\alpha$ is set as $1 / K$ . After that, we conduct the Expectation and Maximization (EM) process for all the local descriptors within each mini-batch. To be concise, we show the key results below and the details can be found in the literature [16].", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Within each mini-batch, for the E-Step, the probability that the $i$ th local descriptor $\\mathbf{v}_i$ belongs to the $k$ th component can be expressed as", + "bbox": [ + 75, + 212, + 468, + 258 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\omega_ {i k} = \\frac {\\alpha_ {k} N \\left(\\mathbf {v} _ {i} ; \\boldsymbol {\\mu} _ {k} , \\Sigma_ {k}\\right)}{\\sum_ {j = 1} ^ {K} \\alpha_ {j} N \\left(\\mathbf {v} _ {i} ; \\boldsymbol {\\mu} _ {j} , \\Sigma_ {j}\\right)} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 268, + 468, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For M-Step, the prior probability, the mean and the covariance are updated as", + "bbox": [ + 76, + 316, + 467, + 347 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {k} \\leftarrow \\alpha_ {k} + \\beta \\left(\\frac {\\sum_ {i} \\omega_ {i k}}{H W} - \\alpha_ {k}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 358, + 328, + 388 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {k} \\leftarrow \\boldsymbol {\\mu} _ {k} + \\beta \\left(\\frac {\\sum_ {i} \\omega_ {i k} \\mathbf {v} _ {i}}{\\sum_ {i} \\omega_ {i k}} - \\boldsymbol {\\mu} _ {k}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 391, + 468, + 422 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {k} ^ {2} \\leftarrow \\sigma_ {k} ^ {2} + \\beta \\Big (\\frac {\\sum_ {i} \\omega_ {i k} \\| \\mathbf {v} _ {i} - \\boldsymbol {\\mu} _ {k} \\| ^ {2}}{\\sum_ {i} \\omega_ {i k}} - \\sigma_ {k} ^ {2} \\Big),\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 425, + 401, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $HW$ is the number of local descriptors obtained from an image, and $\\beta$ is a momentum to make the estimation process more stable in the mini-batch clustering [16]. One E-Step and M-Step are conducted in each iteration during the training.", + "bbox": [ + 76, + 470, + 468, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After the above process, $(\\pmb{\\mu}_1,\\pmb{\\mu}_2,\\dots ,\\pmb{\\mu}_K)$ represents the learned tokens. $\\omega_{i} = (\\omega_{i1},\\omega_{i2},\\dots ,\\omega_{iK})\\in \\mathbb{R}^{K}$ obtained by Eq. (1) can be used as the token-based identification for local descriptor $\\mathbf{v}_i$ since it represents the posterior probability that this descriptor belongs to each of the $K$ components.", + "bbox": [ + 76, + 547, + 468, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Spatial Distribution. To extract spatial distribution information for a local descriptor $\\mathbf{v}_i$ , the distances of this descriptor to all the descriptors $V = \\{\\mathbf{v}_j, j = 1,2,\\dots,HW\\}$ presented on the same feature map should be effectively measured and collected. To achieve this, simply using the coordinate distances among them is inadequate. We utilize a probability transition score obtained by applying random walk on the graph constituted by all the local descriptors as the nodes to measure the distances. By doing so, more possible paths among the local descriptors will be considered and the number of random walk steps could also be used to control the spatial scale in the distance measurement. Inspired by the literature [11], we perform the spatial distribution extraction as an aggregation of the encoded distances between $\\mathbf{v}_i$ and all $\\mathbf{v}_j \\in V$ . By \"coded,\" we mean that the distance is measured by a probability transition process as explained below.", + "bbox": [ + 75, + 643, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an undirected graph with an affinity matrix $A$ , the distance of its nodes $\\nu$ and $u$ can be encoded by a probability transition score $\\zeta$ obtained via $l$ steps of random walk", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\zeta (v, u) ^ {(l)} = \\left(M ^ {l}\\right) _ {v u}, M ^ {1} = A D ^ {- 1}, M ^ {l} = M ^ {l - 1} \\cdot M, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 148, + 890, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M^1$ denotes the random walk matrix, $D^{-1}$ refers to the normalization matrix of the graph, and $l$ is the number of random walk steps. Based on this, the distance of a node $v$ from all nodes $u$ in a target set $S$ can be represented by an aggregation operation as", + "bbox": [ + 498, + 178, + 890, + 253 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\zeta (\\nu , S) ^ {(l)} = \\operatorname {a g g} \\left(\\left\\{\\zeta (\\nu , u) ^ {(l)} \\mid u \\in S \\right\\}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 266, + 890, + 282 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Linking the above result to our case, the undirected graph consists of all the local descriptors $V$ in an image, and they collectively form the target set $S$ in this distance encoding process. In addition, we compute the affinity matrix $A$ based on the coordinate distance on the feature map as", + "bbox": [ + 498, + 297, + 890, + 372 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {i j} = \\exp (- \\operatorname {c o} _ {-} \\operatorname {d i s t} (\\mathbf {v} _ {i}, \\mathbf {v} _ {j})), (1 \\leq i, j \\leq H W), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 386, + 890, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{co\\_dist}(\\cdot, \\cdot)$ denotes the Euclidean distance between the coordinates of two local descriptors. After that, the encoded distance can be obtained by applying Eq. (3). Furthermore, we enrich Eq. (4) by considering the learned token-based identification (i.e., the posteriori probability $\\omega$ obtained in Eq. (1)), and this leads to an instantiated \"agg\" operation in Eq. (4) to produce the spatial context feature for local descriptor $\\mathbf{v}_i$ .", + "bbox": [ + 498, + 415, + 890, + 535 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {s} _ {i} ^ {(l)} \\triangleq \\zeta (v _ {i}, S) ^ {(l)} = \\sum_ {j = 1} ^ {H W} \\zeta (\\mathbf {v} _ {i}, \\mathbf {v} _ {j}) ^ {(l)} \\boldsymbol {\\omega} _ {j}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 547, + 890, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Recall that the token-based identification $\\omega_{i}$ can be treated as a vector of probability transition scores between local descriptor $\\mathbf{v}_i$ and each of the learned tokens $\\pmb{\\mu}$ . By combining the encoded distance and the token-based identification, the spatial context feature $\\mathbf{s}_i$ in Eq. (6) essentially reflects the probability transition scores between node $\\mathbf{v}_i$ and the tokens $\\pmb{\\mu}$ when regarding the spatial structure of the given $H\\times W$ feature map as a (static) transition matrix. This is illustrated in Figure 2. That means the spatial distribution information is used to control the extraction of the spatial context features. In this sense, the spatial distribution information is effectively embedded into the spatial context features. At last, we define the final spatial context feature for the local descriptor $\\mathbf{v}_i$ obtained through an $l$ -step random walk as", + "bbox": [ + 498, + 601, + 890, + 813 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {s} _ {i} = \\mathbf {s} _ {i} ^ {(1)} \\oplus \\mathbf {s} _ {i} ^ {(2)} \\oplus \\dots \\oplus \\mathbf {s} _ {i} ^ {(l)}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 823, + 890, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\oplus$ denotes concatenation operation. The concatenation of the features obtained after each of the $l$ steps considers the spatial context information at various scales.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11253", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f813abe790e495de1e008e840498cc75242bf80e3f649dd11f810b1ad905fc37.jpg", + "image_caption": [ + "Figure 2. Spatial context feature generation. See the detailed description after Eq. (6)." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 472, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Fusion of Visual and Spatial Information", + "text_level": 1, + "bbox": [ + 76, + 383, + 426, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With both visual and spatial context information available, a proper fusion scheme is needed to make them complements to benefit the final feature representation. To accomplish it, various feature fusion schemes could be used, including concatenation, orthogonal fusion [35], Hadamard product, or cross-attention fusion. We utilize a cross-attention module for information fusion in our method since it is commonly used to align features from different modalities in the recent literature. Meanwhile, we provide an ablation study on all the four fusion schemes in the experimental part. For the cross-attention scheme, the spatial context feature $\\mathbf{S} = (\\mathbf{s}_1,\\mathbf{s}_2,\\dots ,\\mathbf{s}_{HW})$ is projected into the same space as the visual feature $\\mathbf{V}$ with a linear projection layer. After that, both of them are flattened into sequences and mapped into Queries (Q), Keys (K), and Values (V), respectively, to put through into the cross-attention layer:", + "bbox": [ + 75, + 407, + 472, + 650 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {Q} = \\operatorname {p r o j} (\\mathbf {V}), \\mathbb {K} = \\operatorname {p r o j} (\\mathbf {S}), \\mathbb {V} = \\operatorname {p r o j} (\\mathbf {S})\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 662, + 408, + 678 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {s p c a} ^ {*} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbb {Q} \\cdot \\mathbb {K} ^ {\\top}}{\\sqrt {D}}\\right) \\cdot \\mathbb {V} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 680, + 468, + 714 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} _ {s p c a} = \\mathbf {F} _ {s p c a} ^ {*} + \\operatorname {M L P} \\left(\\mathbf {F} _ {s p c a} ^ {*}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 717, + 325, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where MLP denotes a feed-forward layer and $\\mathbf{F}_{spca}$ denotes the spatial-context-aware feature sequence. After that, the feature sequence is rearranged as a feature map, followed by a global pooling and a fully-connected layer to generate a global feature representation vector $\\mathbf{f}_{spca}$ .", + "bbox": [ + 75, + 744, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Objective Function for Training", + "text_level": 1, + "bbox": [ + 76, + 830, + 359, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following previous state-of-the-art work [3, 35, 32], we train our model on a dataset with object class annotations and utilize ArcFace margin loss [5] with learnable parame", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ters $\\hat{\\mathbf{W}}\\in \\mathbb{R}^{D\\times N}$ to train the whole model:", + "bbox": [ + 498, + 89, + 771, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = - \\log \\left(\\frac {\\exp \\left(\\gamma \\times A F \\left(\\hat {\\mathbf {w}} _ {t} ^ {\\top} \\hat {\\mathbf {f}} _ {s p c a} , 1\\right)\\right)}{\\sum_ {n} \\exp \\left(\\gamma \\times A F \\left(\\hat {\\mathbf {w}} _ {n} ^ {\\top} \\hat {\\mathbf {f}} _ {s p c a} , y _ {n}\\right)\\right)}\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 114, + 890, + 154 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{w}}_t$ denotes the $t$ th column of $\\hat{\\mathbf{W}}$ and $\\hat{\\mathbf{f}}_{spca}$ is the $L_{2}$ -normalized $\\mathbf{f}_{spca}$ . $y$ is the one-hot label vector and $t$ is the index to indicate the true class (i.e., $y_t = 1$ ). $n$ is the total number of classes in the dataset. $\\gamma$ is a scaling factor. $AF(\\cdot)$ refers to the ArcFace cosine similarity and it is calculated as", + "bbox": [ + 498, + 166, + 893, + 257 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA F (s, c) = \\left\\{ \\begin{array}{l l} \\cos (a \\cos (s) + m), & \\text {i f} c = 1 \\\\ s, & \\text {i f} c = 0 \\end{array} \\right. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 268, + 890, + 304 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s$ is the cosine similarity between $\\hat{\\mathbf{w}}_t$ and $\\hat{\\mathbf{f}}_{spca}$ , $m$ is the ArcFace margin and $c$ indicates if this is the true class.", + "bbox": [ + 498, + 316, + 890, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Result", + "text_level": 1, + "bbox": [ + 498, + 363, + 697, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset and Evaluation Metric", + "text_level": 1, + "bbox": [ + 498, + 388, + 772, + 404 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our model is trained on \"Google Landmark v2 clean\" dataset, which is a clean subset of Google Landmark v2 [31]. It contains 1,580,470 images of 81,313 landmark classes, and it has been widely used in existing methods [35, 32, 3] as the training dataset. To make a fair comparison, we follow the previous work [32, 35] to randomly divide the dataset into two subsets 'train'/'val' with $80\\% / 20\\%$ split. For evaluation, we use two widely used benchmark datasets, ROxford and RParis [19] to test our model. Both datasets have 70 query images but contain 4,993 and 6,322 gallery images, respectively. In addition, a 1M distractor set [19] is added to test our model for the case of large-scale retrieval. We use mean average precision (mAP), as the criterion of retrieval performance for both \"Medium\" and \"Hard\" splits of ROxford and RParis.", + "bbox": [ + 496, + 412, + 890, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 650, + 718, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use ResNet101/ResNet50 [8] as the CNN backbone to learn visual features. For image augmentation, random crop and color jittering are used first, and all the augmented images are resized into $512 \\times 512$ pixels as the model input. The model is trained on 4 Nvidia V100-SXM2-32GB GPU cards with a batch size of 128 for 50 epochs. We use SGD optimizer with a momentum of 0.9. A warming-up of 5-epoch's training is used to initialize the learning rate from 0.0001 to the base learning rate of 0.005. As for the ArcFace loss, the margin $m$ and the scale $\\gamma$ are empirically set as 0.2 and 45. For the global pooling, we utilize GeM [20] pooling with the fixed coefficient $p = 3$ during the whole training. $\\beta$ in the M-Step of GMM is empirically set as 0.999. In addition, we set the number of random walk steps $l$ as 3 and the number of tokens as $K = 16$ . The dimensions of the", + "bbox": [ + 496, + 674, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11254", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/57348d3bc951d83435a6a6f2330f0eca2c548cc9ecaab327e5bcbf580fbe4f5f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMediumHard
ROxfROxf+1MRParRPar+1MROxfROxf+1MRParRPar+1M
Global features + local features re-ranking
R101-DELG [3]+SP81.2069.1087.2071.5064.0047.5072.8048.70
R101-DELG [3]+SP†81.8270.1588.6476.1464.9749.5476.8153.62
Global features
R101-R-MAC [7]60.9039.3078.9054.8032.4012.5059.4028.00
R101-GeM [20]64.7045.2077.2052.3038.5019.9056.3024.70
R101-SOLAR [15]69.9053.5081.6059.2047.9029.9064.5033.40
R101-DELG [3]76.3063.7086.6070.6055.6037.5072.4046.90
R101-GLAM [24]78.6068.0088.5073.5060.2043.5076.8053.10
Swin-S-DALG [25]79.94-90.04-57.55-79.06-
R101-DOLG [35]★81.5077.4391.0283.2961.1054.8180.3066.69
R101-Token [32]82.2870.5289.3476.6666.5747.2778.5655.90
R101-Token [32]†77.8266.7487.9375.2260.1043.0774.6653.19
R101-DOLG [35]†78.35(75.51)(88.48)(78.25)58.59(52.36)(75.39)(61.85)
R101-DELG [3]†79.8267.8587.2172.4561.1642.5873.8450.79
R101-SOLAR [15]†(81.63)71.8488.2172.86(63.29)45.2875.2151.26
R50-SpCaacro (Ours)79.9172.7887.4378.0159.2749.2673.1458.3
R50-SpCaCat (Ours)81.5573.2088.6078.2361.1948.7676.2160.91
R101-SpCaacro (Ours)82.7377.8490.2079.1265.6053.3579.2965.84
R101-SpCaCat (Ours)83.2477.8290.5679.4865.8553.2779.9764.98
", + "bbox": [ + 89, + 87, + 880, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Performance (mAP) comparison with recent state-of-the-art instance image retrieval methods on datasets ROxford5k and RParis6k [19]. R101 and R50 denote ResNet101 and ResNet50. Swin-S denotes Swin-Transformer-small [13]. The subscripts $\\text{cro}$ and $\\text{cat}$ refer to cross-attention and concatenation feature fusion strategies. SP denotes spatial verification via RANSAC. $\\dagger$ denotes our reimplementation. $\\star$ means no query cropping. Results in gray are those reported in the published papers. The best and second best performances are highlighted in bold and with underlines, respectively. The best previous performance is shown in brackets.", + "bbox": [ + 75, + 440, + 893, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "final global feature are set as 2048. For inference, the multiple scales [0.3535, 0.5, 0.7071, 1.0, 1.4142] are applied to each original image to extract the feature representations. To fuse the features obtained from different scales, they are $L_{2}$ -normalized, summed, and normalized again to generate the final global features for retrieval.", + "bbox": [ + 75, + 535, + 470, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 633, + 441, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setting for fair comparison Note that there are setting differences among the previous state-of-the-art methods. For example, they are different at 1) pretrained model sources for initialization (Caffe $^{1}$ , PyTorch $^{2}$ , and Facebook $^{3}$ ); 2) training datasets (SfM-120k [20], GLDv1 [17], GLDv2 [31], and different $80\\% / 20\\%$ split); 3) the number of multiple scales used at the inference stage (e.g., 3, 5, or 7); 4) with or without query cropping scheme. These discrepancies could affect the fairness of the comparison if not well handled. To address this situation, we carefully re-implement multiple SOTA methods by using their officially published codes and the training parameters reported in their papers, while keeping the same settings for the", + "bbox": [ + 75, + 657, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "above factors between these methods and ours. Specifically, to ensure fair comparison, our experimental study utilizes the same $80\\%$ of GLDv2-clean [31] as the training dataset, the same remaining $20\\%$ of GLDv2-clean as the validation dataset, the same pretrained model from PyTorch for initialization, and the same 5 scales with query cropping scheme for inference to conduct instance image retrieval.", + "bbox": [ + 500, + 535, + 890, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Retrieval results Two groups of state-of-the-art methods are compared in this experimental study: 1) methods based on global feature representations. They include two milestone works R-MAC [7] and GeM [20] and another six more recent works including DELG [3], SOLAR [15], GLAM [24], DOLG [35], DALG [25], and Token [32]; 2) a method using global feature based initial retrieval plus local feature based re-ranking scheme, DELG+SP [3], is included as well. Also, note that we focus on global feature based image retrieval in this paper, and we do not consider training a verification model [10] or adding any post-processing steps like diffusion or query expansion to boost retrieval performance [34].", + "bbox": [ + 496, + 657, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The retrieval result is reported in Table 1. The methods under \"Global features\" are partitioned into three sections. The results in gray color are those reported in the original", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1http://cmp.felk.cyut.cz/cnnimageRetrieval/data/networks/imagenet", + "bbox": [ + 93, + 861, + 449, + 875 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{2}$ https://pytorch.org/vision/stable/models/generated/torchvision.models", + "bbox": [ + 96, + 875, + 468, + 887 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3https://github.com/facebookresearch/pycls", + "bbox": [ + 96, + 887, + 326, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11255", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "published papers. Since they involve different settings as discussed above, the results are included here mainly as a reference. Following the gray-colored results are those obtained by our re-implementation for the sake of fair comparison, and they are used to compare with our methods shown at the bottom of this table.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As seen, our method R101-SpCa (where \"SpCa\" is short for \"Spatial-context-aware\"), with either cross-attention ( $-cro$ ) or concatenation ( $-cat$ ) fusion strategy, clearly outperforms the others on all the test cases. Compared with the closest results obtained by DOLG and SOLAR, our method achieves $1.6\\%$ and $2.0\\%$ performance gain on the Medium split of ROxford and RParis, respectively. And higher improvements of $2.5\\%$ and $4.5\\%$ are obtained on the Hard split of the two datasets. After the 1M distractors are added, our method still demonstrates its excellent retrieval performance. All these results validate the efficacy of our method.", + "bbox": [ + 75, + 186, + 468, + 352 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared with the global initial retrieval plus local feature re-ranking scheme, our method still maintains its advantage. As listed in Table 1, even without using the pairwised re-ranking step as done in R101-DELG+SP [3], our method has outperformed it by around $2\\%$ on all dataset splits. More importantly, our method costs no extra inference time as taken by the re-ranking step. In addition, the memory footprint of our global feature representation (i.e., a 2048-dimensional vector per image) is also much less than that used by the local descriptor (there are usually 1,000 vectors per image, each of which is of 128 dimensions) based re-ranking. This again shows the computational advantage brought by our method.", + "bbox": [ + 75, + 357, + 470, + 553 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Computational Overhead We report the number of parameters, feature extraction latency, and memory footprint for different SOTA models in Table 2. As seen, our method is comparable to that of DOLG in terms of computational overhead and comparable to that of Token in terms of the number of parameters. Also, our method takes the same memory footprint as the others that generate 2048-dimensional vectors as feature representations.", + "bbox": [ + 75, + 598, + 468, + 720 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/181b7e1981f60236269d785c508b8271f37ca19619347449a09d7e211edf319b.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Latency is measured on a 1080Ti GPU for a ${1024} \\times {1024}$ image with 3 scaling factors $\\left\\lbrack {1,\\sqrt{2},1/\\sqrt{2}}\\right\\rbrack$ ." + ], + "table_body": "
Method#Para (M)Latency (ms)Mem. (MB) \nOn ROxford
SOLAR [15]52.511039.0
DELG [3]44.510439.0
Token [32]76.611219.5
DOLG [35]61.51509.7
SpCa (Ours)76.815339.0
", + "bbox": [ + 78, + 741, + 478, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 90, + 663, + 104 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this study, we uniformly utilize ResNet50 as the CNN backbone and set the token number and the number of random walk steps as $K = 8$ and $l = 1$ , respectively, for all the following experiments if not mentioned otherwise. In addition, all the models are trained by 25 epochs. More ablation studies utilizing ResNet101 are provided in the Appendix.", + "bbox": [ + 496, + 113, + 890, + 205 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/54a2ea9e6cb5ebbc9f8771cfd7861a9e37f639a0ea850a7a08c86060a062f5a1.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Ablation studies on the impact of different components in the spatial context branch. The baseline containing only the visual feature branch is shown in the first row. OTL and DE denote online token learning and distance encoding, respectively." + ], + "table_body": "
GlobalOTLDEMediumHard
ROxfRParROxfRPar
✓77.5187.8254.7673.82
✓✓78.8288.2158.7374.03
✓✓✓79.6489.0660.9076.97
", + "bbox": [ + 501, + 234, + 888, + 313 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of each component in spatial context branch The proposed spatial context branch consists of two components which are online token learning and distance encoding. We validate the contribution of each of the components by adding them one by one to a bare visual feature branch. In particular, for the first comparison, we directly set the whole probability transition matrix $M$ as a unit matrix (i.e., all of its entries are \"1\") to erase the distance encoding information. By doing so, only the token-based identification generated by the online token learning module is involved in the final global features. As seen in Table 3, with this single module (2nd row), the retrieval performance could be improved from $77.51\\%$ to $78.82\\%$ and $87.82\\%$ to $88.21\\%$ on ROxf-Medium and RPar-Medium, respectively. It shows the benefit of utilizing the tokens to identify the local descriptors. After adding the distance encoding module, the spatial distribution information is involved. It can be seen, with the complete branch (3rd row), the retrieval performance is further improved, especially on Hard splits. The performance (mAP) is increased from $58.73\\%$ to $60.90\\%$ and $74.03\\%$ to $76.97\\%$ on ROxf-Hard and RPar-hard, respectively. This verifies the importance of capturing the spatial distribution information with the distance encoding module. Altogether, this result demonstrates the effectiveness of the spatial context branch as a whole in our method.", + "bbox": [ + 496, + 383, + 890, + 760 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/27a57a7dc677e0b0f0e38506d2567855f66721b5c5c91652bbd84ee8a8e70ca1.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4. Ablation studies on the impact of fusion strategy." + ], + "table_body": "
Fusion StrategyMediumHard
ROxfRParROxfRPar
Orthogonal79.0486.6959.4972.87
Hadamard79.8387.9059.4474.60
Concatenation79.9488.4560.7276.00
Cross-Attention79.6489.0660.9076.97
", + "bbox": [ + 504, + 791, + 887, + 885 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11256", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fusion Strategy We validate the impact of different feature fusion strategies, including concatenation, orthogonal [35], Hadamard product, and cross-attention to fuse the information learned by our two branches in Table 4. As seen, the cross-attention scheme outperforms all the others in most cases except on the Medium split of ROxford. It demonstrates the effectiveness of utilizing cross-attention as the feature fusion strategy. Compared with cross-attention, orthogonal and Hadamard product perform worse. Surprisingly, we find simply concatenating the information from two branches has been able to obtain competitive performance. The result obtained by the concatenation strategy has been included in Table 1 too.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/292b1752cfd3972f0c98bb8a372d4526dad902d728da44ce166f7552519019df.jpg", + "table_caption": [], + "table_footnote": [ + "Table 5. Ablation studies on the impact of token number." + ], + "table_body": "
Token Number (K)MediumHard
ROxfRParROxfRPar
480.7688.3562.0275.33
879.6489.0660.9076.97
1681.2288.6162.4175.78
2480.4689.4261.8777.01
3280.1188.2860.6475.06
", + "bbox": [ + 86, + 316, + 460, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Tokens We investigate the impact of the token number in Table 5. As seen, when the number is 16, the performance on ROxford is much better than other options. Meanwhile, when we utilize 24 tokens, the performance on RParis outperforms the others instead. We believe the optimal token number is related to the characteristic of the test dataset. When the number is too small, only a few visual prototypes could be explored to describe the whole dataset, leading to incomplete spatial context information extraction. Conversely, if the number is too large, more noisy tokens will be included. This could adversely impact the token-based identification process and consequently decrease the final retrieval performance. In our experiment, we just empirically use $K = 16$ since we do not access any test dataset during the training stage.", + "bbox": [ + 75, + 458, + 472, + 685 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/87ff32c3dccdc39577bdbdb0155dfadb5abf7394ce24d8c63ee20cb50d806324.jpg", + "table_caption": [], + "table_footnote": [ + "Table 6. Ablation studies on the impact of random walk steps." + ], + "table_body": "
Random Walk (l)MediumHard
ROxfRParROxfRPar
179.6489.0660.9076.97
280.7688.8862.1576.24
381.3189.6462.5777.48
480.2588.5461.1275.61
", + "bbox": [ + 91, + 717, + 455, + 811 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Random Walk Steps To inspect how many random walk steps are needed to encode the distance for our spatial context information extraction, we apply different number of random walk steps $l = \\{1,2,3,4\\}$ . As seen in", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6, $l = 3$ gives the best performance. When the step number is small (such as 1 or 2), only a small area around the nodes in the matrix $M$ of Eq. (3) is considered for the final distance encoding process. Meanwhile, with the number of steps increased, the random walk process tends to converge and its results become similar (i.e., $\\mathbf{s}^{(l)} \\approx \\mathbf{s}^{(l + 1)}$ in Eq. (6)). Keeping adding or concatenating this information leads to redundant or even noisy information to the distance encoding, and thus adversely impacts the spatial context information extracted and further undermines retrieval.", + "bbox": [ + 496, + 90, + 893, + 242 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Results We demonstrate two images retrieved from ROxford. In addition, we provide the classification activation map obtained by using query feature representation as classification projection weights. As seen in Figure 3, in addition to the most discriminative part of the queried object (as shown in the second column obtained by DELG), the proposed SpCa focuses more on the spatial-context area. This makes the ranking of the true positive image dramatically increased compared with DELG.", + "bbox": [ + 496, + 266, + 893, + 402 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/acd85fac86b11ac3a79ad6abfa5050a8fe103636caae428d13688e5b0eb8b241.jpg", + "image_caption": [ + "Query: ashmolean" + ], + "image_footnote": [], + "bbox": [ + 503, + 417, + 598, + 472 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/35ff8f3b1db00e29bfc50b01dd2a78a98f9b9326cd213ed1fdbc3a73f19a4db5.jpg", + "image_caption": [ + "DELG" + ], + "image_footnote": [], + "bbox": [ + 599, + 417, + 696, + 472 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/294385bd884c6d8639530729122a0e31235397cf9e96c08091f3b507aaab1646.jpg", + "image_caption": [ + "SpCa" + ], + "image_footnote": [], + "bbox": [ + 697, + 417, + 792, + 472 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fa7a743e5d98539444c69ba01e2697c97d59c0f25f23929ba6cf9ccc739f636d.jpg", + "image_caption": [ + "Ranking: 76th -> 20th" + ], + "image_footnote": [], + "bbox": [ + 794, + 417, + 890, + 472 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e685244bba611c8b1f2f9e8700becf381130b45b89b1f3f4c8789d7a5d95a636.jpg", + "image_caption": [ + "Query: cornmarket" + ], + "image_footnote": [], + "bbox": [ + 503, + 484, + 598, + 537 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/acf27e6f11ff0adf21f4f983f474f4671c90f51d66782eb9f7f61d5792e8c49d.jpg", + "image_caption": [ + "DELG" + ], + "image_footnote": [], + "bbox": [ + 601, + 484, + 696, + 537 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ae59ea7bc75ef546de17eab03b338a9a23208027428ccad5f805ebbf1ae70801.jpg", + "image_caption": [ + "SpCa", + "Figure 3. Qualitative results and the activation maps." + ], + "image_footnote": [], + "bbox": [ + 697, + 484, + 792, + 537 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a5892cdb9da9ea5fbda345a666835d91d2c1224f6cfcd0eea81fd17b153b919a.jpg", + "image_caption": [ + "Ranking: 30th -> 11th" + ], + "image_footnote": [], + "bbox": [ + 794, + 484, + 890, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 602, + 617, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Motivated by the benefit of using local descriptor based geometric verification in a re-ranking step, we propose a novel feature learning framework that effectively embeds the spatial context information into the global visual feature representation for instance image retrieval. To mine the spatial context information, a spatial context branch consisting of an online token learning module and a distance encoding module is proposed. The former module is utilized to identify the type of each local descriptor on a feature map. The latter is used to capture the information on how the surrounding descriptors are spatially distributed. By fusing visual and spatial context information together, our framework learns spatial-context-aware global feature representations for images to conduct retrieval. Extensive experiments demonstrate the effectiveness of the proposed framework for retrieval. In future work, we will explore the incorporation of other types of information into global feature representations to further improve instance image retrieval.", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11257", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 78, + 90, + 236, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by the Australian Research Council (grant number DP200101289) and undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government.", + "bbox": [ + 76, + 114, + 468, + 190 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 205, + 173, + 220 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomás Pájdla, and Josef Sivic. 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IEEE Computer Society, 2009. 1" + ], + "bbox": [ + 78, + 90, + 468, + 756 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11259", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_model.json b/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8517b0879fae787793bfe3551629956ea085aa04 --- /dev/null +++ b/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_model.json @@ -0,0 +1,2101 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.807, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.134, + 0.131, + 0.838, + 0.175 + ], + "angle": 0, + "content": "Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.203, + 0.733, + 0.221 + ], + "angle": 0, + "content": "Zhongyan Zhang\\(^{1}\\), Lei Wang\\(^{1}\\), Luping Zhou\\(^{2}\\), Piotr Koniusz\\(^{3,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.221, + 0.885, + 0.24 + ], + "angle": 0, + "content": "University of Wollongong1, University of Sydney2, Data61♥CSIRO3, Australian National University4" + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.242, + 0.851, + 0.256 + ], + "angle": 0, + "content": "zhongyan@uow.edu.au, leiw@uow.edu.au, luping.zhou@sydney.edu.au, peter.koniusz@data61.csiro.au" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.313, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.326, + 0.473, + 0.718 + ], + "angle": 0, + "content": "In instance image retrieval, considering local spatial information within an image has proven effective to boost retrieval performance, as demonstrated by local visual descriptor based geometric verification. Nevertheless, it will be highly valuable to make ordinary global image representations spatial-context-aware because global representation based image retrieval is appealing thanks to its algorithmic simplicity, low memory cost, and being friendly to sophisticated data structures. To this end, we propose a novel feature learning framework for instance image retrieval, which embeds local spatial context information into the learned global feature representations. Specifically, in parallel to the visual feature branch in a CNN backbone, we design a spatial context branch that consists of two modules called online token learning and distance encoding. For each local descriptor learned in CNN, the former module is used to indicate the types of its surrounding descriptors, while their spatial distribution information is captured by the latter module. After that, the visual feature branch and the spatial context branch are fused to produce a single global feature representation per image. As experimentally demonstrated, with the spatial-context-aware characteristic, we can well improve the performance of global representation based image retrieval while maintaining all of its appealing properties. Our code is available at https://github.com/Zy-Zhang/SpCa." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.753, + 0.21, + 0.768 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Given a query image, the purpose of instance-level image retrieval is to search and retrieve the images containing the identical object described by the query from a largescale image dataset. In this task, visual feature representations of images play a crucial role in measuring the similarities between a query and candidate images. A variety of handcrafted feature-based methods [14, 38, 2] have been proposed to significantly improve the performance in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.892, + 0.369 + ], + "angle": 0, + "content": "the past two decades. Recently, due to the development of deep learning technologies, deep feature representations have been overtaking the position of conventional handcrafted ones and bringing great progress in the task of instance image retrieval [1, 3, 17, 28, 15]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.893, + 0.672 + ], + "angle": 0, + "content": "Generally, deep feature representations used in instance image retrieval can be categorized into two types. One type is global feature representation, which describes the visual content of an image as a whole. As a multi-dimensional vector, it can be efficiently used to measure the similarity of two images, say, via Euclidean distance or cosine similarity. For a retrieval task, the total number of global feature representations is just the size of image database, and they can be pre-extracted and economically stored for use. In addition, one global feature representation per image works well with the classic data structures designed for searching. The other type is local descriptors, which describe the local information within an image and collectively reflect the spatial information of the visual cues in an image. In image retrieval, they are important for conducting geometric verification to confirm if two images truly match or not. However, the total number of local descriptors per image could be large (e.g., 1,000) and the verification involves non-trivial computation, making this process expensive in computational cost and memory footprint." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.895, + 0.884 + ], + "angle": 0, + "content": "This situation leads to a wide use of \"two-stage\" paradigm in instance image retrieval [23, 3, 17]. An initial retrieval result is firstly obtained via the global feature representation. After that, a re-ranking step utilizes the local descriptors to refine a small number of top-retrieved images. Nevertheless, this two-stage paradigm not only results in two separate procedures [26, 10] but also considerably increases retrieval time and memory expense for practical retrieval tasks [18], due to the presence of the local descriptor-based spatial verification step. Therefore, it will be highly valuable to make ordinary global image representations spatial-context-aware by considering their appealing properties of algorithmic simplicity, low memory cost, and being friendly to data structures." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To achieve this, we propose a novel feature learning" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11250" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "framework to effectively embed spatial context information into global feature representation of images. Doing so will help to boost the retrieval performance of global feature representation, improving its efficacy when the local descriptor based re-ranking becomes costly or infeasible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.473, + 0.606 + ], + "angle": 0, + "content": "Specifically, two types of information are extracted in our framework. One is conventional visual information obtained by a visual feature branch in a CNN backbone. The other one is spatial context information that describes for each local descriptor learned in CNN, what kind of surrounding local descriptors are and how they spatially distribute on a feature map. To obtain this information, we develop a spatial context branch that operates in parallel to the visual feature branch in CNN. This branch consists of two modules called online token learning and distance encoding. The module of online token learning addresses the \"what kind\" issue. A set of semantic tokens that could be regarded as anchors in the space of local descriptors is learned in an online manner. Comparing the tokens to the visual words in a visual dictionary, each local descriptor can be uniquely labelled via soft coding as a token-based identification. The module of distance encoding cares about the \"spatial distribution\" issue. A probability transition based encoding is devised to reflect the relative spatial distance between each pair of local descriptors, so as to capture their spatial distribution information in a feature map. After that, the token-based identification and the spatial distribution information are integrated to produce a spatial context clue for each local descriptor. With both visual and spatial information, a feature fusion operation is conducted to fuse them together to generate spatial-context-aware local descriptors. Finally, a global pooling followed by a whitening layer is added to embed the context-aware local descriptors into a global feature representation for each image." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.607, + 0.399, + 0.621 + ], + "angle": 0, + "content": "Our contributions are summarised as follows:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.634, + 0.47, + 0.71 + ], + "angle": 0, + "content": "i. We propose an end-to-end feature learning framework to characterise and embed spatial context information into the process of information processing and extraction in CNN. It makes global feature representations become more capable for instance image retrieval." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.722, + 0.47, + 0.813 + ], + "angle": 0, + "content": "ii. To implement the framework, we design a spatial context branch. With its online token learning module, the types of local descriptors are identified and easily compared. With the distance encoding module, the information about the spatial distribution of different types of local descriptors around a given descriptor is obtained." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "iii. To verify the efficacy of the proposed framework, we conduct extensive experiments on instance image retrieval benchmark datasets, ROxford and RParis, with one million distractors. As demonstrated, our global feature representations effectively improve the perfor" + }, + { + "type": "list", + "bbox": [ + 0.075, + 0.634, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "mance of instance image retrieval, making global representation a more competitive option for practical tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.137, + 0.642, + 0.154 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.163, + 0.892, + 0.194 + ], + "angle": 0, + "content": "In this section, we briefly review deep instance image retrieval, including local and global feature learning methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.204, + 0.655, + 0.219 + ], + "angle": 0, + "content": "2.1. Global features" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.228, + 0.892, + 0.606 + ], + "angle": 0, + "content": "Global feature has been widely used to represent the content of images for a wide range of computer vision tasks [21, 13, 8, 36, 37, 12, 11]. Due to its compactness and efficiency, a variety of global methods [24, 32, 35, 15] have been proposed to learn discriminative feature representations via deep models in the instance image retrieval community. Some of the studies focus on applying more effective loss functions, including triplet losses [29], list-wise losses [22], and classification losses [5] to train the model. Others explore how to pool the entire feature maps into a compact feature vector while maintaining their discrepancies. For instance, weighted-sum-pooling (CroW) [9], regional-max-pooling (R-MAC) [29], and GeM pooling [20]. Recently, several methods try to modify the training model architecture to capture more useful information during the training process. SOLAR [15] combines normal training with second-order information by adding self-attention modules in the conventional CNN backbones. Token [32] jointly learns a set of tokens and the corresponding visual representations to mimic the conventional dictionary learning plus feature encoding scheme to represent images. Some other studies [32, 35] propose multiple branches for CNN models to mine more complementary information and fuse them into the final feature vectors. We follow the global feature type to learn compact features to conduct retrieval." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.616, + 0.647, + 0.631 + ], + "angle": 0, + "content": "2.2. Local features" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.64, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Deep local descriptors [28, 30, 33, 17] have been extensively researched and made significant progress in instance image retrieval [4]. The key to their success lies in the spatial information these local descriptors hold, and it is usually utilized by kernel alignment aggregation (e.g., ASMK [27]) or geometric verification (e.g., RANSAC [6]) for image similarity measure. In recent studies, several methods [26, 10] individually train a matching model to directly compare the similarity of two images (or their preextracted local descriptors) in a data-driven manner. However, they need more inference time and memory footprint. Therefore, they are usually applied to only top k retrieved images obtained by a global retrieval method as a reranking." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.854, + 0.864 + ], + "angle": 0, + "content": "2.3. Learning local and global features jointly" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Driven by the complementary properties of global and local features, jointly learning the two types of features" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11251" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.122, + 0.088, + 0.852, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.256, + 0.895, + 0.314 + ], + "angle": 0, + "content": "Figure 1. Overview of our framework. After an initial feature extraction by a CNN backbone, two branches of \"Visual Feature Branch\" and \"Spatial Context Branch\" are used to extract visual and spatial context information. After that, a cross-attention module is used to fuse the visual feature and the corresponding spatial context feature to generate spatial-context-aware visual representations for images. In particular, \"GMM\" denotes the Gaussian Mixture Model process, and \"GP+W\" refers to global pooling followed by whitening." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.473, + 0.655 + ], + "angle": 0, + "content": "becomes a straightforward idea. Recently, several studies demonstrate the advantages of learning features in this manner. DELG [3] creatively unifies the two separate learning processes into one training framework. However, even though the training procedure is unified, the learning processes of the two feature types are still somehow irrelevant. To further explore this approach, DOLG [35] and DALG [25] firstly separate the feature extractor into two branches to learn the local and global features and then fuse them via a manual or learnable way to obtain compact feature representations for images. Both of them try to extract individual visual information from the two types of features to make them complementary to each other. However, the powerful spatial context information held by local features is neither exploited nor embedded into the final feature representations. In this work, we argue that spatial context information is more beneficial than visual information from local descriptors to the final global feature representations for instance image retrieval. To this end, we propose a novel feature learning framework to effectively embed the spatial context information into final global features." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.677, + 0.288, + 0.695 + ], + "angle": 0, + "content": "3. The Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "An overview of our framework is in Figure 1. Given an image \\(I\\), a conventional CNN backbone is used to generate a feature map \\(\\mathbf{V} \\in \\mathbb{R}^{D \\times H \\times W}\\), in which each spatial position corresponds to a \\(D\\)-dimensional local visual descriptor. Besides, a spatial context branch is split from the feature map to extract the spatial context information of all the descriptors, which is represented in the form of \\(\\mathbf{S} \\in \\mathbb{R}^{C \\times H \\times W}\\) with \\(C\\) being the dimensions. After that, for each local descriptor, its two kinds of information are fused together, say, with a cross-attention module or a simple concatenation operation. After the fusion, a global pooling and a fully-connected layer are used to generate the final global spatial-context-aware feature \\(\\mathbf{f}_{spca}\\) to represent the image. In the following," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.337, + 0.892, + 0.368 + ], + "angle": 0, + "content": "we focus on describing the spatial context branch since the visual branch follows its original design in CNN backbones." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.377, + 0.719, + 0.393 + ], + "angle": 0, + "content": "3.1. Spatial Context Branch" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.4, + 0.892, + 0.492 + ], + "angle": 0, + "content": "In the spatial context branch, there are two main issues to be addressed for each spatial position on the feature map: 1) what kinds of local descriptors are there in its surrounding region (i.e., identification task); 2) how they spatially distribute on the feature map (i.e., spatial distribution task). We now introduce how we address the two issues orderly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.893, + 0.84 + ], + "angle": 0, + "content": "Token-based Identification. For existing local feature-based retrieval methods [28, 30, 33], learning tokens to capture discriminative visual patterns in a dataset has proven reliable to identify local descriptors. With the tokens, the encoded features could become more robust against illumination change, the information loss due to occlusion, and the adverse impact of the background in an image. In our framework, we generally follow this \"tokens plus encoding\" pipeline to identify local descriptors. However, in the literature, the tokens are usually learned by clustering (e.g., by k-means) a sampled subset of local descriptors obtained from an image dataset in an offline manner. This way separates the process of token learning from encoding, potentially causing a discrepancy between the training and the inference stages. In addition, using a sampled subset of local descriptors could lead to learning biased tokens since the information available in an image dataset is not fully utilized. To improve this situation, we perform token learning via an online mini-batch based Gaussian Mixture Model (GMM) process. This helps to adequately utilize all the local descriptors to learn tokens and makes our framework fully end-to-end trainable." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Specifically, we model the distribution of local descriptors by a \\(K\\)-component Gaussian mixture model \\(p(\\mathbf{v}|\\Theta) = \\sum_{k}\\alpha_{k}N(\\mathbf{v};\\boldsymbol{\\mu}_{k},\\Sigma_{k})\\), where \\(\\mathbf{v}\\) denotes the a local descriptor, while \\(\\alpha_{k},\\boldsymbol{\\mu}_{k}\\), and \\(\\Sigma_{k} = \\sigma_{k}^{2}I_{D}\\) denote the prior probability, the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11252" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "mean, and the (spherical) covariance matrix for component \\( k \\), respectively. In this case, token learning boils down to the parameter estimation for this Gaussian mixture model. At the beginning, \\( \\mu \\) and \\( \\sigma^2 \\) are randomly generated and \\( \\alpha \\) is set as \\( 1 / K \\). After that, we conduct the Expectation and Maximization (EM) process for all the local descriptors within each mini-batch. To be concise, we show the key results below and the details can be found in the literature [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.47, + 0.259 + ], + "angle": 0, + "content": "Within each mini-batch, for the E-Step, the probability that the \\(i\\)th local descriptor \\(\\mathbf{v}_i\\) belongs to the \\(k\\)th component can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.183, + 0.27, + 0.47, + 0.307 + ], + "angle": 0, + "content": "\\[\n\\omega_ {i k} = \\frac {\\alpha_ {k} N \\left(\\mathbf {v} _ {i} ; \\boldsymbol {\\mu} _ {k} , \\Sigma_ {k}\\right)}{\\sum_ {j = 1} ^ {K} \\alpha_ {j} N \\left(\\mathbf {v} _ {i} ; \\boldsymbol {\\mu} _ {j} , \\Sigma_ {j}\\right)} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.318, + 0.468, + 0.348 + ], + "angle": 0, + "content": "For M-Step, the prior probability, the mean and the covariance are updated as" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.359, + 0.329, + 0.39 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {k} \\leftarrow \\alpha_ {k} + \\beta \\left(\\frac {\\sum_ {i} \\omega_ {i k}}{H W} - \\alpha_ {k}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.392, + 0.469, + 0.424 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {k} \\leftarrow \\boldsymbol {\\mu} _ {k} + \\beta \\left(\\frac {\\sum_ {i} \\omega_ {i k} \\mathbf {v} _ {i}}{\\sum_ {i} \\omega_ {i k}} - \\boldsymbol {\\mu} _ {k}\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.426, + 0.402, + 0.461 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {k} ^ {2} \\leftarrow \\sigma_ {k} ^ {2} + \\beta \\Big (\\frac {\\sum_ {i} \\omega_ {i k} \\| \\mathbf {v} _ {i} - \\boldsymbol {\\mu} _ {k} \\| ^ {2}}{\\sum_ {i} \\omega_ {i k}} - \\sigma_ {k} ^ {2} \\Big),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.471, + 0.469, + 0.546 + ], + "angle": 0, + "content": "where \\( HW \\) is the number of local descriptors obtained from an image, and \\( \\beta \\) is a momentum to make the estimation process more stable in the mini-batch clustering [16]. One E-Step and M-Step are conducted in each iteration during the training." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.548, + 0.469, + 0.623 + ], + "angle": 0, + "content": "After the above process, \\((\\pmb{\\mu}_1,\\pmb{\\mu}_2,\\dots ,\\pmb{\\mu}_K)\\) represents the learned tokens. \\(\\omega_{i} = (\\omega_{i1},\\omega_{i2},\\dots ,\\omega_{iK})\\in \\mathbb{R}^{K}\\) obtained by Eq. (1) can be used as the token-based identification for local descriptor \\(\\mathbf{v}_i\\) since it represents the posterior probability that this descriptor belongs to each of the \\(K\\) components." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Spatial Distribution. To extract spatial distribution information for a local descriptor \\(\\mathbf{v}_i\\), the distances of this descriptor to all the descriptors \\(V = \\{\\mathbf{v}_j, j = 1,2,\\dots,HW\\}\\) presented on the same feature map should be effectively measured and collected. To achieve this, simply using the coordinate distances among them is inadequate. We utilize a probability transition score obtained by applying random walk on the graph constituted by all the local descriptors as the nodes to measure the distances. By doing so, more possible paths among the local descriptors will be considered and the number of random walk steps could also be used to control the spatial scale in the distance measurement. Inspired by the literature [11], we perform the spatial distribution extraction as an aggregation of the encoded distances between \\(\\mathbf{v}_i\\) and all \\(\\mathbf{v}_j \\in V\\). By \"coded,\" we mean that the distance is measured by a probability transition process as explained below." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "Given an undirected graph with an affinity matrix \\( A \\), the distance of its nodes \\( \\nu \\) and \\( u \\) can be encoded by a probability transition score \\( \\zeta \\) obtained via \\( l \\) steps of random walk" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.149, + 0.892, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\zeta (v, u) ^ {(l)} = \\left(M ^ {l}\\right) _ {v u}, M ^ {1} = A D ^ {- 1}, M ^ {l} = M ^ {l - 1} \\cdot M, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.179, + 0.892, + 0.255 + ], + "angle": 0, + "content": "where \\( M^1 \\) denotes the random walk matrix, \\( D^{-1} \\) refers to the normalization matrix of the graph, and \\( l \\) is the number of random walk steps. Based on this, the distance of a node \\( v \\) from all nodes \\( u \\) in a target set \\( S \\) can be represented by an aggregation operation as" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.267, + 0.892, + 0.284 + ], + "angle": 0, + "content": "\\[\n\\zeta (\\nu , S) ^ {(l)} = \\operatorname {a g g} \\left(\\left\\{\\zeta (\\nu , u) ^ {(l)} \\mid u \\in S \\right\\}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.298, + 0.892, + 0.373 + ], + "angle": 0, + "content": "Linking the above result to our case, the undirected graph consists of all the local descriptors \\( V \\) in an image, and they collectively form the target set \\( S \\) in this distance encoding process. In addition, we compute the affinity matrix \\( A \\) based on the coordinate distance on the feature map as" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.387, + 0.892, + 0.404 + ], + "angle": 0, + "content": "\\[\nA _ {i j} = \\exp (- \\operatorname {c o} _ {-} \\operatorname {d i s t} (\\mathbf {v} _ {i}, \\mathbf {v} _ {j})), (1 \\leq i, j \\leq H W), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.416, + 0.892, + 0.536 + ], + "angle": 0, + "content": "where \\(\\mathrm{co\\_dist}(\\cdot, \\cdot)\\) denotes the Euclidean distance between the coordinates of two local descriptors. After that, the encoded distance can be obtained by applying Eq. (3). Furthermore, we enrich Eq. (4) by considering the learned token-based identification (i.e., the posteriori probability \\(\\omega\\) obtained in Eq. (1)), and this leads to an instantiated \"agg\" operation in Eq. (4) to produce the spatial context feature for local descriptor \\(\\mathbf{v}_i\\)." + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.548, + 0.892, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\mathbf {s} _ {i} ^ {(l)} \\triangleq \\zeta (v _ {i}, S) ^ {(l)} = \\sum_ {j = 1} ^ {H W} \\zeta (\\mathbf {v} _ {i}, \\mathbf {v} _ {j}) ^ {(l)} \\boldsymbol {\\omega} _ {j}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.602, + 0.892, + 0.814 + ], + "angle": 0, + "content": "Recall that the token-based identification \\(\\omega_{i}\\) can be treated as a vector of probability transition scores between local descriptor \\(\\mathbf{v}_i\\) and each of the learned tokens \\(\\pmb{\\mu}\\). By combining the encoded distance and the token-based identification, the spatial context feature \\(\\mathbf{s}_i\\) in Eq. (6) essentially reflects the probability transition scores between node \\(\\mathbf{v}_i\\) and the tokens \\(\\pmb{\\mu}\\) when regarding the spatial structure of the given \\(H\\times W\\) feature map as a (static) transition matrix. This is illustrated in Figure 2. That means the spatial distribution information is used to control the extraction of the spatial context features. In this sense, the spatial distribution information is effectively embedded into the spatial context features. At last, we define the final spatial context feature for the local descriptor \\(\\mathbf{v}_i\\) obtained through an \\(l\\)-step random walk as" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.824, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\mathbf {s} _ {i} = \\mathbf {s} _ {i} ^ {(1)} \\oplus \\mathbf {s} _ {i} ^ {(2)} \\oplus \\dots \\oplus \\mathbf {s} _ {i} ^ {(l)}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\oplus\\) denotes concatenation operation. The concatenation of the features obtained after each of the \\(l\\) steps considers the spatial context information at various scales." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11253" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.473, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.332, + 0.47, + 0.361 + ], + "angle": 0, + "content": "Figure 2. Spatial context feature generation. See the detailed description after Eq. (6)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.385, + 0.427, + 0.402 + ], + "angle": 0, + "content": "3.2. Fusion of Visual and Spatial Information" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.473, + 0.651 + ], + "angle": 0, + "content": "With both visual and spatial context information available, a proper fusion scheme is needed to make them complements to benefit the final feature representation. To accomplish it, various feature fusion schemes could be used, including concatenation, orthogonal fusion [35], Hadamard product, or cross-attention fusion. We utilize a cross-attention module for information fusion in our method since it is commonly used to align features from different modalities in the recent literature. Meanwhile, we provide an ablation study on all the four fusion schemes in the experimental part. For the cross-attention scheme, the spatial context feature \\(\\mathbf{S} = (\\mathbf{s}_1,\\mathbf{s}_2,\\dots ,\\mathbf{s}_{HW})\\) is projected into the same space as the visual feature \\(\\mathbf{V}\\) with a linear projection layer. After that, both of them are flattened into sequences and mapped into Queries (Q), Keys (K), and Values (V), respectively, to put through into the cross-attention layer:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.663, + 0.409, + 0.679 + ], + "angle": 0, + "content": "\\[\n\\mathbb {Q} = \\operatorname {p r o j} (\\mathbf {V}), \\mathbb {K} = \\operatorname {p r o j} (\\mathbf {S}), \\mathbb {V} = \\operatorname {p r o j} (\\mathbf {S})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.681, + 0.469, + 0.715 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {s p c a} ^ {*} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbb {Q} \\cdot \\mathbb {K} ^ {\\top}}{\\sqrt {D}}\\right) \\cdot \\mathbb {V} \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.718, + 0.326, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} _ {s p c a} = \\mathbf {F} _ {s p c a} ^ {*} + \\operatorname {M L P} \\left(\\mathbf {F} _ {s p c a} ^ {*}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.47, + 0.824 + ], + "angle": 0, + "content": "where MLP denotes a feed-forward layer and \\(\\mathbf{F}_{spca}\\) denotes the spatial-context-aware feature sequence. After that, the feature sequence is rearranged as a feature map, followed by a global pooling and a fully-connected layer to generate a global feature representation vector \\(\\mathbf{f}_{spca}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.36, + 0.849 + ], + "angle": 0, + "content": "3.3. Objective Function for Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Following previous state-of-the-art work [3, 35, 32], we train our model on a dataset with object class annotations and utilize ArcFace margin loss [5] with learnable parame" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.09, + 0.772, + 0.107 + ], + "angle": 0, + "content": "ters \\(\\hat{\\mathbf{W}}\\in \\mathbb{R}^{D\\times N}\\) to train the whole model:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.116, + 0.892, + 0.155 + ], + "angle": 0, + "content": "\\[\nL = - \\log \\left(\\frac {\\exp \\left(\\gamma \\times A F \\left(\\hat {\\mathbf {w}} _ {t} ^ {\\top} \\hat {\\mathbf {f}} _ {s p c a} , 1\\right)\\right)}{\\sum_ {n} \\exp \\left(\\gamma \\times A F \\left(\\hat {\\mathbf {w}} _ {n} ^ {\\top} \\hat {\\mathbf {f}} _ {s p c a} , y _ {n}\\right)\\right)}\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.167, + 0.894, + 0.258 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{w}}_t\\) denotes the \\(t\\)th column of \\(\\hat{\\mathbf{W}}\\) and \\(\\hat{\\mathbf{f}}_{spca}\\) is the \\(L_{2}\\)-normalized \\(\\mathbf{f}_{spca}\\). \\(y\\) is the one-hot label vector and \\(t\\) is the index to indicate the true class (i.e., \\(y_t = 1\\)). \\(n\\) is the total number of classes in the dataset. \\(\\gamma\\) is a scaling factor. \\(AF(\\cdot)\\) refers to the ArcFace cosine similarity and it is calculated as" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.269, + 0.892, + 0.305 + ], + "angle": 0, + "content": "\\[\nA F (s, c) = \\left\\{ \\begin{array}{l l} \\cos (a \\cos (s) + m), & \\text {i f} c = 1 \\\\ s, & \\text {i f} c = 0 \\end{array} \\right. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.318, + 0.892, + 0.35 + ], + "angle": 0, + "content": "where \\(s\\) is the cosine similarity between \\(\\hat{\\mathbf{w}}_t\\) and \\(\\hat{\\mathbf{f}}_{spca}\\), \\(m\\) is the ArcFace margin and \\(c\\) indicates if this is the true class." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.364, + 0.698, + 0.381 + ], + "angle": 0, + "content": "4. Experimental Result" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.389, + 0.773, + 0.405 + ], + "angle": 0, + "content": "4.1. Dataset and Evaluation Metric" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.892, + 0.64 + ], + "angle": 0, + "content": "Our model is trained on \"Google Landmark v2 clean\" dataset, which is a clean subset of Google Landmark v2 [31]. It contains 1,580,470 images of 81,313 landmark classes, and it has been widely used in existing methods [35, 32, 3] as the training dataset. To make a fair comparison, we follow the previous work [32, 35] to randomly divide the dataset into two subsets 'train'/'val' with \\(80\\% / 20\\%\\) split. For evaluation, we use two widely used benchmark datasets, ROxford and RParis [19] to test our model. Both datasets have 70 query images but contain 4,993 and 6,322 gallery images, respectively. In addition, a 1M distractor set [19] is added to test our model for the case of large-scale retrieval. We use mean average precision (mAP), as the criterion of retrieval performance for both \"Medium\" and \"Hard\" splits of ROxford and RParis." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.651, + 0.719, + 0.667 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We use ResNet101/ResNet50 [8] as the CNN backbone to learn visual features. For image augmentation, random crop and color jittering are used first, and all the augmented images are resized into \\( 512 \\times 512 \\) pixels as the model input. The model is trained on 4 Nvidia V100-SXM2-32GB GPU cards with a batch size of 128 for 50 epochs. We use SGD optimizer with a momentum of 0.9. A warming-up of 5-epoch's training is used to initialize the learning rate from 0.0001 to the base learning rate of 0.005. As for the ArcFace loss, the margin \\( m \\) and the scale \\( \\gamma \\) are empirically set as 0.2 and 45. For the global pooling, we utilize GeM [20] pooling with the fixed coefficient \\( p = 3 \\) during the whole training. \\( \\beta \\) in the M-Step of GMM is empirically set as 0.999. In addition, we set the number of random walk steps \\( l \\) as 3 and the number of tokens as \\( K = 16 \\). The dimensions of the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11254" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.091, + 0.088, + 0.882, + 0.432 + ], + "angle": 0, + "content": "
MethodMediumHard
ROxfROxf+1MRParRPar+1MROxfROxf+1MRParRPar+1M
Global features + local features re-ranking
R101-DELG [3]+SP81.2069.1087.2071.5064.0047.5072.8048.70
R101-DELG [3]+SP†81.8270.1588.6476.1464.9749.5476.8153.62
Global features
R101-R-MAC [7]60.9039.3078.9054.8032.4012.5059.4028.00
R101-GeM [20]64.7045.2077.2052.3038.5019.9056.3024.70
R101-SOLAR [15]69.9053.5081.6059.2047.9029.9064.5033.40
R101-DELG [3]76.3063.7086.6070.6055.6037.5072.4046.90
R101-GLAM [24]78.6068.0088.5073.5060.2043.5076.8053.10
Swin-S-DALG [25]79.94-90.04-57.55-79.06-
R101-DOLG [35]★81.5077.4391.0283.2961.1054.8180.3066.69
R101-Token [32]82.2870.5289.3476.6666.5747.2778.5655.90
R101-Token [32]†77.8266.7487.9375.2260.1043.0774.6653.19
R101-DOLG [35]†78.35(75.51)(88.48)(78.25)58.59(52.36)(75.39)(61.85)
R101-DELG [3]†79.8267.8587.2172.4561.1642.5873.8450.79
R101-SOLAR [15]†(81.63)71.8488.2172.86(63.29)45.2875.2151.26
R50-SpCaacro (Ours)79.9172.7887.4378.0159.2749.2673.1458.3
R50-SpCaCat (Ours)81.5573.2088.6078.2361.1948.7676.2160.91
R101-SpCaacro (Ours)82.7377.8490.2079.1265.6053.3579.2965.84
R101-SpCaCat (Ours)83.2477.8290.5679.4865.8553.2779.9764.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.441, + 0.895, + 0.512 + ], + "angle": 0, + "content": "Table 1. Performance (mAP) comparison with recent state-of-the-art instance image retrieval methods on datasets ROxford5k and RParis6k [19]. R101 and R50 denote ResNet101 and ResNet50. Swin-S denotes Swin-Transformer-small [13]. The subscripts \\( \\text{cro} \\) and \\( \\text{cat} \\) refer to cross-attention and concatenation feature fusion strategies. SP denotes spatial verification via RANSAC. \\( \\dagger \\) denotes our reimplementation. \\( \\star \\) means no query cropping. Results in gray are those reported in the published papers. The best and second best performances are highlighted in bold and with underlines, respectively. The best previous performance is shown in brackets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.471, + 0.628 + ], + "angle": 0, + "content": "final global feature are set as 2048. For inference, the multiple scales [0.3535, 0.5, 0.7071, 1.0, 1.4142] are applied to each original image to extract the feature representations. To fuse the features obtained from different scales, they are \\( L_{2} \\)-normalized, summed, and normalized again to generate the final global features for retrieval." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.442, + 0.651 + ], + "angle": 0, + "content": "4.3. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Setting for fair comparison Note that there are setting differences among the previous state-of-the-art methods. For example, they are different at 1) pretrained model sources for initialization (Caffe\\(^{1}\\), PyTorch\\(^{2}\\), and Facebook\\(^{3}\\)); 2) training datasets (SfM-120k [20], GLDv1 [17], GLDv2 [31], and different \\(80\\% / 20\\%\\) split); 3) the number of multiple scales used at the inference stage (e.g., 3, 5, or 7); 4) with or without query cropping scheme. These discrepancies could affect the fairness of the comparison if not well handled. To address this situation, we carefully re-implement multiple SOTA methods by using their officially published codes and the training parameters reported in their papers, while keeping the same settings for the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.536, + 0.892, + 0.643 + ], + "angle": 0, + "content": "above factors between these methods and ours. Specifically, to ensure fair comparison, our experimental study utilizes the same \\(80\\%\\) of GLDv2-clean [31] as the training dataset, the same remaining \\(20\\%\\) of GLDv2-clean as the validation dataset, the same pretrained model from PyTorch for initialization, and the same 5 scales with query cropping scheme for inference to conduct instance image retrieval." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Retrieval results Two groups of state-of-the-art methods are compared in this experimental study: 1) methods based on global feature representations. They include two milestone works R-MAC [7] and GeM [20] and another six more recent works including DELG [3], SOLAR [15], GLAM [24], DOLG [35], DALG [25], and Token [32]; 2) a method using global feature based initial retrieval plus local feature based re-ranking scheme, DELG+SP [3], is included as well. Also, note that we focus on global feature based image retrieval in this paper, and we do not consider training a verification model [10] or adding any post-processing steps like diffusion or query expansion to boost retrieval performance [34]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The retrieval result is reported in Table 1. The methods under \"Global features\" are partitioned into three sections. The results in gray color are those reported in the original" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.862, + 0.45, + 0.876 + ], + "angle": 0, + "content": "1http://cmp.felk.cyut.cz/cnnimageRetrieval/data/networks/imagenet" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.876, + 0.47, + 0.888 + ], + "angle": 0, + "content": "\\(^{2}\\)https://pytorch.org/vision/stable/models/generated/torchvision.models" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.327, + 0.901 + ], + "angle": 0, + "content": "3https://github.com/facebookresearch/pycls" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.862, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11255" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "published papers. Since they involve different settings as discussed above, the results are included here mainly as a reference. Following the gray-colored results are those obtained by our re-implementation for the sake of fair comparison, and they are used to compare with our methods shown at the bottom of this table." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.187, + 0.47, + 0.353 + ], + "angle": 0, + "content": "As seen, our method R101-SpCa (where \"SpCa\" is short for \"Spatial-context-aware\"), with either cross-attention (\\(-cro\\)) or concatenation (\\(-cat\\)) fusion strategy, clearly outperforms the others on all the test cases. Compared with the closest results obtained by DOLG and SOLAR, our method achieves \\(1.6\\%\\) and \\(2.0\\%\\) performance gain on the Medium split of ROxford and RParis, respectively. And higher improvements of \\(2.5\\%\\) and \\(4.5\\%\\) are obtained on the Hard split of the two datasets. After the 1M distractors are added, our method still demonstrates its excellent retrieval performance. All these results validate the efficacy of our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.471, + 0.554 + ], + "angle": 0, + "content": "Compared with the global initial retrieval plus local feature re-ranking scheme, our method still maintains its advantage. As listed in Table 1, even without using the pairwised re-ranking step as done in R101-DELG+SP [3], our method has outperformed it by around \\(2\\%\\) on all dataset splits. More importantly, our method costs no extra inference time as taken by the re-ranking step. In addition, the memory footprint of our global feature representation (i.e., a 2048-dimensional vector per image) is also much less than that used by the local descriptor (there are usually 1,000 vectors per image, each of which is of 128 dimensions) based re-ranking. This again shows the computational advantage brought by our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.721 + ], + "angle": 0, + "content": "Computational Overhead We report the number of parameters, feature extraction latency, and memory footprint for different SOTA models in Table 2. As seen, our method is comparable to that of DOLG in terms of computational overhead and comparable to that of Token in terms of the number of parameters. Also, our method takes the same memory footprint as the others that generate 2048-dimensional vectors as feature representations." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.742, + 0.48, + 0.85 + ], + "angle": 0, + "content": "
Method#Para (M)Latency (ms)Mem. (MB) \nOn ROxford
SOLAR [15]52.511039.0
DELG [3]44.510439.0
Token [32]76.611219.5
DOLG [35]61.51509.7
SpCa (Ours)76.815339.0
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.851, + 0.472, + 0.879 + ], + "angle": 0, + "content": "Table 2. Latency is measured on a 1080Ti GPU for a \\( {1024} \\times {1024} \\) image with 3 scaling factors \\( \\left\\lbrack {1,\\sqrt{2},1/\\sqrt{2}}\\right\\rbrack \\) ." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.665, + 0.106 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.206 + ], + "angle": 0, + "content": "In this study, we uniformly utilize ResNet50 as the CNN backbone and set the token number and the number of random walk steps as \\( K = 8 \\) and \\( l = 1 \\), respectively, for all the following experiments if not mentioned otherwise. In addition, all the models are trained by 25 epochs. More ablation studies utilizing ResNet101 are provided in the Appendix." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.235, + 0.89, + 0.314 + ], + "angle": 0, + "content": "
GlobalOTLDEMediumHard
ROxfRParROxfRPar
✓77.5187.8254.7673.82
✓✓78.8288.2158.7374.03
✓✓✓79.6489.0660.9076.97
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.498, + 0.314, + 0.892, + 0.369 + ], + "angle": 0, + "content": "Table 3. Ablation studies on the impact of different components in the spatial context branch. The baseline containing only the visual feature branch is shown in the first row. OTL and DE denote online token learning and distance encoding, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Impact of each component in spatial context branch The proposed spatial context branch consists of two components which are online token learning and distance encoding. We validate the contribution of each of the components by adding them one by one to a bare visual feature branch. In particular, for the first comparison, we directly set the whole probability transition matrix \\(M\\) as a unit matrix (i.e., all of its entries are \"1\") to erase the distance encoding information. By doing so, only the token-based identification generated by the online token learning module is involved in the final global features. As seen in Table 3, with this single module (2nd row), the retrieval performance could be improved from \\(77.51\\%\\) to \\(78.82\\%\\) and \\(87.82\\%\\) to \\(88.21\\%\\) on ROxf-Medium and RPar-Medium, respectively. It shows the benefit of utilizing the tokens to identify the local descriptors. After adding the distance encoding module, the spatial distribution information is involved. It can be seen, with the complete branch (3rd row), the retrieval performance is further improved, especially on Hard splits. The performance (mAP) is increased from \\(58.73\\%\\) to \\(60.90\\%\\) and \\(74.03\\%\\) to \\(76.97\\%\\) on ROxf-Hard and RPar-hard, respectively. This verifies the importance of capturing the spatial distribution information with the distance encoding module. Altogether, this result demonstrates the effectiveness of the spatial context branch as a whole in our method." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.792, + 0.888, + 0.886 + ], + "angle": 0, + "content": "
Fusion StrategyMediumHard
ROxfRParROxfRPar
Orthogonal79.0486.6959.4972.87
Hadamard79.8387.9059.4474.60
Concatenation79.9488.4560.7276.00
Cross-Attention79.6489.0660.9076.97
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.522, + 0.886, + 0.865, + 0.899 + ], + "angle": 0, + "content": "Table 4. Ablation studies on the impact of fusion strategy." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11256" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "Fusion Strategy We validate the impact of different feature fusion strategies, including concatenation, orthogonal [35], Hadamard product, and cross-attention to fuse the information learned by our two branches in Table 4. As seen, the cross-attention scheme outperforms all the others in most cases except on the Medium split of ROxford. It demonstrates the effectiveness of utilizing cross-attention as the feature fusion strategy. Compared with cross-attention, orthogonal and Hadamard product perform worse. Surprisingly, we find simply concatenating the information from two branches has been able to obtain competitive performance. The result obtained by the concatenation strategy has been included in Table 1 too." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.318, + 0.462, + 0.428 + ], + "angle": 0, + "content": "
Token Number (K)MediumHard
ROxfRParROxfRPar
480.7688.3562.0275.33
879.6489.0660.9076.97
1681.2288.6162.4175.78
2480.4689.4261.8777.01
3280.1188.2860.6475.06
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.103, + 0.428, + 0.44, + 0.44 + ], + "angle": 0, + "content": "Table 5. Ablation studies on the impact of token number." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.473, + 0.686 + ], + "angle": 0, + "content": "Number of Tokens We investigate the impact of the token number in Table 5. As seen, when the number is 16, the performance on ROxford is much better than other options. Meanwhile, when we utilize 24 tokens, the performance on RParis outperforms the others instead. We believe the optimal token number is related to the characteristic of the test dataset. When the number is too small, only a few visual prototypes could be explored to describe the whole dataset, leading to incomplete spatial context information extraction. Conversely, if the number is too large, more noisy tokens will be included. This could adversely impact the token-based identification process and consequently decrease the final retrieval performance. In our experiment, we just empirically use \\( K = 16 \\) since we do not access any test dataset during the training stage." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.718, + 0.456, + 0.812 + ], + "angle": 0, + "content": "
Random Walk (l)MediumHard
ROxfRParROxfRPar
179.6489.0660.9076.97
280.7688.8862.1576.24
381.3189.6462.5777.48
480.2588.5461.1275.61
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.078, + 0.812, + 0.446, + 0.825 + ], + "angle": 0, + "content": "Table 6. Ablation studies on the impact of random walk steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Number of Random Walk Steps To inspect how many random walk steps are needed to encode the distance for our spatial context information extraction, we apply different number of random walk steps \\( l = \\{1,2,3,4\\} \\). As seen in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.243 + ], + "angle": 0, + "content": "Table 6, \\( l = 3 \\) gives the best performance. When the step number is small (such as 1 or 2), only a small area around the nodes in the matrix \\( M \\) of Eq. (3) is considered for the final distance encoding process. Meanwhile, with the number of steps increased, the random walk process tends to converge and its results become similar (i.e., \\( \\mathbf{s}^{(l)} \\approx \\mathbf{s}^{(l + 1)} \\) in Eq. (6)). Keeping adding or concatenating this information leads to redundant or even noisy information to the distance encoding, and thus adversely impacts the spatial context information extracted and further undermines retrieval." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.895, + 0.404 + ], + "angle": 0, + "content": "Qualitative Results We demonstrate two images retrieved from ROxford. In addition, we provide the classification activation map obtained by using query feature representation as classification projection weights. As seen in Figure 3, in addition to the most discriminative part of the queried object (as shown in the second column obtained by DELG), the proposed SpCa focuses more on the spatial-context area. This makes the ranking of the true positive image dramatically increased compared with DELG." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.418, + 0.599, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.474, + 0.591, + 0.482 + ], + "angle": 0, + "content": "Query: ashmolean" + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.418, + 0.697, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.474, + 0.663, + 0.482 + ], + "angle": 0, + "content": "DELG" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.418, + 0.794, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.733, + 0.474, + 0.759, + 0.482 + ], + "angle": 0, + "content": "SpCa" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.418, + 0.891, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.796, + 0.474, + 0.889, + 0.482 + ], + "angle": 0, + "content": "Ranking: 76th -> 20th" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.485, + 0.599, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.54, + 0.592, + 0.549 + ], + "angle": 0, + "content": "Query: cornmarket" + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.485, + 0.697, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.636, + 0.541, + 0.662, + 0.549 + ], + "angle": 0, + "content": "DELG" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.485, + 0.793, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.733, + 0.541, + 0.758, + 0.549 + ], + "angle": 0, + "content": "SpCa" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.485, + 0.891, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.796, + 0.541, + 0.889, + 0.549 + ], + "angle": 0, + "content": "Ranking: 30th -> 11th" + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.555, + 0.853, + 0.57 + ], + "angle": 0, + "content": "Figure 3. Qualitative results and the activation maps." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.603, + 0.619, + 0.619 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Motivated by the benefit of using local descriptor based geometric verification in a re-ranking step, we propose a novel feature learning framework that effectively embeds the spatial context information into the global visual feature representation for instance image retrieval. To mine the spatial context information, a spatial context branch consisting of an online token learning module and a distance encoding module is proposed. The former module is utilized to identify the type of each local descriptor on a feature map. The latter is used to capture the information on how the surrounding descriptors are spatially distributed. By fusing visual and spatial context information together, our framework learns spatial-context-aware global feature representations for images to conduct retrieval. Extensive experiments demonstrate the effectiveness of the proposed framework for retrieval. In future work, we will explore the incorporation of other types of information into global feature representations to further improve instance image retrieval." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11257" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.091, + 0.237, + 0.108 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.47, + 0.191 + ], + "angle": 0, + "content": "This work is supported by the Australian Research Council (grant number DP200101289) and undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.207, + 0.174, + 0.222 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.232, + 0.47, + 0.288 + ], + "angle": 0, + "content": "[1] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomás Pájdla, and Josef Sivic. 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IEEE Computer Society, 2009. 1" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.757 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11259" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_origin.pdf b/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f435501a4c1771e96bba4c2b4e2cb3aa074c83fe --- /dev/null +++ b/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/4a7da155-d324-4f0d-9452-e7f76abd7205_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bfe8b7c6486cb0768739e4bd02642b1206cf4bfb27b564b3e3a4bedb7af76ce0 +size 3573274 diff --git a/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/full.md b/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/full.md new file mode 100644 index 0000000000000000000000000000000000000000..66f096bbc5eac41f1576c4542f728c0c57a1235a --- /dev/null +++ b/2023/Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval/full.md @@ -0,0 +1,317 @@ +# Learning Spatial-context-aware Global Visual Feature Representation for Instance Image Retrieval + +Zhongyan Zhang $^{1}$ , Lei Wang $^{1}$ , Luping Zhou $^{2}$ , Piotr Koniusz $^{3,4}$ + +University of Wollongong1, University of Sydney2, Data61♥CSIRO3, Australian National University4 + +zhongyan@uow.edu.au, leiw@uow.edu.au, luping.zhou@sydney.edu.au, peter.koniusz@data61.csiro.au + +# Abstract + +In instance image retrieval, considering local spatial information within an image has proven effective to boost retrieval performance, as demonstrated by local visual descriptor based geometric verification. Nevertheless, it will be highly valuable to make ordinary global image representations spatial-context-aware because global representation based image retrieval is appealing thanks to its algorithmic simplicity, low memory cost, and being friendly to sophisticated data structures. To this end, we propose a novel feature learning framework for instance image retrieval, which embeds local spatial context information into the learned global feature representations. Specifically, in parallel to the visual feature branch in a CNN backbone, we design a spatial context branch that consists of two modules called online token learning and distance encoding. For each local descriptor learned in CNN, the former module is used to indicate the types of its surrounding descriptors, while their spatial distribution information is captured by the latter module. After that, the visual feature branch and the spatial context branch are fused to produce a single global feature representation per image. As experimentally demonstrated, with the spatial-context-aware characteristic, we can well improve the performance of global representation based image retrieval while maintaining all of its appealing properties. Our code is available at https://github.com/Zy-Zhang/SpCa. + +# 1. Introduction + +Given a query image, the purpose of instance-level image retrieval is to search and retrieve the images containing the identical object described by the query from a largescale image dataset. In this task, visual feature representations of images play a crucial role in measuring the similarities between a query and candidate images. A variety of handcrafted feature-based methods [14, 38, 2] have been proposed to significantly improve the performance in + +the past two decades. Recently, due to the development of deep learning technologies, deep feature representations have been overtaking the position of conventional handcrafted ones and bringing great progress in the task of instance image retrieval [1, 3, 17, 28, 15]. + +Generally, deep feature representations used in instance image retrieval can be categorized into two types. One type is global feature representation, which describes the visual content of an image as a whole. As a multi-dimensional vector, it can be efficiently used to measure the similarity of two images, say, via Euclidean distance or cosine similarity. For a retrieval task, the total number of global feature representations is just the size of image database, and they can be pre-extracted and economically stored for use. In addition, one global feature representation per image works well with the classic data structures designed for searching. The other type is local descriptors, which describe the local information within an image and collectively reflect the spatial information of the visual cues in an image. In image retrieval, they are important for conducting geometric verification to confirm if two images truly match or not. However, the total number of local descriptors per image could be large (e.g., 1,000) and the verification involves non-trivial computation, making this process expensive in computational cost and memory footprint. + +This situation leads to a wide use of "two-stage" paradigm in instance image retrieval [23, 3, 17]. An initial retrieval result is firstly obtained via the global feature representation. After that, a re-ranking step utilizes the local descriptors to refine a small number of top-retrieved images. Nevertheless, this two-stage paradigm not only results in two separate procedures [26, 10] but also considerably increases retrieval time and memory expense for practical retrieval tasks [18], due to the presence of the local descriptor-based spatial verification step. Therefore, it will be highly valuable to make ordinary global image representations spatial-context-aware by considering their appealing properties of algorithmic simplicity, low memory cost, and being friendly to data structures. + +To achieve this, we propose a novel feature learning + +framework to effectively embed spatial context information into global feature representation of images. Doing so will help to boost the retrieval performance of global feature representation, improving its efficacy when the local descriptor based re-ranking becomes costly or infeasible. + +Specifically, two types of information are extracted in our framework. One is conventional visual information obtained by a visual feature branch in a CNN backbone. The other one is spatial context information that describes for each local descriptor learned in CNN, what kind of surrounding local descriptors are and how they spatially distribute on a feature map. To obtain this information, we develop a spatial context branch that operates in parallel to the visual feature branch in CNN. This branch consists of two modules called online token learning and distance encoding. The module of online token learning addresses the "what kind" issue. A set of semantic tokens that could be regarded as anchors in the space of local descriptors is learned in an online manner. Comparing the tokens to the visual words in a visual dictionary, each local descriptor can be uniquely labelled via soft coding as a token-based identification. The module of distance encoding cares about the "spatial distribution" issue. A probability transition based encoding is devised to reflect the relative spatial distance between each pair of local descriptors, so as to capture their spatial distribution information in a feature map. After that, the token-based identification and the spatial distribution information are integrated to produce a spatial context clue for each local descriptor. With both visual and spatial information, a feature fusion operation is conducted to fuse them together to generate spatial-context-aware local descriptors. Finally, a global pooling followed by a whitening layer is added to embed the context-aware local descriptors into a global feature representation for each image. + +Our contributions are summarised as follows: + +i. We propose an end-to-end feature learning framework to characterise and embed spatial context information into the process of information processing and extraction in CNN. It makes global feature representations become more capable for instance image retrieval. +ii. To implement the framework, we design a spatial context branch. With its online token learning module, the types of local descriptors are identified and easily compared. With the distance encoding module, the information about the spatial distribution of different types of local descriptors around a given descriptor is obtained. +iii. To verify the efficacy of the proposed framework, we conduct extensive experiments on instance image retrieval benchmark datasets, ROxford and RParis, with one million distractors. As demonstrated, our global feature representations effectively improve the perfor + +mance of instance image retrieval, making global representation a more competitive option for practical tasks. + +# 2. Related Work + +In this section, we briefly review deep instance image retrieval, including local and global feature learning methods. + +# 2.1. Global features + +Global feature has been widely used to represent the content of images for a wide range of computer vision tasks [21, 13, 8, 36, 37, 12, 11]. Due to its compactness and efficiency, a variety of global methods [24, 32, 35, 15] have been proposed to learn discriminative feature representations via deep models in the instance image retrieval community. Some of the studies focus on applying more effective loss functions, including triplet losses [29], list-wise losses [22], and classification losses [5] to train the model. Others explore how to pool the entire feature maps into a compact feature vector while maintaining their discrepancies. For instance, weighted-sum-pooling (CroW) [9], regional-max-pooling (R-MAC) [29], and GeM pooling [20]. Recently, several methods try to modify the training model architecture to capture more useful information during the training process. SOLAR [15] combines normal training with second-order information by adding self-attention modules in the conventional CNN backbones. Token [32] jointly learns a set of tokens and the corresponding visual representations to mimic the conventional dictionary learning plus feature encoding scheme to represent images. Some other studies [32, 35] propose multiple branches for CNN models to mine more complementary information and fuse them into the final feature vectors. We follow the global feature type to learn compact features to conduct retrieval. + +# 2.2. Local features + +Deep local descriptors [28, 30, 33, 17] have been extensively researched and made significant progress in instance image retrieval [4]. The key to their success lies in the spatial information these local descriptors hold, and it is usually utilized by kernel alignment aggregation (e.g., ASMK [27]) or geometric verification (e.g., RANSAC [6]) for image similarity measure. In recent studies, several methods [26, 10] individually train a matching model to directly compare the similarity of two images (or their preextracted local descriptors) in a data-driven manner. However, they need more inference time and memory footprint. Therefore, they are usually applied to only top k retrieved images obtained by a global retrieval method as a reranking. + +# 2.3. Learning local and global features jointly + +Driven by the complementary properties of global and local features, jointly learning the two types of features + +![](images/f2251ae6b4e61f4031aaa5f42f3b6e8b4274391297ae37ea7ff703bf923e5c60.jpg) +Figure 1. Overview of our framework. After an initial feature extraction by a CNN backbone, two branches of "Visual Feature Branch" and "Spatial Context Branch" are used to extract visual and spatial context information. After that, a cross-attention module is used to fuse the visual feature and the corresponding spatial context feature to generate spatial-context-aware visual representations for images. In particular, "GMM" denotes the Gaussian Mixture Model process, and "GP+W" refers to global pooling followed by whitening. + +becomes a straightforward idea. Recently, several studies demonstrate the advantages of learning features in this manner. DELG [3] creatively unifies the two separate learning processes into one training framework. However, even though the training procedure is unified, the learning processes of the two feature types are still somehow irrelevant. To further explore this approach, DOLG [35] and DALG [25] firstly separate the feature extractor into two branches to learn the local and global features and then fuse them via a manual or learnable way to obtain compact feature representations for images. Both of them try to extract individual visual information from the two types of features to make them complementary to each other. However, the powerful spatial context information held by local features is neither exploited nor embedded into the final feature representations. In this work, we argue that spatial context information is more beneficial than visual information from local descriptors to the final global feature representations for instance image retrieval. To this end, we propose a novel feature learning framework to effectively embed the spatial context information into final global features. + +# 3. The Proposed Method + +An overview of our framework is in Figure 1. Given an image $I$ , a conventional CNN backbone is used to generate a feature map $\mathbf{V} \in \mathbb{R}^{D \times H \times W}$ , in which each spatial position corresponds to a $D$ -dimensional local visual descriptor. Besides, a spatial context branch is split from the feature map to extract the spatial context information of all the descriptors, which is represented in the form of $\mathbf{S} \in \mathbb{R}^{C \times H \times W}$ with $C$ being the dimensions. After that, for each local descriptor, its two kinds of information are fused together, say, with a cross-attention module or a simple concatenation operation. After the fusion, a global pooling and a fully-connected layer are used to generate the final global spatial-context-aware feature $\mathbf{f}_{spca}$ to represent the image. In the following, + +we focus on describing the spatial context branch since the visual branch follows its original design in CNN backbones. + +# 3.1. Spatial Context Branch + +In the spatial context branch, there are two main issues to be addressed for each spatial position on the feature map: 1) what kinds of local descriptors are there in its surrounding region (i.e., identification task); 2) how they spatially distribute on the feature map (i.e., spatial distribution task). We now introduce how we address the two issues orderly. + +Token-based Identification. For existing local feature-based retrieval methods [28, 30, 33], learning tokens to capture discriminative visual patterns in a dataset has proven reliable to identify local descriptors. With the tokens, the encoded features could become more robust against illumination change, the information loss due to occlusion, and the adverse impact of the background in an image. In our framework, we generally follow this "tokens plus encoding" pipeline to identify local descriptors. However, in the literature, the tokens are usually learned by clustering (e.g., by k-means) a sampled subset of local descriptors obtained from an image dataset in an offline manner. This way separates the process of token learning from encoding, potentially causing a discrepancy between the training and the inference stages. In addition, using a sampled subset of local descriptors could lead to learning biased tokens since the information available in an image dataset is not fully utilized. To improve this situation, we perform token learning via an online mini-batch based Gaussian Mixture Model (GMM) process. This helps to adequately utilize all the local descriptors to learn tokens and makes our framework fully end-to-end trainable. + +Specifically, we model the distribution of local descriptors by a $K$ -component Gaussian mixture model $p(\mathbf{v}|\Theta) = \sum_{k}\alpha_{k}N(\mathbf{v};\boldsymbol{\mu}_{k},\Sigma_{k})$ , where $\mathbf{v}$ denotes the a local descriptor, while $\alpha_{k},\boldsymbol{\mu}_{k}$ , and $\Sigma_{k} = \sigma_{k}^{2}I_{D}$ denote the prior probability, the + +mean, and the (spherical) covariance matrix for component $k$ , respectively. In this case, token learning boils down to the parameter estimation for this Gaussian mixture model. At the beginning, $\mu$ and $\sigma^2$ are randomly generated and $\alpha$ is set as $1 / K$ . After that, we conduct the Expectation and Maximization (EM) process for all the local descriptors within each mini-batch. To be concise, we show the key results below and the details can be found in the literature [16]. + +Within each mini-batch, for the E-Step, the probability that the $i$ th local descriptor $\mathbf{v}_i$ belongs to the $k$ th component can be expressed as + +$$ +\omega_ {i k} = \frac {\alpha_ {k} N \left(\mathbf {v} _ {i} ; \boldsymbol {\mu} _ {k} , \Sigma_ {k}\right)}{\sum_ {j = 1} ^ {K} \alpha_ {j} N \left(\mathbf {v} _ {i} ; \boldsymbol {\mu} _ {j} , \Sigma_ {j}\right)} \tag {1} +$$ + +For M-Step, the prior probability, the mean and the covariance are updated as + +$$ +\alpha_ {k} \leftarrow \alpha_ {k} + \beta \left(\frac {\sum_ {i} \omega_ {i k}}{H W} - \alpha_ {k}\right) +$$ + +$$ +\boldsymbol {\mu} _ {k} \leftarrow \boldsymbol {\mu} _ {k} + \beta \left(\frac {\sum_ {i} \omega_ {i k} \mathbf {v} _ {i}}{\sum_ {i} \omega_ {i k}} - \boldsymbol {\mu} _ {k}\right) \tag {2} +$$ + +$$ +\sigma_ {k} ^ {2} \leftarrow \sigma_ {k} ^ {2} + \beta \Big (\frac {\sum_ {i} \omega_ {i k} \| \mathbf {v} _ {i} - \boldsymbol {\mu} _ {k} \| ^ {2}}{\sum_ {i} \omega_ {i k}} - \sigma_ {k} ^ {2} \Big), +$$ + +where $HW$ is the number of local descriptors obtained from an image, and $\beta$ is a momentum to make the estimation process more stable in the mini-batch clustering [16]. One E-Step and M-Step are conducted in each iteration during the training. + +After the above process, $(\pmb{\mu}_1,\pmb{\mu}_2,\dots ,\pmb{\mu}_K)$ represents the learned tokens. $\omega_{i} = (\omega_{i1},\omega_{i2},\dots ,\omega_{iK})\in \mathbb{R}^{K}$ obtained by Eq. (1) can be used as the token-based identification for local descriptor $\mathbf{v}_i$ since it represents the posterior probability that this descriptor belongs to each of the $K$ components. + +Spatial Distribution. To extract spatial distribution information for a local descriptor $\mathbf{v}_i$ , the distances of this descriptor to all the descriptors $V = \{\mathbf{v}_j, j = 1,2,\dots,HW\}$ presented on the same feature map should be effectively measured and collected. To achieve this, simply using the coordinate distances among them is inadequate. We utilize a probability transition score obtained by applying random walk on the graph constituted by all the local descriptors as the nodes to measure the distances. By doing so, more possible paths among the local descriptors will be considered and the number of random walk steps could also be used to control the spatial scale in the distance measurement. Inspired by the literature [11], we perform the spatial distribution extraction as an aggregation of the encoded distances between $\mathbf{v}_i$ and all $\mathbf{v}_j \in V$ . By "coded," we mean that the distance is measured by a probability transition process as explained below. + +Given an undirected graph with an affinity matrix $A$ , the distance of its nodes $\nu$ and $u$ can be encoded by a probability transition score $\zeta$ obtained via $l$ steps of random walk + +$$ +\zeta (v, u) ^ {(l)} = \left(M ^ {l}\right) _ {v u}, M ^ {1} = A D ^ {- 1}, M ^ {l} = M ^ {l - 1} \cdot M, \tag {3} +$$ + +where $M^1$ denotes the random walk matrix, $D^{-1}$ refers to the normalization matrix of the graph, and $l$ is the number of random walk steps. Based on this, the distance of a node $v$ from all nodes $u$ in a target set $S$ can be represented by an aggregation operation as + +$$ +\zeta (\nu , S) ^ {(l)} = \operatorname {a g g} \left(\left\{\zeta (\nu , u) ^ {(l)} \mid u \in S \right\}\right) \tag {4} +$$ + +Linking the above result to our case, the undirected graph consists of all the local descriptors $V$ in an image, and they collectively form the target set $S$ in this distance encoding process. In addition, we compute the affinity matrix $A$ based on the coordinate distance on the feature map as + +$$ +A _ {i j} = \exp (- \operatorname {c o} _ {-} \operatorname {d i s t} (\mathbf {v} _ {i}, \mathbf {v} _ {j})), (1 \leq i, j \leq H W), \tag {5} +$$ + +where $\mathrm{co\_dist}(\cdot, \cdot)$ denotes the Euclidean distance between the coordinates of two local descriptors. After that, the encoded distance can be obtained by applying Eq. (3). Furthermore, we enrich Eq. (4) by considering the learned token-based identification (i.e., the posteriori probability $\omega$ obtained in Eq. (1)), and this leads to an instantiated "agg" operation in Eq. (4) to produce the spatial context feature for local descriptor $\mathbf{v}_i$ . + +$$ +\mathbf {s} _ {i} ^ {(l)} \triangleq \zeta (v _ {i}, S) ^ {(l)} = \sum_ {j = 1} ^ {H W} \zeta (\mathbf {v} _ {i}, \mathbf {v} _ {j}) ^ {(l)} \boldsymbol {\omega} _ {j}. \tag {6} +$$ + +Recall that the token-based identification $\omega_{i}$ can be treated as a vector of probability transition scores between local descriptor $\mathbf{v}_i$ and each of the learned tokens $\pmb{\mu}$ . By combining the encoded distance and the token-based identification, the spatial context feature $\mathbf{s}_i$ in Eq. (6) essentially reflects the probability transition scores between node $\mathbf{v}_i$ and the tokens $\pmb{\mu}$ when regarding the spatial structure of the given $H\times W$ feature map as a (static) transition matrix. This is illustrated in Figure 2. That means the spatial distribution information is used to control the extraction of the spatial context features. In this sense, the spatial distribution information is effectively embedded into the spatial context features. At last, we define the final spatial context feature for the local descriptor $\mathbf{v}_i$ obtained through an $l$ -step random walk as + +$$ +\mathbf {s} _ {i} = \mathbf {s} _ {i} ^ {(1)} \oplus \mathbf {s} _ {i} ^ {(2)} \oplus \dots \oplus \mathbf {s} _ {i} ^ {(l)}, \tag {7} +$$ + +where $\oplus$ denotes concatenation operation. The concatenation of the features obtained after each of the $l$ steps considers the spatial context information at various scales. + +![](images/f813abe790e495de1e008e840498cc75242bf80e3f649dd11f810b1ad905fc37.jpg) +Figure 2. Spatial context feature generation. See the detailed description after Eq. (6). + +# 3.2. Fusion of Visual and Spatial Information + +With both visual and spatial context information available, a proper fusion scheme is needed to make them complements to benefit the final feature representation. To accomplish it, various feature fusion schemes could be used, including concatenation, orthogonal fusion [35], Hadamard product, or cross-attention fusion. We utilize a cross-attention module for information fusion in our method since it is commonly used to align features from different modalities in the recent literature. Meanwhile, we provide an ablation study on all the four fusion schemes in the experimental part. For the cross-attention scheme, the spatial context feature $\mathbf{S} = (\mathbf{s}_1,\mathbf{s}_2,\dots ,\mathbf{s}_{HW})$ is projected into the same space as the visual feature $\mathbf{V}$ with a linear projection layer. After that, both of them are flattened into sequences and mapped into Queries (Q), Keys (K), and Values (V), respectively, to put through into the cross-attention layer: + +$$ +\mathbb {Q} = \operatorname {p r o j} (\mathbf {V}), \mathbb {K} = \operatorname {p r o j} (\mathbf {S}), \mathbb {V} = \operatorname {p r o j} (\mathbf {S}) +$$ + +$$ +\mathbf {F} _ {s p c a} ^ {*} = \operatorname {s o f t m a x} \left(\frac {\mathbb {Q} \cdot \mathbb {K} ^ {\top}}{\sqrt {D}}\right) \cdot \mathbb {V} \tag {8} +$$ + +$$ +\mathbf {F} _ {s p c a} = \mathbf {F} _ {s p c a} ^ {*} + \operatorname {M L P} \left(\mathbf {F} _ {s p c a} ^ {*}\right) +$$ + +where MLP denotes a feed-forward layer and $\mathbf{F}_{spca}$ denotes the spatial-context-aware feature sequence. After that, the feature sequence is rearranged as a feature map, followed by a global pooling and a fully-connected layer to generate a global feature representation vector $\mathbf{f}_{spca}$ . + +# 3.3. Objective Function for Training + +Following previous state-of-the-art work [3, 35, 32], we train our model on a dataset with object class annotations and utilize ArcFace margin loss [5] with learnable parame + +ters $\hat{\mathbf{W}}\in \mathbb{R}^{D\times N}$ to train the whole model: + +$$ +L = - \log \left(\frac {\exp \left(\gamma \times A F \left(\hat {\mathbf {w}} _ {t} ^ {\top} \hat {\mathbf {f}} _ {s p c a} , 1\right)\right)}{\sum_ {n} \exp \left(\gamma \times A F \left(\hat {\mathbf {w}} _ {n} ^ {\top} \hat {\mathbf {f}} _ {s p c a} , y _ {n}\right)\right)}\right) \tag {9} +$$ + +where $\hat{\mathbf{w}}_t$ denotes the $t$ th column of $\hat{\mathbf{W}}$ and $\hat{\mathbf{f}}_{spca}$ is the $L_{2}$ -normalized $\mathbf{f}_{spca}$ . $y$ is the one-hot label vector and $t$ is the index to indicate the true class (i.e., $y_t = 1$ ). $n$ is the total number of classes in the dataset. $\gamma$ is a scaling factor. $AF(\cdot)$ refers to the ArcFace cosine similarity and it is calculated as + +$$ +A F (s, c) = \left\{ \begin{array}{l l} \cos (a \cos (s) + m), & \text {i f} c = 1 \\ s, & \text {i f} c = 0 \end{array} \right. \tag {10} +$$ + +where $s$ is the cosine similarity between $\hat{\mathbf{w}}_t$ and $\hat{\mathbf{f}}_{spca}$ , $m$ is the ArcFace margin and $c$ indicates if this is the true class. + +# 4. Experimental Result + +# 4.1. Dataset and Evaluation Metric + +Our model is trained on "Google Landmark v2 clean" dataset, which is a clean subset of Google Landmark v2 [31]. It contains 1,580,470 images of 81,313 landmark classes, and it has been widely used in existing methods [35, 32, 3] as the training dataset. To make a fair comparison, we follow the previous work [32, 35] to randomly divide the dataset into two subsets 'train'/'val' with $80\% / 20\%$ split. For evaluation, we use two widely used benchmark datasets, ROxford and RParis [19] to test our model. Both datasets have 70 query images but contain 4,993 and 6,322 gallery images, respectively. In addition, a 1M distractor set [19] is added to test our model for the case of large-scale retrieval. We use mean average precision (mAP), as the criterion of retrieval performance for both "Medium" and "Hard" splits of ROxford and RParis. + +# 4.2. Implementation Details + +We use ResNet101/ResNet50 [8] as the CNN backbone to learn visual features. For image augmentation, random crop and color jittering are used first, and all the augmented images are resized into $512 \times 512$ pixels as the model input. The model is trained on 4 Nvidia V100-SXM2-32GB GPU cards with a batch size of 128 for 50 epochs. We use SGD optimizer with a momentum of 0.9. A warming-up of 5-epoch's training is used to initialize the learning rate from 0.0001 to the base learning rate of 0.005. As for the ArcFace loss, the margin $m$ and the scale $\gamma$ are empirically set as 0.2 and 45. For the global pooling, we utilize GeM [20] pooling with the fixed coefficient $p = 3$ during the whole training. $\beta$ in the M-Step of GMM is empirically set as 0.999. In addition, we set the number of random walk steps $l$ as 3 and the number of tokens as $K = 16$ . The dimensions of the + +
MethodMediumHard
ROxfROxf+1MRParRPar+1MROxfROxf+1MRParRPar+1M
Global features + local features re-ranking
R101-DELG [3]+SP81.2069.1087.2071.5064.0047.5072.8048.70
R101-DELG [3]+SP†81.8270.1588.6476.1464.9749.5476.8153.62
Global features
R101-R-MAC [7]60.9039.3078.9054.8032.4012.5059.4028.00
R101-GeM [20]64.7045.2077.2052.3038.5019.9056.3024.70
R101-SOLAR [15]69.9053.5081.6059.2047.9029.9064.5033.40
R101-DELG [3]76.3063.7086.6070.6055.6037.5072.4046.90
R101-GLAM [24]78.6068.0088.5073.5060.2043.5076.8053.10
Swin-S-DALG [25]79.94-90.04-57.55-79.06-
R101-DOLG [35]★81.5077.4391.0283.2961.1054.8180.3066.69
R101-Token [32]82.2870.5289.3476.6666.5747.2778.5655.90
R101-Token [32]†77.8266.7487.9375.2260.1043.0774.6653.19
R101-DOLG [35]†78.35(75.51)(88.48)(78.25)58.59(52.36)(75.39)(61.85)
R101-DELG [3]†79.8267.8587.2172.4561.1642.5873.8450.79
R101-SOLAR [15]†(81.63)71.8488.2172.86(63.29)45.2875.2151.26
R50-SpCaacro (Ours)79.9172.7887.4378.0159.2749.2673.1458.3
R50-SpCaCat (Ours)81.5573.2088.6078.2361.1948.7676.2160.91
R101-SpCaacro (Ours)82.7377.8490.2079.1265.6053.3579.2965.84
R101-SpCaCat (Ours)83.2477.8290.5679.4865.8553.2779.9764.98
+ +Table 1. Performance (mAP) comparison with recent state-of-the-art instance image retrieval methods on datasets ROxford5k and RParis6k [19]. R101 and R50 denote ResNet101 and ResNet50. Swin-S denotes Swin-Transformer-small [13]. The subscripts $\text{cro}$ and $\text{cat}$ refer to cross-attention and concatenation feature fusion strategies. SP denotes spatial verification via RANSAC. $\dagger$ denotes our reimplementation. $\star$ means no query cropping. Results in gray are those reported in the published papers. The best and second best performances are highlighted in bold and with underlines, respectively. The best previous performance is shown in brackets. + +final global feature are set as 2048. For inference, the multiple scales [0.3535, 0.5, 0.7071, 1.0, 1.4142] are applied to each original image to extract the feature representations. To fuse the features obtained from different scales, they are $L_{2}$ -normalized, summed, and normalized again to generate the final global features for retrieval. + +# 4.3. Comparison with State-of-the-art Methods + +Setting for fair comparison Note that there are setting differences among the previous state-of-the-art methods. For example, they are different at 1) pretrained model sources for initialization (Caffe $^{1}$ , PyTorch $^{2}$ , and Facebook $^{3}$ ); 2) training datasets (SfM-120k [20], GLDv1 [17], GLDv2 [31], and different $80\% / 20\%$ split); 3) the number of multiple scales used at the inference stage (e.g., 3, 5, or 7); 4) with or without query cropping scheme. These discrepancies could affect the fairness of the comparison if not well handled. To address this situation, we carefully re-implement multiple SOTA methods by using their officially published codes and the training parameters reported in their papers, while keeping the same settings for the + +above factors between these methods and ours. Specifically, to ensure fair comparison, our experimental study utilizes the same $80\%$ of GLDv2-clean [31] as the training dataset, the same remaining $20\%$ of GLDv2-clean as the validation dataset, the same pretrained model from PyTorch for initialization, and the same 5 scales with query cropping scheme for inference to conduct instance image retrieval. + +Retrieval results Two groups of state-of-the-art methods are compared in this experimental study: 1) methods based on global feature representations. They include two milestone works R-MAC [7] and GeM [20] and another six more recent works including DELG [3], SOLAR [15], GLAM [24], DOLG [35], DALG [25], and Token [32]; 2) a method using global feature based initial retrieval plus local feature based re-ranking scheme, DELG+SP [3], is included as well. Also, note that we focus on global feature based image retrieval in this paper, and we do not consider training a verification model [10] or adding any post-processing steps like diffusion or query expansion to boost retrieval performance [34]. + +The retrieval result is reported in Table 1. The methods under "Global features" are partitioned into three sections. The results in gray color are those reported in the original + +published papers. Since they involve different settings as discussed above, the results are included here mainly as a reference. Following the gray-colored results are those obtained by our re-implementation for the sake of fair comparison, and they are used to compare with our methods shown at the bottom of this table. + +As seen, our method R101-SpCa (where "SpCa" is short for "Spatial-context-aware"), with either cross-attention ( $-cro$ ) or concatenation ( $-cat$ ) fusion strategy, clearly outperforms the others on all the test cases. Compared with the closest results obtained by DOLG and SOLAR, our method achieves $1.6\%$ and $2.0\%$ performance gain on the Medium split of ROxford and RParis, respectively. And higher improvements of $2.5\%$ and $4.5\%$ are obtained on the Hard split of the two datasets. After the 1M distractors are added, our method still demonstrates its excellent retrieval performance. All these results validate the efficacy of our method. + +Compared with the global initial retrieval plus local feature re-ranking scheme, our method still maintains its advantage. As listed in Table 1, even without using the pairwised re-ranking step as done in R101-DELG+SP [3], our method has outperformed it by around $2\%$ on all dataset splits. More importantly, our method costs no extra inference time as taken by the re-ranking step. In addition, the memory footprint of our global feature representation (i.e., a 2048-dimensional vector per image) is also much less than that used by the local descriptor (there are usually 1,000 vectors per image, each of which is of 128 dimensions) based re-ranking. This again shows the computational advantage brought by our method. + +Computational Overhead We report the number of parameters, feature extraction latency, and memory footprint for different SOTA models in Table 2. As seen, our method is comparable to that of DOLG in terms of computational overhead and comparable to that of Token in terms of the number of parameters. Also, our method takes the same memory footprint as the others that generate 2048-dimensional vectors as feature representations. + +
Method#Para (M)Latency (ms)Mem. (MB) +On ROxford
SOLAR [15]52.511039.0
DELG [3]44.510439.0
Token [32]76.611219.5
DOLG [35]61.51509.7
SpCa (Ours)76.815339.0
+ +Table 2. Latency is measured on a 1080Ti GPU for a ${1024} \times {1024}$ image with 3 scaling factors $\left\lbrack {1,\sqrt{2},1/\sqrt{2}}\right\rbrack$ . + +# 4.4. Ablation Studies + +In this study, we uniformly utilize ResNet50 as the CNN backbone and set the token number and the number of random walk steps as $K = 8$ and $l = 1$ , respectively, for all the following experiments if not mentioned otherwise. In addition, all the models are trained by 25 epochs. More ablation studies utilizing ResNet101 are provided in the Appendix. + +
GlobalOTLDEMediumHard
ROxfRParROxfRPar
✓77.5187.8254.7673.82
✓✓78.8288.2158.7374.03
✓✓✓79.6489.0660.9076.97
+ +Table 3. Ablation studies on the impact of different components in the spatial context branch. The baseline containing only the visual feature branch is shown in the first row. OTL and DE denote online token learning and distance encoding, respectively. + +Impact of each component in spatial context branch The proposed spatial context branch consists of two components which are online token learning and distance encoding. We validate the contribution of each of the components by adding them one by one to a bare visual feature branch. In particular, for the first comparison, we directly set the whole probability transition matrix $M$ as a unit matrix (i.e., all of its entries are "1") to erase the distance encoding information. By doing so, only the token-based identification generated by the online token learning module is involved in the final global features. As seen in Table 3, with this single module (2nd row), the retrieval performance could be improved from $77.51\%$ to $78.82\%$ and $87.82\%$ to $88.21\%$ on ROxf-Medium and RPar-Medium, respectively. It shows the benefit of utilizing the tokens to identify the local descriptors. After adding the distance encoding module, the spatial distribution information is involved. It can be seen, with the complete branch (3rd row), the retrieval performance is further improved, especially on Hard splits. The performance (mAP) is increased from $58.73\%$ to $60.90\%$ and $74.03\%$ to $76.97\%$ on ROxf-Hard and RPar-hard, respectively. This verifies the importance of capturing the spatial distribution information with the distance encoding module. Altogether, this result demonstrates the effectiveness of the spatial context branch as a whole in our method. + +
Fusion StrategyMediumHard
ROxfRParROxfRPar
Orthogonal79.0486.6959.4972.87
Hadamard79.8387.9059.4474.60
Concatenation79.9488.4560.7276.00
Cross-Attention79.6489.0660.9076.97
+ +Table 4. Ablation studies on the impact of fusion strategy. + +Fusion Strategy We validate the impact of different feature fusion strategies, including concatenation, orthogonal [35], Hadamard product, and cross-attention to fuse the information learned by our two branches in Table 4. As seen, the cross-attention scheme outperforms all the others in most cases except on the Medium split of ROxford. It demonstrates the effectiveness of utilizing cross-attention as the feature fusion strategy. Compared with cross-attention, orthogonal and Hadamard product perform worse. Surprisingly, we find simply concatenating the information from two branches has been able to obtain competitive performance. The result obtained by the concatenation strategy has been included in Table 1 too. + +
Token Number (K)MediumHard
ROxfRParROxfRPar
480.7688.3562.0275.33
879.6489.0660.9076.97
1681.2288.6162.4175.78
2480.4689.4261.8777.01
3280.1188.2860.6475.06
+ +Table 5. Ablation studies on the impact of token number. + +Number of Tokens We investigate the impact of the token number in Table 5. As seen, when the number is 16, the performance on ROxford is much better than other options. Meanwhile, when we utilize 24 tokens, the performance on RParis outperforms the others instead. We believe the optimal token number is related to the characteristic of the test dataset. When the number is too small, only a few visual prototypes could be explored to describe the whole dataset, leading to incomplete spatial context information extraction. Conversely, if the number is too large, more noisy tokens will be included. This could adversely impact the token-based identification process and consequently decrease the final retrieval performance. In our experiment, we just empirically use $K = 16$ since we do not access any test dataset during the training stage. + +
Random Walk (l)MediumHard
ROxfRParROxfRPar
179.6489.0660.9076.97
280.7688.8862.1576.24
381.3189.6462.5777.48
480.2588.5461.1275.61
+ +Table 6. Ablation studies on the impact of random walk steps. + +Number of Random Walk Steps To inspect how many random walk steps are needed to encode the distance for our spatial context information extraction, we apply different number of random walk steps $l = \{1,2,3,4\}$ . As seen in + +Table 6, $l = 3$ gives the best performance. When the step number is small (such as 1 or 2), only a small area around the nodes in the matrix $M$ of Eq. (3) is considered for the final distance encoding process. Meanwhile, with the number of steps increased, the random walk process tends to converge and its results become similar (i.e., $\mathbf{s}^{(l)} \approx \mathbf{s}^{(l + 1)}$ in Eq. (6)). Keeping adding or concatenating this information leads to redundant or even noisy information to the distance encoding, and thus adversely impacts the spatial context information extracted and further undermines retrieval. + +Qualitative Results We demonstrate two images retrieved from ROxford. In addition, we provide the classification activation map obtained by using query feature representation as classification projection weights. As seen in Figure 3, in addition to the most discriminative part of the queried object (as shown in the second column obtained by DELG), the proposed SpCa focuses more on the spatial-context area. This makes the ranking of the true positive image dramatically increased compared with DELG. + +![](images/acd85fac86b11ac3a79ad6abfa5050a8fe103636caae428d13688e5b0eb8b241.jpg) +Query: ashmolean + +![](images/35ff8f3b1db00e29bfc50b01dd2a78a98f9b9326cd213ed1fdbc3a73f19a4db5.jpg) +DELG + +![](images/294385bd884c6d8639530729122a0e31235397cf9e96c08091f3b507aaab1646.jpg) +SpCa + +![](images/fa7a743e5d98539444c69ba01e2697c97d59c0f25f23929ba6cf9ccc739f636d.jpg) +Ranking: 76th -> 20th + +![](images/e685244bba611c8b1f2f9e8700becf381130b45b89b1f3f4c8789d7a5d95a636.jpg) +Query: cornmarket + +![](images/acf27e6f11ff0adf21f4f983f474f4671c90f51d66782eb9f7f61d5792e8c49d.jpg) +DELG + +![](images/ae59ea7bc75ef546de17eab03b338a9a23208027428ccad5f805ebbf1ae70801.jpg) +SpCa +Figure 3. Qualitative results and the activation maps. + +![](images/a5892cdb9da9ea5fbda345a666835d91d2c1224f6cfcd0eea81fd17b153b919a.jpg) +Ranking: 30th -> 11th + +# 5. Conclusion + +Motivated by the benefit of using local descriptor based geometric verification in a re-ranking step, we propose a novel feature learning framework that effectively embeds the spatial context information into the global visual feature representation for instance image retrieval. To mine the spatial context information, a spatial context branch consisting of an online token learning module and a distance encoding module is proposed. The former module is utilized to identify the type of each local descriptor on a feature map. The latter is used to capture the information on how the surrounding descriptors are spatially distributed. By fusing visual and spatial context information together, our framework learns spatial-context-aware global feature representations for images to conduct retrieval. Extensive experiments demonstrate the effectiveness of the proposed framework for retrieval. In future work, we will explore the incorporation of other types of information into global feature representations to further improve instance image retrieval. + +# Acknowledgement + +This work is supported by the Australian Research Council (grant number DP200101289) and undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government. + +# References + +[1] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomás Pájdla, and Josef Sivic. Netvlad: CNN architecture for weakly supervised place recognition. In CVPR, pages 5297-5307. IEEE Computer Society, 2016. 1 +[2] Herbert Bay, Andreas Ess, Tinne Tuytelaars, and Luc Van Gool. Speeded-up robust features (SURF). Comput. Vis. Image Underst., 110(3):346-359, 2008. 1 +[3] Bingyi Cao, André Araujo, and Jack Sim. Unifying deep local and global features for image search. In ECCV (20), volume 12365 of Lecture Notes in Computer Science, pages 726-743. 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Nevertheless, it will be highly valuable to make ordinary global image representations spatial-context-aware because global representation based image retrieval is appealing thanks to its algorithmic simplicity, low memory cost, and being friendly to sophisticated data structures. To this end, we propose a novel feature learning framework for instance image retrieval, which embeds local spatial context information into the learned global feature representations. Specifically, in parallel to the visual feature branch in a CNN backbone, we design a spatial context branch that consists of two modules called online token learning and distance encoding. For each local descriptor learned in CNN, the former module is used to indicate the types of its surrounding descriptors, while their spatial distribution information is captured by the latter module. After that, the visual feature branch and the spatial context branch are fused to produce a single global feature representation per image. As experimentally demonstrated, with the spatial-context-aware characteristic, we can well improve the performance of global representation based image retrieval while maintaining all of its appealing properties. Our code is available at https://github.com/Zy-Zhang/SpCa." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "spans": [ + { + "bbox": [ + 47, + 596, + 128, + 608 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "content": "Given a query image, the purpose of instance-level image retrieval is to search and retrieve the images containing the identical object described by the query from a largescale image dataset. In this task, visual feature representations of images play a crucial role in measuring the similarities between a query and candidate images. A variety of handcrafted feature-based methods [14, 38, 2] have been proposed to significantly improve the performance in" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "content": "the past two decades. Recently, due to the development of deep learning technologies, deep feature representations have been overtaking the position of conventional handcrafted ones and bringing great progress in the task of instance image retrieval [1, 3, 17, 28, 15]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 293, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 546, + 532 + ], + "type": "text", + "content": "Generally, deep feature representations used in instance image retrieval can be categorized into two types. One type is global feature representation, which describes the visual content of an image as a whole. As a multi-dimensional vector, it can be efficiently used to measure the similarity of two images, say, via Euclidean distance or cosine similarity. For a retrieval task, the total number of global feature representations is just the size of image database, and they can be pre-extracted and economically stored for use. In addition, one global feature representation per image works well with the classic data structures designed for searching. The other type is local descriptors, which describe the local information within an image and collectively reflect the spatial information of the visual cues in an image. In image retrieval, they are important for conducting geometric verification to confirm if two images truly match or not. However, the total number of local descriptors per image could be large (e.g., 1,000) and the verification involves non-trivial computation, making this process expensive in computational cost and memory footprint." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 700 + ], + "type": "text", + "content": "This situation leads to a wide use of \"two-stage\" paradigm in instance image retrieval [23, 3, 17]. An initial retrieval result is firstly obtained via the global feature representation. After that, a re-ranking step utilizes the local descriptors to refine a small number of top-retrieved images. Nevertheless, this two-stage paradigm not only results in two separate procedures [26, 10] but also considerably increases retrieval time and memory expense for practical retrieval tasks [18], due to the presence of the local descriptor-based spatial verification step. Therefore, it will be highly valuable to make ordinary global image representations spatial-context-aware by considering their appealing properties of algorithmic simplicity, low memory cost, and being friendly to data structures." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "To achieve this, we propose a novel feature learning" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 493, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11250" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "framework to effectively embed spatial context information into global feature representation of images. Doing so will help to boost the retrieval performance of global feature representation, improving its efficacy when the local descriptor based re-ranking becomes costly or infeasible." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 289, + 479 + ], + "type": "text", + "content": "Specifically, two types of information are extracted in our framework. One is conventional visual information obtained by a visual feature branch in a CNN backbone. The other one is spatial context information that describes for each local descriptor learned in CNN, what kind of surrounding local descriptors are and how they spatially distribute on a feature map. To obtain this information, we develop a spatial context branch that operates in parallel to the visual feature branch in CNN. This branch consists of two modules called online token learning and distance encoding. The module of online token learning addresses the \"what kind\" issue. A set of semantic tokens that could be regarded as anchors in the space of local descriptors is learned in an online manner. Comparing the tokens to the visual words in a visual dictionary, each local descriptor can be uniquely labelled via soft coding as a token-based identification. The module of distance encoding cares about the \"spatial distribution\" issue. A probability transition based encoding is devised to reflect the relative spatial distance between each pair of local descriptors, so as to capture their spatial distribution information in a feature map. After that, the token-based identification and the spatial distribution information are integrated to produce a spatial context clue for each local descriptor. With both visual and spatial information, a feature fusion operation is conducted to fuse them together to generate spatial-context-aware local descriptors. Finally, a global pooling followed by a whitening layer is added to embed the context-aware local descriptors into a global feature representation for each image." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 480, + 244, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 480, + 244, + 491 + ], + "spans": [ + { + "bbox": [ + 59, + 480, + 244, + 491 + ], + "type": "text", + "content": "Our contributions are summarised as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 502, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 51, + 502, + 287, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 502, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 51, + 502, + 287, + 562 + ], + "type": "text", + "content": "i. We propose an end-to-end feature learning framework to characterise and embed spatial context information into the process of information processing and extraction in CNN. It makes global feature representations become more capable for instance image retrieval." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 571, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 571, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 48, + 571, + 287, + 643 + ], + "type": "text", + "content": "ii. To implement the framework, we design a spatial context branch. With its online token learning module, the types of local descriptors are identified and easily compared. With the distance encoding module, the information about the spatial distribution of different types of local descriptors around a given descriptor is obtained." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 45, + 653, + 287, + 714 + ], + "type": "text", + "content": "iii. To verify the efficacy of the proposed framework, we conduct extensive experiments on instance image retrieval benchmark datasets, ROxford and RParis, with one million distractors. As demonstrated, our global feature representations effectively improve the perfor" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 320, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 320, + 72, + 545, + 96 + ], + "type": "text", + "content": "mance of instance image retrieval, making global representation a more competitive option for practical tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 108, + 392, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 108, + 392, + 121 + ], + "spans": [ + { + "bbox": [ + 306, + 108, + 392, + 121 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 129, + 545, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 129, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 306, + 129, + 545, + 153 + ], + "type": "text", + "content": "In this section, we briefly review deep instance image retrieval, including local and global feature learning methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 161, + 400, + 173 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 161, + 400, + 173 + ], + "spans": [ + { + "bbox": [ + 306, + 161, + 400, + 173 + ], + "type": "text", + "content": "2.1. Global features" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 180, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 180, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 180, + 545, + 479 + ], + "type": "text", + "content": "Global feature has been widely used to represent the content of images for a wide range of computer vision tasks [21, 13, 8, 36, 37, 12, 11]. Due to its compactness and efficiency, a variety of global methods [24, 32, 35, 15] have been proposed to learn discriminative feature representations via deep models in the instance image retrieval community. Some of the studies focus on applying more effective loss functions, including triplet losses [29], list-wise losses [22], and classification losses [5] to train the model. Others explore how to pool the entire feature maps into a compact feature vector while maintaining their discrepancies. For instance, weighted-sum-pooling (CroW) [9], regional-max-pooling (R-MAC) [29], and GeM pooling [20]. Recently, several methods try to modify the training model architecture to capture more useful information during the training process. SOLAR [15] combines normal training with second-order information by adding self-attention modules in the conventional CNN backbones. Token [32] jointly learns a set of tokens and the corresponding visual representations to mimic the conventional dictionary learning plus feature encoding scheme to represent images. Some other studies [32, 35] propose multiple branches for CNN models to mine more complementary information and fuse them into the final feature vectors. We follow the global feature type to learn compact features to conduct retrieval." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 487, + 395, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 395, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 395, + 499 + ], + "type": "text", + "content": "2.2. Local features" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 506, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 506, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 305, + 506, + 545, + 662 + ], + "type": "text", + "content": "Deep local descriptors [28, 30, 33, 17] have been extensively researched and made significant progress in instance image retrieval [4]. The key to their success lies in the spatial information these local descriptors hold, and it is usually utilized by kernel alignment aggregation (e.g., ASMK [27]) or geometric verification (e.g., RANSAC [6]) for image similarity measure. In recent studies, several methods [26, 10] individually train a matching model to directly compare the similarity of two images (or their preextracted local descriptors) in a data-driven manner. However, they need more inference time and memory footprint. Therefore, they are usually applied to only top k retrieved images obtained by a global retrieval method as a reranking." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 670, + 522, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 522, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 522, + 684 + ], + "type": "text", + "content": "2.3. Learning local and global features jointly" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Driven by the complementary properties of global and local features, jointly learning the two types of features" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11251" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 69, + 521, + 194 + ], + "blocks": [ + { + "bbox": [ + 74, + 69, + 521, + 194 + ], + "lines": [ + { + "bbox": [ + 74, + 69, + 521, + 194 + ], + "spans": [ + { + "bbox": [ + 74, + 69, + 521, + 194 + ], + "type": "image", + "image_path": "f2251ae6b4e61f4031aaa5f42f3b6e8b4274391297ae37ea7ff703bf923e5c60.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 202, + 547, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 202, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 547, + 248 + ], + "type": "text", + "content": "Figure 1. Overview of our framework. After an initial feature extraction by a CNN backbone, two branches of \"Visual Feature Branch\" and \"Spatial Context Branch\" are used to extract visual and spatial context information. After that, a cross-attention module is used to fuse the visual feature and the corresponding spatial context feature to generate spatial-context-aware visual representations for images. In particular, \"GMM\" denotes the Gaussian Mixture Model process, and \"GP+W\" refers to global pooling followed by whitening." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 518 + ], + "type": "text", + "content": "becomes a straightforward idea. Recently, several studies demonstrate the advantages of learning features in this manner. DELG [3] creatively unifies the two separate learning processes into one training framework. However, even though the training procedure is unified, the learning processes of the two feature types are still somehow irrelevant. To further explore this approach, DOLG [35] and DALG [25] firstly separate the feature extractor into two branches to learn the local and global features and then fuse them via a manual or learnable way to obtain compact feature representations for images. Both of them try to extract individual visual information from the two types of features to make them complementary to each other. However, the powerful spatial context information held by local features is neither exploited nor embedded into the final feature representations. In this work, we argue that spatial context information is more beneficial than visual information from local descriptors to the final global feature representations for instance image retrieval. To this end, we propose a novel feature learning framework to effectively embed the spatial context information into final global features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 536, + 176, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 176, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 176, + 550 + ], + "type": "text", + "content": "3. The Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "An overview of our framework is in Figure 1. Given an image " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": ", a conventional CNN backbone is used to generate a feature map " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{D \\times H \\times W}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": ", in which each spatial position corresponds to a " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "-dimensional local visual descriptor. Besides, a spatial context branch is split from the feature map to extract the spatial context information of all the descriptors, which is represented in the form of " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{S} \\in \\mathbb{R}^{C \\times H \\times W}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " being the dimensions. After that, for each local descriptor, its two kinds of information are fused together, say, with a cross-attention module or a simple concatenation operation. After the fusion, a global pooling and a fully-connected layer are used to generate the final global spatial-context-aware feature " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{spca}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " to represent the image. In the following," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 266, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 291 + ], + "type": "text", + "content": "we focus on describing the spatial context branch since the visual branch follows its original design in CNN backbones." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 298, + 440, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 298, + 440, + 311 + ], + "spans": [ + { + "bbox": [ + 305, + 298, + 440, + 311 + ], + "type": "text", + "content": "3.1. Spatial Context Branch" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 316, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 545, + 389 + ], + "type": "text", + "content": "In the spatial context branch, there are two main issues to be addressed for each spatial position on the feature map: 1) what kinds of local descriptors are there in its surrounding region (i.e., identification task); 2) how they spatially distribute on the feature map (i.e., spatial distribution task). We now introduce how we address the two issues orderly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 402, + 546, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 546, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 546, + 665 + ], + "type": "text", + "content": "Token-based Identification. For existing local feature-based retrieval methods [28, 30, 33], learning tokens to capture discriminative visual patterns in a dataset has proven reliable to identify local descriptors. With the tokens, the encoded features could become more robust against illumination change, the information loss due to occlusion, and the adverse impact of the background in an image. In our framework, we generally follow this \"tokens plus encoding\" pipeline to identify local descriptors. However, in the literature, the tokens are usually learned by clustering (e.g., by k-means) a sampled subset of local descriptors obtained from an image dataset in an offline manner. This way separates the process of token learning from encoding, potentially causing a discrepancy between the training and the inference stages. In addition, using a sampled subset of local descriptors could lead to learning biased tokens since the information available in an image dataset is not fully utilized. To improve this situation, we perform token learning via an online mini-batch based Gaussian Mixture Model (GMM) process. This helps to adequately utilize all the local descriptors to learn tokens and makes our framework fully end-to-end trainable." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": "Specifically, we model the distribution of local descriptors by a " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": "-component Gaussian mixture model " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "p(\\mathbf{v}|\\Theta) = \\sum_{k}\\alpha_{k}N(\\mathbf{v};\\boldsymbol{\\mu}_{k},\\Sigma_{k})" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " denotes the a local descriptor, while " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{k},\\boldsymbol{\\mu}_{k}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\Sigma_{k} = \\sigma_{k}^{2}I_{D}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " denote the prior probability, the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11252" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "mean, and the (spherical) covariance matrix for component " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": ", respectively. In this case, token learning boils down to the parameter estimation for this Gaussian mixture model. At the beginning, " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": " are randomly generated and " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": " is set as " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "1 / K" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": ". After that, we conduct the Expectation and Maximization (EM) process for all the local descriptors within each mini-batch. To be concise, we show the key results below and the details can be found in the literature [16]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "content": "Within each mini-batch, for the E-Step, the probability that the " + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "content": "th local descriptor " + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "content": " belongs to the " + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 168, + 287, + 205 + ], + "type": "text", + "content": "th component can be expressed as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 111, + 213, + 287, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 213, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 111, + 213, + 287, + 243 + ], + "type": "interline_equation", + "content": "\\omega_ {i k} = \\frac {\\alpha_ {k} N \\left(\\mathbf {v} _ {i} ; \\boldsymbol {\\mu} _ {k} , \\Sigma_ {k}\\right)}{\\sum_ {j = 1} ^ {K} \\alpha_ {j} N \\left(\\mathbf {v} _ {i} ; \\boldsymbol {\\mu} _ {j} , \\Sigma_ {j}\\right)} \\tag {1}", + "image_path": "636ab4a248893598b2ff19b450f77711e2922fa7fe087e1fc3367eed01dbd5f7.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 251, + 286, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 286, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 286, + 275 + ], + "type": "text", + "content": "For M-Step, the prior probability, the mean and the covariance are updated as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 284, + 201, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 284, + 201, + 308 + ], + "spans": [ + { + "bbox": [ + 88, + 284, + 201, + 308 + ], + "type": "interline_equation", + "content": "\\alpha_ {k} \\leftarrow \\alpha_ {k} + \\beta \\left(\\frac {\\sum_ {i} \\omega_ {i k}}{H W} - \\alpha_ {k}\\right)", + "image_path": "e2170a248a9bd2228e09d68de4743ff6b8efdc89721044de851cae79a5c7525e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 88, + 310, + 287, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 310, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 88, + 310, + 287, + 335 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {k} \\leftarrow \\boldsymbol {\\mu} _ {k} + \\beta \\left(\\frac {\\sum_ {i} \\omega_ {i k} \\mathbf {v} _ {i}}{\\sum_ {i} \\omega_ {i k}} - \\boldsymbol {\\mu} _ {k}\\right) \\tag {2}", + "image_path": "62d926bd68c5b882ff7710c3e7766ae6675478e5d827934a0eb0ac39348f79fe.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 88, + 337, + 246, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 337, + 246, + 365 + ], + "spans": [ + { + "bbox": [ + 88, + 337, + 246, + 365 + ], + "type": "interline_equation", + "content": "\\sigma_ {k} ^ {2} \\leftarrow \\sigma_ {k} ^ {2} + \\beta \\Big (\\frac {\\sum_ {i} \\omega_ {i k} \\| \\mathbf {v} _ {i} - \\boldsymbol {\\mu} _ {k} \\| ^ {2}}{\\sum_ {i} \\omega_ {i k}} - \\sigma_ {k} ^ {2} \\Big),", + "image_path": "d28202935080bcd884ed88b7ebd37065651b14ce879b7a6cdc14de93b454de6d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 373, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 373, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 373, + 287, + 432 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 373, + 287, + 432 + ], + "type": "inline_equation", + "content": "HW" + }, + { + "bbox": [ + 47, + 373, + 287, + 432 + ], + "type": "text", + "content": " is the number of local descriptors obtained from an image, and " + }, + { + "bbox": [ + 47, + 373, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 373, + 287, + 432 + ], + "type": "text", + "content": " is a momentum to make the estimation process more stable in the mini-batch clustering [16]. One E-Step and M-Step are conducted in each iteration during the training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "text", + "content": "After the above process, " + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "inline_equation", + "content": "(\\pmb{\\mu}_1,\\pmb{\\mu}_2,\\dots ,\\pmb{\\mu}_K)" + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "text", + "content": " represents the learned tokens. " + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\omega_{i} = (\\omega_{i1},\\omega_{i2},\\dots ,\\omega_{iK})\\in \\mathbb{R}^{K}" + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "text", + "content": " obtained by Eq. (1) can be used as the token-based identification for local descriptor " + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "text", + "content": " since it represents the posterior probability that this descriptor belongs to each of the " + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 434, + 287, + 493 + ], + "type": "text", + "content": " components." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": "Spatial Distribution. To extract spatial distribution information for a local descriptor " + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": ", the distances of this descriptor to all the descriptors " + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "inline_equation", + "content": "V = \\{\\mathbf{v}_j, j = 1,2,\\dots,HW\\}" + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": " presented on the same feature map should be effectively measured and collected. To achieve this, simply using the coordinate distances among them is inadequate. We utilize a probability transition score obtained by applying random walk on the graph constituted by all the local descriptors as the nodes to measure the distances. By doing so, more possible paths among the local descriptors will be considered and the number of random walk steps could also be used to control the spatial scale in the distance measurement. Inspired by the literature [11], we perform the spatial distribution extraction as an aggregation of the encoded distances between " + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": " and all " + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_j \\in V" + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": ". By \"coded,\" we mean that the distance is measured by a probability transition process as explained below." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "Given an undirected graph with an affinity matrix " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ", the distance of its nodes " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " can be encoded by a probability transition score " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " obtained via " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " steps of random walk" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 322, + 118, + 545, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 118, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 322, + 118, + 545, + 131 + ], + "type": "interline_equation", + "content": "\\zeta (v, u) ^ {(l)} = \\left(M ^ {l}\\right) _ {v u}, M ^ {1} = A D ^ {- 1}, M ^ {l} = M ^ {l - 1} \\cdot M, \\tag {3}", + "image_path": "2e5ad4a65bf32f7080ffd4237b52b245a96ae743d446df002672f9ee7b87886f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "inline_equation", + "content": "M^1" + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "text", + "content": " denotes the random walk matrix, " + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "inline_equation", + "content": "D^{-1}" + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "text", + "content": " refers to the normalization matrix of the graph, and " + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "text", + "content": " is the number of random walk steps. Based on this, the distance of a node " + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "text", + "content": " from all nodes " + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "text", + "content": " in a target set " + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 141, + 545, + 201 + ], + "type": "text", + "content": " can be represented by an aggregation operation as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 359, + 211, + 545, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 211, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 359, + 211, + 545, + 224 + ], + "type": "interline_equation", + "content": "\\zeta (\\nu , S) ^ {(l)} = \\operatorname {a g g} \\left(\\left\\{\\zeta (\\nu , u) ^ {(l)} \\mid u \\in S \\right\\}\\right) \\tag {4}", + "image_path": "0d3aa8f3599acfa2e6d5b10356e26f158e543c3d496219c95b438ca922146ac6.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "type": "text", + "content": "Linking the above result to our case, the undirected graph consists of all the local descriptors " + }, + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "type": "text", + "content": " in an image, and they collectively form the target set " + }, + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "type": "text", + "content": " in this distance encoding process. In addition, we compute the affinity matrix " + }, + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 236, + 545, + 295 + ], + "type": "text", + "content": " based on the coordinate distance on the feature map as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 334, + 306, + 545, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 306, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 334, + 306, + 545, + 319 + ], + "type": "interline_equation", + "content": "A _ {i j} = \\exp (- \\operatorname {c o} _ {-} \\operatorname {d i s t} (\\mathbf {v} _ {i}, \\mathbf {v} _ {j})), (1 \\leq i, j \\leq H W), \\tag {5}", + "image_path": "7925e34dc39c167b981856c8fb6bac740b741c51fe36fdf6a65747e2b659e49c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\mathrm{co\\_dist}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "type": "text", + "content": " denotes the Euclidean distance between the coordinates of two local descriptors. After that, the encoded distance can be obtained by applying Eq. (3). Furthermore, we enrich Eq. (4) by considering the learned token-based identification (i.e., the posteriori probability " + }, + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "type": "text", + "content": " obtained in Eq. (1)), and this leads to an instantiated \"agg\" operation in Eq. (4) to produce the spatial context feature for local descriptor " + }, + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 305, + 329, + 545, + 424 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 354, + 434, + 545, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 434, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 354, + 434, + 545, + 467 + ], + "type": "interline_equation", + "content": "\\mathbf {s} _ {i} ^ {(l)} \\triangleq \\zeta (v _ {i}, S) ^ {(l)} = \\sum_ {j = 1} ^ {H W} \\zeta (\\mathbf {v} _ {i}, \\mathbf {v} _ {j}) ^ {(l)} \\boldsymbol {\\omega} _ {j}. \\tag {6}", + "image_path": "ae7409906ea18c86e7599b61714f84133d05e2f462022302b83363504ba97fd6.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": "Recall that the token-based identification " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\omega_{i}" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": " can be treated as a vector of probability transition scores between local descriptor " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": " and each of the learned tokens " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": ". By combining the encoded distance and the token-based identification, the spatial context feature " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": " in Eq. (6) essentially reflects the probability transition scores between node " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": " and the tokens " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": " when regarding the spatial structure of the given " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": " feature map as a (static) transition matrix. This is illustrated in Figure 2. That means the spatial distribution information is used to control the extraction of the spatial context features. In this sense, the spatial distribution information is effectively embedded into the spatial context features. At last, we define the final spatial context feature for the local descriptor " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_i" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": " obtained through an " + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 476, + 545, + 644 + ], + "type": "text", + "content": "-step random walk as" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 373, + 652, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 652, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 373, + 652, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\mathbf {s} _ {i} = \\mathbf {s} _ {i} ^ {(1)} \\oplus \\mathbf {s} _ {i} ^ {(2)} \\oplus \\dots \\oplus \\mathbf {s} _ {i} ^ {(l)}, \\tag {7}", + "image_path": "dcdb1d7f23bb693bddcc9edef530ea760f667ef83d115b1d4711d208409e9462.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " denotes concatenation operation. The concatenation of the features obtained after each of the " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " steps considers the spatial context information at various scales." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11253" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 289, + 251 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 289, + 251 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 289, + 251 + ], + "type": "image", + "image_path": "f813abe790e495de1e008e840498cc75242bf80e3f649dd11f810b1ad905fc37.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 262, + 287, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 287, + 285 + ], + "type": "text", + "content": "Figure 2. Spatial context feature generation. See the detailed description after Eq. (6)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 304, + 261, + 318 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 261, + 318 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 261, + 318 + ], + "type": "text", + "content": "3.2. Fusion of Visual and Spatial Information" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 323, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 289, + 515 + ], + "type": "text", + "content": "With both visual and spatial context information available, a proper fusion scheme is needed to make them complements to benefit the final feature representation. To accomplish it, various feature fusion schemes could be used, including concatenation, orthogonal fusion [35], Hadamard product, or cross-attention fusion. We utilize a cross-attention module for information fusion in our method since it is commonly used to align features from different modalities in the recent literature. Meanwhile, we provide an ablation study on all the four fusion schemes in the experimental part. For the cross-attention scheme, the spatial context feature " + }, + { + "bbox": [ + 46, + 323, + 289, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{S} = (\\mathbf{s}_1,\\mathbf{s}_2,\\dots ,\\mathbf{s}_{HW})" + }, + { + "bbox": [ + 46, + 323, + 289, + 515 + ], + "type": "text", + "content": " is projected into the same space as the visual feature " + }, + { + "bbox": [ + 46, + 323, + 289, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 46, + 323, + 289, + 515 + ], + "type": "text", + "content": " with a linear projection layer. After that, both of them are flattened into sequences and mapped into Queries (Q), Keys (K), and Values (V), respectively, to put through into the cross-attention layer:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 84, + 525, + 250, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 525, + 250, + 537 + ], + "spans": [ + { + "bbox": [ + 84, + 525, + 250, + 537 + ], + "type": "interline_equation", + "content": "\\mathbb {Q} = \\operatorname {p r o j} (\\mathbf {V}), \\mathbb {K} = \\operatorname {p r o j} (\\mathbf {S}), \\mathbb {V} = \\operatorname {p r o j} (\\mathbf {S})", + "image_path": "b757a2a01bf5d1fa23ccb626c4247d000057c4f58ff16505d36235cd9bbe44bd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 85, + 539, + 287, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 539, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 85, + 539, + 287, + 566 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {s p c a} ^ {*} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbb {Q} \\cdot \\mathbb {K} ^ {\\top}}{\\sqrt {D}}\\right) \\cdot \\mathbb {V} \\tag {8}", + "image_path": "eb1b703e1f0f0e5acb84c325f39ddaf5a89699fe42034511ebc4d9433506f745.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 568, + 199, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 568, + 199, + 582 + ], + "spans": [ + { + "bbox": [ + 85, + 568, + 199, + 582 + ], + "type": "interline_equation", + "content": "\\mathbf {F} _ {s p c a} = \\mathbf {F} _ {s p c a} ^ {*} + \\operatorname {M L P} \\left(\\mathbf {F} _ {s p c a} ^ {*}\\right)", + "image_path": "206cf76c49904dca5e70f5471f086f287919a2f950d39e816546c2684791da85.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 590, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 652 + ], + "type": "text", + "content": "where MLP denotes a feed-forward layer and " + }, + { + "bbox": [ + 46, + 590, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{spca}" + }, + { + "bbox": [ + 46, + 590, + 287, + 652 + ], + "type": "text", + "content": " denotes the spatial-context-aware feature sequence. After that, the feature sequence is rearranged as a feature map, followed by a global pooling and a fully-connected layer to generate a global feature representation vector " + }, + { + "bbox": [ + 46, + 590, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{spca}" + }, + { + "bbox": [ + 46, + 590, + 287, + 652 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 658, + 220, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 220, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 220, + 672 + ], + "type": "text", + "content": "3.3. Objective Function for Training" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Following previous state-of-the-art work [3, 35, 32], we train our model on a dataset with object class annotations and utilize ArcFace margin loss [5] with learnable parame" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 71, + 472, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 472, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 472, + 84 + ], + "type": "text", + "content": "ters " + }, + { + "bbox": [ + 305, + 71, + 472, + 84 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{W}}\\in \\mathbb{R}^{D\\times N}" + }, + { + "bbox": [ + 305, + 71, + 472, + 84 + ], + "type": "text", + "content": " to train the whole model:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 341, + 91, + 545, + 122 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 91, + 545, + 122 + ], + "spans": [ + { + "bbox": [ + 341, + 91, + 545, + 122 + ], + "type": "interline_equation", + "content": "L = - \\log \\left(\\frac {\\exp \\left(\\gamma \\times A F \\left(\\hat {\\mathbf {w}} _ {t} ^ {\\top} \\hat {\\mathbf {f}} _ {s p c a} , 1\\right)\\right)}{\\sum_ {n} \\exp \\left(\\gamma \\times A F \\left(\\hat {\\mathbf {w}} _ {n} ^ {\\top} \\hat {\\mathbf {f}} _ {s p c a} , y _ {n}\\right)\\right)}\\right) \\tag {9}", + "image_path": "435275391486fd3e8dad2701ef83af6406a37a5e717fe55146b81d1ff4a18b30.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}_t" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": "th column of " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{W}}" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{f}}_{spca}" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": "-normalized " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{spca}" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": " is the one-hot label vector and " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": " is the index to indicate the true class (i.e., " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "y_t = 1" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": "). " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": " is the total number of classes in the dataset. " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": " is a scaling factor. " + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "inline_equation", + "content": "AF(\\cdot)" + }, + { + "bbox": [ + 305, + 132, + 547, + 204 + ], + "type": "text", + "content": " refers to the ArcFace cosine similarity and it is calculated as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 341, + 213, + 545, + 241 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 213, + 545, + 241 + ], + "spans": [ + { + "bbox": [ + 341, + 213, + 545, + 241 + ], + "type": "interline_equation", + "content": "A F (s, c) = \\left\\{ \\begin{array}{l l} \\cos (a \\cos (s) + m), & \\text {i f} c = 1 \\\\ s, & \\text {i f} c = 0 \\end{array} \\right. \\tag {10}", + "image_path": "6fae4c19d88f05bb224b9969dacbee6f5be0880d915784360952ee53a7114210.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "text", + "content": " is the cosine similarity between " + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{w}}_t" + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{f}}_{spca}" + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "text", + "content": " is the ArcFace margin and " + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 251, + 545, + 277 + ], + "type": "text", + "content": " indicates if this is the true class." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 288, + 427, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 288, + 427, + 301 + ], + "spans": [ + { + "bbox": [ + 305, + 288, + 427, + 301 + ], + "type": "text", + "content": "4. Experimental Result" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 308, + 473, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 308, + 473, + 320 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 473, + 320 + ], + "type": "text", + "content": "4.1. Dataset and Evaluation Metric" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 327, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 506 + ], + "type": "text", + "content": "Our model is trained on \"Google Landmark v2 clean\" dataset, which is a clean subset of Google Landmark v2 [31]. It contains 1,580,470 images of 81,313 landmark classes, and it has been widely used in existing methods [35, 32, 3] as the training dataset. To make a fair comparison, we follow the previous work [32, 35] to randomly divide the dataset into two subsets 'train'/'val' with " + }, + { + "bbox": [ + 304, + 327, + 545, + 506 + ], + "type": "inline_equation", + "content": "80\\% / 20\\%" + }, + { + "bbox": [ + 304, + 327, + 545, + 506 + ], + "type": "text", + "content": " split. For evaluation, we use two widely used benchmark datasets, ROxford and RParis [19] to test our model. Both datasets have 70 query images but contain 4,993 and 6,322 gallery images, respectively. In addition, a 1M distractor set [19] is added to test our model for the case of large-scale retrieval. We use mean average precision (mAP), as the criterion of retrieval performance for both \"Medium\" and \"Hard\" splits of ROxford and RParis." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 515, + 440, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 515, + 440, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 515, + 440, + 528 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": "We use ResNet101/ResNet50 [8] as the CNN backbone to learn visual features. For image augmentation, random crop and color jittering are used first, and all the augmented images are resized into " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " pixels as the model input. The model is trained on 4 Nvidia V100-SXM2-32GB GPU cards with a batch size of 128 for 50 epochs. We use SGD optimizer with a momentum of 0.9. A warming-up of 5-epoch's training is used to initialize the learning rate from 0.0001 to the base learning rate of 0.005. As for the ArcFace loss, the margin " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " and the scale " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " are empirically set as 0.2 and 45. For the global pooling, we utilize GeM [20] pooling with the fixed coefficient " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "p = 3" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " during the whole training. " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " in the M-Step of GMM is empirically set as 0.999. In addition, we set the number of random walk steps " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " as 3 and the number of tokens as " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "K = 16" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": ". The dimensions of the" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11254" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 69, + 539, + 342 + ], + "blocks": [ + { + "bbox": [ + 55, + 69, + 539, + 342 + ], + "lines": [ + { + "bbox": [ + 55, + 69, + 539, + 342 + ], + "spans": [ + { + "bbox": [ + 55, + 69, + 539, + 342 + ], + "type": "table", + "html": "
MethodMediumHard
ROxfROxf+1MRParRPar+1MROxfROxf+1MRParRPar+1M
Global features + local features re-ranking
R101-DELG [3]+SP81.2069.1087.2071.5064.0047.5072.8048.70
R101-DELG [3]+SP†81.8270.1588.6476.1464.9749.5476.8153.62
Global features
R101-R-MAC [7]60.9039.3078.9054.8032.4012.5059.4028.00
R101-GeM [20]64.7045.2077.2052.3038.5019.9056.3024.70
R101-SOLAR [15]69.9053.5081.6059.2047.9029.9064.5033.40
R101-DELG [3]76.3063.7086.6070.6055.6037.5072.4046.90
R101-GLAM [24]78.6068.0088.5073.5060.2043.5076.8053.10
Swin-S-DALG [25]79.94-90.04-57.55-79.06-
R101-DOLG [35]★81.5077.4391.0283.2961.1054.8180.3066.69
R101-Token [32]82.2870.5289.3476.6666.5747.2778.5655.90
R101-Token [32]†77.8266.7487.9375.2260.1043.0774.6653.19
R101-DOLG [35]†78.35(75.51)(88.48)(78.25)58.59(52.36)(75.39)(61.85)
R101-DELG [3]†79.8267.8587.2172.4561.1642.5873.8450.79
R101-SOLAR [15]†(81.63)71.8488.2172.86(63.29)45.2875.2151.26
R50-SpCaacro (Ours)79.9172.7887.4378.0159.2749.2673.1458.3
R50-SpCaCat (Ours)81.5573.2088.6078.2361.1948.7676.2160.91
R101-SpCaacro (Ours)82.7377.8490.2079.1265.6053.3579.2965.84
R101-SpCaCat (Ours)83.2477.8290.5679.4865.8553.2779.9764.98
", + "image_path": "57348d3bc951d83435a6a6f2330f0eca2c548cc9ecaab327e5bcbf580fbe4f5f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "lines": [ + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "text", + "content": "Table 1. Performance (mAP) comparison with recent state-of-the-art instance image retrieval methods on datasets ROxford5k and RParis6k [19]. R101 and R50 denote ResNet101 and ResNet50. Swin-S denotes Swin-Transformer-small [13]. The subscripts " + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "inline_equation", + "content": "\\text{cro}" + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "inline_equation", + "content": "\\text{cat}" + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "text", + "content": " refer to cross-attention and concatenation feature fusion strategies. SP denotes spatial verification via RANSAC. " + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "text", + "content": " denotes our reimplementation. " + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 46, + 349, + 547, + 405 + ], + "type": "text", + "content": " means no query cropping. Results in gray are those reported in the published papers. The best and second best performances are highlighted in bold and with underlines, respectively. The best previous performance is shown in brackets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 424, + 288, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 288, + 497 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 288, + 497 + ], + "type": "text", + "content": "final global feature are set as 2048. For inference, the multiple scales [0.3535, 0.5, 0.7071, 1.0, 1.4142] are applied to each original image to extract the feature representations. To fuse the features obtained from different scales, they are " + }, + { + "bbox": [ + 46, + 424, + 288, + 497 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 424, + 288, + 497 + ], + "type": "text", + "content": "-normalized, summed, and normalized again to generate the final global features for retrieval." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 502, + 270, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 270, + 515 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 270, + 515 + ], + "type": "text", + "content": "4.3. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "text", + "content": "Setting for fair comparison Note that there are setting differences among the previous state-of-the-art methods. For example, they are different at 1) pretrained model sources for initialization (Caffe" + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "text", + "content": ", PyTorch" + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "text", + "content": ", and Facebook" + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "text", + "content": "); 2) training datasets (SfM-120k [20], GLDv1 [17], GLDv2 [31], and different " + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "inline_equation", + "content": "80\\% / 20\\%" + }, + { + "bbox": [ + 46, + 521, + 287, + 677 + ], + "type": "text", + "content": " split); 3) the number of multiple scales used at the inference stage (e.g., 3, 5, or 7); 4) with or without query cropping scheme. These discrepancies could affect the fairness of the comparison if not well handled. To address this situation, we carefully re-implement multiple SOTA methods by using their officially published codes and the training parameters reported in their papers, while keeping the same settings for the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 424, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 424, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 424, + 545, + 509 + ], + "type": "text", + "content": "above factors between these methods and ours. Specifically, to ensure fair comparison, our experimental study utilizes the same " + }, + { + "bbox": [ + 306, + 424, + 545, + 509 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 306, + 424, + 545, + 509 + ], + "type": "text", + "content": " of GLDv2-clean [31] as the training dataset, the same remaining " + }, + { + "bbox": [ + 306, + 424, + 545, + 509 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 306, + 424, + 545, + 509 + ], + "type": "text", + "content": " of GLDv2-clean as the validation dataset, the same pretrained model from PyTorch for initialization, and the same 5 scales with query cropping scheme for inference to conduct instance image retrieval." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 521, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 676 + ], + "type": "text", + "content": "Retrieval results Two groups of state-of-the-art methods are compared in this experimental study: 1) methods based on global feature representations. They include two milestone works R-MAC [7] and GeM [20] and another six more recent works including DELG [3], SOLAR [15], GLAM [24], DOLG [35], DALG [25], and Token [32]; 2) a method using global feature based initial retrieval plus local feature based re-ranking scheme, DELG+SP [3], is included as well. Also, note that we focus on global feature based image retrieval in this paper, and we do not consider training a verification model [10] or adding any post-processing steps like diffusion or query expansion to boost retrieval performance [34]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "The retrieval result is reported in Table 1. The methods under \"Global features\" are partitioned into three sections. The results in gray color are those reported in the original" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 682, + 275, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 682, + 275, + 693 + ], + "spans": [ + { + "bbox": [ + 57, + 682, + 275, + 693 + ], + "type": "text", + "content": "1http://cmp.felk.cyut.cz/cnnimageRetrieval/data/networks/imagenet" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 693, + 287, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 693, + 287, + 703 + ], + "spans": [ + { + "bbox": [ + 59, + 693, + 287, + 703 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 59, + 693, + 287, + 703 + ], + "type": "text", + "content": "https://pytorch.org/vision/stable/models/generated/torchvision.models" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 703, + 200, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 200, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 200, + 713 + ], + "type": "text", + "content": "3https://github.com/facebookresearch/pycls" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11255" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "published papers. Since they involve different settings as discussed above, the results are included here mainly as a reference. Following the gray-colored results are those obtained by our re-implementation for the sake of fair comparison, and they are used to compare with our methods shown at the bottom of this table." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "text", + "content": "As seen, our method R101-SpCa (where \"SpCa\" is short for \"Spatial-context-aware\"), with either cross-attention (" + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "inline_equation", + "content": "-cro" + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "text", + "content": ") or concatenation (" + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "inline_equation", + "content": "-cat" + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "text", + "content": ") fusion strategy, clearly outperforms the others on all the test cases. Compared with the closest results obtained by DOLG and SOLAR, our method achieves " + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "inline_equation", + "content": "2.0\\%" + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "text", + "content": " performance gain on the Medium split of ROxford and RParis, respectively. And higher improvements of " + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "inline_equation", + "content": "4.5\\%" + }, + { + "bbox": [ + 46, + 148, + 287, + 279 + ], + "type": "text", + "content": " are obtained on the Hard split of the two datasets. After the 1M distractors are added, our method still demonstrates its excellent retrieval performance. All these results validate the efficacy of our method." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 283, + 288, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 288, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 288, + 438 + ], + "type": "text", + "content": "Compared with the global initial retrieval plus local feature re-ranking scheme, our method still maintains its advantage. As listed in Table 1, even without using the pairwised re-ranking step as done in R101-DELG+SP [3], our method has outperformed it by around " + }, + { + "bbox": [ + 46, + 283, + 288, + 438 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 283, + 288, + 438 + ], + "type": "text", + "content": " on all dataset splits. More importantly, our method costs no extra inference time as taken by the re-ranking step. In addition, the memory footprint of our global feature representation (i.e., a 2048-dimensional vector per image) is also much less than that used by the local descriptor (there are usually 1,000 vectors per image, each of which is of 128 dimensions) based re-ranking. This again shows the computational advantage brought by our method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 474, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 571 + ], + "type": "text", + "content": "Computational Overhead We report the number of parameters, feature extraction latency, and memory footprint for different SOTA models in Table 2. As seen, our method is comparable to that of DOLG in terms of computational overhead and comparable to that of Token in terms of the number of parameters. Also, our method takes the same memory footprint as the others that generate 2048-dimensional vectors as feature representations." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 587, + 293, + 673 + ], + "blocks": [ + { + "bbox": [ + 48, + 587, + 293, + 673 + ], + "lines": [ + { + "bbox": [ + 48, + 587, + 293, + 673 + ], + "spans": [ + { + "bbox": [ + 48, + 587, + 293, + 673 + ], + "type": "table", + "html": "
Method#Para (M)Latency (ms)Mem. (MB) \nOn ROxford
SOLAR [15]52.511039.0
DELG [3]44.510439.0
Token [32]76.611219.5
DOLG [35]61.51509.7
SpCa (Ours)76.815339.0
", + "image_path": "181b7e1981f60236269d785c508b8271f37ca19619347449a09d7e211edf319b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 673, + 288, + 696 + ], + "lines": [ + { + "bbox": [ + 46, + 673, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 288, + 696 + ], + "type": "text", + "content": "Table 2. Latency is measured on a 1080Ti GPU for a " + }, + { + "bbox": [ + 46, + 673, + 288, + 696 + ], + "type": "inline_equation", + "content": "{1024} \\times {1024}" + }, + { + "bbox": [ + 46, + 673, + 288, + 696 + ], + "type": "text", + "content": " image with 3 scaling factors " + }, + { + "bbox": [ + 46, + 673, + 288, + 696 + ], + "type": "inline_equation", + "content": "\\left\\lbrack {1,\\sqrt{2},1/\\sqrt{2}}\\right\\rbrack" + }, + { + "bbox": [ + 46, + 673, + 288, + 696 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 90, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 163 + ], + "type": "text", + "content": "In this study, we uniformly utilize ResNet50 as the CNN backbone and set the token number and the number of random walk steps as " + }, + { + "bbox": [ + 304, + 90, + 545, + 163 + ], + "type": "inline_equation", + "content": "K = 8" + }, + { + "bbox": [ + 304, + 90, + 545, + 163 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 90, + 545, + 163 + ], + "type": "inline_equation", + "content": "l = 1" + }, + { + "bbox": [ + 304, + 90, + 545, + 163 + ], + "type": "text", + "content": ", respectively, for all the following experiments if not mentioned otherwise. In addition, all the models are trained by 25 epochs. More ablation studies utilizing ResNet101 are provided in the Appendix." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 186, + 544, + 248 + ], + "blocks": [ + { + "bbox": [ + 307, + 186, + 544, + 248 + ], + "lines": [ + { + "bbox": [ + 307, + 186, + 544, + 248 + ], + "spans": [ + { + "bbox": [ + 307, + 186, + 544, + 248 + ], + "type": "table", + "html": "
GlobalOTLDEMediumHard
ROxfRParROxfRPar
✓77.5187.8254.7673.82
✓✓78.8288.2158.7374.03
✓✓✓79.6489.0660.9076.97
", + "image_path": "54a2ea9e6cb5ebbc9f8771cfd7861a9e37f639a0ea850a7a08c86060a062f5a1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 304, + 248, + 545, + 292 + ], + "lines": [ + { + "bbox": [ + 304, + 248, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 545, + 292 + ], + "type": "text", + "content": "Table 3. Ablation studies on the impact of different components in the spatial context branch. The baseline containing only the visual feature branch is shown in the first row. OTL and DE denote online token learning and distance encoding, respectively." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": "Impact of each component in spatial context branch The proposed spatial context branch consists of two components which are online token learning and distance encoding. We validate the contribution of each of the components by adding them one by one to a bare visual feature branch. In particular, for the first comparison, we directly set the whole probability transition matrix " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " as a unit matrix (i.e., all of its entries are \"1\") to erase the distance encoding information. By doing so, only the token-based identification generated by the online token learning module is involved in the final global features. As seen in Table 3, with this single module (2nd row), the retrieval performance could be improved from " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "77.51\\%" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "78.82\\%" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "87.82\\%" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "88.21\\%" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " on ROxf-Medium and RPar-Medium, respectively. It shows the benefit of utilizing the tokens to identify the local descriptors. After adding the distance encoding module, the spatial distribution information is involved. It can be seen, with the complete branch (3rd row), the retrieval performance is further improved, especially on Hard splits. The performance (mAP) is increased from " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "58.73\\%" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "60.90\\%" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "74.03\\%" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "inline_equation", + "content": "76.97\\%" + }, + { + "bbox": [ + 304, + 304, + 545, + 602 + ], + "type": "text", + "content": " on ROxf-Hard and RPar-hard, respectively. This verifies the importance of capturing the spatial distribution information with the distance encoding module. Altogether, this result demonstrates the effectiveness of the spatial context branch as a whole in our method." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 309, + 627, + 543, + 701 + ], + "blocks": [ + { + "bbox": [ + 309, + 627, + 543, + 701 + ], + "lines": [ + { + "bbox": [ + 309, + 627, + 543, + 701 + ], + "spans": [ + { + "bbox": [ + 309, + 627, + 543, + 701 + ], + "type": "table", + "html": "
Fusion StrategyMediumHard
ROxfRParROxfRPar
Orthogonal79.0486.6959.4972.87
Hadamard79.8387.9059.4474.60
Concatenation79.9488.4560.7276.00
Cross-Attention79.6489.0660.9076.97
", + "image_path": "27a57a7dc677e0b0f0e38506d2567855f66721b5c5c91652bbd84ee8a8e70ca1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 319, + 701, + 529, + 712 + ], + "lines": [ + { + "bbox": [ + 319, + 701, + 529, + 712 + ], + "spans": [ + { + "bbox": [ + 319, + 701, + 529, + 712 + ], + "type": "text", + "content": "Table 4. Ablation studies on the impact of fusion strategy." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11256" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "Fusion Strategy We validate the impact of different feature fusion strategies, including concatenation, orthogonal [35], Hadamard product, and cross-attention to fuse the information learned by our two branches in Table 4. As seen, the cross-attention scheme outperforms all the others in most cases except on the Medium split of ROxford. It demonstrates the effectiveness of utilizing cross-attention as the feature fusion strategy. Compared with cross-attention, orthogonal and Hadamard product perform worse. Surprisingly, we find simply concatenating the information from two branches has been able to obtain competitive performance. The result obtained by the concatenation strategy has been included in Table 1 too." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 251, + 282, + 338 + ], + "blocks": [ + { + "bbox": [ + 53, + 251, + 282, + 338 + ], + "lines": [ + { + "bbox": [ + 53, + 251, + 282, + 338 + ], + "spans": [ + { + "bbox": [ + 53, + 251, + 282, + 338 + ], + "type": "table", + "html": "
Token Number (K)MediumHard
ROxfRParROxfRPar
480.7688.3562.0275.33
879.6489.0660.9076.97
1681.2288.6162.4175.78
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", + "image_path": "292b1752cfd3972f0c98bb8a372d4526dad902d728da44ce166f7552519019df.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 63, + 338, + 269, + 348 + ], + "lines": [ + { + "bbox": [ + 63, + 338, + 269, + 348 + ], + "spans": [ + { + "bbox": [ + 63, + 338, + 269, + 348 + ], + "type": "text", + "content": "Table 5. Ablation studies on the impact of token number." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 363, + 289, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 289, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 289, + 543 + ], + "type": "text", + "content": "Number of Tokens We investigate the impact of the token number in Table 5. As seen, when the number is 16, the performance on ROxford is much better than other options. Meanwhile, when we utilize 24 tokens, the performance on RParis outperforms the others instead. We believe the optimal token number is related to the characteristic of the test dataset. When the number is too small, only a few visual prototypes could be explored to describe the whole dataset, leading to incomplete spatial context information extraction. Conversely, if the number is too large, more noisy tokens will be included. This could adversely impact the token-based identification process and consequently decrease the final retrieval performance. In our experiment, we just empirically use " + }, + { + "bbox": [ + 46, + 363, + 289, + 543 + ], + "type": "inline_equation", + "content": "K = 16" + }, + { + "bbox": [ + 46, + 363, + 289, + 543 + ], + "type": "text", + "content": " since we do not access any test dataset during the training stage." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 56, + 568, + 279, + 643 + ], + "blocks": [ + { + "bbox": [ + 56, + 568, + 279, + 643 + ], + "lines": [ + { + "bbox": [ + 56, + 568, + 279, + 643 + ], + "spans": [ + { + "bbox": [ + 56, + 568, + 279, + 643 + ], + "type": "table", + "html": "
Random Walk (l)MediumHard
ROxfRParROxfRPar
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Ablation studies on the impact of random walk steps." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Number of Random Walk Steps To inspect how many random walk steps are needed to encode the distance for our spatial context information extraction, we apply different number of random walk steps " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "l = \\{1,2,3,4\\}" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": ". As seen in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": "Table 6, " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "l = 3" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " gives the best performance. When the step number is small (such as 1 or 2), only a small area around the nodes in the matrix " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " of Eq. (3) is considered for the final distance encoding process. Meanwhile, with the number of steps increased, the random walk process tends to converge and its results become similar (i.e., " + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{s}^{(l)} \\approx \\mathbf{s}^{(l + 1)}" + }, + { + "bbox": [ + 304, + 72, + 547, + 192 + ], + "type": "text", + "content": " in Eq. (6)). Keeping adding or concatenating this information leads to redundant or even noisy information to the distance encoding, and thus adversely impacts the spatial context information extracted and further undermines retrieval." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 211, + 547, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 547, + 319 + ], + "type": "text", + "content": "Qualitative Results We demonstrate two images retrieved from ROxford. In addition, we provide the classification activation map obtained by using query feature representation as classification projection weights. As seen in Figure 3, in addition to the most discriminative part of the queried object (as shown in the second column obtained by DELG), the proposed SpCa focuses more on the spatial-context area. This makes the ranking of the true positive image dramatically increased compared with DELG." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 331, + 366, + 374 + ], + "blocks": [ + { + "bbox": [ + 308, + 331, + 366, + 374 + ], + "lines": [ + { + "bbox": [ + 308, + 331, + 366, + 374 + ], + "spans": [ + { + "bbox": [ + 308, + 331, + 366, + 374 + ], + "type": "image", + "image_path": "acd85fac86b11ac3a79ad6abfa5050a8fe103636caae428d13688e5b0eb8b241.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 375, + 361, + 381 + ], + "lines": [ + { + "bbox": [ + 313, + 375, + 361, + 381 + ], + "spans": [ + { + "bbox": [ + 313, + 375, + 361, + 381 + ], + "type": "text", + "content": "Query: ashmolean" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 367, + 331, + 426, + 374 + ], + "blocks": [ + { + "bbox": [ + 367, + 331, + 426, + 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"Ranking: 76th -> 20th" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 308, + 384, + 366, + 426 + ], + "blocks": [ + { + "bbox": [ + 308, + 384, + 366, + 426 + ], + "lines": [ + { + "bbox": [ + 308, + 384, + 366, + 426 + ], + "spans": [ + { + "bbox": [ + 308, + 384, + 366, + 426 + ], + "type": "image", + "image_path": "e685244bba611c8b1f2f9e8700becf381130b45b89b1f3f4c8789d7a5d95a636.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 427, + 362, + 434 + ], + "lines": [ + { + "bbox": [ + 312, + 427, + 362, + 434 + ], + "spans": [ + { + "bbox": [ + 312, + 427, + 362, + 434 + ], + "type": "text", + "content": "Query: cornmarket" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 368, + 384, + 426, + 426 + ], + "blocks": [ + { + "bbox": [ + 368, + 384, + 426, + 426 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Qualitative results and the activation maps." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 486, + 384, + 545, + 426 + ], + "blocks": [ + { + "bbox": [ + 486, + 384, + 545, + 426 + ], + "lines": [ + { + "bbox": [ + 486, + 384, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 486, + 384, + 545, + 426 + ], + "type": "image", + "image_path": "a5892cdb9da9ea5fbda345a666835d91d2c1224f6cfcd0eea81fd17b153b919a.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 487, + 428, + 544, + 434 + ], + "lines": [ + { + "bbox": [ + 487, + 428, + 544, + 434 + ], + "spans": [ + { + "bbox": [ + 487, + 428, + 544, + 434 + ], + "type": "text", + "content": "Ranking: 30th -> 11th" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 477, + 378, + 490 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "Motivated by the benefit of using local descriptor based geometric verification in a re-ranking step, we propose a novel feature learning framework that effectively embeds the spatial context information into the global visual feature representation for instance image retrieval. To mine the spatial context information, a spatial context branch consisting of an online token learning module and a distance encoding module is proposed. The former module is utilized to identify the type of each local descriptor on a feature map. The latter is used to capture the information on how the surrounding descriptors are spatially distributed. By fusing visual and spatial context information together, our framework learns spatial-context-aware global feature representations for images to conduct retrieval. Extensive experiments demonstrate the effectiveness of the proposed framework for retrieval. In future work, we will explore the incorporation of other types of information into global feature representations to further improve instance image retrieval." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11257" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 145, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 145, + 85 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 145, + 85 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 151 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 151 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 151 + ], + "type": "text", + "content": "This work is supported by the Australian Research Council (grant number DP200101289) and undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 163, + 106, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 163, + 106, + 175 + ], + "spans": [ + { + "bbox": [ + 48, + 163, + 106, + 175 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 183, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 183, + 287, + 228 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 183, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 53, + 183, + 287, + 228 + ], + "type": "text", + "content": "[1] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomás Pájdla, and Josef Sivic. 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IEEE Computer Society, 2009. 1" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11259" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Support and Trivial Prototypes for Interpretable Image Classification/1bf5aedf-f1e8-4793-8d34-430db9b0cd03_content_list.json b/2023/Learning Support and Trivial Prototypes for Interpretable Image Classification/1bf5aedf-f1e8-4793-8d34-430db9b0cd03_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..51f26f7182b458300e4d30d7ea3c22d79e8add0d --- /dev/null +++ b/2023/Learning Support and Trivial Prototypes for Interpretable Image Classification/1bf5aedf-f1e8-4793-8d34-430db9b0cd03_content_list.json @@ -0,0 +1,1744 @@ +[ + { + "type": "text", + "text": "Learning Support and Trivial Prototypes for Interpretable Image Classification", + "text_level": 1, + "bbox": [ + 84, + 130, + 883, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chong Wang $^{1}$ Yuyuan Liu $^{1}$ Yuanhong Chen $^{1}$ Fengbei Liu $^{1}$ Yu Tian $^{2}$ Davis McCarthy $^{3}$ Helen Frazer $^{4}$ Gustavo Carneiro $^{5}$", + "bbox": [ + 174, + 185, + 815, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Australian Institute for Machine Learning, University of Adelaide \n $^{2}$ Harvard University $^{3}$ St Vincent's Institute of Medical Research \n $^{4}$ St Vincent's Hospital Melbourne $^{5}$ CVSSP, University of Surrey", + "bbox": [ + 228, + 222, + 759, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 306, + 313, + 324 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prototypical part network (ProtoPNet) methods have been designed to achieve interpretable classification by associating predictions with a set of training prototypes, which we refer to as trivial prototypes because they are trained to lie far from the classification boundary in the feature space. Note that it is possible to make an analogy between ProtoPNet and support vector machine (SVM) given that the classification from both methods relies on computing similarity with a set of training points (i.e., trivial prototypes in ProtoPNet, and support vectors in SVM). However, while trivial prototypes are located far from the classification boundary, support vectors are located close to this boundary, and we argue that this discrepancy with the well-established SVM theory can result in ProtoPNet models with inferior classification accuracy. In this paper, we aim to improve the classification of ProtoPNet with a new method to learn support prototypes that lie near the classification boundary in the feature space, as suggested by the SVM theory. In addition, we target the improvement of classification results with a new model, named ST-ProtoPNet, which exploits our support prototypes and the trivial prototypes to provide more effective classification. Experimental results on CUB-200-2011, Stanford Cars, and Stanford Dogs datasets demonstrate that ST-ProtoPNet achieves state-of-the-art classification accuracy and interpretability results. We also show that the proposed support prototypes tend to be better localised in the object of interest rather than in the background region.", + "bbox": [ + 73, + 339, + 473, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 789, + 209, + 805 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep convolutional neural networks (CNN) [28, 30, 16] have had remarkable achievements in various visual tasks, e.g., image recognition [16] and object detection [39]. Despite the excellent feature extraction and discrimination ability, CNNs are generally treated as black-box models due to their complex architectures, high-dimensional fea", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/257bd92a30d8f5af85711e236e4dff2ed11d9626702f1b448d8f59560290594a.jpg", + "image_caption": [ + "(a) The learning of trivial prototypes" + ], + "image_footnote": [], + "bbox": [ + 501, + 306, + 890, + 373 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a1ea86fd4b542a56641457d80ed380227ebd60185eb319f059d0b8ea5cfd5b1f.jpg", + "image_caption": [ + "(b) The learning of support prototypes (ours)", + "Feature vectors $\\star \\star$ Prototypes $\\longrightarrow$ Clustering $\\longrightarrow$ Separation $\\longrightarrow$ Our loss Figure 1. The difference between the learning of trivial and support prototypes. (a) Trivial prototypes: the separation loss pushes the prototypes of different classes as far as possible from the classification boundary. (b) Support prototypes: our new closeness loss enforces the prototypes of different classes to be as close as possible to the classification boundary." + ], + "image_footnote": [], + "bbox": [ + 501, + 383, + 890, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ture spaces, and the enormous number of learnable parameters. Such lack of interpretability hinders their successful application in fields that require understandable and transparent decisions [40], e.g., disease diagnosis [47, 13], financial risk assessment [33], and autonomous driving [23].", + "bbox": [ + 496, + 566, + 890, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, increasing attention has been dedicated to the development of interpretable deep-learning models [25, 1, 4, 3]. A particularly interesting strategy is the prototype-based gray-box models, e.g., prototypical part network (ProtoPNet) [4, 11]. These methods are inherently interpretable since they can explain the model's decisions by showing image classification activation maps associated with a set of class-specific image prototypes. These prototypes are automatically learned from training samples, with classification score being computed by comparing testing image parts to the learned training prototypes.", + "bbox": [ + 496, + 643, + 892, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ProtoPNet [4] is trained to learn a classifier from a set of class-specific prototypes by minimising the cross-entropy classification loss and two additional regularisation losses, namely: 1) a clustering loss that pulls together training image patches to at least one prototype of its own class; and 2) a separation loss that pushes apart training image", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2062", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8b1f49f27fcb87fba8bda1f0e1a84ae8e80e212eeaec170eda5017ae335f2268.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 207, + 143 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e6c9c967a42cc7841459842d5b59555a3388a6aefd22f4876413be3b7f3dc0c3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 88, + 338, + 143 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/56a2b230d561a0ffe03f3bb41c3fcce406d8190b56468c789ce56153e063c9c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 341, + 98, + 467, + 131 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6ecfa48dba624a9aaaff7f7c390c81c51c5a659c8077c2e3aa30386716df617d.jpg", + "image_caption": [ + "(a) Trivial Prototypes", + "Figure 2. Two-moon results. (a) Trivial prototypes and training samples in the feature (top) and data (bottom) spaces from the original ProtoPNet [4]. (b) Support prototypes and training samples in the feature (top) and data (bottom) spaces from our method. (c) Support vectors and training samples from a Radial Basis Function (RBF) kernel based SVM [7]. In (a) and (b), each prototype is projected onto the nearest training sample in the feature space." + ], + "image_footnote": [], + "bbox": [ + 80, + 143, + 207, + 196 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0fd7a59e21f7a3090d3798ff48ca9d04c38113fb40cbedfa3543481f6ed11fb5.jpg", + "image_caption": [ + "(b) Support Prototypes" + ], + "image_footnote": [], + "bbox": [ + 210, + 143, + 336, + 196 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1f3f48ebb9ba59159cc39804b353ab147148c238a85f38c6097d57c5f89794e9.jpg", + "image_caption": [ + "(c) Support vectors from SVM" + ], + "image_footnote": [], + "bbox": [ + 339, + 143, + 467, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "patches from all prototypes of other classes. The combination of these two losses pushes the prototypes as far as possible from the classification boundary, but still within the class distribution, so we call them trivial prototypes, as shown in Fig. 1(a). We also display the trivial prototypes, learned with a feed-forward neural network1, for the two-moon problem in Fig. 2(a). Notice that these trivial prototypes are located far from the classification boundary. In fine-grained visual classification, the trivial prototypes can mistakenly focus on background regions instead of on the object of interest [42, 41], particularly for those classes with subtle foreground (object) differences but large background variations, as shown in Fig. 3. Different from ProtoPNet's trivial prototypes, the support vector machine (SVM) [7] classifier relies on a set of support vectors that are close to the classification boundary, as in Fig. 2(c). These support vectors are often treated as hard samples. Motivated by SVM, we propose the derivation of support (i.e., hard-to-learn) prototypes for ProtoPNet methods.", + "bbox": [ + 75, + 319, + 467, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose an alternative learning strategy for ProtoPNet, which forces the learned prototypes to resemble SVM's support vectors and to be located as close as possible to the classification boundary. The strategy is formulated by a new closeness loss that minimises the distance between prototypes of different classes. As shown in Fig. 1(b), our new loss enforces the prototypes to move closer to the classification boundary, as also demonstrated by Fig. 2(b) revealing that the support prototypes produced by the introduction of our new closeness loss are indeed more similar to the support vectors of SVM in Fig. 2(c). Furthermore, to improve the classification accuracy, we propose a new ST-ProtoPNet method that integrates both the support and trivial prototypes. The ST-ProtoPNet leverages the two distinct and complementary sets of prototypes to capture both hard (i.e., close to the boundary) and easy (i.e., far from the boundary) visual features for classification.", + "bbox": [ + 75, + 607, + 467, + 863 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/62753c07f95b79484d0bcdfd93779e6349c8d5efd7168f7bbebc795a0bb7c39b.jpg", + "image_caption": [ + "Figure 3. Example prototypes sampled from a VGG19-based ProtoPNet [4]. In each class, the left prototype focuses on object features while the right one captures background." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 630, + 146 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/327a68517bc98b9c639fbcf996e52406a2c1182b721808d2561b6e484659c5a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 632, + 90, + 759, + 146 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/956275a2456b859f702e5d6baf6c51544ad71b8964e0d3499903b325598ed141.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 90, + 890, + 146 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The major contributions of this work are:", + "bbox": [ + 517, + 205, + 792, + 219 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We provide the first study that makes an analogy between the prototype learning from ProtoPNet and support vector learning from SVM, where we propose support (i.e., hard-to-learn) prototypes that can improve classification accuracy and interpretability.", + "2. We present a new ST-ProtoPNet method to exploit both support and trivial prototypes for interpretable image classification, where the two sets of prototypes can provide complementary information to improve classification accuracy.", + "3. We conduct extensive experiments on three benchmarks, showing that our ST-ProtoPNet outperforms current state-of-the-art (SOTA) methods in terms of classification accuracy and interpretability." + ], + "bbox": [ + 511, + 227, + 890, + 453 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our experiments, we also demonstrate that the trivial and support prototypes have different characteristics, where the trivial prototypes tend to focus on both local parts of the visual object of interest and the background, while the support prototypes mainly focus on object parts belonging to the visual class of interest.", + "bbox": [ + 496, + 459, + 890, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 565, + 638, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Classification Interpretability", + "text_level": 1, + "bbox": [ + 500, + 590, + 761, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The interpretation of classification results produced by deep neural networks can be achieved by a variety of post-hoc explanation techniques, e.g., explanatory surrogates [34, 56, 44], counterfactual examples [15, 46, 19], and saliency visualisation [45, 55, 59, 43]. Alternatively, prototype-based interpretable techniques can access the model's inner computations. ProtoPNet [4] is the original work that uses class-specific prototypes for interpretable image classification. Similar to ProtoPNet, TesNet [53] constructs class-specific transparent basis concepts on Grassmann manifold for the interpretable classification. Derived from ProtoPNet, Deformable ProtoPNet [11] employs spatially-flexible and deformable prototypes to adaptively capture meaningful object features. In ProtoPShare [42], a data-dependent merge-pruning method is presented to share prototypes among classes, which can reduce the number of prototypes used for classification. In contrast, ProtoPool [41] introduces a fully differentiable prototype assignment strategy to reduce the number of prototypes. In", + "bbox": [ + 496, + 613, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1The network has an input layer of 2 nodes, a hidden layer of 256 nodes (activated by tanh), and an output layer of 2 nodes (activated by sigmoid).", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2063", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Proto2Proto [20], a knowledge distillation method is designed to transfer interpretability from a teacher ProtoPNet to a shallow student ProtoPNet. ProtoTree [35] integrates the prototype learning into a binary neural decision tree that can explain its predictions by tracing a decision path throughout the tree. ViT-NeT [24] further establishes the prototype neural tree structure on visual transformers [12].", + "bbox": [ + 75, + 90, + 467, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Because of the ability to self-explain classification results, prototype-based interpretability (e.g., ProtoPNet) has been widely utilised not only in the computer vision applications above, but also in medical imaging [2, 22, 51] and face recognition [48]. However, an open question faced by these methods is if the prototypes being learned are the ideal ones in terms of classification and interpretability.", + "bbox": [ + 75, + 198, + 467, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. SVM vs Prototype-based Classification", + "text_level": 1, + "bbox": [ + 76, + 314, + 410, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To better understand the role of prototypes, we consider the support vector machine (SVM) [7] classifier that finds support vectors to represent classes. More specifically, SVM learns the maximum-margin classifier defined by a classification boundary that maximises the distance to the closest training samples, which are the support vectors for the classes. The testing of SVM consists of computing a weighted similarity between a testing sample and the support vectors. It is interesting to note that the testing of prototype-based classifiers is also based on measuring the similarity between a testing image and a set of class-specific prototypes learned from the training process. Although the testing of SVM and prototype-based classifiers are similar, their training procedures are different. First, the training of a prototype-based classifier learns a fixed number of prototypes [4, 11], while the SVM classifier learns to weight a variable number of support vectors from the training set. Second, in prototype-based classifiers, the learned prototypes tend to be far from the classification boundary, which is contrary to the SVM training objective mentioned above.", + "bbox": [ + 75, + 337, + 467, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The study of deep learning methods from an SVM theoretical perspective is a rich area of research [9, 38, 6], but there are many practical questions that need to be addressed, e.g., how to scale the kernel computation for large-scale datasets, how to shorten the training process [38], and how to integrate deep-learning features with the learning of the SVM classifier. In this paper, our focus is on adapting the learning of ProtoPNet's prototypes to make them similar to SVM's support vectors, by forcing prototypes to be as close as possible to the classification boundary.", + "bbox": [ + 75, + 640, + 467, + 790 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Interpretable Ensemble Classification", + "text_level": 1, + "bbox": [ + 76, + 801, + 401, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Ensemble classification [10] is a classical machine learning approach that combines the results from multiple classifiers, with the goals of improving learning generalisation and classification calibration. The use of interpretable ensemble strategy has been explored in [4, 53, 35, 11, 41],", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which is achieved by summing the classification logits of multiple prototype-based classifiers (e.g., ProtoPNETs trained with different CNN backbones). In this work, we propose an interpretable ensemble classification by combining the predictions of two ProtoPNETs with highly distinctive prototypes (i.e., support and trivial prototypes), which is different from previous studies where the type of prototypes produced by each classifier is very similar given that the same training objective is used for each classifier.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 237, + 637, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We assume to have a training set $\\mathcal{D} = \\{(\\mathbf{x}_n,\\mathbf{y}_n)\\}_{n = 1}^{|\\mathcal{D}|}$ where $\\mathbf{x}\\in \\mathcal{X}\\subset \\mathbb{R}^{H\\times W\\times R}$ is an image with $R$ colour channels and $\\mathbf{y}\\in \\mathcal{Y}\\subset \\{0,1\\} ^C$ is a one-hot vector representation of the image class label. The interpretable ProtoPNet [4, 11] is trained to learn a set of prototypes $\\mathcal{P} = \\{\\mathbf{p}_m\\}_{m = 1}^M$ , where $\\mathbf{p}_m\\in \\mathbb{R}^{\\rho_1\\times \\rho_2\\times D}$ , with each of the $C$ classes containing $M / C$ prototypes. Without loss of generality, we assume $\\rho_{1} = \\rho_{2} = 1$ , but the extension to general values is trivial. A typical ProtoPNet comprises four components: a CNN backbone, add-on layers, a prototype layer, and a fully connected (FC) layer. An input image $\\mathbf{x}$ is fed to the CNN backbone $f_{\\theta}:X\\to \\mathcal{F}$ (parameterised by $\\theta \\in \\Theta$ , where $\\mathcal{F}\\subset \\mathbb{R}^{H\\times \\bar{W}\\times \\bar{D}}$ ) and then passed on to the add-on layers, denoted by $f_{\\omega}:F\\rightarrow V$ (parameterised by $\\omega \\in \\Omega$ ), to produce a feature map $\\mathbf{V}\\in \\mathcal{V}\\subset \\mathbb{R}^{\\bar{H}\\times \\bar{W}\\times D}$ . The prototype layer computes the similarity between the feature map $\\mathbf{V}$ and the $MD$ dimensional prototypes $\\{\\mathbf{p}_m\\}_{m = 1}^M$ to generate $M$ similarity maps $\\mathbf{S}_m^{(i,j)} = \\mathrm{sim}(\\mathbf{V}(i,j,:),\\mathbf{p}_m)$ , where $i\\in \\{1,\\dots,\\bar{H}\\}$ $j\\in \\{1,\\ldots ,\\bar{W}\\}$ , and $\\mathrm{sim}(\\cdot ,\\cdot)$ represents a similarity measure, e.g., cosine similarity [11] and projection metric [53]. The prototype layer outputs $M$ similarity scores from maxpooling $S = \\left\\{\\max_{i\\in \\{1,\\dots,\\bar{H}\\},j\\in \\{1,\\dots,\\bar{W}\\}}\\mathbf{S}_m^{(i,j)}\\right\\}_{m = 1}^M$ , which are fed to the FC layer $f_{\\phi}:S\\to \\Delta$ parameterised by $\\phi \\in \\Phi$ to produce the classification prediction $\\hat{\\mathbf{y}}\\in \\Delta \\subset [0,1]^C$ where $\\Delta$ denotes the probability space for $C$ classes.", + "bbox": [ + 496, + 256, + 890, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. ST-ProtoPNet", + "text_level": 1, + "bbox": [ + 500, + 678, + 640, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of our proposed ST-ProtoPNet method is illustrated in Fig. 4, which comprises a shared CNN backbone $f_{\\theta}(\\cdot)$ , two interpretable ProtoPNet classification branches, namely: 1) the support ProtoPNet represented by add-on layers $f_{\\omega^{(s)}}(\\cdot)$ , prototype layer with support prototypes $\\mathcal{P}^{(s)}$ , and FC layer $f_{\\phi^{(s)}}(\\cdot)$ which outputs the classification probability distribution $\\hat{\\mathbf{y}}^{(s)} \\in \\Delta$ ; and 2) the trivial ProtoPNet branch with its add-on layers $f_{\\omega^{(t)}}(\\cdot)$ , trivial prototypes $\\mathcal{P}^{(t)}$ , and FC layer $f_{\\phi^{(t)}}(\\cdot)$ that generates probability predictions $\\hat{\\mathbf{y}}^{(t)} \\in \\Delta$ . The final classification is obtained by combining the classification logits from both the support and trivial ProtoP nets. In our implementation, we construct the support and trivial ProtoPNet mainly based on the orig", + "bbox": [ + 496, + 700, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2064", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5a225871a407bdcd8c1652f81c89d811688c20672f9f3666b79577548ceee27f.jpg", + "image_caption": [ + "Figure 4. The architecture of our proposed ST-ProtoPNet method for the interpretable image classification." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 472, + 238 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "inal ProtoPNet [4] and TesNet [53], as explained below.", + "bbox": [ + 76, + 281, + 444, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Support ProtoPNet", + "text_level": 1, + "bbox": [ + 76, + 305, + 261, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The support ProtoPNet is designed to produce support prototypes that are as close as possible to the classification boundary, as shown in Fig. 1(b) and 2(b). The loss function to optimise the support ProtoPNet branch is defined as:", + "bbox": [ + 76, + 329, + 468, + 388 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\theta^ {*}, \\omega^ {(s) *}, \\mathcal {P} ^ {(s) *}, \\phi^ {(s) *} = \\\\ \\arg \\min _ {\\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}} \\sum_ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D}} \\ell_ {s p t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}). \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 398, + 468, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The loss for each training sample $(\\mathbf{x},\\mathbf{y})\\in \\mathcal{D}$ in Eq. (1) above is represented by:", + "bbox": [ + 76, + 483, + 468, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\ell_ {s p t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}) = \\ell_ {c e} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}) \\\\ - \\lambda_ {1} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) \\\\ + \\lambda_ {2} \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) \\\\ - \\lambda_ {3} \\ell_ {c l s} (\\mathcal {P} ^ {(s)}) \\\\ + \\lambda_ {4} \\ell_ {o r t} (\\mathcal {P} ^ {(s)}), \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 523, + 473, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{1},\\lambda_{2},\\lambda_{3}$ , and $\\lambda_{4}$ are hyper-parameters to balance each term, $\\ell_{ce}(\\cdot)$ denotes the cross-entropy classification loss, $\\ell_{ct}(\\cdot)$ and $\\ell_{sp}(\\cdot)$ represent the clustering and separation losses, respectively, which are introduced to regularise the ProtoPNet's training, as follows:", + "bbox": [ + 76, + 656, + 468, + 731 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) = \\max _ {\\mathbf {p} \\in \\mathcal {P} _ {\\mathbf {y}} ^ {(s)}} \\max _ {\\mathbf {v} \\in \\mathbf {V} ^ {(s)}} \\sin (\\mathbf {v}, \\mathbf {p}), (3) \\\\ \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) = \\max _ {\\mathbf {p} \\notin \\mathcal {P} _ {\\mathbf {y}} ^ {(s)}} \\max _ {\\mathbf {v} \\in \\mathbf {V} ^ {(s)}} \\operatorname {s i m} (\\mathbf {v}, \\mathbf {p}), (4) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 739, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{V}^{(s)} = f_{\\omega^{(s)}}(f_{\\theta}(\\mathbf{x}))$ is the feature map extracted from the input image $\\mathbf{x}$ , $\\mathbf{v}$ represents one of the $\\bar{H} \\times \\bar{W}$ feature vectors in $\\mathbf{V}^{(s)}$ obtained by matrix vectorisation, $\\mathbf{p}$ is a normalised prototype (i.e., unit vector) in $\\mathcal{P}^{(s)}$ , $\\sin (\\cdot, \\cdot)$", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is one of the similarity functions defined in Sec. 3, and $\\mathcal{P}_{\\mathbf{y}}^{(s)}$ denotes the set of prototypes of class $\\mathbf{y}$ . The clustering loss in Eq. (3) and separation loss in Eq. (4) aim to learn a meaningful feature space in which the image features of a certain class are clustered around the prototypes of the class, and also well separated from those of other classes.", + "bbox": [ + 496, + 89, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As mentioned in Sec. 1, the effect of the clustering and separation losses above tend to push the prototypes of different classes as far as possible from the classification boundary, resulting in trivial prototypes, as displayed in Fig. 1(a) and Fig. 2(a). In order to learn the proposed support prototypes, we introduce the following novel closeness loss $\\ell_{cls}$ to explicitly enforce the prototypes of different classes to be close to each other, which is formulated as:", + "bbox": [ + 496, + 181, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {c l s} \\left(\\mathcal {P} ^ {(s)}\\right) = \\sum_ {c _ {1} = 1} ^ {C - 1} \\sum_ {c _ {2} = c _ {1} + 1} ^ {C} \\min _ {\\mathbf {p} _ {m} \\in \\mathcal {P} _ {c _ {1}}, \\mathbf {p} _ {n} \\in \\mathcal {P} _ {c _ {2}}} \\mathbf {p} _ {m} ^ {\\top} \\mathbf {p} _ {n}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 311, + 890, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During training, this closeness loss $\\ell_{cls}$ maximises the pair-wise prototype similarity, in the form of dot product $\\mathbf{p}_m^\\top \\mathbf{p}_n$ between different classes in Eq. (5) above, with the goal of pulling the prototypes close to the classification boundary. On the one hand, as the prototypes move gradually towards the classification boundary, they are able to capture harder visual features from training samples. On the other hand, since the prototypes are located near the classification boundary, they can put pressure on the support ProtoPNet's feature learning (i.e., enforce it to learn highly discriminative feature representations for accurate classification), which is beneficial to extract more meaningful semantic information from training samples.", + "bbox": [ + 496, + 364, + 890, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ideally, each prototype of a class should focus on unique object parts of the training images (e.g., head, tail, and claw of birds), so that the prototypes can represent rich and diverse visual patterns. However, there is no particular constraints to guarantee such prototype diversity and the issue of prototype duplication [11] often occurs in the ProtoPNet family of models. To encourage the intra-class prototype diversity, we employ an orthonormality loss [53] so that prototypes within a class can represent dissimilar visual patterns of training samples, which is defined as:", + "bbox": [ + 496, + 561, + 890, + 712 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {o r t} \\left(\\mathcal {P} ^ {(s)}\\right) = \\sum_ {c = 1} ^ {C} \\left\\| \\mathbf {P} _ {c} ^ {\\top} \\mathbf {P} _ {c} - \\mathbf {I} _ {M / C} \\right\\| _ {F} ^ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 723, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\| \\cdot \\| _F^2$ represents Frobenius norm, $\\mathbf{P}_c\\in D\\times \\mathbb{R}^{(M / C)}$ stands for a matrix composed of the prototypes of class $c$ (prototypes in each column of $\\mathbf{P}_c$ are normalised), and $\\mathbf{I}_{M / C}$ is an identity matrix of size $M / C\\times M / C$", + "bbox": [ + 496, + 775, + 890, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Trivial ProtoPNet", + "text_level": 1, + "bbox": [ + 500, + 845, + 671, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As described in Sec. 4.1, the support ProtoPNet is developed to learn support (i.e., hard-to-learn) prototypes by", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2065", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "forcing them to be close to the classification boundary. Considering that training samples contain not only hard visual features but also important easy ones that the support prototypes cannot completely capture, we propose to also learn trivial prototypes to provide complementary classification information, and exploit both the support and trivial prototypes for improved interpretable classification.", + "bbox": [ + 75, + 90, + 467, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The loss objective to optimise the trivial ProtoPNet branch is defined as follows:", + "bbox": [ + 76, + 196, + 467, + 224 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\theta^ {*}, \\omega^ {(t) *}, \\mathcal {P} ^ {(t) *}, \\phi^ {(t) *} = \\\\ \\arg \\min _ {\\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}} \\sum_ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D}} \\ell_ {t r v} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}). \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 232, + 467, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The loss for each training image $(\\mathbf{x},\\mathbf{y})\\in \\mathcal{D}$ in Eq. (7) above is represented by:", + "bbox": [ + 76, + 311, + 467, + 340 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\ell_ {t r v} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}) = \\ell_ {c e} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}) \\\\ - \\lambda_ {1} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {2} \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {3} \\ell_ {d s c} (\\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {4} \\ell_ {\\text {o r t}} (\\mathcal {P} ^ {(t)}), \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 348, + 467, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{1},\\lambda_{2},\\lambda_{3}$ and $\\lambda_{4}$ are hyper-parameters, $\\ell_{ce}(\\cdot)$ is the cross-entropy loss, the clustering loss $\\ell_{ct}$ , separation loss $\\ell_{sp}$ , and orthonormality loss $\\ell_{ort}$ are the same as in the support ProtoPNet defined in Eq. (3), (4) and (6), respectively.", + "bbox": [ + 76, + 474, + 467, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The trivial ProtoPNet targets the learning of easy prototypes that are far from the classification boundary and have a good discrimination ability. To help achieve this, we introduce a new discrimination loss $\\ell_{dsc}$ to facilitate the interclass separability between prototypes of different classes. This is formulated by minimising the pair-wise prototype similarities of different classes, as follows:", + "bbox": [ + 75, + 535, + 467, + 640 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {d s c} \\left(\\mathcal {P} ^ {(t)}\\right) = \\sum_ {c _ {1} = 1} ^ {C - 1} \\sum_ {c _ {2} = c _ {1} + 1} ^ {C} \\max _ {\\mathbf {p} _ {m} \\in \\mathcal {P} _ {c _ {1}}, \\mathbf {p} _ {n} \\in \\mathcal {P} _ {c _ {2}}} \\mathbf {p} _ {m} ^ {\\top} \\mathbf {p} _ {n}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 648, + 467, + 689 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Training and Testing", + "text_level": 1, + "bbox": [ + 76, + 696, + 272, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. Following the training strategies in [4, 11], the training procedure of our ST-ProtoPNet consists of 3 stages: 1) optimisation of the CNN backbone, add-on layers, and prototype layer, using a fixed FC layer initialised with $+1.0$ and -0.5 for correct and incorrect connection weights, respectively. A warm-up of 5 epochs is involved in this stage by updating only the parameters of add-on layers and prototype layer, with a frozen pre-trained CNN backbone. 2) prototype projection by updating each prototype with its nearest latent training image patch; and 3) optimisation of the FC layer, with an additional $L_{1}$ regularisation on the incorrect connection weights (initially fixed at", + "bbox": [ + 75, + 719, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "-0.5). In each stage, we alternate the optimisation of each branch of the ST-ProtoPNet between mini-batches. Notice that our method only brings marginal extra model parameters, computational complexity, and training time since the CNN backbone is shared and optimised by both branches.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Testing. To exploit the complementary results from both branches of ST-ProtoPNet, its final classification is obtained from the summed logits predicted by the two branches. It is worth noticing that this ensemble strategy introduces no loss of interpretability but improved accuracy.", + "bbox": [ + 496, + 171, + 890, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 271, + 630, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform experiments on three fine-grained classification benchmark datasets: CUB-200-2011 [50], Stanford Cars [27], and Stanford Dogs [21]. To achieve fair comparison, we follow previous studies [4, 53] by applying offline data augmentations (e.g., random rotation, skew, shear, and left-right flip) on the cropped CUB and cropped Cars datasets (using the bounding boxes provided). We also validate our method on the full (i.e., uncropped) CUB and Dogs datasets, and employ the same online data augmentation methods (e.g., random affine transformation and left-right flip) as used in Deformable ProtoPNet [11]. All images are resized to $224 \\times 224$ pixels as network input.", + "bbox": [ + 496, + 296, + 890, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 498, + 705, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed ST-ProtoPNet method is evaluated on the following CNN architectures: VGG-16, VGG-19, ResNet-34, ResNet-50, ResNet-152, DenseNet-121, and DenseNet-161. All CNN backbones are pre-trained on ImageNet [8], except for ResNet-50, which is pre-trained on iNaturalist [49] for the experiment on full CUB [11]. The add-on layers include two $1 \\times 1$ convolutional layers. For simplicity, we utilise the same prototype dimension $D = 64$ for all CNN backbones on the three datasets. For cropped CUB and Cars datasets, following [53], we use 10 prototypes (5 support and 5 trivial) per class and the projection metric in the similarity function $\\mathrm{sim}(\\cdot ,\\cdot)$ . In full CUB and Dogs datasets, to ensure comparison fairness with Deformable ProtoPNet [11] that uses $102 \\times 2$ (full CUB) and $103 \\times 3$ (full Dogs) deformable prototypes per class, we utilise the same total number of prototypes, i.e., $401 \\times 1$ (20 support and 20 trivial) for full CUB and $901 \\times 1$ (45 support and 45 trivial) for full Dogs. Also, we employ the cosine similarity in $\\mathrm{sim}(\\cdot ,\\cdot)$ and obtain $14 \\times 14$ ( $\\bar{H} = \\bar{W} = 14$ ) feature maps by upsampling the original $7 \\times 7$ feature maps via a bi-linear interpolation step, as in [11]. Following previous prototype-based methods [4, 53, 11], we set $\\lambda_{1} = 0.8$ , $\\lambda_{2} = 0.48$ and 0.08 for the support and trivial ProtoPNet branches respectively, $\\lambda_{4} = 0.001$ . We choose $\\lambda_{3} = 1.0$ with an ablation provided in the supplementary material.", + "bbox": [ + 496, + 523, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2066", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Interpretability Evaluation", + "text_level": 1, + "bbox": [ + 76, + 90, + 321, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Rather than performing user-based evaluations [60, 41], whose results are often subjective and difficult to reproduce [54], we leverage the annotated object masks to measure interpretability based on the following metrics:", + "bbox": [ + 76, + 109, + 467, + 171 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Content Heatmap (CH) [37]: quantifies the percentage of an activation heatmap that lies within the annotated mask. Hence, we expect this metric to be high.", + "bbox": [ + 76, + 172, + 467, + 217 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Outside-Inside Relevance Ratio (OIRR) [29]: calculates the ratio of mean activation outside the object to mean activation inside the object. A low OIRR indicates a method relies more on the object region and less on the context to support its decision, we thus anticipate OIRR to be low.", + "bbox": [ + 76, + 218, + 467, + 294 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Intersection over Union (IoU) [5]: measures the mean IoU score, where a threshold of 0.5 is applied on the min-max normalised heatmap to select foreground objects.", + "bbox": [ + 76, + 294, + 467, + 340 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Deletion AUC (DAUC) [36]: estimates a decrease in the probability of the predicted class as more and more important/activated pixels are removed. The area under the probability curve is defined as DAUC. Consequently, a sharp drop and a low DAUC mean better interpretation.", + "bbox": [ + 76, + 340, + 467, + 416 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Average Inter-class Prototype Distance (AIPD), Average Inter-class Feature Distance (AIFD): we had earlier stated that support prototypes of different classes should be close to each other and trivial prototypes should be far from each other. Thus, we compute the average inter-class cosine distance for prototypes and their nearest local feature representations, respectively. We expect AIPD $<$ AIFD for support ProtoPNet and AIPD $>$ AIFD for trivial ProtoPNet.", + "bbox": [ + 76, + 417, + 467, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Classification Performance", + "text_level": 1, + "bbox": [ + 76, + 546, + 318, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 presents the classification accuracy (across 5 runs) of our proposed ST-ProtoPNet on cropped CUB and cropped Cars, where the Baseline is represented by non-interpretable black-box CNN models. As can be seen, our ST-ProtoPNet outperforms other competing methods across all backbones for the task of bird species classification. Also, our method achieves the best results for the car model identification task when using VGG and DenseNet architectures as the CNN backbone. In particular, our VGG19-based ST-ProtoPNet reaches an average accuracy of $83.2\\%$ and $91.7\\%$ on CUB and Cars, respectively, surpassing other methods with the most improvements across all backbones. Moreover, the support ProtoPNet generally performs better than methods utilising only trivial prototypes (e.g., ProtoPNet, TesNet, and Trivial ProtoPNet), showing the importance of learning support prototypes for the interpretable classification. It is worth noting that our ST-ProtoPNet produces superior performance over the support ProtoPNet method, indicating that both support and trivial prototypes are useful and can provide complementary information for achieving accurate and interpretable classification.", + "bbox": [ + 76, + 566, + 467, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2 shows the classification results on full CUB and", + "bbox": [ + 96, + 885, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "full Dogs. In both datasets, the classification accuracy of the original ProtoPNet method is generally worse than the non-interpretable counterpart (Baseline) for many CNN backbones. On the other hand, the accuracy by the trivial ProtoPNet and support ProtoPNet are substantially better than those by Baseline, ProtoPNet, and Deformable ProtoPNet. However, our ST-ProtoPNet achieves more significant performance gains and exhibits the best accuracy across most backbones, particularly when using a large number of prototypes (i.e., $401 \\times 1$ prototypes per class for CUB and $901 \\times 1$ prototypes per class for Dogs), demonstrating the effectiveness of utilising both the trivial and support prototypes for the interpretable image classification. Additionally, when using a smaller number of prototypes, i.e., $101 \\times 1$ prototypes per class, our ST-ProtoPNet still has competitive classification accuracy across multiple backbones.", + "bbox": [ + 496, + 90, + 890, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further compare our ST-ProtoPNet with other deep-learning methods that can provide different levels of interpretability on CUB, with results shown in Table 3, where * and ** denote ensemble of models with different backbones. As evident, an ensemble of three ST-ProtoPNETs can achieve high accuracy (87.9% on cropped images, 88.2% on full images), outperforming competing methods that are also based on an ensemble of three models (e.g., ProtoTree, TesNet, and ProtoPool). Moreover, the ensemble of five STProtoPNETs outperforms all other competing methods and obtains the best classification accuracy of 88.1% and 88.4% on cropped and full CUB images, respectively. More results on Cars and Dogs are given in the supplementary material.", + "bbox": [ + 496, + 333, + 890, + 529 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Interpretability Comparison", + "text_level": 1, + "bbox": [ + 500, + 537, + 754, + 553 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We assess the model interpretability on full CUB using the annotated bird segmentation mask $^2$ . Quantitative results on the test set are given in Table 4, where all methods are based on the VGG19 backbone. We use GradCAM [43] for the non-interpretable baseline. For prototype-based methods, we average the activation map of all prototypes of a class to compute the metrics. We can see our proposed support ProtoPNet can effectively improve the interpretableity in all measures, showing the interpretations produced by our support prototypes are more likely to be object-dependent and focus less on context cues. Also, our ST-ProtoPNet method shows better interpretable results than the support ProtoPNet in terms of CH, OIRR, and DAUC. Compared with the original ProtoPNet [4], our ST-ProtoPNet obtains significant interpretability improvements. We show some example activation maps in the supplementary material, and an experiment with prototype pruning is also provided.", + "bbox": [ + 496, + 556, + 890, + 814 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5 presents the computed AIPD and AIFD for the support and trivial ProtoPNet on cropped CUB, using VGG19 and ResNet34 as CNN backbones. As evident, the AIPD is indeed smaller than AIFD for the support ProtoP-", + "bbox": [ + 496, + 814, + 890, + 875 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{2}$ http://www.vision.caltech.edu/datasets/", + "bbox": [ + 517, + 886, + 732, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2067", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c5d10942c36b185c323a35196cc8816b8d88eef4625de7b9aee941e18788006a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCUBCars
VGG16VGG19ResNet34ResNet152Dense121Dense161VGG16VGG19ResNet34ResNet152Dense121Dense161
Baseline73.3 ± 0.274.7 ± 0.482.2 ± 0.380.8 ± 0.481.8 ± 0.182.1 ± 0.287.3 ± 0.488.5 ± 0.392.6 ± 0.392.8 ± 0.492.0 ± 0.392.5 ± 0.3
ProtoPNet [4]77.2 ± 0.277.6 ± 0.278.6 ± 0.179.2 ± 0.379.0 ± 0.280.8 ± 0.388.3 ± 0.289.4 ± 0.288.8 ± 0.188.5 ± 0.387.7 ± 0.189.5 ± 0.2
TesNet [53]81.3 ± 0.281.4 ± 0.182.8 ± 0.182.7 ± 0.284.8 ± 0.284.6 ± 0.390.3 ± 0.290.6 ± 0.290.9 ± 0.292.0 ± 0.291.9 ± 0.392.6 ± 0.3
Trivial ProtoPNet80.8 ± 0.281.2 ± 0.282.5 ± 0.283.1 ± 0.383.9 ± 0.384.6 ± 0.390.1 ± 0.290.7 ± 0.291.1 ± 0.291.5 ± 0.291.4 ± 0.392.4 ± 0.3
Support ProtoPNet81.7 ± 0.281.8 ± 0.383.0 ± 0.183.6 ± 0.284.7 ± 0.285.2 ± 0.390.9 ± 0.290.8 ± 0.291.0 ± 0.291.8 ± 0.291.7 ± 0.292.7 ± 0.3
ST-ProtoPNet (ours)82.9 ± 0.283.2 ± 0.283.5 ± 0.184.1 ± 0.285.4 ± 0.286.1 ± 0.291.1 ± 0.291.7 ± 0.291.4 ± 0.192.0 ± 0.292.3 ± 0.392.7 ± 0.2
", + "bbox": [ + 81, + 88, + 890, + 181 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ce4f997923ea44f2865bae14fa639ba22b5f6cc32c66e26b8dc3b7ba76fdfcd3.jpg", + "table_caption": [ + "Table 1. Classification accuracy (%) on cropped CUB-200-2011 and Stanford Cars by competing methods using different CNN backbones." + ], + "table_footnote": [], + "table_body": "
Method# PrototypeCUB# PrototypeDogs
VGG16VGG19ResNet34ResNet50ResNet152Dense121Dense161VGG16VGG19ResNet34ResNet50ResNet152Dense121Dense161
Baseline-70.971.376.078.779.278.280.0-75.677.381.183.185.281.984.1
ProtoPNet [4]1×1p, 10pc70.372.672.481.174.374.075.41×1p, 10pc70.773.673.476.476.272.077.3
ProtoPNet [4]1×1p, 40pc72.974.274.184.876.076.678.51×1p, 90pc73.975.376.178.179.775.478.8
TesNet [53]1×1p, 10pc75.877.576.286.579.080.279.61×1p, 10pc74.377.180.182.483.880.383.8
TesNet [53]1×1p, 40pc77.679.276.587.380.180.981.31×1p, 90pc78.579.681.283.384.582.185.2
Deformable ProtoPNet [11]2×2p, 10pc75.776.076.886.479.679.081.23×3p, 10pc75.877.980.682.286.580.783.7
Trivial ProtoPNet1×1p, 40pc80.079.577.587.280.881.182.11×1p, 90pc78.680.482.685.087.082.385.9
Support ProtoPNet1×1p, 40pc80.480.078.487.580.281.582.41×1p, 90pc79.080.683.085.187.382.686.2
ST-ProtoPNet (ours)1×1p, 10pc76.877.677.486.678.778.680.61×1p, 10pc74.277.280.884.085.379.484.4
ST-ProtoPNet (ours)1×1p, 40pc81.080.278.288.081.281.882.71×1p, 90pc79.180.983.485.787.282.986.6
", + "bbox": [ + 81, + 212, + 890, + 330 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/022894e2e50c6e5fdb76433494cc25f1ebc0b94d69946bdf508a6934a48f5c97.jpg", + "table_caption": [ + "Table 2. Classification accuracy (%) on full CUB-200-2011 and Stanford Dogs datasets by competing approaches using different CNN backbones, where ${\\rho }_{1} \\times {\\rho }_{2}\\mathrm{p}$ denotes the spatial shape of prototypes and $k\\mathrm{{pc}}$ represents $k$ prototypes per class." + ], + "table_footnote": [], + "table_body": "
Interpretability levelMethodAccuracy (%)
NoneB-CNN [32]85.1 (b)84.1 (f)
Object-level attentionCAM [59]70.5 (b)63.0 (f)
CSG [31]82.6 (b)78.5 (f)
Part-level attentionPA-CNN [26]82.8 (b)-
MG-CNN [52]83.0 (b)81.7 (f)
MA-CNN [57]-86.5 (f)
RA-CNN [14]-85.3 (f)
TASN [58]-87.0 (f)
Part-level attention + PrototypesRegion [17]81.5 (b)80.2 (f)
ProtoPNet* [4]84.8 (b)81.1 (f)
ProtoTree* [35]-86.6 (f)
TesNet* [53]86.2 (b)83.5 (f)
ProtoPool* [41]87.5 (b)-
ST-ProtoPNet* (ours)87.9 (b)88.2 (f)
ProtoTree** [35]-87.2 (f)
Deformable ProtoPNet** [11]-87.8 (f)
ProtoPool** [41]87.6 (b)-
ST-ProtoPNet** (ours)88.1 (b)88.4 (f)
", + "bbox": [ + 81, + 375, + 465, + 587 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6d1bf0cc121f7bece7d0d19fdc61d07c42529c419ac20570179ffb319bb330d7.jpg", + "table_caption": [ + "Table 3. Classification accuracy and interpretability level of different methods on CUB-200-2011. \"b\" and \"f\" denote the model is trained and tested on cropped and full images, respectively. *: Ensemble of three models. **: Ensemble of five models." + ], + "table_footnote": [], + "table_body": "
MetricGradCAM [43]ProtoPNet [4]TesNet [53]DefProto [11]TrvProtoSptProtoST-Proto
CH (%, ↑)52.4648.6659.3852.0963.0563.8766.43
IoU (%, ↑)39.9138.0336.9240.7737.7442.0441.05
OIRR (%, ↓)37.0137.2638.9728.6834.4828.6928.09
DAUC (%, ↓)7.017.395.865.996.065.805.74
", + "bbox": [ + 80, + 657, + 465, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Net while AIPD is larger than AIFD for the trivial ProtoP-Net. This result indicates that the support prototypes of different classes lie closer than their local feature representations and are more inclined to focus on visually similar (i.e., hard-to-learn) object parts of different classes.", + "bbox": [ + 76, + 768, + 468, + 844 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Visualisation Analysis", + "text_level": 1, + "bbox": [ + 76, + 851, + 282, + 867 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To explore the differences between the support and trivial prototypes, we select 5 categories of birds with visu", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2dc5982f5443d80c14a93a17708678ab39af428b9492e28a145222d66f5631b0.jpg", + "table_caption": [ + "Table 4. Quantitative interpretability results on full CUB test set. DefProto = Deformable ProtoPNet, TrvProto = Trivial ProtoPNet, SptProto = Support ProtoPNet, ST-Proto = ST-ProtoPNet." + ], + "table_footnote": [], + "table_body": "
VGG19ResNet34
SupportProtoPNetTrivialProtoPNetSupportProtoPNetTrivialProtoPNet
AIPDAIFDAIPDAIFDAIPDAIFDAIPDAIFD
0.72590.92640.99870.92320.65410.85731.0000.9481
", + "bbox": [ + 503, + 376, + 888, + 421 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Average inter-class prototype distance (AIPD) and average inter-class feature distance (AIFD) for the support and trivial ProtoPNet trained on cropped CUB.", + "bbox": [ + 500, + 425, + 890, + 465 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/83c79ab267d0912173d5809975c3ccf5eb7be6e68b6b5f985411c1e8a549135f.jpg", + "image_caption": [ + "Figure 5. The support (top) and trivial (bottom) prototypes from cropped CUB. In each pair, the first column shows the original image with a prototype marked in a yellow bounding box, the second column is the prototype's corresponding activation map." + ], + "image_footnote": [], + "bbox": [ + 501, + 474, + 890, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ally similar features from cropped CUB to train the support and trivial ProtoPNet methods, with the learned prototypes shown in Fig. 5. We notice the support prototypes can cap", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2068", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c5320708478b8263ae8a62171c8a0f7c9ab52b29de6f99c906d8e076f78b10ea.jpg", + "image_caption": [ + "Figure 6. T-SNE results of support and trivial prototypes. The prototypes and their nearest latent training features are marked with stars and dots, respectively. We show results before the prototype projection stage to better visualise the relation between the prototypes and features. Each colour represents a different class." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 269, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8f698f6fdfeb661718aabd98d51d3d8f5a6d657798fc09b9ab9fc1661b9a723e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 88, + 467, + 193 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ture subtle and fine visual features of different classes and they only focus on relevant bird parts, e.g., head and belly. This is reasonable since our algorithm is designed to produce prototypes that are as close as possible to each other, where the image prototypical parts should not only be discriminative but also share visually similar features among classes. By contrast, the trivial prototypes tend to focus not only on the relevant bird parts but also the background regions. For example, some trivial prototypes of the Laysan Albatross and Sooty Albatross classes capture the sea surface as they often appear with the sea background. We argue that this is because the trivial ProtoPNet may treat the background as an easy pattern to learn, focusing less on the object's visual parts of the class. In Fig. 6, we show the t-SNE result from the 5-category bird classification, where we note the support prototypes of different classes are located closer to each other, in comparison with the trivial prototypes.", + "bbox": [ + 75, + 280, + 468, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 7 shows an example of the interpretable reasoning for our ST-ProtoPNet in classifying a testing bird image. As evident, each ProtoPNet branch calculates its own classification logits (weighted sum of similarity scores), which is then combined to generate the final prediction. Specifically, when classifying a Parakeet Auklet, the support prototypes are quite active on the bird's beak and belly. Meanwhile, the trivial prototypes have high activations on the bird's lower surface and neck. In this case, the support ProtoPNet obtains a relatively higher similarity score (22.925), compared with the trivial branch (20.313). Note that our ST-ProtoPNet exploits both the support and trivial prototypes to capture much richer representations of the object from different perspectives, which enables the realisation of complementary interpretations. More examples on Cars and Dogs are shown in the supplementary material.", + "bbox": [ + 75, + 537, + 470, + 781 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 789, + 230, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The closeness and discrimination losses. To validate the effectiveness of our proposed closeness loss in Eq. (5) and discrimination loss in Eq. (9), we first conduct ablation studies on full CUB and full Dogs by using ResNet50 and ResNet34 as the CNN backbone, respectively. Results are listed in Table 6. We can observe that both the close-", + "bbox": [ + 75, + 809, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7dfb1d14679dbe59deaa77dc6a19d60ac205d535332011c2ab68c1bad1ad1a8b.jpg", + "image_caption": [ + "Figure 7. An example of the interpretable reasoning of our STProtoPNet for classifying a testing Parakeet Auklet image." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 890, + 275 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6ba5d97004fd977e868975f95db7194106b1df997cb69f83e0c784c5d08ab17e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodlctlsplortldscclsAccuracy (%)
CUBDogs
Baseline✓✓✓86.580.9
Trivial ProtoPNet✓✓✓✓87.282.6
Support ProtoPNet✓✓✓✓87.583.0
ST-ProtoPNet (ours)✓✓✓✓✓88.083.4
", + "bbox": [ + 503, + 316, + 888, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation analysis of the closeness loss $\\ell_{cls}$ in Eq. (5) to learn support prototypes, and discrimination loss $\\ell_{dsc}$ in Eq. (9) to learn trivial prototypes on full CUB-200-2011 and Stanford Dogs.", + "bbox": [ + 498, + 383, + 890, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ness and discrimination losses can improve the accuracy, compared with the Baseline ProtoPNet method trained with only clustering, separation, and orthonormality losses. Note that the closeness loss introduces a larger performance improvement, which is attributed to the learning of support (i.e., hard-to-learn) prototypes.", + "bbox": [ + 496, + 438, + 890, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Combining Support and Trivial Prototypes. We also investigate the importance of integrating the two complementary sets of support and trivial prototypes for improved classification. To achieve this, we first train a two-branch model where both branches learn the same type of prototypes and the final result is produced by the ensemble of them (Trivial Ensemble and Support Ensemble). Besides, for our ST-ProtoPNet, we also provide results of its individual branches (Trivial Branch and Support Branch). Table 7 shows the experimental results on cropped CUB. We can notice that combining the two different types of prototypes (ST-ProtoPNet) achieves superior performance over combining only the same type of prototypes (Trivial Ensemble and Support Ensemble), indicating that our performance improvements are from not only the ensemble strategy but also the two complementary sets of prototypes. Also, STProtoPNet indeed exhibits higher accuracy than its individual branches, further verifying that the results from the two branches are complementary, and the combination of them is effective to improve the final classification accuracy.", + "bbox": [ + 496, + 529, + 892, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 500, + 835, + 769, + 852 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed the ST-ProtoPNet to exploit both support (i.e., hard-to-learn) and trivial (i.e., easy-to-learn) prototypes, where the two sets of prototypes can pro", + "bbox": [ + 498, + 854, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2069", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/70f26859fc90953fdfa14e3614377f54cd38e90588b882853049093e6583a859.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodVGG16VGG19ResNet34ResNet152Dense121Dense161
Trivial Ensemble81.4 ± 0.381.8 ± 0.282.7 ± 0.283.2 ± 0.384.4 ± 0.285.0 ± 0.3
Support Ensemble82.1 ± 0.282.4 ± 0.383.0 ± 0.283.7 ± 0.384.8 ± 0.285.5 ± 0.2
Trivial Branch81.0 ± 0.281.1 ± 0.382.4 ± 0.282.9 ± 0.384.1 ± 0.384.8 ± 0.3
Support Branch81.5 ± 0.381.8 ± 0.382.8 ± 0.283.4 ± 0.384.6 ± 0.285.4 ± 0.2
ST-ProtoPNet (ours)82.9 ± 0.283.2 ± 0.283.5 ± 0.184.1 ± 0.285.4 ± 0.286.1 ± 0.2
", + "bbox": [ + 81, + 89, + 465, + 148 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 7. Ablation study of the combination of support and trivial prototypes for improved classification on cropped CUB-200-2011.", + "bbox": [ + 76, + 154, + 467, + 183 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "vide complementary results for the interpretable image classification. Our ST-ProtoPNet is a general approach that can be easily applied to existing prototype-based interpretable models. One limitation for our method is that we empirically adopt the same number of support and trivial prototypes and the same total number of prototypes for each class. Considering the different learning difficulties and imbalanced training samples among classes in other real-world datasets, e.g., ImageNet [8], a better way to adaptively learn a flexible number of support and trivial prototypes is needed and deserves to be further investigated in our future work. Moreover, given that we mimic the behaviour of the support vectors of SVM classifier to obtain the support prototypes by forcing them to be as close as possible to the classification boundary, we plan to develop new methods to learn prototypes with gradient-based kernel techniques, e.g., neural tangent kernel [18] and path kernel [9].", + "bbox": [ + 76, + 196, + 468, + 454 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by funding from the Australian Government under the Medical Research Future Fund - Grant MRFAI000090 for the Transforming Breast Cancer Screening with Artificial Intelligence (BRAIx) Project, and the Australian Research Council through grant FT190100525.", + "bbox": [ + 76, + 467, + 468, + 556 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 574, + 171, + 589 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] David Alvarez Melis and Tommi Jaakkola. Towards robust interpretability with self-explaining neural networks. Advances in Neural Information Processing Systems, 31, 2018.", + "[2] Alina Jade Barnett, Fides Regina Schwartz, Chaofan Tao, Chaofan Chen, Yinhao Ren, Joseph Y Lo, and Cynthia Rudin. A case-based interpretable deep learning model for classification of mass lesions in digital mammography. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3233-3242, 2021." + ], + "bbox": [ + 501, + 92, + 893, + 204 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "2072", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Support and Trivial Prototypes for Interpretable Image Classification/1bf5aedf-f1e8-4793-8d34-430db9b0cd03_model.json b/2023/Learning Support and Trivial Prototypes for Interpretable Image Classification/1bf5aedf-f1e8-4793-8d34-430db9b0cd03_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fb1e56a015b5a54e24eec3d13dada3176380348d --- /dev/null +++ b/2023/Learning Support and Trivial Prototypes for Interpretable Image Classification/1bf5aedf-f1e8-4793-8d34-430db9b0cd03_model.json @@ -0,0 +1,2466 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.131, + 0.885, + 0.154 + ], + "angle": 0, + "content": "Learning Support and Trivial Prototypes for Interpretable Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.186, + 0.816, + 0.223 + ], + "angle": 0, + "content": "Chong Wang\\(^{1}\\) Yuyuan Liu\\(^{1}\\) Yuanhong Chen\\(^{1}\\) Fengbei Liu\\(^{1}\\) Yu Tian\\(^{2}\\) Davis McCarthy\\(^{3}\\) Helen Frazer\\(^{4}\\) Gustavo Carneiro\\(^{5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.223, + 0.761, + 0.277 + ], + "angle": 0, + "content": "\\(^{1}\\) Australian Institute for Machine Learning, University of Adelaide \n\\(^{2}\\) Harvard University \\(^{3}\\) St Vincent's Institute of Medical Research \n\\(^{4}\\) St Vincent's Hospital Melbourne \\(^{5}\\) CVSSP, University of Surrey" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.308, + 0.314, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.34, + 0.474, + 0.765 + ], + "angle": 0, + "content": "Prototypical part network (ProtoPNet) methods have been designed to achieve interpretable classification by associating predictions with a set of training prototypes, which we refer to as trivial prototypes because they are trained to lie far from the classification boundary in the feature space. Note that it is possible to make an analogy between ProtoPNet and support vector machine (SVM) given that the classification from both methods relies on computing similarity with a set of training points (i.e., trivial prototypes in ProtoPNet, and support vectors in SVM). However, while trivial prototypes are located far from the classification boundary, support vectors are located close to this boundary, and we argue that this discrepancy with the well-established SVM theory can result in ProtoPNet models with inferior classification accuracy. In this paper, we aim to improve the classification of ProtoPNet with a new method to learn support prototypes that lie near the classification boundary in the feature space, as suggested by the SVM theory. In addition, we target the improvement of classification results with a new model, named ST-ProtoPNet, which exploits our support prototypes and the trivial prototypes to provide more effective classification. Experimental results on CUB-200-2011, Stanford Cars, and Stanford Dogs datasets demonstrate that ST-ProtoPNet achieves state-of-the-art classification accuracy and interpretability results. We also show that the proposed support prototypes tend to be better localised in the object of interest rather than in the background region." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.79, + 0.21, + 0.806 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Deep convolutional neural networks (CNN) [28, 30, 16] have had remarkable achievements in various visual tasks, e.g., image recognition [16] and object detection [39]. Despite the excellent feature extraction and discrimination ability, CNNs are generally treated as black-box models due to their complex architectures, high-dimensional fea" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.307, + 0.892, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.615, + 0.374, + 0.779, + 0.384 + ], + "angle": 0, + "content": "(a) The learning of trivial prototypes" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.385, + 0.891, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.595, + 0.453, + 0.799, + 0.462 + ], + "angle": 0, + "content": "(b) The learning of support prototypes (ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.463, + 0.891, + 0.556 + ], + "angle": 0, + "content": "Feature vectors \\(\\star \\star\\) Prototypes \\(\\longrightarrow\\) Clustering \\(\\longrightarrow\\) Separation \\(\\longrightarrow\\) Our loss Figure 1. The difference between the learning of trivial and support prototypes. (a) Trivial prototypes: the separation loss pushes the prototypes of different classes as far as possible from the classification boundary. (b) Support prototypes: our new closeness loss enforces the prototypes of different classes to be as close as possible to the classification boundary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.643 + ], + "angle": 0, + "content": "ture spaces, and the enormous number of learnable parameters. Such lack of interpretability hinders their successful application in fields that require understandable and transparent decisions [40], e.g., disease diagnosis [47, 13], financial risk assessment [33], and autonomous driving [23]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.81 + ], + "angle": 0, + "content": "Recently, increasing attention has been dedicated to the development of interpretable deep-learning models [25, 1, 4, 3]. A particularly interesting strategy is the prototype-based gray-box models, e.g., prototypical part network (ProtoPNet) [4, 11]. These methods are inherently interpretable since they can explain the model's decisions by showing image classification activation maps associated with a set of class-specific image prototypes. These prototypes are automatically learned from training samples, with classification score being computed by comparing testing image parts to the learned training prototypes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.902 + ], + "angle": 0, + "content": "ProtoPNet [4] is trained to learn a classifier from a set of class-specific prototypes by minimising the cross-entropy classification loss and two additional regularisation losses, namely: 1) a clustering loss that pulls together training image patches to at least one prototype of its own class; and 2) a separation loss that pushes apart training image" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2062" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.209, + 0.144 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.089, + 0.339, + 0.144 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.099, + 0.468, + 0.132 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.145, + 0.209, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.198, + 0.184, + 0.205 + ], + "angle": 0, + "content": "(a) Trivial Prototypes" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.145, + 0.338, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.231, + 0.198, + 0.317, + 0.205 + ], + "angle": 0, + "content": "(b) Support Prototypes" + }, + { + "type": "image", + "bbox": [ + 0.341, + 0.145, + 0.468, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.347, + 0.198, + 0.459, + 0.205 + ], + "angle": 0, + "content": "(c) Support vectors from SVM" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.209, + 0.47, + 0.306 + ], + "angle": 0, + "content": "Figure 2. Two-moon results. (a) Trivial prototypes and training samples in the feature (top) and data (bottom) spaces from the original ProtoPNet [4]. (b) Support prototypes and training samples in the feature (top) and data (bottom) spaces from our method. (c) Support vectors and training samples from a Radial Basis Function (RBF) kernel based SVM [7]. In (a) and (b), each prototype is projected onto the nearest training sample in the feature space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.468, + 0.606 + ], + "angle": 0, + "content": "patches from all prototypes of other classes. The combination of these two losses pushes the prototypes as far as possible from the classification boundary, but still within the class distribution, so we call them trivial prototypes, as shown in Fig. 1(a). We also display the trivial prototypes, learned with a feed-forward neural network1, for the two-moon problem in Fig. 2(a). Notice that these trivial prototypes are located far from the classification boundary. In fine-grained visual classification, the trivial prototypes can mistakenly focus on background regions instead of on the object of interest [42, 41], particularly for those classes with subtle foreground (object) differences but large background variations, as shown in Fig. 3. Different from ProtoPNet's trivial prototypes, the support vector machine (SVM) [7] classifier relies on a set of support vectors that are close to the classification boundary, as in Fig. 2(c). These support vectors are often treated as hard samples. Motivated by SVM, we propose the derivation of support (i.e., hard-to-learn) prototypes for ProtoPNet methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.468, + 0.864 + ], + "angle": 0, + "content": "In this paper, we propose an alternative learning strategy for ProtoPNet, which forces the learned prototypes to resemble SVM's support vectors and to be located as close as possible to the classification boundary. The strategy is formulated by a new closeness loss that minimises the distance between prototypes of different classes. As shown in Fig. 1(b), our new loss enforces the prototypes to move closer to the classification boundary, as also demonstrated by Fig. 2(b) revealing that the support prototypes produced by the introduction of our new closeness loss are indeed more similar to the support vectors of SVM in Fig. 2(c). Furthermore, to improve the classification accuracy, we propose a new ST-ProtoPNet method that integrates both the support and trivial prototypes. The ST-ProtoPNet leverages the two distinct and complementary sets of prototypes to capture both hard (i.e., close to the boundary) and easy (i.e., far from the boundary) visual features for classification." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.631, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.091, + 0.76, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.091, + 0.891, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.15, + 0.892, + 0.193 + ], + "angle": 0, + "content": "Figure 3. Example prototypes sampled from a VGG19-based ProtoPNet [4]. In each class, the left prototype focuses on object features while the right one captures background." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.206, + 0.793, + 0.22 + ], + "angle": 0, + "content": "The major contributions of this work are:" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.228, + 0.891, + 0.303 + ], + "angle": 0, + "content": "1. We provide the first study that makes an analogy between the prototype learning from ProtoPNet and support vector learning from SVM, where we propose support (i.e., hard-to-learn) prototypes that can improve classification accuracy and interpretability." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.31, + 0.892, + 0.386 + ], + "angle": 0, + "content": "2. We present a new ST-ProtoPNet method to exploit both support and trivial prototypes for interpretable image classification, where the two sets of prototypes can provide complementary information to improve classification accuracy." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.393, + 0.892, + 0.454 + ], + "angle": 0, + "content": "3. We conduct extensive experiments on three benchmarks, showing that our ST-ProtoPNet outperforms current state-of-the-art (SOTA) methods in terms of classification accuracy and interpretability." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.228, + 0.892, + 0.454 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.55 + ], + "angle": 0, + "content": "In our experiments, we also demonstrate that the trivial and support prototypes have different characteristics, where the trivial prototypes tend to focus on both local parts of the visual object of interest and the background, while the support prototypes mainly focus on object parts belonging to the visual class of interest." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.566, + 0.64, + 0.581 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.763, + 0.607 + ], + "angle": 0, + "content": "2.1. Classification Interpretability" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The interpretation of classification results produced by deep neural networks can be achieved by a variety of post-hoc explanation techniques, e.g., explanatory surrogates [34, 56, 44], counterfactual examples [15, 46, 19], and saliency visualisation [45, 55, 59, 43]. Alternatively, prototype-based interpretable techniques can access the model's inner computations. ProtoPNet [4] is the original work that uses class-specific prototypes for interpretable image classification. Similar to ProtoPNet, TesNet [53] constructs class-specific transparent basis concepts on Grassmann manifold for the interpretable classification. Derived from ProtoPNet, Deformable ProtoPNet [11] employs spatially-flexible and deformable prototypes to adaptively capture meaningful object features. In ProtoPShare [42], a data-dependent merge-pruning method is presented to share prototypes among classes, which can reduce the number of prototypes used for classification. In contrast, ProtoPool [41] introduces a fully differentiable prototype assignment strategy to reduce the number of prototypes. In" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "1The network has an input layer of 2 nodes, a hidden layer of 256 nodes (activated by tanh), and an output layer of 2 nodes (activated by sigmoid)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2063" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.198 + ], + "angle": 0, + "content": "Proto2Proto [20], a knowledge distillation method is designed to transfer interpretability from a teacher ProtoPNet to a shallow student ProtoPNet. ProtoTree [35] integrates the prototype learning into a binary neural decision tree that can explain its predictions by tracing a decision path throughout the tree. ViT-NeT [24] further establishes the prototype neural tree structure on visual transformers [12]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.468, + 0.304 + ], + "angle": 0, + "content": "Because of the ability to self-explain classification results, prototype-based interpretability (e.g., ProtoPNet) has been widely utilised not only in the computer vision applications above, but also in medical imaging [2, 22, 51] and face recognition [48]. However, an open question faced by these methods is if the prototypes being learned are the ideal ones in terms of classification and interpretability." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.315, + 0.411, + 0.331 + ], + "angle": 0, + "content": "2.2. SVM vs Prototype-based Classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.468, + 0.639 + ], + "angle": 0, + "content": "To better understand the role of prototypes, we consider the support vector machine (SVM) [7] classifier that finds support vectors to represent classes. More specifically, SVM learns the maximum-margin classifier defined by a classification boundary that maximises the distance to the closest training samples, which are the support vectors for the classes. The testing of SVM consists of computing a weighted similarity between a testing sample and the support vectors. It is interesting to note that the testing of prototype-based classifiers is also based on measuring the similarity between a testing image and a set of class-specific prototypes learned from the training process. Although the testing of SVM and prototype-based classifiers are similar, their training procedures are different. First, the training of a prototype-based classifier learns a fixed number of prototypes [4, 11], while the SVM classifier learns to weight a variable number of support vectors from the training set. Second, in prototype-based classifiers, the learned prototypes tend to be far from the classification boundary, which is contrary to the SVM training objective mentioned above." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.468, + 0.791 + ], + "angle": 0, + "content": "The study of deep learning methods from an SVM theoretical perspective is a rich area of research [9, 38, 6], but there are many practical questions that need to be addressed, e.g., how to scale the kernel computation for large-scale datasets, how to shorten the training process [38], and how to integrate deep-learning features with the learning of the SVM classifier. In this paper, our focus is on adapting the learning of ProtoPNet's prototypes to make them similar to SVM's support vectors, by forcing prototypes to be as close as possible to the classification boundary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.803, + 0.402, + 0.818 + ], + "angle": 0, + "content": "2.3. Interpretable Ensemble Classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Ensemble classification [10] is a classical machine learning approach that combines the results from multiple classifiers, with the goals of improving learning generalisation and classification calibration. The use of interpretable ensemble strategy has been explored in [4, 53, 35, 11, 41]," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "which is achieved by summing the classification logits of multiple prototype-based classifiers (e.g., ProtoPNETs trained with different CNN backbones). In this work, we propose an interpretable ensemble classification by combining the predictions of two ProtoPNETs with highly distinctive prototypes (i.e., support and trivial prototypes), which is different from previous studies where the type of prototypes produced by each classifier is very similar given that the same training objective is used for each classifier." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.238, + 0.638, + 0.254 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.257, + 0.892, + 0.669 + ], + "angle": 0, + "content": "We assume to have a training set \\(\\mathcal{D} = \\{(\\mathbf{x}_n,\\mathbf{y}_n)\\}_{n = 1}^{|\\mathcal{D}|}\\) where \\(\\mathbf{x}\\in \\mathcal{X}\\subset \\mathbb{R}^{H\\times W\\times R}\\) is an image with \\(R\\) colour channels and \\(\\mathbf{y}\\in \\mathcal{Y}\\subset \\{0,1\\} ^C\\) is a one-hot vector representation of the image class label. The interpretable ProtoPNet [4, 11] is trained to learn a set of prototypes \\(\\mathcal{P} = \\{\\mathbf{p}_m\\}_{m = 1}^M\\) , where \\(\\mathbf{p}_m\\in \\mathbb{R}^{\\rho_1\\times \\rho_2\\times D}\\) , with each of the \\(C\\) classes containing \\(M / C\\) prototypes. Without loss of generality, we assume \\(\\rho_{1} = \\rho_{2} = 1\\) , but the extension to general values is trivial. A typical ProtoPNet comprises four components: a CNN backbone, add-on layers, a prototype layer, and a fully connected (FC) layer. An input image \\(\\mathbf{x}\\) is fed to the CNN backbone \\(f_{\\theta}:X\\to \\mathcal{F}\\) (parameterised by \\(\\theta \\in \\Theta\\) , where \\(\\mathcal{F}\\subset \\mathbb{R}^{H\\times \\bar{W}\\times \\bar{D}}\\) ) and then passed on to the add-on layers, denoted by \\(f_{\\omega}:F\\rightarrow V\\) (parameterised by \\(\\omega \\in \\Omega\\) ), to produce a feature map \\(\\mathbf{V}\\in \\mathcal{V}\\subset \\mathbb{R}^{\\bar{H}\\times \\bar{W}\\times D}\\) . The prototype layer computes the similarity between the feature map \\(\\mathbf{V}\\) and the \\(MD\\) dimensional prototypes \\(\\{\\mathbf{p}_m\\}_{m = 1}^M\\) to generate \\(M\\) similarity maps \\(\\mathbf{S}_m^{(i,j)} = \\mathrm{sim}(\\mathbf{V}(i,j,:),\\mathbf{p}_m)\\) , where \\(i\\in \\{1,\\dots,\\bar{H}\\}\\) \\(j\\in \\{1,\\ldots ,\\bar{W}\\}\\) , and \\(\\mathrm{sim}(\\cdot ,\\cdot)\\) represents a similarity measure, e.g., cosine similarity [11] and projection metric [53]. The prototype layer outputs \\(M\\) similarity scores from maxpooling \\(S = \\left\\{\\max_{i\\in \\{1,\\dots,\\bar{H}\\},j\\in \\{1,\\dots,\\bar{W}\\}}\\mathbf{S}_m^{(i,j)}\\right\\}_{m = 1}^M\\) , which are fed to the FC layer \\(f_{\\phi}:S\\to \\Delta\\) parameterised by \\(\\phi \\in \\Phi\\) to produce the classification prediction \\(\\hat{\\mathbf{y}}\\in \\Delta \\subset [0,1]^C\\) where \\(\\Delta\\) denotes the probability space for \\(C\\) classes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.641, + 0.695 + ], + "angle": 0, + "content": "4. ST-ProtoPNet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.901 + ], + "angle": 0, + "content": "An overview of our proposed ST-ProtoPNet method is illustrated in Fig. 4, which comprises a shared CNN backbone \\( f_{\\theta}(\\cdot) \\), two interpretable ProtoPNet classification branches, namely: 1) the support ProtoPNet represented by add-on layers \\( f_{\\omega^{(s)}}(\\cdot) \\), prototype layer with support prototypes \\( \\mathcal{P}^{(s)} \\), and FC layer \\( f_{\\phi^{(s)}}(\\cdot) \\) which outputs the classification probability distribution \\( \\hat{\\mathbf{y}}^{(s)} \\in \\Delta \\); and 2) the trivial ProtoPNet branch with its add-on layers \\( f_{\\omega^{(t)}}(\\cdot) \\), trivial prototypes \\( \\mathcal{P}^{(t)} \\), and FC layer \\( f_{\\phi^{(t)}}(\\cdot) \\) that generates probability predictions \\( \\hat{\\mathbf{y}}^{(t)} \\in \\Delta \\). The final classification is obtained by combining the classification logits from both the support and trivial ProtoP nets. In our implementation, we construct the support and trivial ProtoPNet mainly based on the orig" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2064" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.089, + 0.473, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.242, + 0.47, + 0.27 + ], + "angle": 0, + "content": "Figure 4. The architecture of our proposed ST-ProtoPNet method for the interpretable image classification." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.282, + 0.445, + 0.297 + ], + "angle": 0, + "content": "inal ProtoPNet [4] and TesNet [53], as explained below." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.306, + 0.262, + 0.323 + ], + "angle": 0, + "content": "4.1. Support ProtoPNet" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.33, + 0.47, + 0.39 + ], + "angle": 0, + "content": "The support ProtoPNet is designed to produce support prototypes that are as close as possible to the classification boundary, as shown in Fig. 1(b) and 2(b). The loss function to optimise the support ProtoPNet branch is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.4, + 0.469, + 0.472 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\theta^ {*}, \\omega^ {(s) *}, \\mathcal {P} ^ {(s) *}, \\phi^ {(s) *} = \\\\ \\arg \\min _ {\\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}} \\sum_ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D}} \\ell_ {s p t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}). \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.484, + 0.469, + 0.515 + ], + "angle": 0, + "content": "The loss for each training sample \\((\\mathbf{x},\\mathbf{y})\\in \\mathcal{D}\\) in Eq. (1) above is represented by:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.524, + 0.475, + 0.644 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\ell_ {s p t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}) = \\ell_ {c e} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}) \\\\ - \\lambda_ {1} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) \\\\ + \\lambda_ {2} \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) \\\\ - \\lambda_ {3} \\ell_ {c l s} (\\mathcal {P} ^ {(s)}) \\\\ + \\lambda_ {4} \\ell_ {o r t} (\\mathcal {P} ^ {(s)}), \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.657, + 0.469, + 0.732 + ], + "angle": 0, + "content": "where \\(\\lambda_{1},\\lambda_{2},\\lambda_{3}\\), and \\(\\lambda_{4}\\) are hyper-parameters to balance each term, \\(\\ell_{ce}(\\cdot)\\) denotes the cross-entropy classification loss, \\(\\ell_{ct}(\\cdot)\\) and \\(\\ell_{sp}(\\cdot)\\) represent the clustering and separation losses, respectively, which are introduced to regularise the ProtoPNet's training, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.741, + 0.469, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) = \\max _ {\\mathbf {p} \\in \\mathcal {P} _ {\\mathbf {y}} ^ {(s)}} \\max _ {\\mathbf {v} \\in \\mathbf {V} ^ {(s)}} \\sin (\\mathbf {v}, \\mathbf {p}), (3) \\\\ \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) = \\max _ {\\mathbf {p} \\notin \\mathcal {P} _ {\\mathbf {y}} ^ {(s)}} \\max _ {\\mathbf {v} \\in \\mathbf {V} ^ {(s)}} \\operatorname {s i m} (\\mathbf {v}, \\mathbf {p}), (4) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{V}^{(s)} = f_{\\omega^{(s)}}(f_{\\theta}(\\mathbf{x}))\\) is the feature map extracted from the input image \\(\\mathbf{x}\\), \\(\\mathbf{v}\\) represents one of the \\(\\bar{H} \\times \\bar{W}\\) feature vectors in \\(\\mathbf{V}^{(s)}\\) obtained by matrix vectorisation, \\(\\mathbf{p}\\) is a normalised prototype (i.e., unit vector) in \\(\\mathcal{P}^{(s)}\\), \\(\\sin (\\cdot, \\cdot)\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.182 + ], + "angle": 0, + "content": "is one of the similarity functions defined in Sec. 3, and \\(\\mathcal{P}_{\\mathbf{y}}^{(s)}\\) denotes the set of prototypes of class \\(\\mathbf{y}\\). The clustering loss in Eq. (3) and separation loss in Eq. (4) aim to learn a meaningful feature space in which the image features of a certain class are clustered around the prototypes of the class, and also well separated from those of other classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.303 + ], + "angle": 0, + "content": "As mentioned in Sec. 1, the effect of the clustering and separation losses above tend to push the prototypes of different classes as far as possible from the classification boundary, resulting in trivial prototypes, as displayed in Fig. 1(a) and Fig. 2(a). In order to learn the proposed support prototypes, we introduce the following novel closeness loss \\(\\ell_{cls}\\) to explicitly enforce the prototypes of different classes to be close to each other, which is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.313, + 0.892, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\ell_ {c l s} \\left(\\mathcal {P} ^ {(s)}\\right) = \\sum_ {c _ {1} = 1} ^ {C - 1} \\sum_ {c _ {2} = c _ {1} + 1} ^ {C} \\min _ {\\mathbf {p} _ {m} \\in \\mathcal {P} _ {c _ {1}}, \\mathbf {p} _ {n} \\in \\mathcal {P} _ {c _ {2}}} \\mathbf {p} _ {m} ^ {\\top} \\mathbf {p} _ {n}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.562 + ], + "angle": 0, + "content": "During training, this closeness loss \\(\\ell_{cls}\\) maximises the pair-wise prototype similarity, in the form of dot product \\(\\mathbf{p}_m^\\top \\mathbf{p}_n\\) between different classes in Eq. (5) above, with the goal of pulling the prototypes close to the classification boundary. On the one hand, as the prototypes move gradually towards the classification boundary, they are able to capture harder visual features from training samples. On the other hand, since the prototypes are located near the classification boundary, they can put pressure on the support ProtoPNet's feature learning (i.e., enforce it to learn highly discriminative feature representations for accurate classification), which is beneficial to extract more meaningful semantic information from training samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.713 + ], + "angle": 0, + "content": "Ideally, each prototype of a class should focus on unique object parts of the training images (e.g., head, tail, and claw of birds), so that the prototypes can represent rich and diverse visual patterns. However, there is no particular constraints to guarantee such prototype diversity and the issue of prototype duplication [11] often occurs in the ProtoPNet family of models. To encourage the intra-class prototype diversity, we employ an orthonormality loss [53] so that prototypes within a class can represent dissimilar visual patterns of training samples, which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.724, + 0.892, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\ell_ {o r t} \\left(\\mathcal {P} ^ {(s)}\\right) = \\sum_ {c = 1} ^ {C} \\left\\| \\mathbf {P} _ {c} ^ {\\top} \\mathbf {P} _ {c} - \\mathbf {I} _ {M / C} \\right\\| _ {F} ^ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.776, + 0.892, + 0.84 + ], + "angle": 0, + "content": "where \\(\\| \\cdot \\| _F^2\\) represents Frobenius norm, \\(\\mathbf{P}_c\\in D\\times \\mathbb{R}^{(M / C)}\\) stands for a matrix composed of the prototypes of class \\(c\\) (prototypes in each column of \\(\\mathbf{P}_c\\) are normalised), and \\(\\mathbf{I}_{M / C}\\) is an identity matrix of size \\(M / C\\times M / C\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.673, + 0.862 + ], + "angle": 0, + "content": "4.2. Trivial ProtoPNet" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "As described in Sec. 4.1, the support ProtoPNet is developed to learn support (i.e., hard-to-learn) prototypes by" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "2065" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.198 + ], + "angle": 0, + "content": "forcing them to be close to the classification boundary. Considering that training samples contain not only hard visual features but also important easy ones that the support prototypes cannot completely capture, we propose to also learn trivial prototypes to provide complementary classification information, and exploit both the support and trivial prototypes for improved interpretable classification." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.198, + 0.468, + 0.226 + ], + "angle": 0, + "content": "The loss objective to optimise the trivial ProtoPNet branch is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.233, + 0.468, + 0.303 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\theta^ {*}, \\omega^ {(t) *}, \\mathcal {P} ^ {(t) *}, \\phi^ {(t) *} = \\\\ \\arg \\min _ {\\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}} \\sum_ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D}} \\ell_ {t r v} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}). \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.312, + 0.468, + 0.341 + ], + "angle": 0, + "content": "The loss for each training image \\((\\mathbf{x},\\mathbf{y})\\in \\mathcal{D}\\) in Eq. (7) above is represented by:" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.349, + 0.468, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\ell_ {t r v} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}) = \\ell_ {c e} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}) \\\\ - \\lambda_ {1} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {2} \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {3} \\ell_ {d s c} (\\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {4} \\ell_ {\\text {o r t}} (\\mathcal {P} ^ {(t)}), \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.476, + 0.468, + 0.536 + ], + "angle": 0, + "content": "where \\(\\lambda_{1},\\lambda_{2},\\lambda_{3}\\) and \\(\\lambda_{4}\\) are hyper-parameters, \\(\\ell_{ce}(\\cdot)\\) is the cross-entropy loss, the clustering loss \\(\\ell_{ct}\\), separation loss \\(\\ell_{sp}\\), and orthonormality loss \\(\\ell_{ort}\\) are the same as in the support ProtoPNet defined in Eq. (3), (4) and (6), respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.468, + 0.641 + ], + "angle": 0, + "content": "The trivial ProtoPNet targets the learning of easy prototypes that are far from the classification boundary and have a good discrimination ability. To help achieve this, we introduce a new discrimination loss \\(\\ell_{dsc}\\) to facilitate the interclass separability between prototypes of different classes. This is formulated by minimising the pair-wise prototype similarities of different classes, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.649, + 0.468, + 0.69 + ], + "angle": 0, + "content": "\\[\n\\ell_ {d s c} \\left(\\mathcal {P} ^ {(t)}\\right) = \\sum_ {c _ {1} = 1} ^ {C - 1} \\sum_ {c _ {2} = c _ {1} + 1} ^ {C} \\max _ {\\mathbf {p} _ {m} \\in \\mathcal {P} _ {c _ {1}}, \\mathbf {p} _ {n} \\in \\mathcal {P} _ {c _ {2}}} \\mathbf {p} _ {m} ^ {\\top} \\mathbf {p} _ {n}. \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.274, + 0.713 + ], + "angle": 0, + "content": "4.3. Training and Testing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Training. Following the training strategies in [4, 11], the training procedure of our ST-ProtoPNet consists of 3 stages: 1) optimisation of the CNN backbone, add-on layers, and prototype layer, using a fixed FC layer initialised with \\(+1.0\\) and -0.5 for correct and incorrect connection weights, respectively. A warm-up of 5 epochs is involved in this stage by updating only the parameters of add-on layers and prototype layer, with a frozen pre-trained CNN backbone. 2) prototype projection by updating each prototype with its nearest latent training image patch; and 3) optimisation of the FC layer, with an additional \\(L_{1}\\) regularisation on the incorrect connection weights (initially fixed at" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "-0.5). In each stage, we alternate the optimisation of each branch of the ST-ProtoPNet between mini-batches. Notice that our method only brings marginal extra model parameters, computational complexity, and training time since the CNN backbone is shared and optimised by both branches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.172, + 0.892, + 0.248 + ], + "angle": 0, + "content": "Testing. To exploit the complementary results from both branches of ST-ProtoPNet, its final classification is obtained from the summed logits predicted by the two branches. It is worth noticing that this ensemble strategy introduces no loss of interpretability but improved accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.272, + 0.632, + 0.289 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.892, + 0.478 + ], + "angle": 0, + "content": "We perform experiments on three fine-grained classification benchmark datasets: CUB-200-2011 [50], Stanford Cars [27], and Stanford Dogs [21]. To achieve fair comparison, we follow previous studies [4, 53] by applying offline data augmentations (e.g., random rotation, skew, shear, and left-right flip) on the cropped CUB and cropped Cars datasets (using the bounding boxes provided). We also validate our method on the full (i.e., uncropped) CUB and Dogs datasets, and employ the same online data augmentation methods (e.g., random affine transformation and left-right flip) as used in Deformable ProtoPNet [11]. All images are resized to \\(224 \\times 224\\) pixels as network input." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.499, + 0.706, + 0.515 + ], + "angle": 0, + "content": "5.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The proposed ST-ProtoPNet method is evaluated on the following CNN architectures: VGG-16, VGG-19, ResNet-34, ResNet-50, ResNet-152, DenseNet-121, and DenseNet-161. All CNN backbones are pre-trained on ImageNet [8], except for ResNet-50, which is pre-trained on iNaturalist [49] for the experiment on full CUB [11]. The add-on layers include two \\( 1 \\times 1 \\) convolutional layers. For simplicity, we utilise the same prototype dimension \\( D = 64 \\) for all CNN backbones on the three datasets. For cropped CUB and Cars datasets, following [53], we use 10 prototypes (5 support and 5 trivial) per class and the projection metric in the similarity function \\( \\mathrm{sim}(\\cdot ,\\cdot) \\). In full CUB and Dogs datasets, to ensure comparison fairness with Deformable ProtoPNet [11] that uses \\( 102 \\times 2 \\) (full CUB) and \\( 103 \\times 3 \\) (full Dogs) deformable prototypes per class, we utilise the same total number of prototypes, i.e., \\( 401 \\times 1 \\) (20 support and 20 trivial) for full CUB and \\( 901 \\times 1 \\) (45 support and 45 trivial) for full Dogs. Also, we employ the cosine similarity in \\( \\mathrm{sim}(\\cdot ,\\cdot) \\) and obtain \\( 14 \\times 14 \\) (\\( \\bar{H} = \\bar{W} = 14 \\)) feature maps by upsampling the original \\( 7 \\times 7 \\) feature maps via a bi-linear interpolation step, as in [11]. Following previous prototype-based methods [4, 53, 11], we set \\( \\lambda_{1} = 0.8 \\), \\( \\lambda_{2} = 0.48 \\) and 0.08 for the support and trivial ProtoPNet branches respectively, \\( \\lambda_{4} = 0.001 \\). We choose \\( \\lambda_{3} = 1.0 \\) with an ablation provided in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2066" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.322, + 0.108 + ], + "angle": 0, + "content": "5.2. Interpretability Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.111, + 0.468, + 0.172 + ], + "angle": 0, + "content": "Rather than performing user-based evaluations [60, 41], whose results are often subjective and difficult to reproduce [54], we leverage the annotated object masks to measure interpretability based on the following metrics:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.173, + 0.468, + 0.218 + ], + "angle": 0, + "content": "Content Heatmap (CH) [37]: quantifies the percentage of an activation heatmap that lies within the annotated mask. Hence, we expect this metric to be high." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.219, + 0.468, + 0.295 + ], + "angle": 0, + "content": "Outside-Inside Relevance Ratio (OIRR) [29]: calculates the ratio of mean activation outside the object to mean activation inside the object. A low OIRR indicates a method relies more on the object region and less on the context to support its decision, we thus anticipate OIRR to be low." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.295, + 0.468, + 0.342 + ], + "angle": 0, + "content": "Intersection over Union (IoU) [5]: measures the mean IoU score, where a threshold of 0.5 is applied on the min-max normalised heatmap to select foreground objects." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.342, + 0.468, + 0.417 + ], + "angle": 0, + "content": "Deletion AUC (DAUC) [36]: estimates a decrease in the probability of the predicted class as more and more important/activated pixels are removed. The area under the probability curve is defined as DAUC. Consequently, a sharp drop and a low DAUC mean better interpretation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.418, + 0.468, + 0.538 + ], + "angle": 0, + "content": "Average Inter-class Prototype Distance (AIPD), Average Inter-class Feature Distance (AIFD): we had earlier stated that support prototypes of different classes should be close to each other and trivial prototypes should be far from each other. Thus, we compute the average inter-class cosine distance for prototypes and their nearest local feature representations, respectively. We expect AIPD \\(<\\) AIFD for support ProtoPNet and AIPD \\(>\\) AIFD for trivial ProtoPNet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.547, + 0.32, + 0.563 + ], + "angle": 0, + "content": "5.3. Classification Performance" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.568, + 0.468, + 0.884 + ], + "angle": 0, + "content": "Table 1 presents the classification accuracy (across 5 runs) of our proposed ST-ProtoPNet on cropped CUB and cropped Cars, where the Baseline is represented by non-interpretable black-box CNN models. As can be seen, our ST-ProtoPNet outperforms other competing methods across all backbones for the task of bird species classification. Also, our method achieves the best results for the car model identification task when using VGG and DenseNet architectures as the CNN backbone. In particular, our VGG19-based ST-ProtoPNet reaches an average accuracy of \\(83.2\\%\\) and \\(91.7\\%\\) on CUB and Cars, respectively, surpassing other methods with the most improvements across all backbones. Moreover, the support ProtoPNet generally performs better than methods utilising only trivial prototypes (e.g., ProtoPNet, TesNet, and Trivial ProtoPNet), showing the importance of learning support prototypes for the interpretable classification. It is worth noting that our ST-ProtoPNet produces superior performance over the support ProtoPNet method, indicating that both support and trivial prototypes are useful and can provide complementary information for achieving accurate and interpretable classification." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Table 2 shows the classification results on full CUB and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.333 + ], + "angle": 0, + "content": "full Dogs. In both datasets, the classification accuracy of the original ProtoPNet method is generally worse than the non-interpretable counterpart (Baseline) for many CNN backbones. On the other hand, the accuracy by the trivial ProtoPNet and support ProtoPNet are substantially better than those by Baseline, ProtoPNet, and Deformable ProtoPNet. However, our ST-ProtoPNet achieves more significant performance gains and exhibits the best accuracy across most backbones, particularly when using a large number of prototypes (i.e., \\(401 \\times 1\\) prototypes per class for CUB and \\(901 \\times 1\\) prototypes per class for Dogs), demonstrating the effectiveness of utilising both the trivial and support prototypes for the interpretable image classification. Additionally, when using a smaller number of prototypes, i.e., \\(101 \\times 1\\) prototypes per class, our ST-ProtoPNet still has competitive classification accuracy across multiple backbones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.892, + 0.53 + ], + "angle": 0, + "content": "We further compare our ST-ProtoPNet with other deep-learning methods that can provide different levels of interpretability on CUB, with results shown in Table 3, where * and ** denote ensemble of models with different backbones. As evident, an ensemble of three ST-ProtoPNETs can achieve high accuracy (87.9% on cropped images, 88.2% on full images), outperforming competing methods that are also based on an ensemble of three models (e.g., ProtoTree, TesNet, and ProtoPool). Moreover, the ensemble of five STProtoPNETs outperforms all other competing methods and obtains the best classification accuracy of 88.1% and 88.4% on cropped and full CUB images, respectively. More results on Cars and Dogs are given in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.538, + 0.755, + 0.554 + ], + "angle": 0, + "content": "5.4. Interpretability Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.815 + ], + "angle": 0, + "content": "We assess the model interpretability on full CUB using the annotated bird segmentation mask\\(^2\\). Quantitative results on the test set are given in Table 4, where all methods are based on the VGG19 backbone. We use GradCAM [43] for the non-interpretable baseline. For prototype-based methods, we average the activation map of all prototypes of a class to compute the metrics. We can see our proposed support ProtoPNet can effectively improve the interpretableity in all measures, showing the interpretations produced by our support prototypes are more likely to be object-dependent and focus less on context cues. Also, our ST-ProtoPNet method shows better interpretable results than the support ProtoPNet in terms of CH, OIRR, and DAUC. Compared with the original ProtoPNet [4], our ST-ProtoPNet obtains significant interpretability improvements. We show some example activation maps in the supplementary material, and an experiment with prototype pruning is also provided." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.815, + 0.892, + 0.876 + ], + "angle": 0, + "content": "Table 5 presents the computed AIPD and AIFD for the support and trivial ProtoPNet on cropped CUB, using VGG19 and ResNet34 as CNN backbones. As evident, the AIPD is indeed smaller than AIFD for the support ProtoP-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.733, + 0.9 + ], + "angle": 0, + "content": "\\(^{2}\\)http://www.vision.caltech.edu/datasets/" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2067" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.183 + ], + "angle": 0, + "content": "
MethodCUBCars
VGG16VGG19ResNet34ResNet152Dense121Dense161VGG16VGG19ResNet34ResNet152Dense121Dense161
Baseline73.3 ± 0.274.7 ± 0.482.2 ± 0.380.8 ± 0.481.8 ± 0.182.1 ± 0.287.3 ± 0.488.5 ± 0.392.6 ± 0.392.8 ± 0.492.0 ± 0.392.5 ± 0.3
ProtoPNet [4]77.2 ± 0.277.6 ± 0.278.6 ± 0.179.2 ± 0.379.0 ± 0.280.8 ± 0.388.3 ± 0.289.4 ± 0.288.8 ± 0.188.5 ± 0.387.7 ± 0.189.5 ± 0.2
TesNet [53]81.3 ± 0.281.4 ± 0.182.8 ± 0.182.7 ± 0.284.8 ± 0.284.6 ± 0.390.3 ± 0.290.6 ± 0.290.9 ± 0.292.0 ± 0.291.9 ± 0.392.6 ± 0.3
Trivial ProtoPNet80.8 ± 0.281.2 ± 0.282.5 ± 0.283.1 ± 0.383.9 ± 0.384.6 ± 0.390.1 ± 0.290.7 ± 0.291.1 ± 0.291.5 ± 0.291.4 ± 0.392.4 ± 0.3
Support ProtoPNet81.7 ± 0.281.8 ± 0.383.0 ± 0.183.6 ± 0.284.7 ± 0.285.2 ± 0.390.9 ± 0.290.8 ± 0.291.0 ± 0.291.8 ± 0.291.7 ± 0.292.7 ± 0.3
ST-ProtoPNet (ours)82.9 ± 0.283.2 ± 0.283.5 ± 0.184.1 ± 0.285.4 ± 0.286.1 ± 0.291.1 ± 0.291.7 ± 0.291.4 ± 0.192.0 ± 0.292.3 ± 0.392.7 ± 0.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.188, + 0.891, + 0.202 + ], + "angle": 0, + "content": "Table 1. Classification accuracy (%) on cropped CUB-200-2011 and Stanford Cars by competing methods using different CNN backbones." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.213, + 0.891, + 0.331 + ], + "angle": 0, + "content": "
Method# PrototypeCUB# PrototypeDogs
VGG16VGG19ResNet34ResNet50ResNet152Dense121Dense161VGG16VGG19ResNet34ResNet50ResNet152Dense121Dense161
Baseline-70.971.376.078.779.278.280.0-75.677.381.183.185.281.984.1
ProtoPNet [4]1×1p, 10pc70.372.672.481.174.374.075.41×1p, 10pc70.773.673.476.476.272.077.3
ProtoPNet [4]1×1p, 40pc72.974.274.184.876.076.678.51×1p, 90pc73.975.376.178.179.775.478.8
TesNet [53]1×1p, 10pc75.877.576.286.579.080.279.61×1p, 10pc74.377.180.182.483.880.383.8
TesNet [53]1×1p, 40pc77.679.276.587.380.180.981.31×1p, 90pc78.579.681.283.384.582.185.2
Deformable ProtoPNet [11]2×2p, 10pc75.776.076.886.479.679.081.23×3p, 10pc75.877.980.682.286.580.783.7
Trivial ProtoPNet1×1p, 40pc80.079.577.587.280.881.182.11×1p, 90pc78.680.482.685.087.082.385.9
Support ProtoPNet1×1p, 40pc80.480.078.487.580.281.582.41×1p, 90pc79.080.683.085.187.382.686.2
ST-ProtoPNet (ours)1×1p, 10pc76.877.677.486.678.778.680.61×1p, 10pc74.277.280.884.085.379.484.4
ST-ProtoPNet (ours)1×1p, 40pc81.080.278.288.081.281.882.71×1p, 90pc79.180.983.485.787.282.986.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.334, + 0.891, + 0.362 + ], + "angle": 0, + "content": "Table 2. Classification accuracy (%) on full CUB-200-2011 and Stanford Dogs datasets by competing approaches using different CNN backbones, where \\( {\\rho }_{1} \\times {\\rho }_{2}\\mathrm{p} \\) denotes the spatial shape of prototypes and \\( k\\mathrm{{pc}} \\) represents \\( k \\) prototypes per class." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.376, + 0.466, + 0.588 + ], + "angle": 0, + "content": "
Interpretability levelMethodAccuracy (%)
NoneB-CNN [32]85.1 (b)84.1 (f)
Object-level attentionCAM [59]70.5 (b)63.0 (f)
CSG [31]82.6 (b)78.5 (f)
Part-level attentionPA-CNN [26]82.8 (b)-
MG-CNN [52]83.0 (b)81.7 (f)
MA-CNN [57]-86.5 (f)
RA-CNN [14]-85.3 (f)
TASN [58]-87.0 (f)
Part-level attention + PrototypesRegion [17]81.5 (b)80.2 (f)
ProtoPNet* [4]84.8 (b)81.1 (f)
ProtoTree* [35]-86.6 (f)
TesNet* [53]86.2 (b)83.5 (f)
ProtoPool* [41]87.5 (b)-
ST-ProtoPNet* (ours)87.9 (b)88.2 (f)
ProtoTree** [35]-87.2 (f)
Deformable ProtoPNet** [11]-87.8 (f)
ProtoPool** [41]87.6 (b)-
ST-ProtoPNet** (ours)88.1 (b)88.4 (f)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.59, + 0.47, + 0.646 + ], + "angle": 0, + "content": "Table 3. Classification accuracy and interpretability level of different methods on CUB-200-2011. \"b\" and \"f\" denote the model is trained and tested on cropped and full images, respectively. *: Ensemble of three models. **: Ensemble of five models." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.658, + 0.466, + 0.707 + ], + "angle": 0, + "content": "
MetricGradCAM [43]ProtoPNet [4]TesNet [53]DefProto [11]TrvProtoSptProtoST-Proto
CH (%, ↑)52.4648.6659.3852.0963.0563.8766.43
IoU (%, ↑)39.9138.0336.9240.7737.7442.0441.05
OIRR (%, ↓)37.0137.2638.9728.6834.4828.6928.09
DAUC (%, ↓)7.017.395.865.996.065.805.74
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.71, + 0.468, + 0.751 + ], + "angle": 0, + "content": "Table 4. Quantitative interpretability results on full CUB test set. DefProto = Deformable ProtoPNet, TrvProto = Trivial ProtoPNet, SptProto = Support ProtoPNet, ST-Proto = ST-ProtoPNet." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.769, + 0.469, + 0.845 + ], + "angle": 0, + "content": "Net while AIPD is larger than AIFD for the trivial ProtoP-Net. This result indicates that the support prototypes of different classes lie closer than their local feature representations and are more inclined to focus on visually similar (i.e., hard-to-learn) object parts of different classes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.852, + 0.283, + 0.868 + ], + "angle": 0, + "content": "5.5. Visualisation Analysis" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To explore the differences between the support and trivial prototypes, we select 5 categories of birds with visu" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.377, + 0.889, + 0.422 + ], + "angle": 0, + "content": "
VGG19ResNet34
SupportProtoPNetTrivialProtoPNetSupportProtoPNetTrivialProtoPNet
AIPDAIFDAIPDAIFDAIPDAIFDAIPDAIFD
0.72590.92640.99870.92320.65410.85731.0000.9481
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.426, + 0.892, + 0.467 + ], + "angle": 0, + "content": "Table 5. Average inter-class prototype distance (AIPD) and average inter-class feature distance (AIFD) for the support and trivial ProtoPNet trained on cropped CUB." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.475, + 0.892, + 0.786 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.79, + 0.892, + 0.845 + ], + "angle": 0, + "content": "Figure 5. The support (top) and trivial (bottom) prototypes from cropped CUB. In each pair, the first column shows the original image with a prototype marked in a yellow bounding box, the second column is the prototype's corresponding activation map." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "ally similar features from cropped CUB to train the support and trivial ProtoPNet methods, with the learned prototypes shown in Fig. 5. We notice the support prototypes can cap" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2068" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.27, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.089, + 0.468, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.197, + 0.47, + 0.268 + ], + "angle": 0, + "content": "Figure 6. T-SNE results of support and trivial prototypes. The prototypes and their nearest latent training features are marked with stars and dots, respectively. We show results before the prototype projection stage to better visualise the relation between the prototypes and features. Each colour represents a different class." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.281, + 0.47, + 0.538 + ], + "angle": 0, + "content": "ture subtle and fine visual features of different classes and they only focus on relevant bird parts, e.g., head and belly. This is reasonable since our algorithm is designed to produce prototypes that are as close as possible to each other, where the image prototypical parts should not only be discriminative but also share visually similar features among classes. By contrast, the trivial prototypes tend to focus not only on the relevant bird parts but also the background regions. For example, some trivial prototypes of the Laysan Albatross and Sooty Albatross classes capture the sea surface as they often appear with the sea background. We argue that this is because the trivial ProtoPNet may treat the background as an easy pattern to learn, focusing less on the object's visual parts of the class. In Fig. 6, we show the t-SNE result from the 5-category bird classification, where we note the support prototypes of different classes are located closer to each other, in comparison with the trivial prototypes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.471, + 0.782 + ], + "angle": 0, + "content": "Fig. 7 shows an example of the interpretable reasoning for our ST-ProtoPNet in classifying a testing bird image. As evident, each ProtoPNet branch calculates its own classification logits (weighted sum of similarity scores), which is then combined to generate the final prediction. Specifically, when classifying a Parakeet Auklet, the support prototypes are quite active on the bird's beak and belly. Meanwhile, the trivial prototypes have high activations on the bird's lower surface and neck. In this case, the support ProtoPNet obtains a relatively higher similarity score (22.925), compared with the trivial branch (20.313). Note that our ST-ProtoPNet exploits both the support and trivial prototypes to capture much richer representations of the object from different perspectives, which enables the realisation of complementary interpretations. More examples on Cars and Dogs are shown in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.79, + 0.231, + 0.807 + ], + "angle": 0, + "content": "5.6. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.9 + ], + "angle": 0, + "content": "The closeness and discrimination losses. To validate the effectiveness of our proposed closeness loss in Eq. (5) and discrimination loss in Eq. (9), we first conduct ablation studies on full CUB and full Dogs by using ResNet50 and ResNet34 as the CNN backbone, respectively. Results are listed in Table 6. We can observe that both the close-" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.892, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.279, + 0.892, + 0.307 + ], + "angle": 0, + "content": "Figure 7. An example of the interpretable reasoning of our STProtoPNet for classifying a testing Parakeet Auklet image." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.317, + 0.89, + 0.382 + ], + "angle": 0, + "content": "
MethodlctlsplortldscclsAccuracy (%)
CUBDogs
Baseline✓✓✓86.580.9
Trivial ProtoPNet✓✓✓✓87.282.6
Support ProtoPNet✓✓✓✓87.583.0
ST-ProtoPNet (ours)✓✓✓✓✓88.083.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.385, + 0.892, + 0.428 + ], + "angle": 0, + "content": "Table 6. Ablation analysis of the closeness loss \\(\\ell_{cls}\\) in Eq. (5) to learn support prototypes, and discrimination loss \\(\\ell_{dsc}\\) in Eq. (9) to learn trivial prototypes on full CUB-200-2011 and Stanford Dogs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.529 + ], + "angle": 0, + "content": "ness and discrimination losses can improve the accuracy, compared with the Baseline ProtoPNet method trained with only clustering, separation, and orthonormality losses. Note that the closeness loss introduces a larger performance improvement, which is attributed to the learning of support (i.e., hard-to-learn) prototypes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.893, + 0.832 + ], + "angle": 0, + "content": "Combining Support and Trivial Prototypes. We also investigate the importance of integrating the two complementary sets of support and trivial prototypes for improved classification. To achieve this, we first train a two-branch model where both branches learn the same type of prototypes and the final result is produced by the ensemble of them (Trivial Ensemble and Support Ensemble). Besides, for our ST-ProtoPNet, we also provide results of its individual branches (Trivial Branch and Support Branch). Table 7 shows the experimental results on cropped CUB. We can notice that combining the two different types of prototypes (ST-ProtoPNet) achieves superior performance over combining only the same type of prototypes (Trivial Ensemble and Support Ensemble), indicating that our performance improvements are from not only the ensemble strategy but also the two complementary sets of prototypes. Also, STProtoPNet indeed exhibits higher accuracy than its individual branches, further verifying that the results from the two branches are complementary, and the combination of them is effective to improve the final classification accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.837, + 0.771, + 0.853 + ], + "angle": 0, + "content": "6. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this paper, we proposed the ST-ProtoPNet to exploit both support (i.e., hard-to-learn) and trivial (i.e., easy-to-learn) prototypes, where the two sets of prototypes can pro" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2069" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.467, + 0.15 + ], + "angle": 0, + "content": "
MethodVGG16VGG19ResNet34ResNet152Dense121Dense161
Trivial Ensemble81.4 ± 0.381.8 ± 0.282.7 ± 0.283.2 ± 0.384.4 ± 0.285.0 ± 0.3
Support Ensemble82.1 ± 0.282.4 ± 0.383.0 ± 0.283.7 ± 0.384.8 ± 0.285.5 ± 0.2
Trivial Branch81.0 ± 0.281.1 ± 0.382.4 ± 0.282.9 ± 0.384.1 ± 0.384.8 ± 0.3
Support Branch81.5 ± 0.381.8 ± 0.382.8 ± 0.283.4 ± 0.384.6 ± 0.285.4 ± 0.2
ST-ProtoPNet (ours)82.9 ± 0.283.2 ± 0.283.5 ± 0.184.1 ± 0.285.4 ± 0.286.1 ± 0.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.155, + 0.468, + 0.184 + ], + "angle": 0, + "content": "Table 7. Ablation study of the combination of support and trivial prototypes for improved classification on cropped CUB-200-2011." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.198, + 0.47, + 0.455 + ], + "angle": 0, + "content": "vide complementary results for the interpretable image classification. Our ST-ProtoPNet is a general approach that can be easily applied to existing prototype-based interpretable models. One limitation for our method is that we empirically adopt the same number of support and trivial prototypes and the same total number of prototypes for each class. Considering the different learning difficulties and imbalanced training samples among classes in other real-world datasets, e.g., ImageNet [8], a better way to adaptively learn a flexible number of support and trivial prototypes is needed and deserves to be further investigated in our future work. Moreover, given that we mimic the behaviour of the support vectors of SVM classifier to obtain the support prototypes by forcing them to be as close as possible to the classification boundary, we plan to develop new methods to learn prototypes with gradient-based kernel techniques, e.g., neural tangent kernel [18] and path kernel [9]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.468, + 0.469, + 0.558 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by funding from the Australian Government under the Medical Research Future Fund - Grant MRFAI000090 for the Transforming Breast Cancer Screening with Artificial Intelligence (BRAIx) Project, and the Australian Research Council through grant FT190100525." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.575, + 0.173, + 0.59 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.601, + 0.469, + 0.643 + ], + "angle": 0, + "content": "[1] David Alvarez Melis and Tommi Jaakkola. Towards robust interpretability with self-explaining neural networks. Advances in Neural Information Processing Systems, 31, 2018." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.645, + 0.469, + 0.714 + ], + "angle": 0, + "content": "[2] Alina Jade Barnett, Fides Regina Schwartz, Chaofan Tao, Chaofan Chen, Yinhao Ren, Joseph Y Lo, and Cynthia Rudin. 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Note that it is possible to make an analogy between ProtoPNet and support vector machine (SVM) given that the classification from both methods relies on computing similarity with a set of training points (i.e., trivial prototypes in ProtoPNet, and support vectors in SVM). However, while trivial prototypes are located far from the classification boundary, support vectors are located close to this boundary, and we argue that this discrepancy with the well-established SVM theory can result in ProtoPNet models with inferior classification accuracy. In this paper, we aim to improve the classification of ProtoPNet with a new method to learn support prototypes that lie near the classification boundary in the feature space, as suggested by the SVM theory. In addition, we target the improvement of classification results with a new model, named ST-ProtoPNet, which exploits our support prototypes and the trivial prototypes to provide more effective classification. Experimental results on CUB-200-2011, Stanford Cars, and Stanford Dogs datasets demonstrate that ST-ProtoPNet achieves state-of-the-art classification accuracy and interpretability results. We also show that the proposed support prototypes tend to be better localised in the object of interest rather than in the background region. + +# 1. Introduction + +Deep convolutional neural networks (CNN) [28, 30, 16] have had remarkable achievements in various visual tasks, e.g., image recognition [16] and object detection [39]. Despite the excellent feature extraction and discrimination ability, CNNs are generally treated as black-box models due to their complex architectures, high-dimensional fea + +![](images/257bd92a30d8f5af85711e236e4dff2ed11d9626702f1b448d8f59560290594a.jpg) +(a) The learning of trivial prototypes + +![](images/a1ea86fd4b542a56641457d80ed380227ebd60185eb319f059d0b8ea5cfd5b1f.jpg) +(b) The learning of support prototypes (ours) +Feature vectors $\star \star$ Prototypes $\longrightarrow$ Clustering $\longrightarrow$ Separation $\longrightarrow$ Our loss Figure 1. The difference between the learning of trivial and support prototypes. (a) Trivial prototypes: the separation loss pushes the prototypes of different classes as far as possible from the classification boundary. (b) Support prototypes: our new closeness loss enforces the prototypes of different classes to be as close as possible to the classification boundary. + +ture spaces, and the enormous number of learnable parameters. Such lack of interpretability hinders their successful application in fields that require understandable and transparent decisions [40], e.g., disease diagnosis [47, 13], financial risk assessment [33], and autonomous driving [23]. + +Recently, increasing attention has been dedicated to the development of interpretable deep-learning models [25, 1, 4, 3]. A particularly interesting strategy is the prototype-based gray-box models, e.g., prototypical part network (ProtoPNet) [4, 11]. These methods are inherently interpretable since they can explain the model's decisions by showing image classification activation maps associated with a set of class-specific image prototypes. These prototypes are automatically learned from training samples, with classification score being computed by comparing testing image parts to the learned training prototypes. + +ProtoPNet [4] is trained to learn a classifier from a set of class-specific prototypes by minimising the cross-entropy classification loss and two additional regularisation losses, namely: 1) a clustering loss that pulls together training image patches to at least one prototype of its own class; and 2) a separation loss that pushes apart training image + +![](images/8b1f49f27fcb87fba8bda1f0e1a84ae8e80e212eeaec170eda5017ae335f2268.jpg) + +![](images/e6c9c967a42cc7841459842d5b59555a3388a6aefd22f4876413be3b7f3dc0c3.jpg) + +![](images/56a2b230d561a0ffe03f3bb41c3fcce406d8190b56468c789ce56153e063c9c1.jpg) + +![](images/6ecfa48dba624a9aaaff7f7c390c81c51c5a659c8077c2e3aa30386716df617d.jpg) +(a) Trivial Prototypes +Figure 2. Two-moon results. (a) Trivial prototypes and training samples in the feature (top) and data (bottom) spaces from the original ProtoPNet [4]. (b) Support prototypes and training samples in the feature (top) and data (bottom) spaces from our method. (c) Support vectors and training samples from a Radial Basis Function (RBF) kernel based SVM [7]. In (a) and (b), each prototype is projected onto the nearest training sample in the feature space. + +![](images/0fd7a59e21f7a3090d3798ff48ca9d04c38113fb40cbedfa3543481f6ed11fb5.jpg) +(b) Support Prototypes + +![](images/1f3f48ebb9ba59159cc39804b353ab147148c238a85f38c6097d57c5f89794e9.jpg) +(c) Support vectors from SVM + +patches from all prototypes of other classes. The combination of these two losses pushes the prototypes as far as possible from the classification boundary, but still within the class distribution, so we call them trivial prototypes, as shown in Fig. 1(a). We also display the trivial prototypes, learned with a feed-forward neural network1, for the two-moon problem in Fig. 2(a). Notice that these trivial prototypes are located far from the classification boundary. In fine-grained visual classification, the trivial prototypes can mistakenly focus on background regions instead of on the object of interest [42, 41], particularly for those classes with subtle foreground (object) differences but large background variations, as shown in Fig. 3. Different from ProtoPNet's trivial prototypes, the support vector machine (SVM) [7] classifier relies on a set of support vectors that are close to the classification boundary, as in Fig. 2(c). These support vectors are often treated as hard samples. Motivated by SVM, we propose the derivation of support (i.e., hard-to-learn) prototypes for ProtoPNet methods. + +In this paper, we propose an alternative learning strategy for ProtoPNet, which forces the learned prototypes to resemble SVM's support vectors and to be located as close as possible to the classification boundary. The strategy is formulated by a new closeness loss that minimises the distance between prototypes of different classes. As shown in Fig. 1(b), our new loss enforces the prototypes to move closer to the classification boundary, as also demonstrated by Fig. 2(b) revealing that the support prototypes produced by the introduction of our new closeness loss are indeed more similar to the support vectors of SVM in Fig. 2(c). Furthermore, to improve the classification accuracy, we propose a new ST-ProtoPNet method that integrates both the support and trivial prototypes. The ST-ProtoPNet leverages the two distinct and complementary sets of prototypes to capture both hard (i.e., close to the boundary) and easy (i.e., far from the boundary) visual features for classification. + +![](images/62753c07f95b79484d0bcdfd93779e6349c8d5efd7168f7bbebc795a0bb7c39b.jpg) +Figure 3. Example prototypes sampled from a VGG19-based ProtoPNet [4]. In each class, the left prototype focuses on object features while the right one captures background. + +![](images/327a68517bc98b9c639fbcf996e52406a2c1182b721808d2561b6e484659c5a6.jpg) + +![](images/956275a2456b859f702e5d6baf6c51544ad71b8964e0d3499903b325598ed141.jpg) + +The major contributions of this work are: + +1. We provide the first study that makes an analogy between the prototype learning from ProtoPNet and support vector learning from SVM, where we propose support (i.e., hard-to-learn) prototypes that can improve classification accuracy and interpretability. +2. We present a new ST-ProtoPNet method to exploit both support and trivial prototypes for interpretable image classification, where the two sets of prototypes can provide complementary information to improve classification accuracy. +3. We conduct extensive experiments on three benchmarks, showing that our ST-ProtoPNet outperforms current state-of-the-art (SOTA) methods in terms of classification accuracy and interpretability. + +In our experiments, we also demonstrate that the trivial and support prototypes have different characteristics, where the trivial prototypes tend to focus on both local parts of the visual object of interest and the background, while the support prototypes mainly focus on object parts belonging to the visual class of interest. + +# 2. Related Work + +# 2.1. Classification Interpretability + +The interpretation of classification results produced by deep neural networks can be achieved by a variety of post-hoc explanation techniques, e.g., explanatory surrogates [34, 56, 44], counterfactual examples [15, 46, 19], and saliency visualisation [45, 55, 59, 43]. Alternatively, prototype-based interpretable techniques can access the model's inner computations. ProtoPNet [4] is the original work that uses class-specific prototypes for interpretable image classification. Similar to ProtoPNet, TesNet [53] constructs class-specific transparent basis concepts on Grassmann manifold for the interpretable classification. Derived from ProtoPNet, Deformable ProtoPNet [11] employs spatially-flexible and deformable prototypes to adaptively capture meaningful object features. In ProtoPShare [42], a data-dependent merge-pruning method is presented to share prototypes among classes, which can reduce the number of prototypes used for classification. In contrast, ProtoPool [41] introduces a fully differentiable prototype assignment strategy to reduce the number of prototypes. In + +Proto2Proto [20], a knowledge distillation method is designed to transfer interpretability from a teacher ProtoPNet to a shallow student ProtoPNet. ProtoTree [35] integrates the prototype learning into a binary neural decision tree that can explain its predictions by tracing a decision path throughout the tree. ViT-NeT [24] further establishes the prototype neural tree structure on visual transformers [12]. + +Because of the ability to self-explain classification results, prototype-based interpretability (e.g., ProtoPNet) has been widely utilised not only in the computer vision applications above, but also in medical imaging [2, 22, 51] and face recognition [48]. However, an open question faced by these methods is if the prototypes being learned are the ideal ones in terms of classification and interpretability. + +# 2.2. SVM vs Prototype-based Classification + +To better understand the role of prototypes, we consider the support vector machine (SVM) [7] classifier that finds support vectors to represent classes. More specifically, SVM learns the maximum-margin classifier defined by a classification boundary that maximises the distance to the closest training samples, which are the support vectors for the classes. The testing of SVM consists of computing a weighted similarity between a testing sample and the support vectors. It is interesting to note that the testing of prototype-based classifiers is also based on measuring the similarity between a testing image and a set of class-specific prototypes learned from the training process. Although the testing of SVM and prototype-based classifiers are similar, their training procedures are different. First, the training of a prototype-based classifier learns a fixed number of prototypes [4, 11], while the SVM classifier learns to weight a variable number of support vectors from the training set. Second, in prototype-based classifiers, the learned prototypes tend to be far from the classification boundary, which is contrary to the SVM training objective mentioned above. + +The study of deep learning methods from an SVM theoretical perspective is a rich area of research [9, 38, 6], but there are many practical questions that need to be addressed, e.g., how to scale the kernel computation for large-scale datasets, how to shorten the training process [38], and how to integrate deep-learning features with the learning of the SVM classifier. In this paper, our focus is on adapting the learning of ProtoPNet's prototypes to make them similar to SVM's support vectors, by forcing prototypes to be as close as possible to the classification boundary. + +# 2.3. Interpretable Ensemble Classification + +Ensemble classification [10] is a classical machine learning approach that combines the results from multiple classifiers, with the goals of improving learning generalisation and classification calibration. The use of interpretable ensemble strategy has been explored in [4, 53, 35, 11, 41], + +which is achieved by summing the classification logits of multiple prototype-based classifiers (e.g., ProtoPNETs trained with different CNN backbones). In this work, we propose an interpretable ensemble classification by combining the predictions of two ProtoPNETs with highly distinctive prototypes (i.e., support and trivial prototypes), which is different from previous studies where the type of prototypes produced by each classifier is very similar given that the same training objective is used for each classifier. + +# 3. Preliminaries + +We assume to have a training set $\mathcal{D} = \{(\mathbf{x}_n,\mathbf{y}_n)\}_{n = 1}^{|\mathcal{D}|}$ where $\mathbf{x}\in \mathcal{X}\subset \mathbb{R}^{H\times W\times R}$ is an image with $R$ colour channels and $\mathbf{y}\in \mathcal{Y}\subset \{0,1\} ^C$ is a one-hot vector representation of the image class label. The interpretable ProtoPNet [4, 11] is trained to learn a set of prototypes $\mathcal{P} = \{\mathbf{p}_m\}_{m = 1}^M$ , where $\mathbf{p}_m\in \mathbb{R}^{\rho_1\times \rho_2\times D}$ , with each of the $C$ classes containing $M / C$ prototypes. Without loss of generality, we assume $\rho_{1} = \rho_{2} = 1$ , but the extension to general values is trivial. A typical ProtoPNet comprises four components: a CNN backbone, add-on layers, a prototype layer, and a fully connected (FC) layer. An input image $\mathbf{x}$ is fed to the CNN backbone $f_{\theta}:X\to \mathcal{F}$ (parameterised by $\theta \in \Theta$ , where $\mathcal{F}\subset \mathbb{R}^{H\times \bar{W}\times \bar{D}}$ ) and then passed on to the add-on layers, denoted by $f_{\omega}:F\rightarrow V$ (parameterised by $\omega \in \Omega$ ), to produce a feature map $\mathbf{V}\in \mathcal{V}\subset \mathbb{R}^{\bar{H}\times \bar{W}\times D}$ . The prototype layer computes the similarity between the feature map $\mathbf{V}$ and the $MD$ dimensional prototypes $\{\mathbf{p}_m\}_{m = 1}^M$ to generate $M$ similarity maps $\mathbf{S}_m^{(i,j)} = \mathrm{sim}(\mathbf{V}(i,j,:),\mathbf{p}_m)$ , where $i\in \{1,\dots,\bar{H}\}$ $j\in \{1,\ldots ,\bar{W}\}$ , and $\mathrm{sim}(\cdot ,\cdot)$ represents a similarity measure, e.g., cosine similarity [11] and projection metric [53]. The prototype layer outputs $M$ similarity scores from maxpooling $S = \left\{\max_{i\in \{1,\dots,\bar{H}\},j\in \{1,\dots,\bar{W}\}}\mathbf{S}_m^{(i,j)}\right\}_{m = 1}^M$ , which are fed to the FC layer $f_{\phi}:S\to \Delta$ parameterised by $\phi \in \Phi$ to produce the classification prediction $\hat{\mathbf{y}}\in \Delta \subset [0,1]^C$ where $\Delta$ denotes the probability space for $C$ classes. + +# 4. ST-ProtoPNet + +An overview of our proposed ST-ProtoPNet method is illustrated in Fig. 4, which comprises a shared CNN backbone $f_{\theta}(\cdot)$ , two interpretable ProtoPNet classification branches, namely: 1) the support ProtoPNet represented by add-on layers $f_{\omega^{(s)}}(\cdot)$ , prototype layer with support prototypes $\mathcal{P}^{(s)}$ , and FC layer $f_{\phi^{(s)}}(\cdot)$ which outputs the classification probability distribution $\hat{\mathbf{y}}^{(s)} \in \Delta$ ; and 2) the trivial ProtoPNet branch with its add-on layers $f_{\omega^{(t)}}(\cdot)$ , trivial prototypes $\mathcal{P}^{(t)}$ , and FC layer $f_{\phi^{(t)}}(\cdot)$ that generates probability predictions $\hat{\mathbf{y}}^{(t)} \in \Delta$ . The final classification is obtained by combining the classification logits from both the support and trivial ProtoP nets. In our implementation, we construct the support and trivial ProtoPNet mainly based on the orig + +![](images/5a225871a407bdcd8c1652f81c89d811688c20672f9f3666b79577548ceee27f.jpg) +Figure 4. The architecture of our proposed ST-ProtoPNet method for the interpretable image classification. + +inal ProtoPNet [4] and TesNet [53], as explained below. + +# 4.1. Support ProtoPNet + +The support ProtoPNet is designed to produce support prototypes that are as close as possible to the classification boundary, as shown in Fig. 1(b) and 2(b). The loss function to optimise the support ProtoPNet branch is defined as: + +$$ +\begin{array}{l} \theta^ {*}, \omega^ {(s) *}, \mathcal {P} ^ {(s) *}, \phi^ {(s) *} = \\ \arg \min _ {\theta , \omega^ {(s)}, \mathcal {P} ^ {(s)}, \phi^ {(s)}} \sum_ {(\mathbf {x}, \mathbf {y}) \in \mathcal {D}} \ell_ {s p t} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(s)}, \mathcal {P} ^ {(s)}, \phi^ {(s)}). \tag {1} \\ \end{array} +$$ + +The loss for each training sample $(\mathbf{x},\mathbf{y})\in \mathcal{D}$ in Eq. (1) above is represented by: + +$$ +\begin{array}{l} \ell_ {s p t} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(s)}, \mathcal {P} ^ {(s)}, \phi^ {(s)}) = \ell_ {c e} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(s)}, \mathcal {P} ^ {(s)}, \phi^ {(s)}) \\ - \lambda_ {1} \ell_ {c t} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(s)}, \mathcal {P} ^ {(s)}) \\ + \lambda_ {2} \ell_ {s p} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(s)}, \mathcal {P} ^ {(s)}) \\ - \lambda_ {3} \ell_ {c l s} (\mathcal {P} ^ {(s)}) \\ + \lambda_ {4} \ell_ {o r t} (\mathcal {P} ^ {(s)}), \tag {2} \\ \end{array} +$$ + +where $\lambda_{1},\lambda_{2},\lambda_{3}$ , and $\lambda_{4}$ are hyper-parameters to balance each term, $\ell_{ce}(\cdot)$ denotes the cross-entropy classification loss, $\ell_{ct}(\cdot)$ and $\ell_{sp}(\cdot)$ represent the clustering and separation losses, respectively, which are introduced to regularise the ProtoPNet's training, as follows: + +$$ +\begin{array}{l} \ell_ {c t} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(s)}, \mathcal {P} ^ {(s)}) = \max _ {\mathbf {p} \in \mathcal {P} _ {\mathbf {y}} ^ {(s)}} \max _ {\mathbf {v} \in \mathbf {V} ^ {(s)}} \sin (\mathbf {v}, \mathbf {p}), (3) \\ \ell_ {s p} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(s)}, \mathcal {P} ^ {(s)}) = \max _ {\mathbf {p} \notin \mathcal {P} _ {\mathbf {y}} ^ {(s)}} \max _ {\mathbf {v} \in \mathbf {V} ^ {(s)}} \operatorname {s i m} (\mathbf {v}, \mathbf {p}), (4) \\ \end{array} +$$ + +where $\mathbf{V}^{(s)} = f_{\omega^{(s)}}(f_{\theta}(\mathbf{x}))$ is the feature map extracted from the input image $\mathbf{x}$ , $\mathbf{v}$ represents one of the $\bar{H} \times \bar{W}$ feature vectors in $\mathbf{V}^{(s)}$ obtained by matrix vectorisation, $\mathbf{p}$ is a normalised prototype (i.e., unit vector) in $\mathcal{P}^{(s)}$ , $\sin (\cdot, \cdot)$ + +is one of the similarity functions defined in Sec. 3, and $\mathcal{P}_{\mathbf{y}}^{(s)}$ denotes the set of prototypes of class $\mathbf{y}$ . The clustering loss in Eq. (3) and separation loss in Eq. (4) aim to learn a meaningful feature space in which the image features of a certain class are clustered around the prototypes of the class, and also well separated from those of other classes. + +As mentioned in Sec. 1, the effect of the clustering and separation losses above tend to push the prototypes of different classes as far as possible from the classification boundary, resulting in trivial prototypes, as displayed in Fig. 1(a) and Fig. 2(a). In order to learn the proposed support prototypes, we introduce the following novel closeness loss $\ell_{cls}$ to explicitly enforce the prototypes of different classes to be close to each other, which is formulated as: + +$$ +\ell_ {c l s} \left(\mathcal {P} ^ {(s)}\right) = \sum_ {c _ {1} = 1} ^ {C - 1} \sum_ {c _ {2} = c _ {1} + 1} ^ {C} \min _ {\mathbf {p} _ {m} \in \mathcal {P} _ {c _ {1}}, \mathbf {p} _ {n} \in \mathcal {P} _ {c _ {2}}} \mathbf {p} _ {m} ^ {\top} \mathbf {p} _ {n}. \tag {5} +$$ + +During training, this closeness loss $\ell_{cls}$ maximises the pair-wise prototype similarity, in the form of dot product $\mathbf{p}_m^\top \mathbf{p}_n$ between different classes in Eq. (5) above, with the goal of pulling the prototypes close to the classification boundary. On the one hand, as the prototypes move gradually towards the classification boundary, they are able to capture harder visual features from training samples. On the other hand, since the prototypes are located near the classification boundary, they can put pressure on the support ProtoPNet's feature learning (i.e., enforce it to learn highly discriminative feature representations for accurate classification), which is beneficial to extract more meaningful semantic information from training samples. + +Ideally, each prototype of a class should focus on unique object parts of the training images (e.g., head, tail, and claw of birds), so that the prototypes can represent rich and diverse visual patterns. However, there is no particular constraints to guarantee such prototype diversity and the issue of prototype duplication [11] often occurs in the ProtoPNet family of models. To encourage the intra-class prototype diversity, we employ an orthonormality loss [53] so that prototypes within a class can represent dissimilar visual patterns of training samples, which is defined as: + +$$ +\ell_ {o r t} \left(\mathcal {P} ^ {(s)}\right) = \sum_ {c = 1} ^ {C} \left\| \mathbf {P} _ {c} ^ {\top} \mathbf {P} _ {c} - \mathbf {I} _ {M / C} \right\| _ {F} ^ {2}, \tag {6} +$$ + +where $\| \cdot \| _F^2$ represents Frobenius norm, $\mathbf{P}_c\in D\times \mathbb{R}^{(M / C)}$ stands for a matrix composed of the prototypes of class $c$ (prototypes in each column of $\mathbf{P}_c$ are normalised), and $\mathbf{I}_{M / C}$ is an identity matrix of size $M / C\times M / C$ + +# 4.2. Trivial ProtoPNet + +As described in Sec. 4.1, the support ProtoPNet is developed to learn support (i.e., hard-to-learn) prototypes by + +forcing them to be close to the classification boundary. Considering that training samples contain not only hard visual features but also important easy ones that the support prototypes cannot completely capture, we propose to also learn trivial prototypes to provide complementary classification information, and exploit both the support and trivial prototypes for improved interpretable classification. + +The loss objective to optimise the trivial ProtoPNet branch is defined as follows: + +$$ +\begin{array}{l} \theta^ {*}, \omega^ {(t) *}, \mathcal {P} ^ {(t) *}, \phi^ {(t) *} = \\ \arg \min _ {\theta , \omega^ {(t)}, \mathcal {P} ^ {(t)}, \phi^ {(t)}} \sum_ {(\mathbf {x}, \mathbf {y}) \in \mathcal {D}} \ell_ {t r v} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(t)}, \mathcal {P} ^ {(t)}, \phi^ {(t)}). \tag {7} \\ \end{array} +$$ + +The loss for each training image $(\mathbf{x},\mathbf{y})\in \mathcal{D}$ in Eq. (7) above is represented by: + +$$ +\begin{array}{l} \ell_ {t r v} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(t)}, \mathcal {P} ^ {(t)}, \phi^ {(t)}) = \ell_ {c e} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(t)}, \mathcal {P} ^ {(t)}, \phi^ {(t)}) \\ - \lambda_ {1} \ell_ {c t} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(t)}, \mathcal {P} ^ {(t)}) \\ + \lambda_ {2} \ell_ {s p} (\mathbf {x}, \mathbf {y}, \theta , \omega^ {(t)}, \mathcal {P} ^ {(t)}) \\ + \lambda_ {3} \ell_ {d s c} (\mathcal {P} ^ {(t)}) \\ + \lambda_ {4} \ell_ {\text {o r t}} (\mathcal {P} ^ {(t)}), \tag {8} \\ \end{array} +$$ + +where $\lambda_{1},\lambda_{2},\lambda_{3}$ and $\lambda_{4}$ are hyper-parameters, $\ell_{ce}(\cdot)$ is the cross-entropy loss, the clustering loss $\ell_{ct}$ , separation loss $\ell_{sp}$ , and orthonormality loss $\ell_{ort}$ are the same as in the support ProtoPNet defined in Eq. (3), (4) and (6), respectively. + +The trivial ProtoPNet targets the learning of easy prototypes that are far from the classification boundary and have a good discrimination ability. To help achieve this, we introduce a new discrimination loss $\ell_{dsc}$ to facilitate the interclass separability between prototypes of different classes. This is formulated by minimising the pair-wise prototype similarities of different classes, as follows: + +$$ +\ell_ {d s c} \left(\mathcal {P} ^ {(t)}\right) = \sum_ {c _ {1} = 1} ^ {C - 1} \sum_ {c _ {2} = c _ {1} + 1} ^ {C} \max _ {\mathbf {p} _ {m} \in \mathcal {P} _ {c _ {1}}, \mathbf {p} _ {n} \in \mathcal {P} _ {c _ {2}}} \mathbf {p} _ {m} ^ {\top} \mathbf {p} _ {n}. \tag {9} +$$ + +# 4.3. Training and Testing + +Training. Following the training strategies in [4, 11], the training procedure of our ST-ProtoPNet consists of 3 stages: 1) optimisation of the CNN backbone, add-on layers, and prototype layer, using a fixed FC layer initialised with $+1.0$ and -0.5 for correct and incorrect connection weights, respectively. A warm-up of 5 epochs is involved in this stage by updating only the parameters of add-on layers and prototype layer, with a frozen pre-trained CNN backbone. 2) prototype projection by updating each prototype with its nearest latent training image patch; and 3) optimisation of the FC layer, with an additional $L_{1}$ regularisation on the incorrect connection weights (initially fixed at + +-0.5). In each stage, we alternate the optimisation of each branch of the ST-ProtoPNet between mini-batches. Notice that our method only brings marginal extra model parameters, computational complexity, and training time since the CNN backbone is shared and optimised by both branches. + +Testing. To exploit the complementary results from both branches of ST-ProtoPNet, its final classification is obtained from the summed logits predicted by the two branches. It is worth noticing that this ensemble strategy introduces no loss of interpretability but improved accuracy. + +# 5. Experiments + +We perform experiments on three fine-grained classification benchmark datasets: CUB-200-2011 [50], Stanford Cars [27], and Stanford Dogs [21]. To achieve fair comparison, we follow previous studies [4, 53] by applying offline data augmentations (e.g., random rotation, skew, shear, and left-right flip) on the cropped CUB and cropped Cars datasets (using the bounding boxes provided). We also validate our method on the full (i.e., uncropped) CUB and Dogs datasets, and employ the same online data augmentation methods (e.g., random affine transformation and left-right flip) as used in Deformable ProtoPNet [11]. All images are resized to $224 \times 224$ pixels as network input. + +# 5.1. Experimental Settings + +The proposed ST-ProtoPNet method is evaluated on the following CNN architectures: VGG-16, VGG-19, ResNet-34, ResNet-50, ResNet-152, DenseNet-121, and DenseNet-161. All CNN backbones are pre-trained on ImageNet [8], except for ResNet-50, which is pre-trained on iNaturalist [49] for the experiment on full CUB [11]. The add-on layers include two $1 \times 1$ convolutional layers. For simplicity, we utilise the same prototype dimension $D = 64$ for all CNN backbones on the three datasets. For cropped CUB and Cars datasets, following [53], we use 10 prototypes (5 support and 5 trivial) per class and the projection metric in the similarity function $\mathrm{sim}(\cdot ,\cdot)$ . In full CUB and Dogs datasets, to ensure comparison fairness with Deformable ProtoPNet [11] that uses $102 \times 2$ (full CUB) and $103 \times 3$ (full Dogs) deformable prototypes per class, we utilise the same total number of prototypes, i.e., $401 \times 1$ (20 support and 20 trivial) for full CUB and $901 \times 1$ (45 support and 45 trivial) for full Dogs. Also, we employ the cosine similarity in $\mathrm{sim}(\cdot ,\cdot)$ and obtain $14 \times 14$ ( $\bar{H} = \bar{W} = 14$ ) feature maps by upsampling the original $7 \times 7$ feature maps via a bi-linear interpolation step, as in [11]. Following previous prototype-based methods [4, 53, 11], we set $\lambda_{1} = 0.8$ , $\lambda_{2} = 0.48$ and 0.08 for the support and trivial ProtoPNet branches respectively, $\lambda_{4} = 0.001$ . We choose $\lambda_{3} = 1.0$ with an ablation provided in the supplementary material. + +# 5.2. Interpretability Evaluation + +Rather than performing user-based evaluations [60, 41], whose results are often subjective and difficult to reproduce [54], we leverage the annotated object masks to measure interpretability based on the following metrics: + +Content Heatmap (CH) [37]: quantifies the percentage of an activation heatmap that lies within the annotated mask. Hence, we expect this metric to be high. + +Outside-Inside Relevance Ratio (OIRR) [29]: calculates the ratio of mean activation outside the object to mean activation inside the object. A low OIRR indicates a method relies more on the object region and less on the context to support its decision, we thus anticipate OIRR to be low. + +Intersection over Union (IoU) [5]: measures the mean IoU score, where a threshold of 0.5 is applied on the min-max normalised heatmap to select foreground objects. + +Deletion AUC (DAUC) [36]: estimates a decrease in the probability of the predicted class as more and more important/activated pixels are removed. The area under the probability curve is defined as DAUC. Consequently, a sharp drop and a low DAUC mean better interpretation. + +Average Inter-class Prototype Distance (AIPD), Average Inter-class Feature Distance (AIFD): we had earlier stated that support prototypes of different classes should be close to each other and trivial prototypes should be far from each other. Thus, we compute the average inter-class cosine distance for prototypes and their nearest local feature representations, respectively. We expect AIPD $<$ AIFD for support ProtoPNet and AIPD $>$ AIFD for trivial ProtoPNet. + +# 5.3. Classification Performance + +Table 1 presents the classification accuracy (across 5 runs) of our proposed ST-ProtoPNet on cropped CUB and cropped Cars, where the Baseline is represented by non-interpretable black-box CNN models. As can be seen, our ST-ProtoPNet outperforms other competing methods across all backbones for the task of bird species classification. Also, our method achieves the best results for the car model identification task when using VGG and DenseNet architectures as the CNN backbone. In particular, our VGG19-based ST-ProtoPNet reaches an average accuracy of $83.2\%$ and $91.7\%$ on CUB and Cars, respectively, surpassing other methods with the most improvements across all backbones. Moreover, the support ProtoPNet generally performs better than methods utilising only trivial prototypes (e.g., ProtoPNet, TesNet, and Trivial ProtoPNet), showing the importance of learning support prototypes for the interpretable classification. It is worth noting that our ST-ProtoPNet produces superior performance over the support ProtoPNet method, indicating that both support and trivial prototypes are useful and can provide complementary information for achieving accurate and interpretable classification. + +Table 2 shows the classification results on full CUB and + +full Dogs. In both datasets, the classification accuracy of the original ProtoPNet method is generally worse than the non-interpretable counterpart (Baseline) for many CNN backbones. On the other hand, the accuracy by the trivial ProtoPNet and support ProtoPNet are substantially better than those by Baseline, ProtoPNet, and Deformable ProtoPNet. However, our ST-ProtoPNet achieves more significant performance gains and exhibits the best accuracy across most backbones, particularly when using a large number of prototypes (i.e., $401 \times 1$ prototypes per class for CUB and $901 \times 1$ prototypes per class for Dogs), demonstrating the effectiveness of utilising both the trivial and support prototypes for the interpretable image classification. Additionally, when using a smaller number of prototypes, i.e., $101 \times 1$ prototypes per class, our ST-ProtoPNet still has competitive classification accuracy across multiple backbones. + +We further compare our ST-ProtoPNet with other deep-learning methods that can provide different levels of interpretability on CUB, with results shown in Table 3, where * and ** denote ensemble of models with different backbones. As evident, an ensemble of three ST-ProtoPNETs can achieve high accuracy (87.9% on cropped images, 88.2% on full images), outperforming competing methods that are also based on an ensemble of three models (e.g., ProtoTree, TesNet, and ProtoPool). Moreover, the ensemble of five STProtoPNETs outperforms all other competing methods and obtains the best classification accuracy of 88.1% and 88.4% on cropped and full CUB images, respectively. More results on Cars and Dogs are given in the supplementary material. + +# 5.4. Interpretability Comparison + +We assess the model interpretability on full CUB using the annotated bird segmentation mask $^2$ . Quantitative results on the test set are given in Table 4, where all methods are based on the VGG19 backbone. We use GradCAM [43] for the non-interpretable baseline. For prototype-based methods, we average the activation map of all prototypes of a class to compute the metrics. We can see our proposed support ProtoPNet can effectively improve the interpretableity in all measures, showing the interpretations produced by our support prototypes are more likely to be object-dependent and focus less on context cues. Also, our ST-ProtoPNet method shows better interpretable results than the support ProtoPNet in terms of CH, OIRR, and DAUC. Compared with the original ProtoPNet [4], our ST-ProtoPNet obtains significant interpretability improvements. We show some example activation maps in the supplementary material, and an experiment with prototype pruning is also provided. + +Table 5 presents the computed AIPD and AIFD for the support and trivial ProtoPNet on cropped CUB, using VGG19 and ResNet34 as CNN backbones. As evident, the AIPD is indeed smaller than AIFD for the support ProtoP- + +
MethodCUBCars
VGG16VGG19ResNet34ResNet152Dense121Dense161VGG16VGG19ResNet34ResNet152Dense121Dense161
Baseline73.3 ± 0.274.7 ± 0.482.2 ± 0.380.8 ± 0.481.8 ± 0.182.1 ± 0.287.3 ± 0.488.5 ± 0.392.6 ± 0.392.8 ± 0.492.0 ± 0.392.5 ± 0.3
ProtoPNet [4]77.2 ± 0.277.6 ± 0.278.6 ± 0.179.2 ± 0.379.0 ± 0.280.8 ± 0.388.3 ± 0.289.4 ± 0.288.8 ± 0.188.5 ± 0.387.7 ± 0.189.5 ± 0.2
TesNet [53]81.3 ± 0.281.4 ± 0.182.8 ± 0.182.7 ± 0.284.8 ± 0.284.6 ± 0.390.3 ± 0.290.6 ± 0.290.9 ± 0.292.0 ± 0.291.9 ± 0.392.6 ± 0.3
Trivial ProtoPNet80.8 ± 0.281.2 ± 0.282.5 ± 0.283.1 ± 0.383.9 ± 0.384.6 ± 0.390.1 ± 0.290.7 ± 0.291.1 ± 0.291.5 ± 0.291.4 ± 0.392.4 ± 0.3
Support ProtoPNet81.7 ± 0.281.8 ± 0.383.0 ± 0.183.6 ± 0.284.7 ± 0.285.2 ± 0.390.9 ± 0.290.8 ± 0.291.0 ± 0.291.8 ± 0.291.7 ± 0.292.7 ± 0.3
ST-ProtoPNet (ours)82.9 ± 0.283.2 ± 0.283.5 ± 0.184.1 ± 0.285.4 ± 0.286.1 ± 0.291.1 ± 0.291.7 ± 0.291.4 ± 0.192.0 ± 0.292.3 ± 0.392.7 ± 0.2
+ +Table 1. Classification accuracy (%) on cropped CUB-200-2011 and Stanford Cars by competing methods using different CNN backbones. + +
Method# PrototypeCUB# PrototypeDogs
VGG16VGG19ResNet34ResNet50ResNet152Dense121Dense161VGG16VGG19ResNet34ResNet50ResNet152Dense121Dense161
Baseline-70.971.376.078.779.278.280.0-75.677.381.183.185.281.984.1
ProtoPNet [4]1×1p, 10pc70.372.672.481.174.374.075.41×1p, 10pc70.773.673.476.476.272.077.3
ProtoPNet [4]1×1p, 40pc72.974.274.184.876.076.678.51×1p, 90pc73.975.376.178.179.775.478.8
TesNet [53]1×1p, 10pc75.877.576.286.579.080.279.61×1p, 10pc74.377.180.182.483.880.383.8
TesNet [53]1×1p, 40pc77.679.276.587.380.180.981.31×1p, 90pc78.579.681.283.384.582.185.2
Deformable ProtoPNet [11]2×2p, 10pc75.776.076.886.479.679.081.23×3p, 10pc75.877.980.682.286.580.783.7
Trivial ProtoPNet1×1p, 40pc80.079.577.587.280.881.182.11×1p, 90pc78.680.482.685.087.082.385.9
Support ProtoPNet1×1p, 40pc80.480.078.487.580.281.582.41×1p, 90pc79.080.683.085.187.382.686.2
ST-ProtoPNet (ours)1×1p, 10pc76.877.677.486.678.778.680.61×1p, 10pc74.277.280.884.085.379.484.4
ST-ProtoPNet (ours)1×1p, 40pc81.080.278.288.081.281.882.71×1p, 90pc79.180.983.485.787.282.986.6
+ +Table 2. Classification accuracy (%) on full CUB-200-2011 and Stanford Dogs datasets by competing approaches using different CNN backbones, where ${\rho }_{1} \times {\rho }_{2}\mathrm{p}$ denotes the spatial shape of prototypes and $k\mathrm{{pc}}$ represents $k$ prototypes per class. + +
Interpretability levelMethodAccuracy (%)
NoneB-CNN [32]85.1 (b)84.1 (f)
Object-level attentionCAM [59]70.5 (b)63.0 (f)
CSG [31]82.6 (b)78.5 (f)
Part-level attentionPA-CNN [26]82.8 (b)-
MG-CNN [52]83.0 (b)81.7 (f)
MA-CNN [57]-86.5 (f)
RA-CNN [14]-85.3 (f)
TASN [58]-87.0 (f)
Part-level attention + PrototypesRegion [17]81.5 (b)80.2 (f)
ProtoPNet* [4]84.8 (b)81.1 (f)
ProtoTree* [35]-86.6 (f)
TesNet* [53]86.2 (b)83.5 (f)
ProtoPool* [41]87.5 (b)-
ST-ProtoPNet* (ours)87.9 (b)88.2 (f)
ProtoTree** [35]-87.2 (f)
Deformable ProtoPNet** [11]-87.8 (f)
ProtoPool** [41]87.6 (b)-
ST-ProtoPNet** (ours)88.1 (b)88.4 (f)
+ +Table 3. Classification accuracy and interpretability level of different methods on CUB-200-2011. "b" and "f" denote the model is trained and tested on cropped and full images, respectively. *: Ensemble of three models. **: Ensemble of five models. + +
MetricGradCAM [43]ProtoPNet [4]TesNet [53]DefProto [11]TrvProtoSptProtoST-Proto
CH (%, ↑)52.4648.6659.3852.0963.0563.8766.43
IoU (%, ↑)39.9138.0336.9240.7737.7442.0441.05
OIRR (%, ↓)37.0137.2638.9728.6834.4828.6928.09
DAUC (%, ↓)7.017.395.865.996.065.805.74
+ +Net while AIPD is larger than AIFD for the trivial ProtoP-Net. This result indicates that the support prototypes of different classes lie closer than their local feature representations and are more inclined to focus on visually similar (i.e., hard-to-learn) object parts of different classes. + +# 5.5. Visualisation Analysis + +To explore the differences between the support and trivial prototypes, we select 5 categories of birds with visu + +Table 4. Quantitative interpretability results on full CUB test set. DefProto = Deformable ProtoPNet, TrvProto = Trivial ProtoPNet, SptProto = Support ProtoPNet, ST-Proto = ST-ProtoPNet. + +
VGG19ResNet34
SupportProtoPNetTrivialProtoPNetSupportProtoPNetTrivialProtoPNet
AIPDAIFDAIPDAIFDAIPDAIFDAIPDAIFD
0.72590.92640.99870.92320.65410.85731.0000.9481
+ +Table 5. Average inter-class prototype distance (AIPD) and average inter-class feature distance (AIFD) for the support and trivial ProtoPNet trained on cropped CUB. + +![](images/83c79ab267d0912173d5809975c3ccf5eb7be6e68b6b5f985411c1e8a549135f.jpg) +Figure 5. The support (top) and trivial (bottom) prototypes from cropped CUB. In each pair, the first column shows the original image with a prototype marked in a yellow bounding box, the second column is the prototype's corresponding activation map. + +ally similar features from cropped CUB to train the support and trivial ProtoPNet methods, with the learned prototypes shown in Fig. 5. We notice the support prototypes can cap + +![](images/c5320708478b8263ae8a62171c8a0f7c9ab52b29de6f99c906d8e076f78b10ea.jpg) +Figure 6. T-SNE results of support and trivial prototypes. The prototypes and their nearest latent training features are marked with stars and dots, respectively. We show results before the prototype projection stage to better visualise the relation between the prototypes and features. Each colour represents a different class. + +![](images/8f698f6fdfeb661718aabd98d51d3d8f5a6d657798fc09b9ab9fc1661b9a723e.jpg) + +ture subtle and fine visual features of different classes and they only focus on relevant bird parts, e.g., head and belly. This is reasonable since our algorithm is designed to produce prototypes that are as close as possible to each other, where the image prototypical parts should not only be discriminative but also share visually similar features among classes. By contrast, the trivial prototypes tend to focus not only on the relevant bird parts but also the background regions. For example, some trivial prototypes of the Laysan Albatross and Sooty Albatross classes capture the sea surface as they often appear with the sea background. We argue that this is because the trivial ProtoPNet may treat the background as an easy pattern to learn, focusing less on the object's visual parts of the class. In Fig. 6, we show the t-SNE result from the 5-category bird classification, where we note the support prototypes of different classes are located closer to each other, in comparison with the trivial prototypes. + +Fig. 7 shows an example of the interpretable reasoning for our ST-ProtoPNet in classifying a testing bird image. As evident, each ProtoPNet branch calculates its own classification logits (weighted sum of similarity scores), which is then combined to generate the final prediction. Specifically, when classifying a Parakeet Auklet, the support prototypes are quite active on the bird's beak and belly. Meanwhile, the trivial prototypes have high activations on the bird's lower surface and neck. In this case, the support ProtoPNet obtains a relatively higher similarity score (22.925), compared with the trivial branch (20.313). Note that our ST-ProtoPNet exploits both the support and trivial prototypes to capture much richer representations of the object from different perspectives, which enables the realisation of complementary interpretations. More examples on Cars and Dogs are shown in the supplementary material. + +# 5.6. Ablation Study + +The closeness and discrimination losses. To validate the effectiveness of our proposed closeness loss in Eq. (5) and discrimination loss in Eq. (9), we first conduct ablation studies on full CUB and full Dogs by using ResNet50 and ResNet34 as the CNN backbone, respectively. Results are listed in Table 6. We can observe that both the close- + +![](images/7dfb1d14679dbe59deaa77dc6a19d60ac205d535332011c2ab68c1bad1ad1a8b.jpg) +Figure 7. An example of the interpretable reasoning of our STProtoPNet for classifying a testing Parakeet Auklet image. + +
MethodlctlsplortldscclsAccuracy (%)
CUBDogs
Baseline✓✓✓86.580.9
Trivial ProtoPNet✓✓✓✓87.282.6
Support ProtoPNet✓✓✓✓87.583.0
ST-ProtoPNet (ours)✓✓✓✓✓88.083.4
+ +Table 6. Ablation analysis of the closeness loss $\ell_{cls}$ in Eq. (5) to learn support prototypes, and discrimination loss $\ell_{dsc}$ in Eq. (9) to learn trivial prototypes on full CUB-200-2011 and Stanford Dogs. + +ness and discrimination losses can improve the accuracy, compared with the Baseline ProtoPNet method trained with only clustering, separation, and orthonormality losses. Note that the closeness loss introduces a larger performance improvement, which is attributed to the learning of support (i.e., hard-to-learn) prototypes. + +Combining Support and Trivial Prototypes. We also investigate the importance of integrating the two complementary sets of support and trivial prototypes for improved classification. To achieve this, we first train a two-branch model where both branches learn the same type of prototypes and the final result is produced by the ensemble of them (Trivial Ensemble and Support Ensemble). Besides, for our ST-ProtoPNet, we also provide results of its individual branches (Trivial Branch and Support Branch). Table 7 shows the experimental results on cropped CUB. We can notice that combining the two different types of prototypes (ST-ProtoPNet) achieves superior performance over combining only the same type of prototypes (Trivial Ensemble and Support Ensemble), indicating that our performance improvements are from not only the ensemble strategy but also the two complementary sets of prototypes. Also, STProtoPNet indeed exhibits higher accuracy than its individual branches, further verifying that the results from the two branches are complementary, and the combination of them is effective to improve the final classification accuracy. + +# 6. Conclusion and Future Work + +In this paper, we proposed the ST-ProtoPNet to exploit both support (i.e., hard-to-learn) and trivial (i.e., easy-to-learn) prototypes, where the two sets of prototypes can pro + +
MethodVGG16VGG19ResNet34ResNet152Dense121Dense161
Trivial Ensemble81.4 ± 0.381.8 ± 0.282.7 ± 0.283.2 ± 0.384.4 ± 0.285.0 ± 0.3
Support Ensemble82.1 ± 0.282.4 ± 0.383.0 ± 0.283.7 ± 0.384.8 ± 0.285.5 ± 0.2
Trivial Branch81.0 ± 0.281.1 ± 0.382.4 ± 0.282.9 ± 0.384.1 ± 0.384.8 ± 0.3
Support Branch81.5 ± 0.381.8 ± 0.382.8 ± 0.283.4 ± 0.384.6 ± 0.285.4 ± 0.2
ST-ProtoPNet (ours)82.9 ± 0.283.2 ± 0.283.5 ± 0.184.1 ± 0.285.4 ± 0.286.1 ± 0.2
+ +Table 7. Ablation study of the combination of support and trivial prototypes for improved classification on cropped CUB-200-2011. + +vide complementary results for the interpretable image classification. Our ST-ProtoPNet is a general approach that can be easily applied to existing prototype-based interpretable models. One limitation for our method is that we empirically adopt the same number of support and trivial prototypes and the same total number of prototypes for each class. Considering the different learning difficulties and imbalanced training samples among classes in other real-world datasets, e.g., ImageNet [8], a better way to adaptively learn a flexible number of support and trivial prototypes is needed and deserves to be further investigated in our future work. Moreover, given that we mimic the behaviour of the support vectors of SVM classifier to obtain the support prototypes by forcing them to be as close as possible to the classification boundary, we plan to develop new methods to learn prototypes with gradient-based kernel techniques, e.g., neural tangent kernel [18] and path kernel [9]. + +Acknowledgements. This work was supported by funding from the Australian Government under the Medical Research Future Fund - Grant MRFAI000090 for the Transforming Breast Cancer Screening with Artificial Intelligence (BRAIx) Project, and the Australian Research Council through grant FT190100525. + +# References + +[1] David Alvarez Melis and Tommi Jaakkola. Towards robust interpretability with self-explaining neural networks. Advances in Neural Information Processing Systems, 31, 2018. +[2] Alina Jade Barnett, Fides Regina Schwartz, Chaofan Tao, Chaofan Chen, Yinhao Ren, Joseph Y Lo, and Cynthia Rudin. 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Harvard University " + }, + { + "bbox": [ + 140, + 176, + 465, + 219 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 140, + 176, + 465, + 219 + ], + "type": "text", + "content": " St Vincent's Institute of Medical Research \n" + }, + { + "bbox": [ + 140, + 176, + 465, + 219 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 140, + 176, + 465, + 219 + ], + "type": "text", + "content": " St Vincent's Hospital Melbourne " + }, + { + "bbox": [ + 140, + 176, + 465, + 219 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 140, + 176, + 465, + 219 + ], + "type": "text", + "content": " CVSSP, University of Surrey" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 243, + 192, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 243, + 192, + 257 + ], + "spans": [ + { + "bbox": [ + 143, + 243, + 192, + 257 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 269, + 290, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 269, + 290, + 605 + ], + "spans": [ + { + "bbox": [ + 45, + 269, + 290, + 605 + ], + "type": "text", + "content": "Prototypical part network (ProtoPNet) methods have been designed to achieve interpretable classification by associating predictions with a set of training prototypes, which we refer to as trivial prototypes because they are trained to lie far from the classification boundary in the feature space. Note that it is possible to make an analogy between ProtoPNet and support vector machine (SVM) given that the classification from both methods relies on computing similarity with a set of training points (i.e., trivial prototypes in ProtoPNet, and support vectors in SVM). However, while trivial prototypes are located far from the classification boundary, support vectors are located close to this boundary, and we argue that this discrepancy with the well-established SVM theory can result in ProtoPNet models with inferior classification accuracy. In this paper, we aim to improve the classification of ProtoPNet with a new method to learn support prototypes that lie near the classification boundary in the feature space, as suggested by the SVM theory. In addition, we target the improvement of classification results with a new model, named ST-ProtoPNet, which exploits our support prototypes and the trivial prototypes to provide more effective classification. Experimental results on CUB-200-2011, Stanford Cars, and Stanford Dogs datasets demonstrate that ST-ProtoPNet achieves state-of-the-art classification accuracy and interpretability results. We also show that the proposed support prototypes tend to be better localised in the object of interest rather than in the background region." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 625, + 128, + 638 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 128, + 638 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 128, + 638 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "Deep convolutional neural networks (CNN) [28, 30, 16] have had remarkable achievements in various visual tasks, e.g., image recognition [16] and object detection [39]. Despite the excellent feature extraction and discrimination ability, CNNs are generally treated as black-box models due to their complex architectures, high-dimensional fea" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 243, + 545, + 296 + ], + "blocks": [ + { + "bbox": [ + 307, + 243, + 545, + 296 + ], + "lines": [ + { + "bbox": [ + 307, + 243, + 545, + 296 + ], + "spans": [ + { + "bbox": [ + 307, + 243, + 545, + 296 + ], + "type": "image", + "image_path": "257bd92a30d8f5af85711e236e4dff2ed11d9626702f1b448d8f59560290594a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 376, + 296, + 476, + 304 + ], + "lines": [ + { + "bbox": [ + 376, + 296, + 476, + 304 + ], + "spans": [ + { + "bbox": [ + 376, + 296, + 476, + 304 + ], + "type": "text", + "content": "(a) The learning of trivial prototypes" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 304, + 545, + 358 + ], + "blocks": [ + { + "bbox": [ + 307, + 304, + 545, + 358 + ], + "lines": [ + { + "bbox": [ + 307, + 304, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 307, + 304, + 545, + 358 + ], + "type": "image", + "image_path": "a1ea86fd4b542a56641457d80ed380227ebd60185eb319f059d0b8ea5cfd5b1f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 364, + 358, + 488, + 365 + ], + "lines": [ + { + "bbox": [ + 364, + 358, + 488, + 365 + ], + "spans": [ + { + "bbox": [ + 364, + 358, + 488, + 365 + ], + "type": "text", + "content": "(b) The learning of support prototypes (ours)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "lines": [ + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "text", + "content": "Feature vectors " + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "inline_equation", + "content": "\\star \\star" + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "text", + "content": " Prototypes " + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "inline_equation", + "content": "\\longrightarrow" + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "text", + "content": " Clustering " + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "inline_equation", + "content": "\\longrightarrow" + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "text", + "content": " Separation " + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "inline_equation", + "content": "\\longrightarrow" + }, + { + "bbox": [ + 307, + 366, + 545, + 440 + ], + "type": "text", + "content": " Our loss Figure 1. The difference between the learning of trivial and support prototypes. (a) Trivial prototypes: the separation loss pushes the prototypes of different classes as far as possible from the classification boundary. (b) Support prototypes: our new closeness loss enforces the prototypes of different classes to be as close as possible to the classification boundary." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 509 + ], + "type": "text", + "content": "ture spaces, and the enormous number of learnable parameters. Such lack of interpretability hinders their successful application in fields that require understandable and transparent decisions [40], e.g., disease diagnosis [47, 13], financial risk assessment [33], and autonomous driving [23]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 510, + 546, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 641 + ], + "type": "text", + "content": "Recently, increasing attention has been dedicated to the development of interpretable deep-learning models [25, 1, 4, 3]. A particularly interesting strategy is the prototype-based gray-box models, e.g., prototypical part network (ProtoPNet) [4, 11]. These methods are inherently interpretable since they can explain the model's decisions by showing image classification activation maps associated with a set of class-specific image prototypes. These prototypes are automatically learned from training samples, with classification score being computed by comparing testing image parts to the learned training prototypes." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "ProtoPNet [4] is trained to learn a classifier from a set of class-specific prototypes by minimising the cross-entropy classification loss and two additional regularisation losses, namely: 1) a clustering loss that pulls together training image patches to at least one prototype of its own class; and 2) a separation loss that pushes apart training image" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2062" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 127, + 114 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 127, + 114 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 127, + 114 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 127, + 114 + ], + "type": "image", + "image_path": "8b1f49f27fcb87fba8bda1f0e1a84ae8e80e212eeaec170eda5017ae335f2268.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 129, + 70, + 207, + 114 + ], + "blocks": [ + { + "bbox": [ + 129, + 70, + 207, + 114 + ], + "lines": [ + { + "bbox": [ + 129, + 70, + 207, + 114 + ], + "spans": [ + { + "bbox": [ + 129, + 70, + 207, + 114 + ], + "type": "image", + "image_path": "e6c9c967a42cc7841459842d5b59555a3388a6aefd22f4876413be3b7f3dc0c3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 209, + 78, + 286, + 104 + ], + "blocks": [ + { + "bbox": [ + 209, + 78, + 286, + 104 + ], + "lines": [ + { + "bbox": [ + 209, + 78, + 286, + 104 + ], + "spans": [ + { + "bbox": [ + 209, + 78, + 286, + 104 + ], + "type": "image", + "image_path": "56a2b230d561a0ffe03f3bb41c3fcce406d8190b56468c789ce56153e063c9c1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 49, + 114, + 127, + 156 + ], + "blocks": [ + { + "bbox": [ + 49, + 114, + 127, + 156 + ], + "lines": [ + { + "bbox": [ + 49, + 114, + 127, + 156 + ], + "spans": [ + { + "bbox": [ + 49, + 114, + 127, + 156 + ], + "type": "image", + "image_path": "6ecfa48dba624a9aaaff7f7c390c81c51c5a659c8077c2e3aa30386716df617d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 156, + 112, + 162 + ], + "lines": [ + { + "bbox": [ + 64, + 156, + 112, + 162 + ], + "spans": [ + { + "bbox": [ + 64, + 156, + 112, + 162 + ], + "type": "text", + "content": "(a) Trivial Prototypes" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 165, + 287, + 242 + ], + "type": "text", + "content": "Figure 2. Two-moon results. (a) Trivial prototypes and training samples in the feature (top) and data (bottom) spaces from the original ProtoPNet [4]. (b) Support prototypes and training samples in the feature (top) and data (bottom) spaces from our method. (c) Support vectors and training samples from a Radial Basis Function (RBF) kernel based SVM [7]. In (a) and (b), each prototype is projected onto the nearest training sample in the feature space." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 129, + 114, + 206, + 156 + ], + "blocks": [ + { + "bbox": [ + 129, + 114, + 206, + 156 + ], + "lines": [ + { + "bbox": [ + 129, + 114, + 206, + 156 + ], + "spans": [ + { + "bbox": [ + 129, + 114, + 206, + 156 + ], + "type": "image", + "image_path": "0fd7a59e21f7a3090d3798ff48ca9d04c38113fb40cbedfa3543481f6ed11fb5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 141, + 156, + 194, + 162 + ], + "lines": [ + { + "bbox": [ + 141, + 156, + 194, + 162 + ], + "spans": [ + { + "bbox": [ + 141, + 156, + 194, + 162 + ], + "type": "text", + "content": "(b) Support Prototypes" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 208, + 114, + 286, + 156 + ], + "blocks": [ + { + "bbox": [ + 208, + 114, + 286, + 156 + ], + "lines": [ + { + "bbox": [ + 208, + 114, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 208, + 114, + 286, + 156 + ], + "type": "image", + "image_path": "1f3f48ebb9ba59159cc39804b353ab147148c238a85f38c6097d57c5f89794e9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 212, + 156, + 280, + 162 + ], + "lines": [ + { + "bbox": [ + 212, + 156, + 280, + 162 + ], + "spans": [ + { + "bbox": [ + 212, + 156, + 280, + 162 + ], + "type": "text", + "content": "(c) Support vectors from SVM" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 253, + 286, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 286, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 286, + 479 + ], + "type": "text", + "content": "patches from all prototypes of other classes. The combination of these two losses pushes the prototypes as far as possible from the classification boundary, but still within the class distribution, so we call them trivial prototypes, as shown in Fig. 1(a). We also display the trivial prototypes, learned with a feed-forward neural network1, for the two-moon problem in Fig. 2(a). Notice that these trivial prototypes are located far from the classification boundary. In fine-grained visual classification, the trivial prototypes can mistakenly focus on background regions instead of on the object of interest [42, 41], particularly for those classes with subtle foreground (object) differences but large background variations, as shown in Fig. 3. Different from ProtoPNet's trivial prototypes, the support vector machine (SVM) [7] classifier relies on a set of support vectors that are close to the classification boundary, as in Fig. 2(c). These support vectors are often treated as hard samples. Motivated by SVM, we propose the derivation of support (i.e., hard-to-learn) prototypes for ProtoPNet methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 481, + 286, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 286, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 286, + 684 + ], + "type": "text", + "content": "In this paper, we propose an alternative learning strategy for ProtoPNet, which forces the learned prototypes to resemble SVM's support vectors and to be located as close as possible to the classification boundary. The strategy is formulated by a new closeness loss that minimises the distance between prototypes of different classes. As shown in Fig. 1(b), our new loss enforces the prototypes to move closer to the classification boundary, as also demonstrated by Fig. 2(b) revealing that the support prototypes produced by the introduction of our new closeness loss are indeed more similar to the support vectors of SVM in Fig. 2(c). Furthermore, to improve the classification accuracy, we propose a new ST-ProtoPNet method that integrates both the support and trivial prototypes. The ST-ProtoPNet leverages the two distinct and complementary sets of prototypes to capture both hard (i.e., close to the boundary) and easy (i.e., far from the boundary) visual features for classification." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 386, + 116 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 386, + 116 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 386, + 116 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 386, + 116 + ], + "type": "image", + "image_path": "62753c07f95b79484d0bcdfd93779e6349c8d5efd7168f7bbebc795a0bb7c39b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 118, + 545, + 152 + ], + "lines": [ + { + "bbox": [ + 306, + 118, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 306, + 118, + 545, + 152 + ], + "type": "text", + "content": "Figure 3. Example prototypes sampled from a VGG19-based ProtoPNet [4]. In each class, the left prototype focuses on object features while the right one captures background." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 387, + 72, + 465, + 116 + ], + "blocks": [ + { + "bbox": [ + 387, + 72, + 465, + 116 + ], + "lines": [ + { + "bbox": [ + 387, + 72, + 465, + 116 + ], + "spans": [ + { + "bbox": [ + 387, + 72, + 465, + 116 + ], + "type": "image", + "image_path": "327a68517bc98b9c639fbcf996e52406a2c1182b721808d2561b6e484659c5a6.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 466, + 72, + 545, + 116 + ], + "blocks": [ + { + "bbox": [ + 466, + 72, + 545, + 116 + ], + "lines": [ + { + "bbox": [ + 466, + 72, + 545, + 116 + ], + "spans": [ + { + "bbox": [ + 466, + 72, + 545, + 116 + ], + "type": "image", + "image_path": "956275a2456b859f702e5d6baf6c51544ad71b8964e0d3499903b325598ed141.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 163, + 485, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 163, + 485, + 174 + ], + "spans": [ + { + "bbox": [ + 317, + 163, + 485, + 174 + ], + "type": "text", + "content": "The major contributions of this work are:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 180, + 545, + 359 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 314, + 180, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 180, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 314, + 180, + 545, + 239 + ], + "type": "text", + "content": "1. We provide the first study that makes an analogy between the prototype learning from ProtoPNet and support vector learning from SVM, where we propose support (i.e., hard-to-learn) prototypes that can improve classification accuracy and interpretability." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 245, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 245, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 313, + 245, + 545, + 305 + ], + "type": "text", + "content": "2. We present a new ST-ProtoPNet method to exploit both support and trivial prototypes for interpretable image classification, where the two sets of prototypes can provide complementary information to improve classification accuracy." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 311, + 545, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 311, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 313, + 311, + 545, + 359 + ], + "type": "text", + "content": "3. We conduct extensive experiments on three benchmarks, showing that our ST-ProtoPNet outperforms current state-of-the-art (SOTA) methods in terms of classification accuracy and interpretability." + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 364, + 545, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 435 + ], + "type": "text", + "content": "In our experiments, we also demonstrate that the trivial and support prototypes have different characteristics, where the trivial prototypes tend to focus on both local parts of the visual object of interest and the background, while the support prototypes mainly focus on object parts belonging to the visual class of interest." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 448, + 391, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 448, + 391, + 460 + ], + "spans": [ + { + "bbox": [ + 306, + 448, + 391, + 460 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 468, + 466, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 466, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 466, + 480 + ], + "type": "text", + "content": "2.1. Classification Interpretability" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "type": "text", + "content": "The interpretation of classification results produced by deep neural networks can be achieved by a variety of post-hoc explanation techniques, e.g., explanatory surrogates [34, 56, 44], counterfactual examples [15, 46, 19], and saliency visualisation [45, 55, 59, 43]. Alternatively, prototype-based interpretable techniques can access the model's inner computations. ProtoPNet [4] is the original work that uses class-specific prototypes for interpretable image classification. Similar to ProtoPNet, TesNet [53] constructs class-specific transparent basis concepts on Grassmann manifold for the interpretable classification. Derived from ProtoPNet, Deformable ProtoPNet [11] employs spatially-flexible and deformable prototypes to adaptively capture meaningful object features. In ProtoPShare [42], a data-dependent merge-pruning method is presented to share prototypes among classes, which can reduce the number of prototypes used for classification. In contrast, ProtoPool [41] introduces a fully differentiable prototype assignment strategy to reduce the number of prototypes. In" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "1The network has an input layer of 2 nodes, a hidden layer of 256 nodes (activated by tanh), and an output layer of 2 nodes (activated by sigmoid)." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2063" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "content": "Proto2Proto [20], a knowledge distillation method is designed to transfer interpretability from a teacher ProtoPNet to a shallow student ProtoPNet. ProtoTree [35] integrates the prototype learning into a binary neural decision tree that can explain its predictions by tracing a decision path throughout the tree. ViT-NeT [24] further establishes the prototype neural tree structure on visual transformers [12]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 286, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 286, + 240 + ], + "type": "text", + "content": "Because of the ability to self-explain classification results, prototype-based interpretability (e.g., ProtoPNet) has been widely utilised not only in the computer vision applications above, but also in medical imaging [2, 22, 51] and face recognition [48]. However, an open question faced by these methods is if the prototypes being learned are the ideal ones in terms of classification and interpretability." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 249, + 251, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 249, + 251, + 262 + ], + "spans": [ + { + "bbox": [ + 47, + 249, + 251, + 262 + ], + "type": "text", + "content": "2.2. SVM vs Prototype-based Classification" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 267, + 286, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 286, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 286, + 506 + ], + "type": "text", + "content": "To better understand the role of prototypes, we consider the support vector machine (SVM) [7] classifier that finds support vectors to represent classes. More specifically, SVM learns the maximum-margin classifier defined by a classification boundary that maximises the distance to the closest training samples, which are the support vectors for the classes. The testing of SVM consists of computing a weighted similarity between a testing sample and the support vectors. It is interesting to note that the testing of prototype-based classifiers is also based on measuring the similarity between a testing image and a set of class-specific prototypes learned from the training process. Although the testing of SVM and prototype-based classifiers are similar, their training procedures are different. First, the training of a prototype-based classifier learns a fixed number of prototypes [4, 11], while the SVM classifier learns to weight a variable number of support vectors from the training set. Second, in prototype-based classifiers, the learned prototypes tend to be far from the classification boundary, which is contrary to the SVM training objective mentioned above." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 507, + 286, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 286, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 286, + 626 + ], + "type": "text", + "content": "The study of deep learning methods from an SVM theoretical perspective is a rich area of research [9, 38, 6], but there are many practical questions that need to be addressed, e.g., how to scale the kernel computation for large-scale datasets, how to shorten the training process [38], and how to integrate deep-learning features with the learning of the SVM classifier. In this paper, our focus is on adapting the learning of ProtoPNet's prototypes to make them similar to SVM's support vectors, by forcing prototypes to be as close as possible to the classification boundary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 635, + 246, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 246, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 246, + 647 + ], + "type": "text", + "content": "2.3. Interpretable Ensemble Classification" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "Ensemble classification [10] is a classical machine learning approach that combines the results from multiple classifiers, with the goals of improving learning generalisation and classification calibration. The use of interpretable ensemble strategy has been explored in [4, 53, 35, 11, 41]," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "which is achieved by summing the classification logits of multiple prototype-based classifiers (e.g., ProtoPNETs trained with different CNN backbones). In this work, we propose an interpretable ensemble classification by combining the predictions of two ProtoPNETs with highly distinctive prototypes (i.e., support and trivial prototypes), which is different from previous studies where the type of prototypes produced by each classifier is very similar given that the same training objective is used for each classifier." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 188, + 390, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 188, + 390, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 188, + 390, + 201 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": "We assume to have a training set " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(\\mathbf{x}_n,\\mathbf{y}_n)\\}_{n = 1}^{|\\mathcal{D}|}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{x}\\in \\mathcal{X}\\subset \\mathbb{R}^{H\\times W\\times R}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " is an image with " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " colour channels and " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{y}\\in \\mathcal{Y}\\subset \\{0,1\\} ^C" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " is a one-hot vector representation of the image class label. The interpretable ProtoPNet [4, 11] is trained to learn a set of prototypes " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = \\{\\mathbf{p}_m\\}_{m = 1}^M" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_m\\in \\mathbb{R}^{\\rho_1\\times \\rho_2\\times D}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " , with each of the " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " classes containing " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "M / C" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " prototypes. Without loss of generality, we assume " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\rho_{1} = \\rho_{2} = 1" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " , but the extension to general values is trivial. A typical ProtoPNet comprises four components: a CNN backbone, add-on layers, a prototype layer, and a fully connected (FC) layer. An input image " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " is fed to the CNN backbone " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "f_{\\theta}:X\\to \\mathcal{F}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " (parameterised by " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\theta \\in \\Theta" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{F}\\subset \\mathbb{R}^{H\\times \\bar{W}\\times \\bar{D}}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " ) and then passed on to the add-on layers, denoted by " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "f_{\\omega}:F\\rightarrow V" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " (parameterised by " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\omega \\in \\Omega" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " ), to produce a feature map " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{V}\\in \\mathcal{V}\\subset \\mathbb{R}^{\\bar{H}\\times \\bar{W}\\times D}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " . The prototype layer computes the similarity between the feature map " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "MD" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " dimensional prototypes " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{p}_m\\}_{m = 1}^M" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " to generate " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " similarity maps " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_m^{(i,j)} = \\mathrm{sim}(\\mathbf{V}(i,j,:),\\mathbf{p}_m)" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "i\\in \\{1,\\dots,\\bar{H}\\}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "j\\in \\{1,\\ldots ,\\bar{W}\\}" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " represents a similarity measure, e.g., cosine similarity [11] and projection metric [53]. The prototype layer outputs " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " similarity scores from maxpooling " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "S = \\left\\{\\max_{i\\in \\{1,\\dots,\\bar{H}\\},j\\in \\{1,\\dots,\\bar{W}\\}}\\mathbf{S}_m^{(i,j)}\\right\\}_{m = 1}^M" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " , which are fed to the FC layer " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "f_{\\phi}:S\\to \\Delta" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " parameterised by " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\phi \\in \\Phi" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " to produce the classification prediction " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}\\in \\Delta \\subset [0,1]^C" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " denotes the probability space for " + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 203, + 545, + 529 + ], + "type": "text", + "content": " classes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 537, + 392, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 392, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 392, + 550 + ], + "type": "text", + "content": "4. ST-ProtoPNet" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": "An overview of our proposed ST-ProtoPNet method is illustrated in Fig. 4, which comprises a shared CNN backbone " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": ", two interpretable ProtoPNet classification branches, namely: 1) the support ProtoPNet represented by add-on layers " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\omega^{(s)}}(\\cdot)" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": ", prototype layer with support prototypes " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^{(s)}" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": ", and FC layer " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\phi^{(s)}}(\\cdot)" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": " which outputs the classification probability distribution " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}^{(s)} \\in \\Delta" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": "; and 2) the trivial ProtoPNet branch with its add-on layers " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\omega^{(t)}}(\\cdot)" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": ", trivial prototypes " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^{(t)}" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": ", and FC layer " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\phi^{(t)}}(\\cdot)" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": " that generates probability predictions " + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}^{(t)} \\in \\Delta" + }, + { + "bbox": [ + 304, + 555, + 545, + 713 + ], + "type": "text", + "content": ". The final classification is obtained by combining the classification logits from both the support and trivial ProtoP nets. In our implementation, we construct the support and trivial ProtoPNet mainly based on the orig" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2064" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 289, + 189 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 189 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 189 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 189 + ], + "type": "image", + "image_path": "5a225871a407bdcd8c1652f81c89d811688c20672f9f3666b79577548ceee27f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 191, + 287, + 213 + ], + "lines": [ + { + "bbox": [ + 47, + 191, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 287, + 213 + ], + "type": "text", + "content": "Figure 4. The architecture of our proposed ST-ProtoPNet method for the interpretable image classification." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 223, + 272, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 223, + 272, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 272, + 235 + ], + "type": "text", + "content": "inal ProtoPNet [4] and TesNet [53], as explained below." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 242, + 160, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 242, + 160, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 242, + 160, + 255 + ], + "type": "text", + "content": "4.1. Support ProtoPNet" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 261, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 287, + 308 + ], + "type": "text", + "content": "The support ProtoPNet is designed to produce support prototypes that are as close as possible to the classification boundary, as shown in Fig. 1(b) and 2(b). The loss function to optimise the support ProtoPNet branch is defined as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 316, + 287, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 373 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\theta^ {*}, \\omega^ {(s) *}, \\mathcal {P} ^ {(s) *}, \\phi^ {(s) *} = \\\\ \\arg \\min _ {\\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}} \\sum_ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D}} \\ell_ {s p t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}). \\tag {1} \\\\ \\end{array}", + "image_path": "de175b7a7936f88623c6932e2324c65480828299e5af74cba91df16061481b80.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 383, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 287, + 407 + ], + "type": "text", + "content": "The loss for each training sample " + }, + { + "bbox": [ + 47, + 383, + 287, + 407 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},\\mathbf{y})\\in \\mathcal{D}" + }, + { + "bbox": [ + 47, + 383, + 287, + 407 + ], + "type": "text", + "content": " in Eq. (1) above is represented by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 415, + 290, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 290, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 290, + 510 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\ell_ {s p t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}) = \\ell_ {c e} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}, \\phi^ {(s)}) \\\\ - \\lambda_ {1} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) \\\\ + \\lambda_ {2} \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) \\\\ - \\lambda_ {3} \\ell_ {c l s} (\\mathcal {P} ^ {(s)}) \\\\ + \\lambda_ {4} \\ell_ {o r t} (\\mathcal {P} ^ {(s)}), \\tag {2} \\\\ \\end{array}", + "image_path": "2c5777f7d14c1638df2b75e43ecbac289bec652cb1056f756fff23fe232785eb.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2},\\lambda_{3}" + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\lambda_{4}" + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "text", + "content": " are hyper-parameters to balance each term, " + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\ell_{ce}(\\cdot)" + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "text", + "content": " denotes the cross-entropy classification loss, " + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\ell_{ct}(\\cdot)" + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\ell_{sp}(\\cdot)" + }, + { + "bbox": [ + 47, + 520, + 287, + 579 + ], + "type": "text", + "content": " represent the clustering and separation losses, respectively, which are introduced to regularise the ProtoPNet's training, as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 586, + 287, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 586, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 58, + 586, + 287, + 654 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) = \\max _ {\\mathbf {p} \\in \\mathcal {P} _ {\\mathbf {y}} ^ {(s)}} \\max _ {\\mathbf {v} \\in \\mathbf {V} ^ {(s)}} \\sin (\\mathbf {v}, \\mathbf {p}), (3) \\\\ \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(s)}, \\mathcal {P} ^ {(s)}) = \\max _ {\\mathbf {p} \\notin \\mathcal {P} _ {\\mathbf {y}} ^ {(s)}} \\max _ {\\mathbf {v} \\in \\mathbf {V} ^ {(s)}} \\operatorname {s i m} (\\mathbf {v}, \\mathbf {p}), (4) \\\\ \\end{array}", + "image_path": "67b607c78b017d293c89402d51b6f03089fcf59995baf8d4018300f68fb4b0d7.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{(s)} = f_{\\omega^{(s)}}(f_{\\theta}(\\mathbf{x}))" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " is the feature map extracted from the input image " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " represents one of the " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\bar{H} \\times \\bar{W}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " feature vectors in " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{(s)}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " obtained by matrix vectorisation, " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " is a normalised prototype (i.e., unit vector) in " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^{(s)}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\sin (\\cdot, \\cdot)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 71, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 144 + ], + "type": "text", + "content": "is one of the similarity functions defined in Sec. 3, and " + }, + { + "bbox": [ + 304, + 71, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\mathbf{y}}^{(s)}" + }, + { + "bbox": [ + 304, + 71, + 545, + 144 + ], + "type": "text", + "content": " denotes the set of prototypes of class " + }, + { + "bbox": [ + 304, + 71, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 71, + 545, + 144 + ], + "type": "text", + "content": ". The clustering loss in Eq. (3) and separation loss in Eq. (4) aim to learn a meaningful feature space in which the image features of a certain class are clustered around the prototypes of the class, and also well separated from those of other classes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 144, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 239 + ], + "type": "text", + "content": "As mentioned in Sec. 1, the effect of the clustering and separation losses above tend to push the prototypes of different classes as far as possible from the classification boundary, resulting in trivial prototypes, as displayed in Fig. 1(a) and Fig. 2(a). In order to learn the proposed support prototypes, we introduce the following novel closeness loss " + }, + { + "bbox": [ + 304, + 144, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\ell_{cls}" + }, + { + "bbox": [ + 304, + 144, + 545, + 239 + ], + "type": "text", + "content": " to explicitly enforce the prototypes of different classes to be close to each other, which is formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 319, + 247, + 545, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 247, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 319, + 247, + 545, + 281 + ], + "type": "interline_equation", + "content": "\\ell_ {c l s} \\left(\\mathcal {P} ^ {(s)}\\right) = \\sum_ {c _ {1} = 1} ^ {C - 1} \\sum_ {c _ {2} = c _ {1} + 1} ^ {C} \\min _ {\\mathbf {p} _ {m} \\in \\mathcal {P} _ {c _ {1}}, \\mathbf {p} _ {n} \\in \\mathcal {P} _ {c _ {2}}} \\mathbf {p} _ {m} ^ {\\top} \\mathbf {p} _ {n}. \\tag {5}", + "image_path": "c86157900ee00e826afa1d58ad7afcf902ea71ad687bda07b2af155bc94d0fe3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": "During training, this closeness loss " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\ell_{cls}" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " maximises the pair-wise prototype similarity, in the form of dot product " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_m^\\top \\mathbf{p}_n" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " between different classes in Eq. (5) above, with the goal of pulling the prototypes close to the classification boundary. On the one hand, as the prototypes move gradually towards the classification boundary, they are able to capture harder visual features from training samples. On the other hand, since the prototypes are located near the classification boundary, they can put pressure on the support ProtoPNet's feature learning (i.e., enforce it to learn highly discriminative feature representations for accurate classification), which is beneficial to extract more meaningful semantic information from training samples." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "type": "text", + "content": "Ideally, each prototype of a class should focus on unique object parts of the training images (e.g., head, tail, and claw of birds), so that the prototypes can represent rich and diverse visual patterns. However, there is no particular constraints to guarantee such prototype diversity and the issue of prototype duplication [11] often occurs in the ProtoPNet family of models. To encourage the intra-class prototype diversity, we employ an orthonormality loss [53] so that prototypes within a class can represent dissimilar visual patterns of training samples, which is defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 345, + 573, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 573, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 345, + 573, + 545, + 605 + ], + "type": "interline_equation", + "content": "\\ell_ {o r t} \\left(\\mathcal {P} ^ {(s)}\\right) = \\sum_ {c = 1} ^ {C} \\left\\| \\mathbf {P} _ {c} ^ {\\top} \\mathbf {P} _ {c} - \\mathbf {I} _ {M / C} \\right\\| _ {F} ^ {2}, \\tag {6}", + "image_path": "f90f1fd4594631ae1c0dec76ad8ffd66ef8ac44c9610f04bd74de6db35568cbd.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\| _F^2" + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "text", + "content": " represents Frobenius norm, " + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_c\\in D\\times \\mathbb{R}^{(M / C)}" + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "text", + "content": " stands for a matrix composed of the prototypes of class " + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "text", + "content": " (prototypes in each column of " + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_c" + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "text", + "content": " are normalised), and " + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{M / C}" + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "text", + "content": " is an identity matrix of size " + }, + { + "bbox": [ + 304, + 614, + 545, + 665 + ], + "type": "inline_equation", + "content": "M / C\\times M / C" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 670, + 411, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 411, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 411, + 682 + ], + "type": "text", + "content": "4.2. Trivial ProtoPNet" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "As described in Sec. 4.1, the support ProtoPNet is developed to learn support (i.e., hard-to-learn) prototypes by" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2065" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "content": "forcing them to be close to the classification boundary. Considering that training samples contain not only hard visual features but also important easy ones that the support prototypes cannot completely capture, we propose to also learn trivial prototypes to provide complementary classification information, and exploit both the support and trivial prototypes for improved interpretable classification." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 156, + 286, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 178 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 178 + ], + "type": "text", + "content": "The loss objective to optimise the trivial ProtoPNet branch is defined as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 184, + 286, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 184, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 52, + 184, + 286, + 239 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\theta^ {*}, \\omega^ {(t) *}, \\mathcal {P} ^ {(t) *}, \\phi^ {(t) *} = \\\\ \\arg \\min _ {\\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}} \\sum_ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D}} \\ell_ {t r v} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}). \\tag {7} \\\\ \\end{array}", + "image_path": "2dff1a4497506a0a9544fd77aef2344ea3dbb8002ce2b44fa4733e96648febe9.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 247, + 286, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 286, + 270 + ], + "type": "text", + "content": "The loss for each training image " + }, + { + "bbox": [ + 47, + 247, + 286, + 270 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},\\mathbf{y})\\in \\mathcal{D}" + }, + { + "bbox": [ + 47, + 247, + 286, + 270 + ], + "type": "text", + "content": " in Eq. (7) above is represented by:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 276, + 286, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 276, + 286, + 369 + ], + "spans": [ + { + "bbox": [ + 49, + 276, + 286, + 369 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\ell_ {t r v} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}) = \\ell_ {c e} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}, \\phi^ {(t)}) \\\\ - \\lambda_ {1} \\ell_ {c t} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {2} \\ell_ {s p} (\\mathbf {x}, \\mathbf {y}, \\theta , \\omega^ {(t)}, \\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {3} \\ell_ {d s c} (\\mathcal {P} ^ {(t)}) \\\\ + \\lambda_ {4} \\ell_ {\\text {o r t}} (\\mathcal {P} ^ {(t)}), \\tag {8} \\\\ \\end{array}", + "image_path": "02e477c5b9dc6e9ebe96e97dca86bd526e647c275a9255708405c66d4368506e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2},\\lambda_{3}" + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "inline_equation", + "content": "\\lambda_{4}" + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "text", + "content": " are hyper-parameters, " + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "inline_equation", + "content": "\\ell_{ce}(\\cdot)" + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "text", + "content": " is the cross-entropy loss, the clustering loss " + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "inline_equation", + "content": "\\ell_{ct}" + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "text", + "content": ", separation loss " + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "inline_equation", + "content": "\\ell_{sp}" + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "text", + "content": ", and orthonormality loss " + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "inline_equation", + "content": "\\ell_{ort}" + }, + { + "bbox": [ + 47, + 376, + 286, + 424 + ], + "type": "text", + "content": " are the same as in the support ProtoPNet defined in Eq. (3), (4) and (6), respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 424, + 286, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 286, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 286, + 507 + ], + "type": "text", + "content": "The trivial ProtoPNet targets the learning of easy prototypes that are far from the classification boundary and have a good discrimination ability. To help achieve this, we introduce a new discrimination loss " + }, + { + "bbox": [ + 46, + 424, + 286, + 507 + ], + "type": "inline_equation", + "content": "\\ell_{dsc}" + }, + { + "bbox": [ + 46, + 424, + 286, + 507 + ], + "type": "text", + "content": " to facilitate the interclass separability between prototypes of different classes. This is formulated by minimising the pair-wise prototype similarities of different classes, as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 514, + 286, + 546 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 514, + 286, + 546 + ], + "spans": [ + { + "bbox": [ + 63, + 514, + 286, + 546 + ], + "type": "interline_equation", + "content": "\\ell_ {d s c} \\left(\\mathcal {P} ^ {(t)}\\right) = \\sum_ {c _ {1} = 1} ^ {C - 1} \\sum_ {c _ {2} = c _ {1} + 1} ^ {C} \\max _ {\\mathbf {p} _ {m} \\in \\mathcal {P} _ {c _ {1}}, \\mathbf {p} _ {n} \\in \\mathcal {P} _ {c _ {2}}} \\mathbf {p} _ {m} ^ {\\top} \\mathbf {p} _ {n}. \\tag {9}", + "image_path": "aafcfbfaa8e2398dddb66c48286513acc53c7c285169230c3cc8c54b9d0383df.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 552, + 167, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 167, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 167, + 564 + ], + "type": "text", + "content": "4.3. Training and Testing" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "type": "text", + "content": "Training. Following the training strategies in [4, 11], the training procedure of our ST-ProtoPNet consists of 3 stages: 1) optimisation of the CNN backbone, add-on layers, and prototype layer, using a fixed FC layer initialised with " + }, + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "type": "inline_equation", + "content": "+1.0" + }, + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "type": "text", + "content": " and -0.5 for correct and incorrect connection weights, respectively. A warm-up of 5 epochs is involved in this stage by updating only the parameters of add-on layers and prototype layer, with a frozen pre-trained CNN backbone. 2) prototype projection by updating each prototype with its nearest latent training image patch; and 3) optimisation of the FC layer, with an additional " + }, + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 570, + 286, + 712 + ], + "type": "text", + "content": " regularisation on the incorrect connection weights (initially fixed at" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "-0.5). In each stage, we alternate the optimisation of each branch of the ST-ProtoPNet between mini-batches. Notice that our method only brings marginal extra model parameters, computational complexity, and training time since the CNN backbone is shared and optimised by both branches." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 136, + 545, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 136, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 304, + 136, + 545, + 196 + ], + "type": "text", + "content": "Testing. To exploit the complementary results from both branches of ST-ProtoPNet, its final classification is obtained from the summed logits predicted by the two branches. It is worth noticing that this ensemble strategy introduces no loss of interpretability but improved accuracy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 215, + 386, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 215, + 386, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 215, + 386, + 228 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 235, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 545, + 378 + ], + "type": "text", + "content": "We perform experiments on three fine-grained classification benchmark datasets: CUB-200-2011 [50], Stanford Cars [27], and Stanford Dogs [21]. To achieve fair comparison, we follow previous studies [4, 53] by applying offline data augmentations (e.g., random rotation, skew, shear, and left-right flip) on the cropped CUB and cropped Cars datasets (using the bounding boxes provided). We also validate our method on the full (i.e., uncropped) CUB and Dogs datasets, and employ the same online data augmentation methods (e.g., random affine transformation and left-right flip) as used in Deformable ProtoPNet [11]. All images are resized to " + }, + { + "bbox": [ + 304, + 235, + 545, + 378 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 235, + 545, + 378 + ], + "type": "text", + "content": " pixels as network input." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 395, + 432, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 395, + 432, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 395, + 432, + 407 + ], + "type": "text", + "content": "5.1. Experimental Settings" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": "The proposed ST-ProtoPNet method is evaluated on the following CNN architectures: VGG-16, VGG-19, ResNet-34, ResNet-50, ResNet-152, DenseNet-121, and DenseNet-161. All CNN backbones are pre-trained on ImageNet [8], except for ResNet-50, which is pre-trained on iNaturalist [49] for the experiment on full CUB [11]. The add-on layers include two " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " convolutional layers. For simplicity, we utilise the same prototype dimension " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "D = 64" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " for all CNN backbones on the three datasets. For cropped CUB and Cars datasets, following [53], we use 10 prototypes (5 support and 5 trivial) per class and the projection metric in the similarity function " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": ". In full CUB and Dogs datasets, to ensure comparison fairness with Deformable ProtoPNet [11] that uses " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "102 \\times 2" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " (full CUB) and " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "103 \\times 3" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " (full Dogs) deformable prototypes per class, we utilise the same total number of prototypes, i.e., " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "401 \\times 1" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " (20 support and 20 trivial) for full CUB and " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "901 \\times 1" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " (45 support and 45 trivial) for full Dogs. Also, we employ the cosine similarity in " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " and obtain " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "14 \\times 14" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\bar{H} = \\bar{W} = 14" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": ") feature maps by upsampling the original " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " feature maps via a bi-linear interpolation step, as in [11]. Following previous prototype-based methods [4, 53, 11], we set " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{1} = 0.8" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 0.48" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " and 0.08 for the support and trivial ProtoPNet branches respectively, " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{4} = 0.001" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": ". We choose " + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{3} = 1.0" + }, + { + "bbox": [ + 304, + 415, + 545, + 713 + ], + "type": "text", + "content": " with an ablation provided in the supplementary material." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2066" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 197, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 197, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 197, + 85 + ], + "type": "text", + "content": "5.2. Interpretability Evaluation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 87, + 286, + 136 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 87, + 286, + 136 + ], + "spans": [ + { + "bbox": [ + 47, + 87, + 286, + 136 + ], + "type": "text", + "content": "Rather than performing user-based evaluations [60, 41], whose results are often subjective and difficult to reproduce [54], we leverage the annotated object masks to measure interpretability based on the following metrics:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 137, + 286, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 137, + 286, + 172 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 286, + 172 + ], + "type": "text", + "content": "Content Heatmap (CH) [37]: quantifies the percentage of an activation heatmap that lies within the annotated mask. Hence, we expect this metric to be high." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 173, + 286, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 173, + 286, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 173, + 286, + 233 + ], + "type": "text", + "content": "Outside-Inside Relevance Ratio (OIRR) [29]: calculates the ratio of mean activation outside the object to mean activation inside the object. A low OIRR indicates a method relies more on the object region and less on the context to support its decision, we thus anticipate OIRR to be low." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 233, + 286, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 233, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 233, + 286, + 270 + ], + "type": "text", + "content": "Intersection over Union (IoU) [5]: measures the mean IoU score, where a threshold of 0.5 is applied on the min-max normalised heatmap to select foreground objects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 270, + 286, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 286, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 286, + 330 + ], + "type": "text", + "content": "Deletion AUC (DAUC) [36]: estimates a decrease in the probability of the predicted class as more and more important/activated pixels are removed. The area under the probability curve is defined as DAUC. Consequently, a sharp drop and a low DAUC mean better interpretation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 331, + 286, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 286, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 286, + 426 + ], + "type": "text", + "content": "Average Inter-class Prototype Distance (AIPD), Average Inter-class Feature Distance (AIFD): we had earlier stated that support prototypes of different classes should be close to each other and trivial prototypes should be far from each other. Thus, we compute the average inter-class cosine distance for prototypes and their nearest local feature representations, respectively. We expect AIPD " + }, + { + "bbox": [ + 47, + 331, + 286, + 426 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 47, + 331, + 286, + 426 + ], + "type": "text", + "content": " AIFD for support ProtoPNet and AIPD " + }, + { + "bbox": [ + 47, + 331, + 286, + 426 + ], + "type": "inline_equation", + "content": ">" + }, + { + "bbox": [ + 47, + 331, + 286, + 426 + ], + "type": "text", + "content": " AIFD for trivial ProtoPNet." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 433, + 195, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 195, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 195, + 445 + ], + "type": "text", + "content": "5.3. Classification Performance" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 449, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 286, + 700 + ], + "type": "text", + "content": "Table 1 presents the classification accuracy (across 5 runs) of our proposed ST-ProtoPNet on cropped CUB and cropped Cars, where the Baseline is represented by non-interpretable black-box CNN models. As can be seen, our ST-ProtoPNet outperforms other competing methods across all backbones for the task of bird species classification. Also, our method achieves the best results for the car model identification task when using VGG and DenseNet architectures as the CNN backbone. In particular, our VGG19-based ST-ProtoPNet reaches an average accuracy of " + }, + { + "bbox": [ + 47, + 449, + 286, + 700 + ], + "type": "inline_equation", + "content": "83.2\\%" + }, + { + "bbox": [ + 47, + 449, + 286, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 449, + 286, + 700 + ], + "type": "inline_equation", + "content": "91.7\\%" + }, + { + "bbox": [ + 47, + 449, + 286, + 700 + ], + "type": "text", + "content": " on CUB and Cars, respectively, surpassing other methods with the most improvements across all backbones. Moreover, the support ProtoPNet generally performs better than methods utilising only trivial prototypes (e.g., ProtoPNet, TesNet, and Trivial ProtoPNet), showing the importance of learning support prototypes for the interpretable classification. It is worth noting that our ST-ProtoPNet produces superior performance over the support ProtoPNet method, indicating that both support and trivial prototypes are useful and can provide complementary information for achieving accurate and interpretable classification." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 701, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 712 + ], + "type": "text", + "content": "Table 2 shows the classification results on full CUB and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": "full Dogs. In both datasets, the classification accuracy of the original ProtoPNet method is generally worse than the non-interpretable counterpart (Baseline) for many CNN backbones. On the other hand, the accuracy by the trivial ProtoPNet and support ProtoPNet are substantially better than those by Baseline, ProtoPNet, and Deformable ProtoPNet. However, our ST-ProtoPNet achieves more significant performance gains and exhibits the best accuracy across most backbones, particularly when using a large number of prototypes (i.e., " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "401 \\times 1" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " prototypes per class for CUB and " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "901 \\times 1" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " prototypes per class for Dogs), demonstrating the effectiveness of utilising both the trivial and support prototypes for the interpretable image classification. Additionally, when using a smaller number of prototypes, i.e., " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "101 \\times 1" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " prototypes per class, our ST-ProtoPNet still has competitive classification accuracy across multiple backbones." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 264, + 545, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 545, + 419 + ], + "type": "text", + "content": "We further compare our ST-ProtoPNet with other deep-learning methods that can provide different levels of interpretability on CUB, with results shown in Table 3, where * and ** denote ensemble of models with different backbones. As evident, an ensemble of three ST-ProtoPNETs can achieve high accuracy (87.9% on cropped images, 88.2% on full images), outperforming competing methods that are also based on an ensemble of three models (e.g., ProtoTree, TesNet, and ProtoPool). Moreover, the ensemble of five STProtoPNETs outperforms all other competing methods and obtains the best classification accuracy of 88.1% and 88.4% on cropped and full CUB images, respectively. More results on Cars and Dogs are given in the supplementary material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 426, + 462, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 426, + 462, + 438 + ], + "spans": [ + { + "bbox": [ + 306, + 426, + 462, + 438 + ], + "type": "text", + "content": "5.4. Interpretability Comparison" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 441, + 545, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 645 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 645 + ], + "type": "text", + "content": "We assess the model interpretability on full CUB using the annotated bird segmentation mask" + }, + { + "bbox": [ + 304, + 441, + 545, + 645 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 441, + 545, + 645 + ], + "type": "text", + "content": ". Quantitative results on the test set are given in Table 4, where all methods are based on the VGG19 backbone. We use GradCAM [43] for the non-interpretable baseline. For prototype-based methods, we average the activation map of all prototypes of a class to compute the metrics. We can see our proposed support ProtoPNet can effectively improve the interpretableity in all measures, showing the interpretations produced by our support prototypes are more likely to be object-dependent and focus less on context cues. Also, our ST-ProtoPNet method shows better interpretable results than the support ProtoPNet in terms of CH, OIRR, and DAUC. Compared with the original ProtoPNet [4], our ST-ProtoPNet obtains significant interpretability improvements. We show some example activation maps in the supplementary material, and an experiment with prototype pruning is also provided." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 645, + 545, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 645, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 645, + 545, + 693 + ], + "type": "text", + "content": "Table 5 presents the computed AIPD and AIFD for the support and trivial ProtoPNet on cropped CUB, using VGG19 and ResNet34 as CNN backbones. As evident, the AIPD is indeed smaller than AIFD for the support ProtoP-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 448, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 448, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 448, + 712 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 317, + 702, + 448, + 712 + ], + "type": "text", + "content": "http://www.vision.caltech.edu/datasets/" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2067" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 144 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 144 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 144 + ], + "type": "table", + "html": "
MethodCUBCars
VGG16VGG19ResNet34ResNet152Dense121Dense161VGG16VGG19ResNet34ResNet152Dense121Dense161
Baseline73.3 ± 0.274.7 ± 0.482.2 ± 0.380.8 ± 0.481.8 ± 0.182.1 ± 0.287.3 ± 0.488.5 ± 0.392.6 ± 0.392.8 ± 0.492.0 ± 0.392.5 ± 0.3
ProtoPNet [4]77.2 ± 0.277.6 ± 0.278.6 ± 0.179.2 ± 0.379.0 ± 0.280.8 ± 0.388.3 ± 0.289.4 ± 0.288.8 ± 0.188.5 ± 0.387.7 ± 0.189.5 ± 0.2
TesNet [53]81.3 ± 0.281.4 ± 0.182.8 ± 0.182.7 ± 0.284.8 ± 0.284.6 ± 0.390.3 ± 0.290.6 ± 0.290.9 ± 0.292.0 ± 0.291.9 ± 0.392.6 ± 0.3
Trivial ProtoPNet80.8 ± 0.281.2 ± 0.282.5 ± 0.283.1 ± 0.383.9 ± 0.384.6 ± 0.390.1 ± 0.290.7 ± 0.291.1 ± 0.291.5 ± 0.291.4 ± 0.392.4 ± 0.3
Support ProtoPNet81.7 ± 0.281.8 ± 0.383.0 ± 0.183.6 ± 0.284.7 ± 0.285.2 ± 0.390.9 ± 0.290.8 ± 0.291.0 ± 0.291.8 ± 0.291.7 ± 0.292.7 ± 0.3
ST-ProtoPNet (ours)82.9 ± 0.283.2 ± 0.283.5 ± 0.184.1 ± 0.285.4 ± 0.286.1 ± 0.291.1 ± 0.291.7 ± 0.291.4 ± 0.192.0 ± 0.292.3 ± 0.392.7 ± 0.2
", + "image_path": "c5d10942c36b185c323a35196cc8816b8d88eef4625de7b9aee941e18788006a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 168, + 545, + 262 + ], + "blocks": [ + { + "bbox": [ + 47, + 148, + 545, + 159 + ], + "lines": [ + { + "bbox": [ + 47, + 148, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 545, + 159 + ], + "type": "text", + "content": "Table 1. Classification accuracy (%) on cropped CUB-200-2011 and Stanford Cars by competing methods using different CNN backbones." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 168, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 50, + 168, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 50, + 168, + 545, + 262 + ], + "type": "table", + "html": "
Method# PrototypeCUB# PrototypeDogs
VGG16VGG19ResNet34ResNet50ResNet152Dense121Dense161VGG16VGG19ResNet34ResNet50ResNet152Dense121Dense161
Baseline-70.971.376.078.779.278.280.0-75.677.381.183.185.281.984.1
ProtoPNet [4]1×1p, 10pc70.372.672.481.174.374.075.41×1p, 10pc70.773.673.476.476.272.077.3
ProtoPNet [4]1×1p, 40pc72.974.274.184.876.076.678.51×1p, 90pc73.975.376.178.179.775.478.8
TesNet [53]1×1p, 10pc75.877.576.286.579.080.279.61×1p, 10pc74.377.180.182.483.880.383.8
TesNet [53]1×1p, 40pc77.679.276.587.380.180.981.31×1p, 90pc78.579.681.283.384.582.185.2
Deformable ProtoPNet [11]2×2p, 10pc75.776.076.886.479.679.081.23×3p, 10pc75.877.980.682.286.580.783.7
Trivial ProtoPNet1×1p, 40pc80.079.577.587.280.881.182.11×1p, 90pc78.680.482.685.087.082.385.9
Support ProtoPNet1×1p, 40pc80.480.078.487.580.281.582.41×1p, 90pc79.080.683.085.187.382.686.2
ST-ProtoPNet (ours)1×1p, 10pc76.877.677.486.678.778.680.61×1p, 10pc74.277.280.884.085.379.484.4
ST-ProtoPNet (ours)1×1p, 40pc81.080.278.288.081.281.882.71×1p, 90pc79.180.983.485.787.282.986.6
", + "image_path": "ce4f997923ea44f2865bae14fa639ba22b5f6cc32c66e26b8dc3b7ba76fdfcd3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 50, + 297, + 285, + 465 + ], + "blocks": [ + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "lines": [ + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "type": "text", + "content": "Table 2. Classification accuracy (%) on full CUB-200-2011 and Stanford Dogs datasets by competing approaches using different CNN backbones, where " + }, + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "type": "inline_equation", + "content": "{\\rho }_{1} \\times {\\rho }_{2}\\mathrm{p}" + }, + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "type": "text", + "content": " denotes the spatial shape of prototypes and " + }, + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "type": "inline_equation", + "content": "k\\mathrm{{pc}}" + }, + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "type": "text", + "content": " represents " + }, + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 264, + 545, + 286 + ], + "type": "text", + "content": " prototypes per class." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 297, + 285, + 465 + ], + "lines": [ + { + "bbox": [ + 50, + 297, + 285, + 465 + ], + "spans": [ + { + "bbox": [ + 50, + 297, + 285, + 465 + ], + "type": "table", + "html": "
Interpretability levelMethodAccuracy (%)
NoneB-CNN [32]85.1 (b)84.1 (f)
Object-level attentionCAM [59]70.5 (b)63.0 (f)
CSG [31]82.6 (b)78.5 (f)
Part-level attentionPA-CNN [26]82.8 (b)-
MG-CNN [52]83.0 (b)81.7 (f)
MA-CNN [57]-86.5 (f)
RA-CNN [14]-85.3 (f)
TASN [58]-87.0 (f)
Part-level attention + PrototypesRegion [17]81.5 (b)80.2 (f)
ProtoPNet* [4]84.8 (b)81.1 (f)
ProtoTree* [35]-86.6 (f)
TesNet* [53]86.2 (b)83.5 (f)
ProtoPool* [41]87.5 (b)-
ST-ProtoPNet* (ours)87.9 (b)88.2 (f)
ProtoTree** [35]-87.2 (f)
Deformable ProtoPNet** [11]-87.8 (f)
ProtoPool** [41]87.6 (b)-
ST-ProtoPNet** (ours)88.1 (b)88.4 (f)
", + "image_path": "022894e2e50c6e5fdb76433494cc25f1ebc0b94d69946bdf508a6934a48f5c97.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 49, + 521, + 285, + 559 + ], + "blocks": [ + { + "bbox": [ + 47, + 467, + 287, + 511 + ], + "lines": [ + { + "bbox": [ + 47, + 467, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 287, + 511 + ], + "type": "text", + "content": "Table 3. Classification accuracy and interpretability level of different methods on CUB-200-2011. \"b\" and \"f\" denote the model is trained and tested on cropped and full images, respectively. *: Ensemble of three models. **: Ensemble of five models." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 521, + 285, + 559 + ], + "lines": [ + { + "bbox": [ + 49, + 521, + 285, + 559 + ], + "spans": [ + { + "bbox": [ + 49, + 521, + 285, + 559 + ], + "type": "table", + "html": "
MetricGradCAM [43]ProtoPNet [4]TesNet [53]DefProto [11]TrvProtoSptProtoST-Proto
CH (%, ↑)52.4648.6659.3852.0963.0563.8766.43
IoU (%, ↑)39.9138.0336.9240.7737.7442.0441.05
OIRR (%, ↓)37.0137.2638.9728.6834.4828.6928.09
DAUC (%, ↓)7.017.395.865.996.065.805.74
", + "image_path": "6d1bf0cc121f7bece7d0d19fdc61d07c42529c419ac20570179ffb319bb330d7.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 609, + 287, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 287, + 669 + ], + "type": "text", + "content": "Net while AIPD is larger than AIFD for the trivial ProtoP-Net. This result indicates that the support prototypes of different classes lie closer than their local feature representations and are more inclined to focus on visually similar (i.e., hard-to-learn) object parts of different classes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 674, + 173, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 674, + 173, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 674, + 173, + 687 + ], + "type": "text", + "content": "5.5. Visualisation Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "To explore the differences between the support and trivial prototypes, we select 5 categories of birds with visu" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 308, + 298, + 544, + 334 + ], + "blocks": [ + { + "bbox": [ + 47, + 562, + 286, + 594 + ], + "lines": [ + { + "bbox": [ + 47, + 562, + 286, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 286, + 594 + ], + "type": "text", + "content": "Table 4. Quantitative interpretability results on full CUB test set. DefProto = Deformable ProtoPNet, TrvProto = Trivial ProtoPNet, SptProto = Support ProtoPNet, ST-Proto = ST-ProtoPNet." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 298, + 544, + 334 + ], + "lines": [ + { + "bbox": [ + 308, + 298, + 544, + 334 + ], + "spans": [ + { + "bbox": [ + 308, + 298, + 544, + 334 + ], + "type": "table", + "html": "
VGG19ResNet34
SupportProtoPNetTrivialProtoPNetSupportProtoPNetTrivialProtoPNet
AIPDAIFDAIPDAIFDAIPDAIFDAIPDAIFD
0.72590.92640.99870.92320.65410.85731.0000.9481
", + "image_path": "2dc5982f5443d80c14a93a17708678ab39af428b9492e28a145222d66f5631b0.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 337, + 545, + 369 + ], + "lines": [ + { + "bbox": [ + 306, + 337, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 337, + 545, + 369 + ], + "type": "text", + "content": "Table 5. Average inter-class prototype distance (AIPD) and average inter-class feature distance (AIFD) for the support and trivial ProtoPNet trained on cropped CUB." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 307, + 376, + 545, + 622 + ], + "blocks": [ + { + "bbox": [ + 307, + 376, + 545, + 622 + ], + "lines": [ + { + "bbox": [ + 307, + 376, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 307, + 376, + 545, + 622 + ], + "type": "image", + "image_path": "83c79ab267d0912173d5809975c3ccf5eb7be6e68b6b5f985411c1e8a549135f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 625, + 545, + 669 + ], + "lines": [ + { + "bbox": [ + 305, + 625, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 305, + 625, + 545, + 669 + ], + "type": "text", + "content": "Figure 5. The support (top) and trivial (bottom) prototypes from cropped CUB. In each pair, the first column shows the original image with a prototype marked in a yellow bounding box, the second column is the prototype's corresponding activation map." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "ally similar features from cropped CUB to train the support and trivial ProtoPNet methods, with the learned prototypes shown in Fig. 5. We notice the support prototypes can cap" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2068" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 165, + 153 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 165, + 153 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 165, + 153 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 165, + 153 + ], + "type": "image", + "image_path": "c5320708478b8263ae8a62171c8a0f7c9ab52b29de6f99c906d8e076f78b10ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": "Figure 6. T-SNE results of support and trivial prototypes. The prototypes and their nearest latent training features are marked with stars and dots, respectively. We show results before the prototype projection stage to better visualise the relation between the prototypes and features. Each colour represents a different class." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 171, + 70, + 286, + 153 + ], + "blocks": [ + { + "bbox": [ + 171, + 70, + 286, + 153 + ], + "lines": [ + { + "bbox": [ + 171, + 70, + 286, + 153 + ], + "spans": [ + { + "bbox": [ + 171, + 70, + 286, + 153 + ], + "type": "image", + "image_path": "8f698f6fdfeb661718aabd98d51d3d8f5a6d657798fc09b9ab9fc1661b9a723e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 222, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 222, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 287, + 426 + ], + "type": "text", + "content": "ture subtle and fine visual features of different classes and they only focus on relevant bird parts, e.g., head and belly. This is reasonable since our algorithm is designed to produce prototypes that are as close as possible to each other, where the image prototypical parts should not only be discriminative but also share visually similar features among classes. By contrast, the trivial prototypes tend to focus not only on the relevant bird parts but also the background regions. For example, some trivial prototypes of the Laysan Albatross and Sooty Albatross classes capture the sea surface as they often appear with the sea background. We argue that this is because the trivial ProtoPNet may treat the background as an easy pattern to learn, focusing less on the object's visual parts of the class. In Fig. 6, we show the t-SNE result from the 5-category bird classification, where we note the support prototypes of different classes are located closer to each other, in comparison with the trivial prototypes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 426, + 288, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 619 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 619 + ], + "type": "text", + "content": "Fig. 7 shows an example of the interpretable reasoning for our ST-ProtoPNet in classifying a testing bird image. As evident, each ProtoPNet branch calculates its own classification logits (weighted sum of similarity scores), which is then combined to generate the final prediction. Specifically, when classifying a Parakeet Auklet, the support prototypes are quite active on the bird's beak and belly. Meanwhile, the trivial prototypes have high activations on the bird's lower surface and neck. In this case, the support ProtoPNet obtains a relatively higher similarity score (22.925), compared with the trivial branch (20.313). Note that our ST-ProtoPNet exploits both the support and trivial prototypes to capture much richer representations of the object from different perspectives, which enables the realisation of complementary interpretations. More examples on Cars and Dogs are shown in the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 625, + 141, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 141, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 141, + 639 + ], + "type": "text", + "content": "5.6. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "content": "The closeness and discrimination losses. To validate the effectiveness of our proposed closeness loss in Eq. (5) and discrimination loss in Eq. (9), we first conduct ablation studies on full CUB and full Dogs by using ResNet50 and ResNet34 as the CNN backbone, respectively. Results are listed in Table 6. We can observe that both the close-" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 545, + 218 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 545, + 218 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 545, + 218 + ], + "type": "image", + "image_path": "7dfb1d14679dbe59deaa77dc6a19d60ac205d535332011c2ab68c1bad1ad1a8b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 220, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 306, + 220, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 220, + 545, + 243 + ], + "type": "text", + "content": "Figure 7. An example of the interpretable reasoning of our STProtoPNet for classifying a testing Parakeet Auklet image." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 251, + 544, + 302 + ], + "blocks": [ + { + "bbox": [ + 308, + 251, + 544, + 302 + ], + "lines": [ + { + "bbox": [ + 308, + 251, + 544, + 302 + ], + "spans": [ + { + "bbox": [ + 308, + 251, + 544, + 302 + ], + "type": "table", + "html": "
MethodlctlsplortldscclsAccuracy (%)
CUBDogs
Baseline✓✓✓86.580.9
Trivial ProtoPNet✓✓✓✓87.282.6
Support ProtoPNet✓✓✓✓87.583.0
ST-ProtoPNet (ours)✓✓✓✓✓88.083.4
", + "image_path": "6ba5d97004fd977e868975f95db7194106b1df997cb69f83e0c784c5d08ab17e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 304, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 338 + ], + "type": "text", + "content": "Table 6. Ablation analysis of the closeness loss " + }, + { + "bbox": [ + 305, + 304, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\ell_{cls}" + }, + { + "bbox": [ + 305, + 304, + 545, + 338 + ], + "type": "text", + "content": " in Eq. (5) to learn support prototypes, and discrimination loss " + }, + { + "bbox": [ + 305, + 304, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\ell_{dsc}" + }, + { + "bbox": [ + 305, + 304, + 545, + 338 + ], + "type": "text", + "content": " in Eq. (9) to learn trivial prototypes on full CUB-200-2011 and Stanford Dogs." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 347, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 418 + ], + "type": "text", + "content": "ness and discrimination losses can improve the accuracy, compared with the Baseline ProtoPNet method trained with only clustering, separation, and orthonormality losses. Note that the closeness loss introduces a larger performance improvement, which is attributed to the learning of support (i.e., hard-to-learn) prototypes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 419, + 546, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 546, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 546, + 658 + ], + "type": "text", + "content": "Combining Support and Trivial Prototypes. We also investigate the importance of integrating the two complementary sets of support and trivial prototypes for improved classification. To achieve this, we first train a two-branch model where both branches learn the same type of prototypes and the final result is produced by the ensemble of them (Trivial Ensemble and Support Ensemble). Besides, for our ST-ProtoPNet, we also provide results of its individual branches (Trivial Branch and Support Branch). Table 7 shows the experimental results on cropped CUB. We can notice that combining the two different types of prototypes (ST-ProtoPNet) achieves superior performance over combining only the same type of prototypes (Trivial Ensemble and Support Ensemble), indicating that our performance improvements are from not only the ensemble strategy but also the two complementary sets of prototypes. Also, STProtoPNet indeed exhibits higher accuracy than its individual branches, further verifying that the results from the two branches are complementary, and the combination of them is effective to improve the final classification accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 662, + 471, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 662, + 471, + 675 + ], + "spans": [ + { + "bbox": [ + 306, + 662, + 471, + 675 + ], + "type": "text", + "content": "6. Conclusion and Future Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": "In this paper, we proposed the ST-ProtoPNet to exploit both support (i.e., hard-to-learn) and trivial (i.e., easy-to-learn) prototypes, where the two sets of prototypes can pro" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2069" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 71, + 285, + 118 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 285, + 118 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 285, + 118 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 285, + 118 + ], + "type": "table", + "html": "
MethodVGG16VGG19ResNet34ResNet152Dense121Dense161
Trivial Ensemble81.4 ± 0.381.8 ± 0.282.7 ± 0.283.2 ± 0.384.4 ± 0.285.0 ± 0.3
Support Ensemble82.1 ± 0.282.4 ± 0.383.0 ± 0.283.7 ± 0.384.8 ± 0.285.5 ± 0.2
Trivial Branch81.0 ± 0.281.1 ± 0.382.4 ± 0.282.9 ± 0.384.1 ± 0.384.8 ± 0.3
Support Branch81.5 ± 0.381.8 ± 0.382.8 ± 0.283.4 ± 0.384.6 ± 0.285.4 ± 0.2
ST-ProtoPNet (ours)82.9 ± 0.283.2 ± 0.283.5 ± 0.184.1 ± 0.285.4 ± 0.286.1 ± 0.2
", + "image_path": "70f26859fc90953fdfa14e3614377f54cd38e90588b882853049093e6583a859.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 122, + 286, + 145 + ], + "lines": [ + { + "bbox": [ + 47, + 122, + 286, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 122, + 286, + 145 + ], + "type": "text", + "content": "Table 7. Ablation study of the combination of support and trivial prototypes for improved classification on cropped CUB-200-2011." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 156, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 287, + 360 + ], + "type": "text", + "content": "vide complementary results for the interpretable image classification. Our ST-ProtoPNet is a general approach that can be easily applied to existing prototype-based interpretable models. One limitation for our method is that we empirically adopt the same number of support and trivial prototypes and the same total number of prototypes for each class. Considering the different learning difficulties and imbalanced training samples among classes in other real-world datasets, e.g., ImageNet [8], a better way to adaptively learn a flexible number of support and trivial prototypes is needed and deserves to be further investigated in our future work. Moreover, given that we mimic the behaviour of the support vectors of SVM classifier to obtain the support prototypes by forcing them to be as close as possible to the classification boundary, we plan to develop new methods to learn prototypes with gradient-based kernel techniques, e.g., neural tangent kernel [18] and path kernel [9]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 370, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 287, + 441 + ], + "type": "text", + "content": "Acknowledgements. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3233-3242, 2021." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2072" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Symmetry-Aware Geometry Correspondences for 6D Object Pose Estimation/c3bb6c4d-c63d-4614-92bb-10b441ef4c78_content_list.json b/2023/Learning Symmetry-Aware Geometry Correspondences for 6D Object Pose Estimation/c3bb6c4d-c63d-4614-92bb-10b441ef4c78_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..62b0ba88541f18ca1b70344325ebcb7b76d6ed63 --- /dev/null +++ b/2023/Learning Symmetry-Aware Geometry Correspondences for 6D Object Pose Estimation/c3bb6c4d-c63d-4614-92bb-10b441ef4c78_content_list.json @@ -0,0 +1,2070 @@ +[ + { + "type": "text", + "text": "Learning Symmetry-Aware Geometry Correspondences for 6D Object Pose Estimation", + "text_level": 1, + "bbox": [ + 130, + 130, + 839, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Heng Zhao $^{1,4}$ Shenxing Wei $^{2}$ Dahu Shi $^{1,3*}$ Wenming Tan $^{1*}$", + "bbox": [ + 225, + 200, + 746, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zheyang Li1 Ye Ren1 Xing Wei2 Yi Yang3 Shiliang Pu1", + "bbox": [ + 225, + 220, + 741, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Hikvision Research Institute $^{2}$ Xi'an Jiaotong University $^{3}$ Zhejiang University", + "bbox": [ + 156, + 239, + 812, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "4Key Laboratory of Peace-building Big Data of Zhejiang Province", + "bbox": [ + 222, + 257, + 746, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zhaoheng13,shidahu,tanwenming,lizheyang,renye,pushiliang}@hikvision.com", + "bbox": [ + 166, + 276, + 803, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "wsx1064432511@stu.xjtu.edu.cn, weixing@mail.xjtu.edu.cn, yangyics@zju.edu.cn", + "bbox": [ + 148, + 295, + 820, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Current 6D pose estimation methods focus on handling objects that are previously trained, which limits their applications in real dynamic world. To this end, we propose a geometry correspondence-based framework, termed GCPose, to estimate 6D pose of arbitrary unseen objects without any re-training. Specifically, the proposed method draws the idea from point cloud registration and resorts to object-agnostic geometry features to establish the 3D-3D correspondences between the object-scene point cloud and object-model point cloud. Then the 6D pose parameters are solved by a least-squares fitting algorithm. Taking the symmetry properties of objects into consideration, we design a symmetry-aware matching loss to facilitate the learning of dense point-wise geometry features and improve the performance considerably. Moreover, we introduce an online training data generation with special data augmentation and normalization to empower the network to learn diverse geometry prior. With training on synthetic objects from ShapeNet, our method outperforms previous approaches for unseen object pose estimation by a large margin on T-LESS, LINEMOD, Occluded-LINEMOD, and TUD-L datasets. Code is available at https://github.com/hikvision-research/GCPose.", + "bbox": [ + 75, + 377, + 473, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 756, + 209, + 771 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The 6D pose of an object represents a geometry transformation between the object coordinate system and camera coordinate system, which consists of 3D rotation and 3D translation. Estimating object pose plays an important role in many real-world applications, such as robotic grasping [8] and augmented reality [38].", + "bbox": [ + 75, + 782, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8cd03a2393e3a6a14b2957951055f769457b9f383e5efe62df16611ce8610ac2.jpg", + "image_caption": [ + "(a) Category-Level" + ], + "image_footnote": [], + "bbox": [ + 506, + 344, + 694, + 438 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4d7e099bc442e0044e793e5900ed6ce125156c79be42c84c18e8a3fc3d5748d2.jpg", + "image_caption": [ + "(b) Template-Based" + ], + "image_footnote": [], + "bbox": [ + 697, + 344, + 885, + 438 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eec03ba01786ccefddff44a799e7f8374921bba76d08844a5d778a874b66fa81.jpg", + "image_caption": [ + "(c) Correspondence-Based", + "Figure 1: Comparison of different open-set pose estimation frameworks. Unlike previous methods that rely on category-specific network training (a) or struggle to estimate precise poses (b), our GCPose can perform well on arbitrary unseen objects (c)." + ], + "image_footnote": [], + "bbox": [ + 506, + 463, + 883, + 568 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Driven by the recent developments in deep learning, various methods have been proposed to explore the instance-level 6D pose estimation problem. Some existing works [43, 15] employ CNNs to detect a set of keypoints predefined on the 3D object model. Then the 6D pose can be solved by Perspective-n-Points (PnP) [31] or least-squares fitting algorithm. Since the detected keypoints serve as sparse correspondences, these methods often struggle when objects have view-point changes, occlusions, or lack of texture. Another alternative is to predict pixel-wise 3D coordinates for building dense 2D-3D correspondence maps [42, 59, 51, 36, 22]. They allow for significantly better treatment of occlusions and lead to more precise poses. Al", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14045", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "though instance-level methods can obtain impressive results on existing benchmarks, they are still under the close-set assumption that the object space is identical in both training and testing phases. As a result, laborious data collection and re-training are required when unseen objects appear, which does not adhere to application in the real dynamic world.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To loosen the restriction with generalizability to unseen objects, category-level pose estimation paradigm [60, 33, 7, 35, 62] is proposed, as shown in Figure 1a. These approaches predict the object pose for previously seen or unseen objects from a known set of categories, but can not generalize to new instances having significantly different appearances or shapes [17, 53]. Another way to address the open-set problem is to resort to the template-based mechanism [55, 40, 5, 49, 30], which matches the input image to a series of templates generated from their 3D object models, as shown in Figure 1b. Obviously, these methods struggle to estimate precise poses due to occlusions and the limited number of viewpoints. To remedy this disadvantage, OVE6D [5] presents an in-plane orientation regression network and OSOP [49] introduces an extra network estimating dense 2D-2D correspondences between the input image and the matched template for pose refinement. In general, these methods have cascade pipelines and result in less accurate pose estimation for unseen objects.", + "bbox": [ + 75, + 184, + 473, + 473 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As is known, point cloud registration methods have demonstrated excellent generalization to previously unseen point clouds as the geometry features of the point cloud are generic and object-agnostic. Inspired by this idea, we present an unseen object 6D pose estimation framework based on dense geometry correspondences, termed GCPose. Specifically, given the object-scene point cloud and object-model point cloud as input, GCPose can establish dense 3D-3D correspondences between them through the geometry features. Finding correspondences across two scene-level point clouds is well-studied in point cloud registration [1, 23, 65, 64, 45] field. However, it is challenging to learn 3D-3D matching for object-level point clouds due to ambiguous correspondences caused by symmetric properties in many object models. For instance, a 3D location in the object-scene point cloud may correspond to multiple 3D locations on the surface of the symmetric object, and vice versa. Therefore, exploiting the off-the-shelf point cloud registration method is sub-optimal to building correspondences for object pose estimation. To this end, we design a symmetry-aware matching loss to let the network learn the object symmetries explicitly.", + "bbox": [ + 75, + 474, + 473, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Following the practice in OVE6D [5], we train the network using a large number of synthetic 3D object models from the ShapeNet [6] dataset. Specifically, we introduce a simple yet effective online training data generation with special data augmentation and normalization to empower the network to learn diverse geometry prior. After train-", + "bbox": [ + 75, + 810, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing on synthetic objects with varied shapes, our method is capable of generalizing to an arbitrary unseen object without any re-training. At inference time, the proposed method requires a depth image with a target object mask and the associated object CAD model, which are utilized to generate object-scene and object-model point clouds.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contribution can be summarized as follows:", + "bbox": [ + 517, + 181, + 836, + 196 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) We employ the point cloud registration framework and adapt it to work well for unseen object pose estimation.", + "2) A symmetry-aware matching loss is proposed for building unambiguous and robust 3D-3D correspondences, which improves the performance significantly.", + "3) GCPose achieves state-of-the-art performance on TLESS, LineMOD, Occluded-LineMOD, and TUD-L datasets under an open-set pose estimation setting. Besides, the performance of GCPose can be further improved by scaling up the training data." + ], + "bbox": [ + 509, + 208, + 890, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 398, + 640, + 414 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. 6D Object Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 422, + 741, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Direct Pose Regression Approaches. Some methods directly regress the 6D pose with deep neural networks, such as [63, 25]. Despite these approaches seeming simple, the non-linearity of the rotation space limits their generalization. Some post-refinement methods [58, 29, 24] are generally utilized to refine the pose iteratively.", + "bbox": [ + 496, + 446, + 890, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Correspondence-Based Approaches. Another popular line to estimate the 6D pose relies on pre-defined keypoints on the object model. For instance, PVNet [43] selects $K$ 3D keypoints from the object surface. Then it employs a CNN to predict the offset to the projection of 3D keypoints in 2D images and the 6D pose is calculated by PnP [31]. PVN3D [16] and FFB6D [15] extract the per-point feature from an RGBD image to predict more precise offset to 3D keypoints and improve the performance. Since the keypoints serve as sparse correspondences, above methods often struggle in occluded scenes. An alternative is to generate dense correspondences. Some of the representative works include CDPN [34], EPOS [19], GDR-Net [59], and SO-Pose [11]. Recently, OnePose [53] and FS6D [17] focus on 6D pose estimation under a few-shot setting, which is more challenging.", + "bbox": [ + 496, + 537, + 892, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Template-Based Approaches. To estimate the 6D pose of previously-unseen objects, the template-based mechanism [2, 41, 40, 5, 49] is proposed. These methods compare the input image to a series of templates, which are rendered images of objects associated with the corresponding 6D poses. And the pose of the best-matched template is selected as the final estimation result. Nevertheless, due to the discretization error of the limited number of viewpoints,", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14046", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/875bf7eb59e399247b33693ffcc43474df87dc6f1a550f7f21cd8db23f371396.jpg", + "image_caption": [ + "Figure 2: The training pipeline of GCPose. Firstly, the object-scene point cloud is obtained from the rendered depth image from ShapeNet [6] and the object-model point cloud is generated by uniform sampling on the surface of the object model. Then, a shared backbone network (i.e., KPCov) is utilized to extract multi-level features of the input point clouds. The interleaved self- and cross-attention layers are adopted to enhance the geometry features of both coarse-level superpoints and fine-level points. Finally, a symmetry-aware matching loss is employed to supervise the learning of geometry features for establishing unambiguous and robust 3D-3D correspondences." + ], + "image_footnote": [], + "bbox": [ + 88, + 93, + 875, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "template-based approaches result in inaccurate pose estimation. OVE6D [5] presents an in-plane orientation regression network for rotation refinement. And OSOP [49] proposes an extra network estimating 2D-2D correspondences between the input image and the matched template for pose refinement.", + "bbox": [ + 75, + 440, + 470, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Point Cloud Registration", + "text_level": 1, + "bbox": [ + 76, + 541, + 305, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Point cloud registration aims to align the two input point clouds by estimating a 3D rigid transformation. The typical pipeline contains detecting keypoints [32, 1], extracting feature descriptors [44, 10, 23], and estimating the transformation. Recently, detection-free methods[65, 64, 45] achieve state-of-the-art performance on several point cloud registration benchmarks. These methods generally assume a one-to-one relationship for two input point clouds, which goes against the nature of symmetry existing in object pose estimation. Specially, we propose a symmetry-aware matching loss to supervise the many-to-many relationship for object pose estimation and eliminate the ambiguity of correspondences.", + "bbox": [ + 75, + 565, + 468, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Symmetries in Pose Estimation", + "text_level": 1, + "bbox": [ + 76, + 770, + 352, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multiple poses can be inferred under a specific appearance for symmetric objects, which leads to the problem of pose ambiguity. To relieve this problem, PoseCNN [63], DenseFusion [58], and GDR-Net [59] adopt the ADD-S [63] metric as the loss during training. ES6D [39] designs a symmetry-invariant pose distance metric to make the network converge to the correct state. [37] predicts multiple", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "poses for the object to estimate the specific pose distribution generated by symmetries. EPOS [19] and SurfEmb [13] learn the 2D-3D correspondence distributions over surface fragments or the entire surface and let the network learn the object symmetries implicitly. These methods focus on memorizing the symmetry information of specific objects and the trained network only performs well on a fixed set of objects. In this paper, we leverage the symmetries of objects and supervise the network with many-to-many correspondences in two input point clouds during training. Therefore, our network learns the object symmetries explicitly, which is proven effective for unseen object pose estimation.", + "bbox": [ + 496, + 440, + 893, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 633, + 635, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first present the overall architecture of our GCPose. Next, the training data generation and feature extraction module are introduced. Then, we elaborate on the proposed symmetry-aware matching loss. At last, the inference pipeline of our framework is summarized.", + "bbox": [ + 496, + 657, + 893, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 741, + 609, + 756 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent GeoTransformer [45] achieves outstanding performance in point cloud registration field and shows strong capabilities for finding correspondences. In this paper, we renovate the GeoTransformer [45] pipeline and adapt it for object pose estimation. Specifically, we design a symmetry-aware matching loss to eliminate the ambiguity of correspondences (Section 3.4). To make features more discriminative for establishing correspondence, we enrich fine-level point features with global structural cues (Section 3.3).", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14047", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/f92e632e0b7450ea9c2ccecacd1a11c400297b0ea7df081e505bcd7917f3d967.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AugmentationHyper-parameter
Downscalescale range s ∈ [0.1, 0.3]
Laplace Noisescale param. b ∈ [0, 0.004m]
Median Blurkernel size k = 3, 5
Upscalescale range s ∈ [3.3, 10]
Dropoutarea ratio r ∈ [0.01, 0.1]
", + "bbox": [ + 89, + 88, + 454, + 195 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1: Data augmentation strategies. We adopt these strategies to bridge the domain gap between the synthetic and real-world depth images.", + "bbox": [ + 75, + 199, + 468, + 246 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Moreover, an online training data generation with special data augmentation and normalization is devised to empower the network to learn diverse geometry priors (Section 3.2).", + "bbox": [ + 75, + 272, + 468, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The training pipeline of GCPose is illustrated in Figure 2. Following OVE6D [5], our network is trained using rendered depth images based on 3D object models from ShapeNet [6]. The object-scene point cloud is obtained from the depth image within the object mask and the object-model point cloud is generated by uniform sampling on the surface of the object model. Given the object-scene and object-model point clouds as input, our goal is to estimate the rigid transformation $\\mathbf{T}$ from the object coordinate system to the camera coordinate system, consisting of a 3D rotation $\\mathbf{R} \\in SO(3)$ and a translation vector $\\mathbf{t} \\in \\mathbb{R}^3$ .", + "bbox": [ + 75, + 318, + 468, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Concretely, the KPCov-FPN [56] is employed as the backbone network to extract the multi-level features of the input point clouds. We refer to the coarsest level downsampled points $(\\frac{1}{8}$ resolution of original point cloud) from the backbone as superpoints, denoted as $\\hat{S},\\hat{M}$ for object-scene and object-model point clouds. The first level downsampled points $(\\frac{1}{2}$ resolution of original point cloud), denoted as $S,M$ for object-scene and object-model point clouds, are treated as fine-level points. Besides, we also adopt interleaved self- and cross-attention layers [47, 66, 61, 48] to enhance the geometry features of both coarse-level superpoints and fine-level points. In the end, a symmetry-aware matching loss is proposed to supervise the learning of geometry features for establishing robust 3D-3D correspondences.", + "bbox": [ + 75, + 484, + 468, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Training Data Generation", + "text_level": 1, + "bbox": [ + 76, + 724, + 313, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our network is optimized using synthetic depth images rendered from 3D object models. Specifically, for each 3D object model, the ModernGL library is employed to synthesize the depth images under random poses. After that, we apply a set of data augmentation strategies to bridge the domain gap between the synthetic and real-world depth images. The depth image is first cropped based on the object mask and then resized to a fixed size $(224 \\times 224$ in this paper) for later preprocessing pipeline. Specifically, 1) the depth image is downsampled at a random scale, 2) Median", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/59921321e73b50bffd6d5b2aacc47375df88591fca28f4ec23288002ec9f12ae.jpg", + "image_caption": [ + "(a) Discrete Symmetry", + "Figure 3: Examples of symmetric objects. (a) The object has finite ambiguity poses (4 in the case). (b) The object has infinite ambiguity poses." + ], + "image_footnote": [], + "bbox": [ + 517, + 92, + 689, + 251 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c585ed8434854e7fe71db01a359a541247982eea6fa9a3bc77e649676f7c6743.jpg", + "image_caption": [ + "(b) Continuous Symmetry" + ], + "image_footnote": [], + "bbox": [ + 707, + 95, + 875, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "blur is conducted on it to weaken high-frequency information of synthetic depth image, 3) random Laplace noise is added to simulate salt and pepper noise, 4) the depth image is zoomed into their original size, 5) random square areas are dropped from the image. The detailed hyper-parameters of these data augmentations can be found in Table 1. The resulting depth image with the object mask is converted into the object-scene point cloud using the camera intrinsic matrix. And the object-model point cloud is obtained by uniform surface sampling from the 3D object model.", + "bbox": [ + 496, + 359, + 890, + 512 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In contrast with the training dataset where the set of objects' size is finite, the size of different objects in the real world varies widely. To improve generalization ability of our GCPose, the object-scene and object-model point clouds are normalized before being fed into the network. The normalization scale is calculated as the largest distance between any pair of the object-model point cloud, i.e., the diameter of the smallest circumscribed sphere of the object-model point cloud.", + "bbox": [ + 496, + 516, + 892, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Feature Extraction", + "text_level": 1, + "bbox": [ + 500, + 676, + 681, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The KPCov-FPN [56] only encodes local geometry features which are less distinctive for correspondence search. To capture the global geometry structures and strengthen superpoint features, a self-attention layer is applied to the coarse-level superpoint features extracted from the last downsample stage of KPCov-FPN. Then a cross-attention layer is adopted to enable the bidirectional communication between object-scene and object-model point clouds, which aims to model the inter-point-cloud geometry consistency. In contrast to GeoTransformer [45], to enrich fine-level point features, we inject coarse-level superpoint features with global structural cues into the upsampling stage of KPCov-FPN.", + "bbox": [ + 496, + 704, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14048", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Symmetry-Aware Matching Loss", + "text_level": 1, + "bbox": [ + 76, + 90, + 366, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.1 Symmetries", + "text_level": 1, + "bbox": [ + 76, + 113, + 215, + 128 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Discrete and continuous symmetries are two types of symmetries. As shown in Figure 3, discrete symmetries can be described by a finite transformation set while continuous symmetries are described by an infinite transformation set. The symmetry property of an object can lead to multiple poses with the same visual appearance. In other words, there exist repeated geometry structures on the surface of a symmetry object. Therefore, the extracted geometry feature of a point in the object-scene point cloud should be similar to multiple points features in the symmetric object-model point cloud, and vice versa. To this end, we design a symmetry-aware matching loss to supervise the many-to-many relationship and let the network learn the object symmetries explicitly.", + "bbox": [ + 75, + 137, + 468, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we first use the method described in [39] to calculate the symmetry axes and angles for each object from ShapeNet. After that, we can obtain a set of transformation $\\widehat{\\mathbf{T}} = \\{\\mathbf{T}_0,\\mathbf{T}_1,\\dots,\\mathbf{T}_n\\} ,\\mathbf{T}_i\\in SE(3)$ for each object. The visual appearance of an object remains unchanged under each transformation of $\\widehat{\\mathbf{T}}$ . Here we use $\\mathbf{T}_0$ to represent the identity transformation and the set only containing $\\mathbf{T}_0$ indicates a non-symmetrical object. For continuous symmetries objects, we discretize the rotation angle for obtaining a finite transformation set. Finally, the ground truth pose $\\mathbf{T}$ of an object-scene point cloud can be extended to a pose set, which can be formulated as", + "bbox": [ + 75, + 348, + 472, + 529 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\overline {{\\mathbf {T}}} = \\left\\{\\mathbf {T} \\mathbf {T} _ {i} \\mid \\mathbf {T} _ {i} \\in \\widehat {\\mathbf {T}} \\right\\}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 537, + 468, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\overline{\\mathbf{T}}$ is then used to calculate the following matching loss.", + "bbox": [ + 76, + 566, + 442, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.2 Matching Loss", + "text_level": 1, + "bbox": [ + 76, + 599, + 235, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the ground truth pose set $\\overline{\\mathbf{T}}$ and superpoints $\\hat{S},\\hat{M}$ we calculate the overlap ratio for constructing positive and negative superpoint pairs between object-scene and object-model point clouds. For each superpoint pair $(\\hat{S}_i,\\hat{M}_j)$ , the overlap ratio $o_{ij}$ is computed:", + "bbox": [ + 75, + 622, + 468, + 700 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} o _ {i j} = \\frac {o _ {i \\rightarrow j} + o _ {j \\rightarrow i}}{2} (2) \\\\ O _ {i \\rightarrow j} = \\frac {\\left|\\left\\{p \\in P _ {i} ^ {S} \\mid \\exists q \\in P _ {j} ^ {M} , \\overline {{\\mathbf {T}}} _ {i} \\in \\overline {{\\mathbf {T}}} \\right. \\text {s . t .} \\| \\overline {{\\mathbf {T}}} _ {i} ^ {- 1} (p) - q \\| < \\tau \\} \\right|}{\\left| P _ {i} ^ {S} \\right|} (3) \\\\ O _ {j \\rightarrow i} = \\frac {\\left|\\left\\{q \\in P _ {j} ^ {M} \\mid \\exists p \\in P _ {i} ^ {S} , \\overline {{\\mathbf {T}}} _ {i} \\in \\overline {{\\mathbf {T}}} \\text {s . t .} \\| \\overline {{\\mathbf {T}}} _ {i} (q) - p \\| < \\tau \\right\\}\\right|}{\\left| P _ {j} ^ {M} \\right|} (4) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 709, + 468, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P_{i}^{S}, P_{j}^{M}$ are the set of fine points allocated to $\\hat{S}_{i}, \\hat{M}_{j}$ by point-to-node strategy [65], respectively. $\\tau$ is the distance threshold. $\\|\\cdot\\|$ is the Euclidean norm. $|\\cdot|$ is the set cardinality. $\\overline{\\mathbf{T}}_{i}^{-1}$ is inverse transformation of $\\overline{\\mathbf{T}}_{i}$ . The positive set $\\varepsilon_{p}$ consists of all superpoint pairs with overlap ratio", + "bbox": [ + 75, + 820, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "greater 0.1. Similarly, all superpoint pairs without overlap form the set of negatives $\\varepsilon_{n}$ . Taking $\\varepsilon_{p}, \\varepsilon_{n}$ , and the associated overlap ratio as input, an overlap-aware circle loss [54, 45] is adopted as coarse supervision, denoted as $\\mathcal{L}_c$ .", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a positive superpoint pair $\\langle \\hat{S}_k,\\hat{M}_k\\rangle$ , an optimal transport layer is utilized to extract fine point correspondences. The set of their associated fine points $\\langle P_k^S\\in$ $\\mathbb{R}^{m\\times 3}$ $P_{k}^{M}\\in \\mathbb{R}^{n\\times 3}\\rangle$ are allocated by point-to-node strategy.. Taking their features $\\langle F_k^S\\in \\mathbb{R}^{m\\times d}$ $F_{k}^{M}\\in \\mathbb{R}^{n\\times d}\\rangle$ as input, we firstly compute cost matrix $C^k\\in \\mathbb{R}^{m\\times n}$ by inner product. Then Sinkhorn algorithm [50] is employed to obtain a refined cost matrix $\\mathcal{Z}^k\\in \\mathbb{R}^{m\\times n}$ . Each entry $(i,j)$ in the matrix represents the matching confidence between the point $i$ and point $j$ from $P_{k}^{S}$ and $P_{k}^{M}$ , respectively. If $(i,j)$ is a positive correspondence, the distance of the point $i$ and point $j$ under one pose of $\\overline{\\mathbf{T}}$ less than a matching threshold, and $(i,j)$ is a negative correspondence otherwise. Finally, the fine matching loss $\\mathcal{L}_f^k$ is obtained by minimizing the negative log-likelihood of the cost matrix $\\mathcal{Z}^k$ as in [46, 45].", + "bbox": [ + 496, + 151, + 892, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We randomly sample $N_{c}$ superpoint pairs from $\\varepsilon_{p}$ for fine matching loss. Formally, the overall loss function can be formulated as:", + "bbox": [ + 496, + 378, + 890, + 424 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c} + \\frac {1}{N _ {c}} \\sum_ {k = 1} ^ {N _ {c}} \\mathcal {L} _ {f} ^ {k}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 434, + 890, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Inference", + "text_level": 1, + "bbox": [ + 500, + 486, + 609, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following the setting of OVE6D [5], we obtain the class labels and segmentation masks of objects by the MaskR-CNN [14]. Given a depth image with mask and object model as input, the object-scene and object-model point clouds are first generated. After feature extraction, the coarse similarity matrix $\\hat{C}$ is computed using the coarse features $\\hat{F}^S, \\hat{F}^M$ .", + "bbox": [ + 496, + 508, + 890, + 614 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {c} _ {i, j} = e ^ {- \\left\\| \\hat {f} _ {i} ^ {S} - \\hat {f} _ {j} ^ {M} \\right\\|}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 629, + 613, + 890, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{c}_{i,j} \\in \\hat{C}, \\hat{f}_i^S \\in \\hat{F}^S, \\hat{f}_j^M \\in \\hat{F}^M$ . The largest K entries in $\\hat{C}$ are selected as potential coarse correspondence candidates.", + "bbox": [ + 496, + 638, + 890, + 689 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each selected superpoint pair $\\langle \\hat{S}_k,\\hat{M}_k\\rangle$ , the cost matrix $\\mathcal{Z}^k\\in \\mathbb{R}^{m\\times n}$ is computed as described in 3.4.2. To filter outlier matches, point correspondence candidates are selected by mutual nearest neighbor criteria as described in [52]. These selected dense point pairs are denoted as $\\mathcal{M}^k = \\{\\langle p_u^S,p_v^M\\rangle |p_u^S\\in P_k^S,p_v^M\\in P_k^M\\}$ . A hypothesis pose set $\\{\\mathbf{R}_k,\\mathbf{t}_k\\mid k\\in [1,K]\\}$ is computed:", + "bbox": [ + 496, + 689, + 890, + 797 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R} _ {k}, \\mathbf {t} _ {k} = \\underset {\\mathbf {R}, \\mathbf {t}} {\\arg \\min } \\sum_ {p _ {u} ^ {S}, p _ {v} ^ {M} \\in \\mathcal {M} ^ {k}} z _ {u, v} ^ {k} \\| \\mathbf {R} p _ {v} ^ {M} + \\mathbf {t} - p _ {u} ^ {S} \\|. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 806, + 890, + 843 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{u,v}^{k}$ is the score from cost matrix $\\mathcal{Z}^k$ . The Eq. 7 can be solved by a weighted least-squares fitting algorithm [3]. Then, each hypothesis pose is verified by voting among", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14049", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the entire point correspondences set $\\mathcal{M} = \\bigcup_{k=1}^{K} \\mathcal{M}^k$ . The hypothesis with the largest number of inlier points will be selected as the final estimation result:", + "bbox": [ + 75, + 88, + 468, + 135 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {R}, \\mathbf {t} = \\underset {\\mathbf {R} _ {k}, \\mathbf {t} _ {k}} {\\arg \\max } \\sum_ {p _ {u} ^ {S}, p _ {v} ^ {M} \\in \\mathcal {M}} \\mathbb {I} \\left(\\left\\| \\mathbf {R} _ {k} p _ {v} ^ {M} + \\mathbf {t} _ {k} - p _ {u} ^ {S} \\right\\| < \\delta\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 143, + 467, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbb{I}$ represents the indicator function, $\\delta$ is the voting threshold.", + "bbox": [ + 75, + 191, + 467, + 222 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 234, + 200, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 76, + 260, + 274, + 275 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We evaluate our method on four public benchmark datasets: T-LESS [20], LINEMOD [18], Occluded-LINEMOD [4], and TUD-L [21].", + "bbox": [ + 75, + 284, + 467, + 329 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We follow the evaluation metric used in the BOP Challenge [21]. The performance of pose estimation is evaluated using three errors, i.e., Visible Surface Discrepancy (VSD), Maximum Symmetry-aware Surface Distance (MSSD), and Maximum Symmetry-aware Projection Distance (MSPD). For each of the pose errors, an average recall is computed, i.e., $\\mathrm{AR}_{\\mathrm{VSD}}$ , $\\mathrm{AR}_{\\mathrm{MSSD}}$ , $\\mathrm{AR}_{\\mathrm{MSPD}}$ , based on a set of error thresholds. The AR refers to the average of the three recalls.", + "bbox": [ + 75, + 329, + 467, + 464 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 474, + 294, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use a KPCov-FPN [56] backbone for feature extraction. Adam optimizer [26] is employed to optimize the network with the learning rate of $5 \\times 10^{-5}$ . The weight decay is set to $1 \\times 10^{-6}$ . GCPose is trained for 80 epochs with a batch size of 16 and the learning rate is decayed by 0.95 every 5 epochs. The network is trained on NVIDIA Tesla V100 GPUs.", + "bbox": [ + 75, + 496, + 467, + 601 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following the practice in OVE6D [5], our GCPose is trained using the synthetic 3D objects from ShapeNet [6]. During the test, we first obtain the class labels and segmentation masks of objects by the MaskRCNN [14]. Taking a depth image with mask and object model as input, GCPose is applied to estimate the 6D pose for the object. In addition, the performance using ground truth class labels and segmentation masks is also reported in this paper.", + "bbox": [ + 75, + 602, + 467, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with the State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 76, + 732, + 467, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.1 T-LESS Results", + "text_level": 1, + "bbox": [ + 76, + 756, + 240, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We firstly report pose estimation results on T-LESS dataset in Table 2 in terms of the AR metric. To facilitate comparison to previous works, we re-evaluate the pose estimation results of OVE6D [5] in AR metric using the official trained model. Our method achieves state-of-the-art performance under an open-set pose estimation setting. GCPose outperforms the recent learning-based OVE6D [5] by $15.6\\%$ without ICP refinement [67] and is also $13.3\\%$ higher than", + "bbox": [ + 75, + 779, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4f0cb0cdd250c60fab50f0941db9168063c598d498f6282b7c66f77b42bcf576.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodARVSDARMSSDARMSPDAR
DrostPPF† [12]0.3750.4780.4800.444
VidalPPF† [57]0.4640.5750.5740.538
HybridPPF† [28]0.5800.6890.6960.655
MegaPose [30]---0.543
OVE6D [5]0.5210.5110.5380.523
OVE6D† [5]0.5130.5610.5650.546
GCPose (Ours)0.6430.6910.7020.679
OVE6D* [5]0.6240.5920.6260.614
OVE6D*† [5]0.6010.6370.6370.625
GCPose* (Ours)0.7140.7390.7620.738
", + "bbox": [ + 504, + 88, + 888, + 265 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/689abf79b3c6826bffac702e38ad3b2026287546809415a46b196417561f572b.jpg", + "table_caption": [ + "Table 2: Comparisons on T-LESS dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + ], + "table_footnote": [], + "table_body": "
MethodARvSDARMSSDARMSPDAR
DrostPFP† [12]0.6780.7860.7890.751
OVE6D [5]0.5600.7510.7620.701
OVE6D† [5]0.7360.8820.8860.835
GCPose (Ours)0.7490.8850.8870.841
MatchNorm* [9]0.3190.4900.5290.446
MatchNorm*† [9]0.6160.6800.7370.678
OVE6D* [5]0.7940.8860.9020.860
OVE6D*† [5]0.8060.9520.9560.905
GCPose* (Ours)0.8690.9650.9740.936
", + "bbox": [ + 503, + 329, + 888, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3: Comparisons on LINEMOD dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object.", + "bbox": [ + 498, + 494, + 890, + 541 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "its ICP refinement counterpart. And GCPose also outperforms traditional HybridPPF [28] with ICP refinement by $2.4\\%$ . These results indicate that GCPose performs well on symmetric and texture-less objects. Moreover, given the ground truth masks, GCPose achieves $73.8\\%$ AR, which reveals great potential for performance improvement with better segmentation masks.", + "bbox": [ + 496, + 568, + 890, + 675 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.2 LINEMOD and Occluded-LINEMOD Results", + "text_level": 1, + "bbox": [ + 498, + 694, + 874, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We report pose estimation results on LINEMOD and Occluded-LINEMOD, as shown in Table 3, 4. GCPose still achieves state-of-the-art performance under an open-set pose estimation setting. Specifically, GCPose surpasses OVE6D [5] by $14.0\\%$ on LINEMOD dataset and $15.6\\%$ on Occluded-LINEMOD dataset, respectively. GCPose outperforms the recent MatchNorm [9] by a large margin of $49.0\\%$ on LINEMOD dataset and $37.6\\%$ on Occluded-LINEMOD dataset, respectively. Moreover, our method is superior to OVE6D and MatchNorm, which both use ICP refinement. In contrast to previous works using handcrafted geometry features, GCPose also outperforms DrostPPF", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14050", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/49f5767b96030330f37f849d023002ffa7f98f6d2e3ad56940e618ca6067c8c7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodARVSDARMSSDARMSPDAR
DrostPPF† [12]0.4370.5630.5810.527
VidalPPF† [57]0.4730.6250.6470.582
HybridPPF† [28]0.5170.6750.7030.631
MegaPose [30]---0.583
OVE6D [5]0.3730.5400.5750.496
OVE6D† [5]0.5260.6580.6970.627
GCPose (Ours)0.5430.6910.7210.652
MatchNorm* [9]0.2630.3840.4500.365
MatchNorm*† [9]0.4780.5420.6120.544
OVE6D* [5]0.5390.6400.7030.627
OVE6D*† [5]0.6330.7550.7980.728
GCPose* (Ours)0.6560.7680.7990.741
", + "bbox": [ + 80, + 88, + 467, + 289 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fac35859c81733000792eee074a9fa08a6cf4b12536e9aef8ec80486179b2958.jpg", + "table_caption": [ + "Table 4: Comparisons on Occluded-LINEMOD dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + ], + "table_footnote": [], + "table_body": "
MethodARvSDARMSSDARMSPDAR
DrostPPF† [12]0.7410.7930.7910.775
VidalPPF† [57]0.8110.9100.9070.876
HybridPPF† [28]0.8720.9450.9440.920
MegaPose [30]---0.712
GCPose (Ours)0.8710.9600.9470.926
MatchNorm* [9]0.7000.8530.8520.801
MatchNorm*† [9]0.8590.9140.9350.903
GCPose* (Ours)0.8880.9790.9800.949
", + "bbox": [ + 80, + 356, + 465, + 501 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "[12] and HybridPPF [28] on LINDEMOD and OccludedLINEMOD datasets. These results further demonstrate that GCPose has a strong generalization ability to unseen objects.", + "bbox": [ + 75, + 580, + 468, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.3 TUD-L Results", + "text_level": 1, + "bbox": [ + 76, + 662, + 236, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The pose estimation results on TUD-L dataset are summarized in Table 5. GCPose outperforms the recent MatchNorm [9] by $14.8\\%$ without ICP refinement and is also $4.6\\%$ higher than its ICP refinement counterpart. Besides, GC-Pose is also superior to traditional HybridPPF [28] with ICP refinement, which further indicates the superiority of our learning-based geometry features.", + "bbox": [ + 75, + 686, + 468, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.4 Scaling of Training Data", + "text_level": 1, + "bbox": [ + 76, + 815, + 302, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To investigate the potential of GCPose with more CAD models for training, we scale up the training set to both ShapeNet [6] and ABC [27]. ABC dataset consists of one million CAD models and each model is a collection of ex", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/60ae80b5138c03743714059421322fccea1d537485596653db3539f5a1cb9730.jpg", + "table_caption": [ + "Table 5: Comparisons on TUD-L dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + ], + "table_footnote": [], + "table_body": "
DatasetMethodw/ ABCARvSDARMSSDARMSPDAR
T-LESS [20]GCPose✓0.6430.6910.7020.679
0.6810.7350.7570.724
GCPose*✓0.7140.7390.7620.738
0.7600.8010.8280.796
LM [18]GCPose✓0.7490.8850.8870.841
0.7630.9070.9080.859
GCPose*✓0.8690.9650.9740.936
0.8700.9710.9780.940
O-LM [4]GCPose✓0.5430.6910.7210.652
0.5570.7310.7640.684
GCPose*✓0.6560.7680.7990.741
0.6570.7930.8270.760
TUD-L [21]GCPose✓0.8710.9600.9470.926
0.8750.9780.9740.942
GCPose*✓0.8880.9790.9800.949
0.9040.9810.9850.957
", + "bbox": [ + 504, + 88, + 890, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6: Comparisons on T-LESS, LINEMOD (LM), Occluded-LINEMOD (O-LM), and TUD-L datasets by scaling up training datasets. *: using the ground truth label and mask of the object.", + "bbox": [ + 498, + 359, + 890, + 421 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "plicityly parametrized curves and surfaces. For training efficiency, we only pick the first 100k out of 1000k CAD models from ABC. The pose estimation results are reported in Table 6. GCPose achieves consistent performance improvement on four datasets after being trained with more CAD models.", + "bbox": [ + 498, + 448, + 890, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.5 Visualization", + "text_level": 1, + "bbox": [ + 500, + 556, + 643, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To visualize the learned symmetry-aware geometry features, we reduce the dimension of point-wise features extracted by our backbone network using the t-SNE algorithm. Then the object-model point cloud is colorized according to the low-dimension features. As shown in Figure 5, the geometry feature embeddings among different parts of an object surface are distinguishable clearly and show meaningful similarity among the local structure of symmetry. It demonstrates that our method can predict reasonable geometry representations for unseen objects, which are employed to solve the 6D poses in this paper. We also give some qualitative results of GCPose on T-LESS and LINEMOD datasets, as shown in Figure 4. Compared to OVE6D [5], our method can generate more precise poses.", + "bbox": [ + 496, + 580, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 801, + 651, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct several ablation experiments on the T-LESS dataset. To eliminate the effect of inaccurate segmentation, we use ground truth labels and masks.", + "bbox": [ + 498, + 825, + 890, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Data Augmentation and Normalization. Our method is trained on synthetic data and tested on real-world data.", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14051", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/61a20211846e9d8909fff078053e84c68220125449ccde9b5b78d473dc1d771e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 93, + 104, + 184, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/18ce10262c7b7546a80dbeb46826f25f73d1c0e19ccdd49a65234ac2b09e1161.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 178, + 184, + 251 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/70f36a0f9ae84f2de8a323b60c30e55bc10f8c6614e99af90858c07a1995fc45.jpg", + "image_caption": [ + "Raw", + "Figure 4: Qualitative results. We visualize the results of OVE6D [5] and the proposed GCPose on the T-LESS (left) and the LINEMOD (right) datasets. Raw indicates the original images and GT means the visualization of ground truth poses. GCPose performs well on a wide range of objects, containing view-point changes, and occlusions." + ], + "image_footnote": [], + "bbox": [ + 94, + 253, + 184, + 325 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1908e72477a84c9fba9909297fa1138e4da1db5cbe4a2628feda0c65f7e93a9c.jpg", + "image_caption": [ + "T-LESS" + ], + "image_footnote": [], + "bbox": [ + 189, + 104, + 282, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/71a7878a994454d001421f7438e7b33fc1f1f78be7e68a6265dd49731c4c7850.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 178, + 282, + 251 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9c7ae4ea6cc399302d4fe65ed2f6b58bce9ae4d88916cefedf5e5c5e730ceb78.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 189, + 253, + 282, + 325 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": 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Data AugNormGA FeatSA LossAR
0.635
✓0.669 (+3.4%)
✓✓0.698 (+6.3%)
✓✓✓0.708 (+7.3%)
✓✓✓✓0.738 (+10.3%)
", + "bbox": [ + 89, + 414, + 454, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7: Ablation experiments: the impact of the proposed special data augmentation (Data Aug), normalization (Norm), global-aware fine-level features (GA Feat), and symmetry-aware matching loss (SA Loss).", + "bbox": [ + 75, + 521, + 468, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "So special data augmentation strategies are necessary to improve the generalization to real-world scenes. Besides, we standardize the scale of the input point clouds to facilitate the learning of geometry features. As shown in Table 7, special data augmentation and normalization bring $3.4\\%$ and $2.9\\%$ AR improvement, respectively.", + "bbox": [ + 75, + 611, + 468, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Global-Aware Fine-level Features. As described in Section 3.3, we enhance fine-level point features with global structural cues to make features more discriminative for establishing correspondence. As shown in Table 7, the performance of GCPose is improved from $69.8\\%$ to $70.8\\%$ using global-aware fine-level features.", + "bbox": [ + 75, + 703, + 468, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Symmetry-Aware Matching Loss. To eliminate the ambiguity of the learning of geometry features, as described in Section 3.4, we design a symmetry-aware matching loss to supervise the many-to-many correspondences. The geometry features output by GCPose are meaningful and the features of symmetric structures are visually similar (Figure 5). As shown in Table 7, the symmetry-aware matching loss", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/986b32062250a94daf942762ead66d5cade27384006b5465df705ca4437c0884.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 416, + 570, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e60b3c957a5206e0fa57a7876112642ea08259616c964d1c5e29a87518560971.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 417, + 642, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/15db60fea085cd55d17dc56039d9cfc194481a85d41dd2e949a220c03595be3d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 421, + 751, + 476 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fd5b109093d59048e13ae9b72228024889c9617fea930d902652729a980c1889.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 425, + 877, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/061560be21c8708248ecb766d3a029990bfb7812aea0ea17180a693f5174fc66.jpg", + "image_caption": [ + "Figure 5: t-SNE visualization of learned symmetry-aware geometry features on several unseen objects from T-LESS. The geometry features are distinguishable among different parts within an object and show meaningful similarity among the local structure of symmetry." + ], + "image_footnote": [], + "bbox": [ + 509, + 487, + 570, + 551 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/289cdbb551442b6b868bd7d6b9915265d8cae47b9ac5e2eadc83b0d1ba50d6ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 583, + 488, + 643, + 551 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a8ae1ebb74409c9a26f70a20611e7a24b9cd4af093e879e09498172c239dd0f7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 492, + 750, + 547 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/241326085279413fbf1559363a7366dae737818f1cdcafa18f8381282441c12b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 497, + 877, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "provides $3.0\\%$ AR improvement.", + "bbox": [ + 500, + 661, + 718, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 691, + 617, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a pose estimation framework based on object-agnostic geometry features, which can generalize to arbitrary unseen objects without re-training. Compared with previous methods, GCPose achieves state-of-the-art performance on four benchmarks. We hope that our simple yet effective framework could serve as a strong baseline for unseen object 6D pose estimation and motivate researchers to explore more in this direction.", + "bbox": [ + 496, + 718, + 890, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work is supported by National Key R&D Program of China under Grant No. 2023YFE0204200 and the Fundamental Research Funds for the Central Universities under Grant No. 226-2022-00051.", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14052", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Xuyang Bai, Zixin Luo, Lei Zhou, Hongbo Fu, Long Quan, and Chiew-Lan Tai. D3feat: Joint learning of dense detection and description of 3d local features. In CVPR, 2020. 2, 3", + "[2] Vassileios Balntas, Andreas Douumanoglou, Caner Sahin, Jul Sock, Rigas Kouskouridas, and Tae-Kyun Kim. Pose guided rgbd feature learning for 3d object pose estimation. In ICCV, 2017. 2", + "[3] Paul J Besl and Neil D McKay. 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IJCV, 1994. 6" + ], + "bbox": [ + 503, + 92, + 890, + 892 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14054", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Symmetry-Aware Geometry Correspondences for 6D Object Pose Estimation/c3bb6c4d-c63d-4614-92bb-10b441ef4c78_model.json b/2023/Learning Symmetry-Aware Geometry Correspondences for 6D Object Pose Estimation/c3bb6c4d-c63d-4614-92bb-10b441ef4c78_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3590a62dc15b27edc4e98a0bf5f6e91d86a22909 --- /dev/null +++ b/2023/Learning Symmetry-Aware Geometry Correspondences for 6D Object Pose Estimation/c3bb6c4d-c63d-4614-92bb-10b441ef4c78_model.json @@ -0,0 +1,2860 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.132, + 0.131, + 0.84, + 0.175 + ], + "angle": 0, + "content": "Learning Symmetry-Aware Geometry Correspondences for 6D Object Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.227, + 0.202, + 0.747, + 0.221 + ], + "angle": 0, + "content": "Heng Zhao\\(^{1,4}\\) Shenxing Wei\\(^{2}\\) Dahu Shi\\(^{1,3*}\\) Wenming Tan\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.226, + 0.222, + 0.742, + 0.239 + ], + "angle": 0, + "content": "Zheyang Li1 Ye Ren1 Xing Wei2 Yi Yang3 Shiliang Pu1" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.24, + 0.813, + 0.258 + ], + "angle": 0, + "content": "\\(^{1}\\)Hikvision Research Institute \\(^{2}\\)Xi'an Jiaotong University \\(^{3}\\)Zhejiang University" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.258, + 0.747, + 0.275 + ], + "angle": 0, + "content": "4Key Laboratory of Peace-building Big Data of Zhejiang Province" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.277, + 0.804, + 0.292 + ], + "angle": 0, + "content": "{zhaoheng13,shidahu,tanwenming,lizheyang,renye,pushiliang}@hikvision.com" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.296, + 0.821, + 0.31 + ], + "angle": 0, + "content": "wsx1064432511@stu.xjtu.edu.cn, weixing@mail.xjtu.edu.cn, yangyics@zju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.474, + 0.726 + ], + "angle": 0, + "content": "Current 6D pose estimation methods focus on handling objects that are previously trained, which limits their applications in real dynamic world. To this end, we propose a geometry correspondence-based framework, termed GCPose, to estimate 6D pose of arbitrary unseen objects without any re-training. Specifically, the proposed method draws the idea from point cloud registration and resorts to object-agnostic geometry features to establish the 3D-3D correspondences between the object-scene point cloud and object-model point cloud. Then the 6D pose parameters are solved by a least-squares fitting algorithm. Taking the symmetry properties of objects into consideration, we design a symmetry-aware matching loss to facilitate the learning of dense point-wise geometry features and improve the performance considerably. Moreover, we introduce an online training data generation with special data augmentation and normalization to empower the network to learn diverse geometry prior. With training on synthetic objects from ShapeNet, our method outperforms previous approaches for unseen object pose estimation by a large margin on T-LESS, LINEMOD, Occluded-LINEMOD, and TUD-L datasets. Code is available at https://github.com/hikvision-research/GCPose." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.757, + 0.21, + 0.772 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.47, + 0.875 + ], + "angle": 0, + "content": "The 6D pose of an object represents a geometry transformation between the object coordinate system and camera coordinate system, which consists of 3D rotation and 3D translation. Estimating object pose plays an important role in many real-world applications, such as robotic grasping [8] and augmented reality [38]." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.345, + 0.695, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.444, + 0.658, + 0.458 + ], + "angle": 0, + "content": "(a) Category-Level" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.345, + 0.887, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.444, + 0.853, + 0.458 + ], + "angle": 0, + "content": "(b) Template-Based" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.464, + 0.885, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.614, + 0.574, + 0.776, + 0.588 + ], + "angle": 0, + "content": "(c) Correspondence-Based" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.593, + 0.895, + 0.67 + ], + "angle": 0, + "content": "Figure 1: Comparison of different open-set pose estimation frameworks. Unlike previous methods that rely on category-specific network training (a) or struggle to estimate precise poses (b), our GCPose can perform well on arbitrary unseen objects (c)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Driven by the recent developments in deep learning, various methods have been proposed to explore the instance-level 6D pose estimation problem. Some existing works [43, 15] employ CNNs to detect a set of keypoints predefined on the 3D object model. Then the 6D pose can be solved by Perspective-n-Points (PnP) [31] or least-squares fitting algorithm. Since the detected keypoints serve as sparse correspondences, these methods often struggle when objects have view-point changes, occlusions, or lack of texture. Another alternative is to predict pixel-wise 3D coordinates for building dense 2D-3D correspondence maps [42, 59, 51, 36, 22]. They allow for significantly better treatment of occlusions and lead to more precise poses. Al" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14045" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "though instance-level methods can obtain impressive results on existing benchmarks, they are still under the close-set assumption that the object space is identical in both training and testing phases. As a result, laborious data collection and re-training are required when unseen objects appear, which does not adhere to application in the real dynamic world." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.185, + 0.474, + 0.474 + ], + "angle": 0, + "content": "To loosen the restriction with generalizability to unseen objects, category-level pose estimation paradigm [60, 33, 7, 35, 62] is proposed, as shown in Figure 1a. These approaches predict the object pose for previously seen or unseen objects from a known set of categories, but can not generalize to new instances having significantly different appearances or shapes [17, 53]. Another way to address the open-set problem is to resort to the template-based mechanism [55, 40, 5, 49, 30], which matches the input image to a series of templates generated from their 3D object models, as shown in Figure 1b. Obviously, these methods struggle to estimate precise poses due to occlusions and the limited number of viewpoints. To remedy this disadvantage, OVE6D [5] presents an in-plane orientation regression network and OSOP [49] introduces an extra network estimating dense 2D-2D correspondences between the input image and the matched template for pose refinement. In general, these methods have cascade pipelines and result in less accurate pose estimation for unseen objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.474, + 0.809 + ], + "angle": 0, + "content": "As is known, point cloud registration methods have demonstrated excellent generalization to previously unseen point clouds as the geometry features of the point cloud are generic and object-agnostic. Inspired by this idea, we present an unseen object 6D pose estimation framework based on dense geometry correspondences, termed GCPose. Specifically, given the object-scene point cloud and object-model point cloud as input, GCPose can establish dense 3D-3D correspondences between them through the geometry features. Finding correspondences across two scene-level point clouds is well-studied in point cloud registration [1, 23, 65, 64, 45] field. However, it is challenging to learn 3D-3D matching for object-level point clouds due to ambiguous correspondences caused by symmetric properties in many object models. For instance, a 3D location in the object-scene point cloud may correspond to multiple 3D locations on the surface of the symmetric object, and vice versa. Therefore, exploiting the off-the-shelf point cloud registration method is sub-optimal to building correspondences for object pose estimation. To this end, we design a symmetry-aware matching loss to let the network learn the object symmetries explicitly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Following the practice in OVE6D [5], we train the network using a large number of synthetic 3D object models from the ShapeNet [6] dataset. Specifically, we introduce a simple yet effective online training data generation with special data augmentation and normalization to empower the network to learn diverse geometry prior. After train-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "ing on synthetic objects with varied shapes, our method is capable of generalizing to an arbitrary unseen object without any re-training. At inference time, the proposed method requires a depth image with a target object mask and the associated object CAD model, which are utilized to generate object-scene and object-model point clouds." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.183, + 0.838, + 0.198 + ], + "angle": 0, + "content": "Our contribution can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.209, + 0.892, + 0.24 + ], + "angle": 0, + "content": "1) We employ the point cloud registration framework and adapt it to work well for unseen object pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.251, + 0.892, + 0.298 + ], + "angle": 0, + "content": "2) A symmetry-aware matching loss is proposed for building unambiguous and robust 3D-3D correspondences, which improves the performance significantly." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.308, + 0.892, + 0.385 + ], + "angle": 0, + "content": "3) GCPose achieves state-of-the-art performance on TLESS, LineMOD, Occluded-LineMOD, and TUD-L datasets under an open-set pose estimation setting. Besides, the performance of GCPose can be further improved by scaling up the training data." + }, + { + "type": "list", + "bbox": [ + 0.511, + 0.209, + 0.892, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.399, + 0.642, + 0.415 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.424, + 0.743, + 0.44 + ], + "angle": 0, + "content": "2.1. 6D Object Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.538 + ], + "angle": 0, + "content": "Direct Pose Regression Approaches. Some methods directly regress the 6D pose with deep neural networks, such as [63, 25]. Despite these approaches seeming simple, the non-linearity of the rotation space limits their generalization. Some post-refinement methods [58, 29, 24] are generally utilized to refine the pose iteratively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.893, + 0.78 + ], + "angle": 0, + "content": "Correspondence-Based Approaches. Another popular line to estimate the 6D pose relies on pre-defined keypoints on the object model. For instance, PVNet [43] selects \\(K\\) 3D keypoints from the object surface. Then it employs a CNN to predict the offset to the projection of 3D keypoints in 2D images and the 6D pose is calculated by PnP [31]. PVN3D [16] and FFB6D [15] extract the per-point feature from an RGBD image to predict more precise offset to 3D keypoints and improve the performance. Since the keypoints serve as sparse correspondences, above methods often struggle in occluded scenes. An alternative is to generate dense correspondences. Some of the representative works include CDPN [34], EPOS [19], GDR-Net [59], and SO-Pose [11]. Recently, OnePose [53] and FS6D [17] focus on 6D pose estimation under a few-shot setting, which is more challenging." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Template-Based Approaches. To estimate the 6D pose of previously-unseen objects, the template-based mechanism [2, 41, 40, 5, 49] is proposed. These methods compare the input image to a series of templates, which are rendered images of objects associated with the corresponding 6D poses. And the pose of the best-matched template is selected as the final estimation result. Nevertheless, due to the discretization error of the limited number of viewpoints," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14046" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.094, + 0.877, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.323, + 0.896, + 0.416 + ], + "angle": 0, + "content": "Figure 2: The training pipeline of GCPose. Firstly, the object-scene point cloud is obtained from the rendered depth image from ShapeNet [6] and the object-model point cloud is generated by uniform sampling on the surface of the object model. Then, a shared backbone network (i.e., KPCov) is utilized to extract multi-level features of the input point clouds. The interleaved self- and cross-attention layers are adopted to enhance the geometry features of both coarse-level superpoints and fine-level points. Finally, a symmetry-aware matching loss is employed to supervise the learning of geometry features for establishing unambiguous and robust 3D-3D correspondences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.471, + 0.531 + ], + "angle": 0, + "content": "template-based approaches result in inaccurate pose estimation. OVE6D [5] presents an in-plane orientation regression network for rotation refinement. And OSOP [49] proposes an extra network estimating 2D-2D correspondences between the input image and the matched template for pose refinement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.542, + 0.307, + 0.559 + ], + "angle": 0, + "content": "2.2. Point Cloud Registration" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.761 + ], + "angle": 0, + "content": "Point cloud registration aims to align the two input point clouds by estimating a 3D rigid transformation. The typical pipeline contains detecting keypoints [32, 1], extracting feature descriptors [44, 10, 23], and estimating the transformation. Recently, detection-free methods[65, 64, 45] achieve state-of-the-art performance on several point cloud registration benchmarks. These methods generally assume a one-to-one relationship for two input point clouds, which goes against the nature of symmetry existing in object pose estimation. Specially, we propose a symmetry-aware matching loss to supervise the many-to-many relationship for object pose estimation and eliminate the ambiguity of correspondences." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.353, + 0.789 + ], + "angle": 0, + "content": "2.3. Symmetries in Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Multiple poses can be inferred under a specific appearance for symmetric objects, which leads to the problem of pose ambiguity. To relieve this problem, PoseCNN [63], DenseFusion [58], and GDR-Net [59] adopt the ADD-S [63] metric as the loss during training. ES6D [39] designs a symmetry-invariant pose distance metric to make the network converge to the correct state. [37] predicts multiple" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.895, + 0.624 + ], + "angle": 0, + "content": "poses for the object to estimate the specific pose distribution generated by symmetries. EPOS [19] and SurfEmb [13] learn the 2D-3D correspondence distributions over surface fragments or the entire surface and let the network learn the object symmetries implicitly. These methods focus on memorizing the symmetry information of specific objects and the trained network only performs well on a fixed set of objects. In this paper, we leverage the symmetries of objects and supervise the network with many-to-many correspondences in two input point clouds during training. Therefore, our network learns the object symmetries explicitly, which is proven effective for unseen object pose estimation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.637, + 0.651 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.894, + 0.737 + ], + "angle": 0, + "content": "In this section, we first present the overall architecture of our GCPose. Next, the training data generation and feature extraction module are introduced. Then, we elaborate on the proposed symmetry-aware matching loss. At last, the inference pipeline of our framework is summarized." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.611, + 0.757 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recent GeoTransformer [45] achieves outstanding performance in point cloud registration field and shows strong capabilities for finding correspondences. In this paper, we renovate the GeoTransformer [45] pipeline and adapt it for object pose estimation. Specifically, we design a symmetry-aware matching loss to eliminate the ambiguity of correspondences (Section 3.4). To make features more discriminative for establishing correspondence, we enrich fine-level point features with global structural cues (Section 3.3)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14047" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.089, + 0.455, + 0.196 + ], + "angle": 0, + "content": "
AugmentationHyper-parameter
Downscalescale range s ∈ [0.1, 0.3]
Laplace Noisescale param. b ∈ [0, 0.004m]
Median Blurkernel size k = 3, 5
Upscalescale range s ∈ [3.3, 10]
Dropoutarea ratio r ∈ [0.01, 0.1]
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.2, + 0.47, + 0.247 + ], + "angle": 0, + "content": "Table 1: Data augmentation strategies. We adopt these strategies to bridge the domain gap between the synthetic and real-world depth images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.469, + 0.319 + ], + "angle": 0, + "content": "Moreover, an online training data generation with special data augmentation and normalization is devised to empower the network to learn diverse geometry priors (Section 3.2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.469, + 0.485 + ], + "angle": 0, + "content": "The training pipeline of GCPose is illustrated in Figure 2. Following OVE6D [5], our network is trained using rendered depth images based on 3D object models from ShapeNet [6]. The object-scene point cloud is obtained from the depth image within the object mask and the object-model point cloud is generated by uniform sampling on the surface of the object model. Given the object-scene and object-model point clouds as input, our goal is to estimate the rigid transformation \\(\\mathbf{T}\\) from the object coordinate system to the camera coordinate system, consisting of a 3D rotation \\(\\mathbf{R} \\in SO(3)\\) and a translation vector \\(\\mathbf{t} \\in \\mathbb{R}^3\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Concretely, the KPCov-FPN [56] is employed as the backbone network to extract the multi-level features of the input point clouds. We refer to the coarsest level downsampled points \\((\\frac{1}{8}\\) resolution of original point cloud) from the backbone as superpoints, denoted as \\(\\hat{S},\\hat{M}\\) for object-scene and object-model point clouds. The first level downsampled points \\((\\frac{1}{2}\\) resolution of original point cloud), denoted as \\(S,M\\) for object-scene and object-model point clouds, are treated as fine-level points. Besides, we also adopt interleaved self- and cross-attention layers [47, 66, 61, 48] to enhance the geometry features of both coarse-level superpoints and fine-level points. In the end, a symmetry-aware matching loss is proposed to supervise the learning of geometry features for establishing robust 3D-3D correspondences." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.314, + 0.743 + ], + "angle": 0, + "content": "3.2. Training Data Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Our network is optimized using synthetic depth images rendered from 3D object models. Specifically, for each 3D object model, the ModernGL library is employed to synthesize the depth images under random poses. After that, we apply a set of data augmentation strategies to bridge the domain gap between the synthetic and real-world depth images. The depth image is first cropped based on the object mask and then resized to a fixed size \\((224 \\times 224\\) in this paper) for later preprocessing pipeline. Specifically, 1) the depth image is downsampled at a random scale, 2) Median" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.093, + 0.691, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.255, + 0.663, + 0.267 + ], + "angle": 0, + "content": "(a) Discrete Symmetry" + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.096, + 0.876, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.727, + 0.255, + 0.862, + 0.267 + ], + "angle": 0, + "content": "(b) Continuous Symmetry" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.279, + 0.892, + 0.326 + ], + "angle": 0, + "content": "Figure 3: Examples of symmetric objects. (a) The object has finite ambiguity poses (4 in the case). (b) The object has infinite ambiguity poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.513 + ], + "angle": 0, + "content": "blur is conducted on it to weaken high-frequency information of synthetic depth image, 3) random Laplace noise is added to simulate salt and pepper noise, 4) the depth image is zoomed into their original size, 5) random square areas are dropped from the image. The detailed hyper-parameters of these data augmentations can be found in Table 1. The resulting depth image with the object mask is converted into the object-scene point cloud using the camera intrinsic matrix. And the object-model point cloud is obtained by uniform surface sampling from the 3D object model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.893, + 0.653 + ], + "angle": 0, + "content": "In contrast with the training dataset where the set of objects' size is finite, the size of different objects in the real world varies widely. To improve generalization ability of our GCPose, the object-scene and object-model point clouds are normalized before being fed into the network. The normalization scale is calculated as the largest distance between any pair of the object-model point cloud, i.e., the diameter of the smallest circumscribed sphere of the object-model point cloud." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.677, + 0.682, + 0.691 + ], + "angle": 0, + "content": "3.3. Feature Extraction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.9 + ], + "angle": 0, + "content": "The KPCov-FPN [56] only encodes local geometry features which are less distinctive for correspondence search. To capture the global geometry structures and strengthen superpoint features, a self-attention layer is applied to the coarse-level superpoint features extracted from the last downsample stage of KPCov-FPN. Then a cross-attention layer is adopted to enable the bidirectional communication between object-scene and object-model point clouds, which aims to model the inter-point-cloud geometry consistency. In contrast to GeoTransformer [45], to enrich fine-level point features, we inject coarse-level superpoint features with global structural cues into the upsampling stage of KPCov-FPN." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "14048" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.367, + 0.108 + ], + "angle": 0, + "content": "3.4. Symmetry-Aware Matching Loss" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.114, + 0.216, + 0.129 + ], + "angle": 0, + "content": "3.4.1 Symmetries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.47, + 0.349 + ], + "angle": 0, + "content": "Discrete and continuous symmetries are two types of symmetries. As shown in Figure 3, discrete symmetries can be described by a finite transformation set while continuous symmetries are described by an infinite transformation set. The symmetry property of an object can lead to multiple poses with the same visual appearance. In other words, there exist repeated geometry structures on the surface of a symmetry object. Therefore, the extracted geometry feature of a point in the object-scene point cloud should be similar to multiple points features in the symmetric object-model point cloud, and vice versa. To this end, we design a symmetry-aware matching loss to supervise the many-to-many relationship and let the network learn the object symmetries explicitly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.473, + 0.53 + ], + "angle": 0, + "content": "Specifically, we first use the method described in [39] to calculate the symmetry axes and angles for each object from ShapeNet. After that, we can obtain a set of transformation \\(\\widehat{\\mathbf{T}} = \\{\\mathbf{T}_0,\\mathbf{T}_1,\\dots,\\mathbf{T}_n\\} ,\\mathbf{T}_i\\in SE(3)\\) for each object. The visual appearance of an object remains unchanged under each transformation of \\(\\widehat{\\mathbf{T}}\\) . Here we use \\(\\mathbf{T}_0\\) to represent the identity transformation and the set only containing \\(\\mathbf{T}_0\\) indicates a non-symmetrical object. For continuous symmetries objects, we discretize the rotation angle for obtaining a finite transformation set. Finally, the ground truth pose \\(\\mathbf{T}\\) of an object-scene point cloud can be extended to a pose set, which can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.539, + 0.47, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\overline {{\\mathbf {T}}} = \\left\\{\\mathbf {T} \\mathbf {T} _ {i} \\mid \\mathbf {T} _ {i} \\in \\widehat {\\mathbf {T}} \\right\\}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.567, + 0.444, + 0.584 + ], + "angle": 0, + "content": "\\(\\overline{\\mathbf{T}}\\) is then used to calculate the following matching loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.601, + 0.236, + 0.617 + ], + "angle": 0, + "content": "3.4.2 Matching Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.47, + 0.701 + ], + "angle": 0, + "content": "Given the ground truth pose set \\(\\overline{\\mathbf{T}}\\) and superpoints \\(\\hat{S},\\hat{M}\\) we calculate the overlap ratio for constructing positive and negative superpoint pairs between object-scene and object-model point clouds. For each superpoint pair \\((\\hat{S}_i,\\hat{M}_j)\\), the overlap ratio \\(o_{ij}\\) is computed:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.71, + 0.47, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} o _ {i j} = \\frac {o _ {i \\rightarrow j} + o _ {j \\rightarrow i}}{2} (2) \\\\ O _ {i \\rightarrow j} = \\frac {\\left|\\left\\{p \\in P _ {i} ^ {S} \\mid \\exists q \\in P _ {j} ^ {M} , \\overline {{\\mathbf {T}}} _ {i} \\in \\overline {{\\mathbf {T}}} \\right. \\text {s . t .} \\| \\overline {{\\mathbf {T}}} _ {i} ^ {- 1} (p) - q \\| < \\tau \\} \\right|}{\\left| P _ {i} ^ {S} \\right|} (3) \\\\ O _ {j \\rightarrow i} = \\frac {\\left|\\left\\{q \\in P _ {j} ^ {M} \\mid \\exists p \\in P _ {i} ^ {S} , \\overline {{\\mathbf {T}}} _ {i} \\in \\overline {{\\mathbf {T}}} \\text {s . t .} \\| \\overline {{\\mathbf {T}}} _ {i} (q) - p \\| < \\tau \\right\\}\\right|}{\\left| P _ {j} ^ {M} \\right|} (4) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.821, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(P_{i}^{S}, P_{j}^{M}\\) are the set of fine points allocated to \\(\\hat{S}_{i}, \\hat{M}_{j}\\) by point-to-node strategy [65], respectively. \\(\\tau\\) is the distance threshold. \\(\\|\\cdot\\|\\) is the Euclidean norm. \\(|\\cdot|\\) is the set cardinality. \\(\\overline{\\mathbf{T}}_{i}^{-1}\\) is inverse transformation of \\(\\overline{\\mathbf{T}}_{i}\\). The positive set \\(\\varepsilon_{p}\\) consists of all superpoint pairs with overlap ratio" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "greater 0.1. Similarly, all superpoint pairs without overlap form the set of negatives \\(\\varepsilon_{n}\\). Taking \\(\\varepsilon_{p}, \\varepsilon_{n}\\), and the associated overlap ratio as input, an overlap-aware circle loss [54, 45] is adopted as coarse supervision, denoted as \\(\\mathcal{L}_c\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.893, + 0.38 + ], + "angle": 0, + "content": "Given a positive superpoint pair \\(\\langle \\hat{S}_k,\\hat{M}_k\\rangle\\), an optimal transport layer is utilized to extract fine point correspondences. The set of their associated fine points \\(\\langle P_k^S\\in\\) \\(\\mathbb{R}^{m\\times 3}\\) \\(P_{k}^{M}\\in \\mathbb{R}^{n\\times 3}\\rangle\\) are allocated by point-to-node strategy.. Taking their features \\(\\langle F_k^S\\in \\mathbb{R}^{m\\times d}\\) \\(F_{k}^{M}\\in \\mathbb{R}^{n\\times d}\\rangle\\) as input, we firstly compute cost matrix \\(C^k\\in \\mathbb{R}^{m\\times n}\\) by inner product. Then Sinkhorn algorithm [50] is employed to obtain a refined cost matrix \\(\\mathcal{Z}^k\\in \\mathbb{R}^{m\\times n}\\). Each entry \\((i,j)\\) in the matrix represents the matching confidence between the point \\(i\\) and point \\(j\\) from \\(P_{k}^{S}\\) and \\(P_{k}^{M}\\), respectively. If \\((i,j)\\) is a positive correspondence, the distance of the point \\(i\\) and point \\(j\\) under one pose of \\(\\overline{\\mathbf{T}}\\) less than a matching threshold, and \\((i,j)\\) is a negative correspondence otherwise. Finally, the fine matching loss \\(\\mathcal{L}_f^k\\) is obtained by minimizing the negative log-likelihood of the cost matrix \\(\\mathcal{Z}^k\\) as in [46, 45]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.425 + ], + "angle": 0, + "content": "We randomly sample \\(N_{c}\\) superpoint pairs from \\(\\varepsilon_{p}\\) for fine matching loss. Formally, the overall loss function can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.435, + 0.892, + 0.477 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {c} + \\frac {1}{N _ {c}} \\sum_ {k = 1} ^ {N _ {c}} \\mathcal {L} _ {f} ^ {k}. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.487, + 0.61, + 0.501 + ], + "angle": 0, + "content": "3.5. Inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.615 + ], + "angle": 0, + "content": "Following the setting of OVE6D [5], we obtain the class labels and segmentation masks of objects by the MaskR-CNN [14]. Given a depth image with mask and object model as input, the object-scene and object-model point clouds are first generated. After feature extraction, the coarse similarity matrix \\(\\hat{C}\\) is computed using the coarse features \\(\\hat{F}^S, \\hat{F}^M\\)." + }, + { + "type": "equation", + "bbox": [ + 0.63, + 0.614, + 0.891, + 0.635 + ], + "angle": 0, + "content": "\\[\n\\hat {c} _ {i, j} = e ^ {- \\left\\| \\hat {f} _ {i} ^ {S} - \\hat {f} _ {j} ^ {M} \\right\\|}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.69 + ], + "angle": 0, + "content": "where \\(\\hat{c}_{i,j} \\in \\hat{C}, \\hat{f}_i^S \\in \\hat{F}^S, \\hat{f}_j^M \\in \\hat{F}^M\\). The largest K entries in \\(\\hat{C}\\) are selected as potential coarse correspondence candidates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.798 + ], + "angle": 0, + "content": "For each selected superpoint pair \\(\\langle \\hat{S}_k,\\hat{M}_k\\rangle\\), the cost matrix \\(\\mathcal{Z}^k\\in \\mathbb{R}^{m\\times n}\\) is computed as described in 3.4.2. To filter outlier matches, point correspondence candidates are selected by mutual nearest neighbor criteria as described in [52]. These selected dense point pairs are denoted as \\(\\mathcal{M}^k = \\{\\langle p_u^S,p_v^M\\rangle |p_u^S\\in P_k^S,p_v^M\\in P_k^M\\}\\). A hypothesis pose set \\(\\{\\mathbf{R}_k,\\mathbf{t}_k\\mid k\\in [1,K]\\}\\) is computed:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.808, + 0.892, + 0.844 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R} _ {k}, \\mathbf {t} _ {k} = \\underset {\\mathbf {R}, \\mathbf {t}} {\\arg \\min } \\sum_ {p _ {u} ^ {S}, p _ {v} ^ {M} \\in \\mathcal {M} ^ {k}} z _ {u, v} ^ {k} \\| \\mathbf {R} p _ {v} ^ {M} + \\mathbf {t} - p _ {u} ^ {S} \\|. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.855, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\( z_{u,v}^{k} \\) is the score from cost matrix \\( \\mathcal{Z}^k \\). The Eq. 7 can be solved by a weighted least-squares fitting algorithm [3]. Then, each hypothesis pose is verified by voting among" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14049" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.089, + 0.47, + 0.136 + ], + "angle": 0, + "content": "the entire point correspondences set \\(\\mathcal{M} = \\bigcup_{k=1}^{K} \\mathcal{M}^k\\). The hypothesis with the largest number of inlier points will be selected as the final estimation result:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.145, + 0.468, + 0.192 + ], + "angle": 0, + "content": "\\[\n\\mathbf {R}, \\mathbf {t} = \\underset {\\mathbf {R} _ {k}, \\mathbf {t} _ {k}} {\\arg \\max } \\sum_ {p _ {u} ^ {S}, p _ {v} ^ {M} \\in \\mathcal {M}} \\mathbb {I} \\left(\\left\\| \\mathbf {R} _ {k} p _ {v} ^ {M} + \\mathbf {t} _ {k} - p _ {u} ^ {S} \\right\\| < \\delta\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.193, + 0.468, + 0.223 + ], + "angle": 0, + "content": "where \\(\\mathbb{I}\\) represents the indicator function, \\(\\delta\\) is the voting threshold." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.236, + 0.202, + 0.254 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.261, + 0.276, + 0.276 + ], + "angle": 0, + "content": "4.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.468, + 0.33 + ], + "angle": 0, + "content": "Datasets. We evaluate our method on four public benchmark datasets: T-LESS [20], LINEMOD [18], Occluded-LINEMOD [4], and TUD-L [21]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.468, + 0.465 + ], + "angle": 0, + "content": "Metrics. We follow the evaluation metric used in the BOP Challenge [21]. The performance of pose estimation is evaluated using three errors, i.e., Visible Surface Discrepancy (VSD), Maximum Symmetry-aware Surface Distance (MSSD), and Maximum Symmetry-aware Projection Distance (MSPD). For each of the pose errors, an average recall is computed, i.e., \\(\\mathrm{AR}_{\\mathrm{VSD}}\\), \\(\\mathrm{AR}_{\\mathrm{MSSD}}\\), \\(\\mathrm{AR}_{\\mathrm{MSPD}}\\), based on a set of error thresholds. The AR refers to the average of the three recalls." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.475, + 0.295, + 0.491 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.468, + 0.602 + ], + "angle": 0, + "content": "We use a KPCov-FPN [56] backbone for feature extraction. Adam optimizer [26] is employed to optimize the network with the learning rate of \\( 5 \\times 10^{-5} \\). The weight decay is set to \\( 1 \\times 10^{-6} \\). GCPose is trained for 80 epochs with a batch size of 16 and the learning rate is decayed by 0.95 every 5 epochs. The network is trained on NVIDIA Tesla V100 GPUs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.468, + 0.725 + ], + "angle": 0, + "content": "Following the practice in OVE6D [5], our GCPose is trained using the synthetic 3D objects from ShapeNet [6]. During the test, we first obtain the class labels and segmentation masks of objects by the MaskRCNN [14]. Taking a depth image with mask and object model as input, GCPose is applied to estimate the 6D pose for the object. In addition, the performance using ground truth class labels and segmentation masks is also reported in this paper." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.733, + 0.468, + 0.749 + ], + "angle": 0, + "content": "4.3. Comparison with the State-of-the-Art Methods" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.241, + 0.77 + ], + "angle": 0, + "content": "4.3.1 T-LESS Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We firstly report pose estimation results on T-LESS dataset in Table 2 in terms of the AR metric. To facilitate comparison to previous works, we re-evaluate the pose estimation results of OVE6D [5] in AR metric using the official trained model. Our method achieves state-of-the-art performance under an open-set pose estimation setting. GCPose outperforms the recent learning-based OVE6D [5] by \\(15.6\\%\\) without ICP refinement [67] and is also \\(13.3\\%\\) higher than" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.89, + 0.266 + ], + "angle": 0, + "content": "
MethodARVSDARMSSDARMSPDAR
DrostPPF† [12]0.3750.4780.4800.444
VidalPPF† [57]0.4640.5750.5740.538
HybridPPF† [28]0.5800.6890.6960.655
MegaPose [30]---0.543
OVE6D [5]0.5210.5110.5380.523
OVE6D† [5]0.5130.5610.5650.546
GCPose (Ours)0.6430.6910.7020.679
OVE6D* [5]0.6240.5920.6260.614
OVE6D*† [5]0.6010.6370.6370.625
GCPose* (Ours)0.7140.7390.7620.738
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.269, + 0.892, + 0.316 + ], + "angle": 0, + "content": "Table 2: Comparisons on T-LESS dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.33, + 0.89, + 0.49 + ], + "angle": 0, + "content": "
MethodARvSDARMSSDARMSPDAR
DrostPFP† [12]0.6780.7860.7890.751
OVE6D [5]0.5600.7510.7620.701
OVE6D† [5]0.7360.8820.8860.835
GCPose (Ours)0.7490.8850.8870.841
MatchNorm* [9]0.3190.4900.5290.446
MatchNorm*† [9]0.6160.6800.7370.678
OVE6D* [5]0.7940.8860.9020.860
OVE6D*† [5]0.8060.9520.9560.905
GCPose* (Ours)0.8690.9650.9740.936
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.495, + 0.892, + 0.542 + ], + "angle": 0, + "content": "Table 3: Comparisons on LINEMOD dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.676 + ], + "angle": 0, + "content": "its ICP refinement counterpart. And GCPose also outperforms traditional HybridPPF [28] with ICP refinement by \\(2.4\\%\\). These results indicate that GCPose performs well on symmetric and texture-less objects. Moreover, given the ground truth masks, GCPose achieves \\(73.8\\%\\) AR, which reveals great potential for performance improvement with better segmentation masks." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.695, + 0.875, + 0.71 + ], + "angle": 0, + "content": "4.3.2 LINEMOD and Occluded-LINEMOD Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We report pose estimation results on LINEMOD and Occluded-LINEMOD, as shown in Table 3, 4. GCPose still achieves state-of-the-art performance under an open-set pose estimation setting. Specifically, GCPose surpasses OVE6D [5] by \\(14.0\\%\\) on LINEMOD dataset and \\(15.6\\%\\) on Occluded-LINEMOD dataset, respectively. GCPose outperforms the recent MatchNorm [9] by a large margin of \\(49.0\\%\\) on LINEMOD dataset and \\(37.6\\%\\) on Occluded-LINEMOD dataset, respectively. Moreover, our method is superior to OVE6D and MatchNorm, which both use ICP refinement. In contrast to previous works using handcrafted geometry features, GCPose also outperforms DrostPPF" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14050" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.468, + 0.29 + ], + "angle": 0, + "content": "
MethodARVSDARMSSDARMSPDAR
DrostPPF† [12]0.4370.5630.5810.527
VidalPPF† [57]0.4730.6250.6470.582
HybridPPF† [28]0.5170.6750.7030.631
MegaPose [30]---0.583
OVE6D [5]0.3730.5400.5750.496
OVE6D† [5]0.5260.6580.6970.627
GCPose (Ours)0.5430.6910.7210.652
MatchNorm* [9]0.2630.3840.4500.365
MatchNorm*† [9]0.4780.5420.6120.544
OVE6D* [5]0.5390.6400.7030.627
OVE6D*† [5]0.6330.7550.7980.728
GCPose* (Ours)0.6560.7680.7990.741
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.295, + 0.468, + 0.342 + ], + "angle": 0, + "content": "Table 4: Comparisons on Occluded-LINEMOD dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.357, + 0.466, + 0.502 + ], + "angle": 0, + "content": "
MethodARvSDARMSSDARMSPDAR
DrostPPF† [12]0.7410.7930.7910.775
VidalPPF† [57]0.8110.9100.9070.876
HybridPPF† [28]0.8720.9450.9440.920
MegaPose [30]---0.712
GCPose (Ours)0.8710.9600.9470.926
MatchNorm* [9]0.7000.8530.8520.801
MatchNorm*† [9]0.8590.9140.9350.903
GCPose* (Ours)0.8880.9790.9800.949
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.507, + 0.469, + 0.553 + ], + "angle": 0, + "content": "Table 5: Comparisons on TUD-L dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.469, + 0.643 + ], + "angle": 0, + "content": "[12] and HybridPPF [28] on LINDEMOD and OccludedLINEMOD datasets. These results further demonstrate that GCPose has a strong generalization ability to unseen objects." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.237, + 0.678 + ], + "angle": 0, + "content": "4.3.3 TUD-L Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.794 + ], + "angle": 0, + "content": "The pose estimation results on TUD-L dataset are summarized in Table 5. GCPose outperforms the recent MatchNorm [9] by \\(14.8\\%\\) without ICP refinement and is also \\(4.6\\%\\) higher than its ICP refinement counterpart. Besides, GC-Pose is also superior to traditional HybridPPF [28] with ICP refinement, which further indicates the superiority of our learning-based geometry features." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.303, + 0.831 + ], + "angle": 0, + "content": "4.3.4 Scaling of Training Data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.9 + ], + "angle": 0, + "content": "To investigate the potential of GCPose with more CAD models for training, we scale up the training set to both ShapeNet [6] and ABC [27]. ABC dataset consists of one million CAD models and each model is a collection of ex" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.891, + 0.355 + ], + "angle": 0, + "content": "
DatasetMethodw/ ABCARvSDARMSSDARMSPDAR
T-LESS [20]GCPose✓0.6430.6910.7020.679
0.6810.7350.7570.724
GCPose*✓0.7140.7390.7620.738
0.7600.8010.8280.796
LM [18]GCPose✓0.7490.8850.8870.841
0.7630.9070.9080.859
GCPose*✓0.8690.9650.9740.936
0.8700.9710.9780.940
O-LM [4]GCPose✓0.5430.6910.7210.652
0.5570.7310.7640.684
GCPose*✓0.6560.7680.7990.741
0.6570.7930.8270.760
TUD-L [21]GCPose✓0.8710.9600.9470.926
0.8750.9780.9740.942
GCPose*✓0.8880.9790.9800.949
0.9040.9810.9850.957
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.361, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Table 6: Comparisons on T-LESS, LINEMOD (LM), Occluded-LINEMOD (O-LM), and TUD-L datasets by scaling up training datasets. *: using the ground truth label and mask of the object." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.449, + 0.892, + 0.538 + ], + "angle": 0, + "content": "plicityly parametrized curves and surfaces. For training efficiency, we only pick the first 100k out of 1000k CAD models from ABC. The pose estimation results are reported in Table 6. GCPose achieves consistent performance improvement on four datasets after being trained with more CAD models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.645, + 0.571 + ], + "angle": 0, + "content": "4.3.5 Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.793 + ], + "angle": 0, + "content": "To visualize the learned symmetry-aware geometry features, we reduce the dimension of point-wise features extracted by our backbone network using the t-SNE algorithm. Then the object-model point cloud is colorized according to the low-dimension features. As shown in Figure 5, the geometry feature embeddings among different parts of an object surface are distinguishable clearly and show meaningful similarity among the local structure of symmetry. It demonstrates that our method can predict reasonable geometry representations for unseen objects, which are employed to solve the 6D poses in this paper. We also give some qualitative results of GCPose on T-LESS and LINEMOD datasets, as shown in Figure 4. Compared to OVE6D [5], our method can generate more precise poses." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.652, + 0.818 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.891, + 0.87 + ], + "angle": 0, + "content": "We conduct several ablation experiments on the T-LESS dataset. To eliminate the effect of inaccurate segmentation, we use ground truth labels and masks." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Data Augmentation and Normalization. Our method is trained on synthetic data and tested on real-world data." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14051" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.09, + 0.312, + 0.102 + ], + "angle": 0, + "content": "T-LESS" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.105, + 0.186, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.179, + 0.186, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.255, + 0.186, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.327, + 0.157, + 0.339 + ], + "angle": 0, + "content": "Raw" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.105, + 0.284, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.179, + 0.283, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.255, + 0.283, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.226, + 0.328, + 0.249, + 0.339 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.105, + 0.38, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.179, + 0.38, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.255, + 0.38, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.328, + 0.359, + 0.339 + ], + "angle": 0, + "content": "OVE6D" + }, + { + "type": "image", + "bbox": [ + 0.383, + 0.105, + 0.477, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.383, + 0.179, + 0.477, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.383, + 0.255, + 0.477, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.405, + 0.328, + 0.456, + 0.339 + ], + "angle": 0, + "content": "GCPose" + }, + { + "type": "image_caption", + "bbox": [ + 0.647, + 0.09, + 0.72, + 0.102 + ], + "angle": 0, + "content": "LINEMOD" + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.105, + 0.582, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.179, + 0.582, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.255, + 0.581, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.328, + 0.554, + 0.339 + ], + "angle": 0, + "content": "Raw" + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.105, + 0.68, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.179, + 0.68, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.255, + 0.68, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.623, + 0.328, + 0.646, + 0.339 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.105, + 0.777, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.179, + 0.776, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.255, + 0.776, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.328, + 0.756, + 0.339 + ], + "angle": 0, + "content": "OVE6D" + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.105, + 0.873, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.179, + 0.873, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.255, + 0.873, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.802, + 0.328, + 0.853, + 0.339 + ], + "angle": 0, + "content": "GCPose" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.894, + 0.392 + ], + "angle": 0, + "content": "Figure 4: Qualitative results. We visualize the results of OVE6D [5] and the proposed GCPose on the T-LESS (left) and the LINEMOD (right) datasets. Raw indicates the original images and GT means the visualization of ground truth poses. GCPose performs well on a wide range of objects, containing view-point changes, and occlusions." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.415, + 0.455, + 0.517 + ], + "angle": 0, + "content": "
Data AugNormGA FeatSA LossAR
0.635
✓0.669 (+3.4%)
✓✓0.698 (+6.3%)
✓✓✓0.708 (+7.3%)
✓✓✓✓0.738 (+10.3%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.582 + ], + "angle": 0, + "content": "Table 7: Ablation experiments: the impact of the proposed special data augmentation (Data Aug), normalization (Norm), global-aware fine-level features (GA Feat), and symmetry-aware matching loss (SA Loss)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.702 + ], + "angle": 0, + "content": "So special data augmentation strategies are necessary to improve the generalization to real-world scenes. Besides, we standardize the scale of the input point clouds to facilitate the learning of geometry features. As shown in Table 7, special data augmentation and normalization bring \\(3.4\\%\\) and \\(2.9\\%\\) AR improvement, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Global-Aware Fine-level Features. As described in Section 3.3, we enhance fine-level point features with global structural cues to make features more discriminative for establishing correspondence. As shown in Table 7, the performance of GCPose is improved from \\(69.8\\%\\) to \\(70.8\\%\\) using global-aware fine-level features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Symmetry-Aware Matching Loss. To eliminate the ambiguity of the learning of geometry features, as described in Section 3.4, we design a symmetry-aware matching loss to supervise the many-to-many correspondences. The geometry features output by GCPose are meaningful and the features of symmetric structures are visually similar (Figure 5). As shown in Table 7, the symmetry-aware matching loss" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.417, + 0.571, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.418, + 0.643, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.422, + 0.752, + 0.477 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.426, + 0.878, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.488, + 0.571, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.489, + 0.644, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.493, + 0.751, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.498, + 0.878, + 0.544 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.557, + 0.892, + 0.633 + ], + "angle": 0, + "content": "Figure 5: t-SNE visualization of learned symmetry-aware geometry features on several unseen objects from T-LESS. The geometry features are distinguishable among different parts within an object and show meaningful similarity among the local structure of symmetry." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.662, + 0.72, + 0.677 + ], + "angle": 0, + "content": "provides \\(3.0\\%\\) AR improvement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.619, + 0.708 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.839 + ], + "angle": 0, + "content": "In this paper, we propose a pose estimation framework based on object-agnostic geometry features, which can generalize to arbitrary unseen objects without re-training. Compared with previous methods, GCPose achieves state-of-the-art performance on four benchmarks. We hope that our simple yet effective framework could serve as a strong baseline for unseen object 6D pose estimation and motivate researchers to explore more in this direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments. This work is supported by National Key R&D Program of China under Grant No. 2023YFE0204200 and the Fundamental Research Funds for the Central Universities under Grant No. 226-2022-00051." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14052" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Xuyang Bai, Zixin Luo, Lei Zhou, Hongbo Fu, Long Quan, and Chiew-Lan Tai. 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To this end, we propose a geometry correspondence-based framework, termed GCPose, to estimate 6D pose of arbitrary unseen objects without any re-training. Specifically, the proposed method draws the idea from point cloud registration and resorts to object-agnostic geometry features to establish the 3D-3D correspondences between the object-scene point cloud and object-model point cloud. Then the 6D pose parameters are solved by a least-squares fitting algorithm. Taking the symmetry properties of objects into consideration, we design a symmetry-aware matching loss to facilitate the learning of dense point-wise geometry features and improve the performance considerably. Moreover, we introduce an online training data generation with special data augmentation and normalization to empower the network to learn diverse geometry prior. With training on synthetic objects from ShapeNet, our method outperforms previous approaches for unseen object pose estimation by a large margin on T-LESS, LINEMOD, Occluded-LINEMOD, and TUD-L datasets. Code is available at https://github.com/hikvision-research/GCPose. + +# 1. Introduction + +The 6D pose of an object represents a geometry transformation between the object coordinate system and camera coordinate system, which consists of 3D rotation and 3D translation. Estimating object pose plays an important role in many real-world applications, such as robotic grasping [8] and augmented reality [38]. + +![](images/8cd03a2393e3a6a14b2957951055f769457b9f383e5efe62df16611ce8610ac2.jpg) +(a) Category-Level + +![](images/4d7e099bc442e0044e793e5900ed6ce125156c79be42c84c18e8a3fc3d5748d2.jpg) +(b) Template-Based + +![](images/eec03ba01786ccefddff44a799e7f8374921bba76d08844a5d778a874b66fa81.jpg) +(c) Correspondence-Based +Figure 1: Comparison of different open-set pose estimation frameworks. Unlike previous methods that rely on category-specific network training (a) or struggle to estimate precise poses (b), our GCPose can perform well on arbitrary unseen objects (c). + +Driven by the recent developments in deep learning, various methods have been proposed to explore the instance-level 6D pose estimation problem. Some existing works [43, 15] employ CNNs to detect a set of keypoints predefined on the 3D object model. Then the 6D pose can be solved by Perspective-n-Points (PnP) [31] or least-squares fitting algorithm. Since the detected keypoints serve as sparse correspondences, these methods often struggle when objects have view-point changes, occlusions, or lack of texture. Another alternative is to predict pixel-wise 3D coordinates for building dense 2D-3D correspondence maps [42, 59, 51, 36, 22]. They allow for significantly better treatment of occlusions and lead to more precise poses. Al + +though instance-level methods can obtain impressive results on existing benchmarks, they are still under the close-set assumption that the object space is identical in both training and testing phases. As a result, laborious data collection and re-training are required when unseen objects appear, which does not adhere to application in the real dynamic world. + +To loosen the restriction with generalizability to unseen objects, category-level pose estimation paradigm [60, 33, 7, 35, 62] is proposed, as shown in Figure 1a. These approaches predict the object pose for previously seen or unseen objects from a known set of categories, but can not generalize to new instances having significantly different appearances or shapes [17, 53]. Another way to address the open-set problem is to resort to the template-based mechanism [55, 40, 5, 49, 30], which matches the input image to a series of templates generated from their 3D object models, as shown in Figure 1b. Obviously, these methods struggle to estimate precise poses due to occlusions and the limited number of viewpoints. To remedy this disadvantage, OVE6D [5] presents an in-plane orientation regression network and OSOP [49] introduces an extra network estimating dense 2D-2D correspondences between the input image and the matched template for pose refinement. In general, these methods have cascade pipelines and result in less accurate pose estimation for unseen objects. + +As is known, point cloud registration methods have demonstrated excellent generalization to previously unseen point clouds as the geometry features of the point cloud are generic and object-agnostic. Inspired by this idea, we present an unseen object 6D pose estimation framework based on dense geometry correspondences, termed GCPose. Specifically, given the object-scene point cloud and object-model point cloud as input, GCPose can establish dense 3D-3D correspondences between them through the geometry features. Finding correspondences across two scene-level point clouds is well-studied in point cloud registration [1, 23, 65, 64, 45] field. However, it is challenging to learn 3D-3D matching for object-level point clouds due to ambiguous correspondences caused by symmetric properties in many object models. For instance, a 3D location in the object-scene point cloud may correspond to multiple 3D locations on the surface of the symmetric object, and vice versa. Therefore, exploiting the off-the-shelf point cloud registration method is sub-optimal to building correspondences for object pose estimation. To this end, we design a symmetry-aware matching loss to let the network learn the object symmetries explicitly. + +Following the practice in OVE6D [5], we train the network using a large number of synthetic 3D object models from the ShapeNet [6] dataset. Specifically, we introduce a simple yet effective online training data generation with special data augmentation and normalization to empower the network to learn diverse geometry prior. After train- + +ing on synthetic objects with varied shapes, our method is capable of generalizing to an arbitrary unseen object without any re-training. At inference time, the proposed method requires a depth image with a target object mask and the associated object CAD model, which are utilized to generate object-scene and object-model point clouds. + +Our contribution can be summarized as follows: + +1) We employ the point cloud registration framework and adapt it to work well for unseen object pose estimation. +2) A symmetry-aware matching loss is proposed for building unambiguous and robust 3D-3D correspondences, which improves the performance significantly. +3) GCPose achieves state-of-the-art performance on TLESS, LineMOD, Occluded-LineMOD, and TUD-L datasets under an open-set pose estimation setting. Besides, the performance of GCPose can be further improved by scaling up the training data. + +# 2. Related Work + +# 2.1. 6D Object Pose Estimation + +Direct Pose Regression Approaches. Some methods directly regress the 6D pose with deep neural networks, such as [63, 25]. Despite these approaches seeming simple, the non-linearity of the rotation space limits their generalization. Some post-refinement methods [58, 29, 24] are generally utilized to refine the pose iteratively. + +Correspondence-Based Approaches. Another popular line to estimate the 6D pose relies on pre-defined keypoints on the object model. For instance, PVNet [43] selects $K$ 3D keypoints from the object surface. Then it employs a CNN to predict the offset to the projection of 3D keypoints in 2D images and the 6D pose is calculated by PnP [31]. PVN3D [16] and FFB6D [15] extract the per-point feature from an RGBD image to predict more precise offset to 3D keypoints and improve the performance. Since the keypoints serve as sparse correspondences, above methods often struggle in occluded scenes. An alternative is to generate dense correspondences. Some of the representative works include CDPN [34], EPOS [19], GDR-Net [59], and SO-Pose [11]. Recently, OnePose [53] and FS6D [17] focus on 6D pose estimation under a few-shot setting, which is more challenging. + +Template-Based Approaches. To estimate the 6D pose of previously-unseen objects, the template-based mechanism [2, 41, 40, 5, 49] is proposed. These methods compare the input image to a series of templates, which are rendered images of objects associated with the corresponding 6D poses. And the pose of the best-matched template is selected as the final estimation result. Nevertheless, due to the discretization error of the limited number of viewpoints, + +![](images/875bf7eb59e399247b33693ffcc43474df87dc6f1a550f7f21cd8db23f371396.jpg) +Figure 2: The training pipeline of GCPose. Firstly, the object-scene point cloud is obtained from the rendered depth image from ShapeNet [6] and the object-model point cloud is generated by uniform sampling on the surface of the object model. Then, a shared backbone network (i.e., KPCov) is utilized to extract multi-level features of the input point clouds. The interleaved self- and cross-attention layers are adopted to enhance the geometry features of both coarse-level superpoints and fine-level points. Finally, a symmetry-aware matching loss is employed to supervise the learning of geometry features for establishing unambiguous and robust 3D-3D correspondences. + +template-based approaches result in inaccurate pose estimation. OVE6D [5] presents an in-plane orientation regression network for rotation refinement. And OSOP [49] proposes an extra network estimating 2D-2D correspondences between the input image and the matched template for pose refinement. + +# 2.2. Point Cloud Registration + +Point cloud registration aims to align the two input point clouds by estimating a 3D rigid transformation. The typical pipeline contains detecting keypoints [32, 1], extracting feature descriptors [44, 10, 23], and estimating the transformation. Recently, detection-free methods[65, 64, 45] achieve state-of-the-art performance on several point cloud registration benchmarks. These methods generally assume a one-to-one relationship for two input point clouds, which goes against the nature of symmetry existing in object pose estimation. Specially, we propose a symmetry-aware matching loss to supervise the many-to-many relationship for object pose estimation and eliminate the ambiguity of correspondences. + +# 2.3. Symmetries in Pose Estimation + +Multiple poses can be inferred under a specific appearance for symmetric objects, which leads to the problem of pose ambiguity. To relieve this problem, PoseCNN [63], DenseFusion [58], and GDR-Net [59] adopt the ADD-S [63] metric as the loss during training. ES6D [39] designs a symmetry-invariant pose distance metric to make the network converge to the correct state. [37] predicts multiple + +poses for the object to estimate the specific pose distribution generated by symmetries. EPOS [19] and SurfEmb [13] learn the 2D-3D correspondence distributions over surface fragments or the entire surface and let the network learn the object symmetries implicitly. These methods focus on memorizing the symmetry information of specific objects and the trained network only performs well on a fixed set of objects. In this paper, we leverage the symmetries of objects and supervise the network with many-to-many correspondences in two input point clouds during training. Therefore, our network learns the object symmetries explicitly, which is proven effective for unseen object pose estimation. + +# 3. Methodology + +In this section, we first present the overall architecture of our GCPose. Next, the training data generation and feature extraction module are introduced. Then, we elaborate on the proposed symmetry-aware matching loss. At last, the inference pipeline of our framework is summarized. + +# 3.1. Overview + +Recent GeoTransformer [45] achieves outstanding performance in point cloud registration field and shows strong capabilities for finding correspondences. In this paper, we renovate the GeoTransformer [45] pipeline and adapt it for object pose estimation. Specifically, we design a symmetry-aware matching loss to eliminate the ambiguity of correspondences (Section 3.4). To make features more discriminative for establishing correspondence, we enrich fine-level point features with global structural cues (Section 3.3). + +
AugmentationHyper-parameter
Downscalescale range s ∈ [0.1, 0.3]
Laplace Noisescale param. b ∈ [0, 0.004m]
Median Blurkernel size k = 3, 5
Upscalescale range s ∈ [3.3, 10]
Dropoutarea ratio r ∈ [0.01, 0.1]
+ +Table 1: Data augmentation strategies. We adopt these strategies to bridge the domain gap between the synthetic and real-world depth images. + +Moreover, an online training data generation with special data augmentation and normalization is devised to empower the network to learn diverse geometry priors (Section 3.2). + +The training pipeline of GCPose is illustrated in Figure 2. Following OVE6D [5], our network is trained using rendered depth images based on 3D object models from ShapeNet [6]. The object-scene point cloud is obtained from the depth image within the object mask and the object-model point cloud is generated by uniform sampling on the surface of the object model. Given the object-scene and object-model point clouds as input, our goal is to estimate the rigid transformation $\mathbf{T}$ from the object coordinate system to the camera coordinate system, consisting of a 3D rotation $\mathbf{R} \in SO(3)$ and a translation vector $\mathbf{t} \in \mathbb{R}^3$ . + +Concretely, the KPCov-FPN [56] is employed as the backbone network to extract the multi-level features of the input point clouds. We refer to the coarsest level downsampled points $(\frac{1}{8}$ resolution of original point cloud) from the backbone as superpoints, denoted as $\hat{S},\hat{M}$ for object-scene and object-model point clouds. The first level downsampled points $(\frac{1}{2}$ resolution of original point cloud), denoted as $S,M$ for object-scene and object-model point clouds, are treated as fine-level points. Besides, we also adopt interleaved self- and cross-attention layers [47, 66, 61, 48] to enhance the geometry features of both coarse-level superpoints and fine-level points. In the end, a symmetry-aware matching loss is proposed to supervise the learning of geometry features for establishing robust 3D-3D correspondences. + +# 3.2. Training Data Generation + +Our network is optimized using synthetic depth images rendered from 3D object models. Specifically, for each 3D object model, the ModernGL library is employed to synthesize the depth images under random poses. After that, we apply a set of data augmentation strategies to bridge the domain gap between the synthetic and real-world depth images. The depth image is first cropped based on the object mask and then resized to a fixed size $(224 \times 224$ in this paper) for later preprocessing pipeline. Specifically, 1) the depth image is downsampled at a random scale, 2) Median + +![](images/59921321e73b50bffd6d5b2aacc47375df88591fca28f4ec23288002ec9f12ae.jpg) +(a) Discrete Symmetry +Figure 3: Examples of symmetric objects. (a) The object has finite ambiguity poses (4 in the case). (b) The object has infinite ambiguity poses. + +![](images/c585ed8434854e7fe71db01a359a541247982eea6fa9a3bc77e649676f7c6743.jpg) +(b) Continuous Symmetry + +blur is conducted on it to weaken high-frequency information of synthetic depth image, 3) random Laplace noise is added to simulate salt and pepper noise, 4) the depth image is zoomed into their original size, 5) random square areas are dropped from the image. The detailed hyper-parameters of these data augmentations can be found in Table 1. The resulting depth image with the object mask is converted into the object-scene point cloud using the camera intrinsic matrix. And the object-model point cloud is obtained by uniform surface sampling from the 3D object model. + +In contrast with the training dataset where the set of objects' size is finite, the size of different objects in the real world varies widely. To improve generalization ability of our GCPose, the object-scene and object-model point clouds are normalized before being fed into the network. The normalization scale is calculated as the largest distance between any pair of the object-model point cloud, i.e., the diameter of the smallest circumscribed sphere of the object-model point cloud. + +# 3.3. Feature Extraction + +The KPCov-FPN [56] only encodes local geometry features which are less distinctive for correspondence search. To capture the global geometry structures and strengthen superpoint features, a self-attention layer is applied to the coarse-level superpoint features extracted from the last downsample stage of KPCov-FPN. Then a cross-attention layer is adopted to enable the bidirectional communication between object-scene and object-model point clouds, which aims to model the inter-point-cloud geometry consistency. In contrast to GeoTransformer [45], to enrich fine-level point features, we inject coarse-level superpoint features with global structural cues into the upsampling stage of KPCov-FPN. + +# 3.4. Symmetry-Aware Matching Loss + +# 3.4.1 Symmetries + +Discrete and continuous symmetries are two types of symmetries. As shown in Figure 3, discrete symmetries can be described by a finite transformation set while continuous symmetries are described by an infinite transformation set. The symmetry property of an object can lead to multiple poses with the same visual appearance. In other words, there exist repeated geometry structures on the surface of a symmetry object. Therefore, the extracted geometry feature of a point in the object-scene point cloud should be similar to multiple points features in the symmetric object-model point cloud, and vice versa. To this end, we design a symmetry-aware matching loss to supervise the many-to-many relationship and let the network learn the object symmetries explicitly. + +Specifically, we first use the method described in [39] to calculate the symmetry axes and angles for each object from ShapeNet. After that, we can obtain a set of transformation $\widehat{\mathbf{T}} = \{\mathbf{T}_0,\mathbf{T}_1,\dots,\mathbf{T}_n\} ,\mathbf{T}_i\in SE(3)$ for each object. The visual appearance of an object remains unchanged under each transformation of $\widehat{\mathbf{T}}$ . Here we use $\mathbf{T}_0$ to represent the identity transformation and the set only containing $\mathbf{T}_0$ indicates a non-symmetrical object. For continuous symmetries objects, we discretize the rotation angle for obtaining a finite transformation set. Finally, the ground truth pose $\mathbf{T}$ of an object-scene point cloud can be extended to a pose set, which can be formulated as + +$$ +\overline {{\mathbf {T}}} = \left\{\mathbf {T} \mathbf {T} _ {i} \mid \mathbf {T} _ {i} \in \widehat {\mathbf {T}} \right\}. \tag {1} +$$ + +$\overline{\mathbf{T}}$ is then used to calculate the following matching loss. + +# 3.4.2 Matching Loss + +Given the ground truth pose set $\overline{\mathbf{T}}$ and superpoints $\hat{S},\hat{M}$ we calculate the overlap ratio for constructing positive and negative superpoint pairs between object-scene and object-model point clouds. For each superpoint pair $(\hat{S}_i,\hat{M}_j)$ , the overlap ratio $o_{ij}$ is computed: + +$$ +\begin{array}{l} o _ {i j} = \frac {o _ {i \rightarrow j} + o _ {j \rightarrow i}}{2} (2) \\ O _ {i \rightarrow j} = \frac {\left|\left\{p \in P _ {i} ^ {S} \mid \exists q \in P _ {j} ^ {M} , \overline {{\mathbf {T}}} _ {i} \in \overline {{\mathbf {T}}} \right. \text {s . t .} \| \overline {{\mathbf {T}}} _ {i} ^ {- 1} (p) - q \| < \tau \} \right|}{\left| P _ {i} ^ {S} \right|} (3) \\ O _ {j \rightarrow i} = \frac {\left|\left\{q \in P _ {j} ^ {M} \mid \exists p \in P _ {i} ^ {S} , \overline {{\mathbf {T}}} _ {i} \in \overline {{\mathbf {T}}} \text {s . t .} \| \overline {{\mathbf {T}}} _ {i} (q) - p \| < \tau \right\}\right|}{\left| P _ {j} ^ {M} \right|} (4) \\ \end{array} +$$ + +where $P_{i}^{S}, P_{j}^{M}$ are the set of fine points allocated to $\hat{S}_{i}, \hat{M}_{j}$ by point-to-node strategy [65], respectively. $\tau$ is the distance threshold. $\|\cdot\|$ is the Euclidean norm. $|\cdot|$ is the set cardinality. $\overline{\mathbf{T}}_{i}^{-1}$ is inverse transformation of $\overline{\mathbf{T}}_{i}$ . The positive set $\varepsilon_{p}$ consists of all superpoint pairs with overlap ratio + +greater 0.1. Similarly, all superpoint pairs without overlap form the set of negatives $\varepsilon_{n}$ . Taking $\varepsilon_{p}, \varepsilon_{n}$ , and the associated overlap ratio as input, an overlap-aware circle loss [54, 45] is adopted as coarse supervision, denoted as $\mathcal{L}_c$ . + +Given a positive superpoint pair $\langle \hat{S}_k,\hat{M}_k\rangle$ , an optimal transport layer is utilized to extract fine point correspondences. The set of their associated fine points $\langle P_k^S\in$ $\mathbb{R}^{m\times 3}$ $P_{k}^{M}\in \mathbb{R}^{n\times 3}\rangle$ are allocated by point-to-node strategy.. Taking their features $\langle F_k^S\in \mathbb{R}^{m\times d}$ $F_{k}^{M}\in \mathbb{R}^{n\times d}\rangle$ as input, we firstly compute cost matrix $C^k\in \mathbb{R}^{m\times n}$ by inner product. Then Sinkhorn algorithm [50] is employed to obtain a refined cost matrix $\mathcal{Z}^k\in \mathbb{R}^{m\times n}$ . Each entry $(i,j)$ in the matrix represents the matching confidence between the point $i$ and point $j$ from $P_{k}^{S}$ and $P_{k}^{M}$ , respectively. If $(i,j)$ is a positive correspondence, the distance of the point $i$ and point $j$ under one pose of $\overline{\mathbf{T}}$ less than a matching threshold, and $(i,j)$ is a negative correspondence otherwise. Finally, the fine matching loss $\mathcal{L}_f^k$ is obtained by minimizing the negative log-likelihood of the cost matrix $\mathcal{Z}^k$ as in [46, 45]. + +We randomly sample $N_{c}$ superpoint pairs from $\varepsilon_{p}$ for fine matching loss. Formally, the overall loss function can be formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {c} + \frac {1}{N _ {c}} \sum_ {k = 1} ^ {N _ {c}} \mathcal {L} _ {f} ^ {k}. \tag {5} +$$ + +# 3.5. Inference + +Following the setting of OVE6D [5], we obtain the class labels and segmentation masks of objects by the MaskR-CNN [14]. Given a depth image with mask and object model as input, the object-scene and object-model point clouds are first generated. After feature extraction, the coarse similarity matrix $\hat{C}$ is computed using the coarse features $\hat{F}^S, \hat{F}^M$ . + +$$ +\hat {c} _ {i, j} = e ^ {- \left\| \hat {f} _ {i} ^ {S} - \hat {f} _ {j} ^ {M} \right\|}. \tag {6} +$$ + +where $\hat{c}_{i,j} \in \hat{C}, \hat{f}_i^S \in \hat{F}^S, \hat{f}_j^M \in \hat{F}^M$ . The largest K entries in $\hat{C}$ are selected as potential coarse correspondence candidates. + +For each selected superpoint pair $\langle \hat{S}_k,\hat{M}_k\rangle$ , the cost matrix $\mathcal{Z}^k\in \mathbb{R}^{m\times n}$ is computed as described in 3.4.2. To filter outlier matches, point correspondence candidates are selected by mutual nearest neighbor criteria as described in [52]. These selected dense point pairs are denoted as $\mathcal{M}^k = \{\langle p_u^S,p_v^M\rangle |p_u^S\in P_k^S,p_v^M\in P_k^M\}$ . A hypothesis pose set $\{\mathbf{R}_k,\mathbf{t}_k\mid k\in [1,K]\}$ is computed: + +$$ +\mathbf {R} _ {k}, \mathbf {t} _ {k} = \underset {\mathbf {R}, \mathbf {t}} {\arg \min } \sum_ {p _ {u} ^ {S}, p _ {v} ^ {M} \in \mathcal {M} ^ {k}} z _ {u, v} ^ {k} \| \mathbf {R} p _ {v} ^ {M} + \mathbf {t} - p _ {u} ^ {S} \|. \tag {7} +$$ + +where $z_{u,v}^{k}$ is the score from cost matrix $\mathcal{Z}^k$ . The Eq. 7 can be solved by a weighted least-squares fitting algorithm [3]. Then, each hypothesis pose is verified by voting among + +the entire point correspondences set $\mathcal{M} = \bigcup_{k=1}^{K} \mathcal{M}^k$ . The hypothesis with the largest number of inlier points will be selected as the final estimation result: + +$$ +\mathbf {R}, \mathbf {t} = \underset {\mathbf {R} _ {k}, \mathbf {t} _ {k}} {\arg \max } \sum_ {p _ {u} ^ {S}, p _ {v} ^ {M} \in \mathcal {M}} \mathbb {I} \left(\left\| \mathbf {R} _ {k} p _ {v} ^ {M} + \mathbf {t} _ {k} - p _ {u} ^ {S} \right\| < \delta\right). \tag {8} +$$ + +where $\mathbb{I}$ represents the indicator function, $\delta$ is the voting threshold. + +# 4. Experiment + +# 4.1. Datasets and Metrics + +Datasets. We evaluate our method on four public benchmark datasets: T-LESS [20], LINEMOD [18], Occluded-LINEMOD [4], and TUD-L [21]. + +Metrics. We follow the evaluation metric used in the BOP Challenge [21]. The performance of pose estimation is evaluated using three errors, i.e., Visible Surface Discrepancy (VSD), Maximum Symmetry-aware Surface Distance (MSSD), and Maximum Symmetry-aware Projection Distance (MSPD). For each of the pose errors, an average recall is computed, i.e., $\mathrm{AR}_{\mathrm{VSD}}$ , $\mathrm{AR}_{\mathrm{MSSD}}$ , $\mathrm{AR}_{\mathrm{MSPD}}$ , based on a set of error thresholds. The AR refers to the average of the three recalls. + +# 4.2. Implementation Details + +We use a KPCov-FPN [56] backbone for feature extraction. Adam optimizer [26] is employed to optimize the network with the learning rate of $5 \times 10^{-5}$ . The weight decay is set to $1 \times 10^{-6}$ . GCPose is trained for 80 epochs with a batch size of 16 and the learning rate is decayed by 0.95 every 5 epochs. The network is trained on NVIDIA Tesla V100 GPUs. + +Following the practice in OVE6D [5], our GCPose is trained using the synthetic 3D objects from ShapeNet [6]. During the test, we first obtain the class labels and segmentation masks of objects by the MaskRCNN [14]. Taking a depth image with mask and object model as input, GCPose is applied to estimate the 6D pose for the object. In addition, the performance using ground truth class labels and segmentation masks is also reported in this paper. + +# 4.3. Comparison with the State-of-the-Art Methods + +# 4.3.1 T-LESS Results + +We firstly report pose estimation results on T-LESS dataset in Table 2 in terms of the AR metric. To facilitate comparison to previous works, we re-evaluate the pose estimation results of OVE6D [5] in AR metric using the official trained model. Our method achieves state-of-the-art performance under an open-set pose estimation setting. GCPose outperforms the recent learning-based OVE6D [5] by $15.6\%$ without ICP refinement [67] and is also $13.3\%$ higher than + +
MethodARVSDARMSSDARMSPDAR
DrostPPF† [12]0.3750.4780.4800.444
VidalPPF† [57]0.4640.5750.5740.538
HybridPPF† [28]0.5800.6890.6960.655
MegaPose [30]---0.543
OVE6D [5]0.5210.5110.5380.523
OVE6D† [5]0.5130.5610.5650.546
GCPose (Ours)0.6430.6910.7020.679
OVE6D* [5]0.6240.5920.6260.614
OVE6D*† [5]0.6010.6370.6370.625
GCPose* (Ours)0.7140.7390.7620.738
+ +Table 2: Comparisons on T-LESS dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object. + +
MethodARvSDARMSSDARMSPDAR
DrostPFP† [12]0.6780.7860.7890.751
OVE6D [5]0.5600.7510.7620.701
OVE6D† [5]0.7360.8820.8860.835
GCPose (Ours)0.7490.8850.8870.841
MatchNorm* [9]0.3190.4900.5290.446
MatchNorm*† [9]0.6160.6800.7370.678
OVE6D* [5]0.7940.8860.9020.860
OVE6D*† [5]0.8060.9520.9560.905
GCPose* (Ours)0.8690.9650.9740.936
+ +Table 3: Comparisons on LINEMOD dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object. + +its ICP refinement counterpart. And GCPose also outperforms traditional HybridPPF [28] with ICP refinement by $2.4\%$ . These results indicate that GCPose performs well on symmetric and texture-less objects. Moreover, given the ground truth masks, GCPose achieves $73.8\%$ AR, which reveals great potential for performance improvement with better segmentation masks. + +# 4.3.2 LINEMOD and Occluded-LINEMOD Results + +We report pose estimation results on LINEMOD and Occluded-LINEMOD, as shown in Table 3, 4. GCPose still achieves state-of-the-art performance under an open-set pose estimation setting. Specifically, GCPose surpasses OVE6D [5] by $14.0\%$ on LINEMOD dataset and $15.6\%$ on Occluded-LINEMOD dataset, respectively. GCPose outperforms the recent MatchNorm [9] by a large margin of $49.0\%$ on LINEMOD dataset and $37.6\%$ on Occluded-LINEMOD dataset, respectively. Moreover, our method is superior to OVE6D and MatchNorm, which both use ICP refinement. In contrast to previous works using handcrafted geometry features, GCPose also outperforms DrostPPF + +
MethodARVSDARMSSDARMSPDAR
DrostPPF† [12]0.4370.5630.5810.527
VidalPPF† [57]0.4730.6250.6470.582
HybridPPF† [28]0.5170.6750.7030.631
MegaPose [30]---0.583
OVE6D [5]0.3730.5400.5750.496
OVE6D† [5]0.5260.6580.6970.627
GCPose (Ours)0.5430.6910.7210.652
MatchNorm* [9]0.2630.3840.4500.365
MatchNorm*† [9]0.4780.5420.6120.544
OVE6D* [5]0.5390.6400.7030.627
OVE6D*† [5]0.6330.7550.7980.728
GCPose* (Ours)0.6560.7680.7990.741
+ +Table 4: Comparisons on Occluded-LINEMOD dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object. + +
MethodARvSDARMSSDARMSPDAR
DrostPPF† [12]0.7410.7930.7910.775
VidalPPF† [57]0.8110.9100.9070.876
HybridPPF† [28]0.8720.9450.9440.920
MegaPose [30]---0.712
GCPose (Ours)0.8710.9600.9470.926
MatchNorm* [9]0.7000.8530.8520.801
MatchNorm*† [9]0.8590.9140.9350.903
GCPose* (Ours)0.8880.9790.9800.949
+ +[12] and HybridPPF [28] on LINDEMOD and OccludedLINEMOD datasets. These results further demonstrate that GCPose has a strong generalization ability to unseen objects. + +# 4.3.3 TUD-L Results + +The pose estimation results on TUD-L dataset are summarized in Table 5. GCPose outperforms the recent MatchNorm [9] by $14.8\%$ without ICP refinement and is also $4.6\%$ higher than its ICP refinement counterpart. Besides, GC-Pose is also superior to traditional HybridPPF [28] with ICP refinement, which further indicates the superiority of our learning-based geometry features. + +# 4.3.4 Scaling of Training Data + +To investigate the potential of GCPose with more CAD models for training, we scale up the training set to both ShapeNet [6] and ABC [27]. ABC dataset consists of one million CAD models and each model is a collection of ex + +Table 5: Comparisons on TUD-L dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object. + +
DatasetMethodw/ ABCARvSDARMSSDARMSPDAR
T-LESS [20]GCPose✓0.6430.6910.7020.679
0.6810.7350.7570.724
GCPose*✓0.7140.7390.7620.738
0.7600.8010.8280.796
LM [18]GCPose✓0.7490.8850.8870.841
0.7630.9070.9080.859
GCPose*✓0.8690.9650.9740.936
0.8700.9710.9780.940
O-LM [4]GCPose✓0.5430.6910.7210.652
0.5570.7310.7640.684
GCPose*✓0.6560.7680.7990.741
0.6570.7930.8270.760
TUD-L [21]GCPose✓0.8710.9600.9470.926
0.8750.9780.9740.942
GCPose*✓0.8880.9790.9800.949
0.9040.9810.9850.957
+ +Table 6: Comparisons on T-LESS, LINEMOD (LM), Occluded-LINEMOD (O-LM), and TUD-L datasets by scaling up training datasets. *: using the ground truth label and mask of the object. + +plicityly parametrized curves and surfaces. For training efficiency, we only pick the first 100k out of 1000k CAD models from ABC. The pose estimation results are reported in Table 6. GCPose achieves consistent performance improvement on four datasets after being trained with more CAD models. + +# 4.3.5 Visualization + +To visualize the learned symmetry-aware geometry features, we reduce the dimension of point-wise features extracted by our backbone network using the t-SNE algorithm. Then the object-model point cloud is colorized according to the low-dimension features. As shown in Figure 5, the geometry feature embeddings among different parts of an object surface are distinguishable clearly and show meaningful similarity among the local structure of symmetry. It demonstrates that our method can predict reasonable geometry representations for unseen objects, which are employed to solve the 6D poses in this paper. We also give some qualitative results of GCPose on T-LESS and LINEMOD datasets, as shown in Figure 4. Compared to OVE6D [5], our method can generate more precise poses. + +# 4.4. Ablation Study + +We conduct several ablation experiments on the T-LESS dataset. To eliminate the effect of inaccurate segmentation, we use ground truth labels and masks. + +Data Augmentation and Normalization. Our method is trained on synthetic data and tested on real-world data. + +![](images/61a20211846e9d8909fff078053e84c68220125449ccde9b5b78d473dc1d771e.jpg) + +![](images/18ce10262c7b7546a80dbeb46826f25f73d1c0e19ccdd49a65234ac2b09e1161.jpg) + +![](images/70f36a0f9ae84f2de8a323b60c30e55bc10f8c6614e99af90858c07a1995fc45.jpg) +Raw +Figure 4: Qualitative results. We visualize the results of OVE6D [5] and the proposed GCPose on the T-LESS (left) and the LINEMOD (right) datasets. Raw indicates the original images and GT means the visualization of ground truth poses. GCPose performs well on a wide range of objects, containing view-point changes, and occlusions. + +![](images/1908e72477a84c9fba9909297fa1138e4da1db5cbe4a2628feda0c65f7e93a9c.jpg) +T-LESS + +![](images/71a7878a994454d001421f7438e7b33fc1f1f78be7e68a6265dd49731c4c7850.jpg) + +![](images/9c7ae4ea6cc399302d4fe65ed2f6b58bce9ae4d88916cefedf5e5c5e730ceb78.jpg) +GT + +![](images/304cf4be38f68d6becaa4a5808c4ac87ff58177b4475a338559882a573e1f752.jpg) + +![](images/20f858dc946fabadbcba64e2d7eb296efb993ef3251f25eb5b7fa923b1402416.jpg) + +![](images/2333e31f8fcb2d787dddb24aeb697487b12c707f7b67f09d2f27a5fb0f0ce1e6.jpg) +OVE6D + +![](images/26fef05aeecd603dee2f862b20115cb49d96e8f17ecf1eb1eca65b418e060c7d.jpg) + +![](images/31adccc7910561e4d2363c0fada86705a49233bbcce42460808317472bb9850a.jpg) + +![](images/85f1e98b78ed7731e2275c3b3aec3bbfcd2baf905dab04a77473094af85ed23d.jpg) +GCPose + +![](images/dd1d9dc7b3e757b25755e29a455e1d2c87eba7e89d2a1403112b2a6627abef16.jpg) + +![](images/2fc2f8f9aea51dccc90f469dc638bac31047fa758f4f8988bdf4873362729067.jpg) + +![](images/3bde6ed75d84f5e1fd3d59676b66f814ac6de9fcd9add4e3f776a665cf968435.jpg) +Raw + +![](images/1a842735e2098c34920a1290d2a0b51d0f9d3658c818c11e85740b60e3450f0d.jpg) +LINEMOD + +![](images/0a47aab3c4ba43d322294e62577dcdfc5bb1e8e1ce30db3bc0e44210e6c3dd7c.jpg) + +![](images/8c94b929311b5a0674f8361217f2c15c33ef7051ab5ac1c79dfbf0c56dfd39ca.jpg) +GT + +![](images/af072094bcf6ee4f54965133522255dd4388ec6945ebb4ce7bb7e5e12adb78c4.jpg) + +![](images/7a1ef3ef20287ac0e8ca4e5c64a659f6c108e1a7078c245cf960167e2f2aacdf.jpg) + +![](images/2e0491c30c12601b7a8aa1f3571f4860ba51ebac89d0c3cae7cf04789de3fc9c.jpg) +OVE6D + +![](images/264a71172e8c61ac222a624712d7b013a6366417faeed4699653c3664e7efb7b.jpg) + +![](images/c72f98c6c41f922816ba6efc0d4cfb480ab86bf4de0991a072f8dbe4480f1da7.jpg) + +![](images/55edfd2f9ad808f1b5122a044902eb7c5079427a9f8d0eb442198ee12a728246.jpg) +GCPose + +
Data AugNormGA FeatSA LossAR
0.635
✓0.669 (+3.4%)
✓✓0.698 (+6.3%)
✓✓✓0.708 (+7.3%)
✓✓✓✓0.738 (+10.3%)
+ +Table 7: Ablation experiments: the impact of the proposed special data augmentation (Data Aug), normalization (Norm), global-aware fine-level features (GA Feat), and symmetry-aware matching loss (SA Loss). + +So special data augmentation strategies are necessary to improve the generalization to real-world scenes. Besides, we standardize the scale of the input point clouds to facilitate the learning of geometry features. As shown in Table 7, special data augmentation and normalization bring $3.4\%$ and $2.9\%$ AR improvement, respectively. + +Global-Aware Fine-level Features. As described in Section 3.3, we enhance fine-level point features with global structural cues to make features more discriminative for establishing correspondence. As shown in Table 7, the performance of GCPose is improved from $69.8\%$ to $70.8\%$ using global-aware fine-level features. + +Symmetry-Aware Matching Loss. To eliminate the ambiguity of the learning of geometry features, as described in Section 3.4, we design a symmetry-aware matching loss to supervise the many-to-many correspondences. The geometry features output by GCPose are meaningful and the features of symmetric structures are visually similar (Figure 5). As shown in Table 7, the symmetry-aware matching loss + +![](images/986b32062250a94daf942762ead66d5cade27384006b5465df705ca4437c0884.jpg) + +![](images/e60b3c957a5206e0fa57a7876112642ea08259616c964d1c5e29a87518560971.jpg) + +![](images/15db60fea085cd55d17dc56039d9cfc194481a85d41dd2e949a220c03595be3d.jpg) + +![](images/fd5b109093d59048e13ae9b72228024889c9617fea930d902652729a980c1889.jpg) + +![](images/061560be21c8708248ecb766d3a029990bfb7812aea0ea17180a693f5174fc66.jpg) +Figure 5: t-SNE visualization of learned symmetry-aware geometry features on several unseen objects from T-LESS. The geometry features are distinguishable among different parts within an object and show meaningful similarity among the local structure of symmetry. + +![](images/289cdbb551442b6b868bd7d6b9915265d8cae47b9ac5e2eadc83b0d1ba50d6ba.jpg) + +![](images/a8ae1ebb74409c9a26f70a20611e7a24b9cd4af093e879e09498172c239dd0f7.jpg) + +![](images/241326085279413fbf1559363a7366dae737818f1cdcafa18f8381282441c12b.jpg) + +provides $3.0\%$ AR improvement. + +# 5. Conclusion + +In this paper, we propose a pose estimation framework based on object-agnostic geometry features, which can generalize to arbitrary unseen objects without re-training. Compared with previous methods, GCPose achieves state-of-the-art performance on four benchmarks. We hope that our simple yet effective framework could serve as a strong baseline for unseen object 6D pose estimation and motivate researchers to explore more in this direction. + +Acknowledgments. 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+ { + "bbox": [ + 46, + 299, + 290, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 290, + 574 + ], + "type": "text", + "content": "Current 6D pose estimation methods focus on handling objects that are previously trained, which limits their applications in real dynamic world. To this end, we propose a geometry correspondence-based framework, termed GCPose, to estimate 6D pose of arbitrary unseen objects without any re-training. Specifically, the proposed method draws the idea from point cloud registration and resorts to object-agnostic geometry features to establish the 3D-3D correspondences between the object-scene point cloud and object-model point cloud. Then the 6D pose parameters are solved by a least-squares fitting algorithm. Taking the symmetry properties of objects into consideration, we design a symmetry-aware matching loss to facilitate the learning of dense point-wise geometry features and improve the performance considerably. Moreover, we introduce an online training data generation with special data augmentation and normalization to empower the network to learn diverse geometry prior. With training on synthetic objects from ShapeNet, our method outperforms previous approaches for unseen object pose estimation by a large margin on T-LESS, LINEMOD, Occluded-LINEMOD, and TUD-L datasets. Code is available at https://github.com/hikvision-research/GCPose." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 599, + 128, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 128, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 128, + 611 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 620, + 287, + 693 + ], + "type": "text", + "content": "The 6D pose of an object represents a geometry transformation between the object coordinate system and camera coordinate system, which consists of 3D rotation and 3D translation. Estimating object pose plays an important role in many real-world applications, such as robotic grasping [8] and augmented reality [38]." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 273, + 425, + 347 + ], + "blocks": [ + { + "bbox": [ + 310, + 273, + 425, + 347 + ], + "lines": [ + { + "bbox": [ + 310, + 273, + 425, + 347 + ], + "spans": [ + { + "bbox": [ + 310, + 273, + 425, + 347 + ], + "type": "image", + "image_path": "8cd03a2393e3a6a14b2957951055f769457b9f383e5efe62df16611ce8610ac2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 351, + 402, + 362 + ], + "lines": [ + { + "bbox": [ + 331, + 351, + 402, + 362 + ], + "spans": [ + { + "bbox": [ + 331, + 351, + 402, + 362 + ], + "type": "text", + "content": "(a) Category-Level" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 427, + 273, + 542, + 347 + ], + "blocks": [ + { + "bbox": [ + 427, + 273, + 542, + 347 + ], + "lines": [ + { + "bbox": [ + 427, + 273, + 542, + 347 + ], + "spans": [ + { + "bbox": [ + 427, + 273, + 542, + 347 + ], + "type": "image", + "image_path": "4d7e099bc442e0044e793e5900ed6ce125156c79be42c84c18e8a3fc3d5748d2.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 351, + 522, + 362 + ], + "lines": [ + { + "bbox": [ + 449, + 351, + 522, + 362 + ], + "spans": [ + { + "bbox": [ + 449, + 351, + 522, + 362 + ], + "type": "text", + "content": "(b) Template-Based" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 310, + 367, + 541, + 450 + ], + "blocks": [ + { + "bbox": [ + 310, + 367, + 541, + 450 + ], + "lines": [ + { + "bbox": [ + 310, + 367, + 541, + 450 + ], + "spans": [ + { + "bbox": [ + 310, + 367, + 541, + 450 + ], + "type": "image", + "image_path": "eec03ba01786ccefddff44a799e7f8374921bba76d08844a5d778a874b66fa81.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 375, + 454, + 474, + 465 + ], + "lines": [ + { + "bbox": [ + 375, + 454, + 474, + 465 + ], + "spans": [ + { + "bbox": [ + 375, + 454, + 474, + 465 + ], + "type": "text", + "content": "(c) Correspondence-Based" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 469, + 547, + 530 + ], + "lines": [ + { + "bbox": [ + 304, + 469, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 547, + 530 + ], + "type": "text", + "content": "Figure 1: Comparison of different open-set pose estimation frameworks. Unlike previous methods that rely on category-specific network training (a) or struggle to estimate precise poses (b), our GCPose can perform well on arbitrary unseen objects (c)." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "Driven by the recent developments in deep learning, various methods have been proposed to explore the instance-level 6D pose estimation problem. Some existing works [43, 15] employ CNNs to detect a set of keypoints predefined on the 3D object model. Then the 6D pose can be solved by Perspective-n-Points (PnP) [31] or least-squares fitting algorithm. Since the detected keypoints serve as sparse correspondences, these methods often struggle when objects have view-point changes, occlusions, or lack of texture. Another alternative is to predict pixel-wise 3D coordinates for building dense 2D-3D correspondence maps [42, 59, 51, 36, 22]. They allow for significantly better treatment of occlusions and lead to more precise poses. Al" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14045" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "though instance-level methods can obtain impressive results on existing benchmarks, they are still under the close-set assumption that the object space is identical in both training and testing phases. As a result, laborious data collection and re-training are required when unseen objects appear, which does not adhere to application in the real dynamic world." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 146, + 290, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 146, + 290, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 290, + 375 + ], + "type": "text", + "content": "To loosen the restriction with generalizability to unseen objects, category-level pose estimation paradigm [60, 33, 7, 35, 62] is proposed, as shown in Figure 1a. These approaches predict the object pose for previously seen or unseen objects from a known set of categories, but can not generalize to new instances having significantly different appearances or shapes [17, 53]. Another way to address the open-set problem is to resort to the template-based mechanism [55, 40, 5, 49, 30], which matches the input image to a series of templates generated from their 3D object models, as shown in Figure 1b. Obviously, these methods struggle to estimate precise poses due to occlusions and the limited number of viewpoints. To remedy this disadvantage, OVE6D [5] presents an in-plane orientation regression network and OSOP [49] introduces an extra network estimating dense 2D-2D correspondences between the input image and the matched template for pose refinement. In general, these methods have cascade pipelines and result in less accurate pose estimation for unseen objects." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 376, + 290, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 290, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 290, + 640 + ], + "type": "text", + "content": "As is known, point cloud registration methods have demonstrated excellent generalization to previously unseen point clouds as the geometry features of the point cloud are generic and object-agnostic. Inspired by this idea, we present an unseen object 6D pose estimation framework based on dense geometry correspondences, termed GCPose. Specifically, given the object-scene point cloud and object-model point cloud as input, GCPose can establish dense 3D-3D correspondences between them through the geometry features. Finding correspondences across two scene-level point clouds is well-studied in point cloud registration [1, 23, 65, 64, 45] field. However, it is challenging to learn 3D-3D matching for object-level point clouds due to ambiguous correspondences caused by symmetric properties in many object models. For instance, a 3D location in the object-scene point cloud may correspond to multiple 3D locations on the surface of the symmetric object, and vice versa. Therefore, exploiting the off-the-shelf point cloud registration method is sub-optimal to building correspondences for object pose estimation. To this end, we design a symmetry-aware matching loss to let the network learn the object symmetries explicitly." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "content": "Following the practice in OVE6D [5], we train the network using a large number of synthetic 3D object models from the ShapeNet [6] dataset. Specifically, we introduce a simple yet effective online training data generation with special data augmentation and normalization to empower the network to learn diverse geometry prior. After train-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "ing on synthetic objects with varied shapes, our method is capable of generalizing to an arbitrary unseen object without any re-training. At inference time, the proposed method requires a depth image with a target object mask and the associated object CAD model, which are utilized to generate object-scene and object-model point clouds." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 144, + 512, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 144, + 512, + 156 + ], + "spans": [ + { + "bbox": [ + 317, + 144, + 512, + 156 + ], + "type": "text", + "content": "Our contribution can be summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 312, + 165, + 545, + 304 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 313, + 165, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 165, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 313, + 165, + 545, + 190 + ], + "type": "text", + "content": "1) We employ the point cloud registration framework and adapt it to work well for unseen object pose estimation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 312, + 198, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 198, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 312, + 198, + 545, + 236 + ], + "type": "text", + "content": "2) A symmetry-aware matching loss is proposed for building unambiguous and robust 3D-3D correspondences, which improves the performance significantly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 243, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 243, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 312, + 243, + 545, + 304 + ], + "type": "text", + "content": "3) GCPose achieves state-of-the-art performance on TLESS, LineMOD, Occluded-LineMOD, and TUD-L datasets under an open-set pose estimation setting. Besides, the performance of GCPose can be further improved by scaling up the training data." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 316, + 392, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 392, + 328 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 392, + 328 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 335, + 454, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 454, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 454, + 348 + ], + "type": "text", + "content": "2.1. 6D Object Pose Estimation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 426 + ], + "type": "text", + "content": "Direct Pose Regression Approaches. Some methods directly regress the 6D pose with deep neural networks, such as [63, 25]. Despite these approaches seeming simple, the non-linearity of the rotation space limits their generalization. Some post-refinement methods [58, 29, 24] are generally utilized to refine the pose iteratively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 426, + 546, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 617 + ], + "type": "text", + "content": "Correspondence-Based Approaches. Another popular line to estimate the 6D pose relies on pre-defined keypoints on the object model. For instance, PVNet [43] selects " + }, + { + "bbox": [ + 304, + 426, + 546, + 617 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 426, + 546, + 617 + ], + "type": "text", + "content": " 3D keypoints from the object surface. Then it employs a CNN to predict the offset to the projection of 3D keypoints in 2D images and the 6D pose is calculated by PnP [31]. PVN3D [16] and FFB6D [15] extract the per-point feature from an RGBD image to predict more precise offset to 3D keypoints and improve the performance. Since the keypoints serve as sparse correspondences, above methods often struggle in occluded scenes. An alternative is to generate dense correspondences. Some of the representative works include CDPN [34], EPOS [19], GDR-Net [59], and SO-Pose [11]. Recently, OnePose [53] and FS6D [17] focus on 6D pose estimation under a few-shot setting, which is more challenging." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "Template-Based Approaches. To estimate the 6D pose of previously-unseen objects, the template-based mechanism [2, 41, 40, 5, 49] is proposed. These methods compare the input image to a series of templates, which are rendered images of objects associated with the corresponding 6D poses. And the pose of the best-matched template is selected as the final estimation result. Nevertheless, due to the discretization error of the limited number of viewpoints," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "14046" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 74, + 536, + 250 + ], + "blocks": [ + { + "bbox": [ + 54, + 74, + 536, + 250 + ], + "lines": [ + { + "bbox": [ + 54, + 74, + 536, + 250 + ], + "spans": [ + { + "bbox": [ + 54, + 74, + 536, + 250 + ], + "type": "image", + "image_path": "875bf7eb59e399247b33693ffcc43474df87dc6f1a550f7f21cd8db23f371396.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 255, + 548, + 329 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 548, + 329 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 548, + 329 + ], + "type": "text", + "content": "Figure 2: The training pipeline of GCPose. Firstly, the object-scene point cloud is obtained from the rendered depth image from ShapeNet [6] and the object-model point cloud is generated by uniform sampling on the surface of the object model. Then, a shared backbone network (i.e., KPCov) is utilized to extract multi-level features of the input point clouds. The interleaved self- and cross-attention layers are adopted to enhance the geometry features of both coarse-level superpoints and fine-level points. Finally, a symmetry-aware matching loss is employed to supervise the learning of geometry features for establishing unambiguous and robust 3D-3D correspondences." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 349, + 288, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 288, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 288, + 420 + ], + "type": "text", + "content": "template-based approaches result in inaccurate pose estimation. OVE6D [5] presents an in-plane orientation regression network for rotation refinement. And OSOP [49] proposes an extra network estimating 2D-2D correspondences between the input image and the matched template for pose refinement." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 429, + 187, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 429, + 187, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 187, + 442 + ], + "type": "text", + "content": "2.2. Point Cloud Registration" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 448, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 602 + ], + "type": "text", + "content": "Point cloud registration aims to align the two input point clouds by estimating a 3D rigid transformation. The typical pipeline contains detecting keypoints [32, 1], extracting feature descriptors [44, 10, 23], and estimating the transformation. Recently, detection-free methods[65, 64, 45] achieve state-of-the-art performance on several point cloud registration benchmarks. These methods generally assume a one-to-one relationship for two input point clouds, which goes against the nature of symmetry existing in object pose estimation. Specially, we propose a symmetry-aware matching loss to supervise the many-to-many relationship for object pose estimation and eliminate the ambiguity of correspondences." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 610, + 216, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 216, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 216, + 624 + ], + "type": "text", + "content": "2.3. Symmetries in Pose Estimation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Multiple poses can be inferred under a specific appearance for symmetric objects, which leads to the problem of pose ambiguity. To relieve this problem, PoseCNN [63], DenseFusion [58], and GDR-Net [59] adopt the ADD-S [63] metric as the loss during training. ES6D [39] designs a symmetry-invariant pose distance metric to make the network converge to the correct state. [37] predicts multiple" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 349, + 547, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 547, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 547, + 494 + ], + "type": "text", + "content": "poses for the object to estimate the specific pose distribution generated by symmetries. EPOS [19] and SurfEmb [13] learn the 2D-3D correspondence distributions over surface fragments or the entire surface and let the network learn the object symmetries implicitly. These methods focus on memorizing the symmetry information of specific objects and the trained network only performs well on a fixed set of objects. In this paper, we leverage the symmetries of objects and supervise the network with many-to-many correspondences in two input point clouds during training. Therefore, our network learns the object symmetries explicitly, which is proven effective for unseen object pose estimation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 502, + 389, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 389, + 515 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 389, + 515 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 521, + 547, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 583 + ], + "type": "text", + "content": "In this section, we first present the overall architecture of our GCPose. Next, the training data generation and feature extraction module are introduced. Then, we elaborate on the proposed symmetry-aware matching loss. At last, the inference pipeline of our framework is summarized." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 587, + 373, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 373, + 599 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 373, + 599 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Recent GeoTransformer [45] achieves outstanding performance in point cloud registration field and shows strong capabilities for finding correspondences. In this paper, we renovate the GeoTransformer [45] pipeline and adapt it for object pose estimation. Specifically, we design a symmetry-aware matching loss to eliminate the ambiguity of correspondences (Section 3.4). To make features more discriminative for establishing correspondence, we enrich fine-level point features with global structural cues (Section 3.3)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14047" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 278, + 155 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 278, + 155 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 278, + 155 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 278, + 155 + ], + "type": "table", + "html": "
AugmentationHyper-parameter
Downscalescale range s ∈ [0.1, 0.3]
Laplace Noisescale param. b ∈ [0, 0.004m]
Median Blurkernel size k = 3, 5
Upscalescale range s ∈ [3.3, 10]
Dropoutarea ratio r ∈ [0.01, 0.1]
", + "image_path": "f92e632e0b7450ea9c2ccecacd1a11c400297b0ea7df081e505bcd7917f3d967.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 287, + 195 + ], + "lines": [ + { + "bbox": [ + 46, + 158, + 287, + 195 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 287, + 195 + ], + "type": "text", + "content": "Table 1: Data augmentation strategies. We adopt these strategies to bridge the domain gap between the synthetic and real-world depth images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 216, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 252 + ], + "type": "text", + "content": "Moreover, an online training data generation with special data augmentation and normalization is devised to empower the network to learn diverse geometry priors (Section 3.2)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "type": "text", + "content": "The training pipeline of GCPose is illustrated in Figure 2. Following OVE6D [5], our network is trained using rendered depth images based on 3D object models from ShapeNet [6]. The object-scene point cloud is obtained from the depth image within the object mask and the object-model point cloud is generated by uniform sampling on the surface of the object model. Given the object-scene and object-model point clouds as input, our goal is to estimate the rigid transformation " + }, + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "type": "text", + "content": " from the object coordinate system to the camera coordinate system, consisting of a 3D rotation " + }, + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{R} \\in SO(3)" + }, + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "type": "text", + "content": " and a translation vector " + }, + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{t} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 252, + 287, + 384 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": "Concretely, the KPCov-FPN [56] is employed as the backbone network to extract the multi-level features of the input point clouds. We refer to the coarsest level downsampled points " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "(\\frac{1}{8}" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " resolution of original point cloud) from the backbone as superpoints, denoted as " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\hat{S},\\hat{M}" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " for object-scene and object-model point clouds. The first level downsampled points " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "(\\frac{1}{2}" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " resolution of original point cloud), denoted as " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "S,M" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " for object-scene and object-model point clouds, are treated as fine-level points. Besides, we also adopt interleaved self- and cross-attention layers [47, 66, 61, 48] to enhance the geometry features of both coarse-level superpoints and fine-level points. In the end, a symmetry-aware matching loss is proposed to supervise the learning of geometry features for establishing robust 3D-3D correspondences." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 574, + 192, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 192, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 192, + 588 + ], + "type": "text", + "content": "3.2. Training Data Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "Our network is optimized using synthetic depth images rendered from 3D object models. Specifically, for each 3D object model, the ModernGL library is employed to synthesize the depth images under random poses. After that, we apply a set of data augmentation strategies to bridge the domain gap between the synthetic and real-world depth images. The depth image is first cropped based on the object mask and then resized to a fixed size " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "(224 \\times 224" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " in this paper) for later preprocessing pipeline. Specifically, 1) the depth image is downsampled at a random scale, 2) Median" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 73, + 422, + 199 + ], + "blocks": [ + { + "bbox": [ + 317, + 73, + 422, + 199 + ], + "lines": [ + { + "bbox": [ + 317, + 73, + 422, + 199 + ], + "spans": [ + { + "bbox": [ + 317, + 73, + 422, + 199 + ], + "type": "image", + "image_path": "59921321e73b50bffd6d5b2aacc47375df88591fca28f4ec23288002ec9f12ae.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 201, + 405, + 211 + ], + "lines": [ + { + "bbox": [ + 333, + 201, + 405, + 211 + ], + "spans": [ + { + "bbox": [ + 333, + 201, + 405, + 211 + ], + "type": "text", + "content": "(a) Discrete Symmetry" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 220, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 305, + 220, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 545, + 258 + ], + "type": "text", + "content": "Figure 3: Examples of symmetric objects. (a) The object has finite ambiguity poses (4 in the case). (b) The object has infinite ambiguity poses." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 433, + 76, + 536, + 198 + ], + "blocks": [ + { + "bbox": [ + 433, + 76, + 536, + 198 + ], + "lines": [ + { + "bbox": [ + 433, + 76, + 536, + 198 + ], + "spans": [ + { + "bbox": [ + 433, + 76, + 536, + 198 + ], + "type": "image", + "image_path": "c585ed8434854e7fe71db01a359a541247982eea6fa9a3bc77e649676f7c6743.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 444, + 201, + 527, + 211 + ], + "lines": [ + { + "bbox": [ + 444, + 201, + 527, + 211 + ], + "spans": [ + { + "bbox": [ + 444, + 201, + 527, + 211 + ], + "type": "text", + "content": "(b) Continuous Symmetry" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 285, + 545, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 406 + ], + "type": "text", + "content": "blur is conducted on it to weaken high-frequency information of synthetic depth image, 3) random Laplace noise is added to simulate salt and pepper noise, 4) the depth image is zoomed into their original size, 5) random square areas are dropped from the image. The detailed hyper-parameters of these data augmentations can be found in Table 1. The resulting depth image with the object mask is converted into the object-scene point cloud using the camera intrinsic matrix. And the object-model point cloud is obtained by uniform surface sampling from the 3D object model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 409, + 546, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 546, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 546, + 517 + ], + "type": "text", + "content": "In contrast with the training dataset where the set of objects' size is finite, the size of different objects in the real world varies widely. To improve generalization ability of our GCPose, the object-scene and object-model point clouds are normalized before being fed into the network. The normalization scale is calculated as the largest distance between any pair of the object-model point cloud, i.e., the diameter of the smallest circumscribed sphere of the object-model point cloud." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 536, + 417, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 417, + 547 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 417, + 547 + ], + "type": "text", + "content": "3.3. Feature Extraction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": "The KPCov-FPN [56] only encodes local geometry features which are less distinctive for correspondence search. To capture the global geometry structures and strengthen superpoint features, a self-attention layer is applied to the coarse-level superpoint features extracted from the last downsample stage of KPCov-FPN. Then a cross-attention layer is adopted to enable the bidirectional communication between object-scene and object-model point clouds, which aims to model the inter-point-cloud geometry consistency. In contrast to GeoTransformer [45], to enrich fine-level point features, we inject coarse-level superpoint features with global structural cues into the upsampling stage of KPCov-FPN." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14048" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "text", + "content": "3.4. Symmetry-Aware Matching Loss" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 132, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 132, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 132, + 102 + ], + "type": "text", + "content": "3.4.1 Symmetries" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "text", + "content": "Discrete and continuous symmetries are two types of symmetries. As shown in Figure 3, discrete symmetries can be described by a finite transformation set while continuous symmetries are described by an infinite transformation set. The symmetry property of an object can lead to multiple poses with the same visual appearance. In other words, there exist repeated geometry structures on the surface of a symmetry object. Therefore, the extracted geometry feature of a point in the object-scene point cloud should be similar to multiple points features in the symmetric object-model point cloud, and vice versa. To this end, we design a symmetry-aware matching loss to supervise the many-to-many relationship and let the network learn the object symmetries explicitly." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "text", + "content": "Specifically, we first use the method described in [39] to calculate the symmetry axes and angles for each object from ShapeNet. After that, we can obtain a set of transformation " + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{T}} = \\{\\mathbf{T}_0,\\mathbf{T}_1,\\dots,\\mathbf{T}_n\\} ,\\mathbf{T}_i\\in SE(3)" + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "text", + "content": " for each object. The visual appearance of an object remains unchanged under each transformation of " + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{T}}" + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "text", + "content": " . Here we use " + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_0" + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "text", + "content": " to represent the identity transformation and the set only containing " + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_0" + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "text", + "content": " indicates a non-symmetrical object. For continuous symmetries objects, we discretize the rotation angle for obtaining a finite transformation set. Finally, the ground truth pose " + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 276, + 289, + 419 + ], + "type": "text", + "content": " of an object-scene point cloud can be extended to a pose set, which can be formulated as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 118, + 426, + 287, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 426, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 118, + 426, + 287, + 442 + ], + "type": "interline_equation", + "content": "\\overline {{\\mathbf {T}}} = \\left\\{\\mathbf {T} \\mathbf {T} _ {i} \\mid \\mathbf {T} _ {i} \\in \\widehat {\\mathbf {T}} \\right\\}. \\tag {1}", + "image_path": "1c8bdfd4be4c213ee3de1536b4f2419dbd5d10b19bdce8fe547a7a9c35a2a1a8.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 449, + 271, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 271, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 271, + 462 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{T}}" + }, + { + "bbox": [ + 47, + 449, + 271, + 462 + ], + "type": "text", + "content": " is then used to calculate the following matching loss." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 475, + 144, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 144, + 488 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 144, + 488 + ], + "type": "text", + "content": "3.4.2 Matching Loss" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "text", + "content": "Given the ground truth pose set " + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{T}}" + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "text", + "content": " and superpoints " + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\hat{S},\\hat{M}" + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "text", + "content": " we calculate the overlap ratio for constructing positive and negative superpoint pairs between object-scene and object-model point clouds. For each superpoint pair " + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "inline_equation", + "content": "(\\hat{S}_i,\\hat{M}_j)" + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "text", + "content": ", the overlap ratio " + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "inline_equation", + "content": "o_{ij}" + }, + { + "bbox": [ + 46, + 493, + 287, + 555 + ], + "type": "text", + "content": " is computed:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 562, + 287, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 562, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 52, + 562, + 287, + 647 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} o _ {i j} = \\frac {o _ {i \\rightarrow j} + o _ {j \\rightarrow i}}{2} (2) \\\\ O _ {i \\rightarrow j} = \\frac {\\left|\\left\\{p \\in P _ {i} ^ {S} \\mid \\exists q \\in P _ {j} ^ {M} , \\overline {{\\mathbf {T}}} _ {i} \\in \\overline {{\\mathbf {T}}} \\right. \\text {s . t .} \\| \\overline {{\\mathbf {T}}} _ {i} ^ {- 1} (p) - q \\| < \\tau \\} \\right|}{\\left| P _ {i} ^ {S} \\right|} (3) \\\\ O _ {j \\rightarrow i} = \\frac {\\left|\\left\\{q \\in P _ {j} ^ {M} \\mid \\exists p \\in P _ {i} ^ {S} , \\overline {{\\mathbf {T}}} _ {i} \\in \\overline {{\\mathbf {T}}} \\text {s . t .} \\| \\overline {{\\mathbf {T}}} _ {i} (q) - p \\| < \\tau \\right\\}\\right|}{\\left| P _ {j} ^ {M} \\right|} (4) \\\\ \\end{array}", + "image_path": "d0730c8b2edc9c3a3b57fbc835d7111bd3263c6daa390929413d1cda5d222b91.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_{i}^{S}, P_{j}^{M}" + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": " are the set of fine points allocated to " + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{S}_{i}, \\hat{M}_{j}" + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": " by point-to-node strategy [65], respectively. " + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": " is the distance threshold. " + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\|\\cdot\\|" + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": " is the Euclidean norm. " + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "inline_equation", + "content": "|\\cdot|" + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": " is the set cardinality. " + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{T}}_{i}^{-1}" + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": " is inverse transformation of " + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{T}}_{i}" + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": ". The positive set " + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\varepsilon_{p}" + }, + { + "bbox": [ + 46, + 650, + 287, + 714 + ], + "type": "text", + "content": " consists of all superpoint pairs with overlap ratio" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "greater 0.1. Similarly, all superpoint pairs without overlap form the set of negatives " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\varepsilon_{n}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": ". Taking " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\varepsilon_{p}, \\varepsilon_{n}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": ", and the associated overlap ratio as input, an overlap-aware circle loss [54, 45] is adopted as coarse supervision, denoted as " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": "Given a positive superpoint pair " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\langle \\hat{S}_k,\\hat{M}_k\\rangle" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": ", an optimal transport layer is utilized to extract fine point correspondences. The set of their associated fine points " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\langle P_k^S\\in" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{m\\times 3}" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "P_{k}^{M}\\in \\mathbb{R}^{n\\times 3}\\rangle" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " are allocated by point-to-node strategy.. Taking their features " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\langle F_k^S\\in \\mathbb{R}^{m\\times d}" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "F_{k}^{M}\\in \\mathbb{R}^{n\\times d}\\rangle" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " as input, we firstly compute cost matrix " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "C^k\\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " by inner product. Then Sinkhorn algorithm [50] is employed to obtain a refined cost matrix " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^k\\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": ". Each entry " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " in the matrix represents the matching confidence between the point " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " and point " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "P_{k}^{S}" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "P_{k}^{M}" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": ", respectively. If " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " is a positive correspondence, the distance of the point " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " and point " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " under one pose of " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{T}}" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " less than a matching threshold, and " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " is a negative correspondence otherwise. Finally, the fine matching loss " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_f^k" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " is obtained by minimizing the negative log-likelihood of the cost matrix " + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^k" + }, + { + "bbox": [ + 304, + 120, + 546, + 300 + ], + "type": "text", + "content": " as in [46, 45]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 300, + 545, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 336 + ], + "type": "text", + "content": "We randomly sample " + }, + { + "bbox": [ + 304, + 300, + 545, + 336 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 304, + 300, + 545, + 336 + ], + "type": "text", + "content": " superpoint pairs from " + }, + { + "bbox": [ + 304, + 300, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\varepsilon_{p}" + }, + { + "bbox": [ + 304, + 300, + 545, + 336 + ], + "type": "text", + "content": " for fine matching loss. Formally, the overall loss function can be formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 378, + 344, + 545, + 377 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 344, + 545, + 377 + ], + "spans": [ + { + "bbox": [ + 378, + 344, + 545, + 377 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {c} + \\frac {1}{N _ {c}} \\sum_ {k = 1} ^ {N _ {c}} \\mathcal {L} _ {f} ^ {k}. \\tag {5}", + "image_path": "e7a96a74eb47c96798f45dd8254f8807867c023ef78455832f6451225bd0a225.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 385, + 373, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 385, + 373, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 385, + 373, + 396 + ], + "type": "text", + "content": "3.5. Inference" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": "Following the setting of OVE6D [5], we obtain the class labels and segmentation masks of objects by the MaskR-CNN [14]. Given a depth image with mask and object model as input, the object-scene and object-model point clouds are first generated. After feature extraction, the coarse similarity matrix " + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": " is computed using the coarse features " + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "inline_equation", + "content": "\\hat{F}^S, \\hat{F}^M" + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 385, + 486, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 385, + 486, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 385, + 486, + 545, + 502 + ], + "type": "interline_equation", + "content": "\\hat {c} _ {i, j} = e ^ {- \\left\\| \\hat {f} _ {i} ^ {S} - \\hat {f} _ {j} ^ {M} \\right\\|}. \\tag {6}", + "image_path": "db45f9bca47b9d970f3266ae6d65a67d6ce073479a225f45c77a35fc6a19eee3.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 506, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 546 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 506, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\hat{c}_{i,j} \\in \\hat{C}, \\hat{f}_i^S \\in \\hat{F}^S, \\hat{f}_j^M \\in \\hat{F}^M" + }, + { + "bbox": [ + 304, + 506, + 545, + 546 + ], + "type": "text", + "content": ". The largest K entries in " + }, + { + "bbox": [ + 304, + 506, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 304, + 506, + 545, + 546 + ], + "type": "text", + "content": " are selected as potential coarse correspondence candidates." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "text", + "content": "For each selected superpoint pair " + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\langle \\hat{S}_k,\\hat{M}_k\\rangle" + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "text", + "content": ", the cost matrix " + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^k\\in \\mathbb{R}^{m\\times n}" + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "text", + "content": " is computed as described in 3.4.2. To filter outlier matches, point correspondence candidates are selected by mutual nearest neighbor criteria as described in [52]. These selected dense point pairs are denoted as " + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^k = \\{\\langle p_u^S,p_v^M\\rangle |p_u^S\\in P_k^S,p_v^M\\in P_k^M\\}" + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "text", + "content": ". A hypothesis pose set " + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{R}_k,\\mathbf{t}_k\\mid k\\in [1,K]\\}" + }, + { + "bbox": [ + 304, + 546, + 545, + 632 + ], + "type": "text", + "content": " is computed:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 639, + 545, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 639, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 313, + 639, + 545, + 668 + ], + "type": "interline_equation", + "content": "\\mathbf {R} _ {k}, \\mathbf {t} _ {k} = \\underset {\\mathbf {R}, \\mathbf {t}} {\\arg \\min } \\sum_ {p _ {u} ^ {S}, p _ {v} ^ {M} \\in \\mathcal {M} ^ {k}} z _ {u, v} ^ {k} \\| \\mathbf {R} p _ {v} ^ {M} + \\mathbf {t} - p _ {u} ^ {S} \\|. \\tag {7}", + "image_path": "64c9ac8be32e4af6483586e2369fc0c59d5fa0c67d638abfe9afaae308fd4ca3.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "z_{u,v}^{k}" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " is the score from cost matrix " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}^k" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": ". The Eq. 7 can be solved by a weighted least-squares fitting algorithm [3]. Then, each hypothesis pose is verified by voting among" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14049" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 70, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 70, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 287, + 107 + ], + "type": "text", + "content": "the entire point correspondences set " + }, + { + "bbox": [ + 46, + 70, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathcal{M} = \\bigcup_{k=1}^{K} \\mathcal{M}^k" + }, + { + "bbox": [ + 46, + 70, + 287, + 107 + ], + "type": "text", + "content": ". The hypothesis with the largest number of inlier points will be selected as the final estimation result:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 52, + 114, + 286, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 114, + 286, + 152 + ], + "spans": [ + { + "bbox": [ + 52, + 114, + 286, + 152 + ], + "type": "interline_equation", + "content": "\\mathbf {R}, \\mathbf {t} = \\underset {\\mathbf {R} _ {k}, \\mathbf {t} _ {k}} {\\arg \\max } \\sum_ {p _ {u} ^ {S}, p _ {v} ^ {M} \\in \\mathcal {M}} \\mathbb {I} \\left(\\left\\| \\mathbf {R} _ {k} p _ {v} ^ {M} + \\mathbf {t} _ {k} - p _ {u} ^ {S} \\right\\| < \\delta\\right). \\tag {8}", + "image_path": "a68e49ebcc0c4e45b4eb46bf284ae204903b28f345d35e8cf50b2fd40b0165f8.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 152, + 286, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 152, + 286, + 176 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 286, + 176 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 152, + 286, + 176 + ], + "type": "inline_equation", + "content": "\\mathbb{I}" + }, + { + "bbox": [ + 46, + 152, + 286, + 176 + ], + "type": "text", + "content": " represents the indicator function, " + }, + { + "bbox": [ + 46, + 152, + 286, + 176 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 152, + 286, + 176 + ], + "type": "text", + "content": " is the voting threshold." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 186, + 123, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 186, + 123, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 123, + 201 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 206, + 168, + 218 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 206, + 168, + 218 + ], + "spans": [ + { + "bbox": [ + 47, + 206, + 168, + 218 + ], + "type": "text", + "content": "4.1. Datasets and Metrics" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 225, + 286, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 286, + 261 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 286, + 261 + ], + "type": "text", + "content": "Datasets. We evaluate our method on four public benchmark datasets: T-LESS [20], LINEMOD [18], Occluded-LINEMOD [4], and TUD-L [21]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "type": "text", + "content": "Metrics. We follow the evaluation metric used in the BOP Challenge [21]. The performance of pose estimation is evaluated using three errors, i.e., Visible Surface Discrepancy (VSD), Maximum Symmetry-aware Surface Distance (MSSD), and Maximum Symmetry-aware Projection Distance (MSPD). For each of the pose errors, an average recall is computed, i.e., " + }, + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "type": "inline_equation", + "content": "\\mathrm{AR}_{\\mathrm{VSD}}" + }, + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "type": "inline_equation", + "content": "\\mathrm{AR}_{\\mathrm{MSSD}}" + }, + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "type": "inline_equation", + "content": "\\mathrm{AR}_{\\mathrm{MSPD}}" + }, + { + "bbox": [ + 46, + 261, + 286, + 368 + ], + "type": "text", + "content": ", based on a set of error thresholds. The AR refers to the average of the three recalls." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 376, + 180, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 180, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 180, + 388 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 393, + 286, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 286, + 476 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 286, + 476 + ], + "type": "text", + "content": "We use a KPCov-FPN [56] backbone for feature extraction. Adam optimizer [26] is employed to optimize the network with the learning rate of " + }, + { + "bbox": [ + 46, + 393, + 286, + 476 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-5}" + }, + { + "bbox": [ + 46, + 393, + 286, + 476 + ], + "type": "text", + "content": ". The weight decay is set to " + }, + { + "bbox": [ + 46, + 393, + 286, + 476 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-6}" + }, + { + "bbox": [ + 46, + 393, + 286, + 476 + ], + "type": "text", + "content": ". GCPose is trained for 80 epochs with a batch size of 16 and the learning rate is decayed by 0.95 every 5 epochs. The network is trained on NVIDIA Tesla V100 GPUs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 477, + 286, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 286, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 286, + 574 + ], + "type": "text", + "content": "Following the practice in OVE6D [5], our GCPose is trained using the synthetic 3D objects from ShapeNet [6]. During the test, we first obtain the class labels and segmentation masks of objects by the MaskRCNN [14]. Taking a depth image with mask and object model as input, GCPose is applied to estimate the 6D pose for the object. In addition, the performance using ground truth class labels and segmentation masks is also reported in this paper." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 580, + 286, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 580, + 286, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 580, + 286, + 593 + ], + "type": "text", + "content": "4.3. Comparison with the State-of-the-Art Methods" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 599, + 147, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 147, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 147, + 609 + ], + "type": "text", + "content": "4.3.1 T-LESS Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "We firstly report pose estimation results on T-LESS dataset in Table 2 in terms of the AR metric. To facilitate comparison to previous works, we re-evaluate the pose estimation results of OVE6D [5] in AR metric using the official trained model. Our method achieves state-of-the-art performance under an open-set pose estimation setting. GCPose outperforms the recent learning-based OVE6D [5] by " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "15.6\\%" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " without ICP refinement [67] and is also " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "13.3\\%" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": " higher than" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 544, + 210 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 544, + 210 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 544, + 210 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 544, + 210 + ], + "type": "table", + "html": "
MethodARVSDARMSSDARMSPDAR
DrostPPF† [12]0.3750.4780.4800.444
VidalPPF† [57]0.4640.5750.5740.538
HybridPPF† [28]0.5800.6890.6960.655
MegaPose [30]---0.543
OVE6D [5]0.5210.5110.5380.523
OVE6D† [5]0.5130.5610.5650.546
GCPose (Ours)0.6430.6910.7020.679
OVE6D* [5]0.6240.5920.6260.614
OVE6D*† [5]0.6010.6370.6370.625
GCPose* (Ours)0.7140.7390.7620.738
", + "image_path": "4f0cb0cdd250c60fab50f0941db9168063c598d498f6282b7c66f77b42bcf576.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 308, + 261, + 544, + 388 + ], + "blocks": [ + { + "bbox": [ + 305, + 213, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 305, + 213, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 545, + 250 + ], + "type": "text", + "content": "Table 2: Comparisons on T-LESS dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 261, + 544, + 388 + ], + "lines": [ + { + "bbox": [ + 308, + 261, + 544, + 388 + ], + "spans": [ + { + "bbox": [ + 308, + 261, + 544, + 388 + ], + "type": "table", + "html": "
MethodARvSDARMSSDARMSPDAR
DrostPFP† [12]0.6780.7860.7890.751
OVE6D [5]0.5600.7510.7620.701
OVE6D† [5]0.7360.8820.8860.835
GCPose (Ours)0.7490.8850.8870.841
MatchNorm* [9]0.3190.4900.5290.446
MatchNorm*† [9]0.6160.6800.7370.678
OVE6D* [5]0.7940.8860.9020.860
OVE6D*† [5]0.8060.9520.9560.905
GCPose* (Ours)0.8690.9650.9740.936
", + "image_path": "689abf79b3c6826bffac702e38ad3b2026287546809415a46b196417561f572b.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 392, + 545, + 429 + ], + "lines": [ + { + "bbox": [ + 305, + 392, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 305, + 392, + 545, + 429 + ], + "type": "text", + "content": "Table 3: Comparisons on LINEMOD dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 450, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 535 + ], + "type": "text", + "content": "its ICP refinement counterpart. And GCPose also outperforms traditional HybridPPF [28] with ICP refinement by " + }, + { + "bbox": [ + 304, + 450, + 545, + 535 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 304, + 450, + 545, + 535 + ], + "type": "text", + "content": ". These results indicate that GCPose performs well on symmetric and texture-less objects. Moreover, given the ground truth masks, GCPose achieves " + }, + { + "bbox": [ + 304, + 450, + 545, + 535 + ], + "type": "inline_equation", + "content": "73.8\\%" + }, + { + "bbox": [ + 304, + 450, + 545, + 535 + ], + "type": "text", + "content": " AR, which reveals great potential for performance improvement with better segmentation masks." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 550, + 535, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 550, + 535, + 562 + ], + "spans": [ + { + "bbox": [ + 305, + 550, + 535, + 562 + ], + "type": "text", + "content": "4.3.2 LINEMOD and Occluded-LINEMOD Results" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "We report pose estimation results on LINEMOD and Occluded-LINEMOD, as shown in Table 3, 4. GCPose still achieves state-of-the-art performance under an open-set pose estimation setting. Specifically, GCPose surpasses OVE6D [5] by " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "14.0\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " on LINEMOD dataset and " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "15.6\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " on Occluded-LINEMOD dataset, respectively. GCPose outperforms the recent MatchNorm [9] by a large margin of " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "49.0\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " on LINEMOD dataset and " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "37.6\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " on Occluded-LINEMOD dataset, respectively. Moreover, our method is superior to OVE6D and MatchNorm, which both use ICP refinement. In contrast to previous works using handcrafted geometry features, GCPose also outperforms DrostPPF" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14050" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 286, + 229 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 286, + 229 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 286, + 229 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 286, + 229 + ], + "type": "table", + "html": "
MethodARVSDARMSSDARMSPDAR
DrostPPF† [12]0.4370.5630.5810.527
VidalPPF† [57]0.4730.6250.6470.582
HybridPPF† [28]0.5170.6750.7030.631
MegaPose [30]---0.583
OVE6D [5]0.3730.5400.5750.496
OVE6D† [5]0.5260.6580.6970.627
GCPose (Ours)0.5430.6910.7210.652
MatchNorm* [9]0.2630.3840.4500.365
MatchNorm*† [9]0.4780.5420.6120.544
OVE6D* [5]0.5390.6400.7030.627
OVE6D*† [5]0.6330.7550.7980.728
GCPose* (Ours)0.6560.7680.7990.741
", + "image_path": "49f5767b96030330f37f849d023002ffa7f98f6d2e3ad56940e618ca6067c8c7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 282, + 285, + 397 + ], + "blocks": [ + { + "bbox": [ + 47, + 233, + 286, + 270 + ], + "lines": [ + { + "bbox": [ + 47, + 233, + 286, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 233, + 286, + 270 + ], + "type": "text", + "content": "Table 4: Comparisons on Occluded-LINEMOD dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 282, + 285, + 397 + ], + "lines": [ + { + "bbox": [ + 49, + 282, + 285, + 397 + ], + "spans": [ + { + "bbox": [ + 49, + 282, + 285, + 397 + ], + "type": "table", + "html": "
MethodARvSDARMSSDARMSPDAR
DrostPPF† [12]0.7410.7930.7910.775
VidalPPF† [57]0.8110.9100.9070.876
HybridPPF† [28]0.8720.9450.9440.920
MegaPose [30]---0.712
GCPose (Ours)0.8710.9600.9470.926
MatchNorm* [9]0.7000.8530.8520.801
MatchNorm*† [9]0.8590.9140.9350.903
GCPose* (Ours)0.8880.9790.9800.949
", + "image_path": "fac35859c81733000792eee074a9fa08a6cf4b12536e9aef8ec80486179b2958.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 460, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 509 + ], + "type": "text", + "content": "[12] and HybridPPF [28] on LINDEMOD and OccludedLINEMOD datasets. These results further demonstrate that GCPose has a strong generalization ability to unseen objects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 525, + 145, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 145, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 145, + 536 + ], + "type": "text", + "content": "4.3.3 TUD-L Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": "The pose estimation results on TUD-L dataset are summarized in Table 5. GCPose outperforms the recent MatchNorm [9] by " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "14.8\\%" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": " without ICP refinement and is also " + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "inline_equation", + "content": "4.6\\%" + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": " higher than its ICP refinement counterpart. Besides, GC-Pose is also superior to traditional HybridPPF [28] with ICP refinement, which further indicates the superiority of our learning-based geometry features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 646, + 185, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 185, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 185, + 658 + ], + "type": "text", + "content": "4.3.4 Scaling of Training Data" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "To investigate the potential of GCPose with more CAD models for training, we scale up the training set to both ShapeNet [6] and ABC [27]. ABC dataset consists of one million CAD models and each model is a collection of ex" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 545, + 281 + ], + "blocks": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "content": "Table 5: Comparisons on TUD-L dataset. †: the results are further refined by the ICP algorithm. *: using the ground truth label and mask of the object." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 70, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 281 + ], + "type": "table", + "html": "
DatasetMethodw/ ABCARvSDARMSSDARMSPDAR
T-LESS [20]GCPose✓0.6430.6910.7020.679
0.6810.7350.7570.724
GCPose*✓0.7140.7390.7620.738
0.7600.8010.8280.796
LM [18]GCPose✓0.7490.8850.8870.841
0.7630.9070.9080.859
GCPose*✓0.8690.9650.9740.936
0.8700.9710.9780.940
O-LM [4]GCPose✓0.5430.6910.7210.652
0.5570.7310.7640.684
GCPose*✓0.6560.7680.7990.741
0.6570.7930.8270.760
TUD-L [21]GCPose✓0.8710.9600.9470.926
0.8750.9780.9740.942
GCPose*✓0.8880.9790.9800.949
0.9040.9810.9850.957
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The pose estimation results are reported in Table 6. GCPose achieves consistent performance improvement on four datasets after being trained with more CAD models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 441, + 394, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 394, + 452 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 394, + 452 + ], + "type": "text", + "content": "4.3.5 Visualization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 460, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 628 + ], + "type": "text", + "content": "To visualize the learned symmetry-aware geometry features, we reduce the dimension of point-wise features extracted by our backbone network using the t-SNE algorithm. Then the object-model point cloud is colorized according to the low-dimension features. As shown in Figure 5, the geometry feature embeddings among different parts of an object surface are distinguishable clearly and show meaningful similarity among the local structure of symmetry. It demonstrates that our method can predict reasonable geometry representations for unseen objects, which are employed to solve the 6D poses in this paper. We also give some qualitative results of GCPose on T-LESS and LINEMOD datasets, as shown in Figure 4. Compared to OVE6D [5], our method can generate more precise poses." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 635, + 399, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 399, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 399, + 647 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 654, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 689 + ], + "type": "text", + "content": "We conduct several ablation experiments on the T-LESS dataset. To eliminate the effect of inaccurate segmentation, we use ground truth labels and masks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "Data Augmentation and Normalization. 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Data AugNormGA FeatSA LossAR
0.635
✓0.669 (+3.4%)
✓✓0.698 (+6.3%)
✓✓✓0.708 (+7.3%)
✓✓✓✓0.738 (+10.3%)
", + "image_path": "7037a4acaee18faa0e07ddf1ae25262fe6ade598f1d4eb25408e822feb52d43e.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "table_body" + } + ], + "index": 35 + }, + { + "bbox": [ + 46, + 413, + 287, + 460 + ], + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 460 + ], + "type": "text", + "content": "Table 7: Ablation experiments: the impact of the proposed special data augmentation (Data Aug), normalization (Norm), global-aware fine-level features (GA Feat), and symmetry-aware matching loss (SA Loss)." + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "content": "So special data augmentation strategies are necessary to improve the generalization to real-world scenes. Besides, we standardize the scale of the input point clouds to facilitate the learning of geometry features. As shown in Table 7, special data augmentation and normalization bring " + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "inline_equation", + "content": "3.4\\%" + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "inline_equation", + "content": "2.9\\%" + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "content": " AR improvement, respectively." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 46, + 557, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 628 + ], + "type": "text", + "content": "Global-Aware Fine-level Features. As described in Section 3.3, we enhance fine-level point features with global structural cues to make features more discriminative for establishing correspondence. As shown in Table 7, the performance of GCPose is improved from " + }, + { + "bbox": [ + 46, + 557, + 287, + 628 + ], + "type": "inline_equation", + "content": "69.8\\%" + }, + { + "bbox": [ + 46, + 557, + 287, + 628 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 557, + 287, + 628 + ], + "type": "inline_equation", + "content": "70.8\\%" + }, + { + "bbox": [ + 46, + 557, + 287, + 628 + ], + "type": "text", + "content": " using global-aware fine-level features." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Symmetry-Aware Matching Loss. To eliminate the ambiguity of the learning of geometry features, as described in Section 3.4, we design a symmetry-aware matching loss to supervise the many-to-many correspondences. The geometry features output by GCPose are meaningful and the features of symmetric structures are visually similar (Figure 5). 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The geometry features are distinguishable among different parts within an object and show meaningful similarity among the local structure of symmetry." + } + ] + } + ], + "index": 48, + "angle": 0, + "type": "image_caption" + } + ], + "index": 44 + }, + { + "type": "image", + "bbox": [ + 357, + 387, + 394, + 437 + ], + "blocks": [ + { + "bbox": [ + 357, + 387, + 394, + 437 + ], + "lines": [ + { + "bbox": [ + 357, + 387, + 394, + 437 + ], + "spans": [ + { + "bbox": [ + 357, + 387, + 394, + 437 + ], + "type": "image", + "image_path": "289cdbb551442b6b868bd7d6b9915265d8cae47b9ac5e2eadc83b0d1ba50d6ba.jpg" + } + ] + } + ], + "index": 45, + "angle": 0, + "type": "image_body" + } + ], + "index": 45 + }, + { + "type": "image", + "bbox": [ + 402, + 390, + 459, + 434 + ], + "blocks": [ + { + "bbox": [ + 402, + 390, + 459, + 434 + ], + "lines": [ + { + "bbox": [ + 402, + 390, + 459, + 434 + ], + "spans": [ + { + "bbox": [ + 402, + 390, + 459, + 434 + ], + "type": "image", + "image_path": "a8ae1ebb74409c9a26f70a20611e7a24b9cd4af093e879e09498172c239dd0f7.jpg" + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "image_body" + } + ], + "index": 46 + }, + { + "type": "image", + "bbox": [ + 468, + 394, + 537, + 430 + ], + "blocks": [ + { + "bbox": [ + 468, + 394, + 537, + 430 + ], + "lines": [ + { + "bbox": [ + 468, + 394, + 537, + 430 + ], + "spans": [ + { + "bbox": [ + 468, + 394, + 537, + 430 + ], + "type": "image", + "image_path": "241326085279413fbf1559363a7366dae737818f1cdcafa18f8381282441c12b.jpg" + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "image_body" + } + ], + "index": 47 + }, + { + "bbox": [ + 306, + 524, + 440, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 524, + 440, + 536 + ], + "spans": [ + { + "bbox": [ + 306, + 524, + 440, + 536 + ], + "type": "text", + "content": "provides " + }, + { + "bbox": [ + 306, + 524, + 440, + 536 + ], + "type": "inline_equation", + "content": "3.0\\%" + }, + { + "bbox": [ + 306, + 524, + 440, + 536 + ], + "type": "text", + "content": " AR improvement." + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "text", + "content": "In this paper, we propose a pose estimation framework based on object-agnostic geometry features, which can generalize to arbitrary unseen objects without re-training. Compared with previous methods, GCPose achieves state-of-the-art performance on four benchmarks. We hope that our simple yet effective framework could serve as a strong baseline for unseen object 6D pose estimation and motivate researchers to explore more in this direction." + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments. This work is supported by National Key R&D Program of China under Grant No. 2023YFE0204200 and the Fundamental Research Funds for the Central Universities under Grant No. 226-2022-00051." + } + ] + } + ], + "index": 52 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14052" + } + ] + } + ], + "index": 53 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Xuyang Bai, Zixin Luo, Lei Zhou, Hongbo Fu, Long Quan, and Chiew-Lan Tai. 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IJCV, 1994. 6" + } + ] + } + ], + "index": 33 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "14054" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_content_list.json b/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6bde09910da0dadf395f8914a9f1d90f76335dd6 --- /dev/null +++ b/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_content_list.json @@ -0,0 +1,1889 @@ +[ + { + "type": "text", + "text": "Learning Trajectory-Word Alignments for Video-Language Tasks", + "text_level": 1, + "bbox": [ + 152, + 161, + 816, + 182 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xu Yang $^{1}$ Zhangzikang Li $^{1,2}$ Haiyang Xu $^{2*}$ Hanwang Zhang $^{3}$ Qinghao Ye $^{2}$ Chenliang Li $^{2}$ Ming Yan $^{2}$ Yu Zhang $^{1*}$ Fei Huang $^{2}$ Songfang Huang $^{2}$", + "bbox": [ + 152, + 206, + 816, + 242 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Computer Science & Engineering, Key Lab of New Generation Artificial Intelligence Technology & Its Interdisciplinary Applications (Ministry of Education), Southeast University", + "bbox": [ + 126, + 244, + 843, + 276 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ DAMO Academy, Alibaba Group $^{3}$ School of Computer Science & Engineering, Nanyang Technological University $\\{\\text{xuyang.palm, zhang.yu}\\} @$ seu.edu.cn, lizhangzikang@gmail.com, $\\{\\text{shuofeng.xhy, yeqinghao.yqh, lcl193798, ym119608, f.huang, songfang.hsf}\\} @$ alibaba-inc.com, hanwangzhang@ntu.edu.sg", + "bbox": [ + 90, + 277, + 875, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 356, + 312, + 370 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In a video, an object usually appears as the trajectory, i.e., it spans over a few spatial but longer temporal patches, that contains abundant spatiotemporal contexts. However, modern Video-Language BERTs (VDL-BERTs) neglect this trajectory characteristic that they usually follow image-language BERTs (IL-BERTs) to deploy the patch-to-word (P2W) attention that may over-exploit trivial spatial contexts and neglect significant temporal contexts. To amend this, we propose a novel TW-BERT to learn Trajectory-Word alignment by a newly designed trajectory-to-word (T2W) attention for solving video-language tasks. Moreover, previous VDL-BERTs usually uniformly sample a few frames into the model while different trajectories have diverse graininess, i.e., some trajectories span longer frames and some span shorter, and using a few frames will lose certain useful temporal contexts. However, simply sampling more frames will also make pre-training infeasible due to the largely increased training burdens. To alleviate the problem, during the fine-tuning stage, we insert a novel Hierarchical Frame-Selector (HFS) module into the video encoder. HFS gradually selects the suitable frames conditioned on the text context for the later cross-modal encoder to learn better trajectory-word alignments. By the proposed T2W attention and HFS, our TW-BERT achieves SOTA performances on text-to-video retrieval tasks, and comparable performances on video question-answering tasks with some VDL-BERTs trained on much more data. The code will be available in the supplementary material.", + "bbox": [ + 75, + 385, + 473, + 774 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 796, + 208, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "By witnessing the boom of BERT-like models in single domains, e.g., vision or language[52, 44, 21], researchers", + "bbox": [ + 75, + 819, + 468, + 847 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fa31efdfc99df2e7cad260027e5917e353d6a68c3ee30cb26f6c155a59d004a6.jpg", + "image_caption": [ + "(a) RoI based IL-BERT" + ], + "image_footnote": [], + "bbox": [ + 507, + 358, + 611, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1cd54c442b2f25a3dc41004b99f27b470e1ccfdba412a0cd97d557d251e79fc9.jpg", + "image_caption": [ + "(b) Patch based IL-BERT" + ], + "image_footnote": [], + "bbox": [ + 616, + 362, + 717, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b17a02425cbb3103d51c78e5ffbb5a8166bbbc6c3cad9072616e342b9d19f880.jpg", + "image_caption": [ + "(c) Patch based VDL-BERT" + ], + "image_footnote": [], + "bbox": [ + 727, + 358, + 884, + 429 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cc26e38a9e129cb6d503c1a65683b3cef7b2c2d7fad8959f15794d4a848605ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 507, + 448, + 605, + 516 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/66d7dc9f3f0bf24dd78463c75b609f3bd40439b72ffec187f60fbcf86d90a5ee.jpg", + "image_caption": [ + "(d) TW-BERT Pretraining" + ], + "image_footnote": [], + "bbox": [ + 606, + 448, + 717, + 516 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d70f7835cb0563a554a50a4dc6a98c5e02d30cdec9e855fbc466a4c4263de0ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 448, + 882, + 516 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a590a57ecb7863d30a214386ea98688fcb1d3a28f03bfd4c2a7ffc596f303c6a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 507, + 532, + 605, + 600 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/661c3d1393f1e05f3b81a318f6e587f8240dd14d7b0e96ba4a93cf114e10b154.jpg", + "image_caption": [ + "(e) TW-BERT Fine-Tuning" + ], + "image_footnote": [], + "bbox": [ + 606, + 532, + 717, + 600 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8a118835a4ff3e8a2e56c07d14f72bc936e3b5690ac319f348b40bbfdfb26280.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 717, + 532, + 882, + 600 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A boy is playing basketball.", + "text_level": 1, + "bbox": [ + 608, + 619, + 789, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Figure 1. The comparisons of five different ways to build object-word alignments. In (b), by patch-to-word (P2W) attention, implicit object-word alignment can be built, e.g., the \"ball region\" is aligned with basketball. While in (c), P2W attention may concentrate the attention of an object on only one frame, e.g., basketball only attends over the \"ball region\" of the first frame. (d) When pre-training TW-BERT, the trajectory of an object is constructed, e.g., the \"ball trajectory\" through 4 frames built. Note that we only use 4 frames during pre-training, we show 8 frames for comparing with (e) and the transparent ones denote that they are not input into the model. (e) When fine-tuning TW-BERT, we use HFS to select 4 frames from 8 and we can see that the selected frames are different from the uniformly sampled ones in (d).", + "bbox": [ + 497, + 637, + 890, + 802 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "begin to build vision-language BERTs[3, 61, 10] for learning robust cross-modal associations. Compared with the images, videos provide more details for building robust associations, e.g., the spatiotemporal contexts in videos can", + "bbox": [ + 497, + 809, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 84 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 253, + 48, + 789, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors.", + "bbox": [ + 95, + 853, + 226, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2504", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "better describe the actions. However, directly addressing dynamic videos may cost more storage and computation resources. To circumvent such huge cost, researchers first study image-language BERT (IL-BERT)[17, 25, 8, 27, 61] and then exploit the research fruits to build the challenging, while more pragmatic, video-language BERT (VDLBERT)[47, 2, 26, 36, 13, 35, 46, 37, 54, 51].", + "bbox": [ + 75, + 125, + 468, + 223 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pioneering techniques are directly inherited from IL-BERT into VDL-BERT, e.g., the image encoders are used to embed sampled video frames [23, 62]. However, since image encoders can hardly learn temporal contexts, the resultant VDL-BERTs will degrade to IL-BERT even if they are trained by video-text pairs. To ameliorate it, researchers apply the video encoders [32, 4, 12, 24] to embed spatiotemporal contexts. Though promising improvements are observed, these VDL-BERTs still neglect or ill-consider a significant factor in IL-BERT: the object-word alignment, which helps learn robust associations.", + "bbox": [ + 75, + 224, + 470, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To learn object-word alignments, as Figure 1(a) shows, researchers use an RoI-based extractor to embed an image into a series of RoI features [34, 27, 8]. However, this RoI-based extractor is offline trained by object detection with limited label inventory, which will weaken the IL-BERT since the extractor will not be updated during large-scale pre-training. To enable the end-to-end training, researchers substitute the RoI-based extractor with visual transformers whose outputs are a series of grid embeddings, which will be used to build the cross-modal connections. Although a single grid usually does not construct an integral object, fortunately, the widely applied patch-to-word (P2W) attention of IL-BERT can softly seek the salient visual regions for a given query word. Then the object-word alignments can still be built between this softly detected object and the word, e.g., as shown in Figure 1(b), the object \"basketball\" can be implicitly attended by the corresponding word query.", + "bbox": [ + 75, + 378, + 468, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although the P2W attention remedies the loss of RoI-level features for learning object-word alignments in ILBERT, its effectiveness is weakened in the video case. This is because the objects usually act as the Trajectories which span a few spatial while multiple temporal grids in the videos. Thus, directly applying the P2W attention may over-exploit the trivial spatial contexts while neglecting the significant temporal contexts and then make the model attend to only one or two frames. Figure 1(c) shows this limitation that P2W attention only aligns the \"ball\" in the first frame to the word ball.", + "bbox": [ + 75, + 615, + 468, + 767 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this limitation, we propose to learn Trajectory-to-Word alignments to solve video-language tasks and name this model as TW-BERT. Specifically, such alignment is learnt by a novel designed trajectory-to-word T2W attention, which first uses the word as the query to seek the salient parts of each frame and the sought parts are sequenced to form the trajectory. Then the query word at", + "bbox": [ + 75, + 769, + 468, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tends over the trajectories again for capturing cross-modal associations. In this way, the trivial spatial regions are weakened and the temporal contexts will be strengthened, e.g., as shown in Figure 1(d), the attention weights of the word will be concentrated on the object trajectory instead of only one frame as in (c). In the implementation, we follow most VDL-BERTs to set up the network: two single-modal encoders for the video and text and one cross-modal encoder, which is sketched in Figure 2. For the cross-modal encoder, since our T2W attention does not have the same structure as the word-to-patch (W2P) attention, our cross-modal encoder is asymmetric.", + "bbox": [ + 497, + 125, + 890, + 290 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Moreover, previous VDL-BERTs usually uniformly sample a few frames into the model, which contains two drawbacks. Firstly, using a few frames may lose temporal context and secondly, uniform sampling can hardly capture the varying graininess of the trajectories, i.e., some trajectories span longer frames and some span shorter. However, simply sampling more frames will largely increase the pretraining burdens that are beyond the computation resources we own. To alleviate this problem, in the fine-tuning stage, we sample more frames into the video encoder while only keeping the most relevant frames according to the corresponding text by a novel designed Hierarchical Frame-Selector (HFS). For example, as shown in Figure 1(e), 4 frames are selected by HFS from the 8 uniformly sampled ones for learning trajectory-word alignment. Specifically, HFS inserts a few lightweight layers into the video encoder and these layers can gradually filter frames conditioned on the language context. In this way, HFS learns the coarse-grained trajectory-word alignments, i.e., framework alignments, to help the later T2W attention learn more fine-grained trajectory-word alignments.", + "bbox": [ + 497, + 290, + 892, + 581 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To sum up, our contributions are:", + "bbox": [ + 519, + 581, + 739, + 596 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel perspective to consider the videos that are composed of moving object trajectories, which may inspire the researchers to build more advanced VDL-BERTs.", + "- We propose a simple while effective T2W attention to learn Trajectory-to-Word alignments.", + "- We propose a novel hierarchical frame selector (HFS) in TW-BERT during fine-tuning to capture the varying graininess of the trajectory while not largely increasing the training burdens.", + "- We achieve SOTA performances compared with other VDL-BERTs trained by the same amount of data." + ], + "bbox": [ + 519, + 600, + 890, + 766 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 780, + 640, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image-Language BERT (IL-BERT)", + "text_level": 1, + "bbox": [ + 499, + 802, + 806, + 818 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, various techniques have been proposed in ILBERT to learn vision-language connections. Most of them aim at capturing robust object-word alignments since such", + "bbox": [ + 499, + 824, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2505", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "alignments construct the foundations of visual reasoning. In the beginning, a pre-trained Faster-RCNN [41] is used to extract a series of RoI poolings, where each one contains one or a few salient objects, to facilitate building object-word alignments [34, 48, 8, 27]. However, this Faster-RCNN is usually pre-trained by the object annotations from COCO [7] and VG [20], whose concept space is much narrower than the data used to train IL-BERT, which can be almost unlimedly collected from the websites. Moreover, this Faster-RCNN is not updated during the end-to-end training of the IL-BERT, which means that the visual encoder may hardly learn novel knowledge from the web-collected data. Thus the performances of these IL-BERTs are limited.", + "bbox": [ + 75, + 125, + 472, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To further release the potential of hugely web-collected data, the offline Faster RCNN is switched into vision Transformers [11, 32] and thus a homogeneous IL-BERT, i.e., all the components are transformer-based, is built, which is more easily trained end-to-end [34]. Compared with the RoI-based encoder, the vision Transformer outputs a series of patch embeddings and thus may lose object-level knowledge. To remedy such loss, various strategies are proposed to improve the vision-language alignments. For example, the align-before-fuse strategy [25] aligns the paired image-text embeddings before cross-modal fusion for facilitating the subsequent fusion. And the fine-grained contrastive objective [58] amplifies the local details for learning the object-word alignments.", + "bbox": [ + 75, + 320, + 472, + 514 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Video-Language BERT (VDL-BERT)", + "text_level": 1, + "bbox": [ + 77, + 524, + 401, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the spatiotemporal contexts in videos can hardly be learnt by image extractors, only inheriting the techniques which are successful in IL-BERT to VDL-BERT is not enough. Thus, based on the fruits of IL-BERT, most VDL-BERTs aim at exploiting more spatiotemporal contexts to build cross-modal associations. One straightforward way is to learn such spatiotemporal contexts through video Transformers [4, 28]. Besides this, some more advanced techniques are proposed, e.g., VIOLET [12] tokenizes the dynamic video patches and predicts the labels of these tokens; BridgeFormer [14] erases the words (nouns or verbs) from the text and learn to match the visual embeddings queried by the erased words and the remained texts; or ALPRO [24] computes the similarities between the video embeddings with the generated entity prompts. TS2-Net [31] shifts token features and selects informative tokens in both temporal and spatial dimensions to produce the fine-grained spatial-temporal video representation. Although substantial improvements are observed, these methods use video patches in the cross-modal encoder, which neglects that an object usually acts as the trajectory in the videos, and thus they may over-exploit the trivial spatial contexts. To ameliorate this limitation, we propose TW-BERT to capture", + "bbox": [ + 75, + 548, + 472, + 866 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b5cbebcf78e78d96186340d5f804092d711148f2c73ec9fad719d656e61856ee.jpg", + "image_caption": [ + "Figure 2. The architecture of TW-BET, which contains two single-modal encoders and one asymmetric cross-modal encoder. Totally three losses in the grey blocks are used to train the whole model: $L_{vtc}$ , $L_{mlm}$ , and $L_{vtm}$ . Note that HFS is only used in the fine-tuning stage." + ], + "image_footnote": [], + "bbox": [ + 497, + 122, + 895, + 283 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "trajectory-word alignments for more robust vision-language alignment.", + "bbox": [ + 497, + 355, + 892, + 384 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. TW-BERT", + "text_level": 1, + "bbox": [ + 499, + 396, + 616, + 410 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 sketches TW-BERT, which has two single-modal encoders for embedding the video and text (cf. Sec. 3.1) and one cross-modal encoder for learning videolanguage associations (cf. Sec. 3.2). Different from the previous VDL-BERTs, our cross-modal encoder is an asymmetric one that contains a classic word-to-patch (W2P) attention and a novel proposed trajectory-to-word (T2W) attention (cf. Sec. 3.2) for learning trajectory-word alignments. In Sec. 3.3, we introduce how to use Hierarchical Frame-Selector (HFS) in the fine-tuning stage to gradually filter the frames for capturing coarse-grained frame-word alignments. Lastly, we introduce the losses used to train our TW-BERT in Sec. 3.4.", + "bbox": [ + 497, + 419, + 894, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Single-Modal Encoders", + "text_level": 1, + "bbox": [ + 499, + 609, + 717, + 624 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video Encoder. For a video, we sample a few $224 \\times 224$ frames and input them into the 12-layer TimeSformer [4, 24] for embedding. TimeSformer first partitions each frame into $14 \\times 14$ non-overlapping patches, which are flattened and fed to a linear projection layer to produce a sequence of patch tokens. Then TimeSformer applies self-attention along the temporal and spatial dimensions to calculate per-frame features. These features are further mean-pooled along the height and width dimensions. Learnable spatial positional embeddings are added to each video token in the same spatial location of different frames. The final output embedding set is $\\mathbf{V} = \\{\\mathbf{v}_{cls}, \\mathbf{v}_1, \\dots, \\mathbf{v}_{N_V - 1}\\}$ , where $\\mathbf{v}_n \\in \\mathbb{R}^d$ and $\\mathbf{v}_{cls}$ is the global [CLS] embedding.", + "bbox": [ + 497, + 631, + 892, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text Encoder. For a text, we use a 6-layer transformer to embed it and the output is $\\mathbf{X} = \\{\\pmb{x}_{cls},\\pmb{x}_1,\\dots,\\pmb{x}_{N_X - 1}\\}$ where $\\pmb{x}_n\\in \\mathbb{R}^d$ and $\\pmb{x}_{cls}$ is the global [CLS] embedding. Similar to the video encoder, we also add positional embed", + "bbox": [ + 497, + 811, + 892, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2506", + "bbox": [ + 468, + 889, + 502, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dings to the text tokens.", + "bbox": [ + 77, + 125, + 235, + 138 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Asymmetric Cross-Modal Encoder", + "text_level": 1, + "bbox": [ + 77, + 150, + 379, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After embedding videos and texts, a cross-modal encoder is used to fuse them by calculating bi-directional associations: vision-to-language and language-to-vision. No matter what the direction is, the motivation is to assign semantic knowledge from one domain to another. Since a single word contains integral semantic knowledge, we follow previous VDL-BERT [24, 2, 23, 47] to set a traditional word-to-patch (W2P) attention to assign the words to a patch. However, different from the word, only the object instead of one grid conveys integral semantic knowledge. In videos, an object usually spans both spatial and temporal axes and thus the previously used patch-to-word (P2W) attention may fail to transfer the semantic knowledge. To amend this, we design a novel Trajectory-to-Word (T2W) attention for transferring semantic knowledge from videos to texts. Since W2P and T2W attentions have diverse structures, our cross-encoder is asymmetric.", + "bbox": [ + 75, + 174, + 468, + 408 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, both W2P and T2W attentions are built on the Multi-Head Attention (MHA) operation, here we first formalize MHA and then introduce how to use it to build W2P and T2W attentions. Formally, MHA is*:", + "bbox": [ + 75, + 409, + 468, + 464 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{c} \\text {I n p u t :} \\quad \\mathcal {Q}, \\mathcal {K}, \\mathcal {V} \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 477, + 268, + 491 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A t t}: \\quad \\mathcal {A} _ {i} = \\operatorname {S o f t m a x} (\\frac {\\mathcal {Q W} _ {i} ^ {Q} \\left(\\mathcal {K W} _ {i} ^ {K}\\right) ^ {T}}{\\sqrt {d}})\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 492, + 421, + 522 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H e a d}: \\quad \\mathcal {H} _ {i} = \\mathcal {A} _ {i} \\mathcal {V W} _ {i} ^ {V}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 522, + 468, + 539 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {M u l t i - H e a d}: \\quad \\mathcal {H} = \\left[ \\mathcal {H} _ {1}, \\mathcal {H} _ {2},..., \\mathcal {H} _ {h} \\right] \\mathcal {W} ^ {H},\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 542, + 384, + 557 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {O u t p u t}: \\mathcal {Z} = \\mathrm {L N} (\\mathcal {H} + \\mathcal {Q}),\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 560, + 331, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{W}_i^Q, \\mathcal{W}_i^K, \\mathcal{W}_i^V, \\mathcal{W}_i^H$ are all trainable matrices; $h$ is the head number and $d_h = d / h$ ; $\\mathcal{A}_i$ is the $i$ -th attention matrix corresponding to the $i$ -th head matrix; $[\\cdot]$ is the concatenation operation; and LN is the Layer Normalization.", + "bbox": [ + 75, + 587, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Word-to-Patch (W2P) Attention. To calculate the W2P alignment, we apply the conventional W2P attention [24]:", + "bbox": [ + 75, + 644, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} _ {W 2 P} = \\mathbf {M H A} (\\mathcal {Q} = \\mathbf {V}, \\mathcal {K} = \\mathcal {V} = \\mathbf {X}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 674, + 468, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{V} \\in \\mathbb{R}^{N_V \\times D}$ , $\\mathbf{X} \\in \\mathbb{R}^{N_X \\times D}$ are respectively video and word embedding sets got from two single-modal encoders. By setting the query $\\mathcal{Q}$ to the video patch embeddings, Eq. (2) learns to assign suitable words to each video patch and thus captures the W2P alignment.", + "bbox": [ + 75, + 688, + 468, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Trajectory-to-Word (T2W) Attention. As shown in Figure. 3 (b), we propose the T2W attention that uses two steps to learn the T2W alignment: it first constructs a trajectory for a given word and then uses the word as the query to attend over the trajectory for capturing the associations. For", + "bbox": [ + 75, + 761, + 468, + 830 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b57d3edb8a443743f6444b3a072a33e602ecc73b2ec55405ff7ddab19f1ca6af.jpg", + "image_caption": [ + "Figure 3. The comparisons between Patch-to-Word (P2W) and Trajectory-to-Word (T2W) attentions, where the green block denotes a query word and the blue blocks denote the video patches. In P2W attention, the word attends over all the video patches and may only concentrate on one frame, while in T2W attention, the salient red parts of each frame are found to construct a trajectory, which are connected by the red lines, $e.g., y_1, y_2, y_3$ ." + ], + "image_footnote": [], + "bbox": [ + 500, + 123, + 621, + 207 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/015138560146499c8ae8b166bf94e72b334e605009becc9ae30284f053d959e6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 123, + 768, + 207 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/616dafaae6cb8805152b670366c46a7e841eb366cf41300c761780949cb9565d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 124, + 890, + 207 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "convenience, we introduce how the T2W attention calculates the fusion embedding $z_{T2W}$ for a single word $x$ and it is straightforward to extend it to a sequence of the words.", + "bbox": [ + 497, + 308, + 890, + 350 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the first step, T2W attention uses $x$ as the query to find the salient parts for each frame and then sequence these parts to construct the trajectory. Assuming $V_{t}$ is the embedding set of the $t$ -th frame, the salient part $y_{t}$ is got as:", + "bbox": [ + 497, + 351, + 890, + 406 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {y} _ {t} = \\mathbf {M H A} (\\mathcal {Q} = \\boldsymbol {x}, \\mathcal {K} = \\mathcal {V} = \\boldsymbol {V} _ {t}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 407, + 890, + 423 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then the salient parts at different time frames construct a continuous flow $\\mathbf{Y} = \\{\\pmb{y}_1, \\dots, \\pmb{y}_T\\}$ , which is the trajectory of the given word.", + "bbox": [ + 497, + 425, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the second step, to get the trajectory-to-word fusion embedding $z_{T2W}$ , we treat $x$ as the query again while using the trajectory $Y$ as the key and value in MHA:", + "bbox": [ + 497, + 467, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {z} _ {T 2 W} = \\mathbf {M H A} (\\mathcal {Q} = \\boldsymbol {x}, \\mathcal {K} = \\mathcal {V} = \\boldsymbol {Y}). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 511, + 890, + 524 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By Eq. (3), T2W attention finds the salient parts for the given word at each frame, which enforces Eq. (4) to attend over the continuous frames instead of concentrating the attention only on one or some episodic frames as the previous P2W attentions. In this way, the whole T2W block exploits more temporal contexts to build vision-language associations, which facilitates the video reasoning tasks that usually require the correct recognition of the temporal patterns. Figure. 3 compares P2W and T2W attentions.", + "bbox": [ + 497, + 527, + 890, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Hierarchical Frame-Selector", + "text_level": 1, + "bbox": [ + 499, + 663, + 754, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During fine-tuning, to improve the performance, previous studies tend to sample more frames than pre-training for introducing more temporal information. However, on the one hand, using too many frames will dramatically increase the computational resources, which causes infeasible training. On the other hand, in a video, different trajectories have varying graininess, e.g., some trajectories may cover longer frames and some cover shorter. In this way, uniform sampling may introduce redundant temporal information for these longer trajectories and deficient information for the shorter ones. Interestingly, the time duration of the trajectory is also reflected in the corresponding text. In this way, we can use the text to choose suitable frames and then", + "bbox": [ + 497, + 687, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "*To avoid symbol confusions, we use the calligraphic font (\\mathcal{M}) to denote the built-in variables of the MHA module.", + "bbox": [ + 75, + 843, + 468, + 865 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2507", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8f235540be5a61c6dd1ad91e916d6695bde2a641002ad627ca1ab977f00605c9.jpg", + "image_caption": [ + "Figure 4. The architecture of the proposed Hierarchical Frame-Selector. At beginning, four frames are input into the video encoder and the first frame selector behind the 6-th layer filters out the 2-nd frame. At last, only the tokens of the 1-st and 4-th frames are preserved." + ], + "image_footnote": [], + "bbox": [ + 77, + 128, + 890, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "only input them into the cross-modal attention for learning trajectory-word alignments.", + "bbox": [ + 75, + 255, + 468, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motivated by this, we propose a novel Hierarchical Frame-Selector (HFS) that can gradually select the most relevant video frames to reduce the computational burdens while providing more temporal knowledge. Figure 4 illustrates the architecture of our proposed frame selector module. HFS contains a few frame selector layers which have the same structure with different parameters. For each frame selector layer, given a sequence of video frame [CLS] tokens $V_{cls} = \\{v_{cls}^{1}, v_{cls}^{2}, \\dots, v_{cls}^{T}\\} \\in \\mathbb{R}^{T \\times D}$ , we concatenate the text [CLS] embedding $x_{cls}$ with each $v_{cls}^{t}$ : $f_{t} = [v_{cls}^{t}, x_{cls}] \\in \\mathbb{R}^{2D} (1 \\leq t \\leq T)$ and feed them into a scorer network including a FC layer and a softmax layer:", + "bbox": [ + 75, + 283, + 468, + 448 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {s} = \\operatorname {S o f t m a x} (F C (\\boldsymbol {f})) \\in \\mathbb {R} ^ {T \\times 1}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 448, + 468, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $T$ denotes the number of frames input into the video encoder, and $s \\in \\mathbb{R}^T$ is the score vector of $T$ frames. Then for this frame selector, we keep the tokens of $k$ frames with the top- $k$ $s_t$ for the further embedding in the subsequent video Transformer layers. During training, we employ the perturbed maximum method [5] to construct a differentiable Top-K operator. In the video encoder, we totally insert 2 selector layers and insert them in the 6-th and 12-th layers as in Figure 4.", + "bbox": [ + 75, + 466, + 468, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Objectives", + "text_level": 1, + "bbox": [ + 75, + 600, + 265, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train TW-BERT, as the grey blocks shown in Figure 2, we totally use three losses which are masked language modeling (MLM), video-text matching (VTM), and video-text contrastive loss (VTC).", + "bbox": [ + 75, + 623, + 468, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Masked language Modeling (MLM) [26, 24, 12, 50]. MLM aims to predict the masked word tokens given both the video and the text contexts. To get it, we first randomly replace the input text tokens with the [MASK] token with a probability of $15\\%$ and then use the [MASK] embedding output from the cross-modal encoder to predict the masked word by calculating a cross-entropy loss:", + "bbox": [ + 75, + 679, + 468, + 775 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {M L M} = \\mathbb {E} _ {(V, \\hat {X}) \\sim D} \\mathrm {H} \\left(y ^ {m s k}, p ^ {m s k} (V, \\hat {X})\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 139, + 776, + 468, + 793 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{X}$ is the masked text, $\\mathrm{H}$ is the cross-entropy loss, $y^{msk} / p^{msk}$ are the ground-truth/predicted masked tokens.", + "bbox": [ + 75, + 795, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Video-text Matching (VTM) [24, 12, 50]. VTM calculates whether the given video and text are matched or not. To get it, for a given video-text pair, we first randomly replace the", + "bbox": [ + 75, + 824, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "text with the ones from a different video in the same batch. Then we concatenate the video and text [CLS] embeddings output from the cross-modal encoder and input the concatenated embedding into a binary classifier to judge whether the given video-text pair is matched or not:", + "bbox": [ + 497, + 255, + 890, + 323 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {V T M} = \\mathbb {E} _ {(V, X) \\sim D} \\mathrm {H} \\left(y ^ {v t m}, p ^ {v t m} (V, X)\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 564, + 324, + 890, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y^{vtm} / p^{vtm}(V,X)$ are the ground-truth/predicted values indexing whether $V$ and $X$ are matched or not.", + "bbox": [ + 497, + 340, + 890, + 368 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Video-text Contrastive (VTC) [24, 50, 49, 14, 15, 2, 29]. As detailed in Section 3, VTC contrasts the outputs of two single-modal encoders to pull close their embedding space to help the subsequent cross-modal encoder build more robust vision-language associations. Suppose $s_{ij}$ denotes the similarity score of the $i$ -th video and the $j$ -th text, for each video and text, we calculate the softmax-normalized video-to-text and video-to-image similarity as:", + "bbox": [ + 497, + 369, + 890, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {i j} ^ {v 2 t} (V) = \\frac {\\exp \\left(s _ {i j} / \\tau\\right)}{\\sum_ {j} \\exp \\left(s _ {i j} / \\tau\\right)}, p _ {i j} ^ {t 2 v} (X) = \\frac {\\exp \\left(s _ {i j} / \\tau\\right)}{\\sum_ {i} \\exp \\left(s _ {i j} / \\tau\\right)} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 512, + 486, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is a learnable temperature parameter. Let $y^{v2t}(V)$ and $y^{t2v}(X)$ denote the ground-truth one-hot similarity. This loss contains two symmetric parts, where the left term forces the $i$ -th text embedding to be close to the $i$ -th video embedding compared with the other texts and the right term has a similar effect:", + "bbox": [ + 497, + 524, + 890, + 606 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {V T C} =\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 608, + 571, + 619 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{2} \\mathbb {E} _ {(V, X) \\sim D} [ \\mathrm {H} (y ^ {v 2 t} (V), p ^ {v 2 t} (V)) + \\mathrm {H} (y ^ {t 2 v} (X), p ^ {t 2 v} (X)) ] \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 623, + 890, + 656 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the implementation, we follow [25] to use the momentum queue as a continuously-evolving teacher to provide more negative samples.", + "bbox": [ + 497, + 657, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 499, + 711, + 631, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Pre-training Dataset", + "text_level": 1, + "bbox": [ + 499, + 733, + 692, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following recent work [24, 14, 15, 49, 2], we pre-train TW-BERT on Google Conceptual Captions (CC3M) [45] containing 3.3M image-text pairs and WebVid-2M [2] containing 2.5M video-text pairs. For CC3M, the image is treated as a one-frame video data during pre-training. Note that due to the limited storage and computation resources, we do not use some much larger datasets like HowTo100M [38] containing 136M video-text pairs as [26,", + "bbox": [ + 497, + 755, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2508", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "55]. Also, we do not distill knowledge from CLIP [39], which is pre-trained on 400M image-text pairs, as [36].", + "bbox": [ + 75, + 125, + 467, + 153 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Downstream Tasks", + "text_level": 1, + "bbox": [ + 77, + 163, + 258, + 176 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Text-to-Video Retrieval. (i) MSRVTT contains 10K YouTube videos with 200K descriptions. We follow [56] to use 9K train+val videos for training and report results on the 1K test split. (ii) DiDeMo [16] contains 10K Flickr videos annotated with 40K sentences. (iii) LSMDC consists of 118,081 video clips sourced from 202 movies, where the validation set and the test set contain 7,408 and 1,000 videos. (iv) ActivityNet Caption contains 20K YouTube videos annotated with 100K sentences. The training set contains 10K videos, and we use val1 set with 4.9K videos to report results. For MSRVTT and LSMDC, we perform standard text-to-video retrieval. For DiDeMo and ActivityNet Caption, we concatenate all the text captions in the same video as a single query and evaluate paragraph-to-video retrieval. For two tasks, we measure the performances by average recall at $\\mathrm{K(R@K)}$ and Median Rank on zero-shot and fine-tune setups.", + "bbox": [ + 75, + 184, + 467, + 418 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Video Question Answering. (i) MSRVTT-QA [53] is built upon videos and captions from MSRVTT [56], which contains 10K videos with 243K open-ended questions and 1.5K answer candidates. (ii) MSVD [6] contains 50K question-answer pairs with 2423 answer candidates. We use standard train/val/test splits for the two tasks, and report accuracy.", + "bbox": [ + 75, + 419, + 467, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 77, + 511, + 294, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We initialize our video encoder by ViT-B/16 [42] and the text encoder by the first six BERT-Base layers [9]. For the cross-modal encoder, the self-attentionions in all 3 cross-modal attentions (W2P contains 1 and T2W contains 2) are initialized by the last 6 BERT-Base layers [9]. The model is trained end-to-end during both pre-training and fine-tuning.", + "bbox": [ + 75, + 534, + 467, + 616 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In pre-training, the feature dimension is set to 256 when calculating the contrastive losses and the temperature is set to 0.05. For the momentum queue, the momentum value is 0.995 and the size of the queue is 65,536. The above implementation details follow the recent work [25, 24] for a fair comparison. We pre-train the model on CC3M and WebVid-2M for 10 epochs on 8 NVIDIA A100 GPUs where the batch size is 128. We use AdamW [18] optimizer with a weight decay of 0.001 and betas (0.9, 0.98). The learning rate is first warmed-up to 1e-4 and then decays following a linear decay schedule.", + "bbox": [ + 75, + 617, + 467, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During fine-tuning text-to-video retrieval, We sample 20 frames and use HFS to preserve 8 frames to feed into the cross-modal encoder. The model is trained with both VTC and VTM losses, and we obtain similarity scores from the output of the VTM head during inference. For video question answering, we sample 32 frames per video and preserve 16 frames. Since MSRVTT-QA and MSVD-QA [53]", + "bbox": [ + 75, + 769, + 467, + 865 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "are open-ended VQA, in which the answers are in free-form natural language, it is common to convert the task to a classification task by predicting the answer's label. We input the concatenation of the video and question [CLS] tokens into a two-layer MLP [9] for calculating the cross-entropy loss. All the fine-tuning experiments are conducted on 8 NVIDIA V100 GPUs.", + "bbox": [ + 497, + 125, + 890, + 220 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 499, + 233, + 663, + 247 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct comprehensive ablation studies to evaluate the effectiveness of the proposed trajectory-to-word (T2W) attention and Hierarchical Frame-Selector (HFS) module.", + "bbox": [ + 497, + 255, + 890, + 296 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparing Methods. Base: We use a symmetric cross-modal encoder that contains patch-to-word (P2W) and word-to-patch (W2P) attentions. T2W: We replace P2W attention in Base by our T2W attention. MeanP: Another simple way to consider temporal knowledge is to mean pool the embeddings along the temporal axis. Specifically, we simply average $\\{\\pmb{y}_1,\\dots,\\pmb{y}_T\\}$ . These three ablations are implemented using the zero-shot setting.", + "bbox": [ + 497, + 296, + 890, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[L1,L2]: We insert frame selector layer into the L1-th and L2-th layers. F@T: We sample T frames into the model. F@T1-T2-T3: We use Hierarchical Frame Selector where \"F@T1-T2-T3\" denotes that T1 frames are originally input into the model and then T2 and T3 frames are respectively remained by the first and second frame selector layers. All these ablations are implemented using the fine-tuning setting.", + "bbox": [ + 497, + 408, + 890, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Results. Table 1 compares the performances of diverse baselines. From this table, we can see that T2W outperforms Base, e.g., T2W achieves $3.6\\%$ R@5 improvements on MSRVTT for zero-shot evaluation, which suggests that our T2W attention can exploit more temporal contexts to better solve video-language tasks.", + "bbox": [ + 497, + 519, + 890, + 600 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Also, T2W achieves higher scores than MeanP on different tasks, e.g., T2W achieves $28.4\\%$ of $\\mathbb{R}@\\mathbb{1}$ score in DiDeMo zero-shot text-to-video retrieval task while MeanP only has $27.4\\%$ . Applying mean-pooling strategy indeed fuse all the temporal knowledge, however, simply averaging all $\\pmb{y}_t$ also means that the contexts over the whole time axis are used, while lots of objects may only span a few frames and using all the temporal contexts may introduce trivial or even harmful noises. This proves that our T2W attention can capture more important cross-modal associations in this asymmetric cross-modal encoder case.", + "bbox": [ + 497, + 603, + 890, + 754 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further analyze the impact of the layer settings and frame number on the Hierarchical Frame-Selector module. As shown in Table 2, frame selector in deep layers (e.g. 6-th and 12-th layers) brings better performances on both retrieval and QA tasks. Moving frame selector module into shallower layers deteriorates the scores. For example, the accuracy drops $0.9\\%$ when the frame selector module is placed before the third layer. We hypothesize that discard", + "bbox": [ + 497, + 755, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2509", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/275f77327caa477810a45dde9f8bd76e5bed480d8d25a36ed627c809214224c7.jpg", + "image_caption": [ + "(a) \"A girl practising her arrow tricks\"" + ], + "image_footnote": [], + "bbox": [ + 82, + 119, + 507, + 226 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/19d8d231a44f77172aac4d94ebf6f42f15869fce9464e1acb75f4f2dc6a8d9fd.jpg", + "image_caption": [ + "(b) \"Two people play basketball\"" + ], + "image_footnote": [], + "bbox": [ + 517, + 122, + 890, + 226 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3f8ee20b307dc49c32b0c2cffa27004d52170b8c8503b5f34f0f9e074031866c.jpg", + "image_caption": [ + "(c) \"Adult feeds baby with spoon\"", + "Table 1. Performances of various baselines. R@K and MedR respectively denote recall (\\%) with K retrieval efforts and median ranking for retrieved videos where higher R@K and lower MedR indicate better performance." + ], + "image_footnote": [], + "bbox": [ + 82, + 243, + 507, + 347 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dec8cda2e68dfd55ec6c745614d6af8c8f2dd483a034b7202a4f2477fb2aa326.jpg", + "image_caption": [ + "(d) \"The dog runs away and picks up the cone\"", + "Figure 5. Visualizations of the attention maps from cross-modal encoder. Sample (a) and (b) are from MSRVTT [56], (c) and (d) are from DiDeMo [16] retrieval dataset. TW-BERT attends to the patches related to given query word by Trajectory-to-Word attention." + ], + "image_footnote": [], + "bbox": [ + 517, + 243, + 890, + 347 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e57c7933da83926f4803329c6f8d584870d9047b5417c3e6dfb618b45c1c9f99.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMSRVTT-ZSDiDeMo-ZSMSVD-QA
R@1↑R@5↑R@10↑MedR↓R@1↑R@5↑R@10↑MedR↓Acc.
Base25.146.457.37.026.652.862.75.047.4
T2W26.850.059.95.028.452.964.54.048.2
MeanP25.847.958.06.027.453.164.05.048.0
", + "bbox": [ + 149, + 419, + 811, + 501 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f2e47f260d6cc1962abdd81e82e9f338912c344dd00053b87d14464ba0634e1d.jpg", + "table_caption": [ + "Table 2. Performances comparison with different layer settings of the HFS in fine-tuning." + ], + "table_footnote": [], + "table_body": "
layersMSRVTT-FTMSVD-QA
R@1↑R@5↑R@10↑MedR↓Acc.
[2,4]36.763.274.93.046.2
[3,6]37.463.775.43.046.9
[4,8]38.164.676.23.047.8
[5,10]38.264.976.33.048.3
[6,12]38.465.176.63.048.5
", + "bbox": [ + 80, + 536, + 460, + 641 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6ca5519b8747a54fac49f08e30c485d9acae50f1d048156c6a70cac9a944e2d9.jpg", + "table_caption": [ + "Table 3. Performances comparison with different frame settings of the HFS in fine-tuning." + ], + "table_footnote": [], + "table_body": "
FrameMSRVTT-FTFrameMSVD-QA
R@1↑R@5↑R@10↑MedR↓Acc.
F@135.863.374.23.0F@847.2
F@4-2-135.963.273.93.0F@20-14-847.2
F@437.163.975.33.0F@1247.7
F@8-6-437.564.275.53.0F@24-18-1247.9
F@838.164.976.03.0F@1648.2
F@20-14-838.465.176.63.0F@32-24-1648.5
", + "bbox": [ + 80, + 671, + 465, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing frames too early would result in a lack of temporal knowledge in subsequent ViT layers. We thus choose to insert the frame selector module in the 6-th and 12-th layers in the following experiments. In terms of frame number, as shown in Table 3, on the one hand, as the number of frame we sample increases, both retrieval and QA performance obtain improvements. For example, in MSRVTT", + "bbox": [ + 75, + 769, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fine-tuning text-to-video retrieval task, F@20-14-8 outperforms F@8-6-4 by $0.9\\%$ on R@1 or on MSVD video question answering task, F@32-24-16 outperforms F@24-18-12 by $0.6\\%$ , which suggests that more temporal knowledge benefit our model whether using uniform sampling or our proposed HFS. On the other hand, using HFS gets higher scores than uniform sampling, e.g., F@20-14-8 achieves $38.4\\%$ of R@1 score in MSRVTT retrieval task while F@8 only has $38.1\\%$ , or on MSVD video question answering task, F@32-24-16 outperforms F@16 by $0.3\\%$ , which validates the power of HFS module.", + "bbox": [ + 497, + 515, + 890, + 668 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results. We show the heat maps of the attentions of Base and TW-BERT in Figure 5. We see that TW-BERT can select the most relevant frames according to the whole text, then it implicitly form a trajectory among these frames for a given query word to avoid over-exploiting the trivial spatial contexts as in Base. For example, in (a), TW-BERT first discards the 1-st and 8-th frames which is completely irrelevant to the text, then tracks the hand of the girl in each frame that it keeps according to the query word \"practising\" while Base cannot avoid impact of the irrelevant frames, and in those relevant frames, it only attends to the larger while trivial regions about the whole body of the girl. Moreover, in (d), TW-BERT keeps the 6-th and 7-th frames for these two frames show the dog's action more", + "bbox": [ + 497, + 672, + 892, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2510", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4a907c58568237e29b09351018f2af93ee11d34b88f3852fa50b895868bae6de.jpg", + "table_caption": [ + "Table 4. Experiments of text-to-video retrieval on MSRVTT, DiDeMo and LSMDC datasets. “#PT Pairs” lists the number of video-text pairs for pre-training. We show results with zero-shot evaluation (top) and fine-tuning evaluation (bottom). R@A is the average of R@1, R@5 and R@10." + ], + "table_footnote": [], + "table_body": "
Method#PT PairsDiDeMoLSMDCMSRVTT
R@1↑R@5↑R@10↑R@A↑MedR↓R@1↑R@5↑R@10↑R@A↑MedR↓R@1↑R@5↑R@10↑R@A↑MedR↓
Frozen [2]5.5M21.146.056.241.17.09.322.030.120.551.018.739.551.636.610.0
VIOLET [12]186M23.549.859.844.4------25.949.559.745.0-
OA-Trans [49]5.5M23.550.459.844.66.0-----23.447.555.642.28.0
ALPRO [24]5.5M23.847.357.943.06.0-----24.144.755.441.48.0
BridgeFormer [14]5.5M25.650.661.145.85.012.225.932.223.442.026.046.456.442.97.0
MILES [15]5.5M27.250.363.647.05.011.124.730.622.150.726.147.256.943.47.0
TW-BERT5.5M28.452.964.548.64.014.230.436.026.928.026.850.059.945.65.0
Frozen [2]5.5M31.059.872.454.43.015.030.839.828.520.031.059.570.553.73.0
VIOLET [12]186M32.662.874.756.7-16.136.641.231.3-34.563.073.457.0-
ALPRO [24]5.5M35.967.578.860.73.0-----33.960.773.255.93.0
OA-Trans [49]5.5M34.864.475.158.13.018.234.343.732.118.535.863.476.558.63.0
BridgeFormer [14]5.5M37.062.273.957.73.017.935.444.532.615.037.664.875.159.23.0
MILES [15]5.5M36.663.974.058.23.017.835.644.132.515.537.763.673.858.43.0
TW-BERT5.5M41.871.181.264.72.021.038.849.236.311.038.465.176.660.03.0
", + "bbox": [ + 80, + 157, + 887, + 321 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fa82769894483cf8a170fea100cef8c8841991d5c97749640f83ba6000f98426.jpg", + "table_caption": [ + "Table 5. ActivityNet Caption with fine-tuning setting." + ], + "table_footnote": [], + "table_body": "
Method#PT PairsR@1↑R@5↑R@10↑MedR↓
Dense [19]-14.032.0-34.0
FSE [60]-18.244.8-7.0
CE [30]-18.247.7-6.0
HSE [60]-20.549.3--
Clipbert [23]5.6M21.349.063.56.0
TW-BERT5.5M31.762.374.93.0
", + "bbox": [ + 80, + 334, + 467, + 426 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ed154dc2daf69b6228e4e3091df2097f7e902ca0d9084ba4130a91b28c38f4ba.jpg", + "table_caption": [ + "Table 6. Experiments of video question answering on MSRVTT and MSVD datasets in top-1 accuracy $(\\%)$" + ], + "table_footnote": [], + "table_body": "
Method#PT PairsMSRVTTMSVD
Clipbert [23]5.6M37.4-
ALPRO [24]5.5M42.145.9
SINGULARITY [22]5.5M42.745.9
LGDN [33]15.2M43.1-
SSML [1]100M35.135.1
JustAsk [57]69M41.546.3
MERLOT [59]180M43.1-
VIOLET [12]186M43.947.9
TW-BERT5.5M43.648.5
", + "bbox": [ + 80, + 452, + 465, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "clearly. Then TW-BERT attends to the part where the dog is in contact with the cone according to the query word \"picks\" while Base only focuses on the body of the dog.", + "bbox": [ + 75, + 602, + 468, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Comparisons with SOTA", + "text_level": 1, + "bbox": [ + 77, + 650, + 304, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare TW-BERT with previous methods on two frequently applied tasks: video-text retrieval (VDTR) and video question answering (VDQA). Table 4 and 5 report the performances of VDTR on MSRVTT [56], DiDeMo [16], LSMDC [43], and ActivityNet Caption [19], respectively, where the former three datasets contain both zero-shot and fine-tuning setups and the last one only has fine-tuning setup. Table 6 reports the VDQA on MSRVTT [56] and MSVD [6]. Among the compared models, MILES [15], BridgeFormer [14], OA-Trans [49], Clipbert [23] and VIOLET [12] are SOTA models proposed in recently 1-2 years. Note that VIOLET [12] and ALPRO [24] distill knowledge from additional large-scale BERTs while we do not. Also, we show the number of pre-training video-text pairs in these", + "bbox": [ + 75, + 672, + 468, + 865 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tables for more clear comparisons.", + "bbox": [ + 499, + 330, + 727, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "From these tables, we can find that when the pre-training data is in the same scale, TW-BERT achieves the best performance compared with all the other models on both VDTR and VDQA. For example, on DiDeMo VDTR, TW-BERT outperforms BridgeFormer by $4.8\\%$ on $\\mathbb{R}@\\mathbb{1}$ , or on MSVD VDQA, TW-BERT outperforms ALPRO by $2.6\\%$ . Moreover, compared with the models trained on much more data, TW-BERT can still achieve the best performances on various tasks, e.g., on LSMDC VDTR, TW-BERT outperforms VIOLET by $8.0\\%$ on $\\mathbb{R}@\\mathbb{10}$ or on MSRVTT VDQA, TW-BERT outperforms MERLOT [59] by $0.5\\%$ .", + "bbox": [ + 497, + 356, + 890, + 509 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Note that the videos in LSMDC are longer than MSRVTT and DiDeMo, which means that the videos in this dataset contain more temporal contexts than the other datasets. Then as shown in Table 4, the improvements of TW-BERT over other SOTAs are larger than the improvements on the other datasets. For example, compared with BridgeFormer, TW-BERT has an average $3.5\\%$ improvement in the zero-shot setting, while on DiDeMo dataset, the corresponding average improvement over MILES is only $1.6\\%$ . Such comparisons further validate the effectiveness of TW-BERT in exploiting temporal contexts.", + "bbox": [ + 497, + 521, + 892, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Among these SOTAs, only when compared with VIOLET, which uses an additional large-scale model DALLE [40] and 32 more times pre-training data than ours (180M VS. 5.5M), TW-BERT cannot comprehensively surpass VIOLET on all the tasks. For example, on MSRVTT VDQA, VIOLET achieves $0.3\\%$ higher than TW-BERT, while such marginal improvements are got at the cost of much more training resources. Furthermore, TW-BERT still outperforms VIOLET on the other tasks, e.g., on DiDeMo VDTR, TW-BERT outperforms VIOLET by $9.2\\%$ on R@1 or on MSVD VDQA, TW-BERT outperforms VIOLET by $0.6\\%$ . These comparisons confirm the effectiveness of the proposed TW-BERT.", + "bbox": [ + 497, + 686, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2511", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 77, + 124, + 194, + 138 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We propose a novel Trajectory-Word BERT (TW-BERT) that builds Trajectory-to-Word alignments for solving video-language tasks. In particular, we introduce an asymmetric cross-modal encoder that contains word-to-patch (W2P) and Trajectory-to-Word (T2W) to capture cross-modal associations. Moreover, a novel Hierarchical Frame-Selector (HFS) module is proposed in the fine-tuning stage to filter out irrelevant frames to help the later T2W attention learn better trajectory-word alignments. Extensive experiments across diverse tasks confirm the effectiveness of the proposed TW-BERT.", + "bbox": [ + 75, + 148, + 472, + 302 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 77, + 315, + 265, + 331 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work is supported by National Science Foundation of China (62206048), National Key R&D Program of China (2018AAA0100104, 2018AAA0100100), Natural Science Foundation of Jiangsu Province (BK20220819, BK20211164), and Young Elite Scientists Sponsorship Program of Jiangsu Association for Science and Technology Tj-2022-027.", + "bbox": [ + 75, + 338, + 468, + 435 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 450, + 173, + 464 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Elad Amrani, Rami Ben-Ari, Daniel Rotman, and Alex Bronstein. 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In CVPR, page 8746-8755, 2020. 2" + ], + "bbox": [ + 78, + 125, + 468, + 809 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "2514", + "bbox": [ + 468, + 889, + 500, + 899 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_model.json b/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7398e248135a73af2ecfb71f72391d27e110cbca --- /dev/null +++ b/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_model.json @@ -0,0 +1,2653 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.085 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.088 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.154, + 0.162, + 0.818, + 0.184 + ], + "angle": 0, + "content": "Learning Trajectory-Word Alignments for Video-Language Tasks" + }, + { + "type": "text", + "bbox": [ + 0.153, + 0.207, + 0.818, + 0.243 + ], + "angle": 0, + "content": "Xu Yang\\(^{1}\\) Zhangzikang Li\\(^{1,2}\\) Haiyang Xu\\(^{2*}\\) Hanwang Zhang\\(^{3}\\) Qinghao Ye\\(^{2}\\) Chenliang Li\\(^{2}\\) Ming Yan\\(^{2}\\) Yu Zhang\\(^{1*}\\) Fei Huang\\(^{2}\\) Songfang Huang\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.127, + 0.245, + 0.845, + 0.277 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Computer Science & Engineering, Key Lab of New Generation Artificial Intelligence Technology & Its Interdisciplinary Applications (Ministry of Education), Southeast University" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.278, + 0.876, + 0.326 + ], + "angle": 0, + "content": "\\(^{2}\\)DAMO Academy, Alibaba Group \\(^{3}\\)School of Computer Science & Engineering, Nanyang Technological University \\(\\{\\text{xuyang.palm, zhang.yu}\\} @\\)seu.edu.cn, lizhangzikang@gmail.com, \\(\\{\\text{shuofeng.xhy, yeqinghao.yqh, lcl193798, ym119608, f.huang, songfang.hsf}\\} @\\)alibaba-inc.com, hanwangzhang@ntu.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.357, + 0.313, + 0.371 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.474, + 0.775 + ], + "angle": 0, + "content": "In a video, an object usually appears as the trajectory, i.e., it spans over a few spatial but longer temporal patches, that contains abundant spatiotemporal contexts. However, modern Video-Language BERTs (VDL-BERTs) neglect this trajectory characteristic that they usually follow image-language BERTs (IL-BERTs) to deploy the patch-to-word (P2W) attention that may over-exploit trivial spatial contexts and neglect significant temporal contexts. To amend this, we propose a novel TW-BERT to learn Trajectory-Word alignment by a newly designed trajectory-to-word (T2W) attention for solving video-language tasks. Moreover, previous VDL-BERTs usually uniformly sample a few frames into the model while different trajectories have diverse graininess, i.e., some trajectories span longer frames and some span shorter, and using a few frames will lose certain useful temporal contexts. However, simply sampling more frames will also make pre-training infeasible due to the largely increased training burdens. To alleviate the problem, during the fine-tuning stage, we insert a novel Hierarchical Frame-Selector (HFS) module into the video encoder. HFS gradually selects the suitable frames conditioned on the text context for the later cross-modal encoder to learn better trajectory-word alignments. By the proposed T2W attention and HFS, our TW-BERT achieves SOTA performances on text-to-video retrieval tasks, and comparable performances on video question-answering tasks with some VDL-BERTs trained on much more data. The code will be available in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.797, + 0.21, + 0.81 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.82, + 0.47, + 0.849 + ], + "angle": 0, + "content": "By witnessing the boom of BERT-like models in single domains, e.g., vision or language[52, 44, 21], researchers" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.359, + 0.613, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.434, + 0.606, + 0.442 + ], + "angle": 0, + "content": "(a) RoI based IL-BERT" + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.363, + 0.718, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.618, + 0.434, + 0.72, + 0.442 + ], + "angle": 0, + "content": "(b) Patch based IL-BERT" + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.359, + 0.885, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.749, + 0.434, + 0.859, + 0.442 + ], + "angle": 0, + "content": "(c) Patch based VDL-BERT" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.449, + 0.606, + 0.517 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.449, + 0.718, + 0.517 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.719, + 0.449, + 0.883, + 0.517 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.643, + 0.519, + 0.748, + 0.527 + ], + "angle": 0, + "content": "(d) TW-BERT Pretraining" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.533, + 0.606, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.533, + 0.718, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.719, + 0.533, + 0.884, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.605, + 0.75, + 0.613 + ], + "angle": 0, + "content": "(e) TW-BERT Fine-Tuning" + }, + { + "type": "title", + "bbox": [ + 0.609, + 0.621, + 0.79, + 0.634 + ], + "angle": 0, + "content": "A boy is playing basketball." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.892, + 0.804 + ], + "angle": 0, + "content": "Figure 1. The comparisons of five different ways to build object-word alignments. In (b), by patch-to-word (P2W) attention, implicit object-word alignment can be built, e.g., the \"ball region\" is aligned with basketball. While in (c), P2W attention may concentrate the attention of an object on only one frame, e.g., basketball only attends over the \"ball region\" of the first frame. (d) When pre-training TW-BERT, the trajectory of an object is constructed, e.g., the \"ball trajectory\" through 4 frames built. Note that we only use 4 frames during pre-training, we show 8 frames for comparing with (e) and the transparent ones denote that they are not input into the model. (e) When fine-tuning TW-BERT, we use HFS to select 4 frames from 8 and we can see that the selected frames are different from the uniformly sampled ones in (d)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.868 + ], + "angle": 0, + "content": "begin to build vision-language BERTs[3, 61, 10] for learning robust cross-modal associations. Compared with the images, videos provide more details for building robust associations, e.g., the spatiotemporal contexts in videos can" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.854, + 0.228, + 0.867 + ], + "angle": 0, + "content": "*Corresponding authors." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.502, + 0.901 + ], + "angle": 0, + "content": "2504" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.127, + 0.47, + 0.224 + ], + "angle": 0, + "content": "better describe the actions. However, directly addressing dynamic videos may cost more storage and computation resources. To circumvent such huge cost, researchers first study image-language BERT (IL-BERT)[17, 25, 8, 27, 61] and then exploit the research fruits to build the challenging, while more pragmatic, video-language BERT (VDLBERT)[47, 2, 26, 36, 13, 35, 46, 37, 54, 51]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.225, + 0.471, + 0.378 + ], + "angle": 0, + "content": "Pioneering techniques are directly inherited from IL-BERT into VDL-BERT, e.g., the image encoders are used to embed sampled video frames [23, 62]. However, since image encoders can hardly learn temporal contexts, the resultant VDL-BERTs will degrade to IL-BERT even if they are trained by video-text pairs. To ameliorate it, researchers apply the video encoders [32, 4, 12, 24] to embed spatiotemporal contexts. Though promising improvements are observed, these VDL-BERTs still neglect or ill-consider a significant factor in IL-BERT: the object-word alignment, which helps learn robust associations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.614 + ], + "angle": 0, + "content": "To learn object-word alignments, as Figure 1(a) shows, researchers use an RoI-based extractor to embed an image into a series of RoI features [34, 27, 8]. However, this RoI-based extractor is offline trained by object detection with limited label inventory, which will weaken the IL-BERT since the extractor will not be updated during large-scale pre-training. To enable the end-to-end training, researchers substitute the RoI-based extractor with visual transformers whose outputs are a series of grid embeddings, which will be used to build the cross-modal connections. Although a single grid usually does not construct an integral object, fortunately, the widely applied patch-to-word (P2W) attention of IL-BERT can softly seek the salient visual regions for a given query word. Then the object-word alignments can still be built between this softly detected object and the word, e.g., as shown in Figure 1(b), the object \"basketball\" can be implicitly attended by the corresponding word query." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.768 + ], + "angle": 0, + "content": "Although the P2W attention remedies the loss of RoI-level features for learning object-word alignments in ILBERT, its effectiveness is weakened in the video case. This is because the objects usually act as the Trajectories which span a few spatial while multiple temporal grids in the videos. Thus, directly applying the P2W attention may over-exploit the trivial spatial contexts while neglecting the significant temporal contexts and then make the model attend to only one or two frames. Figure 1(c) shows this limitation that P2W attention only aligns the \"ball\" in the first frame to the word ball." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.47, + 0.868 + ], + "angle": 0, + "content": "To address this limitation, we propose to learn Trajectory-to-Word alignments to solve video-language tasks and name this model as TW-BERT. Specifically, such alignment is learnt by a novel designed trajectory-to-word T2W attention, which first uses the word as the query to seek the salient parts of each frame and the sought parts are sequenced to form the trajectory. Then the query word at" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.292 + ], + "angle": 0, + "content": "tends over the trajectories again for capturing cross-modal associations. In this way, the trivial spatial regions are weakened and the temporal contexts will be strengthened, e.g., as shown in Figure 1(d), the attention weights of the word will be concentrated on the object trajectory instead of only one frame as in (c). In the implementation, we follow most VDL-BERTs to set up the network: two single-modal encoders for the video and text and one cross-modal encoder, which is sketched in Figure 2. For the cross-modal encoder, since our T2W attention does not have the same structure as the word-to-patch (W2P) attention, our cross-modal encoder is asymmetric." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.292, + 0.893, + 0.582 + ], + "angle": 0, + "content": "Moreover, previous VDL-BERTs usually uniformly sample a few frames into the model, which contains two drawbacks. Firstly, using a few frames may lose temporal context and secondly, uniform sampling can hardly capture the varying graininess of the trajectories, i.e., some trajectories span longer frames and some span shorter. However, simply sampling more frames will largely increase the pretraining burdens that are beyond the computation resources we own. To alleviate this problem, in the fine-tuning stage, we sample more frames into the video encoder while only keeping the most relevant frames according to the corresponding text by a novel designed Hierarchical Frame-Selector (HFS). For example, as shown in Figure 1(e), 4 frames are selected by HFS from the 8 uniformly sampled ones for learning trajectory-word alignment. Specifically, HFS inserts a few lightweight layers into the video encoder and these layers can gradually filter frames conditioned on the language context. In this way, HFS learns the coarse-grained trajectory-word alignments, i.e., framework alignments, to help the later T2W attention learn more fine-grained trajectory-word alignments." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.583, + 0.741, + 0.597 + ], + "angle": 0, + "content": "To sum up, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.602, + 0.891, + 0.655 + ], + "angle": 0, + "content": "- We propose a novel perspective to consider the videos that are composed of moving object trajectories, which may inspire the researchers to build more advanced VDL-BERTs." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.657, + 0.89, + 0.684 + ], + "angle": 0, + "content": "- We propose a simple while effective T2W attention to learn Trajectory-to-Word alignments." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.685, + 0.891, + 0.739 + ], + "angle": 0, + "content": "- We propose a novel hierarchical frame selector (HFS) in TW-BERT during fine-tuning to capture the varying graininess of the trajectory while not largely increasing the training burdens." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.74, + 0.891, + 0.767 + ], + "angle": 0, + "content": "- We achieve SOTA performances compared with other VDL-BERTs trained by the same amount of data." + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.602, + 0.891, + 0.767 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.781, + 0.642, + 0.795 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.804, + 0.808, + 0.819 + ], + "angle": 0, + "content": "2.1. Image-Language BERT (IL-BERT)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.825, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Recently, various techniques have been proposed in ILBERT to learn vision-language connections. Most of them aim at capturing robust object-word alignments since such" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.901 + ], + "angle": 0, + "content": "2505" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.127, + 0.473, + 0.319 + ], + "angle": 0, + "content": "alignments construct the foundations of visual reasoning. In the beginning, a pre-trained Faster-RCNN [41] is used to extract a series of RoI poolings, where each one contains one or a few salient objects, to facilitate building object-word alignments [34, 48, 8, 27]. However, this Faster-RCNN is usually pre-trained by the object annotations from COCO [7] and VG [20], whose concept space is much narrower than the data used to train IL-BERT, which can be almost unlimedly collected from the websites. Moreover, this Faster-RCNN is not updated during the end-to-end training of the IL-BERT, which means that the visual encoder may hardly learn novel knowledge from the web-collected data. Thus the performances of these IL-BERTs are limited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.473, + 0.515 + ], + "angle": 0, + "content": "To further release the potential of hugely web-collected data, the offline Faster RCNN is switched into vision Transformers [11, 32] and thus a homogeneous IL-BERT, i.e., all the components are transformer-based, is built, which is more easily trained end-to-end [34]. Compared with the RoI-based encoder, the vision Transformer outputs a series of patch embeddings and thus may lose object-level knowledge. To remedy such loss, various strategies are proposed to improve the vision-language alignments. For example, the align-before-fuse strategy [25] aligns the paired image-text embeddings before cross-modal fusion for facilitating the subsequent fusion. And the fine-grained contrastive objective [58] amplifies the local details for learning the object-word alignments." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.526, + 0.403, + 0.541 + ], + "angle": 0, + "content": "2.2. Video-Language BERT (VDL-BERT)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.473, + 0.868 + ], + "angle": 0, + "content": "Since the spatiotemporal contexts in videos can hardly be learnt by image extractors, only inheriting the techniques which are successful in IL-BERT to VDL-BERT is not enough. Thus, based on the fruits of IL-BERT, most VDL-BERTs aim at exploiting more spatiotemporal contexts to build cross-modal associations. One straightforward way is to learn such spatiotemporal contexts through video Transformers [4, 28]. Besides this, some more advanced techniques are proposed, e.g., VIOLET [12] tokenizes the dynamic video patches and predicts the labels of these tokens; BridgeFormer [14] erases the words (nouns or verbs) from the text and learn to match the visual embeddings queried by the erased words and the remained texts; or ALPRO [24] computes the similarities between the video embeddings with the generated entity prompts. TS2-Net [31] shifts token features and selects informative tokens in both temporal and spatial dimensions to produce the fine-grained spatial-temporal video representation. Although substantial improvements are observed, these methods use video patches in the cross-modal encoder, which neglects that an object usually acts as the trajectory in the videos, and thus they may over-exploit the trivial spatial contexts. To ameliorate this limitation, we propose TW-BERT to capture" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.123, + 0.896, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.285, + 0.894, + 0.35 + ], + "angle": 0, + "content": "Figure 2. The architecture of TW-BET, which contains two single-modal encoders and one asymmetric cross-modal encoder. Totally three losses in the grey blocks are used to train the whole model: \\( L_{vtc} \\), \\( L_{mlm} \\), and \\( L_{vtm} \\). Note that HFS is only used in the fine-tuning stage." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.356, + 0.893, + 0.385 + ], + "angle": 0, + "content": "trajectory-word alignments for more robust vision-language alignment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.397, + 0.617, + 0.411 + ], + "angle": 0, + "content": "3. TW-BERT" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.895, + 0.6 + ], + "angle": 0, + "content": "Figure 2 sketches TW-BERT, which has two single-modal encoders for embedding the video and text (cf. Sec. 3.1) and one cross-modal encoder for learning videolanguage associations (cf. Sec. 3.2). Different from the previous VDL-BERTs, our cross-modal encoder is an asymmetric one that contains a classic word-to-patch (W2P) attention and a novel proposed trajectory-to-word (T2W) attention (cf. Sec. 3.2) for learning trajectory-word alignments. In Sec. 3.3, we introduce how to use Hierarchical Frame-Selector (HFS) in the fine-tuning stage to gradually filter the frames for capturing coarse-grained frame-word alignments. Lastly, we introduce the losses used to train our TW-BERT in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.61, + 0.719, + 0.625 + ], + "angle": 0, + "content": "3.1. Single-Modal Encoders" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.894, + 0.811 + ], + "angle": 0, + "content": "Video Encoder. For a video, we sample a few \\(224 \\times 224\\) frames and input them into the 12-layer TimeSformer [4, 24] for embedding. TimeSformer first partitions each frame into \\(14 \\times 14\\) non-overlapping patches, which are flattened and fed to a linear projection layer to produce a sequence of patch tokens. Then TimeSformer applies self-attention along the temporal and spatial dimensions to calculate per-frame features. These features are further mean-pooled along the height and width dimensions. Learnable spatial positional embeddings are added to each video token in the same spatial location of different frames. The final output embedding set is \\(\\mathbf{V} = \\{\\mathbf{v}_{cls}, \\mathbf{v}_1, \\dots, \\mathbf{v}_{N_V - 1}\\}\\), where \\(\\mathbf{v}_n \\in \\mathbb{R}^d\\) and \\(\\mathbf{v}_{cls}\\) is the global [CLS] embedding." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.812, + 0.894, + 0.868 + ], + "angle": 0, + "content": "Text Encoder. For a text, we use a 6-layer transformer to embed it and the output is \\( \\mathbf{X} = \\{\\pmb{x}_{cls},\\pmb{x}_1,\\dots,\\pmb{x}_{N_X - 1}\\} \\) where \\( \\pmb{x}_n\\in \\mathbb{R}^d \\) and \\( \\pmb{x}_{cls} \\) is the global [CLS] embedding. Similar to the video encoder, we also add positional embed" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.503, + 0.901 + ], + "angle": 0, + "content": "2506" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.127, + 0.236, + 0.14 + ], + "angle": 0, + "content": "dings to the text tokens." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.152, + 0.38, + 0.167 + ], + "angle": 0, + "content": "3.2. Asymmetric Cross-Modal Encoder" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.175, + 0.469, + 0.409 + ], + "angle": 0, + "content": "After embedding videos and texts, a cross-modal encoder is used to fuse them by calculating bi-directional associations: vision-to-language and language-to-vision. No matter what the direction is, the motivation is to assign semantic knowledge from one domain to another. Since a single word contains integral semantic knowledge, we follow previous VDL-BERT [24, 2, 23, 47] to set a traditional word-to-patch (W2P) attention to assign the words to a patch. However, different from the word, only the object instead of one grid conveys integral semantic knowledge. In videos, an object usually spans both spatial and temporal axes and thus the previously used patch-to-word (P2W) attention may fail to transfer the semantic knowledge. To amend this, we design a novel Trajectory-to-Word (T2W) attention for transferring semantic knowledge from videos to texts. Since W2P and T2W attentions have diverse structures, our cross-encoder is asymmetric." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.41, + 0.469, + 0.465 + ], + "angle": 0, + "content": "Specifically, both W2P and T2W attentions are built on the Multi-Head Attention (MHA) operation, here we first formalize MHA and then introduce how to use it to build W2P and T2W attentions. Formally, MHA is*:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.478, + 0.27, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{c} \\text {I n p u t :} \\quad \\mathcal {Q}, \\mathcal {K}, \\mathcal {V} \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.494, + 0.422, + 0.523 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A t t}: \\quad \\mathcal {A} _ {i} = \\operatorname {S o f t m a x} (\\frac {\\mathcal {Q W} _ {i} ^ {Q} \\left(\\mathcal {K W} _ {i} ^ {K}\\right) ^ {T}}{\\sqrt {d}})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.523, + 0.469, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H e a d}: \\quad \\mathcal {H} _ {i} = \\mathcal {A} _ {i} \\mathcal {V W} _ {i} ^ {V}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.543, + 0.385, + 0.558 + ], + "angle": 0, + "content": "\\[\n\\text {M u l t i - H e a d}: \\quad \\mathcal {H} = \\left[ \\mathcal {H} _ {1}, \\mathcal {H} _ {2},..., \\mathcal {H} _ {h} \\right] \\mathcal {W} ^ {H},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.561, + 0.332, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\text {O u t p u t}: \\mathcal {Z} = \\mathrm {L N} (\\mathcal {H} + \\mathcal {Q}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.588, + 0.469, + 0.644 + ], + "angle": 0, + "content": "where \\(\\mathcal{W}_i^Q, \\mathcal{W}_i^K, \\mathcal{W}_i^V, \\mathcal{W}_i^H\\) are all trainable matrices; \\(h\\) is the head number and \\(d_h = d / h\\); \\(\\mathcal{A}_i\\) is the \\(i\\)-th attention matrix corresponding to the \\(i\\)-th head matrix; \\([\\cdot]\\) is the concatenation operation; and LN is the Layer Normalization." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.646, + 0.469, + 0.673 + ], + "angle": 0, + "content": "Word-to-Patch (W2P) Attention. To calculate the W2P alignment, we apply the conventional W2P attention [24]:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.675, + 0.469, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} _ {W 2 P} = \\mathbf {M H A} (\\mathcal {Q} = \\mathbf {V}, \\mathcal {K} = \\mathcal {V} = \\mathbf {X}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.469, + 0.761 + ], + "angle": 0, + "content": "where \\(\\mathbf{V} \\in \\mathbb{R}^{N_V \\times D}\\), \\(\\mathbf{X} \\in \\mathbb{R}^{N_X \\times D}\\) are respectively video and word embedding sets got from two single-modal encoders. By setting the query \\(\\mathcal{Q}\\) to the video patch embeddings, Eq. (2) learns to assign suitable words to each video patch and thus captures the W2P alignment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.762, + 0.469, + 0.831 + ], + "angle": 0, + "content": "Trajectory-to-Word (T2W) Attention. As shown in Figure. 3 (b), we propose the T2W attention that uses two steps to learn the T2W alignment: it first constructs a trajectory for a given word and then uses the word as the query to attend over the trajectory for capturing the associations. For" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.124, + 0.622, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.124, + 0.769, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.125, + 0.892, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.211, + 0.892, + 0.301 + ], + "angle": 0, + "content": "Figure 3. The comparisons between Patch-to-Word (P2W) and Trajectory-to-Word (T2W) attentions, where the green block denotes a query word and the blue blocks denote the video patches. In P2W attention, the word attends over all the video patches and may only concentrate on one frame, while in T2W attention, the salient red parts of each frame are found to construct a trajectory, which are connected by the red lines, \\( e.g., y_1, y_2, y_3 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.892, + 0.351 + ], + "angle": 0, + "content": "convenience, we introduce how the T2W attention calculates the fusion embedding \\( z_{T2W} \\) for a single word \\( x \\) and it is straightforward to extend it to a sequence of the words." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.407 + ], + "angle": 0, + "content": "In the first step, T2W attention uses \\( x \\) as the query to find the salient parts for each frame and then sequence these parts to construct the trajectory. Assuming \\( V_{t} \\) is the embedding set of the \\( t \\)-th frame, the salient part \\( y_{t} \\) is got as:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.408, + 0.891, + 0.424 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {y} _ {t} = \\mathbf {M H A} (\\mathcal {Q} = \\boldsymbol {x}, \\mathcal {K} = \\mathcal {V} = \\boldsymbol {V} _ {t}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.892, + 0.466 + ], + "angle": 0, + "content": "Then the salient parts at different time frames construct a continuous flow \\(\\mathbf{Y} = \\{\\pmb{y}_1, \\dots, \\pmb{y}_T\\}\\), which is the trajectory of the given word." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.891, + 0.509 + ], + "angle": 0, + "content": "In the second step, to get the trajectory-to-word fusion embedding \\( z_{T2W} \\), we treat \\( x \\) as the query again while using the trajectory \\( Y \\) as the key and value in MHA:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.512, + 0.891, + 0.526 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {z} _ {T 2 W} = \\mathbf {M H A} (\\mathcal {Q} = \\boldsymbol {x}, \\mathcal {K} = \\mathcal {V} = \\boldsymbol {Y}). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.652 + ], + "angle": 0, + "content": "By Eq. (3), T2W attention finds the salient parts for the given word at each frame, which enforces Eq. (4) to attend over the continuous frames instead of concentrating the attention only on one or some episodic frames as the previous P2W attentions. In this way, the whole T2W block exploits more temporal contexts to build vision-language associations, which facilitates the video reasoning tasks that usually require the correct recognition of the temporal patterns. Figure. 3 compares P2W and T2W attentions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.665, + 0.755, + 0.678 + ], + "angle": 0, + "content": "3.3. Hierarchical Frame-Selector" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.867 + ], + "angle": 0, + "content": "During fine-tuning, to improve the performance, previous studies tend to sample more frames than pre-training for introducing more temporal information. However, on the one hand, using too many frames will dramatically increase the computational resources, which causes infeasible training. On the other hand, in a video, different trajectories have varying graininess, e.g., some trajectories may cover longer frames and some cover shorter. In this way, uniform sampling may introduce redundant temporal information for these longer trajectories and deficient information for the shorter ones. Interestingly, the time duration of the trajectory is also reflected in the corresponding text. In this way, we can use the text to choose suitable frames and then" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.844, + 0.469, + 0.866 + ], + "angle": 0, + "content": "*To avoid symbol confusions, we use the calligraphic font (\\mathcal{M}) to denote the built-in variables of the MHA module." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.901 + ], + "angle": 0, + "content": "2507" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.129, + 0.891, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.224, + 0.893, + 0.25 + ], + "angle": 0, + "content": "Figure 4. The architecture of the proposed Hierarchical Frame-Selector. At beginning, four frames are input into the video encoder and the first frame selector behind the 6-th layer filters out the 2-nd frame. At last, only the tokens of the 1-st and 4-th frames are preserved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.256, + 0.47, + 0.282 + ], + "angle": 0, + "content": "only input them into the cross-modal attention for learning trajectory-word alignments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.47, + 0.449 + ], + "angle": 0, + "content": "Motivated by this, we propose a novel Hierarchical Frame-Selector (HFS) that can gradually select the most relevant video frames to reduce the computational burdens while providing more temporal knowledge. Figure 4 illustrates the architecture of our proposed frame selector module. HFS contains a few frame selector layers which have the same structure with different parameters. For each frame selector layer, given a sequence of video frame [CLS] tokens \\( V_{cls} = \\{v_{cls}^{1}, v_{cls}^{2}, \\dots, v_{cls}^{T}\\} \\in \\mathbb{R}^{T \\times D} \\), we concatenate the text [CLS] embedding \\( x_{cls} \\) with each \\( v_{cls}^{t} \\): \\( f_{t} = [v_{cls}^{t}, x_{cls}] \\in \\mathbb{R}^{2D} (1 \\leq t \\leq T) \\) and feed them into a scorer network including a FC layer and a softmax layer:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.45, + 0.469, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {s} = \\operatorname {S o f t m a x} (F C (\\boldsymbol {f})) \\in \\mathbb {R} ^ {T \\times 1}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.47, + 0.593 + ], + "angle": 0, + "content": "Here, \\( T \\) denotes the number of frames input into the video encoder, and \\( s \\in \\mathbb{R}^T \\) is the score vector of \\( T \\) frames. Then for this frame selector, we keep the tokens of \\( k \\) frames with the top- \\( k \\) \\( s_t \\) for the further embedding in the subsequent video Transformer layers. During training, we employ the perturbed maximum method [5] to construct a differentiable Top-K operator. In the video encoder, we totally insert 2 selector layers and insert them in the 6-th and 12-th layers as in Figure 4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.267, + 0.618 + ], + "angle": 0, + "content": "3.4. Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.679 + ], + "angle": 0, + "content": "To train TW-BERT, as the grey blocks shown in Figure 2, we totally use three losses which are masked language modeling (MLM), video-text matching (VTM), and video-text contrastive loss (VTC)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.68, + 0.469, + 0.776 + ], + "angle": 0, + "content": "Masked language Modeling (MLM) [26, 24, 12, 50]. MLM aims to predict the masked word tokens given both the video and the text contexts. To get it, we first randomly replace the input text tokens with the [MASK] token with a probability of \\(15\\%\\) and then use the [MASK] embedding output from the cross-modal encoder to predict the masked word by calculating a cross-entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.777, + 0.469, + 0.794 + ], + "angle": 0, + "content": "\\[\nL _ {M L M} = \\mathbb {E} _ {(V, \\hat {X}) \\sim D} \\mathrm {H} \\left(y ^ {m s k}, p ^ {m s k} (V, \\hat {X})\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.825 + ], + "angle": 0, + "content": "where \\(\\hat{X}\\) is the masked text, \\(\\mathrm{H}\\) is the cross-entropy loss, \\(y^{msk} / p^{msk}\\) are the ground-truth/predicted masked tokens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Video-text Matching (VTM) [24, 12, 50]. VTM calculates whether the given video and text are matched or not. To get it, for a given video-text pair, we first randomly replace the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.892, + 0.324 + ], + "angle": 0, + "content": "text with the ones from a different video in the same batch. Then we concatenate the video and text [CLS] embeddings output from the cross-modal encoder and input the concatenated embedding into a binary classifier to judge whether the given video-text pair is matched or not:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.325, + 0.891, + 0.34 + ], + "angle": 0, + "content": "\\[\nL _ {V T M} = \\mathbb {E} _ {(V, X) \\sim D} \\mathrm {H} \\left(y ^ {v t m}, p ^ {v t m} (V, X)\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.369 + ], + "angle": 0, + "content": "where \\( y^{vtm} / p^{vtm}(V,X) \\) are the ground-truth/predicted values indexing whether \\( V \\) and \\( X \\) are matched or not." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.892, + 0.48 + ], + "angle": 0, + "content": "Video-text Contrastive (VTC) [24, 50, 49, 14, 15, 2, 29]. As detailed in Section 3, VTC contrasts the outputs of two single-modal encoders to pull close their embedding space to help the subsequent cross-modal encoder build more robust vision-language associations. Suppose \\( s_{ij} \\) denotes the similarity score of the \\( i \\)-th video and the \\( j \\)-th text, for each video and text, we calculate the softmax-normalized video-to-text and video-to-image similarity as:" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.488, + 0.891, + 0.518 + ], + "angle": 0, + "content": "\\[\np _ {i j} ^ {v 2 t} (V) = \\frac {\\exp \\left(s _ {i j} / \\tau\\right)}{\\sum_ {j} \\exp \\left(s _ {i j} / \\tau\\right)}, p _ {i j} ^ {t 2 v} (X) = \\frac {\\exp \\left(s _ {i j} / \\tau\\right)}{\\sum_ {i} \\exp \\left(s _ {i j} / \\tau\\right)} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.526, + 0.892, + 0.607 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a learnable temperature parameter. Let \\(y^{v2t}(V)\\) and \\(y^{t2v}(X)\\) denote the ground-truth one-hot similarity. This loss contains two symmetric parts, where the left term forces the \\(i\\)-th text embedding to be close to the \\(i\\)-th video embedding compared with the other texts and the right term has a similar effect:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.609, + 0.573, + 0.62 + ], + "angle": 0, + "content": "\\[\nL _ {V T C} =\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.624, + 0.891, + 0.657 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{2} \\mathbb {E} _ {(V, X) \\sim D} [ \\mathrm {H} (y ^ {v 2 t} (V), p ^ {v 2 t} (V)) + \\mathrm {H} (y ^ {t 2 v} (X), p ^ {t 2 v} (X)) ] \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.699 + ], + "angle": 0, + "content": "In the implementation, we follow [25] to use the momentum queue as a continuously-evolving teacher to provide more negative samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.633, + 0.727 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.735, + 0.694, + 0.749 + ], + "angle": 0, + "content": "4.1. Pre-training Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Following recent work [24, 14, 15, 49, 2], we pre-train TW-BERT on Google Conceptual Captions (CC3M) [45] containing 3.3M image-text pairs and WebVid-2M [2] containing 2.5M video-text pairs. For CC3M, the image is treated as a one-frame video data during pre-training. Note that due to the limited storage and computation resources, we do not use some much larger datasets like HowTo100M [38] containing 136M video-text pairs as [26," + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.502, + 0.901 + ], + "angle": 0, + "content": "2508" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.126, + 0.468, + 0.154 + ], + "angle": 0, + "content": "55]. Also, we do not distill knowledge from CLIP [39], which is pre-trained on 400M image-text pairs, as [36]." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.164, + 0.26, + 0.178 + ], + "angle": 0, + "content": "4.2. Downstream Tasks" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.185, + 0.468, + 0.419 + ], + "angle": 0, + "content": "Text-to-Video Retrieval. (i) MSRVTT contains 10K YouTube videos with 200K descriptions. We follow [56] to use 9K train+val videos for training and report results on the 1K test split. (ii) DiDeMo [16] contains 10K Flickr videos annotated with 40K sentences. (iii) LSMDC consists of 118,081 video clips sourced from 202 movies, where the validation set and the test set contain 7,408 and 1,000 videos. (iv) ActivityNet Caption contains 20K YouTube videos annotated with 100K sentences. The training set contains 10K videos, and we use val1 set with 4.9K videos to report results. For MSRVTT and LSMDC, we perform standard text-to-video retrieval. For DiDeMo and ActivityNet Caption, we concatenate all the text captions in the same video as a single query and evaluate paragraph-to-video retrieval. For two tasks, we measure the performances by average recall at \\(\\mathrm{K(R@K)}\\) and Median Rank on zero-shot and fine-tune setups." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.42, + 0.468, + 0.502 + ], + "angle": 0, + "content": "Video Question Answering. (i) MSRVTT-QA [53] is built upon videos and captions from MSRVTT [56], which contains 10K videos with 243K open-ended questions and 1.5K answer candidates. (ii) MSVD [6] contains 50K question-answer pairs with 2423 answer candidates. We use standard train/val/test splits for the two tasks, and report accuracy." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.513, + 0.295, + 0.527 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.535, + 0.468, + 0.617 + ], + "angle": 0, + "content": "We initialize our video encoder by ViT-B/16 [42] and the text encoder by the first six BERT-Base layers [9]. For the cross-modal encoder, the self-attentionions in all 3 cross-modal attentions (W2P contains 1 and T2W contains 2) are initialized by the last 6 BERT-Base layers [9]. The model is trained end-to-end during both pre-training and fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.468, + 0.769 + ], + "angle": 0, + "content": "In pre-training, the feature dimension is set to 256 when calculating the contrastive losses and the temperature is set to 0.05. For the momentum queue, the momentum value is 0.995 and the size of the queue is 65,536. The above implementation details follow the recent work [25, 24] for a fair comparison. We pre-train the model on CC3M and WebVid-2M for 10 epochs on 8 NVIDIA A100 GPUs where the batch size is 128. We use AdamW [18] optimizer with a weight decay of 0.001 and betas (0.9, 0.98). The learning rate is first warmed-up to 1e-4 and then decays following a linear decay schedule." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.468, + 0.866 + ], + "angle": 0, + "content": "During fine-tuning text-to-video retrieval, We sample 20 frames and use HFS to preserve 8 frames to feed into the cross-modal encoder. The model is trained with both VTC and VTM losses, and we obtain similarity scores from the output of the VTM head during inference. For video question answering, we sample 32 frames per video and preserve 16 frames. Since MSRVTT-QA and MSVD-QA [53]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.222 + ], + "angle": 0, + "content": "are open-ended VQA, in which the answers are in free-form natural language, it is common to convert the task to a classification task by predicting the answer's label. We input the concatenation of the video and question [CLS] tokens into a two-layer MLP [9] for calculating the cross-entropy loss. All the fine-tuning experiments are conducted on 8 NVIDIA V100 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.234, + 0.665, + 0.248 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.892, + 0.297 + ], + "angle": 0, + "content": "We conduct comprehensive ablation studies to evaluate the effectiveness of the proposed trajectory-to-word (T2W) attention and Hierarchical Frame-Selector (HFS) module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.298, + 0.892, + 0.408 + ], + "angle": 0, + "content": "Comparing Methods. Base: We use a symmetric cross-modal encoder that contains patch-to-word (P2W) and word-to-patch (W2P) attentions. T2W: We replace P2W attention in Base by our T2W attention. MeanP: Another simple way to consider temporal knowledge is to mean pool the embeddings along the temporal axis. Specifically, we simply average \\(\\{\\pmb{y}_1,\\dots,\\pmb{y}_T\\}\\). These three ablations are implemented using the zero-shot setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.892, + 0.519 + ], + "angle": 0, + "content": "[L1,L2]: We insert frame selector layer into the L1-th and L2-th layers. F@T: We sample T frames into the model. F@T1-T2-T3: We use Hierarchical Frame Selector where \"F@T1-T2-T3\" denotes that T1 frames are originally input into the model and then T2 and T3 frames are respectively remained by the first and second frame selector layers. All these ablations are implemented using the fine-tuning setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.602 + ], + "angle": 0, + "content": "Quantitative Results. Table 1 compares the performances of diverse baselines. From this table, we can see that T2W outperforms Base, e.g., T2W achieves \\(3.6\\%\\) R@5 improvements on MSRVTT for zero-shot evaluation, which suggests that our T2W attention can exploit more temporal contexts to better solve video-language tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.892, + 0.755 + ], + "angle": 0, + "content": "Also, T2W achieves higher scores than MeanP on different tasks, e.g., T2W achieves \\(28.4\\%\\) of \\(\\mathbb{R}@\\mathbb{1}\\) score in DiDeMo zero-shot text-to-video retrieval task while MeanP only has \\(27.4\\%\\). Applying mean-pooling strategy indeed fuse all the temporal knowledge, however, simply averaging all \\(\\pmb{y}_t\\) also means that the contexts over the whole time axis are used, while lots of objects may only span a few frames and using all the temporal contexts may introduce trivial or even harmful noises. This proves that our T2W attention can capture more important cross-modal associations in this asymmetric cross-modal encoder case." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.867 + ], + "angle": 0, + "content": "We further analyze the impact of the layer settings and frame number on the Hierarchical Frame-Selector module. As shown in Table 2, frame selector in deep layers (e.g. 6-th and 12-th layers) brings better performances on both retrieval and QA tasks. Moving frame selector module into shallower layers deteriorates the scores. For example, the accuracy drops \\(0.9\\%\\) when the frame selector module is placed before the third layer. We hypothesize that discard" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.502, + 0.901 + ], + "angle": 0, + "content": "2509" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.12, + 0.509, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.237, + 0.23, + 0.404, + 0.24 + ], + "angle": 0, + "content": "(a) \"A girl practising her arrow tricks\"" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.123, + 0.892, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.23, + 0.776, + 0.24 + ], + "angle": 0, + "content": "(b) \"Two people play basketball\"" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.244, + 0.508, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.351, + 0.371, + 0.361 + ], + "angle": 0, + "content": "(c) \"Adult feeds baby with spoon\"" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.244, + 0.892, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.351, + 0.805, + 0.361 + ], + "angle": 0, + "content": "(d) \"The dog runs away and picks up the cone\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.367, + 0.893, + 0.393 + ], + "angle": 0, + "content": "Figure 5. Visualizations of the attention maps from cross-modal encoder. Sample (a) and (b) are from MSRVTT [56], (c) and (d) are from DiDeMo [16] retrieval dataset. TW-BERT attends to the patches related to given query word by Trajectory-to-Word attention." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.395, + 0.892, + 0.42 + ], + "angle": 0, + "content": "Table 1. Performances of various baselines. R@K and MedR respectively denote recall (\\%) with K retrieval efforts and median ranking for retrieved videos where higher R@K and lower MedR indicate better performance." + }, + { + "type": "table", + "bbox": [ + 0.151, + 0.42, + 0.812, + 0.502 + ], + "angle": 0, + "content": "
MethodMSRVTT-ZSDiDeMo-ZSMSVD-QA
R@1↑R@5↑R@10↑MedR↓R@1↑R@5↑R@10↑MedR↓Acc.
Base25.146.457.37.026.652.862.75.047.4
T2W26.850.059.95.028.452.964.54.048.2
MeanP25.847.958.06.027.453.164.05.048.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.513, + 0.471, + 0.538 + ], + "angle": 0, + "content": "Table 2. Performances comparison with different layer settings of the HFS in fine-tuning." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.538, + 0.462, + 0.642 + ], + "angle": 0, + "content": "
layersMSRVTT-FTMSVD-QA
R@1↑R@5↑R@10↑MedR↓Acc.
[2,4]36.763.274.93.046.2
[3,6]37.463.775.43.046.9
[4,8]38.164.676.23.047.8
[5,10]38.264.976.33.048.3
[6,12]38.465.176.63.048.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.647, + 0.47, + 0.672 + ], + "angle": 0, + "content": "Table 3. Performances comparison with different frame settings of the HFS in fine-tuning." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.672, + 0.466, + 0.76 + ], + "angle": 0, + "content": "
FrameMSRVTT-FTFrameMSVD-QA
R@1↑R@5↑R@10↑MedR↓Acc.
F@135.863.374.23.0F@847.2
F@4-2-135.963.273.93.0F@20-14-847.2
F@437.163.975.33.0F@1247.7
F@8-6-437.564.275.53.0F@24-18-1247.9
F@838.164.976.03.0F@1648.2
F@20-14-838.465.176.63.0F@32-24-1648.5
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.47, + 0.868 + ], + "angle": 0, + "content": "ing frames too early would result in a lack of temporal knowledge in subsequent ViT layers. We thus choose to insert the frame selector module in the 6-th and 12-th layers in the following experiments. In terms of frame number, as shown in Table 3, on the one hand, as the number of frame we sample increases, both retrieval and QA performance obtain improvements. For example, in MSRVTT" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.516, + 0.892, + 0.669 + ], + "angle": 0, + "content": "fine-tuning text-to-video retrieval task, F@20-14-8 outperforms F@8-6-4 by \\(0.9\\%\\) on R@1 or on MSVD video question answering task, F@32-24-16 outperforms F@24-18-12 by \\(0.6\\%\\), which suggests that more temporal knowledge benefit our model whether using uniform sampling or our proposed HFS. On the other hand, using HFS gets higher scores than uniform sampling, e.g., F@20-14-8 achieves \\(38.4\\%\\) of R@1 score in MSRVTT retrieval task while F@8 only has \\(38.1\\%\\), or on MSVD video question answering task, F@32-24-16 outperforms F@16 by \\(0.3\\%\\), which validates the power of HFS module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.893, + 0.868 + ], + "angle": 0, + "content": "Qualitative Results. We show the heat maps of the attentions of Base and TW-BERT in Figure 5. We see that TW-BERT can select the most relevant frames according to the whole text, then it implicitly form a trajectory among these frames for a given query word to avoid over-exploiting the trivial spatial contexts as in Base. For example, in (a), TW-BERT first discards the 1-st and 8-th frames which is completely irrelevant to the text, then tracks the hand of the girl in each frame that it keeps according to the query word \"practising\" while Base cannot avoid impact of the irrelevant frames, and in those relevant frames, it only attends to the larger while trivial regions about the whole body of the girl. Moreover, in (d), TW-BERT keeps the 6-th and 7-th frames for these two frames show the dog's action more" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.502, + 0.901 + ], + "angle": 0, + "content": "2510" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.122, + 0.892, + 0.159 + ], + "angle": 0, + "content": "Table 4. Experiments of text-to-video retrieval on MSRVTT, DiDeMo and LSMDC datasets. “#PT Pairs” lists the number of video-text pairs for pre-training. We show results with zero-shot evaluation (top) and fine-tuning evaluation (bottom). R@A is the average of R@1, R@5 and R@10." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.159, + 0.888, + 0.322 + ], + "angle": 0, + "content": "
Method#PT PairsDiDeMoLSMDCMSRVTT
R@1↑R@5↑R@10↑R@A↑MedR↓R@1↑R@5↑R@10↑R@A↑MedR↓R@1↑R@5↑R@10↑R@A↑MedR↓
Frozen [2]5.5M21.146.056.241.17.09.322.030.120.551.018.739.551.636.610.0
VIOLET [12]186M23.549.859.844.4------25.949.559.745.0-
OA-Trans [49]5.5M23.550.459.844.66.0-----23.447.555.642.28.0
ALPRO [24]5.5M23.847.357.943.06.0-----24.144.755.441.48.0
BridgeFormer [14]5.5M25.650.661.145.85.012.225.932.223.442.026.046.456.442.97.0
MILES [15]5.5M27.250.363.647.05.011.124.730.622.150.726.147.256.943.47.0
TW-BERT5.5M28.452.964.548.64.014.230.436.026.928.026.850.059.945.65.0
Frozen [2]5.5M31.059.872.454.43.015.030.839.828.520.031.059.570.553.73.0
VIOLET [12]186M32.662.874.756.7-16.136.641.231.3-34.563.073.457.0-
ALPRO [24]5.5M35.967.578.860.73.0-----33.960.773.255.93.0
OA-Trans [49]5.5M34.864.475.158.13.018.234.343.732.118.535.863.476.558.63.0
BridgeFormer [14]5.5M37.062.273.957.73.017.935.444.532.615.037.664.875.159.23.0
MILES [15]5.5M36.663.974.058.23.017.835.644.132.515.537.763.673.858.43.0
TW-BERT5.5M41.871.181.264.72.021.038.849.236.311.038.465.176.660.03.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.324, + 0.431, + 0.335 + ], + "angle": 0, + "content": "Table 5. ActivityNet Caption with fine-tuning setting." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.335, + 0.468, + 0.427 + ], + "angle": 0, + "content": "
Method#PT PairsR@1↑R@5↑R@10↑MedR↓
Dense [19]-14.032.0-34.0
FSE [60]-18.244.8-7.0
CE [30]-18.247.7-6.0
HSE [60]-20.549.3--
Clipbert [23]5.6M21.349.063.56.0
TW-BERT5.5M31.762.374.93.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.428, + 0.468, + 0.452 + ], + "angle": 0, + "content": "Table 6. Experiments of video question answering on MSRVTT and MSVD datasets in top-1 accuracy \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.453, + 0.467, + 0.603 + ], + "angle": 0, + "content": "
Method#PT PairsMSRVTTMSVD
Clipbert [23]5.6M37.4-
ALPRO [24]5.5M42.145.9
SINGULARITY [22]5.5M42.745.9
LGDN [33]15.2M43.1-
SSML [1]100M35.135.1
JustAsk [57]69M41.546.3
MERLOT [59]180M43.1-
VIOLET [12]186M43.947.9
TW-BERT5.5M43.648.5
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.603, + 0.469, + 0.644 + ], + "angle": 0, + "content": "clearly. Then TW-BERT attends to the part where the dog is in contact with the cone according to the query word \"picks\" while Base only focuses on the body of the dog." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.652, + 0.305, + 0.667 + ], + "angle": 0, + "content": "4.5. Comparisons with SOTA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.866 + ], + "angle": 0, + "content": "We compare TW-BERT with previous methods on two frequently applied tasks: video-text retrieval (VDTR) and video question answering (VDQA). Table 4 and 5 report the performances of VDTR on MSRVTT [56], DiDeMo [16], LSMDC [43], and ActivityNet Caption [19], respectively, where the former three datasets contain both zero-shot and fine-tuning setups and the last one only has fine-tuning setup. Table 6 reports the VDQA on MSRVTT [56] and MSVD [6]. Among the compared models, MILES [15], BridgeFormer [14], OA-Trans [49], Clipbert [23] and VIOLET [12] are SOTA models proposed in recently 1-2 years. Note that VIOLET [12] and ALPRO [24] distill knowledge from additional large-scale BERTs while we do not. Also, we show the number of pre-training video-text pairs in these" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.331, + 0.729, + 0.345 + ], + "angle": 0, + "content": "tables for more clear comparisons." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.51 + ], + "angle": 0, + "content": "From these tables, we can find that when the pre-training data is in the same scale, TW-BERT achieves the best performance compared with all the other models on both VDTR and VDQA. For example, on DiDeMo VDTR, TW-BERT outperforms BridgeFormer by \\(4.8\\%\\) on \\(\\mathbb{R}@\\mathbb{1}\\), or on MSVD VDQA, TW-BERT outperforms ALPRO by \\(2.6\\%\\). Moreover, compared with the models trained on much more data, TW-BERT can still achieve the best performances on various tasks, e.g., on LSMDC VDTR, TW-BERT outperforms VIOLET by \\(8.0\\%\\) on \\(\\mathbb{R}@\\mathbb{10}\\) or on MSRVTT VDQA, TW-BERT outperforms MERLOT [59] by \\(0.5\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.893, + 0.675 + ], + "angle": 0, + "content": "Note that the videos in LSMDC are longer than MSRVTT and DiDeMo, which means that the videos in this dataset contain more temporal contexts than the other datasets. Then as shown in Table 4, the improvements of TW-BERT over other SOTAs are larger than the improvements on the other datasets. For example, compared with BridgeFormer, TW-BERT has an average \\(3.5\\%\\) improvement in the zero-shot setting, while on DiDeMo dataset, the corresponding average improvement over MILES is only \\(1.6\\%\\). Such comparisons further validate the effectiveness of TW-BERT in exploiting temporal contexts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Among these SOTAs, only when compared with VIOLET, which uses an additional large-scale model DALLE [40] and 32 more times pre-training data than ours (180M VS. 5.5M), TW-BERT cannot comprehensively surpass VIOLET on all the tasks. For example, on MSRVTT VDQA, VIOLET achieves \\(0.3\\%\\) higher than TW-BERT, while such marginal improvements are got at the cost of much more training resources. Furthermore, TW-BERT still outperforms VIOLET on the other tasks, e.g., on DiDeMo VDTR, TW-BERT outperforms VIOLET by \\(9.2\\%\\) on R@1 or on MSVD VDQA, TW-BERT outperforms VIOLET by \\(0.6\\%\\). These comparisons confirm the effectiveness of the proposed TW-BERT." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.901 + ], + "angle": 0, + "content": "2511" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.125, + 0.196, + 0.14 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.149, + 0.473, + 0.304 + ], + "angle": 0, + "content": "We propose a novel Trajectory-Word BERT (TW-BERT) that builds Trajectory-to-Word alignments for solving video-language tasks. In particular, we introduce an asymmetric cross-modal encoder that contains word-to-patch (W2P) and Trajectory-to-Word (T2W) to capture cross-modal associations. Moreover, a novel Hierarchical Frame-Selector (HFS) module is proposed in the fine-tuning stage to filter out irrelevant frames to help the later T2W attention learn better trajectory-word alignments. Extensive experiments across diverse tasks confirm the effectiveness of the proposed TW-BERT." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.316, + 0.266, + 0.332 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.339, + 0.47, + 0.436 + ], + "angle": 0, + "content": "This work is supported by National Science Foundation of China (62206048), National Key R&D Program of China (2018AAA0100104, 2018AAA0100100), Natural Science Foundation of Jiangsu Province (BK20220819, BK20211164), and Young Elite Scientists Sponsorship Program of Jiangsu Association for Science and Technology Tj-2022-027." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.451, + 0.174, + 0.465 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.474, + 0.47, + 0.525 + ], + "angle": 0, + "content": "[1] Elad Amrani, Rami Ben-Ari, Daniel Rotman, and Alex Bronstein. 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In CVPR, page 8746-8755, 2020. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.127, + 0.47, + 0.811 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.9 + ], + "angle": 0, + "content": "2514" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_origin.pdf b/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..feb910f2dd6e0ba0d76870e7901b1647dc7a647b --- /dev/null +++ b/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/e49e204e-97bd-485d-8320-f15ff5bdec7b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:412150cd3a99dbc4354a00fe06be4d951980b559911d775799059d802d2411b8 +size 1373718 diff --git a/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/full.md b/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/full.md new file mode 100644 index 0000000000000000000000000000000000000000..78730cb7877be76ccf4ef5e1e4ec25989b603a84 --- /dev/null +++ b/2023/Learning Trajectory-Word Alignments for Video-Language Tasks/full.md @@ -0,0 +1,388 @@ +# Learning Trajectory-Word Alignments for Video-Language Tasks + +Xu Yang $^{1}$ Zhangzikang Li $^{1,2}$ Haiyang Xu $^{2*}$ Hanwang Zhang $^{3}$ Qinghao Ye $^{2}$ Chenliang Li $^{2}$ Ming Yan $^{2}$ Yu Zhang $^{1*}$ Fei Huang $^{2}$ Songfang Huang $^{2}$ + +$^{1}$ School of Computer Science & Engineering, Key Lab of New Generation Artificial Intelligence Technology & Its Interdisciplinary Applications (Ministry of Education), Southeast University + +$^{2}$ DAMO Academy, Alibaba Group $^{3}$ School of Computer Science & Engineering, Nanyang Technological University $\{\text{xuyang.palm, zhang.yu}\} @$ seu.edu.cn, lizhangzikang@gmail.com, $\{\text{shuofeng.xhy, yeqinghao.yqh, lcl193798, ym119608, f.huang, songfang.hsf}\} @$ alibaba-inc.com, hanwangzhang@ntu.edu.sg + +# Abstract + +In a video, an object usually appears as the trajectory, i.e., it spans over a few spatial but longer temporal patches, that contains abundant spatiotemporal contexts. However, modern Video-Language BERTs (VDL-BERTs) neglect this trajectory characteristic that they usually follow image-language BERTs (IL-BERTs) to deploy the patch-to-word (P2W) attention that may over-exploit trivial spatial contexts and neglect significant temporal contexts. To amend this, we propose a novel TW-BERT to learn Trajectory-Word alignment by a newly designed trajectory-to-word (T2W) attention for solving video-language tasks. Moreover, previous VDL-BERTs usually uniformly sample a few frames into the model while different trajectories have diverse graininess, i.e., some trajectories span longer frames and some span shorter, and using a few frames will lose certain useful temporal contexts. However, simply sampling more frames will also make pre-training infeasible due to the largely increased training burdens. To alleviate the problem, during the fine-tuning stage, we insert a novel Hierarchical Frame-Selector (HFS) module into the video encoder. HFS gradually selects the suitable frames conditioned on the text context for the later cross-modal encoder to learn better trajectory-word alignments. By the proposed T2W attention and HFS, our TW-BERT achieves SOTA performances on text-to-video retrieval tasks, and comparable performances on video question-answering tasks with some VDL-BERTs trained on much more data. The code will be available in the supplementary material. + +# 1. Introduction + +By witnessing the boom of BERT-like models in single domains, e.g., vision or language[52, 44, 21], researchers + +![](images/fa31efdfc99df2e7cad260027e5917e353d6a68c3ee30cb26f6c155a59d004a6.jpg) +(a) RoI based IL-BERT + +![](images/1cd54c442b2f25a3dc41004b99f27b470e1ccfdba412a0cd97d557d251e79fc9.jpg) +(b) Patch based IL-BERT + +![](images/b17a02425cbb3103d51c78e5ffbb5a8166bbbc6c3cad9072616e342b9d19f880.jpg) +(c) Patch based VDL-BERT + +![](images/cc26e38a9e129cb6d503c1a65683b3cef7b2c2d7fad8959f15794d4a848605ee.jpg) + +![](images/66d7dc9f3f0bf24dd78463c75b609f3bd40439b72ffec187f60fbcf86d90a5ee.jpg) +(d) TW-BERT Pretraining + +![](images/d70f7835cb0563a554a50a4dc6a98c5e02d30cdec9e855fbc466a4c4263de0ab.jpg) + +![](images/a590a57ecb7863d30a214386ea98688fcb1d3a28f03bfd4c2a7ffc596f303c6a.jpg) + +![](images/661c3d1393f1e05f3b81a318f6e587f8240dd14d7b0e96ba4a93cf114e10b154.jpg) +(e) TW-BERT Fine-Tuning + +![](images/8a118835a4ff3e8a2e56c07d14f72bc936e3b5690ac319f348b40bbfdfb26280.jpg) + +# A boy is playing basketball. + +Figure 1. The comparisons of five different ways to build object-word alignments. In (b), by patch-to-word (P2W) attention, implicit object-word alignment can be built, e.g., the "ball region" is aligned with basketball. While in (c), P2W attention may concentrate the attention of an object on only one frame, e.g., basketball only attends over the "ball region" of the first frame. (d) When pre-training TW-BERT, the trajectory of an object is constructed, e.g., the "ball trajectory" through 4 frames built. Note that we only use 4 frames during pre-training, we show 8 frames for comparing with (e) and the transparent ones denote that they are not input into the model. (e) When fine-tuning TW-BERT, we use HFS to select 4 frames from 8 and we can see that the selected frames are different from the uniformly sampled ones in (d). + +begin to build vision-language BERTs[3, 61, 10] for learning robust cross-modal associations. Compared with the images, videos provide more details for building robust associations, e.g., the spatiotemporal contexts in videos can + +better describe the actions. However, directly addressing dynamic videos may cost more storage and computation resources. To circumvent such huge cost, researchers first study image-language BERT (IL-BERT)[17, 25, 8, 27, 61] and then exploit the research fruits to build the challenging, while more pragmatic, video-language BERT (VDLBERT)[47, 2, 26, 36, 13, 35, 46, 37, 54, 51]. + +Pioneering techniques are directly inherited from IL-BERT into VDL-BERT, e.g., the image encoders are used to embed sampled video frames [23, 62]. However, since image encoders can hardly learn temporal contexts, the resultant VDL-BERTs will degrade to IL-BERT even if they are trained by video-text pairs. To ameliorate it, researchers apply the video encoders [32, 4, 12, 24] to embed spatiotemporal contexts. Though promising improvements are observed, these VDL-BERTs still neglect or ill-consider a significant factor in IL-BERT: the object-word alignment, which helps learn robust associations. + +To learn object-word alignments, as Figure 1(a) shows, researchers use an RoI-based extractor to embed an image into a series of RoI features [34, 27, 8]. However, this RoI-based extractor is offline trained by object detection with limited label inventory, which will weaken the IL-BERT since the extractor will not be updated during large-scale pre-training. To enable the end-to-end training, researchers substitute the RoI-based extractor with visual transformers whose outputs are a series of grid embeddings, which will be used to build the cross-modal connections. Although a single grid usually does not construct an integral object, fortunately, the widely applied patch-to-word (P2W) attention of IL-BERT can softly seek the salient visual regions for a given query word. Then the object-word alignments can still be built between this softly detected object and the word, e.g., as shown in Figure 1(b), the object "basketball" can be implicitly attended by the corresponding word query. + +Although the P2W attention remedies the loss of RoI-level features for learning object-word alignments in ILBERT, its effectiveness is weakened in the video case. This is because the objects usually act as the Trajectories which span a few spatial while multiple temporal grids in the videos. Thus, directly applying the P2W attention may over-exploit the trivial spatial contexts while neglecting the significant temporal contexts and then make the model attend to only one or two frames. Figure 1(c) shows this limitation that P2W attention only aligns the "ball" in the first frame to the word ball. + +To address this limitation, we propose to learn Trajectory-to-Word alignments to solve video-language tasks and name this model as TW-BERT. Specifically, such alignment is learnt by a novel designed trajectory-to-word T2W attention, which first uses the word as the query to seek the salient parts of each frame and the sought parts are sequenced to form the trajectory. Then the query word at + +tends over the trajectories again for capturing cross-modal associations. In this way, the trivial spatial regions are weakened and the temporal contexts will be strengthened, e.g., as shown in Figure 1(d), the attention weights of the word will be concentrated on the object trajectory instead of only one frame as in (c). In the implementation, we follow most VDL-BERTs to set up the network: two single-modal encoders for the video and text and one cross-modal encoder, which is sketched in Figure 2. For the cross-modal encoder, since our T2W attention does not have the same structure as the word-to-patch (W2P) attention, our cross-modal encoder is asymmetric. + +Moreover, previous VDL-BERTs usually uniformly sample a few frames into the model, which contains two drawbacks. Firstly, using a few frames may lose temporal context and secondly, uniform sampling can hardly capture the varying graininess of the trajectories, i.e., some trajectories span longer frames and some span shorter. However, simply sampling more frames will largely increase the pretraining burdens that are beyond the computation resources we own. To alleviate this problem, in the fine-tuning stage, we sample more frames into the video encoder while only keeping the most relevant frames according to the corresponding text by a novel designed Hierarchical Frame-Selector (HFS). For example, as shown in Figure 1(e), 4 frames are selected by HFS from the 8 uniformly sampled ones for learning trajectory-word alignment. Specifically, HFS inserts a few lightweight layers into the video encoder and these layers can gradually filter frames conditioned on the language context. In this way, HFS learns the coarse-grained trajectory-word alignments, i.e., framework alignments, to help the later T2W attention learn more fine-grained trajectory-word alignments. + +To sum up, our contributions are: + +- We propose a novel perspective to consider the videos that are composed of moving object trajectories, which may inspire the researchers to build more advanced VDL-BERTs. +- We propose a simple while effective T2W attention to learn Trajectory-to-Word alignments. +- We propose a novel hierarchical frame selector (HFS) in TW-BERT during fine-tuning to capture the varying graininess of the trajectory while not largely increasing the training burdens. +- We achieve SOTA performances compared with other VDL-BERTs trained by the same amount of data. + +# 2. Related Work + +# 2.1. Image-Language BERT (IL-BERT) + +Recently, various techniques have been proposed in ILBERT to learn vision-language connections. Most of them aim at capturing robust object-word alignments since such + +alignments construct the foundations of visual reasoning. In the beginning, a pre-trained Faster-RCNN [41] is used to extract a series of RoI poolings, where each one contains one or a few salient objects, to facilitate building object-word alignments [34, 48, 8, 27]. However, this Faster-RCNN is usually pre-trained by the object annotations from COCO [7] and VG [20], whose concept space is much narrower than the data used to train IL-BERT, which can be almost unlimedly collected from the websites. Moreover, this Faster-RCNN is not updated during the end-to-end training of the IL-BERT, which means that the visual encoder may hardly learn novel knowledge from the web-collected data. Thus the performances of these IL-BERTs are limited. + +To further release the potential of hugely web-collected data, the offline Faster RCNN is switched into vision Transformers [11, 32] and thus a homogeneous IL-BERT, i.e., all the components are transformer-based, is built, which is more easily trained end-to-end [34]. Compared with the RoI-based encoder, the vision Transformer outputs a series of patch embeddings and thus may lose object-level knowledge. To remedy such loss, various strategies are proposed to improve the vision-language alignments. For example, the align-before-fuse strategy [25] aligns the paired image-text embeddings before cross-modal fusion for facilitating the subsequent fusion. And the fine-grained contrastive objective [58] amplifies the local details for learning the object-word alignments. + +# 2.2. Video-Language BERT (VDL-BERT) + +Since the spatiotemporal contexts in videos can hardly be learnt by image extractors, only inheriting the techniques which are successful in IL-BERT to VDL-BERT is not enough. Thus, based on the fruits of IL-BERT, most VDL-BERTs aim at exploiting more spatiotemporal contexts to build cross-modal associations. One straightforward way is to learn such spatiotemporal contexts through video Transformers [4, 28]. Besides this, some more advanced techniques are proposed, e.g., VIOLET [12] tokenizes the dynamic video patches and predicts the labels of these tokens; BridgeFormer [14] erases the words (nouns or verbs) from the text and learn to match the visual embeddings queried by the erased words and the remained texts; or ALPRO [24] computes the similarities between the video embeddings with the generated entity prompts. TS2-Net [31] shifts token features and selects informative tokens in both temporal and spatial dimensions to produce the fine-grained spatial-temporal video representation. Although substantial improvements are observed, these methods use video patches in the cross-modal encoder, which neglects that an object usually acts as the trajectory in the videos, and thus they may over-exploit the trivial spatial contexts. To ameliorate this limitation, we propose TW-BERT to capture + +![](images/b5cbebcf78e78d96186340d5f804092d711148f2c73ec9fad719d656e61856ee.jpg) +Figure 2. The architecture of TW-BET, which contains two single-modal encoders and one asymmetric cross-modal encoder. Totally three losses in the grey blocks are used to train the whole model: $L_{vtc}$ , $L_{mlm}$ , and $L_{vtm}$ . Note that HFS is only used in the fine-tuning stage. + +trajectory-word alignments for more robust vision-language alignment. + +# 3. TW-BERT + +Figure 2 sketches TW-BERT, which has two single-modal encoders for embedding the video and text (cf. Sec. 3.1) and one cross-modal encoder for learning videolanguage associations (cf. Sec. 3.2). Different from the previous VDL-BERTs, our cross-modal encoder is an asymmetric one that contains a classic word-to-patch (W2P) attention and a novel proposed trajectory-to-word (T2W) attention (cf. Sec. 3.2) for learning trajectory-word alignments. In Sec. 3.3, we introduce how to use Hierarchical Frame-Selector (HFS) in the fine-tuning stage to gradually filter the frames for capturing coarse-grained frame-word alignments. Lastly, we introduce the losses used to train our TW-BERT in Sec. 3.4. + +# 3.1. Single-Modal Encoders + +Video Encoder. For a video, we sample a few $224 \times 224$ frames and input them into the 12-layer TimeSformer [4, 24] for embedding. TimeSformer first partitions each frame into $14 \times 14$ non-overlapping patches, which are flattened and fed to a linear projection layer to produce a sequence of patch tokens. Then TimeSformer applies self-attention along the temporal and spatial dimensions to calculate per-frame features. These features are further mean-pooled along the height and width dimensions. Learnable spatial positional embeddings are added to each video token in the same spatial location of different frames. The final output embedding set is $\mathbf{V} = \{\mathbf{v}_{cls}, \mathbf{v}_1, \dots, \mathbf{v}_{N_V - 1}\}$ , where $\mathbf{v}_n \in \mathbb{R}^d$ and $\mathbf{v}_{cls}$ is the global [CLS] embedding. + +Text Encoder. For a text, we use a 6-layer transformer to embed it and the output is $\mathbf{X} = \{\pmb{x}_{cls},\pmb{x}_1,\dots,\pmb{x}_{N_X - 1}\}$ where $\pmb{x}_n\in \mathbb{R}^d$ and $\pmb{x}_{cls}$ is the global [CLS] embedding. Similar to the video encoder, we also add positional embed + +dings to the text tokens. + +# 3.2. Asymmetric Cross-Modal Encoder + +After embedding videos and texts, a cross-modal encoder is used to fuse them by calculating bi-directional associations: vision-to-language and language-to-vision. No matter what the direction is, the motivation is to assign semantic knowledge from one domain to another. Since a single word contains integral semantic knowledge, we follow previous VDL-BERT [24, 2, 23, 47] to set a traditional word-to-patch (W2P) attention to assign the words to a patch. However, different from the word, only the object instead of one grid conveys integral semantic knowledge. In videos, an object usually spans both spatial and temporal axes and thus the previously used patch-to-word (P2W) attention may fail to transfer the semantic knowledge. To amend this, we design a novel Trajectory-to-Word (T2W) attention for transferring semantic knowledge from videos to texts. Since W2P and T2W attentions have diverse structures, our cross-encoder is asymmetric. + +Specifically, both W2P and T2W attentions are built on the Multi-Head Attention (MHA) operation, here we first formalize MHA and then introduce how to use it to build W2P and T2W attentions. Formally, MHA is*: + +$$ +\begin{array}{c} \text {I n p u t :} \quad \mathcal {Q}, \mathcal {K}, \mathcal {V} \end{array} +$$ + +$$ +\mathbf {A t t}: \quad \mathcal {A} _ {i} = \operatorname {S o f t m a x} (\frac {\mathcal {Q W} _ {i} ^ {Q} \left(\mathcal {K W} _ {i} ^ {K}\right) ^ {T}}{\sqrt {d}}) +$$ + +$$ +\mathbf {H e a d}: \quad \mathcal {H} _ {i} = \mathcal {A} _ {i} \mathcal {V W} _ {i} ^ {V}, \tag {1} +$$ + +$$ +\text {M u l t i - H e a d}: \quad \mathcal {H} = \left[ \mathcal {H} _ {1}, \mathcal {H} _ {2},..., \mathcal {H} _ {h} \right] \mathcal {W} ^ {H}, +$$ + +$$ +\text {O u t p u t}: \mathcal {Z} = \mathrm {L N} (\mathcal {H} + \mathcal {Q}), +$$ + +where $\mathcal{W}_i^Q, \mathcal{W}_i^K, \mathcal{W}_i^V, \mathcal{W}_i^H$ are all trainable matrices; $h$ is the head number and $d_h = d / h$ ; $\mathcal{A}_i$ is the $i$ -th attention matrix corresponding to the $i$ -th head matrix; $[\cdot]$ is the concatenation operation; and LN is the Layer Normalization. + +Word-to-Patch (W2P) Attention. To calculate the W2P alignment, we apply the conventional W2P attention [24]: + +$$ +\mathbf {Z} _ {W 2 P} = \mathbf {M H A} (\mathcal {Q} = \mathbf {V}, \mathcal {K} = \mathcal {V} = \mathbf {X}), \tag {2} +$$ + +where $\mathbf{V} \in \mathbb{R}^{N_V \times D}$ , $\mathbf{X} \in \mathbb{R}^{N_X \times D}$ are respectively video and word embedding sets got from two single-modal encoders. By setting the query $\mathcal{Q}$ to the video patch embeddings, Eq. (2) learns to assign suitable words to each video patch and thus captures the W2P alignment. + +Trajectory-to-Word (T2W) Attention. As shown in Figure. 3 (b), we propose the T2W attention that uses two steps to learn the T2W alignment: it first constructs a trajectory for a given word and then uses the word as the query to attend over the trajectory for capturing the associations. For + +![](images/b57d3edb8a443743f6444b3a072a33e602ecc73b2ec55405ff7ddab19f1ca6af.jpg) +Figure 3. The comparisons between Patch-to-Word (P2W) and Trajectory-to-Word (T2W) attentions, where the green block denotes a query word and the blue blocks denote the video patches. In P2W attention, the word attends over all the video patches and may only concentrate on one frame, while in T2W attention, the salient red parts of each frame are found to construct a trajectory, which are connected by the red lines, $e.g., y_1, y_2, y_3$ . + +![](images/015138560146499c8ae8b166bf94e72b334e605009becc9ae30284f053d959e6.jpg) + +![](images/616dafaae6cb8805152b670366c46a7e841eb366cf41300c761780949cb9565d.jpg) + +convenience, we introduce how the T2W attention calculates the fusion embedding $z_{T2W}$ for a single word $x$ and it is straightforward to extend it to a sequence of the words. + +In the first step, T2W attention uses $x$ as the query to find the salient parts for each frame and then sequence these parts to construct the trajectory. Assuming $V_{t}$ is the embedding set of the $t$ -th frame, the salient part $y_{t}$ is got as: + +$$ +\boldsymbol {y} _ {t} = \mathbf {M H A} (\mathcal {Q} = \boldsymbol {x}, \mathcal {K} = \mathcal {V} = \boldsymbol {V} _ {t}). \tag {3} +$$ + +Then the salient parts at different time frames construct a continuous flow $\mathbf{Y} = \{\pmb{y}_1, \dots, \pmb{y}_T\}$ , which is the trajectory of the given word. + +In the second step, to get the trajectory-to-word fusion embedding $z_{T2W}$ , we treat $x$ as the query again while using the trajectory $Y$ as the key and value in MHA: + +$$ +\boldsymbol {z} _ {T 2 W} = \mathbf {M H A} (\mathcal {Q} = \boldsymbol {x}, \mathcal {K} = \mathcal {V} = \boldsymbol {Y}). \tag {4} +$$ + +By Eq. (3), T2W attention finds the salient parts for the given word at each frame, which enforces Eq. (4) to attend over the continuous frames instead of concentrating the attention only on one or some episodic frames as the previous P2W attentions. In this way, the whole T2W block exploits more temporal contexts to build vision-language associations, which facilitates the video reasoning tasks that usually require the correct recognition of the temporal patterns. Figure. 3 compares P2W and T2W attentions. + +# 3.3. Hierarchical Frame-Selector + +During fine-tuning, to improve the performance, previous studies tend to sample more frames than pre-training for introducing more temporal information. However, on the one hand, using too many frames will dramatically increase the computational resources, which causes infeasible training. On the other hand, in a video, different trajectories have varying graininess, e.g., some trajectories may cover longer frames and some cover shorter. In this way, uniform sampling may introduce redundant temporal information for these longer trajectories and deficient information for the shorter ones. Interestingly, the time duration of the trajectory is also reflected in the corresponding text. In this way, we can use the text to choose suitable frames and then + +![](images/8f235540be5a61c6dd1ad91e916d6695bde2a641002ad627ca1ab977f00605c9.jpg) +Figure 4. The architecture of the proposed Hierarchical Frame-Selector. At beginning, four frames are input into the video encoder and the first frame selector behind the 6-th layer filters out the 2-nd frame. At last, only the tokens of the 1-st and 4-th frames are preserved. + +only input them into the cross-modal attention for learning trajectory-word alignments. + +Motivated by this, we propose a novel Hierarchical Frame-Selector (HFS) that can gradually select the most relevant video frames to reduce the computational burdens while providing more temporal knowledge. Figure 4 illustrates the architecture of our proposed frame selector module. HFS contains a few frame selector layers which have the same structure with different parameters. For each frame selector layer, given a sequence of video frame [CLS] tokens $V_{cls} = \{v_{cls}^{1}, v_{cls}^{2}, \dots, v_{cls}^{T}\} \in \mathbb{R}^{T \times D}$ , we concatenate the text [CLS] embedding $x_{cls}$ with each $v_{cls}^{t}$ : $f_{t} = [v_{cls}^{t}, x_{cls}] \in \mathbb{R}^{2D} (1 \leq t \leq T)$ and feed them into a scorer network including a FC layer and a softmax layer: + +$$ +\boldsymbol {s} = \operatorname {S o f t m a x} (F C (\boldsymbol {f})) \in \mathbb {R} ^ {T \times 1}. \tag {5} +$$ + +Here, $T$ denotes the number of frames input into the video encoder, and $s \in \mathbb{R}^T$ is the score vector of $T$ frames. Then for this frame selector, we keep the tokens of $k$ frames with the top- $k$ $s_t$ for the further embedding in the subsequent video Transformer layers. During training, we employ the perturbed maximum method [5] to construct a differentiable Top-K operator. In the video encoder, we totally insert 2 selector layers and insert them in the 6-th and 12-th layers as in Figure 4. + +# 3.4. Training Objectives + +To train TW-BERT, as the grey blocks shown in Figure 2, we totally use three losses which are masked language modeling (MLM), video-text matching (VTM), and video-text contrastive loss (VTC). + +Masked language Modeling (MLM) [26, 24, 12, 50]. MLM aims to predict the masked word tokens given both the video and the text contexts. To get it, we first randomly replace the input text tokens with the [MASK] token with a probability of $15\%$ and then use the [MASK] embedding output from the cross-modal encoder to predict the masked word by calculating a cross-entropy loss: + +$$ +L _ {M L M} = \mathbb {E} _ {(V, \hat {X}) \sim D} \mathrm {H} \left(y ^ {m s k}, p ^ {m s k} (V, \hat {X})\right) \tag {6} +$$ + +where $\hat{X}$ is the masked text, $\mathrm{H}$ is the cross-entropy loss, $y^{msk} / p^{msk}$ are the ground-truth/predicted masked tokens. + +Video-text Matching (VTM) [24, 12, 50]. VTM calculates whether the given video and text are matched or not. To get it, for a given video-text pair, we first randomly replace the + +text with the ones from a different video in the same batch. Then we concatenate the video and text [CLS] embeddings output from the cross-modal encoder and input the concatenated embedding into a binary classifier to judge whether the given video-text pair is matched or not: + +$$ +L _ {V T M} = \mathbb {E} _ {(V, X) \sim D} \mathrm {H} \left(y ^ {v t m}, p ^ {v t m} (V, X)\right) \tag {7} +$$ + +where $y^{vtm} / p^{vtm}(V,X)$ are the ground-truth/predicted values indexing whether $V$ and $X$ are matched or not. + +Video-text Contrastive (VTC) [24, 50, 49, 14, 15, 2, 29]. As detailed in Section 3, VTC contrasts the outputs of two single-modal encoders to pull close their embedding space to help the subsequent cross-modal encoder build more robust vision-language associations. Suppose $s_{ij}$ denotes the similarity score of the $i$ -th video and the $j$ -th text, for each video and text, we calculate the softmax-normalized video-to-text and video-to-image similarity as: + +$$ +p _ {i j} ^ {v 2 t} (V) = \frac {\exp \left(s _ {i j} / \tau\right)}{\sum_ {j} \exp \left(s _ {i j} / \tau\right)}, p _ {i j} ^ {t 2 v} (X) = \frac {\exp \left(s _ {i j} / \tau\right)}{\sum_ {i} \exp \left(s _ {i j} / \tau\right)} \tag {8} +$$ + +where $\tau$ is a learnable temperature parameter. Let $y^{v2t}(V)$ and $y^{t2v}(X)$ denote the ground-truth one-hot similarity. This loss contains two symmetric parts, where the left term forces the $i$ -th text embedding to be close to the $i$ -th video embedding compared with the other texts and the right term has a similar effect: + +$$ +L _ {V T C} = +$$ + +$$ +\frac {1}{2} \mathbb {E} _ {(V, X) \sim D} [ \mathrm {H} (y ^ {v 2 t} (V), p ^ {v 2 t} (V)) + \mathrm {H} (y ^ {t 2 v} (X), p ^ {t 2 v} (X)) ] \tag {9} +$$ + +In the implementation, we follow [25] to use the momentum queue as a continuously-evolving teacher to provide more negative samples. + +# 4. Experiments + +# 4.1. Pre-training Dataset + +Following recent work [24, 14, 15, 49, 2], we pre-train TW-BERT on Google Conceptual Captions (CC3M) [45] containing 3.3M image-text pairs and WebVid-2M [2] containing 2.5M video-text pairs. For CC3M, the image is treated as a one-frame video data during pre-training. Note that due to the limited storage and computation resources, we do not use some much larger datasets like HowTo100M [38] containing 136M video-text pairs as [26, + +55]. Also, we do not distill knowledge from CLIP [39], which is pre-trained on 400M image-text pairs, as [36]. + +# 4.2. Downstream Tasks + +Text-to-Video Retrieval. (i) MSRVTT contains 10K YouTube videos with 200K descriptions. We follow [56] to use 9K train+val videos for training and report results on the 1K test split. (ii) DiDeMo [16] contains 10K Flickr videos annotated with 40K sentences. (iii) LSMDC consists of 118,081 video clips sourced from 202 movies, where the validation set and the test set contain 7,408 and 1,000 videos. (iv) ActivityNet Caption contains 20K YouTube videos annotated with 100K sentences. The training set contains 10K videos, and we use val1 set with 4.9K videos to report results. For MSRVTT and LSMDC, we perform standard text-to-video retrieval. For DiDeMo and ActivityNet Caption, we concatenate all the text captions in the same video as a single query and evaluate paragraph-to-video retrieval. For two tasks, we measure the performances by average recall at $\mathrm{K(R@K)}$ and Median Rank on zero-shot and fine-tune setups. + +Video Question Answering. (i) MSRVTT-QA [53] is built upon videos and captions from MSRVTT [56], which contains 10K videos with 243K open-ended questions and 1.5K answer candidates. (ii) MSVD [6] contains 50K question-answer pairs with 2423 answer candidates. We use standard train/val/test splits for the two tasks, and report accuracy. + +# 4.3. Implementation Details + +We initialize our video encoder by ViT-B/16 [42] and the text encoder by the first six BERT-Base layers [9]. For the cross-modal encoder, the self-attentionions in all 3 cross-modal attentions (W2P contains 1 and T2W contains 2) are initialized by the last 6 BERT-Base layers [9]. The model is trained end-to-end during both pre-training and fine-tuning. + +In pre-training, the feature dimension is set to 256 when calculating the contrastive losses and the temperature is set to 0.05. For the momentum queue, the momentum value is 0.995 and the size of the queue is 65,536. The above implementation details follow the recent work [25, 24] for a fair comparison. We pre-train the model on CC3M and WebVid-2M for 10 epochs on 8 NVIDIA A100 GPUs where the batch size is 128. We use AdamW [18] optimizer with a weight decay of 0.001 and betas (0.9, 0.98). The learning rate is first warmed-up to 1e-4 and then decays following a linear decay schedule. + +During fine-tuning text-to-video retrieval, We sample 20 frames and use HFS to preserve 8 frames to feed into the cross-modal encoder. The model is trained with both VTC and VTM losses, and we obtain similarity scores from the output of the VTM head during inference. For video question answering, we sample 32 frames per video and preserve 16 frames. Since MSRVTT-QA and MSVD-QA [53] + +are open-ended VQA, in which the answers are in free-form natural language, it is common to convert the task to a classification task by predicting the answer's label. We input the concatenation of the video and question [CLS] tokens into a two-layer MLP [9] for calculating the cross-entropy loss. All the fine-tuning experiments are conducted on 8 NVIDIA V100 GPUs. + +# 4.4. Ablation Studies + +We conduct comprehensive ablation studies to evaluate the effectiveness of the proposed trajectory-to-word (T2W) attention and Hierarchical Frame-Selector (HFS) module. + +Comparing Methods. Base: We use a symmetric cross-modal encoder that contains patch-to-word (P2W) and word-to-patch (W2P) attentions. T2W: We replace P2W attention in Base by our T2W attention. MeanP: Another simple way to consider temporal knowledge is to mean pool the embeddings along the temporal axis. Specifically, we simply average $\{\pmb{y}_1,\dots,\pmb{y}_T\}$ . These three ablations are implemented using the zero-shot setting. + +[L1,L2]: We insert frame selector layer into the L1-th and L2-th layers. F@T: We sample T frames into the model. F@T1-T2-T3: We use Hierarchical Frame Selector where "F@T1-T2-T3" denotes that T1 frames are originally input into the model and then T2 and T3 frames are respectively remained by the first and second frame selector layers. All these ablations are implemented using the fine-tuning setting. + +Quantitative Results. Table 1 compares the performances of diverse baselines. From this table, we can see that T2W outperforms Base, e.g., T2W achieves $3.6\%$ R@5 improvements on MSRVTT for zero-shot evaluation, which suggests that our T2W attention can exploit more temporal contexts to better solve video-language tasks. + +Also, T2W achieves higher scores than MeanP on different tasks, e.g., T2W achieves $28.4\%$ of $\mathbb{R}@\mathbb{1}$ score in DiDeMo zero-shot text-to-video retrieval task while MeanP only has $27.4\%$ . Applying mean-pooling strategy indeed fuse all the temporal knowledge, however, simply averaging all $\pmb{y}_t$ also means that the contexts over the whole time axis are used, while lots of objects may only span a few frames and using all the temporal contexts may introduce trivial or even harmful noises. This proves that our T2W attention can capture more important cross-modal associations in this asymmetric cross-modal encoder case. + +We further analyze the impact of the layer settings and frame number on the Hierarchical Frame-Selector module. As shown in Table 2, frame selector in deep layers (e.g. 6-th and 12-th layers) brings better performances on both retrieval and QA tasks. Moving frame selector module into shallower layers deteriorates the scores. For example, the accuracy drops $0.9\%$ when the frame selector module is placed before the third layer. We hypothesize that discard + +![](images/275f77327caa477810a45dde9f8bd76e5bed480d8d25a36ed627c809214224c7.jpg) +(a) "A girl practising her arrow tricks" + +![](images/19d8d231a44f77172aac4d94ebf6f42f15869fce9464e1acb75f4f2dc6a8d9fd.jpg) +(b) "Two people play basketball" + +![](images/3f8ee20b307dc49c32b0c2cffa27004d52170b8c8503b5f34f0f9e074031866c.jpg) +(c) "Adult feeds baby with spoon" +Table 1. Performances of various baselines. R@K and MedR respectively denote recall (\%) with K retrieval efforts and median ranking for retrieved videos where higher R@K and lower MedR indicate better performance. + +![](images/dec8cda2e68dfd55ec6c745614d6af8c8f2dd483a034b7202a4f2477fb2aa326.jpg) +(d) "The dog runs away and picks up the cone" +Figure 5. Visualizations of the attention maps from cross-modal encoder. Sample (a) and (b) are from MSRVTT [56], (c) and (d) are from DiDeMo [16] retrieval dataset. TW-BERT attends to the patches related to given query word by Trajectory-to-Word attention. + +
MethodMSRVTT-ZSDiDeMo-ZSMSVD-QA
R@1↑R@5↑R@10↑MedR↓R@1↑R@5↑R@10↑MedR↓Acc.
Base25.146.457.37.026.652.862.75.047.4
T2W26.850.059.95.028.452.964.54.048.2
MeanP25.847.958.06.027.453.164.05.048.0
+ +Table 2. Performances comparison with different layer settings of the HFS in fine-tuning. + +
layersMSRVTT-FTMSVD-QA
R@1↑R@5↑R@10↑MedR↓Acc.
[2,4]36.763.274.93.046.2
[3,6]37.463.775.43.046.9
[4,8]38.164.676.23.047.8
[5,10]38.264.976.33.048.3
[6,12]38.465.176.63.048.5
+ +Table 3. Performances comparison with different frame settings of the HFS in fine-tuning. + +
FrameMSRVTT-FTFrameMSVD-QA
R@1↑R@5↑R@10↑MedR↓Acc.
F@135.863.374.23.0F@847.2
F@4-2-135.963.273.93.0F@20-14-847.2
F@437.163.975.33.0F@1247.7
F@8-6-437.564.275.53.0F@24-18-1247.9
F@838.164.976.03.0F@1648.2
F@20-14-838.465.176.63.0F@32-24-1648.5
+ +ing frames too early would result in a lack of temporal knowledge in subsequent ViT layers. We thus choose to insert the frame selector module in the 6-th and 12-th layers in the following experiments. In terms of frame number, as shown in Table 3, on the one hand, as the number of frame we sample increases, both retrieval and QA performance obtain improvements. For example, in MSRVTT + +fine-tuning text-to-video retrieval task, F@20-14-8 outperforms F@8-6-4 by $0.9\%$ on R@1 or on MSVD video question answering task, F@32-24-16 outperforms F@24-18-12 by $0.6\%$ , which suggests that more temporal knowledge benefit our model whether using uniform sampling or our proposed HFS. On the other hand, using HFS gets higher scores than uniform sampling, e.g., F@20-14-8 achieves $38.4\%$ of R@1 score in MSRVTT retrieval task while F@8 only has $38.1\%$ , or on MSVD video question answering task, F@32-24-16 outperforms F@16 by $0.3\%$ , which validates the power of HFS module. + +Qualitative Results. We show the heat maps of the attentions of Base and TW-BERT in Figure 5. We see that TW-BERT can select the most relevant frames according to the whole text, then it implicitly form a trajectory among these frames for a given query word to avoid over-exploiting the trivial spatial contexts as in Base. For example, in (a), TW-BERT first discards the 1-st and 8-th frames which is completely irrelevant to the text, then tracks the hand of the girl in each frame that it keeps according to the query word "practising" while Base cannot avoid impact of the irrelevant frames, and in those relevant frames, it only attends to the larger while trivial regions about the whole body of the girl. Moreover, in (d), TW-BERT keeps the 6-th and 7-th frames for these two frames show the dog's action more + +Table 4. Experiments of text-to-video retrieval on MSRVTT, DiDeMo and LSMDC datasets. “#PT Pairs” lists the number of video-text pairs for pre-training. We show results with zero-shot evaluation (top) and fine-tuning evaluation (bottom). R@A is the average of R@1, R@5 and R@10. + +
Method#PT PairsDiDeMoLSMDCMSRVTT
R@1↑R@5↑R@10↑R@A↑MedR↓R@1↑R@5↑R@10↑R@A↑MedR↓R@1↑R@5↑R@10↑R@A↑MedR↓
Frozen [2]5.5M21.146.056.241.17.09.322.030.120.551.018.739.551.636.610.0
VIOLET [12]186M23.549.859.844.4------25.949.559.745.0-
OA-Trans [49]5.5M23.550.459.844.66.0-----23.447.555.642.28.0
ALPRO [24]5.5M23.847.357.943.06.0-----24.144.755.441.48.0
BridgeFormer [14]5.5M25.650.661.145.85.012.225.932.223.442.026.046.456.442.97.0
MILES [15]5.5M27.250.363.647.05.011.124.730.622.150.726.147.256.943.47.0
TW-BERT5.5M28.452.964.548.64.014.230.436.026.928.026.850.059.945.65.0
Frozen [2]5.5M31.059.872.454.43.015.030.839.828.520.031.059.570.553.73.0
VIOLET [12]186M32.662.874.756.7-16.136.641.231.3-34.563.073.457.0-
ALPRO [24]5.5M35.967.578.860.73.0-----33.960.773.255.93.0
OA-Trans [49]5.5M34.864.475.158.13.018.234.343.732.118.535.863.476.558.63.0
BridgeFormer [14]5.5M37.062.273.957.73.017.935.444.532.615.037.664.875.159.23.0
MILES [15]5.5M36.663.974.058.23.017.835.644.132.515.537.763.673.858.43.0
TW-BERT5.5M41.871.181.264.72.021.038.849.236.311.038.465.176.660.03.0
+ +Table 5. ActivityNet Caption with fine-tuning setting. + +
Method#PT PairsR@1↑R@5↑R@10↑MedR↓
Dense [19]-14.032.0-34.0
FSE [60]-18.244.8-7.0
CE [30]-18.247.7-6.0
HSE [60]-20.549.3--
Clipbert [23]5.6M21.349.063.56.0
TW-BERT5.5M31.762.374.93.0
+ +Table 6. Experiments of video question answering on MSRVTT and MSVD datasets in top-1 accuracy $(\%)$ + +
Method#PT PairsMSRVTTMSVD
Clipbert [23]5.6M37.4-
ALPRO [24]5.5M42.145.9
SINGULARITY [22]5.5M42.745.9
LGDN [33]15.2M43.1-
SSML [1]100M35.135.1
JustAsk [57]69M41.546.3
MERLOT [59]180M43.1-
VIOLET [12]186M43.947.9
TW-BERT5.5M43.648.5
+ +clearly. Then TW-BERT attends to the part where the dog is in contact with the cone according to the query word "picks" while Base only focuses on the body of the dog. + +# 4.5. Comparisons with SOTA + +We compare TW-BERT with previous methods on two frequently applied tasks: video-text retrieval (VDTR) and video question answering (VDQA). Table 4 and 5 report the performances of VDTR on MSRVTT [56], DiDeMo [16], LSMDC [43], and ActivityNet Caption [19], respectively, where the former three datasets contain both zero-shot and fine-tuning setups and the last one only has fine-tuning setup. Table 6 reports the VDQA on MSRVTT [56] and MSVD [6]. Among the compared models, MILES [15], BridgeFormer [14], OA-Trans [49], Clipbert [23] and VIOLET [12] are SOTA models proposed in recently 1-2 years. Note that VIOLET [12] and ALPRO [24] distill knowledge from additional large-scale BERTs while we do not. Also, we show the number of pre-training video-text pairs in these + +tables for more clear comparisons. + +From these tables, we can find that when the pre-training data is in the same scale, TW-BERT achieves the best performance compared with all the other models on both VDTR and VDQA. For example, on DiDeMo VDTR, TW-BERT outperforms BridgeFormer by $4.8\%$ on $\mathbb{R}@\mathbb{1}$ , or on MSVD VDQA, TW-BERT outperforms ALPRO by $2.6\%$ . Moreover, compared with the models trained on much more data, TW-BERT can still achieve the best performances on various tasks, e.g., on LSMDC VDTR, TW-BERT outperforms VIOLET by $8.0\%$ on $\mathbb{R}@\mathbb{10}$ or on MSRVTT VDQA, TW-BERT outperforms MERLOT [59] by $0.5\%$ . + +Note that the videos in LSMDC are longer than MSRVTT and DiDeMo, which means that the videos in this dataset contain more temporal contexts than the other datasets. Then as shown in Table 4, the improvements of TW-BERT over other SOTAs are larger than the improvements on the other datasets. For example, compared with BridgeFormer, TW-BERT has an average $3.5\%$ improvement in the zero-shot setting, while on DiDeMo dataset, the corresponding average improvement over MILES is only $1.6\%$ . Such comparisons further validate the effectiveness of TW-BERT in exploiting temporal contexts. + +Among these SOTAs, only when compared with VIOLET, which uses an additional large-scale model DALLE [40] and 32 more times pre-training data than ours (180M VS. 5.5M), TW-BERT cannot comprehensively surpass VIOLET on all the tasks. For example, on MSRVTT VDQA, VIOLET achieves $0.3\%$ higher than TW-BERT, while such marginal improvements are got at the cost of much more training resources. Furthermore, TW-BERT still outperforms VIOLET on the other tasks, e.g., on DiDeMo VDTR, TW-BERT outperforms VIOLET by $9.2\%$ on R@1 or on MSVD VDQA, TW-BERT outperforms VIOLET by $0.6\%$ . These comparisons confirm the effectiveness of the proposed TW-BERT. + +# 5. Conclusion + +We propose a novel Trajectory-Word BERT (TW-BERT) that builds Trajectory-to-Word alignments for solving video-language tasks. In particular, we introduce an asymmetric cross-modal encoder that contains word-to-patch (W2P) and Trajectory-to-Word (T2W) to capture cross-modal associations. Moreover, a novel Hierarchical Frame-Selector (HFS) module is proposed in the fine-tuning stage to filter out irrelevant frames to help the later T2W attention learn better trajectory-word alignments. Extensive experiments across diverse tasks confirm the effectiveness of the proposed TW-BERT. + +# 6. Acknowledgements + +This work is supported by National Science Foundation of China (62206048), National Key R&D Program of China (2018AAA0100104, 2018AAA0100100), Natural Science Foundation of Jiangsu Province (BK20220819, BK20211164), and Young Elite Scientists Sponsorship Program of Jiangsu Association for Science and Technology Tj-2022-027. + +# References + +[1] Elad Amrani, Rami Ben-Ari, Daniel Rotman, and Alex Bronstein. Noise estimation using density estimation for self-supervised multimodal learning. In AAAI, pages 6644-6652, 2021. 8 +[2] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In Proceedings of the IEEE/CVF International Conference on Computer Vision, page 1728-1738, 2021. 2, 4, 5, 8 +[3] Hangbo Bao, Li Dong, and Furu Wei. Beit: Bert pre-training of image transformers. arXiv preprint arXiv:2106.08254, 2021. 1 +[4] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. 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+ "type": "image_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 362, + 522, + 470, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 522, + 470, + 533 + ], + "spans": [ + { + "bbox": [ + 362, + 522, + 470, + 533 + ], + "type": "text", + "content": "A boy is playing basketball." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 296, + 537, + 530, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 537, + 530, + 676 + ], + "spans": [ + { + "bbox": [ + 296, + 537, + 530, + 676 + ], + "type": "text", + "content": "Figure 1. The comparisons of five different ways to build object-word alignments. In (b), by patch-to-word (P2W) attention, implicit object-word alignment can be built, e.g., the \"ball region\" is aligned with basketball. While in (c), P2W attention may concentrate the attention of an object on only one frame, e.g., basketball only attends over the \"ball region\" of the first frame. (d) When pre-training TW-BERT, the trajectory of an object is constructed, e.g., the \"ball trajectory\" through 4 frames built. Note that we only use 4 frames during pre-training, we show 8 frames for comparing with (e) and the transparent ones denote that they are not input into the model. (e) When fine-tuning TW-BERT, we use HFS to select 4 frames from 8 and we can see that the selected frames are different from the uniformly sampled ones in (d)." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "type": "text", + "content": "begin to build vision-language BERTs[3, 61, 10] for learning robust cross-modal associations. Compared with the images, videos provide more details for building robust associations, e.g., the spatiotemporal contexts in videos can" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 71 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "spans": [ + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 719, + 135, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 719, + 135, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 719, + 135, + 730 + ], + "type": "text", + "content": "*Corresponding authors." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "2504" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 188 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 188 + ], + "type": "text", + "content": "better describe the actions. However, directly addressing dynamic videos may cost more storage and computation resources. To circumvent such huge cost, researchers first study image-language BERT (IL-BERT)[17, 25, 8, 27, 61] and then exploit the research fruits to build the challenging, while more pragmatic, video-language BERT (VDLBERT)[47, 2, 26, 36, 13, 35, 46, 37, 54, 51]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 189, + 280, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 189, + 280, + 318 + ], + "spans": [ + { + "bbox": [ + 45, + 189, + 280, + 318 + ], + "type": "text", + "content": "Pioneering techniques are directly inherited from IL-BERT into VDL-BERT, e.g., the image encoders are used to embed sampled video frames [23, 62]. However, since image encoders can hardly learn temporal contexts, the resultant VDL-BERTs will degrade to IL-BERT even if they are trained by video-text pairs. To ameliorate it, researchers apply the video encoders [32, 4, 12, 24] to embed spatiotemporal contexts. Though promising improvements are observed, these VDL-BERTs still neglect or ill-consider a significant factor in IL-BERT: the object-word alignment, which helps learn robust associations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 319, + 279, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 319, + 279, + 516 + ], + "spans": [ + { + "bbox": [ + 45, + 319, + 279, + 516 + ], + "type": "text", + "content": "To learn object-word alignments, as Figure 1(a) shows, researchers use an RoI-based extractor to embed an image into a series of RoI features [34, 27, 8]. However, this RoI-based extractor is offline trained by object detection with limited label inventory, which will weaken the IL-BERT since the extractor will not be updated during large-scale pre-training. To enable the end-to-end training, researchers substitute the RoI-based extractor with visual transformers whose outputs are a series of grid embeddings, which will be used to build the cross-modal connections. Although a single grid usually does not construct an integral object, fortunately, the widely applied patch-to-word (P2W) attention of IL-BERT can softly seek the salient visual regions for a given query word. Then the object-word alignments can still be built between this softly detected object and the word, e.g., as shown in Figure 1(b), the object \"basketball\" can be implicitly attended by the corresponding word query." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 518, + 279, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 518, + 279, + 646 + ], + "spans": [ + { + "bbox": [ + 45, + 518, + 279, + 646 + ], + "type": "text", + "content": "Although the P2W attention remedies the loss of RoI-level features for learning object-word alignments in ILBERT, its effectiveness is weakened in the video case. This is because the objects usually act as the Trajectories which span a few spatial while multiple temporal grids in the videos. Thus, directly applying the P2W attention may over-exploit the trivial spatial contexts while neglecting the significant temporal contexts and then make the model attend to only one or two frames. Figure 1(c) shows this limitation that P2W attention only aligns the \"ball\" in the first frame to the word ball." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "type": "text", + "content": "To address this limitation, we propose to learn Trajectory-to-Word alignments to solve video-language tasks and name this model as TW-BERT. Specifically, such alignment is learnt by a novel designed trajectory-to-word T2W attention, which first uses the word as the query to seek the salient parts of each frame and the sought parts are sequenced to form the trajectory. Then the query word at" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 106, + 530, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 245 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 245 + ], + "type": "text", + "content": "tends over the trajectories again for capturing cross-modal associations. In this way, the trivial spatial regions are weakened and the temporal contexts will be strengthened, e.g., as shown in Figure 1(d), the attention weights of the word will be concentrated on the object trajectory instead of only one frame as in (c). In the implementation, we follow most VDL-BERTs to set up the network: two single-modal encoders for the video and text and one cross-modal encoder, which is sketched in Figure 2. For the cross-modal encoder, since our T2W attention does not have the same structure as the word-to-patch (W2P) attention, our cross-modal encoder is asymmetric." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 245, + 531, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 245, + 531, + 490 + ], + "spans": [ + { + "bbox": [ + 296, + 245, + 531, + 490 + ], + "type": "text", + "content": "Moreover, previous VDL-BERTs usually uniformly sample a few frames into the model, which contains two drawbacks. Firstly, using a few frames may lose temporal context and secondly, uniform sampling can hardly capture the varying graininess of the trajectories, i.e., some trajectories span longer frames and some span shorter. However, simply sampling more frames will largely increase the pretraining burdens that are beyond the computation resources we own. To alleviate this problem, in the fine-tuning stage, we sample more frames into the video encoder while only keeping the most relevant frames according to the corresponding text by a novel designed Hierarchical Frame-Selector (HFS). For example, as shown in Figure 1(e), 4 frames are selected by HFS from the 8 uniformly sampled ones for learning trajectory-word alignment. Specifically, HFS inserts a few lightweight layers into the video encoder and these layers can gradually filter frames conditioned on the language context. In this way, HFS learns the coarse-grained trajectory-word alignments, i.e., framework alignments, to help the later T2W attention learn more fine-grained trajectory-word alignments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 309, + 490, + 440, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 490, + 440, + 502 + ], + "spans": [ + { + "bbox": [ + 309, + 490, + 440, + 502 + ], + "type": "text", + "content": "To sum up, our contributions are:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 309, + 506, + 530, + 645 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 309, + 506, + 530, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 506, + 530, + 551 + ], + "spans": [ + { + "bbox": [ + 309, + 506, + 530, + 551 + ], + "type": "text", + "content": "- We propose a novel perspective to consider the videos that are composed of moving object trajectories, which may inspire the researchers to build more advanced VDL-BERTs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 309, + 553, + 529, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 553, + 529, + 575 + ], + "spans": [ + { + "bbox": [ + 309, + 553, + 529, + 575 + ], + "type": "text", + "content": "- We propose a simple while effective T2W attention to learn Trajectory-to-Word alignments." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 309, + 576, + 530, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 576, + 530, + 622 + ], + "spans": [ + { + "bbox": [ + 309, + 576, + 530, + 622 + ], + "type": "text", + "content": "- We propose a novel hierarchical frame selector (HFS) in TW-BERT during fine-tuning to capture the varying graininess of the trajectory while not largely increasing the training burdens." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 309, + 623, + 530, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 623, + 530, + 645 + ], + "spans": [ + { + "bbox": [ + 309, + 623, + 530, + 645 + ], + "type": "text", + "content": "- We achieve SOTA performances compared with other VDL-BERTs trained by the same amount of data." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 297, + 657, + 381, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 657, + 381, + 669 + ], + "spans": [ + { + "bbox": [ + 297, + 657, + 381, + 669 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 676, + 480, + 689 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 676, + 480, + 689 + ], + "spans": [ + { + "bbox": [ + 297, + 676, + 480, + 689 + ], + "type": "text", + "content": "2.1. Image-Language BERT (IL-BERT)" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 297, + 694, + 530, + 730 + ], + "type": "text", + "content": "Recently, various techniques have been proposed in ILBERT to learn vision-language connections. Most of them aim at capturing robust object-word alignments since such" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "2505" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 268 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 268 + ], + "type": "text", + "content": "alignments construct the foundations of visual reasoning. In the beginning, a pre-trained Faster-RCNN [41] is used to extract a series of RoI poolings, where each one contains one or a few salient objects, to facilitate building object-word alignments [34, 48, 8, 27]. However, this Faster-RCNN is usually pre-trained by the object annotations from COCO [7] and VG [20], whose concept space is much narrower than the data used to train IL-BERT, which can be almost unlimedly collected from the websites. Moreover, this Faster-RCNN is not updated during the end-to-end training of the IL-BERT, which means that the visual encoder may hardly learn novel knowledge from the web-collected data. Thus the performances of these IL-BERTs are limited." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 270, + 281, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 270, + 281, + 433 + ], + "spans": [ + { + "bbox": [ + 45, + 270, + 281, + 433 + ], + "type": "text", + "content": "To further release the potential of hugely web-collected data, the offline Faster RCNN is switched into vision Transformers [11, 32] and thus a homogeneous IL-BERT, i.e., all the components are transformer-based, is built, which is more easily trained end-to-end [34]. Compared with the RoI-based encoder, the vision Transformer outputs a series of patch embeddings and thus may lose object-level knowledge. To remedy such loss, various strategies are proposed to improve the vision-language alignments. For example, the align-before-fuse strategy [25] aligns the paired image-text embeddings before cross-modal fusion for facilitating the subsequent fusion. And the fine-grained contrastive objective [58] amplifies the local details for learning the object-word alignments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 442, + 239, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 239, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 239, + 455 + ], + "type": "text", + "content": "2.2. Video-Language BERT (VDL-BERT)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 462, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 462, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 462, + 281, + 730 + ], + "type": "text", + "content": "Since the spatiotemporal contexts in videos can hardly be learnt by image extractors, only inheriting the techniques which are successful in IL-BERT to VDL-BERT is not enough. Thus, based on the fruits of IL-BERT, most VDL-BERTs aim at exploiting more spatiotemporal contexts to build cross-modal associations. One straightforward way is to learn such spatiotemporal contexts through video Transformers [4, 28]. Besides this, some more advanced techniques are proposed, e.g., VIOLET [12] tokenizes the dynamic video patches and predicts the labels of these tokens; BridgeFormer [14] erases the words (nouns or verbs) from the text and learn to match the visual embeddings queried by the erased words and the remained texts; or ALPRO [24] computes the similarities between the video embeddings with the generated entity prompts. TS2-Net [31] shifts token features and selects informative tokens in both temporal and spatial dimensions to produce the fine-grained spatial-temporal video representation. Although substantial improvements are observed, these methods use video patches in the cross-modal encoder, which neglects that an object usually acts as the trajectory in the videos, and thus they may over-exploit the trivial spatial contexts. To ameliorate this limitation, we propose TW-BERT to capture" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 296, + 103, + 533, + 239 + ], + "blocks": [ + { + "bbox": [ + 296, + 103, + 533, + 239 + ], + "lines": [ + { + "bbox": [ + 296, + 103, + 533, + 239 + ], + "spans": [ + { + "bbox": [ + 296, + 103, + 533, + 239 + ], + "type": "image", + "image_path": "b5cbebcf78e78d96186340d5f804092d711148f2c73ec9fad719d656e61856ee.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "lines": [ + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "spans": [ + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "type": "text", + "content": "Figure 2. The architecture of TW-BET, which contains two single-modal encoders and one asymmetric cross-modal encoder. Totally three losses in the grey blocks are used to train the whole model: " + }, + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "type": "inline_equation", + "content": "L_{vtc}" + }, + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "type": "inline_equation", + "content": "L_{mlm}" + }, + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "type": "inline_equation", + "content": "L_{vtm}" + }, + { + "bbox": [ + 296, + 239, + 531, + 294 + ], + "type": "text", + "content": ". Note that HFS is only used in the fine-tuning stage." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 299, + 531, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 299, + 531, + 324 + ], + "spans": [ + { + "bbox": [ + 296, + 299, + 531, + 324 + ], + "type": "text", + "content": "trajectory-word alignments for more robust vision-language alignment." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 297, + 334, + 367, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 334, + 367, + 346 + ], + "spans": [ + { + "bbox": [ + 297, + 334, + 367, + 346 + ], + "type": "text", + "content": "3. TW-BERT" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 353, + 532, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 353, + 532, + 505 + ], + "spans": [ + { + "bbox": [ + 296, + 353, + 532, + 505 + ], + "type": "text", + "content": "Figure 2 sketches TW-BERT, which has two single-modal encoders for embedding the video and text (cf. Sec. 3.1) and one cross-modal encoder for learning videolanguage associations (cf. Sec. 3.2). Different from the previous VDL-BERTs, our cross-modal encoder is an asymmetric one that contains a classic word-to-patch (W2P) attention and a novel proposed trajectory-to-word (T2W) attention (cf. Sec. 3.2) for learning trajectory-word alignments. In Sec. 3.3, we introduce how to use Hierarchical Frame-Selector (HFS) in the fine-tuning stage to gradually filter the frames for capturing coarse-grained frame-word alignments. Lastly, we introduce the losses used to train our TW-BERT in Sec. 3.4." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 297, + 513, + 427, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 513, + 427, + 526 + ], + "spans": [ + { + "bbox": [ + 297, + 513, + 427, + 526 + ], + "type": "text", + "content": "3.1. Single-Modal Encoders" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "spans": [ + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "text", + "content": "Video Encoder. For a video, we sample a few " + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "text", + "content": " frames and input them into the 12-layer TimeSformer [4, 24] for embedding. TimeSformer first partitions each frame into " + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "inline_equation", + "content": "14 \\times 14" + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "text", + "content": " non-overlapping patches, which are flattened and fed to a linear projection layer to produce a sequence of patch tokens. Then TimeSformer applies self-attention along the temporal and spatial dimensions to calculate per-frame features. These features are further mean-pooled along the height and width dimensions. Learnable spatial positional embeddings are added to each video token in the same spatial location of different frames. The final output embedding set is " + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{V} = \\{\\mathbf{v}_{cls}, \\mathbf{v}_1, \\dots, \\mathbf{v}_{N_V - 1}\\}" + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_n \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{cls}" + }, + { + "bbox": [ + 296, + 532, + 531, + 682 + ], + "type": "text", + "content": " is the global [CLS] embedding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "text", + "content": "Text Encoder. For a text, we use a 6-layer transformer to embed it and the output is " + }, + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\{\\pmb{x}_{cls},\\pmb{x}_1,\\dots,\\pmb{x}_{N_X - 1}\\}" + }, + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{x}_n\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{cls}" + }, + { + "bbox": [ + 296, + 683, + 531, + 730 + ], + "type": "text", + "content": " is the global [CLS] embedding. Similar to the video encoder, we also add positional embed" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 299, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 299, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 299, + 758 + ], + "type": "text", + "content": "2506" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 106, + 140, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 106, + 140, + 117 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 140, + 117 + ], + "type": "text", + "content": "dings to the text tokens." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 127, + 226, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 127, + 226, + 140 + ], + "spans": [ + { + "bbox": [ + 46, + 127, + 226, + 140 + ], + "type": "text", + "content": "3.2. Asymmetric Cross-Modal Encoder" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 147, + 279, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 147, + 279, + 344 + ], + "spans": [ + { + "bbox": [ + 45, + 147, + 279, + 344 + ], + "type": "text", + "content": "After embedding videos and texts, a cross-modal encoder is used to fuse them by calculating bi-directional associations: vision-to-language and language-to-vision. No matter what the direction is, the motivation is to assign semantic knowledge from one domain to another. Since a single word contains integral semantic knowledge, we follow previous VDL-BERT [24, 2, 23, 47] to set a traditional word-to-patch (W2P) attention to assign the words to a patch. However, different from the word, only the object instead of one grid conveys integral semantic knowledge. In videos, an object usually spans both spatial and temporal axes and thus the previously used patch-to-word (P2W) attention may fail to transfer the semantic knowledge. To amend this, we design a novel Trajectory-to-Word (T2W) attention for transferring semantic knowledge from videos to texts. Since W2P and T2W attentions have diverse structures, our cross-encoder is asymmetric." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 345, + 279, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 345, + 279, + 391 + ], + "spans": [ + { + "bbox": [ + 45, + 345, + 279, + 391 + ], + "type": "text", + "content": "Specifically, both W2P and T2W attentions are built on the Multi-Head Attention (MHA) operation, here we first formalize MHA and then introduce how to use it to build W2P and T2W attentions. Formally, MHA is*:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 95, + 402, + 160, + 414 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 402, + 160, + 414 + ], + "spans": [ + { + "bbox": [ + 95, + 402, + 160, + 414 + ], + "type": "interline_equation", + "content": "\\begin{array}{c} \\text {I n p u t :} \\quad \\mathcal {Q}, \\mathcal {K}, \\mathcal {V} \\end{array}", + "image_path": "aa58802e41d496303044093e3512ad63daa2e5915148c180f3c4136dff1aaa48.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 415, + 251, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 415, + 251, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 251, + 440 + ], + "type": "interline_equation", + "content": "\\mathbf {A t t}: \\quad \\mathcal {A} _ {i} = \\operatorname {S o f t m a x} (\\frac {\\mathcal {Q W} _ {i} ^ {Q} \\left(\\mathcal {K W} _ {i} ^ {K}\\right) ^ {T}}{\\sqrt {d}})", + "image_path": "93b4299a0720de995b3484dad9c5b45915888c7853faae09ea822035ff3d8630.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 95, + 440, + 279, + 454 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 440, + 279, + 454 + ], + "spans": [ + { + "bbox": [ + 95, + 440, + 279, + 454 + ], + "type": "interline_equation", + "content": "\\mathbf {H e a d}: \\quad \\mathcal {H} _ {i} = \\mathcal {A} _ {i} \\mathcal {V W} _ {i} ^ {V}, \\tag {1}", + "image_path": "5a122fe96a5d93442ae0809ca5216b83accd6e4886b589f2b7743271733a40d0.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 73, + 457, + 229, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 457, + 229, + 469 + ], + "spans": [ + { + "bbox": [ + 73, + 457, + 229, + 469 + ], + "type": "interline_equation", + "content": "\\text {M u l t i - H e a d}: \\quad \\mathcal {H} = \\left[ \\mathcal {H} _ {1}, \\mathcal {H} _ {2},..., \\mathcal {H} _ {h} \\right] \\mathcal {W} ^ {H},", + "image_path": "c35538c4a1b65cf499d86d38535cf10a8bad4dd40eac598b476fd206aa28cc7f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 90, + 472, + 197, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 472, + 197, + 484 + ], + "spans": [ + { + "bbox": [ + 90, + 472, + 197, + 484 + ], + "type": "interline_equation", + "content": "\\text {O u t p u t}: \\mathcal {Z} = \\mathrm {L N} (\\mathcal {H} + \\mathcal {Q}),", + "image_path": "d0b56b40aaee9d861799d4647f1d05c188ecd0bb7d1ea8f6ad59d9371e3b8d92.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "spans": [ + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_i^Q, \\mathcal{W}_i^K, \\mathcal{W}_i^V, \\mathcal{W}_i^H" + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "content": " are all trainable matrices; " + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "content": " is the head number and " + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "inline_equation", + "content": "d_h = d / h" + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_i" + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "content": "-th attention matrix corresponding to the " + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "content": "-th head matrix; " + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "inline_equation", + "content": "[\\cdot]" + }, + { + "bbox": [ + 45, + 495, + 279, + 542 + ], + "type": "text", + "content": " is the concatenation operation; and LN is the Layer Normalization." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 543, + 279, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 543, + 279, + 566 + ], + "spans": [ + { + "bbox": [ + 45, + 543, + 279, + 566 + ], + "type": "text", + "content": "Word-to-Patch (W2P) Attention. To calculate the W2P alignment, we apply the conventional W2P attention [24]:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 82, + 568, + 279, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 568, + 279, + 580 + ], + "spans": [ + { + "bbox": [ + 82, + 568, + 279, + 580 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} _ {W 2 P} = \\mathbf {M H A} (\\mathcal {Q} = \\mathbf {V}, \\mathcal {K} = \\mathcal {V} = \\mathbf {X}), \\tag {2}", + "image_path": "b30a74df60c7c22b352eb8ed5e5b5aab821ca5dadf2663d95b934c9bd03f9225.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "spans": [ + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{N_V \\times D}" + }, + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N_X \\times D}" + }, + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "type": "text", + "content": " are respectively video and word embedding sets got from two single-modal encoders. By setting the query " + }, + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 45, + 580, + 279, + 640 + ], + "type": "text", + "content": " to the video patch embeddings, Eq. (2) learns to assign suitable words to each video patch and thus captures the W2P alignment." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 641, + 279, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 641, + 279, + 699 + ], + "spans": [ + { + "bbox": [ + 45, + 641, + 279, + 699 + ], + "type": "text", + "content": "Trajectory-to-Word (T2W) Attention. As shown in Figure. 3 (b), we propose the T2W attention that uses two steps to learn the T2W alignment: it first constructs a trajectory for a given word and then uses the word as the query to attend over the trajectory for capturing the associations. For" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 298, + 104, + 370, + 175 + ], + "blocks": [ + { + "bbox": [ + 298, + 104, + 370, + 175 + ], + "lines": [ + { + "bbox": [ + 298, + 104, + 370, + 175 + ], + "spans": [ + { + "bbox": [ + 298, + 104, + 370, + 175 + ], + "type": "image", + "image_path": "b57d3edb8a443743f6444b3a072a33e602ecc73b2ec55405ff7ddab19f1ca6af.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 177, + 530, + 253 + ], + "lines": [ + { + "bbox": [ + 296, + 177, + 530, + 253 + ], + "spans": [ + { + "bbox": [ + 296, + 177, + 530, + 253 + ], + "type": "text", + "content": "Figure 3. The comparisons between Patch-to-Word (P2W) and Trajectory-to-Word (T2W) attentions, where the green block denotes a query word and the blue blocks denote the video patches. In P2W attention, the word attends over all the video patches and may only concentrate on one frame, while in T2W attention, the salient red parts of each frame are found to construct a trajectory, which are connected by the red lines, " + }, + { + "bbox": [ + 296, + 177, + 530, + 253 + ], + "type": "inline_equation", + "content": "e.g., y_1, y_2, y_3" + }, + { + "bbox": [ + 296, + 177, + 530, + 253 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 380, + 104, + 457, + 175 + ], + "blocks": [ + { + "bbox": [ + 380, + 104, + 457, + 175 + ], + "lines": [ + { + "bbox": [ + 380, + 104, + 457, + 175 + ], + "spans": [ + { + "bbox": [ + 380, + 104, + 457, + 175 + ], + "type": "image", + "image_path": "015138560146499c8ae8b166bf94e72b334e605009becc9ae30284f053d959e6.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 461, + 105, + 530, + 175 + ], + "blocks": [ + { + "bbox": [ + 461, + 105, + 530, + 175 + ], + "lines": [ + { + "bbox": [ + 461, + 105, + 530, + 175 + ], + "spans": [ + { + "bbox": [ + 461, + 105, + 530, + 175 + ], + "type": "image", + "image_path": "616dafaae6cb8805152b670366c46a7e841eb366cf41300c761780949cb9565d.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 260, + 530, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 260, + 530, + 295 + ], + "spans": [ + { + "bbox": [ + 296, + 260, + 530, + 295 + ], + "type": "text", + "content": "convenience, we introduce how the T2W attention calculates the fusion embedding " + }, + { + "bbox": [ + 296, + 260, + 530, + 295 + ], + "type": "inline_equation", + "content": "z_{T2W}" + }, + { + "bbox": [ + 296, + 260, + 530, + 295 + ], + "type": "text", + "content": " for a single word " + }, + { + "bbox": [ + 296, + 260, + 530, + 295 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 260, + 530, + 295 + ], + "type": "text", + "content": " and it is straightforward to extend it to a sequence of the words." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "spans": [ + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "text", + "content": "In the first step, T2W attention uses " + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "text", + "content": " as the query to find the salient parts for each frame and then sequence these parts to construct the trajectory. Assuming " + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "inline_equation", + "content": "V_{t}" + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "text", + "content": " is the embedding set of the " + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "text", + "content": "-th frame, the salient part " + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 296, + 296, + 530, + 342 + ], + "type": "text", + "content": " is got as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 343, + 343, + 530, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 343, + 530, + 357 + ], + "spans": [ + { + "bbox": [ + 343, + 343, + 530, + 357 + ], + "type": "interline_equation", + "content": "\\boldsymbol {y} _ {t} = \\mathbf {M H A} (\\mathcal {Q} = \\boldsymbol {x}, \\mathcal {K} = \\mathcal {V} = \\boldsymbol {V} _ {t}). \\tag {3}", + "image_path": "0d255b048767ee3ca14e9fb5482306273d39a8e3231668907bbcab45216abf2c.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 296, + 358, + 530, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 358, + 530, + 392 + ], + "spans": [ + { + "bbox": [ + 296, + 358, + 530, + 392 + ], + "type": "text", + "content": "Then the salient parts at different time frames construct a continuous flow " + }, + { + "bbox": [ + 296, + 358, + 530, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} = \\{\\pmb{y}_1, \\dots, \\pmb{y}_T\\}" + }, + { + "bbox": [ + 296, + 358, + 530, + 392 + ], + "type": "text", + "content": ", which is the trajectory of the given word." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "spans": [ + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "type": "text", + "content": "In the second step, to get the trajectory-to-word fusion embedding " + }, + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "type": "inline_equation", + "content": "z_{T2W}" + }, + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "type": "text", + "content": ", we treat " + }, + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "type": "text", + "content": " as the query again while using the trajectory " + }, + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 296, + 394, + 530, + 428 + ], + "type": "text", + "content": " as the key and value in MHA:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 337, + 431, + 530, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 431, + 530, + 442 + ], + "spans": [ + { + "bbox": [ + 337, + 431, + 530, + 442 + ], + "type": "interline_equation", + "content": "\\boldsymbol {z} _ {T 2 W} = \\mathbf {M H A} (\\mathcal {Q} = \\boldsymbol {x}, \\mathcal {K} = \\mathcal {V} = \\boldsymbol {Y}). \\tag {4}", + "image_path": "bfbb49cc1104198f54bf9076a071e82de16b69ffc45e82c8af365b495dcf1990.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 296, + 444, + 530, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 444, + 530, + 548 + ], + "spans": [ + { + "bbox": [ + 296, + 444, + 530, + 548 + ], + "type": "text", + "content": "By Eq. (3), T2W attention finds the salient parts for the given word at each frame, which enforces Eq. (4) to attend over the continuous frames instead of concentrating the attention only on one or some episodic frames as the previous P2W attentions. In this way, the whole T2W block exploits more temporal contexts to build vision-language associations, which facilitates the video reasoning tasks that usually require the correct recognition of the temporal patterns. Figure. 3 compares P2W and T2W attentions." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 297, + 559, + 449, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 559, + 449, + 570 + ], + "spans": [ + { + "bbox": [ + 297, + 559, + 449, + 570 + ], + "type": "text", + "content": "3.3. Hierarchical Frame-Selector" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 296, + 579, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 579, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 579, + 530, + 730 + ], + "type": "text", + "content": "During fine-tuning, to improve the performance, previous studies tend to sample more frames than pre-training for introducing more temporal information. However, on the one hand, using too many frames will dramatically increase the computational resources, which causes infeasible training. On the other hand, in a video, different trajectories have varying graininess, e.g., some trajectories may cover longer frames and some cover shorter. In this way, uniform sampling may introduce redundant temporal information for these longer trajectories and deficient information for the shorter ones. Interestingly, the time duration of the trajectory is also reflected in the corresponding text. In this way, we can use the text to choose suitable frames and then" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 45, + 710, + 279, + 729 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 710, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 710, + 279, + 729 + ], + "type": "text", + "content": "*To avoid symbol confusions, we use the calligraphic font (\\mathcal{M}) to denote the built-in variables of the MHA module." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "2507" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 46, + 108, + 530, + 186 + ], + "blocks": [ + { + "bbox": [ + 46, + 108, + 530, + 186 + ], + "lines": [ + { + "bbox": [ + 46, + 108, + 530, + 186 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 530, + 186 + ], + "type": "image", + "image_path": "8f235540be5a61c6dd1ad91e916d6695bde2a641002ad627ca1ab977f00605c9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 188, + 531, + 210 + ], + "lines": [ + { + "bbox": [ + 45, + 188, + 531, + 210 + ], + "spans": [ + { + "bbox": [ + 45, + 188, + 531, + 210 + ], + "type": "text", + "content": "Figure 4. The architecture of the proposed Hierarchical Frame-Selector. At beginning, four frames are input into the video encoder and the first frame selector behind the 6-th layer filters out the 2-nd frame. At last, only the tokens of the 1-st and 4-th frames are preserved." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 215, + 279, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 215, + 279, + 237 + ], + "spans": [ + { + "bbox": [ + 45, + 215, + 279, + 237 + ], + "type": "text", + "content": "only input them into the cross-modal attention for learning trajectory-word alignments." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "spans": [ + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "text", + "content": "Motivated by this, we propose a novel Hierarchical Frame-Selector (HFS) that can gradually select the most relevant video frames to reduce the computational burdens while providing more temporal knowledge. Figure 4 illustrates the architecture of our proposed frame selector module. HFS contains a few frame selector layers which have the same structure with different parameters. For each frame selector layer, given a sequence of video frame [CLS] tokens " + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "inline_equation", + "content": "V_{cls} = \\{v_{cls}^{1}, v_{cls}^{2}, \\dots, v_{cls}^{T}\\} \\in \\mathbb{R}^{T \\times D}" + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "text", + "content": ", we concatenate the text [CLS] embedding " + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "inline_equation", + "content": "x_{cls}" + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "text", + "content": " with each " + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "inline_equation", + "content": "v_{cls}^{t}" + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "inline_equation", + "content": "f_{t} = [v_{cls}^{t}, x_{cls}] \\in \\mathbb{R}^{2D} (1 \\leq t \\leq T)" + }, + { + "bbox": [ + 45, + 239, + 279, + 378 + ], + "type": "text", + "content": " and feed them into a scorer network including a FC layer and a softmax layer:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 95, + 378, + 279, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 378, + 279, + 392 + ], + "spans": [ + { + "bbox": [ + 95, + 378, + 279, + 392 + ], + "type": "interline_equation", + "content": "\\boldsymbol {s} = \\operatorname {S o f t m a x} (F C (\\boldsymbol {f})) \\in \\mathbb {R} ^ {T \\times 1}. \\tag {5}", + "image_path": "f19c9b0666c63aaaa9a0d156cb0ba5a769c7a8b7d607ec77ad51ae453327045c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "spans": [ + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "text", + "content": " denotes the number of frames input into the video encoder, and " + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "inline_equation", + "content": "s \\in \\mathbb{R}^T" + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "text", + "content": " is the score vector of " + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "text", + "content": " frames. Then for this frame selector, we keep the tokens of " + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "text", + "content": " frames with the top- " + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 45, + 393, + 279, + 499 + ], + "type": "text", + "content": " for the further embedding in the subsequent video Transformer layers. During training, we employ the perturbed maximum method [5] to construct a differentiable Top-K operator. In the video encoder, we totally insert 2 selector layers and insert them in the 6-th and 12-th layers as in Figure 4." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 506, + 158, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 506, + 158, + 520 + ], + "spans": [ + { + "bbox": [ + 45, + 506, + 158, + 520 + ], + "type": "text", + "content": "3.4. Training Objectives" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 525, + 279, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 525, + 279, + 571 + ], + "spans": [ + { + "bbox": [ + 45, + 525, + 279, + 571 + ], + "type": "text", + "content": "To train TW-BERT, as the grey blocks shown in Figure 2, we totally use three losses which are masked language modeling (MLM), video-text matching (VTM), and video-text contrastive loss (VTC)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 572, + 279, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 572, + 279, + 653 + ], + "spans": [ + { + "bbox": [ + 45, + 572, + 279, + 653 + ], + "type": "text", + "content": "Masked language Modeling (MLM) [26, 24, 12, 50]. MLM aims to predict the masked word tokens given both the video and the text contexts. To get it, we first randomly replace the input text tokens with the [MASK] token with a probability of " + }, + { + "bbox": [ + 45, + 572, + 279, + 653 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 45, + 572, + 279, + 653 + ], + "type": "text", + "content": " and then use the [MASK] embedding output from the cross-modal encoder to predict the masked word by calculating a cross-entropy loss:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 83, + 654, + 279, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 654, + 279, + 668 + ], + "spans": [ + { + "bbox": [ + 83, + 654, + 279, + 668 + ], + "type": "interline_equation", + "content": "L _ {M L M} = \\mathbb {E} _ {(V, \\hat {X}) \\sim D} \\mathrm {H} \\left(y ^ {m s k}, p ^ {m s k} (V, \\hat {X})\\right) \\tag {6}", + "image_path": "f620a7ff7d213504fa77151d4316df3517dbc14e068baa623d30fc0e938677bf.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "spans": [ + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "type": "inline_equation", + "content": "\\hat{X}" + }, + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "type": "text", + "content": " is the masked text, " + }, + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "type": "inline_equation", + "content": "\\mathrm{H}" + }, + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "type": "text", + "content": " is the cross-entropy loss, " + }, + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "type": "inline_equation", + "content": "y^{msk} / p^{msk}" + }, + { + "bbox": [ + 45, + 670, + 279, + 694 + ], + "type": "text", + "content": " are the ground-truth/predicted masked tokens." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": "Video-text Matching (VTM) [24, 12, 50]. VTM calculates whether the given video and text are matched or not. To get it, for a given video-text pair, we first randomly replace the" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 215, + 530, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 215, + 530, + 272 + ], + "spans": [ + { + "bbox": [ + 296, + 215, + 530, + 272 + ], + "type": "text", + "content": "text with the ones from a different video in the same batch. Then we concatenate the video and text [CLS] embeddings output from the cross-modal encoder and input the concatenated embedding into a binary classifier to judge whether the given video-text pair is matched or not:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 336, + 273, + 530, + 286 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 273, + 530, + 286 + ], + "spans": [ + { + "bbox": [ + 336, + 273, + 530, + 286 + ], + "type": "interline_equation", + "content": "L _ {V T M} = \\mathbb {E} _ {(V, X) \\sim D} \\mathrm {H} \\left(y ^ {v t m}, p ^ {v t m} (V, X)\\right) \\tag {7}", + "image_path": "d94c82925e4c4414f32f7f056f1514857a4a7ecc921a4f4f5aef99b5ce3c20ad.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "spans": [ + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "type": "inline_equation", + "content": "y^{vtm} / p^{vtm}(V,X)" + }, + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "type": "text", + "content": " are the ground-truth/predicted values indexing whether " + }, + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 296, + 287, + 530, + 310 + ], + "type": "text", + "content": " are matched or not." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "spans": [ + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "type": "text", + "content": "Video-text Contrastive (VTC) [24, 50, 49, 14, 15, 2, 29]. As detailed in Section 3, VTC contrasts the outputs of two single-modal encoders to pull close their embedding space to help the subsequent cross-modal encoder build more robust vision-language associations. Suppose " + }, + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "type": "inline_equation", + "content": "s_{ij}" + }, + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "type": "text", + "content": " denotes the similarity score of the " + }, + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "type": "text", + "content": "-th video and the " + }, + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 296, + 311, + 530, + 404 + ], + "type": "text", + "content": "-th text, for each video and text, we calculate the softmax-normalized video-to-text and video-to-image similarity as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 410, + 530, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 410, + 530, + 436 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 530, + 436 + ], + "type": "interline_equation", + "content": "p _ {i j} ^ {v 2 t} (V) = \\frac {\\exp \\left(s _ {i j} / \\tau\\right)}{\\sum_ {j} \\exp \\left(s _ {i j} / \\tau\\right)}, p _ {i j} ^ {t 2 v} (X) = \\frac {\\exp \\left(s _ {i j} / \\tau\\right)}{\\sum_ {i} \\exp \\left(s _ {i j} / \\tau\\right)} \\tag {8}", + "image_path": "6586fc151ee6458ee17288cbc39193aab180e8d10eeed627de319cba61ccfeda.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "spans": [ + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "text", + "content": " is a learnable temperature parameter. Let " + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "inline_equation", + "content": "y^{v2t}(V)" + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "inline_equation", + "content": "y^{t2v}(X)" + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "text", + "content": " denote the ground-truth one-hot similarity. This loss contains two symmetric parts, where the left term forces the " + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "text", + "content": "-th text embedding to be close to the " + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 442, + 530, + 511 + ], + "type": "text", + "content": "-th video embedding compared with the other texts and the right term has a similar effect:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 512, + 340, + 522 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 340, + 522 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 340, + 522 + ], + "type": "interline_equation", + "content": "L _ {V T C} =", + "image_path": "69e4654f697ac28a73afdfd36adb24bc259566eaa4245d4517f7eb5928592151.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 525, + 530, + 553 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 530, + 553 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 530, + 553 + ], + "type": "interline_equation", + "content": "\\frac {1}{2} \\mathbb {E} _ {(V, X) \\sim D} [ \\mathrm {H} (y ^ {v 2 t} (V), p ^ {v 2 t} (V)) + \\mathrm {H} (y ^ {t 2 v} (X), p ^ {t 2 v} (X)) ] \\tag {9}", + "image_path": "83740dcd0bada7bdd978cd86b45722891c76ef940b4b34bfca6eb5ab696eeeac.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 554, + 530, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 554, + 530, + 588 + ], + "spans": [ + { + "bbox": [ + 296, + 554, + 530, + 588 + ], + "type": "text", + "content": "In the implementation, we follow [25] to use the momentum queue as a continuously-evolving teacher to provide more negative samples." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 297, + 599, + 376, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 599, + 376, + 612 + ], + "spans": [ + { + "bbox": [ + 297, + 599, + 376, + 612 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 297, + 618, + 412, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 618, + 412, + 630 + ], + "spans": [ + { + "bbox": [ + 297, + 618, + 412, + 630 + ], + "type": "text", + "content": "4.1. Pre-training Dataset" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": "Following recent work [24, 14, 15, 49, 2], we pre-train TW-BERT on Google Conceptual Captions (CC3M) [45] containing 3.3M image-text pairs and WebVid-2M [2] containing 2.5M video-text pairs. For CC3M, the image is treated as a one-frame video data during pre-training. Note that due to the limited storage and computation resources, we do not use some much larger datasets like HowTo100M [38] containing 136M video-text pairs as [26," + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "2508" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 278, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 278, + 129 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 278, + 129 + ], + "type": "text", + "content": "55]. Also, we do not distill knowledge from CLIP [39], which is pre-trained on 400M image-text pairs, as [36]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 138, + 154, + 149 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 138, + 154, + 149 + ], + "spans": [ + { + "bbox": [ + 46, + 138, + 154, + 149 + ], + "type": "text", + "content": "4.2. Downstream Tasks" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 155, + 278, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 155, + 278, + 352 + ], + "spans": [ + { + "bbox": [ + 45, + 155, + 278, + 352 + ], + "type": "text", + "content": "Text-to-Video Retrieval. (i) MSRVTT contains 10K YouTube videos with 200K descriptions. We follow [56] to use 9K train+val videos for training and report results on the 1K test split. (ii) DiDeMo [16] contains 10K Flickr videos annotated with 40K sentences. (iii) LSMDC consists of 118,081 video clips sourced from 202 movies, where the validation set and the test set contain 7,408 and 1,000 videos. (iv) ActivityNet Caption contains 20K YouTube videos annotated with 100K sentences. The training set contains 10K videos, and we use val1 set with 4.9K videos to report results. For MSRVTT and LSMDC, we perform standard text-to-video retrieval. For DiDeMo and ActivityNet Caption, we concatenate all the text captions in the same video as a single query and evaluate paragraph-to-video retrieval. For two tasks, we measure the performances by average recall at " + }, + { + "bbox": [ + 45, + 155, + 278, + 352 + ], + "type": "inline_equation", + "content": "\\mathrm{K(R@K)}" + }, + { + "bbox": [ + 45, + 155, + 278, + 352 + ], + "type": "text", + "content": " and Median Rank on zero-shot and fine-tune setups." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 353, + 278, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 353, + 278, + 422 + ], + "spans": [ + { + "bbox": [ + 45, + 353, + 278, + 422 + ], + "type": "text", + "content": "Video Question Answering. (i) MSRVTT-QA [53] is built upon videos and captions from MSRVTT [56], which contains 10K videos with 243K open-ended questions and 1.5K answer candidates. (ii) MSVD [6] contains 50K question-answer pairs with 2423 answer candidates. We use standard train/val/test splits for the two tasks, and report accuracy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 431, + 175, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 175, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 175, + 443 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 450, + 278, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 450, + 278, + 519 + ], + "spans": [ + { + "bbox": [ + 45, + 450, + 278, + 519 + ], + "type": "text", + "content": "We initialize our video encoder by ViT-B/16 [42] and the text encoder by the first six BERT-Base layers [9]. For the cross-modal encoder, the self-attentionions in all 3 cross-modal attentions (W2P contains 1 and T2W contains 2) are initialized by the last 6 BERT-Base layers [9]. The model is trained end-to-end during both pre-training and fine-tuning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 520, + 278, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 520, + 278, + 647 + ], + "spans": [ + { + "bbox": [ + 45, + 520, + 278, + 647 + ], + "type": "text", + "content": "In pre-training, the feature dimension is set to 256 when calculating the contrastive losses and the temperature is set to 0.05. For the momentum queue, the momentum value is 0.995 and the size of the queue is 65,536. The above implementation details follow the recent work [25, 24] for a fair comparison. We pre-train the model on CC3M and WebVid-2M for 10 epochs on 8 NVIDIA A100 GPUs where the batch size is 128. We use AdamW [18] optimizer with a weight decay of 0.001 and betas (0.9, 0.98). The learning rate is first warmed-up to 1e-4 and then decays following a linear decay schedule." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 648, + 278, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 278, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 278, + 729 + ], + "type": "text", + "content": "During fine-tuning text-to-video retrieval, We sample 20 frames and use HFS to preserve 8 frames to feed into the cross-modal encoder. The model is trained with both VTC and VTM losses, and we obtain similarity scores from the output of the VTM head during inference. For video question answering, we sample 32 frames per video and preserve 16 frames. Since MSRVTT-QA and MSVD-QA [53]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 106, + 530, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 186 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 186 + ], + "type": "text", + "content": "are open-ended VQA, in which the answers are in free-form natural language, it is common to convert the task to a classification task by predicting the answer's label. We input the concatenation of the video and question [CLS] tokens into a two-layer MLP [9] for calculating the cross-entropy loss. All the fine-tuning experiments are conducted on 8 NVIDIA V100 GPUs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 297, + 197, + 395, + 208 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 197, + 395, + 208 + ], + "spans": [ + { + "bbox": [ + 297, + 197, + 395, + 208 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 215, + 530, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 215, + 530, + 250 + ], + "spans": [ + { + "bbox": [ + 296, + 215, + 530, + 250 + ], + "type": "text", + "content": "We conduct comprehensive ablation studies to evaluate the effectiveness of the proposed trajectory-to-word (T2W) attention and Hierarchical Frame-Selector (HFS) module." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 250, + 530, + 343 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 250, + 530, + 343 + ], + "spans": [ + { + "bbox": [ + 296, + 250, + 530, + 343 + ], + "type": "text", + "content": "Comparing Methods. Base: We use a symmetric cross-modal encoder that contains patch-to-word (P2W) and word-to-patch (W2P) attentions. T2W: We replace P2W attention in Base by our T2W attention. MeanP: Another simple way to consider temporal knowledge is to mean pool the embeddings along the temporal axis. Specifically, we simply average " + }, + { + "bbox": [ + 296, + 250, + 530, + 343 + ], + "type": "inline_equation", + "content": "\\{\\pmb{y}_1,\\dots,\\pmb{y}_T\\}" + }, + { + "bbox": [ + 296, + 250, + 530, + 343 + ], + "type": "text", + "content": ". These three ablations are implemented using the zero-shot setting." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 344, + 530, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 344, + 530, + 436 + ], + "spans": [ + { + "bbox": [ + 296, + 344, + 530, + 436 + ], + "type": "text", + "content": "[L1,L2]: We insert frame selector layer into the L1-th and L2-th layers. F@T: We sample T frames into the model. F@T1-T2-T3: We use Hierarchical Frame Selector where \"F@T1-T2-T3\" denotes that T1 frames are originally input into the model and then T2 and T3 frames are respectively remained by the first and second frame selector layers. All these ablations are implemented using the fine-tuning setting." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 437, + 530, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 437, + 530, + 506 + ], + "spans": [ + { + "bbox": [ + 296, + 437, + 530, + 506 + ], + "type": "text", + "content": "Quantitative Results. Table 1 compares the performances of diverse baselines. From this table, we can see that T2W outperforms Base, e.g., T2W achieves " + }, + { + "bbox": [ + 296, + 437, + 530, + 506 + ], + "type": "inline_equation", + "content": "3.6\\%" + }, + { + "bbox": [ + 296, + 437, + 530, + 506 + ], + "type": "text", + "content": " R@5 improvements on MSRVTT for zero-shot evaluation, which suggests that our T2W attention can exploit more temporal contexts to better solve video-language tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "spans": [ + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "text", + "content": "Also, T2W achieves higher scores than MeanP on different tasks, e.g., T2W achieves " + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "inline_equation", + "content": "28.4\\%" + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "inline_equation", + "content": "\\mathbb{R}@\\mathbb{1}" + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "text", + "content": " score in DiDeMo zero-shot text-to-video retrieval task while MeanP only has " + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "inline_equation", + "content": "27.4\\%" + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "text", + "content": ". Applying mean-pooling strategy indeed fuse all the temporal knowledge, however, simply averaging all " + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "inline_equation", + "content": "\\pmb{y}_t" + }, + { + "bbox": [ + 296, + 508, + 530, + 635 + ], + "type": "text", + "content": " also means that the contexts over the whole time axis are used, while lots of objects may only span a few frames and using all the temporal contexts may introduce trivial or even harmful noises. This proves that our T2W attention can capture more important cross-modal associations in this asymmetric cross-modal encoder case." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": "We further analyze the impact of the layer settings and frame number on the Hierarchical Frame-Selector module. As shown in Table 2, frame selector in deep layers (e.g. 6-th and 12-th layers) brings better performances on both retrieval and QA tasks. Moving frame selector module into shallower layers deteriorates the scores. For example, the accuracy drops " + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": " when the frame selector module is placed before the third layer. We hypothesize that discard" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "2509" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 101, + 302, + 191 + ], + "blocks": [ + { + "bbox": [ + 49, + 101, + 302, + 191 + ], + "lines": [ + { + "bbox": [ + 49, + 101, + 302, + 191 + ], + "spans": [ + { + "bbox": [ + 49, + 101, + 302, + 191 + ], + "type": "image", + "image_path": "275f77327caa477810a45dde9f8bd76e5bed480d8d25a36ed627c809214224c7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 141, + 193, + 240, + 202 + ], + "lines": [ + { + "bbox": [ + 141, + 193, + 240, + 202 + ], + "spans": [ + { + "bbox": [ + 141, + 193, + 240, + 202 + ], + "type": "text", + "content": "(a) \"A girl practising her arrow tricks\"" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 308, + 103, + 530, + 191 + ], + "blocks": [ + { + "bbox": [ + 308, + 103, + 530, + 191 + ], + "lines": [ + { + "bbox": [ + 308, + 103, + 530, + 191 + ], + "spans": [ + { + "bbox": [ + 308, + 103, + 530, + 191 + ], + "type": "image", + "image_path": "19d8d231a44f77172aac4d94ebf6f42f15869fce9464e1acb75f4f2dc6a8d9fd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 377, + 193, + 461, + 202 + ], + "lines": [ + { + "bbox": [ + 377, + 193, + 461, + 202 + ], + "spans": [ + { + "bbox": [ + 377, + 193, + 461, + 202 + ], + "type": "text", + "content": "(b) \"Two people play basketball\"" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 49, + 205, + 302, + 293 + ], + "blocks": [ + { + "bbox": [ + 49, + 205, + 302, + 293 + ], + "lines": [ + { + "bbox": [ + 49, + 205, + 302, + 293 + ], + "spans": [ + { + "bbox": [ + 49, + 205, + 302, + 293 + ], + "type": "image", + "image_path": "3f8ee20b307dc49c32b0c2cffa27004d52170b8c8503b5f34f0f9e074031866c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 133, + 295, + 220, + 303 + ], + "lines": [ + { + "bbox": [ + 133, + 295, + 220, + 303 + ], + "spans": [ + { + "bbox": [ + 133, + 295, + 220, + 303 + ], + "type": "text", + "content": "(c) \"Adult feeds baby with spoon\"" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 332, + 530, + 353 + ], + "lines": [ + { + "bbox": [ + 45, + 332, + 530, + 353 + ], + "spans": [ + { + "bbox": [ + 45, + 332, + 530, + 353 + ], + "type": "text", + "content": "Table 1. Performances of various baselines. R@K and MedR respectively denote recall (\\%) with K retrieval efforts and median ranking for retrieved videos where higher R@K and lower MedR indicate better performance." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 308, + 205, + 530, + 293 + ], + "blocks": [ + { + "bbox": [ + 308, + 205, + 530, + 293 + ], + "lines": [ + { + "bbox": [ + 308, + 205, + 530, + 293 + ], + "spans": [ + { + "bbox": [ + 308, + 205, + 530, + 293 + ], + "type": "image", + "image_path": "dec8cda2e68dfd55ec6c745614d6af8c8f2dd483a034b7202a4f2477fb2aa326.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 360, + 295, + 478, + 303 + ], + "lines": [ + { + "bbox": [ + 360, + 295, + 478, + 303 + ], + "spans": [ + { + "bbox": [ + 360, + 295, + 478, + 303 + ], + "type": "text", + "content": "(d) \"The dog runs away and picks up the cone\"" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 309, + 531, + 330 + ], + "lines": [ + { + "bbox": [ + 45, + 309, + 531, + 330 + ], + "spans": [ + { + "bbox": [ + 45, + 309, + 531, + 330 + ], + "type": "text", + "content": "Figure 5. Visualizations of the attention maps from cross-modal encoder. Sample (a) and (b) are from MSRVTT [56], (c) and (d) are from DiDeMo [16] retrieval dataset. TW-BERT attends to the patches related to given query word by Trajectory-to-Word attention." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 89, + 353, + 483, + 422 + ], + "blocks": [ + { + "bbox": [ + 89, + 353, + 483, + 422 + ], + "lines": [ + { + "bbox": [ + 89, + 353, + 483, + 422 + ], + "spans": [ + { + "bbox": [ + 89, + 353, + 483, + 422 + ], + "type": "table", + "html": "
MethodMSRVTT-ZSDiDeMo-ZSMSVD-QA
R@1↑R@5↑R@10↑MedR↓R@1↑R@5↑R@10↑MedR↓Acc.
Base25.146.457.37.026.652.862.75.047.4
T2W26.850.059.95.028.452.964.54.048.2
MeanP25.847.958.06.027.453.164.05.048.0
", + "image_path": "e57c7933da83926f4803329c6f8d584870d9047b5417c3e6dfb618b45c1c9f99.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 48, + 452, + 274, + 540 + ], + "blocks": [ + { + "bbox": [ + 45, + 431, + 280, + 452 + ], + "lines": [ + { + "bbox": [ + 45, + 431, + 280, + 452 + ], + "spans": [ + { + "bbox": [ + 45, + 431, + 280, + 452 + ], + "type": "text", + "content": "Table 2. Performances comparison with different layer settings of the HFS in fine-tuning." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 452, + 274, + 540 + ], + "lines": [ + { + "bbox": [ + 48, + 452, + 274, + 540 + ], + "spans": [ + { + "bbox": [ + 48, + 452, + 274, + 540 + ], + "type": "table", + "html": "
layersMSRVTT-FTMSVD-QA
R@1↑R@5↑R@10↑MedR↓Acc.
[2,4]36.763.274.93.046.2
[3,6]37.463.775.43.046.9
[4,8]38.164.676.23.047.8
[5,10]38.264.976.33.048.3
[6,12]38.465.176.63.048.5
", + "image_path": "f2e47f260d6cc1962abdd81e82e9f338912c344dd00053b87d14464ba0634e1d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 48, + 565, + 277, + 639 + ], + "blocks": [ + { + "bbox": [ + 45, + 544, + 279, + 565 + ], + "lines": [ + { + "bbox": [ + 45, + 544, + 279, + 565 + ], + "spans": [ + { + "bbox": [ + 45, + 544, + 279, + 565 + ], + "type": "text", + "content": "Table 3. Performances comparison with different frame settings of the HFS in fine-tuning." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 565, + 277, + 639 + ], + "lines": [ + { + "bbox": [ + 48, + 565, + 277, + 639 + ], + "spans": [ + { + "bbox": [ + 48, + 565, + 277, + 639 + ], + "type": "table", + "html": "
FrameMSRVTT-FTFrameMSVD-QA
R@1↑R@5↑R@10↑MedR↓Acc.
F@135.863.374.23.0F@847.2
F@4-2-135.963.273.93.0F@20-14-847.2
F@437.163.975.33.0F@1247.7
F@8-6-437.564.275.53.0F@24-18-1247.9
F@838.164.976.03.0F@1648.2
F@20-14-838.465.176.63.0F@32-24-1648.5
", + "image_path": "6ca5519b8747a54fac49f08e30c485d9acae50f1d048156c6a70cac9a944e2d9.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 279, + 730 + ], + "type": "text", + "content": "ing frames too early would result in a lack of temporal knowledge in subsequent ViT layers. We thus choose to insert the frame selector module in the 6-th and 12-th layers in the following experiments. In terms of frame number, as shown in Table 3, on the one hand, as the number of frame we sample increases, both retrieval and QA performance obtain improvements. For example, in MSRVTT" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "spans": [ + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "text", + "content": "fine-tuning text-to-video retrieval task, F@20-14-8 outperforms F@8-6-4 by " + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "text", + "content": " on R@1 or on MSVD video question answering task, F@32-24-16 outperforms F@24-18-12 by " + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "text", + "content": ", which suggests that more temporal knowledge benefit our model whether using uniform sampling or our proposed HFS. On the other hand, using HFS gets higher scores than uniform sampling, e.g., F@20-14-8 achieves " + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "inline_equation", + "content": "38.4\\%" + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "text", + "content": " of R@1 score in MSRVTT retrieval task while F@8 only has " + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "inline_equation", + "content": "38.1\\%" + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "text", + "content": ", or on MSVD video question answering task, F@32-24-16 outperforms F@16 by " + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 296, + 434, + 530, + 563 + ], + "type": "text", + "content": ", which validates the power of HFS module." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 566, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 566, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 566, + 531, + 730 + ], + "type": "text", + "content": "Qualitative Results. We show the heat maps of the attentions of Base and TW-BERT in Figure 5. We see that TW-BERT can select the most relevant frames according to the whole text, then it implicitly form a trajectory among these frames for a given query word to avoid over-exploiting the trivial spatial contexts as in Base. For example, in (a), TW-BERT first discards the 1-st and 8-th frames which is completely irrelevant to the text, then tracks the hand of the girl in each frame that it keeps according to the query word \"practising\" while Base cannot avoid impact of the irrelevant frames, and in those relevant frames, it only attends to the larger while trivial regions about the whole body of the girl. Moreover, in (d), TW-BERT keeps the 6-th and 7-th frames for these two frames show the dog's action more" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "2510" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 133, + 528, + 271 + ], + "blocks": [ + { + "bbox": [ + 45, + 102, + 530, + 133 + ], + "lines": [ + { + "bbox": [ + 45, + 102, + 530, + 133 + ], + "spans": [ + { + "bbox": [ + 45, + 102, + 530, + 133 + ], + "type": "text", + "content": "Table 4. Experiments of text-to-video retrieval on MSRVTT, DiDeMo and LSMDC datasets. “#PT Pairs” lists the number of video-text pairs for pre-training. We show results with zero-shot evaluation (top) and fine-tuning evaluation (bottom). R@A is the average of R@1, R@5 and R@10." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 133, + 528, + 271 + ], + "lines": [ + { + "bbox": [ + 48, + 133, + 528, + 271 + ], + "spans": [ + { + "bbox": [ + 48, + 133, + 528, + 271 + ], + "type": "table", + "html": "
Method#PT PairsDiDeMoLSMDCMSRVTT
R@1↑R@5↑R@10↑R@A↑MedR↓R@1↑R@5↑R@10↑R@A↑MedR↓R@1↑R@5↑R@10↑R@A↑MedR↓
Frozen [2]5.5M21.146.056.241.17.09.322.030.120.551.018.739.551.636.610.0
VIOLET [12]186M23.549.859.844.4------25.949.559.745.0-
OA-Trans [49]5.5M23.550.459.844.66.0-----23.447.555.642.28.0
ALPRO [24]5.5M23.847.357.943.06.0-----24.144.755.441.48.0
BridgeFormer [14]5.5M25.650.661.145.85.012.225.932.223.442.026.046.456.442.97.0
MILES [15]5.5M27.250.363.647.05.011.124.730.622.150.726.147.256.943.47.0
TW-BERT5.5M28.452.964.548.64.014.230.436.026.928.026.850.059.945.65.0
Frozen [2]5.5M31.059.872.454.43.015.030.839.828.520.031.059.570.553.73.0
VIOLET [12]186M32.662.874.756.7-16.136.641.231.3-34.563.073.457.0-
ALPRO [24]5.5M35.967.578.860.73.0-----33.960.773.255.93.0
OA-Trans [49]5.5M34.864.475.158.13.018.234.343.732.118.535.863.476.558.63.0
BridgeFormer [14]5.5M37.062.273.957.73.017.935.444.532.615.037.664.875.159.23.0
MILES [15]5.5M36.663.974.058.23.017.835.644.132.515.537.763.673.858.43.0
TW-BERT5.5M41.871.181.264.72.021.038.849.236.311.038.465.176.660.03.0
", + "image_path": "4a907c58568237e29b09351018f2af93ee11d34b88f3852fa50b895868bae6de.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 282, + 278, + 359 + ], + "blocks": [ + { + "bbox": [ + 68, + 272, + 256, + 282 + ], + "lines": [ + { + "bbox": [ + 68, + 272, + 256, + 282 + ], + "spans": [ + { + "bbox": [ + 68, + 272, + 256, + 282 + ], + "type": "text", + "content": "Table 5. ActivityNet Caption with fine-tuning setting." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 282, + 278, + 359 + ], + "lines": [ + { + "bbox": [ + 48, + 282, + 278, + 359 + ], + "spans": [ + { + "bbox": [ + 48, + 282, + 278, + 359 + ], + "type": "table", + "html": "
Method#PT PairsR@1↑R@5↑R@10↑MedR↓
Dense [19]-14.032.0-34.0
FSE [60]-18.244.8-7.0
CE [30]-18.247.7-6.0
HSE [60]-20.549.3--
Clipbert [23]5.6M21.349.063.56.0
TW-BERT5.5M31.762.374.93.0
", + "image_path": "fa82769894483cf8a170fea100cef8c8841991d5c97749640f83ba6000f98426.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 381, + 277, + 507 + ], + "blocks": [ + { + "bbox": [ + 46, + 360, + 278, + 380 + ], + "lines": [ + { + "bbox": [ + 46, + 360, + 278, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 278, + 380 + ], + "type": "text", + "content": "Table 6. Experiments of video question answering on MSRVTT and MSVD datasets in top-1 accuracy " + }, + { + "bbox": [ + 46, + 360, + 278, + 380 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 381, + 277, + 507 + ], + "lines": [ + { + "bbox": [ + 48, + 381, + 277, + 507 + ], + "spans": [ + { + "bbox": [ + 48, + 381, + 277, + 507 + ], + "type": "table", + "html": "
Method#PT PairsMSRVTTMSVD
Clipbert [23]5.6M37.4-
ALPRO [24]5.5M42.145.9
SINGULARITY [22]5.5M42.745.9
LGDN [33]15.2M43.1-
SSML [1]100M35.135.1
JustAsk [57]69M41.546.3
MERLOT [59]180M43.1-
VIOLET [12]186M43.947.9
TW-BERT5.5M43.648.5
", + "image_path": "ed154dc2daf69b6228e4e3091df2097f7e902ca0d9084ba4130a91b28c38f4ba.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 507, + 279, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 507, + 279, + 542 + ], + "spans": [ + { + "bbox": [ + 45, + 507, + 279, + 542 + ], + "type": "text", + "content": "clearly. Then TW-BERT attends to the part where the dog is in contact with the cone according to the query word \"picks\" while Base only focuses on the body of the dog." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 548, + 181, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 181, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 181, + 561 + ], + "type": "text", + "content": "4.5. Comparisons with SOTA" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 566, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 566, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 566, + 279, + 729 + ], + "type": "text", + "content": "We compare TW-BERT with previous methods on two frequently applied tasks: video-text retrieval (VDTR) and video question answering (VDQA). Table 4 and 5 report the performances of VDTR on MSRVTT [56], DiDeMo [16], LSMDC [43], and ActivityNet Caption [19], respectively, where the former three datasets contain both zero-shot and fine-tuning setups and the last one only has fine-tuning setup. Table 6 reports the VDQA on MSRVTT [56] and MSVD [6]. Among the compared models, MILES [15], BridgeFormer [14], OA-Trans [49], Clipbert [23] and VIOLET [12] are SOTA models proposed in recently 1-2 years. Note that VIOLET [12] and ALPRO [24] distill knowledge from additional large-scale BERTs while we do not. Also, we show the number of pre-training video-text pairs in these" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 297, + 278, + 433, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 278, + 433, + 290 + ], + "spans": [ + { + "bbox": [ + 297, + 278, + 433, + 290 + ], + "type": "text", + "content": "tables for more clear comparisons." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "spans": [ + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "text", + "content": "From these tables, we can find that when the pre-training data is in the same scale, TW-BERT achieves the best performance compared with all the other models on both VDTR and VDQA. For example, on DiDeMo VDTR, TW-BERT outperforms BridgeFormer by " + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "inline_equation", + "content": "4.8\\%" + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "inline_equation", + "content": "\\mathbb{R}@\\mathbb{1}" + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "text", + "content": ", or on MSVD VDQA, TW-BERT outperforms ALPRO by " + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "inline_equation", + "content": "2.6\\%" + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "text", + "content": ". Moreover, compared with the models trained on much more data, TW-BERT can still achieve the best performances on various tasks, e.g., on LSMDC VDTR, TW-BERT outperforms VIOLET by " + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "inline_equation", + "content": "8.0\\%" + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "inline_equation", + "content": "\\mathbb{R}@\\mathbb{10}" + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "text", + "content": " or on MSRVTT VDQA, TW-BERT outperforms MERLOT [59] by " + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 296, + 300, + 530, + 429 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 439, + 531, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 439, + 531, + 568 + ], + "spans": [ + { + "bbox": [ + 296, + 439, + 531, + 568 + ], + "type": "text", + "content": "Note that the videos in LSMDC are longer than MSRVTT and DiDeMo, which means that the videos in this dataset contain more temporal contexts than the other datasets. Then as shown in Table 4, the improvements of TW-BERT over other SOTAs are larger than the improvements on the other datasets. For example, compared with BridgeFormer, TW-BERT has an average " + }, + { + "bbox": [ + 296, + 439, + 531, + 568 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 296, + 439, + 531, + 568 + ], + "type": "text", + "content": " improvement in the zero-shot setting, while on DiDeMo dataset, the corresponding average improvement over MILES is only " + }, + { + "bbox": [ + 296, + 439, + 531, + 568 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 296, + 439, + 531, + 568 + ], + "type": "text", + "content": ". Such comparisons further validate the effectiveness of TW-BERT in exploiting temporal contexts." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": "Among these SOTAs, only when compared with VIOLET, which uses an additional large-scale model DALLE [40] and 32 more times pre-training data than ours (180M VS. 5.5M), TW-BERT cannot comprehensively surpass VIOLET on all the tasks. For example, on MSRVTT VDQA, VIOLET achieves " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": " higher than TW-BERT, while such marginal improvements are got at the cost of much more training resources. Furthermore, TW-BERT still outperforms VIOLET on the other tasks, e.g., on DiDeMo VDTR, TW-BERT outperforms VIOLET by " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "9.2\\%" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": " on R@1 or on MSVD VDQA, TW-BERT outperforms VIOLET by " + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 296, + 578, + 530, + 730 + ], + "type": "text", + "content": ". These comparisons confirm the effectiveness of the proposed TW-BERT." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "2511" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 105, + 116, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 105, + 116, + 117 + ], + "spans": [ + { + "bbox": [ + 46, + 105, + 116, + 117 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 125, + 281, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 125, + 281, + 255 + ], + "spans": [ + { + "bbox": [ + 45, + 125, + 281, + 255 + ], + "type": "text", + "content": "We propose a novel Trajectory-Word BERT (TW-BERT) that builds Trajectory-to-Word alignments for solving video-language tasks. In particular, we introduce an asymmetric cross-modal encoder that contains word-to-patch (W2P) and Trajectory-to-Word (T2W) to capture cross-modal associations. Moreover, a novel Hierarchical Frame-Selector (HFS) module is proposed in the fine-tuning stage to filter out irrelevant frames to help the later T2W attention learn better trajectory-word alignments. Extensive experiments across diverse tasks confirm the effectiveness of the proposed TW-BERT." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 266, + 158, + 279 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 158, + 279 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 158, + 279 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 285, + 279, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 285, + 279, + 367 + ], + "spans": [ + { + "bbox": [ + 45, + 285, + 279, + 367 + ], + "type": "text", + "content": "This work is supported by National Science Foundation of China (62206048), National Key R&D Program of China (2018AAA0100104, 2018AAA0100100), Natural Science Foundation of Jiangsu Province (BK20220819, BK20211164), and Young Elite Scientists Sponsorship Program of Jiangsu Association for Science and Technology Tj-2022-027." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 379, + 103, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 379, + 103, + 391 + ], + "spans": [ + { + "bbox": [ + 47, + 379, + 103, + 391 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 399, + 280, + 729 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 51, + 399, + 279, + 442 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 399, + 279, + 442 + ], + "spans": [ + { + "bbox": [ + 51, + 399, + 279, + 442 + ], + "type": "text", + "content": "[1] Elad Amrani, Rami Ben-Ari, Daniel Rotman, and Alex Bronstein. 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In CVPR, page 8746-8755, 2020. 2" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "type": "text", + "content": "2514" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Unified Decompositional and Compositional NeRF for Editable Novel View Synthesis/d796471e-04ce-409b-90cf-4f80b508e362_content_list.json b/2023/Learning Unified Decompositional and Compositional NeRF for Editable Novel View Synthesis/d796471e-04ce-409b-90cf-4f80b508e362_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7a2af0ad60c31eec834a444b07f72f82e5d4aa --- /dev/null +++ b/2023/Learning Unified Decompositional and Compositional NeRF for Editable Novel View Synthesis/d796471e-04ce-409b-90cf-4f80b508e362_content_list.json @@ -0,0 +1,1637 @@ +[ + { + "type": "text", + "text": "Learning Unified Decompositional and Compositional NeRF for Editable Novel View Synthesis", + "text_level": 1, + "bbox": [ + 163, + 130, + 807, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yuxin Wang", + "bbox": [ + 274, + 202, + 383, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wayne $\\mathbf{W}\\mathbf{u}^{2}$", + "bbox": [ + 450, + 203, + 549, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dan $\\mathrm{Xu}^{1*}$", + "bbox": [ + 614, + 203, + 694, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Hong Kong University of Science and Technology $^{2}$ Shanghai Artificial Intelligence Laboratory", + "bbox": [ + 99, + 231, + 870, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ywangom@connect.ust.hk, wuwenyan0503@gmail.com, danxu@cse.ust.hk", + "bbox": [ + 199, + 253, + 767, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 301, + 313, + 318 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Implicit neural representations have shown powerful capacity in modeling real-world 3D scenes, offering superior performance in novel view synthesis. In this paper, we target a more challenging scenario, i.e., joint scene novel view synthesis and editing based on implicit neural scene representations. State-of-the-art methods in this direction typically consider building separate networks for these two tasks (i.e., view synthesis and editing). Thus, the modeling of interactions and correlations between these two tasks is very limited, which, however, is critical for learning high-quality scene representations. To tackle this problem, in this paper, we propose a unified Neural Radiance Field (NeRF) framework to effectively perform joint scene decomposition and composition for modeling real-world scenes. The decomposition aims at learning disentangled 3D representations of different objects and the background, allowing for scene editing, while scene composition models an entire scene representation for novel view synthesis. Specifically, with a two-stage NeRF framework, we learn a coarse stage for predicting a global radiance field as guidance for point sampling, and in the second fine-grained stage, we perform scene decomposition by a novel one-hot object radiance field regularization module and a pseudo supervision via inpainting to handle ambiguous background regions occluded by objects. The decomposed object-level radiance fields are further composed by using activations from the decomposition module. Extensive quantitative and qualitative results show the effectiveness of our method for scene decomposition and composition, outperforming state-of-the-art methods for both novel-view synthesis and editing tasks1.", + "bbox": [ + 75, + 334, + 473, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 809, + 209, + 825 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The reconstruction and rendering of natural scenes are important for computers to understand the 3D physical", + "bbox": [ + 76, + 835, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f55d370e73552652219ebd6f8978ea9bd2bca8a3a90a73655a5cbeeee5e117c6.jpg", + "image_caption": [ + "Figure 1. Illustration of our decomposition-composition design. It enables scene editing and novel view synthesis in a unified NeRF framework. The proposed decomposition targets learning disentangled 3D representations of different foreground objects and the background, allowing for scene editing, while scene composition constructs an entire scene representation for novel view synthesis." + ], + "image_footnote": [], + "bbox": [ + 511, + 301, + 879, + 517 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "world. Fine-grained object-level representations within the scene can bring significant benefits in various applications, such as scene understanding, novel content generation via object editing, and robotic manipulation. The emerging neural rendering techniques [17, 18, 24] allow learning object-level or scene-level representations from multi-view posed images and enable rendering high-quality images from novel views. However, most implicit neural methods model an entire scene and lack fine-grained representations of objects in the scene, which severely limits object-level scene representation and understanding.", + "bbox": [ + 496, + 609, + 892, + 776 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning effective 3D object-aware implicit neural scene representations is still in its infancy. Existing works that tackle this challenging problem typically utilize additional object-level semantic supervision as a priori knowledge in the model optimization [35, 37, 42]. For instance, ObjectSDF [35] considers learning object-level geometries and semantics with an implicit signed distance function (SDF), which achieves effective scene composition from object-", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 875, + 222, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Project: https://w-ted.github.io/publications/udc-nerf", + "bbox": [ + 94, + 887, + 380, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18247", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "level representations. However, it remains challenging for this framework to perform joint object editing and novel view synthesis. On the other hand, ObjectNeRF [37] explores scene modeling with Neural Radiance Fields (NeRF) via introducing learnable object activation codes as switchers to condition the radiance field prediction among different objects. This framework can perform joint scene editing and novel view synthesis benefiting from the radiance field representations. However, it learns two separate networks for these two tasks, a global scene branch for novel view synthesis, and a local object branch for scene editing, without modeling any interaction or correlation among them, which, however, is critical for learning more effective scene representations, due to the simple fact that, global scene and local object representations are two important perspectives of the same scene. The global entire scene representation can model the scene's overall structures and appearance consistency, and the local object-specific representation can learn more fine-grained object details. They are highly complementary for learning a high-quality scene representation.", + "bbox": [ + 76, + 90, + 472, + 395 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To target the above-mentioned problem, this paper proposes a unified decompositional and compositional neural radiance field framework (see Fig. 1), to learn 3D scene representation for joint scene editing and novel view synthesis. The decomposition can provide the functionality of learning disentangled 3D representations of different objects and the background, allowing for scene editing, while scene composition models an entire scene representation for novel view synthesis. These two can be united to facilitate the consistency constraint in the unified optimization framework. Specifically, we design a new two-stage framework for the scene decomposition and composition, consisting a coarse and a fine stage. In the coarse stage, we learn to predict a global scene radiance field as guidance for point sampling, and in the second fine-grained stage, we perform joint scene decomposition and composition. To perform effective scene decomposition, in the fine-stage, we apply a set of learnable object codes to predict distinct object-level radiance fields, and also propose two novel decomposition strategies: (i) 3D one-hot object radiance activation and regularization. For the object or background branches, only one branch is activated during training using a designed Gumbel-Softmax activation function directly applied on the point density predicted from different object/background branches with also a corresponding one-hot regularization; (ii) an in-painting pseudo supervision strategy. A challenge in scene rendering is modeling the appearance and geometry of regions occluded by objects. This causes generation ambiguity especially when the occluded regions are unseen in all the training views. To address this issue, we propose to use a pretrained inpainting model to provide additional pseudo-color supervision for those ambiguous areas. Note that although the 2D inpainting may bring new ambiguity for the regions", + "bbox": [ + 76, + 401, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "seen in other views, the supervision from multi-view consistency is strong enough to suppress most ambiguities. The composition is further performed by utilizing the learned one-hot activation weights for different object-level radiance fields.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, this paper has the following contributions:", + "bbox": [ + 517, + 167, + 883, + 183 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel NeRF framework for joint scene decomposition and composition to effectively learn object-level and scene-level implicit representations for effective scene modeling, allowing object editing and novel view synthesis in a unified pipeline.", + "- To learn a robust scene decomposition, we design two novel strategies, i.e., 3D one-hot radiance regularization and 2D in-painting pseudo supervision, to significantly improve the rendering and editing qualities.", + "- Extensive experiments demonstrate the effectiveness of our approach for scene decomposition and show clear improvements upon state-of-the-art object-compositional methods on two important downstream tasks, i.e. novel-view synthesis and object editing." + ], + "bbox": [ + 517, + 189, + 890, + 405 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 421, + 640, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Implicit Representations. As pioneering methods, [17, 21, 24, 28] introduce neural networks to implicitly parameterize 3D scenes. These works can learn continuous shape and texture from differentiable rendering with [12, 24] or without[21, 28] 3D supervision. Neural Radiance Fields (NeRF) [18] optimize a 3D continuous neural scene representation by using only 2D multiview posed images for training and produce high-quality novel view synthesis with 3D structure awareness. Recent works also extend the generalization of NeRF to more significant scenes [1, 2, 41], or model scenes with fewer perspectives [5, 33, 39]. However, all these works only focus on the entire scene representation, neglecting fine-grained representations of objects/background within the scene. Other researches represent object surfaces with implicit neural function to realize multi-view 3D reconstruction for single objects [22, 32, 38]. The decomposed implicit representation for independently characterizing components within the scene has been studied in not only object scenes [3, 14, 8, 23, 25, 27], but also in the face or body tasks [9, 11, 34]. In contrast to these works, our method targets both scene synthesis and editing, considering joint object- and scene-level implicit representation learning.", + "bbox": [ + 496, + 446, + 890, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object-Compositional Implicit Representation. Representing scenes in an object-compositional manner can benefit both scene synthesis and editing [3, 4, 26, 29, 30, 35, 40, 36]. Compared to decomposed object representations represented by generative models [7, 19, 20], implicit models present more 3D physical meaning during the modeling process, which facilitates image rendering from novel", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18248", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7f548f64d762a0318317ce2902740ad683358c52c7f50faf9bdf1a05232f5ed7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 93, + 467, + 220 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8a472b2ea1c44c8a082c7a5f953949f41703a76b429feb0d17ac953a3716d04b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 473, + 99, + 883, + 191 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fcedf36b74ac6897eb19760ac73b982eeb0400d71b2d582cd58b377ba833ec81.jpg", + "image_caption": [ + "Figure 2. An overview of the proposed unified decompositional and compositional NeRF framework for joint novel view synthesis and scene editing. It has two stages. In the first stage (i.e. the coarse stage), it learns a guidance radiance field for guiding point sampling. In the second stage (i.e. the fine stage), we learn scene decomposition via learnable object codes and two novel decomposition schemes: (i) the 3D one-shot object radiance activation regularization and (ii) color inpainting handling ambiguous generation in occluded background areas. The scene composition is achieved by using one-hot activation weights for different object-level radiance fields learned in the decomposition stage. The decomposition allows scene editing and the composition enables novel view synthesis in the unified framework." + ], + "image_footnote": [], + "bbox": [ + 86, + 222, + 890, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "views. We can categorize the works of object-compositional implicit representations into supervised and unsupervised methods. The unsupervised methods localize objects with different aspects of prior information, such as multiple similar scenes [26, 29, 40], temporal consistency [13], or clustering-based initialization [15]. Specifically, uORF [40] involves a slot-attention [13] module in learning object-level iterative attention masks for each object decomposition. RFP [15] utilizes clustering predictions as initialization and applies a bidirectional color loss to decompose individual objects. However, lacking precise annotation, although these methods can obtain object position clues, they usually suffer from low-resolution [26, 40] issues that restrict generalization ability to high-resolution real-world scenes. The supervised methods usually use object-level annotations, such as semantic masks [35, 37, 42] or scene graphs [23]. Among these works, ObjectNeRF [37] utilizes a two-branch network to learn a scene radiance field with an activation code-conditioned object radiance field supervised by multi-view images and semantic masks. Similarly, ObjectSDF [35] encodes the entire scene by combining the individual Signed Distance Functions (SDF) represented with semantic labels. The most related work to us is ObjectNeRF [37]. In contrast to ObjectNeRF, we model", + "bbox": [ + 75, + 536, + 472, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "an the scene representation via joint scene decomposition and composition, which can effectively model global consistency and rich local details in a unified NeRF framework for a high-quality scene representation.", + "bbox": [ + 498, + 536, + 890, + 597 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Decompositional and Compositional NeRF", + "text_level": 1, + "bbox": [ + 498, + 613, + 880, + 631 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a set of multi-view posed images $\\{x_{i}, i \\in [1, N]\\}$ and their corresponding instance semantic masks $\\{s_{ij}, i \\in [1, N], j \\in [1, K + 1]\\}$ of a static real-world scene, our goal is to learn an entire scene representation based on the composition of a global scene radiance field and explicitly decomposed local radiance fields of different objects and the background. The decomposition allows scene editing and the composition enables novel view synthesis. $N$ is the number of multi-view images, and $K$ is the number of object instances, where we regard the background as an additional instance. We propose a joint decomposition and composition framework to allow simultaneous performing these two tasks.", + "bbox": [ + 496, + 636, + 890, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Framework Overview", + "text_level": 1, + "bbox": [ + 500, + 845, + 705, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overall framework illustration is shown in Fig. 2. It consists of two rendering stages. In the first stage (i.e. the", + "bbox": [ + 500, + 869, + 892, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18249", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "coarse stage), it learns a global scene guidance radiance field for guiding point sampling. In the second stage (i.e. the fine stage), we learn scene decomposition and composition. The decomposition is performed via first applying a set of learnable object codes as conditions to predict $K + 1$ local object/background radiance field components, where $K$ is the number of objects, and the additional 1 represents the background. Following NeRF [18], we use continuous neural radiance fields to represent each local object/background. Considering the composition nature that the whole scene consists of all the $K + 1$ components, we composite all the object and background radiance fields to an entire scene radiance field based on a proposed one-hot object radiance activation module. We also propose an effective color-inpainting strategy to handle the ambiguity in generating occluded background regions. The residual prediction from the first coarse stage is also utilized to benefit from a global scene representation. In the following subsections, we first give a general introduction to the proposed unified framework. Then, we introduce our novel decomposition and composition design and how the method can help disentangle different objects explicitly. After that, we present how our unified framework is optimized and utilized for both novel-view synthesis and editing tasks.", + "bbox": [ + 76, + 90, + 472, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Scene Decomposition", + "text_level": 1, + "bbox": [ + 76, + 465, + 274, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Two-branch network architecture design. For scene decomposition in the fine-stage, we design a two-branch network architecture with a shared MLP backbone to learn generic implicit scene representation from input point coordinates (see Fig. 3). Specifically, the shared backbone takes a sampled 3D point coordinate $\\mathbf{p} = (x,y,z)$ and view direction $\\mathbf{d}$ of a camera ray as input, and predicts a generic scene feature vector $\\mathbf{f}$ . Similar to [37], we also apply a set of learnable codes, each representing the background or an object. We further pass $\\mathbf{f}$ accompanying with background or object codes to the following MLP heads. For better background learning, we use separate the background head and the object head, predicting an RGB color $\\mathbf{c}_{\\mathrm{object}}^i$ and a volume density $\\sigma_{\\mathrm{object}}^i$ for the corresponding background or object $i$ . For simplicity, we refer to the background as a particular object with index $i = 1$ . For efficient point sampling, we apply a coarse-to-fine sampling technique. In the coarse stage, we only adopt several MLPs after the backbone for predicting RGB color $\\mathbf{c}_{\\mathrm{guidance}}$ and volume density $\\sigma_{\\mathrm{guidance}}$ of the global scene. We use the distribution of coarse prediction for the fine point coordinate sampling, so we call these MLPs guidance head. In the fine stage, we also use the prediction of the guidance head as a residual radiance field in the following composition module.", + "bbox": [ + 76, + 489, + 472, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D one-hot density regularization. To achieve effective decomposition of objects/background radiance fields from the scene, we also design a one-hot regularization term for", + "bbox": [ + 76, + 854, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the uncertain regions in the background radiance field. Our motivation is that the 3D points belonging to the foreground objects should not have any volume density in the background radiance field. We thus apply a one-hot regularization loss term, which acts as an additional constraint to the object-specific radiance field optimization objective $\\mathcal{L}_{\\mathrm{object}}$ . In detail, we first obtain the 3D point positions that foreground objects occupy by determining whether the foreground objects take the largest volume density at the points. We thus define a binary occupancy mask $M_{c}$ , and apply a regularization term for the occupied points as follows:", + "bbox": [ + 496, + 90, + 893, + 258 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {c} = \\left[ \\operatorname {a r g m a x} \\left(\\left[ \\sigma_ {\\text {o b j e c t}} ^ {1}, \\sigma_ {\\text {o b j e c t}} ^ {2}, \\sigma_ {\\text {o b j e c t}} ^ {3}, \\dots , \\sigma_ {\\text {o b j e c t}} ^ {K + 1} \\right]\\right) > 1 \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 263, + 890, + 291 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {o n e - h o t}} = M _ {c} \\| \\sigma_ {\\mathrm {o b j e c t}} ^ {1} - \\sigma_ {0} \\| _ {2} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 286, + 704, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\sigma_{\\mathrm{object}}^{1}$ here means we only want to constrain the background radiance field (with index 1). Note that we implement a ReLU operation on the volume density $\\sigma$ to make it positive during the volume rendering process, so if the raw prediction $\\sigma_{\\mathrm{object}}^{1}$ is negative at some points, it will also have no contribution to the rendering results. Therefore, we can set $\\sigma_0$ as any non-positive number here. We put it -0.01 in our experiments from experience.", + "bbox": [ + 496, + 311, + 893, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2D in-painting pseudo supervision. To model a better background-specific radiance field, we need to learn what the scene looks like even if all the foreground objects are removed from the scene. Several occluded regions in the background can be seen in other views, while regions covered by the objects are invisible from all views, which are uncertain regions. We thus do not have any pixel-wise supervision for those regions in the training data, resulting in unsatisfactory extrapolation results on those regions when we learn the background radiance field. To tackle this problem, we involve a pre-trained in-painting model to fill those uncertain regions on the 2D images. Our motivation is that the 2D in-painting model can utilize local context information on an image to fill the regions, providing effective 2D pseudo color supervision. Specifically, we use a famous pre-trained lama [31] model to fill the uncertain 2D background regions and then apply a color loss for the rendered background pixels with a foreground mask $M_{1}(r)^{1}$ :", + "bbox": [ + 496, + 434, + 893, + 708 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o l o r . p s e u d o}} = M _ {1} (r) ^ {1} \\| \\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {1} - C (\\boldsymbol {r}) _ {\\text {p s e u d o}} \\| _ {2} ^ {2} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 714, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intermediate local object rendering. To enforce the decomposition of all object-specific radiance fields, we apply a color consistent loss and an opacity loss with semantic masks as [18, 37] via rendering both 2D color and opacity:", + "bbox": [ + 496, + 741, + 893, + 804 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} = \\sum_ {i = 1} ^ {N} T _ {i} ^ {k} \\left(1 - \\exp \\left(- \\sigma_ {\\text {o b j e c t}} ^ {k} \\delta_ {i}\\right)\\right) \\mathbf {c} _ {\\text {o b j e c t}} ^ {k}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 818, + 890, + 867 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {O} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} = \\sum_ {i = 1} ^ {N} T _ {i} ^ {k} \\left(1 - \\exp \\left(- \\sigma_ {\\text {o b j e c t}} ^ {k} \\delta_ {i}\\right)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 861, + 805, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18250", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T_{i}^{k} = \\exp (-\\sum_{j = 1}^{i - 1}\\sigma_{\\mathrm{object}}^{k}\\delta_{j})$ is the transmittance representing how much light is transmitted along the ray for the $k$ -th object; $N$ is the number of sampled points along the camera ray, and $\\delta_{i}$ is the distance between two adjacent points. Then we apply the following losses:", + "bbox": [ + 75, + 88, + 472, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {o b j e c t}} = \\sum_ {k = 1} ^ {K + 1} M _ {o} (\\boldsymbol {r}) ^ {k} \\| \\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} - C (\\boldsymbol {r}) \\| _ {2} ^ {2} \\tag {4} \\\\ + \\lambda M _ {b} (\\boldsymbol {r}) ^ {1} \\| \\hat {\\boldsymbol {O}} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {1} - M _ {o} (\\boldsymbol {r}) ^ {1} \\| _ {2} ^ {2}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 171, + 468, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $M_{o}(\\boldsymbol{r})$ and $M_{b}(\\boldsymbol{r})$ are 2D spatial weight maps determined by object-level and background-level semantic masks, respectively, which indicates that rendered object-specific pixels are given supervision at the corresponding semantic mask region. The background region in the binary semantic mask can be either real background or occluded by a foreground object, so we use a small weight value (i.e. 0.05) in $M_{b}$ as a balance weight for the uncertain region.", + "bbox": [ + 75, + 239, + 468, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Scene Composition", + "text_level": 1, + "bbox": [ + 76, + 371, + 261, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section presents how the learned global and the local object/background radiance fields are composited for an entire scene radiance field.", + "bbox": [ + 75, + 395, + 468, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gumbel-Softmax one-hot object radiance activation. As shown in Fig. 3, for each sampled point, there are $K + 1$ predictions in the local radiance field decomposition. Considering that each point in the 3D space can only belong to either one object or the background, we use the predicted $(\\mathbf{c}_{\\mathrm{object}}^i,\\sigma_{\\mathrm{object}}^i)$ with the maximum volume density $\\sigma_{\\mathrm{object}}^i$ among all the object instances to construct an activated object-specific radiance field. More specifically, to address the gradient backpropagation problem of the argmax operation, following [10, 16], We employ the Gumbel-Softmax function on volume density as a continuous and differentiable approximation. First, we calculate a soft probability $p_i$ for the $i$ -th object branch as", + "bbox": [ + 75, + 441, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {i} = \\frac {\\exp^ {\\left(\\left(\\sigma_ {\\text {o b j e c t}} ^ {i} + g _ {i}\\right) / t a u\\right)}}{\\sum_ {j} \\exp^ {\\left(\\left(\\sigma_ {\\text {o b j e c t}} ^ {j} + g _ {j}\\right) / t a u\\right)}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 642, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The above $g_{1}, g_{2}, \\ldots, g_{j}$ are the independent and identically distributed samples drawn from $\\mathrm{Gumbel}(0,1)^{1}$ [10]. The symbol $tau$ is the temperature ratio set to 0.1 in our experiments. Then, we can obtain one-hot composition weights from $p_{i}$ for combining the predictions of all the object/background branches, which ensures one-hot activation for all the object/background radiance fields, and enables effective backpropagation for learning object-specific radiance fields and their composition. Specifically, we calculate the one-hot weights $\\mathbf{M}_{obj}$ as Eq. 6. Let us denote $\\mathbf{P}$ as the soft probability vector, containing $K + 1$ predictions calculated by Eq. 5. $\\mathbf{M}_{obj}$ is a one-hot vector of the $K + 1$ elements. The one-hot vector is calculated with a stop gradient operation $f_{sp}$ on $\\mathbf{P}$ , which not only reserves the one-", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/119bd32f91a14af2a1572654b018ca4de6fce02885f6f1d9cc21cd6986ef969d.jpg", + "image_caption": [ + "Figure 3. Illustration of the Composition Module. Our composition module consists of one-hot object radiance activation and global-local radiance field composition (the two green blocks). We first apply Gumbel-Softmax on object-level volume density values to obtain the one-hot mask for object radiance fields. Then, the local compositional radiance field is generated by a weighted sum of the object and background color and density predictions. Finally, the composited radiance is combined with a residual prediction to produce the final scene radiance field." + ], + "image_footnote": [], + "bbox": [ + 501, + 95, + 885, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "hot activation but also allows the gradient backpropagated through $\\mathbf{P}$ . Then, the computation of $\\mathbf{M}_{obj}$ is written as:", + "bbox": [ + 498, + 487, + 890, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {o b j} = f _ {\\mathrm {h}} \\left(\\underset {i} {\\arg \\max } \\left[ g _ {i} + \\log \\sigma_ {\\text {o b j e c t}} ^ {i} \\right]\\right) - f _ {s p} (\\mathbf {P}) + \\mathbf {P}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 542, + 890, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{\\mathrm{h}}(\\cdot)$ denotes a one-hot function; Then, we obtain a composed scene radiance field $(\\mathbf{c}_{\\mathrm{comp}}, \\sigma_{\\mathrm{comp}})$ of all decomposed branches $\\{\\mathbf{c}_{\\mathrm{object}}^k, \\sigma_{\\mathrm{object}}^k\\}_{k=1}^{K+1}$ , by multiplying the above one-hot weights as follows:", + "bbox": [ + 498, + 571, + 890, + 635 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {\\text {c o m p}} = \\sum_ {K + 1} \\mathbf {M} _ {o b j} ^ {k} \\mathbf {c} _ {\\text {o b j e c t}} ^ {k}, \\sigma_ {\\text {c o m p}} = \\sum_ {K + 1} \\mathbf {M} _ {o b j} ^ {k} \\sigma_ {\\text {o b j e c t}} ^ {k}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 648, + 890, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our novel one-hot object radiance activation can not only ensure a reasonable composition of all the object radiance fields but also force that only one object volume density prediction can be activated in the gradient backpropagation, which can also effectively help the object/background decomposition.", + "bbox": [ + 496, + 686, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Residual radiance field composition. After the one-hot object radiance activation, we further combine the composited radiance fields from objects/background branches with the predicted residual radiance field, to produce a final composited scene radiance field, using point-wise average pooling operation applied on the color and density. Then we apply a color loss $\\mathcal{L}_{\\mathrm{comp}}$ for the pixels rendered from the composited radiance field.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18251", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a20b3085627c0852b5559613fb6a4f8f3b11331de4c7dcdd7b2664b9d2076448.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 117, + 88, + 299, + 194 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3d8ca71b8dee949f496125a81203dd6474e620583a2632951c32204202dc4acb.jpg", + "image_caption": [ + "(a) ObjectNeRF" + ], + "image_footnote": [], + "bbox": [ + 125, + 200, + 184, + 250 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/38d5d87aec16a972d1f152b50678187d88f48fbcc7cdc142a43c3790e52da75b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 196, + 295, + 250 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f2acb23477c765a171ea0529de64f170a6680fb5056c75a40ca5be3470c2314e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 88, + 480, + 195 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6379b79d4ebf1c0db6f3727785ac64a98de8717f73a28725a5168440c06fecaa.jpg", + "image_caption": [ + "(b) ObjectSDF" + ], + "image_footnote": [], + "bbox": [ + 308, + 200, + 366, + 250 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5f0d0b681157b1ac72f259e335e3588ce4301754e0b9cb1fa8750a0d91de14b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 374, + 196, + 478, + 253 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bd2ba4c261b85a2cf046e7a698e0095660a25f253b374c74e09d5bd54e7a6100.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 88, + 663, + 195 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/15f752fb87f862776563dd22fd0805e52510a2656682f2a3ddf8ef7f04bb75ba.jpg", + "image_caption": [ + "(c) Our Method" + ], + "image_footnote": [], + "bbox": [ + 491, + 196, + 549, + 252 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4c7a065c6fea920d2ca186e37618e9aa27f82c1ad2244f02dc4a3ca87a1efe0a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 555, + 196, + 660, + 252 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/464595e8e2c723a16f8059bb43da15c57912281dacb8f9476417fdbcb2e4bb66.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 666, + 88, + 846, + 195 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ff58c5f32dfea550760c0181592fd4a2353a2766a4e41e827af2f27fc7488c61.jpg", + "image_caption": [ + "(d) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 674, + 196, + 732, + 252 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cdb2ea0d7073ef1d321806763efe709f9881bb62be4a4d4b17e15aefc2a92594.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 738, + 196, + 844, + 253 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/510c157d9b4fc482a588efc4086d2265cdc14f65372068965650eec50011d471.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Quantitative comparison of different variants of the proposed unified decompositional and compositional NeRF framework on the ToyDesk2." + ], + "table_body": "
MethodsToyDesk2
PSNR ↑SSIM ↑LPIPS ↓
Our Full-Model25.75600.81260.4488
w/o 3D One-hot Density Regularization25.73620.81160.4524
w/o Gumbel-Softmax Activation22.99720.72170.5452
w/o 2D In-painting pseudo Supervision25.68810.81270.4516
w/o Residual Radiance Composition25.22880.80030.4589
", + "bbox": [ + 78, + 318, + 467, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Optimization and Inference", + "text_level": 1, + "bbox": [ + 76, + 460, + 326, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall framework optimization. The overall optimization loss for training the joint framework consists of the following four different loss functions:", + "bbox": [ + 75, + 484, + 468, + 529 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {o v e r a l l}} = \\mathcal {L} _ {\\text {c o m p}} + \\lambda_ {1} \\mathcal {L} _ {\\text {o b j e c t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {c o l o r - p s e u d o}} + \\lambda_ {3} \\mathcal {L} _ {\\text {o n e - h o t}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 541, + 467, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where, $\\lambda_1, \\lambda_2$ , and $\\lambda_3$ are the weights for balancing the learning with the different loss functions.", + "bbox": [ + 75, + 571, + 468, + 601 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Novel View Rendering and Scene Editing After training the joint framework, we can render images of arbitrary perspectives based on the composited radiance field. By reorganizing the object radiance fields, we can generate images with object manipulations, including removal, addition, duplication, and changing position (e.g., rotation).", + "bbox": [ + 75, + 602, + 468, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 705, + 209, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We aim at performing joint scene novel view synthesis and editing based on our proposed unified decompositional and compositional NeRF framework. We thus evaluate our method on both tasks using challenging public benchmarks.", + "bbox": [ + 75, + 731, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 801, + 266, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We use ToyDesk [37] and ScanNet [6] datasets for the evaluation. ToyDesk consists of two sets of indoor multi-view images. In each scene, several toys are put on a desk in the center of the room. The multi-view images are captured by looking at the desk center with 360 degrees", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/094730c13e062a1cea5ebabc252d0989f7bf248de35ec3f4a40f9c9aa1fec05a.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of novel view synthesis on the ToyDesk dataset. We compared with ObjectNeRF [37] and ObjectSDF [35]. The results show that the rendered images of our framework achieve better generation quality for both the foreground objects (e.g., the green dinosaur) and the background (e.g., the chessboard).", + "Figure 5. Qualitative results of the ablation study: (a) Our full model; (b) w/o 3D One-hot Density Regularization; (c) w/o Gumbel-Softmax Activation; (d) w/o 2D In-painting pseudo Supervision. (e) w/o Residual Radiance Composition." + ], + "image_footnote": [], + "bbox": [ + 501, + 321, + 883, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "around the desk, and the camera poses and meshes are provided. The instance semantic labels are annotated on object meshes and then projected onto each perspective to obtain their corresponding 2D semantic label maps. ScanNet is an RGB-D video dataset that contains more than 1500 scans of indoor scenes for multiple 3D understanding tasks. Handheld RGB-D scanners are used for scanning various indoor scenes. Rich annotations such as camera pose, semantic segmentation, and surface reconstruction are also provided. Following ObjectNeRF [37], we choose four scenes, i.e., 0024_00, 0038_00, 0113_00, and 0192_00, from the whole dataset for the experiment.", + "bbox": [ + 496, + 497, + 892, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. Our joint framework consists of a shared backbone, background head, object head, and guidance head. The share backbone is a 4-layer Multi-Layer Perceptron (MLP), and the output generic implicit scene feature has a dimension of 256. The follow-up heads are all three-layer MLPs with a color and density prediction layer to generate corresponding radiance fields. Note that our one-hot regularization and activation module has no parameters to be optimized. We also utilize positional encoding to increase the representation ability for high-frequency details. Specifically, we adopt ten levels for coordinates and four levels for ray directions. The framework is trained end-to-end from scratch, without voxel feature initialization as in [37] or geometric initialization as in [35].", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18252", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cef947f6420594427ccf09bbd419439c6e0df7635377207c897c82a095cf26ad.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 117, + 87, + 297, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b78376b9146c32f99f19df8092247a42efd62b3b88dd0ddbf7404b1d9758f4a9.jpg", + "image_caption": [ + "(a) ObjectNeRF" + ], + "image_footnote": [], + "bbox": [ + 117, + 195, + 297, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/023ffbed22dab1ab677c12954c46abeb8d1ec61224670f4336152a77472e3e5f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 299, + 87, + 480, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cec874fd2ae7d3129c5e84637e61e73b5e9866e91bdcb3865d56b5f69cd517d6.jpg", + "image_caption": [ + "(b) ObjectSDF" + ], + "image_footnote": [], + "bbox": [ + 300, + 195, + 480, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3799752689e992f3f247b07b6cdfa3d970db442e73b15545f352364cdf8ef5e2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 87, + 661, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/972b59886809444c5007f6ee700b219facd9f5ccb79df2fcaeb9f4fe9cbd3892.jpg", + "image_caption": [ + "(c) Our Method" + ], + "image_footnote": [], + "bbox": [ + 480, + 195, + 661, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ad3ed89a27a4b139c4d0aa10ee1ab2ce50940ed7dd2506324b359bfadc1117d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 663, + 87, + 846, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8f99d0fc6e39722e5bd25b77d15310ff5e60ff0a3c984d368ce63c1585d9dfe1.jpg", + "image_caption": [ + "(d) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 663, + 195, + 844, + 299 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a1452280f8e75eb47ca184e3e0d3eb7d6df3bbe3fe9fb85afebc159ab1d301f9.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison of novel view synthesis on the ScanNet dataset. Compared with ObjectNeRF [37] and ObjectSDF [35], our results also achieve better fidelity. We highlight the details in the red boxes.", + "Figure 7. The Decomposition results on the ToyDesk dataset compared with ObjectNeRF [37]. We show the rendered results of our composited radiance field (the first column) and each background/object radiance field (the second and third columns)." + ], + "image_footnote": [], + "bbox": [ + 109, + 354, + 431, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Model Analysis", + "text_level": 1, + "bbox": [ + 76, + 619, + 232, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baseline Models. To verify the effectiveness of our designs for scene decomposition and composition, We conduct several ablation studies considering different variants: (i) 'w/o 3D One-hot Density Regularization' means that we remove the one-hot regularization term for the uncertain regions in the background radiance field. (ii) 'w/o Gumbel-Softmax Activation' indicates that we do not use the Gumbel-Softmax one-hot weight for compositing the object radiance fields. (iii) 'w/o In-painting Supervision' means that we do not apply the in-painting pseudo supervision for the background radiance field. (iv) 'w/o Residual Radiance Composition' means that we do not use the guidance radiance field for fine sampling and remove the residual radiance composition in the fine stage.", + "bbox": [ + 75, + 643, + 468, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of 3D one-hot density regularization. The quantitative results based on different evaluation metrics, i.e., PSNR, SSIM, and LPIPS, are shown in Table 1. Several", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/67d24e50270123e49c4612ccdf7acefdb011272d6880dcb811fe8148f50fb4cd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetMethodsPSNR ↑SSIM ↑LPIPS↓
ToyDeskObject-NeRF [37]22.17360.77230.4711
Object-SDF [35]22.0298--
Our Method23.14350.78990.4691
ScanNetObject-NeRF [37]25.26400.80470.4094
Object-SDF [35]25.2325--
Our Method26.13490.82490.3951
", + "bbox": [ + 504, + 352, + 890, + 459 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison on novel view synthesis. We compared with ObjectNeRF [37] and ObjectSDF [35]. '-' indicates the metrics are not reported by the authors in the paper. The evaluation results show that our synthesis results quantitatively outperform these two SOTA methods on all the shown metrics.", + "bbox": [ + 496, + 462, + 890, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "examples of rendered images from the learned background radiance field are presented in Fig. 5. We evaluate the effectiveness of 3D one-hot density regularization by disabling the loss term. As can be observed from Table 1, our joint full mode with 3D one-hot density regularization achieves better results than the model without it.", + "bbox": [ + 496, + 537, + 890, + 627 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Gumbel-Softmax object radiance activation. We also investigate the effect of using Gumbel-Softmax one-hot activation for the composition of background/object radiance fields. We use an alternative composition method, in which all the local object/background radiance fields that contribute to the same 3D points in the composited field, are directly added instead of using the Gumbel-Softmax one-hot activation weights, as introduced in the method part. As shown in Fig. 5c, without the Gumbel-Softmax one-hot activation, the model cannot successfully learn a decomposed background radiance field (all black), confirming our motivation of using the Gumbel-Softmax activation for a more effective scene representation in a unified framework.", + "bbox": [ + 496, + 628, + 890, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of 2D in-painting pseudo supervision and residual radiance composition. We also show the contribution of the proposed 2D in-painting pseudo-supervision. If we directly disable the pseudo supervision in the framework, the qualitative results are slightly lower, as shown in the", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18253", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a34154ceaac46e51355d317c4bea0455ad16e8c59bd560b13985ec367b3c6904.jpg", + "image_caption": [ + "Figure 8. The Decomposition results on the ScanNet dataset compared with ObjectNeRF [37]. Our background has fewer artifacts when removing the foreground object." + ], + "image_footnote": [], + "bbox": [ + 119, + 87, + 416, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "next to last row in Table. 1. At the same time, as can be seen in Fig. 5, lacking pseudo supervision suffers from significantly downgraded extrapolation in the region occupied by the foreground objects in the 3D space, which indicates that the proposed scheme can effectively help the local object/background disentanglement, especially for learning the radiance field representation of the background on uncertain regions. As shown in Table. 1 and Fig. 5, if we remove the residual radiance composition, the overall qualitative metrics and background decomposition both decline, which demonstrates the importance of using a global radiation field to provide coarse sampling guidance and also further merged as residual information in the fine stage.", + "bbox": [ + 75, + 335, + 470, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Results on Novel View Synthesis", + "text_level": 1, + "bbox": [ + 76, + 542, + 359, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare our methods on the task of novel view synthesis with two state-of-the-art methods, i.e., ObjectNeRF [37] and ObjectSDF [35]. Our train-test split follows ObjectNeRF [37]. We measure the quality of synthesized images on the evaluation metrics of PSNR, SSIM, and LPIPS. In detail, for our joint framework, we use the finally composited entire scene radiance field for the image rendering. For ObjectNeRF and ObjectSDF on the Toydesk dataset, we use the rendered images provided by the authors for comparison. ObjectSDF adopts a different train-test split and label mapping strategy on ScanNet, so we retrain the ObjectSDF on ScanNet following our setting.", + "bbox": [ + 75, + 568, + 468, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 2, our synthesis results quantitatively outperform the comparison methods on all the shown metrics. We also present the image examples rendered from novel views in Fig. 4 and Fig. 6. As can be observed in Fig. 4, the rendered images of our framework achieve better generation quality for both the foreground objects (e.g., the green dinosaur) and the background (e.g., the chessboard) than both ObjectNeRF [37] and ObjectSDF [35], proving the capability of our method in modeling both global scene consistency and local scene details. Fig. 6 shows the synthesized images", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/34d20b9a42b400049fe126a6513010c65266d3f5b2ab57901ba809bbca039c0d.jpg", + "image_caption": [ + "(a) Original view" + ], + "image_footnote": [], + "bbox": [ + 519, + 88, + 692, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4f3966fa82aca8505514fc7b68b2a9aceb7217673826628326c113a3d01f4466.jpg", + "image_caption": [ + "(b) Edited image", + "Figure 9. Illustration of the editing results. (a) shows the image in the original view, and (b) shows the editing result from the same perspective. We do the rotation and duplication for the white triangle and candy by re-composting the learned radiance fields." + ], + "image_footnote": [], + "bbox": [ + 694, + 88, + 867, + 189 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "on ScanNet. We can also observe that our results outperform others in the overall fidelity and local details marked in the red boxes.", + "bbox": [ + 498, + 263, + 890, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Results of Object Decomposition and Editing", + "text_level": 1, + "bbox": [ + 500, + 316, + 880, + 333 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also conduct experiments to show the decomposition effectiveness of our method, especially for the background radiance field. As shown in Fig. 7 and Fig. 8, we rendered the composited radiance field and each local object/background radiance field to show the decomposition results. The background images in Fig. 7 clearly show that our method can generate a clearer table without unsatisfactory artifacts such as strange colors and black shadow effects when removing all the foreground objects on the table. Although with some remained black contours, the rendered pixel colors of the regions below the objects are significantly more reasonable compared to ObjectNeRF [37]. Note that the region under the toys is unseen in any view. Our decomposition module enables clear background and object-specific details, while the composition design helps the rendered entire scene achieve higher quality than the baseline. In Fig. 8, we further show that our pipeline can also provide better background rendering when removing foreground objects on the images from the ScanNet dataset. The better decomposition naturally benefits downstream object editing tasks. Fig. 9 shows that, after learning composited radiance fields, our method can perform rotation and duplication for the white triangle and candy by re-compositing the object and background radiance field representations. We add more editing results in the supplementary materials.", + "bbox": [ + 496, + 340, + 890, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 746, + 617, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a unified NeRF framework with a novel decomposition and composition design to jointly model real-world scenes with both global and local implicit representations. To solve the ambiguous extrapolation problem for unseen areas, we also propose a 3D one-hot density regularization strategy and a 2D in-painting pseudo supervision. Our experimental evaluation demonstrates that our method outperforms the state-of-the-art object-compositional methods for both novel-view synthesis and scene editing tasks.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18254", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 76, + 90, + 256, + 107 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This research is supported in part by HKUST-SAIL joint research funding, the Early Career Scheme of the Research Grants Council (RGC) of the Hong Kong SAR under grant No. 26202321, and HKUST Startup Fund No. R9253.", + "bbox": [ + 76, + 114, + 468, + 176 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 194, + 174, + 209 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In ICCV, 2021. 2", + "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Mip-nerf 360: Unbounded anti-aliased neural radiance fields. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.165, + 0.131, + 0.808, + 0.177 + ], + "angle": 0, + "content": "Learning Unified Decompositional and Compositional NeRF for Editable Novel View Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.203, + 0.384, + 0.222 + ], + "angle": 0, + "content": "Yuxin Wang" + }, + { + "type": "text", + "bbox": [ + 0.452, + 0.204, + 0.55, + 0.222 + ], + "angle": 0, + "content": "Wayne \\(\\mathbf{W}\\mathbf{u}^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.616, + 0.204, + 0.696, + 0.221 + ], + "angle": 0, + "content": "Dan \\(\\mathrm{Xu}^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.232, + 0.871, + 0.252 + ], + "angle": 0, + "content": "\\(^{1}\\)Hong Kong University of Science and Technology \\(^{2}\\)Shanghai Artificial Intelligence Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.254, + 0.768, + 0.267 + ], + "angle": 0, + "content": "ywangom@connect.ust.hk, wuwenyan0503@gmail.com, danxu@cse.ust.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.303, + 0.314, + 0.319 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.474, + 0.789 + ], + "angle": 0, + "content": "Implicit neural representations have shown powerful capacity in modeling real-world 3D scenes, offering superior performance in novel view synthesis. In this paper, we target a more challenging scenario, i.e., joint scene novel view synthesis and editing based on implicit neural scene representations. State-of-the-art methods in this direction typically consider building separate networks for these two tasks (i.e., view synthesis and editing). Thus, the modeling of interactions and correlations between these two tasks is very limited, which, however, is critical for learning high-quality scene representations. To tackle this problem, in this paper, we propose a unified Neural Radiance Field (NeRF) framework to effectively perform joint scene decomposition and composition for modeling real-world scenes. The decomposition aims at learning disentangled 3D representations of different objects and the background, allowing for scene editing, while scene composition models an entire scene representation for novel view synthesis. Specifically, with a two-stage NeRF framework, we learn a coarse stage for predicting a global radiance field as guidance for point sampling, and in the second fine-grained stage, we perform scene decomposition by a novel one-hot object radiance field regularization module and a pseudo supervision via inpainting to handle ambiguous background regions occluded by objects. The decomposed object-level radiance fields are further composed by using activations from the decomposition module. Extensive quantitative and qualitative results show the effectiveness of our method for scene decomposition and composition, outperforming state-of-the-art methods for both novel-view synthesis and editing tasks1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.81, + 0.21, + 0.826 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.836, + 0.47, + 0.867 + ], + "angle": 0, + "content": "The reconstruction and rendering of natural scenes are important for computers to understand the 3D physical" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.303, + 0.88, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.519, + 0.895, + 0.603 + ], + "angle": 0, + "content": "Figure 1. Illustration of our decomposition-composition design. It enables scene editing and novel view synthesis in a unified NeRF framework. The proposed decomposition targets learning disentangled 3D representations of different foreground objects and the background, allowing for scene editing, while scene composition constructs an entire scene representation for novel view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.893, + 0.777 + ], + "angle": 0, + "content": "world. Fine-grained object-level representations within the scene can bring significant benefits in various applications, such as scene understanding, novel content generation via object editing, and robotic manipulation. The emerging neural rendering techniques [17, 18, 24] allow learning object-level or scene-level representations from multi-view posed images and enable rendering high-quality images from novel views. However, most implicit neural methods model an entire scene and lack fine-grained representations of objects in the scene, which severely limits object-level scene representation and understanding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Learning effective 3D object-aware implicit neural scene representations is still in its infancy. Existing works that tackle this challenging problem typically utilize additional object-level semantic supervision as a priori knowledge in the model optimization [35, 37, 42]. For instance, ObjectSDF [35] considers learning object-level geometries and semantics with an implicit signed distance function (SDF), which achieves effective scene composition from object-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.223, + 0.888 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.382, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)Project: https://w-ted.github.io/publications/udc-nerf" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.382, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18247" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.396 + ], + "angle": 0, + "content": "level representations. However, it remains challenging for this framework to perform joint object editing and novel view synthesis. On the other hand, ObjectNeRF [37] explores scene modeling with Neural Radiance Fields (NeRF) via introducing learnable object activation codes as switchers to condition the radiance field prediction among different objects. This framework can perform joint scene editing and novel view synthesis benefiting from the radiance field representations. However, it learns two separate networks for these two tasks, a global scene branch for novel view synthesis, and a local object branch for scene editing, without modeling any interaction or correlation among them, which, however, is critical for learning more effective scene representations, due to the simple fact that, global scene and local object representations are two important perspectives of the same scene. The global entire scene representation can model the scene's overall structures and appearance consistency, and the local object-specific representation can learn more fine-grained object details. They are highly complementary for learning a high-quality scene representation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.402, + 0.473, + 0.904 + ], + "angle": 0, + "content": "To target the above-mentioned problem, this paper proposes a unified decompositional and compositional neural radiance field framework (see Fig. 1), to learn 3D scene representation for joint scene editing and novel view synthesis. The decomposition can provide the functionality of learning disentangled 3D representations of different objects and the background, allowing for scene editing, while scene composition models an entire scene representation for novel view synthesis. These two can be united to facilitate the consistency constraint in the unified optimization framework. Specifically, we design a new two-stage framework for the scene decomposition and composition, consisting a coarse and a fine stage. In the coarse stage, we learn to predict a global scene radiance field as guidance for point sampling, and in the second fine-grained stage, we perform joint scene decomposition and composition. To perform effective scene decomposition, in the fine-stage, we apply a set of learnable object codes to predict distinct object-level radiance fields, and also propose two novel decomposition strategies: (i) 3D one-hot object radiance activation and regularization. For the object or background branches, only one branch is activated during training using a designed Gumbel-Softmax activation function directly applied on the point density predicted from different object/background branches with also a corresponding one-hot regularization; (ii) an in-painting pseudo supervision strategy. A challenge in scene rendering is modeling the appearance and geometry of regions occluded by objects. This causes generation ambiguity especially when the occluded regions are unseen in all the training views. To address this issue, we propose to use a pretrained inpainting model to provide additional pseudo-color supervision for those ambiguous areas. Note that although the 2D inpainting may bring new ambiguity for the regions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "seen in other views, the supervision from multi-view consistency is strong enough to suppress most ambiguities. The composition is further performed by utilizing the learned one-hot activation weights for different object-level radiance fields." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.168, + 0.885, + 0.184 + ], + "angle": 0, + "content": "In summary, this paper has the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.19, + 0.892, + 0.265 + ], + "angle": 0, + "content": "- We propose a novel NeRF framework for joint scene decomposition and composition to effectively learn object-level and scene-level implicit representations for effective scene modeling, allowing object editing and novel view synthesis in a unified pipeline." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.269, + 0.892, + 0.327 + ], + "angle": 0, + "content": "- To learn a robust scene decomposition, we design two novel strategies, i.e., 3D one-hot radiance regularization and 2D in-painting pseudo supervision, to significantly improve the rendering and editing qualities." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.332, + 0.892, + 0.406 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the effectiveness of our approach for scene decomposition and show clear improvements upon state-of-the-art object-compositional methods on two important downstream tasks, i.e. novel-view synthesis and object editing." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.19, + 0.892, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.642, + 0.437 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Neural Implicit Representations. As pioneering methods, [17, 21, 24, 28] introduce neural networks to implicitly parameterize 3D scenes. These works can learn continuous shape and texture from differentiable rendering with [12, 24] or without[21, 28] 3D supervision. Neural Radiance Fields (NeRF) [18] optimize a 3D continuous neural scene representation by using only 2D multiview posed images for training and produce high-quality novel view synthesis with 3D structure awareness. Recent works also extend the generalization of NeRF to more significant scenes [1, 2, 41], or model scenes with fewer perspectives [5, 33, 39]. However, all these works only focus on the entire scene representation, neglecting fine-grained representations of objects/background within the scene. Other researches represent object surfaces with implicit neural function to realize multi-view 3D reconstruction for single objects [22, 32, 38]. The decomposed implicit representation for independently characterizing components within the scene has been studied in not only object scenes [3, 14, 8, 23, 25, 27], but also in the face or body tasks [9, 11, 34]. In contrast to these works, our method targets both scene synthesis and editing, considering joint object- and scene-level implicit representation learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Object-Compositional Implicit Representation. Representing scenes in an object-compositional manner can benefit both scene synthesis and editing [3, 4, 26, 29, 30, 35, 40, 36]. Compared to decomposed object representations represented by generative models [7, 19, 20], implicit models present more 3D physical meaning during the modeling process, which facilitates image rendering from novel" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18248" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.094, + 0.468, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.475, + 0.101, + 0.884, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.223, + 0.891, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.447, + 0.893, + 0.531 + ], + "angle": 0, + "content": "Figure 2. An overview of the proposed unified decompositional and compositional NeRF framework for joint novel view synthesis and scene editing. It has two stages. In the first stage (i.e. the coarse stage), it learns a guidance radiance field for guiding point sampling. In the second stage (i.e. the fine stage), we learn scene decomposition via learnable object codes and two novel decomposition schemes: (i) the 3D one-shot object radiance activation regularization and (ii) color inpainting handling ambiguous generation in occluded background areas. The scene composition is achieved by using one-hot activation weights for different object-level radiance fields learned in the decomposition stage. The decomposition allows scene editing and the composition enables novel view synthesis in the unified framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.473, + 0.9 + ], + "angle": 0, + "content": "views. We can categorize the works of object-compositional implicit representations into supervised and unsupervised methods. The unsupervised methods localize objects with different aspects of prior information, such as multiple similar scenes [26, 29, 40], temporal consistency [13], or clustering-based initialization [15]. Specifically, uORF [40] involves a slot-attention [13] module in learning object-level iterative attention masks for each object decomposition. RFP [15] utilizes clustering predictions as initialization and applies a bidirectional color loss to decompose individual objects. However, lacking precise annotation, although these methods can obtain object position clues, they usually suffer from low-resolution [26, 40] issues that restrict generalization ability to high-resolution real-world scenes. The supervised methods usually use object-level annotations, such as semantic masks [35, 37, 42] or scene graphs [23]. Among these works, ObjectNeRF [37] utilizes a two-branch network to learn a scene radiance field with an activation code-conditioned object radiance field supervised by multi-view images and semantic masks. Similarly, ObjectSDF [35] encodes the entire scene by combining the individual Signed Distance Functions (SDF) represented with semantic labels. The most related work to us is ObjectNeRF [37]. In contrast to ObjectNeRF, we model" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.537, + 0.892, + 0.598 + ], + "angle": 0, + "content": "an the scene representation via joint scene decomposition and composition, which can effectively model global consistency and rich local details in a unified NeRF framework for a high-quality scene representation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.614, + 0.882, + 0.632 + ], + "angle": 0, + "content": "3. Decompositional and Compositional NeRF" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.892, + 0.833 + ], + "angle": 0, + "content": "Given a set of multi-view posed images \\(\\{x_{i}, i \\in [1, N]\\}\\) and their corresponding instance semantic masks \\(\\{s_{ij}, i \\in [1, N], j \\in [1, K + 1]\\}\\) of a static real-world scene, our goal is to learn an entire scene representation based on the composition of a global scene radiance field and explicitly decomposed local radiance fields of different objects and the background. The decomposition allows scene editing and the composition enables novel view synthesis. \\(N\\) is the number of multi-view images, and \\(K\\) is the number of object instances, where we regard the background as an additional instance. We propose a joint decomposition and composition framework to allow simultaneous performing these two tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.707, + 0.862 + ], + "angle": 0, + "content": "3.1. Framework Overview" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.903 + ], + "angle": 0, + "content": "An overall framework illustration is shown in Fig. 2. It consists of two rendering stages. In the first stage (i.e. the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18249" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.455 + ], + "angle": 0, + "content": "coarse stage), it learns a global scene guidance radiance field for guiding point sampling. In the second stage (i.e. the fine stage), we learn scene decomposition and composition. The decomposition is performed via first applying a set of learnable object codes as conditions to predict \\( K + 1 \\) local object/background radiance field components, where \\( K \\) is the number of objects, and the additional 1 represents the background. Following NeRF [18], we use continuous neural radiance fields to represent each local object/background. Considering the composition nature that the whole scene consists of all the \\( K + 1 \\) components, we composite all the object and background radiance fields to an entire scene radiance field based on a proposed one-hot object radiance activation module. We also propose an effective color-inpainting strategy to handle the ambiguity in generating occluded background regions. The residual prediction from the first coarse stage is also utilized to benefit from a global scene representation. In the following subsections, we first give a general introduction to the proposed unified framework. Then, we introduce our novel decomposition and composition design and how the method can help disentangle different objects explicitly. After that, we present how our unified framework is optimized and utilized for both novel-view synthesis and editing tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.466, + 0.276, + 0.482 + ], + "angle": 0, + "content": "3.2. Scene Decomposition" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.491, + 0.473, + 0.854 + ], + "angle": 0, + "content": "Two-branch network architecture design. For scene decomposition in the fine-stage, we design a two-branch network architecture with a shared MLP backbone to learn generic implicit scene representation from input point coordinates (see Fig. 3). Specifically, the shared backbone takes a sampled 3D point coordinate \\(\\mathbf{p} = (x,y,z)\\) and view direction \\(\\mathbf{d}\\) of a camera ray as input, and predicts a generic scene feature vector \\(\\mathbf{f}\\). Similar to [37], we also apply a set of learnable codes, each representing the background or an object. We further pass \\(\\mathbf{f}\\) accompanying with background or object codes to the following MLP heads. For better background learning, we use separate the background head and the object head, predicting an RGB color \\(\\mathbf{c}_{\\mathrm{object}}^i\\) and a volume density \\(\\sigma_{\\mathrm{object}}^i\\) for the corresponding background or object \\(i\\). For simplicity, we refer to the background as a particular object with index \\(i = 1\\). For efficient point sampling, we apply a coarse-to-fine sampling technique. In the coarse stage, we only adopt several MLPs after the backbone for predicting RGB color \\(\\mathbf{c}_{\\mathrm{guidance}}\\) and volume density \\(\\sigma_{\\mathrm{guidance}}\\) of the global scene. We use the distribution of coarse prediction for the fine point coordinate sampling, so we call these MLPs guidance head. In the fine stage, we also use the prediction of the guidance head as a residual radiance field in the following composition module." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.901 + ], + "angle": 0, + "content": "3D one-hot density regularization. To achieve effective decomposition of objects/background radiance fields from the scene, we also design a one-hot regularization term for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.259 + ], + "angle": 0, + "content": "the uncertain regions in the background radiance field. Our motivation is that the 3D points belonging to the foreground objects should not have any volume density in the background radiance field. We thus apply a one-hot regularization loss term, which acts as an additional constraint to the object-specific radiance field optimization objective \\(\\mathcal{L}_{\\mathrm{object}}\\). In detail, we first obtain the 3D point positions that foreground objects occupy by determining whether the foreground objects take the largest volume density at the points. We thus define a binary occupancy mask \\(M_{c}\\), and apply a regularization term for the occupied points as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.264, + 0.892, + 0.292 + ], + "angle": 0, + "content": "\\[\nM _ {c} = \\left[ \\operatorname {a r g m a x} \\left(\\left[ \\sigma_ {\\text {o b j e c t}} ^ {1}, \\sigma_ {\\text {o b j e c t}} ^ {2}, \\sigma_ {\\text {o b j e c t}} ^ {3}, \\dots , \\sigma_ {\\text {o b j e c t}} ^ {K + 1} \\right]\\right) > 1 \\right] \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.287, + 0.705, + 0.306 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {o n e - h o t}} = M _ {c} \\| \\sigma_ {\\mathrm {o b j e c t}} ^ {1} - \\sigma_ {0} \\| _ {2} ^ {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.895, + 0.433 + ], + "angle": 0, + "content": "\\(\\sigma_{\\mathrm{object}}^{1}\\) here means we only want to constrain the background radiance field (with index 1). Note that we implement a ReLU operation on the volume density \\(\\sigma\\) to make it positive during the volume rendering process, so if the raw prediction \\(\\sigma_{\\mathrm{object}}^{1}\\) is negative at some points, it will also have no contribution to the rendering results. Therefore, we can set \\(\\sigma_0\\) as any non-positive number here. We put it -0.01 in our experiments from experience." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.435, + 0.895, + 0.709 + ], + "angle": 0, + "content": "2D in-painting pseudo supervision. To model a better background-specific radiance field, we need to learn what the scene looks like even if all the foreground objects are removed from the scene. Several occluded regions in the background can be seen in other views, while regions covered by the objects are invisible from all views, which are uncertain regions. We thus do not have any pixel-wise supervision for those regions in the training data, resulting in unsatisfactory extrapolation results on those regions when we learn the background radiance field. To tackle this problem, we involve a pre-trained in-painting model to fill those uncertain regions on the 2D images. Our motivation is that the 2D in-painting model can utilize local context information on an image to fill the regions, providing effective 2D pseudo color supervision. Specifically, we use a famous pre-trained lama [31] model to fill the uncertain 2D background regions and then apply a color loss for the rendered background pixels with a foreground mask \\( M_{1}(r)^{1} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.715, + 0.892, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o l o r . p s e u d o}} = M _ {1} (r) ^ {1} \\| \\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {1} - C (\\boldsymbol {r}) _ {\\text {p s e u d o}} \\| _ {2} ^ {2} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.895, + 0.805 + ], + "angle": 0, + "content": "Intermediate local object rendering. To enforce the decomposition of all object-specific radiance fields, we apply a color consistent loss and an opacity loss with semantic masks as [18, 37] via rendering both 2D color and opacity:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.819, + 0.892, + 0.868 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} = \\sum_ {i = 1} ^ {N} T _ {i} ^ {k} \\left(1 - \\exp \\left(- \\sigma_ {\\text {o b j e c t}} ^ {k} \\delta_ {i}\\right)\\right) \\mathbf {c} _ {\\text {o b j e c t}} ^ {k}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.862, + 0.806, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\hat {O} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} = \\sum_ {i = 1} ^ {N} T _ {i} ^ {k} \\left(1 - \\exp \\left(- \\sigma_ {\\text {o b j e c t}} ^ {k} \\delta_ {i}\\right)\\right)\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18250" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.089, + 0.473, + 0.168 + ], + "angle": 0, + "content": "where \\( T_{i}^{k} = \\exp (-\\sum_{j = 1}^{i - 1}\\sigma_{\\mathrm{object}}^{k}\\delta_{j}) \\) is the transmittance representing how much light is transmitted along the ray for the \\( k \\)-th object; \\( N \\) is the number of sampled points along the camera ray, and \\( \\delta_{i} \\) is the distance between two adjacent points. Then we apply the following losses:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.172, + 0.469, + 0.236 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {o b j e c t}} = \\sum_ {k = 1} ^ {K + 1} M _ {o} (\\boldsymbol {r}) ^ {k} \\| \\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} - C (\\boldsymbol {r}) \\| _ {2} ^ {2} \\tag {4} \\\\ + \\lambda M _ {b} (\\boldsymbol {r}) ^ {1} \\| \\hat {\\boldsymbol {O}} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {1} - M _ {o} (\\boldsymbol {r}) ^ {1} \\| _ {2} ^ {2}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.24, + 0.47, + 0.362 + ], + "angle": 0, + "content": "where \\( M_{o}(\\boldsymbol{r}) \\) and \\( M_{b}(\\boldsymbol{r}) \\) are 2D spatial weight maps determined by object-level and background-level semantic masks, respectively, which indicates that rendered object-specific pixels are given supervision at the corresponding semantic mask region. The background region in the binary semantic mask can be either real background or occluded by a foreground object, so we use a small weight value (i.e. 0.05) in \\( M_{b} \\) as a balance weight for the uncertain region." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.372, + 0.262, + 0.389 + ], + "angle": 0, + "content": "3.3. Scene Composition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.47, + 0.44 + ], + "angle": 0, + "content": "This section presents how the learned global and the local object/background radiance fields are composited for an entire scene radiance field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.639 + ], + "angle": 0, + "content": "Gumbel-Softmax one-hot object radiance activation. As shown in Fig. 3, for each sampled point, there are \\( K + 1 \\) predictions in the local radiance field decomposition. Considering that each point in the 3D space can only belong to either one object or the background, we use the predicted \\( (\\mathbf{c}_{\\mathrm{object}}^i,\\sigma_{\\mathrm{object}}^i) \\) with the maximum volume density \\( \\sigma_{\\mathrm{object}}^i \\) among all the object instances to construct an activated object-specific radiance field. More specifically, to address the gradient backpropagation problem of the argmax operation, following [10, 16], We employ the Gumbel-Softmax function on volume density as a continuous and differentiable approximation. First, we calculate a soft probability \\( p_i \\) for the \\( i \\)-th object branch as" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.643, + 0.469, + 0.687 + ], + "angle": 0, + "content": "\\[\np _ {i} = \\frac {\\exp^ {\\left(\\left(\\sigma_ {\\text {o b j e c t}} ^ {i} + g _ {i}\\right) / t a u\\right)}}{\\sum_ {j} \\exp^ {\\left(\\left(\\sigma_ {\\text {o b j e c t}} ^ {j} + g _ {j}\\right) / t a u\\right)}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The above \\( g_{1}, g_{2}, \\ldots, g_{j} \\) are the independent and identically distributed samples drawn from \\( \\mathrm{Gumbel}(0,1)^{1} \\) [10]. The symbol \\( tau \\) is the temperature ratio set to 0.1 in our experiments. Then, we can obtain one-hot composition weights from \\( p_{i} \\) for combining the predictions of all the object/background branches, which ensures one-hot activation for all the object/background radiance fields, and enables effective backpropagation for learning object-specific radiance fields and their composition. Specifically, we calculate the one-hot weights \\( \\mathbf{M}_{obj} \\) as Eq. 6. Let us denote \\( \\mathbf{P} \\) as the soft probability vector, containing \\( K + 1 \\) predictions calculated by Eq. 5. \\( \\mathbf{M}_{obj} \\) is a one-hot vector of the \\( K + 1 \\) elements. The one-hot vector is calculated with a stop gradient operation \\( f_{sp} \\) on \\( \\mathbf{P} \\), which not only reserves the one-" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.096, + 0.887, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.358, + 0.892, + 0.483 + ], + "angle": 0, + "content": "Figure 3. Illustration of the Composition Module. Our composition module consists of one-hot object radiance activation and global-local radiance field composition (the two green blocks). We first apply Gumbel-Softmax on object-level volume density values to obtain the one-hot mask for object radiance fields. Then, the local compositional radiance field is generated by a weighted sum of the object and background color and density predictions. Finally, the composited radiance is combined with a residual prediction to produce the final scene radiance field." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.488, + 0.892, + 0.52 + ], + "angle": 0, + "content": "hot activation but also allows the gradient backpropagated through \\(\\mathbf{P}\\). Then, the computation of \\(\\mathbf{M}_{obj}\\) is written as:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.544, + 0.892, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {o b j} = f _ {\\mathrm {h}} \\left(\\underset {i} {\\arg \\max } \\left[ g _ {i} + \\log \\sigma_ {\\text {o b j e c t}} ^ {i} \\right]\\right) - f _ {s p} (\\mathbf {P}) + \\mathbf {P}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.573, + 0.892, + 0.636 + ], + "angle": 0, + "content": "where \\( f_{\\mathrm{h}}(\\cdot) \\) denotes a one-hot function; Then, we obtain a composed scene radiance field \\( (\\mathbf{c}_{\\mathrm{comp}}, \\sigma_{\\mathrm{comp}}) \\) of all decomposed branches \\( \\{\\mathbf{c}_{\\mathrm{object}}^k, \\sigma_{\\mathrm{object}}^k\\}_{k=1}^{K+1} \\), by multiplying the above one-hot weights as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.649, + 0.892, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {\\text {c o m p}} = \\sum_ {K + 1} \\mathbf {M} _ {o b j} ^ {k} \\mathbf {c} _ {\\text {o b j e c t}} ^ {k}, \\sigma_ {\\text {c o m p}} = \\sum_ {K + 1} \\mathbf {M} _ {o b j} ^ {k} \\sigma_ {\\text {o b j e c t}} ^ {k}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.778 + ], + "angle": 0, + "content": "Our novel one-hot object radiance activation can not only ensure a reasonable composition of all the object radiance fields but also force that only one object volume density prediction can be activated in the gradient backpropagation, which can also effectively help the object/background decomposition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Residual radiance field composition. After the one-hot object radiance activation, we further combine the composited radiance fields from objects/background branches with the predicted residual radiance field, to produce a final composited scene radiance field, using point-wise average pooling operation applied on the color and density. Then we apply a color loss \\(\\mathcal{L}_{\\mathrm{comp}}\\) for the pixels rendered from the composited radiance field." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18251" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.3, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.201, + 0.185, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.19, + 0.197, + 0.296, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.157, + 0.259, + 0.261, + 0.273 + ], + "angle": 0, + "content": "(a) ObjectNeRF" + }, + { + "type": "image", + "bbox": [ + 0.301, + 0.089, + 0.481, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.309, + 0.201, + 0.367, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.198, + 0.48, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.344, + 0.26, + 0.439, + 0.274 + ], + "angle": 0, + "content": "(b) ObjectSDF" + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.089, + 0.665, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.198, + 0.55, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.556, + 0.198, + 0.661, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.259, + 0.625, + 0.272 + ], + "angle": 0, + "content": "(c) Our Method" + }, + { + "type": "image", + "bbox": [ + 0.667, + 0.089, + 0.848, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.198, + 0.733, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.74, + 0.198, + 0.845, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.259, + 0.812, + 0.272 + ], + "angle": 0, + "content": "(d) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.274, + 0.892, + 0.316 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of novel view synthesis on the ToyDesk dataset. We compared with ObjectNeRF [37] and ObjectSDF [35]. The results show that the rendered images of our framework achieve better generation quality for both the foreground objects (e.g., the green dinosaur) and the background (e.g., the chessboard)." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.319, + 0.468, + 0.418 + ], + "angle": 0, + "content": "
MethodsToyDesk2
PSNR ↑SSIM ↑LPIPS ↓
Our Full-Model25.75600.81260.4488
w/o 3D One-hot Density Regularization25.73620.81160.4524
w/o Gumbel-Softmax Activation22.99720.72170.5452
w/o 2D In-painting pseudo Supervision25.68810.81270.4516
w/o Residual Radiance Composition25.22880.80030.4589
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.419, + 0.469, + 0.46 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of different variants of the proposed unified decompositional and compositional NeRF framework on the ToyDesk2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.462, + 0.327, + 0.478 + ], + "angle": 0, + "content": "3.4. Optimization and Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.469, + 0.53 + ], + "angle": 0, + "content": "Overall framework optimization. The overall optimization loss for training the joint framework consists of the following four different loss functions:" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.542, + 0.468, + 0.572 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {o v e r a l l}} = \\mathcal {L} _ {\\text {c o m p}} + \\lambda_ {1} \\mathcal {L} _ {\\text {o b j e c t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {c o l o r - p s e u d o}} + \\lambda_ {3} \\mathcal {L} _ {\\text {o n e - h o t}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.573, + 0.469, + 0.602 + ], + "angle": 0, + "content": "where, \\(\\lambda_1, \\lambda_2\\), and \\(\\lambda_3\\) are the weights for balancing the learning with the different loss functions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.469, + 0.695 + ], + "angle": 0, + "content": "Novel View Rendering and Scene Editing After training the joint framework, we can render images of arbitrary perspectives based on the composited radiance field. By reorganizing the object radiance fields, we can generate images with object manipulations, including removal, addition, duplication, and changing position (e.g., rotation)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.707, + 0.21, + 0.725 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.47, + 0.793 + ], + "angle": 0, + "content": "We aim at performing joint scene novel view synthesis and editing based on our proposed unified decompositional and compositional NeRF framework. We thus evaluate our method on both tasks using challenging public benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.267, + 0.818 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Datasets. We use ToyDesk [37] and ScanNet [6] datasets for the evaluation. ToyDesk consists of two sets of indoor multi-view images. In each scene, several toys are put on a desk in the center of the room. The multi-view images are captured by looking at the desk center with 360 degrees" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.322, + 0.885, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.42, + 0.892, + 0.476 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of the ablation study: (a) Our full model; (b) w/o 3D One-hot Density Regularization; (c) w/o Gumbel-Softmax Activation; (d) w/o 2D In-painting pseudo Supervision. (e) w/o Residual Radiance Composition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.893, + 0.68 + ], + "angle": 0, + "content": "around the desk, and the camera poses and meshes are provided. The instance semantic labels are annotated on object meshes and then projected onto each perspective to obtain their corresponding 2D semantic label maps. ScanNet is an RGB-D video dataset that contains more than 1500 scans of indoor scenes for multiple 3D understanding tasks. Handheld RGB-D scanners are used for scanning various indoor scenes. Rich annotations such as camera pose, semantic segmentation, and surface reconstruction are also provided. Following ObjectNeRF [37], we choose four scenes, i.e., 0024_00, 0038_00, 0113_00, and 0192_00, from the whole dataset for the experiment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Implementation details. Our joint framework consists of a shared backbone, background head, object head, and guidance head. The share backbone is a 4-layer Multi-Layer Perceptron (MLP), and the output generic implicit scene feature has a dimension of 256. The follow-up heads are all three-layer MLPs with a color and density prediction layer to generate corresponding radiance fields. Note that our one-hot regularization and activation module has no parameters to be optimized. We also utilize positional encoding to increase the representation ability for high-frequency details. Specifically, we adopt ten levels for coordinates and four levels for ray directions. The framework is trained end-to-end from scratch, without voxel feature initialization as in [37] or geometric initialization as in [35]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18252" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.088, + 0.298, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.196, + 0.298, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.163, + 0.306, + 0.262, + 0.319 + ], + "angle": 0, + "content": "(a) ObjectNeRF" + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.088, + 0.481, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.301, + 0.196, + 0.481, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.306, + 0.442, + 0.319 + ], + "angle": 0, + "content": "(b) ObjectSDF" + }, + { + "type": "image", + "bbox": [ + 0.481, + 0.088, + 0.663, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.196, + 0.662, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.306, + 0.621, + 0.318 + ], + "angle": 0, + "content": "(c) Our Method" + }, + { + "type": "image", + "bbox": [ + 0.664, + 0.088, + 0.847, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.196, + 0.846, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.306, + 0.807, + 0.319 + ], + "angle": 0, + "content": "(d) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.32, + 0.892, + 0.349 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison of novel view synthesis on the ScanNet dataset. Compared with ObjectNeRF [37] and ObjectSDF [35], our results also achieve better fidelity. We highlight the details in the red boxes." + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.355, + 0.432, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.563, + 0.47, + 0.618 + ], + "angle": 0, + "content": "Figure 7. The Decomposition results on the ToyDesk dataset compared with ObjectNeRF [37]. We show the rendered results of our composited radiance field (the first column) and each background/object radiance field (the second and third columns)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.233, + 0.637 + ], + "angle": 0, + "content": "4.2. Model Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Baseline Models. To verify the effectiveness of our designs for scene decomposition and composition, We conduct several ablation studies considering different variants: (i) 'w/o 3D One-hot Density Regularization' means that we remove the one-hot regularization term for the uncertain regions in the background radiance field. (ii) 'w/o Gumbel-Softmax Activation' indicates that we do not use the Gumbel-Softmax one-hot weight for compositing the object radiance fields. (iii) 'w/o In-painting Supervision' means that we do not apply the in-painting pseudo supervision for the background radiance field. (iv) 'w/o Residual Radiance Composition' means that we do not use the guidance radiance field for fine sampling and remove the residual radiance composition in the fine stage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Effect of 3D one-hot density regularization. The quantitative results based on different evaluation metrics, i.e., PSNR, SSIM, and LPIPS, are shown in Table 1. Several" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.353, + 0.892, + 0.46 + ], + "angle": 0, + "content": "
DatasetMethodsPSNR ↑SSIM ↑LPIPS↓
ToyDeskObject-NeRF [37]22.17360.77230.4711
Object-SDF [35]22.0298--
Our Method23.14350.78990.4691
ScanNetObject-NeRF [37]25.26400.80470.4094
Object-SDF [35]25.2325--
Our Method26.13490.82490.3951
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.532 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison on novel view synthesis. We compared with ObjectNeRF [37] and ObjectSDF [35]. '-' indicates the metrics are not reported by the authors in the paper. The evaluation results show that our synthesis results quantitatively outperform these two SOTA methods on all the shown metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.628 + ], + "angle": 0, + "content": "examples of rendered images from the learned background radiance field are presented in Fig. 5. We evaluate the effectiveness of 3D one-hot density regularization by disabling the loss term. As can be observed from Table 1, our joint full mode with 3D one-hot density regularization achieves better results than the model without it." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Effect of Gumbel-Softmax object radiance activation. We also investigate the effect of using Gumbel-Softmax one-hot activation for the composition of background/object radiance fields. We use an alternative composition method, in which all the local object/background radiance fields that contribute to the same 3D points in the composited field, are directly added instead of using the Gumbel-Softmax one-hot activation weights, as introduced in the method part. As shown in Fig. 5c, without the Gumbel-Softmax one-hot activation, the model cannot successfully learn a decomposed background radiance field (all black), confirming our motivation of using the Gumbel-Softmax activation for a more effective scene representation in a unified framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect of 2D in-painting pseudo supervision and residual radiance composition. We also show the contribution of the proposed 2D in-painting pseudo-supervision. If we directly disable the pseudo supervision in the framework, the qualitative results are slightly lower, as shown in the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18253" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.088, + 0.418, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.287, + 0.47, + 0.33 + ], + "angle": 0, + "content": "Figure 8. The Decomposition results on the ScanNet dataset compared with ObjectNeRF [37]. Our background has fewer artifacts when removing the foreground object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.471, + 0.534 + ], + "angle": 0, + "content": "next to last row in Table. 1. At the same time, as can be seen in Fig. 5, lacking pseudo supervision suffers from significantly downgraded extrapolation in the region occupied by the foreground objects in the 3D space, which indicates that the proposed scheme can effectively help the local object/background disentanglement, especially for learning the radiance field representation of the background on uncertain regions. As shown in Table. 1 and Fig. 5, if we remove the residual radiance composition, the overall qualitative metrics and background decomposition both decline, which demonstrates the importance of using a global radiation field to provide coarse sampling guidance and also further merged as residual information in the fine stage." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.361, + 0.56 + ], + "angle": 0, + "content": "4.3. Results on Novel View Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.749 + ], + "angle": 0, + "content": "We compare our methods on the task of novel view synthesis with two state-of-the-art methods, i.e., ObjectNeRF [37] and ObjectSDF [35]. Our train-test split follows ObjectNeRF [37]. We measure the quality of synthesized images on the evaluation metrics of PSNR, SSIM, and LPIPS. In detail, for our joint framework, we use the finally composited entire scene radiance field for the image rendering. For ObjectNeRF and ObjectSDF on the Toydesk dataset, we use the rendered images provided by the authors for comparison. ObjectSDF adopts a different train-test split and label mapping strategy on ScanNet, so we retrain the ObjectSDF on ScanNet following our setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In Table 2, our synthesis results quantitatively outperform the comparison methods on all the shown metrics. We also present the image examples rendered from novel views in Fig. 4 and Fig. 6. As can be observed in Fig. 4, the rendered images of our framework achieve better generation quality for both the foreground objects (e.g., the green dinosaur) and the background (e.g., the chessboard) than both ObjectNeRF [37] and ObjectSDF [35], proving the capability of our method in modeling both global scene consistency and local scene details. Fig. 6 shows the synthesized images" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.089, + 0.693, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.558, + 0.193, + 0.653, + 0.205 + ], + "angle": 0, + "content": "(a) Original view" + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.089, + 0.868, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.736, + 0.192, + 0.828, + 0.205 + ], + "angle": 0, + "content": "(b) Edited image" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.206, + 0.892, + 0.261 + ], + "angle": 0, + "content": "Figure 9. Illustration of the editing results. (a) shows the image in the original view, and (b) shows the editing result from the same perspective. We do the rotation and duplication for the white triangle and candy by re-composting the learned radiance fields." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.264, + 0.892, + 0.308 + ], + "angle": 0, + "content": "on ScanNet. We can also observe that our results outperform others in the overall fidelity and local details marked in the red boxes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.318, + 0.881, + 0.334 + ], + "angle": 0, + "content": "4.4. Results of Object Decomposition and Editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.734 + ], + "angle": 0, + "content": "We also conduct experiments to show the decomposition effectiveness of our method, especially for the background radiance field. As shown in Fig. 7 and Fig. 8, we rendered the composited radiance field and each local object/background radiance field to show the decomposition results. The background images in Fig. 7 clearly show that our method can generate a clearer table without unsatisfactory artifacts such as strange colors and black shadow effects when removing all the foreground objects on the table. Although with some remained black contours, the rendered pixel colors of the regions below the objects are significantly more reasonable compared to ObjectNeRF [37]. Note that the region under the toys is unseen in any view. Our decomposition module enables clear background and object-specific details, while the composition design helps the rendered entire scene achieve higher quality than the baseline. In Fig. 8, we further show that our pipeline can also provide better background rendering when removing foreground objects on the images from the ScanNet dataset. The better decomposition naturally benefits downstream object editing tasks. Fig. 9 shows that, after learning composited radiance fields, our method can perform rotation and duplication for the white triangle and candy by re-compositing the object and background radiance field representations. We add more editing results in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.747, + 0.619, + 0.761 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We propose a unified NeRF framework with a novel decomposition and composition design to jointly model real-world scenes with both global and local implicit representations. To solve the ambiguous extrapolation problem for unseen areas, we also propose a 3D one-hot density regularization strategy and a 2D in-painting pseudo supervision. Our experimental evaluation demonstrates that our method outperforms the state-of-the-art object-compositional methods for both novel-view synthesis and scene editing tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18254" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.258, + 0.108 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.47, + 0.178 + ], + "angle": 0, + "content": "This research is supported in part by HKUST-SAIL joint research funding, the Early Career Scheme of the Research Grants Council (RGC) of the Hong Kong SAR under grant No. 26202321, and HKUST Startup Fund No. R9253." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.195, + 0.175, + 0.21 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.221, + 0.47, + 0.276 + ], + "angle": 0, + "content": "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In ICCV, 2021. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.279, + 0.472, + 0.32 + ], + "angle": 0, + "content": "[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. 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In this paper, we target a more challenging scenario, i.e., joint scene novel view synthesis and editing based on implicit neural scene representations. State-of-the-art methods in this direction typically consider building separate networks for these two tasks (i.e., view synthesis and editing). Thus, the modeling of interactions and correlations between these two tasks is very limited, which, however, is critical for learning high-quality scene representations. To tackle this problem, in this paper, we propose a unified Neural Radiance Field (NeRF) framework to effectively perform joint scene decomposition and composition for modeling real-world scenes. The decomposition aims at learning disentangled 3D representations of different objects and the background, allowing for scene editing, while scene composition models an entire scene representation for novel view synthesis. Specifically, with a two-stage NeRF framework, we learn a coarse stage for predicting a global radiance field as guidance for point sampling, and in the second fine-grained stage, we perform scene decomposition by a novel one-hot object radiance field regularization module and a pseudo supervision via inpainting to handle ambiguous background regions occluded by objects. The decomposed object-level radiance fields are further composed by using activations from the decomposition module. Extensive quantitative and qualitative results show the effectiveness of our method for scene decomposition and composition, outperforming state-of-the-art methods for both novel-view synthesis and editing tasks1. + +# 1. Introduction + +The reconstruction and rendering of natural scenes are important for computers to understand the 3D physical + +![](images/f55d370e73552652219ebd6f8978ea9bd2bca8a3a90a73655a5cbeeee5e117c6.jpg) +Figure 1. Illustration of our decomposition-composition design. It enables scene editing and novel view synthesis in a unified NeRF framework. The proposed decomposition targets learning disentangled 3D representations of different foreground objects and the background, allowing for scene editing, while scene composition constructs an entire scene representation for novel view synthesis. + +world. Fine-grained object-level representations within the scene can bring significant benefits in various applications, such as scene understanding, novel content generation via object editing, and robotic manipulation. The emerging neural rendering techniques [17, 18, 24] allow learning object-level or scene-level representations from multi-view posed images and enable rendering high-quality images from novel views. However, most implicit neural methods model an entire scene and lack fine-grained representations of objects in the scene, which severely limits object-level scene representation and understanding. + +Learning effective 3D object-aware implicit neural scene representations is still in its infancy. Existing works that tackle this challenging problem typically utilize additional object-level semantic supervision as a priori knowledge in the model optimization [35, 37, 42]. For instance, ObjectSDF [35] considers learning object-level geometries and semantics with an implicit signed distance function (SDF), which achieves effective scene composition from object- + +level representations. However, it remains challenging for this framework to perform joint object editing and novel view synthesis. On the other hand, ObjectNeRF [37] explores scene modeling with Neural Radiance Fields (NeRF) via introducing learnable object activation codes as switchers to condition the radiance field prediction among different objects. This framework can perform joint scene editing and novel view synthesis benefiting from the radiance field representations. However, it learns two separate networks for these two tasks, a global scene branch for novel view synthesis, and a local object branch for scene editing, without modeling any interaction or correlation among them, which, however, is critical for learning more effective scene representations, due to the simple fact that, global scene and local object representations are two important perspectives of the same scene. The global entire scene representation can model the scene's overall structures and appearance consistency, and the local object-specific representation can learn more fine-grained object details. They are highly complementary for learning a high-quality scene representation. + +To target the above-mentioned problem, this paper proposes a unified decompositional and compositional neural radiance field framework (see Fig. 1), to learn 3D scene representation for joint scene editing and novel view synthesis. The decomposition can provide the functionality of learning disentangled 3D representations of different objects and the background, allowing for scene editing, while scene composition models an entire scene representation for novel view synthesis. These two can be united to facilitate the consistency constraint in the unified optimization framework. Specifically, we design a new two-stage framework for the scene decomposition and composition, consisting a coarse and a fine stage. In the coarse stage, we learn to predict a global scene radiance field as guidance for point sampling, and in the second fine-grained stage, we perform joint scene decomposition and composition. To perform effective scene decomposition, in the fine-stage, we apply a set of learnable object codes to predict distinct object-level radiance fields, and also propose two novel decomposition strategies: (i) 3D one-hot object radiance activation and regularization. For the object or background branches, only one branch is activated during training using a designed Gumbel-Softmax activation function directly applied on the point density predicted from different object/background branches with also a corresponding one-hot regularization; (ii) an in-painting pseudo supervision strategy. A challenge in scene rendering is modeling the appearance and geometry of regions occluded by objects. This causes generation ambiguity especially when the occluded regions are unseen in all the training views. To address this issue, we propose to use a pretrained inpainting model to provide additional pseudo-color supervision for those ambiguous areas. Note that although the 2D inpainting may bring new ambiguity for the regions + +seen in other views, the supervision from multi-view consistency is strong enough to suppress most ambiguities. The composition is further performed by utilizing the learned one-hot activation weights for different object-level radiance fields. + +In summary, this paper has the following contributions: + +- We propose a novel NeRF framework for joint scene decomposition and composition to effectively learn object-level and scene-level implicit representations for effective scene modeling, allowing object editing and novel view synthesis in a unified pipeline. +- To learn a robust scene decomposition, we design two novel strategies, i.e., 3D one-hot radiance regularization and 2D in-painting pseudo supervision, to significantly improve the rendering and editing qualities. +- Extensive experiments demonstrate the effectiveness of our approach for scene decomposition and show clear improvements upon state-of-the-art object-compositional methods on two important downstream tasks, i.e. novel-view synthesis and object editing. + +# 2. Related Work + +Neural Implicit Representations. As pioneering methods, [17, 21, 24, 28] introduce neural networks to implicitly parameterize 3D scenes. These works can learn continuous shape and texture from differentiable rendering with [12, 24] or without[21, 28] 3D supervision. Neural Radiance Fields (NeRF) [18] optimize a 3D continuous neural scene representation by using only 2D multiview posed images for training and produce high-quality novel view synthesis with 3D structure awareness. Recent works also extend the generalization of NeRF to more significant scenes [1, 2, 41], or model scenes with fewer perspectives [5, 33, 39]. However, all these works only focus on the entire scene representation, neglecting fine-grained representations of objects/background within the scene. Other researches represent object surfaces with implicit neural function to realize multi-view 3D reconstruction for single objects [22, 32, 38]. The decomposed implicit representation for independently characterizing components within the scene has been studied in not only object scenes [3, 14, 8, 23, 25, 27], but also in the face or body tasks [9, 11, 34]. In contrast to these works, our method targets both scene synthesis and editing, considering joint object- and scene-level implicit representation learning. + +Object-Compositional Implicit Representation. Representing scenes in an object-compositional manner can benefit both scene synthesis and editing [3, 4, 26, 29, 30, 35, 40, 36]. Compared to decomposed object representations represented by generative models [7, 19, 20], implicit models present more 3D physical meaning during the modeling process, which facilitates image rendering from novel + +![](images/7f548f64d762a0318317ce2902740ad683358c52c7f50faf9bdf1a05232f5ed7.jpg) + +![](images/8a472b2ea1c44c8a082c7a5f953949f41703a76b429feb0d17ac953a3716d04b.jpg) + +![](images/fcedf36b74ac6897eb19760ac73b982eeb0400d71b2d582cd58b377ba833ec81.jpg) +Figure 2. An overview of the proposed unified decompositional and compositional NeRF framework for joint novel view synthesis and scene editing. It has two stages. In the first stage (i.e. the coarse stage), it learns a guidance radiance field for guiding point sampling. In the second stage (i.e. the fine stage), we learn scene decomposition via learnable object codes and two novel decomposition schemes: (i) the 3D one-shot object radiance activation regularization and (ii) color inpainting handling ambiguous generation in occluded background areas. The scene composition is achieved by using one-hot activation weights for different object-level radiance fields learned in the decomposition stage. The decomposition allows scene editing and the composition enables novel view synthesis in the unified framework. + +views. We can categorize the works of object-compositional implicit representations into supervised and unsupervised methods. The unsupervised methods localize objects with different aspects of prior information, such as multiple similar scenes [26, 29, 40], temporal consistency [13], or clustering-based initialization [15]. Specifically, uORF [40] involves a slot-attention [13] module in learning object-level iterative attention masks for each object decomposition. RFP [15] utilizes clustering predictions as initialization and applies a bidirectional color loss to decompose individual objects. However, lacking precise annotation, although these methods can obtain object position clues, they usually suffer from low-resolution [26, 40] issues that restrict generalization ability to high-resolution real-world scenes. The supervised methods usually use object-level annotations, such as semantic masks [35, 37, 42] or scene graphs [23]. Among these works, ObjectNeRF [37] utilizes a two-branch network to learn a scene radiance field with an activation code-conditioned object radiance field supervised by multi-view images and semantic masks. Similarly, ObjectSDF [35] encodes the entire scene by combining the individual Signed Distance Functions (SDF) represented with semantic labels. The most related work to us is ObjectNeRF [37]. In contrast to ObjectNeRF, we model + +an the scene representation via joint scene decomposition and composition, which can effectively model global consistency and rich local details in a unified NeRF framework for a high-quality scene representation. + +# 3. Decompositional and Compositional NeRF + +Given a set of multi-view posed images $\{x_{i}, i \in [1, N]\}$ and their corresponding instance semantic masks $\{s_{ij}, i \in [1, N], j \in [1, K + 1]\}$ of a static real-world scene, our goal is to learn an entire scene representation based on the composition of a global scene radiance field and explicitly decomposed local radiance fields of different objects and the background. The decomposition allows scene editing and the composition enables novel view synthesis. $N$ is the number of multi-view images, and $K$ is the number of object instances, where we regard the background as an additional instance. We propose a joint decomposition and composition framework to allow simultaneous performing these two tasks. + +# 3.1. Framework Overview + +An overall framework illustration is shown in Fig. 2. It consists of two rendering stages. In the first stage (i.e. the + +coarse stage), it learns a global scene guidance radiance field for guiding point sampling. In the second stage (i.e. the fine stage), we learn scene decomposition and composition. The decomposition is performed via first applying a set of learnable object codes as conditions to predict $K + 1$ local object/background radiance field components, where $K$ is the number of objects, and the additional 1 represents the background. Following NeRF [18], we use continuous neural radiance fields to represent each local object/background. Considering the composition nature that the whole scene consists of all the $K + 1$ components, we composite all the object and background radiance fields to an entire scene radiance field based on a proposed one-hot object radiance activation module. We also propose an effective color-inpainting strategy to handle the ambiguity in generating occluded background regions. The residual prediction from the first coarse stage is also utilized to benefit from a global scene representation. In the following subsections, we first give a general introduction to the proposed unified framework. Then, we introduce our novel decomposition and composition design and how the method can help disentangle different objects explicitly. After that, we present how our unified framework is optimized and utilized for both novel-view synthesis and editing tasks. + +# 3.2. Scene Decomposition + +Two-branch network architecture design. For scene decomposition in the fine-stage, we design a two-branch network architecture with a shared MLP backbone to learn generic implicit scene representation from input point coordinates (see Fig. 3). Specifically, the shared backbone takes a sampled 3D point coordinate $\mathbf{p} = (x,y,z)$ and view direction $\mathbf{d}$ of a camera ray as input, and predicts a generic scene feature vector $\mathbf{f}$ . Similar to [37], we also apply a set of learnable codes, each representing the background or an object. We further pass $\mathbf{f}$ accompanying with background or object codes to the following MLP heads. For better background learning, we use separate the background head and the object head, predicting an RGB color $\mathbf{c}_{\mathrm{object}}^i$ and a volume density $\sigma_{\mathrm{object}}^i$ for the corresponding background or object $i$ . For simplicity, we refer to the background as a particular object with index $i = 1$ . For efficient point sampling, we apply a coarse-to-fine sampling technique. In the coarse stage, we only adopt several MLPs after the backbone for predicting RGB color $\mathbf{c}_{\mathrm{guidance}}$ and volume density $\sigma_{\mathrm{guidance}}$ of the global scene. We use the distribution of coarse prediction for the fine point coordinate sampling, so we call these MLPs guidance head. In the fine stage, we also use the prediction of the guidance head as a residual radiance field in the following composition module. + +3D one-hot density regularization. To achieve effective decomposition of objects/background radiance fields from the scene, we also design a one-hot regularization term for + +the uncertain regions in the background radiance field. Our motivation is that the 3D points belonging to the foreground objects should not have any volume density in the background radiance field. We thus apply a one-hot regularization loss term, which acts as an additional constraint to the object-specific radiance field optimization objective $\mathcal{L}_{\mathrm{object}}$ . In detail, we first obtain the 3D point positions that foreground objects occupy by determining whether the foreground objects take the largest volume density at the points. We thus define a binary occupancy mask $M_{c}$ , and apply a regularization term for the occupied points as follows: + +$$ +M _ {c} = \left[ \operatorname {a r g m a x} \left(\left[ \sigma_ {\text {o b j e c t}} ^ {1}, \sigma_ {\text {o b j e c t}} ^ {2}, \sigma_ {\text {o b j e c t}} ^ {3}, \dots , \sigma_ {\text {o b j e c t}} ^ {K + 1} \right]\right) > 1 \right] \tag {1} +$$ + +$$ +\mathcal {L} _ {\mathrm {o n e - h o t}} = M _ {c} \| \sigma_ {\mathrm {o b j e c t}} ^ {1} - \sigma_ {0} \| _ {2} ^ {2} +$$ + +$\sigma_{\mathrm{object}}^{1}$ here means we only want to constrain the background radiance field (with index 1). Note that we implement a ReLU operation on the volume density $\sigma$ to make it positive during the volume rendering process, so if the raw prediction $\sigma_{\mathrm{object}}^{1}$ is negative at some points, it will also have no contribution to the rendering results. Therefore, we can set $\sigma_0$ as any non-positive number here. We put it -0.01 in our experiments from experience. + +2D in-painting pseudo supervision. To model a better background-specific radiance field, we need to learn what the scene looks like even if all the foreground objects are removed from the scene. Several occluded regions in the background can be seen in other views, while regions covered by the objects are invisible from all views, which are uncertain regions. We thus do not have any pixel-wise supervision for those regions in the training data, resulting in unsatisfactory extrapolation results on those regions when we learn the background radiance field. To tackle this problem, we involve a pre-trained in-painting model to fill those uncertain regions on the 2D images. Our motivation is that the 2D in-painting model can utilize local context information on an image to fill the regions, providing effective 2D pseudo color supervision. Specifically, we use a famous pre-trained lama [31] model to fill the uncertain 2D background regions and then apply a color loss for the rendered background pixels with a foreground mask $M_{1}(r)^{1}$ : + +$$ +\mathcal {L} _ {\text {c o l o r . p s e u d o}} = M _ {1} (r) ^ {1} \| \hat {C} (\boldsymbol {r}) _ {\text {o b j e c t}} ^ {1} - C (\boldsymbol {r}) _ {\text {p s e u d o}} \| _ {2} ^ {2} \tag {2} +$$ + +Intermediate local object rendering. To enforce the decomposition of all object-specific radiance fields, we apply a color consistent loss and an opacity loss with semantic masks as [18, 37] via rendering both 2D color and opacity: + +$$ +\hat {C} (\boldsymbol {r}) _ {\text {o b j e c t}} ^ {k} = \sum_ {i = 1} ^ {N} T _ {i} ^ {k} \left(1 - \exp \left(- \sigma_ {\text {o b j e c t}} ^ {k} \delta_ {i}\right)\right) \mathbf {c} _ {\text {o b j e c t}} ^ {k}, \tag {3} +$$ + +$$ +\hat {O} (\boldsymbol {r}) _ {\text {o b j e c t}} ^ {k} = \sum_ {i = 1} ^ {N} T _ {i} ^ {k} \left(1 - \exp \left(- \sigma_ {\text {o b j e c t}} ^ {k} \delta_ {i}\right)\right) +$$ + +where $T_{i}^{k} = \exp (-\sum_{j = 1}^{i - 1}\sigma_{\mathrm{object}}^{k}\delta_{j})$ is the transmittance representing how much light is transmitted along the ray for the $k$ -th object; $N$ is the number of sampled points along the camera ray, and $\delta_{i}$ is the distance between two adjacent points. Then we apply the following losses: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {o b j e c t}} = \sum_ {k = 1} ^ {K + 1} M _ {o} (\boldsymbol {r}) ^ {k} \| \hat {C} (\boldsymbol {r}) _ {\text {o b j e c t}} ^ {k} - C (\boldsymbol {r}) \| _ {2} ^ {2} \tag {4} \\ + \lambda M _ {b} (\boldsymbol {r}) ^ {1} \| \hat {\boldsymbol {O}} (\boldsymbol {r}) _ {\text {o b j e c t}} ^ {1} - M _ {o} (\boldsymbol {r}) ^ {1} \| _ {2} ^ {2}, \\ \end{array} +$$ + +where $M_{o}(\boldsymbol{r})$ and $M_{b}(\boldsymbol{r})$ are 2D spatial weight maps determined by object-level and background-level semantic masks, respectively, which indicates that rendered object-specific pixels are given supervision at the corresponding semantic mask region. The background region in the binary semantic mask can be either real background or occluded by a foreground object, so we use a small weight value (i.e. 0.05) in $M_{b}$ as a balance weight for the uncertain region. + +# 3.3. Scene Composition + +This section presents how the learned global and the local object/background radiance fields are composited for an entire scene radiance field. + +Gumbel-Softmax one-hot object radiance activation. As shown in Fig. 3, for each sampled point, there are $K + 1$ predictions in the local radiance field decomposition. Considering that each point in the 3D space can only belong to either one object or the background, we use the predicted $(\mathbf{c}_{\mathrm{object}}^i,\sigma_{\mathrm{object}}^i)$ with the maximum volume density $\sigma_{\mathrm{object}}^i$ among all the object instances to construct an activated object-specific radiance field. More specifically, to address the gradient backpropagation problem of the argmax operation, following [10, 16], We employ the Gumbel-Softmax function on volume density as a continuous and differentiable approximation. First, we calculate a soft probability $p_i$ for the $i$ -th object branch as + +$$ +p _ {i} = \frac {\exp^ {\left(\left(\sigma_ {\text {o b j e c t}} ^ {i} + g _ {i}\right) / t a u\right)}}{\sum_ {j} \exp^ {\left(\left(\sigma_ {\text {o b j e c t}} ^ {j} + g _ {j}\right) / t a u\right)}} \tag {5} +$$ + +The above $g_{1}, g_{2}, \ldots, g_{j}$ are the independent and identically distributed samples drawn from $\mathrm{Gumbel}(0,1)^{1}$ [10]. The symbol $tau$ is the temperature ratio set to 0.1 in our experiments. Then, we can obtain one-hot composition weights from $p_{i}$ for combining the predictions of all the object/background branches, which ensures one-hot activation for all the object/background radiance fields, and enables effective backpropagation for learning object-specific radiance fields and their composition. Specifically, we calculate the one-hot weights $\mathbf{M}_{obj}$ as Eq. 6. Let us denote $\mathbf{P}$ as the soft probability vector, containing $K + 1$ predictions calculated by Eq. 5. $\mathbf{M}_{obj}$ is a one-hot vector of the $K + 1$ elements. The one-hot vector is calculated with a stop gradient operation $f_{sp}$ on $\mathbf{P}$ , which not only reserves the one- + +![](images/119bd32f91a14af2a1572654b018ca4de6fce02885f6f1d9cc21cd6986ef969d.jpg) +Figure 3. Illustration of the Composition Module. Our composition module consists of one-hot object radiance activation and global-local radiance field composition (the two green blocks). We first apply Gumbel-Softmax on object-level volume density values to obtain the one-hot mask for object radiance fields. Then, the local compositional radiance field is generated by a weighted sum of the object and background color and density predictions. Finally, the composited radiance is combined with a residual prediction to produce the final scene radiance field. + +hot activation but also allows the gradient backpropagated through $\mathbf{P}$ . Then, the computation of $\mathbf{M}_{obj}$ is written as: + +$$ +\mathbf {M} _ {o b j} = f _ {\mathrm {h}} \left(\underset {i} {\arg \max } \left[ g _ {i} + \log \sigma_ {\text {o b j e c t}} ^ {i} \right]\right) - f _ {s p} (\mathbf {P}) + \mathbf {P}, \tag {6} +$$ + +where $f_{\mathrm{h}}(\cdot)$ denotes a one-hot function; Then, we obtain a composed scene radiance field $(\mathbf{c}_{\mathrm{comp}}, \sigma_{\mathrm{comp}})$ of all decomposed branches $\{\mathbf{c}_{\mathrm{object}}^k, \sigma_{\mathrm{object}}^k\}_{k=1}^{K+1}$ , by multiplying the above one-hot weights as follows: + +$$ +\mathbf {c} _ {\text {c o m p}} = \sum_ {K + 1} \mathbf {M} _ {o b j} ^ {k} \mathbf {c} _ {\text {o b j e c t}} ^ {k}, \sigma_ {\text {c o m p}} = \sum_ {K + 1} \mathbf {M} _ {o b j} ^ {k} \sigma_ {\text {o b j e c t}} ^ {k}, \tag {7} +$$ + +Our novel one-hot object radiance activation can not only ensure a reasonable composition of all the object radiance fields but also force that only one object volume density prediction can be activated in the gradient backpropagation, which can also effectively help the object/background decomposition. + +Residual radiance field composition. After the one-hot object radiance activation, we further combine the composited radiance fields from objects/background branches with the predicted residual radiance field, to produce a final composited scene radiance field, using point-wise average pooling operation applied on the color and density. Then we apply a color loss $\mathcal{L}_{\mathrm{comp}}$ for the pixels rendered from the composited radiance field. + +![](images/a20b3085627c0852b5559613fb6a4f8f3b11331de4c7dcdd7b2664b9d2076448.jpg) + +![](images/3d8ca71b8dee949f496125a81203dd6474e620583a2632951c32204202dc4acb.jpg) +(a) ObjectNeRF + +![](images/38d5d87aec16a972d1f152b50678187d88f48fbcc7cdc142a43c3790e52da75b.jpg) + +![](images/f2acb23477c765a171ea0529de64f170a6680fb5056c75a40ca5be3470c2314e.jpg) + +![](images/6379b79d4ebf1c0db6f3727785ac64a98de8717f73a28725a5168440c06fecaa.jpg) +(b) ObjectSDF + +![](images/5f0d0b681157b1ac72f259e335e3588ce4301754e0b9cb1fa8750a0d91de14b2.jpg) + +![](images/bd2ba4c261b85a2cf046e7a698e0095660a25f253b374c74e09d5bd54e7a6100.jpg) + +![](images/15f752fb87f862776563dd22fd0805e52510a2656682f2a3ddf8ef7f04bb75ba.jpg) +(c) Our Method + +![](images/4c7a065c6fea920d2ca186e37618e9aa27f82c1ad2244f02dc4a3ca87a1efe0a.jpg) + +![](images/464595e8e2c723a16f8059bb43da15c57912281dacb8f9476417fdbcb2e4bb66.jpg) + +![](images/ff58c5f32dfea550760c0181592fd4a2353a2766a4e41e827af2f27fc7488c61.jpg) +(d) Ground Truth + +![](images/cdb2ea0d7073ef1d321806763efe709f9881bb62be4a4d4b17e15aefc2a92594.jpg) + +
MethodsToyDesk2
PSNR ↑SSIM ↑LPIPS ↓
Our Full-Model25.75600.81260.4488
w/o 3D One-hot Density Regularization25.73620.81160.4524
w/o Gumbel-Softmax Activation22.99720.72170.5452
w/o 2D In-painting pseudo Supervision25.68810.81270.4516
w/o Residual Radiance Composition25.22880.80030.4589
+ +Table 1. Quantitative comparison of different variants of the proposed unified decompositional and compositional NeRF framework on the ToyDesk2. + +# 3.4. Optimization and Inference + +Overall framework optimization. The overall optimization loss for training the joint framework consists of the following four different loss functions: + +$$ +\mathcal {L} _ {\text {o v e r a l l}} = \mathcal {L} _ {\text {c o m p}} + \lambda_ {1} \mathcal {L} _ {\text {o b j e c t}} + \lambda_ {2} \mathcal {L} _ {\text {c o l o r - p s e u d o}} + \lambda_ {3} \mathcal {L} _ {\text {o n e - h o t}}, \tag {8} +$$ + +where, $\lambda_1, \lambda_2$ , and $\lambda_3$ are the weights for balancing the learning with the different loss functions. + +Novel View Rendering and Scene Editing After training the joint framework, we can render images of arbitrary perspectives based on the composited radiance field. By reorganizing the object radiance fields, we can generate images with object manipulations, including removal, addition, duplication, and changing position (e.g., rotation). + +# 4. Experiments + +We aim at performing joint scene novel view synthesis and editing based on our proposed unified decompositional and compositional NeRF framework. We thus evaluate our method on both tasks using challenging public benchmarks. + +# 4.1. Experimental Setup + +Datasets. We use ToyDesk [37] and ScanNet [6] datasets for the evaluation. ToyDesk consists of two sets of indoor multi-view images. In each scene, several toys are put on a desk in the center of the room. The multi-view images are captured by looking at the desk center with 360 degrees + +![](images/094730c13e062a1cea5ebabc252d0989f7bf248de35ec3f4a40f9c9aa1fec05a.jpg) +Figure 4. Qualitative comparison of novel view synthesis on the ToyDesk dataset. We compared with ObjectNeRF [37] and ObjectSDF [35]. The results show that the rendered images of our framework achieve better generation quality for both the foreground objects (e.g., the green dinosaur) and the background (e.g., the chessboard). +Figure 5. Qualitative results of the ablation study: (a) Our full model; (b) w/o 3D One-hot Density Regularization; (c) w/o Gumbel-Softmax Activation; (d) w/o 2D In-painting pseudo Supervision. (e) w/o Residual Radiance Composition. + +around the desk, and the camera poses and meshes are provided. The instance semantic labels are annotated on object meshes and then projected onto each perspective to obtain their corresponding 2D semantic label maps. ScanNet is an RGB-D video dataset that contains more than 1500 scans of indoor scenes for multiple 3D understanding tasks. Handheld RGB-D scanners are used for scanning various indoor scenes. Rich annotations such as camera pose, semantic segmentation, and surface reconstruction are also provided. Following ObjectNeRF [37], we choose four scenes, i.e., 0024_00, 0038_00, 0113_00, and 0192_00, from the whole dataset for the experiment. + +Implementation details. Our joint framework consists of a shared backbone, background head, object head, and guidance head. The share backbone is a 4-layer Multi-Layer Perceptron (MLP), and the output generic implicit scene feature has a dimension of 256. The follow-up heads are all three-layer MLPs with a color and density prediction layer to generate corresponding radiance fields. Note that our one-hot regularization and activation module has no parameters to be optimized. We also utilize positional encoding to increase the representation ability for high-frequency details. Specifically, we adopt ten levels for coordinates and four levels for ray directions. The framework is trained end-to-end from scratch, without voxel feature initialization as in [37] or geometric initialization as in [35]. + +![](images/cef947f6420594427ccf09bbd419439c6e0df7635377207c897c82a095cf26ad.jpg) + +![](images/b78376b9146c32f99f19df8092247a42efd62b3b88dd0ddbf7404b1d9758f4a9.jpg) +(a) ObjectNeRF + +![](images/023ffbed22dab1ab677c12954c46abeb8d1ec61224670f4336152a77472e3e5f.jpg) + +![](images/cec874fd2ae7d3129c5e84637e61e73b5e9866e91bdcb3865d56b5f69cd517d6.jpg) +(b) ObjectSDF + +![](images/3799752689e992f3f247b07b6cdfa3d970db442e73b15545f352364cdf8ef5e2.jpg) + +![](images/972b59886809444c5007f6ee700b219facd9f5ccb79df2fcaeb9f4fe9cbd3892.jpg) +(c) Our Method + +![](images/5ad3ed89a27a4b139c4d0aa10ee1ab2ce50940ed7dd2506324b359bfadc1117d.jpg) + +![](images/8f99d0fc6e39722e5bd25b77d15310ff5e60ff0a3c984d368ce63c1585d9dfe1.jpg) +(d) Ground Truth + +![](images/a1452280f8e75eb47ca184e3e0d3eb7d6df3bbe3fe9fb85afebc159ab1d301f9.jpg) +Figure 6. Qualitative comparison of novel view synthesis on the ScanNet dataset. Compared with ObjectNeRF [37] and ObjectSDF [35], our results also achieve better fidelity. We highlight the details in the red boxes. +Figure 7. The Decomposition results on the ToyDesk dataset compared with ObjectNeRF [37]. We show the rendered results of our composited radiance field (the first column) and each background/object radiance field (the second and third columns). + +# 4.2. Model Analysis + +Baseline Models. To verify the effectiveness of our designs for scene decomposition and composition, We conduct several ablation studies considering different variants: (i) 'w/o 3D One-hot Density Regularization' means that we remove the one-hot regularization term for the uncertain regions in the background radiance field. (ii) 'w/o Gumbel-Softmax Activation' indicates that we do not use the Gumbel-Softmax one-hot weight for compositing the object radiance fields. (iii) 'w/o In-painting Supervision' means that we do not apply the in-painting pseudo supervision for the background radiance field. (iv) 'w/o Residual Radiance Composition' means that we do not use the guidance radiance field for fine sampling and remove the residual radiance composition in the fine stage. + +Effect of 3D one-hot density regularization. The quantitative results based on different evaluation metrics, i.e., PSNR, SSIM, and LPIPS, are shown in Table 1. Several + +
DatasetMethodsPSNR ↑SSIM ↑LPIPS↓
ToyDeskObject-NeRF [37]22.17360.77230.4711
Object-SDF [35]22.0298--
Our Method23.14350.78990.4691
ScanNetObject-NeRF [37]25.26400.80470.4094
Object-SDF [35]25.2325--
Our Method26.13490.82490.3951
+ +Table 2. Quantitative comparison on novel view synthesis. We compared with ObjectNeRF [37] and ObjectSDF [35]. '-' indicates the metrics are not reported by the authors in the paper. The evaluation results show that our synthesis results quantitatively outperform these two SOTA methods on all the shown metrics. + +examples of rendered images from the learned background radiance field are presented in Fig. 5. We evaluate the effectiveness of 3D one-hot density regularization by disabling the loss term. As can be observed from Table 1, our joint full mode with 3D one-hot density regularization achieves better results than the model without it. + +Effect of Gumbel-Softmax object radiance activation. We also investigate the effect of using Gumbel-Softmax one-hot activation for the composition of background/object radiance fields. We use an alternative composition method, in which all the local object/background radiance fields that contribute to the same 3D points in the composited field, are directly added instead of using the Gumbel-Softmax one-hot activation weights, as introduced in the method part. As shown in Fig. 5c, without the Gumbel-Softmax one-hot activation, the model cannot successfully learn a decomposed background radiance field (all black), confirming our motivation of using the Gumbel-Softmax activation for a more effective scene representation in a unified framework. + +Effect of 2D in-painting pseudo supervision and residual radiance composition. We also show the contribution of the proposed 2D in-painting pseudo-supervision. If we directly disable the pseudo supervision in the framework, the qualitative results are slightly lower, as shown in the + +![](images/a34154ceaac46e51355d317c4bea0455ad16e8c59bd560b13985ec367b3c6904.jpg) +Figure 8. The Decomposition results on the ScanNet dataset compared with ObjectNeRF [37]. Our background has fewer artifacts when removing the foreground object. + +next to last row in Table. 1. At the same time, as can be seen in Fig. 5, lacking pseudo supervision suffers from significantly downgraded extrapolation in the region occupied by the foreground objects in the 3D space, which indicates that the proposed scheme can effectively help the local object/background disentanglement, especially for learning the radiance field representation of the background on uncertain regions. As shown in Table. 1 and Fig. 5, if we remove the residual radiance composition, the overall qualitative metrics and background decomposition both decline, which demonstrates the importance of using a global radiation field to provide coarse sampling guidance and also further merged as residual information in the fine stage. + +# 4.3. Results on Novel View Synthesis + +We compare our methods on the task of novel view synthesis with two state-of-the-art methods, i.e., ObjectNeRF [37] and ObjectSDF [35]. Our train-test split follows ObjectNeRF [37]. We measure the quality of synthesized images on the evaluation metrics of PSNR, SSIM, and LPIPS. In detail, for our joint framework, we use the finally composited entire scene radiance field for the image rendering. For ObjectNeRF and ObjectSDF on the Toydesk dataset, we use the rendered images provided by the authors for comparison. ObjectSDF adopts a different train-test split and label mapping strategy on ScanNet, so we retrain the ObjectSDF on ScanNet following our setting. + +In Table 2, our synthesis results quantitatively outperform the comparison methods on all the shown metrics. We also present the image examples rendered from novel views in Fig. 4 and Fig. 6. As can be observed in Fig. 4, the rendered images of our framework achieve better generation quality for both the foreground objects (e.g., the green dinosaur) and the background (e.g., the chessboard) than both ObjectNeRF [37] and ObjectSDF [35], proving the capability of our method in modeling both global scene consistency and local scene details. Fig. 6 shows the synthesized images + +![](images/34d20b9a42b400049fe126a6513010c65266d3f5b2ab57901ba809bbca039c0d.jpg) +(a) Original view + +![](images/4f3966fa82aca8505514fc7b68b2a9aceb7217673826628326c113a3d01f4466.jpg) +(b) Edited image +Figure 9. Illustration of the editing results. (a) shows the image in the original view, and (b) shows the editing result from the same perspective. We do the rotation and duplication for the white triangle and candy by re-composting the learned radiance fields. + +on ScanNet. We can also observe that our results outperform others in the overall fidelity and local details marked in the red boxes. + +# 4.4. Results of Object Decomposition and Editing + +We also conduct experiments to show the decomposition effectiveness of our method, especially for the background radiance field. As shown in Fig. 7 and Fig. 8, we rendered the composited radiance field and each local object/background radiance field to show the decomposition results. The background images in Fig. 7 clearly show that our method can generate a clearer table without unsatisfactory artifacts such as strange colors and black shadow effects when removing all the foreground objects on the table. Although with some remained black contours, the rendered pixel colors of the regions below the objects are significantly more reasonable compared to ObjectNeRF [37]. Note that the region under the toys is unseen in any view. Our decomposition module enables clear background and object-specific details, while the composition design helps the rendered entire scene achieve higher quality than the baseline. In Fig. 8, we further show that our pipeline can also provide better background rendering when removing foreground objects on the images from the ScanNet dataset. The better decomposition naturally benefits downstream object editing tasks. Fig. 9 shows that, after learning composited radiance fields, our method can perform rotation and duplication for the white triangle and candy by re-compositing the object and background radiance field representations. We add more editing results in the supplementary materials. + +# 5. Conclusion + +We propose a unified NeRF framework with a novel decomposition and composition design to jointly model real-world scenes with both global and local implicit representations. To solve the ambiguous extrapolation problem for unseen areas, we also propose a 3D one-hot density regularization strategy and a 2D in-painting pseudo supervision. Our experimental evaluation demonstrates that our method outperforms the state-of-the-art object-compositional methods for both novel-view synthesis and scene editing tasks. + +# 6. Acknowledgments + +This research is supported in part by HKUST-SAIL joint research funding, the Early Career Scheme of the Research Grants Council (RGC) of the Hong Kong SAR under grant No. 26202321, and HKUST Startup Fund No. R9253. + +# References + +[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In ICCV, 2021. 2 +[2] Jonathan T Barron, Ben Mildenhall, Dor Verbin, Pratul P Srinivasan, and Peter Hedman. Mip-nerf 360: Unbounded anti-aliased neural radiance fields. 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In this paper, we target a more challenging scenario, i.e., joint scene novel view synthesis and editing based on implicit neural scene representations. State-of-the-art methods in this direction typically consider building separate networks for these two tasks (i.e., view synthesis and editing). Thus, the modeling of interactions and correlations between these two tasks is very limited, which, however, is critical for learning high-quality scene representations. To tackle this problem, in this paper, we propose a unified Neural Radiance Field (NeRF) framework to effectively perform joint scene decomposition and composition for modeling real-world scenes. The decomposition aims at learning disentangled 3D representations of different objects and the background, allowing for scene editing, while scene composition models an entire scene representation for novel view synthesis. 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Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "content": "The reconstruction and rendering of natural scenes are important for computers to understand the 3D physical" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 313, + 239, + 538, + 410 + ], + "blocks": [ + { + "bbox": [ + 313, + 239, + 538, + 410 + ], + "lines": [ + { + "bbox": [ + 313, + 239, + 538, + 410 + ], + "spans": [ + { + "bbox": [ + 313, + 239, + 538, + 410 + ], + "type": "image", + "image_path": "f55d370e73552652219ebd6f8978ea9bd2bca8a3a90a73655a5cbeeee5e117c6.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 411, + 547, + 477 + ], + "lines": [ + { + "bbox": [ + 305, + 411, + 547, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 411, + 547, + 477 + ], + "type": "text", + "content": "Figure 1. Illustration of our decomposition-composition design. It enables scene editing and novel view synthesis in a unified NeRF framework. The proposed decomposition targets learning disentangled 3D representations of different foreground objects and the background, allowing for scene editing, while scene composition constructs an entire scene representation for novel view synthesis." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 546, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 546, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 546, + 615 + ], + "type": "text", + "content": "world. Fine-grained object-level representations within the scene can bring significant benefits in various applications, such as scene understanding, novel content generation via object editing, and robotic manipulation. The emerging neural rendering techniques [17, 18, 24] allow learning object-level or scene-level representations from multi-view posed images and enable rendering high-quality images from novel views. However, most implicit neural methods model an entire scene and lack fine-grained representations of objects in the scene, which severely limits object-level scene representation and understanding." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Learning effective 3D object-aware implicit neural scene representations is still in its infancy. Existing works that tackle this challenging problem typically utilize additional object-level semantic supervision as a priori knowledge in the model optimization [35, 37, 42]. 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However, it remains challenging for this framework to perform joint object editing and novel view synthesis. On the other hand, ObjectNeRF [37] explores scene modeling with Neural Radiance Fields (NeRF) via introducing learnable object activation codes as switchers to condition the radiance field prediction among different objects. This framework can perform joint scene editing and novel view synthesis benefiting from the radiance field representations. However, it learns two separate networks for these two tasks, a global scene branch for novel view synthesis, and a local object branch for scene editing, without modeling any interaction or correlation among them, which, however, is critical for learning more effective scene representations, due to the simple fact that, global scene and local object representations are two important perspectives of the same scene. The global entire scene representation can model the scene's overall structures and appearance consistency, and the local object-specific representation can learn more fine-grained object details. They are highly complementary for learning a high-quality scene representation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 318, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 318, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 318, + 289, + 715 + ], + "type": "text", + "content": "To target the above-mentioned problem, this paper proposes a unified decompositional and compositional neural radiance field framework (see Fig. 1), to learn 3D scene representation for joint scene editing and novel view synthesis. The decomposition can provide the functionality of learning disentangled 3D representations of different objects and the background, allowing for scene editing, while scene composition models an entire scene representation for novel view synthesis. These two can be united to facilitate the consistency constraint in the unified optimization framework. Specifically, we design a new two-stage framework for the scene decomposition and composition, consisting a coarse and a fine stage. In the coarse stage, we learn to predict a global scene radiance field as guidance for point sampling, and in the second fine-grained stage, we perform joint scene decomposition and composition. To perform effective scene decomposition, in the fine-stage, we apply a set of learnable object codes to predict distinct object-level radiance fields, and also propose two novel decomposition strategies: (i) 3D one-hot object radiance activation and regularization. For the object or background branches, only one branch is activated during training using a designed Gumbel-Softmax activation function directly applied on the point density predicted from different object/background branches with also a corresponding one-hot regularization; (ii) an in-painting pseudo supervision strategy. A challenge in scene rendering is modeling the appearance and geometry of regions occluded by objects. This causes generation ambiguity especially when the occluded regions are unseen in all the training views. To address this issue, we propose to use a pretrained inpainting model to provide additional pseudo-color supervision for those ambiguous areas. Note that although the 2D inpainting may bring new ambiguity for the regions" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "seen in other views, the supervision from multi-view consistency is strong enough to suppress most ambiguities. The composition is further performed by utilizing the learned one-hot activation weights for different object-level radiance fields." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 317, + 133, + 541, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 133, + 541, + 145 + ], + "spans": [ + { + "bbox": [ + 317, + 133, + 541, + 145 + ], + "type": "text", + "content": "In summary, this paper has the following contributions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 150, + 545, + 321 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 317, + 150, + 545, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 150, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 317, + 150, + 545, + 209 + ], + "type": "text", + "content": "- We propose a novel NeRF framework for joint scene decomposition and composition to effectively learn object-level and scene-level implicit representations for effective scene modeling, allowing object editing and novel view synthesis in a unified pipeline." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 213, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 213, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 317, + 213, + 545, + 258 + ], + "type": "text", + "content": "- To learn a robust scene decomposition, we design two novel strategies, i.e., 3D one-hot radiance regularization and 2D in-painting pseudo supervision, to significantly improve the rendering and editing qualities." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 262, + 545, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 262, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 317, + 262, + 545, + 321 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the effectiveness of our approach for scene decomposition and show clear improvements upon state-of-the-art object-compositional methods on two important downstream tasks, i.e. novel-view synthesis and object editing." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 334, + 392, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 392, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 392, + 346 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 354, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 628 + ], + "type": "text", + "content": "Neural Implicit Representations. As pioneering methods, [17, 21, 24, 28] introduce neural networks to implicitly parameterize 3D scenes. These works can learn continuous shape and texture from differentiable rendering with [12, 24] or without[21, 28] 3D supervision. Neural Radiance Fields (NeRF) [18] optimize a 3D continuous neural scene representation by using only 2D multiview posed images for training and produce high-quality novel view synthesis with 3D structure awareness. Recent works also extend the generalization of NeRF to more significant scenes [1, 2, 41], or model scenes with fewer perspectives [5, 33, 39]. However, all these works only focus on the entire scene representation, neglecting fine-grained representations of objects/background within the scene. Other researches represent object surfaces with implicit neural function to realize multi-view 3D reconstruction for single objects [22, 32, 38]. The decomposed implicit representation for independently characterizing components within the scene has been studied in not only object scenes [3, 14, 8, 23, 25, 27], but also in the face or body tasks [9, 11, 34]. In contrast to these works, our method targets both scene synthesis and editing, considering joint object- and scene-level implicit representation learning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Object-Compositional Implicit Representation. Representing scenes in an object-compositional manner can benefit both scene synthesis and editing [3, 4, 26, 29, 30, 35, 40, 36]. Compared to decomposed object representations represented by generative models [7, 19, 20], implicit models present more 3D physical meaning during the modeling process, which facilitates image rendering from novel" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18248" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 74, + 286, + 175 + ], + "blocks": [ + { + "bbox": [ + 53, + 74, + 286, + 175 + ], + "lines": [ + { + "bbox": [ + 53, + 74, + 286, + 175 + ], + "spans": [ + { + "bbox": [ + 53, + 74, + 286, + 175 + ], + "type": "image", + "image_path": "7f548f64d762a0318317ce2902740ad683358c52c7f50faf9bdf1a05232f5ed7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 290, + 79, + 541, + 152 + ], + "blocks": [ + { + "bbox": [ + 290, + 79, + 541, + 152 + ], + "lines": [ + { + "bbox": [ + 290, + 79, + 541, + 152 + ], + "spans": [ + { + "bbox": [ + 290, + 79, + 541, + 152 + ], + "type": "image", + "image_path": "8a472b2ea1c44c8a082c7a5f953949f41703a76b429feb0d17ac953a3716d04b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 53, + 176, + 545, + 350 + ], + "blocks": [ + { + "bbox": [ + 53, + 176, + 545, + 350 + ], + "lines": [ + { + "bbox": [ + 53, + 176, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 53, + 176, + 545, + 350 + ], + "type": "image", + "image_path": "fcedf36b74ac6897eb19760ac73b982eeb0400d71b2d582cd58b377ba833ec81.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 354, + 546, + 420 + ], + "lines": [ + { + "bbox": [ + 46, + 354, + 546, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 546, + 420 + ], + "type": "text", + "content": "Figure 2. An overview of the proposed unified decompositional and compositional NeRF framework for joint novel view synthesis and scene editing. It has two stages. In the first stage (i.e. the coarse stage), it learns a guidance radiance field for guiding point sampling. In the second stage (i.e. the fine stage), we learn scene decomposition via learnable object codes and two novel decomposition schemes: (i) the 3D one-shot object radiance activation regularization and (ii) color inpainting handling ambiguous generation in occluded background areas. The scene composition is achieved by using one-hot activation weights for different object-level radiance fields learned in the decomposition stage. The decomposition allows scene editing and the composition enables novel view synthesis in the unified framework." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 425, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 289, + 712 + ], + "type": "text", + "content": "views. We can categorize the works of object-compositional implicit representations into supervised and unsupervised methods. The unsupervised methods localize objects with different aspects of prior information, such as multiple similar scenes [26, 29, 40], temporal consistency [13], or clustering-based initialization [15]. Specifically, uORF [40] involves a slot-attention [13] module in learning object-level iterative attention masks for each object decomposition. RFP [15] utilizes clustering predictions as initialization and applies a bidirectional color loss to decompose individual objects. However, lacking precise annotation, although these methods can obtain object position clues, they usually suffer from low-resolution [26, 40] issues that restrict generalization ability to high-resolution real-world scenes. The supervised methods usually use object-level annotations, such as semantic masks [35, 37, 42] or scene graphs [23]. Among these works, ObjectNeRF [37] utilizes a two-branch network to learn a scene radiance field with an activation code-conditioned object radiance field supervised by multi-view images and semantic masks. Similarly, ObjectSDF [35] encodes the entire scene by combining the individual Signed Distance Functions (SDF) represented with semantic labels. The most related work to us is ObjectNeRF [37]. In contrast to ObjectNeRF, we model" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 425, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 425, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 305, + 425, + 545, + 473 + ], + "type": "text", + "content": "an the scene representation via joint scene decomposition and composition, which can effectively model global consistency and rich local details in a unified NeRF framework for a high-quality scene representation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 486, + 539, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 539, + 500 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 539, + 500 + ], + "type": "text", + "content": "3. Decompositional and Compositional NeRF" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "text", + "content": "Given a set of multi-view posed images " + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "inline_equation", + "content": "\\{x_{i}, i \\in [1, N]\\}" + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "text", + "content": " and their corresponding instance semantic masks " + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "inline_equation", + "content": "\\{s_{ij}, i \\in [1, N], j \\in [1, K + 1]\\}" + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "text", + "content": " of a static real-world scene, our goal is to learn an entire scene representation based on the composition of a global scene radiance field and explicitly decomposed local radiance fields of different objects and the background. The decomposition allows scene editing and the composition enables novel view synthesis. " + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "text", + "content": " is the number of multi-view images, and " + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 504, + 545, + 659 + ], + "type": "text", + "content": " is the number of object instances, where we regard the background as an additional instance. We propose a joint decomposition and composition framework to allow simultaneous performing these two tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 670, + 432, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 432, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 432, + 682 + ], + "type": "text", + "content": "3.1. Framework Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": "An overall framework illustration is shown in Fig. 2. It consists of two rendering stages. In the first stage (i.e. the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18249" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": "coarse stage), it learns a global scene guidance radiance field for guiding point sampling. In the second stage (i.e. the fine stage), we learn scene decomposition and composition. The decomposition is performed via first applying a set of learnable object codes as conditions to predict " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "K + 1" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " local object/background radiance field components, where " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " is the number of objects, and the additional 1 represents the background. Following NeRF [18], we use continuous neural radiance fields to represent each local object/background. Considering the composition nature that the whole scene consists of all the " + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "inline_equation", + "content": "K + 1" + }, + { + "bbox": [ + 47, + 72, + 289, + 360 + ], + "type": "text", + "content": " components, we composite all the object and background radiance fields to an entire scene radiance field based on a proposed one-hot object radiance activation module. We also propose an effective color-inpainting strategy to handle the ambiguity in generating occluded background regions. The residual prediction from the first coarse stage is also utilized to benefit from a global scene representation. In the following subsections, we first give a general introduction to the proposed unified framework. Then, we introduce our novel decomposition and composition design and how the method can help disentangle different objects explicitly. After that, we present how our unified framework is optimized and utilized for both novel-view synthesis and editing tasks." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 369, + 168, + 381 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 168, + 381 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 168, + 381 + ], + "type": "text", + "content": "3.2. Scene Decomposition" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": "Two-branch network architecture design. For scene decomposition in the fine-stage, we design a two-branch network architecture with a shared MLP backbone to learn generic implicit scene representation from input point coordinates (see Fig. 3). Specifically, the shared backbone takes a sampled 3D point coordinate " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = (x,y,z)" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": " and view direction " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": " of a camera ray as input, and predicts a generic scene feature vector " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": ". Similar to [37], we also apply a set of learnable codes, each representing the background or an object. We further pass " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": " accompanying with background or object codes to the following MLP heads. For better background learning, we use separate the background head and the object head, predicting an RGB color " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{object}}^i" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": " and a volume density " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{object}}^i" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": " for the corresponding background or object " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": ". For simplicity, we refer to the background as a particular object with index " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": ". For efficient point sampling, we apply a coarse-to-fine sampling technique. In the coarse stage, we only adopt several MLPs after the backbone for predicting RGB color " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{guidance}}" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": " and volume density " + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{guidance}}" + }, + { + "bbox": [ + 47, + 388, + 289, + 676 + ], + "type": "text", + "content": " of the global scene. We use the distribution of coarse prediction for the fine point coordinate sampling, so we call these MLPs guidance head. In the fine stage, we also use the prediction of the guidance head as a residual radiance field in the following composition module." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": "3D one-hot density regularization. To achieve effective decomposition of objects/background radiance fields from the scene, we also design a one-hot regularization term for" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": "the uncertain regions in the background radiance field. Our motivation is that the 3D points belonging to the foreground objects should not have any volume density in the background radiance field. We thus apply a one-hot regularization loss term, which acts as an additional constraint to the object-specific radiance field optimization objective " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{object}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": ". In detail, we first obtain the 3D point positions that foreground objects occupy by determining whether the foreground objects take the largest volume density at the points. We thus define a binary occupancy mask " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "M_{c}" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": ", and apply a regularization term for the occupied points as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 311, + 209, + 545, + 231 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 209, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 311, + 209, + 545, + 231 + ], + "type": "interline_equation", + "content": "M _ {c} = \\left[ \\operatorname {a r g m a x} \\left(\\left[ \\sigma_ {\\text {o b j e c t}} ^ {1}, \\sigma_ {\\text {o b j e c t}} ^ {2}, \\sigma_ {\\text {o b j e c t}} ^ {3}, \\dots , \\sigma_ {\\text {o b j e c t}} ^ {K + 1} \\right]\\right) > 1 \\right] \\tag {1}", + "image_path": "8b13f25d7cae586e41dcabffef46d5b6946c088a787706aff4e06450157810d8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 312, + 227, + 431, + 242 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 227, + 431, + 242 + ], + "spans": [ + { + "bbox": [ + 312, + 227, + 431, + 242 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {o n e - h o t}} = M _ {c} \\| \\sigma_ {\\mathrm {o b j e c t}} ^ {1} - \\sigma_ {0} \\| _ {2} ^ {2}", + "image_path": "0347fe35bcc963d9ac20933646466cfe97ac1f9ca92fe6792cfa809ad6014ee9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{object}}^{1}" + }, + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "text", + "content": " here means we only want to constrain the background radiance field (with index 1). Note that we implement a ReLU operation on the volume density " + }, + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "text", + "content": " to make it positive during the volume rendering process, so if the raw prediction " + }, + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{object}}^{1}" + }, + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "text", + "content": " is negative at some points, it will also have no contribution to the rendering results. Therefore, we can set " + }, + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\sigma_0" + }, + { + "bbox": [ + 304, + 247, + 547, + 342 + ], + "type": "text", + "content": " as any non-positive number here. We put it -0.01 in our experiments from experience." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 344, + 547, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 344, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 344, + 547, + 561 + ], + "type": "text", + "content": "2D in-painting pseudo supervision. To model a better background-specific radiance field, we need to learn what the scene looks like even if all the foreground objects are removed from the scene. Several occluded regions in the background can be seen in other views, while regions covered by the objects are invisible from all views, which are uncertain regions. We thus do not have any pixel-wise supervision for those regions in the training data, resulting in unsatisfactory extrapolation results on those regions when we learn the background radiance field. To tackle this problem, we involve a pre-trained in-painting model to fill those uncertain regions on the 2D images. Our motivation is that the 2D in-painting model can utilize local context information on an image to fill the regions, providing effective 2D pseudo color supervision. Specifically, we use a famous pre-trained lama [31] model to fill the uncertain 2D background regions and then apply a color loss for the rendered background pixels with a foreground mask " + }, + { + "bbox": [ + 304, + 344, + 547, + 561 + ], + "type": "inline_equation", + "content": "M_{1}(r)^{1}" + }, + { + "bbox": [ + 304, + 344, + 547, + 561 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 320, + 566, + 545, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 566, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 320, + 566, + 545, + 582 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o l o r . p s e u d o}} = M _ {1} (r) ^ {1} \\| \\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {1} - C (\\boldsymbol {r}) _ {\\text {p s e u d o}} \\| _ {2} ^ {2} \\tag {2}", + "image_path": "07a5a14c9e2b0180c2f3b1b9c3245f7d2118ebf0ca868b7a339e4aa85811e419.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 587, + 547, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 587, + 547, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 587, + 547, + 637 + ], + "type": "text", + "content": "Intermediate local object rendering. To enforce the decomposition of all object-specific radiance fields, we apply a color consistent loss and an opacity loss with semantic masks as [18, 37] via rendering both 2D color and opacity:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 648, + 545, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 648, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 321, + 648, + 545, + 687 + ], + "type": "interline_equation", + "content": "\\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} = \\sum_ {i = 1} ^ {N} T _ {i} ^ {k} \\left(1 - \\exp \\left(- \\sigma_ {\\text {o b j e c t}} ^ {k} \\delta_ {i}\\right)\\right) \\mathbf {c} _ {\\text {o b j e c t}} ^ {k}, \\tag {3}", + "image_path": "eea6e6fb7a68a5c4a9fae7b1dc9f416f6e8bb36eb6e3f3d75787ac79ecb8419d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 322, + 682, + 493, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 682, + 493, + 715 + ], + "spans": [ + { + "bbox": [ + 322, + 682, + 493, + 715 + ], + "type": "interline_equation", + "content": "\\hat {O} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} = \\sum_ {i = 1} ^ {N} T _ {i} ^ {k} \\left(1 - \\exp \\left(- \\sigma_ {\\text {o b j e c t}} ^ {k} \\delta_ {i}\\right)\\right)", + "image_path": "7537e1eed2e4cab2225e56b683193b3891c3aeb8f9f13bca58771454937dc383.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18250" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "inline_equation", + "content": "T_{i}^{k} = \\exp (-\\sum_{j = 1}^{i - 1}\\sigma_{\\mathrm{object}}^{k}\\delta_{j})" + }, + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "text", + "content": " is the transmittance representing how much light is transmitted along the ray for the " + }, + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "text", + "content": "-th object; " + }, + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "text", + "content": " is the number of sampled points along the camera ray, and " + }, + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "inline_equation", + "content": "\\delta_{i}" + }, + { + "bbox": [ + 46, + 70, + 289, + 133 + ], + "type": "text", + "content": " is the distance between two adjacent points. Then we apply the following losses:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 73, + 136, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 136, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 73, + 136, + 287, + 186 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {o b j e c t}} = \\sum_ {k = 1} ^ {K + 1} M _ {o} (\\boldsymbol {r}) ^ {k} \\| \\hat {C} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {k} - C (\\boldsymbol {r}) \\| _ {2} ^ {2} \\tag {4} \\\\ + \\lambda M _ {b} (\\boldsymbol {r}) ^ {1} \\| \\hat {\\boldsymbol {O}} (\\boldsymbol {r}) _ {\\text {o b j e c t}} ^ {1} - M _ {o} (\\boldsymbol {r}) ^ {1} \\| _ {2} ^ {2}, \\\\ \\end{array}", + "image_path": "5a4da38aa20928e563323f7b43062f43b44a4f21a662771cc08230d77d7480a1.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "type": "inline_equation", + "content": "M_{o}(\\boldsymbol{r})" + }, + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "type": "inline_equation", + "content": "M_{b}(\\boldsymbol{r})" + }, + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "type": "text", + "content": " are 2D spatial weight maps determined by object-level and background-level semantic masks, respectively, which indicates that rendered object-specific pixels are given supervision at the corresponding semantic mask region. The background region in the binary semantic mask can be either real background or occluded by a foreground object, so we use a small weight value (i.e. 0.05) in " + }, + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "type": "inline_equation", + "content": "M_{b}" + }, + { + "bbox": [ + 46, + 190, + 287, + 286 + ], + "type": "text", + "content": " as a balance weight for the uncertain region." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 294, + 160, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 294, + 160, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 294, + 160, + 308 + ], + "type": "text", + "content": "3.3. Scene Composition" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 313, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 287, + 348 + ], + "type": "text", + "content": "This section presents how the learned global and the local object/background radiance fields are composited for an entire scene radiance field." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "content": "Gumbel-Softmax one-hot object radiance activation. As shown in Fig. 3, for each sampled point, there are " + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "inline_equation", + "content": "K + 1" + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "content": " predictions in the local radiance field decomposition. Considering that each point in the 3D space can only belong to either one object or the background, we use the predicted " + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_{\\mathrm{object}}^i,\\sigma_{\\mathrm{object}}^i)" + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "content": " with the maximum volume density " + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{object}}^i" + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "content": " among all the object instances to construct an activated object-specific radiance field. More specifically, to address the gradient backpropagation problem of the argmax operation, following [10, 16], We employ the Gumbel-Softmax function on volume density as a continuous and differentiable approximation. First, we calculate a soft probability " + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 350, + 287, + 506 + ], + "type": "text", + "content": "-th object branch as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 509, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 509, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 106, + 509, + 287, + 544 + ], + "type": "interline_equation", + "content": "p _ {i} = \\frac {\\exp^ {\\left(\\left(\\sigma_ {\\text {o b j e c t}} ^ {i} + g _ {i}\\right) / t a u\\right)}}{\\sum_ {j} \\exp^ {\\left(\\left(\\sigma_ {\\text {o b j e c t}} ^ {j} + g _ {j}\\right) / t a u\\right)}} \\tag {5}", + "image_path": "bebb0c92340439005a7ecbb93a4374b257d0057e3a826dff00cc4bb0519cf97e.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "The above " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "g_{1}, g_{2}, \\ldots, g_{j}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " are the independent and identically distributed samples drawn from " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{Gumbel}(0,1)^{1}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " [10]. The symbol " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "tau" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " is the temperature ratio set to 0.1 in our experiments. Then, we can obtain one-hot composition weights from " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "p_{i}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " for combining the predictions of all the object/background branches, which ensures one-hot activation for all the object/background radiance fields, and enables effective backpropagation for learning object-specific radiance fields and their composition. Specifically, we calculate the one-hot weights " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{obj}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " as Eq. 6. Let us denote " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " as the soft probability vector, containing " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "K + 1" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " predictions calculated by Eq. 5. " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{obj}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " is a one-hot vector of the " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "K + 1" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " elements. The one-hot vector is calculated with a stop gradient operation " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{sp}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ", which not only reserves the one-" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 76, + 542, + 277 + ], + "blocks": [ + { + "bbox": [ + 307, + 76, + 542, + 277 + ], + "lines": [ + { + "bbox": [ + 307, + 76, + 542, + 277 + ], + "spans": [ + { + "bbox": [ + 307, + 76, + 542, + 277 + ], + "type": "image", + "image_path": "119bd32f91a14af2a1572654b018ca4de6fce02885f6f1d9cc21cd6986ef969d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 283, + 545, + 382 + ], + "lines": [ + { + "bbox": [ + 304, + 283, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 545, + 382 + ], + "type": "text", + "content": "Figure 3. Illustration of the Composition Module. Our composition module consists of one-hot object radiance activation and global-local radiance field composition (the two green blocks). We first apply Gumbel-Softmax on object-level volume density values to obtain the one-hot mask for object radiance fields. Then, the local compositional radiance field is generated by a weighted sum of the object and background color and density predictions. Finally, the composited radiance is combined with a residual prediction to produce the final scene radiance field." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 386, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 386, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 305, + 386, + 545, + 411 + ], + "type": "text", + "content": "hot activation but also allows the gradient backpropagated through " + }, + { + "bbox": [ + 305, + 386, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 305, + 386, + 545, + 411 + ], + "type": "text", + "content": ". Then, the computation of " + }, + { + "bbox": [ + 305, + 386, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{obj}" + }, + { + "bbox": [ + 305, + 386, + 545, + 411 + ], + "type": "text", + "content": " is written as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 310, + 430, + 545, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 430, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 310, + 430, + 545, + 450 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {o b j} = f _ {\\mathrm {h}} \\left(\\underset {i} {\\arg \\max } \\left[ g _ {i} + \\log \\sigma_ {\\text {o b j e c t}} ^ {i} \\right]\\right) - f _ {s p} (\\mathbf {P}) + \\mathbf {P}, \\tag {6}", + "image_path": "e7e45fbd0399d72486a4aa90cb053981bc9f8bf0a86f2a80ff5756908d3e8d06.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{h}}(\\cdot)" + }, + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "type": "text", + "content": " denotes a one-hot function; Then, we obtain a composed scene radiance field " + }, + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_{\\mathrm{comp}}, \\sigma_{\\mathrm{comp}})" + }, + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "type": "text", + "content": " of all decomposed branches " + }, + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{c}_{\\mathrm{object}}^k, \\sigma_{\\mathrm{object}}^k\\}_{k=1}^{K+1}" + }, + { + "bbox": [ + 305, + 453, + 545, + 503 + ], + "type": "text", + "content": ", by multiplying the above one-hot weights as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 514, + 545, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 514, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 312, + 514, + 545, + 539 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {\\text {c o m p}} = \\sum_ {K + 1} \\mathbf {M} _ {o b j} ^ {k} \\mathbf {c} _ {\\text {o b j e c t}} ^ {k}, \\sigma_ {\\text {c o m p}} = \\sum_ {K + 1} \\mathbf {M} _ {o b j} ^ {k} \\sigma_ {\\text {o b j e c t}} ^ {k}, \\tag {7}", + "image_path": "86fd7311b47c6a49b9b475db4481fd0ac0625bb6b159ddfcd98079f8acb5c828.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "type": "text", + "content": "Our novel one-hot object radiance activation can not only ensure a reasonable composition of all the object radiance fields but also force that only one object volume density prediction can be activated in the gradient backpropagation, which can also effectively help the object/background decomposition." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Residual radiance field composition. After the one-hot object radiance activation, we further combine the composited radiance fields from objects/background branches with the predicted residual radiance field, to produce a final composited scene radiance field, using point-wise average pooling operation applied on the color and density. 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MethodsToyDesk2
PSNR ↑SSIM ↑LPIPS ↓
Our Full-Model25.75600.81260.4488
w/o 3D One-hot Density Regularization25.73620.81160.4524
w/o Gumbel-Softmax Activation22.99720.72170.5452
w/o 2D In-painting pseudo Supervision25.68810.81270.4516
w/o Residual Radiance Composition25.22880.80030.4589
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Optimization and Inference" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 384, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 419 + ], + "type": "text", + "content": "Overall framework optimization. The overall optimization loss for training the joint framework consists of the following four different loss functions:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 50, + 429, + 286, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 429, + 286, + 453 + ], + "spans": [ + { + "bbox": [ + 50, + 429, + 286, + 453 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {o v e r a l l}} = \\mathcal {L} _ {\\text {c o m p}} + \\lambda_ {1} \\mathcal {L} _ {\\text {o b j e c t}} + \\lambda_ {2} \\mathcal {L} _ {\\text {c o l o r - p s e u d o}} + \\lambda_ {3} \\mathcal {L} _ {\\text {o n e - h o t}}, \\tag {8}", + "image_path": "6b42056b531694c8084a2f6203770dab954be39e4cbe48e499af853fda193aef.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 453, + 287, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 476 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 476 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 46, + 453, + 287, + 476 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2" + }, + { + "bbox": [ + 46, + 453, + 287, + 476 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 453, + 287, + 476 + ], + "type": "inline_equation", + "content": "\\lambda_3" + }, + { + "bbox": [ + 46, + 453, + 287, + 476 + ], + "type": "text", + "content": " are the weights for balancing the learning with the different loss functions." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 550 + ], + "type": "text", + "content": "Novel View Rendering and Scene Editing After training the joint framework, we can render images of arbitrary perspectives based on the composited radiance field. By reorganizing the object radiance fields, we can generate images with object manipulations, including removal, addition, duplication, and changing position (e.g., rotation)." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 559, + 128, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 128, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 128, + 574 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 579, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 287, + 628 + ], + "type": "text", + "content": "We aim at performing joint scene novel view synthesis and editing based on our proposed unified decompositional and compositional NeRF framework. We thus evaluate our method on both tasks using challenging public benchmarks." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 47, + 635, + 163, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 163, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 163, + 647 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Datasets. We use ToyDesk [37] and ScanNet [6] datasets for the evaluation. ToyDesk consists of two sets of indoor multi-view images. In each scene, several toys are put on a desk in the center of the room. The multi-view images are captured by looking at the desk center with 360 degrees" + } + ] + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 307, + 255, + 541, + 331 + ], + "blocks": [ + { + "bbox": [ + 46, + 217, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 46, + 217, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 545, + 250 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of novel view synthesis on the ToyDesk dataset. We compared with ObjectNeRF [37] and ObjectSDF [35]. The results show that the rendered images of our framework achieve better generation quality for both the foreground objects (e.g., the green dinosaur) and the background (e.g., the chessboard)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 255, + 541, + 331 + ], + "lines": [ + { + "bbox": [ + 307, + 255, + 541, + 331 + ], + "spans": [ + { + "bbox": [ + 307, + 255, + 541, + 331 + ], + "type": "image", + "image_path": "094730c13e062a1cea5ebabc252d0989f7bf248de35ec3f4a40f9c9aa1fec05a.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 332, + 545, + 376 + ], + "lines": [ + { + "bbox": [ + 305, + 332, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 332, + 545, + 376 + ], + "type": "text", + "content": "Figure 5. Qualitative results of the ablation study: (a) Our full model; (b) w/o 3D One-hot Density Regularization; (c) w/o Gumbel-Softmax Activation; (d) w/o 2D In-painting pseudo Supervision. (e) w/o Residual Radiance Composition." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 394, + 546, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 546, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 546, + 538 + ], + "type": "text", + "content": "around the desk, and the camera poses and meshes are provided. The instance semantic labels are annotated on object meshes and then projected onto each perspective to obtain their corresponding 2D semantic label maps. ScanNet is an RGB-D video dataset that contains more than 1500 scans of indoor scenes for multiple 3D understanding tasks. Handheld RGB-D scanners are used for scanning various indoor scenes. Rich annotations such as camera pose, semantic segmentation, and surface reconstruction are also provided. Following ObjectNeRF [37], we choose four scenes, i.e., 0024_00, 0038_00, 0113_00, and 0192_00, from the whole dataset for the experiment." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Implementation details. Our joint framework consists of a shared backbone, background head, object head, and guidance head. The share backbone is a 4-layer Multi-Layer Perceptron (MLP), and the output generic implicit scene feature has a dimension of 256. The follow-up heads are all three-layer MLPs with a color and density prediction layer to generate corresponding radiance fields. Note that our one-hot regularization and activation module has no parameters to be optimized. 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"type": "text", + "content": "(c) Our Method" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 406, + 69, + 518, + 154 + ], + "blocks": [ + { + "bbox": [ + 406, + 69, + 518, + 154 + ], + "lines": [ + { + "bbox": [ + 406, + 69, + 518, + 154 + ], + "spans": [ + { + "bbox": [ + 406, + 69, + 518, + 154 + ], + "type": "image", + "image_path": "5ad3ed89a27a4b139c4d0aa10ee1ab2ce50940ed7dd2506324b359bfadc1117d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 406, + 155, + 517, + 237 + ], + "blocks": [ + { + "bbox": [ + 406, + 155, + 517, + 237 + ], + "lines": [ + { + "bbox": [ + 406, + 155, + 517, + 237 + ], + "spans": [ + { + "bbox": [ + 406, + 155, + 517, + 237 + ], + "type": "image", + "image_path": "8f99d0fc6e39722e5bd25b77d15310ff5e60ff0a3c984d368ce63c1585d9dfe1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 429, + 242, + 493, + 252 + ], + "lines": [ + { + "bbox": [ + 429, + 242, + 493, + 252 + ], + "spans": [ + { + "bbox": [ + 429, + 242, + 493, + 252 + ], + "type": "text", + "content": "(d) Ground Truth" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 67, + 281, + 264, + 443 + ], + "blocks": [ + { + "bbox": [ + 46, + 253, + 545, + 276 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 545, + 276 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison of novel view synthesis on the ScanNet dataset. Compared with ObjectNeRF [37] and ObjectSDF [35], our results also achieve better fidelity. We highlight the details in the red boxes." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 67, + 281, + 264, + 443 + ], + "lines": [ + { + "bbox": [ + 67, + 281, + 264, + 443 + ], + "spans": [ + { + "bbox": [ + 67, + 281, + 264, + 443 + ], + "type": "image", + "image_path": "a1452280f8e75eb47ca184e3e0d3eb7d6df3bbe3fe9fb85afebc159ab1d301f9.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 445, + 287, + 489 + ], + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 489 + ], + "type": "text", + "content": "Figure 7. The Decomposition results on the ToyDesk dataset compared with ObjectNeRF [37]. We show the rendered results of our composited radiance field (the first column) and each background/object radiance field (the second and third columns)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 491, + 142, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 142, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 142, + 504 + ], + "type": "text", + "content": "4.2. Model Analysis" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 510, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 677 + ], + "type": "text", + "content": "Baseline Models. To verify the effectiveness of our designs for scene decomposition and composition, We conduct several ablation studies considering different variants: (i) 'w/o 3D One-hot Density Regularization' means that we remove the one-hot regularization term for the uncertain regions in the background radiance field. (ii) 'w/o Gumbel-Softmax Activation' indicates that we do not use the Gumbel-Softmax one-hot weight for compositing the object radiance fields. (iii) 'w/o In-painting Supervision' means that we do not apply the in-painting pseudo supervision for the background radiance field. (iv) 'w/o Residual Radiance Composition' means that we do not use the guidance radiance field for fine sampling and remove the residual radiance composition in the fine stage." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Effect of 3D one-hot density regularization. The quantitative results based on different evaluation metrics, i.e., PSNR, SSIM, and LPIPS, are shown in Table 1. Several" + } + ] + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 309, + 279, + 545, + 364 + ], + "blocks": [ + { + "bbox": [ + 309, + 279, + 545, + 364 + ], + "lines": [ + { + "bbox": [ + 309, + 279, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 309, + 279, + 545, + 364 + ], + "type": "table", + "html": "
DatasetMethodsPSNR ↑SSIM ↑LPIPS↓
ToyDeskObject-NeRF [37]22.17360.77230.4711
Object-SDF [35]22.0298--
Our Method23.14350.78990.4691
ScanNetObject-NeRF [37]25.26400.80470.4094
Object-SDF [35]25.2325--
Our Method26.13490.82490.3951
", + "image_path": "67d24e50270123e49c4612ccdf7acefdb011272d6880dcb811fe8148f50fb4cd.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 366, + 545, + 421 + ], + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 421 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on novel view synthesis. We compared with ObjectNeRF [37] and ObjectSDF [35]. '-' indicates the metrics are not reported by the authors in the paper. The evaluation results show that our synthesis results quantitatively outperform these two SOTA methods on all the shown metrics." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 426, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 497 + ], + "type": "text", + "content": "examples of rendered images from the learned background radiance field are presented in Fig. 5. We evaluate the effectiveness of 3D one-hot density regularization by disabling the loss term. As can be observed from Table 1, our joint full mode with 3D one-hot density regularization achieves better results than the model without it." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 498, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 652 + ], + "type": "text", + "content": "Effect of Gumbel-Softmax object radiance activation. We also investigate the effect of using Gumbel-Softmax one-hot activation for the composition of background/object radiance fields. We use an alternative composition method, in which all the local object/background radiance fields that contribute to the same 3D points in the composited field, are directly added instead of using the Gumbel-Softmax one-hot activation weights, as introduced in the method part. As shown in Fig. 5c, without the Gumbel-Softmax one-hot activation, the model cannot successfully learn a decomposed background radiance field (all black), confirming our motivation of using the Gumbel-Softmax activation for a more effective scene representation in a unified framework." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Effect of 2D in-painting pseudo supervision and residual radiance composition. We also show the contribution of the proposed 2D in-painting pseudo-supervision. If we directly disable the pseudo supervision in the framework, the qualitative results are slightly lower, as shown in the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18253" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 69, + 255, + 225 + ], + "blocks": [ + { + "bbox": [ + 73, + 69, + 255, + 225 + ], + "lines": [ + { + "bbox": [ + 73, + 69, + 255, + 225 + ], + "spans": [ + { + "bbox": [ + 73, + 69, + 255, + 225 + ], + "type": "image", + "image_path": "a34154ceaac46e51355d317c4bea0455ad16e8c59bd560b13985ec367b3c6904.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 227, + 287, + 261 + ], + "lines": [ + { + "bbox": [ + 46, + 227, + 287, + 261 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 287, + 261 + ], + "type": "text", + "content": "Figure 8. The Decomposition results on the ScanNet dataset compared with ObjectNeRF [37]. Our background has fewer artifacts when removing the foreground object." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 288, + 422 + ], + "type": "text", + "content": "next to last row in Table. 1. At the same time, as can be seen in Fig. 5, lacking pseudo supervision suffers from significantly downgraded extrapolation in the region occupied by the foreground objects in the 3D space, which indicates that the proposed scheme can effectively help the local object/background disentanglement, especially for learning the radiance field representation of the background on uncertain regions. As shown in Table. 1 and Fig. 5, if we remove the residual radiance composition, the overall qualitative metrics and background decomposition both decline, which demonstrates the importance of using a global radiation field to provide coarse sampling guidance and also further merged as residual information in the fine stage." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 430, + 220, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 220, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 220, + 443 + ], + "type": "text", + "content": "4.3. Results on Novel View Synthesis" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 450, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 593 + ], + "type": "text", + "content": "We compare our methods on the task of novel view synthesis with two state-of-the-art methods, i.e., ObjectNeRF [37] and ObjectSDF [35]. Our train-test split follows ObjectNeRF [37]. We measure the quality of synthesized images on the evaluation metrics of PSNR, SSIM, and LPIPS. In detail, for our joint framework, we use the finally composited entire scene radiance field for the image rendering. For ObjectNeRF and ObjectSDF on the Toydesk dataset, we use the rendered images provided by the authors for comparison. ObjectSDF adopts a different train-test split and label mapping strategy on ScanNet, so we retrain the ObjectSDF on ScanNet following our setting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "In Table 2, our synthesis results quantitatively outperform the comparison methods on all the shown metrics. We also present the image examples rendered from novel views in Fig. 4 and Fig. 6. As can be observed in Fig. 4, the rendered images of our framework achieve better generation quality for both the foreground objects (e.g., the green dinosaur) and the background (e.g., the chessboard) than both ObjectNeRF [37] and ObjectSDF [35], proving the capability of our method in modeling both global scene consistency and local scene details. Fig. 6 shows the synthesized images" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 318, + 70, + 424, + 150 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 424, + 150 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 424, + 150 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 424, + 150 + ], + "type": "image", + "image_path": "34d20b9a42b400049fe126a6513010c65266d3f5b2ab57901ba809bbca039c0d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 341, + 152, + 399, + 162 + ], + "lines": [ + { + "bbox": [ + 341, + 152, + 399, + 162 + ], + "spans": [ + { + "bbox": [ + 341, + 152, + 399, + 162 + ], + "type": "text", + "content": "(a) Original view" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 531, + 150 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 531, + 150 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 531, + 150 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 531, + 150 + ], + "type": "image", + "image_path": "4f3966fa82aca8505514fc7b68b2a9aceb7217673826628326c113a3d01f4466.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 450, + 152, + 506, + 162 + ], + "lines": [ + { + "bbox": [ + 450, + 152, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 450, + 152, + 506, + 162 + ], + "type": "text", + "content": "(b) Edited image" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 163, + 545, + 206 + ], + "lines": [ + { + "bbox": [ + 305, + 163, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 545, + 206 + ], + "type": "text", + "content": "Figure 9. Illustration of the editing results. (a) shows the image in the original view, and (b) shows the editing result from the same perspective. We do the rotation and duplication for the white triangle and candy by re-composting the learned radiance fields." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 209, + 545, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 209, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 545, + 243 + ], + "type": "text", + "content": "on ScanNet. We can also observe that our results outperform others in the overall fidelity and local details marked in the red boxes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 251, + 539, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 539, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 539, + 264 + ], + "type": "text", + "content": "4.4. Results of Object Decomposition and Editing" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 270, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 581 + ], + "type": "text", + "content": "We also conduct experiments to show the decomposition effectiveness of our method, especially for the background radiance field. As shown in Fig. 7 and Fig. 8, we rendered the composited radiance field and each local object/background radiance field to show the decomposition results. The background images in Fig. 7 clearly show that our method can generate a clearer table without unsatisfactory artifacts such as strange colors and black shadow effects when removing all the foreground objects on the table. Although with some remained black contours, the rendered pixel colors of the regions below the objects are significantly more reasonable compared to ObjectNeRF [37]. Note that the region under the toys is unseen in any view. Our decomposition module enables clear background and object-specific details, while the composition design helps the rendered entire scene achieve higher quality than the baseline. In Fig. 8, we further show that our pipeline can also provide better background rendering when removing foreground objects on the images from the ScanNet dataset. The better decomposition naturally benefits downstream object editing tasks. Fig. 9 shows that, after learning composited radiance fields, our method can perform rotation and duplication for the white triangle and candy by re-compositing the object and background radiance field representations. We add more editing results in the supplementary materials." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 591, + 378, + 602 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 591, + 378, + 602 + ], + "spans": [ + { + "bbox": [ + 306, + 591, + 378, + 602 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "We propose a unified NeRF framework with a novel decomposition and composition design to jointly model real-world scenes with both global and local implicit representations. To solve the ambiguous extrapolation problem for unseen areas, we also propose a 3D one-hot density regularization strategy and a 2D in-painting pseudo supervision. Our experimental evaluation demonstrates that our method outperforms the state-of-the-art object-compositional methods for both novel-view synthesis and scene editing tasks." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18254" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 157, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 157, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 157, + 85 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "type": "text", + "content": "This research is supported in part by HKUST-SAIL joint research funding, the Early Career Scheme of the Research Grants Council (RGC) of the Hong Kong SAR under grant No. 26202321, and HKUST Startup Fund No. R9253." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 154, + 107, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 154, + 107, + 166 + ], + "spans": [ + { + "bbox": [ + 48, + 154, + 107, + 166 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 175, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 175, + 287, + 218 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 175, + 287, + 218 + ], + "spans": [ + { + "bbox": [ + 53, + 175, + 287, + 218 + ], + "type": "text", + "content": "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. 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In ICCV, 2021. 1, 3" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "18256" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Versatile 3D Shape Generation with Improved Auto-regressive Models/4e583ffa-62ea-4806-8a7a-46ee129f849e_content_list.json b/2023/Learning Versatile 3D Shape Generation with Improved Auto-regressive Models/4e583ffa-62ea-4806-8a7a-46ee129f849e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e1f6849f8383df069ba3f7c4a232f09a54187310 --- /dev/null +++ b/2023/Learning Versatile 3D Shape Generation with Improved Auto-regressive Models/4e583ffa-62ea-4806-8a7a-46ee129f849e_content_list.json @@ -0,0 +1,1668 @@ +[ + { + "type": "text", + "text": "Learning Versatile 3D Shape Generation with Improved Auto-regressive Models", + "text_level": 1, + "bbox": [ + 81, + 130, + 887, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Simian Luo $^{1,\\ast}$ , Xuelin Qian $^{1,\\ast}$ , Yanwei Fu $^{1,\\dagger}$ , Yinda Zhang $^{2}$ , Ying Tai $^{3}$ , Zhenyu Zhang $^{3}$ , Chengjie Wang $^{3}$ , Xiangyang Xue $^{1}$ , Fudan University; $^{2}$ Google; $^{3}$ Tencent Youtu Lab", + "bbox": [ + 205, + 179, + 763, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{18300180157, xlqian, yanweifu, xyxue}@fudan.edu.cn, yindaz@gmail.com, zhangjesse@foxmail.com, {yingtai,Jasoncjwang}@tencent.com", + "bbox": [ + 184, + 236, + 772, + 268 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/48d89c6b4eb62ed0036688118399a72767d04b263aa980c49f6766b8be3fa3a7.jpg", + "image_caption": [ + "Figure 1: We propose an improved AR model (ImAM) to learn versatile 3D shape generation. ImAM can either generate diverse and faithful shapes with multiple categories via an unconditional way (one column to the left), or can be adapted for conditional generation by incorporating various conditioning inputs given on the left-top (three columns to the right)." + ], + "image_footnote": [], + "bbox": [ + 106, + 297, + 292, + 635 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/85a1e51164a5e386171b2d855af3966cd7e0f7d25e177563860e4605a8c2eed0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 310, + 305, + 480, + 636 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/89f7665b60f21a425d5b9cdf64fef009ed98cb605603dc39ef80482b9f76720a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 301, + 678, + 636 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3b344a6440d290175e5f95bfe7c1502f72936a9a1cef1ce01252c16909cb757f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 315, + 861, + 635 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 698, + 313, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Auto-Regressive (AR) models have achieved impressive results in 2D image generation by modeling joint distributions in the grid space. While this approach has been extended to the 3D domain for powerful shape generation, it still has two limitations: expensive computations on volumetric grids and ambiguous auto-regressive order along grid dimensions. To overcome these limitations, we propose the Improved Auto-regressive Model (ImAM) for 3D shape generation, which applies discrete representation learning", + "bbox": [ + 75, + 729, + 470, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "based on a latent vector instead of volumetric grids. Our approach not only reduces computational costs but also preserves essential geometric details by learning the joint distribution in a more tractable order. Moreover, thanks to the simplicity of our model architecture, we can naturally extend it from unconditional to conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images, and texts. Extensive experiments demonstrate that ImAM can synthesize diverse and faithful shapes of multiple categories, achieving state-of-the-art performance.", + "bbox": [ + 496, + 699, + 893, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14139", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 80, + 89, + 207, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D shape generation has garnered increasing interest in both academia and industry for its extensive applications in robotics [20], autonomous driving [47, 28], augmented reality [35] and virtual reality [34]. Based on whether user prerequisites are provided, shape generation is typically categorized as unconditional or conditional. To be an effective generative model, it is crucial for the synthesized shapes to be both diverse and faithful to the universal cognition of humans or given conditions. These qualities serve as the foundation for other deterministic tasks, such as shape completion, single-view reconstruction, and more. Previous approaches [8, 14, 25] usually utilize an AutoEncoder (AE) to learn latent features by shape reconstruction. Then, a GAN is trained to fit the distributions of the latent features, allowing for the generation of 3D shapes through sampling the latent codes learned in AE. While achieving convincing results, a single embedding for one shape easily encounters the problem of poor scalability and difficulty in training.", + "bbox": [ + 80, + 114, + 467, + 385 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, Auto-Regressive (AR) models have shown remarkable performance in the generation of 2D images [11, 50, 5] and 3D shape [23, 45]. Instead of learning a continuous latent space, these model leverage discrete representation learning to encode each 2D/3D input into grid-based discrete codes. Subsequently, a transformer-based network is employed to jointly model the distribution of all codes, which essentially reflects the underlying prior of objects, facilitating high-quality generation and tractable training. However, applying AR models to 3D still suffers from two limitations. First, as the number of discrete codes increases from squared to cubed, the computational burden of the transformer grows dramatically, making it difficult to converge. Second, discrete codes in the grid space are highly coupled. It is ambiguous to simply flatten them for autoregression (e.g., a top-down row-major order). This may lead to poor quality or even collapse of generated shapes (see Sec. 3.1 and the Supplementary for more details).", + "bbox": [ + 80, + 387, + 467, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose an improved auto-regressive model (ImAM), to enhance the efficient learning of 3D shape generation. Our key idea is to apply discrete representation learning in a one-dimensional space instead of 3D volumetric space. Specifically, we first project volumetric grids encoded from 3D shapes onto three axis-aligned orthogonal planes. This process significantly reduces the computational costs from cubed to squared while maintaining the essential information about the input geometry. Next, we present a coupling network to further encode three planes into a compact and tractable latent space, on which discrete representation learning is performed.", + "bbox": [ + 80, + 659, + 467, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our ImAM is straightforward and effective, simply tackling the aforementioned limitations by two projections. Thus, a vanilla decoder-only transformer can be attached to model the joint distributions of codes from the latent spaces.", + "bbox": [ + 80, + 839, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, the simplicity of the transformer structure allows us to switch freely between unconditional and conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images and texts. Figure 1 showcases the ability of our ImAM to generate diverse and accurate shapes across multiple categories, both with and without the given condition on the top-left corner.", + "bbox": [ + 503, + 90, + 888, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the contributions of this paper are listed as follows. (1) We propose an improved AR Model (ImAM) for 3D shape generation. By applying discrete representation learning in a latent vector instead of volumetric grids, our ImAM enjoys the advantages of lightweight and flexibility. (2) Our proposed ImAM model provides a more unified framework for switching between unconditional and conditional generation for a variety of conditioning inputs, including point clouds, categories, images, and texts. (3) Extensive experiments are conducted on four tasks to demonstrate that our ImAM can generate more faithful and diverse shapes, achieving state-of-the-art results for unconditional and conditional shape generation. Overall, our contributions advance the field of 3D shape generation, providing a powerful tool for researchers and practitioners alike.", + "bbox": [ + 503, + 198, + 888, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 503, + 436, + 635, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D shape generative models. As an extremely challenging task, we review the most previous efforts by using voxel, point clouds, and implicit representations. (1) Standard voxel grids can be easily processed by 3D convolution for learning-based 3D task [19, 44, 10, 41]. However, restricted by its cubic space complexity, voxel representation can not scale to a high resolution, usually limited in $64^{3}$ . Even with efficient data structures like octrees or multi-scale representation [40, 13, 30], such representations still have some limitations in quality. (2) Point clouds extracted from shape surfaces is an alternative 3D representation [12, 43, 27], which is efficient in terms of memory and does not suffer from the restriction of resolution compared with voxel representations. However, these representations can not represent topological relations in 3D space and are also nontrivial to recover shape surfaces from point cloud representation. (3) Recently, implicit representations have gained attention for simplicity in representing 3D shapes [25, 21, 22, 33]. By predicting the signed distance [25, 33] or occupancy label [21, 26] of a given point, and then through Marching cubes [18] methods, the surface can be easily recovered. Follow-up works [21, 25, 8, 26, 15] focus on the design of implicit function representation with global or local shape priors. To sum up, different 3D representations lead to various shape generative models. There are various good previous works such as 3DGAN [41], PC-GAN [1], IM-GAN [8], and GBIF [14]. However, most current generative methods are task-specific. And it is difficult to be directly applied to different generative tasks (e.g., shape completion). Fundamentally,", + "bbox": [ + 503, + 463, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14140", + "bbox": [ + 480, + 946, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ee26ab7ec6f2cbb9beae4e1844c10559e56163a0fa9a23b07ebf6f2da29d01e2.jpg", + "image_caption": [ + "Figure 2: Illustration of auto-regressive generation for grid-based representation. Here, we show three different flattening orders as examples. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 462, + 305 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "they rely on GANs for the generation step, suffering from the known drawbacks such as mode collapse and training instability. In contrast, we propose an improved AR model for 3D shape generation that can synthesize high-quality and diverse shapes while being easily generalized to other multi-modal conditions.", + "bbox": [ + 75, + 392, + 468, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Autoregressive models. AR models are probabilistic generative approaches that have tractable probability density. Using the probability chain rule, the likelihood of a given sample (usually high dimensional data) can be factorized into a series of product of conditional probability. In contrast, GANs do not have such a tractable probability density. Recently, AR models achieve remarkable progress in 2D image generation [11, 37, 29], to a less extent 3D tasks [36, 9, 24]. Most of 3D AR models are struggling with generating high-quality shapes due to the challenges of representation learning with more points or faces. Particularly, we notice two recent works [45, 23] that share similar insights of utilizing AR models for 3D tasks. [45] introduces a sparse representation to only quantize non-empty grids in 3D space, but still follows a monotonic row-major order. [23] presents a non-sequential design to break the orders, but performs on all volumetric grids. However, both of them address only one of the above limitations, and burden the structure design and training of transformer. In contrast, our ImAM applies discrete representation learning in a latent vector instead of volumetric grids. Such a representation offers plenty of advantages, including shorter length of discrete codes, tractable orders from auto-regression, fast convergence, and also preserving essential 3D information. Moreover, benefiting from the simplicity of transformers, we can freely switch from unconditional generation to conditional generation by concatenating various conditions.", + "bbox": [ + 75, + 493, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 89, + 635, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 3 illustrates the schematic of our proposed framework for 3D shape generation, which consists of a two-stage training procedure. It first represents the input as a composition of learned discrete codes (in Sec. 3.2), then utilizes a transformer model to learn their interrelations (in Sec. 3.3). Before beginning, we provide some symbol definitions and necessary preliminaries in Sec. 3.1.", + "bbox": [ + 496, + 114, + 893, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 231, + 629, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Ambiguity. Formally, 'ambiguity' appears in the order of a series of conditional probabilities, which affects the difficulty of likelihood learning, leading to approximation error of the joint distribution. Critically, auto-regressive models require sequential outputs, autoregressively predicting the next code conditioned on all previous ones. Thereby, the order of the flattened sequence determines the order of conditional probabilities. Although some methods (e.g. position embedding [39]) can be aware of positions of codes, it cannot eliminate approximation error caused by the condition order. Notably, this 'ambiguity' phenomenon is also discussed in [11] (in Fig. 47), where the loss curves in Fig. 47 highlight the differences in difficulty for likelihood learning across various orders. Figure 2 illustrates how the flattening order affects the way of autoregressive generation. For grid-based representation, it is ambiguous if the flattening order along axes is $y - x - z$ , $x - z - y$ or other combinations.", + "bbox": [ + 496, + 253, + 893, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Discrete Representation. Given input point clouds $P \\in \\mathbb{R}^{n \\times 3}$ where $n$ means the number of points, an encoder is adopted to extract features for each point cloud and then perform voxelization to get features of regular volumetric grids $f^v \\in \\mathbb{R}^{r \\times r \\times r \\times c}$ , where $r$ denote the resolution of voxels and $c$ is the feature dimension. To learn discrete representation for each 3D shape, a codebook $\\mathbf{q} \\in \\mathbb{R}^{m \\times c}$ is thus introduced whose entry is a learned code describing a particular type of local-part shape in a grid. Formally, for each grid $\\left\\{f_{(h,l,w)}^v\\right\\}_{h,l,w=1}^r$ , vector quantization $\\mathcal{Q}(\\cdot)$ is performed by replacing it with the closest entry in codebooks [11],", + "bbox": [ + 496, + 512, + 893, + 703 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} ^ {v} = \\mathcal {Q} \\left(f ^ {v}\\right) := \\arg \\min _ {\\mathbf {e} _ {i} \\in \\mathbf {q}} \\left| \\left| f _ {(h, l, w)} ^ {v} - \\mathbf {e} _ {i} \\right| \\right| \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 714, + 890, + 738 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{e}_i\\in \\mathbf{q}$ represents the $i$ -th entry in the codebook. Thus, learning the correlations between entries in the second stage can explore the underlying priors for shape generation. However, autoregressive generation [11, 45] requires sequential outputs, facing two limitations. First, the resolution of $\\mathbf{z}^v$ matters the quality of synthesized shapes. If $r$ is too small, it lacks the capacity to represent intricate and detailed geometries, while a large value of $r$ can learn a specific code for each local gird, it inevitably increase the computational complexity since the number of required codes", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14141", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/781c588f7b8cadfeaa7850cea650a4bf4af18f82a2801bb2b0c849a16e1274bc.jpg", + "image_caption": [ + "Figure 3: Overview of our ImAM. Given an arbitrary 3D shape, we first project encoded volumetric grids into the three axis-aligned planes, and then use a coupling network to further project them into a latent vector. Vector quantization is thus performed on it for discrete representation. Taking advantages of such a compact representation with tractable orders, vanilla transformers are adopted to auto-repressively learn shape distributions. Furthermore, we can freely switch from unconditional generation to conditional generation by concatenating various conditions, such as point clouds, categories and images." + ], + "image_footnote": [], + "bbox": [ + 94, + 90, + 877, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "explodes as $r$ grows. Second, the order of $\\mathbf{z}^v$ affects the generation quality. Each grid is highly coupled with neighbors, simply flattening (say, along x-y-z axes) may cause 'ambiguity', leading to sub-optimal generation quality.", + "bbox": [ + 75, + 392, + 470, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Improved Discrete Representation Learning", + "text_level": 1, + "bbox": [ + 76, + 462, + 452, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One possible solution to solve the first limitation is applying vector quantization in spatial grids instead of volumetric grids inspired by [3]. Specifically, after obtaining point cloud features $f^p \\in \\mathbb{R}^{n \\times c}$ , we first project points onto three axis-aligned orthogonal planes. Features of points falling into the same plane grid are aggregated via summation, resulting in three feature maps for the three planes $\\{f^{xy}, f^{yz}, f^{xz}\\} \\in \\mathbb{R}^{l \\times w \\times c}$ . Next, the vector quantization is applied to the three planes separately. The primary advantage of tri-planar representation is efficient and compact. It can dramatically reduce the number of grids from $\\mathcal{O}(r^3)$ to $\\mathcal{O}(r^2)$ while preserving essential 3D information. However, it still suffers from the ambiguity of order, or worse, since it involves the flattening order of three planes and the order of entries of each plane.", + "bbox": [ + 75, + 484, + 468, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, we further introduce a projection by learning a higher latent space for features of the three planes. This is simply achieved by first concatenating three planes with arbitrary order and then feeding them into a coupling network. Finally, the output is flattened as a projected latent vector, formulated as,", + "bbox": [ + 75, + 712, + 468, + 804 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf = \\tau \\left(\\mathcal {G} \\left([ f ^ {x y}; f ^ {y z}; f ^ {x z} ]; \\theta)\\right) \\in \\mathbb {R} ^ {m \\times d} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 816, + 468, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $[\\cdot ;\\cdot ]$ denotes the concatenation operation; $\\mathcal{G}(\\cdot ;\\theta)$ is a series of convolution layers with parameters $\\theta$ . $\\tau (\\cdot)$ means the operation of flatten with row-major order; $m$ and $d$ indicate the length of latent vector and feature dimension. By", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "applying discrete representation learning in the latent vector, we can describe each 3D shape with $\\mathbf{z} = \\mathcal{Q}(f)$ , where $\\mathcal{Q}(\\cdot)$ represents vector quantization in Eq. 1.", + "bbox": [ + 496, + 392, + 890, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark. Different from existing works [23, 45] that rely on structure design and training strategies in second stage to address the problem of ambiguous order, we tackle it by learning the coupling relationship of spatial grids in the first stage with the help of the second projection. By stacking convolution layers, we increase the receptive field of each element in the latent vector. Additionally, since the features of each spatial grid on the three planes are fused and highly encoded, each element does not have a definite position mapping in 3D space, which results in a tractable order for auto-regression. More in-depth discussions can be found in Sec. 4.6 and the supplementary materials.", + "bbox": [ + 496, + 438, + 892, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training Objective. We optimize parameters with reconstruction loss. After getting discrete representation $\\mathbf{z}$ which represents indices of entries in the codebook, we retrieve the corresponding codes with indices, denoted as $\\mathbf{q}_{(\\mathbf{z})}$ . Subsequently, a decoder with symmetric structures of the encoder are designed to decode $\\mathbf{q}_{(\\mathbf{z})}$ back to features of the three planes *. Given sampling points $x\\in \\mathbb{R}^3$ , we query their features by projecting them onto each of the three feature planes and performing bilinear interpolation. Features from three planes are accumulated and fed into an implicit function to predict their occupancy values. Finally, we apply binary cross-entropy loss between the predicted values $y_{o}$ and the ground-truth ones $\\tilde{y_o}$ ,", + "bbox": [ + 496, + 619, + 893, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {o c c} = - \\left(\\tilde {y _ {o}} \\cdot \\log \\left(y _ {o}\\right) + \\left(1 - \\tilde {y _ {o}}\\right) \\cdot \\log \\left(1 - y _ {o}\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 825, + 890, + 842 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further train the codebook, we encourage pulling the", + "bbox": [ + 517, + 851, + 890, + 867 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "*For more details about the first stage architecture, please refer to the Supplementary.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14142", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "distance between features before and after the vector quantization. Thus, the codebook loss is derived as,", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o d e}} = \\beta | | \\operatorname {s g} [ f ] - \\mathbf {q} _ {(\\mathbf {z})} | | _ {2} ^ {2} + | | f - \\operatorname {s g} [ \\mathbf {q} _ {(\\mathbf {z})} ] | | _ {2} ^ {2} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 130, + 468, + 150 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{sg}[\\cdot ]$ denotes the stop-gradient operation [38] and we set $\\beta = 0.4$ by default. In sum, the overall loss for the first stage is $\\mathcal{L}_{rec} = \\mathcal{L}_{occ} + \\mathcal{L}_{code}$", + "bbox": [ + 76, + 157, + 468, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Learning Priors with Vanilla Transformers", + "text_level": 1, + "bbox": [ + 76, + 210, + 444, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Benefiting from a compact composition and tractable order of discrete representation, models in the second stage can absorbly learn the correlation between discrete codes, effectively exploring priors of shape composition. We thus adopt a vanilla decoder-only transformer [11] without any specific-designed module.", + "bbox": [ + 76, + 234, + 468, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For unconditional generation, given discretized indices of latent vector $\\mathbf{z} = \\{\\mathbf{z}_1,\\mathbf{z}_2,\\dots ,\\mathbf{z}_m\\}$ , we feed them into a learnable embedding layer to retrieve features with discrete indices. Then, the transformer with multi-head self-attention mechanism predicts the next possible index by learning the distribution of previous indices, $p(\\mathbf{z}_i\\mid \\mathbf{z}_{< i})$ . This gives the joint distribution of full representation as,", + "bbox": [ + 76, + 325, + 468, + 431 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathbf {z}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {z} _ {i} \\mid \\mathbf {z} _ {< i}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 441, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For conditional generation, users often expect to control the generation process by providing additional conditions. Instead of designing complex modules or training strategies, we simply learn joint distribution given conditions $\\mathbf{c}$ by preponding it to $\\mathbf{z}$ . Equation 5 is thus extended as,", + "bbox": [ + 76, + 489, + 468, + 566 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathbf {z}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {z} _ {i} \\mid \\mathbf {c}, \\mathbf {z} _ {< i}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 574, + 468, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{c}$ denotes a feature vector of given conditions. The simplicity of our model gives the flexibility to learn conditions of any form. Specifically, for 3D conditions such as point clouds, we use our discrete representation learning in Sec. 3.2 to transform them into a vector. As for 2D/1D conditions such as images and classes, we either adopt pretrained models or embedding layers to extract their features. Objective. To train second stage, we minimize negative log-likelihood of Eq. 5 or 6 as $\\mathcal{L}_{nll} = \\mathbb{E}_{x\\sim p(x)}[-\\log p(\\mathbf{z})]$ , where $p(x)$ is the distribution of real data.", + "bbox": [ + 76, + 621, + 468, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference. With both models trained on two stages, we use Eq. 5 or 6 to perform shape generation by progressively sampling the next index with top- $k$ sampling strategy, until all elements in $\\mathbf{z}$ are completed. Then, we feed $\\mathbf{q}_{(\\mathbf{z})}$ into the decoder of the first stage, and query probabilities of occupancy values for all sampled 3D positions (e.g., $128^{3}$ ). The output shapes are extracted with Marching Cubes [18].", + "bbox": [ + 76, + 772, + 468, + 878 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 90, + 633, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section starts with comparing results on unconditional 3D shape generation, showing more faithful and diverse shapes synthesized by our approach in Sec. 4.1. Next, we show extensive studies on four generation tasks, demonstrating the powerful and flexible ability of ImAM (in Sec. $4.2 \\sim 4.5$ ). Lastly, we provide in-depth studies to evaluate the efficacy of our modules and show generalization to real-world data and zero-shot generation (in Sec. 4.6). For all experiments, if necessary, we sample point clouds from output meshes with Poisson Disk Sampling, or reconstruct meshes with our auto-encoder from output points, which is better than Poisson Surface Reconstruction [16]. Please refer to the Supplementary for more details about implementations and qualitative results.", + "bbox": [ + 496, + 114, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Unconditional Shape Generation", + "text_level": 1, + "bbox": [ + 498, + 333, + 787, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data. We consider ShapeNet [4] as our main dataset for generation, following previous literature [14, 8, 36]. We use the same training split and evaluation setup from [14] for fair comparability. Five categories of car, chair, plane, rifle and table are used for testing. As ground-truth, we extract mesh from voxelized models with $256^{3}$ resolution in [13].", + "bbox": [ + 496, + 356, + 890, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compare ImAM with five state-of-the-art models, including GAN-based IM-GAN[8] and GBIF [14], flow-based PointFlow [46], score-based ShapeGF [2] and diffusion-based PVD [51]. We train these methods on the same data split with the official implementation.", + "bbox": [ + 496, + 448, + 890, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics and Settings. The size of the generated set is 5 times the size of the test set, the same as [8, 14]. As suggested by [8], we use the Light Field Descriptor (LFD) [6] as our primary similarity distance metric between two shapes. Coverage (COV) [1], Minimum Matching Distance (MMD) [1] and Edge Count Difference (ECD) [14] are adopted to evaluate the diversity, fidelity and overall quality of synthesized shapes. We also use 1-Nearest Neighbor Accuracy (1-NNA) [46] (with Chamfer Distance) to measure the distribution similarity. The number of sampled points is 2048. Besides, it is well known that COV does not penalize outliers. To rule out the false positive coverage, we introduce CovT, counting as match between a generation and ground truth shape only if LFD between them is smaller than a threshold $t$ . In practice, $t$ could vary across different categories based on the scale and complexity of the shape, and we empirically use mean MMD as the threshold and found it effective in identifying correct matches.", + "bbox": [ + 496, + 523, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results Analysis. Results are reported in Table 1. First, ImAM achieves state-of-the-art performance with regard to ECD and 1-NNA. It significantly demonstrates the superiority of our model over synthesizing high-quality shapes. We notice that the result of Car is not good on the metric of 1-NNA. One possible reason is that ImAM tries to generate meshes of tires and seats inside cars, which may not", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "We reuse the symbol of $\\mathbf{z}$ after embedding for simplicity", + "bbox": [ + 94, + 886, + 401, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14143", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/fbc37d0b927625d443c3e7cf1e888efdf10ec0e4e990c7d179ccd9e4dc500859.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
METRICSMETHODSCATEGORIESAvg
PlaneCarChairRifleTable
ECD ↓IM-GAN [8]92331726583714181108
GBIF [14]9452388354195411858
PointFlow [46]23955318426270835592881
ShapeGF [2]12002547443672114915
PVD [51]66617404126534437453904
Ours236842276531240
1-NNA ↓IM-GAN [8]78.1889.3965.8369.3865.3173.62
GBIF [14]80.2287.1963.9566.9860.9671.86
PointFlow [46]73.6174.7570.1864.7774.8171.62
ShapeGF [2]74.7262.8159.1560.6555.5862.58
PVD [51]81.0957.3762.3677.3274.3170.49
Ours59.9576.5857.3157.2854.7661.17
COV ↑IM-GAN [8]77.0165.3776.3873.2185.7175.53
GBIF [14]80.9678.8580.9577.0085.1380.57
PointFlow [46]65.6464.9757.4948.5271.9561.71
ShapeGF [2]76.6471.8579.4170.6787.5477.22
PVD [51]58.0958.6468.9356.1276.8463.72
Ours79.1173.2580.8174.2684.0178.29
CovT ↑IM-GAN [8]41.0350.6345.6851.6846.5047.10
GBIF [14]32.3852.7639.7750.0043.6843.72
PointFlow [46]35.8547.7628.4834.8130.9835.57
ShapeGF [2]40.1753.6343.6951.0548.5047.41
PVD [51]12.1143.3638.8233.3343.6834.26
Ours45.1256.6449.8255.2748.0350.98
MMD ↓IM-GAN [8]341812902881369125052757
GBIF [14]375413333015386525842910
PointFlow [46]367513933322403829363072
ShapeGF [2]353013072880376224202780
PVD [51]437614323064427426233154
Ours312412132703362823742608
", + "bbox": [ + 80, + 88, + 462, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Results of unconditional generation. Models are trained for each category. The best and second results are highlighted in bold and underlined.", + "bbox": [ + 75, + 488, + 468, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "be very friendly to CD. Second, our model has a clear advantage on both MMD and CovT metrics compared with all competitors, which separately indicates the outstanding fidelity and diversity of our generated shapes. Third, though GBIF achieves relatively good results on COV, it gets worse results on CovT, suggesting that most of the matched samples come from false positive pairs. ImAM, on the contrary, gets second best performance on COV, but higher than GBIF on CovT by about 6 points, showing that our generated shapes enjoy the advantage of high-quality and fewer outliers. Lastly, we visualize shapes with multiple categories in Fig. 4, further supporting the quantitative results and conclusions described above.", + "bbox": [ + 75, + 561, + 468, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Class-guide Generation", + "text_level": 1, + "bbox": [ + 76, + 770, + 294, + 786 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first evaluate the versatility of ImAM on class-guide generation, which requires generating shapes given a category label. It is a basic conditional generation task. We use the same dataset and evaluation metrics as in Sec. 4.1.", + "bbox": [ + 75, + 792, + 468, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We choose two recently-published works as competitors due to the similar motivation. One is two-stage generative model GBIF [14], the other is AR method Au", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e8fe8a8c142680c92100286d72988159abf437d86cf49623eb36f9a3518bf345.jpg", + "image_caption": [ + "Figure 4: Qualitative results of unconditional generation." + ], + "image_footnote": [], + "bbox": [ + 517, + 92, + 867, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "toSDF [23]. We simply modify mask-condition of [14] to class-condition, and additionally add class token to transformers for [23] which is the same as ImAM.", + "bbox": [ + 498, + 459, + 890, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results Analysis. As shown in Tab. 2, ImAM outperforms both competitors across 5 categories by a significant margin, achieving state-of-the-art results on all metrics. Particularly, it gets advantages on the metric of 1-NNA, strongly demonstrating the versatility of ImAM on class-guide generation. Qualitative results of 5 different categories are further illustrated in Fig. 5. As observed, the generated quality of our method is clearly better than GBIF and AutoSDF, while preserving more diversity in types and shapes.", + "bbox": [ + 498, + 505, + 890, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Multi-modal Partial Point Completion", + "text_level": 1, + "bbox": [ + 500, + 650, + 828, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further verify the ability of our model in conditional generation by giving partial point clouds. Here, we advocate the multi-modal completion, since there are many possibilities of the completed shape given the partial shape. It is the essence of generative model, where being faithful to the given partial conditions but using your imagination.", + "bbox": [ + 498, + 674, + 890, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data. We use ShapeNet dataset for testing. Two settings are considered here, (1) perspective completion [49]: randomly sampling a viewpoint and then removing the $25\\% \\sim 75\\%$ furthest points from the viewpoint; (2) bottom-half completion [23]: removing all points from the top half of shapes.", + "bbox": [ + 498, + 765, + 890, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. Four multi-modal completion models are chosen as baselines, including one generative adversarial model cGAN [42], one diffusion model PVD [51], two AR models ShapeFormer [45] and AutoSDF [23].", + "bbox": [ + 498, + 840, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14144", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/eeb26343ca684aedfaaa64be571c19ab92007d9543702683593560e9773458ea.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
METRICSMETHODSCATEGORIESAVG
PlaneCarChairRifleTable
COV ↑GBIF [14]68.7269.6475.9468.9881.7273.00
AutoSDF [23]70.4652.7763.2548.1072.1961.35
Ours81.5871.5883.9875.7485.4879.67
CovT ↑GBIF [14]24.1038.6332.6935.4437.8033.73
AutoSDF [23]30.6640.4931.0034.6036.1034.57
Ours56.4952.7045.0952.7449.3251.27
MMD ↓GBIF [14]473614793220424627633289
AutoSDF [23]370614563249411527443054
Ours319512852871372924302702
ECD ↓GBIF [14]1327275215894348691394
AutoSDF [23]16194256103814434621764
Ours5711889419196285672
1-NNA ↓GBIF [14]91.4792.4375.6183.1270.1982.56
AutoSDF [23]83.3187.7669.3477.4367.2077.01
Ours66.8183.3964.8357.2859.5566.37
", + "bbox": [ + 81, + 88, + 460, + 300 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2: Results of class-guide generation. Models are trained on 13 categories of ShapeNet.", + "bbox": [ + 76, + 309, + 468, + 339 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a61a38d52098f1993df4b8acd904b419a3d866c0ffba072e9e8756a955cb5723.jpg", + "image_caption": [ + "Figure 5: Qualitative results of class-guide generation." + ], + "image_footnote": [], + "bbox": [ + 89, + 359, + 450, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics and Settings. We complete 10 samples for 100 randomly selected shapes of three categories, i.e., chair, sofa and table. Following [42], we use Total Mutual Difference (TMD) to measure the diversity. Minimum Matching Distance [1] (MMD) with Chamfer Distance and Unidirectional Hausdorff Distance (UHD) [32] are adopted to measure the faithfulness of completed shapes.", + "bbox": [ + 75, + 686, + 468, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results Analysis. We first report perspective completion results in Tab. 3. ImAM beats all baselines and achieves state-of-the-art performance. Importantly, we outperform Shapeformer on all classes and metrics, which also utilizes an AR model with transformers to learn shape distribution. On the other hand, we compare with AutoSDF in its bottom-half completion setting. Results from Tab. 4 illus", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7b682522c61d55531ef344649290b3d9f3276eed5646ae3432b47edd0692b928.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 519, + 89, + 879, + 300 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2d11ff8c1db4b6f3173e1b48733a81060ddd20c7fd382c3705d8d556bdc2e243.jpg", + "table_caption": [ + "Figure 6: Qualitative results of partial point completion." + ], + "table_footnote": [], + "table_body": "
METRICSMETHODSCATEGORIESAVG
ChairSofaTable
TMD ↑ (×102)cGAN [42]1.7080.6871.7071.367
PVD [51]1.0980.8110.8390.916
ShapeFormer [45]1.1590.6980.6770.845
Ours2.0421.2211.5381.600
UHD ↓ (×102)cGAN [42]7.8367.0479.4068.096
PVD [51]10.7913.8811.3812.02
ShapeFormer [45]6.8848.6586.6887.410
Ours6.4396.4475.9486.278
MMD ↓ (×103)cGAN [42]1.6651.8131.5961.691
PVD [51]2.3522.0412.1742.189
ShapeFormer [45]1.0551.1001.0661.074
Ours0.9610.8190.8280.869
", + "bbox": [ + 501, + 340, + 887, + 515 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9e1f3da51915ebe2db377ed4211f9c068114a02562ede2839a0bfa2ead794356.jpg", + "table_caption": [ + "Table 3: Results of multi-modal partial point completion. The missing parts vary according to random viewpoints." + ], + "table_footnote": [], + "table_body": "
METRICSMETHODSCATEGORIESAVG
ChairSofaTable
TMD ↑ (×102)AutoSDF [23]2.0461.6093.1162.257
Ours3.6822.67310.305.552
UHD ↓ (×102)AutoSDF [23]6.7939.9508.1228.289
Ours6.9966.59910.878.155
MMD ↓ (×103)AutoSDF [23]1.5011.1542.6001.751
Ours1.4771.1272.9061.837
", + "bbox": [ + 501, + 565, + 888, + 670 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4: Quantitative results of multi-modal partial point completion. The missing parts are always the top half.", + "bbox": [ + 498, + 676, + 890, + 707 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "trates that ImAM outperforms AutoSDF in terms of TMD and MMD. It strongly suggests the flexibility and versatility of our proposed method. Qualitative results in Fig. 6 show the diversity and fidelity of our completed shapes.", + "bbox": [ + 496, + 732, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Image-guide Generation", + "text_level": 1, + "bbox": [ + 500, + 801, + 723, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next, we show the flexibility that ImAM can easily extend to image-guide generation, which is a more challenging task. The flexibility lies in that (1) it is implemented by the easiest way of feature concatenation; (2) the condition form of images is various, which could be 1-D feature", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14145", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/34964c39f9a254de4b73b53d3a4d81b0e6835e71313c09d1f71286aba8ee5968.jpg", + "image_caption": [ + "Figure 7: Visualizations of image-guide shape generation." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 475, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "vector or patch tokens, or 2-D feature maps. For simplicity, we use a pretrained CLIP model (i.e., ViT-B/32) to extract feature vectors of images as conditions. All experiments are conducted on ShapeNet dataset with rendered images.", + "bbox": [ + 76, + 286, + 467, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Baselines. CLIP-Forge [31] is a flow-based model, which is trained with pairs of images and shapes. We take it as our primary baseline for two reasons: (1) it is a generation model instead of reconstruction model, and (2) it originally uses CLIP models to extract image features.", + "bbox": [ + 76, + 347, + 467, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Metrics and Settings. We evaluate models with the test split of 13 categories. For each category, we randomly sample 50 single-view images and then generate 5 shapes for evaluation. As a generation task, TMD is adopted to measure the diversity. We further use MMD with Chamfer Distance and Fréchet Point Cloud distance (FPD) [32] to measure the fidelity compared with the ground truth.", + "bbox": [ + 76, + 424, + 467, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results Analysis. Results are reported in Tab. 5. ImAM wins out in terms of both fidelity and diversity. In particular, we achieve a great advantage on both TMD and FPD, demonstrating the effectiveness of ImAM applied to image-guide generation. It is also successfully echoed by qualitative visualizations in Fig. 7. Our samples are diverse and appear visually faithful to attributes of the object in images.", + "bbox": [ + 76, + 530, + 467, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Text-guide Generation", + "text_level": 1, + "bbox": [ + 76, + 648, + 285, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Encouraged by promising results on image-guide generation, we also turn ImAM to text-to-shape generation. The same pretrained CLIP model is used to extract single embedding for text conditions. Note that we did it on purpose, not using word sequence embedding, but only using a single features vectors in our model to show its efficacy and scalability to the simplest forms of conditions.", + "bbox": [ + 76, + 672, + 467, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Data. To our knowledge, the only existing largest paired text-shape dataset is Text2Shape [7], which provides language descriptions for two objects from ShapeNet, i.e., chair and table. Thereby, we consider it as our main dataset to perform text-guide shape generation.", + "bbox": [ + 76, + 779, + 467, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Baselines. We compare our model with two state-of-the-arts text-to-shape generation model. One is CLIP-Forge [31] under the supervised learning setting, using the same", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/00d1c7d0518e0d275bc5c972daf4ffdd21b80d1a69d84600a7f267985d8d38de.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
METHODTMD (×102) ↑MMD (×103) ↓FPD ↓
AutoSDF [23]2.5231.3832.092
Clip-Forge [31]2.8581.9268.094
Ours4.2741.5901.680
", + "bbox": [ + 506, + 88, + 885, + 140 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5926b96a6425950e319dbc8b9a3bed8fcad5152025336a3e24c17bf05a764342.jpg", + "table_caption": [ + "Table 5: Quantitative results of image-guide generation." + ], + "table_footnote": [], + "table_body": "
METHODTMD (×101) ↑MMD (×103) ↓Acc ↑
ITG [17]N/A2.18729.13
AutoSDF [23]0.3422.16536.95
CLIP-Forge [31]0.4002.13653.68
Ours0.5651.84659.93
", + "bbox": [ + 506, + 180, + 880, + 244 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/594f92b1ffcc0a36aaf437b221d792096aa880560a6f00b35a3c952d0f547ede.jpg", + "table_caption": [ + "(a) Descriptions as text queries" + ], + "table_footnote": [], + "table_body": "
METHODTMD (×10^1) ↑FPD ↓Acc. ↑
AutoSDF [23]0.7525.8441.09
CLIP-Forge [31]0.9614.1455.00
Ours1.2465.3960.87
", + "bbox": [ + 508, + 260, + 879, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(b) Prompts as text queries", + "bbox": [ + 612, + 314, + 772, + 327 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6: Quantitative results of text-guide generation.", + "bbox": [ + 514, + 340, + 867, + 354 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "condition extractor as ours. The other is ITG [17], which adopts BERT to encode texts into sequence embeddings.", + "bbox": [ + 498, + 382, + 890, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Metrics and Settings. All models are trained on the train split of Text2Shape dataset with their official codes. We evaluate our model with two types of text queries: (1) description: the test split of Text2Shape; (2) prompts: customized short phrases provided by [31] containing attributes for chair and table. We additionally use Accuracy (Acc.) [31] to measure the fidelity. The Accuracy is calculated by a pretrained PointNet [27] classifier on ShapeNet.", + "bbox": [ + 498, + 412, + 890, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results Analysis. We report quantitative results of text-guide generation in Tab. 6. ImAM achieves promising results on TMD, MMD and Acc, showing good generalization performance across different conditional generation tasks.", + "bbox": [ + 498, + 534, + 890, + 594 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 604, + 651, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Lastly, we provide in-depth studies to dissect the efficacy of our ImAM framework, and several proposed designs. More discussions are provided in the Supplementary. Design Choices in Discrete Representation Learning. As a key contribution of this paper, we first discuss the efficacy of our improved discrete representation learning. We use 'Vector' to denote our design since we apply vector quantization to latent vector. Similarly, 'Grid' and 'Tri-Plane' refer to baselines applying vector quantization to volumetric grids and the three planes, respectively. Results in Tab. 7 show that 'Grid' gets better IoU performance for shape reconstruction in the first stage, but fails to train transformers in the second stage due to extreme long length of sequence (e.g., $32^{3}$ ). In contrast, our model not only achieves comparable reconstruction results (#0 vs. #2), but also outperforms 'Tri-Plane' by a large margin on generation quality (#1 vs. #2). The latter shows inferior results due to 'ambiguity of order' (see Suppl.) It significantly proves the efficacy", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14146", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9670b3336bc498e8e837c56f0b5ddfae63ba519b7d92516f6181efee997d2da6.jpg", + "image_caption": [ + "Figure 8: Results of real-world image-guide generation. Images are randomly selected from internet." + ], + "image_footnote": [], + "bbox": [ + 94, + 95, + 446, + 281 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/f4dad909d059737be79a5733495fba226513f28d2ff3df3d7cd56949f07e26cd.jpg", + "image_caption": [ + "Figure 9: Results of real-world image-guide generation. Samples are from Pix3D dataset." + ], + "image_footnote": [], + "bbox": [ + 86, + 348, + 464, + 492 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "of our proposed coupling network, improving the plasticity and flexibility of the model. We also explore different design choices in Tab. 7. By gradually increasing feature resolutions or the number of entries in the codebook, we achieve better performance on IoU. This observation is consistent with [48], as the capacity of the discrete representation is affected by these two factors. We do not try larger parameters, as it would significantly increase the computation cost. Image-guide Generation in Real-world. We further investigate the generalizability of our model on real-world images. We use the model trained on ShapeNet as described in Sec. 4.4, and download images from internet as conditions. Figure 8 shows the qualitative results for three categories, i.e., plane, chair and table. Our model sensitively capture major attributes of objects in the image and produce shapes faithful to them (see the first column to the left). Meanwhile, our synthesized samples enjoy the advantage of diversity by partially sticking to the images.", + "bbox": [ + 75, + 565, + 467, + 838 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Figure 9 also show results of our model on Pix3D dataset (trained on ShapeNet, without any finetuning). Compared with other competitors, ImAM is capable of generating high-quality and realistic shapes that highly match the shape", + "bbox": [ + 75, + 839, + 467, + 901 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/0511ae68d408f31568a4a17eb6041682c58a538ce102690902fdb5f0d318d166.jpg", + "image_caption": [ + "Figure 10: Results of zero-shot text-to-shape generation." + ], + "image_footnote": [], + "bbox": [ + 514, + 94, + 875, + 210 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/c3d5a089355fd1c12185605b9af5b5f2dd976ac5d0dbf77239352195cd66ffae.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Num.TYPE#ENTRYRESO.STAGE 1STAGE 2
IoU ↑1-NNA / ECD ↓
0Grid40963288.87×
1Tri-Plane87.8173.67 / 743
2Vector88.0159.95 / 236
340961679.17-
420483286.99
5102486.57
", + "bbox": [ + 501, + 258, + 888, + 359 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 7: Ablation study of auto-encoder design choices. We report 1-NNA/ECD for plane category. 'RESO.' means the resolution of feature map for vector quantization. '×': cannot report due to extreme memory cost. '-': not report. Notably, without the coupling network, our method naturally degenerates into 'Tri-Plane' representation.", + "bbox": [ + 496, + 371, + 890, + 462 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "of objects in real-world images. It significantly highlights the strong generalization ability of our method.", + "bbox": [ + 496, + 478, + 890, + 508 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Zero-shot Text-to-shape Generation. Inspired by CLIP-Forge [31], we utilize the CLIP model to achieve zero-shot text-to-shape generation. At training, we only use the rendered images of 3D shapes. At inference, we substitute image features with text features encoded by the CLIP model. Figure 10 shows our ability of zero-shot generation, where shape attributes are controlled with different prompts.", + "bbox": [ + 496, + 511, + 890, + 617 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 641, + 617, + 657 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We introduce an improved AR model for 3D shape generation. By projecting volumetric grids of encoded input shapes onto three axis-aligned orthogonal feature planes, which are then coupled into a latent vector, we reduce computational costs and create a more tractable order for AR learning. Our compact and tractable representations enable easy switching between unconditional and conditional generation with multi-modal conditioning inputs. Extensive experiments show that our model outperforms previous methods on multiple generation tasks.", + "bbox": [ + 496, + 670, + 890, + 821 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported by China Postdoctoral Science Foundation (2022M710746). Yanwei Fu is with the School of Data Science, Fudan University, and Fudan ISTBI—ZJNU Algorithm Centre for Brain-inspired Intelligence, Zhejiang Normal University, Jinhua, China.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "14147", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5826–5835, 2021. 5, 6, 7" + ], + "bbox": [ + 501, + 92, + 893, + 825 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14149", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Versatile 3D Shape Generation with Improved Auto-regressive Models/4e583ffa-62ea-4806-8a7a-46ee129f849e_model.json b/2023/Learning Versatile 3D Shape Generation with Improved Auto-regressive Models/4e583ffa-62ea-4806-8a7a-46ee129f849e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fd2110c62b18a9aaaf4f1630f29e66887d3ac4cf --- /dev/null +++ b/2023/Learning Versatile 3D Shape Generation with Improved Auto-regressive Models/4e583ffa-62ea-4806-8a7a-46ee129f849e_model.json @@ -0,0 +1,2257 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.131, + 0.888, + 0.155 + ], + "angle": 0, + "content": "Learning Versatile 3D Shape Generation with Improved Auto-regressive Models" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.18, + 0.764, + 0.234 + ], + "angle": 0, + "content": "Simian Luo\\(^{1,\\ast}\\), Xuelin Qian\\(^{1,\\ast}\\), Yanwei Fu\\(^{1,\\dagger}\\), Yinda Zhang\\(^{2}\\), Ying Tai\\(^{3}\\), Zhenyu Zhang\\(^{3}\\), Chengjie Wang\\(^{3}\\), Xiangyang Xue\\(^{1}\\), Fudan University; \\(^{2}\\)Google; \\(^{3}\\)Tencent Youtu Lab" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.237, + 0.774, + 0.27 + ], + "angle": 0, + "content": "{18300180157, xlqian, yanweifu, xyxue}@fudan.edu.cn, yindaz@gmail.com, zhangjesse@foxmail.com, {yingtai,Jasoncjwang}@tencent.com" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.298, + 0.293, + 0.636 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.306, + 0.481, + 0.637 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.303, + 0.679, + 0.637 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.691, + 0.316, + 0.862, + 0.636 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.64, + 0.895, + 0.687 + ], + "angle": 0, + "content": "Figure 1: We propose an improved AR model (ImAM) to learn versatile 3D shape generation. ImAM can either generate diverse and faithful shapes with multiple categories via an unconditional way (one column to the left), or can be adapted for conditional generation by incorporating various conditioning inputs given on the left-top (three columns to the right)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.699, + 0.314, + 0.715 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Auto-Regressive (AR) models have achieved impressive results in 2D image generation by modeling joint distributions in the grid space. While this approach has been extended to the 3D domain for powerful shape generation, it still has two limitations: expensive computations on volumetric grids and ambiguous auto-regressive order along grid dimensions. To overcome these limitations, we propose the Improved Auto-regressive Model (ImAM) for 3D shape generation, which applies discrete representation learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.895, + 0.867 + ], + "angle": 0, + "content": "based on a latent vector instead of volumetric grids. Our approach not only reduces computational costs but also preserves essential geometric details by learning the joint distribution in a more tractable order. Moreover, thanks to the simplicity of our model architecture, we can naturally extend it from unconditional to conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images, and texts. Extensive experiments demonstrate that ImAM can synthesize diverse and faithful shapes of multiple categories, achieving state-of-the-art performance." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.876, + 0.203, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.22, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.876, + 0.22, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14139" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.09, + 0.208, + 0.106 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.116, + 0.468, + 0.386 + ], + "angle": 0, + "content": "3D shape generation has garnered increasing interest in both academia and industry for its extensive applications in robotics [20], autonomous driving [47, 28], augmented reality [35] and virtual reality [34]. Based on whether user prerequisites are provided, shape generation is typically categorized as unconditional or conditional. To be an effective generative model, it is crucial for the synthesized shapes to be both diverse and faithful to the universal cognition of humans or given conditions. These qualities serve as the foundation for other deterministic tasks, such as shape completion, single-view reconstruction, and more. Previous approaches [8, 14, 25] usually utilize an AutoEncoder (AE) to learn latent features by shape reconstruction. Then, a GAN is trained to fit the distributions of the latent features, allowing for the generation of 3D shapes through sampling the latent codes learned in AE. While achieving convincing results, a single embedding for one shape easily encounters the problem of poor scalability and difficulty in training." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.388, + 0.468, + 0.658 + ], + "angle": 0, + "content": "Recently, Auto-Regressive (AR) models have shown remarkable performance in the generation of 2D images [11, 50, 5] and 3D shape [23, 45]. Instead of learning a continuous latent space, these model leverage discrete representation learning to encode each 2D/3D input into grid-based discrete codes. Subsequently, a transformer-based network is employed to jointly model the distribution of all codes, which essentially reflects the underlying prior of objects, facilitating high-quality generation and tractable training. However, applying AR models to 3D still suffers from two limitations. First, as the number of discrete codes increases from squared to cubed, the computational burden of the transformer grows dramatically, making it difficult to converge. Second, discrete codes in the grid space are highly coupled. It is ambiguous to simply flatten them for autoregression (e.g., a top-down row-major order). This may lead to poor quality or even collapse of generated shapes (see Sec. 3.1 and the Supplementary for more details)." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.66, + 0.468, + 0.839 + ], + "angle": 0, + "content": "In this paper, we propose an improved auto-regressive model (ImAM), to enhance the efficient learning of 3D shape generation. Our key idea is to apply discrete representation learning in a one-dimensional space instead of 3D volumetric space. Specifically, we first project volumetric grids encoded from 3D shapes onto three axis-aligned orthogonal planes. This process significantly reduces the computational costs from cubed to squared while maintaining the essential information about the input geometry. Next, we present a coupling network to further encode three planes into a compact and tractable latent space, on which discrete representation learning is performed." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.84, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Our ImAM is straightforward and effective, simply tackling the aforementioned limitations by two projections. Thus, a vanilla decoder-only transformer can be attached to model the joint distributions of codes from the latent spaces." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.197 + ], + "angle": 0, + "content": "Furthermore, the simplicity of the transformer structure allows us to switch freely between unconditional and conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images and texts. Figure 1 showcases the ability of our ImAM to generate diverse and accurate shapes across multiple categories, both with and without the given condition on the top-left corner." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.199, + 0.89, + 0.423 + ], + "angle": 0, + "content": "In summary, the contributions of this paper are listed as follows. (1) We propose an improved AR Model (ImAM) for 3D shape generation. By applying discrete representation learning in a latent vector instead of volumetric grids, our ImAM enjoys the advantages of lightweight and flexibility. (2) Our proposed ImAM model provides a more unified framework for switching between unconditional and conditional generation for a variety of conditioning inputs, including point clouds, categories, images, and texts. (3) Extensive experiments are conducted on four tasks to demonstrate that our ImAM can generate more faithful and diverse shapes, achieving state-of-the-art results for unconditional and conditional shape generation. Overall, our contributions advance the field of 3D shape generation, providing a powerful tool for researchers and practitioners alike." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.438, + 0.636, + 0.453 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.464, + 0.89, + 0.9 + ], + "angle": 0, + "content": "3D shape generative models. As an extremely challenging task, we review the most previous efforts by using voxel, point clouds, and implicit representations. (1) Standard voxel grids can be easily processed by 3D convolution for learning-based 3D task [19, 44, 10, 41]. However, restricted by its cubic space complexity, voxel representation can not scale to a high resolution, usually limited in \\(64^{3}\\). Even with efficient data structures like octrees or multi-scale representation [40, 13, 30], such representations still have some limitations in quality. (2) Point clouds extracted from shape surfaces is an alternative 3D representation [12, 43, 27], which is efficient in terms of memory and does not suffer from the restriction of resolution compared with voxel representations. However, these representations can not represent topological relations in 3D space and are also nontrivial to recover shape surfaces from point cloud representation. (3) Recently, implicit representations have gained attention for simplicity in representing 3D shapes [25, 21, 22, 33]. By predicting the signed distance [25, 33] or occupancy label [21, 26] of a given point, and then through Marching cubes [18] methods, the surface can be easily recovered. Follow-up works [21, 25, 8, 26, 15] focus on the design of implicit function representation with global or local shape priors. To sum up, different 3D representations lead to various shape generative models. There are various good previous works such as 3DGAN [41], PC-GAN [1], IM-GAN [8], and GBIF [14]. However, most current generative methods are task-specific. And it is difficult to be directly applied to different generative tasks (e.g., shape completion). Fundamentally," + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14140" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.464, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.321, + 0.471, + 0.368 + ], + "angle": 0, + "content": "Figure 2: Illustration of auto-regressive generation for grid-based representation. Here, we show three different flattening orders as examples. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.47, + 0.484 + ], + "angle": 0, + "content": "they rely on GANs for the generation step, suffering from the known drawbacks such as mode collapse and training instability. In contrast, we propose an improved AR model for 3D shape generation that can synthesize high-quality and diverse shapes while being easily generalized to other multi-modal conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Autoregressive models. AR models are probabilistic generative approaches that have tractable probability density. Using the probability chain rule, the likelihood of a given sample (usually high dimensional data) can be factorized into a series of product of conditional probability. In contrast, GANs do not have such a tractable probability density. Recently, AR models achieve remarkable progress in 2D image generation [11, 37, 29], to a less extent 3D tasks [36, 9, 24]. Most of 3D AR models are struggling with generating high-quality shapes due to the challenges of representation learning with more points or faces. Particularly, we notice two recent works [45, 23] that share similar insights of utilizing AR models for 3D tasks. [45] introduces a sparse representation to only quantize non-empty grids in 3D space, but still follows a monotonic row-major order. [23] presents a non-sequential design to break the orders, but performs on all volumetric grids. However, both of them address only one of the above limitations, and burden the structure design and training of transformer. In contrast, our ImAM applies discrete representation learning in a latent vector instead of volumetric grids. Such a representation offers plenty of advantages, including shorter length of discrete codes, tractable orders from auto-regression, fast convergence, and also preserving essential 3D information. Moreover, benefiting from the simplicity of transformers, we can freely switch from unconditional generation to conditional generation by concatenating various conditions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.636, + 0.108 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.222 + ], + "angle": 0, + "content": "Figure 3 illustrates the schematic of our proposed framework for 3D shape generation, which consists of a two-stage training procedure. It first represents the input as a composition of learned discrete codes (in Sec. 3.2), then utilizes a transformer model to learn their interrelations (in Sec. 3.3). Before beginning, we provide some symbol definitions and necessary preliminaries in Sec. 3.1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.232, + 0.63, + 0.248 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.255, + 0.895, + 0.512 + ], + "angle": 0, + "content": "Ambiguity. Formally, 'ambiguity' appears in the order of a series of conditional probabilities, which affects the difficulty of likelihood learning, leading to approximation error of the joint distribution. Critically, auto-regressive models require sequential outputs, autoregressively predicting the next code conditioned on all previous ones. Thereby, the order of the flattened sequence determines the order of conditional probabilities. Although some methods (e.g. position embedding [39]) can be aware of positions of codes, it cannot eliminate approximation error caused by the condition order. Notably, this 'ambiguity' phenomenon is also discussed in [11] (in Fig. 47), where the loss curves in Fig. 47 highlight the differences in difficulty for likelihood learning across various orders. Figure 2 illustrates how the flattening order affects the way of autoregressive generation. For grid-based representation, it is ambiguous if the flattening order along axes is \\( y - x - z \\), \\( x - z - y \\) or other combinations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.895, + 0.704 + ], + "angle": 0, + "content": "Discrete Representation. Given input point clouds \\( P \\in \\mathbb{R}^{n \\times 3} \\) where \\( n \\) means the number of points, an encoder is adopted to extract features for each point cloud and then perform voxelization to get features of regular volumetric grids \\( f^v \\in \\mathbb{R}^{r \\times r \\times r \\times c} \\), where \\( r \\) denote the resolution of voxels and \\( c \\) is the feature dimension. To learn discrete representation for each 3D shape, a codebook \\( \\mathbf{q} \\in \\mathbb{R}^{m \\times c} \\) is thus introduced whose entry is a learned code describing a particular type of local-part shape in a grid. Formally, for each grid \\( \\left\\{f_{(h,l,w)}^v\\right\\}_{h,l,w=1}^r \\), vector quantization \\( \\mathcal{Q}(\\cdot) \\) is performed by replacing it with the closest entry in codebooks [11]," + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.715, + 0.892, + 0.739 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} ^ {v} = \\mathcal {Q} \\left(f ^ {v}\\right) := \\arg \\min _ {\\mathbf {e} _ {i} \\in \\mathbf {q}} \\left| \\left| f _ {(h, l, w)} ^ {v} - \\mathbf {e} _ {i} \\right| \\right| \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathbf{e}_i\\in \\mathbf{q}\\) represents the \\(i\\) -th entry in the codebook. Thus, learning the correlations between entries in the second stage can explore the underlying priors for shape generation. However, autoregressive generation [11, 45] requires sequential outputs, facing two limitations. First, the resolution of \\(\\mathbf{z}^v\\) matters the quality of synthesized shapes. If \\(r\\) is too small, it lacks the capacity to represent intricate and detailed geometries, while a large value of \\(r\\) can learn a specific code for each local gird, it inevitably increase the computational complexity since the number of required codes" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14141" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.092, + 0.878, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.29, + 0.896, + 0.37 + ], + "angle": 0, + "content": "Figure 3: Overview of our ImAM. Given an arbitrary 3D shape, we first project encoded volumetric grids into the three axis-aligned planes, and then use a coupling network to further project them into a latent vector. Vector quantization is thus performed on it for discrete representation. Taking advantages of such a compact representation with tractable orders, vanilla transformers are adopted to auto-repressively learn shape distributions. Furthermore, we can freely switch from unconditional generation to conditional generation by concatenating various conditions, such as point clouds, categories and images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.471, + 0.456 + ], + "angle": 0, + "content": "explodes as \\( r \\) grows. Second, the order of \\( \\mathbf{z}^v \\) affects the generation quality. Each grid is highly coupled with neighbors, simply flattening (say, along x-y-z axes) may cause 'ambiguity', leading to sub-optimal generation quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.463, + 0.453, + 0.48 + ], + "angle": 0, + "content": "3.2. Improved Discrete Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.47, + 0.713 + ], + "angle": 0, + "content": "One possible solution to solve the first limitation is applying vector quantization in spatial grids instead of volumetric grids inspired by [3]. Specifically, after obtaining point cloud features \\( f^p \\in \\mathbb{R}^{n \\times c} \\), we first project points onto three axis-aligned orthogonal planes. Features of points falling into the same plane grid are aggregated via summation, resulting in three feature maps for the three planes \\( \\{f^{xy}, f^{yz}, f^{xz}\\} \\in \\mathbb{R}^{l \\times w \\times c} \\). Next, the vector quantization is applied to the three planes separately. The primary advantage of tri-planar representation is efficient and compact. It can dramatically reduce the number of grids from \\( \\mathcal{O}(r^3) \\) to \\( \\mathcal{O}(r^2) \\) while preserving essential 3D information. However, it still suffers from the ambiguity of order, or worse, since it involves the flattening order of three planes and the order of entries of each plane." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.47, + 0.805 + ], + "angle": 0, + "content": "To this end, we further introduce a projection by learning a higher latent space for features of the three planes. This is simply achieved by first concatenating three planes with arbitrary order and then feeding them into a coupling network. Finally, the output is flattened as a projected latent vector, formulated as," + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.817, + 0.47, + 0.836 + ], + "angle": 0, + "content": "\\[\nf = \\tau \\left(\\mathcal {G} \\left([ f ^ {x y}; f ^ {y z}; f ^ {x z} ]; \\theta)\\right) \\in \\mathbb {R} ^ {m \\times d} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "where \\([\\cdot ;\\cdot ]\\) denotes the concatenation operation; \\(\\mathcal{G}(\\cdot ;\\theta)\\) is a series of convolution layers with parameters \\(\\theta\\) . \\(\\tau (\\cdot)\\) means the operation of flatten with row-major order; \\(m\\) and \\(d\\) indicate the length of latent vector and feature dimension. By" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.892, + 0.438 + ], + "angle": 0, + "content": "applying discrete representation learning in the latent vector, we can describe each 3D shape with \\(\\mathbf{z} = \\mathcal{Q}(f)\\), where \\(\\mathcal{Q}(\\cdot)\\) represents vector quantization in Eq. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.893, + 0.62 + ], + "angle": 0, + "content": "Remark. Different from existing works [23, 45] that rely on structure design and training strategies in second stage to address the problem of ambiguous order, we tackle it by learning the coupling relationship of spatial grids in the first stage with the help of the second projection. By stacking convolution layers, we increase the receptive field of each element in the latent vector. Additionally, since the features of each spatial grid on the three planes are fused and highly encoded, each element does not have a definite position mapping in 3D space, which results in a tractable order for auto-regression. More in-depth discussions can be found in Sec. 4.6 and the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.895, + 0.817 + ], + "angle": 0, + "content": "Training Objective. We optimize parameters with reconstruction loss. After getting discrete representation \\(\\mathbf{z}\\) which represents indices of entries in the codebook, we retrieve the corresponding codes with indices, denoted as \\(\\mathbf{q}_{(\\mathbf{z})}\\). Subsequently, a decoder with symmetric structures of the encoder are designed to decode \\(\\mathbf{q}_{(\\mathbf{z})}\\) back to features of the three planes *. Given sampling points \\(x\\in \\mathbb{R}^3\\), we query their features by projecting them onto each of the three feature planes and performing bilinear interpolation. Features from three planes are accumulated and fed into an implicit function to predict their occupancy values. Finally, we apply binary cross-entropy loss between the predicted values \\(y_{o}\\) and the ground-truth ones \\(\\tilde{y_o}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.826, + 0.892, + 0.843 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {o c c} = - \\left(\\tilde {y _ {o}} \\cdot \\log \\left(y _ {o}\\right) + \\left(1 - \\tilde {y _ {o}}\\right) \\cdot \\log \\left(1 - y _ {o}\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.852, + 0.892, + 0.868 + ], + "angle": 0, + "content": "To further train the codebook, we encourage pulling the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "*For more details about the first stage architecture, please refer to the Supplementary." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14142" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "distance between features before and after the vector quantization. Thus, the codebook loss is derived as," + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.131, + 0.47, + 0.151 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o d e}} = \\beta | | \\operatorname {s g} [ f ] - \\mathbf {q} _ {(\\mathbf {z})} | | _ {2} ^ {2} + | | f - \\operatorname {s g} [ \\mathbf {q} _ {(\\mathbf {z})} ] | | _ {2} ^ {2} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.158, + 0.47, + 0.205 + ], + "angle": 0, + "content": "where \\(\\mathrm{sg}[\\cdot ]\\) denotes the stop-gradient operation [38] and we set \\(\\beta = 0.4\\) by default. In sum, the overall loss for the first stage is \\(\\mathcal{L}_{rec} = \\mathcal{L}_{occ} + \\mathcal{L}_{code}\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.212, + 0.445, + 0.229 + ], + "angle": 0, + "content": "3.3. Learning Priors with Vanilla Transformers" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.236, + 0.469, + 0.326 + ], + "angle": 0, + "content": "Benefiting from a compact composition and tractable order of discrete representation, models in the second stage can absorbly learn the correlation between discrete codes, effectively exploring priors of shape composition. We thus adopt a vanilla decoder-only transformer [11] without any specific-designed module." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.327, + 0.469, + 0.433 + ], + "angle": 0, + "content": "For unconditional generation, given discretized indices of latent vector \\(\\mathbf{z} = \\{\\mathbf{z}_1,\\mathbf{z}_2,\\dots ,\\mathbf{z}_m\\}\\), we feed them into a learnable embedding layer to retrieve features with discrete indices. Then, the transformer with multi-head self-attention mechanism predicts the next possible index by learning the distribution of previous indices, \\(p(\\mathbf{z}_i\\mid \\mathbf{z}_{< i})\\). This gives the joint distribution of full representation as," + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.442, + 0.47, + 0.481 + ], + "angle": 0, + "content": "\\[\np (\\mathbf {z}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {z} _ {i} \\mid \\mathbf {z} _ {< i}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.49, + 0.47, + 0.567 + ], + "angle": 0, + "content": "For conditional generation, users often expect to control the generation process by providing additional conditions. Instead of designing complex modules or training strategies, we simply learn joint distribution given conditions \\(\\mathbf{c}\\) by preponding it to \\(\\mathbf{z}\\). Equation 5 is thus extended as," + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.575, + 0.47, + 0.614 + ], + "angle": 0, + "content": "\\[\np (\\mathbf {z}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {z} _ {i} \\mid \\mathbf {c}, \\mathbf {z} _ {< i}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.622, + 0.469, + 0.773 + ], + "angle": 0, + "content": "where \\(\\mathbf{c}\\) denotes a feature vector of given conditions. The simplicity of our model gives the flexibility to learn conditions of any form. Specifically, for 3D conditions such as point clouds, we use our discrete representation learning in Sec. 3.2 to transform them into a vector. As for 2D/1D conditions such as images and classes, we either adopt pretrained models or embedding layers to extract their features. Objective. To train second stage, we minimize negative log-likelihood of Eq. 5 or 6 as \\(\\mathcal{L}_{nll} = \\mathbb{E}_{x\\sim p(x)}[-\\log p(\\mathbf{z})]\\), where \\(p(x)\\) is the distribution of real data." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.773, + 0.469, + 0.88 + ], + "angle": 0, + "content": "Inference. With both models trained on two stages, we use Eq. 5 or 6 to perform shape generation by progressively sampling the next index with top-\\(k\\) sampling strategy, until all elements in \\(\\mathbf{z}\\) are completed. Then, we feed \\(\\mathbf{q}_{(\\mathbf{z})}\\) into the decoder of the first stage, and query probabilities of occupancy values for all sampled 3D positions (e.g., \\(128^{3}\\)). The output shapes are extracted with Marching Cubes [18]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.634, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.327 + ], + "angle": 0, + "content": "This section starts with comparing results on unconditional 3D shape generation, showing more faithful and diverse shapes synthesized by our approach in Sec. 4.1. Next, we show extensive studies on four generation tasks, demonstrating the powerful and flexible ability of ImAM (in Sec. \\(4.2 \\sim 4.5\\)). Lastly, we provide in-depth studies to evaluate the efficacy of our modules and show generalization to real-world data and zero-shot generation (in Sec. 4.6). For all experiments, if necessary, we sample point clouds from output meshes with Poisson Disk Sampling, or reconstruct meshes with our auto-encoder from output points, which is better than Poisson Surface Reconstruction [16]. Please refer to the Supplementary for more details about implementations and qualitative results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.334, + 0.788, + 0.351 + ], + "angle": 0, + "content": "4.1. Unconditional Shape Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.448 + ], + "angle": 0, + "content": "Data. We consider ShapeNet [4] as our main dataset for generation, following previous literature [14, 8, 36]. We use the same training split and evaluation setup from [14] for fair comparability. Five categories of car, chair, plane, rifle and table are used for testing. As ground-truth, we extract mesh from voxelized models with \\(256^{3}\\) resolution in [13]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.524 + ], + "angle": 0, + "content": "Baselines. We compare ImAM with five state-of-the-art models, including GAN-based IM-GAN[8] and GBIF [14], flow-based PointFlow [46], score-based ShapeGF [2] and diffusion-based PVD [51]. We train these methods on the same data split with the official implementation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Metrics and Settings. The size of the generated set is 5 times the size of the test set, the same as [8, 14]. As suggested by [8], we use the Light Field Descriptor (LFD) [6] as our primary similarity distance metric between two shapes. Coverage (COV) [1], Minimum Matching Distance (MMD) [1] and Edge Count Difference (ECD) [14] are adopted to evaluate the diversity, fidelity and overall quality of synthesized shapes. We also use 1-Nearest Neighbor Accuracy (1-NNA) [46] (with Chamfer Distance) to measure the distribution similarity. The number of sampled points is 2048. Besides, it is well known that COV does not penalize outliers. To rule out the false positive coverage, we introduce CovT, counting as match between a generation and ground truth shape only if LFD between them is smaller than a threshold \\( t \\). In practice, \\( t \\) could vary across different categories based on the scale and complexity of the shape, and we empirically use mean MMD as the threshold and found it effective in identifying correct matches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results Analysis. Results are reported in Table 1. First, ImAM achieves state-of-the-art performance with regard to ECD and 1-NNA. It significantly demonstrates the superiority of our model over synthesizing high-quality shapes. We notice that the result of Car is not good on the metric of 1-NNA. One possible reason is that ImAM tries to generate meshes of tires and seats inside cars, which may not" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.402, + 0.901 + ], + "angle": 0, + "content": "We reuse the symbol of \\(\\mathbf{z}\\) after embedding for simplicity" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14143" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.464, + 0.48 + ], + "angle": 0, + "content": "
METRICSMETHODSCATEGORIESAvg
PlaneCarChairRifleTable
ECD ↓IM-GAN [8]92331726583714181108
GBIF [14]9452388354195411858
PointFlow [46]23955318426270835592881
ShapeGF [2]12002547443672114915
PVD [51]66617404126534437453904
Ours236842276531240
1-NNA ↓IM-GAN [8]78.1889.3965.8369.3865.3173.62
GBIF [14]80.2287.1963.9566.9860.9671.86
PointFlow [46]73.6174.7570.1864.7774.8171.62
ShapeGF [2]74.7262.8159.1560.6555.5862.58
PVD [51]81.0957.3762.3677.3274.3170.49
Ours59.9576.5857.3157.2854.7661.17
COV ↑IM-GAN [8]77.0165.3776.3873.2185.7175.53
GBIF [14]80.9678.8580.9577.0085.1380.57
PointFlow [46]65.6464.9757.4948.5271.9561.71
ShapeGF [2]76.6471.8579.4170.6787.5477.22
PVD [51]58.0958.6468.9356.1276.8463.72
Ours79.1173.2580.8174.2684.0178.29
CovT ↑IM-GAN [8]41.0350.6345.6851.6846.5047.10
GBIF [14]32.3852.7639.7750.0043.6843.72
PointFlow [46]35.8547.7628.4834.8130.9835.57
ShapeGF [2]40.1753.6343.6951.0548.5047.41
PVD [51]12.1143.3638.8233.3343.6834.26
Ours45.1256.6449.8255.2748.0350.98
MMD ↓IM-GAN [8]341812902881369125052757
GBIF [14]375413333015386525842910
PointFlow [46]367513933322403829363072
ShapeGF [2]353013072880376224202780
PVD [51]437614323064427426233154
Ours312412132703362823742608
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.489, + 0.47, + 0.534 + ], + "angle": 0, + "content": "Table 1: Results of unconditional generation. Models are trained for each category. The best and second results are highlighted in bold and underlined." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.47, + 0.759 + ], + "angle": 0, + "content": "be very friendly to CD. Second, our model has a clear advantage on both MMD and CovT metrics compared with all competitors, which separately indicates the outstanding fidelity and diversity of our generated shapes. Third, though GBIF achieves relatively good results on COV, it gets worse results on CovT, suggesting that most of the matched samples come from false positive pairs. ImAM, on the contrary, gets second best performance on COV, but higher than GBIF on CovT by about 6 points, showing that our generated shapes enjoy the advantage of high-quality and fewer outliers. Lastly, we visualize shapes with multiple categories in Fig. 4, further supporting the quantitative results and conclusions described above." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.295, + 0.787 + ], + "angle": 0, + "content": "4.2. Class-guide Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.469, + 0.854 + ], + "angle": 0, + "content": "We first evaluate the versatility of ImAM on class-guide generation, which requires generating shapes given a category label. It is a basic conditional generation task. We use the same dataset and evaluation metrics as in Sec. 4.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Baselines. We choose two recently-published works as competitors due to the similar motivation. One is two-stage generative model GBIF [14], the other is AR method Au" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.093, + 0.868, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.419, + 0.88, + 0.433 + ], + "angle": 0, + "content": "Figure 4: Qualitative results of unconditional generation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.46, + 0.892, + 0.505 + ], + "angle": 0, + "content": "toSDF [23]. We simply modify mask-condition of [14] to class-condition, and additionally add class token to transformers for [23] which is the same as ImAM." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.506, + 0.892, + 0.642 + ], + "angle": 0, + "content": "Results Analysis. As shown in Tab. 2, ImAM outperforms both competitors across 5 categories by a significant margin, achieving state-of-the-art results on all metrics. Particularly, it gets advantages on the metric of 1-NNA, strongly demonstrating the versatility of ImAM on class-guide generation. Qualitative results of 5 different categories are further illustrated in Fig. 5. As observed, the generated quality of our method is clearly better than GBIF and AutoSDF, while preserving more diversity in types and shapes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.83, + 0.668 + ], + "angle": 0, + "content": "4.3. Multi-modal Partial Point Completion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.892, + 0.765 + ], + "angle": 0, + "content": "We further verify the ability of our model in conditional generation by giving partial point clouds. Here, we advocate the multi-modal completion, since there are many possibilities of the completed shape given the partial shape. It is the essence of generative model, where being faithful to the given partial conditions but using your imagination." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.766, + 0.892, + 0.841 + ], + "angle": 0, + "content": "Data. We use ShapeNet dataset for testing. Two settings are considered here, (1) perspective completion [49]: randomly sampling a viewpoint and then removing the \\(25\\% \\sim 75\\%\\) furthest points from the viewpoint; (2) bottom-half completion [23]: removing all points from the top half of shapes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Baselines. Four multi-modal completion models are chosen as baselines, including one generative adversarial model cGAN [42], one diffusion model PVD [51], two AR models ShapeFormer [45] and AutoSDF [23]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14144" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.462, + 0.301 + ], + "angle": 0, + "content": "
METRICSMETHODSCATEGORIESAVG
PlaneCarChairRifleTable
COV ↑GBIF [14]68.7269.6475.9468.9881.7273.00
AutoSDF [23]70.4652.7763.2548.1072.1961.35
Ours81.5871.5883.9875.7485.4879.67
CovT ↑GBIF [14]24.1038.6332.6935.4437.8033.73
AutoSDF [23]30.6640.4931.0034.6036.1034.57
Ours56.4952.7045.0952.7449.3251.27
MMD ↓GBIF [14]473614793220424627633289
AutoSDF [23]370614563249411527443054
Ours319512852871372924302702
ECD ↓GBIF [14]1327275215894348691394
AutoSDF [23]16194256103814434621764
Ours5711889419196285672
1-NNA ↓GBIF [14]91.4792.4375.6183.1270.1982.56
AutoSDF [23]83.3187.7669.3477.4367.2077.01
Ours66.8183.3964.8357.2859.5566.37
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.31, + 0.47, + 0.34 + ], + "angle": 0, + "content": "Table 2: Results of class-guide generation. Models are trained on 13 categories of ShapeNet." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.361, + 0.451, + 0.626 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.64, + 0.45, + 0.655 + ], + "angle": 0, + "content": "Figure 5: Qualitative results of class-guide generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Metrics and Settings. We complete 10 samples for 100 randomly selected shapes of three categories, i.e., chair, sofa and table. Following [42], we use Total Mutual Difference (TMD) to measure the diversity. Minimum Matching Distance [1] (MMD) with Chamfer Distance and Unidirectional Hausdorff Distance (UHD) [32] are adopted to measure the faithfulness of completed shapes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Results Analysis. We first report perspective completion results in Tab. 3. ImAM beats all baselines and achieves state-of-the-art performance. Importantly, we outperform Shapeformer on all classes and metrics, which also utilizes an AR model with transformers to learn shape distribution. On the other hand, we compare with AutoSDF in its bottom-half completion setting. Results from Tab. 4 illus" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.09, + 0.88, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.508, + 0.312, + 0.878, + 0.329 + ], + "angle": 0, + "content": "Figure 6: Qualitative results of partial point completion." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.341, + 0.888, + 0.516 + ], + "angle": 0, + "content": "
METRICSMETHODSCATEGORIESAVG
ChairSofaTable
TMD ↑ (×102)cGAN [42]1.7080.6871.7071.367
PVD [51]1.0980.8110.8390.916
ShapeFormer [45]1.1590.6980.6770.845
Ours2.0421.2211.5381.600
UHD ↓ (×102)cGAN [42]7.8367.0479.4068.096
PVD [51]10.7913.8811.3812.02
ShapeFormer [45]6.8848.6586.6887.410
Ours6.4396.4475.9486.278
MMD ↓ (×103)cGAN [42]1.6651.8131.5961.691
PVD [51]2.3522.0412.1742.189
ShapeFormer [45]1.0551.1001.0661.074
Ours0.9610.8190.8280.869
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.522, + 0.892, + 0.554 + ], + "angle": 0, + "content": "Table 3: Results of multi-modal partial point completion. The missing parts vary according to random viewpoints." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.566, + 0.89, + 0.671 + ], + "angle": 0, + "content": "
METRICSMETHODSCATEGORIESAVG
ChairSofaTable
TMD ↑ (×102)AutoSDF [23]2.0461.6093.1162.257
Ours3.6822.67310.305.552
UHD ↓ (×102)AutoSDF [23]6.7939.9508.1228.289
Ours6.9966.59910.878.155
MMD ↓ (×103)AutoSDF [23]1.5011.1542.6001.751
Ours1.4771.1272.9061.837
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.677, + 0.892, + 0.708 + ], + "angle": 0, + "content": "Table 4: Quantitative results of multi-modal partial point completion. The missing parts are always the top half." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.794 + ], + "angle": 0, + "content": "trates that ImAM outperforms AutoSDF in terms of TMD and MMD. It strongly suggests the flexibility and versatility of our proposed method. Qualitative results in Fig. 6 show the diversity and fidelity of our completed shapes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.724, + 0.818 + ], + "angle": 0, + "content": "4.4. Image-guide Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Next, we show the flexibility that ImAM can easily extend to image-guide generation, which is a more challenging task. The flexibility lies in that (1) it is implemented by the easiest way of feature concatenation; (2) the condition form of images is various, which could be 1-D feature" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14145" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.476, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.252, + 0.462, + 0.268 + ], + "angle": 0, + "content": "Figure 7: Visualizations of image-guide shape generation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.287, + 0.468, + 0.348 + ], + "angle": 0, + "content": "vector or patch tokens, or 2-D feature maps. For simplicity, we use a pretrained CLIP model (i.e., ViT-B/32) to extract feature vectors of images as conditions. All experiments are conducted on ShapeNet dataset with rendered images." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.348, + 0.468, + 0.424 + ], + "angle": 0, + "content": "Baselines. CLIP-Forge [31] is a flow-based model, which is trained with pairs of images and shapes. We take it as our primary baseline for two reasons: (1) it is a generation model instead of reconstruction model, and (2) it originally uses CLIP models to extract image features." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.425, + 0.468, + 0.53 + ], + "angle": 0, + "content": "Metrics and Settings. We evaluate models with the test split of 13 categories. For each category, we randomly sample 50 single-view images and then generate 5 shapes for evaluation. As a generation task, TMD is adopted to measure the diversity. We further use MMD with Chamfer Distance and Fréchet Point Cloud distance (FPD) [32] to measure the fidelity compared with the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.531, + 0.468, + 0.637 + ], + "angle": 0, + "content": "Results Analysis. Results are reported in Tab. 5. ImAM wins out in terms of both fidelity and diversity. In particular, we achieve a great advantage on both TMD and FPD, demonstrating the effectiveness of ImAM applied to image-guide generation. It is also successfully echoed by qualitative visualizations in Fig. 7. Our samples are diverse and appear visually faithful to attributes of the object in images." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.649, + 0.286, + 0.665 + ], + "angle": 0, + "content": "4.5. Text-guide Generation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.673, + 0.468, + 0.778 + ], + "angle": 0, + "content": "Encouraged by promising results on image-guide generation, we also turn ImAM to text-to-shape generation. The same pretrained CLIP model is used to extract single embedding for text conditions. Note that we did it on purpose, not using word sequence embedding, but only using a single features vectors in our model to show its efficacy and scalability to the simplest forms of conditions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.78, + 0.468, + 0.855 + ], + "angle": 0, + "content": "Data. To our knowledge, the only existing largest paired text-shape dataset is Text2Shape [7], which provides language descriptions for two objects from ShapeNet, i.e., chair and table. Thereby, we consider it as our main dataset to perform text-guide shape generation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Baselines. We compare our model with two state-of-the-arts text-to-shape generation model. One is CLIP-Forge [31] under the supervised learning setting, using the same" + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.089, + 0.886, + 0.141 + ], + "angle": 0, + "content": "
METHODTMD (×102) ↑MMD (×103) ↓FPD ↓
AutoSDF [23]2.5231.3832.092
Clip-Forge [31]2.8581.9268.094
Ours4.2741.5901.680
" + }, + { + "type": "table_caption", + "bbox": [ + 0.509, + 0.152, + 0.877, + 0.167 + ], + "angle": 0, + "content": "Table 5: Quantitative results of image-guide generation." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.181, + 0.882, + 0.245 + ], + "angle": 0, + "content": "
METHODTMD (×101) ↑MMD (×103) ↓Acc ↑
ITG [17]N/A2.18729.13
AutoSDF [23]0.3422.16536.95
CLIP-Forge [31]0.4002.13653.68
Ours0.5651.84659.93
" + }, + { + "type": "table_caption", + "bbox": [ + 0.603, + 0.248, + 0.787, + 0.26 + ], + "angle": 0, + "content": "(a) Descriptions as text queries" + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.261, + 0.88, + 0.313 + ], + "angle": 0, + "content": "
METHODTMD (×10^1) ↑FPD ↓Acc. ↑
AutoSDF [23]0.7525.8441.09
CLIP-Forge [31]0.9614.1455.00
Ours1.2465.3960.87
" + }, + { + "type": "table_caption", + "bbox": [ + 0.614, + 0.315, + 0.774, + 0.328 + ], + "angle": 0, + "content": "(b) Prompts as text queries" + }, + { + "type": "table_caption", + "bbox": [ + 0.516, + 0.341, + 0.869, + 0.356 + ], + "angle": 0, + "content": "Table 6: Quantitative results of text-guide generation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.383, + 0.892, + 0.414 + ], + "angle": 0, + "content": "condition extractor as ours. The other is ITG [17], which adopts BERT to encode texts into sequence embeddings." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.414, + 0.892, + 0.534 + ], + "angle": 0, + "content": "Metrics and Settings. All models are trained on the train split of Text2Shape dataset with their official codes. We evaluate our model with two types of text queries: (1) description: the test split of Text2Shape; (2) prompts: customized short phrases provided by [31] containing attributes for chair and table. We additionally use Accuracy (Acc.) [31] to measure the fidelity. The Accuracy is calculated by a pretrained PointNet [27] classifier on ShapeNet." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.535, + 0.892, + 0.595 + ], + "angle": 0, + "content": "Results Analysis. We report quantitative results of text-guide generation in Tab. 6. ImAM achieves promising results on TMD, MMD and Acc, showing good generalization performance across different conditional generation tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.653, + 0.621 + ], + "angle": 0, + "content": "4.6. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Lastly, we provide in-depth studies to dissect the efficacy of our ImAM framework, and several proposed designs. More discussions are provided in the Supplementary. Design Choices in Discrete Representation Learning. As a key contribution of this paper, we first discuss the efficacy of our improved discrete representation learning. We use 'Vector' to denote our design since we apply vector quantization to latent vector. Similarly, 'Grid' and 'Tri-Plane' refer to baselines applying vector quantization to volumetric grids and the three planes, respectively. Results in Tab. 7 show that 'Grid' gets better IoU performance for shape reconstruction in the first stage, but fails to train transformers in the second stage due to extreme long length of sequence (e.g., \\(32^{3}\\)). In contrast, our model not only achieves comparable reconstruction results (#0 vs. #2), but also outperforms 'Tri-Plane' by a large margin on generation quality (#1 vs. #2). The latter shows inferior results due to 'ambiguity of order' (see Suppl.) It significantly proves the efficacy" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14146" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.096, + 0.447, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.299, + 0.47, + 0.33 + ], + "angle": 0, + "content": "Figure 8: Results of real-world image-guide generation. Images are randomly selected from internet." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.349, + 0.465, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.505, + 0.468, + 0.534 + ], + "angle": 0, + "content": "Figure 9: Results of real-world image-guide generation. Samples are from Pix3D dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.468, + 0.839 + ], + "angle": 0, + "content": "of our proposed coupling network, improving the plasticity and flexibility of the model. We also explore different design choices in Tab. 7. By gradually increasing feature resolutions or the number of entries in the codebook, we achieve better performance on IoU. This observation is consistent with [48], as the capacity of the discrete representation is affected by these two factors. We do not try larger parameters, as it would significantly increase the computation cost. Image-guide Generation in Real-world. We further investigate the generalizability of our model on real-world images. We use the model trained on ShapeNet as described in Sec. 4.4, and download images from internet as conditions. Figure 8 shows the qualitative results for three categories, i.e., plane, chair and table. Our model sensitively capture major attributes of objects in the image and produce shapes faithful to them (see the first column to the left). Meanwhile, our synthesized samples enjoy the advantage of diversity by partially sticking to the images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Figure 9 also show results of our model on Pix3D dataset (trained on ShapeNet, without any finetuning). Compared with other competitors, ImAM is capable of generating high-quality and realistic shapes that highly match the shape" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.095, + 0.877, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.223, + 0.88, + 0.238 + ], + "angle": 0, + "content": "Figure 10: Results of zero-shot text-to-shape generation." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.259, + 0.89, + 0.361 + ], + "angle": 0, + "content": "
Num.TYPE#ENTRYRESO.STAGE 1STAGE 2
IoU ↑1-NNA / ECD ↓
0Grid40963288.87×
1Tri-Plane87.8173.67 / 743
2Vector88.0159.95 / 236
340961679.17-
420483286.99
5102486.57
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.463 + ], + "angle": 0, + "content": "Table 7: Ablation study of auto-encoder design choices. We report 1-NNA/ECD for plane category. 'RESO.' means the resolution of feature map for vector quantization. '×': cannot report due to extreme memory cost. '-': not report. Notably, without the coupling network, our method naturally degenerates into 'Tri-Plane' representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.479, + 0.891, + 0.509 + ], + "angle": 0, + "content": "of objects in real-world images. It significantly highlights the strong generalization ability of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.892, + 0.618 + ], + "angle": 0, + "content": "Zero-shot Text-to-shape Generation. Inspired by CLIP-Forge [31], we utilize the CLIP model to achieve zero-shot text-to-shape generation. At training, we only use the rendered images of 3D shapes. At inference, we substitute image features with text features encoded by the CLIP model. Figure 10 shows our ability of zero-shot generation, where shape attributes are controlled with different prompts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.619, + 0.658 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.822 + ], + "angle": 0, + "content": "We introduce an improved AR model for 3D shape generation. By projecting volumetric grids of encoded input shapes onto three axis-aligned orthogonal feature planes, which are then coupled into a latent vector, we reduce computational costs and create a more tractable order for AR learning. Our compact and tractable representations enable easy switching between unconditional and conditional generation with multi-modal conditioning inputs. Extensive experiments show that our model outperforms previous methods on multiple generation tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported by China Postdoctoral Science Foundation (2022M710746). Yanwei Fu is with the School of Data Science, Fudan University, and Fudan ISTBI—ZJNU Algorithm Centre for Brain-inspired Intelligence, Zhejiang Normal University, Jinhua, China." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14147" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. 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ImAM can either generate diverse and faithful shapes with multiple categories via an unconditional way (one column to the left), or can be adapted for conditional generation by incorporating various conditioning inputs given on the left-top (three columns to the right). + +![](images/85a1e51164a5e386171b2d855af3966cd7e0f7d25e177563860e4605a8c2eed0.jpg) + +![](images/89f7665b60f21a425d5b9cdf64fef009ed98cb605603dc39ef80482b9f76720a.jpg) + +![](images/3b344a6440d290175e5f95bfe7c1502f72936a9a1cef1ce01252c16909cb757f.jpg) + +# Abstract + +Auto-Regressive (AR) models have achieved impressive results in 2D image generation by modeling joint distributions in the grid space. While this approach has been extended to the 3D domain for powerful shape generation, it still has two limitations: expensive computations on volumetric grids and ambiguous auto-regressive order along grid dimensions. To overcome these limitations, we propose the Improved Auto-regressive Model (ImAM) for 3D shape generation, which applies discrete representation learning + +based on a latent vector instead of volumetric grids. Our approach not only reduces computational costs but also preserves essential geometric details by learning the joint distribution in a more tractable order. Moreover, thanks to the simplicity of our model architecture, we can naturally extend it from unconditional to conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images, and texts. Extensive experiments demonstrate that ImAM can synthesize diverse and faithful shapes of multiple categories, achieving state-of-the-art performance. + +# 1. Introduction + +3D shape generation has garnered increasing interest in both academia and industry for its extensive applications in robotics [20], autonomous driving [47, 28], augmented reality [35] and virtual reality [34]. Based on whether user prerequisites are provided, shape generation is typically categorized as unconditional or conditional. To be an effective generative model, it is crucial for the synthesized shapes to be both diverse and faithful to the universal cognition of humans or given conditions. These qualities serve as the foundation for other deterministic tasks, such as shape completion, single-view reconstruction, and more. Previous approaches [8, 14, 25] usually utilize an AutoEncoder (AE) to learn latent features by shape reconstruction. Then, a GAN is trained to fit the distributions of the latent features, allowing for the generation of 3D shapes through sampling the latent codes learned in AE. While achieving convincing results, a single embedding for one shape easily encounters the problem of poor scalability and difficulty in training. + +Recently, Auto-Regressive (AR) models have shown remarkable performance in the generation of 2D images [11, 50, 5] and 3D shape [23, 45]. Instead of learning a continuous latent space, these model leverage discrete representation learning to encode each 2D/3D input into grid-based discrete codes. Subsequently, a transformer-based network is employed to jointly model the distribution of all codes, which essentially reflects the underlying prior of objects, facilitating high-quality generation and tractable training. However, applying AR models to 3D still suffers from two limitations. First, as the number of discrete codes increases from squared to cubed, the computational burden of the transformer grows dramatically, making it difficult to converge. Second, discrete codes in the grid space are highly coupled. It is ambiguous to simply flatten them for autoregression (e.g., a top-down row-major order). This may lead to poor quality or even collapse of generated shapes (see Sec. 3.1 and the Supplementary for more details). + +In this paper, we propose an improved auto-regressive model (ImAM), to enhance the efficient learning of 3D shape generation. Our key idea is to apply discrete representation learning in a one-dimensional space instead of 3D volumetric space. Specifically, we first project volumetric grids encoded from 3D shapes onto three axis-aligned orthogonal planes. This process significantly reduces the computational costs from cubed to squared while maintaining the essential information about the input geometry. Next, we present a coupling network to further encode three planes into a compact and tractable latent space, on which discrete representation learning is performed. + +Our ImAM is straightforward and effective, simply tackling the aforementioned limitations by two projections. Thus, a vanilla decoder-only transformer can be attached to model the joint distributions of codes from the latent spaces. + +Furthermore, the simplicity of the transformer structure allows us to switch freely between unconditional and conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images and texts. Figure 1 showcases the ability of our ImAM to generate diverse and accurate shapes across multiple categories, both with and without the given condition on the top-left corner. + +In summary, the contributions of this paper are listed as follows. (1) We propose an improved AR Model (ImAM) for 3D shape generation. By applying discrete representation learning in a latent vector instead of volumetric grids, our ImAM enjoys the advantages of lightweight and flexibility. (2) Our proposed ImAM model provides a more unified framework for switching between unconditional and conditional generation for a variety of conditioning inputs, including point clouds, categories, images, and texts. (3) Extensive experiments are conducted on four tasks to demonstrate that our ImAM can generate more faithful and diverse shapes, achieving state-of-the-art results for unconditional and conditional shape generation. Overall, our contributions advance the field of 3D shape generation, providing a powerful tool for researchers and practitioners alike. + +# 2. Related work + +3D shape generative models. As an extremely challenging task, we review the most previous efforts by using voxel, point clouds, and implicit representations. (1) Standard voxel grids can be easily processed by 3D convolution for learning-based 3D task [19, 44, 10, 41]. However, restricted by its cubic space complexity, voxel representation can not scale to a high resolution, usually limited in $64^{3}$ . Even with efficient data structures like octrees or multi-scale representation [40, 13, 30], such representations still have some limitations in quality. (2) Point clouds extracted from shape surfaces is an alternative 3D representation [12, 43, 27], which is efficient in terms of memory and does not suffer from the restriction of resolution compared with voxel representations. However, these representations can not represent topological relations in 3D space and are also nontrivial to recover shape surfaces from point cloud representation. (3) Recently, implicit representations have gained attention for simplicity in representing 3D shapes [25, 21, 22, 33]. By predicting the signed distance [25, 33] or occupancy label [21, 26] of a given point, and then through Marching cubes [18] methods, the surface can be easily recovered. Follow-up works [21, 25, 8, 26, 15] focus on the design of implicit function representation with global or local shape priors. To sum up, different 3D representations lead to various shape generative models. There are various good previous works such as 3DGAN [41], PC-GAN [1], IM-GAN [8], and GBIF [14]. However, most current generative methods are task-specific. And it is difficult to be directly applied to different generative tasks (e.g., shape completion). Fundamentally, + +![](images/ee26ab7ec6f2cbb9beae4e1844c10559e56163a0fa9a23b07ebf6f2da29d01e2.jpg) +Figure 2: Illustration of auto-regressive generation for grid-based representation. Here, we show three different flattening orders as examples. Best viewed in color. + +they rely on GANs for the generation step, suffering from the known drawbacks such as mode collapse and training instability. In contrast, we propose an improved AR model for 3D shape generation that can synthesize high-quality and diverse shapes while being easily generalized to other multi-modal conditions. + +Autoregressive models. AR models are probabilistic generative approaches that have tractable probability density. Using the probability chain rule, the likelihood of a given sample (usually high dimensional data) can be factorized into a series of product of conditional probability. In contrast, GANs do not have such a tractable probability density. Recently, AR models achieve remarkable progress in 2D image generation [11, 37, 29], to a less extent 3D tasks [36, 9, 24]. Most of 3D AR models are struggling with generating high-quality shapes due to the challenges of representation learning with more points or faces. Particularly, we notice two recent works [45, 23] that share similar insights of utilizing AR models for 3D tasks. [45] introduces a sparse representation to only quantize non-empty grids in 3D space, but still follows a monotonic row-major order. [23] presents a non-sequential design to break the orders, but performs on all volumetric grids. However, both of them address only one of the above limitations, and burden the structure design and training of transformer. In contrast, our ImAM applies discrete representation learning in a latent vector instead of volumetric grids. Such a representation offers plenty of advantages, including shorter length of discrete codes, tractable orders from auto-regression, fast convergence, and also preserving essential 3D information. Moreover, benefiting from the simplicity of transformers, we can freely switch from unconditional generation to conditional generation by concatenating various conditions. + +# 3. Methodology + +Figure 3 illustrates the schematic of our proposed framework for 3D shape generation, which consists of a two-stage training procedure. It first represents the input as a composition of learned discrete codes (in Sec. 3.2), then utilizes a transformer model to learn their interrelations (in Sec. 3.3). Before beginning, we provide some symbol definitions and necessary preliminaries in Sec. 3.1. + +# 3.1. Preliminary + +Ambiguity. Formally, 'ambiguity' appears in the order of a series of conditional probabilities, which affects the difficulty of likelihood learning, leading to approximation error of the joint distribution. Critically, auto-regressive models require sequential outputs, autoregressively predicting the next code conditioned on all previous ones. Thereby, the order of the flattened sequence determines the order of conditional probabilities. Although some methods (e.g. position embedding [39]) can be aware of positions of codes, it cannot eliminate approximation error caused by the condition order. Notably, this 'ambiguity' phenomenon is also discussed in [11] (in Fig. 47), where the loss curves in Fig. 47 highlight the differences in difficulty for likelihood learning across various orders. Figure 2 illustrates how the flattening order affects the way of autoregressive generation. For grid-based representation, it is ambiguous if the flattening order along axes is $y - x - z$ , $x - z - y$ or other combinations. + +Discrete Representation. Given input point clouds $P \in \mathbb{R}^{n \times 3}$ where $n$ means the number of points, an encoder is adopted to extract features for each point cloud and then perform voxelization to get features of regular volumetric grids $f^v \in \mathbb{R}^{r \times r \times r \times c}$ , where $r$ denote the resolution of voxels and $c$ is the feature dimension. To learn discrete representation for each 3D shape, a codebook $\mathbf{q} \in \mathbb{R}^{m \times c}$ is thus introduced whose entry is a learned code describing a particular type of local-part shape in a grid. Formally, for each grid $\left\{f_{(h,l,w)}^v\right\}_{h,l,w=1}^r$ , vector quantization $\mathcal{Q}(\cdot)$ is performed by replacing it with the closest entry in codebooks [11], + +$$ +\mathbf {z} ^ {v} = \mathcal {Q} \left(f ^ {v}\right) := \arg \min _ {\mathbf {e} _ {i} \in \mathbf {q}} \left| \left| f _ {(h, l, w)} ^ {v} - \mathbf {e} _ {i} \right| \right| \tag {1} +$$ + +where $\mathbf{e}_i\in \mathbf{q}$ represents the $i$ -th entry in the codebook. Thus, learning the correlations between entries in the second stage can explore the underlying priors for shape generation. However, autoregressive generation [11, 45] requires sequential outputs, facing two limitations. First, the resolution of $\mathbf{z}^v$ matters the quality of synthesized shapes. If $r$ is too small, it lacks the capacity to represent intricate and detailed geometries, while a large value of $r$ can learn a specific code for each local gird, it inevitably increase the computational complexity since the number of required codes + +![](images/781c588f7b8cadfeaa7850cea650a4bf4af18f82a2801bb2b0c849a16e1274bc.jpg) +Figure 3: Overview of our ImAM. Given an arbitrary 3D shape, we first project encoded volumetric grids into the three axis-aligned planes, and then use a coupling network to further project them into a latent vector. Vector quantization is thus performed on it for discrete representation. Taking advantages of such a compact representation with tractable orders, vanilla transformers are adopted to auto-repressively learn shape distributions. Furthermore, we can freely switch from unconditional generation to conditional generation by concatenating various conditions, such as point clouds, categories and images. + +explodes as $r$ grows. Second, the order of $\mathbf{z}^v$ affects the generation quality. Each grid is highly coupled with neighbors, simply flattening (say, along x-y-z axes) may cause 'ambiguity', leading to sub-optimal generation quality. + +# 3.2. Improved Discrete Representation Learning + +One possible solution to solve the first limitation is applying vector quantization in spatial grids instead of volumetric grids inspired by [3]. Specifically, after obtaining point cloud features $f^p \in \mathbb{R}^{n \times c}$ , we first project points onto three axis-aligned orthogonal planes. Features of points falling into the same plane grid are aggregated via summation, resulting in three feature maps for the three planes $\{f^{xy}, f^{yz}, f^{xz}\} \in \mathbb{R}^{l \times w \times c}$ . Next, the vector quantization is applied to the three planes separately. The primary advantage of tri-planar representation is efficient and compact. It can dramatically reduce the number of grids from $\mathcal{O}(r^3)$ to $\mathcal{O}(r^2)$ while preserving essential 3D information. However, it still suffers from the ambiguity of order, or worse, since it involves the flattening order of three planes and the order of entries of each plane. + +To this end, we further introduce a projection by learning a higher latent space for features of the three planes. This is simply achieved by first concatenating three planes with arbitrary order and then feeding them into a coupling network. Finally, the output is flattened as a projected latent vector, formulated as, + +$$ +f = \tau \left(\mathcal {G} \left([ f ^ {x y}; f ^ {y z}; f ^ {x z} ]; \theta)\right) \in \mathbb {R} ^ {m \times d} \right. \tag {2} +$$ + +where $[\cdot ;\cdot ]$ denotes the concatenation operation; $\mathcal{G}(\cdot ;\theta)$ is a series of convolution layers with parameters $\theta$ . $\tau (\cdot)$ means the operation of flatten with row-major order; $m$ and $d$ indicate the length of latent vector and feature dimension. By + +applying discrete representation learning in the latent vector, we can describe each 3D shape with $\mathbf{z} = \mathcal{Q}(f)$ , where $\mathcal{Q}(\cdot)$ represents vector quantization in Eq. 1. + +Remark. Different from existing works [23, 45] that rely on structure design and training strategies in second stage to address the problem of ambiguous order, we tackle it by learning the coupling relationship of spatial grids in the first stage with the help of the second projection. By stacking convolution layers, we increase the receptive field of each element in the latent vector. Additionally, since the features of each spatial grid on the three planes are fused and highly encoded, each element does not have a definite position mapping in 3D space, which results in a tractable order for auto-regression. More in-depth discussions can be found in Sec. 4.6 and the supplementary materials. + +Training Objective. We optimize parameters with reconstruction loss. After getting discrete representation $\mathbf{z}$ which represents indices of entries in the codebook, we retrieve the corresponding codes with indices, denoted as $\mathbf{q}_{(\mathbf{z})}$ . Subsequently, a decoder with symmetric structures of the encoder are designed to decode $\mathbf{q}_{(\mathbf{z})}$ back to features of the three planes *. Given sampling points $x\in \mathbb{R}^3$ , we query their features by projecting them onto each of the three feature planes and performing bilinear interpolation. Features from three planes are accumulated and fed into an implicit function to predict their occupancy values. Finally, we apply binary cross-entropy loss between the predicted values $y_{o}$ and the ground-truth ones $\tilde{y_o}$ , + +$$ +\mathcal {L} _ {o c c} = - \left(\tilde {y _ {o}} \cdot \log \left(y _ {o}\right) + \left(1 - \tilde {y _ {o}}\right) \cdot \log \left(1 - y _ {o}\right)\right) \tag {3} +$$ + +To further train the codebook, we encourage pulling the + +distance between features before and after the vector quantization. Thus, the codebook loss is derived as, + +$$ +\mathcal {L} _ {\text {c o d e}} = \beta | | \operatorname {s g} [ f ] - \mathbf {q} _ {(\mathbf {z})} | | _ {2} ^ {2} + | | f - \operatorname {s g} [ \mathbf {q} _ {(\mathbf {z})} ] | | _ {2} ^ {2} \tag {4} +$$ + +where $\mathrm{sg}[\cdot ]$ denotes the stop-gradient operation [38] and we set $\beta = 0.4$ by default. In sum, the overall loss for the first stage is $\mathcal{L}_{rec} = \mathcal{L}_{occ} + \mathcal{L}_{code}$ + +# 3.3. Learning Priors with Vanilla Transformers + +Benefiting from a compact composition and tractable order of discrete representation, models in the second stage can absorbly learn the correlation between discrete codes, effectively exploring priors of shape composition. We thus adopt a vanilla decoder-only transformer [11] without any specific-designed module. + +For unconditional generation, given discretized indices of latent vector $\mathbf{z} = \{\mathbf{z}_1,\mathbf{z}_2,\dots ,\mathbf{z}_m\}$ , we feed them into a learnable embedding layer to retrieve features with discrete indices. Then, the transformer with multi-head self-attention mechanism predicts the next possible index by learning the distribution of previous indices, $p(\mathbf{z}_i\mid \mathbf{z}_{< i})$ . This gives the joint distribution of full representation as, + +$$ +p (\mathbf {z}) = \prod_ {i = 1} ^ {m} p \left(\mathbf {z} _ {i} \mid \mathbf {z} _ {< i}\right) \tag {5} +$$ + +For conditional generation, users often expect to control the generation process by providing additional conditions. Instead of designing complex modules or training strategies, we simply learn joint distribution given conditions $\mathbf{c}$ by preponding it to $\mathbf{z}$ . Equation 5 is thus extended as, + +$$ +p (\mathbf {z}) = \prod_ {i = 1} ^ {m} p \left(\mathbf {z} _ {i} \mid \mathbf {c}, \mathbf {z} _ {< i}\right) \tag {6} +$$ + +where $\mathbf{c}$ denotes a feature vector of given conditions. The simplicity of our model gives the flexibility to learn conditions of any form. Specifically, for 3D conditions such as point clouds, we use our discrete representation learning in Sec. 3.2 to transform them into a vector. As for 2D/1D conditions such as images and classes, we either adopt pretrained models or embedding layers to extract their features. Objective. To train second stage, we minimize negative log-likelihood of Eq. 5 or 6 as $\mathcal{L}_{nll} = \mathbb{E}_{x\sim p(x)}[-\log p(\mathbf{z})]$ , where $p(x)$ is the distribution of real data. + +Inference. With both models trained on two stages, we use Eq. 5 or 6 to perform shape generation by progressively sampling the next index with top- $k$ sampling strategy, until all elements in $\mathbf{z}$ are completed. Then, we feed $\mathbf{q}_{(\mathbf{z})}$ into the decoder of the first stage, and query probabilities of occupancy values for all sampled 3D positions (e.g., $128^{3}$ ). The output shapes are extracted with Marching Cubes [18]. + +# 4. Experiments + +This section starts with comparing results on unconditional 3D shape generation, showing more faithful and diverse shapes synthesized by our approach in Sec. 4.1. Next, we show extensive studies on four generation tasks, demonstrating the powerful and flexible ability of ImAM (in Sec. $4.2 \sim 4.5$ ). Lastly, we provide in-depth studies to evaluate the efficacy of our modules and show generalization to real-world data and zero-shot generation (in Sec. 4.6). For all experiments, if necessary, we sample point clouds from output meshes with Poisson Disk Sampling, or reconstruct meshes with our auto-encoder from output points, which is better than Poisson Surface Reconstruction [16]. Please refer to the Supplementary for more details about implementations and qualitative results. + +# 4.1. Unconditional Shape Generation + +Data. We consider ShapeNet [4] as our main dataset for generation, following previous literature [14, 8, 36]. We use the same training split and evaluation setup from [14] for fair comparability. Five categories of car, chair, plane, rifle and table are used for testing. As ground-truth, we extract mesh from voxelized models with $256^{3}$ resolution in [13]. + +Baselines. We compare ImAM with five state-of-the-art models, including GAN-based IM-GAN[8] and GBIF [14], flow-based PointFlow [46], score-based ShapeGF [2] and diffusion-based PVD [51]. We train these methods on the same data split with the official implementation. + +Metrics and Settings. The size of the generated set is 5 times the size of the test set, the same as [8, 14]. As suggested by [8], we use the Light Field Descriptor (LFD) [6] as our primary similarity distance metric between two shapes. Coverage (COV) [1], Minimum Matching Distance (MMD) [1] and Edge Count Difference (ECD) [14] are adopted to evaluate the diversity, fidelity and overall quality of synthesized shapes. We also use 1-Nearest Neighbor Accuracy (1-NNA) [46] (with Chamfer Distance) to measure the distribution similarity. The number of sampled points is 2048. Besides, it is well known that COV does not penalize outliers. To rule out the false positive coverage, we introduce CovT, counting as match between a generation and ground truth shape only if LFD between them is smaller than a threshold $t$ . In practice, $t$ could vary across different categories based on the scale and complexity of the shape, and we empirically use mean MMD as the threshold and found it effective in identifying correct matches. + +Results Analysis. Results are reported in Table 1. First, ImAM achieves state-of-the-art performance with regard to ECD and 1-NNA. It significantly demonstrates the superiority of our model over synthesizing high-quality shapes. We notice that the result of Car is not good on the metric of 1-NNA. One possible reason is that ImAM tries to generate meshes of tires and seats inside cars, which may not + +
METRICSMETHODSCATEGORIESAvg
PlaneCarChairRifleTable
ECD ↓IM-GAN [8]92331726583714181108
GBIF [14]9452388354195411858
PointFlow [46]23955318426270835592881
ShapeGF [2]12002547443672114915
PVD [51]66617404126534437453904
Ours236842276531240
1-NNA ↓IM-GAN [8]78.1889.3965.8369.3865.3173.62
GBIF [14]80.2287.1963.9566.9860.9671.86
PointFlow [46]73.6174.7570.1864.7774.8171.62
ShapeGF [2]74.7262.8159.1560.6555.5862.58
PVD [51]81.0957.3762.3677.3274.3170.49
Ours59.9576.5857.3157.2854.7661.17
COV ↑IM-GAN [8]77.0165.3776.3873.2185.7175.53
GBIF [14]80.9678.8580.9577.0085.1380.57
PointFlow [46]65.6464.9757.4948.5271.9561.71
ShapeGF [2]76.6471.8579.4170.6787.5477.22
PVD [51]58.0958.6468.9356.1276.8463.72
Ours79.1173.2580.8174.2684.0178.29
CovT ↑IM-GAN [8]41.0350.6345.6851.6846.5047.10
GBIF [14]32.3852.7639.7750.0043.6843.72
PointFlow [46]35.8547.7628.4834.8130.9835.57
ShapeGF [2]40.1753.6343.6951.0548.5047.41
PVD [51]12.1143.3638.8233.3343.6834.26
Ours45.1256.6449.8255.2748.0350.98
MMD ↓IM-GAN [8]341812902881369125052757
GBIF [14]375413333015386525842910
PointFlow [46]367513933322403829363072
ShapeGF [2]353013072880376224202780
PVD [51]437614323064427426233154
Ours312412132703362823742608
+ +Table 1: Results of unconditional generation. Models are trained for each category. The best and second results are highlighted in bold and underlined. + +be very friendly to CD. Second, our model has a clear advantage on both MMD and CovT metrics compared with all competitors, which separately indicates the outstanding fidelity and diversity of our generated shapes. Third, though GBIF achieves relatively good results on COV, it gets worse results on CovT, suggesting that most of the matched samples come from false positive pairs. ImAM, on the contrary, gets second best performance on COV, but higher than GBIF on CovT by about 6 points, showing that our generated shapes enjoy the advantage of high-quality and fewer outliers. Lastly, we visualize shapes with multiple categories in Fig. 4, further supporting the quantitative results and conclusions described above. + +# 4.2. Class-guide Generation + +We first evaluate the versatility of ImAM on class-guide generation, which requires generating shapes given a category label. It is a basic conditional generation task. We use the same dataset and evaluation metrics as in Sec. 4.1. + +Baselines. We choose two recently-published works as competitors due to the similar motivation. One is two-stage generative model GBIF [14], the other is AR method Au + +![](images/e8fe8a8c142680c92100286d72988159abf437d86cf49623eb36f9a3518bf345.jpg) +Figure 4: Qualitative results of unconditional generation. + +toSDF [23]. We simply modify mask-condition of [14] to class-condition, and additionally add class token to transformers for [23] which is the same as ImAM. + +Results Analysis. As shown in Tab. 2, ImAM outperforms both competitors across 5 categories by a significant margin, achieving state-of-the-art results on all metrics. Particularly, it gets advantages on the metric of 1-NNA, strongly demonstrating the versatility of ImAM on class-guide generation. Qualitative results of 5 different categories are further illustrated in Fig. 5. As observed, the generated quality of our method is clearly better than GBIF and AutoSDF, while preserving more diversity in types and shapes. + +# 4.3. Multi-modal Partial Point Completion + +We further verify the ability of our model in conditional generation by giving partial point clouds. Here, we advocate the multi-modal completion, since there are many possibilities of the completed shape given the partial shape. It is the essence of generative model, where being faithful to the given partial conditions but using your imagination. + +Data. We use ShapeNet dataset for testing. Two settings are considered here, (1) perspective completion [49]: randomly sampling a viewpoint and then removing the $25\% \sim 75\%$ furthest points from the viewpoint; (2) bottom-half completion [23]: removing all points from the top half of shapes. + +Baselines. Four multi-modal completion models are chosen as baselines, including one generative adversarial model cGAN [42], one diffusion model PVD [51], two AR models ShapeFormer [45] and AutoSDF [23]. + +
METRICSMETHODSCATEGORIESAVG
PlaneCarChairRifleTable
COV ↑GBIF [14]68.7269.6475.9468.9881.7273.00
AutoSDF [23]70.4652.7763.2548.1072.1961.35
Ours81.5871.5883.9875.7485.4879.67
CovT ↑GBIF [14]24.1038.6332.6935.4437.8033.73
AutoSDF [23]30.6640.4931.0034.6036.1034.57
Ours56.4952.7045.0952.7449.3251.27
MMD ↓GBIF [14]473614793220424627633289
AutoSDF [23]370614563249411527443054
Ours319512852871372924302702
ECD ↓GBIF [14]1327275215894348691394
AutoSDF [23]16194256103814434621764
Ours5711889419196285672
1-NNA ↓GBIF [14]91.4792.4375.6183.1270.1982.56
AutoSDF [23]83.3187.7669.3477.4367.2077.01
Ours66.8183.3964.8357.2859.5566.37
+ +Table 2: Results of class-guide generation. Models are trained on 13 categories of ShapeNet. + +![](images/a61a38d52098f1993df4b8acd904b419a3d866c0ffba072e9e8756a955cb5723.jpg) +Figure 5: Qualitative results of class-guide generation. + +Metrics and Settings. We complete 10 samples for 100 randomly selected shapes of three categories, i.e., chair, sofa and table. Following [42], we use Total Mutual Difference (TMD) to measure the diversity. Minimum Matching Distance [1] (MMD) with Chamfer Distance and Unidirectional Hausdorff Distance (UHD) [32] are adopted to measure the faithfulness of completed shapes. + +Results Analysis. We first report perspective completion results in Tab. 3. ImAM beats all baselines and achieves state-of-the-art performance. Importantly, we outperform Shapeformer on all classes and metrics, which also utilizes an AR model with transformers to learn shape distribution. On the other hand, we compare with AutoSDF in its bottom-half completion setting. Results from Tab. 4 illus + +![](images/7b682522c61d55531ef344649290b3d9f3276eed5646ae3432b47edd0692b928.jpg) + +Figure 6: Qualitative results of partial point completion. + +
METRICSMETHODSCATEGORIESAVG
ChairSofaTable
TMD ↑ (×102)cGAN [42]1.7080.6871.7071.367
PVD [51]1.0980.8110.8390.916
ShapeFormer [45]1.1590.6980.6770.845
Ours2.0421.2211.5381.600
UHD ↓ (×102)cGAN [42]7.8367.0479.4068.096
PVD [51]10.7913.8811.3812.02
ShapeFormer [45]6.8848.6586.6887.410
Ours6.4396.4475.9486.278
MMD ↓ (×103)cGAN [42]1.6651.8131.5961.691
PVD [51]2.3522.0412.1742.189
ShapeFormer [45]1.0551.1001.0661.074
Ours0.9610.8190.8280.869
+ +Table 3: Results of multi-modal partial point completion. The missing parts vary according to random viewpoints. + +
METRICSMETHODSCATEGORIESAVG
ChairSofaTable
TMD ↑ (×102)AutoSDF [23]2.0461.6093.1162.257
Ours3.6822.67310.305.552
UHD ↓ (×102)AutoSDF [23]6.7939.9508.1228.289
Ours6.9966.59910.878.155
MMD ↓ (×103)AutoSDF [23]1.5011.1542.6001.751
Ours1.4771.1272.9061.837
+ +Table 4: Quantitative results of multi-modal partial point completion. The missing parts are always the top half. + +trates that ImAM outperforms AutoSDF in terms of TMD and MMD. It strongly suggests the flexibility and versatility of our proposed method. Qualitative results in Fig. 6 show the diversity and fidelity of our completed shapes. + +# 4.4. Image-guide Generation + +Next, we show the flexibility that ImAM can easily extend to image-guide generation, which is a more challenging task. The flexibility lies in that (1) it is implemented by the easiest way of feature concatenation; (2) the condition form of images is various, which could be 1-D feature + +![](images/34964c39f9a254de4b73b53d3a4d81b0e6835e71313c09d1f71286aba8ee5968.jpg) +Figure 7: Visualizations of image-guide shape generation. + +vector or patch tokens, or 2-D feature maps. For simplicity, we use a pretrained CLIP model (i.e., ViT-B/32) to extract feature vectors of images as conditions. All experiments are conducted on ShapeNet dataset with rendered images. + +Baselines. CLIP-Forge [31] is a flow-based model, which is trained with pairs of images and shapes. We take it as our primary baseline for two reasons: (1) it is a generation model instead of reconstruction model, and (2) it originally uses CLIP models to extract image features. + +Metrics and Settings. We evaluate models with the test split of 13 categories. For each category, we randomly sample 50 single-view images and then generate 5 shapes for evaluation. As a generation task, TMD is adopted to measure the diversity. We further use MMD with Chamfer Distance and Fréchet Point Cloud distance (FPD) [32] to measure the fidelity compared with the ground truth. + +Results Analysis. Results are reported in Tab. 5. ImAM wins out in terms of both fidelity and diversity. In particular, we achieve a great advantage on both TMD and FPD, demonstrating the effectiveness of ImAM applied to image-guide generation. It is also successfully echoed by qualitative visualizations in Fig. 7. Our samples are diverse and appear visually faithful to attributes of the object in images. + +# 4.5. Text-guide Generation + +Encouraged by promising results on image-guide generation, we also turn ImAM to text-to-shape generation. The same pretrained CLIP model is used to extract single embedding for text conditions. Note that we did it on purpose, not using word sequence embedding, but only using a single features vectors in our model to show its efficacy and scalability to the simplest forms of conditions. + +Data. To our knowledge, the only existing largest paired text-shape dataset is Text2Shape [7], which provides language descriptions for two objects from ShapeNet, i.e., chair and table. Thereby, we consider it as our main dataset to perform text-guide shape generation. + +Baselines. We compare our model with two state-of-the-arts text-to-shape generation model. One is CLIP-Forge [31] under the supervised learning setting, using the same + +
METHODTMD (×102) ↑MMD (×103) ↓FPD ↓
AutoSDF [23]2.5231.3832.092
Clip-Forge [31]2.8581.9268.094
Ours4.2741.5901.680
+ +Table 5: Quantitative results of image-guide generation. + +
METHODTMD (×101) ↑MMD (×103) ↓Acc ↑
ITG [17]N/A2.18729.13
AutoSDF [23]0.3422.16536.95
CLIP-Forge [31]0.4002.13653.68
Ours0.5651.84659.93
+ +(a) Descriptions as text queries + +
METHODTMD (×10^1) ↑FPD ↓Acc. ↑
AutoSDF [23]0.7525.8441.09
CLIP-Forge [31]0.9614.1455.00
Ours1.2465.3960.87
+ +(b) Prompts as text queries + +Table 6: Quantitative results of text-guide generation. + +condition extractor as ours. The other is ITG [17], which adopts BERT to encode texts into sequence embeddings. + +Metrics and Settings. All models are trained on the train split of Text2Shape dataset with their official codes. We evaluate our model with two types of text queries: (1) description: the test split of Text2Shape; (2) prompts: customized short phrases provided by [31] containing attributes for chair and table. We additionally use Accuracy (Acc.) [31] to measure the fidelity. The Accuracy is calculated by a pretrained PointNet [27] classifier on ShapeNet. + +Results Analysis. We report quantitative results of text-guide generation in Tab. 6. ImAM achieves promising results on TMD, MMD and Acc, showing good generalization performance across different conditional generation tasks. + +# 4.6. Ablation Study + +Lastly, we provide in-depth studies to dissect the efficacy of our ImAM framework, and several proposed designs. More discussions are provided in the Supplementary. Design Choices in Discrete Representation Learning. As a key contribution of this paper, we first discuss the efficacy of our improved discrete representation learning. We use 'Vector' to denote our design since we apply vector quantization to latent vector. Similarly, 'Grid' and 'Tri-Plane' refer to baselines applying vector quantization to volumetric grids and the three planes, respectively. Results in Tab. 7 show that 'Grid' gets better IoU performance for shape reconstruction in the first stage, but fails to train transformers in the second stage due to extreme long length of sequence (e.g., $32^{3}$ ). In contrast, our model not only achieves comparable reconstruction results (#0 vs. #2), but also outperforms 'Tri-Plane' by a large margin on generation quality (#1 vs. #2). The latter shows inferior results due to 'ambiguity of order' (see Suppl.) It significantly proves the efficacy + +![](images/9670b3336bc498e8e837c56f0b5ddfae63ba519b7d92516f6181efee997d2da6.jpg) +Figure 8: Results of real-world image-guide generation. Images are randomly selected from internet. + +![](images/f4dad909d059737be79a5733495fba226513f28d2ff3df3d7cd56949f07e26cd.jpg) +Figure 9: Results of real-world image-guide generation. Samples are from Pix3D dataset. + +of our proposed coupling network, improving the plasticity and flexibility of the model. We also explore different design choices in Tab. 7. By gradually increasing feature resolutions or the number of entries in the codebook, we achieve better performance on IoU. This observation is consistent with [48], as the capacity of the discrete representation is affected by these two factors. We do not try larger parameters, as it would significantly increase the computation cost. Image-guide Generation in Real-world. We further investigate the generalizability of our model on real-world images. We use the model trained on ShapeNet as described in Sec. 4.4, and download images from internet as conditions. Figure 8 shows the qualitative results for three categories, i.e., plane, chair and table. Our model sensitively capture major attributes of objects in the image and produce shapes faithful to them (see the first column to the left). Meanwhile, our synthesized samples enjoy the advantage of diversity by partially sticking to the images. + +Figure 9 also show results of our model on Pix3D dataset (trained on ShapeNet, without any finetuning). Compared with other competitors, ImAM is capable of generating high-quality and realistic shapes that highly match the shape + +![](images/0511ae68d408f31568a4a17eb6041682c58a538ce102690902fdb5f0d318d166.jpg) +Figure 10: Results of zero-shot text-to-shape generation. + +
Num.TYPE#ENTRYRESO.STAGE 1STAGE 2
IoU ↑1-NNA / ECD ↓
0Grid40963288.87×
1Tri-Plane87.8173.67 / 743
2Vector88.0159.95 / 236
340961679.17-
420483286.99
5102486.57
+ +Table 7: Ablation study of auto-encoder design choices. We report 1-NNA/ECD for plane category. 'RESO.' means the resolution of feature map for vector quantization. '×': cannot report due to extreme memory cost. '-': not report. Notably, without the coupling network, our method naturally degenerates into 'Tri-Plane' representation. + +of objects in real-world images. It significantly highlights the strong generalization ability of our method. + +Zero-shot Text-to-shape Generation. Inspired by CLIP-Forge [31], we utilize the CLIP model to achieve zero-shot text-to-shape generation. At training, we only use the rendered images of 3D shapes. At inference, we substitute image features with text features encoded by the CLIP model. Figure 10 shows our ability of zero-shot generation, where shape attributes are controlled with different prompts. + +# 5. Conclusion + +We introduce an improved AR model for 3D shape generation. By projecting volumetric grids of encoded input shapes onto three axis-aligned orthogonal feature planes, which are then coupled into a latent vector, we reduce computational costs and create a more tractable order for AR learning. Our compact and tractable representations enable easy switching between unconditional and conditional generation with multi-modal conditioning inputs. Extensive experiments show that our model outperforms previous methods on multiple generation tasks. + +Acknowledgements. This work is supported by China Postdoctoral Science Foundation (2022M710746). Yanwei Fu is with the School of Data Science, Fudan University, and Fudan ISTBI—ZJNU Algorithm Centre for Brain-inspired Intelligence, Zhejiang Normal University, Jinhua, China. + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. 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Advances in Neural Information Processing Systems, 34, 2021. 2 +[51] Linqi Zhou, Yilun Du, and Jiajun Wu. 3d shape generation and completion through point-voxel diffusion. 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ImAM can either generate diverse and faithful shapes with multiple categories via an unconditional way (one column to the left), or can be adapted for conditional generation by incorporating various conditioning inputs given on the left-top (three columns to the right)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 190, + 242, + 294, + 504 + ], + "blocks": [ + { + "bbox": [ + 190, + 242, + 294, + 504 + ], + "lines": [ + { + "bbox": [ + 190, + 242, + 294, + 504 + ], + "spans": [ + { + "bbox": [ + 190, + 242, + 294, + 504 + ], + "type": "image", + "image_path": "85a1e51164a5e386171b2d855af3966cd7e0f7d25e177563860e4605a8c2eed0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 239, + 415, + 504 + ], + "blocks": [ + { + "bbox": [ + 309, + 239, + 415, + 504 + ], + "lines": [ + { + "bbox": [ + 309, + 239, + 415, + 504 + ], + "spans": [ + { + "bbox": [ + 309, + 239, + 415, + 504 + ], + "type": "image", + "image_path": "89f7665b60f21a425d5b9cdf64fef009ed98cb605603dc39ef80482b9f76720a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 422, + 250, + 527, + 503 + ], + "blocks": [ + { + "bbox": [ + 422, + 250, + 527, + 503 + ], + "lines": [ + { + "bbox": [ + 422, + 250, + 527, + 503 + ], + "spans": [ + { + "bbox": [ + 422, + 250, + 527, + 503 + ], + "type": "image", + "image_path": "3b344a6440d290175e5f95bfe7c1502f72936a9a1cef1ce01252c16909cb757f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 553, + 192, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 553, + 192, + 566 + ], + "spans": [ + { + "bbox": [ + 143, + 553, + 192, + 566 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 578, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 288, + 687 + ], + "type": "text", + "content": "Auto-Regressive (AR) models have achieved impressive results in 2D image generation by modeling joint distributions in the grid space. While this approach has been extended to the 3D domain for powerful shape generation, it still has two limitations: expensive computations on volumetric grids and ambiguous auto-regressive order along grid dimensions. To overcome these limitations, we propose the Improved Auto-regressive Model (ImAM) for 3D shape generation, which applies discrete representation learning" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 554, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 547, + 686 + ], + "type": "text", + "content": "based on a latent vector instead of volumetric grids. Our approach not only reduces computational costs but also preserves essential geometric details by learning the joint distribution in a more tractable order. Moreover, thanks to the simplicity of our model architecture, we can naturally extend it from unconditional to conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images, and texts. Extensive experiments demonstrate that ImAM can synthesize diverse and faithful shapes of multiple categories, achieving state-of-the-art performance." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 134, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14139" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 71, + 127, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 71, + 127, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 127, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 91, + 286, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 91, + 286, + 305 + ], + "spans": [ + { + "bbox": [ + 49, + 91, + 286, + 305 + ], + "type": "text", + "content": "3D shape generation has garnered increasing interest in both academia and industry for its extensive applications in robotics [20], autonomous driving [47, 28], augmented reality [35] and virtual reality [34]. Based on whether user prerequisites are provided, shape generation is typically categorized as unconditional or conditional. To be an effective generative model, it is crucial for the synthesized shapes to be both diverse and faithful to the universal cognition of humans or given conditions. These qualities serve as the foundation for other deterministic tasks, such as shape completion, single-view reconstruction, and more. Previous approaches [8, 14, 25] usually utilize an AutoEncoder (AE) to learn latent features by shape reconstruction. Then, a GAN is trained to fit the distributions of the latent features, allowing for the generation of 3D shapes through sampling the latent codes learned in AE. While achieving convincing results, a single embedding for one shape easily encounters the problem of poor scalability and difficulty in training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 307, + 286, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 307, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 49, + 307, + 286, + 521 + ], + "type": "text", + "content": "Recently, Auto-Regressive (AR) models have shown remarkable performance in the generation of 2D images [11, 50, 5] and 3D shape [23, 45]. Instead of learning a continuous latent space, these model leverage discrete representation learning to encode each 2D/3D input into grid-based discrete codes. Subsequently, a transformer-based network is employed to jointly model the distribution of all codes, which essentially reflects the underlying prior of objects, facilitating high-quality generation and tractable training. However, applying AR models to 3D still suffers from two limitations. First, as the number of discrete codes increases from squared to cubed, the computational burden of the transformer grows dramatically, making it difficult to converge. Second, discrete codes in the grid space are highly coupled. It is ambiguous to simply flatten them for autoregression (e.g., a top-down row-major order). This may lead to poor quality or even collapse of generated shapes (see Sec. 3.1 and the Supplementary for more details)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 522, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 522, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 49, + 522, + 286, + 664 + ], + "type": "text", + "content": "In this paper, we propose an improved auto-regressive model (ImAM), to enhance the efficient learning of 3D shape generation. Our key idea is to apply discrete representation learning in a one-dimensional space instead of 3D volumetric space. Specifically, we first project volumetric grids encoded from 3D shapes onto three axis-aligned orthogonal planes. This process significantly reduces the computational costs from cubed to squared while maintaining the essential information about the input geometry. Next, we present a coupling network to further encode three planes into a compact and tractable latent space, on which discrete representation learning is performed." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 665, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 665, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 665, + 286, + 712 + ], + "type": "text", + "content": "Our ImAM is straightforward and effective, simply tackling the aforementioned limitations by two projections. Thus, a vanilla decoder-only transformer can be attached to model the joint distributions of codes from the latent spaces." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 72, + 544, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 156 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 156 + ], + "type": "text", + "content": "Furthermore, the simplicity of the transformer structure allows us to switch freely between unconditional and conditional generation by concatenating various conditioning inputs, such as point clouds, categories, images and texts. Figure 1 showcases the ability of our ImAM to generate diverse and accurate shapes across multiple categories, both with and without the given condition on the top-left corner." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 157, + 544, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 157, + 544, + 335 + ], + "spans": [ + { + "bbox": [ + 308, + 157, + 544, + 335 + ], + "type": "text", + "content": "In summary, the contributions of this paper are listed as follows. (1) We propose an improved AR Model (ImAM) for 3D shape generation. By applying discrete representation learning in a latent vector instead of volumetric grids, our ImAM enjoys the advantages of lightweight and flexibility. (2) Our proposed ImAM model provides a more unified framework for switching between unconditional and conditional generation for a variety of conditioning inputs, including point clouds, categories, images, and texts. (3) Extensive experiments are conducted on four tasks to demonstrate that our ImAM can generate more faithful and diverse shapes, achieving state-of-the-art results for unconditional and conditional shape generation. Overall, our contributions advance the field of 3D shape generation, providing a powerful tool for researchers and practitioners alike." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 346, + 389, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 346, + 389, + 358 + ], + "spans": [ + { + "bbox": [ + 308, + 346, + 389, + 358 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 367, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 367, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 367, + 544, + 712 + ], + "type": "text", + "content": "3D shape generative models. As an extremely challenging task, we review the most previous efforts by using voxel, point clouds, and implicit representations. (1) Standard voxel grids can be easily processed by 3D convolution for learning-based 3D task [19, 44, 10, 41]. However, restricted by its cubic space complexity, voxel representation can not scale to a high resolution, usually limited in " + }, + { + "bbox": [ + 308, + 367, + 544, + 712 + ], + "type": "inline_equation", + "content": "64^{3}" + }, + { + "bbox": [ + 308, + 367, + 544, + 712 + ], + "type": "text", + "content": ". Even with efficient data structures like octrees or multi-scale representation [40, 13, 30], such representations still have some limitations in quality. (2) Point clouds extracted from shape surfaces is an alternative 3D representation [12, 43, 27], which is efficient in terms of memory and does not suffer from the restriction of resolution compared with voxel representations. However, these representations can not represent topological relations in 3D space and are also nontrivial to recover shape surfaces from point cloud representation. (3) Recently, implicit representations have gained attention for simplicity in representing 3D shapes [25, 21, 22, 33]. By predicting the signed distance [25, 33] or occupancy label [21, 26] of a given point, and then through Marching cubes [18] methods, the surface can be easily recovered. Follow-up works [21, 25, 8, 26, 15] focus on the design of implicit function representation with global or local shape priors. To sum up, different 3D representations lead to various shape generative models. There are various good previous works such as 3DGAN [41], PC-GAN [1], IM-GAN [8], and GBIF [14]. However, most current generative methods are task-specific. And it is difficult to be directly applied to different generative tasks (e.g., shape completion). Fundamentally," + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "text", + "content": "14140" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 283, + 242 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 283, + 242 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 283, + 242 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 283, + 242 + ], + "type": "image", + "image_path": "ee26ab7ec6f2cbb9beae4e1844c10559e56163a0fa9a23b07ebf6f2da29d01e2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 254, + 288, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 254, + 288, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 288, + 291 + ], + "type": "text", + "content": "Figure 2: Illustration of auto-regressive generation for grid-based representation. Here, we show three different flattening orders as examples. Best viewed in color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 311, + 287, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 287, + 383 + ], + "type": "text", + "content": "they rely on GANs for the generation step, suffering from the known drawbacks such as mode collapse and training instability. In contrast, we propose an improved AR model for 3D shape generation that can synthesize high-quality and diverse shapes while being easily generalized to other multi-modal conditions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 391, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 288, + 714 + ], + "type": "text", + "content": "Autoregressive models. AR models are probabilistic generative approaches that have tractable probability density. Using the probability chain rule, the likelihood of a given sample (usually high dimensional data) can be factorized into a series of product of conditional probability. In contrast, GANs do not have such a tractable probability density. Recently, AR models achieve remarkable progress in 2D image generation [11, 37, 29], to a less extent 3D tasks [36, 9, 24]. Most of 3D AR models are struggling with generating high-quality shapes due to the challenges of representation learning with more points or faces. Particularly, we notice two recent works [45, 23] that share similar insights of utilizing AR models for 3D tasks. [45] introduces a sparse representation to only quantize non-empty grids in 3D space, but still follows a monotonic row-major order. [23] presents a non-sequential design to break the orders, but performs on all volumetric grids. However, both of them address only one of the above limitations, and burden the structure design and training of transformer. In contrast, our ImAM applies discrete representation learning in a latent vector instead of volumetric grids. Such a representation offers plenty of advantages, including shorter length of discrete codes, tractable orders from auto-regression, fast convergence, and also preserving essential 3D information. Moreover, benefiting from the simplicity of transformers, we can freely switch from unconditional generation to conditional generation by concatenating various conditions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 91, + 547, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 175 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 175 + ], + "type": "text", + "content": "Figure 3 illustrates the schematic of our proposed framework for 3D shape generation, which consists of a two-stage training procedure. It first represents the input as a composition of learned discrete codes (in Sec. 3.2), then utilizes a transformer model to learn their interrelations (in Sec. 3.3). Before beginning, we provide some symbol definitions and necessary preliminaries in Sec. 3.1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 183, + 385, + 196 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 183, + 385, + 196 + ], + "spans": [ + { + "bbox": [ + 306, + 183, + 385, + 196 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 201, + 547, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 201, + 547, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 547, + 405 + ], + "type": "text", + "content": "Ambiguity. Formally, 'ambiguity' appears in the order of a series of conditional probabilities, which affects the difficulty of likelihood learning, leading to approximation error of the joint distribution. Critically, auto-regressive models require sequential outputs, autoregressively predicting the next code conditioned on all previous ones. Thereby, the order of the flattened sequence determines the order of conditional probabilities. Although some methods (e.g. position embedding [39]) can be aware of positions of codes, it cannot eliminate approximation error caused by the condition order. Notably, this 'ambiguity' phenomenon is also discussed in [11] (in Fig. 47), where the loss curves in Fig. 47 highlight the differences in difficulty for likelihood learning across various orders. Figure 2 illustrates how the flattening order affects the way of autoregressive generation. For grid-based representation, it is ambiguous if the flattening order along axes is " + }, + { + "bbox": [ + 304, + 201, + 547, + 405 + ], + "type": "inline_equation", + "content": "y - x - z" + }, + { + "bbox": [ + 304, + 201, + 547, + 405 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 201, + 547, + 405 + ], + "type": "inline_equation", + "content": "x - z - y" + }, + { + "bbox": [ + 304, + 201, + 547, + 405 + ], + "type": "text", + "content": " or other combinations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": "Discrete Representation. Given input point clouds " + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "inline_equation", + "content": "P \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": " means the number of points, an encoder is adopted to extract features for each point cloud and then perform voxelization to get features of regular volumetric grids " + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "inline_equation", + "content": "f^v \\in \\mathbb{R}^{r \\times r \\times r \\times c}" + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": " denote the resolution of voxels and " + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": " is the feature dimension. To learn discrete representation for each 3D shape, a codebook " + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{q} \\in \\mathbb{R}^{m \\times c}" + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": " is thus introduced whose entry is a learned code describing a particular type of local-part shape in a grid. Formally, for each grid " + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "inline_equation", + "content": "\\left\\{f_{(h,l,w)}^v\\right\\}_{h,l,w=1}^r" + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": ", vector quantization " + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}(\\cdot)" + }, + { + "bbox": [ + 304, + 406, + 547, + 557 + ], + "type": "text", + "content": " is performed by replacing it with the closest entry in codebooks [11]," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 341, + 566, + 545, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 566, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 341, + 566, + 545, + 585 + ], + "type": "interline_equation", + "content": "\\mathbf {z} ^ {v} = \\mathcal {Q} \\left(f ^ {v}\\right) := \\arg \\min _ {\\mathbf {e} _ {i} \\in \\mathbf {q}} \\left| \\left| f _ {(h, l, w)} ^ {v} - \\mathbf {e} _ {i} \\right| \\right| \\tag {1}", + "image_path": "8de6f53d7a03e99d95c51c59495676607576a8c63daa22dcba676b2492945248.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i\\in \\mathbf{q}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " -th entry in the codebook. Thus, learning the correlations between entries in the second stage can explore the underlying priors for shape generation. However, autoregressive generation [11, 45] requires sequential outputs, facing two limitations. First, the resolution of " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^v" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " matters the quality of synthesized shapes. If " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " is too small, it lacks the capacity to represent intricate and detailed geometries, while a large value of " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " can learn a specific code for each local gird, it inevitably increase the computational complexity since the number of required codes" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14141" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 72, + 537, + 223 + ], + "blocks": [ + { + "bbox": [ + 58, + 72, + 537, + 223 + ], + "lines": [ + { + "bbox": [ + 58, + 72, + 537, + 223 + ], + "spans": [ + { + "bbox": [ + 58, + 72, + 537, + 223 + ], + "type": "image", + "image_path": "781c588f7b8cadfeaa7850cea650a4bf4af18f82a2801bb2b0c849a16e1274bc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 229, + 548, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 548, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 548, + 293 + ], + "type": "text", + "content": "Figure 3: Overview of our ImAM. Given an arbitrary 3D shape, we first project encoded volumetric grids into the three axis-aligned planes, and then use a coupling network to further project them into a latent vector. Vector quantization is thus performed on it for discrete representation. Taking advantages of such a compact representation with tractable orders, vanilla transformers are adopted to auto-repressively learn shape distributions. Furthermore, we can freely switch from unconditional generation to conditional generation by concatenating various conditions, such as point clouds, categories and images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": "explodes as " + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": " grows. Second, the order of " + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^v" + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": " affects the generation quality. Each grid is highly coupled with neighbors, simply flattening (say, along x-y-z axes) may cause 'ambiguity', leading to sub-optimal generation quality." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 366, + 277, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 277, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 277, + 380 + ], + "type": "text", + "content": "3.2. Improved Discrete Representation Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": "One possible solution to solve the first limitation is applying vector quantization in spatial grids instead of volumetric grids inspired by [3]. Specifically, after obtaining point cloud features " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "f^p \\in \\mathbb{R}^{n \\times c}" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": ", we first project points onto three axis-aligned orthogonal planes. Features of points falling into the same plane grid are aggregated via summation, resulting in three feature maps for the three planes " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\{f^{xy}, f^{yz}, f^{xz}\\} \\in \\mathbb{R}^{l \\times w \\times c}" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": ". Next, the vector quantization is applied to the three planes separately. The primary advantage of tri-planar representation is efficient and compact. It can dramatically reduce the number of grids from " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(r^3)" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(r^2)" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " while preserving essential 3D information. However, it still suffers from the ambiguity of order, or worse, since it involves the flattening order of three planes and the order of entries of each plane." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 564, + 287, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 287, + 637 + ], + "type": "text", + "content": "To this end, we further introduce a projection by learning a higher latent space for features of the three planes. This is simply achieved by first concatenating three planes with arbitrary order and then feeding them into a coupling network. Finally, the output is flattened as a projected latent vector, formulated as," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 82, + 647, + 287, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 647, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 82, + 647, + 287, + 662 + ], + "type": "interline_equation", + "content": "f = \\tau \\left(\\mathcal {G} \\left([ f ^ {x y}; f ^ {y z}; f ^ {x z} ]; \\theta)\\right) \\in \\mathbb {R} ^ {m \\times d} \\right. \\tag {2}", + "image_path": "e5e665791dbc0e2d8ac18129ecab16e71bca04deb12cdffd75062073f7fd7794.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "[\\cdot ;\\cdot ]" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " denotes the concatenation operation; " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\cdot ;\\theta)" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " is a series of convolution layers with parameters " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\tau (\\cdot)" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " means the operation of flatten with row-major order; " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " indicate the length of latent vector and feature dimension. By" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 311, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 545, + 346 + ], + "type": "text", + "content": "applying discrete representation learning in the latent vector, we can describe each 3D shape with " + }, + { + "bbox": [ + 304, + 311, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathcal{Q}(f)" + }, + { + "bbox": [ + 304, + 311, + 545, + 346 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 311, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}(\\cdot)" + }, + { + "bbox": [ + 304, + 311, + 545, + 346 + ], + "type": "text", + "content": " represents vector quantization in Eq. 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 347, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 546, + 491 + ], + "type": "text", + "content": "Remark. Different from existing works [23, 45] that rely on structure design and training strategies in second stage to address the problem of ambiguous order, we tackle it by learning the coupling relationship of spatial grids in the first stage with the help of the second projection. By stacking convolution layers, we increase the receptive field of each element in the latent vector. Additionally, since the features of each spatial grid on the three planes are fused and highly encoded, each element does not have a definite position mapping in 3D space, which results in a tractable order for auto-regression. More in-depth discussions can be found in Sec. 4.6 and the supplementary materials." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "text", + "content": "Training Objective. We optimize parameters with reconstruction loss. After getting discrete representation " + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "text", + "content": " which represents indices of entries in the codebook, we retrieve the corresponding codes with indices, denoted as " + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{(\\mathbf{z})}" + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "text", + "content": ". Subsequently, a decoder with symmetric structures of the encoder are designed to decode " + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{(\\mathbf{z})}" + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "text", + "content": " back to features of the three planes *. Given sampling points " + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "inline_equation", + "content": "x\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "text", + "content": ", we query their features by projecting them onto each of the three feature planes and performing bilinear interpolation. Features from three planes are accumulated and fed into an implicit function to predict their occupancy values. Finally, we apply binary cross-entropy loss between the predicted values " + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "inline_equation", + "content": "y_{o}" + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "text", + "content": " and the ground-truth ones " + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\tilde{y_o}" + }, + { + "bbox": [ + 304, + 491, + 547, + 647 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 318, + 654, + 545, + 667 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 654, + 545, + 667 + ], + "spans": [ + { + "bbox": [ + 318, + 654, + 545, + 667 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {o c c} = - \\left(\\tilde {y _ {o}} \\cdot \\log \\left(y _ {o}\\right) + \\left(1 - \\tilde {y _ {o}}\\right) \\cdot \\log \\left(1 - y _ {o}\\right)\\right) \\tag {3}", + "image_path": "d313201521bc4c33f8b76e5c8ecabc8b92768c815f6f233388dbbfedf6c1f9cc.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 674, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 674, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 317, + 674, + 545, + 687 + ], + "type": "text", + "content": "To further train the codebook, we encourage pulling the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "*For more details about the first stage architecture, please refer to the Supplementary." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14142" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "distance between features before and after the vector quantization. Thus, the codebook loss is derived as," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 63, + 103, + 287, + 119 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 103, + 287, + 119 + ], + "spans": [ + { + "bbox": [ + 63, + 103, + 287, + 119 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o d e}} = \\beta | | \\operatorname {s g} [ f ] - \\mathbf {q} _ {(\\mathbf {z})} | | _ {2} ^ {2} + | | f - \\operatorname {s g} [ \\mathbf {q} _ {(\\mathbf {z})} ] | | _ {2} ^ {2} \\tag {4}", + "image_path": "bbf28d06d354395b506443dc73d484f9d085348e8427287fa449601637b4afff.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 125, + 287, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 125, + 287, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 125, + 287, + 162 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 125, + 287, + 162 + ], + "type": "inline_equation", + "content": "\\mathrm{sg}[\\cdot ]" + }, + { + "bbox": [ + 47, + 125, + 287, + 162 + ], + "type": "text", + "content": " denotes the stop-gradient operation [38] and we set " + }, + { + "bbox": [ + 47, + 125, + 287, + 162 + ], + "type": "inline_equation", + "content": "\\beta = 0.4" + }, + { + "bbox": [ + 47, + 125, + 287, + 162 + ], + "type": "text", + "content": " by default. In sum, the overall loss for the first stage is " + }, + { + "bbox": [ + 47, + 125, + 287, + 162 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec} = \\mathcal{L}_{occ} + \\mathcal{L}_{code}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 167, + 272, + 181 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 167, + 272, + 181 + ], + "spans": [ + { + "bbox": [ + 47, + 167, + 272, + 181 + ], + "type": "text", + "content": "3.3. Learning Priors with Vanilla Transformers" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 186, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 186, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 287, + 258 + ], + "type": "text", + "content": "Benefiting from a compact composition and tractable order of discrete representation, models in the second stage can absorbly learn the correlation between discrete codes, effectively exploring priors of shape composition. We thus adopt a vanilla decoder-only transformer [11] without any specific-designed module." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 258, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 287, + 342 + ], + "type": "text", + "content": "For unconditional generation, given discretized indices of latent vector " + }, + { + "bbox": [ + 47, + 258, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\{\\mathbf{z}_1,\\mathbf{z}_2,\\dots ,\\mathbf{z}_m\\}" + }, + { + "bbox": [ + 47, + 258, + 287, + 342 + ], + "type": "text", + "content": ", we feed them into a learnable embedding layer to retrieve features with discrete indices. Then, the transformer with multi-head self-attention mechanism predicts the next possible index by learning the distribution of previous indices, " + }, + { + "bbox": [ + 47, + 258, + 287, + 342 + ], + "type": "inline_equation", + "content": "p(\\mathbf{z}_i\\mid \\mathbf{z}_{< i})" + }, + { + "bbox": [ + 47, + 258, + 287, + 342 + ], + "type": "text", + "content": ". This gives the joint distribution of full representation as," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 118, + 350, + 287, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 350, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 118, + 350, + 287, + 380 + ], + "type": "interline_equation", + "content": "p (\\mathbf {z}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {z} _ {i} \\mid \\mathbf {z} _ {< i}\\right) \\tag {5}", + "image_path": "c03c071db88085ce271396a9ab84a2872dd40b67fa16a4535f58aba4f44d0b00.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "type": "text", + "content": "For conditional generation, users often expect to control the generation process by providing additional conditions. Instead of designing complex modules or training strategies, we simply learn joint distribution given conditions " + }, + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "type": "text", + "content": " by preponding it to " + }, + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 47, + 388, + 287, + 449 + ], + "type": "text", + "content": ". Equation 5 is thus extended as," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 112, + 455, + 287, + 486 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 455, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 112, + 455, + 287, + 486 + ], + "type": "interline_equation", + "content": "p (\\mathbf {z}) = \\prod_ {i = 1} ^ {m} p \\left(\\mathbf {z} _ {i} \\mid \\mathbf {c}, \\mathbf {z} _ {< i}\\right) \\tag {6}", + "image_path": "9771c15ec6296cdd54ad557d01577fdc21a2475dbc4a021ad6c79dc9e9b2198a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "type": "text", + "content": " denotes a feature vector of given conditions. The simplicity of our model gives the flexibility to learn conditions of any form. Specifically, for 3D conditions such as point clouds, we use our discrete representation learning in Sec. 3.2 to transform them into a vector. As for 2D/1D conditions such as images and classes, we either adopt pretrained models or embedding layers to extract their features. Objective. To train second stage, we minimize negative log-likelihood of Eq. 5 or 6 as " + }, + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{nll} = \\mathbb{E}_{x\\sim p(x)}[-\\log p(\\mathbf{z})]" + }, + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "type": "inline_equation", + "content": "p(x)" + }, + { + "bbox": [ + 47, + 492, + 287, + 612 + ], + "type": "text", + "content": " is the distribution of real data." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "text", + "content": "Inference. With both models trained on two stages, we use Eq. 5 or 6 to perform shape generation by progressively sampling the next index with top-" + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "text", + "content": " sampling strategy, until all elements in " + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "text", + "content": " are completed. Then, we feed " + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{(\\mathbf{z})}" + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "text", + "content": " into the decoder of the first stage, and query probabilities of occupancy values for all sampled 3D positions (e.g., " + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 47, + 612, + 287, + 696 + ], + "type": "text", + "content": "). The output shapes are extracted with Marching Cubes [18]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "text", + "content": "This section starts with comparing results on unconditional 3D shape generation, showing more faithful and diverse shapes synthesized by our approach in Sec. 4.1. Next, we show extensive studies on four generation tasks, demonstrating the powerful and flexible ability of ImAM (in Sec. " + }, + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "inline_equation", + "content": "4.2 \\sim 4.5" + }, + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "text", + "content": "). Lastly, we provide in-depth studies to evaluate the efficacy of our modules and show generalization to real-world data and zero-shot generation (in Sec. 4.6). For all experiments, if necessary, we sample point clouds from output meshes with Poisson Disk Sampling, or reconstruct meshes with our auto-encoder from output points, which is better than Poisson Surface Reconstruction [16]. Please refer to the Supplementary for more details about implementations and qualitative results." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 264, + 482, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 264, + 482, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 264, + 482, + 277 + ], + "type": "text", + "content": "4.1. Unconditional Shape Generation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "text", + "content": "Data. We consider ShapeNet [4] as our main dataset for generation, following previous literature [14, 8, 36]. We use the same training split and evaluation setup from [14] for fair comparability. Five categories of car, chair, plane, rifle and table are used for testing. As ground-truth, we extract mesh from voxelized models with " + }, + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "256^{3}" + }, + { + "bbox": [ + 304, + 282, + 545, + 354 + ], + "type": "text", + "content": " resolution in [13]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 355, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 415 + ], + "type": "text", + "content": "Baselines. We compare ImAM with five state-of-the-art models, including GAN-based IM-GAN[8] and GBIF [14], flow-based PointFlow [46], score-based ShapeGF [2] and diffusion-based PVD [51]. We train these methods on the same data split with the official implementation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 415, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 629 + ], + "type": "text", + "content": "Metrics and Settings. The size of the generated set is 5 times the size of the test set, the same as [8, 14]. As suggested by [8], we use the Light Field Descriptor (LFD) [6] as our primary similarity distance metric between two shapes. Coverage (COV) [1], Minimum Matching Distance (MMD) [1] and Edge Count Difference (ECD) [14] are adopted to evaluate the diversity, fidelity and overall quality of synthesized shapes. We also use 1-Nearest Neighbor Accuracy (1-NNA) [46] (with Chamfer Distance) to measure the distribution similarity. The number of sampled points is 2048. Besides, it is well known that COV does not penalize outliers. To rule out the false positive coverage, we introduce CovT, counting as match between a generation and ground truth shape only if LFD between them is smaller than a threshold " + }, + { + "bbox": [ + 304, + 415, + 545, + 629 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 415, + 545, + 629 + ], + "type": "text", + "content": ". In practice, " + }, + { + "bbox": [ + 304, + 415, + 545, + 629 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 415, + 545, + 629 + ], + "type": "text", + "content": " could vary across different categories based on the scale and complexity of the shape, and we empirically use mean MMD as the threshold and found it effective in identifying correct matches." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Results Analysis. Results are reported in Table 1. First, ImAM achieves state-of-the-art performance with regard to ECD and 1-NNA. It significantly demonstrates the superiority of our model over synthesizing high-quality shapes. We notice that the result of Car is not good on the metric of 1-NNA. One possible reason is that ImAM tries to generate meshes of tires and seats inside cars, which may not" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 246, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 246, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 246, + 713 + ], + "type": "text", + "content": "We reuse the symbol of " + }, + { + "bbox": [ + 58, + 702, + 246, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 58, + 702, + 246, + 713 + ], + "type": "text", + "content": " after embedding for simplicity" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14143" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 283, + 380 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 283, + 380 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 283, + 380 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 283, + 380 + ], + "type": "table", + "html": "
METRICSMETHODSCATEGORIESAvg
PlaneCarChairRifleTable
ECD ↓IM-GAN [8]92331726583714181108
GBIF [14]9452388354195411858
PointFlow [46]23955318426270835592881
ShapeGF [2]12002547443672114915
PVD [51]66617404126534437453904
Ours236842276531240
1-NNA ↓IM-GAN [8]78.1889.3965.8369.3865.3173.62
GBIF [14]80.2287.1963.9566.9860.9671.86
PointFlow [46]73.6174.7570.1864.7774.8171.62
ShapeGF [2]74.7262.8159.1560.6555.5862.58
PVD [51]81.0957.3762.3677.3274.3170.49
Ours59.9576.5857.3157.2854.7661.17
COV ↑IM-GAN [8]77.0165.3776.3873.2185.7175.53
GBIF [14]80.9678.8580.9577.0085.1380.57
PointFlow [46]65.6464.9757.4948.5271.9561.71
ShapeGF [2]76.6471.8579.4170.6787.5477.22
PVD [51]58.0958.6468.9356.1276.8463.72
Ours79.1173.2580.8174.2684.0178.29
CovT ↑IM-GAN [8]41.0350.6345.6851.6846.5047.10
GBIF [14]32.3852.7639.7750.0043.6843.72
PointFlow [46]35.8547.7628.4834.8130.9835.57
ShapeGF [2]40.1753.6343.6951.0548.5047.41
PVD [51]12.1143.3638.8233.3343.6834.26
Ours45.1256.6449.8255.2748.0350.98
MMD ↓IM-GAN [8]341812902881369125052757
GBIF [14]375413333015386525842910
PointFlow [46]367513933322403829363072
ShapeGF [2]353013072880376224202780
PVD [51]437614323064427426233154
Ours312412132703362823742608
", + "image_path": "fbc37d0b927625d443c3e7cf1e888efdf10ec0e4e990c7d179ccd9e4dc500859.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 387, + 287, + 422 + ], + "lines": [ + { + "bbox": [ + 46, + 387, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 287, + 422 + ], + "type": "text", + "content": "Table 1: Results of unconditional generation. Models are trained for each category. The best and second results are highlighted in bold and underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 445, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 601 + ], + "type": "text", + "content": "be very friendly to CD. Second, our model has a clear advantage on both MMD and CovT metrics compared with all competitors, which separately indicates the outstanding fidelity and diversity of our generated shapes. Third, though GBIF achieves relatively good results on COV, it gets worse results on CovT, suggesting that most of the matched samples come from false positive pairs. ImAM, on the contrary, gets second best performance on COV, but higher than GBIF on CovT by about 6 points, showing that our generated shapes enjoy the advantage of high-quality and fewer outliers. Lastly, we visualize shapes with multiple categories in Fig. 4, further supporting the quantitative results and conclusions described above." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 610, + 180, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 180, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 180, + 623 + ], + "type": "text", + "content": "4.2. Class-guide Generation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 628, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 676 + ], + "type": "text", + "content": "We first evaluate the versatility of ImAM on class-guide generation, which requires generating shapes given a category label. It is a basic conditional generation task. We use the same dataset and evaluation metrics as in Sec. 4.1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Baselines. We choose two recently-published works as competitors due to the similar motivation. One is two-stage generative model GBIF [14], the other is AR method Au" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 317, + 73, + 531, + 323 + ], + "blocks": [ + { + "bbox": [ + 317, + 73, + 531, + 323 + ], + "lines": [ + { + "bbox": [ + 317, + 73, + 531, + 323 + ], + "spans": [ + { + "bbox": [ + 317, + 73, + 531, + 323 + ], + "type": "image", + "image_path": "e8fe8a8c142680c92100286d72988159abf437d86cf49623eb36f9a3518bf345.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 331, + 538, + 342 + ], + "lines": [ + { + "bbox": [ + 309, + 331, + 538, + 342 + ], + "spans": [ + { + "bbox": [ + 309, + 331, + 538, + 342 + ], + "type": "text", + "content": "Figure 4: Qualitative results of unconditional generation." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 364, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 364, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 364, + 545, + 399 + ], + "type": "text", + "content": "toSDF [23]. We simply modify mask-condition of [14] to class-condition, and additionally add class token to transformers for [23] which is the same as ImAM." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 400, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 400, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 305, + 400, + 545, + 508 + ], + "type": "text", + "content": "Results Analysis. As shown in Tab. 2, ImAM outperforms both competitors across 5 categories by a significant margin, achieving state-of-the-art results on all metrics. Particularly, it gets advantages on the metric of 1-NNA, strongly demonstrating the versatility of ImAM on class-guide generation. Qualitative results of 5 different categories are further illustrated in Fig. 5. As observed, the generated quality of our method is clearly better than GBIF and AutoSDF, while preserving more diversity in types and shapes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 515, + 507, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 507, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 507, + 529 + ], + "type": "text", + "content": "4.3. Multi-modal Partial Point Completion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 545, + 605 + ], + "type": "text", + "content": "We further verify the ability of our model in conditional generation by giving partial point clouds. Here, we advocate the multi-modal completion, since there are many possibilities of the completed shape given the partial shape. It is the essence of generative model, where being faithful to the given partial conditions but using your imagination." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 606, + 545, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 606, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 305, + 606, + 545, + 666 + ], + "type": "text", + "content": "Data. We use ShapeNet dataset for testing. Two settings are considered here, (1) perspective completion [49]: randomly sampling a viewpoint and then removing the " + }, + { + "bbox": [ + 305, + 606, + 545, + 666 + ], + "type": "inline_equation", + "content": "25\\% \\sim 75\\%" + }, + { + "bbox": [ + 305, + 606, + 545, + 666 + ], + "type": "text", + "content": " furthest points from the viewpoint; (2) bottom-half completion [23]: removing all points from the top half of shapes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "content": "Baselines. Four multi-modal completion models are chosen as baselines, including one generative adversarial model cGAN [42], one diffusion model PVD [51], two AR models ShapeFormer [45] and AutoSDF [23]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14144" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 282, + 238 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 282, + 238 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 282, + 238 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 282, + 238 + ], + "type": "table", + "html": "
METRICSMETHODSCATEGORIESAVG
PlaneCarChairRifleTable
COV ↑GBIF [14]68.7269.6475.9468.9881.7273.00
AutoSDF [23]70.4652.7763.2548.1072.1961.35
Ours81.5871.5883.9875.7485.4879.67
CovT ↑GBIF [14]24.1038.6332.6935.4437.8033.73
AutoSDF [23]30.6640.4931.0034.6036.1034.57
Ours56.4952.7045.0952.7449.3251.27
MMD ↓GBIF [14]473614793220424627633289
AutoSDF [23]370614563249411527443054
Ours319512852871372924302702
ECD ↓GBIF [14]1327275215894348691394
AutoSDF [23]16194256103814434621764
Ours5711889419196285672
1-NNA ↓GBIF [14]91.4792.4375.6183.1270.1982.56
AutoSDF [23]83.3187.7669.3477.4367.2077.01
Ours66.8183.3964.8357.2859.5566.37
", + "image_path": "eeb26343ca684aedfaaa64be571c19ab92007d9543702683593560e9773458ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 245, + 287, + 269 + ], + "lines": [ + { + "bbox": [ + 47, + 245, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 245, + 287, + 269 + ], + "type": "text", + "content": "Table 2: Results of class-guide generation. Models are trained on 13 categories of ShapeNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 55, + 285, + 276, + 495 + ], + "blocks": [ + { + "bbox": [ + 55, + 285, + 276, + 495 + ], + "lines": [ + { + "bbox": [ + 55, + 285, + 276, + 495 + ], + "spans": [ + { + "bbox": [ + 55, + 285, + 276, + 495 + ], + "type": "image", + "image_path": "a61a38d52098f1993df4b8acd904b419a3d866c0ffba072e9e8756a955cb5723.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 506, + 275, + 518 + ], + "lines": [ + { + "bbox": [ + 55, + 506, + 275, + 518 + ], + "spans": [ + { + "bbox": [ + 55, + 506, + 275, + 518 + ], + "type": "text", + "content": "Figure 5: Qualitative results of class-guide generation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": "Metrics and Settings. We complete 10 samples for 100 randomly selected shapes of three categories, i.e., chair, sofa and table. Following [42], we use Total Mutual Difference (TMD) to measure the diversity. Minimum Matching Distance [1] (MMD) with Chamfer Distance and Unidirectional Hausdorff Distance (UHD) [32] are adopted to measure the faithfulness of completed shapes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Results Analysis. We first report perspective completion results in Tab. 3. ImAM beats all baselines and achieves state-of-the-art performance. Importantly, we outperform Shapeformer on all classes and metrics, which also utilizes an AR model with transformers to learn shape distribution. On the other hand, we compare with AutoSDF in its bottom-half completion setting. Results from Tab. 4 illus" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 318, + 71, + 538, + 238 + ], + "blocks": [ + { + "bbox": [ + 318, + 71, + 538, + 238 + ], + "lines": [ + { + "bbox": [ + 318, + 71, + 538, + 238 + ], + "spans": [ + { + "bbox": [ + 318, + 71, + 538, + 238 + ], + "type": "image", + "image_path": "7b682522c61d55531ef344649290b3d9f3276eed5646ae3432b47edd0692b928.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 270, + 543, + 408 + ], + "blocks": [ + { + "bbox": [ + 310, + 247, + 537, + 260 + ], + "lines": [ + { + "bbox": [ + 310, + 247, + 537, + 260 + ], + "spans": [ + { + "bbox": [ + 310, + 247, + 537, + 260 + ], + "type": "text", + "content": "Figure 6: Qualitative results of partial point completion." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 270, + 543, + 408 + ], + "lines": [ + { + "bbox": [ + 307, + 270, + 543, + 408 + ], + "spans": [ + { + "bbox": [ + 307, + 270, + 543, + 408 + ], + "type": "table", + "html": "
METRICSMETHODSCATEGORIESAVG
ChairSofaTable
TMD ↑ (×102)cGAN [42]1.7080.6871.7071.367
PVD [51]1.0980.8110.8390.916
ShapeFormer [45]1.1590.6980.6770.845
Ours2.0421.2211.5381.600
UHD ↓ (×102)cGAN [42]7.8367.0479.4068.096
PVD [51]10.7913.8811.3812.02
ShapeFormer [45]6.8848.6586.6887.410
Ours6.4396.4475.9486.278
MMD ↓ (×103)cGAN [42]1.6651.8131.5961.691
PVD [51]2.3522.0412.1742.189
ShapeFormer [45]1.0551.1001.0661.074
Ours0.9610.8190.8280.869
", + "image_path": "2d11ff8c1db4b6f3173e1b48733a81060ddd20c7fd382c3705d8d556bdc2e243.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 448, + 544, + 531 + ], + "blocks": [ + { + "bbox": [ + 306, + 413, + 545, + 438 + ], + "lines": [ + { + "bbox": [ + 306, + 413, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 545, + 438 + ], + "type": "text", + "content": "Table 3: Results of multi-modal partial point completion. The missing parts vary according to random viewpoints." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 448, + 544, + 531 + ], + "lines": [ + { + "bbox": [ + 307, + 448, + 544, + 531 + ], + "spans": [ + { + "bbox": [ + 307, + 448, + 544, + 531 + ], + "type": "table", + "html": "
METRICSMETHODSCATEGORIESAVG
ChairSofaTable
TMD ↑ (×102)AutoSDF [23]2.0461.6093.1162.257
Ours3.6822.67310.305.552
UHD ↓ (×102)AutoSDF [23]6.7939.9508.1228.289
Ours6.9966.59910.878.155
MMD ↓ (×103)AutoSDF [23]1.5011.1542.6001.751
Ours1.4771.1272.9061.837
", + "image_path": "9e1f3da51915ebe2db377ed4211f9c068114a02562ede2839a0bfa2ead794356.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 536, + 545, + 560 + ], + "lines": [ + { + "bbox": [ + 305, + 536, + 545, + 560 + ], + "spans": [ + { + "bbox": [ + 305, + 536, + 545, + 560 + ], + "type": "text", + "content": "Table 4: Quantitative results of multi-modal partial point completion. The missing parts are always the top half." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 580, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 628 + ], + "type": "text", + "content": "trates that ImAM outperforms AutoSDF in terms of TMD and MMD. It strongly suggests the flexibility and versatility of our proposed method. Qualitative results in Fig. 6 show the diversity and fidelity of our completed shapes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 635, + 443, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 443, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 443, + 647 + ], + "type": "text", + "content": "4.4. Image-guide Generation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Next, we show the flexibility that ImAM can easily extend to image-guide generation, which is a more challenging task. The flexibility lies in that (1) it is implemented by the easiest way of feature concatenation; (2) the condition form of images is various, which could be 1-D feature" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14145" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 291, + 190 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 291, + 190 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 291, + 190 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 291, + 190 + ], + "type": "image", + "image_path": "34964c39f9a254de4b73b53d3a4d81b0e6835e71313c09d1f71286aba8ee5968.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 199, + 282, + 212 + ], + "lines": [ + { + "bbox": [ + 47, + 199, + 282, + 212 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 282, + 212 + ], + "type": "text", + "content": "Figure 7: Visualizations of image-guide shape generation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 227, + 286, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 227, + 286, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 227, + 286, + 275 + ], + "type": "text", + "content": "vector or patch tokens, or 2-D feature maps. For simplicity, we use a pretrained CLIP model (i.e., ViT-B/32) to extract feature vectors of images as conditions. All experiments are conducted on ShapeNet dataset with rendered images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 275, + 286, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 286, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 286, + 335 + ], + "type": "text", + "content": "Baselines. CLIP-Forge [31] is a flow-based model, which is trained with pairs of images and shapes. We take it as our primary baseline for two reasons: (1) it is a generation model instead of reconstruction model, and (2) it originally uses CLIP models to extract image features." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 336, + 286, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 286, + 419 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 286, + 419 + ], + "type": "text", + "content": "Metrics and Settings. We evaluate models with the test split of 13 categories. For each category, we randomly sample 50 single-view images and then generate 5 shapes for evaluation. As a generation task, TMD is adopted to measure the diversity. We further use MMD with Chamfer Distance and Fréchet Point Cloud distance (FPD) [32] to measure the fidelity compared with the ground truth." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 420, + 286, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 286, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 286, + 504 + ], + "type": "text", + "content": "Results Analysis. Results are reported in Tab. 5. ImAM wins out in terms of both fidelity and diversity. In particular, we achieve a great advantage on both TMD and FPD, demonstrating the effectiveness of ImAM applied to image-guide generation. It is also successfully echoed by qualitative visualizations in Fig. 7. Our samples are diverse and appear visually faithful to attributes of the object in images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 514, + 175, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 175, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 175, + 526 + ], + "type": "text", + "content": "4.5. Text-guide Generation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 533, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 286, + 616 + ], + "type": "text", + "content": "Encouraged by promising results on image-guide generation, we also turn ImAM to text-to-shape generation. The same pretrained CLIP model is used to extract single embedding for text conditions. Note that we did it on purpose, not using word sequence embedding, but only using a single features vectors in our model to show its efficacy and scalability to the simplest forms of conditions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 617, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 617, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 617, + 286, + 677 + ], + "type": "text", + "content": "Data. To our knowledge, the only existing largest paired text-shape dataset is Text2Shape [7], which provides language descriptions for two objects from ShapeNet, i.e., chair and table. Thereby, we consider it as our main dataset to perform text-guide shape generation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "Baselines. We compare our model with two state-of-the-arts text-to-shape generation model. One is CLIP-Forge [31] under the supervised learning setting, using the same" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 310, + 70, + 542, + 111 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 542, + 111 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 542, + 111 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 542, + 111 + ], + "type": "table", + "html": "
METHODTMD (×102) ↑MMD (×103) ↓FPD ↓
AutoSDF [23]2.5231.3832.092
Clip-Forge [31]2.8581.9268.094
Ours4.2741.5901.680
", + "image_path": "00d1c7d0518e0d275bc5c972daf4ffdd21b80d1a69d84600a7f267985d8d38de.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 310, + 143, + 539, + 194 + ], + "blocks": [ + { + "bbox": [ + 311, + 120, + 536, + 132 + ], + "lines": [ + { + "bbox": [ + 311, + 120, + 536, + 132 + ], + "spans": [ + { + "bbox": [ + 311, + 120, + 536, + 132 + ], + "type": "text", + "content": "Table 5: Quantitative results of image-guide generation." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 143, + 539, + 194 + ], + "lines": [ + { + "bbox": [ + 310, + 143, + 539, + 194 + ], + "spans": [ + { + "bbox": [ + 310, + 143, + 539, + 194 + ], + "type": "table", + "html": "
METHODTMD (×101) ↑MMD (×103) ↓Acc ↑
ITG [17]N/A2.18729.13
AutoSDF [23]0.3422.16536.95
CLIP-Forge [31]0.4002.13653.68
Ours0.5651.84659.93
", + "image_path": "5926b96a6425950e319dbc8b9a3bed8fcad5152025336a3e24c17bf05a764342.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 311, + 206, + 538, + 247 + ], + "blocks": [ + { + "bbox": [ + 369, + 196, + 481, + 205 + ], + "lines": [ + { + "bbox": [ + 369, + 196, + 481, + 205 + ], + "spans": [ + { + "bbox": [ + 369, + 196, + 481, + 205 + ], + "type": "text", + "content": "(a) Descriptions as text queries" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 311, + 206, + 538, + 247 + ], + "lines": [ + { + "bbox": [ + 311, + 206, + 538, + 247 + ], + "spans": [ + { + "bbox": [ + 311, + 206, + 538, + 247 + ], + "type": "table", + "html": "
METHODTMD (×10^1) ↑FPD ↓Acc. ↑
AutoSDF [23]0.7525.8441.09
CLIP-Forge [31]0.9614.1455.00
Ours1.2465.3960.87
", + "image_path": "594f92b1ffcc0a36aaf437b221d792096aa880560a6f00b35a3c952d0f547ede.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 375, + 249, + 473, + 259 + ], + "lines": [ + { + "bbox": [ + 375, + 249, + 473, + 259 + ], + "spans": [ + { + "bbox": [ + 375, + 249, + 473, + 259 + ], + "type": "text", + "content": "(b) Prompts as text queries" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 315, + 270, + 531, + 281 + ], + "lines": [ + { + "bbox": [ + 315, + 270, + 531, + 281 + ], + "spans": [ + { + "bbox": [ + 315, + 270, + 531, + 281 + ], + "type": "text", + "content": "Table 6: Quantitative results of text-guide generation." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 303, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 303, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 303, + 545, + 327 + ], + "type": "text", + "content": "condition extractor as ours. The other is ITG [17], which adopts BERT to encode texts into sequence embeddings." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 545, + 422 + ], + "type": "text", + "content": "Metrics and Settings. All models are trained on the train split of Text2Shape dataset with their official codes. We evaluate our model with two types of text queries: (1) description: the test split of Text2Shape; (2) prompts: customized short phrases provided by [31] containing attributes for chair and table. We additionally use Accuracy (Acc.) [31] to measure the fidelity. The Accuracy is calculated by a pretrained PointNet [27] classifier on ShapeNet." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 423, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 423, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 305, + 423, + 545, + 471 + ], + "type": "text", + "content": "Results Analysis. We report quantitative results of text-guide generation in Tab. 6. ImAM achieves promising results on TMD, MMD and Acc, showing good generalization performance across different conditional generation tasks." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 479, + 399, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 399, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 399, + 491 + ], + "type": "text", + "content": "4.6. Ablation Study" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "Lastly, we provide in-depth studies to dissect the efficacy of our ImAM framework, and several proposed designs. More discussions are provided in the Supplementary. Design Choices in Discrete Representation Learning. As a key contribution of this paper, we first discuss the efficacy of our improved discrete representation learning. We use 'Vector' to denote our design since we apply vector quantization to latent vector. Similarly, 'Grid' and 'Tri-Plane' refer to baselines applying vector quantization to volumetric grids and the three planes, respectively. Results in Tab. 7 show that 'Grid' gets better IoU performance for shape reconstruction in the first stage, but fails to train transformers in the second stage due to extreme long length of sequence (e.g., " + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "32^{3}" + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "). In contrast, our model not only achieves comparable reconstruction results (#0 vs. #2), but also outperforms 'Tri-Plane' by a large margin on generation quality (#1 vs. #2). The latter shows inferior results due to 'ambiguity of order' (see Suppl.) It significantly proves the efficacy" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14146" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 76, + 273, + 223 + ], + "blocks": [ + { + "bbox": [ + 58, + 76, + 273, + 223 + ], + "lines": [ + { + "bbox": [ + 58, + 76, + 273, + 223 + ], + "spans": [ + { + "bbox": [ + 58, + 76, + 273, + 223 + ], + "type": "image", + "image_path": "9670b3336bc498e8e837c56f0b5ddfae63ba519b7d92516f6181efee997d2da6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 236, + 287, + 261 + ], + "lines": [ + { + "bbox": [ + 47, + 236, + 287, + 261 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 287, + 261 + ], + "type": "text", + "content": "Figure 8: Results of real-world image-guide generation. Images are randomly selected from internet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 276, + 284, + 390 + ], + "blocks": [ + { + "bbox": [ + 53, + 276, + 284, + 390 + ], + "lines": [ + { + "bbox": [ + 53, + 276, + 284, + 390 + ], + "spans": [ + { + "bbox": [ + 53, + 276, + 284, + 390 + ], + "type": "image", + "image_path": "f4dad909d059737be79a5733495fba226513f28d2ff3df3d7cd56949f07e26cd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 399, + 286, + 422 + ], + "lines": [ + { + "bbox": [ + 47, + 399, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 286, + 422 + ], + "type": "text", + "content": "Figure 9: Results of real-world image-guide generation. Samples are from Pix3D dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 448, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 286, + 664 + ], + "type": "text", + "content": "of our proposed coupling network, improving the plasticity and flexibility of the model. We also explore different design choices in Tab. 7. By gradually increasing feature resolutions or the number of entries in the codebook, we achieve better performance on IoU. This observation is consistent with [48], as the capacity of the discrete representation is affected by these two factors. We do not try larger parameters, as it would significantly increase the computation cost. Image-guide Generation in Real-world. We further investigate the generalizability of our model on real-world images. We use the model trained on ShapeNet as described in Sec. 4.4, and download images from internet as conditions. Figure 8 shows the qualitative results for three categories, i.e., plane, chair and table. Our model sensitively capture major attributes of objects in the image and produce shapes faithful to them (see the first column to the left). Meanwhile, our synthesized samples enjoy the advantage of diversity by partially sticking to the images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 714 + ], + "type": "text", + "content": "Figure 9 also show results of our model on Pix3D dataset (trained on ShapeNet, without any finetuning). Compared with other competitors, ImAM is capable of generating high-quality and realistic shapes that highly match the shape" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 315, + 75, + 536, + 167 + ], + "blocks": [ + { + "bbox": [ + 315, + 75, + 536, + 167 + ], + "lines": [ + { + "bbox": [ + 315, + 75, + 536, + 167 + ], + "spans": [ + { + "bbox": [ + 315, + 75, + 536, + 167 + ], + "type": "image", + "image_path": "0511ae68d408f31568a4a17eb6041682c58a538ce102690902fdb5f0d318d166.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 176, + 538, + 188 + ], + "lines": [ + { + "bbox": [ + 309, + 176, + 538, + 188 + ], + "spans": [ + { + "bbox": [ + 309, + 176, + 538, + 188 + ], + "type": "text", + "content": "Figure 10: Results of zero-shot text-to-shape generation." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 205, + 544, + 285 + ], + "blocks": [ + { + "bbox": [ + 307, + 205, + 544, + 285 + ], + "lines": [ + { + "bbox": [ + 307, + 205, + 544, + 285 + ], + "spans": [ + { + "bbox": [ + 307, + 205, + 544, + 285 + ], + "type": "table", + "html": "
Num.TYPE#ENTRYRESO.STAGE 1STAGE 2
IoU ↑1-NNA / ECD ↓
0Grid40963288.87×
1Tri-Plane87.8173.67 / 743
2Vector88.0159.95 / 236
340961679.17-
420483286.99
5102486.57
", + "image_path": "c3d5a089355fd1c12185605b9af5b5f2dd976ac5d0dbf77239352195cd66ffae.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 294, + 545, + 366 + ], + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 366 + ], + "type": "text", + "content": "Table 7: Ablation study of auto-encoder design choices. We report 1-NNA/ECD for plane category. 'RESO.' means the resolution of feature map for vector quantization. '×': cannot report due to extreme memory cost. '-': not report. Notably, without the coupling network, our method naturally degenerates into 'Tri-Plane' representation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 379, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 379, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 545, + 403 + ], + "type": "text", + "content": "of objects in real-world images. It significantly highlights the strong generalization ability of our method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 405, + 545, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 545, + 489 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 545, + 489 + ], + "type": "text", + "content": "Zero-shot Text-to-shape Generation. Inspired by CLIP-Forge [31], we utilize the CLIP model to achieve zero-shot text-to-shape generation. At training, we only use the rendered images of 3D shapes. At inference, we substitute image features with text features encoded by the CLIP model. Figure 10 shows our ability of zero-shot generation, where shape attributes are controlled with different prompts." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 508, + 378, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 378, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 378, + 521 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 531, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 651 + ], + "type": "text", + "content": "We introduce an improved AR model for 3D shape generation. By projecting volumetric grids of encoded input shapes onto three axis-aligned orthogonal feature planes, which are then coupled into a latent vector, we reduce computational costs and create a more tractable order for AR learning. Our compact and tractable representations enable easy switching between unconditional and conditional generation with multi-modal conditioning inputs. Extensive experiments show that our model outperforms previous methods on multiple generation tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work is supported by China Postdoctoral Science Foundation (2022M710746). Yanwei Fu is with the School of Data Science, Fudan University, and Fudan ISTBI—ZJNU Algorithm Centre for Brain-inspired Intelligence, Zhejiang Normal University, Jinhua, China." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14147" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5826–5835, 2021. 5, 6, 7" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "14149" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Vision-and-Language Navigation from YouTube Videos/05335e36-6140-429d-8434-dd018538220c_content_list.json b/2023/Learning Vision-and-Language Navigation from YouTube Videos/05335e36-6140-429d-8434-dd018538220c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..36ef1ce44dcda0f703b1a1ec99b573f62417f2a3 --- /dev/null +++ b/2023/Learning Vision-and-Language Navigation from YouTube Videos/05335e36-6140-429d-8434-dd018538220c_content_list.json @@ -0,0 +1,1454 @@ +[ + { + "type": "text", + "text": "Learning Vision-and-Language Navigation from YouTube Videos", + "text_level": 1, + "bbox": [ + 156, + 161, + 813, + 181 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kunyang Lin $^{1,2*}$ Peihao Chen $^{1*}$ Diwei Huang $^{1}$ Thomas H. Li $^{6}$ Mingkui Tan $^{15\\dagger}$ Chuang Gan $^{34}$", + "bbox": [ + 95, + 206, + 870, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ South China University of Technology, $^{2}$ Information Technology R&D Innovation Center of Peking University, $^{3}$ UMass Amherst, $^{4}$ MIT-IBM Watson AI Lab, $^{5}$ Key Laboratory of Big Data and Intelligent Robot, Ministry of Education, $^{6}$ Peking University Shenzhen Graduate School", + "bbox": [ + 124, + 225, + 843, + 271 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 312, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision-and-language navigation (VLN) requires an embodied agent to navigate in realistic 3D environments using natural language instructions. Existing VLN methods suffer from training on small-scale environments or unreasonable path-instruction datasets, limiting the generalization to unseen environments. There are massive house tour videos on YouTube, providing abundant real navigation experiences and layout information. However, these videos have not been explored for VLN before. In this paper, we propose to learn an agent from these videos by creating a large-scale dataset which comprises reasonable path-instruction pairs from house tour videos and pre-training the agent on it. To achieve this, we have to tackle the challenges of automatically constructing path-instruction pairs and exploiting real layout knowledge from raw and unlabeled videos. To address these, we first leverage an entropy-based method to construct the nodes of a path trajectory. Then, we propose an action-aware generator for generating instructions from unlabeled trajectories. Last, we devise a trajectory judgment pretext task to encourage the agent to mine the layout knowledge. Experimental results show that our method achieves state-of-the-art performance on two popular benchmarks (R2R and REVERIE). Code is available at https://github.com/JeremyLinky/YouTube-VLN", + "bbox": [ + 75, + 334, + 472, + 665 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 669, + 208, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "An important goal of embodied artificial intelligence is to develop agents that can interact with humans in natural language to carry out real-world tasks. Toward this goal, vision-and-language navigation (VLN) [1] is a rudimentary artificial intelligence task, requiring an indoor agent to navigate in unseen environments following natural instructions. VLN has attracted widespread attention in the fields of computer vision and robotics due to its promising applications such as in-home robots [54] and warehouse assistants [29].", + "bbox": [ + 75, + 693, + 468, + 818 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One of the key challenges of VLN is the generaliza", + "bbox": [ + 95, + 818, + 468, + 832 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion ability of agents to unseen environments. Existing VLN methods attempt to cope with this challenge via self-supervised pre-training on vision-and-language datasets. As shown in Figure 1 (a), some previous works [30, 19, 36, 7] learn the agents on simulated navigation environments and manual-labeled data. The other works [14, 13, 42] seek to construct path-instruction pairs by using web image data, which is shown in Figure 1 (b). Despite their promising performance, existing agents still suffer from the following limitations. 1) Training on simulated datasets is limited to a restricted number of environments. 2) Constructing a trajectory by simply concatenating web images leads to unreasonable room layouts, which hamper the agent to learn layout reasoning ability. As a result, VLN agents trained on such data are brittle to adapt to unseen environments.", + "bbox": [ + 499, + 305, + 890, + 511 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fortunately, there are massive house tour videos on YouTube, providing real navigation experiences and layout information but are still under-explored. We can be naturally inspired to let an agent learn VLN ability from such videos, thereby addressing the limitations of existing methods. An intuitive way is to model the navigation experiences as path-instruction pairs to train the agent. Motivated by this, we propose a \"Lily\" agent who Learns Vision-and-Language Navigation from YouTube Videos. Specifically, we first develop an in-domain pre-training dataset from house tour YouTube videos, namely YouTube-VLN, which comprises VLN-like path-instruction pairs. Our YouTube-VLN dataset has the advantages of diverse environments, real layouts, and native actions1, reducing the domain gap with VLN datasets, as illustrated in Figure 1 (c). Then, we pre-train the agent using these path-instruction pairs. Benefiting from in-domain pre-training on our proposed dataset, our agent thus generalizes well to unseen environments.", + "bbox": [ + 497, + 513, + 892, + 761 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Constructing and utilizing such a dataset, however, is still far from trivial work and remains an open problem due to the following challenges. 1) As the nodes in a trajectory are expected to be diverse and informative, it is hard to determine the locations of trajectory nodes from massive video frames and represent the visual content in a node.", + "bbox": [ + 497, + 761, + 890, + 844 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 127, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 253, + 48, + 789, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. Email: {imkunyanglin, phchencs}@gmail.com", + "bbox": [ + 92, + 842, + 457, + 853 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author. Email: mingkuitan@scut.edu.cn", + "bbox": [ + 92, + 853, + 394, + 865 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1The execution actions that objectively exist", + "bbox": [ + 517, + 853, + 754, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8317", + "bbox": [ + 468, + 885, + 500, + 897 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c11408a7f201d573b27741475014fc7813798c4515551140b0e4d5c204daa5bd.jpg", + "image_caption": [ + "(a) Dataset from Simulation Environments" + ], + "image_footnote": [], + "bbox": [ + 80, + 124, + 344, + 244 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c14b03dc69edf64fb69b545e50b9f1d311fab96dfe8bd8402545f487db3fa0c1.jpg", + "image_caption": [ + "(b) Dataset from Web Images Data", + "Figure 1: Comparison of different datasets for pre-training. Existing datasets are built from either simulation environments (a) or web images data (b). The former only covers limited environments, and the latter contains confusing layouts and ambiguous actions. Our dataset built from YouTube videos (c) is able to provide diverse environments, real layouts and native actions simultaneously." + ], + "image_footnote": [], + "bbox": [ + 351, + 124, + 616, + 247 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3a261921a590a6f671e0f8db494f0c3f1e28b5fac03bcf9828da0e6c1f7c3cd2.jpg", + "image_caption": [ + "(c) Dataset from YouTube Videos (Ours)" + ], + "image_footnote": [], + "bbox": [ + 620, + 124, + 889, + 247 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2) Real VLN instructions include various action descriptions, but obtaining corresponding instructions from navigation clips is challenging due to the actions being implicit in videos. Thus it is nontrivial to acquire matching instruction on a trajectory. 3) Layout knowledge from real navigation experience is hard to mine and model, which impedes the agent of learning layout reasoning ability.", + "bbox": [ + 75, + 350, + 468, + 447 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we address the above challenges as follows. To conquer challenge 1), we propose an entropy-based trajectory generation method. Specifically, we first envisage that the nodes of a trajectory should contain as many types of rooms as possible to diversify trajectories. Accordingly, we group the frames with the same room types in videos and consider each group as a node in the trajectory. Then, inspired by that low classification entropy image is reliable and contains rich information relevant to a specific class (room type in our case) [39], the frame with the lowest classification entropy in a group is chosen to represent the visual content in a node. To tackle challenge 2), we introduce an action-aware instruction generation method. Specifically, we adopt an action inverse model to pseudo-label the action along trajectories and fill them in the instructions via hand-designed rules. To grapple with challenge 3), we devise a self-supervised pretext task. As we all know, humans often judge whether a navigation trajectory is reasonable based on the layout of the environment. Therefore, it is believed that an agent equipped with layout reasoning ability should be able to make similar judgment. To this end, we propose trajectory judgment pretext task to ask the agent to identify reasonable navigation trajectories, which further equips the model with the ability to reason environment layouts.", + "bbox": [ + 75, + 448, + 468, + 781 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We empirically show that the diverse entropy-based trajectory generation method and action-aware instruction generator allow us to harvest high-quality path-instruction pairs from YouTube house tour videos, resulting in the YouTube-VLN dataset. By integrating the self-supervised trajectory judgment task in pre-training a VLN agent, our", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Lily agent presents state-of-the-art performance on two mature and solid benchmarks (R2R [1], REVERIE [41]). The proposed Lily agent reaches the first place on the R2R leaderboard in terms of success rate and outperforms the SOTA method under discriminative setting and generative setting by $2\\%$ and $3\\%$ w.r.t. success rate, respectively.", + "bbox": [ + 497, + 350, + 890, + 433 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are as follows:", + "bbox": [ + 517, + 434, + 773, + 446 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We unleash the huge potential of house tour videos for VLN. By leveraging these videos, we introduce a largescale dataset containing real navigation path-instruction pairs for promoting VLN pre-training and a self-supervised pretext task for the learning of layout reasoning.", + "- Our diverse trajectory generation method, together with the action-aware instruction generator, creates informative and diverse trajectory nodes and produces matching instructions, both of which make the path-instruction pairs authentic and of high quality for training a VLN agent.", + "- The proposed trajectory judgment pretext task allows the model to build up an awareness of learning and reasoning the layout knowledge, which is crucial in the VLN task of indoor environments. We also empirically substantiate that the agent indeed learns the layout learning ability." + ], + "bbox": [ + 497, + 448, + 890, + 656 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 669, + 638, + 682 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Vision-and-Language Navigation", + "text_level": 1, + "bbox": [ + 499, + 692, + 786, + 707 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-and-Language Navigation (VLN) [1] is a challenging task and has received continuous and intense attention from the academic community in recent years [4, 12, 25, 31, 46, 27, 6, 45, 9]. Early methods attempt to learn the agent from sequence-to-sequence models [1, 10, 47]. However, these methods can not model the cross-modal relation between language and visual observation well. To address this issue, transformer [48] architecture is adopted to the agents followed by vision-and-language pre-training [35, 50, 57, 37, 13, 42, 5, 38, 24]. PREVALENT [15] pretrains transformer-based agent via masked language mod", + "bbox": [ + 497, + 713, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8318", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "eling and action prediction tasks. Inspired by BERT [8], several works propose to use different variants of BERT for VLN pre-training. VLN-BERT [37] utilizes image-text data [34] to perform path-instruction matching pretext task. Airbert [13] proposes the shuffle loss to improve the ability of the model to learn the order of image-caption pairs. Recently, HOP [42] introduces the history and order-aware pretext tasks. However, these existing pretext tasks do not consider the learning of environment layout reasoning ability and bring limited performance for VLN tasks. In this work, we propose a trajectory judgment task to teach the agent to distinguish reasonable navigation trajectories. By proficiently accomplishing this task, the agent can acquire the ability to reason about environment layout, which enhances its generalization capability to unseen environments.", + "bbox": [ + 75, + 125, + 472, + 333 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Datasets for VLN", + "text_level": 1, + "bbox": [ + 77, + 351, + 248, + 365 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The major difficulty of generalizing a VLN agent to unseen environments is the scarcity of VLN training data. Well-labeled VLN datasets built from the simulators [2, 44, 52] allow the agent to obtain a promising performance, such as R2R [1], R4R [20], RxR [23] and SOON [56]. While the data built from simulators are laborious, Wang et al. [49] and ProbES [30] enrich the navigation instructions via self-exploration in the simulation environments. Some other endeavors [47, 28, 10, 11, 22, 26] seek to augment the data from existing datasets. AutoVLN [7] and Kamath et al. [21] enlarges the VLN data from simulations with a larger number of environments. However, these datasets are limited by the number of scenes in simulators. To ease this problem, VLN-BERT [37] leverages the abundant web image-captions pairs as VLN pre-training data. Airbert [13] further exploits indoor house images and captions from the web to construct path-instruction pairs for VLN pre-training. However, the trajectories constructed by simply splicing pictures may be confusing and ambiguous. In our work, we address these problems by proposing a large-scale in-domain VLN-like pre-training dataset, providing the agent with diverse visual environments and reasonable layouts.", + "bbox": [ + 75, + 375, + 472, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Building VLN Dataset from YouTube Videos", + "text_level": 1, + "bbox": [ + 77, + 701, + 468, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our first step is to develop a large-scale VLN-like dataset that comprises reasonable path-instruction pairs from house tour videos on YouTube, termed YouTube-VLN. YouTube-VLN serves as a cornerstone for facilitating the acquisition of VLN capabilities for Lily, featuring diverse environments, real layouts and native actions. To achieve this goal, we present an entropy-based trajectory generation technique (Section 3.1) and an action-aware generator (Section 3.2) to tackle the arduous tasks of trajectory and instruction generation, respectively.", + "bbox": [ + 75, + 728, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4e676be56851763f7094e83440bfc2926fb1af94666b7c64d1ed83b413a8866e.jpg", + "image_caption": [ + "Figure 2: An example of a generated trajectory from a YouTube house tour video. $\\rightarrow$ represents the direction to go next while $\\rightarrow$ represents the stop action." + ], + "image_footnote": [], + "bbox": [ + 509, + 127, + 884, + 305 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Diverse Trajectory Generation.", + "text_level": 1, + "bbox": [ + 499, + 380, + 774, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We seek to construct discrete navigation trajectories from YouTube videos. Similar to discrete navigation datasets (e.g., R2R [1]), each trajectory comprises $K$ navigation nodes, representing different locations of a navigation path. This entails addressing two major challenges: 1) how to determine the locations composing a trajectory to make the trajectory more diverse and 2) how to represent the visual content at each node location. To tackle these challenges, we first collect large-scale consecutive indoor frames from YouTube videos. Then, we group the adjacent frames according to their room types and consider each group as a node. Last, we present an entropy-based technique to select the most informative frames in a group for representing the visual content in a node.", + "bbox": [ + 497, + 404, + 892, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Collecting Navigation Data from YouTube. Real estate agents typically tour a house in each video. To satisfy the visual diversity and dataset scale, we create the YouTube-VLN dataset from 4078 videos collected from various uploaders, with a total duration of 433 hours. In contrast to prior work [3], which relied on a limited set of videos from a single uploader, our dataset features greater diversity and volume. We also employ sparse sampling and off-the-shelf image classifiers [16, 43] to pre-process the videos, filtering out redundant or noisy frames (those featuring people or outdoor scenes), resulting in a final set of 587k indoor frames suitable for constructing trajectories.", + "bbox": [ + 497, + 600, + 894, + 767 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Determining the Locations of Trajectory Nodes. A real robot often needs to go through different locations for navigating to a goal. To mimic the real navigation process, we expect that our constructed trajectories also contain diverse visual content within the limited navigation nodes. To achieve this, we first utilize the powerful large model CLIP [43] to recognize the room type of each indoor im", + "bbox": [ + 497, + 769, + 894, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8319", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "age. Then, we gather temporally adjacent frames with the same room type as a group and consider this group as one of the navigation nodes. In this sense, the navigation nodes are diversely spread in different rooms and the constructed trajectories are able to mimic the real navigation process. We also call this kind of node a room node. In practice, to increase the visual diversity of trajectories, we also randomly insert transition nodes that are composed of video frames captured during the transition from one room to another one, between two adjacent room nodes.", + "bbox": [ + 75, + 125, + 472, + 264 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Representing Visual Content in a Node. A node consists of a group of images and sometimes the number of images may exceed 100 as the photographer could stay in the same room for a long time. Hence, we have to select the most informative images for representing node features. Inspired by EATA [39], an image with lower classification entropy is more reliable, containing more information relevant to a specific class (room type in our case). We thus propose to select an image with the lowest classification entropy to represent the current view of a node. In order to mimic the panoramic visual context, we then merge $M$ adjacent consecutive images of the current view. It is worth noting that our node features better represent a panoramic view compared with Airbert [13] because we merge adjacent frames that belong to the same place as the current view.", + "bbox": [ + 75, + 264, + 472, + 471 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ultimately, we randomly chose $K$ continuous nodes to construct a trajectory. An example of the constructed trajectory is shown in Figure 2.", + "bbox": [ + 75, + 473, + 470, + 514 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Action-Aware Instruction Generation", + "text_level": 1, + "bbox": [ + 75, + 524, + 401, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition to constructing navigation trajectories, one more important step for building a VLN dataset is to create the corresponding instructions without manual annotation. The main challenge for this step is how to correctly describe visual content and actions along navigation paths. To conquer this challenge, we first generate instruction templates with verb and noun phrase blanks. Then, we describe each node in trajectories using the CLIP [43] model and infer the native actions using an action inverse model [3]. To generate the final instructions, we fill the instruction templates with these visual descriptions and actions.", + "bbox": [ + 75, + 548, + 468, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we first generate templates with verb and noun blanks from instructions in the R2R dataset following Airbert [13]. For noun blanks, we fill them with visual content descriptions about each node. We select the frame with the lowest classification entropy (as described in Sec. 3.1) and use the CLIP model to infer the objects it contains, together with the room type to populate a noun blank. For verb blanks, the existing instruction generation method [13] is unable to fill them with the correct action words because it cannot figure out the actions taken for navigating from one image to another. This makes the agent confused when it observes similar viewpoints transition but is given differ", + "bbox": [ + 75, + 700, + 472, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ent action descriptions. To tackle this problem, we propose an action-aware strategy to fill instruction templates with native actions instead of random inconsistent actions. To be specific, we follow [3] to train an action inverse model, which has $96\\%$ prediction accuracy for predicting native actions, to pseudo-label the trajectory with action labels from one location node to another. The predicted actions are then converted into actionable verbs, i.e., \"go forward\", \"turn left\" and \"turn right\". For each noun blank that has been filled with the description of one node, we find its closest verb phrase blank and fill it with the pseudo-labeled action which is executed to reach the next node. This eventually enables us to create action-aware instructions.", + "bbox": [ + 497, + 125, + 894, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Learning VLN from YouTube Videos", + "text_level": 1, + "bbox": [ + 497, + 319, + 835, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the VLN-like and reasonable path-instruction pairs generated from YouTube videos, we then describe how to learn the Lily agent from these data. As shown in Figure 3, our VLN model consists of two components: a vision-and-language backbone (i.e., Multi-Layer Transformer) that models the relationship between trajectories and instructions and a decision-making module that predicts the next action or a matching score for a path-instruction pair. The vision-and-language backbone can be any type of cross-modal network. We chose ViLBERT [34] for a fair comparison with Airbert [13]. As a common practice, pretext tasks are utilized for pre-training the backbone. We next describe how to pre-train the backbone on our Youtube-VLN dataset using the proposed trajectory judgment pretext task.", + "bbox": [ + 497, + 342, + 894, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Model Architecture", + "text_level": 1, + "bbox": [ + 497, + 560, + 689, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We follow Airbert [13] to leverage a ViLBERT-like [34] architecture as the model backbone. The model encodes the sequential visual region features and the text token via two separate transformers respectively. More formally, the path-instruction pair consists of $K$ nodes $\\{V_k\\}_{k=1}^K$ and $L$ text tokens $\\{w_l\\}_{l=1}^L$ . Each node $V_k$ is composed of $R_k$ visual region features $\\{v_i^k\\}_{i=1}^{R_k}$ . In this way, we represent the visual and text inputs respectively as follows:", + "bbox": [ + 497, + 580, + 892, + 694 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} X _ {V} = \\left[ \\left[ \\operatorname {I M G} \\right], v _ {1} ^ {1}, \\dots , v _ {R _ {1}} ^ {1}, \\dots , \\left[ \\operatorname {I M G} \\right], v _ {1} ^ {K}, \\dots , v _ {R _ {K}} ^ {K} \\right], (1) \\\\ X _ {W} = \\left[ \\left[ \\mathrm {C L S} \\right], w _ {1}, \\dots , w _ {l}, \\dots , w _ {L}, [ \\mathrm {S E P} ] \\right], (2) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 701, + 890, + 745 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where [IMG], [CLS] and [SEP] are special tokens. The encoded visual and text tokens finally interact via a cross-modal transformer encoder. We represent the whole model architecture as \"Multi-Layer Transformer\" in Figure 3.", + "bbox": [ + 497, + 751, + 892, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Learning Layout from Trajectory Judgment", + "text_level": 1, + "bbox": [ + 497, + 815, + 875, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the aforementioned model architecture, we propose to train a VLN agent with a trajectory judgment (TJ)", + "bbox": [ + 497, + 838, + 892, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8320", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/54d51f805e433c01781504cc9c06a427e91f68b33992d33b124ac957f7ca679e.jpg", + "image_caption": [ + "Figure 3: General scheme of our Lily agent for pre-training and downstream stages of VLN tasks. Lily agent learns to leverage the proposed YouTube-VLN dataset for the trajectory judgment task together with the other pretext tasks. After pre-training the VLN model, we adapt it to the downstream datasets and conduct different VLN downstream tasks." + ], + "image_footnote": [], + "bbox": [ + 77, + 122, + 894, + 308 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "task, enabling it to reason about layouts. Herein, we elaborate on the proposed trajectory judgment task.", + "bbox": [ + 75, + 382, + 468, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "**Formulation.** The trajectory judgment task aims to judge the reasonableness of trajectories. We consider the trajectories generated in the way described in Section 3.1 as positive (reasonable) samples and the shuffled trajectories as negative (unreasonable) ones. To finish this task, the agent is required to reason about the visual information and identify the room types, then infer whether the trajectory matches the real environment layout distribution. Specifically, we first calculate the dot product of the output features of [IMG] and [CLS] tokens. Then, we feed this vector feature to a linear layer to predict the probability that indicates whether the trajectory is reasonable. The model aims to minimize the binary cross-entropy loss:", + "bbox": [ + 75, + 410, + 468, + 589 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\left[ w \\cdot y _ {n} \\log (p _ {n}) + (1 - y _ {n}) \\log (1 - p _ {n}) \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 90, + 596, + 468, + 629 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y_{n} = 1$ if the $n^{th}$ trajectory is reasonable, otherwise $y_{n} = 0$ . $p_{n}$ represents the probability that the $n^{th}$ trajectory is predicted as reasonable. $N$ is the number of trajectories in a batch. $w$ is a factor to mitigate the imbalance of positive and negative samples, which equals the ratio of the number of negative samples to the number of positive samples.", + "bbox": [ + 75, + 630, + 468, + 713 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sample Generation. We propose to shuffle the positive sample to generate the negative samples: 1) shuffle only the transition nodes; 2) shuffle all the nodes; 3) keep the order of the room nodes, and randomly insert nodes from other videos. In this way, we create rich and hard negative samples, which increases the task difficulty, helping the agent understand the real layout in a more complex manner.", + "bbox": [ + 75, + 714, + 468, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Combining with Existing Pre-Training Tasks. As depicted in Figure 3, we follow Airbert [13] to pre-train the model backbone using our proposed trajectory judgment task, additionally combining with three other existing", + "bbox": [ + 75, + 811, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pretext tasks, namely masked language modeling (MLM), masked vision modeling (MVM) and path ranking (PR) on YouTube-VLN dataset. For MLM, we randomly mask out the words in instruction and the goal is to recover the masked words. Similar to MLM, MVM is designed to predict masked image regions. PR is a ranking task, which aims to decide the most matching path-instruction pair among a few pairs.", + "bbox": [ + 497, + 382, + 890, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Adapting Pre-trained Backbone for VLN", + "text_level": 1, + "bbox": [ + 497, + 521, + 848, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adapt the pre-trained model to both goal-oriented navigation task and object-oriented navigation task. All the tasks are based on the Matterport3D simulator [2]. We utilize R2R [1] as the benchmark for the goal-oriented navigation task, which is divided into discriminative setting and generative setting. As for the object-oriented task, we evaluate our model on REVERIE [41] in generative setting.", + "bbox": [ + 497, + 549, + 890, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The discriminative setting formulates VLN as a path-selection problem, requiring the agent to choose the path that best matches the instruction from multiple candidate paths. Under the discriminative setting, we utilize the classifier used in the path ranking pretext task for decision-making and fine-tune the Lily agent on the R2R dataset.", + "bbox": [ + 497, + 652, + 890, + 735 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the generative setting, the agent needs to predict actions sequentially to reach the goal (R2R) or simultaneously find the object (REVERIE). We adopt DUET [6] as the architecture for fine-tuning, which feeds the cross-modal feature into a feed-forward network for decision-making. We initialize the text transformer encoder and cross-modal transformer encoder of the generative model with our Lily agent. Note that our Lily agent can apply to any generative model. More details are available in the supplementary.", + "bbox": [ + 497, + 742, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8321", + "bbox": [ + 468, + 887, + 499, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5e82bef7ca8d2e41eff86cb3b36f6a02ff9123beed83063b440e38be298ce124.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
#DatasetPre-training TaskVal SeenVal Unseen
SourceReasonable Navigation PathPseudo-labeled ActionTrajectory JudgmentTLNE↓OSR↑SR↑SPL↑TLNE↓OSR↑SR↑SPL↑
1Airbnb ImagesXXX10.213.4179.0274.120.709.633.9570.9762.840.58
2YouTube VideosXXX10.123.4079.9074.310.709.813.7274.2463.730.59
3YouTube Videos✓XX10.303.4078.6075.100.719.603.7073.5065.000.61
4YouTube Videos✓✓X10.203.3079.8075.400.719.303.6072.7066.100.62
5YouTube Videos✓✓✓9.993.1280.8877.450.749.643.3774.9366.700.62
", + "bbox": [ + 80, + 123, + 889, + 226 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1: Ablation study on YouTube-VLN dataset and trajectory judgment pretext task for pre-training.", + "bbox": [ + 147, + 231, + 821, + 245 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 80, + 256, + 206, + 271 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 80, + 279, + 263, + 293 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and Evaluation Metrics. We conduct our experiments on two VLN benchmarks, i.e., R2R [1] and REVERIE [41]. These two datasets consist of 21,567 path-instruction pairs from 90 scenes in Matterport3D [2]. REVERIE follows the same train/val/test splits as the R2R, while requiring an agent to select the bounding box of the target object bounding box additionally. Following standard settings [13], we adopt five metrics for evaluating R2R, namely success rate (SR), oracle success rate (OSR), success rate weighted by the ratio between the length of the shortest path and the predicted path (SPL), trajectory length (TL) and navigation error (NE). As for REVERIE, we leverage four metrics for evaluating navigation performance, namely SR, OSR, SPL and TL, and two for object grounding performance, namely remote grounding success (RGS) and RGS weighted by path length (RGSPL).", + "bbox": [ + 80, + 299, + 467, + 519 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We implement our method based on Pytorch framework [40] and Matterport3D simulator [2]. Specifically, we divide our training process into two stages, i.e., pre-training and fine-tuning. For the pretraining stage, we distribute training over 4 NVIDIA 3090 GPUs for 500 epochs to convergence. The pre-trained model with the highest accuracy for the path ranking pretext task is selected for fine-tuning. During the fine-tuning stage, we distribute training over 8 NVIDIA 3090 GPUs for 30 epochs to convergence. Following Airbert [13], we use augmented data from EnvDrop [47] for fine-tuning by default. More details are provided in the supplementary.", + "bbox": [ + 80, + 520, + 467, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation Studies on Pre-Training", + "text_level": 1, + "bbox": [ + 80, + 694, + 366, + 707 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We ablate our approach under discriminative setting on R2R benchmark. Considering the time efficiency, we do not use augmented data for fine-tuning on these experiments.", + "bbox": [ + 80, + 714, + 467, + 754 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data Source: Airbnb Images vs. YouTube Videos. One of the main differences between YouTube-VLN dataset and Airbnb dataset [13] is the data source. Airbnb consists of 713k image-caption pairs while YouTube-VLN consists of 587k images extracted from 433 hours of house tour videos. YouTube-VLN has fewer images but provides more information about a room from different camera angles by merging, which better simulates a panorama for down-", + "bbox": [ + 80, + 756, + 467, + 865 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "stream VLN tasks. To evaluate the effect of data source, we follow Airbert [13] to randomly select images in the same house to build a trajectory and its corresponding instruction. We keep the number of instructions the same in pre-training for a fair comparison. In Table 1 (# 1 vs. # 2), YouTube data performs slightly better than Airbnb data, surpassing the SR by $0.89\\%$ on the val unseen split. We speculate this is because data quality is more important than quantity.", + "bbox": [ + 502, + 257, + 889, + 366 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of Reasonable Navigation Trajectory. YouTube-VLN dataset is collected from real house tour videos and is thus able to extract frames in chronological order to build reasonable navigation trajectories instead of combining multiple randomly chosen images. We use the generated reasonable navigation trajectories and shuffled trajectories to train two agents, respectively. In Table 1, the agent trained with reasonable navigation trajectories (# 3) achieves significantly better performance than the shuffled navigation trajectories variant (# 2), with $1.27\\%$ gains on SR under the val unseen split. This suggests that the agent can not well understand and ground the instruction to the trajectory without reasonable navigation paths for learning.", + "bbox": [ + 502, + 368, + 889, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of Pseudo-Labeled Action. The core of the proposed action-aware instruction generator is the pseudo-labeled actions for the instructions. To evaluate the effectiveness of the pseudo-labeled actions, we construct a variant that replaces random action words with the pseudo-labeled actions which are filled in the instructions. The results are shown in Table 1, # 4. Compared to the variant (# 3) that fills the instructions with random action words, this variant boosts the SR metric on both the val unseen (+1.10%) and seen (+0.30%) splits, showing the effectiveness of pseudo-labeled actions. It indicates that with pseudo-labeled actions, the agent can effectively ground the action to the visual observation and recognizes the correct transition from one location to another.", + "bbox": [ + 502, + 547, + 889, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of Trajectory Judgment Pretext Task. To explore the layout knowledge of the YouTube-VLN dataset and equip the agent with layout reasoning ability, we propose a self-supervised trajectory judgment pretext task. In Table 1, the variant with the proposed pretext task improves the performance (#5 vs.#4, +2.05% on val seen and +0.60% on val unseen w.r.t. SR). Moreover, given a room type and visual information of the current node as inputs, this variant predicts the relative orientation of nodes for that", + "bbox": [ + 502, + 742, + 889, + 865 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8322", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/67ae89174462827fc1fd7cb9075ace529d246a5a2620e6c5c94037027aaf4ecb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
#MethodsTLNE↓OSR↑SR↑SPL↑
1Random Sample9.373.5272.8864.410.61
2Temporal Difference9.553.6173.3565.300.61
3Entropy-Based9.643.3774.9366.700.62
", + "bbox": [ + 80, + 123, + 463, + 178 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "room type with a $30\\%$ increase in accuracy (see supplementary for more details). These substantiate the claim of the importance of the proposed trajectory judgment task, which helps the agent learn the layout reasoning ability.", + "bbox": [ + 75, + 222, + 468, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Entropy-Based Trajectory Generation Strategy. In order to acquire an informative frame to represent a node, we propose an entropy-based technique as mentioned in Section 3.1. To demonstrate the effectiveness of our strategy, we construct two variants, i.e., one randomly chooses a frame, and one decides the frame by temporal difference [55]. The second variant computes the temporal pixel difference between every two consecutive frames and picks the frames where the peaks are located as the frames to represent the nodes. In Table 2, our entropy-based method significantly outperforms these two variants, increasing the SR on the val unseen split from $64.41\\%$ and $65.30\\%$ to $66.70\\%$ , respectively. We speculate this is because 1) randomly sampling frames can generate consecutive redundant frames or meaningless frames (e.g., a wall takes up most of the frame); 2) the temporal difference method selects a frame that represents the junction of two different rooms, which is ambiguous and thus confuses the agent. In comparison, our entropy-based method is able to find a reliable frame to represent a node and ensure two adjacent nodes belong to different room types.", + "bbox": [ + 75, + 277, + 468, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Comparison with State-of-the-Arts", + "text_level": 1, + "bbox": [ + 75, + 574, + 381, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on R2R Dataset. We first compare our Lily agent with current methods under the discriminative setting. In Table 3, compared with VLN-BERT that uses image-caption pairs from the web for pre-training, our Lily agent significantly increases the SR by $10.74\\%$ on the val unseen split. This highlights the importance of providing the indomain indoor data for pre-training. Moreover, compared with Airbert which uses in-domain image-caption pairs from online rental marketplaces, Lily still increases the SR from $73.85\\%$ to $79.31\\%$ on val seen and from $68.67\\%$ to $70.00\\%$ on val unseen. We attribute the improvement to our proposed VLN-like YouTube-VLN dataset and trajectory judgment pretext task, which have been thoughtfully evaluated in Section 5.2. When ensembled with the speaker-follower [10], all three methods increase the performance and our Lily agent performs the best.", + "bbox": [ + 75, + 597, + 468, + 817 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 4, we evaluate on R2R test split and our Lily ranks first on the VLN challenge leaderboard compared", + "bbox": [ + 75, + 817, + 468, + 845 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c40504e6a2ef3e78162446cc9db1b855e8325edd0d336630262aee6b0e3f6d21.jpg", + "table_caption": [ + "Table 2: Comparison between different strategies of selecting frames to represent nodes under val unseen split." + ], + "table_footnote": [], + "table_body": "
MethodsVal SeenVal Unseen
TLNE↓SR↑SPL↑TLNE↓SR↑SPL↑
Follower [10]10.403.6865.100.629.575.2052.360.49
Speaker [10]11.193.8060.690.5610.714.2554.660.49
Speaker-Follower [10]10.692.7274.220.7010.103.3267.900.63
ProBES [30]----9.504.0560.280.56
VLN-BERT [36]10.283.7370.200.669.604.1059.260.55
Airbert [13]10.593.2173.850.6910.033.2468.670.63
Lily10.212.8979.310.7610.033.1970.000.65
VLN-BERT* [36]10.612.3581.860.7810.002.7673.610.68
Airbert* [13]10.632.1381.400.779.992.6975.010.70
Lily*10.512.0683.290.809.782.4876.880.72
", + "bbox": [ + 504, + 123, + 887, + 251 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/356caa91ce98daede2e1d1b7cf811833863b76eb7c32c4e5ad337e1ec5669db9.jpg", + "table_caption": [ + "Table 3: Comparison with state-of-the-arts on R2R dataset under discriminative setting. * means results of ensembling with the speaker-follower [10] model." + ], + "table_footnote": [], + "table_body": "
MethodsTLNE↓SPL↑OSR↑SR↑
Speaker-Follower [10]12574.870.019653
Self-Monitoring [35]3734.480.029761
Reinforced CM [51]3584.030.029663
EnvDrop [47]6873.260.019969
AuxRN [57]413.240.218171
VLN-BERT [36]686.822.990.019973
Global Normalization [53]686.862.990.019974
Airbert [13]686.542.580.019977
LiLy686.452.500.019979
", + "bbox": [ + 504, + 305, + 887, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4: Results under discriminative setting on the test unseen split as indicated on the R2R leaderboard ${}^{2}$ .", + "bbox": [ + 499, + 439, + 890, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with the results whose manuscripts are publicly available, achieving the highest SR of $79\\%$ . As we follow Airbert to use 30 candidate trajectories from EnvDrop [47] and the leaderboard considers that our agent has walked through all these paths, the SPL metric is low for both Lily and Airbert.", + "bbox": [ + 497, + 479, + 890, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Besides, our Lily agent also helps to increase the performance on R2R under the generative setting. We enhance the state-of-the-art DUET [6] method by pre-training the agent using our method as mentioned in Section 4. In Table 6, the agent incorporating Lily achieves $2\\%$ and $3\\%$ improvements w.r.t. SR on the val unseen split and test unseen split, respectively, compared to DUET. Notably, our method increases the SPL by $2\\%$ on the val unseen split, indicating the agent is able to reach the goal more efficiently. We attribute this to the agent's acquisition of layout prior knowledge via the proposed trajectory judgment task on our YouTube-VLN dataset, enabling it to plan more efficient routes to the goals in new environments.", + "bbox": [ + 497, + 548, + 890, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on REVERIE Dataset. Compared with R2R, REVERIE is more challenging as its instructions only describe the destinations without detailed path descriptions. This requires the agent to be equipped with common knowledge about the room layouts and to reason the possible paths that lead to the destinations. In Table 5, we outperform the SOTA agent (i.e., DUET) by $1.13\\%$ on SR and increase the SPL from $46.98\\%$ to $48.11\\%$ on the val unseen split. It is worth noting that our method achieves a higher OSR with a shorter TL, indicating that our agent finds the destination", + "bbox": [ + 497, + 728, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "2https://eval.ai/web/challenges/challenge-page/97/leaderboard/270", + "bbox": [ + 95, + 851, + 465, + 864 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8323", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b148e202d8fd012a8b3f24f1af97d9d16bdf1648104eccb62ab2c4bc787cb62a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsVal UnseenTest Unseen
NavigationGroundingNavigationGrounding
TLOSR↑SR↑SPL↑RGS↑RGSPL↑TLOSR↑SR↑SPL↑RGS↑RGSPL↑
Human------21.1886.8381.5383.6677.8451.44
Seq2Seq [1]11.078.074.202.842.161.6310.896.883.993.092.001.58
RCM [51]11.9814.239.296.974.893.8910.6011.687.846.673.673.14
SMNA [35]9.0711.288.156.444.543.619.238.395.804.533.102.39
FM [41]45.2828.2014.407.197.844.6739.0530.6319.8811.6111.286.08
SIA [33]41.5344.6731.5316.2822.4111.5648.6144.5630.8014.8519.029.20
HAMT [5]14.0836.8432.9530.2018.9217.2813.6233.4130.4026.6714.8813.08
RecBERT [18]16.7835.0230.6724.9018.7715.2715.8632.9129.6123.9916.5013.51
ProbES [30]18.0033.2327.6322.7516.8413.9416.8428.2324.9720.1215.1112.32
Airbert [13]18.7134.5127.8921.8818.2314.1817.9134.2030.2823.6116.8313.28
DUET [6]22.1151.0746.9833.7332.1523.0321.3056.9152.5136.0631.8822.06
DUET (Lily)21.8753.7148.1134.4332.1523.4321.9460.5154.3237.3432.0221.94
", + "bbox": [ + 157, + 122, + 803, + 302 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/47cebef36bb987acb804b739db65ccc6ec60c228a1faec6301623a0f961c877e.jpg", + "table_caption": [ + "Table 5: Comparison with state-of-the-arts on REVERIE. Lily agent achieves the state-of-the-art performance on all splits." + ], + "table_footnote": [], + "table_body": "
MethodsVal UnseenTest Unseen
TLNE↓SR↑SPL↑TLNE↓SR↑SPL↑
Seq2Seq [1]8.397.8122-8.137.8520-
EnvDrop [47]10.705.22524811.665.235147
AuxRN [57]-5.285550-5.155551
PREVALENT [14]10.194.71585310.515.305451
RelGraph [17]9.994.73575310.294.755552
RecBERT [18]12.013.93635712.354.096357
ProbES [30]11.584.00615512.434.206256
ADAPT [32]12.333.66665913.164.116357
HOP [42]12.273.80645712.653.836459
HAMT [5]11.462.29666112.273.936560
Airbert [13]11.784.01625612.414.136257
DUET [6]13.943.31726014.733.656959
DUET (Lily)14.582.90746216.133.447260
", + "bbox": [ + 78, + 331, + 463, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "more quickly. We attribute this to the better layout reason ability learned from the large-scale diverse reasonable trajectories in the proposed YouTube-VLN dataset. A similar performance is obtained on the test unseen split, where the Lily agent improves the SR by $1.81\\%$ and the SPL by $1.28\\%$ . Although our objective is solely navigation, we still achieve comparable performance on grounding metrics and even slightly outstrip DUET on most metrics.", + "bbox": [ + 78, + 545, + 467, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Learning Navigation from One Environment", + "text_level": 1, + "bbox": [ + 78, + 665, + 453, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our intuition is that pre-training on the YouTube-VLN dataset can mitigate the domain gap of training from scratch and is able to achieve excellent performance with only a few training environments. To verify this, we conduct a one-shot learning study, where we fine-tune our model on only one environment of the original training environments. Note that the candidate paths are generated from all of the possible paths from the start viewpoints to all navigable points, instead of from the expert model in EnvDrop [47]. All the candidate paths are the shortest paths in the navigation graphs. To reduce the bias, we randomly select 5 sets from the entire environments and report the average results.", + "bbox": [ + 80, + 686, + 467, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 7, our agent outperforms all the existing pre", + "bbox": [ + 97, + 852, + 467, + 865 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/496536ff46320d7b99382834c9627215e151193b82361f2527bd5eef9bbaa60a.jpg", + "table_caption": [ + "Table 6: Comparison with state-of-the-arts on R2R dataset under generative setting." + ], + "table_footnote": [], + "table_body": "
MethodsVal SeenVal Unseen
VLN BERT [36]45.7122.43
AirBERT [13]47.8850.00
Lily49.3150.86
", + "bbox": [ + 581, + 331, + 808, + 380 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7: SR on val seen and val unseen splits of R2R. All the agents access only one environment.", + "bbox": [ + 502, + 385, + 889, + 413 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "training methods. On the val seen split using one-shot finetuning, compared to VLN-BERT and AirBERT, our Lily agent achieves $3.60\\%$ and $1.43\\%$ improvements, respectively. In the val unseen split using one-shot fine-tuning, we achieve $28.43\\%$ improvement compared to VLN-BERT. All these results suggest the effectiveness of our method.", + "bbox": [ + 502, + 423, + 889, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 502, + 517, + 616, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose a new approach Lily to address the limitations of existing vision-and-language navigation (VLN) methods by creating a large-scale VLN-like dataset from real house tour videos to train our embodied agent. We overcome the challenges of automatically generating path-instruction pairs to construct the dataset from raw and unlabeled videos by leveraging an entropy-based method for trajectory construction and an action-aware generator for instruction generation. Additionally, we train the agent to judge the reasonableness of trajectories, improving its layout reasoning ability. Our method achieves state-of-the-art performance on two popular benchmarks (R2R and REVERIE), demonstrating the efficacy. Overall, we hope our work can provide valuable insight into the VLN community by learning embodied VLN from passive videos.", + "bbox": [ + 502, + 541, + 889, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 502, + 760, + 657, + 775 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Prof. Tan and his students were partially supported by the National Natural Science Foundation of China (NSFC) (62072190), National Natural Science Foundation of China (NSFC) 61836003 (key project), Program for Guangdong Introducing Innovative and Entrepreneurial Teams 2017ZT07X183.", + "bbox": [ + 502, + 783, + 889, + 864 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8324", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 173, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] P. 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In CVPR, pages 10009-10019, 2020. 2, 7, 8" + ], + "bbox": [ + 502, + 125, + 890, + 857 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8326", + "bbox": [ + 468, + 887, + 500, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Vision-and-Language Navigation from YouTube Videos/05335e36-6140-429d-8434-dd018538220c_model.json b/2023/Learning Vision-and-Language Navigation from YouTube Videos/05335e36-6140-429d-8434-dd018538220c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..dae3b06f39b26962d625e4d3773f4d179757e92b --- /dev/null +++ b/2023/Learning Vision-and-Language Navigation from YouTube Videos/05335e36-6140-429d-8434-dd018538220c_model.json @@ -0,0 +1,2112 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.129, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.088 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.157, + 0.162, + 0.815, + 0.182 + ], + "angle": 0, + "content": "Learning Vision-and-Language Navigation from YouTube Videos" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.207, + 0.871, + 0.224 + ], + "angle": 0, + "content": "Kunyang Lin\\(^{1,2*}\\) Peihao Chen\\(^{1*}\\) Diwei Huang\\(^{1}\\) Thomas H. Li\\(^{6}\\) Mingkui Tan\\(^{15\\dagger}\\) Chuang Gan\\(^{34}\\)" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.226, + 0.844, + 0.273 + ], + "angle": 0, + "content": "\\(^{1}\\)South China University of Technology, \\(^{2}\\)Information Technology R&D Innovation Center of Peking University, \\(^{3}\\)UMass Amherst, \\(^{4}\\)MIT-IBM Watson AI Lab, \\(^{5}\\)Key Laboratory of Big Data and Intelligent Robot, Ministry of Education, \\(^{6}\\)Peking University Shenzhen Graduate School" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.473, + 0.666 + ], + "angle": 0, + "content": "Vision-and-language navigation (VLN) requires an embodied agent to navigate in realistic 3D environments using natural language instructions. Existing VLN methods suffer from training on small-scale environments or unreasonable path-instruction datasets, limiting the generalization to unseen environments. There are massive house tour videos on YouTube, providing abundant real navigation experiences and layout information. However, these videos have not been explored for VLN before. In this paper, we propose to learn an agent from these videos by creating a large-scale dataset which comprises reasonable path-instruction pairs from house tour videos and pre-training the agent on it. To achieve this, we have to tackle the challenges of automatically constructing path-instruction pairs and exploiting real layout knowledge from raw and unlabeled videos. To address these, we first leverage an entropy-based method to construct the nodes of a path trajectory. Then, we propose an action-aware generator for generating instructions from unlabeled trajectories. Last, we devise a trajectory judgment pretext task to encourage the agent to mine the layout knowledge. Experimental results show that our method achieves state-of-the-art performance on two popular benchmarks (R2R and REVERIE). Code is available at https://github.com/JeremyLinky/YouTube-VLN" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.671, + 0.21, + 0.685 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.694, + 0.47, + 0.819 + ], + "angle": 0, + "content": "An important goal of embodied artificial intelligence is to develop agents that can interact with humans in natural language to carry out real-world tasks. Toward this goal, vision-and-language navigation (VLN) [1] is a rudimentary artificial intelligence task, requiring an indoor agent to navigate in unseen environments following natural instructions. VLN has attracted widespread attention in the fields of computer vision and robotics due to its promising applications such as in-home robots [54] and warehouse assistants [29]." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.819, + 0.469, + 0.833 + ], + "angle": 0, + "content": "One of the key challenges of VLN is the generaliza" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.306, + 0.892, + 0.513 + ], + "angle": 0, + "content": "tion ability of agents to unseen environments. Existing VLN methods attempt to cope with this challenge via self-supervised pre-training on vision-and-language datasets. As shown in Figure 1 (a), some previous works [30, 19, 36, 7] learn the agents on simulated navigation environments and manual-labeled data. The other works [14, 13, 42] seek to construct path-instruction pairs by using web image data, which is shown in Figure 1 (b). Despite their promising performance, existing agents still suffer from the following limitations. 1) Training on simulated datasets is limited to a restricted number of environments. 2) Constructing a trajectory by simply concatenating web images leads to unreasonable room layouts, which hamper the agent to learn layout reasoning ability. As a result, VLN agents trained on such data are brittle to adapt to unseen environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.514, + 0.893, + 0.762 + ], + "angle": 0, + "content": "Fortunately, there are massive house tour videos on YouTube, providing real navigation experiences and layout information but are still under-explored. We can be naturally inspired to let an agent learn VLN ability from such videos, thereby addressing the limitations of existing methods. An intuitive way is to model the navigation experiences as path-instruction pairs to train the agent. Motivated by this, we propose a \"Lily\" agent who Learns Vision-and-Language Navigation from YouTube Videos. Specifically, we first develop an in-domain pre-training dataset from house tour YouTube videos, namely YouTube-VLN, which comprises VLN-like path-instruction pairs. Our YouTube-VLN dataset has the advantages of diverse environments, real layouts, and native actions1, reducing the domain gap with VLN datasets, as illustrated in Figure 1 (c). Then, we pre-train the agent using these path-instruction pairs. Benefiting from in-domain pre-training on our proposed dataset, our agent thus generalizes well to unseen environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.762, + 0.892, + 0.845 + ], + "angle": 0, + "content": "Constructing and utilizing such a dataset, however, is still far from trivial work and remains an open problem due to the following challenges. 1) As the nodes in a trajectory are expected to be diverse and informative, it is hard to determine the locations of trajectory nodes from massive video frames and represent the visual content in a node." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.843, + 0.458, + 0.855 + ], + "angle": 0, + "content": "*Equal contribution. Email: {imkunyanglin, phchencs}@gmail.com" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.855, + 0.395, + 0.866 + ], + "angle": 0, + "content": "†Corresponding author. Email: mingkuitan@scut.edu.cn" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.843, + 0.458, + 0.866 + ], + "angle": 0, + "content": null + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.854, + 0.755, + 0.867 + ], + "angle": 0, + "content": "1The execution actions that objectively exist" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.887, + 0.502, + 0.898 + ], + "angle": 0, + "content": "8317" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.125, + 0.346, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.25, + 0.318, + 0.26 + ], + "angle": 0, + "content": "(a) Dataset from Simulation Environments" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.125, + 0.617, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.401, + 0.25, + 0.57, + 0.261 + ], + "angle": 0, + "content": "(b) Dataset from Web Images Data" + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.125, + 0.89, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.657, + 0.25, + 0.854, + 0.261 + ], + "angle": 0, + "content": "(c) Dataset from YouTube Videos (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.271, + 0.893, + 0.327 + ], + "angle": 0, + "content": "Figure 1: Comparison of different datasets for pre-training. Existing datasets are built from either simulation environments (a) or web images data (b). The former only covers limited environments, and the latter contains confusing layouts and ambiguous actions. Our dataset built from YouTube videos (c) is able to provide diverse environments, real layouts and native actions simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.469, + 0.448 + ], + "angle": 0, + "content": "2) Real VLN instructions include various action descriptions, but obtaining corresponding instructions from navigation clips is challenging due to the actions being implicit in videos. Thus it is nontrivial to acquire matching instruction on a trajectory. 3) Layout knowledge from real navigation experience is hard to mine and model, which impedes the agent of learning layout reasoning ability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.469, + 0.782 + ], + "angle": 0, + "content": "In this paper, we address the above challenges as follows. To conquer challenge 1), we propose an entropy-based trajectory generation method. Specifically, we first envisage that the nodes of a trajectory should contain as many types of rooms as possible to diversify trajectories. Accordingly, we group the frames with the same room types in videos and consider each group as a node in the trajectory. Then, inspired by that low classification entropy image is reliable and contains rich information relevant to a specific class (room type in our case) [39], the frame with the lowest classification entropy in a group is chosen to represent the visual content in a node. To tackle challenge 2), we introduce an action-aware instruction generation method. Specifically, we adopt an action inverse model to pseudo-label the action along trajectories and fill them in the instructions via hand-designed rules. To grapple with challenge 3), we devise a self-supervised pretext task. As we all know, humans often judge whether a navigation trajectory is reasonable based on the layout of the environment. Therefore, it is believed that an agent equipped with layout reasoning ability should be able to make similar judgment. To this end, we propose trajectory judgment pretext task to ask the agent to identify reasonable navigation trajectories, which further equips the model with the ability to reason environment layouts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.469, + 0.867 + ], + "angle": 0, + "content": "We empirically show that the diverse entropy-based trajectory generation method and action-aware instruction generator allow us to harvest high-quality path-instruction pairs from YouTube house tour videos, resulting in the YouTube-VLN dataset. By integrating the self-supervised trajectory judgment task in pre-training a VLN agent, our" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.892, + 0.434 + ], + "angle": 0, + "content": "Lily agent presents state-of-the-art performance on two mature and solid benchmarks (R2R [1], REVERIE [41]). The proposed Lily agent reaches the first place on the R2R leaderboard in terms of success rate and outperforms the SOTA method under discriminative setting and generative setting by \\(2\\%\\) and \\(3\\%\\) w.r.t. success rate, respectively." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.435, + 0.774, + 0.447 + ], + "angle": 0, + "content": "Our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.891, + 0.517 + ], + "angle": 0, + "content": "- We unleash the huge potential of house tour videos for VLN. By leveraging these videos, we introduce a largescale dataset containing real navigation path-instruction pairs for promoting VLN pre-training and a self-supervised pretext task for the learning of layout reasoning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.891, + 0.587 + ], + "angle": 0, + "content": "- Our diverse trajectory generation method, together with the action-aware instruction generator, creates informative and diverse trajectory nodes and produces matching instructions, both of which make the path-instruction pairs authentic and of high quality for training a VLN agent." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.891, + 0.657 + ], + "angle": 0, + "content": "- The proposed trajectory judgment pretext task allows the model to build up an awareness of learning and reasoning the layout knowledge, which is crucial in the VLN task of indoor environments. We also empirically substantiate that the agent indeed learns the layout learning ability." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.449, + 0.891, + 0.657 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.67, + 0.64, + 0.684 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.788, + 0.708 + ], + "angle": 0, + "content": "2.1. Vision-and-Language Navigation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Vision-and-Language Navigation (VLN) [1] is a challenging task and has received continuous and intense attention from the academic community in recent years [4, 12, 25, 31, 46, 27, 6, 45, 9]. Early methods attempt to learn the agent from sequence-to-sequence models [1, 10, 47]. However, these methods can not model the cross-modal relation between language and visual observation well. To address this issue, transformer [48] architecture is adopted to the agents followed by vision-and-language pre-training [35, 50, 57, 37, 13, 42, 5, 38, 24]. PREVALENT [15] pretrains transformer-based agent via masked language mod" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.888, + 0.501, + 0.898 + ], + "angle": 0, + "content": "8318" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.126, + 0.473, + 0.334 + ], + "angle": 0, + "content": "eling and action prediction tasks. Inspired by BERT [8], several works propose to use different variants of BERT for VLN pre-training. VLN-BERT [37] utilizes image-text data [34] to perform path-instruction matching pretext task. Airbert [13] proposes the shuffle loss to improve the ability of the model to learn the order of image-caption pairs. Recently, HOP [42] introduces the history and order-aware pretext tasks. However, these existing pretext tasks do not consider the learning of environment layout reasoning ability and bring limited performance for VLN tasks. In this work, we propose a trajectory judgment task to teach the agent to distinguish reasonable navigation trajectories. By proficiently accomplishing this task, the agent can acquire the ability to reason about environment layout, which enhances its generalization capability to unseen environments." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.352, + 0.249, + 0.366 + ], + "angle": 0, + "content": "2.2. Datasets for VLN" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.376, + 0.473, + 0.681 + ], + "angle": 0, + "content": "The major difficulty of generalizing a VLN agent to unseen environments is the scarcity of VLN training data. Well-labeled VLN datasets built from the simulators [2, 44, 52] allow the agent to obtain a promising performance, such as R2R [1], R4R [20], RxR [23] and SOON [56]. While the data built from simulators are laborious, Wang et al. [49] and ProbES [30] enrich the navigation instructions via self-exploration in the simulation environments. Some other endeavors [47, 28, 10, 11, 22, 26] seek to augment the data from existing datasets. AutoVLN [7] and Kamath et al. [21] enlarges the VLN data from simulations with a larger number of environments. However, these datasets are limited by the number of scenes in simulators. To ease this problem, VLN-BERT [37] leverages the abundant web image-captions pairs as VLN pre-training data. Airbert [13] further exploits indoor house images and captions from the web to construct path-instruction pairs for VLN pre-training. However, the trajectories constructed by simply splicing pictures may be confusing and ambiguous. In our work, we address these problems by proposing a large-scale in-domain VLN-like pre-training dataset, providing the agent with diverse visual environments and reasonable layouts." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.702, + 0.47, + 0.718 + ], + "angle": 0, + "content": "3. Building VLN Dataset from YouTube Videos" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.729, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Our first step is to develop a large-scale VLN-like dataset that comprises reasonable path-instruction pairs from house tour videos on YouTube, termed YouTube-VLN. YouTube-VLN serves as a cornerstone for facilitating the acquisition of VLN capabilities for Lily, featuring diverse environments, real layouts and native actions. To achieve this goal, we present an entropy-based trajectory generation technique (Section 3.1) and an action-aware generator (Section 3.2) to tackle the arduous tasks of trajectory and instruction generation, respectively." + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.128, + 0.885, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.324, + 0.893, + 0.366 + ], + "angle": 0, + "content": "Figure 2: An example of a generated trajectory from a YouTube house tour video. \\(\\rightarrow\\) represents the direction to go next while \\(\\rightarrow\\) represents the stop action." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.381, + 0.776, + 0.397 + ], + "angle": 0, + "content": "3.1. Diverse Trajectory Generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.893, + 0.599 + ], + "angle": 0, + "content": "We seek to construct discrete navigation trajectories from YouTube videos. Similar to discrete navigation datasets (e.g., R2R [1]), each trajectory comprises \\(K\\) navigation nodes, representing different locations of a navigation path. This entails addressing two major challenges: 1) how to determine the locations composing a trajectory to make the trajectory more diverse and 2) how to represent the visual content at each node location. To tackle these challenges, we first collect large-scale consecutive indoor frames from YouTube videos. Then, we group the adjacent frames according to their room types and consider each group as a node. Last, we present an entropy-based technique to select the most informative frames in a group for representing the visual content in a node." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.895, + 0.768 + ], + "angle": 0, + "content": "Collecting Navigation Data from YouTube. Real estate agents typically tour a house in each video. To satisfy the visual diversity and dataset scale, we create the YouTube-VLN dataset from 4078 videos collected from various uploaders, with a total duration of 433 hours. In contrast to prior work [3], which relied on a limited set of videos from a single uploader, our dataset features greater diversity and volume. We also employ sparse sampling and off-the-shelf image classifiers [16, 43] to pre-process the videos, filtering out redundant or noisy frames (those featuring people or outdoor scenes), resulting in a final set of 587k indoor frames suitable for constructing trajectories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Determining the Locations of Trajectory Nodes. A real robot often needs to go through different locations for navigating to a goal. To mimic the real navigation process, we expect that our constructed trajectories also contain diverse visual content within the limited navigation nodes. To achieve this, we first utilize the powerful large model CLIP [43] to recognize the room type of each indoor im" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.888, + 0.502, + 0.898 + ], + "angle": 0, + "content": "8319" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.265 + ], + "angle": 0, + "content": "age. Then, we gather temporally adjacent frames with the same room type as a group and consider this group as one of the navigation nodes. In this sense, the navigation nodes are diversely spread in different rooms and the constructed trajectories are able to mimic the real navigation process. We also call this kind of node a room node. In practice, to increase the visual diversity of trajectories, we also randomly insert transition nodes that are composed of video frames captured during the transition from one room to another one, between two adjacent room nodes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.473, + 0.472 + ], + "angle": 0, + "content": "Representing Visual Content in a Node. A node consists of a group of images and sometimes the number of images may exceed 100 as the photographer could stay in the same room for a long time. Hence, we have to select the most informative images for representing node features. Inspired by EATA [39], an image with lower classification entropy is more reliable, containing more information relevant to a specific class (room type in our case). We thus propose to select an image with the lowest classification entropy to represent the current view of a node. In order to mimic the panoramic visual context, we then merge \\( M \\) adjacent consecutive images of the current view. It is worth noting that our node features better represent a panoramic view compared with Airbert [13] because we merge adjacent frames that belong to the same place as the current view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.472, + 0.515 + ], + "angle": 0, + "content": "Ultimately, we randomly chose \\(K\\) continuous nodes to construct a trajectory. An example of the constructed trajectory is shown in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.526, + 0.403, + 0.54 + ], + "angle": 0, + "content": "3.2. Action-Aware Instruction Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.7 + ], + "angle": 0, + "content": "In addition to constructing navigation trajectories, one more important step for building a VLN dataset is to create the corresponding instructions without manual annotation. The main challenge for this step is how to correctly describe visual content and actions along navigation paths. To conquer this challenge, we first generate instruction templates with verb and noun phrase blanks. Then, we describe each node in trajectories using the CLIP [43] model and infer the native actions using an action inverse model [3]. To generate the final instructions, we fill the instruction templates with these visual descriptions and actions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.473, + 0.868 + ], + "angle": 0, + "content": "Specifically, we first generate templates with verb and noun blanks from instructions in the R2R dataset following Airbert [13]. For noun blanks, we fill them with visual content descriptions about each node. We select the frame with the lowest classification entropy (as described in Sec. 3.1) and use the CLIP model to infer the objects it contains, together with the room type to populate a noun blank. For verb blanks, the existing instruction generation method [13] is unable to fill them with the correct action words because it cannot figure out the actions taken for navigating from one image to another. This makes the agent confused when it observes similar viewpoints transition but is given differ" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.895, + 0.306 + ], + "angle": 0, + "content": "ent action descriptions. To tackle this problem, we propose an action-aware strategy to fill instruction templates with native actions instead of random inconsistent actions. To be specific, we follow [3] to train an action inverse model, which has \\(96\\%\\) prediction accuracy for predicting native actions, to pseudo-label the trajectory with action labels from one location node to another. The predicted actions are then converted into actionable verbs, i.e., \"go forward\", \"turn left\" and \"turn right\". For each noun blank that has been filled with the description of one node, we find its closest verb phrase blank and fill it with the pseudo-labeled action which is executed to reach the next node. This eventually enables us to create action-aware instructions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.32, + 0.836, + 0.336 + ], + "angle": 0, + "content": "4. Learning VLN from YouTube Videos" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.895, + 0.552 + ], + "angle": 0, + "content": "Given the VLN-like and reasonable path-instruction pairs generated from YouTube videos, we then describe how to learn the Lily agent from these data. As shown in Figure 3, our VLN model consists of two components: a vision-and-language backbone (i.e., Multi-Layer Transformer) that models the relationship between trajectories and instructions and a decision-making module that predicts the next action or a matching score for a path-instruction pair. The vision-and-language backbone can be any type of cross-modal network. We chose ViLBERT [34] for a fair comparison with Airbert [13]. As a common practice, pretext tasks are utilized for pre-training the backbone. We next describe how to pre-train the backbone on our Youtube-VLN dataset using the proposed trajectory judgment pretext task." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.561, + 0.69, + 0.575 + ], + "angle": 0, + "content": "4.1. Model Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.894, + 0.695 + ], + "angle": 0, + "content": "We follow Airbert [13] to leverage a ViLBERT-like [34] architecture as the model backbone. The model encodes the sequential visual region features and the text token via two separate transformers respectively. More formally, the path-instruction pair consists of \\(K\\) nodes \\(\\{V_k\\}_{k=1}^K\\) and \\(L\\) text tokens \\(\\{w_l\\}_{l=1}^L\\). Each node \\(V_k\\) is composed of \\(R_k\\) visual region features \\(\\{v_i^k\\}_{i=1}^{R_k}\\). In this way, we represent the visual and text inputs respectively as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.703, + 0.891, + 0.747 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} X _ {V} = \\left[ \\left[ \\operatorname {I M G} \\right], v _ {1} ^ {1}, \\dots , v _ {R _ {1}} ^ {1}, \\dots , \\left[ \\operatorname {I M G} \\right], v _ {1} ^ {K}, \\dots , v _ {R _ {K}} ^ {K} \\right], (1) \\\\ X _ {W} = \\left[ \\left[ \\mathrm {C L S} \\right], w _ {1}, \\dots , w _ {l}, \\dots , w _ {L}, [ \\mathrm {S E P} ] \\right], (2) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.752, + 0.894, + 0.809 + ], + "angle": 0, + "content": "where [IMG], [CLS] and [SEP] are special tokens. The encoded visual and text tokens finally interact via a cross-modal transformer encoder. We represent the whole model architecture as \"Multi-Layer Transformer\" in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.817, + 0.876, + 0.833 + ], + "angle": 0, + "content": "4.2. Learning Layout from Trajectory Judgment" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.839, + 0.894, + 0.868 + ], + "angle": 0, + "content": "Given the aforementioned model architecture, we propose to train a VLN agent with a trajectory judgment (TJ)" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.888, + 0.502, + 0.899 + ], + "angle": 0, + "content": "8320" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.123, + 0.895, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.317, + 0.893, + 0.358 + ], + "angle": 0, + "content": "Figure 3: General scheme of our Lily agent for pre-training and downstream stages of VLN tasks. Lily agent learns to leverage the proposed YouTube-VLN dataset for the trajectory judgment task together with the other pretext tasks. After pre-training the VLN model, we adapt it to the downstream datasets and conduct different VLN downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.469, + 0.41 + ], + "angle": 0, + "content": "task, enabling it to reason about layouts. Herein, we elaborate on the proposed trajectory judgment task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.469, + 0.59 + ], + "angle": 0, + "content": "**Formulation.** The trajectory judgment task aims to judge the reasonableness of trajectories. We consider the trajectories generated in the way described in Section 3.1 as positive (reasonable) samples and the shuffled trajectories as negative (unreasonable) ones. To finish this task, the agent is required to reason about the visual information and identify the room types, then infer whether the trajectory matches the real environment layout distribution. Specifically, we first calculate the dot product of the output features of [IMG] and [CLS] tokens. Then, we feed this vector feature to a linear layer to predict the probability that indicates whether the trajectory is reasonable. The model aims to minimize the binary cross-entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.597, + 0.469, + 0.63 + ], + "angle": 0, + "content": "\\[\nL = - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\left[ w \\cdot y _ {n} \\log (p _ {n}) + (1 - y _ {n}) \\log (1 - p _ {n}) \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.631, + 0.469, + 0.714 + ], + "angle": 0, + "content": "where \\( y_{n} = 1 \\) if the \\( n^{th} \\) trajectory is reasonable, otherwise \\( y_{n} = 0 \\). \\( p_{n} \\) represents the probability that the \\( n^{th} \\) trajectory is predicted as reasonable. \\( N \\) is the number of trajectories in a batch. \\( w \\) is a factor to mitigate the imbalance of positive and negative samples, which equals the ratio of the number of negative samples to the number of positive samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.469, + 0.811 + ], + "angle": 0, + "content": "Sample Generation. We propose to shuffle the positive sample to generate the negative samples: 1) shuffle only the transition nodes; 2) shuffle all the nodes; 3) keep the order of the room nodes, and randomly insert nodes from other videos. In this way, we create rich and hard negative samples, which increases the task difficulty, helping the agent understand the real layout in a more complex manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.812, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Combining with Existing Pre-Training Tasks. As depicted in Figure 3, we follow Airbert [13] to pre-train the model backbone using our proposed trajectory judgment task, additionally combining with three other existing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.494 + ], + "angle": 0, + "content": "pretext tasks, namely masked language modeling (MLM), masked vision modeling (MVM) and path ranking (PR) on YouTube-VLN dataset. For MLM, we randomly mask out the words in instruction and the goal is to recover the masked words. Similar to MLM, MVM is designed to predict masked image regions. PR is a ranking task, which aims to decide the most matching path-instruction pair among a few pairs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.522, + 0.85, + 0.536 + ], + "angle": 0, + "content": "4.3. Adapting Pre-trained Backbone for VLN" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.891, + 0.647 + ], + "angle": 0, + "content": "We adapt the pre-trained model to both goal-oriented navigation task and object-oriented navigation task. All the tasks are based on the Matterport3D simulator [2]. We utilize R2R [1] as the benchmark for the goal-oriented navigation task, which is divided into discriminative setting and generative setting. As for the object-oriented task, we evaluate our model on REVERIE [41] in generative setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.891, + 0.736 + ], + "angle": 0, + "content": "The discriminative setting formulates VLN as a path-selection problem, requiring the agent to choose the path that best matches the instruction from multiple candidate paths. Under the discriminative setting, we utilize the classifier used in the path ranking pretext task for decision-making and fine-tune the Lily agent on the R2R dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.743, + 0.892, + 0.867 + ], + "angle": 0, + "content": "In the generative setting, the agent needs to predict actions sequentially to reach the goal (R2R) or simultaneously find the object (REVERIE). We adopt DUET [6] as the architecture for fine-tuning, which feeds the cross-modal feature into a feed-forward network for decision-making. We initialize the text transformer encoder and cross-modal transformer encoder of the generative model with our Lily agent. Note that our Lily agent can apply to any generative model. More details are available in the supplementary." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.888, + 0.5, + 0.898 + ], + "angle": 0, + "content": "8321" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.124, + 0.89, + 0.227 + ], + "angle": 0, + "content": "
#DatasetPre-training TaskVal SeenVal Unseen
SourceReasonable Navigation PathPseudo-labeled ActionTrajectory JudgmentTLNE↓OSR↑SR↑SPL↑TLNE↓OSR↑SR↑SPL↑
1Airbnb ImagesXXX10.213.4179.0274.120.709.633.9570.9762.840.58
2YouTube VideosXXX10.123.4079.9074.310.709.813.7274.2463.730.59
3YouTube Videos✓XX10.303.4078.6075.100.719.603.7073.5065.000.61
4YouTube Videos✓✓X10.203.3079.8075.400.719.303.6072.7066.100.62
5YouTube Videos✓✓✓9.993.1280.8877.450.749.643.3774.9366.700.62
" + }, + { + "type": "table_caption", + "bbox": [ + 0.148, + 0.232, + 0.822, + 0.246 + ], + "angle": 0, + "content": "Table 1: Ablation study on YouTube-VLN dataset and trajectory judgment pretext task for pre-training." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.257, + 0.208, + 0.272 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.28, + 0.265, + 0.294 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.3, + 0.468, + 0.52 + ], + "angle": 0, + "content": "Dataset and Evaluation Metrics. We conduct our experiments on two VLN benchmarks, i.e., R2R [1] and REVERIE [41]. These two datasets consist of 21,567 path-instruction pairs from 90 scenes in Matterport3D [2]. REVERIE follows the same train/val/test splits as the R2R, while requiring an agent to select the bounding box of the target object bounding box additionally. Following standard settings [13], we adopt five metrics for evaluating R2R, namely success rate (SR), oracle success rate (OSR), success rate weighted by the ratio between the length of the shortest path and the predicted path (SPL), trajectory length (TL) and navigation error (NE). As for REVERIE, we leverage four metrics for evaluating navigation performance, namely SR, OSR, SPL and TL, and two for object grounding performance, namely remote grounding success (RGS) and RGS weighted by path length (RGSPL)." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.521, + 0.468, + 0.687 + ], + "angle": 0, + "content": "Implementation Details. We implement our method based on Pytorch framework [40] and Matterport3D simulator [2]. Specifically, we divide our training process into two stages, i.e., pre-training and fine-tuning. For the pretraining stage, we distribute training over 4 NVIDIA 3090 GPUs for 500 epochs to convergence. The pre-trained model with the highest accuracy for the path ranking pretext task is selected for fine-tuning. During the fine-tuning stage, we distribute training over 8 NVIDIA 3090 GPUs for 30 epochs to convergence. Following Airbert [13], we use augmented data from EnvDrop [47] for fine-tuning by default. More details are provided in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.695, + 0.367, + 0.708 + ], + "angle": 0, + "content": "5.2. Ablation Studies on Pre-Training" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.716, + 0.468, + 0.755 + ], + "angle": 0, + "content": "We ablate our approach under discriminative setting on R2R benchmark. Considering the time efficiency, we do not use augmented data for fine-tuning on these experiments." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.757, + 0.468, + 0.866 + ], + "angle": 0, + "content": "Data Source: Airbnb Images vs. YouTube Videos. One of the main differences between YouTube-VLN dataset and Airbnb dataset [13] is the data source. Airbnb consists of 713k image-caption pairs while YouTube-VLN consists of 587k images extracted from 433 hours of house tour videos. YouTube-VLN has fewer images but provides more information about a room from different camera angles by merging, which better simulates a panorama for down-" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.258, + 0.89, + 0.368 + ], + "angle": 0, + "content": "stream VLN tasks. To evaluate the effect of data source, we follow Airbert [13] to randomly select images in the same house to build a trajectory and its corresponding instruction. We keep the number of instructions the same in pre-training for a fair comparison. In Table 1 (# 1 vs. # 2), YouTube data performs slightly better than Airbnb data, surpassing the SR by \\(0.89\\%\\) on the val unseen split. We speculate this is because data quality is more important than quantity." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.369, + 0.89, + 0.547 + ], + "angle": 0, + "content": "Effectiveness of Reasonable Navigation Trajectory. YouTube-VLN dataset is collected from real house tour videos and is thus able to extract frames in chronological order to build reasonable navigation trajectories instead of combining multiple randomly chosen images. We use the generated reasonable navigation trajectories and shuffled trajectories to train two agents, respectively. In Table 1, the agent trained with reasonable navigation trajectories (# 3) achieves significantly better performance than the shuffled navigation trajectories variant (# 2), with \\(1.27\\%\\) gains on SR under the val unseen split. This suggests that the agent can not well understand and ground the instruction to the trajectory without reasonable navigation paths for learning." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.548, + 0.89, + 0.74 + ], + "angle": 0, + "content": "Effectiveness of Pseudo-Labeled Action. The core of the proposed action-aware instruction generator is the pseudo-labeled actions for the instructions. To evaluate the effectiveness of the pseudo-labeled actions, we construct a variant that replaces random action words with the pseudo-labeled actions which are filled in the instructions. The results are shown in Table 1, # 4. Compared to the variant (# 3) that fills the instructions with random action words, this variant boosts the SR metric on both the val unseen (+1.10%) and seen (+0.30%) splits, showing the effectiveness of pseudo-labeled actions. It indicates that with pseudo-labeled actions, the agent can effectively ground the action to the visual observation and recognizes the correct transition from one location to another." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.743, + 0.89, + 0.866 + ], + "angle": 0, + "content": "Effectiveness of Trajectory Judgment Pretext Task. To explore the layout knowledge of the YouTube-VLN dataset and equip the agent with layout reasoning ability, we propose a self-supervised trajectory judgment pretext task. In Table 1, the variant with the proposed pretext task improves the performance (#5 vs.#4, +2.05% on val seen and +0.60% on val unseen w.r.t. SR). Moreover, given a room type and visual information of the current node as inputs, this variant predicts the relative orientation of nodes for that" + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.501, + 0.898 + ], + "angle": 0, + "content": "8322" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.124, + 0.465, + 0.179 + ], + "angle": 0, + "content": "
#MethodsTLNE↓OSR↑SR↑SPL↑
1Random Sample9.373.5272.8864.410.61
2Temporal Difference9.553.6173.3565.300.61
3Entropy-Based9.643.3774.9366.700.62
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.184, + 0.469, + 0.213 + ], + "angle": 0, + "content": "Table 2: Comparison between different strategies of selecting frames to represent nodes under val unseen split." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.223, + 0.469, + 0.278 + ], + "angle": 0, + "content": "room type with a \\(30\\%\\) increase in accuracy (see supplementary for more details). These substantiate the claim of the importance of the proposed trajectory judgment task, which helps the agent learn the layout reasoning ability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.279, + 0.47, + 0.569 + ], + "angle": 0, + "content": "Effectiveness of Entropy-Based Trajectory Generation Strategy. In order to acquire an informative frame to represent a node, we propose an entropy-based technique as mentioned in Section 3.1. To demonstrate the effectiveness of our strategy, we construct two variants, i.e., one randomly chooses a frame, and one decides the frame by temporal difference [55]. The second variant computes the temporal pixel difference between every two consecutive frames and picks the frames where the peaks are located as the frames to represent the nodes. In Table 2, our entropy-based method significantly outperforms these two variants, increasing the SR on the val unseen split from \\(64.41\\%\\) and \\(65.30\\%\\) to \\(66.70\\%\\), respectively. We speculate this is because 1) randomly sampling frames can generate consecutive redundant frames or meaningless frames (e.g., a wall takes up most of the frame); 2) the temporal difference method selects a frame that represents the junction of two different rooms, which is ambiguous and thus confuses the agent. In comparison, our entropy-based method is able to find a reliable frame to represent a node and ensure two adjacent nodes belong to different room types." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.382, + 0.591 + ], + "angle": 0, + "content": "5.3. Comparison with State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.469, + 0.818 + ], + "angle": 0, + "content": "Results on R2R Dataset. We first compare our Lily agent with current methods under the discriminative setting. In Table 3, compared with VLN-BERT that uses image-caption pairs from the web for pre-training, our Lily agent significantly increases the SR by \\(10.74\\%\\) on the val unseen split. This highlights the importance of providing the indomain indoor data for pre-training. Moreover, compared with Airbert which uses in-domain image-caption pairs from online rental marketplaces, Lily still increases the SR from \\(73.85\\%\\) to \\(79.31\\%\\) on val seen and from \\(68.67\\%\\) to \\(70.00\\%\\) on val unseen. We attribute the improvement to our proposed VLN-like YouTube-VLN dataset and trajectory judgment pretext task, which have been thoughtfully evaluated in Section 5.2. When ensembled with the speaker-follower [10], all three methods increase the performance and our Lily agent performs the best." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.818, + 0.469, + 0.846 + ], + "angle": 0, + "content": "In Table 4, we evaluate on R2R test split and our Lily ranks first on the VLN challenge leaderboard compared" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.124, + 0.888, + 0.252 + ], + "angle": 0, + "content": "
MethodsVal SeenVal Unseen
TLNE↓SR↑SPL↑TLNE↓SR↑SPL↑
Follower [10]10.403.6865.100.629.575.2052.360.49
Speaker [10]11.193.8060.690.5610.714.2554.660.49
Speaker-Follower [10]10.692.7274.220.7010.103.3267.900.63
ProBES [30]----9.504.0560.280.56
VLN-BERT [36]10.283.7370.200.669.604.1059.260.55
Airbert [13]10.593.2173.850.6910.033.2468.670.63
Lily10.212.8979.310.7610.033.1970.000.65
VLN-BERT* [36]10.612.3581.860.7810.002.7673.610.68
Airbert* [13]10.632.1381.400.779.992.6975.010.70
Lily*10.512.0683.290.809.782.4876.880.72
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.257, + 0.892, + 0.3 + ], + "angle": 0, + "content": "Table 3: Comparison with state-of-the-arts on R2R dataset under discriminative setting. * means results of ensembling with the speaker-follower [10] model." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.306, + 0.888, + 0.435 + ], + "angle": 0, + "content": "
MethodsTLNE↓SPL↑OSR↑SR↑
Speaker-Follower [10]12574.870.019653
Self-Monitoring [35]3734.480.029761
Reinforced CM [51]3584.030.029663
EnvDrop [47]6873.260.019969
AuxRN [57]413.240.218171
VLN-BERT [36]686.822.990.019973
Global Normalization [53]686.862.990.019974
Airbert [13]686.542.580.019977
LiLy686.452.500.019979
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.44, + 0.891, + 0.468 + ], + "angle": 0, + "content": "Table 4: Results under discriminative setting on the test unseen split as indicated on the R2R leaderboard \\( {}^{2} \\) ." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.48, + 0.891, + 0.548 + ], + "angle": 0, + "content": "with the results whose manuscripts are publicly available, achieving the highest SR of \\(79\\%\\). As we follow Airbert to use 30 candidate trajectories from EnvDrop [47] and the leaderboard considers that our agent has walked through all these paths, the SPL metric is low for both Lily and Airbert." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.728 + ], + "angle": 0, + "content": "Besides, our Lily agent also helps to increase the performance on R2R under the generative setting. We enhance the state-of-the-art DUET [6] method by pre-training the agent using our method as mentioned in Section 4. In Table 6, the agent incorporating Lily achieves \\(2\\%\\) and \\(3\\%\\) improvements w.r.t. SR on the val unseen split and test unseen split, respectively, compared to DUET. Notably, our method increases the SPL by \\(2\\%\\) on the val unseen split, indicating the agent is able to reach the goal more efficiently. We attribute this to the agent's acquisition of layout prior knowledge via the proposed trajectory judgment task on our YouTube-VLN dataset, enabling it to plan more efficient routes to the goals in new environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Results on REVERIE Dataset. Compared with R2R, REVERIE is more challenging as its instructions only describe the destinations without detailed path descriptions. This requires the agent to be equipped with common knowledge about the room layouts and to reason the possible paths that lead to the destinations. In Table 5, we outperform the SOTA agent (i.e., DUET) by \\(1.13\\%\\) on SR and increase the SPL from \\(46.98\\%\\) to \\(48.11\\%\\) on the val unseen split. It is worth noting that our method achieves a higher OSR with a shorter TL, indicating that our agent finds the destination" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.852, + 0.466, + 0.865 + ], + "angle": 0, + "content": "2https://eval.ai/web/challenges/challenge-page/97/leaderboard/270" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.888, + 0.501, + 0.898 + ], + "angle": 0, + "content": "8323" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.158, + 0.123, + 0.805, + 0.304 + ], + "angle": 0, + "content": "
MethodsVal UnseenTest Unseen
NavigationGroundingNavigationGrounding
TLOSR↑SR↑SPL↑RGS↑RGSPL↑TLOSR↑SR↑SPL↑RGS↑RGSPL↑
Human------21.1886.8381.5383.6677.8451.44
Seq2Seq [1]11.078.074.202.842.161.6310.896.883.993.092.001.58
RCM [51]11.9814.239.296.974.893.8910.6011.687.846.673.673.14
SMNA [35]9.0711.288.156.444.543.619.238.395.804.533.102.39
FM [41]45.2828.2014.407.197.844.6739.0530.6319.8811.6111.286.08
SIA [33]41.5344.6731.5316.2822.4111.5648.6144.5630.8014.8519.029.20
HAMT [5]14.0836.8432.9530.2018.9217.2813.6233.4130.4026.6714.8813.08
RecBERT [18]16.7835.0230.6724.9018.7715.2715.8632.9129.6123.9916.5013.51
ProbES [30]18.0033.2327.6322.7516.8413.9416.8428.2324.9720.1215.1112.32
Airbert [13]18.7134.5127.8921.8818.2314.1817.9134.2030.2823.6116.8313.28
DUET [6]22.1151.0746.9833.7332.1523.0321.3056.9152.5136.0631.8822.06
DUET (Lily)21.8753.7148.1134.4332.1523.4321.9460.5154.3237.3432.0221.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.082, + 0.309, + 0.885, + 0.323 + ], + "angle": 0, + "content": "Table 5: Comparison with state-of-the-arts on REVERIE. Lily agent achieves the state-of-the-art performance on all splits." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.332, + 0.465, + 0.499 + ], + "angle": 0, + "content": "
MethodsVal UnseenTest Unseen
TLNE↓SR↑SPL↑TLNE↓SR↑SPL↑
Seq2Seq [1]8.397.8122-8.137.8520-
EnvDrop [47]10.705.22524811.665.235147
AuxRN [57]-5.285550-5.155551
PREVALENT [14]10.194.71585310.515.305451
RelGraph [17]9.994.73575310.294.755552
RecBERT [18]12.013.93635712.354.096357
ProbES [30]11.584.00615512.434.206256
ADAPT [32]12.333.66665913.164.116357
HOP [42]12.273.80645712.653.836459
HAMT [5]11.462.29666112.273.936560
Airbert [13]11.784.01625612.414.136257
DUET [6]13.943.31726014.733.656959
DUET (Lily)14.582.90746216.133.447260
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.504, + 0.468, + 0.531 + ], + "angle": 0, + "content": "Table 6: Comparison with state-of-the-arts on R2R dataset under generative setting." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.546, + 0.468, + 0.656 + ], + "angle": 0, + "content": "more quickly. We attribute this to the better layout reason ability learned from the large-scale diverse reasonable trajectories in the proposed YouTube-VLN dataset. A similar performance is obtained on the test unseen split, where the Lily agent improves the SR by \\(1.81\\%\\) and the SPL by \\(1.28\\%\\). Although our objective is solely navigation, we still achieve comparable performance on grounding metrics and even slightly outstrip DUET on most metrics." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.666, + 0.454, + 0.68 + ], + "angle": 0, + "content": "5.4. Learning Navigation from One Environment" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.687, + 0.468, + 0.852 + ], + "angle": 0, + "content": "Our intuition is that pre-training on the YouTube-VLN dataset can mitigate the domain gap of training from scratch and is able to achieve excellent performance with only a few training environments. To verify this, we conduct a one-shot learning study, where we fine-tune our model on only one environment of the original training environments. Note that the candidate paths are generated from all of the possible paths from the start viewpoints to all navigable points, instead of from the expert model in EnvDrop [47]. All the candidate paths are the shortest paths in the navigation graphs. To reduce the bias, we randomly select 5 sets from the entire environments and report the average results." + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.853, + 0.468, + 0.866 + ], + "angle": 0, + "content": "In Table 7, our agent outperforms all the existing pre" + }, + { + "type": "table", + "bbox": [ + 0.583, + 0.332, + 0.809, + 0.381 + ], + "angle": 0, + "content": "
MethodsVal SeenVal Unseen
VLN BERT [36]45.7122.43
AirBERT [13]47.8850.00
Lily49.3150.86
" + }, + { + "type": "table_caption", + "bbox": [ + 0.503, + 0.386, + 0.89, + 0.414 + ], + "angle": 0, + "content": "Table 7: SR on val seen and val unseen splits of R2R. All the agents access only one environment." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.425, + 0.89, + 0.506 + ], + "angle": 0, + "content": "training methods. On the val seen split using one-shot finetuning, compared to VLN-BERT and AirBERT, our Lily agent achieves \\(3.60\\%\\) and \\(1.43\\%\\) improvements, respectively. In the val unseen split using one-shot fine-tuning, we achieve \\(28.43\\%\\) improvement compared to VLN-BERT. All these results suggest the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.519, + 0.617, + 0.533 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.542, + 0.89, + 0.748 + ], + "angle": 0, + "content": "In this work, we propose a new approach Lily to address the limitations of existing vision-and-language navigation (VLN) methods by creating a large-scale VLN-like dataset from real house tour videos to train our embodied agent. We overcome the challenges of automatically generating path-instruction pairs to construct the dataset from raw and unlabeled videos by leveraging an entropy-based method for trajectory construction and an action-aware generator for instruction generation. Additionally, we train the agent to judge the reasonableness of trajectories, improving its layout reasoning ability. Our method achieves state-of-the-art performance on two popular benchmarks (R2R and REVERIE), demonstrating the efficacy. Overall, we hope our work can provide valuable insight into the VLN community by learning embodied VLN from passive videos." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.761, + 0.658, + 0.776 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.784, + 0.89, + 0.865 + ], + "angle": 0, + "content": "Prof. Tan and his students were partially supported by the National Natural Science Foundation of China (NSFC) (62072190), National Natural Science Foundation of China (NSFC) 61836003 (key project), Program for Guangdong Introducing Innovative and Entrepreneurial Teams 2017ZT07X183." + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.888, + 0.501, + 0.898 + ], + "angle": 0, + "content": "8324" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.174, + 0.14 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.47, + 0.212 + ], + "angle": 0, + "content": "[1] P. 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Li $^{6}$ Mingkui Tan $^{15\dagger}$ Chuang Gan $^{34}$ + +$^{1}$ South China University of Technology, $^{2}$ Information Technology R&D Innovation Center of Peking University, $^{3}$ UMass Amherst, $^{4}$ MIT-IBM Watson AI Lab, $^{5}$ Key Laboratory of Big Data and Intelligent Robot, Ministry of Education, $^{6}$ Peking University Shenzhen Graduate School + +# Abstract + +Vision-and-language navigation (VLN) requires an embodied agent to navigate in realistic 3D environments using natural language instructions. Existing VLN methods suffer from training on small-scale environments or unreasonable path-instruction datasets, limiting the generalization to unseen environments. There are massive house tour videos on YouTube, providing abundant real navigation experiences and layout information. However, these videos have not been explored for VLN before. In this paper, we propose to learn an agent from these videos by creating a large-scale dataset which comprises reasonable path-instruction pairs from house tour videos and pre-training the agent on it. To achieve this, we have to tackle the challenges of automatically constructing path-instruction pairs and exploiting real layout knowledge from raw and unlabeled videos. To address these, we first leverage an entropy-based method to construct the nodes of a path trajectory. Then, we propose an action-aware generator for generating instructions from unlabeled trajectories. Last, we devise a trajectory judgment pretext task to encourage the agent to mine the layout knowledge. Experimental results show that our method achieves state-of-the-art performance on two popular benchmarks (R2R and REVERIE). Code is available at https://github.com/JeremyLinky/YouTube-VLN + +# 1. Introduction + +An important goal of embodied artificial intelligence is to develop agents that can interact with humans in natural language to carry out real-world tasks. Toward this goal, vision-and-language navigation (VLN) [1] is a rudimentary artificial intelligence task, requiring an indoor agent to navigate in unseen environments following natural instructions. VLN has attracted widespread attention in the fields of computer vision and robotics due to its promising applications such as in-home robots [54] and warehouse assistants [29]. + +One of the key challenges of VLN is the generaliza + +tion ability of agents to unseen environments. Existing VLN methods attempt to cope with this challenge via self-supervised pre-training on vision-and-language datasets. As shown in Figure 1 (a), some previous works [30, 19, 36, 7] learn the agents on simulated navigation environments and manual-labeled data. The other works [14, 13, 42] seek to construct path-instruction pairs by using web image data, which is shown in Figure 1 (b). Despite their promising performance, existing agents still suffer from the following limitations. 1) Training on simulated datasets is limited to a restricted number of environments. 2) Constructing a trajectory by simply concatenating web images leads to unreasonable room layouts, which hamper the agent to learn layout reasoning ability. As a result, VLN agents trained on such data are brittle to adapt to unseen environments. + +Fortunately, there are massive house tour videos on YouTube, providing real navigation experiences and layout information but are still under-explored. We can be naturally inspired to let an agent learn VLN ability from such videos, thereby addressing the limitations of existing methods. An intuitive way is to model the navigation experiences as path-instruction pairs to train the agent. Motivated by this, we propose a "Lily" agent who Learns Vision-and-Language Navigation from YouTube Videos. Specifically, we first develop an in-domain pre-training dataset from house tour YouTube videos, namely YouTube-VLN, which comprises VLN-like path-instruction pairs. Our YouTube-VLN dataset has the advantages of diverse environments, real layouts, and native actions1, reducing the domain gap with VLN datasets, as illustrated in Figure 1 (c). Then, we pre-train the agent using these path-instruction pairs. Benefiting from in-domain pre-training on our proposed dataset, our agent thus generalizes well to unseen environments. + +Constructing and utilizing such a dataset, however, is still far from trivial work and remains an open problem due to the following challenges. 1) As the nodes in a trajectory are expected to be diverse and informative, it is hard to determine the locations of trajectory nodes from massive video frames and represent the visual content in a node. + +![](images/c11408a7f201d573b27741475014fc7813798c4515551140b0e4d5c204daa5bd.jpg) +(a) Dataset from Simulation Environments + +![](images/c14b03dc69edf64fb69b545e50b9f1d311fab96dfe8bd8402545f487db3fa0c1.jpg) +(b) Dataset from Web Images Data +Figure 1: Comparison of different datasets for pre-training. Existing datasets are built from either simulation environments (a) or web images data (b). The former only covers limited environments, and the latter contains confusing layouts and ambiguous actions. Our dataset built from YouTube videos (c) is able to provide diverse environments, real layouts and native actions simultaneously. + +![](images/3a261921a590a6f671e0f8db494f0c3f1e28b5fac03bcf9828da0e6c1f7c3cd2.jpg) +(c) Dataset from YouTube Videos (Ours) + +2) Real VLN instructions include various action descriptions, but obtaining corresponding instructions from navigation clips is challenging due to the actions being implicit in videos. Thus it is nontrivial to acquire matching instruction on a trajectory. 3) Layout knowledge from real navigation experience is hard to mine and model, which impedes the agent of learning layout reasoning ability. + +In this paper, we address the above challenges as follows. To conquer challenge 1), we propose an entropy-based trajectory generation method. Specifically, we first envisage that the nodes of a trajectory should contain as many types of rooms as possible to diversify trajectories. Accordingly, we group the frames with the same room types in videos and consider each group as a node in the trajectory. Then, inspired by that low classification entropy image is reliable and contains rich information relevant to a specific class (room type in our case) [39], the frame with the lowest classification entropy in a group is chosen to represent the visual content in a node. To tackle challenge 2), we introduce an action-aware instruction generation method. Specifically, we adopt an action inverse model to pseudo-label the action along trajectories and fill them in the instructions via hand-designed rules. To grapple with challenge 3), we devise a self-supervised pretext task. As we all know, humans often judge whether a navigation trajectory is reasonable based on the layout of the environment. Therefore, it is believed that an agent equipped with layout reasoning ability should be able to make similar judgment. To this end, we propose trajectory judgment pretext task to ask the agent to identify reasonable navigation trajectories, which further equips the model with the ability to reason environment layouts. + +We empirically show that the diverse entropy-based trajectory generation method and action-aware instruction generator allow us to harvest high-quality path-instruction pairs from YouTube house tour videos, resulting in the YouTube-VLN dataset. By integrating the self-supervised trajectory judgment task in pre-training a VLN agent, our + +Lily agent presents state-of-the-art performance on two mature and solid benchmarks (R2R [1], REVERIE [41]). The proposed Lily agent reaches the first place on the R2R leaderboard in terms of success rate and outperforms the SOTA method under discriminative setting and generative setting by $2\%$ and $3\%$ w.r.t. success rate, respectively. + +Our main contributions are as follows: + +- We unleash the huge potential of house tour videos for VLN. By leveraging these videos, we introduce a largescale dataset containing real navigation path-instruction pairs for promoting VLN pre-training and a self-supervised pretext task for the learning of layout reasoning. +- Our diverse trajectory generation method, together with the action-aware instruction generator, creates informative and diverse trajectory nodes and produces matching instructions, both of which make the path-instruction pairs authentic and of high quality for training a VLN agent. +- The proposed trajectory judgment pretext task allows the model to build up an awareness of learning and reasoning the layout knowledge, which is crucial in the VLN task of indoor environments. We also empirically substantiate that the agent indeed learns the layout learning ability. + +# 2. Related Work + +# 2.1. Vision-and-Language Navigation + +Vision-and-Language Navigation (VLN) [1] is a challenging task and has received continuous and intense attention from the academic community in recent years [4, 12, 25, 31, 46, 27, 6, 45, 9]. Early methods attempt to learn the agent from sequence-to-sequence models [1, 10, 47]. However, these methods can not model the cross-modal relation between language and visual observation well. To address this issue, transformer [48] architecture is adopted to the agents followed by vision-and-language pre-training [35, 50, 57, 37, 13, 42, 5, 38, 24]. PREVALENT [15] pretrains transformer-based agent via masked language mod + +eling and action prediction tasks. Inspired by BERT [8], several works propose to use different variants of BERT for VLN pre-training. VLN-BERT [37] utilizes image-text data [34] to perform path-instruction matching pretext task. Airbert [13] proposes the shuffle loss to improve the ability of the model to learn the order of image-caption pairs. Recently, HOP [42] introduces the history and order-aware pretext tasks. However, these existing pretext tasks do not consider the learning of environment layout reasoning ability and bring limited performance for VLN tasks. In this work, we propose a trajectory judgment task to teach the agent to distinguish reasonable navigation trajectories. By proficiently accomplishing this task, the agent can acquire the ability to reason about environment layout, which enhances its generalization capability to unseen environments. + +# 2.2. Datasets for VLN + +The major difficulty of generalizing a VLN agent to unseen environments is the scarcity of VLN training data. Well-labeled VLN datasets built from the simulators [2, 44, 52] allow the agent to obtain a promising performance, such as R2R [1], R4R [20], RxR [23] and SOON [56]. While the data built from simulators are laborious, Wang et al. [49] and ProbES [30] enrich the navigation instructions via self-exploration in the simulation environments. Some other endeavors [47, 28, 10, 11, 22, 26] seek to augment the data from existing datasets. AutoVLN [7] and Kamath et al. [21] enlarges the VLN data from simulations with a larger number of environments. However, these datasets are limited by the number of scenes in simulators. To ease this problem, VLN-BERT [37] leverages the abundant web image-captions pairs as VLN pre-training data. Airbert [13] further exploits indoor house images and captions from the web to construct path-instruction pairs for VLN pre-training. However, the trajectories constructed by simply splicing pictures may be confusing and ambiguous. In our work, we address these problems by proposing a large-scale in-domain VLN-like pre-training dataset, providing the agent with diverse visual environments and reasonable layouts. + +# 3. Building VLN Dataset from YouTube Videos + +Our first step is to develop a large-scale VLN-like dataset that comprises reasonable path-instruction pairs from house tour videos on YouTube, termed YouTube-VLN. YouTube-VLN serves as a cornerstone for facilitating the acquisition of VLN capabilities for Lily, featuring diverse environments, real layouts and native actions. To achieve this goal, we present an entropy-based trajectory generation technique (Section 3.1) and an action-aware generator (Section 3.2) to tackle the arduous tasks of trajectory and instruction generation, respectively. + +![](images/4e676be56851763f7094e83440bfc2926fb1af94666b7c64d1ed83b413a8866e.jpg) +Figure 2: An example of a generated trajectory from a YouTube house tour video. $\rightarrow$ represents the direction to go next while $\rightarrow$ represents the stop action. + +# 3.1. Diverse Trajectory Generation. + +We seek to construct discrete navigation trajectories from YouTube videos. Similar to discrete navigation datasets (e.g., R2R [1]), each trajectory comprises $K$ navigation nodes, representing different locations of a navigation path. This entails addressing two major challenges: 1) how to determine the locations composing a trajectory to make the trajectory more diverse and 2) how to represent the visual content at each node location. To tackle these challenges, we first collect large-scale consecutive indoor frames from YouTube videos. Then, we group the adjacent frames according to their room types and consider each group as a node. Last, we present an entropy-based technique to select the most informative frames in a group for representing the visual content in a node. + +Collecting Navigation Data from YouTube. Real estate agents typically tour a house in each video. To satisfy the visual diversity and dataset scale, we create the YouTube-VLN dataset from 4078 videos collected from various uploaders, with a total duration of 433 hours. In contrast to prior work [3], which relied on a limited set of videos from a single uploader, our dataset features greater diversity and volume. We also employ sparse sampling and off-the-shelf image classifiers [16, 43] to pre-process the videos, filtering out redundant or noisy frames (those featuring people or outdoor scenes), resulting in a final set of 587k indoor frames suitable for constructing trajectories. + +Determining the Locations of Trajectory Nodes. A real robot often needs to go through different locations for navigating to a goal. To mimic the real navigation process, we expect that our constructed trajectories also contain diverse visual content within the limited navigation nodes. To achieve this, we first utilize the powerful large model CLIP [43] to recognize the room type of each indoor im + +age. Then, we gather temporally adjacent frames with the same room type as a group and consider this group as one of the navigation nodes. In this sense, the navigation nodes are diversely spread in different rooms and the constructed trajectories are able to mimic the real navigation process. We also call this kind of node a room node. In practice, to increase the visual diversity of trajectories, we also randomly insert transition nodes that are composed of video frames captured during the transition from one room to another one, between two adjacent room nodes. + +Representing Visual Content in a Node. A node consists of a group of images and sometimes the number of images may exceed 100 as the photographer could stay in the same room for a long time. Hence, we have to select the most informative images for representing node features. Inspired by EATA [39], an image with lower classification entropy is more reliable, containing more information relevant to a specific class (room type in our case). We thus propose to select an image with the lowest classification entropy to represent the current view of a node. In order to mimic the panoramic visual context, we then merge $M$ adjacent consecutive images of the current view. It is worth noting that our node features better represent a panoramic view compared with Airbert [13] because we merge adjacent frames that belong to the same place as the current view. + +Ultimately, we randomly chose $K$ continuous nodes to construct a trajectory. An example of the constructed trajectory is shown in Figure 2. + +# 3.2. Action-Aware Instruction Generation + +In addition to constructing navigation trajectories, one more important step for building a VLN dataset is to create the corresponding instructions without manual annotation. The main challenge for this step is how to correctly describe visual content and actions along navigation paths. To conquer this challenge, we first generate instruction templates with verb and noun phrase blanks. Then, we describe each node in trajectories using the CLIP [43] model and infer the native actions using an action inverse model [3]. To generate the final instructions, we fill the instruction templates with these visual descriptions and actions. + +Specifically, we first generate templates with verb and noun blanks from instructions in the R2R dataset following Airbert [13]. For noun blanks, we fill them with visual content descriptions about each node. We select the frame with the lowest classification entropy (as described in Sec. 3.1) and use the CLIP model to infer the objects it contains, together with the room type to populate a noun blank. For verb blanks, the existing instruction generation method [13] is unable to fill them with the correct action words because it cannot figure out the actions taken for navigating from one image to another. This makes the agent confused when it observes similar viewpoints transition but is given differ + +ent action descriptions. To tackle this problem, we propose an action-aware strategy to fill instruction templates with native actions instead of random inconsistent actions. To be specific, we follow [3] to train an action inverse model, which has $96\%$ prediction accuracy for predicting native actions, to pseudo-label the trajectory with action labels from one location node to another. The predicted actions are then converted into actionable verbs, i.e., "go forward", "turn left" and "turn right". For each noun blank that has been filled with the description of one node, we find its closest verb phrase blank and fill it with the pseudo-labeled action which is executed to reach the next node. This eventually enables us to create action-aware instructions. + +# 4. Learning VLN from YouTube Videos + +Given the VLN-like and reasonable path-instruction pairs generated from YouTube videos, we then describe how to learn the Lily agent from these data. As shown in Figure 3, our VLN model consists of two components: a vision-and-language backbone (i.e., Multi-Layer Transformer) that models the relationship between trajectories and instructions and a decision-making module that predicts the next action or a matching score for a path-instruction pair. The vision-and-language backbone can be any type of cross-modal network. We chose ViLBERT [34] for a fair comparison with Airbert [13]. As a common practice, pretext tasks are utilized for pre-training the backbone. We next describe how to pre-train the backbone on our Youtube-VLN dataset using the proposed trajectory judgment pretext task. + +# 4.1. Model Architecture + +We follow Airbert [13] to leverage a ViLBERT-like [34] architecture as the model backbone. The model encodes the sequential visual region features and the text token via two separate transformers respectively. More formally, the path-instruction pair consists of $K$ nodes $\{V_k\}_{k=1}^K$ and $L$ text tokens $\{w_l\}_{l=1}^L$ . Each node $V_k$ is composed of $R_k$ visual region features $\{v_i^k\}_{i=1}^{R_k}$ . In this way, we represent the visual and text inputs respectively as follows: + +$$ +\begin{array}{l} X _ {V} = \left[ \left[ \operatorname {I M G} \right], v _ {1} ^ {1}, \dots , v _ {R _ {1}} ^ {1}, \dots , \left[ \operatorname {I M G} \right], v _ {1} ^ {K}, \dots , v _ {R _ {K}} ^ {K} \right], (1) \\ X _ {W} = \left[ \left[ \mathrm {C L S} \right], w _ {1}, \dots , w _ {l}, \dots , w _ {L}, [ \mathrm {S E P} ] \right], (2) \\ \end{array} +$$ + +where [IMG], [CLS] and [SEP] are special tokens. The encoded visual and text tokens finally interact via a cross-modal transformer encoder. We represent the whole model architecture as "Multi-Layer Transformer" in Figure 3. + +# 4.2. Learning Layout from Trajectory Judgment + +Given the aforementioned model architecture, we propose to train a VLN agent with a trajectory judgment (TJ) + +![](images/54d51f805e433c01781504cc9c06a427e91f68b33992d33b124ac957f7ca679e.jpg) +Figure 3: General scheme of our Lily agent for pre-training and downstream stages of VLN tasks. Lily agent learns to leverage the proposed YouTube-VLN dataset for the trajectory judgment task together with the other pretext tasks. After pre-training the VLN model, we adapt it to the downstream datasets and conduct different VLN downstream tasks. + +task, enabling it to reason about layouts. Herein, we elaborate on the proposed trajectory judgment task. + +**Formulation.** The trajectory judgment task aims to judge the reasonableness of trajectories. We consider the trajectories generated in the way described in Section 3.1 as positive (reasonable) samples and the shuffled trajectories as negative (unreasonable) ones. To finish this task, the agent is required to reason about the visual information and identify the room types, then infer whether the trajectory matches the real environment layout distribution. Specifically, we first calculate the dot product of the output features of [IMG] and [CLS] tokens. Then, we feed this vector feature to a linear layer to predict the probability that indicates whether the trajectory is reasonable. The model aims to minimize the binary cross-entropy loss: + +$$ +L = - \frac {1}{N} \sum_ {n = 1} ^ {N} \left[ w \cdot y _ {n} \log (p _ {n}) + (1 - y _ {n}) \log (1 - p _ {n}) \right], \tag {3} +$$ + +where $y_{n} = 1$ if the $n^{th}$ trajectory is reasonable, otherwise $y_{n} = 0$ . $p_{n}$ represents the probability that the $n^{th}$ trajectory is predicted as reasonable. $N$ is the number of trajectories in a batch. $w$ is a factor to mitigate the imbalance of positive and negative samples, which equals the ratio of the number of negative samples to the number of positive samples. + +Sample Generation. We propose to shuffle the positive sample to generate the negative samples: 1) shuffle only the transition nodes; 2) shuffle all the nodes; 3) keep the order of the room nodes, and randomly insert nodes from other videos. In this way, we create rich and hard negative samples, which increases the task difficulty, helping the agent understand the real layout in a more complex manner. + +Combining with Existing Pre-Training Tasks. As depicted in Figure 3, we follow Airbert [13] to pre-train the model backbone using our proposed trajectory judgment task, additionally combining with three other existing + +pretext tasks, namely masked language modeling (MLM), masked vision modeling (MVM) and path ranking (PR) on YouTube-VLN dataset. For MLM, we randomly mask out the words in instruction and the goal is to recover the masked words. Similar to MLM, MVM is designed to predict masked image regions. PR is a ranking task, which aims to decide the most matching path-instruction pair among a few pairs. + +# 4.3. Adapting Pre-trained Backbone for VLN + +We adapt the pre-trained model to both goal-oriented navigation task and object-oriented navigation task. All the tasks are based on the Matterport3D simulator [2]. We utilize R2R [1] as the benchmark for the goal-oriented navigation task, which is divided into discriminative setting and generative setting. As for the object-oriented task, we evaluate our model on REVERIE [41] in generative setting. + +The discriminative setting formulates VLN as a path-selection problem, requiring the agent to choose the path that best matches the instruction from multiple candidate paths. Under the discriminative setting, we utilize the classifier used in the path ranking pretext task for decision-making and fine-tune the Lily agent on the R2R dataset. + +In the generative setting, the agent needs to predict actions sequentially to reach the goal (R2R) or simultaneously find the object (REVERIE). We adopt DUET [6] as the architecture for fine-tuning, which feeds the cross-modal feature into a feed-forward network for decision-making. We initialize the text transformer encoder and cross-modal transformer encoder of the generative model with our Lily agent. Note that our Lily agent can apply to any generative model. More details are available in the supplementary. + +
#DatasetPre-training TaskVal SeenVal Unseen
SourceReasonable Navigation PathPseudo-labeled ActionTrajectory JudgmentTLNE↓OSR↑SR↑SPL↑TLNE↓OSR↑SR↑SPL↑
1Airbnb ImagesXXX10.213.4179.0274.120.709.633.9570.9762.840.58
2YouTube VideosXXX10.123.4079.9074.310.709.813.7274.2463.730.59
3YouTube Videos✓XX10.303.4078.6075.100.719.603.7073.5065.000.61
4YouTube Videos✓✓X10.203.3079.8075.400.719.303.6072.7066.100.62
5YouTube Videos✓✓✓9.993.1280.8877.450.749.643.3774.9366.700.62
+ +Table 1: Ablation study on YouTube-VLN dataset and trajectory judgment pretext task for pre-training. + +# 5. Experiments + +# 5.1. Experimental Setup + +Dataset and Evaluation Metrics. We conduct our experiments on two VLN benchmarks, i.e., R2R [1] and REVERIE [41]. These two datasets consist of 21,567 path-instruction pairs from 90 scenes in Matterport3D [2]. REVERIE follows the same train/val/test splits as the R2R, while requiring an agent to select the bounding box of the target object bounding box additionally. Following standard settings [13], we adopt five metrics for evaluating R2R, namely success rate (SR), oracle success rate (OSR), success rate weighted by the ratio between the length of the shortest path and the predicted path (SPL), trajectory length (TL) and navigation error (NE). As for REVERIE, we leverage four metrics for evaluating navigation performance, namely SR, OSR, SPL and TL, and two for object grounding performance, namely remote grounding success (RGS) and RGS weighted by path length (RGSPL). + +Implementation Details. We implement our method based on Pytorch framework [40] and Matterport3D simulator [2]. Specifically, we divide our training process into two stages, i.e., pre-training and fine-tuning. For the pretraining stage, we distribute training over 4 NVIDIA 3090 GPUs for 500 epochs to convergence. The pre-trained model with the highest accuracy for the path ranking pretext task is selected for fine-tuning. During the fine-tuning stage, we distribute training over 8 NVIDIA 3090 GPUs for 30 epochs to convergence. Following Airbert [13], we use augmented data from EnvDrop [47] for fine-tuning by default. More details are provided in the supplementary. + +# 5.2. Ablation Studies on Pre-Training + +We ablate our approach under discriminative setting on R2R benchmark. Considering the time efficiency, we do not use augmented data for fine-tuning on these experiments. + +Data Source: Airbnb Images vs. YouTube Videos. One of the main differences between YouTube-VLN dataset and Airbnb dataset [13] is the data source. Airbnb consists of 713k image-caption pairs while YouTube-VLN consists of 587k images extracted from 433 hours of house tour videos. YouTube-VLN has fewer images but provides more information about a room from different camera angles by merging, which better simulates a panorama for down- + +stream VLN tasks. To evaluate the effect of data source, we follow Airbert [13] to randomly select images in the same house to build a trajectory and its corresponding instruction. We keep the number of instructions the same in pre-training for a fair comparison. In Table 1 (# 1 vs. # 2), YouTube data performs slightly better than Airbnb data, surpassing the SR by $0.89\%$ on the val unseen split. We speculate this is because data quality is more important than quantity. + +Effectiveness of Reasonable Navigation Trajectory. YouTube-VLN dataset is collected from real house tour videos and is thus able to extract frames in chronological order to build reasonable navigation trajectories instead of combining multiple randomly chosen images. We use the generated reasonable navigation trajectories and shuffled trajectories to train two agents, respectively. In Table 1, the agent trained with reasonable navigation trajectories (# 3) achieves significantly better performance than the shuffled navigation trajectories variant (# 2), with $1.27\%$ gains on SR under the val unseen split. This suggests that the agent can not well understand and ground the instruction to the trajectory without reasonable navigation paths for learning. + +Effectiveness of Pseudo-Labeled Action. The core of the proposed action-aware instruction generator is the pseudo-labeled actions for the instructions. To evaluate the effectiveness of the pseudo-labeled actions, we construct a variant that replaces random action words with the pseudo-labeled actions which are filled in the instructions. The results are shown in Table 1, # 4. Compared to the variant (# 3) that fills the instructions with random action words, this variant boosts the SR metric on both the val unseen (+1.10%) and seen (+0.30%) splits, showing the effectiveness of pseudo-labeled actions. It indicates that with pseudo-labeled actions, the agent can effectively ground the action to the visual observation and recognizes the correct transition from one location to another. + +Effectiveness of Trajectory Judgment Pretext Task. To explore the layout knowledge of the YouTube-VLN dataset and equip the agent with layout reasoning ability, we propose a self-supervised trajectory judgment pretext task. In Table 1, the variant with the proposed pretext task improves the performance (#5 vs.#4, +2.05% on val seen and +0.60% on val unseen w.r.t. SR). Moreover, given a room type and visual information of the current node as inputs, this variant predicts the relative orientation of nodes for that + +
#MethodsTLNE↓OSR↑SR↑SPL↑
1Random Sample9.373.5272.8864.410.61
2Temporal Difference9.553.6173.3565.300.61
3Entropy-Based9.643.3774.9366.700.62
+ +room type with a $30\%$ increase in accuracy (see supplementary for more details). These substantiate the claim of the importance of the proposed trajectory judgment task, which helps the agent learn the layout reasoning ability. + +Effectiveness of Entropy-Based Trajectory Generation Strategy. In order to acquire an informative frame to represent a node, we propose an entropy-based technique as mentioned in Section 3.1. To demonstrate the effectiveness of our strategy, we construct two variants, i.e., one randomly chooses a frame, and one decides the frame by temporal difference [55]. The second variant computes the temporal pixel difference between every two consecutive frames and picks the frames where the peaks are located as the frames to represent the nodes. In Table 2, our entropy-based method significantly outperforms these two variants, increasing the SR on the val unseen split from $64.41\%$ and $65.30\%$ to $66.70\%$ , respectively. We speculate this is because 1) randomly sampling frames can generate consecutive redundant frames or meaningless frames (e.g., a wall takes up most of the frame); 2) the temporal difference method selects a frame that represents the junction of two different rooms, which is ambiguous and thus confuses the agent. In comparison, our entropy-based method is able to find a reliable frame to represent a node and ensure two adjacent nodes belong to different room types. + +# 5.3. Comparison with State-of-the-Arts + +Results on R2R Dataset. We first compare our Lily agent with current methods under the discriminative setting. In Table 3, compared with VLN-BERT that uses image-caption pairs from the web for pre-training, our Lily agent significantly increases the SR by $10.74\%$ on the val unseen split. This highlights the importance of providing the indomain indoor data for pre-training. Moreover, compared with Airbert which uses in-domain image-caption pairs from online rental marketplaces, Lily still increases the SR from $73.85\%$ to $79.31\%$ on val seen and from $68.67\%$ to $70.00\%$ on val unseen. We attribute the improvement to our proposed VLN-like YouTube-VLN dataset and trajectory judgment pretext task, which have been thoughtfully evaluated in Section 5.2. When ensembled with the speaker-follower [10], all three methods increase the performance and our Lily agent performs the best. + +In Table 4, we evaluate on R2R test split and our Lily ranks first on the VLN challenge leaderboard compared + +Table 2: Comparison between different strategies of selecting frames to represent nodes under val unseen split. + +
MethodsVal SeenVal Unseen
TLNE↓SR↑SPL↑TLNE↓SR↑SPL↑
Follower [10]10.403.6865.100.629.575.2052.360.49
Speaker [10]11.193.8060.690.5610.714.2554.660.49
Speaker-Follower [10]10.692.7274.220.7010.103.3267.900.63
ProBES [30]----9.504.0560.280.56
VLN-BERT [36]10.283.7370.200.669.604.1059.260.55
Airbert [13]10.593.2173.850.6910.033.2468.670.63
Lily10.212.8979.310.7610.033.1970.000.65
VLN-BERT* [36]10.612.3581.860.7810.002.7673.610.68
Airbert* [13]10.632.1381.400.779.992.6975.010.70
Lily*10.512.0683.290.809.782.4876.880.72
+ +Table 3: Comparison with state-of-the-arts on R2R dataset under discriminative setting. * means results of ensembling with the speaker-follower [10] model. + +
MethodsTLNE↓SPL↑OSR↑SR↑
Speaker-Follower [10]12574.870.019653
Self-Monitoring [35]3734.480.029761
Reinforced CM [51]3584.030.029663
EnvDrop [47]6873.260.019969
AuxRN [57]413.240.218171
VLN-BERT [36]686.822.990.019973
Global Normalization [53]686.862.990.019974
Airbert [13]686.542.580.019977
LiLy686.452.500.019979
+ +Table 4: Results under discriminative setting on the test unseen split as indicated on the R2R leaderboard ${}^{2}$ . + +with the results whose manuscripts are publicly available, achieving the highest SR of $79\%$ . As we follow Airbert to use 30 candidate trajectories from EnvDrop [47] and the leaderboard considers that our agent has walked through all these paths, the SPL metric is low for both Lily and Airbert. + +Besides, our Lily agent also helps to increase the performance on R2R under the generative setting. We enhance the state-of-the-art DUET [6] method by pre-training the agent using our method as mentioned in Section 4. In Table 6, the agent incorporating Lily achieves $2\%$ and $3\%$ improvements w.r.t. SR on the val unseen split and test unseen split, respectively, compared to DUET. Notably, our method increases the SPL by $2\%$ on the val unseen split, indicating the agent is able to reach the goal more efficiently. We attribute this to the agent's acquisition of layout prior knowledge via the proposed trajectory judgment task on our YouTube-VLN dataset, enabling it to plan more efficient routes to the goals in new environments. + +Results on REVERIE Dataset. Compared with R2R, REVERIE is more challenging as its instructions only describe the destinations without detailed path descriptions. This requires the agent to be equipped with common knowledge about the room layouts and to reason the possible paths that lead to the destinations. In Table 5, we outperform the SOTA agent (i.e., DUET) by $1.13\%$ on SR and increase the SPL from $46.98\%$ to $48.11\%$ on the val unseen split. It is worth noting that our method achieves a higher OSR with a shorter TL, indicating that our agent finds the destination + +
MethodsVal UnseenTest Unseen
NavigationGroundingNavigationGrounding
TLOSR↑SR↑SPL↑RGS↑RGSPL↑TLOSR↑SR↑SPL↑RGS↑RGSPL↑
Human------21.1886.8381.5383.6677.8451.44
Seq2Seq [1]11.078.074.202.842.161.6310.896.883.993.092.001.58
RCM [51]11.9814.239.296.974.893.8910.6011.687.846.673.673.14
SMNA [35]9.0711.288.156.444.543.619.238.395.804.533.102.39
FM [41]45.2828.2014.407.197.844.6739.0530.6319.8811.6111.286.08
SIA [33]41.5344.6731.5316.2822.4111.5648.6144.5630.8014.8519.029.20
HAMT [5]14.0836.8432.9530.2018.9217.2813.6233.4130.4026.6714.8813.08
RecBERT [18]16.7835.0230.6724.9018.7715.2715.8632.9129.6123.9916.5013.51
ProbES [30]18.0033.2327.6322.7516.8413.9416.8428.2324.9720.1215.1112.32
Airbert [13]18.7134.5127.8921.8818.2314.1817.9134.2030.2823.6116.8313.28
DUET [6]22.1151.0746.9833.7332.1523.0321.3056.9152.5136.0631.8822.06
DUET (Lily)21.8753.7148.1134.4332.1523.4321.9460.5154.3237.3432.0221.94
+ +Table 5: Comparison with state-of-the-arts on REVERIE. Lily agent achieves the state-of-the-art performance on all splits. + +
MethodsVal UnseenTest Unseen
TLNE↓SR↑SPL↑TLNE↓SR↑SPL↑
Seq2Seq [1]8.397.8122-8.137.8520-
EnvDrop [47]10.705.22524811.665.235147
AuxRN [57]-5.285550-5.155551
PREVALENT [14]10.194.71585310.515.305451
RelGraph [17]9.994.73575310.294.755552
RecBERT [18]12.013.93635712.354.096357
ProbES [30]11.584.00615512.434.206256
ADAPT [32]12.333.66665913.164.116357
HOP [42]12.273.80645712.653.836459
HAMT [5]11.462.29666112.273.936560
Airbert [13]11.784.01625612.414.136257
DUET [6]13.943.31726014.733.656959
DUET (Lily)14.582.90746216.133.447260
+ +more quickly. We attribute this to the better layout reason ability learned from the large-scale diverse reasonable trajectories in the proposed YouTube-VLN dataset. A similar performance is obtained on the test unseen split, where the Lily agent improves the SR by $1.81\%$ and the SPL by $1.28\%$ . Although our objective is solely navigation, we still achieve comparable performance on grounding metrics and even slightly outstrip DUET on most metrics. + +# 5.4. Learning Navigation from One Environment + +Our intuition is that pre-training on the YouTube-VLN dataset can mitigate the domain gap of training from scratch and is able to achieve excellent performance with only a few training environments. To verify this, we conduct a one-shot learning study, where we fine-tune our model on only one environment of the original training environments. Note that the candidate paths are generated from all of the possible paths from the start viewpoints to all navigable points, instead of from the expert model in EnvDrop [47]. All the candidate paths are the shortest paths in the navigation graphs. To reduce the bias, we randomly select 5 sets from the entire environments and report the average results. + +In Table 7, our agent outperforms all the existing pre + +Table 6: Comparison with state-of-the-arts on R2R dataset under generative setting. + +
MethodsVal SeenVal Unseen
VLN BERT [36]45.7122.43
AirBERT [13]47.8850.00
Lily49.3150.86
+ +Table 7: SR on val seen and val unseen splits of R2R. All the agents access only one environment. + +training methods. On the val seen split using one-shot finetuning, compared to VLN-BERT and AirBERT, our Lily agent achieves $3.60\%$ and $1.43\%$ improvements, respectively. In the val unseen split using one-shot fine-tuning, we achieve $28.43\%$ improvement compared to VLN-BERT. All these results suggest the effectiveness of our method. + +# 6. Conclusion + +In this work, we propose a new approach Lily to address the limitations of existing vision-and-language navigation (VLN) methods by creating a large-scale VLN-like dataset from real house tour videos to train our embodied agent. We overcome the challenges of automatically generating path-instruction pairs to construct the dataset from raw and unlabeled videos by leveraging an entropy-based method for trajectory construction and an action-aware generator for instruction generation. 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Existing VLN methods suffer from training on small-scale environments or unreasonable path-instruction datasets, limiting the generalization to unseen environments. There are massive house tour videos on YouTube, providing abundant real navigation experiences and layout information. However, these videos have not been explored for VLN before. In this paper, we propose to learn an agent from these videos by creating a large-scale dataset which comprises reasonable path-instruction pairs from house tour videos and pre-training the agent on it. To achieve this, we have to tackle the challenges of automatically constructing path-instruction pairs and exploiting real layout knowledge from raw and unlabeled videos. To address these, we first leverage an entropy-based method to construct the nodes of a path trajectory. Then, we propose an action-aware generator for generating instructions from unlabeled trajectories. Last, we devise a trajectory judgment pretext task to encourage the agent to mine the layout knowledge. Experimental results show that our method achieves state-of-the-art performance on two popular benchmarks (R2R and REVERIE). Code is available at https://github.com/JeremyLinky/YouTube-VLN" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 564, + 124, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 124, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 124, + 576 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 584, + 279, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 584, + 279, + 689 + ], + "spans": [ + { + "bbox": [ + 45, + 584, + 279, + 689 + ], + "type": "text", + "content": "An important goal of embodied artificial intelligence is to develop agents that can interact with humans in natural language to carry out real-world tasks. Toward this goal, vision-and-language navigation (VLN) [1] is a rudimentary artificial intelligence task, requiring an indoor agent to navigate in unseen environments following natural instructions. VLN has attracted widespread attention in the fields of computer vision and robotics due to its promising applications such as in-home robots [54] and warehouse assistants [29]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 57, + 689, + 279, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 689, + 279, + 701 + ], + "spans": [ + { + "bbox": [ + 57, + 689, + 279, + 701 + ], + "type": "text", + "content": "One of the key challenges of VLN is the generaliza" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 257, + 530, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 257, + 530, + 431 + ], + "spans": [ + { + "bbox": [ + 297, + 257, + 530, + 431 + ], + "type": "text", + "content": "tion ability of agents to unseen environments. Existing VLN methods attempt to cope with this challenge via self-supervised pre-training on vision-and-language datasets. As shown in Figure 1 (a), some previous works [30, 19, 36, 7] learn the agents on simulated navigation environments and manual-labeled data. The other works [14, 13, 42] seek to construct path-instruction pairs by using web image data, which is shown in Figure 1 (b). Despite their promising performance, existing agents still suffer from the following limitations. 1) Training on simulated datasets is limited to a restricted number of environments. 2) Constructing a trajectory by simply concatenating web images leads to unreasonable room layouts, which hamper the agent to learn layout reasoning ability. As a result, VLN agents trained on such data are brittle to adapt to unseen environments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 432, + 531, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 432, + 531, + 641 + ], + "spans": [ + { + "bbox": [ + 296, + 432, + 531, + 641 + ], + "type": "text", + "content": "Fortunately, there are massive house tour videos on YouTube, providing real navigation experiences and layout information but are still under-explored. We can be naturally inspired to let an agent learn VLN ability from such videos, thereby addressing the limitations of existing methods. An intuitive way is to model the navigation experiences as path-instruction pairs to train the agent. Motivated by this, we propose a \"Lily\" agent who Learns Vision-and-Language Navigation from YouTube Videos. Specifically, we first develop an in-domain pre-training dataset from house tour YouTube videos, namely YouTube-VLN, which comprises VLN-like path-instruction pairs. Our YouTube-VLN dataset has the advantages of diverse environments, real layouts, and native actions1, reducing the domain gap with VLN datasets, as illustrated in Figure 1 (c). Then, we pre-train the agent using these path-instruction pairs. Benefiting from in-domain pre-training on our proposed dataset, our agent thus generalizes well to unseen environments." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 641, + 530, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 641, + 530, + 711 + ], + "spans": [ + { + "bbox": [ + 296, + 641, + 530, + 711 + ], + "type": "text", + "content": "Constructing and utilizing such a dataset, however, is still far from trivial work and remains an open problem due to the following challenges. 1) As the nodes in a trajectory are expected to be diverse and informative, it is hard to determine the locations of trajectory nodes from massive video frames and represent the visual content in a node." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 76, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 76, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "spans": [ + { + "bbox": [ + 151, + 41, + 470, + 74 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 709, + 272, + 719 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 709, + 272, + 719 + ], + "spans": [ + { + "bbox": [ + 55, + 709, + 272, + 719 + ], + "type": "text", + "content": "*Equal contribution. Email: {imkunyanglin, phchencs}@gmail.com" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 55, + 719, + 235, + 729 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 719, + 235, + 729 + ], + "spans": [ + { + "bbox": [ + 55, + 719, + 235, + 729 + ], + "type": "text", + "content": "†Corresponding author. Email: mingkuitan@scut.edu.cn" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 308, + 719, + 449, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 719, + 449, + 730 + ], + "spans": [ + { + "bbox": [ + 308, + 719, + 449, + 730 + ], + "type": "text", + "content": "1The execution actions that objectively exist" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 746, + 298, + 756 + ], + "type": "text", + "content": "8317" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 105, + 205, + 206 + ], + "blocks": [ + { + "bbox": [ + 48, + 105, + 205, + 206 + ], + "lines": [ + { + "bbox": [ + 48, + 105, + 205, + 206 + ], + "spans": [ + { + "bbox": [ + 48, + 105, + 205, + 206 + ], + "type": "image", + "image_path": "c11408a7f201d573b27741475014fc7813798c4515551140b0e4d5c204daa5bd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 210, + 189, + 218 + ], + "lines": [ + { + "bbox": [ + 66, + 210, + 189, + 218 + ], + "spans": [ + { + "bbox": [ + 66, + 210, + 189, + 218 + ], + "type": "text", + "content": "(a) Dataset from Simulation Environments" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 209, + 105, + 367, + 208 + ], + "blocks": [ + { + "bbox": [ + 209, + 105, + 367, + 208 + ], + "lines": [ + { + "bbox": [ + 209, + 105, + 367, + 208 + ], + "spans": [ + { + "bbox": [ + 209, + 105, + 367, + 208 + ], + "type": "image", + "image_path": "c14b03dc69edf64fb69b545e50b9f1d311fab96dfe8bd8402545f487db3fa0c1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 238, + 210, + 339, + 219 + ], + "lines": [ + { + "bbox": [ + 238, + 210, + 339, + 219 + ], + "spans": [ + { + "bbox": [ + 238, + 210, + 339, + 219 + ], + "type": "text", + "content": "(b) Dataset from Web Images Data" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 228, + 531, + 275 + ], + "lines": [ + { + "bbox": [ + 45, + 228, + 531, + 275 + ], + "spans": [ + { + "bbox": [ + 45, + 228, + 531, + 275 + ], + "type": "text", + "content": "Figure 1: Comparison of different datasets for pre-training. Existing datasets are built from either simulation environments (a) or web images data (b). The former only covers limited environments, and the latter contains confusing layouts and ambiguous actions. Our dataset built from YouTube videos (c) is able to provide diverse environments, real layouts and native actions simultaneously." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 369, + 105, + 529, + 208 + ], + "blocks": [ + { + "bbox": [ + 369, + 105, + 529, + 208 + ], + "lines": [ + { + "bbox": [ + 369, + 105, + 529, + 208 + ], + "spans": [ + { + "bbox": [ + 369, + 105, + 529, + 208 + ], + "type": "image", + "image_path": "3a261921a590a6f671e0f8db494f0c3f1e28b5fac03bcf9828da0e6c1f7c3cd2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 390, + 210, + 508, + 219 + ], + "lines": [ + { + "bbox": [ + 390, + 210, + 508, + 219 + ], + "spans": [ + { + "bbox": [ + 390, + 210, + 508, + 219 + ], + "type": "text", + "content": "(c) Dataset from YouTube Videos (Ours)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 295, + 279, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 295, + 279, + 377 + ], + "spans": [ + { + "bbox": [ + 45, + 295, + 279, + 377 + ], + "type": "text", + "content": "2) Real VLN instructions include various action descriptions, but obtaining corresponding instructions from navigation clips is challenging due to the actions being implicit in videos. Thus it is nontrivial to acquire matching instruction on a trajectory. 3) Layout knowledge from real navigation experience is hard to mine and model, which impedes the agent of learning layout reasoning ability." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 378, + 279, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 378, + 279, + 658 + ], + "spans": [ + { + "bbox": [ + 45, + 378, + 279, + 658 + ], + "type": "text", + "content": "In this paper, we address the above challenges as follows. To conquer challenge 1), we propose an entropy-based trajectory generation method. Specifically, we first envisage that the nodes of a trajectory should contain as many types of rooms as possible to diversify trajectories. Accordingly, we group the frames with the same room types in videos and consider each group as a node in the trajectory. Then, inspired by that low classification entropy image is reliable and contains rich information relevant to a specific class (room type in our case) [39], the frame with the lowest classification entropy in a group is chosen to represent the visual content in a node. To tackle challenge 2), we introduce an action-aware instruction generation method. Specifically, we adopt an action inverse model to pseudo-label the action along trajectories and fill them in the instructions via hand-designed rules. To grapple with challenge 3), we devise a self-supervised pretext task. As we all know, humans often judge whether a navigation trajectory is reasonable based on the layout of the environment. Therefore, it is believed that an agent equipped with layout reasoning ability should be able to make similar judgment. To this end, we propose trajectory judgment pretext task to ask the agent to identify reasonable navigation trajectories, which further equips the model with the ability to reason environment layouts." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "We empirically show that the diverse entropy-based trajectory generation method and action-aware instruction generator allow us to harvest high-quality path-instruction pairs from YouTube house tour videos, resulting in the YouTube-VLN dataset. By integrating the self-supervised trajectory judgment task in pre-training a VLN agent, our" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 295, + 530, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 295, + 530, + 365 + ], + "spans": [ + { + "bbox": [ + 296, + 295, + 530, + 365 + ], + "type": "text", + "content": "Lily agent presents state-of-the-art performance on two mature and solid benchmarks (R2R [1], REVERIE [41]). The proposed Lily agent reaches the first place on the R2R leaderboard in terms of success rate and outperforms the SOTA method under discriminative setting and generative setting by " + }, + { + "bbox": [ + 296, + 295, + 530, + 365 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 296, + 295, + 530, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 295, + 530, + 365 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 296, + 295, + 530, + 365 + ], + "type": "text", + "content": " w.r.t. success rate, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 366, + 460, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 366, + 460, + 376 + ], + "spans": [ + { + "bbox": [ + 308, + 366, + 460, + 376 + ], + "type": "text", + "content": "Our main contributions are as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 378, + 530, + 553 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 296, + 378, + 530, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 378, + 530, + 435 + ], + "spans": [ + { + "bbox": [ + 296, + 378, + 530, + 435 + ], + "type": "text", + "content": "- We unleash the huge potential of house tour videos for VLN. By leveraging these videos, we introduce a largescale dataset containing real navigation path-instruction pairs for promoting VLN pre-training and a self-supervised pretext task for the learning of layout reasoning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 436, + 530, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 436, + 530, + 494 + ], + "spans": [ + { + "bbox": [ + 296, + 436, + 530, + 494 + ], + "type": "text", + "content": "- Our diverse trajectory generation method, together with the action-aware instruction generator, creates informative and diverse trajectory nodes and produces matching instructions, both of which make the path-instruction pairs authentic and of high quality for training a VLN agent." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 495, + 530, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 495, + 530, + 553 + ], + "spans": [ + { + "bbox": [ + 296, + 495, + 530, + 553 + ], + "type": "text", + "content": "- The proposed trajectory judgment pretext task allows the model to build up an awareness of learning and reasoning the layout knowledge, which is crucial in the VLN task of indoor environments. We also empirically substantiate that the agent indeed learns the layout learning ability." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 297, + 564, + 380, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 564, + 380, + 575 + ], + "spans": [ + { + "bbox": [ + 297, + 564, + 380, + 575 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 583, + 468, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 583, + 468, + 596 + ], + "spans": [ + { + "bbox": [ + 297, + 583, + 468, + 596 + ], + "type": "text", + "content": "2.1. Vision-and-Language Navigation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 601, + 530, + 730 + ], + "type": "text", + "content": "Vision-and-Language Navigation (VLN) [1] is a challenging task and has received continuous and intense attention from the academic community in recent years [4, 12, 25, 31, 46, 27, 6, 45, 9]. Early methods attempt to learn the agent from sequence-to-sequence models [1, 10, 47]. However, these methods can not model the cross-modal relation between language and visual observation well. To address this issue, transformer [48] architecture is adopted to the agents followed by vision-and-language pre-training [35, 50, 57, 37, 13, 42, 5, 38, 24]. PREVALENT [15] pretrains transformer-based agent via masked language mod" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "8318" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 281 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 281 + ], + "type": "text", + "content": "eling and action prediction tasks. Inspired by BERT [8], several works propose to use different variants of BERT for VLN pre-training. VLN-BERT [37] utilizes image-text data [34] to perform path-instruction matching pretext task. Airbert [13] proposes the shuffle loss to improve the ability of the model to learn the order of image-caption pairs. Recently, HOP [42] introduces the history and order-aware pretext tasks. However, these existing pretext tasks do not consider the learning of environment layout reasoning ability and bring limited performance for VLN tasks. In this work, we propose a trajectory judgment task to teach the agent to distinguish reasonable navigation trajectories. By proficiently accomplishing this task, the agent can acquire the ability to reason about environment layout, which enhances its generalization capability to unseen environments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 296, + 148, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 296, + 148, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 296, + 148, + 308 + ], + "type": "text", + "content": "2.2. Datasets for VLN" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 316, + 281, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 316, + 281, + 573 + ], + "spans": [ + { + "bbox": [ + 45, + 316, + 281, + 573 + ], + "type": "text", + "content": "The major difficulty of generalizing a VLN agent to unseen environments is the scarcity of VLN training data. Well-labeled VLN datasets built from the simulators [2, 44, 52] allow the agent to obtain a promising performance, such as R2R [1], R4R [20], RxR [23] and SOON [56]. While the data built from simulators are laborious, Wang et al. [49] and ProbES [30] enrich the navigation instructions via self-exploration in the simulation environments. Some other endeavors [47, 28, 10, 11, 22, 26] seek to augment the data from existing datasets. AutoVLN [7] and Kamath et al. [21] enlarges the VLN data from simulations with a larger number of environments. However, these datasets are limited by the number of scenes in simulators. To ease this problem, VLN-BERT [37] leverages the abundant web image-captions pairs as VLN pre-training data. Airbert [13] further exploits indoor house images and captions from the web to construct path-instruction pairs for VLN pre-training. However, the trajectories constructed by simply splicing pictures may be confusing and ambiguous. In our work, we address these problems by proposing a large-scale in-domain VLN-like pre-training dataset, providing the agent with diverse visual environments and reasonable layouts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 591, + 279, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 279, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 279, + 604 + ], + "type": "text", + "content": "3. Building VLN Dataset from YouTube Videos" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": "Our first step is to develop a large-scale VLN-like dataset that comprises reasonable path-instruction pairs from house tour videos on YouTube, termed YouTube-VLN. YouTube-VLN serves as a cornerstone for facilitating the acquisition of VLN capabilities for Lily, featuring diverse environments, real layouts and native actions. To achieve this goal, we present an entropy-based trajectory generation technique (Section 3.1) and an action-aware generator (Section 3.2) to tackle the arduous tasks of trajectory and instruction generation, respectively." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 303, + 107, + 526, + 257 + ], + "blocks": [ + { + "bbox": [ + 303, + 107, + 526, + 257 + ], + "lines": [ + { + "bbox": [ + 303, + 107, + 526, + 257 + ], + "spans": [ + { + "bbox": [ + 303, + 107, + 526, + 257 + ], + "type": "image", + "image_path": "4e676be56851763f7094e83440bfc2926fb1af94666b7c64d1ed83b413a8866e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 272, + 531, + 308 + ], + "lines": [ + { + "bbox": [ + 296, + 272, + 531, + 308 + ], + "spans": [ + { + "bbox": [ + 296, + 272, + 531, + 308 + ], + "type": "text", + "content": "Figure 2: An example of a generated trajectory from a YouTube house tour video. " + }, + { + "bbox": [ + 296, + 272, + 531, + 308 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 296, + 272, + 531, + 308 + ], + "type": "text", + "content": " represents the direction to go next while " + }, + { + "bbox": [ + 296, + 272, + 531, + 308 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 296, + 272, + 531, + 308 + ], + "type": "text", + "content": " represents the stop action." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 297, + 320, + 461, + 334 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 320, + 461, + 334 + ], + "spans": [ + { + "bbox": [ + 297, + 320, + 461, + 334 + ], + "type": "text", + "content": "3.1. Diverse Trajectory Generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 341, + 531, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 341, + 531, + 504 + ], + "spans": [ + { + "bbox": [ + 296, + 341, + 531, + 504 + ], + "type": "text", + "content": "We seek to construct discrete navigation trajectories from YouTube videos. Similar to discrete navigation datasets (e.g., R2R [1]), each trajectory comprises " + }, + { + "bbox": [ + 296, + 341, + 531, + 504 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 341, + 531, + 504 + ], + "type": "text", + "content": " navigation nodes, representing different locations of a navigation path. This entails addressing two major challenges: 1) how to determine the locations composing a trajectory to make the trajectory more diverse and 2) how to represent the visual content at each node location. To tackle these challenges, we first collect large-scale consecutive indoor frames from YouTube videos. Then, we group the adjacent frames according to their room types and consider each group as a node. Last, we present an entropy-based technique to select the most informative frames in a group for representing the visual content in a node." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 506, + 532, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 506, + 532, + 646 + ], + "spans": [ + { + "bbox": [ + 296, + 506, + 532, + 646 + ], + "type": "text", + "content": "Collecting Navigation Data from YouTube. Real estate agents typically tour a house in each video. To satisfy the visual diversity and dataset scale, we create the YouTube-VLN dataset from 4078 videos collected from various uploaders, with a total duration of 433 hours. In contrast to prior work [3], which relied on a limited set of videos from a single uploader, our dataset features greater diversity and volume. We also employ sparse sampling and off-the-shelf image classifiers [16, 43] to pre-process the videos, filtering out redundant or noisy frames (those featuring people or outdoor scenes), resulting in a final set of 587k indoor frames suitable for constructing trajectories." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 648, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 532, + 730 + ], + "type": "text", + "content": "Determining the Locations of Trajectory Nodes. A real robot often needs to go through different locations for navigating to a goal. To mimic the real navigation process, we expect that our constructed trajectories also contain diverse visual content within the limited navigation nodes. To achieve this, we first utilize the powerful large model CLIP [43] to recognize the room type of each indoor im" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "8319" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 223 + ], + "type": "text", + "content": "age. Then, we gather temporally adjacent frames with the same room type as a group and consider this group as one of the navigation nodes. In this sense, the navigation nodes are diversely spread in different rooms and the constructed trajectories are able to mimic the real navigation process. We also call this kind of node a room node. In practice, to increase the visual diversity of trajectories, we also randomly insert transition nodes that are composed of video frames captured during the transition from one room to another one, between two adjacent room nodes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 223, + 281, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 223, + 281, + 397 + ], + "spans": [ + { + "bbox": [ + 45, + 223, + 281, + 397 + ], + "type": "text", + "content": "Representing Visual Content in a Node. A node consists of a group of images and sometimes the number of images may exceed 100 as the photographer could stay in the same room for a long time. Hence, we have to select the most informative images for representing node features. Inspired by EATA [39], an image with lower classification entropy is more reliable, containing more information relevant to a specific class (room type in our case). We thus propose to select an image with the lowest classification entropy to represent the current view of a node. In order to mimic the panoramic visual context, we then merge " + }, + { + "bbox": [ + 45, + 223, + 281, + 397 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 223, + 281, + 397 + ], + "type": "text", + "content": " adjacent consecutive images of the current view. It is worth noting that our node features better represent a panoramic view compared with Airbert [13] because we merge adjacent frames that belong to the same place as the current view." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 399, + 280, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 399, + 280, + 433 + ], + "spans": [ + { + "bbox": [ + 45, + 399, + 280, + 433 + ], + "type": "text", + "content": "Ultimately, we randomly chose " + }, + { + "bbox": [ + 45, + 399, + 280, + 433 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 399, + 280, + 433 + ], + "type": "text", + "content": " continuous nodes to construct a trajectory. An example of the constructed trajectory is shown in Figure 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 442, + 239, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 442, + 239, + 454 + ], + "spans": [ + { + "bbox": [ + 45, + 442, + 239, + 454 + ], + "type": "text", + "content": "3.2. Action-Aware Instruction Generation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 462, + 279, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 462, + 279, + 589 + ], + "spans": [ + { + "bbox": [ + 45, + 462, + 279, + 589 + ], + "type": "text", + "content": "In addition to constructing navigation trajectories, one more important step for building a VLN dataset is to create the corresponding instructions without manual annotation. The main challenge for this step is how to correctly describe visual content and actions along navigation paths. To conquer this challenge, we first generate instruction templates with verb and noun phrase blanks. Then, we describe each node in trajectories using the CLIP [43] model and infer the native actions using an action inverse model [3]. To generate the final instructions, we fill the instruction templates with these visual descriptions and actions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 590, + 281, + 730 + ], + "type": "text", + "content": "Specifically, we first generate templates with verb and noun blanks from instructions in the R2R dataset following Airbert [13]. For noun blanks, we fill them with visual content descriptions about each node. We select the frame with the lowest classification entropy (as described in Sec. 3.1) and use the CLIP model to infer the objects it contains, together with the room type to populate a noun blank. For verb blanks, the existing instruction generation method [13] is unable to fill them with the correct action words because it cannot figure out the actions taken for navigating from one image to another. This makes the agent confused when it observes similar viewpoints transition but is given differ" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 106, + 532, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 532, + 257 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 532, + 257 + ], + "type": "text", + "content": "ent action descriptions. To tackle this problem, we propose an action-aware strategy to fill instruction templates with native actions instead of random inconsistent actions. To be specific, we follow [3] to train an action inverse model, which has " + }, + { + "bbox": [ + 296, + 106, + 532, + 257 + ], + "type": "inline_equation", + "content": "96\\%" + }, + { + "bbox": [ + 296, + 106, + 532, + 257 + ], + "type": "text", + "content": " prediction accuracy for predicting native actions, to pseudo-label the trajectory with action labels from one location node to another. The predicted actions are then converted into actionable verbs, i.e., \"go forward\", \"turn left\" and \"turn right\". For each noun blank that has been filled with the description of one node, we find its closest verb phrase blank and fill it with the pseudo-labeled action which is executed to reach the next node. This eventually enables us to create action-aware instructions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 269, + 497, + 282 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 269, + 497, + 282 + ], + "spans": [ + { + "bbox": [ + 296, + 269, + 497, + 282 + ], + "type": "text", + "content": "4. Learning VLN from YouTube Videos" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 288, + 532, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 288, + 532, + 464 + ], + "spans": [ + { + "bbox": [ + 296, + 288, + 532, + 464 + ], + "type": "text", + "content": "Given the VLN-like and reasonable path-instruction pairs generated from YouTube videos, we then describe how to learn the Lily agent from these data. As shown in Figure 3, our VLN model consists of two components: a vision-and-language backbone (i.e., Multi-Layer Transformer) that models the relationship between trajectories and instructions and a decision-making module that predicts the next action or a matching score for a path-instruction pair. The vision-and-language backbone can be any type of cross-modal network. We chose ViLBERT [34] for a fair comparison with Airbert [13]. As a common practice, pretext tasks are utilized for pre-training the backbone. We next describe how to pre-train the backbone on our Youtube-VLN dataset using the proposed trajectory judgment pretext task." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 472, + 410, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 472, + 410, + 484 + ], + "spans": [ + { + "bbox": [ + 296, + 472, + 410, + 484 + ], + "type": "text", + "content": "4.1. Model Architecture" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "spans": [ + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "content": "We follow Airbert [13] to leverage a ViLBERT-like [34] architecture as the model backbone. The model encodes the sequential visual region features and the text token via two separate transformers respectively. More formally, the path-instruction pair consists of " + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "content": " nodes " + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "inline_equation", + "content": "\\{V_k\\}_{k=1}^K" + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "content": " text tokens " + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "inline_equation", + "content": "\\{w_l\\}_{l=1}^L" + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "content": ". Each node " + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "inline_equation", + "content": "V_k" + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "content": " is composed of " + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "inline_equation", + "content": "R_k" + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "content": " visual region features " + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "inline_equation", + "content": "\\{v_i^k\\}_{i=1}^{R_k}" + }, + { + "bbox": [ + 296, + 489, + 531, + 585 + ], + "type": "text", + "content": ". In this way, we represent the visual and text inputs respectively as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 591, + 530, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 591, + 530, + 628 + ], + "spans": [ + { + "bbox": [ + 308, + 591, + 530, + 628 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} X _ {V} = \\left[ \\left[ \\operatorname {I M G} \\right], v _ {1} ^ {1}, \\dots , v _ {R _ {1}} ^ {1}, \\dots , \\left[ \\operatorname {I M G} \\right], v _ {1} ^ {K}, \\dots , v _ {R _ {K}} ^ {K} \\right], (1) \\\\ X _ {W} = \\left[ \\left[ \\mathrm {C L S} \\right], w _ {1}, \\dots , w _ {l}, \\dots , w _ {L}, [ \\mathrm {S E P} ] \\right], (2) \\\\ \\end{array}", + "image_path": "8317575766569b97f22999b626d87661cba0924225a4c7d3f02236b82dc19092.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 633, + 531, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 633, + 531, + 681 + ], + "spans": [ + { + "bbox": [ + 296, + 633, + 531, + 681 + ], + "type": "text", + "content": "where [IMG], [CLS] and [SEP] are special tokens. The encoded visual and text tokens finally interact via a cross-modal transformer encoder. We represent the whole model architecture as \"Multi-Layer Transformer\" in Figure 3." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 687, + 521, + 701 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 687, + 521, + 701 + ], + "spans": [ + { + "bbox": [ + 296, + 687, + 521, + 701 + ], + "type": "text", + "content": "4.2. Learning Layout from Trajectory Judgment" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 706, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 706, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 706, + 531, + 730 + ], + "type": "text", + "content": "Given the aforementioned model architecture, we propose to train a VLN agent with a trajectory judgment (TJ)" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "8320" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 46, + 103, + 532, + 260 + ], + "blocks": [ + { + "bbox": [ + 46, + 103, + 532, + 260 + ], + "lines": [ + { + "bbox": [ + 46, + 103, + 532, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 103, + 532, + 260 + ], + "type": "image", + "image_path": "54d51f805e433c01781504cc9c06a427e91f68b33992d33b124ac957f7ca679e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 266, + 531, + 301 + ], + "lines": [ + { + "bbox": [ + 45, + 266, + 531, + 301 + ], + "spans": [ + { + "bbox": [ + 45, + 266, + 531, + 301 + ], + "type": "text", + "content": "Figure 3: General scheme of our Lily agent for pre-training and downstream stages of VLN tasks. Lily agent learns to leverage the proposed YouTube-VLN dataset for the trajectory judgment task together with the other pretext tasks. After pre-training the VLN model, we adapt it to the downstream datasets and conduct different VLN downstream tasks." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 322, + 279, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 322, + 279, + 345 + ], + "spans": [ + { + "bbox": [ + 45, + 322, + 279, + 345 + ], + "type": "text", + "content": "task, enabling it to reason about layouts. Herein, we elaborate on the proposed trajectory judgment task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 346, + 279, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 346, + 279, + 496 + ], + "spans": [ + { + "bbox": [ + 45, + 346, + 279, + 496 + ], + "type": "text", + "content": "**Formulation.** The trajectory judgment task aims to judge the reasonableness of trajectories. We consider the trajectories generated in the way described in Section 3.1 as positive (reasonable) samples and the shuffled trajectories as negative (unreasonable) ones. To finish this task, the agent is required to reason about the visual information and identify the room types, then infer whether the trajectory matches the real environment layout distribution. Specifically, we first calculate the dot product of the output features of [IMG] and [CLS] tokens. Then, we feed this vector feature to a linear layer to predict the probability that indicates whether the trajectory is reasonable. The model aims to minimize the binary cross-entropy loss:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 502, + 279, + 530 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 502, + 279, + 530 + ], + "spans": [ + { + "bbox": [ + 54, + 502, + 279, + 530 + ], + "type": "interline_equation", + "content": "L = - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\left[ w \\cdot y _ {n} \\log (p _ {n}) + (1 - y _ {n}) \\log (1 - p _ {n}) \\right], \\tag {3}", + "image_path": "fb3f9e054892b8f352e58f1f6ade676fbeea3091c2049ed05726b52f03acf486.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "spans": [ + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "inline_equation", + "content": "y_{n} = 1" + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "content": " if the " + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "inline_equation", + "content": "n^{th}" + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "content": " trajectory is reasonable, otherwise " + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "inline_equation", + "content": "y_{n} = 0" + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "inline_equation", + "content": "p_{n}" + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "content": " represents the probability that the " + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "inline_equation", + "content": "n^{th}" + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "content": " trajectory is predicted as reasonable. " + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "content": " is the number of trajectories in a batch. " + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 531, + 279, + 601 + ], + "type": "text", + "content": " is a factor to mitigate the imbalance of positive and negative samples, which equals the ratio of the number of negative samples to the number of positive samples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 602, + 279, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 602, + 279, + 682 + ], + "spans": [ + { + "bbox": [ + 45, + 602, + 279, + 682 + ], + "type": "text", + "content": "Sample Generation. We propose to shuffle the positive sample to generate the negative samples: 1) shuffle only the transition nodes; 2) shuffle all the nodes; 3) keep the order of the room nodes, and randomly insert nodes from other videos. In this way, we create rich and hard negative samples, which increases the task difficulty, helping the agent understand the real layout in a more complex manner." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 683, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 683, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 683, + 279, + 730 + ], + "type": "text", + "content": "Combining with Existing Pre-Training Tasks. As depicted in Figure 3, we follow Airbert [13] to pre-train the model backbone using our proposed trajectory judgment task, additionally combining with three other existing" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 322, + 530, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 322, + 530, + 415 + ], + "spans": [ + { + "bbox": [ + 296, + 322, + 530, + 415 + ], + "type": "text", + "content": "pretext tasks, namely masked language modeling (MLM), masked vision modeling (MVM) and path ranking (PR) on YouTube-VLN dataset. For MLM, we randomly mask out the words in instruction and the goal is to recover the masked words. Similar to MLM, MVM is designed to predict masked image regions. PR is a ranking task, which aims to decide the most matching path-instruction pair among a few pairs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 439, + 505, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 439, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 296, + 439, + 505, + 451 + ], + "type": "text", + "content": "4.3. Adapting Pre-trained Backbone for VLN" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 463, + 530, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 463, + 530, + 544 + ], + "spans": [ + { + "bbox": [ + 296, + 463, + 530, + 544 + ], + "type": "text", + "content": "We adapt the pre-trained model to both goal-oriented navigation task and object-oriented navigation task. All the tasks are based on the Matterport3D simulator [2]. We utilize R2R [1] as the benchmark for the goal-oriented navigation task, which is divided into discriminative setting and generative setting. As for the object-oriented task, we evaluate our model on REVERIE [41] in generative setting." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 549, + 530, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 549, + 530, + 619 + ], + "spans": [ + { + "bbox": [ + 296, + 549, + 530, + 619 + ], + "type": "text", + "content": "The discriminative setting formulates VLN as a path-selection problem, requiring the agent to choose the path that best matches the instruction from multiple candidate paths. Under the discriminative setting, we utilize the classifier used in the path ranking pretext task for decision-making and fine-tune the Lily agent on the R2R dataset." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 625, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 625, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 625, + 530, + 730 + ], + "type": "text", + "content": "In the generative setting, the agent needs to predict actions sequentially to reach the goal (R2R) or simultaneously find the object (REVERIE). We adopt DUET [6] as the architecture for fine-tuning, which feeds the cross-modal feature into a feed-forward network for decision-making. We initialize the text transformer encoder and cross-modal transformer encoder of the generative model with our Lily agent. Note that our Lily agent can apply to any generative model. More details are available in the supplementary." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 297, + 756 + ], + "type": "text", + "content": "8321" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 104, + 529, + 191 + ], + "blocks": [ + { + "bbox": [ + 48, + 104, + 529, + 191 + ], + "lines": [ + { + "bbox": [ + 48, + 104, + 529, + 191 + ], + "spans": [ + { + "bbox": [ + 48, + 104, + 529, + 191 + ], + "type": "table", + "html": "
#DatasetPre-training TaskVal SeenVal Unseen
SourceReasonable Navigation PathPseudo-labeled ActionTrajectory JudgmentTLNE↓OSR↑SR↑SPL↑TLNE↓OSR↑SR↑SPL↑
1Airbnb ImagesXXX10.213.4179.0274.120.709.633.9570.9762.840.58
2YouTube VideosXXX10.123.4079.9074.310.709.813.7274.2463.730.59
3YouTube Videos✓XX10.303.4078.6075.100.719.603.7073.5065.000.61
4YouTube Videos✓✓X10.203.3079.8075.400.719.303.6072.7066.100.62
5YouTube Videos✓✓✓9.993.1280.8877.450.749.643.3774.9366.700.62
", + "image_path": "5e82bef7ca8d2e41eff86cb3b36f6a02ff9123beed83063b440e38be298ce124.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 88, + 195, + 489, + 207 + ], + "lines": [ + { + "bbox": [ + 88, + 195, + 489, + 207 + ], + "spans": [ + { + "bbox": [ + 88, + 195, + 489, + 207 + ], + "type": "text", + "content": "Table 1: Ablation study on YouTube-VLN dataset and trajectory judgment pretext task for pre-training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 48, + 216, + 123, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 216, + 123, + 229 + ], + "spans": [ + { + "bbox": [ + 48, + 216, + 123, + 229 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 235, + 157, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 235, + 157, + 247 + ], + "spans": [ + { + "bbox": [ + 48, + 235, + 157, + 247 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 252, + 278, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 252, + 278, + 437 + ], + "spans": [ + { + "bbox": [ + 48, + 252, + 278, + 437 + ], + "type": "text", + "content": "Dataset and Evaluation Metrics. We conduct our experiments on two VLN benchmarks, i.e., R2R [1] and REVERIE [41]. These two datasets consist of 21,567 path-instruction pairs from 90 scenes in Matterport3D [2]. REVERIE follows the same train/val/test splits as the R2R, while requiring an agent to select the bounding box of the target object bounding box additionally. Following standard settings [13], we adopt five metrics for evaluating R2R, namely success rate (SR), oracle success rate (OSR), success rate weighted by the ratio between the length of the shortest path and the predicted path (SPL), trajectory length (TL) and navigation error (NE). As for REVERIE, we leverage four metrics for evaluating navigation performance, namely SR, OSR, SPL and TL, and two for object grounding performance, namely remote grounding success (RGS) and RGS weighted by path length (RGSPL)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 438, + 278, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 438, + 278, + 578 + ], + "spans": [ + { + "bbox": [ + 48, + 438, + 278, + 578 + ], + "type": "text", + "content": "Implementation Details. We implement our method based on Pytorch framework [40] and Matterport3D simulator [2]. Specifically, we divide our training process into two stages, i.e., pre-training and fine-tuning. For the pretraining stage, we distribute training over 4 NVIDIA 3090 GPUs for 500 epochs to convergence. The pre-trained model with the highest accuracy for the path ranking pretext task is selected for fine-tuning. During the fine-tuning stage, we distribute training over 8 NVIDIA 3090 GPUs for 30 epochs to convergence. Following Airbert [13], we use augmented data from EnvDrop [47] for fine-tuning by default. More details are provided in the supplementary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 585, + 218, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 585, + 218, + 596 + ], + "spans": [ + { + "bbox": [ + 48, + 585, + 218, + 596 + ], + "type": "text", + "content": "5.2. Ablation Studies on Pre-Training" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 602, + 278, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 602, + 278, + 635 + ], + "spans": [ + { + "bbox": [ + 48, + 602, + 278, + 635 + ], + "type": "text", + "content": "We ablate our approach under discriminative setting on R2R benchmark. Considering the time efficiency, we do not use augmented data for fine-tuning on these experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 48, + 637, + 278, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 637, + 278, + 729 + ], + "spans": [ + { + "bbox": [ + 48, + 637, + 278, + 729 + ], + "type": "text", + "content": "Data Source: Airbnb Images vs. YouTube Videos. One of the main differences between YouTube-VLN dataset and Airbnb dataset [13] is the data source. Airbnb consists of 713k image-caption pairs while YouTube-VLN consists of 587k images extracted from 433 hours of house tour videos. YouTube-VLN has fewer images but provides more information about a room from different camera angles by merging, which better simulates a panorama for down-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 299, + 217, + 529, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 217, + 529, + 309 + ], + "spans": [ + { + "bbox": [ + 299, + 217, + 529, + 309 + ], + "type": "text", + "content": "stream VLN tasks. To evaluate the effect of data source, we follow Airbert [13] to randomly select images in the same house to build a trajectory and its corresponding instruction. We keep the number of instructions the same in pre-training for a fair comparison. In Table 1 (# 1 vs. # 2), YouTube data performs slightly better than Airbnb data, surpassing the SR by " + }, + { + "bbox": [ + 299, + 217, + 529, + 309 + ], + "type": "inline_equation", + "content": "0.89\\%" + }, + { + "bbox": [ + 299, + 217, + 529, + 309 + ], + "type": "text", + "content": " on the val unseen split. We speculate this is because data quality is more important than quantity." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 299, + 310, + 529, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 310, + 529, + 460 + ], + "spans": [ + { + "bbox": [ + 299, + 310, + 529, + 460 + ], + "type": "text", + "content": "Effectiveness of Reasonable Navigation Trajectory. YouTube-VLN dataset is collected from real house tour videos and is thus able to extract frames in chronological order to build reasonable navigation trajectories instead of combining multiple randomly chosen images. We use the generated reasonable navigation trajectories and shuffled trajectories to train two agents, respectively. In Table 1, the agent trained with reasonable navigation trajectories (# 3) achieves significantly better performance than the shuffled navigation trajectories variant (# 2), with " + }, + { + "bbox": [ + 299, + 310, + 529, + 460 + ], + "type": "inline_equation", + "content": "1.27\\%" + }, + { + "bbox": [ + 299, + 310, + 529, + 460 + ], + "type": "text", + "content": " gains on SR under the val unseen split. This suggests that the agent can not well understand and ground the instruction to the trajectory without reasonable navigation paths for learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 299, + 461, + 529, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 461, + 529, + 623 + ], + "spans": [ + { + "bbox": [ + 299, + 461, + 529, + 623 + ], + "type": "text", + "content": "Effectiveness of Pseudo-Labeled Action. The core of the proposed action-aware instruction generator is the pseudo-labeled actions for the instructions. To evaluate the effectiveness of the pseudo-labeled actions, we construct a variant that replaces random action words with the pseudo-labeled actions which are filled in the instructions. The results are shown in Table 1, # 4. Compared to the variant (# 3) that fills the instructions with random action words, this variant boosts the SR metric on both the val unseen (+1.10%) and seen (+0.30%) splits, showing the effectiveness of pseudo-labeled actions. It indicates that with pseudo-labeled actions, the agent can effectively ground the action to the visual observation and recognizes the correct transition from one location to another." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 299, + 625, + 529, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 625, + 529, + 729 + ], + "spans": [ + { + "bbox": [ + 299, + 625, + 529, + 729 + ], + "type": "text", + "content": "Effectiveness of Trajectory Judgment Pretext Task. To explore the layout knowledge of the YouTube-VLN dataset and equip the agent with layout reasoning ability, we propose a self-supervised trajectory judgment pretext task. In Table 1, the variant with the proposed pretext task improves the performance (#5 vs.#4, +2.05% on val seen and +0.60% on val unseen w.r.t. SR). Moreover, given a room type and visual information of the current node as inputs, this variant predicts the relative orientation of nodes for that" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "8322" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 104, + 276, + 150 + ], + "blocks": [ + { + "bbox": [ + 48, + 104, + 276, + 150 + ], + "lines": [ + { + "bbox": [ + 48, + 104, + 276, + 150 + ], + "spans": [ + { + "bbox": [ + 48, + 104, + 276, + 150 + ], + "type": "table", + "html": "
#MethodsTLNE↓OSR↑SR↑SPL↑
1Random Sample9.373.5272.8864.410.61
2Temporal Difference9.553.6173.3565.300.61
3Entropy-Based9.643.3774.9366.700.62
", + "image_path": "67ae89174462827fc1fd7cb9075ace529d246a5a2620e6c5c94037027aaf4ecb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 187, + 279, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 187, + 279, + 234 + ], + "spans": [ + { + "bbox": [ + 45, + 187, + 279, + 234 + ], + "type": "text", + "content": "room type with a " + }, + { + "bbox": [ + 45, + 187, + 279, + 234 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 45, + 187, + 279, + 234 + ], + "type": "text", + "content": " increase in accuracy (see supplementary for more details). These substantiate the claim of the importance of the proposed trajectory judgment task, which helps the agent learn the layout reasoning ability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "spans": [ + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "type": "text", + "content": "Effectiveness of Entropy-Based Trajectory Generation Strategy. In order to acquire an informative frame to represent a node, we propose an entropy-based technique as mentioned in Section 3.1. To demonstrate the effectiveness of our strategy, we construct two variants, i.e., one randomly chooses a frame, and one decides the frame by temporal difference [55]. The second variant computes the temporal pixel difference between every two consecutive frames and picks the frames where the peaks are located as the frames to represent the nodes. In Table 2, our entropy-based method significantly outperforms these two variants, increasing the SR on the val unseen split from " + }, + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "type": "inline_equation", + "content": "64.41\\%" + }, + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "type": "inline_equation", + "content": "65.30\\%" + }, + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "type": "inline_equation", + "content": "66.70\\%" + }, + { + "bbox": [ + 45, + 234, + 279, + 479 + ], + "type": "text", + "content": ", respectively. We speculate this is because 1) randomly sampling frames can generate consecutive redundant frames or meaningless frames (e.g., a wall takes up most of the frame); 2) the temporal difference method selects a frame that represents the junction of two different rooms, which is ambiguous and thus confuses the agent. In comparison, our entropy-based method is able to find a reliable frame to represent a node and ensure two adjacent nodes belong to different room types." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 484, + 227, + 497 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 484, + 227, + 497 + ], + "spans": [ + { + "bbox": [ + 45, + 484, + 227, + 497 + ], + "type": "text", + "content": "5.3. Comparison with State-of-the-Arts" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "spans": [ + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "text", + "content": "Results on R2R Dataset. We first compare our Lily agent with current methods under the discriminative setting. In Table 3, compared with VLN-BERT that uses image-caption pairs from the web for pre-training, our Lily agent significantly increases the SR by " + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "inline_equation", + "content": "10.74\\%" + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "text", + "content": " on the val unseen split. This highlights the importance of providing the indomain indoor data for pre-training. Moreover, compared with Airbert which uses in-domain image-caption pairs from online rental marketplaces, Lily still increases the SR from " + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "inline_equation", + "content": "73.85\\%" + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "inline_equation", + "content": "79.31\\%" + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "text", + "content": " on val seen and from " + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "inline_equation", + "content": "68.67\\%" + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "inline_equation", + "content": "70.00\\%" + }, + { + "bbox": [ + 45, + 503, + 279, + 688 + ], + "type": "text", + "content": " on val unseen. We attribute the improvement to our proposed VLN-like YouTube-VLN dataset and trajectory judgment pretext task, which have been thoughtfully evaluated in Section 5.2. When ensembled with the speaker-follower [10], all three methods increase the performance and our Lily agent performs the best." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 688, + 279, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 688, + 279, + 712 + ], + "spans": [ + { + "bbox": [ + 45, + 688, + 279, + 712 + ], + "type": "text", + "content": "In Table 4, we evaluate on R2R test split and our Lily ranks first on the VLN challenge leaderboard compared" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 300, + 104, + 528, + 212 + ], + "blocks": [ + { + "bbox": [ + 45, + 154, + 279, + 179 + ], + "lines": [ + { + "bbox": [ + 45, + 154, + 279, + 179 + ], + "spans": [ + { + "bbox": [ + 45, + 154, + 279, + 179 + ], + "type": "text", + "content": "Table 2: Comparison between different strategies of selecting frames to represent nodes under val unseen split." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 300, + 104, + 528, + 212 + ], + "lines": [ + { + "bbox": [ + 300, + 104, + 528, + 212 + ], + "spans": [ + { + "bbox": [ + 300, + 104, + 528, + 212 + ], + "type": "table", + "html": "
MethodsVal SeenVal Unseen
TLNE↓SR↑SPL↑TLNE↓SR↑SPL↑
Follower [10]10.403.6865.100.629.575.2052.360.49
Speaker [10]11.193.8060.690.5610.714.2554.660.49
Speaker-Follower [10]10.692.7274.220.7010.103.3267.900.63
ProBES [30]----9.504.0560.280.56
VLN-BERT [36]10.283.7370.200.669.604.1059.260.55
Airbert [13]10.593.2173.850.6910.033.2468.670.63
Lily10.212.8979.310.7610.033.1970.000.65
VLN-BERT* [36]10.612.3581.860.7810.002.7673.610.68
Airbert* [13]10.632.1381.400.779.992.6975.010.70
Lily*10.512.0683.290.809.782.4876.880.72
", + "image_path": "c40504e6a2ef3e78162446cc9db1b855e8325edd0d336630262aee6b0e3f6d21.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 300, + 257, + 528, + 366 + ], + "blocks": [ + { + "bbox": [ + 296, + 216, + 530, + 252 + ], + "lines": [ + { + "bbox": [ + 296, + 216, + 530, + 252 + ], + "spans": [ + { + "bbox": [ + 296, + 216, + 530, + 252 + ], + "type": "text", + "content": "Table 3: Comparison with state-of-the-arts on R2R dataset under discriminative setting. * means results of ensembling with the speaker-follower [10] model." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 300, + 257, + 528, + 366 + ], + "lines": [ + { + "bbox": [ + 300, + 257, + 528, + 366 + ], + "spans": [ + { + "bbox": [ + 300, + 257, + 528, + 366 + ], + "type": "table", + "html": "
MethodsTLNE↓SPL↑OSR↑SR↑
Speaker-Follower [10]12574.870.019653
Self-Monitoring [35]3734.480.029761
Reinforced CM [51]3584.030.029663
EnvDrop [47]6873.260.019969
AuxRN [57]413.240.218171
VLN-BERT [36]686.822.990.019973
Global Normalization [53]686.862.990.019974
Airbert [13]686.542.580.019977
LiLy686.452.500.019979
", + "image_path": "356caa91ce98daede2e1d1b7cf811833863b76eb7c32c4e5ad337e1ec5669db9.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 370, + 530, + 394 + ], + "lines": [ + { + "bbox": [ + 297, + 370, + 530, + 394 + ], + "spans": [ + { + "bbox": [ + 297, + 370, + 530, + 394 + ], + "type": "text", + "content": "Table 4: Results under discriminative setting on the test unseen split as indicated on the R2R leaderboard " + }, + { + "bbox": [ + 297, + 370, + 530, + 394 + ], + "type": "inline_equation", + "content": "{}^{2}" + }, + { + "bbox": [ + 297, + 370, + 530, + 394 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 404, + 530, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 404, + 530, + 461 + ], + "spans": [ + { + "bbox": [ + 296, + 404, + 530, + 461 + ], + "type": "text", + "content": "with the results whose manuscripts are publicly available, achieving the highest SR of " + }, + { + "bbox": [ + 296, + 404, + 530, + 461 + ], + "type": "inline_equation", + "content": "79\\%" + }, + { + "bbox": [ + 296, + 404, + 530, + 461 + ], + "type": "text", + "content": ". As we follow Airbert to use 30 candidate trajectories from EnvDrop [47] and the leaderboard considers that our agent has walked through all these paths, the SPL metric is low for both Lily and Airbert." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "spans": [ + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "type": "text", + "content": "Besides, our Lily agent also helps to increase the performance on R2R under the generative setting. We enhance the state-of-the-art DUET [6] method by pre-training the agent using our method as mentioned in Section 4. In Table 6, the agent incorporating Lily achieves " + }, + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "type": "text", + "content": " improvements w.r.t. SR on the val unseen split and test unseen split, respectively, compared to DUET. Notably, our method increases the SPL by " + }, + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 296, + 462, + 530, + 612 + ], + "type": "text", + "content": " on the val unseen split, indicating the agent is able to reach the goal more efficiently. We attribute this to the agent's acquisition of layout prior knowledge via the proposed trajectory judgment task on our YouTube-VLN dataset, enabling it to plan more efficient routes to the goals in new environments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "text", + "content": "Results on REVERIE Dataset. Compared with R2R, REVERIE is more challenging as its instructions only describe the destinations without detailed path descriptions. This requires the agent to be equipped with common knowledge about the room layouts and to reason the possible paths that lead to the destinations. In Table 5, we outperform the SOTA agent (i.e., DUET) by " + }, + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "inline_equation", + "content": "1.13\\%" + }, + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "text", + "content": " on SR and increase the SPL from " + }, + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "inline_equation", + "content": "46.98\\%" + }, + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "inline_equation", + "content": "48.11\\%" + }, + { + "bbox": [ + 296, + 613, + 530, + 730 + ], + "type": "text", + "content": " on the val unseen split. It is worth noting that our method achieves a higher OSR with a shorter TL, indicating that our agent finds the destination" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 717, + 277, + 728 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 717, + 277, + 728 + ], + "spans": [ + { + "bbox": [ + 57, + 717, + 277, + 728 + ], + "type": "text", + "content": "2https://eval.ai/web/challenges/challenge-page/97/leaderboard/270" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "8323" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 94, + 103, + 478, + 255 + ], + "blocks": [ + { + "bbox": [ + 94, + 103, + 478, + 255 + ], + "lines": [ + { + "bbox": [ + 94, + 103, + 478, + 255 + ], + "spans": [ + { + "bbox": [ + 94, + 103, + 478, + 255 + ], + "type": "table", + "html": "
MethodsVal UnseenTest Unseen
NavigationGroundingNavigationGrounding
TLOSR↑SR↑SPL↑RGS↑RGSPL↑TLOSR↑SR↑SPL↑RGS↑RGSPL↑
Human------21.1886.8381.5383.6677.8451.44
Seq2Seq [1]11.078.074.202.842.161.6310.896.883.993.092.001.58
RCM [51]11.9814.239.296.974.893.8910.6011.687.846.673.673.14
SMNA [35]9.0711.288.156.444.543.619.238.395.804.533.102.39
FM [41]45.2828.2014.407.197.844.6739.0530.6319.8811.6111.286.08
SIA [33]41.5344.6731.5316.2822.4111.5648.6144.5630.8014.8519.029.20
HAMT [5]14.0836.8432.9530.2018.9217.2813.6233.4130.4026.6714.8813.08
RecBERT [18]16.7835.0230.6724.9018.7715.2715.8632.9129.6123.9916.5013.51
ProbES [30]18.0033.2327.6322.7516.8413.9416.8428.2324.9720.1215.1112.32
Airbert [13]18.7134.5127.8921.8818.2314.1817.9134.2030.2823.6116.8313.28
DUET [6]22.1151.0746.9833.7332.1523.0321.3056.9152.5136.0631.8822.06
DUET (Lily)21.8753.7148.1134.4332.1523.4321.9460.5154.3237.3432.0221.94
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MethodsVal UnseenTest Unseen
TLNE↓SR↑SPL↑TLNE↓SR↑SPL↑
Seq2Seq [1]8.397.8122-8.137.8520-
EnvDrop [47]10.705.22524811.665.235147
AuxRN [57]-5.285550-5.155551
PREVALENT [14]10.194.71585310.515.305451
RelGraph [17]9.994.73575310.294.755552
RecBERT [18]12.013.93635712.354.096357
ProbES [30]11.584.00615512.434.206256
ADAPT [32]12.333.66665913.164.116357
HOP [42]12.273.80645712.653.836459
HAMT [5]11.462.29666112.273.936560
Airbert [13]11.784.01625612.414.136257
DUET [6]13.943.31726014.733.656959
DUET (Lily)14.582.90746216.133.447260
", + "image_path": "47cebef36bb987acb804b739db65ccc6ec60c228a1faec6301623a0f961c877e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 459, + 278, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 459, + 278, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 459, + 278, + 552 + ], + "type": "text", + "content": "more quickly. We attribute this to the better layout reason ability learned from the large-scale diverse reasonable trajectories in the proposed YouTube-VLN dataset. A similar performance is obtained on the test unseen split, where the Lily agent improves the SR by " + }, + { + "bbox": [ + 47, + 459, + 278, + 552 + ], + "type": "inline_equation", + "content": "1.81\\%" + }, + { + "bbox": [ + 47, + 459, + 278, + 552 + ], + "type": "text", + "content": " and the SPL by " + }, + { + "bbox": [ + 47, + 459, + 278, + 552 + ], + "type": "inline_equation", + "content": "1.28\\%" + }, + { + "bbox": [ + 47, + 459, + 278, + 552 + ], + "type": "text", + "content": ". Although our objective is solely navigation, we still achieve comparable performance on grounding metrics and even slightly outstrip DUET on most metrics." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 560, + 270, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 270, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 270, + 572 + ], + "type": "text", + "content": "5.4. Learning Navigation from One Environment" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 48, + 578, + 278, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 578, + 278, + 717 + ], + "spans": [ + { + "bbox": [ + 48, + 578, + 278, + 717 + ], + "type": "text", + "content": "Our intuition is that pre-training on the YouTube-VLN dataset can mitigate the domain gap of training from scratch and is able to achieve excellent performance with only a few training environments. To verify this, we conduct a one-shot learning study, where we fine-tune our model on only one environment of the original training environments. Note that the candidate paths are generated from all of the possible paths from the start viewpoints to all navigable points, instead of from the expert model in EnvDrop [47]. All the candidate paths are the shortest paths in the navigation graphs. To reduce the bias, we randomly select 5 sets from the entire environments and report the average results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 718, + 278, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 718, + 278, + 729 + ], + "spans": [ + { + "bbox": [ + 58, + 718, + 278, + 729 + ], + "type": "text", + "content": "In Table 7, our agent outperforms all the existing pre" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 346, + 279, + 481, + 320 + ], + "blocks": [ + { + "bbox": [ + 47, + 424, + 278, + 447 + ], + "lines": [ + { + "bbox": [ + 47, + 424, + 278, + 447 + ], + "spans": [ + { + "bbox": [ + 47, + 424, + 278, + 447 + ], + "type": "text", + "content": "Table 6: Comparison with state-of-the-arts on R2R dataset under generative setting." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 346, + 279, + 481, + 320 + ], + "lines": [ + { + "bbox": [ + 346, + 279, + 481, + 320 + ], + "spans": [ + { + "bbox": [ + 346, + 279, + 481, + 320 + ], + "type": "table", + "html": "
MethodsVal SeenVal Unseen
VLN BERT [36]45.7122.43
AirBERT [13]47.8850.00
Lily49.3150.86
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On the val seen split using one-shot finetuning, compared to VLN-BERT and AirBERT, our Lily agent achieves " + }, + { + "bbox": [ + 299, + 357, + 529, + 426 + ], + "type": "inline_equation", + "content": "3.60\\%" + }, + { + "bbox": [ + 299, + 357, + 529, + 426 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 299, + 357, + 529, + 426 + ], + "type": "inline_equation", + "content": "1.43\\%" + }, + { + "bbox": [ + 299, + 357, + 529, + 426 + ], + "type": "text", + "content": " improvements, respectively. In the val unseen split using one-shot fine-tuning, we achieve " + }, + { + "bbox": [ + 299, + 357, + 529, + 426 + ], + "type": "inline_equation", + "content": "28.43\\%" + }, + { + "bbox": [ + 299, + 357, + 529, + 426 + ], + "type": "text", + "content": " improvement compared to VLN-BERT. All these results suggest the effectiveness of our method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 299, + 436, + 367, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 436, + 367, + 448 + ], + "spans": [ + { + "bbox": [ + 299, + 436, + 367, + 448 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 299, + 456, + 529, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 456, + 529, + 629 + ], + "spans": [ + { + "bbox": [ + 299, + 456, + 529, + 629 + ], + "type": "text", + "content": "In this work, we propose a new approach Lily to address the limitations of existing vision-and-language navigation (VLN) methods by creating a large-scale VLN-like dataset from real house tour videos to train our embodied agent. We overcome the challenges of automatically generating path-instruction pairs to construct the dataset from raw and unlabeled videos by leveraging an entropy-based method for trajectory construction and an action-aware generator for instruction generation. Additionally, we train the agent to judge the reasonableness of trajectories, improving its layout reasoning ability. Our method achieves state-of-the-art performance on two popular benchmarks (R2R and REVERIE), demonstrating the efficacy. Overall, we hope our work can provide valuable insight into the VLN community by learning embodied VLN from passive videos." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 299, + 640, + 391, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 640, + 391, + 653 + ], + "spans": [ + { + "bbox": [ + 299, + 640, + 391, + 653 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 299, + 660, + 529, + 728 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 660, + 529, + 728 + ], + "spans": [ + { + "bbox": [ + 299, + 660, + 529, + 728 + ], + "type": "text", + "content": "Prof. Tan and his students were partially supported by the National Natural Science Foundation of China (NSFC) (62072190), National Natural Science Foundation of China (NSFC) 61836003 (key project), Program for Guangdong Introducing Innovative and Entrepreneurial Teams 2017ZT07X183." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "8324" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 280, + 730 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 178 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 178 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 178 + ], + "type": "text", + "content": "[1] P. 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In CVPR, pages 10009-10019, 2020. 2, 7, 8" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "spans": [ + { + "bbox": [ + 279, + 747, + 298, + 756 + ], + "type": "text", + "content": "8326" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection/918f7816-6b1d-45a6-a6ec-23336f1dbd99_content_list.json b/2023/Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection/918f7816-6b1d-45a6-a6ec-23336f1dbd99_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9da16abc0b20243637364203f142bd1c29f115a4 --- /dev/null +++ b/2023/Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection/918f7816-6b1d-45a6-a6ec-23336f1dbd99_content_list.json @@ -0,0 +1,2200 @@ +[ + { + "type": "text", + "text": "Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection", + "text_level": 1, + "bbox": [ + 78, + 128, + 893, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Junsheng Zhou $^{1,*}$ , Baorui Ma $^{1,2,*}$ , Shujuan Li $^{1}$ , Yu-Shen Liu $^{1\\dagger}$ , Zhizhong Han $^{3}$", + "bbox": [ + 179, + 202, + 790, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "School of Software, Tsinghua University, Beijing, China", + "bbox": [ + 256, + 220, + 712, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Beijing Academy of Artificial Intelligence, Beijing, China", + "bbox": [ + 251, + 238, + 720, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Department of Computer Science, Wayne State University, Detroit, USA", + "bbox": [ + 192, + 256, + 774, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "zhoujs21@mails.tsinghua.edu.cn, brma@baai.ac.cn, lisj22@mails.tsinghua.edu.cn", + "bbox": [ + 138, + 277, + 831, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "liuyushen@tsinghua.edu.cn, h312h@wayne.edu", + "bbox": [ + 294, + 295, + 674, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Latest methods represent shapes with open surfaces using unsigned distance functions (UDFs). They train neural networks to learn UDFs and reconstruct surfaces with the gradients around the zero level set of the UDF. However, the differential networks struggle from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set, resulting in highly fragmented and discontinuous surfaces. To resolve this problem, we propose to learn a more continuous zero level set in UDFs with level set projections. Our insight is to guide the learning of zero level set using the rest non-zero level sets via a projection procedure. Our idea is inspired from the observations that the non-zero level sets are much smoother and more continuous than the zero level set. We pull the non-zero level sets onto the zero level set with gradient constraints which align gradients over different level sets and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous unsigned distance field. We conduct comprehensive experiments in surface reconstruction for point clouds, real scans or depth maps, and further explore the performance in unsupervised point cloud upsampling and unsupervised point normal estimation with the learned UDF, which demonstrate our non-trivial improvements over the state-of-the-art methods. Code is available at https://github.com/junshengzhou/LevelSetUDF.", + "bbox": [ + 76, + 376, + 473, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 796, + 209, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Surface reconstruction from point clouds plays an important role in vision, robotics and graphics. Recently, neural implicit functions [61, 58, 57] have achieved remarkable", + "bbox": [ + 76, + 821, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "results by representing 3D geometries with signed distance functions (SDFs) [51, 13, 73], occupancy [57, 64, 60] or unsigned distance functions (UDFs) [89, 20, 27]. SDFs and occupancy explore the internal-to-external relations, which are limited to reconstruct closed surfaces. Researchers therefore turn to UDFs, which is a more general function, to represent shapes with arbitrary typologies.", + "bbox": [ + 500, + 345, + 893, + 450 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning an accurate zero level set of UDF is the key factor for representing complex geometries and supporting 3D applications [52, 42, 26, 17]. However, the differential neural networks struggle from learning the zero level set where the UDF is not differentiable. This leads to unstable optimizations, which results in large errors on unsigned distances and gradients around the zero level set, causing failures in downstream 3D applications. Taking surface reconstruction for example, SOTA methods [89, 27] extract surfaces from UDFs by judging gradient directions around the zero level set, where the unreliable gradients lead to highly fragmented and discontinuous surfaces.", + "bbox": [ + 496, + 454, + 893, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To resolve this issue, we introduce two novel constraints on the zero level set in forms of losses for learning accurate UDF without ground truth unsigned distances. The key insight is from the observation that despite the unreliable zero level set, the non-zero level sets learned by UDF are quite convincing, which can serve as an accurate guidance for the optimization on zero level set. We therefore propose the level set projection constraint to achieve a smoother and more continuous zero level set of UDF by enforcing the parallelism between the gradient of a query in a non-zero level set and the gradient of its projection to the zero level set. Moreover, we introduce an adaptive weighting strategy to force the neural network to focus more on the optimization nearer to the zero level set.", + "bbox": [ + 496, + 638, + 895, + 851 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The level set projection constraint aims to guide the gradients at zero level set, where we propose another unsigned distance loss as a supplement for correcting distance errors", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 875, + 207, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†The corresponding author is Yu-Shen Liu.", + "bbox": [ + 94, + 887, + 325, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3181", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "at the zero level set. To bring a more robust guidance to the optimization of zero level set, we introduce an addition gradient constraint on queries to learn more accurate and regular non-zero level sets of UDF by encouraging the gradient orthogonal to the tangent plane of the surface.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on our learned stable UDF with an accurate zero level set, we explore three different 3D applications, including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling. Our improvements over unsupervised or even supervised baselines justify both our effectiveness and the importance of an accurate and continuous zero level set to the representation ability of neural unsigned fields.", + "bbox": [ + 75, + 167, + 468, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows.", + "bbox": [ + 96, + 287, + 455, + 301 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose two novel constraints on UDF to achieve a smoother and more continuous zero level set for learning to represent shapes or scenes without ground truth unsigned distances.", + "- We justify that an accurate and continuous zero level set is the key factor to represent complex 3D geometries and supporting 3D downstream applications.", + "- We explore three different 3D applications with our learned UDF, including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling, where we show our superiority over the state-of-the-art supervised / unsupervised methods." + ], + "bbox": [ + 96, + 311, + 468, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 542, + 217, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the rapid development of deep learning, the neural networks have shown great potential in 3D applications [66, 30, 79, 75, 78, 74, 80, 76, 14, 39]. We mainly focus on learning Neural Implicit Functions with networks for representing 3D shapes or scenes.", + "bbox": [ + 75, + 568, + 468, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Implicit Functions. Recently, Neural Implicit Functions (NIFs) have shown promising results in surface reconstruction [61, 51, 57, 16, 29, 15, 38, 55, 53], novel view synthesis [58, 4, 65, 87, 32, 24, 59], image superresolution [68, 59, 11], point normal estimation [44], etc. In the task of surface reconstruction, the NIFs approaches train a neural network to represent shapes and scenes with binary occupancy [57, 64, 19] or signed distance functions (SDFs) [61, 36, 22, 21, 63, 10, 84, 6], and then extract surfaces from the learned implicit functions with the marching cubes algorithm [50]. Previous methods [57, 61] learn a global latent code for each 3D shape with a shared MLP to decode geometries. Some advanced approaches [64, 36] propose to use more latent codes to represent detailed local geometries. Latest studies bring more priors learned from large scale datasets to enhance the representation ability of NIFs. PCP [54] introduces the predictive context priors to", + "bbox": [ + 75, + 643, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "represent large-scale point clouds. OnSurf [52] explores the on-surface prior to reconstruct smooth surfaces from sparse point clouds.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NeRF [58] and the following studies [59, 62, 69, 56, 37, 67, 33, 45] extends NIFs to the task of novel view synthesis. NeuS [73], VolSDF [81] and Unisurf [60] advance the rendering procedure of NeRF for surface reconstruction from multi-view images. ManhattanSDF [28] leverages the man-hattan assumption for representing indoor scenes. NeuRIS [71] and MonoSDF [86] brings the depth prior and normal prior for improving the surface quality.", + "bbox": [ + 496, + 142, + 890, + 263 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Occupancy and SDFs are merely suitable to represent closed shapes. Recently, researchers explore the neural unsigned distances (UDFs) [20, 89, 88, 70, 18, 72, 49, 48] to represent shapes with arbitrary topology. NDF [20] trains a neural network to learn UDFs with the ground truth distance values. GIFS [82] jointly learns UDFs and the relationship of queries. MeshUDF [27] propose a differentiable meshing algorithm for UDF. However, all the previous UDF-based methods fail to reconstruct smooth and continuous surfaces with high-fidelity details due to the disability of learning an accurate and smooth zero level set of UDF.", + "bbox": [ + 496, + 268, + 890, + 434 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Implicit Learning from Raw Point Clouds. With the ground truth signed/unsigned distances or occupancy labels as supervision, previous methods learn NIFs as a regression [20, 61] problem or classification [57] problem. However, these expensive supervisions come from the ground truth meshes which are hard to collect. Moreover, such methods also fail to generalize to unseen cases with large geometry variations to the training data, which limits the application scenarios of such methods. To learn implicit representations directly from raw point clouds without ground truth supervisions, current methods explore the supervision from sign agnostic [2, 3] learning with gradient constraints [25]. Neural-Pull [51] employs a new learning schema to pull space onto surfaces for optimizing SDFs.", + "bbox": [ + 496, + 441, + 890, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Latest work CAP-UDF [89] learns UDF progressively with a field consistency loss. However, the UDF inferred by CAP-UDF are not accurate and the gradients are unreliable, especially in the zero level set which indicates the location of 3D geometries. The key problem is that the differential neural networks struggle from learning non-differentiable zero level set of UDF, leading to highly fragmented and discontinuous surfaces. Since the non-zero level sets of UDF are all differentiable, we propose to pull the non-zero level sets onto the zero level set with gradient constraints which align gradients and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous zero level set of unsigned distance field. Our learning schema involves the constraints for both zero level set and non-zero level sets of UDF, which differentiates our method from the previous ones [89, 2, 3, 51, 20, 61].", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3182", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5c957780ed4d20295f2d52ca39ba8ea24d2e3eecc6c07928d2a6d76e59445437.jpg", + "image_caption": [ + "Figure 1. Overview of our method. (a) The level set projection constraint leverages the gradient $\\nabla f(q)$ at convincing non-zero level set as the guidance to gradient $\\nabla f(\\hat{q})$ at unreliable zero level set. (b) The gradient-surface orthogonal constraint encourages the gradients $\\nabla f(q)$ at query $q$ orthogonal to the tangent plane of the surface at $p'$ which is the nearest point of $q$ in the raw point cloud." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 890, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 281, + 168, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural UDFs and Level Sets. We focus on learning unsigned distance functions for representing 3D shapes or scenes with arbitrary typology. Given a raw point cloud $P = \\{p_i \\in R^3\\}_{i=1}^N$ with $N$ points, we sample a set of queries $Q = \\{q_j \\in R^3\\}_{j=1}^M$ around $P$ . The UDF $f$ predicts the unsigned distances $s^P$ between queries $\\{q_j\\}_{j=1}^M$ and the shape described by $P$ , formulated as:", + "bbox": [ + 75, + 306, + 470, + 416 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns _ {j} ^ {P} = f (q _ {j}). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 426, + 468, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A level set $S_{d}$ of UDF is defined as a region of the 3D space containing a continuous set of 3D points with the same unsigned distance $d$ , formulates as:", + "bbox": [ + 75, + 457, + 468, + 503 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nS _ {d} = \\{q | f (q) = d \\}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 518, + 468, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and the level sets of UDF are defined as $S = \\{S_d\\}_{d > = 0}$", + "bbox": [ + 75, + 542, + 449, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning UDFs from Point Clouds. Inspired by CAP-UDF [89], we leverage the pulling optimization for learning UDFs from raw point clouds without ground truth unsigned distances as supervision. Specifically, given a query $q_{i}$ as input, we move it against the direction of the gradient $g_{i} = \\nabla f(q_{i})$ at $q_{i}$ , the moving operation is formulated as:", + "bbox": [ + 75, + 558, + 468, + 650 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {q} _ {i} = q _ {i} - f \\left(q _ {i}\\right) \\cdot \\nabla f \\left(q _ {i}\\right) / \\left| \\right| \\nabla f \\left(q _ {i}\\right) | | _ {2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 662, + 468, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the chamfer distance between moved queries $\\hat{Q} = \\{\\hat{q}\\}_{i=1}^{M}$ and the raw point cloud $P$ is calculated as the loss function for optimization, formulated as:", + "bbox": [ + 76, + 690, + 468, + 736 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C D}} = \\frac {1}{M} \\sum_ {i \\in [ 1, M ]} \\min _ {j \\in [ 1, N ]} | | \\hat {q} _ {i} - p _ {j} | | _ {2} \\\\ + \\frac {1}{N} \\sum_ {j \\in [ 1, N ]} \\min _ {i \\in [ 1, M ]} \\| p _ {j} - z _ {i} \\| _ {2}, \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 758, + 468, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Zero Level Set of UDF. An accurate zero level set is the key factor for UDF to represent 3D shapes or scenes, since the zero level set indicates the location of 3D geometries. The key problem here is that the differential networks struggle", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/db346aec818d0f395417c0c77778cbb3159315e23a7c944cb3e91d6d76486e1d.jpg", + "image_caption": [ + "(a) w/o ZLS-C" + ], + "image_footnote": [], + "bbox": [ + 501, + 292, + 694, + 368 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d5d35842fbe07c9d982715714b5516242ce10f08651548690048f79c961b7cd4.jpg", + "image_caption": [ + "zero level set" + ], + "image_footnote": [], + "bbox": [ + 501, + 369, + 596, + 428 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ac5e30d14ee521fad2f13f8cdaa464dffb6acd5b1fc66b2d738be09910110cbd.jpg", + "image_caption": [ + "gradient error" + ], + "image_footnote": [], + "bbox": [ + 596, + 369, + 694, + 428 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0bf86a37eeb41930070bb782acaec7972efb7ed0823d646923f570c18c1db568.jpg", + "image_caption": [ + "(b) Ours" + ], + "image_footnote": [], + "bbox": [ + 697, + 292, + 890, + 368 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8da5d3b831b132589c013da705c1854cb0ff2e88df74cbe4f9036598a7c97ac4.jpg", + "image_caption": [ + "zero level set", + "Figure 2. We visualize the fields and the zero level set of UDF learned with or without our designed constraints on the zero level set (ZLS-C). The bluer the color, the smaller the unsigned distances in the field and the errors on gradients." + ], + "image_footnote": [], + "bbox": [ + 697, + 369, + 792, + 428 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2d03c90a6765c7c47ec26aa9407757fd9647cddda1bc5fdb6798e1516cee4acf.jpg", + "image_caption": [ + "gradient error" + ], + "image_footnote": [], + "bbox": [ + 810, + 369, + 890, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set.", + "bbox": [ + 496, + 506, + 890, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We provide a visualization of fields and zero level set of UDF learned with neural networks in Fig. 2. As shown in Fig. 2 (a), the zero level set of UDF learned without proper constraints is highly fragmentary and discontinuous with large errors on the gradients at the space near to the zero level set. On the contrary, we achieve the accurate and continuous zero level set as shown in Fig. 2 (b) by introducing level set projection constraint and gradient-surface orthogonal constraint to the zero level set.", + "bbox": [ + 496, + 551, + 892, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Level Set Projections. For learning accurate zero level set of UDF, we design level set projection constraint to guide the learning of zero level set using the rest non-zero level sets. Our idea comes from the observation that despite the unreliable zero level set, the other level sets of the learned UDF are quite convincing, which can serve as the guidance to the field optimization on the zero level set. As shown in Fig. 2, the gradient errors on the non-zero level set are much less than the errors on the zero level set.", + "bbox": [ + 496, + 688, + 890, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We illustrate our method in Fig. 1, where we pull the non-zero level set onto the zero level set with gradient constraints which align gradients and correct unsigned distance errors on the zero level set. We achieve this by encouraging the parallelism between the gradient at queries $Q = \\{q_i\\}_{i=1}^M$", + "bbox": [ + 496, + 824, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3183", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/90acea61853345eaf455da5ba641005dbd3c748e2cf8f4a97760d4d64cd5c38b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 89, + 267, + 169 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/20cc3fae307f6bd07c5fa1cf1eb25384cc677abf703f21065f63f84534a16408.jpg", + "image_caption": [ + "NDF" + ], + "image_footnote": [], + "bbox": [ + 84, + 167, + 267, + 229 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1a86f838e360a90b0a640fea6f7c57d8cf4dd33236204a4f5c57883872169221.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 89, + 467, + 169 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/656be93e4e8c218875cfce40e2da159ba0e7829a0b2a193920d3e36a3a851b23.jpg", + "image_caption": [ + "CAP-UDF" + ], + "image_footnote": [], + "bbox": [ + 282, + 170, + 467, + 231 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/defe77b78a462a1cfaade2ab7ea74178450af3b75c070f94a10fb29b14f95a48.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 475, + 88, + 671, + 169 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/16cfe1f371564158a3b44cebec48711d68efd7e3d9b10105326acb648577db50.jpg", + "image_caption": [ + "Ours", + "Figure 3. Visual comparisons of surface reconstruction on ShapeNet dataset." + ], + "image_footnote": [], + "bbox": [ + 482, + 170, + 669, + 231 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/701d8418335f6ee86dbc738cdf4da7932c3d480c17b1e912c15a778d4e6c7f59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 683, + 88, + 875, + 169 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/99fbf0f35e98b0f54c75cb6c454a3fdc29d2a9351b901b00ed49e205dcbcdd4b.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 684, + 167, + 872, + 231 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/c55dc890964e84c74e01c2ee6029bb3732987b8951e9ca9d75c86b3f523b7e4d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodChamfer-L2F-ScoreNC
MeanMedian\\( F1^{0.005} \\)\\( F1^{0.01} \\)
Input0.3630.35548.5088.34-
Watertight GT2.6282.29368.8281.60-
GT0.0760.07495.7099.99-
NDF [20]0.2020.19377.4097.9779.1
GIFS [82]0.1280.12388.0599.31-
CAP-UDFBPA0.1410.13884.8499.3381.8
CAP-UDF [89]0.1190.11488.5599.8282.5
Ours0.0980.09792.1899.9085.0
", + "bbox": [ + 81, + 270, + 468, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Surface reconstruction for point cloud on ShapeNet cars dataset (Chamfer-L2×10^4).", + "bbox": [ + 75, + 430, + 468, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and the gradient at their projections $\\hat{Q} = \\{\\hat{q}\\}_{i=1}^{M}$ to the zero level set, formulated as:", + "bbox": [ + 75, + 470, + 468, + 502 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {p r o j}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\gamma_ {i} \\left(1 - \\left| \\frac {\\nabla f (q _ {i}) \\cdot \\nabla f (\\hat {q} _ {i})}{| | \\nabla f (q _ {i}) | | _ {2} \\cdot | | \\nabla f (\\hat {q} _ {i}) | | _ {2}} \\right|\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 512, + 468, + 554 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{i}$ is the factor for weighting the gradient constraint at the query $q_{i}$ , indicating the importance of optimizing query $q_{i}$ , formulated as:", + "bbox": [ + 75, + 563, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma_ {i} = \\exp (- \\lambda | f (q _ {i}) |). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 623, + 468, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We set $\\gamma$ to increase when queries are closer to the zero level set where $\\lambda$ is a hyper-parameter to control the increasing speed. The nonuniform weighting encouraging the network to focus more on the optimizations near the zero level set of UDF.", + "bbox": [ + 75, + 647, + 468, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While $\\mathcal{L}_{proj}$ can provide an effective guidance to the gradients at zero level set, we further explore a more accurate unsigned distance constraint for correcting the distance values at the zero level set of UDF. The implemented loss is defined as:", + "bbox": [ + 75, + 722, + 468, + 795 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} | f (p _ {i}) |, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 794, + 468, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p_i \\in P$ is the raw point cloud indicating the exact surface to be represented.", + "bbox": [ + 75, + 839, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gradient-Surface Orthogonal Constraint. The key idea to guide the learning of zero level set using the rest level sets", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is based on the observation that the non-zero level sets are much more reliable. To bring a more robust guidance to the optimization of zero level set, we introduce an addition gradient constraint on queries to learn a more stable and regular level sets at the non-zero level sets of UDF by enforcing the gradient orthogonal to the tangent plane of the surface. We design a novel loss to encourage the consistency between the gradient direction at a query $q_{i}$ and the direction from $q_{i}$ to its closest point $p_{i}$ on $P$ , formulated as:", + "bbox": [ + 496, + 266, + 890, + 402 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {o r t h}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} (1 - | \\frac {\\nabla f (q _ {i}) \\cdot T (q _ {i} , p _ {i})}{| | \\nabla f (q _ {i}) | | _ {2} \\cdot | | T (q _ {i} , p _ {i}) | | _ {2}} |), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 407, + 890, + 449 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T(q_{i},p_{i})$ is the direction from $q_{i}$ to $p_i$ . The constraint is illustrated in Fig. 1.", + "bbox": [ + 496, + 455, + 890, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A more naive way of introducing the direction vector $T(q_{i},p_{i})$ for learning is to explicitly substitute the gradient $\\nabla f(q_{i})$ with the direction vector $T(q_{i},p_{i})$ , as proposed in GenSDF [21]. However, $T(q_{i},p_{i})$ is obviously not the exact direction for $q_{i}$ to reach the approximated surface since the raw point cloud is the discrete representation of the surface, and $p_{i}$ is not the exact nearest points of $q_{i}$ in the approximated surface, which leads to wrong supervisions for GenSDF.", + "bbox": [ + 496, + 484, + 890, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "On the contrary, We introduce a more flexible way by treating direction vector $T(q_{i},p_{i})$ as an optimization objective, which enables the networks to accommodate the inconsistency between the closest point $p_i$ on $P$ and the closest point $\\hat{q}_i$ predicted by the networks.", + "bbox": [ + 496, + 621, + 890, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Loss Function. Finally, our loss function is formulated as:", + "bbox": [ + 500, + 696, + 887, + 710 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {C D}} + \\alpha_ {1} \\mathcal {L} _ {\\text {p r o j}} + \\alpha_ {2} \\mathcal {L} _ {\\text {d i s t}} + \\alpha_ {3} \\mathcal {L} _ {\\text {o r t h}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 719, + 890, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{1},\\alpha_{2}$ and $\\alpha_{3}$ are the balance weights for our designed three losses to learn accurate zero level set of UDF.", + "bbox": [ + 496, + 742, + 890, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Applications. The zero level set of UDF indicates the location of represented 3D geometries. Thus, a well-learned UDF with accurate and continuous zero level set can be adopt to different 3D applications.", + "bbox": [ + 496, + 772, + 890, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Surface Reconstruction. Following previous methods [89, 27], the surfaces can be extracted from the zero level set of UDF by judging gradient directions, formulated as:", + "bbox": [ + 496, + 832, + 890, + 878 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} \\left(q _ {i}, q _ {j}\\right) = \\nabla f \\left(q _ {i}\\right) \\cdot \\nabla f \\left(q _ {j}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3184", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f652f86e1dd98024bb3591986a12bb7ec79f47fdd487159caa727a8cd8b70af0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 93, + 251, + 175 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0dd16da2b237c0466834b504d1d7d70e640de207eac2a2b2db264b29873b0956.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 93, + 408, + 175 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2f32c6e624c0f9a4cc8e0863094574dd7a0cfabeab655fe4ee8d918979aae06d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 93, + 570, + 175 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a6dae0aee224f911f01228fb0f041d32c272050852ed090d819042c0d32bc626.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 575, + 93, + 728, + 175 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4a6cc4ede02aa033d754009b97b06ab38c7ff00054b15a681beb0e39113aa175.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 92, + 888, + 174 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/efc058f781f640e51fc4dbe4ba299d6ed5f99f06201168f04b5b1cacad023dc2.jpg", + "image_caption": [ + "ConvOcc" + ], + "image_footnote": [], + "bbox": [ + 86, + 176, + 243, + 258 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2d4e050af9f3dcf3c553bb7d06a0fe9ef8cf4fddbfb0da5784fd0591dfbc06ba.jpg", + "image_caption": [ + "NDF" + ], + "image_footnote": [], + "bbox": [ + 245, + 176, + 401, + 258 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b80d7c8b0ad0573789d90c712775fa20e2def5507da8ac345157d41b452b816d.jpg", + "image_caption": [ + "CAP-UDF", + "Figure 4. Visual comparisons of surface reconstruction on 3D Scene dataset. Input contains 1K points / $m^2$" + ], + "image_footnote": [], + "bbox": [ + 401, + 175, + 566, + 261 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/98213426a4f816be03e327fd83b4e2040d3213b0fb7f0a09f1d6c3969450c5a8.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 566, + 175, + 725, + 258 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a0cfbf324b943c4ece9cf616c44e1cae0d3e4ca396f34236affc7def007b7b73.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 728, + 176, + 885, + 261 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d0d7a566dfaa84879516422d0ea29860cbd397433c032bdc9cf7961484684d65.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BurghersLoungeCopyroomStonewallTotempole
L2CDL1CDNCL2CDL1CDNCL2CDL1CDNCL2CDL1CDNCL2CDL1CDNC
500/m2ConvONet [64]26.970.0810.9059.0440.0460.89410.080.0460.88517.700.0630.9092.1650.0240.937
LIG [36]3.0800.0460.8406.7290.0520.8314.0580.0380.8104.9190.0430.8789.380.0620.887
DeepLS [13]0.7140.0200.92310.880.0770.8140.5520.0150.9070.6730.0180.95121.150.1220.927
NDF [20]0.5460.0180.9170.3140.0120.9210.2420.0120.9070.2260.0120.9491.0490.0250.939
OnSurf [52]0.6090.0180.9300.5290.0130.9260.4830.0140.9080.6660.0130.9552.0250.0410.954
CAP-UDF [89]0.1920.0110.9110.0990.0090.9110.1200.0090.9020.0690.0080.9580.1310.0100.954
Ours0.1610.0090.9160.0870.0060.9330.1020.0070.9200.0610.0070.9640.1140.0070.960
1000/m2ConvONet [64]27.460.0790.9079.540.0460.89410.970.0450.89220.460.0690.9052.0540.0210.943
LIG [36]3.0550.0450.8359.6720.0560.8333.610.0360.8105.0320.0420.8799.580.0620.887
DeepLS [13]0.4010.0170.9206.1030.0530.8480.6090.0210.9010.3200.0150.9540.6010.0170.950
NDF [20]1.1680.0270.9010.3930.0140.9100.2690.0130.9080.5090.0190.9362.0200.0360.922
OnSurf [52]1.3390.0310.9290.4320.0140.9340.4050.0140.9140.2660.0140.9571.0890.0290.954
CAP-UDF [89]0.1910.0100.9100.0920.0080.9270.1130.0090.9110.0660.0070.9620.1390.0090.955
Ours0.1460.0090.9210.0680.0060.9410.0930.0070.9250.0500.0050.9700.1070.0070.960
", + "bbox": [ + 81, + 296, + 893, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Surface reconstruction for point clouds under 3D Scene. $\\mathrm{L}2\\mathrm{{CD}} \\times {1000}$ .", + "bbox": [ + 246, + 494, + 718, + 507 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to classify whether two queries $q_{1}$ and $q_{2}$ are in the same $\\mathcal{D}(q_i,q_j) > 0$ or the opposite side $\\mathcal{D}(q_i,q_j) < 0$ of the approximated surface. The marching cubes-like algorithm is then used to extract surfaces.", + "bbox": [ + 75, + 516, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unsupervised Point Normal Estimation. With a well learned zero level set, we compute the gradients at the raw point clouds $P$ as their estimated normals, formulated as:", + "bbox": [ + 75, + 575, + 468, + 622 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {N} (P) = \\{\\nabla f (p) \\}, p \\in P. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 633, + 468, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unsupervised Point Cloud Upsampling. We randomly sample queries around $P$ , and then move them to the zero level set with Eq. 3 as the upsampled points of $P$ . We further filter the queries with unsigned distance values larger than a threshold $\\beta$ for avoiding outliers. The procedure for upsampling $P$ with a factor of $G$ is formulated as:", + "bbox": [ + 75, + 662, + 468, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {U} (P) = \\left\\{\\hat {q} _ {i}, i \\in [ 1, N \\times G ] \\mid f \\left(q _ {i}\\right) < \\beta \\right\\} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 768, + 468, + 786 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 799, + 209, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For evaluating the performance of our method, we conduct experiments on surface reconstruction from raw point clouds of shapes (Sec. 4.1), room-level scenes (Sec. 4.2), and real scans (Sec. 4.4), where we also show our results on large-scale driving scenes obtained by fusing LiDAR", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "depths in Sec. 4.3. We further explore the ability of our learned UDF with accurate zero level set for unsupervised point normal estimation (Sec. 4.5) and unsupervised point upsampling (Sec. 4.6). Finally, we conduct ablation studies in Sec. 4.7.", + "bbox": [ + 496, + 516, + 892, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Surface Reconstruction for Shapes", + "text_level": 1, + "bbox": [ + 498, + 603, + 802, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset and Metrics. To explore the ability of our method in representing shapes with arbitrary topology, we follow previous methods [89, 82] to conduct experiments on the \"Car\" category of ShapeNet dataset which contains the largest number of shapes with multi-layer structures or open surfaces. We sample 10K points per shape as the input for surface reconstruction. For evaluating the performances, we follow the common setting [82] to sample 100K points from the reconstructed surfaces and leverage Chamfer Distance, Normal Consistency [57] and F-score with a threshold of 0.005 / 0.01 as the evaluation metrics.", + "bbox": [ + 496, + 627, + 892, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparisons. We compare our method with the state-of-the-art shape reconstruction methods NDF [20], GIFS [82] and CAP-UDF [89]. We report the quantitative comparison results in Tab. 1, where \"Watertight GT\" is the result of sampling points from the watertight ground truth, indicating the best performance of the methods base on SDF or occupancy. We also show the superior limit of the dataset", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3185", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b4cf5970fcbfd1bb772ed9db7a5d7f4a8ce853325a81a4d1dc72300451e87863.jpg", + "image_caption": [ + "Figure 5. Surface reconstruction results on KITTI odometry dataset (Sequence 00, frame 3000 to 4000)." + ], + "image_footnote": [], + "bbox": [ + 83, + 87, + 890, + 275 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "by sampling points on the ground truth mesh and report the result as \"GT\". Tab. 1 shows that our method achieves the best performance over all the baselines in terms of all metrics. The visual comparison in Fig. 3 further shows that our methods produce more continuous and accurate geometries over all baselines.", + "bbox": [ + 75, + 308, + 470, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Surface Reconstruction for Room-Level Scenes", + "text_level": 1, + "bbox": [ + 76, + 407, + 468, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and Metrics. We further explore our performance on real scene scans to demonstrate the ability of our methods to scale to large-scale point clouds. Following On-Surf [52], we conduct experiments on the 3D Scene dataset consisting of complex scenes with open surfaces and scan noises. The input point cloud is achieved by sampling 500 or 1000 points per $m^2$ uniformly for each scene. We follow the common setting [52, 89] to sample $1M$ points on both the reconstructed and the ground truth meshes. We leverage L1 / L2 Chamfer Distance and Normal Consistency as the evaluation metrics.", + "bbox": [ + 75, + 430, + 468, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons. With different point densities, we compare our method with the state-of-the-art methods ConvONet [64], LIG [36], DeepLS [13], OnSurf [52], NDF [20] and CAP-UDF [89]. The numerical comparison in Tab. 2 demonstrates our superior performance in all scenes. We further present a visual comparison in Fig. 4, where the input point clouds contains 1K points/ $m^2$ . The visualization further shows that our method can reconstruct more detailed and smooth surfaces in complex scenes, where the other UDF-base methods NDF and CAP-UDF produce fragmented surfaces.", + "bbox": [ + 75, + 597, + 470, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Large-Scale Driving Scene Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 771, + 437, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. To further demonstrate our scalability to extremely large scenes, we follow NGS [35] to apply our method to KITTI dataset [23]. We use the LiDAR scans of frame 3000 to 4000 in Squeeze00 subset of KITTI dataset as the full input, which are transformed into world coordinates using the provided camera trajectories. We leverage the slide-window strategy to divide the full scene into 15", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a9006759255c129c7f2176153e85f4e51efcddfa6648673c35f0ee39575b4eaf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodChamfer-L1F-ScoreNC
IGR [25]0.17875.586.9
Point2Mesh [31]0.11664.8-
SPSR [40]0.23273.5-
SAP [63]0.07683.088.6
Neural-Pull [51]0.10679.787.2
NDF [20]0.23868.680.4
CAP-UDF [89]0.07384.588.6
Ours0.07185.191.0
", + "bbox": [ + 513, + 305, + 880, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Surface reconstruction for point cloud on SRB dataset.", + "bbox": [ + 500, + 452, + 875, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "blocks of size $51.2m^3$ , where we sample 300K points per block as the local input to train our network. The final scene is achieve by blending the reconstructed local scenes.", + "bbox": [ + 496, + 472, + 890, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis. The reconstruction results under KITTI scenes is shown in Fig. 5, where our method reproduces visualappealing performances with accurate geometries. Note that: 1) The LiDAR scans contain large amount of noises, especially in the difficult driving scenes. 2) Our method learns to reconstruct surfaces directly from the raw point cloud without learning priors from large-scale datasets.", + "bbox": [ + 496, + 518, + 892, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Surface Reconstruction for Real Scans", + "text_level": 1, + "bbox": [ + 498, + 635, + 831, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and Metrics. We demonstrate our advantages for surface reconstruction from real scans by conducting experiments on the Surface Reconstruction Benchmarks [77] (SRB). We follow previous methods [63, 89] to leverage Chamfer Distance and F-Score with a threshold of $1\\%$ for evaluation. Note that the ground truth of SRB dataset is dense point cloud containing millions of points. For a comprehensive comparison on the reconstruction quality, we further evaluate the Normal Consistency by first converting the ground truth into meshes with BPA [8] algorithm.", + "bbox": [ + 496, + 657, + 890, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons. We first report our numerical comparison under SRB dataset with the classic and learning-based methods in Tab. 3. The compared methods include IGR [25], Point2Mesh [31], Screened Poisson Surface Reconstruction (SPSR) [40], Shape As Points (SAP) [63], Neural-Pull [51], NDF [20] and CAP-UDF [89]. Our method", + "bbox": [ + 496, + 810, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3186", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/994e2d33482fbd100d615528e35b60deb47a125ce9f8d55a259cd9d7f9be067a.jpg", + "image_caption": [ + "Figure 6. Visual comparisons of surface reconstruction on SRB dataset. SRB dataset provides only point clouds as GT." + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 472, + 205 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9d5280b94cedfa4a73da65e2195c30a82eb4d915d25d9aabe12e4f686b596fe3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCleanStripGradientaverage
SupervisedPCPNet [26]9.6611.4713.4211.61
Hough [9]10.2312.4711.0211.24
Nesti-Net [7]6.998.479.008.15
IterNet [41]6.727.737.517.32
DeepFit [5]6.517.927.317.25
UnsupervisedJet [12]12.2313.3913.1312.92
PCA [1]12.2913.6612.8112.92
Ours (w/o ZLS-c)7.307.747.787.61
Ours6.517.457.647.20
", + "bbox": [ + 81, + 250, + 468, + 405 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "achieves the best performance in all metrics as shown in Tab. 3. The visual comparison in Fig. 6 further shows that our methods produce more accurate and smooth geometries over all baselines.", + "bbox": [ + 76, + 430, + 468, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Unsupervised Point Normal Estimation", + "text_level": 1, + "bbox": [ + 76, + 500, + 413, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset and Metrics. We adopt the widely-used PCPNet [26] dataset to evaluate our method on the task of point normal estimation. Each point cloud in the PCPNet dataset contains 100K points. We conduct experiments under three different settings. The inputs of \"Clean\" setting are sampled uniformly on shapes, and two additional settings with varying point densities (Stripes and Gradients) are added to explore our performance in handling irregular data. Following previous methods [5, 26], we sample 5000 points per shape and compute the angle root mean square error (RMSE) between the predicted normals and the ground truth normals as the evaluation metrics.", + "bbox": [ + 75, + 522, + 468, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons. We conduct a comparison with traditional normal estimation methods including PCA [1], Jets [12] and the state-of-the-art learning-based methods PCPNet [26], HoughCNN [9], Nesti-Net [7], Iter-Net [41] and DeepFit [5]. Note that all the previous learning-based methods are designed in a supervised manner which requires a large scale dataset for training, while we extract normals directly from the unsigned distance fields learned from raw point cloud in an unsupervised way. The numerical results in Tab. 4 show that our method achieves a comparable or even better performance than the state-of-the-art supervised methods. The results also show the effectiveness of our method where the performance degrades from 7.20 to 7.61 without", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5fd88d82adf961f6ca3d37a28d9f96b3aa5c116d976091f0cd67a67eddb4f489.jpg", + "image_caption": [ + "Figure 7. Visual comparisons on error maps of point normal estimation on PCPNet dataset." + ], + "image_footnote": [], + "bbox": [ + 506, + 92, + 885, + 496 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0887b8a0fc633d9a67f6c5f039b52085cf75c5edfc439a4c6c63359a5610a2ed.jpg", + "table_caption": [ + "Table 4. Point normal estimation results on the PCPNet dataset." + ], + "table_footnote": [], + "table_body": "
MethodSupervised?P2FCDHD
PU-Net [85]Yes6.840.728.94
MPU [83]Yes3.960.496.11
PU-GAN [42]Yes2.330.284.64
Dis-PU [43]Yes2.010.222.83
EAR [34]No5.820.527.37
L2G-AE [46]No39.376.3163.23
SPU-Net (Tr2T) [47]No5.970.382.24
SPU-Net (All2T)No5.790.372.55
SPU-Net (Te2T)No6.850.412.18
Ours (w/o ZLS-C)No1.430.242.16
OursNo1.020.191.55
", + "bbox": [ + 504, + 539, + 890, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Point cloud upsampling results on the PU-GAN dataset.", + "bbox": [ + 500, + 737, + 883, + 752 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "our constraints. The visual comparison in Fig. 7 shows that our method produces more accurate estimations compared to other methods, especially on the complex geometries.", + "bbox": [ + 498, + 762, + 890, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Unsupervised Point Cloud Upsampling", + "text_level": 1, + "bbox": [ + 500, + 816, + 834, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset and Metrics. For the task of point cloud upsampling, we follow previous methods [47, 43] to conduct experiments on the dataset provided by PU-GAN [42]. We evaluate our method under the setting to generate 8,198", + "bbox": [ + 498, + 839, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3187", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/29496caedd699d5607c87b3b6f95ccaf6f883e73ac91e5c90c24cdb0d67bb907.jpg", + "image_caption": [ + "Figure 8. Visual comparisons of point cloud upsampling on PU-GAN dataset." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 893, + 233 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "points for each sparse input with 2,048 points. We adopt Chamfer Distance (CD), Hausdorff Distance (HD) and Point-to-Surface distance (P2F) as the evaluation metrics.", + "bbox": [ + 75, + 266, + 468, + 310 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparisons. We compare our method with the state-of-the-art supervised methods PU-Net [85], MPU [83], PU-GAN [42], Dis-PU [43] and unsupervised methods EAR [34], L2G-AE [46] and SPU-Net [47]. The quantitative comparison is shown in Tab. 5, where our method outperforms the previous supervised and unsupervised methods significantly. The results also show the effectiveness of our method where the performance degrades from 1.55 to 2.16 in terms of HD without our designed constraints. The visualization in Fig. 8 further shows that our upsampling results are more smooth and uniform even compared with the state-of-the-art supervised methods.", + "bbox": [ + 75, + 311, + 473, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 500, + 243, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct ablation studies to demonstrate the effectiveness of each proposed constraint and explore the effect of some important hyper-parameters. We report the performance under a subset of ShapeNet Cars dataset in terms of L2 Chamfer Distance $(\\times 10^{4})$ and Normal Consistency.", + "bbox": [ + 75, + 523, + 468, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of each Design. We first justify the effectiveness of each proposed constraint in Tab. 6. We report the performance without all the three designed losses as \"w/o ZLS-C\". We explore each loss by reporting the results without level set projection loss as \"w/o $\\mathcal{L}_{\\mathrm{proj}}$ \", surface unsigned distance loss as \"w/o $\\mathcal{L}_{\\mathrm{dist}}$ \", gradient-surface orthogonal loss as \"w/o $\\mathcal{L}_{\\mathrm{orth}}$ \" and adaptive point weight as \"w/o AW\". We replace our level set projection constraint with the GenSDF-style [21] optimization as \"GenSDF-Style\". We further constrain the level set projection loss on a randomly selected non-zero level set other than the zero level set and report the performance as \"Non-zero LSC\". The result demonstrates that the zero level set is the key factor that influence the representation ability of UDF.", + "bbox": [ + 75, + 598, + 468, + 810 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Weight of Level Set Projection Loss. We report the performance with different weights of the level set projection loss $\\mathcal{L}_{\\mathrm{proj}}$ in Tab. 7. We found that a suitable weight of $\\mathcal{L}_{\\mathrm{proj}}$ will improve the reconstruction accuracy, and it may affect the optimization to converge if we weight too much.", + "bbox": [ + 75, + 810, + 468, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Weight of Surface Unsigned Distance Loss. We further", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cbccebd6e8582bd73449ff848a25f2922cce9db83b911eb4877735bbb36216c5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
w/o ZLS-Cw/o Lprojw/o Ldistw/o Lorth
L2CD0.1260.1070.1010.096
NC82.782.983.984.1
w/o AWGenSDF-StyleNon-zero LSCOurs
L2CD0.0960.1010.0980.091
NC84.283.983.584.4
", + "bbox": [ + 504, + 262, + 893, + 349 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6ae2113556c40bb51acc69182ef2408a28ebc76258eb91663eacc28e258e49b8.jpg", + "table_caption": [ + "Table 6. Effect of framework design." + ], + "table_footnote": [], + "table_body": "
0.0010.0020.010.1
L2CD0.0950.0910.1620.359
NC84.284.483.479.6
", + "bbox": [ + 503, + 369, + 892, + 410 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "explore the effect of weights $\\alpha_{2}$ for the surface unsigned distance loss in Tab 8, where we found that a too large or too small weight will degenerate the performance.", + "bbox": [ + 498, + 443, + 893, + 489 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/176f9519ba821e033bf954d804f1bf687361eb2b148135ac5ab73028a0f0f0a7.jpg", + "table_caption": [ + "Table 7. Weight of level set projection loss." + ], + "table_footnote": [], + "table_body": "
0.0010.010.11
L2CD0.1010.1000.0910.449
NC84.184.184.478.9
", + "bbox": [ + 503, + 507, + 892, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Weight of Gradient-Surface Orthogonal Loss. We evaluate the effect of the weight $\\alpha_{3}$ for gradient-surface orthogonal loss in Tab. 9. A proper weight $\\alpha_{3} = 0.01$ brings the best improvement while a too much weight will affect the convergence.", + "bbox": [ + 498, + 560, + 890, + 636 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8715e760e96c7f6f97dd5c8e1ae99d119d69d20003d2c79ca9595383e77fb190.jpg", + "table_caption": [ + "Table 8. Weight of surface unsigned distance loss." + ], + "table_footnote": [], + "table_body": "
0.0010.010.11
L2CD0.0940.0910.3352.55
NC84.284.477.772.9
", + "bbox": [ + 503, + 648, + 890, + 689 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Adaptive per Point Weights. We further report the performance under different $\\lambda$ which controls the increasing speed of adaptive weights for each point in Tab. 10. We found that $\\lambda$ has a relative small impact on the Chamfer Distance with large affect on the Normal Consistency, which indicates that the adaptive per point weight can improve the surface smoothness.", + "bbox": [ + 498, + 712, + 890, + 818 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cf56e9e04fc561e78d77262ccc52fab15184dad8a04775e3fc2f93d671cfa305.jpg", + "table_caption": [ + "Table 9. Weight of gradient-surface orthogonal loss." + ], + "table_footnote": [], + "table_body": "
1101001000
L2CD0.0930.0910.0920.094
NC84.184.483.783.2
", + "bbox": [ + 503, + 830, + 890, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 10. Effect of adaptive per point weights.", + "bbox": [ + 557, + 869, + 831, + 883 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3188", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 89, + 194, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we justify that an accurate and continuous zero level set of unsigned distance functions is the key factor to represent complex 3D geometries. We therefore propose two novel constraints on UDF to achieve a more continuous zero level set by projecting non-zero level set to guide the optimization of zero level set. With the ability of learning consistent and accurate zero level set of UDF, we explore three different 3D applications including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling, where the visual and numerical comparisons with the state-of-the-art supervised/unsupervised methods justify our effectiveness ans show our superiority over the latest methods.", + "bbox": [ + 75, + 114, + 472, + 311 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 76, + 325, + 256, + 343 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data.", + "bbox": [ + 75, + 349, + 468, + 411 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 76, + 422, + 174, + 439 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hervé Abdi and Lynne J Williams. Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2(4):433-459, 2010. 7", + "[2] Matan Atzmon and Yaron Lipman. SAL: Sign agnostic learning of shapes from raw data. 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In Advances in Neural Information Processing Systems (NeurIPS), 2022. 1, 2, 3, 4, 5, 6" + ], + "bbox": [ + 503, + 92, + 890, + 375 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "3192", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection/918f7816-6b1d-45a6-a6ec-23336f1dbd99_model.json b/2023/Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection/918f7816-6b1d-45a6-a6ec-23336f1dbd99_model.json new file mode 100644 index 0000000000000000000000000000000000000000..562fbfa59688600d699c433ffede128002cb9d48 --- /dev/null +++ b/2023/Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection/918f7816-6b1d-45a6-a6ec-23336f1dbd99_model.json @@ -0,0 +1,3326 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.13, + 0.895, + 0.178 + ], + "angle": 0, + "content": "Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection" + }, + { + "type": "text", + "bbox": [ + 0.18, + 0.203, + 0.792, + 0.222 + ], + "angle": 0, + "content": "Junsheng Zhou\\(^{1,*}\\), Baorui Ma\\(^{1,2,*}\\), Shujuan Li\\(^{1}\\), Yu-Shen Liu\\(^{1\\dagger}\\), Zhizhong Han\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.222, + 0.714, + 0.239 + ], + "angle": 0, + "content": "School of Software, Tsinghua University, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.253, + 0.239, + 0.721, + 0.257 + ], + "angle": 0, + "content": "Beijing Academy of Artificial Intelligence, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.257, + 0.776, + 0.275 + ], + "angle": 0, + "content": "Department of Computer Science, Wayne State University, Detroit, USA" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.278, + 0.832, + 0.292 + ], + "angle": 0, + "content": "zhoujs21@mails.tsinghua.edu.cn, brma@baai.ac.cn, lisj22@mails.tsinghua.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.295, + 0.296, + 0.676, + 0.31 + ], + "angle": 0, + "content": "liuyushen@tsinghua.edu.cn, h312h@wayne.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.377, + 0.474, + 0.768 + ], + "angle": 0, + "content": "Latest methods represent shapes with open surfaces using unsigned distance functions (UDFs). They train neural networks to learn UDFs and reconstruct surfaces with the gradients around the zero level set of the UDF. However, the differential networks struggle from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set, resulting in highly fragmented and discontinuous surfaces. To resolve this problem, we propose to learn a more continuous zero level set in UDFs with level set projections. Our insight is to guide the learning of zero level set using the rest non-zero level sets via a projection procedure. Our idea is inspired from the observations that the non-zero level sets are much smoother and more continuous than the zero level set. We pull the non-zero level sets onto the zero level set with gradient constraints which align gradients over different level sets and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous unsigned distance field. We conduct comprehensive experiments in surface reconstruction for point clouds, real scans or depth maps, and further explore the performance in unsupervised point cloud upsampling and unsupervised point normal estimation with the learned UDF, which demonstrate our non-trivial improvements over the state-of-the-art methods. Code is available at https://github.com/junshengzhou/LevelSetUDF." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.797, + 0.21, + 0.812 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.822, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Surface reconstruction from point clouds plays an important role in vision, robotics and graphics. Recently, neural implicit functions [61, 58, 57] have achieved remarkable" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.346, + 0.895, + 0.452 + ], + "angle": 0, + "content": "results by representing 3D geometries with signed distance functions (SDFs) [51, 13, 73], occupancy [57, 64, 60] or unsigned distance functions (UDFs) [89, 20, 27]. SDFs and occupancy explore the internal-to-external relations, which are limited to reconstruct closed surfaces. Researchers therefore turn to UDFs, which is a more general function, to represent shapes with arbitrary typologies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.895, + 0.637 + ], + "angle": 0, + "content": "Learning an accurate zero level set of UDF is the key factor for representing complex geometries and supporting 3D applications [52, 42, 26, 17]. However, the differential neural networks struggle from learning the zero level set where the UDF is not differentiable. This leads to unstable optimizations, which results in large errors on unsigned distances and gradients around the zero level set, causing failures in downstream 3D applications. Taking surface reconstruction for example, SOTA methods [89, 27] extract surfaces from UDFs by judging gradient directions around the zero level set, where the unreliable gradients lead to highly fragmented and discontinuous surfaces." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.896, + 0.852 + ], + "angle": 0, + "content": "To resolve this issue, we introduce two novel constraints on the zero level set in forms of losses for learning accurate UDF without ground truth unsigned distances. The key insight is from the observation that despite the unreliable zero level set, the non-zero level sets learned by UDF are quite convincing, which can serve as an accurate guidance for the optimization on zero level set. We therefore propose the level set projection constraint to achieve a smoother and more continuous zero level set of UDF by enforcing the parallelism between the gradient of a query in a non-zero level set and the gradient of its projection to the zero level set. Moreover, we introduce an adaptive weighting strategy to force the neural network to focus more on the optimization nearer to the zero level set." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The level set projection constraint aims to guide the gradients at zero level set, where we propose another unsigned distance loss as a supplement for correcting distance errors" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.208, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.326, + 0.901 + ], + "angle": 0, + "content": "†The corresponding author is Yu-Shen Liu." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.326, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3181" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "at the zero level set. To bring a more robust guidance to the optimization of zero level set, we introduce an addition gradient constraint on queries to learn more accurate and regular non-zero level sets of UDF by encouraging the gradient orthogonal to the tangent plane of the surface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.47, + 0.287 + ], + "angle": 0, + "content": "Based on our learned stable UDF with an accurate zero level set, we explore three different 3D applications, including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling. Our improvements over unsupervised or even supervised baselines justify both our effectiveness and the importance of an accurate and continuous zero level set to the representation ability of neural unsigned fields." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.289, + 0.457, + 0.303 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.313, + 0.469, + 0.373 + ], + "angle": 0, + "content": "- We propose two novel constraints on UDF to achieve a smoother and more continuous zero level set for learning to represent shapes or scenes without ground truth unsigned distances." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.384, + 0.469, + 0.43 + ], + "angle": 0, + "content": "- We justify that an accurate and continuous zero level set is the key factor to represent complex 3D geometries and supporting 3D downstream applications." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.439, + 0.469, + 0.528 + ], + "angle": 0, + "content": "- We explore three different 3D applications with our learned UDF, including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling, where we show our superiority over the state-of-the-art supervised / unsupervised methods." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.313, + 0.469, + 0.528 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.218, + 0.559 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.644 + ], + "angle": 0, + "content": "With the rapid development of deep learning, the neural networks have shown great potential in 3D applications [66, 30, 79, 75, 78, 74, 80, 76, 14, 39]. We mainly focus on learning Neural Implicit Functions with networks for representing 3D shapes or scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Neural Implicit Functions. Recently, Neural Implicit Functions (NIFs) have shown promising results in surface reconstruction [61, 51, 57, 16, 29, 15, 38, 55, 53], novel view synthesis [58, 4, 65, 87, 32, 24, 59], image superresolution [68, 59, 11], point normal estimation [44], etc. In the task of surface reconstruction, the NIFs approaches train a neural network to represent shapes and scenes with binary occupancy [57, 64, 19] or signed distance functions (SDFs) [61, 36, 22, 21, 63, 10, 84, 6], and then extract surfaces from the learned implicit functions with the marching cubes algorithm [50]. Previous methods [57, 61] learn a global latent code for each 3D shape with a shared MLP to decode geometries. Some advanced approaches [64, 36] propose to use more latent codes to represent detailed local geometries. Latest studies bring more priors learned from large scale datasets to enhance the representation ability of NIFs. PCP [54] introduces the predictive context priors to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "represent large-scale point clouds. OnSurf [52] explores the on-surface prior to reconstruct smooth surfaces from sparse point clouds." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.143, + 0.892, + 0.265 + ], + "angle": 0, + "content": "NeRF [58] and the following studies [59, 62, 69, 56, 37, 67, 33, 45] extends NIFs to the task of novel view synthesis. NeuS [73], VolSDF [81] and Unisurf [60] advance the rendering procedure of NeRF for surface reconstruction from multi-view images. ManhattanSDF [28] leverages the man-hattan assumption for representing indoor scenes. NeuRIS [71] and MonoSDF [86] brings the depth prior and normal prior for improving the surface quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Occupancy and SDFs are merely suitable to represent closed shapes. Recently, researchers explore the neural unsigned distances (UDFs) [20, 89, 88, 70, 18, 72, 49, 48] to represent shapes with arbitrary topology. NDF [20] trains a neural network to learn UDFs with the ground truth distance values. GIFS [82] jointly learns UDFs and the relationship of queries. MeshUDF [27] propose a differentiable meshing algorithm for UDF. However, all the previous UDF-based methods fail to reconstruct smooth and continuous surfaces with high-fidelity details due to the disability of learning an accurate and smooth zero level set of UDF." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.892, + 0.653 + ], + "angle": 0, + "content": "Implicit Learning from Raw Point Clouds. With the ground truth signed/unsigned distances or occupancy labels as supervision, previous methods learn NIFs as a regression [20, 61] problem or classification [57] problem. However, these expensive supervisions come from the ground truth meshes which are hard to collect. Moreover, such methods also fail to generalize to unseen cases with large geometry variations to the training data, which limits the application scenarios of such methods. To learn implicit representations directly from raw point clouds without ground truth supervisions, current methods explore the supervision from sign agnostic [2, 3] learning with gradient constraints [25]. Neural-Pull [51] employs a new learning schema to pull space onto surfaces for optimizing SDFs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Latest work CAP-UDF [89] learns UDF progressively with a field consistency loss. However, the UDF inferred by CAP-UDF are not accurate and the gradients are unreliable, especially in the zero level set which indicates the location of 3D geometries. The key problem is that the differential neural networks struggle from learning non-differentiable zero level set of UDF, leading to highly fragmented and discontinuous surfaces. Since the non-zero level sets of UDF are all differentiable, we propose to pull the non-zero level sets onto the zero level set with gradient constraints which align gradients and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous zero level set of unsigned distance field. Our learning schema involves the constraints for both zero level set and non-zero level sets of UDF, which differentiates our method from the previous ones [89, 2, 3, 51, 20, 61]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3182" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.891, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.894, + 0.278 + ], + "angle": 0, + "content": "Figure 1. Overview of our method. (a) The level set projection constraint leverages the gradient \\(\\nabla f(q)\\) at convincing non-zero level set as the guidance to gradient \\(\\nabla f(\\hat{q})\\) at unreliable zero level set. (b) The gradient-surface orthogonal constraint encourages the gradients \\(\\nabla f(q)\\) at query \\(q\\) orthogonal to the tangent plane of the surface at \\(p'\\) which is the nearest point of \\(q\\) in the raw point cloud." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.282, + 0.169, + 0.298 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.471, + 0.417 + ], + "angle": 0, + "content": "Neural UDFs and Level Sets. We focus on learning unsigned distance functions for representing 3D shapes or scenes with arbitrary typology. Given a raw point cloud \\( P = \\{p_i \\in R^3\\}_{i=1}^N \\) with \\( N \\) points, we sample a set of queries \\( Q = \\{q_j \\in R^3\\}_{j=1}^M \\) around \\( P \\). The UDF \\( f \\) predicts the unsigned distances \\( s^P \\) between queries \\( \\{q_j\\}_{j=1}^M \\) and the shape described by \\( P \\), formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.229, + 0.427, + 0.47, + 0.448 + ], + "angle": 0, + "content": "\\[\ns _ {j} ^ {P} = f (q _ {j}). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.47, + 0.504 + ], + "angle": 0, + "content": "A level set \\( S_{d} \\) of UDF is defined as a region of the 3D space containing a continuous set of 3D points with the same unsigned distance \\( d \\), formulates as:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.52, + 0.47, + 0.537 + ], + "angle": 0, + "content": "\\[\nS _ {d} = \\{q | f (q) = d \\}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.544, + 0.45, + 0.559 + ], + "angle": 0, + "content": "and the level sets of UDF are defined as \\(S = \\{S_d\\}_{d > = 0}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Learning UDFs from Point Clouds. Inspired by CAP-UDF [89], we leverage the pulling optimization for learning UDFs from raw point clouds without ground truth unsigned distances as supervision. Specifically, given a query \\( q_{i} \\) as input, we move it against the direction of the gradient \\( g_{i} = \\nabla f(q_{i}) \\) at \\( q_{i} \\), the moving operation is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.663, + 0.47, + 0.68 + ], + "angle": 0, + "content": "\\[\n\\hat {q} _ {i} = q _ {i} - f \\left(q _ {i}\\right) \\cdot \\nabla f \\left(q _ {i}\\right) / \\left| \\right| \\nabla f \\left(q _ {i}\\right) | | _ {2}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.691, + 0.47, + 0.737 + ], + "angle": 0, + "content": "where the chamfer distance between moved queries \\(\\hat{Q} = \\{\\hat{q}\\}_{i=1}^{M}\\) and the raw point cloud \\(P\\) is calculated as the loss function for optimization, formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.759, + 0.469, + 0.831 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C D}} = \\frac {1}{M} \\sum_ {i \\in [ 1, M ]} \\min _ {j \\in [ 1, N ]} | | \\hat {q} _ {i} - p _ {j} | | _ {2} \\\\ + \\frac {1}{N} \\sum_ {j \\in [ 1, N ]} \\min _ {i \\in [ 1, M ]} \\| p _ {j} - z _ {i} \\| _ {2}, \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Zero Level Set of UDF. An accurate zero level set is the key factor for UDF to represent 3D shapes or scenes, since the zero level set indicates the location of 3D geometries. The key problem here is that the differential networks struggle" + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.282, + 0.629, + 0.292 + ], + "angle": 0, + "content": "(a) w/o ZLS-C" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.293, + 0.696, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.37, + 0.597, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.431, + 0.576, + 0.439 + ], + "angle": 0, + "content": "zero level set" + }, + { + "type": "image", + "bbox": [ + 0.598, + 0.371, + 0.696, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.615, + 0.431, + 0.672, + 0.439 + ], + "angle": 0, + "content": "gradient error" + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.283, + 0.808, + 0.292 + ], + "angle": 0, + "content": "(b) Ours" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.293, + 0.892, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.37, + 0.793, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.717, + 0.431, + 0.772, + 0.439 + ], + "angle": 0, + "content": "zero level set" + }, + { + "type": "image", + "bbox": [ + 0.811, + 0.371, + 0.892, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.811, + 0.431, + 0.868, + 0.439 + ], + "angle": 0, + "content": "gradient error" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.442, + 0.892, + 0.499 + ], + "angle": 0, + "content": "Figure 2. We visualize the fields and the zero level set of UDF learned with or without our designed constraints on the zero level set (ZLS-C). The bluer the color, the smaller the unsigned distances in the field and the errors on gradients." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.552 + ], + "angle": 0, + "content": "from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.893, + 0.688 + ], + "angle": 0, + "content": "We provide a visualization of fields and zero level set of UDF learned with neural networks in Fig. 2. As shown in Fig. 2 (a), the zero level set of UDF learned without proper constraints is highly fragmentary and discontinuous with large errors on the gradients at the space near to the zero level set. On the contrary, we achieve the accurate and continuous zero level set as shown in Fig. 2 (b) by introducing level set projection constraint and gradient-surface orthogonal constraint to the zero level set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Level Set Projections. For learning accurate zero level set of UDF, we design level set projection constraint to guide the learning of zero level set using the rest non-zero level sets. Our idea comes from the observation that despite the unreliable zero level set, the other level sets of the learned UDF are quite convincing, which can serve as the guidance to the field optimization on the zero level set. As shown in Fig. 2, the gradient errors on the non-zero level set are much less than the errors on the zero level set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We illustrate our method in Fig. 1, where we pull the non-zero level set onto the zero level set with gradient constraints which align gradients and correct unsigned distance errors on the zero level set. We achieve this by encouraging the parallelism between the gradient at queries \\( Q = \\{q_i\\}_{i=1}^M \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3183" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.085, + 0.09, + 0.268, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.169, + 0.268, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.234, + 0.19, + 0.244 + ], + "angle": 0, + "content": "NDF" + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.09, + 0.468, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.171, + 0.468, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.347, + 0.234, + 0.403, + 0.244 + ], + "angle": 0, + "content": "CAP-UDF" + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.089, + 0.672, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.171, + 0.671, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.234, + 0.594, + 0.244 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.684, + 0.089, + 0.877, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.169, + 0.874, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.766, + 0.234, + 0.786, + 0.244 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.257, + 0.245, + 0.712, + 0.26 + ], + "angle": 0, + "content": "Figure 3. Visual comparisons of surface reconstruction on ShapeNet dataset." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.271, + 0.47, + 0.426 + ], + "angle": 0, + "content": "
MethodChamfer-L2F-ScoreNC
MeanMedian\\( F1^{0.005} \\)\\( F1^{0.01} \\)
Input0.3630.35548.5088.34-
Watertight GT2.6282.29368.8281.60-
GT0.0760.07495.7099.99-
NDF [20]0.2020.19377.4097.9779.1
GIFS [82]0.1280.12388.0599.31-
CAP-UDFBPA0.1410.13884.8499.3381.8
CAP-UDF [89]0.1190.11488.5599.8282.5
Ours0.0980.09792.1899.9085.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.459 + ], + "angle": 0, + "content": "Table 1. Surface reconstruction for point cloud on ShapeNet cars dataset (Chamfer-L2×10^4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.469, + 0.503 + ], + "angle": 0, + "content": "and the gradient at their projections \\(\\hat{Q} = \\{\\hat{q}\\}_{i=1}^{M}\\) to the zero level set, formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.513, + 0.47, + 0.555 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {p r o j}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\gamma_ {i} \\left(1 - \\left| \\frac {\\nabla f (q _ {i}) \\cdot \\nabla f (\\hat {q} _ {i})}{| | \\nabla f (q _ {i}) | | _ {2} \\cdot | | \\nabla f (\\hat {q} _ {i}) | | _ {2}} \\right|\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.47, + 0.61 + ], + "angle": 0, + "content": "where \\(\\gamma_{i}\\) is the factor for weighting the gradient constraint at the query \\(q_{i}\\), indicating the importance of optimizing query \\(q_{i}\\), formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.624, + 0.469, + 0.643 + ], + "angle": 0, + "content": "\\[\n\\gamma_ {i} = \\exp (- \\lambda | f (q _ {i}) |). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.469, + 0.72 + ], + "angle": 0, + "content": "We set \\(\\gamma\\) to increase when queries are closer to the zero level set where \\(\\lambda\\) is a hyper-parameter to control the increasing speed. The nonuniform weighting encouraging the network to focus more on the optimizations near the zero level set of UDF." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.469, + 0.796 + ], + "angle": 0, + "content": "While \\(\\mathcal{L}_{proj}\\) can provide an effective guidance to the gradients at zero level set, we further explore a more accurate unsigned distance constraint for correcting the distance values at the zero level set of UDF. The implemented loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.795, + 0.469, + 0.836 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i s t}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} | f (p _ {i}) |, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.871 + ], + "angle": 0, + "content": "where \\( p_i \\in P \\) is the raw point cloud indicating the exact surface to be represented." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Gradient-Surface Orthogonal Constraint. The key idea to guide the learning of zero level set using the rest level sets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.403 + ], + "angle": 0, + "content": "is based on the observation that the non-zero level sets are much more reliable. To bring a more robust guidance to the optimization of zero level set, we introduce an addition gradient constraint on queries to learn a more stable and regular level sets at the non-zero level sets of UDF by enforcing the gradient orthogonal to the tangent plane of the surface. We design a novel loss to encourage the consistency between the gradient direction at a query \\( q_{i} \\) and the direction from \\( q_{i} \\) to its closest point \\( p_{i} \\) on \\( P \\), formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.409, + 0.892, + 0.45 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {o r t h}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} (1 - | \\frac {\\nabla f (q _ {i}) \\cdot T (q _ {i} , p _ {i})}{| | \\nabla f (q _ {i}) | | _ {2} \\cdot | | T (q _ {i} , p _ {i}) | | _ {2}} |), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.892, + 0.485 + ], + "angle": 0, + "content": "where \\( T(q_{i},p_{i}) \\) is the direction from \\( q_{i} \\) to \\( p_i \\). The constraint is illustrated in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.621 + ], + "angle": 0, + "content": "A more naive way of introducing the direction vector \\( T(q_{i},p_{i}) \\) for learning is to explicitly substitute the gradient \\( \\nabla f(q_{i}) \\) with the direction vector \\( T(q_{i},p_{i}) \\), as proposed in GenSDF [21]. However, \\( T(q_{i},p_{i}) \\) is obviously not the exact direction for \\( q_{i} \\) to reach the approximated surface since the raw point cloud is the discrete representation of the surface, and \\( p_{i} \\) is not the exact nearest points of \\( q_{i} \\) in the approximated surface, which leads to wrong supervisions for GenSDF." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.697 + ], + "angle": 0, + "content": "On the contrary, We introduce a more flexible way by treating direction vector \\( T(q_{i},p_{i}) \\) as an optimization objective, which enables the networks to accommodate the inconsistency between the closest point \\( p_i \\) on \\( P \\) and the closest point \\( \\hat{q}_i \\) predicted by the networks." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.697, + 0.888, + 0.712 + ], + "angle": 0, + "content": "Loss Function. Finally, our loss function is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.72, + 0.891, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {C D}} + \\alpha_ {1} \\mathcal {L} _ {\\text {p r o j}} + \\alpha_ {2} \\mathcal {L} _ {\\text {d i s t}} + \\alpha_ {3} \\mathcal {L} _ {\\text {o r t h}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.743, + 0.892, + 0.772 + ], + "angle": 0, + "content": "where \\(\\alpha_{1},\\alpha_{2}\\) and \\(\\alpha_{3}\\) are the balance weights for our designed three losses to learn accurate zero level set of UDF." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.773, + 0.892, + 0.833 + ], + "angle": 0, + "content": "Applications. The zero level set of UDF indicates the location of represented 3D geometries. Thus, a well-learned UDF with accurate and continuous zero level set can be adopt to different 3D applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.833, + 0.892, + 0.879 + ], + "angle": 0, + "content": "Surface Reconstruction. Following previous methods [89, 27], the surfaces can be extracted from the zero level set of UDF by judging gradient directions, formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} \\left(q _ {i}, q _ {j}\\right) = \\nabla f \\left(q _ {i}\\right) \\cdot \\nabla f \\left(q _ {j}\\right), \\tag {10}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3184" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.094, + 0.252, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.094, + 0.41, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.094, + 0.571, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.576, + 0.094, + 0.73, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.093, + 0.889, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.177, + 0.245, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.137, + 0.259, + 0.198, + 0.271 + ], + "angle": 0, + "content": "ConvOcc" + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.177, + 0.402, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.26, + 0.341, + 0.272 + ], + "angle": 0, + "content": "NDF" + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.176, + 0.568, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.46, + 0.26, + 0.525, + 0.272 + ], + "angle": 0, + "content": "CAP-UDF" + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.176, + 0.727, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.631, + 0.261, + 0.666, + 0.272 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.729, + 0.178, + 0.886, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.261, + 0.816, + 0.272 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.167, + 0.278, + 0.8, + 0.292 + ], + "angle": 0, + "content": "Figure 4. Visual comparisons of surface reconstruction on 3D Scene dataset. Input contains 1K points / \\(m^2\\)" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.297, + 0.894, + 0.49 + ], + "angle": 0, + "content": "
BurghersLoungeCopyroomStonewallTotempole
L2CDL1CDNCL2CDL1CDNCL2CDL1CDNCL2CDL1CDNCL2CDL1CDNC
500/m2ConvONet [64]26.970.0810.9059.0440.0460.89410.080.0460.88517.700.0630.9092.1650.0240.937
LIG [36]3.0800.0460.8406.7290.0520.8314.0580.0380.8104.9190.0430.8789.380.0620.887
DeepLS [13]0.7140.0200.92310.880.0770.8140.5520.0150.9070.6730.0180.95121.150.1220.927
NDF [20]0.5460.0180.9170.3140.0120.9210.2420.0120.9070.2260.0120.9491.0490.0250.939
OnSurf [52]0.6090.0180.9300.5290.0130.9260.4830.0140.9080.6660.0130.9552.0250.0410.954
CAP-UDF [89]0.1920.0110.9110.0990.0090.9110.1200.0090.9020.0690.0080.9580.1310.0100.954
Ours0.1610.0090.9160.0870.0060.9330.1020.0070.9200.0610.0070.9640.1140.0070.960
1000/m2ConvONet [64]27.460.0790.9079.540.0460.89410.970.0450.89220.460.0690.9052.0540.0210.943
LIG [36]3.0550.0450.8359.6720.0560.8333.610.0360.8105.0320.0420.8799.580.0620.887
DeepLS [13]0.4010.0170.9206.1030.0530.8480.6090.0210.9010.3200.0150.9540.6010.0170.950
NDF [20]1.1680.0270.9010.3930.0140.9100.2690.0130.9080.5090.0190.9362.0200.0360.922
OnSurf [52]1.3390.0310.9290.4320.0140.9340.4050.0140.9140.2660.0140.9571.0890.0290.954
CAP-UDF [89]0.1910.0100.9100.0920.0080.9270.1130.0090.9110.0660.0070.9620.1390.0090.955
Ours0.1460.0090.9210.0680.0060.9410.0930.0070.9250.0500.0050.9700.1070.0070.960
" + }, + { + "type": "table_caption", + "bbox": [ + 0.248, + 0.495, + 0.72, + 0.508 + ], + "angle": 0, + "content": "Table 2. Surface reconstruction for point clouds under 3D Scene. \\( \\mathrm{L}2\\mathrm{{CD}} \\times {1000} \\) ." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.576 + ], + "angle": 0, + "content": "to classify whether two queries \\( q_{1} \\) and \\( q_{2} \\) are in the same \\( \\mathcal{D}(q_i,q_j) > 0 \\) or the opposite side \\( \\mathcal{D}(q_i,q_j) < 0 \\) of the approximated surface. The marching cubes-like algorithm is then used to extract surfaces." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.469, + 0.623 + ], + "angle": 0, + "content": "Unsupervised Point Normal Estimation. With a well learned zero level set, we compute the gradients at the raw point clouds \\( P \\) as their estimated normals, formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.635, + 0.469, + 0.652 + ], + "angle": 0, + "content": "\\[\n\\mathcal {N} (P) = \\{\\nabla f (p) \\}, p \\in P. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.47, + 0.755 + ], + "angle": 0, + "content": "Unsupervised Point Cloud Upsampling. We randomly sample queries around \\( P \\), and then move them to the zero level set with Eq. 3 as the upsampled points of \\( P \\). We further filter the queries with unsigned distance values larger than a threshold \\( \\beta \\) for avoiding outliers. The procedure for upsampling \\( P \\) with a factor of \\( G \\) is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.77, + 0.469, + 0.787 + ], + "angle": 0, + "content": "\\[\n\\mathcal {U} (P) = \\left\\{\\hat {q} _ {i}, i \\in [ 1, N \\times G ] \\mid f \\left(q _ {i}\\right) < \\beta \\right\\} \\tag {12}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.21, + 0.817 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "For evaluating the performance of our method, we conduct experiments on surface reconstruction from raw point clouds of shapes (Sec. 4.1), room-level scenes (Sec. 4.2), and real scans (Sec. 4.4), where we also show our results on large-scale driving scenes obtained by fusing LiDAR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.893, + 0.591 + ], + "angle": 0, + "content": "depths in Sec. 4.3. We further explore the ability of our learned UDF with accurate zero level set for unsupervised point normal estimation (Sec. 4.5) and unsupervised point upsampling (Sec. 4.6). Finally, we conduct ablation studies in Sec. 4.7." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.604, + 0.803, + 0.621 + ], + "angle": 0, + "content": "4.1. Surface Reconstruction for Shapes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.893, + 0.793 + ], + "angle": 0, + "content": "Dataset and Metrics. To explore the ability of our method in representing shapes with arbitrary topology, we follow previous methods [89, 82] to conduct experiments on the \"Car\" category of ShapeNet dataset which contains the largest number of shapes with multi-layer structures or open surfaces. We sample 10K points per shape as the input for surface reconstruction. For evaluating the performances, we follow the common setting [82] to sample 100K points from the reconstructed surfaces and leverage Chamfer Distance, Normal Consistency [57] and F-score with a threshold of 0.005 / 0.01 as the evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Comparisons. We compare our method with the state-of-the-art shape reconstruction methods NDF [20], GIFS [82] and CAP-UDF [89]. We report the quantitative comparison results in Tab. 1, where \"Watertight GT\" is the result of sampling points from the watertight ground truth, indicating the best performance of the methods base on SDF or occupancy. We also show the superior limit of the dataset" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3185" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.891, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.175, + 0.28, + 0.794, + 0.295 + ], + "angle": 0, + "content": "Figure 5. Surface reconstruction results on KITTI odometry dataset (Sequence 00, frame 3000 to 4000)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.309, + 0.471, + 0.399 + ], + "angle": 0, + "content": "by sampling points on the ground truth mesh and report the result as \"GT\". Tab. 1 shows that our method achieves the best performance over all the baselines in terms of all metrics. The visual comparison in Fig. 3 further shows that our methods produce more continuous and accurate geometries over all baselines." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.408, + 0.47, + 0.423 + ], + "angle": 0, + "content": "4.2. Surface Reconstruction for Room-Level Scenes" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.596 + ], + "angle": 0, + "content": "Dataset and Metrics. We further explore our performance on real scene scans to demonstrate the ability of our methods to scale to large-scale point clouds. Following On-Surf [52], we conduct experiments on the 3D Scene dataset consisting of complex scenes with open surfaces and scan noises. The input point cloud is achieved by sampling 500 or 1000 points per \\( m^2 \\) uniformly for each scene. We follow the common setting [52, 89] to sample \\( 1M \\) points on both the reconstructed and the ground truth meshes. We leverage L1 / L2 Chamfer Distance and Normal Consistency as the evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.471, + 0.764 + ], + "angle": 0, + "content": "Comparisons. With different point densities, we compare our method with the state-of-the-art methods ConvONet [64], LIG [36], DeepLS [13], OnSurf [52], NDF [20] and CAP-UDF [89]. The numerical comparison in Tab. 2 demonstrates our superior performance in all scenes. We further present a visual comparison in Fig. 4, where the input point clouds contains 1K points/\\(m^2\\). The visualization further shows that our method can reconstruct more detailed and smooth surfaces in complex scenes, where the other UDF-base methods NDF and CAP-UDF produce fragmented surfaces." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.439, + 0.789 + ], + "angle": 0, + "content": "4.3. Large-Scale Driving Scene Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Dataset. To further demonstrate our scalability to extremely large scenes, we follow NGS [35] to apply our method to KITTI dataset [23]. We use the LiDAR scans of frame 3000 to 4000 in Squeeze00 subset of KITTI dataset as the full input, which are transformed into world coordinates using the provided camera trajectories. We leverage the slide-window strategy to divide the full scene into 15" + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.306, + 0.882, + 0.451 + ], + "angle": 0, + "content": "
MethodChamfer-L1F-ScoreNC
IGR [25]0.17875.586.9
Point2Mesh [31]0.11664.8-
SPSR [40]0.23273.5-
SAP [63]0.07683.088.6
Neural-Pull [51]0.10679.787.2
NDF [20]0.23868.680.4
CAP-UDF [89]0.07384.588.6
Ours0.07185.191.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.453, + 0.877, + 0.466 + ], + "angle": 0, + "content": "Table 3. Surface reconstruction for point cloud on SRB dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.519 + ], + "angle": 0, + "content": "blocks of size \\(51.2m^3\\), where we sample 300K points per block as the local input to train our network. The final scene is achieve by blending the reconstructed local scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.893, + 0.626 + ], + "angle": 0, + "content": "Analysis. The reconstruction results under KITTI scenes is shown in Fig. 5, where our method reproduces visualappealing performances with accurate geometries. Note that: 1) The LiDAR scans contain large amount of noises, especially in the difficult driving scenes. 2) Our method learns to reconstruct surfaces directly from the raw point cloud without learning priors from large-scale datasets." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.636, + 0.833, + 0.651 + ], + "angle": 0, + "content": "4.4. Surface Reconstruction for Real Scans" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Dataset and Metrics. We demonstrate our advantages for surface reconstruction from real scans by conducting experiments on the Surface Reconstruction Benchmarks [77] (SRB). We follow previous methods [63, 89] to leverage Chamfer Distance and F-Score with a threshold of \\(1\\%\\) for evaluation. Note that the ground truth of SRB dataset is dense point cloud containing millions of points. For a comprehensive comparison on the reconstruction quality, we further evaluate the Normal Consistency by first converting the ground truth into meshes with BPA [8] algorithm." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Comparisons. We first report our numerical comparison under SRB dataset with the classic and learning-based methods in Tab. 3. The compared methods include IGR [25], Point2Mesh [31], Screened Poisson Surface Reconstruction (SPSR) [40], Shape As Points (SAP) [63], Neural-Pull [51], NDF [20] and CAP-UDF [89]. Our method" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3186" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.088, + 0.473, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.209, + 0.47, + 0.237 + ], + "angle": 0, + "content": "Figure 6. Visual comparisons of surface reconstruction on SRB dataset. SRB dataset provides only point clouds as GT." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.25, + 0.47, + 0.406 + ], + "angle": 0, + "content": "
MethodCleanStripGradientaverage
SupervisedPCPNet [26]9.6611.4713.4211.61
Hough [9]10.2312.4711.0211.24
Nesti-Net [7]6.998.479.008.15
IterNet [41]6.727.737.517.32
DeepFit [5]6.517.927.317.25
UnsupervisedJet [12]12.2313.3913.1312.92
PCA [1]12.2913.6612.8112.92
Ours (w/o ZLS-c)7.307.747.787.61
Ours6.517.457.647.20
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.41, + 0.455, + 0.423 + ], + "angle": 0, + "content": "Table 4. Point normal estimation results on the PCPNet dataset." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.431, + 0.47, + 0.492 + ], + "angle": 0, + "content": "achieves the best performance in all metrics as shown in Tab. 3. The visual comparison in Fig. 6 further shows that our methods produce more accurate and smooth geometries over all baselines." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.5, + 0.415, + 0.516 + ], + "angle": 0, + "content": "4.5. Unsupervised Point Normal Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.703 + ], + "angle": 0, + "content": "Dataset and Metrics. We adopt the widely-used PCPNet [26] dataset to evaluate our method on the task of point normal estimation. Each point cloud in the PCPNet dataset contains 100K points. We conduct experiments under three different settings. The inputs of \"Clean\" setting are sampled uniformly on shapes, and two additional settings with varying point densities (Stripes and Gradients) are added to explore our performance in handling irregular data. Following previous methods [5, 26], we sample 5000 points per shape and compute the angle root mean square error (RMSE) between the predicted normals and the ground truth normals as the evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Comparisons. We conduct a comparison with traditional normal estimation methods including PCA [1], Jets [12] and the state-of-the-art learning-based methods PCPNet [26], HoughCNN [9], Nesti-Net [7], Iter-Net [41] and DeepFit [5]. Note that all the previous learning-based methods are designed in a supervised manner which requires a large scale dataset for training, while we extract normals directly from the unsigned distance fields learned from raw point cloud in an unsupervised way. The numerical results in Tab. 4 show that our method achieves a comparable or even better performance than the state-of-the-art supervised methods. The results also show the effectiveness of our method where the performance degrades from 7.20 to 7.61 without" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.093, + 0.887, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.501, + 0.892, + 0.528 + ], + "angle": 0, + "content": "Figure 7. Visual comparisons on error maps of point normal estimation on PCPNet dataset." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.54, + 0.892, + 0.732 + ], + "angle": 0, + "content": "
MethodSupervised?P2FCDHD
PU-Net [85]Yes6.840.728.94
MPU [83]Yes3.960.496.11
PU-GAN [42]Yes2.330.284.64
Dis-PU [43]Yes2.010.222.83
EAR [34]No5.820.527.37
L2G-AE [46]No39.376.3163.23
SPU-Net (Tr2T) [47]No5.970.382.24
SPU-Net (All2T)No5.790.372.55
SPU-Net (Te2T)No6.850.412.18
Ours (w/o ZLS-C)No1.430.242.16
OursNo1.020.191.55
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.738, + 0.884, + 0.753 + ], + "angle": 0, + "content": "Table 5. Point cloud upsampling results on the PU-GAN dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.763, + 0.892, + 0.809 + ], + "angle": 0, + "content": "our constraints. The visual comparison in Fig. 7 shows that our method produces more accurate estimations compared to other methods, especially on the complex geometries." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.836, + 0.835 + ], + "angle": 0, + "content": "4.6. Unsupervised Point Cloud Upsampling" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Dataset and Metrics. For the task of point cloud upsampling, we follow previous methods [47, 43] to conduct experiments on the dataset provided by PU-GAN [42]. We evaluate our method under the setting to generate 8,198" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3187" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.253, + 0.238, + 0.715, + 0.253 + ], + "angle": 0, + "content": "Figure 8. Visual comparisons of point cloud upsampling on PU-GAN dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.47, + 0.311 + ], + "angle": 0, + "content": "points for each sparse input with 2,048 points. We adopt Chamfer Distance (CD), Hausdorff Distance (HD) and Point-to-Surface distance (P2F) as the evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.474, + 0.493 + ], + "angle": 0, + "content": "Comparisons. We compare our method with the state-of-the-art supervised methods PU-Net [85], MPU [83], PU-GAN [42], Dis-PU [43] and unsupervised methods EAR [34], L2G-AE [46] and SPU-Net [47]. The quantitative comparison is shown in Tab. 5, where our method outperforms the previous supervised and unsupervised methods significantly. The results also show the effectiveness of our method where the performance degrades from 1.55 to 2.16 in terms of HD without our designed constraints. The visualization in Fig. 8 further shows that our upsampling results are more smooth and uniform even compared with the state-of-the-art supervised methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.5, + 0.245, + 0.515 + ], + "angle": 0, + "content": "4.7. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.599 + ], + "angle": 0, + "content": "We conduct ablation studies to demonstrate the effectiveness of each proposed constraint and explore the effect of some important hyper-parameters. We report the performance under a subset of ShapeNet Cars dataset in terms of L2 Chamfer Distance \\((\\times 10^{4})\\) and Normal Consistency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.811 + ], + "angle": 0, + "content": "Effect of each Design. We first justify the effectiveness of each proposed constraint in Tab. 6. We report the performance without all the three designed losses as \"w/o ZLS-C\". We explore each loss by reporting the results without level set projection loss as \"w/o \\(\\mathcal{L}_{\\mathrm{proj}}\\)\", surface unsigned distance loss as \"w/o \\(\\mathcal{L}_{\\mathrm{dist}}\\)\", gradient-surface orthogonal loss as \"w/o \\(\\mathcal{L}_{\\mathrm{orth}}\\)\" and adaptive point weight as \"w/o AW\". We replace our level set projection constraint with the GenSDF-style [21] optimization as \"GenSDF-Style\". We further constrain the level set projection loss on a randomly selected non-zero level set other than the zero level set and report the performance as \"Non-zero LSC\". The result demonstrates that the zero level set is the key factor that influence the representation ability of UDF." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.886 + ], + "angle": 0, + "content": "Weight of Level Set Projection Loss. We report the performance with different weights of the level set projection loss \\(\\mathcal{L}_{\\mathrm{proj}}\\) in Tab. 7. We found that a suitable weight of \\(\\mathcal{L}_{\\mathrm{proj}}\\) will improve the reconstruction accuracy, and it may affect the optimization to converge if we weight too much." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Weight of Surface Unsigned Distance Loss. We further" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.263, + 0.895, + 0.35 + ], + "angle": 0, + "content": "
w/o ZLS-Cw/o Lprojw/o Ldistw/o Lorth
L2CD0.1260.1070.1010.096
NC82.782.983.984.1
w/o AWGenSDF-StyleNon-zero LSCOurs
L2CD0.0960.1010.0980.091
NC84.283.983.584.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.587, + 0.35, + 0.805, + 0.362 + ], + "angle": 0, + "content": "Table 6. Effect of framework design." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.37, + 0.893, + 0.411 + ], + "angle": 0, + "content": "
0.0010.0020.010.1
L2CD0.0950.0910.1620.359
NC84.284.483.479.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.567, + 0.41, + 0.825, + 0.423 + ], + "angle": 0, + "content": "Table 7. Weight of level set projection loss." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.444, + 0.894, + 0.49 + ], + "angle": 0, + "content": "explore the effect of weights \\(\\alpha_{2}\\) for the surface unsigned distance loss in Tab 8, where we found that a too large or too small weight will degenerate the performance." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.508, + 0.893, + 0.549 + ], + "angle": 0, + "content": "
0.0010.010.11
L2CD0.1010.1000.0910.449
NC84.184.184.478.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.547, + 0.549, + 0.845, + 0.561 + ], + "angle": 0, + "content": "Table 8. Weight of surface unsigned distance loss." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.561, + 0.892, + 0.637 + ], + "angle": 0, + "content": "Weight of Gradient-Surface Orthogonal Loss. We evaluate the effect of the weight \\(\\alpha_{3}\\) for gradient-surface orthogonal loss in Tab. 9. A proper weight \\(\\alpha_{3} = 0.01\\) brings the best improvement while a too much weight will affect the convergence." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.649, + 0.892, + 0.69 + ], + "angle": 0, + "content": "
0.0010.010.11
L2CD0.0940.0910.3352.55
NC84.284.477.772.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.541, + 0.69, + 0.85, + 0.702 + ], + "angle": 0, + "content": "Table 9. Weight of gradient-surface orthogonal loss." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.713, + 0.892, + 0.819 + ], + "angle": 0, + "content": "Effect of Adaptive per Point Weights. We further report the performance under different \\(\\lambda\\) which controls the increasing speed of adaptive weights for each point in Tab. 10. We found that \\(\\lambda\\) has a relative small impact on the Chamfer Distance with large affect on the Normal Consistency, which indicates that the adaptive per point weight can improve the surface smoothness." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.831, + 0.892, + 0.871 + ], + "angle": 0, + "content": "
1101001000
L2CD0.0930.0910.0920.094
NC84.184.483.783.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.558, + 0.871, + 0.833, + 0.884 + ], + "angle": 0, + "content": "Table 10. Effect of adaptive per point weights." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3188" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.196, + 0.106 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.473, + 0.312 + ], + "angle": 0, + "content": "In this paper, we justify that an accurate and continuous zero level set of unsigned distance functions is the key factor to represent complex 3D geometries. We therefore propose two novel constraints on UDF to achieve a more continuous zero level set by projecting non-zero level set to guide the optimization of zero level set. With the ability of learning consistent and accurate zero level set of UDF, we explore three different 3D applications including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling, where the visual and numerical comparisons with the state-of-the-art supervised/unsupervised methods justify our effectiveness ans show our superiority over the latest methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.326, + 0.258, + 0.344 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.47, + 0.412 + ], + "angle": 0, + "content": "This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.424, + 0.175, + 0.44 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.45, + 0.47, + 0.49 + ], + "angle": 0, + "content": "[1] Hervé Abdi and Lynne J Williams. Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2(4):433-459, 2010. 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.492, + 0.472, + 0.547 + ], + "angle": 0, + "content": "[2] Matan Atzmon and Yaron Lipman. SAL: Sign agnostic learning of shapes from raw data. 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They train neural networks to learn UDFs and reconstruct surfaces with the gradients around the zero level set of the UDF. However, the differential networks struggle from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set, resulting in highly fragmented and discontinuous surfaces. To resolve this problem, we propose to learn a more continuous zero level set in UDFs with level set projections. Our insight is to guide the learning of zero level set using the rest non-zero level sets via a projection procedure. Our idea is inspired from the observations that the non-zero level sets are much smoother and more continuous than the zero level set. We pull the non-zero level sets onto the zero level set with gradient constraints which align gradients over different level sets and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous unsigned distance field. We conduct comprehensive experiments in surface reconstruction for point clouds, real scans or depth maps, and further explore the performance in unsupervised point cloud upsampling and unsupervised point normal estimation with the learned UDF, which demonstrate our non-trivial improvements over the state-of-the-art methods. Code is available at https://github.com/junshengzhou/LevelSetUDF. + +# 1. Introduction + +Surface reconstruction from point clouds plays an important role in vision, robotics and graphics. Recently, neural implicit functions [61, 58, 57] have achieved remarkable + +results by representing 3D geometries with signed distance functions (SDFs) [51, 13, 73], occupancy [57, 64, 60] or unsigned distance functions (UDFs) [89, 20, 27]. SDFs and occupancy explore the internal-to-external relations, which are limited to reconstruct closed surfaces. Researchers therefore turn to UDFs, which is a more general function, to represent shapes with arbitrary typologies. + +Learning an accurate zero level set of UDF is the key factor for representing complex geometries and supporting 3D applications [52, 42, 26, 17]. However, the differential neural networks struggle from learning the zero level set where the UDF is not differentiable. This leads to unstable optimizations, which results in large errors on unsigned distances and gradients around the zero level set, causing failures in downstream 3D applications. Taking surface reconstruction for example, SOTA methods [89, 27] extract surfaces from UDFs by judging gradient directions around the zero level set, where the unreliable gradients lead to highly fragmented and discontinuous surfaces. + +To resolve this issue, we introduce two novel constraints on the zero level set in forms of losses for learning accurate UDF without ground truth unsigned distances. The key insight is from the observation that despite the unreliable zero level set, the non-zero level sets learned by UDF are quite convincing, which can serve as an accurate guidance for the optimization on zero level set. We therefore propose the level set projection constraint to achieve a smoother and more continuous zero level set of UDF by enforcing the parallelism between the gradient of a query in a non-zero level set and the gradient of its projection to the zero level set. Moreover, we introduce an adaptive weighting strategy to force the neural network to focus more on the optimization nearer to the zero level set. + +The level set projection constraint aims to guide the gradients at zero level set, where we propose another unsigned distance loss as a supplement for correcting distance errors + +at the zero level set. To bring a more robust guidance to the optimization of zero level set, we introduce an addition gradient constraint on queries to learn more accurate and regular non-zero level sets of UDF by encouraging the gradient orthogonal to the tangent plane of the surface. + +Based on our learned stable UDF with an accurate zero level set, we explore three different 3D applications, including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling. Our improvements over unsupervised or even supervised baselines justify both our effectiveness and the importance of an accurate and continuous zero level set to the representation ability of neural unsigned fields. + +Our main contributions can be summarized as follows. + +- We propose two novel constraints on UDF to achieve a smoother and more continuous zero level set for learning to represent shapes or scenes without ground truth unsigned distances. +- We justify that an accurate and continuous zero level set is the key factor to represent complex 3D geometries and supporting 3D downstream applications. +- We explore three different 3D applications with our learned UDF, including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling, where we show our superiority over the state-of-the-art supervised / unsupervised methods. + +# 2. Related Work + +With the rapid development of deep learning, the neural networks have shown great potential in 3D applications [66, 30, 79, 75, 78, 74, 80, 76, 14, 39]. We mainly focus on learning Neural Implicit Functions with networks for representing 3D shapes or scenes. + +Neural Implicit Functions. Recently, Neural Implicit Functions (NIFs) have shown promising results in surface reconstruction [61, 51, 57, 16, 29, 15, 38, 55, 53], novel view synthesis [58, 4, 65, 87, 32, 24, 59], image superresolution [68, 59, 11], point normal estimation [44], etc. In the task of surface reconstruction, the NIFs approaches train a neural network to represent shapes and scenes with binary occupancy [57, 64, 19] or signed distance functions (SDFs) [61, 36, 22, 21, 63, 10, 84, 6], and then extract surfaces from the learned implicit functions with the marching cubes algorithm [50]. Previous methods [57, 61] learn a global latent code for each 3D shape with a shared MLP to decode geometries. Some advanced approaches [64, 36] propose to use more latent codes to represent detailed local geometries. Latest studies bring more priors learned from large scale datasets to enhance the representation ability of NIFs. PCP [54] introduces the predictive context priors to + +represent large-scale point clouds. OnSurf [52] explores the on-surface prior to reconstruct smooth surfaces from sparse point clouds. + +NeRF [58] and the following studies [59, 62, 69, 56, 37, 67, 33, 45] extends NIFs to the task of novel view synthesis. NeuS [73], VolSDF [81] and Unisurf [60] advance the rendering procedure of NeRF for surface reconstruction from multi-view images. ManhattanSDF [28] leverages the man-hattan assumption for representing indoor scenes. NeuRIS [71] and MonoSDF [86] brings the depth prior and normal prior for improving the surface quality. + +Occupancy and SDFs are merely suitable to represent closed shapes. Recently, researchers explore the neural unsigned distances (UDFs) [20, 89, 88, 70, 18, 72, 49, 48] to represent shapes with arbitrary topology. NDF [20] trains a neural network to learn UDFs with the ground truth distance values. GIFS [82] jointly learns UDFs and the relationship of queries. MeshUDF [27] propose a differentiable meshing algorithm for UDF. However, all the previous UDF-based methods fail to reconstruct smooth and continuous surfaces with high-fidelity details due to the disability of learning an accurate and smooth zero level set of UDF. + +Implicit Learning from Raw Point Clouds. With the ground truth signed/unsigned distances or occupancy labels as supervision, previous methods learn NIFs as a regression [20, 61] problem or classification [57] problem. However, these expensive supervisions come from the ground truth meshes which are hard to collect. Moreover, such methods also fail to generalize to unseen cases with large geometry variations to the training data, which limits the application scenarios of such methods. To learn implicit representations directly from raw point clouds without ground truth supervisions, current methods explore the supervision from sign agnostic [2, 3] learning with gradient constraints [25]. Neural-Pull [51] employs a new learning schema to pull space onto surfaces for optimizing SDFs. + +Latest work CAP-UDF [89] learns UDF progressively with a field consistency loss. However, the UDF inferred by CAP-UDF are not accurate and the gradients are unreliable, especially in the zero level set which indicates the location of 3D geometries. The key problem is that the differential neural networks struggle from learning non-differentiable zero level set of UDF, leading to highly fragmented and discontinuous surfaces. Since the non-zero level sets of UDF are all differentiable, we propose to pull the non-zero level sets onto the zero level set with gradient constraints which align gradients and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous zero level set of unsigned distance field. Our learning schema involves the constraints for both zero level set and non-zero level sets of UDF, which differentiates our method from the previous ones [89, 2, 3, 51, 20, 61]. + +![](images/5c957780ed4d20295f2d52ca39ba8ea24d2e3eecc6c07928d2a6d76e59445437.jpg) +Figure 1. Overview of our method. (a) The level set projection constraint leverages the gradient $\nabla f(q)$ at convincing non-zero level set as the guidance to gradient $\nabla f(\hat{q})$ at unreliable zero level set. (b) The gradient-surface orthogonal constraint encourages the gradients $\nabla f(q)$ at query $q$ orthogonal to the tangent plane of the surface at $p'$ which is the nearest point of $q$ in the raw point cloud. + +# 3. Method + +Neural UDFs and Level Sets. We focus on learning unsigned distance functions for representing 3D shapes or scenes with arbitrary typology. Given a raw point cloud $P = \{p_i \in R^3\}_{i=1}^N$ with $N$ points, we sample a set of queries $Q = \{q_j \in R^3\}_{j=1}^M$ around $P$ . The UDF $f$ predicts the unsigned distances $s^P$ between queries $\{q_j\}_{j=1}^M$ and the shape described by $P$ , formulated as: + +$$ +s _ {j} ^ {P} = f (q _ {j}). \tag {1} +$$ + +A level set $S_{d}$ of UDF is defined as a region of the 3D space containing a continuous set of 3D points with the same unsigned distance $d$ , formulates as: + +$$ +S _ {d} = \{q | f (q) = d \}, \tag {2} +$$ + +and the level sets of UDF are defined as $S = \{S_d\}_{d > = 0}$ + +Learning UDFs from Point Clouds. Inspired by CAP-UDF [89], we leverage the pulling optimization for learning UDFs from raw point clouds without ground truth unsigned distances as supervision. Specifically, given a query $q_{i}$ as input, we move it against the direction of the gradient $g_{i} = \nabla f(q_{i})$ at $q_{i}$ , the moving operation is formulated as: + +$$ +\hat {q} _ {i} = q _ {i} - f \left(q _ {i}\right) \cdot \nabla f \left(q _ {i}\right) / \left| \right| \nabla f \left(q _ {i}\right) | | _ {2}, \tag {3} +$$ + +where the chamfer distance between moved queries $\hat{Q} = \{\hat{q}\}_{i=1}^{M}$ and the raw point cloud $P$ is calculated as the loss function for optimization, formulated as: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {C D}} = \frac {1}{M} \sum_ {i \in [ 1, M ]} \min _ {j \in [ 1, N ]} | | \hat {q} _ {i} - p _ {j} | | _ {2} \\ + \frac {1}{N} \sum_ {j \in [ 1, N ]} \min _ {i \in [ 1, M ]} \| p _ {j} - z _ {i} \| _ {2}, \tag {4} \\ \end{array} +$$ + +Zero Level Set of UDF. An accurate zero level set is the key factor for UDF to represent 3D shapes or scenes, since the zero level set indicates the location of 3D geometries. The key problem here is that the differential networks struggle + +![](images/db346aec818d0f395417c0c77778cbb3159315e23a7c944cb3e91d6d76486e1d.jpg) +(a) w/o ZLS-C + +![](images/d5d35842fbe07c9d982715714b5516242ce10f08651548690048f79c961b7cd4.jpg) +zero level set + +![](images/ac5e30d14ee521fad2f13f8cdaa464dffb6acd5b1fc66b2d738be09910110cbd.jpg) +gradient error + +![](images/0bf86a37eeb41930070bb782acaec7972efb7ed0823d646923f570c18c1db568.jpg) +(b) Ours + +![](images/8da5d3b831b132589c013da705c1854cb0ff2e88df74cbe4f9036598a7c97ac4.jpg) +zero level set +Figure 2. We visualize the fields and the zero level set of UDF learned with or without our designed constraints on the zero level set (ZLS-C). The bluer the color, the smaller the unsigned distances in the field and the errors on gradients. + +![](images/2d03c90a6765c7c47ec26aa9407757fd9647cddda1bc5fdb6798e1516cee4acf.jpg) +gradient error + +from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set. + +We provide a visualization of fields and zero level set of UDF learned with neural networks in Fig. 2. As shown in Fig. 2 (a), the zero level set of UDF learned without proper constraints is highly fragmentary and discontinuous with large errors on the gradients at the space near to the zero level set. On the contrary, we achieve the accurate and continuous zero level set as shown in Fig. 2 (b) by introducing level set projection constraint and gradient-surface orthogonal constraint to the zero level set. + +Level Set Projections. For learning accurate zero level set of UDF, we design level set projection constraint to guide the learning of zero level set using the rest non-zero level sets. Our idea comes from the observation that despite the unreliable zero level set, the other level sets of the learned UDF are quite convincing, which can serve as the guidance to the field optimization on the zero level set. As shown in Fig. 2, the gradient errors on the non-zero level set are much less than the errors on the zero level set. + +We illustrate our method in Fig. 1, where we pull the non-zero level set onto the zero level set with gradient constraints which align gradients and correct unsigned distance errors on the zero level set. We achieve this by encouraging the parallelism between the gradient at queries $Q = \{q_i\}_{i=1}^M$ + +![](images/90acea61853345eaf455da5ba641005dbd3c748e2cf8f4a97760d4d64cd5c38b.jpg) + +![](images/20cc3fae307f6bd07c5fa1cf1eb25384cc677abf703f21065f63f84534a16408.jpg) +NDF + +![](images/1a86f838e360a90b0a640fea6f7c57d8cf4dd33236204a4f5c57883872169221.jpg) + +![](images/656be93e4e8c218875cfce40e2da159ba0e7829a0b2a193920d3e36a3a851b23.jpg) +CAP-UDF + +![](images/defe77b78a462a1cfaade2ab7ea74178450af3b75c070f94a10fb29b14f95a48.jpg) + +![](images/16cfe1f371564158a3b44cebec48711d68efd7e3d9b10105326acb648577db50.jpg) +Ours +Figure 3. Visual comparisons of surface reconstruction on ShapeNet dataset. + +![](images/701d8418335f6ee86dbc738cdf4da7932c3d480c17b1e912c15a778d4e6c7f59.jpg) + +![](images/99fbf0f35e98b0f54c75cb6c454a3fdc29d2a9351b901b00ed49e205dcbcdd4b.jpg) +GT + +
MethodChamfer-L2F-ScoreNC
MeanMedian\( F1^{0.005} \)\( F1^{0.01} \)
Input0.3630.35548.5088.34-
Watertight GT2.6282.29368.8281.60-
GT0.0760.07495.7099.99-
NDF [20]0.2020.19377.4097.9779.1
GIFS [82]0.1280.12388.0599.31-
CAP-UDFBPA0.1410.13884.8499.3381.8
CAP-UDF [89]0.1190.11488.5599.8282.5
Ours0.0980.09792.1899.9085.0
+ +Table 1. Surface reconstruction for point cloud on ShapeNet cars dataset (Chamfer-L2×10^4). + +and the gradient at their projections $\hat{Q} = \{\hat{q}\}_{i=1}^{M}$ to the zero level set, formulated as: + +$$ +\mathcal {L} _ {\mathrm {p r o j}} = \frac {1}{M} \sum_ {i = 1} ^ {M} \gamma_ {i} \left(1 - \left| \frac {\nabla f (q _ {i}) \cdot \nabla f (\hat {q} _ {i})}{| | \nabla f (q _ {i}) | | _ {2} \cdot | | \nabla f (\hat {q} _ {i}) | | _ {2}} \right|\right), \tag {5} +$$ + +where $\gamma_{i}$ is the factor for weighting the gradient constraint at the query $q_{i}$ , indicating the importance of optimizing query $q_{i}$ , formulated as: + +$$ +\gamma_ {i} = \exp (- \lambda | f (q _ {i}) |). \tag {6} +$$ + +We set $\gamma$ to increase when queries are closer to the zero level set where $\lambda$ is a hyper-parameter to control the increasing speed. The nonuniform weighting encouraging the network to focus more on the optimizations near the zero level set of UDF. + +While $\mathcal{L}_{proj}$ can provide an effective guidance to the gradients at zero level set, we further explore a more accurate unsigned distance constraint for correcting the distance values at the zero level set of UDF. The implemented loss is defined as: + +$$ +\mathcal {L} _ {\text {d i s t}} = \frac {1}{N} \sum_ {i = 1} ^ {N} | f (p _ {i}) |, \tag {7} +$$ + +where $p_i \in P$ is the raw point cloud indicating the exact surface to be represented. + +Gradient-Surface Orthogonal Constraint. The key idea to guide the learning of zero level set using the rest level sets + +is based on the observation that the non-zero level sets are much more reliable. To bring a more robust guidance to the optimization of zero level set, we introduce an addition gradient constraint on queries to learn a more stable and regular level sets at the non-zero level sets of UDF by enforcing the gradient orthogonal to the tangent plane of the surface. We design a novel loss to encourage the consistency between the gradient direction at a query $q_{i}$ and the direction from $q_{i}$ to its closest point $p_{i}$ on $P$ , formulated as: + +$$ +\mathcal {L} _ {\text {o r t h}} = \frac {1}{M} \sum_ {i = 1} ^ {M} (1 - | \frac {\nabla f (q _ {i}) \cdot T (q _ {i} , p _ {i})}{| | \nabla f (q _ {i}) | | _ {2} \cdot | | T (q _ {i} , p _ {i}) | | _ {2}} |), \tag {8} +$$ + +where $T(q_{i},p_{i})$ is the direction from $q_{i}$ to $p_i$ . The constraint is illustrated in Fig. 1. + +A more naive way of introducing the direction vector $T(q_{i},p_{i})$ for learning is to explicitly substitute the gradient $\nabla f(q_{i})$ with the direction vector $T(q_{i},p_{i})$ , as proposed in GenSDF [21]. However, $T(q_{i},p_{i})$ is obviously not the exact direction for $q_{i}$ to reach the approximated surface since the raw point cloud is the discrete representation of the surface, and $p_{i}$ is not the exact nearest points of $q_{i}$ in the approximated surface, which leads to wrong supervisions for GenSDF. + +On the contrary, We introduce a more flexible way by treating direction vector $T(q_{i},p_{i})$ as an optimization objective, which enables the networks to accommodate the inconsistency between the closest point $p_i$ on $P$ and the closest point $\hat{q}_i$ predicted by the networks. + +Loss Function. Finally, our loss function is formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {C D}} + \alpha_ {1} \mathcal {L} _ {\text {p r o j}} + \alpha_ {2} \mathcal {L} _ {\text {d i s t}} + \alpha_ {3} \mathcal {L} _ {\text {o r t h}}, \tag {9} +$$ + +where $\alpha_{1},\alpha_{2}$ and $\alpha_{3}$ are the balance weights for our designed three losses to learn accurate zero level set of UDF. + +Applications. The zero level set of UDF indicates the location of represented 3D geometries. Thus, a well-learned UDF with accurate and continuous zero level set can be adopt to different 3D applications. + +Surface Reconstruction. Following previous methods [89, 27], the surfaces can be extracted from the zero level set of UDF by judging gradient directions, formulated as: + +$$ +\mathcal {D} \left(q _ {i}, q _ {j}\right) = \nabla f \left(q _ {i}\right) \cdot \nabla f \left(q _ {j}\right), \tag {10} +$$ + +![](images/f652f86e1dd98024bb3591986a12bb7ec79f47fdd487159caa727a8cd8b70af0.jpg) + +![](images/0dd16da2b237c0466834b504d1d7d70e640de207eac2a2b2db264b29873b0956.jpg) + +![](images/2f32c6e624c0f9a4cc8e0863094574dd7a0cfabeab655fe4ee8d918979aae06d.jpg) + +![](images/a6dae0aee224f911f01228fb0f041d32c272050852ed090d819042c0d32bc626.jpg) + +![](images/4a6cc4ede02aa033d754009b97b06ab38c7ff00054b15a681beb0e39113aa175.jpg) + +![](images/efc058f781f640e51fc4dbe4ba299d6ed5f99f06201168f04b5b1cacad023dc2.jpg) +ConvOcc + +![](images/2d4e050af9f3dcf3c553bb7d06a0fe9ef8cf4fddbfb0da5784fd0591dfbc06ba.jpg) +NDF + +![](images/b80d7c8b0ad0573789d90c712775fa20e2def5507da8ac345157d41b452b816d.jpg) +CAP-UDF +Figure 4. Visual comparisons of surface reconstruction on 3D Scene dataset. Input contains 1K points / $m^2$ + +![](images/98213426a4f816be03e327fd83b4e2040d3213b0fb7f0a09f1d6c3969450c5a8.jpg) +Ours + +![](images/a0cfbf324b943c4ece9cf616c44e1cae0d3e4ca396f34236affc7def007b7b73.jpg) +GT + +
BurghersLoungeCopyroomStonewallTotempole
L2CDL1CDNCL2CDL1CDNCL2CDL1CDNCL2CDL1CDNCL2CDL1CDNC
500/m2ConvONet [64]26.970.0810.9059.0440.0460.89410.080.0460.88517.700.0630.9092.1650.0240.937
LIG [36]3.0800.0460.8406.7290.0520.8314.0580.0380.8104.9190.0430.8789.380.0620.887
DeepLS [13]0.7140.0200.92310.880.0770.8140.5520.0150.9070.6730.0180.95121.150.1220.927
NDF [20]0.5460.0180.9170.3140.0120.9210.2420.0120.9070.2260.0120.9491.0490.0250.939
OnSurf [52]0.6090.0180.9300.5290.0130.9260.4830.0140.9080.6660.0130.9552.0250.0410.954
CAP-UDF [89]0.1920.0110.9110.0990.0090.9110.1200.0090.9020.0690.0080.9580.1310.0100.954
Ours0.1610.0090.9160.0870.0060.9330.1020.0070.9200.0610.0070.9640.1140.0070.960
1000/m2ConvONet [64]27.460.0790.9079.540.0460.89410.970.0450.89220.460.0690.9052.0540.0210.943
LIG [36]3.0550.0450.8359.6720.0560.8333.610.0360.8105.0320.0420.8799.580.0620.887
DeepLS [13]0.4010.0170.9206.1030.0530.8480.6090.0210.9010.3200.0150.9540.6010.0170.950
NDF [20]1.1680.0270.9010.3930.0140.9100.2690.0130.9080.5090.0190.9362.0200.0360.922
OnSurf [52]1.3390.0310.9290.4320.0140.9340.4050.0140.9140.2660.0140.9571.0890.0290.954
CAP-UDF [89]0.1910.0100.9100.0920.0080.9270.1130.0090.9110.0660.0070.9620.1390.0090.955
Ours0.1460.0090.9210.0680.0060.9410.0930.0070.9250.0500.0050.9700.1070.0070.960
+ +Table 2. Surface reconstruction for point clouds under 3D Scene. $\mathrm{L}2\mathrm{{CD}} \times {1000}$ . + +to classify whether two queries $q_{1}$ and $q_{2}$ are in the same $\mathcal{D}(q_i,q_j) > 0$ or the opposite side $\mathcal{D}(q_i,q_j) < 0$ of the approximated surface. The marching cubes-like algorithm is then used to extract surfaces. + +Unsupervised Point Normal Estimation. With a well learned zero level set, we compute the gradients at the raw point clouds $P$ as their estimated normals, formulated as: + +$$ +\mathcal {N} (P) = \{\nabla f (p) \}, p \in P. \tag {11} +$$ + +Unsupervised Point Cloud Upsampling. We randomly sample queries around $P$ , and then move them to the zero level set with Eq. 3 as the upsampled points of $P$ . We further filter the queries with unsigned distance values larger than a threshold $\beta$ for avoiding outliers. The procedure for upsampling $P$ with a factor of $G$ is formulated as: + +$$ +\mathcal {U} (P) = \left\{\hat {q} _ {i}, i \in [ 1, N \times G ] \mid f \left(q _ {i}\right) < \beta \right\} \tag {12} +$$ + +# 4. Experiments + +For evaluating the performance of our method, we conduct experiments on surface reconstruction from raw point clouds of shapes (Sec. 4.1), room-level scenes (Sec. 4.2), and real scans (Sec. 4.4), where we also show our results on large-scale driving scenes obtained by fusing LiDAR + +depths in Sec. 4.3. We further explore the ability of our learned UDF with accurate zero level set for unsupervised point normal estimation (Sec. 4.5) and unsupervised point upsampling (Sec. 4.6). Finally, we conduct ablation studies in Sec. 4.7. + +# 4.1. Surface Reconstruction for Shapes + +Dataset and Metrics. To explore the ability of our method in representing shapes with arbitrary topology, we follow previous methods [89, 82] to conduct experiments on the "Car" category of ShapeNet dataset which contains the largest number of shapes with multi-layer structures or open surfaces. We sample 10K points per shape as the input for surface reconstruction. For evaluating the performances, we follow the common setting [82] to sample 100K points from the reconstructed surfaces and leverage Chamfer Distance, Normal Consistency [57] and F-score with a threshold of 0.005 / 0.01 as the evaluation metrics. + +Comparisons. We compare our method with the state-of-the-art shape reconstruction methods NDF [20], GIFS [82] and CAP-UDF [89]. We report the quantitative comparison results in Tab. 1, where "Watertight GT" is the result of sampling points from the watertight ground truth, indicating the best performance of the methods base on SDF or occupancy. We also show the superior limit of the dataset + +![](images/b4cf5970fcbfd1bb772ed9db7a5d7f4a8ce853325a81a4d1dc72300451e87863.jpg) +Figure 5. Surface reconstruction results on KITTI odometry dataset (Sequence 00, frame 3000 to 4000). + +by sampling points on the ground truth mesh and report the result as "GT". Tab. 1 shows that our method achieves the best performance over all the baselines in terms of all metrics. The visual comparison in Fig. 3 further shows that our methods produce more continuous and accurate geometries over all baselines. + +# 4.2. Surface Reconstruction for Room-Level Scenes + +Dataset and Metrics. We further explore our performance on real scene scans to demonstrate the ability of our methods to scale to large-scale point clouds. Following On-Surf [52], we conduct experiments on the 3D Scene dataset consisting of complex scenes with open surfaces and scan noises. The input point cloud is achieved by sampling 500 or 1000 points per $m^2$ uniformly for each scene. We follow the common setting [52, 89] to sample $1M$ points on both the reconstructed and the ground truth meshes. We leverage L1 / L2 Chamfer Distance and Normal Consistency as the evaluation metrics. + +Comparisons. With different point densities, we compare our method with the state-of-the-art methods ConvONet [64], LIG [36], DeepLS [13], OnSurf [52], NDF [20] and CAP-UDF [89]. The numerical comparison in Tab. 2 demonstrates our superior performance in all scenes. We further present a visual comparison in Fig. 4, where the input point clouds contains 1K points/ $m^2$ . The visualization further shows that our method can reconstruct more detailed and smooth surfaces in complex scenes, where the other UDF-base methods NDF and CAP-UDF produce fragmented surfaces. + +# 4.3. Large-Scale Driving Scene Reconstruction + +Dataset. To further demonstrate our scalability to extremely large scenes, we follow NGS [35] to apply our method to KITTI dataset [23]. We use the LiDAR scans of frame 3000 to 4000 in Squeeze00 subset of KITTI dataset as the full input, which are transformed into world coordinates using the provided camera trajectories. We leverage the slide-window strategy to divide the full scene into 15 + +
MethodChamfer-L1F-ScoreNC
IGR [25]0.17875.586.9
Point2Mesh [31]0.11664.8-
SPSR [40]0.23273.5-
SAP [63]0.07683.088.6
Neural-Pull [51]0.10679.787.2
NDF [20]0.23868.680.4
CAP-UDF [89]0.07384.588.6
Ours0.07185.191.0
+ +Table 3. Surface reconstruction for point cloud on SRB dataset. + +blocks of size $51.2m^3$ , where we sample 300K points per block as the local input to train our network. The final scene is achieve by blending the reconstructed local scenes. + +Analysis. The reconstruction results under KITTI scenes is shown in Fig. 5, where our method reproduces visualappealing performances with accurate geometries. Note that: 1) The LiDAR scans contain large amount of noises, especially in the difficult driving scenes. 2) Our method learns to reconstruct surfaces directly from the raw point cloud without learning priors from large-scale datasets. + +# 4.4. Surface Reconstruction for Real Scans + +Dataset and Metrics. We demonstrate our advantages for surface reconstruction from real scans by conducting experiments on the Surface Reconstruction Benchmarks [77] (SRB). We follow previous methods [63, 89] to leverage Chamfer Distance and F-Score with a threshold of $1\%$ for evaluation. Note that the ground truth of SRB dataset is dense point cloud containing millions of points. For a comprehensive comparison on the reconstruction quality, we further evaluate the Normal Consistency by first converting the ground truth into meshes with BPA [8] algorithm. + +Comparisons. We first report our numerical comparison under SRB dataset with the classic and learning-based methods in Tab. 3. The compared methods include IGR [25], Point2Mesh [31], Screened Poisson Surface Reconstruction (SPSR) [40], Shape As Points (SAP) [63], Neural-Pull [51], NDF [20] and CAP-UDF [89]. Our method + +![](images/994e2d33482fbd100d615528e35b60deb47a125ce9f8d55a259cd9d7f9be067a.jpg) +Figure 6. Visual comparisons of surface reconstruction on SRB dataset. SRB dataset provides only point clouds as GT. + +
MethodCleanStripGradientaverage
SupervisedPCPNet [26]9.6611.4713.4211.61
Hough [9]10.2312.4711.0211.24
Nesti-Net [7]6.998.479.008.15
IterNet [41]6.727.737.517.32
DeepFit [5]6.517.927.317.25
UnsupervisedJet [12]12.2313.3913.1312.92
PCA [1]12.2913.6612.8112.92
Ours (w/o ZLS-c)7.307.747.787.61
Ours6.517.457.647.20
+ +achieves the best performance in all metrics as shown in Tab. 3. The visual comparison in Fig. 6 further shows that our methods produce more accurate and smooth geometries over all baselines. + +# 4.5. Unsupervised Point Normal Estimation + +Dataset and Metrics. We adopt the widely-used PCPNet [26] dataset to evaluate our method on the task of point normal estimation. Each point cloud in the PCPNet dataset contains 100K points. We conduct experiments under three different settings. The inputs of "Clean" setting are sampled uniformly on shapes, and two additional settings with varying point densities (Stripes and Gradients) are added to explore our performance in handling irregular data. Following previous methods [5, 26], we sample 5000 points per shape and compute the angle root mean square error (RMSE) between the predicted normals and the ground truth normals as the evaluation metrics. + +Comparisons. We conduct a comparison with traditional normal estimation methods including PCA [1], Jets [12] and the state-of-the-art learning-based methods PCPNet [26], HoughCNN [9], Nesti-Net [7], Iter-Net [41] and DeepFit [5]. Note that all the previous learning-based methods are designed in a supervised manner which requires a large scale dataset for training, while we extract normals directly from the unsigned distance fields learned from raw point cloud in an unsupervised way. The numerical results in Tab. 4 show that our method achieves a comparable or even better performance than the state-of-the-art supervised methods. The results also show the effectiveness of our method where the performance degrades from 7.20 to 7.61 without + +![](images/5fd88d82adf961f6ca3d37a28d9f96b3aa5c116d976091f0cd67a67eddb4f489.jpg) +Figure 7. Visual comparisons on error maps of point normal estimation on PCPNet dataset. + +Table 4. Point normal estimation results on the PCPNet dataset. + +
MethodSupervised?P2FCDHD
PU-Net [85]Yes6.840.728.94
MPU [83]Yes3.960.496.11
PU-GAN [42]Yes2.330.284.64
Dis-PU [43]Yes2.010.222.83
EAR [34]No5.820.527.37
L2G-AE [46]No39.376.3163.23
SPU-Net (Tr2T) [47]No5.970.382.24
SPU-Net (All2T)No5.790.372.55
SPU-Net (Te2T)No6.850.412.18
Ours (w/o ZLS-C)No1.430.242.16
OursNo1.020.191.55
+ +Table 5. Point cloud upsampling results on the PU-GAN dataset. + +our constraints. The visual comparison in Fig. 7 shows that our method produces more accurate estimations compared to other methods, especially on the complex geometries. + +# 4.6. Unsupervised Point Cloud Upsampling + +Dataset and Metrics. For the task of point cloud upsampling, we follow previous methods [47, 43] to conduct experiments on the dataset provided by PU-GAN [42]. We evaluate our method under the setting to generate 8,198 + +![](images/29496caedd699d5607c87b3b6f95ccaf6f883e73ac91e5c90c24cdb0d67bb907.jpg) +Figure 8. Visual comparisons of point cloud upsampling on PU-GAN dataset. + +points for each sparse input with 2,048 points. We adopt Chamfer Distance (CD), Hausdorff Distance (HD) and Point-to-Surface distance (P2F) as the evaluation metrics. + +Comparisons. We compare our method with the state-of-the-art supervised methods PU-Net [85], MPU [83], PU-GAN [42], Dis-PU [43] and unsupervised methods EAR [34], L2G-AE [46] and SPU-Net [47]. The quantitative comparison is shown in Tab. 5, where our method outperforms the previous supervised and unsupervised methods significantly. The results also show the effectiveness of our method where the performance degrades from 1.55 to 2.16 in terms of HD without our designed constraints. The visualization in Fig. 8 further shows that our upsampling results are more smooth and uniform even compared with the state-of-the-art supervised methods. + +# 4.7. Ablation Studies + +We conduct ablation studies to demonstrate the effectiveness of each proposed constraint and explore the effect of some important hyper-parameters. We report the performance under a subset of ShapeNet Cars dataset in terms of L2 Chamfer Distance $(\times 10^{4})$ and Normal Consistency. + +Effect of each Design. We first justify the effectiveness of each proposed constraint in Tab. 6. We report the performance without all the three designed losses as "w/o ZLS-C". We explore each loss by reporting the results without level set projection loss as "w/o $\mathcal{L}_{\mathrm{proj}}$ ", surface unsigned distance loss as "w/o $\mathcal{L}_{\mathrm{dist}}$ ", gradient-surface orthogonal loss as "w/o $\mathcal{L}_{\mathrm{orth}}$ " and adaptive point weight as "w/o AW". We replace our level set projection constraint with the GenSDF-style [21] optimization as "GenSDF-Style". We further constrain the level set projection loss on a randomly selected non-zero level set other than the zero level set and report the performance as "Non-zero LSC". The result demonstrates that the zero level set is the key factor that influence the representation ability of UDF. + +Weight of Level Set Projection Loss. We report the performance with different weights of the level set projection loss $\mathcal{L}_{\mathrm{proj}}$ in Tab. 7. We found that a suitable weight of $\mathcal{L}_{\mathrm{proj}}$ will improve the reconstruction accuracy, and it may affect the optimization to converge if we weight too much. + +Weight of Surface Unsigned Distance Loss. We further + +
w/o ZLS-Cw/o Lprojw/o Ldistw/o Lorth
L2CD0.1260.1070.1010.096
NC82.782.983.984.1
w/o AWGenSDF-StyleNon-zero LSCOurs
L2CD0.0960.1010.0980.091
NC84.283.983.584.4
+ +Table 6. Effect of framework design. + +
0.0010.0020.010.1
L2CD0.0950.0910.1620.359
NC84.284.483.479.6
+ +explore the effect of weights $\alpha_{2}$ for the surface unsigned distance loss in Tab 8, where we found that a too large or too small weight will degenerate the performance. + +Table 7. Weight of level set projection loss. + +
0.0010.010.11
L2CD0.1010.1000.0910.449
NC84.184.184.478.9
+ +Weight of Gradient-Surface Orthogonal Loss. We evaluate the effect of the weight $\alpha_{3}$ for gradient-surface orthogonal loss in Tab. 9. A proper weight $\alpha_{3} = 0.01$ brings the best improvement while a too much weight will affect the convergence. + +Table 8. Weight of surface unsigned distance loss. + +
0.0010.010.11
L2CD0.0940.0910.3352.55
NC84.284.477.772.9
+ +Effect of Adaptive per Point Weights. We further report the performance under different $\lambda$ which controls the increasing speed of adaptive weights for each point in Tab. 10. We found that $\lambda$ has a relative small impact on the Chamfer Distance with large affect on the Normal Consistency, which indicates that the adaptive per point weight can improve the surface smoothness. + +Table 9. Weight of gradient-surface orthogonal loss. + +
1101001000
L2CD0.0930.0910.0920.094
NC84.184.483.783.2
+ +Table 10. Effect of adaptive per point weights. + +# 5. Conclusion + +In this paper, we justify that an accurate and continuous zero level set of unsigned distance functions is the key factor to represent complex 3D geometries. We therefore propose two novel constraints on UDF to achieve a more continuous zero level set by projecting non-zero level set to guide the optimization of zero level set. With the ability of learning consistent and accurate zero level set of UDF, we explore three different 3D applications including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling, where the visual and numerical comparisons with the state-of-the-art supervised/unsupervised methods justify our effectiveness ans show our superiority over the latest methods. + +# 6. Acknowledgement + +This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data. + +# References + +[1] Hervé Abdi and Lynne J Williams. Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2(4):433-459, 2010. 7 +[2] Matan Atzmon and Yaron Lipman. SAL: Sign agnostic learning of shapes from raw data. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2565-2574, 2020. 2 +[3] Matan Atzmon and Yaron Lipman. SALD: Sign agnostic learning with derivatives. In International Conference on Learning Representations, 2020. 2 +[4] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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"bbox": [ + 47, + 298, + 290, + 608 + ], + "type": "text", + "content": "Latest methods represent shapes with open surfaces using unsigned distance functions (UDFs). They train neural networks to learn UDFs and reconstruct surfaces with the gradients around the zero level set of the UDF. However, the differential networks struggle from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set, resulting in highly fragmented and discontinuous surfaces. To resolve this problem, we propose to learn a more continuous zero level set in UDFs with level set projections. Our insight is to guide the learning of zero level set using the rest non-zero level sets via a projection procedure. Our idea is inspired from the observations that the non-zero level sets are much smoother and more continuous than the zero level set. We pull the non-zero level sets onto the zero level set with gradient constraints which align gradients over different level sets and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous unsigned distance field. We conduct comprehensive experiments in surface reconstruction for point clouds, real scans or depth maps, and further explore the performance in unsupervised point cloud upsampling and unsupervised point normal estimation with the learned UDF, which demonstrate our non-trivial improvements over the state-of-the-art methods. Code is available at https://github.com/junshengzhou/LevelSetUDF." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 651, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 287, + 687 + ], + "type": "text", + "content": "Surface reconstruction from point clouds plays an important role in vision, robotics and graphics. Recently, neural implicit functions [61, 58, 57] have achieved remarkable" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 274, + 547, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 547, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 547, + 357 + ], + "type": "text", + "content": "results by representing 3D geometries with signed distance functions (SDFs) [51, 13, 73], occupancy [57, 64, 60] or unsigned distance functions (UDFs) [89, 20, 27]. SDFs and occupancy explore the internal-to-external relations, which are limited to reconstruct closed surfaces. Researchers therefore turn to UDFs, which is a more general function, to represent shapes with arbitrary typologies." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 360, + 547, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 547, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 547, + 504 + ], + "type": "text", + "content": "Learning an accurate zero level set of UDF is the key factor for representing complex geometries and supporting 3D applications [52, 42, 26, 17]. However, the differential neural networks struggle from learning the zero level set where the UDF is not differentiable. This leads to unstable optimizations, which results in large errors on unsigned distances and gradients around the zero level set, causing failures in downstream 3D applications. Taking surface reconstruction for example, SOTA methods [89, 27] extract surfaces from UDFs by judging gradient directions around the zero level set, where the unreliable gradients lead to highly fragmented and discontinuous surfaces." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 506, + 548, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 548, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 548, + 674 + ], + "type": "text", + "content": "To resolve this issue, we introduce two novel constraints on the zero level set in forms of losses for learning accurate UDF without ground truth unsigned distances. The key insight is from the observation that despite the unreliable zero level set, the non-zero level sets learned by UDF are quite convincing, which can serve as an accurate guidance for the optimization on zero level set. We therefore propose the level set projection constraint to achieve a smoother and more continuous zero level set of UDF by enforcing the parallelism between the gradient of a query in a non-zero level set and the gradient of its projection to the zero level set. Moreover, we introduce an adaptive weighting strategy to force the neural network to focus more on the optimization nearer to the zero level set." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "The level set projection constraint aims to guide the gradients at zero level set, where we propose another unsigned distance loss as a supplement for correcting distance errors" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 58, + 703, + 199, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 199, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 199, + 713 + ], + "type": "text", + "content": "†The corresponding author is Yu-Shen Liu." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3181" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "at the zero level set. To bring a more robust guidance to the optimization of zero level set, we introduce an addition gradient constraint on queries to learn more accurate and regular non-zero level sets of UDF by encouraging the gradient orthogonal to the tangent plane of the surface." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 287, + 227 + ], + "type": "text", + "content": "Based on our learned stable UDF with an accurate zero level set, we explore three different 3D applications, including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling. Our improvements over unsupervised or even supervised baselines justify both our effectiveness and the importance of an accurate and continuous zero level set to the representation ability of neural unsigned fields." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 228, + 279, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 228, + 279, + 239 + ], + "spans": [ + { + "bbox": [ + 59, + 228, + 279, + 239 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 247, + 287, + 418 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 247, + 287, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 247, + 287, + 295 + ], + "spans": [ + { + "bbox": [ + 59, + 247, + 287, + 295 + ], + "type": "text", + "content": "- We propose two novel constraints on UDF to achieve a smoother and more continuous zero level set for learning to represent shapes or scenes without ground truth unsigned distances." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 304, + 287, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 304, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 59, + 304, + 287, + 340 + ], + "type": "text", + "content": "- We justify that an accurate and continuous zero level set is the key factor to represent complex 3D geometries and supporting 3D downstream applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 347, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 347, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 59, + 347, + 287, + 418 + ], + "type": "text", + "content": "- We explore three different 3D applications with our learned UDF, including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling, where we show our superiority over the state-of-the-art supervised / unsupervised methods." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 430, + 133, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 133, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 133, + 442 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 450, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 510 + ], + "type": "text", + "content": "With the rapid development of deep learning, the neural networks have shown great potential in 3D applications [66, 30, 79, 75, 78, 74, 80, 76, 14, 39]. We mainly focus on learning Neural Implicit Functions with networks for representing 3D shapes or scenes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": "Neural Implicit Functions. Recently, Neural Implicit Functions (NIFs) have shown promising results in surface reconstruction [61, 51, 57, 16, 29, 15, 38, 55, 53], novel view synthesis [58, 4, 65, 87, 32, 24, 59], image superresolution [68, 59, 11], point normal estimation [44], etc. In the task of surface reconstruction, the NIFs approaches train a neural network to represent shapes and scenes with binary occupancy [57, 64, 19] or signed distance functions (SDFs) [61, 36, 22, 21, 63, 10, 84, 6], and then extract surfaces from the learned implicit functions with the marching cubes algorithm [50]. Previous methods [57, 61] learn a global latent code for each 3D shape with a shared MLP to decode geometries. Some advanced approaches [64, 36] propose to use more latent codes to represent detailed local geometries. Latest studies bring more priors learned from large scale datasets to enhance the representation ability of NIFs. PCP [54] introduces the predictive context priors to" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "represent large-scale point clouds. OnSurf [52] explores the on-surface prior to reconstruct smooth surfaces from sparse point clouds." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 113, + 545, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 113, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 304, + 113, + 545, + 209 + ], + "type": "text", + "content": "NeRF [58] and the following studies [59, 62, 69, 56, 37, 67, 33, 45] extends NIFs to the task of novel view synthesis. NeuS [73], VolSDF [81] and Unisurf [60] advance the rendering procedure of NeRF for surface reconstruction from multi-view images. ManhattanSDF [28] leverages the man-hattan assumption for representing indoor scenes. NeuRIS [71] and MonoSDF [86] brings the depth prior and normal prior for improving the surface quality." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 213, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 344 + ], + "type": "text", + "content": "Occupancy and SDFs are merely suitable to represent closed shapes. Recently, researchers explore the neural unsigned distances (UDFs) [20, 89, 88, 70, 18, 72, 49, 48] to represent shapes with arbitrary topology. NDF [20] trains a neural network to learn UDFs with the ground truth distance values. GIFS [82] jointly learns UDFs and the relationship of queries. MeshUDF [27] propose a differentiable meshing algorithm for UDF. However, all the previous UDF-based methods fail to reconstruct smooth and continuous surfaces with high-fidelity details due to the disability of learning an accurate and smooth zero level set of UDF." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 350, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 517 + ], + "type": "text", + "content": "Implicit Learning from Raw Point Clouds. With the ground truth signed/unsigned distances or occupancy labels as supervision, previous methods learn NIFs as a regression [20, 61] problem or classification [57] problem. However, these expensive supervisions come from the ground truth meshes which are hard to collect. Moreover, such methods also fail to generalize to unseen cases with large geometry variations to the training data, which limits the application scenarios of such methods. To learn implicit representations directly from raw point clouds without ground truth supervisions, current methods explore the supervision from sign agnostic [2, 3] learning with gradient constraints [25]. Neural-Pull [51] employs a new learning schema to pull space onto surfaces for optimizing SDFs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "Latest work CAP-UDF [89] learns UDF progressively with a field consistency loss. However, the UDF inferred by CAP-UDF are not accurate and the gradients are unreliable, especially in the zero level set which indicates the location of 3D geometries. The key problem is that the differential neural networks struggle from learning non-differentiable zero level set of UDF, leading to highly fragmented and discontinuous surfaces. Since the non-zero level sets of UDF are all differentiable, we propose to pull the non-zero level sets onto the zero level set with gradient constraints which align gradients and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous zero level set of unsigned distance field. Our learning schema involves the constraints for both zero level set and non-zero level sets of UDF, which differentiates our method from the previous ones [89, 2, 3, 51, 20, 61]." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3182" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 545, + 182 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 545, + 182 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 545, + 182 + ], + "type": "image", + "image_path": "5c957780ed4d20295f2d52ca39ba8ea24d2e3eecc6c07928d2a6d76e59445437.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": "Figure 1. Overview of our method. (a) The level set projection constraint leverages the gradient " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "\\nabla f(q)" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " at convincing non-zero level set as the guidance to gradient " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "\\nabla f(\\hat{q})" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " at unreliable zero level set. (b) The gradient-surface orthogonal constraint encourages the gradients " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "\\nabla f(q)" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " at query " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " orthogonal to the tangent plane of the surface at " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "p'" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " which is the nearest point of " + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 186, + 547, + 220 + ], + "type": "text", + "content": " in the raw point cloud." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 223, + 103, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 223, + 103, + 236 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 103, + 236 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": "Neural UDFs and Level Sets. We focus on learning unsigned distance functions for representing 3D shapes or scenes with arbitrary typology. Given a raw point cloud " + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "inline_equation", + "content": "P = \\{p_i \\in R^3\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": " points, we sample a set of queries " + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "inline_equation", + "content": "Q = \\{q_j \\in R^3\\}_{j=1}^M" + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": " around " + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": ". The UDF " + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": " predicts the unsigned distances " + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "inline_equation", + "content": "s^P" + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": " between queries " + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "inline_equation", + "content": "\\{q_j\\}_{j=1}^M" + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": " and the shape described by " + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 243, + 288, + 330 + ], + "type": "text", + "content": ", formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 140, + 338, + 287, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 338, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 140, + 338, + 287, + 354 + ], + "type": "interline_equation", + "content": "s _ {j} ^ {P} = f (q _ {j}). \\tag {1}", + "image_path": "66d7cedb38714be306b9a0bde535493ff204518c37e713f3aad21351edecc046.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 362, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 287, + 399 + ], + "type": "text", + "content": "A level set " + }, + { + "bbox": [ + 46, + 362, + 287, + 399 + ], + "type": "inline_equation", + "content": "S_{d}" + }, + { + "bbox": [ + 46, + 362, + 287, + 399 + ], + "type": "text", + "content": " of UDF is defined as a region of the 3D space containing a continuous set of 3D points with the same unsigned distance " + }, + { + "bbox": [ + 46, + 362, + 287, + 399 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 362, + 287, + 399 + ], + "type": "text", + "content": ", formulates as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 124, + 411, + 287, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 411, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 124, + 411, + 287, + 425 + ], + "type": "interline_equation", + "content": "S _ {d} = \\{q | f (q) = d \\}, \\tag {2}", + "image_path": "71048141d4dcd21586bfd9ef46f79663bd506c7398d7e1a22248fb409bc46126.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 430, + 275, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 275, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 275, + 442 + ], + "type": "text", + "content": "and the level sets of UDF are defined as " + }, + { + "bbox": [ + 46, + 430, + 275, + 442 + ], + "type": "inline_equation", + "content": "S = \\{S_d\\}_{d > = 0}" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": "Learning UDFs from Point Clouds. Inspired by CAP-UDF [89], we leverage the pulling optimization for learning UDFs from raw point clouds without ground truth unsigned distances as supervision. Specifically, given a query " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": " as input, we move it against the direction of the gradient " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "g_{i} = \\nabla f(q_{i})" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 46, + 442, + 287, + 515 + ], + "type": "text", + "content": ", the moving operation is formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 88, + 525, + 287, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 525, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 88, + 525, + 287, + 538 + ], + "type": "interline_equation", + "content": "\\hat {q} _ {i} = q _ {i} - f \\left(q _ {i}\\right) \\cdot \\nabla f \\left(q _ {i}\\right) / \\left| \\right| \\nabla f \\left(q _ {i}\\right) | | _ {2}, \\tag {3}", + "image_path": "f2460237a4778599341853213efa6ca5a8ea2784fea8193f4e00b5fa83427867.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "text", + "content": "where the chamfer distance between moved queries " + }, + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "inline_equation", + "content": "\\hat{Q} = \\{\\hat{q}\\}_{i=1}^{M}" + }, + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "text", + "content": " and the raw point cloud " + }, + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "text", + "content": " is calculated as the loss function for optimization, formulated as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 69, + 601, + 287, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 601, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 69, + 601, + 287, + 658 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C D}} = \\frac {1}{M} \\sum_ {i \\in [ 1, M ]} \\min _ {j \\in [ 1, N ]} | | \\hat {q} _ {i} - p _ {j} | | _ {2} \\\\ + \\frac {1}{N} \\sum_ {j \\in [ 1, N ]} \\min _ {i \\in [ 1, M ]} \\| p _ {j} - z _ {i} \\| _ {2}, \\tag {4} \\\\ \\end{array}", + "image_path": "4ebb059c9df00eb8a0193bf03c712c0bc717366c32eb5131b685fe51ae92b3f2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Zero Level Set of UDF. An accurate zero level set is the key factor for UDF to represent 3D shapes or scenes, since the zero level set indicates the location of 3D geometries. The key problem here is that the differential networks struggle" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 232, + 425, + 292 + ], + "blocks": [ + { + "bbox": [ + 345, + 223, + 384, + 231 + ], + "lines": [ + { + "bbox": [ + 345, + 223, + 384, + 231 + ], + "spans": [ + { + "bbox": [ + 345, + 223, + 384, + 231 + ], + "type": "text", + "content": "(a) w/o ZLS-C" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 232, + 425, + 292 + ], + "lines": [ + { + "bbox": [ + 307, + 232, + 425, + 292 + ], + "spans": [ + { + "bbox": [ + 307, + 232, + 425, + 292 + ], + "type": "image", + "image_path": "db346aec818d0f395417c0c77778cbb3159315e23a7c944cb3e91d6d76486e1d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 307, + 293, + 365, + 339 + ], + "blocks": [ + { + "bbox": [ + 307, + 293, + 365, + 339 + ], + "lines": [ + { + "bbox": [ + 307, + 293, + 365, + 339 + ], + "spans": [ + { + "bbox": [ + 307, + 293, + 365, + 339 + ], + "type": "image", + "image_path": "d5d35842fbe07c9d982715714b5516242ce10f08651548690048f79c961b7cd4.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 341, + 352, + 347 + ], + "lines": [ + { + "bbox": [ + 318, + 341, + 352, + 347 + ], + "spans": [ + { + "bbox": [ + 318, + 341, + 352, + 347 + ], + "type": "text", + "content": "zero level set" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 365, + 293, + 425, + 339 + ], + "blocks": [ + { + "bbox": [ + 365, + 293, + 425, + 339 + ], + "lines": [ + { + "bbox": [ + 365, + 293, + 425, + 339 + ], + "spans": [ + { + "bbox": [ + 365, + 293, + 425, + 339 + ], + "type": "image", + "image_path": "ac5e30d14ee521fad2f13f8cdaa464dffb6acd5b1fc66b2d738be09910110cbd.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 376, + 341, + 411, + 347 + ], + "lines": [ + { + "bbox": [ + 376, + 341, + 411, + 347 + ], + "spans": [ + { + "bbox": [ + 376, + 341, + 411, + 347 + ], + "type": "text", + "content": "gradient error" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 427, + 232, + 545, + 292 + ], + "blocks": [ + { + "bbox": [ + 473, + 224, + 494, + 231 + ], + "lines": [ + { + "bbox": [ + 473, + 224, + 494, + 231 + ], + "spans": [ + { + "bbox": [ + 473, + 224, + 494, + 231 + ], + "type": "text", + "content": "(b) Ours" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 232, + 545, + 292 + ], + "lines": [ + { + "bbox": [ + 427, + 232, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 427, + 232, + 545, + 292 + ], + "type": "image", + "image_path": "0bf86a37eeb41930070bb782acaec7972efb7ed0823d646923f570c18c1db568.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 427, + 293, + 485, + 339 + ], + "blocks": [ + { + "bbox": [ + 427, + 293, + 485, + 339 + ], + "lines": [ + { + "bbox": [ + 427, + 293, + 485, + 339 + ], + "spans": [ + { + "bbox": [ + 427, + 293, + 485, + 339 + ], + "type": "image", + "image_path": "8da5d3b831b132589c013da705c1854cb0ff2e88df74cbe4f9036598a7c97ac4.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 438, + 341, + 472, + 347 + ], + "lines": [ + { + "bbox": [ + 438, + 341, + 472, + 347 + ], + "spans": [ + { + "bbox": [ + 438, + 341, + 472, + 347 + ], + "type": "text", + "content": "zero level set" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 350, + 545, + 395 + ], + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 395 + ], + "type": "text", + "content": "Figure 2. We visualize the fields and the zero level set of UDF learned with or without our designed constraints on the zero level set (ZLS-C). The bluer the color, the smaller the unsigned distances in the field and the errors on gradients." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 496, + 293, + 545, + 339 + ], + "blocks": [ + { + "bbox": [ + 496, + 293, + 545, + 339 + ], + "lines": [ + { + "bbox": [ + 496, + 293, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 496, + 293, + 545, + 339 + ], + "type": "image", + "image_path": "2d03c90a6765c7c47ec26aa9407757fd9647cddda1bc5fdb6798e1516cee4acf.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 496, + 341, + 531, + 347 + ], + "lines": [ + { + "bbox": [ + 496, + 341, + 531, + 347 + ], + "spans": [ + { + "bbox": [ + 496, + 341, + 531, + 347 + ], + "type": "text", + "content": "gradient error" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 401, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 437 + ], + "type": "text", + "content": "from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 437, + 546, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 544 + ], + "type": "text", + "content": "We provide a visualization of fields and zero level set of UDF learned with neural networks in Fig. 2. As shown in Fig. 2 (a), the zero level set of UDF learned without proper constraints is highly fragmentary and discontinuous with large errors on the gradients at the space near to the zero level set. On the contrary, we achieve the accurate and continuous zero level set as shown in Fig. 2 (b) by introducing level set projection constraint and gradient-surface orthogonal constraint to the zero level set." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 545, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 652 + ], + "type": "text", + "content": "Level Set Projections. For learning accurate zero level set of UDF, we design level set projection constraint to guide the learning of zero level set using the rest non-zero level sets. Our idea comes from the observation that despite the unreliable zero level set, the other level sets of the learned UDF are quite convincing, which can serve as the guidance to the field optimization on the zero level set. As shown in Fig. 2, the gradient errors on the non-zero level set are much less than the errors on the zero level set." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "text", + "content": "We illustrate our method in Fig. 1, where we pull the non-zero level set onto the zero level set with gradient constraints which align gradients and correct unsigned distance errors on the zero level set. We achieve this by encouraging the parallelism between the gradient at queries " + }, + { + "bbox": [ + 304, + 653, + 545, + 715 + ], + "type": "inline_equation", + "content": "Q = \\{q_i\\}_{i=1}^M" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3183" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 164, + 134 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 164, + 134 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 164, + 134 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 164, + 134 + ], + "type": "image", + "image_path": "90acea61853345eaf455da5ba641005dbd3c748e2cf8f4a97760d4d64cd5c38b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 133, + 164, + 182 + ], + "blocks": [ + { + "bbox": [ + 52, + 133, + 164, + 182 + ], + "lines": [ + { + "bbox": [ + 52, + 133, + 164, + 182 + ], + "spans": [ + { + "bbox": [ + 52, + 133, + 164, + 182 + ], + "type": "image", + "image_path": "20cc3fae307f6bd07c5fa1cf1eb25384cc677abf703f21065f63f84534a16408.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 99, + 185, + 116, + 193 + ], + "lines": [ + { + "bbox": [ + 99, + 185, + 116, + 193 + ], + "spans": [ + { + "bbox": [ + 99, + 185, + 116, + 193 + ], + "type": "text", + "content": "NDF" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 170, + 71, + 286, + 134 + ], + "blocks": [ + { + "bbox": [ + 170, + 71, + 286, + 134 + ], + "lines": [ + { + "bbox": [ + 170, + 71, + 286, + 134 + ], + "spans": [ + { + "bbox": [ + 170, + 71, + 286, + 134 + ], + "type": "image", + "image_path": "1a86f838e360a90b0a640fea6f7c57d8cf4dd33236204a4f5c57883872169221.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 173, + 135, + 286, + 183 + ], + "blocks": [ + { + "bbox": [ + 173, + 135, + 286, + 183 + ], + "lines": [ + { + "bbox": [ + 173, + 135, + 286, + 183 + ], + "spans": [ + { + "bbox": [ + 173, + 135, + 286, + 183 + ], + "type": "image", + "image_path": "656be93e4e8c218875cfce40e2da159ba0e7829a0b2a193920d3e36a3a851b23.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 212, + 185, + 246, + 193 + ], + "lines": [ + { + "bbox": [ + 212, + 185, + 246, + 193 + ], + "spans": [ + { + "bbox": [ + 212, + 185, + 246, + 193 + ], + "type": "text", + "content": "CAP-UDF" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 291, + 70, + 411, + 134 + ], + "blocks": [ + { + "bbox": [ + 291, + 70, + 411, + 134 + ], + "lines": [ + { + "bbox": [ + 291, + 70, + 411, + 134 + ], + "spans": [ + { + "bbox": [ + 291, + 70, + 411, + 134 + ], + "type": "image", + "image_path": "defe77b78a462a1cfaade2ab7ea74178450af3b75c070f94a10fb29b14f95a48.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 295, + 135, + 410, + 183 + ], + "blocks": [ + { + "bbox": [ + 295, + 135, + 410, + 183 + ], + "lines": [ + { + "bbox": [ + 295, + 135, + 410, + 183 + ], + "spans": [ + { + "bbox": [ + 295, + 135, + 410, + 183 + ], + "type": "image", + "image_path": "16cfe1f371564158a3b44cebec48711d68efd7e3d9b10105326acb648577db50.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 347, + 185, + 363, + 193 + ], + "lines": [ + { + "bbox": [ + 347, + 185, + 363, + 193 + ], + "spans": [ + { + "bbox": [ + 347, + 185, + 363, + 193 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 157, + 194, + 435, + 205 + ], + "lines": [ + { + "bbox": [ + 157, + 194, + 435, + 205 + ], + "spans": [ + { + "bbox": [ + 157, + 194, + 435, + 205 + ], + "type": "text", + "content": "Figure 3. Visual comparisons of surface reconstruction on ShapeNet dataset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 418, + 70, + 536, + 134 + ], + "blocks": [ + { + "bbox": [ + 418, + 70, + 536, + 134 + ], + "lines": [ + { + "bbox": [ + 418, + 70, + 536, + 134 + ], + "spans": [ + { + "bbox": [ + 418, + 70, + 536, + 134 + ], + "type": "image", + "image_path": "701d8418335f6ee86dbc738cdf4da7932c3d480c17b1e912c15a778d4e6c7f59.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 419, + 133, + 534, + 183 + ], + "blocks": [ + { + "bbox": [ + 419, + 133, + 534, + 183 + ], + "lines": [ + { + "bbox": [ + 419, + 133, + 534, + 183 + ], + "spans": [ + { + "bbox": [ + 419, + 133, + 534, + 183 + ], + "type": "image", + "image_path": "99fbf0f35e98b0f54c75cb6c454a3fdc29d2a9351b901b00ed49e205dcbcdd4b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 185, + 481, + 193 + ], + "lines": [ + { + "bbox": [ + 468, + 185, + 481, + 193 + ], + "spans": [ + { + "bbox": [ + 468, + 185, + 481, + 193 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 50, + 214, + 287, + 337 + ], + "blocks": [ + { + "bbox": [ + 50, + 214, + 287, + 337 + ], + "lines": [ + { + "bbox": [ + 50, + 214, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 50, + 214, + 287, + 337 + ], + "type": "table", + "html": "
MethodChamfer-L2F-ScoreNC
MeanMedian\\( F1^{0.005} \\)\\( F1^{0.01} \\)
Input0.3630.35548.5088.34-
Watertight GT2.6282.29368.8281.60-
GT0.0760.07495.7099.99-
NDF [20]0.2020.19377.4097.9779.1
GIFS [82]0.1280.12388.0599.31-
CAP-UDFBPA0.1410.13884.8499.3381.8
CAP-UDF [89]0.1190.11488.5599.8282.5
Ours0.0980.09792.1899.9085.0
", + "image_path": "c55dc890964e84c74e01c2ee6029bb3732987b8951e9ca9d75c86b3f523b7e4d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 341, + 287, + 363 + ], + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 363 + ], + "type": "text", + "content": "Table 1. Surface reconstruction for point cloud on ShapeNet cars dataset (Chamfer-L2×10^4)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 373, + 287, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 398 + ], + "type": "text", + "content": "and the gradient at their projections " + }, + { + "bbox": [ + 46, + 373, + 287, + 398 + ], + "type": "inline_equation", + "content": "\\hat{Q} = \\{\\hat{q}\\}_{i=1}^{M}" + }, + { + "bbox": [ + 46, + 373, + 287, + 398 + ], + "type": "text", + "content": " to the zero level set, formulated as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 55, + 406, + 287, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 406, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 55, + 406, + 287, + 439 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {p r o j}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} \\gamma_ {i} \\left(1 - \\left| \\frac {\\nabla f (q _ {i}) \\cdot \\nabla f (\\hat {q} _ {i})}{| | \\nabla f (q _ {i}) | | _ {2} \\cdot | | \\nabla f (\\hat {q} _ {i}) | | _ {2}} \\right|\\right), \\tag {5}", + "image_path": "9a736dd5ea1cb77dadffa910228270e8ba88aefc45bf59774b5b45a08e28f279.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\gamma_{i}" + }, + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "type": "text", + "content": " is the factor for weighting the gradient constraint at the query " + }, + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "type": "text", + "content": ", indicating the importance of optimizing query " + }, + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 46, + 446, + 287, + 483 + ], + "type": "text", + "content": ", formulated as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 121, + 494, + 287, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 494, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 121, + 494, + 287, + 509 + ], + "type": "interline_equation", + "content": "\\gamma_ {i} = \\exp (- \\lambda | f (q _ {i}) |). \\tag {6}", + "image_path": "70faad301a7b67ae20565772edb78bc52d141bf6f5ee09fcc196be12f8c0ae7c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 513, + 287, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 570 + ], + "type": "text", + "content": "We set " + }, + { + "bbox": [ + 46, + 513, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 513, + 287, + 570 + ], + "type": "text", + "content": " to increase when queries are closer to the zero level set where " + }, + { + "bbox": [ + 46, + 513, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 513, + 287, + 570 + ], + "type": "text", + "content": " is a hyper-parameter to control the increasing speed. The nonuniform weighting encouraging the network to focus more on the optimizations near the zero level set of UDF." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 572, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 287, + 630 + ], + "type": "text", + "content": "While " + }, + { + "bbox": [ + 46, + 572, + 287, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{proj}" + }, + { + "bbox": [ + 46, + 572, + 287, + 630 + ], + "type": "text", + "content": " can provide an effective guidance to the gradients at zero level set, we further explore a more accurate unsigned distance constraint for correcting the distance values at the zero level set of UDF. The implemented loss is defined as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 119, + 629, + 287, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 629, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 119, + 629, + 287, + 662 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i s t}} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} | f (p _ {i}) |, \\tag {7}", + "image_path": "e91a4c22ed0d2ac0ba7b16eb1c278b6bdefda01d847dc707996ae1ff12e4c157.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 665, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 287, + 689 + ], + "type": "inline_equation", + "content": "p_i \\in P" + }, + { + "bbox": [ + 46, + 665, + 287, + 689 + ], + "type": "text", + "content": " is the raw point cloud indicating the exact surface to be represented." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "Gradient-Surface Orthogonal Constraint. The key idea to guide the learning of zero level set using the rest level sets" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "text", + "content": "is based on the observation that the non-zero level sets are much more reliable. To bring a more robust guidance to the optimization of zero level set, we introduce an addition gradient constraint on queries to learn a more stable and regular level sets at the non-zero level sets of UDF by enforcing the gradient orthogonal to the tangent plane of the surface. We design a novel loss to encourage the consistency between the gradient direction at a query " + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "text", + "content": " and the direction from " + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "text", + "content": " to its closest point " + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "inline_equation", + "content": "p_{i}" + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 211, + 545, + 319 + ], + "type": "text", + "content": ", formulated as:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 315, + 323, + 545, + 356 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 323, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 315, + 323, + 545, + 356 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {o r t h}} = \\frac {1}{M} \\sum_ {i = 1} ^ {M} (1 - | \\frac {\\nabla f (q _ {i}) \\cdot T (q _ {i} , p _ {i})}{| | \\nabla f (q _ {i}) | | _ {2} \\cdot | | T (q _ {i} , p _ {i}) | | _ {2}} |), \\tag {8}", + "image_path": "84d634a80d5f3386a7812200181eae721c4d22912e386104a0d97f45dc6a2af0.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "inline_equation", + "content": "T(q_{i},p_{i})" + }, + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "text", + "content": " is the direction from " + }, + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 361, + 545, + 384 + ], + "type": "text", + "content": ". The constraint is illustrated in Fig. 1." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": "A more naive way of introducing the direction vector " + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "inline_equation", + "content": "T(q_{i},p_{i})" + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": " for learning is to explicitly substitute the gradient " + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\nabla f(q_{i})" + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": " with the direction vector " + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "inline_equation", + "content": "T(q_{i},p_{i})" + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": ", as proposed in GenSDF [21]. However, " + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "inline_equation", + "content": "T(q_{i},p_{i})" + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": " is obviously not the exact direction for " + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": " to reach the approximated surface since the raw point cloud is the discrete representation of the surface, and " + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "inline_equation", + "content": "p_{i}" + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": " is not the exact nearest points of " + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": " in the approximated surface, which leads to wrong supervisions for GenSDF." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "text", + "content": "On the contrary, We introduce a more flexible way by treating direction vector " + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "inline_equation", + "content": "T(q_{i},p_{i})" + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "text", + "content": " as an optimization objective, which enables the networks to accommodate the inconsistency between the closest point " + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "text", + "content": " and the closest point " + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\hat{q}_i" + }, + { + "bbox": [ + 304, + 492, + 545, + 552 + ], + "type": "text", + "content": " predicted by the networks." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 552, + 543, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 543, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 543, + 563 + ], + "type": "text", + "content": "Loss Function. Finally, our loss function is formulated as:" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 336, + 570, + 545, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 570, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 336, + 570, + 545, + 583 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {C D}} + \\alpha_ {1} \\mathcal {L} _ {\\text {p r o j}} + \\alpha_ {2} \\mathcal {L} _ {\\text {d i s t}} + \\alpha_ {3} \\mathcal {L} _ {\\text {o r t h}}, \\tag {9}", + "image_path": "5a35e69839e37e8d472e1fbab74188d9f96d44a9a04ca23fceee799ad51c21e7.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 588, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 588, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 588, + 545, + 611 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 588, + 545, + 611 + ], + "type": "inline_equation", + "content": "\\alpha_{1},\\alpha_{2}" + }, + { + "bbox": [ + 304, + 588, + 545, + 611 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 588, + 545, + 611 + ], + "type": "inline_equation", + "content": "\\alpha_{3}" + }, + { + "bbox": [ + 304, + 588, + 545, + 611 + ], + "type": "text", + "content": " are the balance weights for our designed three losses to learn accurate zero level set of UDF." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 612, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 612, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 612, + 545, + 659 + ], + "type": "text", + "content": "Applications. The zero level set of UDF indicates the location of represented 3D geometries. Thus, a well-learned UDF with accurate and continuous zero level set can be adopt to different 3D applications." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 659, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 659, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 659, + 545, + 696 + ], + "type": "text", + "content": "Surface Reconstruction. Following previous methods [89, 27], the surfaces can be extracted from the zero level set of UDF by judging gradient directions, formulated as:" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 364, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 364, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {D} \\left(q _ {i}, q _ {j}\\right) = \\nabla f \\left(q _ {i}\\right) \\cdot \\nabla f \\left(q _ {j}\\right), \\tag {10}", + "image_path": "0e0fb224a899c8210029c965a2165837e7fe13a7f4fedd9045c6e3a920a11fbe.jpg" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3184" + } + ] + } + ], + 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BurghersLoungeCopyroomStonewallTotempole
L2CDL1CDNCL2CDL1CDNCL2CDL1CDNCL2CDL1CDNCL2CDL1CDNC
500/m2ConvONet [64]26.970.0810.9059.0440.0460.89410.080.0460.88517.700.0630.9092.1650.0240.937
LIG [36]3.0800.0460.8406.7290.0520.8314.0580.0380.8104.9190.0430.8789.380.0620.887
DeepLS [13]0.7140.0200.92310.880.0770.8140.5520.0150.9070.6730.0180.95121.150.1220.927
NDF [20]0.5460.0180.9170.3140.0120.9210.2420.0120.9070.2260.0120.9491.0490.0250.939
OnSurf [52]0.6090.0180.9300.5290.0130.9260.4830.0140.9080.6660.0130.9552.0250.0410.954
CAP-UDF [89]0.1920.0110.9110.0990.0090.9110.1200.0090.9020.0690.0080.9580.1310.0100.954
Ours0.1610.0090.9160.0870.0060.9330.1020.0070.9200.0610.0070.9640.1140.0070.960
1000/m2ConvONet [64]27.460.0790.9079.540.0460.89410.970.0450.89220.460.0690.9052.0540.0210.943
LIG [36]3.0550.0450.8359.6720.0560.8333.610.0360.8105.0320.0420.8799.580.0620.887
DeepLS [13]0.4010.0170.9206.1030.0530.8480.6090.0210.9010.3200.0150.9540.6010.0170.950
NDF [20]1.1680.0270.9010.3930.0140.9100.2690.0130.9080.5090.0190.9362.0200.0360.922
OnSurf [52]1.3390.0310.9290.4320.0140.9340.4050.0140.9140.2660.0140.9571.0890.0290.954
CAP-UDF [89]0.1910.0100.9100.0920.0080.9270.1130.0090.9110.0660.0070.9620.1390.0090.955
Ours0.1460.0090.9210.0680.0060.9410.0930.0070.9250.0500.0050.9700.1070.0070.960
", + "image_path": "d0d7a566dfaa84879516422d0ea29860cbd397433c032bdc9cf7961484684d65.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 151, + 392, + 440, + 402 + ], + "lines": [ + { + "bbox": [ + 151, + 392, + 440, + 402 + ], + "spans": [ + { + "bbox": [ + 151, + 392, + 440, + 402 + ], + "type": "text", + "content": "Table 2. Surface reconstruction for point clouds under 3D Scene. " + }, + { + "bbox": [ + 151, + 392, + 440, + 402 + ], + "type": "inline_equation", + "content": "\\mathrm{L}2\\mathrm{{CD}} \\times {1000}" + }, + { + "bbox": [ + 151, + 392, + 440, + 402 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "text", + "content": "to classify whether two queries " + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "inline_equation", + "content": "q_{1}" + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "inline_equation", + "content": "q_{2}" + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "text", + "content": " are in the same " + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(q_i,q_j) > 0" + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "text", + "content": " or the opposite side " + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(q_i,q_j) < 0" + }, + { + "bbox": [ + 46, + 409, + 287, + 456 + ], + "type": "text", + "content": " of the approximated surface. The marching cubes-like algorithm is then used to extract surfaces." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 456, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 493 + ], + "type": "text", + "content": "Unsupervised Point Normal Estimation. With a well learned zero level set, we compute the gradients at the raw point clouds " + }, + { + "bbox": [ + 46, + 456, + 287, + 493 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 456, + 287, + 493 + ], + "type": "text", + "content": " as their estimated normals, formulated as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 111, + 502, + 287, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 502, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 111, + 502, + 287, + 516 + ], + "type": "interline_equation", + "content": "\\mathcal {N} (P) = \\{\\nabla f (p) \\}, p \\in P. \\tag {11}", + "image_path": "313a44ab65b6d00a13de6ca61bec1e04b36f675d46055efb3da84cd3a1d22178.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "text", + "content": "Unsupervised Point Cloud Upsampling. We randomly sample queries around " + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "text", + "content": ", and then move them to the zero level set with Eq. 3 as the upsampled points of " + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "text", + "content": ". We further filter the queries with unsigned distance values larger than a threshold " + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "text", + "content": " for avoiding outliers. The procedure for upsampling " + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "text", + "content": " with a factor of " + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 525, + 287, + 597 + ], + "type": "text", + "content": " is formulated as:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 83, + 609, + 287, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 609, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 83, + 609, + 287, + 623 + ], + "type": "interline_equation", + "content": "\\mathcal {U} (P) = \\left\\{\\hat {q} _ {i}, i \\in [ 1, N \\times G ] \\mid f \\left(q _ {i}\\right) < \\beta \\right\\} \\tag {12}", + "image_path": "52dd251006ed969ab0cd942eca1ff3570061dfe61cadc7166a100b1e978a694f.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 633, + 128, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 128, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 128, + 647 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "For evaluating the performance of our method, we conduct experiments on surface reconstruction from raw point clouds of shapes (Sec. 4.1), room-level scenes (Sec. 4.2), and real scans (Sec. 4.4), where we also show our results on large-scale driving scenes obtained by fusing LiDAR" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 409, + 546, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 546, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 546, + 468 + ], + "type": "text", + "content": "depths in Sec. 4.3. We further explore the ability of our learned UDF with accurate zero level set for unsupervised point normal estimation (Sec. 4.5) and unsupervised point upsampling (Sec. 4.6). Finally, we conduct ablation studies in Sec. 4.7." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 478, + 491, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 478, + 491, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 478, + 491, + 491 + ], + "type": "text", + "content": "4.1. Surface Reconstruction for Shapes" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 497, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 546, + 628 + ], + "type": "text", + "content": "Dataset and Metrics. To explore the ability of our method in representing shapes with arbitrary topology, we follow previous methods [89, 82] to conduct experiments on the \"Car\" category of ShapeNet dataset which contains the largest number of shapes with multi-layer structures or open surfaces. We sample 10K points per shape as the input for surface reconstruction. For evaluating the performances, we follow the common setting [82] to sample 100K points from the reconstructed surfaces and leverage Chamfer Distance, Normal Consistency [57] and F-score with a threshold of 0.005 / 0.01 as the evaluation metrics." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Comparisons. We compare our method with the state-of-the-art shape reconstruction methods NDF [20], GIFS [82] and CAP-UDF [89]. We report the quantitative comparison results in Tab. 1, where \"Watertight GT\" is the result of sampling points from the watertight ground truth, indicating the best performance of the methods base on SDF or occupancy. We also show the superior limit of the dataset" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3185" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 69, + 545, + 218 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 545, + 218 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 545, + 218 + ], + "type": "image", + "image_path": "b4cf5970fcbfd1bb772ed9db7a5d7f4a8ce853325a81a4d1dc72300451e87863.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 221, + 485, + 233 + ], + "lines": [ + { + "bbox": [ + 107, + 221, + 485, + 233 + ], + "spans": [ + { + "bbox": [ + 107, + 221, + 485, + 233 + ], + "type": "text", + "content": "Figure 5. Surface reconstruction results on KITTI odometry dataset (Sequence 00, frame 3000 to 4000)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 244, + 288, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 244, + 288, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 288, + 316 + ], + "type": "text", + "content": "by sampling points on the ground truth mesh and report the result as \"GT\". Tab. 1 shows that our method achieves the best performance over all the baselines in terms of all metrics. The visual comparison in Fig. 3 further shows that our methods produce more continuous and accurate geometries over all baselines." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 287, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 287, + 335 + ], + "type": "text", + "content": "4.2. Surface Reconstruction for Room-Level Scenes" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 341, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 472 + ], + "type": "text", + "content": "Dataset and Metrics. We further explore our performance on real scene scans to demonstrate the ability of our methods to scale to large-scale point clouds. Following On-Surf [52], we conduct experiments on the 3D Scene dataset consisting of complex scenes with open surfaces and scan noises. The input point cloud is achieved by sampling 500 or 1000 points per " + }, + { + "bbox": [ + 46, + 341, + 287, + 472 + ], + "type": "inline_equation", + "content": "m^2" + }, + { + "bbox": [ + 46, + 341, + 287, + 472 + ], + "type": "text", + "content": " uniformly for each scene. We follow the common setting [52, 89] to sample " + }, + { + "bbox": [ + 46, + 341, + 287, + 472 + ], + "type": "inline_equation", + "content": "1M" + }, + { + "bbox": [ + 46, + 341, + 287, + 472 + ], + "type": "text", + "content": " points on both the reconstructed and the ground truth meshes. We leverage L1 / L2 Chamfer Distance and Normal Consistency as the evaluation metrics." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 473, + 288, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 288, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 288, + 605 + ], + "type": "text", + "content": "Comparisons. With different point densities, we compare our method with the state-of-the-art methods ConvONet [64], LIG [36], DeepLS [13], OnSurf [52], NDF [20] and CAP-UDF [89]. The numerical comparison in Tab. 2 demonstrates our superior performance in all scenes. We further present a visual comparison in Fig. 4, where the input point clouds contains 1K points/" + }, + { + "bbox": [ + 46, + 473, + 288, + 605 + ], + "type": "inline_equation", + "content": "m^2" + }, + { + "bbox": [ + 46, + 473, + 288, + 605 + ], + "type": "text", + "content": ". The visualization further shows that our method can reconstruct more detailed and smooth surfaces in complex scenes, where the other UDF-base methods NDF and CAP-UDF produce fragmented surfaces." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 611, + 268, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 268, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 268, + 624 + ], + "type": "text", + "content": "4.3. Large-Scale Driving Scene Reconstruction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "Dataset. To further demonstrate our scalability to extremely large scenes, we follow NGS [35] to apply our method to KITTI dataset [23]. We use the LiDAR scans of frame 3000 to 4000 in Squeeze00 subset of KITTI dataset as the full input, which are transformed into world coordinates using the provided camera trajectories. We leverage the slide-window strategy to divide the full scene into 15" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 314, + 242, + 539, + 357 + ], + "blocks": [ + { + "bbox": [ + 314, + 242, + 539, + 357 + ], + "lines": [ + { + "bbox": [ + 314, + 242, + 539, + 357 + ], + "spans": [ + { + "bbox": [ + 314, + 242, + 539, + 357 + ], + "type": "table", + "html": "
MethodChamfer-L1F-ScoreNC
IGR [25]0.17875.586.9
Point2Mesh [31]0.11664.8-
SPSR [40]0.23273.5-
SAP [63]0.07683.088.6
Neural-Pull [51]0.10679.787.2
NDF [20]0.23868.680.4
CAP-UDF [89]0.07384.588.6
Ours0.07185.191.0
", + "image_path": "a9006759255c129c7f2176153e85f4e51efcddfa6648673c35f0ee39575b4eaf.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 358, + 536, + 369 + ], + "lines": [ + { + "bbox": [ + 306, + 358, + 536, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 536, + 369 + ], + "type": "text", + "content": "Table 3. Surface reconstruction for point cloud on SRB dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 374, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 411 + ], + "type": "text", + "content": "blocks of size " + }, + { + "bbox": [ + 304, + 374, + 545, + 411 + ], + "type": "inline_equation", + "content": "51.2m^3" + }, + { + "bbox": [ + 304, + 374, + 545, + 411 + ], + "type": "text", + "content": ", where we sample 300K points per block as the local input to train our network. The final scene is achieve by blending the reconstructed local scenes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 411, + 546, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 546, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 546, + 495 + ], + "type": "text", + "content": "Analysis. The reconstruction results under KITTI scenes is shown in Fig. 5, where our method reproduces visualappealing performances with accurate geometries. Note that: 1) The LiDAR scans contain large amount of noises, especially in the difficult driving scenes. 2) Our method learns to reconstruct surfaces directly from the raw point cloud without learning priors from large-scale datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 503, + 509, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 503, + 509, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 503, + 509, + 515 + ], + "type": "text", + "content": "4.4. Surface Reconstruction for Real Scans" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 521, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 641 + ], + "type": "text", + "content": "Dataset and Metrics. We demonstrate our advantages for surface reconstruction from real scans by conducting experiments on the Surface Reconstruction Benchmarks [77] (SRB). We follow previous methods [63, 89] to leverage Chamfer Distance and F-Score with a threshold of " + }, + { + "bbox": [ + 304, + 521, + 545, + 641 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 521, + 545, + 641 + ], + "type": "text", + "content": " for evaluation. Note that the ground truth of SRB dataset is dense point cloud containing millions of points. For a comprehensive comparison on the reconstruction quality, we further evaluate the Normal Consistency by first converting the ground truth into meshes with BPA [8] algorithm." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 546, + 713 + ], + "type": "text", + "content": "Comparisons. We first report our numerical comparison under SRB dataset with the classic and learning-based methods in Tab. 3. The compared methods include IGR [25], Point2Mesh [31], Screened Poisson Surface Reconstruction (SPSR) [40], Shape As Points (SAP) [63], Neural-Pull [51], NDF [20] and CAP-UDF [89]. Our method" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3186" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 289, + 163 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 289, + 163 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 289, + 163 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 289, + 163 + ], + "type": "image", + "image_path": "994e2d33482fbd100d615528e35b60deb47a125ce9f8d55a259cd9d7f9be067a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 165, + 287, + 187 + ], + "lines": [ + { + "bbox": [ + 47, + 165, + 287, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 287, + 187 + ], + "type": "text", + "content": "Figure 6. Visual comparisons of surface reconstruction on SRB dataset. SRB dataset provides only point clouds as GT." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 198, + 287, + 321 + ], + "blocks": [ + { + "bbox": [ + 50, + 198, + 287, + 321 + ], + "lines": [ + { + "bbox": [ + 50, + 198, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 50, + 198, + 287, + 321 + ], + "type": "table", + "html": "
MethodCleanStripGradientaverage
SupervisedPCPNet [26]9.6611.4713.4211.61
Hough [9]10.2312.4711.0211.24
Nesti-Net [7]6.998.479.008.15
IterNet [41]6.727.737.517.32
DeepFit [5]6.517.927.317.25
UnsupervisedJet [12]12.2313.3913.1312.92
PCA [1]12.2913.6612.8112.92
Ours (w/o ZLS-c)7.307.747.787.61
Ours6.517.457.647.20
", + "image_path": "9d5280b94cedfa4a73da65e2195c30a82eb4d915d25d9aabe12e4f686b596fe3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 341, + 287, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 287, + 389 + ], + "type": "text", + "content": "achieves the best performance in all metrics as shown in Tab. 3. The visual comparison in Fig. 6 further shows that our methods produce more accurate and smooth geometries over all baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 396, + 253, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 253, + 408 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 253, + 408 + ], + "type": "text", + "content": "4.5. Unsupervised Point Normal Estimation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 414, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 556 + ], + "type": "text", + "content": "Dataset and Metrics. We adopt the widely-used PCPNet [26] dataset to evaluate our method on the task of point normal estimation. Each point cloud in the PCPNet dataset contains 100K points. We conduct experiments under three different settings. The inputs of \"Clean\" setting are sampled uniformly on shapes, and two additional settings with varying point densities (Stripes and Gradients) are added to explore our performance in handling irregular data. Following previous methods [5, 26], we sample 5000 points per shape and compute the angle root mean square error (RMSE) between the predicted normals and the ground truth normals as the evaluation metrics." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "Comparisons. We conduct a comparison with traditional normal estimation methods including PCA [1], Jets [12] and the state-of-the-art learning-based methods PCPNet [26], HoughCNN [9], Nesti-Net [7], Iter-Net [41] and DeepFit [5]. Note that all the previous learning-based methods are designed in a supervised manner which requires a large scale dataset for training, while we extract normals directly from the unsigned distance fields learned from raw point cloud in an unsupervised way. The numerical results in Tab. 4 show that our method achieves a comparable or even better performance than the state-of-the-art supervised methods. The results also show the effectiveness of our method where the performance degrades from 7.20 to 7.61 without" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 73, + 542, + 393 + ], + "blocks": [ + { + "bbox": [ + 310, + 73, + 542, + 393 + ], + "lines": [ + { + "bbox": [ + 310, + 73, + 542, + 393 + ], + "spans": [ + { + "bbox": [ + 310, + 73, + 542, + 393 + ], + "type": "image", + "image_path": "5fd88d82adf961f6ca3d37a28d9f96b3aa5c116d976091f0cd67a67eddb4f489.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 396, + 545, + 418 + ], + "lines": [ + { + "bbox": [ + 306, + 396, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 545, + 418 + ], + "type": "text", + "content": "Figure 7. Visual comparisons on error maps of point normal estimation on PCPNet dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 427, + 545, + 579 + ], + "blocks": [ + { + "bbox": [ + 47, + 324, + 278, + 335 + ], + "lines": [ + { + "bbox": [ + 47, + 324, + 278, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 278, + 335 + ], + "type": "text", + "content": "Table 4. Point normal estimation results on the PCPNet dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 427, + 545, + 579 + ], + "lines": [ + { + "bbox": [ + 309, + 427, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 309, + 427, + 545, + 579 + ], + "type": "table", + "html": "
MethodSupervised?P2FCDHD
PU-Net [85]Yes6.840.728.94
MPU [83]Yes3.960.496.11
PU-GAN [42]Yes2.330.284.64
Dis-PU [43]Yes2.010.222.83
EAR [34]No5.820.527.37
L2G-AE [46]No39.376.3163.23
SPU-Net (Tr2T) [47]No5.970.382.24
SPU-Net (All2T)No5.790.372.55
SPU-Net (Te2T)No6.850.412.18
Ours (w/o ZLS-C)No1.430.242.16
OursNo1.020.191.55
", + "image_path": "0887b8a0fc633d9a67f6c5f039b52085cf75c5edfc439a4c6c63359a5610a2ed.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 584, + 541, + 596 + ], + "lines": [ + { + "bbox": [ + 306, + 584, + 541, + 596 + ], + "spans": [ + { + "bbox": [ + 306, + 584, + 541, + 596 + ], + "type": "text", + "content": "Table 5. Point cloud upsampling results on the PU-GAN dataset." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 604, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 604, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 305, + 604, + 545, + 640 + ], + "type": "text", + "content": "our constraints. The visual comparison in Fig. 7 shows that our method produces more accurate estimations compared to other methods, especially on the complex geometries." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 647, + 511, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 511, + 661 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 511, + 661 + ], + "type": "text", + "content": "4.6. Unsupervised Point Cloud Upsampling" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "content": "Dataset and Metrics. For the task of point cloud upsampling, we follow previous methods [47, 43] to conduct experiments on the dataset provided by PU-GAN [42]. We evaluate our method under the setting to generate 8,198" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3187" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 547, + 185 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 185 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 185 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 185 + ], + "type": "image", + "image_path": "29496caedd699d5607c87b3b6f95ccaf6f883e73ac91e5c90c24cdb0d67bb907.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 154, + 188, + 437, + 200 + ], + "lines": [ + { + "bbox": [ + 154, + 188, + 437, + 200 + ], + "spans": [ + { + "bbox": [ + 154, + 188, + 437, + 200 + ], + "type": "text", + "content": "Figure 8. Visual comparisons of point cloud upsampling on PU-GAN dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 211, + 287, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 287, + 246 + ], + "type": "text", + "content": "points for each sparse input with 2,048 points. We adopt Chamfer Distance (CD), Hausdorff Distance (HD) and Point-to-Surface distance (P2F) as the evaluation metrics." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 290, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 290, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 290, + 390 + ], + "type": "text", + "content": "Comparisons. We compare our method with the state-of-the-art supervised methods PU-Net [85], MPU [83], PU-GAN [42], Dis-PU [43] and unsupervised methods EAR [34], L2G-AE [46] and SPU-Net [47]. The quantitative comparison is shown in Tab. 5, where our method outperforms the previous supervised and unsupervised methods significantly. The results also show the effectiveness of our method where the performance degrades from 1.55 to 2.16 in terms of HD without our designed constraints. The visualization in Fig. 8 further shows that our upsampling results are more smooth and uniform even compared with the state-of-the-art supervised methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 396, + 149, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 149, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 149, + 407 + ], + "type": "text", + "content": "4.7. Ablation Studies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 415, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 474 + ], + "type": "text", + "content": "We conduct ablation studies to demonstrate the effectiveness of each proposed constraint and explore the effect of some important hyper-parameters. We report the performance under a subset of ShapeNet Cars dataset in terms of L2 Chamfer Distance " + }, + { + "bbox": [ + 46, + 415, + 287, + 474 + ], + "type": "inline_equation", + "content": "(\\times 10^{4})" + }, + { + "bbox": [ + 46, + 415, + 287, + 474 + ], + "type": "text", + "content": " and Normal Consistency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "type": "text", + "content": "Effect of each Design. We first justify the effectiveness of each proposed constraint in Tab. 6. We report the performance without all the three designed losses as \"w/o ZLS-C\". We explore each loss by reporting the results without level set projection loss as \"w/o " + }, + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{proj}}" + }, + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "type": "text", + "content": "\", surface unsigned distance loss as \"w/o " + }, + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist}}" + }, + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "type": "text", + "content": "\", gradient-surface orthogonal loss as \"w/o " + }, + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{orth}}" + }, + { + "bbox": [ + 46, + 474, + 287, + 642 + ], + "type": "text", + "content": "\" and adaptive point weight as \"w/o AW\". We replace our level set projection constraint with the GenSDF-style [21] optimization as \"GenSDF-Style\". We further constrain the level set projection loss on a randomly selected non-zero level set other than the zero level set and report the performance as \"Non-zero LSC\". The result demonstrates that the zero level set is the key factor that influence the representation ability of UDF." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 701 + ], + "type": "text", + "content": "Weight of Level Set Projection Loss. We report the performance with different weights of the level set projection loss " + }, + { + "bbox": [ + 46, + 642, + 287, + 701 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{proj}}" + }, + { + "bbox": [ + 46, + 642, + 287, + 701 + ], + "type": "text", + "content": " in Tab. 7. We found that a suitable weight of " + }, + { + "bbox": [ + 46, + 642, + 287, + 701 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{proj}}" + }, + { + "bbox": [ + 46, + 642, + 287, + 701 + ], + "type": "text", + "content": " will improve the reconstruction accuracy, and it may affect the optimization to converge if we weight too much." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "Weight of Surface Unsigned Distance Loss. We further" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 208, + 547, + 277 + ], + "blocks": [ + { + "bbox": [ + 309, + 208, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 309, + 208, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 309, + 208, + 547, + 277 + ], + "type": "table", + "html": "
w/o ZLS-Cw/o Lprojw/o Ldistw/o Lorth
L2CD0.1260.1070.1010.096
NC82.782.983.984.1
w/o AWGenSDF-StyleNon-zero LSCOurs
L2CD0.0960.1010.0980.091
NC84.283.983.584.4
", + "image_path": "cbccebd6e8582bd73449ff848a25f2922cce9db83b911eb4877735bbb36216c5.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 308, + 293, + 546, + 325 + ], + "blocks": [ + { + "bbox": [ + 359, + 277, + 492, + 286 + ], + "lines": [ + { + "bbox": [ + 359, + 277, + 492, + 286 + ], + "spans": [ + { + "bbox": [ + 359, + 277, + 492, + 286 + ], + "type": "text", + "content": "Table 6. Effect of framework design." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 293, + 546, + 325 + ], + "lines": [ + { + "bbox": [ + 308, + 293, + 546, + 325 + ], + "spans": [ + { + "bbox": [ + 308, + 293, + 546, + 325 + ], + "type": "table", + "html": "
0.0010.0020.010.1
L2CD0.0950.0910.1620.359
NC84.284.483.479.6
", + "image_path": "6ae2113556c40bb51acc69182ef2408a28ebc76258eb91663eacc28e258e49b8.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 351, + 547, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 547, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 547, + 388 + ], + "type": "text", + "content": "explore the effect of weights " + }, + { + "bbox": [ + 305, + 351, + 547, + 388 + ], + "type": "inline_equation", + "content": "\\alpha_{2}" + }, + { + "bbox": [ + 305, + 351, + 547, + 388 + ], + "type": "text", + "content": " for the surface unsigned distance loss in Tab 8, where we found that a too large or too small weight will degenerate the performance." + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 308, + 402, + 546, + 434 + ], + "blocks": [ + { + "bbox": [ + 347, + 324, + 504, + 335 + ], + "lines": [ + { + "bbox": [ + 347, + 324, + 504, + 335 + ], + "spans": [ + { + "bbox": [ + 347, + 324, + 504, + 335 + ], + "type": "text", + "content": "Table 7. Weight of level set projection loss." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 402, + 546, + 434 + ], + "lines": [ + { + "bbox": [ + 308, + 402, + 546, + 434 + ], + "spans": [ + { + "bbox": [ + 308, + 402, + 546, + 434 + ], + "type": "table", + "html": "
0.0010.010.11
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Effect of adaptive per point weights." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3188" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 289, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 289, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 289, + 247 + ], + "type": "text", + "content": "In this paper, we justify that an accurate and continuous zero level set of unsigned distance functions is the key factor to represent complex 3D geometries. We therefore propose two novel constraints on UDF to achieve a more continuous zero level set by projecting non-zero level set to guide the optimization of zero level set. With the ability of learning consistent and accurate zero level set of UDF, we explore three different 3D applications including surface reconstruction, unsupervised point normal estimation and unsupervised point cloud upsampling, where the visual and numerical comparisons with the state-of-the-art supervised/unsupervised methods justify our effectiveness ans show our superiority over the latest methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 258, + 157, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 157, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 157, + 272 + ], + "type": "text", + "content": "6. 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Overview and reconstruction results of the Occ-SDF hybrid neural scene representation. Aided with the feature rendering scheme (Sec. 4) and the hybrid representation (Sec. 5), our method yields results with more detailed structures in room-level scenes compared to the state-of-the-art, particularly for those low intensities and detailed structures." + ], + "image_footnote": [], + "bbox": [ + 109, + 323, + 872, + 538 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 596, + 312, + 610 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Implicit neural rendering, using signed distance function (SDF) representation with geometric priors like depth or surface normal, has made impressive strides in the surface reconstruction of large-scale scenes. However, applying this method to reconstruct a room-level scene from images may miss structures in low-intensity areas and/or small, thin objects. We have conducted experiments on three datasets to identify limitations of the original color rendering loss and priors-embedded SDF scene representation.", + "bbox": [ + 75, + 628, + 470, + 752 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our findings show that the color rendering loss creates an optimization bias against low-intensity areas, resulting in gradient vanishing and leaving these areas unoptimized. To address this issue, we propose a feature-based color rendering loss that utilizes non-zero feature values to bring back optimization signals. Additionally, the SDF representation can be influenced by objects along a ray path, disrupting the monotonic change of SDF values when a single", + "bbox": [ + 75, + 757, + 470, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "object is present. Accordingly, we explore using the occupancy representation, which encodes each point separately and is unaffected by objects along a querying ray. Our experimental results demonstrate that the joint forces of the feature-based rendering loss and Occ-SDF hybrid representation scheme can provide high-quality reconstruction results, especially in challenging room-level scenarios. The code is available at https://github.com/shawLyu/Occ-SDF-Hybrid", + "bbox": [ + 497, + 597, + 892, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 747, + 631, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reconstructing a 3D scene from a series of multi-view images is a crucial problem in the realm of computer vision. This process has widespread applications in various fields such as animation, gaming, and virtual/augmented reality (VR/AR). The recent trend is to represent a 3D scene as an implicit function parameterized by a neural network [13, 19, 26, 21], whose optimization is supervised by ex", + "bbox": [ + 497, + 770, + 890, + 868 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 51, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 253, + 48, + 789, + 61 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 332, + 62, + 709, + 74 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 304, + 74, + 739, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8940", + "bbox": [ + 468, + 889, + 502, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "plicit 3D data like point cloud or real SDF value. Recent advancements in neural radiance field (NeRF) [14] further enable learning an implicit 3D representation from purely sparse posed images [35, 15].", + "bbox": [ + 75, + 125, + 468, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, when it comes to producing high-quality novel-view synthesis, these methods frequently utilize volume density [14] to represent the 3D geometry. Unfortunately, this approach does not adequately constrain the 3D geometry in the presence of ambiguities [18], ultimately leading to poor surface reconstructions (as depicted in Fig. 1: Volume Density).", + "bbox": [ + 75, + 182, + 468, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accordingly, research efforts have been made to exploit geometry-friendly representations, including signed distance function (SDF) [32, 34, 19] or occupancy [18], whose zero-level set can be extracted to become the concerned 3D surface. Albeit improving quality, they consider the reconstruction only of a single object, thereby, the performance degrades dramatically when applied to scene-level surface reconstruction, i.e., representing a room (Fig. 1: SDF). An attribute is that reconstructing texture-less areas often suffers from ambiguous visual cues with only RGB loss as the regularization. To address this problem, recent research has attempted to incorporate semantic [8] or geometric priors (depth/normal [36, 31] constraints) to further regularize scene-level reconstruction. With SDF-based representation and geometric priors [36], the reconstruction quality has been greatly improved (Fig. 1: SDF + Geometry Priors), especially concerning large flat areas and objects. However, it still cannot faithfully reconstruct the 3D scene with missing structures in low-intensity dark areas and small/thin objects (Fig. 1: SDF + Geometry Priors).", + "bbox": [ + 75, + 281, + 468, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The above observation motivates us to dive into bridging the remaining missing blocks of existing neural surface representation methods. Notably, we focus on the SDF-based representation as it achieves state-of-the-art performance and has been widely adopted. Our analysis suggests that both the RGB color rendering formulation and SDF representation have clear limitations preventing existing solutions from fully unleashing the potential of implicit neural surface representation for large-scale room-level scenes.", + "bbox": [ + 75, + 560, + 468, + 685 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "First, the color itself can show a significant impact on the optimization of geometric representation relying on the original RGB-based rendering formula [14], namely color bias. In particular, dark pixels with small intensity values will make the partial derivation of the loss with respect to the corresponding SDF value become zero, corrupting the optimization and resulting in missing structures in dark areas (see for example in Fig. 1: Low Intensities). Accordingly, herein instead of directly calculating the weighted color, we first compute weighted features and then use a learnable multi-layer perceptron (MLP) to decode the final rendering color. In such a way, we would still be able to effectively optimize the corresponding geometry represent", + "bbox": [ + 75, + 686, + 468, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tation as long as the feature vector contains non-zero values.", + "bbox": [ + 497, + 125, + 889, + 138 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Second, the vanilla SDF-based neural rendering only considers a single ray directly passing through the object surface from the empty space and ignores objects along the ray [32, 34]. This configuration violates scene-level geometry where the existence of multiple objects clearly affects the distributions of SDF (Fig. 5(a)). Meanwhile, the optimization of thin structures and small objects, which naturally has small sampling probability, will be greatly degraded by this violation even with correct geometry prior and the structure will be erased to minimize the global geometry loss (Fig. 1: Detailed Structures).", + "bbox": [ + 497, + 138, + 890, + 290 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition, although occupancy-based representations are likely to generate unwanted structure and cannot warrant a smooth surface reconstruction (Fig. 1), they are often sufficiently robust to objects along the ray and free from object interference in scene-level data. Therefore, during optimization, we propose to describe the room-level scene using occupancy in conjunction with signed distance functions (SDFs) to compensate for each other's defects.", + "bbox": [ + 497, + 292, + 890, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The technical contributions are as follows:", + "bbox": [ + 517, + 402, + 801, + 415 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We explore an improved feature rendering scheme to overcome the problem of vanishing gradients in neural implicit reconstruction brought by the vanilla color space rendering formula.", + "- We carefully investigate insights and limitations in existing SDF and occupancy representations, and accordingly propose a hybrid representation mingling SDF with occupancy, dubbed Occ-SDF Hybrid, to resolve surfaces with thin structures and small objects.", + "- We conduct a large body of qualitative and quantitative experiments against state-of-the-art, indicating that our Occ-SDF hybrid formula can yield a higher-fidelity room-level scene representation, particularly with successfully resolving small and dark objects." + ], + "bbox": [ + 517, + 426, + 890, + 637 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 649, + 640, + 663 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-view Stereo Conventional algorithms [1, 25, 4] always split the reconstruction into two steps. First, the feature-matching method [22, 17, 24] is applied to estimate the depth of each frame. Then, the resulting depth maps [12] are used to reconstruct the final scene. Notably, the reconstruction may suffer from poor performance in texture-less areas. Learning-based approaches are mainly divided into two categories. Typically, neural networks are embedded into the traditional reconstruction pipeline to replace specific modules, like feature matching [23, 37, 30], depth estimation [33], or depth fusion [5]. These methods often suffer from depth inconsistency problems due to the separately estimated depth maps. Alternatively, neural networks are designed to directly regress input images to trun", + "bbox": [ + 497, + 672, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8941", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cated signed distance functions (TSDFs) [16, 28], but the reconstruction results often lack enough fine details.", + "bbox": [ + 75, + 125, + 468, + 153 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural Scene Representation Recently, coordinate-based neural representations can faithfully model a 3D scene with only posed images. Approaches with an implicit differentiable renderer [35] only use volume density as scene representation which can not extract 3D scenes directly. To address this issue, occupancy-based representation [18] and SDF-based representation [32, 34] are proposed to facilitate 3D reconstruction. Notably, these methods already achieve great performance for object-level scenes but exhibit poorly for room-level scenes, especially in texture-less areas. For the room-level scenes, several existing approaches [9, 39] have demonstrated the ability to employ learned shape priors derived from extensive data to reconstruct scenes from incomplete or noisy point clouds. However, these methods face limitations when it comes to reconstructing scenes solely from image data.", + "bbox": [ + 75, + 157, + 470, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Priors for Indoor Scene Reconstruction Existing methods have attempted to introduce priors to resolve higher-fidelity surfaces in texture-less areas. Manhattan-SDF [8] follows semantic-NeRF[38] to estimate the volume density and semantic label at the same time, and then uses Manhattan-World assumption to regularize the geometry in floor and wall regions. NeuRIS [31] and MonoSDF [36] directly exploit the depth and normal predicted from an off-the-shelf neural network to regularize the geometry of each point, but in many cases, thin structures would disappear. NeuRIS [31] proposes a dynamic scheme to eliminate the wrong supervision signal from inaccurate estimated results, however, based on our investigation that fine structures are still lost even with the correct geometry for supervision. In all, we seek to explore a feature rendering scheme and a hybrid representation to overcome the above problems.", + "bbox": [ + 75, + 384, + 468, + 605 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Overview and Preliminary", + "text_level": 1, + "bbox": [ + 75, + 619, + 324, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to examine the limitations of existing implicit neural surface representations and explore practical solutions for accurately reconstructing large-scale, room-level 3D geometry with fine details from a set of calibrated images. First, we find that the well-adopted color-based rendering formula in [36, 31] will induce optimization bias against low-intensity areas, leaving these areas under-optimized and resulting in missing reconstructions (Sec. 4.1). Accordingly, we propose a simple yet effective feature-based rendering formula to address the problem (Sec. 4.2). Second, our analysis shows that the SDF-based neural surface representation violates scene-level geometry supervised signal and thus prevents the model from obtaining accurate reconstructions, making the model tends to sacrifice small and thin structures (Sec. 5.2). Motivated by this, we propose a hybrid representation mingling occu", + "bbox": [ + 75, + 644, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4e47052f285e56f48ac9ec6e4961cfd62d1195d7152d83141565a388f7d9b0de.jpg", + "image_caption": [ + "Figure 2. Network architecture. The geometry network takes 3D position $(x, y, z)$ after positional encoding (PE) as input and output both SDF and occupancy value. The appearance network takes view direction $(\\theta, \\phi)$ as input and outputs two types of color, the direct color is used in Eq. (4) to directly obtain the pixel color and the decoded color is calculated via the rendering formula (Eq. (8))." + ], + "image_footnote": [], + "bbox": [ + 512, + 125, + 878, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "pancy and SDF for accurate reconstruction (Sec. 5.3).", + "bbox": [ + 497, + 410, + 853, + 423 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We here describe the mathematical preliminary on the state-of-the-art surface representation, namely SDF-based Neural Scene Representation [34], for 3D reconstruction.", + "bbox": [ + 497, + 425, + 890, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For implicit neural reconstruction, we can represent the scene as a signed distance function (SDF) field, which is a continuous function $f$ that calculates the distance between each point and its closest surface", + "bbox": [ + 497, + 467, + 890, + 523 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n1 _ {\\Omega} (\\boldsymbol {p}) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\boldsymbol {p} \\in \\Omega \\\\ 0 & \\text {i f} \\boldsymbol {p} \\notin \\Omega \\end{array} , \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 574, + 524, + 890, + 559 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\boldsymbol {p}) = (- 1) ^ {1 _ {\\Omega} (\\boldsymbol {p})} \\min _ {\\boldsymbol {y} \\in \\mathcal {M}} \\| \\boldsymbol {p} - \\boldsymbol {y} \\|,\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 559, + 813, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $1_{\\Omega}(\\pmb{p})$ is an indicator function to represent whether the space at position $p$ is occupied, $\\mathcal{M} = \\partial \\Omega$ is the boundary surface of occupied space and $||\\cdot ||$ is the standard Euclidean 2-norm. Following the VolSDF [34], we use an MLP to represent the function $f$ and convert the SDF value to Laplace density with the following function", + "bbox": [ + 497, + 583, + 890, + 666 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {i} \\left(\\boldsymbol {p} _ {i}\\right) = \\alpha \\Psi_ {\\beta} (- f \\left(\\boldsymbol {p} _ {i}\\right)), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 605, + 669, + 890, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha, \\beta > 0$ are learnable parameters, and $\\Psi_{\\beta}$ is the cumulative distribution function (CDF) with zero mean and the $\\beta$ scale is defined as", + "bbox": [ + 497, + 687, + 890, + 728 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Psi_ {\\beta} (s) = \\left\\{ \\begin{array}{l l} \\frac {1}{2} \\exp \\left(\\frac {s}{\\beta}\\right) & , \\text {i f} s \\leq 0 \\\\ 1 - \\frac {1}{2} \\exp \\left(- \\frac {s}{\\beta}\\right) & , \\text {i f} s > 0 \\end{array} . \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 730, + 890, + 774 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Color Rendering Formula According to the rendering formula [14], the color for the current ray $r$ is rendered by", + "bbox": [ + 497, + 783, + 889, + 809 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} \\hat {c} _ {i} ^ {r}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 621, + 813, + 890, + 850 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $T_{i}^{r}$ and $\\alpha_{i}$ represent the transmittance and alpha", + "bbox": [ + 499, + 851, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8942", + "bbox": [ + 468, + 889, + 500, + 899 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "value (a.k.a opacity), respectively, of sampled point. And $M$ represent the number of the sampled point along the ray $r$ . They can be computed by", + "bbox": [ + 75, + 125, + 468, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {i} ^ {r} = \\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {i}), \\alpha_ {i} = 1 - \\exp \\left(- \\sigma_ {i} ^ {r} \\delta_ {i} ^ {r}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 169, + 468, + 207 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\delta_r^i$ is the distance between adjacent sample points. Finally, given the rendered color $\\hat{C} (r)$ , the SDF field will be optimized from sparsely sampled images by minimizing the color-based rendering loss as", + "bbox": [ + 75, + 211, + 468, + 267 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r g b}} = \\sum_ {r \\in R} | | \\hat {C} (r) - C (r) | | _ {1}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 270, + 468, + 298 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C(r)$ is the ground-truth color associated with the sampled ray $r$ .", + "bbox": [ + 75, + 301, + 468, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Feature Rendering Formula", + "text_level": 1, + "bbox": [ + 75, + 344, + 337, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Problem of Color-based Rendering", + "text_level": 1, + "bbox": [ + 75, + 366, + 381, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the SDF-based scene representation and the color-based rendering loss $\\mathcal{L}_{\\mathrm{rgb}}$ in Sec. 3, we analyze the derivative of $\\mathcal{L}_{\\mathrm{rgb}}$ to the opacity $\\alpha_{i}$ of a point $p_i$ . Note that for a single point $p_i$ , as $\\alpha_{i}^{r}$ are the same regardless of the rays, we thus omit its dependency on ray $r$ and use $\\alpha_{i}$ for simplicity. For a point $p_i$ , the derivative of the color loss function to its opacity $\\alpha_{i}$ is", + "bbox": [ + 75, + 389, + 468, + 486 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L} _ {r g b}}{\\partial \\alpha_ {i}} = \\pm \\left(\\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {j}) c _ {i} - \\sum_ {k = i + 1} ^ {N} c _ {k} \\alpha_ {k} \\prod_ {j = 1, j \\neq i} ^ {k - 1} (1 - \\alpha_ {j})\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 87, + 488, + 468, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which indicates that when we optimize the SDF value of $p_i$ , the gradient is determined by the color of the current point $p_i$ and points behind it ( $c_k$ and $k \\in \\{i + 1, \\dots, N\\}$ ), and opacity of all points on the entire ray except for the current point ( $\\alpha_j$ and $j \\in \\{1, 2, \\dots, N\\} \\& j \\neq i$ ). Notably, when processing a dark region, saying that the $c_i$ approaches zero, the first term of Eq. (7) will be close to zero. Similarly, if points behind $p_i$ have low opacity ( $\\alpha_k$ and $k \\in \\{i + 1, \\dots, N\\}$ ), the gradient with respect to the SDF value will be small, causing the vanishing problem in dark regions. More generally, the gradient of SDF values can be affected by the color itself, resulting in a biased optimization process that tends to favor high color intensities.", + "bbox": [ + 75, + 534, + 468, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above analysis is also supported by our experiments below. As shown in Fig. 3, we sample rays in the dark regions and the light regions separately and accordingly record the trend of gradient norms in these two regions during the optimization. In the beginning, the gradient norms from these two regions are similar; and the gradient norm in the dark region (red solid line) decreases as the number of training epochs increases, while the gradient norm in the light region remains stable (blue solid line), indicating the dark areas contribute much less to the optimization process. As the optimization process proceeds, if these points are", + "bbox": [ + 75, + 714, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/02408ad68a5c700467f2b2836b9c333cd4eae86b0f1f2f312f80c161d16d24de.jpg", + "image_caption": [ + "Figure 3. The trend for the gradient. The mean and variance of gradient norm (shadowed curves for variance) corresponding to light and dark regions during optimization." + ], + "image_footnote": [], + "bbox": [ + 504, + 124, + 885, + 261 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "predicted as dark colors ( $c_i^r \\to 0$ ), it would lead to the gradient reduction effects as analyzed in Eq. (7). The shadowed regions keep the same trend as the mean values, further affirming our earlier analysis. Note that the gradient of points in these areas will not equal zero due to the influence of other loss functions, like depth consistency loss.", + "bbox": [ + 497, + 315, + 892, + 399 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Feature-based Rendering", + "text_level": 1, + "bbox": [ + 499, + 415, + 729, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To resolve the aforementioned problem, we propose feature-based color rendering loss. As shown in Fig. 2, the Appearance network outputs two predictions for each point $i$ along a ray $r$ : one is the color vector $\\hat{c}_i^r$ , and the other is the hidden feature $F_i^r$ . For direct color $\\hat{c}_i^r$ , we utilize Eq. (4) to obtain the target pixel color $\\hat{C}_c(r)$ . And the hidden feature $F_r^i$ is used to render the ray feature $\\hat{F}(r)$ by", + "bbox": [ + 497, + 439, + 890, + 536 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {F} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} F _ {i} ^ {r}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 618, + 540, + 890, + 576 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The ray feature $\\hat{F}_T$ is further decoded by a decoder $\\mathcal{D}$ to yield the decoded target pixel color,", + "bbox": [ + 497, + 581, + 890, + 610 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} _ {F} (r) = \\mathcal {D} (\\hat {F} (r)), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 626, + 611, + 890, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the decoder $\\mathcal{D}$ is a single-layer perceptron with 256 nodes. Finally, the decoded color $\\hat{C}_F(r)$ from the rendered feature is used to construct the feature-based color rendering loss. As such, the optimization of these dark regions would not be affected by the color itself. As long as there are non-zero values in the rendered feature, there will be non-zero gradients with respect to the volume density of the concerned point. As shown in Fig. 3 (dashed lines), the gradient norm is not influenced by the intensity of colors.", + "bbox": [ + 497, + 630, + 890, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Hybrid Representation Scheme", + "text_level": 1, + "bbox": [ + 499, + 775, + 786, + 790 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Incorporating Geometry Prior Matters", + "text_level": 1, + "bbox": [ + 499, + 800, + 833, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is clear that for room-level scene reconstruction, geometry priors are essential. Existing methods [31, 36] render depth $\\hat{D}(r)$ and normal $\\hat{N}(r)$ of the surface intersecting", + "bbox": [ + 497, + 824, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8943", + "bbox": [ + 468, + 889, + 500, + 899 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the current ray as", + "bbox": [ + 77, + 125, + 194, + 138 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {D} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} ^ {r} t _ {i} ^ {r} \\quad \\text {a n d} \\quad \\hat {N} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} ^ {r} \\hat {n} _ {i} ^ {r}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 141, + 468, + 179 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{T}_r^i$ and $\\hat{\\alpha}_r^i$ have the same meaning as Eq. (4), $t_i^r$ is the distance the ray passing and $n_i^r$ is the normal of point $p_i$ . Next, these methods use depth and normal maps estimated from pre-trained models, such as Omnidata [10], to directly supervise the rendered depth $\\hat{D}(r)$ and normal $\\hat{N}(r)$ using Eq. (11) and Eq. (12), respectively. Overall, the depth loss function is defined as", + "bbox": [ + 75, + 182, + 468, + 280 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d e p t h}} = \\sum_ {r \\in \\mathcal {R}} | | (w \\hat {D} (r) + q) - \\bar {D} (r) | | ^ {2}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 281, + 468, + 309 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w$ and $q$ are the scale and shift computed by the least-squares method [6] to solve scale-ambiguity problem for monocular depth prediction methods. And the normal loss function is", + "bbox": [ + 75, + 312, + 468, + 366 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {n o r m a l}} = \\sum_ {r \\in R} | | \\hat {N} (r) - \\bar {N} (r) | | _ {1} + | | 1 - \\hat {N} (r) ^ {T} \\bar {N} (r) | | _ {1}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 368, + 468, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde{N} (r)$ is the predicted monocular normal transformed to the same coordinate system with angular.", + "bbox": [ + 77, + 400, + 468, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 1, we note that these geometry priors benefit the reconstruction of better surfaces in textureless and sparse-viewed areas. However, thin structures and small objects, such as the yellow flower in Fig. 4, cannot be faithfully reconstructed with geometry priors. Recently, NeuRIS [31] put forward a hypothesis that this phenomenon arises from the inaccurate geometry supervisory signal (i.e. depth and surface normal). However, according to our experiment on Replica synthetic dataset, this problem still exists even though we use the perfect ground-truth depth, normal, and RGB to provide supervisory signals (see Fig. 4).", + "bbox": [ + 75, + 429, + 468, + 581 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Problem of SDF Formula with Geometry Prior", + "text_level": 1, + "bbox": [ + 75, + 593, + 468, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To dive into the SDF representation and explore its limitations for surface reconstruction with geometric priors, we create a simplified scenario and simulate object occlusions as shown in Fig. 5(a). The ground-truth SDF intersecting with a horizontal plane is shown in Fig. 5(a), and the SDF distribution along a ray $r$ intersecting with the blue cube at point $p_s$ is shown in Fig. 5(c). There are many local minima and maxima due to the existence of multiple objects, which differs from the single-object scenario following a monotonic function (blue line in Fig. 5(c)). To examine depth priors for surface reconstruction, we employ the approach proposed in MonoSDF [36] to calculate the depth of $p_s$ following Eq. (10) subject to the ground-truth SDF.", + "bbox": [ + 75, + 615, + 468, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, even with the ground-truth SDF, the estimated depth value (1.59, the red vertical plot in Fig. 5(e)) still deviates from the true depth value (2.94, the green vertical plot in Fig. 5(e)) when multiple objects exist. According to Eq. (10), the estimated normal value would suffer from", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/490ef55cc21e32f5ddce3f9f2cbc5cd761e6955932f1dd6076a295a2a01e59d9.jpg", + "image_caption": [ + "Pseudo Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 510, + 138, + 625, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/caf29d1ae101d75ea88c80affca08444e422a66b0c371ff588ee3b4883dd9f3c.jpg", + "image_caption": [ + "Figure 4. Illustration of failure cases of state-of-the-arts. Even though applying the perfect pseudo ground-truth geometry to supervise the model, existing room-level reconstruction methods like [36] can still fail to resolve accurate 3D structures." + ], + "image_footnote": [], + "bbox": [ + 510, + 223, + 625, + 306 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/254c5eeeceea936dc8b127023a61b64d862b8a568c45bfdcf204d2c522fcbbfb.jpg", + "image_caption": [ + "MonoSDF" + ], + "image_footnote": [], + "bbox": [ + 630, + 137, + 744, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1f95d9a24451ae4fae6a7f245945b3e2005e5f82def5fd2080539fc2b0a04309.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 223, + 744, + 306 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c6997df99b450c116076898e4a4df6296c2fce859c31ce7ea522214f9de56c21.jpg", + "image_caption": [ + "Error" + ], + "image_footnote": [], + "bbox": [ + 749, + 137, + 863, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/888f26ee04977eff42fa287a1d26e115a5eb0b8ad3bc48d52f9ddc558d5f6095.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 749, + 222, + 863, + 306 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6f90db19bded9a33d276c7752c4422dbf1063fe1eb02e4394de3e3ec74465f5c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 863, + 137, + 887, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0cdbb1e86dc402bc6f8586c4533ed4cc805f59c1ceb2a8800a616e0be03d2543.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 863, + 223, + 887, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the same problem. This implies that existing methods incorporating geometry priors [36, 31] to guide the learning of the SDF representation may not necessarily encourage the model to learn the true SDF for scene-level surface reconstruction. In turn, because small objects or thin structures usually have low sampling probability during training, the minimization of $\\mathcal{L}_{\\mathrm{depth}}$ will encourage the model to predict SDF ignoring small objects along the ray $r$ such that the estimated SDF will produce depth values closer to the depth supervision (see Fig. 5(e)) and minimize the overall loss function, attempting to mimic the single object scenario (right part in Fig. 5). In sum, the supervision from geometric priors tends to sacrifice the reconstruction of small objects to preserve large surface reconstruction, which aligns also with our observation presented in Fig. 4.", + "bbox": [ + 497, + 387, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3. Hybrid Occupancy-SDF Representation", + "text_level": 1, + "bbox": [ + 499, + 606, + 842, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The problem above is essentially caused by the SDF representation, which describes the geometry of a scene as a whole and thus suffers from the interference of other objects, especially small objects, and thin structures are prone to be removed to preserve large structures.", + "bbox": [ + 497, + 628, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unlike the SDF representation, occupancy represents each point separately and thus is free from the interference of objects in this challenging scenario. However, occupancy representation only focuses on the intersecting point ignoring the constraint of neighborhood points. Thus, the reconstruction results represented by occupancy will have many floaters and useless structures, as shown in Fig. 1, which can be eliminated in SDF by Eikonal loss [7]. This inspires us to investigate a hybrid of occupancy and SDF as a representation for neural surface reconstruction as shown in Fig. 2. The geometry network $\\theta$ outputs both SDF and occupancy.", + "bbox": [ + 497, + 699, + 890, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, the occupancy represents surfaces as the de", + "bbox": [ + 517, + 852, + 889, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8944", + "bbox": [ + 468, + 889, + 500, + 899 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/329f9c9076933347ff118c3a4694538c3343a127cdb57e91523622f067e61da4.jpg", + "image_caption": [ + "Multi Objects Scene" + ], + "image_footnote": [], + "bbox": [ + 117, + 134, + 257, + 182 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/21fc96f45c6c02e1184be8ac6d7ef5a7404e4a8aef320a80aeafde4d104f7c88.jpg", + "image_caption": [ + "Signed Distance Field" + ], + "image_footnote": [], + "bbox": [ + 265, + 124, + 406, + 191 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/123016b32885614070e3a1f19d49f3d274986ad59d045f97f459e1ebf25e205a.jpg", + "image_caption": [ + "Single Object Scene" + ], + "image_footnote": [], + "bbox": [ + 411, + 134, + 547, + 191 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c8cc49cff12caaf605c56e138731d682719c7f0752492a2cb6d0ef49f0e9e0dc.jpg", + "image_caption": [ + "Signed Distance Field" + ], + "image_footnote": [], + "bbox": [ + 557, + 124, + 695, + 191 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/84f5fae97bed52e500bd27cf9a66ef58fb4b626ef028c2856e654c480831c038.jpg", + "image_caption": [ + "(b) SDF Value at Point P" + ], + "image_footnote": [], + "bbox": [ + 712, + 125, + 863, + 201 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a606b880eab5f424d12e07d06fa7c66201b81b02ec748546ae2442d82ef1ac31.jpg", + "image_caption": [ + "(a) Schematic of the toy 3D structure for the multi-object scene (left) and single object scene (object).", + "(c) SDF $f(\\pmb{p}_i)$", + "Figure 5. Toy experiments for the room-level scene. The left part of 5(a), where we stand in front of the yellow cylinder to observe the entire scene, is a widespread scenario for room-level scale scenes. Unlike the single object scenario, where the distribution of SDF value is a monotonic decreasing function from the observed position to the object, the room-level scenario has complex distributions with multi peaks/valleys along the single ray (5(c)). Following the Laplace density function [34], the density distributions of different situations are shown in 5(d), where room-level scenes have a secondary peak near small objects but the single object scene only has one peak. It is because of the existence of this peak, the weights in the room-level scene (5(e)) exhibit a multi-model distribution, while for the single object case a uni-modal distribution. As such, we note that the rendering depth $\\hat{D}$ deviates from the ground truth in the room-level scene but is close to the ground truth depth object-level scene. 5(b) means the effect of supervised signal in three different representations." + ], + "image_footnote": [], + "bbox": [ + 90, + 224, + 310, + 339 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9d9c3b5e2f02267ac007d1967453a142e87d8d573062de83e195c3055dd102d0.jpg", + "image_caption": [ + "(d) Laplace density $\\delta_i(\\pmb {p}_i)$" + ], + "image_footnote": [], + "bbox": [ + 314, + 224, + 534, + 339 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/53bad4800866f54b47404aaec038a65917be787c9e718615119932ad51ffb731.jpg", + "image_caption": [ + "(e) Weights $T_{r}^{i}\\alpha_{r}^{i}$" + ], + "image_footnote": [], + "bbox": [ + 539, + 226, + 878, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cision boundary of a binary occupancy classifier, parameterized by a neural network $\\theta$", + "bbox": [ + 75, + 480, + 468, + 508 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\no _ {\\theta} (\\mathbf {p}): \\mathbb {R} ^ {3} \\rightarrow [ 0, 1 ], \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 201, + 510, + 468, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{p}$ is a 3D point. The occupancy representation assumes that objects are solid, thus we can rewrite the neural rendering formula [14] to", + "bbox": [ + 75, + 529, + 468, + 571 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (r) = \\sum_ {i = 1} ^ {M} o \\left(\\mathbf {p} _ {i}\\right) \\prod_ {j < i} \\left(1 - o \\left(\\mathbf {x} _ {j}\\right)\\right) c \\left(\\mathbf {p} _ {i}, d\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 573, + 468, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which replaces the opacity $\\alpha$ to a discrete occupancy indicator variable $o\\in 0,1$ , where $o = 0$ indicates the free space while $o = 1$ the occupied space. Thus, this representation will not be affected by the objects along the ray, and the rendering depth will be consistent with ground-truth depth in ground-truth occupancy space. Note that the occupancy-based representation is introduced to facilitate optimization. During inference, the SDF is used for reconstruction.", + "bbox": [ + 75, + 612, + 468, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To understand why and how the hybrid representation helps optimize the SDF field for accurate reconstruction, we conduct the following empirical analysis, using the scenario shown in Fig. 5(a). Here, the orange ray hits a surface point $Q$ of the large blue cube and the blue ray hits the surface point $P$ on the small cylinder. During optimization, the depth/normal loss for point $Q$ along the orange ray will encourage the model to predict a large SDF value (absolute) of point $P$ (Fig. 5(b)) which violates the reconstruction of the small cylinder where a small SDF value is desired. In", + "bbox": [ + 75, + 726, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "contrast, point $Q$ has no effects on point $P$ with occupancy representation. The hybrid representation joins the forces of SDF and occupancy representations, aiming to use occupancy representation to help overcome the issues of SDF representation in optimization. Although the depth/normal loss from the SDF presentation for point $Q$ still has a negative impact on the optimization of point $P$ . The additional occupancy representation will force the network to predict a large occupancy value for a point $P$ and thus will indirectly regularize the network to predict a small SDF value (see Fig. 5(b): the blue up arrow in \"Hybrid\"). We admit that this hybrid representation can only alleviate this problem, and our study is more empirical. Fundamental issues arise from insufficient neural scene representation, which requires further research efforts. We explore further why this combination would bring notable benefits to the supplementary with an example.", + "bbox": [ + 497, + 480, + 890, + 716 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 499, + 733, + 631, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Optimization. In the training stage, we minimize the loss", + "bbox": [ + 499, + 758, + 878, + 773 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {r g b}} ^ {s d f} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {r g b}} ^ {s d f _ {F}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {e i k}} + \\lambda_ {3} \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {o c c}} \\tag {15} \\\\ + \\lambda_ {4} \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {s d f}} + \\lambda_ {5} \\mathcal {L} _ {\\text {n o r m a l}} ^ {\\text {o c c}} + \\lambda_ {6} \\mathcal {L} _ {\\text {n o r m a l}} ^ {\\text {s d f}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 777, + 890, + 817 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{rgb}$ means color-based rendering loss following Eq. (6) but only to SDF representation. The rendering color computed by the feature rendering formula (Eq. (8))", + "bbox": [ + 497, + 824, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8945", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and Eq. (9)) is denoted to $\\mathcal{L}_{rgb}^{sdf_F}$ . Notably, $\\mathcal{L}_{eik}$ means the eikonal loss [7], $\\mathcal{L}_{depth}$ means the depth rendering loss following Eq. (11), and $\\mathcal{L}_{normal}$ means the normal rendering loss following Eq. (12). We apply them for both representations, where the superscript $occ$ indicates the loss computed by occupancy-based representation, while the $sdf$ by SDF-based representation. The network is optimized by the Adam optimizer with a learning rate of $5e^{-4}$ . We set weights $\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4, \\lambda_5, \\lambda_6$ to 1, 0.05, 0.5, 0.1, 0.1, 0.05, respectively. The network architecture and sampling strategy are detailed in the supplement.", + "bbox": [ + 75, + 124, + 472, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets. We use three datasets to assess the performance of our algorithm. ScanNet [2] is a real-world dataset that provides 1,513 scenes captured with Kinect V1 RGB-D camera. The BundleFusion [3] is applied to provide high-quality camera poses and surface reconstructions. For each scene, we uniformly sample roughly 500 frames to train our network. Tanks and Temples [11] is a real-world, large-scale scene dataset. We use four indoor scenes from their advanced split and run on the official server. Replica [27] is a synthetic dataset that provides 18 scenes, with each providing dense geometry, HDR textures, and semantic annotations. We select 8 scenes and use the Habitat simulator [29] to render RGB images following MonoSDF [36] splits. Notably, we conduct ablation studies on this dataset.", + "bbox": [ + 75, + 281, + 472, + 475 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared Methods. (1) UNISURF [18] is an occupancy-based method that unifies surface rendering and volume rendering for neural scene reconstruction. We implement the UNISURF* with normal and depth priors for a fair comparison. (2) MonoSDF [36] is an SDF-based method that adds depth and normal constraints on VolSDF [34]. (3) Manhattan-SDF [8] is an SDF-based method that adds a semantic branch and uses the Manhattan constraint to regularize the geometry in floor and wall regions. (4) COLMAP [25] is a classical multi-view stereo method with Poisson surface reconstruction. (5) NeuRIS [31] is an SDF-based method that introduces pseudo normal prior to the NeUS [32] architecture. Meanwhile, it leverages multiview consistency to eliminate the wrong supervision signal from inaccurate estimated results. (6) NICER-SLAM [39] is an SDF-based dense SLAM system that uses locally implicit map representation and can simultaneously optimize for camera poses and a hierarchical neural implicit map representation. (7) LIG [9] uses the local implicit grid representation to reconstruct the large-scale scene from partial or noise point clouds. (8) Convolutional Occupancy network(Conv-Occ) [21] is a locally implicit representation that integrates local information to get better reconstruction results from noisy point cloud.", + "bbox": [ + 75, + 479, + 472, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Notably, local implicit representation [9, 21] can only reconstruct the scene from point clouds, thus we re-implement them using point clouds generated from scale-aligned pseudo depth and utilize the provided pretrained", + "bbox": [ + 75, + 811, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "models for evaluation. And we directly obtain the results from the main paper of NICER-SLAM [39].", + "bbox": [ + 497, + 125, + 890, + 153 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Metrics. All meshes are evaluated by 5 standard metrics defined in [16]: Accuracy, Completeness, Precision, Recall, and $F$ -score. Their definition will be discussed in the supplementary. For the Replica dataset, we also report the normal consistency following [13, 8, 20]. For the Tanks and Temples dataset, we use the official server to evaluate our results and report the F-score for selected scenes.", + "bbox": [ + 497, + 157, + 892, + 255 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.1. Main Results", + "text_level": 1, + "bbox": [ + 499, + 261, + 638, + 274 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method with state-of-the-art methods on three benchmark datasets.", + "bbox": [ + 497, + 282, + 890, + 309 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6878cb490dc56d94f65d13858ed9a96bc4ab01c627f800f061e79045d79ac68d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAcc ↓Comp ↓C-L1 ↓Prec ↑Recall ↑F-score ↑
COLMAP [25]0.0470.2350.14171.144.153.7
UNISURF [18]0.5540.1640.35921.236.226.7
VolSDF [34]0.4140.1200.26732.139.434.6
NeUS [32]0.1790.2080.19431.327.529.1
Manhattan-SDF [8]0.0720.0680.07062.156.860.2
NeuRIS [31]0.0500.0490.05071.766.969.2
MonoSDF [36]0.0350.0480.04279.968.173.3
Ours0.0390.0410.04080.076.077.9
", + "bbox": [ + 500, + 315, + 892, + 419 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on ScanNet Dataset. We conducted a comparative analysis of our proposed approach against existing implicit reconstruction methods, including ManhattanSDF [8], NeuRIS [31] and MonoSDF [36] using the ScanNet dataset. As revealed in Table 1, our proposed method outperforms state-of-the-art methods, with a significant increase in F-score by 4.6. Additionally, in terms of Recall, our method substantially outperforms MonoSDF by 7.9 without needing extra data. Overall, our approach performs on par with the state-of-art methods in \"Acc\", \"Chamfer- $\\mathcal{L}_1$ (C- $\\mathcal{L}_1$ ) and \"Prec\" and obtain notable performance gains in \"Comp\", \"Recall\" and \"F-score\". This is because these metrics (\"Comp\" and \"Recall\") are better metrics in evaluating how complete and accurate in capturing the shape and details of the scene being reconstructed. Further, Fig. 6 reveals that our method can attain more complete reconstructions with details and for low pixel intensities regions.", + "bbox": [ + 497, + 460, + 890, + 709 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/49634fda1ee66590288f5480634afd92c0ce798976c1c1ec41ad589faeca0c77.jpg", + "table_caption": [ + "Table 1. Quantitative assessments of the proposed model against previous works on the ScanNet dataset." + ], + "table_footnote": [], + "table_body": "
AuditoriumBallroomCourtroomMuseumMean
MonoSDF3.092.4710.005.105.165
Ours5.225.4213.998.598.305
MonoSDF*3.173.7013.755.686.58
Ours*6.197.3319.8011.8511.295
", + "bbox": [ + 500, + 718, + 889, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative assessments of the proposed model against Monosdf on the Tanks and Temples dataset. The evaluation metrics for the Tanks and Temples dataset are F-score. * means that the hash-grid structure is adopted.", + "bbox": [ + 497, + 783, + 890, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Tanks and Temples Dataset. For challenging large-scale indoor scenes, we conduct experiments on", + "bbox": [ + 499, + 838, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8946", + "bbox": [ + 468, + 889, + 502, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3f444be36fc767874bc9b48def4ff54e14800e76edf2de9279a5f81a26788428.jpg", + "image_caption": [ + "UNISRUF*" + ], + "image_footnote": [], + "bbox": [ + 85, + 144, + 243, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9ff79600dc336460ccb6552132b182cbeef8bba2147777bea8f7f782a39aec1a.jpg", + "image_caption": [ + "Replica" + ], + "image_footnote": [], + "bbox": [ + 247, + 144, + 398, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/acf70592dee076c5829fbe744c503a454944d9646815f95f6b59fe63ce3bcdbc.jpg", + "image_caption": [ + "Manhattan-SDF" + ], + "image_footnote": [], + "bbox": [ + 401, + 144, + 559, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/647908f068eacfccdff6dcf3dc6a474eafe9e4d1f661989d97bd00b41f4e9823.jpg", + "image_caption": [ + "ScanNet" + ], + "image_footnote": [], + "bbox": [ + 566, + 143, + 727, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/64a1266fbc7a761a4326ae2dc23b2e47e42a4c7406289fb9a3b072258e02a35d.jpg", + "image_caption": [ + "Tanks and Temples", + "MonoSDF" + ], + "image_footnote": [], + "bbox": [ + 734, + 143, + 887, + 225 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d3ad0a7fe54fc27125e33e223ea412d3fe25f6926fcd17d7e1482975f253a346.jpg", + "image_caption": [ + "MonoSDF" + ], + "image_footnote": [], + "bbox": [ + 85, + 236, + 243, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/db66a1192677b0394eb8b7eccbe16c9008dcdac90b7ea568230c97ab80cb880d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 247, + 236, + 398, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/62cc12b89b0ba6b8f06b753c0a4492df66eb5499ea4601155abd73739515b52a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 400, + 236, + 561, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/18f8c720423e1e604fb2370e50963d3f59ac10d80584bf8dd30dda4a2bb6a282.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 236, + 727, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e6ec9fb1133d79a59aea07efd47a6d71b218cbd5553bf3019e131d3661cabe3f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 734, + 235, + 887, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5287cd10b9264cff33ab0676e269f01635d70ff544d11ba354ef2be7daebe3a6.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 85, + 332, + 243, + 415 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/63cd3da4467f4bc38bbc6c7f8c1d54145f0db268e712e2475016b3f84c8ebc83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 247, + 332, + 396, + 414 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e838a096a846f4160f8a4b963ed76f8203bd518ad9d6af3df366e5332bec98c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 400, + 332, + 559, + 414 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fe6c93eee4ee6ef301e1ce8e38be3922333e1e93f4239e2311e135c90d34afbd.jpg", + "image_caption": [ + "BSDF" + ], + "image_footnote": [], + "bbox": [ + 566, + 332, + 727, + 414 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1df6d92e16d7994b7fd110469b05b332b0194cf60cc28dd572a587aa8bfcca56.jpg", + "image_caption": [ + "Ours (MLP)", + "MonoSDF (Grids)" + ], + "image_footnote": [], + "bbox": [ + 734, + 332, + 887, + 414 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cf1cf04d93509fdad5488a160d238846c356da76bde09806cadf402811f5250b.jpg", + "image_caption": [ + "Ground Truth", + "Figure 6. Reconstruction results on representative datasets of Replica (left), ScanNet (middle), and Tanks and Temples (right). The ground truth is presented on the bottom-most. Red boxes in sub-figures highlight those areas where distinctive differences can be observed." + ], + "image_footnote": [], + "bbox": [ + 85, + 426, + 243, + 507 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/56aa3115f8678b81602522f15db84656a21b0102f8297c04bacb277ac5d8b5e2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 247, + 426, + 396, + 507 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ae27986e6d458c62fcfdea8b84b73f490cccbb4cb075807a73d30f3837ed405c.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 400, + 426, + 559, + 507 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/65bbc042de63ee02bc62524646c17de4cf76d5b763185a5c81e3304fbc5fc3aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 426, + 727, + 507 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3ce84973ff8861014b023f3e587e87017f23f22930b5ba88d04fa79d21e9fe62.jpg", + "image_caption": [ + "Ours (Grids)" + ], + "image_footnote": [], + "bbox": [ + 732, + 425, + 885, + 507 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the advanced Tanks and Temples dataset [11], which features more complicated structures. As alternative methods of neural reconstruction from images are not assessed on this dataset, we implement the best-performing method MonoSDF and compare with it. Thus, the MonoSDF and two versions of our method are implemented. Specifically, one adopts the pure MLP architecture while the other uses the hash grids as the input representation. The quantitative assessments (Table 2) reveal that our method shows better performance on this dataset, regardless of whether an MLP or hash-grid structure is used. And our hybrid representation exhibits excellent generalization abilities across different implicit structures. Overall, our compelling experimental results on the Tanks and Temples dataset further validate the robustness and versatility of the proposed method in reconstructing complex and challenging indoor scenes.", + "bbox": [ + 75, + 566, + 468, + 788 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results on Replica Dataset. Quantitative assessment results on the Replica dataset are presented in Table 3. For this dataset, we compare our methods with both point-based methods [21, 9] and rendering methods [39, 18, 36]. Ours significantly surpasses existing state-of-the-art neural ren", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/345559daf5ba941665584bafb2d0a13a9b4d7cb6be54c4d42c5a0f04d9a27bb4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodNormal C.↑Chamfer- \\( {\\mathcal{L}}_{1} \\downarrow \\)F-score ↑
Conv-Occ [21]85.736.4358.33
LIG [9]89.565.5365.20
NICER-SLAM [39]90.273.91-
UNISURF†[18]90.964.9378.99
MonoSDF†[36]92.112.9486.18
\\( Ours^{\\dagger } \\)93.432.5892.12
", + "bbox": [ + 505, + 567, + 890, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Quantitative assessments of the proposed model against prior works on the Replica dataset. Herein, $\\dagger$ indicates the use of geometry priors as supervision signals.", + "bbox": [ + 497, + 657, + 890, + 697 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dering methods. The results reveal that the SDF-based representation outperforms the occupancy-based ones (i.e. UNISURF*). This is because the SDF usually enforces constraints on the distribution of the entire scene, benefiting to suppressing the occurrence of floaters or unnecessary structures in occupancy-based representation. Notably, our OccSDF Hybrid method can constrain the distribution of the entire scene with SDF representation meanwhile exploiting the occupancy representation to resolve thin structures and small objects. Qualitative comparisons are shown in Fig. 6.", + "bbox": [ + 497, + 726, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8947", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b8332958a86cc83896d92d7a8e5504ed60d3886e74e224c65072077e8820e84f.jpg", + "table_caption": [ + "6.2. Ablation Study" + ], + "table_footnote": [ + "Table 4. Ablation study on the Replica dataset [27], where we progressively add different constraints to assess their impacts. The MonoSDF [36] is set as the baseline model." + ], + "table_body": "
Normal C.↑Chamfer- \\( {\\mathcal{L}}_{1} \\downarrow \\)F-score ↑
MonoSDF92.112.9486.18
+ feature93.012.6491.01
+ hybrid93.222.7790.24
full model93.432.5892.12
", + "bbox": [ + 82, + 152, + 468, + 220 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We conduct ablation studies on the Replica dataset as it provides ground-truth geometry. Four different configurations are investigated to train our model, including (1) MonoSDF with MLP settings (MonoSDF-MLP); (2) MonoSDF-MLP with our feature-based rendering formula; (3) MonoSDF-MLP with our hybrid representation; (4) MonoSDF-MLP with both the feature-based rendering formula and hybrid representation scheme (Full model).", + "bbox": [ + 75, + 271, + 468, + 382 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 4 shows that all metrics are improved when using the feature rendering to reconstruct this scene. Our proposed feature rendering scheme addresses the difficulties in reconstructing areas of low intensities, resulting in better results. On the other hand, the hybrid representation also leads to significant improvements in all metrics. Notably, it improves the completeness of small objects and thin structures, as evidenced by the results in Fig. 6. By leveraging both components, our model achieves an overall improvement of 5.94 in F-score, along with improved normal consistency and Chamfer- $\\mathcal{L}_1$ . We attribute this success to our feature-based color rendering formula and our hybrid representation, which addresses the color-bias issue in optimization and difficulties in reconstructing detailed structures. The visualization results in Fig. 6 show our model's excellent reconstruction performance, especially in low-intensity areas and detailed structures. We will add more ablation studies and visualize results in the supplementary.", + "bbox": [ + 75, + 384, + 468, + 631 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6.3. Parameters Adjusting", + "text_level": 1, + "bbox": [ + 77, + 641, + 284, + 657 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "As shown in Eq. (15), our method newly added three different losses $\\mathcal{L}_{rgb}^{sdf_F},\\mathcal{L}_{depth}^{occ},\\mathcal{L}_{normal}^{occ}$ . In order to verify the sensitivity of our method to hyperparameters, we provided the results of the experiment on the Replica dataset as shown in Fig. 7. It is clear that our method is not very sensitive to hyperparameters, and all the evaluated settings outperform the baseline method (C- $\\mathcal{L}_1$ : 2.94, F-score: 86.18). It is worth noting that our approach demonstrates consistent performance enhancement across diverse datasets using the same parameter set, outperforming the baseline results.", + "bbox": [ + 75, + 663, + 468, + 802 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 77, + 815, + 194, + 828 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We have analyzed the constraints present in current neural scene representation techniques with geometry priors,", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/fc94ad8306528a58fe24577420612fb1ade7800cc574e6486e5f36bda2af3ae3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 125, + 873, + 254 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/2cb135186c9bbf547a3a7a440e952941e6244a228997596f615a7529945abc9e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 257, + 873, + 385 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/f65b8741260a565eb52ecb8a77be0acf42ad48b35775969d1dc0ff5da631e509.jpg", + "image_caption": [ + "Figure 7. Performance with different hyperparameter choices." + ], + "image_footnote": [], + "bbox": [ + 517, + 389, + 873, + 521 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "and have identified issues in their ability to reconstruct detailed structures due to a biased optimization towards high color intensities and the complex SDF distribution. As a result, we have developed a feature rendering scheme that balances color regions and have implemented a hybrid representation to address the limitations of the SDF distribution. Our approach has demonstrated the successful reconstruction of room scenes with a high-fidelity surface, including small objects, detailed structures, and low-intensity pixel regions. We envision our results inspire further research on improving neural scene representation for accurate and large-scale surface reconstruction.", + "bbox": [ + 497, + 553, + 890, + 719 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 499, + 732, + 660, + 748 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We thank Xin Kong for his advising during the rebuttal period. This work has been supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621 and 27212822), General Research Fund Scheme (Grant No. 17202422), and RGC matching fund scheme (RMGS). Part of the described research work is conducted in the JC STEM Lab of Robotics for Soft Materials funded by The Hong Kong Jockey Club Charities Trust.", + "bbox": [ + 497, + 755, + 890, + 866 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "8948", + "bbox": [ + 468, + 889, + 500, + 900 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Motilal Agrawal and Larry S Davis. A probabilistic framework for surface reconstruction from multiple images. In Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, volume 2, pages II-II. IEEE, 2001. 2", + "[2] Angela Dai, Angel X Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. 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Nicer-slam: Neural implicit scene encoding for rgb slam, 2023. 3, 7, 8" + ], + "bbox": [ + 502, + 125, + 892, + 319 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "8950", + "bbox": [ + 468, + 889, + 500, + 899 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/c8aa23d3-c76a-4daf-a8f1-9ca330b3d300_model.json b/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/c8aa23d3-c76a-4daf-a8f1-9ca330b3d300_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e713a93c569f5babe7c5910785026de05a4439d1 --- /dev/null +++ b/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/c8aa23d3-c76a-4daf-a8f1-9ca330b3d300_model.json @@ -0,0 +1,2818 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.052, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.062 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.334, + 0.063, + 0.71, + 0.075 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.305, + 0.076, + 0.74, + 0.088 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.089, + 0.162, + 0.882, + 0.205 + ], + "angle": 0, + "content": "Learning A Room with the Occ-SDF Hybrid: Signed Distance Function Mingled with Occupancy Aids Scene Representation" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.228, + 0.861, + 0.275 + ], + "angle": 0, + "content": "Xiaoyang Lyu\\(^{1}\\), Peng Dai\\(^{1}\\), Zizhang Li\\(^{2}\\), Dongyu Yan\\(^{3}\\), Yi Lin\\(^{4}\\), Yifan Peng\\(^{1}\\), Xiaojuan Qi\\(^{1}\\), \\(^{1}\\)The University of Hong Kong, \\(^{2}\\)Zhejiang University, \\(^{3}\\)Harbin Institute of Technology, \\(^{4}\\)DJI" + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.324, + 0.873, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.542, + 0.893, + 0.581 + ], + "angle": 0, + "content": "Figure 1. Overview and reconstruction results of the Occ-SDF hybrid neural scene representation. Aided with the feature rendering scheme (Sec. 4) and the hybrid representation (Sec. 5), our method yields results with more detailed structures in room-level scenes compared to the state-of-the-art, particularly for those low intensities and detailed structures." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.597, + 0.314, + 0.611 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.471, + 0.754 + ], + "angle": 0, + "content": "Implicit neural rendering, using signed distance function (SDF) representation with geometric priors like depth or surface normal, has made impressive strides in the surface reconstruction of large-scale scenes. However, applying this method to reconstruct a room-level scene from images may miss structures in low-intensity areas and/or small, thin objects. We have conducted experiments on three datasets to identify limitations of the original color rendering loss and priors-embedded SDF scene representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Our findings show that the color rendering loss creates an optimization bias against low-intensity areas, resulting in gradient vanishing and leaving these areas unoptimized. To address this issue, we propose a feature-based color rendering loss that utilizes non-zero feature values to bring back optimization signals. Additionally, the SDF representation can be influenced by objects along a ray path, disrupting the monotonic change of SDF values when a single" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.893, + 0.723 + ], + "angle": 0, + "content": "object is present. Accordingly, we explore using the occupancy representation, which encodes each point separately and is unaffected by objects along a querying ray. Our experimental results demonstrate that the joint forces of the feature-based rendering loss and Occ-SDF hybrid representation scheme can provide high-quality reconstruction results, especially in challenging room-level scenarios. The code is available at https://github.com/shawLyu/Occ-SDF-Hybrid" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.748, + 0.633, + 0.763 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.771, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Reconstructing a 3D scene from a series of multi-view images is a crucial problem in the realm of computer vision. This process has widespread applications in various fields such as animation, gaming, and virtual/augmented reality (VR/AR). The recent trend is to represent a 3D scene as an implicit function parameterized by a neural network [13, 19, 26, 21], whose optimization is supervised by ex" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.503, + 0.901 + ], + "angle": 0, + "content": "8940" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.47, + 0.182 + ], + "angle": 0, + "content": "plicit 3D data like point cloud or real SDF value. Recent advancements in neural radiance field (NeRF) [14] further enable learning an implicit 3D representation from purely sparse posed images [35, 15]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.184, + 0.47, + 0.281 + ], + "angle": 0, + "content": "However, when it comes to producing high-quality novel-view synthesis, these methods frequently utilize volume density [14] to represent the 3D geometry. Unfortunately, this approach does not adequately constrain the 3D geometry in the presence of ambiguities [18], ultimately leading to poor surface reconstructions (as depicted in Fig. 1: Volume Density)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.282, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Accordingly, research efforts have been made to exploit geometry-friendly representations, including signed distance function (SDF) [32, 34, 19] or occupancy [18], whose zero-level set can be extracted to become the concerned 3D surface. Albeit improving quality, they consider the reconstruction only of a single object, thereby, the performance degrades dramatically when applied to scene-level surface reconstruction, i.e., representing a room (Fig. 1: SDF). An attribute is that reconstructing texture-less areas often suffers from ambiguous visual cues with only RGB loss as the regularization. To address this problem, recent research has attempted to incorporate semantic [8] or geometric priors (depth/normal [36, 31] constraints) to further regularize scene-level reconstruction. With SDF-based representation and geometric priors [36], the reconstruction quality has been greatly improved (Fig. 1: SDF + Geometry Priors), especially concerning large flat areas and objects. However, it still cannot faithfully reconstruct the 3D scene with missing structures in low-intensity dark areas and small/thin objects (Fig. 1: SDF + Geometry Priors)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.686 + ], + "angle": 0, + "content": "The above observation motivates us to dive into bridging the remaining missing blocks of existing neural surface representation methods. Notably, we focus on the SDF-based representation as it achieves state-of-the-art performance and has been widely adopted. Our analysis suggests that both the RGB color rendering formulation and SDF representation have clear limitations preventing existing solutions from fully unleashing the potential of implicit neural surface representation for large-scale room-level scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.868 + ], + "angle": 0, + "content": "First, the color itself can show a significant impact on the optimization of geometric representation relying on the original RGB-based rendering formula [14], namely color bias. In particular, dark pixels with small intensity values will make the partial derivation of the loss with respect to the corresponding SDF value become zero, corrupting the optimization and resulting in missing structures in dark areas (see for example in Fig. 1: Low Intensities). Accordingly, herein instead of directly calculating the weighted color, we first compute weighted features and then use a learnable multi-layer perceptron (MLP) to decode the final rendering color. In such a way, we would still be able to effectively optimize the corresponding geometry represent" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.89, + 0.139 + ], + "angle": 0, + "content": "tation as long as the feature vector contains non-zero values." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.14, + 0.892, + 0.292 + ], + "angle": 0, + "content": "Second, the vanilla SDF-based neural rendering only considers a single ray directly passing through the object surface from the empty space and ignores objects along the ray [32, 34]. This configuration violates scene-level geometry where the existence of multiple objects clearly affects the distributions of SDF (Fig. 5(a)). Meanwhile, the optimization of thin structures and small objects, which naturally has small sampling probability, will be greatly degraded by this violation even with correct geometry prior and the structure will be erased to minimize the global geometry loss (Fig. 1: Detailed Structures)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.892, + 0.403 + ], + "angle": 0, + "content": "In addition, although occupancy-based representations are likely to generate unwanted structure and cannot warrant a smooth surface reconstruction (Fig. 1), they are often sufficiently robust to objects along the ray and free from object interference in scene-level data. Therefore, during optimization, we propose to describe the room-level scene using occupancy in conjunction with signed distance functions (SDFs) to compensate for each other's defects." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.403, + 0.802, + 0.416 + ], + "angle": 0, + "content": "The technical contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.427, + 0.892, + 0.482 + ], + "angle": 0, + "content": "- We explore an improved feature rendering scheme to overcome the problem of vanishing gradients in neural implicit reconstruction brought by the vanilla color space rendering formula." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.491, + 0.892, + 0.56 + ], + "angle": 0, + "content": "- We carefully investigate insights and limitations in existing SDF and occupancy representations, and accordingly propose a hybrid representation mingling SDF with occupancy, dubbed Occ-SDF Hybrid, to resolve surfaces with thin structures and small objects." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.569, + 0.892, + 0.638 + ], + "angle": 0, + "content": "- We conduct a large body of qualitative and quantitative experiments against state-of-the-art, indicating that our Occ-SDF hybrid formula can yield a higher-fidelity room-level scene representation, particularly with successfully resolving small and dark objects." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.427, + 0.892, + 0.638 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.642, + 0.665 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Multi-view Stereo Conventional algorithms [1, 25, 4] always split the reconstruction into two steps. First, the feature-matching method [22, 17, 24] is applied to estimate the depth of each frame. Then, the resulting depth maps [12] are used to reconstruct the final scene. Notably, the reconstruction may suffer from poor performance in texture-less areas. Learning-based approaches are mainly divided into two categories. Typically, neural networks are embedded into the traditional reconstruction pipeline to replace specific modules, like feature matching [23, 37, 30], depth estimation [33], or depth fusion [5]. These methods often suffer from depth inconsistency problems due to the separately estimated depth maps. Alternatively, neural networks are designed to directly regress input images to trun" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.901 + ], + "angle": 0, + "content": "8941" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.47, + 0.154 + ], + "angle": 0, + "content": "cated signed distance functions (TSDFs) [16, 28], but the reconstruction results often lack enough fine details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.159, + 0.471, + 0.382 + ], + "angle": 0, + "content": "Neural Scene Representation Recently, coordinate-based neural representations can faithfully model a 3D scene with only posed images. Approaches with an implicit differentiable renderer [35] only use volume density as scene representation which can not extract 3D scenes directly. To address this issue, occupancy-based representation [18] and SDF-based representation [32, 34] are proposed to facilitate 3D reconstruction. Notably, these methods already achieve great performance for object-level scenes but exhibit poorly for room-level scenes, especially in texture-less areas. For the room-level scenes, several existing approaches [9, 39] have demonstrated the ability to employ learned shape priors derived from extensive data to reconstruct scenes from incomplete or noisy point clouds. However, these methods face limitations when it comes to reconstructing scenes solely from image data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.606 + ], + "angle": 0, + "content": "Priors for Indoor Scene Reconstruction Existing methods have attempted to introduce priors to resolve higher-fidelity surfaces in texture-less areas. Manhattan-SDF [8] follows semantic-NeRF[38] to estimate the volume density and semantic label at the same time, and then uses Manhattan-World assumption to regularize the geometry in floor and wall regions. NeuRIS [31] and MonoSDF [36] directly exploit the depth and normal predicted from an off-the-shelf neural network to regularize the geometry of each point, but in many cases, thin structures would disappear. NeuRIS [31] proposes a dynamic scheme to eliminate the wrong supervision signal from inaccurate estimated results, however, based on our investigation that fine structures are still lost even with the correct geometry for supervision. In all, we seek to explore a feature rendering scheme and a hybrid representation to overcome the above problems." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.325, + 0.638 + ], + "angle": 0, + "content": "3. Overview and Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.646, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Our goal is to examine the limitations of existing implicit neural surface representations and explore practical solutions for accurately reconstructing large-scale, room-level 3D geometry with fine details from a set of calibrated images. First, we find that the well-adopted color-based rendering formula in [36, 31] will induce optimization bias against low-intensity areas, leaving these areas under-optimized and resulting in missing reconstructions (Sec. 4.1). Accordingly, we propose a simple yet effective feature-based rendering formula to address the problem (Sec. 4.2). Second, our analysis shows that the SDF-based neural surface representation violates scene-level geometry supervised signal and thus prevents the model from obtaining accurate reconstructions, making the model tends to sacrifice small and thin structures (Sec. 5.2). Motivated by this, we propose a hybrid representation mingling occu" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.127, + 0.88, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.323, + 0.892, + 0.4 + ], + "angle": 0, + "content": "Figure 2. Network architecture. The geometry network takes 3D position \\((x, y, z)\\) after positional encoding (PE) as input and output both SDF and occupancy value. The appearance network takes view direction \\((\\theta, \\phi)\\) as input and outputs two types of color, the direct color is used in Eq. (4) to directly obtain the pixel color and the decoded color is calculated via the rendering formula (Eq. (8))." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.411, + 0.855, + 0.425 + ], + "angle": 0, + "content": "pancy and SDF for accurate reconstruction (Sec. 5.3)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.426, + 0.892, + 0.468 + ], + "angle": 0, + "content": "We here describe the mathematical preliminary on the state-of-the-art surface representation, namely SDF-based Neural Scene Representation [34], for 3D reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.524 + ], + "angle": 0, + "content": "For implicit neural reconstruction, we can represent the scene as a signed distance function (SDF) field, which is a continuous function \\( f \\) that calculates the distance between each point and its closest surface" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.526, + 0.891, + 0.56 + ], + "angle": 0, + "content": "\\[\n1 _ {\\Omega} (\\boldsymbol {p}) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\boldsymbol {p} \\in \\Omega \\\\ 0 & \\text {i f} \\boldsymbol {p} \\notin \\Omega \\end{array} , \\right. \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.56, + 0.815, + 0.581 + ], + "angle": 0, + "content": "\\[\nf (\\boldsymbol {p}) = (- 1) ^ {1 _ {\\Omega} (\\boldsymbol {p})} \\min _ {\\boldsymbol {y} \\in \\mathcal {M}} \\| \\boldsymbol {p} - \\boldsymbol {y} \\|,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.667 + ], + "angle": 0, + "content": "where \\(1_{\\Omega}(\\pmb{p})\\) is an indicator function to represent whether the space at position \\(p\\) is occupied, \\(\\mathcal{M} = \\partial \\Omega\\) is the boundary surface of occupied space and \\(||\\cdot ||\\) is the standard Euclidean 2-norm. Following the VolSDF [34], we use an MLP to represent the function \\(f\\) and convert the SDF value to Laplace density with the following function" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.67, + 0.891, + 0.686 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {i} \\left(\\boldsymbol {p} _ {i}\\right) = \\alpha \\Psi_ {\\beta} (- f \\left(\\boldsymbol {p} _ {i}\\right)), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.891, + 0.729 + ], + "angle": 0, + "content": "where \\(\\alpha, \\beta > 0\\) are learnable parameters, and \\(\\Psi_{\\beta}\\) is the cumulative distribution function (CDF) with zero mean and the \\(\\beta\\) scale is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.731, + 0.891, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\Psi_ {\\beta} (s) = \\left\\{ \\begin{array}{l l} \\frac {1}{2} \\exp \\left(\\frac {s}{\\beta}\\right) & , \\text {i f} s \\leq 0 \\\\ 1 - \\frac {1}{2} \\exp \\left(- \\frac {s}{\\beta}\\right) & , \\text {i f} s > 0 \\end{array} . \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.784, + 0.89, + 0.811 + ], + "angle": 0, + "content": "Color Rendering Formula According to the rendering formula [14], the color for the current ray \\( r \\) is rendered by" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.814, + 0.891, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} \\hat {c} _ {i} ^ {r}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.852, + 0.891, + 0.868 + ], + "angle": 0, + "content": "where \\(T_{i}^{r}\\) and \\(\\alpha_{i}\\) represent the transmittance and alpha" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.502, + 0.9 + ], + "angle": 0, + "content": "8942" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.127, + 0.47, + 0.168 + ], + "angle": 0, + "content": "value (a.k.a opacity), respectively, of sampled point. And \\(M\\) represent the number of the sampled point along the ray \\(r\\). They can be computed by" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.171, + 0.47, + 0.209 + ], + "angle": 0, + "content": "\\[\nT _ {i} ^ {r} = \\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {i}), \\alpha_ {i} = 1 - \\exp \\left(- \\sigma_ {i} ^ {r} \\delta_ {i} ^ {r}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.212, + 0.469, + 0.268 + ], + "angle": 0, + "content": "where \\(\\delta_r^i\\) is the distance between adjacent sample points. Finally, given the rendered color \\(\\hat{C} (r)\\), the SDF field will be optimized from sparsely sampled images by minimizing the color-based rendering loss as" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.271, + 0.469, + 0.299 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r g b}} = \\sum_ {r \\in R} | | \\hat {C} (r) - C (r) | | _ {1}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.469, + 0.331 + ], + "angle": 0, + "content": "where \\(C(r)\\) is the ground-truth color associated with the sampled ray \\(r\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.345, + 0.338, + 0.361 + ], + "angle": 0, + "content": "4. Feature Rendering Formula" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.368, + 0.383, + 0.384 + ], + "angle": 0, + "content": "4.1. Problem of Color-based Rendering" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.39, + 0.469, + 0.487 + ], + "angle": 0, + "content": "Given the SDF-based scene representation and the color-based rendering loss \\(\\mathcal{L}_{\\mathrm{rgb}}\\) in Sec. 3, we analyze the derivative of \\(\\mathcal{L}_{\\mathrm{rgb}}\\) to the opacity \\(\\alpha_{i}\\) of a point \\(p_i\\). Note that for a single point \\(p_i\\), as \\(\\alpha_{i}^{r}\\) are the same regardless of the rays, we thus omit its dependency on ray \\(r\\) and use \\(\\alpha_{i}\\) for simplicity. For a point \\(p_i\\), the derivative of the color loss function to its opacity \\(\\alpha_{i}\\) is" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.489, + 0.469, + 0.533 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L} _ {r g b}}{\\partial \\alpha_ {i}} = \\pm \\left(\\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {j}) c _ {i} - \\sum_ {k = i + 1} ^ {N} c _ {k} \\alpha_ {k} \\prod_ {j = 1, j \\neq i} ^ {k - 1} (1 - \\alpha_ {j})\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.535, + 0.469, + 0.713 + ], + "angle": 0, + "content": "which indicates that when we optimize the SDF value of \\( p_i \\), the gradient is determined by the color of the current point \\( p_i \\) and points behind it (\\( c_k \\) and \\( k \\in \\{i + 1, \\dots, N\\} \\)), and opacity of all points on the entire ray except for the current point (\\( \\alpha_j \\) and \\( j \\in \\{1, 2, \\dots, N\\} \\& j \\neq i \\)). Notably, when processing a dark region, saying that the \\( c_i \\) approaches zero, the first term of Eq. (7) will be close to zero. Similarly, if points behind \\( p_i \\) have low opacity (\\( \\alpha_k \\) and \\( k \\in \\{i + 1, \\dots, N\\} \\)), the gradient with respect to the SDF value will be small, causing the vanishing problem in dark regions. More generally, the gradient of SDF values can be affected by the color itself, resulting in a biased optimization process that tends to favor high color intensities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.469, + 0.867 + ], + "angle": 0, + "content": "The above analysis is also supported by our experiments below. As shown in Fig. 3, we sample rays in the dark regions and the light regions separately and accordingly record the trend of gradient norms in these two regions during the optimization. In the beginning, the gradient norms from these two regions are similar; and the gradient norm in the dark region (red solid line) decreases as the number of training epochs increases, while the gradient norm in the light region remains stable (blue solid line), indicating the dark areas contribute much less to the optimization process. As the optimization process proceeds, if these points are" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.125, + 0.887, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.264, + 0.892, + 0.302 + ], + "angle": 0, + "content": "Figure 3. The trend for the gradient. The mean and variance of gradient norm (shadowed curves for variance) corresponding to light and dark regions during optimization." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.316, + 0.893, + 0.4 + ], + "angle": 0, + "content": "predicted as dark colors (\\(c_i^r \\to 0\\)), it would lead to the gradient reduction effects as analyzed in Eq. (7). The shadowed regions keep the same trend as the mean values, further affirming our earlier analysis. Note that the gradient of points in these areas will not equal zero due to the influence of other loss functions, like depth consistency loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.416, + 0.731, + 0.431 + ], + "angle": 0, + "content": "4.2. Feature-based Rendering" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.44, + 0.892, + 0.538 + ], + "angle": 0, + "content": "To resolve the aforementioned problem, we propose feature-based color rendering loss. As shown in Fig. 2, the Appearance network outputs two predictions for each point \\(i\\) along a ray \\(r\\): one is the color vector \\(\\hat{c}_i^r\\), and the other is the hidden feature \\(F_i^r\\). For direct color \\(\\hat{c}_i^r\\), we utilize Eq. (4) to obtain the target pixel color \\(\\hat{C}_c(r)\\). And the hidden feature \\(F_r^i\\) is used to render the ray feature \\(\\hat{F}(r)\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.541, + 0.891, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\hat {F} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} F _ {i} ^ {r}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.582, + 0.891, + 0.611 + ], + "angle": 0, + "content": "The ray feature \\(\\hat{F}_T\\) is further decoded by a decoder \\(\\mathcal{D}\\) to yield the decoded target pixel color," + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.612, + 0.891, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\hat {C} _ {F} (r) = \\mathcal {D} (\\hat {F} (r)), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.892, + 0.756 + ], + "angle": 0, + "content": "where the decoder \\(\\mathcal{D}\\) is a single-layer perceptron with 256 nodes. Finally, the decoded color \\(\\hat{C}_F(r)\\) from the rendered feature is used to construct the feature-based color rendering loss. As such, the optimization of these dark regions would not be affected by the color itself. As long as there are non-zero values in the rendered feature, there will be non-zero gradients with respect to the volume density of the concerned point. As shown in Fig. 3 (dashed lines), the gradient norm is not influenced by the intensity of colors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.776, + 0.787, + 0.791 + ], + "angle": 0, + "content": "5. Hybrid Representation Scheme" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.835, + 0.816 + ], + "angle": 0, + "content": "5.1. Incorporating Geometry Prior Matters" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.867 + ], + "angle": 0, + "content": "It is clear that for room-level scene reconstruction, geometry priors are essential. Existing methods [31, 36] render depth \\(\\hat{D}(r)\\) and normal \\(\\hat{N}(r)\\) of the surface intersecting" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.9 + ], + "angle": 0, + "content": "8943" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.127, + 0.195, + 0.139 + ], + "angle": 0, + "content": "the current ray as" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.142, + 0.469, + 0.18 + ], + "angle": 0, + "content": "\\[\n\\hat {D} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} ^ {r} t _ {i} ^ {r} \\quad \\text {a n d} \\quad \\hat {N} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} ^ {r} \\hat {n} _ {i} ^ {r}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.184, + 0.469, + 0.281 + ], + "angle": 0, + "content": "where \\(\\hat{T}_r^i\\) and \\(\\hat{\\alpha}_r^i\\) have the same meaning as Eq. (4), \\(t_i^r\\) is the distance the ray passing and \\(n_i^r\\) is the normal of point \\(p_i\\). Next, these methods use depth and normal maps estimated from pre-trained models, such as Omnidata [10], to directly supervise the rendered depth \\(\\hat{D}(r)\\) and normal \\(\\hat{N}(r)\\) using Eq. (11) and Eq. (12), respectively. Overall, the depth loss function is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.282, + 0.469, + 0.311 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d e p t h}} = \\sum_ {r \\in \\mathcal {R}} | | (w \\hat {D} (r) + q) - \\bar {D} (r) | | ^ {2}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.313, + 0.469, + 0.367 + ], + "angle": 0, + "content": "where \\( w \\) and \\( q \\) are the scale and shift computed by the least-squares method [6] to solve scale-ambiguity problem for monocular depth prediction methods. And the normal loss function is" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.369, + 0.469, + 0.397 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {n o r m a l}} = \\sum_ {r \\in R} | | \\hat {N} (r) - \\bar {N} (r) | | _ {1} + | | 1 - \\hat {N} (r) ^ {T} \\bar {N} (r) | | _ {1}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.401, + 0.469, + 0.429 + ], + "angle": 0, + "content": "where \\(\\tilde{N} (r)\\) is the predicted monocular normal transformed to the same coordinate system with angular." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.469, + 0.582 + ], + "angle": 0, + "content": "As shown in Fig. 1, we note that these geometry priors benefit the reconstruction of better surfaces in textureless and sparse-viewed areas. However, thin structures and small objects, such as the yellow flower in Fig. 4, cannot be faithfully reconstructed with geometry priors. Recently, NeuRIS [31] put forward a hypothesis that this phenomenon arises from the inaccurate geometry supervisory signal (i.e. depth and surface normal). However, according to our experiment on Replica synthetic dataset, this problem still exists even though we use the perfect ground-truth depth, normal, and RGB to provide supervisory signals (see Fig. 4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.594, + 0.469, + 0.609 + ], + "angle": 0, + "content": "5.2. Problem of SDF Formula with Geometry Prior" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.469, + 0.797 + ], + "angle": 0, + "content": "To dive into the SDF representation and explore its limitations for surface reconstruction with geometric priors, we create a simplified scenario and simulate object occlusions as shown in Fig. 5(a). The ground-truth SDF intersecting with a horizontal plane is shown in Fig. 5(a), and the SDF distribution along a ray \\( r \\) intersecting with the blue cube at point \\( p_s \\) is shown in Fig. 5(c). There are many local minima and maxima due to the existence of multiple objects, which differs from the single-object scenario following a monotonic function (blue line in Fig. 5(c)). To examine depth priors for surface reconstruction, we employ the approach proposed in MonoSDF [36] to calculate the depth of \\( p_s \\) following Eq. (10) subject to the ground-truth SDF." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.469, + 0.867 + ], + "angle": 0, + "content": "However, even with the ground-truth SDF, the estimated depth value (1.59, the red vertical plot in Fig. 5(e)) still deviates from the true depth value (2.94, the green vertical plot in Fig. 5(e)) when multiple objects exist. According to Eq. (10), the estimated normal value would suffer from" + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.128, + 0.625, + 0.138 + ], + "angle": 0, + "content": "Pseudo Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.139, + 0.626, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.224, + 0.626, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.663, + 0.129, + 0.716, + 0.138 + ], + "angle": 0, + "content": "MonoSDF" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.138, + 0.746, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.224, + 0.745, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.794, + 0.13, + 0.823, + 0.138 + ], + "angle": 0, + "content": "Error" + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.138, + 0.864, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.223, + 0.864, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.865, + 0.138, + 0.889, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.865, + 0.224, + 0.888, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.326, + 0.892, + 0.378 + ], + "angle": 0, + "content": "Figure 4. Illustration of failure cases of state-of-the-arts. Even though applying the perfect pseudo ground-truth geometry to supervise the model, existing room-level reconstruction methods like [36] can still fail to resolve accurate 3D structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.596 + ], + "angle": 0, + "content": "the same problem. This implies that existing methods incorporating geometry priors [36, 31] to guide the learning of the SDF representation may not necessarily encourage the model to learn the true SDF for scene-level surface reconstruction. In turn, because small objects or thin structures usually have low sampling probability during training, the minimization of \\(\\mathcal{L}_{\\mathrm{depth}}\\) will encourage the model to predict SDF ignoring small objects along the ray \\(r\\) such that the estimated SDF will produce depth values closer to the depth supervision (see Fig. 5(e)) and minimize the overall loss function, attempting to mimic the single object scenario (right part in Fig. 5). In sum, the supervision from geometric priors tends to sacrifice the reconstruction of small objects to preserve large surface reconstruction, which aligns also with our observation presented in Fig. 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.607, + 0.843, + 0.622 + ], + "angle": 0, + "content": "5.3. Hybrid Occupancy-SDF Representation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.891, + 0.699 + ], + "angle": 0, + "content": "The problem above is essentially caused by the SDF representation, which describes the geometry of a scene as a whole and thus suffers from the interference of other objects, especially small objects, and thin structures are prone to be removed to preserve large structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.891, + 0.852 + ], + "angle": 0, + "content": "Unlike the SDF representation, occupancy represents each point separately and thus is free from the interference of objects in this challenging scenario. However, occupancy representation only focuses on the intersecting point ignoring the constraint of neighborhood points. Thus, the reconstruction results represented by occupancy will have many floaters and useless structures, as shown in Fig. 1, which can be eliminated in SDF by Eikonal loss [7]. This inspires us to investigate a hybrid of occupancy and SDF as a representation for neural surface reconstruction as shown in Fig. 2. The geometry network \\(\\theta\\) outputs both SDF and occupancy." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.853, + 0.89, + 0.867 + ], + "angle": 0, + "content": "Specifically, the occupancy represents surfaces as the de" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.9 + ], + "angle": 0, + "content": "8944" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.135, + 0.258, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.194, + 0.245, + 0.205 + ], + "angle": 0, + "content": "Multi Objects Scene" + }, + { + "type": "image", + "bbox": [ + 0.267, + 0.125, + 0.408, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.195, + 0.395, + 0.205 + ], + "angle": 0, + "content": "Signed Distance Field" + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.135, + 0.549, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.427, + 0.195, + 0.528, + 0.205 + ], + "angle": 0, + "content": "Single Object Scene" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.125, + 0.697, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.575, + 0.195, + 0.683, + 0.205 + ], + "angle": 0, + "content": "Signed Distance Field" + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.127, + 0.865, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.208, + 0.853, + 0.219 + ], + "angle": 0, + "content": "(b) SDF Value at Point P" + }, + { + "type": "image_caption", + "bbox": [ + 0.134, + 0.212, + 0.667, + 0.224 + ], + "angle": 0, + "content": "(a) Schematic of the toy 3D structure for the multi-object scene (left) and single object scene (object)." + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.225, + 0.311, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.16, + 0.347, + 0.241, + 0.359 + ], + "angle": 0, + "content": "(c) SDF \\( f(\\pmb{p}_i) \\)" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.225, + 0.536, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.345, + 0.496, + 0.358 + ], + "angle": 0, + "content": "(d) Laplace density \\(\\delta_i(\\pmb {p}_i)\\)" + }, + { + "type": "image", + "bbox": [ + 0.54, + 0.228, + 0.88, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.661, + 0.344, + 0.756, + 0.357 + ], + "angle": 0, + "content": "(e) Weights \\(T_{r}^{i}\\alpha_{r}^{i}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.364, + 0.893, + 0.466 + ], + "angle": 0, + "content": "Figure 5. Toy experiments for the room-level scene. The left part of 5(a), where we stand in front of the yellow cylinder to observe the entire scene, is a widespread scenario for room-level scale scenes. Unlike the single object scenario, where the distribution of SDF value is a monotonic decreasing function from the observed position to the object, the room-level scenario has complex distributions with multi peaks/valleys along the single ray (5(c)). Following the Laplace density function [34], the density distributions of different situations are shown in 5(d), where room-level scenes have a secondary peak near small objects but the single object scene only has one peak. It is because of the existence of this peak, the weights in the room-level scene (5(e)) exhibit a multi-model distribution, while for the single object case a uni-modal distribution. As such, we note that the rendering depth \\(\\hat{D}\\) deviates from the ground truth in the room-level scene but is close to the ground truth depth object-level scene. 5(b) means the effect of supervised signal in three different representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.469, + 0.509 + ], + "angle": 0, + "content": "cision boundary of a binary occupancy classifier, parameterized by a neural network \\(\\theta\\)" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.511, + 0.469, + 0.527 + ], + "angle": 0, + "content": "\\[\no _ {\\theta} (\\mathbf {p}): \\mathbb {R} ^ {3} \\rightarrow [ 0, 1 ], \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.47, + 0.572 + ], + "angle": 0, + "content": "where \\(\\mathbf{p}\\) is a 3D point. The occupancy representation assumes that objects are solid, thus we can rewrite the neural rendering formula [14] to" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.574, + 0.469, + 0.612 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (r) = \\sum_ {i = 1} ^ {M} o \\left(\\mathbf {p} _ {i}\\right) \\prod_ {j < i} \\left(1 - o \\left(\\mathbf {x} _ {j}\\right)\\right) c \\left(\\mathbf {p} _ {i}, d\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.725 + ], + "angle": 0, + "content": "which replaces the opacity \\(\\alpha\\) to a discrete occupancy indicator variable \\(o\\in 0,1\\), where \\(o = 0\\) indicates the free space while \\(o = 1\\) the occupied space. Thus, this representation will not be affected by the objects along the ray, and the rendering depth will be consistent with ground-truth depth in ground-truth occupancy space. Note that the occupancy-based representation is introduced to facilitate optimization. During inference, the SDF is used for reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.47, + 0.867 + ], + "angle": 0, + "content": "To understand why and how the hybrid representation helps optimize the SDF field for accurate reconstruction, we conduct the following empirical analysis, using the scenario shown in Fig. 5(a). Here, the orange ray hits a surface point \\( Q \\) of the large blue cube and the blue ray hits the surface point \\( P \\) on the small cylinder. During optimization, the depth/normal loss for point \\( Q \\) along the orange ray will encourage the model to predict a large SDF value (absolute) of point \\( P \\) (Fig. 5(b)) which violates the reconstruction of the small cylinder where a small SDF value is desired. In" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.717 + ], + "angle": 0, + "content": "contrast, point \\( Q \\) has no effects on point \\( P \\) with occupancy representation. The hybrid representation joins the forces of SDF and occupancy representations, aiming to use occupancy representation to help overcome the issues of SDF representation in optimization. Although the depth/normal loss from the SDF presentation for point \\( Q \\) still has a negative impact on the optimization of point \\( P \\). The additional occupancy representation will force the network to predict a large occupancy value for a point \\( P \\) and thus will indirectly regularize the network to predict a small SDF value (see Fig. 5(b): the blue up arrow in \"Hybrid\"). We admit that this hybrid representation can only alleviate this problem, and our study is more empirical. Fundamental issues arise from insufficient neural scene representation, which requires further research efforts. We explore further why this combination would bring notable benefits to the supplementary with an example." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.735, + 0.633, + 0.751 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.76, + 0.88, + 0.774 + ], + "angle": 0, + "content": "Optimization. In the training stage, we minimize the loss" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.779, + 0.891, + 0.818 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {r g b}} ^ {s d f} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {r g b}} ^ {s d f _ {F}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {e i k}} + \\lambda_ {3} \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {o c c}} \\tag {15} \\\\ + \\lambda_ {4} \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {s d f}} + \\lambda_ {5} \\mathcal {L} _ {\\text {n o r m a l}} ^ {\\text {o c c}} + \\lambda_ {6} \\mathcal {L} _ {\\text {n o r m a l}} ^ {\\text {s d f}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.868 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{rgb}\\) means color-based rendering loss following Eq. (6) but only to SDF representation. The rendering color computed by the feature rendering formula (Eq. (8))" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.901 + ], + "angle": 0, + "content": "8945" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.125, + 0.473, + 0.279 + ], + "angle": 0, + "content": "and Eq. (9)) is denoted to \\(\\mathcal{L}_{rgb}^{sdf_F}\\). Notably, \\(\\mathcal{L}_{eik}\\) means the eikonal loss [7], \\(\\mathcal{L}_{depth}\\) means the depth rendering loss following Eq. (11), and \\(\\mathcal{L}_{normal}\\) means the normal rendering loss following Eq. (12). We apply them for both representations, where the superscript \\(occ\\) indicates the loss computed by occupancy-based representation, while the \\(sdf\\) by SDF-based representation. The network is optimized by the Adam optimizer with a learning rate of \\(5e^{-4}\\). We set weights \\(\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4, \\lambda_5, \\lambda_6\\) to 1, 0.05, 0.5, 0.1, 0.1, 0.05, respectively. The network architecture and sampling strategy are detailed in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.282, + 0.473, + 0.476 + ], + "angle": 0, + "content": "Datasets. We use three datasets to assess the performance of our algorithm. ScanNet [2] is a real-world dataset that provides 1,513 scenes captured with Kinect V1 RGB-D camera. The BundleFusion [3] is applied to provide high-quality camera poses and surface reconstructions. For each scene, we uniformly sample roughly 500 frames to train our network. Tanks and Temples [11] is a real-world, large-scale scene dataset. We use four indoor scenes from their advanced split and run on the official server. Replica [27] is a synthetic dataset that provides 18 scenes, with each providing dense geometry, HDR textures, and semantic annotations. We select 8 scenes and use the Habitat simulator [29] to render RGB images following MonoSDF [36] splits. Notably, we conduct ablation studies on this dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.473, + 0.812 + ], + "angle": 0, + "content": "Compared Methods. (1) UNISURF [18] is an occupancy-based method that unifies surface rendering and volume rendering for neural scene reconstruction. We implement the UNISURF* with normal and depth priors for a fair comparison. (2) MonoSDF [36] is an SDF-based method that adds depth and normal constraints on VolSDF [34]. (3) Manhattan-SDF [8] is an SDF-based method that adds a semantic branch and uses the Manhattan constraint to regularize the geometry in floor and wall regions. (4) COLMAP [25] is a classical multi-view stereo method with Poisson surface reconstruction. (5) NeuRIS [31] is an SDF-based method that introduces pseudo normal prior to the NeUS [32] architecture. Meanwhile, it leverages multiview consistency to eliminate the wrong supervision signal from inaccurate estimated results. (6) NICER-SLAM [39] is an SDF-based dense SLAM system that uses locally implicit map representation and can simultaneously optimize for camera poses and a hierarchical neural implicit map representation. (7) LIG [9] uses the local implicit grid representation to reconstruct the large-scale scene from partial or noise point clouds. (8) Convolutional Occupancy network(Conv-Occ) [21] is a locally implicit representation that integrates local information to get better reconstruction results from noisy point cloud." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.812, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Notably, local implicit representation [9, 21] can only reconstruct the scene from point clouds, thus we re-implement them using point clouds generated from scale-aligned pseudo depth and utilize the provided pretrained" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.154 + ], + "angle": 0, + "content": "models for evaluation. And we directly obtain the results from the main paper of NICER-SLAM [39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.158, + 0.894, + 0.256 + ], + "angle": 0, + "content": "Metrics. All meshes are evaluated by 5 standard metrics defined in [16]: Accuracy, Completeness, Precision, Recall, and \\( F \\)-score. Their definition will be discussed in the supplementary. For the Replica dataset, we also report the normal consistency following [13, 8, 20]. For the Tanks and Temples dataset, we use the official server to evaluate our results and report the F-score for selected scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.262, + 0.64, + 0.275 + ], + "angle": 0, + "content": "6.1. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.283, + 0.892, + 0.31 + ], + "angle": 0, + "content": "We compare our method with state-of-the-art methods on three benchmark datasets." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.317, + 0.894, + 0.42 + ], + "angle": 0, + "content": "
MethodAcc ↓Comp ↓C-L1 ↓Prec ↑Recall ↑F-score ↑
COLMAP [25]0.0470.2350.14171.144.153.7
UNISURF [18]0.5540.1640.35921.236.226.7
VolSDF [34]0.4140.1200.26732.139.434.6
NeUS [32]0.1790.2080.19431.327.529.1
Manhattan-SDF [8]0.0720.0680.07062.156.860.2
NeuRIS [31]0.0500.0490.05071.766.969.2
MonoSDF [36]0.0350.0480.04279.968.173.3
Ours0.0390.0410.04080.076.077.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.426, + 0.892, + 0.452 + ], + "angle": 0, + "content": "Table 1. Quantitative assessments of the proposed model against previous works on the ScanNet dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.71 + ], + "angle": 0, + "content": "Results on ScanNet Dataset. We conducted a comparative analysis of our proposed approach against existing implicit reconstruction methods, including ManhattanSDF [8], NeuRIS [31] and MonoSDF [36] using the ScanNet dataset. As revealed in Table 1, our proposed method outperforms state-of-the-art methods, with a significant increase in F-score by 4.6. Additionally, in terms of Recall, our method substantially outperforms MonoSDF by 7.9 without needing extra data. Overall, our approach performs on par with the state-of-art methods in \"Acc\", \"Chamfer-\\(\\mathcal{L}_1\\) (C-\\(\\mathcal{L}_1\\)) and \"Prec\" and obtain notable performance gains in \"Comp\", \"Recall\" and \"F-score\". This is because these metrics (\"Comp\" and \"Recall\") are better metrics in evaluating how complete and accurate in capturing the shape and details of the scene being reconstructed. Further, Fig. 6 reveals that our method can attain more complete reconstructions with details and for low pixel intensities regions." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.719, + 0.89, + 0.78 + ], + "angle": 0, + "content": "
AuditoriumBallroomCourtroomMuseumMean
MonoSDF3.092.4710.005.105.165
Ours5.225.4213.998.598.305
MonoSDF*3.173.7013.755.686.58
Ours*6.197.3319.8011.8511.295
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.784, + 0.892, + 0.835 + ], + "angle": 0, + "content": "Table 2. Quantitative assessments of the proposed model against Monosdf on the Tanks and Temples dataset. The evaluation metrics for the Tanks and Temples dataset are F-score. * means that the hash-grid structure is adopted." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.839, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Results on Tanks and Temples Dataset. For challenging large-scale indoor scenes, we conduct experiments on" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.503, + 0.901 + ], + "angle": 0, + "content": "8946" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.222, + 0.132, + 0.267, + 0.143 + ], + "angle": 0, + "content": "Replica" + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.145, + 0.245, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.145, + 0.399, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.133, + 0.591, + 0.142 + ], + "angle": 0, + "content": "ScanNet" + }, + { + "type": "image", + "bbox": [ + 0.402, + 0.145, + 0.561, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.144, + 0.728, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.133, + 0.866, + 0.143 + ], + "angle": 0, + "content": "Tanks and Temples" + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.144, + 0.888, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.227, + 0.279, + 0.236 + ], + "angle": 0, + "content": "UNISRUF*" + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.237, + 0.245, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.237, + 0.399, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.519, + 0.227, + 0.612, + 0.236 + ], + "angle": 0, + "content": "Manhattan-SDF" + }, + { + "type": "image", + "bbox": [ + 0.401, + 0.237, + 0.562, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.237, + 0.728, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.784, + 0.227, + 0.844, + 0.235 + ], + "angle": 0, + "content": "MonoSDF" + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.236, + 0.888, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.213, + 0.322, + 0.272, + 0.332 + ], + "angle": 0, + "content": "MonoSDF" + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.333, + 0.245, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.333, + 0.398, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.401, + 0.333, + 0.561, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.322, + 0.596, + 0.332 + ], + "angle": 0, + "content": "BSDF" + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.333, + 0.728, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.779, + 0.322, + 0.849, + 0.332 + ], + "angle": 0, + "content": "Ours (MLP)" + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.333, + 0.888, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.416, + 0.258, + 0.425 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.427, + 0.245, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.427, + 0.398, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.401, + 0.427, + 0.561, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.427, + 0.728, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.416, + 0.867, + 0.425 + ], + "angle": 0, + "content": "MonoSDF (Grids)" + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.426, + 0.886, + 0.508 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.2, + 0.509, + 0.282, + 0.518 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.509, + 0.607, + 0.518 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.51, + 0.854, + 0.52 + ], + "angle": 0, + "content": "Ours (Grids)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.523, + 0.892, + 0.549 + ], + "angle": 0, + "content": "Figure 6. Reconstruction results on representative datasets of Replica (left), ScanNet (middle), and Tanks and Temples (right). The ground truth is presented on the bottom-most. Red boxes in sub-figures highlight those areas where distinctive differences can be observed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.789 + ], + "angle": 0, + "content": "the advanced Tanks and Temples dataset [11], which features more complicated structures. As alternative methods of neural reconstruction from images are not assessed on this dataset, we implement the best-performing method MonoSDF and compare with it. Thus, the MonoSDF and two versions of our method are implemented. Specifically, one adopts the pure MLP architecture while the other uses the hash grids as the input representation. The quantitative assessments (Table 2) reveal that our method shows better performance on this dataset, regardless of whether an MLP or hash-grid structure is used. And our hybrid representation exhibits excellent generalization abilities across different implicit structures. Overall, our compelling experimental results on the Tanks and Temples dataset further validate the robustness and versatility of the proposed method in reconstructing complex and challenging indoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.798, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Results on Replica Dataset. Quantitative assessment results on the Replica dataset are presented in Table 3. For this dataset, we compare our methods with both point-based methods [21, 9] and rendering methods [39, 18, 36]. Ours significantly surpasses existing state-of-the-art neural ren" + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.568, + 0.892, + 0.653 + ], + "angle": 0, + "content": "
MethodNormal C.↑Chamfer- \\( {\\mathcal{L}}_{1} \\downarrow \\)F-score ↑
Conv-Occ [21]85.736.4358.33
LIG [9]89.565.5365.20
NICER-SLAM [39]90.273.91-
UNISURF†[18]90.964.9378.99
MonoSDF†[36]92.112.9486.18
\\( Ours^{\\dagger } \\)93.432.5892.12
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.659, + 0.892, + 0.698 + ], + "angle": 0, + "content": "Table 3. Quantitative assessments of the proposed model against prior works on the Replica dataset. Herein, \\(\\dagger\\) indicates the use of geometry priors as supervision signals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.892, + 0.868 + ], + "angle": 0, + "content": "dering methods. The results reveal that the SDF-based representation outperforms the occupancy-based ones (i.e. UNISURF*). This is because the SDF usually enforces constraints on the distribution of the entire scene, benefiting to suppressing the occurrence of floaters or unnecessary structures in occupancy-based representation. Notably, our OccSDF Hybrid method can constrain the distribution of the entire scene with SDF representation meanwhile exploiting the occupancy representation to resolve thin structures and small objects. Qualitative comparisons are shown in Fig. 6." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.901 + ], + "angle": 0, + "content": "8947" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.126, + 0.23, + 0.141 + ], + "angle": 0, + "content": "6.2. Ablation Study" + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.153, + 0.47, + 0.222 + ], + "angle": 0, + "content": "
Normal C.↑Chamfer- \\( {\\mathcal{L}}_{1} \\downarrow \\)F-score ↑
MonoSDF92.112.9486.18
+ feature93.012.6491.01
+ hybrid93.222.7790.24
full model93.432.5892.12
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.227, + 0.47, + 0.265 + ], + "angle": 0, + "content": "Table 4. Ablation study on the Replica dataset [27], where we progressively add different constraints to assess their impacts. The MonoSDF [36] is set as the baseline model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.273, + 0.47, + 0.383 + ], + "angle": 0, + "content": "We conduct ablation studies on the Replica dataset as it provides ground-truth geometry. Four different configurations are investigated to train our model, including (1) MonoSDF with MLP settings (MonoSDF-MLP); (2) MonoSDF-MLP with our feature-based rendering formula; (3) MonoSDF-MLP with our hybrid representation; (4) MonoSDF-MLP with both the feature-based rendering formula and hybrid representation scheme (Full model)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.385, + 0.47, + 0.633 + ], + "angle": 0, + "content": "Table 4 shows that all metrics are improved when using the feature rendering to reconstruct this scene. Our proposed feature rendering scheme addresses the difficulties in reconstructing areas of low intensities, resulting in better results. On the other hand, the hybrid representation also leads to significant improvements in all metrics. Notably, it improves the completeness of small objects and thin structures, as evidenced by the results in Fig. 6. By leveraging both components, our model achieves an overall improvement of 5.94 in F-score, along with improved normal consistency and Chamfer-\\(\\mathcal{L}_1\\). We attribute this success to our feature-based color rendering formula and our hybrid representation, which addresses the color-bias issue in optimization and difficulties in reconstructing detailed structures. The visualization results in Fig. 6 show our model's excellent reconstruction performance, especially in low-intensity areas and detailed structures. We will add more ablation studies and visualize results in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.642, + 0.285, + 0.658 + ], + "angle": 0, + "content": "6.3. Parameters Adjusting" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.664, + 0.469, + 0.803 + ], + "angle": 0, + "content": "As shown in Eq. (15), our method newly added three different losses \\(\\mathcal{L}_{rgb}^{sdf_F},\\mathcal{L}_{depth}^{occ},\\mathcal{L}_{normal}^{occ}\\). In order to verify the sensitivity of our method to hyperparameters, we provided the results of the experiment on the Replica dataset as shown in Fig. 7. It is clear that our method is not very sensitive to hyperparameters, and all the evaluated settings outperform the baseline method (C-\\(\\mathcal{L}_1\\): 2.94, F-score: 86.18). It is worth noting that our approach demonstrates consistent performance enhancement across diverse datasets using the same parameter set, outperforming the baseline results." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.816, + 0.196, + 0.83 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.469, + 0.867 + ], + "angle": 0, + "content": "We have analyzed the constraints present in current neural scene representation techniques with geometry priors," + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.127, + 0.874, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.258, + 0.874, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.39, + 0.874, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.527, + 0.866, + 0.541 + ], + "angle": 0, + "content": "Figure 7. Performance with different hyperparameter choices." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.72 + ], + "angle": 0, + "content": "and have identified issues in their ability to reconstruct detailed structures due to a biased optimization towards high color intensities and the complex SDF distribution. As a result, we have developed a feature rendering scheme that balances color regions and have implemented a hybrid representation to address the limitations of the SDF distribution. Our approach has demonstrated the successful reconstruction of room scenes with a high-fidelity surface, including small objects, detailed structures, and low-intensity pixel regions. We envision our results inspire further research on improving neural scene representation for accurate and large-scale surface reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.733, + 0.661, + 0.749 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.892, + 0.867 + ], + "angle": 0, + "content": "We thank Xin Kong for his advising during the rebuttal period. This work has been supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621 and 27212822), General Research Fund Scheme (Grant No. 17202422), and RGC matching fund scheme (RMGS). 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Nicer-slam: Neural implicit scene encoding for rgb slam, 2023. 3, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.127, + 0.893, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.89, + 0.501, + 0.9 + ], + "angle": 0, + "content": "8950" + } + ] +] \ No newline at end of file diff --git a/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/c8aa23d3-c76a-4daf-a8f1-9ca330b3d300_origin.pdf b/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/c8aa23d3-c76a-4daf-a8f1-9ca330b3d300_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2cf192246f0aa17505f45eb8bc322ed1acd468fc --- /dev/null +++ b/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/c8aa23d3-c76a-4daf-a8f1-9ca330b3d300_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6552085d6d87f5c431b45a832d667033c1d524487b6e8c32238cd81bedfa9371 +size 1897942 diff --git a/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/full.md b/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e0d5fde21edbc8e7213672d5e7d85587093fae81 --- /dev/null +++ b/2023/Learning a Room with the Occ-SDF Hybrid_ Signed Distance Function Mingled with Occupancy Aids Scene Representation/full.md @@ -0,0 +1,428 @@ +# Learning A Room with the Occ-SDF Hybrid: Signed Distance Function Mingled with Occupancy Aids Scene Representation + +Xiaoyang Lyu $^{1}$ , Peng Dai $^{1}$ , Zizhang Li $^{2}$ , Dongyu Yan $^{3}$ , Yi Lin $^{4}$ , Yifan Peng $^{1}$ , Xiaojuan Qi $^{1}$ , $^{1}$ The University of Hong Kong, $^{2}$ Zhejiang University, $^{3}$ Harbin Institute of Technology, $^{4}$ DJI + +![](images/3bffb6de3cfda59b015ae87f8fbd7f1df6a10dcf0348f75996fca8c9cd5d6f47.jpg) +Figure 1. Overview and reconstruction results of the Occ-SDF hybrid neural scene representation. Aided with the feature rendering scheme (Sec. 4) and the hybrid representation (Sec. 5), our method yields results with more detailed structures in room-level scenes compared to the state-of-the-art, particularly for those low intensities and detailed structures. + +# Abstract + +Implicit neural rendering, using signed distance function (SDF) representation with geometric priors like depth or surface normal, has made impressive strides in the surface reconstruction of large-scale scenes. However, applying this method to reconstruct a room-level scene from images may miss structures in low-intensity areas and/or small, thin objects. We have conducted experiments on three datasets to identify limitations of the original color rendering loss and priors-embedded SDF scene representation. + +Our findings show that the color rendering loss creates an optimization bias against low-intensity areas, resulting in gradient vanishing and leaving these areas unoptimized. To address this issue, we propose a feature-based color rendering loss that utilizes non-zero feature values to bring back optimization signals. Additionally, the SDF representation can be influenced by objects along a ray path, disrupting the monotonic change of SDF values when a single + +object is present. Accordingly, we explore using the occupancy representation, which encodes each point separately and is unaffected by objects along a querying ray. Our experimental results demonstrate that the joint forces of the feature-based rendering loss and Occ-SDF hybrid representation scheme can provide high-quality reconstruction results, especially in challenging room-level scenarios. The code is available at https://github.com/shawLyu/Occ-SDF-Hybrid + +# 1. Introduction + +Reconstructing a 3D scene from a series of multi-view images is a crucial problem in the realm of computer vision. This process has widespread applications in various fields such as animation, gaming, and virtual/augmented reality (VR/AR). The recent trend is to represent a 3D scene as an implicit function parameterized by a neural network [13, 19, 26, 21], whose optimization is supervised by ex + +plicit 3D data like point cloud or real SDF value. Recent advancements in neural radiance field (NeRF) [14] further enable learning an implicit 3D representation from purely sparse posed images [35, 15]. + +However, when it comes to producing high-quality novel-view synthesis, these methods frequently utilize volume density [14] to represent the 3D geometry. Unfortunately, this approach does not adequately constrain the 3D geometry in the presence of ambiguities [18], ultimately leading to poor surface reconstructions (as depicted in Fig. 1: Volume Density). + +Accordingly, research efforts have been made to exploit geometry-friendly representations, including signed distance function (SDF) [32, 34, 19] or occupancy [18], whose zero-level set can be extracted to become the concerned 3D surface. Albeit improving quality, they consider the reconstruction only of a single object, thereby, the performance degrades dramatically when applied to scene-level surface reconstruction, i.e., representing a room (Fig. 1: SDF). An attribute is that reconstructing texture-less areas often suffers from ambiguous visual cues with only RGB loss as the regularization. To address this problem, recent research has attempted to incorporate semantic [8] or geometric priors (depth/normal [36, 31] constraints) to further regularize scene-level reconstruction. With SDF-based representation and geometric priors [36], the reconstruction quality has been greatly improved (Fig. 1: SDF + Geometry Priors), especially concerning large flat areas and objects. However, it still cannot faithfully reconstruct the 3D scene with missing structures in low-intensity dark areas and small/thin objects (Fig. 1: SDF + Geometry Priors). + +The above observation motivates us to dive into bridging the remaining missing blocks of existing neural surface representation methods. Notably, we focus on the SDF-based representation as it achieves state-of-the-art performance and has been widely adopted. Our analysis suggests that both the RGB color rendering formulation and SDF representation have clear limitations preventing existing solutions from fully unleashing the potential of implicit neural surface representation for large-scale room-level scenes. + +First, the color itself can show a significant impact on the optimization of geometric representation relying on the original RGB-based rendering formula [14], namely color bias. In particular, dark pixels with small intensity values will make the partial derivation of the loss with respect to the corresponding SDF value become zero, corrupting the optimization and resulting in missing structures in dark areas (see for example in Fig. 1: Low Intensities). Accordingly, herein instead of directly calculating the weighted color, we first compute weighted features and then use a learnable multi-layer perceptron (MLP) to decode the final rendering color. In such a way, we would still be able to effectively optimize the corresponding geometry represent + +tation as long as the feature vector contains non-zero values. + +Second, the vanilla SDF-based neural rendering only considers a single ray directly passing through the object surface from the empty space and ignores objects along the ray [32, 34]. This configuration violates scene-level geometry where the existence of multiple objects clearly affects the distributions of SDF (Fig. 5(a)). Meanwhile, the optimization of thin structures and small objects, which naturally has small sampling probability, will be greatly degraded by this violation even with correct geometry prior and the structure will be erased to minimize the global geometry loss (Fig. 1: Detailed Structures). + +In addition, although occupancy-based representations are likely to generate unwanted structure and cannot warrant a smooth surface reconstruction (Fig. 1), they are often sufficiently robust to objects along the ray and free from object interference in scene-level data. Therefore, during optimization, we propose to describe the room-level scene using occupancy in conjunction with signed distance functions (SDFs) to compensate for each other's defects. + +The technical contributions are as follows: + +- We explore an improved feature rendering scheme to overcome the problem of vanishing gradients in neural implicit reconstruction brought by the vanilla color space rendering formula. +- We carefully investigate insights and limitations in existing SDF and occupancy representations, and accordingly propose a hybrid representation mingling SDF with occupancy, dubbed Occ-SDF Hybrid, to resolve surfaces with thin structures and small objects. +- We conduct a large body of qualitative and quantitative experiments against state-of-the-art, indicating that our Occ-SDF hybrid formula can yield a higher-fidelity room-level scene representation, particularly with successfully resolving small and dark objects. + +# 2. Related Work + +Multi-view Stereo Conventional algorithms [1, 25, 4] always split the reconstruction into two steps. First, the feature-matching method [22, 17, 24] is applied to estimate the depth of each frame. Then, the resulting depth maps [12] are used to reconstruct the final scene. Notably, the reconstruction may suffer from poor performance in texture-less areas. Learning-based approaches are mainly divided into two categories. Typically, neural networks are embedded into the traditional reconstruction pipeline to replace specific modules, like feature matching [23, 37, 30], depth estimation [33], or depth fusion [5]. These methods often suffer from depth inconsistency problems due to the separately estimated depth maps. Alternatively, neural networks are designed to directly regress input images to trun + +cated signed distance functions (TSDFs) [16, 28], but the reconstruction results often lack enough fine details. + +Neural Scene Representation Recently, coordinate-based neural representations can faithfully model a 3D scene with only posed images. Approaches with an implicit differentiable renderer [35] only use volume density as scene representation which can not extract 3D scenes directly. To address this issue, occupancy-based representation [18] and SDF-based representation [32, 34] are proposed to facilitate 3D reconstruction. Notably, these methods already achieve great performance for object-level scenes but exhibit poorly for room-level scenes, especially in texture-less areas. For the room-level scenes, several existing approaches [9, 39] have demonstrated the ability to employ learned shape priors derived from extensive data to reconstruct scenes from incomplete or noisy point clouds. However, these methods face limitations when it comes to reconstructing scenes solely from image data. + +Priors for Indoor Scene Reconstruction Existing methods have attempted to introduce priors to resolve higher-fidelity surfaces in texture-less areas. Manhattan-SDF [8] follows semantic-NeRF[38] to estimate the volume density and semantic label at the same time, and then uses Manhattan-World assumption to regularize the geometry in floor and wall regions. NeuRIS [31] and MonoSDF [36] directly exploit the depth and normal predicted from an off-the-shelf neural network to regularize the geometry of each point, but in many cases, thin structures would disappear. NeuRIS [31] proposes a dynamic scheme to eliminate the wrong supervision signal from inaccurate estimated results, however, based on our investigation that fine structures are still lost even with the correct geometry for supervision. In all, we seek to explore a feature rendering scheme and a hybrid representation to overcome the above problems. + +# 3. Overview and Preliminary + +Our goal is to examine the limitations of existing implicit neural surface representations and explore practical solutions for accurately reconstructing large-scale, room-level 3D geometry with fine details from a set of calibrated images. First, we find that the well-adopted color-based rendering formula in [36, 31] will induce optimization bias against low-intensity areas, leaving these areas under-optimized and resulting in missing reconstructions (Sec. 4.1). Accordingly, we propose a simple yet effective feature-based rendering formula to address the problem (Sec. 4.2). Second, our analysis shows that the SDF-based neural surface representation violates scene-level geometry supervised signal and thus prevents the model from obtaining accurate reconstructions, making the model tends to sacrifice small and thin structures (Sec. 5.2). Motivated by this, we propose a hybrid representation mingling occu + +![](images/4e47052f285e56f48ac9ec6e4961cfd62d1195d7152d83141565a388f7d9b0de.jpg) +Figure 2. Network architecture. The geometry network takes 3D position $(x, y, z)$ after positional encoding (PE) as input and output both SDF and occupancy value. The appearance network takes view direction $(\theta, \phi)$ as input and outputs two types of color, the direct color is used in Eq. (4) to directly obtain the pixel color and the decoded color is calculated via the rendering formula (Eq. (8)). + +pancy and SDF for accurate reconstruction (Sec. 5.3). + +We here describe the mathematical preliminary on the state-of-the-art surface representation, namely SDF-based Neural Scene Representation [34], for 3D reconstruction. + +For implicit neural reconstruction, we can represent the scene as a signed distance function (SDF) field, which is a continuous function $f$ that calculates the distance between each point and its closest surface + +$$ +1 _ {\Omega} (\boldsymbol {p}) = \left\{ \begin{array}{l l} 1 & \text {i f} \boldsymbol {p} \in \Omega \\ 0 & \text {i f} \boldsymbol {p} \notin \Omega \end{array} , \right. \tag {1} +$$ + +$$ +f (\boldsymbol {p}) = (- 1) ^ {1 _ {\Omega} (\boldsymbol {p})} \min _ {\boldsymbol {y} \in \mathcal {M}} \| \boldsymbol {p} - \boldsymbol {y} \|, +$$ + +where $1_{\Omega}(\pmb{p})$ is an indicator function to represent whether the space at position $p$ is occupied, $\mathcal{M} = \partial \Omega$ is the boundary surface of occupied space and $||\cdot ||$ is the standard Euclidean 2-norm. Following the VolSDF [34], we use an MLP to represent the function $f$ and convert the SDF value to Laplace density with the following function + +$$ +\sigma_ {i} \left(\boldsymbol {p} _ {i}\right) = \alpha \Psi_ {\beta} (- f \left(\boldsymbol {p} _ {i}\right)), \tag {2} +$$ + +where $\alpha, \beta > 0$ are learnable parameters, and $\Psi_{\beta}$ is the cumulative distribution function (CDF) with zero mean and the $\beta$ scale is defined as + +$$ +\Psi_ {\beta} (s) = \left\{ \begin{array}{l l} \frac {1}{2} \exp \left(\frac {s}{\beta}\right) & , \text {i f} s \leq 0 \\ 1 - \frac {1}{2} \exp \left(- \frac {s}{\beta}\right) & , \text {i f} s > 0 \end{array} . \right. \tag {3} +$$ + +Color Rendering Formula According to the rendering formula [14], the color for the current ray $r$ is rendered by + +$$ +\hat {C} (r) = \sum_ {i = 1} ^ {M} T _ {i} ^ {r} \alpha_ {i} \hat {c} _ {i} ^ {r}, \tag {4} +$$ + +where $T_{i}^{r}$ and $\alpha_{i}$ represent the transmittance and alpha + +value (a.k.a opacity), respectively, of sampled point. And $M$ represent the number of the sampled point along the ray $r$ . They can be computed by + +$$ +T _ {i} ^ {r} = \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {i}), \alpha_ {i} = 1 - \exp \left(- \sigma_ {i} ^ {r} \delta_ {i} ^ {r}\right), \tag {5} +$$ + +where $\delta_r^i$ is the distance between adjacent sample points. Finally, given the rendered color $\hat{C} (r)$ , the SDF field will be optimized from sparsely sampled images by minimizing the color-based rendering loss as + +$$ +\mathcal {L} _ {\mathrm {r g b}} = \sum_ {r \in R} | | \hat {C} (r) - C (r) | | _ {1}, \tag {6} +$$ + +where $C(r)$ is the ground-truth color associated with the sampled ray $r$ . + +# 4. Feature Rendering Formula + +# 4.1. Problem of Color-based Rendering + +Given the SDF-based scene representation and the color-based rendering loss $\mathcal{L}_{\mathrm{rgb}}$ in Sec. 3, we analyze the derivative of $\mathcal{L}_{\mathrm{rgb}}$ to the opacity $\alpha_{i}$ of a point $p_i$ . Note that for a single point $p_i$ , as $\alpha_{i}^{r}$ are the same regardless of the rays, we thus omit its dependency on ray $r$ and use $\alpha_{i}$ for simplicity. For a point $p_i$ , the derivative of the color loss function to its opacity $\alpha_{i}$ is + +$$ +\frac {\partial \mathcal {L} _ {r g b}}{\partial \alpha_ {i}} = \pm \left(\prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {j}) c _ {i} - \sum_ {k = i + 1} ^ {N} c _ {k} \alpha_ {k} \prod_ {j = 1, j \neq i} ^ {k - 1} (1 - \alpha_ {j})\right), \tag {7} +$$ + +which indicates that when we optimize the SDF value of $p_i$ , the gradient is determined by the color of the current point $p_i$ and points behind it ( $c_k$ and $k \in \{i + 1, \dots, N\}$ ), and opacity of all points on the entire ray except for the current point ( $\alpha_j$ and $j \in \{1, 2, \dots, N\} \& j \neq i$ ). Notably, when processing a dark region, saying that the $c_i$ approaches zero, the first term of Eq. (7) will be close to zero. Similarly, if points behind $p_i$ have low opacity ( $\alpha_k$ and $k \in \{i + 1, \dots, N\}$ ), the gradient with respect to the SDF value will be small, causing the vanishing problem in dark regions. More generally, the gradient of SDF values can be affected by the color itself, resulting in a biased optimization process that tends to favor high color intensities. + +The above analysis is also supported by our experiments below. As shown in Fig. 3, we sample rays in the dark regions and the light regions separately and accordingly record the trend of gradient norms in these two regions during the optimization. In the beginning, the gradient norms from these two regions are similar; and the gradient norm in the dark region (red solid line) decreases as the number of training epochs increases, while the gradient norm in the light region remains stable (blue solid line), indicating the dark areas contribute much less to the optimization process. As the optimization process proceeds, if these points are + +![](images/02408ad68a5c700467f2b2836b9c333cd4eae86b0f1f2f312f80c161d16d24de.jpg) +Figure 3. The trend for the gradient. The mean and variance of gradient norm (shadowed curves for variance) corresponding to light and dark regions during optimization. + +predicted as dark colors ( $c_i^r \to 0$ ), it would lead to the gradient reduction effects as analyzed in Eq. (7). The shadowed regions keep the same trend as the mean values, further affirming our earlier analysis. Note that the gradient of points in these areas will not equal zero due to the influence of other loss functions, like depth consistency loss. + +# 4.2. Feature-based Rendering + +To resolve the aforementioned problem, we propose feature-based color rendering loss. As shown in Fig. 2, the Appearance network outputs two predictions for each point $i$ along a ray $r$ : one is the color vector $\hat{c}_i^r$ , and the other is the hidden feature $F_i^r$ . For direct color $\hat{c}_i^r$ , we utilize Eq. (4) to obtain the target pixel color $\hat{C}_c(r)$ . And the hidden feature $F_r^i$ is used to render the ray feature $\hat{F}(r)$ by + +$$ +\hat {F} (r) = \sum_ {i = 1} ^ {M} T _ {i} ^ {r} \alpha_ {i} F _ {i} ^ {r}. \tag {8} +$$ + +The ray feature $\hat{F}_T$ is further decoded by a decoder $\mathcal{D}$ to yield the decoded target pixel color, + +$$ +\hat {C} _ {F} (r) = \mathcal {D} (\hat {F} (r)), \tag {9} +$$ + +where the decoder $\mathcal{D}$ is a single-layer perceptron with 256 nodes. Finally, the decoded color $\hat{C}_F(r)$ from the rendered feature is used to construct the feature-based color rendering loss. As such, the optimization of these dark regions would not be affected by the color itself. As long as there are non-zero values in the rendered feature, there will be non-zero gradients with respect to the volume density of the concerned point. As shown in Fig. 3 (dashed lines), the gradient norm is not influenced by the intensity of colors. + +# 5. Hybrid Representation Scheme + +# 5.1. Incorporating Geometry Prior Matters + +It is clear that for room-level scene reconstruction, geometry priors are essential. Existing methods [31, 36] render depth $\hat{D}(r)$ and normal $\hat{N}(r)$ of the surface intersecting + +the current ray as + +$$ +\hat {D} (r) = \sum_ {i = 1} ^ {M} T _ {i} ^ {r} \alpha_ {i} ^ {r} t _ {i} ^ {r} \quad \text {a n d} \quad \hat {N} (r) = \sum_ {i = 1} ^ {M} T _ {i} ^ {r} \alpha_ {i} ^ {r} \hat {n} _ {i} ^ {r}, \tag {10} +$$ + +where $\hat{T}_r^i$ and $\hat{\alpha}_r^i$ have the same meaning as Eq. (4), $t_i^r$ is the distance the ray passing and $n_i^r$ is the normal of point $p_i$ . Next, these methods use depth and normal maps estimated from pre-trained models, such as Omnidata [10], to directly supervise the rendered depth $\hat{D}(r)$ and normal $\hat{N}(r)$ using Eq. (11) and Eq. (12), respectively. Overall, the depth loss function is defined as + +$$ +\mathcal {L} _ {\text {d e p t h}} = \sum_ {r \in \mathcal {R}} | | (w \hat {D} (r) + q) - \bar {D} (r) | | ^ {2}, \tag {11} +$$ + +where $w$ and $q$ are the scale and shift computed by the least-squares method [6] to solve scale-ambiguity problem for monocular depth prediction methods. And the normal loss function is + +$$ +\mathcal {L} _ {\text {n o r m a l}} = \sum_ {r \in R} | | \hat {N} (r) - \bar {N} (r) | | _ {1} + | | 1 - \hat {N} (r) ^ {T} \bar {N} (r) | | _ {1}, \tag {12} +$$ + +where $\tilde{N} (r)$ is the predicted monocular normal transformed to the same coordinate system with angular. + +As shown in Fig. 1, we note that these geometry priors benefit the reconstruction of better surfaces in textureless and sparse-viewed areas. However, thin structures and small objects, such as the yellow flower in Fig. 4, cannot be faithfully reconstructed with geometry priors. Recently, NeuRIS [31] put forward a hypothesis that this phenomenon arises from the inaccurate geometry supervisory signal (i.e. depth and surface normal). However, according to our experiment on Replica synthetic dataset, this problem still exists even though we use the perfect ground-truth depth, normal, and RGB to provide supervisory signals (see Fig. 4). + +# 5.2. Problem of SDF Formula with Geometry Prior + +To dive into the SDF representation and explore its limitations for surface reconstruction with geometric priors, we create a simplified scenario and simulate object occlusions as shown in Fig. 5(a). The ground-truth SDF intersecting with a horizontal plane is shown in Fig. 5(a), and the SDF distribution along a ray $r$ intersecting with the blue cube at point $p_s$ is shown in Fig. 5(c). There are many local minima and maxima due to the existence of multiple objects, which differs from the single-object scenario following a monotonic function (blue line in Fig. 5(c)). To examine depth priors for surface reconstruction, we employ the approach proposed in MonoSDF [36] to calculate the depth of $p_s$ following Eq. (10) subject to the ground-truth SDF. + +However, even with the ground-truth SDF, the estimated depth value (1.59, the red vertical plot in Fig. 5(e)) still deviates from the true depth value (2.94, the green vertical plot in Fig. 5(e)) when multiple objects exist. According to Eq. (10), the estimated normal value would suffer from + +![](images/490ef55cc21e32f5ddce3f9f2cbc5cd761e6955932f1dd6076a295a2a01e59d9.jpg) +Pseudo Ground Truth + +![](images/caf29d1ae101d75ea88c80affca08444e422a66b0c371ff588ee3b4883dd9f3c.jpg) +Figure 4. Illustration of failure cases of state-of-the-arts. Even though applying the perfect pseudo ground-truth geometry to supervise the model, existing room-level reconstruction methods like [36] can still fail to resolve accurate 3D structures. + +![](images/254c5eeeceea936dc8b127023a61b64d862b8a568c45bfdcf204d2c522fcbbfb.jpg) +MonoSDF + +![](images/1f95d9a24451ae4fae6a7f245945b3e2005e5f82def5fd2080539fc2b0a04309.jpg) + +![](images/c6997df99b450c116076898e4a4df6296c2fce859c31ce7ea522214f9de56c21.jpg) +Error + +![](images/888f26ee04977eff42fa287a1d26e115a5eb0b8ad3bc48d52f9ddc558d5f6095.jpg) + +![](images/6f90db19bded9a33d276c7752c4422dbf1063fe1eb02e4394de3e3ec74465f5c.jpg) + +![](images/0cdbb1e86dc402bc6f8586c4533ed4cc805f59c1ceb2a8800a616e0be03d2543.jpg) + +the same problem. This implies that existing methods incorporating geometry priors [36, 31] to guide the learning of the SDF representation may not necessarily encourage the model to learn the true SDF for scene-level surface reconstruction. In turn, because small objects or thin structures usually have low sampling probability during training, the minimization of $\mathcal{L}_{\mathrm{depth}}$ will encourage the model to predict SDF ignoring small objects along the ray $r$ such that the estimated SDF will produce depth values closer to the depth supervision (see Fig. 5(e)) and minimize the overall loss function, attempting to mimic the single object scenario (right part in Fig. 5). In sum, the supervision from geometric priors tends to sacrifice the reconstruction of small objects to preserve large surface reconstruction, which aligns also with our observation presented in Fig. 4. + +# 5.3. Hybrid Occupancy-SDF Representation + +The problem above is essentially caused by the SDF representation, which describes the geometry of a scene as a whole and thus suffers from the interference of other objects, especially small objects, and thin structures are prone to be removed to preserve large structures. + +Unlike the SDF representation, occupancy represents each point separately and thus is free from the interference of objects in this challenging scenario. However, occupancy representation only focuses on the intersecting point ignoring the constraint of neighborhood points. Thus, the reconstruction results represented by occupancy will have many floaters and useless structures, as shown in Fig. 1, which can be eliminated in SDF by Eikonal loss [7]. This inspires us to investigate a hybrid of occupancy and SDF as a representation for neural surface reconstruction as shown in Fig. 2. The geometry network $\theta$ outputs both SDF and occupancy. + +Specifically, the occupancy represents surfaces as the de + +![](images/329f9c9076933347ff118c3a4694538c3343a127cdb57e91523622f067e61da4.jpg) +Multi Objects Scene + +![](images/21fc96f45c6c02e1184be8ac6d7ef5a7404e4a8aef320a80aeafde4d104f7c88.jpg) +Signed Distance Field + +![](images/123016b32885614070e3a1f19d49f3d274986ad59d045f97f459e1ebf25e205a.jpg) +Single Object Scene + +![](images/c8cc49cff12caaf605c56e138731d682719c7f0752492a2cb6d0ef49f0e9e0dc.jpg) +Signed Distance Field + +![](images/84f5fae97bed52e500bd27cf9a66ef58fb4b626ef028c2856e654c480831c038.jpg) +(b) SDF Value at Point P + +![](images/a606b880eab5f424d12e07d06fa7c66201b81b02ec748546ae2442d82ef1ac31.jpg) +(a) Schematic of the toy 3D structure for the multi-object scene (left) and single object scene (object). +(c) SDF $f(\pmb{p}_i)$ +Figure 5. Toy experiments for the room-level scene. The left part of 5(a), where we stand in front of the yellow cylinder to observe the entire scene, is a widespread scenario for room-level scale scenes. Unlike the single object scenario, where the distribution of SDF value is a monotonic decreasing function from the observed position to the object, the room-level scenario has complex distributions with multi peaks/valleys along the single ray (5(c)). Following the Laplace density function [34], the density distributions of different situations are shown in 5(d), where room-level scenes have a secondary peak near small objects but the single object scene only has one peak. It is because of the existence of this peak, the weights in the room-level scene (5(e)) exhibit a multi-model distribution, while for the single object case a uni-modal distribution. As such, we note that the rendering depth $\hat{D}$ deviates from the ground truth in the room-level scene but is close to the ground truth depth object-level scene. 5(b) means the effect of supervised signal in three different representations. + +![](images/9d9c3b5e2f02267ac007d1967453a142e87d8d573062de83e195c3055dd102d0.jpg) +(d) Laplace density $\delta_i(\pmb {p}_i)$ + +![](images/53bad4800866f54b47404aaec038a65917be787c9e718615119932ad51ffb731.jpg) +(e) Weights $T_{r}^{i}\alpha_{r}^{i}$ + +cision boundary of a binary occupancy classifier, parameterized by a neural network $\theta$ + +$$ +o _ {\theta} (\mathbf {p}): \mathbb {R} ^ {3} \rightarrow [ 0, 1 ], \tag {13} +$$ + +where $\mathbf{p}$ is a 3D point. The occupancy representation assumes that objects are solid, thus we can rewrite the neural rendering formula [14] to + +$$ +\hat {C} (r) = \sum_ {i = 1} ^ {M} o \left(\mathbf {p} _ {i}\right) \prod_ {j < i} \left(1 - o \left(\mathbf {x} _ {j}\right)\right) c \left(\mathbf {p} _ {i}, d\right), \tag {14} +$$ + +which replaces the opacity $\alpha$ to a discrete occupancy indicator variable $o\in 0,1$ , where $o = 0$ indicates the free space while $o = 1$ the occupied space. Thus, this representation will not be affected by the objects along the ray, and the rendering depth will be consistent with ground-truth depth in ground-truth occupancy space. Note that the occupancy-based representation is introduced to facilitate optimization. During inference, the SDF is used for reconstruction. + +To understand why and how the hybrid representation helps optimize the SDF field for accurate reconstruction, we conduct the following empirical analysis, using the scenario shown in Fig. 5(a). Here, the orange ray hits a surface point $Q$ of the large blue cube and the blue ray hits the surface point $P$ on the small cylinder. During optimization, the depth/normal loss for point $Q$ along the orange ray will encourage the model to predict a large SDF value (absolute) of point $P$ (Fig. 5(b)) which violates the reconstruction of the small cylinder where a small SDF value is desired. In + +contrast, point $Q$ has no effects on point $P$ with occupancy representation. The hybrid representation joins the forces of SDF and occupancy representations, aiming to use occupancy representation to help overcome the issues of SDF representation in optimization. Although the depth/normal loss from the SDF presentation for point $Q$ still has a negative impact on the optimization of point $P$ . The additional occupancy representation will force the network to predict a large occupancy value for a point $P$ and thus will indirectly regularize the network to predict a small SDF value (see Fig. 5(b): the blue up arrow in "Hybrid"). We admit that this hybrid representation can only alleviate this problem, and our study is more empirical. Fundamental issues arise from insufficient neural scene representation, which requires further research efforts. We explore further why this combination would bring notable benefits to the supplementary with an example. + +# 6. Experiments + +Optimization. In the training stage, we minimize the loss + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {\mathrm {r g b}} ^ {s d f} + \lambda_ {1} \mathcal {L} _ {\mathrm {r g b}} ^ {s d f _ {F}} + \lambda_ {2} \mathcal {L} _ {\mathrm {e i k}} + \lambda_ {3} \mathcal {L} _ {\text {d e p t h}} ^ {\text {o c c}} \tag {15} \\ + \lambda_ {4} \mathcal {L} _ {\text {d e p t h}} ^ {\text {s d f}} + \lambda_ {5} \mathcal {L} _ {\text {n o r m a l}} ^ {\text {o c c}} + \lambda_ {6} \mathcal {L} _ {\text {n o r m a l}} ^ {\text {s d f}}, \\ \end{array} +$$ + +where $\mathcal{L}_{rgb}$ means color-based rendering loss following Eq. (6) but only to SDF representation. The rendering color computed by the feature rendering formula (Eq. (8)) + +and Eq. (9)) is denoted to $\mathcal{L}_{rgb}^{sdf_F}$ . Notably, $\mathcal{L}_{eik}$ means the eikonal loss [7], $\mathcal{L}_{depth}$ means the depth rendering loss following Eq. (11), and $\mathcal{L}_{normal}$ means the normal rendering loss following Eq. (12). We apply them for both representations, where the superscript $occ$ indicates the loss computed by occupancy-based representation, while the $sdf$ by SDF-based representation. The network is optimized by the Adam optimizer with a learning rate of $5e^{-4}$ . We set weights $\lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5, \lambda_6$ to 1, 0.05, 0.5, 0.1, 0.1, 0.05, respectively. The network architecture and sampling strategy are detailed in the supplement. + +Datasets. We use three datasets to assess the performance of our algorithm. ScanNet [2] is a real-world dataset that provides 1,513 scenes captured with Kinect V1 RGB-D camera. The BundleFusion [3] is applied to provide high-quality camera poses and surface reconstructions. For each scene, we uniformly sample roughly 500 frames to train our network. Tanks and Temples [11] is a real-world, large-scale scene dataset. We use four indoor scenes from their advanced split and run on the official server. Replica [27] is a synthetic dataset that provides 18 scenes, with each providing dense geometry, HDR textures, and semantic annotations. We select 8 scenes and use the Habitat simulator [29] to render RGB images following MonoSDF [36] splits. Notably, we conduct ablation studies on this dataset. + +Compared Methods. (1) UNISURF [18] is an occupancy-based method that unifies surface rendering and volume rendering for neural scene reconstruction. We implement the UNISURF* with normal and depth priors for a fair comparison. (2) MonoSDF [36] is an SDF-based method that adds depth and normal constraints on VolSDF [34]. (3) Manhattan-SDF [8] is an SDF-based method that adds a semantic branch and uses the Manhattan constraint to regularize the geometry in floor and wall regions. (4) COLMAP [25] is a classical multi-view stereo method with Poisson surface reconstruction. (5) NeuRIS [31] is an SDF-based method that introduces pseudo normal prior to the NeUS [32] architecture. Meanwhile, it leverages multiview consistency to eliminate the wrong supervision signal from inaccurate estimated results. (6) NICER-SLAM [39] is an SDF-based dense SLAM system that uses locally implicit map representation and can simultaneously optimize for camera poses and a hierarchical neural implicit map representation. (7) LIG [9] uses the local implicit grid representation to reconstruct the large-scale scene from partial or noise point clouds. (8) Convolutional Occupancy network(Conv-Occ) [21] is a locally implicit representation that integrates local information to get better reconstruction results from noisy point cloud. + +Notably, local implicit representation [9, 21] can only reconstruct the scene from point clouds, thus we re-implement them using point clouds generated from scale-aligned pseudo depth and utilize the provided pretrained + +models for evaluation. And we directly obtain the results from the main paper of NICER-SLAM [39]. + +Metrics. All meshes are evaluated by 5 standard metrics defined in [16]: Accuracy, Completeness, Precision, Recall, and $F$ -score. Their definition will be discussed in the supplementary. For the Replica dataset, we also report the normal consistency following [13, 8, 20]. For the Tanks and Temples dataset, we use the official server to evaluate our results and report the F-score for selected scenes. + +# 6.1. Main Results + +We compare our method with state-of-the-art methods on three benchmark datasets. + +
MethodAcc ↓Comp ↓C-L1 ↓Prec ↑Recall ↑F-score ↑
COLMAP [25]0.0470.2350.14171.144.153.7
UNISURF [18]0.5540.1640.35921.236.226.7
VolSDF [34]0.4140.1200.26732.139.434.6
NeUS [32]0.1790.2080.19431.327.529.1
Manhattan-SDF [8]0.0720.0680.07062.156.860.2
NeuRIS [31]0.0500.0490.05071.766.969.2
MonoSDF [36]0.0350.0480.04279.968.173.3
Ours0.0390.0410.04080.076.077.9
+ +Results on ScanNet Dataset. We conducted a comparative analysis of our proposed approach against existing implicit reconstruction methods, including ManhattanSDF [8], NeuRIS [31] and MonoSDF [36] using the ScanNet dataset. As revealed in Table 1, our proposed method outperforms state-of-the-art methods, with a significant increase in F-score by 4.6. Additionally, in terms of Recall, our method substantially outperforms MonoSDF by 7.9 without needing extra data. Overall, our approach performs on par with the state-of-art methods in "Acc", "Chamfer- $\mathcal{L}_1$ (C- $\mathcal{L}_1$ ) and "Prec" and obtain notable performance gains in "Comp", "Recall" and "F-score". This is because these metrics ("Comp" and "Recall") are better metrics in evaluating how complete and accurate in capturing the shape and details of the scene being reconstructed. Further, Fig. 6 reveals that our method can attain more complete reconstructions with details and for low pixel intensities regions. + +Table 1. Quantitative assessments of the proposed model against previous works on the ScanNet dataset. + +
AuditoriumBallroomCourtroomMuseumMean
MonoSDF3.092.4710.005.105.165
Ours5.225.4213.998.598.305
MonoSDF*3.173.7013.755.686.58
Ours*6.197.3319.8011.8511.295
+ +Table 2. Quantitative assessments of the proposed model against Monosdf on the Tanks and Temples dataset. The evaluation metrics for the Tanks and Temples dataset are F-score. * means that the hash-grid structure is adopted. + +Results on Tanks and Temples Dataset. For challenging large-scale indoor scenes, we conduct experiments on + +![](images/3f444be36fc767874bc9b48def4ff54e14800e76edf2de9279a5f81a26788428.jpg) +UNISRUF* + +![](images/9ff79600dc336460ccb6552132b182cbeef8bba2147777bea8f7f782a39aec1a.jpg) +Replica + +![](images/acf70592dee076c5829fbe744c503a454944d9646815f95f6b59fe63ce3bcdbc.jpg) +Manhattan-SDF + +![](images/647908f068eacfccdff6dcf3dc6a474eafe9e4d1f661989d97bd00b41f4e9823.jpg) +ScanNet + +![](images/64a1266fbc7a761a4326ae2dc23b2e47e42a4c7406289fb9a3b072258e02a35d.jpg) +Tanks and Temples +MonoSDF + +![](images/d3ad0a7fe54fc27125e33e223ea412d3fe25f6926fcd17d7e1482975f253a346.jpg) +MonoSDF + +![](images/db66a1192677b0394eb8b7eccbe16c9008dcdac90b7ea568230c97ab80cb880d.jpg) + +![](images/62cc12b89b0ba6b8f06b753c0a4492df66eb5499ea4601155abd73739515b52a.jpg) + +![](images/18f8c720423e1e604fb2370e50963d3f59ac10d80584bf8dd30dda4a2bb6a282.jpg) + +![](images/e6ec9fb1133d79a59aea07efd47a6d71b218cbd5553bf3019e131d3661cabe3f.jpg) + +![](images/5287cd10b9264cff33ab0676e269f01635d70ff544d11ba354ef2be7daebe3a6.jpg) +Ours + +![](images/63cd3da4467f4bc38bbc6c7f8c1d54145f0db268e712e2475016b3f84c8ebc83.jpg) + +![](images/8e838a096a846f4160f8a4b963ed76f8203bd518ad9d6af3df366e5332bec98c.jpg) + +![](images/fe6c93eee4ee6ef301e1ce8e38be3922333e1e93f4239e2311e135c90d34afbd.jpg) +BSDF + +![](images/1df6d92e16d7994b7fd110469b05b332b0194cf60cc28dd572a587aa8bfcca56.jpg) +Ours (MLP) +MonoSDF (Grids) + +![](images/cf1cf04d93509fdad5488a160d238846c356da76bde09806cadf402811f5250b.jpg) +Ground Truth +Figure 6. Reconstruction results on representative datasets of Replica (left), ScanNet (middle), and Tanks and Temples (right). The ground truth is presented on the bottom-most. Red boxes in sub-figures highlight those areas where distinctive differences can be observed. + +![](images/56aa3115f8678b81602522f15db84656a21b0102f8297c04bacb277ac5d8b5e2.jpg) + +![](images/ae27986e6d458c62fcfdea8b84b73f490cccbb4cb075807a73d30f3837ed405c.jpg) +Ground Truth + +![](images/65bbc042de63ee02bc62524646c17de4cf76d5b763185a5c81e3304fbc5fc3aa.jpg) + +![](images/3ce84973ff8861014b023f3e587e87017f23f22930b5ba88d04fa79d21e9fe62.jpg) +Ours (Grids) + +the advanced Tanks and Temples dataset [11], which features more complicated structures. As alternative methods of neural reconstruction from images are not assessed on this dataset, we implement the best-performing method MonoSDF and compare with it. Thus, the MonoSDF and two versions of our method are implemented. Specifically, one adopts the pure MLP architecture while the other uses the hash grids as the input representation. The quantitative assessments (Table 2) reveal that our method shows better performance on this dataset, regardless of whether an MLP or hash-grid structure is used. And our hybrid representation exhibits excellent generalization abilities across different implicit structures. Overall, our compelling experimental results on the Tanks and Temples dataset further validate the robustness and versatility of the proposed method in reconstructing complex and challenging indoor scenes. + +Results on Replica Dataset. Quantitative assessment results on the Replica dataset are presented in Table 3. For this dataset, we compare our methods with both point-based methods [21, 9] and rendering methods [39, 18, 36]. Ours significantly surpasses existing state-of-the-art neural ren + +
MethodNormal C.↑Chamfer- \( {\mathcal{L}}_{1} \downarrow \)F-score ↑
Conv-Occ [21]85.736.4358.33
LIG [9]89.565.5365.20
NICER-SLAM [39]90.273.91-
UNISURF†[18]90.964.9378.99
MonoSDF†[36]92.112.9486.18
\( Ours^{\dagger } \)93.432.5892.12
+ +Table 3. Quantitative assessments of the proposed model against prior works on the Replica dataset. Herein, $\dagger$ indicates the use of geometry priors as supervision signals. + +dering methods. The results reveal that the SDF-based representation outperforms the occupancy-based ones (i.e. UNISURF*). This is because the SDF usually enforces constraints on the distribution of the entire scene, benefiting to suppressing the occurrence of floaters or unnecessary structures in occupancy-based representation. Notably, our OccSDF Hybrid method can constrain the distribution of the entire scene with SDF representation meanwhile exploiting the occupancy representation to resolve thin structures and small objects. Qualitative comparisons are shown in Fig. 6. + +6.2. Ablation Study + +
Normal C.↑Chamfer- \( {\mathcal{L}}_{1} \downarrow \)F-score ↑
MonoSDF92.112.9486.18
+ feature93.012.6491.01
+ hybrid93.222.7790.24
full model93.432.5892.12
+ +Table 4. Ablation study on the Replica dataset [27], where we progressively add different constraints to assess their impacts. The MonoSDF [36] is set as the baseline model. + +We conduct ablation studies on the Replica dataset as it provides ground-truth geometry. Four different configurations are investigated to train our model, including (1) MonoSDF with MLP settings (MonoSDF-MLP); (2) MonoSDF-MLP with our feature-based rendering formula; (3) MonoSDF-MLP with our hybrid representation; (4) MonoSDF-MLP with both the feature-based rendering formula and hybrid representation scheme (Full model). + +Table 4 shows that all metrics are improved when using the feature rendering to reconstruct this scene. Our proposed feature rendering scheme addresses the difficulties in reconstructing areas of low intensities, resulting in better results. On the other hand, the hybrid representation also leads to significant improvements in all metrics. Notably, it improves the completeness of small objects and thin structures, as evidenced by the results in Fig. 6. By leveraging both components, our model achieves an overall improvement of 5.94 in F-score, along with improved normal consistency and Chamfer- $\mathcal{L}_1$ . We attribute this success to our feature-based color rendering formula and our hybrid representation, which addresses the color-bias issue in optimization and difficulties in reconstructing detailed structures. The visualization results in Fig. 6 show our model's excellent reconstruction performance, especially in low-intensity areas and detailed structures. We will add more ablation studies and visualize results in the supplementary. + +# 6.3. Parameters Adjusting + +As shown in Eq. (15), our method newly added three different losses $\mathcal{L}_{rgb}^{sdf_F},\mathcal{L}_{depth}^{occ},\mathcal{L}_{normal}^{occ}$ . In order to verify the sensitivity of our method to hyperparameters, we provided the results of the experiment on the Replica dataset as shown in Fig. 7. It is clear that our method is not very sensitive to hyperparameters, and all the evaluated settings outperform the baseline method (C- $\mathcal{L}_1$ : 2.94, F-score: 86.18). It is worth noting that our approach demonstrates consistent performance enhancement across diverse datasets using the same parameter set, outperforming the baseline results. + +# 7. Conclusion + +We have analyzed the constraints present in current neural scene representation techniques with geometry priors, + +![](images/fc94ad8306528a58fe24577420612fb1ade7800cc574e6486e5f36bda2af3ae3.jpg) + +![](images/2cb135186c9bbf547a3a7a440e952941e6244a228997596f615a7529945abc9e.jpg) + +![](images/f65b8741260a565eb52ecb8a77be0acf42ad48b35775969d1dc0ff5da631e509.jpg) +Figure 7. Performance with different hyperparameter choices. + +and have identified issues in their ability to reconstruct detailed structures due to a biased optimization towards high color intensities and the complex SDF distribution. As a result, we have developed a feature rendering scheme that balances color regions and have implemented a hybrid representation to address the limitations of the SDF distribution. Our approach has demonstrated the successful reconstruction of room scenes with a high-fidelity surface, including small objects, detailed structures, and low-intensity pixel regions. We envision our results inspire further research on improving neural scene representation for accurate and large-scale surface reconstruction. + +# Acknowledgement + +We thank Xin Kong for his advising during the rebuttal period. This work has been supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621 and 27212822), General Research Fund Scheme (Grant No. 17202422), and RGC matching fund scheme (RMGS). Part of the described research work is conducted in the JC STEM Lab of Robotics for Soft Materials funded by The Hong Kong Jockey Club Charities Trust. + +# References + +[1] Motilal Agrawal and Larry S Davis. A probabilistic framework for surface reconstruction from multiple images. In Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, volume 2, pages II-II. IEEE, 2001. 2 +[2] Angela Dai, Angel X Chang, Manolis Savva, Maciej Halber, Thomas Funkhouser, and Matthias Nießner. Scannet: Richly-annotated 3d reconstructions of indoor scenes. 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Aided with the feature rendering scheme (Sec. 4) and the hybrid representation (Sec. 5), our method yields results with more detailed structures in room-level scenes compared to the state-of-the-art, particularly for those low intensities and detailed structures." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 139, + 502, + 186, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 502, + 186, + 514 + ], + "spans": [ + { + "bbox": [ + 139, + 502, + 186, + 514 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 529, + 280, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 529, + 280, + 634 + ], + "spans": [ + { + "bbox": [ + 45, + 529, + 280, + 634 + ], + "type": "text", + "content": "Implicit neural rendering, using signed distance function (SDF) representation with geometric priors like depth or surface normal, has made impressive strides in the surface reconstruction of large-scale scenes. However, applying this method to reconstruct a room-level scene from images may miss structures in low-intensity areas and/or small, thin objects. We have conducted experiments on three datasets to identify limitations of the original color rendering loss and priors-embedded SDF scene representation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 638, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 638, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 638, + 280, + 730 + ], + "type": "text", + "content": "Our findings show that the color rendering loss creates an optimization bias against low-intensity areas, resulting in gradient vanishing and leaving these areas unoptimized. To address this issue, we propose a feature-based color rendering loss that utilizes non-zero feature values to bring back optimization signals. Additionally, the SDF representation can be influenced by objects along a ray path, disrupting the monotonic change of SDF values when a single" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 503, + 531, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 503, + 531, + 608 + ], + "spans": [ + { + "bbox": [ + 296, + 503, + 531, + 608 + ], + "type": "text", + "content": "object is present. Accordingly, we explore using the occupancy representation, which encodes each point separately and is unaffected by objects along a querying ray. Our experimental results demonstrate that the joint forces of the feature-based rendering loss and Occ-SDF hybrid representation scheme can provide high-quality reconstruction results, especially in challenging room-level scenarios. The code is available at https://github.com/shawLyu/Occ-SDF-Hybrid" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 298, + 629, + 376, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 629, + 376, + 642 + ], + "spans": [ + { + "bbox": [ + 298, + 629, + 376, + 642 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 649, + 530, + 731 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 649, + 530, + 731 + ], + "spans": [ + { + "bbox": [ + 296, + 649, + 530, + 731 + ], + "type": "text", + "content": "Reconstructing a 3D scene from a series of multi-view images is a crucial problem in the realm of computer vision. This process has widespread applications in various fields such as animation, gaming, and virtual/augmented reality (VR/AR). 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Recent advancements in neural radiance field (NeRF) [14] further enable learning an implicit 3D representation from purely sparse posed images [35, 15]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "spans": [ + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": "However, when it comes to producing high-quality novel-view synthesis, these methods frequently utilize volume density [14] to represent the 3D geometry. Unfortunately, this approach does not adequately constrain the 3D geometry in the presence of ambiguities [18], ultimately leading to poor surface reconstructions (as depicted in Fig. 1: Volume Density)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 237, + 279, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 237, + 279, + 471 + ], + "spans": [ + { + "bbox": [ + 45, + 237, + 279, + 471 + ], + "type": "text", + "content": "Accordingly, research efforts have been made to exploit geometry-friendly representations, including signed distance function (SDF) [32, 34, 19] or occupancy [18], whose zero-level set can be extracted to become the concerned 3D surface. Albeit improving quality, they consider the reconstruction only of a single object, thereby, the performance degrades dramatically when applied to scene-level surface reconstruction, i.e., representing a room (Fig. 1: SDF). An attribute is that reconstructing texture-less areas often suffers from ambiguous visual cues with only RGB loss as the regularization. To address this problem, recent research has attempted to incorporate semantic [8] or geometric priors (depth/normal [36, 31] constraints) to further regularize scene-level reconstruction. With SDF-based representation and geometric priors [36], the reconstruction quality has been greatly improved (Fig. 1: SDF + Geometry Priors), especially concerning large flat areas and objects. However, it still cannot faithfully reconstruct the 3D scene with missing structures in low-intensity dark areas and small/thin objects (Fig. 1: SDF + Geometry Priors)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 472, + 279, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 472, + 279, + 577 + ], + "spans": [ + { + "bbox": [ + 45, + 472, + 279, + 577 + ], + "type": "text", + "content": "The above observation motivates us to dive into bridging the remaining missing blocks of existing neural surface representation methods. Notably, we focus on the SDF-based representation as it achieves state-of-the-art performance and has been widely adopted. Our analysis suggests that both the RGB color rendering formulation and SDF representation have clear limitations preventing existing solutions from fully unleashing the potential of implicit neural surface representation for large-scale room-level scenes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 578, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 578, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 578, + 279, + 730 + ], + "type": "text", + "content": "First, the color itself can show a significant impact on the optimization of geometric representation relying on the original RGB-based rendering formula [14], namely color bias. In particular, dark pixels with small intensity values will make the partial derivation of the loss with respect to the corresponding SDF value become zero, corrupting the optimization and resulting in missing structures in dark areas (see for example in Fig. 1: Low Intensities). Accordingly, herein instead of directly calculating the weighted color, we first compute weighted features and then use a learnable multi-layer perceptron (MLP) to decode the final rendering color. In such a way, we would still be able to effectively optimize the corresponding geometry represent" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 106, + 529, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 529, + 117 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 529, + 117 + ], + "type": "text", + "content": "tation as long as the feature vector contains non-zero values." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 117, + 530, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 117, + 530, + 245 + ], + "spans": [ + { + "bbox": [ + 296, + 117, + 530, + 245 + ], + "type": "text", + "content": "Second, the vanilla SDF-based neural rendering only considers a single ray directly passing through the object surface from the empty space and ignores objects along the ray [32, 34]. This configuration violates scene-level geometry where the existence of multiple objects clearly affects the distributions of SDF (Fig. 5(a)). Meanwhile, the optimization of thin structures and small objects, which naturally has small sampling probability, will be greatly degraded by this violation even with correct geometry prior and the structure will be erased to minimize the global geometry loss (Fig. 1: Detailed Structures)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 246, + 530, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 246, + 530, + 339 + ], + "spans": [ + { + "bbox": [ + 296, + 246, + 530, + 339 + ], + "type": "text", + "content": "In addition, although occupancy-based representations are likely to generate unwanted structure and cannot warrant a smooth surface reconstruction (Fig. 1), they are often sufficiently robust to objects along the ray and free from object interference in scene-level data. Therefore, during optimization, we propose to describe the room-level scene using occupancy in conjunction with signed distance functions (SDFs) to compensate for each other's defects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 339, + 477, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 339, + 477, + 350 + ], + "spans": [ + { + "bbox": [ + 308, + 339, + 477, + 350 + ], + "type": "text", + "content": "The technical contributions are as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 359, + 530, + 537 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 308, + 359, + 530, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 359, + 530, + 405 + ], + "spans": [ + { + "bbox": [ + 308, + 359, + 530, + 405 + ], + "type": "text", + "content": "- We explore an improved feature rendering scheme to overcome the problem of vanishing gradients in neural implicit reconstruction brought by the vanilla color space rendering formula." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 413, + 530, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 413, + 530, + 471 + ], + "spans": [ + { + "bbox": [ + 308, + 413, + 530, + 471 + ], + "type": "text", + "content": "- We carefully investigate insights and limitations in existing SDF and occupancy representations, and accordingly propose a hybrid representation mingling SDF with occupancy, dubbed Occ-SDF Hybrid, to resolve surfaces with thin structures and small objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 479, + 530, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 479, + 530, + 537 + ], + "spans": [ + { + "bbox": [ + 308, + 479, + 530, + 537 + ], + "type": "text", + "content": "- We conduct a large body of qualitative and quantitative experiments against state-of-the-art, indicating that our Occ-SDF hybrid formula can yield a higher-fidelity room-level scene representation, particularly with successfully resolving small and dark objects." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 297, + 547, + 381, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 547, + 381, + 559 + ], + "spans": [ + { + "bbox": [ + 297, + 547, + 381, + 559 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "type": "text", + "content": "Multi-view Stereo Conventional algorithms [1, 25, 4] always split the reconstruction into two steps. First, the feature-matching method [22, 17, 24] is applied to estimate the depth of each frame. Then, the resulting depth maps [12] are used to reconstruct the final scene. Notably, the reconstruction may suffer from poor performance in texture-less areas. Learning-based approaches are mainly divided into two categories. Typically, neural networks are embedded into the traditional reconstruction pipeline to replace specific modules, like feature matching [23, 37, 30], depth estimation [33], or depth fusion [5]. These methods often suffer from depth inconsistency problems due to the separately estimated depth maps. Alternatively, neural networks are designed to directly regress input images to trun" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "8941" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 129 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 129 + ], + "type": "text", + "content": "cated signed distance functions (TSDFs) [16, 28], but the reconstruction results often lack enough fine details." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 133, + 280, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 133, + 280, + 321 + ], + "spans": [ + { + "bbox": [ + 45, + 133, + 280, + 321 + ], + "type": "text", + "content": "Neural Scene Representation Recently, coordinate-based neural representations can faithfully model a 3D scene with only posed images. Approaches with an implicit differentiable renderer [35] only use volume density as scene representation which can not extract 3D scenes directly. To address this issue, occupancy-based representation [18] and SDF-based representation [32, 34] are proposed to facilitate 3D reconstruction. Notably, these methods already achieve great performance for object-level scenes but exhibit poorly for room-level scenes, especially in texture-less areas. For the room-level scenes, several existing approaches [9, 39] have demonstrated the ability to employ learned shape priors derived from extensive data to reconstruct scenes from incomplete or noisy point clouds. However, these methods face limitations when it comes to reconstructing scenes solely from image data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 324, + 279, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 324, + 279, + 510 + ], + "spans": [ + { + "bbox": [ + 45, + 324, + 279, + 510 + ], + "type": "text", + "content": "Priors for Indoor Scene Reconstruction Existing methods have attempted to introduce priors to resolve higher-fidelity surfaces in texture-less areas. Manhattan-SDF [8] follows semantic-NeRF[38] to estimate the volume density and semantic label at the same time, and then uses Manhattan-World assumption to regularize the geometry in floor and wall regions. NeuRIS [31] and MonoSDF [36] directly exploit the depth and normal predicted from an off-the-shelf neural network to regularize the geometry of each point, but in many cases, thin structures would disappear. NeuRIS [31] proposes a dynamic scheme to eliminate the wrong supervision signal from inaccurate estimated results, however, based on our investigation that fine structures are still lost even with the correct geometry for supervision. In all, we seek to explore a feature rendering scheme and a hybrid representation to overcome the above problems." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 522, + 193, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 522, + 193, + 537 + ], + "spans": [ + { + "bbox": [ + 45, + 522, + 193, + 537 + ], + "type": "text", + "content": "3. Overview and Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 543, + 279, + 730 + ], + "type": "text", + "content": "Our goal is to examine the limitations of existing implicit neural surface representations and explore practical solutions for accurately reconstructing large-scale, room-level 3D geometry with fine details from a set of calibrated images. First, we find that the well-adopted color-based rendering formula in [36, 31] will induce optimization bias against low-intensity areas, leaving these areas under-optimized and resulting in missing reconstructions (Sec. 4.1). Accordingly, we propose a simple yet effective feature-based rendering formula to address the problem (Sec. 4.2). Second, our analysis shows that the SDF-based neural surface representation violates scene-level geometry supervised signal and thus prevents the model from obtaining accurate reconstructions, making the model tends to sacrifice small and thin structures (Sec. 5.2). Motivated by this, we propose a hybrid representation mingling occu" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 305, + 106, + 523, + 266 + ], + "blocks": [ + { + "bbox": [ + 305, + 106, + 523, + 266 + ], + "lines": [ + { + "bbox": [ + 305, + 106, + 523, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 106, + 523, + 266 + ], + "type": "image", + "image_path": "4e47052f285e56f48ac9ec6e4961cfd62d1195d7152d83141565a388f7d9b0de.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 271, + 530, + 336 + ], + "lines": [ + { + "bbox": [ + 296, + 271, + 530, + 336 + ], + "spans": [ + { + "bbox": [ + 296, + 271, + 530, + 336 + ], + "type": "text", + "content": "Figure 2. Network architecture. The geometry network takes 3D position " + }, + { + "bbox": [ + 296, + 271, + 530, + 336 + ], + "type": "inline_equation", + "content": "(x, y, z)" + }, + { + "bbox": [ + 296, + 271, + 530, + 336 + ], + "type": "text", + "content": " after positional encoding (PE) as input and output both SDF and occupancy value. The appearance network takes view direction " + }, + { + "bbox": [ + 296, + 271, + 530, + 336 + ], + "type": "inline_equation", + "content": "(\\theta, \\phi)" + }, + { + "bbox": [ + 296, + 271, + 530, + 336 + ], + "type": "text", + "content": " as input and outputs two types of color, the direct color is used in Eq. (4) to directly obtain the pixel color and the decoded color is calculated via the rendering formula (Eq. (8))." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 346, + 508, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 346, + 508, + 357 + ], + "spans": [ + { + "bbox": [ + 296, + 346, + 508, + 357 + ], + "type": "text", + "content": "pancy and SDF for accurate reconstruction (Sec. 5.3)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 358, + 530, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 358, + 530, + 394 + ], + "spans": [ + { + "bbox": [ + 296, + 358, + 530, + 394 + ], + "type": "text", + "content": "We here describe the mathematical preliminary on the state-of-the-art surface representation, namely SDF-based Neural Scene Representation [34], for 3D reconstruction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 394, + 530, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 394, + 530, + 441 + ], + "spans": [ + { + "bbox": [ + 296, + 394, + 530, + 441 + ], + "type": "text", + "content": "For implicit neural reconstruction, we can represent the scene as a signed distance function (SDF) field, which is a continuous function " + }, + { + "bbox": [ + 296, + 394, + 530, + 441 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 296, + 394, + 530, + 441 + ], + "type": "text", + "content": " that calculates the distance between each point and its closest surface" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 342, + 442, + 530, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 442, + 530, + 471 + ], + "spans": [ + { + "bbox": [ + 342, + 442, + 530, + 471 + ], + "type": "interline_equation", + "content": "1 _ {\\Omega} (\\boldsymbol {p}) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\boldsymbol {p} \\in \\Omega \\\\ 0 & \\text {i f} \\boldsymbol {p} \\notin \\Omega \\end{array} , \\right. \\tag {1}", + "image_path": "a91abd7425ac8fcdbcbc274141987e1a81870b65df959bdf66ce2fd6e120ded4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 348, + 471, + 484, + 489 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 471, + 484, + 489 + ], + "spans": [ + { + "bbox": [ + 348, + 471, + 484, + 489 + ], + "type": "interline_equation", + "content": "f (\\boldsymbol {p}) = (- 1) ^ {1 _ {\\Omega} (\\boldsymbol {p})} \\min _ {\\boldsymbol {y} \\in \\mathcal {M}} \\| \\boldsymbol {p} - \\boldsymbol {y} \\|,", + "image_path": "a5273d2262fa70b90a0a0b956ae362bc1d01b7af8c3596150dea1fcff95ecfab.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "spans": [ + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "inline_equation", + "content": "1_{\\Omega}(\\pmb{p})" + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "text", + "content": " is an indicator function to represent whether the space at position " + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "text", + "content": " is occupied, " + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "inline_equation", + "content": "\\mathcal{M} = \\partial \\Omega" + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "text", + "content": " is the boundary surface of occupied space and " + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "inline_equation", + "content": "||\\cdot ||" + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "text", + "content": " is the standard Euclidean 2-norm. Following the VolSDF [34], we use an MLP to represent the function " + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 296, + 491, + 530, + 561 + ], + "type": "text", + "content": " and convert the SDF value to Laplace density with the following function" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 360, + 564, + 530, + 577 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 564, + 530, + 577 + ], + "spans": [ + { + "bbox": [ + 360, + 564, + 530, + 577 + ], + "type": "interline_equation", + "content": "\\sigma_ {i} \\left(\\boldsymbol {p} _ {i}\\right) = \\alpha \\Psi_ {\\beta} (- f \\left(\\boldsymbol {p} _ {i}\\right)), \\tag {2}", + "image_path": "4feac1de9bcf088871ed198009feed0b3e2377b20bbbdc4b45b56829ff876bca.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "spans": [ + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta > 0" + }, + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "type": "text", + "content": " are learnable parameters, and " + }, + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "type": "inline_equation", + "content": "\\Psi_{\\beta}" + }, + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "type": "text", + "content": " is the cumulative distribution function (CDF) with zero mean and the " + }, + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 296, + 579, + 530, + 613 + ], + "type": "text", + "content": " scale is defined as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 329, + 615, + 530, + 652 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 615, + 530, + 652 + ], + "spans": [ + { + "bbox": [ + 329, + 615, + 530, + 652 + ], + "type": "interline_equation", + "content": "\\Psi_ {\\beta} (s) = \\left\\{ \\begin{array}{l l} \\frac {1}{2} \\exp \\left(\\frac {s}{\\beta}\\right) & , \\text {i f} s \\leq 0 \\\\ 1 - \\frac {1}{2} \\exp \\left(- \\frac {s}{\\beta}\\right) & , \\text {i f} s > 0 \\end{array} . \\right. \\tag {3}", + "image_path": "13e9de9d1a7d6b978fee39bfc581add9a3d6175a672ae67d260bc1b3a95b204d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 660, + 529, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 660, + 529, + 682 + ], + "spans": [ + { + "bbox": [ + 296, + 660, + 529, + 682 + ], + "type": "text", + "content": "Color Rendering Formula According to the rendering formula [14], the color for the current ray " + }, + { + "bbox": [ + 296, + 660, + 529, + 682 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 296, + 660, + 529, + 682 + ], + "type": "text", + "content": " is rendered by" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 370, + 685, + 530, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 685, + 530, + 716 + ], + "spans": [ + { + "bbox": [ + 370, + 685, + 530, + 716 + ], + "type": "interline_equation", + "content": "\\hat {C} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} \\hat {c} _ {i} ^ {r}, \\tag {4}", + "image_path": "edcb99b8b4eac8e6c9bba87dba9b71ff7ef0bebe3be3b9de2f803f469adce0e5.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 297, + 717, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 717, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 297, + 717, + 530, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 297, + 717, + 530, + 730 + ], + "type": "inline_equation", + "content": "T_{i}^{r}" + }, + { + "bbox": [ + 297, + 717, + 530, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 297, + 717, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 297, + 717, + 530, + 730 + ], + "type": "text", + "content": " represent the transmittance and alpha" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "type": "text", + "content": "8942" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "content": "value (a.k.a opacity), respectively, of sampled point. And " + }, + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "content": " represent the number of the sampled point along the ray " + }, + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 45, + 106, + 279, + 141 + ], + "type": "text", + "content": ". They can be computed by" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 74, + 143, + 279, + 175 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 143, + 279, + 175 + ], + "spans": [ + { + "bbox": [ + 74, + 143, + 279, + 175 + ], + "type": "interline_equation", + "content": "T _ {i} ^ {r} = \\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {i}), \\alpha_ {i} = 1 - \\exp \\left(- \\sigma_ {i} ^ {r} \\delta_ {i} ^ {r}\\right), \\tag {5}", + "image_path": "1b6b97fa29522afc3f048cb1b95fbcbe2bf0c1cc7efa4333d2566edcaf32bc77.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 178, + 279, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 178, + 279, + 225 + ], + "spans": [ + { + "bbox": [ + 45, + 178, + 279, + 225 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 178, + 279, + 225 + ], + "type": "inline_equation", + "content": "\\delta_r^i" + }, + { + "bbox": [ + 45, + 178, + 279, + 225 + ], + "type": "text", + "content": " is the distance between adjacent sample points. Finally, given the rendered color " + }, + { + "bbox": [ + 45, + 178, + 279, + 225 + ], + "type": "inline_equation", + "content": "\\hat{C} (r)" + }, + { + "bbox": [ + 45, + 178, + 279, + 225 + ], + "type": "text", + "content": ", the SDF field will be optimized from sparsely sampled images by minimizing the color-based rendering loss as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 102, + 228, + 279, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 228, + 279, + 251 + ], + "spans": [ + { + "bbox": [ + 102, + 228, + 279, + 251 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r g b}} = \\sum_ {r \\in R} | | \\hat {C} (r) - C (r) | | _ {1}, \\tag {6}", + "image_path": "cff190f0dedb5efaa4653744a0359c5114359f77725dc779cd7dbfc9d155287d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 254, + 279, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 254, + 279, + 278 + ], + "spans": [ + { + "bbox": [ + 45, + 254, + 279, + 278 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 254, + 279, + 278 + ], + "type": "inline_equation", + "content": "C(r)" + }, + { + "bbox": [ + 45, + 254, + 279, + 278 + ], + "type": "text", + "content": " is the ground-truth color associated with the sampled ray " + }, + { + "bbox": [ + 45, + 254, + 279, + 278 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 45, + 254, + 279, + 278 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 290, + 201, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 290, + 201, + 303 + ], + "spans": [ + { + "bbox": [ + 45, + 290, + 201, + 303 + ], + "type": "text", + "content": "4. Feature Rendering Formula" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 309, + 227, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 309, + 227, + 323 + ], + "spans": [ + { + "bbox": [ + 45, + 309, + 227, + 323 + ], + "type": "text", + "content": "4.1. Problem of Color-based Rendering" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "spans": [ + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": "Given the SDF-based scene representation and the color-based rendering loss " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rgb}}" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": " in Sec. 3, we analyze the derivative of " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rgb}}" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": " to the opacity " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": " of a point " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": ". Note that for a single point " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": ", as " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "\\alpha_{i}^{r}" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": " are the same regardless of the rays, we thus omit its dependency on ray " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": " and use " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": " for simplicity. For a point " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": ", the derivative of the color loss function to its opacity " + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 45, + 328, + 279, + 410 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 52, + 411, + 279, + 448 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 411, + 279, + 448 + ], + "spans": [ + { + "bbox": [ + 52, + 411, + 279, + 448 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L} _ {r g b}}{\\partial \\alpha_ {i}} = \\pm \\left(\\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {j}) c _ {i} - \\sum_ {k = i + 1} ^ {N} c _ {k} \\alpha_ {k} \\prod_ {j = 1, j \\neq i} ^ {k - 1} (1 - \\alpha_ {j})\\right), \\tag {7}", + "image_path": "4e8b0ae7178a0a0f4abdb53ccf5336c39c48695ba1f25c593075c43b5b5a6040.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "spans": [ + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": "which indicates that when we optimize the SDF value of " + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": ", the gradient is determined by the color of the current point " + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": " and points behind it (" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "c_k" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "k \\in \\{i + 1, \\dots, N\\}" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": "), and opacity of all points on the entire ray except for the current point (" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "\\alpha_j" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "j \\in \\{1, 2, \\dots, N\\} \\& j \\neq i" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": "). Notably, when processing a dark region, saying that the " + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": " approaches zero, the first term of Eq. (7) will be close to zero. Similarly, if points behind " + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": " have low opacity (" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "\\alpha_k" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "inline_equation", + "content": "k \\in \\{i + 1, \\dots, N\\}" + }, + { + "bbox": [ + 45, + 450, + 279, + 600 + ], + "type": "text", + "content": "), the gradient with respect to the SDF value will be small, causing the vanishing problem in dark regions. More generally, the gradient of SDF values can be affected by the color itself, resulting in a biased optimization process that tends to favor high color intensities." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 602, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 602, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 602, + 279, + 730 + ], + "type": "text", + "content": "The above analysis is also supported by our experiments below. As shown in Fig. 3, we sample rays in the dark regions and the light regions separately and accordingly record the trend of gradient norms in these two regions during the optimization. In the beginning, the gradient norms from these two regions are similar; and the gradient norm in the dark region (red solid line) decreases as the number of training epochs increases, while the gradient norm in the light region remains stable (blue solid line), indicating the dark areas contribute much less to the optimization process. As the optimization process proceeds, if these points are" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 300, + 105, + 527, + 220 + ], + "blocks": [ + { + "bbox": [ + 300, + 105, + 527, + 220 + ], + "lines": [ + { + "bbox": [ + 300, + 105, + 527, + 220 + ], + "spans": [ + { + "bbox": [ + 300, + 105, + 527, + 220 + ], + "type": "image", + "image_path": "02408ad68a5c700467f2b2836b9c333cd4eae86b0f1f2f312f80c161d16d24de.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 222, + 530, + 254 + ], + "lines": [ + { + "bbox": [ + 296, + 222, + 530, + 254 + ], + "spans": [ + { + "bbox": [ + 296, + 222, + 530, + 254 + ], + "type": "text", + "content": "Figure 3. The trend for the gradient. The mean and variance of gradient norm (shadowed curves for variance) corresponding to light and dark regions during optimization." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 266, + 531, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 266, + 531, + 336 + ], + "spans": [ + { + "bbox": [ + 296, + 266, + 531, + 336 + ], + "type": "text", + "content": "predicted as dark colors (" + }, + { + "bbox": [ + 296, + 266, + 531, + 336 + ], + "type": "inline_equation", + "content": "c_i^r \\to 0" + }, + { + "bbox": [ + 296, + 266, + 531, + 336 + ], + "type": "text", + "content": "), it would lead to the gradient reduction effects as analyzed in Eq. (7). The shadowed regions keep the same trend as the mean values, further affirming our earlier analysis. Note that the gradient of points in these areas will not equal zero due to the influence of other loss functions, like depth consistency loss." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 350, + 434, + 362 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 350, + 434, + 362 + ], + "spans": [ + { + "bbox": [ + 297, + 350, + 434, + 362 + ], + "type": "text", + "content": "4.2. Feature-based Rendering" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "spans": [ + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": "To resolve the aforementioned problem, we propose feature-based color rendering loss. As shown in Fig. 2, the Appearance network outputs two predictions for each point " + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": " along a ray " + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": ": one is the color vector " + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "inline_equation", + "content": "\\hat{c}_i^r" + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": ", and the other is the hidden feature " + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "inline_equation", + "content": "F_i^r" + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": ". For direct color " + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "inline_equation", + "content": "\\hat{c}_i^r" + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": ", we utilize Eq. (4) to obtain the target pixel color " + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "inline_equation", + "content": "\\hat{C}_c(r)" + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": ". And the hidden feature " + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "inline_equation", + "content": "F_r^i" + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": " is used to render the ray feature " + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "inline_equation", + "content": "\\hat{F}(r)" + }, + { + "bbox": [ + 296, + 370, + 530, + 452 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 368, + 455, + 530, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 455, + 530, + 485 + ], + "spans": [ + { + "bbox": [ + 368, + 455, + 530, + 485 + ], + "type": "interline_equation", + "content": "\\hat {F} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} F _ {i} ^ {r}. \\tag {8}", + "image_path": "3a8ec952fd950f08afc5e07f562f9fd5175741543be843e8c64c4aece7d2628e.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 490, + 530, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 490, + 530, + 514 + ], + "spans": [ + { + "bbox": [ + 296, + 490, + 530, + 514 + ], + "type": "text", + "content": "The ray feature " + }, + { + "bbox": [ + 296, + 490, + 530, + 514 + ], + "type": "inline_equation", + "content": "\\hat{F}_T" + }, + { + "bbox": [ + 296, + 490, + 530, + 514 + ], + "type": "text", + "content": " is further decoded by a decoder " + }, + { + "bbox": [ + 296, + 490, + 530, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 296, + 490, + 530, + 514 + ], + "type": "text", + "content": " to yield the decoded target pixel color," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 373, + 515, + 530, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 515, + 530, + 529 + ], + "spans": [ + { + "bbox": [ + 373, + 515, + 530, + 529 + ], + "type": "interline_equation", + "content": "\\hat {C} _ {F} (r) = \\mathcal {D} (\\hat {F} (r)), \\tag {9}", + "image_path": "963891da8deaa2333160b3115102d7123a7967d3b8263b0583ee5c5fe43286de.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 531, + 530, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 531, + 530, + 636 + ], + "spans": [ + { + "bbox": [ + 296, + 531, + 530, + 636 + ], + "type": "text", + "content": "where the decoder " + }, + { + "bbox": [ + 296, + 531, + 530, + 636 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 296, + 531, + 530, + 636 + ], + "type": "text", + "content": " is a single-layer perceptron with 256 nodes. Finally, the decoded color " + }, + { + "bbox": [ + 296, + 531, + 530, + 636 + ], + "type": "inline_equation", + "content": "\\hat{C}_F(r)" + }, + { + "bbox": [ + 296, + 531, + 530, + 636 + ], + "type": "text", + "content": " from the rendered feature is used to construct the feature-based color rendering loss. As such, the optimization of these dark regions would not be affected by the color itself. As long as there are non-zero values in the rendered feature, there will be non-zero gradients with respect to the volume density of the concerned point. As shown in Fig. 3 (dashed lines), the gradient norm is not influenced by the intensity of colors." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 297, + 653, + 468, + 666 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 653, + 468, + 666 + ], + "spans": [ + { + "bbox": [ + 297, + 653, + 468, + 666 + ], + "type": "text", + "content": "5. Hybrid Representation Scheme" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 297, + 674, + 496, + 687 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 674, + 496, + 687 + ], + "spans": [ + { + "bbox": [ + 297, + 674, + 496, + 687 + ], + "type": "text", + "content": "5.1. Incorporating Geometry Prior Matters" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": "It is clear that for room-level scene reconstruction, geometry priors are essential. Existing methods [31, 36] render depth " + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\hat{D}(r)" + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": " and normal " + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\hat{N}(r)" + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": " of the surface intersecting" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "type": "text", + "content": "8943" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 106, + 116, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 106, + 116, + 117 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 116, + 117 + ], + "type": "text", + "content": "the current ray as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 119, + 279, + 151 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 119, + 279, + 151 + ], + "spans": [ + { + "bbox": [ + 53, + 119, + 279, + 151 + ], + "type": "interline_equation", + "content": "\\hat {D} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} ^ {r} t _ {i} ^ {r} \\quad \\text {a n d} \\quad \\hat {N} (r) = \\sum_ {i = 1} ^ {M} T _ {i} ^ {r} \\alpha_ {i} ^ {r} \\hat {n} _ {i} ^ {r}, \\tag {10}", + "image_path": "c9f48c2fc69d83e9162f820b09a259d4b466ee154132d033e86547b870a05fa3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "spans": [ + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "inline_equation", + "content": "\\hat{T}_r^i" + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "inline_equation", + "content": "\\hat{\\alpha}_r^i" + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": " have the same meaning as Eq. (4), " + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "inline_equation", + "content": "t_i^r" + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": " is the distance the ray passing and " + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "inline_equation", + "content": "n_i^r" + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": " is the normal of point " + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": ". Next, these methods use depth and normal maps estimated from pre-trained models, such as Omnidata [10], to directly supervise the rendered depth " + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "inline_equation", + "content": "\\hat{D}(r)" + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": " and normal " + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "inline_equation", + "content": "\\hat{N}(r)" + }, + { + "bbox": [ + 45, + 154, + 279, + 236 + ], + "type": "text", + "content": " using Eq. (11) and Eq. (12), respectively. Overall, the depth loss function is defined as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 82, + 237, + 279, + 261 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 237, + 279, + 261 + ], + "spans": [ + { + "bbox": [ + 82, + 237, + 279, + 261 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d e p t h}} = \\sum_ {r \\in \\mathcal {R}} | | (w \\hat {D} (r) + q) - \\bar {D} (r) | | ^ {2}, \\tag {11}", + "image_path": "9757ff7daf51ff9e460e6de275af255d45abcc2f1d12b280571d0d4e258424f8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 263, + 279, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 263, + 279, + 309 + ], + "spans": [ + { + "bbox": [ + 45, + 263, + 279, + 309 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 263, + 279, + 309 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 45, + 263, + 279, + 309 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 263, + 279, + 309 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 45, + 263, + 279, + 309 + ], + "type": "text", + "content": " are the scale and shift computed by the least-squares method [6] to solve scale-ambiguity problem for monocular depth prediction methods. And the normal loss function is" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 50, + 310, + 279, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 310, + 279, + 334 + ], + "spans": [ + { + "bbox": [ + 50, + 310, + 279, + 334 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {n o r m a l}} = \\sum_ {r \\in R} | | \\hat {N} (r) - \\bar {N} (r) | | _ {1} + | | 1 - \\hat {N} (r) ^ {T} \\bar {N} (r) | | _ {1}, \\tag {12}", + "image_path": "f71ed9b3d6063213b84e0a26e3cdecac4b07352d236cb67248c25347cb7b8c6d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 337, + 279, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 279, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 279, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 337, + 279, + 361 + ], + "type": "inline_equation", + "content": "\\tilde{N} (r)" + }, + { + "bbox": [ + 46, + 337, + 279, + 361 + ], + "type": "text", + "content": " is the predicted monocular normal transformed to the same coordinate system with angular." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 362, + 279, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 362, + 279, + 490 + ], + "spans": [ + { + "bbox": [ + 45, + 362, + 279, + 490 + ], + "type": "text", + "content": "As shown in Fig. 1, we note that these geometry priors benefit the reconstruction of better surfaces in textureless and sparse-viewed areas. However, thin structures and small objects, such as the yellow flower in Fig. 4, cannot be faithfully reconstructed with geometry priors. Recently, NeuRIS [31] put forward a hypothesis that this phenomenon arises from the inaccurate geometry supervisory signal (i.e. depth and surface normal). However, according to our experiment on Replica synthetic dataset, this problem still exists even though we use the perfect ground-truth depth, normal, and RGB to provide supervisory signals (see Fig. 4)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 500, + 279, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 500, + 279, + 512 + ], + "spans": [ + { + "bbox": [ + 45, + 500, + 279, + 512 + ], + "type": "text", + "content": "5.2. Problem of SDF Formula with Geometry Prior" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "spans": [ + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "type": "text", + "content": "To dive into the SDF representation and explore its limitations for surface reconstruction with geometric priors, we create a simplified scenario and simulate object occlusions as shown in Fig. 5(a). The ground-truth SDF intersecting with a horizontal plane is shown in Fig. 5(a), and the SDF distribution along a ray " + }, + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "type": "text", + "content": " intersecting with the blue cube at point " + }, + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "type": "inline_equation", + "content": "p_s" + }, + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "type": "text", + "content": " is shown in Fig. 5(c). There are many local minima and maxima due to the existence of multiple objects, which differs from the single-object scenario following a monotonic function (blue line in Fig. 5(c)). To examine depth priors for surface reconstruction, we employ the approach proposed in MonoSDF [36] to calculate the depth of " + }, + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "type": "inline_equation", + "content": "p_s" + }, + { + "bbox": [ + 45, + 518, + 279, + 671 + ], + "type": "text", + "content": " following Eq. (10) subject to the ground-truth SDF." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "However, even with the ground-truth SDF, the estimated depth value (1.59, the red vertical plot in Fig. 5(e)) still deviates from the true depth value (2.94, the green vertical plot in Fig. 5(e)) when multiple objects exist. According to Eq. (10), the estimated normal value would suffer from" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 304, + 117, + 372, + 187 + ], + "blocks": [ + { + "bbox": [ + 304, + 107, + 371, + 116 + ], + "lines": [ + { + "bbox": [ + 304, + 107, + 371, + 116 + ], + "spans": [ + { + "bbox": [ + 304, + 107, + 371, + 116 + ], + "type": "text", + "content": "Pseudo Ground Truth" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 117, + 372, + 187 + ], + "lines": [ + { + "bbox": [ + 304, + 117, + 372, + 187 + ], + "spans": [ + { + "bbox": [ + 304, + 117, + 372, + 187 + ], + "type": "image", + "image_path": "490ef55cc21e32f5ddce3f9f2cbc5cd761e6955932f1dd6076a295a2a01e59d9.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 304, + 188, + 372, + 258 + ], + "blocks": [ + { + "bbox": [ + 304, + 188, + 372, + 258 + ], + "lines": [ + { + "bbox": [ + 304, + 188, + 372, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 188, + 372, + 258 + ], + "type": "image", + "image_path": "caf29d1ae101d75ea88c80affca08444e422a66b0c371ff588ee3b4883dd9f3c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 274, + 530, + 318 + ], + "lines": [ + { + "bbox": [ + 296, + 274, + 530, + 318 + ], + "spans": [ + { + "bbox": [ + 296, + 274, + 530, + 318 + ], + "type": "text", + "content": "Figure 4. Illustration of failure cases of state-of-the-arts. Even though applying the perfect pseudo ground-truth geometry to supervise the model, existing room-level reconstruction methods like [36] can still fail to resolve accurate 3D structures." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 375, + 116, + 443, + 187 + ], + "blocks": [ + { + "bbox": [ + 394, + 108, + 426, + 116 + ], + "lines": [ + { + "bbox": [ + 394, + 108, + 426, + 116 + ], + "spans": [ + { + "bbox": [ + 394, + 108, + 426, + 116 + ], + "type": "text", + "content": "MonoSDF" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 375, + 116, + 443, + 187 + ], + "lines": [ + { + "bbox": [ + 375, + 116, + 443, + 187 + ], + "spans": [ + { + "bbox": [ + 375, + 116, + 443, + 187 + ], + "type": "image", + "image_path": "254c5eeeceea936dc8b127023a61b64d862b8a568c45bfdcf204d2c522fcbbfb.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 375, + 188, + 443, + 258 + ], + "blocks": [ + { + "bbox": [ + 375, + 188, + 443, + 258 + ], + "lines": [ + { + "bbox": [ + 375, + 188, + 443, + 258 + ], + "spans": [ + { + "bbox": [ + 375, + 188, + 443, + 258 + ], + "type": "image", + "image_path": "1f95d9a24451ae4fae6a7f245945b3e2005e5f82def5fd2080539fc2b0a04309.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 446, + 116, + 514, + 186 + ], + "blocks": [ + { + "bbox": [ + 472, + 109, + 489, + 116 + ], + "lines": [ + { + "bbox": [ + 472, + 109, + 489, + 116 + ], + "spans": [ + { + "bbox": [ + 472, + 109, + 489, + 116 + ], + "type": "text", + "content": "Error" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 446, + 116, + 514, + 186 + ], + "lines": [ + { + "bbox": [ + 446, + 116, + 514, + 186 + ], + "spans": [ + { + "bbox": [ + 446, + 116, + 514, + 186 + ], + "type": "image", + "image_path": "c6997df99b450c116076898e4a4df6296c2fce859c31ce7ea522214f9de56c21.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 446, + 187, + 514, + 258 + ], + "blocks": [ + { + "bbox": [ + 446, + 187, + 514, + 258 + ], + "lines": [ + { + "bbox": [ + 446, + 187, + 514, + 258 + ], + "spans": [ + { + "bbox": [ + 446, + 187, + 514, + 258 + ], + "type": "image", + "image_path": "888f26ee04977eff42fa287a1d26e115a5eb0b8ad3bc48d52f9ddc558d5f6095.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 514, + 116, + 528, + 187 + ], + "blocks": [ + { + "bbox": [ + 514, + 116, + 528, + 187 + ], + "lines": [ + { + "bbox": [ + 514, + 116, + 528, + 187 + ], + "spans": [ + { + "bbox": [ + 514, + 116, + 528, + 187 + ], + "type": "image", + "image_path": "6f90db19bded9a33d276c7752c4422dbf1063fe1eb02e4394de3e3ec74465f5c.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 514, + 188, + 528, + 258 + ], + "blocks": [ + { + "bbox": [ + 514, + 188, + 528, + 258 + ], + "lines": [ + { + "bbox": [ + 514, + 188, + 528, + 258 + ], + "spans": [ + { + "bbox": [ + 514, + 188, + 528, + 258 + ], + "type": "image", + "image_path": "0cdbb1e86dc402bc6f8586c4533ed4cc805f59c1ceb2a8800a616e0be03d2543.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 326, + 530, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 326, + 530, + 501 + ], + "spans": [ + { + "bbox": [ + 296, + 326, + 530, + 501 + ], + "type": "text", + "content": "the same problem. This implies that existing methods incorporating geometry priors [36, 31] to guide the learning of the SDF representation may not necessarily encourage the model to learn the true SDF for scene-level surface reconstruction. In turn, because small objects or thin structures usually have low sampling probability during training, the minimization of " + }, + { + "bbox": [ + 296, + 326, + 530, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{depth}}" + }, + { + "bbox": [ + 296, + 326, + 530, + 501 + ], + "type": "text", + "content": " will encourage the model to predict SDF ignoring small objects along the ray " + }, + { + "bbox": [ + 296, + 326, + 530, + 501 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 296, + 326, + 530, + 501 + ], + "type": "text", + "content": " such that the estimated SDF will produce depth values closer to the depth supervision (see Fig. 5(e)) and minimize the overall loss function, attempting to mimic the single object scenario (right part in Fig. 5). In sum, the supervision from geometric priors tends to sacrifice the reconstruction of small objects to preserve large surface reconstruction, which aligns also with our observation presented in Fig. 4." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 297, + 511, + 501, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 511, + 501, + 523 + ], + "spans": [ + { + "bbox": [ + 297, + 511, + 501, + 523 + ], + "type": "text", + "content": "5.3. Hybrid Occupancy-SDF Representation" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 296, + 529, + 530, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 529, + 530, + 588 + ], + "spans": [ + { + "bbox": [ + 296, + 529, + 530, + 588 + ], + "type": "text", + "content": "The problem above is essentially caused by the SDF representation, which describes the geometry of a scene as a whole and thus suffers from the interference of other objects, especially small objects, and thin structures are prone to be removed to preserve large structures." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 296, + 589, + 530, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 589, + 530, + 717 + ], + "spans": [ + { + "bbox": [ + 296, + 589, + 530, + 717 + ], + "type": "text", + "content": "Unlike the SDF representation, occupancy represents each point separately and thus is free from the interference of objects in this challenging scenario. However, occupancy representation only focuses on the intersecting point ignoring the constraint of neighborhood points. Thus, the reconstruction results represented by occupancy will have many floaters and useless structures, as shown in Fig. 1, which can be eliminated in SDF by Eikonal loss [7]. This inspires us to investigate a hybrid of occupancy and SDF as a representation for neural surface reconstruction as shown in Fig. 2. 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Toy experiments for the room-level scene. The left part of 5(a), where we stand in front of the yellow cylinder to observe the entire scene, is a widespread scenario for room-level scale scenes. Unlike the single object scenario, where the distribution of SDF value is a monotonic decreasing function from the observed position to the object, the room-level scenario has complex distributions with multi peaks/valleys along the single ray (5(c)). Following the Laplace density function [34], the density distributions of different situations are shown in 5(d), where room-level scenes have a secondary peak near small objects but the single object scene only has one peak. It is because of the existence of this peak, the weights in the room-level scene (5(e)) exhibit a multi-model distribution, while for the single object case a uni-modal distribution. 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The occupancy representation assumes that objects are solid, thus we can rewrite the neural rendering formula [14] to" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 79, + 483, + 279, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 483, + 279, + 515 + ], + "spans": [ + { + "bbox": [ + 79, + 483, + 279, + 515 + ], + "type": "interline_equation", + "content": "\\hat {C} (r) = \\sum_ {i = 1} ^ {M} o \\left(\\mathbf {p} _ {i}\\right) \\prod_ {j < i} \\left(1 - o \\left(\\mathbf {x} _ {j}\\right)\\right) c \\left(\\mathbf {p} _ {i}, d\\right), \\tag {14}", + "image_path": "ca39521e9a68cf74434fa8f824dfef1ff2064c02ba9b54e313f6d5de39520f2f.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "spans": [ + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "text", + "content": "which replaces the opacity " + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "text", + "content": " to a discrete occupancy indicator variable " + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "inline_equation", + "content": "o\\in 0,1" + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "inline_equation", + "content": "o = 0" + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "text", + "content": " indicates the free space while " + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "inline_equation", + "content": "o = 1" + }, + { + "bbox": [ + 45, + 516, + 279, + 610 + ], + "type": "text", + "content": " the occupied space. Thus, this representation will not be affected by the objects along the ray, and the rendering depth will be consistent with ground-truth depth in ground-truth occupancy space. Note that the occupancy-based representation is introduced to facilitate optimization. During inference, the SDF is used for reconstruction." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "text", + "content": "To understand why and how the hybrid representation helps optimize the SDF field for accurate reconstruction, we conduct the following empirical analysis, using the scenario shown in Fig. 5(a). Here, the orange ray hits a surface point " + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "text", + "content": " of the large blue cube and the blue ray hits the surface point " + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "text", + "content": " on the small cylinder. During optimization, the depth/normal loss for point " + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "text", + "content": " along the orange ray will encourage the model to predict a large SDF value (absolute) of point " + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 45, + 612, + 279, + 730 + ], + "type": "text", + "content": " (Fig. 5(b)) which violates the reconstruction of the small cylinder where a small SDF value is desired. In" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "spans": [ + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "text", + "content": "contrast, point " + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "text", + "content": " has no effects on point " + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "text", + "content": " with occupancy representation. The hybrid representation joins the forces of SDF and occupancy representations, aiming to use occupancy representation to help overcome the issues of SDF representation in optimization. Although the depth/normal loss from the SDF presentation for point " + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "text", + "content": " still has a negative impact on the optimization of point " + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "text", + "content": ". The additional occupancy representation will force the network to predict a large occupancy value for a point " + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 296, + 405, + 530, + 603 + ], + "type": "text", + "content": " and thus will indirectly regularize the network to predict a small SDF value (see Fig. 5(b): the blue up arrow in \"Hybrid\"). We admit that this hybrid representation can only alleviate this problem, and our study is more empirical. Fundamental issues arise from insufficient neural scene representation, which requires further research efforts. We explore further why this combination would bring notable benefits to the supplementary with an example." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 297, + 618, + 376, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 618, + 376, + 632 + ], + "spans": [ + { + "bbox": [ + 297, + 618, + 376, + 632 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 297, + 639, + 523, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 639, + 523, + 651 + ], + "spans": [ + { + "bbox": [ + 297, + 639, + 523, + 651 + ], + "type": "text", + "content": "Optimization. In the training stage, we minimize the loss" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 332, + 655, + 530, + 688 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 655, + 530, + 688 + ], + "spans": [ + { + "bbox": [ + 332, + 655, + 530, + 688 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\mathrm {r g b}} ^ {s d f} + \\lambda_ {1} \\mathcal {L} _ {\\mathrm {r g b}} ^ {s d f _ {F}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {e i k}} + \\lambda_ {3} \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {o c c}} \\tag {15} \\\\ + \\lambda_ {4} \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {s d f}} + \\lambda_ {5} \\mathcal {L} _ {\\text {n o r m a l}} ^ {\\text {o c c}} + \\lambda_ {6} \\mathcal {L} _ {\\text {n o r m a l}} ^ {\\text {s d f}}, \\\\ \\end{array}", + "image_path": "514c8d6d045bb1da19134a8334855b5ccda217babdf5cb5bbaa86cad2f1ccfe5.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rgb}" + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": " means color-based rendering loss following Eq. (6) but only to SDF representation. The rendering color computed by the feature rendering formula (Eq. (8))" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "8945" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "spans": [ + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": "and Eq. (9)) is denoted to " + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rgb}^{sdf_F}" + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": ". Notably, " + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{eik}" + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": " means the eikonal loss [7], " + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{depth}" + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": " means the depth rendering loss following Eq. (11), and " + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{normal}" + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": " means the normal rendering loss following Eq. (12). We apply them for both representations, where the superscript " + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "inline_equation", + "content": "occ" + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": " indicates the loss computed by occupancy-based representation, while the " + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "inline_equation", + "content": "sdf" + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": " by SDF-based representation. The network is optimized by the Adam optimizer with a learning rate of " + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "inline_equation", + "content": "5e^{-4}" + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": ". We set weights " + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4, \\lambda_5, \\lambda_6" + }, + { + "bbox": [ + 45, + 105, + 281, + 234 + ], + "type": "text", + "content": " to 1, 0.05, 0.5, 0.1, 0.1, 0.05, respectively. The network architecture and sampling strategy are detailed in the supplement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 237, + 281, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 237, + 281, + 400 + ], + "spans": [ + { + "bbox": [ + 45, + 237, + 281, + 400 + ], + "type": "text", + "content": "Datasets. We use three datasets to assess the performance of our algorithm. ScanNet [2] is a real-world dataset that provides 1,513 scenes captured with Kinect V1 RGB-D camera. The BundleFusion [3] is applied to provide high-quality camera poses and surface reconstructions. For each scene, we uniformly sample roughly 500 frames to train our network. Tanks and Temples [11] is a real-world, large-scale scene dataset. We use four indoor scenes from their advanced split and run on the official server. Replica [27] is a synthetic dataset that provides 18 scenes, with each providing dense geometry, HDR textures, and semantic annotations. We select 8 scenes and use the Habitat simulator [29] to render RGB images following MonoSDF [36] splits. Notably, we conduct ablation studies on this dataset." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 404, + 281, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 404, + 281, + 683 + ], + "spans": [ + { + "bbox": [ + 45, + 404, + 281, + 683 + ], + "type": "text", + "content": "Compared Methods. (1) UNISURF [18] is an occupancy-based method that unifies surface rendering and volume rendering for neural scene reconstruction. We implement the UNISURF* with normal and depth priors for a fair comparison. (2) MonoSDF [36] is an SDF-based method that adds depth and normal constraints on VolSDF [34]. (3) Manhattan-SDF [8] is an SDF-based method that adds a semantic branch and uses the Manhattan constraint to regularize the geometry in floor and wall regions. (4) COLMAP [25] is a classical multi-view stereo method with Poisson surface reconstruction. (5) NeuRIS [31] is an SDF-based method that introduces pseudo normal prior to the NeUS [32] architecture. Meanwhile, it leverages multiview consistency to eliminate the wrong supervision signal from inaccurate estimated results. (6) NICER-SLAM [39] is an SDF-based dense SLAM system that uses locally implicit map representation and can simultaneously optimize for camera poses and a hierarchical neural implicit map representation. (7) LIG [9] uses the local implicit grid representation to reconstruct the large-scale scene from partial or noise point clouds. (8) Convolutional Occupancy network(Conv-Occ) [21] is a locally implicit representation that integrates local information to get better reconstruction results from noisy point cloud." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 683, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 683, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 683, + 279, + 730 + ], + "type": "text", + "content": "Notably, local implicit representation [9, 21] can only reconstruct the scene from point clouds, thus we re-implement them using point clouds generated from scale-aligned pseudo depth and utilize the provided pretrained" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "content": "models for evaluation. And we directly obtain the results from the main paper of NICER-SLAM [39]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 133, + 531, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 133, + 531, + 215 + ], + "spans": [ + { + "bbox": [ + 296, + 133, + 531, + 215 + ], + "type": "text", + "content": "Metrics. All meshes are evaluated by 5 standard metrics defined in [16]: Accuracy, Completeness, Precision, Recall, and " + }, + { + "bbox": [ + 296, + 133, + 531, + 215 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 296, + 133, + 531, + 215 + ], + "type": "text", + "content": "-score. Their definition will be discussed in the supplementary. For the Replica dataset, we also report the normal consistency following [13, 8, 20]. For the Tanks and Temples dataset, we use the official server to evaluate our results and report the F-score for selected scenes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 297, + 220, + 380, + 231 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 220, + 380, + 231 + ], + "spans": [ + { + "bbox": [ + 297, + 220, + 380, + 231 + ], + "type": "text", + "content": "6.1. Main Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 238, + 530, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 238, + 530, + 261 + ], + "spans": [ + { + "bbox": [ + 296, + 238, + 530, + 261 + ], + "type": "text", + "content": "We compare our method with state-of-the-art methods on three benchmark datasets." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 298, + 266, + 531, + 353 + ], + "blocks": [ + { + "bbox": [ + 298, + 266, + 531, + 353 + ], + "lines": [ + { + "bbox": [ + 298, + 266, + 531, + 353 + ], + "spans": [ + { + "bbox": [ + 298, + 266, + 531, + 353 + ], + "type": "table", + "html": "
MethodAcc ↓Comp ↓C-L1 ↓Prec ↑Recall ↑F-score ↑
COLMAP [25]0.0470.2350.14171.144.153.7
UNISURF [18]0.5540.1640.35921.236.226.7
VolSDF [34]0.4140.1200.26732.139.434.6
NeUS [32]0.1790.2080.19431.327.529.1
Manhattan-SDF [8]0.0720.0680.07062.156.860.2
NeuRIS [31]0.0500.0490.05071.766.969.2
MonoSDF [36]0.0350.0480.04279.968.173.3
Ours0.0390.0410.04080.076.077.9
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AuditoriumBallroomCourtroomMuseumMean
MonoSDF3.092.4710.005.105.165
Ours5.225.4213.998.598.305
MonoSDF*3.173.7013.755.686.58
Ours*6.197.3319.8011.8511.295
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Reconstruction results on representative datasets of Replica (left), ScanNet (middle), and Tanks and Temples (right). The ground truth is presented on the bottom-most. Red boxes in sub-figures highlight those areas where distinctive differences can be observed." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 147, + 359, + 236, + 427 + ], + "blocks": [ + { + "bbox": [ + 147, + 359, + 236, + 427 + ], + "lines": [ + { + "bbox": [ + 147, + 359, + 236, + 427 + ], + "spans": [ + { + "bbox": [ + 147, + 359, + 236, + 427 + ], + "type": "image", + "image_path": "56aa3115f8678b81602522f15db84656a21b0102f8297c04bacb277ac5d8b5e2.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 238, + 359, + 333, + 427 + ], + "blocks": [ + { + "bbox": [ + 238, + 359, + 333, + 427 + ], + "lines": [ + { + "bbox": [ + 238, + 359, + 333, + 427 + ], + "spans": [ + { + "bbox": [ + 238, + 359, + 333, + 427 + ], + "type": "image", + "image_path": "ae27986e6d458c62fcfdea8b84b73f490cccbb4cb075807a73d30f3837ed405c.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 428, + 361, + 436 + ], + "lines": [ + { + "bbox": [ + 312, + 428, + 361, + 436 + ], + "spans": [ + { + "bbox": [ + 312, + 428, + 361, + 436 + ], + "type": "text", + "content": "Ground Truth" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 337, + 359, + 433, + 427 + ], + "blocks": [ + { + "bbox": [ + 337, + 359, + 433, + 427 + ], + "lines": [ + { + "bbox": [ + 337, + 359, + 433, + 427 + ], + "spans": [ + { + "bbox": [ + 337, + 359, + 433, + 427 + ], + "type": "image", + "image_path": "65bbc042de63ee02bc62524646c17de4cf76d5b763185a5c81e3304fbc5fc3aa.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 436, + 358, + 527, + 427 + ], + "blocks": [ + { + "bbox": [ + 436, + 358, + 527, + 427 + ], + "lines": [ + { + "bbox": [ + 436, + 358, + 527, + 427 + ], + "spans": [ + { + "bbox": [ + 436, + 358, + 527, + 427 + ], + "type": "image", + "image_path": "3ce84973ff8861014b023f3e587e87017f23f22930b5ba88d04fa79d21e9fe62.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 464, + 429, + 508, + 437 + ], + "lines": [ + { + "bbox": [ + 464, + 429, + 508, + 437 + ], + "spans": [ + { + "bbox": [ + 464, + 429, + 508, + 437 + ], + "type": "text", + "content": "Ours (Grids)" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "bbox": [ + 45, + 477, + 279, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 477, + 279, + 664 + ], + "spans": [ + { + "bbox": [ + 45, + 477, + 279, + 664 + ], + "type": "text", + "content": "the advanced Tanks and Temples dataset [11], which features more complicated structures. As alternative methods of neural reconstruction from images are not assessed on this dataset, we implement the best-performing method MonoSDF and compare with it. Thus, the MonoSDF and two versions of our method are implemented. Specifically, one adopts the pure MLP architecture while the other uses the hash grids as the input representation. The quantitative assessments (Table 2) reveal that our method shows better performance on this dataset, regardless of whether an MLP or hash-grid structure is used. And our hybrid representation exhibits excellent generalization abilities across different implicit structures. Overall, our compelling experimental results on the Tanks and Temples dataset further validate the robustness and versatility of the proposed method in reconstructing complex and challenging indoor scenes." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "Results on Replica Dataset. Quantitative assessment results on the Replica dataset are presented in Table 3. For this dataset, we compare our methods with both point-based methods [21, 9] and rendering methods [39, 18, 36]. Ours significantly surpasses existing state-of-the-art neural ren" + } + ] + } + ], + "index": 36 + }, + { + "type": "table", + "bbox": [ + 301, + 478, + 530, + 549 + ], + "blocks": [ + { + "bbox": [ + 301, + 478, + 530, + 549 + ], + "lines": [ + { + "bbox": [ + 301, + 478, + 530, + 549 + ], + "spans": [ + { + "bbox": [ + 301, + 478, + 530, + 549 + ], + "type": "table", + "html": "
MethodNormal C.↑Chamfer- \\( {\\mathcal{L}}_{1} \\downarrow \\)F-score ↑
Conv-Occ [21]85.736.4358.33
LIG [9]89.565.5365.20
NICER-SLAM [39]90.273.91-
UNISURF†[18]90.964.9378.99
MonoSDF†[36]92.112.9486.18
\\( Ours^{\\dagger } \\)93.432.5892.12
", + "image_path": "345559daf5ba941665584bafb2d0a13a9b4d7cb6be54c4d42c5a0f04d9a27bb4.jpg" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "table_body" + } + ], + "index": 37 + }, + { + "bbox": [ + 296, + 554, + 530, + 587 + ], + "lines": [ + { + "bbox": [ + 296, + 554, + 530, + 587 + ], + "spans": [ + { + "bbox": [ + 296, + 554, + 530, + 587 + ], + "type": "text", + "content": "Table 3. Quantitative assessments of the proposed model against prior works on the Replica dataset. Herein, " + }, + { + "bbox": [ + 296, + 554, + 530, + 587 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 296, + 554, + 530, + 587 + ], + "type": "text", + "content": " indicates the use of geometry priors as supervision signals." + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "content": "dering methods. The results reveal that the SDF-based representation outperforms the occupancy-based ones (i.e. UNISURF*). This is because the SDF usually enforces constraints on the distribution of the entire scene, benefiting to suppressing the occurrence of floaters or unnecessary structures in occupancy-based representation. Notably, our OccSDF Hybrid method can constrain the distribution of the entire scene with SDF representation meanwhile exploiting the occupancy representation to resolve thin structures and small objects. Qualitative comparisons are shown in Fig. 6." + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "8947" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 128, + 279, + 186 + ], + "blocks": [ + { + "bbox": [ + 46, + 106, + 136, + 118 + ], + "lines": [ + { + "bbox": [ + 46, + 106, + 136, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 136, + 118 + ], + "type": "text", + "content": "6.2. Ablation Study" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 128, + 279, + 186 + ], + "lines": [ + { + "bbox": [ + 49, + 128, + 279, + 186 + ], + "spans": [ + { + "bbox": [ + 49, + 128, + 279, + 186 + ], + "type": "table", + "html": "
Normal C.↑Chamfer- \\( {\\mathcal{L}}_{1} \\downarrow \\)F-score ↑
MonoSDF92.112.9486.18
+ feature93.012.6491.01
+ hybrid93.222.7790.24
full model93.432.5892.12
", + "image_path": "b8332958a86cc83896d92d7a8e5504ed60d3886e74e224c65072077e8820e84f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 45, + 191, + 279, + 223 + ], + "lines": [ + { + "bbox": [ + 45, + 191, + 279, + 223 + ], + "spans": [ + { + "bbox": [ + 45, + 191, + 279, + 223 + ], + "type": "text", + "content": "Table 4. Ablation study on the Replica dataset [27], where we progressively add different constraints to assess their impacts. The MonoSDF [36] is set as the baseline model." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 229, + 279, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 229, + 279, + 322 + ], + "spans": [ + { + "bbox": [ + 45, + 229, + 279, + 322 + ], + "type": "text", + "content": "We conduct ablation studies on the Replica dataset as it provides ground-truth geometry. Four different configurations are investigated to train our model, including (1) MonoSDF with MLP settings (MonoSDF-MLP); (2) MonoSDF-MLP with our feature-based rendering formula; (3) MonoSDF-MLP with our hybrid representation; (4) MonoSDF-MLP with both the feature-based rendering formula and hybrid representation scheme (Full model)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 324, + 279, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 324, + 279, + 532 + ], + "spans": [ + { + "bbox": [ + 45, + 324, + 279, + 532 + ], + "type": "text", + "content": "Table 4 shows that all metrics are improved when using the feature rendering to reconstruct this scene. Our proposed feature rendering scheme addresses the difficulties in reconstructing areas of low intensities, resulting in better results. On the other hand, the hybrid representation also leads to significant improvements in all metrics. Notably, it improves the completeness of small objects and thin structures, as evidenced by the results in Fig. 6. By leveraging both components, our model achieves an overall improvement of 5.94 in F-score, along with improved normal consistency and Chamfer-" + }, + { + "bbox": [ + 45, + 324, + 279, + 532 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 45, + 324, + 279, + 532 + ], + "type": "text", + "content": ". We attribute this success to our feature-based color rendering formula and our hybrid representation, which addresses the color-bias issue in optimization and difficulties in reconstructing detailed structures. The visualization results in Fig. 6 show our model's excellent reconstruction performance, especially in low-intensity areas and detailed structures. We will add more ablation studies and visualize results in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 540, + 169, + 554 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 169, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 169, + 554 + ], + "type": "text", + "content": "6.3. Parameters Adjusting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 559, + 279, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 559, + 279, + 676 + ], + "spans": [ + { + "bbox": [ + 45, + 559, + 279, + 676 + ], + "type": "text", + "content": "As shown in Eq. (15), our method newly added three different losses " + }, + { + "bbox": [ + 45, + 559, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rgb}^{sdf_F},\\mathcal{L}_{depth}^{occ},\\mathcal{L}_{normal}^{occ}" + }, + { + "bbox": [ + 45, + 559, + 279, + 676 + ], + "type": "text", + "content": ". In order to verify the sensitivity of our method to hyperparameters, we provided the results of the experiment on the Replica dataset as shown in Fig. 7. It is clear that our method is not very sensitive to hyperparameters, and all the evaluated settings outperform the baseline method (C-" + }, + { + "bbox": [ + 45, + 559, + 279, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 45, + 559, + 279, + 676 + ], + "type": "text", + "content": ": 2.94, F-score: 86.18). It is worth noting that our approach demonstrates consistent performance enhancement across diverse datasets using the same parameter set, outperforming the baseline results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 687, + 116, + 698 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 687, + 116, + 698 + ], + "spans": [ + { + "bbox": [ + 46, + 687, + 116, + 698 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "We have analyzed the constraints present in current neural scene representation techniques with geometry priors," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 106, + 520, + 214 + ], + "blocks": [ + { + "bbox": [ + 308, + 106, + 520, + 214 + ], + "lines": [ + { + "bbox": [ + 308, + 106, + 520, + 214 + ], + "spans": [ + { + "bbox": [ + 308, + 106, + 520, + 214 + ], + "type": "image", + "image_path": "fc94ad8306528a58fe24577420612fb1ade7800cc574e6486e5f36bda2af3ae3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 308, + 217, + 520, + 325 + ], + "blocks": [ + { + "bbox": [ + 308, + 217, + 520, + 325 + ], + "lines": [ + { + "bbox": [ + 308, + 217, + 520, + 325 + ], + "spans": [ + { + "bbox": [ + 308, + 217, + 520, + 325 + ], + "type": "image", + "image_path": "2cb135186c9bbf547a3a7a440e952941e6244a228997596f615a7529945abc9e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 308, + 328, + 520, + 439 + ], + "blocks": [ + { + "bbox": [ + 308, + 328, + 520, + 439 + ], + "lines": [ + { + "bbox": [ + 308, + 328, + 520, + 439 + ], + "spans": [ + { + "bbox": [ + 308, + 328, + 520, + 439 + ], + "type": "image", + "image_path": "f65b8741260a565eb52ecb8a77be0acf42ad48b35775969d1dc0ff5da631e509.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 297, + 443, + 515, + 455 + ], + "lines": [ + { + "bbox": [ + 297, + 443, + 515, + 455 + ], + "spans": [ + { + "bbox": [ + 297, + 443, + 515, + 455 + ], + "type": "text", + "content": "Figure 7. Performance with different hyperparameter choices." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 466, + 530, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 466, + 530, + 606 + ], + "spans": [ + { + "bbox": [ + 296, + 466, + 530, + 606 + ], + "type": "text", + "content": "and have identified issues in their ability to reconstruct detailed structures due to a biased optimization towards high color intensities and the complex SDF distribution. As a result, we have developed a feature rendering scheme that balances color regions and have implemented a hybrid representation to address the limitations of the SDF distribution. Our approach has demonstrated the successful reconstruction of room scenes with a high-fidelity surface, including small objects, detailed structures, and low-intensity pixel regions. We envision our results inspire further research on improving neural scene representation for accurate and large-scale surface reconstruction." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 617, + 393, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 617, + 393, + 630 + ], + "spans": [ + { + "bbox": [ + 297, + 617, + 393, + 630 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 530, + 730 + ], + "type": "text", + "content": "We thank Xin Kong for his advising during the rebuttal period. This work has been supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621 and 27212822), General Research Fund Scheme (Grant No. 17202422), and RGC matching fund scheme (RMGS). Part of the described research work is conducted in the JC STEM Lab of Robotics for Soft Materials funded by The Hong Kong Jockey Club Charities Trust." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 758 + ], + "type": "text", + "content": "8948" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 102, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 280, + 730 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 177 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 177 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 177 + ], + "type": "text", + "content": "[1] Motilal Agrawal and Larry S Davis. 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Oswald, Andreas Geiger, and Marc Pollefeys. Nicer-slam: Neural implicit scene encoding for rgb slam, 2023. 3, 7, 8" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "spans": [ + { + "bbox": [ + 279, + 749, + 298, + 757 + ], + "type": "text", + "content": "8950" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning by Sorting_ Self-supervised Learning with Group Ordering Constraints/f7288260-030f-4ffe-bd8d-4ee76970c742_content_list.json b/2023/Learning by Sorting_ Self-supervised Learning with Group Ordering Constraints/f7288260-030f-4ffe-bd8d-4ee76970c742_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..776c260be42aea90753584f538d46839e8946bac --- /dev/null +++ b/2023/Learning by Sorting_ Self-supervised Learning with Group Ordering Constraints/f7288260-030f-4ffe-bd8d-4ee76970c742_content_list.json @@ -0,0 +1,1622 @@ +[ + { + "type": "text", + "text": "Learning by Sorting: Self-supervised Learning with Group Ordering Constraints", + "text_level": 1, + "bbox": [ + 248, + 130, + 722, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nina Shvetsova $^{1,2,3}$ Felix Petersen $^{4}$ Anna Kukleva $^{2}$ Bernt Schiele $^{2}$ Hilde Kuehne $^{1,3,5}$", + "bbox": [ + 122, + 202, + 866, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Goethe University Frankfurt, 2Max-Planck-Institute for Informatics, 3University of Bonn, 4Stanford University, 5MIT-IBM Watson AI Lab {shvetsov@uni-frankfurt.de, mail@felix-petersen.de}", + "bbox": [ + 68, + 222, + 898, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contrastive learning has become an important tool in learning representations from unlabeled data mainly relying on the idea of minimizing distance between positive data pairs, e.g., views from the same images, and maximizing distance between negative data pairs, e.g., views from different images. This paper proposes a new variation of the contrastive learning objective, Group Ordering Constraints (GroCo), that leverages the idea of sorting the distances of positive and negative pairs and computing the respective loss based on how many positive pairs have a larger distance than the negative pairs, and thus are not ordered correctly. To this end, the GroCo loss is based on differentiable sorting networks, which enable training with sorting supervision by matching a differentiable permutation matrix, which is produced by sorting a given set of scores, to a respective ground truth permutation matrix. Applying this idea to groupwise pre-ordered inputs of multiple positive and negative pairs allows introducing the GroCo loss with implicit emphasis on strong positives and negatives, leading to better optimization of the local neighborhood. We evaluate the proposed formulation on various self-supervised learning benchmarks and show that it not only leads to improved results compared to vanilla contrastive learning but also shows competitive performance to comparable methods in linear probing and outperforms current methods in $k$ -NN performance.1", + "bbox": [ + 75, + 323, + 473, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 733, + 209, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Self-supervised learning has become a topic of growing interest over the last years as it allows models to learn representations from large-scale data without the need for human annotation. Many approaches rely on the idea of contrastive learning and were able not only to narrow the gap to the supervised learning performance in vision [23, 14, 60, 30, 3, 63], but also to train state-of-the-art vision-language [52, 56] and multimodal models [40]. All", + "bbox": [ + 75, + 758, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9b23dded58b3e3994358ce72e54c64e5fd38a8990114d1cbb0de78568f2b62ad.jpg", + "image_caption": [ + "Group Ordering Constraints (GroCo) Loss all pos. distances $<$ all neg. distances" + ], + "image_footnote": [], + "bbox": [ + 522, + 311, + 867, + 414 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/072be32b6e16b56f18de4ffbe5345af4f41ab2d5ce373099eb19addf5b2dfd43.jpg", + "image_caption": [ + "Figure 1. The idea of the proposed group ordering constraints loss compared to pairwise contrastive losses: GroCo arranges positive and negative data points so that the largest distance to positives must be smaller than the smallest distance to negative points. To this end, the loss implicitly minimizes the amount of necessary swap operation to achieve the ordering constraint. Thus, it focuses on overlapping positives and negatives compared to standard contrastive losses that minimize resp. maximize all pairwise distances." + ], + "image_footnote": [], + "bbox": [ + 522, + 416, + 867, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of these methods rely on the concept of the pairwise contrastive loss, which is based on the idea that a so-called positive pair, e.g., an image serving as an anchor and an augmentation of the same image, should be closer to each other in an embedding space than a so-called negative pair, e.g., a pair made up of an anchor image and a different image, should be far away from each other. However, it has been noted that the idea of a pairwise contrastive loss also has some limitations, such as the alignment of the embedding space based on individual pairs. Several attempts have been made to address this issue, e.g., combining the contrastive idea with concepts based on local neighborhoods, such as clustering (SwAV [11]), or minimizing distances between multiple positive pairs for the same instance together (Whitening [24]). Another limitation of the contrastive loss is that is that the embedding space is optimized with respect to all negatives, i.e., even negatives that are far away", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": " 0$ denotes an inverse temperature. For $\\beta \\to \\infty$ , the relaxation converges to the discrete swap operation. The differentiable conditional swap operation for the elements $(d_i, d_j)$ can be defined as a permutation matrix $P_{swap(d_i, d_j)} \\in R^{(K + N) \\times (K + N)}$ , which is an identity ma", + "bbox": [ + 496, + 825, + 893, + 904 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16456", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "trix except for entries $P_{ii}, P_{ij}, P_{jj}, P_{ji}$ defined as:", + "bbox": [ + 76, + 90, + 410, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP _ {i i} = P _ {j j} = f \\left(d _ {j} - d _ {i}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 116, + 468, + 140 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP _ {i j} = P _ {j i} = f \\left(d _ {i} - d _ {j}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 136, + 354, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The permutation matrix $P_{s}$ for step $s$ is the product of matrices corresponding to independent (and thus parallel) swap operations in this step $P_{s} = \\prod_{i\\in R}P_{swap(d_{i},d_{i + 1})}$ , where $R$ is the set of odd indices if $s$ is odd and the set of even indices if $s$ is even. The complete permutation matrix $P$ is defined as $P = P_{K + N}\\cdot \\ldots \\cdot P_{1}$ . In the discrete case, each column of a permutation matrix has exactly one entry of 1, indicating the position where the element that corresponds to this column should be placed. In the relaxed version, column values can be seen as a distribution over possible positions of the element. If the correct order of input values is known, we can create a ground truth matrix $Q$ and define the loss as $L = \\frac{1}{(K + N)^2}\\sum_{i,j}\\mathrm{BCE}(P_{ij},Q_{ij})$ where BCE refers to binary cross-entropy.", + "bbox": [ + 75, + 162, + 468, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 GroCo Loss", + "text_level": 1, + "bbox": [ + 76, + 388, + 215, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "If there was a known ground truth order of positives and negatives, the loss could be calculated directly based on this ground truth permutation matrix. However, as the algorithm is based on random augmentations, there are no known orders among positives and among negatives. Thus, the only information available is whether a pair belongs to the positive or the negative group.", + "bbox": [ + 75, + 410, + 468, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To derive a loss to fulfil this group ordering constraint, we start by ordering positives and negatives first separately with respect to the computed distances to the anchor image as $d_1^p \\leq \\ldots \\leq d_K^p$ for positives and $d_1^n \\leq \\ldots \\leq d_N^n$ for negatives. As shown in Figure 3, positive and negative distances are then concatenated in a list as:", + "bbox": [ + 75, + 516, + 468, + 604 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ d _ {1} ^ {p}, \\dots , d _ {K} ^ {p}, d _ {1} ^ {n}, \\dots , d _ {N} ^ {n} \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 616, + 468, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Even though elements in the positive and negative are ordered, it is still open if the constraint $d_i^p < d_j^n$ is fulfilled for any $1 \\leq i \\leq K$ and $1 \\leq j \\leq N$ .", + "bbox": [ + 75, + 643, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A differentiable sorting network is applied to the concatenated list and a differentiable permutation matrix is obtained for sorting the list in non-descending order. As shown in 3, values in the permutation matrix column can be seen as probabilities to sort the corresponding element to the different positions, e.g., $P_{11}$ would be the probability for assigning the first element in the list $(d_1^p)$ to position 1, $P_{21}$ to position 2, etc. Therefore, the sum of the first $K$ elements in a column can be considered as a probability being sorted inside the first $K$ elements. Thus, for a permutation matrix of size $(K + N) \\times (K + N)$ the sum of the first $K$ rows results in probabilities of being sorted in positive places and the later columns (from $K + 1$ to $K + N$ ) in negative places. To enforce positives to be sorted in the positive places and", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "negatives in the negatives places, the respective loss (with $\\mathbb{1}$ as the indicator function) is defined as", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L = \\frac {1}{2 (K + N)} \\sum_ {i = 1} ^ {K + N} \\left(\\operatorname {B C E} \\left(\\sum_ {k = 1} ^ {K} P _ {k i}, \\mathbb {1} _ {i \\leq K}\\right) + \\right. \\tag {6} \\\\ + \\operatorname {B C E} \\left(\\sum_ {k = K + 1} ^ {K + N} P _ {k i}, \\mathbb {1} _ {i > K}\\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 128, + 890, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated in Figure 2, the proposed loss is a relaxation of the sorting supervision in a way that it considers two types of swap operations: swap operations within the group of positive and negative samples, which should not contribute to the loss, and swap operations between the groups, which violate the positive-negative ordering assumption and which are used as the optimization criterion.", + "bbox": [ + 496, + 220, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Role of $\\beta$ . One relevant hyper parameter is the inverse temperature $\\beta$ in differentiable swap operation (Equation 3), which corresponds to the degree of relaxation of the swap operation that converges to a discrete case when $\\beta \\rightarrow \\infty$ (Figure 3). Therefore with lower $\\beta$ the swap operation is more \"soft\", which is beneficial for optimization, but the relaxation error accumulated by each step is larger, and vice versa in the case of larger $\\beta$ . With higher $\\beta$ even a small difference between values results in a high probability for a swap or not swap operation, resulting in a smaller margin between the positive and negatives group.", + "bbox": [ + 496, + 330, + 890, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Number of samples. Since the strongest negatives have the strongest effect on the loss function, the selection can be limited to only the top- $N$ strongest negatives. Further, as more negatives also result in more layers in the sorting network and each layer contributes to the overall differential permutation matrix, more layers also result in a softer swap probabilities. Therefore $\\beta$ should be selected based on a number of elements to sort. An ablation study on this effect is given in Section 4.5.", + "bbox": [ + 496, + 501, + 890, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Role of Pre-ordering. Practically, positives and negatives are pre-ordered among themselves before concatenating and forwarding them to the differentiable sorting network. While the loss will still contrast positives to negatives no matter if the input is ordered or not, it shows that preordering improves the overall performance of the GROCo loss. This can be attributed to the fact that sorting networks perform comparisons between neighboring elements and swap them if they are in the wrong order. If the input was not pre-ordered and, thus, distances from positive and negative pairs would be mixed, this would result in additional swap operations. Using pre-ordered inputs the focus lies on comparing the strongest positives with the strongest negatives. In this way, elements are considered as a group, and the borders of the groups or their overlapping parts are emphasized in the loss. In Section 4.5 and Figure 4, we provide additional discussions and illustrate this behavior.", + "bbox": [ + 496, + 642, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16457", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Evaluation", + "text_level": 1, + "bbox": [ + 76, + 89, + 310, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 111, + 294, + 128 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unless stated otherwise, the following setup is used for all experiments:", + "bbox": [ + 75, + 132, + 468, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model. Following previous works [14, 27, 11, 17] Resnet50 [31] is used as the encoder $g(\\cdot)$ and an MLP block consisting of three fully connected layers with a size of 2048 and followed by a batch normalization layer [33] is used as the projection head $h(\\cdot)$ . All batch normalization layers except the last one are followed by a ReLU activation. The dimensionalities of the representation space and the latent space are both 2048 as in [17].", + "bbox": [ + 75, + 165, + 468, + 286 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. Following previous works [14, 27, 11, 17], we use the train set of the ImageNet ILSVRC-2012 dataset [54] for self-supervised training without any human annotation. To create $m$ augmented views per image (considering $m = 2,3,4$ ), the DINO augmentation setup [12] is used. The model is trained with the SGD optimizer [64] with a learning rate of $6.0 \\times$ (batch size/256) for 100 epochs and $3.0 \\times$ (batch size/256) for 200 and 400 epochs. We use a cosine scheduler without restarts [38] and 10 epochs warm-up for 200 and 400 epochs training and 1 epoch linear warm-up for 100 epochs training (we find it beneficial for our method but not for SimCLR). During training, the stop gradient operation is used following the self-supervised learning setups of [14, 12, 27]; specifically, stop gradient is performed during distance computation $\\mathrm{d}(x^a, x_i) = \\mathrm{d}(x^a, \\text{stop\\_grad}(x_i))$ . While training with stop gradient does not show a direct impact on the overall performance, we observed that it allows training with larger variations of hyperparameters while maintaining stable performance. By default, the top $N = 10$ strongest negatives are sampled from the batch and an inverse temperature of $\\beta = 1$ is used. Due to resource constraints, the model is trained with a batch size of 1024 with mixed precision. On an 8-GPU (NVIDIA A6000) server, training for 100 epochs with $m = 2$ views takes approximately 22 hours.", + "bbox": [ + 75, + 287, + 470, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Procedure", + "text_level": 1, + "bbox": [ + 76, + 669, + 282, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Linear Probing. Linear probing allows to evaluate the learned embedding space by linear evaluation [14, 27, 11, 17], capturing the linear separability of classes. For this, a linear classifier is trained on frozen representations in a fully-supervised way using the ImageNet train set. We follow the standard protocol [17] to train the linear classifier.", + "bbox": [ + 75, + 686, + 468, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$k$ -NN Evaluation. To analyze the local properties of the learned representation, namely how often neighbored data points correspond to the same semantic class, we further evaluate with respect to nearest neighbor classification, predicting the class by a simple weighted $k$ nearest neighbor classifier ( $k$ -NN) with $k = \\{1, 10, 20\\}$ based on cosine distance as used in [12, 11]. Again, we use the ImageNet train set for supervision and test on the val set.", + "bbox": [ + 75, + 779, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/15c1c0800178d849152eb6f43f9091ddd9327679bfaa04d07ec79c075bf172b7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBSViews100 ep200 ep400 ep
Linear Probing (Top-1)
Max-Margin [57]2562×22463.8--
MoCo v2† [16] [17]2562×22467.469.971.0
SimCLR† [14] [17]40962×22466.568.369.8
GroCo (ours)10242×22469.270.471.1
GroCo (ours)10244×22469.670.671.3
SimSiam [17]2562×22468.170.070.8
VICReg [4]20482×22468.6--
Barlow Twins [65]20482×22468.7--
SwAV† [11]40962×22466.569.170.7
ReSSL [67]2562×224-69.9-
BYOL† [27]40962×22466.570.673.2
Whitening [24]40964×22469.4-72.6
k-NN (weighted, k=20)
MoCo v2 [16]2562×224-55.6-
SimCLR† [14] [17]40962×22453.857.259.2
GroCo (ours)10242×22460.562.964.0
GroCo (ours)10244×22461.863.664.8
SimSiam [17]2562×22457.4--
SwAV [11]40962×224--61.3
", + "bbox": [ + 504, + 88, + 890, + 391 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/85d04b3fa39705ac60945940b673170f3014d62808a1359e609d6d00a52cb60d.jpg", + "table_caption": [ + "Table 1. Comparison to state-of-the-art in linear probing $k$ -NN classification on ImageNet. We report results for training for 100, 200, 400 epochs. Backbone=Resnet50. † denotes improved reproductions from SimSiam [17]." + ], + "table_footnote": [], + "table_body": "
MethodEpochsBatch SizeViewsOxfordParis
MHMH
SimSiam [17]1002562×22426.897.0446.9219.31
MoCo v2 [16]2002562×22423.285.0742.817.33
SimCLR [14]40040962×22423.274.5646.9320.19
SwAV [11]40040962×22428.018.3546.2317.4
GroCo (ours)40010242×22429.377.1154.9526.26
", + "bbox": [ + 503, + 463, + 888, + 554 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison to state-of-the-art in image retrieval. We evaluate image retrieval performance on the Medium (M) and Hard (H) splits of the revisited Oxford and Paris datasets [50]. We evaluate nearest neighbor retrieval performance with ImageNet-trained encoders and report MAP. Backbone = Resnet50.", + "bbox": [ + 498, + 561, + 890, + 632 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison to State-of-the-Art", + "text_level": 1, + "bbox": [ + 500, + 646, + 777, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We start with a comparison of the proposed method to state-of-the-art self-supervised learning methods in linear probing and $k$ -NN evaluation on the ImageNet [54], and in image retrieval on the revised Oxford and Paris dataset [50], as well as in transfer learning.", + "bbox": [ + 496, + 670, + 890, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Linear Probing. In the case of linear probing (Table 1), the proposed method is compared to contrastive baselines using positive and negative samples, namely Max-Margin [57], SimCLR [14], and MoCo v2 [16], as well as to alternative methods. We observe that, in the given setting, the proposed loss is able to improve above all contrastive baselines and even outperforms most strong alternative baselines except BYOL [27] and Whitening [24] (in 400 epochs setup) that use $\\times 4$ larger batch size and/or an additional teacher network. Another finding is that in the context of linear", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16458", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b1c358ea5f212854c6749d33e45e9d64d15bf5c205cf907c4c101a611f5be859.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodEpochsBSAircraftCaltech101CarsCifar10Cifar100DTDFlowersFoodPetsSUN397VOC2007Average
MoCo v220025620.178.912.386.961.468.767.347.267.246.973.957.35
SimCLR400409619.377.715.385.461.070.272.551.268.249.073.158.45
SimSiam10025625.480.117.387.465.569.377.352.572.550.072.860.92
SwAV400409625.882.217.888.666.071.174.850.370.452.975.661.41
GroCo (ours)400102427.681.219.186.865.871.079.256.380.652.374.663.14
", + "bbox": [ + 81, + 88, + 890, + 170 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a0c74b21de164e4ec2aec0c8c8a1b7195c0ffa14d15fe5204dc7f273de3f60bc.jpg", + "table_caption": [ + "Table 3. Comparison to state-of-the-art transfer performance in k-NN classification on 11 classification datasets. Models are pretrained on ImageNet. Backbone=Resnet50, views=2x224." + ], + "table_footnote": [], + "table_body": "
MethodBSViews100 ep200 ep400 ep
Linear Probing (Top-1)
SwAV [11]40962×224 + 6×9672.173.974.6
GroCo (ours)10242×224 + 6×9671.872.973.7
k-NN (weighted, k=20)
SwAV [11]40962×224 + 6×9661.763.764.9
GroCo (ours)10242×224 + 6×9662.364.265.2
", + "bbox": [ + 81, + 218, + 467, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "probing, having four positive samples does not significantly improve the approach compared to only two samples. We attribute this to the fact that missing fine-grained differences in the local neighborhood are compensated by the linear layer training, thus the initial pretraining is less relevant with respect to the local neighborhood in this setting.", + "bbox": [ + 75, + 402, + 468, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$k$ -NN Evaluation. Further, the proposed method is evaluated with respect to the $k$ -NN performance and compared to state-of-the-art methods that officially released weights (Table 1). Here, it can be observed that the proposed method outperforms all methods in this setting. The results demonstrate that the margin, by which the loss improves over other methods, is increased compared to linear probing, where, e.g., for SwAV, the results were mainly on par $(+0.4\\%)$ in case of linear probing, while here they show a more substantial improvement $(+2.3\\%)$ . A second hint that the strength of this method is in the optimization of local neighborhoods is given by the fact that the $k$ -NN setting also shows an improved performance by leveraging multiple positive examples. This can be an indication that more positive examples contribute to a better local neighborhood in this setting.", + "bbox": [ + 75, + 498, + 468, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image Retrieval. To further assess the potential of the proposed method in nearest neighbors-based tasks, the model is evaluated on the task of image retrieval in Table 2. Results are reported as the Mean Average Precision (MAP) for the Medium (M) and Hard (H) splits of the datasets as in [12]. Our method outperforms all other methods in this task, confirming good local properties of learned representations.", + "bbox": [ + 75, + 729, + 468, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Transfer Performance. Finally, we compare how well performance transfers on other datasets. In Table 3, we compare ImageNet pre-trained models in zero-shot $k$ -NN evaluation on 11 classification datasets, including FGVC", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2d6f9541cc3feb7feef7bef175c729f77116c56f271d146b253d045c853c8706.jpg", + "table_caption": [ + "Table 4. Comparison to SwAV for the multi-crop augmentation strategy. We report results for training for 100, 200, and 400 epochs. Backbone=Resnet50." + ], + "table_footnote": [], + "table_body": "
MethodViewsk-NN EvaluationLinear Eval.
k=1k=10k=20Top-1Top-5
SimCLR2×224---64.3-
SimCLR‡2×22446.051.551.965.786.7
SimCLR‡3×22444.750.050.665.886.8
SimCLR‡4×22446.352.152.666.587.1
SimCLR‡2×224+6×9646.651.452.067.287.7
GroCo (ours)2×22455.360.360.569.288.4
GroCo (ours)3×22455.861.261.669.588.8
GroCo (ours)4×22456.461.561.869.688.9
GroCo (ours)2×224+6×9657.262.062.371.890.4
", + "bbox": [ + 504, + 219, + 890, + 371 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Comparison to SimCLR as a contrastive baseline on ImageNet. Backbone=Resnet50, #epochs=100, batch size=1024. $\\ddagger$ denotes our reproduction.", + "bbox": [ + 498, + 378, + 890, + 421 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Aircraft [39], Caltech-101 [26], Stanford Cars [35], CIFAR10 [36], CIFAR-100 [36], DTD [19], Oxford 102 Flowers [41], Food-101 [6], Oxford-IIIT Pets [43], SUN397 [61] and Pascal VOC2007 [25]. We observe that the proposed method improves over the SimCLR and MoCo v2 baselines in all classes and on average even outperforms the publicly available SimSiam and SwAV baselines. This can be particularly attributed to the improved performance on the Pets and Food datasets. We credit the increased performance to the fact that both food and animal-related classes often appear in the ImageNet pretraining data, thus, learning a good local embedding helps with those datasets, specifically in the case of $k$ -NN classification.", + "bbox": [ + 496, + 441, + 890, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Multi-crop Augmentation. Since computational cost grows linearly with an increasing number of augmentations, the multi-crop augmentation strategy proposed in SwAV [11] is also considered. The idea is to sample low-resolution local views along with the standard $224 \\times 224$ ones. Use $2 \\times 224 + 6 \\times 96$ scheme, where with two global $224 \\times 224$ augmented views, six local $96 \\times 96$ views are sampled, giving eight views per image. In this case, we follow the \"local-to-global\" correspondence idea [11, 12] and use only global views as positives for both local and global anchor images. While the proposed method shows slightly lower results compared to clustering-based SwAV, it again improves in the case of $k$ -NN classification (Table 4).", + "bbox": [ + 496, + 643, + 892, + 840 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison to Contrastive Loss", + "text_level": 1, + "bbox": [ + 500, + 849, + 784, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate the properties of the proposed method in a direct comparison with the pairwise contrastive loss formula", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16459", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/373e4a96e90cf945a92846eb4f595ca8de1c95c69dbaf46bdf890dd7d8da1755.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodViewsk-NN EvaluationLinear Eval.
k=1k=10k=20Top-1Top-5
MoCo v32×22461.566.666.870.990.2
GroCo (ours)2×22463.167.667.570.889.7
", + "bbox": [ + 81, + 88, + 467, + 154 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a9b3da02b1b71c4f0efeb46b09d1a7a2ee4a15cc100582b03a95aceaf8888cdd.jpg", + "table_caption": [ + "Table 6. Comparison to MoCo v3 as a contrastive baseline on ImageNet. Backbone=ViT-Small, #epochs=100, batch size=1024." + ], + "table_footnote": [], + "table_body": "
k-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Triplet Loss (margin=0.8)46.852.552.863.985.4
Triplet Loss (margin=1.6)47.953.453.764.285.3
Triplet Loss (margin=+∞)47.953.353.864.385.3
GroCo (ours)55.360.360.569.288.4
", + "bbox": [ + 81, + 210, + 465, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion, we compare it further to the classical contrastive learning methods SimCLR [14] and MoCo v3 [18] that use the popular InfoNCE loss [42] as well as to the triplet loss.", + "bbox": [ + 75, + 351, + 468, + 397 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Contrastive Loss. First, we compare the performance to the SimCLR method in Table 5, where we also analyze the properties of losses to align local neighborhood based on more positive data points. To ensure an identical setting for both methods, SimCLR is reproduced with a 3-layer MLP projection head [15]. Since SimCLR originally uses only two augmentations per image, we extend it to a group of positives by applying contrastive loss between all possible positive pairs (see supplementary material). While outperforming the SimCLR baseline by $+3\\%$ (Top-1) in linear probing, the proposed method also advances in $k$ -NN evaluation by more than $+8\\%$ ( $k = 20$ ), demonstrating that the loss helps to learn better representation not only in terms of linear separability but also in terms of local structure. Considering the multi-crop scenario, SimCLR shows mixed results from utilizing more views. While it benefits in linear evaluation, performance slightly decreases in $k$ -NN for $k \\in \\{10, 20\\}$ . The proposed method profits from utilizing more positives in both evaluations, resulting in $+1.7\\%$ in $k$ -NN ( $k = 1$ ), and $+2.4\\%$ in linear evaluation (Top-1). We further compare performance with the more recent and better-engineered MoCo v3 approach [18] with a ViT-Small [22] backbone in Table 6. MoCo v3 additionally utilizes a predictor and a momentum encoder that incur an additional computational cost but are beneficial for contrastive training [18, 12]. We plugin our proposed GroCo loss in MoCo v3 setup (with the same architecture, optimizer, etc.) and perform minimal hyperparameter tuning. Table 6 shows that without any tips and tricks the proposed method outperforms MoCo v3 in all $k$ -NN metrics and has a comparable performance in Top-1 linear probing.", + "bbox": [ + 75, + 398, + 468, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Triplet Loss. We also compare the group ordering loss with the triplet loss formulation $L = \\max \\left(d_{i}^{p} - d_{j}^{n} + r,0\\right)$ ,", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f543366217dd47b9db0afda52a437dec8f54947d726c2f7c82190870b93d48dd.jpg", + "table_caption": [ + "Table 7. Comparison on ImageNet with Triplet Loss. Backbone=Resnet50, #epochs=100, batch size=1024." + ], + "table_footnote": [], + "table_body": "
Inverse temp. βNumber of negatives N
151020
k-NNLin.p.k-NNLin.p.k-NNLin.p.k-NNLin.p.
0.06252.164.5----
0.12552.264.559.268.7--
0.2552.164.459.668.6----
0.5--59.468.460.169.1--
1--59.268.160.569.254.665.5
2----60.268.755.966.0
4------58.667.5
8------59.068.0
16------53.065.8
", + "bbox": [ + 504, + 88, + 880, + 248 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2b4c2006036f76b4ba110d9cd5cc0ff9f8c529990228413fdd80b84339d71241.jpg", + "table_caption": [ + "(a) An inverse temperature $\\beta$ , a number of negatives $N$ ." + ], + "table_footnote": [], + "table_body": "
k-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Randomly ordered54.459.259.568.988.2
Pre-ordered55.360.360.569.288.4
", + "bbox": [ + 522, + 272, + 861, + 334 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/374ee967f16667fd2a93d6d3f749ed77266515e29910251887f3c1bfd38cd650.jpg", + "table_caption": [ + "(b) Pre-ordering in the groups." + ], + "table_footnote": [], + "table_body": "
Batch Sizek-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
25652.457.257.267.888.1
51253.157.958.268.288.0
102455.360.360.569.288.4
", + "bbox": [ + 542, + 356, + 841, + 431 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/71ee334febbc8cb6e8631665054e95d52b4a7254c2c1d09c667493a5e3e7dcf1.jpg", + "table_caption": [ + "(c) Batch size." + ], + "table_footnote": [], + "table_body": "
Batch Samplingk-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Regular55.360.360.569.288.4
With many false negatives51.556.656.967.687.7
", + "bbox": [ + 504, + 454, + 880, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(d) Sensitivity to false negatives in a batch.", + "bbox": [ + 570, + 518, + 808, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Ablation Experiments. For (a), we report $k$ -NN performance with $k = 20$ , and linear probing Top-1, denoted as \"Lin.p\". The best results are bolded. Options used to obtain the main results are highlighted. Backbone=Resnet50, Views=2×224, #epochs=100.", + "bbox": [ + 496, + 539, + 890, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $r$ is a margin (Table 7). For a fair comparison, we consider all positive and the 10 strongest negative samples and evaluate different margin parameters. Here, sorting is superior to a triplet loss with hard margin selection.", + "bbox": [ + 496, + 623, + 890, + 685 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 693, + 653, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inverse Temperature, Number of Negatives. Table 8a shows the influence of the number of nearest neighbor negatives $N$ used in the loss, as well as the value of the inverse temperature parameter $\\beta$ (Equation 2). We observe that usage of too many negatives is not be beneficial for the model. Since our loss focuses on negatives that are sorted incorrectly, increasing the number of negatives at some point does not bring any new learning signal (because more distant samples are unlikely to be sorted incorrectly). However, a larger $N$ results in more steps of the sorting network, increasing the degree of relaxation. Using a larger inverse temperature $\\beta$ (leading to a lower degree of relaxation in the", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16460", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a097399e83434c3bb5ebd661395719d4afc5678016439a7e5e28ff1315d2fc47.jpg", + "image_caption": [ + "Figure 4. A toy experiment where we optimize five real variables, treating one of them as positive similarity and the other four as negatives, with both the GroCo loss and contrastive InfoNCE loss for multiple iterations. While the InfoNCE loss minimizes all negatives, the GroCo loss works behaves more similar to a margin optimization: negatives that further away from the border are optimized to a smaller degree." + ], + "image_footnote": [], + "bbox": [ + 98, + 88, + 472, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/530dd63db45105c11137cc83b9ccd53f4be6f3486f667811ab72afd6b9c73fa4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 88, + 883, + 292 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "swap operation) we can gain some performance; however, the variance of the gradients is larger with a larger $\\beta$ , which is not beneficial for optimization. We found $N = 10$ and $\\beta = 1$ to be an efficient configuration for this setting.", + "bbox": [ + 75, + 363, + 468, + 425 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Pre-ordering. In Table 8b, we analyze the impact of pre-ordering elements within negative and positive groups before forwarding them to the sorting network. We find that it achieves good performance even without pre-ordering, but also that pre-ordering further strengthens the method.", + "bbox": [ + 75, + 428, + 468, + 503 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Batch Size. A large batch size can be an important factor in obtaining good performance for many self-supervised learning methods. Results in Table 8c show that our method also benefits from a large batch size, which we attribute to utilizing stronger negatives from a larger batch.", + "bbox": [ + 75, + 508, + 468, + 584 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "False negatives. To assess the sensitivity of proposed methods to the false negatives, we artificially sample a batch in a way that for each instance, there are three more instances of the same class on average (acting as false negatives). In Table 8d, we observe a performance decline in this scenario (\"With many false negatives\"). Given GroCo's implicit emphasis on strong negatives, enhancing its robustness to false negatives would require further adjustments, which we leave for future work.", + "bbox": [ + 75, + 588, + 468, + 724 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Training Time. We also consider the training time of our model compared to SimCLR baseline. To eliminate the influence of distributed training, we measure the average time of training iteration on one GPU. We find that the iteration time of both models is comparable, 514ms for SimCLR vs 526ms for the proposed methods for a batch size of 128.", + "bbox": [ + 75, + 729, + 468, + 820 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Optimization of Negatives. To better understand the rationale behind GroCo's superiority in $k$ -NN tasks, we analyze the difference between the GroCo loss and contrastive InfoNCE loss (used in SimCLR) in structuring the embedding space. We conduct a toy experiment where we optimize five", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "real variables treating one of them as positive similarity and the other four as negative similarities with both losses for multiple iterations. We demonstrate the optimization process in Figure 4. Although both losses elevate positive similarities and lower negative similarities, they differ in the optimization of the negatives. While the InfoNCE loss minimizes all negatives (even pushing the blue curve substantially below zero), the GroCo loss works behaves more similar to a margin optimization: negatives that are not on the border to the positive are optimized to a smaller degree (the blue curve is pushed only slightly below zero). This highlights GroCo's focus on neighborhood optimization.", + "bbox": [ + 496, + 363, + 893, + 546 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 560, + 619, + 575 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, an alternative approach to the common pairwise contrastive learning formulation is proposed. The group ordering constraints consider positives and negatives as groups and enforce the group of positives to be closer to the anchor image than the negative group. To enforce these constraints, recent progress in the context of differentiable sorting approaches are leveraged to formulate a group ordering loss based on the given sorting supervision. Our evaluation shows that the proposed framework, does not only compete with current contrastive loss baselines, but actually outperforms standard contrastive learning in many settings with regards to $k$ -NN-based metrics.", + "bbox": [ + 496, + 585, + 893, + 768 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 779, + 653, + 795 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Nina Shvetsova is supported by German Federal Ministry of Education and Research (BMBF) project STCL - 01IS22067.", + "bbox": [ + 500, + 803, + 890, + 830 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 845, + 596, + 861 + ], + "page_idx": 8 + }, + { + "type": "ref_text", + "text": "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. 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NeurIPS, 2021. 3, 6" + ], + "bbox": [ + 501, + 92, + 890, + 854 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16463", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning by Sorting_ Self-supervised Learning with Group Ordering Constraints/f7288260-030f-4ffe-bd8d-4ee76970c742_model.json b/2023/Learning by Sorting_ Self-supervised Learning with Group Ordering Constraints/f7288260-030f-4ffe-bd8d-4ee76970c742_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6ba42ce0869e5009b909602ec11589b41ec39d5f --- /dev/null +++ b/2023/Learning by Sorting_ Self-supervised Learning with Group Ordering Constraints/f7288260-030f-4ffe-bd8d-4ee76970c742_model.json @@ -0,0 +1,2378 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.131, + 0.723, + 0.176 + ], + "angle": 0, + "content": "Learning by Sorting: Self-supervised Learning with Group Ordering Constraints" + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.203, + 0.867, + 0.221 + ], + "angle": 0, + "content": "Nina Shvetsova\\(^{1,2,3}\\) Felix Petersen\\(^{4}\\) Anna Kukleva\\(^{2}\\) Bernt Schiele\\(^{2}\\) Hilde Kuehne\\(^{1,3,5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.07, + 0.223, + 0.9, + 0.257 + ], + "angle": 0, + "content": "1Goethe University Frankfurt, 2Max-Planck-Institute for Informatics, 3University of Bonn, 4Stanford University, 5MIT-IBM Watson AI Lab {shvetsov@uni-frankfurt.de, mail@felix-petersen.de}" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.718 + ], + "angle": 0, + "content": "Contrastive learning has become an important tool in learning representations from unlabeled data mainly relying on the idea of minimizing distance between positive data pairs, e.g., views from the same images, and maximizing distance between negative data pairs, e.g., views from different images. This paper proposes a new variation of the contrastive learning objective, Group Ordering Constraints (GroCo), that leverages the idea of sorting the distances of positive and negative pairs and computing the respective loss based on how many positive pairs have a larger distance than the negative pairs, and thus are not ordered correctly. To this end, the GroCo loss is based on differentiable sorting networks, which enable training with sorting supervision by matching a differentiable permutation matrix, which is produced by sorting a given set of scores, to a respective ground truth permutation matrix. Applying this idea to groupwise pre-ordered inputs of multiple positive and negative pairs allows introducing the GroCo loss with implicit emphasis on strong positives and negatives, leading to better optimization of the local neighborhood. We evaluate the proposed formulation on various self-supervised learning benchmarks and show that it not only leads to improved results compared to vanilla contrastive learning but also shows competitive performance to comparable methods in linear probing and outperforms current methods in \\(k\\)-NN performance.1" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.734, + 0.21, + 0.75 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.759, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Self-supervised learning has become a topic of growing interest over the last years as it allows models to learn representations from large-scale data without the need for human annotation. Many approaches rely on the idea of contrastive learning and were able not only to narrow the gap to the supervised learning performance in vision [23, 14, 60, 30, 3, 63], but also to train state-of-the-art vision-language [52, 56] and multimodal models [40]. All" + }, + { + "type": "image_caption", + "bbox": [ + 0.586, + 0.292, + 0.81, + 0.313 + ], + "angle": 0, + "content": "Group Ordering Constraints (GroCo) Loss all pos. distances \\(< \\) all neg. distances" + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.313, + 0.868, + 0.415 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.417, + 0.868, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.515, + 0.895, + 0.627 + ], + "angle": 0, + "content": "Figure 1. The idea of the proposed group ordering constraints loss compared to pairwise contrastive losses: GroCo arranges positive and negative data points so that the largest distance to positives must be smaller than the smallest distance to negative points. To this end, the loss implicitly minimizes the amount of necessary swap operation to achieve the ordering constraint. Thus, it focuses on overlapping positives and negatives compared to standard contrastive losses that minimize resp. maximize all pairwise distances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.903 + ], + "angle": 0, + "content": "of these methods rely on the concept of the pairwise contrastive loss, which is based on the idea that a so-called positive pair, e.g., an image serving as an anchor and an augmentation of the same image, should be closer to each other in an embedding space than a so-called negative pair, e.g., a pair made up of an anchor image and a different image, should be far away from each other. However, it has been noted that the idea of a pairwise contrastive loss also has some limitations, such as the alignment of the embedding space based on individual pairs. Several attempts have been made to address this issue, e.g., combining the contrastive idea with concepts based on local neighborhoods, such as clustering (SwAV [11]), or minimizing distances between multiple positive pairs for the same instance together (Whitening [24]). Another limitation of the contrastive loss is that is that the embedding space is optimized with respect to all negatives, i.e., even negatives that are far away" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.458, + 0.902 + ], + "angle": 0, + "content": " 0\\) denotes an inverse temperature. For \\(\\beta \\to \\infty\\), the relaxation converges to the discrete swap operation. The differentiable conditional swap operation for the elements \\((d_i, d_j)\\) can be defined as a permutation matrix \\(P_{swap(d_i, d_j)} \\in R^{(K + N) \\times (K + N)}\\), which is an identity ma" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16456" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.411, + 0.108 + ], + "angle": 0, + "content": "trix except for entries \\(P_{ii}, P_{ij}, P_{jj}, P_{ji}\\) defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.117, + 0.469, + 0.141 + ], + "angle": 0, + "content": "\\[\nP _ {i i} = P _ {j j} = f \\left(d _ {j} - d _ {i}\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.137, + 0.356, + 0.153 + ], + "angle": 0, + "content": "\\[\nP _ {i j} = P _ {j i} = f \\left(d _ {i} - d _ {j}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.163, + 0.47, + 0.375 + ], + "angle": 0, + "content": "The permutation matrix \\( P_{s} \\) for step \\( s \\) is the product of matrices corresponding to independent (and thus parallel) swap operations in this step \\( P_{s} = \\prod_{i\\in R}P_{swap(d_{i},d_{i + 1})} \\), where \\( R \\) is the set of odd indices if \\( s \\) is odd and the set of even indices if \\( s \\) is even. The complete permutation matrix \\( P \\) is defined as \\( P = P_{K + N}\\cdot \\ldots \\cdot P_{1} \\). In the discrete case, each column of a permutation matrix has exactly one entry of 1, indicating the position where the element that corresponds to this column should be placed. In the relaxed version, column values can be seen as a distribution over possible positions of the element. If the correct order of input values is known, we can create a ground truth matrix \\( Q \\) and define the loss as \\( L = \\frac{1}{(K + N)^2}\\sum_{i,j}\\mathrm{BCE}(P_{ij},Q_{ij}) \\) where BCE refers to binary cross-entropy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.389, + 0.216, + 0.403 + ], + "angle": 0, + "content": "3.3.2 GroCo Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.469, + 0.517 + ], + "angle": 0, + "content": "If there was a known ground truth order of positives and negatives, the loss could be calculated directly based on this ground truth permutation matrix. However, as the algorithm is based on random augmentations, there are no known orders among positives and among negatives. Thus, the only information available is whether a pair belongs to the positive or the negative group." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.469, + 0.606 + ], + "angle": 0, + "content": "To derive a loss to fulfil this group ordering constraint, we start by ordering positives and negatives first separately with respect to the computed distances to the anchor image as \\( d_1^p \\leq \\ldots \\leq d_K^p \\) for positives and \\( d_1^n \\leq \\ldots \\leq d_N^n \\) for negatives. As shown in Figure 3, positive and negative distances are then concatenated in a list as:" + }, + { + "type": "equation", + "bbox": [ + 0.195, + 0.617, + 0.469, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\left[ d _ {1} ^ {p}, \\dots , d _ {K} ^ {p}, d _ {1} ^ {n}, \\dots , d _ {N} ^ {n} \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.469, + 0.689 + ], + "angle": 0, + "content": "Even though elements in the positive and negative are ordered, it is still open if the constraint \\( d_i^p < d_j^n \\) is fulfilled for any \\( 1 \\leq i \\leq K \\) and \\( 1 \\leq j \\leq N \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "A differentiable sorting network is applied to the concatenated list and a differentiable permutation matrix is obtained for sorting the list in non-descending order. As shown in 3, values in the permutation matrix column can be seen as probabilities to sort the corresponding element to the different positions, e.g., \\( P_{11} \\) would be the probability for assigning the first element in the list \\( (d_1^p) \\) to position 1, \\( P_{21} \\) to position 2, etc. Therefore, the sum of the first \\( K \\) elements in a column can be considered as a probability being sorted inside the first \\( K \\) elements. Thus, for a permutation matrix of size \\( (K + N) \\times (K + N) \\) the sum of the first \\( K \\) rows results in probabilities of being sorted in positive places and the later columns (from \\( K + 1 \\) to \\( K + N \\)) in negative places. To enforce positives to be sorted in the positive places and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "negatives in the negatives places, the respective loss (with \\(\\mathbb{1}\\) as the indicator function) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.13, + 0.892, + 0.207 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L = \\frac {1}{2 (K + N)} \\sum_ {i = 1} ^ {K + N} \\left(\\operatorname {B C E} \\left(\\sum_ {k = 1} ^ {K} P _ {k i}, \\mathbb {1} _ {i \\leq K}\\right) + \\right. \\tag {6} \\\\ + \\operatorname {B C E} \\left(\\sum_ {k = K + 1} ^ {K + N} P _ {k i}, \\mathbb {1} _ {i > K}\\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.221, + 0.892, + 0.327 + ], + "angle": 0, + "content": "As illustrated in Figure 2, the proposed loss is a relaxation of the sorting supervision in a way that it considers two types of swap operations: swap operations within the group of positive and negative samples, which should not contribute to the loss, and swap operations between the groups, which violate the positive-negative ordering assumption and which are used as the optimization criterion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.892, + 0.498 + ], + "angle": 0, + "content": "Role of \\(\\beta\\). One relevant hyper parameter is the inverse temperature \\(\\beta\\) in differentiable swap operation (Equation 3), which corresponds to the degree of relaxation of the swap operation that converges to a discrete case when \\(\\beta \\rightarrow \\infty\\) (Figure 3). Therefore with lower \\(\\beta\\) the swap operation is more \"soft\", which is beneficial for optimization, but the relaxation error accumulated by each step is larger, and vice versa in the case of larger \\(\\beta\\). With higher \\(\\beta\\) even a small difference between values results in a high probability for a swap or not swap operation, resulting in a smaller margin between the positive and negatives group." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.892, + 0.638 + ], + "angle": 0, + "content": "Number of samples. Since the strongest negatives have the strongest effect on the loss function, the selection can be limited to only the top-\\(N\\) strongest negatives. Further, as more negatives also result in more layers in the sorting network and each layer contributes to the overall differential permutation matrix, more layers also result in a softer swap probabilities. Therefore \\(\\beta\\) should be selected based on a number of elements to sort. An ablation study on this effect is given in Section 4.5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Role of Pre-ordering. Practically, positives and negatives are pre-ordered among themselves before concatenating and forwarding them to the differentiable sorting network. While the loss will still contrast positives to negatives no matter if the input is ordered or not, it shows that preordering improves the overall performance of the GROCo loss. This can be attributed to the fact that sorting networks perform comparisons between neighboring elements and swap them if they are in the wrong order. If the input was not pre-ordered and, thus, distances from positive and negative pairs would be mixed, this would result in additional swap operations. Using pre-ordered inputs the focus lies on comparing the strongest positives with the strongest negatives. In this way, elements are considered as a group, and the borders of the groups or their overlapping parts are emphasized in the loss. In Section 4.5 and Figure 4, we provide additional discussions and illustrate this behavior." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16457" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.312, + 0.108 + ], + "angle": 0, + "content": "4. Experimental Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.112, + 0.295, + 0.129 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.133, + 0.47, + 0.163 + ], + "angle": 0, + "content": "Unless stated otherwise, the following setup is used for all experiments:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.166, + 0.47, + 0.287 + ], + "angle": 0, + "content": "Model. Following previous works [14, 27, 11, 17] Resnet50 [31] is used as the encoder \\( g(\\cdot) \\) and an MLP block consisting of three fully connected layers with a size of 2048 and followed by a batch normalization layer [33] is used as the projection head \\( h(\\cdot) \\). All batch normalization layers except the last one are followed by a ReLU activation. The dimensionalities of the representation space and the latent space are both 2048 as in [17]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.471, + 0.667 + ], + "angle": 0, + "content": "Training. Following previous works [14, 27, 11, 17], we use the train set of the ImageNet ILSVRC-2012 dataset [54] for self-supervised training without any human annotation. To create \\( m \\) augmented views per image (considering \\( m = 2,3,4 \\)), the DINO augmentation setup [12] is used. The model is trained with the SGD optimizer [64] with a learning rate of \\( 6.0 \\times \\) (batch size/256) for 100 epochs and \\( 3.0 \\times \\) (batch size/256) for 200 and 400 epochs. We use a cosine scheduler without restarts [38] and 10 epochs warm-up for 200 and 400 epochs training and 1 epoch linear warm-up for 100 epochs training (we find it beneficial for our method but not for SimCLR). During training, the stop gradient operation is used following the self-supervised learning setups of [14, 12, 27]; specifically, stop gradient is performed during distance computation \\( \\mathrm{d}(x^a, x_i) = \\mathrm{d}(x^a, \\text{stop\\_grad}(x_i)) \\). While training with stop gradient does not show a direct impact on the overall performance, we observed that it allows training with larger variations of hyperparameters while maintaining stable performance. By default, the top \\( N = 10 \\) strongest negatives are sampled from the batch and an inverse temperature of \\( \\beta = 1 \\) is used. Due to resource constraints, the model is trained with a batch size of 1024 with mixed precision. On an 8-GPU (NVIDIA A6000) server, training for 100 epochs with \\( m = 2 \\) views takes approximately 22 hours." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.67, + 0.283, + 0.685 + ], + "angle": 0, + "content": "4.2. Evaluation Procedure" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.469, + 0.779 + ], + "angle": 0, + "content": "Linear Probing. Linear probing allows to evaluate the learned embedding space by linear evaluation [14, 27, 11, 17], capturing the linear separability of classes. For this, a linear classifier is trained on frozen representations in a fully-supervised way using the ImageNet train set. We follow the standard protocol [17] to train the linear classifier." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\(k\\)-NN Evaluation. To analyze the local properties of the learned representation, namely how often neighbored data points correspond to the same semantic class, we further evaluate with respect to nearest neighbor classification, predicting the class by a simple weighted \\(k\\) nearest neighbor classifier (\\(k\\)-NN) with \\(k = \\{1, 10, 20\\}\\) based on cosine distance as used in [12, 11]. Again, we use the ImageNet train set for supervision and test on the val set." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.891, + 0.392 + ], + "angle": 0, + "content": "
MethodBSViews100 ep200 ep400 ep
Linear Probing (Top-1)
Max-Margin [57]2562×22463.8--
MoCo v2† [16] [17]2562×22467.469.971.0
SimCLR† [14] [17]40962×22466.568.369.8
GroCo (ours)10242×22469.270.471.1
GroCo (ours)10244×22469.670.671.3
SimSiam [17]2562×22468.170.070.8
VICReg [4]20482×22468.6--
Barlow Twins [65]20482×22468.7--
SwAV† [11]40962×22466.569.170.7
ReSSL [67]2562×224-69.9-
BYOL† [27]40962×22466.570.673.2
Whitening [24]40964×22469.4-72.6
k-NN (weighted, k=20)
MoCo v2 [16]2562×224-55.6-
SimCLR† [14] [17]40962×22453.857.259.2
GroCo (ours)10242×22460.562.964.0
GroCo (ours)10244×22461.863.664.8
SimSiam [17]2562×22457.4--
SwAV [11]40962×224--61.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.399, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Table 1. Comparison to state-of-the-art in linear probing \\( k \\)-NN classification on ImageNet. We report results for training for 100, 200, 400 epochs. Backbone=Resnet50. † denotes improved reproductions from SimSiam [17]." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.464, + 0.89, + 0.555 + ], + "angle": 0, + "content": "
MethodEpochsBatch SizeViewsOxfordParis
MHMH
SimSiam [17]1002562×22426.897.0446.9219.31
MoCo v2 [16]2002562×22423.285.0742.817.33
SimCLR [14]40040962×22423.274.5646.9320.19
SwAV [11]40040962×22428.018.3546.2317.4
GroCo (ours)40010242×22429.377.1154.9526.26
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.563, + 0.892, + 0.633 + ], + "angle": 0, + "content": "Table 2. Comparison to state-of-the-art in image retrieval. We evaluate image retrieval performance on the Medium (M) and Hard (H) splits of the revisited Oxford and Paris datasets [50]. We evaluate nearest neighbor retrieval performance with ImageNet-trained encoders and report MAP. Backbone = Resnet50." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.647, + 0.779, + 0.663 + ], + "angle": 0, + "content": "4.3. Comparison to State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.747 + ], + "angle": 0, + "content": "We start with a comparison of the proposed method to state-of-the-art self-supervised learning methods in linear probing and \\( k \\)-NN evaluation on the ImageNet [54], and in image retrieval on the revised Oxford and Paris dataset [50], as well as in transfer learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Linear Probing. In the case of linear probing (Table 1), the proposed method is compared to contrastive baselines using positive and negative samples, namely Max-Margin [57], SimCLR [14], and MoCo v2 [16], as well as to alternative methods. We observe that, in the given setting, the proposed loss is able to improve above all contrastive baselines and even outperforms most strong alternative baselines except BYOL [27] and Whitening [24] (in 400 epochs setup) that use \\(\\times 4\\) larger batch size and/or an additional teacher network. Another finding is that in the context of linear" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16458" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.171 + ], + "angle": 0, + "content": "
MethodEpochsBSAircraftCaltech101CarsCifar10Cifar100DTDFlowersFoodPetsSUN397VOC2007Average
MoCo v220025620.178.912.386.961.468.767.347.267.246.973.957.35
SimCLR400409619.377.715.385.461.070.272.551.268.249.073.158.45
SimSiam10025625.480.117.387.465.569.377.352.572.550.072.860.92
SwAV400409625.882.217.888.666.071.174.850.370.452.975.661.41
GroCo (ours)400102427.681.219.186.865.871.079.256.380.652.374.663.14
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.182, + 0.891, + 0.21 + ], + "angle": 0, + "content": "Table 3. Comparison to state-of-the-art transfer performance in k-NN classification on 11 classification datasets. Models are pretrained on ImageNet. Backbone=Resnet50, views=2x224." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.219, + 0.468, + 0.336 + ], + "angle": 0, + "content": "
MethodBSViews100 ep200 ep400 ep
Linear Probing (Top-1)
SwAV [11]40962×224 + 6×9672.173.974.6
GroCo (ours)10242×224 + 6×9671.872.973.7
k-NN (weighted, k=20)
SwAV [11]40962×224 + 6×9661.763.764.9
GroCo (ours)10242×224 + 6×9662.364.265.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.345, + 0.47, + 0.388 + ], + "angle": 0, + "content": "Table 4. Comparison to SwAV for the multi-crop augmentation strategy. We report results for training for 100, 200, and 400 epochs. Backbone=Resnet50." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.47, + 0.496 + ], + "angle": 0, + "content": "probing, having four positive samples does not significantly improve the approach compared to only two samples. We attribute this to the fact that missing fine-grained differences in the local neighborhood are compensated by the linear layer training, thus the initial pretraining is less relevant with respect to the local neighborhood in this setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.727 + ], + "angle": 0, + "content": "\\(k\\)-NN Evaluation. Further, the proposed method is evaluated with respect to the \\(k\\)-NN performance and compared to state-of-the-art methods that officially released weights (Table 1). Here, it can be observed that the proposed method outperforms all methods in this setting. The results demonstrate that the margin, by which the loss improves over other methods, is increased compared to linear probing, where, e.g., for SwAV, the results were mainly on par \\((+0.4\\%)\\) in case of linear probing, while here they show a more substantial improvement \\((+2.3\\%)\\). A second hint that the strength of this method is in the optimization of local neighborhoods is given by the fact that the \\(k\\)-NN setting also shows an improved performance by leveraging multiple positive examples. This can be an indication that more positive examples contribute to a better local neighborhood in this setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.47, + 0.838 + ], + "angle": 0, + "content": "Image Retrieval. To further assess the potential of the proposed method in nearest neighbors-based tasks, the model is evaluated on the task of image retrieval in Table 2. Results are reported as the Mean Average Precision (MAP) for the Medium (M) and Hard (H) splits of the datasets as in [12]. Our method outperforms all other methods in this task, confirming good local properties of learned representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Transfer Performance. Finally, we compare how well performance transfers on other datasets. In Table 3, we compare ImageNet pre-trained models in zero-shot \\( k \\)-NN evaluation on 11 classification datasets, including FGVC" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.22, + 0.891, + 0.372 + ], + "angle": 0, + "content": "
MethodViewsk-NN EvaluationLinear Eval.
k=1k=10k=20Top-1Top-5
SimCLR2×224---64.3-
SimCLR‡2×22446.051.551.965.786.7
SimCLR‡3×22444.750.050.665.886.8
SimCLR‡4×22446.352.152.666.587.1
SimCLR‡2×224+6×9646.651.452.067.287.7
GroCo (ours)2×22455.360.360.569.288.4
GroCo (ours)3×22455.861.261.669.588.8
GroCo (ours)4×22456.461.561.869.688.9
GroCo (ours)2×224+6×9657.262.062.371.890.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.38, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Table 5. Comparison to SimCLR as a contrastive baseline on ImageNet. Backbone=Resnet50, #epochs=100, batch size=1024. \\(\\ddagger\\) denotes our reproduction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.64 + ], + "angle": 0, + "content": "Aircraft [39], Caltech-101 [26], Stanford Cars [35], CIFAR10 [36], CIFAR-100 [36], DTD [19], Oxford 102 Flowers [41], Food-101 [6], Oxford-IIIT Pets [43], SUN397 [61] and Pascal VOC2007 [25]. We observe that the proposed method improves over the SimCLR and MoCo v2 baselines in all classes and on average even outperforms the publicly available SimSiam and SwAV baselines. This can be particularly attributed to the improved performance on the Pets and Food datasets. We credit the increased performance to the fact that both food and animal-related classes often appear in the ImageNet pretraining data, thus, learning a good local embedding helps with those datasets, specifically in the case of \\(k\\)-NN classification." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.841 + ], + "angle": 0, + "content": "Multi-crop Augmentation. Since computational cost grows linearly with an increasing number of augmentations, the multi-crop augmentation strategy proposed in SwAV [11] is also considered. The idea is to sample low-resolution local views along with the standard \\(224 \\times 224\\) ones. Use \\(2 \\times 224 + 6 \\times 96\\) scheme, where with two global \\(224 \\times 224\\) augmented views, six local \\(96 \\times 96\\) views are sampled, giving eight views per image. In this case, we follow the \"local-to-global\" correspondence idea [11, 12] and use only global views as positives for both local and global anchor images. While the proposed method shows slightly lower results compared to clustering-based SwAV, it again improves in the case of \\(k\\)-NN classification (Table 4)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.85, + 0.785, + 0.866 + ], + "angle": 0, + "content": "4.4. Comparison to Contrastive Loss" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To evaluate the properties of the proposed method in a direct comparison with the pairwise contrastive loss formula" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16459" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.155 + ], + "angle": 0, + "content": "
MethodViewsk-NN EvaluationLinear Eval.
k=1k=10k=20Top-1Top-5
MoCo v32×22461.566.666.870.990.2
GroCo (ours)2×22463.167.667.570.889.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.163, + 0.47, + 0.204 + ], + "angle": 0, + "content": "Table 6. Comparison to MoCo v3 as a contrastive baseline on ImageNet. Backbone=ViT-Small, #epochs=100, batch size=1024." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.212, + 0.466, + 0.299 + ], + "angle": 0, + "content": "
k-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Triplet Loss (margin=0.8)46.852.552.863.985.4
Triplet Loss (margin=1.6)47.953.453.764.285.3
Triplet Loss (margin=+∞)47.953.353.864.385.3
GroCo (ours)55.360.360.569.288.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.308, + 0.468, + 0.336 + ], + "angle": 0, + "content": "Table 7. Comparison on ImageNet with Triplet Loss. Backbone=Resnet50, #epochs=100, batch size=1024." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.469, + 0.398 + ], + "angle": 0, + "content": "tion, we compare it further to the classical contrastive learning methods SimCLR [14] and MoCo v3 [18] that use the popular InfoNCE loss [42] as well as to the triplet loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Contrastive Loss. First, we compare the performance to the SimCLR method in Table 5, where we also analyze the properties of losses to align local neighborhood based on more positive data points. To ensure an identical setting for both methods, SimCLR is reproduced with a 3-layer MLP projection head [15]. Since SimCLR originally uses only two augmentations per image, we extend it to a group of positives by applying contrastive loss between all possible positive pairs (see supplementary material). While outperforming the SimCLR baseline by \\(+3\\%\\) (Top-1) in linear probing, the proposed method also advances in \\(k\\)-NN evaluation by more than \\(+8\\%\\) (\\(k = 20\\)), demonstrating that the loss helps to learn better representation not only in terms of linear separability but also in terms of local structure. Considering the multi-crop scenario, SimCLR shows mixed results from utilizing more views. While it benefits in linear evaluation, performance slightly decreases in \\(k\\)-NN for \\(k \\in \\{10, 20\\}\\). The proposed method profits from utilizing more positives in both evaluations, resulting in \\(+1.7\\%\\) in \\(k\\)-NN (\\(k = 1\\)), and \\(+2.4\\%\\) in linear evaluation (Top-1). We further compare performance with the more recent and better-engineered MoCo v3 approach [18] with a ViT-Small [22] backbone in Table 6. MoCo v3 additionally utilizes a predictor and a momentum encoder that incur an additional computational cost but are beneficial for contrastive training [18, 12]. We plugin our proposed GroCo loss in MoCo v3 setup (with the same architecture, optimizer, etc.) and perform minimal hyperparameter tuning. Table 6 shows that without any tips and tricks the proposed method outperforms MoCo v3 in all \\(k\\)-NN metrics and has a comparable performance in Top-1 linear probing." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Triplet Loss. We also compare the group ordering loss with the triplet loss formulation \\( L = \\max \\left(d_{i}^{p} - d_{j}^{n} + r,0\\right) \\)," + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.882, + 0.249 + ], + "angle": 0, + "content": "
Inverse temp. βNumber of negatives N
151020
k-NNLin.p.k-NNLin.p.k-NNLin.p.k-NNLin.p.
0.06252.164.5----
0.12552.264.559.268.7--
0.2552.164.459.668.6----
0.5--59.468.460.169.1--
1--59.268.160.569.254.665.5
2----60.268.755.966.0
4------58.667.5
8------59.068.0
16------53.065.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.534, + 0.252, + 0.847, + 0.266 + ], + "angle": 0, + "content": "(a) An inverse temperature \\(\\beta\\), a number of negatives \\(N\\)." + }, + { + "type": "table", + "bbox": [ + 0.524, + 0.273, + 0.862, + 0.335 + ], + "angle": 0, + "content": "
k-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Randomly ordered54.459.259.568.988.2
Pre-ordered55.360.360.569.288.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.604, + 0.337, + 0.777, + 0.35 + ], + "angle": 0, + "content": "(b) Pre-ordering in the groups." + }, + { + "type": "table", + "bbox": [ + 0.543, + 0.357, + 0.843, + 0.432 + ], + "angle": 0, + "content": "
Batch Sizek-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
25652.457.257.267.888.1
51253.157.958.268.288.0
102455.360.360.569.288.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.651, + 0.435, + 0.731, + 0.446 + ], + "angle": 0, + "content": "(c) Batch size." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.455, + 0.882, + 0.517 + ], + "angle": 0, + "content": "
Batch Samplingk-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Regular55.360.360.569.288.4
With many false negatives51.556.656.967.687.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.571, + 0.519, + 0.81, + 0.531 + ], + "angle": 0, + "content": "(d) Sensitivity to false negatives in a batch." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.54, + 0.892, + 0.61 + ], + "angle": 0, + "content": "Table 8. Ablation Experiments. For (a), we report \\( k \\)-NN performance with \\( k = 20 \\), and linear probing Top-1, denoted as \"Lin.p\". The best results are bolded. Options used to obtain the main results are highlighted. Backbone=Resnet50, Views=2×224, #epochs=100." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.892, + 0.686 + ], + "angle": 0, + "content": "where \\( r \\) is a margin (Table 7). For a fair comparison, we consider all positive and the 10 strongest negative samples and evaluate different margin parameters. Here, sorting is superior to a triplet loss with hard margin selection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.654, + 0.71 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Inverse Temperature, Number of Negatives. Table 8a shows the influence of the number of nearest neighbor negatives \\(N\\) used in the loss, as well as the value of the inverse temperature parameter \\(\\beta\\) (Equation 2). We observe that usage of too many negatives is not be beneficial for the model. Since our loss focuses on negatives that are sorted incorrectly, increasing the number of negatives at some point does not bring any new learning signal (because more distant samples are unlikely to be sorted incorrectly). However, a larger \\(N\\) results in more steps of the sorting network, increasing the degree of relaxation. Using a larger inverse temperature \\(\\beta\\) (leading to a lower degree of relaxation in the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16460" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.089, + 0.473, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.885, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.304, + 0.895, + 0.348 + ], + "angle": 0, + "content": "Figure 4. A toy experiment where we optimize five real variables, treating one of them as positive similarity and the other four as negatives, with both the GroCo loss and contrastive InfoNCE loss for multiple iterations. While the InfoNCE loss minimizes all negatives, the GroCo loss works behaves more similar to a margin optimization: negatives that further away from the border are optimized to a smaller degree." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.47, + 0.426 + ], + "angle": 0, + "content": "swap operation) we can gain some performance; however, the variance of the gradients is larger with a larger \\(\\beta\\), which is not beneficial for optimization. We found \\(N = 10\\) and \\(\\beta = 1\\) to be an efficient configuration for this setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.47, + 0.505 + ], + "angle": 0, + "content": "Pre-ordering. In Table 8b, we analyze the impact of pre-ordering elements within negative and positive groups before forwarding them to the sorting network. We find that it achieves good performance even without pre-ordering, but also that pre-ordering further strengthens the method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.47, + 0.585 + ], + "angle": 0, + "content": "Batch Size. A large batch size can be an important factor in obtaining good performance for many self-supervised learning methods. Results in Table 8c show that our method also benefits from a large batch size, which we attribute to utilizing stronger negatives from a larger batch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.589, + 0.47, + 0.725 + ], + "angle": 0, + "content": "False negatives. To assess the sensitivity of proposed methods to the false negatives, we artificially sample a batch in a way that for each instance, there are three more instances of the same class on average (acting as false negatives). In Table 8d, we observe a performance decline in this scenario (\"With many false negatives\"). Given GroCo's implicit emphasis on strong negatives, enhancing its robustness to false negatives would require further adjustments, which we leave for future work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.47, + 0.821 + ], + "angle": 0, + "content": "Training Time. We also consider the training time of our model compared to SimCLR baseline. To eliminate the influence of distributed training, we measure the average time of training iteration on one GPU. We find that the iteration time of both models is comparable, 514ms for SimCLR vs 526ms for the proposed methods for a batch size of 128." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Optimization of Negatives. To better understand the rationale behind GroCo's superiority in \\( k \\)-NN tasks, we analyze the difference between the GroCo loss and contrastive InfoNCE loss (used in SimCLR) in structuring the embedding space. We conduct a toy experiment where we optimize five" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.895, + 0.547 + ], + "angle": 0, + "content": "real variables treating one of them as positive similarity and the other four as negative similarities with both losses for multiple iterations. We demonstrate the optimization process in Figure 4. Although both losses elevate positive similarities and lower negative similarities, they differ in the optimization of the negatives. While the InfoNCE loss minimizes all negatives (even pushing the blue curve substantially below zero), the GroCo loss works behaves more similar to a margin optimization: negatives that are not on the border to the positive are optimized to a smaller degree (the blue curve is pushed only slightly below zero). This highlights GroCo's focus on neighborhood optimization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.62, + 0.577 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.895, + 0.77 + ], + "angle": 0, + "content": "In this paper, an alternative approach to the common pairwise contrastive learning formulation is proposed. The group ordering constraints consider positives and negatives as groups and enforce the group of positives to be closer to the anchor image than the negative group. To enforce these constraints, recent progress in the context of differentiable sorting approaches are leveraged to formulate a group ordering loss based on the given sorting supervision. Our evaluation shows that the proposed framework, does not only compete with current contrastive loss baselines, but actually outperforms standard contrastive learning in many settings with regards to \\( k \\)-NN-based metrics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.78, + 0.655, + 0.796 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.804, + 0.892, + 0.832 + ], + "angle": 0, + "content": "Nina Shvetsova is supported by German Federal Ministry of Education and Research (BMBF) project STCL - 01IS22067." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.847, + 0.597, + 0.862 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.873, + 0.892, + 0.901 + ], + "angle": 0, + "content": "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. 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This paper proposes a new variation of the contrastive learning objective, Group Ordering Constraints (GroCo), that leverages the idea of sorting the distances of positive and negative pairs and computing the respective loss based on how many positive pairs have a larger distance than the negative pairs, and thus are not ordered correctly. To this end, the GroCo loss is based on differentiable sorting networks, which enable training with sorting supervision by matching a differentiable permutation matrix, which is produced by sorting a given set of scores, to a respective ground truth permutation matrix. Applying this idea to groupwise pre-ordered inputs of multiple positive and negative pairs allows introducing the GroCo loss with implicit emphasis on strong positives and negatives, leading to better optimization of the local neighborhood. We evaluate the proposed formulation on various self-supervised learning benchmarks and show that it not only leads to improved results compared to vanilla contrastive learning but also shows competitive performance to comparable methods in linear probing and outperforms current methods in $k$ -NN performance.1 + +# 1. Introduction + +Self-supervised learning has become a topic of growing interest over the last years as it allows models to learn representations from large-scale data without the need for human annotation. Many approaches rely on the idea of contrastive learning and were able not only to narrow the gap to the supervised learning performance in vision [23, 14, 60, 30, 3, 63], but also to train state-of-the-art vision-language [52, 56] and multimodal models [40]. All + +![](images/9b23dded58b3e3994358ce72e54c64e5fd38a8990114d1cbb0de78568f2b62ad.jpg) +Group Ordering Constraints (GroCo) Loss all pos. distances $<$ all neg. distances + +![](images/072be32b6e16b56f18de4ffbe5345af4f41ab2d5ce373099eb19addf5b2dfd43.jpg) +Figure 1. The idea of the proposed group ordering constraints loss compared to pairwise contrastive losses: GroCo arranges positive and negative data points so that the largest distance to positives must be smaller than the smallest distance to negative points. To this end, the loss implicitly minimizes the amount of necessary swap operation to achieve the ordering constraint. Thus, it focuses on overlapping positives and negatives compared to standard contrastive losses that minimize resp. maximize all pairwise distances. + +of these methods rely on the concept of the pairwise contrastive loss, which is based on the idea that a so-called positive pair, e.g., an image serving as an anchor and an augmentation of the same image, should be closer to each other in an embedding space than a so-called negative pair, e.g., a pair made up of an anchor image and a different image, should be far away from each other. However, it has been noted that the idea of a pairwise contrastive loss also has some limitations, such as the alignment of the embedding space based on individual pairs. Several attempts have been made to address this issue, e.g., combining the contrastive idea with concepts based on local neighborhoods, such as clustering (SwAV [11]), or minimizing distances between multiple positive pairs for the same instance together (Whitening [24]). Another limitation of the contrastive loss is that is that the embedding space is optimized with respect to all negatives, i.e., even negatives that are far away + +![](images/1ef4e036cbb93f20489ace599470ddce3444dcb6df6c77c6950f1d35db15e91a.jpg) +Figure 2. Overview of the proposed loss: Distances of positives and negatives are computed with respect to an anchor. The concatenated distances are sorted via a differentiable sorting network that computes the swapping probability. The result is a differentiable permutation matrix, in which the column values can be considered as the probabilities of sorting the elements to the corresponding positions. To enforce only the relationships between groups, we sum over the positive and negative rows of the permutation matrix. The loss is then computed as the BCE between the row-wise entries and the ground truth. + +from the anchor will contribute to the optimization of the representation. Other methods were proposed to address this issue, such as hard negative selection by controlling the hardness of examples [53] or negative selection by sparse support vectors [57]. Nevertheless, these methods still require manual selection of the hardness level [53] or incur an additional optimization cost [57]. + +To shift away from the concept of minimizing resp. maximizing all pairwise distances, this paper proposes a variation of the contrastive learning formulation, namely Group Ordering Constraints (GroCo). The idea of GroCo is that positive and negative distances should be sorted in a way that any positive should be closer to an anchor image than any negative, thus forming a group of positive pairs and a group of negative pairs. The idea is illustrated in Figure 1. In comparison to pairwise contrastive losses, the GroCo loss combines the distance information of groups of positive and negative pairs and optimization mainly depends on incorrectly "sorted" pairs. To enforce the group ordering constraints in the projection space, we propose the idea of learning by sorting: we suggest sorting positives and negatives by distance to the anchor image in a differentiable way and swapping them if they are in the wrong order. This leads to a more holistic approach considering all relationships between data points, thereby better utilizing and optimizing the embeddings (esp. for multiple positive pairs), and leading to improved down-stream performance. To create an end-to-end training pipeline, we leverage recent advances in differentiable sorting [21, 28, 44, 45, 46, 47, 48]. Specifically, we utilize a differentiable sorting algorithm to obtain a differentiable permutation matrix for sorting a list of distances to the positive and negative images, as shown in Figure 2. If we would know the full ground truth orderings among positives and negatives (such as which positive sample should be closer to the anchor than another positive sample), we could create a ground truth permutation matrix, and calculate how much the predicted permutation matrix would + +deviate from the ground truth one [28, 21, 45, 47]. Because we do not know the ground truth distance ordering within the positive or the negative groups, we propose the GroCo loss as a relaxed formulation of the original sorting supervision that captures how many negative elements appear in the positive positions and vice versa. The proposed GroCo loss alleviates some aspects of vanilla contrastive learning: first, it treats positive and negative pairs as groups instead of individual pairs, and second, the resulting group ordering focuses on optimizing the local neighborhood around an anchor image by mainly optimizing too close negative and too distant positives, rather than optimizing all data points at once. Thus, it implicitly also focuses on the strongest positive (furthest from the anchor) and strongest negative (closest to the anchor) examples. + +To show the capabilities of the proposed approach, we evaluated it on various competitive self-supervised learning benchmarks, namely in the context of linear probing, $k$ -NN classification, transfer learning, as well as image retrieval. The evaluation shows that the model trained via group ordering constraints outperforms contrastive learning frameworks in linear probing and transfer learning and excels in the context of shaping local neighborhoods on the tasks such as $k$ -NN classification and image retrieval. + +The contributions of this work are summarized as follows: + +- We advance the concept of contrastive learning by introducing Group Ordering Constraints (GroCo) that treat positive and negative elements as groups rather than individual pairs as in conventional contrastive learning. +- To derive a loss that optimizes the proposed constraints, we harness recent differentiable sorting methods and obtain a loss that suggests sorting positive and negative elements and swapping them if they are in the wrong order — thus, we introduce a new contrastive learning method called learning by sorting. +- The proposed method provides embeddings that achieve + +competitive performance in linear probing and are especially suitable to model the local neighborhoods and outperform contrastive learning frameworks on a wide range of nearest-neighbor tasks. + +# 2. Related Work + +# 2.1. Self-supervised Representation Learning + +Contrastive methods: Over the last years, self-supervised learning methods that enforce the model to be robust to different image distortions achieved great performance improvements in self-supervised learning [14, 30, 15, 16]. Such methods generally rely on sampling two augmented views of the image—a positive pair—and minimize the distance between those in the embedding space. To prevent the model from learning a trivial solution for any input, contrastive methods introduce the concept of a negative pair, i.e., two different images, to contrast positive against negative pairs. While earlier contrastive methods relied on the triplet loss [55], the probably most prominent method in many self-supervised learning scenarios is the InfoNCE loss, which is often referred to as a contrastive loss [14, 30, 51, 1], which requires accumulating strong negatives via a memory bank [30] or a large batch size [14]. Many extensions have been proposed to further improve the performance of this idea: data augmentation strategies [14, 62], projection head design [15], hard negative sampling [53], increasing the richness of positives with nearest neighbours [23], or mitigating the effect of false negatives [32]. The variation of the contrastive method proposed in this work should not be considered as opposed but rather as orthogonal to other approaches relying on positive and negative pairs because it changes the loss function itself and can therefore be used, e.g., on top of other techniques. + +Alternative methods: There are also methods [17, 27] that do not rely on negatives and only maximize agreement between positive views. Such methods prevent collapsing of the representation space by using asymmetric architectures applied to different views [17, 27], an additional teacher network [27, 12], stop gradient [17, 27, 12], feature whitening [24], or information maximization [65, 4]. Another set of methods [11, 10, 2] utilizes clustering of latent embeddings. ReSSL [67] leverages relations in an embedding space in a self-labeling way, namely aligning the similarities between weakly-augmented images to the similarities to the similarities between strongly augmented images. SwAV [11] additionally proposes sampling more augmentations in a multi-crop setting, where two full-size augmented images are sampled together with several smaller crops, and Whitening [24] utilized more full-resolution samples. While currently methods relying on positive samples seem to outperform their classical contrastive counterparts, the we show that especially local neighborhood learning can profit from relying on positive and negative samples. + +# 2.2. Differentiable Sorting and Ranking + +Differentiable sorting and ranking methods provide a pipeline that allows training neural networks with ordering supervision in an end-to-end fashion with gradient descent [5, 21, 28, 44, 45, 46, 47, 48, 49]. Earlier pairwise learning-to-rank methods, such as RankNet [8] or LambdaRank [7], and listwise methods, such as SoftRank [59] or ListNet [9], are mostly based on heuristics and aim to optimize ranking metrics, e.g., NDCG. Many of the latest differentiable sorting approaches [21, 28, 44, 45, 47, 48, 49] focus on obtaining a differentiable relaxation for the sorting operator. The sorting operator can be seen as a function returning a permutation matrix that indicates the permutation necessary to sort the sequence of values (the matrix that multiplied with an input vector returns a sorted output vector.) In this context, differentiable sorting refers to relaxing the (hard) permutation matrix to a differentiable permutation matrix via continuous relaxations. The differentiable permutation matrix for a given sequence of values, which can, e.g., be scores predicted by a neural network, can then be used to compute the loss by comparison to a ground truth permutation matrix. Recently, multiple methods for relaxing the permutation matrix have been proposed, including an argsort approximation by unimodal row-stochastic matrices [28, 49], a formulation of entropy-regularized optimal transport [21], as well as networks of differentiable swap operations (differentiable sorting networks) [45, 47]. The latter method composes the full permutation matrix as a product of permutation matrices that arise from comparing only two elements at a time (usually neighbors) and either swapping them or not swapping them. Practically, differentiable sorting has been leveraged in various contexts, including recommender systems [37, 58], image patch selection [20], selection experts in multi-task learning [29], attention mechanisms [66], and audio representation learning [13]. To the best of our knowledge, the proposed method is the first work to leverage ordering supervision for self-supervised learning of visual representations. + +# 3. Method + +Given a dataset of images $\{x_{i}\}_{i = 1}^{M}\subseteq \mathcal{X}$ , the goal is to learn an encoder $g:\mathcal{X}\to \mathbb{R}^d$ that extracts image representations that can later be used for downstream tasks. + +# 3.1. Training Pipeline + +As in standard contrastive losses, the proposed method considers several augmented views of the same image as positive examples, which should be close together in the embedding space, and different images as negative examples, which should be apart in the embedding space. Starting from mini-batches of $B$ images, $m \geq 2$ randomly augmented views are generated for each image, resulting in $m \cdot B$ data points overall per batch. Note that if $m = 2$ , the + +proposed method is close to the original contrastive learning setup [32, 14, 17, 4, 65]. The augmented views are processed with the encoder network $g(\cdot)$ and an MLP projection head $h(\cdot)$ , that maps images to the latent space where distances between views are calculated. For each data point serving as an anchor $x^a$ , there are $m - 1$ positive examples $\{x_i^p\}_{i = 1}^{m - 1}$ and $m \cdot (B - 1)$ negative examples $\{x_i^n\}_{i = 1}^{m \cdot (B - 1)}$ . The measure of distance between data points is the cosine distance defined as: $\mathsf{d}(x,y) = -\frac{x^\top y}{\|x\|\|.y\|}$ . + +# 3.2. Group Ordering Constraints (GroCo) + +In order to consider positives and negatives not individually but instead as a group, the proposed loss extends the contrastive loss to the idea that the group of positives should be closer to the anchor image than the group of negatives in the embedding space resulting in group ordering constraints (GroCo). To simplify the notation, the distance between data point $x^{a}$ and its positive $x_{i}^{p}$ and negative examples $x_{i}^{n}$ is denoted as $d_{i}^{p} = \mathsf{d}(x^{a},x_{i}^{p})$ and $d_{i}^{n} = \mathsf{d}(x^{a},x_{i}^{n})$ . Assuming that $K$ positives $x_{1}^{p},\ldots ,x_{K}^{p}$ are ordered with respect to their distances to the anchor $x^{a}$ as $d_1^p\leq \dots \leq d_K^p$ and $N$ negatives $x_{1}^{n},\ldots ,x_{N}^{n}$ as $d_1^n\leq \dots \leq d_N^n$ , then the group ordering constraints can be defined as + +$$ +d _ {1} ^ {p} \leq \dots \leq d _ {K} ^ {p} < d _ {1} ^ {n} \leq \dots \leq d _ {N} ^ {n}. \tag {1} +$$ + +We note that all elements are considered in the constraints and the relevant constraint is the (bold) $<$ in the center. We remark that, although the constraint is already fulfilled if the largest positive distance $d_K^p$ is smaller than the smallest negative distance $d_1^n$ , it is suboptimal to define loss only on those elements. Comparing only the smallest negative and largest positive ignores other negatives (e.g., the second smallest) and positives (e.g., the second largest) that might also be misaligned, and such a loss would ignore them. In the next section, we propose our novel loss that optimizes the GroCo constraints implicitly. + +# 3.3. Learning by Sorting + +To enforce the constraint, the GroCo loss leverages recent advances in differentiable sorting [45, 47], which allow to derive a loss that fulfills ordering constraints. Namely, the training procedure can be seen as sorting positives and negatives in the embedding space with respect to an anchor image and swapping them if they are in the incorrect order, which relates to the proposed idea of learning by sorting. + +# 3.3.1 Differentiable Sorting Networks + +This section provides a review of the differentiable sorting algorithm differentiable sorting networks [45] used for the proposed loss function. Note that "networks" in "sorting networks" are not "neural networks" but instead refers to a category of sorting algorithms in the computer science literature [34] with no trainable parameters. + +![](images/e23c67aa1f8160dbd6a03ea0cc5ec546fd7600eb48e4f98272bacce80c7c06f8.jpg) +Figure 3. Overview of a differentiable sorting network with odd-even sorting: The network compares neighboring elements starting from odd and even indices alternatingly in each step and applies a differentiable swap operation if elements are in the wrong order. The swap operations on each step $s$ also define a differentiable permutation matrix $P_{s}$ . The network output is a differentiable permutation matrix $P$ , defined as the multiplication of matrices of each step. + +Differentiable sorting networks, e.g., based on the odd-even sorting network, sort an input sequence of $K + N$ elements in non-descending order as shown in Figure 3. They are defined as the concatenation of functions, e.g., representing the swap operations in each layer of an odd-even sorting network, where each function refers to one step of sorting, and pairs of elements of the input sequence are compared and swapped if they are in the wrong order via a conditional swap operation. For the odd-even sorting network, the algorithm compares neighbored elements on odd and even indices alternatingly and requires $K + N$ steps to sort a given input sequence of length $K + N$ . By relaxing the conditional swap operator to a differentiable one, sorting networks can be made differentiable [45]. The conditional swap operation for elements $(d_i, d_j)$ where $i < j$ can be defined as $d_i' = \min(d_i, d_j)$ , $d_j' = \max(d_i, d_j)$ , and the differentiable relaxation [47] of this operation is: + +$$ +\begin{array}{l} d _ {i} ^ {\prime} = \operatorname {s o f t m i n} \left(d _ {i}, d _ {j}\right) = d _ {i} f \left(d _ {j} - d _ {i}\right) + d _ {j} f \left(d _ {i} - d _ {j}\right), \\ d _ {j} ^ {\prime} = \operatorname {s o f t m a x} \left(d _ {i}, d _ {j}\right) = d _ {i} f \left(d _ {i} - d _ {j}\right) + d _ {j} f \left(d _ {j} - d _ {i}\right) \end{array} \tag {2} +$$ + +$$ +f (x) = \frac {1}{\pi} \arctan (\beta x) + 0. 5. \tag {3} +$$ + +The hyperparameter $\beta > 0$ denotes an inverse temperature. For $\beta \to \infty$ , the relaxation converges to the discrete swap operation. The differentiable conditional swap operation for the elements $(d_i, d_j)$ can be defined as a permutation matrix $P_{swap(d_i, d_j)} \in R^{(K + N) \times (K + N)}$ , which is an identity ma + +trix except for entries $P_{ii}, P_{ij}, P_{jj}, P_{ji}$ defined as: + +$$ +P _ {i i} = P _ {j j} = f \left(d _ {j} - d _ {i}\right), \tag {4} +$$ + +$$ +P _ {i j} = P _ {j i} = f \left(d _ {i} - d _ {j}\right). +$$ + +The permutation matrix $P_{s}$ for step $s$ is the product of matrices corresponding to independent (and thus parallel) swap operations in this step $P_{s} = \prod_{i\in R}P_{swap(d_{i},d_{i + 1})}$ , where $R$ is the set of odd indices if $s$ is odd and the set of even indices if $s$ is even. The complete permutation matrix $P$ is defined as $P = P_{K + N}\cdot \ldots \cdot P_{1}$ . In the discrete case, each column of a permutation matrix has exactly one entry of 1, indicating the position where the element that corresponds to this column should be placed. In the relaxed version, column values can be seen as a distribution over possible positions of the element. If the correct order of input values is known, we can create a ground truth matrix $Q$ and define the loss as $L = \frac{1}{(K + N)^2}\sum_{i,j}\mathrm{BCE}(P_{ij},Q_{ij})$ where BCE refers to binary cross-entropy. + +# 3.3.2 GroCo Loss + +If there was a known ground truth order of positives and negatives, the loss could be calculated directly based on this ground truth permutation matrix. However, as the algorithm is based on random augmentations, there are no known orders among positives and among negatives. Thus, the only information available is whether a pair belongs to the positive or the negative group. + +To derive a loss to fulfil this group ordering constraint, we start by ordering positives and negatives first separately with respect to the computed distances to the anchor image as $d_1^p \leq \ldots \leq d_K^p$ for positives and $d_1^n \leq \ldots \leq d_N^n$ for negatives. As shown in Figure 3, positive and negative distances are then concatenated in a list as: + +$$ +\left[ d _ {1} ^ {p}, \dots , d _ {K} ^ {p}, d _ {1} ^ {n}, \dots , d _ {N} ^ {n} \right]. \tag {5} +$$ + +Even though elements in the positive and negative are ordered, it is still open if the constraint $d_i^p < d_j^n$ is fulfilled for any $1 \leq i \leq K$ and $1 \leq j \leq N$ . + +A differentiable sorting network is applied to the concatenated list and a differentiable permutation matrix is obtained for sorting the list in non-descending order. As shown in 3, values in the permutation matrix column can be seen as probabilities to sort the corresponding element to the different positions, e.g., $P_{11}$ would be the probability for assigning the first element in the list $(d_1^p)$ to position 1, $P_{21}$ to position 2, etc. Therefore, the sum of the first $K$ elements in a column can be considered as a probability being sorted inside the first $K$ elements. Thus, for a permutation matrix of size $(K + N) \times (K + N)$ the sum of the first $K$ rows results in probabilities of being sorted in positive places and the later columns (from $K + 1$ to $K + N$ ) in negative places. To enforce positives to be sorted in the positive places and + +negatives in the negatives places, the respective loss (with $\mathbb{1}$ as the indicator function) is defined as + +$$ +\begin{array}{l} L = \frac {1}{2 (K + N)} \sum_ {i = 1} ^ {K + N} \left(\operatorname {B C E} \left(\sum_ {k = 1} ^ {K} P _ {k i}, \mathbb {1} _ {i \leq K}\right) + \right. \tag {6} \\ + \operatorname {B C E} \left(\sum_ {k = K + 1} ^ {K + N} P _ {k i}, \mathbb {1} _ {i > K}\right). \\ \end{array} +$$ + +As illustrated in Figure 2, the proposed loss is a relaxation of the sorting supervision in a way that it considers two types of swap operations: swap operations within the group of positive and negative samples, which should not contribute to the loss, and swap operations between the groups, which violate the positive-negative ordering assumption and which are used as the optimization criterion. + +Role of $\beta$ . One relevant hyper parameter is the inverse temperature $\beta$ in differentiable swap operation (Equation 3), which corresponds to the degree of relaxation of the swap operation that converges to a discrete case when $\beta \rightarrow \infty$ (Figure 3). Therefore with lower $\beta$ the swap operation is more "soft", which is beneficial for optimization, but the relaxation error accumulated by each step is larger, and vice versa in the case of larger $\beta$ . With higher $\beta$ even a small difference between values results in a high probability for a swap or not swap operation, resulting in a smaller margin between the positive and negatives group. + +Number of samples. Since the strongest negatives have the strongest effect on the loss function, the selection can be limited to only the top- $N$ strongest negatives. Further, as more negatives also result in more layers in the sorting network and each layer contributes to the overall differential permutation matrix, more layers also result in a softer swap probabilities. Therefore $\beta$ should be selected based on a number of elements to sort. An ablation study on this effect is given in Section 4.5. + +Role of Pre-ordering. Practically, positives and negatives are pre-ordered among themselves before concatenating and forwarding them to the differentiable sorting network. While the loss will still contrast positives to negatives no matter if the input is ordered or not, it shows that preordering improves the overall performance of the GROCo loss. This can be attributed to the fact that sorting networks perform comparisons between neighboring elements and swap them if they are in the wrong order. If the input was not pre-ordered and, thus, distances from positive and negative pairs would be mixed, this would result in additional swap operations. Using pre-ordered inputs the focus lies on comparing the strongest positives with the strongest negatives. In this way, elements are considered as a group, and the borders of the groups or their overlapping parts are emphasized in the loss. In Section 4.5 and Figure 4, we provide additional discussions and illustrate this behavior. + +# 4. Experimental Evaluation + +# 4.1. Implementation Details + +Unless stated otherwise, the following setup is used for all experiments: + +Model. Following previous works [14, 27, 11, 17] Resnet50 [31] is used as the encoder $g(\cdot)$ and an MLP block consisting of three fully connected layers with a size of 2048 and followed by a batch normalization layer [33] is used as the projection head $h(\cdot)$ . All batch normalization layers except the last one are followed by a ReLU activation. The dimensionalities of the representation space and the latent space are both 2048 as in [17]. + +Training. Following previous works [14, 27, 11, 17], we use the train set of the ImageNet ILSVRC-2012 dataset [54] for self-supervised training without any human annotation. To create $m$ augmented views per image (considering $m = 2,3,4$ ), the DINO augmentation setup [12] is used. The model is trained with the SGD optimizer [64] with a learning rate of $6.0 \times$ (batch size/256) for 100 epochs and $3.0 \times$ (batch size/256) for 200 and 400 epochs. We use a cosine scheduler without restarts [38] and 10 epochs warm-up for 200 and 400 epochs training and 1 epoch linear warm-up for 100 epochs training (we find it beneficial for our method but not for SimCLR). During training, the stop gradient operation is used following the self-supervised learning setups of [14, 12, 27]; specifically, stop gradient is performed during distance computation $\mathrm{d}(x^a, x_i) = \mathrm{d}(x^a, \text{stop\_grad}(x_i))$ . While training with stop gradient does not show a direct impact on the overall performance, we observed that it allows training with larger variations of hyperparameters while maintaining stable performance. By default, the top $N = 10$ strongest negatives are sampled from the batch and an inverse temperature of $\beta = 1$ is used. Due to resource constraints, the model is trained with a batch size of 1024 with mixed precision. On an 8-GPU (NVIDIA A6000) server, training for 100 epochs with $m = 2$ views takes approximately 22 hours. + +# 4.2. Evaluation Procedure + +Linear Probing. Linear probing allows to evaluate the learned embedding space by linear evaluation [14, 27, 11, 17], capturing the linear separability of classes. For this, a linear classifier is trained on frozen representations in a fully-supervised way using the ImageNet train set. We follow the standard protocol [17] to train the linear classifier. + +$k$ -NN Evaluation. To analyze the local properties of the learned representation, namely how often neighbored data points correspond to the same semantic class, we further evaluate with respect to nearest neighbor classification, predicting the class by a simple weighted $k$ nearest neighbor classifier ( $k$ -NN) with $k = \{1, 10, 20\}$ based on cosine distance as used in [12, 11]. Again, we use the ImageNet train set for supervision and test on the val set. + +
MethodBSViews100 ep200 ep400 ep
Linear Probing (Top-1)
Max-Margin [57]2562×22463.8--
MoCo v2† [16] [17]2562×22467.469.971.0
SimCLR† [14] [17]40962×22466.568.369.8
GroCo (ours)10242×22469.270.471.1
GroCo (ours)10244×22469.670.671.3
SimSiam [17]2562×22468.170.070.8
VICReg [4]20482×22468.6--
Barlow Twins [65]20482×22468.7--
SwAV† [11]40962×22466.569.170.7
ReSSL [67]2562×224-69.9-
BYOL† [27]40962×22466.570.673.2
Whitening [24]40964×22469.4-72.6
k-NN (weighted, k=20)
MoCo v2 [16]2562×224-55.6-
SimCLR† [14] [17]40962×22453.857.259.2
GroCo (ours)10242×22460.562.964.0
GroCo (ours)10244×22461.863.664.8
SimSiam [17]2562×22457.4--
SwAV [11]40962×224--61.3
+ +Table 1. Comparison to state-of-the-art in linear probing $k$ -NN classification on ImageNet. We report results for training for 100, 200, 400 epochs. Backbone=Resnet50. † denotes improved reproductions from SimSiam [17]. + +
MethodEpochsBatch SizeViewsOxfordParis
MHMH
SimSiam [17]1002562×22426.897.0446.9219.31
MoCo v2 [16]2002562×22423.285.0742.817.33
SimCLR [14]40040962×22423.274.5646.9320.19
SwAV [11]40040962×22428.018.3546.2317.4
GroCo (ours)40010242×22429.377.1154.9526.26
+ +Table 2. Comparison to state-of-the-art in image retrieval. We evaluate image retrieval performance on the Medium (M) and Hard (H) splits of the revisited Oxford and Paris datasets [50]. We evaluate nearest neighbor retrieval performance with ImageNet-trained encoders and report MAP. Backbone = Resnet50. + +# 4.3. Comparison to State-of-the-Art + +We start with a comparison of the proposed method to state-of-the-art self-supervised learning methods in linear probing and $k$ -NN evaluation on the ImageNet [54], and in image retrieval on the revised Oxford and Paris dataset [50], as well as in transfer learning. + +Linear Probing. In the case of linear probing (Table 1), the proposed method is compared to contrastive baselines using positive and negative samples, namely Max-Margin [57], SimCLR [14], and MoCo v2 [16], as well as to alternative methods. We observe that, in the given setting, the proposed loss is able to improve above all contrastive baselines and even outperforms most strong alternative baselines except BYOL [27] and Whitening [24] (in 400 epochs setup) that use $\times 4$ larger batch size and/or an additional teacher network. Another finding is that in the context of linear + +
MethodEpochsBSAircraftCaltech101CarsCifar10Cifar100DTDFlowersFoodPetsSUN397VOC2007Average
MoCo v220025620.178.912.386.961.468.767.347.267.246.973.957.35
SimCLR400409619.377.715.385.461.070.272.551.268.249.073.158.45
SimSiam10025625.480.117.387.465.569.377.352.572.550.072.860.92
SwAV400409625.882.217.888.666.071.174.850.370.452.975.661.41
GroCo (ours)400102427.681.219.186.865.871.079.256.380.652.374.663.14
+ +Table 3. Comparison to state-of-the-art transfer performance in k-NN classification on 11 classification datasets. Models are pretrained on ImageNet. Backbone=Resnet50, views=2x224. + +
MethodBSViews100 ep200 ep400 ep
Linear Probing (Top-1)
SwAV [11]40962×224 + 6×9672.173.974.6
GroCo (ours)10242×224 + 6×9671.872.973.7
k-NN (weighted, k=20)
SwAV [11]40962×224 + 6×9661.763.764.9
GroCo (ours)10242×224 + 6×9662.364.265.2
+ +probing, having four positive samples does not significantly improve the approach compared to only two samples. We attribute this to the fact that missing fine-grained differences in the local neighborhood are compensated by the linear layer training, thus the initial pretraining is less relevant with respect to the local neighborhood in this setting. + +$k$ -NN Evaluation. Further, the proposed method is evaluated with respect to the $k$ -NN performance and compared to state-of-the-art methods that officially released weights (Table 1). Here, it can be observed that the proposed method outperforms all methods in this setting. The results demonstrate that the margin, by which the loss improves over other methods, is increased compared to linear probing, where, e.g., for SwAV, the results were mainly on par $(+0.4\%)$ in case of linear probing, while here they show a more substantial improvement $(+2.3\%)$ . A second hint that the strength of this method is in the optimization of local neighborhoods is given by the fact that the $k$ -NN setting also shows an improved performance by leveraging multiple positive examples. This can be an indication that more positive examples contribute to a better local neighborhood in this setting. + +Image Retrieval. To further assess the potential of the proposed method in nearest neighbors-based tasks, the model is evaluated on the task of image retrieval in Table 2. Results are reported as the Mean Average Precision (MAP) for the Medium (M) and Hard (H) splits of the datasets as in [12]. Our method outperforms all other methods in this task, confirming good local properties of learned representations. + +Transfer Performance. Finally, we compare how well performance transfers on other datasets. In Table 3, we compare ImageNet pre-trained models in zero-shot $k$ -NN evaluation on 11 classification datasets, including FGVC + +Table 4. Comparison to SwAV for the multi-crop augmentation strategy. We report results for training for 100, 200, and 400 epochs. Backbone=Resnet50. + +
MethodViewsk-NN EvaluationLinear Eval.
k=1k=10k=20Top-1Top-5
SimCLR2×224---64.3-
SimCLR‡2×22446.051.551.965.786.7
SimCLR‡3×22444.750.050.665.886.8
SimCLR‡4×22446.352.152.666.587.1
SimCLR‡2×224+6×9646.651.452.067.287.7
GroCo (ours)2×22455.360.360.569.288.4
GroCo (ours)3×22455.861.261.669.588.8
GroCo (ours)4×22456.461.561.869.688.9
GroCo (ours)2×224+6×9657.262.062.371.890.4
+ +Table 5. Comparison to SimCLR as a contrastive baseline on ImageNet. Backbone=Resnet50, #epochs=100, batch size=1024. $\ddagger$ denotes our reproduction. + +Aircraft [39], Caltech-101 [26], Stanford Cars [35], CIFAR10 [36], CIFAR-100 [36], DTD [19], Oxford 102 Flowers [41], Food-101 [6], Oxford-IIIT Pets [43], SUN397 [61] and Pascal VOC2007 [25]. We observe that the proposed method improves over the SimCLR and MoCo v2 baselines in all classes and on average even outperforms the publicly available SimSiam and SwAV baselines. This can be particularly attributed to the improved performance on the Pets and Food datasets. We credit the increased performance to the fact that both food and animal-related classes often appear in the ImageNet pretraining data, thus, learning a good local embedding helps with those datasets, specifically in the case of $k$ -NN classification. + +Multi-crop Augmentation. Since computational cost grows linearly with an increasing number of augmentations, the multi-crop augmentation strategy proposed in SwAV [11] is also considered. The idea is to sample low-resolution local views along with the standard $224 \times 224$ ones. Use $2 \times 224 + 6 \times 96$ scheme, where with two global $224 \times 224$ augmented views, six local $96 \times 96$ views are sampled, giving eight views per image. In this case, we follow the "local-to-global" correspondence idea [11, 12] and use only global views as positives for both local and global anchor images. While the proposed method shows slightly lower results compared to clustering-based SwAV, it again improves in the case of $k$ -NN classification (Table 4). + +# 4.4. Comparison to Contrastive Loss + +To evaluate the properties of the proposed method in a direct comparison with the pairwise contrastive loss formula + +
MethodViewsk-NN EvaluationLinear Eval.
k=1k=10k=20Top-1Top-5
MoCo v32×22461.566.666.870.990.2
GroCo (ours)2×22463.167.667.570.889.7
+ +Table 6. Comparison to MoCo v3 as a contrastive baseline on ImageNet. Backbone=ViT-Small, #epochs=100, batch size=1024. + +
k-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Triplet Loss (margin=0.8)46.852.552.863.985.4
Triplet Loss (margin=1.6)47.953.453.764.285.3
Triplet Loss (margin=+∞)47.953.353.864.385.3
GroCo (ours)55.360.360.569.288.4
+ +tion, we compare it further to the classical contrastive learning methods SimCLR [14] and MoCo v3 [18] that use the popular InfoNCE loss [42] as well as to the triplet loss. + +Contrastive Loss. First, we compare the performance to the SimCLR method in Table 5, where we also analyze the properties of losses to align local neighborhood based on more positive data points. To ensure an identical setting for both methods, SimCLR is reproduced with a 3-layer MLP projection head [15]. Since SimCLR originally uses only two augmentations per image, we extend it to a group of positives by applying contrastive loss between all possible positive pairs (see supplementary material). While outperforming the SimCLR baseline by $+3\%$ (Top-1) in linear probing, the proposed method also advances in $k$ -NN evaluation by more than $+8\%$ ( $k = 20$ ), demonstrating that the loss helps to learn better representation not only in terms of linear separability but also in terms of local structure. Considering the multi-crop scenario, SimCLR shows mixed results from utilizing more views. While it benefits in linear evaluation, performance slightly decreases in $k$ -NN for $k \in \{10, 20\}$ . The proposed method profits from utilizing more positives in both evaluations, resulting in $+1.7\%$ in $k$ -NN ( $k = 1$ ), and $+2.4\%$ in linear evaluation (Top-1). We further compare performance with the more recent and better-engineered MoCo v3 approach [18] with a ViT-Small [22] backbone in Table 6. MoCo v3 additionally utilizes a predictor and a momentum encoder that incur an additional computational cost but are beneficial for contrastive training [18, 12]. We plugin our proposed GroCo loss in MoCo v3 setup (with the same architecture, optimizer, etc.) and perform minimal hyperparameter tuning. Table 6 shows that without any tips and tricks the proposed method outperforms MoCo v3 in all $k$ -NN metrics and has a comparable performance in Top-1 linear probing. + +Triplet Loss. We also compare the group ordering loss with the triplet loss formulation $L = \max \left(d_{i}^{p} - d_{j}^{n} + r,0\right)$ , + +Table 7. Comparison on ImageNet with Triplet Loss. Backbone=Resnet50, #epochs=100, batch size=1024. + +
Inverse temp. βNumber of negatives N
151020
k-NNLin.p.k-NNLin.p.k-NNLin.p.k-NNLin.p.
0.06252.164.5----
0.12552.264.559.268.7--
0.2552.164.459.668.6----
0.5--59.468.460.169.1--
1--59.268.160.569.254.665.5
2----60.268.755.966.0
4------58.667.5
8------59.068.0
16------53.065.8
+ +(a) An inverse temperature $\beta$ , a number of negatives $N$ . + +
k-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Randomly ordered54.459.259.568.988.2
Pre-ordered55.360.360.569.288.4
+ +(b) Pre-ordering in the groups. + +
Batch Sizek-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
25652.457.257.267.888.1
51253.157.958.268.288.0
102455.360.360.569.288.4
+ +(c) Batch size. + +
Batch Samplingk-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Regular55.360.360.569.288.4
With many false negatives51.556.656.967.687.7
+ +(d) Sensitivity to false negatives in a batch. + +Table 8. Ablation Experiments. For (a), we report $k$ -NN performance with $k = 20$ , and linear probing Top-1, denoted as "Lin.p". The best results are bolded. Options used to obtain the main results are highlighted. Backbone=Resnet50, Views=2×224, #epochs=100. + +where $r$ is a margin (Table 7). For a fair comparison, we consider all positive and the 10 strongest negative samples and evaluate different margin parameters. Here, sorting is superior to a triplet loss with hard margin selection. + +# 4.5. Ablation Study + +Inverse Temperature, Number of Negatives. Table 8a shows the influence of the number of nearest neighbor negatives $N$ used in the loss, as well as the value of the inverse temperature parameter $\beta$ (Equation 2). We observe that usage of too many negatives is not be beneficial for the model. Since our loss focuses on negatives that are sorted incorrectly, increasing the number of negatives at some point does not bring any new learning signal (because more distant samples are unlikely to be sorted incorrectly). However, a larger $N$ results in more steps of the sorting network, increasing the degree of relaxation. Using a larger inverse temperature $\beta$ (leading to a lower degree of relaxation in the + +![](images/a097399e83434c3bb5ebd661395719d4afc5678016439a7e5e28ff1315d2fc47.jpg) +Figure 4. A toy experiment where we optimize five real variables, treating one of them as positive similarity and the other four as negatives, with both the GroCo loss and contrastive InfoNCE loss for multiple iterations. While the InfoNCE loss minimizes all negatives, the GroCo loss works behaves more similar to a margin optimization: negatives that further away from the border are optimized to a smaller degree. + +![](images/530dd63db45105c11137cc83b9ccd53f4be6f3486f667811ab72afd6b9c73fa4.jpg) + +swap operation) we can gain some performance; however, the variance of the gradients is larger with a larger $\beta$ , which is not beneficial for optimization. We found $N = 10$ and $\beta = 1$ to be an efficient configuration for this setting. + +Pre-ordering. In Table 8b, we analyze the impact of pre-ordering elements within negative and positive groups before forwarding them to the sorting network. We find that it achieves good performance even without pre-ordering, but also that pre-ordering further strengthens the method. + +Batch Size. A large batch size can be an important factor in obtaining good performance for many self-supervised learning methods. Results in Table 8c show that our method also benefits from a large batch size, which we attribute to utilizing stronger negatives from a larger batch. + +False negatives. To assess the sensitivity of proposed methods to the false negatives, we artificially sample a batch in a way that for each instance, there are three more instances of the same class on average (acting as false negatives). In Table 8d, we observe a performance decline in this scenario ("With many false negatives"). Given GroCo's implicit emphasis on strong negatives, enhancing its robustness to false negatives would require further adjustments, which we leave for future work. + +Training Time. We also consider the training time of our model compared to SimCLR baseline. To eliminate the influence of distributed training, we measure the average time of training iteration on one GPU. We find that the iteration time of both models is comparable, 514ms for SimCLR vs 526ms for the proposed methods for a batch size of 128. + +Optimization of Negatives. To better understand the rationale behind GroCo's superiority in $k$ -NN tasks, we analyze the difference between the GroCo loss and contrastive InfoNCE loss (used in SimCLR) in structuring the embedding space. We conduct a toy experiment where we optimize five + +real variables treating one of them as positive similarity and the other four as negative similarities with both losses for multiple iterations. We demonstrate the optimization process in Figure 4. Although both losses elevate positive similarities and lower negative similarities, they differ in the optimization of the negatives. While the InfoNCE loss minimizes all negatives (even pushing the blue curve substantially below zero), the GroCo loss works behaves more similar to a margin optimization: negatives that are not on the border to the positive are optimized to a smaller degree (the blue curve is pushed only slightly below zero). This highlights GroCo's focus on neighborhood optimization. + +# 5. Conclusion + +In this paper, an alternative approach to the common pairwise contrastive learning formulation is proposed. The group ordering constraints consider positives and negatives as groups and enforce the group of positives to be closer to the anchor image than the negative group. To enforce these constraints, recent progress in the context of differentiable sorting approaches are leveraged to formulate a group ordering loss based on the given sorting supervision. Our evaluation shows that the proposed framework, does not only compete with current contrastive loss baselines, but actually outperforms standard contrastive learning in many settings with regards to $k$ -NN-based metrics. + +# Acknowledgements + +Nina Shvetsova is supported by German Federal Ministry of Education and Research (BMBF) project STCL - 01IS22067. + +# References + +[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. Vatt: + +Transformers for multimodal self-supervised learning from raw video, audio and text. NeurIPS, 2021. 3 +[2] YM Asano, C Rupprecht, and A Vedaldi. Self-labelling via simultaneous clustering and representation learning. In ICLR, 2020. 3 +[3] Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. NeurIPS, 32, 2019. 1 +[4] Adrien Bardes, Jean Ponce, and Yann LeCun. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 601, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 287, + 696 + ], + "type": "text", + "content": "Self-supervised learning has become a topic of growing interest over the last years as it allows models to learn representations from large-scale data without the need for human annotation. Many approaches rely on the idea of contrastive learning and were able not only to narrow the gap to the supervised learning performance in vision [23, 14, 60, 30, 3, 63], but also to train state-of-the-art vision-language [52, 56] and multimodal models [40]. 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The idea of the proposed group ordering constraints loss compared to pairwise contrastive losses: GroCo arranges positive and negative data points so that the largest distance to positives must be smaller than the smallest distance to negative points. To this end, the loss implicitly minimizes the amount of necessary swap operation to achieve the ordering constraint. Thus, it focuses on overlapping positives and negatives compared to standard contrastive losses that minimize resp. maximize all pairwise distances." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "of these methods rely on the concept of the pairwise contrastive loss, which is based on the idea that a so-called positive pair, e.g., an image serving as an anchor and an augmentation of the same image, should be closer to each other in an embedding space than a so-called negative pair, e.g., a pair made up of an anchor image and a different image, should be far away from each other. However, it has been noted that the idea of a pairwise contrastive loss also has some limitations, such as the alignment of the embedding space based on individual pairs. Several attempts have been made to address this issue, e.g., combining the contrastive idea with concepts based on local neighborhoods, such as clustering (SwAV [11]), or minimizing distances between multiple positive pairs for the same instance together (Whitening [24]). Another limitation of the contrastive loss is that is that the embedding space is optimized with respect to all negatives, i.e., even negatives that are far away" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 280, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 280, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 280, + 714 + ], + "type": "text", + "content": " 0" + }, + { + "bbox": [ + 304, + 654, + 547, + 716 + ], + "type": "text", + "content": " denotes an inverse temperature. For " + }, + { + "bbox": [ + 304, + 654, + 547, + 716 + ], + "type": "inline_equation", + "content": "\\beta \\to \\infty" + }, + { + "bbox": [ + 304, + 654, + 547, + 716 + ], + "type": "text", + "content": ", the relaxation converges to the discrete swap operation. The differentiable conditional swap operation for the elements " + }, + { + "bbox": [ + 304, + 654, + 547, + 716 + ], + "type": "inline_equation", + "content": "(d_i, d_j)" + }, + { + "bbox": [ + 304, + 654, + 547, + 716 + ], + "type": "text", + "content": " can be defined as a permutation matrix " + }, + { + "bbox": [ + 304, + 654, + 547, + 716 + ], + "type": "inline_equation", + "content": "P_{swap(d_i, d_j)} \\in R^{(K + N) \\times (K + N)}" + }, + { + "bbox": [ + 304, + 654, + 547, + 716 + ], + "type": "text", + "content": ", which is an identity ma" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16456" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 251, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 251, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 251, + 85 + ], + "type": "text", + "content": "trix except for entries " + }, + { + "bbox": [ + 47, + 72, + 251, + 85 + ], + "type": "inline_equation", + "content": "P_{ii}, P_{ij}, P_{jj}, P_{ji}" + }, + { + "bbox": [ + 47, + 72, + 251, + 85 + ], + "type": "text", + "content": " defined as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 92, + 287, + 111 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 92, + 287, + 111 + ], + "spans": [ + { + "bbox": [ + 115, + 92, + 287, + 111 + ], + "type": "interline_equation", + "content": "P _ {i i} = P _ {j j} = f \\left(d _ {j} - d _ {i}\\right), \\tag {4}", + "image_path": "3557ac991e76e58150fbda0fbb28368c717627182f1c7bcf41ca93e7e394a3c3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 116, + 108, + 217, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 108, + 217, + 121 + ], + "spans": [ + { + "bbox": [ + 116, + 108, + 217, + 121 + ], + "type": "interline_equation", + "content": "P _ {i j} = P _ {j i} = f \\left(d _ {i} - d _ {j}\\right).", + "image_path": "2704c14d6d319a498354d03e06be15c03364a2769390f951418d36375683829b.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": "The permutation matrix " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "P_{s}" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": " for step " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": " is the product of matrices corresponding to independent (and thus parallel) swap operations in this step " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "P_{s} = \\prod_{i\\in R}P_{swap(d_{i},d_{i + 1})}" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": " is the set of odd indices if " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": " is odd and the set of even indices if " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": " is even. The complete permutation matrix " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": " is defined as " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "P = P_{K + N}\\cdot \\ldots \\cdot P_{1}" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": ". In the discrete case, each column of a permutation matrix has exactly one entry of 1, indicating the position where the element that corresponds to this column should be placed. In the relaxed version, column values can be seen as a distribution over possible positions of the element. If the correct order of input values is known, we can create a ground truth matrix " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": " and define the loss as " + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "inline_equation", + "content": "L = \\frac{1}{(K + N)^2}\\sum_{i,j}\\mathrm{BCE}(P_{ij},Q_{ij})" + }, + { + "bbox": [ + 46, + 129, + 287, + 297 + ], + "type": "text", + "content": " where BCE refers to binary cross-entropy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 308, + 132, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 132, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 132, + 319 + ], + "type": "text", + "content": "3.3.2 GroCo Loss" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 325, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 287, + 409 + ], + "type": "text", + "content": "If there was a known ground truth order of positives and negatives, the loss could be calculated directly based on this ground truth permutation matrix. However, as the algorithm is based on random augmentations, there are no known orders among positives and among negatives. Thus, the only information available is whether a pair belongs to the positive or the negative group." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 409, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 479 + ], + "type": "text", + "content": "To derive a loss to fulfil this group ordering constraint, we start by ordering positives and negatives first separately with respect to the computed distances to the anchor image as " + }, + { + "bbox": [ + 46, + 409, + 287, + 479 + ], + "type": "inline_equation", + "content": "d_1^p \\leq \\ldots \\leq d_K^p" + }, + { + "bbox": [ + 46, + 409, + 287, + 479 + ], + "type": "text", + "content": " for positives and " + }, + { + "bbox": [ + 46, + 409, + 287, + 479 + ], + "type": "inline_equation", + "content": "d_1^n \\leq \\ldots \\leq d_N^n" + }, + { + "bbox": [ + 46, + 409, + 287, + 479 + ], + "type": "text", + "content": " for negatives. As shown in Figure 3, positive and negative distances are then concatenated in a list as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 119, + 488, + 287, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 488, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 119, + 488, + 287, + 504 + ], + "type": "interline_equation", + "content": "\\left[ d _ {1} ^ {p}, \\dots , d _ {K} ^ {p}, d _ {1} ^ {n}, \\dots , d _ {N} ^ {n} \\right]. \\tag {5}", + "image_path": "5d1d041bd7dfa3c31d1af0ba7bd9170e7538654954aec29804a58dee8c40f1f0.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "type": "text", + "content": "Even though elements in the positive and negative are ordered, it is still open if the constraint " + }, + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "type": "inline_equation", + "content": "d_i^p < d_j^n" + }, + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "type": "text", + "content": " is fulfilled for any " + }, + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "type": "inline_equation", + "content": "1 \\leq i \\leq K" + }, + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "type": "inline_equation", + "content": "1 \\leq j \\leq N" + }, + { + "bbox": [ + 46, + 510, + 287, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "A differentiable sorting network is applied to the concatenated list and a differentiable permutation matrix is obtained for sorting the list in non-descending order. As shown in 3, values in the permutation matrix column can be seen as probabilities to sort the corresponding element to the different positions, e.g., " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "P_{11}" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " would be the probability for assigning the first element in the list " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "(d_1^p)" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " to position 1, " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "P_{21}" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " to position 2, etc. Therefore, the sum of the first " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " elements in a column can be considered as a probability being sorted inside the first " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " elements. Thus, for a permutation matrix of size " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "(K + N) \\times (K + N)" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " the sum of the first " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " rows results in probabilities of being sorted in positive places and the later columns (from " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "K + 1" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "K + N" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": ") in negative places. To enforce positives to be sorted in the positive places and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "negatives in the negatives places, the respective loss (with " + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "inline_equation", + "content": "\\mathbb{1}" + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": " as the indicator function) is defined as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 102, + 545, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 102, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 313, + 102, + 545, + 163 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L = \\frac {1}{2 (K + N)} \\sum_ {i = 1} ^ {K + N} \\left(\\operatorname {B C E} \\left(\\sum_ {k = 1} ^ {K} P _ {k i}, \\mathbb {1} _ {i \\leq K}\\right) + \\right. \\tag {6} \\\\ + \\operatorname {B C E} \\left(\\sum_ {k = K + 1} ^ {K + N} P _ {k i}, \\mathbb {1} _ {i > K}\\right). \\\\ \\end{array}", + "image_path": "dd6a383bcf8548fd6bcfe0caece05927d890d96f149c7fba00dcb39e35ef93ae.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 175, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 175, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 545, + 258 + ], + "type": "text", + "content": "As illustrated in Figure 2, the proposed loss is a relaxation of the sorting supervision in a way that it considers two types of swap operations: swap operations within the group of positive and negative samples, which should not contribute to the loss, and swap operations between the groups, which violate the positive-negative ordering assumption and which are used as the optimization criterion." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": "Role of " + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": ". One relevant hyper parameter is the inverse temperature " + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": " in differentiable swap operation (Equation 3), which corresponds to the degree of relaxation of the swap operation that converges to a discrete case when " + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\beta \\rightarrow \\infty" + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": " (Figure 3). Therefore with lower " + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": " the swap operation is more \"soft\", which is beneficial for optimization, but the relaxation error accumulated by each step is larger, and vice versa in the case of larger " + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": ". With higher " + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 262, + 545, + 394 + ], + "type": "text", + "content": " even a small difference between values results in a high probability for a swap or not swap operation, resulting in a smaller margin between the positive and negatives group." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 397, + 545, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 545, + 505 + ], + "type": "text", + "content": "Number of samples. Since the strongest negatives have the strongest effect on the loss function, the selection can be limited to only the top-" + }, + { + "bbox": [ + 304, + 397, + 545, + 505 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 397, + 545, + 505 + ], + "type": "text", + "content": " strongest negatives. Further, as more negatives also result in more layers in the sorting network and each layer contributes to the overall differential permutation matrix, more layers also result in a softer swap probabilities. Therefore " + }, + { + "bbox": [ + 304, + 397, + 545, + 505 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 397, + 545, + 505 + ], + "type": "text", + "content": " should be selected based on a number of elements to sort. An ablation study on this effect is given in Section 4.5." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 509, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 712 + ], + "type": "text", + "content": "Role of Pre-ordering. Practically, positives and negatives are pre-ordered among themselves before concatenating and forwarding them to the differentiable sorting network. While the loss will still contrast positives to negatives no matter if the input is ordered or not, it shows that preordering improves the overall performance of the GROCo loss. This can be attributed to the fact that sorting networks perform comparisons between neighboring elements and swap them if they are in the wrong order. If the input was not pre-ordered and, thus, distances from positive and negative pairs would be mixed, this would result in additional swap operations. Using pre-ordered inputs the focus lies on comparing the strongest positives with the strongest negatives. In this way, elements are considered as a group, and the borders of the groups or their overlapping parts are emphasized in the loss. In Section 4.5 and Figure 4, we provide additional discussions and illustrate this behavior." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16457" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 190, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 190, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 190, + 85 + ], + "type": "text", + "content": "4. Experimental Evaluation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 88, + 180, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 88, + 180, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 88, + 180, + 102 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 105, + 287, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 105, + 287, + 129 + ], + "spans": [ + { + "bbox": [ + 46, + 105, + 287, + 129 + ], + "type": "text", + "content": "Unless stated otherwise, the following setup is used for all experiments:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 131, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 131, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 131, + 287, + 227 + ], + "type": "text", + "content": "Model. Following previous works [14, 27, 11, 17] Resnet50 [31] is used as the encoder " + }, + { + "bbox": [ + 46, + 131, + 287, + 227 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 131, + 287, + 227 + ], + "type": "text", + "content": " and an MLP block consisting of three fully connected layers with a size of 2048 and followed by a batch normalization layer [33] is used as the projection head " + }, + { + "bbox": [ + 46, + 131, + 287, + 227 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 46, + 131, + 287, + 227 + ], + "type": "text", + "content": ". All batch normalization layers except the last one are followed by a ReLU activation. The dimensionalities of the representation space and the latent space are both 2048 as in [17]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": "Training. Following previous works [14, 27, 11, 17], we use the train set of the ImageNet ILSVRC-2012 dataset [54] for self-supervised training without any human annotation. To create " + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": " augmented views per image (considering " + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "inline_equation", + "content": "m = 2,3,4" + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": "), the DINO augmentation setup [12] is used. The model is trained with the SGD optimizer [64] with a learning rate of " + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "inline_equation", + "content": "6.0 \\times" + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": " (batch size/256) for 100 epochs and " + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "inline_equation", + "content": "3.0 \\times" + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": " (batch size/256) for 200 and 400 epochs. We use a cosine scheduler without restarts [38] and 10 epochs warm-up for 200 and 400 epochs training and 1 epoch linear warm-up for 100 epochs training (we find it beneficial for our method but not for SimCLR). During training, the stop gradient operation is used following the self-supervised learning setups of [14, 12, 27]; specifically, stop gradient is performed during distance computation " + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "inline_equation", + "content": "\\mathrm{d}(x^a, x_i) = \\mathrm{d}(x^a, \\text{stop\\_grad}(x_i))" + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": ". While training with stop gradient does not show a direct impact on the overall performance, we observed that it allows training with larger variations of hyperparameters while maintaining stable performance. By default, the top " + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "inline_equation", + "content": "N = 10" + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": " strongest negatives are sampled from the batch and an inverse temperature of " + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": " is used. Due to resource constraints, the model is trained with a batch size of 1024 with mixed precision. On an 8-GPU (NVIDIA A6000) server, training for 100 epochs with " + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "inline_equation", + "content": "m = 2" + }, + { + "bbox": [ + 46, + 228, + 288, + 528 + ], + "type": "text", + "content": " views takes approximately 22 hours." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 530, + 173, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 530, + 173, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 530, + 173, + 542 + ], + "type": "text", + "content": "4.2. Evaluation Procedure" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "type": "text", + "content": "Linear Probing. Linear probing allows to evaluate the learned embedding space by linear evaluation [14, 27, 11, 17], capturing the linear separability of classes. For this, a linear classifier is trained on frozen representations in a fully-supervised way using the ImageNet train set. We follow the standard protocol [17] to train the linear classifier." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": "-NN Evaluation. To analyze the local properties of the learned representation, namely how often neighbored data points correspond to the same semantic class, we further evaluate with respect to nearest neighbor classification, predicting the class by a simple weighted " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " nearest neighbor classifier (" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": "-NN) with " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "k = \\{1, 10, 20\\}" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " based on cosine distance as used in [12, 11]. Again, we use the ImageNet train set for supervision and test on the val set." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 545, + 310 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 545, + 310 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 310 + ], + "type": "table", + "html": "
MethodBSViews100 ep200 ep400 ep
Linear Probing (Top-1)
Max-Margin [57]2562×22463.8--
MoCo v2† [16] [17]2562×22467.469.971.0
SimCLR† [14] [17]40962×22466.568.369.8
GroCo (ours)10242×22469.270.471.1
GroCo (ours)10244×22469.670.671.3
SimSiam [17]2562×22468.170.070.8
VICReg [4]20482×22468.6--
Barlow Twins [65]20482×22468.7--
SwAV† [11]40962×22466.569.170.7
ReSSL [67]2562×224-69.9-
BYOL† [27]40962×22466.570.673.2
Whitening [24]40964×22469.4-72.6
k-NN (weighted, k=20)
MoCo v2 [16]2562×224-55.6-
SimCLR† [14] [17]40962×22453.857.259.2
GroCo (ours)10242×22460.562.964.0
GroCo (ours)10244×22461.863.664.8
SimSiam [17]2562×22457.4--
SwAV [11]40962×224--61.3
", + "image_path": "15c1c0800178d849152eb6f43f9091ddd9327679bfaa04d07ec79c075bf172b7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 367, + 544, + 439 + ], + "blocks": [ + { + "bbox": [ + 305, + 316, + 546, + 361 + ], + "lines": [ + { + "bbox": [ + 305, + 316, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 546, + 361 + ], + "type": "text", + "content": "Table 1. Comparison to state-of-the-art in linear probing " + }, + { + "bbox": [ + 305, + 316, + 546, + 361 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 316, + 546, + 361 + ], + "type": "text", + "content": "-NN classification on ImageNet. We report results for training for 100, 200, 400 epochs. Backbone=Resnet50. † denotes improved reproductions from SimSiam [17]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 367, + 544, + 439 + ], + "lines": [ + { + "bbox": [ + 308, + 367, + 544, + 439 + ], + "spans": [ + { + "bbox": [ + 308, + 367, + 544, + 439 + ], + "type": "table", + "html": "
MethodEpochsBatch SizeViewsOxfordParis
MHMH
SimSiam [17]1002562×22426.897.0446.9219.31
MoCo v2 [16]2002562×22423.285.0742.817.33
SimCLR [14]40040962×22423.274.5646.9320.19
SwAV [11]40040962×22428.018.3546.2317.4
GroCo (ours)40010242×22429.377.1154.9526.26
", + "image_path": "85d04b3fa39705ac60945940b673170f3014d62808a1359e609d6d00a52cb60d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 445, + 545, + 501 + ], + "lines": [ + { + "bbox": [ + 305, + 445, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 545, + 501 + ], + "type": "text", + "content": "Table 2. Comparison to state-of-the-art in image retrieval. We evaluate image retrieval performance on the Medium (M) and Hard (H) splits of the revisited Oxford and Paris datasets [50]. We evaluate nearest neighbor retrieval performance with ImageNet-trained encoders and report MAP. Backbone = Resnet50." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 512, + 476, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 476, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 476, + 525 + ], + "type": "text", + "content": "4.3. Comparison to State-of-the-Art" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 531, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 591 + ], + "type": "text", + "content": "We start with a comparison of the proposed method to state-of-the-art self-supervised learning methods in linear probing and " + }, + { + "bbox": [ + 304, + 531, + 545, + 591 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 531, + 545, + 591 + ], + "type": "text", + "content": "-NN evaluation on the ImageNet [54], and in image retrieval on the revised Oxford and Paris dataset [50], as well as in transfer learning." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "Linear Probing. In the case of linear probing (Table 1), the proposed method is compared to contrastive baselines using positive and negative samples, namely Max-Margin [57], SimCLR [14], and MoCo v2 [16], as well as to alternative methods. We observe that, in the given setting, the proposed loss is able to improve above all contrastive baselines and even outperforms most strong alternative baselines except BYOL [27] and Whitening [24] (in 400 epochs setup) that use " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " larger batch size and/or an additional teacher network. Another finding is that in the context of linear" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16458" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 135 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 135 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 135 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 135 + ], + "type": "table", + "html": "
MethodEpochsBSAircraftCaltech101CarsCifar10Cifar100DTDFlowersFoodPetsSUN397VOC2007Average
MoCo v220025620.178.912.386.961.468.767.347.267.246.973.957.35
SimCLR400409619.377.715.385.461.070.272.551.268.249.073.158.45
SimSiam10025625.480.117.387.465.569.377.352.572.550.072.860.92
SwAV400409625.882.217.888.666.071.174.850.370.452.975.661.41
GroCo (ours)400102427.681.219.186.865.871.079.256.380.652.374.663.14
", + "image_path": "b1c358ea5f212854c6749d33e45e9d64d15bf5c205cf907c4c101a611f5be859.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 173, + 286, + 266 + ], + "blocks": [ + { + "bbox": [ + 47, + 144, + 545, + 166 + ], + "lines": [ + { + "bbox": [ + 47, + 144, + 545, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 545, + 166 + ], + "type": "text", + "content": "Table 3. Comparison to state-of-the-art transfer performance in k-NN classification on 11 classification datasets. Models are pretrained on ImageNet. Backbone=Resnet50, views=2x224." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 173, + 286, + 266 + ], + "lines": [ + { + "bbox": [ + 50, + 173, + 286, + 266 + ], + "spans": [ + { + "bbox": [ + 50, + 173, + 286, + 266 + ], + "type": "table", + "html": "
MethodBSViews100 ep200 ep400 ep
Linear Probing (Top-1)
SwAV [11]40962×224 + 6×9672.173.974.6
GroCo (ours)10242×224 + 6×9671.872.973.7
k-NN (weighted, k=20)
SwAV [11]40962×224 + 6×9661.763.764.9
GroCo (ours)10242×224 + 6×9662.364.265.2
", + "image_path": "a0c74b21de164e4ec2aec0c8c8a1b7195c0ffa14d15fe5204dc7f273de3f60bc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 392 + ], + "type": "text", + "content": "probing, having four positive samples does not significantly improve the approach compared to only two samples. We attribute this to the fact that missing fine-grained differences in the local neighborhood are compensated by the linear layer training, thus the initial pretraining is less relevant with respect to the local neighborhood in this setting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "text", + "content": "-NN Evaluation. Further, the proposed method is evaluated with respect to the " + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "text", + "content": "-NN performance and compared to state-of-the-art methods that officially released weights (Table 1). Here, it can be observed that the proposed method outperforms all methods in this setting. The results demonstrate that the margin, by which the loss improves over other methods, is increased compared to linear probing, where, e.g., for SwAV, the results were mainly on par " + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "inline_equation", + "content": "(+0.4\\%)" + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "text", + "content": " in case of linear probing, while here they show a more substantial improvement " + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "inline_equation", + "content": "(+2.3\\%)" + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "text", + "content": ". A second hint that the strength of this method is in the optimization of local neighborhoods is given by the fact that the " + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 395, + 287, + 575 + ], + "type": "text", + "content": "-NN setting also shows an improved performance by leveraging multiple positive examples. This can be an indication that more positive examples contribute to a better local neighborhood in this setting." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 578, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 663 + ], + "type": "text", + "content": "Image Retrieval. To further assess the potential of the proposed method in nearest neighbors-based tasks, the model is evaluated on the task of image retrieval in Table 2. Results are reported as the Mean Average Precision (MAP) for the Medium (M) and Hard (H) splits of the datasets as in [12]. Our method outperforms all other methods in this task, confirming good local properties of learned representations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Transfer Performance. Finally, we compare how well performance transfers on other datasets. In Table 3, we compare ImageNet pre-trained models in zero-shot " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "-NN evaluation on 11 classification datasets, including FGVC" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 174, + 545, + 294 + ], + "blocks": [ + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "lines": [ + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": "Table 4. Comparison to SwAV for the multi-crop augmentation strategy. We report results for training for 100, 200, and 400 epochs. Backbone=Resnet50." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 174, + 545, + 294 + ], + "lines": [ + { + "bbox": [ + 309, + 174, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 309, + 174, + 545, + 294 + ], + "type": "table", + "html": "
MethodViewsk-NN EvaluationLinear Eval.
k=1k=10k=20Top-1Top-5
SimCLR2×224---64.3-
SimCLR‡2×22446.051.551.965.786.7
SimCLR‡3×22444.750.050.665.886.8
SimCLR‡4×22446.352.152.666.587.1
SimCLR‡2×224+6×9646.651.452.067.287.7
GroCo (ours)2×22455.360.360.569.288.4
GroCo (ours)3×22455.861.261.669.588.8
GroCo (ours)4×22456.461.561.869.688.9
GroCo (ours)2×224+6×9657.262.062.371.890.4
", + "image_path": "2d6f9541cc3feb7feef7bef175c729f77116c56f271d146b253d045c853c8706.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 300, + 545, + 334 + ], + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 334 + ], + "type": "text", + "content": "Table 5. Comparison to SimCLR as a contrastive baseline on ImageNet. Backbone=Resnet50, #epochs=100, batch size=1024. " + }, + { + "bbox": [ + 305, + 300, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 305, + 300, + 545, + 334 + ], + "type": "text", + "content": " denotes our reproduction." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 350, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 506 + ], + "type": "text", + "content": "Aircraft [39], Caltech-101 [26], Stanford Cars [35], CIFAR10 [36], CIFAR-100 [36], DTD [19], Oxford 102 Flowers [41], Food-101 [6], Oxford-IIIT Pets [43], SUN397 [61] and Pascal VOC2007 [25]. We observe that the proposed method improves over the SimCLR and MoCo v2 baselines in all classes and on average even outperforms the publicly available SimSiam and SwAV baselines. This can be particularly attributed to the improved performance on the Pets and Food datasets. We credit the increased performance to the fact that both food and animal-related classes often appear in the ImageNet pretraining data, thus, learning a good local embedding helps with those datasets, specifically in the case of " + }, + { + "bbox": [ + 304, + 350, + 545, + 506 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 350, + 545, + 506 + ], + "type": "text", + "content": "-NN classification." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "text", + "content": "Multi-crop Augmentation. Since computational cost grows linearly with an increasing number of augmentations, the multi-crop augmentation strategy proposed in SwAV [11] is also considered. The idea is to sample low-resolution local views along with the standard " + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "text", + "content": " ones. Use " + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "inline_equation", + "content": "2 \\times 224 + 6 \\times 96" + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "text", + "content": " scheme, where with two global " + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "text", + "content": " augmented views, six local " + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "inline_equation", + "content": "96 \\times 96" + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "text", + "content": " views are sampled, giving eight views per image. In this case, we follow the \"local-to-global\" correspondence idea [11, 12] and use only global views as positives for both local and global anchor images. While the proposed method shows slightly lower results compared to clustering-based SwAV, it again improves in the case of " + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 510, + 546, + 666 + ], + "type": "text", + "content": "-NN classification (Table 4)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 673, + 480, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 673, + 480, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 673, + 480, + 685 + ], + "type": "text", + "content": "4.4. Comparison to Contrastive Loss" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "To evaluate the properties of the proposed method in a direct comparison with the pairwise contrastive loss formula" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16459" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 122 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 122 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 122 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 122 + ], + "type": "table", + "html": "
MethodViewsk-NN EvaluationLinear Eval.
k=1k=10k=20Top-1Top-5
MoCo v32×22461.566.666.870.990.2
GroCo (ours)2×22463.167.667.570.889.7
", + "image_path": "373e4a96e90cf945a92846eb4f595ca8de1c95c69dbaf46bdf890dd7d8da1755.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 167, + 285, + 236 + ], + "blocks": [ + { + "bbox": [ + 47, + 129, + 287, + 161 + ], + "lines": [ + { + "bbox": [ + 47, + 129, + 287, + 161 + ], + "spans": [ + { + "bbox": [ + 47, + 129, + 287, + 161 + ], + "type": "text", + "content": "Table 6. Comparison to MoCo v3 as a contrastive baseline on ImageNet. Backbone=ViT-Small, #epochs=100, batch size=1024." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 167, + 285, + 236 + ], + "lines": [ + { + "bbox": [ + 50, + 167, + 285, + 236 + ], + "spans": [ + { + "bbox": [ + 50, + 167, + 285, + 236 + ], + "type": "table", + "html": "
k-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Triplet Loss (margin=0.8)46.852.552.863.985.4
Triplet Loss (margin=1.6)47.953.453.764.285.3
Triplet Loss (margin=+∞)47.953.353.864.385.3
GroCo (ours)55.360.360.569.288.4
", + "image_path": "a9b3da02b1b71c4f0efeb46b09d1a7a2ee4a15cc100582b03a95aceaf8888cdd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 278, + 287, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 287, + 315 + ], + "type": "text", + "content": "tion, we compare it further to the classical contrastive learning methods SimCLR [14] and MoCo v3 [18] that use the popular InfoNCE loss [42] as well as to the triplet loss." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": "Contrastive Loss. First, we compare the performance to the SimCLR method in Table 5, where we also analyze the properties of losses to align local neighborhood based on more positive data points. To ensure an identical setting for both methods, SimCLR is reproduced with a 3-layer MLP projection head [15]. Since SimCLR originally uses only two augmentations per image, we extend it to a group of positives by applying contrastive loss between all possible positive pairs (see supplementary material). While outperforming the SimCLR baseline by " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "+3\\%" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": " (Top-1) in linear probing, the proposed method also advances in " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": "-NN evaluation by more than " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "+8\\%" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "k = 20" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": "), demonstrating that the loss helps to learn better representation not only in terms of linear separability but also in terms of local structure. Considering the multi-crop scenario, SimCLR shows mixed results from utilizing more views. While it benefits in linear evaluation, performance slightly decreases in " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": "-NN for " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "k \\in \\{10, 20\\}" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": ". The proposed method profits from utilizing more positives in both evaluations, resulting in " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "+1.7\\%" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": "-NN (" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": "), and " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "+2.4\\%" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": " in linear evaluation (Top-1). We further compare performance with the more recent and better-engineered MoCo v3 approach [18] with a ViT-Small [22] backbone in Table 6. MoCo v3 additionally utilizes a predictor and a momentum encoder that incur an additional computational cost but are beneficial for contrastive training [18, 12]. We plugin our proposed GroCo loss in MoCo v3 setup (with the same architecture, optimizer, etc.) and perform minimal hyperparameter tuning. Table 6 shows that without any tips and tricks the proposed method outperforms MoCo v3 in all " + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 316, + 287, + 687 + ], + "type": "text", + "content": "-NN metrics and has a comparable performance in Top-1 linear probing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Triplet Loss. We also compare the group ordering loss with the triplet loss formulation " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "L = \\max \\left(d_{i}^{p} - d_{j}^{n} + r,0\\right)" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 539, + 197 + ], + "blocks": [ + { + "bbox": [ + 47, + 243, + 286, + 266 + ], + "lines": [ + { + "bbox": [ + 47, + 243, + 286, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 286, + 266 + ], + "type": "text", + "content": "Table 7. Comparison on ImageNet with Triplet Loss. Backbone=Resnet50, #epochs=100, batch size=1024." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 70, + 539, + 197 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 539, + 197 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 539, + 197 + ], + "type": "table", + "html": "
Inverse temp. βNumber of negatives N
151020
k-NNLin.p.k-NNLin.p.k-NNLin.p.k-NNLin.p.
0.06252.164.5----
0.12552.264.559.268.7--
0.2552.164.459.668.6----
0.5--59.468.460.169.1--
1--59.268.160.569.254.665.5
2----60.268.755.966.0
4------58.667.5
8------59.068.0
16------53.065.8
", + "image_path": "f543366217dd47b9db0afda52a437dec8f54947d726c2f7c82190870b93d48dd.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 320, + 216, + 527, + 265 + ], + "blocks": [ + { + "bbox": [ + 326, + 199, + 518, + 210 + ], + "lines": [ + { + "bbox": [ + 326, + 199, + 518, + 210 + ], + "spans": [ + { + "bbox": [ + 326, + 199, + 518, + 210 + ], + "type": "text", + "content": "(a) An inverse temperature " + }, + { + "bbox": [ + 326, + 199, + 518, + 210 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 326, + 199, + 518, + 210 + ], + "type": "text", + "content": ", a number of negatives " + }, + { + "bbox": [ + 326, + 199, + 518, + 210 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 326, + 199, + 518, + 210 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 216, + 527, + 265 + ], + "lines": [ + { + "bbox": [ + 320, + 216, + 527, + 265 + ], + "spans": [ + { + "bbox": [ + 320, + 216, + 527, + 265 + ], + "type": "table", + "html": "
k-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Randomly ordered54.459.259.568.988.2
Pre-ordered55.360.360.569.288.4
", + "image_path": "2b4c2006036f76b4ba110d9cd5cc0ff9f8c529990228413fdd80b84339d71241.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 332, + 282, + 515, + 342 + ], + "blocks": [ + { + "bbox": [ + 369, + 266, + 475, + 277 + ], + "lines": [ + { + "bbox": [ + 369, + 266, + 475, + 277 + ], + "spans": [ + { + "bbox": [ + 369, + 266, + 475, + 277 + ], + "type": "text", + "content": "(b) Pre-ordering in the groups." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 332, + 282, + 515, + 342 + ], + "lines": [ + { + "bbox": [ + 332, + 282, + 515, + 342 + ], + "spans": [ + { + "bbox": [ + 332, + 282, + 515, + 342 + ], + "type": "table", + "html": "
Batch Sizek-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
25652.457.257.267.888.1
51253.157.958.268.288.0
102455.360.360.569.288.4
", + "image_path": "374ee967f16667fd2a93d6d3f749ed77266515e29910251887f3c1bfd38cd650.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 309, + 360, + 539, + 409 + ], + "blocks": [ + { + "bbox": [ + 398, + 344, + 447, + 353 + ], + "lines": [ + { + "bbox": [ + 398, + 344, + 447, + 353 + ], + "spans": [ + { + "bbox": [ + 398, + 344, + 447, + 353 + ], + "type": "text", + "content": "(c) Batch size." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 360, + 539, + 409 + ], + "lines": [ + { + "bbox": [ + 309, + 360, + 539, + 409 + ], + "spans": [ + { + "bbox": [ + 309, + 360, + 539, + 409 + ], + "type": "table", + "html": "
Batch Samplingk-NN EvaluationLinear Probing
k=1k=10k=20Top-1Top-5
Regular55.360.360.569.288.4
With many false negatives51.556.656.967.687.7
", + "image_path": "71ee334febbc8cb6e8631665054e95d52b4a7254c2c1d09c667493a5e3e7dcf1.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 349, + 411, + 495, + 420 + ], + "lines": [ + { + "bbox": [ + 349, + 411, + 495, + 420 + ], + "spans": [ + { + "bbox": [ + 349, + 411, + 495, + 420 + ], + "type": "text", + "content": "(d) Sensitivity to false negatives in a batch." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 427, + 545, + 483 + ], + "lines": [ + { + "bbox": [ + 304, + 427, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 427, + 545, + 483 + ], + "type": "text", + "content": "Table 8. Ablation Experiments. For (a), we report " + }, + { + "bbox": [ + 304, + 427, + 545, + 483 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 427, + 545, + 483 + ], + "type": "text", + "content": "-NN performance with " + }, + { + "bbox": [ + 304, + 427, + 545, + 483 + ], + "type": "inline_equation", + "content": "k = 20" + }, + { + "bbox": [ + 304, + 427, + 545, + 483 + ], + "type": "text", + "content": ", and linear probing Top-1, denoted as \"Lin.p\". The best results are bolded. Options used to obtain the main results are highlighted. Backbone=Resnet50, Views=2×224, #epochs=100." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 494, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 545, + 543 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 494, + 545, + 543 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 494, + 545, + 543 + ], + "type": "text", + "content": " is a margin (Table 7). For a fair comparison, we consider all positive and the 10 strongest negative samples and evaluate different margin parameters. Here, sorting is superior to a triplet loss with hard margin selection." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 549, + 400, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 549, + 400, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 549, + 400, + 562 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Inverse Temperature, Number of Negatives. Table 8a shows the influence of the number of nearest neighbor negatives " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " used in the loss, as well as the value of the inverse temperature parameter " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " (Equation 2). We observe that usage of too many negatives is not be beneficial for the model. Since our loss focuses on negatives that are sorted incorrectly, increasing the number of negatives at some point does not bring any new learning signal (because more distant samples are unlikely to be sorted incorrectly). However, a larger " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " results in more steps of the sorting network, increasing the degree of relaxation. Using a larger inverse temperature " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " (leading to a lower degree of relaxation in the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16460" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 70, + 289, + 232 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 289, + 232 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 289, + 232 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 289, + 232 + ], + "type": "image", + "image_path": "a097399e83434c3bb5ebd661395719d4afc5678016439a7e5e28ff1315d2fc47.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 240, + 547, + 275 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 547, + 275 + ], + "type": "text", + "content": "Figure 4. A toy experiment where we optimize five real variables, treating one of them as positive similarity and the other four as negatives, with both the GroCo loss and contrastive InfoNCE loss for multiple iterations. While the InfoNCE loss minimizes all negatives, the GroCo loss works behaves more similar to a margin optimization: negatives that further away from the border are optimized to a smaller degree." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 541, + 232 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 541, + 232 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 541, + 232 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 541, + 232 + ], + "type": "image", + "image_path": "530dd63db45105c11137cc83b9ccd53f4be6f3486f667811ab72afd6b9c73fa4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": "swap operation) we can gain some performance; however, the variance of the gradients is larger with a larger " + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": ", which is not beneficial for optimization. We found " + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "inline_equation", + "content": "N = 10" + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": " to be an efficient configuration for this setting." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 339, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 287, + 399 + ], + "type": "text", + "content": "Pre-ordering. In Table 8b, we analyze the impact of pre-ordering elements within negative and positive groups before forwarding them to the sorting network. We find that it achieves good performance even without pre-ordering, but also that pre-ordering further strengthens the method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 287, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 463 + ], + "type": "text", + "content": "Batch Size. A large batch size can be an important factor in obtaining good performance for many self-supervised learning methods. Results in Table 8c show that our method also benefits from a large batch size, which we attribute to utilizing stronger negatives from a larger batch." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 466, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 466, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 287, + 574 + ], + "type": "text", + "content": "False negatives. To assess the sensitivity of proposed methods to the false negatives, we artificially sample a batch in a way that for each instance, there are three more instances of the same class on average (acting as false negatives). In Table 8d, we observe a performance decline in this scenario (\"With many false negatives\"). Given GroCo's implicit emphasis on strong negatives, enhancing its robustness to false negatives would require further adjustments, which we leave for future work." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 578, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 650 + ], + "type": "text", + "content": "Training Time. We also consider the training time of our model compared to SimCLR baseline. To eliminate the influence of distributed training, we measure the average time of training iteration on one GPU. We find that the iteration time of both models is comparable, 514ms for SimCLR vs 526ms for the proposed methods for a batch size of 128." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "Optimization of Negatives. To better understand the rationale behind GroCo's superiority in " + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "-NN tasks, we analyze the difference between the GroCo loss and contrastive InfoNCE loss (used in SimCLR) in structuring the embedding space. We conduct a toy experiment where we optimize five" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 288, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 547, + 433 + ], + "type": "text", + "content": "real variables treating one of them as positive similarity and the other four as negative similarities with both losses for multiple iterations. We demonstrate the optimization process in Figure 4. Although both losses elevate positive similarities and lower negative similarities, they differ in the optimization of the negatives. While the InfoNCE loss minimizes all negatives (even pushing the blue curve substantially below zero), the GroCo loss works behaves more similar to a margin optimization: negatives that are not on the border to the positive are optimized to a smaller degree (the blue curve is pushed only slightly below zero). This highlights GroCo's focus on neighborhood optimization." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 444, + 379, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 379, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 379, + 456 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 464, + 547, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 547, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 547, + 609 + ], + "type": "text", + "content": "In this paper, an alternative approach to the common pairwise contrastive learning formulation is proposed. The group ordering constraints consider positives and negatives as groups and enforce the group of positives to be closer to the anchor image than the negative group. To enforce these constraints, recent progress in the context of differentiable sorting approaches are leveraged to formulate a group ordering loss based on the given sorting supervision. Our evaluation shows that the proposed framework, does not only compete with current contrastive loss baselines, but actually outperforms standard contrastive learning in many settings with regards to " + }, + { + "bbox": [ + 304, + 464, + 547, + 609 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 464, + 547, + 609 + ], + "type": "text", + "content": "-NN-based metrics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 617, + 400, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 617, + 400, + 630 + ], + "spans": [ + { + "bbox": [ + 306, + 617, + 400, + 630 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 636, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 636, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 636, + 545, + 658 + ], + "type": "text", + "content": "Nina Shvetsova is supported by German Federal Ministry of Education and Research (BMBF) project STCL - 01IS22067." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 670, + 365, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 365, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 365, + 682 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 310, + 691, + 545, + 713 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 691, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 310, + 691, + 545, + 713 + ], + "type": "text", + "content": "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. 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NeurIPS, 2021. 3, 6" + } + ] + } + ], + "index": 32 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16463" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/a3c8a1dc-20e7-4f50-8e36-d4ddc2e6295d_content_list.json b/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/a3c8a1dc-20e7-4f50-8e36-d4ddc2e6295d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c93e90dc78371af07ed911fa66eb5f2d93850020 --- /dev/null +++ b/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/a3c8a1dc-20e7-4f50-8e36-d4ddc2e6295d_content_list.json @@ -0,0 +1,1456 @@ +[ + { + "type": "text", + "text": "Learning with Noisy Data for Semi-Supervised 3D Object Detection", + "text_level": 1, + "bbox": [ + 143, + 130, + 826, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zehui Chen1 Zhenyu Li2 Shuo Wang1 Dengpan Fu3 Feng Zhao1* \n1University of Science and Technology of China \n2Harbin Institute of Technology 3NIO", + "bbox": [ + 189, + 179, + 782, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lovesnow, wangshuo}@mail.ustc.edu.cn zhenyuli17@hit.edu.cn", + "bbox": [ + 215, + 236, + 754, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "dengpan.fu@nio.com fzhao956@ustc.edu.cn", + "bbox": [ + 297, + 255, + 671, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pseudo-Labeling (PL) is a critical approach in semisupervised 3D object detection (SSOD). In PL, delicately selected pseudo-labels, generated by the teacher model, are provided for the student model to supervise the semisupervised detection framework. However, such a paradigm may introduce misclassified labels or loose localized box predictions, resulting in a sub-optimal solution of detection performance. In this paper, we take PL from a noisy learning perspective: instead of directly applying vanilla pseudo-labels, we design a noise-resistant instance supervision module for better generalization. Specifically, we soften the classification targets by considering both the quality of pseudo labels and the network learning ability, and convert the regression task into a probabilistic modeling problem. Besides, considering that self-supervised learning works in the absence of labels, we incorporate dense pixel-wise feature consistency constraints to eliminate the negative impact of noisy labels. To this end, we propose NoiseDet, a simple yet effective framework for semi-supervised 3D object detection. Extensive experiments on competitive ONCE and Waymo benchmarks demonstrate that our method outperforms current semisupervised approaches by a large margin. Notably, our NoiseDet achieves state-of-the-art performance under various dataset scales on ONCE dataset. For example, NoiseDet improves its NoiseStudent baseline from 55.5 mAP to 58.0 mAP, and further reaches 60.2 mAP with enhanced pseudo-label generation. Code will be available at https://github.com/zehuichen123/NoiseDet.", + "bbox": [ + 75, + 335, + 473, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 804, + 209, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D object detection, aiming at detecting instances in the 3D space, is of great importance in various applications. Thanks to the large amount of labeled data, it has achieved", + "bbox": [ + 76, + 830, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ba47aa5978211295c5c78dc171ff36a68d44471b9590419234f610aaaf97b639.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 301, + 885, + 405 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8fe762859dc84524c9f9ddc1fe5b6920baedfa7b8776a66cbb35d3cc81d107f2.jpg", + "image_caption": [ + "Figure 1. The noisy predictions generated by a well-trained 3D object detector. Despite carefully tuning the model and filtering low-confidence score predictions, there are still low-quality bounding boxes left. Directly enforcing the detector to learn from such noisy data on an unlabeled dataset can mislead the model convergence or even deteriorate its performance. In the top figure, we demonstrate an inaccurate heading regression case, and the bottom case shows a false positive prediction. We distinguish the ground truth and model predictions with green and blue, respectively." + ], + "image_footnote": [], + "bbox": [ + 506, + 412, + 885, + 515 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "great success in the past few years [37, 29, 9, 56, 10, 11]. However, labeling a large-scale dataset is extremely time-consuming and labor-intensive [40]. This issue gets much more severe in the 3D object detection task, where 7 degree-of-freedom parameters need to be determined as well as the categorical labels. Therefore, how to further boost the supervised detectors with limited labeled datasets remains a practical and urgent problem.", + "bbox": [ + 496, + 686, + 893, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semi-supervised object detection (SSOD) demonstrates great prospects recently due to its simplicity and weak dependence on costly annotations [46, 20, 39]. By leveraging easily accessible unlabeled data, SSOD approaches enhance the model performance with little human effort [47, 43, 51, 25]. The strategies of current SSOD can be", + "bbox": [ + 496, + 810, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6929", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "categorized into two main streamlines: Mean-Teacher [41] and Pseudo-Labeling [24]. Mean-Teacher adopts a teacher-student paradigm, where the teacher is initialized from the student model via Exponential Moving Average (EMA) to produce supervised signals on the unlabeled data in an end-to-end training fashion. Inspired by this, more advanced ways, including SESS [55], NoisyStudent [45], are built upon the teacher-student paradigm and achieve significant improvements. Despite the superior performance and elegant pipeline, they are not model-agnostic (i.e. the teacher and student should be the same model) and miss the chance to pursuing high-quality pseudo labels, such as off-board label generation [35]. Another line of work is pseudo labeling [53, 36]: the model is first trained on labeled data and then generated pseudo labels on the unlabeled data for later training. Different from MT, it can be easily applied to any detector without adapting the framework to the teacher-student paradigm. These multi-stage approaches obtain reasonably good results, however, the final performance is often impeded by the quality of pseudo labels. To address this issue, 3DIoUMatch [42] proposes to estimate the localization accuracy predicted by the network and utilizes it as a metric to guide the label generation. ProficientTeacher [51] introduces a clustering-based box voting module to filter low-quality predictions without introducing any handcrafted rule. Although the accuracy of pseudo labels gets greatly improved, it may still fail in certain cases, leading to unstable model convergence. Harsh confidence filtering is proven to be worked well [46], however, we observe that it is still hard to remove all misleading instances for generated labels, which can distract the model convergence, shown in Figure 1.", + "bbox": [ + 76, + 90, + 472, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we acknowledge the existence of noise in the generated labels and take PL as a noisy learning task: instead of directly applying vanilla pseudo-labels, we design a noise-resistant instance supervision module for better model generalization. Specifically, for the classification branch, we leverage the confidence predictions from the teacher and the student model learning ability to construct soft categorical targets. Different from previous approaches [47, 28], which simply apply them for loss reweighting, we enforce the network to directly learns from such continual supervision. In this way, our strategy can adaptively learn more knowledge from the teacher's predictions and at the same time develop tolerance to low confidence score labels. As for the regression branch, we find that solely relying on classification scores or IoU predictions is not enough to reflect the learning quality of each attribute of the 3D box. To mitigate this problem, we convert the original smooth L1 regression into a probabilistic modeling task: by enabling the network to output two variables to represent the Gaussian distribution, we maximize the negative log-likelihood of the targets in the distribution. Apart from the label supervi", + "bbox": [ + 76, + 584, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sion on the unlabeled data, we also introduce a novel dense pixel-wise feature self-supervised consistency constraints to further eliminate the negative impact of noisy data. To this end, we propose NoiseDet, a simple semi-supervised 3D object detection framework to address the noise learning problem from the unlabeled data. Our NoiseDet is modal-agnostic and can be easily applied to any 3D object detector with little modification.", + "bbox": [ + 496, + 90, + 893, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our key contributions as follows:", + "bbox": [ + 517, + 212, + 839, + 227 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Instead of directly improving the quality of pseudolabels, we formulate SSOD as a noisy learning problem, where we acknowledge the existence of the noise in pseudo-labels and soften the network supervision for model generalization.", + "- Based on this thought, we propose NoiseDet, a simple yet effective SSOD framework to deal with the noisy data through two core modules: noise-resistant instance supervision and dense pixel-wise feature consistency constraint.", + "- With extensive experiments, we validate the effectiveness of our approach on two competitive benchmarks. Notably, it achieves state-of-the-art performance on the challenging ONCE dataset." + ], + "bbox": [ + 516, + 239, + 890, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 489, + 640, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. LiDAR-based 3D Object Detection", + "text_level": 1, + "bbox": [ + 500, + 513, + 802, + 530 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D object detection aims to detect instances in the 3D space, which is of great importance in various applications, such as autonomous driving, navigation robot, and augmented reality. Current LiDAR detectors [52, 59, 49] mainly voxelize the point cloud into a BEV or voxel representations and adopt traditional 2D convolutions to predict bounding boxes. To improve the inference speed, some works [15, 30] attempt to detect objects directly through the range view. [58] combines both BEV and range-view features together to achieve better performance. VoxelNet [59] adopts PointNet [34] to extract local features through raw point clouds and fill them into the predefined voxel space. PointPillar [22] directly processes points inside a pillar to naturally formulate BEV feature representations, establishing an ultra-fast baseline detector. Inspired by CenterNet [14], CenterPoint [52] introduces a center-based label assignment strategy in 3D object detection, achieving competitive detection accuracy among various approaches. In addition to dense one-stage detectors, many works [8, 38] apply an R-CNN-style two-stage detection paradigm. Point R-CNN [38] propose 3D RoIAlign to aggregate regional features based on the proposals and then refines the detections. PV-RCNN [37] and Voxel R-CNN [13] construct two-parallel branches to extract both point-level and voxel", + "bbox": [ + 496, + 537, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6930", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "level features to enjoy the best of each. However, independently localizing moving instances can introduce misalignment noise, 3D-MAN [50] and MPPNet [7] leverage multi-frame information to further enhance predictions with temporal knowledge.", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Semi-Supervised Learning (SSL)", + "text_level": 1, + "bbox": [ + 76, + 176, + 366, + 193 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semi-supervised learning is an important task in leveraging easy-to-access unlabeled data to improve the supervised model. Most current SSL methods [53, 17, 5, 19] involve adding additional supervision on unlabeled data to regularize the learning of the model. Among them, pseudolabeling is a popular pipeline [4, 24, 18], where unlabeled data is firstly labeled with a supervised model, and then acts in a common training paradigm. In order to guarantee the quality of the generated labels, [24] often filter them with a hard threshold based on the classification score. In addition to hard pseudo-labels, NoisyStudent [45] explores soft supervision to avoid ambiguity problems. Besides, it injects different augmentations to the student and teacher models, to encourage consistency regularization. In light of this, plenty of approaches [44, 2, 26] enforce the model to predict similar results when applying various input permutations. Such strategies are also verified on 2D object detection, where [32] borrows the idea from FixMatch to achieve promising performance. MUM [21] introduces Mix/UnMix augmentation, enforcing students to reconstruct unmixed features for the mixed input images.", + "bbox": [ + 75, + 200, + 472, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Semi-Supervised 3D Object Detection", + "text_level": 1, + "bbox": [ + 76, + 529, + 401, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semi-supervised learning (SSL) has been rapidly developed in both classification and object detection domains and obtains promising results in recent years. There are two main streams in SSOD: consistency learning and pseudo labeling. Consistency-based works [41, 25] apply data augmentations/perturbations to the input, which forms natural regularization for the network predictions. Such a consistency-learning target enforces the model to acquire valid information from the unlabeled data, therefore improving the performance. SESS [55] is the first work to attempt such a paradigm on 3D object detection, where the classification and regression predictions are matched through L2 distance and supervised with the similarity loss on the teacher and student. Inspired by Mean Teacher [41], it also adopts the exponential moving average (EMA) technique to further boost the performance. Apart from the consistency-based approaches, pseudo-labeling is another solution [46, 42]. Most PL works pay attention to the quality enhancement of pseudo labels. 3DIoUMatch [42] proposes to learn the IoU of the network predictions and utilize it to adaptively filter the low-quality pseudo labels. In order to remove the duplicate score threshold search, ProficientTeacher [51] introduces a novel clustering-based box voting", + "bbox": [ + 75, + 553, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "module, replacing the hand-crafted NMS process. Different from the previous approaches, our method views pseudolabeling as a noisy learning problem, therefore delivering more generalization against noisy pseudo-data.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. NoiseDet", + "text_level": 1, + "bbox": [ + 500, + 162, + 601, + 179 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is acknowledged that predictions generated by the teacher model will inevitably encounter false positive (FP) or false negative (FN) problems, despite many efforts that have been devoted to overcoming these issues [51, 46]. Such noises can distract the convergence of the model during the semi-supervised training process, or even deteriorate the final performance.", + "bbox": [ + 496, + 188, + 890, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The main intuition of NoiseDet is to improve the model generalization ability against noisy pseudo labels, which are generated by the baseline model trained on limited labeled data. We start with a vanilla two-stage pseudo-labeling pipeline: assuming that we have access to a (small) set of labeled set $L = \\{x_i^l,y_i^l\\}_{i = 1}^{N_l}$ , and a set of unlabeled set $U = \\{x_i^u\\}_{i = 1}^{N_u}$ , where $N_{l}$ and $N_{u}$ are the numbers of labeled and unlabeled datasets. A teacher model is firstly trained on the labeled set $L$ , and then infer on unlabeled set $U$ to get pseudo labels $\\{y_i^u\\}_{i = 1}^{N_u}$ and formulate the pseudo-labeled set $U_{p} = \\{x_{i}^{u},y_{i}^{u}\\}$ . After that, we initialize the student model from the pretrained teacher and uniformly sample data from both $L$ and $U_{p}$ set to construct each batch for second-stage training. Different from previous works, which mainly focus on improving the quality of pseudo-labels, NoiseDet directly learns knowledge from noise labels $\\{y_i^U\\}_{i = 1}^{N_u}$ .", + "bbox": [ + 496, + 294, + 892, + 539 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Noise-Resistant Instance Supervision", + "text_level": 1, + "bbox": [ + 500, + 545, + 820, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast to standard fully supervised object detection, where labels are carefully human-annotated and verified, the supervisory signals on the unlabeled set are generated by the vanilla teacher model. It may contain unexpected noisy labels, leading to model performance degeneration. Therefore, we propose to transform such hard, deterministic instance supervision into the noise-resistant one to develop the model tolerance to the noisy labels, instead of directly eliminating them.", + "bbox": [ + 496, + 568, + 890, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent works [16, 3] suggests that the confidence score $c$ can be viewed as the noisy level of the network predictions, i.e., the model is more prone to yield a high score for easy-to-detect samples and low score for not-sure samples. Therefore, an intuitive idea is to filter the generated pseudo-labels with a pre-defined score threshold $U_{p} = \\{(x_{i}^{u},c_{i}^{u})|c_{i}^{u}\\geq c_{thres}\\}$ to eliminate the noises for the unlabeled dataset. Though simple, such a strategy does not provide a clear divergence for the rest labels. For instance, the quality of a box with $c = 0.9$ can be different from the quality of the box with $c = 0.5$ . However, they are treated equally with 1/0 labels in the classification branch. To fully exploit a reliable confidence score derived from the", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6931", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ce189c39c234ea83ad8d1231d7ff141194716a07d24fc43bca74f58dea7cc6f4.jpg", + "image_caption": [ + "Figure 2. The overall architecture of the proposed NoiseDet. It consists of two main components: noise-resistant instance supervision and dense feature consistency constraint. It follows the pseudo-labeling practice with a two-stage training paradigm: (i) pseudo labels are pre-generated with a well-trained teacher model on the unlabeled dataset, and (ii) the student model is trained on both labeled (omitted in the figure) and unlabeled LiDAR points in a semi-supervised manner." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 893, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "teacher model, we leverage the $c$ as an indicator to measure the quality of the pseudo label. Specifically, instead of directly assigning each anchor with a deterministic binary label, we soften the categorical label into a value ranging from 0 to 1 given the confidence score $c$ as well as the IoU $\\tau$ between the student predictions and its matched pseudo labels. Different from the one in GFL [27] where the categorical labels are assigned based on the IoU between the network prediction and the ground-truth boxes, we view it as the combination of the quality of the GT boxes itself and the learning ability of the student. Since the standard Focal Loss can only handle discrete binary values, we adopt Quality Focal Loss [27] to conduct the classification supervision on the non-discrete categorical labels:", + "bbox": [ + 75, + 464, + 472, + 675 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\alpha c + (1 - \\alpha) \\tau , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 686, + 468, + 703 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c l s} ^ {U} = - | y - \\hat {y} | ^ {\\beta} ((1 - y) \\log (1 - \\hat {y}) + y \\log (\\hat {y})), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 705, + 468, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{y}$ is the quality score predicted by the teacher and $y$ is the student predictions, $\\alpha$ is set to 0.75. Note that our approach can be easily extended into other continual versions of cross-entropy loss, for instance, Gaussian Focal Loss [23].", + "bbox": [ + 75, + 734, + 468, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition to the classification loss, the boundary targets of the bounding box can present more ambiguities since it contains 7 degree-of-freedom and presents fewer training samples (only positive samples receive the regression supervision). Therefore, how to effectively deal with misleading regression targets is non-trivial. To address this problem,", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we convert the deterministic regression into the probability optimization task. Concretely, we model the network prediction of each bounding box as a Gaussian distribution $h$ given the feature vector $x$ :", + "bbox": [ + 496, + 464, + 892, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {h} = \\mathcal {N} (\\mu (x), \\sigma (x)), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 535, + 892, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu (x)$ and $\\sigma (x)$ denotes the mean and variance of each regression term predicted by the network. After that, the regression loss can be converted into a negative log-likelihood (NLL) loss, where the objective is to maximize the likelihood of each GT $h$ in the predicted distribution:", + "bbox": [ + 496, + 565, + 893, + 642 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e g} = - \\log \\mathcal {N} (h; \\mu (x), \\sigma (x)) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 652, + 890, + 670 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n= - \\log \\frac {1}{\\sigma \\sqrt {2 \\pi}} e ^ {- \\frac {1}{2} \\left(\\frac {h - \\mu}{\\sigma}\\right) ^ {2}}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 672, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By converting the deterministic regression task to a probabilistic estimation problem, the model develops more tolerance against noisy information in the training data, therefore achieving better performance.", + "bbox": [ + 496, + 715, + 890, + 776 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Dense Feature Consistency Constraint", + "text_level": 1, + "bbox": [ + 500, + 786, + 830, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Considering that labels can contain noise information that deteriorates the model performance, we further exploit the incorporation of unsupervised learning to obtain useful knowledge about label-independent features. However, different from the common-studied image classification task that mostly cares about the overall feature representation,", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6932", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D object detection requires estimating instances with various scales and directions. Therefore, learning a scale and rotation-invariant feature extractor for 3D detector is of vital importance. By applying various data augmentation, such as rescaling, rotating, and global transforming, into the input point clouds, and supervising them with the transformed ground-truth boxes, the model can develop robustness to such transformations. However, when the label itself is not so accurate enough, such a strategy may be more harmful.", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To avoid this problem, we propose a dense pixel-wise consistency constraint to enforce the network to acquire such property. Previous literature mainly involves label-level consistency [55, 42, 1, 54] to ensure the model consistency, where the predicted bounding boxes are reversed back to the original space and regularized with Euclidean distance matching. Despite being simple and straightforward, this low-dimensional prediction distribution (number of classes and 7 regression targets) means that only a few amounts of knowledge are encoded, thus limiting the knowledge that can be transferred. Hence, we apply the consistency constraint on the feature level by reversing the BEV features according to the data transformation in the data augmentation and then conducting dense pixel-wise regularization.", + "bbox": [ + 75, + 227, + 470, + 453 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More formally, given one frame of point clouds $P$ and a set of data augmentation policies $\\mathcal{A}$ , we randomly sample two transformations $\\mathcal{A}_1, \\mathcal{A}_2$ from $\\mathcal{A}$ and apply them to the point $P$ to produce two different views of point clouds $P_1, P_2$ . The augmented point clouds are fed into the point feature extractor $\\mathcal{F}$ to generate the BEV feature maps $F$ :", + "bbox": [ + 76, + 454, + 468, + 546 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {1} = \\mathcal {F} (P _ {1}), F _ {2} = \\mathcal {F} (P _ {2}). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 558, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once obtaining the BEV features, we simply reverse them back to the original space with the recorded transformation flow:", + "bbox": [ + 76, + 588, + 468, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {F} _ {1} = \\mathcal {A} _ {1} ^ {- 1} \\left(F _ {1}\\right), \\hat {F} _ {2} = \\mathcal {A} _ {2} ^ {- 1} \\left(F _ {2}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 645, + 468, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $A^{-1}$ denotes the reverse transformation of $A$ . To this end, we can derive the pixel-wise feature consistency constraint with standard L2 loss:", + "bbox": [ + 76, + 676, + 468, + 720 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n s i s t}} = \\left| \\left| \\hat {F} _ {1} - \\hat {F} _ {2} \\right| \\right| _ {2}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 733, + 468, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering that the point-based 3D features can hold meaningful information only if the point exists, mainly due to the characteristics of the LiDAR points, we further introduce a foreground-focusing mask to selectively regularize the augmented BEV features. Different from previous approaches [12] that directly set each foreground GT region with hard supervision, we generate a soft mask to smooth the regularization effect at the boundary regions, similar in [57]. Specifically, we draw a Gaussian distribution for each", + "bbox": [ + 76, + 763, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GT center $(x_{i},y_{i})$ in the BEV space,", + "bbox": [ + 500, + 90, + 743, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {i, x, y} = \\exp \\left(\\frac {\\left(x _ {i} - \\hat {x} _ {i}\\right) ^ {2} + \\left(y _ {i} - \\hat {y} _ {i}\\right) ^ {2}}{2 \\sigma_ {i} ^ {2}}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 117, + 890, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma_{i}$ is a constant (set to 2), indicating the object size standard deviation. Since feature maps are class-agnostic, we merge all $\\phi_{i,x,y}$ into one single mask $\\Phi$ by taking the maximum value across the $i$ dimension. Therefore, the final dense feature consistency constraint is derived as:", + "bbox": [ + 498, + 162, + 890, + 238 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n s i s t}} = \\frac {1}{H W \\Phi} \\sum_ {i} ^ {H} \\sum_ {j} ^ {W} \\max \\left(\\phi_ {i j}\\right) \\left| \\left| \\hat {F} _ {1} - \\hat {F} _ {2} \\right| \\right| _ {2}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 250, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By aligning dense pixel-wise features on the BEV space, the model can gradually learn the ability to extract transform-invariant feature extraction and fully utilize the unlabeled data in a self-supervised manner.", + "bbox": [ + 498, + 305, + 890, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 380, + 630, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 404, + 601, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ONCE dataset [33] is one of the largest autonomous driving datasets with 1 million LiDAR point clouds and 7 million paired images. Only 15,000 samples are annotated with 3D bounding boxes, which are divided into training, validation and testing split with a ratio of $33\\% /20\\% /47\\%$ , respectively. Among all instances, five classes are labeled as interested categories: Car, Bus, Truck, Pedestrian, and Cyclist. According to the official SSL setting, 5,000 samples are selected as labeled set and all the unlabeled sets are divided into 3 scales of subsets: Small, Medium, and Large. The small set contains 70 sequences (100k samples), the medium set contains 321 sequences (500k samples), and the large set contains 560 sequences (about 1M samples). Following the official evaluation tools, we set 0.7, 0.3, and 0.5 for Vehicle, Pedestrian, and Cyclist as the mAP IoU threshold, respectively. Besides, similar to Waymo Open Dataset [40], the evaluation protocol provides metrics based on different perception ranges: '0-30m', '30-50m', and /'50minf' to fully reflect the detection ability of the model.", + "bbox": [ + 498, + 428, + 890, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 726, + 718, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NoiseDet follows the two-stage training pipeline: we first train the teacher network with 80 epochs for ONCE dataset. Then we utilize the STE module proposed in ProficientTeacher [51] to obtain pseudo-labels on the unlabeled dataset. During this process, we can easily incorporate other techniques such as camera/Radar detection or object tracking to further refine the labels. We do not consider such implementations since it is out of the scope of this paper, but it is proven to be effective in [35]. For the semi-supervised training configuration, we uniformly sampled 1 labeled and", + "bbox": [ + 498, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6933", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/cff3cb03fab18b26dc575f1a9cc87182de6e1c57d1916b3a3ff94caa9da00e66.jpg", + "table_caption": [ + "Table 1. Comparison with other state-of-the-art semi-supervised 3D object detection approaches on ONCE validation set with different amounts of unlabeled samples (e.g., \"Small\", \"Medium\" and \"Large\"). We bold the best overall results and list the relative gains based on the baseline model (i.e., SECOND [48] trained on labeled training set only) for better illustration. Most experimental results are borrowed from the official implementations in ONCE [33]." + ], + "table_footnote": [], + "table_body": "
MethodsVehicle AP (%)Pedestrian AP (%)Cyclist AP (%)mAP (%)
overall0-30m30-50m50m-infoverall0-30m30-50m50m-infoverall0-30m30-50m50m-inf
Baseline [48]71.1984.0463.0247.2526.4429.3324.0518.0558.0469.9652.4334.6151.89
Small (100K unlabeled samples)
Pseudo Label72.8084.4664.9751.4625.5028.3622.6618.5155.3765.9550.3434.4251.22 (-0.67)
Noisy Student [45]73.6984.6967.7253.4128.8133.2323.4216.9354.6765.5850.4332.6552.39 (+0.50)
Mean Teacher [41]74.4686.6568.4453.5930.5434.2426.3120.1261.0272.5155.2439.1155.34 (+3.45)
SESS [55]73.3384.5266.2252.8327.3131.1123.9419.0159.5271.0353.9336.6853.39 (+1.50)
3D IoUMatch [42]73.8184.6168.1154.4830.8635.8725.5518.3056.7768.0251.8035.9153.81 (+1.92)
NoiseDet (Ours)75.2686.3667.5255.2937.9642.3632.7823.2860.7772.3155.0338.8758.00 (+6.11)
Medium (500K unlabeled samples)
Pseudo Label73.0386.0665.9651.4224.5627.2820.8117.0053.6165.2648.4433.5850.40 (-1.49)
Noisy Student [45]75.5386.5269.7855.0531.5635.8026.2421.2158.9369.6153.7336.9455.34 (+3.45)
Mean Teacher [41]76.0186.4770.3455.9235.5840.8630.4419.8263.2174.8956.7740.2958.27 (+6.38)
SESS [55]72.1184.0666.4453.6133.4438.5828.1018.6761.8273.2056.6038.7355.79 (+3.90)
3D IoUMatch [42]75.6986.4670.2256.0634.1438.8429.1919.6258.9369.0854.1638.8756.25 (+4.36)
NoiseDet (Ours)77.1487.2169.9458.4440.4544.9135.7124.1162.5973.0457.9842.6760.06 (+8.17)
Large (1M unlabeled samples)
Pseudo Label72.4184.0664.5450.0523.6226.8020.1316.6653.2564.6948.5233.4749.76 (-2.13)
Noisy Student [45]75.5386.5269.7855.0531.5635.8026.2421.2158.9369.6153.7336.9455.34 (+3.45)
MeanTeacher [41]76.3886.4570.9957.4835.9541.7629.0518.8165.5075.7260.0743.6659.28 (+7.39)
SESS [55]75.9586.8370.4555.7634.4340.0027.9219.2063.5874.8558.8839.5157.99 (+6.10)
3D IoUMatch [42]75.8186.1171.8257.8435.7040.6830.3421.1559.6970.6954.9239.0857.07 (+5.18)
NoiseDet (Ours)78.0287.0072.5559.4942.8946.5238.2126.6062.7473.1958.0342.8861.16 (+9.27)
", + "bbox": [ + 84, + 146, + 885, + 426 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/541af94a752b03651caaebc29b7981c82a48e328dbbab569f4ba882166e7a22a.jpg", + "table_caption": [ + "Table 2. Comparison of detection results based on SECOND and CenterPoint with and without NoiseDet on ONCE validation set." + ], + "table_footnote": [], + "table_body": "
DetectorMethodmAP
SECONDNoisyStudent55.50
NoiseDet (Ours)58.01
CenterPointNoisyStudent63.77
NoiseDet (Ours)65.57
", + "bbox": [ + 130, + 488, + 416, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 unlabeled samples for each batch to avoid training collapse. Following the official ONCE benchmark [33], we initialize the student from a pretrained checkpoint on the full labeled set. The student is trained for 25, 50, 75 epochs for small, medium, and large settings on ONCE dataset. The learning rate is set to 1e-4 and the pseudo-labels are updated every 25 epochs. All models are trained on an 8 NVIDIA V100 GPUs machine.", + "bbox": [ + 75, + 618, + 468, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 76, + 753, + 215, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first implement NoiseDet with the standard anchor-based 3D detector, SECOND, following the official benchmark [33], on the Small protocol setting of ONCE dataset. The final performance is shown in Table 2. Our NoiseDet greatly boosts its enhanced baseline NoisyStudent [45] by $2.5\\mathrm{mAP}$ . Then, we also report it on a stronger anchor-free-based detector, CenterPoint [52], which also obtains an improvement of $1.8\\mathrm{mAP}$ , validating the effectiveness and", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "generalization of the proposed method under different 3D detection frameworks. Besides, we also validate NoiseDet on the competitive Waymo Open Dataset [40] in Appendix, which outperforms 3DIoUMatch [42] by a large margin.", + "bbox": [ + 496, + 460, + 890, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Comparison with State-of-the-Arts", + "text_level": 1, + "bbox": [ + 498, + 546, + 805, + 563 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further validate the superiority of our method, we compare NoiseDet with various state-of-the-art semi-supervised approaches, including Pseudo-Label, NoisyStudent, Mean Teacher, SESS, and 3DIouMatch. The experiments are conducted on the three different protocols (Small, Medium, and Large) to fully exploit the extensibility of various strategies and the results are reported in Table 1. We select SECOND as our baseline to keep consistent with other works [33]. NoiseDet surpasses all other counterparts, achieving new state-of-the-art in this competitive benchmark. With the increase of the unlabeled dataset size, NoiseDet can consistently improve the detectors with significant gains: with $6.1\\mathrm{mAP}$ , $8.2\\mathrm{mAP}$ , and $9.3\\mathrm{mAP}$ under Small, Medium, and Large protocols, respectively.", + "bbox": [ + 496, + 575, + 890, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 811, + 665, + 827 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we conduct a series of ablation studies to gain a deeper understanding of NoiseDet. For efficiency, all experiments are conducted on the Small protocol of the ONCE training set and evaluated on the validation set.", + "bbox": [ + 496, + 840, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6934", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/623411059acc594b62e0624a1b9d679aa45d8f7bed142e1a339b6455eb669bcf.jpg", + "table_caption": [ + "Table 3. Effectiveness of each component in our NoiseDet. Results are reported on ONCE validation subset with SECOND." + ], + "table_footnote": [], + "table_body": "
Noise-Resistant Instance Supervision ClassificationRegressionDense Feature Consistency ConstraintmAP
\\( AP_{veh} \\)\\( AP_{ped} \\)\\( AP_{cyc} \\)\\( AP_{overall} \\)
72.0336.8057.7355.50
✓72.7836.4160.7356.80
✓73.8736.7458.3456.39
✓✓74.0536.6261.0357.27
✓✓✓75.2637.9660.7758.01
", + "bbox": [ + 94, + 104, + 874, + 232 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5.1 Main Ablations", + "text_level": 1, + "bbox": [ + 76, + 256, + 240, + 271 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In order to understand the effectiveness of each module contributing to the detection performance in NoiseDet, we test each component separately on the baseline detector SEC-OND and report the results in Table 3. Our baseline is the enhanced implementation of NoisyStudent [45], where its performance starts from $55.5\\mathrm{mAP}$ on the validation dataset. When we add the noise-resistant instance supervision on the classification branch, the mAP score is raised by $1.1\\mathrm{mAP}$ . And then we test the proposed component on the regression branch, which yields another $0.8\\mathrm{mAP}$ . Such a huge improvement validates the correctness of the noise learning strategy on the unknown quality of pseudo-labels and the effectiveness of the proposed noise-resistant instance supervision module. When the dense feature consistency constraint module is applied, the accuracy is promoted by $1.2\\mathrm{mAP}$ , suggesting that consistent regularization provides useful unsupervised hints for model convergence. Finally, we put all techniques together, and NoiseDet achieves 58.0 mAP on the validation subset, indicating a $2.5\\mathrm{mAP}$ performance enhancement.", + "bbox": [ + 75, + 281, + 472, + 583 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5.2 Noise-Resistant Instance Supervision", + "text_level": 1, + "bbox": [ + 76, + 604, + 388, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with other classification supervision. We first compare our proposed noise-resistant classification loss with other supervision approaches. The vanilla strategy is to directly apply Focal Loss on the pseudo labels, similar to the labeled data. Then, we attempt to utilize the predicted score from the teacher to adjust the supervision on the pseudo-labels by reweighting the classification loss. In doing this, we can alleviate the training distraction from low-quality samples by lowering their penalties. Inspired by 3D IoUMatch [42], we consider IoU as another measurement to help decide the loss penalty on the pseudo samples (denoted as IoU Reweight). We also consider Quality Focal Loss proposed in [27] to further integrate IoU into the classification supervision. The final results are shown in Table 4. Incorporating reweighting mechanisms, either IoU or classification score, to balance the supervision across different samples brings about $0.5\\mathrm{mAP}$ improvements. When adapting to QFL, the model improves to $56.2\\mathrm{mAP}$ . Finally,", + "bbox": [ + 75, + 628, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "by both considering localization quality (IoU) and the sample quality (classification score), we obtain the best performance, $56.8\\mathrm{mAP}$ on the validation subset.", + "bbox": [ + 496, + 256, + 890, + 301 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0c8ee0c7e8d23690b894a8de6901796e6c39be9ae8797fe06de84b23394af2ec.jpg", + "table_caption": [ + "Table 4. Comparison with different classification supervision approaches on ONCE validation dataset." + ], + "table_footnote": [], + "table_body": "
Classification LossAPoverall
Focal Loss [31]55.45 ± 0.07
Score Reweight56.09 ± 0.10
IoU Reweight55.90 ± 0.17
QFocal Loss [27]56.20 ± 0.05
Ours56.80 ± 0.08
", + "bbox": [ + 570, + 347, + 820, + 459 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Strategies on $\\hat{y}$ generation. In this part, we explore the best strategy to generate the classification targets $\\hat{y}$ for the Focal Loss. We first consider utilizing the teacher's predicted categorical confidence to replace the original hard pseudo labels, based on the observation that the quality of the generated pseudo-labels is highly correlated with the classification score. On top of this, we also consider the localization quality between the student and teacher's predictions. The main intuition is that when the student model can not perfectly learn the pseudo-targets well, we infer them as noisy labels and downgrade their categorical targets. Actually, this strategy comes to the same formulation as Quality Focal Loss. In order to further improve the representation ability of $\\hat{y}$ , we adopt the combination of IoU and confidence score to fully leverage the information. We consider two types of combinations: multiplication and weighted sum. The experimental results are shown in Table 5. By combining IoU and confidence score with weighted sum, the detection accuracy gets the best performance.", + "bbox": [ + 496, + 477, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with other regression supervision. In addition to classification targets $\\hat{y}$ , properly softening the regression supervision on noisy pseudo labels is also nontrivial. Therefore, we compare different kinds of regression losses and their tolerance against noisy data. The original loss is Smooth L1 loss, which provides more penalty on more accurate predictions (close to GT targets), encouraging the model to pay more attention to high-precision boxes. However, such a strategy is counter to the learning on noisy", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6935", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e1cf45a3fc4084632a7e067f6ed9f55eaaf46407fae85117e2c28c38f522456d.jpg", + "table_caption": [ + "Table 5. Ablations on the strategies to generate the classification target $\\hat{y}$ for categorical supervision." + ], + "table_footnote": [], + "table_body": "
Cls ScoreIoUOperationAPoverall
✓-55.45 ± 0.07
-56.45 ± 0.17
✓-56.11 ± 0.21
✓✓Multiply56.52 ± 0.05
✓✓Weighted-sum56.80 ± 0.08
", + "bbox": [ + 98, + 119, + 444, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/467505eb89dda5528a8282179dee08e3b77daef37e120673d96b955aad675eff.jpg", + "image_caption": [ + "Figure 3. Visualization of the loss curve of different regression approaches on the labeled split in each batch. We also plot the final detection performance (mAP) at the end iteration of each loss. Note that there exists occasional fluctuations during training probably due to the noisy annotations in the training data, empirically it will not affect the final model performance." + ], + "image_footnote": [], + "bbox": [ + 78, + 250, + 472, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "labels: if the network fails to regress the target well, it probably belongs to low-quality samples. Therefore, we directly employ the L1 loss to avoid large misleading gradients on noisy bounding box regression. Another option to improve the tolerance against noisy labels for regression is to convert the regression task into a probabilistic optimization problem. As a result, we consider the Gaussian NLL as an alternative regression objective. We report the results in Figure 3. Gaussian NLL outperforms all other losses, achieving $56.4\\mathrm{mAP}$ on the validation subset, demonstrating the superiority of the probabilistic model on noisy data learning.", + "bbox": [ + 75, + 595, + 468, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5.3 Dense Feature Consistency Constraint", + "text_level": 1, + "bbox": [ + 76, + 785, + 397, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Strategies on consistency regularization. Consistency learning is a crucial component in semi-supervised pipelines. In most previous work [55], such regularization is often conducted on the label level. A key reason is that label encoding is agnostic to any transformation, which is easy to apply to various object detection tasks. Luckily, most in-", + "bbox": [ + 75, + 809, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "put permutations in point clouds can be easily reversed and differentiable. Therefore, we can also explore the feature-level consistency regularization with L2 loss. Followed by the idea of SimSiam [6], we add a projection layer for one branch and detach the gradient in the other branch, and then regularize them with L2 loss. We also consider distance correlation to consider the inner structural similarity in the latent feature space. The final results are shown in Table 6. The vanilla L2 loss on the feature level obtains the best performance. We infer the reason that mutual L2 introduces additional flexibility through the linear projection layer and further promotes the effect of consistent regularization.", + "bbox": [ + 496, + 90, + 890, + 272 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/dc402457f390a05fdb8d4af61c2bef970e49e268ff709993a374288917e26abd.jpg", + "table_caption": [ + "Table 6. Comparison with different approaches for dense feature consistency constraints. \"DC\" denotes distance correlation." + ], + "table_footnote": [], + "table_body": "
Input-levelLossAP
Label-levelL255.45 ± 0.07
Feature-levelDC56.07 ± 0.14
Feature-levelL256.70 ± 0.06
", + "bbox": [ + 563, + 316, + 825, + 397 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Extension to Auto-Labeling Strategy", + "text_level": 1, + "bbox": [ + 500, + 421, + 815, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Auto-Labeling is a simple and effective strategy to improve model prediction. By combing with additional techniques, such as temporal information or object tracking, we can obtain high-quality pseudo-labels [35]. Different from the Mean-Teacher paradigm, the pseudo-labeling pipeline allows the network to pursue more precious labels offline and greatly improves its potential in real-world applications. In this section, we imitate this paradigm and validate the superiority of our framework. Specifically, we generate the pseudo-labels based on two well-tuned CenterPoint models, (CenterPoint and CenterPoint-E), which achieve 62.5 and $70.1\\mathrm{mAP}$ on the ONCE validation subset, respectively, to stimulate the auto-labeling process and utilize it to supervise a SECOND model. The final results are shown in Table 7. With the quality-improved label, our NoiseDet still consistently outperforms the competitive NoisyStudent baseline, yielding a 1.4 and $2.2\\mathrm{mAP}$ on the ONCE validation subset, demonstrating its effectiveness and generalization on semi-supervised learning tasks.", + "bbox": [ + 496, + 444, + 890, + 731 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2ebb9acd84c2e485833793315ab57d52b8921136941e89724d836090e1c75a4a.jpg", + "table_caption": [ + "Table 7. Detection results on different pseudo-label generation with respective teacher models. The results are reported on ONCE validation dataset. CenterPoint-E denotes for the enhanced version of CenterPoint." + ], + "table_footnote": [], + "table_body": "
PL SourceAPvehAPpedAPcycAPoverall
SECOND [48]75.2637.9660.7758.00
CenterPoint [52]75.4240.1962.7359.44
CenterPoint-E [52]76.0141.5663.0160.19
", + "bbox": [ + 501, + 801, + 890, + 882 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6936", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 89, + 194, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we introduce a pseudo-labeling-based semi-supervised 3D object detection framework, namely NoiseDet. By viewing the semi-supervised learning as a noisy learning task, we propose two core modules to overcome the ambiguity detection problem: noise-resistant instance supervision and dense feature consistency regularization. With soft task supervision on the unlabeled data and unsupervised feature consistency regularization, our model develops tolerance towards noisy pseudo-labels and improves the model generalization. Extensive experiments on the ONCE dataset demonstrate the effectiveness and generalization of our approach. We hope NoiseDet can provide a new perspective in dealing with in-sufficient accuracy pseudo labels for semi-supervised 3D object detection.", + "bbox": [ + 75, + 114, + 472, + 327 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 76, + 339, + 236, + 357 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the JKW Research Funds under Grant 20-163-14-LZ-001-004-01, and the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. We acknowledge the support of GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC.", + "bbox": [ + 75, + 364, + 468, + 455 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 76, + 468, + 174, + 484 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Amir Bar, Xin Wang, Vadim Kantorov, Colorado J Reed, Roei Herzig, Gal Chechik, Anna Rohrbach, Trevor Darrell, and Amir Globerson. DETReg: Unsupervised pretraining with region priors for object detection. In CVPR, pages 14605-14615, 2022. 5", + "[2] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: A holistic approach to semi-supervised learning. NeurIPS, 32:1-11, 2019. 3", + "[3] Navaneeth Bodla, Bharat Singh, Rama Chellappa, and Larry S Davis. Soft-NMS-improving object detection with one line of code. 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In CVPR, pages 4490-4499, 2018. 2" + ], + "bbox": [ + 78, + 90, + 467, + 316 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "6939", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/a3c8a1dc-20e7-4f50-8e36-d4ddc2e6295d_model.json b/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/a3c8a1dc-20e7-4f50-8e36-d4ddc2e6295d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4a4417565dfca5de34e8bb7894dce914aee92dc7 --- /dev/null +++ b/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/a3c8a1dc-20e7-4f50-8e36-d4ddc2e6295d_model.json @@ -0,0 +1,2114 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.145, + 0.131, + 0.828, + 0.154 + ], + "angle": 0, + "content": "Learning with Noisy Data for Semi-Supervised 3D Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.191, + 0.18, + 0.784, + 0.234 + ], + "angle": 0, + "content": "Zehui Chen1 Zhenyu Li2 Shuo Wang1 Dengpan Fu3 Feng Zhao1* \n1University of Science and Technology of China \n2Harbin Institute of Technology 3NIO" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.237, + 0.756, + 0.253 + ], + "angle": 0, + "content": "lovesnow, wangshuo}@mail.ustc.edu.cn zhenyuli17@hit.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.299, + 0.256, + 0.672, + 0.269 + ], + "angle": 0, + "content": "dengpan.fu@nio.com fzhao956@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.474, + 0.775 + ], + "angle": 0, + "content": "Pseudo-Labeling (PL) is a critical approach in semisupervised 3D object detection (SSOD). In PL, delicately selected pseudo-labels, generated by the teacher model, are provided for the student model to supervise the semisupervised detection framework. However, such a paradigm may introduce misclassified labels or loose localized box predictions, resulting in a sub-optimal solution of detection performance. In this paper, we take PL from a noisy learning perspective: instead of directly applying vanilla pseudo-labels, we design a noise-resistant instance supervision module for better generalization. Specifically, we soften the classification targets by considering both the quality of pseudo labels and the network learning ability, and convert the regression task into a probabilistic modeling problem. Besides, considering that self-supervised learning works in the absence of labels, we incorporate dense pixel-wise feature consistency constraints to eliminate the negative impact of noisy labels. To this end, we propose NoiseDet, a simple yet effective framework for semi-supervised 3D object detection. Extensive experiments on competitive ONCE and Waymo benchmarks demonstrate that our method outperforms current semisupervised approaches by a large margin. Notably, our NoiseDet achieves state-of-the-art performance under various dataset scales on ONCE dataset. For example, NoiseDet improves its NoiseStudent baseline from 55.5 mAP to 58.0 mAP, and further reaches 60.2 mAP with enhanced pseudo-label generation. Code will be available at https://github.com/zehuichen123/NoiseDet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.805, + 0.21, + 0.82 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.831, + 0.47, + 0.877 + ], + "angle": 0, + "content": "3D object detection, aiming at detecting instances in the 3D space, is of great importance in various applications. Thanks to the large amount of labeled data, it has achieved" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.303, + 0.886, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.414, + 0.886, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.53, + 0.895, + 0.656 + ], + "angle": 0, + "content": "Figure 1. The noisy predictions generated by a well-trained 3D object detector. Despite carefully tuning the model and filtering low-confidence score predictions, there are still low-quality bounding boxes left. Directly enforcing the detector to learn from such noisy data on an unlabeled dataset can mislead the model convergence or even deteriorate its performance. In the top figure, we demonstrate an inaccurate heading regression case, and the bottom case shows a false positive prediction. We distinguish the ground truth and model predictions with green and blue, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.895, + 0.808 + ], + "angle": 0, + "content": "great success in the past few years [37, 29, 9, 56, 10, 11]. However, labeling a large-scale dataset is extremely time-consuming and labor-intensive [40]. This issue gets much more severe in the 3D object detection task, where 7 degree-of-freedom parameters need to be determined as well as the categorical labels. Therefore, how to further boost the supervised detectors with limited labeled datasets remains a practical and urgent problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Semi-supervised object detection (SSOD) demonstrates great prospects recently due to its simplicity and weak dependence on costly annotations [46, 20, 39]. By leveraging easily accessible unlabeled data, SSOD approaches enhance the model performance with little human effort [47, 43, 51, 25]. The strategies of current SSOD can be" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6929" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.575 + ], + "angle": 0, + "content": "categorized into two main streamlines: Mean-Teacher [41] and Pseudo-Labeling [24]. Mean-Teacher adopts a teacher-student paradigm, where the teacher is initialized from the student model via Exponential Moving Average (EMA) to produce supervised signals on the unlabeled data in an end-to-end training fashion. Inspired by this, more advanced ways, including SESS [55], NoisyStudent [45], are built upon the teacher-student paradigm and achieve significant improvements. Despite the superior performance and elegant pipeline, they are not model-agnostic (i.e. the teacher and student should be the same model) and miss the chance to pursuing high-quality pseudo labels, such as off-board label generation [35]. Another line of work is pseudo labeling [53, 36]: the model is first trained on labeled data and then generated pseudo labels on the unlabeled data for later training. Different from MT, it can be easily applied to any detector without adapting the framework to the teacher-student paradigm. These multi-stage approaches obtain reasonably good results, however, the final performance is often impeded by the quality of pseudo labels. To address this issue, 3DIoUMatch [42] proposes to estimate the localization accuracy predicted by the network and utilizes it as a metric to guide the label generation. ProficientTeacher [51] introduces a clustering-based box voting module to filter low-quality predictions without introducing any handcrafted rule. Although the accuracy of pseudo labels gets greatly improved, it may still fail in certain cases, leading to unstable model convergence. Harsh confidence filtering is proven to be worked well [46], however, we observe that it is still hard to remove all misleading instances for generated labels, which can distract the model convergence, shown in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.585, + 0.473, + 0.904 + ], + "angle": 0, + "content": "In this paper, we acknowledge the existence of noise in the generated labels and take PL as a noisy learning task: instead of directly applying vanilla pseudo-labels, we design a noise-resistant instance supervision module for better model generalization. Specifically, for the classification branch, we leverage the confidence predictions from the teacher and the student model learning ability to construct soft categorical targets. Different from previous approaches [47, 28], which simply apply them for loss reweighting, we enforce the network to directly learns from such continual supervision. In this way, our strategy can adaptively learn more knowledge from the teacher's predictions and at the same time develop tolerance to low confidence score labels. As for the regression branch, we find that solely relying on classification scores or IoU predictions is not enough to reflect the learning quality of each attribute of the 3D box. To mitigate this problem, we convert the original smooth L1 regression into a probabilistic modeling task: by enabling the network to output two variables to represent the Gaussian distribution, we maximize the negative log-likelihood of the targets in the distribution. Apart from the label supervi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.212 + ], + "angle": 0, + "content": "sion on the unlabeled data, we also introduce a novel dense pixel-wise feature self-supervised consistency constraints to further eliminate the negative impact of noisy data. To this end, we propose NoiseDet, a simple semi-supervised 3D object detection framework to address the noise learning problem from the unlabeled data. Our NoiseDet is modal-agnostic and can be easily applied to any 3D object detector with little modification." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.213, + 0.84, + 0.228 + ], + "angle": 0, + "content": "We summarize our key contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.24, + 0.892, + 0.316 + ], + "angle": 0, + "content": "- Instead of directly improving the quality of pseudolabels, we formulate SSOD as a noisy learning problem, where we acknowledge the existence of the noise in pseudo-labels and soften the network supervision for model generalization." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.327, + 0.892, + 0.403 + ], + "angle": 0, + "content": "- Based on this thought, we propose NoiseDet, a simple yet effective SSOD framework to deal with the noisy data through two core modules: noise-resistant instance supervision and dense pixel-wise feature consistency constraint." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.415, + 0.892, + 0.475 + ], + "angle": 0, + "content": "- With extensive experiments, we validate the effectiveness of our approach on two competitive benchmarks. Notably, it achieves state-of-the-art performance on the challenging ONCE dataset." + }, + { + "type": "list", + "bbox": [ + 0.517, + 0.24, + 0.892, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.49, + 0.642, + 0.505 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.515, + 0.803, + 0.531 + ], + "angle": 0, + "content": "2.1. LiDAR-based 3D Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.895, + 0.903 + ], + "angle": 0, + "content": "3D object detection aims to detect instances in the 3D space, which is of great importance in various applications, such as autonomous driving, navigation robot, and augmented reality. Current LiDAR detectors [52, 59, 49] mainly voxelize the point cloud into a BEV or voxel representations and adopt traditional 2D convolutions to predict bounding boxes. To improve the inference speed, some works [15, 30] attempt to detect objects directly through the range view. [58] combines both BEV and range-view features together to achieve better performance. VoxelNet [59] adopts PointNet [34] to extract local features through raw point clouds and fill them into the predefined voxel space. PointPillar [22] directly processes points inside a pillar to naturally formulate BEV feature representations, establishing an ultra-fast baseline detector. Inspired by CenterNet [14], CenterPoint [52] introduces a center-based label assignment strategy in 3D object detection, achieving competitive detection accuracy among various approaches. In addition to dense one-stage detectors, many works [8, 38] apply an R-CNN-style two-stage detection paradigm. Point R-CNN [38] propose 3D RoIAlign to aggregate regional features based on the proposals and then refines the detections. PV-RCNN [37] and Voxel R-CNN [13] construct two-parallel branches to extract both point-level and voxel" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6930" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.168 + ], + "angle": 0, + "content": "level features to enjoy the best of each. However, independently localizing moving instances can introduce misalignment noise, 3D-MAN [50] and MPPNet [7] leverage multi-frame information to further enhance predictions with temporal knowledge." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.178, + 0.367, + 0.194 + ], + "angle": 0, + "content": "2.2. Semi-Supervised Learning (SSL)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.201, + 0.473, + 0.52 + ], + "angle": 0, + "content": "Semi-supervised learning is an important task in leveraging easy-to-access unlabeled data to improve the supervised model. Most current SSL methods [53, 17, 5, 19] involve adding additional supervision on unlabeled data to regularize the learning of the model. Among them, pseudolabeling is a popular pipeline [4, 24, 18], where unlabeled data is firstly labeled with a supervised model, and then acts in a common training paradigm. In order to guarantee the quality of the generated labels, [24] often filter them with a hard threshold based on the classification score. In addition to hard pseudo-labels, NoisyStudent [45] explores soft supervision to avoid ambiguity problems. Besides, it injects different augmentations to the student and teacher models, to encourage consistency regularization. In light of this, plenty of approaches [44, 2, 26] enforce the model to predict similar results when applying various input permutations. Such strategies are also verified on 2D object detection, where [32] borrows the idea from FixMatch to achieve promising performance. MUM [21] introduces Mix/UnMix augmentation, enforcing students to reconstruct unmixed features for the mixed input images." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.53, + 0.403, + 0.546 + ], + "angle": 0, + "content": "2.3. Semi-Supervised 3D Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Semi-supervised learning (SSL) has been rapidly developed in both classification and object detection domains and obtains promising results in recent years. There are two main streams in SSOD: consistency learning and pseudo labeling. Consistency-based works [41, 25] apply data augmentations/perturbations to the input, which forms natural regularization for the network predictions. Such a consistency-learning target enforces the model to acquire valid information from the unlabeled data, therefore improving the performance. SESS [55] is the first work to attempt such a paradigm on 3D object detection, where the classification and regression predictions are matched through L2 distance and supervised with the similarity loss on the teacher and student. Inspired by Mean Teacher [41], it also adopts the exponential moving average (EMA) technique to further boost the performance. Apart from the consistency-based approaches, pseudo-labeling is another solution [46, 42]. Most PL works pay attention to the quality enhancement of pseudo labels. 3DIoUMatch [42] proposes to learn the IoU of the network predictions and utilize it to adaptively filter the low-quality pseudo labels. In order to remove the duplicate score threshold search, ProficientTeacher [51] introduces a novel clustering-based box voting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "module, replacing the hand-crafted NMS process. Different from the previous approaches, our method views pseudolabeling as a noisy learning problem, therefore delivering more generalization against noisy pseudo-data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.164, + 0.602, + 0.18 + ], + "angle": 0, + "content": "3. NoiseDet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.189, + 0.892, + 0.295 + ], + "angle": 0, + "content": "It is acknowledged that predictions generated by the teacher model will inevitably encounter false positive (FP) or false negative (FN) problems, despite many efforts that have been devoted to overcoming these issues [51, 46]. Such noises can distract the convergence of the model during the semi-supervised training process, or even deteriorate the final performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.893, + 0.54 + ], + "angle": 0, + "content": "The main intuition of NoiseDet is to improve the model generalization ability against noisy pseudo labels, which are generated by the baseline model trained on limited labeled data. We start with a vanilla two-stage pseudo-labeling pipeline: assuming that we have access to a (small) set of labeled set \\( L = \\{x_i^l,y_i^l\\}_{i = 1}^{N_l} \\), and a set of unlabeled set \\( U = \\{x_i^u\\}_{i = 1}^{N_u} \\), where \\( N_{l} \\) and \\( N_{u} \\) are the numbers of labeled and unlabeled datasets. A teacher model is firstly trained on the labeled set \\( L \\), and then infer on unlabeled set \\( U \\) to get pseudo labels \\( \\{y_i^u\\}_{i = 1}^{N_u} \\) and formulate the pseudo-labeled set \\( U_{p} = \\{x_{i}^{u},y_{i}^{u}\\} \\). After that, we initialize the student model from the pretrained teacher and uniformly sample data from both \\( L \\) and \\( U_{p} \\) set to construct each batch for second-stage training. Different from previous works, which mainly focus on improving the quality of pseudo-labels, NoiseDet directly learns knowledge from noise labels \\( \\{y_i^U\\}_{i = 1}^{N_u} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.546, + 0.821, + 0.562 + ], + "angle": 0, + "content": "3.1. Noise-Resistant Instance Supervision" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.704 + ], + "angle": 0, + "content": "In contrast to standard fully supervised object detection, where labels are carefully human-annotated and verified, the supervisory signals on the unlabeled set are generated by the vanilla teacher model. It may contain unexpected noisy labels, leading to model performance degeneration. Therefore, we propose to transform such hard, deterministic instance supervision into the noise-resistant one to develop the model tolerance to the noisy labels, instead of directly eliminating them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recent works [16, 3] suggests that the confidence score \\( c \\) can be viewed as the noisy level of the network predictions, i.e., the model is more prone to yield a high score for easy-to-detect samples and low score for not-sure samples. Therefore, an intuitive idea is to filter the generated pseudo-labels with a pre-defined score threshold \\( U_{p} = \\{(x_{i}^{u},c_{i}^{u})|c_{i}^{u}\\geq c_{thres}\\} \\) to eliminate the noises for the unlabeled dataset. Though simple, such a strategy does not provide a clear divergence for the rest labels. For instance, the quality of a box with \\( c = 0.9 \\) can be different from the quality of the box with \\( c = 0.5 \\). However, they are treated equally with 1/0 labels in the classification branch. To fully exploit a reliable confidence score derived from the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6931" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.895, + 0.44 + ], + "angle": 0, + "content": "Figure 2. The overall architecture of the proposed NoiseDet. It consists of two main components: noise-resistant instance supervision and dense feature consistency constraint. It follows the pseudo-labeling practice with a two-stage training paradigm: (i) pseudo labels are pre-generated with a well-trained teacher model on the unlabeled dataset, and (ii) the student model is trained on both labeled (omitted in the figure) and unlabeled LiDAR points in a semi-supervised manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.465, + 0.473, + 0.676 + ], + "angle": 0, + "content": "teacher model, we leverage the \\( c \\) as an indicator to measure the quality of the pseudo label. Specifically, instead of directly assigning each anchor with a deterministic binary label, we soften the categorical label into a value ranging from 0 to 1 given the confidence score \\( c \\) as well as the IoU \\( \\tau \\) between the student predictions and its matched pseudo labels. Different from the one in GFL [27] where the categorical labels are assigned based on the IoU between the network prediction and the ground-truth boxes, we view it as the combination of the quality of the GT boxes itself and the learning ability of the student. Since the standard Focal Loss can only handle discrete binary values, we adopt Quality Focal Loss [27] to conduct the classification supervision on the non-discrete categorical labels:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.688, + 0.47, + 0.704 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\alpha c + (1 - \\alpha) \\tau , \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.707, + 0.47, + 0.725 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c l s} ^ {U} = - | y - \\hat {y} | ^ {\\beta} ((1 - y) \\log (1 - \\hat {y}) + y \\log (\\hat {y})), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.81 + ], + "angle": 0, + "content": "where \\(\\hat{y}\\) is the quality score predicted by the teacher and \\(y\\) is the student predictions, \\(\\alpha\\) is set to 0.75. Note that our approach can be easily extended into other continual versions of cross-entropy loss, for instance, Gaussian Focal Loss [23]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In addition to the classification loss, the boundary targets of the bounding box can present more ambiguities since it contains 7 degree-of-freedom and presents fewer training samples (only positive samples receive the regression supervision). Therefore, how to effectively deal with misleading regression targets is non-trivial. To address this problem," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.893, + 0.525 + ], + "angle": 0, + "content": "we convert the deterministic regression into the probability optimization task. Concretely, we model the network prediction of each bounding box as a Gaussian distribution \\( h \\) given the feature vector \\( x \\):" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.536, + 0.893, + 0.556 + ], + "angle": 0, + "content": "\\[\n\\hat {h} = \\mathcal {N} (\\mu (x), \\sigma (x)), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.894, + 0.643 + ], + "angle": 0, + "content": "where \\(\\mu (x)\\) and \\(\\sigma (x)\\) denotes the mean and variance of each regression term predicted by the network. After that, the regression loss can be converted into a negative log-likelihood (NLL) loss, where the objective is to maximize the likelihood of each GT \\(h\\) in the predicted distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.654, + 0.891, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e g} = - \\log \\mathcal {N} (h; \\mu (x), \\sigma (x)) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.674, + 0.892, + 0.706 + ], + "angle": 0, + "content": "\\[\n= - \\log \\frac {1}{\\sigma \\sqrt {2 \\pi}} e ^ {- \\frac {1}{2} \\left(\\frac {h - \\mu}{\\sigma}\\right) ^ {2}}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.777 + ], + "angle": 0, + "content": "By converting the deterministic regression task to a probabilistic estimation problem, the model develops more tolerance against noisy information in the training data, therefore achieving better performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.831, + 0.803 + ], + "angle": 0, + "content": "3.2. Dense Feature Consistency Constraint" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Considering that labels can contain noise information that deteriorates the model performance, we further exploit the incorporation of unsupervised learning to obtain useful knowledge about label-independent features. However, different from the common-studied image classification task that mostly cares about the overall feature representation," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6932" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.227 + ], + "angle": 0, + "content": "3D object detection requires estimating instances with various scales and directions. Therefore, learning a scale and rotation-invariant feature extractor for 3D detector is of vital importance. By applying various data augmentation, such as rescaling, rotating, and global transforming, into the input point clouds, and supervising them with the transformed ground-truth boxes, the model can develop robustness to such transformations. However, when the label itself is not so accurate enough, such a strategy may be more harmful." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.471, + 0.454 + ], + "angle": 0, + "content": "To avoid this problem, we propose a dense pixel-wise consistency constraint to enforce the network to acquire such property. Previous literature mainly involves label-level consistency [55, 42, 1, 54] to ensure the model consistency, where the predicted bounding boxes are reversed back to the original space and regularized with Euclidean distance matching. Despite being simple and straightforward, this low-dimensional prediction distribution (number of classes and 7 regression targets) means that only a few amounts of knowledge are encoded, thus limiting the knowledge that can be transferred. Hence, we apply the consistency constraint on the feature level by reversing the BEV features according to the data transformation in the data augmentation and then conducting dense pixel-wise regularization." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.455, + 0.47, + 0.547 + ], + "angle": 0, + "content": "More formally, given one frame of point clouds \\(P\\) and a set of data augmentation policies \\(\\mathcal{A}\\), we randomly sample two transformations \\(\\mathcal{A}_1, \\mathcal{A}_2\\) from \\(\\mathcal{A}\\) and apply them to the point \\(P\\) to produce two different views of point clouds \\(P_1, P_2\\). The augmented point clouds are fed into the point feature extractor \\(\\mathcal{F}\\) to generate the BEV feature maps \\(F\\):" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.559, + 0.47, + 0.577 + ], + "angle": 0, + "content": "\\[\nF _ {1} = \\mathcal {F} (P _ {1}), F _ {2} = \\mathcal {F} (P _ {2}). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.589, + 0.469, + 0.634 + ], + "angle": 0, + "content": "Once obtaining the BEV features, we simply reverse them back to the original space with the recorded transformation flow:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.646, + 0.469, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\hat {F} _ {1} = \\mathcal {A} _ {1} ^ {- 1} \\left(F _ {1}\\right), \\hat {F} _ {2} = \\mathcal {A} _ {2} ^ {- 1} \\left(F _ {2}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.677, + 0.469, + 0.721 + ], + "angle": 0, + "content": "where \\(A^{-1}\\) denotes the reverse transformation of \\(A\\). To this end, we can derive the pixel-wise feature consistency constraint with standard L2 loss:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.734, + 0.469, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n s i s t}} = \\left| \\left| \\hat {F} _ {1} - \\hat {F} _ {2} \\right| \\right| _ {2}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Considering that the point-based 3D features can hold meaningful information only if the point exists, mainly due to the characteristics of the LiDAR points, we further introduce a foreground-focusing mask to selectively regularize the augmented BEV features. Different from previous approaches [12] that directly set each foreground GT region with hard supervision, we generate a soft mask to smooth the regularization effect at the boundary regions, similar in [57]. Specifically, we draw a Gaussian distribution for each" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.744, + 0.108 + ], + "angle": 0, + "content": "GT center \\((x_{i},y_{i})\\) in the BEV space," + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.118, + 0.892, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\phi_ {i, x, y} = \\exp \\left(\\frac {\\left(x _ {i} - \\hat {x} _ {i}\\right) ^ {2} + \\left(y _ {i} - \\hat {y} _ {i}\\right) ^ {2}}{2 \\sigma_ {i} ^ {2}}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.163, + 0.892, + 0.239 + ], + "angle": 0, + "content": "where \\(\\sigma_{i}\\) is a constant (set to 2), indicating the object size standard deviation. Since feature maps are class-agnostic, we merge all \\(\\phi_{i,x,y}\\) into one single mask \\(\\Phi\\) by taking the maximum value across the \\(i\\) dimension. Therefore, the final dense feature consistency constraint is derived as:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.25, + 0.892, + 0.294 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n s i s t}} = \\frac {1}{H W \\Phi} \\sum_ {i} ^ {H} \\sum_ {j} ^ {W} \\max \\left(\\phi_ {i j}\\right) \\left| \\left| \\hat {F} _ {1} - \\hat {F} _ {2} \\right| \\right| _ {2}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.306, + 0.892, + 0.366 + ], + "angle": 0, + "content": "By aligning dense pixel-wise features on the BEV space, the model can gradually learn the ability to extract transform-invariant feature extraction and fully utilize the unlabeled data in a self-supervised manner." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.381, + 0.632, + 0.397 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.405, + 0.602, + 0.42 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.429, + 0.892, + 0.717 + ], + "angle": 0, + "content": "ONCE dataset [33] is one of the largest autonomous driving datasets with 1 million LiDAR point clouds and 7 million paired images. Only 15,000 samples are annotated with 3D bounding boxes, which are divided into training, validation and testing split with a ratio of \\(33\\% /20\\% /47\\%\\), respectively. Among all instances, five classes are labeled as interested categories: Car, Bus, Truck, Pedestrian, and Cyclist. According to the official SSL setting, 5,000 samples are selected as labeled set and all the unlabeled sets are divided into 3 scales of subsets: Small, Medium, and Large. The small set contains 70 sequences (100k samples), the medium set contains 321 sequences (500k samples), and the large set contains 560 sequences (about 1M samples). Following the official evaluation tools, we set 0.7, 0.3, and 0.5 for Vehicle, Pedestrian, and Cyclist as the mAP IoU threshold, respectively. Besides, similar to Waymo Open Dataset [40], the evaluation protocol provides metrics based on different perception ranges: '0-30m', '30-50m', and /'50minf' to fully reflect the detection ability of the model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.719, + 0.743 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "NoiseDet follows the two-stage training pipeline: we first train the teacher network with 80 epochs for ONCE dataset. Then we utilize the STE module proposed in ProficientTeacher [51] to obtain pseudo-labels on the unlabeled dataset. During this process, we can easily incorporate other techniques such as camera/Radar detection or object tracking to further refine the labels. We do not consider such implementations since it is out of the scope of this paper, but it is proven to be effective in [35]. For the semi-supervised training configuration, we uniformly sampled 1 labeled and" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6933" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.088, + 0.895, + 0.144 + ], + "angle": 0, + "content": "Table 1. Comparison with other state-of-the-art semi-supervised 3D object detection approaches on ONCE validation set with different amounts of unlabeled samples (e.g., \"Small\", \"Medium\" and \"Large\"). We bold the best overall results and list the relative gains based on the baseline model (i.e., SECOND [48] trained on labeled training set only) for better illustration. Most experimental results are borrowed from the official implementations in ONCE [33]." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.147, + 0.887, + 0.427 + ], + "angle": 0, + "content": "
MethodsVehicle AP (%)Pedestrian AP (%)Cyclist AP (%)mAP (%)
overall0-30m30-50m50m-infoverall0-30m30-50m50m-infoverall0-30m30-50m50m-inf
Baseline [48]71.1984.0463.0247.2526.4429.3324.0518.0558.0469.9652.4334.6151.89
Small (100K unlabeled samples)
Pseudo Label72.8084.4664.9751.4625.5028.3622.6618.5155.3765.9550.3434.4251.22 (-0.67)
Noisy Student [45]73.6984.6967.7253.4128.8133.2323.4216.9354.6765.5850.4332.6552.39 (+0.50)
Mean Teacher [41]74.4686.6568.4453.5930.5434.2426.3120.1261.0272.5155.2439.1155.34 (+3.45)
SESS [55]73.3384.5266.2252.8327.3131.1123.9419.0159.5271.0353.9336.6853.39 (+1.50)
3D IoUMatch [42]73.8184.6168.1154.4830.8635.8725.5518.3056.7768.0251.8035.9153.81 (+1.92)
NoiseDet (Ours)75.2686.3667.5255.2937.9642.3632.7823.2860.7772.3155.0338.8758.00 (+6.11)
Medium (500K unlabeled samples)
Pseudo Label73.0386.0665.9651.4224.5627.2820.8117.0053.6165.2648.4433.5850.40 (-1.49)
Noisy Student [45]75.5386.5269.7855.0531.5635.8026.2421.2158.9369.6153.7336.9455.34 (+3.45)
Mean Teacher [41]76.0186.4770.3455.9235.5840.8630.4419.8263.2174.8956.7740.2958.27 (+6.38)
SESS [55]72.1184.0666.4453.6133.4438.5828.1018.6761.8273.2056.6038.7355.79 (+3.90)
3D IoUMatch [42]75.6986.4670.2256.0634.1438.8429.1919.6258.9369.0854.1638.8756.25 (+4.36)
NoiseDet (Ours)77.1487.2169.9458.4440.4544.9135.7124.1162.5973.0457.9842.6760.06 (+8.17)
Large (1M unlabeled samples)
Pseudo Label72.4184.0664.5450.0523.6226.8020.1316.6653.2564.6948.5233.4749.76 (-2.13)
Noisy Student [45]75.5386.5269.7855.0531.5635.8026.2421.2158.9369.6153.7336.9455.34 (+3.45)
MeanTeacher [41]76.3886.4570.9957.4835.9541.7629.0518.8165.5075.7260.0743.6659.28 (+7.39)
SESS [55]75.9586.8370.4555.7634.4340.0027.9219.2063.5874.8558.8839.5157.99 (+6.10)
3D IoUMatch [42]75.8186.1171.8257.8435.7040.6830.3421.1559.6970.6954.9239.0857.07 (+5.18)
NoiseDet (Ours)78.0287.0072.5559.4942.8946.5238.2126.6062.7473.1958.0342.8861.16 (+9.27)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.457, + 0.471, + 0.486 + ], + "angle": 0, + "content": "Table 2. Comparison of detection results based on SECOND and CenterPoint with and without NoiseDet on ONCE validation set." + }, + { + "type": "table", + "bbox": [ + 0.132, + 0.489, + 0.418, + 0.591 + ], + "angle": 0, + "content": "
DetectorMethodmAP
SECONDNoisyStudent55.50
NoiseDet (Ours)58.01
CenterPointNoisyStudent63.77
NoiseDet (Ours)65.57
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.74 + ], + "angle": 0, + "content": "4 unlabeled samples for each batch to avoid training collapse. Following the official ONCE benchmark [33], we initialize the student from a pretrained checkpoint on the full labeled set. The student is trained for 25, 50, 75 epochs for small, medium, and large settings on ONCE dataset. The learning rate is set to 1e-4 and the pseudo-labels are updated every 25 epochs. All models are trained on an 8 NVIDIA V100 GPUs machine." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.216, + 0.77 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We first implement NoiseDet with the standard anchor-based 3D detector, SECOND, following the official benchmark [33], on the Small protocol setting of ONCE dataset. The final performance is shown in Table 2. Our NoiseDet greatly boosts its enhanced baseline NoisyStudent [45] by \\(2.5\\mathrm{mAP}\\). Then, we also report it on a stronger anchor-free-based detector, CenterPoint [52], which also obtains an improvement of \\(1.8\\mathrm{mAP}\\), validating the effectiveness and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.524 + ], + "angle": 0, + "content": "generalization of the proposed method under different 3D detection frameworks. Besides, we also validate NoiseDet on the competitive Waymo Open Dataset [40] in Appendix, which outperforms 3DIoUMatch [42] by a large margin." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.547, + 0.807, + 0.564 + ], + "angle": 0, + "content": "4.4. Comparison with State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.892, + 0.789 + ], + "angle": 0, + "content": "To further validate the superiority of our method, we compare NoiseDet with various state-of-the-art semi-supervised approaches, including Pseudo-Label, NoisyStudent, Mean Teacher, SESS, and 3DIouMatch. The experiments are conducted on the three different protocols (Small, Medium, and Large) to fully exploit the extensibility of various strategies and the results are reported in Table 1. We select SECOND as our baseline to keep consistent with other works [33]. NoiseDet surpasses all other counterparts, achieving new state-of-the-art in this competitive benchmark. With the increase of the unlabeled dataset size, NoiseDet can consistently improve the detectors with significant gains: with \\(6.1\\mathrm{mAP}\\), \\(8.2\\mathrm{mAP}\\), and \\(9.3\\mathrm{mAP}\\) under Small, Medium, and Large protocols, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.812, + 0.666, + 0.828 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.894, + 0.903 + ], + "angle": 0, + "content": "In this section, we conduct a series of ablation studies to gain a deeper understanding of NoiseDet. For efficiency, all experiments are conducted on the Small protocol of the ONCE training set and evaluated on the validation set." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6934" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.119, + 0.088, + 0.851, + 0.102 + ], + "angle": 0, + "content": "Table 3. Effectiveness of each component in our NoiseDet. Results are reported on ONCE validation subset with SECOND." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.106, + 0.875, + 0.233 + ], + "angle": 0, + "content": "
Noise-Resistant Instance Supervision ClassificationRegressionDense Feature Consistency ConstraintmAP
\\( AP_{veh} \\)\\( AP_{ped} \\)\\( AP_{cyc} \\)\\( AP_{overall} \\)
72.0336.8057.7355.50
✓72.7836.4160.7356.80
✓73.8736.7458.3456.39
✓✓74.0536.6261.0357.27
✓✓✓75.2637.9660.7758.01
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.257, + 0.241, + 0.272 + ], + "angle": 0, + "content": "4.5.1 Main Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.282, + 0.473, + 0.584 + ], + "angle": 0, + "content": "In order to understand the effectiveness of each module contributing to the detection performance in NoiseDet, we test each component separately on the baseline detector SEC-OND and report the results in Table 3. Our baseline is the enhanced implementation of NoisyStudent [45], where its performance starts from \\(55.5\\mathrm{mAP}\\) on the validation dataset. When we add the noise-resistant instance supervision on the classification branch, the mAP score is raised by \\(1.1\\mathrm{mAP}\\). And then we test the proposed component on the regression branch, which yields another \\(0.8\\mathrm{mAP}\\). Such a huge improvement validates the correctness of the noise learning strategy on the unknown quality of pseudo-labels and the effectiveness of the proposed noise-resistant instance supervision module. When the dense feature consistency constraint module is applied, the accuracy is promoted by \\(1.2\\mathrm{mAP}\\), suggesting that consistent regularization provides useful unsupervised hints for model convergence. Finally, we put all techniques together, and NoiseDet achieves 58.0 mAP on the validation subset, indicating a \\(2.5\\mathrm{mAP}\\) performance enhancement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.39, + 0.62 + ], + "angle": 0, + "content": "4.5.2 Noise-Resistant Instance Supervision" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Comparison with other classification supervision. We first compare our proposed noise-resistant classification loss with other supervision approaches. The vanilla strategy is to directly apply Focal Loss on the pseudo labels, similar to the labeled data. Then, we attempt to utilize the predicted score from the teacher to adjust the supervision on the pseudo-labels by reweighting the classification loss. In doing this, we can alleviate the training distraction from low-quality samples by lowering their penalties. Inspired by 3D IoUMatch [42], we consider IoU as another measurement to help decide the loss penalty on the pseudo samples (denoted as IoU Reweight). We also consider Quality Focal Loss proposed in [27] to further integrate IoU into the classification supervision. The final results are shown in Table 4. Incorporating reweighting mechanisms, either IoU or classification score, to balance the supervision across different samples brings about \\(0.5\\mathrm{mAP}\\) improvements. When adapting to QFL, the model improves to \\(56.2\\mathrm{mAP}\\). Finally," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.257, + 0.892, + 0.303 + ], + "angle": 0, + "content": "by both considering localization quality (IoU) and the sample quality (classification score), we obtain the best performance, \\(56.8\\mathrm{mAP}\\) on the validation subset." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.315, + 0.892, + 0.343 + ], + "angle": 0, + "content": "Table 4. Comparison with different classification supervision approaches on ONCE validation dataset." + }, + { + "type": "table", + "bbox": [ + 0.571, + 0.348, + 0.821, + 0.46 + ], + "angle": 0, + "content": "
Classification LossAPoverall
Focal Loss [31]55.45 ± 0.07
Score Reweight56.09 ± 0.10
IoU Reweight55.90 ± 0.17
QFocal Loss [27]56.20 ± 0.05
Ours56.80 ± 0.08
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Strategies on \\(\\hat{y}\\) generation. In this part, we explore the best strategy to generate the classification targets \\(\\hat{y}\\) for the Focal Loss. We first consider utilizing the teacher's predicted categorical confidence to replace the original hard pseudo labels, based on the observation that the quality of the generated pseudo-labels is highly correlated with the classification score. On top of this, we also consider the localization quality between the student and teacher's predictions. The main intuition is that when the student model can not perfectly learn the pseudo-targets well, we infer them as noisy labels and downgrade their categorical targets. Actually, this strategy comes to the same formulation as Quality Focal Loss. In order to further improve the representation ability of \\(\\hat{y}\\), we adopt the combination of IoU and confidence score to fully leverage the information. We consider two types of combinations: multiplication and weighted sum. The experimental results are shown in Table 5. By combining IoU and confidence score with weighted sum, the detection accuracy gets the best performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Comparison with other regression supervision. In addition to classification targets \\(\\hat{y}\\), properly softening the regression supervision on noisy pseudo labels is also nontrivial. Therefore, we compare different kinds of regression losses and their tolerance against noisy data. The original loss is Smooth L1 loss, which provides more penalty on more accurate predictions (close to GT targets), encouraging the model to pay more attention to high-precision boxes. However, such a strategy is counter to the learning on noisy" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6935" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.47, + 0.116 + ], + "angle": 0, + "content": "Table 5. Ablations on the strategies to generate the classification target \\(\\hat{y}\\) for categorical supervision." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.12, + 0.446, + 0.238 + ], + "angle": 0, + "content": "
Cls ScoreIoUOperationAPoverall
✓-55.45 ± 0.07
-56.45 ± 0.17
✓-56.11 ± 0.21
✓✓Multiply56.52 ± 0.05
✓✓Weighted-sum56.80 ± 0.08
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.251, + 0.473, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.486, + 0.47, + 0.571 + ], + "angle": 0, + "content": "Figure 3. Visualization of the loss curve of different regression approaches on the labeled split in each batch. We also plot the final detection performance (mAP) at the end iteration of each loss. Note that there exists occasional fluctuations during training probably due to the noisy annotations in the training data, empirically it will not affect the final model performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.765 + ], + "angle": 0, + "content": "labels: if the network fails to regress the target well, it probably belongs to low-quality samples. Therefore, we directly employ the L1 loss to avoid large misleading gradients on noisy bounding box regression. Another option to improve the tolerance against noisy labels for regression is to convert the regression task into a probabilistic optimization problem. As a result, we consider the Gaussian NLL as an alternative regression objective. We report the results in Figure 3. Gaussian NLL outperforms all other losses, achieving \\(56.4\\mathrm{mAP}\\) on the validation subset, demonstrating the superiority of the probabilistic model on noisy data learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.398, + 0.801 + ], + "angle": 0, + "content": "4.5.3 Dense Feature Consistency Constraint" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Strategies on consistency regularization. Consistency learning is a crucial component in semi-supervised pipelines. In most previous work [55], such regularization is often conducted on the label level. A key reason is that label encoding is agnostic to any transformation, which is easy to apply to various object detection tasks. Luckily, most in-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.273 + ], + "angle": 0, + "content": "put permutations in point clouds can be easily reversed and differentiable. Therefore, we can also explore the feature-level consistency regularization with L2 loss. Followed by the idea of SimSiam [6], we add a projection layer for one branch and detach the gradient in the other branch, and then regularize them with L2 loss. We also consider distance correlation to consider the inner structural similarity in the latent feature space. The final results are shown in Table 6. The vanilla L2 loss on the feature level obtains the best performance. We infer the reason that mutual L2 introduces additional flexibility through the linear projection layer and further promotes the effect of consistent regularization." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.284, + 0.892, + 0.313 + ], + "angle": 0, + "content": "Table 6. Comparison with different approaches for dense feature consistency constraints. \"DC\" denotes distance correlation." + }, + { + "type": "table", + "bbox": [ + 0.564, + 0.318, + 0.826, + 0.398 + ], + "angle": 0, + "content": "
Input-levelLossAP
Label-levelL255.45 ± 0.07
Feature-levelDC56.07 ± 0.14
Feature-levelL256.70 ± 0.06
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.816, + 0.439 + ], + "angle": 0, + "content": "4.6. Extension to Auto-Labeling Strategy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.732 + ], + "angle": 0, + "content": "Auto-Labeling is a simple and effective strategy to improve model prediction. By combing with additional techniques, such as temporal information or object tracking, we can obtain high-quality pseudo-labels [35]. Different from the Mean-Teacher paradigm, the pseudo-labeling pipeline allows the network to pursue more precious labels offline and greatly improves its potential in real-world applications. In this section, we imitate this paradigm and validate the superiority of our framework. Specifically, we generate the pseudo-labels based on two well-tuned CenterPoint models, (CenterPoint and CenterPoint-E), which achieve 62.5 and \\(70.1\\mathrm{mAP}\\) on the ONCE validation subset, respectively, to stimulate the auto-labeling process and utilize it to supervise a SECOND model. The final results are shown in Table 7. With the quality-improved label, our NoiseDet still consistently outperforms the competitive NoisyStudent baseline, yielding a 1.4 and \\(2.2\\mathrm{mAP}\\) on the ONCE validation subset, demonstrating its effectiveness and generalization on semi-supervised learning tasks." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.743, + 0.892, + 0.798 + ], + "angle": 0, + "content": "Table 7. Detection results on different pseudo-label generation with respective teacher models. The results are reported on ONCE validation dataset. CenterPoint-E denotes for the enhanced version of CenterPoint." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.803, + 0.892, + 0.883 + ], + "angle": 0, + "content": "
PL SourceAPvehAPpedAPcycAPoverall
SECOND [48]75.2637.9660.7758.00
CenterPoint [52]75.4240.1962.7359.44
CenterPoint-E [52]76.0141.5663.0160.19
" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6936" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.196, + 0.106 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.473, + 0.328 + ], + "angle": 0, + "content": "In this paper, we introduce a pseudo-labeling-based semi-supervised 3D object detection framework, namely NoiseDet. By viewing the semi-supervised learning as a noisy learning task, we propose two core modules to overcome the ambiguity detection problem: noise-resistant instance supervision and dense feature consistency regularization. With soft task supervision on the unlabeled data and unsupervised feature consistency regularization, our model develops tolerance towards noisy pseudo-labels and improves the model generalization. Extensive experiments on the ONCE dataset demonstrate the effectiveness and generalization of our approach. We hope NoiseDet can provide a new perspective in dealing with in-sufficient accuracy pseudo labels for semi-supervised 3D object detection." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.34, + 0.238, + 0.358 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.47, + 0.456 + ], + "angle": 0, + "content": "This work was supported by the JKW Research Funds under Grant 20-163-14-LZ-001-004-01, and the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. We acknowledge the support of GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.469, + 0.175, + 0.485 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.493, + 0.47, + 0.563 + ], + "angle": 0, + "content": "[1] Amir Bar, Xin Wang, Vadim Kantorov, Colorado J Reed, Roei Herzig, Gal Chechik, Anna Rohrbach, Trevor Darrell, and Amir Globerson. DETReg: Unsupervised pretraining with region priors for object detection. In CVPR, pages 14605-14615, 2022. 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.564, + 0.47, + 0.619 + ], + "angle": 0, + "content": "[2] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: A holistic approach to semi-supervised learning. 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In PL, delicately selected pseudo-labels, generated by the teacher model, are provided for the student model to supervise the semisupervised detection framework. However, such a paradigm may introduce misclassified labels or loose localized box predictions, resulting in a sub-optimal solution of detection performance. In this paper, we take PL from a noisy learning perspective: instead of directly applying vanilla pseudo-labels, we design a noise-resistant instance supervision module for better generalization. Specifically, we soften the classification targets by considering both the quality of pseudo labels and the network learning ability, and convert the regression task into a probabilistic modeling problem. Besides, considering that self-supervised learning works in the absence of labels, we incorporate dense pixel-wise feature consistency constraints to eliminate the negative impact of noisy labels. To this end, we propose NoiseDet, a simple yet effective framework for semi-supervised 3D object detection. Extensive experiments on competitive ONCE and Waymo benchmarks demonstrate that our method outperforms current semisupervised approaches by a large margin. Notably, our NoiseDet achieves state-of-the-art performance under various dataset scales on ONCE dataset. For example, NoiseDet improves its NoiseStudent baseline from 55.5 mAP to 58.0 mAP, and further reaches 60.2 mAP with enhanced pseudo-label generation. Code will be available at https://github.com/zehuichen123/NoiseDet. + +# 1. Introduction + +3D object detection, aiming at detecting instances in the 3D space, is of great importance in various applications. Thanks to the large amount of labeled data, it has achieved + +![](images/ba47aa5978211295c5c78dc171ff36a68d44471b9590419234f610aaaf97b639.jpg) + +![](images/8fe762859dc84524c9f9ddc1fe5b6920baedfa7b8776a66cbb35d3cc81d107f2.jpg) +Figure 1. The noisy predictions generated by a well-trained 3D object detector. Despite carefully tuning the model and filtering low-confidence score predictions, there are still low-quality bounding boxes left. Directly enforcing the detector to learn from such noisy data on an unlabeled dataset can mislead the model convergence or even deteriorate its performance. In the top figure, we demonstrate an inaccurate heading regression case, and the bottom case shows a false positive prediction. We distinguish the ground truth and model predictions with green and blue, respectively. + +great success in the past few years [37, 29, 9, 56, 10, 11]. However, labeling a large-scale dataset is extremely time-consuming and labor-intensive [40]. This issue gets much more severe in the 3D object detection task, where 7 degree-of-freedom parameters need to be determined as well as the categorical labels. Therefore, how to further boost the supervised detectors with limited labeled datasets remains a practical and urgent problem. + +Semi-supervised object detection (SSOD) demonstrates great prospects recently due to its simplicity and weak dependence on costly annotations [46, 20, 39]. By leveraging easily accessible unlabeled data, SSOD approaches enhance the model performance with little human effort [47, 43, 51, 25]. The strategies of current SSOD can be + +categorized into two main streamlines: Mean-Teacher [41] and Pseudo-Labeling [24]. Mean-Teacher adopts a teacher-student paradigm, where the teacher is initialized from the student model via Exponential Moving Average (EMA) to produce supervised signals on the unlabeled data in an end-to-end training fashion. Inspired by this, more advanced ways, including SESS [55], NoisyStudent [45], are built upon the teacher-student paradigm and achieve significant improvements. Despite the superior performance and elegant pipeline, they are not model-agnostic (i.e. the teacher and student should be the same model) and miss the chance to pursuing high-quality pseudo labels, such as off-board label generation [35]. Another line of work is pseudo labeling [53, 36]: the model is first trained on labeled data and then generated pseudo labels on the unlabeled data for later training. Different from MT, it can be easily applied to any detector without adapting the framework to the teacher-student paradigm. These multi-stage approaches obtain reasonably good results, however, the final performance is often impeded by the quality of pseudo labels. To address this issue, 3DIoUMatch [42] proposes to estimate the localization accuracy predicted by the network and utilizes it as a metric to guide the label generation. ProficientTeacher [51] introduces a clustering-based box voting module to filter low-quality predictions without introducing any handcrafted rule. Although the accuracy of pseudo labels gets greatly improved, it may still fail in certain cases, leading to unstable model convergence. Harsh confidence filtering is proven to be worked well [46], however, we observe that it is still hard to remove all misleading instances for generated labels, which can distract the model convergence, shown in Figure 1. + +In this paper, we acknowledge the existence of noise in the generated labels and take PL as a noisy learning task: instead of directly applying vanilla pseudo-labels, we design a noise-resistant instance supervision module for better model generalization. Specifically, for the classification branch, we leverage the confidence predictions from the teacher and the student model learning ability to construct soft categorical targets. Different from previous approaches [47, 28], which simply apply them for loss reweighting, we enforce the network to directly learns from such continual supervision. In this way, our strategy can adaptively learn more knowledge from the teacher's predictions and at the same time develop tolerance to low confidence score labels. As for the regression branch, we find that solely relying on classification scores or IoU predictions is not enough to reflect the learning quality of each attribute of the 3D box. To mitigate this problem, we convert the original smooth L1 regression into a probabilistic modeling task: by enabling the network to output two variables to represent the Gaussian distribution, we maximize the negative log-likelihood of the targets in the distribution. Apart from the label supervi + +sion on the unlabeled data, we also introduce a novel dense pixel-wise feature self-supervised consistency constraints to further eliminate the negative impact of noisy data. To this end, we propose NoiseDet, a simple semi-supervised 3D object detection framework to address the noise learning problem from the unlabeled data. Our NoiseDet is modal-agnostic and can be easily applied to any 3D object detector with little modification. + +We summarize our key contributions as follows: + +- Instead of directly improving the quality of pseudolabels, we formulate SSOD as a noisy learning problem, where we acknowledge the existence of the noise in pseudo-labels and soften the network supervision for model generalization. +- Based on this thought, we propose NoiseDet, a simple yet effective SSOD framework to deal with the noisy data through two core modules: noise-resistant instance supervision and dense pixel-wise feature consistency constraint. +- With extensive experiments, we validate the effectiveness of our approach on two competitive benchmarks. Notably, it achieves state-of-the-art performance on the challenging ONCE dataset. + +# 2. Related Work + +# 2.1. LiDAR-based 3D Object Detection + +3D object detection aims to detect instances in the 3D space, which is of great importance in various applications, such as autonomous driving, navigation robot, and augmented reality. Current LiDAR detectors [52, 59, 49] mainly voxelize the point cloud into a BEV or voxel representations and adopt traditional 2D convolutions to predict bounding boxes. To improve the inference speed, some works [15, 30] attempt to detect objects directly through the range view. [58] combines both BEV and range-view features together to achieve better performance. VoxelNet [59] adopts PointNet [34] to extract local features through raw point clouds and fill them into the predefined voxel space. PointPillar [22] directly processes points inside a pillar to naturally formulate BEV feature representations, establishing an ultra-fast baseline detector. Inspired by CenterNet [14], CenterPoint [52] introduces a center-based label assignment strategy in 3D object detection, achieving competitive detection accuracy among various approaches. In addition to dense one-stage detectors, many works [8, 38] apply an R-CNN-style two-stage detection paradigm. Point R-CNN [38] propose 3D RoIAlign to aggregate regional features based on the proposals and then refines the detections. PV-RCNN [37] and Voxel R-CNN [13] construct two-parallel branches to extract both point-level and voxel + +level features to enjoy the best of each. However, independently localizing moving instances can introduce misalignment noise, 3D-MAN [50] and MPPNet [7] leverage multi-frame information to further enhance predictions with temporal knowledge. + +# 2.2. Semi-Supervised Learning (SSL) + +Semi-supervised learning is an important task in leveraging easy-to-access unlabeled data to improve the supervised model. Most current SSL methods [53, 17, 5, 19] involve adding additional supervision on unlabeled data to regularize the learning of the model. Among them, pseudolabeling is a popular pipeline [4, 24, 18], where unlabeled data is firstly labeled with a supervised model, and then acts in a common training paradigm. In order to guarantee the quality of the generated labels, [24] often filter them with a hard threshold based on the classification score. In addition to hard pseudo-labels, NoisyStudent [45] explores soft supervision to avoid ambiguity problems. Besides, it injects different augmentations to the student and teacher models, to encourage consistency regularization. In light of this, plenty of approaches [44, 2, 26] enforce the model to predict similar results when applying various input permutations. Such strategies are also verified on 2D object detection, where [32] borrows the idea from FixMatch to achieve promising performance. MUM [21] introduces Mix/UnMix augmentation, enforcing students to reconstruct unmixed features for the mixed input images. + +# 2.3. Semi-Supervised 3D Object Detection + +Semi-supervised learning (SSL) has been rapidly developed in both classification and object detection domains and obtains promising results in recent years. There are two main streams in SSOD: consistency learning and pseudo labeling. Consistency-based works [41, 25] apply data augmentations/perturbations to the input, which forms natural regularization for the network predictions. Such a consistency-learning target enforces the model to acquire valid information from the unlabeled data, therefore improving the performance. SESS [55] is the first work to attempt such a paradigm on 3D object detection, where the classification and regression predictions are matched through L2 distance and supervised with the similarity loss on the teacher and student. Inspired by Mean Teacher [41], it also adopts the exponential moving average (EMA) technique to further boost the performance. Apart from the consistency-based approaches, pseudo-labeling is another solution [46, 42]. Most PL works pay attention to the quality enhancement of pseudo labels. 3DIoUMatch [42] proposes to learn the IoU of the network predictions and utilize it to adaptively filter the low-quality pseudo labels. In order to remove the duplicate score threshold search, ProficientTeacher [51] introduces a novel clustering-based box voting + +module, replacing the hand-crafted NMS process. Different from the previous approaches, our method views pseudolabeling as a noisy learning problem, therefore delivering more generalization against noisy pseudo-data. + +# 3. NoiseDet + +It is acknowledged that predictions generated by the teacher model will inevitably encounter false positive (FP) or false negative (FN) problems, despite many efforts that have been devoted to overcoming these issues [51, 46]. Such noises can distract the convergence of the model during the semi-supervised training process, or even deteriorate the final performance. + +The main intuition of NoiseDet is to improve the model generalization ability against noisy pseudo labels, which are generated by the baseline model trained on limited labeled data. We start with a vanilla two-stage pseudo-labeling pipeline: assuming that we have access to a (small) set of labeled set $L = \{x_i^l,y_i^l\}_{i = 1}^{N_l}$ , and a set of unlabeled set $U = \{x_i^u\}_{i = 1}^{N_u}$ , where $N_{l}$ and $N_{u}$ are the numbers of labeled and unlabeled datasets. A teacher model is firstly trained on the labeled set $L$ , and then infer on unlabeled set $U$ to get pseudo labels $\{y_i^u\}_{i = 1}^{N_u}$ and formulate the pseudo-labeled set $U_{p} = \{x_{i}^{u},y_{i}^{u}\}$ . After that, we initialize the student model from the pretrained teacher and uniformly sample data from both $L$ and $U_{p}$ set to construct each batch for second-stage training. Different from previous works, which mainly focus on improving the quality of pseudo-labels, NoiseDet directly learns knowledge from noise labels $\{y_i^U\}_{i = 1}^{N_u}$ . + +# 3.1. Noise-Resistant Instance Supervision + +In contrast to standard fully supervised object detection, where labels are carefully human-annotated and verified, the supervisory signals on the unlabeled set are generated by the vanilla teacher model. It may contain unexpected noisy labels, leading to model performance degeneration. Therefore, we propose to transform such hard, deterministic instance supervision into the noise-resistant one to develop the model tolerance to the noisy labels, instead of directly eliminating them. + +Recent works [16, 3] suggests that the confidence score $c$ can be viewed as the noisy level of the network predictions, i.e., the model is more prone to yield a high score for easy-to-detect samples and low score for not-sure samples. Therefore, an intuitive idea is to filter the generated pseudo-labels with a pre-defined score threshold $U_{p} = \{(x_{i}^{u},c_{i}^{u})|c_{i}^{u}\geq c_{thres}\}$ to eliminate the noises for the unlabeled dataset. Though simple, such a strategy does not provide a clear divergence for the rest labels. For instance, the quality of a box with $c = 0.9$ can be different from the quality of the box with $c = 0.5$ . However, they are treated equally with 1/0 labels in the classification branch. To fully exploit a reliable confidence score derived from the + +![](images/ce189c39c234ea83ad8d1231d7ff141194716a07d24fc43bca74f58dea7cc6f4.jpg) +Figure 2. The overall architecture of the proposed NoiseDet. It consists of two main components: noise-resistant instance supervision and dense feature consistency constraint. It follows the pseudo-labeling practice with a two-stage training paradigm: (i) pseudo labels are pre-generated with a well-trained teacher model on the unlabeled dataset, and (ii) the student model is trained on both labeled (omitted in the figure) and unlabeled LiDAR points in a semi-supervised manner. + +teacher model, we leverage the $c$ as an indicator to measure the quality of the pseudo label. Specifically, instead of directly assigning each anchor with a deterministic binary label, we soften the categorical label into a value ranging from 0 to 1 given the confidence score $c$ as well as the IoU $\tau$ between the student predictions and its matched pseudo labels. Different from the one in GFL [27] where the categorical labels are assigned based on the IoU between the network prediction and the ground-truth boxes, we view it as the combination of the quality of the GT boxes itself and the learning ability of the student. Since the standard Focal Loss can only handle discrete binary values, we adopt Quality Focal Loss [27] to conduct the classification supervision on the non-discrete categorical labels: + +$$ +\hat {y} = \alpha c + (1 - \alpha) \tau , \tag {1} +$$ + +$$ +\mathcal {L} _ {c l s} ^ {U} = - | y - \hat {y} | ^ {\beta} ((1 - y) \log (1 - \hat {y}) + y \log (\hat {y})), \tag {2} +$$ + +where $\hat{y}$ is the quality score predicted by the teacher and $y$ is the student predictions, $\alpha$ is set to 0.75. Note that our approach can be easily extended into other continual versions of cross-entropy loss, for instance, Gaussian Focal Loss [23]. + +In addition to the classification loss, the boundary targets of the bounding box can present more ambiguities since it contains 7 degree-of-freedom and presents fewer training samples (only positive samples receive the regression supervision). Therefore, how to effectively deal with misleading regression targets is non-trivial. To address this problem, + +we convert the deterministic regression into the probability optimization task. Concretely, we model the network prediction of each bounding box as a Gaussian distribution $h$ given the feature vector $x$ : + +$$ +\hat {h} = \mathcal {N} (\mu (x), \sigma (x)), \tag {3} +$$ + +where $\mu (x)$ and $\sigma (x)$ denotes the mean and variance of each regression term predicted by the network. After that, the regression loss can be converted into a negative log-likelihood (NLL) loss, where the objective is to maximize the likelihood of each GT $h$ in the predicted distribution: + +$$ +\mathcal {L} _ {r e g} = - \log \mathcal {N} (h; \mu (x), \sigma (x)) \tag {4} +$$ + +$$ += - \log \frac {1}{\sigma \sqrt {2 \pi}} e ^ {- \frac {1}{2} \left(\frac {h - \mu}{\sigma}\right) ^ {2}}. \tag {5} +$$ + +By converting the deterministic regression task to a probabilistic estimation problem, the model develops more tolerance against noisy information in the training data, therefore achieving better performance. + +# 3.2. Dense Feature Consistency Constraint + +Considering that labels can contain noise information that deteriorates the model performance, we further exploit the incorporation of unsupervised learning to obtain useful knowledge about label-independent features. However, different from the common-studied image classification task that mostly cares about the overall feature representation, + +3D object detection requires estimating instances with various scales and directions. Therefore, learning a scale and rotation-invariant feature extractor for 3D detector is of vital importance. By applying various data augmentation, such as rescaling, rotating, and global transforming, into the input point clouds, and supervising them with the transformed ground-truth boxes, the model can develop robustness to such transformations. However, when the label itself is not so accurate enough, such a strategy may be more harmful. + +To avoid this problem, we propose a dense pixel-wise consistency constraint to enforce the network to acquire such property. Previous literature mainly involves label-level consistency [55, 42, 1, 54] to ensure the model consistency, where the predicted bounding boxes are reversed back to the original space and regularized with Euclidean distance matching. Despite being simple and straightforward, this low-dimensional prediction distribution (number of classes and 7 regression targets) means that only a few amounts of knowledge are encoded, thus limiting the knowledge that can be transferred. Hence, we apply the consistency constraint on the feature level by reversing the BEV features according to the data transformation in the data augmentation and then conducting dense pixel-wise regularization. + +More formally, given one frame of point clouds $P$ and a set of data augmentation policies $\mathcal{A}$ , we randomly sample two transformations $\mathcal{A}_1, \mathcal{A}_2$ from $\mathcal{A}$ and apply them to the point $P$ to produce two different views of point clouds $P_1, P_2$ . The augmented point clouds are fed into the point feature extractor $\mathcal{F}$ to generate the BEV feature maps $F$ : + +$$ +F _ {1} = \mathcal {F} (P _ {1}), F _ {2} = \mathcal {F} (P _ {2}). \tag {6} +$$ + +Once obtaining the BEV features, we simply reverse them back to the original space with the recorded transformation flow: + +$$ +\hat {F} _ {1} = \mathcal {A} _ {1} ^ {- 1} \left(F _ {1}\right), \hat {F} _ {2} = \mathcal {A} _ {2} ^ {- 1} \left(F _ {2}\right), \tag {7} +$$ + +where $A^{-1}$ denotes the reverse transformation of $A$ . To this end, we can derive the pixel-wise feature consistency constraint with standard L2 loss: + +$$ +\mathcal {L} _ {\text {c o n s i s t}} = \left| \left| \hat {F} _ {1} - \hat {F} _ {2} \right| \right| _ {2}. \tag {8} +$$ + +Considering that the point-based 3D features can hold meaningful information only if the point exists, mainly due to the characteristics of the LiDAR points, we further introduce a foreground-focusing mask to selectively regularize the augmented BEV features. Different from previous approaches [12] that directly set each foreground GT region with hard supervision, we generate a soft mask to smooth the regularization effect at the boundary regions, similar in [57]. Specifically, we draw a Gaussian distribution for each + +GT center $(x_{i},y_{i})$ in the BEV space, + +$$ +\phi_ {i, x, y} = \exp \left(\frac {\left(x _ {i} - \hat {x} _ {i}\right) ^ {2} + \left(y _ {i} - \hat {y} _ {i}\right) ^ {2}}{2 \sigma_ {i} ^ {2}}\right), \tag {9} +$$ + +where $\sigma_{i}$ is a constant (set to 2), indicating the object size standard deviation. Since feature maps are class-agnostic, we merge all $\phi_{i,x,y}$ into one single mask $\Phi$ by taking the maximum value across the $i$ dimension. Therefore, the final dense feature consistency constraint is derived as: + +$$ +\mathcal {L} _ {\text {c o n s i s t}} = \frac {1}{H W \Phi} \sum_ {i} ^ {H} \sum_ {j} ^ {W} \max \left(\phi_ {i j}\right) \left| \left| \hat {F} _ {1} - \hat {F} _ {2} \right| \right| _ {2}. \tag {10} +$$ + +By aligning dense pixel-wise features on the BEV space, the model can gradually learn the ability to extract transform-invariant feature extraction and fully utilize the unlabeled data in a self-supervised manner. + +# 4. Experiments + +# 4.1. Datasets + +ONCE dataset [33] is one of the largest autonomous driving datasets with 1 million LiDAR point clouds and 7 million paired images. Only 15,000 samples are annotated with 3D bounding boxes, which are divided into training, validation and testing split with a ratio of $33\% /20\% /47\%$ , respectively. Among all instances, five classes are labeled as interested categories: Car, Bus, Truck, Pedestrian, and Cyclist. According to the official SSL setting, 5,000 samples are selected as labeled set and all the unlabeled sets are divided into 3 scales of subsets: Small, Medium, and Large. The small set contains 70 sequences (100k samples), the medium set contains 321 sequences (500k samples), and the large set contains 560 sequences (about 1M samples). Following the official evaluation tools, we set 0.7, 0.3, and 0.5 for Vehicle, Pedestrian, and Cyclist as the mAP IoU threshold, respectively. Besides, similar to Waymo Open Dataset [40], the evaluation protocol provides metrics based on different perception ranges: '0-30m', '30-50m', and /'50minf' to fully reflect the detection ability of the model. + +# 4.2. Implementation Details + +NoiseDet follows the two-stage training pipeline: we first train the teacher network with 80 epochs for ONCE dataset. Then we utilize the STE module proposed in ProficientTeacher [51] to obtain pseudo-labels on the unlabeled dataset. During this process, we can easily incorporate other techniques such as camera/Radar detection or object tracking to further refine the labels. We do not consider such implementations since it is out of the scope of this paper, but it is proven to be effective in [35]. For the semi-supervised training configuration, we uniformly sampled 1 labeled and + +Table 1. Comparison with other state-of-the-art semi-supervised 3D object detection approaches on ONCE validation set with different amounts of unlabeled samples (e.g., "Small", "Medium" and "Large"). We bold the best overall results and list the relative gains based on the baseline model (i.e., SECOND [48] trained on labeled training set only) for better illustration. Most experimental results are borrowed from the official implementations in ONCE [33]. + +
MethodsVehicle AP (%)Pedestrian AP (%)Cyclist AP (%)mAP (%)
overall0-30m30-50m50m-infoverall0-30m30-50m50m-infoverall0-30m30-50m50m-inf
Baseline [48]71.1984.0463.0247.2526.4429.3324.0518.0558.0469.9652.4334.6151.89
Small (100K unlabeled samples)
Pseudo Label72.8084.4664.9751.4625.5028.3622.6618.5155.3765.9550.3434.4251.22 (-0.67)
Noisy Student [45]73.6984.6967.7253.4128.8133.2323.4216.9354.6765.5850.4332.6552.39 (+0.50)
Mean Teacher [41]74.4686.6568.4453.5930.5434.2426.3120.1261.0272.5155.2439.1155.34 (+3.45)
SESS [55]73.3384.5266.2252.8327.3131.1123.9419.0159.5271.0353.9336.6853.39 (+1.50)
3D IoUMatch [42]73.8184.6168.1154.4830.8635.8725.5518.3056.7768.0251.8035.9153.81 (+1.92)
NoiseDet (Ours)75.2686.3667.5255.2937.9642.3632.7823.2860.7772.3155.0338.8758.00 (+6.11)
Medium (500K unlabeled samples)
Pseudo Label73.0386.0665.9651.4224.5627.2820.8117.0053.6165.2648.4433.5850.40 (-1.49)
Noisy Student [45]75.5386.5269.7855.0531.5635.8026.2421.2158.9369.6153.7336.9455.34 (+3.45)
Mean Teacher [41]76.0186.4770.3455.9235.5840.8630.4419.8263.2174.8956.7740.2958.27 (+6.38)
SESS [55]72.1184.0666.4453.6133.4438.5828.1018.6761.8273.2056.6038.7355.79 (+3.90)
3D IoUMatch [42]75.6986.4670.2256.0634.1438.8429.1919.6258.9369.0854.1638.8756.25 (+4.36)
NoiseDet (Ours)77.1487.2169.9458.4440.4544.9135.7124.1162.5973.0457.9842.6760.06 (+8.17)
Large (1M unlabeled samples)
Pseudo Label72.4184.0664.5450.0523.6226.8020.1316.6653.2564.6948.5233.4749.76 (-2.13)
Noisy Student [45]75.5386.5269.7855.0531.5635.8026.2421.2158.9369.6153.7336.9455.34 (+3.45)
MeanTeacher [41]76.3886.4570.9957.4835.9541.7629.0518.8165.5075.7260.0743.6659.28 (+7.39)
SESS [55]75.9586.8370.4555.7634.4340.0027.9219.2063.5874.8558.8839.5157.99 (+6.10)
3D IoUMatch [42]75.8186.1171.8257.8435.7040.6830.3421.1559.6970.6954.9239.0857.07 (+5.18)
NoiseDet (Ours)78.0287.0072.5559.4942.8946.5238.2126.6062.7473.1958.0342.8861.16 (+9.27)
+ +Table 2. Comparison of detection results based on SECOND and CenterPoint with and without NoiseDet on ONCE validation set. + +
DetectorMethodmAP
SECONDNoisyStudent55.50
NoiseDet (Ours)58.01
CenterPointNoisyStudent63.77
NoiseDet (Ours)65.57
+ +4 unlabeled samples for each batch to avoid training collapse. Following the official ONCE benchmark [33], we initialize the student from a pretrained checkpoint on the full labeled set. The student is trained for 25, 50, 75 epochs for small, medium, and large settings on ONCE dataset. The learning rate is set to 1e-4 and the pseudo-labels are updated every 25 epochs. All models are trained on an 8 NVIDIA V100 GPUs machine. + +# 4.3. Main Results + +We first implement NoiseDet with the standard anchor-based 3D detector, SECOND, following the official benchmark [33], on the Small protocol setting of ONCE dataset. The final performance is shown in Table 2. Our NoiseDet greatly boosts its enhanced baseline NoisyStudent [45] by $2.5\mathrm{mAP}$ . Then, we also report it on a stronger anchor-free-based detector, CenterPoint [52], which also obtains an improvement of $1.8\mathrm{mAP}$ , validating the effectiveness and + +generalization of the proposed method under different 3D detection frameworks. Besides, we also validate NoiseDet on the competitive Waymo Open Dataset [40] in Appendix, which outperforms 3DIoUMatch [42] by a large margin. + +# 4.4. Comparison with State-of-the-Arts + +To further validate the superiority of our method, we compare NoiseDet with various state-of-the-art semi-supervised approaches, including Pseudo-Label, NoisyStudent, Mean Teacher, SESS, and 3DIouMatch. The experiments are conducted on the three different protocols (Small, Medium, and Large) to fully exploit the extensibility of various strategies and the results are reported in Table 1. We select SECOND as our baseline to keep consistent with other works [33]. NoiseDet surpasses all other counterparts, achieving new state-of-the-art in this competitive benchmark. With the increase of the unlabeled dataset size, NoiseDet can consistently improve the detectors with significant gains: with $6.1\mathrm{mAP}$ , $8.2\mathrm{mAP}$ , and $9.3\mathrm{mAP}$ under Small, Medium, and Large protocols, respectively. + +# 4.5. Ablation Studies + +In this section, we conduct a series of ablation studies to gain a deeper understanding of NoiseDet. For efficiency, all experiments are conducted on the Small protocol of the ONCE training set and evaluated on the validation set. + +Table 3. Effectiveness of each component in our NoiseDet. Results are reported on ONCE validation subset with SECOND. + +
Noise-Resistant Instance Supervision ClassificationRegressionDense Feature Consistency ConstraintmAP
\( AP_{veh} \)\( AP_{ped} \)\( AP_{cyc} \)\( AP_{overall} \)
72.0336.8057.7355.50
✓72.7836.4160.7356.80
✓73.8736.7458.3456.39
✓✓74.0536.6261.0357.27
✓✓✓75.2637.9660.7758.01
+ +# 4.5.1 Main Ablations + +In order to understand the effectiveness of each module contributing to the detection performance in NoiseDet, we test each component separately on the baseline detector SEC-OND and report the results in Table 3. Our baseline is the enhanced implementation of NoisyStudent [45], where its performance starts from $55.5\mathrm{mAP}$ on the validation dataset. When we add the noise-resistant instance supervision on the classification branch, the mAP score is raised by $1.1\mathrm{mAP}$ . And then we test the proposed component on the regression branch, which yields another $0.8\mathrm{mAP}$ . Such a huge improvement validates the correctness of the noise learning strategy on the unknown quality of pseudo-labels and the effectiveness of the proposed noise-resistant instance supervision module. When the dense feature consistency constraint module is applied, the accuracy is promoted by $1.2\mathrm{mAP}$ , suggesting that consistent regularization provides useful unsupervised hints for model convergence. Finally, we put all techniques together, and NoiseDet achieves 58.0 mAP on the validation subset, indicating a $2.5\mathrm{mAP}$ performance enhancement. + +# 4.5.2 Noise-Resistant Instance Supervision + +Comparison with other classification supervision. We first compare our proposed noise-resistant classification loss with other supervision approaches. The vanilla strategy is to directly apply Focal Loss on the pseudo labels, similar to the labeled data. Then, we attempt to utilize the predicted score from the teacher to adjust the supervision on the pseudo-labels by reweighting the classification loss. In doing this, we can alleviate the training distraction from low-quality samples by lowering their penalties. Inspired by 3D IoUMatch [42], we consider IoU as another measurement to help decide the loss penalty on the pseudo samples (denoted as IoU Reweight). We also consider Quality Focal Loss proposed in [27] to further integrate IoU into the classification supervision. The final results are shown in Table 4. Incorporating reweighting mechanisms, either IoU or classification score, to balance the supervision across different samples brings about $0.5\mathrm{mAP}$ improvements. When adapting to QFL, the model improves to $56.2\mathrm{mAP}$ . Finally, + +by both considering localization quality (IoU) and the sample quality (classification score), we obtain the best performance, $56.8\mathrm{mAP}$ on the validation subset. + +Table 4. Comparison with different classification supervision approaches on ONCE validation dataset. + +
Classification LossAPoverall
Focal Loss [31]55.45 ± 0.07
Score Reweight56.09 ± 0.10
IoU Reweight55.90 ± 0.17
QFocal Loss [27]56.20 ± 0.05
Ours56.80 ± 0.08
+ +Strategies on $\hat{y}$ generation. In this part, we explore the best strategy to generate the classification targets $\hat{y}$ for the Focal Loss. We first consider utilizing the teacher's predicted categorical confidence to replace the original hard pseudo labels, based on the observation that the quality of the generated pseudo-labels is highly correlated with the classification score. On top of this, we also consider the localization quality between the student and teacher's predictions. The main intuition is that when the student model can not perfectly learn the pseudo-targets well, we infer them as noisy labels and downgrade their categorical targets. Actually, this strategy comes to the same formulation as Quality Focal Loss. In order to further improve the representation ability of $\hat{y}$ , we adopt the combination of IoU and confidence score to fully leverage the information. We consider two types of combinations: multiplication and weighted sum. The experimental results are shown in Table 5. By combining IoU and confidence score with weighted sum, the detection accuracy gets the best performance. + +Comparison with other regression supervision. In addition to classification targets $\hat{y}$ , properly softening the regression supervision on noisy pseudo labels is also nontrivial. Therefore, we compare different kinds of regression losses and their tolerance against noisy data. The original loss is Smooth L1 loss, which provides more penalty on more accurate predictions (close to GT targets), encouraging the model to pay more attention to high-precision boxes. However, such a strategy is counter to the learning on noisy + +Table 5. Ablations on the strategies to generate the classification target $\hat{y}$ for categorical supervision. + +
Cls ScoreIoUOperationAPoverall
✓-55.45 ± 0.07
-56.45 ± 0.17
✓-56.11 ± 0.21
✓✓Multiply56.52 ± 0.05
✓✓Weighted-sum56.80 ± 0.08
+ +![](images/467505eb89dda5528a8282179dee08e3b77daef37e120673d96b955aad675eff.jpg) +Figure 3. Visualization of the loss curve of different regression approaches on the labeled split in each batch. We also plot the final detection performance (mAP) at the end iteration of each loss. Note that there exists occasional fluctuations during training probably due to the noisy annotations in the training data, empirically it will not affect the final model performance. + +labels: if the network fails to regress the target well, it probably belongs to low-quality samples. Therefore, we directly employ the L1 loss to avoid large misleading gradients on noisy bounding box regression. Another option to improve the tolerance against noisy labels for regression is to convert the regression task into a probabilistic optimization problem. As a result, we consider the Gaussian NLL as an alternative regression objective. We report the results in Figure 3. Gaussian NLL outperforms all other losses, achieving $56.4\mathrm{mAP}$ on the validation subset, demonstrating the superiority of the probabilistic model on noisy data learning. + +# 4.5.3 Dense Feature Consistency Constraint + +Strategies on consistency regularization. Consistency learning is a crucial component in semi-supervised pipelines. In most previous work [55], such regularization is often conducted on the label level. A key reason is that label encoding is agnostic to any transformation, which is easy to apply to various object detection tasks. Luckily, most in- + +put permutations in point clouds can be easily reversed and differentiable. Therefore, we can also explore the feature-level consistency regularization with L2 loss. Followed by the idea of SimSiam [6], we add a projection layer for one branch and detach the gradient in the other branch, and then regularize them with L2 loss. We also consider distance correlation to consider the inner structural similarity in the latent feature space. The final results are shown in Table 6. The vanilla L2 loss on the feature level obtains the best performance. We infer the reason that mutual L2 introduces additional flexibility through the linear projection layer and further promotes the effect of consistent regularization. + +Table 6. Comparison with different approaches for dense feature consistency constraints. "DC" denotes distance correlation. + +
Input-levelLossAP
Label-levelL255.45 ± 0.07
Feature-levelDC56.07 ± 0.14
Feature-levelL256.70 ± 0.06
+ +# 4.6. Extension to Auto-Labeling Strategy + +Auto-Labeling is a simple and effective strategy to improve model prediction. By combing with additional techniques, such as temporal information or object tracking, we can obtain high-quality pseudo-labels [35]. Different from the Mean-Teacher paradigm, the pseudo-labeling pipeline allows the network to pursue more precious labels offline and greatly improves its potential in real-world applications. In this section, we imitate this paradigm and validate the superiority of our framework. Specifically, we generate the pseudo-labels based on two well-tuned CenterPoint models, (CenterPoint and CenterPoint-E), which achieve 62.5 and $70.1\mathrm{mAP}$ on the ONCE validation subset, respectively, to stimulate the auto-labeling process and utilize it to supervise a SECOND model. The final results are shown in Table 7. With the quality-improved label, our NoiseDet still consistently outperforms the competitive NoisyStudent baseline, yielding a 1.4 and $2.2\mathrm{mAP}$ on the ONCE validation subset, demonstrating its effectiveness and generalization on semi-supervised learning tasks. + +Table 7. Detection results on different pseudo-label generation with respective teacher models. The results are reported on ONCE validation dataset. CenterPoint-E denotes for the enhanced version of CenterPoint. + +
PL SourceAPvehAPpedAPcycAPoverall
SECOND [48]75.2637.9660.7758.00
CenterPoint [52]75.4240.1962.7359.44
CenterPoint-E [52]76.0141.5663.0160.19
+ +# 5. Conclusion + +In this paper, we introduce a pseudo-labeling-based semi-supervised 3D object detection framework, namely NoiseDet. By viewing the semi-supervised learning as a noisy learning task, we propose two core modules to overcome the ambiguity detection problem: noise-resistant instance supervision and dense feature consistency regularization. With soft task supervision on the unlabeled data and unsupervised feature consistency regularization, our model develops tolerance towards noisy pseudo-labels and improves the model generalization. Extensive experiments on the ONCE dataset demonstrate the effectiveness and generalization of our approach. We hope NoiseDet can provide a new perspective in dealing with in-sufficient accuracy pseudo labels for semi-supervised 3D object detection. + +# Acknowledgments + +This work was supported by the JKW Research Funds under Grant 20-163-14-LZ-001-004-01, and the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. We acknowledge the support of GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC. + +# References + +[1] Amir Bar, Xin Wang, Vadim Kantorov, Colorado J Reed, Roei Herzig, Gal Chechik, Anna Rohrbach, Trevor Darrell, and Amir Globerson. DETReg: Unsupervised pretraining with region priors for object detection. In CVPR, pages 14605-14615, 2022. 5 +[2] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: A holistic approach to semi-supervised learning. NeurIPS, 32:1-11, 2019. 3 +[3] Navaneeth Bodla, Bharat Singh, Rama Chellappa, and Larry S Davis. Soft-NMS-improving object detection with one line of code. In Proceedings of the IEEE international conference on computer vision, pages 5561-5569, 2017. 3 +[4] Paola Cascante-Bonilla, Fuwen Tan, Yanjun Qi, and Vicente Ordonez. Curriculum labeling: Revisiting pseudo-labeling for semi-supervised learning. 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In CVPR, pages 4490-4499, 2018. 2 \ No newline at end of file diff --git a/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/images.zip b/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7acb15671b073744be48d7b9a795ccd44e313a48 --- /dev/null +++ b/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:424de2cb62a9f8283678b0e36e2c295ab95b209cb34ed25522530d383a612972 +size 529138 diff --git a/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/layout.json b/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..8e95dd4f2ab1b6b45df0f4804f3c5bb645bac423 --- /dev/null +++ b/2023/Learning from Noisy Data for Semi-Supervised 3D Object Detection/layout.json @@ -0,0 +1,7692 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "spans": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "type": "text", + "content": "Learning with Noisy Data for Semi-Supervised 3D Object Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 142, + 479, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 142, + 479, + 185 + ], + "spans": [ + { + "bbox": [ + 116, + 142, + 479, + 185 + ], + "type": "text", + "content": "Zehui Chen1 Zhenyu Li2 Shuo Wang1 Dengpan Fu3 Feng Zhao1* \n1University of Science and Technology of China \n2Harbin Institute of Technology 3NIO" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 132, + 187, + 462, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 187, + 462, + 200 + ], + "spans": [ + { + "bbox": [ + 132, + 187, + 462, + 200 + ], + "type": "text", + "content": "lovesnow, wangshuo}@mail.ustc.edu.cn zhenyuli17@hit.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 182, + 202, + 411, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 202, + 411, + 213 + ], + "spans": [ + { + "bbox": [ + 182, + 202, + 411, + 213 + ], + "type": "text", + "content": "dengpan.fu@nio.com fzhao956@ustc.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 241, + 192, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 241, + 192, + 253 + ], + "spans": [ + { + "bbox": [ + 143, + 241, + 192, + 253 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 266, + 290, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 290, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 290, + 613 + ], + "type": "text", + "content": "Pseudo-Labeling (PL) is a critical approach in semisupervised 3D object detection (SSOD). In PL, delicately selected pseudo-labels, generated by the teacher model, are provided for the student model to supervise the semisupervised detection framework. However, such a paradigm may introduce misclassified labels or loose localized box predictions, resulting in a sub-optimal solution of detection performance. In this paper, we take PL from a noisy learning perspective: instead of directly applying vanilla pseudo-labels, we design a noise-resistant instance supervision module for better generalization. Specifically, we soften the classification targets by considering both the quality of pseudo labels and the network learning ability, and convert the regression task into a probabilistic modeling problem. Besides, considering that self-supervised learning works in the absence of labels, we incorporate dense pixel-wise feature consistency constraints to eliminate the negative impact of noisy labels. To this end, we propose NoiseDet, a simple yet effective framework for semi-supervised 3D object detection. Extensive experiments on competitive ONCE and Waymo benchmarks demonstrate that our method outperforms current semisupervised approaches by a large margin. Notably, our NoiseDet achieves state-of-the-art performance under various dataset scales on ONCE dataset. For example, NoiseDet improves its NoiseStudent baseline from 55.5 mAP to 58.0 mAP, and further reaches 60.2 mAP with enhanced pseudo-label generation. Code will be available at https://github.com/zehuichen123/NoiseDet." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 637, + 128, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 637, + 128, + 649 + ], + "spans": [ + { + "bbox": [ + 47, + 637, + 128, + 649 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 658, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 287, + 694 + ], + "type": "text", + "content": "3D object detection, aiming at detecting instances in the 3D space, is of great importance in various applications. Thanks to the large amount of labeled data, it has achieved" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 311, + 239, + 542, + 321 + ], + "blocks": [ + { + "bbox": [ + 311, + 239, + 542, + 321 + ], + "lines": [ + { + "bbox": [ + 311, + 239, + 542, + 321 + ], + "spans": [ + { + "bbox": [ + 311, + 239, + 542, + 321 + ], + "type": "image", + "image_path": "ba47aa5978211295c5c78dc171ff36a68d44471b9590419234f610aaaf97b639.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 327, + 542, + 408 + ], + "blocks": [ + { + "bbox": [ + 310, + 327, + 542, + 408 + ], + "lines": [ + { + "bbox": [ + 310, + 327, + 542, + 408 + ], + "spans": [ + { + "bbox": [ + 310, + 327, + 542, + 408 + ], + "type": "image", + "image_path": "8fe762859dc84524c9f9ddc1fe5b6920baedfa7b8776a66cbb35d3cc81d107f2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 419, + 547, + 519 + ], + "lines": [ + { + "bbox": [ + 304, + 419, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 547, + 519 + ], + "type": "text", + "content": "Figure 1. The noisy predictions generated by a well-trained 3D object detector. Despite carefully tuning the model and filtering low-confidence score predictions, there are still low-quality bounding boxes left. Directly enforcing the detector to learn from such noisy data on an unlabeled dataset can mislead the model convergence or even deteriorate its performance. In the top figure, we demonstrate an inaccurate heading regression case, and the bottom case shows a false positive prediction. We distinguish the ground truth and model predictions with green and blue, respectively." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "text", + "content": "great success in the past few years [37, 29, 9, 56, 10, 11]. However, labeling a large-scale dataset is extremely time-consuming and labor-intensive [40]. This issue gets much more severe in the 3D object detection task, where 7 degree-of-freedom parameters need to be determined as well as the categorical labels. Therefore, how to further boost the supervised detectors with limited labeled datasets remains a practical and urgent problem." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 642, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 548, + 714 + ], + "type": "text", + "content": "Semi-supervised object detection (SSOD) demonstrates great prospects recently due to its simplicity and weak dependence on costly annotations [46, 20, 39]. By leveraging easily accessible unlabeled data, SSOD approaches enhance the model performance with little human effort [47, 43, 51, 25]. The strategies of current SSOD can be" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6929" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 455 + ], + "type": "text", + "content": "categorized into two main streamlines: Mean-Teacher [41] and Pseudo-Labeling [24]. Mean-Teacher adopts a teacher-student paradigm, where the teacher is initialized from the student model via Exponential Moving Average (EMA) to produce supervised signals on the unlabeled data in an end-to-end training fashion. Inspired by this, more advanced ways, including SESS [55], NoisyStudent [45], are built upon the teacher-student paradigm and achieve significant improvements. Despite the superior performance and elegant pipeline, they are not model-agnostic (i.e. the teacher and student should be the same model) and miss the chance to pursuing high-quality pseudo labels, such as off-board label generation [35]. Another line of work is pseudo labeling [53, 36]: the model is first trained on labeled data and then generated pseudo labels on the unlabeled data for later training. Different from MT, it can be easily applied to any detector without adapting the framework to the teacher-student paradigm. These multi-stage approaches obtain reasonably good results, however, the final performance is often impeded by the quality of pseudo labels. To address this issue, 3DIoUMatch [42] proposes to estimate the localization accuracy predicted by the network and utilizes it as a metric to guide the label generation. ProficientTeacher [51] introduces a clustering-based box voting module to filter low-quality predictions without introducing any handcrafted rule. Although the accuracy of pseudo labels gets greatly improved, it may still fail in certain cases, leading to unstable model convergence. Harsh confidence filtering is proven to be worked well [46], however, we observe that it is still hard to remove all misleading instances for generated labels, which can distract the model convergence, shown in Figure 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 463, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we acknowledge the existence of noise in the generated labels and take PL as a noisy learning task: instead of directly applying vanilla pseudo-labels, we design a noise-resistant instance supervision module for better model generalization. Specifically, for the classification branch, we leverage the confidence predictions from the teacher and the student model learning ability to construct soft categorical targets. Different from previous approaches [47, 28], which simply apply them for loss reweighting, we enforce the network to directly learns from such continual supervision. In this way, our strategy can adaptively learn more knowledge from the teacher's predictions and at the same time develop tolerance to low confidence score labels. As for the regression branch, we find that solely relying on classification scores or IoU predictions is not enough to reflect the learning quality of each attribute of the 3D box. To mitigate this problem, we convert the original smooth L1 regression into a probabilistic modeling task: by enabling the network to output two variables to represent the Gaussian distribution, we maximize the negative log-likelihood of the targets in the distribution. Apart from the label supervi" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "content": "sion on the unlabeled data, we also introduce a novel dense pixel-wise feature self-supervised consistency constraints to further eliminate the negative impact of noisy data. To this end, we propose NoiseDet, a simple semi-supervised 3D object detection framework to address the noise learning problem from the unlabeled data. Our NoiseDet is modal-agnostic and can be easily applied to any 3D object detector with little modification." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 317, + 168, + 514, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 168, + 514, + 180 + ], + "spans": [ + { + "bbox": [ + 317, + 168, + 514, + 180 + ], + "type": "text", + "content": "We summarize our key contributions as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 316, + 190, + 545, + 376 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 316, + 190, + 545, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 190, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 316, + 190, + 545, + 250 + ], + "type": "text", + "content": "- Instead of directly improving the quality of pseudolabels, we formulate SSOD as a noisy learning problem, where we acknowledge the existence of the noise in pseudo-labels and soften the network supervision for model generalization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 316, + 258, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 258, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 316, + 258, + 545, + 319 + ], + "type": "text", + "content": "- Based on this thought, we propose NoiseDet, a simple yet effective SSOD framework to deal with the noisy data through two core modules: noise-resistant instance supervision and dense pixel-wise feature consistency constraint." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 316, + 328, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 328, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 316, + 328, + 545, + 376 + ], + "type": "text", + "content": "- With extensive experiments, we validate the effectiveness of our approach on two competitive benchmarks. Notably, it achieves state-of-the-art performance on the challenging ONCE dataset." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 388, + 392, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 388, + 392, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 388, + 392, + 399 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 407, + 491, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 407, + 491, + 420 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 491, + 420 + ], + "type": "text", + "content": "2.1. LiDAR-based 3D Object Detection" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 426, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 715 + ], + "type": "text", + "content": "3D object detection aims to detect instances in the 3D space, which is of great importance in various applications, such as autonomous driving, navigation robot, and augmented reality. Current LiDAR detectors [52, 59, 49] mainly voxelize the point cloud into a BEV or voxel representations and adopt traditional 2D convolutions to predict bounding boxes. To improve the inference speed, some works [15, 30] attempt to detect objects directly through the range view. [58] combines both BEV and range-view features together to achieve better performance. VoxelNet [59] adopts PointNet [34] to extract local features through raw point clouds and fill them into the predefined voxel space. PointPillar [22] directly processes points inside a pillar to naturally formulate BEV feature representations, establishing an ultra-fast baseline detector. Inspired by CenterNet [14], CenterPoint [52] introduces a center-based label assignment strategy in 3D object detection, achieving competitive detection accuracy among various approaches. In addition to dense one-stage detectors, many works [8, 38] apply an R-CNN-style two-stage detection paradigm. Point R-CNN [38] propose 3D RoIAlign to aggregate regional features based on the proposals and then refines the detections. PV-RCNN [37] and Voxel R-CNN [13] construct two-parallel branches to extract both point-level and voxel" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6930" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "level features to enjoy the best of each. However, independently localizing moving instances can introduce misalignment noise, 3D-MAN [50] and MPPNet [7] leverage multi-frame information to further enhance predictions with temporal knowledge." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 140, + 224, + 153 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 224, + 153 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 224, + 153 + ], + "type": "text", + "content": "2.2. Semi-Supervised Learning (SSL)" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 159, + 289, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 159, + 289, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 289, + 411 + ], + "type": "text", + "content": "Semi-supervised learning is an important task in leveraging easy-to-access unlabeled data to improve the supervised model. Most current SSL methods [53, 17, 5, 19] involve adding additional supervision on unlabeled data to regularize the learning of the model. Among them, pseudolabeling is a popular pipeline [4, 24, 18], where unlabeled data is firstly labeled with a supervised model, and then acts in a common training paradigm. In order to guarantee the quality of the generated labels, [24] often filter them with a hard threshold based on the classification score. In addition to hard pseudo-labels, NoisyStudent [45] explores soft supervision to avoid ambiguity problems. Besides, it injects different augmentations to the student and teacher models, to encourage consistency regularization. In light of this, plenty of approaches [44, 2, 26] enforce the model to predict similar results when applying various input permutations. Such strategies are also verified on 2D object detection, where [32] borrows the idea from FixMatch to achieve promising performance. MUM [21] introduces Mix/UnMix augmentation, enforcing students to reconstruct unmixed features for the mixed input images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 419, + 246, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 419, + 246, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 419, + 246, + 432 + ], + "type": "text", + "content": "2.3. Semi-Supervised 3D Object Detection" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": "Semi-supervised learning (SSL) has been rapidly developed in both classification and object detection domains and obtains promising results in recent years. There are two main streams in SSOD: consistency learning and pseudo labeling. Consistency-based works [41, 25] apply data augmentations/perturbations to the input, which forms natural regularization for the network predictions. Such a consistency-learning target enforces the model to acquire valid information from the unlabeled data, therefore improving the performance. SESS [55] is the first work to attempt such a paradigm on 3D object detection, where the classification and regression predictions are matched through L2 distance and supervised with the similarity loss on the teacher and student. Inspired by Mean Teacher [41], it also adopts the exponential moving average (EMA) technique to further boost the performance. Apart from the consistency-based approaches, pseudo-labeling is another solution [46, 42]. Most PL works pay attention to the quality enhancement of pseudo labels. 3DIoUMatch [42] proposes to learn the IoU of the network predictions and utilize it to adaptively filter the low-quality pseudo labels. In order to remove the duplicate score threshold search, ProficientTeacher [51] introduces a novel clustering-based box voting" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "module, replacing the hand-crafted NMS process. Different from the previous approaches, our method views pseudolabeling as a noisy learning problem, therefore delivering more generalization against noisy pseudo-data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 129, + 368, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 129, + 368, + 142 + ], + "spans": [ + { + "bbox": [ + 306, + 129, + 368, + 142 + ], + "type": "text", + "content": "3. NoiseDet" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "type": "text", + "content": "It is acknowledged that predictions generated by the teacher model will inevitably encounter false positive (FP) or false negative (FN) problems, despite many efforts that have been devoted to overcoming these issues [51, 46]. Such noises can distract the convergence of the model during the semi-supervised training process, or even deteriorate the final performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": "The main intuition of NoiseDet is to improve the model generalization ability against noisy pseudo labels, which are generated by the baseline model trained on limited labeled data. We start with a vanilla two-stage pseudo-labeling pipeline: assuming that we have access to a (small) set of labeled set " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "L = \\{x_i^l,y_i^l\\}_{i = 1}^{N_l}" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": ", and a set of unlabeled set " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "U = \\{x_i^u\\}_{i = 1}^{N_u}" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": " are the numbers of labeled and unlabeled datasets. A teacher model is firstly trained on the labeled set " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": ", and then infer on unlabeled set " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": " to get pseudo labels " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "\\{y_i^u\\}_{i = 1}^{N_u}" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": " and formulate the pseudo-labeled set " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "U_{p} = \\{x_{i}^{u},y_{i}^{u}\\}" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": ". After that, we initialize the student model from the pretrained teacher and uniformly sample data from both " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "U_{p}" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": " set to construct each batch for second-stage training. Different from previous works, which mainly focus on improving the quality of pseudo-labels, NoiseDet directly learns knowledge from noise labels " + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "inline_equation", + "content": "\\{y_i^U\\}_{i = 1}^{N_u}" + }, + { + "bbox": [ + 304, + 233, + 546, + 427 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 432, + 502, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 432, + 502, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 432, + 502, + 445 + ], + "type": "text", + "content": "3.1. Noise-Resistant Instance Supervision" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 450, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 557 + ], + "type": "text", + "content": "In contrast to standard fully supervised object detection, where labels are carefully human-annotated and verified, the supervisory signals on the unlabeled set are generated by the vanilla teacher model. It may contain unexpected noisy labels, leading to model performance degeneration. Therefore, we propose to transform such hard, deterministic instance supervision into the noise-resistant one to develop the model tolerance to the noisy labels, instead of directly eliminating them." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Recent works [16, 3] suggests that the confidence score " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " can be viewed as the noisy level of the network predictions, i.e., the model is more prone to yield a high score for easy-to-detect samples and low score for not-sure samples. Therefore, an intuitive idea is to filter the generated pseudo-labels with a pre-defined score threshold " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "U_{p} = \\{(x_{i}^{u},c_{i}^{u})|c_{i}^{u}\\geq c_{thres}\\}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " to eliminate the noises for the unlabeled dataset. Though simple, such a strategy does not provide a clear divergence for the rest labels. For instance, the quality of a box with " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "c = 0.9" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " can be different from the quality of the box with " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "c = 0.5" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ". However, they are treated equally with 1/0 labels in the classification branch. To fully exploit a reliable confidence score derived from the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6931" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 547, + 289 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 289 + ], + "type": "image", + "image_path": "ce189c39c234ea83ad8d1231d7ff141194716a07d24fc43bca74f58dea7cc6f4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "type": "text", + "content": "Figure 2. The overall architecture of the proposed NoiseDet. It consists of two main components: noise-resistant instance supervision and dense feature consistency constraint. It follows the pseudo-labeling practice with a two-stage training paradigm: (i) pseudo labels are pre-generated with a well-trained teacher model on the unlabeled dataset, and (ii) the student model is trained on both labeled (omitted in the figure) and unlabeled LiDAR points in a semi-supervised manner." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "type": "text", + "content": "teacher model, we leverage the " + }, + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "type": "text", + "content": " as an indicator to measure the quality of the pseudo label. Specifically, instead of directly assigning each anchor with a deterministic binary label, we soften the categorical label into a value ranging from 0 to 1 given the confidence score " + }, + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "type": "text", + "content": " as well as the IoU " + }, + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 368, + 289, + 535 + ], + "type": "text", + "content": " between the student predictions and its matched pseudo labels. Different from the one in GFL [27] where the categorical labels are assigned based on the IoU between the network prediction and the ground-truth boxes, we view it as the combination of the quality of the GT boxes itself and the learning ability of the student. Since the standard Focal Loss can only handle discrete binary values, we adopt Quality Focal Loss [27] to conduct the classification supervision on the non-discrete categorical labels:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 124, + 544, + 287, + 557 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 544, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 124, + 544, + 287, + 557 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\alpha c + (1 - \\alpha) \\tau , \\tag {1}", + "image_path": "48a3808d1f023eeaecfd1222ed5d2cf373ad5f5946e338eebb28d6d761fc811c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 60, + 559, + 287, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 559, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 60, + 559, + 287, + 574 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c l s} ^ {U} = - | y - \\hat {y} | ^ {\\beta} ((1 - y) \\log (1 - \\hat {y}) + y \\log (\\hat {y})), \\tag {2}", + "image_path": "4214d88e97d9862ea11a1138b117cb01551defbe181bee4b89e8da98a0486e2f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "text", + "content": " is the quality score predicted by the teacher and " + }, + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "text", + "content": " is the student predictions, " + }, + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 582, + 287, + 641 + ], + "type": "text", + "content": " is set to 0.75. Note that our approach can be easily extended into other continual versions of cross-entropy loss, for instance, Gaussian Focal Loss [23]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "In addition to the classification loss, the boundary targets of the bounding box can present more ambiguities since it contains 7 degree-of-freedom and presents fewer training samples (only positive samples receive the regression supervision). Therefore, how to effectively deal with misleading regression targets is non-trivial. To address this problem," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 368, + 546, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 546, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 546, + 415 + ], + "type": "text", + "content": "we convert the deterministic regression into the probability optimization task. Concretely, we model the network prediction of each bounding box as a Gaussian distribution " + }, + { + "bbox": [ + 304, + 368, + 546, + 415 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 368, + 546, + 415 + ], + "type": "text", + "content": " given the feature vector " + }, + { + "bbox": [ + 304, + 368, + 546, + 415 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 368, + 546, + 415 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 382, + 424, + 546, + 440 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 424, + 546, + 440 + ], + "spans": [ + { + "bbox": [ + 382, + 424, + 546, + 440 + ], + "type": "interline_equation", + "content": "\\hat {h} = \\mathcal {N} (\\mu (x), \\sigma (x)), \\tag {3}", + "image_path": "861e4cd623cedb270f5e2b571dc91b60e589b6a7192d53580330469fb2156e44.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "type": "inline_equation", + "content": "\\mu (x)" + }, + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "type": "inline_equation", + "content": "\\sigma (x)" + }, + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "type": "text", + "content": " denotes the mean and variance of each regression term predicted by the network. After that, the regression loss can be converted into a negative log-likelihood (NLL) loss, where the objective is to maximize the likelihood of each GT " + }, + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 448, + 547, + 509 + ], + "type": "text", + "content": " in the predicted distribution:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 359, + 517, + 545, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 517, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 359, + 517, + 545, + 531 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e g} = - \\log \\mathcal {N} (h; \\mu (x), \\sigma (x)) \\tag {4}", + "image_path": "e5a24c262298cdf983430a4820ed32908b197f4ccd0804b362c2ed8e08931232.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 383, + 533, + 545, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 533, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 383, + 533, + 545, + 559 + ], + "type": "interline_equation", + "content": "= - \\log \\frac {1}{\\sigma \\sqrt {2 \\pi}} e ^ {- \\frac {1}{2} \\left(\\frac {h - \\mu}{\\sigma}\\right) ^ {2}}. \\tag {5}", + "image_path": "e48f11f417969f8f5d12adf62bed94741999e6aaf16e9176f63c79bb30292a4c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 567, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 615 + ], + "type": "text", + "content": "By converting the deterministic regression task to a probabilistic estimation problem, the model develops more tolerance against noisy information in the training data, therefore achieving better performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 623, + 508, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 508, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 508, + 635 + ], + "type": "text", + "content": "3.2. Dense Feature Consistency Constraint" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "Considering that labels can contain noise information that deteriorates the model performance, we further exploit the incorporation of unsupervised learning to obtain useful knowledge about label-independent features. However, different from the common-studied image classification task that mostly cares about the overall feature representation," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6932" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "3D object detection requires estimating instances with various scales and directions. Therefore, learning a scale and rotation-invariant feature extractor for 3D detector is of vital importance. By applying various data augmentation, such as rescaling, rotating, and global transforming, into the input point clouds, and supervising them with the transformed ground-truth boxes, the model can develop robustness to such transformations. However, when the label itself is not so accurate enough, such a strategy may be more harmful." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 288, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 359 + ], + "type": "text", + "content": "To avoid this problem, we propose a dense pixel-wise consistency constraint to enforce the network to acquire such property. Previous literature mainly involves label-level consistency [55, 42, 1, 54] to ensure the model consistency, where the predicted bounding boxes are reversed back to the original space and regularized with Euclidean distance matching. Despite being simple and straightforward, this low-dimensional prediction distribution (number of classes and 7 regression targets) means that only a few amounts of knowledge are encoded, thus limiting the knowledge that can be transferred. Hence, we apply the consistency constraint on the feature level by reversing the BEV features according to the data transformation in the data augmentation and then conducting dense pixel-wise regularization." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": "More formally, given one frame of point clouds " + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": " and a set of data augmentation policies " + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": ", we randomly sample two transformations " + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_1, \\mathcal{A}_2" + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": " and apply them to the point " + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": " to produce two different views of point clouds " + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "inline_equation", + "content": "P_1, P_2" + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": ". The augmented point clouds are fed into the point feature extractor " + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": " to generate the BEV feature maps " + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 47, + 360, + 287, + 433 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 111, + 442, + 287, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 442, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 111, + 442, + 287, + 456 + ], + "type": "interline_equation", + "content": "F _ {1} = \\mathcal {F} (P _ {1}), F _ {2} = \\mathcal {F} (P _ {2}). \\tag {6}", + "image_path": "bfcccd98518dd36e87fe2b60a781845c4f3844055f9ee252518e60d4cc4ff077.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 466, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 287, + 502 + ], + "type": "text", + "content": "Once obtaining the BEV features, we simply reverse them back to the original space with the recorded transformation flow:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 100, + 511, + 287, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 511, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 100, + 511, + 287, + 526 + ], + "type": "interline_equation", + "content": "\\hat {F} _ {1} = \\mathcal {A} _ {1} ^ {- 1} \\left(F _ {1}\\right), \\hat {F} _ {2} = \\mathcal {A} _ {2} ^ {- 1} \\left(F _ {2}\\right), \\tag {7}", + "image_path": "8232c763b78940ab907c12916333139c9f5b0151728dbff4d1c9e4dfbbd52c9b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 536, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 287, + 571 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 536, + 287, + 571 + ], + "type": "inline_equation", + "content": "A^{-1}" + }, + { + "bbox": [ + 47, + 536, + 287, + 571 + ], + "type": "text", + "content": " denotes the reverse transformation of " + }, + { + "bbox": [ + 47, + 536, + 287, + 571 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 536, + 287, + 571 + ], + "type": "text", + "content": ". To this end, we can derive the pixel-wise feature consistency constraint with standard L2 loss:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 581, + 287, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 581, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 116, + 581, + 287, + 596 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n s i s t}} = \\left| \\left| \\hat {F} _ {1} - \\hat {F} _ {2} \\right| \\right| _ {2}. \\tag {8}", + "image_path": "5a9fb10ae53c166cf6db1f293389d9eadbe760aee0d787258b952a43b7de77b8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "text", + "content": "Considering that the point-based 3D features can hold meaningful information only if the point exists, mainly due to the characteristics of the LiDAR points, we further introduce a foreground-focusing mask to selectively regularize the augmented BEV features. Different from previous approaches [12] that directly set each foreground GT region with hard supervision, we generate a soft mask to smooth the regularization effect at the boundary regions, similar in [57]. Specifically, we draw a Gaussian distribution for each" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 455, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 455, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 455, + 85 + ], + "type": "text", + "content": "GT center " + }, + { + "bbox": [ + 306, + 72, + 455, + 85 + ], + "type": "inline_equation", + "content": "(x_{i},y_{i})" + }, + { + "bbox": [ + 306, + 72, + 455, + 85 + ], + "type": "text", + "content": " in the BEV space," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 344, + 93, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 93, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 344, + 93, + 545, + 121 + ], + "type": "interline_equation", + "content": "\\phi_ {i, x, y} = \\exp \\left(\\frac {\\left(x _ {i} - \\hat {x} _ {i}\\right) ^ {2} + \\left(y _ {i} - \\hat {y} _ {i}\\right) ^ {2}}{2 \\sigma_ {i} ^ {2}}\\right), \\tag {9}", + "image_path": "8eca2e524f015e1109f18f024db6556976435579cefb6aea94dad2add58f3571.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "spans": [ + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "text", + "content": " is a constant (set to 2), indicating the object size standard deviation. Since feature maps are class-agnostic, we merge all " + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "inline_equation", + "content": "\\phi_{i,x,y}" + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "text", + "content": " into one single mask " + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "text", + "content": " by taking the maximum value across the " + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 129, + 545, + 189 + ], + "type": "text", + "content": " dimension. Therefore, the final dense feature consistency constraint is derived as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 198, + 545, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 198, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 314, + 198, + 545, + 232 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n s i s t}} = \\frac {1}{H W \\Phi} \\sum_ {i} ^ {H} \\sum_ {j} ^ {W} \\max \\left(\\phi_ {i j}\\right) \\left| \\left| \\hat {F} _ {1} - \\hat {F} _ {2} \\right| \\right| _ {2}. \\tag {10}", + "image_path": "bed18849dbd34a9e47fb807e4df117abc8bcdefa5b15fd3fc6d92dbfac1387cb.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 242, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 242, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 242, + 545, + 289 + ], + "type": "text", + "content": "By aligning dense pixel-wise features on the BEV space, the model can gradually learn the ability to extract transform-invariant feature extraction and fully utilize the unlabeled data in a self-supervised manner." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 301, + 386, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 301, + 386, + 314 + ], + "spans": [ + { + "bbox": [ + 306, + 301, + 386, + 314 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 320, + 368, + 332 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 320, + 368, + 332 + ], + "spans": [ + { + "bbox": [ + 306, + 320, + 368, + 332 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 339, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 339, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 305, + 339, + 545, + 567 + ], + "type": "text", + "content": "ONCE dataset [33] is one of the largest autonomous driving datasets with 1 million LiDAR point clouds and 7 million paired images. Only 15,000 samples are annotated with 3D bounding boxes, which are divided into training, validation and testing split with a ratio of " + }, + { + "bbox": [ + 305, + 339, + 545, + 567 + ], + "type": "inline_equation", + "content": "33\\% /20\\% /47\\%" + }, + { + "bbox": [ + 305, + 339, + 545, + 567 + ], + "type": "text", + "content": ", respectively. Among all instances, five classes are labeled as interested categories: Car, Bus, Truck, Pedestrian, and Cyclist. According to the official SSL setting, 5,000 samples are selected as labeled set and all the unlabeled sets are divided into 3 scales of subsets: Small, Medium, and Large. The small set contains 70 sequences (100k samples), the medium set contains 321 sequences (500k samples), and the large set contains 560 sequences (about 1M samples). Following the official evaluation tools, we set 0.7, 0.3, and 0.5 for Vehicle, Pedestrian, and Cyclist as the mAP IoU threshold, respectively. Besides, similar to Waymo Open Dataset [40], the evaluation protocol provides metrics based on different perception ranges: '0-30m', '30-50m', and /'50minf' to fully reflect the detection ability of the model." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 575, + 440, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 440, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 440, + 588 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 594, + 545, + 713 + ], + "type": "text", + "content": "NoiseDet follows the two-stage training pipeline: we first train the teacher network with 80 epochs for ONCE dataset. Then we utilize the STE module proposed in ProficientTeacher [51] to obtain pseudo-labels on the unlabeled dataset. During this process, we can easily incorporate other techniques such as camera/Radar detection or object tracking to further refine the labels. We do not consider such implementations since it is out of the scope of this paper, but it is proven to be effective in [35]. For the semi-supervised training configuration, we uniformly sampled 1 labeled and" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6933" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 116, + 542, + 338 + ], + "blocks": [ + { + "bbox": [ + 46, + 69, + 547, + 114 + ], + "lines": [ + { + "bbox": [ + 46, + 69, + 547, + 114 + ], + "spans": [ + { + "bbox": [ + 46, + 69, + 547, + 114 + ], + "type": "text", + "content": "Table 1. Comparison with other state-of-the-art semi-supervised 3D object detection approaches on ONCE validation set with different amounts of unlabeled samples (e.g., \"Small\", \"Medium\" and \"Large\"). We bold the best overall results and list the relative gains based on the baseline model (i.e., SECOND [48] trained on labeled training set only) for better illustration. Most experimental results are borrowed from the official implementations in ONCE [33]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 116, + 542, + 338 + ], + "lines": [ + { + "bbox": [ + 52, + 116, + 542, + 338 + ], + "spans": [ + { + "bbox": [ + 52, + 116, + 542, + 338 + ], + "type": "table", + "html": "
MethodsVehicle AP (%)Pedestrian AP (%)Cyclist AP (%)mAP (%)
overall0-30m30-50m50m-infoverall0-30m30-50m50m-infoverall0-30m30-50m50m-inf
Baseline [48]71.1984.0463.0247.2526.4429.3324.0518.0558.0469.9652.4334.6151.89
Small (100K unlabeled samples)
Pseudo Label72.8084.4664.9751.4625.5028.3622.6618.5155.3765.9550.3434.4251.22 (-0.67)
Noisy Student [45]73.6984.6967.7253.4128.8133.2323.4216.9354.6765.5850.4332.6552.39 (+0.50)
Mean Teacher [41]74.4686.6568.4453.5930.5434.2426.3120.1261.0272.5155.2439.1155.34 (+3.45)
SESS [55]73.3384.5266.2252.8327.3131.1123.9419.0159.5271.0353.9336.6853.39 (+1.50)
3D IoUMatch [42]73.8184.6168.1154.4830.8635.8725.5518.3056.7768.0251.8035.9153.81 (+1.92)
NoiseDet (Ours)75.2686.3667.5255.2937.9642.3632.7823.2860.7772.3155.0338.8758.00 (+6.11)
Medium (500K unlabeled samples)
Pseudo Label73.0386.0665.9651.4224.5627.2820.8117.0053.6165.2648.4433.5850.40 (-1.49)
Noisy Student [45]75.5386.5269.7855.0531.5635.8026.2421.2158.9369.6153.7336.9455.34 (+3.45)
Mean Teacher [41]76.0186.4770.3455.9235.5840.8630.4419.8263.2174.8956.7740.2958.27 (+6.38)
SESS [55]72.1184.0666.4453.6133.4438.5828.1018.6761.8273.2056.6038.7355.79 (+3.90)
3D IoUMatch [42]75.6986.4670.2256.0634.1438.8429.1919.6258.9369.0854.1638.8756.25 (+4.36)
NoiseDet (Ours)77.1487.2169.9458.4440.4544.9135.7124.1162.5973.0457.9842.6760.06 (+8.17)
Large (1M unlabeled samples)
Pseudo Label72.4184.0664.5450.0523.6226.8020.1316.6653.2564.6948.5233.4749.76 (-2.13)
Noisy Student [45]75.5386.5269.7855.0531.5635.8026.2421.2158.9369.6153.7336.9455.34 (+3.45)
MeanTeacher [41]76.3886.4570.9957.4835.9541.7629.0518.8165.5075.7260.0743.6659.28 (+7.39)
SESS [55]75.9586.8370.4555.7634.4340.0027.9219.2063.5874.8558.8839.5157.99 (+6.10)
3D IoUMatch [42]75.8186.1171.8257.8435.7040.6830.3421.1559.6970.6954.9239.0857.07 (+5.18)
NoiseDet (Ours)78.0287.0072.5559.4942.8946.5238.2126.6062.7473.1958.0342.8861.16 (+9.27)
", + "image_path": "cff3cb03fab18b26dc575f1a9cc87182de6e1c57d1916b3a3ff94caa9da00e66.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 80, + 387, + 255, + 468 + ], + "blocks": [ + { + "bbox": [ + 47, + 361, + 288, + 384 + ], + "lines": [ + { + "bbox": [ + 47, + 361, + 288, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 288, + 384 + ], + "type": "text", + "content": "Table 2. Comparison of detection results based on SECOND and CenterPoint with and without NoiseDet on ONCE validation set." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 80, + 387, + 255, + 468 + ], + "lines": [ + { + "bbox": [ + 80, + 387, + 255, + 468 + ], + "spans": [ + { + "bbox": [ + 80, + 387, + 255, + 468 + ], + "type": "table", + "html": "
DetectorMethodmAP
SECONDNoisyStudent55.50
NoiseDet (Ours)58.01
CenterPointNoisyStudent63.77
NoiseDet (Ours)65.57
", + "image_path": "541af94a752b03651caaebc29b7981c82a48e328dbbab569f4ba882166e7a22a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 490, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 586 + ], + "type": "text", + "content": "4 unlabeled samples for each batch to avoid training collapse. Following the official ONCE benchmark [33], we initialize the student from a pretrained checkpoint on the full labeled set. The student is trained for 25, 50, 75 epochs for small, medium, and large settings on ONCE dataset. The learning rate is set to 1e-4 and the pseudo-labels are updated every 25 epochs. All models are trained on an 8 NVIDIA V100 GPUs machine." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 132, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 132, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 132, + 609 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "We first implement NoiseDet with the standard anchor-based 3D detector, SECOND, following the official benchmark [33], on the Small protocol setting of ONCE dataset. The final performance is shown in Table 2. Our NoiseDet greatly boosts its enhanced baseline NoisyStudent [45] by " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "2.5\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": ". Then, we also report it on a stronger anchor-free-based detector, CenterPoint [52], which also obtains an improvement of " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "1.8\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": ", validating the effectiveness and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 365, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 415 + ], + "type": "text", + "content": "generalization of the proposed method under different 3D detection frameworks. Besides, we also validate NoiseDet on the competitive Waymo Open Dataset [40] in Appendix, which outperforms 3DIoUMatch [42] by a large margin." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 433, + 493, + 446 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 433, + 493, + 446 + ], + "spans": [ + { + "bbox": [ + 305, + 433, + 493, + 446 + ], + "type": "text", + "content": "4.4. Comparison with State-of-the-Arts" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": "To further validate the superiority of our method, we compare NoiseDet with various state-of-the-art semi-supervised approaches, including Pseudo-Label, NoisyStudent, Mean Teacher, SESS, and 3DIouMatch. The experiments are conducted on the three different protocols (Small, Medium, and Large) to fully exploit the extensibility of various strategies and the results are reported in Table 1. We select SECOND as our baseline to keep consistent with other works [33]. NoiseDet surpasses all other counterparts, achieving new state-of-the-art in this competitive benchmark. With the increase of the unlabeled dataset size, NoiseDet can consistently improve the detectors with significant gains: with " + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "inline_equation", + "content": "6.1\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "inline_equation", + "content": "8.2\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "inline_equation", + "content": "9.3\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 456, + 545, + 624 + ], + "type": "text", + "content": " under Small, Medium, and Large protocols, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 643, + 407, + 655 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 407, + 655 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 407, + 655 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "content": "In this section, we conduct a series of ablation studies to gain a deeper understanding of NoiseDet. For efficiency, all experiments are conducted on the Small protocol of the ONCE training set and evaluated on the validation set." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6934" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 83, + 535, + 184 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 520, + 80 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 520, + 80 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 520, + 80 + ], + "type": "text", + "content": "Table 3. Effectiveness of each component in our NoiseDet. Results are reported on ONCE validation subset with SECOND." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 83, + 535, + 184 + ], + "lines": [ + { + "bbox": [ + 58, + 83, + 535, + 184 + ], + "spans": [ + { + "bbox": [ + 58, + 83, + 535, + 184 + ], + "type": "table", + "html": "
Noise-Resistant Instance Supervision ClassificationRegressionDense Feature Consistency ConstraintmAP
\\( AP_{veh} \\)\\( AP_{ped} \\)\\( AP_{cyc} \\)\\( AP_{overall} \\)
72.0336.8057.7355.50
✓72.7836.4160.7356.80
✓73.8736.7458.3456.39
✓✓74.0536.6261.0357.27
✓✓✓75.2637.9660.7758.01
", + "image_path": "623411059acc594b62e0624a1b9d679aa45d8f7bed142e1a339b6455eb669bcf.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 203, + 147, + 215 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 203, + 147, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 203, + 147, + 215 + ], + "type": "text", + "content": "4.5.1 Main Ablations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "text", + "content": "In order to understand the effectiveness of each module contributing to the detection performance in NoiseDet, we test each component separately on the baseline detector SEC-OND and report the results in Table 3. Our baseline is the enhanced implementation of NoisyStudent [45], where its performance starts from " + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "inline_equation", + "content": "55.5\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "text", + "content": " on the validation dataset. When we add the noise-resistant instance supervision on the classification branch, the mAP score is raised by " + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "inline_equation", + "content": "1.1\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "text", + "content": ". And then we test the proposed component on the regression branch, which yields another " + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "inline_equation", + "content": "0.8\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "text", + "content": ". Such a huge improvement validates the correctness of the noise learning strategy on the unknown quality of pseudo-labels and the effectiveness of the proposed noise-resistant instance supervision module. When the dense feature consistency constraint module is applied, the accuracy is promoted by " + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "inline_equation", + "content": "1.2\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "text", + "content": ", suggesting that consistent regularization provides useful unsupervised hints for model convergence. Finally, we put all techniques together, and NoiseDet achieves 58.0 mAP on the validation subset, indicating a " + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "inline_equation", + "content": "2.5\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 223, + 289, + 462 + ], + "type": "text", + "content": " performance enhancement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 479, + 238, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 238, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 238, + 491 + ], + "type": "text", + "content": "4.5.2 Noise-Resistant Instance Supervision" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": "Comparison with other classification supervision. We first compare our proposed noise-resistant classification loss with other supervision approaches. The vanilla strategy is to directly apply Focal Loss on the pseudo labels, similar to the labeled data. Then, we attempt to utilize the predicted score from the teacher to adjust the supervision on the pseudo-labels by reweighting the classification loss. In doing this, we can alleviate the training distraction from low-quality samples by lowering their penalties. Inspired by 3D IoUMatch [42], we consider IoU as another measurement to help decide the loss penalty on the pseudo samples (denoted as IoU Reweight). We also consider Quality Focal Loss proposed in [27] to further integrate IoU into the classification supervision. The final results are shown in Table 4. Incorporating reweighting mechanisms, either IoU or classification score, to balance the supervision across different samples brings about " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " improvements. When adapting to QFL, the model improves to " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "56.2\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": ". Finally," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "content": "by both considering localization quality (IoU) and the sample quality (classification score), we obtain the best performance, " + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "inline_equation", + "content": "56.8\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 203, + 545, + 239 + ], + "type": "text", + "content": " on the validation subset." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 349, + 275, + 502, + 364 + ], + "blocks": [ + { + "bbox": [ + 304, + 249, + 545, + 271 + ], + "lines": [ + { + "bbox": [ + 304, + 249, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 304, + 249, + 545, + 271 + ], + "type": "text", + "content": "Table 4. Comparison with different classification supervision approaches on ONCE validation dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 349, + 275, + 502, + 364 + ], + "lines": [ + { + "bbox": [ + 349, + 275, + 502, + 364 + ], + "spans": [ + { + "bbox": [ + 349, + 275, + 502, + 364 + ], + "type": "table", + "html": "
Classification LossAPoverall
Focal Loss [31]55.45 ± 0.07
Score Reweight56.09 ± 0.10
IoU Reweight55.90 ± 0.17
QFocal Loss [27]56.20 ± 0.05
Ours56.80 ± 0.08
", + "image_path": "0c8ee0c7e8d23690b894a8de6901796e6c39be9ae8797fe06de84b23394af2ec.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "type": "text", + "content": "Strategies on " + }, + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "type": "text", + "content": " generation. In this part, we explore the best strategy to generate the classification targets " + }, + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "type": "text", + "content": " for the Focal Loss. We first consider utilizing the teacher's predicted categorical confidence to replace the original hard pseudo labels, based on the observation that the quality of the generated pseudo-labels is highly correlated with the classification score. On top of this, we also consider the localization quality between the student and teacher's predictions. The main intuition is that when the student model can not perfectly learn the pseudo-targets well, we infer them as noisy labels and downgrade their categorical targets. Actually, this strategy comes to the same formulation as Quality Focal Loss. In order to further improve the representation ability of " + }, + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 378, + 545, + 604 + ], + "type": "text", + "content": ", we adopt the combination of IoU and confidence score to fully leverage the information. We consider two types of combinations: multiplication and weighted sum. The experimental results are shown in Table 5. By combining IoU and confidence score with weighted sum, the detection accuracy gets the best performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "Comparison with other regression supervision. In addition to classification targets " + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": ", properly softening the regression supervision on noisy pseudo labels is also nontrivial. Therefore, we compare different kinds of regression losses and their tolerance against noisy data. The original loss is Smooth L1 loss, which provides more penalty on more accurate predictions (close to GT targets), encouraging the model to pay more attention to high-precision boxes. However, such a strategy is counter to the learning on noisy" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6935" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 95, + 272, + 188 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "type": "text", + "content": "Table 5. Ablations on the strategies to generate the classification target " + }, + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 47, + 69, + 287, + 91 + ], + "type": "text", + "content": " for categorical supervision." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 95, + 272, + 188 + ], + "lines": [ + { + "bbox": [ + 60, + 95, + 272, + 188 + ], + "spans": [ + { + "bbox": [ + 60, + 95, + 272, + 188 + ], + "type": "table", + "html": "
Cls ScoreIoUOperationAPoverall
✓-55.45 ± 0.07
-56.45 ± 0.17
✓-56.11 ± 0.21
✓✓Multiply56.52 ± 0.05
✓✓Weighted-sum56.80 ± 0.08
", + "image_path": "e1cf45a3fc4084632a7e067f6ed9f55eaaf46407fae85117e2c28c38f522456d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 198, + 289, + 373 + ], + "blocks": [ + { + "bbox": [ + 48, + 198, + 289, + 373 + ], + "lines": [ + { + "bbox": [ + 48, + 198, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 48, + 198, + 289, + 373 + ], + "type": "image", + "image_path": "467505eb89dda5528a8282179dee08e3b77daef37e120673d96b955aad675eff.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 384, + 287, + 452 + ], + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 452 + ], + "type": "text", + "content": "Figure 3. Visualization of the loss curve of different regression approaches on the labeled split in each batch. We also plot the final detection performance (mAP) at the end iteration of each loss. Note that there exists occasional fluctuations during training probably due to the noisy annotations in the training data, empirically it will not affect the final model performance." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 472, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 605 + ], + "type": "text", + "content": "labels: if the network fails to regress the target well, it probably belongs to low-quality samples. Therefore, we directly employ the L1 loss to avoid large misleading gradients on noisy bounding box regression. Another option to improve the tolerance against noisy labels for regression is to convert the regression task into a probabilistic optimization problem. As a result, we consider the Gaussian NLL as an alternative regression objective. We report the results in Figure 3. Gaussian NLL outperforms all other losses, achieving " + }, + { + "bbox": [ + 46, + 472, + 287, + 605 + ], + "type": "inline_equation", + "content": "56.4\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 472, + 287, + 605 + ], + "type": "text", + "content": " on the validation subset, demonstrating the superiority of the probabilistic model on noisy data learning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 622, + 243, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 243, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 243, + 634 + ], + "type": "text", + "content": "4.5.3 Dense Feature Consistency Constraint" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 715 + ], + "type": "text", + "content": "Strategies on consistency regularization. Consistency learning is a crucial component in semi-supervised pipelines. In most previous work [55], such regularization is often conducted on the label level. A key reason is that label encoding is agnostic to any transformation, which is easy to apply to various object detection tasks. Luckily, most in-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": "put permutations in point clouds can be easily reversed and differentiable. Therefore, we can also explore the feature-level consistency regularization with L2 loss. Followed by the idea of SimSiam [6], we add a projection layer for one branch and detach the gradient in the other branch, and then regularize them with L2 loss. We also consider distance correlation to consider the inner structural similarity in the latent feature space. The final results are shown in Table 6. The vanilla L2 loss on the feature level obtains the best performance. We infer the reason that mutual L2 introduces additional flexibility through the linear projection layer and further promotes the effect of consistent regularization." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 345, + 251, + 505, + 315 + ], + "blocks": [ + { + "bbox": [ + 305, + 224, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 247 + ], + "type": "text", + "content": "Table 6. Comparison with different approaches for dense feature consistency constraints. \"DC\" denotes distance correlation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 345, + 251, + 505, + 315 + ], + "lines": [ + { + "bbox": [ + 345, + 251, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 345, + 251, + 505, + 315 + ], + "type": "table", + "html": "
Input-levelLossAP
Label-levelL255.45 ± 0.07
Feature-levelDC56.07 ± 0.14
Feature-levelL256.70 ± 0.06
", + "image_path": "dc402457f390a05fdb8d4af61c2bef970e49e268ff709993a374288917e26abd.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 334, + 499, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 499, + 347 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 499, + 347 + ], + "type": "text", + "content": "4.6. Extension to Auto-Labeling Strategy" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 352, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 579 + ], + "type": "text", + "content": "Auto-Labeling is a simple and effective strategy to improve model prediction. By combing with additional techniques, such as temporal information or object tracking, we can obtain high-quality pseudo-labels [35]. Different from the Mean-Teacher paradigm, the pseudo-labeling pipeline allows the network to pursue more precious labels offline and greatly improves its potential in real-world applications. In this section, we imitate this paradigm and validate the superiority of our framework. Specifically, we generate the pseudo-labels based on two well-tuned CenterPoint models, (CenterPoint and CenterPoint-E), which achieve 62.5 and " + }, + { + "bbox": [ + 304, + 352, + 545, + 579 + ], + "type": "inline_equation", + "content": "70.1\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 352, + 545, + 579 + ], + "type": "text", + "content": " on the ONCE validation subset, respectively, to stimulate the auto-labeling process and utilize it to supervise a SECOND model. The final results are shown in Table 7. With the quality-improved label, our NoiseDet still consistently outperforms the competitive NoisyStudent baseline, yielding a 1.4 and " + }, + { + "bbox": [ + 304, + 352, + 545, + 579 + ], + "type": "inline_equation", + "content": "2.2\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 352, + 545, + 579 + ], + "type": "text", + "content": " on the ONCE validation subset, demonstrating its effectiveness and generalization on semi-supervised learning tasks." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 307, + 635, + 545, + 699 + ], + "blocks": [ + { + "bbox": [ + 305, + 588, + 545, + 632 + ], + "lines": [ + { + "bbox": [ + 305, + 588, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 305, + 588, + 545, + 632 + ], + "type": "text", + "content": "Table 7. Detection results on different pseudo-label generation with respective teacher models. The results are reported on ONCE validation dataset. CenterPoint-E denotes for the enhanced version of CenterPoint." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 635, + 545, + 699 + ], + "lines": [ + { + "bbox": [ + 307, + 635, + 545, + 699 + ], + "spans": [ + { + "bbox": [ + 307, + 635, + 545, + 699 + ], + "type": "table", + "html": "
PL SourceAPvehAPpedAPcycAPoverall
SECOND [48]75.2637.9660.7758.00
CenterPoint [52]75.4240.1962.7359.44
CenterPoint-E [52]76.0141.5663.0160.19
", + "image_path": "2ebb9acd84c2e485833793315ab57d52b8921136941e89724d836090e1c75a4a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6936" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 119, + 83 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 289, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 289, + 259 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 289, + 259 + ], + "type": "text", + "content": "In this paper, we introduce a pseudo-labeling-based semi-supervised 3D object detection framework, namely NoiseDet. By viewing the semi-supervised learning as a noisy learning task, we propose two core modules to overcome the ambiguity detection problem: noise-resistant instance supervision and dense feature consistency regularization. With soft task supervision on the unlabeled data and unsupervised feature consistency regularization, our model develops tolerance towards noisy pseudo-labels and improves the model generalization. Extensive experiments on the ONCE dataset demonstrate the effectiveness and generalization of our approach. We hope NoiseDet can provide a new perspective in dealing with in-sufficient accuracy pseudo labels for semi-supervised 3D object detection." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 269, + 145, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 269, + 145, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 269, + 145, + 283 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 361 + ], + "type": "text", + "content": "This work was supported by the JKW Research Funds under Grant 20-163-14-LZ-001-004-01, and the Anhui Provincial Natural Science Foundation under Grant 2108085UD12. 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In CVPR, pages 4490-4499, 2018. 2" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6939" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/911172cc-132a-4651-a728-4f623936c716_content_list.json b/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/911172cc-132a-4651-a728-4f623936c716_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..421e1a148a1f9bd0cf5b17abff8dc7b409ac0755 --- /dev/null +++ b/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/911172cc-132a-4651-a728-4f623936c716_content_list.json @@ -0,0 +1,1556 @@ +[ + { + "type": "text", + "text": "Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization", + "text_level": 1, + "bbox": [ + 197, + 130, + 772, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kun Xia $^{1,3\\dagger}$ Le Wang $^{1*}$ Sanping Zhou $^{1}$ Gang Hua $^{2}$ Wei Tang $^{3}$ $^{1}$ National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University \n $^{2}$ Wormpex AI Research $^{3}$ University of Illinois Chicago", + "bbox": [ + 169, + 202, + 800, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 325, + 313, + 343 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semi-Supervised Temporal Action Localization (SS-TAL) aims to improve the generalization ability of action detectors with large-scale unlabeled videos. Albeit the recent advancement, one of the major challenges still remains: noisy pseudo labels hinder efficient learning on abundant unlabeled videos, embodied as location biases and category errors. In this paper, we dive deep into such an important but understudied dilemma. To this end, we propose a unified framework, termed Noisy Pseudo-Label Learning, to handle both location biases and category errors. Specifically, our method is featured with (1) Noisy Label Ranking to rank pseudo labels based on the semantic confidence and boundary reliability, (2) Noisy Label Filtering to address the class-imbalance problem of pseudo labels caused by category errors, (3) Noisy Label Learning to penalize inconsistent boundary predictions to achieve noise-tolerant learning for heavy location biases. As a result, our method could effectively handle the label noise problem and improve the utilization of a large amount of unlabeled videos. Extensive experiments on THUMOS14 and ActivityNet v1.3 demonstrate the effectiveness of our method. The code is available at github.com/kunnxia/NPL.", + "bbox": [ + 75, + 358, + 473, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 720, + 209, + 736 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Temporal Action Localization (TAL) aims at detecting action instances of interest in an untrimmed video by locating their temporal boundaries and recognizing their action categories. Most existing TAL methods rely on dense temporal annotations for the training videos. However, labeling human actions is very tedious and time-consuming. As a remedy, Semi-Supervised TAL (SS-TAL) requires only a few", + "bbox": [ + 75, + 744, + 470, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/58e266e1acd772d3f4fbc5c3447c4b4baba82ebdca7dd54b2cadf2a9fee5d9e0.jpg", + "image_caption": [ + "Figure 1. Illustration of label noise. Two examples demonstrate that pseudo labels may contain location biases and category errors. The fewer labeled videos are available, the heavier the noise of the pseudo labels will be." + ], + "image_footnote": [], + "bbox": [ + 506, + 328, + 885, + 579 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "labeled videos in conjunction with a large amount of unlabeled videos. It has attracted growing attention in academia and industry.", + "bbox": [ + 496, + 670, + 893, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing SS-TAL methods [12, 37, 28] are based on consistency regularization or self-training. Consistency-based methods [12, 37] aim to generate consistent action proposals for the same video subject to different augmentations, e.g., time warping [12] and temporal feature shift [37]. In contrast, the self-training-based method [28] achieves new state-of-the-art performance by alternating between pseudo-labeling and re-training. It focuses on designing a proposal-free framework to address proposal error propagation from [12, 37] but neglects the important role of pseudo labels. Albeit its advancement, label noise still remains a core challenge, hindering efficient learning on abundant un", + "bbox": [ + 496, + 719, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 107, + 862, + 233, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Part of this work was done while Kun Xia was a visiting scholar at University of Illinois Chicago.", + "bbox": [ + 78, + 875, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10160", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "labeled videos. From Figure 1, we can observe that label noise commonly leads to two intractable issues, i.e., location bias and category error, which become worse as the amount of labeled videos decreases. As a result, noisy pseudo labels will significantly degrade the performance of SS-TAL.", + "bbox": [ + 75, + 90, + 468, + 166 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a Noisy Pseudo-Label Learning (NPL) framework tailored for SS-TAL to combat detrimental label noise. It follows the self-training paradigm that alternates between pseudo-labeling and model training. But unlike all previous self-training methods, our NPL includes three novel components, termed Noisy Label Ranking, Noisy Label Filtering, and Noisy Label Learning, respectively, which alleviate the negative effects caused by location biases and category errors in a unified framework.", + "bbox": [ + 75, + 167, + 470, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "First, Noisy Label Ranking aims to rank and select high-quality pseudo labels based on both semantic confidence and boundary reliability. Classification scores have been widely used in self-training to measure the quality of pseudo labels, but they only reflect semantic confidence and fail to account for localization reliability. To close this gap, we explicitly model the localization reliability of a detected action instance in an unlabeled video as the variance of the boundary predictions from dense snippets within the action. We then introduce a new integrated metric of semantic confidence and boundary reliability to rank the pseudo labels.", + "bbox": [ + 75, + 301, + 470, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Second, Noisy Label Filtering aims at addressing the class-imbalance problem in noisy pseudo labels. Owing to the category error, the class-imbalance problem occurs regardless of whether pseudo labels are sampled based on a confidence threshold or the number of samples. The model will be dominated by redundant noisy pseudo labels in training, especially for the ones of category errors, and further harm its generalization ability. To address this issue, we introduce an adaptive filtering strategy to regularize the distribution of pseudo labels and adaptively assign class-balanced pseudo labels to unlabeled videos.", + "bbox": [ + 75, + 468, + 470, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Last, Noisy Label Learning aims to improve the robustness of training to location bias. While noisy label ranking and filtering can improve the quality of sampled pseudo labels, location bias will not be removed completely. Training on biased boundary labels hinders the convergence of the model and further impedes accurate action localization. To this end, we propose a noise-tolerant training algorithm based on an unsupervised temporal consistency loss, which penalizes inconsistent predictions from adjacent action frames.", + "bbox": [ + 75, + 633, + 470, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions are summarized as follows:", + "bbox": [ + 96, + 785, + 434, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- This paper introduces a Noisy Pseudo-Label Learning (NPL) framework tailored for SS-TAL, which handles both the location bias and category error in a unified framework. Extensive experiments conducted on THUMOS14 [13] and ActivityNet v1.3 [2] demonstrate the effectiveness of the proposed method.", + "bbox": [ + 94, + 809, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a Noisy Label Ranking method to rank and select high-quality pseudo labels based on a new integrated metric of semantic confidence and boundary reliability.", + "- We propose a Noisy Label Filtering method to tackle the largely ignored class-imbalance problem in pseudo labels based on a new adaptive filtering strategy.", + "- We introduce a Noisy Label Learning method, which adopts an unsupervised temporal consistency loss to penalize inconsistent predictions from adjacent frames for noise-tolerant learning." + ], + "bbox": [ + 517, + 90, + 890, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 301, + 640, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Temporal Action Localization. The recent significant advancement of TAL arguably owes to the availability of large-scale and well-annotated datasets. We can roughly categorize existing TAL methods into three groups. Anchor-based methods [43, 5, 45, 52, 36] employ multiscale anchors that may contain an action and refine them via a boundary regression head. GTAN [25] dynamically optimizes the scale of each anchor via Gaussian kernels. G-TAD [45] improves temporal anchor representation with semantic and temporal context. Anchor-free methods [54, 29, 18, 27, 40, 39, 41] directly learn to predict action proposals by grouping possible start/end locations [20, 19] or regressing the distance to action boundaries [18, 49]. Transformer-based methods [31, 24, 49, 8] adopt the Transformer architecture [33, 3] for action localization and achieve remarkable performance on TAL benchmarks. In addition, unsupervised temporal action localization [11, 50] has made remarkable achievements without requiring any annotations.", + "bbox": [ + 496, + 325, + 893, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semi-Supervised Learning. Semi-Supervised Learning (SSL) methods mostly focus on image classification. They can be classified into two categories. Consistency-based methods [32, 26, 51, 1] enforce the model to produce consistent predictions across label-preserving image augmentations. Self-training methods [42, 15, 10] retrain the model with high-confidence pseudo labels of unlabeled raw data. Thereby, the final performance is largely limited by the quality of pseudo labels generated by an inaccurate model trained using a few labeled data. Much effort tries to remedy noisy pseudo labels [16, 23, 44, 55, 17, 46]. Li et al. [16] train a noise-tolerant model, which is encouraged to produce consistent predictions under a variety of noisy synthetic labels. DSL [7] directly ignores the gradient computation and propagation for ambiguous pseudo labels. Wang et al. [38] propose an iterative training method to identify and down-weigh noisy samples. Chen et al. [6] address severe confirmation bias during self-training and generate unbiased pseudo labels to drive student learning. In this paper, we focus on the challenging SS-TAL problem.", + "bbox": [ + 496, + 598, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10161", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b60c2c584f2b6aa971674514e2f323d7b013950153b0c7824142c7eb80743e4d.jpg", + "image_caption": [ + "Figure 2. An overview of our proposed Noisy Pseudo-Label Learning framework. The training data contain both labeled and unlabeled videos. We first obtain a pre-trained model using a small amount of labeled videos and generate pseudo labels on unlabeled videos. To deal with noise in pseudo labels, Noisy Label Ranking first assesses the quality of pseudo labels through both semantic confidence and boundary reliability. Noisy Label Filtering then adaptively filters pseudo labels so that the model learning will not be dominated by pseudo labels with category errors. To make the training robust to label noise, we introduce dense temporal consistency training with $L_{u}^{\\mathrm{cons}}$ . The model can be optimized by the final loss, which is the sum of $L_{s}$ , $L_{u}^{\\mathrm{cls}}$ , and $L_{u}^{\\mathrm{cons}}$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 98, + 890, + 342 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semi-Supervised Temporal Action Localization. SS-TAL is a worthwhile but under-explored field. Existing works [12, 37, 9, 28] are intrinsically driven by SSL. Some works [12, 37, 9] aim to improve the consistent predictions of the teacher-student network when video features are augmented by different temporal perturbations, e.g., time warping/masking [12], temporal feature shift/flip [37] or spatiotemporal feature crossover [9]. The other one [28] focuses on addressing proposal error propagation, which alternates between predicting and applying pseudo labels. However, all these approaches fail to dive deep into the major challenge of SS-TAL, i.e., noisy pseudo labels hindering efficient learning on unlabeled videos. We attribute the label noise problem of pseudo labels from unlabeled videos to the semantic uncertainty and boundary ambiguity of labeled actions. This paper tackles both the location bias and category error of pseudo labels into a unified framework for efficient learning from unlabeled videos.", + "bbox": [ + 75, + 455, + 472, + 727 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 743, + 169, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 768, + 207, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Problem Setting. Semi-supervised temporal action localization (SS-TAL) aims to perform TAL from a small amount of labeled videos $\\{X_{i}|_{i = 1}^{N_{l}}\\}$ and a large amount of unlabeled videos $\\{U_i|_{i = 1}^{N_u}\\}$ , where $N_{l}$ and $N_{u}$ are the numbers of labeled and unlabeled videos, respectively. In a labeled video, its annotation is a set of action instances, and each action instance could be represented as $(t_s,t_e,c)$ , where $t_s,t_e,$ and $c$", + "bbox": [ + 75, + 792, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "denote the start time, end time, and action class, respectively.", + "bbox": [ + 498, + 455, + 893, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature Encoding. Following conventions [45, 47], we sample a video snippet from every few consecutive frames. Then, we adopt a fine-tuned two-stream network to extract RGB and optical flow features at each video snippet.", + "bbox": [ + 498, + 470, + 893, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. Recent anchor-free TAL methods [18, 49, 27] are more attractive and practical since they are powerful and portable to be deployed in many real-world applications. We take the anchor-free detector [49] as our baseline, where each video snippet is directly supervised by the corresponding labels, i.e., distances to boundaries and the action category.", + "bbox": [ + 496, + 532, + 893, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our SS-TAL framework follows the self-training paradigm [30], which can be decomposed into two steps. In the first step, we obtain a pre-trained model based on labeled videos with a supervised loss and then generate pseudo labels on unlabeled videos. In the second step, we update the model parameters with a semi-supervised training objective, including a supervised loss and an unsupervised loss:", + "bbox": [ + 496, + 625, + 893, + 729 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {s} + \\alpha \\mathcal {L} _ {u}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 743, + 890, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_s$ and $\\mathcal{L}_u$ denote the supervised loss of labeled videos and the unsupervised loss of unlabeled videos, respectively, and $\\alpha$ controls the contribution of the unsupervised loss. Both of them are normalized by the corresponding numbers of training samples as follows:", + "bbox": [ + 496, + 773, + 893, + 849 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} = \\frac {1}{N _ {l}} \\sum_ {i = 1} ^ {N _ {l}} \\left(\\mathcal {L} _ {s} ^ {\\mathrm {c l s}} \\left(X _ {i}\\right) + \\mathcal {L} _ {s} ^ {\\mathrm {r e g}} \\left(X _ {i}\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 862, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10162", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {u} = \\frac {1}{N _ {u}} \\sum_ {i = 1} ^ {N _ {u}} \\left(\\mathcal {L} _ {u} ^ {\\mathrm {c l s}} \\left(U _ {i}\\right) + \\mathcal {L} _ {u} ^ {\\mathrm {r e g}} \\left(U _ {i}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 102, + 470, + 143 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}^{\\mathrm{cls}}$ is a classification loss, $\\mathcal{L}^{\\mathrm{reg}}$ is a regression loss, and $N_{l}$ and $N_{u}$ denote the number of training samples for labeled and unlabeled videos, respectively.", + "bbox": [ + 76, + 150, + 470, + 195 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We claim that the major obstacle that hinders self-training performance lies in label noise, which leads to two issues: location biases and category errors. In this paper, we propose a Noisy Pseudo-Label Learning framework (NPL) to alleviate the negative effects caused by location biases and category errors for SS-TAL. The pipeline of our method is illustrated in Figure 2. It includes three novel components: Noisy Label Ranking, Noisy Label Filtering, and Noisy Label Learning, described in the following sections.", + "bbox": [ + 75, + 196, + 470, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Noisy Label Ranking", + "text_level": 1, + "bbox": [ + 76, + 340, + 274, + 357 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In SS-TAL, the quality of pseudo labels can be measured from two perspectives, i.e., semantic confidence and boundary reliability. It is desirable to have high-quality pseudo labels for semi-supervised learning.", + "bbox": [ + 76, + 364, + 468, + 424 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The majority of TAL frameworks [20, 53, 52, 36] rely on the foreground score of an anchor or a proposal to measure its quality. However, the foreground score only reflects semantic confidence and cannot account for boundary reliability. From Figure 3 (a), we can observe that foreground scores may not strongly correlate with the localization quality (i.e., IoU w.r.t. ground truth). Thus, it is necessary to measure the quality of pseudo labels from both aspects of action classification and boundary localization.", + "bbox": [ + 75, + 424, + 470, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For labeled videos, anchors or proposals corresponding to the same action instance are supervised by the same ground truth during training. Thus, they are gradually regressed to the similar temporal boundary locations. This motivates us to use the consistency of the boundary predictions to measure their location reliability. Specifically, taking our anchor-free framework as an example, we can obtain dense predictions of action instances before the post-processing phase. Given a prediction $p_j = (\\hat{t}_{s,j}, \\hat{t}_{e,j}, c_j)$ where $\\hat{t}_{s,j}$ and $\\hat{t}_{e,j}$ are the predicted start and end boundaries of the $j$ -th video snippet respectively and $c_j$ is its foreground score, we can obtain a set of predictions $\\{p_n\\}_{n=1}^{N_a}$ from its $N_a$ adjacent snippets. Then, we formulate the boundary ambiguity of $p_j$ as follows:", + "bbox": [ + 75, + 560, + 470, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\sigma} _ {j} = \\hat {\\sigma} _ {s, j} + \\hat {\\sigma} _ {e, j},\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 770, + 338, + 786 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {s, j} = \\frac {\\sigma_ {s , j}}{d (p _ {j})}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 787, + 470, + 818 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {e, j} = \\frac {\\sigma_ {e , j}}{d (p _ {j})},\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 820, + 308, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma_{s,j}$ and $\\sigma_{e,j}$ are the variances of the start and end boundaries of $\\{p_n\\}_{n = 1}^{N_a}$ , respectively. $\\hat{\\sigma}_{s,j}$ and $\\hat{\\sigma}_{e,j}$ are normalized by their duration $d(p_j)$ . A smaller boundary vari", + "bbox": [ + 76, + 854, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7522465f91e375b8547b389e360714b0faaef39f9f45bb9a8c1a78367ec816d4.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 501, + 93, + 694, + 210 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ed119a7fc26802ee0327b2821b440629fe797274eed6dd2dfd73ce57fcabda63.jpg", + "image_caption": [ + "(b)", + "Figure 3. Each star represents a prediction result (i.e., a pseudo label) on $60\\%$ unlabeled videos based on the model trained with $40\\%$ labeled videos on THUMOS14. (a) depicts the correlation between the foreground score and the IoU with ground truth. (b) depicts the correlation between the boundary variance and the IoU with ground truth. It can be observed that the boundary variance highly correlates with the localization quality." + ], + "image_footnote": [], + "bbox": [ + 694, + 94, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ance $\\bar{\\sigma}_j$ indicates lower boundary ambiguity of the prediction $p_j$ , thus leading to higher localization reliability. In Figure 3 (b), we experimentally illustrate the correlation between the boundary variance and IoU w.r.t ground truth. We can observe that boundary variances could better measure the localization quality of pseudo labels than the classification scores. Particularly, this motivates us to define the confidence score of $p_j$ as:", + "bbox": [ + 496, + 349, + 893, + 472 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {j} = \\frac {c _ {j}}{\\bar {\\sigma} _ {j}}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 661, + 482, + 890, + 512 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Eq. (5) provides a comprehensive metric to measure the quality of pseudo labels by their semantic confidence (foreground score $c$ ) and boundary ambiguity (boundary variance $\\bar{\\sigma}$ ). As a result, our Noisy Label Ranking could improve the quality of pseudo labels only from intrinsic video snippets without requiring additional learnable networks or hyperparameters.", + "bbox": [ + 496, + 521, + 893, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Noisy Label Filtering", + "text_level": 1, + "bbox": [ + 500, + 635, + 700, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training on a few labeled videos inevitably produces noisy pseudo labels with category errors on unlabeled videos. As a result, the frequencies of some action categories in the selected pseudo labels will be much larger or smaller than their natural frequencies in the videos, regardless of whether pseudo labels are sampled based on a confidence threshold or the number of samples. We call this phenomenon the class-imbalance problem of pseudo labels in SS-TAL, illustrated in Figure 4. For example, the frequency of \"Golf Swing\" in pseudo labels is much higher than that in ground truth labels, while the frequency of \"Throw Discus\" is much lower in the pseudo labels.", + "bbox": [ + 496, + 659, + 893, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Under this class-imbalance problem, overwhelming pseudo labels with category errors will dominate the model learning and further aggravate the semantic uncertainty of actions of category errors, resulting in limited gains.", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10163", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/435e98c65b58e57a78c7aea01d3577a620c66b8100197909f0c6e09fc01b2c10.jpg", + "image_caption": [ + "Figure 4. Illustration of the class-imbalance problem of pseudo labels obtained on $60\\%$ unlabeled THUMOS14. The horizontal axis of the histogram represents the class name, and the vertical axis represents the ratio between the number of pseudo labels and the number of ground truth labels. It can be observed that our Noisy Label Filtering could alleviate the class-imbalance problem of pseudo labels." + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 446, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address this class-imbalance problem, we introduce an adaptive filtering strategy to regularize the distribution of pseudo labels for each category. Concretely, we arrange dense labels according to the category of actions and the number of pseudo labels in an unlabeled video, as follows:", + "bbox": [ + 75, + 417, + 468, + 494 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nK _ {a d p} = \\frac {\\left| \\left\\{p _ {n} ^ {c} \\right\\} _ {n = 1} ^ {N _ {v}} \\right|}{N _ {v}} \\cdot N _ {p o s}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 503, + 468, + 541 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{v}$ is the total number of pseudo labels within a video, and $N_{pos}$ is a hyper-parameter to control the number of positive predictions. Eq. (6) is used to adaptively select the number $K_{adp}$ of class-specific pseudo labels for the category $c$ in each unlabeled video. From Figure 4, we experimentally demonstrate that our adaptive filtering strategy could address the class-imbalance distribution of pseudo labels. As a result, our Noisy Label Filtering could not only assign accurate pseudo labels to improve the model learning but also prevent the pseudo labels from being dominated by overwhelming pseudo labels with category errors, while it also avoids tediously adjusting heuristic thresholds.", + "bbox": [ + 75, + 550, + 472, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Noisy Label Learning", + "text_level": 1, + "bbox": [ + 76, + 741, + 281, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The boundary ambiguity of labeled actions gives rise to noisy pseudo labels with location biases. Subsequently, training on the biased boundaries results in the boundary ambiguity of unlabeled actions and impedes accurate action localization.", + "bbox": [ + 75, + 763, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To remedy it, we propose a noise-tolerant training algorithm for unlabeled videos with heavy location biases. It aims to penalize inconsistency boundary predictions from adjacent feature locations within a video feature sequence.", + "bbox": [ + 75, + 840, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our unsupervised temporal consistency loss is defined as follows:", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {u} ^ {\\text {c o n s}} = \\frac {1}{M _ {u} \\left(M _ {p} - 1\\right)} \\sum_ {j = 1} ^ {M _ {u}} \\sum_ {i = 1} ^ {M _ {p} - 1} \\left| b _ {i + 1} ^ {j} - b _ {i} ^ {j} \\right|, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 128, + 893, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $M_{u}$ denotes the number of pseudo labels within an unlabeled video. $M_{p}$ represents the number of the training snippets within an action. $b_{i}$ represents the predicted start/end boundary locations from the $i$ -th snippet. In this way, the model could learn to produce more reliable predictions. Consequently, our complete unsupervised loss is denoted below:", + "bbox": [ + 498, + 185, + 893, + 289 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {u} = \\frac {1}{N _ {u}} \\sum_ {i = 1} ^ {N _ {u}} \\left(\\mathcal {L} _ {u} ^ {\\mathrm {c l s}} \\left(U _ {i}\\right) + \\mathcal {L} _ {u} ^ {\\mathrm {c o n s}} \\left(U _ {i}\\right)\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 299, + 890, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Noisy Label Learning makes the training robust to location biases in the pseudo labels. Finally, the model can be optimized by the sum of $\\mathcal{L}_s$ and $\\mathcal{L}_u$ on all videos.", + "bbox": [ + 498, + 352, + 890, + 397 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 411, + 632, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 500, + 436, + 697, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Datasets. We evaluate our proposed method on two benchmark TAL datasets, i.e., THUMOS14 [13] and ActivityNet v1.3 [2]. THUMOS14 [13] is a standard benchmark for TAL. It contains 200 validation videos and 213 testing videos, including 20 action categories. It is very challenging since each video has more than 15 action instances. Following the common setting [48], we use the validation set for training and evaluate on the testing set.", + "bbox": [ + 498, + 459, + 890, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ActivityNet v1.3 [2] is a large-scale benchmark for video-based action localization. It contains 10k training videos and 5k validation videos corresponding to 200 different actions. Following the standard practice [22], we train our method on the training set and test it on the validation set.", + "bbox": [ + 498, + 580, + 893, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We use the mean Average Precision (mAP) as the evaluation metric. The tIoU thresholds are $[0.3:0.1:0.7]$ for THUMOS14 and $[0.5:0.05:0.95]$ for ActivityNet v1.3. We report the average mAP of the IoU thresholds between 0.5 and 0.95 with the step of 0.05 on ActivityNet v1.3. Also, we present the average mAP of the tIoU thresholds from 0.3 to 0.7 on THUMOS14.", + "bbox": [ + 498, + 656, + 893, + 760 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The goal of SS-TAL is to use a large amount of unlabeled data to improve a well-trained detector on a small amount of labeled data. We randomly sample $10\\%$ , $20\\%$ , $40\\%$ , and $60\\%$ of the training data as labeled data and treat the remainder as unlabeled data.", + "bbox": [ + 498, + 761, + 890, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 847, + 715, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We implement our semi-supervised action localization framework based on the recent prevalent anchor-free detector", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10164", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0927ee05a046cf22c79576b85ec9e1fdb0e790a9534944fd9234f3dd69e797ea.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Performance comparison with state-of-the-art SS-TAL methods on THUMOS14 testing set and ActivityNet v1.3 validation set. Notably, SSP and SSTAP employ UntrimmedNet [34] trained with $100\\%$ class labels for proposal classification. ActF refers to ActionFormer [49]. \\* means using only labeled training videos." + ], + "table_body": "
LabelMethodBackboneTHUMOS14 (%)ActivityNet v1.3 (%)
0.30.40.50.60.7Avg.0.50.750.95Avg.
10%ActF* [49]I3D28.522.914.18.24.115.647.824.21.725.6
ActF [49] + MixUp [51]I3D29.724.214.59.65.416.749.427.93.128.8
NPL (ActF)I3D32.829.620.111.77.220.351.933.43.632.5
SSP [12]TSN44.234.124.616.99.325.838.928.78.427.6
SSTAP [37]TSN45.635.226.317.510.727.040.729.69.028.2
SPOT [28]TSN49.440.431.522.912.431.349.931.18.332.1
NPL (BMN)TSN50.041.733.523.613.432.450.932.07.932.6
20%ActF* [49]I3D49.141.632.621.512.131.451.234.33.832.9
ActF [49] + MixUp [51]I3D51.243.234.023.914.133.352.934.73.933.3
NPL (ActF)I3D54.547.139.329.718.537.853.135.83.933.8
SPOT [28]TSN52.643.934.125.216.234.451.732.06.932.3
NPL (BMN)TSN53.945.636.226.916.535.852.132.97.932.9
40%ActF* [49]I3D69.060.449.331.519.345.953.235.73.834.2
ActF [49] + MixUp [51]I3D69.761.952.434.420.147.753.136.04.334.5
NPL (ActF)I3D71.965.455.740.923.451.553.636.54.635.3
SPOT [28]TSN54.445.837.229.719.437.353.333.06.633.2
NPL (BMN)TSN56.246.738.830.319.538.353.433.98.133.8
60%ActF* [49]I3D71.565.659.947.332.755.453.936.15.735.0
ActF [49] + MixUp [51]I3D72.267.561.248.734.056.754.136.45.735.2
NPL (ActF)I3D74.569.962.851.136.659.054.336.76.535.8
SSP [12]TSN53.246.839.329.719.837.849.834.57.033.5
SSTAP [37]TSN56.449.541.030.921.639.950.134.97.434.0
SPOT [28]TSN58.950.142.333.522.941.552.835.08.135.2
NPL (BMN)TSN59.051.442.934.323.342.253.935.88.535.7
", + "bbox": [ + 122, + 88, + 848, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ActionFormer [49], which is composed of a self-attention backbone [33], an FPN [21] neck and two parallel heads. Also, we combine the proposed semi-supervised method with BMN [19], which is a two-stage proposal-based detector. For video feature encoding, we used two popular backbones, i.e., two-stream network [35] and I3D [4] pretrained on Kinetics [14] to extract the video features, following [18, 49]. For THUMOS14, the initial learning rate is $1e - 4$ , and a cosine learning rate decay is used. The minibatch size is 2, and a weight decay of $1e - 4$ is used. For ActivityNet v1.3, the learning rate is $1e - 3$ , the mini-batch size is 32, and the weight decay is $1e - 4$ .", + "bbox": [ + 75, + 560, + 473, + 743 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For semi-supervised configurations, an initial model is trained on available labeled videos, where labeling ratios are set to $10\\%$ , $20\\%$ , $40\\%$ , and $60\\%$ . Further using this well-trained model generates pseudo labels. For the re-training phase, we pre-train the model on the labeled data and then compute the supervised loss and unsupervised loss for 40 epochs (THUMOS14) and 15 epochs (ActivityNet v1.3). We set $\\alpha = 1$ and $N_{pos} = 15$ . We apply background data augmentation to $10\\%$ of unlabeled videos for performance improvements. Additional implementation details and more", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "attempts for SS-TAL refer to the supplementary material.", + "bbox": [ + 500, + 560, + 877, + 577 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 500, + 588, + 864, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "THUMOS14. We compare the proposed method NPL with existing SS-TAL methods in Table 1, where we combine two different frameworks, ActionFormer [49] and BMN [19] with our NPL. We report mAP at different tIoU thresholds as well as average mAP between 0.3 and 0.7 with the step of 0.1. Also, we reproduce the SPOT [28] results of $20\\%$ and $40\\%$ labeling ratios from the source code for comparison. When labeled data is scarce (i.e., $10\\%$ and $20\\%$ labeling ratios), our method achieves the competitive performance compared to existing methods. Especially, our method outperforms the baseline, semi-supervised ActF [49], by a large margin with $10\\%$ labeled THUMOS14. When more labeled data is accessible (i.e., $40\\%$ and $60\\%$ labeling ratios), our method outperforms all the competing methods, demonstrating the effectiveness and superiority of our method.", + "bbox": [ + 496, + 612, + 893, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ActivityNet v1.3. We also conduct experiments on the more challenging benchmark ActivityNet v1.3. As depicted in Table 1, the proposed method also achieves significant performance gains over all the compared methods. When", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10165", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/154761691da79e3ba1a8fa529286a3f420d6c8b94ea39be557db3c743df1c1e4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
LabelMethodmAP (%)
0.30.50.7Avg.
10%baseline29.515.85.016.8
+NR30.716.96.318.0
+NF32.018.56.919.1
+NL32.820.17.220.3
40%baseline70.149.520.247.1
+NR70.752.120.748.5
+NF71.654.421.350.3
+NL71.955.723.451.5
", + "bbox": [ + 130, + 88, + 416, + 250 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/097043c8320d48ac3f0948e60b0294f040ae6542f0b742cfc46d88499fa8e24d.jpg", + "table_caption": [ + "Table 2. Ablation study on effectiveness of each component of the proposed method on THUMOS14, using $10\\%$ and $40\\%$ labeled videos. + means training by the proposed method." + ], + "table_footnote": [], + "table_body": "
LabelMethodClass (%)Avg. tIoU (%)
10%baseline21.027.4
NPL25.936.2
40%baseline73.054.2
NPL74.459.0
", + "bbox": [ + 120, + 304, + 426, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "there are more unlabeled data introduced, our method also can improve the average mAP, which mainly comes from the high-quality pseudo labels for effective training.", + "bbox": [ + 75, + 460, + 468, + 506 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 513, + 230, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To better understand how the proposed method works, we conduct a series of ablation studies, where we use ActionFormer [49] as the localization framework with I3D [4].", + "bbox": [ + 75, + 537, + 470, + 584 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of individual component. To validate our key designs, we ablate the effects of the proposed Noisy Label Ranking (NR), Noisy Label Filtering (NF), and Noisy Label Learning (NL). The results are shown in Table 2. Under the $40\\%$ labeling ratio, one can see that our model equipped with NR improves performance by $1.4\\%$ . Further applying our adaptive filtering strategy and the temporal consistency learning, the performance reaches an average mAP of $51.5\\%$ . In summary, our designs significantly improve the utilization of unlabeled data for effectively semi-supervised learning.", + "bbox": [ + 75, + 598, + 468, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quality improvements of pseudo labels. The quality of pseudo labels is the important indicator for the SS-TAL performance improvement. We further study the quality of pseudo labels from their average temporal IoU (tIoU) w.r.t ground truth and classification accuracy (Acc.). We report the comparison results in Table 3. It can be observed that the significant improvements attribute to our Noisy Label Ranking to rank and select high-quality pseudo labels based on the comprehensive metric, i.e., semantic confidence and localization reliability, as well as our Noisy Label Filtering to", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3c69396b2137a2a3549217a76e661c8ae9357d844df92a737b7337880d6dfffc.jpg", + "image_caption": [ + "Figure 5. Curves of averaged IoU vs. foreground score or boundary variance, where each averaged IoU is calculated by the foreground scores or boundary variances of the samples in different intervals." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 692, + 196 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b5aaad6a9f933727e8715d3e0600a244bcf46b02257794c41640934f03d1934d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 88, + 887, + 198 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d258888c711ce0cccfbfa95682e0f1e631c458ee8f8d4eca41291e20866fe6b7.jpg", + "table_caption": [ + "Table 3. Ablation study on the quality of pseudo labels in terms of action classification accuracy (Class) and average tIoU (Avg. tIoU), using $10\\%$ and $40\\%$ labeled videos." + ], + "table_footnote": [], + "table_body": "
MethodmAP (%)
0.30.40.50.60.7Avg.
\\( \\theta_s = 0.3 \\)70.163.552.937.422.249.2
top-1071.063.353.438.122.849.7
NF71.965.455.740.923.451.5
", + "bbox": [ + 542, + 255, + 849, + 348 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Comparison of pseudo-label filtering strategies on THUMOS14 with ${40}\\%$ labeled videos and ${60}\\%$ unlabeled videos.", + "bbox": [ + 500, + 349, + 893, + 376 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "adaptively assign class-balanced pseudo labels for training.", + "bbox": [ + 500, + 401, + 888, + 415 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of noisy label ranking. To further support our motivation of the noisy label ranking, we add a curve of averaged IoU (between pseudo labels and ground truth) versus foreground score or boundary variance, where each averaged IoU corresponds to the foreground scores or boundary variances of the samples in different intervals, as shown in Figure 5. Particularly, the Pearson correlation coefficient between IoU and boundary variance is 0.496, while that between IoU and foreground score is 0.449.", + "bbox": [ + 496, + 416, + 893, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Superiority of adaptive filtering strategy. Our Noisy Label Filtering (NF) could alleviate the class-imbalance problem of pseudo labels caused by the category error. In addition, it also could avoid tediously adjusting hard-crafted thresholds or numbers for pseudo-label filtering. To demonstrate this superiority, we experiment with two common approaches as a reference, i.e., single thresholding and fixed number strategies. More specifically, we empirically set the foreground score threshold $\\theta_{s}$ to 0.3, where instances are regarded as foreground if their scores are above the threshold and background otherwise. Besides, we also empirically select top-10 confidence predictions for each unlabeled video. As shown in Table 4, these approaches cannot achieve satisfactory performance. In contrast, our adaptive filtering strategy could adaptively sample class-specific pseudo labels, showing its effectiveness and importance.", + "bbox": [ + 496, + 551, + 893, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of temporal consistency. Our Noisy Label Learning introduces a temporal consistency loss to tackle the location bias problem by penalizing inconsistent boundary predictions from each intrinsic video snippet. We conduct an ablation study on this key design, where we train the pre-trained model with and without the temporal consistency only on $60\\%$ unlabeled videos, as shown in Figure 6. Based", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10166", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3b5c425a40e81c755ce3abf15b041b5386bd0a40b85d15f61e3d7cb9f6ba58af.jpg", + "image_caption": [ + "Figure 6. Comparison of model performance and convergence speed with and without the temporal consistency loss on THU-MOS14." + ], + "image_footnote": [], + "bbox": [ + 130, + 89, + 421, + 258 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2d8f4b2ad0df5ca3dd5f8ff7ea0269f323df84b28ea5a5c43d3888e4c3c1ed45.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NposmAP (%)
0.30.50.7Avg.
571.555.222.851.0
1571.955.723.451.5
3071.055.322.550.7
", + "bbox": [ + 178, + 316, + 370, + 405 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f01bbc4590ba98ddd78a6ca9b90351e1878b4033a292ad3ebd2fd7ece2d37158.jpg", + "table_caption": [ + "Table 5. Comparison of mAP with various values of $N_{pos}$ using $40\\%$ labeled THUMOS14." + ], + "table_footnote": [], + "table_body": "
Label100%60%40%20%10%
mAP@0.5 (%)71.062.855.739.320.1
mAP@Avg (%)66.859.051.537.820.3
", + "bbox": [ + 109, + 443, + 437, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Comparison of mAP with various labeling ratios on THU-MOS14, where the remainder is treated as unlabeled data.", + "bbox": [ + 75, + 500, + 470, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "on the temporal consistency, it obtains a $1.2\\%$ improvement on the average mAP. Apart from the performance gain, our contribution can also significantly boost the convergence speed. Both of these advances validate the effectiveness of the proposed Noisy Label Learning.", + "bbox": [ + 75, + 551, + 468, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Choice of hyper-parameters. $N_{pos}$ is a pre-defined value to handle the number of positive samples for unlabeled videos. We conduct an ablation study on the hyper-parameter $N_{pos}$ under $40\\%$ labeling ratio. From Table 5, it can be observed that the performance peaks around $N_{pos} = 15$ . A large value such as $N_{pos} = 30$ will introduce more low-quality pseudo labels and confuse the model in training, while a small value such as $N_{pos} = 5$ only provides a small number of samples for training so as to obtain limited gains.", + "bbox": [ + 75, + 628, + 470, + 765 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Bottleneck of our NPL. The performance limitation of SS-TAL following self-training lies in the noise level of pseudo labels. To explore the performance bottleneck, we train a fully-supervised model with $100\\%$ labeled videos on THUMOS14. The experimental results in Table 6 show that our method still has great room for improvement. Also, it demonstrates that the negative impacts of the label noise problem cannot be ignored in semi-supervised learning.", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/63f654c453e52d6017d722912392e1215238aa71424ab5f7ea30ca714398cddf.jpg", + "image_caption": [ + "Figure 7. Qualitative SS-TAL result comparison of our proposed method with SPOT [28] on two untrimmed videos from (a) ActivityNet v1.3 and (b) THUMOS14, respectively." + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 890, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Visualization Analysis", + "text_level": 1, + "bbox": [ + 498, + 369, + 705, + 386 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further validate the effectiveness of the proposed method, we provide some qualitative results by prior art SPOT [28] and our model with $10\\%$ and $40\\%$ labeled data on both ActivityNet v1.3 and THUMOS14. From the illustration in Figure 7, we can observe that our method can localize the target actions more accurately, demonstrating the effectiveness and superiority of our method.", + "bbox": [ + 496, + 393, + 893, + 501 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 515, + 619, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel Noisy Pseudo-Label Learning framework tailored for SS-TAL to tackle the label noise problem. Specifically, we first present a new integrated metric of semantic confidence and boundary reliability for ranking high-quality pseudo labels. Then, an adaptive filtering strategy alleviates the class-imbalance distribution of pseudo labels caused by the category error. Finally, we introduce an unsupervised temporal consistency loss to tackle biased boundary labels for noise-tolerant learning. Experiments show that the effectiveness of our method on both THUMOS14 and ActivityNet v1.3.", + "bbox": [ + 496, + 541, + 893, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation. The number of positive snippets inside an action instance affects our method for quality ranking and noisetolerant training, which indicates that tackling short action instances remains a challenging problem.", + "bbox": [ + 496, + 708, + 893, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 784, + 660, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported partly by National Key R&D Program of China under Grant 2021YFB1714700, NSFC under Grants 62088102 and 62106192, Natural Science Foundation of Shaanxi Province under Grant 2022JC-41, and Fundamental Research Funds for the Central Universities under Grant XTR042021005.", + "bbox": [ + 496, + 809, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10167", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abulikemu AbuDuweili, Xingjian Li, Humphrey Shi, ChengZhong Xu, and Dejing Dou. 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In ECCV, pages 35-50, 2022. 2" + ], + "bbox": [ + 501, + 90, + 893, + 488 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10169", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/911172cc-132a-4651-a728-4f623936c716_model.json b/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/911172cc-132a-4651-a728-4f623936c716_model.json new file mode 100644 index 0000000000000000000000000000000000000000..619d568e82b9cb76bbb8f339cb6b2224d5bd4397 --- /dev/null +++ b/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/911172cc-132a-4651-a728-4f623936c716_model.json @@ -0,0 +1,2211 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.199, + 0.131, + 0.773, + 0.177 + ], + "angle": 0, + "content": "Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.203, + 0.802, + 0.294 + ], + "angle": 0, + "content": "Kun Xia\\(^{1,3\\dagger}\\) Le Wang\\(^{1*}\\) Sanping Zhou\\(^{1}\\) Gang Hua\\(^{2}\\) Wei Tang\\(^{3}\\) \n\\(^{1}\\)National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University \n\\(^{2}\\)Wormpex AI Research \\(^{3}\\)University of Illinois Chicago" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.474, + 0.691 + ], + "angle": 0, + "content": "Semi-Supervised Temporal Action Localization (SS-TAL) aims to improve the generalization ability of action detectors with large-scale unlabeled videos. Albeit the recent advancement, one of the major challenges still remains: noisy pseudo labels hinder efficient learning on abundant unlabeled videos, embodied as location biases and category errors. In this paper, we dive deep into such an important but understudied dilemma. To this end, we propose a unified framework, termed Noisy Pseudo-Label Learning, to handle both location biases and category errors. Specifically, our method is featured with (1) Noisy Label Ranking to rank pseudo labels based on the semantic confidence and boundary reliability, (2) Noisy Label Filtering to address the class-imbalance problem of pseudo labels caused by category errors, (3) Noisy Label Learning to penalize inconsistent boundary predictions to achieve noise-tolerant learning for heavy location biases. As a result, our method could effectively handle the label noise problem and improve the utilization of a large amount of unlabeled videos. Extensive experiments on THUMOS14 and ActivityNet v1.3 demonstrate the effectiveness of our method. The code is available at github.com/kunnxia/NPL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.721, + 0.21, + 0.737 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.471, + 0.854 + ], + "angle": 0, + "content": "Temporal Action Localization (TAL) aims at detecting action instances of interest in an untrimmed video by locating their temporal boundaries and recognizing their action categories. Most existing TAL methods rely on dense temporal annotations for the training videos. However, labeling human actions is very tedious and time-consuming. As a remedy, Semi-Supervised TAL (SS-TAL) requires only a few" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.329, + 0.887, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.584, + 0.895, + 0.641 + ], + "angle": 0, + "content": "Figure 1. Illustration of label noise. Two examples demonstrate that pseudo labels may contain location biases and category errors. The fewer labeled videos are available, the heavier the noise of the pseudo labels will be." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.895, + 0.717 + ], + "angle": 0, + "content": "labeled videos in conjunction with a large amount of unlabeled videos. It has attracted growing attention in academia and industry." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Existing SS-TAL methods [12, 37, 28] are based on consistency regularization or self-training. Consistency-based methods [12, 37] aim to generate consistent action proposals for the same video subject to different augmentations, e.g., time warping [12] and temporal feature shift [37]. In contrast, the self-training-based method [28] achieves new state-of-the-art performance by alternating between pseudo-labeling and re-training. It focuses on designing a proposal-free framework to address proposal error propagation from [12, 37] but neglects the important role of pseudo labels. Albeit its advancement, label noise still remains a core challenge, hindering efficient learning on abundant un" + }, + { + "type": "page_footnote", + "bbox": [ + 0.108, + 0.863, + 0.235, + 0.876 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_footnote", + "bbox": [ + 0.08, + 0.876, + 0.47, + 0.901 + ], + "angle": 0, + "content": "† Part of this work was done while Kun Xia was a visiting scholar at University of Illinois Chicago." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10160" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.167 + ], + "angle": 0, + "content": "labeled videos. From Figure 1, we can observe that label noise commonly leads to two intractable issues, i.e., location bias and category error, which become worse as the amount of labeled videos decreases. As a result, noisy pseudo labels will significantly degrade the performance of SS-TAL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.471, + 0.302 + ], + "angle": 0, + "content": "In this paper, we propose a Noisy Pseudo-Label Learning (NPL) framework tailored for SS-TAL to combat detrimental label noise. It follows the self-training paradigm that alternates between pseudo-labeling and model training. But unlike all previous self-training methods, our NPL includes three novel components, termed Noisy Label Ranking, Noisy Label Filtering, and Noisy Label Learning, respectively, which alleviate the negative effects caused by location biases and category errors in a unified framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.471, + 0.469 + ], + "angle": 0, + "content": "First, Noisy Label Ranking aims to rank and select high-quality pseudo labels based on both semantic confidence and boundary reliability. Classification scores have been widely used in self-training to measure the quality of pseudo labels, but they only reflect semantic confidence and fail to account for localization reliability. To close this gap, we explicitly model the localization reliability of a detected action instance in an unlabeled video as the variance of the boundary predictions from dense snippets within the action. We then introduce a new integrated metric of semantic confidence and boundary reliability to rank the pseudo labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.471, + 0.635 + ], + "angle": 0, + "content": "Second, Noisy Label Filtering aims at addressing the class-imbalance problem in noisy pseudo labels. Owing to the category error, the class-imbalance problem occurs regardless of whether pseudo labels are sampled based on a confidence threshold or the number of samples. The model will be dominated by redundant noisy pseudo labels in training, especially for the ones of category errors, and further harm its generalization ability. To address this issue, we introduce an adaptive filtering strategy to regularize the distribution of pseudo labels and adaptively assign class-balanced pseudo labels to unlabeled videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.471, + 0.785 + ], + "angle": 0, + "content": "Last, Noisy Label Learning aims to improve the robustness of training to location bias. While noisy label ranking and filtering can improve the quality of sampled pseudo labels, location bias will not be removed completely. Training on biased boundary labels hinders the convergence of the model and further impedes accurate action localization. To this end, we propose a noise-tolerant training algorithm based on an unsupervised temporal consistency loss, which penalizes inconsistent predictions from adjacent action frames." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.786, + 0.436, + 0.801 + ], + "angle": 0, + "content": "The main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.81, + 0.472, + 0.902 + ], + "angle": 0, + "content": "- This paper introduces a Noisy Pseudo-Label Learning (NPL) framework tailored for SS-TAL, which handles both the location bias and category error in a unified framework. Extensive experiments conducted on THUMOS14 [13] and ActivityNet v1.3 [2] demonstrate the effectiveness of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "- We propose a Noisy Label Ranking method to rank and select high-quality pseudo labels based on a new integrated metric of semantic confidence and boundary reliability." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.162, + 0.892, + 0.208 + ], + "angle": 0, + "content": "- We propose a Noisy Label Filtering method to tackle the largely ignored class-imbalance problem in pseudo labels based on a new adaptive filtering strategy." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.218, + 0.892, + 0.278 + ], + "angle": 0, + "content": "- We introduce a Noisy Label Learning method, which adopts an unsupervised temporal consistency loss to penalize inconsistent predictions from adjacent frames for noise-tolerant learning." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.302, + 0.642, + 0.318 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.895, + 0.599 + ], + "angle": 0, + "content": "Temporal Action Localization. The recent significant advancement of TAL arguably owes to the availability of large-scale and well-annotated datasets. We can roughly categorize existing TAL methods into three groups. Anchor-based methods [43, 5, 45, 52, 36] employ multiscale anchors that may contain an action and refine them via a boundary regression head. GTAN [25] dynamically optimizes the scale of each anchor via Gaussian kernels. G-TAD [45] improves temporal anchor representation with semantic and temporal context. Anchor-free methods [54, 29, 18, 27, 40, 39, 41] directly learn to predict action proposals by grouping possible start/end locations [20, 19] or regressing the distance to action boundaries [18, 49]. Transformer-based methods [31, 24, 49, 8] adopt the Transformer architecture [33, 3] for action localization and achieve remarkable performance on TAL benchmarks. In addition, unsupervised temporal action localization [11, 50] has made remarkable achievements without requiring any annotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Semi-Supervised Learning. Semi-Supervised Learning (SSL) methods mostly focus on image classification. They can be classified into two categories. Consistency-based methods [32, 26, 51, 1] enforce the model to produce consistent predictions across label-preserving image augmentations. Self-training methods [42, 15, 10] retrain the model with high-confidence pseudo labels of unlabeled raw data. Thereby, the final performance is largely limited by the quality of pseudo labels generated by an inaccurate model trained using a few labeled data. Much effort tries to remedy noisy pseudo labels [16, 23, 44, 55, 17, 46]. Li et al. [16] train a noise-tolerant model, which is encouraged to produce consistent predictions under a variety of noisy synthetic labels. DSL [7] directly ignores the gradient computation and propagation for ambiguous pseudo labels. Wang et al. [38] propose an iterative training method to identify and down-weigh noisy samples. Chen et al. [6] address severe confirmation bias during self-training and generate unbiased pseudo labels to drive student learning. In this paper, we focus on the challenging SS-TAL problem." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10161" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.099, + 0.892, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.347, + 0.895, + 0.434 + ], + "angle": 0, + "content": "Figure 2. An overview of our proposed Noisy Pseudo-Label Learning framework. The training data contain both labeled and unlabeled videos. We first obtain a pre-trained model using a small amount of labeled videos and generate pseudo labels on unlabeled videos. To deal with noise in pseudo labels, Noisy Label Ranking first assesses the quality of pseudo labels through both semantic confidence and boundary reliability. Noisy Label Filtering then adaptively filters pseudo labels so that the model learning will not be dominated by pseudo labels with category errors. To make the training robust to label noise, we introduce dense temporal consistency training with \\( L_{u}^{\\mathrm{cons}} \\). The model can be optimized by the final loss, which is the sum of \\( L_{s} \\), \\( L_{u}^{\\mathrm{cls}} \\), and \\( L_{u}^{\\mathrm{cons}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.473, + 0.728 + ], + "angle": 0, + "content": "Semi-Supervised Temporal Action Localization. SS-TAL is a worthwhile but under-explored field. Existing works [12, 37, 9, 28] are intrinsically driven by SSL. Some works [12, 37, 9] aim to improve the consistent predictions of the teacher-student network when video features are augmented by different temporal perturbations, e.g., time warping/masking [12], temporal feature shift/flip [37] or spatiotemporal feature crossover [9]. The other one [28] focuses on addressing proposal error propagation, which alternates between predicting and applying pseudo labels. However, all these approaches fail to dive deep into the major challenge of SS-TAL, i.e., noisy pseudo labels hindering efficient learning on unlabeled videos. We attribute the label noise problem of pseudo labels from unlabeled videos to the semantic uncertainty and boundary ambiguity of labeled actions. This paper tackles both the location bias and category error of pseudo labels into a unified framework for efficient learning from unlabeled videos." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.744, + 0.17, + 0.76 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.208, + 0.787 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Problem Setting. Semi-supervised temporal action localization (SS-TAL) aims to perform TAL from a small amount of labeled videos \\(\\{X_{i}|_{i = 1}^{N_{l}}\\}\\) and a large amount of unlabeled videos \\(\\{U_i|_{i = 1}^{N_u}\\}\\), where \\(N_{l}\\) and \\(N_{u}\\) are the numbers of labeled and unlabeled videos, respectively. In a labeled video, its annotation is a set of action instances, and each action instance could be represented as \\((t_s,t_e,c)\\), where \\(t_s,t_e,\\) and \\(c\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.456, + 0.895, + 0.471 + ], + "angle": 0, + "content": "denote the start time, end time, and action class, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.472, + 0.894, + 0.533 + ], + "angle": 0, + "content": "Feature Encoding. Following conventions [45, 47], we sample a video snippet from every few consecutive frames. Then, we adopt a fine-tuned two-stream network to extract RGB and optical flow features at each video snippet." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.894, + 0.624 + ], + "angle": 0, + "content": "Overview. Recent anchor-free TAL methods [18, 49, 27] are more attractive and practical since they are powerful and portable to be deployed in many real-world applications. We take the anchor-free detector [49] as our baseline, where each video snippet is directly supervised by the corresponding labels, i.e., distances to boundaries and the action category." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.895, + 0.731 + ], + "angle": 0, + "content": "Our SS-TAL framework follows the self-training paradigm [30], which can be decomposed into two steps. In the first step, we obtain a pre-trained model based on labeled videos with a supervised loss and then generate pseudo labels on unlabeled videos. In the second step, we update the model parameters with a semi-supervised training objective, including a supervised loss and an unsupervised loss:" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.744, + 0.892, + 0.761 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {s} + \\alpha \\mathcal {L} _ {u}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.774, + 0.895, + 0.85 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_s\\) and \\(\\mathcal{L}_u\\) denote the supervised loss of labeled videos and the unsupervised loss of unlabeled videos, respectively, and \\(\\alpha\\) controls the contribution of the unsupervised loss. Both of them are normalized by the corresponding numbers of training samples as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.863, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} = \\frac {1}{N _ {l}} \\sum_ {i = 1} ^ {N _ {l}} \\left(\\mathcal {L} _ {s} ^ {\\mathrm {c l s}} \\left(X _ {i}\\right) + \\mathcal {L} _ {s} ^ {\\mathrm {r e g}} \\left(X _ {i}\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10162" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.141, + 0.103, + 0.471, + 0.144 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {u} = \\frac {1}{N _ {u}} \\sum_ {i = 1} ^ {N _ {u}} \\left(\\mathcal {L} _ {u} ^ {\\mathrm {c l s}} \\left(U _ {i}\\right) + \\mathcal {L} _ {u} ^ {\\mathrm {r e g}} \\left(U _ {i}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.151, + 0.471, + 0.196 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}^{\\mathrm{cls}}\\) is a classification loss, \\(\\mathcal{L}^{\\mathrm{reg}}\\) is a regression loss, and \\(N_{l}\\) and \\(N_{u}\\) denote the number of training samples for labeled and unlabeled videos, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.472, + 0.332 + ], + "angle": 0, + "content": "We claim that the major obstacle that hinders self-training performance lies in label noise, which leads to two issues: location biases and category errors. In this paper, we propose a Noisy Pseudo-Label Learning framework (NPL) to alleviate the negative effects caused by location biases and category errors for SS-TAL. The pipeline of our method is illustrated in Figure 2. It includes three novel components: Noisy Label Ranking, Noisy Label Filtering, and Noisy Label Learning, described in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.342, + 0.276, + 0.358 + ], + "angle": 0, + "content": "3.2. Noisy Label Ranking" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.365, + 0.47, + 0.425 + ], + "angle": 0, + "content": "In SS-TAL, the quality of pseudo labels can be measured from two perspectives, i.e., semantic confidence and boundary reliability. It is desirable to have high-quality pseudo labels for semi-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.471, + 0.56 + ], + "angle": 0, + "content": "The majority of TAL frameworks [20, 53, 52, 36] rely on the foreground score of an anchor or a proposal to measure its quality. However, the foreground score only reflects semantic confidence and cannot account for boundary reliability. From Figure 3 (a), we can observe that foreground scores may not strongly correlate with the localization quality (i.e., IoU w.r.t. ground truth). Thus, it is necessary to measure the quality of pseudo labels from both aspects of action classification and boundary localization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.472, + 0.76 + ], + "angle": 0, + "content": "For labeled videos, anchors or proposals corresponding to the same action instance are supervised by the same ground truth during training. Thus, they are gradually regressed to the similar temporal boundary locations. This motivates us to use the consistency of the boundary predictions to measure their location reliability. Specifically, taking our anchor-free framework as an example, we can obtain dense predictions of action instances before the post-processing phase. Given a prediction \\( p_j = (\\hat{t}_{s,j}, \\hat{t}_{e,j}, c_j) \\) where \\( \\hat{t}_{s,j} \\) and \\( \\hat{t}_{e,j} \\) are the predicted start and end boundaries of the \\( j \\)-th video snippet respectively and \\( c_j \\) is its foreground score, we can obtain a set of predictions \\( \\{p_n\\}_{n=1}^{N_a} \\) from its \\( N_a \\) adjacent snippets. Then, we formulate the boundary ambiguity of \\( p_j \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.771, + 0.339, + 0.787 + ], + "angle": 0, + "content": "\\[\n\\bar {\\sigma} _ {j} = \\hat {\\sigma} _ {s, j} + \\hat {\\sigma} _ {e, j},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.209, + 0.789, + 0.471, + 0.819 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {s, j} = \\frac {\\sigma_ {s , j}}{d (p _ {j})}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.209, + 0.821, + 0.309, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {e, j} = \\frac {\\sigma_ {e , j}}{d (p _ {j})},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.472, + 0.902 + ], + "angle": 0, + "content": "where \\(\\sigma_{s,j}\\) and \\(\\sigma_{e,j}\\) are the variances of the start and end boundaries of \\(\\{p_n\\}_{n = 1}^{N_a}\\), respectively. \\(\\hat{\\sigma}_{s,j}\\) and \\(\\hat{\\sigma}_{e,j}\\) are normalized by their duration \\(d(p_j)\\). A smaller boundary vari" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.094, + 0.695, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.602, + 0.213, + 0.621, + 0.224 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.095, + 0.891, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.798, + 0.214, + 0.817, + 0.225 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.23, + 0.894, + 0.327 + ], + "angle": 0, + "content": "Figure 3. Each star represents a prediction result (i.e., a pseudo label) on \\(60\\%\\) unlabeled videos based on the model trained with \\(40\\%\\) labeled videos on THUMOS14. (a) depicts the correlation between the foreground score and the IoU with ground truth. (b) depicts the correlation between the boundary variance and the IoU with ground truth. It can be observed that the boundary variance highly correlates with the localization quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.895, + 0.473 + ], + "angle": 0, + "content": "ance \\(\\bar{\\sigma}_j\\) indicates lower boundary ambiguity of the prediction \\(p_j\\), thus leading to higher localization reliability. In Figure 3 (b), we experimentally illustrate the correlation between the boundary variance and IoU w.r.t ground truth. We can observe that boundary variances could better measure the localization quality of pseudo labels than the classification scores. Particularly, this motivates us to define the confidence score of \\(p_j\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.663, + 0.483, + 0.892, + 0.513 + ], + "angle": 0, + "content": "\\[\ns _ {j} = \\frac {c _ {j}}{\\bar {\\sigma} _ {j}}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.894, + 0.627 + ], + "angle": 0, + "content": "Eq. (5) provides a comprehensive metric to measure the quality of pseudo labels by their semantic confidence (foreground score \\( c \\)) and boundary ambiguity (boundary variance \\( \\bar{\\sigma} \\)). As a result, our Noisy Label Ranking could improve the quality of pseudo labels only from intrinsic video snippets without requiring additional learnable networks or hyperparameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.702, + 0.653 + ], + "angle": 0, + "content": "3.3. Noisy Label Filtering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.894, + 0.839 + ], + "angle": 0, + "content": "Training on a few labeled videos inevitably produces noisy pseudo labels with category errors on unlabeled videos. As a result, the frequencies of some action categories in the selected pseudo labels will be much larger or smaller than their natural frequencies in the videos, regardless of whether pseudo labels are sampled based on a confidence threshold or the number of samples. We call this phenomenon the class-imbalance problem of pseudo labels in SS-TAL, illustrated in Figure 4. For example, the frequency of \"Golf Swing\" in pseudo labels is much higher than that in ground truth labels, while the frequency of \"Throw Discus\" is much lower in the pseudo labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Under this class-imbalance problem, overwhelming pseudo labels with category errors will dominate the model learning and further aggravate the semantic uncertainty of actions of category errors, resulting in limited gains." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10163" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.091, + 0.447, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.471, + 0.395 + ], + "angle": 0, + "content": "Figure 4. Illustration of the class-imbalance problem of pseudo labels obtained on \\(60\\%\\) unlabeled THUMOS14. The horizontal axis of the histogram represents the class name, and the vertical axis represents the ratio between the number of pseudo labels and the number of ground truth labels. It can be observed that our Noisy Label Filtering could alleviate the class-imbalance problem of pseudo labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.47, + 0.496 + ], + "angle": 0, + "content": "To address this class-imbalance problem, we introduce an adaptive filtering strategy to regularize the distribution of pseudo labels for each category. Concretely, we arrange dense labels according to the category of actions and the number of pseudo labels in an unlabeled video, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.505, + 0.47, + 0.542 + ], + "angle": 0, + "content": "\\[\nK _ {a d p} = \\frac {\\left| \\left\\{p _ {n} ^ {c} \\right\\} _ {n = 1} ^ {N _ {v}} \\right|}{N _ {v}} \\cdot N _ {p o s}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.473, + 0.732 + ], + "angle": 0, + "content": "where \\( N_{v} \\) is the total number of pseudo labels within a video, and \\( N_{pos} \\) is a hyper-parameter to control the number of positive predictions. Eq. (6) is used to adaptively select the number \\( K_{adp} \\) of class-specific pseudo labels for the category \\( c \\) in each unlabeled video. From Figure 4, we experimentally demonstrate that our adaptive filtering strategy could address the class-imbalance distribution of pseudo labels. As a result, our Noisy Label Filtering could not only assign accurate pseudo labels to improve the model learning but also prevent the pseudo labels from being dominated by overwhelming pseudo labels with category errors, while it also avoids tediously adjusting heuristic thresholds." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.282, + 0.759 + ], + "angle": 0, + "content": "3.4. Noisy Label Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.839 + ], + "angle": 0, + "content": "The boundary ambiguity of labeled actions gives rise to noisy pseudo labels with location biases. Subsequently, training on the biased boundaries results in the boundary ambiguity of unlabeled actions and impedes accurate action localization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.471, + 0.902 + ], + "angle": 0, + "content": "To remedy it, we propose a noise-tolerant training algorithm for unlabeled videos with heavy location biases. It aims to penalize inconsistency boundary predictions from adjacent feature locations within a video feature sequence." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "Our unsupervised temporal consistency loss is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.13, + 0.894, + 0.174 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {u} ^ {\\text {c o n s}} = \\frac {1}{M _ {u} \\left(M _ {p} - 1\\right)} \\sum_ {j = 1} ^ {M _ {u}} \\sum_ {i = 1} ^ {M _ {p} - 1} \\left| b _ {i + 1} ^ {j} - b _ {i} ^ {j} \\right|, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.186, + 0.895, + 0.29 + ], + "angle": 0, + "content": "where \\( M_{u} \\) denotes the number of pseudo labels within an unlabeled video. \\( M_{p} \\) represents the number of the training snippets within an action. \\( b_{i} \\) represents the predicted start/end boundary locations from the \\( i \\)-th snippet. In this way, the model could learn to produce more reliable predictions. Consequently, our complete unsupervised loss is denoted below:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.3, + 0.892, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {u} = \\frac {1}{N _ {u}} \\sum_ {i = 1} ^ {N _ {u}} \\left(\\mathcal {L} _ {u} ^ {\\mathrm {c l s}} \\left(U _ {i}\\right) + \\mathcal {L} _ {u} ^ {\\mathrm {c o n s}} \\left(U _ {i}\\right)\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.353, + 0.892, + 0.398 + ], + "angle": 0, + "content": "The Noisy Label Learning makes the training robust to location biases in the pseudo labels. Finally, the model can be optimized by the sum of \\(\\mathcal{L}_s\\) and \\(\\mathcal{L}_u\\) on all videos." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.412, + 0.633, + 0.429 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.698, + 0.451 + ], + "angle": 0, + "content": "4.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.46, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Evaluation Datasets. We evaluate our proposed method on two benchmark TAL datasets, i.e., THUMOS14 [13] and ActivityNet v1.3 [2]. THUMOS14 [13] is a standard benchmark for TAL. It contains 200 validation videos and 213 testing videos, including 20 action categories. It is very challenging since each video has more than 15 action instances. Following the common setting [48], we use the validation set for training and evaluate on the testing set." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.894, + 0.656 + ], + "angle": 0, + "content": "ActivityNet v1.3 [2] is a large-scale benchmark for video-based action localization. It contains 10k training videos and 5k validation videos corresponding to 200 different actions. Following the standard practice [22], we train our method on the training set and test it on the validation set." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.657, + 0.894, + 0.761 + ], + "angle": 0, + "content": "Evaluation Metrics. We use the mean Average Precision (mAP) as the evaluation metric. The tIoU thresholds are \\([0.3:0.1:0.7]\\) for THUMOS14 and \\([0.5:0.05:0.95]\\) for ActivityNet v1.3. We report the average mAP of the IoU thresholds between 0.5 and 0.95 with the step of 0.05 on ActivityNet v1.3. Also, we present the average mAP of the tIoU thresholds from 0.3 to 0.7 on THUMOS14." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.762, + 0.892, + 0.837 + ], + "angle": 0, + "content": "The goal of SS-TAL is to use a large amount of unlabeled data to improve a well-trained detector on a small amount of labeled data. We randomly sample \\(10\\%\\), \\(20\\%\\), \\(40\\%\\), and \\(60\\%\\) of the training data as labeled data and treat the remainder as unlabeled data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.716, + 0.864 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We implement our semi-supervised action localization framework based on the recent prevalent anchor-free detector" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10164" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.089, + 0.849, + 0.495 + ], + "angle": 0, + "content": "
LabelMethodBackboneTHUMOS14 (%)ActivityNet v1.3 (%)
0.30.40.50.60.7Avg.0.50.750.95Avg.
10%ActF* [49]I3D28.522.914.18.24.115.647.824.21.725.6
ActF [49] + MixUp [51]I3D29.724.214.59.65.416.749.427.93.128.8
NPL (ActF)I3D32.829.620.111.77.220.351.933.43.632.5
SSP [12]TSN44.234.124.616.99.325.838.928.78.427.6
SSTAP [37]TSN45.635.226.317.510.727.040.729.69.028.2
SPOT [28]TSN49.440.431.522.912.431.349.931.18.332.1
NPL (BMN)TSN50.041.733.523.613.432.450.932.07.932.6
20%ActF* [49]I3D49.141.632.621.512.131.451.234.33.832.9
ActF [49] + MixUp [51]I3D51.243.234.023.914.133.352.934.73.933.3
NPL (ActF)I3D54.547.139.329.718.537.853.135.83.933.8
SPOT [28]TSN52.643.934.125.216.234.451.732.06.932.3
NPL (BMN)TSN53.945.636.226.916.535.852.132.97.932.9
40%ActF* [49]I3D69.060.449.331.519.345.953.235.73.834.2
ActF [49] + MixUp [51]I3D69.761.952.434.420.147.753.136.04.334.5
NPL (ActF)I3D71.965.455.740.923.451.553.636.54.635.3
SPOT [28]TSN54.445.837.229.719.437.353.333.06.633.2
NPL (BMN)TSN56.246.738.830.319.538.353.433.98.133.8
60%ActF* [49]I3D71.565.659.947.332.755.453.936.15.735.0
ActF [49] + MixUp [51]I3D72.267.561.248.734.056.754.136.45.735.2
NPL (ActF)I3D74.569.962.851.136.659.054.336.76.535.8
SSP [12]TSN53.246.839.329.719.837.849.834.57.033.5
SSTAP [37]TSN56.449.541.030.921.639.950.134.97.434.0
SPOT [28]TSN58.950.142.333.522.941.552.835.08.135.2
NPL (BMN)TSN59.051.442.934.323.342.253.935.88.535.7
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.495, + 0.895, + 0.539 + ], + "angle": 0, + "content": "Table 1. Performance comparison with state-of-the-art SS-TAL methods on THUMOS14 testing set and ActivityNet v1.3 validation set. Notably, SSP and SSTAP employ UntrimmedNet [34] trained with \\(100\\%\\) class labels for proposal classification. ActF refers to ActionFormer [49]. \\* means using only labeled training videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.475, + 0.744 + ], + "angle": 0, + "content": "ActionFormer [49], which is composed of a self-attention backbone [33], an FPN [21] neck and two parallel heads. Also, we combine the proposed semi-supervised method with BMN [19], which is a two-stage proposal-based detector. For video feature encoding, we used two popular backbones, i.e., two-stream network [35] and I3D [4] pretrained on Kinetics [14] to extract the video features, following [18, 49]. For THUMOS14, the initial learning rate is \\(1e - 4\\), and a cosine learning rate decay is used. The minibatch size is 2, and a weight decay of \\(1e - 4\\) is used. For ActivityNet v1.3, the learning rate is \\(1e - 3\\), the mini-batch size is 32, and the weight decay is \\(1e - 4\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "For semi-supervised configurations, an initial model is trained on available labeled videos, where labeling ratios are set to \\(10\\%\\), \\(20\\%\\), \\(40\\%\\), and \\(60\\%\\). Further using this well-trained model generates pseudo labels. For the re-training phase, we pre-train the model on the labeled data and then compute the supervised loss and unsupervised loss for 40 epochs (THUMOS14) and 15 epochs (ActivityNet v1.3). We set \\(\\alpha = 1\\) and \\(N_{pos} = 15\\). We apply background data augmentation to \\(10\\%\\) of unlabeled videos for performance improvements. Additional implementation details and more" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.561, + 0.879, + 0.578 + ], + "angle": 0, + "content": "attempts for SS-TAL refer to the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.866, + 0.605 + ], + "angle": 0, + "content": "4.3. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.895, + 0.84 + ], + "angle": 0, + "content": "THUMOS14. We compare the proposed method NPL with existing SS-TAL methods in Table 1, where we combine two different frameworks, ActionFormer [49] and BMN [19] with our NPL. We report mAP at different tIoU thresholds as well as average mAP between 0.3 and 0.7 with the step of 0.1. Also, we reproduce the SPOT [28] results of \\(20\\%\\) and \\(40\\%\\) labeling ratios from the source code for comparison. When labeled data is scarce (i.e., \\(10\\%\\) and \\(20\\%\\) labeling ratios), our method achieves the competitive performance compared to existing methods. Especially, our method outperforms the baseline, semi-supervised ActF [49], by a large margin with \\(10\\%\\) labeled THUMOS14. When more labeled data is accessible (i.e., \\(40\\%\\) and \\(60\\%\\) labeling ratios), our method outperforms all the competing methods, demonstrating the effectiveness and superiority of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "ActivityNet v1.3. We also conduct experiments on the more challenging benchmark ActivityNet v1.3. As depicted in Table 1, the proposed method also achieves significant performance gains over all the compared methods. When" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10165" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.132, + 0.089, + 0.418, + 0.251 + ], + "angle": 0, + "content": "
LabelMethodmAP (%)
0.30.50.7Avg.
10%baseline29.515.85.016.8
+NR30.716.96.318.0
+NF32.018.56.919.1
+NL32.820.17.220.3
40%baseline70.149.520.247.1
+NR70.752.120.748.5
+NF71.654.421.350.3
+NL71.955.723.451.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.252, + 0.47, + 0.294 + ], + "angle": 0, + "content": "Table 2. Ablation study on effectiveness of each component of the proposed method on THUMOS14, using \\(10\\%\\) and \\(40\\%\\) labeled videos. + means training by the proposed method." + }, + { + "type": "table", + "bbox": [ + 0.121, + 0.305, + 0.427, + 0.394 + ], + "angle": 0, + "content": "
LabelMethodClass (%)Avg. tIoU (%)
10%baseline21.027.4
NPL25.936.2
40%baseline73.054.2
NPL74.459.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.395, + 0.472, + 0.437 + ], + "angle": 0, + "content": "Table 3. Ablation study on the quality of pseudo labels in terms of action classification accuracy (Class) and average tIoU (Avg. tIoU), using \\(10\\%\\) and \\(40\\%\\) labeled videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.507 + ], + "angle": 0, + "content": "there are more unlabeled data introduced, our method also can improve the average mAP, which mainly comes from the high-quality pseudo labels for effective training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.515, + 0.231, + 0.531 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.472, + 0.585 + ], + "angle": 0, + "content": "To better understand how the proposed method works, we conduct a series of ablation studies, where we use ActionFormer [49] as the localization framework with I3D [4]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.75 + ], + "angle": 0, + "content": "Effectiveness of individual component. To validate our key designs, we ablate the effects of the proposed Noisy Label Ranking (NR), Noisy Label Filtering (NF), and Noisy Label Learning (NL). The results are shown in Table 2. Under the \\(40\\%\\) labeling ratio, one can see that our model equipped with NR improves performance by \\(1.4\\%\\). Further applying our adaptive filtering strategy and the temporal consistency learning, the performance reaches an average mAP of \\(51.5\\%\\). In summary, our designs significantly improve the utilization of unlabeled data for effectively semi-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Quality improvements of pseudo labels. The quality of pseudo labels is the important indicator for the SS-TAL performance improvement. We further study the quality of pseudo labels from their average temporal IoU (tIoU) w.r.t ground truth and classification accuracy (Acc.). We report the comparison results in Table 3. It can be observed that the significant improvements attribute to our Noisy Label Ranking to rank and select high-quality pseudo labels based on the comprehensive metric, i.e., semantic confidence and localization reliability, as well as our Noisy Label Filtering to" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.089, + 0.693, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.089, + 0.888, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.201, + 0.892, + 0.243 + ], + "angle": 0, + "content": "Figure 5. Curves of averaged IoU vs. foreground score or boundary variance, where each averaged IoU is calculated by the foreground scores or boundary variances of the samples in different intervals." + }, + { + "type": "table", + "bbox": [ + 0.543, + 0.256, + 0.85, + 0.349 + ], + "angle": 0, + "content": "
MethodmAP (%)
0.30.40.50.60.7Avg.
\\( \\theta_s = 0.3 \\)70.163.552.937.422.249.2
top-1071.063.353.438.122.849.7
NF71.965.455.740.923.451.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.35, + 0.894, + 0.377 + ], + "angle": 0, + "content": "Table 4. Comparison of pseudo-label filtering strategies on THUMOS14 with \\( {40}\\% \\) labeled videos and \\( {60}\\% \\) unlabeled videos." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.402, + 0.89, + 0.416 + ], + "angle": 0, + "content": "adaptively assign class-balanced pseudo labels for training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.894, + 0.552 + ], + "angle": 0, + "content": "Visualization of noisy label ranking. To further support our motivation of the noisy label ranking, we add a curve of averaged IoU (between pseudo labels and ground truth) versus foreground score or boundary variance, where each averaged IoU corresponds to the foreground scores or boundary variances of the samples in different intervals, as shown in Figure 5. Particularly, the Pearson correlation coefficient between IoU and boundary variance is 0.496, while that between IoU and foreground score is 0.449." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.895, + 0.794 + ], + "angle": 0, + "content": "Superiority of adaptive filtering strategy. Our Noisy Label Filtering (NF) could alleviate the class-imbalance problem of pseudo labels caused by the category error. In addition, it also could avoid tediously adjusting hard-crafted thresholds or numbers for pseudo-label filtering. To demonstrate this superiority, we experiment with two common approaches as a reference, i.e., single thresholding and fixed number strategies. More specifically, we empirically set the foreground score threshold \\(\\theta_{s}\\) to 0.3, where instances are regarded as foreground if their scores are above the threshold and background otherwise. Besides, we also empirically select top-10 confidence predictions for each unlabeled video. As shown in Table 4, these approaches cannot achieve satisfactory performance. In contrast, our adaptive filtering strategy could adaptively sample class-specific pseudo labels, showing its effectiveness and importance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Analysis of temporal consistency. Our Noisy Label Learning introduces a temporal consistency loss to tackle the location bias problem by penalizing inconsistent boundary predictions from each intrinsic video snippet. We conduct an ablation study on this key design, where we train the pre-trained model with and without the temporal consistency only on \\(60\\%\\) unlabeled videos, as shown in Figure 6. Based" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10166" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.131, + 0.09, + 0.422, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.264, + 0.473, + 0.306 + ], + "angle": 0, + "content": "Figure 6. Comparison of model performance and convergence speed with and without the temporal consistency loss on THU-MOS14." + }, + { + "type": "table", + "bbox": [ + 0.179, + 0.317, + 0.372, + 0.406 + ], + "angle": 0, + "content": "
NposmAP (%)
0.30.50.7Avg.
571.555.222.851.0
1571.955.723.451.5
3071.055.322.550.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.406, + 0.47, + 0.433 + ], + "angle": 0, + "content": "Table 5. Comparison of mAP with various values of \\(N_{pos}\\) using \\(40\\%\\) labeled THUMOS14." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.444, + 0.438, + 0.499 + ], + "angle": 0, + "content": "
Label100%60%40%20%10%
mAP@0.5 (%)71.062.855.739.320.1
mAP@Avg (%)66.859.051.537.820.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.5, + 0.472, + 0.527 + ], + "angle": 0, + "content": "Table 6. Comparison of mAP with various labeling ratios on THU-MOS14, where the remainder is treated as unlabeled data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.629 + ], + "angle": 0, + "content": "on the temporal consistency, it obtains a \\(1.2\\%\\) improvement on the average mAP. Apart from the performance gain, our contribution can also significantly boost the convergence speed. Both of these advances validate the effectiveness of the proposed Noisy Label Learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.472, + 0.766 + ], + "angle": 0, + "content": "Choice of hyper-parameters. \\(N_{pos}\\) is a pre-defined value to handle the number of positive samples for unlabeled videos. We conduct an ablation study on the hyper-parameter \\(N_{pos}\\) under \\(40\\%\\) labeling ratio. From Table 5, it can be observed that the performance peaks around \\(N_{pos} = 15\\). A large value such as \\(N_{pos} = 30\\) will introduce more low-quality pseudo labels and confuse the model in training, while a small value such as \\(N_{pos} = 5\\) only provides a small number of samples for training so as to obtain limited gains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Bottleneck of our NPL. The performance limitation of SS-TAL following self-training lies in the noise level of pseudo labels. To explore the performance bottleneck, we train a fully-supervised model with \\(100\\%\\) labeled videos on THUMOS14. The experimental results in Table 6 show that our method still has great room for improvement. Also, it demonstrates that the negative impacts of the label noise problem cannot be ignored in semi-supervised learning." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.891, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.304, + 0.895, + 0.348 + ], + "angle": 0, + "content": "Figure 7. Qualitative SS-TAL result comparison of our proposed method with SPOT [28] on two untrimmed videos from (a) ActivityNet v1.3 and (b) THUMOS14, respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.371, + 0.707, + 0.387 + ], + "angle": 0, + "content": "4.5. Visualization Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.895, + 0.502 + ], + "angle": 0, + "content": "To further validate the effectiveness of the proposed method, we provide some qualitative results by prior art SPOT [28] and our model with \\(10\\%\\) and \\(40\\%\\) labeled data on both ActivityNet v1.3 and THUMOS14. From the illustration in Figure 7, we can observe that our method can localize the target actions more accurately, demonstrating the effectiveness and superiority of our method." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.516, + 0.62, + 0.532 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.895, + 0.708 + ], + "angle": 0, + "content": "In this paper, we propose a novel Noisy Pseudo-Label Learning framework tailored for SS-TAL to tackle the label noise problem. Specifically, we first present a new integrated metric of semantic confidence and boundary reliability for ranking high-quality pseudo labels. Then, an adaptive filtering strategy alleviates the class-imbalance distribution of pseudo labels caused by the category error. Finally, we introduce an unsupervised temporal consistency loss to tackle biased boundary labels for noise-tolerant learning. Experiments show that the effectiveness of our method on both THUMOS14 and ActivityNet v1.3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.709, + 0.895, + 0.77 + ], + "angle": 0, + "content": "Limitation. The number of positive snippets inside an action instance affects our method for quality ranking and noisetolerant training, which indicates that tackling short action instances remains a challenging problem." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.661, + 0.802 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.9 + ], + "angle": 0, + "content": "This work was supported partly by National Key R&D Program of China under Grant 2021YFB1714700, NSFC under Grants 62088102 and 62106192, Natural Science Foundation of Shaanxi Province under Grant 2022JC-41, and Fundamental Research Funds for the Central Universities under Grant XTR042021005." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10167" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.472, + 0.17 + ], + "angle": 0, + "content": "[1] Abulikemu AbuDuweili, Xingjian Li, Humphrey Shi, ChengZhong Xu, and Dejing Dou. 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Albeit the recent advancement, one of the major challenges still remains: noisy pseudo labels hinder efficient learning on abundant unlabeled videos, embodied as location biases and category errors. In this paper, we dive deep into such an important but understudied dilemma. To this end, we propose a unified framework, termed Noisy Pseudo-Label Learning, to handle both location biases and category errors. Specifically, our method is featured with (1) Noisy Label Ranking to rank pseudo labels based on the semantic confidence and boundary reliability, (2) Noisy Label Filtering to address the class-imbalance problem of pseudo labels caused by category errors, (3) Noisy Label Learning to penalize inconsistent boundary predictions to achieve noise-tolerant learning for heavy location biases. As a result, our method could effectively handle the label noise problem and improve the utilization of a large amount of unlabeled videos. Extensive experiments on THUMOS14 and ActivityNet v1.3 demonstrate the effectiveness of our method. The code is available at github.com/kunnxia/NPL. + +# 1. Introduction + +Temporal Action Localization (TAL) aims at detecting action instances of interest in an untrimmed video by locating their temporal boundaries and recognizing their action categories. Most existing TAL methods rely on dense temporal annotations for the training videos. However, labeling human actions is very tedious and time-consuming. As a remedy, Semi-Supervised TAL (SS-TAL) requires only a few + +![](images/58e266e1acd772d3f4fbc5c3447c4b4baba82ebdca7dd54b2cadf2a9fee5d9e0.jpg) +Figure 1. Illustration of label noise. Two examples demonstrate that pseudo labels may contain location biases and category errors. The fewer labeled videos are available, the heavier the noise of the pseudo labels will be. + +labeled videos in conjunction with a large amount of unlabeled videos. It has attracted growing attention in academia and industry. + +Existing SS-TAL methods [12, 37, 28] are based on consistency regularization or self-training. Consistency-based methods [12, 37] aim to generate consistent action proposals for the same video subject to different augmentations, e.g., time warping [12] and temporal feature shift [37]. In contrast, the self-training-based method [28] achieves new state-of-the-art performance by alternating between pseudo-labeling and re-training. It focuses on designing a proposal-free framework to address proposal error propagation from [12, 37] but neglects the important role of pseudo labels. Albeit its advancement, label noise still remains a core challenge, hindering efficient learning on abundant un + +labeled videos. From Figure 1, we can observe that label noise commonly leads to two intractable issues, i.e., location bias and category error, which become worse as the amount of labeled videos decreases. As a result, noisy pseudo labels will significantly degrade the performance of SS-TAL. + +In this paper, we propose a Noisy Pseudo-Label Learning (NPL) framework tailored for SS-TAL to combat detrimental label noise. It follows the self-training paradigm that alternates between pseudo-labeling and model training. But unlike all previous self-training methods, our NPL includes three novel components, termed Noisy Label Ranking, Noisy Label Filtering, and Noisy Label Learning, respectively, which alleviate the negative effects caused by location biases and category errors in a unified framework. + +First, Noisy Label Ranking aims to rank and select high-quality pseudo labels based on both semantic confidence and boundary reliability. Classification scores have been widely used in self-training to measure the quality of pseudo labels, but they only reflect semantic confidence and fail to account for localization reliability. To close this gap, we explicitly model the localization reliability of a detected action instance in an unlabeled video as the variance of the boundary predictions from dense snippets within the action. We then introduce a new integrated metric of semantic confidence and boundary reliability to rank the pseudo labels. + +Second, Noisy Label Filtering aims at addressing the class-imbalance problem in noisy pseudo labels. Owing to the category error, the class-imbalance problem occurs regardless of whether pseudo labels are sampled based on a confidence threshold or the number of samples. The model will be dominated by redundant noisy pseudo labels in training, especially for the ones of category errors, and further harm its generalization ability. To address this issue, we introduce an adaptive filtering strategy to regularize the distribution of pseudo labels and adaptively assign class-balanced pseudo labels to unlabeled videos. + +Last, Noisy Label Learning aims to improve the robustness of training to location bias. While noisy label ranking and filtering can improve the quality of sampled pseudo labels, location bias will not be removed completely. Training on biased boundary labels hinders the convergence of the model and further impedes accurate action localization. To this end, we propose a noise-tolerant training algorithm based on an unsupervised temporal consistency loss, which penalizes inconsistent predictions from adjacent action frames. + +The main contributions are summarized as follows: + +- This paper introduces a Noisy Pseudo-Label Learning (NPL) framework tailored for SS-TAL, which handles both the location bias and category error in a unified framework. Extensive experiments conducted on THUMOS14 [13] and ActivityNet v1.3 [2] demonstrate the effectiveness of the proposed method. + +- We propose a Noisy Label Ranking method to rank and select high-quality pseudo labels based on a new integrated metric of semantic confidence and boundary reliability. +- We propose a Noisy Label Filtering method to tackle the largely ignored class-imbalance problem in pseudo labels based on a new adaptive filtering strategy. +- We introduce a Noisy Label Learning method, which adopts an unsupervised temporal consistency loss to penalize inconsistent predictions from adjacent frames for noise-tolerant learning. + +# 2. Related Work + +Temporal Action Localization. The recent significant advancement of TAL arguably owes to the availability of large-scale and well-annotated datasets. We can roughly categorize existing TAL methods into three groups. Anchor-based methods [43, 5, 45, 52, 36] employ multiscale anchors that may contain an action and refine them via a boundary regression head. GTAN [25] dynamically optimizes the scale of each anchor via Gaussian kernels. G-TAD [45] improves temporal anchor representation with semantic and temporal context. Anchor-free methods [54, 29, 18, 27, 40, 39, 41] directly learn to predict action proposals by grouping possible start/end locations [20, 19] or regressing the distance to action boundaries [18, 49]. Transformer-based methods [31, 24, 49, 8] adopt the Transformer architecture [33, 3] for action localization and achieve remarkable performance on TAL benchmarks. In addition, unsupervised temporal action localization [11, 50] has made remarkable achievements without requiring any annotations. + +Semi-Supervised Learning. Semi-Supervised Learning (SSL) methods mostly focus on image classification. They can be classified into two categories. Consistency-based methods [32, 26, 51, 1] enforce the model to produce consistent predictions across label-preserving image augmentations. Self-training methods [42, 15, 10] retrain the model with high-confidence pseudo labels of unlabeled raw data. Thereby, the final performance is largely limited by the quality of pseudo labels generated by an inaccurate model trained using a few labeled data. Much effort tries to remedy noisy pseudo labels [16, 23, 44, 55, 17, 46]. Li et al. [16] train a noise-tolerant model, which is encouraged to produce consistent predictions under a variety of noisy synthetic labels. DSL [7] directly ignores the gradient computation and propagation for ambiguous pseudo labels. Wang et al. [38] propose an iterative training method to identify and down-weigh noisy samples. Chen et al. [6] address severe confirmation bias during self-training and generate unbiased pseudo labels to drive student learning. In this paper, we focus on the challenging SS-TAL problem. + +![](images/b60c2c584f2b6aa971674514e2f323d7b013950153b0c7824142c7eb80743e4d.jpg) +Figure 2. An overview of our proposed Noisy Pseudo-Label Learning framework. The training data contain both labeled and unlabeled videos. We first obtain a pre-trained model using a small amount of labeled videos and generate pseudo labels on unlabeled videos. To deal with noise in pseudo labels, Noisy Label Ranking first assesses the quality of pseudo labels through both semantic confidence and boundary reliability. Noisy Label Filtering then adaptively filters pseudo labels so that the model learning will not be dominated by pseudo labels with category errors. To make the training robust to label noise, we introduce dense temporal consistency training with $L_{u}^{\mathrm{cons}}$ . The model can be optimized by the final loss, which is the sum of $L_{s}$ , $L_{u}^{\mathrm{cls}}$ , and $L_{u}^{\mathrm{cons}}$ . + +Semi-Supervised Temporal Action Localization. SS-TAL is a worthwhile but under-explored field. Existing works [12, 37, 9, 28] are intrinsically driven by SSL. Some works [12, 37, 9] aim to improve the consistent predictions of the teacher-student network when video features are augmented by different temporal perturbations, e.g., time warping/masking [12], temporal feature shift/flip [37] or spatiotemporal feature crossover [9]. The other one [28] focuses on addressing proposal error propagation, which alternates between predicting and applying pseudo labels. However, all these approaches fail to dive deep into the major challenge of SS-TAL, i.e., noisy pseudo labels hindering efficient learning on unlabeled videos. We attribute the label noise problem of pseudo labels from unlabeled videos to the semantic uncertainty and boundary ambiguity of labeled actions. This paper tackles both the location bias and category error of pseudo labels into a unified framework for efficient learning from unlabeled videos. + +# 3. Method + +# 3.1. Preliminary + +Problem Setting. Semi-supervised temporal action localization (SS-TAL) aims to perform TAL from a small amount of labeled videos $\{X_{i}|_{i = 1}^{N_{l}}\}$ and a large amount of unlabeled videos $\{U_i|_{i = 1}^{N_u}\}$ , where $N_{l}$ and $N_{u}$ are the numbers of labeled and unlabeled videos, respectively. In a labeled video, its annotation is a set of action instances, and each action instance could be represented as $(t_s,t_e,c)$ , where $t_s,t_e,$ and $c$ + +denote the start time, end time, and action class, respectively. + +Feature Encoding. Following conventions [45, 47], we sample a video snippet from every few consecutive frames. Then, we adopt a fine-tuned two-stream network to extract RGB and optical flow features at each video snippet. + +Overview. Recent anchor-free TAL methods [18, 49, 27] are more attractive and practical since they are powerful and portable to be deployed in many real-world applications. We take the anchor-free detector [49] as our baseline, where each video snippet is directly supervised by the corresponding labels, i.e., distances to boundaries and the action category. + +Our SS-TAL framework follows the self-training paradigm [30], which can be decomposed into two steps. In the first step, we obtain a pre-trained model based on labeled videos with a supervised loss and then generate pseudo labels on unlabeled videos. In the second step, we update the model parameters with a semi-supervised training objective, including a supervised loss and an unsupervised loss: + +$$ +\mathcal {L} = \mathcal {L} _ {s} + \alpha \mathcal {L} _ {u}, \tag {1} +$$ + +where $\mathcal{L}_s$ and $\mathcal{L}_u$ denote the supervised loss of labeled videos and the unsupervised loss of unlabeled videos, respectively, and $\alpha$ controls the contribution of the unsupervised loss. Both of them are normalized by the corresponding numbers of training samples as follows: + +$$ +\mathcal {L} _ {s} = \frac {1}{N _ {l}} \sum_ {i = 1} ^ {N _ {l}} \left(\mathcal {L} _ {s} ^ {\mathrm {c l s}} \left(X _ {i}\right) + \mathcal {L} _ {s} ^ {\mathrm {r e g}} \left(X _ {i}\right)\right), \tag {2} +$$ + +$$ +\mathcal {L} _ {u} = \frac {1}{N _ {u}} \sum_ {i = 1} ^ {N _ {u}} \left(\mathcal {L} _ {u} ^ {\mathrm {c l s}} \left(U _ {i}\right) + \mathcal {L} _ {u} ^ {\mathrm {r e g}} \left(U _ {i}\right)\right), \tag {3} +$$ + +where $\mathcal{L}^{\mathrm{cls}}$ is a classification loss, $\mathcal{L}^{\mathrm{reg}}$ is a regression loss, and $N_{l}$ and $N_{u}$ denote the number of training samples for labeled and unlabeled videos, respectively. + +We claim that the major obstacle that hinders self-training performance lies in label noise, which leads to two issues: location biases and category errors. In this paper, we propose a Noisy Pseudo-Label Learning framework (NPL) to alleviate the negative effects caused by location biases and category errors for SS-TAL. The pipeline of our method is illustrated in Figure 2. It includes three novel components: Noisy Label Ranking, Noisy Label Filtering, and Noisy Label Learning, described in the following sections. + +# 3.2. Noisy Label Ranking + +In SS-TAL, the quality of pseudo labels can be measured from two perspectives, i.e., semantic confidence and boundary reliability. It is desirable to have high-quality pseudo labels for semi-supervised learning. + +The majority of TAL frameworks [20, 53, 52, 36] rely on the foreground score of an anchor or a proposal to measure its quality. However, the foreground score only reflects semantic confidence and cannot account for boundary reliability. From Figure 3 (a), we can observe that foreground scores may not strongly correlate with the localization quality (i.e., IoU w.r.t. ground truth). Thus, it is necessary to measure the quality of pseudo labels from both aspects of action classification and boundary localization. + +For labeled videos, anchors or proposals corresponding to the same action instance are supervised by the same ground truth during training. Thus, they are gradually regressed to the similar temporal boundary locations. This motivates us to use the consistency of the boundary predictions to measure their location reliability. Specifically, taking our anchor-free framework as an example, we can obtain dense predictions of action instances before the post-processing phase. Given a prediction $p_j = (\hat{t}_{s,j}, \hat{t}_{e,j}, c_j)$ where $\hat{t}_{s,j}$ and $\hat{t}_{e,j}$ are the predicted start and end boundaries of the $j$ -th video snippet respectively and $c_j$ is its foreground score, we can obtain a set of predictions $\{p_n\}_{n=1}^{N_a}$ from its $N_a$ adjacent snippets. Then, we formulate the boundary ambiguity of $p_j$ as follows: + +$$ +\bar {\sigma} _ {j} = \hat {\sigma} _ {s, j} + \hat {\sigma} _ {e, j}, +$$ + +$$ +\hat {\sigma} _ {s, j} = \frac {\sigma_ {s , j}}{d (p _ {j})}, \tag {4} +$$ + +$$ +\hat {\sigma} _ {e, j} = \frac {\sigma_ {e , j}}{d (p _ {j})}, +$$ + +where $\sigma_{s,j}$ and $\sigma_{e,j}$ are the variances of the start and end boundaries of $\{p_n\}_{n = 1}^{N_a}$ , respectively. $\hat{\sigma}_{s,j}$ and $\hat{\sigma}_{e,j}$ are normalized by their duration $d(p_j)$ . A smaller boundary vari + +![](images/7522465f91e375b8547b389e360714b0faaef39f9f45bb9a8c1a78367ec816d4.jpg) +(a) + +![](images/ed119a7fc26802ee0327b2821b440629fe797274eed6dd2dfd73ce57fcabda63.jpg) +(b) +Figure 3. Each star represents a prediction result (i.e., a pseudo label) on $60\%$ unlabeled videos based on the model trained with $40\%$ labeled videos on THUMOS14. (a) depicts the correlation between the foreground score and the IoU with ground truth. (b) depicts the correlation between the boundary variance and the IoU with ground truth. It can be observed that the boundary variance highly correlates with the localization quality. + +ance $\bar{\sigma}_j$ indicates lower boundary ambiguity of the prediction $p_j$ , thus leading to higher localization reliability. In Figure 3 (b), we experimentally illustrate the correlation between the boundary variance and IoU w.r.t ground truth. We can observe that boundary variances could better measure the localization quality of pseudo labels than the classification scores. Particularly, this motivates us to define the confidence score of $p_j$ as: + +$$ +s _ {j} = \frac {c _ {j}}{\bar {\sigma} _ {j}}. \tag {5} +$$ + +Eq. (5) provides a comprehensive metric to measure the quality of pseudo labels by their semantic confidence (foreground score $c$ ) and boundary ambiguity (boundary variance $\bar{\sigma}$ ). As a result, our Noisy Label Ranking could improve the quality of pseudo labels only from intrinsic video snippets without requiring additional learnable networks or hyperparameters. + +# 3.3. Noisy Label Filtering + +Training on a few labeled videos inevitably produces noisy pseudo labels with category errors on unlabeled videos. As a result, the frequencies of some action categories in the selected pseudo labels will be much larger or smaller than their natural frequencies in the videos, regardless of whether pseudo labels are sampled based on a confidence threshold or the number of samples. We call this phenomenon the class-imbalance problem of pseudo labels in SS-TAL, illustrated in Figure 4. For example, the frequency of "Golf Swing" in pseudo labels is much higher than that in ground truth labels, while the frequency of "Throw Discus" is much lower in the pseudo labels. + +Under this class-imbalance problem, overwhelming pseudo labels with category errors will dominate the model learning and further aggravate the semantic uncertainty of actions of category errors, resulting in limited gains. + +![](images/435e98c65b58e57a78c7aea01d3577a620c66b8100197909f0c6e09fc01b2c10.jpg) +Figure 4. Illustration of the class-imbalance problem of pseudo labels obtained on $60\%$ unlabeled THUMOS14. The horizontal axis of the histogram represents the class name, and the vertical axis represents the ratio between the number of pseudo labels and the number of ground truth labels. It can be observed that our Noisy Label Filtering could alleviate the class-imbalance problem of pseudo labels. + +To address this class-imbalance problem, we introduce an adaptive filtering strategy to regularize the distribution of pseudo labels for each category. Concretely, we arrange dense labels according to the category of actions and the number of pseudo labels in an unlabeled video, as follows: + +$$ +K _ {a d p} = \frac {\left| \left\{p _ {n} ^ {c} \right\} _ {n = 1} ^ {N _ {v}} \right|}{N _ {v}} \cdot N _ {p o s}, \tag {6} +$$ + +where $N_{v}$ is the total number of pseudo labels within a video, and $N_{pos}$ is a hyper-parameter to control the number of positive predictions. Eq. (6) is used to adaptively select the number $K_{adp}$ of class-specific pseudo labels for the category $c$ in each unlabeled video. From Figure 4, we experimentally demonstrate that our adaptive filtering strategy could address the class-imbalance distribution of pseudo labels. As a result, our Noisy Label Filtering could not only assign accurate pseudo labels to improve the model learning but also prevent the pseudo labels from being dominated by overwhelming pseudo labels with category errors, while it also avoids tediously adjusting heuristic thresholds. + +# 3.4. Noisy Label Learning + +The boundary ambiguity of labeled actions gives rise to noisy pseudo labels with location biases. Subsequently, training on the biased boundaries results in the boundary ambiguity of unlabeled actions and impedes accurate action localization. + +To remedy it, we propose a noise-tolerant training algorithm for unlabeled videos with heavy location biases. It aims to penalize inconsistency boundary predictions from adjacent feature locations within a video feature sequence. + +Our unsupervised temporal consistency loss is defined as follows: + +$$ +\mathcal {L} _ {u} ^ {\text {c o n s}} = \frac {1}{M _ {u} \left(M _ {p} - 1\right)} \sum_ {j = 1} ^ {M _ {u}} \sum_ {i = 1} ^ {M _ {p} - 1} \left| b _ {i + 1} ^ {j} - b _ {i} ^ {j} \right|, \tag {7} +$$ + +where $M_{u}$ denotes the number of pseudo labels within an unlabeled video. $M_{p}$ represents the number of the training snippets within an action. $b_{i}$ represents the predicted start/end boundary locations from the $i$ -th snippet. In this way, the model could learn to produce more reliable predictions. Consequently, our complete unsupervised loss is denoted below: + +$$ +\mathcal {L} _ {u} = \frac {1}{N _ {u}} \sum_ {i = 1} ^ {N _ {u}} \left(\mathcal {L} _ {u} ^ {\mathrm {c l s}} \left(U _ {i}\right) + \mathcal {L} _ {u} ^ {\mathrm {c o n s}} \left(U _ {i}\right)\right). \tag {8} +$$ + +The Noisy Label Learning makes the training robust to location biases in the pseudo labels. Finally, the model can be optimized by the sum of $\mathcal{L}_s$ and $\mathcal{L}_u$ on all videos. + +# 4. Experiments + +# 4.1. Datasets and Metrics + +Evaluation Datasets. We evaluate our proposed method on two benchmark TAL datasets, i.e., THUMOS14 [13] and ActivityNet v1.3 [2]. THUMOS14 [13] is a standard benchmark for TAL. It contains 200 validation videos and 213 testing videos, including 20 action categories. It is very challenging since each video has more than 15 action instances. Following the common setting [48], we use the validation set for training and evaluate on the testing set. + +ActivityNet v1.3 [2] is a large-scale benchmark for video-based action localization. It contains 10k training videos and 5k validation videos corresponding to 200 different actions. Following the standard practice [22], we train our method on the training set and test it on the validation set. + +Evaluation Metrics. We use the mean Average Precision (mAP) as the evaluation metric. The tIoU thresholds are $[0.3:0.1:0.7]$ for THUMOS14 and $[0.5:0.05:0.95]$ for ActivityNet v1.3. We report the average mAP of the IoU thresholds between 0.5 and 0.95 with the step of 0.05 on ActivityNet v1.3. Also, we present the average mAP of the tIoU thresholds from 0.3 to 0.7 on THUMOS14. + +The goal of SS-TAL is to use a large amount of unlabeled data to improve a well-trained detector on a small amount of labeled data. We randomly sample $10\%$ , $20\%$ , $40\%$ , and $60\%$ of the training data as labeled data and treat the remainder as unlabeled data. + +# 4.2. Implementation Details + +We implement our semi-supervised action localization framework based on the recent prevalent anchor-free detector + +
LabelMethodBackboneTHUMOS14 (%)ActivityNet v1.3 (%)
0.30.40.50.60.7Avg.0.50.750.95Avg.
10%ActF* [49]I3D28.522.914.18.24.115.647.824.21.725.6
ActF [49] + MixUp [51]I3D29.724.214.59.65.416.749.427.93.128.8
NPL (ActF)I3D32.829.620.111.77.220.351.933.43.632.5
SSP [12]TSN44.234.124.616.99.325.838.928.78.427.6
SSTAP [37]TSN45.635.226.317.510.727.040.729.69.028.2
SPOT [28]TSN49.440.431.522.912.431.349.931.18.332.1
NPL (BMN)TSN50.041.733.523.613.432.450.932.07.932.6
20%ActF* [49]I3D49.141.632.621.512.131.451.234.33.832.9
ActF [49] + MixUp [51]I3D51.243.234.023.914.133.352.934.73.933.3
NPL (ActF)I3D54.547.139.329.718.537.853.135.83.933.8
SPOT [28]TSN52.643.934.125.216.234.451.732.06.932.3
NPL (BMN)TSN53.945.636.226.916.535.852.132.97.932.9
40%ActF* [49]I3D69.060.449.331.519.345.953.235.73.834.2
ActF [49] + MixUp [51]I3D69.761.952.434.420.147.753.136.04.334.5
NPL (ActF)I3D71.965.455.740.923.451.553.636.54.635.3
SPOT [28]TSN54.445.837.229.719.437.353.333.06.633.2
NPL (BMN)TSN56.246.738.830.319.538.353.433.98.133.8
60%ActF* [49]I3D71.565.659.947.332.755.453.936.15.735.0
ActF [49] + MixUp [51]I3D72.267.561.248.734.056.754.136.45.735.2
NPL (ActF)I3D74.569.962.851.136.659.054.336.76.535.8
SSP [12]TSN53.246.839.329.719.837.849.834.57.033.5
SSTAP [37]TSN56.449.541.030.921.639.950.134.97.434.0
SPOT [28]TSN58.950.142.333.522.941.552.835.08.135.2
NPL (BMN)TSN59.051.442.934.323.342.253.935.88.535.7
+ +Table 1. Performance comparison with state-of-the-art SS-TAL methods on THUMOS14 testing set and ActivityNet v1.3 validation set. Notably, SSP and SSTAP employ UntrimmedNet [34] trained with $100\%$ class labels for proposal classification. ActF refers to ActionFormer [49]. \* means using only labeled training videos. + +ActionFormer [49], which is composed of a self-attention backbone [33], an FPN [21] neck and two parallel heads. Also, we combine the proposed semi-supervised method with BMN [19], which is a two-stage proposal-based detector. For video feature encoding, we used two popular backbones, i.e., two-stream network [35] and I3D [4] pretrained on Kinetics [14] to extract the video features, following [18, 49]. For THUMOS14, the initial learning rate is $1e - 4$ , and a cosine learning rate decay is used. The minibatch size is 2, and a weight decay of $1e - 4$ is used. For ActivityNet v1.3, the learning rate is $1e - 3$ , the mini-batch size is 32, and the weight decay is $1e - 4$ . + +For semi-supervised configurations, an initial model is trained on available labeled videos, where labeling ratios are set to $10\%$ , $20\%$ , $40\%$ , and $60\%$ . Further using this well-trained model generates pseudo labels. For the re-training phase, we pre-train the model on the labeled data and then compute the supervised loss and unsupervised loss for 40 epochs (THUMOS14) and 15 epochs (ActivityNet v1.3). We set $\alpha = 1$ and $N_{pos} = 15$ . We apply background data augmentation to $10\%$ of unlabeled videos for performance improvements. Additional implementation details and more + +attempts for SS-TAL refer to the supplementary material. + +# 4.3. Comparison with State-of-the-art Methods + +THUMOS14. We compare the proposed method NPL with existing SS-TAL methods in Table 1, where we combine two different frameworks, ActionFormer [49] and BMN [19] with our NPL. We report mAP at different tIoU thresholds as well as average mAP between 0.3 and 0.7 with the step of 0.1. Also, we reproduce the SPOT [28] results of $20\%$ and $40\%$ labeling ratios from the source code for comparison. When labeled data is scarce (i.e., $10\%$ and $20\%$ labeling ratios), our method achieves the competitive performance compared to existing methods. Especially, our method outperforms the baseline, semi-supervised ActF [49], by a large margin with $10\%$ labeled THUMOS14. When more labeled data is accessible (i.e., $40\%$ and $60\%$ labeling ratios), our method outperforms all the competing methods, demonstrating the effectiveness and superiority of our method. + +ActivityNet v1.3. We also conduct experiments on the more challenging benchmark ActivityNet v1.3. As depicted in Table 1, the proposed method also achieves significant performance gains over all the compared methods. When + +
LabelMethodmAP (%)
0.30.50.7Avg.
10%baseline29.515.85.016.8
+NR30.716.96.318.0
+NF32.018.56.919.1
+NL32.820.17.220.3
40%baseline70.149.520.247.1
+NR70.752.120.748.5
+NF71.654.421.350.3
+NL71.955.723.451.5
+ +Table 2. Ablation study on effectiveness of each component of the proposed method on THUMOS14, using $10\%$ and $40\%$ labeled videos. + means training by the proposed method. + +
LabelMethodClass (%)Avg. tIoU (%)
10%baseline21.027.4
NPL25.936.2
40%baseline73.054.2
NPL74.459.0
+ +there are more unlabeled data introduced, our method also can improve the average mAP, which mainly comes from the high-quality pseudo labels for effective training. + +# 4.4. Ablation Study + +To better understand how the proposed method works, we conduct a series of ablation studies, where we use ActionFormer [49] as the localization framework with I3D [4]. + +Effectiveness of individual component. To validate our key designs, we ablate the effects of the proposed Noisy Label Ranking (NR), Noisy Label Filtering (NF), and Noisy Label Learning (NL). The results are shown in Table 2. Under the $40\%$ labeling ratio, one can see that our model equipped with NR improves performance by $1.4\%$ . Further applying our adaptive filtering strategy and the temporal consistency learning, the performance reaches an average mAP of $51.5\%$ . In summary, our designs significantly improve the utilization of unlabeled data for effectively semi-supervised learning. + +Quality improvements of pseudo labels. The quality of pseudo labels is the important indicator for the SS-TAL performance improvement. We further study the quality of pseudo labels from their average temporal IoU (tIoU) w.r.t ground truth and classification accuracy (Acc.). We report the comparison results in Table 3. It can be observed that the significant improvements attribute to our Noisy Label Ranking to rank and select high-quality pseudo labels based on the comprehensive metric, i.e., semantic confidence and localization reliability, as well as our Noisy Label Filtering to + +![](images/3c69396b2137a2a3549217a76e661c8ae9357d844df92a737b7337880d6dfffc.jpg) +Figure 5. Curves of averaged IoU vs. foreground score or boundary variance, where each averaged IoU is calculated by the foreground scores or boundary variances of the samples in different intervals. + +![](images/b5aaad6a9f933727e8715d3e0600a244bcf46b02257794c41640934f03d1934d.jpg) + +Table 3. Ablation study on the quality of pseudo labels in terms of action classification accuracy (Class) and average tIoU (Avg. tIoU), using $10\%$ and $40\%$ labeled videos. + +
MethodmAP (%)
0.30.40.50.60.7Avg.
\( \theta_s = 0.3 \)70.163.552.937.422.249.2
top-1071.063.353.438.122.849.7
NF71.965.455.740.923.451.5
+ +Table 4. Comparison of pseudo-label filtering strategies on THUMOS14 with ${40}\%$ labeled videos and ${60}\%$ unlabeled videos. + +adaptively assign class-balanced pseudo labels for training. + +Visualization of noisy label ranking. To further support our motivation of the noisy label ranking, we add a curve of averaged IoU (between pseudo labels and ground truth) versus foreground score or boundary variance, where each averaged IoU corresponds to the foreground scores or boundary variances of the samples in different intervals, as shown in Figure 5. Particularly, the Pearson correlation coefficient between IoU and boundary variance is 0.496, while that between IoU and foreground score is 0.449. + +Superiority of adaptive filtering strategy. Our Noisy Label Filtering (NF) could alleviate the class-imbalance problem of pseudo labels caused by the category error. In addition, it also could avoid tediously adjusting hard-crafted thresholds or numbers for pseudo-label filtering. To demonstrate this superiority, we experiment with two common approaches as a reference, i.e., single thresholding and fixed number strategies. More specifically, we empirically set the foreground score threshold $\theta_{s}$ to 0.3, where instances are regarded as foreground if their scores are above the threshold and background otherwise. Besides, we also empirically select top-10 confidence predictions for each unlabeled video. As shown in Table 4, these approaches cannot achieve satisfactory performance. In contrast, our adaptive filtering strategy could adaptively sample class-specific pseudo labels, showing its effectiveness and importance. + +Analysis of temporal consistency. Our Noisy Label Learning introduces a temporal consistency loss to tackle the location bias problem by penalizing inconsistent boundary predictions from each intrinsic video snippet. We conduct an ablation study on this key design, where we train the pre-trained model with and without the temporal consistency only on $60\%$ unlabeled videos, as shown in Figure 6. Based + +![](images/3b5c425a40e81c755ce3abf15b041b5386bd0a40b85d15f61e3d7cb9f6ba58af.jpg) +Figure 6. Comparison of model performance and convergence speed with and without the temporal consistency loss on THU-MOS14. + +
NposmAP (%)
0.30.50.7Avg.
571.555.222.851.0
1571.955.723.451.5
3071.055.322.550.7
+ +Table 5. Comparison of mAP with various values of $N_{pos}$ using $40\%$ labeled THUMOS14. + +
Label100%60%40%20%10%
mAP@0.5 (%)71.062.855.739.320.1
mAP@Avg (%)66.859.051.537.820.3
+ +Table 6. Comparison of mAP with various labeling ratios on THU-MOS14, where the remainder is treated as unlabeled data. + +on the temporal consistency, it obtains a $1.2\%$ improvement on the average mAP. Apart from the performance gain, our contribution can also significantly boost the convergence speed. Both of these advances validate the effectiveness of the proposed Noisy Label Learning. + +Choice of hyper-parameters. $N_{pos}$ is a pre-defined value to handle the number of positive samples for unlabeled videos. We conduct an ablation study on the hyper-parameter $N_{pos}$ under $40\%$ labeling ratio. From Table 5, it can be observed that the performance peaks around $N_{pos} = 15$ . A large value such as $N_{pos} = 30$ will introduce more low-quality pseudo labels and confuse the model in training, while a small value such as $N_{pos} = 5$ only provides a small number of samples for training so as to obtain limited gains. + +Bottleneck of our NPL. The performance limitation of SS-TAL following self-training lies in the noise level of pseudo labels. To explore the performance bottleneck, we train a fully-supervised model with $100\%$ labeled videos on THUMOS14. The experimental results in Table 6 show that our method still has great room for improvement. Also, it demonstrates that the negative impacts of the label noise problem cannot be ignored in semi-supervised learning. + +![](images/63f654c453e52d6017d722912392e1215238aa71424ab5f7ea30ca714398cddf.jpg) +Figure 7. Qualitative SS-TAL result comparison of our proposed method with SPOT [28] on two untrimmed videos from (a) ActivityNet v1.3 and (b) THUMOS14, respectively. + +# 4.5. Visualization Analysis + +To further validate the effectiveness of the proposed method, we provide some qualitative results by prior art SPOT [28] and our model with $10\%$ and $40\%$ labeled data on both ActivityNet v1.3 and THUMOS14. From the illustration in Figure 7, we can observe that our method can localize the target actions more accurately, demonstrating the effectiveness and superiority of our method. + +# 5. Conclusion + +In this paper, we propose a novel Noisy Pseudo-Label Learning framework tailored for SS-TAL to tackle the label noise problem. Specifically, we first present a new integrated metric of semantic confidence and boundary reliability for ranking high-quality pseudo labels. Then, an adaptive filtering strategy alleviates the class-imbalance distribution of pseudo labels caused by the category error. Finally, we introduce an unsupervised temporal consistency loss to tackle biased boundary labels for noise-tolerant learning. Experiments show that the effectiveness of our method on both THUMOS14 and ActivityNet v1.3. + +Limitation. 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In CVPR, pages 10156-10165, 2020. 2, 3 +[46] Qize Yang, Xihan Wei, Biao Wang, Xian-Sheng Hua, and Lei Zhang. Interactive self-training with mean teachers for semi-supervised object detection. In CVPR, pages 5941-5950, 2021. 2 +[47] Runhao Zeng, Wenbing Huang, Mingkui Tan, Yu Rong, Peilin Zhao, Junzhou Huang, and Chuang Gan. Graph convolutional networks for temporal action localization. In ICCV, pages 7094-7103, 2019. 3 + +[48] Runhao Zeng, Wenbing Huang, Mingkui Tan, Yu Rong, Peilin Zhao, Junzhou Huang, and Chuang Gan. Graph convolutional module for temporal action localization in videos. IEEE T-PAMI, 44(10):6209-6223, 2022. 5 +[49] Chenlin Zhang, Jianxin Wu, and Yin Li. ActionFormer: Localizing moments of actions with transformers. In ECCV, pages 492-510, 2022. 2, 3, 6, 7 +[50] Can Zhang, Tianyu Yang, Junwu Weng, Meng Cao, Jue Wang, and Yuexian Zou. Unsupervised pre-training for temporal action localization tasks. In CVPR, pages 14031-14041, 2022. 2 +[51] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In ICLR, 2018. 2, 6 +[52] Chen Zhao, Ali K Thabet, and Bernard Ghanem. Video self-stitching graph network for temporal action localization. In ICCV, pages 13658-13667, 2021. 2, 4 +[53] Peisen Zhao, Lingxi Xie, Chen Ju, Ya Zhang, Yanfeng Wang, and Qi Tian. Bottom-up temporal action localization with mutual regularization. In ECCV, pages 539-555, 2020. 4 +[54] Yue Zhao, Yuanjun Xiong, Limin Wang, Zhirong Wu, Xiaou Tang, and Dahua Lin. Temporal action detection with structured segment networks. In ICCV, pages 2914-2923, 2017. 2 +[55] Hongyu Zhou, Zheng Ge, Songtao Liu, Weixin Mao, Zeming Li, Haiyan Yu, and Jian Sun. Dense teacher: Dense pseudolabels for semi-supervised object detection. In ECCV, pages 35-50, 2022. 2 \ No newline at end of file diff --git a/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/images.zip b/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7328a01b83c8f31ea48d7a10cf372c5639aac3a6 --- /dev/null +++ b/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e8aa39abc929f1542f9ffaf6e28d12c9e96282a32faeabb48cdf4b3cca89c8a9 +size 643825 diff --git a/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/layout.json b/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7fd7cc2040d33604a6ff5bddfaa6788b2ca16a58 --- /dev/null +++ b/2023/Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization/layout.json @@ -0,0 +1,8851 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 121, + 103, + 473, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 103, + 473, + 140 + ], + "spans": [ + { + "bbox": [ + 121, + 103, + 473, + 140 + ], + "type": "text", + "content": "Learning from Noisy Pseudo Labels for Semi-Supervised Temporal Action Localization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "spans": [ + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "content": "Kun Xia" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "inline_equation", + "content": "^{1,3\\dagger}" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "content": " Le Wang" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "content": " Sanping Zhou" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "content": " Gang Hua" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "content": " Wei Tang" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "content": "National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University \n" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "content": "Wormpex AI Research " + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 104, + 160, + 490, + 232 + ], + "type": "text", + "content": "University of Illinois Chicago" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "spans": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 284, + 290, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 290, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 290, + 547 + ], + "type": "text", + "content": "Semi-Supervised Temporal Action Localization (SS-TAL) aims to improve the generalization ability of action detectors with large-scale unlabeled videos. Albeit the recent advancement, one of the major challenges still remains: noisy pseudo labels hinder efficient learning on abundant unlabeled videos, embodied as location biases and category errors. In this paper, we dive deep into such an important but understudied dilemma. To this end, we propose a unified framework, termed Noisy Pseudo-Label Learning, to handle both location biases and category errors. Specifically, our method is featured with (1) Noisy Label Ranking to rank pseudo labels based on the semantic confidence and boundary reliability, (2) Noisy Label Filtering to address the class-imbalance problem of pseudo labels caused by category errors, (3) Noisy Label Learning to penalize inconsistent boundary predictions to achieve noise-tolerant learning for heavy location biases. As a result, our method could effectively handle the label noise problem and improve the utilization of a large amount of unlabeled videos. Extensive experiments on THUMOS14 and ActivityNet v1.3 demonstrate the effectiveness of our method. The code is available at github.com/kunnxia/NPL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 128, + 583 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 590, + 288, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 288, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 288, + 676 + ], + "type": "text", + "content": "Temporal Action Localization (TAL) aims at detecting action instances of interest in an untrimmed video by locating their temporal boundaries and recognizing their action categories. Most existing TAL methods rely on dense temporal annotations for the training videos. However, labeling human actions is very tedious and time-consuming. As a remedy, Semi-Supervised TAL (SS-TAL) requires only a few" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 260, + 542, + 459 + ], + "blocks": [ + { + "bbox": [ + 310, + 260, + 542, + 459 + ], + "lines": [ + { + "bbox": [ + 310, + 260, + 542, + 459 + ], + "spans": [ + { + "bbox": [ + 310, + 260, + 542, + 459 + ], + "type": "image", + "image_path": "58e266e1acd772d3f4fbc5c3447c4b4baba82ebdca7dd54b2cadf2a9fee5d9e0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 462, + 547, + 507 + ], + "lines": [ + { + "bbox": [ + 305, + 462, + 547, + 507 + ], + "spans": [ + { + "bbox": [ + 305, + 462, + 547, + 507 + ], + "type": "text", + "content": "Figure 1. Illustration of label noise. Two examples demonstrate that pseudo labels may contain location biases and category errors. The fewer labeled videos are available, the heavier the noise of the pseudo labels will be." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 531, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 547, + 567 + ], + "type": "text", + "content": "labeled videos in conjunction with a large amount of unlabeled videos. It has attracted growing attention in academia and industry." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 714 + ], + "type": "text", + "content": "Existing SS-TAL methods [12, 37, 28] are based on consistency regularization or self-training. Consistency-based methods [12, 37] aim to generate consistent action proposals for the same video subject to different augmentations, e.g., time warping [12] and temporal feature shift [37]. In contrast, the self-training-based method [28] achieves new state-of-the-art performance by alternating between pseudo-labeling and re-training. It focuses on designing a proposal-free framework to address proposal error propagation from [12, 37] but neglects the important role of pseudo labels. Albeit its advancement, label noise still remains a core challenge, hindering efficient learning on abundant un" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 683, + 143, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 683, + 143, + 693 + ], + "spans": [ + { + "bbox": [ + 66, + 683, + 143, + 693 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 48, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 48, + 693, + 287, + 713 + ], + "type": "text", + "content": "† Part of this work was done while Kun Xia was a visiting scholar at University of Illinois Chicago." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10160" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": "labeled videos. From Figure 1, we can observe that label noise commonly leads to two intractable issues, i.e., location bias and category error, which become worse as the amount of labeled videos decreases. As a result, noisy pseudo labels will significantly degrade the performance of SS-TAL." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 239 + ], + "type": "text", + "content": "In this paper, we propose a Noisy Pseudo-Label Learning (NPL) framework tailored for SS-TAL to combat detrimental label noise. It follows the self-training paradigm that alternates between pseudo-labeling and model training. But unlike all previous self-training methods, our NPL includes three novel components, termed Noisy Label Ranking, Noisy Label Filtering, and Noisy Label Learning, respectively, which alleviate the negative effects caused by location biases and category errors in a unified framework." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 239, + 288, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 288, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 288, + 371 + ], + "type": "text", + "content": "First, Noisy Label Ranking aims to rank and select high-quality pseudo labels based on both semantic confidence and boundary reliability. Classification scores have been widely used in self-training to measure the quality of pseudo labels, but they only reflect semantic confidence and fail to account for localization reliability. To close this gap, we explicitly model the localization reliability of a detected action instance in an unlabeled video as the variance of the boundary predictions from dense snippets within the action. We then introduce a new integrated metric of semantic confidence and boundary reliability to rank the pseudo labels." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 371, + 288, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 288, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 288, + 502 + ], + "type": "text", + "content": "Second, Noisy Label Filtering aims at addressing the class-imbalance problem in noisy pseudo labels. Owing to the category error, the class-imbalance problem occurs regardless of whether pseudo labels are sampled based on a confidence threshold or the number of samples. The model will be dominated by redundant noisy pseudo labels in training, especially for the ones of category errors, and further harm its generalization ability. To address this issue, we introduce an adaptive filtering strategy to regularize the distribution of pseudo labels and adaptively assign class-balanced pseudo labels to unlabeled videos." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 502, + 288, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 288, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 288, + 621 + ], + "type": "text", + "content": "Last, Noisy Label Learning aims to improve the robustness of training to location bias. While noisy label ranking and filtering can improve the quality of sampled pseudo labels, location bias will not be removed completely. Training on biased boundary labels hinders the convergence of the model and further impedes accurate action localization. To this end, we propose a noise-tolerant training algorithm based on an unsupervised temporal consistency loss, which penalizes inconsistent predictions from adjacent action frames." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 622, + 266, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 622, + 266, + 634 + ], + "spans": [ + { + "bbox": [ + 59, + 622, + 266, + 634 + ], + "type": "text", + "content": "The main contributions are summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "type": "text", + "content": "- This paper introduces a Noisy Pseudo-Label Learning (NPL) framework tailored for SS-TAL, which handles both the location bias and category error in a unified framework. Extensive experiments conducted on THUMOS14 [13] and ActivityNet v1.3 [2] demonstrate the effectiveness of the proposed method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 72, + 545, + 220 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 120 + ], + "type": "text", + "content": "- We propose a Noisy Label Ranking method to rank and select high-quality pseudo labels based on a new integrated metric of semantic confidence and boundary reliability." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 128, + 545, + 164 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 128, + 545, + 164 + ], + "spans": [ + { + "bbox": [ + 317, + 128, + 545, + 164 + ], + "type": "text", + "content": "- We propose a Noisy Label Filtering method to tackle the largely ignored class-imbalance problem in pseudo labels based on a new adaptive filtering strategy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 172, + 545, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 172, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 317, + 172, + 545, + 220 + ], + "type": "text", + "content": "- We introduce a Noisy Label Learning method, which adopts an unsupervised temporal consistency loss to penalize inconsistent predictions from adjacent frames for noise-tolerant learning." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 239, + 392, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 392, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 392, + 251 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 258, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 547, + 474 + ], + "type": "text", + "content": "Temporal Action Localization. The recent significant advancement of TAL arguably owes to the availability of large-scale and well-annotated datasets. We can roughly categorize existing TAL methods into three groups. Anchor-based methods [43, 5, 45, 52, 36] employ multiscale anchors that may contain an action and refine them via a boundary regression head. GTAN [25] dynamically optimizes the scale of each anchor via Gaussian kernels. G-TAD [45] improves temporal anchor representation with semantic and temporal context. Anchor-free methods [54, 29, 18, 27, 40, 39, 41] directly learn to predict action proposals by grouping possible start/end locations [20, 19] or regressing the distance to action boundaries [18, 49]. Transformer-based methods [31, 24, 49, 8] adopt the Transformer architecture [33, 3] for action localization and achieve remarkable performance on TAL benchmarks. In addition, unsupervised temporal action localization [11, 50] has made remarkable achievements without requiring any annotations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 714 + ], + "type": "text", + "content": "Semi-Supervised Learning. Semi-Supervised Learning (SSL) methods mostly focus on image classification. They can be classified into two categories. Consistency-based methods [32, 26, 51, 1] enforce the model to produce consistent predictions across label-preserving image augmentations. Self-training methods [42, 15, 10] retrain the model with high-confidence pseudo labels of unlabeled raw data. Thereby, the final performance is largely limited by the quality of pseudo labels generated by an inaccurate model trained using a few labeled data. Much effort tries to remedy noisy pseudo labels [16, 23, 44, 55, 17, 46]. Li et al. [16] train a noise-tolerant model, which is encouraged to produce consistent predictions under a variety of noisy synthetic labels. DSL [7] directly ignores the gradient computation and propagation for ambiguous pseudo labels. Wang et al. [38] propose an iterative training method to identify and down-weigh noisy samples. Chen et al. [6] address severe confirmation bias during self-training and generate unbiased pseudo labels to drive student learning. In this paper, we focus on the challenging SS-TAL problem." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10161" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 78, + 545, + 271 + ], + "blocks": [ + { + "bbox": [ + 50, + 78, + 545, + 271 + ], + "lines": [ + { + "bbox": [ + 50, + 78, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 50, + 78, + 545, + 271 + ], + "type": "image", + "image_path": "b60c2c584f2b6aa971674514e2f323d7b013950153b0c7824142c7eb80743e4d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "text", + "content": "Figure 2. An overview of our proposed Noisy Pseudo-Label Learning framework. The training data contain both labeled and unlabeled videos. We first obtain a pre-trained model using a small amount of labeled videos and generate pseudo labels on unlabeled videos. To deal with noise in pseudo labels, Noisy Label Ranking first assesses the quality of pseudo labels through both semantic confidence and boundary reliability. Noisy Label Filtering then adaptively filters pseudo labels so that the model learning will not be dominated by pseudo labels with category errors. To make the training robust to label noise, we introduce dense temporal consistency training with " + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "inline_equation", + "content": "L_{u}^{\\mathrm{cons}}" + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "text", + "content": ". The model can be optimized by the final loss, which is the sum of " + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "inline_equation", + "content": "L_{s}" + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "inline_equation", + "content": "L_{u}^{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "inline_equation", + "content": "L_{u}^{\\mathrm{cons}}" + }, + { + "bbox": [ + 46, + 274, + 547, + 343 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 361, + 289, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 289, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 289, + 576 + ], + "type": "text", + "content": "Semi-Supervised Temporal Action Localization. SS-TAL is a worthwhile but under-explored field. Existing works [12, 37, 9, 28] are intrinsically driven by SSL. Some works [12, 37, 9] aim to improve the consistent predictions of the teacher-student network when video features are augmented by different temporal perturbations, e.g., time warping/masking [12], temporal feature shift/flip [37] or spatiotemporal feature crossover [9]. The other one [28] focuses on addressing proposal error propagation, which alternates between predicting and applying pseudo labels. However, all these approaches fail to dive deep into the major challenge of SS-TAL, i.e., noisy pseudo labels hindering efficient learning on unlabeled videos. We attribute the label noise problem of pseudo labels from unlabeled videos to the semantic uncertainty and boundary ambiguity of labeled actions. This paper tackles both the location bias and category error of pseudo labels into a unified framework for efficient learning from unlabeled videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 589, + 104, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 589, + 104, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 589, + 104, + 601 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 609, + 127, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 127, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 127, + 623 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "text", + "content": "Problem Setting. Semi-supervised temporal action localization (SS-TAL) aims to perform TAL from a small amount of labeled videos " + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{X_{i}|_{i = 1}^{N_{l}}\\}" + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "text", + "content": " and a large amount of unlabeled videos " + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{U_i|_{i = 1}^{N_u}\\}" + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "text", + "content": " are the numbers of labeled and unlabeled videos, respectively. In a labeled video, its annotation is a set of action instances, and each action instance could be represented as " + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "inline_equation", + "content": "(t_s,t_e,c)" + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "inline_equation", + "content": "t_s,t_e," + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 628, + 289, + 715 + ], + "type": "inline_equation", + "content": "c" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 361, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 361, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 547, + 373 + ], + "type": "text", + "content": "denote the start time, end time, and action class, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 373, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 373, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 373, + 547, + 422 + ], + "type": "text", + "content": "Feature Encoding. Following conventions [45, 47], we sample a video snippet from every few consecutive frames. Then, we adopt a fine-tuned two-stream network to extract RGB and optical flow features at each video snippet." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 494 + ], + "type": "text", + "content": "Overview. Recent anchor-free TAL methods [18, 49, 27] are more attractive and practical since they are powerful and portable to be deployed in many real-world applications. We take the anchor-free detector [49] as our baseline, where each video snippet is directly supervised by the corresponding labels, i.e., distances to boundaries and the action category." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 495, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 578 + ], + "type": "text", + "content": "Our SS-TAL framework follows the self-training paradigm [30], which can be decomposed into two steps. In the first step, we obtain a pre-trained model based on labeled videos with a supervised loss and then generate pseudo labels on unlabeled videos. In the second step, we update the model parameters with a semi-supervised training objective, including a supervised loss and an unsupervised loss:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 392, + 589, + 545, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 589, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 392, + 589, + 545, + 602 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {s} + \\alpha \\mathcal {L} _ {u}, \\tag {1}", + "image_path": "5ef7f07a47b00a8475785925cc1eb8fb3cb7c1b417724672d0a7682722144ced.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_u" + }, + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "type": "text", + "content": " denote the supervised loss of labeled videos and the unsupervised loss of unlabeled videos, respectively, and " + }, + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 613, + 547, + 673 + ], + "type": "text", + "content": " controls the contribution of the unsupervised loss. Both of them are normalized by the corresponding numbers of training samples as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 345, + 683, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 683, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 345, + 683, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s} = \\frac {1}{N _ {l}} \\sum_ {i = 1} ^ {N _ {l}} \\left(\\mathcal {L} _ {s} ^ {\\mathrm {c l s}} \\left(X _ {i}\\right) + \\mathcal {L} _ {s} ^ {\\mathrm {r e g}} \\left(X _ {i}\\right)\\right), \\tag {2}", + "image_path": "8a29a3a5a71968a57600e6b295ad00564f2584e98007f8d46f0129eb496d3d74.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10162" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 86, + 81, + 288, + 114 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 81, + 288, + 114 + ], + "spans": [ + { + "bbox": [ + 86, + 81, + 288, + 114 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {u} = \\frac {1}{N _ {u}} \\sum_ {i = 1} ^ {N _ {u}} \\left(\\mathcal {L} _ {u} ^ {\\mathrm {c l s}} \\left(U _ {i}\\right) + \\mathcal {L} _ {u} ^ {\\mathrm {r e g}} \\left(U _ {i}\\right)\\right), \\tag {3}", + "image_path": "992e376d2f44ef601cb14f55351b212eb6e63c3ebc469f085eabb38360f3df9a.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "spans": [ + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{\\mathrm{cls}}" + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "text", + "content": " is a classification loss, " + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^{\\mathrm{reg}}" + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "text", + "content": " is a regression loss, and " + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 47, + 119, + 288, + 155 + ], + "type": "text", + "content": " denote the number of training samples for labeled and unlabeled videos, respectively." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 156, + 288, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 288, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 288, + 262 + ], + "type": "text", + "content": "We claim that the major obstacle that hinders self-training performance lies in label noise, which leads to two issues: location biases and category errors. In this paper, we propose a Noisy Pseudo-Label Learning framework (NPL) to alleviate the negative effects caused by location biases and category errors for SS-TAL. The pipeline of our method is illustrated in Figure 2. It includes three novel components: Noisy Label Ranking, Noisy Label Filtering, and Noisy Label Learning, described in the following sections." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 270, + 168, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 168, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 168, + 283 + ], + "type": "text", + "content": "3.2. Noisy Label Ranking" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 289, + 287, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 287, + 336 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 287, + 336 + ], + "type": "text", + "content": "In SS-TAL, the quality of pseudo labels can be measured from two perspectives, i.e., semantic confidence and boundary reliability. It is desirable to have high-quality pseudo labels for semi-supervised learning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 336, + 288, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 288, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 288, + 443 + ], + "type": "text", + "content": "The majority of TAL frameworks [20, 53, 52, 36] rely on the foreground score of an anchor or a proposal to measure its quality. However, the foreground score only reflects semantic confidence and cannot account for boundary reliability. From Figure 3 (a), we can observe that foreground scores may not strongly correlate with the localization quality (i.e., IoU w.r.t. ground truth). Thus, it is necessary to measure the quality of pseudo labels from both aspects of action classification and boundary localization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": "For labeled videos, anchors or proposals corresponding to the same action instance are supervised by the same ground truth during training. Thus, they are gradually regressed to the similar temporal boundary locations. This motivates us to use the consistency of the boundary predictions to measure their location reliability. Specifically, taking our anchor-free framework as an example, we can obtain dense predictions of action instances before the post-processing phase. Given a prediction " + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "inline_equation", + "content": "p_j = (\\hat{t}_{s,j}, \\hat{t}_{e,j}, c_j)" + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "inline_equation", + "content": "\\hat{t}_{s,j}" + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "inline_equation", + "content": "\\hat{t}_{e,j}" + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": " are the predicted start and end boundaries of the " + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": "-th video snippet respectively and " + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "inline_equation", + "content": "c_j" + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": " is its foreground score, we can obtain a set of predictions " + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "inline_equation", + "content": "\\{p_n\\}_{n=1}^{N_a}" + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": " from its " + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "inline_equation", + "content": "N_a" + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": " adjacent snippets. Then, we formulate the boundary ambiguity of " + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "inline_equation", + "content": "p_j" + }, + { + "bbox": [ + 46, + 444, + 288, + 601 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 133, + 610, + 207, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 610, + 207, + 623 + ], + "spans": [ + { + "bbox": [ + 133, + 610, + 207, + 623 + ], + "type": "interline_equation", + "content": "\\bar {\\sigma} _ {j} = \\hat {\\sigma} _ {s, j} + \\hat {\\sigma} _ {e, j},", + "image_path": "82061e85ec30c5a9d2e47af32482688a67be4ff9ba05d861086db12e195ba833.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 127, + 624, + 288, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 624, + 288, + 648 + ], + "spans": [ + { + "bbox": [ + 127, + 624, + 288, + 648 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {s, j} = \\frac {\\sigma_ {s , j}}{d (p _ {j})}, \\tag {4}", + "image_path": "88e0b67d932bb5be9158b3db7b5db3d5de6b37fc55132460b1e5abda7b151811.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 127, + 650, + 189, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 650, + 189, + 673 + ], + "spans": [ + { + "bbox": [ + 127, + 650, + 189, + 673 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {e, j} = \\frac {\\sigma_ {e , j}}{d (p _ {j})},", + "image_path": "cfc347e08b02487e00e3fe635657256ad472ccbd37c896c90467f76a9dc4a6fe.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{s,j}" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{e,j}" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": " are the variances of the start and end boundaries of " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\{p_n\\}_{n = 1}^{N_a}" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_{s,j}" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_{e,j}" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": " are normalized by their duration " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "d(p_j)" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": ". A smaller boundary vari" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 74, + 425, + 167 + ], + "blocks": [ + { + "bbox": [ + 307, + 74, + 425, + 167 + ], + "lines": [ + { + "bbox": [ + 307, + 74, + 425, + 167 + ], + "spans": [ + { + "bbox": [ + 307, + 74, + 425, + 167 + ], + "type": "image", + "image_path": "7522465f91e375b8547b389e360714b0faaef39f9f45bb9a8c1a78367ec816d4.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 368, + 168, + 380, + 177 + ], + "lines": [ + { + "bbox": [ + 368, + 168, + 380, + 177 + ], + "spans": [ + { + "bbox": [ + 368, + 168, + 380, + 177 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 425, + 75, + 545, + 168 + ], + "blocks": [ + { + "bbox": [ + 425, + 75, + 545, + 168 + ], + "lines": [ + { + "bbox": [ + 425, + 75, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 425, + 75, + 545, + 168 + ], + "type": "image", + "image_path": "ed119a7fc26802ee0327b2821b440629fe797274eed6dd2dfd73ce57fcabda63.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 488, + 169, + 500, + 178 + ], + "lines": [ + { + "bbox": [ + 488, + 169, + 500, + 178 + ], + "spans": [ + { + "bbox": [ + 488, + 169, + 500, + 178 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 182, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 258 + ], + "type": "text", + "content": "Figure 3. Each star represents a prediction result (i.e., a pseudo label) on " + }, + { + "bbox": [ + 304, + 182, + 547, + 258 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 182, + 547, + 258 + ], + "type": "text", + "content": " unlabeled videos based on the model trained with " + }, + { + "bbox": [ + 304, + 182, + 547, + 258 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 182, + 547, + 258 + ], + "type": "text", + "content": " labeled videos on THUMOS14. (a) depicts the correlation between the foreground score and the IoU with ground truth. (b) depicts the correlation between the boundary variance and the IoU with ground truth. It can be observed that the boundary variance highly correlates with the localization quality." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "type": "text", + "content": "ance " + }, + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "type": "inline_equation", + "content": "\\bar{\\sigma}_j" + }, + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "type": "text", + "content": " indicates lower boundary ambiguity of the prediction " + }, + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "type": "inline_equation", + "content": "p_j" + }, + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "type": "text", + "content": ", thus leading to higher localization reliability. In Figure 3 (b), we experimentally illustrate the correlation between the boundary variance and IoU w.r.t ground truth. We can observe that boundary variances could better measure the localization quality of pseudo labels than the classification scores. Particularly, this motivates us to define the confidence score of " + }, + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "type": "inline_equation", + "content": "p_j" + }, + { + "bbox": [ + 304, + 277, + 547, + 374 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 405, + 382, + 545, + 406 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 382, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 405, + 382, + 545, + 406 + ], + "type": "interline_equation", + "content": "s _ {j} = \\frac {c _ {j}}{\\bar {\\sigma} _ {j}}. \\tag {5}", + "image_path": "ce4a5a388eea7d1f9bb38b24a79eab40a689309ee1a131a79f6721af976b17c8.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 413, + 547, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 547, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 547, + 496 + ], + "type": "text", + "content": "Eq. (5) provides a comprehensive metric to measure the quality of pseudo labels by their semantic confidence (foreground score " + }, + { + "bbox": [ + 304, + 413, + 547, + 496 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 413, + 547, + 496 + ], + "type": "text", + "content": ") and boundary ambiguity (boundary variance " + }, + { + "bbox": [ + 304, + 413, + 547, + 496 + ], + "type": "inline_equation", + "content": "\\bar{\\sigma}" + }, + { + "bbox": [ + 304, + 413, + 547, + 496 + ], + "type": "text", + "content": "). As a result, our Noisy Label Ranking could improve the quality of pseudo labels only from intrinsic video snippets without requiring additional learnable networks or hyperparameters." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 503, + 429, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 429, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 429, + 517 + ], + "type": "text", + "content": "3.3. Noisy Label Filtering" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 522, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 547, + 664 + ], + "type": "text", + "content": "Training on a few labeled videos inevitably produces noisy pseudo labels with category errors on unlabeled videos. As a result, the frequencies of some action categories in the selected pseudo labels will be much larger or smaller than their natural frequencies in the videos, regardless of whether pseudo labels are sampled based on a confidence threshold or the number of samples. We call this phenomenon the class-imbalance problem of pseudo labels in SS-TAL, illustrated in Figure 4. For example, the frequency of \"Golf Swing\" in pseudo labels is much higher than that in ground truth labels, while the frequency of \"Throw Discus\" is much lower in the pseudo labels." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "Under this class-imbalance problem, overwhelming pseudo labels with category errors will dominate the model learning and further aggravate the semantic uncertainty of actions of category errors, resulting in limited gains." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10163" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 273, + 232 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 273, + 232 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 273, + 232 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 273, + 232 + ], + "type": "image", + "image_path": "435e98c65b58e57a78c7aea01d3577a620c66b8100197909f0c6e09fc01b2c10.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 288, + 312 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 312 + ], + "type": "text", + "content": "Figure 4. Illustration of the class-imbalance problem of pseudo labels obtained on " + }, + { + "bbox": [ + 46, + 235, + 288, + 312 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 46, + 235, + 288, + 312 + ], + "type": "text", + "content": " unlabeled THUMOS14. The horizontal axis of the histogram represents the class name, and the vertical axis represents the ratio between the number of pseudo labels and the number of ground truth labels. It can be observed that our Noisy Label Filtering could alleviate the class-imbalance problem of pseudo labels." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 392 + ], + "type": "text", + "content": "To address this class-imbalance problem, we introduce an adaptive filtering strategy to regularize the distribution of pseudo labels for each category. Concretely, we arrange dense labels according to the category of actions and the number of pseudo labels in an unlabeled video, as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 109, + 399, + 287, + 429 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 399, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 109, + 399, + 287, + 429 + ], + "type": "interline_equation", + "content": "K _ {a d p} = \\frac {\\left| \\left\\{p _ {n} ^ {c} \\right\\} _ {n = 1} ^ {N _ {v}} \\right|}{N _ {v}} \\cdot N _ {p o s}, \\tag {6}", + "image_path": "1fa9ce444c6fc8874660f52b12ba14a8b8170a466f18f67baa68b94acde82ec0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "inline_equation", + "content": "N_{v}" + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "text", + "content": " is the total number of pseudo labels within a video, and " + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "inline_equation", + "content": "N_{pos}" + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "text", + "content": " is a hyper-parameter to control the number of positive predictions. Eq. (6) is used to adaptively select the number " + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "inline_equation", + "content": "K_{adp}" + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "text", + "content": " of class-specific pseudo labels for the category " + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 436, + 289, + 579 + ], + "type": "text", + "content": " in each unlabeled video. From Figure 4, we experimentally demonstrate that our adaptive filtering strategy could address the class-imbalance distribution of pseudo labels. As a result, our Noisy Label Filtering could not only assign accurate pseudo labels to improve the model learning but also prevent the pseudo labels from being dominated by overwhelming pseudo labels with category errors, while it also avoids tediously adjusting heuristic thresholds." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 587, + 172, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 172, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 172, + 601 + ], + "type": "text", + "content": "3.4. Noisy Label Learning" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 664 + ], + "type": "text", + "content": "The boundary ambiguity of labeled actions gives rise to noisy pseudo labels with location biases. Subsequently, training on the biased boundaries results in the boundary ambiguity of unlabeled actions and impedes accurate action localization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "content": "To remedy it, we propose a noise-tolerant training algorithm for unlabeled videos with heavy location biases. It aims to penalize inconsistency boundary predictions from adjacent feature locations within a video feature sequence." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "Our unsupervised temporal consistency loss is defined as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 335, + 102, + 547, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 102, + 547, + 137 + ], + "spans": [ + { + "bbox": [ + 335, + 102, + 547, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {u} ^ {\\text {c o n s}} = \\frac {1}{M _ {u} \\left(M _ {p} - 1\\right)} \\sum_ {j = 1} ^ {M _ {u}} \\sum_ {i = 1} ^ {M _ {p} - 1} \\left| b _ {i + 1} ^ {j} - b _ {i} ^ {j} \\right|, \\tag {7}", + "image_path": "64b0a627bff6a1c892b2bcb273ee4dacdf8f8735a43d274d1884be7e935fad37.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "spans": [ + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "inline_equation", + "content": "M_{u}" + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "text", + "content": " denotes the number of pseudo labels within an unlabeled video. " + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "inline_equation", + "content": "M_{p}" + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "text", + "content": " represents the number of the training snippets within an action. " + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "text", + "content": " represents the predicted start/end boundary locations from the " + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 147, + 547, + 229 + ], + "type": "text", + "content": "-th snippet. In this way, the model could learn to produce more reliable predictions. Consequently, our complete unsupervised loss is denoted below:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 344, + 237, + 545, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 237, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 344, + 237, + 545, + 270 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {u} = \\frac {1}{N _ {u}} \\sum_ {i = 1} ^ {N _ {u}} \\left(\\mathcal {L} _ {u} ^ {\\mathrm {c l s}} \\left(U _ {i}\\right) + \\mathcal {L} _ {u} ^ {\\mathrm {c o n s}} \\left(U _ {i}\\right)\\right). \\tag {8}", + "image_path": "06bbd19a34966c1eba4974940a8fcb3beaa0b1004639206bcfb015d87b0ddf02.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "spans": [ + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": "The Noisy Label Learning makes the training robust to location biases in the pseudo labels. Finally, the model can be optimized by the sum of " + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_u" + }, + { + "bbox": [ + 305, + 279, + 545, + 315 + ], + "type": "text", + "content": " on all videos." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 326, + 387, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 326, + 387, + 339 + ], + "spans": [ + { + "bbox": [ + 306, + 326, + 387, + 339 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 346, + 427, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 427, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 427, + 357 + ], + "type": "text", + "content": "4.1. Datasets and Metrics" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 364, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 364, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 364, + 545, + 460 + ], + "type": "text", + "content": "Evaluation Datasets. We evaluate our proposed method on two benchmark TAL datasets, i.e., THUMOS14 [13] and ActivityNet v1.3 [2]. THUMOS14 [13] is a standard benchmark for TAL. It contains 200 validation videos and 213 testing videos, including 20 action categories. It is very challenging since each video has more than 15 action instances. Following the common setting [48], we use the validation set for training and evaluate on the testing set." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 460, + 547, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 547, + 519 + ], + "type": "text", + "content": "ActivityNet v1.3 [2] is a large-scale benchmark for video-based action localization. It contains 10k training videos and 5k validation videos corresponding to 200 different actions. Following the standard practice [22], we train our method on the training set and test it on the validation set." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 520, + 547, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 520, + 547, + 602 + ], + "spans": [ + { + "bbox": [ + 305, + 520, + 547, + 602 + ], + "type": "text", + "content": "Evaluation Metrics. We use the mean Average Precision (mAP) as the evaluation metric. The tIoU thresholds are " + }, + { + "bbox": [ + 305, + 520, + 547, + 602 + ], + "type": "inline_equation", + "content": "[0.3:0.1:0.7]" + }, + { + "bbox": [ + 305, + 520, + 547, + 602 + ], + "type": "text", + "content": " for THUMOS14 and " + }, + { + "bbox": [ + 305, + 520, + 547, + 602 + ], + "type": "inline_equation", + "content": "[0.5:0.05:0.95]" + }, + { + "bbox": [ + 305, + 520, + 547, + 602 + ], + "type": "text", + "content": " for ActivityNet v1.3. We report the average mAP of the IoU thresholds between 0.5 and 0.95 with the step of 0.05 on ActivityNet v1.3. Also, we present the average mAP of the tIoU thresholds from 0.3 to 0.7 on THUMOS14." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "text", + "content": "The goal of SS-TAL is to use a large amount of unlabeled data to improve a well-trained detector on a small amount of labeled data. We randomly sample " + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 305, + 603, + 545, + 662 + ], + "type": "text", + "content": " of the training data as labeled data and treat the remainder as unlabeled data." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 671, + 438, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 438, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 438, + 684 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "We implement our semi-supervised action localization framework based on the recent prevalent anchor-free detector" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10164" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 70, + 519, + 392 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 519, + 392 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 519, + 392 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 519, + 392 + ], + "type": "table", + "html": "
LabelMethodBackboneTHUMOS14 (%)ActivityNet v1.3 (%)
0.30.40.50.60.7Avg.0.50.750.95Avg.
10%ActF* [49]I3D28.522.914.18.24.115.647.824.21.725.6
ActF [49] + MixUp [51]I3D29.724.214.59.65.416.749.427.93.128.8
NPL (ActF)I3D32.829.620.111.77.220.351.933.43.632.5
SSP [12]TSN44.234.124.616.99.325.838.928.78.427.6
SSTAP [37]TSN45.635.226.317.510.727.040.729.69.028.2
SPOT [28]TSN49.440.431.522.912.431.349.931.18.332.1
NPL (BMN)TSN50.041.733.523.613.432.450.932.07.932.6
20%ActF* [49]I3D49.141.632.621.512.131.451.234.33.832.9
ActF [49] + MixUp [51]I3D51.243.234.023.914.133.352.934.73.933.3
NPL (ActF)I3D54.547.139.329.718.537.853.135.83.933.8
SPOT [28]TSN52.643.934.125.216.234.451.732.06.932.3
NPL (BMN)TSN53.945.636.226.916.535.852.132.97.932.9
40%ActF* [49]I3D69.060.449.331.519.345.953.235.73.834.2
ActF [49] + MixUp [51]I3D69.761.952.434.420.147.753.136.04.334.5
NPL (ActF)I3D71.965.455.740.923.451.553.636.54.635.3
SPOT [28]TSN54.445.837.229.719.437.353.333.06.633.2
NPL (BMN)TSN56.246.738.830.319.538.353.433.98.133.8
60%ActF* [49]I3D71.565.659.947.332.755.453.936.15.735.0
ActF [49] + MixUp [51]I3D72.267.561.248.734.056.754.136.45.735.2
NPL (ActF)I3D74.569.962.851.136.659.054.336.76.535.8
SSP [12]TSN53.246.839.329.719.837.849.834.57.033.5
SSTAP [37]TSN56.449.541.030.921.639.950.134.97.434.0
SPOT [28]TSN58.950.142.333.522.941.552.835.08.135.2
NPL (BMN)TSN59.051.442.934.323.342.253.935.88.535.7
", + "image_path": "0927ee05a046cf22c79576b85ec9e1fdb0e790a9534944fd9234f3dd69e797ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 392, + 547, + 426 + ], + "lines": [ + { + "bbox": [ + 46, + 392, + 547, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 547, + 426 + ], + "type": "text", + "content": "Table 1. Performance comparison with state-of-the-art SS-TAL methods on THUMOS14 testing set and ActivityNet v1.3 validation set. Notably, SSP and SSTAP employ UntrimmedNet [34] trained with " + }, + { + "bbox": [ + 46, + 392, + 547, + 426 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 392, + 547, + 426 + ], + "type": "text", + "content": " class labels for proposal classification. ActF refers to ActionFormer [49]. \\* means using only labeled training videos." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "text", + "content": "ActionFormer [49], which is composed of a self-attention backbone [33], an FPN [21] neck and two parallel heads. Also, we combine the proposed semi-supervised method with BMN [19], which is a two-stage proposal-based detector. For video feature encoding, we used two popular backbones, i.e., two-stream network [35] and I3D [4] pretrained on Kinetics [14] to extract the video features, following [18, 49]. For THUMOS14, the initial learning rate is " + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "text", + "content": ", and a cosine learning rate decay is used. The minibatch size is 2, and a weight decay of " + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "text", + "content": " is used. For ActivityNet v1.3, the learning rate is " + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "inline_equation", + "content": "1e - 3" + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "text", + "content": ", the mini-batch size is 32, and the weight decay is " + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 46, + 444, + 290, + 589 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "For semi-supervised configurations, an initial model is trained on available labeled videos, where labeling ratios are set to " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ". Further using this well-trained model generates pseudo labels. For the re-training phase, we pre-train the model on the labeled data and then compute the supervised loss and unsupervised loss for 40 epochs (THUMOS14) and 15 epochs (ActivityNet v1.3). We set " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "N_{pos} = 15" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ". We apply background data augmentation to " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " of unlabeled videos for performance improvements. Additional implementation details and more" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 444, + 537, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 537, + 457 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 537, + 457 + ], + "type": "text", + "content": "attempts for SS-TAL refer to the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 466, + 529, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 529, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 529, + 479 + ], + "type": "text", + "content": "4.3. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": "THUMOS14. We compare the proposed method NPL with existing SS-TAL methods in Table 1, where we combine two different frameworks, ActionFormer [49] and BMN [19] with our NPL. We report mAP at different tIoU thresholds as well as average mAP between 0.3 and 0.7 with the step of 0.1. Also, we reproduce the SPOT [28] results of " + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": " labeling ratios from the source code for comparison. When labeled data is scarce (i.e., " + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": " labeling ratios), our method achieves the competitive performance compared to existing methods. Especially, our method outperforms the baseline, semi-supervised ActF [49], by a large margin with " + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": " labeled THUMOS14. When more labeled data is accessible (i.e., " + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": " labeling ratios), our method outperforms all the competing methods, demonstrating the effectiveness and superiority of our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "ActivityNet v1.3. We also conduct experiments on the more challenging benchmark ActivityNet v1.3. As depicted in Table 1, the proposed method also achieves significant performance gains over all the compared methods. When" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10165" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 80, + 70, + 255, + 198 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 255, + 198 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 255, + 198 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 255, + 198 + ], + "type": "table", + "html": "
LabelMethodmAP (%)
0.30.50.7Avg.
10%baseline29.515.85.016.8
+NR30.716.96.318.0
+NF32.018.56.919.1
+NL32.820.17.220.3
40%baseline70.149.520.247.1
+NR70.752.120.748.5
+NF71.654.421.350.3
+NL71.955.723.451.5
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LabelMethodClass (%)Avg. tIoU (%)
10%baseline21.027.4
NPL25.936.2
40%baseline73.054.2
NPL74.459.0
", + "image_path": "097043c8320d48ac3f0948e60b0294f040ae6542f0b742cfc46d88499fa8e24d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 401 + ], + "type": "text", + "content": "there are more unlabeled data introduced, our method also can improve the average mAP, which mainly comes from the high-quality pseudo labels for effective training." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 407, + 141, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 141, + 420 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 141, + 420 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 426, + 288, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 463 + ], + "type": "text", + "content": "To better understand how the proposed method works, we conduct a series of ablation studies, where we use ActionFormer [49] as the localization framework with I3D [4]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "type": "text", + "content": "Effectiveness of individual component. To validate our key designs, we ablate the effects of the proposed Noisy Label Ranking (NR), Noisy Label Filtering (NF), and Noisy Label Learning (NL). The results are shown in Table 2. Under the " + }, + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "type": "text", + "content": " labeling ratio, one can see that our model equipped with NR improves performance by " + }, + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "type": "text", + "content": ". Further applying our adaptive filtering strategy and the temporal consistency learning, the performance reaches an average mAP of " + }, + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "type": "inline_equation", + "content": "51.5\\%" + }, + { + "bbox": [ + 46, + 474, + 287, + 594 + ], + "type": "text", + "content": ". In summary, our designs significantly improve the utilization of unlabeled data for effectively semi-supervised learning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Quality improvements of pseudo labels. The quality of pseudo labels is the important indicator for the SS-TAL performance improvement. We further study the quality of pseudo labels from their average temporal IoU (tIoU) w.r.t ground truth and classification accuracy (Acc.). We report the comparison results in Table 3. It can be observed that the significant improvements attribute to our Noisy Label Ranking to rank and select high-quality pseudo labels based on the comprehensive metric, i.e., semantic confidence and localization reliability, as well as our Noisy Label Filtering to" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 424, + 156 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 424, + 156 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 424, + 156 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 424, + 156 + ], + "type": "image", + "image_path": "3c69396b2137a2a3549217a76e661c8ae9357d844df92a737b7337880d6dfffc.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 159, + 545, + 192 + ], + "lines": [ + { + "bbox": [ + 305, + 159, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 159, + 545, + 192 + ], + "type": "text", + "content": "Figure 5. Curves of averaged IoU vs. foreground score or boundary variance, where each averaged IoU is calculated by the foreground scores or boundary variances of the samples in different intervals." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 543, + 157 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 543, + 157 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 543, + 157 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 543, + 157 + ], + "type": "image", + "image_path": "b5aaad6a9f933727e8715d3e0600a244bcf46b02257794c41640934f03d1934d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 332, + 202, + 520, + 276 + ], + "blocks": [ + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "text", + "content": "Table 3. Ablation study on the quality of pseudo labels in terms of action classification accuracy (Class) and average tIoU (Avg. tIoU), using " + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 312, + 288, + 346 + ], + "type": "text", + "content": " labeled videos." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 332, + 202, + 520, + 276 + ], + "lines": [ + { + "bbox": [ + 332, + 202, + 520, + 276 + ], + "spans": [ + { + "bbox": [ + 332, + 202, + 520, + 276 + ], + "type": "table", + "html": "
MethodmAP (%)
0.30.40.50.60.7Avg.
\\( \\theta_s = 0.3 \\)70.163.552.937.422.249.2
top-1071.063.353.438.122.849.7
NF71.965.455.740.923.451.5
", + "image_path": "d258888c711ce0cccfbfa95682e0f1e631c458ee8f8d4eca41291e20866fe6b7.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 277, + 547, + 298 + ], + "lines": [ + { + "bbox": [ + 306, + 277, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 306, + 277, + 547, + 298 + ], + "type": "text", + "content": "Table 4. Comparison of pseudo-label filtering strategies on THUMOS14 with " + }, + { + "bbox": [ + 306, + 277, + 547, + 298 + ], + "type": "inline_equation", + "content": "{40}\\%" + }, + { + "bbox": [ + 306, + 277, + 547, + 298 + ], + "type": "text", + "content": " labeled videos and " + }, + { + "bbox": [ + 306, + 277, + 547, + 298 + ], + "type": "inline_equation", + "content": "{60}\\%" + }, + { + "bbox": [ + 306, + 277, + 547, + 298 + ], + "type": "text", + "content": " unlabeled videos." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 318, + 544, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 318, + 544, + 329 + ], + "spans": [ + { + "bbox": [ + 306, + 318, + 544, + 329 + ], + "type": "text", + "content": "adaptively assign class-balanced pseudo labels for training." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 330, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 547, + 437 + ], + "type": "text", + "content": "Visualization of noisy label ranking. To further support our motivation of the noisy label ranking, we add a curve of averaged IoU (between pseudo labels and ground truth) versus foreground score or boundary variance, where each averaged IoU corresponds to the foreground scores or boundary variances of the samples in different intervals, as shown in Figure 5. Particularly, the Pearson correlation coefficient between IoU and boundary variance is 0.496, while that between IoU and foreground score is 0.449." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "type": "text", + "content": "Superiority of adaptive filtering strategy. Our Noisy Label Filtering (NF) could alleviate the class-imbalance problem of pseudo labels caused by the category error. In addition, it also could avoid tediously adjusting hard-crafted thresholds or numbers for pseudo-label filtering. To demonstrate this superiority, we experiment with two common approaches as a reference, i.e., single thresholding and fixed number strategies. More specifically, we empirically set the foreground score threshold " + }, + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\theta_{s}" + }, + { + "bbox": [ + 304, + 437, + 547, + 628 + ], + "type": "text", + "content": " to 0.3, where instances are regarded as foreground if their scores are above the threshold and background otherwise. Besides, we also empirically select top-10 confidence predictions for each unlabeled video. As shown in Table 4, these approaches cannot achieve satisfactory performance. In contrast, our adaptive filtering strategy could adaptively sample class-specific pseudo labels, showing its effectiveness and importance." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Analysis of temporal consistency. Our Noisy Label Learning introduces a temporal consistency loss to tackle the location bias problem by penalizing inconsistent boundary predictions from each intrinsic video snippet. We conduct an ablation study on this key design, where we train the pre-trained model with and without the temporal consistency only on " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " unlabeled videos, as shown in Figure 6. Based" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10166" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 71, + 258, + 205 + ], + "blocks": [ + { + "bbox": [ + 80, + 71, + 258, + 205 + ], + "lines": [ + { + "bbox": [ + 80, + 71, + 258, + 205 + ], + "spans": [ + { + "bbox": [ + 80, + 71, + 258, + 205 + ], + "type": "image", + "image_path": "3b5c425a40e81c755ce3abf15b041b5386bd0a40b85d15f61e3d7cb9f6ba58af.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 289, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 289, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 289, + 242 + ], + "type": "text", + "content": "Figure 6. Comparison of model performance and convergence speed with and without the temporal consistency loss on THU-MOS14." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 109, + 251, + 227, + 321 + ], + "blocks": [ + { + "bbox": [ + 109, + 251, + 227, + 321 + ], + "lines": [ + { + "bbox": [ + 109, + 251, + 227, + 321 + ], + "spans": [ + { + "bbox": [ + 109, + 251, + 227, + 321 + ], + "type": "table", + "html": "
NposmAP (%)
0.30.50.7Avg.
571.555.222.851.0
1571.955.723.451.5
3071.055.322.550.7
", + "image_path": "2d8f4b2ad0df5ca3dd5f8ff7ea0269f323df84b28ea5a5c43d3888e4c3c1ed45.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 67, + 351, + 268, + 395 + ], + "blocks": [ + { + "bbox": [ + 46, + 321, + 287, + 342 + ], + "lines": [ + { + "bbox": [ + 46, + 321, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 287, + 342 + ], + "type": "text", + "content": "Table 5. Comparison of mAP with various values of " + }, + { + "bbox": [ + 46, + 321, + 287, + 342 + ], + "type": "inline_equation", + "content": "N_{pos}" + }, + { + "bbox": [ + 46, + 321, + 287, + 342 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 46, + 321, + 287, + 342 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 321, + 287, + 342 + ], + "type": "text", + "content": " labeled THUMOS14." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 351, + 268, + 395 + ], + "lines": [ + { + "bbox": [ + 67, + 351, + 268, + 395 + ], + "spans": [ + { + "bbox": [ + 67, + 351, + 268, + 395 + ], + "type": "table", + "html": "
Label100%60%40%20%10%
mAP@0.5 (%)71.062.855.739.320.1
mAP@Avg (%)66.859.051.537.820.3
", + "image_path": "f01bbc4590ba98ddd78a6ca9b90351e1878b4033a292ad3ebd2fd7ece2d37158.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 396, + 288, + 417 + ], + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 417 + ], + "type": "text", + "content": "Table 6. Comparison of mAP with various labeling ratios on THU-MOS14, where the remainder is treated as unlabeled data." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 437, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 498 + ], + "type": "text", + "content": "on the temporal consistency, it obtains a " + }, + { + "bbox": [ + 46, + 437, + 287, + 498 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 498 + ], + "type": "text", + "content": " improvement on the average mAP. Apart from the performance gain, our contribution can also significantly boost the convergence speed. Both of these advances validate the effectiveness of the proposed Noisy Label Learning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "text", + "content": "Choice of hyper-parameters. " + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "inline_equation", + "content": "N_{pos}" + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "text", + "content": " is a pre-defined value to handle the number of positive samples for unlabeled videos. We conduct an ablation study on the hyper-parameter " + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "inline_equation", + "content": "N_{pos}" + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "text", + "content": " under " + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "text", + "content": " labeling ratio. From Table 5, it can be observed that the performance peaks around " + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "inline_equation", + "content": "N_{pos} = 15" + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "text", + "content": ". A large value such as " + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "inline_equation", + "content": "N_{pos} = 30" + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "text", + "content": " will introduce more low-quality pseudo labels and confuse the model in training, while a small value such as " + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "inline_equation", + "content": "N_{pos} = 5" + }, + { + "bbox": [ + 46, + 498, + 288, + 606 + ], + "type": "text", + "content": " only provides a small number of samples for training so as to obtain limited gains." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "Bottleneck of our NPL. The performance limitation of SS-TAL following self-training lies in the noise level of pseudo labels. To explore the performance bottleneck, we train a fully-supervised model with " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " labeled videos on THUMOS14. The experimental results in Table 6 show that our method still has great room for improvement. Also, it demonstrates that the negative impacts of the label noise problem cannot be ignored in semi-supervised learning." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 545, + 239 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 545, + 239 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 239 + ], + "type": "image", + "image_path": "63f654c453e52d6017d722912392e1215238aa71424ab5f7ea30ca714398cddf.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 240, + 547, + 275 + ], + "lines": [ + { + "bbox": [ + 305, + 240, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 547, + 275 + ], + "type": "text", + "content": "Figure 7. Qualitative SS-TAL result comparison of our proposed method with SPOT [28] on two untrimmed videos from (a) ActivityNet v1.3 and (b) THUMOS14, respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 293, + 432, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 432, + 306 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 432, + 306 + ], + "type": "text", + "content": "4.5. Visualization Analysis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 312, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 547, + 397 + ], + "type": "text", + "content": "To further validate the effectiveness of the proposed method, we provide some qualitative results by prior art SPOT [28] and our model with " + }, + { + "bbox": [ + 304, + 312, + 547, + 397 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 312, + 547, + 397 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 312, + 547, + 397 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 312, + 547, + 397 + ], + "type": "text", + "content": " labeled data on both ActivityNet v1.3 and THUMOS14. From the illustration in Figure 7, we can observe that our method can localize the target actions more accurately, demonstrating the effectiveness and superiority of our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 408, + 379, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 408, + 379, + 421 + ], + "spans": [ + { + "bbox": [ + 305, + 408, + 379, + 421 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 429, + 547, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 547, + 560 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 547, + 560 + ], + "type": "text", + "content": "In this paper, we propose a novel Noisy Pseudo-Label Learning framework tailored for SS-TAL to tackle the label noise problem. Specifically, we first present a new integrated metric of semantic confidence and boundary reliability for ranking high-quality pseudo labels. Then, an adaptive filtering strategy alleviates the class-imbalance distribution of pseudo labels caused by the category error. Finally, we introduce an unsupervised temporal consistency loss to tackle biased boundary labels for noise-tolerant learning. Experiments show that the effectiveness of our method on both THUMOS14 and ActivityNet v1.3." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 561, + 547, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 561, + 547, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 561, + 547, + 609 + ], + "type": "text", + "content": "Limitation. The number of positive snippets inside an action instance affects our method for quality ranking and noisetolerant training, which indicates that tackling short action instances remains a challenging problem." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 621, + 404, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 404, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 404, + 635 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 641, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 712 + ], + "type": "text", + "content": "This work was supported partly by National Key R&D Program of China under Grant 2021YFB1714700, NSFC under Grants 62088102 and 62106192, Natural Science Foundation of Shaanxi Province under Grant 2022JC-41, and Fundamental Research Funds for the Central Universities under Grant XTR042021005." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10167" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "type": "text", + "content": "[1] Abulikemu AbuDuweili, Xingjian Li, Humphrey Shi, ChengZhong Xu, and Dejing Dou. 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In this case, the model aims to learn comprehensive multiview representations while the cross-view semantic information exhibits variations. We propose Semantics-based Unpaired Multiview Learning (SUM-L) to tackle this unpaired multiview learning problem. The key idea is to build cross-view pseudopairs and do view-invariant alignment by leveraging the semantic information of videos. To facilitate the data efficiency of multiview learning, we further perform video-text alignment for first-person and third-person videos, to fully leverage the semantic knowledge to improve video representations. Extensive experiments on multiple benchmark datasets verify the effectiveness of our framework. Our method also outperforms multiple existing view-alignment methods, under the more challenging scenario than typical paired or unpaired multimodal or multiview learning. Our code is available at https://github.com/wqtwjt1996/SUM-I.", + "bbox": [ + 75, + 324, + 473, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 645, + 209, + 660 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have witnessed a tremendous increase in the research regarding egocentric video understanding and learning [22, 26, 20, 41, 29, 30, 14, 42, 7, 31, 46, 9]. In parallel, a recent study [22] verifies that the activity of third-person videos in fact positively inform first-person video learning. Early works [39, 51] of egocentric video learning and understanding pay a lot of attention to paired multiview data representation learning. However, synchronized first-person and third-person video pairs are difficult to collect. This severely limits the data scale and scope of multiview learning for egocentric data.", + "bbox": [ + 75, + 672, + 468, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, egocentric video datasets [4, 5, 10] with larger scale have become available. However, since head-mounted cameras were not available until recent years, very few first-person videos have paired third-person videos [15].", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/11a6d8139ef43551d88f6400794318ec6f6ded9d1228e8e3930b331978303bf6.jpg", + "image_caption": [ + "Figure 1. (a) The typical multiview video learning method learns view-invariant representations from paired first-person and third-person videos. (b) Recent multimodal study [19] is interested in the alignment between unpaired samples which share identical semantics. In this paper, we study a more challenging scenario than existing works: unpaired multiview samples alignment with partially similar semantics, such as videos with (c) the same verb only, or (d) the same object only. The verb-object phrases above the video clips denote the semantic information of videos." + ], + "image_footnote": [], + "bbox": [ + 506, + 290, + 885, + 465 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fortunately, there exist third-person videos from different datasets [12, 16]. It is worth noting that unpaired third-person videos are relatively easier to capture and obtain compared with paired ones. Therefore, in this paper, we study an interesting yet seldom investigated problem: how to leverage unpaired third-person videos to help egocentric video learning?", + "bbox": [ + 496, + 626, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unpaired multiview learning is rarely studied. While recent works [28, 27, 38, 53] study the scenario where paired modalities are missing. But they do not leverage the potential of unpaired data from diverse datasets. Moreover, to align the unpaired multimodal samples, Kundu et al. [19] propose one relation distillation method to align the unpaired samples. They assume that unpaired data need to share identical semantic information. However, in the unpaired first-person and third-person video learning scenario, for the vast majority of egocentric videos, it is almost impossible to mine the third-person samples with identical", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3307", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cb778db156a5a2f6d004a5483ee0b2d46aa73fb607ca0235f5f3bef666eeb58a.jpg", + "image_caption": [ + "Semantic Similarity Statistics of Multiview Pseudo Pairs (%)", + "Figure 2. Statistics of semantic similarities between the first-person samples in [39, 4, 5] and the most similar single-agent third-person samples they can find from the LEMMA [15] dataset. The semantic similarity is the cosine distance between textual phrase vectors of videos encoded by a large language model [34]. Each bar in the figure represents the percentage of action classes that fall within one semantic similarity range (e.g., [0.8, 1.0]) in an egocentric dataset compared to all action classes in this dataset. In all of the three popular egocentric datasets, very few first-person videos are able to find third-person videos with identical semantics. For reference, in the studies for paired multiview data [43, 39, 51, 54], all the semantic similarities of cross-view data pairs are (or very close to) “1.0”." + ], + "image_footnote": [], + "bbox": [ + 114, + 119, + 851, + 251 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "semantics. The only alternatives are partially semantics-similar unpaired third-person videos. For example, for one egocentric video clip with \"cut watermelon\" semantics, the most similar third-person video is those with \"cut lemon\" (same verb) or \"eat watermelon\" (same object) semantics. Examples and comparisons between our scenario and typical paired or unpaired multiview or multimodal learning are shown in Figure 1, and we display comprehensive semantics similarity statistics of multiview data studied in this paper (see Figure 2). Therefore, how to employ the unpaired and partially semantics-similar third-person views to help first-person view learning is an open problem. Intuitively, compared with previous research, our setting is more challenging since most of the first-person videos only share partially similar semantics with third-person views.", + "bbox": [ + 75, + 372, + 472, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we are interested in view-invariant alignment in the partially semantics-similar pseudo-pair setting. We propose Semantics-based Unpaired Multiview Learning (SUM-L), where multiview pseudo-pairs with high similarities are aligned in a semantics-aware manner. In our method, we also employ video-text alignment to permit all first-person videos to obtain knowledge from samples with different views or modalities. We highlight that our SUM-L employs the large language model [34] to help align cross-view and cross-modality data. This is different from [22], which proposes to distill beneficial knowledge from unpaired third-person videos [16], mostly with the help of the off-the-shelf image recognition model [6] and hand-object detector [37]. Moreover, our method is better than existing view-invariant alignment methods, such as typical contrastive learning [44, 43, 50, 54] and triplet loss based learning [35, 51] in the new setting, since they naively reduce multiview feature distance, which leads to learning suboptimal first-person representations.", + "bbox": [ + 75, + 613, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contribution is three-fold:", + "bbox": [ + 519, + 372, + 816, + 386 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We study a new problem: in the partially semantics-similar multiview setting, how to leverage unpaired third-person videos to help first-person video learning.", + "- We propose SUM-L for this new problem, which is more effective than existing view-alignment methods in our unpaired multiview learning scenario.", + "- Experiments in standard benchmark datasets including Charades-Ego [39], EPIC-Kitchens [4], and EPIC-Kitchens-100 [5] validate the competitive performance of our methods over existing view-alignment methods including typical contrastive learning and triplet loss based learning." + ], + "bbox": [ + 517, + 398, + 890, + 608 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 625, + 640, + 640 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Egocentric Video Learning", + "text_level": 1, + "bbox": [ + 500, + 648, + 743, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The study of egocentric video learning has attracted a large volume of attention in recent years. To verify the quality of model learning, there are multiple egocentric-related tasks, including action recognition [29, 42, 46], video summarization [26, 20], engagement detection [41], scene affordance [30], gaze prediction [14], video question answering [7], and activity anticipation [31, 9]. Nevertheless, aforementioned studies utilize knowledge from first-person videos only [26, 20, 41, 14, 42, 31, 9], or make use of extra supervision from off-the-shelf models [29, 30], or naively pretrain on large-scale datasets [7, 46]. More specifically, these methods do not consider tackling the domain mismatch between different multiview datasets or abstaining from extra supervision. Recently, Li et al. [22] try to discover latent signals in the third-person videos which", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3308", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "are predictive of key egocentric-specific properties. Similar to [29, 30], however, this method heavily relies on the knowledge of off-the-shelf image or video models.", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. First-person Video Representation Learning with Joint Third-person Videos", + "text_level": 1, + "bbox": [ + 76, + 143, + 468, + 175 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The paired first-person and third-person videos, as descriptions of the same actions from different perspectives, are potential to provide beneficial knowledge to each other, yielding more generalizable joint representations. Recent studies [39, 40] propose paired first-person and third-person datasets and learn joint representations of multiview videos. They show the potential of transferring knowledge from third-person videos to first-person videos. In order to extract more useful joint knowledge, Yu et al. [52] make use of the shared attention regions between different views with spatial constraints, in a self-supervised and simultaneous manner. However, nowadays very few first-person videos have paired third-person videos [15]. Moreover, we find that existing multiview methods [44, 43, 35, 51] learn suboptimal first-person representations from unpaired third-person videos, that are relatively easier to capture and obtain compared with paired data. Instead, our methodology can better distill unpaired third-person video knowledge to first-person videos, and it is more efficient and applicable than existing view-alignment methods [44, 43, 35, 51].", + "bbox": [ + 75, + 181, + 472, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Unpaired Multimodal Learning", + "text_level": 1, + "bbox": [ + 76, + 492, + 356, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the relatively difficult acquisition of paired multimodal samples and the limited number of them, unpaired multimodal learning recently has attracted the interest of some researchers. Kundu et al. [19] treat unpaired 3D pose learning as a self-supervised adaptation problem that aims to transfer the task knowledge from a labeled paired source domain to a completely unpaired target domain. Next, it proposes the relation distillation method to align the unpaired target videos and unpaired 3D pose sequences. However, this work makes the assumption that there exist semantically identical cross-modal data in the unpaired target domain, which is almost unavailable in unpaired first- and third-person video representation learning. Therefore, in this paper, we study a more challenging problem: how to make unpaired multiview alignment in an incompletely semantics-similar situation.", + "bbox": [ + 75, + 515, + 472, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 768, + 210, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following sections, we first describe our pseudopair construction method (Sec. 3.1). Then we introduce the traditional contrastive framework for paired multiview or multimodal data (Sec. 3.2). Next, we introduce our proposed cross-view and cross-modal methods (Sec. 3.3). Finally, we present our full training and evaluation pipeline in Sec. 3.4.", + "bbox": [ + 75, + 794, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Semantics-based Pseudo-pair Mining", + "text_level": 1, + "bbox": [ + 498, + 90, + 823, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from the previous joint multiview learning approaches [39, 40, 51], first-person and third-person videos are not automatically paired in the cross-dataset setting. Hence, before model training, it is essential to construct pseudo multiview pairs.", + "bbox": [ + 496, + 113, + 890, + 188 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Every first-person and third-person video has one unique textual narration, which describes the key semantic information of it. Therefore, we employ the large language model [34] to encode textual narrations of multiview videos to vectors. Then for each first-person video, we mine the third-person video with the highest textual semantic similarity from the third-person video pool to construct the pseudopair. We compute the cosine distance between cross-view video textual narrations as the criterion of semantic similarity between first-person and third-person video clips:", + "bbox": [ + 496, + 189, + 892, + 340 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {s i m} _ {\\left(\\mathbf {z} _ {\\mathrm {f}}, \\mathbf {z} _ {\\mathrm {t}}\\right)} = \\frac {\\mathbf {d} _ {\\mathrm {f}} \\cdot \\mathbf {d} _ {\\mathrm {t}}}{\\| \\mathbf {d} _ {\\mathrm {f}} \\| \\cdot \\| \\mathbf {d} _ {\\mathrm {t}} \\|}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 347, + 890, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{d_f}$ and $\\mathbf{d_t}$ denote textual narration vectors of first-person and third-person videos, respectively.", + "bbox": [ + 496, + 387, + 890, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Typical Multiview Alignment", + "text_level": 1, + "bbox": [ + 498, + 426, + 761, + 443 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing contrastive-based multiview [43, 25, 54] or multimodal [21, 49, 32, 48] methods propose to learn the view-invariant representations via the alignment of the features. Specifically, they learn to align features between different views or modalities by minimizing the distance between paired samples and maximizing the distance between negative (unpaired) samples.", + "bbox": [ + 496, + 449, + 890, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a batch of $N$ normalized first-person features $\\{\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}$ and third-person features $\\{\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{N}}\\}$ , these methods calculate the contrastive multiview Info-NCE [43, 33] loss as:", + "bbox": [ + 500, + 555, + 890, + 614 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {c} = L _ {c} ^ {(f, t)} + L _ {c} ^ {(t, f)}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 613, + 890, + 631 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {c} ^ {\\left(v _ {1}, v _ {2}\\right)} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\log \\left[ \\frac {\\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}} , \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {i}} \\right\\rangle / \\tau\\right)}{\\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}} , \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {i}} \\right\\rangle / \\tau\\right) + S _ {i}} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 656, + 890, + 710 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i} = \\sum_ {j \\in [ 1, N ], j \\neq i} e x p \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}}, \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {j}} \\right\\rangle / \\tau\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 722, + 890, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{v}_1$ and $\\mathbf{v}_2$ are two views and $\\tau$ is the temperature.", + "bbox": [ + 500, + 761, + 874, + 775 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For an input video clip $\\mathbf{x}_{\\mathbf{v_k}}$ , its normalized feature representation is extracted by the encoder $f_{v_k}(\\cdot)$ following the projection network $h_{v_k}(\\cdot)$ as:", + "bbox": [ + 496, + 776, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {\\mathbf {v} _ {\\mathbf {k}}} = \\frac {h _ {v _ {k}} \\left(A v g P o o l \\left(f _ {v _ {k}} \\left(\\mathbf {x} _ {\\mathbf {v} _ {\\mathbf {k}}}\\right)\\right)\\right)}{\\| h _ {v _ {k}} \\left(A v g P o o l \\left(f _ {v _ {k}} \\left(\\mathbf {x} _ {\\mathbf {v} _ {\\mathbf {k}}}\\right)\\right)\\right) \\| _ {2}}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 829, + 890, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The optimization of contrastive learning methods is often computationally expensive, which requires large batch", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3309", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b8a7d8cb2e698ee65391a298bf0b9b214b534ca325145b30c60261e58512e41b.jpg", + "image_caption": [ + "Figure 3. Illustration of our framework. First, one batch (batch size = 4) of multiview pseudo-pairs is built from unpaired first-person and third-person videos. The pseudo-pairs are built based on mining the most semantics-similar third-person video for every first-person video. During training, the global features for multiview alignment $(z_{f}, z_{t})$ are extracted by their corresponding encoders following the projection networks $(h_{f}, h_{t})$ . In addition, textual features $(d_{f}, d_{t})$ are extracted by a large language model [34] from textual narrations of first-person and third-person videos. The semantic similarity between $d_{f}$ and $d_{t}$ is calculated to filter out the multiview pseudo-pairs with low semantic similarity. Then the multiview pairs with high semantic similarity are employed to learn the view-invariant representations with the contrastive learning method. To further improve data efficiency, we employ all the first-person and third-person videos in the batch to learn contrastive multimodal relations. Finally, the task-specific heads $(g_{f}, g_{t})$ for both first-person and third-person videos are trained to make predictions for their corresponding downstream tasks. During testing, we only use the first-person encoder and task-specific head $(g_{f})$ to make first-person video predictions." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 888, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "sizes and a large volume of training epochs. To tackle this issue, Yeh et al. [50] refine the InfoNCE loss by removing the positive term from the denominator in Equation 3 and significantly improve the learning efficiency. To be specific, it rewrites Equation 3 as:", + "bbox": [ + 75, + 568, + 470, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {d c} ^ {\\left(v _ {1}, v _ {2}\\right)} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\log \\left[ \\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathrm {i}}, \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathrm {i}} \\right\\rangle / \\tau\\right) / S _ {i} \\right]. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 650, + 468, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the context of our unpaired multiview learning, we argue that directly employing the above vanilla contrastive learning method is an obstacle that hinders further acquiring knowledge from third-person videos. On the one hand, in the unpaired first-person and third-person video multiview representation learning, very few first-person views have the third-person views which share the same semantics. On the other hand, typical contrastive multiview representation learning is designed to minimize the feature distance between samples with identical semantics, e.g., recordings from camera views for the same objects [18], images with different visuals belonging to the same class [17], one image applying multiple independent [2] or asymmetric [11]", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "data augmentations, etc. Naively reducing multiview feature distances in our unpaired multiview learning will lead to learning suboptimal first-person video representations.", + "bbox": [ + 496, + 568, + 893, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Semantics-based Multiview Learning", + "text_level": 1, + "bbox": [ + 498, + 630, + 821, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address the above issue, we propose a representation learning method, namely Semantics-based Unpaired Multiview Learning. We employ contrastive alignment as a tool to align the unpaired multiview videos. Different from existing view-alignment methods, our proposed method introduces the following two novel alignments: (1) Semantics-based Cross-view Alignment, which employs the semantic information from textual narrations of multiview videos to align high-similar unpaired data; (2) Video-text Modal Alignment, which permits all first-person video obtaining knowledge from samples with different views or modalities. Next, we will introduce our framework step-by-step.", + "bbox": [ + 496, + 656, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Semantics-based Cross-view Alignment. We believe that pseudo-pairs with high semantic similarities can better help learn view-invariant information in first-person videos. Therefore, given cross-view pseudo-pairs $(\\mathbf{z_f},\\mathbf{z_t})$ in one", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3310", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "batch, we pick pseudo-pairs $(^{*}\\mathbf{z}_{\\mathbf{f}},^{*}\\mathbf{z}_{\\mathbf{t}})$ which have relatively higher textual semantic similarities. Then the first-person and third-person video alignment loss $(L_{a})$ is defined as the decoupled contrastive learning loss [50] of high semantic similarity pseudo-pairs:", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a} = L _ {d c} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} + L _ {d c} ^ {\\left(^ {*} \\mathrm {t}, ^ {*} \\mathrm {f}\\right)}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 176, + 468, + 198 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides, we hypothesize that the employed large language model [34] is a strong teacher: by encoding the textual descriptions of videos into vectors, the similarity between vectors implicitly provides a reference to measure the semantic similarity between videos. To make better use of these textual descriptions of first-person and third-person videos, inspired by [50], we further introduce a semantic-based weighting function for the positive pseudopairs. More specifically, we first rewrite our cross-view video alignment loss $L_{a}$ in Equation 7 as $L_{aw}$ , where:", + "bbox": [ + 75, + 207, + 470, + 358 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a w} = L _ {a w} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} + L _ {a w} ^ {\\left(^ {*} \\mathrm {t}, ^ {*} \\mathrm {f}\\right)}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 368, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then given views $(^{*}\\mathrm{f},^{*}\\mathrm{t})$ , we have:", + "bbox": [ + 76, + 398, + 313, + 414 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a w} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\log \\left(S _ {i}\\right) - \\omega \\left(^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathrm {i}}, ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathrm {i}}\\right) \\cdot \\left\\langle^ {*} \\mathrm {z} _ {\\mathbf {f}} ^ {\\mathrm {i}}, ^ {*} \\mathrm {z} _ {\\mathbf {t}} ^ {\\mathrm {i}} \\right\\rangle / \\tau \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 426, + 473, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the definition of $S_{i}$ is the same as Equation 4. Here we implement the weighting function as:", + "bbox": [ + 76, + 479, + 468, + 511 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\omega \\left(^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}}, ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}}\\right) = \\frac {\\exp \\left(\\left\\langle {} ^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}} , ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}} / \\sigma \\right\\rangle\\right)}{\\mathbb {E} _ {i} \\left[ \\exp \\left(\\left\\langle {} ^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}} , ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}} / \\sigma \\right\\rangle\\right) \\right]}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 520, + 468, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the higher textual similarity pseudo-pair has, the more learning signal the pseudo-pair needs to be provided, and vice versa. In this case, our multiview alignment is semantics-aware, which is different from existing multiview alignment methods [43, 51] that evenly align multiview data with different semantic similarities.", + "bbox": [ + 75, + 583, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Video-text Modal Alignment. Until now, although the above statement provides a seemingly finalized solution in the case where the multiview pseudo-pair semantic information is not exactly the same, it is not data-efficient for every first-person sample. This is because it cannot help first-person videos in pseudo-pairs with low semantic similarities gain learning signals from others.", + "bbox": [ + 75, + 672, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to permit all first-person videos to obtain knowledge from samples with different views or modalities, we employ video-text contrastive alignment to make the model training more data-efficient. As we mentioned before that every first-person and third-person video has an accurate textual description of their semantic information, this multimodal alignment can further help the neural network learn useful knowledge from these phrases.", + "bbox": [ + 75, + 780, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Technically, given a batch of $N$ normalized first-person and third-person features $\\{\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}$ and $\\{\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}$ , and their corresponding normalized textual description vectors $\\{\\mathbf{d}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{d}_{\\mathbf{f}}^{\\mathbf{N}}\\}$ and $\\{\\mathbf{d}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{d}_{\\mathbf{t}}^{\\mathbf{N}}\\}$ , the multimodal contrastive alignment loss $(L_{m})$ for both first-person videos and third-person videos is defined as:", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {m} = L _ {d c} ^ {\\left(\\mathbf {z} _ {\\mathrm {f}}, \\mathbf {d} _ {\\mathrm {f}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {d} _ {\\mathrm {f}}, \\mathbf {z} _ {\\mathrm {f}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {z} _ {\\mathrm {t}}, \\mathbf {d} _ {\\mathrm {t}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {d} _ {\\mathrm {t}}, \\mathbf {z} _ {\\mathrm {t}}\\right)}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 186, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training and Evaluation Pipelines", + "text_level": 1, + "bbox": [ + 500, + 215, + 797, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The two proposed cross-view and cross-modal losses, along with the task-specific losses for both first-person videos $(L_{f})$ and third-person videos $(L_{t})$ , are combined together during the training procedure to construct the final training loss:", + "bbox": [ + 496, + 238, + 890, + 314 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {L} = L _ {f} + w _ {t} \\cdot L _ {t} + w _ {a w} \\cdot L _ {a w} + w _ {m} \\cdot L _ {m}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 323, + 890, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that our model is trained in multiple stages. First, both first-person and third-person video encoders are initialized by weights pretrained on Kinetics-400 [16]. Then we train the third-person video encoder and task-specific head on the third-person video dataset with third-person video task-specific loss $(L_{t})$ only. Next, we load this trained weight for the third-person video encoder and task-specific head and do training for the whole framework with the overall loss in Equation 12. Finally, we evaluate the first-person video performance of our method using the first-person video encoder and task-specific head.", + "bbox": [ + 496, + 348, + 890, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The specific task for both first-person and third-person videos we discussed in this paper is video classification. Therefore, both $L_{f}$ and $L_{t}$ are classification losses; $w_{t}$ , $w_{aw}$ , and $w_{m}$ are the loss weights.", + "bbox": [ + 496, + 513, + 890, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 587, + 633, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 500, + 612, + 692, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Dataset", + "text_level": 1, + "bbox": [ + 500, + 635, + 607, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we introduce the standard benchmarks we used for evaluation in the experiments.", + "bbox": [ + 496, + 659, + 890, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LEMMA [15] contains 648 third-person videos and 445 first-person videos. Among them, 136 activities were performed in kitchens, and the remaining 188 were in the living rooms. It contains 25 verb classes, 64 noun classes, and 863 action classes in their action recognition task, and includes not only single-agent but also multi-agent videos. We utilize single-agent third-person videos only as our unpaired third-person samples.", + "bbox": [ + 496, + 688, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Charades-Ego [39, 40] contains 68,536 activity instances in paired 68.8 hours of first-person and third-person videos. It includes 157 action classes. We only utilize first-person videos during training and inference.", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "EPIC-Kitchens [4] is a large-scale egocentric video benchmark recorded in kitchen environments. It contains", + "bbox": [ + 496, + 869, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3311", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "55 hours of video with a total of 39.6K action segments and is labeled with 352 object and 125 verb classes.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "EPIC-Kitchens-100 [5] extends EPIC-Kitchens [4] to 100 hours and 89,977 action segments. We employ this as well as EPIC-Kitchens [4] to validate our approach.", + "bbox": [ + 76, + 122, + 468, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.2 Baseline Methods", + "text_level": 1, + "bbox": [ + 76, + 193, + 253, + 207 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the proposed approach with the following baseline methods, including typical multiview representation learning methods:", + "bbox": [ + 76, + 219, + 467, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FPV Only is trained with first-person (FPV) video data only. Its framework is composed of first-person video encoder and first-person video classification head.", + "bbox": [ + 76, + 266, + 467, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Typical CL is widely employed for view- or modal-invariant contrastive learning (CL) [43, 54], and vision-language models [32, 48, 21, 49, 24, 55]. Here we implement it with the loss function in Equation 6. Similar to our framework, videos from different views are fed to different encoders. We employ the same pseudo-pair construction method and the same inference strategy as our framework for this baseline method.", + "bbox": [ + 75, + 311, + 467, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Triplet is another widely used multiview representation learning method [51, 39]. We employ the same implementation protocol following [51]. Moreover, we leverage this method to tackle our problem following the same procedures as \"Typical CL\".", + "bbox": [ + 76, + 434, + 467, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.3 Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 535, + 294, + 549 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To ensure fairness, we keep all hyperparameters the exact same for all baselines and our method. For Charades-Ego [39, 40], we use the base learning rate of 0.25, batch size of 32 and maximum epoch of 60. For EPIC-Kitchens [4] and EPIC-Kitchens-100 [5], we use the base learning rate of 0.01, weight decay of 0.0001, batch size of 64 and maximum epoch of 30. Following [22], all models are trained using the stochastic gradient descent optimizer [1] with the momentum of 0.9. For Charades-Ego [39, 40], we use the cosine learning rate decay. For EPIC-Kitchens [4] and EPIC-Kitchens-100 [5], we use sequential learning rate decay. The backbones we use are ResNet-3D-50 [13] and SlowFast [8]. More details about the implementation of backbones will be provided in the following experimental sections.", + "bbox": [ + 75, + 561, + 467, + 786 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Validity of Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 800, + 333, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 shows the performance of different training strategies, where all methods are implemented with the ResNet-3D-50 [13] encoder. Our proposed method outperforms the \"FPV only\" baseline model on both Charades-Ego and EPIC-Kitchens $(+1.6\\%)$ mAP on Charades-Ego,", + "bbox": [ + 76, + 825, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/245562b91d06382fe4fd88fa7047bd144fa190694459b3f91600706060cdc1a5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetC-EgoEK-55 (Verb)EK-55 (Noun)
EvaluationsmAP (%)Top-1 acc. (%)Top-5 acc. (%)Top-1 acc. (%)Top-5 acc. (%)
FPV Only24.761.187.145.870.4
Typical CL25.160.586.245.368.6
Triplet25.261.586.845.769.7
SUM-L (Ours)26.362.387.247.370.9
", + "bbox": [ + 511, + 88, + 883, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Comparison with baseline methods. The backbone we use is R3D-50 [13] for all methods. \"C-Ego\" denotes Charades-Ego [39] dataset and \"EK-55\" denotes EPIC-Kitchens [4] dataset.", + "bbox": [ + 500, + 191, + 890, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and $+1.2\\% / + 1.5\\%$ on EPIC-Kitchens verbs/nouns top-1 accuracies). This demonstrates that under partially similar semantics situations, with our method, the third-person videos can help to improve first-person video representations.", + "bbox": [ + 498, + 261, + 890, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Moreover, different from our method, previous multiview learning methods (\"Typical CL\" and \"Triplet\") cannot bring significant and consistent improvement compared with \"FPV only\". For example, \"Typical CL\" brings only $0.4\\%$ improvement on Charades-Ego (far less than ours) and even deteriorates performance on EPIC-Kitchens. Instead, our proposed method outperforms existing alignment methods up to $+1.2\\%$ mAP on Charades-Ego and $+1.8\\% / + 2.0\\%$ on EPIC-Kitchens verbs/nouns top-1 accuracies. We believe this is due to the following reasons. (1) Our method semantics-awarely aligns unpaired data, instead of evenly aligning pseudo-pairs with different semantic similarities. (2) Our method filters the negative effects caused by multiview pseudo-pairs of low semantic similarity. This is different from typical multiview methods which naively align all the pairs. (3) Our method permits all first-person videos to obtain knowledge from samples with different views or modalities, which improves data efficiency.", + "bbox": [ + 496, + 323, + 892, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further verify the effectiveness of our proposed method with a larger backbone, SlowFast [8], as the encoder, and we compare with recent state-of-the-art methods on three popular egocentric action recognition benchmarks, Charades-Ego [39], EPIC-Kitchens [4], and EPIC-Kitchens-100 [5]. Note that evaluation scores of state-of-the-arts are reported directly from their paper. The experimental results employing SlowFast [8] encoder confirm the following findings. (1) Our method is effective for cross-view pseudo-pair alignment when there is only partially same multiview semantics. (2) Compared with existing multiview alignment methods, the improvement based on \"FPV Only\" of our method is still more significant and consistent. Next, we analyze the important details of the experiments.", + "bbox": [ + 496, + 597, + 890, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison on Charades-Ego Table 2 demonstrates the effectiveness of our method for cross-view pseudopair alignment when there is only partially same semantics. Note that our method and Ego-Exo [22] complement each other. Thus, we can also incorporate our method into Ego", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3312", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ced477b48605d4923ac00c9a535eb99e38077ad84fd5d3893df5cd08d5e22632.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodologymAP (%)
state-of-the-artsActor [39]20.0
SSDA [3]23.1
I3D [22]25.8
Ego-Exo [22]28.7
Ego-Exo* [22]30.1
w/o “EE”FPV Only27.4
Typical CL27.9
Triplet28.1
SUM-L (Ours)28.5
w/ “EE”FPV Only29.5
Typical CL29.1
Triplet28.6
SUM-L (Ours)30.7
", + "bbox": [ + 122, + 88, + 421, + 286 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/44b0f2d0edc14c3dafff7a5058e1f6599d1994f765dfdd2d256a766e1b00e1e3.jpg", + "table_caption": [ + "Table 2. Comparison on Charades-Ego. Our method and all baseline methods are implemented with SlowFast-R101 [8] backbone. \"EE\" denotes training based on pretrained weights provided by [22]." + ], + "table_footnote": [], + "table_body": "
MethodologyVerb (%)Noun (%)
state-of-the-artsSlowFast-R50 [8]64.148.6
Ego-Exo [22]66.049.4
Ego-Exo* [22]66.449.8
w/o “EE”FPV Only63.148.4
Typical CL63.949.6
Triplet63.948.8
SUM-L (Ours)65.049.5
w/ “EE”FPV Only65.849.5
Typical CL63.848.4
Triplet63.949.6
SUM-L (Ours)66.750.2
", + "bbox": [ + 84, + 366, + 464, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Exo [22]. As shown in Table 2, based on pretrained weight on [22], our proposed method further improves the performance of \"FPV only\" by $1.2\\%$ mAP, and achieves a new state-of-the-art on Charades-Ego [39].", + "bbox": [ + 75, + 625, + 468, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on EPIC-Kitchens As we can see from Table 3, our method still brings clear improvement compared with \"FPV Only\" method $(+1.9\\% / +1.1\\%$ verbs/nouns top-1 accuracies). Furthermore, with the help of pretrained weights from [22], our method still outperforms most state-of-the-art methodologies, which indicates the effectiveness of our method. Last but not least, our method outperforms existing alignment methods up to $+2.9\\% / +1.8\\%$ of verbs/nouns top-1 accuracies.", + "bbox": [ + 75, + 686, + 468, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on EPIC-Kitchens-100 As shown in table 4, our method also obtains competitive results on EPIC-Kitchens-100 [5] dataset when trained based on weights from [22]. It is worth noting that our method gains the first place in noun accuracy and third place in verb accu", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5712936af90c7038972f025a2b37be6e715eafb62ca53c53ba7e016b649f4071.jpg", + "table_caption": [ + "Table 3. Comparison on EPIC-Kitchens. The accuracies are measured by top-1 verb & noun classification accuracies. Our method and all baseline methods are implemented with SlowFast-R50 [8] backbone." + ], + "table_footnote": [], + "table_body": "
MethodologyVerb (%)Noun (%)
state-of-the-artsTSN [45]60.246.0
TSM [23]67.949.0
TempAgg [36]59.945.1
Ego-Exo [22]67.052.9
Ego-Exo* [22]67.552.9
IPL [47]68.651.2
w/ “EE”SUM-L (Ours)67.053.4
", + "bbox": [ + 506, + 87, + 888, + 200 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ec24b3a1cc016c134ff6ba723b373a19e27c226dbb55761b085293582902a7f7.jpg", + "table_caption": [ + "Table 4. Comparison on EPIC-Kitchens-100 with state-of-the-arts that implement CNN backbone. The accuracies are measured by top-1 verb & noun classification accuracies. We implement SlowFast-R101 [8] backbone." + ], + "table_footnote": [], + "table_body": "
LaLawLmmAP (%)
×××24.7
×✓×25.6
×✓✓26.3
✓×✓26.1
", + "bbox": [ + 606, + 279, + 781, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Different training task combinations of our proposed method. Combining semantics-aware unpaired cross-view alignment with video-text alignment, our method clearly improves egocentric classification performance on the Charades-Ego dataset.", + "bbox": [ + 498, + 368, + 890, + 425 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "racy compared with state-of-the-art methodologies which employ convolutional neural network backbones.", + "bbox": [ + 498, + 454, + 890, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 500, + 663, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct the ablation studies on Charades-Ego [39] dataset. The backbone we employ is ResNet-3D-50 [13].", + "bbox": [ + 498, + 525, + 890, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.1 Impact of Different Alignment Tasks", + "text_level": 1, + "bbox": [ + 500, + 601, + 808, + 616 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The experiment results are shown in Table 5. We find our proposed unpaired cross-view alignment method itself brings $0.9\\%$ mAP improvement comparing with the \"FPV Only\" method. It denotes that the method can help learn useful knowledge from unpaired third-person view samples when the cross-view semantic information is not identical. Moreover, our proposed video-text modal alignment method further boosts first-person performance by $0.7\\%$ mAP compared with implementation with cross-view alignment only. We think this is because the proposed video-text modal alignment ensures the alignment of all first-person video samples, and further improves the semantics utilization for both first-person and third-person videos. Besides, implementing our cross-view alignment without semantic weighting causes a slight $0.2\\%$ drop, which manifests the usefulness of knowledge from the large language model. This knowledge provides a reference to measure the semantic similarity between cross-view videos.", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3313", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4893ed8504c1e2be008de05734bf4b428554b7ee04efcb261dbe2014e8d98598.jpg", + "image_caption": [ + "First-person frame heatmaps from \"FPV Only\"" + ], + "image_footnote": [], + "bbox": [ + 104, + 109, + 225, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a39c545060fe2122fa4c28d7efe85ea5663ce0b0e2c5a0ab2b31c97ecc8566ee.jpg", + "image_caption": [ + "First-person frame heatmaps from our method" + ], + "image_footnote": [], + "bbox": [ + 228, + 109, + 354, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/03f3b4c0b84f621f4178fc5da4b27766eb1c2ac4ecfb312f0b9c0c49bf7abac0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 109, + 480, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2f5a611efdd4bc6ba581b577847e89a7510b6ac9680873c0e6b2726b542c31d6.jpg", + "image_caption": [ + "Third-person frame heatmaps from our method" + ], + "image_footnote": [], + "bbox": [ + 483, + 109, + 609, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0661c1ed5b9b94a4794ed9e4f7bc1ad55a44ccb466c32f7f5fa9fae7e235944c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 109, + 743, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/821b24b956eb1adc563f4ae8a53c68203e964dfd5786cd7194bff875ec6d28a4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 109, + 872, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5481096a6acc31744e5ec2cdd54abf4943b4a1086e15e463ff8e75e2aca2427e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 102, + 212, + 225, + 309 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5b24d1052755c8de474d34b8928a8f60fab00d094ef0cf0082a237883ec823e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 228, + 212, + 354, + 309 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2b8a3cb728af9692ff6f6cdb6602134dd2efecef19b0d0f206432c6b127548fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 212, + 480, + 309 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d9e16e5624f1ade00ed80cf7d3751b0be34b70c8246b34f5c61d32cef8441c7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 212, + 609, + 309 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2a0c985fa33df04f16f2e3cf9e0ad972d202672de48fc8030068096421c51b6f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 212, + 743, + 309 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/32f23936d82ba7a88adf0775d09682da3e07c9e5ad54d6e8ec6a6ccda18c4a19.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 212, + 872, + 309 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/63c6de48fb055918a0e51ba026555385805012e0900a675fe933e3031f6587bc.jpg", + "image_caption": [ + "Figure 4. Comparison of class activation map visualizations between the \"FPV Only\" method and our method. The cross-view similar semantics for data in the first row is \"holding pan\". The cross-view similar semantics for data in the second and third rows is \"take\"." + ], + "image_footnote": [], + "bbox": [ + 102, + 321, + 225, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/75383de40adc9d6d5b901d26f23edfdd8e7beb0639ee8ec64c035295356af224.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 228, + 321, + 352, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/35e9c8c41ed28ad72c3348c6afea1915b584dac24dc72621e971155ad0bbc471.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 321, + 480, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eefcefe7d0dfa58dc6f9ee637216db49be3ae2124d87f88e1f0b0a3e445a1e28.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 321, + 609, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ab572a88bf961648c9c0400a185b5d0fae0f239649ed0c2acd450ca0578c0c9e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 321, + 743, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9efc0311a88430b460ad002c318eea4c8c4d44737e05f873d4f91b8b360527ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 321, + 872, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.2 Impact of Third-person View Backbone", + "text_level": 1, + "bbox": [ + 76, + 489, + 408, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The original setup of the third-person video encoder is mentioned in Sec. 3.4. Here we study the effect of other intuitively feasible third-person video encoder implementations. The experiment results are shown in Table 6.", + "bbox": [ + 75, + 549, + 468, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "First, we load the pretrained weight of the third-person video and freeze it during the training process for the whole framework shown in Figure 3. We find freezing the third-person video encoder causes a $0.5\\%$ mAP drop compared with the original setup. This indicates that for the pretrained third-person video encoder, allowing training more parameters can better help first-person video learn effective information from third-person samples. Moreover, naively employing shared encoder weights for different views, which follows [2], can cause clear performance drop ( $1.0\\%$ mAP drop) to first-person video learning. We think this is due to the big variances between first-person and third-person samples. Finally, the same initialization (pretrained on Kinetics-400 [16]) for both first-person and third-person video encoders causes a slight $0.2\\%$ mAP drop. It indicates that for the third-person video encoder, employing existing weights of third-person samples for optimization has a positive effect on first-person video learning.", + "bbox": [ + 75, + 628, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5dc4a09a6552333094ab9a2a18258c5f29bf637d6b964c39dbc6014fc18431fe.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SetupmAP (%)
Freezed TPV Backbone25.8
Shared Multiview Encoder Weights25.3
Same Initialization with FPV Encoder26.1
Original26.3
", + "bbox": [ + 517, + 487, + 870, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Impact of different third-person video encoder implementations. The \"Original\" setup is described in Sec. 3.4.", + "bbox": [ + 500, + 575, + 890, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Visualization", + "text_level": 1, + "bbox": [ + 500, + 632, + 637, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We visualize the first-person and third-person video class activation maps (CAM) [56] on EPIC-Kitchens [4] dataset. We employ first-person video encoder weights from \"FPV Only\" method (61.1% & 45.8% top-1 verb & noun accuracies) and our method (62.3% & 47.3% top-1 verb & noun accuracies). As shown in the first and second columns of Figure 4, comparing with \"FPV Only\" method, our method can help the model be more responsive to positive spatiotemporal locations of video clips.", + "bbox": [ + 496, + 657, + 890, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Moreover, from the third column of Figure 4, we find that our model also has a strong response to the third-person video locations which have overlapped semantics with the first-person video (see bright green bounding boxes of Figure 4). It shows that our method successfully utilizes knowledge from unpaired third-person videos to help learn first-person video representations.", + "bbox": [ + 496, + 795, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3314", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 76, + 89, + 204, + 104 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we tackle a new problem in first-person and third-person video learning and propose SUM-L. It can distill knowledge from unpaired, cross-dataset third-person video without exact same multiview semantic information. Our experiments show the validity of our proposed method. Besides, under the more challenging scenario than typical paired or unpaired multimodal or multiview learning, our method outperforms existing view-alignment methods.", + "bbox": [ + 76, + 114, + 467, + 236 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "However, improvements from SUM-L are not very significant. One possible reason is due to the relatively small amount of third-person data. It will be interesting to explore more unpaired third-person video datasets. It will be also interesting to study more downstream tasks, such as unpaired cross-view retrieval. We leave these as future work.", + "bbox": [ + 76, + 237, + 467, + 325 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements This work is partially supported by National Science Foundation (NSF) CMMI-2039857, and University of Delaware Research Foundation (UDRF). We thank Florian Schroff and Hartwig Adam from Google Research for supporting this project.", + "bbox": [ + 76, + 328, + 467, + 404 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 417, + 173, + 434 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shun-ichi Amari. Backpropagation and stochastic gradient descent method. Neurocomputing, 5(4-5):185-196, 1993. 6", + "[2] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In International conference on machine learning, pages 1597-1607. 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In Proceedings of the IEEE conference on" + ], + "bbox": [ + 78, + 90, + 470, + 900 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "computer vision and pattern recognition, pages 2921-2929, 2016.8", + "bbox": [ + 535, + 92, + 890, + 118 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "3317", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning from Semantic Alignment between Unpaired Multiviews for Egocentric Video Recognition/3976a321-a1a8-401c-abba-91b9fbe78433_model.json b/2023/Learning from Semantic Alignment between Unpaired Multiviews for Egocentric Video Recognition/3976a321-a1a8-401c-abba-91b9fbe78433_model.json new file mode 100644 index 0000000000000000000000000000000000000000..15eb7ca967b774b9da0695b0702ba4d83a56a98a --- /dev/null +++ b/2023/Learning from Semantic Alignment between Unpaired Multiviews for Egocentric Video Recognition/3976a321-a1a8-401c-abba-91b9fbe78433_model.json @@ -0,0 +1,2510 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.135, + 0.13, + 0.838, + 0.177 + ], + "angle": 0, + "content": "Learning from Semantic Alignment between Unpaired Multiviews for Egocentric Video Recognition" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.203, + 0.747, + 0.24 + ], + "angle": 0, + "content": "Qitong Wang\\(^{1}\\), Long Zhao\\(^{2}\\), Liangzhe Yuan\\(^{2}\\), Ting Liu\\(^{2}\\), Xi Peng\\(^{1}\\) \n\\(^{1}\\)University of Delaware, \\(^{2}\\)Google Research" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.242, + 0.748, + 0.259 + ], + "angle": 0, + "content": "{wqtwjxipeng}@udel.edu {longzh,lzyuan,liuti} \\(@\\) google.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.474, + 0.613 + ], + "angle": 0, + "content": "We are concerned with a challenging scenario in unpaired multiview video learning. In this case, the model aims to learn comprehensive multiview representations while the cross-view semantic information exhibits variations. We propose Semantics-based Unpaired Multiview Learning (SUM-L) to tackle this unpaired multiview learning problem. The key idea is to build cross-view pseudopairs and do view-invariant alignment by leveraging the semantic information of videos. To facilitate the data efficiency of multiview learning, we further perform video-text alignment for first-person and third-person videos, to fully leverage the semantic knowledge to improve video representations. Extensive experiments on multiple benchmark datasets verify the effectiveness of our framework. Our method also outperforms multiple existing view-alignment methods, under the more challenging scenario than typical paired or unpaired multimodal or multiview learning. Our code is available at https://github.com/wqtwjt1996/SUM-I." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.646, + 0.21, + 0.661 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Recent years have witnessed a tremendous increase in the research regarding egocentric video understanding and learning [22, 26, 20, 41, 29, 30, 14, 42, 7, 31, 46, 9]. In parallel, a recent study [22] verifies that the activity of third-person videos in fact positively inform first-person video learning. Early works [39, 51] of egocentric video learning and understanding pay a lot of attention to paired multiview data representation learning. However, synchronized first-person and third-person video pairs are difficult to collect. This severely limits the data scale and scope of multiview learning for egocentric data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Recently, egocentric video datasets [4, 5, 10] with larger scale have become available. However, since head-mounted cameras were not available until recent years, very few first-person videos have paired third-person videos [15]." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.291, + 0.887, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.473, + 0.895, + 0.6 + ], + "angle": 0, + "content": "Figure 1. (a) The typical multiview video learning method learns view-invariant representations from paired first-person and third-person videos. (b) Recent multimodal study [19] is interested in the alignment between unpaired samples which share identical semantics. In this paper, we study a more challenging scenario than existing works: unpaired multiview samples alignment with partially similar semantics, such as videos with (c) the same verb only, or (d) the same object only. The verb-object phrases above the video clips denote the semantic information of videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Fortunately, there exist third-person videos from different datasets [12, 16]. It is worth noting that unpaired third-person videos are relatively easier to capture and obtain compared with paired ones. Therefore, in this paper, we study an interesting yet seldom investigated problem: how to leverage unpaired third-person videos to help egocentric video learning?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Unpaired multiview learning is rarely studied. While recent works [28, 27, 38, 53] study the scenario where paired modalities are missing. But they do not leverage the potential of unpaired data from diverse datasets. Moreover, to align the unpaired multimodal samples, Kundu et al. [19] propose one relation distillation method to align the unpaired samples. They assume that unpaired data need to share identical semantic information. However, in the unpaired first-person and third-person video learning scenario, for the vast majority of egocentric videos, it is almost impossible to mine the third-person samples with identical" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3307" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.295, + 0.103, + 0.677, + 0.117 + ], + "angle": 0, + "content": "Semantic Similarity Statistics of Multiview Pseudo Pairs (%)" + }, + { + "type": "image", + "bbox": [ + 0.115, + 0.121, + 0.852, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.264, + 0.895, + 0.349 + ], + "angle": 0, + "content": "Figure 2. Statistics of semantic similarities between the first-person samples in [39, 4, 5] and the most similar single-agent third-person samples they can find from the LEMMA [15] dataset. The semantic similarity is the cosine distance between textual phrase vectors of videos encoded by a large language model [34]. Each bar in the figure represents the percentage of action classes that fall within one semantic similarity range (e.g., [0.8, 1.0]) in an egocentric dataset compared to all action classes in this dataset. In all of the three popular egocentric datasets, very few first-person videos are able to find third-person videos with identical semantics. For reference, in the studies for paired multiview data [43, 39, 51, 54], all the semantic similarities of cross-view data pairs are (or very close to) “1.0”." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.473, + 0.601 + ], + "angle": 0, + "content": "semantics. The only alternatives are partially semantics-similar unpaired third-person videos. For example, for one egocentric video clip with \"cut watermelon\" semantics, the most similar third-person video is those with \"cut lemon\" (same verb) or \"eat watermelon\" (same object) semantics. Examples and comparisons between our scenario and typical paired or unpaired multiview or multimodal learning are shown in Figure 1, and we display comprehensive semantics similarity statistics of multiview data studied in this paper (see Figure 2). Therefore, how to employ the unpaired and partially semantics-similar third-person views to help first-person view learning is an open problem. Intuitively, compared with previous research, our setting is more challenging since most of the first-person videos only share partially similar semantics with third-person views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, we are interested in view-invariant alignment in the partially semantics-similar pseudo-pair setting. We propose Semantics-based Unpaired Multiview Learning (SUM-L), where multiview pseudo-pairs with high similarities are aligned in a semantics-aware manner. In our method, we also employ video-text alignment to permit all first-person videos to obtain knowledge from samples with different views or modalities. We highlight that our SUM-L employs the large language model [34] to help align cross-view and cross-modality data. This is different from [22], which proposes to distill beneficial knowledge from unpaired third-person videos [16], mostly with the help of the off-the-shelf image recognition model [6] and hand-object detector [37]. Moreover, our method is better than existing view-invariant alignment methods, such as typical contrastive learning [44, 43, 50, 54] and triplet loss based learning [35, 51] in the new setting, since they naively reduce multiview feature distance, which leads to learning suboptimal first-person representations." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.373, + 0.818, + 0.387 + ], + "angle": 0, + "content": "To summarize, our contribution is three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.4, + 0.892, + 0.448 + ], + "angle": 0, + "content": "- We study a new problem: in the partially semantics-similar multiview setting, how to leverage unpaired third-person videos to help first-person video learning." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.459, + 0.892, + 0.505 + ], + "angle": 0, + "content": "- We propose SUM-L for this new problem, which is more effective than existing view-alignment methods in our unpaired multiview learning scenario." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.518, + 0.892, + 0.609 + ], + "angle": 0, + "content": "- Experiments in standard benchmark datasets including Charades-Ego [39], EPIC-Kitchens [4], and EPIC-Kitchens-100 [5] validate the competitive performance of our methods over existing view-alignment methods including typical contrastive learning and triplet loss based learning." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.4, + 0.892, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.642, + 0.641 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.744, + 0.667 + ], + "angle": 0, + "content": "2.1. Egocentric Video Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The study of egocentric video learning has attracted a large volume of attention in recent years. To verify the quality of model learning, there are multiple egocentric-related tasks, including action recognition [29, 42, 46], video summarization [26, 20], engagement detection [41], scene affordance [30], gaze prediction [14], video question answering [7], and activity anticipation [31, 9]. Nevertheless, aforementioned studies utilize knowledge from first-person videos only [26, 20, 41, 14, 42, 31, 9], or make use of extra supervision from off-the-shelf models [29, 30], or naively pretrain on large-scale datasets [7, 46]. More specifically, these methods do not consider tackling the domain mismatch between different multiview datasets or abstaining from extra supervision. Recently, Li et al. [22] try to discover latent signals in the third-person videos which" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3308" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "are predictive of key egocentric-specific properties. Similar to [29, 30], however, this method heavily relies on the knowledge of off-the-shelf image or video models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.145, + 0.47, + 0.176 + ], + "angle": 0, + "content": "2.2. First-person Video Representation Learning with Joint Third-person Videos" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.473, + 0.486 + ], + "angle": 0, + "content": "The paired first-person and third-person videos, as descriptions of the same actions from different perspectives, are potential to provide beneficial knowledge to each other, yielding more generalizable joint representations. Recent studies [39, 40] propose paired first-person and third-person datasets and learn joint representations of multiview videos. They show the potential of transferring knowledge from third-person videos to first-person videos. In order to extract more useful joint knowledge, Yu et al. [52] make use of the shared attention regions between different views with spatial constraints, in a self-supervised and simultaneous manner. However, nowadays very few first-person videos have paired third-person videos [15]. Moreover, we find that existing multiview methods [44, 43, 35, 51] learn suboptimal first-person representations from unpaired third-person videos, that are relatively easier to capture and obtain compared with paired data. Instead, our methodology can better distill unpaired third-person video knowledge to first-person videos, and it is more efficient and applicable than existing view-alignment methods [44, 43, 35, 51]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.493, + 0.357, + 0.509 + ], + "angle": 0, + "content": "2.3. Unpaired Multimodal Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.473, + 0.759 + ], + "angle": 0, + "content": "Due to the relatively difficult acquisition of paired multimodal samples and the limited number of them, unpaired multimodal learning recently has attracted the interest of some researchers. Kundu et al. [19] treat unpaired 3D pose learning as a self-supervised adaptation problem that aims to transfer the task knowledge from a labeled paired source domain to a completely unpaired target domain. Next, it proposes the relation distillation method to align the unpaired target videos and unpaired 3D pose sequences. However, this work makes the assumption that there exist semantically identical cross-modal data in the unpaired target domain, which is almost unavailable in unpaired first- and third-person video representation learning. Therefore, in this paper, we study a more challenging problem: how to make unpaired multiview alignment in an incompletely semantics-similar situation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.212, + 0.788 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.9 + ], + "angle": 0, + "content": "In the following sections, we first describe our pseudopair construction method (Sec. 3.1). Then we introduce the traditional contrastive framework for paired multiview or multimodal data (Sec. 3.2). Next, we introduce our proposed cross-view and cross-modal methods (Sec. 3.3). Finally, we present our full training and evaluation pipeline in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.824, + 0.108 + ], + "angle": 0, + "content": "3.1. Semantics-based Pseudo-pair Mining" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.189 + ], + "angle": 0, + "content": "Different from the previous joint multiview learning approaches [39, 40, 51], first-person and third-person videos are not automatically paired in the cross-dataset setting. Hence, before model training, it is essential to construct pseudo multiview pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.19, + 0.893, + 0.342 + ], + "angle": 0, + "content": "Every first-person and third-person video has one unique textual narration, which describes the key semantic information of it. Therefore, we employ the large language model [34] to encode textual narrations of multiview videos to vectors. Then for each first-person video, we mine the third-person video with the highest textual semantic similarity from the third-person video pool to construct the pseudopair. We compute the cosine distance between cross-view video textual narrations as the criterion of semantic similarity between first-person and third-person video clips:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.348, + 0.892, + 0.381 + ], + "angle": 0, + "content": "\\[\n\\operatorname {s i m} _ {\\left(\\mathbf {z} _ {\\mathrm {f}}, \\mathbf {z} _ {\\mathrm {t}}\\right)} = \\frac {\\mathbf {d} _ {\\mathrm {f}} \\cdot \\mathbf {d} _ {\\mathrm {t}}}{\\| \\mathbf {d} _ {\\mathrm {f}} \\| \\cdot \\| \\mathbf {d} _ {\\mathrm {t}} \\|}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.419 + ], + "angle": 0, + "content": "where \\(\\mathbf{d_f}\\) and \\(\\mathbf{d_t}\\) denote textual narration vectors of first-person and third-person videos, respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.427, + 0.762, + 0.444 + ], + "angle": 0, + "content": "3.2. Typical Multiview Alignment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.892, + 0.555 + ], + "angle": 0, + "content": "Existing contrastive-based multiview [43, 25, 54] or multimodal [21, 49, 32, 48] methods propose to learn the view-invariant representations via the alignment of the features. Specifically, they learn to align features between different views or modalities by minimizing the distance between paired samples and maximizing the distance between negative (unpaired) samples." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.556, + 0.892, + 0.615 + ], + "angle": 0, + "content": "Given a batch of \\(N\\) normalized first-person features \\(\\{\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}\\) and third-person features \\(\\{\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{N}}\\}\\), these methods calculate the contrastive multiview Info-NCE [43, 33] loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.614, + 0.892, + 0.632 + ], + "angle": 0, + "content": "\\[\nL _ {c} = L _ {c} ^ {(f, t)} + L _ {c} ^ {(t, f)}, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.657, + 0.891, + 0.711 + ], + "angle": 0, + "content": "\\[\nL _ {c} ^ {\\left(v _ {1}, v _ {2}\\right)} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\log \\left[ \\frac {\\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}} , \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {i}} \\right\\rangle / \\tau\\right)}{\\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}} , \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {i}} \\right\\rangle / \\tau\\right) + S _ {i}} \\right], \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.723, + 0.892, + 0.758 + ], + "angle": 0, + "content": "\\[\nS _ {i} = \\sum_ {j \\in [ 1, N ], j \\neq i} e x p \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}}, \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {j}} \\right\\rangle / \\tau\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.762, + 0.875, + 0.776 + ], + "angle": 0, + "content": "where \\(\\mathbf{v}_1\\) and \\(\\mathbf{v}_2\\) are two views and \\(\\tau\\) is the temperature." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.777, + 0.892, + 0.823 + ], + "angle": 0, + "content": "For an input video clip \\(\\mathbf{x}_{\\mathbf{v_k}}\\), its normalized feature representation is extracted by the encoder \\(f_{v_k}(\\cdot)\\) following the projection network \\(h_{v_k}(\\cdot)\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.83, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {\\mathbf {v} _ {\\mathbf {k}}} = \\frac {h _ {v _ {k}} \\left(A v g P o o l \\left(f _ {v _ {k}} \\left(\\mathbf {x} _ {\\mathbf {v} _ {\\mathbf {k}}}\\right)\\right)\\right)}{\\| h _ {v _ {k}} \\left(A v g P o o l \\left(f _ {v _ {k}} \\left(\\mathbf {x} _ {\\mathbf {v} _ {\\mathbf {k}}}\\right)\\right)\\right) \\| _ {2}}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The optimization of contrastive learning methods is often computationally expensive, which requires large batch" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3309" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.089, + 0.889, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.405, + 0.896, + 0.545 + ], + "angle": 0, + "content": "Figure 3. Illustration of our framework. First, one batch (batch size = 4) of multiview pseudo-pairs is built from unpaired first-person and third-person videos. The pseudo-pairs are built based on mining the most semantics-similar third-person video for every first-person video. During training, the global features for multiview alignment \\((z_{f}, z_{t})\\) are extracted by their corresponding encoders following the projection networks \\((h_{f}, h_{t})\\). In addition, textual features \\((d_{f}, d_{t})\\) are extracted by a large language model [34] from textual narrations of first-person and third-person videos. The semantic similarity between \\(d_{f}\\) and \\(d_{t}\\) is calculated to filter out the multiview pseudo-pairs with low semantic similarity. Then the multiview pairs with high semantic similarity are employed to learn the view-invariant representations with the contrastive learning method. To further improve data efficiency, we employ all the first-person and third-person videos in the batch to learn contrastive multimodal relations. Finally, the task-specific heads \\((g_{f}, g_{t})\\) for both first-person and third-person videos are trained to make predictions for their corresponding downstream tasks. During testing, we only use the first-person encoder and task-specific head \\((g_{f})\\) to make first-person video predictions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.471, + 0.645 + ], + "angle": 0, + "content": "sizes and a large volume of training epochs. To tackle this issue, Yeh et al. [50] refine the InfoNCE loss by removing the positive term from the denominator in Equation 3 and significantly improve the learning efficiency. To be specific, it rewrites Equation 3 as:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.651, + 0.47, + 0.704 + ], + "angle": 0, + "content": "\\[\nL _ {d c} ^ {\\left(v _ {1}, v _ {2}\\right)} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\log \\left[ \\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathrm {i}}, \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathrm {i}} \\right\\rangle / \\tau\\right) / S _ {i} \\right]. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In the context of our unpaired multiview learning, we argue that directly employing the above vanilla contrastive learning method is an obstacle that hinders further acquiring knowledge from third-person videos. On the one hand, in the unpaired first-person and third-person video multiview representation learning, very few first-person views have the third-person views which share the same semantics. On the other hand, typical contrastive multiview representation learning is designed to minimize the feature distance between samples with identical semantics, e.g., recordings from camera views for the same objects [18], images with different visuals belonging to the same class [17], one image applying multiple independent [2] or asymmetric [11]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.895, + 0.616 + ], + "angle": 0, + "content": "data augmentations, etc. Naively reducing multiview feature distances in our unpaired multiview learning will lead to learning suboptimal first-person video representations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.631, + 0.822, + 0.648 + ], + "angle": 0, + "content": "3.3. Semantics-based Multiview Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.839 + ], + "angle": 0, + "content": "To address the above issue, we propose a representation learning method, namely Semantics-based Unpaired Multiview Learning. We employ contrastive alignment as a tool to align the unpaired multiview videos. Different from existing view-alignment methods, our proposed method introduces the following two novel alignments: (1) Semantics-based Cross-view Alignment, which employs the semantic information from textual narrations of multiview videos to align high-similar unpaired data; (2) Video-text Modal Alignment, which permits all first-person video obtaining knowledge from samples with different views or modalities. Next, we will introduce our framework step-by-step." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Semantics-based Cross-view Alignment. We believe that pseudo-pairs with high semantic similarities can better help learn view-invariant information in first-person videos. Therefore, given cross-view pseudo-pairs \\((\\mathbf{z_f},\\mathbf{z_t})\\) in one" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3310" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "batch, we pick pseudo-pairs \\((^{*}\\mathbf{z}_{\\mathbf{f}},^{*}\\mathbf{z}_{\\mathbf{t}})\\) which have relatively higher textual semantic similarities. Then the first-person and third-person video alignment loss \\((L_{a})\\) is defined as the decoupled contrastive learning loss [50] of high semantic similarity pseudo-pairs:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.177, + 0.47, + 0.199 + ], + "angle": 0, + "content": "\\[\nL _ {a} = L _ {d c} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} + L _ {d c} ^ {\\left(^ {*} \\mathrm {t}, ^ {*} \\mathrm {f}\\right)}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.208, + 0.471, + 0.359 + ], + "angle": 0, + "content": "Besides, we hypothesize that the employed large language model [34] is a strong teacher: by encoding the textual descriptions of videos into vectors, the similarity between vectors implicitly provides a reference to measure the semantic similarity between videos. To make better use of these textual descriptions of first-person and third-person videos, inspired by [50], we further introduce a semantic-based weighting function for the positive pseudopairs. More specifically, we first rewrite our cross-view video alignment loss \\( L_{a} \\) in Equation 7 as \\( L_{aw} \\), where:" + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.369, + 0.47, + 0.389 + ], + "angle": 0, + "content": "\\[\nL _ {a w} = L _ {a w} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} + L _ {a w} ^ {\\left(^ {*} \\mathrm {t}, ^ {*} \\mathrm {f}\\right)}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.399, + 0.314, + 0.415 + ], + "angle": 0, + "content": "Then given views \\((^{*}\\mathrm{f},^{*}\\mathrm{t})\\) , we have:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.427, + 0.475, + 0.479 + ], + "angle": 0, + "content": "\\[\nL _ {a w} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\log \\left(S _ {i}\\right) - \\omega \\left(^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathrm {i}}, ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathrm {i}}\\right) \\cdot \\left\\langle^ {*} \\mathrm {z} _ {\\mathbf {f}} ^ {\\mathrm {i}}, ^ {*} \\mathrm {z} _ {\\mathbf {t}} ^ {\\mathrm {i}} \\right\\rangle / \\tau \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.481, + 0.47, + 0.512 + ], + "angle": 0, + "content": "where the definition of \\( S_{i} \\) is the same as Equation 4. Here we implement the weighting function as:" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.521, + 0.469, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\omega \\left(^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}}, ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}}\\right) = \\frac {\\exp \\left(\\left\\langle {} ^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}} , ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}} / \\sigma \\right\\rangle\\right)}{\\mathbb {E} _ {i} \\left[ \\exp \\left(\\left\\langle {} ^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}} , ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}} / \\sigma \\right\\rangle\\right) \\right]}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.469, + 0.673 + ], + "angle": 0, + "content": "where the higher textual similarity pseudo-pair has, the more learning signal the pseudo-pair needs to be provided, and vice versa. In this case, our multiview alignment is semantics-aware, which is different from existing multiview alignment methods [43, 51] that evenly align multiview data with different semantic similarities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Video-text Modal Alignment. Until now, although the above statement provides a seemingly finalized solution in the case where the multiview pseudo-pair semantic information is not exactly the same, it is not data-efficient for every first-person sample. This is because it cannot help first-person videos in pseudo-pairs with low semantic similarities gain learning signals from others." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In order to permit all first-person videos to obtain knowledge from samples with different views or modalities, we employ video-text contrastive alignment to make the model training more data-efficient. As we mentioned before that every first-person and third-person video has an accurate textual description of their semantic information, this multimodal alignment can further help the neural network learn useful knowledge from these phrases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "Technically, given a batch of \\(N\\) normalized first-person and third-person features \\(\\{\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}\\) and \\(\\{\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}\\), and their corresponding normalized textual description vectors \\(\\{\\mathbf{d}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{d}_{\\mathbf{f}}^{\\mathbf{N}}\\}\\) and \\(\\{\\mathbf{d}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{d}_{\\mathbf{t}}^{\\mathbf{N}}\\}\\), the multimodal contrastive alignment loss \\((L_{m})\\) for both first-person videos and third-person videos is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.188, + 0.892, + 0.211 + ], + "angle": 0, + "content": "\\[\nL _ {m} = L _ {d c} ^ {\\left(\\mathbf {z} _ {\\mathrm {f}}, \\mathbf {d} _ {\\mathrm {f}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {d} _ {\\mathrm {f}}, \\mathbf {z} _ {\\mathrm {f}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {z} _ {\\mathrm {t}}, \\mathbf {d} _ {\\mathrm {t}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {d} _ {\\mathrm {t}}, \\mathbf {z} _ {\\mathrm {t}}\\right)}. \\tag {11}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.216, + 0.799, + 0.233 + ], + "angle": 0, + "content": "3.4. Training and Evaluation Pipelines" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.239, + 0.892, + 0.315 + ], + "angle": 0, + "content": "The two proposed cross-view and cross-modal losses, along with the task-specific losses for both first-person videos \\((L_{f})\\) and third-person videos \\((L_{t})\\), are combined together during the training procedure to construct the final training loss:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.324, + 0.892, + 0.341 + ], + "angle": 0, + "content": "\\[\n\\mathbb {L} = L _ {f} + w _ {t} \\cdot L _ {t} + w _ {a w} \\cdot L _ {a w} + w _ {m} \\cdot L _ {m}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.515 + ], + "angle": 0, + "content": "Note that our model is trained in multiple stages. First, both first-person and third-person video encoders are initialized by weights pretrained on Kinetics-400 [16]. Then we train the third-person video encoder and task-specific head on the third-person video dataset with third-person video task-specific loss \\((L_{t})\\) only. Next, we load this trained weight for the third-person video encoder and task-specific head and do training for the whole framework with the overall loss in Equation 12. Finally, we evaluate the first-person video performance of our method using the first-person video encoder and task-specific head." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.576 + ], + "angle": 0, + "content": "The specific task for both first-person and third-person videos we discussed in this paper is video classification. Therefore, both \\( L_{f} \\) and \\( L_{t} \\) are classification losses; \\( w_{t} \\), \\( w_{aw} \\), and \\( w_{m} \\) are the loss weights." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.588, + 0.634, + 0.605 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.613, + 0.693, + 0.629 + ], + "angle": 0, + "content": "4.1. Experiment Settings" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.608, + 0.65 + ], + "angle": 0, + "content": "4.1.1 Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.689 + ], + "angle": 0, + "content": "In this section, we introduce the standard benchmarks we used for evaluation in the experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.81 + ], + "angle": 0, + "content": "LEMMA [15] contains 648 third-person videos and 445 first-person videos. Among them, 136 activities were performed in kitchens, and the remaining 188 were in the living rooms. It contains 25 verb classes, 64 noun classes, and 863 action classes in their action recognition task, and includes not only single-agent but also multi-agent videos. We utilize single-agent third-person videos only as our unpaired third-person samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Charades-Ego [39, 40] contains 68,536 activity instances in paired 68.8 hours of first-person and third-person videos. It includes 157 action classes. We only utilize first-person videos during training and inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "EPIC-Kitchens [4] is a large-scale egocentric video benchmark recorded in kitchen environments. It contains" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3311" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "55 hours of video with a total of 39.6K action segments and is labeled with 352 object and 125 verb classes." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.123, + 0.47, + 0.169 + ], + "angle": 0, + "content": "EPIC-Kitchens-100 [5] extends EPIC-Kitchens [4] to 100 hours and 89,977 action segments. We employ this as well as EPIC-Kitchens [4] to validate our approach." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.194, + 0.254, + 0.208 + ], + "angle": 0, + "content": "4.1.2 Baseline Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.22, + 0.468, + 0.265 + ], + "angle": 0, + "content": "We compare the proposed approach with the following baseline methods, including typical multiview representation learning methods:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.267, + 0.468, + 0.311 + ], + "angle": 0, + "content": "FPV Only is trained with first-person (FPV) video data only. Its framework is composed of first-person video encoder and first-person video classification head." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.468, + 0.432 + ], + "angle": 0, + "content": "Typical CL is widely employed for view- or modal-invariant contrastive learning (CL) [43, 54], and vision-language models [32, 48, 21, 49, 24, 55]. Here we implement it with the loss function in Equation 6. Similar to our framework, videos from different views are fed to different encoders. We employ the same pseudo-pair construction method and the same inference strategy as our framework for this baseline method." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.435, + 0.468, + 0.51 + ], + "angle": 0, + "content": "Triplet is another widely used multiview representation learning method [51, 39]. We employ the same implementation protocol following [51]. Moreover, we leverage this method to tackle our problem following the same procedures as \"Typical CL\"." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.536, + 0.295, + 0.55 + ], + "angle": 0, + "content": "4.1.3 Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.468, + 0.787 + ], + "angle": 0, + "content": "To ensure fairness, we keep all hyperparameters the exact same for all baselines and our method. For Charades-Ego [39, 40], we use the base learning rate of 0.25, batch size of 32 and maximum epoch of 60. For EPIC-Kitchens [4] and EPIC-Kitchens-100 [5], we use the base learning rate of 0.01, weight decay of 0.0001, batch size of 64 and maximum epoch of 30. Following [22], all models are trained using the stochastic gradient descent optimizer [1] with the momentum of 0.9. For Charades-Ego [39, 40], we use the cosine learning rate decay. For EPIC-Kitchens [4] and EPIC-Kitchens-100 [5], we use sequential learning rate decay. The backbones we use are ResNet-3D-50 [13] and SlowFast [8]. More details about the implementation of backbones will be provided in the following experimental sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.334, + 0.817 + ], + "angle": 0, + "content": "4.2. Validity of Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Table 1 shows the performance of different training strategies, where all methods are implemented with the ResNet-3D-50 [13] encoder. Our proposed method outperforms the \"FPV only\" baseline model on both Charades-Ego and EPIC-Kitchens \\((+1.6\\%)\\) mAP on Charades-Ego," + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.089, + 0.885, + 0.183 + ], + "angle": 0, + "content": "
DatasetC-EgoEK-55 (Verb)EK-55 (Noun)
EvaluationsmAP (%)Top-1 acc. (%)Top-5 acc. (%)Top-1 acc. (%)Top-5 acc. (%)
FPV Only24.761.187.145.870.4
Typical CL25.160.586.245.368.6
Triplet25.261.586.845.769.7
SUM-L (Ours)26.362.387.247.370.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.192, + 0.892, + 0.234 + ], + "angle": 0, + "content": "Table 1. Comparison with baseline methods. The backbone we use is R3D-50 [13] for all methods. \"C-Ego\" denotes Charades-Ego [39] dataset and \"EK-55\" denotes EPIC-Kitchens [4] dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.262, + 0.892, + 0.323 + ], + "angle": 0, + "content": "and \\(+1.2\\% / + 1.5\\%\\) on EPIC-Kitchens verbs/nouns top-1 accuracies). This demonstrates that under partially similar semantics situations, with our method, the third-person videos can help to improve first-person video representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.893, + 0.596 + ], + "angle": 0, + "content": "Moreover, different from our method, previous multiview learning methods (\"Typical CL\" and \"Triplet\") cannot bring significant and consistent improvement compared with \"FPV only\". For example, \"Typical CL\" brings only \\(0.4\\%\\) improvement on Charades-Ego (far less than ours) and even deteriorates performance on EPIC-Kitchens. Instead, our proposed method outperforms existing alignment methods up to \\(+1.2\\%\\) mAP on Charades-Ego and \\(+1.8\\% / + 2.0\\%\\) on EPIC-Kitchens verbs/nouns top-1 accuracies. We believe this is due to the following reasons. (1) Our method semantics-awarely aligns unpaired data, instead of evenly aligning pseudo-pairs with different semantic similarities. (2) Our method filters the negative effects caused by multiview pseudo-pairs of low semantic similarity. This is different from typical multiview methods which naively align all the pairs. (3) Our method permits all first-person videos to obtain knowledge from samples with different views or modalities, which improves data efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.824 + ], + "angle": 0, + "content": "We further verify the effectiveness of our proposed method with a larger backbone, SlowFast [8], as the encoder, and we compare with recent state-of-the-art methods on three popular egocentric action recognition benchmarks, Charades-Ego [39], EPIC-Kitchens [4], and EPIC-Kitchens-100 [5]. Note that evaluation scores of state-of-the-arts are reported directly from their paper. The experimental results employing SlowFast [8] encoder confirm the following findings. (1) Our method is effective for cross-view pseudo-pair alignment when there is only partially same multiview semantics. (2) Compared with existing multiview alignment methods, the improvement based on \"FPV Only\" of our method is still more significant and consistent. Next, we analyze the important details of the experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparison on Charades-Ego Table 2 demonstrates the effectiveness of our method for cross-view pseudopair alignment when there is only partially same semantics. Note that our method and Ego-Exo [22] complement each other. Thus, we can also incorporate our method into Ego" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3312" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.089, + 0.422, + 0.287 + ], + "angle": 0, + "content": "
MethodologymAP (%)
state-of-the-artsActor [39]20.0
SSDA [3]23.1
I3D [22]25.8
Ego-Exo [22]28.7
Ego-Exo* [22]30.1
w/o “EE”FPV Only27.4
Typical CL27.9
Triplet28.1
SUM-L (Ours)28.5
w/ “EE”FPV Only29.5
Typical CL29.1
Triplet28.6
SUM-L (Ours)30.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.296, + 0.47, + 0.354 + ], + "angle": 0, + "content": "Table 2. Comparison on Charades-Ego. Our method and all baseline methods are implemented with SlowFast-R101 [8] backbone. \"EE\" denotes training based on pretrained weights provided by [22]." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.367, + 0.465, + 0.535 + ], + "angle": 0, + "content": "
MethodologyVerb (%)Noun (%)
state-of-the-artsSlowFast-R50 [8]64.148.6
Ego-Exo [22]66.049.4
Ego-Exo* [22]66.449.8
w/o “EE”FPV Only63.148.4
Typical CL63.949.6
Triplet63.948.8
SUM-L (Ours)65.049.5
w/ “EE”FPV Only65.849.5
Typical CL63.848.4
Triplet63.949.6
SUM-L (Ours)66.750.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.599 + ], + "angle": 0, + "content": "Table 3. Comparison on EPIC-Kitchens. The accuracies are measured by top-1 verb & noun classification accuracies. Our method and all baseline methods are implemented with SlowFast-R50 [8] backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.469, + 0.687 + ], + "angle": 0, + "content": "Exo [22]. As shown in Table 2, based on pretrained weight on [22], our proposed method further improves the performance of \"FPV only\" by \\(1.2\\%\\) mAP, and achieves a new state-of-the-art on Charades-Ego [39]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.824 + ], + "angle": 0, + "content": "Comparison on EPIC-Kitchens As we can see from Table 3, our method still brings clear improvement compared with \"FPV Only\" method \\((+1.9\\% / +1.1\\%\\) verbs/nouns top-1 accuracies). Furthermore, with the help of pretrained weights from [22], our method still outperforms most state-of-the-art methodologies, which indicates the effectiveness of our method. Last but not least, our method outperforms existing alignment methods up to \\(+2.9\\% / +1.8\\%\\) of verbs/nouns top-1 accuracies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Comparison on EPIC-Kitchens-100 As shown in table 4, our method also obtains competitive results on EPIC-Kitchens-100 [5] dataset when trained based on weights from [22]. It is worth noting that our method gains the first place in noun accuracy and third place in verb accu" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.088, + 0.89, + 0.201 + ], + "angle": 0, + "content": "
MethodologyVerb (%)Noun (%)
state-of-the-artsTSN [45]60.246.0
TSM [23]67.949.0
TempAgg [36]59.945.1
Ego-Exo [22]67.052.9
Ego-Exo* [22]67.552.9
IPL [47]68.651.2
w/ “EE”SUM-L (Ours)67.053.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.208, + 0.892, + 0.265 + ], + "angle": 0, + "content": "Table 4. Comparison on EPIC-Kitchens-100 with state-of-the-arts that implement CNN backbone. The accuracies are measured by top-1 verb & noun classification accuracies. We implement SlowFast-R101 [8] backbone." + }, + { + "type": "table", + "bbox": [ + 0.607, + 0.28, + 0.782, + 0.361 + ], + "angle": 0, + "content": "
LaLawLmmAP (%)
×××24.7
×✓×25.6
×✓✓26.3
✓×✓26.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.369, + 0.892, + 0.426 + ], + "angle": 0, + "content": "Table 5. Different training task combinations of our proposed method. Combining semantics-aware unpaired cross-view alignment with video-text alignment, our method clearly improves egocentric classification performance on the Charades-Ego dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.455, + 0.892, + 0.484 + ], + "angle": 0, + "content": "racy compared with state-of-the-art methodologies which employ convolutional neural network backbones." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.501, + 0.665, + 0.515 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.526, + 0.892, + 0.572 + ], + "angle": 0, + "content": "In this section, we conduct the ablation studies on Charades-Ego [39] dataset. The backbone we employ is ResNet-3D-50 [13]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.602, + 0.81, + 0.617 + ], + "angle": 0, + "content": "4.3.1 Impact of Different Alignment Tasks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The experiment results are shown in Table 5. We find our proposed unpaired cross-view alignment method itself brings \\(0.9\\%\\) mAP improvement comparing with the \"FPV Only\" method. It denotes that the method can help learn useful knowledge from unpaired third-person view samples when the cross-view semantic information is not identical. Moreover, our proposed video-text modal alignment method further boosts first-person performance by \\(0.7\\%\\) mAP compared with implementation with cross-view alignment only. We think this is because the proposed video-text modal alignment ensures the alignment of all first-person video samples, and further improves the semantics utilization for both first-person and third-person videos. Besides, implementing our cross-view alignment without semantic weighting causes a slight \\(0.2\\%\\) drop, which manifests the usefulness of knowledge from the large language model. This knowledge provides a reference to measure the semantic similarity between cross-view videos." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3313" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.095, + 0.345, + 0.108 + ], + "angle": 0, + "content": "First-person frame heatmaps from \"FPV Only\"" + }, + { + "type": "image", + "bbox": [ + 0.105, + 0.111, + 0.227, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.23, + 0.111, + 0.355, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.365, + 0.095, + 0.6, + 0.107 + ], + "angle": 0, + "content": "First-person frame heatmaps from our method" + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.111, + 0.482, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.111, + 0.611, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.623, + 0.095, + 0.863, + 0.107 + ], + "angle": 0, + "content": "Third-person frame heatmaps from our method" + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.111, + 0.744, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.111, + 0.874, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.213, + 0.227, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.23, + 0.213, + 0.355, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.213, + 0.482, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.213, + 0.61, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.213, + 0.745, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.748, + 0.213, + 0.874, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.322, + 0.227, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.23, + 0.322, + 0.354, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.322, + 0.482, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.322, + 0.61, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.322, + 0.745, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.748, + 0.322, + 0.873, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.438, + 0.894, + 0.467 + ], + "angle": 0, + "content": "Figure 4. Comparison of class activation map visualizations between the \"FPV Only\" method and our method. The cross-view similar semantics for data in the first row is \"holding pan\". The cross-view similar semantics for data in the second and third rows is \"take\"." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.491, + 0.409, + 0.507 + ], + "angle": 0, + "content": "4.3.2 Impact of Third-person View Backbone" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.611 + ], + "angle": 0, + "content": "The original setup of the third-person video encoder is mentioned in Sec. 3.4. Here we study the effect of other intuitively feasible third-person video encoder implementations. The experiment results are shown in Table 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.903 + ], + "angle": 0, + "content": "First, we load the pretrained weight of the third-person video and freeze it during the training process for the whole framework shown in Figure 3. We find freezing the third-person video encoder causes a \\(0.5\\%\\) mAP drop compared with the original setup. This indicates that for the pretrained third-person video encoder, allowing training more parameters can better help first-person video learn effective information from third-person samples. Moreover, naively employing shared encoder weights for different views, which follows [2], can cause clear performance drop (\\(1.0\\%\\) mAP drop) to first-person video learning. We think this is due to the big variances between first-person and third-person samples. Finally, the same initialization (pretrained on Kinetics-400 [16]) for both first-person and third-person video encoders causes a slight \\(0.2\\%\\) mAP drop. It indicates that for the third-person video encoder, employing existing weights of third-person samples for optimization has a positive effect on first-person video learning." + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.488, + 0.872, + 0.569 + ], + "angle": 0, + "content": "
SetupmAP (%)
Freezed TPV Backbone25.8
Shared Multiview Encoder Weights25.3
Same Initialization with FPV Encoder26.1
Original26.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.577, + 0.892, + 0.606 + ], + "angle": 0, + "content": "Table 6. Impact of different third-person video encoder implementations. The \"Original\" setup is described in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.638, + 0.648 + ], + "angle": 0, + "content": "4.4. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.794 + ], + "angle": 0, + "content": "We visualize the first-person and third-person video class activation maps (CAM) [56] on EPIC-Kitchens [4] dataset. We employ first-person video encoder weights from \"FPV Only\" method (61.1% & 45.8% top-1 verb & noun accuracies) and our method (62.3% & 47.3% top-1 verb & noun accuracies). As shown in the first and second columns of Figure 4, comparing with \"FPV Only\" method, our method can help the model be more responsive to positive spatiotemporal locations of video clips." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Moreover, from the third column of Figure 4, we find that our model also has a strong response to the third-person video locations which have overlapped semantics with the first-person video (see bright green bounding boxes of Figure 4). It shows that our method successfully utilizes knowledge from unpaired third-person videos to help learn first-person video representations." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3314" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.205, + 0.106 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.468, + 0.237 + ], + "angle": 0, + "content": "In this paper, we tackle a new problem in first-person and third-person video learning and propose SUM-L. It can distill knowledge from unpaired, cross-dataset third-person video without exact same multiview semantic information. Our experiments show the validity of our proposed method. Besides, under the more challenging scenario than typical paired or unpaired multimodal or multiview learning, our method outperforms existing view-alignment methods." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.238, + 0.468, + 0.327 + ], + "angle": 0, + "content": "However, improvements from SUM-L are not very significant. One possible reason is due to the relatively small amount of third-person data. It will be interesting to explore more unpaired third-person video datasets. It will be also interesting to study more downstream tasks, such as unpaired cross-view retrieval. We leave these as future work." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.329, + 0.468, + 0.405 + ], + "angle": 0, + "content": "Acknowledgements This work is partially supported by National Science Foundation (NSF) CMMI-2039857, and University of Delaware Research Foundation (UDRF). We thank Florian Schroff and Hartwig Adam from Google Research for supporting this project." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.419, + 0.174, + 0.435 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.445, + 0.468, + 0.473 + ], + "angle": 0, + "content": "[1] Shun-ichi Amari. Backpropagation and stochastic gradient descent method. Neurocomputing, 5(4-5):185-196, 1993. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.476, + 0.468, + 0.53 + ], + "angle": 0, + "content": "[2] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. 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In this case, the model aims to learn comprehensive multiview representations while the cross-view semantic information exhibits variations. We propose Semantics-based Unpaired Multiview Learning (SUM-L) to tackle this unpaired multiview learning problem. The key idea is to build cross-view pseudopairs and do view-invariant alignment by leveraging the semantic information of videos. To facilitate the data efficiency of multiview learning, we further perform video-text alignment for first-person and third-person videos, to fully leverage the semantic knowledge to improve video representations. Extensive experiments on multiple benchmark datasets verify the effectiveness of our framework. Our method also outperforms multiple existing view-alignment methods, under the more challenging scenario than typical paired or unpaired multimodal or multiview learning. Our code is available at https://github.com/wqtwjt1996/SUM-I. + +# 1. Introduction + +Recent years have witnessed a tremendous increase in the research regarding egocentric video understanding and learning [22, 26, 20, 41, 29, 30, 14, 42, 7, 31, 46, 9]. In parallel, a recent study [22] verifies that the activity of third-person videos in fact positively inform first-person video learning. Early works [39, 51] of egocentric video learning and understanding pay a lot of attention to paired multiview data representation learning. However, synchronized first-person and third-person video pairs are difficult to collect. This severely limits the data scale and scope of multiview learning for egocentric data. + +Recently, egocentric video datasets [4, 5, 10] with larger scale have become available. However, since head-mounted cameras were not available until recent years, very few first-person videos have paired third-person videos [15]. + +![](images/11a6d8139ef43551d88f6400794318ec6f6ded9d1228e8e3930b331978303bf6.jpg) +Figure 1. (a) The typical multiview video learning method learns view-invariant representations from paired first-person and third-person videos. (b) Recent multimodal study [19] is interested in the alignment between unpaired samples which share identical semantics. In this paper, we study a more challenging scenario than existing works: unpaired multiview samples alignment with partially similar semantics, such as videos with (c) the same verb only, or (d) the same object only. The verb-object phrases above the video clips denote the semantic information of videos. + +Fortunately, there exist third-person videos from different datasets [12, 16]. It is worth noting that unpaired third-person videos are relatively easier to capture and obtain compared with paired ones. Therefore, in this paper, we study an interesting yet seldom investigated problem: how to leverage unpaired third-person videos to help egocentric video learning? + +Unpaired multiview learning is rarely studied. While recent works [28, 27, 38, 53] study the scenario where paired modalities are missing. But they do not leverage the potential of unpaired data from diverse datasets. Moreover, to align the unpaired multimodal samples, Kundu et al. [19] propose one relation distillation method to align the unpaired samples. They assume that unpaired data need to share identical semantic information. However, in the unpaired first-person and third-person video learning scenario, for the vast majority of egocentric videos, it is almost impossible to mine the third-person samples with identical + +![](images/cb778db156a5a2f6d004a5483ee0b2d46aa73fb607ca0235f5f3bef666eeb58a.jpg) +Semantic Similarity Statistics of Multiview Pseudo Pairs (%) +Figure 2. Statistics of semantic similarities between the first-person samples in [39, 4, 5] and the most similar single-agent third-person samples they can find from the LEMMA [15] dataset. The semantic similarity is the cosine distance between textual phrase vectors of videos encoded by a large language model [34]. Each bar in the figure represents the percentage of action classes that fall within one semantic similarity range (e.g., [0.8, 1.0]) in an egocentric dataset compared to all action classes in this dataset. In all of the three popular egocentric datasets, very few first-person videos are able to find third-person videos with identical semantics. For reference, in the studies for paired multiview data [43, 39, 51, 54], all the semantic similarities of cross-view data pairs are (or very close to) “1.0”. + +semantics. The only alternatives are partially semantics-similar unpaired third-person videos. For example, for one egocentric video clip with "cut watermelon" semantics, the most similar third-person video is those with "cut lemon" (same verb) or "eat watermelon" (same object) semantics. Examples and comparisons between our scenario and typical paired or unpaired multiview or multimodal learning are shown in Figure 1, and we display comprehensive semantics similarity statistics of multiview data studied in this paper (see Figure 2). Therefore, how to employ the unpaired and partially semantics-similar third-person views to help first-person view learning is an open problem. Intuitively, compared with previous research, our setting is more challenging since most of the first-person videos only share partially similar semantics with third-person views. + +In this paper, we are interested in view-invariant alignment in the partially semantics-similar pseudo-pair setting. We propose Semantics-based Unpaired Multiview Learning (SUM-L), where multiview pseudo-pairs with high similarities are aligned in a semantics-aware manner. In our method, we also employ video-text alignment to permit all first-person videos to obtain knowledge from samples with different views or modalities. We highlight that our SUM-L employs the large language model [34] to help align cross-view and cross-modality data. This is different from [22], which proposes to distill beneficial knowledge from unpaired third-person videos [16], mostly with the help of the off-the-shelf image recognition model [6] and hand-object detector [37]. Moreover, our method is better than existing view-invariant alignment methods, such as typical contrastive learning [44, 43, 50, 54] and triplet loss based learning [35, 51] in the new setting, since they naively reduce multiview feature distance, which leads to learning suboptimal first-person representations. + +To summarize, our contribution is three-fold: + +- We study a new problem: in the partially semantics-similar multiview setting, how to leverage unpaired third-person videos to help first-person video learning. +- We propose SUM-L for this new problem, which is more effective than existing view-alignment methods in our unpaired multiview learning scenario. +- Experiments in standard benchmark datasets including Charades-Ego [39], EPIC-Kitchens [4], and EPIC-Kitchens-100 [5] validate the competitive performance of our methods over existing view-alignment methods including typical contrastive learning and triplet loss based learning. + +# 2. Related Work + +# 2.1. Egocentric Video Learning + +The study of egocentric video learning has attracted a large volume of attention in recent years. To verify the quality of model learning, there are multiple egocentric-related tasks, including action recognition [29, 42, 46], video summarization [26, 20], engagement detection [41], scene affordance [30], gaze prediction [14], video question answering [7], and activity anticipation [31, 9]. Nevertheless, aforementioned studies utilize knowledge from first-person videos only [26, 20, 41, 14, 42, 31, 9], or make use of extra supervision from off-the-shelf models [29, 30], or naively pretrain on large-scale datasets [7, 46]. More specifically, these methods do not consider tackling the domain mismatch between different multiview datasets or abstaining from extra supervision. Recently, Li et al. [22] try to discover latent signals in the third-person videos which + +are predictive of key egocentric-specific properties. Similar to [29, 30], however, this method heavily relies on the knowledge of off-the-shelf image or video models. + +# 2.2. First-person Video Representation Learning with Joint Third-person Videos + +The paired first-person and third-person videos, as descriptions of the same actions from different perspectives, are potential to provide beneficial knowledge to each other, yielding more generalizable joint representations. Recent studies [39, 40] propose paired first-person and third-person datasets and learn joint representations of multiview videos. They show the potential of transferring knowledge from third-person videos to first-person videos. In order to extract more useful joint knowledge, Yu et al. [52] make use of the shared attention regions between different views with spatial constraints, in a self-supervised and simultaneous manner. However, nowadays very few first-person videos have paired third-person videos [15]. Moreover, we find that existing multiview methods [44, 43, 35, 51] learn suboptimal first-person representations from unpaired third-person videos, that are relatively easier to capture and obtain compared with paired data. Instead, our methodology can better distill unpaired third-person video knowledge to first-person videos, and it is more efficient and applicable than existing view-alignment methods [44, 43, 35, 51]. + +# 2.3. Unpaired Multimodal Learning + +Due to the relatively difficult acquisition of paired multimodal samples and the limited number of them, unpaired multimodal learning recently has attracted the interest of some researchers. Kundu et al. [19] treat unpaired 3D pose learning as a self-supervised adaptation problem that aims to transfer the task knowledge from a labeled paired source domain to a completely unpaired target domain. Next, it proposes the relation distillation method to align the unpaired target videos and unpaired 3D pose sequences. However, this work makes the assumption that there exist semantically identical cross-modal data in the unpaired target domain, which is almost unavailable in unpaired first- and third-person video representation learning. Therefore, in this paper, we study a more challenging problem: how to make unpaired multiview alignment in an incompletely semantics-similar situation. + +# 3. Methodology + +In the following sections, we first describe our pseudopair construction method (Sec. 3.1). Then we introduce the traditional contrastive framework for paired multiview or multimodal data (Sec. 3.2). Next, we introduce our proposed cross-view and cross-modal methods (Sec. 3.3). Finally, we present our full training and evaluation pipeline in Sec. 3.4. + +# 3.1. Semantics-based Pseudo-pair Mining + +Different from the previous joint multiview learning approaches [39, 40, 51], first-person and third-person videos are not automatically paired in the cross-dataset setting. Hence, before model training, it is essential to construct pseudo multiview pairs. + +Every first-person and third-person video has one unique textual narration, which describes the key semantic information of it. Therefore, we employ the large language model [34] to encode textual narrations of multiview videos to vectors. Then for each first-person video, we mine the third-person video with the highest textual semantic similarity from the third-person video pool to construct the pseudopair. We compute the cosine distance between cross-view video textual narrations as the criterion of semantic similarity between first-person and third-person video clips: + +$$ +\operatorname {s i m} _ {\left(\mathbf {z} _ {\mathrm {f}}, \mathbf {z} _ {\mathrm {t}}\right)} = \frac {\mathbf {d} _ {\mathrm {f}} \cdot \mathbf {d} _ {\mathrm {t}}}{\| \mathbf {d} _ {\mathrm {f}} \| \cdot \| \mathbf {d} _ {\mathrm {t}} \|}, \tag {1} +$$ + +where $\mathbf{d_f}$ and $\mathbf{d_t}$ denote textual narration vectors of first-person and third-person videos, respectively. + +# 3.2. Typical Multiview Alignment + +Existing contrastive-based multiview [43, 25, 54] or multimodal [21, 49, 32, 48] methods propose to learn the view-invariant representations via the alignment of the features. Specifically, they learn to align features between different views or modalities by minimizing the distance between paired samples and maximizing the distance between negative (unpaired) samples. + +Given a batch of $N$ normalized first-person features $\{\mathbf{z}_{\mathbf{f}}^{\mathbf{1}},\dots,\mathbf{z}_{\mathbf{f}}^{\mathbf{N}}\}$ and third-person features $\{\mathbf{z}_{\mathbf{t}}^{\mathbf{1}},\dots,\mathbf{z}_{\mathbf{t}}^{\mathbf{N}}\}$ , these methods calculate the contrastive multiview Info-NCE [43, 33] loss as: + +$$ +L _ {c} = L _ {c} ^ {(f, t)} + L _ {c} ^ {(t, f)}, \tag {2} +$$ + +$$ +L _ {c} ^ {\left(v _ {1}, v _ {2}\right)} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \log \left[ \frac {\exp \left(\left\langle \mathbf {z} _ {\mathbf {v} _ {1}} ^ {\mathbf {i}} , \mathbf {z} _ {\mathbf {v} _ {2}} ^ {\mathbf {i}} \right\rangle / \tau\right)}{\exp \left(\left\langle \mathbf {z} _ {\mathbf {v} _ {1}} ^ {\mathbf {i}} , \mathbf {z} _ {\mathbf {v} _ {2}} ^ {\mathbf {i}} \right\rangle / \tau\right) + S _ {i}} \right], \tag {3} +$$ + +$$ +S _ {i} = \sum_ {j \in [ 1, N ], j \neq i} e x p \left(\left\langle \mathbf {z} _ {\mathbf {v} _ {1}} ^ {\mathbf {i}}, \mathbf {z} _ {\mathbf {v} _ {2}} ^ {\mathbf {j}} \right\rangle / \tau\right), \tag {4} +$$ + +where $\mathbf{v}_1$ and $\mathbf{v}_2$ are two views and $\tau$ is the temperature. + +For an input video clip $\mathbf{x}_{\mathbf{v_k}}$ , its normalized feature representation is extracted by the encoder $f_{v_k}(\cdot)$ following the projection network $h_{v_k}(\cdot)$ as: + +$$ +\mathbf {z} _ {\mathbf {v} _ {\mathbf {k}}} = \frac {h _ {v _ {k}} \left(A v g P o o l \left(f _ {v _ {k}} \left(\mathbf {x} _ {\mathbf {v} _ {\mathbf {k}}}\right)\right)\right)}{\| h _ {v _ {k}} \left(A v g P o o l \left(f _ {v _ {k}} \left(\mathbf {x} _ {\mathbf {v} _ {\mathbf {k}}}\right)\right)\right) \| _ {2}}. \tag {5} +$$ + +The optimization of contrastive learning methods is often computationally expensive, which requires large batch + +![](images/b8a7d8cb2e698ee65391a298bf0b9b214b534ca325145b30c60261e58512e41b.jpg) +Figure 3. Illustration of our framework. First, one batch (batch size = 4) of multiview pseudo-pairs is built from unpaired first-person and third-person videos. The pseudo-pairs are built based on mining the most semantics-similar third-person video for every first-person video. During training, the global features for multiview alignment $(z_{f}, z_{t})$ are extracted by their corresponding encoders following the projection networks $(h_{f}, h_{t})$ . In addition, textual features $(d_{f}, d_{t})$ are extracted by a large language model [34] from textual narrations of first-person and third-person videos. The semantic similarity between $d_{f}$ and $d_{t}$ is calculated to filter out the multiview pseudo-pairs with low semantic similarity. Then the multiview pairs with high semantic similarity are employed to learn the view-invariant representations with the contrastive learning method. To further improve data efficiency, we employ all the first-person and third-person videos in the batch to learn contrastive multimodal relations. Finally, the task-specific heads $(g_{f}, g_{t})$ for both first-person and third-person videos are trained to make predictions for their corresponding downstream tasks. During testing, we only use the first-person encoder and task-specific head $(g_{f})$ to make first-person video predictions. + +sizes and a large volume of training epochs. To tackle this issue, Yeh et al. [50] refine the InfoNCE loss by removing the positive term from the denominator in Equation 3 and significantly improve the learning efficiency. To be specific, it rewrites Equation 3 as: + +$$ +L _ {d c} ^ {\left(v _ {1}, v _ {2}\right)} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \log \left[ \exp \left(\left\langle \mathbf {z} _ {\mathbf {v} _ {1}} ^ {\mathrm {i}}, \mathbf {z} _ {\mathbf {v} _ {2}} ^ {\mathrm {i}} \right\rangle / \tau\right) / S _ {i} \right]. \tag {6} +$$ + +In the context of our unpaired multiview learning, we argue that directly employing the above vanilla contrastive learning method is an obstacle that hinders further acquiring knowledge from third-person videos. On the one hand, in the unpaired first-person and third-person video multiview representation learning, very few first-person views have the third-person views which share the same semantics. On the other hand, typical contrastive multiview representation learning is designed to minimize the feature distance between samples with identical semantics, e.g., recordings from camera views for the same objects [18], images with different visuals belonging to the same class [17], one image applying multiple independent [2] or asymmetric [11] + +data augmentations, etc. Naively reducing multiview feature distances in our unpaired multiview learning will lead to learning suboptimal first-person video representations. + +# 3.3. Semantics-based Multiview Learning + +To address the above issue, we propose a representation learning method, namely Semantics-based Unpaired Multiview Learning. We employ contrastive alignment as a tool to align the unpaired multiview videos. Different from existing view-alignment methods, our proposed method introduces the following two novel alignments: (1) Semantics-based Cross-view Alignment, which employs the semantic information from textual narrations of multiview videos to align high-similar unpaired data; (2) Video-text Modal Alignment, which permits all first-person video obtaining knowledge from samples with different views or modalities. Next, we will introduce our framework step-by-step. + +Semantics-based Cross-view Alignment. We believe that pseudo-pairs with high semantic similarities can better help learn view-invariant information in first-person videos. Therefore, given cross-view pseudo-pairs $(\mathbf{z_f},\mathbf{z_t})$ in one + +batch, we pick pseudo-pairs $(^{*}\mathbf{z}_{\mathbf{f}},^{*}\mathbf{z}_{\mathbf{t}})$ which have relatively higher textual semantic similarities. Then the first-person and third-person video alignment loss $(L_{a})$ is defined as the decoupled contrastive learning loss [50] of high semantic similarity pseudo-pairs: + +$$ +L _ {a} = L _ {d c} ^ {\left(^ {*} \mathrm {f}, ^ {*} \mathrm {t}\right)} + L _ {d c} ^ {\left(^ {*} \mathrm {t}, ^ {*} \mathrm {f}\right)}. \tag {7} +$$ + +Besides, we hypothesize that the employed large language model [34] is a strong teacher: by encoding the textual descriptions of videos into vectors, the similarity between vectors implicitly provides a reference to measure the semantic similarity between videos. To make better use of these textual descriptions of first-person and third-person videos, inspired by [50], we further introduce a semantic-based weighting function for the positive pseudopairs. More specifically, we first rewrite our cross-view video alignment loss $L_{a}$ in Equation 7 as $L_{aw}$ , where: + +$$ +L _ {a w} = L _ {a w} ^ {\left(^ {*} \mathrm {f}, ^ {*} \mathrm {t}\right)} + L _ {a w} ^ {\left(^ {*} \mathrm {t}, ^ {*} \mathrm {f}\right)}. \tag {8} +$$ + +Then given views $(^{*}\mathrm{f},^{*}\mathrm{t})$ , we have: + +$$ +L _ {a w} ^ {\left(^ {*} \mathrm {f}, ^ {*} \mathrm {t}\right)} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left[ \log \left(S _ {i}\right) - \omega \left(^ {*} \mathrm {d} _ {\mathbf {f}} ^ {\mathrm {i}}, ^ {*} \mathrm {d} _ {\mathbf {t}} ^ {\mathrm {i}}\right) \cdot \left\langle^ {*} \mathrm {z} _ {\mathbf {f}} ^ {\mathrm {i}}, ^ {*} \mathrm {z} _ {\mathbf {t}} ^ {\mathrm {i}} \right\rangle / \tau \right], \tag {9} +$$ + +where the definition of $S_{i}$ is the same as Equation 4. Here we implement the weighting function as: + +$$ +\omega \left(^ {*} \mathrm {d} _ {\mathbf {f}} ^ {\mathbf {i}}, ^ {*} \mathrm {d} _ {\mathbf {t}} ^ {\mathbf {i}}\right) = \frac {\exp \left(\left\langle {} ^ {*} \mathrm {d} _ {\mathbf {f}} ^ {\mathbf {i}} , ^ {*} \mathrm {d} _ {\mathbf {t}} ^ {\mathbf {i}} / \sigma \right\rangle\right)}{\mathbb {E} _ {i} \left[ \exp \left(\left\langle {} ^ {*} \mathrm {d} _ {\mathbf {f}} ^ {\mathbf {i}} , ^ {*} \mathrm {d} _ {\mathbf {t}} ^ {\mathbf {i}} / \sigma \right\rangle\right) \right]}, \tag {10} +$$ + +where the higher textual similarity pseudo-pair has, the more learning signal the pseudo-pair needs to be provided, and vice versa. In this case, our multiview alignment is semantics-aware, which is different from existing multiview alignment methods [43, 51] that evenly align multiview data with different semantic similarities. + +Video-text Modal Alignment. Until now, although the above statement provides a seemingly finalized solution in the case where the multiview pseudo-pair semantic information is not exactly the same, it is not data-efficient for every first-person sample. This is because it cannot help first-person videos in pseudo-pairs with low semantic similarities gain learning signals from others. + +In order to permit all first-person videos to obtain knowledge from samples with different views or modalities, we employ video-text contrastive alignment to make the model training more data-efficient. As we mentioned before that every first-person and third-person video has an accurate textual description of their semantic information, this multimodal alignment can further help the neural network learn useful knowledge from these phrases. + +Technically, given a batch of $N$ normalized first-person and third-person features $\{\mathbf{z}_{\mathbf{f}}^{\mathbf{1}},\dots,\mathbf{z}_{\mathbf{f}}^{\mathbf{N}}\}$ and $\{\mathbf{z}_{\mathbf{t}}^{\mathbf{1}},\dots,\mathbf{z}_{\mathbf{f}}^{\mathbf{N}}\}$ , and their corresponding normalized textual description vectors $\{\mathbf{d}_{\mathbf{f}}^{\mathbf{1}},\dots,\mathbf{d}_{\mathbf{f}}^{\mathbf{N}}\}$ and $\{\mathbf{d}_{\mathbf{t}}^{\mathbf{1}},\dots,\mathbf{d}_{\mathbf{t}}^{\mathbf{N}}\}$ , the multimodal contrastive alignment loss $(L_{m})$ for both first-person videos and third-person videos is defined as: + +$$ +L _ {m} = L _ {d c} ^ {\left(\mathbf {z} _ {\mathrm {f}}, \mathbf {d} _ {\mathrm {f}}\right)} + L _ {d c} ^ {\left(\mathbf {d} _ {\mathrm {f}}, \mathbf {z} _ {\mathrm {f}}\right)} + L _ {d c} ^ {\left(\mathbf {z} _ {\mathrm {t}}, \mathbf {d} _ {\mathrm {t}}\right)} + L _ {d c} ^ {\left(\mathbf {d} _ {\mathrm {t}}, \mathbf {z} _ {\mathrm {t}}\right)}. \tag {11} +$$ + +# 3.4. Training and Evaluation Pipelines + +The two proposed cross-view and cross-modal losses, along with the task-specific losses for both first-person videos $(L_{f})$ and third-person videos $(L_{t})$ , are combined together during the training procedure to construct the final training loss: + +$$ +\mathbb {L} = L _ {f} + w _ {t} \cdot L _ {t} + w _ {a w} \cdot L _ {a w} + w _ {m} \cdot L _ {m}. \tag {12} +$$ + +Note that our model is trained in multiple stages. First, both first-person and third-person video encoders are initialized by weights pretrained on Kinetics-400 [16]. Then we train the third-person video encoder and task-specific head on the third-person video dataset with third-person video task-specific loss $(L_{t})$ only. Next, we load this trained weight for the third-person video encoder and task-specific head and do training for the whole framework with the overall loss in Equation 12. Finally, we evaluate the first-person video performance of our method using the first-person video encoder and task-specific head. + +The specific task for both first-person and third-person videos we discussed in this paper is video classification. Therefore, both $L_{f}$ and $L_{t}$ are classification losses; $w_{t}$ , $w_{aw}$ , and $w_{m}$ are the loss weights. + +# 4. Experiments + +# 4.1. Experiment Settings + +# 4.1.1 Dataset + +In this section, we introduce the standard benchmarks we used for evaluation in the experiments. + +LEMMA [15] contains 648 third-person videos and 445 first-person videos. Among them, 136 activities were performed in kitchens, and the remaining 188 were in the living rooms. It contains 25 verb classes, 64 noun classes, and 863 action classes in their action recognition task, and includes not only single-agent but also multi-agent videos. We utilize single-agent third-person videos only as our unpaired third-person samples. + +Charades-Ego [39, 40] contains 68,536 activity instances in paired 68.8 hours of first-person and third-person videos. It includes 157 action classes. We only utilize first-person videos during training and inference. + +EPIC-Kitchens [4] is a large-scale egocentric video benchmark recorded in kitchen environments. It contains + +55 hours of video with a total of 39.6K action segments and is labeled with 352 object and 125 verb classes. + +EPIC-Kitchens-100 [5] extends EPIC-Kitchens [4] to 100 hours and 89,977 action segments. We employ this as well as EPIC-Kitchens [4] to validate our approach. + +# 4.1.2 Baseline Methods + +We compare the proposed approach with the following baseline methods, including typical multiview representation learning methods: + +FPV Only is trained with first-person (FPV) video data only. Its framework is composed of first-person video encoder and first-person video classification head. + +Typical CL is widely employed for view- or modal-invariant contrastive learning (CL) [43, 54], and vision-language models [32, 48, 21, 49, 24, 55]. Here we implement it with the loss function in Equation 6. Similar to our framework, videos from different views are fed to different encoders. We employ the same pseudo-pair construction method and the same inference strategy as our framework for this baseline method. + +Triplet is another widely used multiview representation learning method [51, 39]. We employ the same implementation protocol following [51]. Moreover, we leverage this method to tackle our problem following the same procedures as "Typical CL". + +# 4.1.3 Implementation Details + +To ensure fairness, we keep all hyperparameters the exact same for all baselines and our method. For Charades-Ego [39, 40], we use the base learning rate of 0.25, batch size of 32 and maximum epoch of 60. For EPIC-Kitchens [4] and EPIC-Kitchens-100 [5], we use the base learning rate of 0.01, weight decay of 0.0001, batch size of 64 and maximum epoch of 30. Following [22], all models are trained using the stochastic gradient descent optimizer [1] with the momentum of 0.9. For Charades-Ego [39, 40], we use the cosine learning rate decay. For EPIC-Kitchens [4] and EPIC-Kitchens-100 [5], we use sequential learning rate decay. The backbones we use are ResNet-3D-50 [13] and SlowFast [8]. More details about the implementation of backbones will be provided in the following experimental sections. + +# 4.2. Validity of Proposed Method + +Table 1 shows the performance of different training strategies, where all methods are implemented with the ResNet-3D-50 [13] encoder. Our proposed method outperforms the "FPV only" baseline model on both Charades-Ego and EPIC-Kitchens $(+1.6\%)$ mAP on Charades-Ego, + +
DatasetC-EgoEK-55 (Verb)EK-55 (Noun)
EvaluationsmAP (%)Top-1 acc. (%)Top-5 acc. (%)Top-1 acc. (%)Top-5 acc. (%)
FPV Only24.761.187.145.870.4
Typical CL25.160.586.245.368.6
Triplet25.261.586.845.769.7
SUM-L (Ours)26.362.387.247.370.9
+ +Table 1. Comparison with baseline methods. The backbone we use is R3D-50 [13] for all methods. "C-Ego" denotes Charades-Ego [39] dataset and "EK-55" denotes EPIC-Kitchens [4] dataset. + +and $+1.2\% / + 1.5\%$ on EPIC-Kitchens verbs/nouns top-1 accuracies). This demonstrates that under partially similar semantics situations, with our method, the third-person videos can help to improve first-person video representations. + +Moreover, different from our method, previous multiview learning methods ("Typical CL" and "Triplet") cannot bring significant and consistent improvement compared with "FPV only". For example, "Typical CL" brings only $0.4\%$ improvement on Charades-Ego (far less than ours) and even deteriorates performance on EPIC-Kitchens. Instead, our proposed method outperforms existing alignment methods up to $+1.2\%$ mAP on Charades-Ego and $+1.8\% / + 2.0\%$ on EPIC-Kitchens verbs/nouns top-1 accuracies. We believe this is due to the following reasons. (1) Our method semantics-awarely aligns unpaired data, instead of evenly aligning pseudo-pairs with different semantic similarities. (2) Our method filters the negative effects caused by multiview pseudo-pairs of low semantic similarity. This is different from typical multiview methods which naively align all the pairs. (3) Our method permits all first-person videos to obtain knowledge from samples with different views or modalities, which improves data efficiency. + +We further verify the effectiveness of our proposed method with a larger backbone, SlowFast [8], as the encoder, and we compare with recent state-of-the-art methods on three popular egocentric action recognition benchmarks, Charades-Ego [39], EPIC-Kitchens [4], and EPIC-Kitchens-100 [5]. Note that evaluation scores of state-of-the-arts are reported directly from their paper. The experimental results employing SlowFast [8] encoder confirm the following findings. (1) Our method is effective for cross-view pseudo-pair alignment when there is only partially same multiview semantics. (2) Compared with existing multiview alignment methods, the improvement based on "FPV Only" of our method is still more significant and consistent. Next, we analyze the important details of the experiments. + +Comparison on Charades-Ego Table 2 demonstrates the effectiveness of our method for cross-view pseudopair alignment when there is only partially same semantics. Note that our method and Ego-Exo [22] complement each other. Thus, we can also incorporate our method into Ego + +
MethodologymAP (%)
state-of-the-artsActor [39]20.0
SSDA [3]23.1
I3D [22]25.8
Ego-Exo [22]28.7
Ego-Exo* [22]30.1
w/o “EE”FPV Only27.4
Typical CL27.9
Triplet28.1
SUM-L (Ours)28.5
w/ “EE”FPV Only29.5
Typical CL29.1
Triplet28.6
SUM-L (Ours)30.7
+ +Table 2. Comparison on Charades-Ego. Our method and all baseline methods are implemented with SlowFast-R101 [8] backbone. "EE" denotes training based on pretrained weights provided by [22]. + +
MethodologyVerb (%)Noun (%)
state-of-the-artsSlowFast-R50 [8]64.148.6
Ego-Exo [22]66.049.4
Ego-Exo* [22]66.449.8
w/o “EE”FPV Only63.148.4
Typical CL63.949.6
Triplet63.948.8
SUM-L (Ours)65.049.5
w/ “EE”FPV Only65.849.5
Typical CL63.848.4
Triplet63.949.6
SUM-L (Ours)66.750.2
+ +Exo [22]. As shown in Table 2, based on pretrained weight on [22], our proposed method further improves the performance of "FPV only" by $1.2\%$ mAP, and achieves a new state-of-the-art on Charades-Ego [39]. + +Comparison on EPIC-Kitchens As we can see from Table 3, our method still brings clear improvement compared with "FPV Only" method $(+1.9\% / +1.1\%$ verbs/nouns top-1 accuracies). Furthermore, with the help of pretrained weights from [22], our method still outperforms most state-of-the-art methodologies, which indicates the effectiveness of our method. Last but not least, our method outperforms existing alignment methods up to $+2.9\% / +1.8\%$ of verbs/nouns top-1 accuracies. + +Comparison on EPIC-Kitchens-100 As shown in table 4, our method also obtains competitive results on EPIC-Kitchens-100 [5] dataset when trained based on weights from [22]. It is worth noting that our method gains the first place in noun accuracy and third place in verb accu + +Table 3. Comparison on EPIC-Kitchens. The accuracies are measured by top-1 verb & noun classification accuracies. Our method and all baseline methods are implemented with SlowFast-R50 [8] backbone. + +
MethodologyVerb (%)Noun (%)
state-of-the-artsTSN [45]60.246.0
TSM [23]67.949.0
TempAgg [36]59.945.1
Ego-Exo [22]67.052.9
Ego-Exo* [22]67.552.9
IPL [47]68.651.2
w/ “EE”SUM-L (Ours)67.053.4
+ +Table 4. Comparison on EPIC-Kitchens-100 with state-of-the-arts that implement CNN backbone. The accuracies are measured by top-1 verb & noun classification accuracies. We implement SlowFast-R101 [8] backbone. + +
LaLawLmmAP (%)
×××24.7
×✓×25.6
×✓✓26.3
✓×✓26.1
+ +Table 5. Different training task combinations of our proposed method. Combining semantics-aware unpaired cross-view alignment with video-text alignment, our method clearly improves egocentric classification performance on the Charades-Ego dataset. + +racy compared with state-of-the-art methodologies which employ convolutional neural network backbones. + +# 4.3. Ablation Studies + +In this section, we conduct the ablation studies on Charades-Ego [39] dataset. The backbone we employ is ResNet-3D-50 [13]. + +# 4.3.1 Impact of Different Alignment Tasks + +The experiment results are shown in Table 5. We find our proposed unpaired cross-view alignment method itself brings $0.9\%$ mAP improvement comparing with the "FPV Only" method. It denotes that the method can help learn useful knowledge from unpaired third-person view samples when the cross-view semantic information is not identical. Moreover, our proposed video-text modal alignment method further boosts first-person performance by $0.7\%$ mAP compared with implementation with cross-view alignment only. We think this is because the proposed video-text modal alignment ensures the alignment of all first-person video samples, and further improves the semantics utilization for both first-person and third-person videos. Besides, implementing our cross-view alignment without semantic weighting causes a slight $0.2\%$ drop, which manifests the usefulness of knowledge from the large language model. This knowledge provides a reference to measure the semantic similarity between cross-view videos. + +![](images/4893ed8504c1e2be008de05734bf4b428554b7ee04efcb261dbe2014e8d98598.jpg) +First-person frame heatmaps from "FPV Only" + +![](images/a39c545060fe2122fa4c28d7efe85ea5663ce0b0e2c5a0ab2b31c97ecc8566ee.jpg) +First-person frame heatmaps from our method + +![](images/03f3b4c0b84f621f4178fc5da4b27766eb1c2ac4ecfb312f0b9c0c49bf7abac0.jpg) + +![](images/2f5a611efdd4bc6ba581b577847e89a7510b6ac9680873c0e6b2726b542c31d6.jpg) +Third-person frame heatmaps from our method + +![](images/0661c1ed5b9b94a4794ed9e4f7bc1ad55a44ccb466c32f7f5fa9fae7e235944c.jpg) + +![](images/821b24b956eb1adc563f4ae8a53c68203e964dfd5786cd7194bff875ec6d28a4.jpg) + +![](images/5481096a6acc31744e5ec2cdd54abf4943b4a1086e15e463ff8e75e2aca2427e.jpg) + +![](images/5b24d1052755c8de474d34b8928a8f60fab00d094ef0cf0082a237883ec823e4.jpg) + +![](images/2b8a3cb728af9692ff6f6cdb6602134dd2efecef19b0d0f206432c6b127548fe.jpg) + +![](images/0d9e16e5624f1ade00ed80cf7d3751b0be34b70c8246b34f5c61d32cef8441c7.jpg) + +![](images/2a0c985fa33df04f16f2e3cf9e0ad972d202672de48fc8030068096421c51b6f.jpg) + +![](images/32f23936d82ba7a88adf0775d09682da3e07c9e5ad54d6e8ec6a6ccda18c4a19.jpg) + +![](images/63c6de48fb055918a0e51ba026555385805012e0900a675fe933e3031f6587bc.jpg) +Figure 4. Comparison of class activation map visualizations between the "FPV Only" method and our method. The cross-view similar semantics for data in the first row is "holding pan". The cross-view similar semantics for data in the second and third rows is "take". + +![](images/75383de40adc9d6d5b901d26f23edfdd8e7beb0639ee8ec64c035295356af224.jpg) + +![](images/35e9c8c41ed28ad72c3348c6afea1915b584dac24dc72621e971155ad0bbc471.jpg) + +![](images/eefcefe7d0dfa58dc6f9ee637216db49be3ae2124d87f88e1f0b0a3e445a1e28.jpg) + +![](images/ab572a88bf961648c9c0400a185b5d0fae0f239649ed0c2acd450ca0578c0c9e.jpg) + +![](images/9efc0311a88430b460ad002c318eea4c8c4d44737e05f873d4f91b8b360527ba.jpg) + +# 4.3.2 Impact of Third-person View Backbone + +The original setup of the third-person video encoder is mentioned in Sec. 3.4. Here we study the effect of other intuitively feasible third-person video encoder implementations. The experiment results are shown in Table 6. + +First, we load the pretrained weight of the third-person video and freeze it during the training process for the whole framework shown in Figure 3. We find freezing the third-person video encoder causes a $0.5\%$ mAP drop compared with the original setup. This indicates that for the pretrained third-person video encoder, allowing training more parameters can better help first-person video learn effective information from third-person samples. Moreover, naively employing shared encoder weights for different views, which follows [2], can cause clear performance drop ( $1.0\%$ mAP drop) to first-person video learning. We think this is due to the big variances between first-person and third-person samples. Finally, the same initialization (pretrained on Kinetics-400 [16]) for both first-person and third-person video encoders causes a slight $0.2\%$ mAP drop. It indicates that for the third-person video encoder, employing existing weights of third-person samples for optimization has a positive effect on first-person video learning. + +
SetupmAP (%)
Freezed TPV Backbone25.8
Shared Multiview Encoder Weights25.3
Same Initialization with FPV Encoder26.1
Original26.3
+ +Table 6. Impact of different third-person video encoder implementations. The "Original" setup is described in Sec. 3.4. + +# 4.4. Visualization + +We visualize the first-person and third-person video class activation maps (CAM) [56] on EPIC-Kitchens [4] dataset. We employ first-person video encoder weights from "FPV Only" method (61.1% & 45.8% top-1 verb & noun accuracies) and our method (62.3% & 47.3% top-1 verb & noun accuracies). As shown in the first and second columns of Figure 4, comparing with "FPV Only" method, our method can help the model be more responsive to positive spatiotemporal locations of video clips. + +Moreover, from the third column of Figure 4, we find that our model also has a strong response to the third-person video locations which have overlapped semantics with the first-person video (see bright green bounding boxes of Figure 4). It shows that our method successfully utilizes knowledge from unpaired third-person videos to help learn first-person video representations. + +# 5. Conclusions + +In this paper, we tackle a new problem in first-person and third-person video learning and propose SUM-L. It can distill knowledge from unpaired, cross-dataset third-person video without exact same multiview semantic information. Our experiments show the validity of our proposed method. Besides, under the more challenging scenario than typical paired or unpaired multimodal or multiview learning, our method outperforms existing view-alignment methods. + +However, improvements from SUM-L are not very significant. One possible reason is due to the relatively small amount of third-person data. It will be interesting to explore more unpaired third-person video datasets. It will be also interesting to study more downstream tasks, such as unpaired cross-view retrieval. We leave these as future work. + +Acknowledgements This work is partially supported by National Science Foundation (NSF) CMMI-2039857, and University of Delaware Research Foundation (UDRF). We thank Florian Schroff and Hartwig Adam from Google Research for supporting this project. + +# References + +[1] Shun-ichi Amari. Backpropagation and stochastic gradient descent method. Neurocomputing, 5(4-5):185-196, 1993. 6 +[2] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In International conference on machine learning, pages 1597-1607. PMLR, 2020. 4, 8 +[3] Jinwoo Choi, Gaurav Sharma, Manmohan Chandraker, and Jia-Bin Huang. Unsupervised and semi-supervised domain adaptation for action recognition from drones. 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In this case, the model aims to learn comprehensive multiview representations while the cross-view semantic information exhibits variations. We propose Semantics-based Unpaired Multiview Learning (SUM-L) to tackle this unpaired multiview learning problem. The key idea is to build cross-view pseudopairs and do view-invariant alignment by leveraging the semantic information of videos. To facilitate the data efficiency of multiview learning, we further perform video-text alignment for first-person and third-person videos, to fully leverage the semantic knowledge to improve video representations. Extensive experiments on multiple benchmark datasets verify the effectiveness of our framework. Our method also outperforms multiple existing view-alignment methods, under the more challenging scenario than typical paired or unpaired multimodal or multiview learning. Our code is available at https://github.com/wqtwjt1996/SUM-I." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 511, + 128, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 128, + 523 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 128, + 523 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 664 + ], + "type": "text", + "content": "Recent years have witnessed a tremendous increase in the research regarding egocentric video understanding and learning [22, 26, 20, 41, 29, 30, 14, 42, 7, 31, 46, 9]. In parallel, a recent study [22] verifies that the activity of third-person videos in fact positively inform first-person video learning. Early works [39, 51] of egocentric video learning and understanding pay a lot of attention to paired multiview data representation learning. However, synchronized first-person and third-person video pairs are difficult to collect. This severely limits the data scale and scope of multiview learning for egocentric data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Recently, egocentric video datasets [4, 5, 10] with larger scale have become available. However, since head-mounted cameras were not available until recent years, very few first-person videos have paired third-person videos [15]." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 230, + 542, + 369 + ], + "blocks": [ + { + "bbox": [ + 310, + 230, + 542, + 369 + ], + "lines": [ + { + "bbox": [ + 310, + 230, + 542, + 369 + ], + "spans": [ + { + "bbox": [ + 310, + 230, + 542, + 369 + ], + "type": "image", + "image_path": "11a6d8139ef43551d88f6400794318ec6f6ded9d1228e8e3930b331978303bf6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 374, + 547, + 475 + ], + "lines": [ + { + "bbox": [ + 304, + 374, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 547, + 475 + ], + "type": "text", + "content": "Figure 1. (a) The typical multiview video learning method learns view-invariant representations from paired first-person and third-person videos. (b) Recent multimodal study [19] is interested in the alignment between unpaired samples which share identical semantics. In this paper, we study a more challenging scenario than existing works: unpaired multiview samples alignment with partially similar semantics, such as videos with (c) the same verb only, or (d) the same object only. The verb-object phrases above the video clips denote the semantic information of videos." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 496, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 547, + 581 + ], + "type": "text", + "content": "Fortunately, there exist third-person videos from different datasets [12, 16]. It is worth noting that unpaired third-person videos are relatively easier to capture and obtain compared with paired ones. Therefore, in this paper, we study an interesting yet seldom investigated problem: how to leverage unpaired third-person videos to help egocentric video learning?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "Unpaired multiview learning is rarely studied. While recent works [28, 27, 38, 53] study the scenario where paired modalities are missing. But they do not leverage the potential of unpaired data from diverse datasets. Moreover, to align the unpaired multimodal samples, Kundu et al. [19] propose one relation distillation method to align the unpaired samples. They assume that unpaired data need to share identical semantic information. However, in the unpaired first-person and third-person video learning scenario, for the vast majority of egocentric videos, it is almost impossible to mine the third-person samples with identical" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3307" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 95, + 521, + 199 + ], + "blocks": [ + { + "bbox": [ + 180, + 81, + 414, + 92 + ], + "lines": [ + { + "bbox": [ + 180, + 81, + 414, + 92 + ], + "spans": [ + { + "bbox": [ + 180, + 81, + 414, + 92 + ], + "type": "text", + "content": "Semantic Similarity Statistics of Multiview Pseudo Pairs (%)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 70, + 95, + 521, + 199 + ], + "lines": [ + { + "bbox": [ + 70, + 95, + 521, + 199 + ], + "spans": [ + { + "bbox": [ + 70, + 95, + 521, + 199 + ], + "type": "image", + "image_path": "cb778db156a5a2f6d004a5483ee0b2d46aa73fb607ca0235f5f3bef666eeb58a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 547, + 276 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 547, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 547, + 276 + ], + "type": "text", + "content": "Figure 2. Statistics of semantic similarities between the first-person samples in [39, 4, 5] and the most similar single-agent third-person samples they can find from the LEMMA [15] dataset. The semantic similarity is the cosine distance between textual phrase vectors of videos encoded by a large language model [34]. Each bar in the figure represents the percentage of action classes that fall within one semantic similarity range (e.g., [0.8, 1.0]) in an egocentric dataset compared to all action classes in this dataset. In all of the three popular egocentric datasets, very few first-person videos are able to find third-person videos with identical semantics. For reference, in the studies for paired multiview data [43, 39, 51, 54], all the semantic similarities of cross-view data pairs are (or very close to) “1.0”." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 295, + 289, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 289, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 289, + 475 + ], + "type": "text", + "content": "semantics. The only alternatives are partially semantics-similar unpaired third-person videos. For example, for one egocentric video clip with \"cut watermelon\" semantics, the most similar third-person video is those with \"cut lemon\" (same verb) or \"eat watermelon\" (same object) semantics. Examples and comparisons between our scenario and typical paired or unpaired multiview or multimodal learning are shown in Figure 1, and we display comprehensive semantics similarity statistics of multiview data studied in this paper (see Figure 2). Therefore, how to employ the unpaired and partially semantics-similar third-person views to help first-person view learning is an open problem. Intuitively, compared with previous research, our setting is more challenging since most of the first-person videos only share partially similar semantics with third-person views." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we are interested in view-invariant alignment in the partially semantics-similar pseudo-pair setting. We propose Semantics-based Unpaired Multiview Learning (SUM-L), where multiview pseudo-pairs with high similarities are aligned in a semantics-aware manner. In our method, we also employ video-text alignment to permit all first-person videos to obtain knowledge from samples with different views or modalities. We highlight that our SUM-L employs the large language model [34] to help align cross-view and cross-modality data. This is different from [22], which proposes to distill beneficial knowledge from unpaired third-person videos [16], mostly with the help of the off-the-shelf image recognition model [6] and hand-object detector [37]. Moreover, our method is better than existing view-invariant alignment methods, such as typical contrastive learning [44, 43, 50, 54] and triplet loss based learning [35, 51] in the new setting, since they naively reduce multiview feature distance, which leads to learning suboptimal first-person representations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 318, + 295, + 500, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 295, + 500, + 306 + ], + "spans": [ + { + "bbox": [ + 318, + 295, + 500, + 306 + ], + "type": "text", + "content": "To summarize, our contribution is three-fold:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 316, + 545, + 482 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 316, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 316, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 317, + 316, + 545, + 354 + ], + "type": "text", + "content": "- We study a new problem: in the partially semantics-similar multiview setting, how to leverage unpaired third-person videos to help first-person video learning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 363, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 363, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 317, + 363, + 545, + 399 + ], + "type": "text", + "content": "- We propose SUM-L for this new problem, which is more effective than existing view-alignment methods in our unpaired multiview learning scenario." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 410, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 410, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 317, + 410, + 545, + 482 + ], + "type": "text", + "content": "- Experiments in standard benchmark datasets including Charades-Ego [39], EPIC-Kitchens [4], and EPIC-Kitchens-100 [5] validate the competitive performance of our methods over existing view-alignment methods including typical contrastive learning and triplet loss based learning." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 495, + 392, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 392, + 507 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 392, + 507 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 514, + 455, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 455, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 455, + 528 + ], + "type": "text", + "content": "2.1. Egocentric Video Learning" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "The study of egocentric video learning has attracted a large volume of attention in recent years. To verify the quality of model learning, there are multiple egocentric-related tasks, including action recognition [29, 42, 46], video summarization [26, 20], engagement detection [41], scene affordance [30], gaze prediction [14], video question answering [7], and activity anticipation [31, 9]. Nevertheless, aforementioned studies utilize knowledge from first-person videos only [26, 20, 41, 14, 42, 31, 9], or make use of extra supervision from off-the-shelf models [29, 30], or naively pretrain on large-scale datasets [7, 46]. More specifically, these methods do not consider tackling the domain mismatch between different multiview datasets or abstaining from extra supervision. Recently, Li et al. [22] try to discover latent signals in the third-person videos which" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3308" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "are predictive of key egocentric-specific properties. Similar to [29, 30], however, this method heavily relies on the knowledge of off-the-shelf image or video models." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 114, + 287, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 114, + 287, + 139 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 287, + 139 + ], + "type": "text", + "content": "2.2. First-person Video Representation Learning with Joint Third-person Videos" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 144, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 289, + 384 + ], + "type": "text", + "content": "The paired first-person and third-person videos, as descriptions of the same actions from different perspectives, are potential to provide beneficial knowledge to each other, yielding more generalizable joint representations. Recent studies [39, 40] propose paired first-person and third-person datasets and learn joint representations of multiview videos. They show the potential of transferring knowledge from third-person videos to first-person videos. In order to extract more useful joint knowledge, Yu et al. [52] make use of the shared attention regions between different views with spatial constraints, in a self-supervised and simultaneous manner. However, nowadays very few first-person videos have paired third-person videos [15]. Moreover, we find that existing multiview methods [44, 43, 35, 51] learn suboptimal first-person representations from unpaired third-person videos, that are relatively easier to capture and obtain compared with paired data. Instead, our methodology can better distill unpaired third-person video knowledge to first-person videos, and it is more efficient and applicable than existing view-alignment methods [44, 43, 35, 51]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 390, + 218, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 218, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 218, + 403 + ], + "type": "text", + "content": "2.3. Unpaired Multimodal Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 408, + 289, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 289, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 289, + 601 + ], + "type": "text", + "content": "Due to the relatively difficult acquisition of paired multimodal samples and the limited number of them, unpaired multimodal learning recently has attracted the interest of some researchers. Kundu et al. [19] treat unpaired 3D pose learning as a self-supervised adaptation problem that aims to transfer the task knowledge from a labeled paired source domain to a completely unpaired target domain. Next, it proposes the relation distillation method to align the unpaired target videos and unpaired 3D pose sequences. However, this work makes the assumption that there exist semantically identical cross-modal data in the unpaired target domain, which is almost unavailable in unpaired first- and third-person video representation learning. Therefore, in this paper, we study a more challenging problem: how to make unpaired multiview alignment in an incompletely semantics-similar situation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 609, + 129, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 129, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 129, + 624 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 712 + ], + "type": "text", + "content": "In the following sections, we first describe our pseudopair construction method (Sec. 3.1). Then we introduce the traditional contrastive framework for paired multiview or multimodal data (Sec. 3.2). Next, we introduce our proposed cross-view and cross-modal methods (Sec. 3.3). Finally, we present our full training and evaluation pipeline in Sec. 3.4." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 504, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 504, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 504, + 85 + ], + "type": "text", + "content": "3.1. Semantics-based Pseudo-pair Mining" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 149 + ], + "type": "text", + "content": "Different from the previous joint multiview learning approaches [39, 40, 51], first-person and third-person videos are not automatically paired in the cross-dataset setting. Hence, before model training, it is essential to construct pseudo multiview pairs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 150, + 546, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 150, + 546, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 150, + 546, + 270 + ], + "type": "text", + "content": "Every first-person and third-person video has one unique textual narration, which describes the key semantic information of it. Therefore, we employ the large language model [34] to encode textual narrations of multiview videos to vectors. Then for each first-person video, we mine the third-person video with the highest textual semantic similarity from the third-person video pool to construct the pseudopair. We compute the cosine distance between cross-view video textual narrations as the criterion of semantic similarity between first-person and third-person video clips:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 370, + 275, + 545, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 275, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 370, + 275, + 545, + 301 + ], + "type": "interline_equation", + "content": "\\operatorname {s i m} _ {\\left(\\mathbf {z} _ {\\mathrm {f}}, \\mathbf {z} _ {\\mathrm {t}}\\right)} = \\frac {\\mathbf {d} _ {\\mathrm {f}} \\cdot \\mathbf {d} _ {\\mathrm {t}}}{\\| \\mathbf {d} _ {\\mathrm {f}} \\| \\cdot \\| \\mathbf {d} _ {\\mathrm {t}} \\|}, \\tag {1}", + "image_path": "3c754d82b7d3db9b46a9acdedbbfa74ffaf32e3423bd43b406b28993f47bbd7f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 307, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 331 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 307, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{d_f}" + }, + { + "bbox": [ + 304, + 307, + 545, + 331 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 307, + 545, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{d_t}" + }, + { + "bbox": [ + 304, + 307, + 545, + 331 + ], + "type": "text", + "content": " denote textual narration vectors of first-person and third-person videos, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 338, + 466, + 351 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 338, + 466, + 351 + ], + "spans": [ + { + "bbox": [ + 305, + 338, + 466, + 351 + ], + "type": "text", + "content": "3.2. Typical Multiview Alignment" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 356, + 545, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 545, + 439 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 545, + 439 + ], + "type": "text", + "content": "Existing contrastive-based multiview [43, 25, 54] or multimodal [21, 49, 32, 48] methods propose to learn the view-invariant representations via the alignment of the features. Specifically, they learn to align features between different views or modalities by minimizing the distance between paired samples and maximizing the distance between negative (unpaired) samples." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "type": "text", + "content": "Given a batch of " + }, + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "type": "text", + "content": " normalized first-person features " + }, + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}" + }, + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "type": "text", + "content": " and third-person features " + }, + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{N}}\\}" + }, + { + "bbox": [ + 306, + 440, + 545, + 487 + ], + "type": "text", + "content": ", these methods calculate the contrastive multiview Info-NCE [43, 33] loss as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 381, + 486, + 545, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 486, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 381, + 486, + 545, + 500 + ], + "type": "interline_equation", + "content": "L _ {c} = L _ {c} ^ {(f, t)} + L _ {c} ^ {(t, f)}, \\tag {2}", + "image_path": "c6da4b4d566af846a22ca97794ad6be70da6569527f4fcb70c73d44134db95ba.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 520, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 520, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 315, + 520, + 545, + 563 + ], + "type": "interline_equation", + "content": "L _ {c} ^ {\\left(v _ {1}, v _ {2}\\right)} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\log \\left[ \\frac {\\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}} , \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {i}} \\right\\rangle / \\tau\\right)}{\\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}} , \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {i}} \\right\\rangle / \\tau\\right) + S _ {i}} \\right], \\tag {3}", + "image_path": "8e93f91f6c127a4b65467fffa54f515e461c372af48897e017b31941f6bc5167.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 347, + 572, + 545, + 600 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 572, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 347, + 572, + 545, + 600 + ], + "type": "interline_equation", + "content": "S _ {i} = \\sum_ {j \\in [ 1, N ], j \\neq i} e x p \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathbf {i}}, \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathbf {j}} \\right\\rangle / \\tau\\right), \\tag {4}", + "image_path": "595069c3452266a497250a4416542639bd3bca4f7aec9375911579dbd2b28d73.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "spans": [ + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_1" + }, + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_2" + }, + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "type": "text", + "content": " are two views and " + }, + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 603, + 535, + 614 + ], + "type": "text", + "content": " is the temperature." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "type": "text", + "content": "For an input video clip " + }, + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathbf{v_k}}" + }, + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "type": "text", + "content": ", its normalized feature representation is extracted by the encoder " + }, + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "type": "inline_equation", + "content": "f_{v_k}(\\cdot)" + }, + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "type": "text", + "content": " following the projection network " + }, + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "type": "inline_equation", + "content": "h_{v_k}(\\cdot)" + }, + { + "bbox": [ + 304, + 615, + 545, + 651 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 344, + 657, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 657, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 344, + 657, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {\\mathbf {v} _ {\\mathbf {k}}} = \\frac {h _ {v _ {k}} \\left(A v g P o o l \\left(f _ {v _ {k}} \\left(\\mathbf {x} _ {\\mathbf {v} _ {\\mathbf {k}}}\\right)\\right)\\right)}{\\| h _ {v _ {k}} \\left(A v g P o o l \\left(f _ {v _ {k}} \\left(\\mathbf {x} _ {\\mathbf {v} _ {\\mathbf {k}}}\\right)\\right)\\right) \\| _ {2}}. \\tag {5}", + "image_path": "09a052c8a247b117e635abf1b1cf58caf562b8ae97d01d34d0ff70ce201bdb64.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "The optimization of contrastive learning methods is often computationally expensive, which requires large batch" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3309" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 544, + 312 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 544, + 312 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 544, + 312 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 544, + 312 + ], + "type": "image", + "image_path": "b8a7d8cb2e698ee65391a298bf0b9b214b534ca325145b30c60261e58512e41b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "lines": [ + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "text", + "content": "Figure 3. Illustration of our framework. First, one batch (batch size = 4) of multiview pseudo-pairs is built from unpaired first-person and third-person videos. The pseudo-pairs are built based on mining the most semantics-similar third-person video for every first-person video. During training, the global features for multiview alignment " + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "inline_equation", + "content": "(z_{f}, z_{t})" + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "text", + "content": " are extracted by their corresponding encoders following the projection networks " + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "inline_equation", + "content": "(h_{f}, h_{t})" + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "text", + "content": ". In addition, textual features " + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "inline_equation", + "content": "(d_{f}, d_{t})" + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "text", + "content": " are extracted by a large language model [34] from textual narrations of first-person and third-person videos. The semantic similarity between " + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "inline_equation", + "content": "d_{f}" + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "inline_equation", + "content": "d_{t}" + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "text", + "content": " is calculated to filter out the multiview pseudo-pairs with low semantic similarity. Then the multiview pairs with high semantic similarity are employed to learn the view-invariant representations with the contrastive learning method. To further improve data efficiency, we employ all the first-person and third-person videos in the batch to learn contrastive multimodal relations. Finally, the task-specific heads " + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "inline_equation", + "content": "(g_{f}, g_{t})" + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "text", + "content": " for both first-person and third-person videos are trained to make predictions for their corresponding downstream tasks. During testing, we only use the first-person encoder and task-specific head " + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "inline_equation", + "content": "(g_{f})" + }, + { + "bbox": [ + 46, + 320, + 548, + 431 + ], + "type": "text", + "content": " to make first-person video predictions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 450, + 288, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 288, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 288, + 510 + ], + "type": "text", + "content": "sizes and a large volume of training epochs. To tackle this issue, Yeh et al. [50] refine the InfoNCE loss by removing the positive term from the denominator in Equation 3 and significantly improve the learning efficiency. To be specific, it rewrites Equation 3 as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 515, + 287, + 557 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 515, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 56, + 515, + 287, + 557 + ], + "type": "interline_equation", + "content": "L _ {d c} ^ {\\left(v _ {1}, v _ {2}\\right)} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\log \\left[ \\exp \\left(\\left\\langle \\mathbf {z} _ {\\mathbf {v} _ {1}} ^ {\\mathrm {i}}, \\mathbf {z} _ {\\mathbf {v} _ {2}} ^ {\\mathrm {i}} \\right\\rangle / \\tau\\right) / S _ {i} \\right]. \\tag {6}", + "image_path": "5abf4f6339cd7b653f0050d72edb0f5fcf8ec1de09efcb43ec631c7e5a45f13d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "In the context of our unpaired multiview learning, we argue that directly employing the above vanilla contrastive learning method is an obstacle that hinders further acquiring knowledge from third-person videos. On the one hand, in the unpaired first-person and third-person video multiview representation learning, very few first-person views have the third-person views which share the same semantics. On the other hand, typical contrastive multiview representation learning is designed to minimize the feature distance between samples with identical semantics, e.g., recordings from camera views for the same objects [18], images with different visuals belonging to the same class [17], one image applying multiple independent [2] or asymmetric [11]" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 450, + 547, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 547, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 547, + 487 + ], + "type": "text", + "content": "data augmentations, etc. Naively reducing multiview feature distances in our unpaired multiview learning will lead to learning suboptimal first-person video representations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 499, + 503, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 499, + 503, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 499, + 503, + 513 + ], + "type": "text", + "content": "3.3. Semantics-based Multiview Learning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 520, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 664 + ], + "type": "text", + "content": "To address the above issue, we propose a representation learning method, namely Semantics-based Unpaired Multiview Learning. We employ contrastive alignment as a tool to align the unpaired multiview videos. Different from existing view-alignment methods, our proposed method introduces the following two novel alignments: (1) Semantics-based Cross-view Alignment, which employs the semantic information from textual narrations of multiview videos to align high-similar unpaired data; (2) Video-text Modal Alignment, which permits all first-person video obtaining knowledge from samples with different views or modalities. Next, we will introduce our framework step-by-step." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Semantics-based Cross-view Alignment. We believe that pseudo-pairs with high semantic similarities can better help learn view-invariant information in first-person videos. Therefore, given cross-view pseudo-pairs " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "(\\mathbf{z_f},\\mathbf{z_t})" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " in one" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3310" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "batch, we pick pseudo-pairs " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "(^{*}\\mathbf{z}_{\\mathbf{f}},^{*}\\mathbf{z}_{\\mathbf{t}})" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " which have relatively higher textual semantic similarities. Then the first-person and third-person video alignment loss " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "(L_{a})" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " is defined as the decoupled contrastive learning loss [50] of high semantic similarity pseudo-pairs:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 116, + 140, + 287, + 157 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 140, + 287, + 157 + ], + "spans": [ + { + "bbox": [ + 116, + 140, + 287, + 157 + ], + "type": "interline_equation", + "content": "L _ {a} = L _ {d c} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} + L _ {d c} ^ {\\left(^ {*} \\mathrm {t}, ^ {*} \\mathrm {f}\\right)}. \\tag {7}", + "image_path": "6a6053d873e58eea91c6a5cea6dd2b4ecdf0da15efc57a39796522fc6394f88a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 164, + 288, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 164, + 288, + 284 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 288, + 284 + ], + "type": "text", + "content": "Besides, we hypothesize that the employed large language model [34] is a strong teacher: by encoding the textual descriptions of videos into vectors, the similarity between vectors implicitly provides a reference to measure the semantic similarity between videos. To make better use of these textual descriptions of first-person and third-person videos, inspired by [50], we further introduce a semantic-based weighting function for the positive pseudopairs. More specifically, we first rewrite our cross-view video alignment loss " + }, + { + "bbox": [ + 46, + 164, + 288, + 284 + ], + "type": "inline_equation", + "content": "L_{a}" + }, + { + "bbox": [ + 46, + 164, + 288, + 284 + ], + "type": "text", + "content": " in Equation 7 as " + }, + { + "bbox": [ + 46, + 164, + 288, + 284 + ], + "type": "inline_equation", + "content": "L_{aw}" + }, + { + "bbox": [ + 46, + 164, + 288, + 284 + ], + "type": "text", + "content": ", where:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 114, + 292, + 287, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 292, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 114, + 292, + 287, + 308 + ], + "type": "interline_equation", + "content": "L _ {a w} = L _ {a w} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} + L _ {a w} ^ {\\left(^ {*} \\mathrm {t}, ^ {*} \\mathrm {f}\\right)}. \\tag {8}", + "image_path": "f9bd529edb8d679177e9ed5a688e4fb6a1e31303f18a0dde0fc770c0b5aa22a9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 316, + 192, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 192, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 192, + 328 + ], + "type": "text", + "content": "Then given views " + }, + { + "bbox": [ + 47, + 316, + 192, + 328 + ], + "type": "inline_equation", + "content": "(^{*}\\mathrm{f},^{*}\\mathrm{t})" + }, + { + "bbox": [ + 47, + 316, + 192, + 328 + ], + "type": "text", + "content": " , we have:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 338, + 290, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 338, + 290, + 379 + ], + "spans": [ + { + "bbox": [ + 47, + 338, + 290, + 379 + ], + "type": "interline_equation", + "content": "L _ {a w} ^ {\\left(^ {*} \\mathrm {f}, ^ {*} \\mathrm {t}\\right)} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left[ \\log \\left(S _ {i}\\right) - \\omega \\left(^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathrm {i}}, ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathrm {i}}\\right) \\cdot \\left\\langle^ {*} \\mathrm {z} _ {\\mathbf {f}} ^ {\\mathrm {i}}, ^ {*} \\mathrm {z} _ {\\mathbf {t}} ^ {\\mathrm {i}} \\right\\rangle / \\tau \\right], \\tag {9}", + "image_path": "8927a60df4e42dc9aeaef311e647c189f1c54d64efa4db92e1268849151b3fb5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 380, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 287, + 405 + ], + "type": "text", + "content": "where the definition of " + }, + { + "bbox": [ + 47, + 380, + 287, + 405 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 47, + 380, + 287, + 405 + ], + "type": "text", + "content": " is the same as Equation 4. Here we implement the weighting function as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 412, + 287, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 412, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 69, + 412, + 287, + 455 + ], + "type": "interline_equation", + "content": "\\omega \\left(^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}}, ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}}\\right) = \\frac {\\exp \\left(\\left\\langle {} ^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}} , ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}} / \\sigma \\right\\rangle\\right)}{\\mathbb {E} _ {i} \\left[ \\exp \\left(\\left\\langle {} ^ {*} \\mathrm {d} _ {\\mathbf {f}} ^ {\\mathbf {i}} , ^ {*} \\mathrm {d} _ {\\mathbf {t}} ^ {\\mathbf {i}} / \\sigma \\right\\rangle\\right) \\right]}, \\tag {10}", + "image_path": "ce0768cf8954e08b78dacacba325cef113f5177375c5a7f977cfc7c12a1576b3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "content": "where the higher textual similarity pseudo-pair has, the more learning signal the pseudo-pair needs to be provided, and vice versa. In this case, our multiview alignment is semantics-aware, which is different from existing multiview alignment methods [43, 51] that evenly align multiview data with different semantic similarities." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": "Video-text Modal Alignment. Until now, although the above statement provides a seemingly finalized solution in the case where the multiview pseudo-pair semantic information is not exactly the same, it is not data-efficient for every first-person sample. This is because it cannot help first-person videos in pseudo-pairs with low semantic similarities gain learning signals from others." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 714 + ], + "type": "text", + "content": "In order to permit all first-person videos to obtain knowledge from samples with different views or modalities, we employ video-text contrastive alignment to make the model training more data-efficient. As we mentioned before that every first-person and third-person video has an accurate textual description of their semantic information, this multimodal alignment can further help the neural network learn useful knowledge from these phrases." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "Technically, given a batch of " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " normalized first-person and third-person features " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{z}_{\\mathbf{f}}^{\\mathbf{N}}\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", and their corresponding normalized textual description vectors " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{d}_{\\mathbf{f}}^{\\mathbf{1}},\\dots,\\mathbf{d}_{\\mathbf{f}}^{\\mathbf{N}}\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{d}_{\\mathbf{t}}^{\\mathbf{1}},\\dots,\\mathbf{d}_{\\mathbf{t}}^{\\mathbf{N}}\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", the multimodal contrastive alignment loss " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "(L_{m})" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " for both first-person videos and third-person videos is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 148, + 545, + 167 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 148, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 318, + 148, + 545, + 167 + ], + "type": "interline_equation", + "content": "L _ {m} = L _ {d c} ^ {\\left(\\mathbf {z} _ {\\mathrm {f}}, \\mathbf {d} _ {\\mathrm {f}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {d} _ {\\mathrm {f}}, \\mathbf {z} _ {\\mathrm {f}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {z} _ {\\mathrm {t}}, \\mathbf {d} _ {\\mathrm {t}}\\right)} + L _ {d c} ^ {\\left(\\mathbf {d} _ {\\mathrm {t}}, \\mathbf {z} _ {\\mathrm {t}}\\right)}. \\tag {11}", + "image_path": "f555a654ab9a5a391ba0bee785d67c7b1cb2e5386afa93e5cdae360183aa5c26.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 171, + 488, + 184 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 171, + 488, + 184 + ], + "spans": [ + { + "bbox": [ + 306, + 171, + 488, + 184 + ], + "type": "text", + "content": "3.4. Training and Evaluation Pipelines" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 189, + 545, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 189, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 304, + 189, + 545, + 249 + ], + "type": "text", + "content": "The two proposed cross-view and cross-modal losses, along with the task-specific losses for both first-person videos " + }, + { + "bbox": [ + 304, + 189, + 545, + 249 + ], + "type": "inline_equation", + "content": "(L_{f})" + }, + { + "bbox": [ + 304, + 189, + 545, + 249 + ], + "type": "text", + "content": " and third-person videos " + }, + { + "bbox": [ + 304, + 189, + 545, + 249 + ], + "type": "inline_equation", + "content": "(L_{t})" + }, + { + "bbox": [ + 304, + 189, + 545, + 249 + ], + "type": "text", + "content": ", are combined together during the training procedure to construct the final training loss:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 325, + 256, + 545, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 256, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 325, + 256, + 545, + 270 + ], + "type": "interline_equation", + "content": "\\mathbb {L} = L _ {f} + w _ {t} \\cdot L _ {t} + w _ {a w} \\cdot L _ {a w} + w _ {m} \\cdot L _ {m}. \\tag {12}", + "image_path": "bb9665712a8c909493d3d7af51e869bc486b729193113a22b4089ad15fb3353b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 276, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 407 + ], + "type": "text", + "content": "Note that our model is trained in multiple stages. First, both first-person and third-person video encoders are initialized by weights pretrained on Kinetics-400 [16]. Then we train the third-person video encoder and task-specific head on the third-person video dataset with third-person video task-specific loss " + }, + { + "bbox": [ + 304, + 276, + 545, + 407 + ], + "type": "inline_equation", + "content": "(L_{t})" + }, + { + "bbox": [ + 304, + 276, + 545, + 407 + ], + "type": "text", + "content": " only. Next, we load this trained weight for the third-person video encoder and task-specific head and do training for the whole framework with the overall loss in Equation 12. Finally, we evaluate the first-person video performance of our method using the first-person video encoder and task-specific head." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "text", + "content": "The specific task for both first-person and third-person videos we discussed in this paper is video classification. Therefore, both " + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "inline_equation", + "content": "L_{f}" + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "inline_equation", + "content": "L_{t}" + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "text", + "content": " are classification losses; " + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "inline_equation", + "content": "w_{aw}" + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "inline_equation", + "content": "w_{m}" + }, + { + "bbox": [ + 304, + 407, + 545, + 456 + ], + "type": "text", + "content": " are the loss weights." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 465, + 388, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 388, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 388, + 479 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 485, + 424, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 485, + 424, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 485, + 424, + 498 + ], + "type": "text", + "content": "4.1. Experiment Settings" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 503, + 372, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 372, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 372, + 514 + ], + "type": "text", + "content": "4.1.1 Dataset" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 522, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 545 + ], + "type": "text", + "content": "In this section, we introduce the standard benchmarks we used for evaluation in the experiments." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "content": "LEMMA [15] contains 648 third-person videos and 445 first-person videos. Among them, 136 activities were performed in kitchens, and the remaining 188 were in the living rooms. It contains 25 verb classes, 64 noun classes, and 863 action classes in their action recognition task, and includes not only single-agent but also multi-agent videos. We utilize single-agent third-person videos only as our unpaired third-person samples." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": "Charades-Ego [39, 40] contains 68,536 activity instances in paired 68.8 hours of first-person and third-person videos. It includes 157 action classes. We only utilize first-person videos during training and inference." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "content": "EPIC-Kitchens [4] is a large-scale egocentric video benchmark recorded in kitchen environments. It contains" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3311" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "55 hours of video with a total of 39.6K action segments and is labeled with 352 object and 125 verb classes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 97, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 97, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 97, + 287, + 133 + ], + "type": "text", + "content": "EPIC-Kitchens-100 [5] extends EPIC-Kitchens [4] to 100 hours and 89,977 action segments. We employ this as well as EPIC-Kitchens [4] to validate our approach." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 153, + 155, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 153, + 155, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 153, + 155, + 164 + ], + "type": "text", + "content": "4.1.2 Baseline Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 174, + 286, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 174, + 286, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 174, + 286, + 209 + ], + "type": "text", + "content": "We compare the proposed approach with the following baseline methods, including typical multiview representation learning methods:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 211, + 286, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 211, + 286, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 211, + 286, + 246 + ], + "type": "text", + "content": "FPV Only is trained with first-person (FPV) video data only. Its framework is composed of first-person video encoder and first-person video classification head." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "text", + "content": "Typical CL is widely employed for view- or modal-invariant contrastive learning (CL) [43, 54], and vision-language models [32, 48, 21, 49, 24, 55]. Here we implement it with the loss function in Equation 6. Similar to our framework, videos from different views are fed to different encoders. We employ the same pseudo-pair construction method and the same inference strategy as our framework for this baseline method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 344, + 286, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 286, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 286, + 403 + ], + "type": "text", + "content": "Triplet is another widely used multiview representation learning method [51, 39]. We employ the same implementation protocol following [51]. Moreover, we leverage this method to tackle our problem following the same procedures as \"Typical CL\"." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 424, + 180, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 424, + 180, + 435 + ], + "spans": [ + { + "bbox": [ + 47, + 424, + 180, + 435 + ], + "type": "text", + "content": "4.1.3 Implementation Details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 445, + 286, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 286, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 286, + 623 + ], + "type": "text", + "content": "To ensure fairness, we keep all hyperparameters the exact same for all baselines and our method. For Charades-Ego [39, 40], we use the base learning rate of 0.25, batch size of 32 and maximum epoch of 60. For EPIC-Kitchens [4] and EPIC-Kitchens-100 [5], we use the base learning rate of 0.01, weight decay of 0.0001, batch size of 64 and maximum epoch of 30. Following [22], all models are trained using the stochastic gradient descent optimizer [1] with the momentum of 0.9. For Charades-Ego [39, 40], we use the cosine learning rate decay. For EPIC-Kitchens [4] and EPIC-Kitchens-100 [5], we use sequential learning rate decay. The backbones we use are ResNet-3D-50 [13] and SlowFast [8]. More details about the implementation of backbones will be provided in the following experimental sections." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 634, + 204, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 204, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 204, + 647 + ], + "type": "text", + "content": "4.2. Validity of Proposed Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "type": "text", + "content": "Table 1 shows the performance of different training strategies, where all methods are implemented with the ResNet-3D-50 [13] encoder. Our proposed method outperforms the \"FPV only\" baseline model on both Charades-Ego and EPIC-Kitchens " + }, + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "type": "inline_equation", + "content": "(+1.6\\%)" + }, + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "type": "text", + "content": " mAP on Charades-Ego," + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 313, + 70, + 541, + 144 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 541, + 144 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 541, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 541, + 144 + ], + "type": "table", + "html": "
DatasetC-EgoEK-55 (Verb)EK-55 (Noun)
EvaluationsmAP (%)Top-1 acc. (%)Top-5 acc. (%)Top-1 acc. (%)Top-5 acc. (%)
FPV Only24.761.187.145.870.4
Typical CL25.160.586.245.368.6
Triplet25.261.586.845.769.7
SUM-L (Ours)26.362.387.247.370.9
", + "image_path": "245562b91d06382fe4fd88fa7047bd144fa190694459b3f91600706060cdc1a5.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 152, + 545, + 185 + ], + "lines": [ + { + "bbox": [ + 306, + 152, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 306, + 152, + 545, + 185 + ], + "type": "text", + "content": "Table 1. Comparison with baseline methods. The backbone we use is R3D-50 [13] for all methods. \"C-Ego\" denotes Charades-Ego [39] dataset and \"EK-55\" denotes EPIC-Kitchens [4] dataset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 207, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 207, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 207, + 545, + 255 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 305, + 207, + 545, + 255 + ], + "type": "inline_equation", + "content": "+1.2\\% / + 1.5\\%" + }, + { + "bbox": [ + 305, + 207, + 545, + 255 + ], + "type": "text", + "content": " on EPIC-Kitchens verbs/nouns top-1 accuracies). This demonstrates that under partially similar semantics situations, with our method, the third-person videos can help to improve first-person video representations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "text", + "content": "Moreover, different from our method, previous multiview learning methods (\"Typical CL\" and \"Triplet\") cannot bring significant and consistent improvement compared with \"FPV only\". For example, \"Typical CL\" brings only " + }, + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "text", + "content": " improvement on Charades-Ego (far less than ours) and even deteriorates performance on EPIC-Kitchens. Instead, our proposed method outperforms existing alignment methods up to " + }, + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "inline_equation", + "content": "+1.2\\%" + }, + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "text", + "content": " mAP on Charades-Ego and " + }, + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "inline_equation", + "content": "+1.8\\% / + 2.0\\%" + }, + { + "bbox": [ + 304, + 256, + 546, + 472 + ], + "type": "text", + "content": " on EPIC-Kitchens verbs/nouns top-1 accuracies. We believe this is due to the following reasons. (1) Our method semantics-awarely aligns unpaired data, instead of evenly aligning pseudo-pairs with different semantic similarities. (2) Our method filters the negative effects caused by multiview pseudo-pairs of low semantic similarity. This is different from typical multiview methods which naively align all the pairs. (3) Our method permits all first-person videos to obtain knowledge from samples with different views or modalities, which improves data efficiency." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 473, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 652 + ], + "type": "text", + "content": "We further verify the effectiveness of our proposed method with a larger backbone, SlowFast [8], as the encoder, and we compare with recent state-of-the-art methods on three popular egocentric action recognition benchmarks, Charades-Ego [39], EPIC-Kitchens [4], and EPIC-Kitchens-100 [5]. Note that evaluation scores of state-of-the-arts are reported directly from their paper. The experimental results employing SlowFast [8] encoder confirm the following findings. (1) Our method is effective for cross-view pseudo-pair alignment when there is only partially same multiview semantics. (2) Compared with existing multiview alignment methods, the improvement based on \"FPV Only\" of our method is still more significant and consistent. Next, we analyze the important details of the experiments." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Comparison on Charades-Ego Table 2 demonstrates the effectiveness of our method for cross-view pseudopair alignment when there is only partially same semantics. Note that our method and Ego-Exo [22] complement each other. Thus, we can also incorporate our method into Ego" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3312" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 70, + 258, + 227 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 258, + 227 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 258, + 227 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 258, + 227 + ], + "type": "table", + "html": "
MethodologymAP (%)
state-of-the-artsActor [39]20.0
SSDA [3]23.1
I3D [22]25.8
Ego-Exo [22]28.7
Ego-Exo* [22]30.1
w/o “EE”FPV Only27.4
Typical CL27.9
Triplet28.1
SUM-L (Ours)28.5
w/ “EE”FPV Only29.5
Typical CL29.1
Triplet28.6
SUM-L (Ours)30.7
", + "image_path": "ced477b48605d4923ac00c9a535eb99e38077ad84fd5d3893df5cd08d5e22632.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 290, + 284, + 423 + ], + "blocks": [ + { + "bbox": [ + 46, + 234, + 287, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 287, + 280 + ], + "type": "text", + "content": "Table 2. Comparison on Charades-Ego. Our method and all baseline methods are implemented with SlowFast-R101 [8] backbone. \"EE\" denotes training based on pretrained weights provided by [22]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 290, + 284, + 423 + ], + "lines": [ + { + "bbox": [ + 52, + 290, + 284, + 423 + ], + "spans": [ + { + "bbox": [ + 52, + 290, + 284, + 423 + ], + "type": "table", + "html": "
MethodologyVerb (%)Noun (%)
state-of-the-artsSlowFast-R50 [8]64.148.6
Ego-Exo [22]66.049.4
Ego-Exo* [22]66.449.8
w/o “EE”FPV Only63.148.4
Typical CL63.949.6
Triplet63.948.8
SUM-L (Ours)65.049.5
w/ “EE”FPV Only65.849.5
Typical CL63.848.4
Triplet63.949.6
SUM-L (Ours)66.750.2
", + "image_path": "44b0f2d0edc14c3dafff7a5058e1f6599d1994f765dfdd2d256a766e1b00e1e3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 495, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 544 + ], + "type": "text", + "content": "Exo [22]. As shown in Table 2, based on pretrained weight on [22], our proposed method further improves the performance of \"FPV only\" by " + }, + { + "bbox": [ + 46, + 495, + 287, + 544 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 544 + ], + "type": "text", + "content": " mAP, and achieves a new state-of-the-art on Charades-Ego [39]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": "Comparison on EPIC-Kitchens As we can see from Table 3, our method still brings clear improvement compared with \"FPV Only\" method " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "(+1.9\\% / +1.1\\%" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " verbs/nouns top-1 accuracies). Furthermore, with the help of pretrained weights from [22], our method still outperforms most state-of-the-art methodologies, which indicates the effectiveness of our method. Last but not least, our method outperforms existing alignment methods up to " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "+2.9\\% / +1.8\\%" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " of verbs/nouns top-1 accuracies." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Comparison on EPIC-Kitchens-100 As shown in table 4, our method also obtains competitive results on EPIC-Kitchens-100 [5] dataset when trained based on weights from [22]. It is worth noting that our method gains the first place in noun accuracy and third place in verb accu" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 310, + 69, + 544, + 159 + ], + "blocks": [ + { + "bbox": [ + 46, + 430, + 287, + 474 + ], + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 474 + ], + "type": "text", + "content": "Table 3. Comparison on EPIC-Kitchens. The accuracies are measured by top-1 verb & noun classification accuracies. Our method and all baseline methods are implemented with SlowFast-R50 [8] backbone." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 69, + 544, + 159 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 544, + 159 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 544, + 159 + ], + "type": "table", + "html": "
MethodologyVerb (%)Noun (%)
state-of-the-artsTSN [45]60.246.0
TSM [23]67.949.0
TempAgg [36]59.945.1
Ego-Exo [22]67.052.9
Ego-Exo* [22]67.552.9
IPL [47]68.651.2
w/ “EE”SUM-L (Ours)67.053.4
", + "image_path": "5712936af90c7038972f025a2b37be6e715eafb62ca53c53ba7e016b649f4071.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 371, + 221, + 478, + 285 + ], + "blocks": [ + { + "bbox": [ + 305, + 164, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 305, + 164, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 305, + 164, + 545, + 209 + ], + "type": "text", + "content": "Table 4. Comparison on EPIC-Kitchens-100 with state-of-the-arts that implement CNN backbone. The accuracies are measured by top-1 verb & noun classification accuracies. We implement SlowFast-R101 [8] backbone." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 371, + 221, + 478, + 285 + ], + "lines": [ + { + "bbox": [ + 371, + 221, + 478, + 285 + ], + "spans": [ + { + "bbox": [ + 371, + 221, + 478, + 285 + ], + "type": "table", + "html": "
LaLawLmmAP (%)
×××24.7
×✓×25.6
×✓✓26.3
✓×✓26.1
", + "image_path": "ec24b3a1cc016c134ff6ba723b373a19e27c226dbb55761b085293582902a7f7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 292, + 545, + 337 + ], + "lines": [ + { + "bbox": [ + 305, + 292, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 305, + 292, + 545, + 337 + ], + "type": "text", + "content": "Table 5. Different training task combinations of our proposed method. Combining semantics-aware unpaired cross-view alignment with video-text alignment, our method clearly improves egocentric classification performance on the Charades-Ego dataset." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 360, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 360, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 360, + 545, + 383 + ], + "type": "text", + "content": "racy compared with state-of-the-art methodologies which employ convolutional neural network backbones." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 396, + 406, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 406, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 406, + 407 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 416, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 416, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 416, + 545, + 453 + ], + "type": "text", + "content": "In this section, we conduct the ablation studies on Charades-Ego [39] dataset. The backbone we employ is ResNet-3D-50 [13]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 476, + 495, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 476, + 495, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 476, + 495, + 488 + ], + "type": "text", + "content": "4.3.1 Impact of Different Alignment Tasks" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "The experiment results are shown in Table 5. We find our proposed unpaired cross-view alignment method itself brings " + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": " mAP improvement comparing with the \"FPV Only\" method. It denotes that the method can help learn useful knowledge from unpaired third-person view samples when the cross-view semantic information is not identical. Moreover, our proposed video-text modal alignment method further boosts first-person performance by " + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": " mAP compared with implementation with cross-view alignment only. We think this is because the proposed video-text modal alignment ensures the alignment of all first-person video samples, and further improves the semantics utilization for both first-person and third-person videos. Besides, implementing our cross-view alignment without semantic weighting causes a slight " + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": " drop, which manifests the usefulness of knowledge from the large language model. This knowledge provides a reference to measure the semantic similarity between cross-view videos." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3313" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 64, + 87, + 138, + 163 + ], + "blocks": [ + { + "bbox": [ + 66, + 75, + 211, + 85 + ], + "lines": [ + { + "bbox": [ + 66, + 75, + 211, + 85 + ], + "spans": [ + { + "bbox": [ + 66, + 75, + 211, + 85 + ], + "type": "text", + "content": "First-person frame heatmaps from \"FPV Only\"" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 64, + 87, + 138, + 163 + ], + "lines": [ + { + "bbox": [ + 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Comparison of class activation map visualizations between the \"FPV Only\" method and our method. The cross-view similar semantics for data in the first row is \"holding pan\". 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Here we study the effect of other intuitively feasible third-person video encoder implementations. The experiment results are shown in Table 6." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": "First, we load the pretrained weight of the third-person video and freeze it during the training process for the whole framework shown in Figure 3. We find freezing the third-person video encoder causes a " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " mAP drop compared with the original setup. This indicates that for the pretrained third-person video encoder, allowing training more parameters can better help first-person video learn effective information from third-person samples. Moreover, naively employing shared encoder weights for different views, which follows [2], can cause clear performance drop (" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " mAP drop) to first-person video learning. We think this is due to the big variances between first-person and third-person samples. Finally, the same initialization (pretrained on Kinetics-400 [16]) for both first-person and third-person video encoders causes a slight " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " mAP drop. It indicates that for the third-person video encoder, employing existing weights of third-person samples for optimization has a positive effect on first-person video learning." + } + ] + } + ], + "index": 24 + }, + { + "type": "table", + "bbox": [ + 317, + 386, + 533, + 450 + ], + "blocks": [ + { + "bbox": [ + 317, + 386, + 533, + 450 + ], + "lines": [ + { + "bbox": [ + 317, + 386, + 533, + 450 + ], + "spans": [ + { + "bbox": [ + 317, + 386, + 533, + 450 + ], + "type": "table", + "html": "
SetupmAP (%)
Freezed TPV Backbone25.8
Shared Multiview Encoder Weights25.3
Same Initialization with FPV Encoder26.1
Original26.3
", + "image_path": "5dc4a09a6552333094ab9a2a18258c5f29bf637d6b964c39dbc6014fc18431fe.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "table_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 456, + 545, + 479 + ], + "lines": [ + { + "bbox": [ + 306, + 456, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 545, + 479 + ], + "type": "text", + "content": "Table 6. Impact of different third-person video encoder implementations. The \"Original\" setup is described in Sec. 3.4." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 501, + 390, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 390, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 390, + 513 + ], + "type": "text", + "content": "4.4. Visualization" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": "We visualize the first-person and third-person video class activation maps (CAM) [56] on EPIC-Kitchens [4] dataset. We employ first-person video encoder weights from \"FPV Only\" method (61.1% & 45.8% top-1 verb & noun accuracies) and our method (62.3% & 47.3% top-1 verb & noun accuracies). As shown in the first and second columns of Figure 4, comparing with \"FPV Only\" method, our method can help the model be more responsive to positive spatiotemporal locations of video clips." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 630, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 715 + ], + "type": "text", + "content": "Moreover, from the third column of Figure 4, we find that our model also has a strong response to the third-person video locations which have overlapped semantics with the first-person video (see bright green bounding boxes of Figure 4). It shows that our method successfully utilizes knowledge from unpaired third-person videos to help learn first-person video representations." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3314" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 125, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 125, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 125, + 83 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 286, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 286, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 286, + 187 + ], + "type": "text", + "content": "In this paper, we tackle a new problem in first-person and third-person video learning and propose SUM-L. It can distill knowledge from unpaired, cross-dataset third-person video without exact same multiview semantic information. Our experiments show the validity of our proposed method. Besides, under the more challenging scenario than typical paired or unpaired multimodal or multiview learning, our method outperforms existing view-alignment methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 188, + 286, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 188, + 286, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 188, + 286, + 258 + ], + "type": "text", + "content": "However, improvements from SUM-L are not very significant. One possible reason is due to the relatively small amount of third-person data. It will be interesting to explore more unpaired third-person video datasets. It will be also interesting to study more downstream tasks, such as unpaired cross-view retrieval. We leave these as future work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 260, + 286, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 260, + 286, + 320 + ], + "spans": [ + { + "bbox": [ + 47, + 260, + 286, + 320 + ], + "type": "text", + "content": "Acknowledgements This work is partially supported by National Science Foundation (NSF) CMMI-2039857, and University of Delaware Research Foundation (UDRF). We thank Florian Schroff and Hartwig Adam from Google Research for supporting this project." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 331, + 106, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 331, + 106, + 344 + ], + "spans": [ + { + "bbox": [ + 48, + 331, + 106, + 344 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 352, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 352, + 286, + 374 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 352, + 286, + 374 + ], + "spans": [ + { + "bbox": [ + 53, + 352, + 286, + 374 + ], + "type": "text", + "content": "[1] Shun-ichi Amari. Backpropagation and stochastic gradient descent method. 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Unfortunately, this assumption is unrealistic in large-scale MLC data that has long-tailed (LT) distribution and partial labels (PL). To address the problem, we introduce a novel task, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), to jointly consider the above two imperfect learning environments. Not surprisingly, we find that most LT-MLC and PL-MLC approaches fail to solve the PLT-MLC, resulting in significant performance degradation on the two proposed PLT-MLC benchmarks. Therefore, we propose an end-to-end learning framework: $\\mathbf{C}\\mathbf{O}\\mathbf{R}\\mathbf{e}\\mathbf{r}\\mathbf{o}\\mathbf{r}\\mathbf{c}\\rightarrow$ Modification $\\rightarrow$ balanCe, abbreviated as COMIC. Our bootstrapping philosophy is to simultaneously correct the missing labels (Correction) with convinced prediction confidence over a class-aware threshold and to learn from these recall labels during training. We next propose a novel multi-focal modifier loss that simultaneously addresses head-tail imbalance and positive-negative imbalance to adaptively modify the attention to different samples (Modification) under the LT class distribution. In addition, we develop a balanced training strategy by distilling the model's learning effect from head and tail samples, and thus design a balanced classifier (Balance) conditioned on the head and tail learning effect to maintain stable performance for all samples. Our experimental study shows that the proposed COMIC significantly outperforms general MLC, LT-MLC and PL-MLC methods in terms of effectiveness and robustness on our newly created PLT-MLC datasets. Codes and benchmarks are available on the link https://https://github.com/wannature/COMIC", + "bbox": [ + 76, + 359, + 473, + 815 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 849, + 209, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, the development of deep learning prosperity to the field of computer vision [20, 17, 19, 16, 23, 22, 25,", + "bbox": [ + 75, + 869, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "24, 43, 42, 18]. Images typically contain multiple objects and concepts, highlighting the importance of multi-label classification (MLC) [34] for real-world tasks. Along with the wide adoption of deep learning, recent MLC approaches have made remarkable progress in visual recognition [36, 38], but the performance is limited by two common assumptions: all categories have comparable numbers of instances and each training instance has been fully annotated with all the relevant labels. While this conventional setting provides a perfect training environment for various studies, it conceals a number of complexities that typically arise in real-world applications: i) Long-Tailed (LT) Class Distribution. With the growth of digital data, the crux of making a large-scale dataset is no longer about where to collect, but how to balance it [33]. However, the cost of expanding the dataset to a larger class vocabulary with balanced data is not linear — but exponential — since the data is inevitably long-tailed following Zipf's distribution [30]. ii) Partial Labels (PL) of Instances. In the case of a large number of categories, it is difficult and even impractical to fully annotate all relevant labels for each image [39, 46]. Intuitively, humans tend to focus on different aspects of image contents due to human bias, i.e., their preference, personality and sentiment [41], which indirectly affects how and what we annotate. In fact, LT and PL are often co-occurring, and therefore, the MLC model must be sufficiently robust to handle different data distributions and imperfect datasets.", + "bbox": [ + 496, + 327, + 895, + 736 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present a new challenge for MLC at scale, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), with concomitant existence of both PL setting [39] and LT distribution [33] problems. As captured in the overview of PLT-MLC in Figure 1 (a), it has the following three challenges: i) False Negative Training. Under the PL setting, the MLC model treats the un-annotated labels $(\\odot)$ as negatives $(\\odot)$ , which may produce sub-optimal decision boundary as it adds noise of false negative labels (Figure 1 (b)). The situation is further exacerbated in the", + "bbox": [ + 496, + 750, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1423", + "bbox": [ + 482, + 946, + 514, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3252a6d42f8a56a86a3850c4d575d0ca94145d1ff7a844cbfe3f1bb36d5b442c.jpg", + "image_caption": [ + "Figure 1: (a) illustrates an overview of the proposed PLT-MLC task. (b) depicts three key challenges of a PLT-MLC task. (c) depicts a concise version of our proposed model for facilitating the PLT-MLC. $(\\bullet : positive, \\bullet : negative, \\circ : false, \\circ :$ corrected positive)" + ], + "image_footnote": [], + "bbox": [ + 124, + 88, + 411, + 273 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e4930b6aa52408b836b771c2cc1735cf3f7e08ad25c2068e503468c17bc0d196.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 418, + 88, + 846, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LT class distribution as some tail categories are prone to missing annotations in practice. For instance, in Figure 1 (a), \"person\" is the head class in the PLT-MLC dataset and is often notable in an image to labeling for annotators. In contrast, the \"tie\" often occupies a tiny region in the scene compared with the \"person\". The annotator may miss the \"tie\" object, which will aggravate the LT distribution and further increase the difficulty of learning from tail classes. ii) Head-Tail and Positive-Negative Imbalance. There are two imbalance issues in a PLT-MLC task: inter-instance head-tail imbalance and intra-instance positive-negative imbalance. As shown in Figure 1 (b), the inter-instance ratio of head positive ( $\\odot$ ) \"person\" ( $\\odot$ ): tail positive ( $\\odot$ \"tie $\\odot$ ) $\\approx$ 32 under the LT data distribution, and the intra-instance ratio of tail negative ( $\\odot$ ) categories: tail positive ( $\\odot$ \"tie $\\odot$ ) = 78 as an image only contains a small fraction of the positive labels. Consequently, a robust PLT-MLC model should address the co-occurring imbalances simultaneously. iii) Head Overfitting and Tail Underfitting. Different from the general LT distribution, the classification model downplays the minor tail and overplays the major head. The PLT-MLC has an extreme LT distribution and Figure 1(c) illustrates an interesting phenomenon of MLC model learning: the general classification model is prone to overfitting to head class with extensive samples and underfitting to tail classes with a few samples. This figure also indicates that only the medium class shows a steady growth in performance, which means that existing LT methods focusing on lifting up the tail performance may not solve the PLT-MLC problem satisfactorily.", + "bbox": [ + 75, + 352, + 472, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Suppose a trained model is used to correct the missing labels and then an LT classifier is trained using the updated labels, we might not be able to obtain a satisfying PLT-MLC performance, either. While machine learning methods can easily detect the head samples, they may have difficulty in identifying the tail samples. As a result, the corrected labels", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "may still exhibit an LT distribution that inevitably hurts balanced learning. Moreover, even when a general LT classifier affords the trade-off to improve the tail performance conditioned on the head performance drop, it is still incapable of simultaneously addressing the issue of head overfitting and tail underfitting problem. Further, the decoupled learning paradigm is impractical since it needs the \"stop\" training and human \"re-start\" training, i.e., an end-to-end learning scheme is more desirable. Thus, these limitations motivate us to reconsider the solution for the PLT-MLC task.", + "bbox": [ + 496, + 352, + 893, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose an end-to-end PLT-MLC framework: COrrection $\\rightarrow$ ModificatIon $\\rightarrow$ balanCe (Figure 1), called COMIC, which progressively addresses the three key PLT-MLC challenges. Step 1: The Correction module aims to gradually correct the missing labels according to the predicted confidence and dynamically adjusts the classified loss of the corrected samples under the real-time estimated class distribution. Step 2: After the label correction, the Modification module introduces a novel Multi-Focal Modifier (MFM) Loss, which contains two focal factors to address the two imbalance issues in PLT-MLC independently. Motivated by [3], the first is an intra-instance positive-negative factor that determines the concentration of learning on hard negatives and positives with different exponential decay factors. The second is an inter-instance head-tail factor that increases the impact of rare categories, ensuring that the loss contribution of rare samples will not be overwhelmed by frequent ones. Step 3: Finally, the Balance module measures the model's optimization direction with a calculated moving average vector of the gradient over all past samples. And thus, we devise a head model and a tail model by subtracting or adding this moving vector, which can respectively improve head and tail performance. Subsequently, a balanced classifier deduces a balanced learning effect under the supervision of the head classifier and tail classifier. It protects the model training from being too medium biased, and hence", + "bbox": [ + 496, + 508, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1424", + "bbox": [ + 483, + 946, + 514, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the balanced classifier is able to achieve the balanced learning schema. Notably, our solution is an end-to-end learning framework, which is re-training-free and effectively enables balanced prediction.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our contributions are three-fold: (1) We present a new challenging task: Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), together with two newly designed benchmarks: PLT-COCO and PLT-VOC. (2) We propose an end-to-end PLT-MLC learning framework, called COMIC, to effectively perform the PLT-MLC task as a progressive learning paradigm, i.e., Correction $\\rightarrow$ Modification $\\rightarrow$ Balance. (3) Through an extensive experimental study, we show that our method improves all the prevalent LT and ML line-ups on PLT-MLC benchmarks by a large margin.", + "bbox": [ + 75, + 152, + 472, + 305 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 324, + 225, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Long-Tailed MLC. [37] is the first work that addresses the LT-MLC by extending the re-balanced sampling and cost-sensitive re-weighting methods. It proposes an optimized DB Focal method, which does improve the recognition performance of tail classes. Later work, [10] performs uniform and re-balanced samplings from the same training set. Then a two-branch network is developed to enforce the consistency between two branches for collaborative learning on both uniform and re-balanced samplings. However, the above works require careful data initialization, i.e., re-sampling, which is undesirable in practice. Moreover, these methods have not yet considered the missing labeling case, which may not sufficiently deal with the PLT-MLC.", + "bbox": [ + 75, + 352, + 472, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "MLC with Partial Labels. Multi-label tasks often involve incomplete training data, hence several methods have been proposed to solve the problem of multi-label learning with missing labels. A simple solution is to treat the missing labels as negative labels [31, 21, 4]. However, performance will drop because a lot of ground-truth positive labels are initialized as negative labels [12]. Current works on PL-MLC mainly focus on the design of networks and training schemes. The common practice is to utilize the customized networks to learn label correlations or classification confidence to realize correct recognition of missing labels [7, 44]. However, the corrected labels learned from a trained model are imbalanced due to the previous training dataset having an LT distribution. Using such recall labels will aggravate the LT distribution in the PLT-MLC dataset and result in an imbalanced performance.", + "bbox": [ + 75, + 551, + 470, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Other Works. [40] learns to generate concept-invariant samples in the environment with semantic gap, which enables the model to classify the samples through causal intervention, yielding improved generalization guarantees; [18] collaborates a cascade of foundation models, thus learning superior interleaved multi-modal instruction-following ability from imperfect supervision.", + "bbox": [ + 75, + 794, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 89, + 635, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section describes the proposed PLT-MLC framework. We will present each module and its training strategy.", + "bbox": [ + 498, + 114, + 893, + 146 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 152, + 702, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before presenting our method, we first introduce some basic notions and terminologies. We consider a partially annotated MLC dataset contains $C$ classes and $N$ i.i.d training samples $\\mathcal{S} = \\{(\\mathcal{I}^{(1)},y^{(1)}),\\dots ,(\\mathcal{I}^{(N)},y^{(N)})\\}$ , where $\\mathcal{I}^{(i)}$ denote $i^{th}$ image and label $y^{(i)} = [y_1^{(i)},\\dots ,y_c^{(i)}]\\in \\{0,1\\}^C$ . For a given $i^{th}$ example and category $c$ , $y_{c}^{(i)} = 0$ , 1 respectively means the category is unknown and present. Our proposed COMIC solves the PLT-MLC problem in an end-to-end learning manner: Correction $\\rightarrow$ Modification $\\rightarrow$ Balance, with Reflective Label Corrector (RLC, in Sec.3.2), Multi-Focal Modifier (MFM, in Sec.3.3) and Head-Tail Balancer (HTB, in Sec.3.3), as illustrated in Figure 2.", + "bbox": [ + 496, + 176, + 893, + 361 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "These three modules are designed to seek a balanced model $\\mathcal{M}_b(\\cdot ;\\Theta_b)$ , parameterized by $\\Theta_{b}$ , to predict the presence or absence of each class given an input image. We denote $p = [p_1,\\dots ,p_c]$ as the class prediction, computed by the model: $p_c = \\sigma (z_c)$ where $\\sigma$ is the sigmoid function, and $z_{c}$ is the output logit corresponding to class $c$ . The optimized goal of COMIC can be defined as follows:", + "bbox": [ + 496, + 362, + 893, + 468 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underbrace {\\mathcal {L} ((\\mathcal {S}) ; \\Theta_ {b})} _ {\\text {C O M I C L o s s}} = \\underbrace {\\lambda_ {c} \\cdot \\mathcal {L} _ {r l c}} _ {\\text {R L C L o s s}} + \\underbrace {\\lambda_ {m} \\cdot \\mathcal {L} _ {m f m}} _ {\\text {M F M L o s s}} + \\underbrace {\\lambda_ {b} \\cdot \\mathcal {L} _ {h t b}} _ {\\text {H T B L o s s}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 474, + 890, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{rlc}$ , $\\mathcal{L}_{mfm}$ and $\\mathcal{L}_{htb}$ denote the loss of RLC, MFM and HTB, respectively. $\\lambda_{c},\\lambda_{m}$ and $\\lambda_{b}$ are hyperparameters.", + "bbox": [ + 496, + 515, + 893, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Reflective Label Corrector", + "text_level": 1, + "bbox": [ + 500, + 553, + 740, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reflective Label Corrector (RLC) presents a real-time label correction method for missing labels to alleviate the effect of partially labeled samples. The core idea is to examine the label likelihood $p$ of each training image and recall the labels with convinced prediction confidence during training. Interestingly, we found that the model can distinguish a large number of missing labels with high prediction confidence in the early training stage, which implies that we can recall these missing labels during training to boost PTL-MLC learning. Here, we first define a threshold $\\tau$ and then check the input sample's label likelihood $p$ to check whether it is greater than $\\tau$ and then calculate the average category possibility $P_{c}$ of past trained data with class $c$ . If predicted probabilities $p_{c}$ are highly confident, i.e., $p_{c} > \\max \\{\\tau, P_{c}\\}$ , we regard that the sample misses the label of class $c$ and set a pseudo-label $\\hat{y}_{c}$ .", + "bbox": [ + 496, + 575, + 893, + 818 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {c} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} p _ {c} > \\max \\left\\{\\tau , P _ {c} \\right\\}, y _ {c} = 0 \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 824, + 890, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Thus, the loss of RLC module, i.e., $\\mathcal{L}_{rlc}$ utilizes the MFM loss (refer the details in Sec. 3.3) with these corrected label", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1425", + "bbox": [ + 483, + 946, + 514, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/437ca58d174d331935450d64630aba60fdedf08c66ee8ef204d10a6878493963.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 122, + 90, + 478, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cd98ecdd00a0baf3356e99f6bc9751210e4786ae428eb5f6658ce3721c5d23c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 90, + 846, + 171 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0624ea5a4d27a76d03897b0a9d85ab81025a16befa67f2f1d4a45e7c4c693ad4.jpg", + "image_caption": [ + "Figure 2: Overview of COMIC. RLC module (Correction) corrects the missing labels along with the training and dynamically re-weights the sample weight according to the estimated class distribution. MFM module (Modification) adjusts the focal of different instances according to head-tail and positive-negative imbalance under the extreme LT distribution. HTB module (Balance) measures the model's optimization direction and correspondingly develops a balanced learning scheme to produce stable PLT-MLC performance." + ], + "image_footnote": [], + "bbox": [ + 122, + 172, + 707, + 380 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/63ae493d2d175e533a774d3b7850adcb61a85997ebf393e3934bc729b6e8b9fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 172, + 843, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\hat{y}$ for model training:", + "bbox": [ + 76, + 498, + 217, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r l c} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {m f m} ^ {+} (p), & \\text {i f} \\hat {y} = 1 \\\\ \\mathbb {1} _ {(y = 1)} \\mathcal {L} _ {m f m} ^ {+} (p) + \\mathbb {1} _ {(\\hat {y} = 0)} \\mathcal {L} _ {m f m} ^ {-} (p), & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 68, + 529, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{mfm}^{+}(p)$ and $\\mathcal{L}_{mfm}^{-}(p)$ refer to the generalized MFM loss function for positives and negatives. Notably, we find that most of the corrected labels belong to head class, which may aggravate the LT distribution. To address this issue, we dynamically adjust the inter-sample head-tail factor $\\gamma_{ht}^{(i)}$ (details of this factor are explained in Sec. 3.3) according to the dynamic class distribution $\\mathcal{D}_t$ , which can increase the focal weight for tail samples. In addition, we also multiply $\\mathcal{L}_{rlc}(p)$ by a coefficient $\\frac{\\mathcal{B}_s}{\\mathcal{N}_t}$ in each training batch to constrain the loss value, where $\\mathcal{B}_s$ is the batch size and $\\mathcal{N}_t$ is the number of corrected labels.", + "bbox": [ + 75, + 582, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Through this, RLC can gradually and dynamically correct the potential missing labels during training, which efficiently improves the classifier's performance with recalled labels.", + "bbox": [ + 75, + 752, + 468, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Multi-Focal Modifier", + "text_level": 1, + "bbox": [ + 76, + 814, + 274, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first revisit the focal loss [26], which is a widely-used solution in the positive-negative imbalance problem. It redistributes the loss contribution of easy samples and hard samples, which greatly weakens the influence of the majority", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of negative samples.", + "bbox": [ + 500, + 500, + 635, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f l} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {f l} ^ {+} = (1 - p) ^ {\\gamma} \\log (p), & \\text {i f} y = 1 \\\\ \\mathcal {L} _ {f l} ^ {-} = p ^ {\\gamma} \\log (1 - p), & \\text {i f} y = 0 \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 527, + 890, + 568 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma$ is the focusing parameter, $\\gamma = 0$ yields binary cross-entropy. By setting $\\gamma > 0$ , the contribution of easy negatives (with low probability, $p \\ll 0.5$ ) can be down-weighted in the loss, enabling the model to focus on harder samples.", + "bbox": [ + 496, + 580, + 890, + 641 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the focal loss may not satisfactorily resolve the PLT-MLC problem due to two key aspects:", + "bbox": [ + 498, + 643, + 890, + 672 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Tail Positive Gradient Elimination. When using focal loss for multi-label training, there is an inner trade-off: high $\\gamma$ sufficiently down-weights the contribution from easy negatives, but may eliminate the gradients from the tail positive samples [3].", + "- Head-Tail Imbalance. Imbalance among the positive categories also exists in MLC, i.e., head positive-tail positive imbalance. Rare categories suffer more from severe imbalance issues than frequent ones." + ], + "bbox": [ + 517, + 686, + 890, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, we propose a Multi-Focal Modifier (MFM) loss that decouples $\\gamma$ at two granularities of focal factors, i.e., an intra-sample positive-negative (P-N) factor $\\gamma_{pn}$ and an", + "bbox": [ + 498, + 854, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1426", + "bbox": [ + 483, + 946, + 514, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "inter-sample head-tail (H-T) factor $\\gamma_{ht}$ .", + "bbox": [ + 76, + 90, + 341, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma^ {(i)} = \\left\\{ \\begin{array}{l l} \\gamma^ {(i) +} = \\gamma_ {p n} ^ {+} + w ^ {+} \\cdot \\gamma_ {h t} ^ {(i)}, & \\text {i f} y = 1 \\\\ \\gamma^ {(i) -} = \\gamma_ {p n} ^ {-} + w ^ {-} \\cdot \\gamma_ {h t} ^ {(i)}, & \\text {i f} y = 0 \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 116, + 470, + 157 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma^{(i) + }$ and $\\gamma^{(i) - }$ control the focal of samples with $i^{th}$ class. Similar to [3], $\\gamma_{pn}^{+}$ and $\\gamma_{pn}^{-}$ decouple the original decay rate $\\gamma$ as two factors, which respectively control the focal of the positive and negative samples. Since we are interested in emphasizing the contribution of positive samples, we set $\\gamma_{pn}^{-}\\geq \\gamma_{pn}^{+}$ . We achieve better control over the contribution of positive and negative samples through the designed loss function, which assists the network to learn meaningful features from positive samples, despite their rarity. Another focal factor $\\gamma_{ht}^{(i)}$ is a variable parameter $(\\geq 1)$ associated with the imbalance degree of the $i^{th}$ class. A bigger value of $\\gamma_{ht}^{(i)}$ will increase the weight of tail samples to encourage the model to pay more attention to the positive tail samples, and vice versa. $w^{+}$ and $w^{-}$ are the coefficients that adjust the weight at a fine-grained level. The $\\gamma_{ht}^{(i)}$ is the static class distribution $\\mathcal{D}$ of training set with max normalization function $\\psi (\\cdot)$ [29] to adjust the head-tail focal.", + "bbox": [ + 75, + 167, + 472, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After applying the decoupled $\\gamma^{(i) + }$ and $\\gamma^{(i) - }$ into our MFM loss, we obtain the loss function as follows (more discussions in the Appendix.):", + "bbox": [ + 75, + 431, + 470, + 478 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m f m} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {m f m} ^ {+} = \\sum_ {i = 1} ^ {C} (1 - p) ^ {\\gamma^ {(i) +}} \\log (p), & \\text {i f} y = 1 \\\\ \\mathcal {L} _ {m f m} ^ {-} = \\sum_ {i = 1} ^ {C} p ^ {\\gamma^ {(i) -}} \\log (1 - p), & \\text {i f} y = 0 \\end{array} \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 66, + 488, + 468, + 540 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By doing so, the MFM module utilizes the multi-grained focal to alleviate the two imbalance problems in the PLT-MLC task, yielding better classification results.", + "bbox": [ + 75, + 541, + 472, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Head-Tail Balancer", + "text_level": 1, + "bbox": [ + 76, + 595, + 264, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As discussed in the introduction, the extreme LT dataset with numerous head samples and a small number of tail samples result in a head overfitting and tail underfitting learning effect. Only the medium samples present a superior performance during training, which fails to obtain the balanced performance for the overall samples. To address this issue, we develop a balanced strategy that measures the balanced learning effect under the supervision of the head classifier and tail classifier to achieve balanced results. Before we delve into the balanced learning, we first measure the moving average of the gradient in the SGD-based optimizer [32]:", + "bbox": [ + 75, + 619, + 472, + 785 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {t} = \\mu \\cdot \\mathbf {e} _ {t - 1} + \\operatorname {s u m} \\left(g _ {t}\\right), \\forall t = 1, \\dots , T. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 797, + 468, + 814 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{sum}(g_t)$ is the accumulated gradient at iteration $t$ , $\\mu$ is the momentum decay. The average moving vector $\\mathbf{e}_t$ records the model's optimization tendency by $\\mathbf{e}_{t-1}$ and $\\mathrm{sum}(g_t)$ .", + "bbox": [ + 75, + 824, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our empirical study, we observe that only the medium samples obtain a stable learning effect from the early to late", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "training stage, mainly due to the extreme LT distribution. To simulate the learning effect towards head/tail samples, as depicted in Figure 2(c), we reduce/add the moving vector $\\mathbf{e}_t$ at each step in head model $\\mathcal{M}_h$ and tail model $\\mathcal{M}_t$ respectively, to assist the balanced model $\\mathcal{M}_b$ for balanced learning. Notably, we set different learning rate decays for each model to further explore the balanced learning effect. The three models are parallel-trained with their own backbone and classifier. In the feature learning stage, we develop an additive attention [1] that computes the relevance of balanced features $\\hat{\\mathbf{f}}_b$ , and head features $\\mathbf{f}_h$ , tail features $\\mathbf{f}_t$ extracted from corresponding backbones.", + "bbox": [ + 496, + 90, + 893, + 272 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {b} = \\operatorname {A t t n} \\left(\\hat {\\mathbf {f}} _ {b}, \\left[ \\mathbf {f} _ {h}, \\mathbf {f} _ {t} \\right]\\right)) + \\hat {\\mathbf {f}} _ {b} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 282, + 892, + 300 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Attn(\\cdot)$ is the additive attention mechanism.", + "bbox": [ + 498, + 310, + 836, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then updated $\\mathbf{f}_b$ , $\\mathbf{f}_h$ , $\\mathbf{f}_t$ are input to their classifiers to obtain their logits. We develop the multi-head classifier with normalization [9, 28, 33], which has already been embraced by various methods of empirical practice. The multi-head strategy [35] equally divides the channel of weights and features into $N_g$ groups, which can be considered as $N_g$ times of fine-grained sampling.", + "bbox": [ + 496, + 325, + 893, + 431 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {x} = \\frac {\\rho}{N _ {g}} \\sum_ {k = 1} ^ {N _ {g}} \\frac {w _ {k} ^ {\\top} \\mathbf {f} _ {x}}{(| | w _ {k} | | + \\eta) | | \\mathbf {f} _ {x} | |}, x \\in \\{h, t, b \\} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 441, + 892, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\rho$ is a scaling factor akin to the inverse temperature in Gibbs distribution, $\\eta$ is a class-agnostic baseline energy. $w_{k}$ is the $k^{th}$ learned parameter matrix.", + "bbox": [ + 496, + 494, + 890, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Subsequently, we measure the head and tail learning effect by subtracting and adding the average moving vector $\\mathbf{e}_t$ to the logits of head model and tail model, respectively:", + "bbox": [ + 496, + 540, + 893, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {z}} _ {x} = \\mathbf {z} _ {x} \\pm \\frac {\\rho}{N _ {g}} \\sum_ {k = 1} ^ {N _ {g}} \\frac {\\sin \\left(\\mathbf {z} _ {x} , \\mathbf {e} _ {t}\\right) \\cdot \\left(w _ {j}\\right) ^ {\\top} \\mathbf {e} _ {t}}{| | w _ {k} | | + \\eta}, x \\in \\{h, t \\} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 595, + 892, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $sim(\\cdot, \\cdot)$ measures the cosine similarity of vectors.", + "bbox": [ + 498, + 648, + 879, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining the logits of $\\hat{\\mathbf{z}}_h$ , $\\hat{\\mathbf{z}}_t$ and $\\mathbf{z}_b$ , the balanced learning effect needs to distill the head and tail knowledge from $\\hat{\\mathbf{z}}_h$ and $\\hat{\\mathbf{z}}_t$ to enable the stable learning for all samples. Hence, we develop the head-tail loss:", + "bbox": [ + 496, + 664, + 893, + 724 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {h t b} = \\kappa_ {h} \\cdot \\mathcal {L} \\left(\\phi \\left(\\hat {\\mathbf {z}} _ {h}\\right) \\cdot \\phi \\left(\\mathbf {z} _ {b}\\right)\\right) + \\kappa_ {t} \\cdot \\mathcal {L} \\left(\\phi \\left(\\hat {\\mathbf {z}} _ {t}\\right) \\cdot \\phi \\left(\\mathbf {z} _ {b}\\right)\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 734, + 892, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}$ is $\\mathcal{L}_{mfm}$ and $\\phi (\\cdot)$ is softmax function. $\\kappa_{h}$ and $\\kappa_{t}$ are adaptive weights for head and tail learning that calculated by $\\kappa_{h} = \\frac{(\\mathcal{L}(\\hat{z}_{h}))^{\\alpha}}{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha} + (\\mathcal{L}(\\hat{z}_{h}))^{\\alpha}}$ and $\\kappa_{t} = \\frac{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha}}{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha} + (\\mathcal{L}(z_{h}))^{\\alpha}}$ , respectively. $\\alpha$ is a scaling factor and we study its effect in Sec. 4.3. Such loss can be regarded as the empirical risk minimization (ERM) [6], which adaptively distills the knowledge from the head and tail models, enabling the balanced model is not biased to medium samples and produces a balanced learning effect for the PLT-MLC task.", + "bbox": [ + 496, + 762, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1427", + "bbox": [ + 483, + 946, + 514, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3e29340e466b67f82deca78f23b158aa5b498259cd271450224b3ed94adbc4b9.jpg", + "table_caption": [ + "Table 1: Performance comparison of the proposed method and baselines on PLT-MLC datasets (PLT-COCO and PLT-VOC). $E2E^{*}$ indicates that the PLT model is learned in an end-to-end manner. A larger score has better performance. Improv. indicates performance improvement. Acronym notations of baselines can be found in Sec. 4.1. We color each row as the best, second best and lowest score." + ], + "table_footnote": [], + "table_body": "
CategoryMethodsE2E*PLT-COCO DatasetPLT-VOC Dataset
Many ShotMedium ShotFew ShotTotal ShotMany ShotMedium ShotFew ShotTotal Shot
MLCBCE [45]✔42.57±0.1156.67±0.1946.40±0.6048.92±0.2367.37±0.1888.27±0.3983.79±0.4178.79±0.14
Focal [26]✔41.05±0.0758.33±0.1253.58±0.3151.39±0.1567.02±0.1187.49±0.1882.82±0.7878.13±0.23
ASL [3]✔41.60±0.1758.15±0.1552.67±0.1751.20±0.0867.67±0.1087.79±0.1382.23±0.5578.35±0.11
LT-MLCDB [37]✔44.83±0.3158.96±0.2453.82±0.4752.16±0.3669.22±0.2888.56±0.4283.72±0.3578.86±0.23
DB-Focal [37]✔45.76±0.2559.74±0.2153.85±0.1652.57±0.2768.96±0.2288.89±0.1883.42±0.2078.90±0.26
LWS [13]-44.86±0.5858.79±0.6353.48±0.5152.86±0.6069.08±0.4488.24±0.5583.46±0.4778.28±0.49
PL-MLCPseudo-Label [15]-41.41±0.4157.46±0.3553.12±0.3351.67±0.3767.38±0.2487.58±0.3583.26±0.4278.32±0.30
ML-GCN [5]✔43.43±0.5358.46±0.6153.74±0.4852.14±0.5568.46±0.4488.17±0.6182.46±0.3879.02±0.56
Hill [44]✔42.50±0.1656.89±0.1947.31±0.3749.28±0.0968.79±0.1586.70±0.1778.15±0.9977.40±0.22
P-ASL [2]✔43.09±0.0557.67±0.0753.46±0.2251.75±0.1768.95±0.2287.24±0.1383.37±0.3378.96±0.16
PLT-MLCHead Model (Ours)✔47.59±0.0959.07±0.1252.35±0.2853.30±0.1972.91±0.2888.59±0.3182.12±0.2780.70±0.30
Tail Model (Ours)✔46.30±0.2558.76±0.2953.38±0.1453.09±0.2771.65±0.3488.68±0.4183.51±0.2480.58±0.36
COMIC (Ours)✔49.21±0.2260.08±0.1355.36±0.2155.08±0.1473.10±0.3589.18±0.4584.53±0.4881.53±0.35
Improv. ↑--1.62 ~ 8.160.34 ~ 3.410.53 ~ 8.961.78 ~ 6.160.19 ~ 6.080.29 ~ 2.48-0.3 ~ 6.380.83 ~ 4.13
", + "bbox": [ + 88, + 162, + 877, + 392 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/eab436315f3754e590ef808f4405e20399cf78ece5619fd47674aa3e3480e2ab.jpg", + "table_caption": [ + "Table 2: Ablation study of different modules. M,C,B represent correction, modification and balance learning, respectively." + ], + "table_footnote": [], + "table_body": "
ModelsSettingPLT-COCO Dataset
MCBTotal mAPAverage mAPRecall
-RLC✔✔54.70±0.1354.42±0.1585.26±0.08
-MFM✔✔54.60±0.1354.33±0.1384.59±0.19
-HTB✔✔53.65±0.3153.36±0.3184.19±0.23
COMIC✔✔✔55.08±0.1454.88±0.1988.19±0.22
", + "bbox": [ + 84, + 472, + 465, + 579 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 606, + 209, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 632, + 266, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset Construction. The proposed method is analyzed on the created LT versions of two MLC benchmarks (COCO [27] and VOC [8]), called PLT-COCO and PLT-VOC, respectively. The missing rate of PLT-COCO is $40\\%$ and it contains 2,962 images from 80 classes. The maximum training number for each class is 1,240 and the minimum number is 6. We select 5000 images from the test set of COCO2017 for evaluation. PLT-VOC has the same missing rate setting and contains 2,569 images from 20 classes, in which the maximum training number for each class is 1,117 and the minimum number is 7. We evaluate the performance on VOC2007 test set with 4,952 images. More details about the dataset construction can be found in the Appendix.", + "bbox": [ + 75, + 657, + 468, + 867 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We employ the ResNet-50 [11] as the backbone model to conduct the PLT-MLC task. We train", + "bbox": [ + 75, + 869, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "our model with a standard Adam [14] optimizer in all the experiments. The images will be randomly cropped and resized to $224 \\times 224$ together with standard data augmentation. Besides, we use an identical set of hyperparameters ( $B = 32$ , $Mo = 0.9$ , $E_{max} = 40$ ) across all the datasets. More details of implementation are in Appendix.", + "bbox": [ + 496, + 416, + 890, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. Following [37], we split these classes into three groups according to the number of their training examples: each head class contains over 100 samples as a many shot, each medium class has 20 to 100 samples as a medium shot, and each tail class has less than 20 samples as a low shot. The total shot indicates all the test samples. We evaluate mean average precision (mAP) for all the classes and recall for missing label settings.", + "bbox": [ + 496, + 508, + 890, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison of the Methods. To quantify the efficacy of the proposed framework, we use several baselines for performance comparison according to different aspects $^2$ . MLC methods: BCE [45], Focal [26], ASL [3]. LT-MLC methods: DB [37], DB-Focal [37] and LWS [13]. PL-MLC methods: Hill [44], Pseudo-Label [15], ML-GCN [5] and P-ASL [2].", + "bbox": [ + 496, + 628, + 890, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Overall Performance", + "text_level": 1, + "bbox": [ + 498, + 732, + 697, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 summarizes the quantitative PLT-MLC results of our framework and baselines on PLT-COCO and PLT-VOC. We make the following observations: 1) In general, irrespective of the different shot scenarios, compared to SoTAs, COMIC achieves the best performance on almost all the metrics across both datasets. In particular, COMIC outperforms other baselines in terms of total shot's mAP by", + "bbox": [ + 496, + 756, + 893, + 862 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "${}^{1}B$ and ${Mo}$ refer to the batch size and momentum in the Adam.", + "bbox": [ + 514, + 875, + 857, + 887 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2We only compare with the approaches that have open source code.", + "bbox": [ + 514, + 887, + 872, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1428", + "bbox": [ + 482, + 946, + 514, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4d47860ae9f4b1b6540fe4fb8de5f06f237289bc2638750c28e7dcacfcbbf5cc.jpg", + "table_caption": [ + "Table 3: Performance comparison under different missing labeled settings. $0\\%$ indicates an LT dataset that is fully labeled." + ], + "table_footnote": [], + "table_body": "
Missing RatioPLT-COCO Dataset
Total ShotMany ShotMedium ShotLow Shot
0%57.07±0.0952.21±0.1159.98±0.1261.12±0.24
30%55.80±0.1749.97±0.1162.59±0.1554.56±0.17
40%54.75±0.1948.93±0.2460.31±0.2154.14±0.21
50%54.69±0.1548.74±0.1256.68±0.1657.25±0.24
", + "bbox": [ + 83, + 146, + 467, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/005ad87dbfe387cb83433f3194c62d4a1d971419db7e1904c10463300cc25d0b.jpg", + "image_caption": [ + "(a) mAρ of different α" + ], + "image_footnote": [], + "bbox": [ + 81, + 262, + 279, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f81bcb1f38fb03b613df93f7a6a64989131f9b856123b61a676511094d8c084a.jpg", + "image_caption": [ + "(b) mAp of different tau" + ], + "image_footnote": [], + "bbox": [ + 279, + 261, + 478, + 375 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/be42b607a22028f8cbe7155ba3aa1bbb6b9b65d852e076a529c5c2194be29983.jpg", + "image_caption": [ + "Figure 3: Ablations with respect to coefficient $\\alpha$ and $\\tau$ .", + "(a) Performance Comparison of Losses", + "Figure 4: MLT-MLC results using different losses." + ], + "image_footnote": [], + "bbox": [ + 81, + 431, + 282, + 558 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fb9a2877c01e1e2bce889431f12c1eae1269292cb3a7eb069491dc401bdadde3.jpg", + "image_caption": [ + "(b) Loss Visualization" + ], + "image_footnote": [], + "bbox": [ + 282, + 431, + 483, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a large margin (PLT-COCO: $1.78\\% \\sim 6.16\\%$ , PLT-VOC: $0.83\\% \\sim 4.13\\%$ ) for PLT-MLC task. 2) Besides, we can observe from Table 1 that the LT methods outperform PL baselines in most $X$ -shot situations. We believe the underlying reason behind this is that LT data distribution hurts the classification capability for MLC models more seriously than PL. Besides, the label correction may have aggravated the LT issue and further result in performance reduction. 3) Benefiting from the carefully designed HTB module, our COMIC not only achieves the highest total mAP score but also yields balanced results with a narrowed performance gap in different shot metrics. These results demonstrate the superiority of our proposed model.", + "bbox": [ + 75, + 625, + 472, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 830, + 230, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Each Component. We conduct an ablation study to illustrate the effectiveness of each component in Table 2. Comparing COMIC and COMIC(-RLC) (Row 1 v.s", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2902bda875f0852c90ce9796f191ccde0c163c689709e12ff401b91899ce1548.jpg", + "image_caption": [ + "(a) Number of TP and FP" + ], + "image_footnote": [], + "bbox": [ + 506, + 89, + 707, + 204 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/70e574376d45e16082c83a35855a516ecb578bdd741ca825c79d8000f731f880.jpg", + "image_caption": [ + "(b) Dynamic Distribution Heat Map", + "Figure 5: In-depth analysis of label correction." + ], + "image_footnote": [], + "bbox": [ + 709, + 88, + 905, + 204 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c6a3fb7c19c10a3af4d2b46a6fd260a96098dea6cab73989cebf02805d65b5e0.jpg", + "table_caption": [ + "Table 4: Ablation of MFM. $\\downarrow$ indicates the mAP decay." + ], + "table_footnote": [], + "table_body": "
MFM FactorPLT-COCO Dataset
P-NH-TTotal ShotMany ShotMedium ShotLow Shot
✔54.44 (↓0.64)48.65 (↓0.56)60.00 (↓0.08)53.81 (↓1.55)
♥53.70 (↓1.38)48.38 (↓0.83)58.99 (↓1.09)52.91 (↓2.45)
✔55.0849.2160.0855.36
", + "bbox": [ + 506, + 273, + 888, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Row 4), the label (Correction) mechanism contributes $0.38\\%$ improvement on total mAP. The results of Row 2 show the mAP improvement of the MFM (Modification). Meanwhile, Row 3 indicates that it suffers from noticeable performance degradation without the (Balance) learning. To sum up, we can observe that the improvement of each module is distinguishable. Combining all the components, our COMIC exhibits steady improvement over the baselines.", + "bbox": [ + 496, + 380, + 893, + 502 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation of Missing Rate. To study the effect of partial labels that affect COMIC's results, we evaluate the performance under different missing rates (MR) of labels (from $0\\% \\sim 50\\%$ ). Not surprisingly, when the MR decreases, the accuracy of COMIC increases on all the metrics. We also find that the performance gap between different shots is consistently small in all MR settings. The results demonstrate the generalizability of the proposed COMIC that it can produce stable and balanced results under different MR settings.", + "bbox": [ + 496, + 502, + 893, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hyperparameter $\\alpha$ and $\\tau$ . We investigate the impact of hyper-parameter $\\alpha$ and $\\tau$ for the PLT-MLC task. The mAPs of different hyper-parameter settings on PLT-COCO are shown in Figure 3. This figure suggests that the optimal choices of $\\alpha$ and $\\tau$ are around 2 and 0.7, respectively. Either increasing or decreasing these values results in performance decay.", + "bbox": [ + 496, + 638, + 893, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. In-Depth Analysis", + "text_level": 1, + "bbox": [ + 500, + 755, + 674, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further validate several vital issues of the proposed Correction $\\rightarrow$ Modification $\\rightarrow$ Balance learning paradigm by answering the three questions as follows.", + "bbox": [ + 496, + 779, + 890, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Q1: Can the model trust the recalled labels distinguished by RLC? To build the insight on the effectiveness of the label correction mechanism in COMIC, we visualize the true positive (TP) and false positive (FP) in Figure 5(a)). This figure suggests that the RLC module can distinguish a large", + "bbox": [ + 496, + 825, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1429", + "bbox": [ + 483, + 946, + 514, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7c2451c28e0e07cfb3cb89aafefea4540503dc212f51dc9945657ec632050826.jpg", + "image_caption": [ + "(a) Separate Training", + "Figure 6: Analysis of balanced learning of COMIC. (a) and (b) depict the total mAP of separate and joint training of COMIC within the 40 epochs. (c) summarizes the loss visualization of head, balanced and tail models with joint training. (d) demonstrates head and tail models respectively optimize the head and tail class's performance." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 284, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4f4b5391f2e69ce724ba454ca76b41940cf8668aecb6a36ceb2e4d7eff1f5ae2.jpg", + "image_caption": [ + "(b) Joint Training" + ], + "image_footnote": [], + "bbox": [ + 285, + 90, + 486, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2d9b55bf08e9622b71937a4e4490ca7d8e2a65a36d0198596dc7ebb2f5a960c5.jpg", + "image_caption": [ + "(c) Loss Visualization" + ], + "image_footnote": [], + "bbox": [ + 491, + 90, + 673, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dabb023a5fc1da4b7324811cca887d6db1babefc97fcc27073a1e8de5a8f126c.jpg", + "image_caption": [ + "(c) Head v.s Tail" + ], + "image_footnote": [], + "bbox": [ + 676, + 90, + 875, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "number of missing labels with high prediction confidence in the early training stage, meanwhile, $\\mathrm{sum(TP)}\\gg \\mathrm{sum(FP)}$ . However, Figure 5(b) of corrected samples also reveals LT class distribution with respect to the original training set. To address this issue, we dynamically adjust the sample weight conditioned on the real-time distribution to produce a stable performance.", + "bbox": [ + 75, + 301, + 470, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Q2: How does the MFM module affect the PLT-MLC performance? Here, we evaluate the effectiveness of the multi-focal modifier (MFM) loss compared with different loss functions. Figure 4(a) shows the loss ablation results using different losses in our COMIC. Our developed MFM outperforms existing losses, as the designed loss considers the key point of the head-tail and positive-negative imbalance under the extreme LT distribution in the PLT-MLC task. There are two components in MFM, which are the positive-negative (P-N) factor and head-tail (H-T) factor. To demonstrate the effect of each component, we train the model with the individual factor in the proposed MFM. As shown in Table. 4, both the P-N factor and the H-T factor play significant roles in MFM. For the H-T factor, it achieves an improvement from $53.7\\%$ mAP to $55.08\\%$ mAP. Meanwhile, it brings a significant gain on tail categories with $2.45\\%$ mAP improvement, indicating its effectiveness to alleviate the severe positive-negative imbalance problems in the LT class distribution. As for the P-N factor, it brings a steady boost on all shot settings which means it can further alleviate the positive-negative issue. Additionally, Figure 4(b) indicates that the MFM loss decreases faster and smoother than the two variants of MFM without different factors, demonstrating its superiority in the PLT-MLC task further.", + "bbox": [ + 75, + 412, + 470, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Q3: How does the HTB module benefit the balanced learning? We systematically present the explicit benefits of the balanced learning strategy in multi-view. 1) Figure 6 (a) and (b) show the comparison between separate and joint training of head, balanced and tail model with respect to the total mAP on PLT-COCO dataset. An interesting phenomenon is that the detached head and tail models slightly outperform the joint head and tail models but suffer", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "from an unstable performance. In contrast, the accuracy of the joint trained balanced model increases much faster and smoother than the detached balanced model which also yields a stable performance and faster convergence speed. This phenomenon is reasonable as the main optimization objective in joint training is to improve the balanced model's performance. It can be regarded as the knowledge distillation effect that enables the balanced model to learn from the head biased and tail biased model, and this in turn facilitates the PLT-MLC learning. 2) During the competition of head v.s tail, the head model's loss drops faster (shown in Figure 6 (c)) and is biased to optimizing the head samples, while the tail model produces an opposite result. Such head and tail biased results form a foundation that enables our COMIC to be trained in a balanced and stable learning effect. 3) We also perform the analysis of the different balanced learning blocks in our COMIC. As presented in Table 6 (in the Appendix), the DL, NC and AMV contribute $0.05\\%$ , $1.08\\%$ and $0.37\\%$ improvement on total shot mAP. The observations and analysis verify the effectiveness of balanced learning for being able to study from the head and tail models, thereby achieving the PLT-MLC improvement.", + "bbox": [ + 496, + 301, + 893, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 657, + 625, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a fire-new task called PLT-MLC and correspondingly developed a novel framework, named COMIC. COMIC simultaneously addresses the partial labeling and long-tailed environments in a Correction $\\rightarrow$ Modification $\\rightarrow$ Balance learning manner. On two newly proposed benchmarks, PLT-COCO and PLT-VOC, we demonstrate that the proposed framework significantly outperforms existing MLC, LT-MLC and PL-MLC approaches.", + "bbox": [ + 496, + 685, + 893, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This research is supported by Singapore Ministry of Education Academic Research Fund Tier 3 under MOE's official grant number MOE2017-T3-1-007, Zhejiang NSF (LR21F020004), the NSFC (No. 62272411), Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, and Ant Group.", + "bbox": [ + 496, + 809, + 893, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1430", + "bbox": [ + 483, + 946, + 514, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 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Pattern Recognition, 74:488-502, 2018." + ], + "bbox": [ + 501, + 92, + 893, + 458 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1432", + "bbox": [ + 483, + 946, + 514, + 957 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning in Imperfect Environment_ Multi-Label Classification with Long-Tailed Distribution and Partial Labels/0590a041-a804-4736-ab7e-fab59b5b776d_model.json b/2023/Learning in Imperfect Environment_ Multi-Label Classification with Long-Tailed Distribution and Partial Labels/0590a041-a804-4736-ab7e-fab59b5b776d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4b442dece62d5c50af462b5e8652aa650a1503b0 --- /dev/null +++ b/2023/Learning in Imperfect Environment_ Multi-Label Classification with Long-Tailed Distribution and Partial Labels/0590a041-a804-4736-ab7e-fab59b5b776d_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.165, + 0.13, + 0.806, + 0.175 + ], + "angle": 0, + "content": "Learning in Imperfect Environment: Multi-Label Classification with Long-Tailed Distribution and Partial Labels" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.202, + 0.874, + 0.24 + ], + "angle": 0, + "content": "Wenqiao Zhang 1 Changshuo Liu 2 Lingze Zeng 2 Bengchin Ooi 2 Siliang Tang 1 Yueting Zhuang 1" + }, + { + "type": "text", + "bbox": [ + 0.263, + 0.242, + 0.721, + 0.256 + ], + "angle": 0, + "content": "\\(^{1}\\) Zhejiang University, China, \\(^{2}\\) National University of Singapore, Singapore," + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.26, + 0.89, + 0.275 + ], + "angle": 0, + "content": "wenqiao zhang@zju.edu.cn, liu717@comp.nus.edu.sg, Zenglz_pro@163.com, ooibc@comp.nus.edu.sg," + }, + { + "type": "text", + "bbox": [ + 0.318, + 0.278, + 0.655, + 0.292 + ], + "angle": 0, + "content": "siliang@zju.edu.cn, yzhuang@zju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.361, + 0.474, + 0.816 + ], + "angle": 0, + "content": "Conventional multi-label classification (MLC) methods assume that all samples are fully labeled and identically distributed. Unfortunately, this assumption is unrealistic in large-scale MLC data that has long-tailed (LT) distribution and partial labels (PL). To address the problem, we introduce a novel task, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), to jointly consider the above two imperfect learning environments. Not surprisingly, we find that most LT-MLC and PL-MLC approaches fail to solve the PLT-MLC, resulting in significant performance degradation on the two proposed PLT-MLC benchmarks. Therefore, we propose an end-to-end learning framework: \\( \\mathbf{C}\\mathbf{O}\\mathbf{R}\\mathbf{e}\\mathbf{r}\\mathbf{o}\\mathbf{r}\\mathbf{c}\\rightarrow \\) Modification \\( \\rightarrow \\) balanCe, abbreviated as COMIC. Our bootstrapping philosophy is to simultaneously correct the missing labels (Correction) with convinced prediction confidence over a class-aware threshold and to learn from these recall labels during training. We next propose a novel multi-focal modifier loss that simultaneously addresses head-tail imbalance and positive-negative imbalance to adaptively modify the attention to different samples (Modification) under the LT class distribution. In addition, we develop a balanced training strategy by distilling the model's learning effect from head and tail samples, and thus design a balanced classifier (Balance) conditioned on the head and tail learning effect to maintain stable performance for all samples. Our experimental study shows that the proposed COMIC significantly outperforms general MLC, LT-MLC and PL-MLC methods in terms of effectiveness and robustness on our newly created PLT-MLC datasets. Codes and benchmarks are available on the link https://https://github.com/wannature/COMIC" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.85, + 0.21, + 0.866 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "In recent years, the development of deep learning prosperity to the field of computer vision [20, 17, 19, 16, 23, 22, 25," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.896, + 0.737 + ], + "angle": 0, + "content": "24, 43, 42, 18]. Images typically contain multiple objects and concepts, highlighting the importance of multi-label classification (MLC) [34] for real-world tasks. Along with the wide adoption of deep learning, recent MLC approaches have made remarkable progress in visual recognition [36, 38], but the performance is limited by two common assumptions: all categories have comparable numbers of instances and each training instance has been fully annotated with all the relevant labels. While this conventional setting provides a perfect training environment for various studies, it conceals a number of complexities that typically arise in real-world applications: i) Long-Tailed (LT) Class Distribution. With the growth of digital data, the crux of making a large-scale dataset is no longer about where to collect, but how to balance it [33]. However, the cost of expanding the dataset to a larger class vocabulary with balanced data is not linear — but exponential — since the data is inevitably long-tailed following Zipf's distribution [30]. ii) Partial Labels (PL) of Instances. In the case of a large number of categories, it is difficult and even impractical to fully annotate all relevant labels for each image [39, 46]. Intuitively, humans tend to focus on different aspects of image contents due to human bias, i.e., their preference, personality and sentiment [41], which indirectly affects how and what we annotate. In fact, LT and PL are often co-occurring, and therefore, the MLC model must be sufficiently robust to handle different data distributions and imperfect datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.902 + ], + "angle": 0, + "content": "In this paper, we present a new challenge for MLC at scale, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), with concomitant existence of both PL setting [39] and LT distribution [33] problems. As captured in the overview of PLT-MLC in Figure 1 (a), it has the following three challenges: i) False Negative Training. Under the PL setting, the MLC model treats the un-annotated labels \\((\\odot)\\) as negatives \\((\\odot)\\), which may produce sub-optimal decision boundary as it adds noise of false negative labels (Figure 1 (b)). The situation is further exacerbated in the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1423" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.125, + 0.089, + 0.412, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.089, + 0.847, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.897, + 0.335 + ], + "angle": 0, + "content": "Figure 1: (a) illustrates an overview of the proposed PLT-MLC task. (b) depicts three key challenges of a PLT-MLC task. (c) depicts a concise version of our proposed model for facilitating the PLT-MLC. \\((\\bullet : positive, \\bullet : negative, \\circ : false, \\circ :\\) corrected positive)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.473, + 0.807 + ], + "angle": 0, + "content": "LT class distribution as some tail categories are prone to missing annotations in practice. For instance, in Figure 1 (a), \"person\" is the head class in the PLT-MLC dataset and is often notable in an image to labeling for annotators. In contrast, the \"tie\" often occupies a tiny region in the scene compared with the \"person\". The annotator may miss the \"tie\" object, which will aggravate the LT distribution and further increase the difficulty of learning from tail classes. ii) Head-Tail and Positive-Negative Imbalance. There are two imbalance issues in a PLT-MLC task: inter-instance head-tail imbalance and intra-instance positive-negative imbalance. As shown in Figure 1 (b), the inter-instance ratio of head positive (\\(\\odot\\)) \"person\" (\\(\\odot\\)): tail positive (\\(\\odot\\)\"tie\\(\\odot\\)) \\(\\approx\\) 32 under the LT data distribution, and the intra-instance ratio of tail negative (\\(\\odot\\)) categories: tail positive (\\(\\odot\\)\"tie\\(\\odot\\)) = 78 as an image only contains a small fraction of the positive labels. Consequently, a robust PLT-MLC model should address the co-occurring imbalances simultaneously. iii) Head Overfitting and Tail Underfitting. Different from the general LT distribution, the classification model downplays the minor tail and overplays the major head. The PLT-MLC has an extreme LT distribution and Figure 1(c) illustrates an interesting phenomenon of MLC model learning: the general classification model is prone to overfitting to head class with extensive samples and underfitting to tail classes with a few samples. This figure also indicates that only the medium class shows a steady growth in performance, which means that existing LT methods focusing on lifting up the tail performance may not solve the PLT-MLC problem satisfactorily." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Suppose a trained model is used to correct the missing labels and then an LT classifier is trained using the updated labels, we might not be able to obtain a satisfying PLT-MLC performance, either. While machine learning methods can easily detect the head samples, they may have difficulty in identifying the tail samples. As a result, the corrected labels" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.895, + 0.504 + ], + "angle": 0, + "content": "may still exhibit an LT distribution that inevitably hurts balanced learning. Moreover, even when a general LT classifier affords the trade-off to improve the tail performance conditioned on the head performance drop, it is still incapable of simultaneously addressing the issue of head overfitting and tail underfitting problem. Further, the decoupled learning paradigm is impractical since it needs the \"stop\" training and human \"re-start\" training, i.e., an end-to-end learning scheme is more desirable. Thus, these limitations motivate us to reconsider the solution for the PLT-MLC task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.896, + 0.903 + ], + "angle": 0, + "content": "To this end, we propose an end-to-end PLT-MLC framework: COrrection \\(\\rightarrow\\) ModificatIon \\(\\rightarrow\\) balanCe (Figure 1), called COMIC, which progressively addresses the three key PLT-MLC challenges. Step 1: The Correction module aims to gradually correct the missing labels according to the predicted confidence and dynamically adjusts the classified loss of the corrected samples under the real-time estimated class distribution. Step 2: After the label correction, the Modification module introduces a novel Multi-Focal Modifier (MFM) Loss, which contains two focal factors to address the two imbalance issues in PLT-MLC independently. Motivated by [3], the first is an intra-instance positive-negative factor that determines the concentration of learning on hard negatives and positives with different exponential decay factors. The second is an inter-instance head-tail factor that increases the impact of rare categories, ensuring that the loss contribution of rare samples will not be overwhelmed by frequent ones. Step 3: Finally, the Balance module measures the model's optimization direction with a calculated moving average vector of the gradient over all past samples. And thus, we devise a head model and a tail model by subtracting or adding this moving vector, which can respectively improve head and tail performance. Subsequently, a balanced classifier deduces a balanced learning effect under the supervision of the head classifier and tail classifier. It protects the model training from being too medium biased, and hence" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1424" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "the balanced classifier is able to achieve the balanced learning schema. Notably, our solution is an end-to-end learning framework, which is re-training-free and effectively enables balanced prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.154, + 0.473, + 0.306 + ], + "angle": 0, + "content": "Our contributions are three-fold: (1) We present a new challenging task: Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), together with two newly designed benchmarks: PLT-COCO and PLT-VOC. (2) We propose an end-to-end PLT-MLC learning framework, called COMIC, to effectively perform the PLT-MLC task as a progressive learning paradigm, i.e., Correction \\(\\rightarrow\\) Modification \\(\\rightarrow\\) Balance. (3) Through an extensive experimental study, we show that our method improves all the prevalent LT and ML line-ups on PLT-MLC benchmarks by a large margin." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.325, + 0.226, + 0.34 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.473, + 0.549 + ], + "angle": 0, + "content": "Long-Tailed MLC. [37] is the first work that addresses the LT-MLC by extending the re-balanced sampling and cost-sensitive re-weighting methods. It proposes an optimized DB Focal method, which does improve the recognition performance of tail classes. Later work, [10] performs uniform and re-balanced samplings from the same training set. Then a two-branch network is developed to enforce the consistency between two branches for collaborative learning on both uniform and re-balanced samplings. However, the above works require careful data initialization, i.e., re-sampling, which is undesirable in practice. Moreover, these methods have not yet considered the missing labeling case, which may not sufficiently deal with the PLT-MLC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.472, + 0.793 + ], + "angle": 0, + "content": "MLC with Partial Labels. Multi-label tasks often involve incomplete training data, hence several methods have been proposed to solve the problem of multi-label learning with missing labels. A simple solution is to treat the missing labels as negative labels [31, 21, 4]. However, performance will drop because a lot of ground-truth positive labels are initialized as negative labels [12]. Current works on PL-MLC mainly focus on the design of networks and training schemes. The common practice is to utilize the customized networks to learn label correlations or classification confidence to realize correct recognition of missing labels [7, 44]. However, the corrected labels learned from a trained model are imbalanced due to the previous training dataset having an LT distribution. Using such recall labels will aggravate the LT distribution in the PLT-MLC dataset and result in an imbalanced performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Other Works. [40] learns to generate concept-invariant samples in the environment with semantic gap, which enables the model to classify the samples through causal intervention, yielding improved generalization guarantees; [18] collaborates a cascade of foundation models, thus learning superior interleaved multi-modal instruction-following ability from imperfect supervision." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.636, + 0.108 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.115, + 0.894, + 0.147 + ], + "angle": 0, + "content": "This section describes the proposed PLT-MLC framework. We will present each module and its training strategy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.153, + 0.704, + 0.168 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.177, + 0.895, + 0.362 + ], + "angle": 0, + "content": "Before presenting our method, we first introduce some basic notions and terminologies. We consider a partially annotated MLC dataset contains \\(C\\) classes and \\(N\\) i.i.d training samples \\(\\mathcal{S} = \\{(\\mathcal{I}^{(1)},y^{(1)}),\\dots ,(\\mathcal{I}^{(N)},y^{(N)})\\}\\), where \\(\\mathcal{I}^{(i)}\\) denote \\(i^{th}\\) image and label \\(y^{(i)} = [y_1^{(i)},\\dots ,y_c^{(i)}]\\in \\{0,1\\}^C\\). For a given \\(i^{th}\\) example and category \\(c\\), \\(y_{c}^{(i)} = 0\\), 1 respectively means the category is unknown and present. Our proposed COMIC solves the PLT-MLC problem in an end-to-end learning manner: Correction \\(\\rightarrow\\) Modification \\(\\rightarrow\\) Balance, with Reflective Label Corrector (RLC, in Sec.3.2), Multi-Focal Modifier (MFM, in Sec.3.3) and Head-Tail Balancer (HTB, in Sec.3.3), as illustrated in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.363, + 0.894, + 0.469 + ], + "angle": 0, + "content": "These three modules are designed to seek a balanced model \\(\\mathcal{M}_b(\\cdot ;\\Theta_b)\\), parameterized by \\(\\Theta_{b}\\), to predict the presence or absence of each class given an input image. We denote \\(p = [p_1,\\dots ,p_c]\\) as the class prediction, computed by the model: \\(p_c = \\sigma (z_c)\\) where \\(\\sigma\\) is the sigmoid function, and \\(z_{c}\\) is the output logit corresponding to class \\(c\\). The optimized goal of COMIC can be defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.475, + 0.892, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\underbrace {\\mathcal {L} ((\\mathcal {S}) ; \\Theta_ {b})} _ {\\text {C O M I C L o s s}} = \\underbrace {\\lambda_ {c} \\cdot \\mathcal {L} _ {r l c}} _ {\\text {R L C L o s s}} + \\underbrace {\\lambda_ {m} \\cdot \\mathcal {L} _ {m f m}} _ {\\text {M F M L o s s}} + \\underbrace {\\lambda_ {b} \\cdot \\mathcal {L} _ {h t b}} _ {\\text {H T B L o s s}} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.516, + 0.894, + 0.547 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{rlc}\\), \\(\\mathcal{L}_{mfm}\\) and \\(\\mathcal{L}_{htb}\\) denote the loss of RLC, MFM and HTB, respectively. \\(\\lambda_{c},\\lambda_{m}\\) and \\(\\lambda_{b}\\) are hyperparameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.554, + 0.741, + 0.568 + ], + "angle": 0, + "content": "3.2. Reflective Label Corrector" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.895, + 0.819 + ], + "angle": 0, + "content": "Reflective Label Corrector (RLC) presents a real-time label correction method for missing labels to alleviate the effect of partially labeled samples. The core idea is to examine the label likelihood \\( p \\) of each training image and recall the labels with convinced prediction confidence during training. Interestingly, we found that the model can distinguish a large number of missing labels with high prediction confidence in the early training stage, which implies that we can recall these missing labels during training to boost PTL-MLC learning. Here, we first define a threshold \\( \\tau \\) and then check the input sample's label likelihood \\( p \\) to check whether it is greater than \\( \\tau \\) and then calculate the average category possibility \\( P_{c} \\) of past trained data with class \\( c \\). If predicted probabilities \\( p_{c} \\) are highly confident, i.e., \\( p_{c} > \\max \\{\\tau, P_{c}\\} \\), we regard that the sample misses the label of class \\( c \\) and set a pseudo-label \\( \\hat{y}_{c} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.825, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {c} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} p _ {c} > \\max \\left\\{\\tau , P _ {c} \\right\\}, y _ {c} = 0 \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Thus, the loss of RLC module, i.e., \\(\\mathcal{L}_{rlc}\\) utilizes the MFM loss (refer the details in Sec. 3.3) with these corrected label" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1425" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.092, + 0.48, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.092, + 0.847, + 0.172 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.174, + 0.709, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.714, + 0.174, + 0.844, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.396, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Figure 2: Overview of COMIC. RLC module (Correction) corrects the missing labels along with the training and dynamically re-weights the sample weight according to the estimated class distribution. MFM module (Modification) adjusts the focal of different instances according to head-tail and positive-negative imbalance under the extreme LT distribution. HTB module (Balance) measures the model's optimization direction and correspondingly develops a balanced learning scheme to produce stable PLT-MLC performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.499, + 0.218, + 0.515 + ], + "angle": 0, + "content": "\\(\\hat{y}\\) for model training:" + }, + { + "type": "equation", + "bbox": [ + 0.069, + 0.53, + 0.47, + 0.582 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r l c} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {m f m} ^ {+} (p), & \\text {i f} \\hat {y} = 1 \\\\ \\mathbb {1} _ {(y = 1)} \\mathcal {L} _ {m f m} ^ {+} (p) + \\mathbb {1} _ {(\\hat {y} = 0)} \\mathcal {L} _ {m f m} ^ {-} (p), & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.75 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{mfm}^{+}(p)\\) and \\(\\mathcal{L}_{mfm}^{-}(p)\\) refer to the generalized MFM loss function for positives and negatives. Notably, we find that most of the corrected labels belong to head class, which may aggravate the LT distribution. To address this issue, we dynamically adjust the inter-sample head-tail factor \\(\\gamma_{ht}^{(i)}\\) (details of this factor are explained in Sec. 3.3) according to the dynamic class distribution \\(\\mathcal{D}_t\\), which can increase the focal weight for tail samples. In addition, we also multiply \\(\\mathcal{L}_{rlc}(p)\\) by a coefficient \\(\\frac{\\mathcal{B}_s}{\\mathcal{N}_t}\\) in each training batch to constrain the loss value, where \\(\\mathcal{B}_s\\) is the batch size and \\(\\mathcal{N}_t\\) is the number of corrected labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.753, + 0.47, + 0.799 + ], + "angle": 0, + "content": "Through this, RLC can gradually and dynamically correct the potential missing labels during training, which efficiently improves the classifier's performance with recalled labels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.275, + 0.83 + ], + "angle": 0, + "content": "3.3. Multi-Focal Modifier" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We first revisit the focal loss [26], which is a widely-used solution in the positive-negative imbalance problem. It redistributes the loss contribution of easy samples and hard samples, which greatly weakens the influence of the majority" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.5, + 0.637, + 0.515 + ], + "angle": 0, + "content": "of negative samples." + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.529, + 0.892, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f l} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {f l} ^ {+} = (1 - p) ^ {\\gamma} \\log (p), & \\text {i f} y = 1 \\\\ \\mathcal {L} _ {f l} ^ {-} = p ^ {\\gamma} \\log (1 - p), & \\text {i f} y = 0 \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.642 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is the focusing parameter, \\(\\gamma = 0\\) yields binary cross-entropy. By setting \\(\\gamma > 0\\), the contribution of easy negatives (with low probability, \\(p \\ll 0.5\\)) can be down-weighted in the loss, enabling the model to focus on harder samples." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.644, + 0.891, + 0.674 + ], + "angle": 0, + "content": "However, the focal loss may not satisfactorily resolve the PLT-MLC problem due to two key aspects:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.688, + 0.892, + 0.765 + ], + "angle": 0, + "content": "- Tail Positive Gradient Elimination. When using focal loss for multi-label training, there is an inner trade-off: high \\(\\gamma\\) sufficiently down-weights the contribution from easy negatives, but may eliminate the gradients from the tail positive samples [3]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.78, + 0.892, + 0.841 + ], + "angle": 0, + "content": "- Head-Tail Imbalance. Imbalance among the positive categories also exists in MLC, i.e., head positive-tail positive imbalance. Rare categories suffer more from severe imbalance issues than frequent ones." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.688, + 0.892, + 0.841 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Thus, we propose a Multi-Focal Modifier (MFM) loss that decouples \\(\\gamma\\) at two granularities of focal factors, i.e., an intra-sample positive-negative (P-N) factor \\(\\gamma_{pn}\\) and an" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1426" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.342, + 0.107 + ], + "angle": 0, + "content": "inter-sample head-tail (H-T) factor \\(\\gamma_{ht}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.117, + 0.471, + 0.159 + ], + "angle": 0, + "content": "\\[\n\\gamma^ {(i)} = \\left\\{ \\begin{array}{l l} \\gamma^ {(i) +} = \\gamma_ {p n} ^ {+} + w ^ {+} \\cdot \\gamma_ {h t} ^ {(i)}, & \\text {i f} y = 1 \\\\ \\gamma^ {(i) -} = \\gamma_ {p n} ^ {-} + w ^ {-} \\cdot \\gamma_ {h t} ^ {(i)}, & \\text {i f} y = 0 \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.169, + 0.473, + 0.432 + ], + "angle": 0, + "content": "where \\(\\gamma^{(i) + }\\) and \\(\\gamma^{(i) - }\\) control the focal of samples with \\(i^{th}\\) class. Similar to [3], \\(\\gamma_{pn}^{+}\\) and \\(\\gamma_{pn}^{-}\\) decouple the original decay rate \\(\\gamma\\) as two factors, which respectively control the focal of the positive and negative samples. Since we are interested in emphasizing the contribution of positive samples, we set \\(\\gamma_{pn}^{-}\\geq \\gamma_{pn}^{+}\\). We achieve better control over the contribution of positive and negative samples through the designed loss function, which assists the network to learn meaningful features from positive samples, despite their rarity. Another focal factor \\(\\gamma_{ht}^{(i)}\\) is a variable parameter \\((\\geq 1)\\) associated with the imbalance degree of the \\(i^{th}\\) class. A bigger value of \\(\\gamma_{ht}^{(i)}\\) will increase the weight of tail samples to encourage the model to pay more attention to the positive tail samples, and vice versa. \\(w^{+}\\) and \\(w^{-}\\) are the coefficients that adjust the weight at a fine-grained level. The \\(\\gamma_{ht}^{(i)}\\) is the static class distribution \\(\\mathcal{D}\\) of training set with max normalization function \\(\\psi (\\cdot)\\) [29] to adjust the head-tail focal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.472, + 0.479 + ], + "angle": 0, + "content": "After applying the decoupled \\(\\gamma^{(i) + }\\) and \\(\\gamma^{(i) - }\\) into our MFM loss, we obtain the loss function as follows (more discussions in the Appendix.):" + }, + { + "type": "equation", + "bbox": [ + 0.067, + 0.489, + 0.47, + 0.541 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m f m} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {m f m} ^ {+} = \\sum_ {i = 1} ^ {C} (1 - p) ^ {\\gamma^ {(i) +}} \\log (p), & \\text {i f} y = 1 \\\\ \\mathcal {L} _ {m f m} ^ {-} = \\sum_ {i = 1} ^ {C} p ^ {\\gamma^ {(i) -}} \\log (1 - p), & \\text {i f} y = 0 \\end{array} \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.473, + 0.587 + ], + "angle": 0, + "content": "By doing so, the MFM module utilizes the multi-grained focal to alleviate the two imbalance problems in the PLT-MLC task, yielding better classification results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.596, + 0.265, + 0.611 + ], + "angle": 0, + "content": "3.4. Head-Tail Balancer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.473, + 0.786 + ], + "angle": 0, + "content": "As discussed in the introduction, the extreme LT dataset with numerous head samples and a small number of tail samples result in a head overfitting and tail underfitting learning effect. Only the medium samples present a superior performance during training, which fails to obtain the balanced performance for the overall samples. To address this issue, we develop a balanced strategy that measures the balanced learning effect under the supervision of the head classifier and tail classifier to achieve balanced results. Before we delve into the balanced learning, we first measure the moving average of the gradient in the SGD-based optimizer [32]:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.798, + 0.47, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {t} = \\mu \\cdot \\mathbf {e} _ {t - 1} + \\operatorname {s u m} \\left(g _ {t}\\right), \\forall t = 1, \\dots , T. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.871 + ], + "angle": 0, + "content": "where \\(\\mathrm{sum}(g_t)\\) is the accumulated gradient at iteration \\(t\\), \\(\\mu\\) is the momentum decay. The average moving vector \\(\\mathbf{e}_t\\) records the model's optimization tendency by \\(\\mathbf{e}_{t-1}\\) and \\(\\mathrm{sum}(g_t)\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In our empirical study, we observe that only the medium samples obtain a stable learning effect from the early to late" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.273 + ], + "angle": 0, + "content": "training stage, mainly due to the extreme LT distribution. To simulate the learning effect towards head/tail samples, as depicted in Figure 2(c), we reduce/add the moving vector \\(\\mathbf{e}_t\\) at each step in head model \\(\\mathcal{M}_h\\) and tail model \\(\\mathcal{M}_t\\) respectively, to assist the balanced model \\(\\mathcal{M}_b\\) for balanced learning. Notably, we set different learning rate decays for each model to further explore the balanced learning effect. The three models are parallel-trained with their own backbone and classifier. In the feature learning stage, we develop an additive attention [1] that computes the relevance of balanced features \\(\\hat{\\mathbf{f}}_b\\), and head features \\(\\mathbf{f}_h\\), tail features \\(\\mathbf{f}_t\\) extracted from corresponding backbones." + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.283, + 0.893, + 0.301 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {b} = \\operatorname {A t t n} \\left(\\hat {\\mathbf {f}} _ {b}, \\left[ \\mathbf {f} _ {h}, \\mathbf {f} _ {t} \\right]\\right)) + \\hat {\\mathbf {f}} _ {b} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.311, + 0.838, + 0.326 + ], + "angle": 0, + "content": "where \\( Attn(\\cdot) \\) is the additive attention mechanism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.894, + 0.433 + ], + "angle": 0, + "content": "Then updated \\(\\mathbf{f}_b\\), \\(\\mathbf{f}_h\\), \\(\\mathbf{f}_t\\) are input to their classifiers to obtain their logits. We develop the multi-head classifier with normalization [9, 28, 33], which has already been embraced by various methods of empirical practice. The multi-head strategy [35] equally divides the channel of weights and features into \\(N_g\\) groups, which can be considered as \\(N_g\\) times of fine-grained sampling." + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.443, + 0.893, + 0.486 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {x} = \\frac {\\rho}{N _ {g}} \\sum_ {k = 1} ^ {N _ {g}} \\frac {w _ {k} ^ {\\top} \\mathbf {f} _ {x}}{(| | w _ {k} | | + \\eta) | | \\mathbf {f} _ {x} | |}, x \\in \\{h, t, b \\} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.495, + 0.892, + 0.54 + ], + "angle": 0, + "content": "where \\(\\rho\\) is a scaling factor akin to the inverse temperature in Gibbs distribution, \\(\\eta\\) is a class-agnostic baseline energy. \\(w_{k}\\) is the \\(k^{th}\\) learned parameter matrix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.541, + 0.894, + 0.587 + ], + "angle": 0, + "content": "Subsequently, we measure the head and tail learning effect by subtracting and adding the average moving vector \\(\\mathbf{e}_t\\) to the logits of head model and tail model, respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.596, + 0.893, + 0.64 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {z}} _ {x} = \\mathbf {z} _ {x} \\pm \\frac {\\rho}{N _ {g}} \\sum_ {k = 1} ^ {N _ {g}} \\frac {\\sin \\left(\\mathbf {z} _ {x} , \\mathbf {e} _ {t}\\right) \\cdot \\left(w _ {j}\\right) ^ {\\top} \\mathbf {e} _ {t}}{| | w _ {k} | | + \\eta}, x \\in \\{h, t \\} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.65, + 0.88, + 0.665 + ], + "angle": 0, + "content": "where \\(sim(\\cdot, \\cdot)\\) measures the cosine similarity of vectors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.665, + 0.894, + 0.726 + ], + "angle": 0, + "content": "After obtaining the logits of \\(\\hat{\\mathbf{z}}_h\\), \\(\\hat{\\mathbf{z}}_t\\) and \\(\\mathbf{z}_b\\), the balanced learning effect needs to distill the head and tail knowledge from \\(\\hat{\\mathbf{z}}_h\\) and \\(\\hat{\\mathbf{z}}_t\\) to enable the stable learning for all samples. Hence, we develop the head-tail loss:" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.736, + 0.893, + 0.754 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {h t b} = \\kappa_ {h} \\cdot \\mathcal {L} \\left(\\phi \\left(\\hat {\\mathbf {z}} _ {h}\\right) \\cdot \\phi \\left(\\mathbf {z} _ {b}\\right)\\right) + \\kappa_ {t} \\cdot \\mathcal {L} \\left(\\phi \\left(\\hat {\\mathbf {z}} _ {t}\\right) \\cdot \\phi \\left(\\mathbf {z} _ {b}\\right)\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.895, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}\\) is \\(\\mathcal{L}_{mfm}\\) and \\(\\phi (\\cdot)\\) is softmax function. \\(\\kappa_{h}\\) and \\(\\kappa_{t}\\) are adaptive weights for head and tail learning that calculated by \\(\\kappa_{h} = \\frac{(\\mathcal{L}(\\hat{z}_{h}))^{\\alpha}}{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha} + (\\mathcal{L}(\\hat{z}_{h}))^{\\alpha}}\\) and \\(\\kappa_{t} = \\frac{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha}}{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha} + (\\mathcal{L}(z_{h}))^{\\alpha}}\\), respectively. \\(\\alpha\\) is a scaling factor and we study its effect in Sec. 4.3. Such loss can be regarded as the empirical risk minimization (ERM) [6], which adaptively distills the knowledge from the head and tail models, enabling the balanced model is not biased to medium samples and produces a balanced learning effect for the PLT-MLC task." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1427" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.154 + ], + "angle": 0, + "content": "Table 1: Performance comparison of the proposed method and baselines on PLT-MLC datasets (PLT-COCO and PLT-VOC). \\(E2E^{*}\\) indicates that the PLT model is learned in an end-to-end manner. A larger score has better performance. Improv. indicates performance improvement. Acronym notations of baselines can be found in Sec. 4.1. We color each row as the best, second best and lowest score." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.163, + 0.879, + 0.393 + ], + "angle": 0, + "content": "
CategoryMethodsE2E*PLT-COCO DatasetPLT-VOC Dataset
Many ShotMedium ShotFew ShotTotal ShotMany ShotMedium ShotFew ShotTotal Shot
MLCBCE [45]✔42.57±0.1156.67±0.1946.40±0.6048.92±0.2367.37±0.1888.27±0.3983.79±0.4178.79±0.14
Focal [26]✔41.05±0.0758.33±0.1253.58±0.3151.39±0.1567.02±0.1187.49±0.1882.82±0.7878.13±0.23
ASL [3]✔41.60±0.1758.15±0.1552.67±0.1751.20±0.0867.67±0.1087.79±0.1382.23±0.5578.35±0.11
LT-MLCDB [37]✔44.83±0.3158.96±0.2453.82±0.4752.16±0.3669.22±0.2888.56±0.4283.72±0.3578.86±0.23
DB-Focal [37]✔45.76±0.2559.74±0.2153.85±0.1652.57±0.2768.96±0.2288.89±0.1883.42±0.2078.90±0.26
LWS [13]-44.86±0.5858.79±0.6353.48±0.5152.86±0.6069.08±0.4488.24±0.5583.46±0.4778.28±0.49
PL-MLCPseudo-Label [15]-41.41±0.4157.46±0.3553.12±0.3351.67±0.3767.38±0.2487.58±0.3583.26±0.4278.32±0.30
ML-GCN [5]✔43.43±0.5358.46±0.6153.74±0.4852.14±0.5568.46±0.4488.17±0.6182.46±0.3879.02±0.56
Hill [44]✔42.50±0.1656.89±0.1947.31±0.3749.28±0.0968.79±0.1586.70±0.1778.15±0.9977.40±0.22
P-ASL [2]✔43.09±0.0557.67±0.0753.46±0.2251.75±0.1768.95±0.2287.24±0.1383.37±0.3378.96±0.16
PLT-MLCHead Model (Ours)✔47.59±0.0959.07±0.1252.35±0.2853.30±0.1972.91±0.2888.59±0.3182.12±0.2780.70±0.30
Tail Model (Ours)✔46.30±0.2558.76±0.2953.38±0.1453.09±0.2771.65±0.3488.68±0.4183.51±0.2480.58±0.36
COMIC (Ours)✔49.21±0.2260.08±0.1355.36±0.2155.08±0.1473.10±0.3589.18±0.4584.53±0.4881.53±0.35
Improv. ↑--1.62 ~ 8.160.34 ~ 3.410.53 ~ 8.961.78 ~ 6.160.19 ~ 6.080.29 ~ 2.48-0.3 ~ 6.380.83 ~ 4.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.415, + 0.471, + 0.461 + ], + "angle": 0, + "content": "Table 2: Ablation study of different modules. M,C,B represent correction, modification and balance learning, respectively." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.473, + 0.466, + 0.58 + ], + "angle": 0, + "content": "
ModelsSettingPLT-COCO Dataset
MCBTotal mAPAverage mAPRecall
-RLC✔✔54.70±0.1354.42±0.1585.26±0.08
-MFM✔✔54.60±0.1354.33±0.1384.59±0.19
-HTB✔✔53.65±0.3153.36±0.3184.19±0.23
COMIC✔✔✔55.08±0.1454.88±0.1988.19±0.22
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.607, + 0.21, + 0.625 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.633, + 0.267, + 0.65 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Dataset Construction. The proposed method is analyzed on the created LT versions of two MLC benchmarks (COCO [27] and VOC [8]), called PLT-COCO and PLT-VOC, respectively. The missing rate of PLT-COCO is \\(40\\%\\) and it contains 2,962 images from 80 classes. The maximum training number for each class is 1,240 and the minimum number is 6. We select 5000 images from the test set of COCO2017 for evaluation. PLT-VOC has the same missing rate setting and contains 2,569 images from 20 classes, in which the maximum training number for each class is 1,117 and the minimum number is 7. We evaluate the performance on VOC2007 test set with 4,952 images. More details about the dataset construction can be found in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Implementation Details. We employ the ResNet-50 [11] as the backbone model to conduct the PLT-MLC task. We train" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.508 + ], + "angle": 0, + "content": "our model with a standard Adam [14] optimizer in all the experiments. The images will be randomly cropped and resized to \\(224 \\times 224\\) together with standard data augmentation. Besides, we use an identical set of hyperparameters (\\(B = 32\\), \\(Mo = 0.9\\), \\(E_{max} = 40\\)) across all the datasets. More details of implementation are in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Evaluation Metrics. Following [37], we split these classes into three groups according to the number of their training examples: each head class contains over 100 samples as a many shot, each medium class has 20 to 100 samples as a medium shot, and each tail class has less than 20 samples as a low shot. The total shot indicates all the test samples. We evaluate mean average precision (mAP) for all the classes and recall for missing label settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.722 + ], + "angle": 0, + "content": "Comparison of the Methods. To quantify the efficacy of the proposed framework, we use several baselines for performance comparison according to different aspects\\(^2\\). MLC methods: BCE [45], Focal [26], ASL [3]. LT-MLC methods: DB [37], DB-Focal [37] and LWS [13]. PL-MLC methods: Hill [44], Pseudo-Label [15], ML-GCN [5] and P-ASL [2]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.733, + 0.698, + 0.749 + ], + "angle": 0, + "content": "4.2. Overall Performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.757, + 0.894, + 0.863 + ], + "angle": 0, + "content": "Table 1 summarizes the quantitative PLT-MLC results of our framework and baselines on PLT-COCO and PLT-VOC. We make the following observations: 1) In general, irrespective of the different shot scenarios, compared to SoTAs, COMIC achieves the best performance on almost all the metrics across both datasets. In particular, COMIC outperforms other baselines in terms of total shot's mAP by" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.875, + 0.858, + 0.888 + ], + "angle": 0, + "content": "\\( {}^{1}B \\) and \\( {Mo} \\) refer to the batch size and momentum in the Adam." + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.888, + 0.874, + 0.901 + ], + "angle": 0, + "content": "2We only compare with the approaches that have open source code." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.875, + 0.874, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1428" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.473, + 0.135 + ], + "angle": 0, + "content": "Table 3: Performance comparison under different missing labeled settings. \\(0\\%\\) indicates an LT dataset that is fully labeled." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.147, + 0.468, + 0.248 + ], + "angle": 0, + "content": "
Missing RatioPLT-COCO Dataset
Total ShotMany ShotMedium ShotLow Shot
0%57.07±0.0952.21±0.1159.98±0.1261.12±0.24
30%55.80±0.1749.97±0.1162.59±0.1554.56±0.17
40%54.75±0.1948.93±0.2460.31±0.2154.14±0.21
50%54.69±0.1548.74±0.1256.68±0.1657.25±0.24
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.263, + 0.28, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.379, + 0.245, + 0.388 + ], + "angle": 0, + "content": "(a) mAρ of different α" + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.262, + 0.48, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.328, + 0.378, + 0.45, + 0.389 + ], + "angle": 0, + "content": "(b) mAp of different tau" + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.402, + 0.465, + 0.418 + ], + "angle": 0, + "content": "Figure 3: Ablations with respect to coefficient \\(\\alpha\\) and \\(\\tau\\)." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.433, + 0.283, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.561, + 0.284, + 0.57 + ], + "angle": 0, + "content": "(a) Performance Comparison of Losses" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.433, + 0.484, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.346, + 0.56, + 0.442, + 0.57 + ], + "angle": 0, + "content": "(b) Loss Visualization" + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.583, + 0.449, + 0.599 + ], + "angle": 0, + "content": "Figure 4: MLT-MLC results using different losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.473, + 0.822 + ], + "angle": 0, + "content": "a large margin (PLT-COCO: \\(1.78\\% \\sim 6.16\\%\\), PLT-VOC: \\(0.83\\% \\sim 4.13\\%\\)) for PLT-MLC task. 2) Besides, we can observe from Table 1 that the LT methods outperform PL baselines in most \\(X\\)-shot situations. We believe the underlying reason behind this is that LT data distribution hurts the classification capability for MLC models more seriously than PL. Besides, the label correction may have aggravated the LT issue and further result in performance reduction. 3) Benefiting from the carefully designed HTB module, our COMIC not only achieves the highest total mAP score but also yields balanced results with a narrowed performance gap in different shot metrics. These results demonstrate the superiority of our proposed model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.232, + 0.849 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Effectiveness of Each Component. We conduct an ablation study to illustrate the effectiveness of each component in Table 2. Comparing COMIC and COMIC(-RLC) (Row 1 v.s" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.09, + 0.708, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.206, + 0.682, + 0.216 + ], + "angle": 0, + "content": "(a) Number of TP and FP" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.089, + 0.906, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.205, + 0.889, + 0.215 + ], + "angle": 0, + "content": "(b) Dynamic Distribution Heat Map" + }, + { + "type": "image_caption", + "bbox": [ + 0.533, + 0.228, + 0.857, + 0.243 + ], + "angle": 0, + "content": "Figure 5: In-depth analysis of label correction." + }, + { + "type": "table_caption", + "bbox": [ + 0.51, + 0.248, + 0.881, + 0.264 + ], + "angle": 0, + "content": "Table 4: Ablation of MFM. \\( \\downarrow \\) indicates the mAP decay." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.275, + 0.89, + 0.355 + ], + "angle": 0, + "content": "
MFM FactorPLT-COCO Dataset
P-NH-TTotal ShotMany ShotMedium ShotLow Shot
✔54.44 (↓0.64)48.65 (↓0.56)60.00 (↓0.08)53.81 (↓1.55)
♥53.70 (↓1.38)48.38 (↓0.83)58.99 (↓1.09)52.91 (↓2.45)
✔55.0849.2160.0855.36
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.895, + 0.503 + ], + "angle": 0, + "content": "Row 4), the label (Correction) mechanism contributes \\(0.38\\%\\) improvement on total mAP. The results of Row 2 show the mAP improvement of the MFM (Modification). Meanwhile, Row 3 indicates that it suffers from noticeable performance degradation without the (Balance) learning. To sum up, we can observe that the improvement of each module is distinguishable. Combining all the components, our COMIC exhibits steady improvement over the baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.895, + 0.639 + ], + "angle": 0, + "content": "Ablation of Missing Rate. To study the effect of partial labels that affect COMIC's results, we evaluate the performance under different missing rates (MR) of labels (from \\(0\\% \\sim 50\\%\\)). Not surprisingly, when the MR decreases, the accuracy of COMIC increases on all the metrics. We also find that the performance gap between different shots is consistently small in all MR settings. The results demonstrate the generalizability of the proposed COMIC that it can produce stable and balanced results under different MR settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.894, + 0.746 + ], + "angle": 0, + "content": "Hyperparameter \\(\\alpha\\) and \\(\\tau\\). We investigate the impact of hyper-parameter \\(\\alpha\\) and \\(\\tau\\) for the PLT-MLC task. The mAPs of different hyper-parameter settings on PLT-COCO are shown in Figure 3. This figure suggests that the optimal choices of \\(\\alpha\\) and \\(\\tau\\) are around 2 and 0.7, respectively. Either increasing or decreasing these values results in performance decay." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.756, + 0.676, + 0.772 + ], + "angle": 0, + "content": "4.4. In-Depth Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.825 + ], + "angle": 0, + "content": "We further validate several vital issues of the proposed Correction \\(\\rightarrow\\) Modification \\(\\rightarrow\\) Balance learning paradigm by answering the three questions as follows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Q1: Can the model trust the recalled labels distinguished by RLC? To build the insight on the effectiveness of the label correction mechanism in COMIC, we visualize the true positive (TP) and false positive (FP) in Figure 5(a)). This figure suggests that the RLC module can distinguish a large" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1429" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.285, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.207, + 0.252, + 0.218 + ], + "angle": 0, + "content": "(a) Separate Training" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.092, + 0.488, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.207, + 0.444, + 0.218 + ], + "angle": 0, + "content": "(b) Joint Training" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.092, + 0.674, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.207, + 0.65, + 0.218 + ], + "angle": 0, + "content": "(c) Loss Visualization" + }, + { + "type": "image", + "bbox": [ + 0.677, + 0.092, + 0.876, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.207, + 0.827, + 0.218 + ], + "angle": 0, + "content": "(c) Head v.s Tail" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.895, + 0.276 + ], + "angle": 0, + "content": "Figure 6: Analysis of balanced learning of COMIC. (a) and (b) depict the total mAP of separate and joint training of COMIC within the 40 epochs. (c) summarizes the loss visualization of head, balanced and tail models with joint training. (d) demonstrates head and tail models respectively optimize the head and tail class's performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.471, + 0.408 + ], + "angle": 0, + "content": "number of missing labels with high prediction confidence in the early training stage, meanwhile, \\(\\mathrm{sum(TP)}\\gg \\mathrm{sum(FP)}\\). However, Figure 5(b) of corrected samples also reveals LT class distribution with respect to the original training set. To address this issue, we dynamically adjust the sample weight conditioned on the real-time distribution to produce a stable performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.471, + 0.775 + ], + "angle": 0, + "content": "Q2: How does the MFM module affect the PLT-MLC performance? Here, we evaluate the effectiveness of the multi-focal modifier (MFM) loss compared with different loss functions. Figure 4(a) shows the loss ablation results using different losses in our COMIC. Our developed MFM outperforms existing losses, as the designed loss considers the key point of the head-tail and positive-negative imbalance under the extreme LT distribution in the PLT-MLC task. There are two components in MFM, which are the positive-negative (P-N) factor and head-tail (H-T) factor. To demonstrate the effect of each component, we train the model with the individual factor in the proposed MFM. As shown in Table. 4, both the P-N factor and the H-T factor play significant roles in MFM. For the H-T factor, it achieves an improvement from \\(53.7\\%\\) mAP to \\(55.08\\%\\) mAP. Meanwhile, it brings a significant gain on tail categories with \\(2.45\\%\\) mAP improvement, indicating its effectiveness to alleviate the severe positive-negative imbalance problems in the LT class distribution. As for the P-N factor, it brings a steady boost on all shot settings which means it can further alleviate the positive-negative issue. Additionally, Figure 4(b) indicates that the MFM loss decreases faster and smoother than the two variants of MFM without different factors, demonstrating its superiority in the PLT-MLC task further." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Q3: How does the HTB module benefit the balanced learning? We systematically present the explicit benefits of the balanced learning strategy in multi-view. 1) Figure 6 (a) and (b) show the comparison between separate and joint training of head, balanced and tail model with respect to the total mAP on PLT-COCO dataset. An interesting phenomenon is that the detached head and tail models slightly outperform the joint head and tail models but suffer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.302, + 0.895, + 0.635 + ], + "angle": 0, + "content": "from an unstable performance. In contrast, the accuracy of the joint trained balanced model increases much faster and smoother than the detached balanced model which also yields a stable performance and faster convergence speed. This phenomenon is reasonable as the main optimization objective in joint training is to improve the balanced model's performance. It can be regarded as the knowledge distillation effect that enables the balanced model to learn from the head biased and tail biased model, and this in turn facilitates the PLT-MLC learning. 2) During the competition of head v.s tail, the head model's loss drops faster (shown in Figure 6 (c)) and is biased to optimizing the head samples, while the tail model produces an opposite result. Such head and tail biased results form a foundation that enables our COMIC to be trained in a balanced and stable learning effect. 3) We also perform the analysis of the different balanced learning blocks in our COMIC. As presented in Table 6 (in the Appendix), the DL, NC and AMV contribute \\(0.05\\%\\), \\(1.08\\%\\) and \\(0.37\\%\\) improvement on total shot mAP. The observations and analysis verify the effectiveness of balanced learning for being able to study from the head and tail models, thereby achieving the PLT-MLC improvement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.658, + 0.627, + 0.673 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.895, + 0.808 + ], + "angle": 0, + "content": "We have presented a fire-new task called PLT-MLC and correspondingly developed a novel framework, named COMIC. COMIC simultaneously addresses the partial labeling and long-tailed environments in a Correction \\(\\rightarrow\\) Modification \\(\\rightarrow\\) Balance learning manner. On two newly proposed benchmarks, PLT-COCO and PLT-VOC, we demonstrate that the proposed framework significantly outperforms existing MLC, LT-MLC and PL-MLC approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Acknowledgement This research is supported by Singapore Ministry of Education Academic Research Fund Tier 3 under MOE's official grant number MOE2017-T3-1-007, Zhejiang NSF (LR21F020004), the NSFC (No. 62272411), Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, and Ant Group." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1430" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.159 + ], + "angle": 0, + "content": "[1] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 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Unfortunately, this assumption is unrealistic in large-scale MLC data that has long-tailed (LT) distribution and partial labels (PL). To address the problem, we introduce a novel task, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), to jointly consider the above two imperfect learning environments. Not surprisingly, we find that most LT-MLC and PL-MLC approaches fail to solve the PLT-MLC, resulting in significant performance degradation on the two proposed PLT-MLC benchmarks. Therefore, we propose an end-to-end learning framework: $\mathbf{C}\mathbf{O}\mathbf{R}\mathbf{e}\mathbf{r}\mathbf{o}\mathbf{r}\mathbf{c}\rightarrow$ Modification $\rightarrow$ balanCe, abbreviated as COMIC. Our bootstrapping philosophy is to simultaneously correct the missing labels (Correction) with convinced prediction confidence over a class-aware threshold and to learn from these recall labels during training. We next propose a novel multi-focal modifier loss that simultaneously addresses head-tail imbalance and positive-negative imbalance to adaptively modify the attention to different samples (Modification) under the LT class distribution. In addition, we develop a balanced training strategy by distilling the model's learning effect from head and tail samples, and thus design a balanced classifier (Balance) conditioned on the head and tail learning effect to maintain stable performance for all samples. Our experimental study shows that the proposed COMIC significantly outperforms general MLC, LT-MLC and PL-MLC methods in terms of effectiveness and robustness on our newly created PLT-MLC datasets. Codes and benchmarks are available on the link https://https://github.com/wannature/COMIC + +# 1. Introduction + +In recent years, the development of deep learning prosperity to the field of computer vision [20, 17, 19, 16, 23, 22, 25, + +24, 43, 42, 18]. Images typically contain multiple objects and concepts, highlighting the importance of multi-label classification (MLC) [34] for real-world tasks. Along with the wide adoption of deep learning, recent MLC approaches have made remarkable progress in visual recognition [36, 38], but the performance is limited by two common assumptions: all categories have comparable numbers of instances and each training instance has been fully annotated with all the relevant labels. While this conventional setting provides a perfect training environment for various studies, it conceals a number of complexities that typically arise in real-world applications: i) Long-Tailed (LT) Class Distribution. With the growth of digital data, the crux of making a large-scale dataset is no longer about where to collect, but how to balance it [33]. However, the cost of expanding the dataset to a larger class vocabulary with balanced data is not linear — but exponential — since the data is inevitably long-tailed following Zipf's distribution [30]. ii) Partial Labels (PL) of Instances. In the case of a large number of categories, it is difficult and even impractical to fully annotate all relevant labels for each image [39, 46]. Intuitively, humans tend to focus on different aspects of image contents due to human bias, i.e., their preference, personality and sentiment [41], which indirectly affects how and what we annotate. In fact, LT and PL are often co-occurring, and therefore, the MLC model must be sufficiently robust to handle different data distributions and imperfect datasets. + +In this paper, we present a new challenge for MLC at scale, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), with concomitant existence of both PL setting [39] and LT distribution [33] problems. As captured in the overview of PLT-MLC in Figure 1 (a), it has the following three challenges: i) False Negative Training. Under the PL setting, the MLC model treats the un-annotated labels $(\odot)$ as negatives $(\odot)$ , which may produce sub-optimal decision boundary as it adds noise of false negative labels (Figure 1 (b)). The situation is further exacerbated in the + +![](images/3252a6d42f8a56a86a3850c4d575d0ca94145d1ff7a844cbfe3f1bb36d5b442c.jpg) +Figure 1: (a) illustrates an overview of the proposed PLT-MLC task. (b) depicts three key challenges of a PLT-MLC task. (c) depicts a concise version of our proposed model for facilitating the PLT-MLC. $(\bullet : positive, \bullet : negative, \circ : false, \circ :$ corrected positive) + +![](images/e4930b6aa52408b836b771c2cc1735cf3f7e08ad25c2068e503468c17bc0d196.jpg) + +LT class distribution as some tail categories are prone to missing annotations in practice. For instance, in Figure 1 (a), "person" is the head class in the PLT-MLC dataset and is often notable in an image to labeling for annotators. In contrast, the "tie" often occupies a tiny region in the scene compared with the "person". The annotator may miss the "tie" object, which will aggravate the LT distribution and further increase the difficulty of learning from tail classes. ii) Head-Tail and Positive-Negative Imbalance. There are two imbalance issues in a PLT-MLC task: inter-instance head-tail imbalance and intra-instance positive-negative imbalance. As shown in Figure 1 (b), the inter-instance ratio of head positive ( $\odot$ ) "person" ( $\odot$ ): tail positive ( $\odot$ "tie $\odot$ ) $\approx$ 32 under the LT data distribution, and the intra-instance ratio of tail negative ( $\odot$ ) categories: tail positive ( $\odot$ "tie $\odot$ ) = 78 as an image only contains a small fraction of the positive labels. Consequently, a robust PLT-MLC model should address the co-occurring imbalances simultaneously. iii) Head Overfitting and Tail Underfitting. Different from the general LT distribution, the classification model downplays the minor tail and overplays the major head. The PLT-MLC has an extreme LT distribution and Figure 1(c) illustrates an interesting phenomenon of MLC model learning: the general classification model is prone to overfitting to head class with extensive samples and underfitting to tail classes with a few samples. This figure also indicates that only the medium class shows a steady growth in performance, which means that existing LT methods focusing on lifting up the tail performance may not solve the PLT-MLC problem satisfactorily. + +Suppose a trained model is used to correct the missing labels and then an LT classifier is trained using the updated labels, we might not be able to obtain a satisfying PLT-MLC performance, either. While machine learning methods can easily detect the head samples, they may have difficulty in identifying the tail samples. As a result, the corrected labels + +may still exhibit an LT distribution that inevitably hurts balanced learning. Moreover, even when a general LT classifier affords the trade-off to improve the tail performance conditioned on the head performance drop, it is still incapable of simultaneously addressing the issue of head overfitting and tail underfitting problem. Further, the decoupled learning paradigm is impractical since it needs the "stop" training and human "re-start" training, i.e., an end-to-end learning scheme is more desirable. Thus, these limitations motivate us to reconsider the solution for the PLT-MLC task. + +To this end, we propose an end-to-end PLT-MLC framework: COrrection $\rightarrow$ ModificatIon $\rightarrow$ balanCe (Figure 1), called COMIC, which progressively addresses the three key PLT-MLC challenges. Step 1: The Correction module aims to gradually correct the missing labels according to the predicted confidence and dynamically adjusts the classified loss of the corrected samples under the real-time estimated class distribution. Step 2: After the label correction, the Modification module introduces a novel Multi-Focal Modifier (MFM) Loss, which contains two focal factors to address the two imbalance issues in PLT-MLC independently. Motivated by [3], the first is an intra-instance positive-negative factor that determines the concentration of learning on hard negatives and positives with different exponential decay factors. The second is an inter-instance head-tail factor that increases the impact of rare categories, ensuring that the loss contribution of rare samples will not be overwhelmed by frequent ones. Step 3: Finally, the Balance module measures the model's optimization direction with a calculated moving average vector of the gradient over all past samples. And thus, we devise a head model and a tail model by subtracting or adding this moving vector, which can respectively improve head and tail performance. Subsequently, a balanced classifier deduces a balanced learning effect under the supervision of the head classifier and tail classifier. It protects the model training from being too medium biased, and hence + +the balanced classifier is able to achieve the balanced learning schema. Notably, our solution is an end-to-end learning framework, which is re-training-free and effectively enables balanced prediction. + +Our contributions are three-fold: (1) We present a new challenging task: Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), together with two newly designed benchmarks: PLT-COCO and PLT-VOC. (2) We propose an end-to-end PLT-MLC learning framework, called COMIC, to effectively perform the PLT-MLC task as a progressive learning paradigm, i.e., Correction $\rightarrow$ Modification $\rightarrow$ Balance. (3) Through an extensive experimental study, we show that our method improves all the prevalent LT and ML line-ups on PLT-MLC benchmarks by a large margin. + +# 2. Related Works + +Long-Tailed MLC. [37] is the first work that addresses the LT-MLC by extending the re-balanced sampling and cost-sensitive re-weighting methods. It proposes an optimized DB Focal method, which does improve the recognition performance of tail classes. Later work, [10] performs uniform and re-balanced samplings from the same training set. Then a two-branch network is developed to enforce the consistency between two branches for collaborative learning on both uniform and re-balanced samplings. However, the above works require careful data initialization, i.e., re-sampling, which is undesirable in practice. Moreover, these methods have not yet considered the missing labeling case, which may not sufficiently deal with the PLT-MLC. + +MLC with Partial Labels. Multi-label tasks often involve incomplete training data, hence several methods have been proposed to solve the problem of multi-label learning with missing labels. A simple solution is to treat the missing labels as negative labels [31, 21, 4]. However, performance will drop because a lot of ground-truth positive labels are initialized as negative labels [12]. Current works on PL-MLC mainly focus on the design of networks and training schemes. The common practice is to utilize the customized networks to learn label correlations or classification confidence to realize correct recognition of missing labels [7, 44]. However, the corrected labels learned from a trained model are imbalanced due to the previous training dataset having an LT distribution. Using such recall labels will aggravate the LT distribution in the PLT-MLC dataset and result in an imbalanced performance. + +Other Works. [40] learns to generate concept-invariant samples in the environment with semantic gap, which enables the model to classify the samples through causal intervention, yielding improved generalization guarantees; [18] collaborates a cascade of foundation models, thus learning superior interleaved multi-modal instruction-following ability from imperfect supervision. + +# 3. Methodology + +This section describes the proposed PLT-MLC framework. We will present each module and its training strategy. + +# 3.1. Problem Formulation + +Before presenting our method, we first introduce some basic notions and terminologies. We consider a partially annotated MLC dataset contains $C$ classes and $N$ i.i.d training samples $\mathcal{S} = \{(\mathcal{I}^{(1)},y^{(1)}),\dots ,(\mathcal{I}^{(N)},y^{(N)})\}$ , where $\mathcal{I}^{(i)}$ denote $i^{th}$ image and label $y^{(i)} = [y_1^{(i)},\dots ,y_c^{(i)}]\in \{0,1\}^C$ . For a given $i^{th}$ example and category $c$ , $y_{c}^{(i)} = 0$ , 1 respectively means the category is unknown and present. Our proposed COMIC solves the PLT-MLC problem in an end-to-end learning manner: Correction $\rightarrow$ Modification $\rightarrow$ Balance, with Reflective Label Corrector (RLC, in Sec.3.2), Multi-Focal Modifier (MFM, in Sec.3.3) and Head-Tail Balancer (HTB, in Sec.3.3), as illustrated in Figure 2. + +These three modules are designed to seek a balanced model $\mathcal{M}_b(\cdot ;\Theta_b)$ , parameterized by $\Theta_{b}$ , to predict the presence or absence of each class given an input image. We denote $p = [p_1,\dots ,p_c]$ as the class prediction, computed by the model: $p_c = \sigma (z_c)$ where $\sigma$ is the sigmoid function, and $z_{c}$ is the output logit corresponding to class $c$ . The optimized goal of COMIC can be defined as follows: + +$$ +\underbrace {\mathcal {L} ((\mathcal {S}) ; \Theta_ {b})} _ {\text {C O M I C L o s s}} = \underbrace {\lambda_ {c} \cdot \mathcal {L} _ {r l c}} _ {\text {R L C L o s s}} + \underbrace {\lambda_ {m} \cdot \mathcal {L} _ {m f m}} _ {\text {M F M L o s s}} + \underbrace {\lambda_ {b} \cdot \mathcal {L} _ {h t b}} _ {\text {H T B L o s s}} \tag {1} +$$ + +where $\mathcal{L}_{rlc}$ , $\mathcal{L}_{mfm}$ and $\mathcal{L}_{htb}$ denote the loss of RLC, MFM and HTB, respectively. $\lambda_{c},\lambda_{m}$ and $\lambda_{b}$ are hyperparameters. + +# 3.2. Reflective Label Corrector + +Reflective Label Corrector (RLC) presents a real-time label correction method for missing labels to alleviate the effect of partially labeled samples. The core idea is to examine the label likelihood $p$ of each training image and recall the labels with convinced prediction confidence during training. Interestingly, we found that the model can distinguish a large number of missing labels with high prediction confidence in the early training stage, which implies that we can recall these missing labels during training to boost PTL-MLC learning. Here, we first define a threshold $\tau$ and then check the input sample's label likelihood $p$ to check whether it is greater than $\tau$ and then calculate the average category possibility $P_{c}$ of past trained data with class $c$ . If predicted probabilities $p_{c}$ are highly confident, i.e., $p_{c} > \max \{\tau, P_{c}\}$ , we regard that the sample misses the label of class $c$ and set a pseudo-label $\hat{y}_{c}$ . + +$$ +\hat {y} _ {c} = \left\{ \begin{array}{l l} 1, & \text {i f} p _ {c} > \max \left\{\tau , P _ {c} \right\}, y _ {c} = 0 \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {2} +$$ + +Thus, the loss of RLC module, i.e., $\mathcal{L}_{rlc}$ utilizes the MFM loss (refer the details in Sec. 3.3) with these corrected label + +![](images/437ca58d174d331935450d64630aba60fdedf08c66ee8ef204d10a6878493963.jpg) + +![](images/cd98ecdd00a0baf3356e99f6bc9751210e4786ae428eb5f6658ce3721c5d23c8.jpg) + +![](images/0624ea5a4d27a76d03897b0a9d85ab81025a16befa67f2f1d4a45e7c4c693ad4.jpg) +Figure 2: Overview of COMIC. RLC module (Correction) corrects the missing labels along with the training and dynamically re-weights the sample weight according to the estimated class distribution. MFM module (Modification) adjusts the focal of different instances according to head-tail and positive-negative imbalance under the extreme LT distribution. HTB module (Balance) measures the model's optimization direction and correspondingly develops a balanced learning scheme to produce stable PLT-MLC performance. + +![](images/63ae493d2d175e533a774d3b7850adcb61a85997ebf393e3934bc729b6e8b9fe.jpg) + +$\hat{y}$ for model training: + +$$ +\mathcal {L} _ {r l c} (p) = \left\{ \begin{array}{l l} \mathcal {L} _ {m f m} ^ {+} (p), & \text {i f} \hat {y} = 1 \\ \mathbb {1} _ {(y = 1)} \mathcal {L} _ {m f m} ^ {+} (p) + \mathbb {1} _ {(\hat {y} = 0)} \mathcal {L} _ {m f m} ^ {-} (p), & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +where $\mathcal{L}_{mfm}^{+}(p)$ and $\mathcal{L}_{mfm}^{-}(p)$ refer to the generalized MFM loss function for positives and negatives. Notably, we find that most of the corrected labels belong to head class, which may aggravate the LT distribution. To address this issue, we dynamically adjust the inter-sample head-tail factor $\gamma_{ht}^{(i)}$ (details of this factor are explained in Sec. 3.3) according to the dynamic class distribution $\mathcal{D}_t$ , which can increase the focal weight for tail samples. In addition, we also multiply $\mathcal{L}_{rlc}(p)$ by a coefficient $\frac{\mathcal{B}_s}{\mathcal{N}_t}$ in each training batch to constrain the loss value, where $\mathcal{B}_s$ is the batch size and $\mathcal{N}_t$ is the number of corrected labels. + +Through this, RLC can gradually and dynamically correct the potential missing labels during training, which efficiently improves the classifier's performance with recalled labels. + +# 3.3. Multi-Focal Modifier + +We first revisit the focal loss [26], which is a widely-used solution in the positive-negative imbalance problem. It redistributes the loss contribution of easy samples and hard samples, which greatly weakens the influence of the majority + +of negative samples. + +$$ +\mathcal {L} _ {f l} (p) = \left\{ \begin{array}{l l} \mathcal {L} _ {f l} ^ {+} = (1 - p) ^ {\gamma} \log (p), & \text {i f} y = 1 \\ \mathcal {L} _ {f l} ^ {-} = p ^ {\gamma} \log (1 - p), & \text {i f} y = 0 \end{array} \right. \tag {4} +$$ + +where $\gamma$ is the focusing parameter, $\gamma = 0$ yields binary cross-entropy. By setting $\gamma > 0$ , the contribution of easy negatives (with low probability, $p \ll 0.5$ ) can be down-weighted in the loss, enabling the model to focus on harder samples. + +However, the focal loss may not satisfactorily resolve the PLT-MLC problem due to two key aspects: + +- Tail Positive Gradient Elimination. When using focal loss for multi-label training, there is an inner trade-off: high $\gamma$ sufficiently down-weights the contribution from easy negatives, but may eliminate the gradients from the tail positive samples [3]. +- Head-Tail Imbalance. Imbalance among the positive categories also exists in MLC, i.e., head positive-tail positive imbalance. Rare categories suffer more from severe imbalance issues than frequent ones. + +Thus, we propose a Multi-Focal Modifier (MFM) loss that decouples $\gamma$ at two granularities of focal factors, i.e., an intra-sample positive-negative (P-N) factor $\gamma_{pn}$ and an + +inter-sample head-tail (H-T) factor $\gamma_{ht}$ . + +$$ +\gamma^ {(i)} = \left\{ \begin{array}{l l} \gamma^ {(i) +} = \gamma_ {p n} ^ {+} + w ^ {+} \cdot \gamma_ {h t} ^ {(i)}, & \text {i f} y = 1 \\ \gamma^ {(i) -} = \gamma_ {p n} ^ {-} + w ^ {-} \cdot \gamma_ {h t} ^ {(i)}, & \text {i f} y = 0 \end{array} \right. \tag {5} +$$ + +where $\gamma^{(i) + }$ and $\gamma^{(i) - }$ control the focal of samples with $i^{th}$ class. Similar to [3], $\gamma_{pn}^{+}$ and $\gamma_{pn}^{-}$ decouple the original decay rate $\gamma$ as two factors, which respectively control the focal of the positive and negative samples. Since we are interested in emphasizing the contribution of positive samples, we set $\gamma_{pn}^{-}\geq \gamma_{pn}^{+}$ . We achieve better control over the contribution of positive and negative samples through the designed loss function, which assists the network to learn meaningful features from positive samples, despite their rarity. Another focal factor $\gamma_{ht}^{(i)}$ is a variable parameter $(\geq 1)$ associated with the imbalance degree of the $i^{th}$ class. A bigger value of $\gamma_{ht}^{(i)}$ will increase the weight of tail samples to encourage the model to pay more attention to the positive tail samples, and vice versa. $w^{+}$ and $w^{-}$ are the coefficients that adjust the weight at a fine-grained level. The $\gamma_{ht}^{(i)}$ is the static class distribution $\mathcal{D}$ of training set with max normalization function $\psi (\cdot)$ [29] to adjust the head-tail focal. + +After applying the decoupled $\gamma^{(i) + }$ and $\gamma^{(i) - }$ into our MFM loss, we obtain the loss function as follows (more discussions in the Appendix.): + +$$ +\mathcal {L} _ {m f m} (p) = \left\{ \begin{array}{l l} \mathcal {L} _ {m f m} ^ {+} = \sum_ {i = 1} ^ {C} (1 - p) ^ {\gamma^ {(i) +}} \log (p), & \text {i f} y = 1 \\ \mathcal {L} _ {m f m} ^ {-} = \sum_ {i = 1} ^ {C} p ^ {\gamma^ {(i) -}} \log (1 - p), & \text {i f} y = 0 \end{array} \right. \tag {6} +$$ + +By doing so, the MFM module utilizes the multi-grained focal to alleviate the two imbalance problems in the PLT-MLC task, yielding better classification results. + +# 3.4. Head-Tail Balancer + +As discussed in the introduction, the extreme LT dataset with numerous head samples and a small number of tail samples result in a head overfitting and tail underfitting learning effect. Only the medium samples present a superior performance during training, which fails to obtain the balanced performance for the overall samples. To address this issue, we develop a balanced strategy that measures the balanced learning effect under the supervision of the head classifier and tail classifier to achieve balanced results. Before we delve into the balanced learning, we first measure the moving average of the gradient in the SGD-based optimizer [32]: + +$$ +\mathbf {e} _ {t} = \mu \cdot \mathbf {e} _ {t - 1} + \operatorname {s u m} \left(g _ {t}\right), \forall t = 1, \dots , T. \tag {7} +$$ + +where $\mathrm{sum}(g_t)$ is the accumulated gradient at iteration $t$ , $\mu$ is the momentum decay. The average moving vector $\mathbf{e}_t$ records the model's optimization tendency by $\mathbf{e}_{t-1}$ and $\mathrm{sum}(g_t)$ . + +In our empirical study, we observe that only the medium samples obtain a stable learning effect from the early to late + +training stage, mainly due to the extreme LT distribution. To simulate the learning effect towards head/tail samples, as depicted in Figure 2(c), we reduce/add the moving vector $\mathbf{e}_t$ at each step in head model $\mathcal{M}_h$ and tail model $\mathcal{M}_t$ respectively, to assist the balanced model $\mathcal{M}_b$ for balanced learning. Notably, we set different learning rate decays for each model to further explore the balanced learning effect. The three models are parallel-trained with their own backbone and classifier. In the feature learning stage, we develop an additive attention [1] that computes the relevance of balanced features $\hat{\mathbf{f}}_b$ , and head features $\mathbf{f}_h$ , tail features $\mathbf{f}_t$ extracted from corresponding backbones. + +$$ +\mathbf {f} _ {b} = \operatorname {A t t n} \left(\hat {\mathbf {f}} _ {b}, \left[ \mathbf {f} _ {h}, \mathbf {f} _ {t} \right]\right)) + \hat {\mathbf {f}} _ {b} \tag {8} +$$ + +where $Attn(\cdot)$ is the additive attention mechanism. + +Then updated $\mathbf{f}_b$ , $\mathbf{f}_h$ , $\mathbf{f}_t$ are input to their classifiers to obtain their logits. We develop the multi-head classifier with normalization [9, 28, 33], which has already been embraced by various methods of empirical practice. The multi-head strategy [35] equally divides the channel of weights and features into $N_g$ groups, which can be considered as $N_g$ times of fine-grained sampling. + +$$ +\mathbf {z} _ {x} = \frac {\rho}{N _ {g}} \sum_ {k = 1} ^ {N _ {g}} \frac {w _ {k} ^ {\top} \mathbf {f} _ {x}}{(| | w _ {k} | | + \eta) | | \mathbf {f} _ {x} | |}, x \in \{h, t, b \} \tag {9} +$$ + +where $\rho$ is a scaling factor akin to the inverse temperature in Gibbs distribution, $\eta$ is a class-agnostic baseline energy. $w_{k}$ is the $k^{th}$ learned parameter matrix. + +Subsequently, we measure the head and tail learning effect by subtracting and adding the average moving vector $\mathbf{e}_t$ to the logits of head model and tail model, respectively: + +$$ +\hat {\mathbf {z}} _ {x} = \mathbf {z} _ {x} \pm \frac {\rho}{N _ {g}} \sum_ {k = 1} ^ {N _ {g}} \frac {\sin \left(\mathbf {z} _ {x} , \mathbf {e} _ {t}\right) \cdot \left(w _ {j}\right) ^ {\top} \mathbf {e} _ {t}}{| | w _ {k} | | + \eta}, x \in \{h, t \} \tag {10} +$$ + +where $sim(\cdot, \cdot)$ measures the cosine similarity of vectors. + +After obtaining the logits of $\hat{\mathbf{z}}_h$ , $\hat{\mathbf{z}}_t$ and $\mathbf{z}_b$ , the balanced learning effect needs to distill the head and tail knowledge from $\hat{\mathbf{z}}_h$ and $\hat{\mathbf{z}}_t$ to enable the stable learning for all samples. Hence, we develop the head-tail loss: + +$$ +\mathcal {L} _ {h t b} = \kappa_ {h} \cdot \mathcal {L} \left(\phi \left(\hat {\mathbf {z}} _ {h}\right) \cdot \phi \left(\mathbf {z} _ {b}\right)\right) + \kappa_ {t} \cdot \mathcal {L} \left(\phi \left(\hat {\mathbf {z}} _ {t}\right) \cdot \phi \left(\mathbf {z} _ {b}\right)\right) \tag {11} +$$ + +where $\mathcal{L}$ is $\mathcal{L}_{mfm}$ and $\phi (\cdot)$ is softmax function. $\kappa_{h}$ and $\kappa_{t}$ are adaptive weights for head and tail learning that calculated by $\kappa_{h} = \frac{(\mathcal{L}(\hat{z}_{h}))^{\alpha}}{(\mathcal{L}(\hat{z}_{t}))^{\alpha} + (\mathcal{L}(\hat{z}_{h}))^{\alpha}}$ and $\kappa_{t} = \frac{(\mathcal{L}(\hat{z}_{t}))^{\alpha}}{(\mathcal{L}(\hat{z}_{t}))^{\alpha} + (\mathcal{L}(z_{h}))^{\alpha}}$ , respectively. $\alpha$ is a scaling factor and we study its effect in Sec. 4.3. Such loss can be regarded as the empirical risk minimization (ERM) [6], which adaptively distills the knowledge from the head and tail models, enabling the balanced model is not biased to medium samples and produces a balanced learning effect for the PLT-MLC task. + +Table 1: Performance comparison of the proposed method and baselines on PLT-MLC datasets (PLT-COCO and PLT-VOC). $E2E^{*}$ indicates that the PLT model is learned in an end-to-end manner. A larger score has better performance. Improv. indicates performance improvement. Acronym notations of baselines can be found in Sec. 4.1. We color each row as the best, second best and lowest score. + +
CategoryMethodsE2E*PLT-COCO DatasetPLT-VOC Dataset
Many ShotMedium ShotFew ShotTotal ShotMany ShotMedium ShotFew ShotTotal Shot
MLCBCE [45]✔42.57±0.1156.67±0.1946.40±0.6048.92±0.2367.37±0.1888.27±0.3983.79±0.4178.79±0.14
Focal [26]✔41.05±0.0758.33±0.1253.58±0.3151.39±0.1567.02±0.1187.49±0.1882.82±0.7878.13±0.23
ASL [3]✔41.60±0.1758.15±0.1552.67±0.1751.20±0.0867.67±0.1087.79±0.1382.23±0.5578.35±0.11
LT-MLCDB [37]✔44.83±0.3158.96±0.2453.82±0.4752.16±0.3669.22±0.2888.56±0.4283.72±0.3578.86±0.23
DB-Focal [37]✔45.76±0.2559.74±0.2153.85±0.1652.57±0.2768.96±0.2288.89±0.1883.42±0.2078.90±0.26
LWS [13]-44.86±0.5858.79±0.6353.48±0.5152.86±0.6069.08±0.4488.24±0.5583.46±0.4778.28±0.49
PL-MLCPseudo-Label [15]-41.41±0.4157.46±0.3553.12±0.3351.67±0.3767.38±0.2487.58±0.3583.26±0.4278.32±0.30
ML-GCN [5]✔43.43±0.5358.46±0.6153.74±0.4852.14±0.5568.46±0.4488.17±0.6182.46±0.3879.02±0.56
Hill [44]✔42.50±0.1656.89±0.1947.31±0.3749.28±0.0968.79±0.1586.70±0.1778.15±0.9977.40±0.22
P-ASL [2]✔43.09±0.0557.67±0.0753.46±0.2251.75±0.1768.95±0.2287.24±0.1383.37±0.3378.96±0.16
PLT-MLCHead Model (Ours)✔47.59±0.0959.07±0.1252.35±0.2853.30±0.1972.91±0.2888.59±0.3182.12±0.2780.70±0.30
Tail Model (Ours)✔46.30±0.2558.76±0.2953.38±0.1453.09±0.2771.65±0.3488.68±0.4183.51±0.2480.58±0.36
COMIC (Ours)✔49.21±0.2260.08±0.1355.36±0.2155.08±0.1473.10±0.3589.18±0.4584.53±0.4881.53±0.35
Improv. ↑--1.62 ~ 8.160.34 ~ 3.410.53 ~ 8.961.78 ~ 6.160.19 ~ 6.080.29 ~ 2.48-0.3 ~ 6.380.83 ~ 4.13
+ +Table 2: Ablation study of different modules. M,C,B represent correction, modification and balance learning, respectively. + +
ModelsSettingPLT-COCO Dataset
MCBTotal mAPAverage mAPRecall
-RLC✔✔54.70±0.1354.42±0.1585.26±0.08
-MFM✔✔54.60±0.1354.33±0.1384.59±0.19
-HTB✔✔53.65±0.3153.36±0.3184.19±0.23
COMIC✔✔✔55.08±0.1454.88±0.1988.19±0.22
+ +# 4. Experiments + +# 4.1. Experimental Setup + +Dataset Construction. The proposed method is analyzed on the created LT versions of two MLC benchmarks (COCO [27] and VOC [8]), called PLT-COCO and PLT-VOC, respectively. The missing rate of PLT-COCO is $40\%$ and it contains 2,962 images from 80 classes. The maximum training number for each class is 1,240 and the minimum number is 6. We select 5000 images from the test set of COCO2017 for evaluation. PLT-VOC has the same missing rate setting and contains 2,569 images from 20 classes, in which the maximum training number for each class is 1,117 and the minimum number is 7. We evaluate the performance on VOC2007 test set with 4,952 images. More details about the dataset construction can be found in the Appendix. + +Implementation Details. We employ the ResNet-50 [11] as the backbone model to conduct the PLT-MLC task. We train + +our model with a standard Adam [14] optimizer in all the experiments. The images will be randomly cropped and resized to $224 \times 224$ together with standard data augmentation. Besides, we use an identical set of hyperparameters ( $B = 32$ , $Mo = 0.9$ , $E_{max} = 40$ ) across all the datasets. More details of implementation are in Appendix. + +Evaluation Metrics. Following [37], we split these classes into three groups according to the number of their training examples: each head class contains over 100 samples as a many shot, each medium class has 20 to 100 samples as a medium shot, and each tail class has less than 20 samples as a low shot. The total shot indicates all the test samples. We evaluate mean average precision (mAP) for all the classes and recall for missing label settings. + +Comparison of the Methods. To quantify the efficacy of the proposed framework, we use several baselines for performance comparison according to different aspects $^2$ . MLC methods: BCE [45], Focal [26], ASL [3]. LT-MLC methods: DB [37], DB-Focal [37] and LWS [13]. PL-MLC methods: Hill [44], Pseudo-Label [15], ML-GCN [5] and P-ASL [2]. + +# 4.2. Overall Performance + +Table 1 summarizes the quantitative PLT-MLC results of our framework and baselines on PLT-COCO and PLT-VOC. We make the following observations: 1) In general, irrespective of the different shot scenarios, compared to SoTAs, COMIC achieves the best performance on almost all the metrics across both datasets. In particular, COMIC outperforms other baselines in terms of total shot's mAP by + +Table 3: Performance comparison under different missing labeled settings. $0\%$ indicates an LT dataset that is fully labeled. + +
Missing RatioPLT-COCO Dataset
Total ShotMany ShotMedium ShotLow Shot
0%57.07±0.0952.21±0.1159.98±0.1261.12±0.24
30%55.80±0.1749.97±0.1162.59±0.1554.56±0.17
40%54.75±0.1948.93±0.2460.31±0.2154.14±0.21
50%54.69±0.1548.74±0.1256.68±0.1657.25±0.24
+ +![](images/005ad87dbfe387cb83433f3194c62d4a1d971419db7e1904c10463300cc25d0b.jpg) +(a) mAρ of different α + +![](images/f81bcb1f38fb03b613df93f7a6a64989131f9b856123b61a676511094d8c084a.jpg) +(b) mAp of different tau + +![](images/be42b607a22028f8cbe7155ba3aa1bbb6b9b65d852e076a529c5c2194be29983.jpg) +Figure 3: Ablations with respect to coefficient $\alpha$ and $\tau$ . +(a) Performance Comparison of Losses +Figure 4: MLT-MLC results using different losses. + +![](images/fb9a2877c01e1e2bce889431f12c1eae1269292cb3a7eb069491dc401bdadde3.jpg) +(b) Loss Visualization + +a large margin (PLT-COCO: $1.78\% \sim 6.16\%$ , PLT-VOC: $0.83\% \sim 4.13\%$ ) for PLT-MLC task. 2) Besides, we can observe from Table 1 that the LT methods outperform PL baselines in most $X$ -shot situations. We believe the underlying reason behind this is that LT data distribution hurts the classification capability for MLC models more seriously than PL. Besides, the label correction may have aggravated the LT issue and further result in performance reduction. 3) Benefiting from the carefully designed HTB module, our COMIC not only achieves the highest total mAP score but also yields balanced results with a narrowed performance gap in different shot metrics. These results demonstrate the superiority of our proposed model. + +# 4.3. Ablation Study + +Effectiveness of Each Component. We conduct an ablation study to illustrate the effectiveness of each component in Table 2. Comparing COMIC and COMIC(-RLC) (Row 1 v.s + +![](images/2902bda875f0852c90ce9796f191ccde0c163c689709e12ff401b91899ce1548.jpg) +(a) Number of TP and FP + +![](images/70e574376d45e16082c83a35855a516ecb578bdd741ca825c79d8000f731f880.jpg) +(b) Dynamic Distribution Heat Map +Figure 5: In-depth analysis of label correction. + +Table 4: Ablation of MFM. $\downarrow$ indicates the mAP decay. + +
MFM FactorPLT-COCO Dataset
P-NH-TTotal ShotMany ShotMedium ShotLow Shot
✔54.44 (↓0.64)48.65 (↓0.56)60.00 (↓0.08)53.81 (↓1.55)
♥53.70 (↓1.38)48.38 (↓0.83)58.99 (↓1.09)52.91 (↓2.45)
✔55.0849.2160.0855.36
+ +Row 4), the label (Correction) mechanism contributes $0.38\%$ improvement on total mAP. The results of Row 2 show the mAP improvement of the MFM (Modification). Meanwhile, Row 3 indicates that it suffers from noticeable performance degradation without the (Balance) learning. To sum up, we can observe that the improvement of each module is distinguishable. Combining all the components, our COMIC exhibits steady improvement over the baselines. + +Ablation of Missing Rate. To study the effect of partial labels that affect COMIC's results, we evaluate the performance under different missing rates (MR) of labels (from $0\% \sim 50\%$ ). Not surprisingly, when the MR decreases, the accuracy of COMIC increases on all the metrics. We also find that the performance gap between different shots is consistently small in all MR settings. The results demonstrate the generalizability of the proposed COMIC that it can produce stable and balanced results under different MR settings. + +Hyperparameter $\alpha$ and $\tau$ . We investigate the impact of hyper-parameter $\alpha$ and $\tau$ for the PLT-MLC task. The mAPs of different hyper-parameter settings on PLT-COCO are shown in Figure 3. This figure suggests that the optimal choices of $\alpha$ and $\tau$ are around 2 and 0.7, respectively. Either increasing or decreasing these values results in performance decay. + +# 4.4. In-Depth Analysis + +We further validate several vital issues of the proposed Correction $\rightarrow$ Modification $\rightarrow$ Balance learning paradigm by answering the three questions as follows. + +Q1: Can the model trust the recalled labels distinguished by RLC? To build the insight on the effectiveness of the label correction mechanism in COMIC, we visualize the true positive (TP) and false positive (FP) in Figure 5(a)). This figure suggests that the RLC module can distinguish a large + +![](images/7c2451c28e0e07cfb3cb89aafefea4540503dc212f51dc9945657ec632050826.jpg) +(a) Separate Training +Figure 6: Analysis of balanced learning of COMIC. (a) and (b) depict the total mAP of separate and joint training of COMIC within the 40 epochs. (c) summarizes the loss visualization of head, balanced and tail models with joint training. (d) demonstrates head and tail models respectively optimize the head and tail class's performance. + +![](images/4f4b5391f2e69ce724ba454ca76b41940cf8668aecb6a36ceb2e4d7eff1f5ae2.jpg) +(b) Joint Training + +![](images/2d9b55bf08e9622b71937a4e4490ca7d8e2a65a36d0198596dc7ebb2f5a960c5.jpg) +(c) Loss Visualization + +![](images/dabb023a5fc1da4b7324811cca887d6db1babefc97fcc27073a1e8de5a8f126c.jpg) +(c) Head v.s Tail + +number of missing labels with high prediction confidence in the early training stage, meanwhile, $\mathrm{sum(TP)}\gg \mathrm{sum(FP)}$ . However, Figure 5(b) of corrected samples also reveals LT class distribution with respect to the original training set. To address this issue, we dynamically adjust the sample weight conditioned on the real-time distribution to produce a stable performance. + +Q2: How does the MFM module affect the PLT-MLC performance? Here, we evaluate the effectiveness of the multi-focal modifier (MFM) loss compared with different loss functions. Figure 4(a) shows the loss ablation results using different losses in our COMIC. Our developed MFM outperforms existing losses, as the designed loss considers the key point of the head-tail and positive-negative imbalance under the extreme LT distribution in the PLT-MLC task. There are two components in MFM, which are the positive-negative (P-N) factor and head-tail (H-T) factor. To demonstrate the effect of each component, we train the model with the individual factor in the proposed MFM. As shown in Table. 4, both the P-N factor and the H-T factor play significant roles in MFM. For the H-T factor, it achieves an improvement from $53.7\%$ mAP to $55.08\%$ mAP. Meanwhile, it brings a significant gain on tail categories with $2.45\%$ mAP improvement, indicating its effectiveness to alleviate the severe positive-negative imbalance problems in the LT class distribution. As for the P-N factor, it brings a steady boost on all shot settings which means it can further alleviate the positive-negative issue. Additionally, Figure 4(b) indicates that the MFM loss decreases faster and smoother than the two variants of MFM without different factors, demonstrating its superiority in the PLT-MLC task further. + +Q3: How does the HTB module benefit the balanced learning? We systematically present the explicit benefits of the balanced learning strategy in multi-view. 1) Figure 6 (a) and (b) show the comparison between separate and joint training of head, balanced and tail model with respect to the total mAP on PLT-COCO dataset. An interesting phenomenon is that the detached head and tail models slightly outperform the joint head and tail models but suffer + +from an unstable performance. In contrast, the accuracy of the joint trained balanced model increases much faster and smoother than the detached balanced model which also yields a stable performance and faster convergence speed. This phenomenon is reasonable as the main optimization objective in joint training is to improve the balanced model's performance. It can be regarded as the knowledge distillation effect that enables the balanced model to learn from the head biased and tail biased model, and this in turn facilitates the PLT-MLC learning. 2) During the competition of head v.s tail, the head model's loss drops faster (shown in Figure 6 (c)) and is biased to optimizing the head samples, while the tail model produces an opposite result. Such head and tail biased results form a foundation that enables our COMIC to be trained in a balanced and stable learning effect. 3) We also perform the analysis of the different balanced learning blocks in our COMIC. As presented in Table 6 (in the Appendix), the DL, NC and AMV contribute $0.05\%$ , $1.08\%$ and $0.37\%$ improvement on total shot mAP. The observations and analysis verify the effectiveness of balanced learning for being able to study from the head and tail models, thereby achieving the PLT-MLC improvement. + +# 5. Conclusions + +We have presented a fire-new task called PLT-MLC and correspondingly developed a novel framework, named COMIC. COMIC simultaneously addresses the partial labeling and long-tailed environments in a Correction $\rightarrow$ Modification $\rightarrow$ Balance learning manner. On two newly proposed benchmarks, PLT-COCO and PLT-VOC, we demonstrate that the proposed framework significantly outperforms existing MLC, LT-MLC and PL-MLC approaches. + +Acknowledgement This research is supported by Singapore Ministry of Education Academic Research Fund Tier 3 under MOE's official grant number MOE2017-T3-1-007, Zhejiang NSF (LR21F020004), the NSFC (No. 62272411), Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, and Ant Group. + +# References + +[1] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 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Unfortunately, this assumption is unrealistic in large-scale MLC data that has long-tailed (LT) distribution and partial labels (PL). To address the problem, we introduce a novel task, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), to jointly consider the above two imperfect learning environments. Not surprisingly, we find that most LT-MLC and PL-MLC approaches fail to solve the PLT-MLC, resulting in significant performance degradation on the two proposed PLT-MLC benchmarks. Therefore, we propose an end-to-end learning framework: " + }, + { + "bbox": [ + 47, + 285, + 290, + 646 + ], + "type": "inline_equation", + "content": "\\mathbf{C}\\mathbf{O}\\mathbf{R}\\mathbf{e}\\mathbf{r}\\mathbf{o}\\mathbf{r}\\mathbf{c}\\rightarrow" + }, + { + "bbox": [ + 47, + 285, + 290, + 646 + ], + "type": "text", + "content": " Modification " + }, + { + "bbox": [ + 47, + 285, + 290, + 646 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 285, + 290, + 646 + ], + "type": "text", + "content": " balanCe, abbreviated as COMIC. Our bootstrapping philosophy is to simultaneously correct the missing labels (Correction) with convinced prediction confidence over a class-aware threshold and to learn from these recall labels during training. We next propose a novel multi-focal modifier loss that simultaneously addresses head-tail imbalance and positive-negative imbalance to adaptively modify the attention to different samples (Modification) under the LT class distribution. In addition, we develop a balanced training strategy by distilling the model's learning effect from head and tail samples, and thus design a balanced classifier (Balance) conditioned on the head and tail learning effect to maintain stable performance for all samples. Our experimental study shows that the proposed COMIC significantly outperforms general MLC, LT-MLC and PL-MLC methods in terms of effectiveness and robustness on our newly created PLT-MLC datasets. Codes and benchmarks are available on the link https://https://github.com/wannature/COMIC" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 673, + 128, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 128, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 128, + 685 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": "In recent years, the development of deep learning prosperity to the field of computer vision [20, 17, 19, 16, 23, 22, 25," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 259, + 548, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 548, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 548, + 583 + ], + "type": "text", + "content": "24, 43, 42, 18]. Images typically contain multiple objects and concepts, highlighting the importance of multi-label classification (MLC) [34] for real-world tasks. Along with the wide adoption of deep learning, recent MLC approaches have made remarkable progress in visual recognition [36, 38], but the performance is limited by two common assumptions: all categories have comparable numbers of instances and each training instance has been fully annotated with all the relevant labels. While this conventional setting provides a perfect training environment for various studies, it conceals a number of complexities that typically arise in real-world applications: i) Long-Tailed (LT) Class Distribution. With the growth of digital data, the crux of making a large-scale dataset is no longer about where to collect, but how to balance it [33]. However, the cost of expanding the dataset to a larger class vocabulary with balanced data is not linear — but exponential — since the data is inevitably long-tailed following Zipf's distribution [30]. ii) Partial Labels (PL) of Instances. In the case of a large number of categories, it is difficult and even impractical to fully annotate all relevant labels for each image [39, 46]. Intuitively, humans tend to focus on different aspects of image contents due to human bias, i.e., their preference, personality and sentiment [41], which indirectly affects how and what we annotate. In fact, LT and PL are often co-occurring, and therefore, the MLC model must be sufficiently robust to handle different data distributions and imperfect datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": "In this paper, we present a new challenge for MLC at scale, Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), with concomitant existence of both PL setting [39] and LT distribution [33] problems. As captured in the overview of PLT-MLC in Figure 1 (a), it has the following three challenges: i) False Negative Training. Under the PL setting, the MLC model treats the un-annotated labels " + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "inline_equation", + "content": "(\\odot)" + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": " as negatives " + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "inline_equation", + "content": "(\\odot)" + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": ", which may produce sub-optimal decision boundary as it adds noise of false negative labels (Figure 1 (b)). 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "type": "text", + "content": "1423" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 70, + 252, + 217 + ], + "blocks": [ + { + "bbox": [ + 76, + 70, + 252, + 217 + ], + "lines": [ + { + "bbox": [ + 76, + 70, + 252, + 217 + ], + "spans": [ + { + "bbox": [ + 76, + 70, + 252, + 217 + ], + "type": "image", + "image_path": "3252a6d42f8a56a86a3850c4d575d0ca94145d1ff7a844cbfe3f1bb36d5b442c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 548, + 265 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 548, + 265 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 548, + 265 + ], + "type": "text", + "content": "Figure 1: (a) illustrates an overview of the proposed PLT-MLC task. (b) depicts three key challenges of a PLT-MLC task. (c) depicts a concise version of our proposed model for facilitating the PLT-MLC. " + }, + { + "bbox": [ + 46, + 228, + 548, + 265 + ], + "type": "inline_equation", + "content": "(\\bullet : positive, \\bullet : negative, \\circ : false, \\circ :" + }, + { + "bbox": [ + 46, + 228, + 548, + 265 + ], + "type": "text", + "content": " corrected positive)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 256, + 70, + 518, + 216 + ], + "blocks": [ + { + "bbox": [ + 256, + 70, + 518, + 216 + ], + "lines": [ + { + "bbox": [ + 256, + 70, + 518, + 216 + ], + "spans": [ + { + "bbox": [ + 256, + 70, + 518, + 216 + ], + "type": "image", + "image_path": "e4930b6aa52408b836b771c2cc1735cf3f7e08ad25c2068e503468c17bc0d196.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": "LT class distribution as some tail categories are prone to missing annotations in practice. For instance, in Figure 1 (a), \"person\" is the head class in the PLT-MLC dataset and is often notable in an image to labeling for annotators. In contrast, the \"tie\" often occupies a tiny region in the scene compared with the \"person\". The annotator may miss the \"tie\" object, which will aggravate the LT distribution and further increase the difficulty of learning from tail classes. ii) Head-Tail and Positive-Negative Imbalance. There are two imbalance issues in a PLT-MLC task: inter-instance head-tail imbalance and intra-instance positive-negative imbalance. As shown in Figure 1 (b), the inter-instance ratio of head positive (" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": ") \"person\" (" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": "): tail positive (" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": "\"tie" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": ") " + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\approx" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": " 32 under the LT data distribution, and the intra-instance ratio of tail negative (" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": ") categories: tail positive (" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": "\"tie" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 279, + 289, + 639 + ], + "type": "text", + "content": ") = 78 as an image only contains a small fraction of the positive labels. Consequently, a robust PLT-MLC model should address the co-occurring imbalances simultaneously. iii) Head Overfitting and Tail Underfitting. Different from the general LT distribution, the classification model downplays the minor tail and overplays the major head. The PLT-MLC has an extreme LT distribution and Figure 1(c) illustrates an interesting phenomenon of MLC model learning: the general classification model is prone to overfitting to head class with extensive samples and underfitting to tail classes with a few samples. This figure also indicates that only the medium class shows a steady growth in performance, which means that existing LT methods focusing on lifting up the tail performance may not solve the PLT-MLC problem satisfactorily." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Suppose a trained model is used to correct the missing labels and then an LT classifier is trained using the updated labels, we might not be able to obtain a satisfying PLT-MLC performance, either. While machine learning methods can easily detect the head samples, they may have difficulty in identifying the tail samples. As a result, the corrected labels" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 279, + 547, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 547, + 399 + ], + "type": "text", + "content": "may still exhibit an LT distribution that inevitably hurts balanced learning. Moreover, even when a general LT classifier affords the trade-off to improve the tail performance conditioned on the head performance drop, it is still incapable of simultaneously addressing the issue of head overfitting and tail underfitting problem. Further, the decoupled learning paradigm is impractical since it needs the \"stop\" training and human \"re-start\" training, i.e., an end-to-end learning scheme is more desirable. Thus, these limitations motivate us to reconsider the solution for the PLT-MLC task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 403, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 548, + 715 + ], + "type": "text", + "content": "To this end, we propose an end-to-end PLT-MLC framework: COrrection " + }, + { + "bbox": [ + 304, + 403, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 403, + 548, + 715 + ], + "type": "text", + "content": " ModificatIon " + }, + { + "bbox": [ + 304, + 403, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 403, + 548, + 715 + ], + "type": "text", + "content": " balanCe (Figure 1), called COMIC, which progressively addresses the three key PLT-MLC challenges. Step 1: The Correction module aims to gradually correct the missing labels according to the predicted confidence and dynamically adjusts the classified loss of the corrected samples under the real-time estimated class distribution. Step 2: After the label correction, the Modification module introduces a novel Multi-Focal Modifier (MFM) Loss, which contains two focal factors to address the two imbalance issues in PLT-MLC independently. Motivated by [3], the first is an intra-instance positive-negative factor that determines the concentration of learning on hard negatives and positives with different exponential decay factors. The second is an inter-instance head-tail factor that increases the impact of rare categories, ensuring that the loss contribution of rare samples will not be overwhelmed by frequent ones. Step 3: Finally, the Balance module measures the model's optimization direction with a calculated moving average vector of the gradient over all past samples. And thus, we devise a head model and a tail model by subtracting or adding this moving vector, which can respectively improve head and tail performance. Subsequently, a balanced classifier deduces a balanced learning effect under the supervision of the head classifier and tail classifier. It protects the model training from being too medium biased, and hence" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "text", + "content": "1424" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "the balanced classifier is able to achieve the balanced learning schema. Notably, our solution is an end-to-end learning framework, which is re-training-free and effectively enables balanced prediction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 289, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 289, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 289, + 242 + ], + "type": "text", + "content": "Our contributions are three-fold: (1) We present a new challenging task: Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), together with two newly designed benchmarks: PLT-COCO and PLT-VOC. (2) We propose an end-to-end PLT-MLC learning framework, called COMIC, to effectively perform the PLT-MLC task as a progressive learning paradigm, i.e., Correction " + }, + { + "bbox": [ + 46, + 121, + 289, + 242 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 121, + 289, + 242 + ], + "type": "text", + "content": " Modification " + }, + { + "bbox": [ + 46, + 121, + 289, + 242 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 121, + 289, + 242 + ], + "type": "text", + "content": " Balance. (3) Through an extensive experimental study, we show that our method improves all the prevalent LT and ML line-ups on PLT-MLC benchmarks by a large margin." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 257, + 138, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 257, + 138, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 257, + 138, + 269 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 279, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 289, + 434 + ], + "type": "text", + "content": "Long-Tailed MLC. [37] is the first work that addresses the LT-MLC by extending the re-balanced sampling and cost-sensitive re-weighting methods. It proposes an optimized DB Focal method, which does improve the recognition performance of tail classes. Later work, [10] performs uniform and re-balanced samplings from the same training set. Then a two-branch network is developed to enforce the consistency between two branches for collaborative learning on both uniform and re-balanced samplings. However, the above works require careful data initialization, i.e., re-sampling, which is undesirable in practice. Moreover, these methods have not yet considered the missing labeling case, which may not sufficiently deal with the PLT-MLC." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 288, + 628 + ], + "type": "text", + "content": "MLC with Partial Labels. Multi-label tasks often involve incomplete training data, hence several methods have been proposed to solve the problem of multi-label learning with missing labels. A simple solution is to treat the missing labels as negative labels [31, 21, 4]. However, performance will drop because a lot of ground-truth positive labels are initialized as negative labels [12]. Current works on PL-MLC mainly focus on the design of networks and training schemes. The common practice is to utilize the customized networks to learn label correlations or classification confidence to realize correct recognition of missing labels [7, 44]. However, the corrected labels learned from a trained model are imbalanced due to the previous training dataset having an LT distribution. Using such recall labels will aggravate the LT distribution in the PLT-MLC dataset and result in an imbalanced performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "content": "Other Works. [40] learns to generate concept-invariant samples in the environment with semantic gap, which enables the model to classify the samples through causal intervention, yielding improved generalization guarantees; [18] collaborates a cascade of foundation models, thus learning superior interleaved multi-modal instruction-following ability from imperfect supervision." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 389, + 85 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 91, + 547, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 91, + 547, + 116 + ], + "spans": [ + { + "bbox": [ + 305, + 91, + 547, + 116 + ], + "type": "text", + "content": "This section describes the proposed PLT-MLC framework. We will present each module and its training strategy." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 121, + 430, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 121, + 430, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 430, + 133 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": "Before presenting our method, we first introduce some basic notions and terminologies. We consider a partially annotated MLC dataset contains " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": " classes and " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": " i.i.d training samples " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "\\mathcal{S} = \\{(\\mathcal{I}^{(1)},y^{(1)}),\\dots ,(\\mathcal{I}^{(N)},y^{(N)})\\}" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^{(i)}" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": " denote " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": " image and label " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "y^{(i)} = [y_1^{(i)},\\dots ,y_c^{(i)}]\\in \\{0,1\\}^C" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": ". For a given " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": " example and category " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "y_{c}^{(i)} = 0" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": ", 1 respectively means the category is unknown and present. Our proposed COMIC solves the PLT-MLC problem in an end-to-end learning manner: Correction " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": " Modification " + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 140, + 547, + 286 + ], + "type": "text", + "content": " Balance, with Reflective Label Corrector (RLC, in Sec.3.2), Multi-Focal Modifier (MFM, in Sec.3.3) and Head-Tail Balancer (HTB, in Sec.3.3), as illustrated in Figure 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "content": "These three modules are designed to seek a balanced model " + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_b(\\cdot ;\\Theta_b)" + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "content": ", parameterized by " + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "inline_equation", + "content": "\\Theta_{b}" + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "content": ", to predict the presence or absence of each class given an input image. We denote " + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "inline_equation", + "content": "p = [p_1,\\dots ,p_c]" + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "content": " as the class prediction, computed by the model: " + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "inline_equation", + "content": "p_c = \\sigma (z_c)" + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "content": " is the sigmoid function, and " + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "inline_equation", + "content": "z_{c}" + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "content": " is the output logit corresponding to class " + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 287, + 547, + 371 + ], + "type": "text", + "content": ". The optimized goal of COMIC can be defined as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 319, + 376, + 545, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 376, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 319, + 376, + 545, + 403 + ], + "type": "interline_equation", + "content": "\\underbrace {\\mathcal {L} ((\\mathcal {S}) ; \\Theta_ {b})} _ {\\text {C O M I C L o s s}} = \\underbrace {\\lambda_ {c} \\cdot \\mathcal {L} _ {r l c}} _ {\\text {R L C L o s s}} + \\underbrace {\\lambda_ {m} \\cdot \\mathcal {L} _ {m f m}} _ {\\text {M F M L o s s}} + \\underbrace {\\lambda_ {b} \\cdot \\mathcal {L} _ {h t b}} _ {\\text {H T B L o s s}} \\tag {1}", + "image_path": "d64829f135f4f34b09942763677d0e200d6de676a594e2cc3535fd260629f456.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rlc}" + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mfm}" + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{htb}" + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "text", + "content": " denote the loss of RLC, MFM and HTB, respectively. " + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "inline_equation", + "content": "\\lambda_{c},\\lambda_{m}" + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "inline_equation", + "content": "\\lambda_{b}" + }, + { + "bbox": [ + 304, + 408, + 547, + 433 + ], + "type": "text", + "content": " are hyperparameters." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 438, + 453, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 438, + 453, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 438, + 453, + 449 + ], + "type": "text", + "content": "3.2. Reflective Label Corrector" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": "Reflective Label Corrector (RLC) presents a real-time label correction method for missing labels to alleviate the effect of partially labeled samples. The core idea is to examine the label likelihood " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": " of each training image and recall the labels with convinced prediction confidence during training. Interestingly, we found that the model can distinguish a large number of missing labels with high prediction confidence in the early training stage, which implies that we can recall these missing labels during training to boost PTL-MLC learning. Here, we first define a threshold " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": " and then check the input sample's label likelihood " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": " to check whether it is greater than " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": " and then calculate the average category possibility " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "P_{c}" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": " of past trained data with class " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": ". If predicted probabilities " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "p_{c}" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": " are highly confident, i.e., " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "p_{c} > \\max \\{\\tau, P_{c}\\}" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": ", we regard that the sample misses the label of class " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": " and set a pseudo-label " + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "inline_equation", + "content": "\\hat{y}_{c}" + }, + { + "bbox": [ + 304, + 456, + 547, + 648 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 343, + 653, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 653, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 343, + 653, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {c} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} p _ {c} > \\max \\left\\{\\tau , P _ {c} \\right\\}, y _ {c} = 0 \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {2}", + "image_path": "d139b09464d2a7bce0381eb9dcf6decccee52c524c2751a7b0500e2b47ca2bbf.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "Thus, the loss of RLC module, i.e., " + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rlc}" + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": " utilizes the MFM loss (refer the details in Sec. 3.3) with these corrected label" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "text", + "content": "1425" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 72, + 293, + 137 + ], + "blocks": [ + { + "bbox": [ + 75, + 72, + 293, + 137 + ], + "lines": [ + { + "bbox": [ + 75, + 72, + 293, + 137 + ], + "spans": [ + { + "bbox": [ + 75, + 72, + 293, + 137 + ], + "type": "image", + "image_path": "437ca58d174d331935450d64630aba60fdedf08c66ee8ef204d10a6878493963.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 299, + 72, + 518, + 136 + ], + "blocks": [ + { + "bbox": [ + 299, + 72, + 518, + 136 + ], + "lines": [ + { + "bbox": [ + 299, + 72, + 518, + 136 + ], + "spans": [ + { + "bbox": [ + 299, + 72, + 518, + 136 + ], + "type": "image", + "image_path": "cd98ecdd00a0baf3356e99f6bc9751210e4786ae428eb5f6658ce3721c5d23c8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 75, + 137, + 433, + 301 + ], + "blocks": [ + { + "bbox": [ + 75, + 137, + 433, + 301 + ], + "lines": [ + { + "bbox": [ + 75, + 137, + 433, + 301 + ], + "spans": [ + { + "bbox": [ + 75, + 137, + 433, + 301 + ], + "type": "image", + "image_path": "0624ea5a4d27a76d03897b0a9d85ab81025a16befa67f2f1d4a45e7c4c693ad4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 313, + 545, + 373 + ], + "lines": [ + { + "bbox": [ + 45, + 313, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 45, + 313, + 545, + 373 + ], + "type": "text", + "content": "Figure 2: Overview of COMIC. RLC module (Correction) corrects the missing labels along with the training and dynamically re-weights the sample weight according to the estimated class distribution. MFM module (Modification) adjusts the focal of different instances according to head-tail and positive-negative imbalance under the extreme LT distribution. HTB module (Balance) measures the model's optimization direction and correspondingly develops a balanced learning scheme to produce stable PLT-MLC performance." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 436, + 137, + 516, + 292 + ], + "blocks": [ + { + "bbox": [ + 436, + 137, + 516, + 292 + ], + "lines": [ + { + "bbox": [ + 436, + 137, + 516, + 292 + ], + "spans": [ + { + "bbox": [ + 436, + 137, + 516, + 292 + ], + "type": "image", + "image_path": "63ae493d2d175e533a774d3b7850adcb61a85997ebf393e3934bc729b6e8b9fe.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 395, + 133, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 395, + 133, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 395, + 133, + 407 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 47, + 395, + 133, + 407 + ], + "type": "text", + "content": " for model training:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 42, + 419, + 287, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 42, + 419, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 42, + 419, + 287, + 460 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r l c} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {m f m} ^ {+} (p), & \\text {i f} \\hat {y} = 1 \\\\ \\mathbb {1} _ {(y = 1)} \\mathcal {L} _ {m f m} ^ {+} (p) + \\mathbb {1} _ {(\\hat {y} = 0)} \\mathcal {L} _ {m f m} ^ {-} (p), & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}", + "image_path": "e0b9dc5a085dd233fa3d7ef6a811bebe8a78ed220f5f73ac3bb001f9344880b6.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mfm}^{+}(p)" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mfm}^{-}(p)" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " refer to the generalized MFM loss function for positives and negatives. Notably, we find that most of the corrected labels belong to head class, which may aggravate the LT distribution. To address this issue, we dynamically adjust the inter-sample head-tail factor " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\gamma_{ht}^{(i)}" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " (details of this factor are explained in Sec. 3.3) according to the dynamic class distribution " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": ", which can increase the focal weight for tail samples. In addition, we also multiply " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rlc}(p)" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " by a coefficient " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\frac{\\mathcal{B}_s}{\\mathcal{N}_t}" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " in each training batch to constrain the loss value, where " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_s" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " is the batch size and " + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_t" + }, + { + "bbox": [ + 46, + 461, + 287, + 594 + ], + "type": "text", + "content": " is the number of corrected labels." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 596, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 596, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 596, + 287, + 632 + ], + "type": "text", + "content": "Through this, RLC can gradually and dynamically correct the potential missing labels during training, which efficiently improves the classifier's performance with recalled labels." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 645, + 168, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 168, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 168, + 657 + ], + "type": "text", + "content": "3.3. Multi-Focal Modifier" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "We first revisit the focal loss [26], which is a widely-used solution in the positive-negative imbalance problem. It redistributes the loss contribution of easy samples and hard samples, which greatly weakens the influence of the majority" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 396, + 389, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 389, + 407 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 389, + 407 + ], + "type": "text", + "content": "of negative samples." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 331, + 418, + 545, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 418, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 331, + 418, + 545, + 450 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f l} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {f l} ^ {+} = (1 - p) ^ {\\gamma} \\log (p), & \\text {i f} y = 1 \\\\ \\mathcal {L} _ {f l} ^ {-} = p ^ {\\gamma} \\log (1 - p), & \\text {i f} y = 0 \\end{array} \\right. \\tag {4}", + "image_path": "21ab6664764802e76d11472d50baf0f79f92877368d07d5c068ce0900530473a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "content": " is the focusing parameter, " + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\gamma = 0" + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "content": " yields binary cross-entropy. By setting " + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "inline_equation", + "content": "\\gamma > 0" + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "content": ", the contribution of easy negatives (with low probability, " + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "inline_equation", + "content": "p \\ll 0.5" + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "content": ") can be down-weighted in the loss, enabling the model to focus on harder samples." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 510, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 510, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 510, + 545, + 533 + ], + "type": "text", + "content": "However, the focal loss may not satisfactorily resolve the PLT-MLC problem due to two key aspects:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 544, + 545, + 666 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 317, + 544, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 544, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 317, + 544, + 545, + 605 + ], + "type": "text", + "content": "- Tail Positive Gradient Elimination. When using focal loss for multi-label training, there is an inner trade-off: high " + }, + { + "bbox": [ + 317, + 544, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 317, + 544, + 545, + 605 + ], + "type": "text", + "content": " sufficiently down-weights the contribution from easy negatives, but may eliminate the gradients from the tail positive samples [3]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 617, + 545, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 617, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 317, + 617, + 545, + 666 + ], + "type": "text", + "content": "- Head-Tail Imbalance. Imbalance among the positive categories also exists in MLC, i.e., head positive-tail positive imbalance. Rare categories suffer more from severe imbalance issues than frequent ones." + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": "Thus, we propose a Multi-Focal Modifier (MFM) loss that decouples " + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": " at two granularities of focal factors, i.e., an intra-sample positive-negative (P-N) factor " + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\gamma_{pn}" + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": " and an" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "text", + "content": "1426" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 209, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 209, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 209, + 84 + ], + "type": "text", + "content": "inter-sample head-tail (H-T) factor " + }, + { + "bbox": [ + 47, + 72, + 209, + 84 + ], + "type": "inline_equation", + "content": "\\gamma_{ht}" + }, + { + "bbox": [ + 47, + 72, + 209, + 84 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 74, + 92, + 288, + 125 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 92, + 288, + 125 + ], + "spans": [ + { + "bbox": [ + 74, + 92, + 288, + 125 + ], + "type": "interline_equation", + "content": "\\gamma^ {(i)} = \\left\\{ \\begin{array}{l l} \\gamma^ {(i) +} = \\gamma_ {p n} ^ {+} + w ^ {+} \\cdot \\gamma_ {h t} ^ {(i)}, & \\text {i f} y = 1 \\\\ \\gamma^ {(i) -} = \\gamma_ {p n} ^ {-} + w ^ {-} \\cdot \\gamma_ {h t} ^ {(i)}, & \\text {i f} y = 0 \\end{array} \\right. \\tag {5}", + "image_path": "c2f56ca79f05bbd68a79ee56c6bd8928fd1174330cb0d0f8e1c3cdb17f90da5d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma^{(i) + }" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma^{(i) - }" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " control the focal of samples with " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " class. Similar to [3], " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma_{pn}^{+}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma_{pn}^{-}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " decouple the original decay rate " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " as two factors, which respectively control the focal of the positive and negative samples. Since we are interested in emphasizing the contribution of positive samples, we set " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma_{pn}^{-}\\geq \\gamma_{pn}^{+}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": ". We achieve better control over the contribution of positive and negative samples through the designed loss function, which assists the network to learn meaningful features from positive samples, despite their rarity. Another focal factor " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma_{ht}^{(i)}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " is a variable parameter " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "(\\geq 1)" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " associated with the imbalance degree of the " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " class. A bigger value of " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma_{ht}^{(i)}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " will increase the weight of tail samples to encourage the model to pay more attention to the positive tail samples, and vice versa. " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "w^{+}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "w^{-}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " are the coefficients that adjust the weight at a fine-grained level. The " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\gamma_{ht}^{(i)}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " is the static class distribution " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " of training set with max normalization function " + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\psi (\\cdot)" + }, + { + "bbox": [ + 46, + 133, + 289, + 342 + ], + "type": "text", + "content": " [29] to adjust the head-tail focal." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 342, + 288, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 288, + 379 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 288, + 379 + ], + "type": "text", + "content": "After applying the decoupled " + }, + { + "bbox": [ + 46, + 342, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\gamma^{(i) + }" + }, + { + "bbox": [ + 46, + 342, + 288, + 379 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 342, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\gamma^{(i) - }" + }, + { + "bbox": [ + 46, + 342, + 288, + 379 + ], + "type": "text", + "content": " into our MFM loss, we obtain the loss function as follows (more discussions in the Appendix.):" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 41, + 387, + 287, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 41, + 387, + 287, + 428 + ], + "spans": [ + { + "bbox": [ + 41, + 387, + 287, + 428 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m f m} (p) = \\left\\{ \\begin{array}{l l} \\mathcal {L} _ {m f m} ^ {+} = \\sum_ {i = 1} ^ {C} (1 - p) ^ {\\gamma^ {(i) +}} \\log (p), & \\text {i f} y = 1 \\\\ \\mathcal {L} _ {m f m} ^ {-} = \\sum_ {i = 1} ^ {C} p ^ {\\gamma^ {(i) -}} \\log (1 - p), & \\text {i f} y = 0 \\end{array} \\right. \\tag {6}", + "image_path": "ff7aacb3a71a5c294f8f53d1ba68e6caa81f633b6db5d08c9900368e8f86e290.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 429, + 289, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 289, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 289, + 464 + ], + "type": "text", + "content": "By doing so, the MFM module utilizes the multi-grained focal to alleviate the two imbalance problems in the PLT-MLC task, yielding better classification results." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 472, + 162, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 162, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 162, + 483 + ], + "type": "text", + "content": "3.4. Head-Tail Balancer" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 491, + 289, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 289, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 289, + 622 + ], + "type": "text", + "content": "As discussed in the introduction, the extreme LT dataset with numerous head samples and a small number of tail samples result in a head overfitting and tail underfitting learning effect. Only the medium samples present a superior performance during training, which fails to obtain the balanced performance for the overall samples. To address this issue, we develop a balanced strategy that measures the balanced learning effect under the supervision of the head classifier and tail classifier to achieve balanced results. Before we delve into the balanced learning, we first measure the moving average of the gradient in the SGD-based optimizer [32]:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 83, + 632, + 287, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 632, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 83, + 632, + 287, + 645 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {t} = \\mu \\cdot \\mathbf {e} _ {t - 1} + \\operatorname {s u m} \\left(g _ {t}\\right), \\forall t = 1, \\dots , T. \\tag {7}", + "image_path": "14fc31f39a8899f8b165efcf4561e273ca63fe2e33cb23072608fabd12245882.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{sum}(g_t)" + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": " is the accumulated gradient at iteration " + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": " is the momentum decay. The average moving vector " + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_t" + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": " records the model's optimization tendency by " + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_{t-1}" + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{sum}(g_t)" + }, + { + "bbox": [ + 46, + 653, + 287, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "In our empirical study, we observe that only the medium samples obtain a stable learning effect from the early to late" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": "training stage, mainly due to the extreme LT distribution. To simulate the learning effect towards head/tail samples, as depicted in Figure 2(c), we reduce/add the moving vector " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_t" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " at each step in head model " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_h" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " and tail model " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_t" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " respectively, to assist the balanced model " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_b" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " for balanced learning. Notably, we set different learning rate decays for each model to further explore the balanced learning effect. The three models are parallel-trained with their own backbone and classifier. In the feature learning stage, we develop an additive attention [1] that computes the relevance of balanced features " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{f}}_b" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": ", and head features " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_h" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": ", tail features " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_t" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " extracted from corresponding backbones." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 368, + 224, + 546, + 238 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 224, + 546, + 238 + ], + "spans": [ + { + "bbox": [ + 368, + 224, + 546, + 238 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {b} = \\operatorname {A t t n} \\left(\\hat {\\mathbf {f}} _ {b}, \\left[ \\mathbf {f} _ {h}, \\mathbf {f} _ {t} \\right]\\right)) + \\hat {\\mathbf {f}} _ {b} \\tag {8}", + "image_path": "2c4d6c125a1f02f2d3067b1f4dd1ebad9f98a38e50bde0fcdd7a6d8b530ed5fe.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 246, + 512, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 246, + 512, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 246, + 512, + 258 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 246, + 512, + 258 + ], + "type": "inline_equation", + "content": "Attn(\\cdot)" + }, + { + "bbox": [ + 305, + 246, + 512, + 258 + ], + "type": "text", + "content": " is the additive attention mechanism." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "text", + "content": "Then updated " + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_b" + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_h" + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_t" + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "text", + "content": " are input to their classifiers to obtain their logits. We develop the multi-head classifier with normalization [9, 28, 33], which has already been embraced by various methods of empirical practice. The multi-head strategy [35] equally divides the channel of weights and features into " + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "inline_equation", + "content": "N_g" + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "text", + "content": " groups, which can be considered as " + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "inline_equation", + "content": "N_g" + }, + { + "bbox": [ + 304, + 258, + 547, + 342 + ], + "type": "text", + "content": " times of fine-grained sampling." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 333, + 350, + 546, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 350, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 333, + 350, + 546, + 384 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {x} = \\frac {\\rho}{N _ {g}} \\sum_ {k = 1} ^ {N _ {g}} \\frac {w _ {k} ^ {\\top} \\mathbf {f} _ {x}}{(| | w _ {k} | | + \\eta) | | \\mathbf {f} _ {x} | |}, x \\in \\{h, t, b \\} \\tag {9}", + "image_path": "0fb47c9b2c7755ace173b3cfa2ad103e1dd7d34a27056d786d272e1c74401d7e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "text", + "content": " is a scaling factor akin to the inverse temperature in Gibbs distribution, " + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "text", + "content": " is a class-agnostic baseline energy. " + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "inline_equation", + "content": "w_{k}" + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 304, + 392, + 545, + 427 + ], + "type": "text", + "content": " learned parameter matrix." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 428, + 547, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 547, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 547, + 464 + ], + "type": "text", + "content": "Subsequently, we measure the head and tail learning effect by subtracting and adding the average moving vector " + }, + { + "bbox": [ + 304, + 428, + 547, + 464 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_t" + }, + { + "bbox": [ + 304, + 428, + 547, + 464 + ], + "type": "text", + "content": " to the logits of head model and tail model, respectively:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 472, + 546, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 472, + 546, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 546, + 506 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {z}} _ {x} = \\mathbf {z} _ {x} \\pm \\frac {\\rho}{N _ {g}} \\sum_ {k = 1} ^ {N _ {g}} \\frac {\\sin \\left(\\mathbf {z} _ {x} , \\mathbf {e} _ {t}\\right) \\cdot \\left(w _ {j}\\right) ^ {\\top} \\mathbf {e} _ {t}}{| | w _ {k} | | + \\eta}, x \\in \\{h, t \\} \\tag {10}", + "image_path": "4b02cad2e0a4f668814cbc164a4be4f227ce8dc9272794df54c69416f3d3aa0b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 514, + 538, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 514, + 538, + 526 + ], + "spans": [ + { + "bbox": [ + 305, + 514, + 538, + 526 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 514, + 538, + 526 + ], + "type": "inline_equation", + "content": "sim(\\cdot, \\cdot)" + }, + { + "bbox": [ + 305, + 514, + 538, + 526 + ], + "type": "text", + "content": " measures the cosine similarity of vectors." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "text", + "content": "After obtaining the logits of " + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_h" + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_t" + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_b" + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "text", + "content": ", the balanced learning effect needs to distill the head and tail knowledge from " + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_h" + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_t" + }, + { + "bbox": [ + 304, + 526, + 547, + 574 + ], + "type": "text", + "content": " to enable the stable learning for all samples. Hence, we develop the head-tail loss:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 582, + 546, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 546, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 546, + 597 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {h t b} = \\kappa_ {h} \\cdot \\mathcal {L} \\left(\\phi \\left(\\hat {\\mathbf {z}} _ {h}\\right) \\cdot \\phi \\left(\\mathbf {z} _ {b}\\right)\\right) + \\kappa_ {t} \\cdot \\mathcal {L} \\left(\\phi \\left(\\hat {\\mathbf {z}} _ {t}\\right) \\cdot \\phi \\left(\\mathbf {z} _ {b}\\right)\\right) \\tag {11}", + "image_path": "26c97392209a8478137c0d4efe0373eb1d3e44b912638643d8ff72ff38317791.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mfm}" + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot)" + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": " is softmax function. " + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\kappa_{h}" + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\kappa_{t}" + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": " are adaptive weights for head and tail learning that calculated by " + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\kappa_{h} = \\frac{(\\mathcal{L}(\\hat{z}_{h}))^{\\alpha}}{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha} + (\\mathcal{L}(\\hat{z}_{h}))^{\\alpha}}" + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\kappa_{t} = \\frac{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha}}{(\\mathcal{L}(\\hat{z}_{t}))^{\\alpha} + (\\mathcal{L}(z_{h}))^{\\alpha}}" + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 604, + 547, + 713 + ], + "type": "text", + "content": " is a scaling factor and we study its effect in Sec. 4.3. Such loss can be regarded as the empirical risk minimization (ERM) [6], which adaptively distills the knowledge from the head and tail models, enabling the balanced model is not biased to medium samples and produces a balanced learning effect for the PLT-MLC task." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "text", + "content": "1427" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 54, + 129, + 537, + 311 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 121 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 121 + ], + "type": "text", + "content": "Table 1: Performance comparison of the proposed method and baselines on PLT-MLC datasets (PLT-COCO and PLT-VOC). " + }, + { + "bbox": [ + 46, + 70, + 545, + 121 + ], + "type": "inline_equation", + "content": "E2E^{*}" + }, + { + "bbox": [ + 46, + 70, + 545, + 121 + ], + "type": "text", + "content": " indicates that the PLT model is learned in an end-to-end manner. A larger score has better performance. Improv. indicates performance improvement. Acronym notations of baselines can be found in Sec. 4.1. We color each row as the best, second best and lowest score." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 54, + 129, + 537, + 311 + ], + "lines": [ + { + "bbox": [ + 54, + 129, + 537, + 311 + ], + "spans": [ + { + "bbox": [ + 54, + 129, + 537, + 311 + ], + "type": "table", + "html": "
CategoryMethodsE2E*PLT-COCO DatasetPLT-VOC Dataset
Many ShotMedium ShotFew ShotTotal ShotMany ShotMedium ShotFew ShotTotal Shot
MLCBCE [45]✔42.57±0.1156.67±0.1946.40±0.6048.92±0.2367.37±0.1888.27±0.3983.79±0.4178.79±0.14
Focal [26]✔41.05±0.0758.33±0.1253.58±0.3151.39±0.1567.02±0.1187.49±0.1882.82±0.7878.13±0.23
ASL [3]✔41.60±0.1758.15±0.1552.67±0.1751.20±0.0867.67±0.1087.79±0.1382.23±0.5578.35±0.11
LT-MLCDB [37]✔44.83±0.3158.96±0.2453.82±0.4752.16±0.3669.22±0.2888.56±0.4283.72±0.3578.86±0.23
DB-Focal [37]✔45.76±0.2559.74±0.2153.85±0.1652.57±0.2768.96±0.2288.89±0.1883.42±0.2078.90±0.26
LWS [13]-44.86±0.5858.79±0.6353.48±0.5152.86±0.6069.08±0.4488.24±0.5583.46±0.4778.28±0.49
PL-MLCPseudo-Label [15]-41.41±0.4157.46±0.3553.12±0.3351.67±0.3767.38±0.2487.58±0.3583.26±0.4278.32±0.30
ML-GCN [5]✔43.43±0.5358.46±0.6153.74±0.4852.14±0.5568.46±0.4488.17±0.6182.46±0.3879.02±0.56
Hill [44]✔42.50±0.1656.89±0.1947.31±0.3749.28±0.0968.79±0.1586.70±0.1778.15±0.9977.40±0.22
P-ASL [2]✔43.09±0.0557.67±0.0753.46±0.2251.75±0.1768.95±0.2287.24±0.1383.37±0.3378.96±0.16
PLT-MLCHead Model (Ours)✔47.59±0.0959.07±0.1252.35±0.2853.30±0.1972.91±0.2888.59±0.3182.12±0.2780.70±0.30
Tail Model (Ours)✔46.30±0.2558.76±0.2953.38±0.1453.09±0.2771.65±0.3488.68±0.4183.51±0.2480.58±0.36
COMIC (Ours)✔49.21±0.2260.08±0.1355.36±0.2155.08±0.1473.10±0.3589.18±0.4584.53±0.4881.53±0.35
Improv. ↑--1.62 ~ 8.160.34 ~ 3.410.53 ~ 8.961.78 ~ 6.160.19 ~ 6.080.29 ~ 2.48-0.3 ~ 6.380.83 ~ 4.13
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ModelsSettingPLT-COCO Dataset
MCBTotal mAPAverage mAPRecall
-RLC✔✔54.70±0.1354.42±0.1585.26±0.08
-MFM✔✔54.60±0.1354.33±0.1384.59±0.19
-HTB✔✔53.65±0.3153.36±0.3184.19±0.23
COMIC✔✔✔55.08±0.1454.88±0.1988.19±0.22
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Experimental Setup" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "content": "Dataset Construction. The proposed method is analyzed on the created LT versions of two MLC benchmarks (COCO [27] and VOC [8]), called PLT-COCO and PLT-VOC, respectively. The missing rate of PLT-COCO is " + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "content": " and it contains 2,962 images from 80 classes. The maximum training number for each class is 1,240 and the minimum number is 6. We select 5000 images from the test set of COCO2017 for evaluation. PLT-VOC has the same missing rate setting and contains 2,569 images from 20 classes, in which the maximum training number for each class is 1,117 and the minimum number is 7. We evaluate the performance on VOC2007 test set with 4,952 images. More details about the dataset construction can be found in the Appendix." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "content": "Implementation Details. We employ the ResNet-50 [11] as the backbone model to conduct the PLT-MLC task. We train" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "text", + "content": "our model with a standard Adam [14] optimizer in all the experiments. The images will be randomly cropped and resized to " + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "text", + "content": " together with standard data augmentation. Besides, we use an identical set of hyperparameters (" + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "inline_equation", + "content": "B = 32" + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "inline_equation", + "content": "Mo = 0.9" + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "inline_equation", + "content": "E_{max} = 40" + }, + { + "bbox": [ + 304, + 330, + 545, + 402 + ], + "type": "text", + "content": ") across all the datasets. More details of implementation are in Appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": "Evaluation Metrics. Following [37], we split these classes into three groups according to the number of their training examples: each head class contains over 100 samples as a many shot, each medium class has 20 to 100 samples as a medium shot, and each tail class has less than 20 samples as a low shot. The total shot indicates all the test samples. We evaluate mean average precision (mAP) for all the classes and recall for missing label settings." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 498, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 571 + ], + "type": "text", + "content": "Comparison of the Methods. To quantify the efficacy of the proposed framework, we use several baselines for performance comparison according to different aspects" + }, + { + "bbox": [ + 304, + 498, + 545, + 571 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 498, + 545, + 571 + ], + "type": "text", + "content": ". MLC methods: BCE [45], Focal [26], ASL [3]. LT-MLC methods: DB [37], DB-Focal [37] and LWS [13]. PL-MLC methods: Hill [44], Pseudo-Label [15], ML-GCN [5] and P-ASL [2]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 580, + 427, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 580, + 427, + 593 + ], + "spans": [ + { + "bbox": [ + 305, + 580, + 427, + 593 + ], + "type": "text", + "content": "4.2. Overall Performance" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 599, + 547, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 599, + 547, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 547, + 683 + ], + "type": "text", + "content": "Table 1 summarizes the quantitative PLT-MLC results of our framework and baselines on PLT-COCO and PLT-VOC. We make the following observations: 1) In general, irrespective of the different shot scenarios, compared to SoTAs, COMIC achieves the best performance on almost all the metrics across both datasets. In particular, COMIC outperforms other baselines in terms of total shot's mAP by" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 693, + 525, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 693, + 525, + 703 + ], + "spans": [ + { + "bbox": [ + 315, + 693, + 525, + 703 + ], + "type": "inline_equation", + "content": "{}^{1}B" + }, + { + "bbox": [ + 315, + 693, + 525, + 703 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 315, + 693, + 525, + 703 + ], + "type": "inline_equation", + "content": "{Mo}" + }, + { + "bbox": [ + 315, + 693, + 525, + 703 + ], + "type": "text", + "content": " refer to the batch size and momentum in the Adam." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 703, + 534, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 703, + 534, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 703, + 534, + 713 + ], + "type": "text", + "content": "2We only compare with the approaches that have open source code." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "type": "text", + "content": "1428" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 116, + 286, + 196 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 106 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 106 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 106 + ], + "type": "text", + "content": "Table 3: Performance comparison under different missing labeled settings. 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Missing RatioPLT-COCO Dataset
Total ShotMany ShotMedium ShotLow Shot
0%57.07±0.0952.21±0.1159.98±0.1261.12±0.24
30%55.80±0.1749.97±0.1162.59±0.1554.56±0.17
40%54.75±0.1948.93±0.2460.31±0.2154.14±0.21
50%54.69±0.1548.74±0.1256.68±0.1657.25±0.24
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outperform PL baselines in most " + }, + { + "bbox": [ + 46, + 495, + 289, + 651 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 495, + 289, + 651 + ], + "type": "text", + "content": "-shot situations. We believe the underlying reason behind this is that LT data distribution hurts the classification capability for MLC models more seriously than PL. Besides, the label correction may have aggravated the LT issue and further result in performance reduction. 3) Benefiting from the carefully designed HTB module, our COMIC not only achieves the highest total mAP score but also yields balanced results with a narrowed performance gap in different shot metrics. These results demonstrate the superiority of our proposed model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 658, + 141, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 141, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 141, + 672 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Effectiveness of Each Component. We conduct an ablation study to illustrate the effectiveness of each component in Table 2. Comparing COMIC and COMIC(-RLC) (Row 1 v.s" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 310, + 71, + 433, + 162 + ], + "blocks": [ + { + "bbox": [ + 310, + 71, + 433, + 162 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 433, + 162 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 433, + 162 + ], + "type": "image", + "image_path": "2902bda875f0852c90ce9796f191ccde0c163c689709e12ff401b91899ce1548.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 163, + 417, + 171 + ], + "lines": [ + { + "bbox": [ + 340, + 163, + 417, + 171 + ], + "spans": [ + { + "bbox": [ + 340, + 163, + 417, + 171 + ], + "type": "text", + "content": "(a) Number of TP and FP" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 434, + 70, + 554, + 162 + ], + "blocks": [ + { + "bbox": [ + 434, + 70, + 554, + 162 + ], + "lines": [ + { + "bbox": [ + 434, + 70, + 554, + 162 + ], + "spans": [ + { + "bbox": [ + 434, + 70, + 554, + 162 + ], + "type": "image", + "image_path": "70e574376d45e16082c83a35855a516ecb578bdd741ca825c79d8000f731f880.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 436, + 162, + 544, + 170 + ], + "lines": [ + { + "bbox": [ + 436, + 162, + 544, + 170 + ], + "spans": [ + { + "bbox": [ + 436, + 162, + 544, + 170 + ], + "type": "text", + "content": "(b) Dynamic Distribution Heat Map" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 326, + 180, + 524, + 192 + ], + "lines": [ + { + "bbox": [ + 326, + 180, + 524, + 192 + ], + "spans": [ + { + "bbox": [ + 326, + 180, + 524, + 192 + ], + "type": "text", + "content": "Figure 5: In-depth analysis of label correction." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 310, + 217, + 544, + 281 + ], + "blocks": [ + { + "bbox": [ + 312, + 196, + 539, + 209 + ], + "lines": [ + { + "bbox": [ + 312, + 196, + 539, + 209 + ], + "spans": [ + { + "bbox": [ + 312, + 196, + 539, + 209 + ], + "type": "text", + "content": "Table 4: Ablation of MFM. " + }, + { + "bbox": [ + 312, + 196, + 539, + 209 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 312, + 196, + 539, + 209 + ], + "type": "text", + "content": " indicates the mAP decay." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 217, + 544, + 281 + ], + "lines": [ + { + "bbox": [ + 310, + 217, + 544, + 281 + ], + "spans": [ + { + "bbox": [ + 310, + 217, + 544, + 281 + ], + "type": "table", + "html": "
MFM FactorPLT-COCO Dataset
P-NH-TTotal ShotMany ShotMedium ShotLow Shot
✔54.44 (↓0.64)48.65 (↓0.56)60.00 (↓0.08)53.81 (↓1.55)
♥53.70 (↓1.38)48.38 (↓0.83)58.99 (↓1.09)52.91 (↓2.45)
✔55.0849.2160.0855.36
", + "image_path": "c6a3fb7c19c10a3af4d2b46a6fd260a96098dea6cab73989cebf02805d65b5e0.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 301, + 547, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 547, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 547, + 398 + ], + "type": "text", + "content": "Row 4), the label (Correction) mechanism contributes " + }, + { + "bbox": [ + 304, + 301, + 547, + 398 + ], + "type": "inline_equation", + "content": "0.38\\%" + }, + { + "bbox": [ + 304, + 301, + 547, + 398 + ], + "type": "text", + "content": " improvement on total mAP. The results of Row 2 show the mAP improvement of the MFM (Modification). Meanwhile, Row 3 indicates that it suffers from noticeable performance degradation without the (Balance) learning. To sum up, we can observe that the improvement of each module is distinguishable. Combining all the components, our COMIC exhibits steady improvement over the baselines." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 398, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 547, + 506 + ], + "type": "text", + "content": "Ablation of Missing Rate. To study the effect of partial labels that affect COMIC's results, we evaluate the performance under different missing rates (MR) of labels (from " + }, + { + "bbox": [ + 304, + 398, + 547, + 506 + ], + "type": "inline_equation", + "content": "0\\% \\sim 50\\%" + }, + { + "bbox": [ + 304, + 398, + 547, + 506 + ], + "type": "text", + "content": "). Not surprisingly, when the MR decreases, the accuracy of COMIC increases on all the metrics. We also find that the performance gap between different shots is consistently small in all MR settings. The results demonstrate the generalizability of the proposed COMIC that it can produce stable and balanced results under different MR settings." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": "Hyperparameter " + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": ". We investigate the impact of hyper-parameter " + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": " for the PLT-MLC task. The mAPs of different hyper-parameter settings on PLT-COCO are shown in Figure 3. This figure suggests that the optimal choices of " + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 506, + 547, + 590 + ], + "type": "text", + "content": " are around 2 and 0.7, respectively. Either increasing or decreasing these values results in performance decay." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 598, + 413, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 598, + 413, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 598, + 413, + 611 + ], + "type": "text", + "content": "4.4. In-Depth Analysis" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "text", + "content": "We further validate several vital issues of the proposed Correction " + }, + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "text", + "content": " Modification " + }, + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "text", + "content": " Balance learning paradigm by answering the three questions as follows." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": "Q1: Can the model trust the recalled labels distinguished by RLC? To build the insight on the effectiveness of the label correction mechanism in COMIC, we visualize the true positive (TP) and false positive (FP) in Figure 5(a)). This figure suggests that the RLC module can distinguish a large" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "text", + "content": "1429" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 174, + 163 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 174, + 163 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 174, + 163 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 174, + 163 + ], + "type": "image", + "image_path": "7c2451c28e0e07cfb3cb89aafefea4540503dc212f51dc9945657ec632050826.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 86, + 163, + 154, + 172 + ], + "lines": [ + { + "bbox": [ + 86, + 163, + 154, + 172 + ], + "spans": [ + { + "bbox": [ + 86, + 163, + 154, + 172 + ], + "type": "text", + "content": "(a) Separate Training" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 182, + 547, + 218 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 547, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 547, + 218 + ], + "type": "text", + "content": "Figure 6: Analysis of balanced learning of COMIC. (a) and (b) depict the total mAP of separate and joint training of COMIC within the 40 epochs. (c) summarizes the loss visualization of head, balanced and tail models with joint training. (d) demonstrates head and tail models respectively optimize the head and tail class's performance." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 72, + 298, + 163 + ], + "blocks": [ + { + "bbox": [ + 175, + 72, + 298, + 163 + ], + "lines": [ + { + "bbox": [ + 175, + 72, + 298, + 163 + ], + "spans": [ + { + "bbox": [ + 175, + 72, + 298, + 163 + ], + "type": "image", + "image_path": "4f4b5391f2e69ce724ba454ca76b41940cf8668aecb6a36ceb2e4d7eff1f5ae2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 163, + 271, + 172 + ], + "lines": [ + { + "bbox": [ + 214, + 163, + 271, + 172 + ], + "spans": [ + { + "bbox": [ + 214, + 163, + 271, + 172 + ], + "type": "text", + "content": "(b) Joint Training" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 301, + 72, + 412, + 163 + ], + "blocks": [ + { + "bbox": [ + 301, + 72, + 412, + 163 + ], + "lines": [ + { + "bbox": [ + 301, + 72, + 412, + 163 + ], + "spans": [ + { + "bbox": [ + 301, + 72, + 412, + 163 + ], + "type": "image", + "image_path": "2d9b55bf08e9622b71937a4e4490ca7d8e2a65a36d0198596dc7ebb2f5a960c5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 163, + 397, + 172 + ], + "lines": [ + { + "bbox": [ + 329, + 163, + 397, + 172 + ], + "spans": [ + { + "bbox": [ + 329, + 163, + 397, + 172 + ], + "type": "text", + "content": "(c) Loss Visualization" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 414, + 72, + 536, + 163 + ], + "blocks": [ + { + "bbox": [ + 414, + 72, + 536, + 163 + ], + "lines": [ + { + "bbox": [ + 414, + 72, + 536, + 163 + ], + "spans": [ + { + "bbox": [ + 414, + 72, + 536, + 163 + ], + "type": "image", + "image_path": "dabb023a5fc1da4b7324811cca887d6db1babefc97fcc27073a1e8de5a8f126c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 455, + 163, + 506, + 172 + ], + "lines": [ + { + "bbox": [ + 455, + 163, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 455, + 163, + 506, + 172 + ], + "type": "text", + "content": "(c) Head v.s Tail" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 239, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 288, + 323 + ], + "type": "text", + "content": "number of missing labels with high prediction confidence in the early training stage, meanwhile, " + }, + { + "bbox": [ + 46, + 239, + 288, + 323 + ], + "type": "inline_equation", + "content": "\\mathrm{sum(TP)}\\gg \\mathrm{sum(FP)}" + }, + { + "bbox": [ + 46, + 239, + 288, + 323 + ], + "type": "text", + "content": ". However, Figure 5(b) of corrected samples also reveals LT class distribution with respect to the original training set. To address this issue, we dynamically adjust the sample weight conditioned on the real-time distribution to produce a stable performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "type": "text", + "content": "Q2: How does the MFM module affect the PLT-MLC performance? Here, we evaluate the effectiveness of the multi-focal modifier (MFM) loss compared with different loss functions. Figure 4(a) shows the loss ablation results using different losses in our COMIC. Our developed MFM outperforms existing losses, as the designed loss considers the key point of the head-tail and positive-negative imbalance under the extreme LT distribution in the PLT-MLC task. There are two components in MFM, which are the positive-negative (P-N) factor and head-tail (H-T) factor. To demonstrate the effect of each component, we train the model with the individual factor in the proposed MFM. As shown in Table. 4, both the P-N factor and the H-T factor play significant roles in MFM. For the H-T factor, it achieves an improvement from " + }, + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "type": "inline_equation", + "content": "53.7\\%" + }, + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "type": "text", + "content": " mAP to " + }, + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "type": "inline_equation", + "content": "55.08\\%" + }, + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "type": "text", + "content": " mAP. Meanwhile, it brings a significant gain on tail categories with " + }, + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "type": "inline_equation", + "content": "2.45\\%" + }, + { + "bbox": [ + 46, + 327, + 288, + 613 + ], + "type": "text", + "content": " mAP improvement, indicating its effectiveness to alleviate the severe positive-negative imbalance problems in the LT class distribution. As for the P-N factor, it brings a steady boost on all shot settings which means it can further alleviate the positive-negative issue. Additionally, Figure 4(b) indicates that the MFM loss decreases faster and smoother than the two variants of MFM without different factors, demonstrating its superiority in the PLT-MLC task further." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Q3: How does the HTB module benefit the balanced learning? We systematically present the explicit benefits of the balanced learning strategy in multi-view. 1) Figure 6 (a) and (b) show the comparison between separate and joint training of head, balanced and tail model with respect to the total mAP on PLT-COCO dataset. An interesting phenomenon is that the detached head and tail models slightly outperform the joint head and tail models but suffer" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "type": "text", + "content": "from an unstable performance. In contrast, the accuracy of the joint trained balanced model increases much faster and smoother than the detached balanced model which also yields a stable performance and faster convergence speed. This phenomenon is reasonable as the main optimization objective in joint training is to improve the balanced model's performance. It can be regarded as the knowledge distillation effect that enables the balanced model to learn from the head biased and tail biased model, and this in turn facilitates the PLT-MLC learning. 2) During the competition of head v.s tail, the head model's loss drops faster (shown in Figure 6 (c)) and is biased to optimizing the head samples, while the tail model produces an opposite result. Such head and tail biased results form a foundation that enables our COMIC to be trained in a balanced and stable learning effect. 3) We also perform the analysis of the different balanced learning blocks in our COMIC. As presented in Table 6 (in the Appendix), the DL, NC and AMV contribute " + }, + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "type": "inline_equation", + "content": "0.05\\%" + }, + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "type": "inline_equation", + "content": "1.08\\%" + }, + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "type": "inline_equation", + "content": "0.37\\%" + }, + { + "bbox": [ + 304, + 239, + 547, + 502 + ], + "type": "text", + "content": " improvement on total shot mAP. The observations and analysis verify the effectiveness of balanced learning for being able to study from the head and tail models, thereby achieving the PLT-MLC improvement." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 521, + 383, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 383, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 383, + 533 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "content": "We have presented a fire-new task called PLT-MLC and correspondingly developed a novel framework, named COMIC. COMIC simultaneously addresses the partial labeling and long-tailed environments in a Correction " + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "content": " Modification " + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 543, + 547, + 639 + ], + "type": "text", + "content": " Balance learning manner. On two newly proposed benchmarks, PLT-COCO and PLT-VOC, we demonstrate that the proposed framework significantly outperforms existing MLC, LT-MLC and PL-MLC approaches." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "content": "Acknowledgement This research is supported by Singapore Ministry of Education Academic Research Fund Tier 3 under MOE's official grant number MOE2017-T3-1-007, Zhejiang NSF (LR21F020004), the NSFC (No. 62272411), Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, and Ant Group." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "text", + "content": "1430" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "text", + "content": "[1] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 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Pattern Recognition, 74:488-502, 2018." + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 315, + 758 + ], + "type": "text", + "content": "1432" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning to Distill Global Representation for Sparse-View CT/816ad801-b997-48a5-9faf-a09a225c6e9c_content_list.json b/2023/Learning to Distill Global Representation for Sparse-View CT/816ad801-b997-48a5-9faf-a09a225c6e9c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9f6bf592b9e9e68905b464d9b86832acd6d71d1a --- /dev/null +++ b/2023/Learning to Distill Global Representation for Sparse-View CT/816ad801-b997-48a5-9faf-a09a225c6e9c_content_list.json @@ -0,0 +1,1682 @@ +[ + { + "type": "text", + "text": "Learning to Distill Global Representation for Sparse-View CT", + "text_level": 1, + "bbox": [ + 171, + 130, + 797, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zilong Li $^{1}$ Chenglong Ma $^{2}$ Jie Chen $^{1}$ Junping Zhang $^{1}$ Hongming Shan $^{2,3*}$", + "bbox": [ + 122, + 179, + 843, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Shanghai Key Lab of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai 200433, China", + "bbox": [ + 137, + 198, + 831, + 233 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "$^{2}$ Institute of Science and Technology for Brain-inspired Intelligence and MOE Frontiers Center for Brain Science, Fudan University, Shanghai 200433, China", + "$^{3}$ Shanghai Center for Brain Science and Brain-inspired Technology, Shanghai 200031, China {zilongli21, clma22}@m.fudan.edu.cn, {chenj19, jpzhang, hmshan}@fudan.edu.cn" + ], + "bbox": [ + 107, + 233, + 861, + 305 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 339, + 313, + 354 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sparse-view computed tomography (CT)—using a small number of projections for tomographic reconstruction—enables much lower radiation dose to patients and accelerated data acquisition. The reconstructed images, however, suffer from strong artifacts, greatly limiting their diagnostic value. Current trends for sparse-view CT turn to the raw data for better information recovery. The resultant dual-domain methods, nonetheless, suffer from secondary artifacts, especially in ultra-sparse view scenarios, and their generalization to other scanners/protocols is greatly limited. A crucial question arises: have the image post-processing methods reached the limit? Our answer is not yet. In this paper, we stick to image post-processing methods due to great flexibility and propose global representation(GloRe) distillation framework for sparse-view CT, termed GloReDi. First, we propose to learn GloRe with Fourier convolution, so each element in GloRe has an image-wide receptive field. Second, unlike methods that only use the full-view images for supervision, we propose to distill GloRe from intermediate-view reconstructed images that are readily available but not explored in previous literature. The success of GloRe distillation is attributed to two key components: representation directional distillation to align the GloRe directions, and band-pass-specific contrastive distillation to gain clinically important details. Extensive experiments demonstrate the superiority of the proposed GloReDi over the state-of-the-art methods, including dual-domain ones. The source code is available at https://github.com/longzilicart/GloReDi.", + "bbox": [ + 76, + 372, + 473, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 844, + 209, + 859 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "X-ray CT is one of the major modalities widely used in clinical screening and diagnosis. Despite the benefits,", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/756a567b6fc751570ebf1d8c919d160bd8f9c82ad12f97be762f6581b45d0a72.jpg", + "image_caption": [ + "Figure 1. Sparse-view CT only uses a few projection views for tomographic reconstruction, thus providing fast and low-dose CT scanning. However, the reconstruction results of the conventional method suffer from severe global streak artifacts." + ], + "image_footnote": [], + "bbox": [ + 506, + 339, + 890, + 520 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "there have been growing concerns that X-ray radiation exposure could increase the risk of cancer induction [47]. Following the \"As Low As Reasonably Achievable\" principle in the medical community [36], efforts have been made to lower the radiation dose while maintaining imaging quality [20]. Sparse-view CT is one of the effective solutions which reduces the radiation by sampling part of the projection data, a.k.a sinogram, for image reconstruction, as shown in Fig. 1. However, analytical reconstruction algorithms such as filtered back projection (FBP) produce inferior image quality with globally severe streak artifacts, significantly compromising its diagnosis value. How to effectively reconstruct the sparse-view CT remains challenging and, hence, is gaining increasing attention in the computer vision and medical imaging communities.", + "bbox": [ + 496, + 613, + 892, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image-domain methods regard sparse-view CT reconstruction as an image post-processing task on the FBP-reconstructed images and have achieved exciting performance on streak artifacts removal and structure preserva", + "bbox": [ + 496, + 840, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21196", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion [5, 22, 32, 58]. However, due to the limited receptive field, these methods have difficulty in modeling global information efficiently, thus leading to suboptimal results. Current dominant methods turn to the help of sinogram by restoring the sinogram and performing CT image postprocessing simultaneously [17, 29, 31, 46]. Specifically, in addition to the image domain methods, deep neural networks are also applied to interpolate the missing data in sinogram so that the reconstructed images can be recovered in a global manner [10, 25].", + "bbox": [ + 80, + 90, + 467, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the common success of dual-domain methods, they suffer from unsatisfactory and unstable performance due to the following reasons. First, the processing of sinogram data is sensitive and even subtle changes may remarkably affect the reconstructed images and introduce stubborn secondary artifacts that are hard to be eliminated. Second, in ultra sparse-view scenarios, inpainting methods are unable to accurately restore the excessive missing raw data; e.g., inpainting sparse CT data of 18 views to the full CT data of 720 views only retains about $2.5\\%$ of the valid information, in which the involvement of sinogram processing makes the learning more difficult and compromise the performance [29,46]. Third, it is often impractical to access sinogram data given the privacy and commercial concerns, and if accessible, the requirement of raw data greatly limits the generalization to other scanners/protocols.", + "bbox": [ + 80, + 243, + 467, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivation. Given the great flexibility of the image domain methods, we raise a critical question in this paper: have the image domain (post-processing) methods reached the limits? Our answer is not yet, given the following observations. First, existing image-domain methods typically suffer from limited receptive field, which fails to extract and recover the global information efficiently [43], given that streak artifacts are spread globally on the reconstructed images as shown in Fig. 1. Second, existing image-domain methods only utilize the full-view images as the unique supervision on the result [22, 58]. They ignore the importance of representation learning, especially global representation (GloRe), making the artifact removal and detail recovery entangled, and leading to sub-optimal results due to the significant gap between sparse- and full-view. Third, the intermediate-view reconstructed images can be readily available during data preparation, but to the best of our knowledge, they are surprisingly neglected in the past literature. We argue that they can provide extra information and build bridges for sparse- and full-view CT reconstruction.", + "bbox": [ + 80, + 491, + 467, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the abovementioned issues, we propose a novel image-domain method for sparse-view CT reconstruction. First, to address the limited receptive field inherent in conventional convolutional neural networks, we propose to learn GloRe with fast Fourier convolution (FFC) [7], so each element in GloRe has an image-wide receptive field. This global nature allows artifacts and information,", + "bbox": [ + 80, + 795, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "spread over the entire image, to be better modeled while also easing the alignment of the representations from different views. Second, to leverage extra supervision from intermediate-view CT images, we propose a novel distillation framework to learn better GloRe, termed GloReDi, which contains a parallel teacher network to distill knowledge from the readily intermediate-view images to provide high-quality and appropriate guidance for learning the GloRe of sparse-view CT images. Specifically, we first leverage intermediate-view reconstructed images to train a teacher network, which is then used to guide the learning of the student model (i.e. the sparse-view CT). The distillation scheme benefits GloRe in two folds: (1) representation directional distillation that aligns the directions between the student and teacher GloRe, which provides appropriate supervision considering the massive information loss due to the domain gaps between CT images with different views; and (2) band-pass-specific contrastive distillation that utilizes contrastive learning solely on the band-pass components to help distill the specific clinical value of each CT image without compromising the reconstruction accuracy.", + "bbox": [ + 503, + 90, + 888, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. In summary, our contributions are listed as follows. First, we propose the global representation (GloRe) learning for sparse-view CT with Fourier convolution, which, to the best of our knowledge, is the first study to emphasize on the representation learning for image post-processing in sparse-view CT. Second, we propose a novel GloRe distillation framework, which can leverage the extra supervision from intermediate-view reconstructed images for high-quality information recovery and reconstruction. Third, we present representation directional distillation and band-pass-specific contrastive distillation for distilling GloRe to align the representation directions and gain clinically important details. Last, extensive experimental results demonstrate the superiority of GloReDi over the state-of-the-art sparse-view CT reconstruction methods in terms of quantitative metrics and visual comparison.", + "bbox": [ + 503, + 412, + 888, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Detailed Related Work", + "text_level": 1, + "bbox": [ + 503, + 670, + 712, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Deep-learning-based Sparse-view CT", + "text_level": 1, + "bbox": [ + 503, + 696, + 818, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Numerous model-based iterative reconstruction (IR) methods have been developed to solve the sparse-view CT problem, mainly utilizing the sparsity of the total variation (TV) of the image [4, 12, 23, 33, 37, 51, 52]. However, most of them suffer from over-smoothed results, handcrafted tuning for each image, and extremely high computation cost [46], limiting their clinical application. In contrast, deep learning methods are often faster and more accessible, thus arousing attention in this field. Among them, most image-domain methods regard sparse-view CT reconstruction as an image post-processing task. RedCNN [5], FBPCovNet [22], and DDNet [58] are proposed to recon", + "bbox": [ + 503, + 720, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21197", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/39079075f1fa3780726c8ebc0a0477b51833038f6a895045ed41fd3019596138.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 89, + 179, + 165 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0bf62877d0ea5293afe999f9d3218964e512e2cf7bc01242c979df77b2a6dfca.jpg", + "image_caption": [ + "Band-Pass-Specific Contrastive Distillation", + "Encoders" + ], + "image_footnote": [], + "bbox": [ + 187, + 147, + 387, + 220 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0122f267d596d11874f8856b683d78bcd835e2b3bf29a85e592ee24ad1927033.jpg", + "image_caption": [ + "EncoderT" + ], + "image_footnote": [], + "bbox": [ + 395, + 95, + 656, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1cc431bf19aeb136ef42253f2eb05f9a5cf7285fd13965f97f7ec21143ac409c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 666, + 89, + 888, + 172 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c26dd8f5a24d2d555cef451aa7ed4691a522a2ec6885498ebeba8e7d9c2a0f33.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed GloReDi for sparse-view CT reconstruction. GloReDi facilitates efficient information recovery by learning to distill the global representation from intermediate-view images." + ], + "image_footnote": [], + "bbox": [ + 666, + 179, + 888, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "struct the sparse-view CT by the convolutional neural network (CNN). These methods achieve competitive performance on streak artifact removal and structure preservation compared to conventional ones, but most of them fail to capture the global context and underperform in global reconstruction and artifact removal. Since streak artifacts result directly from the incomplete projection views, various methods are proposed to remove the artifacts by interpolating sinogram data [10, 25]. Further, dual-domain methods were becoming popular for their superior reconstruction performance by combining the knowledge of both domains. DuDoNet [31] first proposed a novel Radon inversion layer linking the gradient between the image and sinogram domain networks. Furthermore, various techniques have been proposed to enhance dual domain approaches through network design [1,6] and unrolling architecture [57]. Recently, Transformer [45] has been introduced to dual-domain methods for its capability of capturing long-range dependencies, achieving superior performance [29, 46, 49]. However, the problems of the irreversible secondary artifacts and additional computational costs are not well addressed, and the requirement of raw data greatly limits their generalizability to other CT scanners/protocols. In this work, we challenge reconstructing sparse-view CT without raw data while still achieving state-of-the-art results.", + "bbox": [ + 75, + 323, + 472, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Knowledge Distillation", + "text_level": 1, + "bbox": [ + 76, + 710, + 287, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge distillation transfers rich knowledge from teacher models to lightweight student models in the label or feature domains, mainly applied in model compression and acceleration [15, 41]. Among various approaches, feature-based knowledge distillation is extensively applied in image restoration tasks such as image super-resolution [14, 16, 27, 38]. It minimizes the distance between feature representations to learn richer information from the teacher model compared to softened labels [48]. Further, contrastive representation distillation is proposed to exploit the structural characteristics among different samples by harnessing the", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "discriminative representations, thereby enhancing differentiation within data [8, 19, 44]. This work distills knowledge from the intermediate-view images to enhance the sparse-view CT reconstruction.", + "bbox": [ + 496, + 323, + 890, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Frequency Methods in Deep Learning", + "text_level": 1, + "bbox": [ + 498, + 393, + 828, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Frequency methods have been widely used in digital image processing and machine learning [2]. Wavelet convolution [32] and fast Fourier convolution [7] have been proposed to provide a larger/global receptive field, achieving great success in image restoration tasks [43]. Frequency methods have also yielded promising results in domain adaption and image translation, mainly by taking advantage of domain-invariant spectrum components [3, 18, 54-56]. Previous research also shows that particular features and details can be better extracted in the frequency domain, leading to improvements in camouflaged object detection [59], face forgery detection [21, 28], and face editing [9]. Frequency-based networks have also made notable strides in CT reconstruction. Previous studies [1, 26] employ multi-wavelet CNN [32] in both sinogram and image domain to suppress artifacts, substituting the pooling operator with wavelet transforms to achieve a larger receptive field. However, since both the Haar filter-based wavelet transform and convolution are applied on the spatial feature map, these methods struggle to capture global representation effectively. Recent research has demonstrated that employing convolution in the Fourier domain can efficiently eliminate the global artifacts [30, 34]. In this work, we utilize a frequency-based network for global representation learning, enhancing clinically critical features by band-pass-specific contrastive distillation.", + "bbox": [ + 496, + 416, + 892, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 821, + 589, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 500, + 845, + 681, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Assume we have a two-dimensional (2D) CT slice of size $N\\times N$ $\\pmb {I}\\in \\mathbb{R}^{N\\times N}$ , where each pixel contains the attenua", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21198", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion coefficient of the corresponding human body. The raw data or sinogram from the CT scanning, $S \\in \\mathbb{R}^{N_{\\mathrm{v}} \\times N_{\\mathrm{d}}}$ , can be obtained via the Radon transform [39], where $N_{\\mathrm{v}}$ and $N_{\\mathrm{d}}$ denote the number of projection views and the number of the detectors, respectively. Inversely, the image reconstruction process can be expressed as $\\boldsymbol{I} = \\mathcal{R}^{-1}(\\boldsymbol{S})$ , where $\\mathcal{R}^{-1}$ denotes the inverse Radon transform such as FBP. Ideally, when $N_{\\mathrm{v}}$ is sufficiently large, FBP can produce pleasing image quality. However, when $N_{\\mathrm{v}}$ is fairly small, the image reconstruction of so-called sparse-view CT becomes an undetermined problem.", + "bbox": [ + 75, + 90, + 472, + 256 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we use $I_{\\mathrm{F}}$ and $I_{\\mathrm{S}}$ to represent the reconstructed images from full view (i.e. ground-truth) and sparse view, respectively. The image-domain methods for sparse-view CT are to improve the image quality of $I_{\\mathrm{S}}$ towards $I_{\\mathrm{F}}$ through a neural network $\\mathcal{F}$ . That is, the output of the network, $\\widehat{I}_{\\mathrm{S}} = \\mathcal{F}(I_{\\mathrm{S}})$ , is expected to be of comparable quality to the full-view ground-truth. In addition, we also use the images, $I_{\\mathrm{T}}$ , reconstructed from an intermediate number of projection views that are between sparse and full views, as the teacher supervision, forming a student-teacher framework where the teacher encoder with $I_{\\mathrm{T}}$ supervises the training of student encoder with $I_{\\mathrm{S}}$ .", + "bbox": [ + 75, + 257, + 472, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overview of Our GloReDi", + "text_level": 1, + "bbox": [ + 76, + 446, + 316, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 2 presents the proposed GloReDi, which mainly consists of four parts: two encoders to learn global representations (GloRe) from sparse- and intermediate-view reconstructed images, $I_{\\mathrm{S}}$ , and $I_{\\mathrm{T}}$ , respectively, and two decoders to produce the final processed images from GloRe. In addition to learning GloRe with Fourier convolution, we have two novel modules to perform distillation from the teacher network: (1) representation directional distillation to align the directions between the student and teacher GloRes; and (2) band-pass-specific contrastive distillation to distill the clinically important features for better detail recovery.", + "bbox": [ + 75, + 469, + 472, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we detail each of the proposed components.", + "bbox": [ + 96, + 651, + 426, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Global Representation Learning", + "text_level": 1, + "bbox": [ + 76, + 674, + 362, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The key technique behind the proposed network is the global representation learning with fast Fourier convolution (FFC) [7]. Concretely, FFC first applies real Fourier transform to get the frequency feature map and then performs convolution on frequency components before finally back transforming the frequency features as shown in Fig. 2. Therefore, GloRe from sparse-view images $I_{\\mathrm{S}}$ is learned by a Fourier-based encoder network as follows:", + "bbox": [ + 75, + 698, + 468, + 818 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {Z} _ {\\mathrm {S}} = \\operatorname {e n c o d e r S} (\\boldsymbol {I} _ {\\mathrm {S}}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 828, + 468, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Z_{\\mathrm{S}} \\in \\mathbb{R}^{N_{\\mathrm{w}} \\times N_{\\mathrm{h}} \\times N_{\\mathrm{c}}}$ denotes GloRe extracted from the sparse-view reconstructed image $I_{\\mathrm{S}}$ through the (student) encoder encoderS and $N_{\\mathrm{w}} \\times N_{\\mathrm{h}} \\times N_{\\mathrm{c}}$ denotes the", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "width, height, and channel size of GloRe. Compared to the vanilla convolution with a limited receptive field, FFC works in the frequency domain, so each element in GloRe contains global information of the sparse-view image by using an image-wide receptive field, representing patterns of artifacts and the image contents simultaneously. Furthermore, such global nature can aid in modeling the artifact and information distributed throughout the image while easing the alignment between GloRe of different views.", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Global Representation Distillation", + "text_level": 1, + "bbox": [ + 498, + 234, + 799, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the context of sparse-view CT, images with an intermediate view $I_{\\mathrm{T}}$ can be easily obtained from the full-view sinogram as extra supervision. To get the teacher representation from $I_{\\mathrm{T}}$ , a parallel teacher encoder encoderT, using the same architecture as encoderS but with different weights, takes $I_{\\mathrm{T}}$ as input and yields teacher GloRe $Z_{\\mathrm{T}}$ of the same shape with $Z_{\\mathrm{S}}$ as follows:", + "bbox": [ + 496, + 258, + 893, + 364 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {Z} _ {\\mathrm {T}} = \\operatorname {e n c o d e r} \\mathrm {T} \\left(\\boldsymbol {I} _ {\\mathrm {T}}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 375, + 890, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$Z_{\\mathrm{T}}$ can be regarded as a high-quality pseudo target for student GloRe in the same latent space since richer information can be extracted from $I_{\\mathrm{T}}$ . Exploring distillation from $I_{\\mathrm{T}}$ is obviously easier than that of $I_{\\mathrm{F}}$ given the significant gap between $I_{\\mathrm{S}}$ and $I_{\\mathrm{F}}$ .", + "bbox": [ + 496, + 398, + 890, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, $Z_{\\mathrm{S}}$ should be similar to $Z_{\\mathrm{T}}$ if the artifact-free target information is precisely encoded. Therefore, a natural way for distillation is to use $Z_{\\mathrm{T}}$ as the supervision for $Z_{\\mathrm{S}}$ by minimizing their Euclidean distance. However, this could harm the reconstruction performance since the student encoder has to partially recover $I_{\\mathrm{T}}$ . Finding an effective solution to distilling the information in $Z_{\\mathrm{T}}$ for sparse-view CT reconstruction is one of the highlights in this work. Our idea is to separate the distillation process. First, we present representation directional distillation to align the representation directions so the images of different views are along the same direction. Second, we propose a band-pass-specific contrastive distillation to enhance clinically critical details.", + "bbox": [ + 496, + 474, + 892, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We detail these two distillation techniques as follows.", + "bbox": [ + 519, + 671, + 872, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4.1 Representation Directional Distillation", + "text_level": 1, + "bbox": [ + 498, + 704, + 823, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given that $I_{\\mathrm{S}}$ and $I_{\\mathrm{T}}$ share the same ground truth $I_{\\mathrm{F}}$ , but differ mainly in artifact patterns, student and teacher GloRe should at least demonstrate a consistent direction for reconstruction with high confidence. Therefore, We define the directional distillation loss for $Z_{\\mathrm{S}}$ as follows:", + "bbox": [ + 496, + 727, + 890, + 803 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r d d}} = \\frac {1}{N _ {\\mathrm {w}} N _ {\\mathrm {h}}} \\sum_ {i, j} \\left(1 - \\operatorname {C o s S i m} \\left(\\left[ \\mathbf {Z} _ {\\mathrm {S}} \\right] _ {i, j}, \\left[ \\mathbf {Z} _ {\\mathrm {T}} \\right] _ {i, j}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 809, + 890, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\operatorname{CosSim}$ denotes the cosine similarity, defined as $\\operatorname{CosSim}(\\mathbf{a},\\mathbf{b}) = \\mathbf{a}^{\\mathrm{T}}\\mathbf{b} / \\max (\\|\\mathbf{a}\\|_2\\|\\mathbf{b}\\|_2,\\epsilon)$ with $\\epsilon$ set to $1\\times 10^{-8}$ to avoid division by zero.", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21199", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f009c71cebac14b4dc2b7355b8a2dc1c82e95cdd82450d3609d7b02df326d2b0.jpg", + "image_caption": [ + "Figure 3. The difference between representation distillation (left) and band-pass-specific contrastive distillation (right). Global representation distillation fails to distinguish clinical details due to high similarity among similar body parts, e.g., adjacent lung slices. Band-pass-specific contrastive distillation further projects the representation to the DCT domain, enabling distillation of specific clinical details on corresponding DCT components." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.2 Band-Pass-Specific Contrastive Distillation", + "text_level": 1, + "bbox": [ + 76, + 368, + 429, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The directional distillation aligns the directions of student representation $Z_{\\mathrm{S}}$ and the teacher representation $Z_{\\mathrm{T}}$ in the view-independent space, which, however, does not guarantee a high-quality reconstruction of the image. What distinguishes sparse-view CT reconstruction task from classic image restoration one (e.g. denoising, deraining, etc.) is that the former is more demanding in terms of fine-grained details for diseases identification, organs delineation, and low-contrast lesions detection, etc [11]. In other words, it places more emphasis on learning the image-specific representation.", + "bbox": [ + 75, + 393, + 468, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrastive representation learning, as a self-supervised approach, encourages the model to maximize the difference among representations of different samples so that model can emphasize those category-specific representations. However, directly implementing these losses would lead to imprecise reconstruction results because most CT images are inherently similar in intensity distribution, especially for images of the same body parts, as shown in Fig. 3. Recent methods have achieved great success learning on specific DCT spectrum [18, 50, 54], due to its strong energy compaction property, making it simple to select specific frequency components [40]. Therefore, we distilled the image-specific details by applying contrastive distillation on specific discrete cosine transform (DCT) spectrums. On the one hand, detailed knowledge can be better distilled from specific frequency components of teacher GloRe. On the other hand, contrastive against different CT slices can further enhance image-specific details on corresponding DCT components.", + "bbox": [ + 75, + 561, + 470, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Discrete cosine transform. Discrete cosine transform (DCT) is widely used for data compression in low-frequency components. The basis function of 2D DCT is", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "defined as follows:", + "bbox": [ + 500, + 90, + 627, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nB _ {w, h} ^ {i, j} = \\cos \\left(\\frac {\\pi w}{N _ {\\mathrm {w}}} \\left(i + \\frac {1}{2}\\right)\\right) \\cos \\left(\\frac {\\pi h}{N _ {\\mathrm {h}}} \\left(j + \\frac {1}{2}\\right)\\right), \\quad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 112, + 893, + 140 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{\\mathrm{w}}$ and $N_{\\mathrm{h}}$ represent the width and height of the input, respectively. Then, 2D DCT of the latent feature $\\mathbf{Z}$ can be written as:", + "bbox": [ + 498, + 147, + 893, + 191 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {w, h} (\\boldsymbol {Z}) = \\sum_ {i = 0} ^ {N _ {\\mathrm {w}} - 1} \\sum_ {j = 0} ^ {N _ {\\mathrm {h}} - 1} [ \\boldsymbol {Z} ] _ {i, j} B _ {w, h} ^ {i, j}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 200, + 892, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w\\in \\{0,1,\\ldots ,N_{\\mathrm{w}} - 1\\} ,h\\in \\{0,1,\\ldots ,N_{\\mathrm{h}} - 1\\}$ The $f(\\pmb {Z})\\in \\mathbb{R}^{N_{\\mathrm{w}}\\times N_{\\mathrm{h}}}$ represents the 2D DCT frequency spectrum of $\\pmb{Z}$ . Thus, frequency components can be easily selected by a mask $M\\in \\{0,1\\}^{N_{\\mathrm{w}}\\times N_{\\mathrm{h}}}$", + "bbox": [ + 498, + 238, + 892, + 300 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Band-pass-specific contrastive distillation. Crucially, the low-frequency components of GloRe contribute most to the reconstruction accuracy, while high-frequency may contain inherent noise and artifacts of CT images. We therefore use a band-pass supervised contrastive loss for the distillation, where a band-pass mask $M$ is incorporated to filter out the mid-frequency part in the frequency domain, containing main structure as well as the necessary detail information. The proposed band-pass supervised contrastive loss can be written as:", + "bbox": [ + 498, + 303, + 890, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {z} = \\text {f l a t t e n} \\left(\\operatorname {c r o p} \\left(f _ {w, h} (\\boldsymbol {Z}), \\boldsymbol {M}\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 465, + 890, + 483 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where crop operator will keep the value at locations where $M = 1$ while the flatten operator flattens the 2D spectrum map into 1D representation.", + "bbox": [ + 498, + 493, + 890, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is to be observed that the clinical details in the CT images vary from case by case and are each very critical for diagnosis, requiring more sophisticated instance-level distinction. To this end, we consider all representations from different CT slices as negative samples to maximize image-specific features while updating the memory bank $\\mathcal{M}$ with the widely applied First-In-First-Out mechanism per iteration from the previous mini-batches. The proposed band-pass-specific contrastive distillation loss for sample $z_{\\mathrm{S}}$ can be written as follows:", + "bbox": [ + 496, + 539, + 892, + 689 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {b c d}} = - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {\\mathrm {S}} ^ {\\mathrm {T}} \\boldsymbol {z} _ {\\mathrm {T}} / \\tau\\right)}{\\sum_ {\\boldsymbol {z} \\in \\mathcal {M}} \\exp \\left(\\boldsymbol {z} _ {\\mathrm {S}} ^ {\\mathrm {T}} \\boldsymbol {z} / \\tau\\right)}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 696, + 890, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z_{\\mathrm{S}}, z_{\\mathrm{T}}$ , and $z$ are frequency representations of $Z_{\\mathrm{S}}, Z_{\\mathrm{T}}$ , and negative samples from memory bank $\\mathcal{M}$ of size $N_{\\mathrm{mem}}$ , respectively. $\\tau$ is the temperature term used to adjust the sensitivity of negative samples.", + "bbox": [ + 498, + 742, + 890, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Loss Function and Training Procedure", + "text_level": 1, + "bbox": [ + 500, + 811, + 831, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Teacher reconstruction. To constrain the GloRe extracted from $I_{\\mathrm{S}}$ and $I_{\\mathrm{T}}$ in the same latent space, a naive solution is to share the same decoder in the training phase, which, however, brings instability. Therefore, we adopt the widely", + "bbox": [ + 498, + 839, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21200", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 The training process of GloReDi." + ], + "code_body": "Require: encoderS, encoderT, decoderS, decoderT; Input images: $I_{\\mathrm{S}}, I_{\\mathrm{T}}, I_{\\mathrm{F}}$ ; momentum $m$ and Memory bank \n1: for iter = 0 to Max_Iter do \n2: Update decoderT using Eq. (8) \n3: $\\widehat{I}_{\\mathrm{T}}, Z_{\\mathrm{T}} = \\text{decoderT}(\\text{encoderT}(I_{\\mathrm{T}}))$ \n4: Optimize encoderT using Eq. (9) \n5: $\\widehat{I}_{\\mathrm{S}}, Z_{\\mathrm{S}} = \\text{decoderS}(\\text{encoderS}(I_{\\mathrm{S}}))$ \n6: Optimize encoderS+decoderS using Eq. (11) \n7: Update memory bank \n8: end for \nReturn: encoderS+ decoderS", + "bbox": [ + 78, + 107, + 468, + 290 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "used Exponential Moving Average (EMA) with momentum $m$ to update the parameters $\\theta$ of the teacher decoder by the student decoder [13]:", + "bbox": [ + 76, + 316, + 468, + 363 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {\\text {d e c o d e r T}} = m \\theta_ {\\text {d e c o d e r T}} + (1 - m) \\theta_ {\\text {d e c o d e r S}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 376, + 468, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then, the global representation $Z_{\\mathrm{T}}$ learned by the teacher is fed into to the decoder to obtain the teacher reconstruction result $\\widehat{I}_{\\mathrm{T}}$ , and we use $\\ell_1$ loss to measure the pixel-wise difference between $\\widehat{I}_{\\mathrm{T}}$ and the full-view ground-truth $I_{\\mathrm{F}}$ and train the teacher:", + "bbox": [ + 76, + 404, + 468, + 478 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p i x e l T}} = \\left\\| \\operatorname {d e c o d e r T} \\left(\\boldsymbol {Z} _ {\\mathrm {T}}\\right) - \\boldsymbol {I} _ {\\mathrm {F}} \\right\\| _ {1}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 491, + 468, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Student reconstruction. The pixel-wise error measurement for the student is defined in a similar way:", + "bbox": [ + 76, + 525, + 468, + 555 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p i x e l S}} = \\left\\| \\operatorname {d e c o d e r S} \\left(\\boldsymbol {Z} _ {\\mathrm {S}}\\right) - \\boldsymbol {I} _ {\\mathrm {F}} \\right\\| _ {1}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 566, + 468, + 584 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, a compound loss function combining pixel-wise error and two distillation losses, respectively defined in Eq. (3) and Eq. (7) is introduced for student network training to achieve high-quality sparse-view CT reconstruction:", + "bbox": [ + 76, + 595, + 468, + 657 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {S t u}} = \\mathcal {L} _ {\\mathrm {p i x e l S}} + \\alpha \\mathcal {L} _ {\\mathrm {r d d}} + \\beta \\mathcal {L} _ {\\mathrm {b c d}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 684, + 468, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GloReDi is trained following the process summarized in Algorithm 1, where the student and teacher encoder are trained iteratively.", + "bbox": [ + 76, + 712, + 468, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 772, + 281, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 797, + 266, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We use DeepLesion dataset [53] and \"2016 NIH-AAPM-Mayo Clinic Low-Dose CT Grand Challenge\" AAPM dataset [35] to demonstrate the effectiveness of the proposed GloReDi. The DeepLesion dataset is the largest multi-lesion real-world CT dataset made available to the", + "bbox": [ + 76, + 824, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "public, from which 40,000 images of 303 patients are selected as the training set while 1000 images of another 18 patients are selected as the test set. AAPM dataset contains routine dose CT data from 10 patients, where a total of 5,410 slices from 9 patients are chosen for training and 526 slices from the remaining 1 patient for testing. All images are resized to $256 \\times 256$ . We simulate the forward and back projection using fan-beam geometry under $120\\mathrm{kVp}$ and $500\\mathrm{mA}$ with TorchRadon toolbox [42]. The distance from X-ray source to the rotation center is $59.5\\mathrm{cm}$ , and the number of detectors is set to 672. Sparse-view CT images are generated from $N_{\\mathrm{v}} = 18,36,72,144$ projection views uniformly sampled from full 720 views covering $[0,2\\pi]$ . To simulate the photon noise presented in real-world CT, an intensity of $1 \\times 10^{6}$ Poisson noise is added to the sinograms.", + "bbox": [ + 496, + 90, + 890, + 318 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. Our model is implemented in PyTorch. We use Adam optimizer [24] with $(\\beta_{1},\\beta_{2}) = (0.5,0.999)$ to train the model. The learning rate starts from $1\\times 10^{-3}$ and is halved for every 40 epochs. For each method, four models of different $N_{\\mathrm{v}}$ are trained separately on 4 NVIDIA RTX 3090 GPUs for 120 epochs with a batch size of 8. For hyperparameters in GloReDi, we set $\\alpha$ and $\\beta$ in Eq. (11) empirically to 0.1 and 0.0002 to fit the scale between losses. The momentum $m$ and temperature $\\tau$ are set to 0.9 and 1.0, respectively, while the size $L$ of the memory bank is set to 300 to balance the performance and computational cost. We set intermediate-view as $N_{\\mathrm{v}}\\times 2$ by default. More details, including the network architecture, can be found in the Supplementary Material.", + "bbox": [ + 496, + 321, + 890, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. For quantitative evaluation, we use peak signal-to-noise ratio (PSNR), structural similarity (SSIM) [60] and root mean square error (RMSE); all of them are widely adopted for image quality assessment.", + "bbox": [ + 496, + 540, + 890, + 599 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 498, + 613, + 867, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare GloReDi with the following state-of-the-art methods: DDNet [58], FBPCovNet [22], DuDoNet [31], DDPTrans [29], and DuDoTrans [46]. In addition, we name the network without the distillation from $I_{\\mathrm{T}}$ as the frequency encoder and decoder network (Fred-Net), optimized with only the pixel-wise loss in Eq. (10). FBP directly applies Radon transform to reconstruct the image from the sparse-view sinogram. DDNet and FBPCovNet are image-domain deep-learning methods taking FBP results as input. DuDoNet is a state-of-the-art dual-domain method that restores the CT image using two U-Nets in sinogram and image domains. Furthermore, DDPTrans and DuDoTrans adopt Transformer on both domains to restore the image by utilizing the long-range dependency. We try our best to reproduce these methods and then train and test them on the same dataset for a fair comparison.", + "bbox": [ + 496, + 638, + 890, + 878 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative comparison. Table 1 presents the quantita", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21201", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/23081cb199a5ac3c80912953a6229b4339a42f1dc2c6a7da64a4ed434a4a2a33.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methods\\(N_{\\mathrm{v}}=18\\)\\(N_{\\mathrm{v}}=36\\)\\(N_{\\mathrm{v}}=72\\)\\(N_{\\mathrm{v}}=144\\)
PSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSE
FBP22.2235.360.079525.4947.490.054330.8863.810.029337.1282.940.0144
DDNet [58]34.5791.940.018738.2494.910.012641.6697.270.008346.7598.790.0048
FBPCovNet [22]35.9593.620.016439.7996.130.010643.7697.470.006648.4698.600.0039
DuDoNet [31]35.6993.960.016940.3696.940.010344.8698.390.005949.3399.230.0036
DDPTRans [29]35.1193.480.018138.6895.990.012143.5698.160.006948.7299.220.0038
DuDoTrans [46]36.0893.280.016140.7596.670.009545.1698.440.005749.9699.280.0034
Fred-Net (ours)38.0895.200.012940.8696.810.009344.4398.180.006348.4599.080.0039
GloReDi (ours)38.6595.870.012041.2597.050.009045.1898.430.005748.9699.210.0037
", + "bbox": [ + 78, + 87, + 893, + 231 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Quantitative evaluation [PSNR (db), SSIM (%) and RMSE] for state-of-the-art methods on DeepLesion dataset.", + "bbox": [ + 127, + 234, + 839, + 250 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ed20eca4f47123ee893b8a48a6c3f78d989483843ffcf29a1d59afd80dac083.jpg", + "image_caption": [ + "Figure 4. Visual comparison of state-of-the-art methods on DeepLesion dataset: (a) Ground Truth, (b) FBP, (c) DDNet, (d) FBPCovNet, (e) DuDoNet, (f) DDPTrans, (g) DuDoTrans, and (h) GloReDi. From top to bottom: the results under $N_{\\mathrm{v}} = 18$ , 36, 72; display window is set to [-1000, 2000] HU for the first two rows and [-200, 300] HU for the third row." + ], + "image_footnote": [], + "bbox": [ + 78, + 262, + 890, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tive comparison. Generally, dual-domain methods perform better than single-domain methods, especially in the case of $N_{\\mathrm{v}} = 72$ , 144 thanks to the sinogram inpainting network. However, we highlight in ultra sparse-view scenarios where $N_{\\mathrm{v}} = 18$ , that dual-domain methods like DuDoNet perform worse than classical image-domain-only methods such as FBPCovNet. This can be attributed to the secondary artifacts introduced by the unsuccessful sinogram inpainting; e.g., when $N_{\\mathrm{v}} = 18$ in our setting, restoring the sinogram can be recognized as a $40 \\times$ super-resolution task, which is rather challenging. DuDoTrans is superior to DuDoNet to some extent, indicating the importance of long-range dependency in reconstruction. DDPTrans fails to surpass DuDoNet because of the limited parameter number though most transformers are memory-consuming.", + "bbox": [ + 75, + 584, + 472, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared with the previous works, the proposed GloReDi achieves competitive results by learning to distill GloRe for high-quality reconstruction. Particularly in ultrasparse scenarios, e.g., when $N_{\\mathrm{v}} = 18$ , GloReDi has 2.57db and 2.70db improvement on PSNR over DuDoTrans and", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "FBPCovNet, respectively. As $N_{\\mathrm{v}}$ increases, the advantage of GloReDi decreases, mainly due to a shift towards artifacts removal tasks rather than reconstruction. We highlight that the fewer projection views indicate less radiation dose and more speedup. We notice that global representation distillation further improves the performance of GloReDi from 0.51db to 0.89db compared to Fred-Net. The results show that the proposed GloReDi successfully inspire the potential of image post-processing methods and is significantly superior to the state-of-the-art methods under various settings.", + "bbox": [ + 496, + 584, + 890, + 737 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual comparison. Fig. 4 presents the visualization results of three sparse-view CT. DDNet and FBPCovNet cannot remove the artifact thoroughly, while the reconstruction results are over-smooth in the boundary of organs and bones. Such effects can be easily observed in the second row of Figs. 4(c) and 4(d) on the spine where the anatomical structure is complicated. Although dual-domain methods perform better in general, their accuracy in details is even worse than FBPCovNet in comparison with Figs. 4(d) and 4(e)-(g). Among all these methods, Glo", + "bbox": [ + 496, + 750, + 892, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21202", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b3073c8f663b5ec5305221ae4fd8cbd9a9f753ed2502a07b05d39ffca260deed.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methods\\(N_{\\mathrm{v}}=18\\)\\(N_{\\mathrm{v}}=36\\)\\(N_{\\mathrm{v}}=72\\)\\(N_{\\mathrm{v}}=144\\)
PSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSE
FBP22.7335.060.073226.2747.520.048631.3664.560.027037.8584.570.0128
DDNet [58]34.2989.680.019436.9593.030.014240.4196.040.009644.3598.050.0061
FBPCovNet [22]35.7392.840.016537.9593.730.012742.9297.190.007247.3598.760.0043
DuDoNet [31]34.8293.000.019639.8995.990.010244.0698.020.006248.3999.110.0038
DDPTRans [29]34.4791.950.019138.1394.830.012542.7797.650.007347.8499.060.0041
DuDoTrans [46]35.8593.070.016240.0496.020.010044.2098.070.006249.0299.210.0036
Fred-Net (ours)37.2093.900.014041.4696.840.008543.6497.840.006647.5099.030.0042
GloReDi (ours)37.9194.580.012841.5796.700.008444.2498.030.006248.1099.080.0040
", + "bbox": [ + 78, + 87, + 893, + 233 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1226c91ee7a8df6895ef469430ee3aad5f89e3550f68f6e71526642aecc97c42.jpg", + "image_caption": [ + "Figure 5. Visual comparison of state-of-the-art methods on AAPM dataset: (a) Ground Truth, (b) FBP, (c) DDNet, (d) FBPCovNet, (e) DuDoNet, (f) DDPTrans, (g) DuDoTrans, and (h) GloReDi. From top to bottom: $N_{\\mathrm{v}} = 18$ , 36; the display window is [-1000, 2000] HU." + ], + "image_footnote": [], + "bbox": [ + 78, + 255, + 890, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ReDi best reconstructs the structures and details, especially in ultra-sparse scenarios. In the first two rows of Fig. 4(h), only GloReDi precisely recovers those clinically important details such as soft tissue and corrupted pulmonary alveoli.", + "bbox": [ + 75, + 479, + 468, + 540 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 551, + 230, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We first evaluate the effectiveness of each component in GloReDi. We use Fred-Net as the baseline to add components. The configurations involved in Table 3 are mainly four groups: (1) the baseline Fred-Net using pixel-wise loss to train student model without distillation components (a); (2) the baseline without Fourier convolutions $(\\mathbf{b} - \\mathbf{c})$ ; (3) the baseline with distillation from intermediate-view reconstructed images $(\\mathbf{d} - \\mathbf{g})$ ; and (4) the dual-domain version with raw data processed by sinogram-domain sub-network of DuDoNet [31] $(\\mathbf{h})$ . Unless noted otherwise, the pixelwise loss is involved in training.", + "bbox": [ + 75, + 577, + 468, + 743 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablations on global representations. The results between a) and b) in Table 3 confirm that learning global representations with the image-wide receptive field by Fourier convolution is beneficial for sparse CT reconstruction. Also, we notice that in Tables 1 and 2, our baseline Fred-Net still outperforms state-of-the-art methods when $N_{\\mathrm{v}} = 18$ and 36. Interestingly, we found that c) performs even worse than b) in Table 3. This suggests that global representation is essential for bridging the gap between images of different views. Generally, learning global representations is pow", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/97716c31ccd9ce2eae2413f816db9e7c652eae209d897942f3152d0a70664f1d.jpg", + "table_caption": [ + "Table 2. Quantitative evaluation [PSNR (db), SSIM (%) and RMSE] for state-of-the-art methods transferred to AAPM dataset." + ], + "table_footnote": [], + "table_body": "
config.PSNR
a)Fred-Net38.09
b)Fred-Net w/o Fourier36.52
c)Fred-Net w/o Fourier + Lrdd + Lbcd36.30
d)Fred-Net + data augmentation34.41
e)Fred-Net + Lrdd38.39
f)Fred-Net + Lbcd38.42
g)Fred-Net + Lrdd + Lbcd = GloReDi38.65
h)Fred-Net + raw data38.44
", + "bbox": [ + 529, + 476, + 859, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Quantitative evaluation of different configurations.", + "bbox": [ + 500, + 604, + 849, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "erful and provides a new perspective for sparse-view CT reconstruction, which also answers that the limit of image post-processing methods is still far beyond reach.", + "bbox": [ + 496, + 638, + 890, + 685 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablations on global representation distillation. Through a comparison between Fred-Net and the one trained with intermediate-view images as data augmentation (a vs. d) in Table 3, we found that directly applying data augmentation had a negative impact, resulting in a 3.67db PSNR drop. This indicates that the network failed to benefit from denser-view images directly because of the significant domain gap among images of different views. By comparing a), e) and f) in Table 3, we can see that both e) representation directional distillation and f) band-pass-specific contrastive distillation can improve the performance of a), showing that end-to-end supervision cannot thoroughly unlock the potential of the GloRe. By training with both distillation loss, g) further boosts the performance and outperforms all other", + "bbox": [ + 496, + 688, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21203", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/89e688447428635419147dadbe15aca227a33c45bb68482aa1ca749b17bdbf26.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4. PSNR evaluation of GloReDi trained with different intermediate-view images for 60 epochs. The first and second rows show the results of sparse-view images with $N_{\\mathrm{v}} = 18$ , 72 distilled from images of $N_{\\mathrm{v}} \\times 2$ , 3, 4 and 720 (full view), respectively." + ], + "table_body": "
config.Nv×2Nv×3Nv×4720
Nv=1838.3838.2938.2838.02
Nv=7244.8444.4644.7244.38
", + "bbox": [ + 107, + 88, + 434, + 131 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "configurations. By comparing a), g) and h), we found unsurprisingly that using raw data does improve the performance of the image-domain network. However, our method GloReDi yields even better performance by effectively distilling GloRe from intermediate-view image data.", + "bbox": [ + 76, + 217, + 467, + 292 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Ablations on intermediate views for distillation. Selecting a suitable intermediate view for distillation is crucial in realizing the full potential of GloReDi. Images reconstructed from a denser view can provide richer information to the teacher GloRe while introducing a more significant domain gap. As presented in Table 4, we found that models distilled from $N_{\\mathrm{v}} \\times 2$ views exhibit the best performance. Interestingly, models distilled from the full-view image yield the worst performance, primarily because of the considerable domain gap between the input data. Please refer to Supplementary Material for more ablation studies on framework designs, configurations of residual blocks, and distillation loss.", + "bbox": [ + 75, + 299, + 468, + 494 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.4. Transfer to Other Dataset", + "text_level": 1, + "bbox": [ + 76, + 512, + 312, + 527 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "To test the generalizability and robustness of GloReDi along with other state-of-the-art methods, we finetune each model for another ten epochs on AAPM dataset to bridge the domain gap following the same setting. In Table 2, the proposed GloReDi shows excellent transferability over all other state-of-the-art methods in (ultra) sparse-view scenarios ( $N_{\\mathrm{v}} = 18,36,72$ ) and still achieves performance comparable with the dual-domain methods when $N_{\\mathrm{v}} = 72$ . Specifically, when $N_{\\mathrm{v}} = 18$ , we notice GloReDi has 2.06db and 2.18db improvements on PSNR compared to DuDoTrans and FBPCovNet, respectively, indicating that our method is significantly superior in ultra sparse-view scenarios. Fig. 5 shows images with $N_{\\mathrm{v}} = 18$ and 36, which are corrupted severely by FBP as shown in Fig. 5(b), thus losing its clinical value. Previous image-domain methods remove the artifact to some extent but lose most of the details, as shown in Figs. 5(c) and (d). Although the state-of-the-art dual-domain methods gain better results in general, we notice that clinical details such as lesion and bone, as pointed out by the blue arrows, are not accurately reconstructed in Figs. 5(e)-(g) while severe secondary artifacts are introduced, especially when $N_{\\mathrm{v}} = 18$ . In contrast, the proposed GloReDi excels at reconstructing the details and greatly improves the clinical value of sparse-view CT.", + "bbox": [ + 75, + 537, + 470, + 902 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 89, + 746, + 106 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In this paper, we challenge the sparse-view CT reconstruction in the absence of sinogram data and demonstrate that, with appropriate design, the image post-processing method can outperform the state-of-the-art dual-domain method. We propose to learn GloRe with Fourier convolution for image-wide receptive field and present directional and band-pass-specific contrastive distillation for high-quality reconstruction. Our method is particularly advantageous in ultra-sparse scenarios.", + "bbox": [ + 496, + 130, + 890, + 267 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We emphasize that our contributions can be easily extended to dual-domain methods when sinogram data are available. On the one hand, learning to distill GloRe can also benefit the image-domain network in a dual-domain framework. On the other hand, the proposed method can also be used to enhance the sinogram recovery by distilling the sinogram with intermediate views. Future work can concentrate on extending GloReDi to dual domain methods and other CT reconstruction tasks, such as limited-views CT reconstruction and metal artifact reduction. Although the teacher network is trained alongside the student network in the current version, it is valuable to explore the utilization of pre-trained teacher models, enabling GloReDi to progressively distill the GloRe from a series of teacher models.", + "bbox": [ + 496, + 281, + 892, + 492 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We also acknowledge some limitations. First, the teacher network will introduce additional computational costs during the training phase. It is possible to study how to distill knowledge from a pretrained teacher network. Second, although there are clear improvements in quantitative and visual results, it is desirable to have feedback from radiologists for clinical practice. The generalizability and robustness of the trained networks in clinical applications require further investigation. Third, we only considered 2D cases in the paper due to memory respect. If GPU memory permits, one can extend GloReDi to 3D by replacing 2D convolutions with 3D ones by applying high-dimension kernels for FFCs [7]. Lastly, GloReDi failed to surpass the dual-domain methods in denser view scenarios when sinogram can provide effective information for performance improvement. Studying how to improve the performance given an arbitrary $N_{\\mathrm{v}}$ would be of great value for future research.", + "bbox": [ + 496, + 508, + 892, + 765 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported in part by National Natural Science Foundation of China (Nos. 62101136 and 62176059), Shanghai Sailing Program (No. 21YF1402800), Shanghai Municipal Science and Technology Major Project (No. 2018SHZDZX01), ZJ Lab, Shanghai Municipal of Science and Technology Project (No. 20JC1419500), and Shanghai Center for Brain Science and Brain-inspired Technology.", + "bbox": [ + 496, + 780, + 890, + 901 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "21204", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jielin Bai, Yitong Liu, and Hongwen Yang. 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IEEE Transactions on Image Processing, 13(4), 2004. 6" + ], + "bbox": [ + 78, + 90, + 470, + 642 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "21207", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Learning to Distill Global Representation for Sparse-View CT/816ad801-b997-48a5-9faf-a09a225c6e9c_model.json b/2023/Learning to Distill Global Representation for Sparse-View CT/816ad801-b997-48a5-9faf-a09a225c6e9c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8fc6c39a2e1531dd8419982e909642addab4c7cd --- /dev/null +++ b/2023/Learning to Distill Global Representation for Sparse-View CT/816ad801-b997-48a5-9faf-a09a225c6e9c_model.json @@ -0,0 +1,2369 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.172, + 0.131, + 0.799, + 0.154 + ], + "angle": 0, + "content": "Learning to Distill Global Representation for Sparse-View CT" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.18, + 0.844, + 0.199 + ], + "angle": 0, + "content": "Zilong Li\\(^{1}\\) Chenglong Ma\\(^{2}\\) Jie Chen\\(^{1}\\) Junping Zhang\\(^{1}\\) Hongming Shan\\(^{2,3*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.138, + 0.199, + 0.832, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\) Shanghai Key Lab of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai 200433, China" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.234, + 0.862, + 0.269 + ], + "angle": 0, + "content": "\\(^{2}\\) Institute of Science and Technology for Brain-inspired Intelligence and MOE Frontiers Center for Brain Science, Fudan University, Shanghai 200433, China" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.269, + 0.854, + 0.306 + ], + "angle": 0, + "content": "\\(^{3}\\) Shanghai Center for Brain Science and Brain-inspired Technology, Shanghai 200031, China {zilongli21, clma22}@m.fudan.edu.cn, {chenj19, jpzhang, hmshan}@fudan.edu.cn" + }, + { + "type": "list", + "bbox": [ + 0.108, + 0.234, + 0.862, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.34, + 0.314, + 0.356 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.373, + 0.474, + 0.812 + ], + "angle": 0, + "content": "Sparse-view computed tomography (CT)—using a small number of projections for tomographic reconstruction—enables much lower radiation dose to patients and accelerated data acquisition. The reconstructed images, however, suffer from strong artifacts, greatly limiting their diagnostic value. Current trends for sparse-view CT turn to the raw data for better information recovery. The resultant dual-domain methods, nonetheless, suffer from secondary artifacts, especially in ultra-sparse view scenarios, and their generalization to other scanners/protocols is greatly limited. A crucial question arises: have the image post-processing methods reached the limit? Our answer is not yet. In this paper, we stick to image post-processing methods due to great flexibility and propose global representation(GloRe) distillation framework for sparse-view CT, termed GloReDi. First, we propose to learn GloRe with Fourier convolution, so each element in GloRe has an image-wide receptive field. Second, unlike methods that only use the full-view images for supervision, we propose to distill GloRe from intermediate-view reconstructed images that are readily available but not explored in previous literature. The success of GloRe distillation is attributed to two key components: representation directional distillation to align the GloRe directions, and band-pass-specific contrastive distillation to gain clinically important details. Extensive experiments demonstrate the superiority of the proposed GloReDi over the state-of-the-art methods, including dual-domain ones. The source code is available at https://github.com/longzilicart/GloReDi." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.845, + 0.21, + 0.86 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "X-ray CT is one of the major modalities widely used in clinical screening and diagnosis. Despite the benefits," + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.34, + 0.891, + 0.521 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.54, + 0.894, + 0.596 + ], + "angle": 0, + "content": "Figure 1. Sparse-view CT only uses a few projection views for tomographic reconstruction, thus providing fast and low-dose CT scanning. However, the reconstruction results of the conventional method suffer from severe global streak artifacts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.84 + ], + "angle": 0, + "content": "there have been growing concerns that X-ray radiation exposure could increase the risk of cancer induction [47]. Following the \"As Low As Reasonably Achievable\" principle in the medical community [36], efforts have been made to lower the radiation dose while maintaining imaging quality [20]. Sparse-view CT is one of the effective solutions which reduces the radiation by sampling part of the projection data, a.k.a sinogram, for image reconstruction, as shown in Fig. 1. However, analytical reconstruction algorithms such as filtered back projection (FBP) produce inferior image quality with globally severe streak artifacts, significantly compromising its diagnosis value. How to effectively reconstruct the sparse-view CT remains challenging and, hence, is gaining increasing attention in the computer vision and medical imaging communities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Image-domain methods regard sparse-view CT reconstruction as an image post-processing task on the FBP-reconstructed images and have achieved exciting performance on streak artifacts removal and structure preserva" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21196" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.242 + ], + "angle": 0, + "content": "tion [5, 22, 32, 58]. However, due to the limited receptive field, these methods have difficulty in modeling global information efficiently, thus leading to suboptimal results. Current dominant methods turn to the help of sinogram by restoring the sinogram and performing CT image postprocessing simultaneously [17, 29, 31, 46]. Specifically, in addition to the image domain methods, deep neural networks are also applied to interpolate the missing data in sinogram so that the reconstructed images can be recovered in a global manner [10, 25]." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.244, + 0.468, + 0.485 + ], + "angle": 0, + "content": "Despite the common success of dual-domain methods, they suffer from unsatisfactory and unstable performance due to the following reasons. First, the processing of sinogram data is sensitive and even subtle changes may remarkably affect the reconstructed images and introduce stubborn secondary artifacts that are hard to be eliminated. Second, in ultra sparse-view scenarios, inpainting methods are unable to accurately restore the excessive missing raw data; e.g., inpainting sparse CT data of 18 views to the full CT data of 720 views only retains about \\(2.5\\%\\) of the valid information, in which the involvement of sinogram processing makes the learning more difficult and compromise the performance [29,46]. Third, it is often impractical to access sinogram data given the privacy and commercial concerns, and if accessible, the requirement of raw data greatly limits the generalization to other scanners/protocols." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.492, + 0.468, + 0.793 + ], + "angle": 0, + "content": "Motivation. Given the great flexibility of the image domain methods, we raise a critical question in this paper: have the image domain (post-processing) methods reached the limits? Our answer is not yet, given the following observations. First, existing image-domain methods typically suffer from limited receptive field, which fails to extract and recover the global information efficiently [43], given that streak artifacts are spread globally on the reconstructed images as shown in Fig. 1. Second, existing image-domain methods only utilize the full-view images as the unique supervision on the result [22, 58]. They ignore the importance of representation learning, especially global representation (GloRe), making the artifact removal and detail recovery entangled, and leading to sub-optimal results due to the significant gap between sparse- and full-view. Third, the intermediate-view reconstructed images can be readily available during data preparation, but to the best of our knowledge, they are surprisingly neglected in the past literature. We argue that they can provide extra information and build bridges for sparse- and full-view CT reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.796, + 0.468, + 0.9 + ], + "angle": 0, + "content": "To address the abovementioned issues, we propose a novel image-domain method for sparse-view CT reconstruction. First, to address the limited receptive field inherent in conventional convolutional neural networks, we propose to learn GloRe with fast Fourier convolution (FFC) [7], so each element in GloRe has an image-wide receptive field. This global nature allows artifacts and information," + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.408 + ], + "angle": 0, + "content": "spread over the entire image, to be better modeled while also easing the alignment of the representations from different views. Second, to leverage extra supervision from intermediate-view CT images, we propose a novel distillation framework to learn better GloRe, termed GloReDi, which contains a parallel teacher network to distill knowledge from the readily intermediate-view images to provide high-quality and appropriate guidance for learning the GloRe of sparse-view CT images. Specifically, we first leverage intermediate-view reconstructed images to train a teacher network, which is then used to guide the learning of the student model (i.e. the sparse-view CT). The distillation scheme benefits GloRe in two folds: (1) representation directional distillation that aligns the directions between the student and teacher GloRe, which provides appropriate supervision considering the massive information loss due to the domain gaps between CT images with different views; and (2) band-pass-specific contrastive distillation that utilizes contrastive learning solely on the band-pass components to help distill the specific clinical value of each CT image without compromising the reconstruction accuracy." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.414, + 0.89, + 0.654 + ], + "angle": 0, + "content": "Contributions. In summary, our contributions are listed as follows. First, we propose the global representation (GloRe) learning for sparse-view CT with Fourier convolution, which, to the best of our knowledge, is the first study to emphasize on the representation learning for image post-processing in sparse-view CT. Second, we propose a novel GloRe distillation framework, which can leverage the extra supervision from intermediate-view reconstructed images for high-quality information recovery and reconstruction. Third, we present representation directional distillation and band-pass-specific contrastive distillation for distilling GloRe to align the representation directions and gain clinically important details. Last, extensive experimental results demonstrate the superiority of GloReDi over the state-of-the-art sparse-view CT reconstruction methods in terms of quantitative metrics and visual comparison." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.671, + 0.714, + 0.687 + ], + "angle": 0, + "content": "2. Detailed Related Work" + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.697, + 0.819, + 0.712 + ], + "angle": 0, + "content": "2.1. Deep-learning-based Sparse-view CT" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.721, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Numerous model-based iterative reconstruction (IR) methods have been developed to solve the sparse-view CT problem, mainly utilizing the sparsity of the total variation (TV) of the image [4, 12, 23, 33, 37, 51, 52]. However, most of them suffer from over-smoothed results, handcrafted tuning for each image, and extremely high computation cost [46], limiting their clinical application. In contrast, deep learning methods are often faster and more accessible, thus arousing attention in this field. Among them, most image-domain methods regard sparse-view CT reconstruction as an image post-processing task. RedCNN [5], FBPCovNet [22], and DDNet [58] are proposed to recon" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21197" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.181, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.109, + 0.294, + 0.12 + ], + "angle": 0, + "content": "EncoderT" + }, + { + "type": "image_caption", + "bbox": [ + 0.193, + 0.135, + 0.387, + 0.146 + ], + "angle": 0, + "content": "Band-Pass-Specific Contrastive Distillation" + }, + { + "type": "image", + "bbox": [ + 0.189, + 0.148, + 0.388, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.238, + 0.293, + 0.248 + ], + "angle": 0, + "content": "Encoders" + }, + { + "type": "image", + "bbox": [ + 0.396, + 0.096, + 0.657, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.667, + 0.09, + 0.89, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.18, + 0.89, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.27, + 0.893, + 0.3 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed GloReDi for sparse-view CT reconstruction. GloReDi facilitates efficient information recovery by learning to distill the global representation from intermediate-view images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.473, + 0.701 + ], + "angle": 0, + "content": "struct the sparse-view CT by the convolutional neural network (CNN). These methods achieve competitive performance on streak artifact removal and structure preservation compared to conventional ones, but most of them fail to capture the global context and underperform in global reconstruction and artifact removal. Since streak artifacts result directly from the incomplete projection views, various methods are proposed to remove the artifacts by interpolating sinogram data [10, 25]. Further, dual-domain methods were becoming popular for their superior reconstruction performance by combining the knowledge of both domains. DuDoNet [31] first proposed a novel Radon inversion layer linking the gradient between the image and sinogram domain networks. Furthermore, various techniques have been proposed to enhance dual domain approaches through network design [1,6] and unrolling architecture [57]. Recently, Transformer [45] has been introduced to dual-domain methods for its capability of capturing long-range dependencies, achieving superior performance [29, 46, 49]. However, the problems of the irreversible secondary artifacts and additional computational costs are not well addressed, and the requirement of raw data greatly limits their generalizability to other CT scanners/protocols. In this work, we challenge reconstructing sparse-view CT without raw data while still achieving state-of-the-art results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.711, + 0.289, + 0.727 + ], + "angle": 0, + "content": "2.2. Knowledge Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Knowledge distillation transfers rich knowledge from teacher models to lightweight student models in the label or feature domains, mainly applied in model compression and acceleration [15, 41]. Among various approaches, feature-based knowledge distillation is extensively applied in image restoration tasks such as image super-resolution [14, 16, 27, 38]. It minimizes the distance between feature representations to learn richer information from the teacher model compared to softened labels [48]. Further, contrastive representation distillation is proposed to exploit the structural characteristics among different samples by harnessing the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.385 + ], + "angle": 0, + "content": "discriminative representations, thereby enhancing differentiation within data [8, 19, 44]. This work distills knowledge from the intermediate-view images to enhance the sparse-view CT reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.394, + 0.829, + 0.41 + ], + "angle": 0, + "content": "2.3. Frequency Methods in Deep Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.893, + 0.81 + ], + "angle": 0, + "content": "Frequency methods have been widely used in digital image processing and machine learning [2]. Wavelet convolution [32] and fast Fourier convolution [7] have been proposed to provide a larger/global receptive field, achieving great success in image restoration tasks [43]. Frequency methods have also yielded promising results in domain adaption and image translation, mainly by taking advantage of domain-invariant spectrum components [3, 18, 54-56]. Previous research also shows that particular features and details can be better extracted in the frequency domain, leading to improvements in camouflaged object detection [59], face forgery detection [21, 28], and face editing [9]. Frequency-based networks have also made notable strides in CT reconstruction. Previous studies [1, 26] employ multi-wavelet CNN [32] in both sinogram and image domain to suppress artifacts, substituting the pooling operator with wavelet transforms to achieve a larger receptive field. However, since both the Haar filter-based wavelet transform and convolution are applied on the spatial feature map, these methods struggle to capture global representation effectively. Recent research has demonstrated that employing convolution in the Fourier domain can efficiently eliminate the global artifacts [30, 34]. In this work, we utilize a frequency-based network for global representation learning, enhancing clinically critical features by band-pass-specific contrastive distillation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.822, + 0.591, + 0.837 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.682, + 0.862 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Assume we have a two-dimensional (2D) CT slice of size \\(N\\times N\\) \\(\\pmb {I}\\in \\mathbb{R}^{N\\times N}\\) , where each pixel contains the attenua" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21198" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.257 + ], + "angle": 0, + "content": "tion coefficient of the corresponding human body. The raw data or sinogram from the CT scanning, \\(S \\in \\mathbb{R}^{N_{\\mathrm{v}} \\times N_{\\mathrm{d}}}\\), can be obtained via the Radon transform [39], where \\(N_{\\mathrm{v}}\\) and \\(N_{\\mathrm{d}}\\) denote the number of projection views and the number of the detectors, respectively. Inversely, the image reconstruction process can be expressed as \\(\\boldsymbol{I} = \\mathcal{R}^{-1}(\\boldsymbol{S})\\), where \\(\\mathcal{R}^{-1}\\) denotes the inverse Radon transform such as FBP. Ideally, when \\(N_{\\mathrm{v}}\\) is sufficiently large, FBP can produce pleasing image quality. However, when \\(N_{\\mathrm{v}}\\) is fairly small, the image reconstruction of so-called sparse-view CT becomes an undetermined problem." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.473, + 0.44 + ], + "angle": 0, + "content": "Here, we use \\( I_{\\mathrm{F}} \\) and \\( I_{\\mathrm{S}} \\) to represent the reconstructed images from full view (i.e. ground-truth) and sparse view, respectively. The image-domain methods for sparse-view CT are to improve the image quality of \\( I_{\\mathrm{S}} \\) towards \\( I_{\\mathrm{F}} \\) through a neural network \\( \\mathcal{F} \\). That is, the output of the network, \\( \\widehat{I}_{\\mathrm{S}} = \\mathcal{F}(I_{\\mathrm{S}}) \\), is expected to be of comparable quality to the full-view ground-truth. In addition, we also use the images, \\( I_{\\mathrm{T}} \\), reconstructed from an intermediate number of projection views that are between sparse and full views, as the teacher supervision, forming a student-teacher framework where the teacher encoder with \\( I_{\\mathrm{T}} \\) supervises the training of student encoder with \\( I_{\\mathrm{S}} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.447, + 0.317, + 0.461 + ], + "angle": 0, + "content": "3.2. Overview of Our GloReDi" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.473, + 0.652 + ], + "angle": 0, + "content": "Fig. 2 presents the proposed GloReDi, which mainly consists of four parts: two encoders to learn global representations (GloRe) from sparse- and intermediate-view reconstructed images, \\( I_{\\mathrm{S}} \\), and \\( I_{\\mathrm{T}} \\), respectively, and two decoders to produce the final processed images from GloRe. In addition to learning GloRe with Fourier convolution, we have two novel modules to perform distillation from the teacher network: (1) representation directional distillation to align the directions between the student and teacher GloRes; and (2) band-pass-specific contrastive distillation to distill the clinically important features for better detail recovery." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.652, + 0.427, + 0.667 + ], + "angle": 0, + "content": "Next, we detail each of the proposed components." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.675, + 0.364, + 0.692 + ], + "angle": 0, + "content": "3.3. Global Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.47, + 0.819 + ], + "angle": 0, + "content": "The key technique behind the proposed network is the global representation learning with fast Fourier convolution (FFC) [7]. Concretely, FFC first applies real Fourier transform to get the frequency feature map and then performs convolution on frequency components before finally back transforming the frequency features as shown in Fig. 2. Therefore, GloRe from sparse-view images \\( I_{\\mathrm{S}} \\) is learned by a Fourier-based encoder network as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.829, + 0.47, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {Z} _ {\\mathrm {S}} = \\operatorname {e n c o d e r S} (\\boldsymbol {I} _ {\\mathrm {S}}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.855, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\(Z_{\\mathrm{S}} \\in \\mathbb{R}^{N_{\\mathrm{w}} \\times N_{\\mathrm{h}} \\times N_{\\mathrm{c}}}\\) denotes GloRe extracted from the sparse-view reconstructed image \\(I_{\\mathrm{S}}\\) through the (student) encoder encoderS and \\(N_{\\mathrm{w}} \\times N_{\\mathrm{h}} \\times N_{\\mathrm{c}}\\) denotes the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "width, height, and channel size of GloRe. Compared to the vanilla convolution with a limited receptive field, FFC works in the frequency domain, so each element in GloRe contains global information of the sparse-view image by using an image-wide receptive field, representing patterns of artifacts and the image contents simultaneously. Furthermore, such global nature can aid in modeling the artifact and information distributed throughout the image while easing the alignment between GloRe of different views." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.236, + 0.8, + 0.252 + ], + "angle": 0, + "content": "3.4. Global Representation Distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.894, + 0.366 + ], + "angle": 0, + "content": "In the context of sparse-view CT, images with an intermediate view \\( I_{\\mathrm{T}} \\) can be easily obtained from the full-view sinogram as extra supervision. To get the teacher representation from \\( I_{\\mathrm{T}} \\), a parallel teacher encoder encoderT, using the same architecture as encoderS but with different weights, takes \\( I_{\\mathrm{T}} \\) as input and yields teacher GloRe \\( Z_{\\mathrm{T}} \\) of the same shape with \\( Z_{\\mathrm{S}} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.375, + 0.892, + 0.39 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {Z} _ {\\mathrm {T}} = \\operatorname {e n c o d e r} \\mathrm {T} \\left(\\boldsymbol {I} _ {\\mathrm {T}}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.892, + 0.474 + ], + "angle": 0, + "content": "\\(Z_{\\mathrm{T}}\\) can be regarded as a high-quality pseudo target for student GloRe in the same latent space since richer information can be extracted from \\(I_{\\mathrm{T}}\\). Exploring distillation from \\(I_{\\mathrm{T}}\\) is obviously easier than that of \\(I_{\\mathrm{F}}\\) given the significant gap between \\(I_{\\mathrm{S}}\\) and \\(I_{\\mathrm{F}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.893, + 0.672 + ], + "angle": 0, + "content": "Intuitively, \\( Z_{\\mathrm{S}} \\) should be similar to \\( Z_{\\mathrm{T}} \\) if the artifact-free target information is precisely encoded. Therefore, a natural way for distillation is to use \\( Z_{\\mathrm{T}} \\) as the supervision for \\( Z_{\\mathrm{S}} \\) by minimizing their Euclidean distance. However, this could harm the reconstruction performance since the student encoder has to partially recover \\( I_{\\mathrm{T}} \\). Finding an effective solution to distilling the information in \\( Z_{\\mathrm{T}} \\) for sparse-view CT reconstruction is one of the highlights in this work. Our idea is to separate the distillation process. First, we present representation directional distillation to align the representation directions so the images of different views are along the same direction. Second, we propose a band-pass-specific contrastive distillation to enhance clinically critical details." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.672, + 0.874, + 0.687 + ], + "angle": 0, + "content": "We detail these two distillation techniques as follows." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.705, + 0.824, + 0.72 + ], + "angle": 0, + "content": "3.4.1 Representation Directional Distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.892, + 0.804 + ], + "angle": 0, + "content": "Given that \\( I_{\\mathrm{S}} \\) and \\( I_{\\mathrm{T}} \\) share the same ground truth \\( I_{\\mathrm{F}} \\), but differ mainly in artifact patterns, student and teacher GloRe should at least demonstrate a consistent direction for reconstruction with high confidence. Therefore, We define the directional distillation loss for \\( Z_{\\mathrm{S}} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.81, + 0.892, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r d d}} = \\frac {1}{N _ {\\mathrm {w}} N _ {\\mathrm {h}}} \\sum_ {i, j} \\left(1 - \\operatorname {C o s S i m} \\left(\\left[ \\mathbf {Z} _ {\\mathrm {S}} \\right] _ {i, j}, \\left[ \\mathbf {Z} _ {\\mathrm {T}} \\right] _ {i, j}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "where \\(\\operatorname{CosSim}\\) denotes the cosine similarity, defined as \\(\\operatorname{CosSim}(\\mathbf{a},\\mathbf{b}) = \\mathbf{a}^{\\mathrm{T}}\\mathbf{b} / \\max (\\|\\mathbf{a}\\|_2\\|\\mathbf{b}\\|_2,\\epsilon)\\) with \\(\\epsilon\\) set to \\(1\\times 10^{-8}\\) to avoid division by zero." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21199" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.342 + ], + "angle": 0, + "content": "Figure 3. The difference between representation distillation (left) and band-pass-specific contrastive distillation (right). Global representation distillation fails to distinguish clinical details due to high similarity among similar body parts, e.g., adjacent lung slices. Band-pass-specific contrastive distillation further projects the representation to the DCT domain, enabling distillation of specific clinical details on corresponding DCT components." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.369, + 0.43, + 0.384 + ], + "angle": 0, + "content": "3.4.2 Band-Pass-Specific Contrastive Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.47, + 0.56 + ], + "angle": 0, + "content": "The directional distillation aligns the directions of student representation \\( Z_{\\mathrm{S}} \\) and the teacher representation \\( Z_{\\mathrm{T}} \\) in the view-independent space, which, however, does not guarantee a high-quality reconstruction of the image. What distinguishes sparse-view CT reconstruction task from classic image restoration one (e.g. denoising, deraining, etc.) is that the former is more demanding in terms of fine-grained details for diseases identification, organs delineation, and low-contrast lesions detection, etc [11]. In other words, it places more emphasis on learning the image-specific representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.471, + 0.851 + ], + "angle": 0, + "content": "Contrastive representation learning, as a self-supervised approach, encourages the model to maximize the difference among representations of different samples so that model can emphasize those category-specific representations. However, directly implementing these losses would lead to imprecise reconstruction results because most CT images are inherently similar in intensity distribution, especially for images of the same body parts, as shown in Fig. 3. Recent methods have achieved great success learning on specific DCT spectrum [18, 50, 54], due to its strong energy compaction property, making it simple to select specific frequency components [40]. Therefore, we distilled the image-specific details by applying contrastive distillation on specific discrete cosine transform (DCT) spectrums. On the one hand, detailed knowledge can be better distilled from specific frequency components of teacher GloRe. On the other hand, contrastive against different CT slices can further enhance image-specific details on corresponding DCT components." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Discrete cosine transform. Discrete cosine transform (DCT) is widely used for data compression in low-frequency components. The basis function of 2D DCT is" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.628, + 0.106 + ], + "angle": 0, + "content": "defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.113, + 0.894, + 0.141 + ], + "angle": 0, + "content": "\\[\nB _ {w, h} ^ {i, j} = \\cos \\left(\\frac {\\pi w}{N _ {\\mathrm {w}}} \\left(i + \\frac {1}{2}\\right)\\right) \\cos \\left(\\frac {\\pi h}{N _ {\\mathrm {h}}} \\left(j + \\frac {1}{2}\\right)\\right), \\quad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.148, + 0.894, + 0.193 + ], + "angle": 0, + "content": "where \\(N_{\\mathrm{w}}\\) and \\(N_{\\mathrm{h}}\\) represent the width and height of the input, respectively. Then, 2D DCT of the latent feature \\(\\mathbf{Z}\\) can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.201, + 0.893, + 0.231 + ], + "angle": 0, + "content": "\\[\nf _ {w, h} (\\boldsymbol {Z}) = \\sum_ {i = 0} ^ {N _ {\\mathrm {w}} - 1} \\sum_ {j = 0} ^ {N _ {\\mathrm {h}} - 1} [ \\boldsymbol {Z} ] _ {i, j} B _ {w, h} ^ {i, j}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.239, + 0.893, + 0.301 + ], + "angle": 0, + "content": "where \\(w\\in \\{0,1,\\ldots ,N_{\\mathrm{w}} - 1\\} ,h\\in \\{0,1,\\ldots ,N_{\\mathrm{h}} - 1\\}\\) The \\(f(\\pmb {Z})\\in \\mathbb{R}^{N_{\\mathrm{w}}\\times N_{\\mathrm{h}}}\\) represents the 2D DCT frequency spectrum of \\(\\pmb{Z}\\) . Thus, frequency components can be easily selected by a mask \\(M\\in \\{0,1\\}^{N_{\\mathrm{w}}\\times N_{\\mathrm{h}}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.304, + 0.892, + 0.456 + ], + "angle": 0, + "content": "Band-pass-specific contrastive distillation. Crucially, the low-frequency components of GloRe contribute most to the reconstruction accuracy, while high-frequency may contain inherent noise and artifacts of CT images. We therefore use a band-pass supervised contrastive loss for the distillation, where a band-pass mask \\( M \\) is incorporated to filter out the mid-frequency part in the frequency domain, containing main structure as well as the necessary detail information. The proposed band-pass supervised contrastive loss can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.467, + 0.892, + 0.484 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {z} = \\text {f l a t t e n} \\left(\\operatorname {c r o p} \\left(f _ {w, h} (\\boldsymbol {Z}), \\boldsymbol {M}\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.494, + 0.892, + 0.539 + ], + "angle": 0, + "content": "where crop operator will keep the value at locations where \\( M = 1 \\) while the flatten operator flattens the 2D spectrum map into 1D representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.54, + 0.893, + 0.69 + ], + "angle": 0, + "content": "It is to be observed that the clinical details in the CT images vary from case by case and are each very critical for diagnosis, requiring more sophisticated instance-level distinction. To this end, we consider all representations from different CT slices as negative samples to maximize image-specific features while updating the memory bank \\(\\mathcal{M}\\) with the widely applied First-In-First-Out mechanism per iteration from the previous mini-batches. The proposed band-pass-specific contrastive distillation loss for sample \\(z_{\\mathrm{S}}\\) can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.697, + 0.892, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {b c d}} = - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {\\mathrm {S}} ^ {\\mathrm {T}} \\boldsymbol {z} _ {\\mathrm {T}} / \\tau\\right)}{\\sum_ {\\boldsymbol {z} \\in \\mathcal {M}} \\exp \\left(\\boldsymbol {z} _ {\\mathrm {S}} ^ {\\mathrm {T}} \\boldsymbol {z} / \\tau\\right)}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.743, + 0.892, + 0.805 + ], + "angle": 0, + "content": "where \\(z_{\\mathrm{S}}, z_{\\mathrm{T}}\\), and \\(z\\) are frequency representations of \\(Z_{\\mathrm{S}}, Z_{\\mathrm{T}}\\), and negative samples from memory bank \\(\\mathcal{M}\\) of size \\(N_{\\mathrm{mem}}\\), respectively. \\(\\tau\\) is the temperature term used to adjust the sensitivity of negative samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.813, + 0.833, + 0.83 + ], + "angle": 0, + "content": "3.5. Loss Function and Training Procedure" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Teacher reconstruction. To constrain the GloRe extracted from \\( I_{\\mathrm{S}} \\) and \\( I_{\\mathrm{T}} \\) in the same latent space, a naive solution is to share the same decoder in the training phase, which, however, brings instability. Therefore, we adopt the widely" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21200" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.081, + 0.092, + 0.387, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 The training process of GloReDi." + }, + { + "type": "algorithm", + "bbox": [ + 0.08, + 0.108, + 0.47, + 0.291 + ], + "angle": 0, + "content": "Require: encoderS, encoderT, decoderS, decoderT; Input images: \\(I_{\\mathrm{S}}, I_{\\mathrm{T}}, I_{\\mathrm{F}}\\); momentum \\(m\\) and Memory bank \n1: for iter = 0 to Max_Iter do \n2: Update decoderT using Eq. (8) \n3: \\(\\widehat{I}_{\\mathrm{T}}, Z_{\\mathrm{T}} = \\text{decoderT}(\\text{encoderT}(I_{\\mathrm{T}}))\\) \n4: Optimize encoderT using Eq. (9) \n5: \\(\\widehat{I}_{\\mathrm{S}}, Z_{\\mathrm{S}} = \\text{decoderS}(\\text{encoderS}(I_{\\mathrm{S}}))\\) \n6: Optimize encoderS+decoderS using Eq. (11) \n7: Update memory bank \n8: end for \nReturn: encoderS+ decoderS" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.318, + 0.47, + 0.364 + ], + "angle": 0, + "content": "used Exponential Moving Average (EMA) with momentum \\( m \\) to update the parameters \\( \\theta \\) of the teacher decoder by the student decoder [13]:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.377, + 0.469, + 0.392 + ], + "angle": 0, + "content": "\\[\n\\theta_ {\\text {d e c o d e r T}} = m \\theta_ {\\text {d e c o d e r T}} + (1 - m) \\theta_ {\\text {d e c o d e r S}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.405, + 0.469, + 0.479 + ], + "angle": 0, + "content": "Then, the global representation \\( Z_{\\mathrm{T}} \\) learned by the teacher is fed into to the decoder to obtain the teacher reconstruction result \\( \\widehat{I}_{\\mathrm{T}} \\), and we use \\( \\ell_1 \\) loss to measure the pixel-wise difference between \\( \\widehat{I}_{\\mathrm{T}} \\) and the full-view ground-truth \\( I_{\\mathrm{F}} \\) and train the teacher:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.492, + 0.469, + 0.509 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p i x e l T}} = \\left\\| \\operatorname {d e c o d e r T} \\left(\\boldsymbol {Z} _ {\\mathrm {T}}\\right) - \\boldsymbol {I} _ {\\mathrm {F}} \\right\\| _ {1}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.526, + 0.469, + 0.556 + ], + "angle": 0, + "content": "Student reconstruction. The pixel-wise error measurement for the student is defined in a similar way:" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.568, + 0.469, + 0.585 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p i x e l S}} = \\left\\| \\operatorname {d e c o d e r S} \\left(\\boldsymbol {Z} _ {\\mathrm {S}}\\right) - \\boldsymbol {I} _ {\\mathrm {F}} \\right\\| _ {1}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.597, + 0.469, + 0.658 + ], + "angle": 0, + "content": "Finally, a compound loss function combining pixel-wise error and two distillation losses, respectively defined in Eq. (3) and Eq. (7) is introduced for student network training to achieve high-quality sparse-view CT reconstruction:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.685, + 0.469, + 0.701 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {S t u}} = \\mathcal {L} _ {\\mathrm {p i x e l S}} + \\alpha \\mathcal {L} _ {\\mathrm {r d d}} + \\beta \\mathcal {L} _ {\\mathrm {b c d}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.713, + 0.469, + 0.759 + ], + "angle": 0, + "content": "GloReDi is trained following the process summarized in Algorithm 1, where the student and teacher encoder are trained iteratively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.773, + 0.282, + 0.789 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.798, + 0.267, + 0.814 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Dataset. We use DeepLesion dataset [53] and \"2016 NIH-AAPM-Mayo Clinic Low-Dose CT Grand Challenge\" AAPM dataset [35] to demonstrate the effectiveness of the proposed GloReDi. The DeepLesion dataset is the largest multi-lesion real-world CT dataset made available to the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.319 + ], + "angle": 0, + "content": "public, from which 40,000 images of 303 patients are selected as the training set while 1000 images of another 18 patients are selected as the test set. AAPM dataset contains routine dose CT data from 10 patients, where a total of 5,410 slices from 9 patients are chosen for training and 526 slices from the remaining 1 patient for testing. All images are resized to \\(256 \\times 256\\). We simulate the forward and back projection using fan-beam geometry under \\(120\\mathrm{kVp}\\) and \\(500\\mathrm{mA}\\) with TorchRadon toolbox [42]. The distance from X-ray source to the rotation center is \\(59.5\\mathrm{cm}\\), and the number of detectors is set to 672. Sparse-view CT images are generated from \\(N_{\\mathrm{v}} = 18,36,72,144\\) projection views uniformly sampled from full 720 views covering \\([0,2\\pi]\\). To simulate the photon noise presented in real-world CT, an intensity of \\(1 \\times 10^{6}\\) Poisson noise is added to the sinograms." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.323, + 0.892, + 0.536 + ], + "angle": 0, + "content": "Implementation details. Our model is implemented in PyTorch. We use Adam optimizer [24] with \\((\\beta_{1},\\beta_{2}) = (0.5,0.999)\\) to train the model. The learning rate starts from \\(1\\times 10^{-3}\\) and is halved for every 40 epochs. For each method, four models of different \\(N_{\\mathrm{v}}\\) are trained separately on 4 NVIDIA RTX 3090 GPUs for 120 epochs with a batch size of 8. For hyperparameters in GloReDi, we set \\(\\alpha\\) and \\(\\beta\\) in Eq. (11) empirically to 0.1 and 0.0002 to fit the scale between losses. The momentum \\(m\\) and temperature \\(\\tau\\) are set to 0.9 and 1.0, respectively, while the size \\(L\\) of the memory bank is set to 300 to balance the performance and computational cost. We set intermediate-view as \\(N_{\\mathrm{v}}\\times 2\\) by default. More details, including the network architecture, can be found in the Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.541, + 0.892, + 0.601 + ], + "angle": 0, + "content": "Evaluation metrics. For quantitative evaluation, we use peak signal-to-noise ratio (PSNR), structural similarity (SSIM) [60] and root mean square error (RMSE); all of them are widely adopted for image quality assessment." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.614, + 0.868, + 0.631 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.88 + ], + "angle": 0, + "content": "We compare GloReDi with the following state-of-the-art methods: DDNet [58], FBPCovNet [22], DuDoNet [31], DDPTrans [29], and DuDoTrans [46]. In addition, we name the network without the distillation from \\( I_{\\mathrm{T}} \\) as the frequency encoder and decoder network (Fred-Net), optimized with only the pixel-wise loss in Eq. (10). FBP directly applies Radon transform to reconstruct the image from the sparse-view sinogram. DDNet and FBPCovNet are image-domain deep-learning methods taking FBP results as input. DuDoNet is a state-of-the-art dual-domain method that restores the CT image using two U-Nets in sinogram and image domains. Furthermore, DDPTrans and DuDoTrans adopt Transformer on both domains to restore the image by utilizing the long-range dependency. We try our best to reproduce these methods and then train and test them on the same dataset for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.891, + 0.902 + ], + "angle": 0, + "content": "Quantitative comparison. Table 1 presents the quantita" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21201" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.088, + 0.895, + 0.232 + ], + "angle": 0, + "content": "
Methods\\(N_{\\mathrm{v}}=18\\)\\(N_{\\mathrm{v}}=36\\)\\(N_{\\mathrm{v}}=72\\)\\(N_{\\mathrm{v}}=144\\)
PSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSE
FBP22.2235.360.079525.4947.490.054330.8863.810.029337.1282.940.0144
DDNet [58]34.5791.940.018738.2494.910.012641.6697.270.008346.7598.790.0048
FBPCovNet [22]35.9593.620.016439.7996.130.010643.7697.470.006648.4698.600.0039
DuDoNet [31]35.6993.960.016940.3696.940.010344.8698.390.005949.3399.230.0036
DDPTRans [29]35.1193.480.018138.6895.990.012143.5698.160.006948.7299.220.0038
DuDoTrans [46]36.0893.280.016140.7596.670.009545.1698.440.005749.9699.280.0034
Fred-Net (ours)38.0895.200.012940.8696.810.009344.4398.180.006348.4599.080.0039
GloReDi (ours)38.6595.870.012041.2597.050.009045.1898.430.005748.9699.210.0037
" + }, + { + "type": "table_caption", + "bbox": [ + 0.129, + 0.236, + 0.841, + 0.251 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation [PSNR (db), SSIM (%) and RMSE] for state-of-the-art methods on DeepLesion dataset." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.263, + 0.891, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.519, + 0.893, + 0.561 + ], + "angle": 0, + "content": "Figure 4. Visual comparison of state-of-the-art methods on DeepLesion dataset: (a) Ground Truth, (b) FBP, (c) DDNet, (d) FBPCovNet, (e) DuDoNet, (f) DDPTrans, (g) DuDoTrans, and (h) GloReDi. From top to bottom: the results under \\( N_{\\mathrm{v}} = 18 \\), 36, 72; display window is set to [-1000, 2000] HU for the first two rows and [-200, 300] HU for the third row." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.473, + 0.812 + ], + "angle": 0, + "content": "tive comparison. Generally, dual-domain methods perform better than single-domain methods, especially in the case of \\( N_{\\mathrm{v}} = 72 \\), 144 thanks to the sinogram inpainting network. However, we highlight in ultra sparse-view scenarios where \\( N_{\\mathrm{v}} = 18 \\), that dual-domain methods like DuDoNet perform worse than classical image-domain-only methods such as FBPCovNet. This can be attributed to the secondary artifacts introduced by the unsuccessful sinogram inpainting; e.g., when \\( N_{\\mathrm{v}} = 18 \\) in our setting, restoring the sinogram can be recognized as a \\( 40 \\times \\) super-resolution task, which is rather challenging. DuDoTrans is superior to DuDoNet to some extent, indicating the importance of long-range dependency in reconstruction. DDPTrans fails to surpass DuDoNet because of the limited parameter number though most transformers are memory-consuming." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Compared with the previous works, the proposed GloReDi achieves competitive results by learning to distill GloRe for high-quality reconstruction. Particularly in ultrasparse scenarios, e.g., when \\( N_{\\mathrm{v}} = 18 \\), GloReDi has 2.57db and 2.70db improvement on PSNR over DuDoTrans and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.892, + 0.738 + ], + "angle": 0, + "content": "FBPCovNet, respectively. As \\( N_{\\mathrm{v}} \\) increases, the advantage of GloReDi decreases, mainly due to a shift towards artifacts removal tasks rather than reconstruction. We highlight that the fewer projection views indicate less radiation dose and more speedup. We notice that global representation distillation further improves the performance of GloReDi from 0.51db to 0.89db compared to Fred-Net. The results show that the proposed GloReDi successfully inspire the potential of image post-processing methods and is significantly superior to the state-of-the-art methods under various settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Visual comparison. Fig. 4 presents the visualization results of three sparse-view CT. DDNet and FBPCovNet cannot remove the artifact thoroughly, while the reconstruction results are over-smooth in the boundary of organs and bones. Such effects can be easily observed in the second row of Figs. 4(c) and 4(d) on the spine where the anatomical structure is complicated. Although dual-domain methods perform better in general, their accuracy in details is even worse than FBPCovNet in comparison with Figs. 4(d) and 4(e)-(g). Among all these methods, Glo" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21202" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.088, + 0.895, + 0.234 + ], + "angle": 0, + "content": "
Methods\\(N_{\\mathrm{v}}=18\\)\\(N_{\\mathrm{v}}=36\\)\\(N_{\\mathrm{v}}=72\\)\\(N_{\\mathrm{v}}=144\\)
PSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSE
FBP22.7335.060.073226.2747.520.048631.3664.560.027037.8584.570.0128
DDNet [58]34.2989.680.019436.9593.030.014240.4196.040.009644.3598.050.0061
FBPCovNet [22]35.7392.840.016537.9593.730.012742.9297.190.007247.3598.760.0043
DuDoNet [31]34.8293.000.019639.8995.990.010244.0698.020.006248.3999.110.0038
DDPTRans [29]34.4791.950.019138.1394.830.012542.7797.650.007347.8499.060.0041
DuDoTrans [46]35.8593.070.016240.0496.020.010044.2098.070.006249.0299.210.0036
Fred-Net (ours)37.2093.900.014041.4696.840.008543.6497.840.006647.5099.030.0042
GloReDi (ours)37.9194.580.012841.5796.700.008444.2498.030.006248.1099.080.0040
" + }, + { + "type": "table_caption", + "bbox": [ + 0.11, + 0.236, + 0.856, + 0.25 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluation [PSNR (db), SSIM (%) and RMSE] for state-of-the-art methods transferred to AAPM dataset." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.256, + 0.891, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.433, + 0.893, + 0.463 + ], + "angle": 0, + "content": "Figure 5. Visual comparison of state-of-the-art methods on AAPM dataset: (a) Ground Truth, (b) FBP, (c) DDNet, (d) FBPCovNet, (e) DuDoNet, (f) DDPTrans, (g) DuDoTrans, and (h) GloReDi. From top to bottom: \\( N_{\\mathrm{v}} = 18 \\), 36; the display window is [-1000, 2000] HU." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.47, + 0.541 + ], + "angle": 0, + "content": "ReDi best reconstructs the structures and details, especially in ultra-sparse scenarios. In the first two rows of Fig. 4(h), only GloReDi precisely recovers those clinically important details such as soft tissue and corrupted pulmonary alveoli." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.553, + 0.231, + 0.57 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.47, + 0.744 + ], + "angle": 0, + "content": "We first evaluate the effectiveness of each component in GloReDi. We use Fred-Net as the baseline to add components. The configurations involved in Table 3 are mainly four groups: (1) the baseline Fred-Net using pixel-wise loss to train student model without distillation components (a); (2) the baseline without Fourier convolutions \\((\\mathbf{b} - \\mathbf{c})\\); (3) the baseline with distillation from intermediate-view reconstructed images \\((\\mathbf{d} - \\mathbf{g})\\); and (4) the dual-domain version with raw data processed by sinogram-domain sub-network of DuDoNet [31] \\((\\mathbf{h})\\). Unless noted otherwise, the pixelwise loss is involved in training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Ablations on global representations. The results between a) and b) in Table 3 confirm that learning global representations with the image-wide receptive field by Fourier convolution is beneficial for sparse CT reconstruction. Also, we notice that in Tables 1 and 2, our baseline Fred-Net still outperforms state-of-the-art methods when \\( N_{\\mathrm{v}} = 18 \\) and 36. Interestingly, we found that c) performs even worse than b) in Table 3. This suggests that global representation is essential for bridging the gap between images of different views. Generally, learning global representations is pow" + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.477, + 0.86, + 0.606 + ], + "angle": 0, + "content": "
config.PSNR
a)Fred-Net38.09
b)Fred-Net w/o Fourier36.52
c)Fred-Net w/o Fourier + Lrdd + Lbcd36.30
d)Fred-Net + data augmentation34.41
e)Fred-Net + Lrdd38.39
f)Fred-Net + Lbcd38.42
g)Fred-Net + Lrdd + Lbcd = GloReDi38.65
h)Fred-Net + raw data38.44
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.605, + 0.851, + 0.618 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation of different configurations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.686 + ], + "angle": 0, + "content": "erful and provides a new perspective for sparse-view CT reconstruction, which also answers that the limit of image post-processing methods is still far beyond reach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Ablations on global representation distillation. Through a comparison between Fred-Net and the one trained with intermediate-view images as data augmentation (a vs. d) in Table 3, we found that directly applying data augmentation had a negative impact, resulting in a 3.67db PSNR drop. This indicates that the network failed to benefit from denser-view images directly because of the significant domain gap among images of different views. By comparing a), e) and f) in Table 3, we can see that both e) representation directional distillation and f) band-pass-specific contrastive distillation can improve the performance of a), showing that end-to-end supervision cannot thoroughly unlock the potential of the GloRe. By training with both distillation loss, g) further boosts the performance and outperforms all other" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21203" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.109, + 0.089, + 0.435, + 0.132 + ], + "angle": 0, + "content": "
config.Nv×2Nv×3Nv×4720
Nv=1838.3838.2938.2838.02
Nv=7244.8444.4644.7244.38
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.133, + 0.47, + 0.188 + ], + "angle": 0, + "content": "Table 4. PSNR evaluation of GloReDi trained with different intermediate-view images for 60 epochs. The first and second rows show the results of sparse-view images with \\( N_{\\mathrm{v}} = 18 \\), 72 distilled from images of \\( N_{\\mathrm{v}} \\times 2 \\), 3, 4 and 720 (full view), respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.218, + 0.468, + 0.293 + ], + "angle": 0, + "content": "configurations. By comparing a), g) and h), we found unsurprisingly that using raw data does improve the performance of the image-domain network. However, our method GloReDi yields even better performance by effectively distilling GloRe from intermediate-view image data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.47, + 0.495 + ], + "angle": 0, + "content": "Ablations on intermediate views for distillation. Selecting a suitable intermediate view for distillation is crucial in realizing the full potential of GloReDi. Images reconstructed from a denser view can provide richer information to the teacher GloRe while introducing a more significant domain gap. As presented in Table 4, we found that models distilled from \\( N_{\\mathrm{v}} \\times 2 \\) views exhibit the best performance. Interestingly, models distilled from the full-view image yield the worst performance, primarily because of the considerable domain gap between the input data. Please refer to Supplementary Material for more ablation studies on framework designs, configurations of residual blocks, and distillation loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.513, + 0.313, + 0.528 + ], + "angle": 0, + "content": "4.4. Transfer to Other Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To test the generalizability and robustness of GloReDi along with other state-of-the-art methods, we finetune each model for another ten epochs on AAPM dataset to bridge the domain gap following the same setting. In Table 2, the proposed GloReDi shows excellent transferability over all other state-of-the-art methods in (ultra) sparse-view scenarios (\\(N_{\\mathrm{v}} = 18,36,72\\)) and still achieves performance comparable with the dual-domain methods when \\(N_{\\mathrm{v}} = 72\\). Specifically, when \\(N_{\\mathrm{v}} = 18\\), we notice GloReDi has 2.06db and 2.18db improvements on PSNR compared to DuDoTrans and FBPCovNet, respectively, indicating that our method is significantly superior in ultra sparse-view scenarios. Fig. 5 shows images with \\(N_{\\mathrm{v}} = 18\\) and 36, which are corrupted severely by FBP as shown in Fig. 5(b), thus losing its clinical value. Previous image-domain methods remove the artifact to some extent but lose most of the details, as shown in Figs. 5(c) and (d). Although the state-of-the-art dual-domain methods gain better results in general, we notice that clinical details such as lesion and bone, as pointed out by the blue arrows, are not accurately reconstructed in Figs. 5(e)-(g) while severe secondary artifacts are introduced, especially when \\(N_{\\mathrm{v}} = 18\\). In contrast, the proposed GloReDi excels at reconstructing the details and greatly improves the clinical value of sparse-view CT." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.748, + 0.107 + ], + "angle": 0, + "content": "5. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.131, + 0.892, + 0.268 + ], + "angle": 0, + "content": "In this paper, we challenge the sparse-view CT reconstruction in the absence of sinogram data and demonstrate that, with appropriate design, the image post-processing method can outperform the state-of-the-art dual-domain method. We propose to learn GloRe with Fourier convolution for image-wide receptive field and present directional and band-pass-specific contrastive distillation for high-quality reconstruction. Our method is particularly advantageous in ultra-sparse scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.893, + 0.493 + ], + "angle": 0, + "content": "We emphasize that our contributions can be easily extended to dual-domain methods when sinogram data are available. On the one hand, learning to distill GloRe can also benefit the image-domain network in a dual-domain framework. On the other hand, the proposed method can also be used to enhance the sinogram recovery by distilling the sinogram with intermediate views. Future work can concentrate on extending GloReDi to dual domain methods and other CT reconstruction tasks, such as limited-views CT reconstruction and metal artifact reduction. Although the teacher network is trained alongside the student network in the current version, it is valuable to explore the utilization of pre-trained teacher models, enabling GloReDi to progressively distill the GloRe from a series of teacher models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.893, + 0.766 + ], + "angle": 0, + "content": "We also acknowledge some limitations. First, the teacher network will introduce additional computational costs during the training phase. It is possible to study how to distill knowledge from a pretrained teacher network. Second, although there are clear improvements in quantitative and visual results, it is desirable to have feedback from radiologists for clinical practice. The generalizability and robustness of the trained networks in clinical applications require further investigation. Third, we only considered 2D cases in the paper due to memory respect. If GPU memory permits, one can extend GloReDi to 3D by replacing 2D convolutions with 3D ones by applying high-dimension kernels for FFCs [7]. Lastly, GloReDi failed to surpass the dual-domain methods in denser view scenarios when sinogram can provide effective information for performance improvement. Studying how to improve the performance given an arbitrary \\( N_{\\mathrm{v}} \\) would be of great value for future research." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Acknowledgement This work was supported in part by National Natural Science Foundation of China (Nos. 62101136 and 62176059), Shanghai Sailing Program (No. 21YF1402800), Shanghai Municipal Science and Technology Major Project (No. 2018SHZDZX01), ZJ Lab, Shanghai Municipal of Science and Technology Project (No. 20JC1419500), and Shanghai Center for Brain Science and Brain-inspired Technology." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21204" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Jielin Bai, Yitong Liu, and Hongwen Yang. 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The reconstructed images, however, suffer from strong artifacts, greatly limiting their diagnostic value. Current trends for sparse-view CT turn to the raw data for better information recovery. The resultant dual-domain methods, nonetheless, suffer from secondary artifacts, especially in ultra-sparse view scenarios, and their generalization to other scanners/protocols is greatly limited. A crucial question arises: have the image post-processing methods reached the limit? Our answer is not yet. In this paper, we stick to image post-processing methods due to great flexibility and propose global representation(GloRe) distillation framework for sparse-view CT, termed GloReDi. First, we propose to learn GloRe with Fourier convolution, so each element in GloRe has an image-wide receptive field. Second, unlike methods that only use the full-view images for supervision, we propose to distill GloRe from intermediate-view reconstructed images that are readily available but not explored in previous literature. The success of GloRe distillation is attributed to two key components: representation directional distillation to align the GloRe directions, and band-pass-specific contrastive distillation to gain clinically important details. Extensive experiments demonstrate the superiority of the proposed GloReDi over the state-of-the-art methods, including dual-domain ones. The source code is available at https://github.com/longzilicart/GloReDi. + +# 1. Introduction + +X-ray CT is one of the major modalities widely used in clinical screening and diagnosis. Despite the benefits, + +![](images/756a567b6fc751570ebf1d8c919d160bd8f9c82ad12f97be762f6581b45d0a72.jpg) +Figure 1. Sparse-view CT only uses a few projection views for tomographic reconstruction, thus providing fast and low-dose CT scanning. However, the reconstruction results of the conventional method suffer from severe global streak artifacts. + +there have been growing concerns that X-ray radiation exposure could increase the risk of cancer induction [47]. Following the "As Low As Reasonably Achievable" principle in the medical community [36], efforts have been made to lower the radiation dose while maintaining imaging quality [20]. Sparse-view CT is one of the effective solutions which reduces the radiation by sampling part of the projection data, a.k.a sinogram, for image reconstruction, as shown in Fig. 1. However, analytical reconstruction algorithms such as filtered back projection (FBP) produce inferior image quality with globally severe streak artifacts, significantly compromising its diagnosis value. How to effectively reconstruct the sparse-view CT remains challenging and, hence, is gaining increasing attention in the computer vision and medical imaging communities. + +Image-domain methods regard sparse-view CT reconstruction as an image post-processing task on the FBP-reconstructed images and have achieved exciting performance on streak artifacts removal and structure preserva + +tion [5, 22, 32, 58]. However, due to the limited receptive field, these methods have difficulty in modeling global information efficiently, thus leading to suboptimal results. Current dominant methods turn to the help of sinogram by restoring the sinogram and performing CT image postprocessing simultaneously [17, 29, 31, 46]. Specifically, in addition to the image domain methods, deep neural networks are also applied to interpolate the missing data in sinogram so that the reconstructed images can be recovered in a global manner [10, 25]. + +Despite the common success of dual-domain methods, they suffer from unsatisfactory and unstable performance due to the following reasons. First, the processing of sinogram data is sensitive and even subtle changes may remarkably affect the reconstructed images and introduce stubborn secondary artifacts that are hard to be eliminated. Second, in ultra sparse-view scenarios, inpainting methods are unable to accurately restore the excessive missing raw data; e.g., inpainting sparse CT data of 18 views to the full CT data of 720 views only retains about $2.5\%$ of the valid information, in which the involvement of sinogram processing makes the learning more difficult and compromise the performance [29,46]. Third, it is often impractical to access sinogram data given the privacy and commercial concerns, and if accessible, the requirement of raw data greatly limits the generalization to other scanners/protocols. + +Motivation. Given the great flexibility of the image domain methods, we raise a critical question in this paper: have the image domain (post-processing) methods reached the limits? Our answer is not yet, given the following observations. First, existing image-domain methods typically suffer from limited receptive field, which fails to extract and recover the global information efficiently [43], given that streak artifacts are spread globally on the reconstructed images as shown in Fig. 1. Second, existing image-domain methods only utilize the full-view images as the unique supervision on the result [22, 58]. They ignore the importance of representation learning, especially global representation (GloRe), making the artifact removal and detail recovery entangled, and leading to sub-optimal results due to the significant gap between sparse- and full-view. Third, the intermediate-view reconstructed images can be readily available during data preparation, but to the best of our knowledge, they are surprisingly neglected in the past literature. We argue that they can provide extra information and build bridges for sparse- and full-view CT reconstruction. + +To address the abovementioned issues, we propose a novel image-domain method for sparse-view CT reconstruction. First, to address the limited receptive field inherent in conventional convolutional neural networks, we propose to learn GloRe with fast Fourier convolution (FFC) [7], so each element in GloRe has an image-wide receptive field. This global nature allows artifacts and information, + +spread over the entire image, to be better modeled while also easing the alignment of the representations from different views. Second, to leverage extra supervision from intermediate-view CT images, we propose a novel distillation framework to learn better GloRe, termed GloReDi, which contains a parallel teacher network to distill knowledge from the readily intermediate-view images to provide high-quality and appropriate guidance for learning the GloRe of sparse-view CT images. Specifically, we first leverage intermediate-view reconstructed images to train a teacher network, which is then used to guide the learning of the student model (i.e. the sparse-view CT). The distillation scheme benefits GloRe in two folds: (1) representation directional distillation that aligns the directions between the student and teacher GloRe, which provides appropriate supervision considering the massive information loss due to the domain gaps between CT images with different views; and (2) band-pass-specific contrastive distillation that utilizes contrastive learning solely on the band-pass components to help distill the specific clinical value of each CT image without compromising the reconstruction accuracy. + +Contributions. In summary, our contributions are listed as follows. First, we propose the global representation (GloRe) learning for sparse-view CT with Fourier convolution, which, to the best of our knowledge, is the first study to emphasize on the representation learning for image post-processing in sparse-view CT. Second, we propose a novel GloRe distillation framework, which can leverage the extra supervision from intermediate-view reconstructed images for high-quality information recovery and reconstruction. Third, we present representation directional distillation and band-pass-specific contrastive distillation for distilling GloRe to align the representation directions and gain clinically important details. Last, extensive experimental results demonstrate the superiority of GloReDi over the state-of-the-art sparse-view CT reconstruction methods in terms of quantitative metrics and visual comparison. + +# 2. Detailed Related Work + +# 2.1. Deep-learning-based Sparse-view CT + +Numerous model-based iterative reconstruction (IR) methods have been developed to solve the sparse-view CT problem, mainly utilizing the sparsity of the total variation (TV) of the image [4, 12, 23, 33, 37, 51, 52]. However, most of them suffer from over-smoothed results, handcrafted tuning for each image, and extremely high computation cost [46], limiting their clinical application. In contrast, deep learning methods are often faster and more accessible, thus arousing attention in this field. Among them, most image-domain methods regard sparse-view CT reconstruction as an image post-processing task. RedCNN [5], FBPCovNet [22], and DDNet [58] are proposed to recon + +![](images/39079075f1fa3780726c8ebc0a0477b51833038f6a895045ed41fd3019596138.jpg) + +![](images/0bf62877d0ea5293afe999f9d3218964e512e2cf7bc01242c979df77b2a6dfca.jpg) +Band-Pass-Specific Contrastive Distillation +Encoders + +![](images/0122f267d596d11874f8856b683d78bcd835e2b3bf29a85e592ee24ad1927033.jpg) +EncoderT + +![](images/1cc431bf19aeb136ef42253f2eb05f9a5cf7285fd13965f97f7ec21143ac409c.jpg) + +![](images/c26dd8f5a24d2d555cef451aa7ed4691a522a2ec6885498ebeba8e7d9c2a0f33.jpg) +Figure 2. Overview of the proposed GloReDi for sparse-view CT reconstruction. GloReDi facilitates efficient information recovery by learning to distill the global representation from intermediate-view images. + +struct the sparse-view CT by the convolutional neural network (CNN). These methods achieve competitive performance on streak artifact removal and structure preservation compared to conventional ones, but most of them fail to capture the global context and underperform in global reconstruction and artifact removal. Since streak artifacts result directly from the incomplete projection views, various methods are proposed to remove the artifacts by interpolating sinogram data [10, 25]. Further, dual-domain methods were becoming popular for their superior reconstruction performance by combining the knowledge of both domains. DuDoNet [31] first proposed a novel Radon inversion layer linking the gradient between the image and sinogram domain networks. Furthermore, various techniques have been proposed to enhance dual domain approaches through network design [1,6] and unrolling architecture [57]. Recently, Transformer [45] has been introduced to dual-domain methods for its capability of capturing long-range dependencies, achieving superior performance [29, 46, 49]. However, the problems of the irreversible secondary artifacts and additional computational costs are not well addressed, and the requirement of raw data greatly limits their generalizability to other CT scanners/protocols. In this work, we challenge reconstructing sparse-view CT without raw data while still achieving state-of-the-art results. + +# 2.2. Knowledge Distillation + +Knowledge distillation transfers rich knowledge from teacher models to lightweight student models in the label or feature domains, mainly applied in model compression and acceleration [15, 41]. Among various approaches, feature-based knowledge distillation is extensively applied in image restoration tasks such as image super-resolution [14, 16, 27, 38]. It minimizes the distance between feature representations to learn richer information from the teacher model compared to softened labels [48]. Further, contrastive representation distillation is proposed to exploit the structural characteristics among different samples by harnessing the + +discriminative representations, thereby enhancing differentiation within data [8, 19, 44]. This work distills knowledge from the intermediate-view images to enhance the sparse-view CT reconstruction. + +# 2.3. Frequency Methods in Deep Learning + +Frequency methods have been widely used in digital image processing and machine learning [2]. Wavelet convolution [32] and fast Fourier convolution [7] have been proposed to provide a larger/global receptive field, achieving great success in image restoration tasks [43]. Frequency methods have also yielded promising results in domain adaption and image translation, mainly by taking advantage of domain-invariant spectrum components [3, 18, 54-56]. Previous research also shows that particular features and details can be better extracted in the frequency domain, leading to improvements in camouflaged object detection [59], face forgery detection [21, 28], and face editing [9]. Frequency-based networks have also made notable strides in CT reconstruction. Previous studies [1, 26] employ multi-wavelet CNN [32] in both sinogram and image domain to suppress artifacts, substituting the pooling operator with wavelet transforms to achieve a larger receptive field. However, since both the Haar filter-based wavelet transform and convolution are applied on the spatial feature map, these methods struggle to capture global representation effectively. Recent research has demonstrated that employing convolution in the Fourier domain can efficiently eliminate the global artifacts [30, 34]. In this work, we utilize a frequency-based network for global representation learning, enhancing clinically critical features by band-pass-specific contrastive distillation. + +# 3. Method + +# 3.1. Problem Definition + +Assume we have a two-dimensional (2D) CT slice of size $N\times N$ $\pmb {I}\in \mathbb{R}^{N\times N}$ , where each pixel contains the attenua + +tion coefficient of the corresponding human body. The raw data or sinogram from the CT scanning, $S \in \mathbb{R}^{N_{\mathrm{v}} \times N_{\mathrm{d}}}$ , can be obtained via the Radon transform [39], where $N_{\mathrm{v}}$ and $N_{\mathrm{d}}$ denote the number of projection views and the number of the detectors, respectively. Inversely, the image reconstruction process can be expressed as $\boldsymbol{I} = \mathcal{R}^{-1}(\boldsymbol{S})$ , where $\mathcal{R}^{-1}$ denotes the inverse Radon transform such as FBP. Ideally, when $N_{\mathrm{v}}$ is sufficiently large, FBP can produce pleasing image quality. However, when $N_{\mathrm{v}}$ is fairly small, the image reconstruction of so-called sparse-view CT becomes an undetermined problem. + +Here, we use $I_{\mathrm{F}}$ and $I_{\mathrm{S}}$ to represent the reconstructed images from full view (i.e. ground-truth) and sparse view, respectively. The image-domain methods for sparse-view CT are to improve the image quality of $I_{\mathrm{S}}$ towards $I_{\mathrm{F}}$ through a neural network $\mathcal{F}$ . That is, the output of the network, $\widehat{I}_{\mathrm{S}} = \mathcal{F}(I_{\mathrm{S}})$ , is expected to be of comparable quality to the full-view ground-truth. In addition, we also use the images, $I_{\mathrm{T}}$ , reconstructed from an intermediate number of projection views that are between sparse and full views, as the teacher supervision, forming a student-teacher framework where the teacher encoder with $I_{\mathrm{T}}$ supervises the training of student encoder with $I_{\mathrm{S}}$ . + +# 3.2. Overview of Our GloReDi + +Fig. 2 presents the proposed GloReDi, which mainly consists of four parts: two encoders to learn global representations (GloRe) from sparse- and intermediate-view reconstructed images, $I_{\mathrm{S}}$ , and $I_{\mathrm{T}}$ , respectively, and two decoders to produce the final processed images from GloRe. In addition to learning GloRe with Fourier convolution, we have two novel modules to perform distillation from the teacher network: (1) representation directional distillation to align the directions between the student and teacher GloRes; and (2) band-pass-specific contrastive distillation to distill the clinically important features for better detail recovery. + +Next, we detail each of the proposed components. + +# 3.3. Global Representation Learning + +The key technique behind the proposed network is the global representation learning with fast Fourier convolution (FFC) [7]. Concretely, FFC first applies real Fourier transform to get the frequency feature map and then performs convolution on frequency components before finally back transforming the frequency features as shown in Fig. 2. Therefore, GloRe from sparse-view images $I_{\mathrm{S}}$ is learned by a Fourier-based encoder network as follows: + +$$ +\boldsymbol {Z} _ {\mathrm {S}} = \operatorname {e n c o d e r S} (\boldsymbol {I} _ {\mathrm {S}}), \tag {1} +$$ + +where $Z_{\mathrm{S}} \in \mathbb{R}^{N_{\mathrm{w}} \times N_{\mathrm{h}} \times N_{\mathrm{c}}}$ denotes GloRe extracted from the sparse-view reconstructed image $I_{\mathrm{S}}$ through the (student) encoder encoderS and $N_{\mathrm{w}} \times N_{\mathrm{h}} \times N_{\mathrm{c}}$ denotes the + +width, height, and channel size of GloRe. Compared to the vanilla convolution with a limited receptive field, FFC works in the frequency domain, so each element in GloRe contains global information of the sparse-view image by using an image-wide receptive field, representing patterns of artifacts and the image contents simultaneously. Furthermore, such global nature can aid in modeling the artifact and information distributed throughout the image while easing the alignment between GloRe of different views. + +# 3.4. Global Representation Distillation + +In the context of sparse-view CT, images with an intermediate view $I_{\mathrm{T}}$ can be easily obtained from the full-view sinogram as extra supervision. To get the teacher representation from $I_{\mathrm{T}}$ , a parallel teacher encoder encoderT, using the same architecture as encoderS but with different weights, takes $I_{\mathrm{T}}$ as input and yields teacher GloRe $Z_{\mathrm{T}}$ of the same shape with $Z_{\mathrm{S}}$ as follows: + +$$ +\boldsymbol {Z} _ {\mathrm {T}} = \operatorname {e n c o d e r} \mathrm {T} \left(\boldsymbol {I} _ {\mathrm {T}}\right). \tag {2} +$$ + +$Z_{\mathrm{T}}$ can be regarded as a high-quality pseudo target for student GloRe in the same latent space since richer information can be extracted from $I_{\mathrm{T}}$ . Exploring distillation from $I_{\mathrm{T}}$ is obviously easier than that of $I_{\mathrm{F}}$ given the significant gap between $I_{\mathrm{S}}$ and $I_{\mathrm{F}}$ . + +Intuitively, $Z_{\mathrm{S}}$ should be similar to $Z_{\mathrm{T}}$ if the artifact-free target information is precisely encoded. Therefore, a natural way for distillation is to use $Z_{\mathrm{T}}$ as the supervision for $Z_{\mathrm{S}}$ by minimizing their Euclidean distance. However, this could harm the reconstruction performance since the student encoder has to partially recover $I_{\mathrm{T}}$ . Finding an effective solution to distilling the information in $Z_{\mathrm{T}}$ for sparse-view CT reconstruction is one of the highlights in this work. Our idea is to separate the distillation process. First, we present representation directional distillation to align the representation directions so the images of different views are along the same direction. Second, we propose a band-pass-specific contrastive distillation to enhance clinically critical details. + +We detail these two distillation techniques as follows. + +# 3.4.1 Representation Directional Distillation + +Given that $I_{\mathrm{S}}$ and $I_{\mathrm{T}}$ share the same ground truth $I_{\mathrm{F}}$ , but differ mainly in artifact patterns, student and teacher GloRe should at least demonstrate a consistent direction for reconstruction with high confidence. Therefore, We define the directional distillation loss for $Z_{\mathrm{S}}$ as follows: + +$$ +\mathcal {L} _ {\mathrm {r d d}} = \frac {1}{N _ {\mathrm {w}} N _ {\mathrm {h}}} \sum_ {i, j} \left(1 - \operatorname {C o s S i m} \left(\left[ \mathbf {Z} _ {\mathrm {S}} \right] _ {i, j}, \left[ \mathbf {Z} _ {\mathrm {T}} \right] _ {i, j}\right)\right), \tag {3} +$$ + +where $\operatorname{CosSim}$ denotes the cosine similarity, defined as $\operatorname{CosSim}(\mathbf{a},\mathbf{b}) = \mathbf{a}^{\mathrm{T}}\mathbf{b} / \max (\|\mathbf{a}\|_2\|\mathbf{b}\|_2,\epsilon)$ with $\epsilon$ set to $1\times 10^{-8}$ to avoid division by zero. + +![](images/f009c71cebac14b4dc2b7355b8a2dc1c82e95cdd82450d3609d7b02df326d2b0.jpg) +Figure 3. The difference between representation distillation (left) and band-pass-specific contrastive distillation (right). Global representation distillation fails to distinguish clinical details due to high similarity among similar body parts, e.g., adjacent lung slices. Band-pass-specific contrastive distillation further projects the representation to the DCT domain, enabling distillation of specific clinical details on corresponding DCT components. + +# 3.4.2 Band-Pass-Specific Contrastive Distillation + +The directional distillation aligns the directions of student representation $Z_{\mathrm{S}}$ and the teacher representation $Z_{\mathrm{T}}$ in the view-independent space, which, however, does not guarantee a high-quality reconstruction of the image. What distinguishes sparse-view CT reconstruction task from classic image restoration one (e.g. denoising, deraining, etc.) is that the former is more demanding in terms of fine-grained details for diseases identification, organs delineation, and low-contrast lesions detection, etc [11]. In other words, it places more emphasis on learning the image-specific representation. + +Contrastive representation learning, as a self-supervised approach, encourages the model to maximize the difference among representations of different samples so that model can emphasize those category-specific representations. However, directly implementing these losses would lead to imprecise reconstruction results because most CT images are inherently similar in intensity distribution, especially for images of the same body parts, as shown in Fig. 3. Recent methods have achieved great success learning on specific DCT spectrum [18, 50, 54], due to its strong energy compaction property, making it simple to select specific frequency components [40]. Therefore, we distilled the image-specific details by applying contrastive distillation on specific discrete cosine transform (DCT) spectrums. On the one hand, detailed knowledge can be better distilled from specific frequency components of teacher GloRe. On the other hand, contrastive against different CT slices can further enhance image-specific details on corresponding DCT components. + +Discrete cosine transform. Discrete cosine transform (DCT) is widely used for data compression in low-frequency components. The basis function of 2D DCT is + +defined as follows: + +$$ +B _ {w, h} ^ {i, j} = \cos \left(\frac {\pi w}{N _ {\mathrm {w}}} \left(i + \frac {1}{2}\right)\right) \cos \left(\frac {\pi h}{N _ {\mathrm {h}}} \left(j + \frac {1}{2}\right)\right), \quad (4) +$$ + +where $N_{\mathrm{w}}$ and $N_{\mathrm{h}}$ represent the width and height of the input, respectively. Then, 2D DCT of the latent feature $\mathbf{Z}$ can be written as: + +$$ +f _ {w, h} (\boldsymbol {Z}) = \sum_ {i = 0} ^ {N _ {\mathrm {w}} - 1} \sum_ {j = 0} ^ {N _ {\mathrm {h}} - 1} [ \boldsymbol {Z} ] _ {i, j} B _ {w, h} ^ {i, j}, \tag {5} +$$ + +where $w\in \{0,1,\ldots ,N_{\mathrm{w}} - 1\} ,h\in \{0,1,\ldots ,N_{\mathrm{h}} - 1\}$ The $f(\pmb {Z})\in \mathbb{R}^{N_{\mathrm{w}}\times N_{\mathrm{h}}}$ represents the 2D DCT frequency spectrum of $\pmb{Z}$ . Thus, frequency components can be easily selected by a mask $M\in \{0,1\}^{N_{\mathrm{w}}\times N_{\mathrm{h}}}$ + +Band-pass-specific contrastive distillation. Crucially, the low-frequency components of GloRe contribute most to the reconstruction accuracy, while high-frequency may contain inherent noise and artifacts of CT images. We therefore use a band-pass supervised contrastive loss for the distillation, where a band-pass mask $M$ is incorporated to filter out the mid-frequency part in the frequency domain, containing main structure as well as the necessary detail information. The proposed band-pass supervised contrastive loss can be written as: + +$$ +\boldsymbol {z} = \text {f l a t t e n} \left(\operatorname {c r o p} \left(f _ {w, h} (\boldsymbol {Z}), \boldsymbol {M}\right)\right), \tag {6} +$$ + +where crop operator will keep the value at locations where $M = 1$ while the flatten operator flattens the 2D spectrum map into 1D representation. + +It is to be observed that the clinical details in the CT images vary from case by case and are each very critical for diagnosis, requiring more sophisticated instance-level distinction. To this end, we consider all representations from different CT slices as negative samples to maximize image-specific features while updating the memory bank $\mathcal{M}$ with the widely applied First-In-First-Out mechanism per iteration from the previous mini-batches. The proposed band-pass-specific contrastive distillation loss for sample $z_{\mathrm{S}}$ can be written as follows: + +$$ +\mathcal {L} _ {\mathrm {b c d}} = - \log \frac {\exp \left(\boldsymbol {z} _ {\mathrm {S}} ^ {\mathrm {T}} \boldsymbol {z} _ {\mathrm {T}} / \tau\right)}{\sum_ {\boldsymbol {z} \in \mathcal {M}} \exp \left(\boldsymbol {z} _ {\mathrm {S}} ^ {\mathrm {T}} \boldsymbol {z} / \tau\right)}, \tag {7} +$$ + +where $z_{\mathrm{S}}, z_{\mathrm{T}}$ , and $z$ are frequency representations of $Z_{\mathrm{S}}, Z_{\mathrm{T}}$ , and negative samples from memory bank $\mathcal{M}$ of size $N_{\mathrm{mem}}$ , respectively. $\tau$ is the temperature term used to adjust the sensitivity of negative samples. + +# 3.5. Loss Function and Training Procedure + +Teacher reconstruction. To constrain the GloRe extracted from $I_{\mathrm{S}}$ and $I_{\mathrm{T}}$ in the same latent space, a naive solution is to share the same decoder in the training phase, which, however, brings instability. Therefore, we adopt the widely + +Algorithm 1 The training process of GloReDi. +Require: encoderS, encoderT, decoderS, decoderT; Input images: $I_{\mathrm{S}}, I_{\mathrm{T}}, I_{\mathrm{F}}$ ; momentum $m$ and Memory bank +1: for iter = 0 to Max_Iter do +2: Update decoderT using Eq. (8) +3: $\widehat{I}_{\mathrm{T}}, Z_{\mathrm{T}} = \text{decoderT}(\text{encoderT}(I_{\mathrm{T}}))$ +4: Optimize encoderT using Eq. (9) +5: $\widehat{I}_{\mathrm{S}}, Z_{\mathrm{S}} = \text{decoderS}(\text{encoderS}(I_{\mathrm{S}}))$ +6: Optimize encoderS+decoderS using Eq. (11) +7: Update memory bank +8: end for +Return: encoderS+ decoderS + +used Exponential Moving Average (EMA) with momentum $m$ to update the parameters $\theta$ of the teacher decoder by the student decoder [13]: + +$$ +\theta_ {\text {d e c o d e r T}} = m \theta_ {\text {d e c o d e r T}} + (1 - m) \theta_ {\text {d e c o d e r S}}. \tag {8} +$$ + +Then, the global representation $Z_{\mathrm{T}}$ learned by the teacher is fed into to the decoder to obtain the teacher reconstruction result $\widehat{I}_{\mathrm{T}}$ , and we use $\ell_1$ loss to measure the pixel-wise difference between $\widehat{I}_{\mathrm{T}}$ and the full-view ground-truth $I_{\mathrm{F}}$ and train the teacher: + +$$ +\mathcal {L} _ {\text {p i x e l T}} = \left\| \operatorname {d e c o d e r T} \left(\boldsymbol {Z} _ {\mathrm {T}}\right) - \boldsymbol {I} _ {\mathrm {F}} \right\| _ {1}. \tag {9} +$$ + +Student reconstruction. The pixel-wise error measurement for the student is defined in a similar way: + +$$ +\mathcal {L} _ {\text {p i x e l S}} = \left\| \operatorname {d e c o d e r S} \left(\boldsymbol {Z} _ {\mathrm {S}}\right) - \boldsymbol {I} _ {\mathrm {F}} \right\| _ {1}. \tag {10} +$$ + +Finally, a compound loss function combining pixel-wise error and two distillation losses, respectively defined in Eq. (3) and Eq. (7) is introduced for student network training to achieve high-quality sparse-view CT reconstruction: + +$$ +\mathcal {L} _ {\mathrm {S t u}} = \mathcal {L} _ {\mathrm {p i x e l S}} + \alpha \mathcal {L} _ {\mathrm {r d d}} + \beta \mathcal {L} _ {\mathrm {b c d}}, \tag {11} +$$ + +GloReDi is trained following the process summarized in Algorithm 1, where the student and teacher encoder are trained iteratively. + +# 4. Experimental Results + +# 4.1. Experimental Setup + +Dataset. We use DeepLesion dataset [53] and "2016 NIH-AAPM-Mayo Clinic Low-Dose CT Grand Challenge" AAPM dataset [35] to demonstrate the effectiveness of the proposed GloReDi. The DeepLesion dataset is the largest multi-lesion real-world CT dataset made available to the + +public, from which 40,000 images of 303 patients are selected as the training set while 1000 images of another 18 patients are selected as the test set. AAPM dataset contains routine dose CT data from 10 patients, where a total of 5,410 slices from 9 patients are chosen for training and 526 slices from the remaining 1 patient for testing. All images are resized to $256 \times 256$ . We simulate the forward and back projection using fan-beam geometry under $120\mathrm{kVp}$ and $500\mathrm{mA}$ with TorchRadon toolbox [42]. The distance from X-ray source to the rotation center is $59.5\mathrm{cm}$ , and the number of detectors is set to 672. Sparse-view CT images are generated from $N_{\mathrm{v}} = 18,36,72,144$ projection views uniformly sampled from full 720 views covering $[0,2\pi]$ . To simulate the photon noise presented in real-world CT, an intensity of $1 \times 10^{6}$ Poisson noise is added to the sinograms. + +Implementation details. Our model is implemented in PyTorch. We use Adam optimizer [24] with $(\beta_{1},\beta_{2}) = (0.5,0.999)$ to train the model. The learning rate starts from $1\times 10^{-3}$ and is halved for every 40 epochs. For each method, four models of different $N_{\mathrm{v}}$ are trained separately on 4 NVIDIA RTX 3090 GPUs for 120 epochs with a batch size of 8. For hyperparameters in GloReDi, we set $\alpha$ and $\beta$ in Eq. (11) empirically to 0.1 and 0.0002 to fit the scale between losses. The momentum $m$ and temperature $\tau$ are set to 0.9 and 1.0, respectively, while the size $L$ of the memory bank is set to 300 to balance the performance and computational cost. We set intermediate-view as $N_{\mathrm{v}}\times 2$ by default. More details, including the network architecture, can be found in the Supplementary Material. + +Evaluation metrics. For quantitative evaluation, we use peak signal-to-noise ratio (PSNR), structural similarity (SSIM) [60] and root mean square error (RMSE); all of them are widely adopted for image quality assessment. + +# 4.2. Comparison with State-of-the-Art Methods + +We compare GloReDi with the following state-of-the-art methods: DDNet [58], FBPCovNet [22], DuDoNet [31], DDPTrans [29], and DuDoTrans [46]. In addition, we name the network without the distillation from $I_{\mathrm{T}}$ as the frequency encoder and decoder network (Fred-Net), optimized with only the pixel-wise loss in Eq. (10). FBP directly applies Radon transform to reconstruct the image from the sparse-view sinogram. DDNet and FBPCovNet are image-domain deep-learning methods taking FBP results as input. DuDoNet is a state-of-the-art dual-domain method that restores the CT image using two U-Nets in sinogram and image domains. Furthermore, DDPTrans and DuDoTrans adopt Transformer on both domains to restore the image by utilizing the long-range dependency. We try our best to reproduce these methods and then train and test them on the same dataset for a fair comparison. + +Quantitative comparison. Table 1 presents the quantita + +
Methods\(N_{\mathrm{v}}=18\)\(N_{\mathrm{v}}=36\)\(N_{\mathrm{v}}=72\)\(N_{\mathrm{v}}=144\)
PSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSE
FBP22.2235.360.079525.4947.490.054330.8863.810.029337.1282.940.0144
DDNet [58]34.5791.940.018738.2494.910.012641.6697.270.008346.7598.790.0048
FBPCovNet [22]35.9593.620.016439.7996.130.010643.7697.470.006648.4698.600.0039
DuDoNet [31]35.6993.960.016940.3696.940.010344.8698.390.005949.3399.230.0036
DDPTRans [29]35.1193.480.018138.6895.990.012143.5698.160.006948.7299.220.0038
DuDoTrans [46]36.0893.280.016140.7596.670.009545.1698.440.005749.9699.280.0034
Fred-Net (ours)38.0895.200.012940.8696.810.009344.4398.180.006348.4599.080.0039
GloReDi (ours)38.6595.870.012041.2597.050.009045.1898.430.005748.9699.210.0037
+ +Table 1. Quantitative evaluation [PSNR (db), SSIM (%) and RMSE] for state-of-the-art methods on DeepLesion dataset. + +![](images/5ed20eca4f47123ee893b8a48a6c3f78d989483843ffcf29a1d59afd80dac083.jpg) +Figure 4. Visual comparison of state-of-the-art methods on DeepLesion dataset: (a) Ground Truth, (b) FBP, (c) DDNet, (d) FBPCovNet, (e) DuDoNet, (f) DDPTrans, (g) DuDoTrans, and (h) GloReDi. From top to bottom: the results under $N_{\mathrm{v}} = 18$ , 36, 72; display window is set to [-1000, 2000] HU for the first two rows and [-200, 300] HU for the third row. + +tive comparison. Generally, dual-domain methods perform better than single-domain methods, especially in the case of $N_{\mathrm{v}} = 72$ , 144 thanks to the sinogram inpainting network. However, we highlight in ultra sparse-view scenarios where $N_{\mathrm{v}} = 18$ , that dual-domain methods like DuDoNet perform worse than classical image-domain-only methods such as FBPCovNet. This can be attributed to the secondary artifacts introduced by the unsuccessful sinogram inpainting; e.g., when $N_{\mathrm{v}} = 18$ in our setting, restoring the sinogram can be recognized as a $40 \times$ super-resolution task, which is rather challenging. DuDoTrans is superior to DuDoNet to some extent, indicating the importance of long-range dependency in reconstruction. DDPTrans fails to surpass DuDoNet because of the limited parameter number though most transformers are memory-consuming. + +Compared with the previous works, the proposed GloReDi achieves competitive results by learning to distill GloRe for high-quality reconstruction. Particularly in ultrasparse scenarios, e.g., when $N_{\mathrm{v}} = 18$ , GloReDi has 2.57db and 2.70db improvement on PSNR over DuDoTrans and + +FBPCovNet, respectively. As $N_{\mathrm{v}}$ increases, the advantage of GloReDi decreases, mainly due to a shift towards artifacts removal tasks rather than reconstruction. We highlight that the fewer projection views indicate less radiation dose and more speedup. We notice that global representation distillation further improves the performance of GloReDi from 0.51db to 0.89db compared to Fred-Net. The results show that the proposed GloReDi successfully inspire the potential of image post-processing methods and is significantly superior to the state-of-the-art methods under various settings. + +Visual comparison. Fig. 4 presents the visualization results of three sparse-view CT. DDNet and FBPCovNet cannot remove the artifact thoroughly, while the reconstruction results are over-smooth in the boundary of organs and bones. Such effects can be easily observed in the second row of Figs. 4(c) and 4(d) on the spine where the anatomical structure is complicated. Although dual-domain methods perform better in general, their accuracy in details is even worse than FBPCovNet in comparison with Figs. 4(d) and 4(e)-(g). Among all these methods, Glo + +
Methods\(N_{\mathrm{v}}=18\)\(N_{\mathrm{v}}=36\)\(N_{\mathrm{v}}=72\)\(N_{\mathrm{v}}=144\)
PSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSE
FBP22.7335.060.073226.2747.520.048631.3664.560.027037.8584.570.0128
DDNet [58]34.2989.680.019436.9593.030.014240.4196.040.009644.3598.050.0061
FBPCovNet [22]35.7392.840.016537.9593.730.012742.9297.190.007247.3598.760.0043
DuDoNet [31]34.8293.000.019639.8995.990.010244.0698.020.006248.3999.110.0038
DDPTRans [29]34.4791.950.019138.1394.830.012542.7797.650.007347.8499.060.0041
DuDoTrans [46]35.8593.070.016240.0496.020.010044.2098.070.006249.0299.210.0036
Fred-Net (ours)37.2093.900.014041.4696.840.008543.6497.840.006647.5099.030.0042
GloReDi (ours)37.9194.580.012841.5796.700.008444.2498.030.006248.1099.080.0040
+ +![](images/1226c91ee7a8df6895ef469430ee3aad5f89e3550f68f6e71526642aecc97c42.jpg) +Figure 5. Visual comparison of state-of-the-art methods on AAPM dataset: (a) Ground Truth, (b) FBP, (c) DDNet, (d) FBPCovNet, (e) DuDoNet, (f) DDPTrans, (g) DuDoTrans, and (h) GloReDi. From top to bottom: $N_{\mathrm{v}} = 18$ , 36; the display window is [-1000, 2000] HU. + +ReDi best reconstructs the structures and details, especially in ultra-sparse scenarios. In the first two rows of Fig. 4(h), only GloReDi precisely recovers those clinically important details such as soft tissue and corrupted pulmonary alveoli. + +# 4.3. Ablation Study + +We first evaluate the effectiveness of each component in GloReDi. We use Fred-Net as the baseline to add components. The configurations involved in Table 3 are mainly four groups: (1) the baseline Fred-Net using pixel-wise loss to train student model without distillation components (a); (2) the baseline without Fourier convolutions $(\mathbf{b} - \mathbf{c})$ ; (3) the baseline with distillation from intermediate-view reconstructed images $(\mathbf{d} - \mathbf{g})$ ; and (4) the dual-domain version with raw data processed by sinogram-domain sub-network of DuDoNet [31] $(\mathbf{h})$ . Unless noted otherwise, the pixelwise loss is involved in training. + +Ablations on global representations. The results between a) and b) in Table 3 confirm that learning global representations with the image-wide receptive field by Fourier convolution is beneficial for sparse CT reconstruction. Also, we notice that in Tables 1 and 2, our baseline Fred-Net still outperforms state-of-the-art methods when $N_{\mathrm{v}} = 18$ and 36. Interestingly, we found that c) performs even worse than b) in Table 3. This suggests that global representation is essential for bridging the gap between images of different views. Generally, learning global representations is pow + +Table 2. Quantitative evaluation [PSNR (db), SSIM (%) and RMSE] for state-of-the-art methods transferred to AAPM dataset. + +
config.PSNR
a)Fred-Net38.09
b)Fred-Net w/o Fourier36.52
c)Fred-Net w/o Fourier + Lrdd + Lbcd36.30
d)Fred-Net + data augmentation34.41
e)Fred-Net + Lrdd38.39
f)Fred-Net + Lbcd38.42
g)Fred-Net + Lrdd + Lbcd = GloReDi38.65
h)Fred-Net + raw data38.44
+ +Table 3. Quantitative evaluation of different configurations. + +erful and provides a new perspective for sparse-view CT reconstruction, which also answers that the limit of image post-processing methods is still far beyond reach. + +Ablations on global representation distillation. Through a comparison between Fred-Net and the one trained with intermediate-view images as data augmentation (a vs. d) in Table 3, we found that directly applying data augmentation had a negative impact, resulting in a 3.67db PSNR drop. This indicates that the network failed to benefit from denser-view images directly because of the significant domain gap among images of different views. By comparing a), e) and f) in Table 3, we can see that both e) representation directional distillation and f) band-pass-specific contrastive distillation can improve the performance of a), showing that end-to-end supervision cannot thoroughly unlock the potential of the GloRe. By training with both distillation loss, g) further boosts the performance and outperforms all other + +
config.Nv×2Nv×3Nv×4720
Nv=1838.3838.2938.2838.02
Nv=7244.8444.4644.7244.38
+ +Table 4. PSNR evaluation of GloReDi trained with different intermediate-view images for 60 epochs. The first and second rows show the results of sparse-view images with $N_{\mathrm{v}} = 18$ , 72 distilled from images of $N_{\mathrm{v}} \times 2$ , 3, 4 and 720 (full view), respectively. + +configurations. By comparing a), g) and h), we found unsurprisingly that using raw data does improve the performance of the image-domain network. However, our method GloReDi yields even better performance by effectively distilling GloRe from intermediate-view image data. + +Ablations on intermediate views for distillation. Selecting a suitable intermediate view for distillation is crucial in realizing the full potential of GloReDi. Images reconstructed from a denser view can provide richer information to the teacher GloRe while introducing a more significant domain gap. As presented in Table 4, we found that models distilled from $N_{\mathrm{v}} \times 2$ views exhibit the best performance. Interestingly, models distilled from the full-view image yield the worst performance, primarily because of the considerable domain gap between the input data. Please refer to Supplementary Material for more ablation studies on framework designs, configurations of residual blocks, and distillation loss. + +# 4.4. Transfer to Other Dataset + +To test the generalizability and robustness of GloReDi along with other state-of-the-art methods, we finetune each model for another ten epochs on AAPM dataset to bridge the domain gap following the same setting. In Table 2, the proposed GloReDi shows excellent transferability over all other state-of-the-art methods in (ultra) sparse-view scenarios ( $N_{\mathrm{v}} = 18,36,72$ ) and still achieves performance comparable with the dual-domain methods when $N_{\mathrm{v}} = 72$ . Specifically, when $N_{\mathrm{v}} = 18$ , we notice GloReDi has 2.06db and 2.18db improvements on PSNR compared to DuDoTrans and FBPCovNet, respectively, indicating that our method is significantly superior in ultra sparse-view scenarios. Fig. 5 shows images with $N_{\mathrm{v}} = 18$ and 36, which are corrupted severely by FBP as shown in Fig. 5(b), thus losing its clinical value. Previous image-domain methods remove the artifact to some extent but lose most of the details, as shown in Figs. 5(c) and (d). Although the state-of-the-art dual-domain methods gain better results in general, we notice that clinical details such as lesion and bone, as pointed out by the blue arrows, are not accurately reconstructed in Figs. 5(e)-(g) while severe secondary artifacts are introduced, especially when $N_{\mathrm{v}} = 18$ . In contrast, the proposed GloReDi excels at reconstructing the details and greatly improves the clinical value of sparse-view CT. + +# 5. Discussion and Conclusion + +In this paper, we challenge the sparse-view CT reconstruction in the absence of sinogram data and demonstrate that, with appropriate design, the image post-processing method can outperform the state-of-the-art dual-domain method. We propose to learn GloRe with Fourier convolution for image-wide receptive field and present directional and band-pass-specific contrastive distillation for high-quality reconstruction. Our method is particularly advantageous in ultra-sparse scenarios. + +We emphasize that our contributions can be easily extended to dual-domain methods when sinogram data are available. On the one hand, learning to distill GloRe can also benefit the image-domain network in a dual-domain framework. On the other hand, the proposed method can also be used to enhance the sinogram recovery by distilling the sinogram with intermediate views. Future work can concentrate on extending GloReDi to dual domain methods and other CT reconstruction tasks, such as limited-views CT reconstruction and metal artifact reduction. Although the teacher network is trained alongside the student network in the current version, it is valuable to explore the utilization of pre-trained teacher models, enabling GloReDi to progressively distill the GloRe from a series of teacher models. + +We also acknowledge some limitations. First, the teacher network will introduce additional computational costs during the training phase. It is possible to study how to distill knowledge from a pretrained teacher network. Second, although there are clear improvements in quantitative and visual results, it is desirable to have feedback from radiologists for clinical practice. The generalizability and robustness of the trained networks in clinical applications require further investigation. Third, we only considered 2D cases in the paper due to memory respect. If GPU memory permits, one can extend GloReDi to 3D by replacing 2D convolutions with 3D ones by applying high-dimension kernels for FFCs [7]. Lastly, GloReDi failed to surpass the dual-domain methods in denser view scenarios when sinogram can provide effective information for performance improvement. Studying how to improve the performance given an arbitrary $N_{\mathrm{v}}$ would be of great value for future research. + +Acknowledgement This work was supported in part by National Natural Science Foundation of China (Nos. 62101136 and 62176059), Shanghai Sailing Program (No. 21YF1402800), Shanghai Municipal Science and Technology Major Project (No. 2018SHZDZX01), ZJ Lab, Shanghai Municipal of Science and Technology Project (No. 20JC1419500), and Shanghai Center for Brain Science and Brain-inspired Technology. + +# References + +[1] Jielin Bai, Yitong Liu, and Hongwen Yang. Sparse-view CT reconstruction based on a hybrid domain model with multi-level wavelet transform. 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The reconstructed images, however, suffer from strong artifacts, greatly limiting their diagnostic value. Current trends for sparse-view CT turn to the raw data for better information recovery. The resultant dual-domain methods, nonetheless, suffer from secondary artifacts, especially in ultra-sparse view scenarios, and their generalization to other scanners/protocols is greatly limited. A crucial question arises: have the image post-processing methods reached the limit? Our answer is not yet. In this paper, we stick to image post-processing methods due to great flexibility and propose global representation(GloRe) distillation framework for sparse-view CT, termed GloReDi. First, we propose to learn GloRe with Fourier convolution, so each element in GloRe has an image-wide receptive field. Second, unlike methods that only use the full-view images for supervision, we propose to distill GloRe from intermediate-view reconstructed images that are readily available but not explored in previous literature. The success of GloRe distillation is attributed to two key components: representation directional distillation to align the GloRe directions, and band-pass-specific contrastive distillation to gain clinically important details. Extensive experiments demonstrate the superiority of the proposed GloReDi over the state-of-the-art methods, including dual-domain ones. The source code is available at https://github.com/longzilicart/GloReDi." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 669, + 128, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 128, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 128, + 681 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "X-ray CT is one of the major modalities widely used in clinical screening and diagnosis. Despite the benefits," + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 269, + 545, + 412 + ], + "blocks": [ + { + "bbox": [ + 310, + 269, + 545, + 412 + ], + "lines": [ + { + "bbox": [ + 310, + 269, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 310, + 269, + 545, + 412 + ], + "type": "image", + "image_path": "756a567b6fc751570ebf1d8c919d160bd8f9c82ad12f97be762f6581b45d0a72.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 427, + 547, + 472 + ], + "lines": [ + { + "bbox": [ + 305, + 427, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 427, + 547, + 472 + ], + "type": "text", + "content": "Figure 1. Sparse-view CT only uses a few projection views for tomographic reconstruction, thus providing fast and low-dose CT scanning. However, the reconstruction results of the conventional method suffer from severe global streak artifacts." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 486, + 546, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 665 + ], + "type": "text", + "content": "there have been growing concerns that X-ray radiation exposure could increase the risk of cancer induction [47]. Following the \"As Low As Reasonably Achievable\" principle in the medical community [36], efforts have been made to lower the radiation dose while maintaining imaging quality [20]. Sparse-view CT is one of the effective solutions which reduces the radiation by sampling part of the projection data, a.k.a sinogram, for image reconstruction, as shown in Fig. 1. However, analytical reconstruction algorithms such as filtered back projection (FBP) produce inferior image quality with globally severe streak artifacts, significantly compromising its diagnosis value. How to effectively reconstruct the sparse-view CT remains challenging and, hence, is gaining increasing attention in the computer vision and medical imaging communities." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "content": "Image-domain methods regard sparse-view CT reconstruction as an image post-processing task on the FBP-reconstructed images and have achieved exciting performance on streak artifacts removal and structure preserva" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21196" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 286, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 286, + 191 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 286, + 191 + ], + "type": "text", + "content": "tion [5, 22, 32, 58]. However, due to the limited receptive field, these methods have difficulty in modeling global information efficiently, thus leading to suboptimal results. Current dominant methods turn to the help of sinogram by restoring the sinogram and performing CT image postprocessing simultaneously [17, 29, 31, 46]. Specifically, in addition to the image domain methods, deep neural networks are also applied to interpolate the missing data in sinogram so that the reconstructed images can be recovered in a global manner [10, 25]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 193, + 286, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 193, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 49, + 193, + 286, + 384 + ], + "type": "text", + "content": "Despite the common success of dual-domain methods, they suffer from unsatisfactory and unstable performance due to the following reasons. First, the processing of sinogram data is sensitive and even subtle changes may remarkably affect the reconstructed images and introduce stubborn secondary artifacts that are hard to be eliminated. Second, in ultra sparse-view scenarios, inpainting methods are unable to accurately restore the excessive missing raw data; e.g., inpainting sparse CT data of 18 views to the full CT data of 720 views only retains about " + }, + { + "bbox": [ + 49, + 193, + 286, + 384 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 49, + 193, + 286, + 384 + ], + "type": "text", + "content": " of the valid information, in which the involvement of sinogram processing makes the learning more difficult and compromise the performance [29,46]. Third, it is often impractical to access sinogram data given the privacy and commercial concerns, and if accessible, the requirement of raw data greatly limits the generalization to other scanners/protocols." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 389, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 389, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 49, + 389, + 286, + 628 + ], + "type": "text", + "content": "Motivation. Given the great flexibility of the image domain methods, we raise a critical question in this paper: have the image domain (post-processing) methods reached the limits? Our answer is not yet, given the following observations. First, existing image-domain methods typically suffer from limited receptive field, which fails to extract and recover the global information efficiently [43], given that streak artifacts are spread globally on the reconstructed images as shown in Fig. 1. Second, existing image-domain methods only utilize the full-view images as the unique supervision on the result [22, 58]. They ignore the importance of representation learning, especially global representation (GloRe), making the artifact removal and detail recovery entangled, and leading to sub-optimal results due to the significant gap between sparse- and full-view. Third, the intermediate-view reconstructed images can be readily available during data preparation, but to the best of our knowledge, they are surprisingly neglected in the past literature. We argue that they can provide extra information and build bridges for sparse- and full-view CT reconstruction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 630, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 630, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 630, + 286, + 712 + ], + "type": "text", + "content": "To address the abovementioned issues, we propose a novel image-domain method for sparse-view CT reconstruction. First, to address the limited receptive field inherent in conventional convolutional neural networks, we propose to learn GloRe with fast Fourier convolution (FFC) [7], so each element in GloRe has an image-wide receptive field. This global nature allows artifacts and information," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 308, + 72, + 544, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 323 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 323 + ], + "type": "text", + "content": "spread over the entire image, to be better modeled while also easing the alignment of the representations from different views. Second, to leverage extra supervision from intermediate-view CT images, we propose a novel distillation framework to learn better GloRe, termed GloReDi, which contains a parallel teacher network to distill knowledge from the readily intermediate-view images to provide high-quality and appropriate guidance for learning the GloRe of sparse-view CT images. Specifically, we first leverage intermediate-view reconstructed images to train a teacher network, which is then used to guide the learning of the student model (i.e. the sparse-view CT). The distillation scheme benefits GloRe in two folds: (1) representation directional distillation that aligns the directions between the student and teacher GloRe, which provides appropriate supervision considering the massive information loss due to the domain gaps between CT images with different views; and (2) band-pass-specific contrastive distillation that utilizes contrastive learning solely on the band-pass components to help distill the specific clinical value of each CT image without compromising the reconstruction accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 327, + 544, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 327, + 544, + 517 + ], + "spans": [ + { + "bbox": [ + 308, + 327, + 544, + 517 + ], + "type": "text", + "content": "Contributions. In summary, our contributions are listed as follows. First, we propose the global representation (GloRe) learning for sparse-view CT with Fourier convolution, which, to the best of our knowledge, is the first study to emphasize on the representation learning for image post-processing in sparse-view CT. Second, we propose a novel GloRe distillation framework, which can leverage the extra supervision from intermediate-view reconstructed images for high-quality information recovery and reconstruction. Third, we present representation directional distillation and band-pass-specific contrastive distillation for distilling GloRe to align the representation directions and gain clinically important details. Last, extensive experimental results demonstrate the superiority of GloReDi over the state-of-the-art sparse-view CT reconstruction methods in terms of quantitative metrics and visual comparison." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 531, + 436, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 531, + 436, + 544 + ], + "spans": [ + { + "bbox": [ + 308, + 531, + 436, + 544 + ], + "type": "text", + "content": "2. Detailed Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 552, + 501, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 552, + 501, + 563 + ], + "spans": [ + { + "bbox": [ + 308, + 552, + 501, + 563 + ], + "type": "text", + "content": "2.1. Deep-learning-based Sparse-view CT" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 571, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 571, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 571, + 544, + 712 + ], + "type": "text", + "content": "Numerous model-based iterative reconstruction (IR) methods have been developed to solve the sparse-view CT problem, mainly utilizing the sparsity of the total variation (TV) of the image [4, 12, 23, 33, 37, 51, 52]. However, most of them suffer from over-smoothed results, handcrafted tuning for each image, and extremely high computation cost [46], limiting their clinical application. In contrast, deep learning methods are often faster and more accessible, thus arousing attention in this field. Among them, most image-domain methods regard sparse-view CT reconstruction as an image post-processing task. RedCNN [5], FBPCovNet [22], and DDNet [58] are proposed to recon" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "21197" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 110, + 131 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 110, + 131 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 110, + 131 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 110, + 131 + ], + "type": "image", + "image_path": "39079075f1fa3780726c8ebc0a0477b51833038f6a895045ed41fd3019596138.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 115, + 117, + 237, + 175 + ], + "blocks": [ + { + "bbox": [ + 118, + 106, + 236, + 115 + ], + "lines": [ + { + "bbox": [ + 118, + 106, + 236, + 115 + ], + "spans": [ + { + "bbox": [ + 118, + 106, + 236, + 115 + ], + "type": "text", + "content": "Band-Pass-Specific Contrastive Distillation" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 115, + 117, + 237, + 175 + ], + "lines": [ + { + "bbox": [ + 115, + 117, + 237, + 175 + ], + "spans": [ + { + "bbox": [ + 115, + 117, + 237, + 175 + ], + "type": "image", + "image_path": "0bf62877d0ea5293afe999f9d3218964e512e2cf7bc01242c979df77b2a6dfca.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 136, + 188, + 179, + 196 + ], + "lines": [ + { + "bbox": [ + 136, + 188, + 179, + 196 + ], + "spans": [ + { + "bbox": [ + 136, + 188, + 179, + 196 + ], + "type": "text", + "content": "Encoders" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 242, + 76, + 402, + 208 + ], + "blocks": [ + { + "bbox": [ + 136, + 86, + 179, + 95 + ], + "lines": [ + { + "bbox": [ + 136, + 86, + 179, + 95 + ], + "spans": [ + { + "bbox": [ + 136, + 86, + 179, + 95 + ], + "type": "text", + "content": "EncoderT" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 242, + 76, + 402, + 208 + ], + "lines": [ + { + "bbox": [ + 242, + 76, + 402, + 208 + ], + "spans": [ + { + "bbox": [ + 242, + 76, + 402, + 208 + ], + "type": "image", + "image_path": "0122f267d596d11874f8856b683d78bcd835e2b3bf29a85e592ee24ad1927033.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 408, + 71, + 544, + 137 + ], + "blocks": [ + { + "bbox": [ + 408, + 71, + 544, + 137 + ], + "lines": [ + { + "bbox": [ + 408, + 71, + 544, + 137 + ], + "spans": [ + { + "bbox": [ + 408, + 71, + 544, + 137 + ], + "type": "image", + "image_path": "1cc431bf19aeb136ef42253f2eb05f9a5cf7285fd13965f97f7ec21143ac409c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 408, + 142, + 544, + 209 + ], + "blocks": [ + { + "bbox": [ + 408, + 142, + 544, + 209 + ], + "lines": [ + { + "bbox": [ + 408, + 142, + 544, + 209 + ], + "spans": [ + { + "bbox": [ + 408, + 142, + 544, + 209 + ], + "type": "image", + "image_path": "c26dd8f5a24d2d555cef451aa7ed4691a522a2ec6885498ebeba8e7d9c2a0f33.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 546, + 237 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 546, + 237 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 546, + 237 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed GloReDi for sparse-view CT reconstruction. GloReDi facilitates efficient information recovery by learning to distill the global representation from intermediate-view images." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 256, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 289, + 555 + ], + "type": "text", + "content": "struct the sparse-view CT by the convolutional neural network (CNN). These methods achieve competitive performance on streak artifact removal and structure preservation compared to conventional ones, but most of them fail to capture the global context and underperform in global reconstruction and artifact removal. Since streak artifacts result directly from the incomplete projection views, various methods are proposed to remove the artifacts by interpolating sinogram data [10, 25]. Further, dual-domain methods were becoming popular for their superior reconstruction performance by combining the knowledge of both domains. DuDoNet [31] first proposed a novel Radon inversion layer linking the gradient between the image and sinogram domain networks. Furthermore, various techniques have been proposed to enhance dual domain approaches through network design [1,6] and unrolling architecture [57]. Recently, Transformer [45] has been introduced to dual-domain methods for its capability of capturing long-range dependencies, achieving superior performance [29, 46, 49]. However, the problems of the irreversible secondary artifacts and additional computational costs are not well addressed, and the requirement of raw data greatly limits their generalizability to other CT scanners/protocols. In this work, we challenge reconstructing sparse-view CT without raw data while still achieving state-of-the-art results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 563, + 176, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 176, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 176, + 575 + ], + "type": "text", + "content": "2.2. Knowledge Distillation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "Knowledge distillation transfers rich knowledge from teacher models to lightweight student models in the label or feature domains, mainly applied in model compression and acceleration [15, 41]. Among various approaches, feature-based knowledge distillation is extensively applied in image restoration tasks such as image super-resolution [14, 16, 27, 38]. It minimizes the distance between feature representations to learn richer information from the teacher model compared to softened labels [48]. Further, contrastive representation distillation is proposed to exploit the structural characteristics among different samples by harnessing the" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 256, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 304 + ], + "type": "text", + "content": "discriminative representations, thereby enhancing differentiation within data [8, 19, 44]. This work distills knowledge from the intermediate-view images to enhance the sparse-view CT reconstruction." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 312, + 507, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 507, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 507, + 324 + ], + "type": "text", + "content": "2.3. Frequency Methods in Deep Learning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 330, + 546, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 546, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 546, + 641 + ], + "type": "text", + "content": "Frequency methods have been widely used in digital image processing and machine learning [2]. Wavelet convolution [32] and fast Fourier convolution [7] have been proposed to provide a larger/global receptive field, achieving great success in image restoration tasks [43]. Frequency methods have also yielded promising results in domain adaption and image translation, mainly by taking advantage of domain-invariant spectrum components [3, 18, 54-56]. Previous research also shows that particular features and details can be better extracted in the frequency domain, leading to improvements in camouflaged object detection [59], face forgery detection [21, 28], and face editing [9]. Frequency-based networks have also made notable strides in CT reconstruction. Previous studies [1, 26] employ multi-wavelet CNN [32] in both sinogram and image domain to suppress artifacts, substituting the pooling operator with wavelet transforms to achieve a larger receptive field. However, since both the Haar filter-based wavelet transform and convolution are applied on the spatial feature map, these methods struggle to capture global representation effectively. Recent research has demonstrated that employing convolution in the Fourier domain can efficiently eliminate the global artifacts [30, 34]. In this work, we utilize a frequency-based network for global representation learning, enhancing clinically critical features by band-pass-specific contrastive distillation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 651, + 361, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 361, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 361, + 662 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 670, + 417, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 417, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 417, + 682 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Assume we have a two-dimensional (2D) CT slice of size " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "N\\times N" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb {I}\\in \\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " , where each pixel contains the attenua" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21198" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": "tion coefficient of the corresponding human body. The raw data or sinogram from the CT scanning, " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{N_{\\mathrm{v}} \\times N_{\\mathrm{d}}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": ", can be obtained via the Radon transform [39], where " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": " denote the number of projection views and the number of the detectors, respectively. Inversely, the image reconstruction process can be expressed as " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "\\boldsymbol{I} = \\mathcal{R}^{-1}(\\boldsymbol{S})" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "\\mathcal{R}^{-1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": " denotes the inverse Radon transform such as FBP. Ideally, when " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": " is sufficiently large, FBP can produce pleasing image quality. However, when " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": " is fairly small, the image reconstruction of so-called sparse-view CT becomes an undetermined problem." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": "Here, we use " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{F}}" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": " to represent the reconstructed images from full view (i.e. ground-truth) and sparse view, respectively. The image-domain methods for sparse-view CT are to improve the image quality of " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": " towards " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{F}}" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": " through a neural network " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": ". That is, the output of the network, " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "\\widehat{I}_{\\mathrm{S}} = \\mathcal{F}(I_{\\mathrm{S}})" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": ", is expected to be of comparable quality to the full-view ground-truth. In addition, we also use the images, " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": ", reconstructed from an intermediate number of projection views that are between sparse and full views, as the teacher supervision, forming a student-teacher framework where the teacher encoder with " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": " supervises the training of student encoder with " + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 204, + 289, + 348 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 354, + 194, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 194, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 194, + 365 + ], + "type": "text", + "content": "3.2. Overview of Our GloReDi" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 372, + 289, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 289, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 289, + 516 + ], + "type": "text", + "content": "Fig. 2 presents the proposed GloReDi, which mainly consists of four parts: two encoders to learn global representations (GloRe) from sparse- and intermediate-view reconstructed images, " + }, + { + "bbox": [ + 46, + 372, + 289, + 516 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 372, + 289, + 516 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 372, + 289, + 516 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 46, + 372, + 289, + 516 + ], + "type": "text", + "content": ", respectively, and two decoders to produce the final processed images from GloRe. In addition to learning GloRe with Fourier convolution, we have two novel modules to perform distillation from the teacher network: (1) representation directional distillation to align the directions between the student and teacher GloRes; and (2) band-pass-specific contrastive distillation to distill the clinically important features for better detail recovery." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 516, + 261, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 516, + 261, + 528 + ], + "spans": [ + { + "bbox": [ + 59, + 516, + 261, + 528 + ], + "type": "text", + "content": "Next, we detail each of the proposed components." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 534, + 222, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 222, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 222, + 548 + ], + "type": "text", + "content": "3.3. Global Representation Learning" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 553, + 287, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 648 + ], + "type": "text", + "content": "The key technique behind the proposed network is the global representation learning with fast Fourier convolution (FFC) [7]. Concretely, FFC first applies real Fourier transform to get the frequency feature map and then performs convolution on frequency components before finally back transforming the frequency features as shown in Fig. 2. Therefore, GloRe from sparse-view images " + }, + { + "bbox": [ + 46, + 553, + 287, + 648 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 553, + 287, + 648 + ], + "type": "text", + "content": " is learned by a Fourier-based encoder network as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 118, + 656, + 287, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 656, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 118, + 656, + 287, + 669 + ], + "type": "interline_equation", + "content": "\\boldsymbol {Z} _ {\\mathrm {S}} = \\operatorname {e n c o d e r S} (\\boldsymbol {I} _ {\\mathrm {S}}), \\tag {1}", + "image_path": "8a8e8e3672529d87197bb5e60b3dcdde093d919a6de225069464a9629792f0c2.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{S}} \\in \\mathbb{R}^{N_{\\mathrm{w}} \\times N_{\\mathrm{h}} \\times N_{\\mathrm{c}}}" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": " denotes GloRe extracted from the sparse-view reconstructed image " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": " through the (student) encoder encoderS and " + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{w}} \\times N_{\\mathrm{h}} \\times N_{\\mathrm{c}}" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": " denotes the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "width, height, and channel size of GloRe. Compared to the vanilla convolution with a limited receptive field, FFC works in the frequency domain, so each element in GloRe contains global information of the sparse-view image by using an image-wide receptive field, representing patterns of artifacts and the image contents simultaneously. Furthermore, such global nature can aid in modeling the artifact and information distributed throughout the image while easing the alignment between GloRe of different views." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 186, + 489, + 199 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 186, + 489, + 199 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 489, + 199 + ], + "type": "text", + "content": "3.4. Global Representation Distillation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "text", + "content": "In the context of sparse-view CT, images with an intermediate view " + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "text", + "content": " can be easily obtained from the full-view sinogram as extra supervision. To get the teacher representation from " + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "text", + "content": ", a parallel teacher encoder encoderT, using the same architecture as encoderS but with different weights, takes " + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "text", + "content": " as input and yields teacher GloRe " + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "text", + "content": " of the same shape with " + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 205, + 547, + 289 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 375, + 297, + 545, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 297, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 375, + 297, + 545, + 308 + ], + "type": "interline_equation", + "content": "\\boldsymbol {Z} _ {\\mathrm {T}} = \\operatorname {e n c o d e r} \\mathrm {T} \\left(\\boldsymbol {I} _ {\\mathrm {T}}\\right). \\tag {2}", + "image_path": "9d305140b6078ab93f48318fdf1ac605fbd0f0a576a0cc5353c82dfd8f82ddb4.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "text", + "content": " can be regarded as a high-quality pseudo target for student GloRe in the same latent space since richer information can be extracted from " + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "text", + "content": ". Exploring distillation from " + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "text", + "content": " is obviously easier than that of " + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{F}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "text", + "content": " given the significant gap between " + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{F}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 375 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "text", + "content": "Intuitively, " + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "text", + "content": " should be similar to " + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "text", + "content": " if the artifact-free target information is precisely encoded. Therefore, a natural way for distillation is to use " + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "text", + "content": " as the supervision for " + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "text", + "content": " by minimizing their Euclidean distance. However, this could harm the reconstruction performance since the student encoder has to partially recover " + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "text", + "content": ". Finding an effective solution to distilling the information in " + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 376, + 546, + 532 + ], + "type": "text", + "content": " for sparse-view CT reconstruction is one of the highlights in this work. Our idea is to separate the distillation process. First, we present representation directional distillation to align the representation directions so the images of different views are along the same direction. Second, we propose a band-pass-specific contrastive distillation to enhance clinically critical details." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 532, + 534, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 532, + 534, + 544 + ], + "spans": [ + { + "bbox": [ + 318, + 532, + 534, + 544 + ], + "type": "text", + "content": "We detail these two distillation techniques as follows." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 558, + 504, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 504, + 570 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 504, + 570 + ], + "type": "text", + "content": "3.4.1 Representation Directional Distillation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "text", + "content": "Given that " + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "text", + "content": " share the same ground truth " + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{F}}" + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "text", + "content": ", but differ mainly in artifact patterns, student and teacher GloRe should at least demonstrate a consistent direction for reconstruction with high confidence. Therefore, We define the directional distillation loss for " + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 576, + 545, + 636 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 314, + 641, + 545, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 641, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 314, + 641, + 545, + 671 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r d d}} = \\frac {1}{N _ {\\mathrm {w}} N _ {\\mathrm {h}}} \\sum_ {i, j} \\left(1 - \\operatorname {C o s S i m} \\left(\\left[ \\mathbf {Z} _ {\\mathrm {S}} \\right] _ {i, j}, \\left[ \\mathbf {Z} _ {\\mathrm {T}} \\right] _ {i, j}\\right)\\right), \\tag {3}", + "image_path": "a2ca9e2449ba44095e748d59172c8ad2df3226fda5635c896d7668c92a595c68.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\operatorname{CosSim}" + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": " denotes the cosine similarity, defined as " + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\operatorname{CosSim}(\\mathbf{a},\\mathbf{b}) = \\mathbf{a}^{\\mathrm{T}}\\mathbf{b} / \\max (\\|\\mathbf{a}\\|_2\\|\\mathbf{b}\\|_2,\\epsilon)" + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": " set to " + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "1\\times 10^{-8}" + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": " to avoid division by zero." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21199" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 178 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 178 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 178 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 178 + ], + "type": "image", + "image_path": "f009c71cebac14b4dc2b7355b8a2dc1c82e95cdd82450d3609d7b02df326d2b0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 192, + 289, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 270 + ], + "type": "text", + "content": "Figure 3. The difference between representation distillation (left) and band-pass-specific contrastive distillation (right). Global representation distillation fails to distinguish clinical details due to high similarity among similar body parts, e.g., adjacent lung slices. Band-pass-specific contrastive distillation further projects the representation to the DCT domain, enabling distillation of specific clinical details on corresponding DCT components." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 292, + 263, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 292, + 263, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 292, + 263, + 304 + ], + "type": "text", + "content": "3.4.2 Band-Pass-Specific Contrastive Distillation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": "The directional distillation aligns the directions of student representation " + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": " and the teacher representation " + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{T}}" + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": " in the view-independent space, which, however, does not guarantee a high-quality reconstruction of the image. What distinguishes sparse-view CT reconstruction task from classic image restoration one (e.g. denoising, deraining, etc.) is that the former is more demanding in terms of fine-grained details for diseases identification, organs delineation, and low-contrast lesions detection, etc [11]. In other words, it places more emphasis on learning the image-specific representation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 445, + 288, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 288, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 288, + 673 + ], + "type": "text", + "content": "Contrastive representation learning, as a self-supervised approach, encourages the model to maximize the difference among representations of different samples so that model can emphasize those category-specific representations. However, directly implementing these losses would lead to imprecise reconstruction results because most CT images are inherently similar in intensity distribution, especially for images of the same body parts, as shown in Fig. 3. Recent methods have achieved great success learning on specific DCT spectrum [18, 50, 54], due to its strong energy compaction property, making it simple to select specific frequency components [40]. Therefore, we distilled the image-specific details by applying contrastive distillation on specific discrete cosine transform (DCT) spectrums. On the one hand, detailed knowledge can be better distilled from specific frequency components of teacher GloRe. On the other hand, contrastive against different CT slices can further enhance image-specific details on corresponding DCT components." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Discrete cosine transform. Discrete cosine transform (DCT) is widely used for data compression in low-frequency components. The basis function of 2D DCT is" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 384, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 384, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 384, + 83 + ], + "type": "text", + "content": "defined as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 330, + 89, + 547, + 111 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 89, + 547, + 111 + ], + "spans": [ + { + "bbox": [ + 330, + 89, + 547, + 111 + ], + "type": "interline_equation", + "content": "B _ {w, h} ^ {i, j} = \\cos \\left(\\frac {\\pi w}{N _ {\\mathrm {w}}} \\left(i + \\frac {1}{2}\\right)\\right) \\cos \\left(\\frac {\\pi h}{N _ {\\mathrm {h}}} \\left(j + \\frac {1}{2}\\right)\\right), \\quad (4)", + "image_path": "547d1321086295773a86a14d219860d089aef50be306c2bacb5f95eef3c60b69.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "spans": [ + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{w}}" + }, + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{h}}" + }, + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "text", + "content": " represent the width and height of the input, respectively. Then, 2D DCT of the latent feature " + }, + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}" + }, + { + "bbox": [ + 305, + 117, + 547, + 152 + ], + "type": "text", + "content": " can be written as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 339, + 159, + 546, + 182 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 159, + 546, + 182 + ], + "spans": [ + { + "bbox": [ + 339, + 159, + 546, + 182 + ], + "type": "interline_equation", + "content": "f _ {w, h} (\\boldsymbol {Z}) = \\sum_ {i = 0} ^ {N _ {\\mathrm {w}} - 1} \\sum_ {j = 0} ^ {N _ {\\mathrm {h}} - 1} [ \\boldsymbol {Z} ] _ {i, j} B _ {w, h} ^ {i, j}, \\tag {5}", + "image_path": "784241c22dcdcdb4c061dabcd612c8f66957c03d2a355b9c0e1bdf5acc022c23.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "spans": [ + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "inline_equation", + "content": "w\\in \\{0,1,\\ldots ,N_{\\mathrm{w}} - 1\\} ,h\\in \\{0,1,\\ldots ,N_{\\mathrm{h}} - 1\\}" + }, + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "text", + "content": " The " + }, + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "inline_equation", + "content": "f(\\pmb {Z})\\in \\mathbb{R}^{N_{\\mathrm{w}}\\times N_{\\mathrm{h}}}" + }, + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "text", + "content": " represents the 2D DCT frequency spectrum of " + }, + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "inline_equation", + "content": "\\pmb{Z}" + }, + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "text", + "content": " . Thus, frequency components can be easily selected by a mask " + }, + { + "bbox": [ + 305, + 189, + 546, + 238 + ], + "type": "inline_equation", + "content": "M\\in \\{0,1\\}^{N_{\\mathrm{w}}\\times N_{\\mathrm{h}}}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 240, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 240, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 545, + 361 + ], + "type": "text", + "content": "Band-pass-specific contrastive distillation. Crucially, the low-frequency components of GloRe contribute most to the reconstruction accuracy, while high-frequency may contain inherent noise and artifacts of CT images. We therefore use a band-pass supervised contrastive loss for the distillation, where a band-pass mask " + }, + { + "bbox": [ + 305, + 240, + 545, + 361 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 240, + 545, + 361 + ], + "type": "text", + "content": " is incorporated to filter out the mid-frequency part in the frequency domain, containing main structure as well as the necessary detail information. The proposed band-pass supervised contrastive loss can be written as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 343, + 369, + 545, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 369, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 343, + 369, + 545, + 383 + ], + "type": "interline_equation", + "content": "\\boldsymbol {z} = \\text {f l a t t e n} \\left(\\operatorname {c r o p} \\left(f _ {w, h} (\\boldsymbol {Z}), \\boldsymbol {M}\\right)\\right), \\tag {6}", + "image_path": "9762a00f410f833b63347e03124bbbd1bed05ad52eb23cdaafe2ebe796334bc9.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 391, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 391, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 391, + 545, + 426 + ], + "type": "text", + "content": "where crop operator will keep the value at locations where " + }, + { + "bbox": [ + 305, + 391, + 545, + 426 + ], + "type": "inline_equation", + "content": "M = 1" + }, + { + "bbox": [ + 305, + 391, + 545, + 426 + ], + "type": "text", + "content": " while the flatten operator flattens the 2D spectrum map into 1D representation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 427, + 546, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 427, + 546, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 427, + 546, + 546 + ], + "type": "text", + "content": "It is to be observed that the clinical details in the CT images vary from case by case and are each very critical for diagnosis, requiring more sophisticated instance-level distinction. To this end, we consider all representations from different CT slices as negative samples to maximize image-specific features while updating the memory bank " + }, + { + "bbox": [ + 304, + 427, + 546, + 546 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 427, + 546, + 546 + ], + "type": "text", + "content": " with the widely applied First-In-First-Out mechanism per iteration from the previous mini-batches. The proposed band-pass-specific contrastive distillation loss for sample " + }, + { + "bbox": [ + 304, + 427, + 546, + 546 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 427, + 546, + 546 + ], + "type": "text", + "content": " can be written as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 552, + 545, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 552, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 350, + 552, + 545, + 583 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {b c d}} = - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {\\mathrm {S}} ^ {\\mathrm {T}} \\boldsymbol {z} _ {\\mathrm {T}} / \\tau\\right)}{\\sum_ {\\boldsymbol {z} \\in \\mathcal {M}} \\exp \\left(\\boldsymbol {z} _ {\\mathrm {S}} ^ {\\mathrm {T}} \\boldsymbol {z} / \\tau\\right)}, \\tag {7}", + "image_path": "36d4e3c8bf7d3b5753b4bbe0be8aa5b1128153370dcf39090095fd610370c1ce.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{S}}, z_{\\mathrm{T}}" + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "text", + "content": " are frequency representations of " + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{S}}, Z_{\\mathrm{T}}" + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "text", + "content": ", and negative samples from memory bank " + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{mem}}" + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 588, + 545, + 637 + ], + "type": "text", + "content": " is the temperature term used to adjust the sensitivity of negative samples." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 643, + 509, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 643, + 509, + 657 + ], + "spans": [ + { + "bbox": [ + 306, + 643, + 509, + 657 + ], + "type": "text", + "content": "3.5. Loss Function and Training Procedure" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": "Teacher reconstruction. To constrain the GloRe extracted from " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " in the same latent space, a naive solution is to share the same decoder in the training phase, which, however, brings instability. Therefore, we adopt the widely" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21200" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 48, + 85, + 287, + 230 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 236, + 83 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 236, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 236, + 83 + ], + "type": "text", + "content": "Algorithm 1 The training process of GloReDi." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "lines": [ + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "spans": [ + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "text", + "content": "Require: encoderS, encoderT, decoderS, decoderT; Input images: " + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{S}}, I_{\\mathrm{T}}, I_{\\mathrm{F}}" + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "text", + "content": "; momentum " + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "text", + "content": " and Memory bank \n1: for iter = 0 to Max_Iter do \n2: Update decoderT using Eq. (8) \n3: " + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "inline_equation", + "content": "\\widehat{I}_{\\mathrm{T}}, Z_{\\mathrm{T}} = \\text{decoderT}(\\text{encoderT}(I_{\\mathrm{T}}))" + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "text", + "content": " \n4: Optimize encoderT using Eq. (9) \n5: " + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "inline_equation", + "content": "\\widehat{I}_{\\mathrm{S}}, Z_{\\mathrm{S}} = \\text{decoderS}(\\text{encoderS}(I_{\\mathrm{S}}))" + }, + { + "bbox": [ + 48, + 85, + 287, + 230 + ], + "type": "text", + "content": " \n6: Optimize encoderS+decoderS using Eq. (11) \n7: Update memory bank \n8: end for \nReturn: encoderS+ decoderS" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 251, + 287, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 287, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 287, + 288 + ], + "type": "text", + "content": "used Exponential Moving Average (EMA) with momentum " + }, + { + "bbox": [ + 47, + 251, + 287, + 288 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 251, + 287, + 288 + ], + "type": "text", + "content": " to update the parameters " + }, + { + "bbox": [ + 47, + 251, + 287, + 288 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 251, + 287, + 288 + ], + "type": "text", + "content": " of the teacher decoder by the student decoder [13]:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 298, + 287, + 310 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 298, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 71, + 298, + 287, + 310 + ], + "type": "interline_equation", + "content": "\\theta_ {\\text {d e c o d e r T}} = m \\theta_ {\\text {d e c o d e r T}} + (1 - m) \\theta_ {\\text {d e c o d e r S}}. \\tag {8}", + "image_path": "618c828d826840fade60015cf3a24d2c9d75480812c85a8189dc81732656f88d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "text", + "content": "Then, the global representation " + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "inline_equation", + "content": "Z_{\\mathrm{T}}" + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "text", + "content": " learned by the teacher is fed into to the decoder to obtain the teacher reconstruction result " + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\widehat{I}_{\\mathrm{T}}" + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "text", + "content": ", and we use " + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "text", + "content": " loss to measure the pixel-wise difference between " + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "inline_equation", + "content": "\\widehat{I}_{\\mathrm{T}}" + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "text", + "content": " and the full-view ground-truth " + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{F}}" + }, + { + "bbox": [ + 47, + 320, + 287, + 379 + ], + "type": "text", + "content": " and train the teacher:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 88, + 389, + 287, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 389, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 88, + 389, + 287, + 403 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p i x e l T}} = \\left\\| \\operatorname {d e c o d e r T} \\left(\\boldsymbol {Z} _ {\\mathrm {T}}\\right) - \\boldsymbol {I} _ {\\mathrm {F}} \\right\\| _ {1}. \\tag {9}", + "image_path": "eb51e533408b79e61d7a795b1ce5a5c47368253ab264fbcef09e01e6bf996d39.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 416, + 287, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 287, + 440 + ], + "type": "text", + "content": "Student reconstruction. The pixel-wise error measurement for the student is defined in a similar way:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 90, + 449, + 287, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 449, + 287, + 463 + ], + "spans": [ + { + "bbox": [ + 90, + 449, + 287, + 463 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p i x e l S}} = \\left\\| \\operatorname {d e c o d e r S} \\left(\\boldsymbol {Z} _ {\\mathrm {S}}\\right) - \\boldsymbol {I} _ {\\mathrm {F}} \\right\\| _ {1}. \\tag {10}", + "image_path": "f799207f25cc7e3d7440ae473dc1703ae6144405305af112bb1ace2fce3aa8f4.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 472, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 287, + 521 + ], + "type": "text", + "content": "Finally, a compound loss function combining pixel-wise error and two distillation losses, respectively defined in Eq. (3) and Eq. (7) is introduced for student network training to achieve high-quality sparse-view CT reconstruction:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 95, + 542, + 287, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 542, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 95, + 542, + 287, + 555 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {S t u}} = \\mathcal {L} _ {\\mathrm {p i x e l S}} + \\alpha \\mathcal {L} _ {\\mathrm {r d d}} + \\beta \\mathcal {L} _ {\\mathrm {b c d}}, \\tag {11}", + "image_path": "7e718a5beaaac2c3a62d42b0f93b993610b9574d9c04da988952181dbd708b0e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 564, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 564, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 564, + 287, + 601 + ], + "type": "text", + "content": "GloReDi is trained following the process summarized in Algorithm 1, where the student and teacher encoder are trained iteratively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 612, + 172, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 612, + 172, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 612, + 172, + 624 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 632, + 163, + 644 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 632, + 163, + 644 + ], + "spans": [ + { + "bbox": [ + 47, + 632, + 163, + 644 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 712 + ], + "type": "text", + "content": "Dataset. We use DeepLesion dataset [53] and \"2016 NIH-AAPM-Mayo Clinic Low-Dose CT Grand Challenge\" AAPM dataset [35] to demonstrate the effectiveness of the proposed GloReDi. The DeepLesion dataset is the largest multi-lesion real-world CT dataset made available to the" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": "public, from which 40,000 images of 303 patients are selected as the training set while 1000 images of another 18 patients are selected as the test set. AAPM dataset contains routine dose CT data from 10 patients, where a total of 5,410 slices from 9 patients are chosen for training and 526 slices from the remaining 1 patient for testing. All images are resized to " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": ". We simulate the forward and back projection using fan-beam geometry under " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "120\\mathrm{kVp}" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "500\\mathrm{mA}" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " with TorchRadon toolbox [42]. The distance from X-ray source to the rotation center is " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "59.5\\mathrm{cm}" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": ", and the number of detectors is set to 672. Sparse-view CT images are generated from " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18,36,72,144" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " projection views uniformly sampled from full 720 views covering " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "[0,2\\pi]" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": ". To simulate the photon noise presented in real-world CT, an intensity of " + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "inline_equation", + "content": "1 \\times 10^{6}" + }, + { + "bbox": [ + 304, + 72, + 545, + 252 + ], + "type": "text", + "content": " Poisson noise is added to the sinograms." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": "Implementation details. Our model is implemented in PyTorch. We use Adam optimizer [24] with " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "(\\beta_{1},\\beta_{2}) = (0.5,0.999)" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " to train the model. The learning rate starts from " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "1\\times 10^{-3}" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " and is halved for every 40 epochs. For each method, four models of different " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}}" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " are trained separately on 4 NVIDIA RTX 3090 GPUs for 120 epochs with a batch size of 8. For hyperparameters in GloReDi, we set " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " in Eq. (11) empirically to 0.1 and 0.0002 to fit the scale between losses. The momentum " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " and temperature " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " are set to 0.9 and 1.0, respectively, while the size " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " of the memory bank is set to 300 to balance the performance and computational cost. We set intermediate-view as " + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}}\\times 2" + }, + { + "bbox": [ + 304, + 255, + 545, + 424 + ], + "type": "text", + "content": " by default. More details, including the network architecture, can be found in the Supplementary Material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 428, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 545, + 475 + ], + "type": "text", + "content": "Evaluation metrics. For quantitative evaluation, we use peak signal-to-noise ratio (PSNR), structural similarity (SSIM) [60] and root mean square error (RMSE); all of them are widely adopted for image quality assessment." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 486, + 531, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 531, + 499 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 531, + 499 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-Art Methods" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "content": "We compare GloReDi with the following state-of-the-art methods: DDNet [58], FBPCovNet [22], DuDoNet [31], DDPTrans [29], and DuDoTrans [46]. In addition, we name the network without the distillation from " + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{T}}" + }, + { + "bbox": [ + 304, + 506, + 545, + 696 + ], + "type": "text", + "content": " as the frequency encoder and decoder network (Fred-Net), optimized with only the pixel-wise loss in Eq. (10). FBP directly applies Radon transform to reconstruct the image from the sparse-view sinogram. DDNet and FBPCovNet are image-domain deep-learning methods taking FBP results as input. DuDoNet is a state-of-the-art dual-domain method that restores the CT image using two U-Nets in sinogram and image domains. Furthermore, DDPTrans and DuDoTrans adopt Transformer on both domains to restore the image by utilizing the long-range dependency. We try our best to reproduce these methods and then train and test them on the same dataset for a fair comparison." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Quantitative comparison. Table 1 presents the quantita" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21201" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 69, + 547, + 183 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 547, + 183 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 547, + 183 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 547, + 183 + ], + "type": "table", + "html": "
Methods\\(N_{\\mathrm{v}}=18\\)\\(N_{\\mathrm{v}}=36\\)\\(N_{\\mathrm{v}}=72\\)\\(N_{\\mathrm{v}}=144\\)
PSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSE
FBP22.2235.360.079525.4947.490.054330.8863.810.029337.1282.940.0144
DDNet [58]34.5791.940.018738.2494.910.012641.6697.270.008346.7598.790.0048
FBPCovNet [22]35.9593.620.016439.7996.130.010643.7697.470.006648.4698.600.0039
DuDoNet [31]35.6993.960.016940.3696.940.010344.8698.390.005949.3399.230.0036
DDPTRans [29]35.1193.480.018138.6895.990.012143.5698.160.006948.7299.220.0038
DuDoTrans [46]36.0893.280.016140.7596.670.009545.1698.440.005749.9699.280.0034
Fred-Net (ours)38.0895.200.012940.8696.810.009344.4398.180.006348.4599.080.0039
GloReDi (ours)38.6595.870.012041.2597.050.009045.1898.430.005748.9699.210.0037
", + "image_path": "23081cb199a5ac3c80912953a6229b4339a42f1dc2c6a7da64a4ed434a4a2a33.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 78, + 186, + 514, + 198 + ], + "lines": [ + { + "bbox": [ + 78, + 186, + 514, + 198 + ], + "spans": [ + { + "bbox": [ + 78, + 186, + 514, + 198 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation [PSNR (db), SSIM (%) and RMSE] for state-of-the-art methods on DeepLesion dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 48, + 208, + 545, + 407 + ], + "blocks": [ + { + "bbox": [ + 48, + 208, + 545, + 407 + ], + "lines": [ + { + "bbox": [ + 48, + 208, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 48, + 208, + 545, + 407 + ], + "type": "image", + "image_path": "5ed20eca4f47123ee893b8a48a6c3f78d989483843ffcf29a1d59afd80dac083.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 411, + 546, + 444 + ], + "lines": [ + { + "bbox": [ + 46, + 411, + 546, + 444 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 546, + 444 + ], + "type": "text", + "content": "Figure 4. Visual comparison of state-of-the-art methods on DeepLesion dataset: (a) Ground Truth, (b) FBP, (c) DDNet, (d) FBPCovNet, (e) DuDoNet, (f) DDPTrans, (g) DuDoTrans, and (h) GloReDi. From top to bottom: the results under " + }, + { + "bbox": [ + 46, + 411, + 546, + 444 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 411, + 546, + 444 + ], + "type": "text", + "content": ", 36, 72; display window is set to [-1000, 2000] HU for the first two rows and [-200, 300] HU for the third row." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "text", + "content": "tive comparison. Generally, dual-domain methods perform better than single-domain methods, especially in the case of " + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 72" + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "text", + "content": ", 144 thanks to the sinogram inpainting network. However, we highlight in ultra sparse-view scenarios where " + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "text", + "content": ", that dual-domain methods like DuDoNet perform worse than classical image-domain-only methods such as FBPCovNet. This can be attributed to the secondary artifacts introduced by the unsuccessful sinogram inpainting; e.g., when " + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "text", + "content": " in our setting, restoring the sinogram can be recognized as a " + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "inline_equation", + "content": "40 \\times" + }, + { + "bbox": [ + 46, + 463, + 289, + 643 + ], + "type": "text", + "content": " super-resolution task, which is rather challenging. DuDoTrans is superior to DuDoNet to some extent, indicating the importance of long-range dependency in reconstruction. DDPTrans fails to surpass DuDoNet because of the limited parameter number though most transformers are memory-consuming." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "Compared with the previous works, the proposed GloReDi achieves competitive results by learning to distill GloRe for high-quality reconstruction. Particularly in ultrasparse scenarios, e.g., when " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": ", GloReDi has 2.57db and 2.70db improvement on PSNR over DuDoTrans and" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 463, + 545, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 463, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 304, + 463, + 545, + 584 + ], + "type": "text", + "content": "FBPCovNet, respectively. As " + }, + { + "bbox": [ + 304, + 463, + 545, + 584 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}}" + }, + { + "bbox": [ + 304, + 463, + 545, + 584 + ], + "type": "text", + "content": " increases, the advantage of GloReDi decreases, mainly due to a shift towards artifacts removal tasks rather than reconstruction. We highlight that the fewer projection views indicate less radiation dose and more speedup. We notice that global representation distillation further improves the performance of GloReDi from 0.51db to 0.89db compared to Fred-Net. The results show that the proposed GloReDi successfully inspire the potential of image post-processing methods and is significantly superior to the state-of-the-art methods under various settings." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 594, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 715 + ], + "type": "text", + "content": "Visual comparison. Fig. 4 presents the visualization results of three sparse-view CT. DDNet and FBPCovNet cannot remove the artifact thoroughly, while the reconstruction results are over-smooth in the boundary of organs and bones. Such effects can be easily observed in the second row of Figs. 4(c) and 4(d) on the spine where the anatomical structure is complicated. Although dual-domain methods perform better in general, their accuracy in details is even worse than FBPCovNet in comparison with Figs. 4(d) and 4(e)-(g). Among all these methods, Glo" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21202" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 69, + 547, + 185 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 547, + 185 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 547, + 185 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 547, + 185 + ], + "type": "table", + "html": "
Methods\\(N_{\\mathrm{v}}=18\\)\\(N_{\\mathrm{v}}=36\\)\\(N_{\\mathrm{v}}=72\\)\\(N_{\\mathrm{v}}=144\\)
PSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSEPSNRSSIMRMSE
FBP22.7335.060.073226.2747.520.048631.3664.560.027037.8584.570.0128
DDNet [58]34.2989.680.019436.9593.030.014240.4196.040.009644.3598.050.0061
FBPCovNet [22]35.7392.840.016537.9593.730.012742.9297.190.007247.3598.760.0043
DuDoNet [31]34.8293.000.019639.8995.990.010244.0698.020.006248.3999.110.0038
DDPTRans [29]34.4791.950.019138.1394.830.012542.7797.650.007347.8499.060.0041
DuDoTrans [46]35.8593.070.016240.0496.020.010044.2098.070.006249.0299.210.0036
Fred-Net (ours)37.2093.900.014041.4696.840.008543.6497.840.006647.5099.030.0042
GloReDi (ours)37.9194.580.012841.5796.700.008444.2498.030.006248.1099.080.0040
", + "image_path": "b3073c8f663b5ec5305221ae4fd8cbd9a9f753ed2502a07b05d39ffca260deed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 202, + 545, + 339 + ], + "blocks": [ + { + "bbox": [ + 48, + 202, + 545, + 339 + ], + "lines": [ + { + "bbox": [ + 48, + 202, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 48, + 202, + 545, + 339 + ], + "type": "image", + "image_path": "1226c91ee7a8df6895ef469430ee3aad5f89e3550f68f6e71526642aecc97c42.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 342, + 546, + 366 + ], + "lines": [ + { + "bbox": [ + 46, + 342, + 546, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 546, + 366 + ], + "type": "text", + "content": "Figure 5. Visual comparison of state-of-the-art methods on AAPM dataset: (a) Ground Truth, (b) FBP, (c) DDNet, (d) FBPCovNet, (e) DuDoNet, (f) DDPTrans, (g) DuDoTrans, and (h) GloReDi. From top to bottom: " + }, + { + "bbox": [ + 46, + 342, + 546, + 366 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 342, + 546, + 366 + ], + "type": "text", + "content": ", 36; the display window is [-1000, 2000] HU." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 380, + 287, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 428 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 428 + ], + "type": "text", + "content": "ReDi best reconstructs the structures and details, especially in ultra-sparse scenarios. In the first two rows of Fig. 4(h), only GloReDi precisely recovers those clinically important details such as soft tissue and corrupted pulmonary alveoli." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 437, + 141, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 141, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 141, + 451 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "type": "text", + "content": "We first evaluate the effectiveness of each component in GloReDi. We use Fred-Net as the baseline to add components. The configurations involved in Table 3 are mainly four groups: (1) the baseline Fred-Net using pixel-wise loss to train student model without distillation components (a); (2) the baseline without Fourier convolutions " + }, + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "type": "inline_equation", + "content": "(\\mathbf{b} - \\mathbf{c})" + }, + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "type": "text", + "content": "; (3) the baseline with distillation from intermediate-view reconstructed images " + }, + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "type": "inline_equation", + "content": "(\\mathbf{d} - \\mathbf{g})" + }, + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "type": "text", + "content": "; and (4) the dual-domain version with raw data processed by sinogram-domain sub-network of DuDoNet [31] " + }, + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "type": "inline_equation", + "content": "(\\mathbf{h})" + }, + { + "bbox": [ + 46, + 457, + 287, + 589 + ], + "type": "text", + "content": ". Unless noted otherwise, the pixelwise loss is involved in training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Ablations on global representations. The results between a) and b) in Table 3 confirm that learning global representations with the image-wide receptive field by Fourier convolution is beneficial for sparse CT reconstruction. Also, we notice that in Tables 1 and 2, our baseline Fred-Net still outperforms state-of-the-art methods when " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " and 36. Interestingly, we found that c) performs even worse than b) in Table 3. This suggests that global representation is essential for bridging the gap between images of different views. Generally, learning global representations is pow" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 324, + 377, + 526, + 479 + ], + "blocks": [ + { + "bbox": [ + 67, + 186, + 523, + 198 + ], + "lines": [ + { + "bbox": [ + 67, + 186, + 523, + 198 + ], + "spans": [ + { + "bbox": [ + 67, + 186, + 523, + 198 + ], + "type": "text", + "content": "Table 2. Quantitative evaluation [PSNR (db), SSIM (%) and RMSE] for state-of-the-art methods transferred to AAPM dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 324, + 377, + 526, + 479 + ], + "lines": [ + { + "bbox": [ + 324, + 377, + 526, + 479 + ], + "spans": [ + { + "bbox": [ + 324, + 377, + 526, + 479 + ], + "type": "table", + "html": "
config.PSNR
a)Fred-Net38.09
b)Fred-Net w/o Fourier36.52
c)Fred-Net w/o Fourier + Lrdd + Lbcd36.30
d)Fred-Net + data augmentation34.41
e)Fred-Net + Lrdd38.39
f)Fred-Net + Lbcd38.42
g)Fred-Net + Lrdd + Lbcd = GloReDi38.65
h)Fred-Net + raw data38.44
", + "image_path": "97716c31ccd9ce2eae2413f816db9e7c652eae209d897942f3152d0a70664f1d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 479, + 520, + 489 + ], + "lines": [ + { + "bbox": [ + 306, + 479, + 520, + 489 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 520, + 489 + ], + "type": "text", + "content": "Table 3. Quantitative evaluation of different configurations." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 506, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 543 + ], + "type": "text", + "content": "erful and provides a new perspective for sparse-view CT reconstruction, which also answers that the limit of image post-processing methods is still far beyond reach." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": "Ablations on global representation distillation. Through a comparison between Fred-Net and the one trained with intermediate-view images as data augmentation (a vs. d) in Table 3, we found that directly applying data augmentation had a negative impact, resulting in a 3.67db PSNR drop. This indicates that the network failed to benefit from denser-view images directly because of the significant domain gap among images of different views. By comparing a), e) and f) in Table 3, we can see that both e) representation directional distillation and f) band-pass-specific contrastive distillation can improve the performance of a), showing that end-to-end supervision cannot thoroughly unlock the potential of the GloRe. By training with both distillation loss, g) further boosts the performance and outperforms all other" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21203" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 70, + 266, + 104 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 266, + 104 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 266, + 104 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 266, + 104 + ], + "type": "table", + "html": "
config.Nv×2Nv×3Nv×4720
Nv=1838.3838.2938.2838.02
Nv=7244.8444.4644.7244.38
", + "image_path": "89e688447428635419147dadbe15aca227a33c45bb68482aa1ca749b17bdbf26.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 105, + 287, + 148 + ], + "lines": [ + { + "bbox": [ + 47, + 105, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 287, + 148 + ], + "type": "text", + "content": "Table 4. PSNR evaluation of GloReDi trained with different intermediate-view images for 60 epochs. The first and second rows show the results of sparse-view images with " + }, + { + "bbox": [ + 47, + 105, + 287, + 148 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 47, + 105, + 287, + 148 + ], + "type": "text", + "content": ", 72 distilled from images of " + }, + { + "bbox": [ + 47, + 105, + 287, + 148 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} \\times 2" + }, + { + "bbox": [ + 47, + 105, + 287, + 148 + ], + "type": "text", + "content": ", 3, 4 and 720 (full view), respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 172, + 286, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 172, + 286, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 172, + 286, + 232 + ], + "type": "text", + "content": "configurations. By comparing a), g) and h), we found unsurprisingly that using raw data does improve the performance of the image-domain network. However, our method GloReDi yields even better performance by effectively distilling GloRe from intermediate-view image data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 237, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 287, + 392 + ], + "type": "text", + "content": "Ablations on intermediate views for distillation. Selecting a suitable intermediate view for distillation is crucial in realizing the full potential of GloReDi. Images reconstructed from a denser view can provide richer information to the teacher GloRe while introducing a more significant domain gap. As presented in Table 4, we found that models distilled from " + }, + { + "bbox": [ + 46, + 237, + 287, + 392 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} \\times 2" + }, + { + "bbox": [ + 46, + 237, + 287, + 392 + ], + "type": "text", + "content": " views exhibit the best performance. Interestingly, models distilled from the full-view image yield the worst performance, primarily because of the considerable domain gap between the input data. Please refer to Supplementary Material for more ablation studies on framework designs, configurations of residual blocks, and distillation loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 406, + 191, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 191, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 191, + 418 + ], + "type": "text", + "content": "4.4. Transfer to Other Dataset" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "content": "To test the generalizability and robustness of GloReDi along with other state-of-the-art methods, we finetune each model for another ten epochs on AAPM dataset to bridge the domain gap following the same setting. In Table 2, the proposed GloReDi shows excellent transferability over all other state-of-the-art methods in (ultra) sparse-view scenarios (" + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18,36,72" + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "content": ") and still achieves performance comparable with the dual-domain methods when " + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 72" + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "content": ". Specifically, when " + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "content": ", we notice GloReDi has 2.06db and 2.18db improvements on PSNR compared to DuDoTrans and FBPCovNet, respectively, indicating that our method is significantly superior in ultra sparse-view scenarios. Fig. 5 shows images with " + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "content": " and 36, which are corrupted severely by FBP as shown in Fig. 5(b), thus losing its clinical value. Previous image-domain methods remove the artifact to some extent but lose most of the details, as shown in Figs. 5(c) and (d). Although the state-of-the-art dual-domain methods gain better results in general, we notice that clinical details such as lesion and bone, as pointed out by the blue arrows, are not accurately reconstructed in Figs. 5(e)-(g) while severe secondary artifacts are introduced, especially when " + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}} = 18" + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "content": ". In contrast, the proposed GloReDi excels at reconstructing the details and greatly improves the clinical value of sparse-view CT." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 71, + 457, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 457, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 457, + 84 + ], + "type": "text", + "content": "5. Discussion and Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 103, + 545, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 103, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 103, + 545, + 212 + ], + "type": "text", + "content": "In this paper, we challenge the sparse-view CT reconstruction in the absence of sinogram data and demonstrate that, with appropriate design, the image post-processing method can outperform the state-of-the-art dual-domain method. We propose to learn GloRe with Fourier convolution for image-wide receptive field and present directional and band-pass-specific contrastive distillation for high-quality reconstruction. Our method is particularly advantageous in ultra-sparse scenarios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 223, + 546, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 546, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 546, + 390 + ], + "type": "text", + "content": "We emphasize that our contributions can be easily extended to dual-domain methods when sinogram data are available. On the one hand, learning to distill GloRe can also benefit the image-domain network in a dual-domain framework. On the other hand, the proposed method can also be used to enhance the sinogram recovery by distilling the sinogram with intermediate views. Future work can concentrate on extending GloReDi to dual domain methods and other CT reconstruction tasks, such as limited-views CT reconstruction and metal artifact reduction. Although the teacher network is trained alongside the student network in the current version, it is valuable to explore the utilization of pre-trained teacher models, enabling GloReDi to progressively distill the GloRe from a series of teacher models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 403, + 546, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 546, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 546, + 606 + ], + "type": "text", + "content": "We also acknowledge some limitations. First, the teacher network will introduce additional computational costs during the training phase. It is possible to study how to distill knowledge from a pretrained teacher network. Second, although there are clear improvements in quantitative and visual results, it is desirable to have feedback from radiologists for clinical practice. The generalizability and robustness of the trained networks in clinical applications require further investigation. Third, we only considered 2D cases in the paper due to memory respect. If GPU memory permits, one can extend GloReDi to 3D by replacing 2D convolutions with 3D ones by applying high-dimension kernels for FFCs [7]. Lastly, GloReDi failed to surpass the dual-domain methods in denser view scenarios when sinogram can provide effective information for performance improvement. Studying how to improve the performance given an arbitrary " + }, + { + "bbox": [ + 304, + 403, + 546, + 606 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{v}}" + }, + { + "bbox": [ + 304, + 403, + 546, + 606 + ], + "type": "text", + "content": " would be of great value for future research." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 618, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 714 + ], + "type": "text", + "content": "Acknowledgement This work was supported in part by National Natural Science Foundation of China (Nos. 62101136 and 62176059), Shanghai Sailing Program (No. 21YF1402800), Shanghai Municipal Science and Technology Major Project (No. 2018SHZDZX01), ZJ Lab, Shanghai Municipal of Science and Technology Project (No. 20JC1419500), and Shanghai Center for Brain Science and Brain-inspired Technology." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "21204" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Jielin Bai, Yitong Liu, and Hongwen Yang. 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IEEE Transactions on Image Processing, 13(4), 2004. 6" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21207" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_content_list.json b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..54a8606be1c60e61ef02d9327d82e2ff571b5b6f --- /dev/null +++ b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_content_list.json @@ -0,0 +1,2003 @@ +[ + { + "type": "text", + "text": "Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis", + "text_level": 1, + "bbox": [ + 147, + 162, + 821, + 204 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Minho Park*, Jooyeol Yun*, Seunghwan Choi, Jaegul Choo \nKorea Advanced Institute of Science and Technology (KAIST) \nDaejeon, Korea", + "bbox": [ + 218, + 228, + 749, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{m.park, blizzard072, shadow2496, jchoo}@kaist.ac.kr", + "bbox": [ + 253, + 279, + 712, + 293 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 324, + 312, + 339 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing text-to-image generation approaches have set high standards for photorealism and text-image correspondence, largely benefiting from web-scale text-image datasets, which can include up to 5 billion pairs. However, text-to-image generation models trained on domain-specific datasets, such as urban scenes, medical images, and faces, still suffer from low text-image correspondence due to the lack of text-image pairs. Additionally, collecting billions of text-image pairs for a specific domain can be time-consuming and costly. Thus, ensuring high text-image correspondence without relying on web-scale text-image datasets remains a challenging task. In this paper, we present a novel approach for enhancing text-image correspondence by leveraging available semantic layouts. Specifically, we propose a Gaussian-categorical diffusion process that simultaneously generates both images and corresponding layout pairs. Our experiments reveal that we can guide text-to-image generation models to be aware of the semantics of different image regions, by training the model to generate semantic labels for each pixel. We demonstrate that our approach achieves higher text-image correspondence compared to existing text-to-image generation approaches in the Multi-Modal CelebA-HQ and the Cityscapes dataset, where text-image pairs are scarce. Codes are available at https://pmh9960.github.io/research/GCDP.", + "bbox": [ + 75, + 353, + 472, + 713 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 720, + 208, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-to-image generation aims to materialize text descriptions into images, where the main challenge comes from ensuring high image quality and correspondence between input text and output images. While texts convey intuitive semantic depictions of images, they often lack detailed spatial descriptions. For example, text descriptions such as \"A woman is wearing earrings.\" do not describe where the earrings are located within the image. Thus, when a small number of text-image pairs are given, it is challenging", + "bbox": [ + 75, + 739, + 468, + 865 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1828bea502eb09d6cf3965dcf0134f9638046958d03c353ff32e7c7489211a3f.jpg", + "image_caption": [ + "Figure 1. Recall of facial attributes specified in the text descriptions. Text-to-image generation approaches trained on a subset of the Multi-Modal CelebA-HQ [17,22] often fail to reflect text conditions. Facial attributes are classified with a pretrained attribute classifier [30]." + ], + "image_footnote": [], + "bbox": [ + 509, + 326, + 884, + 416 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing for a generative model to learn what part of the image corresponds to which words in the text.", + "bbox": [ + 497, + 490, + 890, + 517 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Overcome this hurdle, recent text-to-image generation approaches [28, 29, 31, 32] leverage web-scale text-image datasets [29, 33] containing up to 5 billion text-image pairs. With access to such data, generative models can fully learn the correspondence between input texts and output images and synthesize photorealistic images while properly reflecting text descriptions.", + "bbox": [ + 497, + 519, + 890, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the cost of such large-scale training remains a major obstacle, often requiring weeks of training even with hundreds of GPUs, which limits participation in the subject to only a few researchers. Moreover, when generating images in a specific domain, such as faces or urban scenes, collecting billions of text-image pairs can be challenging due to the difficulties in collecting images. Even with a general-purpose pretrained model, finetuning on datasets with large domain gaps (e.g., urban scenes or medical images) leads to poor image quality and low text-image correspondence. Recent text-to-image models trained on specific domains often fail to reflect text conditions in the absence of web-scale text-image pairs. To examine the issue in data-scarce scenarios, we evaluate text-to-image generation models trained on a subset of the Multi-Modal CelebA-HQ [17,22] dataset. As shown in Figure 1, existing models struggle to generate certain attributes specified in the given text conditions. Thus, ensuring high text-image correspondence remains a", + "bbox": [ + 497, + 617, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 253, + 48, + 789, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "${}^{1}$ * indicates equal contribution.", + "bbox": [ + 95, + 872, + 267, + 885 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7591", + "bbox": [ + 468, + 896, + 500, + 907 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "challenge for domain-specific generation.", + "bbox": [ + 75, + 125, + 352, + 138 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present a novel approach to achieve high text-image correspondence for domain-specific text-to-image generation by leveraging semantic layouts. Rather than solely generating images based on text descriptions, we propose to concurrently generate both images and their corresponding semantic layouts. To this end, we design a Gaussian-categorical diffusion process that models the joint distribution of image layout pairs. To the best of our knowledge, this is the first approach to combine Gaussian and categorical diffusion processes into a unified diffusion process. By generating semantic labels for each pixel in the image, our generative model can learn the semantics of different parts of the image, allowing it to effectively learn which text descriptions correspond to which locations in the image, even with limited text-image pairs.", + "bbox": [ + 75, + 138, + 468, + 345 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We experiment our approach on subsets of the MultiModal CelebA-HQ [19, 22] to simulate cases where text-image pairs are limited and semantic layouts are available. We also add text descriptions to the Cityscapes dataset [6] to evaluate text-to-image generation in complex scenes with multiple objects, where learning text-image correspondence can be challenging. Our experiments and analyses reveal that modeling the joint image layout distribution can effectively facilitate text-to-image generation models to achieve high text-image correspondence when web-scale text-image pairs are unavailable. We also demonstrate potential applications of the Gaussian-categorical diffusion models in semantic image synthesis and semantic segmentation, through cross-modal outpainting.", + "bbox": [ + 75, + 347, + 468, + 540 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are threefold:", + "bbox": [ + 95, + 540, + 307, + 552 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We define a Gaussian-categorical diffusion process for modeling joint image-Layout distributions, which is the first approach to unify two diffusion processes for image-Layout generation.", + "- Our experiments reveal that generating image layout pairs can be a practical alternative to increase text-image correspondence in circumstances where collecting web-scale text-image pairs is infeasible.", + "- We present cross-modal outpainting, which demonstrates that Gaussian-categorical diffusion models are also capable of modeling conditional distributions for semantic image synthesis and semantic segmentation." + ], + "bbox": [ + 95, + 557, + 468, + 730 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 75, + 739, + 215, + 752 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-image generation. Text-to-image generation [39, 40, 42, 43] have consistently advanced over the years benefiting from large pretrained text encoders [27, 29] and generative models [8, 12, 29]. Recent approaches [25, 28, 31, 32] tackle zero-shot text-to-image generation by training diffusion-based generative models on web-scale text-image datasets, such as the LAION-5B [33] or the DALL-E dataset [29], which scale from 250M to 5B text-image", + "bbox": [ + 75, + 755, + 468, + 865 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/64d8fd9cc52cd4e8b0811996384f1770545a310a54b8a42779d90b410f9a506a.jpg", + "image_caption": [ + "\"He is wearing earrings. He has high cheekbones, and goatee. He is smiling.\"", + "Figure 2. Samples of image, text, and layout triplets from the MM CelebA-HQ [17, 19, 22] and the Cityscapes dataset [6]." + ], + "image_footnote": [], + "bbox": [ + 505, + 125, + 633, + 214 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e7621a6ef494ea44ac6c931c0b9d8c5b395345af62193f84094e8fb6a9cf80ea.jpg", + "image_caption": [ + "\"An image of an urban street view with Poles, Sidewalks, People, Bicycles, Traffic signs, Cars, Buildings, Vegetations, Walls, Riders, Roads, Skies, Traffic lights and Terrains.\"" + ], + "image_footnote": [], + "bbox": [ + 635, + 125, + 887, + 214 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "pairs. While zero-shot text-to-image generation can synthesize realistic images given general text descriptions, these approaches heavily rely on the large number of text-image pairs used for training to achieve high text-image correspondence. Thus, when these models are trained on specific datasets (e.g., MM CelebA-HQ [17, 19, 22, 38]) to generate images within a certain domain, they often fail to satisfy the given text conditions as seen in Figure 1. Collecting enough text-image pairs for a specific domain to ensure high text-image correspondence may be overly expensive since obtaining text descriptions often require human captioning. In this paper, we present an alternative approach for enhancing text-image correspondence without additional text-image pairs by leveraging semantic layouts.", + "bbox": [ + 497, + 269, + 890, + 463 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generating image layout pairs. Modeling the joint image layout distribution $p(x, y)$ is an emerging field in image synthesis, where the goal is to generate both the image $x$ and the corresponding semantic layout $y$ . For the purpose of training semantic segmentation models with strong data augmentation, DatasetGAN [41] and Dataset-DDPM [3] represent the joint image layout distribution as a composition of two models: an image generation model $p(x)$ and a classifier $p(y|x)$ . During inference, the internal representations of $p(x)$ (i.e., feature maps) are used as inputs of $p(y|x)$ , which then classifies each pixel to obtain an image layout pair.", + "bbox": [ + 497, + 464, + 890, + 630 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "On the other hand, SB-GAN [2] and Semantic Palette [18] discover that joint modeling of the image layout distribution can be advantageous for generating complex scenes. Specifically, they decompose the generation process into two steps, a layout generation step $p(y)$ followed by a conditional image generation step $p(x|y)$ given the generated layout. The authors argue that generating layouts with appropriate class proportions can effectively facilitate the scene generation process.", + "bbox": [ + 497, + 630, + 890, + 754 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SemanticGAN [20] models $p(x, y)$ with a single GAN [8] in the pursuit of semantic segmentation with out-of-domain generalization. The results demonstrate that images and layouts can exhibit high alignment when generated through a single model.", + "bbox": [ + 497, + 755, + 890, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a Gaussian-categorical diffusion process to model $p(x,y)$ with a single diffusion process. Our joint image-Layout generation model is extended", + "bbox": [ + 497, + 824, + 890, + 865 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7592", + "bbox": [ + 468, + 896, + 500, + 906 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b3890f5d30b18c6d4e8b92592be07f6bff1ee796b17434cac42a70204b276db3.jpg", + "image_caption": [ + "Figure 3. Illustration of the Gaussian-categorical diffusion process on the image layout distribution of MM CelebA-HQ [19, 22]." + ], + "image_footnote": [], + "bbox": [ + 80, + 123, + 467, + 269 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to the text-to-image generation task, where we achieve high text-image correspondence without requiring web-scale text-image datasets. Specifically, we provide analyses demonstrating that our model is aware of the semantics of the generated image and properly reflects the text conditions.", + "bbox": [ + 75, + 302, + 468, + 384 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion process in arbitrary domains. Diffusion models [7, 12, 24, 35] synthesize data $\\mathbf{x}_0$ in an iterative manner by repeatedly denoising pure noise $\\mathbf{x}_T$ . In image generation, the forward noisng process $q(\\mathbf{x}_t|\\mathbf{x}_{t - 1})$ and the reverse denoising process $p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)$ are defined using a predefined noise schedule $\\beta_{t}$ ,", + "bbox": [ + 75, + 385, + 468, + 467 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) := \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} I\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 126, + 477, + 468, + 494 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) := \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\mathbf {x} _ {t}\\right), \\sigma_ {t} ^ {2} \\boldsymbol {I}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 136, + 496, + 468, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $t\\in [1,2,\\dots,T]$", + "bbox": [ + 75, + 523, + 226, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the true reverse process $q(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t)$ is intractable, the reverse process is approximated by minimizing the KL divergence with the posterior $q(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t, \\mathbf{x}_0)$ with", + "bbox": [ + 75, + 536, + 468, + 579 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t} = D _ {\\mathrm {K L}} \\left(q \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}, \\mathbf {x} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right)\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 121, + 590, + 468, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To extend diffusion processes to categorical data [1, 15] such as text or semantic labels, a categorical noise is defined for the forward process, and the denoising diffusion process is constructed in a similar manner. For instance, Hoogeboom et al. [15] defines a categorical noise as", + "bbox": [ + 75, + 617, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) := \\mathcal {C} \\left(\\mathbf {x} _ {t}; (1 - \\beta_ {t}) \\mathbf {x} _ {t - 1} + \\beta_ {t} / K\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 697, + 468, + 713 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) := \\mathcal {C} \\left(\\mathbf {x} _ {t - 1}; \\boldsymbol {\\Theta} _ {\\theta} \\left(\\mathbf {x} _ {t}\\right)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 154, + 714, + 468, + 730 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{C}$ denotes a categorical distribution, $K$ is the number of categories, and $\\Theta$ is the probability mass function (PMF) of the categorical distribution.", + "bbox": [ + 75, + 741, + 468, + 781 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The key idea for defining a diffusion process in a certain distribution is to define a forward noising process $q(\\mathbf{x}_t|\\mathbf{x}_{t - 1})$ and derive a posterior $q\\left(\\mathbf{x}_{t - 1}|\\mathbf{x}_t,\\mathbf{x}_0\\right)$ . In the following section, we define the forward and reverse processes of the Gaussian-categorical distribution, which can model the joint distribution of image layout pairs.", + "bbox": [ + 75, + 783, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e4c22eec590cc2b1e0725600f367f6d67432aa64ff943771cfd101dd5bb65799.jpg", + "image_caption": [ + "Figure 4. Visualization of a Gaussian-categorical distribution with a single variable ( $N = 1$ , $M = 1$ , $K = 4$ , and $S = 4$ )." + ], + "image_footnote": [], + "bbox": [ + 591, + 125, + 842, + 238 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 499, + 283, + 589, + 296 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Gaussian-categorical distribution", + "text_level": 1, + "bbox": [ + 499, + 300, + 789, + 314 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we define the joint distribution of the Gaussian variable $X$ and categorical variable $Y$ . We parameterize the Gaussian-categorical distribution as follows,", + "bbox": [ + 497, + 321, + 890, + 363 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n(X, Y) \\sim \\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 382, + 890, + 397 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nX = \\left[ X _ {1}, X _ {2},..., X _ {N} \\right] \\in \\mathbb {R} ^ {N},\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 401, + 796, + 416 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nY = \\left[ Y _ {1}, Y _ {2}, \\dots , Y _ {M} \\right] \\in \\{1, 2, \\dots , K \\} ^ {M} \\subset \\mathbb {R} ^ {M},\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 420, + 848, + 437 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} \\in \\mathbb {R} ^ {S \\times N}, \\boldsymbol {\\Sigma} \\in \\mathbb {R} ^ {S \\times N \\times N}, \\boldsymbol {\\Theta} \\in \\mathbb {R} ^ {M \\times K}.\n$$\n", + "text_format": "latex", + "bbox": [ + 556, + 439, + 833, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $\\mu, \\Sigma$ are the mean and variance of the Gaussian distribution, and $\\Theta$ is the probability mass function (PMF) of the categorical distribution. Also, $K$ is the number of possible states for $Y_{i}$ and $S = K^{M}$ is the total number of states of $Y$ . It is worth noting that the dimensions of $\\mu$ and $\\Sigma$ , which indicates that there is a Gaussian mean and variance for all possible categorical states in $Y$ .", + "bbox": [ + 497, + 467, + 890, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The joint distribution of two random variables can be written as a product of a conditional and marginal distribution. Therefore, we can also express the Gaussian-categorical distribution as", + "bbox": [ + 497, + 565, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}) = \\mathcal {C} (\\mathbf {y}; \\boldsymbol {\\Theta}) \\cdot \\mathcal {N} (\\mathbf {x}; \\boldsymbol {\\mu} _ {\\mathbf {y}}, \\boldsymbol {\\Sigma} _ {\\mathbf {y}}) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 536, + 633, + 890, + 649 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {\\mathbf {y}} \\in \\mathbb {R} ^ {N}, \\boldsymbol {\\Sigma} _ {\\mathbf {y}} \\in \\mathbb {R} ^ {N \\times N}.\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 650, + 779, + 668 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The probability density function (PDF) can be written as a weighted Gaussian distribution for each unique $\\mathbf{y} \\in \\{1, 2, \\dots, K\\}^M$ as", + "bbox": [ + 497, + 679, + 890, + 722 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}) = \\left(\\prod_ {i = 1} ^ {M} \\boldsymbol {\\Theta} _ {i}, \\mathbf {y} _ {i}\\right) (2 \\pi) ^ {- \\frac {N}{2}} | \\boldsymbol {\\Sigma} _ {\\mathbf {y}} | ^ {- \\frac {1}{2}} \\\\ \\exp \\Big (- \\frac {1}{2} (\\mathbf {x} - \\boldsymbol {\\mu_ {\\mathbf {y}}}) ^ {\\top} \\boldsymbol {\\Sigma_ {\\mathbf {y}} ^ {- 1}} (\\mathbf {x} - \\boldsymbol {\\mu_ {\\mathbf {y}}}) \\Big), \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 497, + 733, + 905, + 812 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Theta_{i,\\mathbf{y}_i}$ denotes the probability of $Y_{i} = \\mathbf{y}_{i}$ , and $\\pmb{\\mu}_{\\mathbf{y}}$ , $\\pmb{\\Sigma}_{\\mathbf{y}}$ indicates the mean and variance corresponding to state $\\mathbf{y}$ , respectively.", + "bbox": [ + 497, + 824, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7593", + "bbox": [ + 468, + 896, + 500, + 906 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Gaussian-categorical diffusion process", + "text_level": 1, + "bbox": [ + 77, + 125, + 406, + 140 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similar to the diffusion process for images, we define our reverse process of image layout distributions as a Gaussian-categorical transition with a Markov property. Specifically, we define the transition probability $p_{\\theta}\\left(\\mathbf{z}_{t - 1} \\mid \\mathbf{z}_t\\right)$ as", + "bbox": [ + 75, + 146, + 468, + 201 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\boldsymbol {\\Sigma} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\boldsymbol {\\Theta} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 92, + 212, + 468, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{z}$ represents the tuple $(\\mathbf{x},\\mathbf{y})$ for simplicity.", + "bbox": [ + 77, + 241, + 403, + 254 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We define the forward process of image layout pairs $\\mathbf{z}_0$ under the Markov assumption as", + "bbox": [ + 75, + 254, + 468, + 281 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t}; \\left[ \\boldsymbol {\\mu} _ {t \\mid t - 1} \\right] _ {\\times S}, \\left[ \\boldsymbol {\\Sigma} _ {t \\mid t - 1} \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {t \\mid t - 1}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 77, + 290, + 468, + 326 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {t \\mid t - 1} := \\sqrt {1 - \\beta_ {t} ^ {N}} \\mathbf {x} _ {t - 1},\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 333, + 334, + 350 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {t \\mid t - 1} := \\beta_ {t} ^ {N} \\boldsymbol {I},\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 351, + 268, + 366 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Theta} _ {t | t - 1} := \\left(1 - \\beta_ {t} ^ {c}\\right) \\mathbf {y} _ {t - 1} + \\beta_ {t} ^ {c} / K,\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 369, + 386, + 385 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta^c$ and $\\beta^{N}$ are predefined noise schedules. We use the notation $[\\mathbf{v}]_{\\times S}$ to indicate row-wise duplication of a vector $\\mathbf{v}$ (i.e., $[\\mathbf{v},\\mathbf{v},\\dots,\\mathbf{v}]^T)$ .", + "bbox": [ + 75, + 394, + 468, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, the forward process is defined as independently applying the Gaussian and categorical noises following a normal distribution $\\mathcal{N}(\\mathbf{0},\\mathbf{I})$ and a categorical distribution with uniform probability $\\mathcal{C}(1 / K)$ , according to predefined noise schedules $\\beta^{\\mathcal{N}},\\beta^{\\mathcal{C}}$ . Given a large $T$ and appropriate noise schedules, the forward process leads to an isotropic Gaussian distribution and a uniform categorical distribution at the final state $\\mathbf{z}_T$ .", + "bbox": [ + 75, + 435, + 468, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With $\\alpha_{t} \\coloneqq 1 - \\beta_{t}$ and $\\bar{\\alpha}_{t} \\coloneqq \\prod_{s=1}^{t} \\alpha_{s}$ , we can derive a forward process to an arbitrary timestep as", + "bbox": [ + 75, + 545, + 468, + 574 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N C} \\left(\\mathbf {z} _ {t}; \\left[ \\boldsymbol {\\mu} _ {t | 0} \\right] _ {\\times S}, \\left[ \\boldsymbol {\\Sigma} _ {t | 0} \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {t | 0}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 584, + 468, + 608 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {t | 0} := \\sqrt {\\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {0},\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 619, + 292, + 637 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {t | 0} := \\left(1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}\\right) \\boldsymbol {I},\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 638, + 309, + 654 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Theta} _ {t \\mid 0} := (1 - \\bar {\\alpha} _ {t} ^ {c}) \\mathbf {y} _ {0} + \\bar {\\alpha} _ {t} ^ {c} / K.\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 656, + 371, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, using Bayes theorem, we can derive the posterior $q(\\mathbf{z}_{t - 1} \\mid \\mathbf{z}_t, \\mathbf{z}_0)$ , which is summarized into the following form of a Gaussian-categorical distribution", + "bbox": [ + 75, + 682, + 468, + 723 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) = \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\left[ \\tilde {\\boldsymbol {\\mu}} _ {t} \\right] _ {\\times S}, \\left[ \\tilde {\\boldsymbol {\\Sigma}} _ {t} \\right] _ {\\times S}, \\tilde {\\boldsymbol {\\Theta}} _ {t}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 95, + 726, + 468, + 763 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\boldsymbol {\\mu}} _ {t} := \\frac {\\sqrt {\\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}}} \\beta_ {t} ^ {\\mathcal {N}}}{1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {0} + \\frac {\\sqrt {\\alpha_ {t} ^ {\\mathcal {N}}} (1 - \\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}})}{1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {t},\n$$\n", + "text_format": "latex", + "bbox": [ + 126, + 769, + 418, + 802 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\boldsymbol {\\Sigma}} _ {t} := \\left(\\left(1 - \\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}}\\right) \\beta_ {t} ^ {\\mathcal {N}} / \\left(1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}\\right)\\right) \\boldsymbol {I},\n$$\n", + "text_format": "latex", + "bbox": [ + 152, + 804, + 393, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\boldsymbol {\\Theta}} _ {t} := Z \\left[ \\alpha_ {t} ^ {c} \\mathbf {y} _ {t} + \\left(1 - \\alpha_ {t} ^ {c}\\right) / K \\right] \\odot \\left[ \\bar {\\alpha} _ {t} ^ {c} \\mathbf {y} _ {0} + \\left(1 - \\bar {\\alpha} _ {t - 1} ^ {c}\\right) / K \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 825, + 467, + 842 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Z$ is a normalizing constant and $\\odot$ is the element-", + "bbox": [ + 80, + 852, + 468, + 865 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "wise product. Detailed proofs for each step are provided in the appendix.", + "bbox": [ + 497, + 125, + 890, + 152 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that parameters $\\pmb{\\mu}$ and $\\pmb{\\Sigma}$ of the posterior are expressed in terms of $\\widetilde{\\pmb{\\mu}}_t\\in \\mathbb{R}^N$ and $\\widetilde{\\Sigma}_t\\in \\mathbb{R}^{N\\times N}$ , which have a reduced dimensions than the original parameters in Equation (6). This is due to the definition in Equation (10), where the Gaussian noise is applied independently of the categorical variable.", + "bbox": [ + 497, + 153, + 890, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can write the variational lower bound (VLB) as", + "bbox": [ + 517, + 236, + 857, + 249 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {V L B}} := L _ {0} + L _ {1} + L _ {2} + \\dots + L _ {T}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 254, + 890, + 269 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {0} := - \\log p _ {\\theta} \\left(\\mathbf {z} _ {0} \\mid \\mathbf {z} _ {1}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 613, + 271, + 890, + 286 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t - 1} := D _ {K L} \\left(q \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right)\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 289, + 890, + 302 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {T} := D _ {K L} \\left(q \\left(\\mathbf {z} _ {T} \\mid \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {T}\\right)\\right). \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 579, + 306, + 890, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the posterior $q(\\mathbf{z}_{t - 1}|\\mathbf{z}_t,\\mathbf{z}_0)$ is parameterized by $\\widetilde{\\boldsymbol{\\mu}}_t$ and $\\widetilde{\\Sigma}_t$ , we can also re-parameterize $p_{\\theta}$ as", + "bbox": [ + 497, + 327, + 890, + 356 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\left[ \\widetilde {\\boldsymbol {\\mu}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\right] _ {\\times S}, \\left[ \\widetilde {\\boldsymbol {\\Sigma}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {\\theta}\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 502, + 362, + 890, + 391 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\boldsymbol {\\mu}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\in \\mathbb {R} ^ {N}, \\widetilde {\\boldsymbol {\\Sigma}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\in \\mathbb {R} ^ {N \\times N}, \\boldsymbol {\\Theta} _ {\\theta} \\in \\mathbb {R} ^ {M \\times K}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 395, + 890, + 413 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, we can predict a reduced number of parameters to minimize the KL divergence term in Equation (15),", + "bbox": [ + 497, + 420, + 890, + 447 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD _ {K L} \\left(q \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right)\\right) \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 454, + 890, + 469 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n= \\mathbb {E} _ {q} \\left[ \\frac {1}{2 \\sigma_ {t} ^ {2}} \\| \\widetilde {\\boldsymbol {\\mu}} _ {t} - \\widetilde {\\boldsymbol {\\mu}} _ {\\theta} (\\mathbf {z} _ {t}) \\| ^ {2} \\right] + D _ {\\mathrm {K L}} \\left(\\widetilde {\\boldsymbol {\\Theta}} _ {t} \\| \\boldsymbol {\\Theta} _ {\\theta} (\\mathbf {z} _ {t})\\right) + C,\n$$\n", + "text_format": "latex", + "bbox": [ + 507, + 472, + 887, + 501 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C$ is a constant irrelevant to learnable parameters $\\theta$ . $L_{0}$ is directly minimized through a closed-form solution and $L_{T}$ does not involve any learnable parameters.", + "bbox": [ + 497, + 505, + 890, + 543 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Architectural design", + "text_level": 1, + "bbox": [ + 499, + 551, + 692, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to treat image-Layout pairs as a single data sample, we embed the semantic layouts (i.e., one-hot vectors) into 3-channel vectors via learnable parameters and concatenate them with images along the channel dimension $(\\mathbf{z} \\in \\mathbb{R}^{N \\times N \\times 6})$ . We adopt the U-Net [24] and the Efficient U-Net [32] following existing diffusion models and modify the input/output channels for image-Layout input/outputs. For text conditioning, we utilize the T5-L [27] text encoder and condition the U-Net model similarly to Imagen [32].", + "bbox": [ + 497, + 573, + 890, + 697 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We follow the cascaded diffusion [13] framework to generate high-resolution image layout pairs, which involves a sequence of an image generation model followed by a super-resolution model. We find that resizing layouts to a small resolution (e.g., $64 \\times 64$ ) often damages the integrity of semantic labels due to nearest-neighbor sampling on extreme scales. Thus, we generate $128 \\times 128$ resolution images and then upsample to $256 \\times 256$ resolution with a Gaussian-categorical super-resolution model. The super-resolution model upsamples both images and layouts following the Gaussian-categorical diffusion. We adopt the classifier-free guidance on both the generation model and the super-resolution model.", + "bbox": [ + 497, + 697, + 890, + 876 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7594", + "bbox": [ + 468, + 896, + 500, + 906 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b16a793ffaaffa1879eaaf411fd0e6a6ae4f651cd9e4009100f3d7fe25398942.jpg", + "image_caption": [ + "Figure 5. Examples of text-guided generation of image layout pairs from the Gaussian-categorical diffusion trained on MM CelebA-HQ-100 [17,22] and Cityscapes [6]. The text descriptions on the bottom are given as conditions to generate the image-label pairs." + ], + "image_footnote": [], + "bbox": [ + 87, + 128, + 830, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 75, + 453, + 208, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Text-image datasets", + "text_level": 1, + "bbox": [ + 75, + 476, + 265, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multi-Modal CelebA-HQ. MM CelebA-HQ [17,22,38] is a collection of different annotations for the 30,000 images in the CelebA-HQ dataset [17,22], including text descriptions, face attribute labels, and part-level segmentation labels. Part-level segmentation labels consist of 19 different classes ( $K = 19$ ) including all facial components and accessories. To train the Gaussian-categorical diffusion model, we use both the segmentation labels and the text descriptions provided in the dataset. We also construct subsets of the data, MM CelebA-HQ-25 and MM CelebA-HQ-50, by randomly selecting $25\\%$ and $50\\%$ of the images, respectively, to simulate data-scarce scenarios. We train and evaluate our models on $256 \\times 256$ resolution images.", + "bbox": [ + 75, + 497, + 468, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cityscapes. Cityscapes [6] is an urban scene dataset with 3475 image layout pairs of complex scenes containing multiple objects, including 20 different semantic classes ( $K = 20$ ). To add text descriptions to each image, we list the class names in the following format:", + "bbox": [ + 75, + 678, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "\"An image of an urban scene with {classes}.", + "bbox": [ + 119, + 752, + 423, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where classes are the unique class names in the corresponding semantic layout. The Cityscapes dataset presents a challenging domain for generating realistic images due to the limited number of available images and the diverse object locations in urban scenes. Since Cityscapes images have a unique aspect ratio of 2:1, we generate $512 \\times 256$ resolution images. We include example text-image pairs in Figure 2.", + "bbox": [ + 75, + 773, + 470, + 872 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 499, + 453, + 714, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For synthesizing image layout pairs, $N$ and $M$ are equally set to the number of pixels in the image. Although the Gaussian-categorical diffusion process allows different noise schedules $\\beta^{\\mathcal{N}}$ and $\\beta^{c}$ for images and layouts, we set both schedules to the cosine schedule [24]. We provide experiments on the effect of different noise schedules for $\\beta^{c}$ in the supplementary section. We set $T = 1000$ and sample with 100 timesteps using the accelerated sampling technique [35].", + "bbox": [ + 497, + 475, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Evaluating text-to-image generation", + "text_level": 1, + "bbox": [ + 499, + 600, + 811, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Text-to-image generation models are evaluated from two perspectives, image fidelity and text-image correspondence. We use the Fréchet Inception Distance (FID) [10] to measure the image fidelity. After the release of CLIP [26], the CLIP score [9] is often used to evaluate text-image correspondence for text-to-image generation. However, the CLIP score is known to have poor generalization abilities [26] when evaluating scenes with large domain gaps (i.e., Cityscapes) and also lacks interpretability in terms of understanding what element in the image causes a low or high CLIP score. In order to compensate for this drawback, we propose Semantic Recall to precisely measure the text-image correspondence for Cityscapes generation.", + "bbox": [ + 497, + 616, + 890, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Semantic Recall. The Semantic Recall is analogous to the Semantic Object Accuracy (SOA) [11], which evaluates the generation of specific objects in text-to-image generation by utilizing pretrained object detectors. In our work, we use a pretrained semantic segmentation model [37] to detect the", + "bbox": [ + 497, + 796, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7595", + "bbox": [ + 468, + 896, + 500, + 906 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ce751d195d36b7a0ff1bcb1d12a7204c6abf463a804d34a1ae20a30604074b1f.jpg", + "image_caption": [ + "(a) FID-Semantic Recall" + ], + "image_footnote": [], + "bbox": [ + 134, + 133, + 433, + 294 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/26fea2cb71c198eac4e2c9da5ddf6b25499da4293ee8be1c82b983cb7dfb9e5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 514, + 128, + 855, + 206 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/00607728f06dcccdfc5763976d602c2d3291438eb0f10513fd272b55df2a06fb.jpg", + "image_caption": [ + "(b) Class-wise Semantic Recall", + "(c) Class Proportion in Cityscapes", + "Figure 6. (a) FID-Semantic Recall trade-off in the Cityscapes dataset. (b) Semantic Recall for minor classes. Semantic Recall is measured using the HRNet-w48 [37] model. (c) Proportion of each semantic class in the entire Cityscapes dataset. Class proportion is compared in log-scale for visibility." + ], + "image_footnote": [], + "bbox": [ + 512, + 220, + 875, + 309 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "presence of classes described in text conditions. We determine that a class is detected in a generated image if it appears in the segmentation layout. The ground-truth classes for each image are identified by searching for class names in text descriptions. For example, an image generated with the text description \"An urban scene with cars, roads, and traffic signs.\", would be evaluated with the existence of cars, roads, and traffic signs. Therefore, we compute the Semantic Recall as the average ratio of correctly detected classes in the generated image to the total number of classes in the ground-truth layouts,", + "bbox": [ + 73, + 378, + 468, + 532 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{| \\mathcal {G} |} \\sum_ {x _ {i}, y _ {i} \\in \\mathcal {G}} \\frac {\\left| \\text {C l a s s e s i n} F \\left(x _ {i}\\right) \\cap \\text {C l a s s e s i n} y _ {i} \\right|}{\\left| \\text {C l a s s e s i n} y _ {i} \\right|},\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 541, + 436, + 578 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{G}$ is the set of generated image layout pairs $(x_{i},y_{i})$ and $|\\cdot |$ indicates the cardinality of a given set. $F(\\cdot)$ is the pretrained semantic segmentation model [37].", + "bbox": [ + 75, + 589, + 468, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We compare our approach with state-of-the-art performing diffusion-based models, Imagen [32] and the latent diffusion model (LDM) [31]. We also train a high-performing GAN-based approach Lafite [42] trained on MM CelebA-HQ and Cityscapes. For training LDM, we utilize the pretrained autoencoder from the Stable Diffusion project. Diffusion-based approaches utilize the classifier-free guidance [14] to control the performance trade-off between text-image correspondence and image fidelity. Thus, for these approaches, we sweep the guidance scale until the text-image correspondence measures saturate and report all FID-Semantic Recall or FID-CLIP score pairs.", + "bbox": [ + 75, + 631, + 468, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on Cityscapes. For the Cityscapes dataset [6], we report the FID and Semantic Recall performance trade-off and also provide detailed recall scores for each class in Figure 6. Given the small number of text-image pairs (3475 pairs), existing text-to-image models face", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "challenges in learning the text-image correspondence and achieving high text-image correspondence. However, the Gaussian-categorical diffusion effectively generates complex Cityscapes scenes while maintaining high Semantic Recall even with limited data. Additionally, the model achieves high recall rates for minor classes, such as the bicycle or the motorcycle class, which only constitute a small portion of the dataset. This indicates that generating semantic labels for each pixel facilitates the model to establish high text-image correspondence, especially for underrepresented classes.", + "bbox": [ + 497, + 378, + 890, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on MM CelebA-HQ. We further evaluate our method on the MM CelebA-HQ-25, 50, and 100, and report the FID-CLIP scores for each dataset. As shown in Figure 7, the Gaussian-categorical diffusion consistently outperforms existing text-to-image approaches at datasets with varying numbers of text-image pairs, exhibiting low FIDs and a high CLIP scores. We provide qualitative results of the Gaussian-categorical diffusion in Figure 5 and also compare the results with existing approaches in the supplementary material.", + "bbox": [ + 497, + 530, + 892, + 669 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Analyzing the internal representations", + "text_level": 1, + "bbox": [ + 499, + 679, + 828, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to visualize the advantages of jointly generating image-Layout pairs, we train a Gaussian diffusion model which generates images without corresponding semantic layouts. Then, we collect the internal features from the two models at different timesteps and cluster the features in an unsupervised manner with K-means clustering. As shown in Figure 8, the internal features of the Gaussian-categorical model form distinct clusters that correspond to different facial regions. Specifically, the internal features of the Gaussian-categorical diffusion model form clusters even in the early stages of generation $(t = 800)$ , correctly distinguishing hair, glasses and the background region.", + "bbox": [ + 497, + 700, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7596", + "bbox": [ + 468, + 896, + 500, + 906 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c36a1ab08a379a68417e123542a2fc9396eea69d219cd31e3d0effdb84df4b08.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 107, + 127, + 344, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f724f67f38e302c852f37afe1c044473cc61db82ea26ace94b3b586b6b083df1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 127, + 660, + 279 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8aa05d2a01ba7e38e588dc306fdfbf819dd14ca8e1cb47156452a418510a74b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 613, + 128, + 848, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/781007feb0d468d7aa1007c9e11fa38ff7dd48bf40b9a53480b366687e5abfa7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 314, + 285, + 660, + 302 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9b504da7a451afc2a30509f75fbfc89ee42cd2b995b982d9e2914142b56f9035.jpg", + "image_caption": [ + "Figure 7. FID-CLIP score pairs for text-to-image generation models on different subsets of the MM CelebA-HQ dataset. The CLIP scores are measured with the ViT-L/14-336 model. The guidance scale is swept starting from 1 until saturation.", + "Figure 8. Visualization of clustering results between the internal features of the Gaussian-categorical diffusion and the Gaussian diffusion." + ], + "image_footnote": [], + "bbox": [ + 82, + 347, + 467, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results reveal that the Gaussian-categorical diffusion model is highly aware of the semantics of the image during the generation process. This characteristic is advantageous in scenarios where a generative model needs to learn how to match specific parts of the image with corresponding input text descriptions, as the model is capable of understanding the semantic structure of the image. As such, training a Gaussian-categorical diffusion is a promising approach for achieving high correspondence between text descriptions and image pixels, particularly when there is a scarcity of text-image pairs available.", + "bbox": [ + 75, + 541, + 472, + 693 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Image layout fidelity and alignment", + "text_level": 1, + "bbox": [ + 75, + 705, + 386, + 720 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we evaluate whether generated images and layouts closely model the real distribution, and whether the generated pairs are semantically aligned. Following Semantic Palette [2, 18] we evaluate the image-Layout alignment using the mean intersection over union (mIoU) between the generated layouts and the segmentation labels predicted by a pretrained HRNet [37]. Additionally, we use the Fréchet Segmentation Distance (FSD) [4], which replaces the Inception-V3 [36] features in the FID score [10] to pixel counts for each class, to evaluate the quality of gen", + "bbox": [ + 75, + 728, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2554efeaf4d2f301f343b156a556c064be115f9c56a2dbdebade98199582330f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsFID ↓mIoU ↑FSD ↓
GANformer [16]24.86-481.5
DatasetDDPM [3]55.3833.8890.31
Semantic Palette [18]52.1353.1748.29
Ours20.3665.8042.22
", + "bbox": [ + 504, + 346, + 885, + 435 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Image-Layout alignment and FID of different Imagelayout generation approaches for scene generation in the Cityscapes [6] dataset.", + "bbox": [ + 497, + 438, + 890, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "erated layouts. Similar to the FID score, a low FSD indicates that the class distributions are close to the real distribution.", + "bbox": [ + 497, + 496, + 890, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our results with existing unconditional image layout generation approaches [3, 18] on the Cityscapes dataset. Additionally, we introduce a simple baseline (i.e., GANformer [16]) for image layout generation, in which we generate images using a well-trained unconditional image generation model [16] and segment the images using a pretrained segmentation model [37]. Note that we cannot measure the mIoU for this baseline since the semantic layouts are predicted using the same pretrained network.", + "bbox": [ + 497, + 543, + 890, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 1, the Gaussian-categorical diffusion process is highly effective in modeling the joint distribution of images and layouts even for complex urban scenes. By using a unified diffusion process, we are able to generate image layout pairs that exhibit high alignment, closely resembling the real distribution. The ability of the Gaussian-categorical diffusion to effectively model the joint distribution of images and layouts offers promising avenues for future research in generative modeling. By leveraging the theoretical foundations established by our method, researchers can explore new approaches for dataset generation in a range of domains, from images and audiios to semantic layouts and texts.", + "bbox": [ + 497, + 686, + 892, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7597", + "bbox": [ + 468, + 896, + 500, + 906 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d4abe812daed03d04a7c5cfc1cd2bbaf52417dbc95478fb5e793f96edef526cc.jpg", + "image_caption": [ + "(a) Text-guided Image-to-Layout Generation" + ], + "image_footnote": [], + "bbox": [ + 82, + 123, + 480, + 269 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/799914a679d802c6143cfbc9f1682771d39574c8f0f47504200805f05e8b4af1.jpg", + "image_caption": [ + "(b) Text-guided Layout-to-Image Generation", + "Figure 9. Cross-modal outpainting for (a) text-guided image-to-Layout generation and (b) text-guided layout-to-image generation. Segmentation layouts are generated with $n = 1$ resampling steps and images are generated with $n = 5$ resampling steps for each timestep." + ], + "image_footnote": [], + "bbox": [ + 490, + 123, + 887, + 269 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Cross-modal outpainting", + "text_level": 1, + "bbox": [ + 75, + 331, + 305, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "RePaint [23] enables existing diffusion models to inpaint a masked image by iteratively denoising the masked region given the known image (i.e., condition image). Specifically, for each timestep $t$ , images are inpainted as follows:", + "bbox": [ + 75, + 352, + 468, + 409 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t - 1} ^ {\\mathrm {k n o w n}} \\sim \\mathcal {N} (\\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) I),\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 418, + 383, + 435 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t - 1} ^ {\\text {u n k n o w n}} \\sim \\mathcal {N} (\\boldsymbol {\\mu} _ {\\theta} (x _ {t}, t), \\boldsymbol {\\Sigma} _ {\\theta} (x _ {t}, t)),\n$$\n", + "text_format": "latex", + "bbox": [ + 154, + 437, + 391, + 454 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t - 1} = m \\odot x _ {t - 1} ^ {\\text {k n o w n}} + (1 - m) \\odot x _ {t - 1} ^ {\\text {u n k n o w n}},\n$$\n", + "text_format": "latex", + "bbox": [ + 131, + 456, + 415, + 473 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $m$ is the mask for the known image. To ensure consistency between the inpainted regions and known regions, Repaint iterates the denoising process $n$ times for each timestep.", + "bbox": [ + 75, + 483, + 468, + 539 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Repaint technique allows us to use the Gaussian-categorical diffusion model as a text-guided layout-to-image generation model (i.e., semantic image synthesis) by considering the layouts as an image layout pair with the image part masked. Similarly, we can perform text-guided image-to layout generation (i.e., semantic segmentation) by masking the layout in the image layout pair. As shown in Figure 9, the Gaussian-categorical diffusion generates realistic images or layouts conditioned on text descriptions. The results demonstrate that a well-trained Gaussian-categorical diffusion can serve as a generative prior for conditional generation tasks. We describe the algorithm for cross-modal outpainting in the supplementary material.", + "bbox": [ + 75, + 539, + 468, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation", + "text_level": 1, + "bbox": [ + 75, + 731, + 191, + 745 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although the Gaussian-categorical diffusion offers means for achieving high text-image correspondence without training on web-scale text-image pairs, training a Gaussian-categorical diffusion model requires additional semantic layout annotations of images. However, with the assistance of recent data annotation tools [5,34], annotating existing data can be a cost-effective option for text-to-image generation in scenarios where obtaining web-scale text", + "bbox": [ + 75, + 755, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "image pairs is costly (e.g., medical images, urban scenes, and aerial images).", + "bbox": [ + 497, + 331, + 889, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We observe that training the Gaussian-categorical diffusion model on the MS-COCO dataset [21] produces poor quality images and layouts. We suspect that this is due to the highly diverse scenes in the COCO dataset, with 171 categories in the semantic layouts. Analyzing the challenges of training on the MS-COCO dataset is a potential area for future research. Nevertheless, we propose an effective approach for text-to-image generation in data-scarce scenarios, where collecting data is expensive and annotating existing images is affordable.", + "bbox": [ + 497, + 361, + 892, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 499, + 517, + 618, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we define the Gaussian-categorical diffusion process to model the joint distribution of image layout pairs. Our experiments demonstrate that the proposed model can ensure high text-image correspondence for text-to-image generation in specific domains, without relying on web-scale text-image pairs. Our approach outperforms existing approaches in terms of image quality and text-image correspondence.", + "bbox": [ + 497, + 543, + 890, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our visualizations of the internal representations of the Gaussian-categorical distribution demonstrate that the proposed model is aware of the semantics of the image, bridging the gap between highly semantic text descriptions and image pixels. Additionally, the high image layout alignment of generated image layout pairs and the results of cross-modal outpainting show that the model precisely captures the relationship between images and labels.", + "bbox": [ + 497, + 656, + 890, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Overall, the Gaussian-categorical diffusion enables text-to-image models to achieve high text-image correspondence by leveraging semantic labels when trained on a specific domain with limited text-image pairs. Our proposed model can also be utilized as a generative prior for conditional generation tasks, such as text-guided semantic image synthesis and text-guided semantic segmentation.", + "bbox": [ + 497, + 769, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7598", + "bbox": [ + 468, + 896, + 500, + 906 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 78, + 124, + 236, + 140 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B02001913), Electronics and Telecommunications Research Institute (ETRI) grant funded by the Korean government [22ZS1200, Fundamental Technology Research for Human-Centric Autonomous Intelligent Systems], and the KAIST-NAVER hypercreative AI center.", + "bbox": [ + 75, + 148, + 468, + 258 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 274, + 171, + 288 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. 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In CVPR, 2019. 2" + ], + "bbox": [ + 502, + 125, + 890, + 228 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7600", + "bbox": [ + 468, + 896, + 500, + 906 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_model.json b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..337c0cc7fdd22faab171249ac09e379e2ff6a3bb --- /dev/null +++ b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_model.json @@ -0,0 +1,2541 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.254, + 0.049, + 0.79, + 0.088 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.149, + 0.163, + 0.823, + 0.205 + ], + "angle": 0, + "content": "Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.229, + 0.751, + 0.278 + ], + "angle": 0, + "content": "Minho Park*, Jooyeol Yun*, Seunghwan Choi, Jaegul Choo \nKorea Advanced Institute of Science and Technology (KAIST) \nDaejeon, Korea" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.28, + 0.714, + 0.294 + ], + "angle": 0, + "content": "{m.park, blizzard072, shadow2496, jchoo}@kaist.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.325, + 0.314, + 0.34 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.355, + 0.473, + 0.714 + ], + "angle": 0, + "content": "Existing text-to-image generation approaches have set high standards for photorealism and text-image correspondence, largely benefiting from web-scale text-image datasets, which can include up to 5 billion pairs. However, text-to-image generation models trained on domain-specific datasets, such as urban scenes, medical images, and faces, still suffer from low text-image correspondence due to the lack of text-image pairs. Additionally, collecting billions of text-image pairs for a specific domain can be time-consuming and costly. Thus, ensuring high text-image correspondence without relying on web-scale text-image datasets remains a challenging task. In this paper, we present a novel approach for enhancing text-image correspondence by leveraging available semantic layouts. Specifically, we propose a Gaussian-categorical diffusion process that simultaneously generates both images and corresponding layout pairs. Our experiments reveal that we can guide text-to-image generation models to be aware of the semantics of different image regions, by training the model to generate semantic labels for each pixel. We demonstrate that our approach achieves higher text-image correspondence compared to existing text-to-image generation approaches in the Multi-Modal CelebA-HQ and the Cityscapes dataset, where text-image pairs are scarce. Codes are available at https://pmh9960.github.io/research/GCDP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.721, + 0.21, + 0.735 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.741, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Text-to-image generation aims to materialize text descriptions into images, where the main challenge comes from ensuring high image quality and correspondence between input text and output images. While texts convey intuitive semantic depictions of images, they often lack detailed spatial descriptions. For example, text descriptions such as \"A woman is wearing earrings.\" do not describe where the earrings are located within the image. Thus, when a small number of text-image pairs are given, it is challenging" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.327, + 0.885, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.421, + 0.893, + 0.485 + ], + "angle": 0, + "content": "Figure 1. Recall of facial attributes specified in the text descriptions. Text-to-image generation approaches trained on a subset of the Multi-Modal CelebA-HQ [17,22] often fail to reflect text conditions. Facial attributes are classified with a pretrained attribute classifier [30]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.491, + 0.892, + 0.518 + ], + "angle": 0, + "content": "ing for a generative model to learn what part of the image corresponds to which words in the text." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.617 + ], + "angle": 0, + "content": "Overcome this hurdle, recent text-to-image generation approaches [28, 29, 31, 32] leverage web-scale text-image datasets [29, 33] containing up to 5 billion text-image pairs. With access to such data, generative models can fully learn the correspondence between input texts and output images and synthesize photorealistic images while properly reflecting text descriptions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.893, + 0.867 + ], + "angle": 0, + "content": "However, the cost of such large-scale training remains a major obstacle, often requiring weeks of training even with hundreds of GPUs, which limits participation in the subject to only a few researchers. Moreover, when generating images in a specific domain, such as faces or urban scenes, collecting billions of text-image pairs can be challenging due to the difficulties in collecting images. Even with a general-purpose pretrained model, finetuning on datasets with large domain gaps (e.g., urban scenes or medical images) leads to poor image quality and low text-image correspondence. Recent text-to-image models trained on specific domains often fail to reflect text conditions in the absence of web-scale text-image pairs. To examine the issue in data-scarce scenarios, we evaluate text-to-image generation models trained on a subset of the Multi-Modal CelebA-HQ [17,22] dataset. As shown in Figure 1, existing models struggle to generate certain attributes specified in the given text conditions. Thus, ensuring high text-image correspondence remains a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.873, + 0.268, + 0.886 + ], + "angle": 0, + "content": "\\( {}^{1} \\) * indicates equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.897, + 0.501, + 0.908 + ], + "angle": 0, + "content": "7591" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.127, + 0.353, + 0.14 + ], + "angle": 0, + "content": "challenge for domain-specific generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.469, + 0.346 + ], + "angle": 0, + "content": "In this paper, we present a novel approach to achieve high text-image correspondence for domain-specific text-to-image generation by leveraging semantic layouts. Rather than solely generating images based on text descriptions, we propose to concurrently generate both images and their corresponding semantic layouts. To this end, we design a Gaussian-categorical diffusion process that models the joint distribution of image layout pairs. To the best of our knowledge, this is the first approach to combine Gaussian and categorical diffusion processes into a unified diffusion process. By generating semantic labels for each pixel in the image, our generative model can learn the semantics of different parts of the image, allowing it to effectively learn which text descriptions correspond to which locations in the image, even with limited text-image pairs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.469, + 0.541 + ], + "angle": 0, + "content": "We experiment our approach on subsets of the MultiModal CelebA-HQ [19, 22] to simulate cases where text-image pairs are limited and semantic layouts are available. We also add text descriptions to the Cityscapes dataset [6] to evaluate text-to-image generation in complex scenes with multiple objects, where learning text-image correspondence can be challenging. Our experiments and analyses reveal that modeling the joint image layout distribution can effectively facilitate text-to-image generation models to achieve high text-image correspondence when web-scale text-image pairs are unavailable. We also demonstrate potential applications of the Gaussian-categorical diffusion models in semantic image synthesis and semantic segmentation, through cross-modal outpainting." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.541, + 0.308, + 0.553 + ], + "angle": 0, + "content": "Our contributions are threefold:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.558, + 0.469, + 0.613 + ], + "angle": 0, + "content": "- We define a Gaussian-categorical diffusion process for modeling joint image-Layout distributions, which is the first approach to unify two diffusion processes for image-Layout generation." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.617, + 0.469, + 0.672 + ], + "angle": 0, + "content": "- Our experiments reveal that generating image layout pairs can be a practical alternative to increase text-image correspondence in circumstances where collecting web-scale text-image pairs is infeasible." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.676, + 0.469, + 0.731 + ], + "angle": 0, + "content": "- We present cross-modal outpainting, which demonstrates that Gaussian-categorical diffusion models are also capable of modeling conditional distributions for semantic image synthesis and semantic segmentation." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.558, + 0.469, + 0.731 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.216, + 0.753 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.469, + 0.866 + ], + "angle": 0, + "content": "Text-to-image generation. Text-to-image generation [39, 40, 42, 43] have consistently advanced over the years benefiting from large pretrained text encoders [27, 29] and generative models [8, 12, 29]. Recent approaches [25, 28, 31, 32] tackle zero-shot text-to-image generation by training diffusion-based generative models on web-scale text-image datasets, such as the LAION-5B [33] or the DALL-E dataset [29], which scale from 250M to 5B text-image" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.127, + 0.634, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.218, + 0.635, + 0.241 + ], + "angle": 0, + "content": "\"He is wearing earrings. He has high cheekbones, and goatee. He is smiling.\"" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.127, + 0.888, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.636, + 0.218, + 0.882, + 0.24 + ], + "angle": 0, + "content": "\"An image of an urban street view with Poles, Sidewalks, People, Bicycles, Traffic signs, Cars, Buildings, Vegetations, Walls, Riders, Roads, Skies, Traffic lights and Terrains.\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.241, + 0.89, + 0.266 + ], + "angle": 0, + "content": "Figure 2. Samples of image, text, and layout triplets from the MM CelebA-HQ [17, 19, 22] and the Cityscapes dataset [6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.891, + 0.464 + ], + "angle": 0, + "content": "pairs. While zero-shot text-to-image generation can synthesize realistic images given general text descriptions, these approaches heavily rely on the large number of text-image pairs used for training to achieve high text-image correspondence. Thus, when these models are trained on specific datasets (e.g., MM CelebA-HQ [17, 19, 22, 38]) to generate images within a certain domain, they often fail to satisfy the given text conditions as seen in Figure 1. Collecting enough text-image pairs for a specific domain to ensure high text-image correspondence may be overly expensive since obtaining text descriptions often require human captioning. In this paper, we present an alternative approach for enhancing text-image correspondence without additional text-image pairs by leveraging semantic layouts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.891, + 0.631 + ], + "angle": 0, + "content": "Generating image layout pairs. Modeling the joint image layout distribution \\( p(x, y) \\) is an emerging field in image synthesis, where the goal is to generate both the image \\( x \\) and the corresponding semantic layout \\( y \\). For the purpose of training semantic segmentation models with strong data augmentation, DatasetGAN [41] and Dataset-DDPM [3] represent the joint image layout distribution as a composition of two models: an image generation model \\( p(x) \\) and a classifier \\( p(y|x) \\). During inference, the internal representations of \\( p(x) \\) (i.e., feature maps) are used as inputs of \\( p(y|x) \\), which then classifies each pixel to obtain an image layout pair." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.891, + 0.755 + ], + "angle": 0, + "content": "On the other hand, SB-GAN [2] and Semantic Palette [18] discover that joint modeling of the image layout distribution can be advantageous for generating complex scenes. Specifically, they decompose the generation process into two steps, a layout generation step \\( p(y) \\) followed by a conditional image generation step \\( p(x|y) \\) given the generated layout. The authors argue that generating layouts with appropriate class proportions can effectively facilitate the scene generation process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.891, + 0.824 + ], + "angle": 0, + "content": "SemanticGAN [20] models \\( p(x, y) \\) with a single GAN [8] in the pursuit of semantic segmentation with out-of-domain generalization. The results demonstrate that images and layouts can exhibit high alignment when generated through a single model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.891, + 0.866 + ], + "angle": 0, + "content": "In this work, we propose a Gaussian-categorical diffusion process to model \\( p(x,y) \\) with a single diffusion process. Our joint image-Layout generation model is extended" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.897, + 0.501, + 0.907 + ], + "angle": 0, + "content": "7592" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.124, + 0.468, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.274, + 0.469, + 0.3 + ], + "angle": 0, + "content": "Figure 3. Illustration of the Gaussian-categorical diffusion process on the image layout distribution of MM CelebA-HQ [19, 22]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.469, + 0.385 + ], + "angle": 0, + "content": "to the text-to-image generation task, where we achieve high text-image correspondence without requiring web-scale text-image datasets. Specifically, we provide analyses demonstrating that our model is aware of the semantics of the generated image and properly reflects the text conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.469, + 0.469 + ], + "angle": 0, + "content": "Diffusion process in arbitrary domains. Diffusion models [7, 12, 24, 35] synthesize data \\(\\mathbf{x}_0\\) in an iterative manner by repeatedly denoising pure noise \\(\\mathbf{x}_T\\). In image generation, the forward noisng process \\(q(\\mathbf{x}_t|\\mathbf{x}_{t - 1})\\) and the reverse denoising process \\(p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)\\) are defined using a predefined noise schedule \\(\\beta_{t}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.478, + 0.469, + 0.495 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) := \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} I\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.497, + 0.469, + 0.513 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) := \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\mathbf {x} _ {t}\\right), \\sigma_ {t} ^ {2} \\boldsymbol {I}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.524, + 0.228, + 0.538 + ], + "angle": 0, + "content": "where \\(t\\in [1,2,\\dots,T]\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.469, + 0.58 + ], + "angle": 0, + "content": "Since the true reverse process \\( q(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t) \\) is intractable, the reverse process is approximated by minimizing the KL divergence with the posterior \\( q(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t, \\mathbf{x}_0) \\) with" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.591, + 0.469, + 0.607 + ], + "angle": 0, + "content": "\\[\nL _ {t} = D _ {\\mathrm {K L}} \\left(q \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}, \\mathbf {x} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right)\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.469, + 0.687 + ], + "angle": 0, + "content": "To extend diffusion processes to categorical data [1, 15] such as text or semantic labels, a categorical noise is defined for the forward process, and the denoising diffusion process is constructed in a similar manner. For instance, Hoogeboom et al. [15] defines a categorical noise as" + }, + { + "type": "equation", + "bbox": [ + 0.119, + 0.698, + 0.469, + 0.714 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) := \\mathcal {C} \\left(\\mathbf {x} _ {t}; (1 - \\beta_ {t}) \\mathbf {x} _ {t - 1} + \\beta_ {t} / K\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.716, + 0.469, + 0.731 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) := \\mathcal {C} \\left(\\mathbf {x} _ {t - 1}; \\boldsymbol {\\Theta} _ {\\theta} \\left(\\mathbf {x} _ {t}\\right)\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.469, + 0.782 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}\\) denotes a categorical distribution, \\(K\\) is the number of categories, and \\(\\Theta\\) is the probability mass function (PMF) of the categorical distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.469, + 0.867 + ], + "angle": 0, + "content": "The key idea for defining a diffusion process in a certain distribution is to define a forward noising process \\(q(\\mathbf{x}_t|\\mathbf{x}_{t - 1})\\) and derive a posterior \\(q\\left(\\mathbf{x}_{t - 1}|\\mathbf{x}_t,\\mathbf{x}_0\\right)\\). In the following section, we define the forward and reverse processes of the Gaussian-categorical distribution, which can model the joint distribution of image layout pairs." + }, + { + "type": "image", + "bbox": [ + 0.592, + 0.126, + 0.843, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.249, + 0.892, + 0.274 + ], + "angle": 0, + "content": "Figure 4. Visualization of a Gaussian-categorical distribution with a single variable (\\(N = 1\\), \\(M = 1\\), \\(K = 4\\), and \\(S = 4\\))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.284, + 0.59, + 0.297 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.301, + 0.791, + 0.315 + ], + "angle": 0, + "content": "3.1. Gaussian-categorical distribution" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.323, + 0.892, + 0.364 + ], + "angle": 0, + "content": "In this section, we define the joint distribution of the Gaussian variable \\(X\\) and categorical variable \\(Y\\). We parameterize the Gaussian-categorical distribution as follows," + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.383, + 0.891, + 0.399 + ], + "angle": 0, + "content": "\\[\n(X, Y) \\sim \\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}), \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.402, + 0.797, + 0.418 + ], + "angle": 0, + "content": "\\[\nX = \\left[ X _ {1}, X _ {2},..., X _ {N} \\right] \\in \\mathbb {R} ^ {N},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.421, + 0.85, + 0.438 + ], + "angle": 0, + "content": "\\[\nY = \\left[ Y _ {1}, Y _ {2}, \\dots , Y _ {M} \\right] \\in \\{1, 2, \\dots , K \\} ^ {M} \\subset \\mathbb {R} ^ {M},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.44, + 0.835, + 0.456 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} \\in \\mathbb {R} ^ {S \\times N}, \\boldsymbol {\\Sigma} \\in \\mathbb {R} ^ {S \\times N \\times N}, \\boldsymbol {\\Theta} \\in \\mathbb {R} ^ {M \\times K}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.566 + ], + "angle": 0, + "content": "Here, \\(\\mu, \\Sigma\\) are the mean and variance of the Gaussian distribution, and \\(\\Theta\\) is the probability mass function (PMF) of the categorical distribution. Also, \\(K\\) is the number of possible states for \\(Y_{i}\\) and \\(S = K^{M}\\) is the total number of states of \\(Y\\). It is worth noting that the dimensions of \\(\\mu\\) and \\(\\Sigma\\), which indicates that there is a Gaussian mean and variance for all possible categorical states in \\(Y\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.891, + 0.621 + ], + "angle": 0, + "content": "The joint distribution of two random variables can be written as a product of a conditional and marginal distribution. Therefore, we can also express the Gaussian-categorical distribution as" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.634, + 0.891, + 0.65 + ], + "angle": 0, + "content": "\\[\n\\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}) = \\mathcal {C} (\\mathbf {y}; \\boldsymbol {\\Theta}) \\cdot \\mathcal {N} (\\mathbf {x}; \\boldsymbol {\\mu} _ {\\mathbf {y}}, \\boldsymbol {\\Sigma} _ {\\mathbf {y}}) \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.652, + 0.78, + 0.669 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {\\mathbf {y}} \\in \\mathbb {R} ^ {N}, \\boldsymbol {\\Sigma} _ {\\mathbf {y}} \\in \\mathbb {R} ^ {N \\times N}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.68, + 0.891, + 0.723 + ], + "angle": 0, + "content": "The probability density function (PDF) can be written as a weighted Gaussian distribution for each unique \\(\\mathbf{y} \\in \\{1, 2, \\dots, K\\}^M\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.734, + 0.907, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}) = \\left(\\prod_ {i = 1} ^ {M} \\boldsymbol {\\Theta} _ {i}, \\mathbf {y} _ {i}\\right) (2 \\pi) ^ {- \\frac {N}{2}} | \\boldsymbol {\\Sigma} _ {\\mathbf {y}} | ^ {- \\frac {1}{2}} \\\\ \\exp \\Big (- \\frac {1}{2} (\\mathbf {x} - \\boldsymbol {\\mu_ {\\mathbf {y}}}) ^ {\\top} \\boldsymbol {\\Sigma_ {\\mathbf {y}} ^ {- 1}} (\\mathbf {x} - \\boldsymbol {\\mu_ {\\mathbf {y}}}) \\Big), \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.867 + ], + "angle": 0, + "content": "where \\(\\Theta_{i,\\mathbf{y}_i}\\) denotes the probability of \\(Y_{i} = \\mathbf{y}_{i}\\), and \\(\\pmb{\\mu}_{\\mathbf{y}}\\), \\(\\pmb{\\Sigma}_{\\mathbf{y}}\\) indicates the mean and variance corresponding to state \\(\\mathbf{y}\\), respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.897, + 0.501, + 0.907 + ], + "angle": 0, + "content": "7593" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.126, + 0.408, + 0.141 + ], + "angle": 0, + "content": "3.2. Gaussian-categorical diffusion process" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.147, + 0.47, + 0.203 + ], + "angle": 0, + "content": "Similar to the diffusion process for images, we define our reverse process of image layout distributions as a Gaussian-categorical transition with a Markov property. Specifically, we define the transition probability \\( p_{\\theta}\\left(\\mathbf{z}_{t - 1} \\mid \\mathbf{z}_t\\right) \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.213, + 0.469, + 0.24 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\boldsymbol {\\Sigma} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\boldsymbol {\\Theta} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.242, + 0.405, + 0.255 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}\\) represents the tuple \\((\\mathbf{x},\\mathbf{y})\\) for simplicity." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.255, + 0.469, + 0.282 + ], + "angle": 0, + "content": "We define the forward process of image layout pairs \\(\\mathbf{z}_0\\) under the Markov assumption as" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.292, + 0.47, + 0.327 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t}; \\left[ \\boldsymbol {\\mu} _ {t \\mid t - 1} \\right] _ {\\times S}, \\left[ \\boldsymbol {\\Sigma} _ {t \\mid t - 1} \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {t \\mid t - 1}\\right), \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.334, + 0.336, + 0.351 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {t \\mid t - 1} := \\sqrt {1 - \\beta_ {t} ^ {N}} \\mathbf {x} _ {t - 1},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.352, + 0.269, + 0.368 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {t \\mid t - 1} := \\beta_ {t} ^ {N} \\boldsymbol {I},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.37, + 0.387, + 0.386 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Theta} _ {t | t - 1} := \\left(1 - \\beta_ {t} ^ {c}\\right) \\mathbf {y} _ {t - 1} + \\beta_ {t} ^ {c} / K,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.395, + 0.469, + 0.436 + ], + "angle": 0, + "content": "where \\(\\beta^c\\) and \\(\\beta^{N}\\) are predefined noise schedules. We use the notation \\([\\mathbf{v}]_{\\times S}\\) to indicate row-wise duplication of a vector \\(\\mathbf{v}\\) (i.e., \\([\\mathbf{v},\\mathbf{v},\\dots,\\mathbf{v}]^T)\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.437, + 0.469, + 0.546 + ], + "angle": 0, + "content": "Intuitively, the forward process is defined as independently applying the Gaussian and categorical noises following a normal distribution \\(\\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) and a categorical distribution with uniform probability \\(\\mathcal{C}(1 / K)\\), according to predefined noise schedules \\(\\beta^{\\mathcal{N}},\\beta^{\\mathcal{C}}\\). Given a large \\(T\\) and appropriate noise schedules, the forward process leads to an isotropic Gaussian distribution and a uniform categorical distribution at the final state \\(\\mathbf{z}_T\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.546, + 0.469, + 0.575 + ], + "angle": 0, + "content": "With \\(\\alpha_{t} \\coloneqq 1 - \\beta_{t}\\) and \\(\\bar{\\alpha}_{t} \\coloneqq \\prod_{s=1}^{t} \\alpha_{s}\\), we can derive a forward process to an arbitrary timestep as" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.585, + 0.47, + 0.609 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N C} \\left(\\mathbf {z} _ {t}; \\left[ \\boldsymbol {\\mu} _ {t | 0} \\right] _ {\\times S}, \\left[ \\boldsymbol {\\Sigma} _ {t | 0} \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {t | 0}\\right), \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.62, + 0.294, + 0.638 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {t | 0} := \\sqrt {\\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {0},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.64, + 0.31, + 0.655 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {t | 0} := \\left(1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}\\right) \\boldsymbol {I},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.657, + 0.372, + 0.672 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Theta} _ {t \\mid 0} := (1 - \\bar {\\alpha} _ {t} ^ {c}) \\mathbf {y} _ {0} + \\bar {\\alpha} _ {t} ^ {c} / K.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.683, + 0.469, + 0.724 + ], + "angle": 0, + "content": "Finally, using Bayes theorem, we can derive the posterior \\( q(\\mathbf{z}_{t - 1} \\mid \\mathbf{z}_t, \\mathbf{z}_0) \\), which is summarized into the following form of a Gaussian-categorical distribution" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.728, + 0.469, + 0.764 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) = \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\left[ \\tilde {\\boldsymbol {\\mu}} _ {t} \\right] _ {\\times S}, \\left[ \\tilde {\\boldsymbol {\\Sigma}} _ {t} \\right] _ {\\times S}, \\tilde {\\boldsymbol {\\Theta}} _ {t}\\right), \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.77, + 0.419, + 0.804 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\boldsymbol {\\mu}} _ {t} := \\frac {\\sqrt {\\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}}} \\beta_ {t} ^ {\\mathcal {N}}}{1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {0} + \\frac {\\sqrt {\\alpha_ {t} ^ {\\mathcal {N}}} (1 - \\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}})}{1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {t},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.805, + 0.394, + 0.823 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\boldsymbol {\\Sigma}} _ {t} := \\left(\\left(1 - \\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}}\\right) \\beta_ {t} ^ {\\mathcal {N}} / \\left(1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}\\right)\\right) \\boldsymbol {I},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.826, + 0.468, + 0.843 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\boldsymbol {\\Theta}} _ {t} := Z \\left[ \\alpha_ {t} ^ {c} \\mathbf {y} _ {t} + \\left(1 - \\alpha_ {t} ^ {c}\\right) / K \\right] \\odot \\left[ \\bar {\\alpha} _ {t} ^ {c} \\mathbf {y} _ {0} + \\left(1 - \\bar {\\alpha} _ {t - 1} ^ {c}\\right) / K \\right],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.853, + 0.469, + 0.866 + ], + "angle": 0, + "content": "where \\( Z \\) is a normalizing constant and \\( \\odot \\) is the element-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.892, + 0.153 + ], + "angle": 0, + "content": "wise product. Detailed proofs for each step are provided in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.154, + 0.892, + 0.235 + ], + "angle": 0, + "content": "Note that parameters \\(\\pmb{\\mu}\\) and \\(\\pmb{\\Sigma}\\) of the posterior are expressed in terms of \\(\\widetilde{\\pmb{\\mu}}_t\\in \\mathbb{R}^N\\) and \\(\\widetilde{\\Sigma}_t\\in \\mathbb{R}^{N\\times N}\\), which have a reduced dimensions than the original parameters in Equation (6). This is due to the definition in Equation (10), where the Gaussian noise is applied independently of the categorical variable." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.237, + 0.858, + 0.25 + ], + "angle": 0, + "content": "We can write the variational lower bound (VLB) as" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.255, + 0.891, + 0.27 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {V L B}} := L _ {0} + L _ {1} + L _ {2} + \\dots + L _ {T}, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.272, + 0.891, + 0.287 + ], + "angle": 0, + "content": "\\[\nL _ {0} := - \\log p _ {\\theta} \\left(\\mathbf {z} _ {0} \\mid \\mathbf {z} _ {1}\\right), \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.29, + 0.891, + 0.304 + ], + "angle": 0, + "content": "\\[\nL _ {t - 1} := D _ {K L} \\left(q \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right)\\right), \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.307, + 0.891, + 0.322 + ], + "angle": 0, + "content": "\\[\nL _ {T} := D _ {K L} \\left(q \\left(\\mathbf {z} _ {T} \\mid \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {T}\\right)\\right). \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.328, + 0.891, + 0.357 + ], + "angle": 0, + "content": "Since the posterior \\(q(\\mathbf{z}_{t - 1}|\\mathbf{z}_t,\\mathbf{z}_0)\\) is parameterized by \\(\\widetilde{\\boldsymbol{\\mu}}_t\\) and \\(\\widetilde{\\Sigma}_t\\), we can also re-parameterize \\(p_{\\theta}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.503, + 0.363, + 0.891, + 0.393 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\left[ \\widetilde {\\boldsymbol {\\mu}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\right] _ {\\times S}, \\left[ \\widetilde {\\boldsymbol {\\Sigma}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {\\theta}\\right), \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.396, + 0.891, + 0.414 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\boldsymbol {\\mu}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\in \\mathbb {R} ^ {N}, \\widetilde {\\boldsymbol {\\Sigma}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\in \\mathbb {R} ^ {N \\times N}, \\boldsymbol {\\Theta} _ {\\theta} \\in \\mathbb {R} ^ {M \\times K}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.421, + 0.891, + 0.448 + ], + "angle": 0, + "content": "Thus, we can predict a reduced number of parameters to minimize the KL divergence term in Equation (15)," + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.455, + 0.891, + 0.47 + ], + "angle": 0, + "content": "\\[\nD _ {K L} \\left(q \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right)\\right) \\tag {19}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.473, + 0.888, + 0.502 + ], + "angle": 0, + "content": "\\[\n= \\mathbb {E} _ {q} \\left[ \\frac {1}{2 \\sigma_ {t} ^ {2}} \\| \\widetilde {\\boldsymbol {\\mu}} _ {t} - \\widetilde {\\boldsymbol {\\mu}} _ {\\theta} (\\mathbf {z} _ {t}) \\| ^ {2} \\right] + D _ {\\mathrm {K L}} \\left(\\widetilde {\\boldsymbol {\\Theta}} _ {t} \\| \\boldsymbol {\\Theta} _ {\\theta} (\\mathbf {z} _ {t})\\right) + C,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.891, + 0.545 + ], + "angle": 0, + "content": "where \\(C\\) is a constant irrelevant to learnable parameters \\(\\theta\\). \\(L_{0}\\) is directly minimized through a closed-form solution and \\(L_{T}\\) does not involve any learnable parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.552, + 0.694, + 0.567 + ], + "angle": 0, + "content": "3.3. Architectural design" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.892, + 0.698 + ], + "angle": 0, + "content": "In order to treat image-Layout pairs as a single data sample, we embed the semantic layouts (i.e., one-hot vectors) into 3-channel vectors via learnable parameters and concatenate them with images along the channel dimension \\((\\mathbf{z} \\in \\mathbb{R}^{N \\times N \\times 6})\\). We adopt the U-Net [24] and the Efficient U-Net [32] following existing diffusion models and modify the input/output channels for image-Layout input/outputs. For text conditioning, we utilize the T5-L [27] text encoder and condition the U-Net model similarly to Imagen [32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.698, + 0.892, + 0.877 + ], + "angle": 0, + "content": "We follow the cascaded diffusion [13] framework to generate high-resolution image layout pairs, which involves a sequence of an image generation model followed by a super-resolution model. We find that resizing layouts to a small resolution (e.g., \\(64 \\times 64\\)) often damages the integrity of semantic labels due to nearest-neighbor sampling on extreme scales. Thus, we generate \\(128 \\times 128\\) resolution images and then upsample to \\(256 \\times 256\\) resolution with a Gaussian-categorical super-resolution model. The super-resolution model upsamples both images and layouts following the Gaussian-categorical diffusion. We adopt the classifier-free guidance on both the generation model and the super-resolution model." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.897, + 0.501, + 0.907 + ], + "angle": 0, + "content": "7594" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.129, + 0.831, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.42, + 0.893, + 0.446 + ], + "angle": 0, + "content": "Figure 5. Examples of text-guided generation of image layout pairs from the Gaussian-categorical diffusion trained on MM CelebA-HQ-100 [17,22] and Cityscapes [6]. The text descriptions on the bottom are given as conditions to generate the image-label pairs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.454, + 0.21, + 0.469 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.477, + 0.266, + 0.492 + ], + "angle": 0, + "content": "4.1. Text-image datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.498, + 0.47, + 0.679 + ], + "angle": 0, + "content": "Multi-Modal CelebA-HQ. MM CelebA-HQ [17,22,38] is a collection of different annotations for the 30,000 images in the CelebA-HQ dataset [17,22], including text descriptions, face attribute labels, and part-level segmentation labels. Part-level segmentation labels consist of 19 different classes (\\(K = 19\\)) including all facial components and accessories. To train the Gaussian-categorical diffusion model, we use both the segmentation labels and the text descriptions provided in the dataset. We also construct subsets of the data, MM CelebA-HQ-25 and MM CelebA-HQ-50, by randomly selecting \\(25\\%\\) and \\(50\\%\\) of the images, respectively, to simulate data-scarce scenarios. We train and evaluate our models on \\(256 \\times 256\\) resolution images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Cityscapes. Cityscapes [6] is an urban scene dataset with 3475 image layout pairs of complex scenes containing multiple objects, including 20 different semantic classes (\\(K = 20\\)). To add text descriptions to each image, we list the class names in the following format:" + }, + { + "type": "text", + "bbox": [ + 0.121, + 0.754, + 0.425, + 0.769 + ], + "angle": 0, + "content": "\"An image of an urban scene with {classes}." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.774, + 0.471, + 0.873 + ], + "angle": 0, + "content": "where classes are the unique class names in the corresponding semantic layout. The Cityscapes dataset presents a challenging domain for generating realistic images due to the limited number of available images and the diverse object locations in urban scenes. Since Cityscapes images have a unique aspect ratio of 2:1, we generate \\(512 \\times 256\\) resolution images. We include example text-image pairs in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.454, + 0.715, + 0.469 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.6 + ], + "angle": 0, + "content": "For synthesizing image layout pairs, \\(N\\) and \\(M\\) are equally set to the number of pixels in the image. Although the Gaussian-categorical diffusion process allows different noise schedules \\(\\beta^{\\mathcal{N}}\\) and \\(\\beta^{c}\\) for images and layouts, we set both schedules to the cosine schedule [24]. We provide experiments on the effect of different noise schedules for \\(\\beta^{c}\\) in the supplementary section. We set \\(T = 1000\\) and sample with 100 timesteps using the accelerated sampling technique [35]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.602, + 0.813, + 0.617 + ], + "angle": 0, + "content": "4.3. Evaluating text-to-image generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.617, + 0.892, + 0.797 + ], + "angle": 0, + "content": "Text-to-image generation models are evaluated from two perspectives, image fidelity and text-image correspondence. We use the Fréchet Inception Distance (FID) [10] to measure the image fidelity. After the release of CLIP [26], the CLIP score [9] is often used to evaluate text-image correspondence for text-to-image generation. However, the CLIP score is known to have poor generalization abilities [26] when evaluating scenes with large domain gaps (i.e., Cityscapes) and also lacks interpretability in terms of understanding what element in the image causes a low or high CLIP score. In order to compensate for this drawback, we propose Semantic Recall to precisely measure the text-image correspondence for Cityscapes generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Semantic Recall. The Semantic Recall is analogous to the Semantic Object Accuracy (SOA) [11], which evaluates the generation of specific objects in text-to-image generation by utilizing pretrained object detectors. In our work, we use a pretrained semantic segmentation model [37] to detect the" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.897, + 0.501, + 0.907 + ], + "angle": 0, + "content": "7595" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.136, + 0.134, + 0.435, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.219, + 0.303, + 0.378, + 0.317 + ], + "angle": 0, + "content": "(a) FID-Semantic Recall" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.129, + 0.857, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.596, + 0.212, + 0.8, + 0.224 + ], + "angle": 0, + "content": "(b) Class-wise Semantic Recall" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.221, + 0.877, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.313, + 0.809, + 0.327 + ], + "angle": 0, + "content": "(c) Class Proportion in Cityscapes" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.332, + 0.893, + 0.371 + ], + "angle": 0, + "content": "Figure 6. (a) FID-Semantic Recall trade-off in the Cityscapes dataset. (b) Semantic Recall for minor classes. Semantic Recall is measured using the HRNet-w48 [37] model. (c) Proportion of each semantic class in the entire Cityscapes dataset. Class proportion is compared in log-scale for visibility." + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.38, + 0.47, + 0.533 + ], + "angle": 0, + "content": "presence of classes described in text conditions. We determine that a class is detected in a generated image if it appears in the segmentation layout. The ground-truth classes for each image are identified by searching for class names in text descriptions. For example, an image generated with the text description \"An urban scene with cars, roads, and traffic signs.\", would be evaluated with the existence of cars, roads, and traffic signs. Therefore, we compute the Semantic Recall as the average ratio of correctly detected classes in the generated image to the total number of classes in the ground-truth layouts," + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.542, + 0.438, + 0.579 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{| \\mathcal {G} |} \\sum_ {x _ {i}, y _ {i} \\in \\mathcal {G}} \\frac {\\left| \\text {C l a s s e s i n} F \\left(x _ {i}\\right) \\cap \\text {C l a s s e s i n} y _ {i} \\right|}{\\left| \\text {C l a s s e s i n} y _ {i} \\right|},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.469, + 0.631 + ], + "angle": 0, + "content": "where \\(\\mathcal{G}\\) is the set of generated image layout pairs \\((x_{i},y_{i})\\) and \\(|\\cdot |\\) indicates the cardinality of a given set. \\(F(\\cdot)\\) is the pretrained semantic segmentation model [37]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.469, + 0.797 + ], + "angle": 0, + "content": "Baselines. We compare our approach with state-of-the-art performing diffusion-based models, Imagen [32] and the latent diffusion model (LDM) [31]. We also train a high-performing GAN-based approach Lafite [42] trained on MM CelebA-HQ and Cityscapes. For training LDM, we utilize the pretrained autoencoder from the Stable Diffusion project. Diffusion-based approaches utilize the classifier-free guidance [14] to control the performance trade-off between text-image correspondence and image fidelity. Thus, for these approaches, we sweep the guidance scale until the text-image correspondence measures saturate and report all FID-Semantic Recall or FID-CLIP score pairs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Evaluation on Cityscapes. For the Cityscapes dataset [6], we report the FID and Semantic Recall performance trade-off and also provide detailed recall scores for each class in Figure 6. Given the small number of text-image pairs (3475 pairs), existing text-to-image models face" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.531 + ], + "angle": 0, + "content": "challenges in learning the text-image correspondence and achieving high text-image correspondence. However, the Gaussian-categorical diffusion effectively generates complex Cityscapes scenes while maintaining high Semantic Recall even with limited data. Additionally, the model achieves high recall rates for minor classes, such as the bicycle or the motorcycle class, which only constitute a small portion of the dataset. This indicates that generating semantic labels for each pixel facilitates the model to establish high text-image correspondence, especially for underrepresented classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.893, + 0.671 + ], + "angle": 0, + "content": "Evaluation on MM CelebA-HQ. We further evaluate our method on the MM CelebA-HQ-25, 50, and 100, and report the FID-CLIP scores for each dataset. As shown in Figure 7, the Gaussian-categorical diffusion consistently outperforms existing text-to-image approaches at datasets with varying numbers of text-image pairs, exhibiting low FIDs and a high CLIP scores. We provide qualitative results of the Gaussian-categorical diffusion in Figure 5 and also compare the results with existing approaches in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.83, + 0.695 + ], + "angle": 0, + "content": "4.4. Analyzing the internal representations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.867 + ], + "angle": 0, + "content": "In order to visualize the advantages of jointly generating image-Layout pairs, we train a Gaussian diffusion model which generates images without corresponding semantic layouts. Then, we collect the internal features from the two models at different timesteps and cluster the features in an unsupervised manner with K-means clustering. As shown in Figure 8, the internal features of the Gaussian-categorical model form distinct clusters that correspond to different facial regions. Specifically, the internal features of the Gaussian-categorical diffusion model form clusters even in the early stages of generation \\((t = 800)\\), correctly distinguishing hair, glasses and the background region." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.897, + 0.502, + 0.907 + ], + "angle": 0, + "content": "7596" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.108, + 0.128, + 0.345, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.128, + 0.661, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.129, + 0.85, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.286, + 0.662, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.315, + 0.892, + 0.341 + ], + "angle": 0, + "content": "Figure 7. FID-CLIP score pairs for text-to-image generation models on different subsets of the MM CelebA-HQ dataset. The CLIP scores are measured with the ViT-L/14-336 model. The guidance scale is swept starting from 1 until saturation." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.349, + 0.468, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.53 + ], + "angle": 0, + "content": "Figure 8. Visualization of clustering results between the internal features of the Gaussian-categorical diffusion and the Gaussian diffusion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.473, + 0.694 + ], + "angle": 0, + "content": "The results reveal that the Gaussian-categorical diffusion model is highly aware of the semantics of the image during the generation process. This characteristic is advantageous in scenarios where a generative model needs to learn how to match specific parts of the image with corresponding input text descriptions, as the model is capable of understanding the semantic structure of the image. As such, training a Gaussian-categorical diffusion is a promising approach for achieving high correspondence between text descriptions and image pixels, particularly when there is a scarcity of text-image pairs available." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.706, + 0.388, + 0.721 + ], + "angle": 0, + "content": "4.5. Image layout fidelity and alignment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.47, + 0.868 + ], + "angle": 0, + "content": "In this section, we evaluate whether generated images and layouts closely model the real distribution, and whether the generated pairs are semantically aligned. Following Semantic Palette [2, 18] we evaluate the image-Layout alignment using the mean intersection over union (mIoU) between the generated layouts and the segmentation labels predicted by a pretrained HRNet [37]. Additionally, we use the Fréchet Segmentation Distance (FSD) [4], which replaces the Inception-V3 [36] features in the FID score [10] to pixel counts for each class, to evaluate the quality of gen" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.347, + 0.886, + 0.437 + ], + "angle": 0, + "content": "
MethodsFID ↓mIoU ↑FSD ↓
GANformer [16]24.86-481.5
DatasetDDPM [3]55.3833.8890.31
Semantic Palette [18]52.1353.1748.29
Ours20.3665.8042.22
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.439, + 0.892, + 0.478 + ], + "angle": 0, + "content": "Table 1. Image-Layout alignment and FID of different Imagelayout generation approaches for scene generation in the Cityscapes [6] dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.497, + 0.891, + 0.538 + ], + "angle": 0, + "content": "erated layouts. Similar to the FID score, a low FSD indicates that the class distributions are close to the real distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.544, + 0.892, + 0.681 + ], + "angle": 0, + "content": "We compare our results with existing unconditional image layout generation approaches [3, 18] on the Cityscapes dataset. Additionally, we introduce a simple baseline (i.e., GANformer [16]) for image layout generation, in which we generate images using a well-trained unconditional image generation model [16] and segment the images using a pretrained segmentation model [37]. Note that we cannot measure the mIoU for this baseline since the semantic layouts are predicted using the same pretrained network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.893, + 0.867 + ], + "angle": 0, + "content": "As shown in Table 1, the Gaussian-categorical diffusion process is highly effective in modeling the joint distribution of images and layouts even for complex urban scenes. By using a unified diffusion process, we are able to generate image layout pairs that exhibit high alignment, closely resembling the real distribution. The ability of the Gaussian-categorical diffusion to effectively model the joint distribution of images and layouts offers promising avenues for future research in generative modeling. By leveraging the theoretical foundations established by our method, researchers can explore new approaches for dataset generation in a range of domains, from images and audiios to semantic layouts and texts." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.897, + 0.501, + 0.907 + ], + "angle": 0, + "content": "7597" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.124, + 0.482, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.169, + 0.272, + 0.405, + 0.284 + ], + "angle": 0, + "content": "(a) Text-guided Image-to-Layout Generation" + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.124, + 0.888, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.574, + 0.272, + 0.81, + 0.284 + ], + "angle": 0, + "content": "(b) Text-guided Layout-to-Image Generation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.291, + 0.893, + 0.318 + ], + "angle": 0, + "content": "Figure 9. Cross-modal outpainting for (a) text-guided image-to-Layout generation and (b) text-guided layout-to-image generation. Segmentation layouts are generated with \\( n = 1 \\) resampling steps and images are generated with \\( n = 5 \\) resampling steps for each timestep." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.332, + 0.307, + 0.348 + ], + "angle": 0, + "content": "4.6. Cross-modal outpainting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.47, + 0.41 + ], + "angle": 0, + "content": "RePaint [23] enables existing diffusion models to inpaint a masked image by iteratively denoising the masked region given the known image (i.e., condition image). Specifically, for each timestep \\( t \\), images are inpainted as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.419, + 0.384, + 0.437 + ], + "angle": 0, + "content": "\\[\nx _ {t - 1} ^ {\\mathrm {k n o w n}} \\sim \\mathcal {N} (\\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) I),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.438, + 0.393, + 0.455 + ], + "angle": 0, + "content": "\\[\nx _ {t - 1} ^ {\\text {u n k n o w n}} \\sim \\mathcal {N} (\\boldsymbol {\\mu} _ {\\theta} (x _ {t}, t), \\boldsymbol {\\Sigma} _ {\\theta} (x _ {t}, t)),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.457, + 0.416, + 0.474 + ], + "angle": 0, + "content": "\\[\nx _ {t - 1} = m \\odot x _ {t - 1} ^ {\\text {k n o w n}} + (1 - m) \\odot x _ {t - 1} ^ {\\text {u n k n o w n}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.484, + 0.47, + 0.54 + ], + "angle": 0, + "content": "where \\(m\\) is the mask for the known image. To ensure consistency between the inpainted regions and known regions, Repaint iterates the denoising process \\(n\\) times for each timestep." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.47, + 0.721 + ], + "angle": 0, + "content": "The Repaint technique allows us to use the Gaussian-categorical diffusion model as a text-guided layout-to-image generation model (i.e., semantic image synthesis) by considering the layouts as an image layout pair with the image part masked. Similarly, we can perform text-guided image-to layout generation (i.e., semantic segmentation) by masking the layout in the image layout pair. As shown in Figure 9, the Gaussian-categorical diffusion generates realistic images or layouts conditioned on text descriptions. The results demonstrate that a well-trained Gaussian-categorical diffusion can serve as a generative prior for conditional generation tasks. We describe the algorithm for cross-modal outpainting in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.732, + 0.192, + 0.747 + ], + "angle": 0, + "content": "5. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Although the Gaussian-categorical diffusion offers means for achieving high text-image correspondence without training on web-scale text-image pairs, training a Gaussian-categorical diffusion model requires additional semantic layout annotations of images. However, with the assistance of recent data annotation tools [5,34], annotating existing data can be a cost-effective option for text-to-image generation in scenarios where obtaining web-scale text" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.89, + 0.361 + ], + "angle": 0, + "content": "image pairs is costly (e.g., medical images, urban scenes, and aerial images)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.893, + 0.501 + ], + "angle": 0, + "content": "We observe that training the Gaussian-categorical diffusion model on the MS-COCO dataset [21] produces poor quality images and layouts. We suspect that this is due to the highly diverse scenes in the COCO dataset, with 171 categories in the semantic layouts. Analyzing the challenges of training on the MS-COCO dataset is a potential area for future research. Nevertheless, we propose an effective approach for text-to-image generation in data-scarce scenarios, where collecting data is expensive and annotating existing images is affordable." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.519, + 0.619, + 0.533 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.892, + 0.656 + ], + "angle": 0, + "content": "In this paper, we define the Gaussian-categorical diffusion process to model the joint distribution of image layout pairs. Our experiments demonstrate that the proposed model can ensure high text-image correspondence for text-to-image generation in specific domains, without relying on web-scale text-image pairs. Our approach outperforms existing approaches in terms of image quality and text-image correspondence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.768 + ], + "angle": 0, + "content": "Our visualizations of the internal representations of the Gaussian-categorical distribution demonstrate that the proposed model is aware of the semantics of the image, bridging the gap between highly semantic text descriptions and image pixels. Additionally, the high image layout alignment of generated image layout pairs and the results of cross-modal outpainting show that the model precisely captures the relationship between images and labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Overall, the Gaussian-categorical diffusion enables text-to-image models to achieve high text-image correspondence by leveraging semantic labels when trained on a specific domain with limited text-image pairs. Our proposed model can also be utilized as a generative prior for conditional generation tasks, such as text-guided semantic image synthesis and text-guided semantic segmentation." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.897, + 0.502, + 0.907 + ], + "angle": 0, + "content": "7598" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.125, + 0.237, + 0.141 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.149, + 0.47, + 0.26 + ], + "angle": 0, + "content": "This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B02001913), Electronics and Telecommunications Research Institute (ETRI) grant funded by the Korean government [22ZS1200, Fundamental Technology Research for Human-Centric Autonomous Intelligent Systems], and the KAIST-NAVER hypercreative AI center." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.275, + 0.173, + 0.289 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.3, + 0.47, + 0.35 + ], + "angle": 0, + "content": "[1] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. 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In CVPR, 2019. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.127, + 0.892, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.47, + 0.897, + 0.501, + 0.907 + ], + "angle": 0, + "content": "7600" + } + ] +] \ No newline at end of file diff --git a/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_origin.pdf b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c8bcf306daa32312ff9102a787b58091c25ba2c5 --- /dev/null +++ b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/580abc17-52d1-48f0-9975-3f39f0fd195f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:758b0d08183a24d4ada1b1cabd55bb523dac742ab42cf9154fde2379e4bce382 +size 2083885 diff --git a/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/full.md b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/full.md new file mode 100644 index 0000000000000000000000000000000000000000..de2c7182e68ad618cd4cba31c5afdc77018c1dbe --- /dev/null +++ b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/full.md @@ -0,0 +1,439 @@ +# Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis + +Minho Park*, Jooyeol Yun*, Seunghwan Choi, Jaegul Choo +Korea Advanced Institute of Science and Technology (KAIST) +Daejeon, Korea + +{m.park, blizzard072, shadow2496, jchoo}@kaist.ac.kr + +# Abstract + +Existing text-to-image generation approaches have set high standards for photorealism and text-image correspondence, largely benefiting from web-scale text-image datasets, which can include up to 5 billion pairs. However, text-to-image generation models trained on domain-specific datasets, such as urban scenes, medical images, and faces, still suffer from low text-image correspondence due to the lack of text-image pairs. Additionally, collecting billions of text-image pairs for a specific domain can be time-consuming and costly. Thus, ensuring high text-image correspondence without relying on web-scale text-image datasets remains a challenging task. In this paper, we present a novel approach for enhancing text-image correspondence by leveraging available semantic layouts. Specifically, we propose a Gaussian-categorical diffusion process that simultaneously generates both images and corresponding layout pairs. Our experiments reveal that we can guide text-to-image generation models to be aware of the semantics of different image regions, by training the model to generate semantic labels for each pixel. We demonstrate that our approach achieves higher text-image correspondence compared to existing text-to-image generation approaches in the Multi-Modal CelebA-HQ and the Cityscapes dataset, where text-image pairs are scarce. Codes are available at https://pmh9960.github.io/research/GCDP. + +# 1. Introduction + +Text-to-image generation aims to materialize text descriptions into images, where the main challenge comes from ensuring high image quality and correspondence between input text and output images. While texts convey intuitive semantic depictions of images, they often lack detailed spatial descriptions. For example, text descriptions such as "A woman is wearing earrings." do not describe where the earrings are located within the image. Thus, when a small number of text-image pairs are given, it is challenging + +![](images/1828bea502eb09d6cf3965dcf0134f9638046958d03c353ff32e7c7489211a3f.jpg) +Figure 1. Recall of facial attributes specified in the text descriptions. Text-to-image generation approaches trained on a subset of the Multi-Modal CelebA-HQ [17,22] often fail to reflect text conditions. Facial attributes are classified with a pretrained attribute classifier [30]. + +ing for a generative model to learn what part of the image corresponds to which words in the text. + +Overcome this hurdle, recent text-to-image generation approaches [28, 29, 31, 32] leverage web-scale text-image datasets [29, 33] containing up to 5 billion text-image pairs. With access to such data, generative models can fully learn the correspondence between input texts and output images and synthesize photorealistic images while properly reflecting text descriptions. + +However, the cost of such large-scale training remains a major obstacle, often requiring weeks of training even with hundreds of GPUs, which limits participation in the subject to only a few researchers. Moreover, when generating images in a specific domain, such as faces or urban scenes, collecting billions of text-image pairs can be challenging due to the difficulties in collecting images. Even with a general-purpose pretrained model, finetuning on datasets with large domain gaps (e.g., urban scenes or medical images) leads to poor image quality and low text-image correspondence. Recent text-to-image models trained on specific domains often fail to reflect text conditions in the absence of web-scale text-image pairs. To examine the issue in data-scarce scenarios, we evaluate text-to-image generation models trained on a subset of the Multi-Modal CelebA-HQ [17,22] dataset. As shown in Figure 1, existing models struggle to generate certain attributes specified in the given text conditions. Thus, ensuring high text-image correspondence remains a + +challenge for domain-specific generation. + +In this paper, we present a novel approach to achieve high text-image correspondence for domain-specific text-to-image generation by leveraging semantic layouts. Rather than solely generating images based on text descriptions, we propose to concurrently generate both images and their corresponding semantic layouts. To this end, we design a Gaussian-categorical diffusion process that models the joint distribution of image layout pairs. To the best of our knowledge, this is the first approach to combine Gaussian and categorical diffusion processes into a unified diffusion process. By generating semantic labels for each pixel in the image, our generative model can learn the semantics of different parts of the image, allowing it to effectively learn which text descriptions correspond to which locations in the image, even with limited text-image pairs. + +We experiment our approach on subsets of the MultiModal CelebA-HQ [19, 22] to simulate cases where text-image pairs are limited and semantic layouts are available. We also add text descriptions to the Cityscapes dataset [6] to evaluate text-to-image generation in complex scenes with multiple objects, where learning text-image correspondence can be challenging. Our experiments and analyses reveal that modeling the joint image layout distribution can effectively facilitate text-to-image generation models to achieve high text-image correspondence when web-scale text-image pairs are unavailable. We also demonstrate potential applications of the Gaussian-categorical diffusion models in semantic image synthesis and semantic segmentation, through cross-modal outpainting. + +Our contributions are threefold: + +- We define a Gaussian-categorical diffusion process for modeling joint image-Layout distributions, which is the first approach to unify two diffusion processes for image-Layout generation. +- Our experiments reveal that generating image layout pairs can be a practical alternative to increase text-image correspondence in circumstances where collecting web-scale text-image pairs is infeasible. +- We present cross-modal outpainting, which demonstrates that Gaussian-categorical diffusion models are also capable of modeling conditional distributions for semantic image synthesis and semantic segmentation. + +# 2. Related work + +Text-to-image generation. Text-to-image generation [39, 40, 42, 43] have consistently advanced over the years benefiting from large pretrained text encoders [27, 29] and generative models [8, 12, 29]. Recent approaches [25, 28, 31, 32] tackle zero-shot text-to-image generation by training diffusion-based generative models on web-scale text-image datasets, such as the LAION-5B [33] or the DALL-E dataset [29], which scale from 250M to 5B text-image + +![](images/64d8fd9cc52cd4e8b0811996384f1770545a310a54b8a42779d90b410f9a506a.jpg) +"He is wearing earrings. He has high cheekbones, and goatee. He is smiling." +Figure 2. Samples of image, text, and layout triplets from the MM CelebA-HQ [17, 19, 22] and the Cityscapes dataset [6]. + +![](images/e7621a6ef494ea44ac6c931c0b9d8c5b395345af62193f84094e8fb6a9cf80ea.jpg) +"An image of an urban street view with Poles, Sidewalks, People, Bicycles, Traffic signs, Cars, Buildings, Vegetations, Walls, Riders, Roads, Skies, Traffic lights and Terrains." + +pairs. While zero-shot text-to-image generation can synthesize realistic images given general text descriptions, these approaches heavily rely on the large number of text-image pairs used for training to achieve high text-image correspondence. Thus, when these models are trained on specific datasets (e.g., MM CelebA-HQ [17, 19, 22, 38]) to generate images within a certain domain, they often fail to satisfy the given text conditions as seen in Figure 1. Collecting enough text-image pairs for a specific domain to ensure high text-image correspondence may be overly expensive since obtaining text descriptions often require human captioning. In this paper, we present an alternative approach for enhancing text-image correspondence without additional text-image pairs by leveraging semantic layouts. + +Generating image layout pairs. Modeling the joint image layout distribution $p(x, y)$ is an emerging field in image synthesis, where the goal is to generate both the image $x$ and the corresponding semantic layout $y$ . For the purpose of training semantic segmentation models with strong data augmentation, DatasetGAN [41] and Dataset-DDPM [3] represent the joint image layout distribution as a composition of two models: an image generation model $p(x)$ and a classifier $p(y|x)$ . During inference, the internal representations of $p(x)$ (i.e., feature maps) are used as inputs of $p(y|x)$ , which then classifies each pixel to obtain an image layout pair. + +On the other hand, SB-GAN [2] and Semantic Palette [18] discover that joint modeling of the image layout distribution can be advantageous for generating complex scenes. Specifically, they decompose the generation process into two steps, a layout generation step $p(y)$ followed by a conditional image generation step $p(x|y)$ given the generated layout. The authors argue that generating layouts with appropriate class proportions can effectively facilitate the scene generation process. + +SemanticGAN [20] models $p(x, y)$ with a single GAN [8] in the pursuit of semantic segmentation with out-of-domain generalization. The results demonstrate that images and layouts can exhibit high alignment when generated through a single model. + +In this work, we propose a Gaussian-categorical diffusion process to model $p(x,y)$ with a single diffusion process. Our joint image-Layout generation model is extended + +![](images/b3890f5d30b18c6d4e8b92592be07f6bff1ee796b17434cac42a70204b276db3.jpg) +Figure 3. Illustration of the Gaussian-categorical diffusion process on the image layout distribution of MM CelebA-HQ [19, 22]. + +to the text-to-image generation task, where we achieve high text-image correspondence without requiring web-scale text-image datasets. Specifically, we provide analyses demonstrating that our model is aware of the semantics of the generated image and properly reflects the text conditions. + +Diffusion process in arbitrary domains. Diffusion models [7, 12, 24, 35] synthesize data $\mathbf{x}_0$ in an iterative manner by repeatedly denoising pure noise $\mathbf{x}_T$ . In image generation, the forward noisng process $q(\mathbf{x}_t|\mathbf{x}_{t - 1})$ and the reverse denoising process $p_{\theta}(\mathbf{x}_{t - 1}|\mathbf{x}_t)$ are defined using a predefined noise schedule $\beta_{t}$ , + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right) := \mathcal {N} \left(\mathbf {x} _ {t}; \sqrt {1 - \beta_ {t}} \mathbf {x} _ {t - 1}, \beta_ {t} I\right), \tag {1} +$$ + +$$ +p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) := \mathcal {N} \left(\mathbf {x} _ {t - 1}; \boldsymbol {\mu} _ {\theta} \left(\mathbf {x} _ {t}\right), \sigma_ {t} ^ {2} \boldsymbol {I}\right), \tag {2} +$$ + +where $t\in [1,2,\dots,T]$ + +Since the true reverse process $q(\mathbf{x}_{t - 1} \mid \mathbf{x}_t)$ is intractable, the reverse process is approximated by minimizing the KL divergence with the posterior $q(\mathbf{x}_{t - 1} \mid \mathbf{x}_t, \mathbf{x}_0)$ with + +$$ +L _ {t} = D _ {\mathrm {K L}} \left(q \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}, \mathbf {x} _ {0}\right) \| p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right)\right). \tag {3} +$$ + +To extend diffusion processes to categorical data [1, 15] such as text or semantic labels, a categorical noise is defined for the forward process, and the denoising diffusion process is constructed in a similar manner. For instance, Hoogeboom et al. [15] defines a categorical noise as + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {t - 1}\right) := \mathcal {C} \left(\mathbf {x} _ {t}; (1 - \beta_ {t}) \mathbf {x} _ {t - 1} + \beta_ {t} / K\right), \tag {4} +$$ + +$$ +p _ {\theta} \left(\mathbf {x} _ {t - 1} \mid \mathbf {x} _ {t}\right) := \mathcal {C} \left(\mathbf {x} _ {t - 1}; \boldsymbol {\Theta} _ {\theta} \left(\mathbf {x} _ {t}\right)\right), \tag {5} +$$ + +where $\mathcal{C}$ denotes a categorical distribution, $K$ is the number of categories, and $\Theta$ is the probability mass function (PMF) of the categorical distribution. + +The key idea for defining a diffusion process in a certain distribution is to define a forward noising process $q(\mathbf{x}_t|\mathbf{x}_{t - 1})$ and derive a posterior $q\left(\mathbf{x}_{t - 1}|\mathbf{x}_t,\mathbf{x}_0\right)$ . In the following section, we define the forward and reverse processes of the Gaussian-categorical distribution, which can model the joint distribution of image layout pairs. + +![](images/e4c22eec590cc2b1e0725600f367f6d67432aa64ff943771cfd101dd5bb65799.jpg) +Figure 4. Visualization of a Gaussian-categorical distribution with a single variable ( $N = 1$ , $M = 1$ , $K = 4$ , and $S = 4$ ). + +# 3. Method + +# 3.1. Gaussian-categorical distribution + +In this section, we define the joint distribution of the Gaussian variable $X$ and categorical variable $Y$ . We parameterize the Gaussian-categorical distribution as follows, + +$$ +(X, Y) \sim \mathcal {N C} (\mathbf {x}, \mathbf {y}; \boldsymbol {\mu}, \boldsymbol {\Sigma}, \boldsymbol {\Theta}), \tag {6} +$$ + +$$ +X = \left[ X _ {1}, X _ {2},..., X _ {N} \right] \in \mathbb {R} ^ {N}, +$$ + +$$ +Y = \left[ Y _ {1}, Y _ {2}, \dots , Y _ {M} \right] \in \{1, 2, \dots , K \} ^ {M} \subset \mathbb {R} ^ {M}, +$$ + +$$ +\boldsymbol {\mu} \in \mathbb {R} ^ {S \times N}, \boldsymbol {\Sigma} \in \mathbb {R} ^ {S \times N \times N}, \boldsymbol {\Theta} \in \mathbb {R} ^ {M \times K}. +$$ + +Here, $\mu, \Sigma$ are the mean and variance of the Gaussian distribution, and $\Theta$ is the probability mass function (PMF) of the categorical distribution. Also, $K$ is the number of possible states for $Y_{i}$ and $S = K^{M}$ is the total number of states of $Y$ . It is worth noting that the dimensions of $\mu$ and $\Sigma$ , which indicates that there is a Gaussian mean and variance for all possible categorical states in $Y$ . + +The joint distribution of two random variables can be written as a product of a conditional and marginal distribution. Therefore, we can also express the Gaussian-categorical distribution as + +$$ +\mathcal {N C} (\mathbf {x}, \mathbf {y}; \boldsymbol {\mu}, \boldsymbol {\Sigma}, \boldsymbol {\Theta}) = \mathcal {C} (\mathbf {y}; \boldsymbol {\Theta}) \cdot \mathcal {N} (\mathbf {x}; \boldsymbol {\mu} _ {\mathbf {y}}, \boldsymbol {\Sigma} _ {\mathbf {y}}) \tag {7} +$$ + +$$ +\boldsymbol {\mu} _ {\mathbf {y}} \in \mathbb {R} ^ {N}, \boldsymbol {\Sigma} _ {\mathbf {y}} \in \mathbb {R} ^ {N \times N}. +$$ + +The probability density function (PDF) can be written as a weighted Gaussian distribution for each unique $\mathbf{y} \in \{1, 2, \dots, K\}^M$ as + +$$ +\begin{array}{l} \mathcal {N C} (\mathbf {x}, \mathbf {y}; \boldsymbol {\mu}, \boldsymbol {\Sigma}, \boldsymbol {\Theta}) = \left(\prod_ {i = 1} ^ {M} \boldsymbol {\Theta} _ {i}, \mathbf {y} _ {i}\right) (2 \pi) ^ {- \frac {N}{2}} | \boldsymbol {\Sigma} _ {\mathbf {y}} | ^ {- \frac {1}{2}} \\ \exp \Big (- \frac {1}{2} (\mathbf {x} - \boldsymbol {\mu_ {\mathbf {y}}}) ^ {\top} \boldsymbol {\Sigma_ {\mathbf {y}} ^ {- 1}} (\mathbf {x} - \boldsymbol {\mu_ {\mathbf {y}}}) \Big), \tag {8} \\ \end{array} +$$ + +where $\Theta_{i,\mathbf{y}_i}$ denotes the probability of $Y_{i} = \mathbf{y}_{i}$ , and $\pmb{\mu}_{\mathbf{y}}$ , $\pmb{\Sigma}_{\mathbf{y}}$ indicates the mean and variance corresponding to state $\mathbf{y}$ , respectively. + +# 3.2. Gaussian-categorical diffusion process + +Similar to the diffusion process for images, we define our reverse process of image layout distributions as a Gaussian-categorical transition with a Markov property. Specifically, we define the transition probability $p_{\theta}\left(\mathbf{z}_{t - 1} \mid \mathbf{z}_t\right)$ as + +$$ +p _ {\theta} \left(\mathbf {z} _ {t - 1} \mid \mathbf {z} _ {t}\right) := \mathcal {N C} \left(\mathbf {z} _ {t - 1}; \boldsymbol {\mu} _ {\theta} \left(\mathbf {z} _ {t}\right), \boldsymbol {\Sigma} _ {\theta} \left(\mathbf {z} _ {t}\right), \boldsymbol {\Theta} _ {\theta} \left(\mathbf {z} _ {t}\right)\right), \tag {9} +$$ + +where $\mathbf{z}$ represents the tuple $(\mathbf{x},\mathbf{y})$ for simplicity. + +We define the forward process of image layout pairs $\mathbf{z}_0$ under the Markov assumption as + +$$ +q \left(\mathbf {z} _ {t} \mid \mathbf {z} _ {t - 1}\right) := \mathcal {N C} \left(\mathbf {z} _ {t}; \left[ \boldsymbol {\mu} _ {t \mid t - 1} \right] _ {\times S}, \left[ \boldsymbol {\Sigma} _ {t \mid t - 1} \right] _ {\times S}, \boldsymbol {\Theta} _ {t \mid t - 1}\right), \tag {10} +$$ + +$$ +\boldsymbol {\mu} _ {t \mid t - 1} := \sqrt {1 - \beta_ {t} ^ {N}} \mathbf {x} _ {t - 1}, +$$ + +$$ +\boldsymbol {\Sigma} _ {t \mid t - 1} := \beta_ {t} ^ {N} \boldsymbol {I}, +$$ + +$$ +\boldsymbol {\Theta} _ {t | t - 1} := \left(1 - \beta_ {t} ^ {c}\right) \mathbf {y} _ {t - 1} + \beta_ {t} ^ {c} / K, +$$ + +where $\beta^c$ and $\beta^{N}$ are predefined noise schedules. We use the notation $[\mathbf{v}]_{\times S}$ to indicate row-wise duplication of a vector $\mathbf{v}$ (i.e., $[\mathbf{v},\mathbf{v},\dots,\mathbf{v}]^T)$ . + +Intuitively, the forward process is defined as independently applying the Gaussian and categorical noises following a normal distribution $\mathcal{N}(\mathbf{0},\mathbf{I})$ and a categorical distribution with uniform probability $\mathcal{C}(1 / K)$ , according to predefined noise schedules $\beta^{\mathcal{N}},\beta^{\mathcal{C}}$ . Given a large $T$ and appropriate noise schedules, the forward process leads to an isotropic Gaussian distribution and a uniform categorical distribution at the final state $\mathbf{z}_T$ . + +With $\alpha_{t} \coloneqq 1 - \beta_{t}$ and $\bar{\alpha}_{t} \coloneqq \prod_{s=1}^{t} \alpha_{s}$ , we can derive a forward process to an arbitrary timestep as + +$$ +q \left(\mathbf {z} _ {t} \mid \mathbf {z} _ {0}\right) = \mathcal {N C} \left(\mathbf {z} _ {t}; \left[ \boldsymbol {\mu} _ {t | 0} \right] _ {\times S}, \left[ \boldsymbol {\Sigma} _ {t | 0} \right] _ {\times S}, \boldsymbol {\Theta} _ {t | 0}\right), \tag {11} +$$ + +$$ +\boldsymbol {\mu} _ {t | 0} := \sqrt {\bar {\alpha} _ {t} ^ {\mathcal {N}}} \mathbf {x} _ {0}, +$$ + +$$ +\boldsymbol {\Sigma} _ {t | 0} := \left(1 - \bar {\alpha} _ {t} ^ {\mathcal {N}}\right) \boldsymbol {I}, +$$ + +$$ +\boldsymbol {\Theta} _ {t \mid 0} := (1 - \bar {\alpha} _ {t} ^ {c}) \mathbf {y} _ {0} + \bar {\alpha} _ {t} ^ {c} / K. +$$ + +Finally, using Bayes theorem, we can derive the posterior $q(\mathbf{z}_{t - 1} \mid \mathbf{z}_t, \mathbf{z}_0)$ , which is summarized into the following form of a Gaussian-categorical distribution + +$$ +q \left(\mathbf {z} _ {t - 1} \mid \mathbf {z} _ {t}, \mathbf {z} _ {0}\right) = \mathcal {N C} \left(\mathbf {z} _ {t - 1}; \left[ \tilde {\boldsymbol {\mu}} _ {t} \right] _ {\times S}, \left[ \tilde {\boldsymbol {\Sigma}} _ {t} \right] _ {\times S}, \tilde {\boldsymbol {\Theta}} _ {t}\right), \tag {12} +$$ + +$$ +\widetilde {\boldsymbol {\mu}} _ {t} := \frac {\sqrt {\bar {\alpha} _ {t - 1} ^ {\mathcal {N}}} \beta_ {t} ^ {\mathcal {N}}}{1 - \bar {\alpha} _ {t} ^ {\mathcal {N}}} \mathbf {x} _ {0} + \frac {\sqrt {\alpha_ {t} ^ {\mathcal {N}}} (1 - \bar {\alpha} _ {t - 1} ^ {\mathcal {N}})}{1 - \bar {\alpha} _ {t} ^ {\mathcal {N}}} \mathbf {x} _ {t}, +$$ + +$$ +\widetilde {\boldsymbol {\Sigma}} _ {t} := \left(\left(1 - \bar {\alpha} _ {t - 1} ^ {\mathcal {N}}\right) \beta_ {t} ^ {\mathcal {N}} / \left(1 - \bar {\alpha} _ {t} ^ {\mathcal {N}}\right)\right) \boldsymbol {I}, +$$ + +$$ +\widetilde {\boldsymbol {\Theta}} _ {t} := Z \left[ \alpha_ {t} ^ {c} \mathbf {y} _ {t} + \left(1 - \alpha_ {t} ^ {c}\right) / K \right] \odot \left[ \bar {\alpha} _ {t} ^ {c} \mathbf {y} _ {0} + \left(1 - \bar {\alpha} _ {t - 1} ^ {c}\right) / K \right], +$$ + +where $Z$ is a normalizing constant and $\odot$ is the element- + +wise product. Detailed proofs for each step are provided in the appendix. + +Note that parameters $\pmb{\mu}$ and $\pmb{\Sigma}$ of the posterior are expressed in terms of $\widetilde{\pmb{\mu}}_t\in \mathbb{R}^N$ and $\widetilde{\Sigma}_t\in \mathbb{R}^{N\times N}$ , which have a reduced dimensions than the original parameters in Equation (6). This is due to the definition in Equation (10), where the Gaussian noise is applied independently of the categorical variable. + +We can write the variational lower bound (VLB) as + +$$ +L _ {\mathrm {V L B}} := L _ {0} + L _ {1} + L _ {2} + \dots + L _ {T}, \tag {13} +$$ + +$$ +L _ {0} := - \log p _ {\theta} \left(\mathbf {z} _ {0} \mid \mathbf {z} _ {1}\right), \tag {14} +$$ + +$$ +L _ {t - 1} := D _ {K L} \left(q \left(\mathbf {z} _ {t - 1} \mid \mathbf {z} _ {t}, \mathbf {z} _ {0}\right) \| p _ {\theta} \left(\mathbf {z} _ {t - 1} \mid \mathbf {z} _ {t}\right)\right), \tag {15} +$$ + +$$ +L _ {T} := D _ {K L} \left(q \left(\mathbf {z} _ {T} \mid \mathbf {z} _ {0}\right) \| p _ {\theta} \left(\mathbf {z} _ {T}\right)\right). \tag {16} +$$ + +Since the posterior $q(\mathbf{z}_{t - 1}|\mathbf{z}_t,\mathbf{z}_0)$ is parameterized by $\widetilde{\boldsymbol{\mu}}_t$ and $\widetilde{\Sigma}_t$ , we can also re-parameterize $p_{\theta}$ as + +$$ +p _ {\theta} \left(\mathbf {z} _ {t - 1} \mid \mathbf {z} _ {t}\right) := \mathcal {N C} \left(\mathbf {z} _ {t - 1}; \left[ \widetilde {\boldsymbol {\mu}} _ {\theta} \left(\mathbf {z} _ {t}\right) \right] _ {\times S}, \left[ \widetilde {\boldsymbol {\Sigma}} _ {\theta} \left(\mathbf {z} _ {t}\right) \right] _ {\times S}, \boldsymbol {\Theta} _ {\theta}\right), \tag {17} +$$ + +$$ +\widetilde {\boldsymbol {\mu}} _ {\theta} \left(\mathbf {z} _ {t}\right) \in \mathbb {R} ^ {N}, \widetilde {\boldsymbol {\Sigma}} _ {\theta} \left(\mathbf {z} _ {t}\right) \in \mathbb {R} ^ {N \times N}, \boldsymbol {\Theta} _ {\theta} \in \mathbb {R} ^ {M \times K}, \tag {18} +$$ + +Thus, we can predict a reduced number of parameters to minimize the KL divergence term in Equation (15), + +$$ +D _ {K L} \left(q \left(\mathbf {z} _ {t - 1} \mid \mathbf {z} _ {t}, \mathbf {z} _ {0}\right) \| p _ {\theta} \left(\mathbf {z} _ {t - 1} \mid \mathbf {z} _ {t}\right)\right) \tag {19} +$$ + +$$ += \mathbb {E} _ {q} \left[ \frac {1}{2 \sigma_ {t} ^ {2}} \| \widetilde {\boldsymbol {\mu}} _ {t} - \widetilde {\boldsymbol {\mu}} _ {\theta} (\mathbf {z} _ {t}) \| ^ {2} \right] + D _ {\mathrm {K L}} \left(\widetilde {\boldsymbol {\Theta}} _ {t} \| \boldsymbol {\Theta} _ {\theta} (\mathbf {z} _ {t})\right) + C, +$$ + +where $C$ is a constant irrelevant to learnable parameters $\theta$ . $L_{0}$ is directly minimized through a closed-form solution and $L_{T}$ does not involve any learnable parameters. + +# 3.3. Architectural design + +In order to treat image-Layout pairs as a single data sample, we embed the semantic layouts (i.e., one-hot vectors) into 3-channel vectors via learnable parameters and concatenate them with images along the channel dimension $(\mathbf{z} \in \mathbb{R}^{N \times N \times 6})$ . We adopt the U-Net [24] and the Efficient U-Net [32] following existing diffusion models and modify the input/output channels for image-Layout input/outputs. For text conditioning, we utilize the T5-L [27] text encoder and condition the U-Net model similarly to Imagen [32]. + +We follow the cascaded diffusion [13] framework to generate high-resolution image layout pairs, which involves a sequence of an image generation model followed by a super-resolution model. We find that resizing layouts to a small resolution (e.g., $64 \times 64$ ) often damages the integrity of semantic labels due to nearest-neighbor sampling on extreme scales. Thus, we generate $128 \times 128$ resolution images and then upsample to $256 \times 256$ resolution with a Gaussian-categorical super-resolution model. The super-resolution model upsamples both images and layouts following the Gaussian-categorical diffusion. We adopt the classifier-free guidance on both the generation model and the super-resolution model. + +![](images/b16a793ffaaffa1879eaaf411fd0e6a6ae4f651cd9e4009100f3d7fe25398942.jpg) +Figure 5. Examples of text-guided generation of image layout pairs from the Gaussian-categorical diffusion trained on MM CelebA-HQ-100 [17,22] and Cityscapes [6]. The text descriptions on the bottom are given as conditions to generate the image-label pairs. + +# 4. Experiments + +# 4.1. Text-image datasets + +Multi-Modal CelebA-HQ. MM CelebA-HQ [17,22,38] is a collection of different annotations for the 30,000 images in the CelebA-HQ dataset [17,22], including text descriptions, face attribute labels, and part-level segmentation labels. Part-level segmentation labels consist of 19 different classes ( $K = 19$ ) including all facial components and accessories. To train the Gaussian-categorical diffusion model, we use both the segmentation labels and the text descriptions provided in the dataset. We also construct subsets of the data, MM CelebA-HQ-25 and MM CelebA-HQ-50, by randomly selecting $25\%$ and $50\%$ of the images, respectively, to simulate data-scarce scenarios. We train and evaluate our models on $256 \times 256$ resolution images. + +Cityscapes. Cityscapes [6] is an urban scene dataset with 3475 image layout pairs of complex scenes containing multiple objects, including 20 different semantic classes ( $K = 20$ ). To add text descriptions to each image, we list the class names in the following format: + +"An image of an urban scene with {classes}. + +where classes are the unique class names in the corresponding semantic layout. The Cityscapes dataset presents a challenging domain for generating realistic images due to the limited number of available images and the diverse object locations in urban scenes. Since Cityscapes images have a unique aspect ratio of 2:1, we generate $512 \times 256$ resolution images. We include example text-image pairs in Figure 2. + +# 4.2. Implementation details + +For synthesizing image layout pairs, $N$ and $M$ are equally set to the number of pixels in the image. Although the Gaussian-categorical diffusion process allows different noise schedules $\beta^{\mathcal{N}}$ and $\beta^{c}$ for images and layouts, we set both schedules to the cosine schedule [24]. We provide experiments on the effect of different noise schedules for $\beta^{c}$ in the supplementary section. We set $T = 1000$ and sample with 100 timesteps using the accelerated sampling technique [35]. + +# 4.3. Evaluating text-to-image generation + +Text-to-image generation models are evaluated from two perspectives, image fidelity and text-image correspondence. We use the Fréchet Inception Distance (FID) [10] to measure the image fidelity. After the release of CLIP [26], the CLIP score [9] is often used to evaluate text-image correspondence for text-to-image generation. However, the CLIP score is known to have poor generalization abilities [26] when evaluating scenes with large domain gaps (i.e., Cityscapes) and also lacks interpretability in terms of understanding what element in the image causes a low or high CLIP score. In order to compensate for this drawback, we propose Semantic Recall to precisely measure the text-image correspondence for Cityscapes generation. + +Semantic Recall. The Semantic Recall is analogous to the Semantic Object Accuracy (SOA) [11], which evaluates the generation of specific objects in text-to-image generation by utilizing pretrained object detectors. In our work, we use a pretrained semantic segmentation model [37] to detect the + +![](images/ce751d195d36b7a0ff1bcb1d12a7204c6abf463a804d34a1ae20a30604074b1f.jpg) +(a) FID-Semantic Recall + +![](images/26fea2cb71c198eac4e2c9da5ddf6b25499da4293ee8be1c82b983cb7dfb9e5e.jpg) + +![](images/00607728f06dcccdfc5763976d602c2d3291438eb0f10513fd272b55df2a06fb.jpg) +(b) Class-wise Semantic Recall +(c) Class Proportion in Cityscapes +Figure 6. (a) FID-Semantic Recall trade-off in the Cityscapes dataset. (b) Semantic Recall for minor classes. Semantic Recall is measured using the HRNet-w48 [37] model. (c) Proportion of each semantic class in the entire Cityscapes dataset. Class proportion is compared in log-scale for visibility. + +presence of classes described in text conditions. We determine that a class is detected in a generated image if it appears in the segmentation layout. The ground-truth classes for each image are identified by searching for class names in text descriptions. For example, an image generated with the text description "An urban scene with cars, roads, and traffic signs.", would be evaluated with the existence of cars, roads, and traffic signs. Therefore, we compute the Semantic Recall as the average ratio of correctly detected classes in the generated image to the total number of classes in the ground-truth layouts, + +$$ +\frac {1}{| \mathcal {G} |} \sum_ {x _ {i}, y _ {i} \in \mathcal {G}} \frac {\left| \text {C l a s s e s i n} F \left(x _ {i}\right) \cap \text {C l a s s e s i n} y _ {i} \right|}{\left| \text {C l a s s e s i n} y _ {i} \right|}, +$$ + +where $\mathcal{G}$ is the set of generated image layout pairs $(x_{i},y_{i})$ and $|\cdot |$ indicates the cardinality of a given set. $F(\cdot)$ is the pretrained semantic segmentation model [37]. + +Baselines. We compare our approach with state-of-the-art performing diffusion-based models, Imagen [32] and the latent diffusion model (LDM) [31]. We also train a high-performing GAN-based approach Lafite [42] trained on MM CelebA-HQ and Cityscapes. For training LDM, we utilize the pretrained autoencoder from the Stable Diffusion project. Diffusion-based approaches utilize the classifier-free guidance [14] to control the performance trade-off between text-image correspondence and image fidelity. Thus, for these approaches, we sweep the guidance scale until the text-image correspondence measures saturate and report all FID-Semantic Recall or FID-CLIP score pairs. + +Evaluation on Cityscapes. For the Cityscapes dataset [6], we report the FID and Semantic Recall performance trade-off and also provide detailed recall scores for each class in Figure 6. Given the small number of text-image pairs (3475 pairs), existing text-to-image models face + +challenges in learning the text-image correspondence and achieving high text-image correspondence. However, the Gaussian-categorical diffusion effectively generates complex Cityscapes scenes while maintaining high Semantic Recall even with limited data. Additionally, the model achieves high recall rates for minor classes, such as the bicycle or the motorcycle class, which only constitute a small portion of the dataset. This indicates that generating semantic labels for each pixel facilitates the model to establish high text-image correspondence, especially for underrepresented classes. + +Evaluation on MM CelebA-HQ. We further evaluate our method on the MM CelebA-HQ-25, 50, and 100, and report the FID-CLIP scores for each dataset. As shown in Figure 7, the Gaussian-categorical diffusion consistently outperforms existing text-to-image approaches at datasets with varying numbers of text-image pairs, exhibiting low FIDs and a high CLIP scores. We provide qualitative results of the Gaussian-categorical diffusion in Figure 5 and also compare the results with existing approaches in the supplementary material. + +# 4.4. Analyzing the internal representations + +In order to visualize the advantages of jointly generating image-Layout pairs, we train a Gaussian diffusion model which generates images without corresponding semantic layouts. Then, we collect the internal features from the two models at different timesteps and cluster the features in an unsupervised manner with K-means clustering. As shown in Figure 8, the internal features of the Gaussian-categorical model form distinct clusters that correspond to different facial regions. Specifically, the internal features of the Gaussian-categorical diffusion model form clusters even in the early stages of generation $(t = 800)$ , correctly distinguishing hair, glasses and the background region. + +![](images/c36a1ab08a379a68417e123542a2fc9396eea69d219cd31e3d0effdb84df4b08.jpg) + +![](images/f724f67f38e302c852f37afe1c044473cc61db82ea26ace94b3b586b6b083df1.jpg) + +![](images/8aa05d2a01ba7e38e588dc306fdfbf819dd14ca8e1cb47156452a418510a74b2.jpg) + +![](images/781007feb0d468d7aa1007c9e11fa38ff7dd48bf40b9a53480b366687e5abfa7.jpg) + +![](images/9b504da7a451afc2a30509f75fbfc89ee42cd2b995b982d9e2914142b56f9035.jpg) +Figure 7. FID-CLIP score pairs for text-to-image generation models on different subsets of the MM CelebA-HQ dataset. The CLIP scores are measured with the ViT-L/14-336 model. The guidance scale is swept starting from 1 until saturation. +Figure 8. Visualization of clustering results between the internal features of the Gaussian-categorical diffusion and the Gaussian diffusion. + +The results reveal that the Gaussian-categorical diffusion model is highly aware of the semantics of the image during the generation process. This characteristic is advantageous in scenarios where a generative model needs to learn how to match specific parts of the image with corresponding input text descriptions, as the model is capable of understanding the semantic structure of the image. As such, training a Gaussian-categorical diffusion is a promising approach for achieving high correspondence between text descriptions and image pixels, particularly when there is a scarcity of text-image pairs available. + +# 4.5. Image layout fidelity and alignment + +In this section, we evaluate whether generated images and layouts closely model the real distribution, and whether the generated pairs are semantically aligned. Following Semantic Palette [2, 18] we evaluate the image-Layout alignment using the mean intersection over union (mIoU) between the generated layouts and the segmentation labels predicted by a pretrained HRNet [37]. Additionally, we use the Fréchet Segmentation Distance (FSD) [4], which replaces the Inception-V3 [36] features in the FID score [10] to pixel counts for each class, to evaluate the quality of gen + +
MethodsFID ↓mIoU ↑FSD ↓
GANformer [16]24.86-481.5
DatasetDDPM [3]55.3833.8890.31
Semantic Palette [18]52.1353.1748.29
Ours20.3665.8042.22
+ +Table 1. Image-Layout alignment and FID of different Imagelayout generation approaches for scene generation in the Cityscapes [6] dataset. + +erated layouts. Similar to the FID score, a low FSD indicates that the class distributions are close to the real distribution. + +We compare our results with existing unconditional image layout generation approaches [3, 18] on the Cityscapes dataset. Additionally, we introduce a simple baseline (i.e., GANformer [16]) for image layout generation, in which we generate images using a well-trained unconditional image generation model [16] and segment the images using a pretrained segmentation model [37]. Note that we cannot measure the mIoU for this baseline since the semantic layouts are predicted using the same pretrained network. + +As shown in Table 1, the Gaussian-categorical diffusion process is highly effective in modeling the joint distribution of images and layouts even for complex urban scenes. By using a unified diffusion process, we are able to generate image layout pairs that exhibit high alignment, closely resembling the real distribution. The ability of the Gaussian-categorical diffusion to effectively model the joint distribution of images and layouts offers promising avenues for future research in generative modeling. By leveraging the theoretical foundations established by our method, researchers can explore new approaches for dataset generation in a range of domains, from images and audiios to semantic layouts and texts. + +![](images/d4abe812daed03d04a7c5cfc1cd2bbaf52417dbc95478fb5e793f96edef526cc.jpg) +(a) Text-guided Image-to-Layout Generation + +![](images/799914a679d802c6143cfbc9f1682771d39574c8f0f47504200805f05e8b4af1.jpg) +(b) Text-guided Layout-to-Image Generation +Figure 9. Cross-modal outpainting for (a) text-guided image-to-Layout generation and (b) text-guided layout-to-image generation. Segmentation layouts are generated with $n = 1$ resampling steps and images are generated with $n = 5$ resampling steps for each timestep. + +# 4.6. Cross-modal outpainting + +RePaint [23] enables existing diffusion models to inpaint a masked image by iteratively denoising the masked region given the known image (i.e., condition image). Specifically, for each timestep $t$ , images are inpainted as follows: + +$$ +x _ {t - 1} ^ {\mathrm {k n o w n}} \sim \mathcal {N} (\sqrt {\bar {\alpha} _ {t}} x _ {0}, (1 - \bar {\alpha} _ {t}) I), +$$ + +$$ +x _ {t - 1} ^ {\text {u n k n o w n}} \sim \mathcal {N} (\boldsymbol {\mu} _ {\theta} (x _ {t}, t), \boldsymbol {\Sigma} _ {\theta} (x _ {t}, t)), +$$ + +$$ +x _ {t - 1} = m \odot x _ {t - 1} ^ {\text {k n o w n}} + (1 - m) \odot x _ {t - 1} ^ {\text {u n k n o w n}}, +$$ + +where $m$ is the mask for the known image. To ensure consistency between the inpainted regions and known regions, Repaint iterates the denoising process $n$ times for each timestep. + +The Repaint technique allows us to use the Gaussian-categorical diffusion model as a text-guided layout-to-image generation model (i.e., semantic image synthesis) by considering the layouts as an image layout pair with the image part masked. Similarly, we can perform text-guided image-to layout generation (i.e., semantic segmentation) by masking the layout in the image layout pair. As shown in Figure 9, the Gaussian-categorical diffusion generates realistic images or layouts conditioned on text descriptions. The results demonstrate that a well-trained Gaussian-categorical diffusion can serve as a generative prior for conditional generation tasks. We describe the algorithm for cross-modal outpainting in the supplementary material. + +# 5. Limitation + +Although the Gaussian-categorical diffusion offers means for achieving high text-image correspondence without training on web-scale text-image pairs, training a Gaussian-categorical diffusion model requires additional semantic layout annotations of images. However, with the assistance of recent data annotation tools [5,34], annotating existing data can be a cost-effective option for text-to-image generation in scenarios where obtaining web-scale text + +image pairs is costly (e.g., medical images, urban scenes, and aerial images). + +We observe that training the Gaussian-categorical diffusion model on the MS-COCO dataset [21] produces poor quality images and layouts. We suspect that this is due to the highly diverse scenes in the COCO dataset, with 171 categories in the semantic layouts. Analyzing the challenges of training on the MS-COCO dataset is a potential area for future research. Nevertheless, we propose an effective approach for text-to-image generation in data-scarce scenarios, where collecting data is expensive and annotating existing images is affordable. + +# 6. Conclusion + +In this paper, we define the Gaussian-categorical diffusion process to model the joint distribution of image layout pairs. Our experiments demonstrate that the proposed model can ensure high text-image correspondence for text-to-image generation in specific domains, without relying on web-scale text-image pairs. Our approach outperforms existing approaches in terms of image quality and text-image correspondence. + +Our visualizations of the internal representations of the Gaussian-categorical distribution demonstrate that the proposed model is aware of the semantics of the image, bridging the gap between highly semantic text descriptions and image pixels. Additionally, the high image layout alignment of generated image layout pairs and the results of cross-modal outpainting show that the model precisely captures the relationship between images and labels. + +Overall, the Gaussian-categorical diffusion enables text-to-image models to achieve high text-image correspondence by leveraging semantic labels when trained on a specific domain with limited text-image pairs. Our proposed model can also be utilized as a generative prior for conditional generation tasks, such as text-guided semantic image synthesis and text-guided semantic segmentation. + +# Acknowledgement + +This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B02001913), Electronics and Telecommunications Research Institute (ETRI) grant funded by the Korean government [22ZS1200, Fundamental Technology Research for Human-Centric Autonomous Intelligent Systems], and the KAIST-NAVER hypercreative AI center. + +# References + +[1] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. Structured denoising diffusion models in discrete state-spaces. NeurIPS, 34:17981-17993, 2021. 3 +[2] Samaneh Azadi, Michael Tschannen, Eric Tzeng, Sylvain Gelly, Trevor Darrell, and Mario Lucic. 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In CVPR, 2019. 2 \ No newline at end of file diff --git a/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/images.zip b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..db7b098333a3625d26099922b93c354185a978f5 --- /dev/null +++ b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:897971b5002c7a51e53741df6b9fb89d804041d2400912d930137b11a3cece15 +size 599175 diff --git a/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/layout.json b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4e59ed92ca2ccaf342ba5442c9c241bcfe5a40e4 --- /dev/null +++ b/2023/Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis/layout.json @@ -0,0 +1,9860 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 88, + 137, + 489, + 172 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 137, + 489, + 172 + ], + "spans": [ + { + "bbox": [ + 88, + 137, + 489, + 172 + ], + "type": "text", + "content": "Learning to Generate Semantic Layouts for Higher Text-Image Correspondence in Text-to-Image Synthesis" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 130, + 192, + 446, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 192, + 446, + 234 + ], + "spans": [ + { + "bbox": [ + 130, + 192, + 446, + 234 + ], + "type": "text", + "content": "Minho Park*, Jooyeol Yun*, Seunghwan Choi, Jaegul Choo \nKorea Advanced Institute of Science and Technology (KAIST) \nDaejeon, Korea" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 235, + 424, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 235, + 424, + 247 + ], + "spans": [ + { + "bbox": [ + 151, + 235, + 424, + 247 + ], + "type": "text", + "content": "{m.park, blizzard072, shadow2496, jchoo}@kaist.ac.kr" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 139, + 273, + 186, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 273, + 186, + 286 + ], + "spans": [ + { + "bbox": [ + 139, + 273, + 186, + 286 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 298, + 281, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 298, + 281, + 601 + ], + "spans": [ + { + "bbox": [ + 45, + 298, + 281, + 601 + ], + "type": "text", + "content": "Existing text-to-image generation approaches have set high standards for photorealism and text-image correspondence, largely benefiting from web-scale text-image datasets, which can include up to 5 billion pairs. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 623, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 623, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 623, + 279, + 729 + ], + "type": "text", + "content": "Text-to-image generation aims to materialize text descriptions into images, where the main challenge comes from ensuring high image quality and correspondence between input text and output images. While texts convey intuitive semantic depictions of images, they often lack detailed spatial descriptions. For example, text descriptions such as \"A woman is wearing earrings.\" do not describe where the earrings are located within the image. 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With access to such data, generative models can fully learn the correspondence between input texts and output images and synthesize photorealistic images while properly reflecting text descriptions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 520, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 520, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 520, + 531, + 730 + ], + "type": "text", + "content": "However, the cost of such large-scale training remains a major obstacle, often requiring weeks of training even with hundreds of GPUs, which limits participation in the subject to only a few researchers. Moreover, when generating images in a specific domain, such as faces or urban scenes, collecting billions of text-image pairs can be challenging due to the difficulties in collecting images. Even with a general-purpose pretrained model, finetuning on datasets with large domain gaps (e.g., urban scenes or medical images) leads to poor image quality and low text-image correspondence. Recent text-to-image models trained on specific domains often fail to reflect text conditions in the absence of web-scale text-image pairs. To examine the issue in data-scarce scenarios, we evaluate text-to-image generation models trained on a subset of the Multi-Modal CelebA-HQ [17,22] dataset. As shown in Figure 1, existing models struggle to generate certain attributes specified in the given text conditions. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 735, + 159, + 746 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 735, + 159, + 746 + ], + "spans": [ + { + "bbox": [ + 57, + 735, + 159, + 746 + ], + "type": "inline_equation", + "content": "{}^{1}" + }, + { + "bbox": [ + 57, + 735, + 159, + 746 + ], + "type": "text", + "content": " * indicates equal contribution." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 279, + 755, + 298, + 764 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 755, + 298, + 764 + ], + "spans": [ + { + "bbox": [ + 279, + 755, + 298, + 764 + ], + "type": "text", + "content": "7591" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 210, + 117 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 210, + 117 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 210, + 117 + ], + "type": "text", + "content": "challenge for domain-specific generation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 117, + 279, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 117, + 279, + 291 + ], + "spans": [ + { + "bbox": [ + 45, + 117, + 279, + 291 + ], + "type": "text", + "content": "In this paper, we present a novel approach to achieve high text-image correspondence for domain-specific text-to-image generation by leveraging semantic layouts. Rather than solely generating images based on text descriptions, we propose to concurrently generate both images and their corresponding semantic layouts. To this end, we design a Gaussian-categorical diffusion process that models the joint distribution of image layout pairs. To the best of our knowledge, this is the first approach to combine Gaussian and categorical diffusion processes into a unified diffusion process. By generating semantic labels for each pixel in the image, our generative model can learn the semantics of different parts of the image, allowing it to effectively learn which text descriptions correspond to which locations in the image, even with limited text-image pairs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 293, + 279, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 293, + 279, + 455 + ], + "spans": [ + { + "bbox": [ + 45, + 293, + 279, + 455 + ], + "type": "text", + "content": "We experiment our approach on subsets of the MultiModal CelebA-HQ [19, 22] to simulate cases where text-image pairs are limited and semantic layouts are available. We also add text descriptions to the Cityscapes dataset [6] to evaluate text-to-image generation in complex scenes with multiple objects, where learning text-image correspondence can be challenging. Our experiments and analyses reveal that modeling the joint image layout distribution can effectively facilitate text-to-image generation models to achieve high text-image correspondence when web-scale text-image pairs are unavailable. We also demonstrate potential applications of the Gaussian-categorical diffusion models in semantic image synthesis and semantic segmentation, through cross-modal outpainting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 455, + 183, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 455, + 183, + 465 + ], + "spans": [ + { + "bbox": [ + 57, + 455, + 183, + 465 + ], + "type": "text", + "content": "Our contributions are threefold:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 469, + 279, + 615 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 57, + 469, + 279, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 469, + 279, + 516 + ], + "spans": [ + { + "bbox": [ + 57, + 469, + 279, + 516 + ], + "type": "text", + "content": "- We define a Gaussian-categorical diffusion process for modeling joint image-Layout distributions, which is the first approach to unify two diffusion processes for image-Layout generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 519, + 279, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 519, + 279, + 565 + ], + "spans": [ + { + "bbox": [ + 57, + 519, + 279, + 565 + ], + "type": "text", + "content": "- Our experiments reveal that generating image layout pairs can be a practical alternative to increase text-image correspondence in circumstances where collecting web-scale text-image pairs is infeasible." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 569, + 279, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 569, + 279, + 615 + ], + "spans": [ + { + "bbox": [ + 57, + 569, + 279, + 615 + ], + "type": "text", + "content": "- We present cross-modal outpainting, which demonstrates that Gaussian-categorical diffusion models are also capable of modeling conditional distributions for semantic image synthesis and semantic segmentation." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 45, + 623, + 128, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 623, + 128, + 634 + ], + "spans": [ + { + "bbox": [ + 45, + 623, + 128, + 634 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 636, + 279, + 729 + ], + "type": "text", + "content": "Text-to-image generation. Text-to-image generation [39, 40, 42, 43] have consistently advanced over the years benefiting from large pretrained text encoders [27, 29] and generative models [8, 12, 29]. Recent approaches [25, 28, 31, 32] tackle zero-shot text-to-image generation by training diffusion-based generative models on web-scale text-image datasets, such as the LAION-5B [33] or the DALL-E dataset [29], which scale from 250M to 5B text-image" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 301, + 106, + 377, + 181 + ], + "blocks": [ + { + "bbox": [ + 301, + 106, + 377, + 181 + ], + "lines": [ + { + "bbox": [ + 301, + 106, + 377, + 181 + ], + "spans": [ + { + "bbox": [ + 301, + 106, + 377, + 181 + ], + "type": "image", + "image_path": "64d8fd9cc52cd4e8b0811996384f1770545a310a54b8a42779d90b410f9a506a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 302, + 183, + 377, + 202 + ], + "lines": [ + { + "bbox": [ + 302, + 183, + 377, + 202 + ], + "spans": [ + { + "bbox": [ + 302, + 183, + 377, + 202 + ], + "type": "text", + "content": "\"He is wearing earrings. He has high cheekbones, and goatee. He is smiling.\"" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 296, + 202, + 529, + 223 + ], + "lines": [ + { + "bbox": [ + 296, + 202, + 529, + 223 + ], + "spans": [ + { + "bbox": [ + 296, + 202, + 529, + 223 + ], + "type": "text", + "content": "Figure 2. Samples of image, text, and layout triplets from the MM CelebA-HQ [17, 19, 22] and the Cityscapes dataset [6]." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 378, + 106, + 528, + 181 + ], + "blocks": [ + { + "bbox": [ + 378, + 106, + 528, + 181 + ], + "lines": [ + { + "bbox": [ + 378, + 106, + 528, + 181 + ], + "spans": [ + { + "bbox": [ + 378, + 106, + 528, + 181 + ], + "type": "image", + "image_path": "e7621a6ef494ea44ac6c931c0b9d8c5b395345af62193f84094e8fb6a9cf80ea.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 378, + 183, + 524, + 202 + ], + "lines": [ + { + "bbox": [ + 378, + 183, + 524, + 202 + ], + "spans": [ + { + "bbox": [ + 378, + 183, + 524, + 202 + ], + "type": "text", + "content": "\"An image of an urban street view with Poles, Sidewalks, People, Bicycles, Traffic signs, Cars, Buildings, Vegetations, Walls, Riders, Roads, Skies, Traffic lights and Terrains.\"" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 227, + 530, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 227, + 530, + 390 + ], + "spans": [ + { + "bbox": [ + 296, + 227, + 530, + 390 + ], + "type": "text", + "content": "pairs. While zero-shot text-to-image generation can synthesize realistic images given general text descriptions, these approaches heavily rely on the large number of text-image pairs used for training to achieve high text-image correspondence. Thus, when these models are trained on specific datasets (e.g., MM CelebA-HQ [17, 19, 22, 38]) to generate images within a certain domain, they often fail to satisfy the given text conditions as seen in Figure 1. Collecting enough text-image pairs for a specific domain to ensure high text-image correspondence may be overly expensive since obtaining text descriptions often require human captioning. In this paper, we present an alternative approach for enhancing text-image correspondence without additional text-image pairs by leveraging semantic layouts." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "spans": [ + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "content": "Generating image layout pairs. Modeling the joint image layout distribution " + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "inline_equation", + "content": "p(x, y)" + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "content": " is an emerging field in image synthesis, where the goal is to generate both the image " + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "content": " and the corresponding semantic layout " + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "content": ". For the purpose of training semantic segmentation models with strong data augmentation, DatasetGAN [41] and Dataset-DDPM [3] represent the joint image layout distribution as a composition of two models: an image generation model " + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "inline_equation", + "content": "p(x)" + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "content": " and a classifier " + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "inline_equation", + "content": "p(y|x)" + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "content": ". During inference, the internal representations of " + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "inline_equation", + "content": "p(x)" + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "content": " (i.e., feature maps) are used as inputs of " + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "inline_equation", + "content": "p(y|x)" + }, + { + "bbox": [ + 296, + 391, + 530, + 531 + ], + "type": "text", + "content": ", which then classifies each pixel to obtain an image layout pair." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 531, + 530, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 531, + 530, + 635 + ], + "spans": [ + { + "bbox": [ + 296, + 531, + 530, + 635 + ], + "type": "text", + "content": "On the other hand, SB-GAN [2] and Semantic Palette [18] discover that joint modeling of the image layout distribution can be advantageous for generating complex scenes. Specifically, they decompose the generation process into two steps, a layout generation step " + }, + { + "bbox": [ + 296, + 531, + 530, + 635 + ], + "type": "inline_equation", + "content": "p(y)" + }, + { + "bbox": [ + 296, + 531, + 530, + 635 + ], + "type": "text", + "content": " followed by a conditional image generation step " + }, + { + "bbox": [ + 296, + 531, + 530, + 635 + ], + "type": "inline_equation", + "content": "p(x|y)" + }, + { + "bbox": [ + 296, + 531, + 530, + 635 + ], + "type": "text", + "content": " given the generated layout. The authors argue that generating layouts with appropriate class proportions can effectively facilitate the scene generation process." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 636, + 530, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 636, + 530, + 693 + ], + "spans": [ + { + "bbox": [ + 296, + 636, + 530, + 693 + ], + "type": "text", + "content": "SemanticGAN [20] models " + }, + { + "bbox": [ + 296, + 636, + 530, + 693 + ], + "type": "inline_equation", + "content": "p(x, y)" + }, + { + "bbox": [ + 296, + 636, + 530, + 693 + ], + "type": "text", + "content": " with a single GAN [8] in the pursuit of semantic segmentation with out-of-domain generalization. The results demonstrate that images and layouts can exhibit high alignment when generated through a single model." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 694, + 530, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 729 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 729 + ], + "type": "text", + "content": "In this work, we propose a Gaussian-categorical diffusion process to model " + }, + { + "bbox": [ + 296, + 694, + 530, + 729 + ], + "type": "inline_equation", + "content": "p(x,y)" + }, + { + "bbox": [ + 296, + 694, + 530, + 729 + ], + "type": "text", + "content": " with a single diffusion process. Our joint image-Layout generation model is extended" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "spans": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "text", + "content": "7592" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 104, + 278, + 227 + ], + "blocks": [ + { + "bbox": [ + 48, + 104, + 278, + 227 + ], + "lines": [ + { + "bbox": [ + 48, + 104, + 278, + 227 + ], + "spans": [ + { + "bbox": [ + 48, + 104, + 278, + 227 + ], + "type": "image", + "image_path": "b3890f5d30b18c6d4e8b92592be07f6bff1ee796b17434cac42a70204b276db3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 230, + 279, + 252 + ], + "lines": [ + { + "bbox": [ + 45, + 230, + 279, + 252 + ], + "spans": [ + { + "bbox": [ + 45, + 230, + 279, + 252 + ], + "type": "text", + "content": "Figure 3. Illustration of the Gaussian-categorical diffusion process on the image layout distribution of MM CelebA-HQ [19, 22]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 255, + 279, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 255, + 279, + 324 + ], + "spans": [ + { + "bbox": [ + 45, + 255, + 279, + 324 + ], + "type": "text", + "content": "to the text-to-image generation task, where we achieve high text-image correspondence without requiring web-scale text-image datasets. Specifically, we provide analyses demonstrating that our model is aware of the semantics of the generated image and properly reflects the text conditions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "spans": [ + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "text", + "content": "Diffusion process in arbitrary domains. Diffusion models [7, 12, 24, 35] synthesize data " + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "text", + "content": " in an iterative manner by repeatedly denoising pure noise " + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_T" + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "text", + "content": ". In image generation, the forward noisng process " + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_t|\\mathbf{x}_{t - 1})" + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "text", + "content": " and the reverse denoising process " + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{x}_{t - 1}|\\mathbf{x}_t)" + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "text", + "content": " are defined using a predefined noise schedule " + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 45, + 325, + 279, + 394 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 75, + 402, + 279, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 402, + 279, + 416 + ], + "spans": [ + { + "bbox": [ + 75, + 402, + 279, + 416 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) := \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\sqrt {1 - \\beta_ {t}} \\mathbf {x} _ {t - 1}, \\beta_ {t} I\\right), \\tag {1}", + "image_path": "e9aff6cb25e3125c5c081371fdec8a5778876d0b90f6de932a2c214802f4ea9c.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 81, + 418, + 279, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 418, + 279, + 431 + ], + "spans": [ + { + "bbox": [ + 81, + 418, + 279, + 431 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) := \\mathcal {N} \\left(\\mathbf {x} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\mathbf {x} _ {t}\\right), \\sigma_ {t} ^ {2} \\boldsymbol {I}\\right), \\tag {2}", + "image_path": "a2be3a860eebcc0d60a450d03ca2036273a6be90b840165f4950762f14c497b6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 441, + 135, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 441, + 135, + 452 + ], + "spans": [ + { + "bbox": [ + 45, + 441, + 135, + 452 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 441, + 135, + 452 + ], + "type": "inline_equation", + "content": "t\\in [1,2,\\dots,T]" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 452, + 279, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 452, + 279, + 488 + ], + "spans": [ + { + "bbox": [ + 45, + 452, + 279, + 488 + ], + "type": "text", + "content": "Since the true reverse process " + }, + { + "bbox": [ + 45, + 452, + 279, + 488 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t)" + }, + { + "bbox": [ + 45, + 452, + 279, + 488 + ], + "type": "text", + "content": " is intractable, the reverse process is approximated by minimizing the KL divergence with the posterior " + }, + { + "bbox": [ + 45, + 452, + 279, + 488 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_{t - 1} \\mid \\mathbf{x}_t, \\mathbf{x}_0)" + }, + { + "bbox": [ + 45, + 452, + 279, + 488 + ], + "type": "text", + "content": " with" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 72, + 497, + 279, + 511 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 497, + 279, + 511 + ], + "spans": [ + { + "bbox": [ + 72, + 497, + 279, + 511 + ], + "type": "interline_equation", + "content": "L _ {t} = D _ {\\mathrm {K L}} \\left(q \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}, \\mathbf {x} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right)\\right). \\tag {3}", + "image_path": "a0a0b18e2c1b4669ce98974f18119fa360f0d4eea3cf004de1197a3afb18a370.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 520, + 279, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 520, + 279, + 578 + ], + "spans": [ + { + "bbox": [ + 45, + 520, + 279, + 578 + ], + "type": "text", + "content": "To extend diffusion processes to categorical data [1, 15] such as text or semantic labels, a categorical noise is defined for the forward process, and the denoising diffusion process is constructed in a similar manner. For instance, Hoogeboom et al. [15] defines a categorical noise as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 70, + 587, + 279, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 587, + 279, + 601 + ], + "spans": [ + { + "bbox": [ + 70, + 587, + 279, + 601 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {t - 1}\\right) := \\mathcal {C} \\left(\\mathbf {x} _ {t}; (1 - \\beta_ {t}) \\mathbf {x} _ {t - 1} + \\beta_ {t} / K\\right), \\tag {4}", + "image_path": "1621da9e5c71a74c18278cf3e8bb09750bda68dc71d37d011aaec939f56e387a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 92, + 602, + 279, + 615 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 602, + 279, + 615 + ], + "spans": [ + { + "bbox": [ + 92, + 602, + 279, + 615 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {x} _ {t - 1} \\mid \\mathbf {x} _ {t}\\right) := \\mathcal {C} \\left(\\mathbf {x} _ {t - 1}; \\boldsymbol {\\Theta} _ {\\theta} \\left(\\mathbf {x} _ {t}\\right)\\right), \\tag {5}", + "image_path": "154b8beaac105ba653bd0583a1d29e260ebdd883d9b2dc1d7bff5200a581eb51.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "spans": [ + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "type": "text", + "content": " denotes a categorical distribution, " + }, + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "type": "text", + "content": " is the number of categories, and " + }, + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 45, + 624, + 279, + 658 + ], + "type": "text", + "content": " is the probability mass function (PMF) of the categorical distribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": "The key idea for defining a diffusion process in a certain distribution is to define a forward noising process " + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_t|\\mathbf{x}_{t - 1})" + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": " and derive a posterior " + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "inline_equation", + "content": "q\\left(\\mathbf{x}_{t - 1}|\\mathbf{x}_t,\\mathbf{x}_0\\right)" + }, + { + "bbox": [ + 45, + 660, + 279, + 730 + ], + "type": "text", + "content": ". In the following section, we define the forward and reverse processes of the Gaussian-categorical distribution, which can model the joint distribution of image layout pairs." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 352, + 106, + 501, + 201 + ], + "blocks": [ + { + "bbox": [ + 352, + 106, + 501, + 201 + ], + "lines": [ + { + "bbox": [ + 352, + 106, + 501, + 201 + ], + "spans": [ + { + "bbox": [ + 352, + 106, + 501, + 201 + ], + "type": "image", + "image_path": "e4c22eec590cc2b1e0725600f367f6d67432aa64ff943771cfd101dd5bb65799.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "lines": [ + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "spans": [ + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "text", + "content": "Figure 4. Visualization of a Gaussian-categorical distribution with a single variable (" + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "inline_equation", + "content": "N = 1" + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "inline_equation", + "content": "M = 1" + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "inline_equation", + "content": "S = 4" + }, + { + "bbox": [ + 296, + 209, + 530, + 230 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 239, + 351, + 250 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 239, + 351, + 250 + ], + "spans": [ + { + "bbox": [ + 297, + 239, + 351, + 250 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 253, + 470, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 253, + 470, + 265 + ], + "spans": [ + { + "bbox": [ + 297, + 253, + 470, + 265 + ], + "type": "text", + "content": "3.1. Gaussian-categorical distribution" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 271, + 530, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 271, + 530, + 306 + ], + "spans": [ + { + "bbox": [ + 296, + 271, + 530, + 306 + ], + "type": "text", + "content": "In this section, we define the joint distribution of the Gaussian variable " + }, + { + "bbox": [ + 296, + 271, + 530, + 306 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 296, + 271, + 530, + 306 + ], + "type": "text", + "content": " and categorical variable " + }, + { + "bbox": [ + 296, + 271, + 530, + 306 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 296, + 271, + 530, + 306 + ], + "type": "text", + "content": ". We parameterize the Gaussian-categorical distribution as follows," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 351, + 322, + 530, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 322, + 530, + 335 + ], + "spans": [ + { + "bbox": [ + 351, + 322, + 530, + 335 + ], + "type": "interline_equation", + "content": "(X, Y) \\sim \\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}), \\tag {6}", + "image_path": "36e08df8200d653a9764fd9b1747f8ea91ea160fd5270556977803ff269e7999.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 355, + 338, + 474, + 351 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 338, + 474, + 351 + ], + "spans": [ + { + "bbox": [ + 355, + 338, + 474, + 351 + ], + "type": "interline_equation", + "content": "X = \\left[ X _ {1}, X _ {2},..., X _ {N} \\right] \\in \\mathbb {R} ^ {N},", + "image_path": "f457b29c7e160ce3184faf19e88c3b7140368aeaece3d78c870113f07695c1d8.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 321, + 354, + 505, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 354, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 321, + 354, + 505, + 368 + ], + "type": "interline_equation", + "content": "Y = \\left[ Y _ {1}, Y _ {2}, \\dots , Y _ {M} \\right] \\in \\{1, 2, \\dots , K \\} ^ {M} \\subset \\mathbb {R} ^ {M},", + "image_path": "a97ec6cdd913d0f67cbec3e3b26311a3901d52ff1c5ff0de5c8bf9803266f168.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 331, + 370, + 496, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 370, + 496, + 383 + ], + "spans": [ + { + "bbox": [ + 331, + 370, + 496, + 383 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} \\in \\mathbb {R} ^ {S \\times N}, \\boldsymbol {\\Sigma} \\in \\mathbb {R} ^ {S \\times N \\times N}, \\boldsymbol {\\Theta} \\in \\mathbb {R} ^ {M \\times K}.", + "image_path": "f7bb82ef4e9d10c2764f92d0029c8231f66db0b41efb33e1aefbc53f4cbd3419.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "spans": [ + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "\\mu, \\Sigma" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": " are the mean and variance of the Gaussian distribution, and " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": " is the probability mass function (PMF) of the categorical distribution. Also, " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": " is the number of possible states for " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "Y_{i}" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "S = K^{M}" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": " is the total number of states of " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": ". It is worth noting that the dimensions of " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": ", which indicates that there is a Gaussian mean and variance for all possible categorical states in " + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 296, + 394, + 530, + 476 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 296, + 476, + 530, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 476, + 530, + 522 + ], + "spans": [ + { + "bbox": [ + 296, + 476, + 530, + 522 + ], + "type": "text", + "content": "The joint distribution of two random variables can be written as a product of a conditional and marginal distribution. Therefore, we can also express the Gaussian-categorical distribution as" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 319, + 533, + 530, + 547 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 533, + 530, + 547 + ], + "spans": [ + { + "bbox": [ + 319, + 533, + 530, + 547 + ], + "type": "interline_equation", + "content": "\\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}) = \\mathcal {C} (\\mathbf {y}; \\boldsymbol {\\Theta}) \\cdot \\mathcal {N} (\\mathbf {x}; \\boldsymbol {\\mu} _ {\\mathbf {y}}, \\boldsymbol {\\Sigma} _ {\\mathbf {y}}) \\tag {7}", + "image_path": "ad704ba7e96e0adb4e240c317f92c6793d91052070d64aa736846f34485e2f1c.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 364, + 548, + 464, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 548, + 464, + 563 + ], + "spans": [ + { + "bbox": [ + 364, + 548, + 464, + 563 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {\\mathbf {y}} \\in \\mathbb {R} ^ {N}, \\boldsymbol {\\Sigma} _ {\\mathbf {y}} \\in \\mathbb {R} ^ {N \\times N}.", + "image_path": "a698b4065f9c68ae985702c761c869337d86d62518d7f554c8a8b3274eb10046.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 296, + 572, + 530, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 572, + 530, + 608 + ], + "spans": [ + { + "bbox": [ + 296, + 572, + 530, + 608 + ], + "type": "text", + "content": "The probability density function (PDF) can be written as a weighted Gaussian distribution for each unique " + }, + { + "bbox": [ + 296, + 572, + 530, + 608 + ], + "type": "inline_equation", + "content": "\\mathbf{y} \\in \\{1, 2, \\dots, K\\}^M" + }, + { + "bbox": [ + 296, + 572, + 530, + 608 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 296, + 618, + 539, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 618, + 539, + 684 + ], + "spans": [ + { + "bbox": [ + 296, + 618, + 539, + 684 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {N C} (\\mathbf {x}, \\mathbf {y}; \\boldsymbol {\\mu}, \\boldsymbol {\\Sigma}, \\boldsymbol {\\Theta}) = \\left(\\prod_ {i = 1} ^ {M} \\boldsymbol {\\Theta} _ {i}, \\mathbf {y} _ {i}\\right) (2 \\pi) ^ {- \\frac {N}{2}} | \\boldsymbol {\\Sigma} _ {\\mathbf {y}} | ^ {- \\frac {1}{2}} \\\\ \\exp \\Big (- \\frac {1}{2} (\\mathbf {x} - \\boldsymbol {\\mu_ {\\mathbf {y}}}) ^ {\\top} \\boldsymbol {\\Sigma_ {\\mathbf {y}} ^ {- 1}} (\\mathbf {x} - \\boldsymbol {\\mu_ {\\mathbf {y}}}) \\Big), \\tag {8} \\\\ \\end{array}", + "image_path": "1c7c43cbe2b03e0fa782a611b88121793541c7acdc957f7818e1ac644dd07af6.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\Theta_{i,\\mathbf{y}_i}" + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": " denotes the probability of " + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "inline_equation", + "content": "Y_{i} = \\mathbf{y}_{i}" + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{\\mathbf{y}}" + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_{\\mathbf{y}}" + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": " indicates the mean and variance corresponding to state " + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 296, + 694, + 530, + 730 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "spans": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "text", + "content": "7593" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 106, + 242, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 106, + 242, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 242, + 118 + ], + "type": "text", + "content": "3.2. Gaussian-categorical diffusion process" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 123, + 279, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 123, + 279, + 170 + ], + "spans": [ + { + "bbox": [ + 45, + 123, + 279, + 170 + ], + "type": "text", + "content": "Similar to the diffusion process for images, we define our reverse process of image layout distributions as a Gaussian-categorical transition with a Markov property. Specifically, we define the transition probability " + }, + { + "bbox": [ + 45, + 123, + 279, + 170 + ], + "type": "inline_equation", + "content": "p_{\\theta}\\left(\\mathbf{z}_{t - 1} \\mid \\mathbf{z}_t\\right)" + }, + { + "bbox": [ + 45, + 123, + 279, + 170 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 179, + 279, + 202 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 179, + 279, + 202 + ], + "spans": [ + { + "bbox": [ + 55, + 179, + 279, + 202 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\boldsymbol {\\Sigma} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\boldsymbol {\\Theta} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right), \\tag {9}", + "image_path": "98a63d8340b6d0ba437a711d9a17f18577a52f23fbc0dac96d6f0fa7901ba83f.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 203, + 240, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 203, + 240, + 214 + ], + "spans": [ + { + "bbox": [ + 46, + 203, + 240, + 214 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 203, + 240, + 214 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 203, + 240, + 214 + ], + "type": "text", + "content": " represents the tuple " + }, + { + "bbox": [ + 46, + 203, + 240, + 214 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},\\mathbf{y})" + }, + { + "bbox": [ + 46, + 203, + 240, + 214 + ], + "type": "text", + "content": " for simplicity." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 214, + 279, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 214, + 279, + 237 + ], + "spans": [ + { + "bbox": [ + 45, + 214, + 279, + 237 + ], + "type": "text", + "content": "We define the forward process of image layout pairs " + }, + { + "bbox": [ + 45, + 214, + 279, + 237 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 45, + 214, + 279, + 237 + ], + "type": "text", + "content": " under the Markov assumption as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 245, + 279, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 279, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 279, + 275 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t}; \\left[ \\boldsymbol {\\mu} _ {t \\mid t - 1} \\right] _ {\\times S}, \\left[ \\boldsymbol {\\Sigma} _ {t \\mid t - 1} \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {t \\mid t - 1}\\right), \\tag {10}", + "image_path": "af2e59498c28c2d0f373b0539da919f59a28cb16779b35f628173ef06ca196bf.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 95, + 281, + 199, + 295 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 281, + 199, + 295 + ], + "spans": [ + { + "bbox": [ + 95, + 281, + 199, + 295 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {t \\mid t - 1} := \\sqrt {1 - \\beta_ {t} ^ {N}} \\mathbf {x} _ {t - 1},", + "image_path": "842d0813fed0deda1274660fb71bab33d86c34de3c6baeb14a97ae7b2166debc.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 95, + 296, + 160, + 309 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 296, + 160, + 309 + ], + "spans": [ + { + "bbox": [ + 95, + 296, + 160, + 309 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {t \\mid t - 1} := \\beta_ {t} ^ {N} \\boldsymbol {I},", + "image_path": "c62f598cf9860f0960574f414f11a3b2f2550bf4bb6a5b75ed88f22af79d0836.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 95, + 311, + 230, + 325 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 311, + 230, + 325 + ], + "spans": [ + { + "bbox": [ + 95, + 311, + 230, + 325 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Theta} _ {t | t - 1} := \\left(1 - \\beta_ {t} ^ {c}\\right) \\mathbf {y} _ {t - 1} + \\beta_ {t} ^ {c} / K,", + "image_path": "ed9e15e0e809da003bb1dd9db4de0045cc4a734e2056c762cd9bda592907b31a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "spans": [ + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "inline_equation", + "content": "\\beta^c" + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "inline_equation", + "content": "\\beta^{N}" + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "text", + "content": " are predefined noise schedules. We use the notation " + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "inline_equation", + "content": "[\\mathbf{v}]_{\\times S}" + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "text", + "content": " to indicate row-wise duplication of a vector " + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "inline_equation", + "content": "[\\mathbf{v},\\mathbf{v},\\dots,\\mathbf{v}]^T)" + }, + { + "bbox": [ + 45, + 332, + 279, + 367 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "spans": [ + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "text", + "content": "Intuitively, the forward process is defined as independently applying the Gaussian and categorical noises following a normal distribution " + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "text", + "content": " and a categorical distribution with uniform probability " + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(1 / K)" + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "text", + "content": ", according to predefined noise schedules " + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "inline_equation", + "content": "\\beta^{\\mathcal{N}},\\beta^{\\mathcal{C}}" + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "text", + "content": ". Given a large " + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "text", + "content": " and appropriate noise schedules, the forward process leads to an isotropic Gaussian distribution and a uniform categorical distribution at the final state " + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 45, + 367, + 279, + 459 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 459, + 279, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 459, + 279, + 484 + ], + "spans": [ + { + "bbox": [ + 45, + 459, + 279, + 484 + ], + "type": "text", + "content": "With " + }, + { + "bbox": [ + 45, + 459, + 279, + 484 + ], + "type": "inline_equation", + "content": "\\alpha_{t} \\coloneqq 1 - \\beta_{t}" + }, + { + "bbox": [ + 45, + 459, + 279, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 459, + 279, + 484 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} \\coloneqq \\prod_{s=1}^{t} \\alpha_{s}" + }, + { + "bbox": [ + 45, + 459, + 279, + 484 + ], + "type": "text", + "content": ", we can derive a forward process to an arbitrary timestep as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 56, + 492, + 279, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 492, + 279, + 512 + ], + "spans": [ + { + "bbox": [ + 56, + 492, + 279, + 512 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N C} \\left(\\mathbf {z} _ {t}; \\left[ \\boldsymbol {\\mu} _ {t | 0} \\right] _ {\\times S}, \\left[ \\boldsymbol {\\Sigma} _ {t | 0} \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {t | 0}\\right), \\tag {11}", + "image_path": "76b9db87767523d9183893d714913f296500b60aecf1f0900cea668888838adf.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 522, + 174, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 522, + 174, + 537 + ], + "spans": [ + { + "bbox": [ + 104, + 522, + 174, + 537 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {t | 0} := \\sqrt {\\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {0},", + "image_path": "828ae2f1cbc029794f5541e85c28ca2b90759bcb18a9fe5ec7a0af07a3ace150.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 538, + 184, + 551 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 538, + 184, + 551 + ], + "spans": [ + { + "bbox": [ + 104, + 538, + 184, + 551 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {t | 0} := \\left(1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}\\right) \\boldsymbol {I},", + "image_path": "a7ea79e318bc5dfcf6d59ad841f930d3535983bc0729d0034864da1e7b245ee1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 553, + 221, + 565 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 553, + 221, + 565 + ], + "spans": [ + { + "bbox": [ + 104, + 553, + 221, + 565 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Theta} _ {t \\mid 0} := (1 - \\bar {\\alpha} _ {t} ^ {c}) \\mathbf {y} _ {0} + \\bar {\\alpha} _ {t} ^ {c} / K.", + "image_path": "c69c050c3664e97023a63eed3279c1838a605bf7481199c5a7f25b0d17aa67e9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 45, + 575, + 279, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 575, + 279, + 609 + ], + "spans": [ + { + "bbox": [ + 45, + 575, + 279, + 609 + ], + "type": "text", + "content": "Finally, using Bayes theorem, we can derive the posterior " + }, + { + "bbox": [ + 45, + 575, + 279, + 609 + ], + "type": "inline_equation", + "content": "q(\\mathbf{z}_{t - 1} \\mid \\mathbf{z}_t, \\mathbf{z}_0)" + }, + { + "bbox": [ + 45, + 575, + 279, + 609 + ], + "type": "text", + "content": ", which is summarized into the following form of a Gaussian-categorical distribution" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 57, + 612, + 279, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 612, + 279, + 643 + ], + "spans": [ + { + "bbox": [ + 57, + 612, + 279, + 643 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) = \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\left[ \\tilde {\\boldsymbol {\\mu}} _ {t} \\right] _ {\\times S}, \\left[ \\tilde {\\boldsymbol {\\Sigma}} _ {t} \\right] _ {\\times S}, \\tilde {\\boldsymbol {\\Theta}} _ {t}\\right), \\tag {12}", + "image_path": "fc570d74e33d5eea4df353cd3a6c8017a2da61d5f512f0b0fac912b016c49003.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 75, + 648, + 249, + 676 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 648, + 249, + 676 + ], + "spans": [ + { + "bbox": [ + 75, + 648, + 249, + 676 + ], + "type": "interline_equation", + "content": "\\widetilde {\\boldsymbol {\\mu}} _ {t} := \\frac {\\sqrt {\\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}}} \\beta_ {t} ^ {\\mathcal {N}}}{1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {0} + \\frac {\\sqrt {\\alpha_ {t} ^ {\\mathcal {N}}} (1 - \\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}})}{1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}} \\mathbf {x} _ {t},", + "image_path": "86289de874823ffbf1d86621666b440672a40055b17cb6101bf5fe5b1155b799.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 91, + 677, + 234, + 692 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 677, + 234, + 692 + ], + "spans": [ + { + "bbox": [ + 91, + 677, + 234, + 692 + ], + "type": "interline_equation", + "content": "\\widetilde {\\boldsymbol {\\Sigma}} _ {t} := \\left(\\left(1 - \\bar {\\alpha} _ {t - 1} ^ {\\mathcal {N}}\\right) \\beta_ {t} ^ {\\mathcal {N}} / \\left(1 - \\bar {\\alpha} _ {t} ^ {\\mathcal {N}}\\right)\\right) \\boldsymbol {I},", + "image_path": "3a8bb595c5033b6d41c5f7268d5218c0bb0dfb35f0abf098bdda655b139c3ed8.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 695, + 278, + 709 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 695, + 278, + 709 + ], + "spans": [ + { + "bbox": [ + 47, + 695, + 278, + 709 + ], + "type": "interline_equation", + "content": "\\widetilde {\\boldsymbol {\\Theta}} _ {t} := Z \\left[ \\alpha_ {t} ^ {c} \\mathbf {y} _ {t} + \\left(1 - \\alpha_ {t} ^ {c}\\right) / K \\right] \\odot \\left[ \\bar {\\alpha} _ {t} ^ {c} \\mathbf {y} _ {0} + \\left(1 - \\bar {\\alpha} _ {t - 1} ^ {c}\\right) / K \\right],", + "image_path": "5be13aec17021fb132d0e0a9b2d754d5fcb6a29597e60ddc92435044992f4427.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 48, + 718, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 718, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 48, + 718, + 279, + 729 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 48, + 718, + 279, + 729 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 48, + 718, + 279, + 729 + ], + "type": "text", + "content": " is a normalizing constant and " + }, + { + "bbox": [ + 48, + 718, + 279, + 729 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 48, + 718, + 279, + 729 + ], + "type": "text", + "content": " is the element-" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 106, + 530, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 128 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 128 + ], + "type": "text", + "content": "wise product. Detailed proofs for each step are provided in the appendix." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "spans": [ + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "text", + "content": "Note that parameters " + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}" + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}" + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "text", + "content": " of the posterior are expressed in terms of " + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "inline_equation", + "content": "\\widetilde{\\pmb{\\mu}}_t\\in \\mathbb{R}^N" + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "inline_equation", + "content": "\\widetilde{\\Sigma}_t\\in \\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 296, + 129, + 530, + 197 + ], + "type": "text", + "content": ", which have a reduced dimensions than the original parameters in Equation (6). This is due to the definition in Equation (10), where the Gaussian noise is applied independently of the categorical variable." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 308, + 199, + 510, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 199, + 510, + 210 + ], + "spans": [ + { + "bbox": [ + 308, + 199, + 510, + 210 + ], + "type": "text", + "content": "We can write the variational lower bound (VLB) as" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 343, + 214, + 530, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 214, + 530, + 227 + ], + "spans": [ + { + "bbox": [ + 343, + 214, + 530, + 227 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {V L B}} := L _ {0} + L _ {1} + L _ {2} + \\dots + L _ {T}, \\tag {13}", + "image_path": "9f0d0593d23e0a6b3c45a01f8153995215ffb5f2fb7fc84b75af0e8afadc11d4.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 365, + 229, + 530, + 241 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 229, + 530, + 241 + ], + "spans": [ + { + "bbox": [ + 365, + 229, + 530, + 241 + ], + "type": "interline_equation", + "content": "L _ {0} := - \\log p _ {\\theta} \\left(\\mathbf {z} _ {0} \\mid \\mathbf {z} _ {1}\\right), \\tag {14}", + "image_path": "713f95d6b88261dba70824bec3e507a1721220eb4fa4045e82054ec38cb5bc90.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 311, + 244, + 530, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 244, + 530, + 255 + ], + "spans": [ + { + "bbox": [ + 311, + 244, + 530, + 255 + ], + "type": "interline_equation", + "content": "L _ {t - 1} := D _ {K L} \\left(q \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right)\\right), \\tag {15}", + "image_path": "0ab68c46a877247f555ccb4052d7ac22d142cfc7b6a2acab00e2e7897d14d352.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 345, + 258, + 530, + 271 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 258, + 530, + 271 + ], + "spans": [ + { + "bbox": [ + 345, + 258, + 530, + 271 + ], + "type": "interline_equation", + "content": "L _ {T} := D _ {K L} \\left(q \\left(\\mathbf {z} _ {T} \\mid \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {T}\\right)\\right). \\tag {16}", + "image_path": "f31a51360a57a3c99bf59039e093e488b17dd219847caa951eeec9be887dccb5.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "spans": [ + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "text", + "content": "Since the posterior " + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "inline_equation", + "content": "q(\\mathbf{z}_{t - 1}|\\mathbf{z}_t,\\mathbf{z}_0)" + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "text", + "content": " is parameterized by " + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "inline_equation", + "content": "\\widetilde{\\boldsymbol{\\mu}}_t" + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "inline_equation", + "content": "\\widetilde{\\Sigma}_t" + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "text", + "content": ", we can also re-parameterize " + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 296, + 276, + 530, + 300 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 299, + 305, + 530, + 330 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 305, + 530, + 330 + ], + "spans": [ + { + "bbox": [ + 299, + 305, + 530, + 330 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right) := \\mathcal {N C} \\left(\\mathbf {z} _ {t - 1}; \\left[ \\widetilde {\\boldsymbol {\\mu}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\right] _ {\\times S}, \\left[ \\widetilde {\\boldsymbol {\\Sigma}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\right] _ {\\times S}, \\boldsymbol {\\Theta} _ {\\theta}\\right), \\tag {17}", + "image_path": "7b5f104181a338800d6c42289903bbb6428baf5f135483724e5127601072a170.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 311, + 333, + 530, + 348 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 333, + 530, + 348 + ], + "spans": [ + { + "bbox": [ + 311, + 333, + 530, + 348 + ], + "type": "interline_equation", + "content": "\\widetilde {\\boldsymbol {\\mu}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\in \\mathbb {R} ^ {N}, \\widetilde {\\boldsymbol {\\Sigma}} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right) \\in \\mathbb {R} ^ {N \\times N}, \\boldsymbol {\\Theta} _ {\\theta} \\in \\mathbb {R} ^ {M \\times K}, \\tag {18}", + "image_path": "0d467d872da7ed47b220ae7ebdd5373a4a74b49c51518d458d2f47e0ea668524.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 296, + 354, + 530, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 354, + 530, + 377 + ], + "spans": [ + { + "bbox": [ + 296, + 354, + 530, + 377 + ], + "type": "text", + "content": "Thus, we can predict a reduced number of parameters to minimize the KL divergence term in Equation (15)," + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 300, + 383, + 530, + 395 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 383, + 530, + 395 + ], + "spans": [ + { + "bbox": [ + 300, + 383, + 530, + 395 + ], + "type": "interline_equation", + "content": "D _ {K L} \\left(q \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}, \\mathbf {z} _ {0}\\right) \\| p _ {\\theta} \\left(\\mathbf {z} _ {t - 1} \\mid \\mathbf {z} _ {t}\\right)\\right) \\tag {19}", + "image_path": "30ed512f55ffd91b5f7ea101e6022b628e49f74cdaa3c33450548052beabf020.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 302, + 398, + 528, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 398, + 528, + 422 + ], + "spans": [ + { + "bbox": [ + 302, + 398, + 528, + 422 + ], + "type": "interline_equation", + "content": "= \\mathbb {E} _ {q} \\left[ \\frac {1}{2 \\sigma_ {t} ^ {2}} \\| \\widetilde {\\boldsymbol {\\mu}} _ {t} - \\widetilde {\\boldsymbol {\\mu}} _ {\\theta} (\\mathbf {z} _ {t}) \\| ^ {2} \\right] + D _ {\\mathrm {K L}} \\left(\\widetilde {\\boldsymbol {\\Theta}} _ {t} \\| \\boldsymbol {\\Theta} _ {\\theta} (\\mathbf {z} _ {t})\\right) + C,", + "image_path": "dfeec0d7b39d2f190890384185efc36d36adfe9b07466fc37b401bc233674fff.jpg" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "spans": [ + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "text", + "content": " is a constant irrelevant to learnable parameters " + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "inline_equation", + "content": "L_{0}" + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "text", + "content": " is directly minimized through a closed-form solution and " + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "inline_equation", + "content": "L_{T}" + }, + { + "bbox": [ + 296, + 426, + 530, + 458 + ], + "type": "text", + "content": " does not involve any learnable parameters." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 297, + 464, + 412, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 464, + 412, + 477 + ], + "spans": [ + { + "bbox": [ + 297, + 464, + 412, + 477 + ], + "type": "text", + "content": "3.3. Architectural design" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 296, + 483, + 530, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 483, + 530, + 587 + ], + "spans": [ + { + "bbox": [ + 296, + 483, + 530, + 587 + ], + "type": "text", + "content": "In order to treat image-Layout pairs as a single data sample, we embed the semantic layouts (i.e., one-hot vectors) into 3-channel vectors via learnable parameters and concatenate them with images along the channel dimension " + }, + { + "bbox": [ + 296, + 483, + 530, + 587 + ], + "type": "inline_equation", + "content": "(\\mathbf{z} \\in \\mathbb{R}^{N \\times N \\times 6})" + }, + { + "bbox": [ + 296, + 483, + 530, + 587 + ], + "type": "text", + "content": ". We adopt the U-Net [24] and the Efficient U-Net [32] following existing diffusion models and modify the input/output channels for image-Layout input/outputs. For text conditioning, we utilize the T5-L [27] text encoder and condition the U-Net model similarly to Imagen [32]." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "spans": [ + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "type": "text", + "content": "We follow the cascaded diffusion [13] framework to generate high-resolution image layout pairs, which involves a sequence of an image generation model followed by a super-resolution model. We find that resizing layouts to a small resolution (e.g., " + }, + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "type": "text", + "content": ") often damages the integrity of semantic labels due to nearest-neighbor sampling on extreme scales. Thus, we generate " + }, + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "type": "text", + "content": " resolution images and then upsample to " + }, + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 296, + 587, + 530, + 738 + ], + "type": "text", + "content": " resolution with a Gaussian-categorical super-resolution model. The super-resolution model upsamples both images and layouts following the Gaussian-categorical diffusion. We adopt the classifier-free guidance on both the generation model and the super-resolution model." + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "spans": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "text", + "content": "7594" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 108, + 494, + 351 + ], + "blocks": [ + { + "bbox": [ + 52, + 108, + 494, + 351 + ], + "lines": [ + { + "bbox": [ + 52, + 108, + 494, + 351 + ], + "spans": [ + { + "bbox": [ + 52, + 108, + 494, + 351 + ], + "type": "image", + "image_path": "b16a793ffaaffa1879eaaf411fd0e6a6ae4f651cd9e4009100f3d7fe25398942.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 353, + 531, + 375 + ], + "lines": [ + { + "bbox": [ + 45, + 353, + 531, + 375 + ], + "spans": [ + { + "bbox": [ + 45, + 353, + 531, + 375 + ], + "type": "text", + "content": "Figure 5. Examples of text-guided generation of image layout pairs from the Gaussian-categorical diffusion trained on MM CelebA-HQ-100 [17,22] and Cityscapes [6]. The text descriptions on the bottom are given as conditions to generate the image-label pairs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 382, + 124, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 382, + 124, + 394 + ], + "spans": [ + { + "bbox": [ + 45, + 382, + 124, + 394 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 401, + 158, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 401, + 158, + 414 + ], + "spans": [ + { + "bbox": [ + 45, + 401, + 158, + 414 + ], + "type": "text", + "content": "4.1. Text-image datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "spans": [ + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "text", + "content": "Multi-Modal CelebA-HQ. MM CelebA-HQ [17,22,38] is a collection of different annotations for the 30,000 images in the CelebA-HQ dataset [17,22], including text descriptions, face attribute labels, and part-level segmentation labels. Part-level segmentation labels consist of 19 different classes (" + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "inline_equation", + "content": "K = 19" + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "text", + "content": ") including all facial components and accessories. To train the Gaussian-categorical diffusion model, we use both the segmentation labels and the text descriptions provided in the dataset. We also construct subsets of the data, MM CelebA-HQ-25 and MM CelebA-HQ-50, by randomly selecting " + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "text", + "content": " of the images, respectively, to simulate data-scarce scenarios. We train and evaluate our models on " + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 45, + 419, + 279, + 571 + ], + "type": "text", + "content": " resolution images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 571, + 279, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 571, + 279, + 630 + ], + "spans": [ + { + "bbox": [ + 45, + 571, + 279, + 630 + ], + "type": "text", + "content": "Cityscapes. Cityscapes [6] is an urban scene dataset with 3475 image layout pairs of complex scenes containing multiple objects, including 20 different semantic classes (" + }, + { + "bbox": [ + 45, + 571, + 279, + 630 + ], + "type": "inline_equation", + "content": "K = 20" + }, + { + "bbox": [ + 45, + 571, + 279, + 630 + ], + "type": "text", + "content": "). To add text descriptions to each image, we list the class names in the following format:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 71, + 634, + 252, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 634, + 252, + 647 + ], + "spans": [ + { + "bbox": [ + 71, + 634, + 252, + 647 + ], + "type": "text", + "content": "\"An image of an urban scene with {classes}." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 651, + 280, + 735 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 651, + 280, + 735 + ], + "spans": [ + { + "bbox": [ + 45, + 651, + 280, + 735 + ], + "type": "text", + "content": "where classes are the unique class names in the corresponding semantic layout. The Cityscapes dataset presents a challenging domain for generating realistic images due to the limited number of available images and the diverse object locations in urban scenes. Since Cityscapes images have a unique aspect ratio of 2:1, we generate " + }, + { + "bbox": [ + 45, + 651, + 280, + 735 + ], + "type": "inline_equation", + "content": "512 \\times 256" + }, + { + "bbox": [ + 45, + 651, + 280, + 735 + ], + "type": "text", + "content": " resolution images. We include example text-image pairs in Figure 2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 297, + 382, + 425, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 382, + 425, + 394 + ], + "spans": [ + { + "bbox": [ + 297, + 382, + 425, + 394 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "spans": [ + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "text", + "content": "For synthesizing image layout pairs, " + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "text", + "content": " are equally set to the number of pixels in the image. Although the Gaussian-categorical diffusion process allows different noise schedules " + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "inline_equation", + "content": "\\beta^{\\mathcal{N}}" + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "inline_equation", + "content": "\\beta^{c}" + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "text", + "content": " for images and layouts, we set both schedules to the cosine schedule [24]. We provide experiments on the effect of different noise schedules for " + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "inline_equation", + "content": "\\beta^{c}" + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "text", + "content": " in the supplementary section. We set " + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "inline_equation", + "content": "T = 1000" + }, + { + "bbox": [ + 296, + 400, + 530, + 505 + ], + "type": "text", + "content": " and sample with 100 timesteps using the accelerated sampling technique [35]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 506, + 483, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 506, + 483, + 519 + ], + "spans": [ + { + "bbox": [ + 297, + 506, + 483, + 519 + ], + "type": "text", + "content": "4.3. Evaluating text-to-image generation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 519, + 530, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 519, + 530, + 671 + ], + "spans": [ + { + "bbox": [ + 296, + 519, + 530, + 671 + ], + "type": "text", + "content": "Text-to-image generation models are evaluated from two perspectives, image fidelity and text-image correspondence. We use the Fréchet Inception Distance (FID) [10] to measure the image fidelity. After the release of CLIP [26], the CLIP score [9] is often used to evaluate text-image correspondence for text-to-image generation. However, the CLIP score is known to have poor generalization abilities [26] when evaluating scenes with large domain gaps (i.e., Cityscapes) and also lacks interpretability in terms of understanding what element in the image causes a low or high CLIP score. In order to compensate for this drawback, we propose Semantic Recall to precisely measure the text-image correspondence for Cityscapes generation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 671, + 530, + 730 + ], + "type": "text", + "content": "Semantic Recall. The Semantic Recall is analogous to the Semantic Object Accuracy (SOA) [11], which evaluates the generation of specific objects in text-to-image generation by utilizing pretrained object detectors. In our work, we use a pretrained semantic segmentation model [37] to detect the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "spans": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "text", + "content": "7595" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 112, + 258, + 248 + ], + "blocks": [ + { + "bbox": [ + 80, + 112, + 258, + 248 + ], + "lines": [ + { + "bbox": [ + 80, + 112, + 258, + 248 + ], + "spans": [ + { + "bbox": [ + 80, + 112, + 258, + 248 + ], + "type": "image", + "image_path": "ce751d195d36b7a0ff1bcb1d12a7204c6abf463a804d34a1ae20a30604074b1f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 130, + 255, + 224, + 266 + ], + "lines": [ + { + "bbox": [ + 130, + 255, + 224, + 266 + ], + "spans": [ + { + "bbox": [ + 130, + 255, + 224, + 266 + ], + "type": "text", + "content": "(a) FID-Semantic Recall" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 306, + 108, + 509, + 174 + ], + "blocks": [ + { + "bbox": [ + 306, + 108, + 509, + 174 + ], + "lines": [ + { + "bbox": [ + 306, + 108, + 509, + 174 + ], + "spans": [ + { + "bbox": [ + 306, + 108, + 509, + 174 + ], + "type": "image", + "image_path": "26fea2cb71c198eac4e2c9da5ddf6b25499da4293ee8be1c82b983cb7dfb9e5e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 305, + 186, + 521, + 261 + ], + "blocks": [ + { + "bbox": [ + 354, + 178, + 476, + 188 + ], + "lines": [ + { + "bbox": [ + 354, + 178, + 476, + 188 + ], + "spans": [ + { + "bbox": [ + 354, + 178, + 476, + 188 + ], + "type": "text", + "content": "(b) Class-wise Semantic Recall" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 186, + 521, + 261 + ], + "lines": [ + { + "bbox": [ + 305, + 186, + 521, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 521, + 261 + ], + "type": "image", + "image_path": "00607728f06dcccdfc5763976d602c2d3291438eb0f10513fd272b55df2a06fb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 349, + 263, + 481, + 275 + ], + "lines": [ + { + "bbox": [ + 349, + 263, + 481, + 275 + ], + "spans": [ + { + "bbox": [ + 349, + 263, + 481, + 275 + ], + "type": "text", + "content": "(c) Class Proportion in Cityscapes" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 44, + 279, + 531, + 312 + ], + "lines": [ + { + "bbox": [ + 44, + 279, + 531, + 312 + ], + "spans": [ + { + "bbox": [ + 44, + 279, + 531, + 312 + ], + "type": "text", + "content": "Figure 6. (a) FID-Semantic Recall trade-off in the Cityscapes dataset. (b) Semantic Recall for minor classes. Semantic Recall is measured using the HRNet-w48 [37] model. (c) Proportion of each semantic class in the entire Cityscapes dataset. Class proportion is compared in log-scale for visibility." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 44, + 319, + 279, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 319, + 279, + 448 + ], + "spans": [ + { + "bbox": [ + 44, + 319, + 279, + 448 + ], + "type": "text", + "content": "presence of classes described in text conditions. We determine that a class is detected in a generated image if it appears in the segmentation layout. The ground-truth classes for each image are identified by searching for class names in text descriptions. For example, an image generated with the text description \"An urban scene with cars, roads, and traffic signs.\", would be evaluated with the existence of cars, roads, and traffic signs. Therefore, we compute the Semantic Recall as the average ratio of correctly detected classes in the generated image to the total number of classes in the ground-truth layouts," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 64, + 456, + 260, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 456, + 260, + 487 + ], + "spans": [ + { + "bbox": [ + 64, + 456, + 260, + 487 + ], + "type": "interline_equation", + "content": "\\frac {1}{| \\mathcal {G} |} \\sum_ {x _ {i}, y _ {i} \\in \\mathcal {G}} \\frac {\\left| \\text {C l a s s e s i n} F \\left(x _ {i}\\right) \\cap \\text {C l a s s e s i n} y _ {i} \\right|}{\\left| \\text {C l a s s e s i n} y _ {i} \\right|},", + "image_path": "232cc961fb0ac98acd20d2a2896f55391f09dc4e5ca16f5ffc931e10ec70b123.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "spans": [ + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "text", + "content": " is the set of generated image layout pairs " + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "inline_equation", + "content": "(x_{i},y_{i})" + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "inline_equation", + "content": "|\\cdot |" + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "text", + "content": " indicates the cardinality of a given set. " + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "inline_equation", + "content": "F(\\cdot)" + }, + { + "bbox": [ + 45, + 496, + 279, + 531 + ], + "type": "text", + "content": " is the pretrained semantic segmentation model [37]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 532, + 279, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 532, + 279, + 671 + ], + "spans": [ + { + "bbox": [ + 45, + 532, + 279, + 671 + ], + "type": "text", + "content": "Baselines. We compare our approach with state-of-the-art performing diffusion-based models, Imagen [32] and the latent diffusion model (LDM) [31]. We also train a high-performing GAN-based approach Lafite [42] trained on MM CelebA-HQ and Cityscapes. For training LDM, we utilize the pretrained autoencoder from the Stable Diffusion project. Diffusion-based approaches utilize the classifier-free guidance [14] to control the performance trade-off between text-image correspondence and image fidelity. Thus, for these approaches, we sweep the guidance scale until the text-image correspondence measures saturate and report all FID-Semantic Recall or FID-CLIP score pairs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "Evaluation on Cityscapes. For the Cityscapes dataset [6], we report the FID and Semantic Recall performance trade-off and also provide detailed recall scores for each class in Figure 6. Given the small number of text-image pairs (3475 pairs), existing text-to-image models face" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 319, + 530, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 319, + 530, + 447 + ], + "spans": [ + { + "bbox": [ + 296, + 319, + 530, + 447 + ], + "type": "text", + "content": "challenges in learning the text-image correspondence and achieving high text-image correspondence. However, the Gaussian-categorical diffusion effectively generates complex Cityscapes scenes while maintaining high Semantic Recall even with limited data. Additionally, the model achieves high recall rates for minor classes, such as the bicycle or the motorcycle class, which only constitute a small portion of the dataset. This indicates that generating semantic labels for each pixel facilitates the model to establish high text-image correspondence, especially for underrepresented classes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 447, + 531, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 447, + 531, + 564 + ], + "spans": [ + { + "bbox": [ + 296, + 447, + 531, + 564 + ], + "type": "text", + "content": "Evaluation on MM CelebA-HQ. We further evaluate our method on the MM CelebA-HQ-25, 50, and 100, and report the FID-CLIP scores for each dataset. As shown in Figure 7, the Gaussian-categorical diffusion consistently outperforms existing text-to-image approaches at datasets with varying numbers of text-image pairs, exhibiting low FIDs and a high CLIP scores. We provide qualitative results of the Gaussian-categorical diffusion in Figure 5 and also compare the results with existing approaches in the supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 572, + 493, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 572, + 493, + 585 + ], + "spans": [ + { + "bbox": [ + 297, + 572, + 493, + 585 + ], + "type": "text", + "content": "4.4. Analyzing the internal representations" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": "In order to visualize the advantages of jointly generating image-Layout pairs, we train a Gaussian diffusion model which generates images without corresponding semantic layouts. Then, we collect the internal features from the two models at different timesteps and cluster the features in an unsupervised manner with K-means clustering. As shown in Figure 8, the internal features of the Gaussian-categorical model form distinct clusters that correspond to different facial regions. Specifically, the internal features of the Gaussian-categorical diffusion model form clusters even in the early stages of generation " + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "inline_equation", + "content": "(t = 800)" + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": ", correctly distinguishing hair, glasses and the background region." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "spans": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "text", + "content": "7596" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 64, + 107, + 205, + 234 + ], + "blocks": [ + { + "bbox": [ + 64, + 107, + 205, + 234 + ], + "lines": [ + { + "bbox": [ + 64, + 107, + 205, + 234 + ], + "spans": [ + { + "bbox": [ + 64, + 107, + 205, + 234 + ], + "type": "image", + "image_path": "c36a1ab08a379a68417e123542a2fc9396eea69d219cd31e3d0effdb84df4b08.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 214, + 107, + 393, + 235 + ], + "blocks": [ + { + "bbox": [ + 214, + 107, + 393, + 235 + ], + "lines": [ + { + "bbox": [ + 214, + 107, + 393, + 235 + ], + "spans": [ + { + "bbox": [ + 214, + 107, + 393, + 235 + ], + "type": "image", + "image_path": "f724f67f38e302c852f37afe1c044473cc61db82ea26ace94b3b586b6b083df1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 365, + 108, + 505, + 234 + ], + "blocks": [ + { + "bbox": [ + 365, + 108, + 505, + 234 + ], + "lines": [ + { + "bbox": [ + 365, + 108, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 365, + 108, + 505, + 234 + ], + "type": "image", + "image_path": "8aa05d2a01ba7e38e588dc306fdfbf819dd14ca8e1cb47156452a418510a74b2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 187, + 240, + 393, + 255 + ], + "blocks": [ + { + "bbox": [ + 187, + 240, + 393, + 255 + ], + "lines": [ + { + "bbox": [ + 187, + 240, + 393, + 255 + ], + "spans": [ + { + "bbox": [ + 187, + 240, + 393, + 255 + ], + "type": "image", + "image_path": "781007feb0d468d7aa1007c9e11fa38ff7dd48bf40b9a53480b366687e5abfa7.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 49, + 293, + 278, + 410 + ], + "blocks": [ + { + "bbox": [ + 45, + 265, + 530, + 287 + ], + "lines": [ + { + "bbox": [ + 45, + 265, + 530, + 287 + ], + "spans": [ + { + "bbox": [ + 45, + 265, + 530, + 287 + ], + "type": "text", + "content": "Figure 7. FID-CLIP score pairs for text-to-image generation models on different subsets of the MM CelebA-HQ dataset. The CLIP scores are measured with the ViT-L/14-336 model. The guidance scale is swept starting from 1 until saturation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 293, + 278, + 410 + ], + "lines": [ + { + "bbox": [ + 49, + 293, + 278, + 410 + ], + "spans": [ + { + "bbox": [ + 49, + 293, + 278, + 410 + ], + "type": "image", + "image_path": "9b504da7a451afc2a30509f75fbfc89ee42cd2b995b982d9e2914142b56f9035.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 415, + 279, + 446 + ], + "lines": [ + { + "bbox": [ + 45, + 415, + 279, + 446 + ], + "spans": [ + { + "bbox": [ + 45, + 415, + 279, + 446 + ], + "type": "text", + "content": "Figure 8. Visualization of clustering results between the internal features of the Gaussian-categorical diffusion and the Gaussian diffusion." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 456, + 281, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 456, + 281, + 584 + ], + "spans": [ + { + "bbox": [ + 45, + 456, + 281, + 584 + ], + "type": "text", + "content": "The results reveal that the Gaussian-categorical diffusion model is highly aware of the semantics of the image during the generation process. This characteristic is advantageous in scenarios where a generative model needs to learn how to match specific parts of the image with corresponding input text descriptions, as the model is capable of understanding the semantic structure of the image. As such, training a Gaussian-categorical diffusion is a promising approach for achieving high correspondence between text descriptions and image pixels, particularly when there is a scarcity of text-image pairs available." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 594, + 230, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 594, + 230, + 607 + ], + "spans": [ + { + "bbox": [ + 45, + 594, + 230, + 607 + ], + "type": "text", + "content": "4.5. Image layout fidelity and alignment" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": "In this section, we evaluate whether generated images and layouts closely model the real distribution, and whether the generated pairs are semantically aligned. Following Semantic Palette [2, 18] we evaluate the image-Layout alignment using the mean intersection over union (mIoU) between the generated layouts and the segmentation labels predicted by a pretrained HRNet [37]. Additionally, we use the Fréchet Segmentation Distance (FSD) [4], which replaces the Inception-V3 [36] features in the FID score [10] to pixel counts for each class, to evaluate the quality of gen" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 300, + 292, + 527, + 367 + ], + "blocks": [ + { + "bbox": [ + 300, + 292, + 527, + 367 + ], + "lines": [ + { + "bbox": [ + 300, + 292, + 527, + 367 + ], + "spans": [ + { + "bbox": [ + 300, + 292, + 527, + 367 + ], + "type": "table", + "html": "
MethodsFID ↓mIoU ↑FSD ↓
GANformer [16]24.86-481.5
DatasetDDPM [3]55.3833.8890.31
Semantic Palette [18]52.1353.1748.29
Ours20.3665.8042.22
", + "image_path": "2554efeaf4d2f301f343b156a556c064be115f9c56a2dbdebade98199582330f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 369, + 530, + 402 + ], + "lines": [ + { + "bbox": [ + 296, + 369, + 530, + 402 + ], + "spans": [ + { + "bbox": [ + 296, + 369, + 530, + 402 + ], + "type": "text", + "content": "Table 1. Image-Layout alignment and FID of different Imagelayout generation approaches for scene generation in the Cityscapes [6] dataset." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 296, + 418, + 530, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 418, + 530, + 452 + ], + "spans": [ + { + "bbox": [ + 296, + 418, + 530, + 452 + ], + "type": "text", + "content": "erated layouts. Similar to the FID score, a low FSD indicates that the class distributions are close to the real distribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 458, + 530, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 458, + 530, + 573 + ], + "spans": [ + { + "bbox": [ + 296, + 458, + 530, + 573 + ], + "type": "text", + "content": "We compare our results with existing unconditional image layout generation approaches [3, 18] on the Cityscapes dataset. Additionally, we introduce a simple baseline (i.e., GANformer [16]) for image layout generation, in which we generate images using a well-trained unconditional image generation model [16] and segment the images using a pretrained segmentation model [37]. Note that we cannot measure the mIoU for this baseline since the semantic layouts are predicted using the same pretrained network." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 578, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 578, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 578, + 531, + 730 + ], + "type": "text", + "content": "As shown in Table 1, the Gaussian-categorical diffusion process is highly effective in modeling the joint distribution of images and layouts even for complex urban scenes. By using a unified diffusion process, we are able to generate image layout pairs that exhibit high alignment, closely resembling the real distribution. The ability of the Gaussian-categorical diffusion to effectively model the joint distribution of images and layouts offers promising avenues for future research in generative modeling. By leveraging the theoretical foundations established by our method, researchers can explore new approaches for dataset generation in a range of domains, from images and audiios to semantic layouts and texts." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "spans": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "text", + "content": "7597" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 104, + 286, + 227 + ], + "blocks": [ + { + "bbox": [ + 49, + 104, + 286, + 227 + ], + "lines": [ + { + "bbox": [ + 49, + 104, + 286, + 227 + ], + "spans": [ + { + "bbox": [ + 49, + 104, + 286, + 227 + ], + "type": "image", + "image_path": "d4abe812daed03d04a7c5cfc1cd2bbaf52417dbc95478fb5e793f96edef526cc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 100, + 229, + 240, + 239 + ], + "lines": [ + { + "bbox": [ + 100, + 229, + 240, + 239 + ], + "spans": [ + { + "bbox": [ + 100, + 229, + 240, + 239 + ], + "type": "text", + "content": "(a) Text-guided Image-to-Layout Generation" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 292, + 104, + 528, + 227 + ], + "blocks": [ + { + "bbox": [ + 292, + 104, + 528, + 227 + ], + "lines": [ + { + "bbox": [ + 292, + 104, + 528, + 227 + ], + "spans": [ + { + "bbox": [ + 292, + 104, + 528, + 227 + ], + "type": "image", + "image_path": "799914a679d802c6143cfbc9f1682771d39574c8f0f47504200805f05e8b4af1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 341, + 229, + 481, + 239 + ], + "lines": [ + { + "bbox": [ + 341, + 229, + 481, + 239 + ], + "spans": [ + { + "bbox": [ + 341, + 229, + 481, + 239 + ], + "type": "text", + "content": "(b) Text-guided Layout-to-Image Generation" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 245, + 531, + 267 + ], + "lines": [ + { + "bbox": [ + 45, + 245, + 531, + 267 + ], + "spans": [ + { + "bbox": [ + 45, + 245, + 531, + 267 + ], + "type": "text", + "content": "Figure 9. Cross-modal outpainting for (a) text-guided image-to-Layout generation and (b) text-guided layout-to-image generation. Segmentation layouts are generated with " + }, + { + "bbox": [ + 45, + 245, + 531, + 267 + ], + "type": "inline_equation", + "content": "n = 1" + }, + { + "bbox": [ + 45, + 245, + 531, + 267 + ], + "type": "text", + "content": " resampling steps and images are generated with " + }, + { + "bbox": [ + 45, + 245, + 531, + 267 + ], + "type": "inline_equation", + "content": "n = 5" + }, + { + "bbox": [ + 45, + 245, + 531, + 267 + ], + "type": "text", + "content": " resampling steps for each timestep." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 279, + 182, + 293 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 279, + 182, + 293 + ], + "spans": [ + { + "bbox": [ + 45, + 279, + 182, + 293 + ], + "type": "text", + "content": "4.6. Cross-modal outpainting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 297, + 279, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 297, + 279, + 345 + ], + "spans": [ + { + "bbox": [ + 45, + 297, + 279, + 345 + ], + "type": "text", + "content": "RePaint [23] enables existing diffusion models to inpaint a masked image by iteratively denoising the masked region given the known image (i.e., condition image). Specifically, for each timestep " + }, + { + "bbox": [ + 45, + 297, + 279, + 345 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 45, + 297, + 279, + 345 + ], + "type": "text", + "content": ", images are inpainted as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 96, + 352, + 228, + 367 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 352, + 228, + 367 + ], + "spans": [ + { + "bbox": [ + 96, + 352, + 228, + 367 + ], + "type": "interline_equation", + "content": "x _ {t - 1} ^ {\\mathrm {k n o w n}} \\sim \\mathcal {N} (\\sqrt {\\bar {\\alpha} _ {t}} x _ {0}, (1 - \\bar {\\alpha} _ {t}) I),", + "image_path": "49dd1b7a9947e82e29b3c840ab875e0e76e68e29d45470555f99452fb27d0206.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 92, + 368, + 233, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 368, + 233, + 383 + ], + "spans": [ + { + "bbox": [ + 92, + 368, + 233, + 383 + ], + "type": "interline_equation", + "content": "x _ {t - 1} ^ {\\text {u n k n o w n}} \\sim \\mathcal {N} (\\boldsymbol {\\mu} _ {\\theta} (x _ {t}, t), \\boldsymbol {\\Sigma} _ {\\theta} (x _ {t}, t)),", + "image_path": "0a7df7820d37e82d37a7d6e04544dbc235101452ece488448e0348ec4e65c47d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 78, + 384, + 247, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 384, + 247, + 399 + ], + "spans": [ + { + "bbox": [ + 78, + 384, + 247, + 399 + ], + "type": "interline_equation", + "content": "x _ {t - 1} = m \\odot x _ {t - 1} ^ {\\text {k n o w n}} + (1 - m) \\odot x _ {t - 1} ^ {\\text {u n k n o w n}},", + "image_path": "350c7e6a12224195a30e3752b55f77be34086dc6ff6db2e7dfa3ca9808072fd1.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 407, + 279, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 407, + 279, + 454 + ], + "spans": [ + { + "bbox": [ + 45, + 407, + 279, + 454 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 407, + 279, + 454 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 45, + 407, + 279, + 454 + ], + "type": "text", + "content": " is the mask for the known image. To ensure consistency between the inpainted regions and known regions, Repaint iterates the denoising process " + }, + { + "bbox": [ + 45, + 407, + 279, + 454 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 45, + 407, + 279, + 454 + ], + "type": "text", + "content": " times for each timestep." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 454, + 279, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 454, + 279, + 607 + ], + "spans": [ + { + "bbox": [ + 45, + 454, + 279, + 607 + ], + "type": "text", + "content": "The Repaint technique allows us to use the Gaussian-categorical diffusion model as a text-guided layout-to-image generation model (i.e., semantic image synthesis) by considering the layouts as an image layout pair with the image part masked. Similarly, we can perform text-guided image-to layout generation (i.e., semantic segmentation) by masking the layout in the image layout pair. As shown in Figure 9, the Gaussian-categorical diffusion generates realistic images or layouts conditioned on text descriptions. The results demonstrate that a well-trained Gaussian-categorical diffusion can serve as a generative prior for conditional generation tasks. We describe the algorithm for cross-modal outpainting in the supplementary material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 616, + 114, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 616, + 114, + 628 + ], + "spans": [ + { + "bbox": [ + 45, + 616, + 114, + 628 + ], + "type": "text", + "content": "5. Limitation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 636, + 279, + 730 + ], + "type": "text", + "content": "Although the Gaussian-categorical diffusion offers means for achieving high text-image correspondence without training on web-scale text-image pairs, training a Gaussian-categorical diffusion model requires additional semantic layout annotations of images. However, with the assistance of recent data annotation tools [5,34], annotating existing data can be a cost-effective option for text-to-image generation in scenarios where obtaining web-scale text" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 279, + 529, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 279, + 529, + 303 + ], + "spans": [ + { + "bbox": [ + 296, + 279, + 529, + 303 + ], + "type": "text", + "content": "image pairs is costly (e.g., medical images, urban scenes, and aerial images)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 304, + 531, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 304, + 531, + 421 + ], + "spans": [ + { + "bbox": [ + 296, + 304, + 531, + 421 + ], + "type": "text", + "content": "We observe that training the Gaussian-categorical diffusion model on the MS-COCO dataset [21] produces poor quality images and layouts. We suspect that this is due to the highly diverse scenes in the COCO dataset, with 171 categories in the semantic layouts. Analyzing the challenges of training on the MS-COCO dataset is a potential area for future research. Nevertheless, we propose an effective approach for text-to-image generation in data-scarce scenarios, where collecting data is expensive and annotating existing images is affordable." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 436, + 368, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 436, + 368, + 448 + ], + "spans": [ + { + "bbox": [ + 297, + 436, + 368, + 448 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 458, + 530, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 458, + 530, + 552 + ], + "spans": [ + { + "bbox": [ + 296, + 458, + 530, + 552 + ], + "type": "text", + "content": "In this paper, we define the Gaussian-categorical diffusion process to model the joint distribution of image layout pairs. Our experiments demonstrate that the proposed model can ensure high text-image correspondence for text-to-image generation in specific domains, without relying on web-scale text-image pairs. Our approach outperforms existing approaches in terms of image quality and text-image correspondence." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 553, + 530, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 553, + 530, + 646 + ], + "spans": [ + { + "bbox": [ + 296, + 553, + 530, + 646 + ], + "type": "text", + "content": "Our visualizations of the internal representations of the Gaussian-categorical distribution demonstrate that the proposed model is aware of the semantics of the image, bridging the gap between highly semantic text descriptions and image pixels. Additionally, the high image layout alignment of generated image layout pairs and the results of cross-modal outpainting show that the model precisely captures the relationship between images and labels." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 530, + 730 + ], + "type": "text", + "content": "Overall, the Gaussian-categorical diffusion enables text-to-image models to achieve high text-image correspondence by leveraging semantic labels when trained on a specific domain with limited text-image pairs. Our proposed model can also be utilized as a generative prior for conditional generation tasks, such as text-guided semantic image synthesis and text-guided semantic segmentation." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "spans": [ + { + "bbox": [ + 279, + 755, + 298, + 763 + ], + "type": "text", + "content": "7598" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 141, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 141, + 118 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 141, + 118 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 125, + 279, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 125, + 279, + 218 + ], + "spans": [ + { + "bbox": [ + 45, + 125, + 279, + 218 + ], + "type": "text", + "content": "This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B02001913), Electronics and Telecommunications Research Institute (ETRI) grant funded by the Korean government [22ZS1200, Fundamental Technology Research for Human-Centric Autonomous Intelligent Systems], and the KAIST-NAVER hypercreative AI center." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 231, + 102, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 231, + 102, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 231, + 102, + 243 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 252, + 279, + 729 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 51, + 252, + 279, + 294 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 252, + 279, + 294 + ], + "spans": [ + { + "bbox": [ + 51, + 252, + 279, + 294 + ], + "type": "text", + "content": "[1] Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. 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To deal with the scarcity of labeled data at scale, we source the step descriptions from a language knowledge base (wikiHow) containing instructional articles for a large variety of procedural tasks. Without any form of manual supervision, our model learns to temporally ground the steps of procedural articles in how-to videos by matching three modalities: frames, narrations, and step descriptions. Specifically, our method aligns steps to video by fusing information from two distinct pathways: i) direct alignment of step descriptions to frames, ii) indirect alignment obtained by composing steps-to-narrations with narrations-to-video correspondences. Notably, our approach performs global temporal grounding of all steps in an article at once by exploiting order information, and is trained with step pseudo-labels which are iteratively refined and aggressively filtered. In order to validate our model we introduce a new benchmark - HT-Step - obtained by manually annotating a 124-hour subset of HowTo100M1 with steps sourced from wikiHow articles. Experiments on this benchmark as well as zero-shot evaluations on CrossTask demonstrate that our multi-modality alignment yields dramatic gains over several baselines and prior works. Finally, we show that our inner module for matching narration-to-video outperforms by a large margin the state of the art on the HTM-Align narration-video alignment benchmark.", + "bbox": [ + 76, + 300, + 473, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 737, + 209, + 752 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Instructional videos have emerged as a popular means for people to learn new skills and improve their abilities in executing complex procedural activities, such as cooking a recipe, performing home improvements, or fixing things. In addition to being useful teaching materials for humans, how-to videos are a promising medium for learning by ma", + "bbox": [ + 75, + 762, + 468, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4431a922b1eca13386407057d143a3cc1255f4166af6c28f0b619ab8d371d2a8.jpg", + "image_caption": [ + "Figure 1: Our proposed Video, Instructions, and Narrations Aligner (VINA) learns to simultaneously ground narrations and instruction steps in how-to videos from an uncurated set of narrated videos and a separate knowledge base of instructional articles, without any manual annotations. This is contrary to prior work that learns how to align a video with a single sequence of sentences by leveraging ground-truth pairs of video-text sequences, e.g., a video and its narrations [22], or a video and an annotated, ordered list of steps demonstrated in it [16]." + ], + "image_footnote": [], + "bbox": [ + 509, + 273, + 859, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "chines, as they provide revealing visual demonstrations of complex activities and show elaborate human-object interactions in a variety of domains. Motivated by this observation, in this work we look at the task of temporally localizing the steps of procedural activities in instructional videos. This problem is foundational to the broader goal of human-procedure understanding and advances on this task promise to enable breakthrough applications, such as AI-powered skill coaching and human-to-robot imitation learning.", + "bbox": [ + 496, + 732, + 893, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior work has tackled procedural step localization by leveraging either (a) fully-annotated datasets where the task", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 238, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution\n1A test server is accessible at https://eval.ai/web/challenges/challenge-page/2082.", + "bbox": [ + 93, + 863, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15201", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "shown in the video is given (video-level labeling) and manually annotated temporal segments are provided for each step (segment-level labeling) [59] or (b) weakly-annotated training sets where the task and the order in which the steps appear in the video is given [79]. However, due to the inherent manual cost involved in collecting step annotations, these works have relied on datasets that are small-scale both in the number of tasks (e.g., at most few hundreds [79]) and in the number of video samples (e.g., 12k videos [59]). These limitations affect both the generality and the complexity of the models that can be trained on these benchmarks. In this paper, we therefore pose the following question: can we leverage large-scale, unlabeled video datasets to train a model that can ground procedural steps in how-to videos?", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To answer this question, we propose a novel training framework for weakly-supervised step grounding that utilizes two freely available sources of information: (a) instructional articles which define ordered lists of steps for a wide variety of tasks (e.g., from wikiHow) and (b) narrations which provide instance-specific rich commentaries of the execution of the task in the video, e.g., from ASR transcriptions. Our work treats the former as an abstraction of the latter and uses the video-specific narrations to support the grounding of the article steps. Specifically, during training, our method leverages narrations as an auxiliary signal to (i) identify the task shown in the video, (ii) temporally ground the article steps that are visually-demonstrated and (iii) filter out steps that are not executed in the given instance. To further motivate this mechanism, let us look at the example in Figure 1. The narrations help disambiguate the task (make a pumpkin puree), enabling the automatic retrieval of relevant instructional articles for the video. Furthermore, the narrations can be matched to steps described in the articles to roughly localize the steps that are represented in the video. In this example, the timestamp of \"First thing you'll need to do is cut off the stem\" provides a loose temporal prior for the matching step \"Cut the pumpkins.\" On the other hand, steps that do not have any matching narrations (e.g., \"Wash the pumpkins\") are unlikely to be represented in the video and thus can be rejected. Based on this intuition, we propose a procedure that learns to align steps to video by fusing information from two pathways. The first is an indirect pathway inferring step-frame alignments by composing step-to-narration assignments with narration-to-frame correspondences. The second is a direct pathway that learns associations between step descriptions and frames by leveraging information from all videos having steps in common.", + "bbox": [ + 75, + 305, + 472, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our experiments we demonstrate that our multimodality alignment leads to significant performance gains over several baselines, including single-pathway temporal grounding, as well adaptations of prior works to our problem. During inference, the direct pathway can be used by", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "itself to temporally ground steps in absence of transcribed narrations. When narrations are available at test time, our method improves further the accuracy of temporal grounding by fusing the inference outputs of the two pathways.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our work makes the following contributions: 1) we learn to align steps to frames in how-to videos, using only weak supervision in the form of noisy ASR narrations and instructional articles; 2) we propose a novel approach for joint dense temporal grounding of instructional steps and video narrations; 3) we introduce a new benchmark for evaluating instructional step grounding which we will make available to the community; 4) we demonstrate state-of-the-art results on multiple benchmarks for both step as well as narration grounding.", + "bbox": [ + 496, + 152, + 893, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 316, + 640, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Procedural step recognition. Going beyond classifying a trimmed segment video to a procedural step [9, 32, 41, 76], there has been active research in untrimmed video segmentation [10, 59, 72, 77], step anticipation [40, 47, 48], unsupervised step discovery [18, 19], procedure planning [6, 12, 74] and step description [68, 72]. In this work we focus on parsing untrimmed procedural videos into a sequence of step segments. Prior approaches can be categorized into two groups: action localization-based methods [3, 29, 50, 59] use fixed taxonomies of step classes and are not able to recognize unseen steps, while grounding-based methods [2, 5, 21], including ours, operate in an open-world setting, treating the problem as video-text alignment. Grounding-based approaches can be further subdivided into single step grounding, where single steps are queried over the whole video[27, 57] and dense temporal grounding methods [14, 22] where the objective is to jointly ground a sequence of steps or whole article into the video. Chen et al. [14] use video-level instructional step labels for (weak) supervision of a model that grounds instructional articles to videos. Their approach attempts to localize steps without using any narration information during training. Instead, we argue that narrations provide a much richer source of supervision for training step grounding models, while essentially coming for free.", + "bbox": [ + 496, + 340, + 893, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Weakly-supervised approaches Existing methods also vary by the level of supervision used during training. One option is leveraging fully-annotated datasets with known temporal segments for each step [10, 26, 29, 50, 53, 60, 71, 80]. Other works use weakly-annotated training sets where the task and the order in which the steps appear in the video are known [7, 8, 11, 16, 20, 28, 45, 79], or only the task and potential steps are known [44], or only loose association between video and instructional articles is given [14, 17]. More related to our work are approaches that are trained using weak supervision coming for free from instructional video narrations [1, 20, 36, 49, 75]. Narrations", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15202", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and their timestamps have been used to discover procedural steps in videos and then align them with visual clusters [1, 51], to obtain temporal constraints for the location of steps in videos [20, 79], and to roughly localized steps by leveraging their textual similarity with ASR narrations [36]. In this work we utilize narrations, and in particular the estimated video-narration alignment, via multi-task learning and complementary inference pathways [73] for training a step grounding model.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instructional articles have been recently used for learning strong video representations [32, 40] by replacing noisy ASR narrations with steps mined from instructional articles using their semantic similarity. Although we also associate steps from wikiHow articles to video frames through the use of narrations, our work differs from prior work in several aspects: we align steps to video by a global procedure that takes into account all ordered steps in the article (inspired by dense temporal grounding methods [5]) and temporally grounds them in the whole video, instead of matching individual video clips to an orderless collection of steps; our step grounding uses video in addition to steps and narrations while the method proposed in Lin et al. [32] relies purely on text-matching narrations to step descriptions; finally, the works differ in objectives with our aim being step grounding in long how-to videos rather than learning video-clip representations. In summary, our model is trained by combining supervision signals from video narrations and instructional articles, and can be applied for aligning procedural steps to videos with and without narrations.", + "bbox": [ + 75, + 227, + 472, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video-Text alignment The availability of large-scale video-text datasets such as HowTo100M has prompted many works on joint video-language embedding training [10, 24, 32, 33, 37, 46, 52, 70]. A form of contrastive loss is often adopted for bringing together the representations of the two modalities [4, 34, 35, 37, 42, 43, 66, 69], while masked objectives are also gaining popularity [15, 23, 31, 35, 56, 57, 58, 61, 78]. Some works perform end-to-end representation learning [37, 38], while others freeze representation and focus on longer-term temporal modelling, which aims to capture context [66]. Recently Han et al. investigated directly aligning contextualized narration representations to video frames [22]. We build our method off of this approach – we note however that our objective is complementary: rather than aligning a video's narrations as an end-goal, we use this functionality to ground a set of independent steps sourced from instructional articles; in that process we show that the synergy that develops while training jointly on the two tasks results in improved performance for both.", + "bbox": [ + 75, + 529, + 472, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Narration-Aided Step Grounding", + "text_level": 1, + "bbox": [ + 76, + 844, + 382, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first present our architecture for joint narration and step grounding (Sec. 3.2), followed by learning objectives", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(Sec. 3.3.1) and pseudo-labeling strategy (Sec. 3.3.3); we discuss inferring the video task in (Section 3.3.2).", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 128, + 702, + 143 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $(\\mathcal{V},\\mathcal{N})$ be a video-narration pair, consisting of $T$ video frames and a sequence of $N$ narrations. Also, let $S$ be an ordered list of $S$ steps from an instructional article for a candidate task $\\tau$ . Our objective is to ground each step of $S$ to the video, conditioned on the other steps and the ASR transcript2. In particular, the desired output of our model is an alignment matrix $Y^{SV} \\in \\{0,1\\}^{S \\times T}$ , where $Y_{st} = 1$ only if frame $t$ is depicting the $s$ -th step of task $\\tau$ , and zero otherwise. Note that some steps might not be represented in the video.", + "bbox": [ + 496, + 152, + 893, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Joint Narration and Article Step Grounder", + "text_level": 1, + "bbox": [ + 498, + 311, + 867, + 329 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 2, our proposed VINA model follows the popular paradigm of leveraging Transformers for modeling multimodal interactions [62, 67].", + "bbox": [ + 496, + 335, + 893, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unimodal Encoders. Before feeding the video, narrations and article steps to our model, we preprocess them to extract a sequence of tokens. Given a video-narration pair $(\\mathcal{V}, \\mathcal{N})$ we extract visual features, $X^v \\in \\mathbb{R}^{T \\times D_v}$ and narration features $X^n \\in \\mathbb{R}^{N \\times D_n}$ using standard backbone networks (e.g., a frozen S3D [65] network for visual features, and pooled Word2Vec [39] embeddings for narration features). Similarly, we encode the sequence of steps in a sequence of features $X^s \\in \\mathbb{R}^{S \\times D_s}$ . The features of each modality $m$ are embedded into a common embedding space of dimensionality $D$ using a Unimodal Encoder that consists of a modality-specific MLP network, and then learnable, modality-specific positional embeddings $P^m$ are added to them:", + "bbox": [ + 496, + 383, + 893, + 595 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nH ^ {m} = M L P \\left(X ^ {m}; \\theta_ {m}\\right) + P ^ {m}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 588, + 604, + 890, + 622 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $m\\in \\{v,n,s\\}$ denotes the modality.", + "bbox": [ + 498, + 631, + 782, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multimodal Encoder. The outputs of the Unimodal Encoders are concatenated into a sequence of tokens: $H = [H^v; H^n; H^s] \\in \\mathbb{R}^{(T + N + S) \\times D}$ and fed to the Multimodal Encoder, which is a standard Transformer with multiple layers of multi-head self-attention:", + "bbox": [ + 498, + 648, + 893, + 724 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nZ = \\operatorname {T r a n s f o r m e r} (H) \\in \\mathbb {R} ^ {(T + N + S) \\times D}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 733, + 890, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The contextualized embeddings $Z = [Z^v; Z^n; Z^s]$ computed by the Multimodal Encoder capture interactions within each modality (e.g., temporal relationships within the video and context among steps of an article) and across modalities. We can then compute cosine similarity matrices between all pairs of modalities: narrations-to-video $A^{NV} \\in \\mathbb{R}^{N \\times T}$ , steps-to-video $A^{SV} \\in \\mathbb{R}^{S \\times T}$ ,", + "bbox": [ + 496, + 760, + 893, + 867 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "$^{2}$ ASR transcripts are assumed to be always available for training and optionally during inference.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15203", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4348eaf538f96c16d5e3b00ab4000ebb9c79479df70e2032a5991b68b31ba595.jpg", + "image_caption": [ + "Figure 2: (left) Schematic illustration of our system. First, it extracts representations for each modality (video, ASR narrations, task steps) with three Unimodal Encoders. These representations are fed to a Transformer-based Multimodal Encoder for capturing interactions among video frames as well as among the textual modalities and the video. The contextualized embeddings for video frames, narrations and steps are used to compute correspondences between all pairs of modalities. Step grounding is achieved by fusing the output of two pathways: a direct pathway aligning steps to video $(A^{SV})$ and an indirect pathway that composes steps-to-narration $(A^{SN})$ with narration-to-video $(A^{NV})$ alignments to produce a second step-to-video alignment $(A^{SNV})$ . We train our model using a teacher-student strategy with iteratively refined and filtered step pseudo-labels. (right) Qualitative examples of our learned steps-to-video alignment and steps-to-narrations alignment matrices for a video snippet." + ], + "image_footnote": [], + "bbox": [ + 155, + 88, + 810, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and steps-to-narrations $A^{SN} \\in \\mathbb{R}^{S \\times N}$ . For example, the narrations-to-video similarity matrix $A^{NV}$ is obtained by simply computing the cosine similarity between each frame embedding and each narration embedding: $A_{nt}^{NV} = \\mathbf{z}_n^{n\\top}\\mathbf{z}_t^v / (||\\mathbf{z}_n^n||||\\mathbf{z}_t^v||)$ .", + "bbox": [ + 75, + 516, + 468, + 593 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Narration-aided Step Grounding. A straightforward inference path for temporally grounding the steps in the video is directly through the $A^{SV}$ similarity matrix, which captures the similarity of each video frame with each instructional step. However, this alignment does not explicitly take into account the narrations of the video (only implicitly, through the Multimodal Transformer). We observe that an alternative way to ground steps in a video is to first identify narrations in the ASR transcript that are relevant to the step and then exploit the similarity of those narrations with video frames to get a loose prior over the step location. This is computed by combining the information captured in the steps-to-narrations and narrations-to-video alignment matrices $A^{SN}$ and $A^{NV}$ :", + "bbox": [ + 75, + 593, + 468, + 808 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA ^ {S N V} = \\tilde {A} ^ {S N} A ^ {N V} \\in \\mathbb {R} ^ {S \\times T}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 819, + 468, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tilde{A}^{SN}$ is the predicted steps-to-narrations alignment matrix $A^{SN}$ after being normalized with a softmax function with temperature $\\xi$ : $\\tilde{A}_{sn}^{SN} = \\frac{\\exp(A_{sn} / \\xi)}{\\sum_{j=1}^{N}\\exp(A_{sj} / \\xi)}$ .", + "bbox": [ + 76, + 848, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The resulting $A^{SV}$ and $A^{SNV}$ alignment matrices provide two complementary inference paths to align steps to video frames. The mutual agreement between the direct steps-to-video alignment provided by $A^{SV}$ and indirect, narration-based steps-to-video alignment provided by $A^{SNV}$ can be used to better ground steps. Intuitively, if a frame is both very similar to a step in the joint embedding space learned by the Multimodal Transformer, and also very similar to a narration that is relevant to the step, then it is more likely to be indeed relevant to the step. Hence, we fuse the $A^{SV}$ and $A^{SNV}$ alignment matrices to a matrix $A^{F} = (A^{SV} + A^{SNV}) / 2$ .", + "bbox": [ + 498, + 516, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Weakly-Supervised Training from Narrated Instructional Videos", + "text_level": 1, + "bbox": [ + 500, + 750, + 888, + 780 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we discuss how to supervise the VINA model in order to learn steps-to-video alignment and narrations-to-video alignment. We first present the training objective assuming that the ground-truth temporal segments for each narration and step in the video are given. Then we describe our approach for obtaining automatic pseudo-labels for the temporal segments.", + "bbox": [ + 496, + 801, + 890, + 909 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15204", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Learning on Labeled Data", + "text_level": 1, + "bbox": [ + 76, + 90, + 316, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $\\mathcal{B} = \\{\\mathcal{V}_i, \\mathcal{N}_i, \\mathcal{S}_i, Y_i^{NV}, Y_i^{SV}\\}_{i=1}^B$ denote a set of training tuples, each comprising a video-narration pair, an ordered list of relevant task steps, and the target video-narrations and video-steps alignment matrices, we train the VINA model by optimising the following objective:", + "bbox": [ + 75, + 117, + 468, + 195 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\frac {1}{B} \\left[ \\sum_ {i = 1} ^ {B} \\lambda_ {N V} \\mathcal {H} \\left(Y _ {i} ^ {N V}, A _ {i} ^ {N V}\\right) + \\lambda_ {S V} \\mathcal {H} \\left(Y _ {i} ^ {S V}, A _ {i} ^ {S V}\\right) \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 210, + 468, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{H}(\\cdot, \\cdot)$ is the modified InfoNCE loss used by [22] for aligning video with text using noisy ground-truth temporal segments:", + "bbox": [ + 75, + 282, + 468, + 330 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {H} (Y, A) = - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\log \\frac {\\sum_ {t} Y _ {t , k} \\exp \\left(A _ {t , k} / \\eta\\right)}{\\sum_ {t} \\exp \\left(A _ {t , k} / \\eta\\right)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 345, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\eta$ is a temperature constant. Note that although we do not explicitly supervise the steps-narrations alignment $A^{SN}$ , meaningful alignments emerge during training due to the joint grounding of narrations and steps to the same video samples, as seen in Figure 2. Note that although we do not directly supervise the steps-to-narrations alignment, our model is able to learn meaningful correspondences, which go beyond simple pairwise textual matching.", + "bbox": [ + 75, + 402, + 470, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Pairing Videos with Articles", + "text_level": 1, + "bbox": [ + 76, + 555, + 326, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We assume access to a set of instructional articles $\\mathcal{A} = \\{\\mathcal{S}_j, \\tau_j\\}_{j=1}^W$ , where $\\tau_j$ denotes the article title and $\\mathcal{S}_j$ the associated set of steps. To assign a set of steps to a given video from our training set $\\mathcal{B}$ we need to associate it with an article from $\\mathcal{A}$ . If our video dataset provides metadata (e.g., a task id for every video), then this can be used to obtain the association – although there is no guarantee that this will result in the best article-match for the video (see discussion in supplementary materials for more analysis). If such metadata is not available, we can predict a task id, using the similarity between the narration and the titles of the available articles. To that end we use an off-the-shelf language model (e.g. MPNet [55]) to compute semantic embeddings of the ASR captions of every video and the title of each article $\\tau_j \\in \\mathcal{W}$ . For every video $\\mathcal{V}_i$ we then calculate the semantic similarity between all the $N$ captions in $\\mathcal{N}_i$ and all task titles $\\tau_j \\in \\mathcal{W}$ , and assign $N$ votes; the vote of every caption goes to the task that best matches it. Finally the video is assigned the task with the most votes. Alternatively, in order to obtain multiple sets of steps for a video, we rank the tasks by the number of votes.", + "bbox": [ + 75, + 583, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Narration-Aided Pseudo-Labeling", + "text_level": 1, + "bbox": [ + 500, + 90, + 794, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once a task $\\tau_{j}$ has been associated with a video, we have access to a list of steps $S_{j}$ from the article of the task. However, whether these steps appear in the video and their temporal location remain unknown. Inspired by self-labeling approaches from the SSL literature [30, 54, 64], we follow a teacher-student approach where a teacher version of our models generates pseudo-labeled temporal segments for training the student. For every step represented by a row in the learned steps-to-video alignment matrix we obtain a pseudo-ground truth segment by finding the maximal activation (peak) and expanding a temporal segment on both sides until the activation falls below an adaptive threshold $\\zeta$ (e.g., $70\\%$ of the peak). To avoid training with unreliable pseudo-labels, we filter out pseudo-labels with low confidence: if the peak activation is below a fixed threshold $\\gamma$ , the alignment of that step is treated as unreliable for pseudo-labeling, and is altogether ignored.", + "bbox": [ + 496, + 114, + 893, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training curriculum. For the first $E_{b}$ epochs we perform burn-in training of the student model on fixed pseudo-labels generated by feeding the video and the list of steps $S_{j}$ to TAN [22], an off-the-shelf model pre-trained on the task of video-text alignment. Afterwards, we switch to using pseudo-labels generated from the teacher, where the teacher is initialized by duplicating the burn-in student model and then updated every $\\nu$ epochs. During both stages, we utilize the original ASR timestamps for supervising the video-to-narrations alignment.", + "bbox": [ + 496, + 375, + 893, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 539, + 633, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 500, + 564, + 697, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our models on narrated videos from the HowTo100M dataset by leveraging the dataset release of wikiHow instructional articles [25], without using any form of manual annotations. In order to evaluate the effectiveness of our method, we evaluate: step grounding on HT-Step (a new benchmark, described below), narration alignment on HTM-Align [22], and zero-shot step localization on CrossTask [79]. A statistics summary of all the datasets used for training and evaluation is provided in Table 1.", + "bbox": [ + 496, + 587, + 893, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "HowTo100M (Training). The HowTo100M dataset [38] contains instructional videos from YouTube. Following Han et al. [22], we use the Food & Entertainment subset containing approximately $370K$ videos, where each video is complemented by the \"sentencified\" ASR transcription of its audio narration.", + "bbox": [ + 496, + 726, + 893, + 818 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "wikiHow (Training). We train using 14,541 cooking tasks from the wikiHow-Dataset [25]. For each task, we generate an ordered list of steps by extracting the step headlines.", + "bbox": [ + 496, + 820, + 890, + 867 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CrossTask (Evaluation). We use this established instructional video benchmark for zero-shot grounding, i.e., by", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15205", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3c9f8c217e5cc3002f6794a3a75df146691f4a4cf707228478644927543fcd66.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetStep Annot.# Videos# Activities# Steps# Segments
HowTo100M [38]X1.2M25k--
HTM-Align [22]X8080--
CrossTask [79]✓4.8k (2.8k)83 (18)13320.9k
HT-Step (val)✓6001201,2043,441
HT-Step (test)✓6001201,2423,631
wikiHow-14k100k-
", + "bbox": [ + 78, + 88, + 475, + 195 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "directly evaluating on CrossTask our model learned from HowTo100M. Following common practices, we use two evaluation protocols: the first one - step localization - aims at predicting a single timestamp for each occurring step in videos from 18 primary tasks [79]. Performance is evaluated by computing the recall (denoted as Avg. R@1) of the most confident prediction for each task and averaging the results over all query steps in a video, where R@1 measures whether the predicted timestamp for a step falls within the ground truth boundaries. We report average results over 20 random sets of 1850 videos [79]. The second task - article grounding - requires predicting temporal segments for each step of an instructional article describing the task represented in the video. We use the mapping between CrossTask and simplified wikiHow article steps provided in Chen et al. [14] and report results on 2407 videos of 15 primary tasks obtained excluding three primary tasks following the protocol of [14] (see supplementary materials for details). Performance for this task is measured with Recall@ $K$ at different IoU thresholds [14].", + "bbox": [ + 73, + 286, + 472, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "HTM-Align (Evaluation). This benchmark is used to evaluate our model on narration grounding. It contains 80 videos where the ASR transcriptions have been manually aligned temporally with the video. We report the R@1 metric [22], which evaluates whether the model can correctly localize the narrations that are alignable with the video.", + "bbox": [ + 75, + 599, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "HT-Step (Evaluation). To evaluate the effectiveness of our model in grounding article steps, we introduce an evaluation benchmark consisting of 1200 HowTo100M narrated videos spanning a total of 216 unique tasks, with each video manually annotated with temporal segments for each occurring step. For each video, annotators were provided with the task name (e.g., Make Pumpkin Puree) and candidate recipe steps from the corresponding wikiHow article. We refer the reader to supplementary materials for details about the data annotation. We split the annotated videos into a validation and a test set, each containing 600 videos, with 5 videos per task. We ensure that our validation set does not contain videos from HTM-Align.", + "bbox": [ + 75, + 703, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 90, + 718, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As video encoder we adopt the S3D [65] backbone pretrained with the MIL-NCE objective on HowTo100M [37]. Following previous work [22, 66], we keep this module frozen and use it to extract clip-level features (one feature per second for video decoded at 16 fps). For extracting context-aware features for each sentence (step or narration), we follow the Bag-of-word (BoW) approach based on Word2Vec embeddings [39]. Our methods hyperparameters were selected on the HT-Step validation set and are: $\\lambda_{SV} = \\lambda_{NV} = 1$ , temperatures $\\eta, \\xi = 0.07$ , and threshold $\\gamma = 0.65$ . We train our model for 12 epochs, with 3 epochs burn-in and then we update the teacher every 3 epochs. Pseudo-labels are obtained based on the steps-to-video alignment matrix. To obtain temporal segment detections from the step-to-video alignment output of our model (e.g. for evaluating on the CrossTask article grounding setting) we use a simple 1D blob detector [63]. Unless otherwise specified, we use the fused alignment matrix for step grounding when narrations are available during inference time. More details are included in supplementary materials.", + "bbox": [ + 496, + 112, + 893, + 417 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4f40f908c8e0ee1f29220affb4d192fb767d39be1c0413ab17f22fa620c51da5.jpg", + "table_caption": [ + "Table 1: Summary statistics for the datasets in our work. For CrossTask, the statistics for primary activities only are shown in parentheses." + ], + "table_footnote": [], + "table_body": "
MethodTrain.Inp.HT-Step ↑R@1HTM-Align ↑R@1
w/o nar.w/ nar.
CLIP (ViT-B/32) [43]---23.4
MIL-NCE [37]N30.7-34.2
TAN (Joint+Dual, S2) [22]N--49.4
TAN* (Joint, S1, LC) [22]N31.2-47.1
TAN* (Joint, S1, PE+LC) [22]N7.9-63.0
OursN+S35.6 ± 0.437.4 ± 0.466.5 ± 0.9
", + "bbox": [ + 500, + 426, + 910, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2: Comparison with state-of-the-art methods for step and narration grounding. We report results on the HT-Step and HTM-Align test sets, respectively. TAN* refers to our improved baselines of [22]. S1 and S2 refer to the training stages followed in [22]. PE denotes the addition of positional encoding to the output of the narration encoder. LC denotes long context, i.e., our improved TAN* baseline using 1024 seconds of context as opposed to 64 for TAN. Previous best results are shown underlined. Our VINA results are reported after 5 random runs. VINA clearly outperforms all previous work – as well as our improved TAN baselines – by large margins on both narration alignment and step grounding.", + "bbox": [ + 496, + 547, + 893, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Results", + "text_level": 1, + "bbox": [ + 500, + 770, + 591, + 784 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.1 Comparison with the State of the Art", + "text_level": 1, + "bbox": [ + 498, + 792, + 812, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Weakly-Supervised Narration and Step Grounding. Table 2 compares the step and narration grounding performance of our method with recent state-of-the-art video-text alignment methods trained on HowTo100M using ASR narrations: MIL-NCE [37] and TAN [22]. When using them for narration alignment, we feed them with ASR as input.", + "bbox": [ + 496, + 809, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15206", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "But we also evaluate them as strong baselines for zero-shot step grounding by feeding them with the sequence of steps as input. Our model achieves $66.5\\%$ R@1 on narration alignment on HTM-Align, leading to an absolute improvement of $17.1\\%$ over the previously reported state-of-the-art $(49.4\\%)$ . Notably, on HTM-Align our method surpasses TAN* (Joint, S1, PE, LC) which is a new version of TAN [22] implemented by us and much stronger in video-narration alignment. Our re-implementation uses positional encodings for ASR narrations, is trained on long-form videos (up to 17 minutes) only with original ASR timestamps, while TAN was trained on 1 min video-clips with refined narration timestamps and used a fusion of two models during inference (Joint+Dual). Our method also outperforms all baselines for step grounding on HT-Step even when seeing only steps during inference, while being trained with (video, narrations, steps) triplets. It also outperforms TAN* (Joint, S1, LC), which is a second re-implementation of TAN designed for maximum performance on the task of step grounding. Additionally, VINA is able to use ASR transcripts of videos during test time, if available, to further boost the performance.", + "bbox": [ + 75, + 90, + 472, + 422 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e4718563f8491f1671ed0bb71a83657643d39376c5d38288a7efbddba14d0888.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method↑Avg. R@ 1 (%)
Supervised
TempCLR [70]52.5
Zero-Shot
Zhukov [79]22.4
HT100M [38]33.6
VideoCLIP [66]33.9
MCN [13]35.1
DWSA [51]35.3
MIL-NCE [37]40.5
VT-TWINS* [24]40.7
UniVL [33]42.0
Ours w/o nar.44.1
Ours w/ nar.44.8
", + "bbox": [ + 161, + 450, + 385, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3: Comparison with state-of-the-art methods for zero-shot action step localization on the CrossTask dataset. The performance of the state-of-the-art fully-supervised method (TempCLR [70]) is reported as an upper-bound to the zero-shot approaches. * denotes results reported on different test splits, and hence not directly comparable with the rest. Our model outperforms all previous works by a clear margin (2.1% absolute improvement over the previous best result on the standard split). When providing narrations as additional inputs during inference (only text, not the timings), we obtain a further 0.7% boost.", + "bbox": [ + 75, + 657, + 470, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Step localization on CrossTask. In Table 3 we compare our model against the state-of-the-art in step localization on the CrossTask benchmark. Our approach sets a new state-of-the-art for zero-shot step localization on this challenging", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "benchmark. Importantly, most approaches are evaluated on this dataset by feeding their predicted steps-to-frames alignment matrix to a dynamic programming algorithm which finds the optimal assignment of each step with exactly one short clip assuming a canonical, fixed ordering of steps for each task. In contrast, our method, which is naturally aware of context and ordering by densely grounding steps, can outperform prior results without imposing any constraints during inference.", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/17744c5ebd31741a7063e606bfa8a87f62590238cc3513da7070a668580a1051.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Model↑R@50(IOU)↑R@100(IOU)
0.10.30.50.10.30.5
MIL-NCE-max [37]33.512.04.939.714.35.9
MIL-NCE-avg [37]42.924.312.956.832.117.0
WSAG [14]40.123.110.154.331.314.0
Ours87.159.030.090.661.130.9
", + "bbox": [ + 503, + 241, + 888, + 342 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4: Comparison with state-of-the-art approaches for article grounding on the CrossTask dataset.", + "bbox": [ + 498, + 356, + 890, + 388 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Article grounding on CrossTask. VINA is robust to the type of language in which task steps are described. It can handle both atomic phrases (as demonstrated by our results on step localization on CrossTask), but also rich, natural language step descriptions, as evidenced by performance on HT-Step. To further demonstrate this, we compare against the state-of-the-art on the article grounding task of CrossTask in Table 4. Our model outperforms all previous works by a large margin. We emphasize the performance improvement we obtain compared to WSAG, which highlights the importance of exploiting the narration information for training.", + "bbox": [ + 496, + 415, + 890, + 598 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.2 Ablation Studies", + "text_level": 1, + "bbox": [ + 498, + 608, + 669, + 623 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform ablations to assess the impact of the various design choices in our method by measuring step grounding performance on the HT-Step validation set and video-narration alignment performance on HTM-Align.", + "bbox": [ + 496, + 633, + 890, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of weak supervision from instructional articles. Row 3 in Table 5 shows the step grounding results obtained from an instance of our model that includes only the direct video-step alignment pathway and that is trained just on wikiHow steps (without narrations) using the fixed step pseudo-labels from TAN* [22] without any form of iterative pseudo-labeling (row 1). Remarkably, this variant improves by $3.3\\%$ over the step-grounding performance of TAN*. When we let this variant update the step pseudo-labels (row 4), the recall improves further ( $5.1\\%$ over TAN*). These results provide evidence of the strong benefits of utilizing instructional articles for the learning of step grounding.", + "bbox": [ + 496, + 719, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15207", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d22aef2b73bbfa8b0dd5caa18e98ca05e0b071a41571806708674dac380036c4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTrain.Inp.Iter.Pseudo.HT-Step ↑R@1HTM-Align
w/o nar.w/ nar.
Baseline/Initial Step Pseudo-labels
(1) TAN Joint S1N30.7-47.1
Single-Task Training
(2) OursN--63.2
(3) OursS34.0--
(4) OursS✓35.8--
Multi-Task Training
(5) OursN+S34.336.164.8
(6) OursN+S✓36.939.167.0
", + "bbox": [ + 78, + 88, + 480, + 255 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5: Ablation of main components of our framework. We study the contribution of (a) multi-task training for narration and step grounding, (b) iterative step pseudo-labeling (Iter. Pseudo), and (c) narration-aware step grounding $(w / n a r)$ . We report results on the HT-Step val set for STG and HTM-Align for NG. We compare training only with narrations (N), only with wikiHow steps (S), and training with narrations-steps sequence pairs $(\\mathrm{N} + \\mathrm{S})$ . We also compare the performance with and without providing narrations during inference.", + "bbox": [ + 75, + 265, + 468, + 416 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of multimodal training and inference. Training our model with multi-modal textual inputs (steps and narrations), we observe an improvement of $1.6\\%$ in narration grounding (row 5 of Table 5) compared to its single-task counterpart (row 2). However the gain in step grounding is marginal when seeing only video frames during inference ( $w/o$ nar, $34\\%$ in row 3 vs $34.3\\%$ in row 5). Our conjecture is that the missing modality (narrations) leads to some drop in performance. Providing both steps and narrations during inference leads to a stronger step grounding performance, which surpasses the TAN* baseline by $5.4\\%$ ( $30.7 \\rightarrow 36.1$ ).", + "bbox": [ + 75, + 419, + 468, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of iterative pseudo-labeling. By comparing row 5 to row 6 of Table 5 we observe a clear boost in performance on both step grounding and narration alignment. This is a clear indication of the gains produced by iteratively refining the pseudo-labels using our model as a teacher during training.", + "bbox": [ + 75, + 593, + 468, + 685 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/56374483eb0fdcc6efbe452b3093d46abcecd8ff174c63121a508aa0fea15127.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AlignmentS → VS → NN → VHT-Step ↑R@1
S → Vlearned--34.3
S → N → V-learnedlearned30.5
S → N → V-learnedASR27.9
S → N → V-MPNet [55]ASR19.0
Fusedlearnedlearnedlearned36.1
", + "bbox": [ + 78, + 696, + 470, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6: Impact of the alignment matrix used during inference with narrations. The same model is used for all results (corresponding to row 5 in Table 5).", + "bbox": [ + 75, + 796, + 468, + 843 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of pathways during inference. In Table 6 we study the effects of using different pathways and alignment information during inference. All results are produced", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/84f8776646ffa6760f84144db1fb7fc5f3849df770f3b3aa09166832dc4d3d1e.jpg", + "image_caption": [ + "Figure 3: Step grounding performance and minimum retained step ratio as a function of the filtering threshold. Aggressive unreliable pseudo-label filtering with high confidence thresholds (large maximum step discard ratio) leads to improved performance." + ], + "image_footnote": [], + "bbox": [ + 542, + 90, + 851, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "from the same model trained for joint narration and step grounding with fixed pseudo-labels from TAN (row 5 in Table 5). Grounding steps using the indirect steps-to-video alignment only lags by $3.8\\%$ behind the direct steps-to-video alignment that directly computes the similarity between steps and video frames $(30.5\\%)$ vs $34.3\\%$ . Their fusion outperforms their individual grounding performance. This suggests that they capture complementary information. We also explore substituting our learned steps-to-narrations alignment with an alignment computed with an off-the-shelf language model. This significantly degrades performance (19.0) showing that our joint steps and narrations grounding model learns relationships between steps and narrations that go beyond textual similarity between pairs of sentences. Similarly, substituting our learned narrations-to-video alignment with an alignment based on the original ASR timestamps reduces performance by $2.6\\%$ (see additional details in supplementary materials).", + "bbox": [ + 496, + 340, + 890, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of pseudo-label filtering threshold. In Figure 3 we study the effect of the filtering threshold used in the iterative pseudo-labeling stage. We can observe that using aggressive filtering (i.e., high thresholds translating to a high maximum percentage of pseudo-labels that are discarded) is key to observing gains from iterative pseudo-labeling compared to training with fixed pseudo-labels from TAN. Intuitively, a large percentage of steps described in wikiHow articles are not represented in the given instructional video due to task mismatch, variations in recipe execution, and some steps being optional. Therefore, starting with a small subset of reliable pseudo-labels can facilitate step grounding.", + "bbox": [ + 496, + 619, + 890, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Task selection. In Table 7 we investigate different strategies to select the wikiHow articles during training. This selection determines the set of steps to be grounded. We evaluate two strategies for video-task association from narratives and compare them with using the task id provided in", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15208", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bbb2d0a7df83b63b4f8e76734e4c7d648fd79782ffb66b68c73b3fdcbf1a110f.jpg", + "image_caption": [ + "Figure 4: Visualization of sample frames per step, ground-truth segments (colored bars) and a single predicted timestamp per step (dashed lines) for the groundable steps of three HT-step validation videos demonstrating (a) a Mini-Stromboli recipe, (b) a Make Tabouli recipe, and (c) a Bake a Sweet Potato Pie recipe. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 91, + 97, + 509, + 292 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/c3bbc8296be48e918ebe5ce17fa97fae7d2ccc0f7111655366e659fbc730a026.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 527, + 119, + 746, + 289 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/f141fe8b373930461d1fc09c8698f01074e6c56b8bcb073eba83a575db32c2b4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Task ID selectionHT-Step ↑R@1
HT100M metadata34.3
Top-1 prediction34.7
Random / top-5 pred34.3
", + "bbox": [ + 153, + 380, + 393, + 446 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Table 7: Sensitivity to task id selection. We assess how the performance of our method changes when using different strategies to associate videos with articles. We experiment with using the task ids available from HT100M, as well as the two predictive strategies presented in Section 3.3.2. We conclude that our method is robust to the task selection, and the task labels are not necessary for training.", + "bbox": [ + 75, + 455, + 472, + 564 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "the HowTo100M metadata for each video3. We see that our automatic selection approaches yield results on par with or even slightly better than those based on metadata.", + "bbox": [ + 75, + 575, + 470, + 625 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.3.3 Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 641, + 264, + 657 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Qualitative grounding results obtained with the proposed VINA model are presented in Figure 4. These examples showcase that our model can successfully retrieve complex and fine-grained steps, such as combining multiple ingredients in a mixing bowl or tapping a filled pie pan for the Bake a Sweet Potato Pie recipe. Failure cases include discriminating between steps that involve the same ingredients, such as mixing the milk and eggs versus adding the mixture to the existing mix.", + "bbox": [ + 75, + 665, + 468, + 801 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 809, + 194, + 825 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We have presented a method for learning how to temporally ground sequences of steps in instructional videos,", + "bbox": [ + 76, + 835, + 468, + 866 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "without any manual supervision. Our proposed method exploits the weak supervision naturally provided in such videos through their narrations, and solves for joint alignment of narrations and steps, while fusing two complementary pathways for step-to-video alignment. We demonstrated strong quantitative performance, surpassing the state-of-the-art on multiple benchmarks for both narration and step grounding.", + "bbox": [ + 496, + 383, + 892, + 505 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements. We thank Huiyu Wang, Yale Song, Mandy Toh, and Tengda Han for helpful discussions.", + "bbox": [ + 498, + 507, + 890, + 537 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 549, + 596, + 565 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Piotr Bojanowski, Nishant Agrawal, Josef Sivic, Ivan Laptev, and Simon Lacoste-Julien. Unsupervised learning from narrated instruction videos. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4575-4583, 2016. 2, 3", + "[2] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In Proceedings of the IEEE international conference on computer vision, pages 5803-5812, 2017. 2", + "[3] Kumar Ashutosh, Santhosh Kumar Ramakrishnan, Triantafyllos Afouras, and Kristen Grauman. 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In International Conference on 3D Vision (3DV), 2022. 2" + ], + "bbox": [ + 78, + 90, + 468, + 241 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "15213", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2023/Learning to Ground Instructional Articles in Videos through Narrations/a5da633a-33ad-4510-84f7-55e37a75aa45_model.json b/2023/Learning to Ground Instructional Articles in Videos through Narrations/a5da633a-33ad-4510-84f7-55e37a75aa45_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b6819e6fa254687fe282f5757190402c982693b2 --- /dev/null +++ b/2023/Learning to Ground Instructional Articles in Videos through Narrations/a5da633a-33ad-4510-84f7-55e37a75aa45_model.json @@ -0,0 +1,2459 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.239, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.122, + 0.131, + 0.85, + 0.154 + ], + "angle": 0, + "content": "Learning to Ground Instructional Articles in Videos through Narrations" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.181, + 0.735, + 0.216 + ], + "angle": 0, + "content": "Effrosyni Mavroudi; Triantafyllos Afouras; Lorenzo Torresani Meta AI" + }, + { + "type": "text", + "bbox": [ + 0.305, + 0.22, + 0.667, + 0.234 + ], + "angle": 0, + "content": "{emavroudi, afourast, torresani}@meta.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.301, + 0.474, + 0.71 + ], + "angle": 0, + "content": "In this paper we present an approach for localizing steps of procedural activities in narrated how-to videos. To deal with the scarcity of labeled data at scale, we source the step descriptions from a language knowledge base (wikiHow) containing instructional articles for a large variety of procedural tasks. Without any form of manual supervision, our model learns to temporally ground the steps of procedural articles in how-to videos by matching three modalities: frames, narrations, and step descriptions. Specifically, our method aligns steps to video by fusing information from two distinct pathways: i) direct alignment of step descriptions to frames, ii) indirect alignment obtained by composing steps-to-narrations with narrations-to-video correspondences. Notably, our approach performs global temporal grounding of all steps in an article at once by exploiting order information, and is trained with step pseudo-labels which are iteratively refined and aggressively filtered. In order to validate our model we introduce a new benchmark - HT-Step - obtained by manually annotating a 124-hour subset of HowTo100M1 with steps sourced from wikiHow articles. Experiments on this benchmark as well as zero-shot evaluations on CrossTask demonstrate that our multi-modality alignment yields dramatic gains over several baselines and prior works. Finally, we show that our inner module for matching narration-to-video outperforms by a large margin the state of the art on the HTM-Align narration-video alignment benchmark." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.738, + 0.21, + 0.753 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Instructional videos have emerged as a popular means for people to learn new skills and improve their abilities in executing complex procedural activities, such as cooking a recipe, performing home improvements, or fixing things. In addition to being useful teaching materials for humans, how-to videos are a promising medium for learning by ma" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.274, + 0.86, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.57, + 0.895, + 0.722 + ], + "angle": 0, + "content": "Figure 1: Our proposed Video, Instructions, and Narrations Aligner (VINA) learns to simultaneously ground narrations and instruction steps in how-to videos from an uncurated set of narrated videos and a separate knowledge base of instructional articles, without any manual annotations. This is contrary to prior work that learns how to align a video with a single sequence of sentences by leveraging ground-truth pairs of video-text sequences, e.g., a video and its narrations [22], or a video and an annotated, ordered list of steps demonstrated in it [16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.895, + 0.87 + ], + "angle": 0, + "content": "chines, as they provide revealing visual demonstrations of complex activities and show elaborate human-object interactions in a variety of domains. Motivated by this observation, in this work we look at the task of temporally localizing the steps of procedural activities in instructional videos. This problem is foundational to the broader goal of human-procedure understanding and advances on this task promise to enable breakthrough applications, such as AI-powered skill coaching and human-to-robot imitation learning." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Prior work has tackled procedural step localization by leveraging either (a) fully-annotated datasets where the task" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.864, + 0.468, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution\n1A test server is accessible at https://eval.ai/web/challenges/challenge-page/2082." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15201" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "shown in the video is given (video-level labeling) and manually annotated temporal segments are provided for each step (segment-level labeling) [59] or (b) weakly-annotated training sets where the task and the order in which the steps appear in the video is given [79]. However, due to the inherent manual cost involved in collecting step annotations, these works have relied on datasets that are small-scale both in the number of tasks (e.g., at most few hundreds [79]) and in the number of video samples (e.g., 12k videos [59]). These limitations affect both the generality and the complexity of the models that can be trained on these benchmarks. In this paper, we therefore pose the following question: can we leverage large-scale, unlabeled video datasets to train a model that can ground procedural steps in how-to videos?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.473, + 0.822 + ], + "angle": 0, + "content": "To answer this question, we propose a novel training framework for weakly-supervised step grounding that utilizes two freely available sources of information: (a) instructional articles which define ordered lists of steps for a wide variety of tasks (e.g., from wikiHow) and (b) narrations which provide instance-specific rich commentaries of the execution of the task in the video, e.g., from ASR transcriptions. Our work treats the former as an abstraction of the latter and uses the video-specific narrations to support the grounding of the article steps. Specifically, during training, our method leverages narrations as an auxiliary signal to (i) identify the task shown in the video, (ii) temporally ground the article steps that are visually-demonstrated and (iii) filter out steps that are not executed in the given instance. To further motivate this mechanism, let us look at the example in Figure 1. The narrations help disambiguate the task (make a pumpkin puree), enabling the automatic retrieval of relevant instructional articles for the video. Furthermore, the narrations can be matched to steps described in the articles to roughly localize the steps that are represented in the video. In this example, the timestamp of \"First thing you'll need to do is cut off the stem\" provides a loose temporal prior for the matching step \"Cut the pumpkins.\" On the other hand, steps that do not have any matching narrations (e.g., \"Wash the pumpkins\") are unlikely to be represented in the video and thus can be rejected. Based on this intuition, we propose a procedure that learns to align steps to video by fusing information from two pathways. The first is an indirect pathway inferring step-frame alignments by composing step-to-narration assignments with narration-to-frame correspondences. The second is a direct pathway that learns associations between step descriptions and frames by leveraging information from all videos having steps in common." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In our experiments we demonstrate that our multimodality alignment leads to significant performance gains over several baselines, including single-pathway temporal grounding, as well adaptations of prior works to our problem. During inference, the direct pathway can be used by" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "itself to temporally ground steps in absence of transcribed narrations. When narrations are available at test time, our method improves further the accuracy of temporal grounding by fusing the inference outputs of the two pathways." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.895, + 0.304 + ], + "angle": 0, + "content": "To summarize, our work makes the following contributions: 1) we learn to align steps to frames in how-to videos, using only weak supervision in the form of noisy ASR narrations and instructional articles; 2) we propose a novel approach for joint dense temporal grounding of instructional steps and video narrations; 3) we introduce a new benchmark for evaluating instructional step grounding which we will make available to the community; 4) we demonstrate state-of-the-art results on multiple benchmarks for both step as well as narration grounding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.317, + 0.642, + 0.332 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.895, + 0.719 + ], + "angle": 0, + "content": "Procedural step recognition. Going beyond classifying a trimmed segment video to a procedural step [9, 32, 41, 76], there has been active research in untrimmed video segmentation [10, 59, 72, 77], step anticipation [40, 47, 48], unsupervised step discovery [18, 19], procedure planning [6, 12, 74] and step description [68, 72]. In this work we focus on parsing untrimmed procedural videos into a sequence of step segments. Prior approaches can be categorized into two groups: action localization-based methods [3, 29, 50, 59] use fixed taxonomies of step classes and are not able to recognize unseen steps, while grounding-based methods [2, 5, 21], including ours, operate in an open-world setting, treating the problem as video-text alignment. Grounding-based approaches can be further subdivided into single step grounding, where single steps are queried over the whole video[27, 57] and dense temporal grounding methods [14, 22] where the objective is to jointly ground a sequence of steps or whole article into the video. Chen et al. [14] use video-level instructional step labels for (weak) supervision of a model that grounds instructional articles to videos. Their approach attempts to localize steps without using any narration information during training. Instead, we argue that narrations provide a much richer source of supervision for training step grounding models, while essentially coming for free." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Weakly-supervised approaches Existing methods also vary by the level of supervision used during training. One option is leveraging fully-annotated datasets with known temporal segments for each step [10, 26, 29, 50, 53, 60, 71, 80]. Other works use weakly-annotated training sets where the task and the order in which the steps appear in the video are known [7, 8, 11, 16, 20, 28, 45, 79], or only the task and potential steps are known [44], or only loose association between video and instructional articles is given [14, 17]. More related to our work are approaches that are trained using weak supervision coming for free from instructional video narrations [1, 20, 36, 49, 75]. Narrations" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15202" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "and their timestamps have been used to discover procedural steps in videos and then align them with visual clusters [1, 51], to obtain temporal constraints for the location of steps in videos [20, 79], and to roughly localized steps by leveraging their textual similarity with ASR narrations [36]. In this work we utilize narrations, and in particular the estimated video-narration alignment, via multi-task learning and complementary inference pathways [73] for training a step grounding model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.529 + ], + "angle": 0, + "content": "Instructional articles have been recently used for learning strong video representations [32, 40] by replacing noisy ASR narrations with steps mined from instructional articles using their semantic similarity. Although we also associate steps from wikiHow articles to video frames through the use of narrations, our work differs from prior work in several aspects: we align steps to video by a global procedure that takes into account all ordered steps in the article (inspired by dense temporal grounding methods [5]) and temporally grounds them in the whole video, instead of matching individual video clips to an orderless collection of steps; our step grounding uses video in addition to steps and narrations while the method proposed in Lin et al. [32] relies purely on text-matching narrations to step descriptions; finally, the works differ in objectives with our aim being step grounding in long how-to videos rather than learning video-clip representations. In summary, our model is trained by combining supervision signals from video narrations and instructional articles, and can be applied for aligning procedural steps to videos with and without narrations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.473, + 0.833 + ], + "angle": 0, + "content": "Video-Text alignment The availability of large-scale video-text datasets such as HowTo100M has prompted many works on joint video-language embedding training [10, 24, 32, 33, 37, 46, 52, 70]. A form of contrastive loss is often adopted for bringing together the representations of the two modalities [4, 34, 35, 37, 42, 43, 66, 69], while masked objectives are also gaining popularity [15, 23, 31, 35, 56, 57, 58, 61, 78]. Some works perform end-to-end representation learning [37, 38], while others freeze representation and focus on longer-term temporal modelling, which aims to capture context [66]. Recently Han et al. investigated directly aligning contextualized narration representations to video frames [22]. We build our method off of this approach – we note however that our objective is complementary: rather than aligning a video's narrations as an end-goal, we use this functionality to ground a set of independent steps sourced from instructional articles; in that process we show that the synergy that develops while training jointly on the two tasks results in improved performance for both." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.383, + 0.864 + ], + "angle": 0, + "content": "3. Narration-Aided Step Grounding" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We first present our architecture for joint narration and step grounding (Sec. 3.2), followed by learning objectives" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "(Sec. 3.3.1) and pseudo-labeling strategy (Sec. 3.3.3); we discuss inferring the video task in (Section 3.3.2)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.13, + 0.704, + 0.145 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Let \\((\\mathcal{V},\\mathcal{N})\\) be a video-narration pair, consisting of \\(T\\) video frames and a sequence of \\(N\\) narrations. Also, let \\(S\\) be an ordered list of \\(S\\) steps from an instructional article for a candidate task \\(\\tau\\). Our objective is to ground each step of \\(S\\) to the video, conditioned on the other steps and the ASR transcript2. In particular, the desired output of our model is an alignment matrix \\(Y^{SV} \\in \\{0,1\\}^{S \\times T}\\), where \\(Y_{st} = 1\\) only if frame \\(t\\) is depicting the \\(s\\)-th step of task \\(\\tau\\), and zero otherwise. Note that some steps might not be represented in the video." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.313, + 0.868, + 0.33 + ], + "angle": 0, + "content": "3.2. Joint Narration and Article Step Grounder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.894, + 0.382 + ], + "angle": 0, + "content": "As shown in Figure 2, our proposed VINA model follows the popular paradigm of leveraging Transformers for modeling multimodal interactions [62, 67]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.895, + 0.596 + ], + "angle": 0, + "content": "Unimodal Encoders. Before feeding the video, narrations and article steps to our model, we preprocess them to extract a sequence of tokens. Given a video-narration pair \\((\\mathcal{V}, \\mathcal{N})\\) we extract visual features, \\(X^v \\in \\mathbb{R}^{T \\times D_v}\\) and narration features \\(X^n \\in \\mathbb{R}^{N \\times D_n}\\) using standard backbone networks (e.g., a frozen S3D [65] network for visual features, and pooled Word2Vec [39] embeddings for narration features). Similarly, we encode the sequence of steps in a sequence of features \\(X^s \\in \\mathbb{R}^{S \\times D_s}\\). The features of each modality \\(m\\) are embedded into a common embedding space of dimensionality \\(D\\) using a Unimodal Encoder that consists of a modality-specific MLP network, and then learnable, modality-specific positional embeddings \\(P^m\\) are added to them:" + }, + { + "type": "equation", + "bbox": [ + 0.589, + 0.606, + 0.892, + 0.623 + ], + "angle": 0, + "content": "\\[\nH ^ {m} = M L P \\left(X ^ {m}; \\theta_ {m}\\right) + P ^ {m}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.632, + 0.783, + 0.648 + ], + "angle": 0, + "content": "where \\(m\\in \\{v,n,s\\}\\) denotes the modality." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.65, + 0.894, + 0.726 + ], + "angle": 0, + "content": "Multimodal Encoder. The outputs of the Unimodal Encoders are concatenated into a sequence of tokens: \\( H = [H^v; H^n; H^s] \\in \\mathbb{R}^{(T + N + S) \\times D} \\) and fed to the Multimodal Encoder, which is a standard Transformer with multiple layers of multi-head self-attention:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.734, + 0.892, + 0.753 + ], + "angle": 0, + "content": "\\[\nZ = \\operatorname {T r a n s f o r m e r} (H) \\in \\mathbb {R} ^ {(T + N + S) \\times D}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.761, + 0.894, + 0.868 + ], + "angle": 0, + "content": "The contextualized embeddings \\( Z = [Z^v; Z^n; Z^s] \\) computed by the Multimodal Encoder capture interactions within each modality (e.g., temporal relationships within the video and context among steps of an article) and across modalities. We can then compute cosine similarity matrices between all pairs of modalities: narrations-to-video \\( A^{NV} \\in \\mathbb{R}^{N \\times T} \\), steps-to-video \\( A^{SV} \\in \\mathbb{R}^{S \\times T} \\)," + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(^{2}\\)ASR transcripts are assumed to be always available for training and optionally during inference." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15203" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.089, + 0.812, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.355, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Figure 2: (left) Schematic illustration of our system. First, it extracts representations for each modality (video, ASR narrations, task steps) with three Unimodal Encoders. These representations are fed to a Transformer-based Multimodal Encoder for capturing interactions among video frames as well as among the textual modalities and the video. The contextualized embeddings for video frames, narrations and steps are used to compute correspondences between all pairs of modalities. Step grounding is achieved by fusing the output of two pathways: a direct pathway aligning steps to video \\((A^{SV})\\) and an indirect pathway that composes steps-to-narration \\((A^{SN})\\) with narration-to-video \\((A^{NV})\\) alignments to produce a second step-to-video alignment \\((A^{SNV})\\). We train our model using a teacher-student strategy with iteratively refined and filtered step pseudo-labels. (right) Qualitative examples of our learned steps-to-video alignment and steps-to-narrations alignment matrices for a video snippet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.469, + 0.594 + ], + "angle": 0, + "content": "and steps-to-narrations \\(A^{SN} \\in \\mathbb{R}^{S \\times N}\\). For example, the narrations-to-video similarity matrix \\(A^{NV}\\) is obtained by simply computing the cosine similarity between each frame embedding and each narration embedding: \\(A_{nt}^{NV} = \\mathbf{z}_n^{n\\top}\\mathbf{z}_t^v / (||\\mathbf{z}_n^n||||\\mathbf{z}_t^v||)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.469, + 0.809 + ], + "angle": 0, + "content": "Narration-aided Step Grounding. A straightforward inference path for temporally grounding the steps in the video is directly through the \\(A^{SV}\\) similarity matrix, which captures the similarity of each video frame with each instructional step. However, this alignment does not explicitly take into account the narrations of the video (only implicitly, through the Multimodal Transformer). We observe that an alternative way to ground steps in a video is to first identify narrations in the ASR transcript that are relevant to the step and then exploit the similarity of those narrations with video frames to get a loose prior over the step location. This is computed by combining the information captured in the steps-to-narrations and narrations-to-video alignment matrices \\(A^{SN}\\) and \\(A^{NV}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.82, + 0.469, + 0.838 + ], + "angle": 0, + "content": "\\[\nA ^ {S N V} = \\tilde {A} ^ {S N} A ^ {N V} \\in \\mathbb {R} ^ {S \\times T}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.849, + 0.469, + 0.904 + ], + "angle": 0, + "content": "where \\(\\tilde{A}^{SN}\\) is the predicted steps-to-narrations alignment matrix \\(A^{SN}\\) after being normalized with a softmax function with temperature \\(\\xi\\): \\(\\tilde{A}_{sn}^{SN} = \\frac{\\exp(A_{sn} / \\xi)}{\\sum_{j=1}^{N}\\exp(A_{sj} / \\xi)}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.517, + 0.892, + 0.701 + ], + "angle": 0, + "content": "The resulting \\( A^{SV} \\) and \\( A^{SNV} \\) alignment matrices provide two complementary inference paths to align steps to video frames. The mutual agreement between the direct steps-to-video alignment provided by \\( A^{SV} \\) and indirect, narration-based steps-to-video alignment provided by \\( A^{SNV} \\) can be used to better ground steps. Intuitively, if a frame is both very similar to a step in the joint embedding space learned by the Multimodal Transformer, and also very similar to a narration that is relevant to the step, then it is more likely to be indeed relevant to the step. Hence, we fuse the \\( A^{SV} \\) and \\( A^{SNV} \\) alignment matrices to a matrix \\( A^{F} = (A^{SV} + A^{SNV}) / 2 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.75, + 0.89, + 0.781 + ], + "angle": 0, + "content": "3.3. Weakly-Supervised Training from Narrated Instructional Videos" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.803, + 0.892, + 0.91 + ], + "angle": 0, + "content": "Next, we discuss how to supervise the VINA model in order to learn steps-to-video alignment and narrations-to-video alignment. We first present the training objective assuming that the ground-truth temporal segments for each narration and step in the video are given. Then we describe our approach for obtaining automatic pseudo-labels for the temporal segments." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15204" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.092, + 0.317, + 0.108 + ], + "angle": 0, + "content": "3.3.1 Learning on Labeled Data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.118, + 0.47, + 0.196 + ], + "angle": 0, + "content": "Let \\(\\mathcal{B} = \\{\\mathcal{V}_i, \\mathcal{N}_i, \\mathcal{S}_i, Y_i^{NV}, Y_i^{SV}\\}_{i=1}^B\\) denote a set of training tuples, each comprising a video-narration pair, an ordered list of relevant task steps, and the target video-narrations and video-steps alignment matrices, we train the VINA model by optimising the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.212, + 0.469, + 0.268 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\frac {1}{B} \\left[ \\sum_ {i = 1} ^ {B} \\lambda_ {N V} \\mathcal {H} \\left(Y _ {i} ^ {N V}, A _ {i} ^ {N V}\\right) + \\lambda_ {S V} \\mathcal {H} \\left(Y _ {i} ^ {S V}, A _ {i} ^ {S V}\\right) \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.47, + 0.332 + ], + "angle": 0, + "content": "where \\(\\mathcal{H}(\\cdot, \\cdot)\\) is the modified InfoNCE loss used by [22] for aligning video with text using noisy ground-truth temporal segments:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.347, + 0.47, + 0.389 + ], + "angle": 0, + "content": "\\[\n\\mathcal {H} (Y, A) = - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\log \\frac {\\sum_ {t} Y _ {t , k} \\exp \\left(A _ {t , k} / \\eta\\right)}{\\sum_ {t} \\exp \\left(A _ {t , k} / \\eta\\right)}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.471, + 0.526 + ], + "angle": 0, + "content": "where \\(\\eta\\) is a temperature constant. Note that although we do not explicitly supervise the steps-narrations alignment \\(A^{SN}\\), meaningful alignments emerge during training due to the joint grounding of narrations and steps to the same video samples, as seen in Figure 2. Note that although we do not directly supervise the steps-to-narrations alignment, our model is able to learn meaningful correspondences, which go beyond simple pairwise textual matching." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.556, + 0.328, + 0.57 + ], + "angle": 0, + "content": "3.3.2 Pairing Videos with Articles" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.473, + 0.902 + ], + "angle": 0, + "content": "We assume access to a set of instructional articles \\(\\mathcal{A} = \\{\\mathcal{S}_j, \\tau_j\\}_{j=1}^W\\), where \\(\\tau_j\\) denotes the article title and \\(\\mathcal{S}_j\\) the associated set of steps. To assign a set of steps to a given video from our training set \\(\\mathcal{B}\\) we need to associate it with an article from \\(\\mathcal{A}\\). If our video dataset provides metadata (e.g., a task id for every video), then this can be used to obtain the association – although there is no guarantee that this will result in the best article-match for the video (see discussion in supplementary materials for more analysis). If such metadata is not available, we can predict a task id, using the similarity between the narration and the titles of the available articles. To that end we use an off-the-shelf language model (e.g. MPNet [55]) to compute semantic embeddings of the ASR captions of every video and the title of each article \\(\\tau_j \\in \\mathcal{W}\\). For every video \\(\\mathcal{V}_i\\) we then calculate the semantic similarity between all the \\(N\\) captions in \\(\\mathcal{N}_i\\) and all task titles \\(\\tau_j \\in \\mathcal{W}\\), and assign \\(N\\) votes; the vote of every caption goes to the task that best matches it. Finally the video is assigned the task with the most votes. Alternatively, in order to obtain multiple sets of steps for a video, we rank the tasks by the number of votes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.795, + 0.108 + ], + "angle": 0, + "content": "3.3.3 Narration-Aided Pseudo-Labeling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.373 + ], + "angle": 0, + "content": "Once a task \\(\\tau_{j}\\) has been associated with a video, we have access to a list of steps \\(S_{j}\\) from the article of the task. However, whether these steps appear in the video and their temporal location remain unknown. Inspired by self-labeling approaches from the SSL literature [30, 54, 64], we follow a teacher-student approach where a teacher version of our models generates pseudo-labeled temporal segments for training the student. For every step represented by a row in the learned steps-to-video alignment matrix we obtain a pseudo-ground truth segment by finding the maximal activation (peak) and expanding a temporal segment on both sides until the activation falls below an adaptive threshold \\(\\zeta\\) (e.g., \\(70\\%\\) of the peak). To avoid training with unreliable pseudo-labels, we filter out pseudo-labels with low confidence: if the peak activation is below a fixed threshold \\(\\gamma\\), the alignment of that step is treated as unreliable for pseudo-labeling, and is altogether ignored." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.895, + 0.527 + ], + "angle": 0, + "content": "Training curriculum. For the first \\( E_{b} \\) epochs we perform burn-in training of the student model on fixed pseudo-labels generated by feeding the video and the list of steps \\( S_{j} \\) to TAN [22], an off-the-shelf model pre-trained on the task of video-text alignment. Afterwards, we switch to using pseudo-labels generated from the teacher, where the teacher is initialized by duplicating the burn-in student model and then updated every \\( \\nu \\) epochs. During both stages, we utilize the original ASR timestamps for supervising the video-to-narrations alignment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.54, + 0.634, + 0.557 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.565, + 0.698, + 0.58 + ], + "angle": 0, + "content": "4.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.894, + 0.725 + ], + "angle": 0, + "content": "We train our models on narrated videos from the HowTo100M dataset by leveraging the dataset release of wikiHow instructional articles [25], without using any form of manual annotations. In order to evaluate the effectiveness of our method, we evaluate: step grounding on HT-Step (a new benchmark, described below), narration alignment on HTM-Align [22], and zero-shot step localization on CrossTask [79]. A statistics summary of all the datasets used for training and evaluation is provided in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.894, + 0.819 + ], + "angle": 0, + "content": "HowTo100M (Training). The HowTo100M dataset [38] contains instructional videos from YouTube. Following Han et al. [22], we use the Food & Entertainment subset containing approximately \\(370K\\) videos, where each video is complemented by the \"sentencified\" ASR transcription of its audio narration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.821, + 0.892, + 0.868 + ], + "angle": 0, + "content": "wikiHow (Training). We train using 14,541 cooking tasks from the wikiHow-Dataset [25]. For each task, we generate an ordered list of steps by extracting the step headlines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.87, + 0.892, + 0.902 + ], + "angle": 0, + "content": "CrossTask (Evaluation). We use this established instructional video benchmark for zero-shot grounding, i.e., by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15205" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.477, + 0.196 + ], + "angle": 0, + "content": "
DatasetStep Annot.# Videos# Activities# Steps# Segments
HowTo100M [38]X1.2M25k--
HTM-Align [22]X8080--
CrossTask [79]✓4.8k (2.8k)83 (18)13320.9k
HT-Step (val)✓6001201,2043,441
HT-Step (test)✓6001201,2423,631
wikiHow-14k100k-
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.206, + 0.471, + 0.252 + ], + "angle": 0, + "content": "Table 1: Summary statistics for the datasets in our work. For CrossTask, the statistics for primary activities only are shown in parentheses." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.287, + 0.473, + 0.591 + ], + "angle": 0, + "content": "directly evaluating on CrossTask our model learned from HowTo100M. Following common practices, we use two evaluation protocols: the first one - step localization - aims at predicting a single timestamp for each occurring step in videos from 18 primary tasks [79]. Performance is evaluated by computing the recall (denoted as Avg. R@1) of the most confident prediction for each task and averaging the results over all query steps in a video, where R@1 measures whether the predicted timestamp for a step falls within the ground truth boundaries. We report average results over 20 random sets of 1850 videos [79]. The second task - article grounding - requires predicting temporal segments for each step of an instructional article describing the task represented in the video. We use the mapping between CrossTask and simplified wikiHow article steps provided in Chen et al. [14] and report results on 2407 videos of 15 primary tasks obtained excluding three primary tasks following the protocol of [14] (see supplementary materials for details). Performance for this task is measured with Recall@ \\( K \\) at different IoU thresholds [14]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.47, + 0.693 + ], + "angle": 0, + "content": "HTM-Align (Evaluation). This benchmark is used to evaluate our model on narration grounding. It contains 80 videos where the ASR transcriptions have been manually aligned temporally with the video. We report the R@1 metric [22], which evaluates whether the model can correctly localize the narrations that are alignable with the video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.903 + ], + "angle": 0, + "content": "HT-Step (Evaluation). To evaluate the effectiveness of our model in grounding article steps, we introduce an evaluation benchmark consisting of 1200 HowTo100M narrated videos spanning a total of 216 unique tasks, with each video manually annotated with temporal segments for each occurring step. For each video, annotators were provided with the task name (e.g., Make Pumpkin Puree) and candidate recipe steps from the corresponding wikiHow article. We refer the reader to supplementary materials for details about the data annotation. We split the annotated videos into a validation and a test set, each containing 600 videos, with 5 videos per task. We ensure that our validation set does not contain videos from HTM-Align." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.719, + 0.108 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.113, + 0.895, + 0.418 + ], + "angle": 0, + "content": "As video encoder we adopt the S3D [65] backbone pretrained with the MIL-NCE objective on HowTo100M [37]. Following previous work [22, 66], we keep this module frozen and use it to extract clip-level features (one feature per second for video decoded at 16 fps). For extracting context-aware features for each sentence (step or narration), we follow the Bag-of-word (BoW) approach based on Word2Vec embeddings [39]. Our methods hyperparameters were selected on the HT-Step validation set and are: \\(\\lambda_{SV} = \\lambda_{NV} = 1\\), temperatures \\(\\eta, \\xi = 0.07\\), and threshold \\(\\gamma = 0.65\\). We train our model for 12 epochs, with 3 epochs burn-in and then we update the teacher every 3 epochs. Pseudo-labels are obtained based on the steps-to-video alignment matrix. To obtain temporal segment detections from the step-to-video alignment output of our model (e.g. for evaluating on the CrossTask article grounding setting) we use a simple 1D blob detector [63]. Unless otherwise specified, we use the fused alignment matrix for step grounding when narrations are available during inference time. More details are included in supplementary materials." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.428, + 0.911, + 0.54 + ], + "angle": 0, + "content": "
MethodTrain.Inp.HT-Step ↑R@1HTM-Align ↑R@1
w/o nar.w/ nar.
CLIP (ViT-B/32) [43]---23.4
MIL-NCE [37]N30.7-34.2
TAN (Joint+Dual, S2) [22]N--49.4
TAN* (Joint, S1, LC) [22]N31.2-47.1
TAN* (Joint, S1, PE+LC) [22]N7.9-63.0
OursN+S35.6 ± 0.437.4 ± 0.466.5 ± 0.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.548, + 0.895, + 0.747 + ], + "angle": 0, + "content": "Table 2: Comparison with state-of-the-art methods for step and narration grounding. We report results on the HT-Step and HTM-Align test sets, respectively. TAN* refers to our improved baselines of [22]. S1 and S2 refer to the training stages followed in [22]. PE denotes the addition of positional encoding to the output of the narration encoder. LC denotes long context, i.e., our improved TAN* baseline using 1024 seconds of context as opposed to 64 for TAN. Previous best results are shown underlined. Our VINA results are reported after 5 random runs. VINA clearly outperforms all previous work – as well as our improved TAN baselines – by large margins on both narration alignment and step grounding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.593, + 0.785 + ], + "angle": 0, + "content": "4.3. Results" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.794, + 0.813, + 0.809 + ], + "angle": 0, + "content": "4.3.1 Comparison with the State of the Art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Weakly-Supervised Narration and Step Grounding. Table 2 compares the step and narration grounding performance of our method with recent state-of-the-art video-text alignment methods trained on HowTo100M using ASR narrations: MIL-NCE [37] and TAN [22]. When using them for narration alignment, we feed them with ASR as input." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15206" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.424 + ], + "angle": 0, + "content": "But we also evaluate them as strong baselines for zero-shot step grounding by feeding them with the sequence of steps as input. Our model achieves \\(66.5\\%\\) R@1 on narration alignment on HTM-Align, leading to an absolute improvement of \\(17.1\\%\\) over the previously reported state-of-the-art \\((49.4\\%)\\). Notably, on HTM-Align our method surpasses TAN* (Joint, S1, PE, LC) which is a new version of TAN [22] implemented by us and much stronger in video-narration alignment. Our re-implementation uses positional encodings for ASR narrations, is trained on long-form videos (up to 17 minutes) only with original ASR timestamps, while TAN was trained on 1 min video-clips with refined narration timestamps and used a fusion of two models during inference (Joint+Dual). Our method also outperforms all baselines for step grounding on HT-Step even when seeing only steps during inference, while being trained with (video, narrations, steps) triplets. It also outperforms TAN* (Joint, S1, LC), which is a second re-implementation of TAN designed for maximum performance on the task of step grounding. Additionally, VINA is able to use ASR transcripts of videos during test time, if available, to further boost the performance." + }, + { + "type": "table", + "bbox": [ + 0.162, + 0.452, + 0.387, + 0.649 + ], + "angle": 0, + "content": "
Method↑Avg. R@ 1 (%)
Supervised
TempCLR [70]52.5
Zero-Shot
Zhukov [79]22.4
HT100M [38]33.6
VideoCLIP [66]33.9
MCN [13]35.1
DWSA [51]35.3
MIL-NCE [37]40.5
VT-TWINS* [24]40.7
UniVL [33]42.0
Ours w/o nar.44.1
Ours w/ nar.44.8
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.472, + 0.827 + ], + "angle": 0, + "content": "Table 3: Comparison with state-of-the-art methods for zero-shot action step localization on the CrossTask dataset. The performance of the state-of-the-art fully-supervised method (TempCLR [70]) is reported as an upper-bound to the zero-shot approaches. * denotes results reported on different test splits, and hence not directly comparable with the rest. Our model outperforms all previous works by a clear margin (2.1% absolute improvement over the previous best result on the standard split). When providing narrations as additional inputs during inference (only text, not the timings), we obtain a further 0.7% boost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Step localization on CrossTask. In Table 3 we compare our model against the state-of-the-art in step localization on the CrossTask benchmark. Our approach sets a new state-of-the-art for zero-shot step localization on this challenging" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "benchmark. Importantly, most approaches are evaluated on this dataset by feeding their predicted steps-to-frames alignment matrix to a dynamic programming algorithm which finds the optimal assignment of each step with exactly one short clip assuming a canonical, fixed ordering of steps for each task. In contrast, our method, which is naturally aware of context and ordering by densely grounding steps, can outperform prior results without imposing any constraints during inference." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.242, + 0.89, + 0.343 + ], + "angle": 0, + "content": "
Model↑R@50(IOU)↑R@100(IOU)
0.10.30.50.10.30.5
MIL-NCE-max [37]33.512.04.939.714.35.9
MIL-NCE-avg [37]42.924.312.956.832.117.0
WSAG [14]40.123.110.154.331.314.0
Ours87.159.030.090.661.130.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.357, + 0.892, + 0.389 + ], + "angle": 0, + "content": "Table 4: Comparison with state-of-the-art approaches for article grounding on the CrossTask dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Article grounding on CrossTask. VINA is robust to the type of language in which task steps are described. It can handle both atomic phrases (as demonstrated by our results on step localization on CrossTask), but also rich, natural language step descriptions, as evidenced by performance on HT-Step. To further demonstrate this, we compare against the state-of-the-art on the article grounding task of CrossTask in Table 4. Our model outperforms all previous works by a large margin. We emphasize the performance improvement we obtain compared to WSAG, which highlights the importance of exploiting the narration information for training." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.609, + 0.671, + 0.624 + ], + "angle": 0, + "content": "4.3.2 Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.892, + 0.697 + ], + "angle": 0, + "content": "We perform ablations to assess the impact of the various design choices in our method by measuring step grounding performance on the HT-Step validation set and video-narration alignment performance on HTM-Align." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Effect of weak supervision from instructional articles. Row 3 in Table 5 shows the step grounding results obtained from an instance of our model that includes only the direct video-step alignment pathway and that is trained just on wikiHow steps (without narrations) using the fixed step pseudo-labels from TAN* [22] without any form of iterative pseudo-labeling (row 1). Remarkably, this variant improves by \\(3.3\\%\\) over the step-grounding performance of TAN*. When we let this variant update the step pseudo-labels (row 4), the recall improves further (\\(5.1\\%\\) over TAN*). These results provide evidence of the strong benefits of utilizing instructional articles for the learning of step grounding." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15207" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.482, + 0.256 + ], + "angle": 0, + "content": "
MethodTrain.Inp.Iter.Pseudo.HT-Step ↑R@1HTM-Align
w/o nar.w/ nar.
Baseline/Initial Step Pseudo-labels
(1) TAN Joint S1N30.7-47.1
Single-Task Training
(2) OursN--63.2
(3) OursS34.0--
(4) OursS✓35.8--
Multi-Task Training
(5) OursN+S34.336.164.8
(6) OursN+S✓36.939.167.0
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.47, + 0.417 + ], + "angle": 0, + "content": "Table 5: Ablation of main components of our framework. We study the contribution of (a) multi-task training for narration and step grounding, (b) iterative step pseudo-labeling (Iter. Pseudo), and (c) narration-aware step grounding \\((w / n a r)\\). We report results on the HT-Step val set for STG and HTM-Align for NG. We compare training only with narrations (N), only with wikiHow steps (S), and training with narrations-steps sequence pairs \\((\\mathrm{N} + \\mathrm{S})\\). We also compare the performance with and without providing narrations during inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.47, + 0.587 + ], + "angle": 0, + "content": "Effect of multimodal training and inference. Training our model with multi-modal textual inputs (steps and narrations), we observe an improvement of \\(1.6\\%\\) in narration grounding (row 5 of Table 5) compared to its single-task counterpart (row 2). However the gain in step grounding is marginal when seeing only video frames during inference (\\(w/o\\) nar, \\(34\\%\\) in row 3 vs \\(34.3\\%\\) in row 5). Our conjecture is that the missing modality (narrations) leads to some drop in performance. Providing both steps and narrations during inference leads to a stronger step grounding performance, which surpasses the TAN* baseline by \\(5.4\\%\\) (\\(30.7 \\rightarrow 36.1\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.47, + 0.686 + ], + "angle": 0, + "content": "Effect of iterative pseudo-labeling. By comparing row 5 to row 6 of Table 5 we observe a clear boost in performance on both step grounding and narration alignment. This is a clear indication of the gains produced by iteratively refining the pseudo-labels using our model as a teacher during training." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.698, + 0.472, + 0.786 + ], + "angle": 0, + "content": "
AlignmentS → VS → NN → VHT-Step ↑R@1
S → Vlearned--34.3
S → N → V-learnedlearned30.5
S → N → V-learnedASR27.9
S → N → V-MPNet [55]ASR19.0
Fusedlearnedlearnedlearned36.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.797, + 0.47, + 0.844 + ], + "angle": 0, + "content": "Table 6: Impact of the alignment matrix used during inference with narrations. The same model is used for all results (corresponding to row 5 in Table 5)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Impact of pathways during inference. In Table 6 we study the effects of using different pathways and alignment information during inference. All results are produced" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.091, + 0.852, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.238, + 0.892, + 0.314 + ], + "angle": 0, + "content": "Figure 3: Step grounding performance and minimum retained step ratio as a function of the filtering threshold. Aggressive unreliable pseudo-label filtering with high confidence thresholds (large maximum step discard ratio) leads to improved performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.614 + ], + "angle": 0, + "content": "from the same model trained for joint narration and step grounding with fixed pseudo-labels from TAN (row 5 in Table 5). Grounding steps using the indirect steps-to-video alignment only lags by \\(3.8\\%\\) behind the direct steps-to-video alignment that directly computes the similarity between steps and video frames \\((30.5\\%)\\) vs \\(34.3\\%\\). Their fusion outperforms their individual grounding performance. This suggests that they capture complementary information. We also explore substituting our learned steps-to-narrations alignment with an alignment computed with an off-the-shelf language model. This significantly degrades performance (19.0) showing that our joint steps and narrations grounding model learns relationships between steps and narrations that go beyond textual similarity between pairs of sentences. Similarly, substituting our learned narrations-to-video alignment with an alignment based on the original ASR timestamps reduces performance by \\(2.6\\%\\) (see additional details in supplementary materials)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.892, + 0.817 + ], + "angle": 0, + "content": "Impact of pseudo-label filtering threshold. In Figure 3 we study the effect of the filtering threshold used in the iterative pseudo-labeling stage. We can observe that using aggressive filtering (i.e., high thresholds translating to a high maximum percentage of pseudo-labels that are discarded) is key to observing gains from iterative pseudo-labeling compared to training with fixed pseudo-labels from TAN. Intuitively, a large percentage of steps described in wikiHow articles are not represented in the given instructional video due to task mismatch, variations in recipe execution, and some steps being optional. Therefore, starting with a small subset of reliable pseudo-labels can facilitate step grounding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Task selection. In Table 7 we investigate different strategies to select the wikiHow articles during training. This selection determines the set of steps to be grounded. We evaluate two strategies for video-task association from narratives and compare them with using the task id provided in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15208" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.098, + 0.511, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.121, + 0.748, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.313, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Figure 4: Visualization of sample frames per step, ground-truth segments (colored bars) and a single predicted timestamp per step (dashed lines) for the groundable steps of three HT-step validation videos demonstrating (a) a Mini-Stromboli recipe, (b) a Make Tabouli recipe, and (c) a Bake a Sweet Potato Pie recipe. Best viewed in color." + }, + { + "type": "table", + "bbox": [ + 0.155, + 0.381, + 0.394, + 0.448 + ], + "angle": 0, + "content": "
Task ID selectionHT-Step ↑R@1
HT100M metadata34.3
Top-1 prediction34.7
Random / top-5 pred34.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.457, + 0.473, + 0.565 + ], + "angle": 0, + "content": "Table 7: Sensitivity to task id selection. We assess how the performance of our method changes when using different strategies to associate videos with articles. We experiment with using the task ids available from HT100M, as well as the two predictive strategies presented in Section 3.3.2. We conclude that our method is robust to the task selection, and the task labels are not necessary for training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.472, + 0.625 + ], + "angle": 0, + "content": "the HowTo100M metadata for each video3. We see that our automatic selection approaches yield results on par with or even slightly better than those based on metadata." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.642, + 0.265, + 0.658 + ], + "angle": 0, + "content": "4.3.3 Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.666, + 0.47, + 0.803 + ], + "angle": 0, + "content": "Qualitative grounding results obtained with the proposed VINA model are presented in Figure 4. These examples showcase that our model can successfully retrieve complex and fine-grained steps, such as combining multiple ingredients in a mixing bowl or tapping a filled pie pan for the Bake a Sweet Potato Pie recipe. Failure cases include discriminating between steps that involve the same ingredients, such as mixing the milk and eggs versus adding the mixture to the existing mix." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.81, + 0.196, + 0.826 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.836, + 0.47, + 0.867 + ], + "angle": 0, + "content": "We have presented a method for learning how to temporally ground sequences of steps in instructional videos," + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.471, + 0.903 + ], + "angle": 0, + "content": "3During inference, metadata task ids are used in all of our HowTo100M experiments in order to evaluate against the ground-truth step annotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.893, + 0.506 + ], + "angle": 0, + "content": "without any manual supervision. Our proposed method exploits the weak supervision naturally provided in such videos through their narrations, and solves for joint alignment of narrations and steps, while fusing two complementary pathways for step-to-video alignment. We demonstrated strong quantitative performance, surpassing the state-of-the-art on multiple benchmarks for both narration and step grounding." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.508, + 0.892, + 0.539 + ], + "angle": 0, + "content": "Acknowledgements. We thank Huiyu Wang, Yale Song, Mandy Toh, and Tengda Han for helpful discussions." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.55, + 0.597, + 0.566 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.575, + 0.895, + 0.644 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Piotr Bojanowski, Nishant Agrawal, Josef Sivic, Ivan Laptev, and Simon Lacoste-Julien. Unsupervised learning from narrated instruction videos. 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To deal with the scarcity of labeled data at scale, we source the step descriptions from a language knowledge base (wikiHow) containing instructional articles for a large variety of procedural tasks. Without any form of manual supervision, our model learns to temporally ground the steps of procedural articles in how-to videos by matching three modalities: frames, narrations, and step descriptions. Specifically, our method aligns steps to video by fusing information from two distinct pathways: i) direct alignment of step descriptions to frames, ii) indirect alignment obtained by composing steps-to-narrations with narrations-to-video correspondences. Notably, our approach performs global temporal grounding of all steps in an article at once by exploiting order information, and is trained with step pseudo-labels which are iteratively refined and aggressively filtered. In order to validate our model we introduce a new benchmark - HT-Step - obtained by manually annotating a 124-hour subset of HowTo100M1 with steps sourced from wikiHow articles. Experiments on this benchmark as well as zero-shot evaluations on CrossTask demonstrate that our multi-modality alignment yields dramatic gains over several baselines and prior works. Finally, we show that our inner module for matching narration-to-video outperforms by a large margin the state of the art on the HTM-Align narration-video alignment benchmark. + +# 1. Introduction + +Instructional videos have emerged as a popular means for people to learn new skills and improve their abilities in executing complex procedural activities, such as cooking a recipe, performing home improvements, or fixing things. In addition to being useful teaching materials for humans, how-to videos are a promising medium for learning by ma + +![](images/4431a922b1eca13386407057d143a3cc1255f4166af6c28f0b619ab8d371d2a8.jpg) +Figure 1: Our proposed Video, Instructions, and Narrations Aligner (VINA) learns to simultaneously ground narrations and instruction steps in how-to videos from an uncurated set of narrated videos and a separate knowledge base of instructional articles, without any manual annotations. This is contrary to prior work that learns how to align a video with a single sequence of sentences by leveraging ground-truth pairs of video-text sequences, e.g., a video and its narrations [22], or a video and an annotated, ordered list of steps demonstrated in it [16]. + +chines, as they provide revealing visual demonstrations of complex activities and show elaborate human-object interactions in a variety of domains. Motivated by this observation, in this work we look at the task of temporally localizing the steps of procedural activities in instructional videos. This problem is foundational to the broader goal of human-procedure understanding and advances on this task promise to enable breakthrough applications, such as AI-powered skill coaching and human-to-robot imitation learning. + +Prior work has tackled procedural step localization by leveraging either (a) fully-annotated datasets where the task + +shown in the video is given (video-level labeling) and manually annotated temporal segments are provided for each step (segment-level labeling) [59] or (b) weakly-annotated training sets where the task and the order in which the steps appear in the video is given [79]. However, due to the inherent manual cost involved in collecting step annotations, these works have relied on datasets that are small-scale both in the number of tasks (e.g., at most few hundreds [79]) and in the number of video samples (e.g., 12k videos [59]). These limitations affect both the generality and the complexity of the models that can be trained on these benchmarks. In this paper, we therefore pose the following question: can we leverage large-scale, unlabeled video datasets to train a model that can ground procedural steps in how-to videos? + +To answer this question, we propose a novel training framework for weakly-supervised step grounding that utilizes two freely available sources of information: (a) instructional articles which define ordered lists of steps for a wide variety of tasks (e.g., from wikiHow) and (b) narrations which provide instance-specific rich commentaries of the execution of the task in the video, e.g., from ASR transcriptions. Our work treats the former as an abstraction of the latter and uses the video-specific narrations to support the grounding of the article steps. Specifically, during training, our method leverages narrations as an auxiliary signal to (i) identify the task shown in the video, (ii) temporally ground the article steps that are visually-demonstrated and (iii) filter out steps that are not executed in the given instance. To further motivate this mechanism, let us look at the example in Figure 1. The narrations help disambiguate the task (make a pumpkin puree), enabling the automatic retrieval of relevant instructional articles for the video. Furthermore, the narrations can be matched to steps described in the articles to roughly localize the steps that are represented in the video. In this example, the timestamp of "First thing you'll need to do is cut off the stem" provides a loose temporal prior for the matching step "Cut the pumpkins." On the other hand, steps that do not have any matching narrations (e.g., "Wash the pumpkins") are unlikely to be represented in the video and thus can be rejected. Based on this intuition, we propose a procedure that learns to align steps to video by fusing information from two pathways. The first is an indirect pathway inferring step-frame alignments by composing step-to-narration assignments with narration-to-frame correspondences. The second is a direct pathway that learns associations between step descriptions and frames by leveraging information from all videos having steps in common. + +In our experiments we demonstrate that our multimodality alignment leads to significant performance gains over several baselines, including single-pathway temporal grounding, as well adaptations of prior works to our problem. During inference, the direct pathway can be used by + +itself to temporally ground steps in absence of transcribed narrations. When narrations are available at test time, our method improves further the accuracy of temporal grounding by fusing the inference outputs of the two pathways. + +To summarize, our work makes the following contributions: 1) we learn to align steps to frames in how-to videos, using only weak supervision in the form of noisy ASR narrations and instructional articles; 2) we propose a novel approach for joint dense temporal grounding of instructional steps and video narrations; 3) we introduce a new benchmark for evaluating instructional step grounding which we will make available to the community; 4) we demonstrate state-of-the-art results on multiple benchmarks for both step as well as narration grounding. + +# 2. Related Work + +Procedural step recognition. Going beyond classifying a trimmed segment video to a procedural step [9, 32, 41, 76], there has been active research in untrimmed video segmentation [10, 59, 72, 77], step anticipation [40, 47, 48], unsupervised step discovery [18, 19], procedure planning [6, 12, 74] and step description [68, 72]. In this work we focus on parsing untrimmed procedural videos into a sequence of step segments. Prior approaches can be categorized into two groups: action localization-based methods [3, 29, 50, 59] use fixed taxonomies of step classes and are not able to recognize unseen steps, while grounding-based methods [2, 5, 21], including ours, operate in an open-world setting, treating the problem as video-text alignment. Grounding-based approaches can be further subdivided into single step grounding, where single steps are queried over the whole video[27, 57] and dense temporal grounding methods [14, 22] where the objective is to jointly ground a sequence of steps or whole article into the video. Chen et al. [14] use video-level instructional step labels for (weak) supervision of a model that grounds instructional articles to videos. Their approach attempts to localize steps without using any narration information during training. Instead, we argue that narrations provide a much richer source of supervision for training step grounding models, while essentially coming for free. + +Weakly-supervised approaches Existing methods also vary by the level of supervision used during training. One option is leveraging fully-annotated datasets with known temporal segments for each step [10, 26, 29, 50, 53, 60, 71, 80]. Other works use weakly-annotated training sets where the task and the order in which the steps appear in the video are known [7, 8, 11, 16, 20, 28, 45, 79], or only the task and potential steps are known [44], or only loose association between video and instructional articles is given [14, 17]. More related to our work are approaches that are trained using weak supervision coming for free from instructional video narrations [1, 20, 36, 49, 75]. Narrations + +and their timestamps have been used to discover procedural steps in videos and then align them with visual clusters [1, 51], to obtain temporal constraints for the location of steps in videos [20, 79], and to roughly localized steps by leveraging their textual similarity with ASR narrations [36]. In this work we utilize narrations, and in particular the estimated video-narration alignment, via multi-task learning and complementary inference pathways [73] for training a step grounding model. + +Instructional articles have been recently used for learning strong video representations [32, 40] by replacing noisy ASR narrations with steps mined from instructional articles using their semantic similarity. Although we also associate steps from wikiHow articles to video frames through the use of narrations, our work differs from prior work in several aspects: we align steps to video by a global procedure that takes into account all ordered steps in the article (inspired by dense temporal grounding methods [5]) and temporally grounds them in the whole video, instead of matching individual video clips to an orderless collection of steps; our step grounding uses video in addition to steps and narrations while the method proposed in Lin et al. [32] relies purely on text-matching narrations to step descriptions; finally, the works differ in objectives with our aim being step grounding in long how-to videos rather than learning video-clip representations. In summary, our model is trained by combining supervision signals from video narrations and instructional articles, and can be applied for aligning procedural steps to videos with and without narrations. + +Video-Text alignment The availability of large-scale video-text datasets such as HowTo100M has prompted many works on joint video-language embedding training [10, 24, 32, 33, 37, 46, 52, 70]. A form of contrastive loss is often adopted for bringing together the representations of the two modalities [4, 34, 35, 37, 42, 43, 66, 69], while masked objectives are also gaining popularity [15, 23, 31, 35, 56, 57, 58, 61, 78]. Some works perform end-to-end representation learning [37, 38], while others freeze representation and focus on longer-term temporal modelling, which aims to capture context [66]. Recently Han et al. investigated directly aligning contextualized narration representations to video frames [22]. We build our method off of this approach – we note however that our objective is complementary: rather than aligning a video's narrations as an end-goal, we use this functionality to ground a set of independent steps sourced from instructional articles; in that process we show that the synergy that develops while training jointly on the two tasks results in improved performance for both. + +# 3. Narration-Aided Step Grounding + +We first present our architecture for joint narration and step grounding (Sec. 3.2), followed by learning objectives + +(Sec. 3.3.1) and pseudo-labeling strategy (Sec. 3.3.3); we discuss inferring the video task in (Section 3.3.2). + +# 3.1. Problem Formulation + +Let $(\mathcal{V},\mathcal{N})$ be a video-narration pair, consisting of $T$ video frames and a sequence of $N$ narrations. Also, let $S$ be an ordered list of $S$ steps from an instructional article for a candidate task $\tau$ . Our objective is to ground each step of $S$ to the video, conditioned on the other steps and the ASR transcript2. In particular, the desired output of our model is an alignment matrix $Y^{SV} \in \{0,1\}^{S \times T}$ , where $Y_{st} = 1$ only if frame $t$ is depicting the $s$ -th step of task $\tau$ , and zero otherwise. Note that some steps might not be represented in the video. + +# 3.2. Joint Narration and Article Step Grounder + +As shown in Figure 2, our proposed VINA model follows the popular paradigm of leveraging Transformers for modeling multimodal interactions [62, 67]. + +Unimodal Encoders. Before feeding the video, narrations and article steps to our model, we preprocess them to extract a sequence of tokens. Given a video-narration pair $(\mathcal{V}, \mathcal{N})$ we extract visual features, $X^v \in \mathbb{R}^{T \times D_v}$ and narration features $X^n \in \mathbb{R}^{N \times D_n}$ using standard backbone networks (e.g., a frozen S3D [65] network for visual features, and pooled Word2Vec [39] embeddings for narration features). Similarly, we encode the sequence of steps in a sequence of features $X^s \in \mathbb{R}^{S \times D_s}$ . The features of each modality $m$ are embedded into a common embedding space of dimensionality $D$ using a Unimodal Encoder that consists of a modality-specific MLP network, and then learnable, modality-specific positional embeddings $P^m$ are added to them: + +$$ +H ^ {m} = M L P \left(X ^ {m}; \theta_ {m}\right) + P ^ {m}, \tag {1} +$$ + +where $m\in \{v,n,s\}$ denotes the modality. + +Multimodal Encoder. The outputs of the Unimodal Encoders are concatenated into a sequence of tokens: $H = [H^v; H^n; H^s] \in \mathbb{R}^{(T + N + S) \times D}$ and fed to the Multimodal Encoder, which is a standard Transformer with multiple layers of multi-head self-attention: + +$$ +Z = \operatorname {T r a n s f o r m e r} (H) \in \mathbb {R} ^ {(T + N + S) \times D}. \tag {2} +$$ + +The contextualized embeddings $Z = [Z^v; Z^n; Z^s]$ computed by the Multimodal Encoder capture interactions within each modality (e.g., temporal relationships within the video and context among steps of an article) and across modalities. We can then compute cosine similarity matrices between all pairs of modalities: narrations-to-video $A^{NV} \in \mathbb{R}^{N \times T}$ , steps-to-video $A^{SV} \in \mathbb{R}^{S \times T}$ , + +![](images/4348eaf538f96c16d5e3b00ab4000ebb9c79479df70e2032a5991b68b31ba595.jpg) +Figure 2: (left) Schematic illustration of our system. First, it extracts representations for each modality (video, ASR narrations, task steps) with three Unimodal Encoders. These representations are fed to a Transformer-based Multimodal Encoder for capturing interactions among video frames as well as among the textual modalities and the video. The contextualized embeddings for video frames, narrations and steps are used to compute correspondences between all pairs of modalities. Step grounding is achieved by fusing the output of two pathways: a direct pathway aligning steps to video $(A^{SV})$ and an indirect pathway that composes steps-to-narration $(A^{SN})$ with narration-to-video $(A^{NV})$ alignments to produce a second step-to-video alignment $(A^{SNV})$ . We train our model using a teacher-student strategy with iteratively refined and filtered step pseudo-labels. (right) Qualitative examples of our learned steps-to-video alignment and steps-to-narrations alignment matrices for a video snippet. + +and steps-to-narrations $A^{SN} \in \mathbb{R}^{S \times N}$ . For example, the narrations-to-video similarity matrix $A^{NV}$ is obtained by simply computing the cosine similarity between each frame embedding and each narration embedding: $A_{nt}^{NV} = \mathbf{z}_n^{n\top}\mathbf{z}_t^v / (||\mathbf{z}_n^n||||\mathbf{z}_t^v||)$ . + +Narration-aided Step Grounding. A straightforward inference path for temporally grounding the steps in the video is directly through the $A^{SV}$ similarity matrix, which captures the similarity of each video frame with each instructional step. However, this alignment does not explicitly take into account the narrations of the video (only implicitly, through the Multimodal Transformer). We observe that an alternative way to ground steps in a video is to first identify narrations in the ASR transcript that are relevant to the step and then exploit the similarity of those narrations with video frames to get a loose prior over the step location. This is computed by combining the information captured in the steps-to-narrations and narrations-to-video alignment matrices $A^{SN}$ and $A^{NV}$ : + +$$ +A ^ {S N V} = \tilde {A} ^ {S N} A ^ {N V} \in \mathbb {R} ^ {S \times T}, \tag {3} +$$ + +where $\tilde{A}^{SN}$ is the predicted steps-to-narrations alignment matrix $A^{SN}$ after being normalized with a softmax function with temperature $\xi$ : $\tilde{A}_{sn}^{SN} = \frac{\exp(A_{sn} / \xi)}{\sum_{j=1}^{N}\exp(A_{sj} / \xi)}$ . + +The resulting $A^{SV}$ and $A^{SNV}$ alignment matrices provide two complementary inference paths to align steps to video frames. The mutual agreement between the direct steps-to-video alignment provided by $A^{SV}$ and indirect, narration-based steps-to-video alignment provided by $A^{SNV}$ can be used to better ground steps. Intuitively, if a frame is both very similar to a step in the joint embedding space learned by the Multimodal Transformer, and also very similar to a narration that is relevant to the step, then it is more likely to be indeed relevant to the step. Hence, we fuse the $A^{SV}$ and $A^{SNV}$ alignment matrices to a matrix $A^{F} = (A^{SV} + A^{SNV}) / 2$ . + +# 3.3. Weakly-Supervised Training from Narrated Instructional Videos + +Next, we discuss how to supervise the VINA model in order to learn steps-to-video alignment and narrations-to-video alignment. We first present the training objective assuming that the ground-truth temporal segments for each narration and step in the video are given. Then we describe our approach for obtaining automatic pseudo-labels for the temporal segments. + +# 3.3.1 Learning on Labeled Data + +Let $\mathcal{B} = \{\mathcal{V}_i, \mathcal{N}_i, \mathcal{S}_i, Y_i^{NV}, Y_i^{SV}\}_{i=1}^B$ denote a set of training tuples, each comprising a video-narration pair, an ordered list of relevant task steps, and the target video-narrations and video-steps alignment matrices, we train the VINA model by optimising the following objective: + +$$ +\mathcal {L} = \frac {1}{B} \left[ \sum_ {i = 1} ^ {B} \lambda_ {N V} \mathcal {H} \left(Y _ {i} ^ {N V}, A _ {i} ^ {N V}\right) + \lambda_ {S V} \mathcal {H} \left(Y _ {i} ^ {S V}, A _ {i} ^ {S V}\right) \right], \tag {4} +$$ + +where $\mathcal{H}(\cdot, \cdot)$ is the modified InfoNCE loss used by [22] for aligning video with text using noisy ground-truth temporal segments: + +$$ +\mathcal {H} (Y, A) = - \frac {1}{K} \sum_ {k = 1} ^ {K} \log \frac {\sum_ {t} Y _ {t , k} \exp \left(A _ {t , k} / \eta\right)}{\sum_ {t} \exp \left(A _ {t , k} / \eta\right)}, \tag {5} +$$ + +where $\eta$ is a temperature constant. Note that although we do not explicitly supervise the steps-narrations alignment $A^{SN}$ , meaningful alignments emerge during training due to the joint grounding of narrations and steps to the same video samples, as seen in Figure 2. Note that although we do not directly supervise the steps-to-narrations alignment, our model is able to learn meaningful correspondences, which go beyond simple pairwise textual matching. + +# 3.3.2 Pairing Videos with Articles + +We assume access to a set of instructional articles $\mathcal{A} = \{\mathcal{S}_j, \tau_j\}_{j=1}^W$ , where $\tau_j$ denotes the article title and $\mathcal{S}_j$ the associated set of steps. To assign a set of steps to a given video from our training set $\mathcal{B}$ we need to associate it with an article from $\mathcal{A}$ . If our video dataset provides metadata (e.g., a task id for every video), then this can be used to obtain the association – although there is no guarantee that this will result in the best article-match for the video (see discussion in supplementary materials for more analysis). If such metadata is not available, we can predict a task id, using the similarity between the narration and the titles of the available articles. To that end we use an off-the-shelf language model (e.g. MPNet [55]) to compute semantic embeddings of the ASR captions of every video and the title of each article $\tau_j \in \mathcal{W}$ . For every video $\mathcal{V}_i$ we then calculate the semantic similarity between all the $N$ captions in $\mathcal{N}_i$ and all task titles $\tau_j \in \mathcal{W}$ , and assign $N$ votes; the vote of every caption goes to the task that best matches it. Finally the video is assigned the task with the most votes. Alternatively, in order to obtain multiple sets of steps for a video, we rank the tasks by the number of votes. + +# 3.3.3 Narration-Aided Pseudo-Labeling + +Once a task $\tau_{j}$ has been associated with a video, we have access to a list of steps $S_{j}$ from the article of the task. However, whether these steps appear in the video and their temporal location remain unknown. Inspired by self-labeling approaches from the SSL literature [30, 54, 64], we follow a teacher-student approach where a teacher version of our models generates pseudo-labeled temporal segments for training the student. For every step represented by a row in the learned steps-to-video alignment matrix we obtain a pseudo-ground truth segment by finding the maximal activation (peak) and expanding a temporal segment on both sides until the activation falls below an adaptive threshold $\zeta$ (e.g., $70\%$ of the peak). To avoid training with unreliable pseudo-labels, we filter out pseudo-labels with low confidence: if the peak activation is below a fixed threshold $\gamma$ , the alignment of that step is treated as unreliable for pseudo-labeling, and is altogether ignored. + +Training curriculum. For the first $E_{b}$ epochs we perform burn-in training of the student model on fixed pseudo-labels generated by feeding the video and the list of steps $S_{j}$ to TAN [22], an off-the-shelf model pre-trained on the task of video-text alignment. Afterwards, we switch to using pseudo-labels generated from the teacher, where the teacher is initialized by duplicating the burn-in student model and then updated every $\nu$ epochs. During both stages, we utilize the original ASR timestamps for supervising the video-to-narrations alignment. + +# 4. Experiments + +# 4.1. Datasets and Metrics + +We train our models on narrated videos from the HowTo100M dataset by leveraging the dataset release of wikiHow instructional articles [25], without using any form of manual annotations. In order to evaluate the effectiveness of our method, we evaluate: step grounding on HT-Step (a new benchmark, described below), narration alignment on HTM-Align [22], and zero-shot step localization on CrossTask [79]. A statistics summary of all the datasets used for training and evaluation is provided in Table 1. + +HowTo100M (Training). The HowTo100M dataset [38] contains instructional videos from YouTube. Following Han et al. [22], we use the Food & Entertainment subset containing approximately $370K$ videos, where each video is complemented by the "sentencified" ASR transcription of its audio narration. + +wikiHow (Training). We train using 14,541 cooking tasks from the wikiHow-Dataset [25]. For each task, we generate an ordered list of steps by extracting the step headlines. + +CrossTask (Evaluation). We use this established instructional video benchmark for zero-shot grounding, i.e., by + +
DatasetStep Annot.# Videos# Activities# Steps# Segments
HowTo100M [38]X1.2M25k--
HTM-Align [22]X8080--
CrossTask [79]✓4.8k (2.8k)83 (18)13320.9k
HT-Step (val)✓6001201,2043,441
HT-Step (test)✓6001201,2423,631
wikiHow-14k100k-
+ +directly evaluating on CrossTask our model learned from HowTo100M. Following common practices, we use two evaluation protocols: the first one - step localization - aims at predicting a single timestamp for each occurring step in videos from 18 primary tasks [79]. Performance is evaluated by computing the recall (denoted as Avg. R@1) of the most confident prediction for each task and averaging the results over all query steps in a video, where R@1 measures whether the predicted timestamp for a step falls within the ground truth boundaries. We report average results over 20 random sets of 1850 videos [79]. The second task - article grounding - requires predicting temporal segments for each step of an instructional article describing the task represented in the video. We use the mapping between CrossTask and simplified wikiHow article steps provided in Chen et al. [14] and report results on 2407 videos of 15 primary tasks obtained excluding three primary tasks following the protocol of [14] (see supplementary materials for details). Performance for this task is measured with Recall@ $K$ at different IoU thresholds [14]. + +HTM-Align (Evaluation). This benchmark is used to evaluate our model on narration grounding. It contains 80 videos where the ASR transcriptions have been manually aligned temporally with the video. We report the R@1 metric [22], which evaluates whether the model can correctly localize the narrations that are alignable with the video. + +HT-Step (Evaluation). To evaluate the effectiveness of our model in grounding article steps, we introduce an evaluation benchmark consisting of 1200 HowTo100M narrated videos spanning a total of 216 unique tasks, with each video manually annotated with temporal segments for each occurring step. For each video, annotators were provided with the task name (e.g., Make Pumpkin Puree) and candidate recipe steps from the corresponding wikiHow article. We refer the reader to supplementary materials for details about the data annotation. We split the annotated videos into a validation and a test set, each containing 600 videos, with 5 videos per task. We ensure that our validation set does not contain videos from HTM-Align. + +# 4.2. Implementation Details + +As video encoder we adopt the S3D [65] backbone pretrained with the MIL-NCE objective on HowTo100M [37]. Following previous work [22, 66], we keep this module frozen and use it to extract clip-level features (one feature per second for video decoded at 16 fps). For extracting context-aware features for each sentence (step or narration), we follow the Bag-of-word (BoW) approach based on Word2Vec embeddings [39]. Our methods hyperparameters were selected on the HT-Step validation set and are: $\lambda_{SV} = \lambda_{NV} = 1$ , temperatures $\eta, \xi = 0.07$ , and threshold $\gamma = 0.65$ . We train our model for 12 epochs, with 3 epochs burn-in and then we update the teacher every 3 epochs. Pseudo-labels are obtained based on the steps-to-video alignment matrix. To obtain temporal segment detections from the step-to-video alignment output of our model (e.g. for evaluating on the CrossTask article grounding setting) we use a simple 1D blob detector [63]. Unless otherwise specified, we use the fused alignment matrix for step grounding when narrations are available during inference time. More details are included in supplementary materials. + +Table 1: Summary statistics for the datasets in our work. For CrossTask, the statistics for primary activities only are shown in parentheses. + +
MethodTrain.Inp.HT-Step ↑R@1HTM-Align ↑R@1
w/o nar.w/ nar.
CLIP (ViT-B/32) [43]---23.4
MIL-NCE [37]N30.7-34.2
TAN (Joint+Dual, S2) [22]N--49.4
TAN* (Joint, S1, LC) [22]N31.2-47.1
TAN* (Joint, S1, PE+LC) [22]N7.9-63.0
OursN+S35.6 ± 0.437.4 ± 0.466.5 ± 0.9
+ +Table 2: Comparison with state-of-the-art methods for step and narration grounding. We report results on the HT-Step and HTM-Align test sets, respectively. TAN* refers to our improved baselines of [22]. S1 and S2 refer to the training stages followed in [22]. PE denotes the addition of positional encoding to the output of the narration encoder. LC denotes long context, i.e., our improved TAN* baseline using 1024 seconds of context as opposed to 64 for TAN. Previous best results are shown underlined. Our VINA results are reported after 5 random runs. VINA clearly outperforms all previous work – as well as our improved TAN baselines – by large margins on both narration alignment and step grounding. + +# 4.3. Results + +# 4.3.1 Comparison with the State of the Art + +Weakly-Supervised Narration and Step Grounding. Table 2 compares the step and narration grounding performance of our method with recent state-of-the-art video-text alignment methods trained on HowTo100M using ASR narrations: MIL-NCE [37] and TAN [22]. When using them for narration alignment, we feed them with ASR as input. + +But we also evaluate them as strong baselines for zero-shot step grounding by feeding them with the sequence of steps as input. Our model achieves $66.5\%$ R@1 on narration alignment on HTM-Align, leading to an absolute improvement of $17.1\%$ over the previously reported state-of-the-art $(49.4\%)$ . Notably, on HTM-Align our method surpasses TAN* (Joint, S1, PE, LC) which is a new version of TAN [22] implemented by us and much stronger in video-narration alignment. Our re-implementation uses positional encodings for ASR narrations, is trained on long-form videos (up to 17 minutes) only with original ASR timestamps, while TAN was trained on 1 min video-clips with refined narration timestamps and used a fusion of two models during inference (Joint+Dual). Our method also outperforms all baselines for step grounding on HT-Step even when seeing only steps during inference, while being trained with (video, narrations, steps) triplets. It also outperforms TAN* (Joint, S1, LC), which is a second re-implementation of TAN designed for maximum performance on the task of step grounding. Additionally, VINA is able to use ASR transcripts of videos during test time, if available, to further boost the performance. + +
Method↑Avg. R@ 1 (%)
Supervised
TempCLR [70]52.5
Zero-Shot
Zhukov [79]22.4
HT100M [38]33.6
VideoCLIP [66]33.9
MCN [13]35.1
DWSA [51]35.3
MIL-NCE [37]40.5
VT-TWINS* [24]40.7
UniVL [33]42.0
Ours w/o nar.44.1
Ours w/ nar.44.8
+ +Table 3: Comparison with state-of-the-art methods for zero-shot action step localization on the CrossTask dataset. The performance of the state-of-the-art fully-supervised method (TempCLR [70]) is reported as an upper-bound to the zero-shot approaches. * denotes results reported on different test splits, and hence not directly comparable with the rest. Our model outperforms all previous works by a clear margin (2.1% absolute improvement over the previous best result on the standard split). When providing narrations as additional inputs during inference (only text, not the timings), we obtain a further 0.7% boost. + +Step localization on CrossTask. In Table 3 we compare our model against the state-of-the-art in step localization on the CrossTask benchmark. Our approach sets a new state-of-the-art for zero-shot step localization on this challenging + +benchmark. Importantly, most approaches are evaluated on this dataset by feeding their predicted steps-to-frames alignment matrix to a dynamic programming algorithm which finds the optimal assignment of each step with exactly one short clip assuming a canonical, fixed ordering of steps for each task. In contrast, our method, which is naturally aware of context and ordering by densely grounding steps, can outperform prior results without imposing any constraints during inference. + +
Model↑R@50(IOU)↑R@100(IOU)
0.10.30.50.10.30.5
MIL-NCE-max [37]33.512.04.939.714.35.9
MIL-NCE-avg [37]42.924.312.956.832.117.0
WSAG [14]40.123.110.154.331.314.0
Ours87.159.030.090.661.130.9
+ +Table 4: Comparison with state-of-the-art approaches for article grounding on the CrossTask dataset. + +Article grounding on CrossTask. VINA is robust to the type of language in which task steps are described. It can handle both atomic phrases (as demonstrated by our results on step localization on CrossTask), but also rich, natural language step descriptions, as evidenced by performance on HT-Step. To further demonstrate this, we compare against the state-of-the-art on the article grounding task of CrossTask in Table 4. Our model outperforms all previous works by a large margin. We emphasize the performance improvement we obtain compared to WSAG, which highlights the importance of exploiting the narration information for training. + +# 4.3.2 Ablation Studies + +We perform ablations to assess the impact of the various design choices in our method by measuring step grounding performance on the HT-Step validation set and video-narration alignment performance on HTM-Align. + +Effect of weak supervision from instructional articles. Row 3 in Table 5 shows the step grounding results obtained from an instance of our model that includes only the direct video-step alignment pathway and that is trained just on wikiHow steps (without narrations) using the fixed step pseudo-labels from TAN* [22] without any form of iterative pseudo-labeling (row 1). Remarkably, this variant improves by $3.3\%$ over the step-grounding performance of TAN*. When we let this variant update the step pseudo-labels (row 4), the recall improves further ( $5.1\%$ over TAN*). These results provide evidence of the strong benefits of utilizing instructional articles for the learning of step grounding. + +
MethodTrain.Inp.Iter.Pseudo.HT-Step ↑R@1HTM-Align
w/o nar.w/ nar.
Baseline/Initial Step Pseudo-labels
(1) TAN Joint S1N30.7-47.1
Single-Task Training
(2) OursN--63.2
(3) OursS34.0--
(4) OursS✓35.8--
Multi-Task Training
(5) OursN+S34.336.164.8
(6) OursN+S✓36.939.167.0
+ +Table 5: Ablation of main components of our framework. We study the contribution of (a) multi-task training for narration and step grounding, (b) iterative step pseudo-labeling (Iter. Pseudo), and (c) narration-aware step grounding $(w / n a r)$ . We report results on the HT-Step val set for STG and HTM-Align for NG. We compare training only with narrations (N), only with wikiHow steps (S), and training with narrations-steps sequence pairs $(\mathrm{N} + \mathrm{S})$ . We also compare the performance with and without providing narrations during inference. + +Effect of multimodal training and inference. Training our model with multi-modal textual inputs (steps and narrations), we observe an improvement of $1.6\%$ in narration grounding (row 5 of Table 5) compared to its single-task counterpart (row 2). However the gain in step grounding is marginal when seeing only video frames during inference ( $w/o$ nar, $34\%$ in row 3 vs $34.3\%$ in row 5). Our conjecture is that the missing modality (narrations) leads to some drop in performance. Providing both steps and narrations during inference leads to a stronger step grounding performance, which surpasses the TAN* baseline by $5.4\%$ ( $30.7 \rightarrow 36.1$ ). + +Effect of iterative pseudo-labeling. By comparing row 5 to row 6 of Table 5 we observe a clear boost in performance on both step grounding and narration alignment. This is a clear indication of the gains produced by iteratively refining the pseudo-labels using our model as a teacher during training. + +
AlignmentS → VS → NN → VHT-Step ↑R@1
S → Vlearned--34.3
S → N → V-learnedlearned30.5
S → N → V-learnedASR27.9
S → N → V-MPNet [55]ASR19.0
Fusedlearnedlearnedlearned36.1
+ +Table 6: Impact of the alignment matrix used during inference with narrations. The same model is used for all results (corresponding to row 5 in Table 5). + +Impact of pathways during inference. In Table 6 we study the effects of using different pathways and alignment information during inference. All results are produced + +![](images/84f8776646ffa6760f84144db1fb7fc5f3849df770f3b3aa09166832dc4d3d1e.jpg) +Figure 3: Step grounding performance and minimum retained step ratio as a function of the filtering threshold. Aggressive unreliable pseudo-label filtering with high confidence thresholds (large maximum step discard ratio) leads to improved performance. + +from the same model trained for joint narration and step grounding with fixed pseudo-labels from TAN (row 5 in Table 5). Grounding steps using the indirect steps-to-video alignment only lags by $3.8\%$ behind the direct steps-to-video alignment that directly computes the similarity between steps and video frames $(30.5\%)$ vs $34.3\%$ . Their fusion outperforms their individual grounding performance. This suggests that they capture complementary information. We also explore substituting our learned steps-to-narrations alignment with an alignment computed with an off-the-shelf language model. This significantly degrades performance (19.0) showing that our joint steps and narrations grounding model learns relationships between steps and narrations that go beyond textual similarity between pairs of sentences. Similarly, substituting our learned narrations-to-video alignment with an alignment based on the original ASR timestamps reduces performance by $2.6\%$ (see additional details in supplementary materials). + +Impact of pseudo-label filtering threshold. In Figure 3 we study the effect of the filtering threshold used in the iterative pseudo-labeling stage. We can observe that using aggressive filtering (i.e., high thresholds translating to a high maximum percentage of pseudo-labels that are discarded) is key to observing gains from iterative pseudo-labeling compared to training with fixed pseudo-labels from TAN. Intuitively, a large percentage of steps described in wikiHow articles are not represented in the given instructional video due to task mismatch, variations in recipe execution, and some steps being optional. Therefore, starting with a small subset of reliable pseudo-labels can facilitate step grounding. + +Task selection. In Table 7 we investigate different strategies to select the wikiHow articles during training. This selection determines the set of steps to be grounded. We evaluate two strategies for video-task association from narratives and compare them with using the task id provided in + +![](images/bbb2d0a7df83b63b4f8e76734e4c7d648fd79782ffb66b68c73b3fdcbf1a110f.jpg) +Figure 4: Visualization of sample frames per step, ground-truth segments (colored bars) and a single predicted timestamp per step (dashed lines) for the groundable steps of three HT-step validation videos demonstrating (a) a Mini-Stromboli recipe, (b) a Make Tabouli recipe, and (c) a Bake a Sweet Potato Pie recipe. Best viewed in color. + +![](images/c3bbc8296be48e918ebe5ce17fa97fae7d2ccc0f7111655366e659fbc730a026.jpg) + +
Task ID selectionHT-Step ↑R@1
HT100M metadata34.3
Top-1 prediction34.7
Random / top-5 pred34.3
+ +Table 7: Sensitivity to task id selection. We assess how the performance of our method changes when using different strategies to associate videos with articles. We experiment with using the task ids available from HT100M, as well as the two predictive strategies presented in Section 3.3.2. We conclude that our method is robust to the task selection, and the task labels are not necessary for training. + +the HowTo100M metadata for each video3. We see that our automatic selection approaches yield results on par with or even slightly better than those based on metadata. + +# 4.3.3 Qualitative Results + +Qualitative grounding results obtained with the proposed VINA model are presented in Figure 4. These examples showcase that our model can successfully retrieve complex and fine-grained steps, such as combining multiple ingredients in a mixing bowl or tapping a filled pie pan for the Bake a Sweet Potato Pie recipe. Failure cases include discriminating between steps that involve the same ingredients, such as mixing the milk and eggs versus adding the mixture to the existing mix. + +# 5. Conclusion + +We have presented a method for learning how to temporally ground sequences of steps in instructional videos, + +without any manual supervision. Our proposed method exploits the weak supervision naturally provided in such videos through their narrations, and solves for joint alignment of narrations and steps, while fusing two complementary pathways for step-to-video alignment. We demonstrated strong quantitative performance, surpassing the state-of-the-art on multiple benchmarks for both narration and step grounding. + +Acknowledgements. We thank Huiyu Wang, Yale Song, Mandy Toh, and Tengda Han for helpful discussions. + +# References + +[1] Jean-Baptiste Alayrac, Piotr Bojanowski, Nishant Agrawal, Josef Sivic, Ivan Laptev, and Simon Lacoste-Julien. 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In International Conference on 3D Vision (3DV), 2022. 2 \ No newline at end of file diff --git a/2023/Learning to Ground Instructional Articles in Videos through Narrations/images.zip b/2023/Learning to Ground Instructional Articles in Videos through Narrations/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..015dd986cf1720d810302e38a87828187df6c273 --- /dev/null +++ b/2023/Learning to Ground Instructional Articles in Videos through Narrations/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1404bd48aef523990a14f14ebd7b9981724c2f7e3e9c916b4c4b26b0f5dc3a6a +size 426340 diff --git a/2023/Learning to Ground Instructional Articles in Videos through Narrations/layout.json b/2023/Learning to Ground Instructional Articles in Videos through Narrations/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..17e4395b399a3361edf9712ecfbe39ca53662a20 --- /dev/null +++ b/2023/Learning to Ground Instructional Articles in Videos through Narrations/layout.json @@ -0,0 +1,9256 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 74, + 103, + 520, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 103, + 520, + 121 + ], + "spans": [ + { + "bbox": [ + 74, + 103, + 520, + 121 + ], + "type": "text", + "content": "Learning to Ground Instructional Articles in Videos through Narrations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 143, + 449, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 143, + 449, + 171 + ], + "spans": [ + { + "bbox": [ + 143, + 143, + 449, + 171 + ], + "type": "text", + "content": "Effrosyni Mavroudi; Triantafyllos Afouras; Lorenzo Torresani Meta AI" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 186, + 174, + 408, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 186, + 174, + 408, + 185 + ], + "spans": [ + { + "bbox": [ + 186, + 174, + 408, + 185 + ], + "type": "text", + "content": "{emavroudi, afourast, torresani}@meta.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 238, + 290, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 238, + 290, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 238, + 290, + 562 + ], + "type": "text", + "content": "In this paper we present an approach for localizing steps of procedural activities in narrated how-to videos. To deal with the scarcity of labeled data at scale, we source the step descriptions from a language knowledge base (wikiHow) containing instructional articles for a large variety of procedural tasks. Without any form of manual supervision, our model learns to temporally ground the steps of procedural articles in how-to videos by matching three modalities: frames, narrations, and step descriptions. Specifically, our method aligns steps to video by fusing information from two distinct pathways: i) direct alignment of step descriptions to frames, ii) indirect alignment obtained by composing steps-to-narrations with narrations-to-video correspondences. Notably, our approach performs global temporal grounding of all steps in an article at once by exploiting order information, and is trained with step pseudo-labels which are iteratively refined and aggressively filtered. In order to validate our model we introduce a new benchmark - HT-Step - obtained by manually annotating a 124-hour subset of HowTo100M1 with steps sourced from wikiHow articles. Experiments on this benchmark as well as zero-shot evaluations on CrossTask demonstrate that our multi-modality alignment yields dramatic gains over several baselines and prior works. Finally, we show that our inner module for matching narration-to-video outperforms by a large margin the state of the art on the HTM-Align narration-video alignment benchmark." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 584, + 128, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 584, + 128, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 584, + 128, + 596 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 604, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 676 + ], + "type": "text", + "content": "Instructional videos have emerged as a popular means for people to learn new skills and improve their abilities in executing complex procedural activities, such as cooking a recipe, performing home improvements, or fixing things. In addition to being useful teaching materials for humans, how-to videos are a promising medium for learning by ma" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 217, + 526, + 441 + ], + "blocks": [ + { + "bbox": [ + 312, + 217, + 526, + 441 + ], + "lines": [ + { + "bbox": [ + 312, + 217, + 526, + 441 + ], + "spans": [ + { + "bbox": [ + 312, + 217, + 526, + 441 + ], + "type": "image", + "image_path": "4431a922b1eca13386407057d143a3cc1255f4166af6c28f0b619ab8d371d2a8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 451, + 547, + 571 + ], + "lines": [ + { + "bbox": [ + 304, + 451, + 547, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 547, + 571 + ], + "type": "text", + "content": "Figure 1: Our proposed Video, Instructions, and Narrations Aligner (VINA) learns to simultaneously ground narrations and instruction steps in how-to videos from an uncurated set of narrated videos and a separate knowledge base of instructional articles, without any manual annotations. This is contrary to prior work that learns how to align a video with a single sequence of sentences by leveraging ground-truth pairs of video-text sequences, e.g., a video and its narrations [22], or a video and an annotated, ordered list of steps demonstrated in it [16]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 580, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 689 + ], + "type": "text", + "content": "chines, as they provide revealing visual demonstrations of complex activities and show elaborate human-object interactions in a variety of domains. Motivated by this observation, in this work we look at the task of temporally localizing the steps of procedural activities in instructional videos. This problem is foundational to the broader goal of human-procedure understanding and advances on this task promise to enable breakthrough applications, such as AI-powered skill coaching and human-to-robot imitation learning." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "Prior work has tackled procedural step localization by leveraging either (a) fully-annotated datasets where the task" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 146, + 0, + 494, + 37 + ], + "type": "text", + "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 684, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 684, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 684, + 286, + 713 + ], + "type": "text", + "content": "*Equal contribution\n1A test server is accessible at https://eval.ai/web/challenges/challenge-page/2082." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15201" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "shown in the video is given (video-level labeling) and manually annotated temporal segments are provided for each step (segment-level labeling) [59] or (b) weakly-annotated training sets where the task and the order in which the steps appear in the video is given [79]. However, due to the inherent manual cost involved in collecting step annotations, these works have relied on datasets that are small-scale both in the number of tasks (e.g., at most few hundreds [79]) and in the number of video samples (e.g., 12k videos [59]). These limitations affect both the generality and the complexity of the models that can be trained on these benchmarks. In this paper, we therefore pose the following question: can we leverage large-scale, unlabeled video datasets to train a model that can ground procedural steps in how-to videos?" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 242, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 289, + 651 + ], + "type": "text", + "content": "To answer this question, we propose a novel training framework for weakly-supervised step grounding that utilizes two freely available sources of information: (a) instructional articles which define ordered lists of steps for a wide variety of tasks (e.g., from wikiHow) and (b) narrations which provide instance-specific rich commentaries of the execution of the task in the video, e.g., from ASR transcriptions. Our work treats the former as an abstraction of the latter and uses the video-specific narrations to support the grounding of the article steps. Specifically, during training, our method leverages narrations as an auxiliary signal to (i) identify the task shown in the video, (ii) temporally ground the article steps that are visually-demonstrated and (iii) filter out steps that are not executed in the given instance. To further motivate this mechanism, let us look at the example in Figure 1. The narrations help disambiguate the task (make a pumpkin puree), enabling the automatic retrieval of relevant instructional articles for the video. Furthermore, the narrations can be matched to steps described in the articles to roughly localize the steps that are represented in the video. In this example, the timestamp of \"First thing you'll need to do is cut off the stem\" provides a loose temporal prior for the matching step \"Cut the pumpkins.\" On the other hand, steps that do not have any matching narrations (e.g., \"Wash the pumpkins\") are unlikely to be represented in the video and thus can be rejected. Based on this intuition, we propose a procedure that learns to align steps to video by fusing information from two pathways. The first is an indirect pathway inferring step-frame alignments by composing step-to-narration assignments with narration-to-frame correspondences. The second is a direct pathway that learns associations between step descriptions and frames by leveraging information from all videos having steps in common." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "In our experiments we demonstrate that our multimodality alignment leads to significant performance gains over several baselines, including single-pathway temporal grounding, as well adaptations of prior works to our problem. During inference, the direct pathway can be used by" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "itself to temporally ground steps in absence of transcribed narrations. When narrations are available at test time, our method improves further the accuracy of temporal grounding by fusing the inference outputs of the two pathways." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": "To summarize, our work makes the following contributions: 1) we learn to align steps to frames in how-to videos, using only weak supervision in the form of noisy ASR narrations and instructional articles; 2) we propose a novel approach for joint dense temporal grounding of instructional steps and video narrations; 3) we introduce a new benchmark for evaluating instructional step grounding which we will make available to the community; 4) we demonstrate state-of-the-art results on multiple benchmarks for both step as well as narration grounding." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 270, + 547, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 547, + 569 + ], + "type": "text", + "content": "Procedural step recognition. Going beyond classifying a trimmed segment video to a procedural step [9, 32, 41, 76], there has been active research in untrimmed video segmentation [10, 59, 72, 77], step anticipation [40, 47, 48], unsupervised step discovery [18, 19], procedure planning [6, 12, 74] and step description [68, 72]. In this work we focus on parsing untrimmed procedural videos into a sequence of step segments. Prior approaches can be categorized into two groups: action localization-based methods [3, 29, 50, 59] use fixed taxonomies of step classes and are not able to recognize unseen steps, while grounding-based methods [2, 5, 21], including ours, operate in an open-world setting, treating the problem as video-text alignment. Grounding-based approaches can be further subdivided into single step grounding, where single steps are queried over the whole video[27, 57] and dense temporal grounding methods [14, 22] where the objective is to jointly ground a sequence of steps or whole article into the video. Chen et al. [14] use video-level instructional step labels for (weak) supervision of a model that grounds instructional articles to videos. Their approach attempts to localize steps without using any narration information during training. Instead, we argue that narrations provide a much richer source of supervision for training step grounding models, while essentially coming for free." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Weakly-supervised approaches Existing methods also vary by the level of supervision used during training. One option is leveraging fully-annotated datasets with known temporal segments for each step [10, 26, 29, 50, 53, 60, 71, 80]. Other works use weakly-annotated training sets where the task and the order in which the steps appear in the video are known [7, 8, 11, 16, 20, 28, 45, 79], or only the task and potential steps are known [44], or only loose association between video and instructional articles is given [14, 17]. More related to our work are approaches that are trained using weak supervision coming for free from instructional video narrations [1, 20, 36, 49, 75]. Narrations" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15202" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "and their timestamps have been used to discover procedural steps in videos and then align them with visual clusters [1, 51], to obtain temporal constraints for the location of steps in videos [20, 79], and to roughly localized steps by leveraging their textual similarity with ASR narrations [36]. In this work we utilize narrations, and in particular the estimated video-narration alignment, via multi-task learning and complementary inference pathways [73] for training a step grounding model." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 289, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 418 + ], + "type": "text", + "content": "Instructional articles have been recently used for learning strong video representations [32, 40] by replacing noisy ASR narrations with steps mined from instructional articles using their semantic similarity. Although we also associate steps from wikiHow articles to video frames through the use of narrations, our work differs from prior work in several aspects: we align steps to video by a global procedure that takes into account all ordered steps in the article (inspired by dense temporal grounding methods [5]) and temporally grounds them in the whole video, instead of matching individual video clips to an orderless collection of steps; our step grounding uses video in addition to steps and narrations while the method proposed in Lin et al. [32] relies purely on text-matching narrations to step descriptions; finally, the works differ in objectives with our aim being step grounding in long how-to videos rather than learning video-clip representations. In summary, our model is trained by combining supervision signals from video narrations and instructional articles, and can be applied for aligning procedural steps to videos with and without narrations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 419, + 289, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 289, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 289, + 659 + ], + "type": "text", + "content": "Video-Text alignment The availability of large-scale video-text datasets such as HowTo100M has prompted many works on joint video-language embedding training [10, 24, 32, 33, 37, 46, 52, 70]. A form of contrastive loss is often adopted for bringing together the representations of the two modalities [4, 34, 35, 37, 42, 43, 66, 69], while masked objectives are also gaining popularity [15, 23, 31, 35, 56, 57, 58, 61, 78]. Some works perform end-to-end representation learning [37, 38], while others freeze representation and focus on longer-term temporal modelling, which aims to capture context [66]. Recently Han et al. investigated directly aligning contextualized narration representations to video frames [22]. We build our method off of this approach – we note however that our objective is complementary: rather than aligning a video's narrations as an end-goal, we use this functionality to ground a set of independent steps sourced from instructional articles; in that process we show that the synergy that develops while training jointly on the two tasks results in improved performance for both." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 669, + 234, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 234, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 234, + 684 + ], + "type": "text", + "content": "3. Narration-Aided Step Grounding" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "We first present our architecture for joint narration and step grounding (Sec. 3.2), followed by learning objectives" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "(Sec. 3.3.1) and pseudo-labeling strategy (Sec. 3.3.3); we discuss inferring the video task in (Section 3.3.2)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 102, + 430, + 114 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 102, + 430, + 114 + ], + "spans": [ + { + "bbox": [ + 306, + 102, + 430, + 114 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "(\\mathcal{V},\\mathcal{N})" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": " be a video-narration pair, consisting of " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": " video frames and a sequence of " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": " narrations. Also, let " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": " be an ordered list of " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": " steps from an instructional article for a candidate task " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": ". Our objective is to ground each step of " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": " to the video, conditioned on the other steps and the ASR transcript2. In particular, the desired output of our model is an alignment matrix " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "Y^{SV} \\in \\{0,1\\}^{S \\times T}" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "Y_{st} = 1" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": " only if frame " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": " is depicting the " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": "-th step of task " + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 121, + 547, + 240 + ], + "type": "text", + "content": ", and zero otherwise. Note that some steps might not be represented in the video." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 247, + 531, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 247, + 531, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 531, + 261 + ], + "type": "text", + "content": "3.2. Joint Narration and Article Step Grounder" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 266, + 547, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 547, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 547, + 302 + ], + "type": "text", + "content": "As shown in Figure 2, our proposed VINA model follows the popular paradigm of leveraging Transformers for modeling multimodal interactions [62, 67]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": "Unimodal Encoders. Before feeding the video, narrations and article steps to our model, we preprocess them to extract a sequence of tokens. Given a video-narration pair " + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "inline_equation", + "content": "(\\mathcal{V}, \\mathcal{N})" + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": " we extract visual features, " + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "inline_equation", + "content": "X^v \\in \\mathbb{R}^{T \\times D_v}" + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": " and narration features " + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "inline_equation", + "content": "X^n \\in \\mathbb{R}^{N \\times D_n}" + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": " using standard backbone networks (e.g., a frozen S3D [65] network for visual features, and pooled Word2Vec [39] embeddings for narration features). Similarly, we encode the sequence of steps in a sequence of features " + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "inline_equation", + "content": "X^s \\in \\mathbb{R}^{S \\times D_s}" + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": ". The features of each modality " + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": " are embedded into a common embedding space of dimensionality " + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": " using a Unimodal Encoder that consists of a modality-specific MLP network, and then learnable, modality-specific positional embeddings " + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "inline_equation", + "content": "P^m" + }, + { + "bbox": [ + 304, + 304, + 547, + 472 + ], + "type": "text", + "content": " are added to them:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 360, + 479, + 545, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 479, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 360, + 479, + 545, + 493 + ], + "type": "interline_equation", + "content": "H ^ {m} = M L P \\left(X ^ {m}; \\theta_ {m}\\right) + P ^ {m}, \\tag {1}", + "image_path": "711d5cf33026117be711ad6cfd16fc8e6f120d0d04d70dd8d5d211caaaee0ce5.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 500, + 479, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 500, + 479, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 500, + 479, + 513 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 500, + 479, + 513 + ], + "type": "inline_equation", + "content": "m\\in \\{v,n,s\\}" + }, + { + "bbox": [ + 305, + 500, + 479, + 513 + ], + "type": "text", + "content": " denotes the modality." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 514, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 514, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 305, + 514, + 547, + 574 + ], + "type": "text", + "content": "Multimodal Encoder. The outputs of the Unimodal Encoders are concatenated into a sequence of tokens: " + }, + { + "bbox": [ + 305, + 514, + 547, + 574 + ], + "type": "inline_equation", + "content": "H = [H^v; H^n; H^s] \\in \\mathbb{R}^{(T + N + S) \\times D}" + }, + { + "bbox": [ + 305, + 514, + 547, + 574 + ], + "type": "text", + "content": " and fed to the Multimodal Encoder, which is a standard Transformer with multiple layers of multi-head self-attention:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 342, + 581, + 545, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 581, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 342, + 581, + 545, + 596 + ], + "type": "interline_equation", + "content": "Z = \\operatorname {T r a n s f o r m e r} (H) \\in \\mathbb {R} ^ {(T + N + S) \\times D}. \\tag {2}", + "image_path": "0c2dbd7b3c3dce8d24dc74574e16c38f051ed62984f1e8d6dde8b9dcfd8efa77.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "text", + "content": "The contextualized embeddings " + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "inline_equation", + "content": "Z = [Z^v; Z^n; Z^s]" + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "text", + "content": " computed by the Multimodal Encoder capture interactions within each modality (e.g., temporal relationships within the video and context among steps of an article) and across modalities. We can then compute cosine similarity matrices between all pairs of modalities: narrations-to-video " + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "inline_equation", + "content": "A^{NV} \\in \\mathbb{R}^{N \\times T}" + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "text", + "content": ", steps-to-video " + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "inline_equation", + "content": "A^{SV} \\in \\mathbb{R}^{S \\times T}" + }, + { + "bbox": [ + 304, + 602, + 547, + 687 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "ASR transcripts are assumed to be always available for training and optionally during inference." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15203" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 95, + 70, + 496, + 273 + ], + "blocks": [ + { + "bbox": [ + 95, + 70, + 496, + 273 + ], + "lines": [ + { + "bbox": [ + 95, + 70, + 496, + 273 + ], + "spans": [ + { + "bbox": [ + 95, + 70, + 496, + 273 + ], + "type": "image", + "image_path": "4348eaf538f96c16d5e3b00ab4000ebb9c79479df70e2032a5991b68b31ba595.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "lines": [ + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "text", + "content": "Figure 2: (left) Schematic illustration of our system. First, it extracts representations for each modality (video, ASR narrations, task steps) with three Unimodal Encoders. These representations are fed to a Transformer-based Multimodal Encoder for capturing interactions among video frames as well as among the textual modalities and the video. The contextualized embeddings for video frames, narrations and steps are used to compute correspondences between all pairs of modalities. Step grounding is achieved by fusing the output of two pathways: a direct pathway aligning steps to video " + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "inline_equation", + "content": "(A^{SV})" + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "text", + "content": " and an indirect pathway that composes steps-to-narration " + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "inline_equation", + "content": "(A^{SN})" + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "text", + "content": " with narration-to-video " + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "inline_equation", + "content": "(A^{NV})" + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "text", + "content": " alignments to produce a second step-to-video alignment " + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "inline_equation", + "content": "(A^{SNV})" + }, + { + "bbox": [ + 46, + 281, + 545, + 388 + ], + "type": "text", + "content": ". We train our model using a teacher-student strategy with iteratively refined and filtered step pseudo-labels. (right) Qualitative examples of our learned steps-to-video alignment and steps-to-narrations alignment matrices for a video snippet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "type": "text", + "content": "and steps-to-narrations " + }, + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "type": "inline_equation", + "content": "A^{SN} \\in \\mathbb{R}^{S \\times N}" + }, + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "type": "text", + "content": ". For example, the narrations-to-video similarity matrix " + }, + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "type": "inline_equation", + "content": "A^{NV}" + }, + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "type": "text", + "content": " is obtained by simply computing the cosine similarity between each frame embedding and each narration embedding: " + }, + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "type": "inline_equation", + "content": "A_{nt}^{NV} = \\mathbf{z}_n^{n\\top}\\mathbf{z}_t^v / (||\\mathbf{z}_n^n||||\\mathbf{z}_t^v||)" + }, + { + "bbox": [ + 46, + 409, + 287, + 470 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "type": "text", + "content": "Narration-aided Step Grounding. A straightforward inference path for temporally grounding the steps in the video is directly through the " + }, + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "type": "inline_equation", + "content": "A^{SV}" + }, + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "type": "text", + "content": " similarity matrix, which captures the similarity of each video frame with each instructional step. However, this alignment does not explicitly take into account the narrations of the video (only implicitly, through the Multimodal Transformer). We observe that an alternative way to ground steps in a video is to first identify narrations in the ASR transcript that are relevant to the step and then exploit the similarity of those narrations with video frames to get a loose prior over the step location. This is computed by combining the information captured in the steps-to-narrations and narrations-to-video alignment matrices " + }, + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "type": "inline_equation", + "content": "A^{SN}" + }, + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "type": "inline_equation", + "content": "A^{NV}" + }, + { + "bbox": [ + 46, + 470, + 287, + 640 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 649, + 287, + 663 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 649, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 104, + 649, + 287, + 663 + ], + "type": "interline_equation", + "content": "A ^ {S N V} = \\tilde {A} ^ {S N} A ^ {N V} \\in \\mathbb {R} ^ {S \\times T}, \\tag {3}", + "image_path": "4434f7a1f99114fec6742fe58fe68f769dff9e1c09c97a8733ac07755f85fb81.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{A}^{SN}" + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "text", + "content": " is the predicted steps-to-narrations alignment matrix " + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "inline_equation", + "content": "A^{SN}" + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "text", + "content": " after being normalized with a softmax function with temperature " + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{A}_{sn}^{SN} = \\frac{\\exp(A_{sn} / \\xi)}{\\sum_{j=1}^{N}\\exp(A_{sj} / \\xi)}" + }, + { + "bbox": [ + 47, + 672, + 287, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "content": "The resulting " + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "inline_equation", + "content": "A^{SV}" + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "inline_equation", + "content": "A^{SNV}" + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "content": " alignment matrices provide two complementary inference paths to align steps to video frames. The mutual agreement between the direct steps-to-video alignment provided by " + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "inline_equation", + "content": "A^{SV}" + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "content": " and indirect, narration-based steps-to-video alignment provided by " + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "inline_equation", + "content": "A^{SNV}" + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "content": " can be used to better ground steps. Intuitively, if a frame is both very similar to a step in the joint embedding space learned by the Multimodal Transformer, and also very similar to a narration that is relevant to the step, then it is more likely to be indeed relevant to the step. Hence, we fuse the " + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "inline_equation", + "content": "A^{SV}" + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "inline_equation", + "content": "A^{SNV}" + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "content": " alignment matrices to a matrix " + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "inline_equation", + "content": "A^{F} = (A^{SV} + A^{SNV}) / 2" + }, + { + "bbox": [ + 305, + 409, + 545, + 555 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 594, + 544, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 544, + 618 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 544, + 618 + ], + "type": "text", + "content": "3.3. Weakly-Supervised Training from Narrated Instructional Videos" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 635, + 545, + 720 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 635, + 545, + 720 + ], + "spans": [ + { + "bbox": [ + 304, + 635, + 545, + 720 + ], + "type": "text", + "content": "Next, we discuss how to supervise the VINA model in order to learn steps-to-video alignment and narrations-to-video alignment. We first present the training objective assuming that the ground-truth temporal segments for each narration and step in the video are given. Then we describe our approach for obtaining automatic pseudo-labels for the temporal segments." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15204" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 194, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 194, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 194, + 85 + ], + "type": "text", + "content": "3.3.1 Learning on Labeled Data" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 93, + 287, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 93, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 46, + 93, + 287, + 155 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 93, + 287, + 155 + ], + "type": "inline_equation", + "content": "\\mathcal{B} = \\{\\mathcal{V}_i, \\mathcal{N}_i, \\mathcal{S}_i, Y_i^{NV}, Y_i^{SV}\\}_{i=1}^B" + }, + { + "bbox": [ + 46, + 93, + 287, + 155 + ], + "type": "text", + "content": " denote a set of training tuples, each comprising a video-narration pair, an ordered list of relevant task steps, and the target video-narrations and video-steps alignment matrices, we train the VINA model by optimising the following objective:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 167, + 287, + 212 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 167, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 48, + 167, + 287, + 212 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\frac {1}{B} \\left[ \\sum_ {i = 1} ^ {B} \\lambda_ {N V} \\mathcal {H} \\left(Y _ {i} ^ {N V}, A _ {i} ^ {N V}\\right) + \\lambda_ {S V} \\mathcal {H} \\left(Y _ {i} ^ {S V}, A _ {i} ^ {S V}\\right) \\right], \\tag {4}", + "image_path": "7fd4e570655816cf18ad20908f64fcdc398bb361683960fea7c3c8e468999cd7.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "content": " is the modified InfoNCE loss used by [22] for aligning video with text using noisy ground-truth temporal segments:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 64, + 274, + 287, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 274, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 64, + 274, + 287, + 308 + ], + "type": "interline_equation", + "content": "\\mathcal {H} (Y, A) = - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\log \\frac {\\sum_ {t} Y _ {t , k} \\exp \\left(A _ {t , k} / \\eta\\right)}{\\sum_ {t} \\exp \\left(A _ {t , k} / \\eta\\right)}, \\tag {5}", + "image_path": "1524b31b1d5c79d75f6513f3e7c5c1112690469d321d62cbac2cec39584e9a46.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 319, + 288, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 288, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 288, + 416 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 319, + 288, + 416 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 319, + 288, + 416 + ], + "type": "text", + "content": " is a temperature constant. Note that although we do not explicitly supervise the steps-narrations alignment " + }, + { + "bbox": [ + 46, + 319, + 288, + 416 + ], + "type": "inline_equation", + "content": "A^{SN}" + }, + { + "bbox": [ + 46, + 319, + 288, + 416 + ], + "type": "text", + "content": ", meaningful alignments emerge during training due to the joint grounding of narrations and steps to the same video samples, as seen in Figure 2. Note that although we do not directly supervise the steps-to-narrations alignment, our model is able to learn meaningful correspondences, which go beyond simple pairwise textual matching." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 440, + 200, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 440, + 200, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 440, + 200, + 451 + ], + "type": "text", + "content": "3.3.2 Pairing Videos with Articles" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": "We assume access to a set of instructional articles " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{A} = \\{\\mathcal{S}_j, \\tau_j\\}_{j=1}^W" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\tau_j" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": " denotes the article title and " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_j" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": " the associated set of steps. To assign a set of steps to a given video from our training set " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": " we need to associate it with an article from " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": ". If our video dataset provides metadata (e.g., a task id for every video), then this can be used to obtain the association – although there is no guarantee that this will result in the best article-match for the video (see discussion in supplementary materials for more analysis). If such metadata is not available, we can predict a task id, using the similarity between the narration and the titles of the available articles. To that end we use an off-the-shelf language model (e.g. MPNet [55]) to compute semantic embeddings of the ASR captions of every video and the title of each article " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\tau_j \\in \\mathcal{W}" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": ". For every video " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_i" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": " we then calculate the semantic similarity between all the " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": " captions in " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": " and all task titles " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\tau_j \\in \\mathcal{W}" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": ", and assign " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": " votes; the vote of every caption goes to the task that best matches it. Finally the video is assigned the task with the most votes. Alternatively, in order to obtain multiple sets of steps for a video, we rank the tasks by the number of votes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 486, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 486, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 486, + 85 + ], + "type": "text", + "content": "3.3.3 Narration-Aided Pseudo-Labeling" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "content": "Once a task " + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\tau_{j}" + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "content": " has been associated with a video, we have access to a list of steps " + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "inline_equation", + "content": "S_{j}" + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "content": " from the article of the task. However, whether these steps appear in the video and their temporal location remain unknown. Inspired by self-labeling approaches from the SSL literature [30, 54, 64], we follow a teacher-student approach where a teacher version of our models generates pseudo-labeled temporal segments for training the student. For every step represented by a row in the learned steps-to-video alignment matrix we obtain a pseudo-ground truth segment by finding the maximal activation (peak) and expanding a temporal segment on both sides until the activation falls below an adaptive threshold " + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "content": " (e.g., " + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "content": " of the peak). To avoid training with unreliable pseudo-labels, we filter out pseudo-labels with low confidence: if the peak activation is below a fixed threshold " + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 91, + 547, + 295 + ], + "type": "text", + "content": ", the alignment of that step is treated as unreliable for pseudo-labeling, and is altogether ignored." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": "Training curriculum. For the first " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "E_{b}" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": " epochs we perform burn-in training of the student model on fixed pseudo-labels generated by feeding the video and the list of steps " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "S_{j}" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": " to TAN [22], an off-the-shelf model pre-trained on the task of video-text alignment. Afterwards, we switch to using pseudo-labels generated from the teacher, where the teacher is initialized by duplicating the burn-in student model and then updated every " + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 304, + 297, + 547, + 417 + ], + "type": "text", + "content": " epochs. During both stages, we utilize the original ASR timestamps for supervising the video-to-narrations alignment." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 427, + 388, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 427, + 388, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 427, + 388, + 441 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 447, + 427, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 447, + 427, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 447, + 427, + 459 + ], + "type": "text", + "content": "4.1. Datasets and Metrics" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 465, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 547, + 574 + ], + "type": "text", + "content": "We train our models on narrated videos from the HowTo100M dataset by leveraging the dataset release of wikiHow instructional articles [25], without using any form of manual annotations. In order to evaluate the effectiveness of our method, we evaluate: step grounding on HT-Step (a new benchmark, described below), narration alignment on HTM-Align [22], and zero-shot step localization on CrossTask [79]. A statistics summary of all the datasets used for training and evaluation is provided in Table 1." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 575, + 547, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 547, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 547, + 648 + ], + "type": "text", + "content": "HowTo100M (Training). The HowTo100M dataset [38] contains instructional videos from YouTube. Following Han et al. [22], we use the Food & Entertainment subset containing approximately " + }, + { + "bbox": [ + 304, + 575, + 547, + 648 + ], + "type": "inline_equation", + "content": "370K" + }, + { + "bbox": [ + 304, + 575, + 547, + 648 + ], + "type": "text", + "content": " videos, where each video is complemented by the \"sentencified\" ASR transcription of its audio narration." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 650, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 650, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 650, + 545, + 687 + ], + "type": "text", + "content": "wikiHow (Training). We train using 14,541 cooking tasks from the wikiHow-Dataset [25]. For each task, we generate an ordered list of steps by extracting the step headlines." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "CrossTask (Evaluation). We use this established instructional video benchmark for zero-shot grounding, i.e., by" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15205" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 291, + 155 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 291, + 155 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 291, + 155 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 291, + 155 + ], + "type": "table", + "html": "
DatasetStep Annot.# Videos# Activities# Steps# Segments
HowTo100M [38]X1.2M25k--
HTM-Align [22]X8080--
CrossTask [79]✓4.8k (2.8k)83 (18)13320.9k
HT-Step (val)✓6001201,2043,441
HT-Step (test)✓6001201,2423,631
wikiHow-14k100k-
", + "image_path": "3c9f8c217e5cc3002f6794a3a75df146691f4a4cf707228478644927543fcd66.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 227, + 289, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 227, + 289, + 468 + ], + "spans": [ + { + "bbox": [ + 45, + 227, + 289, + 468 + ], + "type": "text", + "content": "directly evaluating on CrossTask our model learned from HowTo100M. Following common practices, we use two evaluation protocols: the first one - step localization - aims at predicting a single timestamp for each occurring step in videos from 18 primary tasks [79]. Performance is evaluated by computing the recall (denoted as Avg. R@1) of the most confident prediction for each task and averaging the results over all query steps in a video, where R@1 measures whether the predicted timestamp for a step falls within the ground truth boundaries. We report average results over 20 random sets of 1850 videos [79]. The second task - article grounding - requires predicting temporal segments for each step of an instructional article describing the task represented in the video. We use the mapping between CrossTask and simplified wikiHow article steps provided in Chen et al. [14] and report results on 2407 videos of 15 primary tasks obtained excluding three primary tasks following the protocol of [14] (see supplementary materials for details). Performance for this task is measured with Recall@ " + }, + { + "bbox": [ + 45, + 227, + 289, + 468 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 227, + 289, + 468 + ], + "type": "text", + "content": " at different IoU thresholds [14]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "content": "HTM-Align (Evaluation). This benchmark is used to evaluate our model on narration grounding. It contains 80 videos where the ASR transcriptions have been manually aligned temporally with the video. We report the R@1 metric [22], which evaluates whether the model can correctly localize the narrations that are alignable with the video." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "HT-Step (Evaluation). To evaluate the effectiveness of our model in grounding article steps, we introduce an evaluation benchmark consisting of 1200 HowTo100M narrated videos spanning a total of 216 unique tasks, with each video manually annotated with temporal segments for each occurring step. For each video, annotators were provided with the task name (e.g., Make Pumpkin Puree) and candidate recipe steps from the corresponding wikiHow article. We refer the reader to supplementary materials for details about the data annotation. We split the annotated videos into a validation and a test set, each containing 600 videos, with 5 videos per task. We ensure that our validation set does not contain videos from HTM-Align." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 440, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 440, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 440, + 85 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "type": "text", + "content": "As video encoder we adopt the S3D [65] backbone pretrained with the MIL-NCE objective on HowTo100M [37]. Following previous work [22, 66], we keep this module frozen and use it to extract clip-level features (one feature per second for video decoded at 16 fps). For extracting context-aware features for each sentence (step or narration), we follow the Bag-of-word (BoW) approach based on Word2Vec embeddings [39]. Our methods hyperparameters were selected on the HT-Step validation set and are: " + }, + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\lambda_{SV} = \\lambda_{NV} = 1" + }, + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "type": "text", + "content": ", temperatures " + }, + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\eta, \\xi = 0.07" + }, + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "type": "text", + "content": ", and threshold " + }, + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\gamma = 0.65" + }, + { + "bbox": [ + 304, + 89, + 547, + 331 + ], + "type": "text", + "content": ". We train our model for 12 epochs, with 3 epochs burn-in and then we update the teacher every 3 epochs. Pseudo-labels are obtained based on the steps-to-video alignment matrix. To obtain temporal segment detections from the step-to-video alignment output of our model (e.g. for evaluating on the CrossTask article grounding setting) we use a simple 1D blob detector [63]. Unless otherwise specified, we use the fused alignment matrix for step grounding when narrations are available during inference time. More details are included in supplementary materials." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 338, + 557, + 427 + ], + "blocks": [ + { + "bbox": [ + 46, + 163, + 288, + 199 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 288, + 199 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 288, + 199 + ], + "type": "text", + "content": "Table 1: Summary statistics for the datasets in our work. For CrossTask, the statistics for primary activities only are shown in parentheses." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 338, + 557, + 427 + ], + "lines": [ + { + "bbox": [ + 306, + 338, + 557, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 338, + 557, + 427 + ], + "type": "table", + "html": "
MethodTrain.Inp.HT-Step ↑R@1HTM-Align ↑R@1
w/o nar.w/ nar.
CLIP (ViT-B/32) [43]---23.4
MIL-NCE [37]N30.7-34.2
TAN (Joint+Dual, S2) [22]N--49.4
TAN* (Joint, S1, LC) [22]N31.2-47.1
TAN* (Joint, S1, PE+LC) [22]N7.9-63.0
OursN+S35.6 ± 0.437.4 ± 0.466.5 ± 0.9
", + "image_path": "4f40f908c8e0ee1f29220affb4d192fb767d39be1c0413ab17f22fa620c51da5.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 434, + 547, + 591 + ], + "lines": [ + { + "bbox": [ + 304, + 434, + 547, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 547, + 591 + ], + "type": "text", + "content": "Table 2: Comparison with state-of-the-art methods for step and narration grounding. We report results on the HT-Step and HTM-Align test sets, respectively. TAN* refers to our improved baselines of [22]. S1 and S2 refer to the training stages followed in [22]. PE denotes the addition of positional encoding to the output of the narration encoder. LC denotes long context, i.e., our improved TAN* baseline using 1024 seconds of context as opposed to 64 for TAN. Previous best results are shown underlined. Our VINA results are reported after 5 random runs. VINA clearly outperforms all previous work – as well as our improved TAN baselines – by large margins on both narration alignment and step grounding." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 610, + 362, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 362, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 362, + 621 + ], + "type": "text", + "content": "4.3. Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 628, + 497, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 628, + 497, + 640 + ], + "spans": [ + { + "bbox": [ + 305, + 628, + 497, + 640 + ], + "type": "text", + "content": "4.3.1 Comparison with the State of the Art" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": "Weakly-Supervised Narration and Step Grounding. Table 2 compares the step and narration grounding performance of our method with recent state-of-the-art video-text alignment methods trained on HowTo100M using ASR narrations: MIL-NCE [37] and TAN [22]. When using them for narration alignment, we feed them with ASR as input." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15206" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "type": "text", + "content": "But we also evaluate them as strong baselines for zero-shot step grounding by feeding them with the sequence of steps as input. Our model achieves " + }, + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "type": "inline_equation", + "content": "66.5\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "type": "text", + "content": " R@1 on narration alignment on HTM-Align, leading to an absolute improvement of " + }, + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "type": "inline_equation", + "content": "17.1\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "type": "text", + "content": " over the previously reported state-of-the-art " + }, + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "type": "inline_equation", + "content": "(49.4\\%)" + }, + { + "bbox": [ + 46, + 72, + 289, + 335 + ], + "type": "text", + "content": ". Notably, on HTM-Align our method surpasses TAN* (Joint, S1, PE, LC) which is a new version of TAN [22] implemented by us and much stronger in video-narration alignment. Our re-implementation uses positional encodings for ASR narrations, is trained on long-form videos (up to 17 minutes) only with original ASR timestamps, while TAN was trained on 1 min video-clips with refined narration timestamps and used a fusion of two models during inference (Joint+Dual). Our method also outperforms all baselines for step grounding on HT-Step even when seeing only steps during inference, while being trained with (video, narrations, steps) triplets. It also outperforms TAN* (Joint, S1, LC), which is a second re-implementation of TAN designed for maximum performance on the task of step grounding. Additionally, VINA is able to use ASR transcripts of videos during test time, if available, to further boost the performance." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 99, + 357, + 236, + 514 + ], + "blocks": [ + { + "bbox": [ + 99, + 357, + 236, + 514 + ], + "lines": [ + { + "bbox": [ + 99, + 357, + 236, + 514 + ], + "spans": [ + { + "bbox": [ + 99, + 357, + 236, + 514 + ], + "type": "table", + "html": "
Method↑Avg. R@ 1 (%)
Supervised
TempCLR [70]52.5
Zero-Shot
Zhukov [79]22.4
HT100M [38]33.6
VideoCLIP [66]33.9
MCN [13]35.1
DWSA [51]35.3
MIL-NCE [37]40.5
VT-TWINS* [24]40.7
UniVL [33]42.0
Ours w/o nar.44.1
Ours w/ nar.44.8
", + "image_path": "e4718563f8491f1671ed0bb71a83657643d39376c5d38288a7efbddba14d0888.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 521, + 288, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 654 + ], + "type": "text", + "content": "Table 3: Comparison with state-of-the-art methods for zero-shot action step localization on the CrossTask dataset. The performance of the state-of-the-art fully-supervised method (TempCLR [70]) is reported as an upper-bound to the zero-shot approaches. * denotes results reported on different test splits, and hence not directly comparable with the rest. Our model outperforms all previous works by a clear margin (2.1% absolute improvement over the previous best result on the standard split). When providing narrations as additional inputs during inference (only text, not the timings), we obtain a further 0.7% boost." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Step localization on CrossTask. In Table 3 we compare our model against the state-of-the-art in step localization on the CrossTask benchmark. Our approach sets a new state-of-the-art for zero-shot step localization on this challenging" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "benchmark. Importantly, most approaches are evaluated on this dataset by feeding their predicted steps-to-frames alignment matrix to a dynamic programming algorithm which finds the optimal assignment of each step with exactly one short clip assuming a canonical, fixed ordering of steps for each task. In contrast, our method, which is naturally aware of context and ordering by densely grounding steps, can outperform prior results without imposing any constraints during inference." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 308, + 191, + 544, + 271 + ], + "blocks": [ + { + "bbox": [ + 308, + 191, + 544, + 271 + ], + "lines": [ + { + "bbox": [ + 308, + 191, + 544, + 271 + ], + "spans": [ + { + "bbox": [ + 308, + 191, + 544, + 271 + ], + "type": "table", + "html": "
Model↑R@50(IOU)↑R@100(IOU)
0.10.30.50.10.30.5
MIL-NCE-max [37]33.512.04.939.714.35.9
MIL-NCE-avg [37]42.924.312.956.832.117.0
WSAG [14]40.123.110.154.331.314.0
Ours87.159.030.090.661.130.9
", + "image_path": "17744c5ebd31741a7063e606bfa8a87f62590238cc3513da7070a668580a1051.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 282, + 545, + 308 + ], + "lines": [ + { + "bbox": [ + 305, + 282, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 282, + 545, + 308 + ], + "type": "text", + "content": "Table 4: Comparison with state-of-the-art approaches for article grounding on the CrossTask dataset." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 329, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 474 + ], + "type": "text", + "content": "Article grounding on CrossTask. VINA is robust to the type of language in which task steps are described. It can handle both atomic phrases (as demonstrated by our results on step localization on CrossTask), but also rich, natural language step descriptions, as evidenced by performance on HT-Step. To further demonstrate this, we compare against the state-of-the-art on the article grounding task of CrossTask in Table 4. Our model outperforms all previous works by a large margin. We emphasize the performance improvement we obtain compared to WSAG, which highlights the importance of exploiting the narration information for training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 482, + 410, + 494 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 482, + 410, + 494 + ], + "spans": [ + { + "bbox": [ + 305, + 482, + 410, + 494 + ], + "type": "text", + "content": "4.3.2 Ablation Studies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 502, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 552 + ], + "type": "text", + "content": "We perform ablations to assess the impact of the various design choices in our method by measuring step grounding performance on the HT-Step validation set and video-narration alignment performance on HTM-Align." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "text", + "content": "Effect of weak supervision from instructional articles. Row 3 in Table 5 shows the step grounding results obtained from an instance of our model that includes only the direct video-step alignment pathway and that is trained just on wikiHow steps (without narrations) using the fixed step pseudo-labels from TAN* [22] without any form of iterative pseudo-labeling (row 1). Remarkably, this variant improves by " + }, + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "text", + "content": " over the step-grounding performance of TAN*. When we let this variant update the step pseudo-labels (row 4), the recall improves further (" + }, + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "inline_equation", + "content": "5.1\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 714 + ], + "type": "text", + "content": " over TAN*). These results provide evidence of the strong benefits of utilizing instructional articles for the learning of step grounding." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15207" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 294, + 202 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 294, + 202 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 294, + 202 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 294, + 202 + ], + "type": "table", + "html": "
MethodTrain.Inp.Iter.Pseudo.HT-Step ↑R@1HTM-Align
w/o nar.w/ nar.
Baseline/Initial Step Pseudo-labels
(1) TAN Joint S1N30.7-47.1
Single-Task Training
(2) OursN--63.2
(3) OursS34.0--
(4) OursS✓35.8--
Multi-Task Training
(5) OursN+S34.336.164.8
(6) OursN+S✓36.939.167.0
", + "image_path": "d22aef2b73bbfa8b0dd5caa18e98ca05e0b071a41571806708674dac380036c4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 210, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 287, + 330 + ], + "type": "text", + "content": "Table 5: Ablation of main components of our framework. We study the contribution of (a) multi-task training for narration and step grounding, (b) iterative step pseudo-labeling (Iter. Pseudo), and (c) narration-aware step grounding " + }, + { + "bbox": [ + 46, + 210, + 287, + 330 + ], + "type": "inline_equation", + "content": "(w / n a r)" + }, + { + "bbox": [ + 46, + 210, + 287, + 330 + ], + "type": "text", + "content": ". We report results on the HT-Step val set for STG and HTM-Align for NG. We compare training only with narrations (N), only with wikiHow steps (S), and training with narrations-steps sequence pairs " + }, + { + "bbox": [ + 46, + 210, + 287, + 330 + ], + "type": "inline_equation", + "content": "(\\mathrm{N} + \\mathrm{S})" + }, + { + "bbox": [ + 46, + 210, + 287, + 330 + ], + "type": "text", + "content": ". We also compare the performance with and without providing narrations during inference." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "text", + "content": "Effect of multimodal training and inference. Training our model with multi-modal textual inputs (steps and narrations), we observe an improvement of " + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "text", + "content": " in narration grounding (row 5 of Table 5) compared to its single-task counterpart (row 2). However the gain in step grounding is marginal when seeing only video frames during inference (" + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "text", + "content": " nar, " + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "inline_equation", + "content": "34\\%" + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "text", + "content": " in row 3 vs " + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "inline_equation", + "content": "34.3\\%" + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "text", + "content": " in row 5). Our conjecture is that the missing modality (narrations) leads to some drop in performance. Providing both steps and narrations during inference leads to a stronger step grounding performance, which surpasses the TAN* baseline by " + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "inline_equation", + "content": "30.7 \\rightarrow 36.1" + }, + { + "bbox": [ + 46, + 332, + 287, + 464 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 470, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 543 + ], + "type": "text", + "content": "Effect of iterative pseudo-labeling. By comparing row 5 to row 6 of Table 5 we observe a clear boost in performance on both step grounding and narration alignment. This is a clear indication of the gains produced by iteratively refining the pseudo-labels using our model as a teacher during training." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 552, + 288, + 622 + ], + "blocks": [ + { + "bbox": [ + 48, + 552, + 288, + 622 + ], + "lines": [ + { + "bbox": [ + 48, + 552, + 288, + 622 + ], + "spans": [ + { + "bbox": [ + 48, + 552, + 288, + 622 + ], + "type": "table", + "html": "
AlignmentS → VS → NN → VHT-Step ↑R@1
S → Vlearned--34.3
S → N → V-learnedlearned30.5
S → N → V-learnedASR27.9
S → N → V-MPNet [55]ASR19.0
Fusedlearnedlearnedlearned36.1
", + "image_path": "56374483eb0fdcc6efbe452b3093d46abcecd8ff174c63121a508aa0fea15127.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 631, + 287, + 668 + ], + "lines": [ + { + "bbox": [ + 46, + 631, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 46, + 631, + 287, + 668 + ], + "type": "text", + "content": "Table 6: Impact of the alignment matrix used during inference with narrations. The same model is used for all results (corresponding to row 5 in Table 5)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "Impact of pathways during inference. In Table 6 we study the effects of using different pathways and alignment information during inference. All results are produced" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 332, + 72, + 521, + 178 + ], + "blocks": [ + { + "bbox": [ + 332, + 72, + 521, + 178 + ], + "lines": [ + { + "bbox": [ + 332, + 72, + 521, + 178 + ], + "spans": [ + { + "bbox": [ + 332, + 72, + 521, + 178 + ], + "type": "image", + "image_path": "84f8776646ffa6760f84144db1fb7fc5f3849df770f3b3aa09166832dc4d3d1e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 188, + 545, + 248 + ], + "lines": [ + { + "bbox": [ + 304, + 188, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 188, + 545, + 248 + ], + "type": "text", + "content": "Figure 3: Step grounding performance and minimum retained step ratio as a function of the filtering threshold. Aggressive unreliable pseudo-label filtering with high confidence thresholds (large maximum step discard ratio) leads to improved performance." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "text", + "content": "from the same model trained for joint narration and step grounding with fixed pseudo-labels from TAN (row 5 in Table 5). Grounding steps using the indirect steps-to-video alignment only lags by " + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "inline_equation", + "content": "3.8\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "text", + "content": " behind the direct steps-to-video alignment that directly computes the similarity between steps and video frames " + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "inline_equation", + "content": "(30.5\\%)" + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "text", + "content": " vs " + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "inline_equation", + "content": "34.3\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "text", + "content": ". Their fusion outperforms their individual grounding performance. This suggests that they capture complementary information. We also explore substituting our learned steps-to-narrations alignment with an alignment computed with an off-the-shelf language model. This significantly degrades performance (19.0) showing that our joint steps and narrations grounding model learns relationships between steps and narrations that go beyond textual similarity between pairs of sentences. Similarly, substituting our learned narrations-to-video alignment with an alignment based on the original ASR timestamps reduces performance by " + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "inline_equation", + "content": "2.6\\%" + }, + { + "bbox": [ + 304, + 270, + 545, + 486 + ], + "type": "text", + "content": " (see additional details in supplementary materials)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 647 + ], + "type": "text", + "content": "Impact of pseudo-label filtering threshold. In Figure 3 we study the effect of the filtering threshold used in the iterative pseudo-labeling stage. We can observe that using aggressive filtering (i.e., high thresholds translating to a high maximum percentage of pseudo-labels that are discarded) is key to observing gains from iterative pseudo-labeling compared to training with fixed pseudo-labels from TAN. Intuitively, a large percentage of steps described in wikiHow articles are not represented in the given instructional video due to task mismatch, variations in recipe execution, and some steps being optional. Therefore, starting with a small subset of reliable pseudo-labels can facilitate step grounding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Task selection. In Table 7 we investigate different strategies to select the wikiHow articles during training. This selection determines the set of steps to be grounded. We evaluate two strategies for video-task association from narratives and compare them with using the task id provided in" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15208" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 77, + 312, + 232 + ], + "blocks": [ + { + "bbox": [ + 56, + 77, + 312, + 232 + ], + "lines": [ + { + "bbox": [ + 56, + 77, + 312, + 232 + ], + "spans": [ + { + "bbox": [ + 56, + 77, + 312, + 232 + ], + "type": "image", + "image_path": "bbb2d0a7df83b63b4f8e76734e4c7d648fd79782ffb66b68c73b3fdcbf1a110f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 285 + ], + "type": "text", + "content": "Figure 4: Visualization of sample frames per step, ground-truth segments (colored bars) and a single predicted timestamp per step (dashed lines) for the groundable steps of three HT-step validation videos demonstrating (a) a Mini-Stromboli recipe, (b) a Make Tabouli recipe, and (c) a Bake a Sweet Potato Pie recipe. Best viewed in color." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 323, + 95, + 457, + 229 + ], + "blocks": [ + { + "bbox": [ + 323, + 95, + 457, + 229 + ], + "lines": [ + { + "bbox": [ + 323, + 95, + 457, + 229 + ], + "spans": [ + { + "bbox": [ + 323, + 95, + 457, + 229 + ], + "type": "image", + "image_path": "c3bbc8296be48e918ebe5ce17fa97fae7d2ccc0f7111655366e659fbc730a026.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 94, + 301, + 241, + 354 + ], + "blocks": [ + { + "bbox": [ + 94, + 301, + 241, + 354 + ], + "lines": [ + { + "bbox": [ + 94, + 301, + 241, + 354 + ], + "spans": [ + { + "bbox": [ + 94, + 301, + 241, + 354 + ], + "type": "table", + "html": "
Task ID selectionHT-Step ↑R@1
HT100M metadata34.3
Top-1 prediction34.7
Random / top-5 pred34.3
", + "image_path": "f141fe8b373930461d1fc09c8698f01074e6c56b8bcb073eba83a575db32c2b4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 361, + 289, + 447 + ], + "lines": [ + { + "bbox": [ + 46, + 361, + 289, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 289, + 447 + ], + "type": "text", + "content": "Table 7: Sensitivity to task id selection. We assess how the performance of our method changes when using different strategies to associate videos with articles. We experiment with using the task ids available from HT100M, as well as the two predictive strategies presented in Section 3.3.2. We conclude that our method is robust to the task selection, and the task labels are not necessary for training." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 456, + 288, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 288, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 288, + 495 + ], + "type": "text", + "content": "the HowTo100M metadata for each video3. We see that our automatic selection approaches yield results on par with or even slightly better than those based on metadata." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 508, + 162, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 508, + 162, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 508, + 162, + 521 + ], + "type": "text", + "content": "4.3.3 Qualitative Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 527, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 527, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 527, + 287, + 635 + ], + "type": "text", + "content": "Qualitative grounding results obtained with the proposed VINA model are presented in Figure 4. These examples showcase that our model can successfully retrieve complex and fine-grained steps, such as combining multiple ingredients in a mixing bowl or tapping a filled pie pan for the Bake a Sweet Potato Pie recipe. Failure cases include discriminating between steps that involve the same ingredients, such as mixing the milk and eggs versus adding the mixture to the existing mix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 641, + 119, + 654 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 119, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 119, + 654 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "content": "We have presented a method for learning how to temporally ground sequences of steps in instructional videos," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 304, + 546, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 546, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 546, + 400 + ], + "type": "text", + "content": "without any manual supervision. Our proposed method exploits the weak supervision naturally provided in such videos through their narrations, and solves for joint alignment of narrations and steps, while fusing two complementary pathways for step-to-video alignment. We demonstrated strong quantitative performance, surpassing the state-of-the-art on multiple benchmarks for both narration and step grounding." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 402, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 402, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 402, + 545, + 426 + ], + "type": "text", + "content": "Acknowledgements. We thank Huiyu Wang, Yale Song, Mandy Toh, and Tengda Han for helpful discussions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 435, + 365, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 365, + 448 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 365, + 448 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 455, + 547, + 714 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 310, + 455, + 547, + 510 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 455, + 547, + 510 + ], + "spans": [ + { + "bbox": [ + 310, + 455, + 547, + 510 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Piotr Bojanowski, Nishant Agrawal, Josef Sivic, Ivan Laptev, and Simon Lacoste-Julien. Unsupervised learning from narrated instruction videos. 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Procedure planning" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "type": "text", + "content": "3During inference, metadata task ids are used in all of our HowTo100M experiments in order to evaluate against the ground-truth step annotations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15209" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 288, + 709 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 66, + 72, + 287, + 115 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 72, + 287, + 115 + ], + "spans": [ + { + "bbox": [ + 66, + 72, + 287, + 115 + ], + "type": "text", + "content": "in instructional videos via contextual modeling and model-based policy learning. 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